Finite Group Databasebeta

← #11675800

Subgroups — #11675800

Order 768.

1750 conjugacy classes of subgroups.

The subgroup lattice has 1208 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#86277C211yesmaximal, characteristic
2C2×#5685C211yesmaximal, characteristic, complemented
3C3×#3166C211yesmaximal, characteristic, complemented
4#83367C211yesmaximal, characteristic, complemented
5#83017C211yesmaximal, characteristic
6#81971C212yesmaximal, complemented
7#81969C212yesmaximal, complemented
8#81967C212yesmaximal, complemented
9#81966C212yesmaximal, complemented
10#81932C212yesmaximal, complemented
11#81930C212yesmaximal, complemented
12#81914C212yesmaximal, complemented
13#81913C212yesmaximal, complemented
14#79245C211yesmaximal, characteristic, complemented
15#79245C211yesmaximal, characteristic, complemented
16#79241C211yesmaximal, characteristic
17#79240C211yesmaximal, characteristic
18#79204C211yesmaximal, characteristic, complemented
19#79203C211yesmaximal, characteristic, complemented
20#79200C211yesmaximal, characteristic
21#79200C211yesmaximal, characteristic
22C4×#909C211yesmaximal, characteristic
23M16×Dic6C211yesmaximal, characteristic, complemented
24#61369—31nomaximal, Sylow
25C3×#533C2211yescharacteristic
26C2×C3×#125C2211yescharacteristic
27C2×#909C2211yescharacteristic
28#5730C2211yescharacteristic
29#5727C2211yescharacteristic
30#5722C2211yescharacteristic
31#5721C2211yescharacteristic
32#5690C2211yescharacteristic
33#5690C2211yescharacteristic
34#5685—21no—
35#5685—21no—
36#5685—21no—
37#5685—21no—
38#5685C2211yescharacteristic
39#5685C2211yescharacteristic
40#5685C2212yes—
41#5685C2212yes—
42#5685C2212yes—
43#5685C2212yes—
44#5636—21no—
45#5636—21no—
46#5635—21no—
47#5632—21no—
48#5578—21no—
49#5578—21no—
50#5578—21no—
51C4×D3×Q8—21no—
52#5522C2211yescharacteristic
53#5522C2211yescharacteristic
54#5517C2211yescharacteristic
55#5517C2211yescharacteristic
56C2×#890C2211yescharacteristic
57C2×#889—21no—
58C2×#889—21no—
59C2×#888—21no—
60C2×#888C2211yescharacteristic
61C2×#887—21no—
62C2×#887C2211yescharacteristic
63C2×#887C2211yescharacteristic
64C4×#235C2211yescharacteristic
65C2×C4×Dic6C2211yescharacteristic
66C2×C4×Dic6C2211yescharacteristic
67C3×#501C2212yes—
68C3×#501C2212yes—
69C3×#499C2212yes—
70C3×#499C2212yes—
71C3×#428C2211yescharacteristic
72C3×#428C2211yescharacteristic
73C3×#428C2211yescharacteristic
74C3×#428C2211yescharacteristic
75C3×C4×M16C2211yescharacteristic
76#5133C2211yescharacteristic
77#5121C2211yescharacteristic
78#5120C2211yescharacteristic
79#5118C2211yescharacteristic
80#5118C2211yescharacteristic
81Dic3×M16C2211yescharacteristic
82Dic3×M16C2211yescharacteristic
83#5094C2212yes—
84#5091C2212yes—
85#5066C2212yes—
86#5066C2212yes—
87#5063C2212yes—
88#5063C2212yes—
89#5063C2212yes—
90#5063C2212yes—
91#5004C2211yescharacteristic
92#5004C2211yescharacteristic
93#4995C2211yescharacteristic
94#4995C2211yescharacteristic
95#4966C2211yescharacteristic
96#4966C2211yescharacteristic
97#4964C2211yescharacteristic
98#4964C2211yescharacteristic
99#4924C2211yescharacteristic
100#4891C2212yes—
101#4890C2212yes—
102#4889C2212yes—
103#4889C2212yes—
104#4878C2212yes—
105#4877C2212yes—
106#4877C2212yes—
107#4877C2212yes—
108#4876C2212yes—
109#4876C2212yes—
110#4875C2212yes—
111#4875C2212yes—
112#4875C2212yes—
113#4874C2212yes—
114#4873C2212yes—
115#4873C2212yes—
116#4871C2212yes—
117#4870C2212yes—
118#4858C2212yes—
119#4857C2212yes—
120#4857C2212yes—
121#4857C2212yes—
122#4856C2212yes—
123#4856C2212yes—
124#4855C2212yes—
125#4854C2212yes—
126#4854C2212yes—
127#4854C2212yes—
128#4853C2212yes—
129#4853C2212yes—
130#4852C2212yes—
131#4852C2212yes—
132#4716C2212yes—
133#4710C2212yes—
134#4701C2212yes—
135#4701C2212yes—
136C4×Dic12C2212yes—
137C4×#204C2212yes—
138#4679C2212yes—
139C8×Dic6C2212yes—
140Q8×#41—31no—
141C2×#557—31no—
142#3390—32no—
143#3390—32no—
144#3388—32no—
145#3388—32no—
146#3387—32no—
147#3386—32no—
148#3383—32no—
149#3381—32no—
150#3166—31no—
151#3166D311yescharacteristic, complemented
152#3165—31no—
153#3080—31no—
154#3080—31no—
155#3079—31no—
156#3078—31no—
157#3078—31no—
158#3078—31no—
159Q8×M16—31no—
160C4×#137—31no—
161C4×#137—31no—
162C4×#137—31no—
163C2×D3×Q8—21no—
164C2×#235C2311yescharacteristic
165C22×Dic6—21no—
166C22×Dic6D411yescharacteristic
167C22×Dic6C2311yescharacteristic
168C2×C3×M16C2311yescharacteristic
169C2×C3×M16C2311yescharacteristic
170C3×C4⋊Q8C2311yescharacteristic
171C3×C4⋊Q8C2311yescharacteristic
172C3×#125—21no—
173C3×#125—21no—
174C3×#125C2312yes—
175C3×#125C2312yes—
176C3×#125C2311yescharacteristic
177C3×#125C2311yescharacteristic
178C3×C22⋊Q8—21no—
179C3×C22⋊Q8—21no—
180C3×C4×Q8—21no—
181C3×C4×Q8—21no—
182C3×#117C2311yescharacteristic
183C3×#117C2311yescharacteristic
184C2×C3×C4⋊C4—21no—
185C2×C3×C4⋊C4—21no—
186C2×C3×C4⋊C4C2311yescharacteristic
187C2×C3×C4⋊C4C2311yescharacteristic
188C2×C3×C42C2311yescharacteristic
189#946—21no—
190#946—21no—
191#946—21no—
192Q8×Dic3—21no—
193#944—21no—
194#944—21no—
195#944—21no—
196C4×#67—21no—
197C4×#67—21no—
198#926C2311yescharacteristic
199C2×C4⋊Dic3—21no—
200C2×C4⋊Dic3D411yescharacteristic
201C2×C4⋊Dic3C2311yescharacteristic
202C2×Dic3⋊C4—21no—
203C2×Dic3⋊C4—21no—
204C2×Dic3⋊C4—21no—
205C2×Dic3⋊C4—21no—
206C2×Dic3⋊C4—21no—
207C2×Dic3⋊C4D411yescharacteristic
208C2×Dic3⋊C4D411yescharacteristic
209C2×C4×Dic3—21no—
210C2×C4×Dic3—21no—
211C2×C4×Dic3—21no—
212C2×C4×Dic3C2311yescharacteristic
213C2×C4×Dic3C2311yescharacteristic
214C2×#208C2311yescharacteristic
215C2×#208C2311yescharacteristic
216#909Q818yescomplemented
217C2×Dic12C2312yes—
218C2×#204C2312yes—
219#897—21no—
220#897—21no—
221#897—21no—
222#896—21no—
223#896—21no—
224#896—21no—
225#896—21no—
226#896—21no—
227#896—21no—
228#893C2311yescharacteristic
229#893C2311yescharacteristic
230#893C2311yescharacteristic
231#893C2311yescharacteristic
232D3×C4⋊C4—21no—
233D3×C4⋊C4—21no—
234D3×C4⋊C4—21no—
235#890—21no—
236#890—21no—
237#890C2312yes—
238#890C2311yescharacteristic
239#890C2311yescharacteristic
240#890C2311yescharacteristic
241#890C2311yescharacteristic
242#890C2312yes—
243#889—21no—
244#889—21no—
245#889—22no—
246#889—22no—
247#889—22no—
248#889—22no—
249#889—21no—
250#889—21no—
251#889—21no—
252#889—21no—
253#889—22no—
254#889—22no—
255#889—22no—
256#889—22no—
257#888—21no—
258#888—21no—
259#888—22no—
260#888—22no—
261#888—22no—
262#888—22no—
263#888—21no—
264#888—21no—
265#888—21no—
266#888C2312yes—
267#888C2311yescharacteristic
268#888C2312yes—
269#888C2311yescharacteristic
270#888C2311yescharacteristic
271#888C2311yescharacteristic
272#887—21no—
273#887—21no—
274#887—21no—
275#887—22no—
276#887—22no—
277#887—22no—
278#887—22no—
279#887—21no—
280#887—21no—
281#887—21no—
282#887—21no—
283#887C2311yescharacteristic
284#887C2311yescharacteristic
285#887C2312yes—
286#887C2312yes—
287#887C2311yescharacteristic
288#887C2312yes—
289#887C2311yescharacteristic
290#887C2312yes—
291#67⋊C4—21no—
292#67⋊C4—21no—
293#67⋊C4—21no—
294#67⋊C4—21no—
295#878—21no—
296#878—21no—
297#878—21no—
298#878—21no—
299C4×D12C2311yescharacteristic
300C4×D12C2311yescharacteristic
301#872—21no—
302#872—21no—
303#872—21no—
304C42×D3—21no—
305C42×D3—21no—
306C42×D3—21no—
307C4×Dic6—21no—
308C4×Dic6—21no—
309C4×Dic6—21no—
310C4×Dic6—21no—
311C4×Dic6—21no—
312C4×Dic6—21no—
313C4×Dic6D411yescharacteristic
314C4×Dic6D411yescharacteristic
315C4×Dic6D411yescharacteristic
316C4×Dic6D411yescharacteristic
317C4×Dic6C2312yes—
318C4×Dic6C2311yescharacteristic
319C4×Dic6C2312yes—
320C4×Dic6C2311yescharacteristic
321C4×Dic6C2311yescharacteristic
322C4×Dic6C2311yescharacteristic
323C4×Dic6C2311yescharacteristic
324C4×Dic6C2311yescharacteristic
325C3×#107C2312yes—
326C3×#107C2312yes—
327C3×#107C2312yes—
328C3×#107C2312yes—
329C3×#106C2312yes—
330C3×#106C2312yes—
331C3×#106C2312yes—
332C3×#106C2312yes—
333C3×#97C2312yes—
334C3×C4×C8C2312yes—
335#821C2312yes—
336#818C2312yes—
337#817C2312yes—
338#816C2312yes—
339#816C2312yes—
340#816C2312yes—
341#815C2312yes—
342#815C2312yes—
343Dic3⋊C8C2312yes—
344Dic3⋊C8C2312yes—
345Dic3⋊C8C2312yes—
346Dic3⋊C8C2312yes—
347C8×Dic3C2312yes—
348C8×Dic3C2312yes—
349#810C2312yes—
350#810C2312yes—
351#810C2312yes—
352#810C2312yes—
353#810C2312yes—
354#810C2312yes—
355#809C2312yes—
356#809C2312yes—
357#808C2312yes—
358#808C2312yes—
359#808C2312yes—
360#808C2312yes—
361#807C2312yes—
362#807C2312yes—
363#807C2312yes—
364#807C2312yes—
365C4⋊(C3⋊C8)C2312yes—
366C4⋊(C3⋊C8)C2312yes—
367C2×#137—31no—
368Q82—31no—
369#557—31no—
370#557—32no—
371#557—31no—
372#557—32no—
373#557—32no—
374#557—32no—
375#557—31no—
376#557—61no—
377#557—61no—
378#557—61no—
379#557—61no—
380#554—31no—
381#554—31no—
382#554—31no—
383#554—61no—
384#554—61no—
385#554—61no—
386D4×Q8—31no—
387D4×Q8—61no—
388#533—31no—
389#533—31no—
390#533—61no—
391#533—61no—
392#533—61no—
393#533C2×D311yescharacteristic
394C2×C4⋊Q8—31no—
395C2×C4⋊Q8—61no—
396C2×#125—31no—
397C2×#125—61no—
398C2×#125—61no—
399C2×#125C2×D311yescharacteristic
400C4×#41—31no—
401C4×#41—31no—
402C4×#41—31no—
403C2×C4×Q8—31no—
404C2×C4×Q8—31no—
405C2×C4×Q8—31no—
406C2×C4×Q8—31no—
407C2×C4×Q8—61no—
408C2×C4×Q8—61no—
409#501—32no—
410#501—32no—
411#501—32no—
412#501—32no—
413#501C2×D312yes—
414#501C2×D312yes—
415#500—32no—
416#499—32no—
417#499—32no—
418#499C2×D312yes—
419#499C2×D312yes—
420#498—32no—
421#479—32no—
422#479—32no—
423#479—32no—
424#479—32no—
425#479—32no—
426#479—32no—
427#479—32no—
428#479—32no—
429#479—32no—
430#479—32no—
431#478—32no—
432#478—32no—
433#478—32no—
434#478—32no—
435#477—32no—
436#477—32no—
437#477—32no—
438#477—32no—
439#476—32no—
440#475—32no—
441#475—32no—
442#475—32no—
443#475—32no—
444#474—32no—
445#446—32no—
446#446—32no—
447#446—32no—
448C8×Q8—32no—
449#441—32no—
450#441—32no—
451#441—32no—
452#440—32no—
453#440—32no—
454#440—32no—
455C4×Q16—32no—
456C4×Q16—32no—
457C4×Q16—32no—
458C4×SD16—32no—
459C4×SD16—32no—
460C4×SD16—32no—
461#428—31no—
462#428—31no—
463#428—31no—
464#428—31no—
465#428—31no—
466#428C2×D311yescharacteristic
467#428C2×D311yescharacteristic
468#428C2×D311yescharacteristic
469#428C2×D311yescharacteristic
470#423—31no—
471#423—31no—
472#423—31no—
473#419—31no—
474#419—31no—
475#419—31no—
476#417—31no—
477#417—31no—
478#417—31no—
479C4×M16—31no—
480C4×M16—31no—
481C4×M16C2×D311yescharacteristic
482C2×C3×Q8—21no—
483C2×C3×Q8—21no—
484C22×C3×C4—21no—
485C22×C3×C4—21no—
486C22×C3×C4C2×D411yescharacteristic
487C22×C3×C4C2×D411yescharacteristic
488C22×C3×C4C2411yescharacteristic
489C2×#67—21no—
490C22×Dic3—21no—
491C22×Dic3—21no—
492C22×Dic3C2×D411yescharacteristic
493C22×Dic3C2×D411yescharacteristic
494C22×Dic3C2×D411yescharacteristic
495C22×Dic3C2×D411yescharacteristic
496D3×Q8—44no—
497#235—22no—
498#235C2×Q814yes—
499C2×D12C2411yescharacteristic
500C2×C4×D3—21no—
501C2×C4×D3—21no—
502C2×C4×D3—21no—
503C2×C4×D3—21no—
504C2×C4×D3—21no—
505C2×C4×D3—21no—
506C2×C4×D3—21no—
507C2×Dic6—21no—
508C2×Dic6—22no—
509C2×Dic6—21no—
510C2×Dic6—21no—
511C2×Dic6—22no—
512C2×Dic6—22no—
513C2×Dic6—21no—
514C2×Dic6—21no—
515C2×Dic6—42no—
516C2×Dic6—44no—
517C2×Dic6C2×D411yescharacteristic
518C2×Dic6C2×D411yescharacteristic
519C2×Dic6C2×D411yescharacteristic
520C2×Dic6C2×D411yescharacteristic
521C2×Dic6C2×Q814yescomplemented
522C2×Dic6C2412yes—
523C2×Dic6C2411yescharacteristic
524C3×M16—22no—
525C3×M16C2×Q814yescomplemented
526C2×C3×C8C2412yes—
527C2×C3×C8C2412yes—
528C3×C4⋊C4—21no—
529C3×C4⋊C4—22no—
530C3×C4⋊C4—22no—
531C3×C4⋊C4—21no—
532C3×C4⋊C4—21no—
533C3×C4⋊C4—21no—
534C3×C4⋊C4—21no—
535C3×C4⋊C4—22no—
536C3×C4⋊C4—22no—
537C3×C4⋊C4—21no—
538C3×C4⋊C4—21no—
539C3×C4⋊C4—21no—
540C3×C4⋊C4C2411yescharacteristic
541C3×C4⋊C4C2411yescharacteristic
542C3×C4⋊C4C2412yes—
543C3×C4⋊C4C2412yes—
544C3×C4⋊C4C2411yescharacteristic
545C3×C4⋊C4C2411yescharacteristic
546C3×C22⋊C4—21no—
547C3×C22⋊C4—21no—
548C3×C42—21no—
549C3×C42—21no—
550C3×C42C2×D411yescharacteristic
551C3×C42C2×D411yescharacteristic
552C3×C42C2411yescharacteristic
553C3×C42C2411yescharacteristic
554#217—21no—
555(C2×D3)⋊C4—21no—
556(C2×D3)⋊C4—21no—
557(C2×D3)⋊C4—21no—
558(C2×D3)⋊C4—21no—
559(C2×D3)⋊C4—21no—
560(C2×D3)⋊C4—21no—
561C4⋊Dic3—21no—
562C4⋊Dic3—21no—
563C4⋊Dic3—21no—
564C4⋊Dic3—21no—
565C4⋊Dic3—21no—
566C4⋊Dic3—22no—
567C4⋊Dic3—22no—
568C4⋊Dic3C2×D411yescharacteristic
569C4⋊Dic3C2×D411yescharacteristic
570C4⋊Dic3C2×D411yescharacteristic
571C4⋊Dic3C2×D411yescharacteristic
572C4⋊Dic3C2411yescharacteristic
573C4⋊Dic3C2411yescharacteristic
574C4⋊Dic3C2412yes—
575Dic3⋊C4—22no—
576Dic3⋊C4—22no—
577Dic3⋊C4—21no—
578Dic3⋊C4—21no—
579Dic3⋊C4—21no—
580Dic3⋊C4—21no—
581Dic3⋊C4—21no—
582Dic3⋊C4—21no—
583Dic3⋊C4—21no—
584Dic3⋊C4—21no—
585Dic3⋊C4—21no—
586Dic3⋊C4—21no—
587Dic3⋊C4—21no—
588Dic3⋊C4—21no—
589Dic3⋊C4—21no—
590Dic3⋊C4—21no—
591Dic3⋊C4—22no—
592Dic3⋊C4—22no—
593Dic3⋊C4—22no—
594Dic3⋊C4—22no—
595Dic3⋊C4—22no—
596Dic3⋊C4—22no—
597Dic3⋊C4—22no—
598Dic3⋊C4—22no—
599Dic3⋊C4C2×D411yescharacteristic
600Dic3⋊C4C2×D411yescharacteristic
601Dic3⋊C4C2×D411yescharacteristic
602Dic3⋊C4C2×D411yescharacteristic
603Dic3⋊C4C2×D411yescharacteristic
604Dic3⋊C4C2×D411yescharacteristic
605Dic3⋊C4C2×D411yescharacteristic
606Dic3⋊C4C2×D411yescharacteristic
607C4×Dic3—21no—
608C4×Dic3—22no—
609C4×Dic3—22no—
610C4×Dic3—21no—
611C4×Dic3—21no—
612C4×Dic3—21no—
613C4×Dic3—21no—
614C4×Dic3—21no—
615C4×Dic3—21no—
616C4×Dic3—22no—
617C4×Dic3—22no—
618C4×Dic3—22no—
619C4×Dic3—22no—
620C4×Dic3C2×D411yescharacteristic
621C4×Dic3C2×D411yescharacteristic
622C4×Dic3C2×D411yescharacteristic
623C4×Dic3C2×D411yescharacteristic
624C4×Dic3C2411yescharacteristic
625C4×Dic3C2411yescharacteristic
626C4×Dic3C2411yescharacteristic
627C4×Dic3C2411yescharacteristic
628#208—22no—
629#208—22no—
630C2×C3⋊C8C2412yes—
631C2×C3⋊C8C2412yes—
632Dic12C2×Q818yescomplemented
633#204C2×Q818yescomplemented
634C2×#41—31no—
635C22×Q8—31no—
636C22×Q8—31no—
637C22×Q8—61no—
638C22×Q8—61no—
639#137—38no—
640C2×Q16—32no—
641C2×SD16—32no—
642C2×M16—31no—
643C2×M16—31no—
644C2×M16C22×D311yescharacteristic
645C2×M16C22×D311yescharacteristic
646C4⋊Q8—32no—
647C4⋊Q8—32no—
648C4⋊Q8—31no—
649C4⋊Q8—31no—
650C4⋊Q8—31no—
651C4⋊Q8—31no—
652C4⋊Q8—61no—
653C4⋊Q8—61no—
654C4⋊Q8—61no—
655C4⋊Q8—62no—
656C4⋊Q8—62no—
657C4⋊Q8—62no—
658C4⋊Q8—62no—
659C4⋊Q8—61no—
660C4⋊Q8—61no—
661C4⋊Q8—61no—
662C4⋊Q8—61no—
663C4⋊Q8—61no—
664C4⋊Q8C22×D311yescharacteristic
665C4⋊Q8C22×D311yescharacteristic
666#125—21no—
667#125—21no—
668#125—32no—
669#125—32no—
670#125—31no—
671#125—31no—
672#125—31no—
673#125—31no—
674#125—61no—
675#125—61no—
676#125—62no—
677#125—62no—
678#125—62no—
679#125—62no—
680#125—62no—
681#125—62no—
682#125—62no—
683#125—62no—
684#125—61no—
685#125—61no—
686#125—61no—
687#125—61no—
688#125—61no—
689#125—61no—
690#125C22×D312yes—
691#125C22×D312yes—
692#125C22×D311yescharacteristic
693#125C22×D311yescharacteristic
694C22⋊Q8—21no—
695C22⋊Q8—21no—
696C22⋊Q8—61no—
697C22⋊Q8—61no—
698C22⋊Q8—61no—
699C22⋊Q8—61no—
700C22⋊Q8—61no—
701C22⋊Q8—61no—
702C22⋊Q8—61no—
703C22⋊Q8—61no—
704C22⋊Q8—61no—
705C22⋊Q8—61no—
706C22⋊Q8—61no—
707C22⋊Q8—61no—
708C22⋊Q8—61no—
709C22⋊Q8—61no—
710C22⋊Q8—61no—
711C22⋊Q8—61no—
712C4×Q8—21no—
713C4×Q8—21no—
714C4×Q8—31no—
715C4×Q8—31no—
716C4×Q8—31no—
717C4×Q8—31no—
718C4×Q8—31no—
719C4×Q8—31no—
720C4×Q8—31no—
721C4×Q8—31no—
722C4×Q8—32no—
723C4×Q8—32no—
724C4×Q8—32no—
725C4×Q8—32no—
726C4×Q8—31no—
727C4×Q8—31no—
728C4×Q8—31no—
729C4×Q8—31no—
730C4×Q8—32no—
731C4×Q8—32no—
732C4×Q8—31no—
733C4×Q8—31no—
734C4×Q8—61no—
735C4×Q8—61no—
736C4×Q8—61no—
737C4×Q8—61no—
738C4×Q8—61no—
739C4×Q8—61no—
740C4×Q8—61no—
741C4×Q8—61no—
742C4×Q8—61no—
743C4×Q8—61no—
744C4×Q8—62no—
745C4×Q8—62no—
746C4×Q8—62no—
747C4×Q8—62no—
748C4×Q8—61no—
749C4×Q8—61no—
750C4×Q8—61no—
751C4×Q8—61no—
752C4×D4—31no—
753C4×D4—31no—
754C4×D4—31no—
755C4×D4—31no—
756C4×D4—31no—
757C4×D4—31no—
758C4×D4—61no—
759C4×D4—61no—
760C4×D4—61no—
761C4×D4—61no—
762C4×D4—61no—
763C4×D4—61no—
764#117—31no—
765#117—61no—
766#117—61no—
767#117—61no—
768#117C22×D311yescharacteristic
769#117C22×D311yescharacteristic
770C2×C4⋊C4—21no—
771C2×C4⋊C4—21no—
772C2×C4⋊C4—31no—
773C2×C4⋊C4—31no—
774C2×C4⋊C4—31no—
775C2×C4⋊C4—31no—
776C2×C4⋊C4—61no—
777C2×C4⋊C4—61no—
778C2×C4⋊C4—61no—
779C2×C4⋊C4—61no—
780C2×C4⋊C4—61no—
781C2×C4⋊C4—61no—
782C2×C4⋊C4—61no—
783C2×C4⋊C4—61no—
784C2×C4⋊C4—61no—
785C2×C4⋊C4C22×D311yescharacteristic
786C2×C4⋊C4C22×D311yescharacteristic
787C2×C42—31no—
788C2×C42—31no—
789C2×C42—61no—
790C2×C42—61no—
791C2×C42—61no—
792C2×C42—61no—
793C2×C42—61no—
794C2×C42—61no—
795C2×C42C22×D311yescharacteristic
796#107—32no—
797#107—32no—
798#107—32no—
799#107—32no—
800#107—32no—
801#107C22×D312yes—
802#107C22×D312yes—
803#107C22×D312yes—
804#107C22×D312yes—
805#106—32no—
806#106—32no—
807#106—32no—
808#106—32no—
809#106—32no—
810#106C22×D312yes—
811#106C22×D312yes—
812#106C22×D312yes—
813#106C22×D312yes—
814C4⋊C8—32no—
815C4⋊C8—32no—
816C4⋊C8—32no—
817C4⋊C8—32no—
818C4⋊C8—32no—
819C4⋊C8—32no—
820#103—32no—
821#103—32no—
822#103—32no—
823#103—32no—
824#103—32no—
825#103—32no—
826#103—32no—
827#103—32no—
828#103—32no—
829#102—32no—
830#102—32no—
831#102—32no—
832#97—32no—
833#97—32no—
834#97C22×D312yes—
835C4×C8—32no—
836C4×C8—32no—
837C4×C8C22×D312yes—
838C23×C3C22×D411yescharacteristic
839C22×D3—21no—
840C3×Q8—42no—
841C3×Q8—81no—
842C2×C3×C4—22no—
843C2×C3×C4—22no—
844C2×C3×C4—21no—
845C2×C3×C4—21no—
846C2×C3×C4—21no—
847C2×C3×C4—21no—
848C2×C3×C4—41no—
849C2×C3×C4—41no—
850C2×C3×C4—42no—
851C2×C3×C4—42no—
852C2×C3×C4C22×D411yescharacteristic
853C2×C3×C4C22×D411yescharacteristic
854C2×C3×C4C22×D411yescharacteristic
855C2×C3×C4C22×D411yescharacteristic
856C2×C3×C4C22×D411yescharacteristic
857C2×C3×C4C22×Q812yes—
858C2×C3×C42−1+412yes—
859C2×C3×C4C2511yescharacteristic
860#67—24no—
861C2×Dic3—24no—
862C2×Dic3—22no—
863C2×Dic3—21no—
864C2×Dic3—22no—
865C2×Dic3—22no—
866C2×Dic3—21no—
867C2×Dic3—21no—
868C2×Dic3—41no—
869C2×Dic3—41no—
870C2×Dic3—41no—
871C2×Dic3—42no—
872C2×Dic3C22×D411yescharacteristic
873C2×Dic3C22×D411yescharacteristic
874C2×Dic3C22×D411yescharacteristic
875C2×Dic3C22×D411yescharacteristic
876C2×Dic3C22×D411yescharacteristic
877C2×Dic3C22×D411yescharacteristic
878C2×Dic3C22×D411yescharacteristic
879C2×Dic3C22×D411yescharacteristic
880D12—21no—
881D12C22×Q812yes—
882C4×D3—24no—
883C4×D3—42no—
884C4×D3—42no—
885C4×D3—42no—
886C4×D3—81no—
887C4×D3—81no—
888C4×D3—81no—
889Dic6—24no—
890Dic6—22no—
891Dic6—21no—
892Dic6—22no—
893Dic6—22no—
894Dic6—41no—
895Dic6—41no—
896Dic6—44no—
897Dic6—42no—
898Dic6—44no—
899Dic6—42no—
900Dic6—81no—
901Dic6—81no—
902Dic6C22×Q814yes—
903Dic6C22×Q812yes—
904C3×C8—22no—
905C3×C8C22×Q814yes—
906C3⋊C8—22no—
907C3⋊C8—22no—
908#41—34no—
909#41—62no—
910C2×Q8—21no—
911C2×Q8—21no—
912C2×Q8—31no—
913C2×Q8—31no—
914C2×Q8—31no—
915C2×Q8—31no—
916C2×Q8—34no—
917C2×Q8—32no—
918C2×Q8—31no—
919C2×Q8—61no—
920C2×Q8—61no—
921C2×Q8—62no—
922C2×Q8—62no—
923C2×Q8—61no—
924C2×Q8—61no—
925C2×Q8—61no—
926C2×Q8—62no—
927C2×Q8—122no—
928C2×Q8—124no—
929C2×Q8—124no—
930C2×D4—31no—
931C2×D4—61no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—31no—
935C22×C4—31no—
936C22×C4—31no—
937C22×C4—31no—
938C22×C4—61no—
939C22×C4—61no—
940C22×C4—61no—
941C22×C4—61no—
942C22×C4—61no—
943C22×C4—61no—
944C22×C4—61no—
945C22×C4—61no—
946C22×C4—61no—
947C22×C4D3×D411yescharacteristic
948C22×C4D3×D411yescharacteristic
949C22×C4C23×D311yescharacteristic
950Q16—38no—
951SD16—38no—
952M16—22no—
953M16—62no—
954M16—62no—
955M16D3×Q814yescomplemented
956C2×C8—32no—
957C2×C8—32no—
958C2×C8C23×D312yes—
959C2×C8C23×D312yes—
960C4⋊C4—22no—
961C4⋊C4—22no—
962C4⋊C4—22no—
963C4⋊C4—22no—
964C4⋊C4—21no—
965C4⋊C4—21no—
966C4⋊C4—21no—
967C4⋊C4—21no—
968C4⋊C4—21no—
969C4⋊C4—21no—
970C4⋊C4—21no—
971C4⋊C4—21no—
972C4⋊C4—31no—
973C4⋊C4—31no—
974C4⋊C4—31no—
975C4⋊C4—31no—
976C4⋊C4—31no—
977C4⋊C4—31no—
978C4⋊C4—31no—
979C4⋊C4—31no—
980C4⋊C4—31no—
981C4⋊C4—31no—
982C4⋊C4—31no—
983C4⋊C4—31no—
984C4⋊C4—32no—
985C4⋊C4—31no—
986C4⋊C4—31no—
987C4⋊C4—62no—
988C4⋊C4—62no—
989C4⋊C4—62no—
990C4⋊C4—62no—
991C4⋊C4—61no—
992C4⋊C4—61no—
993C4⋊C4—61no—
994C4⋊C4—61no—
995C4⋊C4—61no—
996C4⋊C4—61no—
997C4⋊C4—62no—
998C4⋊C4—62no—
999C4⋊C4—62no—
1000C4⋊C4—62no—
1001C4⋊C4—62no—
1002C4⋊C4—62no—
1003C4⋊C4—61no—
1004C4⋊C4—61no—
1005C4⋊C4—61no—
1006C4⋊C4—61no—
1007C4⋊C4—61no—
1008C4⋊C4—61no—
1009C4⋊C4—61no—
1010C4⋊C4—61no—
1011C4⋊C4—61no—
1012C4⋊C4—61no—
1013C4⋊C4—61no—
1014C4⋊C4—62no—
1015C4⋊C4—62no—
1016C4⋊C4—61no—
1017C4⋊C4—61no—
1018C4⋊C4C23×D312yes—
1019C4⋊C4C23×D312yes—
1020C4⋊C4C23×D311yescharacteristic
1021C4⋊C4C23×D311yescharacteristic
1022C4⋊C4C23×D311yescharacteristic
1023C4⋊C4C23×D311yescharacteristic
1024C22⋊C4—21no—
1025C22⋊C4—21no—
1026C22⋊C4—61no—
1027C22⋊C4—61no—
1028C22⋊C4—61no—
1029C22⋊C4—61no—
1030C22⋊C4—61no—
1031C22⋊C4—61no—
1032C22⋊C4—61no—
1033C42—21no—
1034C42—21no—
1035C42—31no—
1036C42—31no—
1037C42—31no—
1038C42—31no—
1039C42—31no—
1040C42—31no—
1041C42—31no—
1042C42—31no—
1043C42—61no—
1044C42—61no—
1045C42—61no—
1046C42—61no—
1047C42—62no—
1048C42—62no—
1049C42—62no—
1050C42—62no—
1051C42—61no—
1052C42—61no—
1053C42—61no—
1054C42—62no—
1055C42—62no—
1056C42D3×D411yescharacteristic
1057C42D3×D411yescharacteristic
1058C42C23×D311yescharacteristic
1059C42C23×D311yescharacteristic
1060C22×C3—21no—
1061C22×C3—21no—
1062C22×C3D4×Q812yes—
1063C22×C3C23×D411yescharacteristic
1064C2×D3—22no—
1065C2×D3—41no—
1066C2×D3—41no—
1067C3×C4—21no—
1068C3×C4—21no—
1069C3×C4—21no—
1070C3×C4—21no—
1071C3×C4—41no—
1072C3×C4—41no—
1073C3×C4—42no—
1074C3×C4—42no—
1075C3×C4—41no—
1076C3×C4—41no—
1077C3×C4D4×Q812yes—
1078C3×C4C23×Q811yescharacteristic
1079C3×C4C2×2−1+411yescharacteristic
1080Dic3—21no—
1081Dic3—21no—
1082Dic3—21no—
1083Dic3—21no—
1084Dic3—24no—
1085Dic3—22no—
1086Dic3—21no—
1087Dic3—21no—
1088Dic3—21no—
1089Dic3—41no—
1090Dic3—41no—
1091Dic3—42no—
1092Dic3#57512yes—
1093C23—61no—
1094C23C2×D3×D411yescharacteristic
1095Q8—34no—
1096Q8—32no—
1097Q8—42no—
1098Q8—62no—
1099Q8—62no—
1100Q8—62no—
1101Q8—61no—
1102Q8—64no—
1103Q8—81no—
1104Q8—121no—
1105Q8—121no—
1106Q8—124no—
1107Q8—122no—
1108Q8—124no—
1109Q8—122no—
1110Q8—241no—
1111Q8—241no—
1112D4—32no—
1113D4—64no—
1114D4—61no—
1115C2×C4—21no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—21no—
1119C2×C4—22no—
1120C2×C4—22no—
1121C2×C4—31no—
1122C2×C4—31no—
1123C2×C4—31no—
1124C2×C4—31no—
1125C2×C4—31no—
1126C2×C4—31no—
1127C2×C4—31no—
1128C2×C4—31no—
1129C2×C4—41no—
1130C2×C4—41no—
1131C2×C4—42no—
1132C2×C4—42no—
1133C2×C4—62no—
1134C2×C4—61no—
1135C2×C4—62no—
1136C2×C4—64no—
1137C2×C4—64no—
1138C2×C4—61no—
1139C2×C4—61no—
1140C2×C4—62no—
1141C2×C4—122no—
1142C2×C4—122no—
1143C2×C4—122no—
1144C2×C4—121no—
1145C2×C4—121no—
1146C2×C4—121no—
1147C2×C4—122no—
1148C2×C4—241no—
1149C2×C4—241no—
1150C2×C4—241no—
1151C2×C4C2×D3×D411yescharacteristic
1152C2×C4C2×D3×D411yescharacteristic
1153C2×C4C2×D3×D411yescharacteristic
1154C2×C4C2×D3×D411yescharacteristic
1155C2×C4C2×D3×D411yescharacteristic
1156C2×C4C2×D3×Q812yes—
1157C2×C4#100712yes—
1158C2×C4C24×D311yescharacteristic
1159C8—22no—
1160C8—62no—
1161C8—62no—
1162C8C2×D3×Q814yes—
1163C2×C3—22no—
1164C2×C3C2×D4×Q811yescharacteristic
1165C2×C3C2×#57511yescharacteristic
1166C2×C3#358611yescharacteristic
1167D3—42no—
1168C22—21no—
1169C22—21no—
1170C22—62no—
1171C22—121no—
1172C22—121no—
1173C22#572712yes—
1174C22C22×D3×D411yescharacteristic
1175C4—21no—
1176C4—21no—
1177C4—21no—
1178C4—21no—
1179C4—32no—
1180C4—42no—
1181C4—41no—
1182C4—41no—
1183C4—42no—
1184C4—41no—
1185C4—41no—
1186C4—61no—
1187C4—61no—
1188C4—61no—
1189C4—61no—
1190C4—61no—
1191C4—61no—
1192C4—61no—
1193C4—62no—
1194C4—64no—
1195C4—121no—
1196C4—122no—
1197C4—121no—
1198C4#572712yes—
1199C4C22×D3×Q811yescharacteristic
1200C4C2×#100711yescharacteristic
1201C3#6136911yescharacteristic, complemented, Sylow
1202C2—22no—
1203C2—122no—
1204C2C2×#572711yescharacteristic
1205C2D3×#57511yescharacteristic
1206C2#8720111yescharacteristic
subgroupG/H
centerC22C22×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#3166C2
socleC22×C3C23×D4
prime radicalC2×#235C23
hypercenter#3166D3
hypocenterC3#61369
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3166

Complements

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

NH ≅ G/Ntype
2. C2×#5685C2semidirect
3. C3×#3166C2semidirect
4. #83367C2semidirect
6. #81971C2semidirect
7. #81969C2semidirect
8. #81967C2semidirect
9. #81966C2semidirect
10. #81932C2semidirect
11. #81930C2semidirect
12. #81914C2semidirect
13. #81913C2semidirect
14. #79245C2semidirect
15. #79245C2semidirect
18. #79204C2semidirect
19. #79203C2semidirect
23. M16×Dic6C2semidirect
151. #3166D3semidirect
216. #909Q8semidirect
521. C2×Dic6C2×Q8semidirect
525. C3×M16C2×Q8semidirect
632. Dic12C2×Q8semidirect
633. #204C2×Q8semidirect
955. M16D3×Q8semidirect
1201. C3#61369semidirect

Maximal subgroups

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

subgroupindex
#862772
C2×#56852
C3×#31662
#833672
#830172
#819712
#819692
#819672
#819662
#819322
#819302
#819142
#819132
#792452
#792412
#792402
#792042
#792032
#792002
C4×#9092
M16×Dic62
#613693