Finite Group Databasebeta

← #7687352

Subgroups — #7687352

Order 512.

5420 conjugacy classes of subgroups.

The subgroup lattice has 1357 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59933C213yesmaximal, complemented
2#59769C213yesmaximal, complemented
3#59481C213yesmaximal, complemented
4#59383C213yesmaximal, complemented
5#59282C213yesmaximal, complemented
6#45305C213yesmaximal, complemented
7#45250C213yesmaximal, complemented
8#44962C213yesmaximal, complemented
9#44918C213yesmaximal, complemented
10#39563C213yesmaximal, complemented
11#39041C213yesmaximal, complemented
12#38253C213yesmaximal, complemented
13#37973C213yesmaximal, complemented
14#36578C211yesmaximal, characteristic, complemented
15#36577C211yesmaximal, characteristic, complemented
16Q8×#123C211yesmaximal, characteristic, complemented
17#36467C211yesmaximal, characteristic, complemented
18#36458C211yesmaximal, characteristic, complemented
19#36381C213yesmaximal, complemented
20#36379C213yesmaximal, complemented
21#35898C211yesmaximal, characteristic, complemented
22#35786C211yesmaximal, characteristic, complemented
23#35723C211yesmaximal, characteristic, complemented
24#35687C211yesmaximal, characteristic
25#34861C213yesmaximal, complemented
26#34291C211yesmaximal, characteristic, complemented
27#34262C211yesmaximal, characteristic, complemented
28#34257C211yesmaximal, characteristic, complemented
29#34257C211yesmaximal, characteristic, complemented
30C4×D4×Q8C211yesmaximal, characteristic, complemented
31#34128C211yesmaximal, characteristic, complemented
32C22×2−1+4C2211yescharacteristic
33C2×#557C2211yescharacteristic
34C2×D4×Q8C2211yescharacteristic
35C2×D4×Q8C2211yescharacteristic
36C2×#548C2211yescharacteristic
37C2×#519C2211yescharacteristic
38C2×#519C2211yescharacteristic
39C22×C4×Q8C2211yescharacteristic
40C22×C4×Q8C2211yescharacteristic
41C22×C4×Q8C2211yescharacteristic
42#2861C2213yes—
43#2860C2213yes—
44#2857C2213yes—
45#2855C2213yes—
46#2854C2213yes—
47#2799C2216yes—
48#2796C2216yes—
49#2786C2216yes—
50#2762C2216yes—
51#2761C2216yes—
52#2758C2216yes—
53#2757C2216yes—
54#2751C2216yes—
55#2750C2216yes—
56#2749C2216yes—
57#2748C2216yes—
58#2747C2216yes—
59#2747C2216yes—
60#2722C2216yes—
61#2644C2213yes—
62#2629C2213yes—
63#2625C2213yes—
64#2616C2213yes—
65#2612C2216yes—
66#2605C2213yes—
67#2603C2213yes—
68#2601C2216yes—
69#2601C2213yes—
70#2598C2213yes—
71#2597C2213yes—
72#2592C2213yes—
73#2589C2213yes—
74#2589C2216yes—
75#2588C2216yes—
76#2582C2213yes—
77#2582C2213yes—
78#2578C2216yes—
79#2577C2216yes—
80#2576C2213yes—
81#2574C2216yes—
82#2568C2213yes—
83#2565C2213yes—
84#2562C2213yes—
85#2560C2216yes—
86#2557C2213yes—
87#2553C2216yes—
88#2531C2216yes—
89#2531C2213yes—
90#2530C2216yes—
91#2530C2216yes—
92#2527C2213yes—
93#2526C2216yes—
94#2523C2216yes—
95#2522C2216yes—
96#2522C2216yes—
97#2520C2213yes—
98#2516C2213yes—
99#2513C2213yes—
100#2513C2213yes—
101#2512C2213yes—
102#2512C2213yes—
103#2512C2213yes—
104#2512C2213yes—
105#2504C2213yes—
106#2502C2213yes—
107#2499C2213yes—
108#2497C2213yes—
109#2497C2213yes—
110#2496C2213yes—
111#2496C2213yes—
112#2495C2213yes—
113#2494C2213yes—
114#2492C2213yes—
115#2491C2213yes—
116#2490C2213yes—
117#2489C2213yes—
118#2487C2213yes—
119#2487C2213yes—
120#2485C2213yes—
121#2479C2216yes—
122#2477C2213yes—
123#2471C2213yes—
124#2467C2216yes—
125#2461C2213yes—
126#2457C2211yescharacteristic
127#2453C2213yes—
128#2453C2213yes—
129#2453C2213yes—
130#2451C2213yes—
131#2448C2213yes—
132#2448C2213yes—
133#2446C2213yes—
134#2446C2213yes—
135#2446C2213yes—
136#2446C2213yes—
137#2442C2213yes—
138#2442C2213yes—
139#2441C2213yes—
140#2439C2213yes—
141#2434C2213yes—
142#2432C2213yes—
143#2432C2213yes—
144#2423C2213yes—
145#2423C2213yes—
146#2423C2213yes—
147#2421C2213yes—
148#2421C2213yes—
149#2421C2213yes—
150#2409C2213yes—
151#2407C2213yes—
152#2407C2213yes—
153#2401C2213yes—
154#2396C2213yes—
155#2395C2213yes—
156#2388C2213yes—
157#2373C2216yes—
158#2373C2216yes—
159#2372C2216yes—
160#2365C2213yes—
161#2365C2213yes—
162#2362C2213yes—
163#2360C2213yes—
164#2360C2213yes—
165#2360C2213yes—
166#2356C2213yes—
167#2356C2213yes—
168#2356C2213yes—
169#2355C2213yes—
170#2352C2213yes—
171#2351C2211yescharacteristic
172#2351C2211yescharacteristic
173#2351C2211yescharacteristic
174#2351C2211yescharacteristic
175Q8×C4⋊C4C2211yescharacteristic
176Q8×C4⋊C4C2211yescharacteristic
177Q8×C4⋊C4C2211yescharacteristic
178Q8×C4⋊C4C2211yescharacteristic
179D4×C4⋊C4C2213yes—
180#2347C2213yes—
181#2346C2213yes—
182#2344C2213yes—
183#2344C2213yes—
184#2341C2213yes—
185#2341C2213yes—
186#2341C2211yescharacteristic
187#2341C2211yescharacteristic
188#2341C2211yescharacteristic
189#2341C2211yescharacteristic
190#2341C2211yescharacteristic
191#2341C2213yes—
192#2341C2213yes—
193Q8×C22⋊C4C2213yes—
194Q8×C22⋊C4C2213yes—
195Q8×C22⋊C4C2211yescharacteristic
196Q8×C22⋊C4C2211yescharacteristic
197Q8×C22⋊C4C2213yes—
198Q8×C22⋊C4C2211yescharacteristic
199Q8×C22⋊C4C2211yescharacteristic
200Q8×C22⋊C4C2211yescharacteristic
201Q8×C22⋊C4C2211yescharacteristic
202Q8×C22⋊C4C2211yescharacteristic
203Q8×C22⋊C4C2211yescharacteristic
204Q8×C22⋊C4C2211yescharacteristic
205Q8×C22⋊C4C2213yes—
206#2327C2213yes—
207#2323C2213yes—
208#2320C2213yes—
209#2314C2213yes—
210#2311C2213yes—
211#2311C2213yes—
212#2311C2213yes—
213#2311C2213yes—
214C4×C4⋊Q8C2213yes—
215C4×#126C2213yes—
216C4×#124C2213yes—
217C4×C22⋊Q8C2213yes—
218C4×C22⋊Q8C2213yes—
219C4×C22⋊Q8C2213yes—
220C4×C22⋊Q8C2213yes—
221C4×#123C2213yes—
222C4×#123C2213yes—
223#2298C2213yes—
224#2297C2213yes—
225#2297C2213yes—
226#2297C2213yes—
227#2297C2213yes—
228#2295C2213yes—
229#2295C2213yes—
230#2295C2213yes—
231#2290C2213yes—
232#2283C2213yes—
233#2276C2211yescharacteristic
234C42×Q8C2211yescharacteristic
235C42×Q8C2211yescharacteristic
236C42×D4C2213yes—
237C4×#117C2213yes—
238C2×2−1+4—28no—
239C2×2−1+4—28no—
240C2×2−1+4—44no—
241C22×#41C2311yescharacteristic
242C22×#41C2313yes—
243C22×#41C2313yes—
244C22×#41C2313yes—
245C23×Q8C2311yescharacteristic
246C23×Q8C2313yes—
247C23×Q8C2311yescharacteristic
248C23×Q8C2311yescharacteristic
249#557—44no—
250D4×Q8—28no—
251D4×Q8—28no—
252#548—44no—
253C2×C4⋊Q8C2313yes—
254C2×C4⋊Q8C2313yes—
255C2×C4⋊Q8C2313yes—
256C2×#126C2313yes—
257C2×#126C2316yes—
258C2×#126C2316yes—
259C2×#125C2313yes—
260C2×#125C2313yes—
261C2×#124C2313yes—
262C2×#124C2313yes—
263C2×#123C2311yescharacteristic
264C2×#123C2313yes—
265C2×C22⋊Q8C2313yes—
266C2×C22⋊Q8C2313yes—
267C2×C22⋊Q8C2313yes—
268C2×C22⋊Q8C2313yes—
269C2×C22⋊Q8C2313yes—
270C2×C22⋊Q8C2313yes—
271C2×#121C2313yes—
272#519—28no—
273#519—44no—
274C2×C4×Q8—28no—
275C2×C4×Q8—44no—
276C2×C4×Q8—44no—
277C2×C4×Q8C2313yes—
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×Q8C2311yescharacteristic
288C2×C4×Q8C2311yescharacteristic
289C2×C4×Q8C2313yes—
290C2×C4×Q8C2313yes—
291C2×C4×Q8C2313yes—
292C2×C4×Q8C2313yes—
293C2×C4×Q8C2313yes—
294C2×C4×Q8C2313yes—
295C2×C4×Q8C2313yes—
296C2×C4×Q8C2313yes—
297C2×C4×Q8C2313yes—
298C2×C4×Q8C2313yes—
299C2×C4×D4C2313yes—
300C2×C4×D4C2313yes—
301C2×C4×D4C2311yescharacteristic
302C2×C4×D4C2313yes—
303C2×C4×D4C2313yes—
304C2×#117C2313yes—
305C2×#117C2313yes—
306C2×#117C2313yes—
307C2×#117C2313yes—
308C2×#117C2313yes—
309C2×#117C2313yes—
310C22×C4⋊C4C2313yes—
311C22×C4⋊C4C2313yes—
312C22×C4⋊C4C2313yes—
313C22×C42C2313yes—
314C22×C42C2313yes—
315C22×C42C2313yes—
316#401C2313yes—
317#400C2316yes—
318#400C2316yes—
319#400C2316yes—
320#400C2316yes—
321#400C2316yes—
322#400C2313yes—
323#400C2316yes—
324#400C2313yes—
325#400C2313yes—
326#400C2311yescharacteristic
327#400C2313yes—
328#400C2316yes—
329#399C2313yes—
330#399C2316yes—
331#399C2313yes—
332#399C2316yes—
333#398C2316yes—
334#398C2313yes—
335#398C2316yes—
336#398C2313yes—
337#398C2316yes—
338#398C2316yes—
339#398C2316yes—
340#398C2316yes—
341#398C2313yes—
342#398C2316yes—
343#397C2316yes—
344#397C2313yes—
345#397C2316yes—
346#397C2316yes—
347#397C2313yes—
348#397C2316yes—
349#397C2313yes—
350#397C2313yes—
351#397C2313yes—
352#397C2316yes—
353#397C2313yes—
354#397C2316yes—
355#397C2316yes—
356#397C2316yes—
357#396C2313yes—
358#396C2313yes—
359#396C2311yescharacteristic
360#396C2316yes—
361#396C2316yes—
362#396C2316yes—
363#395C2313yes—
364#395C2316yes—
365#395C2313yes—
366#394C2316yes—
367#394C2316yes—
368#394C2313yes—
369#394C2313yes—
370#394C2313yes—
371#394C2316yes—
372#394C2313yes—
373#394C2311yescharacteristic
374#393C2316yes—
375#393C2313yes—
376#393C2313yes—
377#392C2311yescharacteristic
378#392C2313yes—
379#392C2313yes—
380#391C2316yes—
381#391C2313yes—
382#391C2313yes—
383#391C2313yes—
384#391C2313yes—
385#391C2313yes—
386#391C2313yes—
387#391C2313yes—
388#391C2316yes—
389#391C2316yes—
390#391C2313yes—
391#391C2316yes—
392#391C2313yes—
393#391C2313yes—
394#391C2313yes—
395#391C2313yes—
396#391C2313yes—
397#391C2313yes—
398#391C2313yes—
399#391C2313yes—
400#391C2313yes—
401#391C2313yes—
402#391C2313yes—
403#391C2313yes—
404#391C2313yes—
405#391C2313yes—
406#391C2313yes—
407#391C2313yes—
408#390C2316yes—
409#390C2313yes—
410#390C2313yes—
411#390C2313yes—
412#390C2313yes—
413#390C2316yes—
414#390C2313yes—
415#390C2313yes—
416#390C2313yes—
417#390C2313yes—
418#390C2313yes—
419#390C2313yes—
420#390C2313yes—
421#390C2313yes—
422#390C2313yes—
423#390C2313yes—
424#390C2313yes—
425#389C2316yes—
426#389C2316yes—
427#389C2313yes—
428#389C2313yes—
429#389C2313yes—
430#389C2316yes—
431#389C2313yes—
432#389C2316yes—
433#389C2313yes—
434#389C2313yes—
435#389C2313yes—
436#389C2316yes—
437#389C2313yes—
438#389C2313yes—
439#389C2313yes—
440#389C2313yes—
441#389C2313yes—
442#389C2313yes—
443#389C2313yes—
444#389C2313yes—
445#389C2313yes—
446#389C2313yes—
447#388C2313yes—
448#388C2313yes—
449#388C2313yes—
450#388C2316yes—
451#388C2316yes—
452#388C2316yes—
453#388C2313yes—
454#388C2316yes—
455#388C2313yes—
456#388C2316yes—
457#388C2316yes—
458#388C2313yes—
459#388C2313yes—
460#388C2313yes—
461#388C2316yes—
462#388C2316yes—
463#388C2311yescharacteristic
464#388C2313yes—
465#388C2316yes—
466#388C2313yes—
467#388C2311yescharacteristic
468#388C2313yes—
469#388C2313yes—
470#388C2313yes—
471#388C2313yes—
472#388C2316yes—
473#388C2316yes—
474#388C2316yes—
475#388C2313yes—
476#387C2311yescharacteristic
477#387C2313yes—
478#387C2313yes—
479#387C2316yes—
480#387C2316yes—
481#387C2316yes—
482#387C2316yes—
483#387C2316yes—
484#387C2316yes—
485#387C2316yes—
486#387C2316yes—
487#387C2313yes—
488#387C2313yes—
489#387C2313yes—
490#387C2313yes—
491#387C2316yes—
492#387C2313yes—
493#387C2316yes—
494#387C2316yes—
495#387C2313yes—
496#387C2316yes—
497#387C2316yes—
498#387C2313yes—
499#387C2313yes—
500#387C2316yes—
501#387C2316yes—
502#387C2316yes—
503#387C2313yes—
504#387C2313yes—
505#387C2313yes—
506#387C2316yes—
507#387C2316yes—
508#387C2313yes—
509#387C2316yes—
510#386C2313yes—
511#386C2313yes—
512#386C2313yes—
513#386C2313yes—
514#386C2313yes—
515#386C2316yes—
516#386C2316yes—
517#386C2311yescharacteristic
518#386C2313yes—
519#386C2316yes—
520#386C2313yes—
521#386C2313yes—
522#386C2316yes—
523#386C2311yescharacteristic
524#386C2311yescharacteristic
525#386C2313yes—
526#385C2316yes—
527#385C2313yes—
528#385C2316yes—
529#385C2316yes—
530#385C2313yes—
531#385C2313yes—
532#385C2313yes—
533#385C2316yes—
534#385C2313yes—
535#385C2316yes—
536#385C2316yes—
537#385C2313yes—
538#384C2313yes—
539#384C2313yes—
540#384C2313yes—
541#384C2313yes—
542#383C2313yes—
543#383C2316yes—
544#383C2316yes—
545#382C2313yes—
546#382C2313yes—
547#382C2313yes—
548#382C2316yes—
549#382C2313yes—
550#382C2313yes—
551#381C2313yes—
552#381C2316yes—
553#381C2311yescharacteristic
554#380C2313yes—
555#380C2313yes—
556#380C2313yes—
557#380C2313yes—
558#380C2313yes—
559#380C2316yes—
560#380C2316yes—
561#380C2316yes—
562#380C2313yes—
563#380C2313yes—
564#380C2313yes—
565#380C2313yes—
566#380C2313yes—
567#380C2316yes—
568#380C2313yes—
569#380C2313yes—
570#380C2313yes—
571#380C2313yes—
572#380C2316yes—
573#380C2311yescharacteristic
574C4×C4⋊C4C2313yes—
575C4×C4⋊C4C2313yes—
576C4×C4⋊C4C2313yes—
577C4×C4⋊C4C2316yes—
578C4×C4⋊C4C2313yes—
579C4×C4⋊C4C2313yes—
580C4×C4⋊C4C2316yes—
581C4×C4⋊C4C2313yes—
582C4×C4⋊C4C2313yes—
583C4×C4⋊C4C2313yes—
584C4×C4⋊C4C2313yes—
585C4×C4⋊C4C2313yes—
586C4×C4⋊C4C2313yes—
587C4×C4⋊C4C2316yes—
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×C22⋊C4C2313yes—
599C4×C22⋊C4C2313yes—
600C4×C22⋊C4C2313yes—
601C4×C22⋊C4C2313yes—
602C4×C22⋊C4C2316yes—
603C4×C22⋊C4C2313yes—
604C4×C22⋊C4C2313yes—
605C4×C22⋊C4C2316yes—
606C4×C22⋊C4C2316yes—
607C4×C22⋊C4C2316yes—
608C4×C22⋊C4C2313yes—
609C4×C22⋊C4C2313yes—
610C4×C22⋊C4C2313yes—
611C4×C22⋊C4C2316yes—
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—
621C4×C22⋊C4C2311yescharacteristic
622C4×C22⋊C4C2313yes—
623#376C2313yes—
624#376C2316yes—
625#376C2313yes—
626#376C2313yes—
627#376C2316yes—
628C43C2313yes—
629C43C2313yes—
6302−1+4—464no—
631C2×#41—212no—
632C2×#41—212no—
633C2×#41—24no—
634C2×#41—24no—
635C2×#41—24no—
636C2×#41—212no—
637C2×#41—212no—
638C2×#41—212no—
639C2×#41—212no—
640C2×#41—46no—
641C2×#41—46no—
642C2×#41—46no—
643C22×Q8—24no—
644C22×Q8—24no—
645C22×Q8—24no—
646C22×Q8—24no—
647C22×Q8—24no—
648C22×Q8—24no—
649C22×Q8—212no—
650C22×Q8—212no—
651C22×Q8—24no—
652C22×Q8—46no—
653C22×Q8#4118yes—
654C22×Q8#4118yes—
655C22×Q8C2413yes—
656C22×Q8C2413yes—
657C22×Q8C2413yes—
658C22×Q8C2413yes—
659C22×Q8C2413yes—
660C22×Q8C2411yescharacteristic
661C22×D4C2411yescharacteristic
662C22×D4C2413yes—
663C22×D4C2411yescharacteristic
664C22×D4C2411yescharacteristic
665C22×D4C2413yes—
666C22×D4C2413yes—
667C22×D4C2413yes—
668C23×C4C2413yes—
669C23×C4C2413yes—
670C23×C4C2411yescharacteristic
671C23×C4C2411yescharacteristic
672C23×C4C2411yescharacteristic
673C23×C4C2416yes—
674C23×C4C2413yes—
675C23×C4C2413yes—
676C23×C4C2413yes—
677C23×C4C2413yes—
678C23×C4C2413yes—
679C4⋊Q8—212no—
680C4⋊Q8—212no—
681C4⋊Q8—46no—
682#126—46no—
683#126—412no—
684#126—412no—
685#125—46no—
686#125—46no—
687#124—212no—
688#124—46no—
689#123—24no—
690#123—46no—
691C22⋊Q8—212no—
692C22⋊Q8—212no—
693C22⋊Q8—212no—
694C22⋊Q8—212no—
695C22⋊Q8—46no—
696C22⋊Q8—46no—
697#121—46no—
698C4×Q8—212no—
699C4×Q8—212no—
700C4×Q8—24no—
701C4×Q8—24no—
702C4×Q8—212no—
703C4×Q8—212no—
704C4×Q8—24no—
705C4×Q8—24no—
706C4×Q8—24no—
707C4×Q8—24no—
708C4×Q8—24no—
709C4×Q8—24no—
710C4×Q8—24no—
711C4×Q8—24no—
712C4×Q8—24no—
713C4×Q8—46no—
714C4×Q8—46no—
715C4×Q8—46no—
716C4×Q8—46no—
717C4×Q8—46no—
718C4×Q8—46no—
719C4×Q8—46no—
720C4×D4—212no—
721C4×D4—212no—
722C4×D4—24no—
723C4×D4—46no—
724C4×D4—46no—
725#117—212no—
726#117—212no—
727#117—46no—
728#117—46no—
729#117—46no—
730#117—46no—
731C2×C4⋊C4—212no—
732C2×C4⋊C4—46no—
733C2×C4⋊C4—46no—
734C2×C4⋊C4C2413yes—
735C2×C4⋊C4C2413yes—
736C2×C4⋊C4C2413yes—
737C2×C4⋊C4C2413yes—
738C2×C4⋊C4C2413yes—
739C2×C4⋊C4C2416yes—
740C2×C4⋊C4C2413yes—
741C2×C4⋊C4C2413yes—
742C2×C4⋊C4C2413yes—
743C2×C4⋊C4C2413yes—
744C2×C4⋊C4C2413yes—
745C2×C4⋊C4C2413yes—
746C2×C4⋊C4C2413yes—
747C2×C4⋊C4C2413yes—
748C2×C4⋊C4C2413yes—
749C2×C4⋊C4C2413yes—
750C2×C4⋊C4C2411yescharacteristic
751C2×C4⋊C4C2413yes—
752C2×C4⋊C4C2413yes—
753C2×C4⋊C4C2413yes—
754C2×C4⋊C4C2416yes—
755C2×C4⋊C4C2416yes—
756C2×C4⋊C4C2413yes—
757C2×C4⋊C4C2411yescharacteristic
758C2×C4⋊C4C2411yescharacteristic
759C2×C4⋊C4C2411yescharacteristic
760C2×C4⋊C4C2416yes—
761C2×C4⋊C4C2416yes—
762C2×C4⋊C4C2413yes—
763C2×C4⋊C4C2413yes—
764C2×C4⋊C4C2413yes—
765C2×C4⋊C4C2413yes—
766C2×C4⋊C4C2413yes—
767C2×C4⋊C4C2411yescharacteristic
768C2×C4⋊C4C2413yes—
769C2×C4⋊C4C2413yes—
770C2×C4⋊C4C2413yes—
771C2×C4⋊C4C2413yes—
772C2×C4⋊C4C2416yes—
773C2×C4⋊C4C2416yes—
774C2×C4⋊C4C2413yes—
775C2×C4⋊C4C2413yes—
776C2×C4⋊C4C2416yes—
777C2×C4⋊C4C2416yes—
778C2×C4⋊C4C2413yes—
779C2×C4⋊C4C2413yes—
780C2×C4⋊C4C2416yes—
781C2×C22⋊C4C2411yescharacteristic
782C2×C22⋊C4C2411yescharacteristic
783C2×C22⋊C4C2413yes—
784C2×C22⋊C4C2411yescharacteristic
785C2×C22⋊C4C2413yes—
786C2×C22⋊C4C2413yes—
787C2×C22⋊C4C2413yes—
788C2×C22⋊C4C2413yes—
789C2×C22⋊C4C2411yescharacteristic
790C2×C22⋊C4C2413yes—
791C2×C22⋊C4C2411yescharacteristic
792C2×C22⋊C4C2411yescharacteristic
793C2×C22⋊C4C2413yes—
794C2×C22⋊C4C2413yes—
795C2×C22⋊C4C2413yes—
796C2×C22⋊C4C2413yes—
797C2×C22⋊C4C2413yes—
798C2×C22⋊C4C2411yescharacteristic
799C2×C22⋊C4C2413yes—
800C2×C22⋊C4C2413yes—
801C2×C22⋊C4C2411yescharacteristic
802C2×C22⋊C4C2413yes—
803C2×C22⋊C4C2413yes—
804C2×C22⋊C4C2413yes—
805C2×C22⋊C4C2416yes—
806C2×C22⋊C4C2413yes—
807C2×C22⋊C4C2413yes—
808C2×C22⋊C4C2413yes—
809C2×C22⋊C4C2413yes—
810C2×C22⋊C4C2416yes—
811C2×C22⋊C4C2413yes—
812C2×C22⋊C4C2416yes—
813C2×C22⋊C4C2416yes—
814C2×C22⋊C4C2413yes—
815C2×C22⋊C4C2416yes—
816C2×C22⋊C4C2411yescharacteristic
817C2×C22⋊C4C2411yescharacteristic
818C2×C22⋊C4C2411yescharacteristic
819C2×C22⋊C4C2413yes—
820C2×C22⋊C4C2413yes—
821C2×C22⋊C4C2416yes—
822C2×C22⋊C4C2413yes—
823C2×C22⋊C4C2413yes—
824C2×C22⋊C4C2411yescharacteristic
825C2×C42—212no—
826C2×C42—46no—
827C2×C42—46no—
828C2×C42C2413yes—
829C2×C42C2413yes—
830C2×C42C2413yes—
831C2×C42C2413yes—
832C2×C42C2416yes—
833C2×C42C2413yes—
834C2×C42C2413yes—
835C2×C42C2413yes—
836C2×C42C2413yes—
837C2×C42C2413yes—
838C2×C42C2411yescharacteristic
839C2×C42C2413yes—
840C2×C42C2413yes—
841C2×C42C2413yes—
842C2×C42C2413yes—
843C2×C42C2413yes—
844C2×C42C2413yes—
845C2×C42C2413yes—
846C2×C42C2416yes—
847C2×C42C2413yes—
848C2×C42C2413yes—
849C2×C42C2413yes—
850C2×C42C2413yes—
851C2×C42C2413yes—
852C2×C42C2413yes—
853C2×C42C2416yes—
854C2×C42C2411yescharacteristic
855C2×C42C2413yes—
856#95C2411yescharacteristic
857#95C2411yescharacteristic
858#95C2411yescharacteristic
859#95C2413yes—
860#95C2413yes—
861#95C2413yes—
862#95C2416yes—
863#95C2413yes—
864#95C2413yes—
865#95C2413yes—
866#95C2413yes—
867#95C2413yes—
868#95C2413yes—
869#95C2413yes—
870#95C2413yes—
871#95C2416yes—
872#95C2416yes—
873#95C2416yes—
874#95C2416yes—
875#95C2416yes—
876#95C2411yescharacteristic
877#95C2411yescharacteristic
878#95C2411yescharacteristic
879#95C2411yescharacteristic
880#95C2413yes—
881#95C2413yes—
882#95C2411yescharacteristic
883#95C2413yes—
884#95C2413yes—
885#95C2413yes—
886#95C2413yes—
887#95C2413yes—
888#95C2416yes—
889#95C2413yes—
890#95C2413yes—
891#95C2413yes—
892#95C2413yes—
893#95C2413yes—
894#95C2413yes—
895#95C2413yes—
896#95C2416yes—
897#95C2416yes—
898#95C2413yes—
899#95C2416yes—
900#95C2413yes—
901#95C2413yes—
902#95C2413yes—
903#95C2413yes—
904#95C2413yes—
905#95C2411yescharacteristic
906#95C2416yes—
907#95C2416yes—
908#95C2411yescharacteristic
909#95C2416yes—
910#95C2416yes—
911#95C2413yes—
912#95C2413yes—
913#95C2413yes—
914#95C2413yes—
915#95C2413yes—
916#95C2413yes—
917#95C2413yes—
918#95C2416yes—
919C24C2513yes—
920C24C2511yescharacteristic
921C24C2511yescharacteristic
922C24C2511yescharacteristic
923#41—448no—
924#41—448no—
925#41—448no—
926#41—416no—
927C2×Q8—232no—
928C2×Q8—232no—
929C2×Q8—26no—
930C2×Q8—26no—
931C2×Q8—26no—
932C2×Q8—26no—
933C2×Q8—26no—
934C2×Q8—26no—
935C2×Q8—26no—
936C2×Q8—26no—
937C2×Q8—26no—
938C2×Q8—26no—
939C2×Q8—43no—
940C2×Q8—43no—
941C2×Q8—43no—
942C2×Q8—448no—
943C2×Q8—416no—
944C2×Q8C2×#41112yes—
945C2×Q8C2×#41112yes—
946C2×Q8C2×#4114yes—
947C2×Q8C2×#4114yes—
948C2×Q8H(5,𝔽2)14yes—
949C2×D4—22no—
950C2×D4—22no—
951C2×D4—22no—
952C2×D4—26no—
953C2×D4—26no—
954C2×D4—22no—
955C2×D4—22no—
956C2×D4—22no—
957C2×D4—26no—
958C2×D4—26no—
959C2×D4—26no—
960C2×D4—26no—
961C2×D4—26no—
962C2×D4—26no—
963C2×D4—22no—
964C2×D4—41no—
965C2×D4—43no—
966C2×D4—43no—
967C2×D4—41no—
968C2×D4—43no—
969C2×D4—43no—
970C22×C4—26no—
971C22×C4—26no—
972C22×C4—26no—
973C22×C4—26no—
974C22×C4—22no—
975C22×C4—26no—
976C22×C4—22no—
977C22×C4—26no—
978C22×C4—26no—
979C22×C4—212no—
980C22×C4—212no—
981C22×C4—26no—
982C22×C4—26no—
983C22×C4—26no—
984C22×C4—26no—
985C22×C4—22no—
986C22×C4—22no—
987C22×C4—22no—
988C22×C4—22no—
989C22×C4—41no—
990C22×C4—41no—
991C22×C4—43no—
992C22×C4—43no—
993C22×C4—41no—
994C22×C4—46no—
995C22×C4—43no—
996C22×C4—43no—
997C22×C4—43no—
998C22×C4—43no—
999C22×C4—43no—
1000C22×C4—43no—
1001C22×C4C2×#41112yes—
1002C22×C4C2×#41112yes—
1003C22×C4C2511yescharacteristic
1004C22×C4C2511yescharacteristic
1005C22×C4C2511yescharacteristic
1006C22×C4C2513yes—
1007C22×C4C2511yescharacteristic
1008C22×C4C2513yes—
1009C22×C4C2511yescharacteristic
1010C22×C4C2513yes—
1011C22×C4C2511yescharacteristic
1012C22×C4C2513yes—
1013C22×C4C2513yes—
1014C22×C4C2513yes—
1015C22×C4C2513yes—
1016C22×C4C2513yes—
1017C22×C4C2513yes—
1018C22×C4C2513yes—
1019C22×C4C2513yes—
1020C22×C4C2513yes—
1021C22×C4C2511yescharacteristic
1022C22×C4C2511yescharacteristic
1023C22×C4C2513yes—
1024C22×C4C2513yes—
1025C22×C4C2511yescharacteristic
1026C22×C4C2511yescharacteristic
1027C22×C4C2511yescharacteristic
1028C22×C4C2511yescharacteristic
1029C22×C4C2513yes—
1030C4⋊C4—212no—
1031C4⋊C4—26no—
1032C4⋊C4—26no—
1033C4⋊C4—26no—
1034C4⋊C4—26no—
1035C4⋊C4—26no—
1036C4⋊C4—26no—
1037C4⋊C4—26no—
1038C4⋊C4—26no—
1039C4⋊C4—26no—
1040C4⋊C4—26no—
1041C4⋊C4—212no—
1042C4⋊C4—212no—
1043C4⋊C4—26no—
1044C4⋊C4—26no—
1045C4⋊C4—26no—
1046C4⋊C4—26no—
1047C4⋊C4—26no—
1048C4⋊C4—22no—
1049C4⋊C4—22no—
1050C4⋊C4—22no—
1051C4⋊C4—26no—
1052C4⋊C4—26no—
1053C4⋊C4—26no—
1054C4⋊C4—26no—
1055C4⋊C4—22no—
1056C4⋊C4—46no—
1057C4⋊C4—46no—
1058C4⋊C4—43no—
1059C4⋊C4—43no—
1060C4⋊C4—46no—
1061C4⋊C4—43no—
1062C4⋊C4—43no—
1063C4⋊C4—43no—
1064C4⋊C4—43no—
1065C4⋊C4—43no—
1066C4⋊C4—41no—
1067C4⋊C4—43no—
1068C4⋊C4—43no—
1069C4⋊C4—43no—
1070C4⋊C4—43no—
1071C4⋊C4—46no—
1072C4⋊C4—43no—
1073C4⋊C4—46no—
1074C4⋊C4—46no—
1075C4⋊C4—43no—
1076C4⋊C4—46no—
1077C22⋊C4—22no—
1078C22⋊C4—26no—
1079C22⋊C4—26no—
1080C22⋊C4—26no—
1081C22⋊C4—22no—
1082C22⋊C4—26no—
1083C22⋊C4—26no—
1084C22⋊C4—26no—
1085C22⋊C4—22no—
1086C22⋊C4—22no—
1087C22⋊C4—26no—
1088C22⋊C4—26no—
1089C22⋊C4—22no—
1090C22⋊C4—22no—
1091C22⋊C4—26no—
1092C22⋊C4—26no—
1093C22⋊C4—41no—
1094C22⋊C4—43no—
1095C22⋊C4—46no—
1096C22⋊C4—41no—
1097C22⋊C4—43no—
1098C22⋊C4—41no—
1099C22⋊C4—43no—
1100C22⋊C4—43no—
1101C22⋊C4—43no—
1102C22⋊C4—43no—
1103C22⋊C4—41no—
1104C22⋊C4—43no—
1105C22⋊C4—43no—
1106C22⋊C4—43no—
1107C22⋊C4—41no—
1108C22⋊C4—43no—
1109C22⋊C4—46no—
1110C22⋊C4—43no—
1111C22⋊C4—43no—
1112C22⋊C4—43no—
1113C22⋊C4—43no—
1114C22⋊C4—43no—
1115C22⋊C4—46no—
1116C22⋊C4—46no—
1117C22⋊C4—43no—
1118C22⋊C4—46no—
1119C22⋊C4—46no—
1120C22⋊C42−1+414yescomplemented
1121C42—26no—
1122C42—26no—
1123C42—26no—
1124C42—26no—
1125C42—212no—
1126C42—26no—
1127C42—26no—
1128C42—26no—
1129C42—26no—
1130C42—26no—
1131C42—26no—
1132C42—26no—
1133C42—26no—
1134C42—26no—
1135C42—22no—
1136C42—26no—
1137C42—26no—
1138C42—26no—
1139C42—43no—
1140C42—43no—
1141C42—43no—
1142C42—43no—
1143C42—41no—
1144C42—43no—
1145C42—43no—
1146C42—43no—
1147C42—46no—
1148C42—46no—
1149C23—21no—
1150C23—21no—
1151C23—21no—
1152C23—21no—
1153C23—21no—
1154C23—21no—
1155C23—21no—
1156C23—21no—
1157C23—21no—
1158C23—21no—
1159C23—21no—
1160C23—21no—
1161C23—21no—
1162C23—21no—
1163C23—21no—
1164C23—21no—
1165C23—21no—
1166C23—21no—
1167C23—23no—
1168C23—23no—
1169C23—23no—
1170C23—23no—
1171C23—23no—
1172C23—23no—
1173C23—23no—
1174C23C22×#4112yes—
1175C23C22×#4112yes—
1176C23C2×2−1+412yes—
1177C23C2611yescharacteristic
1178Q8—224no—
1179Q8—224no—
1180Q8—412no—
1181Q8—412no—
1182Q8—86no—
1183Q8#551116yes—
1184D4—28no—
1185D4—412no—
1186D4—412no—
1187D4—44no—
1188D4—44no—
1189D4—412no—
1190D4—86no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—23no—
1194C2×C4—23no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—23no—
1198C2×C4—23no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—224no—
1204C2×C4—224no—
1205C2×C4—21no—
1206C2×C4—21no—
1207C2×C4—23no—
1208C2×C4—23no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—23no—
1212C2×C4—23no—
1213C2×C4—23no—
1214C2×C4—23no—
1215C2×C4—23no—
1216C2×C4—23no—
1217C2×C4—21no—
1218C2×C4—21no—
1219C2×C4—21no—
1220C2×C4—21no—
1221C2×C4—21no—
1222C2×C4—23no—
1223C2×C4—23no—
1224C2×C4—23no—
1225C2×C4—23no—
1226C2×C4—23no—
1227C2×C4—23no—
1228C2×C4—21no—
1229C2×C4—23no—
1230C2×C4—23no—
1231C2×C4—21no—
1232C2×C4—23no—
1233C2×C4—21no—
1234C2×C4—21no—
1235C2×C4—21no—
1236C2×C4—23no—
1237C2×C4—23no—
1238C2×C4—23no—
1239C2×C4—23no—
1240C2×C4—21no—
1241C2×C4—21no—
1242C2×C4—23no—
1243C2×C4—23no—
1244C2×C4—23no—
1245C2×C4—23no—
1246C2×C4—23no—
1247C2×C4—21no—
1248C2×C4—23no—
1249C2×C4—21no—
1250C2×C4—23no—
1251C2×C4—23no—
1252C2×C4—23no—
1253C2×C4—21no—
1254C2×C4—23no—
1255C2×C4—21no—
1256C2×C4—23no—
1257C2×C4—23no—
1258C2×C4—21no—
1259C2×C4—21no—
1260C2×C4—21no—
1261C2×C4—23no—
1262C2×C4—21no—
1263C2×C4—23no—
1264C2×C4—23no—
1265C2×C4—44no—
1266C2×C4—424no—
1267C2×C4—44no—
1268C2×C4—44no—
1269C2×C4—412no—
1270C2×C4—412no—
1271C2×C4—412no—
1272C2×C4—86no—
1273C2×C4—86no—
1274C2×C4C22×#4116yes—
1275C2×C4C22×#4116yes—
1276C2×C4C22×#4116yes—
1277C2×C4C22×#4116yes—
1278C2×C4C2×H(5,𝔽2)16yes—
1279C2×C4C2×2−1+412yes—
1280C2×C4C2×2−1+412yes—
1281C2×C4#58512yes—
1282C2×C4#58512yes—
1283C22—22no—
1284C22—22no—
1285C22—22no—
1286C22—22no—
1287C22—22no—
1288C22—22no—
1289C22—22no—
1290C22—22no—
1291C22—22no—
1292C22—41no—
1293C22—41no—
1294C22—41no—
1295C22—41no—
1296C22—41no—
1297C22—41no—
1298C22—41no—
1299C22—41no—
1300C22—41no—
1301C22—41no—
1302C22—41no—
1303C22—41no—
1304C22—43no—
1305C22—43no—
1306C22—43no—
1307C22—43no—
1308C22—43no—
1309C22—43no—
1310C22—43no—
1311C22C23×#4111yescharacteristic
1312C22C23×#4111yescharacteristic
1313C22C22×H(5,𝔽2)11yescharacteristic
1314C22C22×2−1+411yescharacteristic
1315C22C2×#58511yescharacteristic
1316C22C2×#58511yescharacteristic
1317C222−1+611yescharacteristic
1318C4—22no—
1319C4—22no—
1320C4—22no—
1321C4—22no—
1322C4—26no—
1323C4—26no—
1324C4—41no—
1325C4—41no—
1326C4—41no—
1327C4—43no—
1328C4—43no—
1329C4—41no—
1330C4—43no—
1331C4—43no—
1332C4—43no—
1333C4—41no—
1334C4—43no—
1335C4—43no—
1336C4—43no—
1337C4—41no—
1338C4—41no—
1339C4—43no—
1340C4—43no—
1341C4—43no—
1342C4—41no—
1343C4—43no—
1344C4C2×#551112yes—
1345C2—42no—
1346C2—42no—
1347C2—42no—
1348C2—83no—
1349C2C22×#55111yescharacteristic
1350C2#6278811yescharacteristic
1351C2#6279311yescharacteristic
1352C2#6292211yescharacteristic
1353C2#6299811yescharacteristic
1354C2#6300711yescharacteristic
1355C2#6301511yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35687C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59933C2semidirect
2. #59769C2semidirect
3. #59481C2semidirect
4. #59383C2semidirect
5. #59282C2semidirect
6. #45305C2semidirect
7. #45250C2semidirect
8. #44962C2semidirect
9. #44918C2semidirect
10. #39563C2semidirect
11. #39041C2semidirect
12. #38253C2semidirect
13. #37973C2semidirect
14. #36578C2semidirect
15. #36577C2semidirect
16. Q8×#123C2semidirect
17. #36467C2semidirect
18. #36458C2semidirect
19. #36381C2semidirect
20. #36379C2semidirect
21. #35898C2semidirect
22. #35786C2semidirect
23. #35723C2semidirect
25. #34861C2semidirect
26. #34291C2semidirect
27. #34262C2semidirect
28. #34257C2semidirect
29. #34257C2semidirect
30. C4×D4×Q8C2semidirect
31. #34128C2semidirect
1120. C22⋊C42−1+4semidirect

Maximal subgroups

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

subgroupindex
#599332
#597692
#594812
#593832
#592822
#453052
#452502
#449622
#449182
#395632
#390412
#382532
#379732
#365782
#365772
Q8×#1232
#364672
#364582
#363812
#363792
#358982
#357862
#357232
#356872
#348612
#342912
#342622
#342572
C4×D4×Q82
#341282