Finite Group Databasebeta

← #33978582

Subgroups — #33978582

Order 18688.

1856 conjugacy classes of subgroups.

The subgroup lattice has 1756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22623885C211yesmaximal, characteristic, complemented
2#22623550C211yesmaximal, characteristic, complemented
3#22622987C211yesmaximal, characteristic, complemented
4#22622963C211yesmaximal, characteristic, complemented
5#22622720C211yesmaximal, characteristic, complemented
6#22622652C211yesmaximal, characteristic, complemented
7#22622210C211yesmaximal, characteristic, complemented
8#22622160C211yesmaximal, characteristic, complemented
9#22621995C211yesmaximal, characteristic, complemented
10#22621963C211yesmaximal, characteristic, complemented
11#22621961C211yesmaximal, characteristic, complemented
12#22621570C211yesmaximal, characteristic, complemented
13#22621528C211yesmaximal, characteristic, complemented
14#22621487C211yesmaximal, characteristic, complemented
15#22621483C211yesmaximal, characteristic, complemented
16#22621461C211yesmaximal, characteristic, complemented
17#22621460C211yesmaximal, characteristic, complemented
18#22621307C211yesmaximal, characteristic, complemented
19#22621297C211yesmaximal, characteristic, complemented
20#22621263C211yesmaximal, characteristic, complemented
21#22620935C211yesmaximal, characteristic, complemented
22#22620933C211yesmaximal, characteristic, complemented
23#22620885C211yesmaximal, characteristic, complemented
24#22620046C211yesmaximal, characteristic, complemented
25#22620035C211yesmaximal, characteristic, complemented
26#22619952C211yesmaximal, characteristic, complemented
27#22619428C211yesmaximal, characteristic, complemented
28#22619422C211yesmaximal, characteristic, complemented
29#22619384C211yesmaximal, characteristic, complemented
30#22619043C211yesmaximal, characteristic, complemented
31C73×#3313C211yesmaximal, characteristic, complemented
32C2×#14556623C2211yescharacteristic, complemented
33C2×#14556622C2211yescharacteristic, complemented
34C2×#14556619C2211yescharacteristic
35C2×#14556618C2211yescharacteristic
36C2×#14556613C2211yescharacteristic, complemented
37C2×#14556611C2211yescharacteristic, complemented
38#17989319C2211yescharacteristic
39#17989315C2211yescharacteristic, complemented
40#17989309C2211yescharacteristic
41#17989305C2211yescharacteristic
42#17989305C2211yescharacteristic, complemented
43#17989299—21no—
44#17989278—21no—
45#17989273—21no—
46#17989273—21no—
47#17989266—21no—
48#17989264—21no—
49#17989252C2211yescharacteristic, complemented
50Q8×C22⋊D73C2211yescharacteristic
51#17989247C2211yescharacteristic
52#17989245—21no—
53#17989242C2211yescharacteristic, complemented
54#17989239C2211yescharacteristic
55#17989239C2211yescharacteristic, complemented
56#17989233C2211yescharacteristic
57#17989226—21no—
58#17989225C2211yescharacteristic
59#17989221C2211yescharacteristic
60#17989207—21no—
61#17989174—21no—
62#17989171—21no—
63#17989142C2211yescharacteristic, complemented
64#17989139C2211yescharacteristic, complemented
65#17989139C2211yescharacteristic, complemented
66#17989133C2211yescharacteristic
67#17989124C2211yescharacteristic
68#17989123C2211yescharacteristic
69#17989120—21no—
70#17989120—21no—
71#17989118C2211yescharacteristic
72#17989116—21no—
73C2×#14556580C2211yescharacteristic
74#124×D73C2211yescharacteristic
75#17989059—21no—
76C4×#11924029C2211yescharacteristic, complemented
77#17989055C2211yescharacteristic, complemented
78#17989055C2211yescharacteristic, complemented
79C4×#11924027C2211yescharacteristic
80C4×Q8×D73—21no—
81#17988982C2211yescharacteristic, complemented
82#17988981C2211yescharacteristic
83#17988980C2211yescharacteristic
84#17988980C2211yescharacteristic, complemented
85#17988965C2211yescharacteristic, complemented
86#17988958C2211yescharacteristic
87#17988949C2211yescharacteristic
88#17988948C2211yescharacteristic
89#17988948C2211yescharacteristic, complemented
90#17988936C2211yescharacteristic, complemented
91#17988932C2211yescharacteristic
92#17988928C2211yescharacteristic, complemented
93#17988926C2211yescharacteristic, complemented
94#17988913C2211yescharacteristic
95#17988911C2211yescharacteristic
96#17988893C2211yescharacteristic, complemented
97#17988893C2211yescharacteristic, complemented
98#17988892C2211yescharacteristic, complemented
99#17988886C2211yescharacteristic, complemented
100#17988881C2211yescharacteristic, complemented
101#17988875C2211yescharacteristic, complemented
102#17988874C2211yescharacteristic, complemented
103#17988870C2211yescharacteristic, complemented
104#17988866C2211yescharacteristic
105#17988845C2211yescharacteristic, complemented
106#17988844C2211yescharacteristic, complemented
107#17988844C2211yescharacteristic, complemented
108#17988843C2211yescharacteristic, complemented
109#17988834C2211yescharacteristic
110#17988834C2211yescharacteristic
111#17988831C2211yescharacteristic
112#17988826C2211yescharacteristic, complemented
113#17988818C2211yescharacteristic
114#17988816C2211yescharacteristic
115#17988812C2211yescharacteristic
116#17988812C2211yescharacteristic
117#17988812C2211yescharacteristic
118#17988812C2211yescharacteristic, complemented
119#17988812C2211yescharacteristic, complemented
120#17988812C2211yescharacteristic, complemented
121#17988811C2211yescharacteristic
122#17988811C2211yescharacteristic, complemented
123#17988809C2211yescharacteristic
124#17988808C2211yescharacteristic, complemented
125#17988808C2211yescharacteristic, complemented
126#17988807C2211yescharacteristic, complemented
127#17988805C2211yescharacteristic
128#17988805C2211yescharacteristic
129#17988805C2211yescharacteristic, complemented
130#17988805C2211yescharacteristic, complemented
131#17988803C2211yescharacteristic
132#17988801C2211yescharacteristic, complemented
133#17988799C2211yescharacteristic, complemented
134#17988797C2211yescharacteristic, complemented
135#17988796C2211yescharacteristic, complemented
136#17988796C2211yescharacteristic, complemented
137#17988795C2211yescharacteristic, complemented
138#17988793C2211yescharacteristic, complemented
139#17988791C2211yescharacteristic
140#17988791C2211yescharacteristic, complemented
141#17988790C2211yescharacteristic, complemented
142#17988786C2211yescharacteristic
143#17988781C2211yescharacteristic
144#17988751C2211yescharacteristic, complemented
145#17988751C2211yescharacteristic, complemented
146#17988749C2211yescharacteristic, complemented
147#17988748C2211yescharacteristic, complemented
148#17988747C2211yescharacteristic, complemented
149#17988747C2211yescharacteristic, complemented
150#17988744C2211yescharacteristic, complemented
151#17988744C2211yescharacteristic, complemented
152#17988743C2211yescharacteristic, complemented
153#17988740C2211yescharacteristic
154#17988739C2211yescharacteristic
155#17988739C2211yescharacteristic
156#17988737C2211yescharacteristic
157#17988735C2211yescharacteristic
158#17988734C2211yescharacteristic
159#17988730C2211yescharacteristic
160#17988716C2211yescharacteristic, complemented
161#17988715C2211yescharacteristic, complemented
162#17988700C2211yescharacteristic, complemented
163#17988696C2211yescharacteristic, complemented
164#17988693C2211yescharacteristic, complemented
165#17988686C2211yescharacteristic, complemented
166#17988685C2211yescharacteristic, complemented
167#17988685C2211yescharacteristic, complemented
168#17988684C2211yescharacteristic, complemented
169#17988679C2211yescharacteristic, complemented
170#17988674C2211yescharacteristic
171#17988672C2211yescharacteristic, complemented
172#17988669C2211yescharacteristic
173#17988663C2211yescharacteristic
174#17988662C2211yescharacteristic
175#17988659C2211yescharacteristic, complemented
176#17988658C2211yescharacteristic, complemented
177#17988655C2211yescharacteristic, complemented
178#17988642C2211yescharacteristic, complemented
179#17988641C2211yescharacteristic, complemented
180#17988637C2211yescharacteristic, complemented
181#17988610C2211yescharacteristic, complemented
182#17988609C2211yescharacteristic, complemented
183C2×#14556520C2211yescharacteristic, complemented
184#17988594C2211yescharacteristic, complemented
185#17988591C2211yescharacteristic
186#17988590C2211yescharacteristic
187#17988581C2211yescharacteristic, complemented
188#556×C73C2211yescharacteristic, complemented
189#548×C73C2211yescharacteristic
190#489×C73C2211yescharacteristic, complemented
191#485×C73C2211yescharacteristic, complemented
192#482×C73C2211yescharacteristic
193#477×C73C2211yescharacteristic, complemented
194#468×C73C2211yescharacteristic
195#467×C73C2211yescharacteristic, complemented
196#464×C73C2211yescharacteristic, complemented
197#452×C73C2211yescharacteristic, complemented
198#451×C73C2211yescharacteristic, complemented
199#441×C73C2211yescharacteristic, complemented
200#435×C73C2211yescharacteristic, complemented
201#419×C73C2211yescharacteristic, complemented
202#416×C73C2211yescharacteristic, complemented
203C2×#11924029C2311yescharacteristic
204C2×#11924028C2311yescharacteristic
205C2×#11924028C2311yescharacteristic
206C2×#11924028C2311yescharacteristic
207C2×#11924027D411yescharacteristic
208C2×Q8×D73—21no—
209C2×Q8×D73C2311yescharacteristic
210C22×D292C2311yescharacteristic
211C2×D4×D73—21no—
212C2×D4×D73C2311yescharacteristic
213#14556623—42no—
214#14556622—42no—
215#14556619—42no—
216#14556618—42no—
217#14556613—42no—
218#14556611—42no—
219C2×Dic292C2311yescharacteristic
220C2×Dic292C2311yescharacteristic
221C2×#11924018C2311yescharacteristic
222C2×#11924018C2311yescharacteristic
223C2×#11924018C2311yescharacteristic
224C2×#11924018C2311yescharacteristic
225C2×#11924018C2311yescharacteristic
226C2×#11924017C2311yescharacteristic
227C2×#11924017C2311yescharacteristic
228C2×#11924017C2311yescharacteristic
229C2×#11924017C2311yescharacteristic
230C2×#11924017C2311yescharacteristic
231C2×#11924016C2311yescharacteristic
232C2×#11924016C2311yescharacteristic
233C2×#11924015C2311yescharacteristic
234C2×#11924015C2311yescharacteristic
235C2×#11924015C2311yescharacteristic
236C2×#11924015C2311yescharacteristic
237C2×D584C2311yescharacteristic
238C2×D584C2311yescharacteristic
239C2×#11924013C2311yescharacteristic
240C2×#11924012C2311yescharacteristic
241C2×#11924011C2311yescharacteristic
242C2×#11924011C2311yescharacteristic
243C22×#10596831C2311yescharacteristic
244#14556591C2311yescharacteristic
245#14556590C2311yescharacteristic
246#14556590C2311yescharacteristic
247#14556589—21no—
248#14556589C2311yescharacteristic
249#14556589C2311yescharacteristic
250#14556589C2311yescharacteristic
251#14556587C2311yescharacteristic
252#14556586—21no—
253#14556586—21no—
254#14556586—21no—
255#14556585—21no—
256#14556585—21no—
257#14556585—21no—
258#14556584—21no—
259#14556584—21no—
260#14556584—21no—
261#14556583—21no—
262#14556582—21no—
263#14556582C2311yescharacteristic
264#14556581—21no—
265#14556581—21no—
266#14556581—21no—
267#14556581—21no—
268#14556580—21no—
269#14556580—21no—
270#14556580C2311yescharacteristic
271#14556580C2311yescharacteristic
272#14556580C2311yescharacteristic
273#14556580C2311yescharacteristic
274#14556579C2311yescharacteristic
275#14556578C2311yescharacteristic
276#14556577—21no—
277#14556577—21no—
278#14556577—21no—
279#14556577—21no—
280#14556577—21no—
281#14556577—21no—
282#14556576—21no—
283#14556576—21no—
284#14556576—21no—
285#14556576—21no—
286#14556575—21no—
287#14556575—21no—
288#14556574—21no—
289#14556573—21no—
290#14556573—21no—
291#14556573—21no—
292#14556573—21no—
293#14556573—21no—
294#14556572—21no—
295#14556571C2311yescharacteristic
296#14556571C2311yescharacteristic
297#14556570—21no—
298#14556570C2311yescharacteristic
299#14556570C2311yescharacteristic
300#14556570C2311yescharacteristic
301#14556569—21no—
302#14556569—21no—
303#14556569—21no—
304#14556569—21no—
305#14556568—21no—
306#14556568—21no—
307#14556567—21no—
308#14556567—21no—
309#14556567—21no—
310#14556567C2311yescharacteristic
311#14556566C2311yescharacteristic
312#14556565C2311yescharacteristic
313#14556564—21no—
314#14556564—21no—
315#14556564—21no—
316#14556564—21no—
317#14556564—21no—
318#14556563—21no—
319#14556563—21no—
320#14556563—21no—
321#14556562—21no—
322#14556561—21no—
323#14556559—21no—
324#14556559—21no—
325#14556559—21no—
326Q8×Dic73—21no—
327Q8×Dic73C2311yescharacteristic
328Q8×Dic73C2311yescharacteristic
329C4×Dic146—21no—
330C4×Dic146—21no—
331C4×Dic146—21no—
332C4×Dic146C2311yescharacteristic
333#14556556—21no—
334#14556556—21no—
335#14556556D411yescharacteristic
336#14556556C2311yescharacteristic
337#14556556C2311yescharacteristic
338#14556556C2311yescharacteristic
339#14556556C2311yescharacteristic
340#14556556C2311yescharacteristic
341C4×D292—21no—
342C4×D292—21no—
343C4×D292C2311yescharacteristic
344C4×D292C2311yescharacteristic
345D4×Dic73—21no—
346D4×Dic73D411yescharacteristic
347D4×Dic73C2311yescharacteristic
348#14556553—21no—
349#14556553—21no—
350#14556553C2311yescharacteristic
351#14556553C2311yescharacteristic
352#14556553C2311yescharacteristic
353#14556553C2311yescharacteristic
354C4×C22⋊D73—21no—
355C4×C22⋊D73—21no—
356C4×C22⋊D73—21no—
357C4×C22⋊D73C2311yescharacteristic
358C4×C22⋊D73C2311yescharacteristic
359#14556551—21no—
360#14556551—21no—
361#14556551—21no—
362#14556551—21no—
363#14556551—21no—
364#14556551—21no—
365#14556551D411yescharacteristic
366#14556551D411yescharacteristic
367#14556549—21no—
368#14556549—21no—
369#14556549—21no—
370#14556549D411yescharacteristic
371#14556549C2311yescharacteristic
372#14556548—21no—
373#14556548—21no—
374#14556548—21no—
375#14556548—21no—
376#14556547—21no—
377#14556547—21no—
378#14556547—21no—
379#14556547D411yescharacteristic
380#14556547D411yescharacteristic
381C4⋊C4×D73—21no—
382C4⋊C4×D73—21no—
383C4⋊C4×D73—21no—
384C2×#11924005—21no—
385C2×#11924005—21no—
386C2×#11924005—21no—
387C22⋊C4×D73—21no—
388C22⋊C4×D73—21no—
389C22⋊C4×D73—21no—
390C2×C4×Dic73C2311yescharacteristic
391C2×C4×Dic73C2311yescharacteristic
392C42×D73—21no—
393C42×D73—21no—
394C42×D73—21no—
395C42×D73C2311yescharacteristic
396#14556524C2311yescharacteristic
397#14556524C2311yescharacteristic
398#14556523C2311yescharacteristic
399#14556522C2311yescharacteristic
400#14556522C2311yescharacteristic
401C4⋊#10596831C2311yescharacteristic
402#14556520C2311yescharacteristic
403#14556520C2311yescharacteristic
404#14556520C2311yescharacteristic
405#14556520C2311yescharacteristic
406#14556520C2311yescharacteristic
407#14556520C2311yescharacteristic
408#14556520C2311yescharacteristic
409#14556520C2311yescharacteristic
410#14556516C2311yescharacteristic
411#14556516C2311yescharacteristic
412#14556516C2311yescharacteristic
413#14556515C2311yescharacteristic
414#14556515C2311yescharacteristic
415#14556515C2311yescharacteristic
416#14556514C2311yescharacteristic
417#14556514C2311yescharacteristic
418#14556514C2311yescharacteristic
419#14556514C2311yescharacteristic
420#14556514C2311yescharacteristic
421#14556513C2311yescharacteristic
422#14556513C2311yescharacteristic
423#14556513C2311yescharacteristic
424#14556512C2311yescharacteristic
425#14556511C2311yescharacteristic
426#14556511C2311yescharacteristic
427#14556511C2311yescharacteristic
428#14556511C2311yescharacteristic
429#14556511C2311yescharacteristic
430#14556511C2311yescharacteristic
431#14556511C2311yescharacteristic
432C22⋊#10596831C2311yescharacteristic
433C22⋊#10596831C2311yescharacteristic
434#14556503C2311yescharacteristic
435#14556503C2311yescharacteristic
436#14556502C2311yescharacteristic
437#14556501C2311yescharacteristic
438#14556501C2311yescharacteristic
439C8×Dic73C2311yescharacteristic
440C8×Dic73C2311yescharacteristic
441C2×#41×C73C2311yescharacteristic
442C22×Q8×C73C2311yescharacteristic
443C2×Q16×C73C2311yescharacteristic
444C2×Q16×C73C2311yescharacteristic
445C2×SD16×C73C2311yescharacteristic
446C2×M16×C73C2311yescharacteristic
447C22×C8×C73C2311yescharacteristic
448C4⋊Q8×C73C2311yescharacteristic
449#126×C73—21no—
450#126×C73—21no—
451#124×C73—21no—
452#124×C73—21no—
453#124×C73C2311yescharacteristic
454C22⋊Q8×C73—21no—
455C22⋊Q8×C73C2311yescharacteristic
456C22⋊Q8×C73C2311yescharacteristic
457C22⋊Q8×C73C2311yescharacteristic
458#121×C73—21no—
459#121×C73C2311yescharacteristic
460C4×Q8×C73—21no—
461C4×Q8×C73C2311yescharacteristic
462C4×Q8×C73C2311yescharacteristic
463C4×D4×C73—21no—
464C4×D4×C73C2311yescharacteristic
465#117×C73C2311yescharacteristic
466#117×C73C2311yescharacteristic
467#107×C73C2311yescharacteristic
468#107×C73C2311yescharacteristic
469#106×C73C2311yescharacteristic
470C4⋊C8×C73C2311yescharacteristic
471#103×C73C2311yescharacteristic
472#103×C73C2311yescharacteristic
473#103×C73C2311yescharacteristic
474#103×C73C2311yescharacteristic
475#103×C73C2311yescharacteristic
476#103×C73C2311yescharacteristic
477#103×C73C2311yescharacteristic
478#102×C73C2311yescharacteristic
479#102×C73C2311yescharacteristic
480#102×C73C2311yescharacteristic
481C22⋊C8×C73C2311yescharacteristic
482C22⋊C8×C73C2311yescharacteristic
483#97×C73C2311yescharacteristic
484C23×D73—21no—
485C23×D73—21no—
486#11924029—22no—
487#11924029—41no—
488#11924028—22no—
489#11924028—22no—
490#11924028—41no—
491#11924028—41no—
492#11924028—41no—
493#11924028—41no—
494#11924027—42no—
495C2×Dic146—21no—
496C2×Dic146—21no—
497C2×Dic146—21no—
498C2×Dic146C2×D411yescharacteristic
499C2×Dic146C2411yescharacteristic
500C2×Dic146C2411yescharacteristic
501C2×Dic146C2411yescharacteristic
502Q8×D73—44no—
503Q8×D73—41no—
504Q8×D73—41no—
505C2×D292—21no—
506C2×D292—21no—
507C2×D292—21no—
508C2×D292—41no—
509C2×D292—41no—
510C2×D292C2411yescharacteristic
511C2×D292C2411yescharacteristic
512C2×D292C2411yescharacteristic
513C2×C22⋊D73—21no—
514C2×C22⋊D73—21no—
515C2×C22⋊D73—21no—
516C2×C22⋊D73—21no—
517C2×C22⋊D73—21no—
518C2×C22⋊D73—21no—
519C2×C22⋊D73—21no—
520C2×C22⋊D73C2×D411yescharacteristic
521C2×C22⋊D73C2×D411yescharacteristic
522D4×D73—41no—
523D4×D73—41no—
524D4×D73—44no—
525C22×Dic73—21no—
526C22×Dic73C2×D411yescharacteristic
527C22×Dic73C2×D411yescharacteristic
528C22×Dic73C2×D411yescharacteristic
529C22×Dic73C2×D411yescharacteristic
530C2×C4×D73—21no—
531C2×C4×D73—21no—
532C2×C4×D73—21no—
533C2×C4×D73—21no—
534C2×C4×D73—21no—
535C2×C4×D73—21no—
536C2×C4×D73—21no—
537C2×C4×D73—21no—
538C2×C4×D73—21no—
539C2×C4×D73—21no—
540C2×C4×D73—21no—
541C2×C4×D73C2×D411yescharacteristic
542C2×C4×D73C2×D411yescharacteristic
543C2×C4×D73C2411yescharacteristic
544Dic292—41no—
545Dic292—41no—
546#11924018—41no—
547#11924018—41no—
548#11924018—41no—
549#11924018—41no—
550#11924018—41no—
551#11924017—22no—
552#11924017—41no—
553#11924017—41no—
554#11924017—41no—
555#11924017—41no—
556#11924016—41no—
557#11924016—41no—
558#11924015—22no—
559#11924015—22no—
560#11924015—41no—
561#11924015—41no—
562D584—22no—
563D584—22no—
564#11924013—22no—
565#11924012—41no—
566#11924011—41no—
567#11924011—41no—
568C2×#10596831—41no—
569C2×#10596831C2411yescharacteristic
570C2×#10596831C2411yescharacteristic
571C2×#10596831C2411yescharacteristic
572C2×#10596831C2411yescharacteristic
573C4⋊Dic73—21no—
574C4⋊Dic73—21no—
575C4⋊Dic73—21no—
576C4⋊Dic73—21no—
577C4⋊Dic73—21no—
578C4⋊Dic73—21no—
579C4⋊Dic73—21no—
580C4⋊Dic73C2×D411yescharacteristic
581C4⋊Dic73C2411yescharacteristic
582C4⋊Dic73C2411yescharacteristic
583#11924007—21no—
584#11924007—21no—
585#11924007—21no—
586#11924007—21no—
587#11924007—21no—
588#11924007—21no—
589#11924007—21no—
590#11924007—21no—
591#11924007—21no—
592#11924007—21no—
593#11924007—21no—
594#11924007—21no—
595#11924007—21no—
596#11924007—21no—
597#11924007—21no—
598#11924007—21no—
599#11924007—21no—
600#11924007—21no—
601#11924007C2×D411yescharacteristic
602#11924007C2×D411yescharacteristic
603#11924007C2×D411yescharacteristic
604#11924007C2×D411yescharacteristic
605C22⋊Dic73—21no—
606C22⋊Dic73—21no—
607C22⋊Dic73—21no—
608C22⋊Dic73—21no—
609C22⋊Dic73—21no—
610C22⋊Dic73—21no—
611C22⋊Dic73C2×D411yescharacteristic
612C22⋊Dic73C2×D411yescharacteristic
613#11924005—21no—
614#11924005—21no—
615#11924005—21no—
616#11924005—21no—
617#11924005—21no—
618#11924005—21no—
619#11924005—21no—
620#11924005—21no—
621#11924005—21no—
622#11924005—21no—
623#11924005—21no—
624#11924005—21no—
625#11924005—21no—
626#11924005—21no—
627#11924005—21no—
628#11924005—21no—
629#11924005—21no—
630#11924005—21no—
631#11924005—21no—
632#11924005—21no—
633#11924005—21no—
634#11924005—21no—
635#11924005C2×D411yescharacteristic
636#11924005C2×D411yescharacteristic
637C4×Dic73—21no—
638C4×Dic73—21no—
639C4×Dic73—21no—
640C4×Dic73—21no—
641C4×Dic73—21no—
642C4×Dic73—21no—
643C4×Dic73—21no—
644C4×Dic73—21no—
645C4×Dic73C2×D411yescharacteristic
646C4×Dic73C2×D411yescharacteristic
647C4×Dic73C2×D411yescharacteristic
648C4×Dic73C2×D411yescharacteristic
649C4×Dic73C2×D411yescharacteristic
650C4×Dic73C2×D411yescharacteristic
651C4×Dic73C2411yescharacteristic
652C4×Dic73C2411yescharacteristic
653C4×Dic73C2411yescharacteristic
654#41×C73—41no—
655#41×C73—41no—
656C2×Q8×C73—21no—
657C2×Q8×C73—21no—
658C2×Q8×C73—41no—
659C2×Q8×C73—41no—
660C2×Q8×C73C2411yescharacteristic
661C2×Q8×C73C2411yescharacteristic
662C2×Q8×C73C2411yescharacteristic
663C2×D4×C73—21no—
664C2×D4×C73—21no—
665C2×D4×C73C2×D411yescharacteristic
666C2×D4×C73C2411yescharacteristic
667C22×C4×C73—21no—
668C22×C4×C73—21no—
669C22×C4×C73C2411yescharacteristic
670C22×C4×C73C2411yescharacteristic
671Q16×C73—41no—
672Q16×C73—41no—
673SD16×C73—41no—
674M16×C73—41no—
675C2×C8×C73—41no—
676C2×C8×C73C2411yescharacteristic
677C2×C8×C73C2411yescharacteristic
678C2×C8×C73C2411yescharacteristic
679C2×C8×C73C2411yescharacteristic
680C4⋊C4×C73—21no—
681C4⋊C4×C73—21no—
682C4⋊C4×C73—21no—
683C4⋊C4×C73—21no—
684C4⋊C4×C73—21no—
685C4⋊C4×C73—21no—
686C4⋊C4×C73C2×D411yescharacteristic
687C4⋊C4×C73C2411yescharacteristic
688C4⋊C4×C73C2411yescharacteristic
689C4⋊C4×C73C2411yescharacteristic
690C4⋊C4×C73C2411yescharacteristic
691C22⋊C4×C73—21no—
692C22⋊C4×C73—21no—
693C22⋊C4×C73—21no—
694C22⋊C4×C73—21no—
695C22⋊C4×C73—21no—
696C22⋊C4×C73—21no—
697C22⋊C4×C73—21no—
698C22⋊C4×C73—21no—
699C22⋊C4×C73C2×D411yescharacteristic
700C22⋊C4×C73C2×D411yescharacteristic
701C42×C73—21no—
702C42×C73—21no—
703C42×C73—21no—
704C42×C73—21no—
705C42×C73C2411yescharacteristic
706C23×C73—21no—
707C23×C73C22×D411yescharacteristic
708C23×C73C22×D411yescharacteristic
709C22×D73—21no—
710C22×D73—21no—
711C22×D73—21no—
712C22×D73—42no—
713C22×D73—42no—
714C22×D73—81no—
715C22×D73—81no—
716C22×D73—81no—
717C22×D73—81no—
718C22×D73C22×D411yescharacteristic
719Q8×C73—21no—
720Q8×C73—21no—
721Q8×C73—21no—
722Q8×C73—21no—
723Q8×C73—21no—
724Q8×C73—21no—
725Q8×C73—42no—
726Q8×C73—81no—
727D4×C73—21no—
728D4×C73—21no—
729D4×C73—41no—
730D4×C73—42no—
731D4×C73—81no—
732C2×C4×C73—21no—
733C2×C4×C73—21no—
734C2×C4×C73—21no—
735C2×C4×C73—21no—
736C2×C4×C73—21no—
737C2×C4×C73—21no—
738C2×C4×C73—21no—
739C2×C4×C73—21no—
740C2×C4×C73—21no—
741C2×C4×C73—21no—
742C2×C4×C73—21no—
743C2×C4×C73—81no—
744C2×C4×C73—81no—
745C2×C4×C73C22×D411yescharacteristic
746C2×C4×C73C22×D411yescharacteristic
747C2×C4×C73C22×D411yescharacteristic
748C2×C4×C73C22×D411yescharacteristic
749C2×C4×C73C2511yescharacteristic
750C22⋊D73—22no—
751C22⋊D73—41no—
752C22⋊D73—42no—
753C22⋊D73—42no—
754C22⋊D73—42no—
755C22⋊D73—81no—
756C22⋊D73—81no—
757C22⋊D73—81no—
758C22⋊D73—81no—
759C2×Dic73—22no—
760C2×Dic73—21no—
761C2×Dic73—21no—
762C2×Dic73—21no—
763C2×Dic73—21no—
764C2×Dic73—21no—
765C2×Dic73—41no—
766C2×Dic73—41no—
767C2×Dic73—41no—
768C2×Dic73—81no—
769C2×Dic73C22×D411yescharacteristic
770C2×Dic73C22×D411yescharacteristic
771C2×Dic73C22×D411yescharacteristic
772C2×Dic73C22×D411yescharacteristic
773C2×Dic73C22×D411yescharacteristic
774C2×Dic73C22×D411yescharacteristic
775C2×Dic73C22×D411yescharacteristic
776D292—21no—
777D292—21no—
778D292—21no—
779D292—21no—
780D292—21no—
781D292—42no—
782D292—42no—
783D292—81no—
784D292H(5,𝔽2)12yes—
785C4×D73—21no—
786C4×D73—21no—
787C4×D73—41no—
788C4×D73—41no—
789C4×D73—42no—
790C4×D73—42no—
791C4×D73—42no—
792C4×D73—42no—
793C4×D73—42no—
794C4×D73—42no—
795C4×D73—42no—
796C4×D73—42no—
797C4×D73—81no—
798C4×D73—81no—
799C4×D73—81no—
800Dic146—22no—
801Dic146—21no—
802Dic146—21no—
803Dic146—21no—
804Dic146—21no—
805Dic146—21no—
806Dic146—21no—
807Dic146—42no—
808Dic146—42no—
809Dic146—81no—
810C8×C73—21no—
811C8×C73—21no—
812C8×C73—21no—
813C8×C73—21no—
814#10596831—21no—
815#10596831—21no—
816#10596831—21no—
817#10596831—21no—
818C22×C73—21no—
819C22×C73—21no—
820C22×C73—21no—
821C22×C73—21no—
822C22×C73—21no—
823C22×C73—21no—
824C22×C73—41no—
825C22×C73—41no—
826C22×C73—41no—
827C22×C73C23×D411yescharacteristic
828C2×D73—21no—
829C2×D73—21no—
830C2×D73—22no—
831C2×D73—21no—
832C2×D73—41no—
833C2×D73—41no—
834C2×D73—41no—
835C2×D73—41no—
836C2×D73—41no—
837C2×D73—41no—
838C2×D73—41no—
839C2×D73—41no—
840C2×D73—162no—
841C2×D73—162no—
842C4×C73—21no—
843C4×C73—21no—
844C4×C73—21no—
845C4×C73—21no—
846C4×C73—41no—
847C4×C73—41no—
848C4×C73—41no—
849C4×C73—41no—
850C4×C73—41no—
851C4×C73—41no—
852C4×C73—41no—
853C4×C73C2×H(5,𝔽2)11yescharacteristic
854C4×C73#58511yescharacteristic
855Dic73—21no—
856Dic73—21no—
857Dic73—21no—
858Dic73—21no—
859Dic73—21no—
860Dic73—21no—
861Dic73—41no—
862Dic73—41no—
863Dic73—41no—
864Dic73—41no—
865Dic73—41no—
866Dic73#57512yes—
867#61973—731nomaximal, Sylow
868C2×C73—41no—
869C2×C73—41no—
870C2×C73—81no—
871C2×C73#348811yescharacteristic
872C2×C73C2×#57511yescharacteristic
873C2×C73#358611yescharacteristic
874D73—41no—
875D73—42no—
876D73—81no—
877D73—81no—
878#3514—731no—
879#3482—731no—
880#3400—731no—
881#3398—731no—
882#3373—731no—
883#3367—731no—
884#3328—731no—
885#3324—731no—
886#3313—731no—
887#3313D7311yescharacteristic, complemented
888#3311—731no—
889#3311—731no—
890#3276—731no—
891#3272—731no—
892#3269—731no—
893#3269—731no—
894#3267—731no—
895#3267—731no—
896#3252—731no—
897#3252—731no—
898#3248—731no—
899#3215—731no—
900#3215—731no—
901#3210—731no—
902#3111—731no—
903#3111—731no—
904#3102—731no—
905#3040—731no—
906#3040—731no—
907#3035—731no—
908#2989—731no—
909C73#6197311yescharacteristic, complemented, Sylow
910C2×#137—731no—
911C2×#137—731no—
912C2×AGL(1,ℤ/8)—731no—
913C2×AGL(1,ℤ/8)—731no—
914C2×#135—731no—
915C2×#135—731no—
916#559—731no—
917#557—731no—
918#556—731no—
919#556—731no—
920#556—731no—
921#556C2×D7311yescharacteristic, complemented
922#555—1461no—
923#552—1461no—
924#552—1461no—
925#552—1461no—
926#551—1461no—
927#551—1461no—
928D4×Q8—731no—
929D4×Q8—731no—
930#548—731no—
931#548—1461no—
932#548C2×D7311yescharacteristic
933#547—731no—
934#547—731no—
935#547—731no—
936#546—731no—
937#546—731no—
938#546—1461no—
939D42—731no—
940#542—1461no—
941#538—1461no—
942#538—1461no—
943#533—731no—
944#533—731no—
945#533—731no—
946#532—731no—
947#529—731no—
948#529—731no—
949#529—731no—
950#529—1461no—
951#529—1461no—
952#529—1461no—
953C2×#124—731no—
954C2×#124—731no—
955#518—1461no—
956C4×#41—731no—
957C4×#41—731no—
958C4×#41—731no—
959C4×#41—731no—
960C2×C4×Q8—1461no—
961#497—731no—
962#497—731no—
963#497—731no—
964#497—731no—
965#494—731no—
966#492—731no—
967#489—731no—
968#489—731no—
969#489—731no—
970#489C2×D7311yescharacteristic, complemented
971#487—731no—
972#486—731no—
973#485—731no—
974#485—731no—
975#485C2×D7311yescharacteristic, complemented
976#482—731no—
977#482—731no—
978#482C2×D7311yescharacteristic
979#479—731no—
980#479—731no—
981#479—731no—
982#478—731no—
983#477—731no—
984#477C2×D7311yescharacteristic, complemented
985#476—731no—
986#476—731no—
987#475—731no—
988#474—731no—
989#470—731no—
990#470—731no—
991#470—731no—
992#470—731no—
993#468—731no—
994#468—731no—
995#468—731no—
996#468C2×D7311yescharacteristic
997#467—731no—
998#467C2×D7311yescharacteristic, complemented
999#465—731no—
1000#465—731no—
1001#464—731no—
1002#464—731no—
1003#464—731no—
1004#464—731no—
1005#464—731no—
1006#464—731no—
1007#464—731no—
1008#464—731no—
1009#464—731no—
1010#464—731no—
1011#464—731no—
1012#464—731no—
1013#464C2×D7311yescharacteristic, complemented
1014#463—731no—
1015#463—731no—
1016#463—731no—
1017#463—731no—
1018#463—731no—
1019#463—731no—
1020#463—731no—
1021#462—731no—
1022#462—731no—
1023#462—731no—
1024#462—731no—
1025#461—731no—
1026#461—731no—
1027#461—731no—
1028#461—731no—
1029#460—731no—
1030#459—731no—
1031#452—731no—
1032#452—731no—
1033#452—731no—
1034#452—731no—
1035#452—731no—
1036#452—731no—
1037#452C2×D7311yescharacteristic, complemented
1038#451—731no—
1039#451—731no—
1040#451—731no—
1041#451C2×D7311yescharacteristic, complemented
1042#450—731no—
1043#450—731no—
1044#450—731no—
1045#450—731no—
1046#449—731no—
1047#449—731no—
1048#449—731no—
1049#446—731no—
1050#446—731no—
1051#442—731no—
1052#442—731no—
1053#441—731no—
1054#441C2×D7311yescharacteristic, complemented
1055#440—731no—
1056#440—731no—
1057#440—731no—
1058#440—731no—
1059C4×Q16—731no—
1060C4×SD16—731no—
1061C4×SD16—731no—
1062C4×D8—731no—
1063#436—731no—
1064#436—731no—
1065#435—731no—
1066#435—731no—
1067#435—731no—
1068#435C2×D7311yescharacteristic, complemented
1069#432—731no—
1070#432—731no—
1071#431—731no—
1072#423—731no—
1073#423—731no—
1074C2×C4⋊C8—731no—
1075#419—731no—
1076#419C2×D7311yescharacteristic, complemented
1077#418—731no—
1078#418—731no—
1079#416—731no—
1080#416C2×D7311yescharacteristic, complemented
1081C2×#41—731no—
1082C2×#41—731no—
1083C2×#41—731no—
1084C2×#41—731no—
1085C2×#41—731no—
1086C2×#41C22×D7311yescharacteristic
1087C22×Q8—731no—
1088C22×Q8—1461no—
1089C22×Q8C22×D7311yescharacteristic
1090C22×D4—731no—
1091C22×D4—731no—
1092C22×D4—1461no—
1093#137—2922no—
1094#137—2922no—
1095AGL(1,ℤ/8)—2922no—
1096AGL(1,ℤ/8)—2922no—
1097#135—2922no—
1098#135—2922no—
1099C2×Q16—731no—
1100C2×Q16—731no—
1101C2×Q16—731no—
1102C2×Q16—731no—
1103C2×Q16—731no—
1104C2×Q16—731no—
1105C2×Q16—731no—
1106C2×Q16C22×D7311yescharacteristic
1107C2×Q16C22×D7311yescharacteristic
1108C2×SD16—731no—
1109C2×SD16—731no—
1110C2×SD16—731no—
1111C2×SD16—731no—
1112C2×SD16—731no—
1113C2×SD16—731no—
1114C2×SD16—731no—
1115C2×SD16—731no—
1116C2×SD16—731no—
1117C2×SD16—731no—
1118C2×SD16—731no—
1119C2×SD16C22×D7311yescharacteristic
1120C2×D8—731no—
1121C2×D8—731no—
1122C2×D8—731no—
1123C2×M16—731no—
1124C2×M16—731no—
1125C2×M16—731no—
1126C2×M16C22×D7311yescharacteristic
1127C22×C8—731no—
1128C22×C8C22×D7311yescharacteristic
1129C4⋊Q8—731no—
1130C4⋊Q8—731no—
1131C4⋊Q8—731no—
1132C4⋊Q8—731no—
1133C4⋊Q8—731no—
1134C4⋊Q8—731no—
1135C4⋊Q8—1461no—
1136C4⋊Q8C22×D7311yescharacteristic
1137#127—731no—
1138#126—21no—
1139#126—21no—
1140#126—1461no—
1141#126—1461no—
1142#126—1461no—
1143#126—1461no—
1144#126—1461no—
1145#126—1461no—
1146#126—1461no—
1147#126—1461no—
1148#126—1461no—
1149#125—731no—
1150#125—1461no—
1151#125—1461no—
1152#125—1461no—
1153#125—1461no—
1154#125—1461no—
1155#125—1461no—
1156#124—21no—
1157#124—21no—
1158#124—731no—
1159#124—731no—
1160#124—731no—
1161#124—731no—
1162#124—731no—
1163#124—731no—
1164#124—1461no—
1165#124—1461no—
1166#124—1461no—
1167#124—1461no—
1168#124—1461no—
1169#124—1461no—
1170#124—1461no—
1171#124—1461no—
1172#124C22×D7311yescharacteristic
1173#123—1461no—
1174#123—1461no—
1175#123—1461no—
1176#123—1461no—
1177#123—1461no—
1178#123—1461no—
1179#123—1461no—
1180#123—1461no—
1181#123—1461no—
1182#123—1461no—
1183#123—1461no—
1184#123—1461no—
1185#123—1461no—
1186C22⋊Q8—21no—
1187C22⋊Q8—731no—
1188C22⋊Q8—731no—
1189C22⋊Q8—731no—
1190C22⋊Q8—731no—
1191C22⋊Q8—731no—
1192C22⋊Q8—731no—
1193C22⋊Q8—1461no—
1194C22⋊Q8—1461no—
1195C22⋊Q8—1461no—
1196C22⋊Q8—1461no—
1197C22⋊Q8—1461no—
1198C22⋊Q8—1461no—
1199C22⋊Q8—1461no—
1200C22⋊Q8—1461no—
1201C22⋊Q8—1461no—
1202C22⋊Q8—1461no—
1203C22⋊Q8C22×D7311yescharacteristic
1204C22⋊Q8C22×D7311yescharacteristic
1205C22⋊Q8C22×D7311yescharacteristic
1206#121—21no—
1207#121—731no—
1208#121—731no—
1209#121—1461no—
1210#121—1461no—
1211#121—1461no—
1212#121—1461no—
1213#121—1461no—
1214#121—1461no—
1215#121—1461no—
1216#121—1461no—
1217#121—1461no—
1218#121C22×D7311yescharacteristic
1219#120—1461no—
1220#120—1461no—
1221#120—1461no—
1222#120—1461no—
1223C4×Q8—21no—
1224C4×Q8—731no—
1225C4×Q8—731no—
1226C4×Q8—731no—
1227C4×Q8—731no—
1228C4×Q8—731no—
1229C4×Q8—731no—
1230C4×Q8—731no—
1231C4×Q8—731no—
1232C4×Q8—731no—
1233C4×Q8—1461no—
1234C4×Q8—1461no—
1235C4×Q8—1461no—
1236C4×Q8—1461no—
1237C4×Q8—1461no—
1238C4×Q8—1461no—
1239C4×Q8C22×D7311yescharacteristic
1240C4×Q8C22×D7311yescharacteristic
1241C4×D4—21no—
1242C4×D4—731no—
1243C4×D4—731no—
1244C4×D4—731no—
1245C4×D4—731no—
1246C4×D4—731no—
1247C4×D4—731no—
1248C4×D4—731no—
1249C4×D4—731no—
1250C4×D4—731no—
1251C4×D4—731no—
1252C4×D4—731no—
1253C4×D4—731no—
1254C4×D4—1461no—
1255C4×D4—1461no—
1256C4×D4—1461no—
1257C4×D4—1461no—
1258C4×D4—1461no—
1259C4×D4—1461no—
1260C4×D4—1461no—
1261C4×D4—1461no—
1262C4×D4—1461no—
1263C4×D4—1461no—
1264C4×D4—1461no—
1265C4×D4—1461no—
1266C4×D4—1461no—
1267C4×D4—1461no—
1268C4×D4C22×D7311yescharacteristic
1269#117—731no—
1270#117—731no—
1271#117—731no—
1272#117—731no—
1273#117—1461no—
1274#117—1461no—
1275#117—1461no—
1276#117—1461no—
1277#117—1461no—
1278#117—1461no—
1279#117—1461no—
1280#117—1461no—
1281#117—1461no—
1282#117—1461no—
1283#117C22×D7311yescharacteristic
1284#117C22×D7311yescharacteristic
1285C2×C4⋊C4—1461no—
1286C2×C4⋊C4—1461no—
1287C2×C4⋊C4—1461no—
1288C2×C22⋊C4—1461no—
1289C2×C22⋊C4—1461no—
1290C2×C22⋊C4—1461no—
1291C2×C22⋊C4—1461no—
1292C2×C22⋊C4—1461no—
1293C2×C22⋊C4—1461no—
1294C2×C42—731no—
1295C2×C42—731no—
1296C2×C42—731no—
1297C2×C42—1461no—
1298C2×C42—1461no—
1299C2×C42—1461no—
1300#107—731no—
1301#107—731no—
1302#107C22×D7311yescharacteristic
1303#107C22×D7311yescharacteristic
1304#106—731no—
1305#106—731no—
1306#106—731no—
1307#106C22×D7311yescharacteristic
1308C4⋊C8—731no—
1309C4⋊C8—731no—
1310C4⋊C8—731no—
1311C4⋊C8—731no—
1312C4⋊C8—731no—
1313C4⋊C8—731no—
1314C4⋊C8—731no—
1315C4⋊C8—731no—
1316C4⋊C8—731no—
1317C4⋊C8C22×D7311yescharacteristic
1318#103—731no—
1319#103—731no—
1320#103—731no—
1321#103—731no—
1322#103—731no—
1323#103—731no—
1324#103—731no—
1325#103—731no—
1326#103—731no—
1327#103—731no—
1328#103—731no—
1329#103C22×D7311yescharacteristic
1330#103C22×D7311yescharacteristic
1331#103C22×D7311yescharacteristic
1332#103C22×D7311yescharacteristic
1333#103C22×D7311yescharacteristic
1334#103C22×D7311yescharacteristic
1335#103C22×D7311yescharacteristic
1336#102—731no—
1337#102—731no—
1338#102—731no—
1339#102—731no—
1340#102—731no—
1341#102—731no—
1342#102—731no—
1343#102—731no—
1344#102—731no—
1345#102—731no—
1346#102—731no—
1347#102C22×D7311yescharacteristic
1348#102C22×D7311yescharacteristic
1349#102C22×D7311yescharacteristic
1350C22⋊C8—731no—
1351C22⋊C8—731no—
1352C22⋊C8—731no—
1353C22⋊C8—731no—
1354C22⋊C8C22×D7311yescharacteristic
1355C22⋊C8C22×D7311yescharacteristic
1356#97—731no—
1357#97—731no—
1358#97—731no—
1359#97C22×D7311yescharacteristic
1360C4×C8—731no—
1361C4×C8—731no—
1362C24—1461no—
1363C24—1461no—
1364#41—41no—
1365#41—41no—
1366#41—2921no—
1367#41—2921no—
1368#41—2921no—
1369#41—2921no—
1370#41—2922no—
1371#41—2921no—
1372#41—1462no—
1373#41—1462no—
1374#41—1462no—
1375C2×Q8—21no—
1376C2×Q8—21no—
1377C2×Q8—41no—
1378C2×Q8—41no—
1379C2×Q8—2924no—
1380C2×Q8—2921no—
1381C2×Q8—2921no—
1382C2×Q8—731no—
1383C2×Q8—731no—
1384C2×Q8—731no—
1385C2×Q8—731no—
1386C2×Q8—1461no—
1387C2×Q8—1461no—
1388C2×Q8—1461no—
1389C2×Q8C23×D7311yescharacteristic
1390C2×Q8C23×D7311yescharacteristic
1391C2×Q8C23×D7311yescharacteristic
1392C2×D4—21no—
1393C2×D4—21no—
1394C2×D4—2921no—
1395C2×D4—2921no—
1396C2×D4—2924no—
1397C2×D4—2921no—
1398C2×D4—2921no—
1399C2×D4—731no—
1400C2×D4—731no—
1401C2×D4—731no—
1402C2×D4—731no—
1403C2×D4—731no—
1404C2×D4—1461no—
1405C2×D4—1461no—
1406C2×D4—1461no—
1407C2×D4—1461no—
1408C2×D4—1461no—
1409C2×D4—1461no—
1410C2×D4—1461no—
1411C2×D4—1461no—
1412C2×D4—1461no—
1413C2×D4—1461no—
1414C2×D4D4×D7311yescharacteristic
1415C2×D4C23×D7311yescharacteristic
1416C22×C4—21no—
1417C22×C4—21no—
1418C22×C4—731no—
1419C22×C4—731no—
1420C22×C4—731no—
1421C22×C4—731no—
1422C22×C4—731no—
1423C22×C4—731no—
1424C22×C4—731no—
1425C22×C4—1461no—
1426C22×C4—1461no—
1427C22×C4—1461no—
1428C22×C4—1461no—
1429C22×C4—1461no—
1430C22×C4—1461no—
1431C22×C4—1461no—
1432C22×C4—1461no—
1433C22×C4—1461no—
1434C22×C4—1461no—
1435C22×C4—1461no—
1436C22×C4—1461no—
1437C22×C4C23×D7311yescharacteristic
1438C22×C4C23×D7311yescharacteristic
1439Q16—41no—
1440Q16—41no—
1441Q16—2921no—
1442Q16—2921no—
1443Q16—2921no—
1444Q16—2921no—
1445Q16—2921no—
1446Q16—2921no—
1447Q16—2921no—
1448SD16—41no—
1449SD16—2921no—
1450SD16—2921no—
1451SD16—2921no—
1452SD16—2921no—
1453SD16—2921no—
1454SD16—2921no—
1455SD16—2921no—
1456SD16—2921no—
1457SD16—1462no—
1458SD16—1462no—
1459SD16—1462no—
1460D8—1462no—
1461D8—1462no—
1462D8—1462no—
1463M16—41no—
1464M16—2921no—
1465M16—2921no—
1466M16—2921no—
1467C2×C8—41no—
1468C2×C8—2921no—
1469C2×C8—731no—
1470C2×C8—731no—
1471C2×C8—731no—
1472C2×C8—731no—
1473C2×C8C23×D7311yescharacteristic
1474C2×C8C23×D7311yescharacteristic
1475C2×C8C23×D7311yescharacteristic
1476C2×C8C23×D7311yescharacteristic
1477C4⋊C4—21no—
1478C4⋊C4—21no—
1479C4⋊C4—21no—
1480C4⋊C4—21no—
1481C4⋊C4—21no—
1482C4⋊C4—21no—
1483C4⋊C4—731no—
1484C4⋊C4—731no—
1485C4⋊C4—731no—
1486C4⋊C4—731no—
1487C4⋊C4—731no—
1488C4⋊C4—731no—
1489C4⋊C4—731no—
1490C4⋊C4—1461no—
1491C4⋊C4—1461no—
1492C4⋊C4—1461no—
1493C4⋊C4—1461no—
1494C4⋊C4—1461no—
1495C4⋊C4—1461no—
1496C4⋊C4—1461no—
1497C4⋊C4—1461no—
1498C4⋊C4—1461no—
1499C4⋊C4—1461no—
1500C4⋊C4—1461no—
1501C4⋊C4—1461no—
1502C4⋊C4—1461no—
1503C4⋊C4—1461no—
1504C4⋊C4—1461no—
1505C4⋊C4—1461no—
1506C4⋊C4—1461no—
1507C4⋊C4—1461no—
1508C4⋊C4—1461no—
1509C4⋊C4—1461no—
1510C4⋊C4—1461no—
1511C4⋊C4—1461no—
1512C4⋊C4—1461no—
1513C4⋊C4—1461no—
1514C4⋊C4—1461no—
1515C4⋊C4D4×D7311yescharacteristic
1516C4⋊C4C23×D7311yescharacteristic
1517C4⋊C4C23×D7311yescharacteristic
1518C4⋊C4C23×D7311yescharacteristic
1519C4⋊C4C23×D7311yescharacteristic
1520C22⋊C4—21no—
1521C22⋊C4—21no—
1522C22⋊C4—21no—
1523C22⋊C4—21no—
1524C22⋊C4—21no—
1525C22⋊C4—21no—
1526C22⋊C4—21no—
1527C22⋊C4—21no—
1528C22⋊C4—731no—
1529C22⋊C4—731no—
1530C22⋊C4—731no—
1531C22⋊C4—731no—
1532C22⋊C4—1461no—
1533C22⋊C4—1461no—
1534C22⋊C4—1461no—
1535C22⋊C4—1461no—
1536C22⋊C4—1461no—
1537C22⋊C4—1461no—
1538C22⋊C4—1461no—
1539C22⋊C4—1461no—
1540C22⋊C4—1461no—
1541C22⋊C4—1461no—
1542C22⋊C4—1461no—
1543C22⋊C4—1461no—
1544C22⋊C4—1461no—
1545C22⋊C4—1461no—
1546C22⋊C4—1461no—
1547C22⋊C4—1461no—
1548C22⋊C4—1461no—
1549C22⋊C4—1461no—
1550C22⋊C4—1461no—
1551C22⋊C4—1461no—
1552C22⋊C4—1461no—
1553C22⋊C4—1461no—
1554C22⋊C4—1461no—
1555C22⋊C4—1461no—
1556C22⋊C4—1461no—
1557C22⋊C4—1461no—
1558C22⋊C4—1461no—
1559C22⋊C4—1461no—
1560C22⋊C4D4×D7311yescharacteristic
1561C22⋊C4D4×D7311yescharacteristic
1562C42—21no—
1563C42—21no—
1564C42—21no—
1565C42—21no—
1566C42—731no—
1567C42—731no—
1568C42—731no—
1569C42—731no—
1570C42—731no—
1571C42—731no—
1572C42—731no—
1573C42—731no—
1574C42—731no—
1575C42—1461no—
1576C42—1461no—
1577C42—1461no—
1578C42—1461no—
1579C42—1461no—
1580C42—1461no—
1581C42—1461no—
1582C42—1461no—
1583C42C23×D7311yescharacteristic
1584C23—21no—
1585C23—2922no—
1586C23—2922no—
1587C23—5841no—
1588C23—5841no—
1589C23—5841no—
1590C23—5841no—
1591C23—731no—
1592C23—1461no—
1593C23—1461no—
1594C23—1461no—
1595C23C2×D4×D7311yescharacteristic
1596C23C2×D4×D7311yescharacteristic
1597Q8—21no—
1598Q8—21no—
1599Q8—21no—
1600Q8—21no—
1601Q8—21no—
1602Q8—21no—
1603Q8—42no—
1604Q8—81no—
1605Q8—2922no—
1606Q8—2922no—
1607Q8—5841no—
1608Q8—1462no—
1609Q8—1461no—
1610Q8—1461no—
1611Q8—1461no—
1612Q8—1461no—
1613Q8—1461no—
1614Q8—1461no—
1615D4—21no—
1616D4—21no—
1617D4—41no—
1618D4—42no—
1619D4—81no—
1620D4—2922no—
1621D4—2922no—
1622D4—2922no—
1623D4—2922no—
1624D4—2922no—
1625D4—2921no—
1626D4—5841no—
1627D4—5841no—
1628D4—5841no—
1629D4—5841no—
1630D4—5841no—
1631D4—732no—
1632D4—1462no—
1633D4—1461no—
1634D4—1461no—
1635D4—1461no—
1636D4—1461no—
1637D4—1461no—
1638C2×C4—21no—
1639C2×C4—21no—
1640C2×C4—21no—
1641C2×C4—21no—
1642C2×C4—21no—
1643C2×C4—21no—
1644C2×C4—21no—
1645C2×C4—21no—
1646C2×C4—21no—
1647C2×C4—21no—
1648C2×C4—21no—
1649C2×C4—81no—
1650C2×C4—81no—
1651C2×C4—2922no—
1652C2×C4—2922no—
1653C2×C4—2922no—
1654C2×C4—2921no—
1655C2×C4—2921no—
1656C2×C4—2922no—
1657C2×C4—2922no—
1658C2×C4—2922no—
1659C2×C4—2922no—
1660C2×C4—2922no—
1661C2×C4—2921no—
1662C2×C4—2921no—
1663C2×C4—2921no—
1664C2×C4—5841no—
1665C2×C4—5841no—
1666C2×C4—5841no—
1667C2×C4—5841no—
1668C2×C4—731no—
1669C2×C4—731no—
1670C2×C4—731no—
1671C2×C4—731no—
1672C2×C4—731no—
1673C2×C4—731no—
1674C2×C4—731no—
1675C2×C4—1461no—
1676C2×C4—1461no—
1677C2×C4—1461no—
1678C2×C4—1461no—
1679C2×C4—1461no—
1680C2×C4—1462no—
1681C2×C4—1461no—
1682C2×C4—1461no—
1683C2×C4C2×D4×D7311yescharacteristic
1684C2×C4C2×D4×D7311yescharacteristic
1685C2×C4C2×D4×D7311yescharacteristic
1686C2×C4C2×D4×D7311yescharacteristic
1687C2×C4C24×D7311yescharacteristic
1688C8—21no—
1689C8—21no—
1690C8—21no—
1691C8—21no—
1692C8—1461no—
1693C8—1461no—
1694C8—1461no—
1695C8—1461no—
1696C22—21no—
1697C22—21no—
1698C22—21no—
1699C22—21no—
1700C22—21no—
1701C22—21no—
1702C22—41no—
1703C22—41no—
1704C22—41no—
1705C22—2921no—
1706C22—2921no—
1707C22—2921no—
1708C22—2921no—
1709C22—2921no—
1710C22—2921no—
1711C22—2921no—
1712C22—2921no—
1713C22—11682no—
1714C22—11682no—
1715C22—1462no—
1716C22—1461no—
1717C22—1461no—
1718C22—1461no—
1719C22C22×D4×D7311yescharacteristic
1720C4—21no—
1721C4—21no—
1722C4—21no—
1723C4—21no—
1724C4—41no—
1725C4—41no—
1726C4—41no—
1727C4—41no—
1728C4—41no—
1729C4—41no—
1730C4—41no—
1731C4—2921no—
1732C4—2921no—
1733C4—2921no—
1734C4—2921no—
1735C4—2921no—
1736C4—732no—
1737C4—1461no—
1738C4—1461no—
1739C4—1461no—
1740C4—1461no—
1741C4—1461no—
1742C4—1461no—
1743C4H(5,𝔽2)×D7311yescharacteristic
1744C4#1798942311yescharacteristic
1745C2—41no—
1746C2—41no—
1747C2—81no—
1748C2—2922no—
1749C2—2921no—
1750C2—5841no—
1751C2—5841no—
1752C2#2262359411yescharacteristic
1753C2#575×D7311yescharacteristic
1754C2#2262471611yescharacteristic
subgroupG/H
centerC22C22×D4×D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC73×#3313C2
socleC22×C73C23×D4
hypercenter#3313D73
hypocenterC73#61973
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C4×D4 ◁ #3313

Complements

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

NH ≅ G/Ntype
1. #22623885C2semidirect
2. #22623550C2semidirect
3. #22622987C2semidirect
4. #22622963C2semidirect
5. #22622720C2semidirect
6. #22622652C2semidirect
7. #22622210C2semidirect
8. #22622160C2semidirect
9. #22621995C2semidirect
10. #22621963C2semidirect
11. #22621961C2semidirect
12. #22621570C2semidirect
13. #22621528C2semidirect
14. #22621487C2semidirect
15. #22621483C2semidirect
16. #22621461C2semidirect
17. #22621460C2semidirect
18. #22621307C2semidirect
19. #22621297C2semidirect
20. #22621263C2semidirect
21. #22620935C2semidirect
22. #22620933C2semidirect
23. #22620885C2semidirect
24. #22620046C2semidirect
25. #22620035C2semidirect
26. #22619952C2semidirect
27. #22619428C2semidirect
28. #22619422C2semidirect
29. #22619384C2semidirect
30. #22619043C2semidirect
31. C73×#3313C2semidirect
32. C2×#14556623C22semidirect
33. C2×#14556622C22semidirect
36. C2×#14556613C22semidirect
37. C2×#14556611C22semidirect
39. #17989315C22semidirect
42. #17989305C22semidirect
49. #17989252C22semidirect
53. #17989242C22semidirect
55. #17989239C22semidirect
63. #17989142C22semidirect
64. #17989139C22semidirect
65. #17989139C22semidirect
76. C4×#11924029C22semidirect
77. #17989055C22semidirect
78. #17989055C22semidirect
81. #17988982C22semidirect
84. #17988980C22semidirect
85. #17988965C22semidirect
89. #17988948C22semidirect
90. #17988936C22semidirect
92. #17988928C22semidirect
93. #17988926C22semidirect
96. #17988893C22semidirect
97. #17988893C22semidirect
98. #17988892C22semidirect
99. #17988886C22semidirect
100. #17988881C22semidirect
101. #17988875C22semidirect
102. #17988874C22semidirect
103. #17988870C22semidirect
105. #17988845C22semidirect
106. #17988844C22semidirect
107. #17988844C22semidirect
108. #17988843C22semidirect
112. #17988826C22semidirect
118. #17988812C22semidirect
119. #17988812C22semidirect
120. #17988812C22semidirect
122. #17988811C22semidirect
124. #17988808C22semidirect
125. #17988808C22semidirect
126. #17988807C22semidirect
129. #17988805C22semidirect
130. #17988805C22semidirect
132. #17988801C22semidirect
133. #17988799C22semidirect
134. #17988797C22semidirect
135. #17988796C22semidirect
136. #17988796C22semidirect
137. #17988795C22semidirect
138. #17988793C22semidirect
140. #17988791C22semidirect
141. #17988790C22semidirect
144. #17988751C22semidirect
145. #17988751C22semidirect
146. #17988749C22semidirect
147. #17988748C22semidirect
148. #17988747C22semidirect
149. #17988747C22semidirect
150. #17988744C22semidirect
151. #17988744C22semidirect
152. #17988743C22semidirect
160. #17988716C22semidirect
161. #17988715C22semidirect
162. #17988700C22semidirect
163. #17988696C22semidirect
164. #17988693C22semidirect
165. #17988686C22semidirect
166. #17988685C22semidirect
167. #17988685C22semidirect
168. #17988684C22semidirect
169. #17988679C22semidirect
171. #17988672C22semidirect
175. #17988659C22semidirect
176. #17988658C22semidirect
177. #17988655C22semidirect
178. #17988642C22semidirect
179. #17988641C22semidirect
180. #17988637C22semidirect
181. #17988610C22semidirect
182. #17988609C22semidirect
183. C2×#14556520C22semidirect
184. #17988594C22semidirect
187. #17988581C22semidirect
188. #556×C73C22semidirect
190. #489×C73C22semidirect
191. #485×C73C22semidirect
193. #477×C73C22semidirect
195. #467×C73C22semidirect
196. #464×C73C22semidirect
197. #452×C73C22semidirect
198. #451×C73C22semidirect
199. #441×C73C22semidirect
200. #435×C73C22semidirect
201. #419×C73C22semidirect
202. #416×C73C22semidirect
887. #3313D73semidirect
909. C73#61973semidirect
921. #556C2×D73semidirect
970. #489C2×D73semidirect
975. #485C2×D73semidirect
984. #477C2×D73semidirect
998. #467C2×D73semidirect
1013. #464C2×D73semidirect
1037. #452C2×D73semidirect
1041. #451C2×D73semidirect
1054. #441C2×D73semidirect
1068. #435C2×D73semidirect
1076. #419C2×D73semidirect
1080. #416C2×D73semidirect

Maximal subgroups

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

subgroupindex
#226238852
#226235502
#226229872
#226229632
#226227202
#226226522
#226222102
#226221602
#226219952
#226219632
#226219612
#226215702
#226215282
#226214872
#226214832
#226214612
#226214602
#226213072
#226212972
#226212632
#226209352
#226209332
#226208852
#226200462
#226200352
#226199522
#226194282
#226194222
#226193842
#226190432
C73×#33132
#6197373