Finite Group Databasebeta

← #7662483

Subgroups — #7662483

Order 512.

4534 conjugacy classes of subgroups.

The subgroup lattice has 1243 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#52290C213yesmaximal, complemented
2#42498C213yesmaximal, complemented
3#42498C213yesmaximal, complemented
4#42496C213yesmaximal, complemented
5#42495C213yesmaximal, complemented
6#42492C213yesmaximal, complemented
7#42489C213yesmaximal, complemented
8#39973C213yesmaximal, complemented
9#39972C213yesmaximal, complemented
10#39497C213yesmaximal, complemented
11#39178C213yesmaximal, complemented
12#38966C213yesmaximal, complemented
13#38963C213yesmaximal, complemented
14#37429C213yesmaximal, complemented
15#37427C213yesmaximal, complemented
16#37312C213yesmaximal, complemented
17#36593C211yesmaximal, characteristic, complemented
18#36475C211yesmaximal, characteristic, complemented
19#36475C211yesmaximal, characteristic, complemented
20#36466C211yesmaximal, characteristic, complemented
21#36431C211yesmaximal, characteristic
22#36431C211yesmaximal, characteristic
23#35971C211yesmaximal, characteristic, complemented
24#35957C211yesmaximal, characteristic, complemented
25#35957C211yesmaximal, characteristic, complemented
26#35868C211yesmaximal, characteristic, complemented
27#35816C211yesmaximal, characteristic
28#35816C211yesmaximal, characteristic
29#34263C211yesmaximal, characteristic
30#34263C211yesmaximal, characteristic
31#34250C211yesmaximal, characteristic
32C2×#557C2211yescharacteristic
33C2×#557C2211yescharacteristic
34C2×#557C2211yescharacteristic
35C2×#557C2211yescharacteristic
36C2×#520C2211yescharacteristic
37C2×#520C2211yescharacteristic
38C2×C4×#41C2211yescharacteristic
39#2868C2213yes—
40#2864C2213yes—
41#2864C2213yes—
42#2859C2213yes—
43#2851C2213yes—
44#2851C2213yes—
45#2841C2216yes—
46#2841C2216yes—
47#2806C2213yes—
48#2805C2213yes—
49#2802C2216yes—
50#2792C2216yes—
51#2791C2216yes—
52#2791C2213yes—
53#2791C2216yes—
54#2791C2216yes—
55#2791C2211yescharacteristic
56#2790C2216yes—
57#2790C2216yes—
58#2790C2216yes—
59#2790C2216yes—
60#2790C2216yes—
61#2790C2216yes—
62#2788C2216yes—
63#2788C2213yes—
64#2788C2213yes—
65#2774C2213yes—
66#2774C2213yes—
67#2768C2216yes—
68#2768C2213yes—
69#2768C2213yes—
70#2755C2216yes—
71#2742C2216yes—
72#2734C2213yes—
73#2729C2213yes—
74#2729C2216yes—
75#2729C2213yes—
76#2726C2213yes—
77#2720C2213yes—
78#2720C2216yes—
79#2720C2213yes—
80#2713C2216yes—
81#2677C2216yes—
82#2667C2216yes—
83#2665C2216yes—
84#2660C2213yes—
85#2660C2213yes—
86#2647C2213yes—
87#2647C2213yes—
88#2646C2216yes—
89#2629C2216yes—
90#2629C2216yes—
91#2629C2213yes—
92#2629C2213yes—
93#2627C2216yes—
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#2566C2213yes—
112#2566C2213yes—
113#2552C2213yes—
114#2552C2213yes—
115#2552C2213yes—
116#2552C2213yes—
117#2552C2213yes—
118#2552C2213yes—
119#2552C2213yes—
120#2552C2213yes—
121#2552C2213yes—
122#2552C2213yes—
123#2551C2213yes—
124#2550C2213yes—
125#2550C2213yes—
126#2550C2213yes—
127#2550C2213yes—
128#2550C2213yes—
129#2550C2213yes—
130#2546C2213yes—
131#2546C2213yes—
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#2442C2216yes—
160#2442C2213yes—
161#2441C2216yes—
162#2441C2213yes—
163#2441C2213yes—
164#2440C2216yes—
165#2440C2213yes—
166#2440C2213yes—
167#2439C2216yes—
168#2439C2213yes—
169#2439C2213yes—
170#2438C2216yes—
171#2438C2216yes—
172#2402C2213yes—
173#2402C2213yes—
174#2399C2213yes—
175#2399C2213yes—
176#2396C2213yes—
177#2396C2213yes—
178#2357C2213yes—
179#2357C2213yes—
180#2354C2213yes—
181#2354C2213yes—
182#2351C2211yescharacteristic
183#2351C2211yescharacteristic
184#2351C2211yescharacteristic
185#2351C2211yescharacteristic
186#2351C2211yescharacteristic
187#2351C2211yescharacteristic
188#2351C2211yescharacteristic
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
199Q8×C4⋊C4C2211yescharacteristic
200Q8×C4⋊C4C2211yescharacteristic
201Q8×C4⋊C4C2211yescharacteristic
202#2349C2213yes—
203#2349C2213yes—
204D4×C4⋊C4C2213yes—
205D4×C4⋊C4C2213yes—
206#2345C2213yes—
207#2345C2213yes—
208#2344C2213yes—
209#2344C2213yes—
210#2341C2211yescharacteristic
211#2341C2211yescharacteristic
212#2341C2211yescharacteristic
213#2341C2211yescharacteristic
214#2329C2216yes—
215#2319C2213yes—
216#2319C2213yes—
217#2317C2216yes—
218#2317C2213yes—
219#2316C2213yes—
220#2314C2213yes—
221#2314C2213yes—
222C4×C4⋊Q8C2213yes—
223C4×C4⋊Q8C2213yes—
224C4×#125C2213yes—
225C4×#125C2213yes—
226C4×C22⋊Q8C2213yes—
227C4×C22⋊Q8C2213yes—
228#2298C2213yes—
229#2298C2213yes—
230#2296C2213yes—
231#2293C2213yes—
232#2293C2213yes—
233C2×#389C2213yes—
234#2276C2211yescharacteristic
235#2276C2211yescharacteristic
236C42×Q8C2211yescharacteristic
237C42×Q8C2211yescharacteristic
238C22×#41C2311yescharacteristic
239#557—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⋊Q8C2316yes—
250C2×#125C2313yes—
251C2×#125C2313yes—
252C2×#125C2313yes—
253C2×#125C2313yes—
254C2×#125C2313yes—
255C2×#125C2313yes—
256C2×#125C2313yes—
257C2×#125C2313yes—
258C2×#125C2313yes—
259C2×#125C2313yes—
260C2×#125C2316yes—
261C2×C22⋊Q8C2316yes—
262C2×C22⋊Q8C2313yes—
263C2×C22⋊Q8C2313yes—
264C2×C22⋊Q8C2316yes—
265#520—44no—
266#520Q8116yescomplemented
267C4×#41—44no—
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×#117C2316yes—
295C2×#117C2316yes—
296C2×#117C2313yes—
297C22×C4⋊C4C2313yes—
298C22×C4⋊C4C2316yes—
299C22×C4⋊C4C2313yes—
300C22×C42C2313yes—
301#400C2313yes—
302#400C2316yes—
303#400C2316yes—
304#400C2316yes—
305#400C2316yes—
306#400C2316yes—
307#400C2313yes—
308#400C2316yes—
309#400C2316yes—
310#400C2313yes—
311#400C2313yes—
312#400C2313yes—
313#400C2313yes—
314#400C2313yes—
315#400C2311yescharacteristic
316#400C2313yes—
317#400C2313yes—
318#399C2316yes—
319#399C2316yes—
320#399C2313yes—
321#399C2313yes—
322#398C2313yes—
323#398C2316yes—
324#398C2316yes—
325#398C2316yes—
326#398C2316yes—
327#398C2316yes—
328#398C2313yes—
329#398C2313yes—
330#398C2316yes—
331#398C2316yes—
332#398C2313yes—
333#398C2313yes—
334#398C2313yes—
335#398C2316yes—
336#398C2316yes—
337#398C2316yes—
338#398C2316yes—
339#398C2313yes—
340#398C2313yes—
341#398C2313yes—
342#398C2313yes—
343#398C2316yes—
344#398C2316yes—
345#398C2316yes—
346#398C2316yes—
347#398C2316yes—
348#398C2313yes—
349#398C2311yescharacteristic
350#398C2311yescharacteristic
351#398C2311yescharacteristic
352#398C2311yescharacteristic
353#398C2313yes—
354#398C2313yes—
355#398C2313yes—
356#398C2311yescharacteristic
357#398C2313yes—
358#398C2316yes—
359#398C2316yes—
360#398C2316yes—
361#396C2313yes—
362#396C2313yes—
363#396C2316yes—
364#396C2316yes—
365#396C2316yes—
366#396C2316yes—
367#396C2316yes—
368#396C2316yes—
369#396C2316yes—
370#396C2316yes—
371#396C2313yes—
372#396C2313yes—
373#395C2313yes—
374#395C2313yes—
375#395C2316yes—
376#395C2316yes—
377#395C2316yes—
378#395C2316yes—
379#395C2313yes—
380#395C2313yes—
381#395C2313yes—
382#395C2313yes—
383#395C2313yes—
384#395C2313yes—
385#395C2313yes—
386#395C2313yes—
387#393C2316yes—
388#393C2316yes—
389#393C2313yes—
390#393C2313yes—
391#391C2313yes—
392#391C2313yes—
393#391C2313yes—
394#391C2313yes—
395#391C2316yes—
396#391C2316yes—
397#391C2313yes—
398#391C2313yes—
399#390C2313yes—
400#390C2313yes—
401#390C2313yes—
402#390C2313yes—
403#390C2313yes—
404#390C2313yes—
405#390C2313yes—
406#390C2313yes—
407#389C2313yes—
408#389C2313yes—
409#389C2313yes—
410#389C2313yes—
411#389C2311yescharacteristic
412#389C2313yes—
413#389C2313yes—
414#389C2313yes—
415#389C2313yes—
416#389C2313yes—
417#389C2313yes—
418#389C2313yes—
419#389C2313yes—
420#389C2313yes—
421#389C2313yes—
422#389C2313yes—
423#389C2313yes—
424#389C2313yes—
425#389C2313yes—
426#389C2313yes—
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#389C2316yes—
440#389C2313yes—
441#389C2316yes—
442#389C2313yes—
443#389C2313yes—
444#389C2313yes—
445#389C2313yes—
446#389C2316yes—
447#389C2316yes—
448#389C2316yes—
449#389C2313yes—
450#389C2313yes—
451#389C2313yes—
452#389C2313yes—
453#389C2313yes—
454#389C2313yes—
455#389C2316yes—
456#389C2316yes—
457#389C2313yes—
458#389C2313yes—
459#389C2313yes—
460#389C2313yes—
461#389C2313yes—
462#389C2316yes—
463#389C2316yes—
464#389C2313yes—
465#389C2313yes—
466#389C2316yes—
467#389C2313yes—
468#389C2313yes—
469#389C2313yes—
470#389C2313yes—
471#389C2313yes—
472#389C2313yes—
473#389C2313yes—
474#389C2311yescharacteristic
475#388C2316yes—
476#388C2316yes—
477#388C2316yes—
478#388C2316yes—
479#388C2313yes—
480#388C2313yes—
481#388C2313yes—
482#388C2313yes—
483#388C2313yes—
484#388C2313yes—
485#388C2313yes—
486#388C2313yes—
487#387C2311yescharacteristic
488#387C2311yescharacteristic
489#387C2313yes—
490#387C2313yes—
491#387C2313yes—
492#387C2313yes—
493#387C2313yes—
494#387C2313yes—
495#387C2313yes—
496#387C2313yes—
497#387C2316yes—
498#387C2316yes—
499#387C2316yes—
500#387C2316yes—
501#387C2316yes—
502#387C2316yes—
503#387C2316yes—
504#387C2316yes—
505#387C2316yes—
506#387C2316yes—
507#387C2313yes—
508#387C2313yes—
509#387C2316yes—
510#387C2316yes—
511#387C2313yes—
512#387C2313yes—
513#387C2313yes—
514#387C2313yes—
515#387C2316yes—
516#387C2316yes—
517#387C2311yescharacteristic
518#387C2311yescharacteristic
519#387C2311yescharacteristic
520#387C2311yescharacteristic
521#385C2313yes—
522#385C2313yes—
523#385C2316yes—
524#385C2316yes—
525#385C2316yes—
526#385C2316yes—
527#385C2316yes—
528#385C2316yes—
529#385C2316yes—
530#385C2316yes—
531#385C2316yes—
532#385C2313yes—
533#385C2313yes—
534#385C2316yes—
535#385C2313yes—
536#385C2313yes—
537#385C2313yes—
538#385C2313yes—
539#384C2311yescharacteristic
540#384C2313yes—
541#384C2313yes—
542#384C2313yes—
543#384C2313yes—
544#384C2313yes—
545#384C2316yes—
546#384C2316yes—
547#384C2313yes—
548#384C2313yes—
549#384C2313yes—
550#384C2313yes—
551#384C2313yes—
552#384C2313yes—
553#384C2316yes—
554#384C2316yes—
555#382C2313yes—
556#382C2313yes—
557#382C2313yes—
558#382C2313yes—
559#382C2313yes—
560#382C2313yes—
561#382C2313yes—
562#382C2313yes—
563#382C2313yes—
564#382C2313yes—
565#382C2313yes—
566#382C2313yes—
567#382C2316yes—
568#381C2316yes—
569#381C2316yes—
570#380C2313yes—
571#380C2313yes—
572#380C2313yes—
573#380C2313yes—
574#380C2316yes—
575#380C2316yes—
576#380C2316yes—
577#380C2316yes—
578#380C2316yes—
579#380C2316yes—
580#380C2313yes—
581#380C2313yes—
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⋊C4C2313yes—
608C4×C4⋊C4C2313yes—
609C4×C4⋊C4C2313yes—
610C4×C4⋊C4C2313yes—
611C4×C4⋊C4C2313yes—
612C4×C4⋊C4C2313yes—
613C4×C4⋊C4C2313yes—
614C4×C22⋊C4C2316yes—
615C4×C22⋊C4C2316yes—
616C4×C22⋊C4C2313yes—
617C4×C22⋊C4C2313yes—
618C4×C22⋊C4C2313yes—
619C4×C22⋊C4C2313yes—
620#376C2313yes—
621#376C2313yes—
622C2×#95C2316yes—
623C43C2313yes—
624C43C2313yes—
625C2×#41—24no—
626C2×#41—24no—
627C2×#41C2×Q818yes—
628C22×Q8C2413yes—
629C22×Q8C2413yes—
630C22×Q8C2413yes—
631C22×Q8C2413yes—
632C22×Q8C2411yescharacteristic
633C22×D4C2413yes—
634C23×C4C2413yes—
635C23×C4C2416yes—
636C23×C4C2413yes—
637C23×C4C2413yes—
638C23×C4C2416yes—
639C4⋊Q8—46no—
640C4⋊Q8—46no—
641C4⋊Q8—46no—
642C4⋊Q8—46no—
643C4⋊Q8—46no—
644C4⋊Q8—46no—
645C4⋊Q8—86no—
646#125—46no—
647#125—46no—
648#125—46no—
649#125—46no—
650#125—46no—
651#125—46no—
652#125—46no—
653#125—46no—
654#125—46no—
655#125—46no—
656#125—86no—
657C22⋊Q8—46no—
658C22⋊Q8—46no—
659C22⋊Q8—412no—
660C22⋊Q8—86no—
661C4×Q8—24no—
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—46no—
674C4×Q8—46no—
675C4×Q8—46no—
676C4×Q8—46no—
677C4×Q8C2×Q818yes—
678C4×Q8C2×Q818yes—
679C4×D4—46no—
680C4×D4—46no—
681C4×D4—46no—
682C4×D4—46no—
683C4×D4C2×Q8124yes—
684C4×D4C2×Q8124yes—
685#117—46no—
686#117—412no—
687#117—46no—
688#117—86no—
689#117C2×Q8124yes—
690C2×C4⋊C4—46no—
691C2×C4⋊C4—86no—
692C2×C4⋊C4C2×Q8124yes—
693C2×C4⋊C4C2413yes—
694C2×C4⋊C4C2413yes—
695C2×C4⋊C4C2413yes—
696C2×C4⋊C4C2413yes—
697C2×C4⋊C4C2413yes—
698C2×C4⋊C4C2413yes—
699C2×C4⋊C4C2413yes—
700C2×C4⋊C4C2413yes—
701C2×C4⋊C4C2413yes—
702C2×C4⋊C4C2413yes—
703C2×C4⋊C4C2413yes—
704C2×C4⋊C4C2413yes—
705C2×C4⋊C4C2413yes—
706C2×C4⋊C4C2411yescharacteristic
707C2×C4⋊C4C2411yescharacteristic
708C2×C4⋊C4C2413yes—
709C2×C4⋊C4C2413yes—
710C2×C4⋊C4C2411yescharacteristic
711C2×C4⋊C4C2411yescharacteristic
712C2×C4⋊C4C2411yescharacteristic
713C2×C4⋊C4C2413yes—
714C2×C4⋊C4C2413yes—
715C2×C4⋊C4C2413yes—
716C2×C4⋊C4C2416yes—
717C2×C4⋊C4C2416yes—
718C2×C4⋊C4C2411yescharacteristic
719C2×C4⋊C4C2413yes—
720C2×C4⋊C4C2416yes—
721C2×C4⋊C4C2416yes—
722C2×C4⋊C4C2411yescharacteristic
723C2×C4⋊C4C2411yescharacteristic
724C2×C4⋊C4C2411yescharacteristic
725C2×C4⋊C4C2411yescharacteristic
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⋊C4C2416yes—
736C2×C4⋊C4C2416yes—
737C2×C4⋊C4C2413yes—
738C2×C4⋊C4C2413yes—
739C2×C4⋊C4C2413yes—
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⋊C4C2416yes—
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⋊C4C2411yescharacteristic
764C2×C4⋊C4C2411yescharacteristic
765C2×C4⋊C4C2411yescharacteristic
766C2×C4⋊C4C2411yescharacteristic
767C2×C4⋊C4C2411yescharacteristic
768C2×C4⋊C4C2413yes—
769C2×C4⋊C4C2413yes—
770C2×C4⋊C4C2413yes—
771C2×C4⋊C4C2413yes—
772C2×C4⋊C4C2416yes—
773C2×C4⋊C4C2413yes—
774C2×C4⋊C4C2413yes—
775C2×C4⋊C4C2413yes—
776C2×C4⋊C4C2411yescharacteristic
777C2×C22⋊C4C2413yes—
778C2×C22⋊C4C2413yes—
779C2×C22⋊C4C2413yes—
780C2×C22⋊C4C2416yes—
781C2×C22⋊C4C2413yes—
782C2×C22⋊C4C2413yes—
783C2×C22⋊C4C2416yes—
784C2×C22⋊C4C2416yes—
785C2×C22⋊C4C2413yes—
786C2×C22⋊C4C2413yes—
787C2×C22⋊C4C2413yes—
788C2×C22⋊C4C2416yes—
789C2×C22⋊C4C2413yes—
790C2×C22⋊C4C2416yes—
791C2×C22⋊C4C2413yes—
792C2×C22⋊C4C2413yes—
793C2×C22⋊C4C2413yes—
794C2×C42—46no—
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×C42C2411yescharacteristic
809C2×C42C2413yes—
810C2×C42C2413yes—
811C2×C42C2416yes—
812C2×C42C2416yes—
813C2×C42C2413yes—
814C2×C42C2413yes—
815C2×C42C2413yes—
816C2×C42C2411yescharacteristic
817C2×C42C2413yes—
818C2×C42C2411yescharacteristic
819C2×C42C2413yes—
820C2×C42C2413yes—
821#95C2413yes—
822#95C2413yes—
823#95C2416yes—
824#95C2416yes—
825#95C2411yescharacteristic
826#95C2411yescharacteristic
827#95C2413yes—
828#95C2413yes—
829#95C2413yes—
830#95C2413yes—
831#95C2413yes—
832#95C2413yes—
833#95C2411yescharacteristic
834#95C2411yescharacteristic
835#95C2411yescharacteristic
836#95C2411yescharacteristic
837#95C2413yes—
838#95C2413yes—
839#95C2413yes—
840#95C2413yes—
841#95C2413yes—
842#95C2413yes—
843#95C2416yes—
844#95C2416yes—
845#95C2411yescharacteristic
846#95C2411yescharacteristic
847#95C2416yes—
848#95C2416yes—
849#95C2411yescharacteristic
850#95C2411yescharacteristic
851#95C2411yescharacteristic
852#95C2411yescharacteristic
853#95C2411yescharacteristic
854#95C2411yescharacteristic
855#95C2411yescharacteristic
856#95C2411yescharacteristic
857#95C2413yes—
858#95C2413yes—
859#95C2413yes—
860#95C2413yes—
861#95C2413yes—
862#95C2413yes—
863#95C2413yes—
864#95C2413yes—
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—26no—
892C2×Q8—26no—
893C2×Q8—43no—
894C2×Q8—43no—
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×Q8C22×Q814yes—
904C2×Q8H(5,𝔽2)14yes—
905C2×Q82−1+414yes—
906C2×D4—26no—
907C2×D4—26no—
908C2×D4C22×Q8112yes—
909C22×C4—26no—
910C22×C4—26no—
911C22×C4—46no—
912C22×C4—46no—
913C22×C4—43no—
914C22×C4—43no—
915C22×C4—43no—
916C22×C4—43no—
917C22×C4—43no—
918C22×C4—43no—
919C22×C4—46no—
920C22×C4—46no—
921C22×C4—46no—
922C22×C4C22×Q8112yes—
923C22×C4C22×Q8124yes—
924C22×C4C2511yescharacteristic
925C22×C4C2511yescharacteristic
926C22×C4C2511yescharacteristic
927C22×C4C2511yescharacteristic
928C22×C4C2513yes—
929C22×C4C2513yes—
930C22×C4C2513yes—
931C22×C4C2513yes—
932C22×C4C2511yescharacteristic
933C22×C4C2513yes—
934C22×C4C2511yescharacteristic
935C22×C4C2513yes—
936C22×C4C2511yescharacteristic
937C22×C4C2513yes—
938C22×C4C2513yes—
939C22×C4C2511yescharacteristic
940C22×C4C2511yescharacteristic
941C22×C4C2511yescharacteristic
942C22×C4C2513yes—
943C22×C4C2513yes—
944C22×C4C2513yes—
945C22×C4C2513yes—
946C22×C4C2511yescharacteristic
947C22×C4C2511yescharacteristic
948C22×C4C2511yescharacteristic
949C22×C4C2513yes—
950C22×C4C2513yes—
951C22×C4C2511yescharacteristic
952C22×C4C2511yescharacteristic
953C22×C4C2513yes—
954C4⋊C4—26no—
955C4⋊C4—26no—
956C4⋊C4—26no—
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—22no—
968C4⋊C4—22no—
969C4⋊C4—26no—
970C4⋊C4—26no—
971C4⋊C4—22no—
972C4⋊C4—22no—
973C4⋊C4—22no—
974C4⋊C4—43no—
975C4⋊C4—43no—
976C4⋊C4—43no—
977C4⋊C4—46no—
978C4⋊C4—46no—
979C4⋊C4—41no—
980C4⋊C4—41no—
981C4⋊C4—43no—
982C4⋊C4—41no—
983C4⋊C4—43no—
984C4⋊C4—43no—
985C4⋊C4—46no—
986C4⋊C4—41no—
987C4⋊C4—41no—
988C4⋊C4—43no—
989C4⋊C4—46no—
990C4⋊C4—41no—
991C4⋊C4—43no—
992C4⋊C4—46no—
993C4⋊C4—41no—
994C4⋊C4—41no—
995C4⋊C4—41no—
996C4⋊C4—41no—
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—43no—
1006C4⋊C4—46no—
1007C4⋊C4—43no—
1008C4⋊C4—43no—
1009C4⋊C4—46no—
1010C4⋊C4—43no—
1011C4⋊C4—46no—
1012C4⋊C4—46no—
1013C4⋊C4—43no—
1014C4⋊C4—43no—
1015C4⋊C4—43no—
1016C4⋊C4—43no—
1017C4⋊C4—43no—
1018C4⋊C4—43no—
1019C4⋊C4—43no—
1020C4⋊C4—46no—
1021C4⋊C4—46no—
1022C4⋊C4—46no—
1023C4⋊C4—46no—
1024C4⋊C4—43no—
1025C4⋊C4—43no—
1026C4⋊C4—43no—
1027C4⋊C4—46no—
1028C4⋊C4—43no—
1029C4⋊C4—43no—
1030C4⋊C4—43no—
1031C4⋊C4—43no—
1032C4⋊C4—43no—
1033C4⋊C4—43no—
1034C4⋊C4C22×Q8112yes—
1035C4⋊C4C22×Q8112yes—
1036C4⋊C4C22×Q8112yes—
1037C4⋊C4C22×Q814yes—
1038C22⋊C4—26no—
1039C22⋊C4—26no—
1040C22⋊C4—43no—
1041C22⋊C4—46no—
1042C22⋊C4—43no—
1043C22⋊C4—46no—
1044C22⋊C4—43no—
1045C22⋊C4—43no—
1046C22⋊C4—46no—
1047C22⋊C4—43no—
1048C22⋊C4—46no—
1049C22⋊C4—46no—
1050C22⋊C4—43no—
1051C22⋊C4—43no—
1052C22⋊C4—43no—
1053C22⋊C4C22×Q8112yes—
1054C22⋊C4C22×Q8112yes—
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—22no—
1069C42—41no—
1070C42—43no—
1071C42—43no—
1072C42—41no—
1073C42—46no—
1074C42—43no—
1075C42—46no—
1076C42—43no—
1077C42—43no—
1078C42—43no—
1079C42C22×Q8112yes—
1080C42C22×Q8112yes—
1081C23—23no—
1082C23—23no—
1083C23—23no—
1084C23—23no—
1085C23—23no—
1086C23—23no—
1087C23C23×Q816yes—
1088C23C2611yescharacteristic
1089Q8—86no—
1090Q8—86no—
1091Q8—86no—
1092Q8—86no—
1093Q8#544116yes—
1094D4—224no—
1095C2×C4—21no—
1096C2×C4—21no—
1097C2×C4—21no—
1098C2×C4—21no—
1099C2×C4—23no—
1100C2×C4—21no—
1101C2×C4—21no—
1102C2×C4—21no—
1103C2×C4—23no—
1104C2×C4—23no—
1105C2×C4—21no—
1106C2×C4—23no—
1107C2×C4—21no—
1108C2×C4—21no—
1109C2×C4—224no—
1110C2×C4—21no—
1111C2×C4—21no—
1112C2×C4—21no—
1113C2×C4—21no—
1114C2×C4—21no—
1115C2×C4—21no—
1116C2×C4—21no—
1117C2×C4—23no—
1118C2×C4—23no—
1119C2×C4—23no—
1120C2×C4—23no—
1121C2×C4—23no—
1122C2×C4—23no—
1123C2×C4—23no—
1124C2×C4—23no—
1125C2×C4—21no—
1126C2×C4—21no—
1127C2×C4—21no—
1128C2×C4—23no—
1129C2×C4—23no—
1130C2×C4—23no—
1131C2×C4—23no—
1132C2×C4—23no—
1133C2×C4—21no—
1134C2×C4—23no—
1135C2×C4—23no—
1136C2×C4—23no—
1137C2×C4—23no—
1138C2×C4—23no—
1139C2×C4—23no—
1140C2×C4—21no—
1141C2×C4—21no—
1142C2×C4—23no—
1143C2×C4—21no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—23no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—23no—
1150C2×C4—21no—
1151C2×C4—23no—
1152C2×C4—23no—
1153C2×C4—21no—
1154C2×C4—23no—
1155C2×C4—23no—
1156C2×C4—23no—
1157C2×C4—23no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—23no—
1161C2×C4—21no—
1162C2×C4—23no—
1163C2×C4—23no—
1164C2×C4—21no—
1165C2×C4—23no—
1166C2×C4—23no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—23no—
1170C2×C4—23no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—23no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—424no—
1177C2×C4—86no—
1178C2×C4—86no—
1179C2×C4—166no—
1180C2×C4C23×Q812yes—
1181C2×C4C23×Q812yes—
1182C2×C4C23×Q816yes—
1183C2×C4C23×Q816yes—
1184C2×C4C23×Q812yes—
1185C2×C4C23×Q816yes—
1186C2×C4C2×H(5,𝔽2)16yes—
1187C2×C4C2×2−1+416yes—
1188C2×C4#58512yes—
1189C2×C4#58512yes—
1190C22—26no—
1191C22—26no—
1192C22—26no—
1193C22—43no—
1194C22—43no—
1195C22—43no—
1196C22—43no—
1197C22C24×Q811yescharacteristic
1198C22C22×H(5,𝔽2)11yescharacteristic
1199C22C22×2−1+411yescharacteristic
1200C22C2×#58511yescharacteristic
1201C22C2×#58511yescharacteristic
1202C22H(7,𝔽2)11yescharacteristic
1203C222−1+611yescharacteristic
1204C4—26no—
1205C4—26no—
1206C4—22no—
1207C4—22no—
1208C4—22no—
1209C4—22no—
1210C4—22no—
1211C4—41no—
1212C4—43no—
1213C4—43no—
1214C4—41no—
1215C4—41no—
1216C4—43no—
1217C4—43no—
1218C4—41no—
1219C4—43no—
1220C4—43no—
1221C4—43no—
1222C4—43no—
1223C4—43no—
1224C4—41no—
1225C4—41no—
1226C4—41no—
1227C4—41no—
1228C4—43no—
1229C4—41no—
1230C4—43no—
1231C4—43no—
1232C4—41no—
1233C4C2×#544112yes—
1234C2—46no—
1235C2C22×#54411yescharacteristic
1236C2#6289911yescharacteristic
1237C2#6292211yescharacteristic
1238C2#6298911yescharacteristic
1239C2#6300411yescharacteristic
1240C2#6303311yescharacteristic
1241C2#6306111yescharacteristic
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. #52290C2semidirect
2. #42498C2semidirect
3. #42498C2semidirect
4. #42496C2semidirect
5. #42495C2semidirect
6. #42492C2semidirect
7. #42489C2semidirect
8. #39973C2semidirect
9. #39972C2semidirect
10. #39497C2semidirect
11. #39178C2semidirect
12. #38966C2semidirect
13. #38963C2semidirect
14. #37429C2semidirect
15. #37427C2semidirect
16. #37312C2semidirect
17. #36593C2semidirect
18. #36475C2semidirect
19. #36475C2semidirect
20. #36466C2semidirect
23. #35971C2semidirect
24. #35957C2semidirect
25. #35957C2semidirect
26. #35868C2semidirect
266. #520Q8semidirect

Maximal subgroups

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

subgroupindex
#522902
#424982
#424962
#424952
#424922
#424892
#399732
#399722
#394972
#391782
#389662
#389632
#374292
#374272
#373122
#365932
#364752
#364662
#364312
#359712
#359572
#358682
#358162
#342632
#342502