Finite Group Databasebeta

← #8096424

Subgroups — #8096424

Order 512.

4343 conjugacy classes of subgroups.

The subgroup lattice has 1258 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53109C213yesmaximal, complemented
2#53081C213yesmaximal, complemented
3#53048C213yesmaximal, complemented
4#53035C213yesmaximal, complemented
5#53020C213yesmaximal, complemented
6#52998C213yesmaximal, complemented
7#52300C213yesmaximal, complemented
8#46343C213yesmaximal, complemented
9#46341C213yesmaximal, complemented
10#46062C213yesmaximal, complemented
11#46051C213yesmaximal, complemented
12#46019C213yesmaximal, complemented
13#46011C213yesmaximal, complemented
14#45618C213yesmaximal, complemented
15#45605C213yesmaximal, complemented
16#45499C213yesmaximal, complemented
17Q8×C4⋊Q8C211yesmaximal, characteristic, complemented
18Q8×#126C211yesmaximal, characteristic, complemented
19#36474C211yesmaximal, characteristic, complemented
20#36458C211yesmaximal, characteristic, complemented
21#36458C211yesmaximal, characteristic, complemented
22#36456C211yesmaximal, characteristic, complemented
23#36448C211yesmaximal, characteristic, complemented
24#36432C211yesmaximal, characteristic
25#36431C211yesmaximal, characteristic, complemented
26#35971C211yesmaximal, characteristic, complemented
27#35948C211yesmaximal, characteristic
28#35868C211yesmaximal, characteristic, complemented
29#35801C211yesmaximal, characteristic
30#35786C211yesmaximal, characteristic, complemented
31#35711C211yesmaximal, characteristic, complemented
32C2×Q82C2211yescharacteristic
33C2×Q82C2211yescharacteristic
34C2×#557C2211yescharacteristic
35C2×#548C2211yescharacteristic
36C2×#519C2211yescharacteristic
37C2×C4×#41C2211yescharacteristic
38#2868C2213yes—
39#2863C2213yes—
40#2863C2213yes—
41#2862C2213yes—
42#2860C2213yes—
43#2860C2213yes—
44#2857C2213yes—
45#2855C2213yes—
46#2851C2213yes—
47#2841C2216yes—
48#2838C2216yes—
49#2836C2216yes—
50#2835C2216yes—
51#2832C2216yes—
52#2831C2216yes—
53#2831C2216yes—
54#2831C2216yes—
55#2823C2216yes—
56#2821C2216yes—
57#2820C2216yes—
58#2805C2216yes—
59#2799C2216yes—
60#2794C2216yes—
61#2793C2216yes—
62#2791C2213yes—
63#2791C2213yes—
64#2777C2213yes—
65#2777C2213yes—
66#2775C2216yes—
67#2771C2213yes—
68#2770C2216yes—
69#2764C2213yes—
70#2762C2216yes—
71#2759C2216yes—
72#2758C2213yes—
73#2758C2213yes—
74#2745C2216yes—
75#2731C2216yes—
76#2729C2216yes—
77#2722C2213yes—
78#2721C2216yes—
79#2720C2216yes—
80#2718C2213yes—
81#2718C2213yes—
82#2716C2216yes—
83#2716C2216yes—
84#2716C2216yes—
85#2716C2211yescharacteristic
86#2716C2213yes—
87#2715C2216yes—
88#2713C2216yes—
89#2702C2213yes—
90#2702C2213yes—
91#2698C2216yes—
92#2689C2216yes—
93#2677C2213yes—
94#2674C2216yes—
95#2647C2213yes—
96#2647C2213yes—
97#2640C2213yes—
98#2629C2213yes—
99#2628C2213yes—
100#2624C2213yes—
101#2592C2213yes—
102#2582C2213yes—
103#2581C2213yes—
104#2580C2213yes—
105#2571C2213yes—
106#2570C2213yes—
107#2570C2213yes—
108#2568C2213yes—
109#2567C2213yes—
110#2567C2213yes—
111#2567C2213yes—
112#2566C2213yes—
113#2565C2213yes—
114#2563C2213yes—
115#2552C2213yes—
116#2551C2213yes—
117#2551C2213yes—
118#2551C2213yes—
119#2551C2213yes—
120#2550C2213yes—
121#2550C2213yes—
122#2550C2213yes—
123#2550C2213yes—
124#2547C2213yes—
125#2546C2213yes—
126#2538C2213yes—
127#2514C2213yes—
128#2514C2213yes—
129#2513C2213yes—
130#2513C2213yes—
131#2512C2213yes—
132#2512C2213yes—
133#2512C2213yes—
134#2512C2213yes—
135#2511C2213yes—
136#2511C2213yes—
137#2511C2213yes—
138#2511C2213yes—
139#2509C2213yes—
140#2509C2213yes—
141#2508C2213yes—
142#2508C2213yes—
143#2507C2213yes—
144#2507C2213yes—
145#2506C2213yes—
146#2506C2213yes—
147#2500C2213yes—
148#2499C2213yes—
149#2497C2213yes—
150#2497C2213yes—
151#2497C2213yes—
152#2497C2213yes—
153#2497C2213yes—
154#2496C2213yes—
155#2496C2213yes—
156#2496C2213yes—
157#2495C2213yes—
158#2495C2213yes—
159#2495C2213yes—
160#2494C2213yes—
161#2492C2213yes—
162#2492C2213yes—
163#2491C2213yes—
164#2491C2213yes—
165#2485C2213yes—
166#2485C2213yes—
167#2454C2213yes—
168#2453C2213yes—
169#2452C2213yes—
170#2452C2213yes—
171#2452C2213yes—
172#2451C2213yes—
173#2451C2213yes—
174#2451C2213yes—
175#2448C2213yes—
176#2448C2213yes—
177#2447C2213yes—
178#2447C2213yes—
179#2441C2213yes—
180#2441C2213yes—
181#2439C2213yes—
182#2439C2213yes—
183#2439C2213yes—
184#2439C2213yes—
185#2439C2213yes—
186#2439C2213yes—
187#2423C2213yes—
188#2422C2213yes—
189#2421C2213yes—
190#2420C2213yes—
191#2402C2213yes—
192#2402C2213yes—
193#2398C2213yes—
194#2396C2213yes—
195#2396C2213yes—
196#2395C2213yes—
197#2383C2216yes—
198#2381C2216yes—
199#2378C2216yes—
200#2351C2211yescharacteristic
201#2351C2211yescharacteristic
202#2351C2211yescharacteristic
203#2351C2211yescharacteristic
204#2351C2211yescharacteristic
205#2351C2211yescharacteristic
206#2351C2211yescharacteristic
207#2351C2211yescharacteristic
208Q8×C4⋊C4C2211yescharacteristic
209Q8×C4⋊C4C2211yescharacteristic
210Q8×C4⋊C4C2211yescharacteristic
211Q8×C4⋊C4C2211yescharacteristic
212Q8×C4⋊C4C2211yescharacteristic
213Q8×C4⋊C4C2211yescharacteristic
214Q8×C4⋊C4C2211yescharacteristic
215Q8×C4⋊C4C2211yescharacteristic
216#2341C2211yescharacteristic
217#2341C2211yescharacteristic
218#2341C2211yescharacteristic
219#2341C2211yescharacteristic
220#2341C2211yescharacteristic
221Q8×C22⋊C4C2211yescharacteristic
222Q8×C22⋊C4C2211yescharacteristic
223Q8×C22⋊C4C2211yescharacteristic
224Q8×C22⋊C4C2211yescharacteristic
225Q8×C22⋊C4C2211yescharacteristic
226C4×C4⋊Q8C2213yes—
227C4×C4⋊Q8C2213yes—
228C4×#126C2213yes—
229C4×#126C2213yes—
230C4×#126C2213yes—
231C4×#126C2213yes—
232C4×C22⋊Q8C2213yes—
233C4×C22⋊Q8C2213yes—
234C4×#123C2213yes—
235#2276C2211yescharacteristic
236C42×Q8C2211yescharacteristic
237C42×Q8C2211yescharacteristic
238C22×#41C2311yescharacteristic
239C23×Q8C2311yescharacteristic
240Q82—44no—
241Q82—44no—
242#557—44no—
243#548—44no—
244C2×C4⋊Q8C2311yescharacteristic
245C2×C4⋊Q8C2313yes—
246C2×C4⋊Q8C2313yes—
247C2×C4⋊Q8C2316yes—
248C2×C4⋊Q8C2313yes—
249C2×C4⋊Q8C2313yes—
250C2×C4⋊Q8C2313yes—
251C2×C4⋊Q8C2313yes—
252C2×C4⋊Q8C2313yes—
253C2×C4⋊Q8C2313yes—
254C2×C4⋊Q8C2316yes—
255C2×#126C2311yescharacteristic
256C2×#126C2313yes—
257C2×#126C2313yes—
258C2×#126C2313yes—
259C2×#126C2316yes—
260C2×#126C2316yes—
261C2×#125C2313yes—
262C2×#125C2313yes—
263C2×#125C2316yes—
264C2×#124C2313yes—
265C2×#124C2316yes—
266C2×#123C2313yes—
267C2×C22⋊Q8C2313yes—
268C2×C22⋊Q8C2313yes—
269C2×C22⋊Q8C2313yes—
270C2×C22⋊Q8C2316yes—
271C2×#121C2313yes—
272#519—44no—
273C4×#41—44no—
274C2×C4×Q8C2311yescharacteristic
275C2×C4×Q8C2311yescharacteristic
276C2×C4×Q8C2311yescharacteristic
277C2×C4×Q8C2311yescharacteristic
278C2×C4×Q8C2311yescharacteristic
279C2×C4×Q8C2311yescharacteristic
280C2×C4×Q8C2311yescharacteristic
281C2×C4×Q8C2311yescharacteristic
282C2×C4×Q8C2311yescharacteristic
283C2×C4×Q8C2311yescharacteristic
284C2×C4×Q8C2311yescharacteristic
285C2×C4×Q8C2311yescharacteristic
286C2×C4×Q8C2311yescharacteristic
287C2×C4×Q8C2313yes—
288C2×C4×Q8C2313yes—
289C2×C4×Q8C2313yes—
290C2×C4×Q8C2313yes—
291C2×C4×Q8C2313yes—
292C2×C4×D4C2313yes—
293C2×C4×D4C2313yes—
294C2×C4×D4C2313yes—
295C2×#117C2313yes—
296C2×#117C2313yes—
297C2×#117C2313yes—
298C22×C42C2313yes—
299#401C2316yes—
300#400C2316yes—
301#400C2316yes—
302#400C2313yes—
303#400C2316yes—
304#400C2313yes—
305#400C2313yes—
306#400C2316yes—
307#400C2313yes—
308#400C2313yes—
309#400C2316yes—
310#400C2316yes—
311#400C2316yes—
312#400C2316yes—
313#400C2313yes—
314#400C2316yes—
315#400C2316yes—
316#400C2313yes—
317#400C2316yes—
318#400C2313yes—
319#400C2313yes—
320#400C2313yes—
321#400C2311yescharacteristic
322#400C2313yes—
323#400C2313yes—
324#399C2313yes—
325#399C2316yes—
326#399C2316yes—
327#399C2313yes—
328#399C2313yes—
329#398C2313yes—
330#398C2316yes—
331#398C2313yes—
332#398C2316yes—
333#398C2316yes—
334#398C2316yes—
335#398C2313yes—
336#398C2316yes—
337#398C2313yes—
338#398C2316yes—
339#398C2316yes—
340#398C2313yes—
341#398C2313yes—
342#398C2313yes—
343#398C2313yes—
344#398C2313yes—
345#398C2313yes—
346#398C2311yescharacteristic
347#398C2313yes—
348#398C2313yes—
349#397C2316yes—
350#397C2316yes—
351#397C2316yes—
352#397C2316yes—
353#397C2313yes—
354#397C2313yes—
355#397C2313yes—
356#397C2316yes—
357#397C2316yes—
358#397C2316yes—
359#397C2316yes—
360#397C2316yes—
361#397C2316yes—
362#397C2313yes—
363#397C2311yescharacteristic
364#396C2313yes—
365#396C2316yes—
366#396C2316yes—
367#396C2316yes—
368#396C2316yes—
369#396C2316yes—
370#396C2313yes—
371#396C2316yes—
372#396C2316yes—
373#396C2316yes—
374#396C2311yescharacteristic
375#396C2313yes—
376#395C2316yes—
377#395C2316yes—
378#395C2316yes—
379#395C2316yes—
380#395C2316yes—
381#395C2316yes—
382#395C2316yes—
383#395C2313yes—
384#395C2313yes—
385#394C2313yes—
386#394C2316yes—
387#394C2313yes—
388#394C2316yes—
389#394C2313yes—
390#394C2313yes—
391#393C2316yes—
392#393C2316yes—
393#393C2316yes—
394#393C2316yes—
395#393C2316yes—
396#393C2313yes—
397#393C2316yes—
398#393C2313yes—
399#393C2311yescharacteristic
400#393C2311yescharacteristic
401#391C2311yescharacteristic
402#391C2313yes—
403#391C2313yes—
404#391C2313yes—
405#391C2313yes—
406#391C2313yes—
407#391C2316yes—
408#391C2316yes—
409#391C2313yes—
410#391C2313yes—
411#391C2316yes—
412#391C2316yes—
413#391C2316yes—
414#391C2313yes—
415#391C2313yes—
416#391C2313yes—
417#391C2313yes—
418#391C2316yes—
419#391C2313yes—
420#391C2313yes—
421#391C2316yes—
422#391C2316yes—
423#391C2313yes—
424#391C2311yescharacteristic
425#390C2313yes—
426#390C2313yes—
427#390C2313yes—
428#390C2313yes—
429#390C2313yes—
430#390C2313yes—
431#390C2313yes—
432#390C2313yes—
433#390C2313yes—
434#390C2313yes—
435#389C2313yes—
436#389C2313yes—
437#389C2313yes—
438#389C2313yes—
439#389C2313yes—
440#389C2313yes—
441#389C2313yes—
442#389C2313yes—
443#389C2313yes—
444#389C2313yes—
445#389C2313yes—
446#389C2313yes—
447#389C2313yes—
448#389C2313yes—
449#389C2313yes—
450#389C2313yes—
451#389C2313yes—
452#389C2313yes—
453#389C2313yes—
454#389C2313yes—
455#389C2313yes—
456#389C2313yes—
457#389C2313yes—
458#389C2313yes—
459#389C2316yes—
460#389C2313yes—
461#389C2313yes—
462#389C2313yes—
463#389C2313yes—
464#389C2316yes—
465#389C2313yes—
466#389C2313yes—
467#389C2313yes—
468#389C2313yes—
469#389C2313yes—
470#389C2313yes—
471#389C2313yes—
472#389C2313yes—
473#389C2313yes—
474#389C2313yes—
475#389C2313yes—
476#389C2313yes—
477#389C2313yes—
478#389C2316yes—
479#389C2313yes—
480#388C2311yescharacteristic
481#388C2313yes—
482#388C2313yes—
483#388C2313yes—
484#388C2313yes—
485#388C2313yes—
486#388C2313yes—
487#388C2313yes—
488#388C2313yes—
489#388C2313yes—
490#388C2313yes—
491#388C2313yes—
492#388C2313yes—
493#388C2316yes—
494#388C2316yes—
495#388C2316yes—
496#388C2316yes—
497#388C2316yes—
498#388C2316yes—
499#388C2316yes—
500#388C2316yes—
501#388C2316yes—
502#388C2311yescharacteristic
503#387C2311yescharacteristic
504#387C2311yescharacteristic
505#387C2313yes—
506#387C2313yes—
507#387C2313yes—
508#387C2313yes—
509#387C2313yes—
510#387C2313yes—
511#387C2313yes—
512#387C2313yes—
513#387C2313yes—
514#387C2313yes—
515#387C2316yes—
516#387C2316yes—
517#387C2316yes—
518#387C2316yes—
519#387C2316yes—
520#387C2316yes—
521#387C2316yes—
522#387C2316yes—
523#387C2316yes—
524#387C2316yes—
525#387C2316yes—
526#387C2316yes—
527#387C2313yes—
528#387C2313yes—
529#387C2316yes—
530#387C2316yes—
531#387C2316yes—
532#387C2313yes—
533#387C2316yes—
534#387C2313yes—
535#387C2313yes—
536#387C2311yescharacteristic
537#386C2313yes—
538#385C2313yes—
539#385C2316yes—
540#385C2313yes—
541#385C2316yes—
542#385C2313yes—
543#385C2316yes—
544#385C2313yes—
545#385C2313yes—
546#384C2313yes—
547#384C2313yes—
548#384C2313yes—
549#384C2313yes—
550#384C2316yes—
551#384C2313yes—
552#384C2313yes—
553#384C2313yes—
554#384C2313yes—
555#384C2313yes—
556#384C2313yes—
557#383C2313yes—
558#383C2313yes—
559#383C2313yes—
560#383C2313yes—
561#383C2316yes—
562#382C2313yes—
563#382C2313yes—
564#382C2316yes—
565#382C2313yes—
566#382C2313yes—
567#382C2313yes—
568#382C2313yes—
569#382C2313yes—
570#382C2313yes—
571#381C2316yes—
572#381C2313yes—
573#380C2313yes—
574#380C2316yes—
575#380C2313yes—
576#380C2313yes—
577#380C2313yes—
578#380C2313yes—
579#380C2313yes—
580#380C2313yes—
581#380C2313yes—
582#380C2313yes—
583#380C2313yes—
584#380C2313yes—
585#380C2313yes—
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×C22⋊C4C2313yes—
612C4×C22⋊C4C2313yes—
613C4×C22⋊C4C2313yes—
614C4×C22⋊C4C2313yes—
615C4×C22⋊C4C2313yes—
616C4×C22⋊C4C2313yes—
617C4×C22⋊C4C2313yes—
618C4×C22⋊C4C2313yes—
619C4×C22⋊C4C2313yes—
620C4×C22⋊C4C2313yes—
621#376C2313yes—
622C43C2313yes—
623C43C2313yes—
624C2×#41—24no—
625C2×#41—24no—
626C2×#41—24no—
627C22×Q8—24no—
628C22×Q8—24no—
629C22×Q8—24no—
630C22×Q8C2413yes—
631C22×Q8C2411yescharacteristic
632C22×Q8C2411yescharacteristic
633C22×Q8C2413yes—
634C22×Q8C2416yes—
635C22×Q8C2416yes—
636C22×Q8C2411yescharacteristic
637C22×D4C2413yes—
638C22×D4C2413yes—
639C23×C4C2413yes—
640C23×C4C2413yes—
641C23×C4C2413yes—
642C23×C4C2413yes—
643C4⋊Q8—24no—
644C4⋊Q8—412no—
645C4⋊Q8—46no—
646C4⋊Q8—46no—
647C4⋊Q8—46no—
648C4⋊Q8—46no—
649C4⋊Q8—46no—
650C4⋊Q8—46no—
651C4⋊Q8—46no—
652C4⋊Q8—46no—
653C4⋊Q8—86no—
654#126—24no—
655#126—412no—
656#126—46no—
657#126—46no—
658#126—46no—
659#126—86no—
660#125—46no—
661#125—46no—
662#125—86no—
663#124—46no—
664#124—86no—
665#123—46no—
666C22⋊Q8—212no—
667C22⋊Q8—46no—
668C22⋊Q8—46no—
669C22⋊Q8—86no—
670#121—46no—
671C4×Q8—24no—
672C4×Q8—24no—
673C4×Q8—24no—
674C4×Q8—24no—
675C4×Q8—24no—
676C4×Q8—24no—
677C4×Q8—24no—
678C4×Q8—24no—
679C4×Q8—24no—
680C4×Q8—24no—
681C4×Q8—24no—
682C4×Q8—24no—
683C4×Q8—24no—
684C4×Q8—46no—
685C4×Q8—46no—
686C4×Q8—46no—
687C4×Q8—46no—
688C4×Q8—46no—
689C4×D4—46no—
690C4×D4—46no—
691C4×D4—46no—
692#117—46no—
693#117—46no—
694#117—46no—
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⋊C4C2413yes—
707C2×C4⋊C4C2413yes—
708C2×C4⋊C4C2413yes—
709C2×C4⋊C4C2413yes—
710C2×C4⋊C4C2413yes—
711C2×C4⋊C4C2413yes—
712C2×C4⋊C4C2411yescharacteristic
713C2×C4⋊C4C2411yescharacteristic
714C2×C4⋊C4C2413yes—
715C2×C4⋊C4C2413yes—
716C2×C4⋊C4C2411yescharacteristic
717C2×C4⋊C4C2411yescharacteristic
718C2×C4⋊C4C2411yescharacteristic
719C2×C4⋊C4C2411yescharacteristic
720C2×C4⋊C4C2411yescharacteristic
721C2×C4⋊C4C2413yes—
722C2×C4⋊C4C2413yes—
723C2×C4⋊C4C2413yes—
724C2×C4⋊C4C2411yescharacteristic
725C2×C4⋊C4C2413yes—
726C2×C4⋊C4C2413yes—
727C2×C4⋊C4C2413yes—
728C2×C4⋊C4C2413yes—
729C2×C4⋊C4C2413yes—
730C2×C4⋊C4C2413yes—
731C2×C4⋊C4C2413yes—
732C2×C4⋊C4C2413yes—
733C2×C4⋊C4C2413yes—
734C2×C4⋊C4C2413yes—
735C2×C4⋊C4C2416yes—
736C2×C4⋊C4C2413yes—
737C2×C4⋊C4C2413yes—
738C2×C4⋊C4C2413yes—
739C2×C4⋊C4C2416yes—
740C2×C4⋊C4C2413yes—
741C2×C4⋊C4C2413yes—
742C2×C4⋊C4C2413yes—
743C2×C4⋊C4C2416yes—
744C2×C4⋊C4C2416yes—
745C2×C4⋊C4C2413yes—
746C2×C4⋊C4C2416yes—
747C2×C4⋊C4C2413yes—
748C2×C4⋊C4C2413yes—
749C2×C4⋊C4C2413yes—
750C2×C4⋊C4C2413yes—
751C2×C4⋊C4C2413yes—
752C2×C4⋊C4C2416yes—
753C2×C4⋊C4C2416yes—
754C2×C4⋊C4C2413yes—
755C2×C4⋊C4C2413yes—
756C2×C4⋊C4C2413yes—
757C2×C4⋊C4C2413yes—
758C2×C4⋊C4C2416yes—
759C2×C4⋊C4C2416yes—
760C2×C4⋊C4C2411yescharacteristic
761C2×C22⋊C4C2413yes—
762C2×C22⋊C4C2413yes—
763C2×C22⋊C4C2413yes—
764C2×C22⋊C4C2411yescharacteristic
765C2×C22⋊C4C2413yes—
766C2×C22⋊C4C2411yescharacteristic
767C2×C22⋊C4C2411yescharacteristic
768C2×C22⋊C4C2411yescharacteristic
769C2×C22⋊C4C2411yescharacteristic
770C2×C22⋊C4C2413yes—
771C2×C22⋊C4C2411yescharacteristic
772C2×C22⋊C4C2416yes—
773C2×C22⋊C4C2411yescharacteristic
774C2×C22⋊C4C2413yes—
775C2×C22⋊C4C2416yes—
776C2×C22⋊C4C2416yes—
777C2×C22⋊C4C2416yes—
778C2×C22⋊C4C2413yes—
779C2×C22⋊C4C2413yes—
780C2×C22⋊C4C2413yes—
781C2×C22⋊C4C2413yes—
782C2×C22⋊C4C2416yes—
783C2×C22⋊C4C2413yes—
784C2×C22⋊C4C2413yes—
785C2×C22⋊C4C2413yes—
786C2×C22⋊C4C2413yes—
787C2×C22⋊C4C2413yes—
788C2×C22⋊C4C2413yes—
789C2×C22⋊C4C2413yes—
790C2×C22⋊C4C2416yes—
791C2×C22⋊C4C2416yes—
792C2×C42—46no—
793C2×C42C2413yes—
794C2×C42C2413yes—
795C2×C42C2413yes—
796C2×C42C2413yes—
797C2×C42C2413yes—
798C2×C42C2413yes—
799C2×C42C2413yes—
800C2×C42C2413yes—
801C2×C42C2413yes—
802C2×C42C2413yes—
803C2×C42C2413yes—
804C2×C42C2413yes—
805C2×C42C2413yes—
806C2×C42C2413yes—
807C2×C42C2413yes—
808C2×C42C2411yescharacteristic
809C2×C42C2411yescharacteristic
810C2×C42C2413yes—
811C2×C42C2416yes—
812C2×C42C2416yes—
813C2×C42C2413yes—
814C2×C42C2413yes—
815C2×C42C2413yes—
816C2×C42C2413yes—
817C2×C42C2411yescharacteristic
818#95C2411yescharacteristic
819#95C2413yes—
820#95C2413yes—
821#95C2413yes—
822#95C2411yescharacteristic
823#95C2411yescharacteristic
824#95C2411yescharacteristic
825#95C2411yescharacteristic
826#95C2411yescharacteristic
827#95C2413yes—
828#95C2413yes—
829#95C2413yes—
830#95C2413yes—
831#95C2413yes—
832#95C2413yes—
833#95C2413yes—
834#95C2413yes—
835#95C2413yes—
836#95C2413yes—
837#95C2413yes—
838#95C2413yes—
839#95C2413yes—
840#95C2413yes—
841#95C2413yes—
842#95C2411yescharacteristic
843#95C2411yescharacteristic
844#95C2411yescharacteristic
845#95C2411yescharacteristic
846#95C2411yescharacteristic
847#95C2411yescharacteristic
848#95C2411yescharacteristic
849#95C2411yescharacteristic
850#95C2416yes—
851#95C2416yes—
852#95C2413yes—
853#95C2413yes—
854#95C2413yes—
855#95C2413yes—
856#95C2413yes—
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#95C2416yes—
877#95C2416yes—
878#95C2416yes—
879#95C2416yes—
880#95C2416yes—
881#95C2416yes—
882#95C2416yes—
883#95C2416yes—
884#95C2416yes—
885#95C2416yes—
886#95C2416yes—
887#95C2416yes—
888#95C2416yes—
889C24C2511yescharacteristic
890C24C2513yes—
891#41—416no—
892C2×Q8—26no—
893C2×Q8—22no—
894C2×Q8—22no—
895C2×Q8—26no—
896C2×Q8—26no—
897C2×Q8—26no—
898C2×Q8—22no—
899C2×Q8—22no—
900C2×Q8—41no—
901C2×Q8—41no—
902C2×Q8—43no—
903C2×Q8—43no—
904C2×Q8—46no—
905C2×Q8—46no—
906C2×Q8—46no—
907C2×Q8—46no—
908C2×Q8—46no—
909C2×Q8—46no—
910C2×Q8—416no—
911C2×Q8H(5,𝔽2)14yes—
912C2×Q82−1+414yes—
913C2×Q82−1+414yes—
914C2×D4—26no—
915C2×D4—26no—
916C2×D4—26no—
917C2×D4—43no—
918C2×D4—43no—
919C2×D4—43no—
920C22×C4—26no—
921C22×C4—26no—
922C22×C4—26no—
923C22×C4—26no—
924C22×C4—26no—
925C22×C4—26no—
926C22×C4—26no—
927C22×C4—43no—
928C22×C4—43no—
929C22×C4—43no—
930C22×C4—43no—
931C22×C4—43no—
932C22×C4C2511yescharacteristic
933C22×C4C2513yes—
934C22×C4C2511yescharacteristic
935C22×C4C2511yescharacteristic
936C22×C4C2511yescharacteristic
937C22×C4C2513yes—
938C22×C4C2511yescharacteristic
939C22×C4C2513yes—
940C22×C4C2513yes—
941C22×C4C2513yes—
942C22×C4C2513yes—
943C22×C4C2513yes—
944C22×C4C2513yes—
945C22×C4C2511yescharacteristic
946C22×C4C2511yescharacteristic
947C22×C4C2513yes—
948C22×C4C2513yes—
949C22×C4C2511yescharacteristic
950C22×C4C2513yes—
951C22×C4C2513yes—
952C22×C4C2513yes—
953C22×C4C2513yes—
954C22×C4C2511yescharacteristic
955C22×C4C2511yescharacteristic
956C22×C4C2511yescharacteristic
957C22×C4C2511yescharacteristic
958C22×C4C2511yescharacteristic
959C22×C4C2511yescharacteristic
960C22×C4C2513yes—
961C4⋊C4—26no—
962C4⋊C4—26no—
963C4⋊C4—26no—
964C4⋊C4—26no—
965C4⋊C4—26no—
966C4⋊C4—26no—
967C4⋊C4—26no—
968C4⋊C4—26no—
969C4⋊C4—26no—
970C4⋊C4—26no—
971C4⋊C4—26no—
972C4⋊C4—26no—
973C4⋊C4—26no—
974C4⋊C4—26no—
975C4⋊C4—26no—
976C4⋊C4—22no—
977C4⋊C4—22no—
978C4⋊C4—22no—
979C4⋊C4—22no—
980C4⋊C4—22no—
981C4⋊C4—26no—
982C4⋊C4—26no—
983C4⋊C4—22no—
984C4⋊C4—22no—
985C4⋊C4—26no—
986C4⋊C4—26no—
987C4⋊C4—43no—
988C4⋊C4—43no—
989C4⋊C4—43no—
990C4⋊C4—41no—
991C4⋊C4—43no—
992C4⋊C4—43no—
993C4⋊C4—43no—
994C4⋊C4—43no—
995C4⋊C4—43no—
996C4⋊C4—43no—
997C4⋊C4—43no—
998C4⋊C4—43no—
999C4⋊C4—43no—
1000C4⋊C4—43no—
1001C4⋊C4—43no—
1002C4⋊C4—43no—
1003C4⋊C4—46no—
1004C4⋊C4—43no—
1005C4⋊C4—46no—
1006C4⋊C4—43no—
1007C4⋊C4—43no—
1008C4⋊C4—43no—
1009C4⋊C4—46no—
1010C4⋊C4—46no—
1011C4⋊C4—43no—
1012C4⋊C4—46no—
1013C4⋊C4—46no—
1014C4⋊C4—43no—
1015C4⋊C4—43no—
1016C4⋊C4—43no—
1017C4⋊C4—43no—
1018C4⋊C4—43no—
1019C4⋊C4—46no—
1020C4⋊C4—46no—
1021C4⋊C4—46no—
1022C4⋊C4—43no—
1023C4⋊C4—43no—
1024C4⋊C4—43no—
1025C4⋊C4—43no—
1026C4⋊C42−1+414yes—
1027C22⋊C4—26no—
1028C22⋊C4—26no—
1029C22⋊C4—22no—
1030C22⋊C4—22no—
1031C22⋊C4—22no—
1032C22⋊C4—26no—
1033C22⋊C4—22no—
1034C22⋊C4—26no—
1035C22⋊C4—22no—
1036C22⋊C4—41no—
1037C22⋊C4—43no—
1038C22⋊C4—46no—
1039C22⋊C4—41no—
1040C22⋊C4—43no—
1041C22⋊C4—46no—
1042C22⋊C4—43no—
1043C22⋊C4—46no—
1044C22⋊C4—46no—
1045C22⋊C4—43no—
1046C22⋊C4—43no—
1047C22⋊C4—43no—
1048C22⋊C4—46no—
1049C22⋊C4—43no—
1050C22⋊C4—46no—
1051C22⋊C4—46no—
1052C22⋊C4—43no—
1053C22⋊C4—43no—
1054C22⋊C4—43no—
1055C22⋊C4—43no—
1056C22⋊C4—43no—
1057C22⋊C4—43no—
1058C42—26no—
1059C42—26no—
1060C42—26no—
1061C42—26no—
1062C42—26no—
1063C42—26no—
1064C42—26no—
1065C42—26no—
1066C42—26no—
1067C42—26no—
1068C42—26no—
1069C42—26no—
1070C42—26no—
1071C42—22no—
1072C42—22no—
1073C42—26no—
1074C42—26no—
1075C42—41no—
1076C42—43no—
1077C42—46no—
1078C42—46no—
1079C42—43no—
1080C42—43no—
1081C42—43no—
1082C42—43no—
1083C23—21no—
1084C23—23no—
1085C23—21no—
1086C23—23no—
1087C23—21no—
1088C23—21no—
1089C23—23no—
1090C23—23no—
1091C23—21no—
1092C23—23no—
1093C23—23no—
1094C23—21no—
1095C23—23no—
1096C23—21no—
1097C23C2611yescharacteristic
1098Q8—44no—
1099Q8—44no—
1100Q8—412no—
1101Q8—86no—
1102Q8—166no—
1103Q8—166no—
1104Q8#563116yes—
1105D4—412no—
1106D4—86no—
1107C2×C4—21no—
1108C2×C4—21no—
1109C2×C4—21no—
1110C2×C4—21no—
1111C2×C4—21no—
1112C2×C4—21no—
1113C2×C4—21no—
1114C2×C4—21no—
1115C2×C4—21no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—21no—
1119C2×C4—21no—
1120C2×C4—21no—
1121C2×C4—23no—
1122C2×C4—23no—
1123C2×C4—23no—
1124C2×C4—23no—
1125C2×C4—23no—
1126C2×C4—23no—
1127C2×C4—23no—
1128C2×C4—21no—
1129C2×C4—23no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—21no—
1136C2×C4—23no—
1137C2×C4—23no—
1138C2×C4—23no—
1139C2×C4—23no—
1140C2×C4—23no—
1141C2×C4—23no—
1142C2×C4—21no—
1143C2×C4—23no—
1144C2×C4—23no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—23no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—23no—
1151C2×C4—23no—
1152C2×C4—23no—
1153C2×C4—23no—
1154C2×C4—23no—
1155C2×C4—23no—
1156C2×C4—21no—
1157C2×C4—23no—
1158C2×C4—23no—
1159C2×C4—23no—
1160C2×C4—23no—
1161C2×C4—21no—
1162C2×C4—23no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—23no—
1169C2×C4—23no—
1170C2×C4—23no—
1171C2×C4—23no—
1172C2×C4—23no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—23no—
1176C2×C4—23no—
1177C2×C4—23no—
1178C2×C4—23no—
1179C2×C4—23no—
1180C2×C4—23no—
1181C2×C4—23no—
1182C2×C4—23no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—23no—
1186C2×C4—412no—
1187C2×C4—412no—
1188C2×C4—86no—
1189C2×C4—86no—
1190C2×C4C2×H(5,𝔽2)16yes—
1191C2×C4C2×2−1+412yes—
1192C2×C4C2×2−1+412yes—
1193C2×C4C2×2−1+412yes—
1194C2×C4C2×2−1+416yes—
1195C2×C4C2×2−1+416yes—
1196C2×C4#58512yes—
1197C2×C4#58512yes—
1198C22—43no—
1199C22—41no—
1200C22—41no—
1201C22—43no—
1202C22—41no—
1203C22—43no—
1204C22—43no—
1205C22—41no—
1206C22—41no—
1207C22—43no—
1208C22—41no—
1209C22—43no—
1210C22—41no—
1211C22—43no—
1212C22C22×H(5,𝔽2)11yescharacteristic
1213C22C22×2−1+411yescharacteristic
1214C22C22×2−1+411yescharacteristic
1215C22C22×2−1+411yescharacteristic
1216C22C2×#58511yescharacteristic
1217C22C2×#58511yescharacteristic
1218C22H(7,𝔽2)11yescharacteristic
1219C4—22no—
1220C4—22no—
1221C4—22no—
1222C4—22no—
1223C4—22no—
1224C4—43no—
1225C4—41no—
1226C4—41no—
1227C4—43no—
1228C4—41no—
1229C4—43no—
1230C4—43no—
1231C4—41no—
1232C4—41no—
1233C4—41no—
1234C4—41no—
1235C4—43no—
1236C4—43no—
1237C4—43no—
1238C4—43no—
1239C4—43no—
1240C4—41no—
1241C4—43no—
1242C4—41no—
1243C4—43no—
1244C4—43no—
1245C4—43no—
1246C4—43no—
1247C4C2×#563112yes—
1248C2—83no—
1249C2—81no—
1250C2C22×#56311yescharacteristic
1251C2#6292311yescharacteristic
1252C2#6294311yescharacteristic
1253C2#6295211yescharacteristic
1254C2#6301511yescharacteristic
1255C2#6303411yescharacteristic
1256C2#6303811yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#548C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #53109C2semidirect
2. #53081C2semidirect
3. #53048C2semidirect
4. #53035C2semidirect
5. #53020C2semidirect
6. #52998C2semidirect
7. #52300C2semidirect
8. #46343C2semidirect
9. #46341C2semidirect
10. #46062C2semidirect
11. #46051C2semidirect
12. #46019C2semidirect
13. #46011C2semidirect
14. #45618C2semidirect
15. #45605C2semidirect
16. #45499C2semidirect
17. Q8×C4⋊Q8C2semidirect
18. Q8×#126C2semidirect
19. #36474C2semidirect
20. #36458C2semidirect
21. #36458C2semidirect
22. #36456C2semidirect
23. #36448C2semidirect
25. #36431C2semidirect
26. #35971C2semidirect
28. #35868C2semidirect
30. #35786C2semidirect
31. #35711C2semidirect

Maximal subgroups

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

subgroupindex
#531092
#530812
#530482
#530352
#530202
#529982
#523002
#463432
#463412
#460622
#460512
#460192
#460112
#456182
#456052
#454992
Q8×C4⋊Q82
Q8×#1262
#364742
#364582
#364562
#364482
#364322
#364312
#359712
#359482
#358682
#358012
#357862
#357112