Finite Group Databasebeta

← #33972026

Subgroups — #33972026

Order 18688.

2114 conjugacy classes of subgroups.

The subgroup lattice has 1918 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22624191C211yesmaximal, characteristic, complemented
2#22622199C211yesmaximal, characteristic, complemented
3#22622184C211yesmaximal, characteristic, complemented
4#22622072C211yesmaximal, characteristic, complemented
5#22622057C211yesmaximal, characteristic, complemented
6#22621952C211yesmaximal, characteristic, complemented
7#22621937C211yesmaximal, characteristic, complemented
8#22621781C211yesmaximal, characteristic, complemented
9#22621766C211yesmaximal, characteristic, complemented
10#22621687C211yesmaximal, characteristic, complemented
11#22621661C211yesmaximal, characteristic, complemented
12#22621547C211yesmaximal, characteristic, complemented
13#22621527C211yesmaximal, characteristic, complemented
14#22621517C211yesmaximal, characteristic, complemented
15#22621487C211yesmaximal, characteristic, complemented
16#22621467C211yesmaximal, characteristic, complemented
17#22621452C211yesmaximal, characteristic, complemented
18#22621003C211yesmaximal, characteristic, complemented
19#22620981C211yesmaximal, characteristic, complemented
20#22620837C211yesmaximal, characteristic, complemented
21#22620828C211yesmaximal, characteristic, complemented
22#22620745C211yesmaximal, characteristic, complemented
23#22620696C211yesmaximal, characteristic, complemented
24#22620145C211yesmaximal, characteristic, complemented
25#22620130C211yesmaximal, characteristic, complemented
26#22619235C211yesmaximal, characteristic, complemented
27#22619235C211yesmaximal, characteristic, complemented
28#22619173C211yesmaximal, characteristic, complemented
29#22619149C211yesmaximal, characteristic, complemented
30#22618979C211yesmaximal, characteristic, complemented
31C73×#3488C211yesmaximal, characteristic, complemented
32C2×#14556622C2211yescharacteristic, complemented
33C2×#14556617C2211yescharacteristic, complemented
34C2×#14556617C2211yescharacteristic, complemented
35C2×#14556617C2211yescharacteristic, complemented
36C2×#14556611C2211yescharacteristic, complemented
37C2×#14556611C2211yescharacteristic, complemented
38C2×#14556611C2211yescharacteristic, complemented
39C2×#14556611C2211yescharacteristic, complemented
40#17989326—21no—
41#17989326—21no—
42#17989283C2211yescharacteristic, complemented
43#17989283C2211yescharacteristic, complemented
44#17989282—21no—
45#17989282—21no—
46#17989277C2211yescharacteristic, complemented
47#17989277C2211yescharacteristic, complemented
48#17989258C2211yescharacteristic, complemented
49#17989258C2211yescharacteristic, complemented
50#17989242C2211yescharacteristic, complemented
51#17989242C2211yescharacteristic, complemented
52#17989199C2211yescharacteristic, complemented
53#17989192C2211yescharacteristic, complemented
54#17989187—21no—
55#17989187—21no—
56#17989183—21no—
57#17989183—21no—
58#17989165C2211yescharacteristic, complemented
59#17989165C2211yescharacteristic, complemented
60#17989098C2211yescharacteristic, complemented
61#17989098C2211yescharacteristic, complemented
62#17988982C2211yescharacteristic, complemented
63#17988977C2211yescharacteristic, complemented
64#17988963C2211yescharacteristic, complemented
65#17988959C2211yescharacteristic, complemented
66#17988951C2211yescharacteristic, complemented
67#17988951C2211yescharacteristic, complemented
68#17988941C2211yescharacteristic, complemented
69#17988941C2211yescharacteristic, complemented
70#17988922C2211yescharacteristic, complemented
71#17988920C2211yescharacteristic, complemented
72#17988917C2211yescharacteristic, complemented
73#17988915C2211yescharacteristic, complemented
74#17988908C2211yescharacteristic, complemented
75#17988908C2211yescharacteristic, complemented
76#17988908C2211yescharacteristic, complemented
77#17988908C2211yescharacteristic, complemented
78#17988905C2211yescharacteristic, complemented
79#17988903C2211yescharacteristic, complemented
80#17988900C2211yescharacteristic, complemented
81#17988898C2211yescharacteristic, complemented
82#17988894C2211yescharacteristic, complemented
83#17988894C2211yescharacteristic, complemented
84#17988887C2211yescharacteristic, complemented
85#17988887C2211yescharacteristic, complemented
86#17988843C2211yescharacteristic, complemented
87#17988838C2211yescharacteristic, complemented
88#17988838C2211yescharacteristic, complemented
89#17988838C2211yescharacteristic, complemented
90#17988835C2211yescharacteristic, complemented
91#17988831C2211yescharacteristic, complemented
92#17988831C2211yescharacteristic, complemented
93#17988831C2211yescharacteristic, complemented
94#17988826C2211yescharacteristic, complemented
95#17988821C2211yescharacteristic, complemented
96#17988821C2211yescharacteristic, complemented
97#17988821C2211yescharacteristic, complemented
98#17988818C2211yescharacteristic, complemented
99#17988814C2211yescharacteristic, complemented
100#17988814C2211yescharacteristic, complemented
101#17988814C2211yescharacteristic, complemented
102#17988806C2211yescharacteristic, complemented
103#17988806C2211yescharacteristic, complemented
104#17988799C2211yescharacteristic, complemented
105#17988799C2211yescharacteristic, complemented
106#17988797C2211yescharacteristic, complemented
107#17988792C2211yescharacteristic, complemented
108#17988787C2211yescharacteristic, complemented
109#17988784C2211yescharacteristic, complemented
110#17988784C2211yescharacteristic, complemented
111#17988782C2211yescharacteristic, complemented
112#17988779C2211yescharacteristic, complemented
113#17988779C2211yescharacteristic, complemented
114#17988749C2211yescharacteristic
115#17988749C2211yescharacteristic
116#17988749C2211yescharacteristic, complemented
117#17988749C2211yescharacteristic, complemented
118#17988749C2211yescharacteristic, complemented
119#17988749C2211yescharacteristic, complemented
120#17988749C2211yescharacteristic, complemented
121#17988749C2211yescharacteristic, complemented
122#17988747C2211yescharacteristic, complemented
123#17988747C2211yescharacteristic, complemented
124#17988743C2211yescharacteristic, complemented
125#17988738C2211yescharacteristic, complemented
126#17988738C2211yescharacteristic, complemented
127#17988738C2211yescharacteristic, complemented
128#17988738C2211yescharacteristic, complemented
129#17988738C2211yescharacteristic, complemented
130#17988732C2211yescharacteristic
131#17988732C2211yescharacteristic
132#17988732C2211yescharacteristic, complemented
133#17988732C2211yescharacteristic, complemented
134#17988732C2211yescharacteristic, complemented
135#17988732C2211yescharacteristic, complemented
136#17988732C2211yescharacteristic, complemented
137#17988732C2211yescharacteristic, complemented
138#17988730C2211yescharacteristic, complemented
139#17988730C2211yescharacteristic, complemented
140#17988730C2211yescharacteristic, complemented
141#17988730C2211yescharacteristic, complemented
142#17988730C2211yescharacteristic, complemented
143#17988730C2211yescharacteristic, complemented
144#17988726C2211yescharacteristic, complemented
145#17988721C2211yescharacteristic, complemented
146#17988721C2211yescharacteristic, complemented
147#17988721C2211yescharacteristic, complemented
148#17988721C2211yescharacteristic, complemented
149#17988721C2211yescharacteristic, complemented
150#17988697C2211yescharacteristic, complemented
151#17988692C2211yescharacteristic, complemented
152#17988687C2211yescharacteristic, complemented
153#17988685C2211yescharacteristic, complemented
154C4×#11924018C2211yescharacteristic, complemented
155C4×#11924015C2211yescharacteristic, complemented
156C4×#11924016C2211yescharacteristic, complemented
157C4×#11924013C2211yescharacteristic, complemented
158#17988665C2211yescharacteristic, complemented
159#17988665C2211yescharacteristic, complemented
160#17988659C2211yescharacteristic, complemented
161#17988659C2211yescharacteristic, complemented
162#17988659C2211yescharacteristic, complemented
163#17988659C2211yescharacteristic, complemented
164D4×#10596831C2211yescharacteristic, complemented
165D4×#10596831C2211yescharacteristic, complemented
166#17988648C2211yescharacteristic, complemented
167#17988648C2211yescharacteristic, complemented
168#17988596C2211yescharacteristic, complemented
169#17988592C2211yescharacteristic, complemented
170#17988588C2211yescharacteristic, complemented
171#17988588C2211yescharacteristic, complemented
172#17988583C2211yescharacteristic, complemented
173#17988583C2211yescharacteristic, complemented
174C2×#14556512C2211yescharacteristic, complemented
175C2×#14556512C2211yescharacteristic, complemented
176#17988554C2211yescharacteristic, complemented
177#17988554C2211yescharacteristic, complemented
178#17988551C2211yescharacteristic, complemented
179C2×C22⋊#10596831C2211yescharacteristic, complemented
180C2×H(5,𝔽2)×C73C2211yescharacteristic
181C22×#41×C73C2211yescharacteristic
182#550×C73C2211yescharacteristic
183#550×C73C2211yescharacteristic
184#548×C73C2211yescharacteristic
185#548×C73C2211yescharacteristic
186#546×C73—21no—
187#546×C73—21no—
188#546×C73C2211yescharacteristic
189#546×C73C2211yescharacteristic
190D42×C73—21no—
191D42×C73—21no—
192D42×C73C2211yescharacteristic
193D42×C73C2211yescharacteristic
194#537×C73—21no—
195#537×C73C2211yescharacteristic
196#535×C73—21no—
197#535×C73C2211yescharacteristic
198#525×C73—21no—
199#525×C73C2211yescharacteristic
200C2×#121×C73—21no—
201C2×#121×C73C2211yescharacteristic
202#520×C73C2211yescharacteristic
203C2×#11924028C2311yescharacteristic
204C2×#11924028C2311yescharacteristic
205C2×#11924028C2311yescharacteristic
206C2×#11924028C2311yescharacteristic
207#14556622—42no—
208#14556617—42no—
209#14556617—42no—
210#14556617—42no—
211#14556611—42no—
212#14556611—42no—
213#14556611—42no—
214#14556611—42no—
215C2×#11924018C2311yescharacteristic
216C2×#11924018C2311yescharacteristic
217C2×#11924018C2311yescharacteristic
218C2×#11924018C2311yescharacteristic
219C2×#11924016C2311yescharacteristic
220C2×#11924016C2311yescharacteristic
221C2×#11924016C2311yescharacteristic
222C2×#11924016C2311yescharacteristic
223C2×#11924016C2311yescharacteristic
224C2×#11924016C2311yescharacteristic
225C2×#11924016C2311yescharacteristic
226C2×#11924016C2311yescharacteristic
227C2×#11924015C2311yescharacteristic
228C2×#11924015C2311yescharacteristic
229C2×#11924015C2311yescharacteristic
230C2×#11924015C2311yescharacteristic
231C2×#11924013C2311yescharacteristic
232C2×#11924013C2311yescharacteristic
233C2×#11924013C2311yescharacteristic
234C2×#11924013C2311yescharacteristic
235C2×#11924013C2311yescharacteristic
236C2×#11924013C2311yescharacteristic
237C2×#11924013C2311yescharacteristic
238C2×#11924013C2311yescharacteristic
239C2×#11924012C2311yescharacteristic
240C2×#11924012C2311yescharacteristic
241C2×#11924012C2311yescharacteristic
242C2×#11924012C2311yescharacteristic
243C22×#10596831C2311yescharacteristic
244C22×#10596831C2311yescharacteristic
245C22×#10596831C2311yescharacteristic
246C22×#10596831C2311yescharacteristic
247#14556591C2311yescharacteristic
248#14556588C2311yescharacteristic
249#14556587—21no—
250#14556587—21no—
251#14556586—21no—
252#14556586—21no—
253#14556584—21no—
254#14556584—21no—
255#14556584—21no—
256#14556584—21no—
257#14556583C2311yescharacteristic
258#14556583C2311yescharacteristic
259#14556581—21no—
260#14556581—21no—
261#14556581—21no—
262#14556581—21no—
263#14556576—21no—
264#14556576—21no—
265#14556574—21no—
266#14556574—21no—
267#14556573—21no—
268#14556573—21no—
269#14556573—21no—
270#14556573—21no—
271#14556573—21no—
272#14556573—21no—
273#14556572—21no—
274#14556572—21no—
275#14556570C2311yescharacteristic
276#14556570C2311yescharacteristic
277#14556570C2311yescharacteristic
278#14556570C2311yescharacteristic
279#14556570C2311yescharacteristic
280#14556570C2311yescharacteristic
281#14556567—21no—
282#14556567—21no—
283#14556565C2311yescharacteristic
284#14556565C2311yescharacteristic
285#14556565C2311yescharacteristic
286#14556565C2311yescharacteristic
287#14556565C2311yescharacteristic
288#14556565C2311yescharacteristic
289#14556564—21no—
290#14556564—21no—
291#14556564—21no—
292#14556564—21no—
293#14556564—21no—
294#14556564—21no—
295#14556563—21no—
296#14556563—21no—
297#14556563—21no—
298#14556563—21no—
299#14556563—21no—
300#14556563—21no—
301#14556562—21no—
302#14556562—21no—
303#14556562—21no—
304#14556562—21no—
305#14556560—21no—
306#14556560—21no—
307C4×Dic146C2311yescharacteristic
308C4×Dic146C2311yescharacteristic
309C4×D292C2311yescharacteristic
310C4×D292C2311yescharacteristic
311#14556553—21no—
312#14556553—21no—
313C4×C22⋊D73—21no—
314C4×C22⋊D73—21no—
315C4×C22⋊D73—21no—
316C4×C22⋊D73—21no—
317#14556551—21no—
318#14556551—21no—
319#14556550C2311yescharacteristic
320#14556550C2311yescharacteristic
321#14556547—21no—
322#14556547—21no—
323C2×C4⋊Dic73C2311yescharacteristic
324C2×C4⋊Dic73C2311yescharacteristic
325C4⋊C4×D73—21no—
326C4⋊C4×D73—21no—
327#14556524C2311yescharacteristic
328#14556524C2311yescharacteristic
329#14556524C2311yescharacteristic
330#14556524C2311yescharacteristic
331#14556522C2311yescharacteristic
332#14556522C2311yescharacteristic
333#14556522C2311yescharacteristic
334#14556522C2311yescharacteristic
335C4⋊#10596831C2311yescharacteristic
336C4⋊#10596831C2311yescharacteristic
337C4⋊#10596831C2311yescharacteristic
338C4⋊#10596831C2311yescharacteristic
339#14556515C2311yescharacteristic
340#14556515C2311yescharacteristic
341#14556515C2311yescharacteristic
342#14556515C2311yescharacteristic
343#14556515C2311yescharacteristic
344#14556515C2311yescharacteristic
345#14556515C2311yescharacteristic
346#14556515C2311yescharacteristic
347#14556514C2311yescharacteristic
348#14556514C2311yescharacteristic
349#14556514C2311yescharacteristic
350#14556514C2311yescharacteristic
351#14556512C2311yescharacteristic
352#14556512C2311yescharacteristic
353#14556512C2311yescharacteristic
354#14556512C2311yescharacteristic
355#14556512C2311yescharacteristic
356#14556512C2311yescharacteristic
357#14556512C2311yescharacteristic
358#14556512C2311yescharacteristic
359#14556512C2311yescharacteristic
360#14556512C2311yescharacteristic
361#14556512C2311yescharacteristic
362#14556512C2311yescharacteristic
363#14556512C2311yescharacteristic
364#14556512C2311yescharacteristic
365#14556512C2311yescharacteristic
366#14556512C2311yescharacteristic
367#14556511C2311yescharacteristic
368#14556511C2311yescharacteristic
369#14556511C2311yescharacteristic
370#14556511C2311yescharacteristic
371C22⋊#10596831C2311yescharacteristic
372C22⋊#10596831C2311yescharacteristic
373C22⋊#10596831C2311yescharacteristic
374C22⋊#10596831C2311yescharacteristic
375C22⋊#10596831C2311yescharacteristic
376C22⋊#10596831C2311yescharacteristic
377C22⋊#10596831C2311yescharacteristic
378C22⋊#10596831C2311yescharacteristic
379C22⋊#10596831C2311yescharacteristic
380C22⋊#10596831C2311yescharacteristic
381C22⋊#10596831C2311yescharacteristic
382C22⋊#10596831C2311yescharacteristic
383#14556502C2311yescharacteristic
384#14556502C2311yescharacteristic
385C4×#10596831C2311yescharacteristic
386C4×#10596831C2311yescharacteristic
387H(5,𝔽2)×C73—42no—
388H(5,𝔽2)×C73—42no—
389C2×#41×C73—21no—
390C2×#41×C73—21no—
391C2×#41×C73—21no—
392C2×#41×C73—42no—
393C2×#41×C73—42no—
394C2×#41×C73C2311yescharacteristic
395C2×#41×C73C2311yescharacteristic
396C2×#41×C73C2311yescharacteristic
397C2×#41×C73C2311yescharacteristic
398C2×#41×C73C2311yescharacteristic
399C2×#41×C73C2311yescharacteristic
400C2×#41×C73C2311yescharacteristic
401C22×Q8×C73C2311yescharacteristic
402C22×D4×C73—21no—
403C22×D4×C73—21no—
404C22×D4×C73—21no—
405C22×D4×C73—21no—
406C22×D4×C73—21no—
407C22×D4×C73—21no—
408C22×D4×C73—21no—
409C22×D4×C73C2311yescharacteristic
410C22×D4×C73C2311yescharacteristic
411C22×D4×C73C2311yescharacteristic
412C22×D4×C73C2311yescharacteristic
413C23×C4×C73—21no—
414C23×C4×C73C2311yescharacteristic
415#127×C73—21no—
416#127×C73—21no—
417#127×C73C2311yescharacteristic
418#127×C73C2311yescharacteristic
419#124×C73—21no—
420#124×C73—21no—
421#124×C73C2311yescharacteristic
422#124×C73C2311yescharacteristic
423#123×C73—21no—
424#123×C73—21no—
425#123×C73D411yescharacteristic
426#123×C73D411yescharacteristic
427C22⋊Q8×C73—21no—
428C22⋊Q8×C73—21no—
429C22⋊Q8×C73—21no—
430C22⋊Q8×C73D411yescharacteristic
431C22⋊Q8×C73D411yescharacteristic
432C22⋊Q8×C73C2311yescharacteristic
433C22⋊Q8×C73C2311yescharacteristic
434#121×C73—21no—
435#121×C73—21no—
436#121×C73—21no—
437#121×C73—21no—
438#121×C73—21no—
439#121×C73—21no—
440#121×C73—21no—
441#121×C73—21no—
442#121×C73—21no—
443#121×C73—21no—
444#121×C73—21no—
445#121×C73—21no—
446#121×C73—21no—
447#121×C73—21no—
448#121×C73—21no—
449#121×C73—21no—
450#121×C73—21no—
451#121×C73D411yescharacteristic
452#121×C73D411yescharacteristic
453#121×C73C2311yescharacteristic
454#121×C73C2311yescharacteristic
455#121×C73C2311yescharacteristic
456#121×C73C2311yescharacteristic
457#121×C73C2311yescharacteristic
458#121×C73C2311yescharacteristic
459#120×C73—21no—
460#120×C73—21no—
461#120×C73—21no—
462#120×C73—21no—
463#120×C73—21no—
464#120×C73—21no—
465#120×C73—21no—
466#120×C73—21no—
467#120×C73D411yescharacteristic
468#120×C73D411yescharacteristic
469C4×Q8×C73C2311yescharacteristic
470C4×Q8×C73C2311yescharacteristic
471C4×D4×C73—21no—
472C4×D4×C73—21no—
473C4×D4×C73—21no—
474C4×D4×C73—21no—
475C4×D4×C73—21no—
476C4×D4×C73—21no—
477C4×D4×C73C2311yescharacteristic
478C4×D4×C73C2311yescharacteristic
479C4×D4×C73C2311yescharacteristic
480C4×D4×C73C2311yescharacteristic
481C4×D4×C73C2311yescharacteristic
482C4×D4×C73C2311yescharacteristic
483#117×C73—21no—
484#117×C73C2311yescharacteristic
485C2×C4⋊C4×C73—21no—
486C2×C4⋊C4×C73C2311yescharacteristic
487C2×C22⋊C4×C73—21no—
488C2×C22⋊C4×C73—21no—
489C2×C22⋊C4×C73—21no—
490#11924028—41no—
491#11924028—41no—
492#11924028—41no—
493#11924028—41no—
494#11924028—41no—
495#11924028—41no—
496#11924028—41no—
497#11924028—41no—
498C2×Dic146C2411yescharacteristic
499C2×Dic146C2411yescharacteristic
500C2×D292—21no—
501C2×D292—21no—
502C2×D292C2411yescharacteristic
503C2×D292C2411yescharacteristic
504C2×C22⋊D73—21no—
505C2×C22⋊D73—21no—
506C2×C22⋊D73—21no—
507C2×C22⋊D73—21no—
508C2×C22⋊D73—21no—
509C2×C22⋊D73—21no—
510C2×C22⋊D73—21no—
511C2×C22⋊D73—21no—
512C2×C22⋊D73—21no—
513C2×C22⋊D73—21no—
514C22×Dic73—21no—
515C22×Dic73—21no—
516C2×C4×D73—21no—
517C2×C4×D73—21no—
518C2×C4×D73—21no—
519C2×C4×D73—21no—
520C2×C4×D73—21no—
521C2×C4×D73—21no—
522#11924018—22no—
523#11924018—22no—
524#11924018—41no—
525#11924018—41no—
526#11924016—22no—
527#11924016—22no—
528#11924016—41no—
529#11924016—41no—
530#11924016—41no—
531#11924016—41no—
532#11924016—41no—
533#11924016—41no—
534#11924015—22no—
535#11924015—22no—
536#11924015—41no—
537#11924015—41no—
538#11924013—22no—
539#11924013—22no—
540#11924013—41no—
541#11924013—41no—
542#11924013—41no—
543#11924013—41no—
544#11924013—41no—
545#11924013—41no—
546#11924012—41no—
547#11924012—41no—
548#11924012—41no—
549#11924012—41no—
550C2×#10596831—41no—
551C2×#10596831—41no—
552C2×#10596831—41no—
553C2×#10596831—41no—
554C2×#10596831C2411yescharacteristic
555C2×#10596831C2411yescharacteristic
556C2×#10596831C2411yescharacteristic
557C2×#10596831C2411yescharacteristic
558C2×#10596831C2411yescharacteristic
559C2×#10596831C2411yescharacteristic
560C2×#10596831C2411yescharacteristic
561C2×#10596831C2411yescharacteristic
562C4⋊Dic73—21no—
563C4⋊Dic73—21no—
564C4⋊Dic73—21no—
565C4⋊Dic73—21no—
566C4⋊Dic73C2411yescharacteristic
567C4⋊Dic73C2411yescharacteristic
568C4⋊Dic73C2411yescharacteristic
569C4⋊Dic73C2411yescharacteristic
570#11924007—21no—
571#11924007—21no—
572#11924007—21no—
573#11924007—21no—
574#11924007—21no—
575#11924007—21no—
576#11924007—21no—
577#11924007—21no—
578#11924007—21no—
579#11924007—21no—
580#11924007—21no—
581#11924007—21no—
582C22⋊Dic73—21no—
583C22⋊Dic73—21no—
584C22⋊Dic73—21no—
585C22⋊Dic73—21no—
586C22⋊Dic73—21no—
587C22⋊Dic73—21no—
588C22⋊Dic73—21no—
589C22⋊Dic73—21no—
590#11924005—21no—
591#11924005—21no—
592#11924005—21no—
593#11924005—21no—
594#11924005—21no—
595#11924005—21no—
596#11924005—21no—
597#11924005—21no—
598C4×Dic73—21no—
599C4×Dic73—21no—
600C4×Dic73—21no—
601C4×Dic73—21no—
602C24×C73—21no—
603C24×C73—21no—
604C24×C73—21no—
605C24×C73—21no—
606C24×C73C2×D411yescharacteristic
607#41×C73—22no—
608#41×C73—22no—
609#41×C73—22no—
610#41×C73—22no—
611#41×C73—22no—
612#41×C73—22no—
613#41×C73—41no—
614#41×C73—41no—
615#41×C73—41no—
616#41×C73—41no—
617#41×C73—41no—
618#41×C73—41no—
619#41×C73—41no—
620#41×C73—41no—
621#41×C73—44no—
622#41×C73—44no—
623#41×C73—44no—
624C2×Q8×C73—21no—
625C2×Q8×C73—22no—
626C2×Q8×C73—41no—
627C2×Q8×C73C2×D411yescharacteristic
628C2×Q8×C73C2411yescharacteristic
629C2×Q8×C73C2411yescharacteristic
630C2×D4×C73—21no—
631C2×D4×C73—22no—
632C2×D4×C73—22no—
633C2×D4×C73—22no—
634C2×D4×C73—21no—
635C2×D4×C73—21no—
636C2×D4×C73—21no—
637C2×D4×C73—21no—
638C2×D4×C73—21no—
639C2×D4×C73—21no—
640C2×D4×C73—21no—
641C2×D4×C73—21no—
642C2×D4×C73—21no—
643C2×D4×C73—21no—
644C2×D4×C73—21no—
645C2×D4×C73—21no—
646C2×D4×C73—21no—
647C2×D4×C73—21no—
648C2×D4×C73—21no—
649C2×D4×C73—21no—
650C2×D4×C73—21no—
651C2×D4×C73—21no—
652C2×D4×C73—21no—
653C2×D4×C73—41no—
654C2×D4×C73—41no—
655C2×D4×C73—41no—
656C2×D4×C73—41no—
657C2×D4×C73—41no—
658C2×D4×C73—44no—
659C2×D4×C73—44no—
660C2×D4×C73—44no—
661C2×D4×C73—44no—
662C2×D4×C73—82no—
663C2×D4×C73—82no—
664C2×D4×C73—82no—
665C2×D4×C73C2×D411yescharacteristic
666C2×D4×C73C2×D411yescharacteristic
667C2×D4×C73C2×D411yescharacteristic
668C2×D4×C73C2×D411yescharacteristic
669C2×D4×C73C2×D411yescharacteristic
670C2×D4×C73C2×D411yescharacteristic
671C2×D4×C73C2×D411yescharacteristic
672C2×D4×C73C2411yescharacteristic
673C2×D4×C73C2411yescharacteristic
674C2×D4×C73C2411yescharacteristic
675C2×D4×C73C2411yescharacteristic
676C22×C4×C73—21no—
677C22×C4×C73—21no—
678C22×C4×C73—21no—
679C22×C4×C73—21no—
680C22×C4×C73—21no—
681C22×C4×C73—21no—
682C22×C4×C73—21no—
683C22×C4×C73—21no—
684C22×C4×C73—21no—
685C22×C4×C73—21no—
686C22×C4×C73—41no—
687C22×C4×C73—41no—
688C22×C4×C73—44no—
689C22×C4×C73C2×D411yescharacteristic
690C22×C4×C73C2×D411yescharacteristic
691C22×C4×C73C2×D411yescharacteristic
692C22×C4×C73C2411yescharacteristic
693C22×C4×C73C2411yescharacteristic
694C22×C4×C73C2411yescharacteristic
695C22×C4×C73C2411yescharacteristic
696C22×C4×C73C2411yescharacteristic
697C4⋊C4×C73—21no—
698C4⋊C4×C73—21no—
699C4⋊C4×C73—21no—
700C4⋊C4×C73—21no—
701C4⋊C4×C73—21no—
702C4⋊C4×C73C2×D411yescharacteristic
703C4⋊C4×C73C2×D411yescharacteristic
704C4⋊C4×C73C2×D411yescharacteristic
705C4⋊C4×C73C2×D411yescharacteristic
706C4⋊C4×C73C2×D411yescharacteristic
707C4⋊C4×C73C2×D411yescharacteristic
708C4⋊C4×C73C2411yescharacteristic
709C4⋊C4×C73C2411yescharacteristic
710C22⋊C4×C73—21no—
711C22⋊C4×C73—21no—
712C22⋊C4×C73—21no—
713C22⋊C4×C73—21no—
714C22⋊C4×C73—21no—
715C22⋊C4×C73—21no—
716C22⋊C4×C73—21no—
717C22⋊C4×C73—21no—
718C22⋊C4×C73—21no—
719C22⋊C4×C73—21no—
720C22⋊C4×C73—21no—
721C22⋊C4×C73—21no—
722C22⋊C4×C73—21no—
723C22⋊C4×C73—21no—
724C22⋊C4×C73C2×D411yescharacteristic
725C22⋊C4×C73C2×D411yescharacteristic
726C22⋊C4×C73C2×D411yescharacteristic
727C22⋊C4×C73C2×D411yescharacteristic
728C22⋊C4×C73C2×D411yescharacteristic
729C22⋊C4×C73C2×D411yescharacteristic
730C22⋊C4×C73C2×D411yescharacteristic
731C22⋊C4×C73C2×D411yescharacteristic
732C22⋊C4×C73C2×D411yescharacteristic
733C22⋊C4×C73C2×D411yescharacteristic
734C42×C73—21no—
735C42×C73—21no—
736C42×C73C2411yescharacteristic
737C42×C73C2411yescharacteristic
738C23×C73—21no—
739C23×C73—21no—
740C23×C73—21no—
741C23×C73—21no—
742C23×C73—41no—
743C23×C73—41no—
744C23×C73—41no—
745C23×C73—42no—
746C23×C73—42no—
747C23×C73—42no—
748C23×C73—42no—
749C23×C73—42no—
750C23×C73—81no—
751C23×C73—81no—
752C23×C73—81no—
753C23×C73—81no—
754C23×C73—81no—
755C23×C73—81no—
756C23×C73—81no—
757C23×C73C22×D411yescharacteristic
758C23×C73C22×D411yescharacteristic
759C23×C73C22×D411yescharacteristic
760C23×C73C22×D411yescharacteristic
761C23×C73C22×D411yescharacteristic
762C22×D73—21no—
763C22×D73—21no—
764Q8×C73—21no—
765Q8×C73—21no—
766Q8×C73—21no—
767Q8×C73—41no—
768Q8×C73—42no—
769Q8×C73H(5,𝔽2)12yes—
770D4×C73—24no—
771D4×C73—21no—
772D4×C73—21no—
773D4×C73—21no—
774D4×C73—21no—
775D4×C73—21no—
776D4×C73—21no—
777D4×C73—21no—
778D4×C73—41no—
779D4×C73—41no—
780D4×C73—41no—
781D4×C73—41no—
782D4×C73—41no—
783D4×C73—41no—
784D4×C73—41no—
785D4×C73—42no—
786D4×C73—42no—
787D4×C73—42no—
788D4×C73—42no—
789D4×C73—42no—
790D4×C73—42no—
791D4×C73—42no—
792D4×C73—42no—
793D4×C73—42no—
794D4×C73—42no—
795D4×C73—42no—
796D4×C73—81no—
797D4×C73—81no—
798D4×C73—81no—
799D4×C73—81no—
800D4×C73—81no—
801D4×C73—81no—
802D4×C73—81no—
803D4×C73—81no—
804D4×C73H(5,𝔽2)12yes—
805C2×C4×C73—24no—
806C2×C4×C73—21no—
807C2×C4×C73—21no—
808C2×C4×C73—21no—
809C2×C4×C73—21no—
810C2×C4×C73—21no—
811C2×C4×C73—21no—
812C2×C4×C73—21no—
813C2×C4×C73—21no—
814C2×C4×C73—21no—
815C2×C4×C73—21no—
816C2×C4×C73—21no—
817C2×C4×C73—21no—
818C2×C4×C73—21no—
819C2×C4×C73—21no—
820C2×C4×C73—41no—
821C2×C4×C73—41no—
822C2×C4×C73—41no—
823C2×C4×C73—42no—
824C2×C4×C73—42no—
825C2×C4×C73—42no—
826C2×C4×C73—42no—
827C2×C4×C73—42no—
828C2×C4×C73—42no—
829C2×C4×C73—81no—
830C2×C4×C73—81no—
831C2×C4×C73—81no—
832C2×C4×C73C22×D411yescharacteristic
833C2×C4×C73C22×D411yescharacteristic
834C2×C4×C73C22×D411yescharacteristic
835C2×C4×C73C22×D411yescharacteristic
836C2×C4×C73C22×D411yescharacteristic
837C2×C4×C73C22×D411yescharacteristic
838C2×C4×C73C22×D411yescharacteristic
839C2×C4×C73C22×D411yescharacteristic
840C2×C4×C73C22×D411yescharacteristic
841C2×C4×C73C2511yescharacteristic
842C22⋊D73—81no—
843C22⋊D73—81no—
844C22⋊D73—81no—
845C22⋊D73—81no—
846C22⋊D73—81no—
847C22⋊D73—81no—
848C22⋊D73—81no—
849C22⋊D73—81no—
850C22⋊D73—81no—
851C22⋊D73—81no—
852C2×Dic73—21no—
853C2×Dic73—21no—
854C2×Dic73—21no—
855C2×Dic73—21no—
856C2×Dic73—21no—
857C2×Dic73—21no—
858C2×Dic73—81no—
859C2×Dic73—81no—
860D292—21no—
861D292—21no—
862D292—21no—
863D292—21no—
864D292—81no—
865D292—81no—
866C4×D73—81no—
867C4×D73—81no—
868C4×D73—81no—
869C4×D73—81no—
870C4×D73—81no—
871C4×D73—81no—
872Dic146—21no—
873Dic146—21no—
874Dic146—21no—
875Dic146—21no—
876#10596831—21no—
877#10596831—21no—
878#10596831—21no—
879#10596831—21no—
880#10596831—21no—
881#10596831—21no—
882#10596831—21no—
883#10596831—21no—
884C22×C73—21no—
885C22×C73—21no—
886C22×C73—21no—
887C22×C73—21no—
888C22×C73—21no—
889C22×C73—21no—
890C22×C73—21no—
891C22×C73—21no—
892C22×C73—21no—
893C22×C73—21no—
894C22×C73—21no—
895C22×C73—21no—
896C22×C73—21no—
897C22×C73—21no—
898C22×C73—21no—
899C22×C73—22no—
900C22×C73—41no—
901C22×C73—41no—
902C22×C73—41no—
903C22×C73—41no—
904C22×C73—41no—
905C22×C73—41no—
906C22×C73—41no—
907C22×C73—41no—
908C22×C73—41no—
909C22×C73—41no—
910C22×C73—41no—
911C22×C73—82no—
912C22×C73—84no—
913C22×C73—162no—
914C22×C73—162no—
915C22×C73—162no—
916C22×C73C23×D411yescharacteristic
917C2×D73—41no—
918C2×D73—41no—
919C2×D73—41no—
920C2×D73—41no—
921C2×D73—41no—
922C2×D73—41no—
923C4×C73—21no—
924C4×C73—21no—
925C4×C73—21no—
926C4×C73—21no—
927C4×C73—21no—
928C4×C73—21no—
929C4×C73—21no—
930C4×C73—21no—
931C4×C73—21no—
932C4×C73—22no—
933C4×C73—41no—
934C4×C73—41no—
935C4×C73—41no—
936C4×C73C2×H(5,𝔽2)11yescharacteristic
937C4×C73C2×H(5,𝔽2)11yescharacteristic
938Dic73—41no—
939Dic73—41no—
940Dic73—41no—
941Dic73—41no—
942Dic73—41no—
943Dic73—41no—
944#61628—731nomaximal, Sylow
945C2×C73—41no—
946C2×C73—41no—
947C2×C73—41no—
948C2×C73—41no—
949C2×C73—41no—
950C2×C73—42no—
951C2×C73—81no—
952C2×C73—81no—
953C2×C73—81no—
954C2×C73#348411yescharacteristic
955C2×C73#358411yescharacteristic
956C2×C73#358511yescharacteristic
957D73—81no—
958D73—81no—
959#3539—731no—
960#3488D7311yescharacteristic, complemented
961#3327—731no—
962#3326—731no—
963#3318—731no—
964#3317—731no—
965#3310—731no—
966#3309—731no—
967#3297—731no—
968#3296—731no—
969#3287—731no—
970#3284—731no—
971#3274—731no—
972#3272—731no—
973#3271—731no—
974#3269—731no—
975#3268—731no—
976#3267—731no—
977#3222—731no—
978#3220—731no—
979#3204—731no—
980#3203—731no—
981#3194—731no—
982#3188—731no—
983#3120—731no—
984#3119—731no—
985#3012—731no—
986#3012—731no—
987#3005—731no—
988#3002—731no—
989#2976—731no—
990C73#6162811yescharacteristic, complemented, Sylow
991C2×H(5,𝔽2)C2×D7311yescharacteristic
992C22×#41C2×D7311yescharacteristic
993C2×#137—731no—
994C2×AGL(1,ℤ/8)—731no—
995C2×AGL(1,ℤ/8)—731no—
996C2×AGL(1,ℤ/8)—731no—
997C2×#135—731no—
998C2×#135—731no—
999C2×#135—731no—
1000C2×#135—731no—
1001#560—1461no—
1002#560—1461no—
1003#553—731no—
1004#553—731no—
1005#553—1461no—
1006#553—1461no—
1007#552—731no—
1008#552—731no—
1009#550—731no—
1010#550—731no—
1011#550C2×D7311yescharacteristic
1012#550C2×D7311yescharacteristic
1013#548C2×D7311yescharacteristic
1014#548C2×D7311yescharacteristic
1015#547—731no—
1016#547—731no—
1017#546—21no—
1018#546—21no—
1019#546C2×D7311yescharacteristic
1020#546C2×D7311yescharacteristic
1021D42—21no—
1022D42—21no—
1023D42C2×D7311yescharacteristic
1024D42C2×D7311yescharacteristic
1025#541—731no—
1026#540—731no—
1027#540—1461no—
1028#540—1461no—
1029#539—1461no—
1030#539—1461no—
1031#537—21no—
1032#537—731no—
1033#537—731no—
1034#537C2×D7311yescharacteristic
1035#535—21no—
1036#535C2×D7311yescharacteristic
1037#525—21no—
1038#525—731no—
1039#525—731no—
1040#525C2×D7311yescharacteristic
1041C2×#121—21no—
1042C2×#121C2×D7311yescharacteristic
1043#520C2×D7311yescharacteristic
1044#497—731no—
1045#496—731no—
1046#493—731no—
1047#492—731no—
1048#490—731no—
1049#490—731no—
1050#488—731no—
1051#488—731no—
1052#484—731no—
1053#484—731no—
1054#483—731no—
1055#483—731no—
1056#482—731no—
1057#482—731no—
1058#482—731no—
1059#482—731no—
1060#481—731no—
1061#481—731no—
1062#480—731no—
1063#480—731no—
1064#479—731no—
1065#479—731no—
1066#478—731no—
1067#478—731no—
1068#470—731no—
1069#469—731no—
1070#469—731no—
1071#469—731no—
1072#468—731no—
1073#468—731no—
1074#468—731no—
1075#468—731no—
1076#467—731no—
1077#466—731no—
1078#466—731no—
1079#466—731no—
1080#465—731no—
1081#465—731no—
1082#465—731no—
1083#465—731no—
1084#464—731no—
1085#464—731no—
1086#463—731no—
1087#463—731no—
1088#462—731no—
1089#461—731no—
1090#460—731no—
1091#460—731no—
1092#460—731no—
1093#459—731no—
1094#459—731no—
1095#459—731no—
1096#452—731no—
1097#452—731no—
1098#452—731no—
1099#452—731no—
1100#452—731no—
1101#452—731no—
1102#452—731no—
1103#452—731no—
1104#452—731no—
1105#452—731no—
1106#451—731no—
1107#450—731no—
1108#450—731no—
1109#450—731no—
1110#450—731no—
1111#450—731no—
1112#449—731no—
1113#449—731no—
1114#449—731no—
1115#449—731no—
1116#449—731no—
1117#449—731no—
1118#449—731no—
1119#449—731no—
1120#449—731no—
1121#449—731no—
1122#449—731no—
1123#449—731no—
1124#449—731no—
1125#449—731no—
1126#448—731no—
1127#447—731no—
1128#447—731no—
1129#447—731no—
1130#447—731no—
1131#447—731no—
1132#442—731no—
1133#441—731no—
1134#440—731no—
1135#440—731no—
1136C4×Q16—731no—
1137C4×SD16—731no—
1138C4×SD16—731no—
1139C4×D8—731no—
1140#436—731no—
1141#436—731no—
1142#435—731no—
1143#435—731no—
1144#435—731no—
1145#435—731no—
1146C8×D4—731no—
1147C8×D4—731no—
1148#433—731no—
1149#433—731no—
1150#419—731no—
1151#418—731no—
1152#417—731no—
1153#417—731no—
1154#416—731no—
1155#416—731no—
1156C2×#102—731no—
1157C2×#102—731no—
1158#408—731no—
1159#408—731no—
1160#407—731no—
1161C2×C22⋊C8—731no—
1162H(5,𝔽2)—42no—
1163H(5,𝔽2)—42no—
1164C2×#41—21no—
1165C2×#41—21no—
1166C2×#41—21no—
1167C2×#41—42no—
1168C2×#41—42no—
1169C2×#41—731no—
1170C2×#41—731no—
1171C2×#41—731no—
1172C2×#41—731no—
1173C2×#41C22×D7311yescharacteristic
1174C2×#41C22×D7311yescharacteristic
1175C2×#41C22×D7311yescharacteristic
1176C2×#41C22×D7311yescharacteristic
1177C2×#41C22×D7311yescharacteristic
1178C2×#41C22×D7311yescharacteristic
1179C2×#41C22×D7311yescharacteristic
1180C22×Q8C22×D7311yescharacteristic
1181C22×D4—21no—
1182C22×D4—21no—
1183C22×D4—21no—
1184C22×D4—21no—
1185C22×D4—21no—
1186C22×D4—21no—
1187C22×D4—21no—
1188C22×D4C22×D7311yescharacteristic
1189C22×D4C22×D7311yescharacteristic
1190C22×D4C22×D7311yescharacteristic
1191C22×D4C22×D7311yescharacteristic
1192C23×C4—21no—
1193C23×C4C22×D7311yescharacteristic
1194#137—2922no—
1195AGL(1,ℤ/8)—2922no—
1196AGL(1,ℤ/8)—2922no—
1197AGL(1,ℤ/8)—2922no—
1198#135—2922no—
1199#135—2922no—
1200#135—2922no—
1201#135—2922no—
1202C2×Q16—731no—
1203C2×Q16—731no—
1204C2×Q16—731no—
1205C2×Q16—731no—
1206C2×SD16—731no—
1207C2×SD16—731no—
1208C2×SD16—731no—
1209C2×SD16—731no—
1210C2×SD16—731no—
1211C2×SD16—731no—
1212C2×SD16—731no—
1213C2×SD16—731no—
1214C2×SD16—731no—
1215C2×SD16—731no—
1216C2×SD16—731no—
1217C2×SD16—731no—
1218C2×D8—731no—
1219C2×D8—731no—
1220C2×D8—731no—
1221C2×D8—731no—
1222C2×D8—731no—
1223C2×D8—731no—
1224C2×D8—731no—
1225C2×D8—731no—
1226C2×M16—731no—
1227C2×M16—731no—
1228C2×M16—731no—
1229C2×M16—731no—
1230C22×C8—731no—
1231C22×C8—731no—
1232C22×C8—731no—
1233C22×C8—731no—
1234C4⋊Q8—731no—
1235#127—21no—
1236#127—21no—
1237#127—731no—
1238#127—1461no—
1239#127—1461no—
1240#127C22×D7311yescharacteristic
1241#127C22×D7311yescharacteristic
1242#126—1461no—
1243#126—1461no—
1244#126—1461no—
1245#126—1461no—
1246#126—1461no—
1247#126—1461no—
1248#125—731no—
1249#125—731no—
1250#125—1461no—
1251#125—1461no—
1252#125—1461no—
1253#125—1461no—
1254#124—21no—
1255#124—21no—
1256#124C22×D7311yescharacteristic
1257#124C22×D7311yescharacteristic
1258#123—21no—
1259#123—21no—
1260#123—1461no—
1261#123—1461no—
1262#123—1461no—
1263#123—1461no—
1264#123—1461no—
1265#123—1461no—
1266#123—1461no—
1267#123—1461no—
1268#123—1461no—
1269#123—1461no—
1270#123—1461no—
1271#123—1461no—
1272#123C22⋊D7311yescharacteristic
1273#123C22⋊D7311yescharacteristic
1274C22⋊Q8—21no—
1275C22⋊Q8—21no—
1276C22⋊Q8—21no—
1277C22⋊Q8—731no—
1278C22⋊Q8—731no—
1279C22⋊Q8—731no—
1280C22⋊Q8—731no—
1281C22⋊Q8—731no—
1282C22⋊Q8—731no—
1283C22⋊Q8—1461no—
1284C22⋊Q8—1461no—
1285C22⋊Q8C22⋊D7311yescharacteristic
1286C22⋊Q8C22⋊D7311yescharacteristic
1287C22⋊Q8C22×D7311yescharacteristic
1288C22⋊Q8C22×D7311yescharacteristic
1289#121—21no—
1290#121—21no—
1291#121—21no—
1292#121—21no—
1293#121—21no—
1294#121—21no—
1295#121—21no—
1296#121—21no—
1297#121—21no—
1298#121—21no—
1299#121—21no—
1300#121—21no—
1301#121—21no—
1302#121—21no—
1303#121—21no—
1304#121—21no—
1305#121—21no—
1306#121—731no—
1307#121—731no—
1308#121—731no—
1309#121—731no—
1310#121—731no—
1311#121—731no—
1312#121—1461no—
1313#121—1461no—
1314#121—1461no—
1315#121—1461no—
1316#121—1461no—
1317#121—1461no—
1318#121—1461no—
1319#121—1461no—
1320#121—1461no—
1321#121—1461no—
1322#121—1461no—
1323#121—1461no—
1324#121—1461no—
1325#121—1461no—
1326#121—1461no—
1327#121—1461no—
1328#121C22⋊D7311yescharacteristic
1329#121C22⋊D7311yescharacteristic
1330#121C22×D7311yescharacteristic
1331#121C22×D7311yescharacteristic
1332#121C22×D7311yescharacteristic
1333#121C22×D7311yescharacteristic
1334#121C22×D7311yescharacteristic
1335#121C22×D7311yescharacteristic
1336#120—21no—
1337#120—21no—
1338#120—21no—
1339#120—21no—
1340#120—21no—
1341#120—21no—
1342#120—21no—
1343#120—21no—
1344#120—1461no—
1345#120—1461no—
1346#120C22⋊D7311yescharacteristic
1347#120C22⋊D7311yescharacteristic
1348C4×Q8—731no—
1349C4×Q8—731no—
1350C4×Q8C22×D7311yescharacteristic
1351C4×Q8C22×D7311yescharacteristic
1352C4×D4—21no—
1353C4×D4—21no—
1354C4×D4—21no—
1355C4×D4—21no—
1356C4×D4—21no—
1357C4×D4—21no—
1358C4×D4—731no—
1359C4×D4—731no—
1360C4×D4—1461no—
1361C4×D4—1461no—
1362C4×D4—1461no—
1363C4×D4—1461no—
1364C4×D4—1461no—
1365C4×D4—1461no—
1366C4×D4—1461no—
1367C4×D4—1461no—
1368C4×D4C22×D7311yescharacteristic
1369C4×D4C22×D7311yescharacteristic
1370C4×D4C22×D7311yescharacteristic
1371C4×D4C22×D7311yescharacteristic
1372C4×D4C22×D7311yescharacteristic
1373C4×D4C22×D7311yescharacteristic
1374#117—21no—
1375#117—731no—
1376#117—731no—
1377#117—1461no—
1378#117—1461no—
1379#117C22×D7311yescharacteristic
1380C2×C4⋊C4—21no—
1381C2×C4⋊C4—731no—
1382C2×C4⋊C4—731no—
1383C2×C4⋊C4—1461no—
1384C2×C4⋊C4—1461no—
1385C2×C4⋊C4C22×D7311yescharacteristic
1386C2×C22⋊C4—21no—
1387C2×C22⋊C4—21no—
1388C2×C22⋊C4—21no—
1389#107—731no—
1390#107—731no—
1391#107—731no—
1392#107—731no—
1393#106—731no—
1394#106—731no—
1395#106—731no—
1396#106—731no—
1397C4⋊C8—731no—
1398C4⋊C8—731no—
1399C4⋊C8—731no—
1400C4⋊C8—731no—
1401#103—731no—
1402#103—731no—
1403#103—731no—
1404#103—731no—
1405#103—731no—
1406#103—731no—
1407#103—731no—
1408#103—731no—
1409#103—731no—
1410#103—731no—
1411#103—731no—
1412#103—731no—
1413#102—731no—
1414#102—731no—
1415#102—731no—
1416#102—731no—
1417#102—731no—
1418#102—731no—
1419#102—731no—
1420#102—731no—
1421#102—731no—
1422#102—731no—
1423#102—731no—
1424#102—731no—
1425#102—731no—
1426#102—731no—
1427#102—731no—
1428#102—731no—
1429#102—731no—
1430#102—731no—
1431#102—731no—
1432#102—731no—
1433C22⋊C8—731no—
1434C22⋊C8—731no—
1435C22⋊C8—731no—
1436C22⋊C8—731no—
1437C22⋊C8—731no—
1438C22⋊C8—731no—
1439C22⋊C8—731no—
1440C22⋊C8—731no—
1441C22⋊C8—731no—
1442C22⋊C8—731no—
1443C22⋊C8—731no—
1444C22⋊C8—731no—
1445#97—731no—
1446#97—731no—
1447C4×C8—731no—
1448C4×C8—731no—
1449C24—21no—
1450C24—21no—
1451C24—21no—
1452C24—21no—
1453C24C2×C22⋊D7311yescharacteristic
1454#41—22no—
1455#41—22no—
1456#41—22no—
1457#41—22no—
1458#41—22no—
1459#41—22no—
1460#41—41no—
1461#41—41no—
1462#41—41no—
1463#41—41no—
1464#41—41no—
1465#41—41no—
1466#41—41no—
1467#41—41no—
1468#41—44no—
1469#41—44no—
1470#41—44no—
1471#41—2921no—
1472#41—2921no—
1473#41—2921no—
1474#41—2921no—
1475#41—2921no—
1476#41—2921no—
1477#41—2921no—
1478#41—2921no—
1479C2×Q8—21no—
1480C2×Q8—22no—
1481C2×Q8—41no—
1482C2×Q8—731no—
1483C2×Q8—731no—
1484C2×Q8C2×C22⋊D7311yescharacteristic
1485C2×Q8C23×D7311yescharacteristic
1486C2×Q8C23×D7311yescharacteristic
1487C2×D4—21no—
1488C2×D4—22no—
1489C2×D4—22no—
1490C2×D4—22no—
1491C2×D4—21no—
1492C2×D4—21no—
1493C2×D4—21no—
1494C2×D4—21no—
1495C2×D4—21no—
1496C2×D4—21no—
1497C2×D4—21no—
1498C2×D4—21no—
1499C2×D4—21no—
1500C2×D4—21no—
1501C2×D4—21no—
1502C2×D4—21no—
1503C2×D4—21no—
1504C2×D4—21no—
1505C2×D4—21no—
1506C2×D4—21no—
1507C2×D4—21no—
1508C2×D4—21no—
1509C2×D4—21no—
1510C2×D4—41no—
1511C2×D4—41no—
1512C2×D4—41no—
1513C2×D4—41no—
1514C2×D4—41no—
1515C2×D4—44no—
1516C2×D4—44no—
1517C2×D4—44no—
1518C2×D4—44no—
1519C2×D4—82no—
1520C2×D4—82no—
1521C2×D4—82no—
1522C2×D4—731no—
1523C2×D4—731no—
1524C2×D4—1461no—
1525C2×D4—1461no—
1526C2×D4—1461no—
1527C2×D4—1461no—
1528C2×D4—1461no—
1529C2×D4—1461no—
1530C2×D4—1461no—
1531C2×D4—1461no—
1532C2×D4—1461no—
1533C2×D4—1461no—
1534C2×D4—1461no—
1535C2×D4—1461no—
1536C2×D4C2×C22⋊D7311yescharacteristic
1537C2×D4C2×C22⋊D7311yescharacteristic
1538C2×D4C2×C22⋊D7311yescharacteristic
1539C2×D4C2×C22⋊D7311yescharacteristic
1540C2×D4C2×C22⋊D7311yescharacteristic
1541C2×D4C2×C22⋊D7311yescharacteristic
1542C2×D4C2×C22⋊D7311yescharacteristic
1543C2×D4C23×D7311yescharacteristic
1544C2×D4C23×D7311yescharacteristic
1545C2×D4C23×D7311yescharacteristic
1546C2×D4C23×D7311yescharacteristic
1547C22×C4—21no—
1548C22×C4—21no—
1549C22×C4—21no—
1550C22×C4—21no—
1551C22×C4—21no—
1552C22×C4—21no—
1553C22×C4—21no—
1554C22×C4—21no—
1555C22×C4—21no—
1556C22×C4—21no—
1557C22×C4—41no—
1558C22×C4—41no—
1559C22×C4—44no—
1560C22×C4—1461no—
1561C22×C4—1461no—
1562C22×C4—1461no—
1563C22×C4—1461no—
1564C22×C4—1461no—
1565C22×C4—1461no—
1566C22×C4—1461no—
1567C22×C4—1461no—
1568C22×C4C2×C22⋊D7311yescharacteristic
1569C22×C4C2×C22⋊D7311yescharacteristic
1570C22×C4C2×C22⋊D7311yescharacteristic
1571C22×C4C23×D7311yescharacteristic
1572C22×C4C23×D7311yescharacteristic
1573C22×C4C23×D7311yescharacteristic
1574C22×C4C23×D7311yescharacteristic
1575C22×C4C23×D7311yescharacteristic
1576Q16—2921no—
1577Q16—2921no—
1578Q16—1462no—
1579Q16—1462no—
1580SD16—2921no—
1581SD16—2921no—
1582SD16—2921no—
1583SD16—2921no—
1584SD16—2921no—
1585SD16—2921no—
1586SD16—2921no—
1587SD16—2921no—
1588SD16—1462no—
1589SD16—1462no—
1590SD16—1462no—
1591SD16—1462no—
1592D8—2921no—
1593D8—2921no—
1594D8—2921no—
1595D8—2921no—
1596D8—2921no—
1597D8—2921no—
1598D8—1462no—
1599D8—1462no—
1600M16—2921no—
1601M16—2921no—
1602M16—2921no—
1603M16—2921no—
1604C2×C8—2921no—
1605C2×C8—2921no—
1606C2×C8—2921no—
1607C2×C8—2921no—
1608C2×C8—731no—
1609C2×C8—731no—
1610C2×C8—731no—
1611C2×C8—731no—
1612C2×C8—731no—
1613C2×C8—731no—
1614C2×C8—731no—
1615C2×C8—731no—
1616C4⋊C4—21no—
1617C4⋊C4—21no—
1618C4⋊C4—21no—
1619C4⋊C4—21no—
1620C4⋊C4—21no—
1621C4⋊C4—731no—
1622C4⋊C4—731no—
1623C4⋊C4—731no—
1624C4⋊C4—731no—
1625C4⋊C4—1461no—
1626C4⋊C4—1461no—
1627C4⋊C4—1461no—
1628C4⋊C4—1461no—
1629C4⋊C4—1461no—
1630C4⋊C4—1461no—
1631C4⋊C4—1461no—
1632C4⋊C4—1461no—
1633C4⋊C4—1461no—
1634C4⋊C4—1461no—
1635C4⋊C4—1461no—
1636C4⋊C4—1461no—
1637C4⋊C4—1461no—
1638C4⋊C4—1461no—
1639C4⋊C4—1461no—
1640C4⋊C4—1461no—
1641C4⋊C4C2×C22⋊D7311yescharacteristic
1642C4⋊C4C2×C22⋊D7311yescharacteristic
1643C4⋊C4C2×C22⋊D7311yescharacteristic
1644C4⋊C4C2×C22⋊D7311yescharacteristic
1645C4⋊C4C2×C22⋊D7311yescharacteristic
1646C4⋊C4C2×C22⋊D7311yescharacteristic
1647C4⋊C4C23×D7311yescharacteristic
1648C4⋊C4C23×D7311yescharacteristic
1649C22⋊C4—21no—
1650C22⋊C4—21no—
1651C22⋊C4—21no—
1652C22⋊C4—21no—
1653C22⋊C4—21no—
1654C22⋊C4—21no—
1655C22⋊C4—21no—
1656C22⋊C4—21no—
1657C22⋊C4—21no—
1658C22⋊C4—21no—
1659C22⋊C4—21no—
1660C22⋊C4—21no—
1661C22⋊C4—21no—
1662C22⋊C4—21no—
1663C22⋊C4—1461no—
1664C22⋊C4—1461no—
1665C22⋊C4—1461no—
1666C22⋊C4—1461no—
1667C22⋊C4—1461no—
1668C22⋊C4—1461no—
1669C22⋊C4—1461no—
1670C22⋊C4—1461no—
1671C22⋊C4—1461no—
1672C22⋊C4—1461no—
1673C22⋊C4—1461no—
1674C22⋊C4—1461no—
1675C22⋊C4—1461no—
1676C22⋊C4—1461no—
1677C22⋊C4—1461no—
1678C22⋊C4—1461no—
1679C22⋊C4C2×C22⋊D7311yescharacteristic
1680C22⋊C4C2×C22⋊D7311yescharacteristic
1681C22⋊C4C2×C22⋊D7311yescharacteristic
1682C22⋊C4C2×C22⋊D7311yescharacteristic
1683C22⋊C4C2×C22⋊D7311yescharacteristic
1684C22⋊C4C2×C22⋊D7311yescharacteristic
1685C22⋊C4C2×C22⋊D7311yescharacteristic
1686C22⋊C4C2×C22⋊D7311yescharacteristic
1687C22⋊C4C2×C22⋊D7311yescharacteristic
1688C22⋊C4C2×C22⋊D7311yescharacteristic
1689C42—21no—
1690C42—21no—
1691C42—1461no—
1692C42—1461no—
1693C42—1461no—
1694C42—1461no—
1695C42C23×D7311yescharacteristic
1696C42C23×D7311yescharacteristic
1697C23—21no—
1698C23—21no—
1699C23—21no—
1700C23—21no—
1701C23—41no—
1702C23—41no—
1703C23—41no—
1704C23—42no—
1705C23—42no—
1706C23—42no—
1707C23—42no—
1708C23—42no—
1709C23—81no—
1710C23—81no—
1711C23—81no—
1712C23—81no—
1713C23—81no—
1714C23—81no—
1715C23—81no—
1716C23—1461no—
1717C23—1461no—
1718C23C22×C22⋊D7311yescharacteristic
1719C23C22×C22⋊D7311yescharacteristic
1720C23C22×C22⋊D7311yescharacteristic
1721C23C22×C22⋊D7311yescharacteristic
1722C23C22×C22⋊D7311yescharacteristic
1723Q8—21no—
1724Q8—21no—
1725Q8—21no—
1726Q8—41no—
1727Q8—42no—
1728Q8—1461no—
1729Q8—1461no—
1730Q8—1461no—
1731Q8—1461no—
1732Q8#1455663612yes—
1733D4—24no—
1734D4—21no—
1735D4—21no—
1736D4—21no—
1737D4—21no—
1738D4—21no—
1739D4—21no—
1740D4—21no—
1741D4—41no—
1742D4—41no—
1743D4—41no—
1744D4—41no—
1745D4—41no—
1746D4—41no—
1747D4—41no—
1748D4—42no—
1749D4—42no—
1750D4—42no—
1751D4—42no—
1752D4—42no—
1753D4—42no—
1754D4—42no—
1755D4—42no—
1756D4—42no—
1757D4—42no—
1758D4—42no—
1759D4—81no—
1760D4—81no—
1761D4—81no—
1762D4—81no—
1763D4—81no—
1764D4—81no—
1765D4—81no—
1766D4—81no—
1767D4—5841no—
1768D4—5841no—
1769D4—5841no—
1770D4—5841no—
1771D4—5841no—
1772D4—5841no—
1773D4—5841no—
1774D4—5841no—
1775D4—5841no—
1776D4—5841no—
1777D4—5841no—
1778D4—5841no—
1779D4—1461no—
1780D4—1461no—
1781D4—1461no—
1782D4—1461no—
1783D4#1455663612yes—
1784C2×C4—24no—
1785C2×C4—21no—
1786C2×C4—21no—
1787C2×C4—21no—
1788C2×C4—21no—
1789C2×C4—21no—
1790C2×C4—21no—
1791C2×C4—21no—
1792C2×C4—21no—
1793C2×C4—21no—
1794C2×C4—21no—
1795C2×C4—21no—
1796C2×C4—21no—
1797C2×C4—21no—
1798C2×C4—21no—
1799C2×C4—41no—
1800C2×C4—41no—
1801C2×C4—41no—
1802C2×C4—42no—
1803C2×C4—42no—
1804C2×C4—42no—
1805C2×C4—42no—
1806C2×C4—42no—
1807C2×C4—42no—
1808C2×C4—81no—
1809C2×C4—81no—
1810C2×C4—81no—
1811C2×C4—5841no—
1812C2×C4—5841no—
1813C2×C4—5841no—
1814C2×C4—5841no—
1815C2×C4—5841no—
1816C2×C4—5841no—
1817C2×C4—5841no—
1818C2×C4—5841no—
1819C2×C4—1461no—
1820C2×C4—1461no—
1821C2×C4—1461no—
1822C2×C4—1461no—
1823C2×C4—1461no—
1824C2×C4—1461no—
1825C2×C4C22×C22⋊D7311yescharacteristic
1826C2×C4C22×C22⋊D7311yescharacteristic
1827C2×C4C22×C22⋊D7311yescharacteristic
1828C2×C4C22×C22⋊D7311yescharacteristic
1829C2×C4C22×C22⋊D7311yescharacteristic
1830C2×C4C22×C22⋊D7311yescharacteristic
1831C2×C4C22×C22⋊D7311yescharacteristic
1832C2×C4C22×C22⋊D7311yescharacteristic
1833C2×C4C22×C22⋊D7311yescharacteristic
1834C2×C4C24×D7311yescharacteristic
1835C8—1461no—
1836C8—1461no—
1837C8—1461no—
1838C8—1461no—
1839C8—1461no—
1840C8—1461no—
1841C8—1461no—
1842C8—1461no—
1843C22—21no—
1844C22—21no—
1845C22—22no—
1846C22—21no—
1847C22—21no—
1848C22—21no—
1849C22—21no—
1850C22—21no—
1851C22—21no—
1852C22—21no—
1853C22—21no—
1854C22—21no—
1855C22—21no—
1856C22—21no—
1857C22—21no—
1858C22—21no—
1859C22—41no—
1860C22—41no—
1861C22—41no—
1862C22—41no—
1863C22—41no—
1864C22—41no—
1865C22—41no—
1866C22—41no—
1867C22—41no—
1868C22—41no—
1869C22—41no—
1870C22—82no—
1871C22—84no—
1872C22—162no—
1873C22—162no—
1874C22—162no—
1875C22—2921no—
1876C22—2921no—
1877C22—2921no—
1878C22—2921no—
1879C22—2921no—
1880C22—2921no—
1881C22C23×C22⋊D7311yescharacteristic
1882C4—21no—
1883C4—22no—
1884C4—21no—
1885C4—21no—
1886C4—21no—
1887C4—21no—
1888C4—21no—
1889C4—21no—
1890C4—21no—
1891C4—21no—
1892C4—41no—
1893C4—41no—
1894C4—41no—
1895C4—2921no—
1896C4—2921no—
1897C4—2921no—
1898C4—2921no—
1899C4—2921no—
1900C4—2921no—
1901C4C2×#1455663611yescharacteristic
1902C4C2×#1455663611yescharacteristic
1903C2—41no—
1904C2—41no—
1905C2—41no—
1906C2—41no—
1907C2—41no—
1908C2—42no—
1909C2—81no—
1910C2—81no—
1911C2—81no—
1912C2—5841no—
1913C2—5841no—
1914C2#2262356611yescharacteristic
1915C2#2262470211yescharacteristic
1916C2#2262471111yescharacteristic
subgroupG/H
centerC22C23×C22⋊D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC73×#3488C2
socleC22×C73C23×D4
hypercenter#3488D73
hypocenterC73#61628
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ #525 ◁ #3488

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #22624191C2semidirect
2. #22622199C2semidirect
3. #22622184C2semidirect
4. #22622072C2semidirect
5. #22622057C2semidirect
6. #22621952C2semidirect
7. #22621937C2semidirect
8. #22621781C2semidirect
9. #22621766C2semidirect
10. #22621687C2semidirect
11. #22621661C2semidirect
12. #22621547C2semidirect
13. #22621527C2semidirect
14. #22621517C2semidirect
15. #22621487C2semidirect
16. #22621467C2semidirect
17. #22621452C2semidirect
18. #22621003C2semidirect
19. #22620981C2semidirect
20. #22620837C2semidirect
21. #22620828C2semidirect
22. #22620745C2semidirect
23. #22620696C2semidirect
24. #22620145C2semidirect
25. #22620130C2semidirect
26. #22619235C2semidirect
27. #22619235C2semidirect
28. #22619173C2semidirect
29. #22619149C2semidirect
30. #22618979C2semidirect
31. C73×#3488C2semidirect
32. C2×#14556622C22semidirect
33. C2×#14556617C22semidirect
34. C2×#14556617C22semidirect
35. C2×#14556617C22semidirect
36. C2×#14556611C22semidirect
37. C2×#14556611C22semidirect
38. C2×#14556611C22semidirect
39. C2×#14556611C22semidirect
42. #17989283C22semidirect
43. #17989283C22semidirect
46. #17989277C22semidirect
47. #17989277C22semidirect
48. #17989258C22semidirect
49. #17989258C22semidirect
50. #17989242C22semidirect
51. #17989242C22semidirect
52. #17989199C22semidirect
53. #17989192C22semidirect
58. #17989165C22semidirect
59. #17989165C22semidirect
60. #17989098C22semidirect
61. #17989098C22semidirect
62. #17988982C22semidirect
63. #17988977C22semidirect
64. #17988963C22semidirect
65. #17988959C22semidirect
66. #17988951C22semidirect
67. #17988951C22semidirect
68. #17988941C22semidirect
69. #17988941C22semidirect
70. #17988922C22semidirect
71. #17988920C22semidirect
72. #17988917C22semidirect
73. #17988915C22semidirect
74. #17988908C22semidirect
75. #17988908C22semidirect
76. #17988908C22semidirect
77. #17988908C22semidirect
78. #17988905C22semidirect
79. #17988903C22semidirect
80. #17988900C22semidirect
81. #17988898C22semidirect
82. #17988894C22semidirect
83. #17988894C22semidirect
84. #17988887C22semidirect
85. #17988887C22semidirect
86. #17988843C22semidirect
87. #17988838C22semidirect
88. #17988838C22semidirect
89. #17988838C22semidirect
90. #17988835C22semidirect
91. #17988831C22semidirect
92. #17988831C22semidirect
93. #17988831C22semidirect
94. #17988826C22semidirect
95. #17988821C22semidirect
96. #17988821C22semidirect
97. #17988821C22semidirect
98. #17988818C22semidirect
99. #17988814C22semidirect
100. #17988814C22semidirect
101. #17988814C22semidirect
102. #17988806C22semidirect
103. #17988806C22semidirect
104. #17988799C22semidirect
105. #17988799C22semidirect
106. #17988797C22semidirect
107. #17988792C22semidirect
108. #17988787C22semidirect
109. #17988784C22semidirect
110. #17988784C22semidirect
111. #17988782C22semidirect
112. #17988779C22semidirect
113. #17988779C22semidirect
116. #17988749C22semidirect
117. #17988749C22semidirect
118. #17988749C22semidirect
119. #17988749C22semidirect
120. #17988749C22semidirect
121. #17988749C22semidirect
122. #17988747C22semidirect
123. #17988747C22semidirect
124. #17988743C22semidirect
125. #17988738C22semidirect
126. #17988738C22semidirect
127. #17988738C22semidirect
128. #17988738C22semidirect
129. #17988738C22semidirect
132. #17988732C22semidirect
133. #17988732C22semidirect
134. #17988732C22semidirect
135. #17988732C22semidirect
136. #17988732C22semidirect
137. #17988732C22semidirect
138. #17988730C22semidirect
139. #17988730C22semidirect
140. #17988730C22semidirect
141. #17988730C22semidirect
142. #17988730C22semidirect
143. #17988730C22semidirect
144. #17988726C22semidirect
145. #17988721C22semidirect
146. #17988721C22semidirect
147. #17988721C22semidirect
148. #17988721C22semidirect
149. #17988721C22semidirect
150. #17988697C22semidirect
151. #17988692C22semidirect
152. #17988687C22semidirect
153. #17988685C22semidirect
154. C4×#11924018C22semidirect
155. C4×#11924015C22semidirect
156. C4×#11924016C22semidirect
157. C4×#11924013C22semidirect
158. #17988665C22semidirect
159. #17988665C22semidirect
160. #17988659C22semidirect
161. #17988659C22semidirect
162. #17988659C22semidirect
163. #17988659C22semidirect
164. D4×#10596831C22semidirect
165. D4×#10596831C22semidirect
166. #17988648C22semidirect
167. #17988648C22semidirect
168. #17988596C22semidirect
169. #17988592C22semidirect
170. #17988588C22semidirect
171. #17988588C22semidirect
172. #17988583C22semidirect
173. #17988583C22semidirect
174. C2×#14556512C22semidirect
175. C2×#14556512C22semidirect
176. #17988554C22semidirect
177. #17988554C22semidirect
178. #17988551C22semidirect
179. C2×C22⋊#10596831C22semidirect
960. #3488D73semidirect
990. C73#61628semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#226241912
#226221992
#226221842
#226220722
#226220572
#226219522
#226219372
#226217812
#226217662
#226216872
#226216612
#226215472
#226215272
#226215172
#226214872
#226214672
#226214522
#226210032
#226209812
#226208372
#226208282
#226207452
#226206962
#226201452
#226201302
#226192352
#226191732
#226191492
#226189792
C73×#34882
#6162873