Finite Group Databasebeta

← #7660747

Subgroups — #7660747

Order 512.

5067 conjugacy classes of subgroups.

The subgroup lattice has 1327 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#52247C213yesmaximal, complemented
2#42601C213yesmaximal, complemented
3#42572C213yesmaximal, complemented
4#42559C213yesmaximal, complemented
5#42551C213yesmaximal, complemented
6#42521C213yesmaximal, complemented
7#42506C213yesmaximal, complemented
8#40165C213yesmaximal, complemented
9#40045C213yesmaximal, complemented
10#39604C213yesmaximal, complemented
11#39404C213yesmaximal, complemented
12#39400C213yesmaximal, complemented
13#39348C213yesmaximal, complemented
14#37342C213yesmaximal, complemented
15#37339C213yesmaximal, complemented
16#37287C213yesmaximal, complemented
17Q8×#125C211yesmaximal, characteristic, complemented
18Q8×C22⋊Q8C211yesmaximal, characteristic, complemented
19#36483C211yesmaximal, characteristic, complemented
20#36448C211yesmaximal, characteristic, complemented
21#36433C211yesmaximal, characteristic, complemented
22#36432C211yesmaximal, characteristic, complemented
23#35996C211yesmaximal, characteristic, complemented
24#35898C211yesmaximal, characteristic, complemented
25#35868C211yesmaximal, characteristic, complemented
26#35831C211yesmaximal, characteristic
27#35748C211yesmaximal, characteristic, complemented
28#35748C211yesmaximal, characteristic, complemented
29#34313C211yesmaximal, characteristic, complemented
30#34294C211yesmaximal, characteristic, complemented
31#34183C211yesmaximal, characteristic, complemented
32C2×Q82C2211yescharacteristic
33C2×#550C2211yescharacteristic
34C2×#548C2211yescharacteristic
35C2×#548C2211yescharacteristic
36C2×#539C2216yes—
37C2×#520C2211yescharacteristic
38C2×#520C2211yescharacteristic
39C2×#520C2211yescharacteristic
40C2×C4×#41C2211yescharacteristic
41C22×C4×Q8C2211yescharacteristic
42#2863C2213yes—
43#2859C2213yes—
44#2857C2213yes—
45#2855C2213yes—
46#2854C2213yes—
47#2854C2213yes—
48#2834C2216yes—
49#2827C2216yes—
50#2796C2216yes—
51#2793C2213yes—
52#2792C2216yes—
53#2791C2213yes—
54#2790C2216yes—
55#2781C2213yes—
56#2775C2213yes—
57#2775C2216yes—
58#2770C2216yes—
59#2767C2213yes—
60#2765C2213yes—
61#2765C2216yes—
62#2757C2216yes—
63#2746C2216yes—
64#2745C2213yes—
65#2743C2213yes—
66#2740C2213yes—
67#2738C2213yes—
68#2737C2216yes—
69#2728C2216yes—
70#2723C2216yes—
71#2721C2216yes—
72#2720C2211yescharacteristic
73#2720C2216yes—
74#2718C2213yes—
75#2708C2216yes—
76#2707C2213yes—
77#2706C2213yes—
78#2696C2213yes—
79#2695C2213yes—
80#2694C2216yes—
81#2690C2216yes—
82#2687C2216yes—
83#2681C2216yes—
84#2680C2216yes—
85#2653C2216yes—
86#2647C2213yes—
87#2644C2213yes—
88#2638C2216yes—
89#2638C2216yes—
90#2633C2216yes—
91#2628C2213yes—
92#2628C2213yes—
93#2627C2216yes—
94#2625C2213yes—
95#2623C2216yes—
96#2620C2213yes—
97#2582C2213yes—
98#2580C2213yes—
99#2580C2213yes—
100#2570C2213yes—
101#2567C2213yes—
102#2552C2213yes—
103#2552C2213yes—
104#2552C2213yes—
105#2544C2213yes—
106#2542C2213yes—
107#2542C2213yes—
108#2537C2213yes—
109#2514C2213yes—
110#2514C2213yes—
111#2513C2213yes—
112#2512C2213yes—
113#2512C2213yes—
114#2511C2213yes—
115#2509C2213yes—
116#2507C2213yes—
117#2507C2213yes—
118#2507C2213yes—
119#2507C2213yes—
120#2507C2213yes—
121#2506C2213yes—
122#2506C2213yes—
123#2502C2213yes—
124#2501C2213yes—
125#2500C2213yes—
126#2499C2213yes—
127#2497C2213yes—
128#2496C2213yes—
129#2496C2213yes—
130#2495C2213yes—
131#2494C2213yes—
132#2494C2213yes—
133#2486C2213yes—
134#2486C2213yes—
135#2485C2213yes—
136#2485C2213yes—
137#2473C2216yes—
138#2466C2216yes—
139#2455C2216yes—
140#2452C2213yes—
141#2452C2213yes—
142#2452C2213yes—
143#2452C2213yes—
144#2451C2213yes—
145#2451C2213yes—
146#2449C2216yes—
147#2449C2216yes—
148#2448C2213yes—
149#2448C2213yes—
150#2447C2213yes—
151#2447C2213yes—
152#2447C2213yes—
153#2447C2213yes—
154#2445C2213yes—
155#2445C2213yes—
156#2443C2216yes—
157#2440C2213yes—
158#2440C2213yes—
159#2440C2213yes—
160#2440C2213yes—
161#2440C2213yes—
162#2440C2213yes—
163#2428C2213yes—
164#2427C2213yes—
165#2423C2213yes—
166#2423C2213yes—
167#2422C2213yes—
168#2422C2213yes—
169#2422C2213yes—
170#2422C2213yes—
171#2420C2213yes—
172#2420C2213yes—
173#2417C2213yes—
174#2416C2213yes—
175#2402C2213yes—
176#2401C2213yes—
177#2396C2213yes—
178#2396C2213yes—
179#2395C2213yes—
180#2392C2213yes—
181#2367C2213yes—
182#2366C2213yes—
183#2361C2213yes—
184#2361C2213yes—
185#2361C2213yes—
186#2360C2213yes—
187#2351C2211yescharacteristic
188#2351C2211yescharacteristic
189#2351C2211yescharacteristic
190Q8×C4⋊C4C2211yescharacteristic
191Q8×C4⋊C4C2211yescharacteristic
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
201D4×C4⋊C4C2213yes—
202D4×C4⋊C4C2213yes—
203D4×C4⋊C4C2213yes—
204D4×C4⋊C4C2213yes—
205D4×C4⋊C4C2213yes—
206D4×C4⋊C4C2213yes—
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#2326C2213yes—
218#2324C2213yes—
219#2324C2213yes—
220#2323C2213yes—
221#2322C2216yes—
222#2317C2213yes—
223#2317C2213yes—
224C4×#127C2213yes—
225C4×#125C2213yes—
226C4×#126C2213yes—
227C4×C22⋊Q8C2213yes—
228C4×#123C2213yes—
229C4×#123C2213yes—
230C4×#123C2213yes—
231C4×#121C2213yes—
232#2293C2213yes—
233#2290C2213yes—
234#2285C2213yes—
235C2×#384C2213yes—
236#2276C2211yescharacteristic
237C42×Q8C2211yescharacteristic
238C22×#41C2311yescharacteristic
239C22×#41C2311yescharacteristic
240C23×Q8C2311yescharacteristic
241Q82—44no—
242#550—28no—
243#548—28no—
244#548—44no—
245#539—424no—
246C2×C4⋊Q8C2313yes—
247C2×C4⋊Q8C2313yes—
248C2×C4⋊Q8C2313yes—
249C2×#127C2313yes—
250C2×#126C2313yes—
251C2×#126C2316yes—
252C2×#125C2311yescharacteristic
253C2×#125C2316yes—
254C2×#125C2316yes—
255C2×#124C2313yes—
256C2×#124C2313yes—
257C2×#123C2313yes—
258C2×#123C2313yes—
259C2×#123C2313yes—
260C2×#123C2316yes—
261C2×#123C2316yes—
262C2×#123C2316yes—
263C2×C22⋊Q8C2313yes—
264C2×C22⋊Q8C2311yescharacteristic
265C2×C22⋊Q8C2316yes—
266C2×C22⋊Q8C2313yes—
267C2×C22⋊Q8C2316yes—
268C2×C22⋊Q8C2316yes—
269C2×C22⋊Q8C2316yes—
270C2×C22⋊Q8C2316yes—
271C2×#121C2313yes—
272C2×#121C2313yes—
273C2×#121C2313yes—
274C2×#121C2313yes—
275C2×#121C2316yes—
276#520—44no—
277#520—44no—
278#520—44no—
279C4×#41—28no—
280C2×C4×Q8—44no—
281C2×C4×Q8C2311yescharacteristic
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×Q8C2313yes—
294C2×C4×Q8C2313yes—
295C2×C4×Q8C2313yes—
296C2×C4×D4C2313yes—
297C2×C4×D4C2313yes—
298C2×C4×D4C2313yes—
299C2×C4×D4C2313yes—
300C2×C4×D4C2313yes—
301C2×C4×D4C2313yes—
302C2×C4×D4C2316yes—
303C2×C4×D4C2313yes—
304C2×C4×D4C2313yes—
305C2×C4×D4C2313yes—
306C2×C4×D4C2313yes—
307C2×C4×D4C2316yes—
308C2×C4×D4C2313yes—
309C2×C4×D4C2316yes—
310C2×#117C2313yes—
311C2×#117C2313yes—
312C2×#117C2313yes—
313C2×#117C2313yes—
314C22×C4⋊C4C2313yes—
315C22×C4⋊C4C2313yes—
316C22×C4⋊C4C2316yes—
317C22×C4⋊C4C2313yes—
318C22×C4⋊C4C2313yes—
319C22×C4⋊C4C2316yes—
320C22×C42C2313yes—
321C22×C42C2313yes—
322#401C2313yes—
323#401C2316yes—
324#400C2313yes—
325#400C2316yes—
326#400C2313yes—
327#400C2316yes—
328#400C2313yes—
329#400C2313yes—
330#400C2313yes—
331#400C2313yes—
332#400C2313yes—
333#400C2316yes—
334#400C2311yescharacteristic
335#400C2313yes—
336#400C2313yes—
337#399C2316yes—
338#399C2316yes—
339#399C2313yes—
340#399C2316yes—
341#399C2313yes—
342#399C2316yes—
343#399C2311yescharacteristic
344#398C2316yes—
345#398C2316yes—
346#398C2316yes—
347#398C2313yes—
348#398C2316yes—
349#398C2316yes—
350#398C2316yes—
351#398C2316yes—
352#398C2316yes—
353#398C2313yes—
354#398C2316yes—
355#398C2313yes—
356#398C2313yes—
357#398C2313yes—
358#398C2313yes—
359#398C2313yes—
360#398C2316yes—
361#398C2311yescharacteristic
362#398C2313yes—
363#398C2313yes—
364#397C2313yes—
365#397C2316yes—
366#397C2316yes—
367#397C2313yes—
368#397C2316yes—
369#397C2316yes—
370#397C2316yes—
371#397C2316yes—
372#397C2316yes—
373#397C2313yes—
374#397C2316yes—
375#397C2313yes—
376#397C2316yes—
377#397C2313yes—
378#397C2316yes—
379#397C2313yes—
380#397C2313yes—
381#396C2313yes—
382#396C2316yes—
383#396C2313yes—
384#396C2316yes—
385#396C2311yescharacteristic
386#396C2313yes—
387#396C2313yes—
388#396C2313yes—
389#396C2313yes—
390#395C2316yes—
391#395C2316yes—
392#395C2316yes—
393#395C2316yes—
394#395C2311yescharacteristic
395#395C2311yescharacteristic
396#394C2316yes—
397#394C2316yes—
398#394C2316yes—
399#394C2313yes—
400#394C2313yes—
401#394C2316yes—
402#394C2316yes—
403#394C2313yes—
404#394C2313yes—
405#394C2313yes—
406#394C2316yes—
407#393C2313yes—
408#393C2313yes—
409#393C2316yes—
410#393C2316yes—
411#392C2313yes—
412#391C2313yes—
413#391C2313yes—
414#391C2313yes—
415#391C2313yes—
416#391C2313yes—
417#391C2313yes—
418#391C2313yes—
419#391C2313yes—
420#391C2313yes—
421#391C2316yes—
422#390C2313yes—
423#390C2316yes—
424#390C2313yes—
425#390C2313yes—
426#390C2313yes—
427#390C2313yes—
428#390C2313yes—
429#390C2313yes—
430#390C2313yes—
431#390C2313yes—
432#390C2313yes—
433#390C2313yes—
434#390C2313yes—
435#390C2313yes—
436#390C2313yes—
437#389C2313yes—
438#389C2313yes—
439#389C2313yes—
440#389C2316yes—
441#389C2313yes—
442#389C2313yes—
443#389C2313yes—
444#389C2313yes—
445#389C2313yes—
446#389C2313yes—
447#389C2313yes—
448#389C2313yes—
449#389C2313yes—
450#389C2316yes—
451#389C2313yes—
452#389C2316yes—
453#389C2313yes—
454#389C2313yes—
455#389C2313yes—
456#389C2313yes—
457#389C2313yes—
458#389C2313yes—
459#389C2313yes—
460#389C2313yes—
461#389C2313yes—
462#389C2313yes—
463#389C2316yes—
464#389C2316yes—
465#389C2313yes—
466#389C2313yes—
467#389C2313yes—
468#389C2313yes—
469#389C2313yes—
470#389C2313yes—
471#389C2313yes—
472#389C2313yes—
473#389C2313yes—
474#389C2311yescharacteristic
475#388C2311yescharacteristic
476#388C2313yes—
477#388C2313yes—
478#388C2316yes—
479#388C2316yes—
480#388C2316yes—
481#388C2316yes—
482#388C2313yes—
483#388C2313yes—
484#388C2313yes—
485#388C2313yes—
486#388C2316yes—
487#388C2316yes—
488#388C2313yes—
489#388C2313yes—
490#388C2313yes—
491#388C2316yes—
492#388C2313yes—
493#388C2313yes—
494#388C2313yes—
495#388C2311yescharacteristic
496#388C2313yes—
497#387C2313yes—
498#387C2313yes—
499#387C2313yes—
500#387C2313yes—
501#387C2313yes—
502#387C2313yes—
503#387C2313yes—
504#387C2316yes—
505#387C2316yes—
506#387C2316yes—
507#387C2313yes—
508#387C2313yes—
509#387C2316yes—
510#387C2316yes—
511#387C2313yes—
512#387C2316yes—
513#387C2313yes—
514#387C2313yes—
515#387C2313yes—
516#387C2313yes—
517#387C2311yescharacteristic
518#387C2313yes—
519#387C2313yes—
520#386C2316yes—
521#386C2316yes—
522#386C2316yes—
523#386C2313yes—
524#386C2316yes—
525#386C2313yes—
526#386C2316yes—
527#386C2313yes—
528#386C2313yes—
529#386C2313yes—
530#385C2316yes—
531#385C2316yes—
532#385C2316yes—
533#385C2316yes—
534#385C2316yes—
535#385C2316yes—
536#385C2316yes—
537#385C2316yes—
538#385C2316yes—
539#385C2316yes—
540#385C2316yes—
541#385C2316yes—
542#385C2316yes—
543#385C2316yes—
544#385C2313yes—
545#385C2316yes—
546#385C2313yes—
547#385C2311yescharacteristic
548#385C2313yes—
549#385C2313yes—
550#385C2313yes—
551#385C2311yescharacteristic
552#384C2313yes—
553#384C2313yes—
554#384C2313yes—
555#384C2316yes—
556#384C2313yes—
557#384C2313yes—
558#384C2313yes—
559#384C2313yes—
560#384C2313yes—
561#384C2313yes—
562#384C2313yes—
563#384C2313yes—
564#384C2313yes—
565#384C2311yescharacteristic
566#383C2313yes—
567#383C2316yes—
568#382C2313yes—
569#382C2313yes—
570#382C2313yes—
571#382C2313yes—
572#382C2313yes—
573#382C2313yes—
574#381C2316yes—
575#381C2313yes—
576#381C2313yes—
577#381C2313yes—
578#381C2316yes—
579#380C2313yes—
580#380C2313yes—
581#380C2313yes—
582#380C2313yes—
583#380C2313yes—
584#380C2313yes—
585#380C2313yes—
586#380C2313yes—
587#380C2313yes—
588#380C2313yes—
589#380C2313yes—
590#380C2313yes—
591#380C2313yes—
592#380C2313yes—
593#380C2313yes—
594#380C2316yes—
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×C4⋊C4C2313yes—
615C4×C22⋊C4C2313yes—
616C4×C22⋊C4C2313yes—
617C4×C22⋊C4C2313yes—
618C4×C22⋊C4C2316yes—
619C4×C22⋊C4C2313yes—
620C4×C22⋊C4C2313yes—
621C4×C22⋊C4C2313yes—
622C4×C22⋊C4C2313yes—
623C4×C22⋊C4C2313yes—
624C4×C22⋊C4C2313yes—
625C4×C22⋊C4C2313yes—
626#376C2313yes—
627C43C2313yes—
628C2×#41—24no—
629C2×#41—24no—
630C2×#41—24no—
631C2×#41—24no—
632C2×#41—24no—
633C2×#41#4118yes—
634C22×Q8—24no—
635C22×Q8—24no—
636C22×Q8—24no—
637C22×Q8C2413yes—
638C22×Q8C2411yescharacteristic
639C22×Q8C2416yes—
640C22×Q8C2411yescharacteristic
641C22×D4C2413yes—
642C22×D4C2413yes—
643C22×D4C2413yes—
644C22×D4C2413yes—
645C22×D4C2413yes—
646C22×D4C2416yes—
647C23×C4C2413yes—
648C23×C4C2413yes—
649C23×C4C2413yes—
650C23×C4C2413yes—
651C23×C4C2413yes—
652C23×C4C2413yes—
653C23×C4C2411yescharacteristic
654C23×C4C2416yes—
655C23×C4C2416yes—
656C23×C4C2416yes—
657C4⋊Q8—46no—
658C4⋊Q8—46no—
659C4⋊Q8—46no—
660#127—212no—
661#126—212no—
662#126—412no—
663#125—24no—
664#125—412no—
665#125—412no—
666#124—212no—
667#124—46no—
668#123—212no—
669#123—212no—
670#123—212no—
671#123—412no—
672#123—412no—
673#123—86no—
674C22⋊Q8—212no—
675C22⋊Q8—24no—
676C22⋊Q8—412no—
677C22⋊Q8—412no—
678C22⋊Q8—412no—
679C22⋊Q8—46no—
680C22⋊Q8—86no—
681C22⋊Q8—86no—
682#121—212no—
683#121—212no—
684#121—212no—
685#121—412no—
686#121—46no—
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—24no—
696C4×Q8—24no—
697C4×Q8—24no—
698C4×Q8—24no—
699C4×Q8—46no—
700C4×Q8—46no—
701C4×Q8—46no—
702C4×D4—212no—
703C4×D4—212no—
704C4×D4—212no—
705C4×D4—212no—
706C4×D4—412no—
707C4×D4—46no—
708C4×D4—46no—
709C4×D4—46no—
710C4×D4—46no—
711C4×D4—46no—
712C4×D4—46no—
713C4×D4—46no—
714C4×D4—412no—
715C4×D4—86no—
716#117—212no—
717#117—46no—
718#117—46no—
719#117—46no—
720C2×C4⋊C4—46no—
721C2×C4⋊C4—46no—
722C2×C4⋊C4—46no—
723C2×C4⋊C4—46no—
724C2×C4⋊C4—412no—
725C2×C4⋊C4—86no—
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⋊C4C2411yescharacteristic
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⋊C4C2411yescharacteristic
746C2×C4⋊C4C2411yescharacteristic
747C2×C4⋊C4C2413yes—
748C2×C4⋊C4C2413yes—
749C2×C4⋊C4C2413yes—
750C2×C4⋊C4C2411yescharacteristic
751C2×C4⋊C4C2411yescharacteristic
752C2×C4⋊C4C2411yescharacteristic
753C2×C4⋊C4C2411yescharacteristic
754C2×C4⋊C4C2411yescharacteristic
755C2×C4⋊C4C2413yes—
756C2×C4⋊C4C2413yes—
757C2×C4⋊C4C2413yes—
758C2×C4⋊C4C2413yes—
759C2×C4⋊C4C2413yes—
760C2×C4⋊C4C2416yes—
761C2×C4⋊C4C2416yes—
762C2×C4⋊C4C2416yes—
763C2×C4⋊C4C2416yes—
764C2×C4⋊C4C2416yes—
765C2×C4⋊C4C2411yescharacteristic
766C2×C4⋊C4C2411yescharacteristic
767C2×C4⋊C4C2411yescharacteristic
768C2×C4⋊C4C2413yes—
769C2×C4⋊C4C2413yes—
770C2×C4⋊C4C2416yes—
771C2×C4⋊C4C2416yes—
772C2×C4⋊C4C2413yes—
773C2×C4⋊C4C2413yes—
774C2×C4⋊C4C2413yes—
775C2×C4⋊C4C2416yes—
776C2×C4⋊C4C2413yes—
777C2×C4⋊C4C2413yes—
778C2×C4⋊C4C2413yes—
779C2×C4⋊C4C2413yes—
780C2×C4⋊C4C2416yes—
781C2×C4⋊C4C2416yes—
782C2×C4⋊C4C2416yes—
783C2×C4⋊C4C2411yescharacteristic
784C2×C4⋊C4C2411yescharacteristic
785C2×C4⋊C4C2411yescharacteristic
786C2×C4⋊C4C2413yes—
787C2×C4⋊C4C2413yes—
788C2×C4⋊C4C2416yes—
789C2×C4⋊C4C2411yescharacteristic
790C2×C22⋊C4C2416yes—
791C2×C22⋊C4C2411yescharacteristic
792C2×C22⋊C4C2413yes—
793C2×C22⋊C4C2413yes—
794C2×C22⋊C4C2413yes—
795C2×C22⋊C4C2413yes—
796C2×C22⋊C4C2413yes—
797C2×C22⋊C4C2413yes—
798C2×C22⋊C4C2413yes—
799C2×C22⋊C4C2416yes—
800C2×C22⋊C4C2413yes—
801C2×C22⋊C4C2413yes—
802C2×C22⋊C4C2411yescharacteristic
803C2×C22⋊C4C2411yescharacteristic
804C2×C22⋊C4C2413yes—
805C2×C22⋊C4C2413yes—
806C2×C22⋊C4C2413yes—
807C2×C22⋊C4C2413yes—
808C2×C22⋊C4C2413yes—
809C2×C22⋊C4C2413yes—
810C2×C22⋊C4C2413yes—
811C2×C22⋊C4C2413yes—
812C2×C22⋊C4C2413yes—
813C2×C22⋊C4C2411yescharacteristic
814C2×C22⋊C4C2416yes—
815C2×C22⋊C4C2416yes—
816C2×C22⋊C4C2416yes—
817C2×C22⋊C4C2413yes—
818C2×C22⋊C4C2416yes—
819C2×C22⋊C4C2416yes—
820C2×C22⋊C4C2413yes—
821C2×C22⋊C4C2413yes—
822C2×C22⋊C4C2416yes—
823C2×C22⋊C4C2416yes—
824C2×C22⋊C4C2413yes—
825C2×C22⋊C4C2411yescharacteristic
826C2×C22⋊C4C2413yes—
827C2×C22⋊C4C2413yes—
828C2×C22⋊C4C2413yes—
829C2×C22⋊C4C2413yes—
830C2×C22⋊C4C2411yescharacteristic
831C2×C42—212no—
832C2×C42—46no—
833C2×C42C2413yes—
834C2×C42C2413yes—
835C2×C42C2413yes—
836C2×C42C2413yes—
837C2×C42C2413yes—
838C2×C42C2413yes—
839C2×C42C2413yes—
840C2×C42C2413yes—
841C2×C42C2413yes—
842C2×C42C2413yes—
843C2×C42C2413yes—
844C2×C42C2413yes—
845C2×C42C2413yes—
846C2×C42C2413yes—
847C2×C42C2411yescharacteristic
848C2×C42C2411yescharacteristic
849C2×C42C2413yes—
850C2×C42C2416yes—
851C2×C42C2413yes—
852C2×C42C2413yes—
853C2×C42C2413yes—
854#95C2411yescharacteristic
855#95C2413yes—
856#95C2413yes—
857#95C2413yes—
858#95C2411yescharacteristic
859#95C2411yescharacteristic
860#95C2411yescharacteristic
861#95C2411yescharacteristic
862#95C2411yescharacteristic
863#95C2411yescharacteristic
864#95C2413yes—
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#95C2413yes—
879#95C2413yes—
880#95C2411yescharacteristic
881#95C2411yescharacteristic
882#95C2416yes—
883#95C2411yescharacteristic
884#95C2413yes—
885#95C2413yes—
886#95C2413yes—
887#95C2413yes—
888#95C2413yes—
889#95C2413yes—
890#95C2413yes—
891#95C2413yes—
892#95C2413yes—
893#95C2413yes—
894#95C2413yes—
895#95C2413yes—
896#95C2413yes—
897#95C2413yes—
898#95C2413yes—
899#95C2413yes—
900#95C2413yes—
901#95C2413yes—
902#95C2413yes—
903#95C2413yes—
904#95C2413yes—
905#95C2413yes—
906#95C2413yes—
907#95C2413yes—
908#95C2416yes—
909#95C2416yes—
910#95C2416yes—
911#95C2416yes—
912#95C2416yes—
913#95C2416yes—
914C24C2513yes—
915C24C2513yes—
916C24C2511yescharacteristic
917#41—232no—
918#41—416no—
919C2×Q8—26no—
920C2×Q8—26no—
921C2×Q8—22no—
922C2×Q8—26no—
923C2×Q8—41no—
924C2×Q8—41no—
925C2×Q8—46no—
926C2×Q8—46no—
927C2×Q8—46no—
928C2×Q8—416no—
929C2×Q8C2×#4114yes—
930C2×Q8H(5,𝔽2)14yes—
931C2×Q82−1+414yes—
932C2×D4—26no—
933C2×D4—26no—
934C2×D4—26no—
935C2×D4—212no—
936C2×D4—26no—
937C2×D4—26no—
938C2×D4—26no—
939C2×D4—26no—
940C2×D4—26no—
941C2×D4—26no—
942C2×D4—26no—
943C2×D4—43no—
944C2×D4—43no—
945C2×D4—43no—
946C2×D4—46no—
947C2×D4—43no—
948C2×D4—46no—
949C2×D4C2×#41112yes—
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—26no—
959C22×C4—26no—
960C22×C4—22no—
961C22×C4—26no—
962C22×C4—26no—
963C22×C4—26no—
964C22×C4—41no—
965C22×C4—43no—
966C22×C4—41no—
967C22×C4—43no—
968C22×C4—43no—
969C22×C4—43no—
970C22×C4—46no—
971C22×C4—46no—
972C22×C4—46no—
973C22×C4—46no—
974C22×C4—46no—
975C22×C4—46no—
976C22×C4—46no—
977C22×C4—46no—
978C22×C4—46no—
979C22×C4C2×#41112yes—
980C22×C4C2513yes—
981C22×C4C2511yescharacteristic
982C22×C4C2511yescharacteristic
983C22×C4C2513yes—
984C22×C4C2511yescharacteristic
985C22×C4C2513yes—
986C22×C4C2511yescharacteristic
987C22×C4C2511yescharacteristic
988C22×C4C2513yes—
989C22×C4C2511yescharacteristic
990C22×C4C2511yescharacteristic
991C22×C4C2511yescharacteristic
992C22×C4C2513yes—
993C22×C4C2513yes—
994C22×C4C2513yes—
995C22×C4C2513yes—
996C22×C4C2513yes—
997C22×C4C2513yes—
998C22×C4C2513yes—
999C22×C4C2513yes—
1000C22×C4C2513yes—
1001C22×C4C2511yescharacteristic
1002C22×C4C2511yescharacteristic
1003C22×C4C2511yescharacteristic
1004C22×C4C2511yescharacteristic
1005C22×C4C2511yescharacteristic
1006C22×C4C2511yescharacteristic
1007C22×C4C2513yes—
1008C4⋊C4—26no—
1009C4⋊C4—26no—
1010C4⋊C4—22no—
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—22no—
1030C4⋊C4—22no—
1031C4⋊C4—26no—
1032C4⋊C4—22no—
1033C4⋊C4—22no—
1034C4⋊C4—22no—
1035C4⋊C4—22no—
1036C4⋊C4—22no—
1037C4⋊C4—43no—
1038C4⋊C4—43no—
1039C4⋊C4—43no—
1040C4⋊C4—46no—
1041C4⋊C4—46no—
1042C4⋊C4—46no—
1043C4⋊C4—43no—
1044C4⋊C4—43no—
1045C4⋊C4—46no—
1046C4⋊C4—46no—
1047C4⋊C4—43no—
1048C4⋊C4—41no—
1049C4⋊C4—41no—
1050C4⋊C4—46no—
1051C4⋊C4—43no—
1052C4⋊C4—41no—
1053C4⋊C4—41no—
1054C4⋊C4—41no—
1055C4⋊C4—41no—
1056C4⋊C4—43no—
1057C4⋊C4—46no—
1058C4⋊C4—46no—
1059C4⋊C4—43no—
1060C4⋊C4—43no—
1061C4⋊C4—43no—
1062C4⋊C4—43no—
1063C4⋊C4—46no—
1064C4⋊C4—46no—
1065C4⋊C4—46no—
1066C4⋊C4—43no—
1067C4⋊C4—43no—
1068C4⋊C4—43no—
1069C4⋊C4—43no—
1070C4⋊C4—46no—
1071C4⋊C42−1+414yes—
1072C22⋊C4—212no—
1073C22⋊C4—26no—
1074C22⋊C4—26no—
1075C22⋊C4—212no—
1076C22⋊C4—26no—
1077C22⋊C4—26no—
1078C22⋊C4—26no—
1079C22⋊C4—22no—
1080C22⋊C4—26no—
1081C22⋊C4—26no—
1082C22⋊C4—26no—
1083C22⋊C4—26no—
1084C22⋊C4—22no—
1085C22⋊C4—22no—
1086C22⋊C4—26no—
1087C22⋊C4—26no—
1088C22⋊C4—26no—
1089C22⋊C4—41no—
1090C22⋊C4—43no—
1091C22⋊C4—43no—
1092C22⋊C4—43no—
1093C22⋊C4—43no—
1094C22⋊C4—43no—
1095C22⋊C4—43no—
1096C22⋊C4—43no—
1097C22⋊C4—43no—
1098C22⋊C4—43no—
1099C22⋊C4—43no—
1100C22⋊C4—41no—
1101C22⋊C4—46no—
1102C22⋊C4—43no—
1103C22⋊C4—46no—
1104C22⋊C4—46no—
1105C22⋊C4—46no—
1106C22⋊C4—46no—
1107C22⋊C4—43no—
1108C22⋊C4—43no—
1109C22⋊C4—46no—
1110C22⋊C4—46no—
1111C22⋊C4—43no—
1112C22⋊C4H(5,𝔽2)14yes—
1113C42—22no—
1114C42—26no—
1115C42—26no—
1116C42—26no—
1117C42—26no—
1118C42—26no—
1119C42—26no—
1120C42—26no—
1121C42—26no—
1122C42—26no—
1123C42—26no—
1124C42—26no—
1125C42—26no—
1126C42—26no—
1127C42—26no—
1128C42—22no—
1129C42—43no—
1130C42—43no—
1131C42—43no—
1132C42—46no—
1133C42—43no—
1134C23—21no—
1135C23—23no—
1136C23—23no—
1137C23—21no—
1138C23—21no—
1139C23—23no—
1140C23—21no—
1141C23—23no—
1142C23—23no—
1143C23—21no—
1144C23—23no—
1145C23—21no—
1146C23—23no—
1147C23—23no—
1148C23—23no—
1149C23—23no—
1150C23—23no—
1151C23—23no—
1152C23—23no—
1153C23C22×#4116yes—
1154C23C2×H(5,𝔽2)12yes—
1155C23C2611yescharacteristic
1156Q8—44no—
1157Q8—412no—
1158Q8—166no—
1159Q8#539116yescomplemented
1160D4—224no—
1161D4—412no—
1162D4—412no—
1163D4—412no—
1164D4—812no—
1165D4—86no—
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—21no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—224no—
1179C2×C4—21no—
1180C2×C4—23no—
1181C2×C4—23no—
1182C2×C4—23no—
1183C2×C4—23no—
1184C2×C4—21no—
1185C2×C4—23no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—21no—
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—23no—
1201C2×C4—23no—
1202C2×C4—23no—
1203C2×C4—23no—
1204C2×C4—23no—
1205C2×C4—23no—
1206C2×C4—23no—
1207C2×C4—21no—
1208C2×C4—23no—
1209C2×C4—21no—
1210C2×C4—23no—
1211C2×C4—23no—
1212C2×C4—21no—
1213C2×C4—23no—
1214C2×C4—23no—
1215C2×C4—21no—
1216C2×C4—21no—
1217C2×C4—21no—
1218C2×C4—21no—
1219C2×C4—21no—
1220C2×C4—21no—
1221C2×C4—23no—
1222C2×C4—23no—
1223C2×C4—23no—
1224C2×C4—21no—
1225C2×C4—21no—
1226C2×C4—23no—
1227C2×C4—23no—
1228C2×C4—23no—
1229C2×C4—23no—
1230C2×C4—23no—
1231C2×C4—23no—
1232C2×C4—21no—
1233C2×C4—23no—
1234C2×C4—23no—
1235C2×C4—21no—
1236C2×C4—21no—
1237C2×C4—21no—
1238C2×C4—21no—
1239C2×C4—23no—
1240C2×C4—23no—
1241C2×C4—21no—
1242C2×C4—412no—
1243C2×C4—412no—
1244C2×C4—44no—
1245C2×C4—412no—
1246C2×C4—412no—
1247C2×C4—86no—
1248C2×C4—166no—
1249C2×C4—166no—
1250C2×C4—166no—
1251C2×C4C22×#4112yes—
1252C2×C4C22×#4116yes—
1253C2×C4C2×H(5,𝔽2)12yes—
1254C2×C4C2×H(5,𝔽2)12yes—
1255C2×C4C2×H(5,𝔽2)16yes—
1256C2×C4C2×2−1+412yes—
1257C2×C4C2×2−1+412yes—
1258C2×C4C2×2−1+412yes—
1259C2×C4C2×2−1+416yes—
1260C22—26no—
1261C22—22no—
1262C22—26no—
1263C22—22no—
1264C22—22no—
1265C22—26no—
1266C22—41no—
1267C22—43no—
1268C22—41no—
1269C22—43no—
1270C22—41no—
1271C22—43no—
1272C22—43no—
1273C22—41no—
1274C22—43no—
1275C22—43no—
1276C22—43no—
1277C22—43no—
1278C22—43no—
1279C22—43no—
1280C22—43no—
1281C22C23×#4111yescharacteristic
1282C22C22×H(5,𝔽2)11yescharacteristic
1283C22C22×H(5,𝔽2)11yescharacteristic
1284C22C22×2−1+411yescharacteristic
1285C22C22×2−1+411yescharacteristic
1286C22H(7,𝔽2)11yescharacteristic
1287C222−1+611yescharacteristic
1288C4—22no—
1289C4—22no—
1290C4—22no—
1291C4—22no—
1292C4—22no—
1293C4—22no—
1294C4—43no—
1295C4—43no—
1296C4—43no—
1297C4—41no—
1298C4—43no—
1299C4—43no—
1300C4—41no—
1301C4—43no—
1302C4—41no—
1303C4—41no—
1304C4—41no—
1305C4—41no—
1306C4—41no—
1307C4—43no—
1308C4—43no—
1309C4—43no—
1310C4—43no—
1311C4—43no—
1312C4—43no—
1313C4—41no—
1314C4—43no—
1315C4C2×#539112yes—
1316C2—46no—
1317C2—42no—
1318C2—83no—
1319C2C22×#53911yescharacteristic
1320C2#6291311yescharacteristic
1321C2#6291611yescharacteristic
1322C2#6298511yescharacteristic
1323C2#6300011yescharacteristic
1324C2#6303711yescharacteristic
1325C2#6306111yescharacteristic
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. #52247C2semidirect
2. #42601C2semidirect
3. #42572C2semidirect
4. #42559C2semidirect
5. #42551C2semidirect
6. #42521C2semidirect
7. #42506C2semidirect
8. #40165C2semidirect
9. #40045C2semidirect
10. #39604C2semidirect
11. #39404C2semidirect
12. #39400C2semidirect
13. #39348C2semidirect
14. #37342C2semidirect
15. #37339C2semidirect
16. #37287C2semidirect
17. Q8×#125C2semidirect
18. Q8×C22⋊Q8C2semidirect
19. #36483C2semidirect
20. #36448C2semidirect
21. #36433C2semidirect
22. #36432C2semidirect
23. #35996C2semidirect
24. #35898C2semidirect
25. #35868C2semidirect
27. #35748C2semidirect
28. #35748C2semidirect
29. #34313C2semidirect
30. #34294C2semidirect
31. #34183C2semidirect
1159. Q8#539semidirect

Maximal subgroups

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

subgroupindex
#522472
#426012
#425722
#425592
#425512
#425212
#425062
#401652
#400452
#396042
#394042
#394002
#393482
#373422
#373392
#372872
Q8×#1252
Q8×C22⋊Q82
#364832
#364482
#364332
#364322
#359962
#358982
#358682
#358312
#357482
#343132
#342942
#341832