Finite Group Databasebeta

← #7655996

Subgroups — #7655996

Order 512.

5580 conjugacy classes of subgroups.

The subgroup lattice has 1442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42759C213yesmaximal, complemented
2#42752C213yesmaximal, complemented
3#42617C213yesmaximal, complemented
4#42608C213yesmaximal, complemented
5#42529C213yesmaximal, complemented
6#42508C213yesmaximal, complemented
7#42471C213yesmaximal, complemented
8#42460C213yesmaximal, complemented
9#40054C213yesmaximal, complemented
10#40046C213yesmaximal, complemented
11#39410C213yesmaximal, complemented
12#39402C213yesmaximal, complemented
13#37587C213yesmaximal, complemented
14#37570C213yesmaximal, complemented
15#36578C211yesmaximal, characteristic, complemented
16#36576C211yesmaximal, characteristic, complemented
17#36455C211yesmaximal, characteristic, complemented
18#36433C211yesmaximal, characteristic, complemented
19#36066C211yesmaximal, characteristic, complemented
20#36029C211yesmaximal, characteristic, complemented
21#36029C211yesmaximal, characteristic, complemented
22#36005C211yesmaximal, characteristic, complemented
23#35996C211yesmaximal, characteristic, complemented
24#35868C211yesmaximal, characteristic, complemented
25#35831C211yesmaximal, characteristic, complemented
26#35831C211yesmaximal, characteristic, complemented
27#35171C213yesmaximal, complemented
28#34597C213yesmaximal, complemented
29#34313C211yesmaximal, characteristic, complemented
30#34263C211yesmaximal, characteristic, complemented
31C4×#548C211yesmaximal, characteristic, complemented
32C2×#550C2211yescharacteristic
33C2×#550C2211yescharacteristic
34C2×#550C2211yescharacteristic
35C2×#550C2211yescharacteristic
36C2×#550C2211yescharacteristic
37C2×#550C2211yescharacteristic
38C2×#548C2211yescharacteristic
39C2×#548C2211yescharacteristic
40C2×#548C2211yescharacteristic
41C2×#548C2211yescharacteristic
42C2×#540C2216yes—
43C2×#520C2211yescharacteristic
44C2×#520C2211yescharacteristic
45C2×#520C2211yescharacteristic
46C2×C4×#41C2211yescharacteristic
47C22×C4×Q8C2211yescharacteristic
48#2856C2213yes—
49#2856C2213yes—
50#2854C2213yes—
51#2854C2213yes—
52#2837C2216yes—
53#2829C2216yes—
54#2828C2216yes—
55#2828C2216yes—
56#2797C2216yes—
57#2786C2216yes—
58#2780C2216yes—
59#2748C2216yes—
60#2743C2216yes—
61#2711C2216yes—
62#2709C2216yes—
63#2707C2216yes—
64#2703C2216yes—
65#2701C2216yes—
66#2699C2216yes—
67#2688C2216yes—
68#2688C2216yes—
69#2673C2216yes—
70#2671C2216yes—
71#2671C2216yes—
72#2667C2211yescharacteristic
73#2667C2213yes—
74#2661C2213yes—
75#2661C2213yes—
76#2661C2216yes—
77#2657C2213yes—
78#2654C2213yes—
79#2654C2213yes—
80#2651C2213yes—
81#2651C2213yes—
82#2649C2213yes—
83#2649C2213yes—
84#2648C2216yes—
85#2648C2216yes—
86#2648C2213yes—
87#2648C2213yes—
88#2647C2213yes—
89#2635C2216yes—
90#2635C2213yes—
91#2635C2213yes—
92#2630C2213yes—
93#2630C2213yes—
94#2630C2216yes—
95#2625C2213yes—
96#2624C2213yes—
97#2620C2213yes—
98#2620C2213yes—
99#2619C2213yes—
100#2619C2213yes—
101#2570C2213yes—
102#2552C2213yes—
103#2548C2213yes—
104#2544C2213yes—
105#2544C2213yes—
106#2541C2213yes—
107#2541C2213yes—
108#2541C2213yes—
109#2541C2213yes—
110#2541C2213yes—
111#2541C2213yes—
112#2540C2213yes—
113#2540C2213yes—
114#2540C2213yes—
115#2538C2213yes—
116#2537C2213yes—
117#2537C2213yes—
118#2537C2213yes—
119#2535C2213yes—
120#2535C2213yes—
121#2509C2213yes—
122#2507C2213yes—
123#2506C2213yes—
124#2506C2213yes—
125#2504C2213yes—
126#2502C2213yes—
127#2501C2213yes—
128#2500C2213yes—
129#2490C2216yes—
130#2487C2213yes—
131#2487C2213yes—
132#2486C2213yes—
133#2485C2213yes—
134#2476C2216yes—
135#2471C2216yes—
136#2464C2216yes—
137#2464C2216yes—
138#2464C2216yes—
139#2457C2216yes—
140#2448C2213yes—
141#2448C2213yes—
142#2447C2213yes—
143#2447C2213yes—
144#2445C2213yes—
145#2445C2213yes—
146#2445C2213yes—
147#2445C2213yes—
148#2428C2213yes—
149#2428C2213yes—
150#2428C2216yes—
151#2428C2213yes—
152#2428C2213yes—
153#2428C2213yes—
154#2428C2213yes—
155#2428C2213yes—
156#2428C2213yes—
157#2427C2213yes—
158#2427C2213yes—
159#2426C2213yes—
160#2426C2213yes—
161#2422C2213yes—
162#2422C2213yes—
163#2422C2213yes—
164#2422C2213yes—
165#2422C2213yes—
166#2421C2213yes—
167#2421C2213yes—
168#2420C2213yes—
169#2417C2213yes—
170#2417C2213yes—
171#2416C2213yes—
172#2416C2213yes—
173#2416C2213yes—
174#2416C2213yes—
175#2416C2213yes—
176#2416C2213yes—
177#2416C2213yes—
178#2416C2213yes—
179#2414C2213yes—
180#2414C2213yes—
181#2402C2213yes—
182#2397C2213yes—
183#2395C2213yes—
184#2395C2213yes—
185#2392C2213yes—
186#2392C2213yes—
187#2392C2213yes—
188#2392C2213yes—
189#2367C2213yes—
190#2366C2213yes—
191#2362C2213yes—
192#2361C2213yes—
193#2361C2213yes—
194#2361C2213yes—
195#2357C2213yes—
196#2354C2213yes—
197#2352C2213yes—
198#2351C2211yescharacteristic
199#2351C2211yescharacteristic
200#2351C2211yescharacteristic
201Q8×C4⋊C4C2211yescharacteristic
202Q8×C4⋊C4C2211yescharacteristic
203Q8×C4⋊C4C2211yescharacteristic
204Q8×C4⋊C4C2211yescharacteristic
205Q8×C4⋊C4C2211yescharacteristic
206D4×C4⋊C4C2213yes—
207#2345C2213yes—
208#2344C2213yes—
209#2341C2211yescharacteristic
210#2341C2211yescharacteristic
211#2341C2211yescharacteristic
212#2341C2211yescharacteristic
213#2341C2211yescharacteristic
214#2341C2211yescharacteristic
215#2341C2211yescharacteristic
216#2341C2211yescharacteristic
217Q8×C22⋊C4C2211yescharacteristic
218Q8×C22⋊C4C2211yescharacteristic
219#2324C2213yes—
220#2324C2213yes—
221#2324C2216yes—
222#2319C2213yes—
223#2314C2213yes—
224C4×#127C2213yes—
225C4×#124C2213yes—
226C4×C22⋊Q8C2213yes—
227C4×#123C2213yes—
228C4×#123C2213yes—
229C4×#121C2213yes—
230C4×#121C2213yes—
231C4×#121C2213yes—
232#2298C2213yes—
233#2293C2213yes—
234#2293C2213yes—
235#2276C2211yescharacteristic
236C42×Q8C2211yescharacteristic
237C42×D4C2213yes—
238C22×#41C2311yescharacteristic
239C22×#41C2311yescharacteristic
240C22×#41C2311yescharacteristic
241C22×#41C2311yescharacteristic
242C23×Q8C2311yescharacteristic
243#550—28no—
244#550—44no—
245#550—44no—
246#550—44no—
247#550—44no—
248#550—44no—
249#548—28no—
250#548—44no—
251#548—44no—
252#548—44no—
253#540—424no—
254C2×#127C2313yes—
255C2×#127C2313yes—
256C2×#127C2313yes—
257C2×#127C2313yes—
258C2×#127C2313yes—
259C2×#127C2313yes—
260C2×#127C2316yes—
261C2×#125C2316yes—
262C2×#124C2313yes—
263C2×#124C2313yes—
264C2×#124C2313yes—
265C2×#124C2313yes—
266C2×#123C2313yes—
267C2×#123C2316yes—
268C2×#123C2313yes—
269C2×#123C2316yes—
270C2×#123C2316yes—
271C2×#123C2316yes—
272C2×C22⋊Q8C2313yes—
273C2×C22⋊Q8C2313yes—
274C2×C22⋊Q8C2313yes—
275C2×C22⋊Q8C2313yes—
276C2×#121C2313yes—
277C2×#121C2313yes—
278C2×#121C2313yes—
279C2×#121C2313yes—
280C2×#121C2316yes—
281C2×#121C2313yes—
282C2×#121C2313yes—
283C2×#121C2316yes—
284C2×#121C2313yes—
285C2×#121C2313yes—
286C2×#121C2313yes—
287C2×#121C2313yes—
288C2×#121C2313yes—
289C2×#121C2313yes—
290C2×#121C2313yes—
291C2×#121C2313yes—
292C2×#121C2313yes—
293C2×#121C2313yes—
294C2×#121C2313yes—
295C2×#121C2313yes—
296C2×#121C2316yes—
297C2×#121C2316yes—
298C2×#121C2316yes—
299C2×#121C2316yes—
300C2×#121C2316yes—
301C2×#121C2316yes—
302C2×#121C2316yes—
303#520—28no—
304#520—44no—
305#520—44no—
306C4×#41—44no—
307C2×C4×Q8—44no—
308C2×C4×Q8C2311yescharacteristic
309C2×C4×Q8C2311yescharacteristic
310C2×C4×Q8C2311yescharacteristic
311C2×C4×Q8C2311yescharacteristic
312C2×C4×Q8C2311yescharacteristic
313C2×C4×Q8C2311yescharacteristic
314C2×C4×Q8C2311yescharacteristic
315C2×C4×Q8C2311yescharacteristic
316C2×C4×Q8C2311yescharacteristic
317C2×C4×Q8C2313yes—
318C2×C4×Q8C2313yes—
319C2×C4×Q8C2311yescharacteristic
320C2×C4×D4C2313yes—
321C2×C4×D4C2313yes—
322C2×C4×D4C2313yes—
323C2×C4×D4C2313yes—
324C2×C4×D4C2313yes—
325C2×C4×D4C2316yes—
326C2×C4×D4C2313yes—
327C2×C4×D4C2313yes—
328C2×C4×D4C2313yes—
329C2×C4×D4C2313yes—
330C2×C4×D4C2313yes—
331C2×C4×D4C2313yes—
332C2×C4×D4C2313yes—
333C2×C4×D4C2313yes—
334C2×C4×D4C2313yes—
335C2×C4×D4C2313yes—
336C2×C4×D4C2313yes—
337C2×C4×D4C2313yes—
338C2×C4×D4C2313yes—
339C2×C4×D4C2313yes—
340C2×C4×D4C2313yes—
341C2×C4×D4C2316yes—
342C2×#117C2313yes—
343C2×#117C2316yes—
344C2×#117C2313yes—
345C2×#117C2313yes—
346C2×#117C2313yes—
347C22×C4⋊C4C2313yes—
348C22×C4⋊C4C2313yes—
349C22×C4⋊C4C2313yes—
350C22×C4⋊C4C2313yes—
351C22×C42C2313yes—
352C22×C42C2313yes—
353#400C2313yes—
354#400C2316yes—
355#400C2316yes—
356#400C2313yes—
357#400C2313yes—
358#400C2313yes—
359#400C2313yes—
360#400C2313yes—
361#399C2316yes—
362#399C2313yes—
363#399C2316yes—
364#399C2311yescharacteristic
365#399C2313yes—
366#399C2311yescharacteristic
367#399C2313yes—
368#399C2313yes—
369#398C2316yes—
370#398C2316yes—
371#398C2316yes—
372#398C2313yes—
373#398C2313yes—
374#398C2311yescharacteristic
375#398C2311yescharacteristic
376#398C2313yes—
377#398C2313yes—
378#398C2311yescharacteristic
379#398C2313yes—
380#398C2311yescharacteristic
381#398C2313yes—
382#397C2313yes—
383#397C2316yes—
384#397C2316yes—
385#397C2316yes—
386#397C2313yes—
387#397C2316yes—
388#397C2313yes—
389#397C2316yes—
390#397C2313yes—
391#397C2313yes—
392#397C2313yes—
393#397C2313yes—
394#397C2313yes—
395#397C2313yes—
396#397C2313yes—
397#396C2316yes—
398#396C2316yes—
399#396C2316yes—
400#396C2316yes—
401#396C2313yes—
402#396C2313yes—
403#396C2311yescharacteristic
404#396C2313yes—
405#396C2313yes—
406#396C2313yes—
407#396C2311yescharacteristic
408#396C2313yes—
409#394C2313yes—
410#394C2313yes—
411#394C2316yes—
412#394C2316yes—
413#394C2316yes—
414#394C2316yes—
415#394C2316yes—
416#394C2316yes—
417#394C2316yes—
418#394C2316yes—
419#394C2313yes—
420#394C2316yes—
421#394C2316yes—
422#394C2316yes—
423#394C2316yes—
424#394C2316yes—
425#394C2316yes—
426#394C2316yes—
427#394C2313yes—
428#394C2313yes—
429#394C2313yes—
430#394C2313yes—
431#394C2313yes—
432#394C2313yes—
433#394C2313yes—
434#394C2313yes—
435#394C2313yes—
436#394C2313yes—
437#394C2313yes—
438#394C2313yes—
439#394C2313yes—
440#392C2316yes—
441#392C2316yes—
442#392C2316yes—
443#392C2316yes—
444#392C2316yes—
445#392C2316yes—
446#392C2316yes—
447#392C2316yes—
448#392C2316yes—
449#392C2313yes—
450#392C2313yes—
451#392C2313yes—
452#392C2313yes—
453#392C2313yes—
454#392C2313yes—
455#392C2313yes—
456#392C2313yes—
457#391C2313yes—
458#391C2313yes—
459#391C2313yes—
460#391C2313yes—
461#390C2313yes—
462#390C2316yes—
463#390C2313yes—
464#390C2313yes—
465#390C2313yes—
466#390C2313yes—
467#390C2313yes—
468#390C2313yes—
469#390C2313yes—
470#390C2313yes—
471#390C2316yes—
472#390C2316yes—
473#390C2313yes—
474#390C2313yes—
475#390C2313yes—
476#390C2313yes—
477#390C2313yes—
478#390C2313yes—
479#390C2313yes—
480#390C2313yes—
481#390C2313yes—
482#390C2313yes—
483#390C2316yes—
484#390C2316yes—
485#390C2316yes—
486#390C2316yes—
487#390C2313yes—
488#389C2313yes—
489#389C2313yes—
490#389C2313yes—
491#389C2313yes—
492#389C2313yes—
493#389C2313yes—
494#389C2316yes—
495#389C2313yes—
496#389C2313yes—
497#389C2313yes—
498#389C2313yes—
499#389C2313yes—
500#389C2313yes—
501#389C2313yes—
502#389C2313yes—
503#389C2313yes—
504#389C2313yes—
505#389C2313yes—
506#389C2311yescharacteristic
507#389C2311yescharacteristic
508#389C2313yes—
509#388C2316yes—
510#388C2316yes—
511#388C2313yes—
512#388C2316yes—
513#388C2316yes—
514#388C2313yes—
515#388C2313yes—
516#388C2313yes—
517#388C2313yes—
518#388C2316yes—
519#388C2316yes—
520#388C2316yes—
521#388C2313yes—
522#388C2313yes—
523#388C2313yes—
524#388C2316yes—
525#388C2313yes—
526#388C2313yes—
527#388C2313yes—
528#388C2313yes—
529#388C2313yes—
530#388C2313yes—
531#388C2313yes—
532#388C2313yes—
533#387C2313yes—
534#387C2316yes—
535#387C2316yes—
536#387C2316yes—
537#387C2313yes—
538#387C2313yes—
539#387C2316yes—
540#387C2311yescharacteristic
541#387C2313yes—
542#387C2313yes—
543#387C2311yescharacteristic
544#387C2313yes—
545#386C2316yes—
546#386C2316yes—
547#386C2316yes—
548#386C2316yes—
549#386C2316yes—
550#386C2316yes—
551#386C2316yes—
552#386C2313yes—
553#386C2313yes—
554#386C2316yes—
555#386C2313yes—
556#386C2313yes—
557#386C2313yes—
558#386C2313yes—
559#386C2316yes—
560#386C2316yes—
561#386C2316yes—
562#386C2316yes—
563#386C2316yes—
564#386C2316yes—
565#385C2316yes—
566#385C2316yes—
567#385C2316yes—
568#385C2316yes—
569#385C2316yes—
570#385C2313yes—
571#385C2313yes—
572#385C2316yes—
573#384C2313yes—
574#384C2313yes—
575#384C2313yes—
576#384C2313yes—
577#384C2313yes—
578#382C2313yes—
579#382C2313yes—
580#382C2313yes—
581#381C2316yes—
582#381C2311yescharacteristic
583#381C2313yes—
584#381C2316yes—
585#380C2313yes—
586#380C2313yes—
587#380C2316yes—
588#380C2313yes—
589#380C2313yes—
590#380C2316yes—
591#380C2313yes—
592#380C2313yes—
593#380C2313yes—
594#380C2313yes—
595#380C2313yes—
596#380C2313yes—
597#380C2311yescharacteristic
598#380C2313yes—
599#380C2316yes—
600C4×C4⋊C4C2313yes—
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×C4⋊C4C2313yes—
611C4×C4⋊C4C2313yes—
612C4×C4⋊C4C2313yes—
613C4×C4⋊C4C2313yes—
614C4×C4⋊C4C2313yes—
615C4×C4⋊C4C2313yes—
616C4×C22⋊C4C2313yes—
617C4×C22⋊C4C2313yes—
618C4×C22⋊C4C2313yes—
619C4×C22⋊C4C2313yes—
620C4×C22⋊C4C2313yes—
621C4×C22⋊C4C2313yes—
622C4×C22⋊C4C2313yes—
623C4×C22⋊C4C2313yes—
624C4×C22⋊C4C2313yes—
625C4×C22⋊C4C2313yes—
626C4×C22⋊C4C2316yes—
627C4×C22⋊C4C2313yes—
628C4×C22⋊C4C2313yes—
629C4×C22⋊C4C2313yes—
630C4×C22⋊C4C2311yescharacteristic
631C4×C22⋊C4C2316yes—
632#376C2313yes—
633C43C2313yes—
634C2×#41—24no—
635C2×#41—24no—
636C2×#41—24no—
637C2×#41—24no—
638C2×#41—24no—
639C2×#41—24no—
640C2×#41—24no—
641C2×#41—24no—
642C2×#41—24no—
643C2×#41—24no—
644C2×#41—24no—
645C2×#41—24no—
646C22×Q8—24no—
647C22×Q8—24no—
648C22×Q8—24no—
649C22×Q8C2413yes—
650C22×Q8C2411yescharacteristic
651C22×D4C2413yes—
652C22×D4C2413yes—
653C22×D4C2413yes—
654C22×D4C2413yes—
655C22×D4C2413yes—
656C22×D4C2413yes—
657C22×D4C2413yes—
658C22×D4C2413yes—
659C22×D4C2413yes—
660C22×D4C2413yes—
661C22×D4C2413yes—
662C22×D4C2416yes—
663C22×D4C2413yes—
664C22×D4C2413yes—
665C22×D4C2413yes—
666C22×D4C2416yes—
667C22×D4C2416yes—
668C22×D4C2416yes—
669C22×D4C2416yes—
670C22×D4C2416yes—
671C23×C4C2413yes—
672C23×C4C2413yes—
673C23×C4C2413yes—
674C23×C4C2413yes—
675C23×C4C2413yes—
676C23×C4C2416yes—
677C23×C4C2413yes—
678C23×C4C2413yes—
679C23×C4C2413yes—
680C23×C4C2416yes—
681C23×C4C2416yes—
682C23×C4C2411yescharacteristic
683#127—212no—
684#127—46no—
685#127—46no—
686#127—46no—
687#127—46no—
688#127—46no—
689#127—412no—
690#125—412no—
691#124—212no—
692#124—46no—
693#124—46no—
694#124—46no—
695#123—212no—
696#123—412no—
697#123—412no—
698#123—46no—
699#123—412no—
700#123—86no—
701C22⋊Q8—212no—
702C22⋊Q8—46no—
703C22⋊Q8—46no—
704C22⋊Q8—46no—
705#121—212no—
706#121—212no—
707#121—212no—
708#121—212no—
709#121—412no—
710#121—412no—
711#121—412no—
712#121—412no—
713#121—412no—
714#121—412no—
715#121—46no—
716#121—46no—
717#121—46no—
718#121—46no—
719#121—46no—
720#121—46no—
721#121—46no—
722#121—46no—
723#121—46no—
724#121—46no—
725#121—46no—
726#121—46no—
727#121—46no—
728#121—46no—
729#121—86no—
730#121—86no—
731#121—86no—
732C4×Q8—24no—
733C4×Q8—24no—
734C4×Q8—24no—
735C4×Q8—24no—
736C4×Q8—24no—
737C4×Q8—24no—
738C4×Q8—24no—
739C4×Q8—24no—
740C4×Q8—24no—
741C4×Q8—46no—
742C4×Q8—46no—
743C4×Q8#4118yes—
744C4×D4—212no—
745C4×D4—212no—
746C4×D4—212no—
747C4×D4—212no—
748C4×D4—212no—
749C4×D4—412no—
750C4×D4—46no—
751C4×D4—46no—
752C4×D4—46no—
753C4×D4—46no—
754C4×D4—46no—
755C4×D4—46no—
756C4×D4—46no—
757C4×D4—46no—
758C4×D4—46no—
759C4×D4—46no—
760C4×D4—46no—
761C4×D4—46no—
762C4×D4—46no—
763C4×D4—46no—
764C4×D4—46no—
765C4×D4—86no—
766#117—212no—
767#117—46no—
768#117—46no—
769#117—412no—
770#117—46no—
771C2×C4⋊C4—212no—
772C2×C4⋊C4—46no—
773C2×C4⋊C4—46no—
774C2×C4⋊C4—46no—
775C2×C4⋊C4C2413yes—
776C2×C4⋊C4C2413yes—
777C2×C4⋊C4C2413yes—
778C2×C4⋊C4C2413yes—
779C2×C4⋊C4C2413yes—
780C2×C4⋊C4C2413yes—
781C2×C4⋊C4C2413yes—
782C2×C4⋊C4C2411yescharacteristic
783C2×C4⋊C4C2413yes—
784C2×C4⋊C4C2413yes—
785C2×C4⋊C4C2411yescharacteristic
786C2×C4⋊C4C2413yes—
787C2×C4⋊C4C2413yes—
788C2×C4⋊C4C2413yes—
789C2×C4⋊C4C2413yes—
790C2×C4⋊C4C2413yes—
791C2×C4⋊C4C2411yescharacteristic
792C2×C4⋊C4C2413yes—
793C2×C4⋊C4C2413yes—
794C2×C4⋊C4C2411yescharacteristic
795C2×C4⋊C4C2413yes—
796C2×C4⋊C4C2413yes—
797C2×C4⋊C4C2416yes—
798C2×C4⋊C4C2411yescharacteristic
799C2×C4⋊C4C2411yescharacteristic
800C2×C4⋊C4C2416yes—
801C2×C4⋊C4C2411yescharacteristic
802C2×C4⋊C4C2411yescharacteristic
803C2×C4⋊C4C2411yescharacteristic
804C2×C4⋊C4C2411yescharacteristic
805C2×C4⋊C4C2411yescharacteristic
806C2×C4⋊C4C2413yes—
807C2×C4⋊C4C2416yes—
808C2×C4⋊C4C2413yes—
809C2×C4⋊C4C2413yes—
810C2×C4⋊C4C2413yes—
811C2×C4⋊C4C2413yes—
812C2×C4⋊C4C2413yes—
813C2×C4⋊C4C2416yes—
814C2×C4⋊C4C2416yes—
815C2×C4⋊C4C2416yes—
816C2×C4⋊C4C2413yes—
817C2×C4⋊C4C2413yes—
818C2×C4⋊C4C2411yescharacteristic
819C2×C4⋊C4C2411yescharacteristic
820C2×C4⋊C4C2411yescharacteristic
821C2×C4⋊C4C2413yes—
822C2×C4⋊C4C2413yes—
823C2×C22⋊C4C2413yes—
824C2×C22⋊C4C2413yes—
825C2×C22⋊C4C2413yes—
826C2×C22⋊C4C2411yescharacteristic
827C2×C22⋊C4C2411yescharacteristic
828C2×C22⋊C4C2413yes—
829C2×C22⋊C4C2413yes—
830C2×C22⋊C4C2413yes—
831C2×C22⋊C4C2413yes—
832C2×C22⋊C4C2413yes—
833C2×C22⋊C4C2413yes—
834C2×C22⋊C4C2413yes—
835C2×C22⋊C4C2413yes—
836C2×C22⋊C4C2413yes—
837C2×C22⋊C4C2413yes—
838C2×C22⋊C4C2416yes—
839C2×C22⋊C4C2413yes—
840C2×C22⋊C4C2413yes—
841C2×C22⋊C4C2416yes—
842C2×C22⋊C4C2413yes—
843C2×C22⋊C4C2413yes—
844C2×C22⋊C4C2416yes—
845C2×C22⋊C4C2411yescharacteristic
846C2×C22⋊C4C2411yescharacteristic
847C2×C22⋊C4C2411yescharacteristic
848C2×C22⋊C4C2413yes—
849C2×C22⋊C4C2413yes—
850C2×C22⋊C4C2413yes—
851C2×C22⋊C4C2413yes—
852C2×C22⋊C4C2413yes—
853C2×C22⋊C4C2413yes—
854C2×C22⋊C4C2413yes—
855C2×C22⋊C4C2413yes—
856C2×C22⋊C4C2413yes—
857C2×C22⋊C4C2413yes—
858C2×C22⋊C4C2416yes—
859C2×C22⋊C4C2416yes—
860C2×C22⋊C4C2413yes—
861C2×C22⋊C4C2413yes—
862C2×C22⋊C4C2413yes—
863C2×C22⋊C4C2413yes—
864C2×C22⋊C4C2413yes—
865C2×C22⋊C4C2416yes—
866C2×C22⋊C4C2416yes—
867C2×C22⋊C4C2416yes—
868C2×C22⋊C4C2416yes—
869C2×C22⋊C4C2416yes—
870C2×C22⋊C4C2416yes—
871C2×C22⋊C4C2416yes—
872C2×C22⋊C4C2413yes—
873C2×C22⋊C4C2413yes—
874C2×C22⋊C4C2416yes—
875C2×C22⋊C4C2413yes—
876C2×C22⋊C4C2413yes—
877C2×C22⋊C4C2413yes—
878C2×C22⋊C4C2413yes—
879C2×C22⋊C4C2411yescharacteristic
880C2×C22⋊C4C2413yes—
881C2×C22⋊C4C2413yes—
882C2×C42—46no—
883C2×C42—46no—
884C2×C42C2413yes—
885C2×C42C2413yes—
886C2×C42C2413yes—
887C2×C42C2413yes—
888C2×C42C2413yes—
889C2×C42C2413yes—
890C2×C42C2413yes—
891C2×C42C2413yes—
892C2×C42C2413yes—
893C2×C42C2413yes—
894C2×C42C2413yes—
895C2×C42C2416yes—
896C2×C42C2413yes—
897C2×C42C2413yes—
898C2×C42C2413yes—
899C2×C42C2413yes—
900C2×C42C2411yescharacteristic
901C2×C42C2411yescharacteristic
902C2×C42C2413yes—
903#95C2411yescharacteristic
904#95C2413yes—
905#95C2413yes—
906#95C2413yes—
907#95C2411yescharacteristic
908#95C2411yescharacteristic
909#95C2411yescharacteristic
910#95C2411yescharacteristic
911#95C2411yescharacteristic
912#95C2411yescharacteristic
913#95C2411yescharacteristic
914#95C2411yescharacteristic
915#95C2411yescharacteristic
916#95C2413yes—
917#95C2413yes—
918#95C2413yes—
919#95C2413yes—
920#95C2413yes—
921#95C2413yes—
922#95C2413yes—
923#95C2413yes—
924#95C2413yes—
925#95C2413yes—
926#95C2416yes—
927#95C2413yes—
928#95C2413yes—
929#95C2416yes—
930#95C2416yes—
931#95C2413yes—
932#95C2413yes—
933#95C2416yes—
934#95C2411yescharacteristic
935#95C2411yescharacteristic
936#95C2413yes—
937#95C2413yes—
938#95C2413yes—
939#95C2413yes—
940#95C2413yes—
941#95C2413yes—
942#95C2413yes—
943#95C2413yes—
944#95C2413yes—
945#95C2413yes—
946#95C2413yes—
947#95C2416yes—
948#95C2416yes—
949C24C2513yes—
950C24C2513yes—
951C24C2513yes—
952C24C2513yes—
953C24C2511yescharacteristic
954#41—416no—
955#41—416no—
956#41—416no—
957#41—416no—
958C2×Q8—26no—
959C2×Q8—26no—
960C2×Q8—26no—
961C2×Q8—416no—
962C2×Q8C2×#4114yes—
963C2×Q8H(5,𝔽2)14yes—
964C2×Q8H(5,𝔽2)14yes—
965C2×D4—26no—
966C2×D4—26no—
967C2×D4—26no—
968C2×D4—26no—
969C2×D4—26no—
970C2×D4—26no—
971C2×D4—26no—
972C2×D4—26no—
973C2×D4—26no—
974C2×D4—26no—
975C2×D4—212no—
976C2×D4—26no—
977C2×D4—26no—
978C2×D4—26no—
979C2×D4—26no—
980C2×D4—26no—
981C2×D4—26no—
982C2×D4—26no—
983C2×D4—26no—
984C2×D4—26no—
985C2×D4—26no—
986C2×D4—43no—
987C2×D4—43no—
988C2×D4—43no—
989C2×D4—43no—
990C2×D4—43no—
991C2×D4—43no—
992C2×D4—46no—
993C2×D4—43no—
994C2×D4—43no—
995C2×D4—43no—
996C2×D4—43no—
997C2×D4—43no—
998C2×D4—46no—
999C2×D4—43no—
1000C2×D4—43no—
1001C2×D4—43no—
1002C2×D4—43no—
1003C2×D4—43no—
1004C2×D4—43no—
1005C2×D4—43no—
1006C2×D4—43no—
1007C2×D4—43no—
1008C2×D4—43no—
1009C2×D4—43no—
1010C2×D4—46no—
1011C2×D4—46no—
1012C2×D4—46no—
1013C2×D4—46no—
1014C2×D4—46no—
1015C2×D4—46no—
1016C2×D4—46no—
1017C2×D4—46no—
1018C2×D4—46no—
1019C2×D4—46no—
1020C2×D4—46no—
1021C2×D4—46no—
1022C2×D4—46no—
1023C2×D4—46no—
1024C2×D4—46no—
1025C22×C4—26no—
1026C22×C4—26no—
1027C22×C4—26no—
1028C22×C4—26no—
1029C22×C4—26no—
1030C22×C4—26no—
1031C22×C4—26no—
1032C22×C4—26no—
1033C22×C4—26no—
1034C22×C4—26no—
1035C22×C4—26no—
1036C22×C4—26no—
1037C22×C4—26no—
1038C22×C4—26no—
1039C22×C4—26no—
1040C22×C4—212no—
1041C22×C4—26no—
1042C22×C4—26no—
1043C22×C4—41no—
1044C22×C4—41no—
1045C22×C4—43no—
1046C22×C4—43no—
1047C22×C4—43no—
1048C22×C4—46no—
1049C22×C4—43no—
1050C22×C4—46no—
1051C22×C4—43no—
1052C22×C4—43no—
1053C22×C4—43no—
1054C22×C4—46no—
1055C22×C4—46no—
1056C22×C4—46no—
1057C22×C4—46no—
1058C22×C4—46no—
1059C22×C4—46no—
1060C22×C4H(5,𝔽2)14yes—
1061C22×C4C2511yescharacteristic
1062C22×C4C2511yescharacteristic
1063C22×C4C2511yescharacteristic
1064C22×C4C2511yescharacteristic
1065C22×C4C2513yes—
1066C22×C4C2513yes—
1067C22×C4C2513yes—
1068C22×C4C2513yes—
1069C22×C4C2511yescharacteristic
1070C22×C4C2513yes—
1071C22×C4C2511yescharacteristic
1072C22×C4C2511yescharacteristic
1073C22×C4C2513yes—
1074C22×C4C2513yes—
1075C22×C4C2513yes—
1076C22×C4C2511yescharacteristic
1077C22×C4C2511yescharacteristic
1078C22×C4C2511yescharacteristic
1079C22×C4C2513yes—
1080C22×C4C2513yes—
1081C22×C4C2511yescharacteristic
1082C22×C4C2513yes—
1083C22×C4C2511yescharacteristic
1084C22×C4C2511yescharacteristic
1085C22×C4C2511yescharacteristic
1086C22×C4C2513yes—
1087C4⋊C4—26no—
1088C4⋊C4—26no—
1089C4⋊C4—22no—
1090C4⋊C4—22no—
1091C4⋊C4—26no—
1092C4⋊C4—26no—
1093C4⋊C4—26no—
1094C4⋊C4—26no—
1095C4⋊C4—26no—
1096C4⋊C4—26no—
1097C4⋊C4—26no—
1098C4⋊C4—26no—
1099C4⋊C4—26no—
1100C4⋊C4—26no—
1101C4⋊C4—26no—
1102C4⋊C4—26no—
1103C4⋊C4—26no—
1104C4⋊C4—26no—
1105C4⋊C4—22no—
1106C4⋊C4—22no—
1107C4⋊C4—43no—
1108C4⋊C4—43no—
1109C4⋊C4—46no—
1110C4⋊C4—41no—
1111C4⋊C4—41no—
1112C4⋊C4—41no—
1113C4⋊C4—43no—
1114C4⋊C4—41no—
1115C4⋊C4—41no—
1116C4⋊C4—46no—
1117C4⋊C4—41no—
1118C4⋊C4—41no—
1119C4⋊C4—41no—
1120C4⋊C4—41no—
1121C4⋊C4—41no—
1122C4⋊C4—46no—
1123C4⋊C4—43no—
1124C4⋊C4—43no—
1125C4⋊C4—43no—
1126C4⋊C4—43no—
1127C4⋊C4—46no—
1128C4⋊C4—46no—
1129C4⋊C4—43no—
1130C4⋊C4—43no—
1131C4⋊C4—46no—
1132C4⋊C4—43no—
1133C4⋊C4—43no—
1134C4⋊C4C2×#41112yes—
1135C22⋊C4—26no—
1136C22⋊C4—26no—
1137C22⋊C4—26no—
1138C22⋊C4—26no—
1139C22⋊C4—22no—
1140C22⋊C4—26no—
1141C22⋊C4—26no—
1142C22⋊C4—26no—
1143C22⋊C4—212no—
1144C22⋊C4—26no—
1145C22⋊C4—26no—
1146C22⋊C4—26no—
1147C22⋊C4—26no—
1148C22⋊C4—26no—
1149C22⋊C4—22no—
1150C22⋊C4—26no—
1151C22⋊C4—43no—
1152C22⋊C4—43no—
1153C22⋊C4—41no—
1154C22⋊C4—43no—
1155C22⋊C4—43no—
1156C22⋊C4—43no—
1157C22⋊C4—43no—
1158C22⋊C4—46no—
1159C22⋊C4—46no—
1160C22⋊C4—43no—
1161C22⋊C4—41no—
1162C22⋊C4—41no—
1163C22⋊C4—41no—
1164C22⋊C4—43no—
1165C22⋊C4—43no—
1166C22⋊C4—43no—
1167C22⋊C4—43no—
1168C22⋊C4—43no—
1169C22⋊C4—43no—
1170C22⋊C4—43no—
1171C22⋊C4—43no—
1172C22⋊C4—43no—
1173C22⋊C4—43no—
1174C22⋊C4—43no—
1175C22⋊C4—43no—
1176C22⋊C4—43no—
1177C22⋊C4—46no—
1178C22⋊C4—46no—
1179C22⋊C4—43no—
1180C22⋊C4—43no—
1181C22⋊C4—46no—
1182C22⋊C4—46no—
1183C22⋊C4—46no—
1184C22⋊C4—46no—
1185C22⋊C4—46no—
1186C22⋊C4—46no—
1187C22⋊C4—46no—
1188C22⋊C4—43no—
1189C22⋊C4—46no—
1190C22⋊C4—43no—
1191C22⋊C4—43no—
1192C22⋊C4—43no—
1193C22⋊C4—43no—
1194C42—26no—
1195C42—26no—
1196C42—26no—
1197C42—26no—
1198C42—26no—
1199C42—26no—
1200C42—26no—
1201C42—26no—
1202C42—26no—
1203C42—26no—
1204C42—41no—
1205C42—43no—
1206C42—43no—
1207C42—43no—
1208C42—41no—
1209C42—46no—
1210C42—43no—
1211C42—43no—
1212C42C2×#41112yes—
1213C23—21no—
1214C23—21no—
1215C23—21no—
1216C23—21no—
1217C23—21no—
1218C23—21no—
1219C23—23no—
1220C23—23no—
1221C23—23no—
1222C23—23no—
1223C23—23no—
1224C23—23no—
1225C23—23no—
1226C23—23no—
1227C23—23no—
1228C23—23no—
1229C23—23no—
1230C23—23no—
1231C23—23no—
1232C23—23no—
1233C23—23no—
1234C23—23no—
1235C23—23no—
1236C23—23no—
1237C23—23no—
1238C23—23no—
1239C23—23no—
1240C23—23no—
1241C23—23no—
1242C23—23no—
1243C23—23no—
1244C23—23no—
1245C23—23no—
1246C23—23no—
1247C23C2×H(5,𝔽2)12yes—
1248C23C2611yescharacteristic
1249Q8—412no—
1250Q8#540116yescomplemented
1251D4—412no—
1252D4—412no—
1253D4—412no—
1254D4—412no—
1255D4—412no—
1256D4—412no—
1257D4—812no—
1258D4—86no—
1259D4—86no—
1260D4—86no—
1261D4—86no—
1262D4—86no—
1263D4—86no—
1264D4—86no—
1265D4—86no—
1266D4—166no—
1267D4—166no—
1268D4—166no—
1269D4—166no—
1270D4—166no—
1271C2×C4—21no—
1272C2×C4—21no—
1273C2×C4—21no—
1274C2×C4—23no—
1275C2×C4—23no—
1276C2×C4—21no—
1277C2×C4—21no—
1278C2×C4—21no—
1279C2×C4—21no—
1280C2×C4—21no—
1281C2×C4—21no—
1282C2×C4—23no—
1283C2×C4—21no—
1284C2×C4—21no—
1285C2×C4—23no—
1286C2×C4—21no—
1287C2×C4—21no—
1288C2×C4—21no—
1289C2×C4—21no—
1290C2×C4—21no—
1291C2×C4—21no—
1292C2×C4—21no—
1293C2×C4—23no—
1294C2×C4—23no—
1295C2×C4—23no—
1296C2×C4—23no—
1297C2×C4—23no—
1298C2×C4—23no—
1299C2×C4—23no—
1300C2×C4—23no—
1301C2×C4—23no—
1302C2×C4—21no—
1303C2×C4—23no—
1304C2×C4—23no—
1305C2×C4—23no—
1306C2×C4—23no—
1307C2×C4—23no—
1308C2×C4—23no—
1309C2×C4—23no—
1310C2×C4—21no—
1311C2×C4—21no—
1312C2×C4—21no—
1313C2×C4—23no—
1314C2×C4—21no—
1315C2×C4—21no—
1316C2×C4—21no—
1317C2×C4—21no—
1318C2×C4—21no—
1319C2×C4—23no—
1320C2×C4—23no—
1321C2×C4—21no—
1322C2×C4—23no—
1323C2×C4—21no—
1324C2×C4—21no—
1325C2×C4—21no—
1326C2×C4—23no—
1327C2×C4—23no—
1328C2×C4—21no—
1329C2×C4—23no—
1330C2×C4—23no—
1331C2×C4—21no—
1332C2×C4—23no—
1333C2×C4—23no—
1334C2×C4—21no—
1335C2×C4—21no—
1336C2×C4—23no—
1337C2×C4—23no—
1338C2×C4—21no—
1339C2×C4—21no—
1340C2×C4—21no—
1341C2×C4—44no—
1342C2×C4—412no—
1343C2×C4—412no—
1344C2×C4—412no—
1345C2×C4—412no—
1346C2×C4—412no—
1347C2×C4—812no—
1348C2×C4—86no—
1349C2×C4—86no—
1350C2×C4—86no—
1351C2×C4—166no—
1352C2×C4—166no—
1353C2×C4C22×#4112yes—
1354C2×C4C22×#4116yes—
1355C2×C4C22×#4116yes—
1356C2×C4C2×H(5,𝔽2)12yes—
1357C2×C4C2×H(5,𝔽2)12yes—
1358C2×C4C2×H(5,𝔽2)16yes—
1359C2×C4C2×H(5,𝔽2)16yes—
1360C2×C4#58512yes—
1361C22—22no—
1362C22—22no—
1363C22—22no—
1364C22—41no—
1365C22—41no—
1366C22—41no—
1367C22—41no—
1368C22—43no—
1369C22—43no—
1370C22—43no—
1371C22—43no—
1372C22—43no—
1373C22—43no—
1374C22—43no—
1375C22—43no—
1376C22—43no—
1377C22—43no—
1378C22—43no—
1379C22—43no—
1380C22—43no—
1381C22—43no—
1382C22—43no—
1383C22—43no—
1384C22—43no—
1385C22—43no—
1386C22—43no—
1387C22—43no—
1388C22—43no—
1389C22—43no—
1390C22—43no—
1391C22—43no—
1392C22—43no—
1393C22—43no—
1394C22—43no—
1395C22—43no—
1396C22C23×#4111yescharacteristic
1397C22C22×H(5,𝔽2)11yescharacteristic
1398C22C22×H(5,𝔽2)11yescharacteristic
1399C22C22×H(5,𝔽2)11yescharacteristic
1400C22C2×#58511yescharacteristic
1401C22H(7,𝔽2)11yescharacteristic
1402C222−1+611yescharacteristic
1403C4—26no—
1404C4—22no—
1405C4—22no—
1406C4—22no—
1407C4—22no—
1408C4—43no—
1409C4—41no—
1410C4—43no—
1411C4—43no—
1412C4—43no—
1413C4—43no—
1414C4—41no—
1415C4—43no—
1416C4—43no—
1417C4—43no—
1418C4—43no—
1419C4—41no—
1420C4—41no—
1421C4—41no—
1422C4—41no—
1423C4—41no—
1424C4—41no—
1425C4—41no—
1426C4—41no—
1427C4—43no—
1428C4C2×#540112yes—
1429C2—42no—
1430C2—83no—
1431C2—83no—
1432C2—83no—
1433C2—83no—
1434C2C22×#54011yescharacteristic
1435C2#6280011yescharacteristic
1436C2#6285111yescharacteristic
1437C2#6289511yescharacteristic
1438C2#6289911yescharacteristic
1439C2#6291611yescharacteristic
1440C2#6292211yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42759C2semidirect
2. #42752C2semidirect
3. #42617C2semidirect
4. #42608C2semidirect
5. #42529C2semidirect
6. #42508C2semidirect
7. #42471C2semidirect
8. #42460C2semidirect
9. #40054C2semidirect
10. #40046C2semidirect
11. #39410C2semidirect
12. #39402C2semidirect
13. #37587C2semidirect
14. #37570C2semidirect
15. #36578C2semidirect
16. #36576C2semidirect
17. #36455C2semidirect
18. #36433C2semidirect
19. #36066C2semidirect
20. #36029C2semidirect
21. #36029C2semidirect
22. #36005C2semidirect
23. #35996C2semidirect
24. #35868C2semidirect
25. #35831C2semidirect
26. #35831C2semidirect
27. #35171C2semidirect
28. #34597C2semidirect
29. #34313C2semidirect
30. #34263C2semidirect
31. C4×#548C2semidirect
1250. Q8#540semidirect

Maximal subgroups

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

subgroupindex
#427592
#427522
#426172
#426082
#425292
#425082
#424712
#424602
#400542
#400462
#394102
#394022
#375872
#375702
#365782
#365762
#364552
#364332
#360662
#360292
#360052
#359962
#358682
#358312
#351712
#345972
#343132
#342632
C4×#5482