Finite Group Databasebeta

← #33979767

Subgroups — #33979767

Order 18688.

1860 conjugacy classes of subgroups.

The subgroup lattice has 1790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22623875C211yesmaximal, characteristic, complemented
2#22622997C211yesmaximal, characteristic, complemented
3#22622939C211yesmaximal, characteristic, complemented
4#22622678C211yesmaximal, characteristic, complemented
5#22622576C211yesmaximal, characteristic, complemented
6#22622236C211yesmaximal, characteristic, complemented
7#22622199C211yesmaximal, characteristic, complemented
8#22622184C211yesmaximal, characteristic, complemented
9#22622057C211yesmaximal, characteristic, complemented
10#22621892C211yesmaximal, characteristic, complemented
11#22621781C211yesmaximal, characteristic, complemented
12#22621639C211yesmaximal, characteristic, complemented
13#22621551C211yesmaximal, characteristic, complemented
14#22621538C211yesmaximal, characteristic, complemented
15#22621538C211yesmaximal, characteristic, complemented
16#22621457C211yesmaximal, characteristic, complemented
17#22621427C211yesmaximal, characteristic, complemented
18#22621372C211yesmaximal, characteristic, complemented
19#22621336C211yesmaximal, characteristic, complemented
20#22621327C211yesmaximal, characteristic, complemented
21#22621040C211yesmaximal, characteristic, complemented
22#22620981C211yesmaximal, characteristic, complemented
23#22620907C211yesmaximal, characteristic, complemented
24#22620169C211yesmaximal, characteristic, complemented
25#22620139C211yesmaximal, characteristic, complemented
26#22619974C211yesmaximal, characteristic, complemented
27#22619466C211yesmaximal, characteristic, complemented
28#22619439C211yesmaximal, characteristic, complemented
29#22619391C211yesmaximal, characteristic, complemented
30#22619080C211yesmaximal, characteristic, complemented
31C73×#3562C211yesmaximal, characteristic, complemented
32C2×#14556617C2211yescharacteristic
33C2×#14556616C2211yescharacteristic
34C2×#14556616C2211yescharacteristic
35C2×#14556616C2211yescharacteristic, complemented
36C2×#14556611C2211yescharacteristic
37C22×#11924015C2211yescharacteristic, complemented
38#17989322C2211yescharacteristic, complemented
39#17989297C2211yescharacteristic, complemented
40#17989288—21no—
41#17989283C2211yescharacteristic
42#17989277C2211yescharacteristic, complemented
43#17989264—21no—
44#17989262—21no—
45#17989241C2211yescharacteristic
46#17989233C2211yescharacteristic
47#17989233C2211yescharacteristic
48#17989226—21no—
49D4×D292C2211yescharacteristic, complemented
50#17989208C2211yescharacteristic, complemented
51#17989192C2211yescharacteristic
52#17989185—21no—
53#17989171—21no—
54#17989121C2211yescharacteristic, complemented
55#17989095—21no—
56#123×D73—21no—
57#17989067C2211yescharacteristic
58#17989061C2211yescharacteristic, complemented
59C2×C4×D292C2211yescharacteristic, complemented
60#17988979C2211yescharacteristic, complemented
61#17988977C2211yescharacteristic
62#17988969C2211yescharacteristic, complemented
63#17988969C2211yescharacteristic, complemented
64#17988969C2211yescharacteristic, complemented
65#17988963C2211yescharacteristic
66#17988951C2211yescharacteristic, complemented
67#17988946C2211yescharacteristic, complemented
68#17988941C2211yescharacteristic, complemented
69#17988941C2211yescharacteristic, complemented
70#17988941C2211yescharacteristic, complemented
71#17988937C2211yescharacteristic, complemented
72#17988920C2211yescharacteristic, complemented
73#17988920C2211yescharacteristic, complemented
74#17988915C2211yescharacteristic, complemented
75#17988908C2211yescharacteristic, complemented
76#17988908C2211yescharacteristic, complemented
77#17988903C2211yescharacteristic, complemented
78#17988894C2211yescharacteristic, complemented
79#17988894C2211yescharacteristic, complemented
80#17988894C2211yescharacteristic, complemented
81#17988891C2211yescharacteristic, complemented
82#17988887C2211yescharacteristic, complemented
83#17988884C2211yescharacteristic, complemented
84#17988884C2211yescharacteristic, complemented
85#17988884C2211yescharacteristic, complemented
86#17988877C2211yescharacteristic, complemented
87#17988867C2211yescharacteristic, complemented
88#17988843C2211yescharacteristic, complemented
89#17988838C2211yescharacteristic
90#17988838C2211yescharacteristic, complemented
91#17988835C2211yescharacteristic, complemented
92#17988835C2211yescharacteristic, complemented
93#17988835C2211yescharacteristic, complemented
94#17988831C2211yescharacteristic, complemented
95#17988831C2211yescharacteristic, complemented
96#17988821C2211yescharacteristic
97#17988818C2211yescharacteristic, complemented
98#17988818C2211yescharacteristic, complemented
99#17988814C2211yescharacteristic, complemented
100#17988809C2211yescharacteristic, complemented
101#17988806C2211yescharacteristic, complemented
102#17988806C2211yescharacteristic, complemented
103#17988802C2211yescharacteristic, complemented
104#17988802C2211yescharacteristic, complemented
105#17988802C2211yescharacteristic, complemented
106#17988799C2211yescharacteristic
107#17988799C2211yescharacteristic
108#17988799C2211yescharacteristic
109#17988799C2211yescharacteristic
110#17988799C2211yescharacteristic, complemented
111#17988799C2211yescharacteristic, complemented
112#17988799C2211yescharacteristic, complemented
113#17988799C2211yescharacteristic, complemented
114#17988799C2211yescharacteristic, complemented
115#17988799C2211yescharacteristic, complemented
116#17988794C2211yescharacteristic, complemented
117#17988789C2211yescharacteristic, complemented
118#17988789C2211yescharacteristic, complemented
119#17988789C2211yescharacteristic, complemented
120#17988789C2211yescharacteristic, complemented
121#17988789C2211yescharacteristic, complemented
122#17988787C2211yescharacteristic, complemented
123#17988787C2211yescharacteristic, complemented
124#17988784C2211yescharacteristic, complemented
125#17988784C2211yescharacteristic, complemented
126#17988779C2211yescharacteristic
127#17988779C2211yescharacteristic
128#17988779C2211yescharacteristic, complemented
129#17988779C2211yescharacteristic, complemented
130#17988749C2211yescharacteristic, complemented
131#17988749C2211yescharacteristic, complemented
132#17988749C2211yescharacteristic, complemented
133#17988747C2211yescharacteristic
134#17988747C2211yescharacteristic
135#17988743C2211yescharacteristic, complemented
136#17988737C2211yescharacteristic, complemented
137#17988732C2211yescharacteristic
138#17988732C2211yescharacteristic
139#17988732C2211yescharacteristic, complemented
140#17988732C2211yescharacteristic, complemented
141#17988732C2211yescharacteristic, complemented
142#17988726C2211yescharacteristic, complemented
143#17988721C2211yescharacteristic, complemented
144#17988721C2211yescharacteristic, complemented
145#17988720C2211yescharacteristic
146#17988720C2211yescharacteristic
147#17988720C2211yescharacteristic, complemented
148#17988718C2211yescharacteristic, complemented
149Q8×#10596831C2211yescharacteristic, complemented
150#17988697C2211yescharacteristic, complemented
151#17988697C2211yescharacteristic, complemented
152#17988692C2211yescharacteristic, complemented
153#17988685C2211yescharacteristic, complemented
154C4×#11924018C2211yescharacteristic, complemented
155C4×#11924015C2211yescharacteristic, complemented
156C4×#11924015C2211yescharacteristic, complemented
157C4×#11924015C2211yescharacteristic, complemented
158C4×#11924013C2211yescharacteristic
159C4×#11924013C2211yescharacteristic
160C4×#11924013C2211yescharacteristic, complemented
161C4×#11924013C2211yescharacteristic, complemented
162#17988665C2211yescharacteristic, complemented
163#17988665C2211yescharacteristic, complemented
164#17988665C2211yescharacteristic, complemented
165#17988659C2211yescharacteristic, complemented
166#17988659C2211yescharacteristic, complemented
167D4×#10596831C2211yescharacteristic, complemented
168#17988648C2211yescharacteristic, complemented
169#17988648C2211yescharacteristic, complemented
170#17988640C2211yescharacteristic, complemented
171#17988614C2211yescharacteristic, complemented
172#17988614C2211yescharacteristic, complemented
173#17988611C2211yescharacteristic, complemented
174#17988596C2211yescharacteristic, complemented
175#17988588C2211yescharacteristic, complemented
176#17988588C2211yescharacteristic, complemented
177#17988588C2211yescharacteristic, complemented
178#17988583C2211yescharacteristic, complemented
179C2×#14556512C2211yescharacteristic, complemented
180#562×C73—21no—
181#560×C73—21no—
182#559×C73C2211yescharacteristic, complemented
183#556×C73C2211yescharacteristic, complemented
184#553×C73—21no—
185#551×C73—21no—
186#550×C73C2211yescharacteristic
187#548×C73C2211yescharacteristic
188#548×C73C2211yescharacteristic, complemented
189#547×C73C2211yescharacteristic, complemented
190#546×C73C2211yescharacteristic, complemented
191#546×C73C2211yescharacteristic, complemented
192#541×C73C2211yescharacteristic, complemented
193#540×C73—21no—
194#540×C73C2211yescharacteristic, complemented
195#539×C73—21no—
196#538×C73—21no—
197#538×C73—21no—
198#536×C73C2211yescharacteristic, complemented
199#535×C73C2211yescharacteristic, complemented
200#532×C73C2211yescharacteristic, complemented
201#529×C73C2211yescharacteristic
202#529×C73C2211yescharacteristic, complemented
203C2×#11924028C2311yescharacteristic
204C2×#11924027—21no—
205C22×D292C2311yescharacteristic
206C22×D292C2311yescharacteristic
207C2×D4×D73—21no—
208C22×C4×D73—21no—
209#14556617—42no—
210#14556616—42no—
211#14556616—42no—
212#14556616—42no—
213#14556611—42no—
214C2×#11924018C2311yescharacteristic
215C2×#11924018C2311yescharacteristic
216C2×#11924018C2311yescharacteristic
217C2×#11924016C2311yescharacteristic
218C2×#11924016C2311yescharacteristic
219C2×#11924016C2311yescharacteristic
220C2×#11924015—42no—
221C2×#11924015C2311yescharacteristic
222C2×#11924015C2311yescharacteristic
223C2×#11924015C2311yescharacteristic
224C2×#11924015C2311yescharacteristic
225C2×#11924015C2311yescharacteristic
226C2×#11924015C2311yescharacteristic
227C2×#11924015C2311yescharacteristic
228C2×#11924015C2311yescharacteristic
229C2×#11924015C2311yescharacteristic
230C2×#11924013C2311yescharacteristic
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
245#14556591C2311yescharacteristic
246#14556588C2311yescharacteristic
247#14556586—21no—
248#14556586—21no—
249#14556585—21no—
250#14556584—21no—
251#14556583C2311yescharacteristic
252#14556583C2311yescharacteristic
253#14556581—21no—
254#14556580—21no—
255#14556579C2311yescharacteristic
256#14556579C2311yescharacteristic
257#14556577—21no—
258#14556576—21no—
259#14556576—21no—
260#14556576—21no—
261#14556576—21no—
262#14556576—21no—
263#14556576—21no—
264#14556575—21no—
265#14556575—21no—
266#14556574—21no—
267#14556573—21no—
268#14556573—21no—
269#14556572—21no—
270#14556571—21no—
271#14556570C2311yescharacteristic
272#14556570C2311yescharacteristic
273#14556569—21no—
274#14556569—21no—
275#14556569—21no—
276#14556567—21no—
277#14556566—21no—
278#14556565C2311yescharacteristic
279#14556565C2311yescharacteristic
280#14556565C2311yescharacteristic
281#14556565C2311yescharacteristic
282#14556564—21no—
283#14556564—21no—
284#14556564—21no—
285#14556564—21no—
286#14556563—21no—
287#14556561—21no—
288#14556561—21no—
289#14556559—21no—
290#14556559—21no—
291C4×Dic146C2311yescharacteristic
292C4×Dic146C2311yescharacteristic
293C4×D292—21no—
294C4×D292—21no—
295C4×D292C2311yescharacteristic
296C4×D292C2311yescharacteristic
297C4×D292C2311yescharacteristic
298C4×D292C2311yescharacteristic
299C4×D292C2311yescharacteristic
300C4×D292C2311yescharacteristic
301C4×D292C2311yescharacteristic
302C4×D292C2311yescharacteristic
303#14556553—21no—
304#14556553—21no—
305#14556553—21no—
306C4×C22⋊D73—21no—
307#14556551—21no—
308#14556551—21no—
309#14556551—21no—
310#14556550C2311yescharacteristic
311#14556549—21no—
312#14556548—21no—
313#14556547—21no—
314C2×C4⋊Dic73C2311yescharacteristic
315C2×C4⋊Dic73C2311yescharacteristic
316C4⋊C4×D73—21no—
317C4⋊C4×D73—21no—
318C2×#11924005—21no—
319C22⋊C4×D73—21no—
320C22⋊C4×D73—21no—
321C22⋊C4×D73—21no—
322C22⋊C4×D73—21no—
323#14556524C2311yescharacteristic
324#14556524C2311yescharacteristic
325#14556524C2311yescharacteristic
326#14556524C2311yescharacteristic
327#14556522C2311yescharacteristic
328#14556522C2311yescharacteristic
329#14556522C2311yescharacteristic
330#14556522C2311yescharacteristic
331C4⋊#10596831C2311yescharacteristic
332C4⋊#10596831C2311yescharacteristic
333C4⋊#10596831C2311yescharacteristic
334C4⋊#10596831C2311yescharacteristic
335C4⋊#10596831C2311yescharacteristic
336C4⋊#10596831C2311yescharacteristic
337C4⋊#10596831C2311yescharacteristic
338C4⋊#10596831C2311yescharacteristic
339C4⋊#10596831C2311yescharacteristic
340C4⋊#10596831C2311yescharacteristic
341#14556515C2311yescharacteristic
342#14556515C2311yescharacteristic
343#14556515C2311yescharacteristic
344#14556515C2311yescharacteristic
345#14556515C2311yescharacteristic
346#14556515C2311yescharacteristic
347#14556515C2311yescharacteristic
348#14556515C2311yescharacteristic
349#14556515C2311yescharacteristic
350#14556515C2311yescharacteristic
351#14556515C2311yescharacteristic
352#14556515C2311yescharacteristic
353#14556514C2311yescharacteristic
354#14556514C2311yescharacteristic
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
371#14556511C2311yescharacteristic
372#14556511C2311yescharacteristic
373C22⋊#10596831C2311yescharacteristic
374C22⋊#10596831C2311yescharacteristic
375C22⋊#10596831C2311yescharacteristic
376C22⋊#10596831C2311yescharacteristic
377C22⋊#10596831C2311yescharacteristic
378C22⋊#10596831C2311yescharacteristic
379#14556502C2311yescharacteristic
380#14556502C2311yescharacteristic
381C4×#10596831C2311yescharacteristic
382C4×#10596831C2311yescharacteristic
383C4×#10596831C2311yescharacteristic
384C4×#10596831C2311yescharacteristic
385C2×#41×C73C2311yescharacteristic
386C2×#41×C73C2311yescharacteristic
387C2×#41×C73C2311yescharacteristic
388C2×#41×C73C2311yescharacteristic
389C22×Q8×C73C2311yescharacteristic
390C22×D4×C73C2311yescharacteristic
391C4⋊Q8×C73C2311yescharacteristic
392C4⋊Q8×C73C2311yescharacteristic
393#127×C73—21no—
394#127×C73C2311yescharacteristic
395#127×C73C2311yescharacteristic
396#126×C73—21no—
397#126×C73—21no—
398#126×C73—21no—
399#126×C73—21no—
400#126×C73—21no—
401#126×C73D411yescharacteristic
402#126×C73D411yescharacteristic
403#125×C73—21no—
404#125×C73—21no—
405#125×C73D411yescharacteristic
406#125×C73C2311yescharacteristic
407#124×C73—21no—
408#124×C73—21no—
409#124×C73—21no—
410#124×C73D411yescharacteristic
411#124×C73C2311yescharacteristic
412#124×C73C2311yescharacteristic
413#124×C73C2311yescharacteristic
414#124×C73C2311yescharacteristic
415#124×C73C2311yescharacteristic
416#123×C73—21no—
417#123×C73—21no—
418#123×C73—21no—
419#123×C73—21no—
420#123×C73—21no—
421#123×C73—21no—
422#123×C73—21no—
423#123×C73—21no—
424#123×C73—21no—
425#123×C73—21no—
426#123×C73—21no—
427#123×C73D411yescharacteristic
428#123×C73D411yescharacteristic
429C22⋊Q8×C73—21no—
430C22⋊Q8×C73—21no—
431C22⋊Q8×C73—21no—
432C22⋊Q8×C73—21no—
433C22⋊Q8×C73—21no—
434C22⋊Q8×C73D411yescharacteristic
435C22⋊Q8×C73C2311yescharacteristic
436C22⋊Q8×C73C2311yescharacteristic
437C22⋊Q8×C73C2311yescharacteristic
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×C73C2311yescharacteristic
453#121×C73C2311yescharacteristic
454#121×C73C2311yescharacteristic
455#120×C73—21no—
456#120×C73—21no—
457#120×C73—21no—
458#120×C73—21no—
459C4×Q8×C73C2311yescharacteristic
460C4×Q8×C73C2311yescharacteristic
461C4×Q8×C73C2311yescharacteristic
462C4×Q8×C73C2311yescharacteristic
463C4×D4×C73—21no—
464C4×D4×C73—21no—
465C4×D4×C73—21no—
466C4×D4×C73—21no—
467C4×D4×C73—21no—
468C4×D4×C73—21no—
469C4×D4×C73—21no—
470C4×D4×C73C2311yescharacteristic
471C4×D4×C73C2311yescharacteristic
472C4×D4×C73C2311yescharacteristic
473C4×D4×C73C2311yescharacteristic
474C4×D4×C73C2311yescharacteristic
475C4×D4×C73C2311yescharacteristic
476#117×C73—21no—
477#117×C73—21no—
478#117×C73C2311yescharacteristic
479#117×C73C2311yescharacteristic
480C2×C4⋊C4×C73—21no—
481C2×C22⋊C4×C73—21no—
482C2×C22⋊C4×C73—21no—
483C2×C42×C73C2311yescharacteristic
484C23×D73—21no—
485C23×D73—21no—
486#11924028—22no—
487#11924028—41no—
488#11924027—82no—
489C2×Dic146—21no—
490C2×Dic146C2411yescharacteristic
491C2×D292—22no—
492C2×D292—22no—
493C2×D292—21no—
494C2×D292—21no—
495C2×D292—21no—
496C2×D292—21no—
497C2×D292—41no—
498C2×D292—41no—
499C2×D292C2411yescharacteristic
500C2×D292C2411yescharacteristic
501C2×D292C2411yescharacteristic
502C2×C22⋊D73—21no—
503C2×C22⋊D73—21no—
504C2×C22⋊D73—21no—
505C2×C22⋊D73—21no—
506C2×C22⋊D73—21no—
507D4×D73—82no—
508C22×Dic73—21no—
509C22×Dic73—21no—
510C2×C4×D73—21no—
511C2×C4×D73—21no—
512C2×C4×D73—21no—
513C2×C4×D73—21no—
514C2×C4×D73—21no—
515C2×C4×D73—21no—
516C2×C4×D73—21no—
517C2×C4×D73—21no—
518C2×C4×D73—21no—
519C2×C4×D73—82no—
520#11924018—41no—
521#11924018—41no—
522#11924018—41no—
523#11924016—41no—
524#11924016—41no—
525#11924016—41no—
526#11924015—22no—
527#11924015—22no—
528#11924015—22no—
529#11924015—41no—
530#11924015—41no—
531#11924015—41no—
532#11924015—41no—
533#11924015—41no—
534#11924015—41no—
535#11924013—22no—
536#11924013—22no—
537#11924013—22no—
538#11924013—41no—
539#11924013—41no—
540#11924013—41no—
541#11924013—41no—
542#11924013—41no—
543#11924013—41no—
544#11924012—41no—
545#11924012—41no—
546#11924012—41no—
547#11924012—41no—
548C2×#10596831—41no—
549C2×#10596831—41no—
550C2×#10596831C2411yescharacteristic
551C2×#10596831C2411yescharacteristic
552C2×#10596831C2411yescharacteristic
553C2×#10596831C2411yescharacteristic
554C2×#10596831C2411yescharacteristic
555C2×#10596831C2411yescharacteristic
556C2×#10596831C2411yescharacteristic
557C2×#10596831C2411yescharacteristic
558C4⋊Dic73—21no—
559C4⋊Dic73—21no—
560C4⋊Dic73—21no—
561C4⋊Dic73C2411yescharacteristic
562C4⋊Dic73C2411yescharacteristic
563C4⋊Dic73C2411yescharacteristic
564C4⋊Dic73C2411yescharacteristic
565#11924007—21no—
566#11924007—21no—
567#11924007—21no—
568#11924007—21no—
569#11924007—21no—
570#11924007—21no—
571#11924007—21no—
572#11924007—21no—
573C22⋊Dic73—21no—
574C22⋊Dic73—21no—
575C22⋊Dic73—21no—
576#11924005—21no—
577#11924005—21no—
578#11924005—21no—
579#11924005—21no—
580#11924005—21no—
581#11924005—21no—
582#11924005—21no—
583#11924005—21no—
584#11924005—21no—
585#11924005—21no—
586#11924005—21no—
587#11924005—21no—
588#11924005—21no—
589#11924005—21no—
590#11924005—21no—
591#11924005—21no—
592C4×Dic73—21no—
593C4×Dic73—21no—
594C4×Dic73—21no—
595C24×C73—21no—
596#41×C73—41no—
597#41×C73—41no—
598#41×C73—41no—
599#41×C73—41no—
600#41×C73—41no—
601#41×C73—41no—
602#41×C73—41no—
603#41×C73—41no—
604C2×Q8×C73—21no—
605C2×Q8×C73—41no—
606C2×Q8×C73—41no—
607C2×Q8×C73C2×D411yescharacteristic
608C2×Q8×C73C2411yescharacteristic
609C2×Q8×C73C2411yescharacteristic
610C2×Q8×C73C2411yescharacteristic
611C2×D4×C73—21no—
612C2×D4×C73—21no—
613C2×D4×C73—21no—
614C2×D4×C73—21no—
615C2×D4×C73—21no—
616C2×D4×C73—21no—
617C2×D4×C73—21no—
618C2×D4×C73—21no—
619C2×D4×C73—21no—
620C2×D4×C73—21no—
621C2×D4×C73—21no—
622C2×D4×C73—21no—
623C2×D4×C73—41no—
624C2×D4×C73—41no—
625C2×D4×C73C2×D411yescharacteristic
626C2×D4×C73C2×D411yescharacteristic
627C2×D4×C73C2×D411yescharacteristic
628C2×D4×C73C2411yescharacteristic
629C2×D4×C73C2411yescharacteristic
630C2×D4×C73C2411yescharacteristic
631C22×C4×C73—21no—
632C22×C4×C73—21no—
633C22×C4×C73—21no—
634C22×C4×C73—21no—
635C22×C4×C73—21no—
636C22×C4×C73—21no—
637C22×C4×C73—21no—
638C22×C4×C73—21no—
639C22×C4×C73C2×D411yescharacteristic
640C22×C4×C73C2×D411yescharacteristic
641C22×C4×C73C2411yescharacteristic
642C22×C4×C73C2411yescharacteristic
643C22×C4×C73C2411yescharacteristic
644C4⋊C4×C73—21no—
645C4⋊C4×C73—21no—
646C4⋊C4×C73—21no—
647C4⋊C4×C73—21no—
648C4⋊C4×C73—21no—
649C4⋊C4×C73—21no—
650C4⋊C4×C73—21no—
651C4⋊C4×C73—21no—
652C4⋊C4×C73—21no—
653C4⋊C4×C73—21no—
654C4⋊C4×C73—21no—
655C4⋊C4×C73—21no—
656C4⋊C4×C73C2×D411yescharacteristic
657C4⋊C4×C73C2×D411yescharacteristic
658C4⋊C4×C73C2×D411yescharacteristic
659C4⋊C4×C73C2×D411yescharacteristic
660C4⋊C4×C73C2×D411yescharacteristic
661C4⋊C4×C73C2×D411yescharacteristic
662C4⋊C4×C73C2×D411yescharacteristic
663C4⋊C4×C73C2×D411yescharacteristic
664C4⋊C4×C73C2×D411yescharacteristic
665C4⋊C4×C73C2×D411yescharacteristic
666C4⋊C4×C73C2411yescharacteristic
667C4⋊C4×C73C2411yescharacteristic
668C22⋊C4×C73—21no—
669C22⋊C4×C73—21no—
670C22⋊C4×C73—21no—
671C22⋊C4×C73—21no—
672C22⋊C4×C73—21no—
673C22⋊C4×C73—21no—
674C22⋊C4×C73—21no—
675C22⋊C4×C73—21no—
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—21no—
687C22⋊C4×C73C2×D411yescharacteristic
688C22⋊C4×C73C2×D411yescharacteristic
689C22⋊C4×C73C2×D411yescharacteristic
690C22⋊C4×C73C2×D411yescharacteristic
691C22⋊C4×C73C2×D411yescharacteristic
692C22⋊C4×C73C2×D411yescharacteristic
693C22⋊C4×C73C2×D411yescharacteristic
694C22⋊C4×C73C2×D411yescharacteristic
695C22⋊C4×C73C2×D411yescharacteristic
696C22⋊C4×C73C2×D411yescharacteristic
697C42×C73—21no—
698C42×C73—21no—
699C42×C73—21no—
700C42×C73C2×D411yescharacteristic
701C42×C73C2×D411yescharacteristic
702C42×C73C2411yescharacteristic
703C42×C73C2411yescharacteristic
704C42×C73C2411yescharacteristic
705C42×C73C2411yescharacteristic
706C23×C73—21no—
707C23×C73—21no—
708C23×C73—21no—
709C23×C73—81no—
710C23×C73—81no—
711C23×C73—81no—
712C23×C73C22×D411yescharacteristic
713C23×C73C22×D411yescharacteristic
714C23×C73C22×D411yescharacteristic
715C22×D73—21no—
716C22×D73—21no—
717C22×D73—21no—
718C22×D73—42no—
719C22×D73—42no—
720C22×D73—42no—
721C22×D73—81no—
722C22×D73—81no—
723C22×D73—81no—
724Q8×C73—21no—
725Q8×C73—21no—
726Q8×C73—21no—
727Q8×C73—21no—
728Q8×C73—21no—
729Q8×C73—21no—
730Q8×C73—41no—
731Q8×C73—81no—
732D4×C73—21no—
733D4×C73—21no—
734D4×C73—21no—
735D4×C73—21no—
736D4×C73—21no—
737D4×C73—21no—
738D4×C73—41no—
739D4×C73—41no—
740D4×C73—41no—
741D4×C73—81no—
742D4×C73—81no—
743D4×C73—81no—
744D4×C73—81no—
745D4×C73—81no—
746D4×C73—81no—
747D4×C73—81no—
748D4×C73—81no—
749D4×C73—81no—
750D4×C73—81no—
751D4×C73—81no—
752D4×C73—81no—
753C2×C4×C73—21no—
754C2×C4×C73—21no—
755C2×C4×C73—21no—
756C2×C4×C73—21no—
757C2×C4×C73—21no—
758C2×C4×C73—21no—
759C2×C4×C73—21no—
760C2×C4×C73—21no—
761C2×C4×C73—21no—
762C2×C4×C73—21no—
763C2×C4×C73—21no—
764C2×C4×C73—41no—
765C2×C4×C73—41no—
766C2×C4×C73—81no—
767C2×C4×C73—81no—
768C2×C4×C73—81no—
769C2×C4×C73—81no—
770C2×C4×C73—81no—
771C2×C4×C73—81no—
772C2×C4×C73—81no—
773C2×C4×C73—81no—
774C2×C4×C73C22×D411yescharacteristic
775C2×C4×C73C22×D411yescharacteristic
776C2×C4×C73C22×D411yescharacteristic
777C2×C4×C73C22×D411yescharacteristic
778C2×C4×C73C22×D411yescharacteristic
779C2×C4×C73C22×D411yescharacteristic
780C2×C4×C73C22×D411yescharacteristic
781C2×C4×C73C22×D411yescharacteristic
782C2×C4×C73C22×D411yescharacteristic
783C2×C4×C73C22×D411yescharacteristic
784C2×C4×C73C22×D411yescharacteristic
785C2×C4×C73C2511yescharacteristic
786C22⋊D73—42no—
787C22⋊D73—42no—
788C22⋊D73—81no—
789C22⋊D73—81no—
790C22⋊D73—81no—
791C2×Dic73—21no—
792C2×Dic73—21no—
793C2×Dic73—21no—
794C2×Dic73—21no—
795C2×Dic73—21no—
796C2×Dic73—42no—
797C2×Dic73—81no—
798D292—21no—
799D292—21no—
800D292—21no—
801D292—21no—
802D292—21no—
803D292—42no—
804D292—42no—
805D292—81no—
806D292—81no—
807D292H(5,𝔽2)12yes—
808C4×D73—42no—
809C4×D73—81no—
810C4×D73—81no—
811C4×D73—81no—
812C4×D73—81no—
813C4×D73—81no—
814C4×D73—81no—
815C4×D73—81no—
816C4×D73—81no—
817Dic146—21no—
818Dic146—21no—
819Dic146—81no—
820#10596831—21no—
821#10596831—21no—
822#10596831—21no—
823#10596831—21no—
824#10596831—21no—
825#10596831—21no—
826#10596831—21no—
827#10596831—21no—
828C22×C73—21no—
829C22×C73—21no—
830C22×C73—21no—
831C22×C73—21no—
832C22×C73—21no—
833C22×C73—21no—
834C22×C73—21no—
835C22×C73—21no—
836C22×C73—21no—
837C22×C73—41no—
838C22×C73—41no—
839C22×C73—41no—
840C22×C73—41no—
841C22×C73—41no—
842C22×C73—41no—
843C22×C73—41no—
844C22×C73—41no—
845C22×C73—41no—
846C22×C73—162no—
847C22×C73C23×D411yescharacteristic
848C2×D73—22no—
849C2×D73—41no—
850C2×D73—41no—
851C2×D73—41no—
852C2×D73—41no—
853C2×D73—41no—
854C2×D73—41no—
855C2×D73—41no—
856C2×D73—41no—
857C2×D73—84no—
858C2×D73—162no—
859C4×C73—21no—
860C4×C73—21no—
861C4×C73—21no—
862C4×C73—21no—
863C4×C73—21no—
864C4×C73—21no—
865C4×C73—21no—
866C4×C73—21no—
867C4×C73—21no—
868C4×C73—21no—
869C4×C73—21no—
870C4×C73—41no—
871C4×C73—41no—
872C4×C73—41no—
873C4×C73—41no—
874C4×C73—41no—
875C4×C73C2×H(5,𝔽2)11yescharacteristic
876C4×C73#58511yescharacteristic
877Dic73—41no—
878Dic73—41no—
879Dic73—41no—
880Dic73—41no—
881Dic73—41no—
882#62027—731nomaximal, Sylow
883C2×C73—41no—
884C2×C73—41no—
885C2×C73—41no—
886C2×C73—81no—
887C2×C73—81no—
888C2×C73—81no—
889C2×C73#348811yescharacteristic
890C2×C73#358411yescharacteristic
891C2×C73#358511yescharacteristic
892D73—42no—
893D73—81no—
894D73—81no—
895#3562D7311yescharacteristic, complemented
896#3513—731no—
897#3401—731no—
898#3396—731no—
899#3370—731no—
900#3360—731no—
901#3330—731no—
902#3327—731no—
903#3326—731no—
904#3317—731no—
905#3306—731no—
906#3297—731no—
907#3282—731no—
908#3274—731no—
909#3273—731no—
910#3273—731no—
911#3267—731no—
912#3265—731no—
913#3260—731no—
914#3257—731no—
915#3256—731no—
916#3225—731no—
917#3220—731no—
918#3212—731no—
919#3122—731no—
920#3120—731no—
921#3105—731no—
922#3045—731no—
923#3042—731no—
924#3036—731no—
925#2993—731no—
926C73#6202711yescharacteristic, complemented, Sylow
927C2×AGL(1,ℤ/8)—731no—
928C2×AGL(1,ℤ/8)—731no—
929C2×AGL(1,ℤ/8)—731no—
930C2×AGL(1,ℤ/8)—731no—
931C2×#135—731no—
932C22×SD16—731no—
933#562—21no—
934#560—21no—
935#559—731no—
936#559C2×D7311yescharacteristic, complemented
937#556C2×D7311yescharacteristic, complemented
938#554—731no—
939#553—21no—
940#553—731no—
941#553—1461no—
942#552—731no—
943#551—21no—
944#551—1461no—
945#551—1461no—
946#550C2×D7311yescharacteristic
947#548C2×D7311yescharacteristic
948#548C2×D7311yescharacteristic, complemented
949#547—731no—
950#547C2×D7311yescharacteristic, complemented
951#546—731no—
952#546—731no—
953#546—1461no—
954#546C2×D7311yescharacteristic, complemented
955#546C2×D7311yescharacteristic, complemented
956D42—731no—
957#542—731no—
958#541C2×D7311yescharacteristic, complemented
959#540—21no—
960#540—731no—
961#540C2×D7311yescharacteristic, complemented
962#539—21no—
963#539—1461no—
964#538—21no—
965#538—21no—
966#538—1461no—
967#536C2×D7311yescharacteristic, complemented
968#535C2×D7311yescharacteristic, complemented
969#532C2×D7311yescharacteristic, complemented
970#529—731no—
971#529C2×D7311yescharacteristic
972#529C2×D7311yescharacteristic, complemented
973#525—1461no—
974C2×#123—1461no—
975#520—731no—
976#518—731no—
977C2×C4×D4—731no—
978#497—731no—
979#496—731no—
980#495—731no—
981#495—731no—
982#495—731no—
983#493—731no—
984#490—731no—
985#489—731no—
986#488—731no—
987#488—731no—
988#488—731no—
989#487—731no—
990#484—731no—
991#484—731no—
992#483—731no—
993#482—731no—
994#482—731no—
995#481—731no—
996#479—731no—
997#479—731no—
998#479—731no—
999#479—731no—
1000#478—731no—
1001#478—731no—
1002#478—731no—
1003#478—731no—
1004#476—731no—
1005#474—731no—
1006#470—731no—
1007#469—731no—
1008#469—731no—
1009#468—731no—
1010#468—731no—
1011#468—731no—
1012#468—731no—
1013#468—731no—
1014#466—731no—
1015#465—731no—
1016#465—731no—
1017#465—731no—
1018#464—731no—
1019#464—731no—
1020#464—731no—
1021#463—731no—
1022#463—731no—
1023#463—731no—
1024#463—731no—
1025#463—731no—
1026#463—731no—
1027#463—731no—
1028#463—731no—
1029#463—731no—
1030#463—731no—
1031#463—731no—
1032#463—731no—
1033#463—731no—
1034#462—731no—
1035#461—731no—
1036#461—731no—
1037#461—731no—
1038#461—731no—
1039#461—731no—
1040#460—731no—
1041#460—731no—
1042#460—731no—
1043#460—731no—
1044#459—731no—
1045#459—731no—
1046#459—731no—
1047#459—731no—
1048#452—731no—
1049#452—731no—
1050#452—731no—
1051#452—731no—
1052#452—731no—
1053#451—731no—
1054#450—731no—
1055#449—731no—
1056#449—731no—
1057#449—731no—
1058#449—731no—
1059#449—731no—
1060#448—731no—
1061#447—731no—
1062#447—731no—
1063#447—731no—
1064#447—731no—
1065#447—731no—
1066#446—731no—
1067C8×Q8—731no—
1068#442—731no—
1069#442—731no—
1070#441—731no—
1071#440—731no—
1072C4×Q16—731no—
1073C4×SD16—731no—
1074C4×SD16—731no—
1075C4×SD16—731no—
1076C4×D8—731no—
1077C4×D8—731no—
1078C4×D8—731no—
1079C4×D8—731no—
1080#436—731no—
1081#436—731no—
1082#436—731no—
1083#435—731no—
1084#435—731no—
1085C8×D4—731no—
1086#433—731no—
1087#433—731no—
1088#431—731no—
1089#424—731no—
1090#424—731no—
1091#423—731no—
1092#419—731no—
1093#417—731no—
1094#417—731no—
1095#417—731no—
1096#416—731no—
1097C2×#102—731no—
1098C2×#41—731no—
1099C2×#41—1461no—
1100C2×#41C22×D7311yescharacteristic
1101C2×#41C22×D7311yescharacteristic
1102C2×#41C22×D7311yescharacteristic
1103C2×#41C22×D7311yescharacteristic
1104C22×Q8C22×D7311yescharacteristic
1105C22×D4—731no—
1106C22×D4—731no—
1107C22×D4—1461no—
1108C22×D4C22×D7311yescharacteristic
1109C23×C4—1461no—
1110AGL(1,ℤ/8)—2922no—
1111AGL(1,ℤ/8)—2922no—
1112AGL(1,ℤ/8)—2922no—
1113AGL(1,ℤ/8)—2922no—
1114#135—2922no—
1115C2×Q16—731no—
1116C2×Q16—731no—
1117C2×Q16—731no—
1118C2×SD16—2922no—
1119C2×SD16—731no—
1120C2×SD16—731no—
1121C2×SD16—731no—
1122C2×SD16—731no—
1123C2×SD16—731no—
1124C2×SD16—731no—
1125C2×SD16—731no—
1126C2×SD16—731no—
1127C2×SD16—731no—
1128C2×SD16—731no—
1129C2×SD16—731no—
1130C2×SD16—731no—
1131C2×D8—731no—
1132C2×D8—731no—
1133C2×D8—731no—
1134C2×D8—731no—
1135C2×D8—731no—
1136C2×D8—731no—
1137C2×D8—731no—
1138C2×D8—731no—
1139C2×D8—731no—
1140C2×M16—731no—
1141C2×M16—731no—
1142C2×M16—731no—
1143C2×M16—731no—
1144C22×C8—731no—
1145C22×C8—731no—
1146C4⋊Q8—731no—
1147C4⋊Q8C22×D7311yescharacteristic
1148C4⋊Q8C22×D7311yescharacteristic
1149#127—21no—
1150#127—731no—
1151#127C22×D7311yescharacteristic
1152#127C22×D7311yescharacteristic
1153#126—21no—
1154#126—21no—
1155#126—21no—
1156#126—21no—
1157#126—21no—
1158#126—1461no—
1159#126—1461no—
1160#126—1461no—
1161#126—1461no—
1162#126C22⋊D7311yescharacteristic
1163#126C22⋊D7311yescharacteristic
1164#125—21no—
1165#125—21no—
1166#125—731no—
1167#125—731no—
1168#125—1461no—
1169#125C22⋊D7311yescharacteristic
1170#125C22×D7311yescharacteristic
1171#124—21no—
1172#124—21no—
1173#124—21no—
1174#124—731no—
1175#124—731no—
1176#124—1461no—
1177#124—1461no—
1178#124C22⋊D7311yescharacteristic
1179#124C22×D7311yescharacteristic
1180#124C22×D7311yescharacteristic
1181#124C22×D7311yescharacteristic
1182#124C22×D7311yescharacteristic
1183#124C22×D7311yescharacteristic
1184#123—21no—
1185#123—21no—
1186#123—21no—
1187#123—21no—
1188#123—21no—
1189#123—21no—
1190#123—21no—
1191#123—21no—
1192#123—21no—
1193#123—21no—
1194#123—21no—
1195#123—1461no—
1196#123—1461no—
1197#123—1461no—
1198#123—1461no—
1199#123—1461no—
1200#123—1461no—
1201#123—1461no—
1202#123—1461no—
1203#123—1461no—
1204#123—1461no—
1205#123—1461no—
1206#123—1461no—
1207#123C22⋊D7311yescharacteristic
1208#123C22⋊D7311yescharacteristic
1209C22⋊Q8—21no—
1210C22⋊Q8—21no—
1211C22⋊Q8—21no—
1212C22⋊Q8—21no—
1213C22⋊Q8—21no—
1214C22⋊Q8—731no—
1215C22⋊Q8—731no—
1216C22⋊Q8—1461no—
1217C22⋊Q8—1461no—
1218C22⋊Q8—1461no—
1219C22⋊Q8—1461no—
1220C22⋊Q8—1461no—
1221C22⋊Q8C22⋊D7311yescharacteristic
1222C22⋊Q8C22×D7311yescharacteristic
1223C22⋊Q8C22×D7311yescharacteristic
1224C22⋊Q8C22×D7311yescharacteristic
1225#121—21no—
1226#121—21no—
1227#121—21no—
1228#121—21no—
1229#121—21no—
1230#121—21no—
1231#121—21no—
1232#121—21no—
1233#121—21no—
1234#121—21no—
1235#121—21no—
1236#121—21no—
1237#121—21no—
1238#121—731no—
1239#121—731no—
1240#121—731no—
1241#121—731no—
1242#121—1461no—
1243#121—1461no—
1244#121—1461no—
1245#121—1461no—
1246#121—1461no—
1247#121—1461no—
1248#121C22⋊D7311yescharacteristic
1249#121C22×D7311yescharacteristic
1250#121C22×D7311yescharacteristic
1251#121C22×D7311yescharacteristic
1252#120—21no—
1253#120—21no—
1254#120—21no—
1255#120—21no—
1256#120—1461no—
1257#120—1461no—
1258#120—1461no—
1259#120—1461no—
1260C4×Q8—731no—
1261C4×Q8—731no—
1262C4×Q8C22×D7311yescharacteristic
1263C4×Q8C22×D7311yescharacteristic
1264C4×Q8C22×D7311yescharacteristic
1265C4×Q8C22×D7311yescharacteristic
1266C4×D4—21no—
1267C4×D4—21no—
1268C4×D4—21no—
1269C4×D4—21no—
1270C4×D4—21no—
1271C4×D4—21no—
1272C4×D4—21no—
1273C4×D4—731no—
1274C4×D4—731no—
1275C4×D4—731no—
1276C4×D4—731no—
1277C4×D4—731no—
1278C4×D4—731no—
1279C4×D4—731no—
1280C4×D4—731no—
1281C4×D4—1461no—
1282C4×D4—1461no—
1283C4×D4—1461no—
1284C4×D4—1461no—
1285C4×D4—1461no—
1286C4×D4—1461no—
1287C4×D4—1461no—
1288C4×D4—1461no—
1289C4×D4—1461no—
1290C4×D4C22×D7311yescharacteristic
1291C4×D4C22×D7311yescharacteristic
1292C4×D4C22×D7311yescharacteristic
1293C4×D4C22×D7311yescharacteristic
1294C4×D4C22×D7311yescharacteristic
1295C4×D4C22×D7311yescharacteristic
1296#117—21no—
1297#117—21no—
1298#117—731no—
1299#117—1461no—
1300#117—1461no—
1301#117—1461no—
1302#117C22×D7311yescharacteristic
1303#117C22×D7311yescharacteristic
1304C2×C4⋊C4—21no—
1305C2×C4⋊C4—731no—
1306C2×C4⋊C4—731no—
1307C2×C4⋊C4—1461no—
1308C2×C4⋊C4—1461no—
1309C2×C22⋊C4—21no—
1310C2×C22⋊C4—21no—
1311C2×C22⋊C4—1461no—
1312C2×C22⋊C4—1461no—
1313C2×C22⋊C4—1461no—
1314C2×C22⋊C4—1461no—
1315C2×C22⋊C4—1461no—
1316C2×C42C22×D7311yescharacteristic
1317#107—731no—
1318#107—731no—
1319#107—731no—
1320#107—731no—
1321#106—731no—
1322#106—731no—
1323#106—731no—
1324#106—731no—
1325C4⋊C8—731no—
1326C4⋊C8—731no—
1327C4⋊C8—731no—
1328C4⋊C8—731no—
1329C4⋊C8—731no—
1330C4⋊C8—731no—
1331C4⋊C8—731no—
1332C4⋊C8—731no—
1333C4⋊C8—731no—
1334C4⋊C8—731no—
1335#103—731no—
1336#103—731no—
1337#103—731no—
1338#103—731no—
1339#103—731no—
1340#103—731no—
1341#103—731no—
1342#103—731no—
1343#103—731no—
1344#103—731no—
1345#103—731no—
1346#103—731no—
1347#103—731no—
1348#103—731no—
1349#102—731no—
1350#102—731no—
1351#102—731no—
1352#102—731no—
1353#102—731no—
1354#102—731no—
1355#102—731no—
1356#102—731no—
1357#102—731no—
1358#102—731no—
1359#102—731no—
1360#102—731no—
1361#102—731no—
1362#102—731no—
1363#102—731no—
1364#102—731no—
1365#102—731no—
1366#102—731no—
1367C22⋊C8—731no—
1368C22⋊C8—731no—
1369C22⋊C8—731no—
1370C22⋊C8—731no—
1371C22⋊C8—731no—
1372C22⋊C8—731no—
1373#97—731no—
1374#97—731no—
1375C4×C8—731no—
1376C4×C8—731no—
1377C4×C8—731no—
1378C4×C8—731no—
1379C24—21no—
1380C24—1461no—
1381C24—1461no—
1382#41—41no—
1383#41—41no—
1384#41—41no—
1385#41—41no—
1386#41—41no—
1387#41—41no—
1388#41—41no—
1389#41—41no—
1390#41—2921no—
1391#41—5842no—
1392#41—1462no—
1393C2×Q8—21no—
1394C2×Q8—41no—
1395C2×Q8—41no—
1396C2×Q8—731no—
1397C2×Q8—1461no—
1398C2×Q8C2×C22⋊D7311yescharacteristic
1399C2×Q8C23×D7311yescharacteristic
1400C2×Q8C23×D7311yescharacteristic
1401C2×Q8C23×D7311yescharacteristic
1402C2×D4—21no—
1403C2×D4—21no—
1404C2×D4—21no—
1405C2×D4—21no—
1406C2×D4—21no—
1407C2×D4—21no—
1408C2×D4—21no—
1409C2×D4—21no—
1410C2×D4—21no—
1411C2×D4—21no—
1412C2×D4—21no—
1413C2×D4—21no—
1414C2×D4—41no—
1415C2×D4—41no—
1416C2×D4—2921no—
1417C2×D4—2921no—
1418C2×D4—5842no—
1419C2×D4—731no—
1420C2×D4—731no—
1421C2×D4—731no—
1422C2×D4—1462no—
1423C2×D4—1462no—
1424C2×D4—1461no—
1425C2×D4—1461no—
1426C2×D4—1461no—
1427C2×D4—1461no—
1428C2×D4—1461no—
1429C2×D4—1461no—
1430C2×D4—1461no—
1431C2×D4—1461no—
1432C2×D4—1461no—
1433C2×D4C2×C22⋊D7311yescharacteristic
1434C2×D4C2×C22⋊D7311yescharacteristic
1435C2×D4C2×C22⋊D7311yescharacteristic
1436C2×D4C23×D7311yescharacteristic
1437C2×D4C23×D7311yescharacteristic
1438C2×D4C23×D7311yescharacteristic
1439C22×C4—21no—
1440C22×C4—21no—
1441C22×C4—21no—
1442C22×C4—21no—
1443C22×C4—21no—
1444C22×C4—21no—
1445C22×C4—21no—
1446C22×C4—21no—
1447C22×C4—5842no—
1448C22×C4—1461no—
1449C22×C4—1461no—
1450C22×C4—1461no—
1451C22×C4—1461no—
1452C22×C4—1461no—
1453C22×C4—1461no—
1454C22×C4—1461no—
1455C22×C4—1461no—
1456C22×C4—1461no—
1457C22×C4—1461no—
1458C22×C4—1461no—
1459C22×C4C2×C22⋊D7311yescharacteristic
1460C22×C4C2×C22⋊D7311yescharacteristic
1461C22×C4C23×D7311yescharacteristic
1462C22×C4C23×D7311yescharacteristic
1463C22×C4C23×D7311yescharacteristic
1464Q16—2921no—
1465Q16—2921no—
1466Q16—2921no—
1467SD16—2921no—
1468SD16—2921no—
1469SD16—2921no—
1470SD16—2921no—
1471SD16—2921no—
1472SD16—2921no—
1473SD16—2921no—
1474SD16—2921no—
1475SD16—2921no—
1476SD16—1462no—
1477SD16—1462no—
1478SD16—1462no—
1479D8—2921no—
1480D8—2921no—
1481D8—2921no—
1482D8—2921no—
1483D8—2921no—
1484D8—2921no—
1485D8—1462no—
1486D8—1462no—
1487D8—1462no—
1488M16—2921no—
1489M16—2921no—
1490M16—2921no—
1491M16—2921no—
1492C2×C8—2921no—
1493C2×C8—2921no—
1494C2×C8—731no—
1495C2×C8—731no—
1496C2×C8—731no—
1497C2×C8—731no—
1498C2×C8—731no—
1499C2×C8—731no—
1500C2×C8—731no—
1501C2×C8—731no—
1502C4⋊C4—21no—
1503C4⋊C4—21no—
1504C4⋊C4—21no—
1505C4⋊C4—21no—
1506C4⋊C4—21no—
1507C4⋊C4—21no—
1508C4⋊C4—21no—
1509C4⋊C4—21no—
1510C4⋊C4—21no—
1511C4⋊C4—21no—
1512C4⋊C4—21no—
1513C4⋊C4—21no—
1514C4⋊C4—731no—
1515C4⋊C4—731no—
1516C4⋊C4—731no—
1517C4⋊C4—731no—
1518C4⋊C4—1461no—
1519C4⋊C4—1461no—
1520C4⋊C4—1461no—
1521C4⋊C4—1461no—
1522C4⋊C4—1461no—
1523C4⋊C4—1461no—
1524C4⋊C4—1461no—
1525C4⋊C4—1461no—
1526C4⋊C4—1461no—
1527C4⋊C4—1461no—
1528C4⋊C4—1461no—
1529C4⋊C4C2×C22⋊D7311yescharacteristic
1530C4⋊C4C2×C22⋊D7311yescharacteristic
1531C4⋊C4C2×C22⋊D7311yescharacteristic
1532C4⋊C4C2×C22⋊D7311yescharacteristic
1533C4⋊C4C2×C22⋊D7311yescharacteristic
1534C4⋊C4C2×C22⋊D7311yescharacteristic
1535C4⋊C4C2×C22⋊D7311yescharacteristic
1536C4⋊C4C2×C22⋊D7311yescharacteristic
1537C4⋊C4C2×C22⋊D7311yescharacteristic
1538C4⋊C4C2×C22⋊D7311yescharacteristic
1539C4⋊C4C23×D7311yescharacteristic
1540C4⋊C4C23×D7311yescharacteristic
1541C22⋊C4—21no—
1542C22⋊C4—21no—
1543C22⋊C4—21no—
1544C22⋊C4—21no—
1545C22⋊C4—21no—
1546C22⋊C4—21no—
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—21no—
1558C22⋊C4—21no—
1559C22⋊C4—21no—
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⋊C4—1461no—
1569C22⋊C4—1461no—
1570C22⋊C4—1461no—
1571C22⋊C4—1461no—
1572C22⋊C4—1461no—
1573C22⋊C4—1461no—
1574C22⋊C4—1461no—
1575C22⋊C4—1461no—
1576C22⋊C4—1461no—
1577C22⋊C4—1461no—
1578C22⋊C4—1461no—
1579C22⋊C4C2×C22⋊D7311yescharacteristic
1580C22⋊C4C2×C22⋊D7311yescharacteristic
1581C22⋊C4C2×C22⋊D7311yescharacteristic
1582C22⋊C4C2×C22⋊D7311yescharacteristic
1583C22⋊C4C2×C22⋊D7311yescharacteristic
1584C22⋊C4C2×C22⋊D7311yescharacteristic
1585C22⋊C4C2×C22⋊D7311yescharacteristic
1586C22⋊C4C2×C22⋊D7311yescharacteristic
1587C22⋊C4C2×C22⋊D7311yescharacteristic
1588C22⋊C4C2×C22⋊D7311yescharacteristic
1589C42—21no—
1590C42—21no—
1591C42—21no—
1592C42—1461no—
1593C42—1461no—
1594C42—1461no—
1595C42C2×C22⋊D7311yescharacteristic
1596C42C2×C22⋊D7311yescharacteristic
1597C42C23×D7311yescharacteristic
1598C42C23×D7311yescharacteristic
1599C42C23×D7311yescharacteristic
1600C42C23×D7311yescharacteristic
1601C23—21no—
1602C23—21no—
1603C23—21no—
1604C23—81no—
1605C23—81no—
1606C23—81no—
1607C23—2922no—
1608C23—2922no—
1609C23—2922no—
1610C23—5841no—
1611C23—5841no—
1612C23—5841no—
1613C23—1461no—
1614C23—1461no—
1615C23—1461no—
1616C23C22×C22⋊D7311yescharacteristic
1617C23C22×C22⋊D7311yescharacteristic
1618C23C22×C22⋊D7311yescharacteristic
1619Q8—21no—
1620Q8—21no—
1621Q8—21no—
1622Q8—21no—
1623Q8—21no—
1624Q8—21no—
1625Q8—41no—
1626Q8—81no—
1627Q8—5841no—
1628Q8—1461no—
1629Q8—1461no—
1630D4—21no—
1631D4—21no—
1632D4—21no—
1633D4—21no—
1634D4—21no—
1635D4—21no—
1636D4—41no—
1637D4—41no—
1638D4—41no—
1639D4—81no—
1640D4—81no—
1641D4—81no—
1642D4—81no—
1643D4—81no—
1644D4—81no—
1645D4—81no—
1646D4—81no—
1647D4—81no—
1648D4—81no—
1649D4—81no—
1650D4—81no—
1651D4—2922no—
1652D4—2922no—
1653D4—2922no—
1654D4—2922no—
1655D4—5841no—
1656D4—5841no—
1657D4—5841no—
1658D4—5841no—
1659D4—5841no—
1660D4—732no—
1661D4—1461no—
1662D4—1461no—
1663D4—1461no—
1664D4—1461no—
1665D4—1461no—
1666C2×C4—21no—
1667C2×C4—21no—
1668C2×C4—21no—
1669C2×C4—21no—
1670C2×C4—21no—
1671C2×C4—21no—
1672C2×C4—21no—
1673C2×C4—21no—
1674C2×C4—21no—
1675C2×C4—21no—
1676C2×C4—21no—
1677C2×C4—41no—
1678C2×C4—41no—
1679C2×C4—81no—
1680C2×C4—81no—
1681C2×C4—81no—
1682C2×C4—81no—
1683C2×C4—81no—
1684C2×C4—81no—
1685C2×C4—81no—
1686C2×C4—81no—
1687C2×C4—2922no—
1688C2×C4—2922no—
1689C2×C4—5841no—
1690C2×C4—5841no—
1691C2×C4—5841no—
1692C2×C4—5841no—
1693C2×C4—5841no—
1694C2×C4—5841no—
1695C2×C4—5841no—
1696C2×C4—5841no—
1697C2×C4—5841no—
1698C2×C4—1461no—
1699C2×C4—1461no—
1700C2×C4—1461no—
1701C2×C4—1461no—
1702C2×C4—1461no—
1703C2×C4C22×C22⋊D7311yescharacteristic
1704C2×C4C22×C22⋊D7311yescharacteristic
1705C2×C4C22×C22⋊D7311yescharacteristic
1706C2×C4C22×C22⋊D7311yescharacteristic
1707C2×C4C22×C22⋊D7311yescharacteristic
1708C2×C4C22×C22⋊D7311yescharacteristic
1709C2×C4C22×C22⋊D7311yescharacteristic
1710C2×C4C22×C22⋊D7311yescharacteristic
1711C2×C4C22×C22⋊D7311yescharacteristic
1712C2×C4C22×C22⋊D7311yescharacteristic
1713C2×C4C22×C22⋊D7311yescharacteristic
1714C2×C4C24×D7311yescharacteristic
1715C8—1461no—
1716C8—1461no—
1717C8—1461no—
1718C8—1461no—
1719C8—1461no—
1720C8—1461no—
1721C8—1461no—
1722C8—1461no—
1723C22—21no—
1724C22—21no—
1725C22—21no—
1726C22—21no—
1727C22—21no—
1728C22—21no—
1729C22—21no—
1730C22—21no—
1731C22—21no—
1732C22—41no—
1733C22—41no—
1734C22—41no—
1735C22—41no—
1736C22—41no—
1737C22—41no—
1738C22—41no—
1739C22—41no—
1740C22—41no—
1741C22—162no—
1742C22—2921no—
1743C22—2921no—
1744C22—2921no—
1745C22—2921no—
1746C22—2921no—
1747C22—2921no—
1748C22—2921no—
1749C22—2921no—
1750C22—5844no—
1751C22—11682no—
1752C22—1462no—
1753C22C23×C22⋊D7311yescharacteristic
1754C4—21no—
1755C4—21no—
1756C4—21no—
1757C4—21no—
1758C4—21no—
1759C4—21no—
1760C4—21no—
1761C4—21no—
1762C4—21no—
1763C4—21no—
1764C4—21no—
1765C4—41no—
1766C4—41no—
1767C4—41no—
1768C4—41no—
1769C4—41no—
1770C4—2921no—
1771C4—2921no—
1772C4—2921no—
1773C4—2921no—
1774C4—2921no—
1775C4H(5,𝔽2)×D7311yescharacteristic
1776C4#1798942211yescharacteristic
1777C2—41no—
1778C2—41no—
1779C2—41no—
1780C2—81no—
1781C2—81no—
1782C2—81no—
1783C2—2922no—
1784C2—5841no—
1785C2—5841no—
1786C2#2262359311yescharacteristic
1787C2#2262470211yescharacteristic
1788C2#2262471011yescharacteristic
subgroupG/H
centerC22C23×C22⋊D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC73×#3562C2
socleC22×C73C23×D4
hypercenter#3562D73
hypocenterC73#62027
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ #529 ◁ #3562

Complements

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

NH ≅ G/Ntype
1. #22623875C2semidirect
2. #22622997C2semidirect
3. #22622939C2semidirect
4. #22622678C2semidirect
5. #22622576C2semidirect
6. #22622236C2semidirect
7. #22622199C2semidirect
8. #22622184C2semidirect
9. #22622057C2semidirect
10. #22621892C2semidirect
11. #22621781C2semidirect
12. #22621639C2semidirect
13. #22621551C2semidirect
14. #22621538C2semidirect
15. #22621538C2semidirect
16. #22621457C2semidirect
17. #22621427C2semidirect
18. #22621372C2semidirect
19. #22621336C2semidirect
20. #22621327C2semidirect
21. #22621040C2semidirect
22. #22620981C2semidirect
23. #22620907C2semidirect
24. #22620169C2semidirect
25. #22620139C2semidirect
26. #22619974C2semidirect
27. #22619466C2semidirect
28. #22619439C2semidirect
29. #22619391C2semidirect
30. #22619080C2semidirect
31. C73×#3562C2semidirect
35. C2×#14556616C22semidirect
37. C22×#11924015C22semidirect
38. #17989322C22semidirect
39. #17989297C22semidirect
42. #17989277C22semidirect
49. D4×D292C22semidirect
50. #17989208C22semidirect
54. #17989121C22semidirect
58. #17989061C22semidirect
59. C2×C4×D292C22semidirect
60. #17988979C22semidirect
62. #17988969C22semidirect
63. #17988969C22semidirect
64. #17988969C22semidirect
66. #17988951C22semidirect
67. #17988946C22semidirect
68. #17988941C22semidirect
69. #17988941C22semidirect
70. #17988941C22semidirect
71. #17988937C22semidirect
72. #17988920C22semidirect
73. #17988920C22semidirect
74. #17988915C22semidirect
75. #17988908C22semidirect
76. #17988908C22semidirect
77. #17988903C22semidirect
78. #17988894C22semidirect
79. #17988894C22semidirect
80. #17988894C22semidirect
81. #17988891C22semidirect
82. #17988887C22semidirect
83. #17988884C22semidirect
84. #17988884C22semidirect
85. #17988884C22semidirect
86. #17988877C22semidirect
87. #17988867C22semidirect
88. #17988843C22semidirect
90. #17988838C22semidirect
91. #17988835C22semidirect
92. #17988835C22semidirect
93. #17988835C22semidirect
94. #17988831C22semidirect
95. #17988831C22semidirect
97. #17988818C22semidirect
98. #17988818C22semidirect
99. #17988814C22semidirect
100. #17988809C22semidirect
101. #17988806C22semidirect
102. #17988806C22semidirect
103. #17988802C22semidirect
104. #17988802C22semidirect
105. #17988802C22semidirect
110. #17988799C22semidirect
111. #17988799C22semidirect
112. #17988799C22semidirect
113. #17988799C22semidirect
114. #17988799C22semidirect
115. #17988799C22semidirect
116. #17988794C22semidirect
117. #17988789C22semidirect
118. #17988789C22semidirect
119. #17988789C22semidirect
120. #17988789C22semidirect
121. #17988789C22semidirect
122. #17988787C22semidirect
123. #17988787C22semidirect
124. #17988784C22semidirect
125. #17988784C22semidirect
128. #17988779C22semidirect
129. #17988779C22semidirect
130. #17988749C22semidirect
131. #17988749C22semidirect
132. #17988749C22semidirect
135. #17988743C22semidirect
136. #17988737C22semidirect
139. #17988732C22semidirect
140. #17988732C22semidirect
141. #17988732C22semidirect
142. #17988726C22semidirect
143. #17988721C22semidirect
144. #17988721C22semidirect
147. #17988720C22semidirect
148. #17988718C22semidirect
149. Q8×#10596831C22semidirect
150. #17988697C22semidirect
151. #17988697C22semidirect
152. #17988692C22semidirect
153. #17988685C22semidirect
154. C4×#11924018C22semidirect
155. C4×#11924015C22semidirect
156. C4×#11924015C22semidirect
157. C4×#11924015C22semidirect
160. C4×#11924013C22semidirect
161. C4×#11924013C22semidirect
162. #17988665C22semidirect
163. #17988665C22semidirect
164. #17988665C22semidirect
165. #17988659C22semidirect
166. #17988659C22semidirect
167. D4×#10596831C22semidirect
168. #17988648C22semidirect
169. #17988648C22semidirect
170. #17988640C22semidirect
171. #17988614C22semidirect
172. #17988614C22semidirect
173. #17988611C22semidirect
174. #17988596C22semidirect
175. #17988588C22semidirect
176. #17988588C22semidirect
177. #17988588C22semidirect
178. #17988583C22semidirect
179. C2×#14556512C22semidirect
182. #559×C73C22semidirect
183. #556×C73C22semidirect
188. #548×C73C22semidirect
189. #547×C73C22semidirect
190. #546×C73C22semidirect
191. #546×C73C22semidirect
192. #541×C73C22semidirect
194. #540×C73C22semidirect
198. #536×C73C22semidirect
199. #535×C73C22semidirect
200. #532×C73C22semidirect
202. #529×C73C22semidirect
895. #3562D73semidirect
926. C73#62027semidirect
936. #559C2×D73semidirect
937. #556C2×D73semidirect
948. #548C2×D73semidirect
950. #547C2×D73semidirect
954. #546C2×D73semidirect
955. #546C2×D73semidirect
958. #541C2×D73semidirect
961. #540C2×D73semidirect
967. #536C2×D73semidirect
968. #535C2×D73semidirect
969. #532C2×D73semidirect
972. #529C2×D73semidirect

Maximal subgroups

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

subgroupindex
#226238752
#226229972
#226229392
#226226782
#226225762
#226222362
#226221992
#226221842
#226220572
#226218922
#226217812
#226216392
#226215512
#226215382
#226214572
#226214272
#226213722
#226213362
#226213272
#226210402
#226209812
#226209072
#226201692
#226201392
#226199742
#226194662
#226194392
#226193912
#226190802
C73×#35622
#6202773