Finite Group Databasebeta

← #7656986

Subgroups — #7656986

Order 512.

4532 conjugacy classes of subgroups.

The subgroup lattice has 1244 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42981C213yesmaximal, complemented
2#42973C213yesmaximal, complemented
3#42972C213yesmaximal, complemented
4#42972C213yesmaximal, complemented
5#42498C213yesmaximal, complemented
6#42497C213yesmaximal, complemented
7#42494C213yesmaximal, complemented
8#42493C213yesmaximal, complemented
9#39977C213yesmaximal, complemented
10#39976C213yesmaximal, complemented
11#39973C213yesmaximal, complemented
12#39972C213yesmaximal, complemented
13#37624C213yesmaximal, complemented
14#37561C213yesmaximal, complemented
15#36475C211yesmaximal, characteristic, complemented
16#36475C211yesmaximal, characteristic, complemented
17#36474C211yesmaximal, characteristic, complemented
18#36466C211yesmaximal, characteristic, complemented
19#36040C211yesmaximal, characteristic
20#35971C211yesmaximal, characteristic, complemented
21#35957C211yesmaximal, characteristic, complemented
22#35937C211yesmaximal, characteristic, complemented
23#35868C211yesmaximal, characteristic, complemented
24#35816C211yesmaximal, characteristic
25#35816C211yesmaximal, characteristic
26#35748C211yesmaximal, characteristic
27#35132C213yesmaximal, complemented
28#34625C213yesmaximal, complemented
29#34197C211yesmaximal, characteristic
30#34184C211yesmaximal, characteristic
31#34129C211yesmaximal, characteristic
32C2×Q82C2211yescharacteristic
33C2×#557C2211yescharacteristic
34C2×#557C2211yescharacteristic
35C2×#557C2211yescharacteristic
36C2×#520C2211yescharacteristic
37C2×#520C2211yescharacteristic
38C2×C4×#41C2211yescharacteristic
39#2864C2213yes—
40#2864C2213yes—
41#2862C2213yes—
42#2859C2213yes—
43#2845C2216yes—
44#2844C2216yes—
45#2841C2216yes—
46#2841C2216yes—
47#2807C2216yes—
48#2790C2216yes—
49#2790C2216yes—
50#2788C2216yes—
51#2788C2216yes—
52#2768C2216yes—
53#2768C2216yes—
54#2763C2216yes—
55#2742C2216yes—
56#2729C2216yes—
57#2729C2216yes—
58#2720C2216yes—
59#2720C2216yes—
60#2704C2216yes—
61#2704C2216yes—
62#2677C2216yes—
63#2667C2213yes—
64#2667C2213yes—
65#2666C2213yes—
66#2666C2216yes—
67#2666C2211yescharacteristic
68#2666C2213yes—
69#2666C2213yes—
70#2665C2213yes—
71#2665C2213yes—
72#2660C2213yes—
73#2660C2213yes—
74#2660C2213yes—
75#2660C2213yes—
76#2660C2216yes—
77#2659C2216yes—
78#2647C2213yes—
79#2647C2213yes—
80#2647C2213yes—
81#2647C2213yes—
82#2647C2216yes—
83#2646C2216yes—
84#2629C2213yes—
85#2629C2213yes—
86#2629C2213yes—
87#2629C2213yes—
88#2628C2213yes—
89#2628C2213yes—
90#2628C2213yes—
91#2628C2213yes—
92#2612C2216yes—
93#2612C2216yes—
94#2584C2213yes—
95#2584C2213yes—
96#2584C2213yes—
97#2584C2213yes—
98#2580C2213yes—
99#2580C2213yes—
100#2571C2213yes—
101#2570C2213yes—
102#2570C2213yes—
103#2570C2213yes—
104#2570C2213yes—
105#2570C2213yes—
106#2570C2213yes—
107#2567C2213yes—
108#2567C2213yes—
109#2566C2213yes—
110#2566C2213yes—
111#2563C2213yes—
112#2552C2213yes—
113#2552C2213yes—
114#2552C2213yes—
115#2552C2213yes—
116#2551C2213yes—
117#2551C2213yes—
118#2551C2213yes—
119#2550C2213yes—
120#2550C2213yes—
121#2550C2213yes—
122#2550C2213yes—
123#2550C2213yes—
124#2550C2213yes—
125#2550C2213yes—
126#2550C2213yes—
127#2550C2213yes—
128#2550C2213yes—
129#2546C2213yes—
130#2546C2213yes—
131#2542C2213yes—
132#2538C2213yes—
133#2538C2213yes—
134#2509C2213yes—
135#2509C2213yes—
136#2509C2213yes—
137#2509C2213yes—
138#2508C2213yes—
139#2508C2213yes—
140#2508C2213yes—
141#2508C2213yes—
142#2507C2213yes—
143#2507C2213yes—
144#2507C2213yes—
145#2507C2213yes—
146#2506C2213yes—
147#2506C2213yes—
148#2506C2213yes—
149#2506C2213yes—
150#2454C2213yes—
151#2454C2213yes—
152#2454C2213yes—
153#2454C2213yes—
154#2452C2213yes—
155#2452C2213yes—
156#2452C2213yes—
157#2452C2213yes—
158#2442C2213yes—
159#2442C2213yes—
160#2442C2213yes—
161#2442C2213yes—
162#2441C2216yes—
163#2440C2213yes—
164#2440C2213yes—
165#2440C2213yes—
166#2440C2213yes—
167#2439C2216yes—
168#2438C2216yes—
169#2438C2216yes—
170#2438C2216yes—
171#2438C2216yes—
172#2402C2213yes—
173#2402C2213yes—
174#2399C2213yes—
175#2399C2213yes—
176#2396C2213yes—
177#2396C2213yes—
178#2396C2213yes—
179#2396C2213yes—
180#2357C2213yes—
181#2357C2213yes—
182#2354C2213yes—
183#2354C2213yes—
184#2351C2211yescharacteristic
185#2351C2211yescharacteristic
186#2351C2211yescharacteristic
187#2351C2211yescharacteristic
188#2351C2211yescharacteristic
189#2351C2211yescharacteristic
190#2351C2211yescharacteristic
191#2351C2211yescharacteristic
192#2351C2211yescharacteristic
193#2351C2211yescharacteristic
194#2351C2211yescharacteristic
195#2351C2211yescharacteristic
196Q8×C4⋊C4C2211yescharacteristic
197Q8×C4⋊C4C2211yescharacteristic
198Q8×C4⋊C4C2211yescharacteristic
199Q8×C4⋊C4C2211yescharacteristic
200Q8×C4⋊C4C2211yescharacteristic
201Q8×C4⋊C4C2211yescharacteristic
202Q8×C4⋊C4C2211yescharacteristic
203Q8×C4⋊C4C2211yescharacteristic
204#2349C2213yes—
205#2349C2213yes—
206#2349C2213yes—
207#2349C2213yes—
208#2346C2213yes—
209#2346C2213yes—
210#2346C2213yes—
211#2346C2213yes—
212#2341C2211yescharacteristic
213#2341C2211yescharacteristic
214#2341C2211yescharacteristic
215#2341C2211yescharacteristic
216#2329C2216yes—
217#2329C2216yes—
218#2319C2213yes—
219#2319C2213yes—
220#2317C2213yes—
221#2317C2213yes—
222C4×C4⋊Q8C2213yes—
223C4×C4⋊Q8C2213yes—
224C4×#125C2213yes—
225C4×#125C2213yes—
226#2293C2213yes—
227#2293C2213yes—
228#2285C2213yes—
229#2285C2213yes—
230#2283C2213yes—
231#2283C2213yes—
232C2×#382C2213yes—
233#2276C2211yescharacteristic
234#2276C2211yescharacteristic
235C42×Q8C2211yescharacteristic
236C42×Q8C2211yescharacteristic
237C4×#117C2213yes—
238C22×#41C2311yescharacteristic
239Q82—44no—
240#557—44no—
241#557—44no—
242#557—44no—
243C2×C4⋊Q8C2313yes—
244C2×C4⋊Q8C2313yes—
245C2×C4⋊Q8C2313yes—
246C2×C4⋊Q8C2313yes—
247C2×C4⋊Q8C2313yes—
248C2×C4⋊Q8C2313yes—
249C2×C4⋊Q8C2313yes—
250C2×C4⋊Q8C2313yes—
251C2×C4⋊Q8C2316yes—
252C2×#125C2313yes—
253C2×#125C2313yes—
254C2×#125C2313yes—
255C2×#125C2313yes—
256C2×#125C2313yes—
257C2×#125C2313yes—
258C2×#125C2313yes—
259C2×#125C2313yes—
260C2×#125C2316yes—
261C2×C22⋊Q8C2316yes—
262C2×C22⋊Q8C2316yes—
263C2×C22⋊Q8C2316yes—
264C2×C22⋊Q8C2316yes—
265#520—44no—
266#520—44no—
267C4×#41Q8116yescomplemented
268C2×C4×Q8C2311yescharacteristic
269C2×C4×Q8C2311yescharacteristic
270C2×C4×Q8C2311yescharacteristic
271C2×C4×Q8C2311yescharacteristic
272C2×C4×Q8C2311yescharacteristic
273C2×C4×Q8C2311yescharacteristic
274C2×C4×Q8C2311yescharacteristic
275C2×C4×Q8C2311yescharacteristic
276C2×C4×Q8C2311yescharacteristic
277C2×C4×Q8C2311yescharacteristic
278C2×C4×Q8C2311yescharacteristic
279C2×C4×Q8C2311yescharacteristic
280C2×C4×Q8C2313yes—
281C2×C4×Q8C2313yes—
282C2×C4×Q8C2313yes—
283C2×C4×Q8C2313yes—
284C2×C4×Q8C2311yescharacteristic
285C2×C4×Q8C2311yescharacteristic
286C2×C4×D4C2313yes—
287C2×C4×D4C2313yes—
288C2×C4×D4C2313yes—
289C2×C4×D4C2313yes—
290C2×C4×D4C2313yes—
291C2×C4×D4C2313yes—
292C2×#117C2313yes—
293C2×#117C2313yes—
294C2×#117C2313yes—
295C2×#117C2313yes—
296C2×#117C2316yes—
297C2×#117C2313yes—
298C22×C4⋊C4C2313yes—
299C22×C4⋊C4C2313yes—
300C22×C42C2313yes—
301#400C2313yes—
302#400C2316yes—
303#400C2316yes—
304#400C2316yes—
305#400C2316yes—
306#400C2316yes—
307#400C2313yes—
308#400C2313yes—
309#400C2316yes—
310#400C2316yes—
311#400C2316yes—
312#400C2313yes—
313#400C2311yescharacteristic
314#400C2313yes—
315#400C2313yes—
316#400C2311yescharacteristic
317#400C2313yes—
318#400C2313yes—
319#400C2313yes—
320#400C2313yes—
321#399C2313yes—
322#399C2316yes—
323#399C2316yes—
324#399C2313yes—
325#399C2313yes—
326#399C2313yes—
327#398C2313yes—
328#398C2316yes—
329#398C2316yes—
330#398C2316yes—
331#398C2316yes—
332#398C2316yes—
333#398C2313yes—
334#398C2316yes—
335#398C2316yes—
336#398C2316yes—
337#398C2313yes—
338#398C2313yes—
339#398C2316yes—
340#398C2316yes—
341#398C2313yes—
342#398C2313yes—
343#398C2316yes—
344#398C2316yes—
345#398C2316yes—
346#398C2316yes—
347#398C2316yes—
348#398C2316yes—
349#398C2313yes—
350#398C2313yes—
351#398C2311yescharacteristic
352#398C2311yescharacteristic
353#398C2313yes—
354#398C2313yes—
355#398C2313yes—
356#398C2313yes—
357#398C2313yes—
358#398C2311yescharacteristic
359#398C2313yes—
360#398C2313yes—
361#398C2313yes—
362#398C2311yescharacteristic
363#398C2313yes—
364#398C2313yes—
365#398C2313yes—
366#398C2313yes—
367#396C2313yes—
368#396C2313yes—
369#396C2316yes—
370#396C2316yes—
371#396C2316yes—
372#396C2316yes—
373#396C2313yes—
374#396C2313yes—
375#396C2313yes—
376#396C2313yes—
377#396C2313yes—
378#396C2313yes—
379#395C2313yes—
380#395C2316yes—
381#395C2316yes—
382#395C2316yes—
383#395C2313yes—
384#395C2316yes—
385#395C2316yes—
386#395C2313yes—
387#395C2316yes—
388#395C2313yes—
389#395C2316yes—
390#395C2316yes—
391#395C2313yes—
392#395C2311yescharacteristic
393#395C2313yes—
394#395C2313yes—
395#395C2313yes—
396#395C2311yescharacteristic
397#395C2313yes—
398#395C2313yes—
399#393C2313yes—
400#393C2316yes—
401#393C2313yes—
402#393C2316yes—
403#393C2313yes—
404#393C2313yes—
405#391C2311yescharacteristic
406#391C2313yes—
407#391C2313yes—
408#391C2313yes—
409#391C2316yes—
410#391C2316yes—
411#391C2316yes—
412#391C2316yes—
413#391C2316yes—
414#390C2313yes—
415#390C2313yes—
416#390C2313yes—
417#390C2313yes—
418#390C2313yes—
419#390C2313yes—
420#390C2313yes—
421#390C2313yes—
422#389C2313yes—
423#389C2313yes—
424#389C2313yes—
425#389C2313yes—
426#389C2311yescharacteristic
427#389C2313yes—
428#389C2313yes—
429#389C2313yes—
430#389C2313yes—
431#389C2313yes—
432#389C2313yes—
433#389C2313yes—
434#389C2313yes—
435#389C2313yes—
436#389C2313yes—
437#389C2313yes—
438#389C2313yes—
439#389C2313yes—
440#389C2313yes—
441#389C2313yes—
442#389C2313yes—
443#389C2313yes—
444#389C2313yes—
445#389C2313yes—
446#389C2313yes—
447#389C2313yes—
448#389C2313yes—
449#389C2313yes—
450#389C2313yes—
451#389C2313yes—
452#389C2313yes—
453#389C2313yes—
454#389C2313yes—
455#389C2316yes—
456#389C2313yes—
457#389C2313yes—
458#389C2313yes—
459#389C2313yes—
460#389C2313yes—
461#389C2313yes—
462#389C2313yes—
463#389C2313yes—
464#389C2313yes—
465#389C2313yes—
466#389C2313yes—
467#389C2313yes—
468#389C2316yes—
469#389C2316yes—
470#389C2316yes—
471#389C2313yes—
472#389C2313yes—
473#389C2313yes—
474#389C2313yes—
475#389C2316yes—
476#389C2316yes—
477#389C2316yes—
478#389C2313yes—
479#389C2313yes—
480#389C2316yes—
481#389C2313yes—
482#389C2316yes—
483#388C2316yes—
484#388C2316yes—
485#388C2316yes—
486#388C2316yes—
487#388C2316yes—
488#388C2316yes—
489#388C2316yes—
490#388C2316yes—
491#387C2311yescharacteristic
492#387C2311yescharacteristic
493#387C2313yes—
494#387C2313yes—
495#387C2313yes—
496#387C2313yes—
497#387C2313yes—
498#387C2313yes—
499#387C2316yes—
500#387C2316yes—
501#387C2316yes—
502#387C2316yes—
503#387C2316yes—
504#387C2316yes—
505#387C2316yes—
506#387C2316yes—
507#387C2316yes—
508#387C2316yes—
509#385C2316yes—
510#385C2316yes—
511#385C2316yes—
512#385C2316yes—
513#385C2316yes—
514#385C2316yes—
515#385C2316yes—
516#385C2316yes—
517#385C2316yes—
518#385C2316yes—
519#385C2316yes—
520#385C2316yes—
521#384C2313yes—
522#384C2313yes—
523#384C2313yes—
524#384C2313yes—
525#384C2316yes—
526#384C2313yes—
527#384C2313yes—
528#384C2313yes—
529#384C2313yes—
530#384C2313yes—
531#384C2313yes—
532#384C2313yes—
533#384C2313yes—
534#383C2311yescharacteristic
535#383C2313yes—
536#382C2313yes—
537#382C2313yes—
538#382C2313yes—
539#382C2313yes—
540#382C2313yes—
541#382C2313yes—
542#382C2313yes—
543#382C2313yes—
544#382C2313yes—
545#382C2313yes—
546#382C2313yes—
547#382C2313yes—
548#382C2313yes—
549#382C2316yes—
550#382C2316yes—
551#382C2313yes—
552#382C2316yes—
553#382C2313yes—
554#382C2313yes—
555#382C2313yes—
556#382C2311yescharacteristic
557#381C2316yes—
558#381C2313yes—
559#381C2313yes—
560#380C2316yes—
561#380C2316yes—
562#380C2313yes—
563#380C2313yes—
564#380C2316yes—
565#380C2313yes—
566#380C2313yes—
567#380C2316yes—
568#380C2313yes—
569#380C2313yes—
570#380C2313yes—
571#380C2313yes—
572#380C2313yes—
573#380C2313yes—
574#380C2316yes—
575C4×C4⋊C4C2313yes—
576C4×C4⋊C4C2313yes—
577C4×C4⋊C4C2313yes—
578C4×C4⋊C4C2313yes—
579C4×C4⋊C4C2313yes—
580C4×C4⋊C4C2313yes—
581C4×C4⋊C4C2313yes—
582C4×C4⋊C4C2313yes—
583C4×C4⋊C4C2313yes—
584C4×C4⋊C4C2313yes—
585C4×C4⋊C4C2313yes—
586C4×C4⋊C4C2313yes—
587C4×C4⋊C4C2313yes—
588C4×C4⋊C4C2313yes—
589C4×C4⋊C4C2313yes—
590C4×C4⋊C4C2313yes—
591C4×C4⋊C4C2313yes—
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⋊C4C2313yes—
601C4×C4⋊C4C2313yes—
602C4×C4⋊C4C2313yes—
603C4×C4⋊C4C2313yes—
604C4×C4⋊C4C2313yes—
605C4×C4⋊C4C2313yes—
606C4×C4⋊C4C2313yes—
607C4×C4⋊C4C2311yescharacteristic
608C4×C4⋊C4C2313yes—
609C4×C22⋊C4C2316yes—
610C4×C22⋊C4C2313yes—
611C4×C22⋊C4C2313yes—
612C4×C22⋊C4C2313yes—
613C4×C22⋊C4C2313yes—
614C4×C22⋊C4C2313yes—
615C4×C22⋊C4C2313yes—
616#376C2313yes—
617#376C2313yes—
618#376C2313yes—
619#376C2316yes—
620#376C2313yes—
621C2×#95C2316yes—
622C2×#95C2316yes—
623C43C2313yes—
624C43C2313yes—
625C2×#41—24no—
626C2×#41—24no—
627C2×#41C2×Q818yes—
628C22×Q8C2411yescharacteristic
629C22×Q8C2413yes—
630C22×Q8C2413yes—
631C22×Q8C2413yes—
632C22×Q8C2416yes—
633C22×Q8C2411yescharacteristic
634C22×D4C2413yes—
635C23×C4C2413yes—
636C23×C4C2416yes—
637C23×C4C2416yes—
638C23×C4C2413yes—
639C23×C4C2413yes—
640C4⋊Q8—46no—
641C4⋊Q8—46no—
642C4⋊Q8—46no—
643C4⋊Q8—46no—
644C4⋊Q8—46no—
645C4⋊Q8—46no—
646C4⋊Q8—46no—
647C4⋊Q8—46no—
648C4⋊Q8—86no—
649#125—46no—
650#125—46no—
651#125—46no—
652#125—46no—
653#125—46no—
654#125—46no—
655#125—46no—
656#125—46no—
657#125—86no—
658C22⋊Q8—412no—
659C22⋊Q8—412no—
660C22⋊Q8—86no—
661C22⋊Q8—86no—
662C4×Q8—24no—
663C4×Q8—24no—
664C4×Q8—24no—
665C4×Q8—24no—
666C4×Q8—24no—
667C4×Q8—24no—
668C4×Q8—24no—
669C4×Q8—24no—
670C4×Q8—24no—
671C4×Q8—24no—
672C4×Q8—24no—
673C4×Q8—24no—
674C4×Q8—46no—
675C4×Q8—46no—
676C4×Q8—46no—
677C4×Q8—46no—
678C4×Q8C2×Q818yes—
679C4×Q8C2×Q818yes—
680C4×D4—46no—
681C4×D4—46no—
682C4×D4—46no—
683C4×D4—46no—
684C4×D4C2×Q8124yes—
685C4×D4C2×Q8124yes—
686#117—46no—
687#117—46no—
688#117—46no—
689#117—46no—
690#117—86no—
691#117C2×Q8124yes—
692C2×C4⋊C4—46no—
693C2×C4⋊C4—46no—
694C2×C4⋊C4C2413yes—
695C2×C4⋊C4C2413yes—
696C2×C4⋊C4C2413yes—
697C2×C4⋊C4C2413yes—
698C2×C4⋊C4C2411yescharacteristic
699C2×C4⋊C4C2411yescharacteristic
700C2×C4⋊C4C2413yes—
701C2×C4⋊C4C2413yes—
702C2×C4⋊C4C2413yes—
703C2×C4⋊C4C2413yes—
704C2×C4⋊C4C2413yes—
705C2×C4⋊C4C2413yes—
706C2×C4⋊C4C2413yes—
707C2×C4⋊C4C2413yes—
708C2×C4⋊C4C2413yes—
709C2×C4⋊C4C2413yes—
710C2×C4⋊C4C2413yes—
711C2×C4⋊C4C2411yescharacteristic
712C2×C4⋊C4C2411yescharacteristic
713C2×C4⋊C4C2411yescharacteristic
714C2×C4⋊C4C2413yes—
715C2×C4⋊C4C2413yes—
716C2×C4⋊C4C2411yescharacteristic
717C2×C4⋊C4C2411yescharacteristic
718C2×C4⋊C4C2416yes—
719C2×C4⋊C4C2416yes—
720C2×C4⋊C4C2413yes—
721C2×C4⋊C4C2413yes—
722C2×C4⋊C4C2411yescharacteristic
723C2×C4⋊C4C2411yescharacteristic
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⋊C4C2413yes—
736C2×C4⋊C4C2413yes—
737C2×C4⋊C4C2416yes—
738C2×C4⋊C4C2416yes—
739C2×C4⋊C4C2416yes—
740C2×C4⋊C4C2416yes—
741C2×C4⋊C4C2416yes—
742C2×C4⋊C4C2416yes—
743C2×C4⋊C4C2416yes—
744C2×C4⋊C4C2416yes—
745C2×C4⋊C4C2416yes—
746C2×C4⋊C4C2413yes—
747C2×C4⋊C4C2413yes—
748C2×C4⋊C4C2413yes—
749C2×C4⋊C4C2413yes—
750C2×C4⋊C4C2413yes—
751C2×C4⋊C4C2413yes—
752C2×C4⋊C4C2413yes—
753C2×C4⋊C4C2413yes—
754C2×C4⋊C4C2413yes—
755C2×C4⋊C4C2413yes—
756C2×C4⋊C4C2413yes—
757C2×C4⋊C4C2413yes—
758C2×C4⋊C4C2413yes—
759C2×C4⋊C4C2413yes—
760C2×C4⋊C4C2413yes—
761C2×C4⋊C4C2413yes—
762C2×C4⋊C4C2413yes—
763C2×C4⋊C4C2413yes—
764C2×C4⋊C4C2413yes—
765C2×C4⋊C4C2411yescharacteristic
766C2×C4⋊C4C2411yescharacteristic
767C2×C4⋊C4C2411yescharacteristic
768C2×C4⋊C4C2413yes—
769C2×C4⋊C4C2413yes—
770C2×C4⋊C4C2413yes—
771C2×C4⋊C4C2413yes—
772C2×C4⋊C4C2413yes—
773C2×C4⋊C4C2413yes—
774C2×C4⋊C4C2413yes—
775C2×C22⋊C4C2413yes—
776C2×C22⋊C4C2413yes—
777C2×C22⋊C4C2413yes—
778C2×C22⋊C4C2413yes—
779C2×C22⋊C4C2413yes—
780C2×C22⋊C4C2413yes—
781C2×C22⋊C4C2416yes—
782C2×C22⋊C4C2416yes—
783C2×C22⋊C4C2413yes—
784C2×C22⋊C4C2413yes—
785C2×C22⋊C4C2413yes—
786C2×C22⋊C4C2413yes—
787C2×C22⋊C4C2416yes—
788C2×C22⋊C4C2416yes—
789C2×C22⋊C4C2413yes—
790C2×C22⋊C4C2413yes—
791C2×C22⋊C4C2416yes—
792C2×C42C2×Q8124yes—
793C2×C42C2413yes—
794C2×C42C2413yes—
795C2×C42C2413yes—
796C2×C42C2413yes—
797C2×C42C2413yes—
798C2×C42C2413yes—
799C2×C42C2413yes—
800C2×C42C2413yes—
801C2×C42C2413yes—
802C2×C42C2413yes—
803C2×C42C2413yes—
804C2×C42C2413yes—
805C2×C42C2413yes—
806C2×C42C2413yes—
807C2×C42C2413yes—
808C2×C42C2413yes—
809C2×C42C2413yes—
810C2×C42C2413yes—
811C2×C42C2416yes—
812C2×C42C2411yescharacteristic
813C2×C42C2411yescharacteristic
814C2×C42C2416yes—
815C2×C42C2413yes—
816C2×C42C2413yes—
817C2×C42C2413yes—
818C2×C42C2411yescharacteristic
819#95C2413yes—
820#95C2413yes—
821#95C2413yes—
822#95C2413yes—
823#95C2416yes—
824#95C2416yes—
825#95C2416yes—
826#95C2416yes—
827#95C2411yescharacteristic
828#95C2411yescharacteristic
829#95C2411yescharacteristic
830#95C2411yescharacteristic
831#95C2413yes—
832#95C2413yes—
833#95C2413yes—
834#95C2413yes—
835#95C2413yes—
836#95C2413yes—
837#95C2413yes—
838#95C2413yes—
839#95C2413yes—
840#95C2413yes—
841#95C2413yes—
842#95C2413yes—
843#95C2413yes—
844#95C2413yes—
845#95C2416yes—
846#95C2416yes—
847#95C2411yescharacteristic
848#95C2411yescharacteristic
849#95C2413yes—
850#95C2413yes—
851#95C2411yescharacteristic
852#95C2411yescharacteristic
853#95C2411yescharacteristic
854#95C2411yescharacteristic
855#95C2416yes—
856#95C2416yes—
857#95C2411yescharacteristic
858#95C2411yescharacteristic
859#95C2411yescharacteristic
860#95C2411yescharacteristic
861#95C2411yescharacteristic
862#95C2411yescharacteristic
863#95C2411yescharacteristic
864#95C2411yescharacteristic
865#95C2413yes—
866#95C2413yes—
867#95C2413yes—
868#95C2413yes—
869#95C2413yes—
870#95C2413yes—
871#95C2413yes—
872#95C2413yes—
873#95C2413yes—
874#95C2413yes—
875#95C2413yes—
876#95C2413yes—
877#95C2413yes—
878#95C2413yes—
879#95C2413yes—
880#95C2413yes—
881#95C2413yes—
882#95C2413yes—
883#95C2416yes—
884#95C2416yes—
885#95C2416yes—
886#95C2416yes—
887#95C2416yes—
888#95C2416yes—
889C24C2513yes—
890#41—232no—
891C2×Q8—22no—
892C2×Q8—26no—
893C2×Q8—41no—
894C2×Q8—41no—
895C2×Q8—43no—
896C2×Q8—43no—
897C2×Q8—43no—
898C2×Q8—43no—
899C2×Q8—43no—
900C2×Q8—43no—
901C2×Q8—43no—
902C2×Q8—43no—
903C2×Q8—46no—
904C2×Q8—46no—
905C2×Q8—46no—
906C2×Q8C22×Q814yes—
907C2×Q8H(5,𝔽2)14yes—
908C2×Q82−1+414yes—
909C2×D4—26no—
910C2×D4—26no—
911C2×D4C22×Q8112yes—
912C22×C4—26no—
913C22×C4—26no—
914C22×C4—43no—
915C22×C4—43no—
916C22×C4—43no—
917C22×C4—43no—
918C22×C4—46no—
919C22×C4—46no—
920C22×C4—46no—
921C22×C4—46no—
922C22×C4—46no—
923C22×C4—46no—
924C22×C4C22×Q8112yes—
925C22×C4C22×Q8112yes—
926C22×C4C22×Q8112yes—
927C22×C4C2511yescharacteristic
928C22×C4C2511yescharacteristic
929C22×C4C2513yes—
930C22×C4C2513yes—
931C22×C4C2511yescharacteristic
932C22×C4C2513yes—
933C22×C4C2513yes—
934C22×C4C2513yes—
935C22×C4C2513yes—
936C22×C4C2513yes—
937C22×C4C2511yescharacteristic
938C22×C4C2511yescharacteristic
939C22×C4C2513yes—
940C22×C4C2511yescharacteristic
941C22×C4C2511yescharacteristic
942C22×C4C2513yes—
943C22×C4C2513yes—
944C22×C4C2511yescharacteristic
945C22×C4C2511yescharacteristic
946C22×C4C2513yes—
947C22×C4C2513yes—
948C22×C4C2511yescharacteristic
949C22×C4C2511yescharacteristic
950C22×C4C2511yescharacteristic
951C22×C4C2511yescharacteristic
952C22×C4C2513yes—
953C22×C4C2513yes—
954C22×C4C2511yescharacteristic
955C22×C4C2511yescharacteristic
956C22×C4C2513yes—
957C4⋊C4—26no—
958C4⋊C4—26no—
959C4⋊C4—26no—
960C4⋊C4—26no—
961C4⋊C4—26no—
962C4⋊C4—26no—
963C4⋊C4—26no—
964C4⋊C4—26no—
965C4⋊C4—26no—
966C4⋊C4—26no—
967C4⋊C4—26no—
968C4⋊C4—26no—
969C4⋊C4—22no—
970C4⋊C4—22no—
971C4⋊C4—26no—
972C4⋊C4—26no—
973C4⋊C4—26no—
974C4⋊C4—22no—
975C4⋊C4—22no—
976C4⋊C4—22no—
977C4⋊C4—43no—
978C4⋊C4—43no—
979C4⋊C4—43no—
980C4⋊C4—43no—
981C4⋊C4—43no—
982C4⋊C4—41no—
983C4⋊C4—43no—
984C4⋊C4—43no—
985C4⋊C4—41no—
986C4⋊C4—41no—
987C4⋊C4—43no—
988C4⋊C4—43no—
989C4⋊C4—41no—
990C4⋊C4—41no—
991C4⋊C4—46no—
992C4⋊C4—46no—
993C4⋊C4—41no—
994C4⋊C4—41no—
995C4⋊C4—41no—
996C4⋊C4—43no—
997C4⋊C4—43no—
998C4⋊C4—43no—
999C4⋊C4—43no—
1000C4⋊C4—43no—
1001C4⋊C4—43no—
1002C4⋊C4—43no—
1003C4⋊C4—43no—
1004C4⋊C4—43no—
1005C4⋊C4—46no—
1006C4⋊C4—46no—
1007C4⋊C4—46no—
1008C4⋊C4—43no—
1009C4⋊C4—43no—
1010C4⋊C4—43no—
1011C4⋊C4—46no—
1012C4⋊C4—46no—
1013C4⋊C4—46no—
1014C4⋊C4—43no—
1015C4⋊C4—43no—
1016C4⋊C4—43no—
1017C4⋊C4—43no—
1018C4⋊C4—43no—
1019C4⋊C4—43no—
1020C4⋊C4—43no—
1021C4⋊C4—43no—
1022C4⋊C4—46no—
1023C4⋊C4—46no—
1024C4⋊C4—46no—
1025C4⋊C4—43no—
1026C4⋊C4—43no—
1027C4⋊C4—43no—
1028C4⋊C4—43no—
1029C4⋊C4—43no—
1030C4⋊C4—43no—
1031C4⋊C4—43no—
1032C4⋊C4—43no—
1033C4⋊C4—43no—
1034C4⋊C4—43no—
1035C4⋊C4—43no—
1036C4⋊C4C22×Q8112yes—
1037C4⋊C4C22×Q8112yes—
1038C22⋊C4—26no—
1039C22⋊C4—26no—
1040C22⋊C4—43no—
1041C22⋊C4—43no—
1042C22⋊C4—43no—
1043C22⋊C4—43no—
1044C22⋊C4—43no—
1045C22⋊C4—43no—
1046C22⋊C4—43no—
1047C22⋊C4—43no—
1048C22⋊C4—46no—
1049C22⋊C4—46no—
1050C22⋊C4—46no—
1051C22⋊C4—46no—
1052C22⋊C4—43no—
1053C22⋊C4—43no—
1054C22⋊C4C22×Q8124yes—
1055C42—26no—
1056C42—26no—
1057C42—26no—
1058C42—26no—
1059C42—26no—
1060C42—26no—
1061C42—26no—
1062C42—26no—
1063C42—26no—
1064C42—26no—
1065C42—26no—
1066C42—26no—
1067C42—26no—
1068C42—26no—
1069C42—46no—
1070C42—41no—
1071C42—41no—
1072C42—43no—
1073C42—43no—
1074C42—43no—
1075C42—43no—
1076C42—46no—
1077C42C22×Q814yes—
1078C42C22×Q8112yes—
1079C42C22×Q8112yes—
1080C42C22×Q8112yes—
1081C23—23no—
1082C23—23no—
1083C23—23no—
1084C23—23no—
1085C23—23no—
1086C23—23no—
1087C23C23×Q816yes—
1088C23C2611yescharacteristic
1089Q8—44no—
1090Q8—86no—
1091Q8—86no—
1092Q8—86no—
1093Q8—166no—
1094Q8#544116yes—
1095D4—224no—
1096C2×C4—21no—
1097C2×C4—21no—
1098C2×C4—21no—
1099C2×C4—21no—
1100C2×C4—23no—
1101C2×C4—23no—
1102C2×C4—21no—
1103C2×C4—21no—
1104C2×C4—21no—
1105C2×C4—23no—
1106C2×C4—23no—
1107C2×C4—21no—
1108C2×C4—21no—
1109C2×C4—21no—
1110C2×C4—224no—
1111C2×C4—21no—
1112C2×C4—21no—
1113C2×C4—21no—
1114C2×C4—21no—
1115C2×C4—21no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—23no—
1119C2×C4—23no—
1120C2×C4—23no—
1121C2×C4—23no—
1122C2×C4—23no—
1123C2×C4—23no—
1124C2×C4—23no—
1125C2×C4—23no—
1126C2×C4—21no—
1127C2×C4—21no—
1128C2×C4—21no—
1129C2×C4—23no—
1130C2×C4—23no—
1131C2×C4—23no—
1132C2×C4—23no—
1133C2×C4—23no—
1134C2×C4—23no—
1135C2×C4—21no—
1136C2×C4—21no—
1137C2×C4—23no—
1138C2×C4—23no—
1139C2×C4—23no—
1140C2×C4—23no—
1141C2×C4—23no—
1142C2×C4—23no—
1143C2×C4—21no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—23no—
1148C2×C4—23no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—23no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—23no—
1155C2×C4—23no—
1156C2×C4—23no—
1157C2×C4—23no—
1158C2×C4—23no—
1159C2×C4—23no—
1160C2×C4—23no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—23no—
1165C2×C4—21no—
1166C2×C4—23no—
1167C2×C4—23no—
1168C2×C4—23no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—23no—
1176C2×C4—23no—
1177C2×C4—412no—
1178C2×C4—412no—
1179C2×C4—166no—
1180C2×C4—166no—
1181C2×C4C23×Q812yes—
1182C2×C4C23×Q812yes—
1183C2×C4C23×Q812yes—
1184C2×C4C23×Q816yes—
1185C2×C4C23×Q816yes—
1186C2×C4C23×Q816yes—
1187C2×C4C2×H(5,𝔽2)16yes—
1188C2×C4C2×2−1+416yes—
1189C2×C4#58512yes—
1190C2×C4#58512yes—
1191C22—26no—
1192C22—26no—
1193C22—26no—
1194C22—43no—
1195C22—43no—
1196C22—43no—
1197C22—43no—
1198C22C24×Q811yescharacteristic
1199C22C22×H(5,𝔽2)11yescharacteristic
1200C22C22×2−1+411yescharacteristic
1201C22C2×#58511yescharacteristic
1202C22C2×#58511yescharacteristic
1203C22H(7,𝔽2)11yescharacteristic
1204C222−1+611yescharacteristic
1205C4—22no—
1206C4—26no—
1207C4—22no—
1208C4—26no—
1209C4—22no—
1210C4—22no—
1211C4—22no—
1212C4—41no—
1213C4—41no—
1214C4—43no—
1215C4—43no—
1216C4—41no—
1217C4—41no—
1218C4—43no—
1219C4—41no—
1220C4—43no—
1221C4—43no—
1222C4—43no—
1223C4—41no—
1224C4—41no—
1225C4—43no—
1226C4—43no—
1227C4—41no—
1228C4—41no—
1229C4—43no—
1230C4—41no—
1231C4—43no—
1232C4—43no—
1233C4—43no—
1234C4C2×#544112yes—
1235C2—46no—
1236C2C22×#54411yescharacteristic
1237C2#6281311yescharacteristic
1238C2#6285411yescharacteristic
1239C2#6291911yescharacteristic
1240C2#6292311yescharacteristic
1241C2#6294911yescharacteristic
1242C2#6295211yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC22×#41C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42981C2semidirect
2. #42973C2semidirect
3. #42972C2semidirect
4. #42972C2semidirect
5. #42498C2semidirect
6. #42497C2semidirect
7. #42494C2semidirect
8. #42493C2semidirect
9. #39977C2semidirect
10. #39976C2semidirect
11. #39973C2semidirect
12. #39972C2semidirect
13. #37624C2semidirect
14. #37561C2semidirect
15. #36475C2semidirect
16. #36475C2semidirect
17. #36474C2semidirect
18. #36466C2semidirect
20. #35971C2semidirect
21. #35957C2semidirect
22. #35937C2semidirect
23. #35868C2semidirect
27. #35132C2semidirect
28. #34625C2semidirect
267. C4×#41Q8semidirect

Maximal subgroups

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

subgroupindex
#429812
#429732
#429722
#424982
#424972
#424942
#424932
#399772
#399762
#399732
#399722
#376242
#375612
#364752
#364742
#364662
#360402
#359712
#359572
#359372
#358682
#358162
#357482
#351322
#346252
#341972
#341842
#341292