Finite Group Databasebeta

← #7659892

Subgroups — #7659892

Order 512.

4794 conjugacy classes of subgroups.

The subgroup lattice has 1316 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#52250C213yesmaximal, complemented
2#42707C213yesmaximal, complemented
3#42699C213yesmaximal, complemented
4#42635C213yesmaximal, complemented
5#42632C213yesmaximal, complemented
6#42554C213yesmaximal, complemented
7#42514C213yesmaximal, complemented
8#40174C213yesmaximal, complemented
9#40127C213yesmaximal, complemented
10#40050C213yesmaximal, complemented
11#39925C213yesmaximal, complemented
12#39608C213yesmaximal, complemented
13#39216C213yesmaximal, complemented
14#37345C213yesmaximal, complemented
15#37333C213yesmaximal, complemented
16#37294C213yesmaximal, complemented
17#36578C211yesmaximal, characteristic, complemented
18Q8×#126C211yesmaximal, characteristic, complemented
19Q8×C22⋊Q8C211yesmaximal, characteristic, complemented
20#36457C211yesmaximal, characteristic, complemented
21#36445C211yesmaximal, characteristic, complemented
22#36430C211yesmaximal, characteristic
23#36005C211yesmaximal, characteristic, complemented
24#35937C211yesmaximal, characteristic, complemented
25#35898C211yesmaximal, characteristic, complemented
26#35854C211yesmaximal, characteristic, complemented
27#35854C211yesmaximal, characteristic, complemented
28#35816C211yesmaximal, characteristic, complemented
29#34336C211yesmaximal, characteristic, complemented
30#34294C211yesmaximal, characteristic, complemented
31#34193C211yesmaximal, characteristic, complemented
32C2×Q82C2211yescharacteristic
33C2×#557C2211yescharacteristic
34C2×#557C2211yescharacteristic
35C2×#550C2211yescharacteristic
36C2×#548C2211yescharacteristic
37C2×#548C2211yescharacteristic
38C2×#520C2211yescharacteristic
39C2×C4×#41C2211yescharacteristic
40C22×C4×Q8C2211yescharacteristic
41#2863C2213yes—
42#2858C2213yes—
43#2857C2213yes—
44#2857C2213yes—
45#2854C2213yes—
46#2850C2213yes—
47#2838C2216yes—
48#2837C2216yes—
49#2800C2216yes—
50#2775C2216yes—
51#2773C2216yes—
52#2772C2213yes—
53#2770C2216yes—
54#2766C2213yes—
55#2763C2213yes—
56#2763C2216yes—
57#2758C2213yes—
58#2757C2213yes—
59#2757C2216yes—
60#2754C2213yes—
61#2754C2216yes—
62#2747C2213yes—
63#2746C2213yes—
64#2742C2213yes—
65#2741C2216yes—
66#2737C2213yes—
67#2737C2213yes—
68#2731C2216yes—
69#2730C2216yes—
70#2717C2216yes—
71#2717C2216yes—
72#2705C2216yes—
73#2702C2216yes—
74#2700C2213yes—
75#2700C2216yes—
76#2698C2211yescharacteristic
77#2692C2216yes—
78#2692C2216yes—
79#2691C2213yes—
80#2687C2216yes—
81#2687C2213yes—
82#2674C2216yes—
83#2672C2213yes—
84#2663C2216yes—
85#2660C2213yes—
86#2654C2216yes—
87#2651C2216yes—
88#2650C2216yes—
89#2644C2213yes—
90#2640C2213yes—
91#2640C2213yes—
92#2630C2216yes—
93#2629C2213yes—
94#2628C2216yes—
95#2624C2213yes—
96#2592C2213yes—
97#2592C2213yes—
98#2584C2213yes—
99#2582C2213yes—
100#2567C2213yes—
101#2566C2213yes—
102#2563C2213yes—
103#2563C2213yes—
104#2563C2213yes—
105#2551C2213yes—
106#2551C2213yes—
107#2550C2213yes—
108#2550C2213yes—
109#2548C2213yes—
110#2546C2213yes—
111#2544C2213yes—
112#2542C2213yes—
113#2538C2213yes—
114#2538C2213yes—
115#2535C2213yes—
116#2521C2216yes—
117#2513C2213yes—
118#2512C2213yes—
119#2512C2213yes—
120#2511C2213yes—
121#2511C2213yes—
122#2511C2213yes—
123#2508C2216yes—
124#2504C2213yes—
125#2501C2213yes—
126#2497C2213yes—
127#2497C2213yes—
128#2497C2213yes—
129#2497C2213yes—
130#2496C2213yes—
131#2494C2213yes—
132#2491C2213yes—
133#2491C2213yes—
134#2491C2213yes—
135#2491C2213yes—
136#2490C2213yes—
137#2490C2213yes—
138#2490C2213yes—
139#2490C2213yes—
140#2489C2213yes—
141#2489C2213yes—
142#2489C2213yes—
143#2489C2213yes—
144#2487C2213yes—
145#2487C2213yes—
146#2474C2216yes—
147#2470C2216yes—
148#2461C2216yes—
149#2454C2213yes—
150#2454C2213yes—
151#2454C2213yes—
152#2452C2216yes—
153#2452C2213yes—
154#2451C2213yes—
155#2451C2213yes—
156#2448C2213yes—
157#2448C2213yes—
158#2445C2213yes—
159#2445C2213yes—
160#2442C2213yes—
161#2441C2213yes—
162#2441C2213yes—
163#2440C2213yes—
164#2440C2213yes—
165#2440C2213yes—
166#2428C2213yes—
167#2427C2213yes—
168#2422C2213yes—
169#2422C2213yes—
170#2421C2213yes—
171#2421C2213yes—
172#2415C2213yes—
173#2414C2213yes—
174#2401C2213yes—
175#2399C2213yes—
176#2398C2213yes—
177#2398C2213yes—
178#2396C2213yes—
179#2395C2213yes—
180#2370C2213yes—
181#2370C2213yes—
182#2369C2213yes—
183#2367C2213yes—
184#2361C2213yes—
185#2360C2213yes—
186#2355C2213yes—
187#2354C2213yes—
188#2354C2213yes—
189#2351C2211yescharacteristic
190#2351C2211yescharacteristic
191#2351C2211yescharacteristic
192Q8×C4⋊C4C2211yescharacteristic
193Q8×C4⋊C4C2211yescharacteristic
194Q8×C4⋊C4C2211yescharacteristic
195Q8×C4⋊C4C2211yescharacteristic
196Q8×C4⋊C4C2211yescharacteristic
197Q8×C4⋊C4C2211yescharacteristic
198Q8×C4⋊C4C2211yescharacteristic
199D4×C4⋊C4C2213yes—
200#2347C2213yes—
201#2347C2213yes—
202#2341C2211yescharacteristic
203#2341C2211yescharacteristic
204#2341C2211yescharacteristic
205#2341C2211yescharacteristic
206#2341C2211yescharacteristic
207#2341C2211yescharacteristic
208#2341C2211yescharacteristic
209#2341C2211yescharacteristic
210Q8×C22⋊C4C2211yescharacteristic
211Q8×C22⋊C4C2211yescharacteristic
212Q8×C22⋊C4C2211yescharacteristic
213Q8×C22⋊C4C2211yescharacteristic
214#2334C2216yes—
215#2331C2213yes—
216#2330C2213yes—
217#2326C2213yes—
218#2324C2216yes—
219#2323C2213yes—
220#2319C2213yes—
221#2319C2213yes—
222C4×#125C2213yes—
223C4×#126C2213yes—
224C4×#124C2213yes—
225C4×C22⋊Q8C2213yes—
226C4×C22⋊Q8C2213yes—
227C4×#123C2213yes—
228C4×#121C2213yes—
229C4×#121C2213yes—
230#2295C2213yes—
231#2290C2213yes—
232#2285C2213yes—
233#2283C2213yes—
234#2276C2211yescharacteristic
235#2276C2211yescharacteristic
236#2276C2211yescharacteristic
237C42×Q8C2211yescharacteristic
238C22×#41C2311yescharacteristic
239C22×#41C2311yescharacteristic
240C23×Q8C2311yescharacteristic
241Q82—44no—
242#557—28no—
243#557—44no—
244#550—44no—
245#548—28no—
246#548—44no—
247C2×C4⋊Q8C2313yes—
248C2×C4⋊Q8C2313yes—
249C2×C4⋊Q8C2313yes—
250C2×C4⋊Q8C2313yes—
251C2×C4⋊Q8C2313yes—
252C2×C4⋊Q8C2316yes—
253C2×#127C2313yes—
254C2×#126C2311yescharacteristic
255C2×#126C2316yes—
256C2×#125C2313yes—
257C2×#125C2313yes—
258C2×#125C2313yes—
259C2×#125C2313yes—
260C2×#124C2313yes—
261C2×#124C2313yes—
262C2×#124C2313yes—
263C2×#124C2316yes—
264C2×#124C2316yes—
265C2×#123C2313yes—
266C2×#123C2316yes—
267C2×#123C2316yes—
268C2×C22⋊Q8C2313yes—
269C2×C22⋊Q8C2311yescharacteristic
270C2×C22⋊Q8C2313yes—
271C2×C22⋊Q8C2313yes—
272C2×C22⋊Q8C2316yes—
273C2×C22⋊Q8C2316yes—
274C2×C22⋊Q8C2316yes—
275C2×#121C2313yes—
276C2×#121C2313yes—
277C2×#121C2313yes—
278C2×#121C2313yes—
279C2×#121C2313yes—
280#520—44no—
281C4×#41—28no—
282C2×C4×Q8—44no—
283C2×C4×Q8C2313yes—
284C2×C4×Q8C2311yescharacteristic
285C2×C4×Q8C2311yescharacteristic
286C2×C4×Q8C2311yescharacteristic
287C2×C4×Q8C2311yescharacteristic
288C2×C4×Q8C2311yescharacteristic
289C2×C4×Q8C2311yescharacteristic
290C2×C4×Q8C2311yescharacteristic
291C2×C4×Q8C2311yescharacteristic
292C2×C4×Q8C2311yescharacteristic
293C2×C4×Q8C2311yescharacteristic
294C2×C4×Q8C2311yescharacteristic
295C2×C4×Q8C2313yes—
296C2×C4×Q8C2313yes—
297C2×C4×Q8C2313yes—
298C2×C4×Q8C2313yes—
299C2×C4×Q8C2311yescharacteristic
300C2×C4×D4C2313yes—
301C2×C4×D4C2313yes—
302C2×C4×D4C2313yes—
303C2×C4×D4C2313yes—
304C2×C4×D4C2313yes—
305C2×C4×D4C2313yes—
306C2×C4×D4C2313yes—
307C2×C4×D4C2316yes—
308C2×#117C2313yes—
309C2×#117C2313yes—
310C2×#117C2316yes—
311C22×C4⋊C4C2313yes—
312C22×C4⋊C4C2313yes—
313C22×C42C2313yes—
314C22×C42C2313yes—
315#401C2313yes—
316#400C2316yes—
317#400C2313yes—
318#400C2316yes—
319#400C2313yes—
320#400C2316yes—
321#400C2313yes—
322#400C2316yes—
323#400C2313yes—
324#400C2313yes—
325#400C2313yes—
326#400C2313yes—
327#400C2311yescharacteristic
328#400C2313yes—
329#399C2316yes—
330#399C2316yes—
331#399C2313yes—
332#399C2316yes—
333#399C2313yes—
334#399C2316yes—
335#398C2313yes—
336#398C2316yes—
337#398C2316yes—
338#398C2316yes—
339#398C2316yes—
340#398C2313yes—
341#398C2311yescharacteristic
342#398C2313yes—
343#398C2311yescharacteristic
344#398C2313yes—
345#398C2313yes—
346#397C2313yes—
347#397C2316yes—
348#397C2316yes—
349#397C2316yes—
350#397C2316yes—
351#397C2313yes—
352#397C2313yes—
353#397C2316yes—
354#397C2316yes—
355#397C2316yes—
356#397C2313yes—
357#397C2316yes—
358#397C2313yes—
359#397C2313yes—
360#397C2311yescharacteristic
361#397C2311yescharacteristic
362#397C2316yes—
363#397C2313yes—
364#397C2313yes—
365#396C2313yes—
366#396C2316yes—
367#396C2313yes—
368#396C2316yes—
369#396C2316yes—
370#396C2316yes—
371#396C2316yes—
372#396C2316yes—
373#396C2313yes—
374#395C2316yes—
375#395C2316yes—
376#395C2316yes—
377#395C2313yes—
378#395C2313yes—
379#395C2311yescharacteristic
380#395C2313yes—
381#395C2313yes—
382#395C2316yes—
383#394C2316yes—
384#394C2316yes—
385#394C2316yes—
386#394C2316yes—
387#394C2313yes—
388#394C2313yes—
389#394C2313yes—
390#394C2313yes—
391#394C2316yes—
392#394C2313yes—
393#394C2313yes—
394#394C2316yes—
395#393C2313yes—
396#393C2313yes—
397#393C2316yes—
398#393C2316yes—
399#393C2316yes—
400#393C2316yes—
401#393C2313yes—
402#393C2313yes—
403#393C2313yes—
404#392C2316yes—
405#391C2313yes—
406#391C2313yes—
407#391C2313yes—
408#391C2313yes—
409#391C2313yes—
410#391C2313yes—
411#391C2313yes—
412#391C2313yes—
413#391C2316yes—
414#391C2313yes—
415#391C2313yes—
416#391C2313yes—
417#391C2316yes—
418#391C2313yes—
419#391C2316yes—
420#391C2311yescharacteristic
421#390C2316yes—
422#390C2316yes—
423#390C2316yes—
424#390C2313yes—
425#390C2313yes—
426#390C2313yes—
427#390C2313yes—
428#390C2313yes—
429#390C2313yes—
430#390C2313yes—
431#390C2313yes—
432#390C2313yes—
433#390C2313yes—
434#390C2313yes—
435#390C2313yes—
436#390C2313yes—
437#390C2313yes—
438#390C2313yes—
439#390C2313yes—
440#390C2313yes—
441#390C2313yes—
442#389C2313yes—
443#389C2313yes—
444#389C2313yes—
445#389C2316yes—
446#389C2313yes—
447#389C2313yes—
448#389C2313yes—
449#389C2313yes—
450#389C2316yes—
451#389C2313yes—
452#389C2316yes—
453#389C2316yes—
454#389C2316yes—
455#389C2313yes—
456#389C2313yes—
457#389C2313yes—
458#389C2313yes—
459#389C2313yes—
460#389C2313yes—
461#389C2313yes—
462#389C2313yes—
463#389C2313yes—
464#389C2313yes—
465#389C2316yes—
466#389C2313yes—
467#389C2313yes—
468#389C2313yes—
469#389C2313yes—
470#389C2313yes—
471#389C2313yes—
472#389C2311yescharacteristic
473#388C2313yes—
474#388C2313yes—
475#388C2313yes—
476#388C2316yes—
477#388C2316yes—
478#388C2316yes—
479#388C2316yes—
480#388C2316yes—
481#388C2316yes—
482#388C2316yes—
483#388C2313yes—
484#388C2313yes—
485#388C2316yes—
486#388C2316yes—
487#388C2316yes—
488#388C2316yes—
489#388C2316yes—
490#388C2313yes—
491#388C2316yes—
492#388C2316yes—
493#388C2313yes—
494#388C2316yes—
495#388C2313yes—
496#388C2313yes—
497#388C2313yes—
498#388C2311yescharacteristic
499#388C2313yes—
500#388C2313yes—
501#387C2313yes—
502#387C2313yes—
503#387C2313yes—
504#387C2313yes—
505#387C2316yes—
506#387C2313yes—
507#387C2316yes—
508#387C2316yes—
509#387C2313yes—
510#387C2313yes—
511#387C2316yes—
512#387C2316yes—
513#387C2316yes—
514#387C2313yes—
515#387C2313yes—
516#387C2313yes—
517#387C2313yes—
518#387C2316yes—
519#387C2313yes—
520#387C2311yescharacteristic
521#387C2313yes—
522#387C2313yes—
523#386C2316yes—
524#386C2316yes—
525#386C2316yes—
526#386C2316yes—
527#386C2313yes—
528#386C2313yes—
529#386C2313yes—
530#386C2313yes—
531#386C2313yes—
532#385C2316yes—
533#385C2316yes—
534#385C2313yes—
535#385C2316yes—
536#385C2316yes—
537#385C2316yes—
538#385C2313yes—
539#385C2313yes—
540#385C2313yes—
541#385C2311yescharacteristic
542#385C2313yes—
543#385C2313yes—
544#384C2313yes—
545#384C2313yes—
546#384C2313yes—
547#384C2313yes—
548#384C2313yes—
549#384C2313yes—
550#384C2313yes—
551#383C2313yes—
552#383C2313yes—
553#383C2313yes—
554#382C2313yes—
555#382C2313yes—
556#382C2316yes—
557#382C2316yes—
558#382C2313yes—
559#382C2313yes—
560#382C2311yescharacteristic
561#382C2313yes—
562#381C2313yes—
563#381C2313yes—
564#381C2311yescharacteristic
565#380C2313yes—
566#380C2313yes—
567#380C2313yes—
568#380C2313yes—
569#380C2313yes—
570#380C2313yes—
571#380C2313yes—
572#380C2313yes—
573#380C2313yes—
574#380C2316yes—
575#380C2316yes—
576#380C2313yes—
577#380C2313yes—
578#380C2313yes—
579#380C2313yes—
580#380C2313yes—
581#380C2313yes—
582#380C2313yes—
583#380C2316yes—
584#380C2313yes—
585C4×C4⋊C4C2313yes—
586C4×C4⋊C4C2313yes—
587C4×C4⋊C4C2313yes—
588C4×C4⋊C4C2316yes—
589C4×C4⋊C4C2313yes—
590C4×C4⋊C4C2313yes—
591C4×C4⋊C4C2316yes—
592C4×C4⋊C4C2313yes—
593C4×C4⋊C4C2313yes—
594C4×C4⋊C4C2313yes—
595C4×C4⋊C4C2313yes—
596C4×C4⋊C4C2313yes—
597C4×C4⋊C4C2313yes—
598C4×C4⋊C4C2313yes—
599C4×C4⋊C4C2313yes—
600C4×C4⋊C4C2316yes—
601C4×C4⋊C4C2313yes—
602C4×C4⋊C4C2313yes—
603C4×C4⋊C4C2313yes—
604C4×C4⋊C4C2313yes—
605C4×C4⋊C4C2313yes—
606C4×C4⋊C4C2313yes—
607C4×C4⋊C4C2313yes—
608C4×C4⋊C4C2313yes—
609C4×C4⋊C4C2313yes—
610C4×C22⋊C4C2313yes—
611C4×C22⋊C4C2313yes—
612C4×C22⋊C4C2313yes—
613C4×C22⋊C4C2316yes—
614C4×C22⋊C4C2313yes—
615C4×C22⋊C4C2313yes—
616C4×C22⋊C4C2313yes—
617C4×C22⋊C4C2313yes—
618C4×C22⋊C4C2313yes—
619C4×C22⋊C4C2313yes—
620C4×C22⋊C4C2313yes—
621C4×C22⋊C4C2313yes—
622C4×C22⋊C4C2313yes—
623#376C2313yes—
624#376C2313yes—
625#376C2313yes—
626C43C2313yes—
627C2×#41—24no—
628C2×#41—24no—
629C2×#41—24no—
630C2×#41—24no—
631C2×#41—24no—
632C2×#41—24no—
633C22×Q8—24no—
634C22×Q8—24no—
635C22×Q8—24no—
636C22×Q8C2413yes—
637C22×Q8C2411yescharacteristic
638C22×Q8C2413yes—
639C22×Q8C2413yes—
640C22×Q8C2416yes—
641C22×Q8C2411yescharacteristic
642C22×D4C2413yes—
643C22×D4C2413yes—
644C22×D4C2413yes—
645C22×D4C2413yes—
646C22×D4C2413yes—
647C22×D4C2416yes—
648C23×C4C2413yes—
649C23×C4C2413yes—
650C23×C4C2413yes—
651C23×C4C2413yes—
652C23×C4C2411yescharacteristic
653C23×C4C2413yes—
654C23×C4C2413yes—
655C23×C4C2416yes—
656C4⋊Q8—212no—
657C4⋊Q8—46no—
658C4⋊Q8—46no—
659C4⋊Q8—46no—
660C4⋊Q8—46no—
661C4⋊Q8—86no—
662#127—46no—
663#126—24no—
664#126—412no—
665#125—212no—
666#125—212no—
667#125—46no—
668#125—46no—
669#124—212no—
670#124—46no—
671#124—46no—
672#124—86no—
673#124—86no—
674#123—46no—
675#123—86no—
676#123—86no—
677C22⋊Q8—212no—
678C22⋊Q8—24no—
679C22⋊Q8—46no—
680C22⋊Q8—46no—
681C22⋊Q8—86no—
682C22⋊Q8—86no—
683C22⋊Q8—86no—
684#121—212no—
685#121—212no—
686#121—46no—
687#121—46no—
688#121—46no—
689C4×Q8—24no—
690C4×Q8—24no—
691C4×Q8—24no—
692C4×Q8—24no—
693C4×Q8—24no—
694C4×Q8—24no—
695C4×Q8—24no—
696C4×Q8—24no—
697C4×Q8—24no—
698C4×Q8—24no—
699C4×Q8—24no—
700C4×Q8—212no—
701C4×Q8—46no—
702C4×Q8—46no—
703C4×Q8—46no—
704C4×Q8—46no—
705C4×Q8#4118yes—
706C4×D4—212no—
707C4×D4—212no—
708C4×D4—212no—
709C4×D4—46no—
710C4×D4—46no—
711C4×D4—46no—
712C4×D4—46no—
713C4×D4—86no—
714#117—212no—
715#117—46no—
716#117—86no—
717C2×C4⋊C4—46no—
718C2×C4⋊C4—46no—
719C2×C4⋊C4C2413yes—
720C2×C4⋊C4C2413yes—
721C2×C4⋊C4C2413yes—
722C2×C4⋊C4C2413yes—
723C2×C4⋊C4C2413yes—
724C2×C4⋊C4C2411yescharacteristic
725C2×C4⋊C4C2413yes—
726C2×C4⋊C4C2413yes—
727C2×C4⋊C4C2413yes—
728C2×C4⋊C4C2413yes—
729C2×C4⋊C4C2413yes—
730C2×C4⋊C4C2413yes—
731C2×C4⋊C4C2413yes—
732C2×C4⋊C4C2413yes—
733C2×C4⋊C4C2413yes—
734C2×C4⋊C4C2413yes—
735C2×C4⋊C4C2411yescharacteristic
736C2×C4⋊C4C2413yes—
737C2×C4⋊C4C2411yescharacteristic
738C2×C4⋊C4C2411yescharacteristic
739C2×C4⋊C4C2411yescharacteristic
740C2×C4⋊C4C2413yes—
741C2×C4⋊C4C2416yes—
742C2×C4⋊C4C2411yescharacteristic
743C2×C4⋊C4C2411yescharacteristic
744C2×C4⋊C4C2411yescharacteristic
745C2×C4⋊C4C2413yes—
746C2×C4⋊C4C2416yes—
747C2×C4⋊C4C2411yescharacteristic
748C2×C4⋊C4C2413yes—
749C2×C4⋊C4C2413yes—
750C2×C4⋊C4C2411yescharacteristic
751C2×C4⋊C4C2413yes—
752C2×C4⋊C4C2416yes—
753C2×C4⋊C4C2411yescharacteristic
754C2×C4⋊C4C2413yes—
755C2×C4⋊C4C2413yes—
756C2×C4⋊C4C2413yes—
757C2×C4⋊C4C2413yes—
758C2×C4⋊C4C2413yes—
759C2×C4⋊C4C2413yes—
760C2×C4⋊C4C2416yes—
761C2×C4⋊C4C2413yes—
762C2×C4⋊C4C2416yes—
763C2×C4⋊C4C2416yes—
764C2×C4⋊C4C2416yes—
765C2×C4⋊C4C2413yes—
766C2×C4⋊C4C2413yes—
767C2×C4⋊C4C2413yes—
768C2×C4⋊C4C2416yes—
769C2×C4⋊C4C2413yes—
770C2×C4⋊C4C2416yes—
771C2×C4⋊C4C2416yes—
772C2×C4⋊C4C2413yes—
773C2×C4⋊C4C2413yes—
774C2×C4⋊C4C2413yes—
775C2×C22⋊C4C2416yes—
776C2×C22⋊C4C2411yescharacteristic
777C2×C22⋊C4C2413yes—
778C2×C22⋊C4C2416yes—
779C2×C22⋊C4C2413yes—
780C2×C22⋊C4C2413yes—
781C2×C22⋊C4C2411yescharacteristic
782C2×C22⋊C4C2413yes—
783C2×C22⋊C4C2411yescharacteristic
784C2×C22⋊C4C2411yescharacteristic
785C2×C22⋊C4C2413yes—
786C2×C22⋊C4C2413yes—
787C2×C22⋊C4C2416yes—
788C2×C22⋊C4C2416yes—
789C2×C22⋊C4C2411yescharacteristic
790C2×C22⋊C4C2413yes—
791C2×C22⋊C4C2413yes—
792C2×C22⋊C4C2413yes—
793C2×C22⋊C4C2413yes—
794C2×C22⋊C4C2416yes—
795C2×C22⋊C4C2416yes—
796C2×C22⋊C4C2413yes—
797C2×C22⋊C4C2413yes—
798C2×C22⋊C4C2413yes—
799C2×C22⋊C4C2416yes—
800C2×C22⋊C4C2416yes—
801C2×C22⋊C4C2416yes—
802C2×C22⋊C4C2413yes—
803C2×C22⋊C4C2413yes—
804C2×C22⋊C4C2413yes—
805C2×C22⋊C4C2413yes—
806C2×C22⋊C4C2413yes—
807C2×C22⋊C4C2413yes—
808C2×C22⋊C4C2413yes—
809C2×C22⋊C4C2413yes—
810C2×C22⋊C4C2413yes—
811C2×C22⋊C4C2413yes—
812C2×C22⋊C4C2413yes—
813C2×C22⋊C4C2413yes—
814C2×C22⋊C4C2413yes—
815C2×C22⋊C4C2416yes—
816C2×C22⋊C4C2416yes—
817C2×C22⋊C4C2411yescharacteristic
818C2×C42—212no—
819C2×C42—46no—
820C2×C42C2413yes—
821C2×C42C2413yes—
822C2×C42C2413yes—
823C2×C42C2413yes—
824C2×C42C2413yes—
825C2×C42C2413yes—
826C2×C42C2413yes—
827C2×C42C2413yes—
828C2×C42C2413yes—
829C2×C42C2413yes—
830C2×C42C2413yes—
831C2×C42C2413yes—
832C2×C42C2411yescharacteristic
833C2×C42C2411yescharacteristic
834C2×C42C2416yes—
835C2×C42C2416yes—
836C2×C42C2413yes—
837C2×C42C2413yes—
838C2×C42C2413yes—
839C2×C42C2413yes—
840C2×C42C2413yes—
841C2×C42C2416yes—
842C2×C42C2413yes—
843#95C2411yescharacteristic
844#95C2411yescharacteristic
845#95C2411yescharacteristic
846#95C2413yes—
847#95C2413yes—
848#95C2413yes—
849#95C2413yes—
850#95C2413yes—
851#95C2413yes—
852#95C2413yes—
853#95C2413yes—
854#95C2413yes—
855#95C2411yescharacteristic
856#95C2411yescharacteristic
857#95C2411yescharacteristic
858#95C2411yescharacteristic
859#95C2411yescharacteristic
860#95C2411yescharacteristic
861#95C2411yescharacteristic
862#95C2411yescharacteristic
863#95C2413yes—
864#95C2413yes—
865#95C2413yes—
866#95C2413yes—
867#95C2413yes—
868#95C2413yes—
869#95C2413yes—
870#95C2413yes—
871#95C2413yes—
872#95C2416yes—
873#95C2413yes—
874#95C2413yes—
875#95C2413yes—
876#95C2413yes—
877#95C2413yes—
878#95C2413yes—
879#95C2413yes—
880#95C2413yes—
881#95C2411yescharacteristic
882#95C2411yescharacteristic
883#95C2413yes—
884#95C2413yes—
885#95C2411yescharacteristic
886#95C2416yes—
887#95C2413yes—
888#95C2413yes—
889#95C2413yes—
890#95C2413yes—
891#95C2416yes—
892#95C2413yes—
893#95C2413yes—
894#95C2413yes—
895#95C2413yes—
896#95C2413yes—
897#95C2413yes—
898#95C2413yes—
899#95C2416yes—
900#95C2413yes—
901#95C2413yes—
902#95C2413yes—
903#95C2416yes—
904#95C2416yes—
905#95C2416yes—
906#95C2416yes—
907C24C2513yes—
908C24C2513yes—
909C24C2511yescharacteristic
910#41—416no—
911#41—416no—
912C2×Q8—26no—
913C2×Q8—26no—
914C2×Q8—26no—
915C2×Q8—22no—
916C2×Q8—26no—
917C2×Q8—22no—
918C2×Q8—41no—
919C2×Q8—43no—
920C2×Q8—43no—
921C2×Q8—43no—
922C2×Q8—43no—
923C2×Q8—43no—
924C2×Q8—46no—
925C2×Q8—46no—
926C2×Q8—46no—
927C2×Q8—416no—
928C2×Q8C2×#4114yes—
929C2×Q8H(5,𝔽2)14yes—
930C2×Q82−1+414yes—
931C2×D4—26no—
932C2×D4—26no—
933C2×D4—26no—
934C2×D4—26no—
935C2×D4—26no—
936C2×D4—26no—
937C2×D4—26no—
938C2×D4—26no—
939C2×D4—26no—
940C2×D4—26no—
941C2×D4—43no—
942C2×D4—43no—
943C2×D4—43no—
944C2×D4—43no—
945C2×D4—43no—
946C2×D4—46no—
947C2×D4—46no—
948C2×D4—46no—
949C22×C4—22no—
950C22×C4—26no—
951C22×C4—26no—
952C22×C4—26no—
953C22×C4—26no—
954C22×C4—26no—
955C22×C4—26no—
956C22×C4—26no—
957C22×C4—26no—
958C22×C4—26no—
959C22×C4—26no—
960C22×C4—26no—
961C22×C4—22no—
962C22×C4—26no—
963C22×C4—41no—
964C22×C4—43no—
965C22×C4—43no—
966C22×C4—43no—
967C22×C4—43no—
968C22×C4—43no—
969C22×C4—43no—
970C22×C4—46no—
971C22×C4—46no—
972C22×C4—46no—
973C22×C4C2511yescharacteristic
974C22×C4C2511yescharacteristic
975C22×C4C2511yescharacteristic
976C22×C4C2513yes—
977C22×C4C2511yescharacteristic
978C22×C4C2511yescharacteristic
979C22×C4C2513yes—
980C22×C4C2511yescharacteristic
981C22×C4C2511yescharacteristic
982C22×C4C2513yes—
983C22×C4C2511yescharacteristic
984C22×C4C2513yes—
985C22×C4C2511yescharacteristic
986C22×C4C2513yes—
987C22×C4C2513yes—
988C22×C4C2513yes—
989C22×C4C2513yes—
990C22×C4C2513yes—
991C22×C4C2511yescharacteristic
992C22×C4C2513yes—
993C22×C4C2513yes—
994C22×C4C2513yes—
995C22×C4C2511yescharacteristic
996C22×C4C2513yes—
997C22×C4C2511yescharacteristic
998C22×C4C2511yescharacteristic
999C22×C4C2511yescharacteristic
1000C22×C4C2513yes—
1001C4⋊C4—26no—
1002C4⋊C4—26no—
1003C4⋊C4—22no—
1004C4⋊C4—26no—
1005C4⋊C4—26no—
1006C4⋊C4—26no—
1007C4⋊C4—26no—
1008C4⋊C4—212no—
1009C4⋊C4—26no—
1010C4⋊C4—26no—
1011C4⋊C4—26no—
1012C4⋊C4—26no—
1013C4⋊C4—26no—
1014C4⋊C4—26no—
1015C4⋊C4—26no—
1016C4⋊C4—26no—
1017C4⋊C4—26no—
1018C4⋊C4—22no—
1019C4⋊C4—22no—
1020C4⋊C4—22no—
1021C4⋊C4—22no—
1022C4⋊C4—22no—
1023C4⋊C4—22no—
1024C4⋊C4—22no—
1025C4⋊C4—26no—
1026C4⋊C4—26no—
1027C4⋊C4—43no—
1028C4⋊C4—46no—
1029C4⋊C4—41no—
1030C4⋊C4—43no—
1031C4⋊C4—43no—
1032C4⋊C4—41no—
1033C4⋊C4—43no—
1034C4⋊C4—46no—
1035C4⋊C4—41no—
1036C4⋊C4—43no—
1037C4⋊C4—43no—
1038C4⋊C4—43no—
1039C4⋊C4—43no—
1040C4⋊C4—43no—
1041C4⋊C4—43no—
1042C4⋊C4—43no—
1043C4⋊C4—43no—
1044C4⋊C4—46no—
1045C4⋊C4—46no—
1046C4⋊C4—46no—
1047C4⋊C4—46no—
1048C4⋊C4—43no—
1049C4⋊C4—43no—
1050C4⋊C4—43no—
1051C4⋊C4—46no—
1052C4⋊C4—46no—
1053C4⋊C4—46no—
1054C4⋊C4—43no—
1055C4⋊C4—43no—
1056C4⋊C4C2×#41112yes—
1057C22⋊C4—22no—
1058C22⋊C4—22no—
1059C22⋊C4—22no—
1060C22⋊C4—212no—
1061C22⋊C4—22no—
1062C22⋊C4—26no—
1063C22⋊C4—212no—
1064C22⋊C4—26no—
1065C22⋊C4—26no—
1066C22⋊C4—26no—
1067C22⋊C4—43no—
1068C22⋊C4—43no—
1069C22⋊C4—46no—
1070C22⋊C4—46no—
1071C22⋊C4—41no—
1072C22⋊C4—43no—
1073C22⋊C4—43no—
1074C22⋊C4—43no—
1075C22⋊C4—43no—
1076C22⋊C4—46no—
1077C22⋊C4—46no—
1078C22⋊C4—43no—
1079C22⋊C4—43no—
1080C22⋊C4—43no—
1081C22⋊C4—43no—
1082C22⋊C4—46no—
1083C22⋊C4—46no—
1084C22⋊C4—46no—
1085C22⋊C4—43no—
1086C22⋊C4—43no—
1087C22⋊C4—43no—
1088C22⋊C4—43no—
1089C22⋊C4—43no—
1090C22⋊C4—43no—
1091C22⋊C4—43no—
1092C22⋊C4—43no—
1093C22⋊C4—43no—
1094C22⋊C4—43no—
1095C22⋊C4—43no—
1096C22⋊C4—43no—
1097C22⋊C4—46no—
1098C22⋊C4—46no—
1099C22⋊C42−1+414yes—
1100C42—22no—
1101C42—26no—
1102C42—26no—
1103C42—26no—
1104C42—26no—
1105C42—26no—
1106C42—26no—
1107C42—26no—
1108C42—26no—
1109C42—26no—
1110C42—26no—
1111C42—26no—
1112C42—26no—
1113C42—22no—
1114C42—43no—
1115C42—43no—
1116C42—46no—
1117C42—46no—
1118C42—43no—
1119C42—43no—
1120C42—43no—
1121C42—46no—
1122C42C2×#41112yes—
1123C23—21no—
1124C23—21no—
1125C23—21no—
1126C23—21no—
1127C23—21no—
1128C23—21no—
1129C23—23no—
1130C23—23no—
1131C23—23no—
1132C23—23no—
1133C23—23no—
1134C23—23no—
1135C23—23no—
1136C23—23no—
1137C23—23no—
1138C23—23no—
1139C23—23no—
1140C23—23no—
1141C23—23no—
1142C23—23no—
1143C23C2×2−1+412yes—
1144C23C2611yescharacteristic
1145Q8—44no—
1146Q8—412no—
1147Q8—86no—
1148Q8—86no—
1149Q8—166no—
1150Q8#542116yes—
1151D4—412no—
1152D4—412no—
1153D4—412no—
1154D4—86no—
1155D4—86no—
1156D4—166no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—23no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—23no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—23no—
1171C2×C4—23no—
1172C2×C4—23no—
1173C2×C4—23no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—23no—
1180C2×C4—23no—
1181C2×C4—23no—
1182C2×C4—23no—
1183C2×C4—23no—
1184C2×C4—23no—
1185C2×C4—23no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—23no—
1193C2×C4—23no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—23no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—23no—
1203C2×C4—23no—
1204C2×C4—23no—
1205C2×C4—23no—
1206C2×C4—23no—
1207C2×C4—21no—
1208C2×C4—23no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—23no—
1212C2×C4—21no—
1213C2×C4—21no—
1214C2×C4—23no—
1215C2×C4—23no—
1216C2×C4—23no—
1217C2×C4—23no—
1218C2×C4—23no—
1219C2×C4—23no—
1220C2×C4—23no—
1221C2×C4—21no—
1222C2×C4—21no—
1223C2×C4—23no—
1224C2×C4—23no—
1225C2×C4—23no—
1226C2×C4—23no—
1227C2×C4—21no—
1228C2×C4—23no—
1229C2×C4—23no—
1230C2×C4—23no—
1231C2×C4—23no—
1232C2×C4—21no—
1233C2×C4—412no—
1234C2×C4—44no—
1235C2×C4—412no—
1236C2×C4—412no—
1237C2×C4—412no—
1238C2×C4—86no—
1239C2×C4—86no—
1240C2×C4—166no—
1241C2×C4C22×#4112yes—
1242C2×C4C22×#4116yes—
1243C2×C4C22×#4116yes—
1244C2×C4C2×H(5,𝔽2)16yes—
1245C2×C4C2×2−1+412yes—
1246C2×C4C2×2−1+412yes—
1247C2×C4C2×2−1+416yes—
1248C2×C4#58512yes—
1249C22—22no—
1250C22—22no—
1251C22—22no—
1252C22—41no—
1253C22—41no—
1254C22—41no—
1255C22—41no—
1256C22—43no—
1257C22—43no—
1258C22—43no—
1259C22—43no—
1260C22—43no—
1261C22—43no—
1262C22—43no—
1263C22—43no—
1264C22—43no—
1265C22—43no—
1266C22—43no—
1267C22—43no—
1268C22—43no—
1269C22—43no—
1270C22C23×#4111yescharacteristic
1271C22C22×H(5,𝔽2)11yescharacteristic
1272C22C22×2−1+411yescharacteristic
1273C22C22×2−1+411yescharacteristic
1274C22C2×#58511yescharacteristic
1275C22H(7,𝔽2)11yescharacteristic
1276C22H(7,𝔽2)11yescharacteristic
1277C4—22no—
1278C4—26no—
1279C4—22no—
1280C4—22no—
1281C4—22no—
1282C4—41no—
1283C4—41no—
1284C4—43no—
1285C4—43no—
1286C4—43no—
1287C4—41no—
1288C4—41no—
1289C4—43no—
1290C4—41no—
1291C4—43no—
1292C4—43no—
1293C4—43no—
1294C4—43no—
1295C4—41no—
1296C4—43no—
1297C4—41no—
1298C4—41no—
1299C4—43no—
1300C4—41no—
1301C4—41no—
1302C4—43no—
1303C4—43no—
1304C4C2×#542112yes—
1305C2—42no—
1306C2—83no—
1307C2—83no—
1308C2C22×#54211yescharacteristic
1309C2#6294311yescharacteristic
1310C2#6295211yescharacteristic
1311C2#6300011yescharacteristic
1312C2#6300611yescharacteristic
1313C2#6301511yescharacteristic
1314C2#6306611yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#36430C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #52250C2semidirect
2. #42707C2semidirect
3. #42699C2semidirect
4. #42635C2semidirect
5. #42632C2semidirect
6. #42554C2semidirect
7. #42514C2semidirect
8. #40174C2semidirect
9. #40127C2semidirect
10. #40050C2semidirect
11. #39925C2semidirect
12. #39608C2semidirect
13. #39216C2semidirect
14. #37345C2semidirect
15. #37333C2semidirect
16. #37294C2semidirect
17. #36578C2semidirect
18. Q8×#126C2semidirect
19. Q8×C22⋊Q8C2semidirect
20. #36457C2semidirect
21. #36445C2semidirect
23. #36005C2semidirect
24. #35937C2semidirect
25. #35898C2semidirect
26. #35854C2semidirect
27. #35854C2semidirect
28. #35816C2semidirect
29. #34336C2semidirect
30. #34294C2semidirect
31. #34193C2semidirect

Maximal subgroups

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

subgroupindex
#522502
#427072
#426992
#426352
#426322
#425542
#425142
#401742
#401272
#400502
#399252
#396082
#392162
#373452
#373332
#372942
#365782
Q8×#1262
Q8×C22⋊Q82
#364572
#364452
#364302
#360052
#359372
#358982
#358542
#358162
#343362
#342942
#341932