Finite Group Databasebeta

← #33966625

Subgroups — #33966625

Order 18688.

1750 conjugacy classes of subgroups.

The subgroup lattice has 1598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22623738C211yesmaximal, characteristic, complemented
2#22623730C211yesmaximal, characteristic
3#22622882C211yesmaximal, characteristic, complemented
4#22622878C211yesmaximal, characteristic, complemented
5#22622872C211yesmaximal, characteristic, complemented
6#22622853C211yesmaximal, characteristic, complemented
7#22622849C211yesmaximal, characteristic, complemented
8#22622842C211yesmaximal, characteristic, complemented
9#22622838C211yesmaximal, characteristic, complemented
10#22622809C211yesmaximal, characteristic, complemented
11#22622809C211yesmaximal, characteristic, complemented
12#22622806C211yesmaximal, characteristic, complemented
13#22622802C211yesmaximal, characteristic, complemented
14#22622801C211yesmaximal, characteristic, complemented
15#22622801C211yesmaximal, characteristic, complemented
16#22622790C211yesmaximal, characteristic, complemented
17#22622786C211yesmaximal, characteristic, complemented
18#22620458C211yesmaximal, characteristic, complemented
19#22620458C211yesmaximal, characteristic, complemented
20#22620444C211yesmaximal, characteristic, complemented
21#22619770C211yesmaximal, characteristic, complemented
22#22619766C211yesmaximal, characteristic, complemented
23#22619761C211yesmaximal, characteristic
24#22619757C211yesmaximal, characteristic
25#22619734C211yesmaximal, characteristic, complemented
26#22619726C211yesmaximal, characteristic
27#22618862C211yesmaximal, characteristic, complemented
28#22618787C211yesmaximal, characteristic
29#22618787C211yesmaximal, characteristic
30C4×SD16×D73C211yesmaximal, characteristic
31C73×#3388C211yesmaximal, characteristic, complemented
32C2×SD16×D73C2211yescharacteristic
33Q8×Dic146C2211yescharacteristic, complemented
34#17989317—21no—
35#17989317C2211yescharacteristic, complemented
36#17989315—21no—
37#17989315C2211yescharacteristic, complemented
38#17989314—21no—
39#17989314—21no—
40#17989314C2211yescharacteristic, complemented
41#17989314C2211yescharacteristic, complemented
42#17989313C2211yescharacteristic, complemented
43#17989313C2211yescharacteristic, complemented
44#17989297C2211yescharacteristic
45#17989296C2211yescharacteristic
46#17989296C2211yescharacteristic
47#17989293C2211yescharacteristic
48#17989293C2211yescharacteristic
49#17989292—21no—
50#17989291—21no—
51#17989291—21no—
52D4×Dic146C2211yescharacteristic
53#17989252C2211yescharacteristic
54#17989250—21no—
55#17989217—21no—
56#17989217C2211yescharacteristic
57#17989217C2211yescharacteristic
58#17989214—21no—
59#17989214C2211yescharacteristic
60#17989214C2211yescharacteristic
61#17989212—21no—
62#17989212—21no—
63#17989143—21no—
64#17989143C2211yescharacteristic
65#17989143C2211yescharacteristic
66#17989141—21no—
67#17989141C2211yescharacteristic
68C2×#14556569—21no—
69C22⋊Q8×D73—21no—
70#17989063C2211yescharacteristic
71#17989063C2211yescharacteristic
72#17989059C2211yescharacteristic
73#17989059C2211yescharacteristic
74C4×Q8×D73C2211yescharacteristic
75C4×D4×D73C2211yescharacteristic
76#17988996C2211yescharacteristic, complemented
77#17988996C2211yescharacteristic, complemented
78#17988995C2211yescharacteristic, complemented
79#17988995C2211yescharacteristic, complemented
80#17988994C2211yescharacteristic, complemented
81#17988994C2211yescharacteristic, complemented
82#17988991C2211yescharacteristic, complemented
83#17988991C2211yescharacteristic, complemented
84#17988989C2211yescharacteristic, complemented
85#17988988C2211yescharacteristic, complemented
86#17988988C2211yescharacteristic, complemented
87#17988986C2211yescharacteristic, complemented
88#17988986C2211yescharacteristic, complemented
89#17988986C2211yescharacteristic, complemented
90#17988986C2211yescharacteristic, complemented
91#17988984C2211yescharacteristic, complemented
92#17988984C2211yescharacteristic, complemented
93#17988984C2211yescharacteristic, complemented
94#17988984C2211yescharacteristic, complemented
95#17988983C2211yescharacteristic, complemented
96#17988983C2211yescharacteristic, complemented
97#17988897C2211yescharacteristic, complemented
98#17988897C2211yescharacteristic, complemented
99#17988895C2211yescharacteristic, complemented
100#17988895C2211yescharacteristic, complemented
101#17988894C2211yescharacteristic, complemented
102#17988894C2211yescharacteristic, complemented
103#17988892C2211yescharacteristic, complemented
104#17988892C2211yescharacteristic, complemented
105#17988891C2211yescharacteristic, complemented
106#17988891C2211yescharacteristic, complemented
107#17988889C2211yescharacteristic
108#17988889C2211yescharacteristic
109#17988888C2211yescharacteristic
110#17988888C2211yescharacteristic
111#17988887C2211yescharacteristic
112#17988887C2211yescharacteristic
113#17988886C2211yescharacteristic
114#17988886C2211yescharacteristic
115#17988884C2211yescharacteristic
116#17988884C2211yescharacteristic
117#17988882C2211yescharacteristic, complemented
118#17988881C2211yescharacteristic, complemented
119#17988881C2211yescharacteristic, complemented
120#17988880C2211yescharacteristic, complemented
121#17988880C2211yescharacteristic, complemented
122#17988879C2211yescharacteristic, complemented
123#17988878C2211yescharacteristic
124#17988876C2211yescharacteristic
125#17988876C2211yescharacteristic
126#17988875C2211yescharacteristic
127#17988875C2211yescharacteristic
128#17988873C2211yescharacteristic, complemented
129#17988871C2211yescharacteristic, complemented
130#17988871C2211yescharacteristic, complemented
131#17988870C2211yescharacteristic, complemented
132#17988870C2211yescharacteristic, complemented
133#17988867C2211yescharacteristic
134#17988866C2211yescharacteristic
135#17988866C2211yescharacteristic
136#17988865C2211yescharacteristic
137#17988865C2211yescharacteristic
138#17988864C2211yescharacteristic
139#17988717C2211yescharacteristic, complemented
140#17988715C2211yescharacteristic, complemented
141#17988715C2211yescharacteristic, complemented
142Q8×#10596831C2211yescharacteristic, complemented
143#17988711C2211yescharacteristic, complemented
144#17988711C2211yescharacteristic, complemented
145#17988711C2211yescharacteristic, complemented
146#17988689C2211yescharacteristic
147#17988689C2211yescharacteristic
148#17988688C2211yescharacteristic
149#17988688C2211yescharacteristic
150#17988686C2211yescharacteristic
151#17988686C2211yescharacteristic
152#17988678C2211yescharacteristic
153#17988678C2211yescharacteristic
154#17988678C2211yescharacteristic
155C4×#11924017C2211yescharacteristic
156SD16×Dic73C2211yescharacteristic
157C4×#11924015C2211yescharacteristic
158C4×#11924015C2211yescharacteristic
159C4×#11924015C2211yescharacteristic
160#17988674C2211yescharacteristic
161C4×#11924016C2211yescharacteristic
162C4×#11924016C2211yescharacteristic
163C4×#11924016C2211yescharacteristic
164#17988672C2211yescharacteristic
165#17988672C2211yescharacteristic
166#17988672C2211yescharacteristic
167#17988628C2211yescharacteristic
168#17988628C2211yescharacteristic
169#17988626C2211yescharacteristic
170#17988626C2211yescharacteristic
171#17988624C2211yescharacteristic
172#17988624C2211yescharacteristic
173#17988622C2211yescharacteristic
174#17988622C2211yescharacteristic
175#106×D73C2211yescharacteristic
176#17988612C2211yescharacteristic
177#17988612C2211yescharacteristic
178#17988609C2211yescharacteristic
179#17988594C2211yescharacteristic
180#17988594C2211yescharacteristic
181#17988590C2211yescharacteristic
182#17988590C2211yescharacteristic
183#103×D73C2211yescharacteristic
184#102×D73C2211yescharacteristic
185#17988544C2211yescharacteristic
186#17988544C2211yescharacteristic
187C4×C8×D73C2211yescharacteristic
188#557×C73C2211yescharacteristic, complemented
189#554×C73C2211yescharacteristic
190#501×C73C2211yescharacteristic, complemented
191#501×C73C2211yescharacteristic, complemented
192#499×C73C2211yescharacteristic, complemented
193#479×C73C2211yescharacteristic, complemented
194#479×C73C2211yescharacteristic, complemented
195#478×C73C2211yescharacteristic
196#478×C73C2211yescharacteristic
197#476×C73C2211yescharacteristic
198#475×C73C2211yescharacteristic, complemented
199#446×C73C2211yescharacteristic, complemented
200#440×C73C2211yescharacteristic
201#440×C73C2211yescharacteristic
202C4×SD16×C73C2211yescharacteristic
203C22×Dic146—21no—
204C2×Q8×D73—21no—
205C2×Q8×D73C2311yescharacteristic
206C2×D4×D73C2311yescharacteristic
207C22×C4×D73—21no—
208C2×#11924017C2311yescharacteristic
209C2×#11924016C2311yescharacteristic
210C2×#11924015C2311yescharacteristic
211SD16×D73Q818yescomplemented
212C2×#11924011C2311yescharacteristic
213C2×#11924011C2311yescharacteristic
214C2×C8×D73C2311yescharacteristic
215C2×C8×D73C2311yescharacteristic
216#14556591—21no—
217#14556591C2311yescharacteristic
218#14556591C2311yescharacteristic
219#14556590—21no—
220#14556590—21no—
221#14556590—21no—
222#14556590—21no—
223#14556590—21no—
224#14556590—21no—
225#14556590—21no—
226#14556590—21no—
227#14556590—21no—
228#14556590D411yescharacteristic
229#14556590C2311yescharacteristic
230#14556590C2311yescharacteristic
231#14556590C2311yescharacteristic
232#14556590C2311yescharacteristic
233#14556590C2311yescharacteristic
234#14556590C2311yescharacteristic
235#14556590C2311yescharacteristic
236#14556590C2311yescharacteristic
237#14556589—21no—
238#14556589—21no—
239#14556589—21no—
240#14556589—21no—
241#14556589—21no—
242#14556589D411yescharacteristic
243#14556583—21no—
244#14556583—21no—
245#14556583C2311yescharacteristic
246#14556583C2311yescharacteristic
247#14556583C2311yescharacteristic
248#14556583C2311yescharacteristic
249#14556582—21no—
250#14556582—21no—
251#14556582C2311yescharacteristic
252#14556582C2311yescharacteristic
253#14556582C2311yescharacteristic
254#14556582C2311yescharacteristic
255#14556581—21no—
256#14556581—21no—
257#14556581—21no—
258#14556581—21no—
259#14556581—21no—
260#14556581—21no—
261#14556581—21no—
262#14556581—21no—
263#14556581—21no—
264#14556581—21no—
265#14556581D411yescharacteristic
266#14556581D411yescharacteristic
267#14556571—21no—
268#14556571—21no—
269#14556571—21no—
270#14556571—21no—
271#14556571D411yescharacteristic
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#14556569—21no—
290#14556569—21no—
291#14556569D411yescharacteristic
292#14556569D411yescharacteristic
293#14556568—21no—
294#14556568—21no—
295#14556568—21no—
296#14556568—21no—
297#14556568—21no—
298#14556568—21no—
299#14556567—21no—
300#14556567—21no—
301#14556567—21no—
302#14556567—21no—
303#14556567D411yescharacteristic
304Q8×Dic73C2311yescharacteristic
305Q8×Dic73C2311yescharacteristic
306Q8×Dic73C2311yescharacteristic
307C4×Dic146—21no—
308C4×Dic146—21no—
309C4×Dic146—21no—
310C4×Dic146—21no—
311C4×Dic146—21no—
312C4×Dic146—21no—
313C4×Dic146C2311yescharacteristic
314C4×Dic146C2311yescharacteristic
315C4×Dic146C2311yescharacteristic
316C4×Dic146C2311yescharacteristic
317C4×Dic146C2311yescharacteristic
318C4×Dic146C2311yescharacteristic
319#14556556—21no—
320#14556556—21no—
321#14556556—21no—
322#14556556—21no—
323#14556556—21no—
324#14556556—21no—
325#14556556—21no—
326#14556556—21no—
327#14556556—21no—
328#14556556—21no—
329#14556556—21no—
330#14556556C2311yescharacteristic
331#14556556C2311yescharacteristic
332#14556556C2311yescharacteristic
333C4×D292C2311yescharacteristic
334C4×D292C2311yescharacteristic
335C4×D292C2311yescharacteristic
336D4×Dic73C2311yescharacteristic
337D4×Dic73C2311yescharacteristic
338D4×Dic73C2311yescharacteristic
339#14556553C2311yescharacteristic
340#14556553C2311yescharacteristic
341#14556553C2311yescharacteristic
342C4×C22⋊D73—21no—
343C4×C22⋊D73—21no—
344C4×C22⋊D73—21no—
345#14556551—21no—
346#14556551—21no—
347#14556551—21no—
348#14556549—21no—
349#14556549—21no—
350#14556549C2311yescharacteristic
351#14556549C2311yescharacteristic
352#14556549C2311yescharacteristic
353#14556549C2311yescharacteristic
354#14556548—21no—
355#14556548—21no—
356#14556548C2311yescharacteristic
357#14556548C2311yescharacteristic
358C2×#11924007—21no—
359C2×#11924007—21no—
360C4⋊C4×D73—21no—
361C4⋊C4×D73—21no—
362C4⋊C4×D73—21no—
363C4⋊C4×D73—21no—
364C4⋊C4×D73C2311yescharacteristic
365C4⋊C4×D73C2311yescharacteristic
366C2×#11924005—21no—
367C2×#11924005—21no—
368C22⋊C4×D73—21no—
369C22⋊C4×D73—21no—
370C22⋊C4×D73—21no—
371C42×D73—21no—
372C42×D73C2311yescharacteristic
373#14556525C2311yescharacteristic
374#14556525C2311yescharacteristic
375#14556525C2311yescharacteristic
376#14556525C2311yescharacteristic
377#14556524C2311yescharacteristic
378#14556524C2311yescharacteristic
379#14556524C2311yescharacteristic
380#14556524C2311yescharacteristic
381#14556524C2311yescharacteristic
382#14556524C2311yescharacteristic
383#14556524C2311yescharacteristic
384#14556524C2311yescharacteristic
385#14556523C2311yescharacteristic
386#14556523C2311yescharacteristic
387#14556523C2311yescharacteristic
388#14556523C2311yescharacteristic
389#14556523C2311yescharacteristic
390#14556522C2311yescharacteristic
391#14556522C2311yescharacteristic
392#14556522C2311yescharacteristic
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#14556515C2311yescharacteristic
413#14556515C2311yescharacteristic
414#14556515C2311yescharacteristic
415#14556514C2311yescharacteristic
416#14556514C2311yescharacteristic
417#14556514C2311yescharacteristic
418#14556513C2311yescharacteristic
419#14556513C2311yescharacteristic
420#14556513C2311yescharacteristic
421#14556512C2311yescharacteristic
422#14556512C2311yescharacteristic
423#14556512C2311yescharacteristic
424#14556511C2311yescharacteristic
425#14556511C2311yescharacteristic
426#14556511C2311yescharacteristic
427#14556501C2311yescharacteristic
428#14556501C2311yescharacteristic
429C4×#10596831C2311yescharacteristic
430C4×#10596831C2311yescharacteristic
431C4×#10596831C2311yescharacteristic
432C8×Dic73C2311yescharacteristic
433C8×Dic73C2311yescharacteristic
434C8×Dic73C2311yescharacteristic
435C8×Dic73C2311yescharacteristic
436C2×SD16×C73C2311yescharacteristic
437C4⋊Q8×C73—21no—
438C4⋊Q8×C73C2311yescharacteristic
439C4⋊Q8×C73C2311yescharacteristic
440#125×C73—21no—
441#125×C73—21no—
442#125×C73C2311yescharacteristic
443#125×C73C2311yescharacteristic
444#125×C73C2311yescharacteristic
445#125×C73C2311yescharacteristic
446C22⋊Q8×C73—21no—
447C22⋊Q8×C73—21no—
448C22⋊Q8×C73—21no—
449C4×Q8×C73—21no—
450C4×Q8×C73C2311yescharacteristic
451C4×Q8×C73C2311yescharacteristic
452C4×Q8×C73C2311yescharacteristic
453C4×Q8×C73C2311yescharacteristic
454C4×D4×C73C2311yescharacteristic
455C4×D4×C73C2311yescharacteristic
456C4×D4×C73C2311yescharacteristic
457C2×C4⋊C4×C73—21no—
458#107×C73C2311yescharacteristic
459#107×C73C2311yescharacteristic
460#107×C73C2311yescharacteristic
461#107×C73C2311yescharacteristic
462#106×C73C2311yescharacteristic
463#106×C73C2311yescharacteristic
464#106×C73C2311yescharacteristic
465#106×C73C2311yescharacteristic
466#106×C73C2311yescharacteristic
467C4⋊C8×C73C2311yescharacteristic
468C4⋊C8×C73C2311yescharacteristic
469C4⋊C8×C73C2311yescharacteristic
470#103×C73C2311yescharacteristic
471#103×C73C2311yescharacteristic
472#103×C73C2311yescharacteristic
473#102×C73C2311yescharacteristic
474#102×C73C2311yescharacteristic
475#102×C73C2311yescharacteristic
476#97×C73C2311yescharacteristic
477#97×C73C2311yescharacteristic
478C4×C8×C73C2311yescharacteristic
479C23×D73—21no—
480C2×Dic146—21no—
481C2×Dic146—21no—
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—82no—
492C2×Dic146C2×D411yescharacteristic
493C2×Dic146C2×D411yescharacteristic
494C2×Dic146C2×D411yescharacteristic
495C2×Dic146C2411yescharacteristic
496Q8×D73—22no—
497Q8×D73—82no—
498Q8×D73C2×Q814yescomplemented
499C2×D292C2411yescharacteristic
500C2×C22⋊D73—21no—
501D4×D73—22no—
502D4×D73C2×Q814yes—
503C22×Dic73—21no—
504C22×Dic73—21no—
505C22×Dic73—21no—
506C2×C4×D73—21no—
507C2×C4×D73—21no—
508C2×C4×D73—21no—
509C2×C4×D73—21no—
510C2×C4×D73—21no—
511C2×C4×D73—21no—
512C2×C4×D73—21no—
513C2×C4×D73—21no—
514C2×C4×D73—21no—
515C2×C4×D73—82no—
516C2×C4×D73C2×D411yescharacteristic
517C2×C4×D73C2×D411yescharacteristic
518C2×C4×D73C2411yescharacteristic
519#11924017C2×Q814yescomplemented
520#11924016C2×Q814yescomplemented
521#11924015C2×Q814yescomplemented
522#11924011—22no—
523#11924011—22no—
524C2×#10596831C2411yescharacteristic
525C2×#10596831C2411yescharacteristic
526C2×#10596831C2411yescharacteristic
527C2×#10596831C2411yescharacteristic
528C8×D73—22no—
529C8×D73C2×Q814yescomplemented
530C4⋊Dic73—21no—
531C4⋊Dic73—21no—
532C4⋊Dic73—21no—
533C4⋊Dic73—21no—
534C4⋊Dic73—21no—
535C4⋊Dic73—21no—
536C4⋊Dic73—21no—
537C4⋊Dic73—21no—
538C4⋊Dic73—21no—
539C4⋊Dic73C2×D411yescharacteristic
540C4⋊Dic73C2×D411yescharacteristic
541C4⋊Dic73C2×D411yescharacteristic
542C4⋊Dic73C2411yescharacteristic
543C4⋊Dic73C2411yescharacteristic
544C4⋊Dic73C2411yescharacteristic
545C4⋊Dic73C2411yescharacteristic
546C4⋊Dic73C2411yescharacteristic
547C4⋊Dic73C2411yescharacteristic
548#11924007—21no—
549#11924007—21no—
550#11924007—21no—
551#11924007—21no—
552#11924007—21no—
553#11924007—21no—
554#11924007—21no—
555#11924007—21no—
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#11924007C2×D411yescharacteristic
577#11924007C2×D411yescharacteristic
578#11924007C2×D411yescharacteristic
579#11924007C2×D411yescharacteristic
580#11924007C2×D411yescharacteristic
581#11924007C2×D411yescharacteristic
582#11924007C2×D411yescharacteristic
583#11924007C2×D411yescharacteristic
584#11924007C2×D411yescharacteristic
585#11924007C2×D411yescharacteristic
586C22⋊Dic73—21no—
587C22⋊Dic73—21no—
588C22⋊Dic73—21no—
589#11924005—21no—
590#11924005—21no—
591#11924005—21no—
592#11924005—21no—
593#11924005—21no—
594#11924005—21no—
595#11924005—21no—
596#11924005—21no—
597#11924005—21no—
598#11924005—21no—
599#11924005C2×D411yescharacteristic
600#11924005C2×D411yescharacteristic
601#11924005C2×D411yescharacteristic
602#11924005C2×D411yescharacteristic
603C4×Dic73—21no—
604C4×Dic73—21no—
605C4×Dic73—21no—
606C4×Dic73—21no—
607C4×Dic73—21no—
608C4×Dic73—21no—
609C4×Dic73—21no—
610C4×Dic73—21no—
611C4×Dic73—21no—
612C4×Dic73—21no—
613C4×Dic73—21no—
614C4×Dic73—21no—
615C4×Dic73—21no—
616C4×Dic73C2×D411yescharacteristic
617C4×Dic73C2×D411yescharacteristic
618C4×Dic73C2411yescharacteristic
619C4×Dic73C2411yescharacteristic
620C4×Dic73C2411yescharacteristic
621C2×Q8×C73—21no—
622C2×Q8×C73—21no—
623C2×Q8×C73C2×D411yescharacteristic
624C2×Q8×C73C2411yescharacteristic
625C2×D4×C73C2411yescharacteristic
626C22×C4×C73—21no—
627C22×C4×C73—21no—
628C22×C4×C73—21no—
629SD16×C73C2×Q814yescomplemented
630C2×C8×C73C2411yescharacteristic
631C2×C8×C73C2411yescharacteristic
632C2×C8×C73C2411yescharacteristic
633C2×C8×C73C2411yescharacteristic
634C4⋊C4×C73—21no—
635C4⋊C4×C73—21no—
636C4⋊C4×C73—21no—
637C4⋊C4×C73—21no—
638C4⋊C4×C73—21no—
639C4⋊C4×C73—21no—
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×C73C2×D411yescharacteristic
648C4⋊C4×C73C2×D411yescharacteristic
649C4⋊C4×C73C2×D411yescharacteristic
650C4⋊C4×C73C2411yescharacteristic
651C4⋊C4×C73C2411yescharacteristic
652C4⋊C4×C73C2411yescharacteristic
653C4⋊C4×C73C2411yescharacteristic
654C4⋊C4×C73C2411yescharacteristic
655C4⋊C4×C73C2411yescharacteristic
656C22⋊C4×C73—21no—
657C22⋊C4×C73—21no—
658C22⋊C4×C73—21no—
659C42×C73—21no—
660C42×C73—21no—
661C42×C73—21no—
662C42×C73C2411yescharacteristic
663C42×C73C2411yescharacteristic
664C42×C73C2411yescharacteristic
665C23×C73—21no—
666C22×D73—21no—
667C22×D73—24no—
668C22×D73—81no—
669C22×D73—81no—
670C22×D73C22×D411yescharacteristic
671Q8×C73—21no—
672Q8×C73—41no—
673Q8×C73—81no—
674Q8×C73—81no—
675Q8×C73C22×Q812yes—
676D4×C73—21no—
677D4×C73C22×Q812yes—
678C2×C4×C73—21no—
679C2×C4×C73—21no—
680C2×C4×C73—21no—
681C2×C4×C73—21no—
682C2×C4×C73—21no—
683C2×C4×C73—21no—
684C2×C4×C73—21no—
685C2×C4×C73—81no—
686C2×C4×C73—81no—
687C2×C4×C73—81no—
688C2×C4×C73C22×D411yescharacteristic
689C2×C4×C73C22×D411yescharacteristic
690C2×C4×C73C22×D411yescharacteristic
691C2×C4×C73C22×D411yescharacteristic
692C2×C4×C73C22×D411yescharacteristic
693C2×C4×C73C22×D411yescharacteristic
694C2×C4×C73C2511yescharacteristic
695C22⋊D73—24no—
696C2×Dic73—21no—
697C2×Dic73—21no—
698C2×Dic73—21no—
699C2×Dic73—21no—
700C2×Dic73—21no—
701C2×Dic73—21no—
702C2×Dic73—21no—
703C2×Dic73—42no—
704C2×Dic73—81no—
705C2×Dic73—81no—
706C2×Dic73C22×D411yescharacteristic
707C2×Dic73C22×D411yescharacteristic
708C2×Dic73C22×D411yescharacteristic
709C2×Dic73C22×D411yescharacteristic
710C2×Dic73C22×D411yescharacteristic
711C2×Dic73C22×D411yescharacteristic
712C2×Dic73C22×D411yescharacteristic
713D292—21no—
714D292C22×Q812yes—
715C4×D73—24no—
716C4×D73—22no—
717C4×D73—41no—
718C4×D73—42no—
719C4×D73—81no—
720C4×D73—81no—
721C4×D73—81no—
722C4×D73—81no—
723C4×D73—81no—
724C4×D73—81no—
725C4×D73—81no—
726C4×D73C22×Q812yes—
727C4×D732−1+412yes—
728Dic146—21no—
729Dic146—24no—
730Dic146—22no—
731Dic146—22no—
732Dic146—41no—
733Dic146—42no—
734Dic146—42no—
735Dic146—81no—
736Dic146—81no—
737Dic146—81no—
738Dic146—81no—
739Dic146—81no—
740Dic146—81no—
741Dic146—81no—
742Dic146—81no—
743Dic146C22×Q812yes—
744C8×C73—21no—
745C8×C73—21no—
746C8×C73—21no—
747C8×C73C22×Q812yes—
748#10596831—21no—
749#10596831—21no—
750#10596831—21no—
751#10596831C22×Q812yes—
752C22×C73—22no—
753C22×C73—41no—
754C22×C73—41no—
755C22×C73C23×D411yescharacteristic
756C2×D73—21no—
757C2×D73—21no—
758C2×D73—22no—
759C2×D73—41no—
760C2×D73—41no—
761C2×D73—84no—
762C2×D73D4×Q812yes—
763C4×C73—21no—
764C4×C73—21no—
765C4×C73—21no—
766C4×C73—22no—
767C4×C73—21no—
768C4×C73—21no—
769C4×C73—21no—
770C4×C73—41no—
771C4×C73—41no—
772C4×C73—41no—
773C4×C73—41no—
774C4×C73—41no—
775C4×C73—41no—
776C4×C73C23×Q811yescharacteristic
777C4×C73C2×2−1+411yescharacteristic
778Dic73—21no—
779Dic73—21no—
780Dic73—21no—
781Dic73—22no—
782Dic73—21no—
783Dic73—21no—
784Dic73—41no—
785Dic73—41no—
786Dic73—41no—
787Dic73—41no—
788Dic73—41no—
789Dic73—41no—
790Dic73D4×Q812yes—
791Dic73#57712yes—
792#61371—731nomaximal, Sylow
793C2×C73—42no—
794C2×C73C2×D4×Q811yescharacteristic
795C2×C73C2×#57711yescharacteristic
796C2×C73#358411yescharacteristic
797D73—22no—
798D73—42no—
799#3502—731no—
800#3501—731no—
801#3388—731no—
802#3388—731no—
803#3388—731no—
804#3388D7311yescharacteristic, complemented
805#3386—731no—
806#3386—731no—
807#3385—731no—
808#3385—731no—
809#3381—731no—
810#3381—731no—
811#3381—731no—
812#3381—731no—
813#3381—731no—
814#3381—731no—
815Q8×SD16—731no—
816Q8×SD16—731no—
817#3163—731no—
818#3163—731no—
819#3160—731no—
820#3082—731no—
821#3082—731no—
822#3081—731no—
823#3081—731no—
824#3078—731no—
825#3077—731no—
826#2960—731no—
827#2949—731no—
828#2949—731no—
829C2×C4×SD16—731no—
830C73#6137111yescharacteristic, complemented, Sylow
831C22×SD16—731no—
832Q82—731no—
833Q82—731no—
834Q82—1461no—
835#557—731no—
836#557—731no—
837#557—731no—
838#557—731no—
839#557—731no—
840#557—1461no—
841#557—1461no—
842#557—1461no—
843#557C2×D7311yescharacteristic, complemented
844#554—731no—
845#554—731no—
846#554—731no—
847#554—731no—
848#554—731no—
849#554—1461no—
850#554—1461no—
851#554—1461no—
852#554C2×D7311yescharacteristic
853D4×Q8—731no—
854D4×Q8—731no—
855D4×Q8—1461no—
856#544—731no—
857#544—731no—
858#544—731no—
859#544—731no—
860#544—1461no—
861#544—1461no—
862#543—1461no—
863#543—1461no—
864#533—731no—
865#533—731no—
866#533—731no—
867#533—1461no—
868#533—1461no—
869C2×C22⋊Q8—1461no—
870C2×C22⋊Q8—1461no—
871#519—731no—
872#519—731no—
873#518—731no—
874#518—731no—
875C2×C4×Q8—731no—
876C2×C4×D4—731no—
877#501—731no—
878#501—731no—
879#501—731no—
880#501—731no—
881#501—731no—
882#501—731no—
883#501C2×D7311yescharacteristic, complemented
884#501C2×D7311yescharacteristic, complemented
885#500—731no—
886#500—731no—
887#499—731no—
888#499—731no—
889#499—731no—
890#499—731no—
891#499—731no—
892#499—731no—
893#499—731no—
894#499C2×D7311yescharacteristic, complemented
895#498—731no—
896#498—731no—
897#498—731no—
898#498—731no—
899#498—731no—
900#498—731no—
901#479—731no—
902#479—731no—
903#479—731no—
904#479—731no—
905#479—731no—
906#479—731no—
907#479—731no—
908#479—731no—
909#479—731no—
910#479—731no—
911#479C2×D7311yescharacteristic, complemented
912#479C2×D7311yescharacteristic, complemented
913#478—731no—
914#478—731no—
915#478—731no—
916#478—731no—
917#478—731no—
918#478—731no—
919#478—731no—
920#478—731no—
921#478—731no—
922#478—731no—
923#478C2×D7311yescharacteristic
924#478C2×D7311yescharacteristic
925#477—731no—
926#477—731no—
927#477—731no—
928#477—731no—
929#477—731no—
930#477—731no—
931#476—731no—
932#476—731no—
933#476—731no—
934#476—731no—
935#476—731no—
936#476C2×D7311yescharacteristic
937#475—731no—
938#475—731no—
939#475—731no—
940#475—731no—
941#475—731no—
942#475C2×D7311yescharacteristic, complemented
943#474—731no—
944#474—731no—
945#474—731no—
946#474—731no—
947#474—731no—
948#474—731no—
949#446—731no—
950#446—731no—
951#446—731no—
952#446C2×D7311yescharacteristic, complemented
953C8×Q8—731no—
954C8×Q8—731no—
955C8×Q8—731no—
956C8×Q8—731no—
957#440—731no—
958#440—731no—
959#440—731no—
960#440—731no—
961#440—731no—
962#440—731no—
963#440C2×D7311yescharacteristic
964#440C2×D7311yescharacteristic
965C4×SD16—731no—
966C4×SD16—731no—
967C4×SD16—731no—
968C4×SD16—731no—
969C4×SD16—731no—
970C4×SD16—731no—
971C4×SD16—731no—
972C4×SD16—731no—
973C4×SD16—731no—
974C4×SD16—731no—
975C4×SD16—731no—
976C4×SD16—731no—
977C4×SD16—731no—
978C4×SD16—731no—
979C4×SD16—731no—
980C4×SD16C2×D7311yescharacteristic
981#428—731no—
982#428—731no—
983#428—731no—
984#428—731no—
985#427—731no—
986#427—731no—
987#427—731no—
988#427—731no—
989C2×#106—731no—
990#424—731no—
991#424—731no—
992#423—731no—
993#419—731no—
994#419—731no—
995#418—731no—
996#418—731no—
997C2×#103—731no—
998C2×#102—731no—
999#405—731no—
1000#405—731no—
1001C2×C4×C8—731no—
1002C22×Q8—731no—
1003C22×Q8—1461no—
1004C22×Q8—1461no—
1005C22×D4—731no—
1006C23×C4—1461no—
1007C2×SD16—731no—
1008C2×SD16—731no—
1009C2×SD16—738no—
1010C2×SD16—731no—
1011C2×SD16C22×D7311yescharacteristic
1012C2×M16—731no—
1013C2×M16—731no—
1014C22×C8—731no—
1015C22×C8—731no—
1016C4⋊Q8—21no—
1017C4⋊Q8—731no—
1018C4⋊Q8—731no—
1019C4⋊Q8—731no—
1020C4⋊Q8—731no—
1021C4⋊Q8—731no—
1022C4⋊Q8—731no—
1023C4⋊Q8—731no—
1024C4⋊Q8—731no—
1025C4⋊Q8—731no—
1026C4⋊Q8—731no—
1027C4⋊Q8—731no—
1028C4⋊Q8—731no—
1029C4⋊Q8—1461no—
1030C4⋊Q8—1461no—
1031C4⋊Q8—1461no—
1032C4⋊Q8—1461no—
1033C4⋊Q8—1461no—
1034C4⋊Q8—1461no—
1035C4⋊Q8—1461no—
1036C4⋊Q8—1461no—
1037C4⋊Q8—1461no—
1038C4⋊Q8—1461no—
1039C4⋊Q8—1461no—
1040C4⋊Q8—1461no—
1041C4⋊Q8—1461no—
1042C4⋊Q8—1461no—
1043C4⋊Q8—1461no—
1044C4⋊Q8C22×D7311yescharacteristic
1045C4⋊Q8C22×D7311yescharacteristic
1046#125—21no—
1047#125—21no—
1048#125—731no—
1049#125—731no—
1050#125—731no—
1051#125—731no—
1052#125—731no—
1053#125—731no—
1054#125—731no—
1055#125—731no—
1056#125—731no—
1057#125—731no—
1058#125—1461no—
1059#125—1461no—
1060#125—1461no—
1061#125—1461no—
1062#125—1461no—
1063#125—1461no—
1064#125—1461no—
1065#125—1461no—
1066#125—1461no—
1067#125—1461no—
1068#125—1461no—
1069#125—1461no—
1070#125—1461no—
1071#125—1461no—
1072#125C22×D7311yescharacteristic
1073#125C22×D7311yescharacteristic
1074#125C22×D7311yescharacteristic
1075#125C22×D7311yescharacteristic
1076C22⋊Q8—21no—
1077C22⋊Q8—21no—
1078C22⋊Q8—21no—
1079C22⋊Q8—731no—
1080C22⋊Q8—731no—
1081C22⋊Q8—731no—
1082C22⋊Q8—731no—
1083C22⋊Q8—1461no—
1084C22⋊Q8—1461no—
1085C22⋊Q8—1461no—
1086C22⋊Q8—1461no—
1087C22⋊Q8—1461no—
1088C22⋊Q8—1461no—
1089C22⋊Q8—1461no—
1090C22⋊Q8—1461no—
1091C22⋊Q8—1461no—
1092C22⋊Q8—1461no—
1093C22⋊Q8—1461no—
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—
1116C4×Q8—21no—
1117C4×Q8—731no—
1118C4×Q8—731no—
1119C4×Q8—731no—
1120C4×Q8—731no—
1121C4×Q8—731no—
1122C4×Q8—731no—
1123C4×Q8—731no—
1124C4×Q8—731no—
1125C4×Q8—731no—
1126C4×Q8—731no—
1127C4×Q8—731no—
1128C4×Q8—731no—
1129C4×Q8—1461no—
1130C4×Q8—1461no—
1131C4×Q8—1461no—
1132C4×Q8—1461no—
1133C4×Q8—1461no—
1134C4×Q8—1461no—
1135C4×Q8—1461no—
1136C4×Q8—1461no—
1137C4×Q8—1461no—
1138C4×Q8—1461no—
1139C4×Q8—1461no—
1140C4×Q8—1461no—
1141C4×Q8—1461no—
1142C4×Q8—1461no—
1143C4×Q8—1461no—
1144C4×Q8—1461no—
1145C4×Q8—1461no—
1146C4×Q8C22×D7311yescharacteristic
1147C4×Q8C22×D7311yescharacteristic
1148C4×Q8C22×D7311yescharacteristic
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—1461no—
1160C4×D4—1461no—
1161C4×D4—1461no—
1162C4×D4—1461no—
1163C4×D4—1461no—
1164C4×D4—1461no—
1165C4×D4C22×D7311yescharacteristic
1166C4×D4C22×D7311yescharacteristic
1167C4×D4C22×D7311yescharacteristic
1168#117—731no—
1169#117—731no—
1170#117—731no—
1171#117—731no—
1172#117—731no—
1173#117—731no—
1174#117—1461no—
1175#117—1461no—
1176#117—1461no—
1177#117—1461no—
1178C2×C4⋊C4—21no—
1179C2×C4⋊C4—731no—
1180C2×C4⋊C4—731no—
1181C2×C4⋊C4—1461no—
1182C2×C4⋊C4—1461no—
1183C2×C4⋊C4—1461no—
1184C2×C4⋊C4—1461no—
1185C2×C4⋊C4—1461no—
1186C2×C4⋊C4—1461no—
1187C2×C22⋊C4—1461no—
1188C2×C22⋊C4—1461no—
1189C2×C22⋊C4—1461no—
1190C2×C22⋊C4—1461no—
1191C2×C22⋊C4—1461no—
1192C2×C42—731no—
1193C2×C42—1461no—
1194#107—731no—
1195#107—731no—
1196#107—731no—
1197#107—731no—
1198#107—731no—
1199#107—731no—
1200#107—731no—
1201#107—731no—
1202#107—731no—
1203#107—731no—
1204#107—731no—
1205#107—731no—
1206#107C22×D7311yescharacteristic
1207#107C22×D7311yescharacteristic
1208#107C22×D7311yescharacteristic
1209#107C22×D7311yescharacteristic
1210#106—731no—
1211#106—731no—
1212#106—731no—
1213#106—731no—
1214#106—731no—
1215#106—731no—
1216#106—731no—
1217#106—731no—
1218#106—731no—
1219#106—731no—
1220#106—731no—
1221#106—731no—
1222#106—731no—
1223#106—731no—
1224#106—731no—
1225#106C22×D7311yescharacteristic
1226#106C22×D7311yescharacteristic
1227#106C22×D7311yescharacteristic
1228#106C22×D7311yescharacteristic
1229#106C22×D7311yescharacteristic
1230C4⋊C8—731no—
1231C4⋊C8—731no—
1232C4⋊C8—731no—
1233C4⋊C8—731no—
1234C4⋊C8—731no—
1235C4⋊C8—731no—
1236C4⋊C8—731no—
1237C4⋊C8—731no—
1238C4⋊C8—731no—
1239C4⋊C8C22×D7311yescharacteristic
1240C4⋊C8C22×D7311yescharacteristic
1241C4⋊C8C22×D7311yescharacteristic
1242#103—731no—
1243#103—731no—
1244#103—731no—
1245#103—731no—
1246#103—731no—
1247#103—731no—
1248#103—731no—
1249#103—731no—
1250#103—731no—
1251#103C22×D7311yescharacteristic
1252#103C22×D7311yescharacteristic
1253#103C22×D7311yescharacteristic
1254#102—731no—
1255#102—731no—
1256#102—731no—
1257#102—731no—
1258#102—731no—
1259#102—731no—
1260#102—731no—
1261#102—731no—
1262#102—731no—
1263#102C22×D7311yescharacteristic
1264#102C22×D7311yescharacteristic
1265#102C22×D7311yescharacteristic
1266#97—731no—
1267#97—731no—
1268#97C22×D7311yescharacteristic
1269#97C22×D7311yescharacteristic
1270C4×C8—731no—
1271C4×C8—731no—
1272C4×C8—731no—
1273C4×C8—731no—
1274C4×C8—731no—
1275C4×C8—731no—
1276C4×C8—731no—
1277C4×C8C22×D7311yescharacteristic
1278C24—1461no—
1279C2×Q8—21no—
1280C2×Q8—21no—
1281C2×Q8—5842no—
1282C2×Q8—5842no—
1283C2×Q8—731no—
1284C2×Q8—731no—
1285C2×Q8—731no—
1286C2×Q8—734no—
1287C2×Q8—731no—
1288C2×Q8—1461no—
1289C2×Q8—1461no—
1290C2×Q8—1461no—
1291C2×Q8—1461no—
1292C2×Q8—1461no—
1293C2×Q8—1461no—
1294C2×Q8—1461no—
1295C2×Q8—1461no—
1296C2×Q8—1461no—
1297C2×Q8—1462no—
1298C2×Q8—1461no—
1299C2×Q8—1461no—
1300C2×Q8D4×D7311yescharacteristic
1301C2×Q8C23×D7311yescharacteristic
1302C2×D4—734no—
1303C2×D4—731no—
1304C2×D4—1462no—
1305C2×D4—1461no—
1306C2×D4C23×D7311yescharacteristic
1307C22×C4—21no—
1308C22×C4—21no—
1309C22×C4—21no—
1310C22×C4—5842no—
1311C22×C4—731no—
1312C22×C4—731no—
1313C22×C4—731no—
1314C22×C4—1461no—
1315C22×C4—1461no—
1316C22×C4—1461no—
1317C22×C4—1461no—
1318C22×C4—1461no—
1319C22×C4—1461no—
1320C22×C4—1461no—
1321C22×C4—1461no—
1322C22×C4—1461no—
1323C22×C4—1461no—
1324C22×C4—1461no—
1325C22×C4—1461no—
1326SD16—734no—
1327SD16—734no—
1328SD16—734no—
1329SD16Q8×D7314yescomplemented
1330M16—1462no—
1331M16—1462no—
1332C2×C8—731no—
1333C2×C8—734no—
1334C2×C8—731no—
1335C2×C8—731no—
1336C2×C8—731no—
1337C2×C8—1462no—
1338C2×C8C23×D7311yescharacteristic
1339C2×C8C23×D7311yescharacteristic
1340C2×C8C23×D7311yescharacteristic
1341C2×C8C23×D7311yescharacteristic
1342C4⋊C4—21no—
1343C4⋊C4—21no—
1344C4⋊C4—21no—
1345C4⋊C4—21no—
1346C4⋊C4—21no—
1347C4⋊C4—21no—
1348C4⋊C4—21no—
1349C4⋊C4—21no—
1350C4⋊C4—21no—
1351C4⋊C4—21no—
1352C4⋊C4—21no—
1353C4⋊C4—21no—
1354C4⋊C4—21no—
1355C4⋊C4—731no—
1356C4⋊C4—731no—
1357C4⋊C4—731no—
1358C4⋊C4—731no—
1359C4⋊C4—731no—
1360C4⋊C4—731no—
1361C4⋊C4—731no—
1362C4⋊C4—731no—
1363C4⋊C4—731no—
1364C4⋊C4—731no—
1365C4⋊C4—731no—
1366C4⋊C4—731no—
1367C4⋊C4—731no—
1368C4⋊C4—731no—
1369C4⋊C4—731no—
1370C4⋊C4—731no—
1371C4⋊C4—731no—
1372C4⋊C4—731no—
1373C4⋊C4—731no—
1374C4⋊C4—1461no—
1375C4⋊C4—1461no—
1376C4⋊C4—1461no—
1377C4⋊C4—1461no—
1378C4⋊C4—1461no—
1379C4⋊C4—1461no—
1380C4⋊C4—1461no—
1381C4⋊C4—1461no—
1382C4⋊C4—1461no—
1383C4⋊C4—1461no—
1384C4⋊C4—1461no—
1385C4⋊C4—1461no—
1386C4⋊C4—1461no—
1387C4⋊C4—1461no—
1388C4⋊C4—1461no—
1389C4⋊C4—1461no—
1390C4⋊C4—1461no—
1391C4⋊C4—1461no—
1392C4⋊C4—1461no—
1393C4⋊C4—1461no—
1394C4⋊C4—1461no—
1395C4⋊C4—1461no—
1396C4⋊C4—1461no—
1397C4⋊C4—1461no—
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⋊C4D4×D7311yescharacteristic
1412C4⋊C4D4×D7311yescharacteristic
1413C4⋊C4D4×D7311yescharacteristic
1414C4⋊C4C23×D7311yescharacteristic
1415C4⋊C4C23×D7311yescharacteristic
1416C4⋊C4C23×D7311yescharacteristic
1417C4⋊C4C23×D7311yescharacteristic
1418C4⋊C4C23×D7311yescharacteristic
1419C4⋊C4C23×D7311yescharacteristic
1420C22⋊C4—21no—
1421C22⋊C4—21no—
1422C22⋊C4—21no—
1423C22⋊C4—731no—
1424C22⋊C4—731no—
1425C22⋊C4—731no—
1426C22⋊C4—731no—
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⋊C4—1461no—
1438C22⋊C4—1461no—
1439C22⋊C4—1461no—
1440C42—21no—
1441C42—21no—
1442C42—21no—
1443C42—731no—
1444C42—731no—
1445C42—731no—
1446C42—731no—
1447C42—731no—
1448C42—1461no—
1449C42—1461no—
1450C42—1461no—
1451C42—1461no—
1452C42—1461no—
1453C42—1461no—
1454C42—1461no—
1455C42—1461no—
1456C42—1461no—
1457C42—1461no—
1458C42—1461no—
1459C42—1461no—
1460C42—1461no—
1461C42C23×D7311yescharacteristic
1462C42C23×D7311yescharacteristic
1463C42C23×D7311yescharacteristic
1464C23—21no—
1465C23—5841no—
1466C23—5841no—
1467C23—731no—
1468C23—1464no—
1469C23—1461no—
1470Q8—21no—
1471Q8—41no—
1472Q8—81no—
1473Q8—81no—
1474Q8—2921no—
1475Q8—2922no—
1476Q8—2922no—
1477Q8—5841no—
1478Q8—5841no—
1479Q8—5841no—
1480Q8—5841no—
1481Q8—5841no—
1482Q8—5841no—
1483Q8—5841no—
1484Q8—5841no—
1485Q8—732no—
1486Q8—1462no—
1487Q8—1462no—
1488Q8—1464no—
1489Q8—1461no—
1490Q8C2×Q8×D7312yes—
1491D4—21no—
1492D4—732no—
1493D4—1464no—
1494D4—1461no—
1495D4C2×Q8×D7312yes—
1496C2×C4—21no—
1497C2×C4—21no—
1498C2×C4—21no—
1499C2×C4—21no—
1500C2×C4—21no—
1501C2×C4—21no—
1502C2×C4—21no—
1503C2×C4—81no—
1504C2×C4—81no—
1505C2×C4—81no—
1506C2×C4—2921no—
1507C2×C4—2922no—
1508C2×C4—2922no—
1509C2×C4—5841no—
1510C2×C4—5841no—
1511C2×C4—5841no—
1512C2×C4—5841no—
1513C2×C4—5841no—
1514C2×C4—5841no—
1515C2×C4—5841no—
1516C2×C4—5841no—
1517C2×C4—5841no—
1518C2×C4—731no—
1519C2×C4—731no—
1520C2×C4—732no—
1521C2×C4—732no—
1522C2×C4—731no—
1523C2×C4—731no—
1524C2×C4—731no—
1525C2×C4—731no—
1526C2×C4—731no—
1527C2×C4—1462no—
1528C2×C4—1464no—
1529C2×C4—1461no—
1530C2×C4—1461no—
1531C2×C4—1461no—
1532C2×C4—1461no—
1533C2×C4—1461no—
1534C2×C4—1461no—
1535C2×C4—1461no—
1536C2×C4C2×D4×D7311yescharacteristic
1537C2×C4C2×D4×D7311yescharacteristic
1538C2×C4C2×D4×D7311yescharacteristic
1539C2×C4C2×D4×D7311yescharacteristic
1540C2×C4C2×D4×D7311yescharacteristic
1541C2×C4C2×D4×D7311yescharacteristic
1542C2×C4C24×D7311yescharacteristic
1543C8—21no—
1544C8—21no—
1545C8—21no—
1546C8—732no—
1547C8—1461no—
1548C8—1461no—
1549C8—1461no—
1550C8C2×Q8×D7312yes—
1551C22—22no—
1552C22—41no—
1553C22—41no—
1554C22—2921no—
1555C22—2921no—
1556C22—5844no—
1557C22—732no—
1558C22—1462no—
1559C22—1461no—
1560C22—1461no—
1561C22C22×D4×D7311yescharacteristic
1562C4—22no—
1563C4—21no—
1564C4—21no—
1565C4—21no—
1566C4—21no—
1567C4—21no—
1568C4—21no—
1569C4—41no—
1570C4—41no—
1571C4—41no—
1572C4—41no—
1573C4—41no—
1574C4—41no—
1575C4—2921no—
1576C4—2921no—
1577C4—2921no—
1578C4—2921no—
1579C4—2921no—
1580C4—2921no—
1581C4—732no—
1582C4—732no—
1583C4—1462no—
1584C4—1461no—
1585C4—1461no—
1586C4—1461no—
1587C4—1461no—
1588C4—1461no—
1589C4C22×Q8×D7311yescharacteristic
1590C42−1+4×D7311yescharacteristic
1591C2—42no—
1592C2—2922no—
1593C2—1462no—
1594C2D4×Q8×D7311yescharacteristic
1595C2#577×D7311yescharacteristic
1596C2#2262470411yescharacteristic
subgroupG/H
centerC22C22×D4×D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC73×#3388C2
socleC22×C73C23×D4
prime radicalC2×D4×D73C23
hypercenter#3388D73
hypocenterC73#61371
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #3388

Complements

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

NH ≅ G/Ntype
1. #22623738C2semidirect
3. #22622882C2semidirect
4. #22622878C2semidirect
5. #22622872C2semidirect
6. #22622853C2semidirect
7. #22622849C2semidirect
8. #22622842C2semidirect
9. #22622838C2semidirect
10. #22622809C2semidirect
11. #22622809C2semidirect
12. #22622806C2semidirect
13. #22622802C2semidirect
14. #22622801C2semidirect
15. #22622801C2semidirect
16. #22622790C2semidirect
17. #22622786C2semidirect
18. #22620458C2semidirect
19. #22620458C2semidirect
20. #22620444C2semidirect
21. #22619770C2semidirect
22. #22619766C2semidirect
25. #22619734C2semidirect
27. #22618862C2semidirect
31. C73×#3388C2semidirect
33. Q8×Dic146C22semidirect
35. #17989317C22semidirect
37. #17989315C22semidirect
40. #17989314C22semidirect
41. #17989314C22semidirect
42. #17989313C22semidirect
43. #17989313C22semidirect
76. #17988996C22semidirect
77. #17988996C22semidirect
78. #17988995C22semidirect
79. #17988995C22semidirect
80. #17988994C22semidirect
81. #17988994C22semidirect
82. #17988991C22semidirect
83. #17988991C22semidirect
84. #17988989C22semidirect
85. #17988988C22semidirect
86. #17988988C22semidirect
87. #17988986C22semidirect
88. #17988986C22semidirect
89. #17988986C22semidirect
90. #17988986C22semidirect
91. #17988984C22semidirect
92. #17988984C22semidirect
93. #17988984C22semidirect
94. #17988984C22semidirect
95. #17988983C22semidirect
96. #17988983C22semidirect
97. #17988897C22semidirect
98. #17988897C22semidirect
99. #17988895C22semidirect
100. #17988895C22semidirect
101. #17988894C22semidirect
102. #17988894C22semidirect
103. #17988892C22semidirect
104. #17988892C22semidirect
105. #17988891C22semidirect
106. #17988891C22semidirect
117. #17988882C22semidirect
118. #17988881C22semidirect
119. #17988881C22semidirect
120. #17988880C22semidirect
121. #17988880C22semidirect
122. #17988879C22semidirect
128. #17988873C22semidirect
129. #17988871C22semidirect
130. #17988871C22semidirect
131. #17988870C22semidirect
132. #17988870C22semidirect
139. #17988717C22semidirect
140. #17988715C22semidirect
141. #17988715C22semidirect
142. Q8×#10596831C22semidirect
143. #17988711C22semidirect
144. #17988711C22semidirect
145. #17988711C22semidirect
188. #557×C73C22semidirect
190. #501×C73C22semidirect
191. #501×C73C22semidirect
192. #499×C73C22semidirect
193. #479×C73C22semidirect
194. #479×C73C22semidirect
198. #475×C73C22semidirect
199. #446×C73C22semidirect
211. SD16×D73Q8semidirect
498. Q8×D73C2×Q8semidirect
519. #11924017C2×Q8semidirect
520. #11924016C2×Q8semidirect
521. #11924015C2×Q8semidirect
529. C8×D73C2×Q8semidirect
629. SD16×C73C2×Q8semidirect
804. #3388D73semidirect
830. C73#61371semidirect
843. #557C2×D73semidirect
883. #501C2×D73semidirect
884. #501C2×D73semidirect
894. #499C2×D73semidirect
911. #479C2×D73semidirect
912. #479C2×D73semidirect
942. #475C2×D73semidirect
952. #446C2×D73semidirect
1329. SD16Q8×D73semidirect

Maximal subgroups

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

subgroupindex
#226237382
#226237302
#226228822
#226228782
#226228722
#226228532
#226228492
#226228422
#226228382
#226228092
#226228062
#226228022
#226228012
#226227902
#226227862
#226204582
#226204442
#226197702
#226197662
#226197612
#226197572
#226197342
#226197262
#226188622
#226187872
C4×SD16×D732
C73×#33882
#6137173