Finite Group Databasebeta

← #7657060

Subgroups — #7657060

Order 512.

4779 conjugacy classes of subgroups.

The subgroup lattice has 1313 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42699C213yesmaximal, complemented
2#42671C213yesmaximal, complemented
3#42628C213yesmaximal, complemented
4#42621C213yesmaximal, complemented
5#42585C213yesmaximal, complemented
6#42579C213yesmaximal, complemented
7#42515C213yesmaximal, complemented
8#42459C213yesmaximal, complemented
9#40226C213yesmaximal, complemented
10#40188C213yesmaximal, complemented
11#39789C213yesmaximal, complemented
12#39652C213yesmaximal, complemented
13#37627C213yesmaximal, complemented
14#37593C213yesmaximal, complemented
15#36583C211yesmaximal, characteristic, complemented
16Q8×#126C211yesmaximal, characteristic, complemented
17#36467C211yesmaximal, characteristic, complemented
18#36458C211yesmaximal, characteristic, complemented
19#36005C211yesmaximal, characteristic, complemented
20#35957C211yesmaximal, characteristic, complemented
21#35948C211yesmaximal, characteristic, complemented
22#35831C211yesmaximal, characteristic
23#35816C211yesmaximal, characteristic, complemented
24#35801C211yesmaximal, characteristic, complemented
25#35786C211yesmaximal, characteristic, complemented
26#35748C211yesmaximal, characteristic, complemented
27#35114C213yesmaximal, complemented
28#34603C213yesmaximal, complemented
29#34312C211yesmaximal, characteristic, complemented
30#34263C211yesmaximal, characteristic, complemented
31C4×Q82C211yesmaximal, characteristic, complemented
32C2×Q82C2211yescharacteristic
33C2×#557C2211yescharacteristic
34C2×#557C2211yescharacteristic
35C2×#550C2211yescharacteristic
36C2×#548C2211yescharacteristic
37C2×#548C2211yescharacteristic
38C2×#520C2211yescharacteristic
39C2×#520C2211yescharacteristic
40C2×#519C2211yescharacteristic
41#2863C2213yes—
42#2861C2213yes—
43#2860C2213yes—
44#2858C2213yes—
45#2837C2216yes—
46#2837C2216yes—
47#2832C2216yes—
48#2831C2216yes—
49#2800C2216yes—
50#2799C2216yes—
51#2798C2216yes—
52#2790C2216yes—
53#2772C2216yes—
54#2742C2216yes—
55#2738C2216yes—
56#2718C2216yes—
57#2715C2216yes—
58#2712C2216yes—
59#2702C2216yes—
60#2701C2216yes—
61#2700C2216yes—
62#2692C2216yes—
63#2687C2216yes—
64#2672C2216yes—
65#2666C2213yes—
66#2666C2213yes—
67#2663C2216yes—
68#2662C2213yes—
69#2662C2213yes—
70#2660C2213yes—
71#2654C2213yes—
72#2654C2213yes—
73#2652C2216yes—
74#2651C2216yes—
75#2651C2213yes—
76#2651C2213yes—
77#2651C2213yes—
78#2651C2213yes—
79#2650C2213yes—
80#2650C2213yes—
81#2640C2213yes—
82#2637C2211yescharacteristic
83#2637C2213yes—
84#2632C2213yes—
85#2632C2213yes—
86#2629C2213yes—
87#2629C2213yes—
88#2628C2213yes—
89#2625C2216yes—
90#2624C2213yes—
91#2624C2213yes—
92#2620C2216yes—
93#2620C2213yes—
94#2592C2213yes—
95#2592C2213yes—
96#2584C2213yes—
97#2582C2213yes—
98#2580C2213yes—
99#2567C2213yes—
100#2566C2213yes—
101#2565C2213yes—
102#2562C2213yes—
103#2552C2213yes—
104#2552C2213yes—
105#2550C2213yes—
106#2550C2213yes—
107#2548C2213yes—
108#2547C2213yes—
109#2547C2213yes—
110#2544C2213yes—
111#2542C2213yes—
112#2538C2213yes—
113#2537C2213yes—
114#2521C2216yes—
115#2513C2213yes—
116#2512C2213yes—
117#2512C2213yes—
118#2511C2213yes—
119#2511C2213yes—
120#2511C2213yes—
121#2501C2213yes—
122#2500C2213yes—
123#2497C2213yes—
124#2497C2213yes—
125#2497C2213yes—
126#2497C2213yes—
127#2496C2213yes—
128#2495C2213yes—
129#2492C2213yes—
130#2492C2213yes—
131#2492C2213yes—
132#2491C2213yes—
133#2491C2213yes—
134#2491C2213yes—
135#2490C2213yes—
136#2490C2213yes—
137#2490C2213yes—
138#2490C2213yes—
139#2490C2213yes—
140#2489C2213yes—
141#2487C2213yes—
142#2485C2213yes—
143#2479C2216yes—
144#2474C2216yes—
145#2465C2216yes—
146#2458C2216yes—
147#2458C2216yes—
148#2454C2213yes—
149#2453C2213yes—
150#2452C2213yes—
151#2452C2213yes—
152#2452C2213yes—
153#2451C2213yes—
154#2448C2213yes—
155#2448C2213yes—
156#2445C2213yes—
157#2445C2213yes—
158#2442C2213yes—
159#2441C2213yes—
160#2440C2213yes—
161#2440C2213yes—
162#2440C2213yes—
163#2439C2213yes—
164#2428C2213yes—
165#2427C2213yes—
166#2426C2216yes—
167#2423C2216yes—
168#2423C2213yes—
169#2422C2213yes—
170#2422C2213yes—
171#2421C2213yes—
172#2417C2213yes—
173#2416C2213yes—
174#2399C2213yes—
175#2398C2213yes—
176#2396C2213yes—
177#2396C2213yes—
178#2396C2213yes—
179#2395C2213yes—
180#2395C2213yes—
181#2392C2213yes—
182#2369C2213yes—
183#2369C2213yes—
184#2369C2213yes—
185#2367C2213yes—
186#2363C2213yes—
187#2360C2213yes—
188#2357C2213yes—
189#2354C2213yes—
190#2352C2213yes—
191#2351C2211yescharacteristic
192#2351C2211yescharacteristic
193#2351C2211yescharacteristic
194Q8×C4⋊C4C2213yes—
195Q8×C4⋊C4C2211yescharacteristic
196Q8×C4⋊C4C2211yescharacteristic
197Q8×C4⋊C4C2211yescharacteristic
198Q8×C4⋊C4C2211yescharacteristic
199Q8×C4⋊C4C2211yescharacteristic
200Q8×C4⋊C4C2211yescharacteristic
201Q8×C4⋊C4C2211yescharacteristic
202#2345C2213yes—
203#2344C2213yes—
204#2341C2211yescharacteristic
205#2341C2211yescharacteristic
206#2341C2211yescharacteristic
207#2341C2211yescharacteristic
208#2341C2211yescharacteristic
209#2341C2211yescharacteristic
210#2341C2211yescharacteristic
211#2341C2211yescharacteristic
212Q8×C22⋊C4C2211yescharacteristic
213Q8×C22⋊C4C2211yescharacteristic
214Q8×C22⋊C4C2211yescharacteristic
215Q8×C22⋊C4C2211yescharacteristic
216#2337C2216yes—
217#2335C2216yes—
218#2324C2213yes—
219#2323C2213yes—
220#2319C2213yes—
221#2314C2213yes—
222C4×C4⋊Q8C2213yes—
223C4×C4⋊Q8C2213yes—
224C4×C4⋊Q8C2213yes—
225C4×#126C2213yes—
226C4×#126C2213yes—
227C4×#124C2213yes—
228C4×#124C2213yes—
229C4×#124C2213yes—
230#2298C2213yes—
231#2293C2213yes—
232#2293C2213yes—
233#2276C2211yescharacteristic
234C42×Q8C2211yescharacteristic
235C42×Q8C2213yes—
236C42×Q8C2211yescharacteristic
237C42×Q8C2211yescharacteristic
238C22×#41C2311yescharacteristic
239C22×#41C2311yescharacteristic
240C23×Q8C2311yescharacteristic
241Q82—28no—
242#557—44no—
243#557—44no—
244#550—44no—
245#548—28no—
246#548—44no—
247C2×C4⋊Q8C2313yes—
248C2×C4⋊Q8C2313yes—
249C2×C4⋊Q8C2313yes—
250C2×C4⋊Q8C2313yes—
251C2×C4⋊Q8C2313yes—
252C2×#127C2313yes—
253C2×#126C2311yescharacteristic
254C2×#126C2313yes—
255C2×#126C2316yes—
256C2×#125C2313yes—
257C2×#125C2313yes—
258C2×#125C2313yes—
259C2×#125C2313yes—
260C2×#124C2313yes—
261C2×#124C2313yes—
262C2×#124C2313yes—
263C2×#124C2313yes—
264C2×#124C2316yes—
265C2×#124C2316yes—
266C2×#123C2316yes—
267C2×#123C2316yes—
268C2×C22⋊Q8C2313yes—
269C2×C22⋊Q8C2313yes—
270C2×C22⋊Q8C2316yes—
271C2×C22⋊Q8C2316yes—
272C2×C22⋊Q8C2316yes—
273C2×#121C2313yes—
274C2×#121C2313yes—
275C2×#121C2313yes—
276C2×#121C2313yes—
277C2×#121C2316yes—
278#520—28no—
279#520—44no—
280#519—44no—
281C2×C4×Q8C2313yes—
282C2×C4×Q8C2311yescharacteristic
283C2×C4×Q8C2311yescharacteristic
284C2×C4×Q8C2311yescharacteristic
285C2×C4×Q8C2311yescharacteristic
286C2×C4×Q8C2311yescharacteristic
287C2×C4×Q8C2311yescharacteristic
288C2×C4×Q8C2311yescharacteristic
289C2×C4×Q8C2311yescharacteristic
290C2×C4×Q8C2311yescharacteristic
291C2×C4×Q8C2311yescharacteristic
292C2×C4×Q8C2311yescharacteristic
293C2×C4×Q8C2311yescharacteristic
294C2×C4×Q8C2313yes—
295C2×C4×Q8C2313yes—
296C2×C4×Q8C2313yes—
297C2×C4×Q8C2313yes—
298C2×C4×Q8C2313yes—
299C2×C4×Q8C2316yes—
300C2×C4×Q8C2311yescharacteristic
301C2×C4×D4C2313yes—
302C2×C4×D4C2313yes—
303C2×C4×D4C2313yes—
304C2×C4×D4C2313yes—
305C2×C4×D4C2313yes—
306C2×C4×D4C2313yes—
307C2×C4×D4C2313yes—
308C2×#117C2313yes—
309C2×#117C2313yes—
310C2×#117C2313yes—
311C2×#117C2313yes—
312C2×#117C2316yes—
313C22×C4⋊C4C2313yes—
314C22×C4⋊C4C2313yes—
315#400C2316yes—
316#400C2313yes—
317#400C2316yes—
318#400C2313yes—
319#400C2316yes—
320#400C2316yes—
321#400C2316yes—
322#400C2313yes—
323#400C2313yes—
324#400C2313yes—
325#400C2313yes—
326#400C2313yes—
327#399C2316yes—
328#399C2313yes—
329#399C2316yes—
330#399C2316yes—
331#399C2313yes—
332#399C2313yes—
333#399C2313yes—
334#399C2313yes—
335#398C2313yes—
336#398C2316yes—
337#398C2316yes—
338#398C2316yes—
339#398C2313yes—
340#398C2316yes—
341#398C2316yes—
342#398C2313yes—
343#398C2313yes—
344#398C2313yes—
345#398C2311yescharacteristic
346#398C2313yes—
347#398C2311yescharacteristic
348#398C2311yescharacteristic
349#398C2313yes—
350#398C2313yes—
351#398C2313yes—
352#398C2313yes—
353#397C2313yes—
354#397C2316yes—
355#397C2316yes—
356#397C2316yes—
357#397C2316yes—
358#397C2313yes—
359#397C2316yes—
360#397C2316yes—
361#397C2316yes—
362#397C2313yes—
363#397C2311yescharacteristic
364#397C2313yes—
365#397C2313yes—
366#397C2313yes—
367#397C2313yes—
368#397C2313yes—
369#396C2313yes—
370#396C2316yes—
371#396C2316yes—
372#396C2316yes—
373#396C2316yes—
374#396C2316yes—
375#396C2316yes—
376#396C2313yes—
377#396C2313yes—
378#396C2311yescharacteristic
379#396C2311yescharacteristic
380#396C2313yes—
381#396C2313yes—
382#396C2313yes—
383#395C2313yes—
384#395C2316yes—
385#395C2316yes—
386#395C2313yes—
387#395C2313yes—
388#395C2313yes—
389#395C2313yes—
390#395C2311yescharacteristic
391#395C2313yes—
392#394C2316yes—
393#394C2316yes—
394#394C2316yes—
395#394C2316yes—
396#394C2313yes—
397#394C2316yes—
398#394C2316yes—
399#394C2316yes—
400#394C2316yes—
401#394C2313yes—
402#394C2313yes—
403#394C2313yes—
404#394C2313yes—
405#394C2313yes—
406#394C2313yes—
407#394C2313yes—
408#394C2313yes—
409#393C2316yes—
410#393C2313yes—
411#393C2316yes—
412#393C2316yes—
413#393C2316yes—
414#393C2313yes—
415#393C2313yes—
416#393C2311yescharacteristic
417#393C2313yes—
418#392C2313yes—
419#391C2316yes—
420#391C2316yes—
421#391C2316yes—
422#391C2313yes—
423#391C2313yes—
424#391C2316yes—
425#391C2313yes—
426#391C2313yes—
427#391C2316yes—
428#391C2313yes—
429#391C2313yes—
430#391C2313yes—
431#391C2313yes—
432#391C2316yes—
433#391C2313yes—
434#391C2313yes—
435#390C2313yes—
436#390C2313yes—
437#390C2313yes—
438#390C2313yes—
439#390C2313yes—
440#390C2313yes—
441#390C2313yes—
442#390C2313yes—
443#390C2316yes—
444#390C2313yes—
445#390C2313yes—
446#390C2313yes—
447#390C2313yes—
448#390C2313yes—
449#390C2313yes—
450#390C2313yes—
451#390C2313yes—
452#390C2313yes—
453#390C2316yes—
454#390C2313yes—
455#390C2313yes—
456#390C2313yes—
457#389C2313yes—
458#389C2316yes—
459#389C2313yes—
460#389C2313yes—
461#389C2313yes—
462#389C2313yes—
463#389C2316yes—
464#389C2313yes—
465#389C2316yes—
466#389C2313yes—
467#389C2313yes—
468#389C2313yes—
469#389C2313yes—
470#389C2313yes—
471#389C2313yes—
472#389C2313yes—
473#389C2313yes—
474#389C2313yes—
475#389C2316yes—
476#389C2316yes—
477#389C2313yes—
478#389C2313yes—
479#389C2316yes—
480#389C2313yes—
481#389C2313yes—
482#389C2313yes—
483#389C2313yes—
484#389C2313yes—
485#388C2313yes—
486#388C2313yes—
487#388C2313yes—
488#388C2313yes—
489#388C2313yes—
490#388C2313yes—
491#388C2313yes—
492#388C2316yes—
493#388C2316yes—
494#388C2316yes—
495#388C2313yes—
496#388C2316yes—
497#388C2313yes—
498#388C2316yes—
499#388C2313yes—
500#388C2313yes—
501#388C2313yes—
502#388C2316yes—
503#388C2316yes—
504#388C2313yes—
505#388C2316yes—
506#388C2316yes—
507#388C2316yes—
508#388C2316yes—
509#388C2316yes—
510#388C2316yes—
511#388C2313yes—
512#388C2313yes—
513#388C2313yes—
514#388C2313yes—
515#388C2311yescharacteristic
516#388C2311yescharacteristic
517#388C2313yes—
518#388C2313yes—
519#388C2313yes—
520#388C2316yes—
521#387C2311yescharacteristic
522#387C2313yes—
523#387C2313yes—
524#387C2313yes—
525#387C2313yes—
526#387C2313yes—
527#387C2316yes—
528#387C2316yes—
529#387C2313yes—
530#387C2316yes—
531#387C2313yes—
532#387C2316yes—
533#387C2316yes—
534#387C2313yes—
535#387C2316yes—
536#387C2316yes—
537#387C2311yescharacteristic
538#387C2316yes—
539#386C2316yes—
540#386C2316yes—
541#386C2316yes—
542#386C2316yes—
543#385C2316yes—
544#385C2316yes—
545#385C2316yes—
546#385C2316yes—
547#385C2316yes—
548#385C2316yes—
549#384C2313yes—
550#384C2313yes—
551#384C2313yes—
552#384C2316yes—
553#384C2313yes—
554#384C2313yes—
555#384C2313yes—
556#384C2313yes—
557#383C2313yes—
558#383C2313yes—
559#382C2313yes—
560#382C2313yes—
561#382C2313yes—
562#382C2311yescharacteristic
563#382C2313yes—
564#381C2316yes—
565#380C2313yes—
566#380C2313yes—
567#380C2313yes—
568#380C2313yes—
569#380C2313yes—
570#380C2316yes—
571#380C2313yes—
572#380C2316yes—
573#380C2313yes—
574#380C2313yes—
575#380C2313yes—
576#380C2313yes—
577#380C2313yes—
578#380C2313yes—
579#380C2316yes—
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⋊C4C2313yes—
608C4×C22⋊C4C2313yes—
609C4×C22⋊C4C2313yes—
610C4×C22⋊C4C2313yes—
611C4×C22⋊C4C2313yes—
612C4×C22⋊C4C2313yes—
613C4×C22⋊C4C2313yes—
614C4×C22⋊C4C2316yes—
615C4×C22⋊C4C2316yes—
616C4×C22⋊C4C2313yes—
617C4×C22⋊C4C2313yes—
618C4×C22⋊C4C2313yes—
619C4×C22⋊C4C2313yes—
620C4×C22⋊C4C2313yes—
621C4×C22⋊C4C2313yes—
622C4×C22⋊C4C2316yes—
623#376C2313yes—
624C43C2313yes—
625C43C2313yes—
626C43C2313yes—
627C2×#41—24no—
628C2×#41—24no—
629C2×#41—24no—
630C2×#41—24no—
631C2×#41—24no—
632C2×#41—24no—
633C22×Q8—24no—
634C22×Q8—24no—
635C22×Q8—24no—
636C22×Q8C2411yescharacteristic
637C22×Q8C2413yes—
638C22×Q8C2416yes—
639C22×Q8C2413yes—
640C22×Q8C2413yes—
641C22×Q8C2411yescharacteristic
642C22×D4C2413yes—
643C22×D4C2413yes—
644C22×D4C2413yes—
645C22×D4C2413yes—
646C22×D4C2413yes—
647C22×D4C2416yes—
648C23×C4C2413yes—
649C23×C4C2413yes—
650C23×C4C2413yes—
651C23×C4C2416yes—
652C23×C4C2416yes—
653C4⋊Q8—212no—
654C4⋊Q8—212no—
655C4⋊Q8—212no—
656C4⋊Q8—46no—
657C4⋊Q8—46no—
658#127—46no—
659#126—24no—
660#126—46no—
661#126—86no—
662#125—46no—
663#125—46no—
664#125—46no—
665#125—46no—
666#124—212no—
667#124—212no—
668#124—46no—
669#124—46no—
670#124—86no—
671#124—86no—
672#123—412no—
673#123—86no—
674C22⋊Q8—212no—
675C22⋊Q8—46no—
676C22⋊Q8—86no—
677C22⋊Q8—86no—
678C22⋊Q8—86no—
679#121—212no—
680#121—46no—
681#121—46no—
682#121—46no—
683#121—86no—
684C4×Q8—24no—
685C4×Q8—24no—
686C4×Q8—24no—
687C4×Q8—24no—
688C4×Q8—24no—
689C4×Q8—24no—
690C4×Q8—24no—
691C4×Q8—24no—
692C4×Q8—24no—
693C4×Q8—24no—
694C4×Q8—24no—
695C4×Q8—212no—
696C4×Q8—24no—
697C4×Q8—46no—
698C4×Q8—46no—
699C4×Q8—46no—
700C4×Q8—46no—
701C4×Q8—46no—
702C4×Q8—86no—
703C4×Q8#4118yes—
704C4×D4—212no—
705C4×D4—212no—
706C4×D4—212no—
707C4×D4—46no—
708C4×D4—46no—
709C4×D4—46no—
710C4×D4—46no—
711#117—212no—
712#117—46no—
713#117—46no—
714#117—46no—
715#117—86no—
716C2×C4⋊C4—212no—
717C2×C4⋊C4—46no—
718C2×C4⋊C4C2413yes—
719C2×C4⋊C4C2413yes—
720C2×C4⋊C4C2413yes—
721C2×C4⋊C4C2413yes—
722C2×C4⋊C4C2411yescharacteristic
723C2×C4⋊C4C2413yes—
724C2×C4⋊C4C2413yes—
725C2×C4⋊C4C2413yes—
726C2×C4⋊C4C2413yes—
727C2×C4⋊C4C2413yes—
728C2×C4⋊C4C2413yes—
729C2×C4⋊C4C2413yes—
730C2×C4⋊C4C2413yes—
731C2×C4⋊C4C2413yes—
732C2×C4⋊C4C2413yes—
733C2×C4⋊C4C2413yes—
734C2×C4⋊C4C2413yes—
735C2×C4⋊C4C2411yescharacteristic
736C2×C4⋊C4C2411yescharacteristic
737C2×C4⋊C4C2411yescharacteristic
738C2×C4⋊C4C2413yes—
739C2×C4⋊C4C2411yescharacteristic
740C2×C4⋊C4C2411yescharacteristic
741C2×C4⋊C4C2411yescharacteristic
742C2×C4⋊C4C2411yescharacteristic
743C2×C4⋊C4C2413yes—
744C2×C4⋊C4C2411yescharacteristic
745C2×C4⋊C4C2413yes—
746C2×C4⋊C4C2413yes—
747C2×C4⋊C4C2413yes—
748C2×C4⋊C4C2416yes—
749C2×C4⋊C4C2411yescharacteristic
750C2×C4⋊C4C2413yes—
751C2×C4⋊C4C2411yescharacteristic
752C2×C4⋊C4C2411yescharacteristic
753C2×C4⋊C4C2416yes—
754C2×C4⋊C4C2416yes—
755C2×C4⋊C4C2416yes—
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⋊C4C2413yes—
766C2×C4⋊C4C2413yes—
767C2×C4⋊C4C2416yes—
768C2×C4⋊C4C2416yes—
769C2×C4⋊C4C2413yes—
770C2×C4⋊C4C2416yes—
771C2×C4⋊C4C2416yes—
772C2×C4⋊C4C2416yes—
773C2×C4⋊C4C2413yes—
774C2×C4⋊C4C2413yes—
775C2×C4⋊C4C2413yes—
776C2×C4⋊C4C2413yes—
777C2×C22⋊C4C2413yes—
778C2×C22⋊C4C2413yes—
779C2×C22⋊C4C2411yescharacteristic
780C2×C22⋊C4C2413yes—
781C2×C22⋊C4C2416yes—
782C2×C22⋊C4C2413yes—
783C2×C22⋊C4C2413yes—
784C2×C22⋊C4C2411yescharacteristic
785C2×C22⋊C4C2413yes—
786C2×C22⋊C4C2413yes—
787C2×C22⋊C4C2413yes—
788C2×C22⋊C4C2413yes—
789C2×C22⋊C4C2411yescharacteristic
790C2×C22⋊C4C2411yescharacteristic
791C2×C22⋊C4C2411yescharacteristic
792C2×C22⋊C4C2413yes—
793C2×C22⋊C4C2411yescharacteristic
794C2×C22⋊C4C2413yes—
795C2×C22⋊C4C2413yes—
796C2×C22⋊C4C2413yes—
797C2×C22⋊C4C2416yes—
798C2×C22⋊C4C2411yescharacteristic
799C2×C22⋊C4C2413yes—
800C2×C22⋊C4C2413yes—
801C2×C22⋊C4C2413yes—
802C2×C22⋊C4C2413yes—
803C2×C22⋊C4C2416yes—
804C2×C22⋊C4C2416yes—
805C2×C22⋊C4C2413yes—
806C2×C22⋊C4C2413yes—
807C2×C22⋊C4C2413yes—
808C2×C22⋊C4C2416yes—
809C2×C22⋊C4C2416yes—
810C2×C22⋊C4C2413yes—
811C2×C22⋊C4C2413yes—
812C2×C22⋊C4C2416yes—
813C2×C22⋊C4C2413yes—
814C2×C22⋊C4C2413yes—
815C2×C22⋊C4C2416yes—
816C2×C22⋊C4C2416yes—
817C2×C22⋊C4C2416yes—
818C2×C22⋊C4C2413yes—
819C2×C22⋊C4C2413yes—
820C2×C22⋊C4C2413yes—
821C2×C22⋊C4C2413yes—
822C2×C22⋊C4C2413yes—
823C2×C42C2413yes—
824C2×C42C2413yes—
825C2×C42C2413yes—
826C2×C42C2413yes—
827C2×C42C2413yes—
828C2×C42C2413yes—
829C2×C42C2413yes—
830C2×C42C2413yes—
831C2×C42C2413yes—
832C2×C42C2413yes—
833C2×C42C2413yes—
834C2×C42C2411yescharacteristic
835C2×C42C2411yescharacteristic
836C2×C42C2413yes—
837C2×C42C2413yes—
838C2×C42C2416yes—
839C2×C42C2416yes—
840C2×C42C2413yes—
841C2×C42C2413yes—
842C2×C42C2413yes—
843C2×C42C2413yes—
844C2×C42C2413yes—
845C2×C42C2413yes—
846C2×C42C2413yes—
847C2×C42C2413yes—
848C2×C42C2411yescharacteristic
849#95C2411yescharacteristic
850#95C2413yes—
851#95C2413yes—
852#95C2413yes—
853#95C2411yescharacteristic
854#95C2411yescharacteristic
855#95C2411yescharacteristic
856#95C2411yescharacteristic
857#95C2411yescharacteristic
858#95C2411yescharacteristic
859#95C2413yes—
860#95C2411yescharacteristic
861#95C2411yescharacteristic
862#95C2413yes—
863#95C2413yes—
864#95C2413yes—
865#95C2413yes—
866#95C2413yes—
867#95C2413yes—
868#95C2413yes—
869#95C2413yes—
870#95C2413yes—
871#95C2413yes—
872#95C2416yes—
873#95C2416yes—
874#95C2416yes—
875#95C2413yes—
876#95C2413yes—
877#95C2413yes—
878#95C2413yes—
879#95C2413yes—
880#95C2413yes—
881#95C2413yes—
882#95C2413yes—
883#95C2416yes—
884#95C2413yes—
885#95C2413yes—
886#95C2413yes—
887#95C2411yescharacteristic
888#95C2411yescharacteristic
889#95C2411yescharacteristic
890#95C2413yes—
891#95C2416yes—
892#95C2413yes—
893#95C2416yes—
894#95C2413yes—
895#95C2413yes—
896#95C2413yes—
897#95C2413yes—
898#95C2413yes—
899#95C2413yes—
900#95C2413yes—
901#95C2413yes—
902#95C2413yes—
903#95C2416yes—
904#95C2416yes—
905#95C2416yes—
906#95C2416yes—
907C24C2513yes—
908C24C2513yes—
909C24C2511yescharacteristic
910#41—416no—
911#41—416no—
912C2×Q8—22no—
913C2×Q8—26no—
914C2×Q8—212no—
915C2×Q8—26no—
916C2×Q8—22no—
917C2×Q8—26no—
918C2×Q8—26no—
919C2×Q8—22no—
920C2×Q8—43no—
921C2×Q8—43no—
922C2×Q8—46no—
923C2×Q8—43no—
924C2×Q8—46no—
925C2×Q8—43no—
926C2×Q8—43no—
927C2×Q8—416no—
928C2×Q8C2×#4114yes—
929C2×Q8H(5,𝔽2)14yes—
930C2×Q82−1+414yes—
931C2×D4—26no—
932C2×D4—26no—
933C2×D4—26no—
934C2×D4—26no—
935C2×D4—26no—
936C2×D4—26no—
937C2×D4—26no—
938C2×D4—26no—
939C2×D4—43no—
940C2×D4—43no—
941C2×D4—43no—
942C2×D4—43no—
943C2×D4—43no—
944C2×D4—43no—
945C2×D4—43no—
946C2×D4—46no—
947C2×D4—46no—
948C2×D4—46no—
949C22×C4—26no—
950C22×C4—26no—
951C22×C4—26no—
952C22×C4—26no—
953C22×C4—26no—
954C22×C4—26no—
955C22×C4—26no—
956C22×C4—26no—
957C22×C4—26no—
958C22×C4—212no—
959C22×C4—46no—
960C22×C4—46no—
961C22×C4—46no—
962C22×C4—46no—
963C22×C4—46no—
964C22×C4C2511yescharacteristic
965C22×C4C2513yes—
966C22×C4C2511yescharacteristic
967C22×C4C2511yescharacteristic
968C22×C4C2511yescharacteristic
969C22×C4C2513yes—
970C22×C4C2513yes—
971C22×C4C2513yes—
972C22×C4C2513yes—
973C22×C4C2513yes—
974C22×C4C2513yes—
975C22×C4C2511yescharacteristic
976C22×C4C2513yes—
977C22×C4C2513yes—
978C22×C4C2511yescharacteristic
979C22×C4C2511yescharacteristic
980C22×C4C2513yes—
981C22×C4C2511yescharacteristic
982C22×C4C2513yes—
983C22×C4C2513yes—
984C22×C4C2511yescharacteristic
985C22×C4C2511yescharacteristic
986C22×C4C2513yes—
987C22×C4C2511yescharacteristic
988C22×C4C2511yescharacteristic
989C22×C4C2511yescharacteristic
990C22×C4C2511yescharacteristic
991C22×C4C2513yes—
992C4⋊C4—26no—
993C4⋊C4—26no—
994C4⋊C4—22no—
995C4⋊C4—26no—
996C4⋊C4—26no—
997C4⋊C4—26no—
998C4⋊C4—26no—
999C4⋊C4—26no—
1000C4⋊C4—26no—
1001C4⋊C4—26no—
1002C4⋊C4—26no—
1003C4⋊C4—26no—
1004C4⋊C4—26no—
1005C4⋊C4—26no—
1006C4⋊C4—26no—
1007C4⋊C4—22no—
1008C4⋊C4—22no—
1009C4⋊C4—22no—
1010C4⋊C4—26no—
1011C4⋊C4—26no—
1012C4⋊C4—22no—
1013C4⋊C4—22no—
1014C4⋊C4—22no—
1015C4⋊C4—26no—
1016C4⋊C4—22no—
1017C4⋊C4—43no—
1018C4⋊C4—41no—
1019C4⋊C4—43no—
1020C4⋊C4—43no—
1021C4⋊C4—43no—
1022C4⋊C4—46no—
1023C4⋊C4—41no—
1024C4⋊C4—43no—
1025C4⋊C4—43no—
1026C4⋊C4—43no—
1027C4⋊C4—41no—
1028C4⋊C4—41no—
1029C4⋊C4—43no—
1030C4⋊C4—43no—
1031C4⋊C4—43no—
1032C4⋊C4—43no—
1033C4⋊C4—46no—
1034C4⋊C4—46no—
1035C4⋊C4—46no—
1036C4⋊C4—43no—
1037C4⋊C4—43no—
1038C4⋊C4—43no—
1039C4⋊C4—43no—
1040C4⋊C4—46no—
1041C4⋊C4—43no—
1042C4⋊C4—46no—
1043C4⋊C4—46no—
1044C4⋊C4—43no—
1045C4⋊C4—46no—
1046C4⋊C4—46no—
1047C4⋊C4—43no—
1048C4⋊C4—43no—
1049C4⋊C4—43no—
1050C4⋊C4C2×#41112yes—
1051C22⋊C4—26no—
1052C22⋊C4—26no—
1053C22⋊C4—22no—
1054C22⋊C4—26no—
1055C22⋊C4—212no—
1056C22⋊C4—26no—
1057C22⋊C4—26no—
1058C22⋊C4—26no—
1059C22⋊C4—26no—
1060C22⋊C4—22no—
1061C22⋊C4—22no—
1062C22⋊C4—22no—
1063C22⋊C4—26no—
1064C22⋊C4—26no—
1065C22⋊C4—22no—
1066C22⋊C4—41no—
1067C22⋊C4—43no—
1068C22⋊C4—43no—
1069C22⋊C4—43no—
1070C22⋊C4—43no—
1071C22⋊C4—46no—
1072C22⋊C4—41no—
1073C22⋊C4—43no—
1074C22⋊C4—43no—
1075C22⋊C4—43no—
1076C22⋊C4—46no—
1077C22⋊C4—43no—
1078C22⋊C4—46no—
1079C22⋊C4—43no—
1080C22⋊C4—43no—
1081C22⋊C4—43no—
1082C22⋊C4—46no—
1083C22⋊C4—46no—
1084C22⋊C4—46no—
1085C22⋊C4—43no—
1086C22⋊C4—43no—
1087C22⋊C4—43no—
1088C22⋊C4—43no—
1089C22⋊C4—46no—
1090C22⋊C4—43no—
1091C22⋊C4—43no—
1092C22⋊C4—46no—
1093C22⋊C4—46no—
1094C22⋊C4—43no—
1095C22⋊C4—43no—
1096C22⋊C4—43no—
1097C42—26no—
1098C42—26no—
1099C42—26no—
1100C42—26no—
1101C42—26no—
1102C42—26no—
1103C42—26no—
1104C42—26no—
1105C42—26no—
1106C42—26no—
1107C42—22no—
1108C42—22no—
1109C42—26no—
1110C42—26no—
1111C42—46no—
1112C42—43no—
1113C42—46no—
1114C42—43no—
1115C42—43no—
1116C42—43no—
1117C42—43no—
1118C42—43no—
1119C42—43no—
1120C42—43no—
1121C42C2×#41112yes—
1122C422−1+414yes—
1123C23—23no—
1124C23—23no—
1125C23—21no—
1126C23—21no—
1127C23—23no—
1128C23—23no—
1129C23—21no—
1130C23—23no—
1131C23—23no—
1132C23—21no—
1133C23—23no—
1134C23—23no—
1135C23—21no—
1136C23—23no—
1137C23—23no—
1138C23—23no—
1139C23—23no—
1140C23—21no—
1141C23—23no—
1142C23—23no—
1143C23—21no—
1144C23C2611yescharacteristic
1145Q8—28no—
1146Q8—412no—
1147Q8—812no—
1148Q8—86no—
1149Q8—86no—
1150Q8#542116yes—
1151D4—412no—
1152D4—412no—
1153D4—86no—
1154D4—86no—
1155D4—86no—
1156D4—166no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—23no—
1167C2×C4—21no—
1168C2×C4—23no—
1169C2×C4—21no—
1170C2×C4—23no—
1171C2×C4—23no—
1172C2×C4—23no—
1173C2×C4—23no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—21no—
1181C2×C4—23no—
1182C2×C4—23no—
1183C2×C4—23no—
1184C2×C4—23no—
1185C2×C4—23no—
1186C2×C4—23no—
1187C2×C4—23no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—23no—
1194C2×C4—23no—
1195C2×C4—23no—
1196C2×C4—23no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—23no—
1203C2×C4—23no—
1204C2×C4—23no—
1205C2×C4—23no—
1206C2×C4—23no—
1207C2×C4—21no—
1208C2×C4—23no—
1209C2×C4—23no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—23no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—23no—
1216C2×C4—23no—
1217C2×C4—23no—
1218C2×C4—23no—
1219C2×C4—23no—
1220C2×C4—23no—
1221C2×C4—23no—
1222C2×C4—23no—
1223C2×C4—23no—
1224C2×C4—21no—
1225C2×C4—23no—
1226C2×C4—21no—
1227C2×C4—21no—
1228C2×C4—23no—
1229C2×C4—21no—
1230C2×C4—23no—
1231C2×C4—23no—
1232C2×C4—412no—
1233C2×C4—412no—
1234C2×C4—412no—
1235C2×C4—812no—
1236C2×C4—166no—
1237C2×C4C22×#4112yes—
1238C2×C4C22×#4116yes—
1239C2×C4C22×#4116yes—
1240C2×C4C2×H(5,𝔽2)16yes—
1241C2×C4C2×2−1+412yes—
1242C2×C4C2×2−1+412yes—
1243C2×C4C2×2−1+412yes—
1244C2×C4C2×2−1+416yes—
1245C2×C4#58512yes—
1246C22—43no—
1247C22—43no—
1248C22—41no—
1249C22—43no—
1250C22—41no—
1251C22—43no—
1252C22—43no—
1253C22—43no—
1254C22—41no—
1255C22—43no—
1256C22—41no—
1257C22—43no—
1258C22—41no—
1259C22—43no—
1260C22—43no—
1261C22—41no—
1262C22—43no—
1263C22—43no—
1264C22—41no—
1265C22—43no—
1266C22—43no—
1267C22C23×#4111yescharacteristic
1268C22C22×H(5,𝔽2)11yescharacteristic
1269C22C22×2−1+411yescharacteristic
1270C22C22×2−1+411yescharacteristic
1271C22C2×#58511yescharacteristic
1272C22H(7,𝔽2)11yescharacteristic
1273C22H(7,𝔽2)11yescharacteristic
1274C4—22no—
1275C4—22no—
1276C4—22no—
1277C4—26no—
1278C4—22no—
1279C4—22no—
1280C4—41no—
1281C4—43no—
1282C4—43no—
1283C4—43no—
1284C4—41no—
1285C4—41no—
1286C4—41no—
1287C4—43no—
1288C4—43no—
1289C4—41no—
1290C4—43no—
1291C4—43no—
1292C4—43no—
1293C4—43no—
1294C4—41no—
1295C4—41no—
1296C4—41no—
1297C4—43no—
1298C4—41no—
1299C4—43no—
1300C4—43no—
1301C4C2×#542112yes—
1302C2—83no—
1303C2—81no—
1304C2—83no—
1305C2C22×#54211yescharacteristic
1306C2#6278811yescharacteristic
1307C2#6285811yescharacteristic
1308C2#6291711yescharacteristic
1309C2#6292311yescharacteristic
1310C2#6294311yescharacteristic
1311C2#6295211yescharacteristic
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. #42699C2semidirect
2. #42671C2semidirect
3. #42628C2semidirect
4. #42621C2semidirect
5. #42585C2semidirect
6. #42579C2semidirect
7. #42515C2semidirect
8. #42459C2semidirect
9. #40226C2semidirect
10. #40188C2semidirect
11. #39789C2semidirect
12. #39652C2semidirect
13. #37627C2semidirect
14. #37593C2semidirect
15. #36583C2semidirect
16. Q8×#126C2semidirect
17. #36467C2semidirect
18. #36458C2semidirect
19. #36005C2semidirect
20. #35957C2semidirect
21. #35948C2semidirect
23. #35816C2semidirect
24. #35801C2semidirect
25. #35786C2semidirect
26. #35748C2semidirect
27. #35114C2semidirect
28. #34603C2semidirect
29. #34312C2semidirect
30. #34263C2semidirect
31. C4×Q82C2semidirect

Maximal subgroups

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

subgroupindex
#426992
#426712
#426282
#426212
#425852
#425792
#425152
#424592
#402262
#401882
#397892
#396522
#376272
#375932
#365832
Q8×#1262
#364672
#364582
#360052
#359572
#359482
#358312
#358162
#358012
#357862
#357482
#351142
#346032
#343122
#342632
C4×Q822