Finite Group Databasebeta

← #33966770

Subgroups — #33966770

Order 18688.

1794 conjugacy classes of subgroups.

The subgroup lattice has 1628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22623745C211yesmaximal, characteristic, complemented
2#22623730C211yesmaximal, characteristic, complemented
3#22622890C211yesmaximal, characteristic, complemented
4#22622888C211yesmaximal, characteristic, complemented
5#22622885C211yesmaximal, characteristic, complemented
6#22622849C211yesmaximal, characteristic, complemented
7#22622847C211yesmaximal, characteristic, complemented
8#22622843C211yesmaximal, characteristic, complemented
9#22622841C211yesmaximal, characteristic, complemented
10#22622838C211yesmaximal, characteristic, complemented
11#22622836C211yesmaximal, characteristic, complemented
12#22622833C211yesmaximal, characteristic, complemented
13#22622831C211yesmaximal, characteristic, complemented
14#22622803C211yesmaximal, characteristic, complemented
15#22622801C211yesmaximal, characteristic, complemented
16D8×Dic146C211yesmaximal, characteristic, complemented
17#22622781C211yesmaximal, characteristic, complemented
18#22620476C211yesmaximal, characteristic, complemented
19#22620468C211yesmaximal, characteristic, complemented
20#22620466C211yesmaximal, characteristic, complemented
21#22619783C211yesmaximal, characteristic, complemented
22#22619777C211yesmaximal, characteristic, complemented
23#22619761C211yesmaximal, characteristic, complemented
24#22619759C211yesmaximal, characteristic, complemented
25#22619716C211yesmaximal, characteristic, complemented
26#474×D73C211yesmaximal, characteristic, complemented
27#22618876C211yesmaximal, characteristic, complemented
28#22618760C211yesmaximal, characteristic
29#22618756C211yesmaximal, characteristic
30#22618742C211yesmaximal, characteristic
31C73×#3389C211yesmaximal, characteristic, complemented
32C2×#14556615C2211yescharacteristic
33Q8×Dic146C2211yescharacteristic, complemented
34#17989317C2211yescharacteristic, complemented
35#17989314C2211yescharacteristic, complemented
36#17989314C2211yescharacteristic, complemented
37#17989297C2211yescharacteristic
38#17989296C2211yescharacteristic
39#17989296C2211yescharacteristic
40#17989295—21no—
41#17989294C2211yescharacteristic, complemented
42#17989293C2211yescharacteristic
43#17989293C2211yescharacteristic
44#17989292—21no—
45#17989292—21no—
46#17989291—21no—
47#17989291—21no—
48D4×Dic146C2211yescharacteristic
49D4×Dic146C2211yescharacteristic, complemented
50D4×Dic146C2211yescharacteristic, complemented
51#17989252C2211yescharacteristic
52#17989250—21no—
53#17989250—21no—
54#17989250—21no—
55#17989217C2211yescharacteristic
56#17989217C2211yescharacteristic
57#17989217C2211yescharacteristic
58#17989216—21no—
59#17989216—21no—
60#17989214C2211yescharacteristic
61#17989212—21no—
62#17989212—21no—
63#17989143C2211yescharacteristic
64#17989141C2211yescharacteristic
65#17989139—21no—
66C2×#14556590—21no—
67C4⋊Q8×D73C2211yescharacteristic
68C2×#14556569—21no—
69C22⋊Q8×D73—21no—
70#17989066C2211yescharacteristic
71#17989066C2211yescharacteristic
72#17989059C2211yescharacteristic
73#17989059C2211yescharacteristic
74C4×#11924027C2211yescharacteristic
75C4×D4×D73C2211yescharacteristic
76#17988997C2211yescharacteristic, complemented
77#17988997C2211yescharacteristic, complemented
78#17988997C2211yescharacteristic, complemented
79#17988996C2211yescharacteristic, complemented
80#17988996C2211yescharacteristic, complemented
81#17988995C2211yescharacteristic, complemented
82#17988994C2211yescharacteristic, complemented
83#17988994C2211yescharacteristic, complemented
84#17988994C2211yescharacteristic, complemented
85#17988993C2211yescharacteristic, complemented
86#17988992C2211yescharacteristic, complemented
87#17988991C2211yescharacteristic, complemented
88#17988991C2211yescharacteristic, complemented
89#17988991C2211yescharacteristic, complemented
90#17988991C2211yescharacteristic, complemented
91#17988990C2211yescharacteristic, complemented
92#17988988C2211yescharacteristic, complemented
93#17988987C2211yescharacteristic, complemented
94#17988986C2211yescharacteristic, complemented
95#17988984C2211yescharacteristic, complemented
96#17988984C2211yescharacteristic, complemented
97#17988897C2211yescharacteristic, complemented
98#17988895C2211yescharacteristic, complemented
99#17988895C2211yescharacteristic, complemented
100#17988893C2211yescharacteristic, complemented
101#17988891C2211yescharacteristic, complemented
102#17988891C2211yescharacteristic, complemented
103#17988890C2211yescharacteristic
104#17988889C2211yescharacteristic
105#17988889C2211yescharacteristic, complemented
106#17988887C2211yescharacteristic, complemented
107#17988887C2211yescharacteristic, complemented
108#17988886C2211yescharacteristic
109#17988885C2211yescharacteristic
110#17988885C2211yescharacteristic, complemented
111#17988884C2211yescharacteristic
112#17988884C2211yescharacteristic
113#17988883C2211yescharacteristic, complemented
114#17988881C2211yescharacteristic, complemented
115#17988881C2211yescharacteristic, complemented
116#17988881C2211yescharacteristic, complemented
117#17988879C2211yescharacteristic, complemented
118#17988878C2211yescharacteristic
119#17988877C2211yescharacteristic
120#17988876C2211yescharacteristic
121#17988875C2211yescharacteristic
122#17988875C2211yescharacteristic, complemented
123#17988871C2211yescharacteristic, complemented
124#17988868C2211yescharacteristic
125#17988868C2211yescharacteristic
126#17988867C2211yescharacteristic
127#17988867C2211yescharacteristic
128#17988867C2211yescharacteristic, complemented
129#17988866C2211yescharacteristic
130#17988866C2211yescharacteristic
131#17988866C2211yescharacteristic
132#17988865C2211yescharacteristic
133#17988865C2211yescharacteristic
134#17988865C2211yescharacteristic
135#17988865C2211yescharacteristic, complemented
136#17988865C2211yescharacteristic, complemented
137#17988865C2211yescharacteristic, complemented
138#17988864C2211yescharacteristic
139#17988718C2211yescharacteristic, complemented
140#17988716C2211yescharacteristic, complemented
141#17988716C2211yescharacteristic, complemented
142#17988715C2211yescharacteristic, complemented
143#17988715C2211yescharacteristic, complemented
144C8×Dic146C2211yescharacteristic, complemented
145#17988711C2211yescharacteristic, complemented
146#17988699C2211yescharacteristic
147#17988697C2211yescharacteristic
148#17988697C2211yescharacteristic
149#17988696C2211yescharacteristic
150#17988689C2211yescharacteristic
151#17988689C2211yescharacteristic
152#17988687C2211yescharacteristic
153#17988687C2211yescharacteristic
154#17988686C2211yescharacteristic
155#17988684C2211yescharacteristic
156#17988678C2211yescharacteristic
157#17988678C2211yescharacteristic
158C4×#11924017C2211yescharacteristic
159#17988674C2211yescharacteristic
160#17988674C2211yescharacteristic
161C4×#11924016C2211yescharacteristic
162D8×Dic73C2211yescharacteristic
163D8×Dic73C2211yescharacteristic
164C4×#11924013C2211yescharacteristic
165#17988667C2211yescharacteristic
166#17988667C2211yescharacteristic
167#17988628C2211yescharacteristic
168#17988628C2211yescharacteristic
169#17988626C2211yescharacteristic
170#17988626C2211yescharacteristic
171#17988626C2211yescharacteristic
172#17988624C2211yescharacteristic
173#17988622C2211yescharacteristic
174#107×D73C2211yescharacteristic
175#107×D73C2211yescharacteristic
176#17988612C2211yescharacteristic
177#17988612C2211yescharacteristic
178C4⋊C8×D73C2211yescharacteristic
179#17988590C2211yescharacteristic
180#17988585C2211yescharacteristic
181#17988580C2211yescharacteristic
182#17988580C2211yescharacteristic
183#102×D73C2211yescharacteristic
184#102×D73C2211yescharacteristic
185#17988544C2211yescharacteristic
186#17988541C2211yescharacteristic
187#17988539C2211yescharacteristic
188#554×C73C2211yescharacteristic
189#554×C73C2211yescharacteristic, complemented
190#501×C73C2211yescharacteristic, complemented
191#501×C73C2211yescharacteristic, complemented
192#499×C73C2211yescharacteristic, complemented
193#478×C73C2211yescharacteristic
194#478×C73C2211yescharacteristic
195#478×C73C2211yescharacteristic, complemented
196#478×C73C2211yescharacteristic, complemented
197#474×C73C2211yescharacteristic
198#474×C73C2211yescharacteristic, complemented
199#446×C73C2211yescharacteristic, complemented
200#442×C73C2211yescharacteristic
201#442×C73C2211yescharacteristic
202C4×D8×C73C2211yescharacteristic
203C2×#11924027C2311yescharacteristic
204C22×Dic146—21no—
205C22×Dic146—21no—
206C22×Dic146—21no—
207C2×Q8×D73—21no—
208C2×Q8×D73—21no—
209C2×D4×D73C2311yescharacteristic
210C22×C4×D73—21no—
211#14556615Q818yescomplemented
212C2×#11924017C2311yescharacteristic
213C2×#11924016C2311yescharacteristic
214C2×#11924013C2311yescharacteristic
215C2×#11924011C2311yescharacteristic
216C2×#11924011C2311yescharacteristic
217C2×C8×D73C2311yescharacteristic
218C2×C8×D73C2311yescharacteristic
219#14556591C2311yescharacteristic
220#14556591C2311yescharacteristic
221#14556591C2311yescharacteristic
222#14556591C2311yescharacteristic
223#14556590—21no—
224#14556590—21no—
225#14556590—21no—
226#14556590—21no—
227#14556590—21no—
228#14556590—21no—
229#14556590—21no—
230#14556590—21no—
231#14556590—21no—
232#14556590—21no—
233#14556590D411yescharacteristic
234#14556590C2311yescharacteristic
235#14556590C2311yescharacteristic
236#14556590C2311yescharacteristic
237#14556590C2311yescharacteristic
238#14556590C2311yescharacteristic
239#14556590C2311yescharacteristic
240#14556590C2311yescharacteristic
241#14556590C2311yescharacteristic
242#14556589—21no—
243#14556589—21no—
244#14556589—21no—
245#14556589—21no—
246#14556589D411yescharacteristic
247#14556583C2311yescharacteristic
248#14556583C2311yescharacteristic
249#14556582C2311yescharacteristic
250#14556582C2311yescharacteristic
251#14556582C2311yescharacteristic
252#14556582C2311yescharacteristic
253#14556581—21no—
254#14556581—21no—
255#14556581—21no—
256#14556581—21no—
257#14556581—21no—
258#14556581—21no—
259#14556581—21no—
260#14556581—21no—
261#14556581D411yescharacteristic
262#14556581D411yescharacteristic
263#14556571—21no—
264#14556571—21no—
265#14556571—21no—
266#14556571—21no—
267#14556571—21no—
268#14556571D411yescharacteristic
269#14556570—21no—
270#14556570—21no—
271#14556570—21no—
272#14556570—21no—
273#14556570—21no—
274#14556570—21no—
275#14556569—21no—
276#14556569—21no—
277#14556569—21no—
278#14556569—21no—
279#14556569—21no—
280#14556569—21no—
281#14556569—21no—
282#14556569—21no—
283#14556569—21no—
284#14556569—21no—
285#14556569—21no—
286#14556569—21no—
287#14556569—21no—
288#14556569—21no—
289#14556569D411yescharacteristic
290#14556569D411yescharacteristic
291#14556568—21no—
292#14556568—21no—
293#14556568—21no—
294#14556568—21no—
295#14556568—21no—
296#14556568—21no—
297#14556568—21no—
298#14556568—21no—
299#14556568—21no—
300#14556568—21no—
301#14556568—21no—
302#14556568—21no—
303#14556567—21no—
304#14556567—21no—
305#14556567—21no—
306#14556567D411yescharacteristic
307Q8×Dic73—21no—
308C4×Dic146C2311yescharacteristic
309C4×Dic146C2311yescharacteristic
310C4×Dic146C2311yescharacteristic
311C4×Dic146C2311yescharacteristic
312C4×Dic146C2311yescharacteristic
313C4×Dic146C2311yescharacteristic
314#14556556—21no—
315#14556556—21no—
316#14556556—21no—
317#14556556—21no—
318#14556556—21no—
319#14556556C2311yescharacteristic
320#14556556C2311yescharacteristic
321#14556556C2311yescharacteristic
322C4×D292C2311yescharacteristic
323C4×D292C2311yescharacteristic
324C4×D292C2311yescharacteristic
325D4×Dic73C2311yescharacteristic
326D4×Dic73C2311yescharacteristic
327D4×Dic73C2311yescharacteristic
328D4×Dic73C2311yescharacteristic
329D4×Dic73C2311yescharacteristic
330D4×Dic73C2311yescharacteristic
331#14556553C2311yescharacteristic
332#14556553C2311yescharacteristic
333#14556553C2311yescharacteristic
334C4×C22⋊D73—21no—
335C4×C22⋊D73—21no—
336C4×C22⋊D73—21no—
337C4×C22⋊D73—21no—
338C4×C22⋊D73—21no—
339C4×C22⋊D73—21no—
340#14556551—21no—
341#14556551—21no—
342#14556551—21no—
343#14556551—21no—
344#14556551—21no—
345#14556551—21no—
346#14556549C2311yescharacteristic
347#14556549C2311yescharacteristic
348#14556549C2311yescharacteristic
349#14556548C2311yescharacteristic
350#14556548C2311yescharacteristic
351#14556547—21no—
352#14556547—21no—
353#14556547—21no—
354C2×C4⋊Dic73—21no—
355C2×#11924007—21no—
356C2×#11924007—21no—
357C2×#11924007—21no—
358C2×#11924007—21no—
359C4⋊C4×D73—21no—
360C4⋊C4×D73—21no—
361C4⋊C4×D73—21no—
362C4⋊C4×D73—21no—
363C4⋊C4×D73C2311yescharacteristic
364C4⋊C4×D73C2311yescharacteristic
365C4⋊C4×D73C2311yescharacteristic
366C2×#11924005—21no—
367C2×#11924005—21no—
368C22⋊C4×D73—21no—
369C22⋊C4×D73—21no—
370C22⋊C4×D73—21no—
371C2×C4×Dic73—21no—
372C42×D73C2311yescharacteristic
373#14556525C2311yescharacteristic
374#14556525C2311yescharacteristic
375#14556525C2311yescharacteristic
376#14556525C2311yescharacteristic
377#14556525C2311yescharacteristic
378#14556525C2311yescharacteristic
379#14556524C2311yescharacteristic
380#14556524C2311yescharacteristic
381#14556524C2311yescharacteristic
382#14556524C2311yescharacteristic
383#14556524C2311yescharacteristic
384#14556524C2311yescharacteristic
385#14556524C2311yescharacteristic
386#14556524C2311yescharacteristic
387#14556524C2311yescharacteristic
388#14556524C2311yescharacteristic
389#14556524C2311yescharacteristic
390#14556523C2311yescharacteristic
391#14556523C2311yescharacteristic
392#14556523C2311yescharacteristic
393#14556522C2311yescharacteristic
394#14556522C2311yescharacteristic
395#14556522C2311yescharacteristic
396#14556522C2311yescharacteristic
397#14556522C2311yescharacteristic
398#14556522C2311yescharacteristic
399#14556522C2311yescharacteristic
400C4⋊#10596831C2311yescharacteristic
401C4⋊#10596831C2311yescharacteristic
402C4⋊#10596831C2311yescharacteristic
403#14556520C2311yescharacteristic
404#14556520C2311yescharacteristic
405#14556520C2311yescharacteristic
406#14556520C2311yescharacteristic
407#14556520C2311yescharacteristic
408#14556520C2311yescharacteristic
409#14556516C2311yescharacteristic
410#14556516C2311yescharacteristic
411#14556516C2311yescharacteristic
412#14556514C2311yescharacteristic
413#14556514C2311yescharacteristic
414#14556514C2311yescharacteristic
415#14556513C2311yescharacteristic
416#14556513C2311yescharacteristic
417#14556513C2311yescharacteristic
418#14556512C2311yescharacteristic
419#14556512C2311yescharacteristic
420#14556512C2311yescharacteristic
421#14556512C2311yescharacteristic
422#14556512C2311yescharacteristic
423#14556512C2311yescharacteristic
424#14556511C2311yescharacteristic
425#14556511C2311yescharacteristic
426#14556511C2311yescharacteristic
427#14556502C2311yescharacteristic
428#14556502C2311yescharacteristic
429#14556501C2311yescharacteristic
430#14556501C2311yescharacteristic
431C4×#10596831C2311yescharacteristic
432C8×Dic73C2311yescharacteristic
433C8×Dic73C2311yescharacteristic
434C8×Dic73C2311yescharacteristic
435C8×Dic73C2311yescharacteristic
436C2×D8×C73C2311yescharacteristic
437C4⋊Q8×C73C2311yescharacteristic
438C4⋊Q8×C73C2311yescharacteristic
439#125×C73C2311yescharacteristic
440#125×C73C2311yescharacteristic
441#125×C73C2311yescharacteristic
442#125×C73C2311yescharacteristic
443C22⋊Q8×C73—21no—
444C22⋊Q8×C73—21no—
445C22⋊Q8×C73—21no—
446C22⋊Q8×C73—21no—
447C22⋊Q8×C73—21no—
448C22⋊Q8×C73—21no—
449C4×Q8×C73C2311yescharacteristic
450C4×D4×C73C2311yescharacteristic
451C4×D4×C73C2311yescharacteristic
452C4×D4×C73C2311yescharacteristic
453C4×D4×C73C2311yescharacteristic
454C4×D4×C73C2311yescharacteristic
455C4×D4×C73C2311yescharacteristic
456C2×C4⋊C4×C73—21no—
457C2×C4⋊C4×C73—21no—
458#107×C73C2311yescharacteristic
459#107×C73C2311yescharacteristic
460#107×C73C2311yescharacteristic
461#107×C73C2311yescharacteristic
462#107×C73C2311yescharacteristic
463#106×C73C2311yescharacteristic
464#106×C73C2311yescharacteristic
465#106×C73C2311yescharacteristic
466#106×C73C2311yescharacteristic
467C4⋊C8×C73C2311yescharacteristic
468C4⋊C8×C73C2311yescharacteristic
469C4⋊C8×C73C2311yescharacteristic
470#102×C73C2311yescharacteristic
471#102×C73C2311yescharacteristic
472#102×C73C2311yescharacteristic
473#102×C73C2311yescharacteristic
474#102×C73C2311yescharacteristic
475#102×C73C2311yescharacteristic
476#97×C73C2311yescharacteristic
477#97×C73C2311yescharacteristic
478C4×C8×C73C2311yescharacteristic
479C23×D73—21no—
480#11924027—22no—
481#11924027C2×Q814yescomplemented
482C2×Dic146—21no—
483C2×Dic146—21no—
484C2×Dic146—21no—
485C2×Dic146—21no—
486C2×Dic146—21no—
487C2×Dic146—21no—
488C2×Dic146—21no—
489C2×Dic146—21no—
490C2×Dic146—21no—
491C2×Dic146—21no—
492C2×Dic146—21no—
493C2×Dic146—21no—
494C2×Dic146—82no—
495C2×Dic146—82no—
496C2×Dic146—82no—
497C2×Dic146C2×D411yescharacteristic
498C2×Dic146C2×D411yescharacteristic
499C2×Dic146C2×D411yescharacteristic
500C2×Dic146C2411yescharacteristic
501Q8×D73—82no—
502Q8×D73—82no—
503C2×D292C2411yescharacteristic
504C2×C22⋊D73—21no—
505C2×C22⋊D73—21no—
506D4×D73—22no—
507D4×D73C2×Q814yescomplemented
508C22×Dic73—21no—
509C22×Dic73—21no—
510C22×Dic73—21no—
511C22×Dic73—21no—
512C22×Dic73—21no—
513C22×Dic73—21no—
514C22×Dic73—21no—
515C2×C4×D73—21no—
516C2×C4×D73—21no—
517C2×C4×D73—21no—
518C2×C4×D73—21no—
519C2×C4×D73—21no—
520C2×C4×D73—21no—
521C2×C4×D73—21no—
522C2×C4×D73—21no—
523C2×C4×D73—21no—
524C2×C4×D73—82no—
525C2×C4×D73C2×D411yescharacteristic
526C2×C4×D73C2×D411yescharacteristic
527C2×C4×D73C2411yescharacteristic
528#11924017C2×Q814yescomplemented
529#11924016C2×Q814yescomplemented
530#11924013C2×Q814yescomplemented
531#11924011—22no—
532#11924011C2×Q814yescomplemented
533C2×#10596831C2411yescharacteristic
534C2×#10596831C2411yescharacteristic
535C2×#10596831C2411yescharacteristic
536C2×#10596831C2411yescharacteristic
537C8×D73—22no—
538C8×D73—22no—
539C4⋊Dic73—21no—
540C4⋊Dic73—21no—
541C4⋊Dic73—21no—
542C4⋊Dic73—21no—
543C4⋊Dic73—21no—
544C4⋊Dic73—21no—
545C4⋊Dic73—21no—
546C4⋊Dic73—21no—
547C4⋊Dic73C2×D411yescharacteristic
548C4⋊Dic73C2×D411yescharacteristic
549C4⋊Dic73C2×D411yescharacteristic
550C4⋊Dic73C2411yescharacteristic
551C4⋊Dic73C2411yescharacteristic
552C4⋊Dic73C2411yescharacteristic
553C4⋊Dic73C2411yescharacteristic
554C4⋊Dic73C2411yescharacteristic
555C4⋊Dic73C2411yescharacteristic
556#11924007—21no—
557#11924007—21no—
558#11924007—21no—
559#11924007—21no—
560#11924007—21no—
561#11924007—21no—
562#11924007—21no—
563#11924007—21no—
564#11924007—21no—
565#11924007—21no—
566#11924007—21no—
567#11924007—21no—
568#11924007—21no—
569#11924007—21no—
570#11924007—21no—
571#11924007—21no—
572#11924007—21no—
573#11924007—21no—
574#11924007—21no—
575#11924007—21no—
576#11924007—21no—
577#11924007—21no—
578#11924007—21no—
579#11924007—21no—
580#11924007—21no—
581#11924007C2×D411yescharacteristic
582#11924007C2×D411yescharacteristic
583#11924007C2×D411yescharacteristic
584#11924007C2×D411yescharacteristic
585#11924007C2×D411yescharacteristic
586#11924007C2×D411yescharacteristic
587#11924007C2×D411yescharacteristic
588#11924007C2×D411yescharacteristic
589#11924007C2×D411yescharacteristic
590#11924007C2×D411yescharacteristic
591C22⋊Dic73—21no—
592C22⋊Dic73—21no—
593C22⋊Dic73—21no—
594C22⋊Dic73—21no—
595C22⋊Dic73—21no—
596C22⋊Dic73—21no—
597#11924005—21no—
598#11924005—21no—
599#11924005—21no—
600#11924005—21no—
601#11924005—21no—
602#11924005—21no—
603#11924005—21no—
604#11924005—21no—
605#11924005—21no—
606#11924005C2×D411yescharacteristic
607#11924005C2×D411yescharacteristic
608#11924005C2×D411yescharacteristic
609#11924005C2×D411yescharacteristic
610C4×Dic73—21no—
611C4×Dic73—21no—
612C4×Dic73—21no—
613C4×Dic73—21no—
614C4×Dic73—21no—
615C4×Dic73—21no—
616C4×Dic73—21no—
617C4×Dic73—21no—
618C4×Dic73—21no—
619C4×Dic73C2×D411yescharacteristic
620C4×Dic73C2×D411yescharacteristic
621C4×Dic73C2411yescharacteristic
622C4×Dic73C2411yescharacteristic
623C4×Dic73C2411yescharacteristic
624C2×Q8×C73—21no—
625C2×Q8×C73—21no—
626C2×Q8×C73C2×D411yescharacteristic
627C2×D4×C73C2411yescharacteristic
628C2×D4×C73C2411yescharacteristic
629C22×C4×C73—21no—
630C22×C4×C73—21no—
631C22×C4×C73—21no—
632C22×C4×C73—21no—
633C22×C4×C73—21no—
634C22×C4×C73—21no—
635D8×C73C2×Q814yescomplemented
636C2×C8×C73C2411yescharacteristic
637C2×C8×C73C2411yescharacteristic
638C2×C8×C73C2411yescharacteristic
639C2×C8×C73C2411yescharacteristic
640C4⋊C4×C73—21no—
641C4⋊C4×C73—21no—
642C4⋊C4×C73—21no—
643C4⋊C4×C73—21no—
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×C73C2×D411yescharacteristic
651C4⋊C4×C73C2×D411yescharacteristic
652C4⋊C4×C73C2×D411yescharacteristic
653C4⋊C4×C73C2411yescharacteristic
654C4⋊C4×C73C2411yescharacteristic
655C4⋊C4×C73C2411yescharacteristic
656C4⋊C4×C73C2411yescharacteristic
657C4⋊C4×C73C2411yescharacteristic
658C4⋊C4×C73C2411yescharacteristic
659C22⋊C4×C73—21no—
660C22⋊C4×C73—21no—
661C22⋊C4×C73—21no—
662C22⋊C4×C73—21no—
663C22⋊C4×C73—21no—
664C22⋊C4×C73—21no—
665C42×C73C2411yescharacteristic
666C42×C73C2411yescharacteristic
667C42×C73C2411yescharacteristic
668C23×C73—21no—
669C23×C73—21no—
670C22×D73—21no—
671C22×D73—24no—
672C22×D73—81no—
673C22×D73—81no—
674C22×D73C22×D411yescharacteristic
675Q8×C73—41no—
676Q8×C73—81no—
677Q8×C73—81no—
678D4×C73—21no—
679D4×C73—21no—
680D4×C73C22×Q812yes—
681D4×C73C22×Q812yes—
682C2×C4×C73—21no—
683C2×C4×C73—21no—
684C2×C4×C73—21no—
685C2×C4×C73—21no—
686C2×C4×C73—21no—
687C2×C4×C73—21no—
688C2×C4×C73—42no—
689C2×C4×C73—81no—
690C2×C4×C73—81no—
691C2×C4×C73—81no—
692C2×C4×C73—81no—
693C2×C4×C73—81no—
694C2×C4×C73C22×D411yescharacteristic
695C2×C4×C73C22×D411yescharacteristic
696C2×C4×C73C22×D411yescharacteristic
697C2×C4×C73C22×D411yescharacteristic
698C2×C4×C73C22×D411yescharacteristic
699C2×C4×C73C22×D411yescharacteristic
700C2×C4×C73C2511yescharacteristic
701C22⋊D73—24no—
702C22⋊D73—24no—
703C2×Dic73—21no—
704C2×Dic73—24no—
705C2×Dic73—21no—
706C2×Dic73—21no—
707C2×Dic73—21no—
708C2×Dic73—21no—
709C2×Dic73—21no—
710C2×Dic73—21no—
711C2×Dic73—42no—
712C2×Dic73—42no—
713C2×Dic73—81no—
714C2×Dic73—81no—
715C2×Dic73—81no—
716C2×Dic73—81no—
717C2×Dic73C22×D411yescharacteristic
718C2×Dic73C22×D411yescharacteristic
719C2×Dic73C22×D411yescharacteristic
720C2×Dic73C22×D411yescharacteristic
721C2×Dic73C22×D411yescharacteristic
722C2×Dic73C22×D411yescharacteristic
723C2×Dic73C22×D411yescharacteristic
724D292—21no—
725D292C22×Q812yes—
726C4×D73—22no—
727C4×D73—41no—
728C4×D73—42no—
729C4×D73—81no—
730C4×D73—81no—
731C4×D73—81no—
732C4×D73—81no—
733C4×D73—81no—
734C4×D73—81no—
735C4×D73—81no—
736C4×D73—81no—
737C4×D73C22×Q812yes—
738C4×D732−1+412yes—
739Dic146—21no—
740Dic146—22no—
741Dic146—22no—
742Dic146—41no—
743Dic146—42no—
744Dic146—42no—
745Dic146—42no—
746Dic146—81no—
747Dic146—81no—
748Dic146—81no—
749Dic146—81no—
750Dic146—81no—
751Dic146—81no—
752Dic146—81no—
753Dic146—81no—
754Dic146—81no—
755Dic146C22×Q812yes—
756C8×C73—21no—
757C8×C73—21no—
758C8×C73—21no—
759C8×C73C22×Q812yes—
760#10596831—21no—
761#10596831—21no—
762#10596831—21no—
763#10596831C22×Q812yes—
764C22×C73—22no—
765C22×C73—22no—
766C22×C73—41no—
767C22×C73—41no—
768C22×C73—41no—
769C22×C73—41no—
770C22×C73C23×D411yescharacteristic
771C2×D73—21no—
772C2×D73—21no—
773C2×D73—22no—
774C2×D73—41no—
775C2×D73—41no—
776C2×D73—84no—
777C2×D73D4×Q812yes—
778C4×C73—21no—
779C4×C73—21no—
780C4×C73—21no—
781C4×C73—21no—
782C4×C73—21no—
783C4×C73—21no—
784C4×C73—41no—
785C4×C73—41no—
786C4×C73—41no—
787C4×C73—41no—
788C4×C73—41no—
789C4×C73—41no—
790C4×C73C23×Q811yescharacteristic
791C4×C73C2×2−1+411yescharacteristic
792Dic73—21no—
793Dic73—21no—
794Dic73—21no—
795Dic73—22no—
796Dic73—21no—
797Dic73—21no—
798Dic73—41no—
799Dic73—41no—
800Dic73—41no—
801Dic73—41no—
802Dic73—41no—
803Dic73—41no—
804Dic73D4×Q812yes—
805Dic73#57612yes—
806#61381—731nomaximal, Sylow
807C2×C73—42no—
808C2×C73—42no—
809C2×C73C2×D4×Q811yescharacteristic
810C2×C73C2×#57611yescharacteristic
811C2×C73#358611yescharacteristic
812D73—22no—
813D73—42no—
814#3503—731no—
815#3501—731no—
816#3389—731no—
817#3389—731no—
818#3389—731no—
819#3389D7311yescharacteristic, complemented
820#3386—731no—
821#3386—731no—
822#3385—731no—
823#3385—731no—
824#3385—731no—
825#3385—731no—
826#3384—731no—
827#3384—731no—
828#3381—731no—
829#3381—731no—
830Q8×D8—731no—
831Q8×D8—731no—
832#3165—731no—
833#3164—731no—
834#3164—731no—
835#3083—731no—
836#3083—731no—
837#3081—731no—
838#3081—731no—
839#3076—731no—
840C2×#474—731no—
841#2962—731no—
842#2946—731no—
843#2946—731no—
844C4×AGL(1,ℤ/8)—731no—
845C73#6138111yescharacteristic, complemented, Sylow
846C2×AGL(1,ℤ/8)—731no—
847Q82—731no—
848Q82—731no—
849#557—731no—
850#557—731no—
851#554—731no—
852#554—731no—
853#554—731no—
854#554—731no—
855#554—731no—
856#554—731no—
857#554—1461no—
858#554—1461no—
859#554—1461no—
860#554—1461no—
861#554—1461no—
862#554C2×D7311yescharacteristic
863#554C2×D7311yescharacteristic, complemented
864D4×Q8—731no—
865D4×Q8—731no—
866D4×Q8—731no—
867D4×Q8—731no—
868D4×Q8—1461no—
869D4×Q8—1461no—
870D4×Q8—1461no—
871#544—731no—
872#544—731no—
873#544—731no—
874#544—731no—
875#544—1461no—
876#544—1461no—
877#543—1461no—
878#543—1461no—
879#533—731no—
880#533—731no—
881#533—1461no—
882C2×C4⋊Q8—731no—
883C2×C4⋊Q8—1461no—
884C2×C22⋊Q8—1461no—
885C2×C22⋊Q8—1461no—
886#520—731no—
887#520—731no—
888#518—731no—
889#518—731no—
890C4×#41—731no—
891C2×C4×D4—731no—
892#501—731no—
893#501—731no—
894#501—731no—
895#501—731no—
896#501—731no—
897#501—731no—
898#501—731no—
899#501—731no—
900#501—731no—
901#501—731no—
902#501C2×D7311yescharacteristic, complemented
903#501C2×D7311yescharacteristic, complemented
904#500—731no—
905#500—731no—
906#500—731no—
907#500—731no—
908#500—731no—
909#500—731no—
910#499—731no—
911#499—731no—
912#499—731no—
913#499C2×D7311yescharacteristic, complemented
914#498—731no—
915#498—731no—
916#479—731no—
917#479—731no—
918#479—731no—
919#479—731no—
920#479—731no—
921#479—731no—
922#478—731no—
923#478—731no—
924#478—731no—
925#478—731no—
926#478—731no—
927#478—731no—
928#478—731no—
929#478—731no—
930#478—731no—
931#478—731no—
932#478C2×D7311yescharacteristic
933#478C2×D7311yescharacteristic
934#478C2×D7311yescharacteristic, complemented
935#478C2×D7311yescharacteristic, complemented
936#477—731no—
937#477—731no—
938#477—731no—
939#477—731no—
940#477—731no—
941#476—731no—
942#476—731no—
943#476—731no—
944#476—731no—
945#476—731no—
946#475—731no—
947#474—731no—
948#474—731no—
949#474—731no—
950#474—731no—
951#474—731no—
952#474—731no—
953#474—731no—
954#474—731no—
955#474—731no—
956#474—731no—
957#474—731no—
958#474—731no—
959#474—731no—
960#474—731no—
961#474—731no—
962#474C2×D7311yescharacteristic
963#474C2×D7311yescharacteristic, complemented
964#446—731no—
965#446—731no—
966#446—731no—
967#446—731no—
968#446—731no—
969#446C2×D7311yescharacteristic, complemented
970C8×Q8—731no—
971C8×Q8—731no—
972#442—731no—
973#442—731no—
974#442—731no—
975#442—731no—
976#442C2×D7311yescharacteristic
977#442C2×D7311yescharacteristic
978#440—731no—
979#440—731no—
980#440—731no—
981#440—731no—
982#440—731no—
983#440—731no—
984C4×SD16—731no—
985C4×SD16—731no—
986C4×SD16—731no—
987C4×SD16—731no—
988C4×SD16—731no—
989C4×SD16—731no—
990C4×D8—731no—
991C4×D8—731no—
992C4×D8—731no—
993C4×D8—731no—
994C4×D8—731no—
995C4×D8C2×D7311yescharacteristic
996#428—731no—
997#428—731no—
998#428—731no—
999#428—731no—
1000#428—731no—
1001#427—731no—
1002#427—731no—
1003C2×#107—731no—
1004C2×#107—731no—
1005#424—731no—
1006#424—731no—
1007C2×C4⋊C8—731no—
1008#418—731no—
1009#417—731no—
1010#416—731no—
1011#416—731no—
1012C2×#102—731no—
1013C2×#102—731no—
1014#405—731no—
1015#405—731no—
1016C4×M16—731no—
1017C2×#41—731no—
1018C22×Q8—1461no—
1019C22×Q8—1461no—
1020C22×Q8—1461no—
1021C22×Q8—1461no—
1022C22×Q8—1461no—
1023C22×D4—731no—
1024C23×C4—1461no—
1025AGL(1,ℤ/8)—738no—
1026C2×SD16—731no—
1027C2×SD16—731no—
1028C2×D8—731no—
1029C2×D8C22×D7311yescharacteristic
1030C2×M16—731no—
1031C2×M16—731no—
1032C22×C8—731no—
1033C22×C8—731no—
1034C4⋊Q8—731no—
1035C4⋊Q8—731no—
1036C4⋊Q8—731no—
1037C4⋊Q8—731no—
1038C4⋊Q8—731no—
1039C4⋊Q8—731no—
1040C4⋊Q8—731no—
1041C4⋊Q8—731no—
1042C4⋊Q8—731no—
1043C4⋊Q8—731no—
1044C4⋊Q8—731no—
1045C4⋊Q8—731no—
1046C4⋊Q8—731no—
1047C4⋊Q8—731no—
1048C4⋊Q8—1461no—
1049C4⋊Q8—1461no—
1050C4⋊Q8—1461no—
1051C4⋊Q8—1461no—
1052C4⋊Q8—1461no—
1053C4⋊Q8—1461no—
1054C4⋊Q8—1461no—
1055C4⋊Q8—1461no—
1056C4⋊Q8—1461no—
1057C4⋊Q8—1461no—
1058C4⋊Q8—1461no—
1059C4⋊Q8—1461no—
1060C4⋊Q8—1461no—
1061C4⋊Q8—1461no—
1062C4⋊Q8C22×D7311yescharacteristic
1063C4⋊Q8C22×D7311yescharacteristic
1064#125—731no—
1065#125—731no—
1066#125—731no—
1067#125—731no—
1068#125—731no—
1069#125—731no—
1070#125—731no—
1071#125—731no—
1072#125—1461no—
1073#125—1461no—
1074#125—1461no—
1075#125—1461no—
1076#125—1461no—
1077#125—1461no—
1078#125—1461no—
1079#125—1461no—
1080#125C22×D7311yescharacteristic
1081#125C22×D7311yescharacteristic
1082#125C22×D7311yescharacteristic
1083#125C22×D7311yescharacteristic
1084C22⋊Q8—21no—
1085C22⋊Q8—21no—
1086C22⋊Q8—21no—
1087C22⋊Q8—21no—
1088C22⋊Q8—21no—
1089C22⋊Q8—21no—
1090C22⋊Q8—731no—
1091C22⋊Q8—731no—
1092C22⋊Q8—731no—
1093C22⋊Q8—731no—
1094C22⋊Q8—1461no—
1095C22⋊Q8—1461no—
1096C22⋊Q8—1461no—
1097C22⋊Q8—1461no—
1098C22⋊Q8—1461no—
1099C22⋊Q8—1461no—
1100C22⋊Q8—1461no—
1101C22⋊Q8—1461no—
1102C22⋊Q8—1461no—
1103C22⋊Q8—1461no—
1104C22⋊Q8—1461no—
1105C22⋊Q8—1461no—
1106C22⋊Q8—1461no—
1107C22⋊Q8—1461no—
1108C22⋊Q8—1461no—
1109C22⋊Q8—1461no—
1110C22⋊Q8—1461no—
1111C22⋊Q8—1461no—
1112C22⋊Q8—1461no—
1113C22⋊Q8—1461no—
1114C22⋊Q8—1461no—
1115C22⋊Q8—1461no—
1116C22⋊Q8—1461no—
1117C22⋊Q8—1461no—
1118C22⋊Q8—1461no—
1119C22⋊Q8—1461no—
1120C22⋊Q8—1461no—
1121C22⋊Q8—1461no—
1122C22⋊Q8—1461no—
1123C22⋊Q8—1461no—
1124C22⋊Q8—1461no—
1125C22⋊Q8—1461no—
1126C22⋊Q8—1461no—
1127C22⋊Q8—1461no—
1128C22⋊Q8—1461no—
1129C22⋊Q8—1461no—
1130C22⋊Q8—1461no—
1131C22⋊Q8—1461no—
1132C22⋊Q8—1461no—
1133C22⋊Q8—1461no—
1134C4×Q8—731no—
1135C4×Q8—731no—
1136C4×Q8—731no—
1137C4×Q8—731no—
1138C4×Q8—731no—
1139C4×Q8—731no—
1140C4×Q8—731no—
1141C4×Q8—731no—
1142C4×Q8—731no—
1143C4×Q8—1461no—
1144C4×Q8—1461no—
1145C4×Q8—1461no—
1146C4×Q8—1461no—
1147C4×Q8—1461no—
1148C4×Q8—1461no—
1149C4×Q8C22×D7311yescharacteristic
1150C4×D4—731no—
1151C4×D4—731no—
1152C4×D4—731no—
1153C4×D4—731no—
1154C4×D4—731no—
1155C4×D4—731no—
1156C4×D4—731no—
1157C4×D4—731no—
1158C4×D4—731no—
1159C4×D4—731no—
1160C4×D4—731no—
1161C4×D4—731no—
1162C4×D4—1461no—
1163C4×D4—1461no—
1164C4×D4—1461no—
1165C4×D4—1461no—
1166C4×D4—1461no—
1167C4×D4—1461no—
1168C4×D4—1461no—
1169C4×D4—1461no—
1170C4×D4—1461no—
1171C4×D4—1461no—
1172C4×D4—1461no—
1173C4×D4—1461no—
1174C4×D4C22×D7311yescharacteristic
1175C4×D4C22×D7311yescharacteristic
1176C4×D4C22×D7311yescharacteristic
1177C4×D4C22×D7311yescharacteristic
1178C4×D4C22×D7311yescharacteristic
1179C4×D4C22×D7311yescharacteristic
1180#117—731no—
1181#117—731no—
1182#117—731no—
1183#117—731no—
1184#117—731no—
1185#117—1461no—
1186#117—1461no—
1187#117—1461no—
1188C2×C4⋊C4—21no—
1189C2×C4⋊C4—21no—
1190C2×C4⋊C4—731no—
1191C2×C4⋊C4—731no—
1192C2×C4⋊C4—731no—
1193C2×C4⋊C4—1461no—
1194C2×C4⋊C4—1461no—
1195C2×C4⋊C4—1461no—
1196C2×C4⋊C4—1461no—
1197C2×C4⋊C4—1461no—
1198C2×C4⋊C4—1461no—
1199C2×C4⋊C4—1461no—
1200C2×C4⋊C4—1461no—
1201C2×C4⋊C4—1461no—
1202C2×C22⋊C4—1461no—
1203C2×C22⋊C4—1461no—
1204C2×C22⋊C4—1461no—
1205C2×C22⋊C4—1461no—
1206C2×C22⋊C4—1461no—
1207C2×C42—731no—
1208C2×C42—1461no—
1209#107—731no—
1210#107—731no—
1211#107—731no—
1212#107—731no—
1213#107—731no—
1214#107—731no—
1215#107—731no—
1216#107—731no—
1217#107—731no—
1218#107—731no—
1219#107—731no—
1220#107—731no—
1221#107—731no—
1222#107—731no—
1223#107—731no—
1224#107—731no—
1225#107—731no—
1226#107C22×D7311yescharacteristic
1227#107C22×D7311yescharacteristic
1228#107C22×D7311yescharacteristic
1229#107C22×D7311yescharacteristic
1230#107C22×D7311yescharacteristic
1231#106—731no—
1232#106—731no—
1233#106—731no—
1234#106—731no—
1235#106—731no—
1236#106—731no—
1237#106—731no—
1238#106—731no—
1239#106—731no—
1240#106—731no—
1241#106C22×D7311yescharacteristic
1242#106C22×D7311yescharacteristic
1243#106C22×D7311yescharacteristic
1244#106C22×D7311yescharacteristic
1245C4⋊C8—731no—
1246C4⋊C8—731no—
1247C4⋊C8—731no—
1248C4⋊C8—731no—
1249C4⋊C8—731no—
1250C4⋊C8—731no—
1251C4⋊C8—731no—
1252C4⋊C8—731no—
1253C4⋊C8—731no—
1254C4⋊C8C22×D7311yescharacteristic
1255C4⋊C8C22×D7311yescharacteristic
1256C4⋊C8C22×D7311yescharacteristic
1257#103—731no—
1258#103—731no—
1259#103—731no—
1260#103—731no—
1261#103—731no—
1262#103—731no—
1263#102—731no—
1264#102—731no—
1265#102—731no—
1266#102—731no—
1267#102—731no—
1268#102—731no—
1269#102—731no—
1270#102—731no—
1271#102—731no—
1272#102—731no—
1273#102—731no—
1274#102—731no—
1275#102C22×D7311yescharacteristic
1276#102C22×D7311yescharacteristic
1277#102C22×D7311yescharacteristic
1278#102C22×D7311yescharacteristic
1279#102C22×D7311yescharacteristic
1280#102C22×D7311yescharacteristic
1281#97—731no—
1282#97—731no—
1283#97—731no—
1284#97—731no—
1285#97C22×D7311yescharacteristic
1286#97C22×D7311yescharacteristic
1287C4×C8—731no—
1288C4×C8—731no—
1289C4×C8—731no—
1290C4×C8—731no—
1291C4×C8—731no—
1292C4×C8C22×D7311yescharacteristic
1293C24—1461no—
1294#41—734no—
1295#41—1462no—
1296C2×Q8—21no—
1297C2×Q8—21no—
1298C2×Q8—5842no—
1299C2×Q8—5842no—
1300C2×Q8—5842no—
1301C2×Q8—5842no—
1302C2×Q8—5842no—
1303C2×Q8—731no—
1304C2×Q8—731no—
1305C2×Q8—731no—
1306C2×Q8—731no—
1307C2×Q8—1461no—
1308C2×Q8—1461no—
1309C2×Q8—1461no—
1310C2×Q8—1461no—
1311C2×Q8—1461no—
1312C2×Q8—1461no—
1313C2×Q8—1461no—
1314C2×Q8—1461no—
1315C2×Q8—1461no—
1316C2×Q8—1461no—
1317C2×Q8—1461no—
1318C2×Q8—1461no—
1319C2×Q8D4×D7311yescharacteristic
1320C2×D4—734no—
1321C2×D4—731no—
1322C2×D4—1462no—
1323C2×D4—1461no—
1324C2×D4—1461no—
1325C2×D4C23×D7311yescharacteristic
1326C2×D4C23×D7311yescharacteristic
1327C22×C4—21no—
1328C22×C4—21no—
1329C22×C4—21no—
1330C22×C4—21no—
1331C22×C4—21no—
1332C22×C4—21no—
1333C22×C4—5842no—
1334C22×C4—731no—
1335C22×C4—731no—
1336C22×C4—731no—
1337C22×C4—1461no—
1338C22×C4—1461no—
1339C22×C4—1461no—
1340C22×C4—1461no—
1341C22×C4—1461no—
1342C22×C4—1461no—
1343C22×C4—1461no—
1344C22×C4—1461no—
1345C22×C4—1461no—
1346C22×C4—1461no—
1347C22×C4—1461no—
1348C22×C4—1461no—
1349C22×C4—1461no—
1350C22×C4—1461no—
1351C22×C4—1461no—
1352C22×C4—1461no—
1353SD16—734no—
1354SD16—734no—
1355D8—734no—
1356D8Q8×D7314yescomplemented
1357M16—734no—
1358M16—1462no—
1359C2×C8—731no—
1360C2×C8—731no—
1361C2×C8—731no—
1362C2×C8—731no—
1363C2×C8—1462no—
1364C2×C8—1462no—
1365C2×C8C23×D7311yescharacteristic
1366C2×C8C23×D7311yescharacteristic
1367C2×C8C23×D7311yescharacteristic
1368C2×C8C23×D7311yescharacteristic
1369C4⋊C4—21no—
1370C4⋊C4—21no—
1371C4⋊C4—21no—
1372C4⋊C4—21no—
1373C4⋊C4—21no—
1374C4⋊C4—21no—
1375C4⋊C4—21no—
1376C4⋊C4—21no—
1377C4⋊C4—21no—
1378C4⋊C4—21no—
1379C4⋊C4—731no—
1380C4⋊C4—731no—
1381C4⋊C4—731no—
1382C4⋊C4—731no—
1383C4⋊C4—731no—
1384C4⋊C4—731no—
1385C4⋊C4—731no—
1386C4⋊C4—731no—
1387C4⋊C4—731no—
1388C4⋊C4—731no—
1389C4⋊C4—731no—
1390C4⋊C4—731no—
1391C4⋊C4—731no—
1392C4⋊C4—731no—
1393C4⋊C4—731no—
1394C4⋊C4—731no—
1395C4⋊C4—731no—
1396C4⋊C4—731no—
1397C4⋊C4—731no—
1398C4⋊C4—1461no—
1399C4⋊C4—1461no—
1400C4⋊C4—1461no—
1401C4⋊C4—1461no—
1402C4⋊C4—1461no—
1403C4⋊C4—1461no—
1404C4⋊C4—1461no—
1405C4⋊C4—1461no—
1406C4⋊C4—1461no—
1407C4⋊C4—1461no—
1408C4⋊C4—1461no—
1409C4⋊C4—1461no—
1410C4⋊C4—1461no—
1411C4⋊C4—1461no—
1412C4⋊C4—1461no—
1413C4⋊C4—1461no—
1414C4⋊C4—1461no—
1415C4⋊C4—1461no—
1416C4⋊C4—1461no—
1417C4⋊C4—1461no—
1418C4⋊C4—1461no—
1419C4⋊C4—1461no—
1420C4⋊C4—1461no—
1421C4⋊C4—1461no—
1422C4⋊C4—1461no—
1423C4⋊C4—1461no—
1424C4⋊C4—1461no—
1425C4⋊C4—1461no—
1426C4⋊C4—1461no—
1427C4⋊C4—1461no—
1428C4⋊C4—1461no—
1429C4⋊C4—1461no—
1430C4⋊C4—1461no—
1431C4⋊C4D4×D7311yescharacteristic
1432C4⋊C4D4×D7311yescharacteristic
1433C4⋊C4D4×D7311yescharacteristic
1434C4⋊C4C23×D7311yescharacteristic
1435C4⋊C4C23×D7311yescharacteristic
1436C4⋊C4C23×D7311yescharacteristic
1437C4⋊C4C23×D7311yescharacteristic
1438C4⋊C4C23×D7311yescharacteristic
1439C4⋊C4C23×D7311yescharacteristic
1440C22⋊C4—21no—
1441C22⋊C4—21no—
1442C22⋊C4—21no—
1443C22⋊C4—21no—
1444C22⋊C4—21no—
1445C22⋊C4—21no—
1446C22⋊C4—731no—
1447C22⋊C4—731no—
1448C22⋊C4—731no—
1449C22⋊C4—731no—
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⋊C4—1461no—
1460C22⋊C4—1461no—
1461C22⋊C4—1461no—
1462C22⋊C4—1461no—
1463C22⋊C4—1461no—
1464C22⋊C4—1461no—
1465C42—731no—
1466C42—731no—
1467C42—731no—
1468C42—731no—
1469C42—731no—
1470C42—1461no—
1471C42—1461no—
1472C42—1461no—
1473C42—1461no—
1474C42—1461no—
1475C42—1461no—
1476C42—1461no—
1477C42—1461no—
1478C42—1461no—
1479C42C23×D7311yescharacteristic
1480C42C23×D7311yescharacteristic
1481C42C23×D7311yescharacteristic
1482C23—21no—
1483C23—21no—
1484C23—5841no—
1485C23—5841no—
1486C23—731no—
1487C23—1464no—
1488C23—1461no—
1489Q8—41no—
1490Q8—81no—
1491Q8—81no—
1492Q8—2921no—
1493Q8—2922no—
1494Q8—2922no—
1495Q8—2922no—
1496Q8—5841no—
1497Q8—5841no—
1498Q8—5841no—
1499Q8—5841no—
1500Q8—5841no—
1501Q8—5841no—
1502Q8—5841no—
1503Q8—5841no—
1504Q8—5841no—
1505Q8—732no—
1506Q8—1462no—
1507Q8—1462no—
1508Q8—1461no—
1509D4—21no—
1510D4—21no—
1511D4—732no—
1512D4—1464no—
1513D4—1464no—
1514D4—1461no—
1515D4C2×Q8×D7312yes—
1516D4C2×Q8×D7312yes—
1517C2×C4—21no—
1518C2×C4—21no—
1519C2×C4—21no—
1520C2×C4—21no—
1521C2×C4—21no—
1522C2×C4—21no—
1523C2×C4—42no—
1524C2×C4—81no—
1525C2×C4—81no—
1526C2×C4—81no—
1527C2×C4—81no—
1528C2×C4—81no—
1529C2×C4—2921no—
1530C2×C4—2922no—
1531C2×C4—2922no—
1532C2×C4—2922no—
1533C2×C4—5841no—
1534C2×C4—5841no—
1535C2×C4—5841no—
1536C2×C4—5841no—
1537C2×C4—5841no—
1538C2×C4—5841no—
1539C2×C4—5841no—
1540C2×C4—5841no—
1541C2×C4—5841no—
1542C2×C4—5841no—
1543C2×C4—5841no—
1544C2×C4—5841no—
1545C2×C4—731no—
1546C2×C4—731no—
1547C2×C4—732no—
1548C2×C4—732no—
1549C2×C4—731no—
1550C2×C4—731no—
1551C2×C4—731no—
1552C2×C4—731no—
1553C2×C4—731no—
1554C2×C4—1462no—
1555C2×C4—1461no—
1556C2×C4—1461no—
1557C2×C4—1461no—
1558C2×C4—1461no—
1559C2×C4—1461no—
1560C2×C4—1461no—
1561C2×C4—1464no—
1562C2×C4—1461no—
1563C2×C4C2×D4×D7311yescharacteristic
1564C2×C4C2×D4×D7311yescharacteristic
1565C2×C4C2×D4×D7311yescharacteristic
1566C2×C4C2×D4×D7311yescharacteristic
1567C2×C4C2×D4×D7311yescharacteristic
1568C2×C4C2×D4×D7311yescharacteristic
1569C2×C4C24×D7311yescharacteristic
1570C8—21no—
1571C8—21no—
1572C8—21no—
1573C8—732no—
1574C8—1461no—
1575C8—1461no—
1576C8—1461no—
1577C8C2×Q8×D7312yes—
1578C22—22no—
1579C22—22no—
1580C22—41no—
1581C22—41no—
1582C22—41no—
1583C22—41no—
1584C22—2921no—
1585C22—2921no—
1586C22—5844no—
1587C22—732no—
1588C22—1462no—
1589C22—1461no—
1590C22—1461no—
1591C22C22×D4×D7311yescharacteristic
1592C4—21no—
1593C4—21no—
1594C4—21no—
1595C4—21no—
1596C4—21no—
1597C4—21no—
1598C4—41no—
1599C4—41no—
1600C4—41no—
1601C4—41no—
1602C4—41no—
1603C4—41no—
1604C4—2921no—
1605C4—2921no—
1606C4—2921no—
1607C4—2921no—
1608C4—2921no—
1609C4—2921no—
1610C4—732no—
1611C4—732no—
1612C4—1461no—
1613C4—1461no—
1614C4—1462no—
1615C4—1461no—
1616C4—1461no—
1617C4—1461no—
1618C4C22×Q8×D7311yescharacteristic
1619C42−1+4×D7311yescharacteristic
1620C2—42no—
1621C2—42no—
1622C2—2922no—
1623C2—1462no—
1624C2D4×Q8×D7311yescharacteristic
1625C2#576×D7311yescharacteristic
1626C2#2262471511yescharacteristic
subgroupG/H
centerC22C22×D4×D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC73×#3389C2
socleC22×C73C23×D4
prime radicalC2×#14556615C22
hypercenter#3389D73
hypocenterC73#61381
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #3389

Complements

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

NH ≅ G/Ntype
1. #22623745C2semidirect
2. #22623730C2semidirect
3. #22622890C2semidirect
4. #22622888C2semidirect
5. #22622885C2semidirect
6. #22622849C2semidirect
7. #22622847C2semidirect
8. #22622843C2semidirect
9. #22622841C2semidirect
10. #22622838C2semidirect
11. #22622836C2semidirect
12. #22622833C2semidirect
13. #22622831C2semidirect
14. #22622803C2semidirect
15. #22622801C2semidirect
16. D8×Dic146C2semidirect
17. #22622781C2semidirect
18. #22620476C2semidirect
19. #22620468C2semidirect
20. #22620466C2semidirect
21. #22619783C2semidirect
22. #22619777C2semidirect
23. #22619761C2semidirect
24. #22619759C2semidirect
25. #22619716C2semidirect
26. #474×D73C2semidirect
27. #22618876C2semidirect
31. C73×#3389C2semidirect
33. Q8×Dic146C22semidirect
34. #17989317C22semidirect
35. #17989314C22semidirect
36. #17989314C22semidirect
41. #17989294C22semidirect
49. D4×Dic146C22semidirect
50. D4×Dic146C22semidirect
76. #17988997C22semidirect
77. #17988997C22semidirect
78. #17988997C22semidirect
79. #17988996C22semidirect
80. #17988996C22semidirect
81. #17988995C22semidirect
82. #17988994C22semidirect
83. #17988994C22semidirect
84. #17988994C22semidirect
85. #17988993C22semidirect
86. #17988992C22semidirect
87. #17988991C22semidirect
88. #17988991C22semidirect
89. #17988991C22semidirect
90. #17988991C22semidirect
91. #17988990C22semidirect
92. #17988988C22semidirect
93. #17988987C22semidirect
94. #17988986C22semidirect
95. #17988984C22semidirect
96. #17988984C22semidirect
97. #17988897C22semidirect
98. #17988895C22semidirect
99. #17988895C22semidirect
100. #17988893C22semidirect
101. #17988891C22semidirect
102. #17988891C22semidirect
105. #17988889C22semidirect
106. #17988887C22semidirect
107. #17988887C22semidirect
110. #17988885C22semidirect
113. #17988883C22semidirect
114. #17988881C22semidirect
115. #17988881C22semidirect
116. #17988881C22semidirect
117. #17988879C22semidirect
122. #17988875C22semidirect
123. #17988871C22semidirect
128. #17988867C22semidirect
135. #17988865C22semidirect
136. #17988865C22semidirect
137. #17988865C22semidirect
139. #17988718C22semidirect
140. #17988716C22semidirect
141. #17988716C22semidirect
142. #17988715C22semidirect
143. #17988715C22semidirect
144. C8×Dic146C22semidirect
145. #17988711C22semidirect
189. #554×C73C22semidirect
190. #501×C73C22semidirect
191. #501×C73C22semidirect
192. #499×C73C22semidirect
195. #478×C73C22semidirect
196. #478×C73C22semidirect
198. #474×C73C22semidirect
199. #446×C73C22semidirect
211. #14556615Q8semidirect
481. #11924027C2×Q8semidirect
507. D4×D73C2×Q8semidirect
528. #11924017C2×Q8semidirect
529. #11924016C2×Q8semidirect
530. #11924013C2×Q8semidirect
532. #11924011C2×Q8semidirect
635. D8×C73C2×Q8semidirect
819. #3389D73semidirect
845. C73#61381semidirect
863. #554C2×D73semidirect
902. #501C2×D73semidirect
903. #501C2×D73semidirect
913. #499C2×D73semidirect
934. #478C2×D73semidirect
935. #478C2×D73semidirect
963. #474C2×D73semidirect
969. #446C2×D73semidirect
1356. D8Q8×D73semidirect

Maximal subgroups

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

subgroupindex
#226237452
#226237302
#226228902
#226228882
#226228852
#226228492
#226228472
#226228432
#226228412
#226228382
#226228362
#226228332
#226228312
#226228032
#226228012
D8×Dic1462
#226227812
#226204762
#226204682
#226204662
#226197832
#226197772
#226197612
#226197592
#226197162
#474×D732
#226188762
#226187602
#226187562
#226187422
C73×#33892
#6138173