Finite Group Databasebeta

← #7655981

Subgroups — #7655981

Order 512.

4952 conjugacy classes of subgroups.

The subgroup lattice has 1320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42756C213yesmaximal, complemented
2#42754C213yesmaximal, complemented
3#42699C213yesmaximal, complemented
4#42693C213yesmaximal, complemented
5#42671C213yesmaximal, complemented
6#42661C213yesmaximal, complemented
7#42613C213yesmaximal, complemented
8#42611C213yesmaximal, complemented
9#40055C213yesmaximal, complemented
10#40047C213yesmaximal, complemented
11#39411C213yesmaximal, complemented
12#39403C213yesmaximal, complemented
13#37593C213yesmaximal, complemented
14#37572C213yesmaximal, complemented
15#36578C211yesmaximal, characteristic, complemented
16#36577C211yesmaximal, characteristic, complemented
17#36456C211yesmaximal, characteristic, complemented
18#36433C211yesmaximal, characteristic, complemented
19#36049C211yesmaximal, characteristic, complemented
20#35948C211yesmaximal, characteristic, complemented
21#35948C211yesmaximal, characteristic, complemented
22#35937C211yesmaximal, characteristic, complemented
23#35920C211yesmaximal, characteristic, complemented
24#35898C211yesmaximal, characteristic, complemented
25#35831C211yesmaximal, characteristic
26#35748C211yesmaximal, characteristic, complemented
27#35170C213yesmaximal, complemented
28#34596C213yesmaximal, complemented
29#34335C211yesmaximal, characteristic, complemented
30#34263C211yesmaximal, characteristic, complemented
31C4×#548C211yesmaximal, characteristic, complemented
32C2×Q82C2211yescharacteristic
33C2×Q82C2211yescharacteristic
34C2×#557C2211yescharacteristic
35C2×#550C2211yescharacteristic
36C2×#548C2211yescharacteristic
37C2×#548C2211yescharacteristic
38C2×#542C2216yes—
39C2×#520C2211yescharacteristic
40C2×C4×#41C2211yescharacteristic
41C22×C4×Q8C2211yescharacteristic
42#2857C2213yes—
43#2857C2213yes—
44#2854C2213yes—
45#2854C2213yes—
46#2837C2216yes—
47#2832C2216yes—
48#2832C2216yes—
49#2831C2216yes—
50#2799C2216yes—
51#2798C2216yes—
52#2779C2216yes—
53#2747C2216yes—
54#2745C2216yes—
55#2739C2216yes—
56#2731C2216yes—
57#2716C2216yes—
58#2715C2216yes—
59#2712C2216yes—
60#2702C2216yes—
61#2700C2216yes—
62#2692C2216yes—
63#2691C2216yes—
64#2687C2216yes—
65#2686C2216yes—
66#2665C2211yescharacteristic
67#2665C2213yes—
68#2663C2213yes—
69#2663C2213yes—
70#2663C2216yes—
71#2660C2213yes—
72#2655C2213yes—
73#2655C2213yes—
74#2653C2216yes—
75#2653C2213yes—
76#2653C2213yes—
77#2652C2213yes—
78#2652C2213yes—
79#2651C2216yes—
80#2650C2213yes—
81#2650C2213yes—
82#2650C2216yes—
83#2649C2216yes—
84#2645C2213yes—
85#2644C2213yes—
86#2641C2213yes—
87#2640C2213yes—
88#2640C2213yes—
89#2638C2213yes—
90#2638C2213yes—
91#2630C2213yes—
92#2630C2213yes—
93#2628C2213yes—
94#2620C2213yes—
95#2592C2213yes—
96#2592C2213yes—
97#2584C2213yes—
98#2582C2213yes—
99#2580C2213yes—
100#2568C2213yes—
101#2563C2213yes—
102#2562C2213yes—
103#2551C2213yes—
104#2551C2213yes—
105#2550C2213yes—
106#2550C2213yes—
107#2548C2213yes—
108#2547C2213yes—
109#2547C2213yes—
110#2546C2213yes—
111#2544C2213yes—
112#2542C2213yes—
113#2538C2213yes—
114#2537C2213yes—
115#2521C2216yes—
116#2521C2216yes—
117#2513C2213yes—
118#2512C2213yes—
119#2512C2213yes—
120#2511C2213yes—
121#2511C2213yes—
122#2511C2213yes—
123#2504C2213yes—
124#2500C2213yes—
125#2497C2213yes—
126#2496C2213yes—
127#2496C2213yes—
128#2496C2213yes—
129#2496C2213yes—
130#2494C2213yes—
131#2492C2216yes—
132#2492C2213yes—
133#2492C2213yes—
134#2492C2213yes—
135#2492C2213yes—
136#2491C2213yes—
137#2491C2213yes—
138#2491C2213yes—
139#2491C2213yes—
140#2491C2213yes—
141#2491C2213yes—
142#2490C2213yes—
143#2490C2213yes—
144#2487C2213yes—
145#2485C2213yes—
146#2477C2216yes—
147#2470C2216yes—
148#2465C2216yes—
149#2458C2216yes—
150#2453C2213yes—
151#2453C2213yes—
152#2452C2213yes—
153#2452C2213yes—
154#2452C2213yes—
155#2452C2213yes—
156#2448C2213yes—
157#2448C2213yes—
158#2445C2213yes—
159#2445C2213yes—
160#2442C2213yes—
161#2442C2213yes—
162#2440C2213yes—
163#2440C2213yes—
164#2439C2213yes—
165#2439C2213yes—
166#2428C2213yes—
167#2427C2213yes—
168#2427C2216yes—
169#2422C2213yes—
170#2421C2213yes—
171#2421C2213yes—
172#2420C2213yes—
173#2417C2213yes—
174#2416C2213yes—
175#2401C2213yes—
176#2401C2213yes—
177#2399C2213yes—
178#2398C2213yes—
179#2398C2213yes—
180#2398C2213yes—
181#2396C2213yes—
182#2392C2213yes—
183#2369C2213yes—
184#2367C2213yes—
185#2365C2213yes—
186#2365C2213yes—
187#2362C2213yes—
188#2361C2213yes—
189#2357C2213yes—
190#2355C2213yes—
191#2354C2213yes—
192#2352C2213yes—
193#2351C2211yescharacteristic
194#2351C2211yescharacteristic
195#2351C2211yescharacteristic
196#2351C2211yescharacteristic
197#2351C2211yescharacteristic
198Q8×C4⋊C4C2211yescharacteristic
199Q8×C4⋊C4C2211yescharacteristic
200Q8×C4⋊C4C2211yescharacteristic
201Q8×C4⋊C4C2211yescharacteristic
202Q8×C4⋊C4C2211yescharacteristic
203#2345C2213yes—
204#2344C2213yes—
205#2341C2211yescharacteristic
206#2341C2211yescharacteristic
207#2341C2211yescharacteristic
208#2341C2211yescharacteristic
209#2341C2211yescharacteristic
210#2341C2211yescharacteristic
211#2341C2211yescharacteristic
212#2341C2211yescharacteristic
213Q8×C22⋊C4C2211yescharacteristic
214Q8×C22⋊C4C2211yescharacteristic
215Q8×C22⋊C4C2211yescharacteristic
216Q8×C22⋊C4C2211yescharacteristic
217#2331C2213yes—
218#2331C2213yes—
219#2323C2216yes—
220#2319C2213yes—
221#2314C2213yes—
222C4×C4⋊Q8C2213yes—
223C4×#124C2213yes—
224C4×C22⋊Q8C2213yes—
225C4×C22⋊Q8C2213yes—
226C4×C22⋊Q8C2213yes—
227C4×#123C2213yes—
228C4×#123C2213yes—
229C4×#121C2213yes—
230#2298C2213yes—
231#2295C2213yes—
232#2293C2213yes—
233#2276C2211yescharacteristic
234#2276C2211yescharacteristic
235#2276C2211yescharacteristic
236C42×Q8C2211yescharacteristic
237C42×D4C2213yes—
238C22×#41C2311yescharacteristic
239C22×#41C2311yescharacteristic
240C23×Q8C2311yescharacteristic
241Q82—28no—
242Q82—44no—
243#557—44no—
244#550—44no—
245#548—28no—
246#548—44no—
247#542—424no—
248C2×C4⋊Q8C2313yes—
249C2×C4⋊Q8C2313yes—
250C2×C4⋊Q8C2313yes—
251C2×C4⋊Q8C2313yes—
252C2×C4⋊Q8C2313yes—
253C2×C4⋊Q8C2313yes—
254C2×C4⋊Q8C2313yes—
255C2×C4⋊Q8C2316yes—
256C2×#127C2313yes—
257C2×#126C2316yes—
258C2×#126C2316yes—
259C2×#125C2313yes—
260C2×#125C2313yes—
261C2×#124C2313yes—
262C2×#124C2313yes—
263C2×#124C2316yes—
264C2×#124C2316yes—
265C2×#124C2316yes—
266C2×#123C2313yes—
267C2×#123C2316yes—
268C2×#123C2313yes—
269C2×C22⋊Q8C2313yes—
270C2×C22⋊Q8C2313yes—
271C2×C22⋊Q8C2316yes—
272C2×C22⋊Q8C2316yes—
273C2×C22⋊Q8C2313yes—
274C2×C22⋊Q8C2313yes—
275C2×C22⋊Q8C2316yes—
276C2×#121C2313yes—
277C2×#121C2313yes—
278C2×#121C2313yes—
279C2×#121C2313yes—
280C2×#121C2316yes—
281#520—28no—
282C4×#41—44no—
283C2×C4×Q8—44no—
284C2×C4×Q8C2313yes—
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×Q8C2311yescharacteristic
296C2×C4×Q8C2316yes—
297C2×C4×Q8C2313yes—
298C2×C4×Q8C2313yes—
299C2×C4×Q8C2313yes—
300C2×C4×Q8C2313yes—
301C2×C4×Q8C2311yescharacteristic
302C2×C4×D4C2313yes—
303C2×C4×D4C2313yes—
304C2×C4×D4C2313yes—
305C2×C4×D4C2313yes—
306C2×C4×D4C2313yes—
307C2×C4×D4C2313yes—
308C2×C4×D4C2313yes—
309C2×C4×D4C2313yes—
310C2×C4×D4C2313yes—
311C2×#117C2313yes—
312C2×#117C2316yes—
313C2×#117C2313yes—
314C22×C4⋊C4C2313yes—
315C22×C4⋊C4C2313yes—
316C22×C42C2313yes—
317C22×C42C2313yes—
318#401C2313yes—
319#401C2313yes—
320#400C2313yes—
321#400C2316yes—
322#400C2316yes—
323#400C2313yes—
324#400C2316yes—
325#400C2316yes—
326#400C2313yes—
327#400C2316yes—
328#400C2316yes—
329#400C2313yes—
330#400C2311yescharacteristic
331#400C2313yes—
332#400C2313yes—
333#400C2313yes—
334#400C2313yes—
335#400C2311yescharacteristic
336#400C2313yes—
337#400C2313yes—
338#400C2313yes—
339#399C2316yes—
340#399C2316yes—
341#399C2313yes—
342#398C2316yes—
343#398C2316yes—
344#398C2313yes—
345#398C2316yes—
346#398C2313yes—
347#398C2313yes—
348#398C2313yes—
349#398C2313yes—
350#398C2313yes—
351#398C2313yes—
352#397C2313yes—
353#397C2316yes—
354#397C2316yes—
355#397C2313yes—
356#397C2316yes—
357#397C2316yes—
358#397C2316yes—
359#397C2316yes—
360#397C2316yes—
361#397C2313yes—
362#397C2313yes—
363#397C2313yes—
364#397C2313yes—
365#397C2313yes—
366#397C2313yes—
367#397C2313yes—
368#397C2313yes—
369#397C2313yes—
370#397C2313yes—
371#397C2313yes—
372#396C2316yes—
373#396C2316yes—
374#396C2316yes—
375#396C2316yes—
376#396C2313yes—
377#396C2311yescharacteristic
378#396C2313yes—
379#396C2313yes—
380#396C2313yes—
381#396C2311yescharacteristic
382#395C2316yes—
383#395C2316yes—
384#395C2316yes—
385#395C2313yes—
386#395C2313yes—
387#395C2311yescharacteristic
388#395C2311yescharacteristic
389#395C2313yes—
390#394C2316yes—
391#394C2316yes—
392#394C2316yes—
393#394C2316yes—
394#394C2316yes—
395#394C2316yes—
396#394C2316yes—
397#394C2313yes—
398#394C2316yes—
399#394C2313yes—
400#394C2313yes—
401#394C2313yes—
402#394C2313yes—
403#394C2313yes—
404#394C2313yes—
405#394C2313yes—
406#394C2313yes—
407#393C2316yes—
408#393C2316yes—
409#393C2316yes—
410#393C2313yes—
411#393C2313yes—
412#393C2316yes—
413#393C2316yes—
414#393C2316yes—
415#393C2316yes—
416#393C2313yes—
417#393C2311yescharacteristic
418#393C2313yes—
419#393C2313yes—
420#393C2311yescharacteristic
421#392C2313yes—
422#391C2316yes—
423#391C2313yes—
424#391C2316yes—
425#391C2313yes—
426#391C2313yes—
427#391C2313yes—
428#391C2316yes—
429#391C2313yes—
430#391C2313yes—
431#391C2316yes—
432#391C2316yes—
433#391C2313yes—
434#391C2313yes—
435#391C2313yes—
436#391C2313yes—
437#391C2316yes—
438#391C2311yescharacteristic
439#391C2316yes—
440#391C2311yescharacteristic
441#391C2316yes—
442#390C2313yes—
443#390C2313yes—
444#390C2313yes—
445#390C2313yes—
446#390C2313yes—
447#390C2313yes—
448#390C2313yes—
449#390C2313yes—
450#390C2313yes—
451#390C2313yes—
452#390C2313yes—
453#390C2313yes—
454#390C2313yes—
455#390C2313yes—
456#390C2313yes—
457#390C2313yes—
458#390C2316yes—
459#389C2313yes—
460#389C2313yes—
461#389C2313yes—
462#389C2313yes—
463#389C2313yes—
464#389C2313yes—
465#389C2316yes—
466#389C2316yes—
467#389C2313yes—
468#389C2313yes—
469#389C2313yes—
470#389C2313yes—
471#389C2313yes—
472#389C2313yes—
473#389C2313yes—
474#389C2313yes—
475#389C2313yes—
476#389C2316yes—
477#389C2313yes—
478#389C2313yes—
479#389C2313yes—
480#389C2313yes—
481#389C2313yes—
482#389C2313yes—
483#389C2313yes—
484#389C2313yes—
485#389C2313yes—
486#388C2316yes—
487#388C2316yes—
488#388C2316yes—
489#388C2316yes—
490#388C2313yes—
491#388C2316yes—
492#388C2313yes—
493#388C2316yes—
494#388C2313yes—
495#388C2316yes—
496#388C2316yes—
497#388C2316yes—
498#388C2316yes—
499#388C2316yes—
500#388C2316yes—
501#388C2316yes—
502#388C2313yes—
503#388C2316yes—
504#388C2313yes—
505#388C2313yes—
506#388C2313yes—
507#388C2316yes—
508#388C2316yes—
509#388C2313yes—
510#387C2313yes—
511#387C2316yes—
512#387C2313yes—
513#387C2316yes—
514#387C2316yes—
515#387C2313yes—
516#387C2313yes—
517#387C2316yes—
518#387C2316yes—
519#387C2313yes—
520#387C2316yes—
521#387C2313yes—
522#387C2313yes—
523#387C2313yes—
524#387C2313yes—
525#387C2316yes—
526#387C2316yes—
527#387C2311yescharacteristic
528#387C2313yes—
529#387C2313yes—
530#387C2313yes—
531#387C2313yes—
532#387C2311yescharacteristic
533#387C2313yes—
534#386C2316yes—
535#386C2316yes—
536#386C2316yes—
537#386C2313yes—
538#386C2313yes—
539#386C2316yes—
540#386C2316yes—
541#385C2316yes—
542#385C2316yes—
543#385C2316yes—
544#385C2313yes—
545#385C2313yes—
546#385C2313yes—
547#385C2313yes—
548#385C2313yes—
549#385C2313yes—
550#384C2313yes—
551#384C2313yes—
552#384C2313yes—
553#384C2313yes—
554#384C2313yes—
555#382C2313yes—
556#382C2313yes—
557#382C2313yes—
558#382C2313yes—
559#382C2313yes—
560#381C2316yes—
561#381C2311yescharacteristic
562#381C2313yes—
563#380C2313yes—
564#380C2313yes—
565#380C2313yes—
566#380C2313yes—
567#380C2313yes—
568#380C2316yes—
569#380C2313yes—
570#380C2316yes—
571#380C2316yes—
572#380C2313yes—
573#380C2313yes—
574#380C2313yes—
575#380C2313yes—
576#380C2313yes—
577#380C2313yes—
578#380C2313yes—
579#380C2316yes—
580#380C2311yescharacteristic
581C4×C4⋊C4C2313yes—
582C4×C4⋊C4C2313yes—
583C4×C4⋊C4C2313yes—
584C4×C4⋊C4C2316yes—
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×C22⋊C4C2313yes—
607C4×C22⋊C4C2313yes—
608C4×C22⋊C4C2313yes—
609C4×C22⋊C4C2313yes—
610C4×C22⋊C4C2313yes—
611C4×C22⋊C4C2313yes—
612C4×C22⋊C4C2313yes—
613C4×C22⋊C4C2313yes—
614C4×C22⋊C4C2313yes—
615C4×C22⋊C4C2313yes—
616C4×C22⋊C4C2313yes—
617C4×C22⋊C4C2313yes—
618C4×C22⋊C4C2316yes—
619C4×C22⋊C4C2313yes—
620C4×C22⋊C4C2313yes—
621C4×C22⋊C4C2313yes—
622C4×C22⋊C4C2311yescharacteristic
623C4×C22⋊C4C2316yes—
624#376C2313yes—
625#376C2313yes—
626#376C2313yes—
627C43C2313yes—
628C2×#41—24no—
629C2×#41—24no—
630C2×#41—24no—
631C2×#41—24no—
632C2×#41—24no—
633C2×#41—24no—
634C22×Q8—24no—
635C22×Q8—24no—
636C22×Q8—24no—
637C22×Q8C2413yes—
638C22×Q8C2411yescharacteristic
639C22×Q8C2411yescharacteristic
640C22×Q8C2416yes—
641C22×Q8C2413yes—
642C22×Q8C2416yes—
643C22×Q8C2411yescharacteristic
644C22×D4C2413yes—
645C22×D4C2413yes—
646C22×D4C2413yes—
647C22×D4C2413yes—
648C22×D4C2413yes—
649C22×D4C2416yes—
650C23×C4C2413yes—
651C23×C4C2413yes—
652C23×C4C2413yes—
653C23×C4C2416yes—
654C23×C4C2413yes—
655C23×C4C2413yes—
656C23×C4C2413yes—
657C23×C4C2411yescharacteristic
658C4⋊Q8—212no—
659C4⋊Q8—212no—
660C4⋊Q8—212no—
661C4⋊Q8—46no—
662C4⋊Q8—46no—
663C4⋊Q8—46no—
664C4⋊Q8—46no—
665C4⋊Q8—412no—
666#127—46no—
667#126—412no—
668#126—412no—
669#125—46no—
670#125—46no—
671#124—212no—
672#124—46no—
673#124—412no—
674#124—412no—
675#124—412no—
676#123—212no—
677#123—46no—
678#123—412no—
679C22⋊Q8—212no—
680C22⋊Q8—212no—
681C22⋊Q8—412no—
682C22⋊Q8—412no—
683C22⋊Q8—412no—
684C22⋊Q8—46no—
685C22⋊Q8—46no—
686#121—212no—
687#121—412no—
688#121—46no—
689#121—46no—
690#121—46no—
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—24no—
701C4×Q8—24no—
702C4×Q8—212no—
703C4×Q8—46no—
704C4×Q8—46no—
705C4×Q8—412no—
706C4×Q8—46no—
707C4×Q8—46no—
708C4×Q8#4118yes—
709C4×D4—212no—
710C4×D4—212no—
711C4×D4—212no—
712C4×D4—212no—
713C4×D4—46no—
714C4×D4—46no—
715C4×D4—46no—
716C4×D4—46no—
717C4×D4—46no—
718#117—212no—
719#117—412no—
720#117—46no—
721C2×C4⋊C4—212no—
722C2×C4⋊C4—46no—
723C2×C4⋊C4C2413yes—
724C2×C4⋊C4C2413yes—
725C2×C4⋊C4C2413yes—
726C2×C4⋊C4C2413yes—
727C2×C4⋊C4C2411yescharacteristic
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⋊C4C2413yes—
738C2×C4⋊C4C2413yes—
739C2×C4⋊C4C2413yes—
740C2×C4⋊C4C2413yes—
741C2×C4⋊C4C2413yes—
742C2×C4⋊C4C2413yes—
743C2×C4⋊C4C2413yes—
744C2×C4⋊C4C2413yes—
745C2×C4⋊C4C2413yes—
746C2×C4⋊C4C2413yes—
747C2×C4⋊C4C2411yescharacteristic
748C2×C4⋊C4C2413yes—
749C2×C4⋊C4C2416yes—
750C2×C4⋊C4C2416yes—
751C2×C4⋊C4C2411yescharacteristic
752C2×C4⋊C4C2413yes—
753C2×C4⋊C4C2411yescharacteristic
754C2×C4⋊C4C2416yes—
755C2×C4⋊C4C2413yes—
756C2×C4⋊C4C2413yes—
757C2×C4⋊C4C2413yes—
758C2×C4⋊C4C2413yes—
759C2×C4⋊C4C2413yes—
760C2×C4⋊C4C2416yes—
761C2×C4⋊C4C2413yes—
762C2×C4⋊C4C2413yes—
763C2×C4⋊C4C2416yes—
764C2×C4⋊C4C2416yes—
765C2×C4⋊C4C2413yes—
766C2×C4⋊C4C2416yes—
767C2×C4⋊C4C2411yescharacteristic
768C2×C4⋊C4C2411yescharacteristic
769C2×C4⋊C4C2413yes—
770C2×C4⋊C4C2411yescharacteristic
771C2×C4⋊C4C2411yescharacteristic
772C2×C4⋊C4C2413yes—
773C2×C4⋊C4C2413yes—
774C2×C4⋊C4C2413yes—
775C2×C4⋊C4C2413yes—
776C2×C22⋊C4C2413yes—
777C2×C22⋊C4C2413yes—
778C2×C22⋊C4C2413yes—
779C2×C22⋊C4C2411yescharacteristic
780C2×C22⋊C4C2411yescharacteristic
781C2×C22⋊C4C2413yes—
782C2×C22⋊C4C2413yes—
783C2×C22⋊C4C2413yes—
784C2×C22⋊C4C2413yes—
785C2×C22⋊C4C2416yes—
786C2×C22⋊C4C2413yes—
787C2×C22⋊C4C2413yes—
788C2×C22⋊C4C2413yes—
789C2×C22⋊C4C2413yes—
790C2×C22⋊C4C2416yes—
791C2×C22⋊C4C2416yes—
792C2×C22⋊C4C2411yescharacteristic
793C2×C22⋊C4C2413yes—
794C2×C22⋊C4C2413yes—
795C2×C22⋊C4C2413yes—
796C2×C22⋊C4C2413yes—
797C2×C22⋊C4C2416yes—
798C2×C22⋊C4C2416yes—
799C2×C22⋊C4C2416yes—
800C2×C22⋊C4C2416yes—
801C2×C22⋊C4C2413yes—
802C2×C22⋊C4C2413yes—
803C2×C22⋊C4C2416yes—
804C2×C22⋊C4C2416yes—
805C2×C22⋊C4C2413yes—
806C2×C22⋊C4C2413yes—
807C2×C22⋊C4C2411yescharacteristic
808C2×C22⋊C4C2411yescharacteristic
809C2×C22⋊C4C2411yescharacteristic
810C2×C22⋊C4C2413yes—
811C2×C22⋊C4C2416yes—
812C2×C22⋊C4C2413yes—
813C2×C22⋊C4C2416yes—
814C2×C22⋊C4C2413yes—
815C2×C22⋊C4C2413yes—
816C2×C22⋊C4C2413yes—
817C2×C22⋊C4C2413yes—
818C2×C22⋊C4C2413yes—
819C2×C42—46no—
820C2×C42—46no—
821C2×C42C2413yes—
822C2×C42C2413yes—
823C2×C42C2413yes—
824C2×C42C2413yes—
825C2×C42C2413yes—
826C2×C42C2413yes—
827C2×C42C2413yes—
828C2×C42C2413yes—
829C2×C42C2413yes—
830C2×C42C2413yes—
831C2×C42C2413yes—
832C2×C42C2413yes—
833C2×C42C2413yes—
834C2×C42C2416yes—
835C2×C42C2413yes—
836C2×C42C2413yes—
837C2×C42C2413yes—
838C2×C42C2416yes—
839C2×C42C2416yes—
840C2×C42C2411yescharacteristic
841C2×C42C2413yes—
842C2×C42C2411yescharacteristic
843C2×C42C2413yes—
844#95C2411yescharacteristic
845#95C2411yescharacteristic
846#95C2411yescharacteristic
847#95C2413yes—
848#95C2413yes—
849#95C2413yes—
850#95C2413yes—
851#95C2413yes—
852#95C2413yes—
853#95C2413yes—
854#95C2413yes—
855#95C2413yes—
856#95C2411yescharacteristic
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#95C2416yes—
872#95C2413yes—
873#95C2413yes—
874#95C2413yes—
875#95C2413yes—
876#95C2413yes—
877#95C2413yes—
878#95C2416yes—
879#95C2416yes—
880#95C2413yes—
881#95C2413yes—
882#95C2413yes—
883#95C2413yes—
884#95C2413yes—
885#95C2413yes—
886#95C2416yes—
887#95C2411yescharacteristic
888#95C2411yescharacteristic
889#95C2411yescharacteristic
890#95C2411yescharacteristic
891#95C2413yes—
892#95C2413yes—
893#95C2416yes—
894#95C2416yes—
895#95C2413yes—
896#95C2413yes—
897#95C2413yes—
898#95C2413yes—
899#95C2413yes—
900#95C2413yes—
901#95C2413yes—
902#95C2413yes—
903#95C2413yes—
904#95C2413yes—
905#95C2413yes—
906#95C2416yes—
907#95C2416yes—
908#95C2416yes—
909#95C2416yes—
910C24C2513yes—
911C24C2513yes—
912C24C2511yescharacteristic
913#41—416no—
914#41—416no—
915C2×Q8—22no—
916C2×Q8—26no—
917C2×Q8—212no—
918C2×Q8—26no—
919C2×Q8—26no—
920C2×Q8—26no—
921C2×Q8—22no—
922C2×Q8—41no—
923C2×Q8—41no—
924C2×Q8—41no—
925C2×Q8—41no—
926C2×Q8—46no—
927C2×Q8—43no—
928C2×Q8—46no—
929C2×Q8—43no—
930C2×Q8—46no—
931C2×Q8—46no—
932C2×Q8—46no—
933C2×Q8—416no—
934C2×Q8C2×#4114yes—
935C2×Q8H(5,𝔽2)14yes—
936C2×Q82−1+414yes—
937C2×D4—26no—
938C2×D4—26no—
939C2×D4—26no—
940C2×D4—26no—
941C2×D4—26no—
942C2×D4—26no—
943C2×D4—26no—
944C2×D4—26no—
945C2×D4—26no—
946C2×D4—43no—
947C2×D4—43no—
948C2×D4—43no—
949C2×D4—43no—
950C2×D4—43no—
951C2×D4—43no—
952C2×D4—46no—
953C2×D4—46no—
954C2×D4—46no—
955C22×C4—26no—
956C22×C4—26no—
957C22×C4—26no—
958C22×C4—26no—
959C22×C4—26no—
960C22×C4—26no—
961C22×C4—26no—
962C22×C4—26no—
963C22×C4—26no—
964C22×C4—212no—
965C22×C4—26no—
966C22×C4—26no—
967C22×C4—41no—
968C22×C4—41no—
969C22×C4—43no—
970C22×C4—43no—
971C22×C4—43no—
972C22×C4—46no—
973C22×C4—43no—
974C22×C4—46no—
975C22×C4—43no—
976C22×C4—43no—
977C22×C4—43no—
978C22×C4H(5,𝔽2)14yes—
979C22×C4C2511yescharacteristic
980C22×C4C2511yescharacteristic
981C22×C4C2511yescharacteristic
982C22×C4C2511yescharacteristic
983C22×C4C2511yescharacteristic
984C22×C4C2513yes—
985C22×C4C2511yescharacteristic
986C22×C4C2511yescharacteristic
987C22×C4C2511yescharacteristic
988C22×C4C2513yes—
989C22×C4C2513yes—
990C22×C4C2513yes—
991C22×C4C2511yescharacteristic
992C22×C4C2511yescharacteristic
993C22×C4C2513yes—
994C22×C4C2513yes—
995C22×C4C2513yes—
996C22×C4C2513yes—
997C22×C4C2513yes—
998C22×C4C2513yes—
999C22×C4C2513yes—
1000C22×C4C2513yes—
1001C22×C4C2511yescharacteristic
1002C22×C4C2513yes—
1003C22×C4C2511yescharacteristic
1004C22×C4C2511yescharacteristic
1005C22×C4C2511yescharacteristic
1006C22×C4C2513yes—
1007C4⋊C4—26no—
1008C4⋊C4—26no—
1009C4⋊C4—22no—
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—26no—
1019C4⋊C4—26no—
1020C4⋊C4—26no—
1021C4⋊C4—26no—
1022C4⋊C4—26no—
1023C4⋊C4—26no—
1024C4⋊C4—26no—
1025C4⋊C4—26no—
1026C4⋊C4—26no—
1027C4⋊C4—26no—
1028C4⋊C4—26no—
1029C4⋊C4—26no—
1030C4⋊C4—26no—
1031C4⋊C4—26no—
1032C4⋊C4—22no—
1033C4⋊C4—46no—
1034C4⋊C4—41no—
1035C4⋊C4—43no—
1036C4⋊C4—41no—
1037C4⋊C4—41no—
1038C4⋊C4—41no—
1039C4⋊C4—43no—
1040C4⋊C4—43no—
1041C4⋊C4—43no—
1042C4⋊C4—46no—
1043C4⋊C4—41no—
1044C4⋊C4—43no—
1045C4⋊C4—41no—
1046C4⋊C4—46no—
1047C4⋊C4—43no—
1048C4⋊C4—43no—
1049C4⋊C4—43no—
1050C4⋊C4—43no—
1051C4⋊C4—43no—
1052C4⋊C4—43no—
1053C4⋊C4—43no—
1054C4⋊C4—46no—
1055C4⋊C4—46no—
1056C4⋊C4—43no—
1057C4⋊C4—46no—
1058C4⋊C4—46no—
1059C4⋊C4C2×#41112yes—
1060C22⋊C4—26no—
1061C22⋊C4—26no—
1062C22⋊C4—26no—
1063C22⋊C4—26no—
1064C22⋊C4—26no—
1065C22⋊C4—26no—
1066C22⋊C4—22no—
1067C22⋊C4—26no—
1068C22⋊C4—212no—
1069C22⋊C4—26no—
1070C22⋊C4—26no—
1071C22⋊C4—26no—
1072C22⋊C4—22no—
1073C22⋊C4—26no—
1074C22⋊C4—43no—
1075C22⋊C4—46no—
1076C22⋊C4—43no—
1077C22⋊C4—46no—
1078C22⋊C4—41no—
1079C22⋊C4—43no—
1080C22⋊C4—43no—
1081C22⋊C4—41no—
1082C22⋊C4—43no—
1083C22⋊C4—43no—
1084C22⋊C4—43no—
1085C22⋊C4—41no—
1086C22⋊C4—46no—
1087C22⋊C4—46no—
1088C22⋊C4—43no—
1089C22⋊C4—41no—
1090C22⋊C4—43no—
1091C22⋊C4—43no—
1092C22⋊C4—43no—
1093C22⋊C4—46no—
1094C22⋊C4—46no—
1095C22⋊C4—46no—
1096C22⋊C4—43no—
1097C22⋊C4—43no—
1098C22⋊C4—46no—
1099C22⋊C4—46no—
1100C22⋊C4—43no—
1101C22⋊C4—43no—
1102C22⋊C4—46no—
1103C42—26no—
1104C42—26no—
1105C42—26no—
1106C42—26no—
1107C42—26no—
1108C42—26no—
1109C42—26no—
1110C42—26no—
1111C42—26no—
1112C42—26no—
1113C42—26no—
1114C42—26no—
1115C42—41no—
1116C42—43no—
1117C42—43no—
1118C42—43no—
1119C42—43no—
1120C42—41no—
1121C42—46no—
1122C42—43no—
1123C42—46no—
1124C42—46no—
1125C42C2×#41112yes—
1126C23—21no—
1127C23—21no—
1128C23—21no—
1129C23—21no—
1130C23—21no—
1131C23—21no—
1132C23—23no—
1133C23—23no—
1134C23—23no—
1135C23—23no—
1136C23—23no—
1137C23—23no—
1138C23—23no—
1139C23—23no—
1140C23—23no—
1141C23—23no—
1142C23—23no—
1143C23—23no—
1144C23—23no—
1145C23—23no—
1146C23C2×H(5,𝔽2)12yes—
1147C23C2611yescharacteristic
1148Q8—44no—
1149Q8—44no—
1150Q8—412no—
1151Q8—812no—
1152Q8—86no—
1153Q8—166no—
1154Q8#542116yescomplemented
1155D4—412no—
1156D4—412no—
1157D4—412no—
1158D4—86no—
1159D4—86no—
1160D4—166no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—23no—
1165C2×C4—23no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—23no—
1175C2×C4—23no—
1176C2×C4—23no—
1177C2×C4—23no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—21no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—23no—
1184C2×C4—23no—
1185C2×C4—23no—
1186C2×C4—23no—
1187C2×C4—23no—
1188C2×C4—23no—
1189C2×C4—23no—
1190C2×C4—21no—
1191C2×C4—23no—
1192C2×C4—23no—
1193C2×C4—23no—
1194C2×C4—23no—
1195C2×C4—23no—
1196C2×C4—23no—
1197C2×C4—23no—
1198C2×C4—23no—
1199C2×C4—23no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—23no—
1204C2×C4—23no—
1205C2×C4—21no—
1206C2×C4—21no—
1207C2×C4—23no—
1208C2×C4—21no—
1209C2×C4—23no—
1210C2×C4—23no—
1211C2×C4—21no—
1212C2×C4—23no—
1213C2×C4—23no—
1214C2×C4—21no—
1215C2×C4—21no—
1216C2×C4—23no—
1217C2×C4—21no—
1218C2×C4—23no—
1219C2×C4—21no—
1220C2×C4—23no—
1221C2×C4—21no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—21no—
1225C2×C4—23no—
1226C2×C4—23no—
1227C2×C4—21no—
1228C2×C4—21no—
1229C2×C4—23no—
1230C2×C4—21no—
1231C2×C4—21no—
1232C2×C4—23no—
1233C2×C4—21no—
1234C2×C4—23no—
1235C2×C4—21no—
1236C2×C4—23no—
1237C2×C4—44no—
1238C2×C4—412no—
1239C2×C4—412no—
1240C2×C4—412no—
1241C2×C4—812no—
1242C2×C4—86no—
1243C2×C4—86no—
1244C2×C4—86no—
1245C2×C4C22×#4112yes—
1246C2×C4C22×#4116yes—
1247C2×C4C22×#4116yes—
1248C2×C4C2×H(5,𝔽2)12yes—
1249C2×C4C2×H(5,𝔽2)12yes—
1250C2×C4C2×H(5,𝔽2)16yes—
1251C2×C4C2×2−1+416yes—
1252C2×C4#58512yes—
1253C22—22no—
1254C22—22no—
1255C22—22no—
1256C22—41no—
1257C22—41no—
1258C22—41no—
1259C22—41no—
1260C22—43no—
1261C22—43no—
1262C22—43no—
1263C22—43no—
1264C22—43no—
1265C22—43no—
1266C22—43no—
1267C22—43no—
1268C22—43no—
1269C22—43no—
1270C22—43no—
1271C22—43no—
1272C22—43no—
1273C22—43no—
1274C22C23×#4111yescharacteristic
1275C22C22×H(5,𝔽2)11yescharacteristic
1276C22C22×H(5,𝔽2)11yescharacteristic
1277C22C22×2−1+411yescharacteristic
1278C22C2×#58511yescharacteristic
1279C222−1+611yescharacteristic
1280C222−1+611yescharacteristic
1281C4—26no—
1282C4—22no—
1283C4—22no—
1284C4—22no—
1285C4—22no—
1286C4—43no—
1287C4—43no—
1288C4—43no—
1289C4—41no—
1290C4—41no—
1291C4—41no—
1292C4—43no—
1293C4—43no—
1294C4—43no—
1295C4—43no—
1296C4—43no—
1297C4—43no—
1298C4—41no—
1299C4—41no—
1300C4—41no—
1301C4—41no—
1302C4—41no—
1303C4—43no—
1304C4—43no—
1305C4—43no—
1306C4—41no—
1307C4—41no—
1308C4C2×#542112yes—
1309C2—42no—
1310C2—83no—
1311C2—83no—
1312C2C22×#54211yescharacteristic
1313C2#6280011yescharacteristic
1314C2#6285011yescharacteristic
1315C2#6289511yescharacteristic
1316C2#6289711yescharacteristic
1317C2#6294611yescharacteristic
1318C2#6295311yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35831C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42756C2semidirect
2. #42754C2semidirect
3. #42699C2semidirect
4. #42693C2semidirect
5. #42671C2semidirect
6. #42661C2semidirect
7. #42613C2semidirect
8. #42611C2semidirect
9. #40055C2semidirect
10. #40047C2semidirect
11. #39411C2semidirect
12. #39403C2semidirect
13. #37593C2semidirect
14. #37572C2semidirect
15. #36578C2semidirect
16. #36577C2semidirect
17. #36456C2semidirect
18. #36433C2semidirect
19. #36049C2semidirect
20. #35948C2semidirect
21. #35948C2semidirect
22. #35937C2semidirect
23. #35920C2semidirect
24. #35898C2semidirect
26. #35748C2semidirect
27. #35170C2semidirect
28. #34596C2semidirect
29. #34335C2semidirect
30. #34263C2semidirect
31. C4×#548C2semidirect
1154. Q8#542semidirect

Maximal subgroups

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

subgroupindex
#427562
#427542
#426992
#426932
#426712
#426612
#426132
#426112
#400552
#400472
#394112
#394032
#375932
#375722
#365782
#365772
#364562
#364332
#360492
#359482
#359372
#359202
#358982
#358312
#357482
#351702
#345962
#343352
#342632
C4×#5482