Finite Group Databasebeta

← #7683826

Subgroups — #7683826

Order 512.

4524 conjugacy classes of subgroups.

The subgroup lattice has 1317 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59796C214yesmaximal, complemented
2#59747C214yesmaximal, complemented
3#59725C214yesmaximal, complemented
4#59451C212yesmaximal, complemented
5#59433C212yesmaximal, complemented
6#59433C214yesmaximal, complemented
7#59243C212yesmaximal, complemented
8#59140C212yesmaximal, complemented
9#45432C211yesmaximal, characteristic, complemented
10#45400C211yesmaximal, characteristic, complemented
11#45396C212yesmaximal, complemented
12#45152C211yesmaximal, characteristic, complemented
13#44982C211yesmaximal, characteristic, complemented
14#44977C212yesmaximal, complemented
15#44556C214yesmaximal, complemented
16#44550C214yesmaximal, complemented
17#44121C214yesmaximal, complemented
18#44108C214yesmaximal, complemented
19#35652C212yesmaximal, complemented
20#35635C212yesmaximal, complemented
21#35609C212yesmaximal, complemented
22#34880C211yesmaximal, characteristic
23#34793C212yesmaximal, complemented
24#34300C212yesmaximal, complemented
25#34281C211yesmaximal, characteristic, complemented
26#34242C212yesmaximal, complemented
27#34217C211yesmaximal, characteristic, complemented
28C2×#552C2212yes—
29C2×#541C2211yescharacteristic
30C2×#529C2212yes—
31C22×#125C2211yescharacteristic
32#2803C2214yes—
33#2803C2214yes—
34#2802C2214yes—
35#2801C2214yes—
36#2789C2214yes—
37#2789C2214yes—
38#2786C2214yes—
39#2786C2214yes—
40#2786C2214yes—
41#2786C2214yes—
42#2783C2214yes—
43#2779C2214yes—
44#2773C2214yes—
45#2773C2214yes—
46#2767C2214yes—
47#2756C2214yes—
48#2747C2214yes—
49#2741C2214yes—
50#2726C2214yes—
51#2725C2214yes—
52#2721C2214yes—
53#2719C2214yes—
54#2707C2214yes—
55#2705C2214yes—
56#2606C2214yes—
57#2596C2214yes—
58#2596C2214yes—
59#2596C2214yes—
60#2596C2214yes—
61#2596C2214yes—
62#2595C2214yes—
63#2594C2214yes—
64#2594C2214yes—
65#2594C2214yes—
66#2594C2214yes—
67#2594C2214yes—
68#2594C2214yes—
69#2590C2214yes—
70#2590C2214yes—
71#2588C2214yes—
72#2585C2214yes—
73#2584C2212yes—
74#2584C2214yes—
75#2577C2214yes—
76#2570C2214yes—
77#2568C2212yes—
78#2565C2212yes—
79#2562C2212yes—
80#2562C2212yes—
81#2562C2214yes—
82#2559C2214yes—
83#2558C2214yes—
84#2556C2214yes—
85#2556C2212yes—
86#2555C2212yes—
87#2554C2212yes—
88#2553C2212yes—
89#2553C2214yes—
90#2552C2212yes—
91#2542C2212yes—
92#2538C2212yes—
93#2531C2214yes—
94#2531C2214yes—
95#2531C2214yes—
96#2530C2214yes—
97#2528C2214yes—
98#2528C2214yes—
99#2528C2214yes—
100#2528C2214yes—
101#2525C2214yes—
102#2524C2214yes—
103#2522C2214yes—
104#2522C2214yes—
105#2521C2212yes—
106#2521C2214yes—
107#2521C2214yes—
108#2519C2214yes—
109#2519C2214yes—
110#2519C2214yes—
111#2519C2212yes—
112#2517C2214yes—
113#2514C2212yes—
114#2513C2214yes—
115#2513C2214yes—
116#2511C2212yes—
117#2507C2212yes—
118#2506C2214yes—
119#2506C2212yes—
120#2499C2212yes—
121#2499C2212yes—
122#2496C2214yes—
123#2496C2212yes—
124#2494C2214yes—
125#2494C2214yes—
126#2494C2212yes—
127#2494C2214yes—
128#2494C2214yes—
129#2494C2212yes—
130#2494C2212yes—
131#2490C2214yes—
132#2489C2212yes—
133#2489C2212yes—
134#2485C2212yes—
135#2485C2212yes—
136#2481C2214yes—
137#2479C2214yes—
138#2475C2214yes—
139#2475C2214yes—
140#2471C2214yes—
141#2467C2214yes—
142#2464C2212yes—
143#2462C2214yes—
144#2461C2212yes—
145#2460C2214yes—
146#2448C2214yes—
147#2443C2214yes—
148#2442C2214yes—
149#2442C2212yes—
150#2441C2212yes—
151#2441C2214yes—
152#2423C2212yes—
153#2423C2212yes—
154#2417C2212yes—
155#2417C2212yes—
156#2417C2212yes—
157#2415C2212yes—
158#2415C2212yes—
159#2415C2212yes—
160#2401C2214yes—
161#2399C2211yescharacteristic
162#2397C2211yescharacteristic
163#2395C2214yes—
164#2392C2211yescharacteristic
165#2392C2211yescharacteristic
166#2374C2214yes—
167#2373C2214yes—
168#2373C2214yes—
169#2373C2214yes—
170#2373C2214yes—
171#2373C2214yes—
172#2373C2214yes—
173#2371C2214yes—
174#2371C2214yes—
175#2370C2212yes—
176#2370C2214yes—
177#2370C2214yes—
178#2370C2214yes—
179#2370C2214yes—
180#2363C2214yes—
181#2362C2212yes—
182#2362C2212yes—
183#2362C2214yes—
184#2355C2214yes—
185#2355C2212yes—
186#2355C2212yes—
187#2354C2212yes—
188#2354C2212yes—
189#2354C2212yes—
190#2354C2212yes—
191#2352C2214yes—
192#2352C2212yes—
193#2352C2212yes—
194Q8×C4⋊C4C2212yes—
195D4×C4⋊C4C2212yes—
196#2346C2214yes—
197#2346C2212yes—
198#2345C2214yes—
199#2345C2214yes—
200#2345C2212yes—
201#2335C2214yes—
202#2335C2214yes—
203#2335C2214yes—
204#2334C2214yes—
205#2330C2211yescharacteristic
206#2330C2211yescharacteristic
207#2330C2211yescharacteristic
208#2330C2211yescharacteristic
209#2330C2211yescharacteristic
210#2327C2211yescharacteristic
211#2323C2212yes—
212#2323C2212yes—
213#2323C2212yes—
214#2316C2212yes—
215#2314C2212yes—
216#2314C2211yescharacteristic
217C4×C4⋊Q8C2211yescharacteristic
218C4×#125C2211yescharacteristic
219C4×#125C2212yes—
220C4×#125C2214yes—
221C4×#125C2214yes—
222C4×#125C2212yes—
223C4×#125C2214yes—
224C4×#124C2212yes—
225C4×#124C2214yes—
226C4×C22⋊Q8C2212yes—
227C4×C22⋊Q8C2212yes—
228C4×C22⋊Q8C2212yes—
229C4×#121C2212yes—
230#2298C2214yes—
231#2298C2214yes—
232#2295C2212yes—
233#2293C2211yescharacteristic
234#2290C2212yes—
235#2285C2212yes—
236#2285C2211yescharacteristic
237#2276C2212yes—
238#2274C2212yes—
239#2274C2212yes—
240C42×D4C2211yescharacteristic
241C4×#117C2211yescharacteristic
242C4×#117C2212yes—
243#552—216no—
244#541—28no—
245C2×C4⋊Q8C2311yescharacteristic
246#529—216no—
247C2×#126C2314yes—
248C2×#126C2312yes—
249C2×#126C2312yes—
250C2×#126C2314yes—
251C2×#126C2314yes—
252C2×#125—28no—
253C2×#125C2312yes—
254C2×#125C2312yes—
255C2×#125C2311yescharacteristic
256C2×#125C2314yes—
257C2×#125C2311yescharacteristic
258C2×#125C2314yes—
259C2×#125C2314yes—
260C2×#125C2314yes—
261C2×#125C2314yes—
262C2×#125C2311yescharacteristic
263C2×#124C2312yes—
264C2×#124C2312yes—
265C2×#123C2312yes—
266C2×#123C2312yes—
267C2×#123C2314yes—
268C2×C22⋊Q8C2312yes—
269C2×C22⋊Q8C2312yes—
270C2×C22⋊Q8C2312yes—
271C2×C22⋊Q8C2312yes—
272C2×C22⋊Q8C2312yes—
273C2×C22⋊Q8C2312yes—
274C2×#121C2312yes—
275C2×#121C2312yes—
276C2×C4×Q8C2312yes—
277C2×C4×Q8C2312yes—
278C2×C4×Q8C2312yes—
279C2×C4×Q8C2312yes—
280C2×C4×Q8C2314yes—
281C2×C4×D4C2312yes—
282C2×C4×D4C2312yes—
283C2×C4×D4C2312yes—
284C2×C4×D4C2312yes—
285C2×C4×D4C2314yes—
286C2×C4×D4C2311yescharacteristic
287C2×C4×D4C2311yescharacteristic
288C2×C4×D4C2312yes—
289C2×#117C2312yes—
290C2×#117C2312yes—
291C2×#117C2314yes—
292C2×#117C2311yescharacteristic
293C2×#117C2312yes—
294C2×#117C2312yes—
295C2×#117C2312yes—
296C2×#117C2314yes—
297C2×#117C2311yescharacteristic
298C22×C4⋊C4C2312yes—
299C22×C4⋊C4C2314yes—
300C22×C4⋊C4C2312yes—
301C22×C42C2311yescharacteristic
302C22×C42C2312yes—
303#401C2314yes—
304#401C2314yes—
305#401C2314yes—
306#401C2314yes—
307#400C2314yes—
308#400C2314yes—
309#400C2314yes—
310#400C2314yes—
311#400C2314yes—
312#400C2314yes—
313#400C2314yes—
314#400C2314yes—
315#400C2314yes—
316#400C2314yes—
317#400C2314yes—
318#400C2314yes—
319#399C2312yes—
320#399C2312yes—
321#399C2314yes—
322#399C2314yes—
323#399C2314yes—
324#399C2314yes—
325#399C2314yes—
326#398C2314yes—
327#398C2314yes—
328#398C2314yes—
329#398C2314yes—
330#398C2314yes—
331#398C2314yes—
332#398C2314yes—
333#398C2314yes—
334#398C2314yes—
335#398C2314yes—
336#398C2314yes—
337#398C2311yescharacteristic
338#398C2314yes—
339#398C2314yes—
340#398C2314yes—
341#398C2311yescharacteristic
342#398C2312yes—
343#398C2312yes—
344#397C2314yes—
345#397C2314yes—
346#397C2314yes—
347#397C2314yes—
348#397C2314yes—
349#397C2314yes—
350#397C2314yes—
351#397C2314yes—
352#397C2314yes—
353#397C2314yes—
354#397C2311yescharacteristic
355#397C2311yescharacteristic
356#397C2314yes—
357#397C2314yes—
358#397C2314yes—
359#397C2314yes—
360#397C2314yes—
361#396C2312yes—
362#396C2314yes—
363#396C2314yes—
364#396C2314yes—
365#396C2314yes—
366#396C2312yes—
367#396C2314yes—
368#396C2314yes—
369#395C2312yes—
370#395C2314yes—
371#395C2312yes—
372#394C2312yes—
373#394C2314yes—
374#394C2314yes—
375#394C2314yes—
376#394C2314yes—
377#394C2311yescharacteristic
378#394C2312yes—
379#394C2311yescharacteristic
380#394C2314yes—
381#394C2314yes—
382#394C2314yes—
383#392C2311yescharacteristic
384#392C2311yescharacteristic
385#392C2312yes—
386#392C2312yes—
387#391C2312yes—
388#391C2312yes—
389#391C2312yes—
390#391C2312yes—
391#391C2314yes—
392#391C2312yes—
393#391C2312yes—
394#391C2314yes—
395#391C2312yes—
396#390C2314yes—
397#390C2314yes—
398#390C2314yes—
399#390C2312yes—
400#390C2314yes—
401#390C2314yes—
402#390C2314yes—
403#390C2312yes—
404#390C2312yes—
405#389C2312yes—
406#389C2312yes—
407#389C2312yes—
408#389C2312yes—
409#389C2314yes—
410#389C2314yes—
411#389C2314yes—
412#389C2314yes—
413#389C2314yes—
414#389C2314yes—
415#389C2312yes—
416#389C2314yes—
417#389C2314yes—
418#389C2314yes—
419#389C2314yes—
420#389C2312yes—
421#389C2312yes—
422#389C2314yes—
423#389C2312yes—
424#389C2314yes—
425#389C2314yes—
426#389C2314yes—
427#389C2314yes—
428#389C2314yes—
429#389C2314yes—
430#389C2314yes—
431#389C2314yes—
432#389C2314yes—
433#389C2312yes—
434#389C2312yes—
435#389C2312yes—
436#389C2314yes—
437#389C2314yes—
438#389C2314yes—
439#389C2314yes—
440#389C2314yes—
441#389C2312yes—
442#388C2314yes—
443#388C2314yes—
444#388C2314yes—
445#388C2314yes—
446#388C2314yes—
447#388C2314yes—
448#388C2314yes—
449#388C2314yes—
450#388C2314yes—
451#388C2314yes—
452#388C2314yes—
453#388C2312yes—
454#388C2314yes—
455#388C2314yes—
456#388C2314yes—
457#388C2314yes—
458#388C2314yes—
459#388C2314yes—
460#388C2314yes—
461#388C2314yes—
462#388C2314yes—
463#388C2314yes—
464#388C2314yes—
465#388C2314yes—
466#388C2314yes—
467#388C2314yes—
468#388C2314yes—
469#388C2314yes—
470#388C2312yes—
471#388C2314yes—
472#388C2312yes—
473#388C2312yes—
474#388C2312yes—
475#388C2312yes—
476#388C2314yes—
477#388C2314yes—
478#388C2314yes—
479#388C2314yes—
480#388C2314yes—
481#388C2314yes—
482#388C2314yes—
483#388C2314yes—
484#388C2312yes—
485#388C2314yes—
486#388C2312yes—
487#388C2314yes—
488#388C2314yes—
489#388C2314yes—
490#388C2312yes—
491#388C2314yes—
492#388C2312yes—
493#387C2312yes—
494#387C2314yes—
495#387C2314yes—
496#387C2314yes—
497#387C2314yes—
498#387C2314yes—
499#387C2314yes—
500#387C2314yes—
501#387C2314yes—
502#387C2314yes—
503#387C2314yes—
504#387C2314yes—
505#387C2314yes—
506#387C2314yes—
507#387C2314yes—
508#387C2314yes—
509#387C2314yes—
510#387C2314yes—
511#387C2314yes—
512#387C2314yes—
513#387C2314yes—
514#387C2314yes—
515#387C2314yes—
516#387C2314yes—
517#387C2314yes—
518#387C2314yes—
519#387C2314yes—
520#387C2314yes—
521#387C2314yes—
522#387C2314yes—
523#387C2314yes—
524#387C2314yes—
525#387C2314yes—
526#387C2314yes—
527#387C2314yes—
528#387C2314yes—
529#387C2314yes—
530#387C2314yes—
531#387C2314yes—
532#387C2314yes—
533#387C2312yes—
534#387C2314yes—
535#387C2314yes—
536#387C2314yes—
537#387C2314yes—
538#387C2314yes—
539#387C2314yes—
540#387C2314yes—
541#387C2314yes—
542#387C2314yes—
543#387C2314yes—
544#387C2314yes—
545#387C2314yes—
546#387C2314yes—
547#387C2314yes—
548#387C2314yes—
549#387C2314yes—
550#386C2312yes—
551#386C2314yes—
552#386C2314yes—
553#386C2314yes—
554#386C2312yes—
555#386C2314yes—
556#386C2312yes—
557#386C2314yes—
558#386C2312yes—
559#385C2314yes—
560#385C2312yes—
561#385C2314yes—
562#385C2314yes—
563#385C2314yes—
564#385C2314yes—
565#385C2312yes—
566#385C2314yes—
567#384C2311yescharacteristic
568#384C2312yes—
569#384C2312yes—
570#384C2314yes—
571#384C2311yescharacteristic
572#384C2311yescharacteristic
573#384C2312yes—
574#383C2314yes—
575#382C2312yes—
576#382C2311yescharacteristic
577#382C2314yes—
578#382C2314yes—
579#382C2314yes—
580#382C2312yes—
581#382C2314yes—
582#382C2312yes—
583#382C2314yes—
584#382C2314yes—
585#380C2312yes—
586#380C2312yes—
587#380C2312yes—
588#380C2314yes—
589#380C2314yes—
590#380C2312yes—
591#380C2314yes—
592#380C2312yes—
593#380C2312yes—
594#380C2314yes—
595#380C2312yes—
596#380C2312yes—
597#380C2314yes—
598#380C2314yes—
599#380C2314yes—
600#380C2312yes—
601#380C2314yes—
602#380C2314yes—
603#380C2312yes—
604C4×C4⋊C4C2314yes—
605C4×C4⋊C4C2312yes—
606C4×C4⋊C4C2312yes—
607C4×C4⋊C4C2314yes—
608C4×C4⋊C4C2312yes—
609C4×C4⋊C4C2314yes—
610C4×C4⋊C4C2314yes—
611C4×C4⋊C4C2314yes—
612C4×C4⋊C4C2312yes—
613C4×C4⋊C4C2312yes—
614C4×C4⋊C4C2312yes—
615C4×C4⋊C4C2314yes—
616C4×C4⋊C4C2314yes—
617C4×C4⋊C4C2314yes—
618C4×C4⋊C4C2314yes—
619C4×C4⋊C4C2314yes—
620C4×C4⋊C4C2314yes—
621C4×C4⋊C4C2314yes—
622C4×C4⋊C4C2314yes—
623C4×C4⋊C4C2314yes—
624C4×C4⋊C4C2314yes—
625C4×C4⋊C4C2314yes—
626C4×C4⋊C4C2314yes—
627C4×C4⋊C4C2314yes—
628C4×C4⋊C4C2314yes—
629C4×C4⋊C4C2314yes—
630C4×C4⋊C4C2314yes—
631C4×C4⋊C4C2312yes—
632C4×C4⋊C4C2314yes—
633C4×C4⋊C4C2312yes—
634C4×C4⋊C4C2312yes—
635C4×C4⋊C4C2314yes—
636C4×C4⋊C4C2314yes—
637C4×C4⋊C4C2314yes—
638C4×C4⋊C4C2312yes—
639C4×C4⋊C4C2312yes—
640C4×C4⋊C4C2312yes—
641C4×C4⋊C4C2312yes—
642C4×C4⋊C4C2314yes—
643C4×C4⋊C4C2312yes—
644C4×C4⋊C4C2312yes—
645C4×C4⋊C4C2314yes—
646C4×C4⋊C4C2314yes—
647C4×C4⋊C4C2311yescharacteristic
648C4×C4⋊C4C2311yescharacteristic
649C4×C22⋊C4C2314yes—
650C4×C22⋊C4C2314yes—
651C4×C22⋊C4C2314yes—
652C4×C22⋊C4C2314yes—
653C4×C22⋊C4C2314yes—
654C4×C22⋊C4C2312yes—
655C4×C22⋊C4C2312yes—
656C4×C22⋊C4C2312yes—
657C4×C22⋊C4C2314yes—
658C4×C22⋊C4C2312yes—
659C4×C22⋊C4C2314yes—
660C4×C22⋊C4C2314yes—
661C4×C22⋊C4C2314yes—
662C4×C22⋊C4C2314yes—
663C4×C22⋊C4C2314yes—
664C4×C22⋊C4C2314yes—
665C4×C22⋊C4C2312yes—
666C4×C22⋊C4C2312yes—
667C4×C22⋊C4C2312yes—
668C4×C22⋊C4C2312yes—
669#376C2311yescharacteristic
670#376C2311yescharacteristic
671#376C2314yes—
672#376C2314yes—
673#376C2314yes—
674#376C2314yes—
675C43C2311yescharacteristic
676C43C2314yes—
677C43C2311yescharacteristic
678C22×Q8C2412yes—
679C22×Q8C2412yes—
680C22×D4C2412yes—
681C22×D4C2412yes—
682C22×D4C2412yes—
683C22×D4C2412yes—
684C22×D4C2411yescharacteristic
685C22×D4C2411yescharacteristic
686C23×C4C2412yes—
687C23×C4C2412yes—
688C23×C4C2412yes—
689C23×C4C2411yescharacteristic
690C23×C4C2414yes—
691C23×C4C2412yes—
692C23×C4C2414yes—
693C23×C4C2412yes—
694C4⋊Q8—24no—
695#126—28no—
696#126—216no—
697#126—28no—
698#126—216no—
699#126—48no—
700#125—28no—
701#125—216no—
702#125—28no—
703#125—216no—
704#125—216no—
705#125—24no—
706#125—24no—
707#125—48no—
708#125—48no—
709#125#4118yes—
710#124—28no—
711#124—44no—
712#123—28no—
713#123—216no—
714#123—28no—
715C22⋊Q8—28no—
716C22⋊Q8—28no—
717C22⋊Q8—28no—
718C22⋊Q8—28no—
719C22⋊Q8—44no—
720C22⋊Q8—44no—
721#121—28no—
722#121—44no—
723C4×Q8—28no—
724C4×Q8—28no—
725C4×Q8—28no—
726C4×Q8—44no—
727C4×Q8—48no—
728C4×D4—28no—
729C4×D4—28no—
730C4×D4—28no—
731C4×D4—28no—
732C4×D4—48no—
733C4×D4—42no—
734C4×D4—42no—
735C4×D4—44no—
736#117—28no—
737#117—216no—
738#117—28no—
739#117—42no—
740#117—44no—
741#117—44no—
742#117—44no—
743#117—48no—
744#117#4118yes—
745C2×C4⋊C4—28no—
746C2×C4⋊C4—216no—
747C2×C4⋊C4—28no—
748C2×C4⋊C4C2412yes—
749C2×C4⋊C4C2412yes—
750C2×C4⋊C4C2414yes—
751C2×C4⋊C4C2414yes—
752C2×C4⋊C4C2414yes—
753C2×C4⋊C4C2414yes—
754C2×C4⋊C4C2414yes—
755C2×C4⋊C4C2412yes—
756C2×C4⋊C4C2412yes—
757C2×C4⋊C4C2414yes—
758C2×C4⋊C4C2414yes—
759C2×C4⋊C4C2412yes—
760C2×C4⋊C4C2414yes—
761C2×C4⋊C4C2412yes—
762C2×C4⋊C4C2412yes—
763C2×C4⋊C4C2412yes—
764C2×C4⋊C4C2412yes—
765C2×C4⋊C4C2412yes—
766C2×C4⋊C4C2412yes—
767C2×C4⋊C4C2412yes—
768C2×C4⋊C4C2412yes—
769C2×C4⋊C4C2412yes—
770C2×C4⋊C4C2414yes—
771C2×C4⋊C4C2412yes—
772C2×C4⋊C4C2412yes—
773C2×C4⋊C4C2414yes—
774C2×C4⋊C4C2412yes—
775C2×C4⋊C4C2414yes—
776C2×C4⋊C4C2414yes—
777C2×C4⋊C4C2414yes—
778C2×C4⋊C4C2414yes—
779C2×C4⋊C4C2414yes—
780C2×C4⋊C4C2411yescharacteristic
781C2×C4⋊C4C2411yescharacteristic
782C2×C4⋊C4C2411yescharacteristic
783C2×C4⋊C4C2411yescharacteristic
784C2×C4⋊C4C2414yes—
785C2×C4⋊C4C2414yes—
786C2×C4⋊C4C2414yes—
787C2×C4⋊C4C2414yes—
788C2×C4⋊C4C2414yes—
789C2×C4⋊C4C2414yes—
790C2×C4⋊C4C2414yes—
791C2×C4⋊C4C2414yes—
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2414yes—
794C2×C4⋊C4C2414yes—
795C2×C4⋊C4C2414yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2414yes—
799C2×C4⋊C4C2414yes—
800C2×C4⋊C4C2414yes—
801C2×C4⋊C4C2412yes—
802C2×C4⋊C4C2414yes—
803C2×C4⋊C4C2414yes—
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2414yes—
807C2×C4⋊C4C2412yes—
808C2×C22⋊C4C2412yes—
809C2×C22⋊C4C2412yes—
810C2×C22⋊C4C2414yes—
811C2×C22⋊C4C2412yes—
812C2×C22⋊C4C2414yes—
813C2×C22⋊C4C2412yes—
814C2×C22⋊C4C2412yes—
815C2×C22⋊C4C2412yes—
816C2×C22⋊C4C2412yes—
817C2×C22⋊C4C2412yes—
818C2×C22⋊C4C2412yes—
819C2×C22⋊C4C2412yes—
820C2×C22⋊C4C2412yes—
821C2×C22⋊C4C2414yes—
822C2×C22⋊C4C2414yes—
823C2×C22⋊C4C2412yes—
824C2×C22⋊C4C2411yescharacteristic
825C2×C22⋊C4C2411yescharacteristic
826C2×C22⋊C4C2414yes—
827C2×C22⋊C4C2414yes—
828C2×C22⋊C4C2414yes—
829C2×C22⋊C4C2414yes—
830C2×C22⋊C4C2414yes—
831C2×C22⋊C4C2414yes—
832C2×C22⋊C4C2412yes—
833C2×C22⋊C4C2412yes—
834C2×C22⋊C4C2412yes—
835C2×C22⋊C4C2414yes—
836C2×C22⋊C4C2412yes—
837C2×C22⋊C4C2414yes—
838C2×C22⋊C4C2414yes—
839C2×C22⋊C4C2412yes—
840C2×C22⋊C4C2412yes—
841C2×C22⋊C4C2414yes—
842C2×C22⋊C4C2414yes—
843C2×C22⋊C4C2412yes—
844C2×C22⋊C4C2414yes—
845C2×C22⋊C4C2414yes—
846C2×C22⋊C4C2414yes—
847C2×C22⋊C4C2412yes—
848C2×C22⋊C4C2412yes—
849C2×C42—24no—
850C2×C42—28no—
851C2×C42C2414yes—
852C2×C42C2411yescharacteristic
853C2×C42C2412yes—
854C2×C42C2411yescharacteristic
855C2×C42C2414yes—
856C2×C42C2414yes—
857C2×C42C2412yes—
858C2×C42C2414yes—
859C2×C42C2412yes—
860C2×C42C2411yescharacteristic
861C2×C42C2412yes—
862C2×C42C2412yes—
863C2×C42C2414yes—
864C2×C42C2414yes—
865C2×C42C2414yes—
866C2×C42C2414yes—
867C2×C42C2414yes—
868C2×C42C2412yes—
869C2×C42C2414yes—
870C2×C42C2414yes—
871C2×C42C2414yes—
872C2×C42C2412yes—
873C2×C42C2414yes—
874C2×C42C2414yes—
875C2×C42C2412yes—
876C2×C42C2414yes—
877C2×C42C2414yes—
878C2×C42C2412yes—
879C2×C42C2414yes—
880C2×C42C2414yes—
881C2×C42C2411yescharacteristic
882C2×C42C2411yescharacteristic
883C2×C42C2411yescharacteristic
884#95C2412yes—
885#95C2414yes—
886#95C2412yes—
887#95C2414yes—
888#95C2412yes—
889#95C2414yes—
890#95C2414yes—
891#95C2414yes—
892#95C2414yes—
893#95C2412yes—
894#95C2412yes—
895#95C2414yes—
896#95C2414yes—
897#95C2414yes—
898#95C2414yes—
899#95C2414yes—
900#95C2414yes—
901#95C2414yes—
902#95C2412yes—
903#95C2412yes—
904#95C2414yes—
905#95C2411yescharacteristic
906#95C2411yescharacteristic
907#95C2414yes—
908#95C2414yes—
909#95C2414yes—
910#95C2412yes—
911#95C2414yes—
912#95C2414yes—
913#95C2414yes—
914#95C2412yes—
915#95C2414yes—
916#95C2414yes—
917#95C2414yes—
918#95C2414yes—
919#95C2412yes—
920#95C2414yes—
921#95C2414yes—
922#95C2412yes—
923#95C2412yes—
924#95C2414yes—
925#95C2414yes—
926#95C2414yes—
927#95C2414yes—
928#95C2412yes—
929#95C2414yes—
930#95C2414yes—
931#95C2414yes—
932#95C2414yes—
933#95C2414yes—
934#95C2414yes—
935#95C2414yes—
936#95C2414yes—
937#95C2414yes—
938#95C2414yes—
939#95C2414yes—
940#95C2414yes—
941#95C2414yes—
942#95C2411yescharacteristic
943#95C2412yes—
944#95C2411yescharacteristic
945#95C2414yes—
946#95C2414yes—
947#95C2414yes—
948#95C2414yes—
949C24C2512yes—
950C24C2512yes—
951C24C2511yescharacteristic
952C2×Q8—24no—
953C2×Q8—24no—
954C2×Q8—24no—
955C2×Q8—24no—
956C2×Q8—24no—
957C2×Q8—42no—
958C2×D4—24no—
959C2×D4—24no—
960C2×D4—24no—
961C2×D4—24no—
962C2×D4—24no—
963C2×D4—41no—
964C2×D4—42no—
965C2×D4—42no—
966C2×D4—41no—
967C2×D4—42no—
968C2×D4—42no—
969C2×D4—42no—
970C2×D4—42no—
971C2×D4—42no—
972C2×D4—42no—
973C2×D4—42no—
974C22×C4—22no—
975C22×C4—22no—
976C22×C4—24no—
977C22×C4—24no—
978C22×C4—24no—
979C22×C4—24no—
980C22×C4—24no—
981C22×C4—24no—
982C22×C4—24no—
983C22×C4—24no—
984C22×C4—24no—
985C22×C4—24no—
986C22×C4—28no—
987C22×C4—28no—
988C22×C4—42no—
989C22×C4—44no—
990C22×C4—44no—
991C22×C4—42no—
992C22×C4—42no—
993C22×C4—42no—
994C22×C4—44no—
995C22×C4—44no—
996C22×C4—42no—
997C22×C4C2×#4114yes—
998C22×C4C2511yescharacteristic
999C22×C4C2511yescharacteristic
1000C22×C4C2514yes—
1001C22×C4C2514yes—
1002C22×C4C2512yes—
1003C22×C4C2512yes—
1004C22×C4C2512yes—
1005C22×C4C2512yes—
1006C22×C4C2514yes—
1007C22×C4C2512yes—
1008C22×C4C2514yes—
1009C22×C4C2514yes—
1010C22×C4C2511yescharacteristic
1011C22×C4C2512yes—
1012C22×C4C2514yes—
1013C22×C4C2511yescharacteristic
1014C22×C4C2514yes—
1015C22×C4C2512yes—
1016C22×C4C2512yes—
1017C22×C4C2512yes—
1018C22×C4C2514yes—
1019C22×C4C2511yescharacteristic
1020C22×C4C2512yes—
1021C22×C4C2511yescharacteristic
1022C4⋊C4—24no—
1023C4⋊C4—28no—
1024C4⋊C4—28no—
1025C4⋊C4—28no—
1026C4⋊C4—28no—
1027C4⋊C4—24no—
1028C4⋊C4—28no—
1029C4⋊C4—28no—
1030C4⋊C4—24no—
1031C4⋊C4—24no—
1032C4⋊C4—24no—
1033C4⋊C4—24no—
1034C4⋊C4—24no—
1035C4⋊C4—24no—
1036C4⋊C4—24no—
1037C4⋊C4—24no—
1038C4⋊C4—28no—
1039C4⋊C4—24no—
1040C4⋊C4—24no—
1041C4⋊C4—28no—
1042C4⋊C4—28no—
1043C4⋊C4—28no—
1044C4⋊C4—28no—
1045C4⋊C4—28no—
1046C4⋊C4—24no—
1047C4⋊C4—24no—
1048C4⋊C4—28no—
1049C4⋊C4—28no—
1050C4⋊C4—24no—
1051C4⋊C4—24no—
1052C4⋊C4—24no—
1053C4⋊C4—28no—
1054C4⋊C4—44no—
1055C4⋊C4—44no—
1056C4⋊C4—44no—
1057C4⋊C4—42no—
1058C4⋊C4—42no—
1059C4⋊C4—44no—
1060C4⋊C4—44no—
1061C4⋊C4—44no—
1062C4⋊C4—41no—
1063C4⋊C4—41no—
1064C4⋊C4—41no—
1065C4⋊C4—41no—
1066C4⋊C4—44no—
1067C4⋊C4—44no—
1068C4⋊C4—44no—
1069C4⋊C4—44no—
1070C4⋊C4—44no—
1071C4⋊C4—44no—
1072C4⋊C4—44no—
1073C4⋊C4—44no—
1074C4⋊C4—44no—
1075C4⋊C4—44no—
1076C4⋊C4—44no—
1077C4⋊C4—44no—
1078C4⋊C4—44no—
1079C4⋊C4C2×#4118yes—
1080C4⋊C4C2×#41116yes—
1081C4⋊C4C2×#4118yes—
1082C22⋊C4—24no—
1083C22⋊C4—24no—
1084C22⋊C4—28no—
1085C22⋊C4—24no—
1086C22⋊C4—24no—
1087C22⋊C4—28no—
1088C22⋊C4—24no—
1089C22⋊C4—28no—
1090C22⋊C4—24no—
1091C22⋊C4—24no—
1092C22⋊C4—24no—
1093C22⋊C4—24no—
1094C22⋊C4—24no—
1095C22⋊C4—28no—
1096C22⋊C4—24no—
1097C22⋊C4—24no—
1098C22⋊C4—44no—
1099C22⋊C4—42no—
1100C22⋊C4—42no—
1101C22⋊C4—44no—
1102C22⋊C4—44no—
1103C22⋊C4—41no—
1104C22⋊C4—41no—
1105C22⋊C4—44no—
1106C22⋊C4—44no—
1107C22⋊C4—44no—
1108C22⋊C4—44no—
1109C22⋊C4—44no—
1110C22⋊C4—42no—
1111C22⋊C4—42no—
1112C22⋊C4—44no—
1113C22⋊C4—44no—
1114C22⋊C4—42no—
1115C22⋊C4—42no—
1116C22⋊C4—44no—
1117C22⋊C4—44no—
1118C22⋊C4—42no—
1119C22⋊C4—42no—
1120C22⋊C4—44no—
1121C22⋊C4—44no—
1122C22⋊C4C2×#4118yes—
1123C42—24no—
1124C42—24no—
1125C42—24no—
1126C42—22no—
1127C42—24no—
1128C42—28no—
1129C42—24no—
1130C42—28no—
1131C42—28no—
1132C42—22no—
1133C42—22no—
1134C42—28no—
1135C42—44no—
1136C42—42no—
1137C42—44no—
1138C42—42no—
1139C42—44no—
1140C42—44no—
1141C42—44no—
1142C42—44no—
1143C42—44no—
1144C42—44no—
1145C42—44no—
1146C42—42no—
1147C42—44no—
1148C42—44no—
1149C42—44no—
1150C42—42no—
1151C42—44no—
1152C42—44no—
1153C42C2×#4114yes—
1154C42C2×#4114yes—
1155C42C2×#4114yes—
1156C23—21no—
1157C23—21no—
1158C23—22no—
1159C23—22no—
1160C23—22no—
1161C23—22no—
1162C23—22no—
1163C23—22no—
1164C23—22no—
1165C23—22no—
1166C23—22no—
1167C23—22no—
1168C23—22no—
1169C23—22no—
1170C23—22no—
1171C23—22no—
1172C23—22no—
1173C23—22no—
1174C23C22×#4112yes—
1175C23C2611yescharacteristic
1176Q8—48no—
1177Q8—48no—
1178D4—48no—
1179D4—44no—
1180D4—84no—
1181D4—84no—
1182D4—84no—
1183D4—82no—
1184C2×C4—21no—
1185C2×C4—22no—
1186C2×C4—24no—
1187C2×C4—22no—
1188C2×C4—21no—
1189C2×C4—22no—
1190C2×C4—22no—
1191C2×C4—22no—
1192C2×C4—22no—
1193C2×C4—22no—
1194C2×C4—24no—
1195C2×C4—22no—
1196C2×C4—28no—
1197C2×C4—22no—
1198C2×C4—22no—
1199C2×C4—24no—
1200C2×C4—22no—
1201C2×C4—22no—
1202C2×C4—22no—
1203C2×C4—24no—
1204C2×C4—24no—
1205C2×C4—22no—
1206C2×C4—24no—
1207C2×C4—22no—
1208C2×C4—22no—
1209C2×C4—24no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—24no—
1214C2×C4—21no—
1215C2×C4—22no—
1216C2×C4—24no—
1217C2×C4—24no—
1218C2×C4—24no—
1219C2×C4—22no—
1220C2×C4—24no—
1221C2×C4—22no—
1222C2×C4—24no—
1223C2×C4—24no—
1224C2×C4—22no—
1225C2×C4—22no—
1226C2×C4—24no—
1227C2×C4—24no—
1228C2×C4—24no—
1229C2×C4—22no—
1230C2×C4—24no—
1231C2×C4—22no—
1232C2×C4—22no—
1233C2×C4—24no—
1234C2×C4—22no—
1235C2×C4—24no—
1236C2×C4—22no—
1237C2×C4—22no—
1238C2×C4—24no—
1239C2×C4—24no—
1240C2×C4—22no—
1241C2×C4—24no—
1242C2×C4—22no—
1243C2×C4—22no—
1244C2×C4—48no—
1245C2×C4—48no—
1246C2×C4—48no—
1247C2×C4—84no—
1248C2×C4—88no—
1249C2×C4—88no—
1250C2×C4—84no—
1251C2×C4C22×#4114yes—
1252C2×C4C22×#4114yes—
1253C2×C4C22×#4118yes—
1254C2×C4C22×#4114yes—
1255C2×C4C22×#4112yes—
1256C2×C4C22×#4112yes—
1257C2×C4C22×#4112yes—
1258C2×C4#58514yes—
1259C2×C4#58512yes—
1260C22—24no—
1261C22—22no—
1262C22—42no—
1263C22—41no—
1264C22—41no—
1265C22—42no—
1266C22—42no—
1267C22—42no—
1268C22—42no—
1269C22—42no—
1270C22—42no—
1271C22—42no—
1272C22—42no—
1273C22—42no—
1274C22—42no—
1275C22—42no—
1276C22—42no—
1277C22—42no—
1278C22—42no—
1279C22C23×#4111yescharacteristic
1280C22C23×#4111yescharacteristic
1281C22C2×#58512yes—
1282C22C2×#58511yescharacteristic
1283C222−1+612yes—
1284C4—24no—
1285C4—24no—
1286C4—24no—
1287C4—28no—
1288C4—24no—
1289C4—22no—
1290C4—44no—
1291C4—42no—
1292C4—42no—
1293C4—42no—
1294C4—44no—
1295C4—42no—
1296C4—44no—
1297C4—44no—
1298C4—41no—
1299C4—44no—
1300C4—41no—
1301C4—41no—
1302C4—44no—
1303C4—41no—
1304C4—42no—
1305C4—42no—
1306C4—44no—
1307C4#348014yes—
1308C2—42no—
1309C2—82no—
1310C2—82no—
1311C2C2×#348011yescharacteristic
1312C2#6284011yescharacteristic
1313C2#6289011yescharacteristic
1314C2#6299312yes—
1315C2#6300912yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#34880C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59796C2semidirect
2. #59747C2semidirect
3. #59725C2semidirect
4. #59451C2semidirect
5. #59433C2semidirect
6. #59433C2semidirect
7. #59243C2semidirect
8. #59140C2semidirect
9. #45432C2semidirect
10. #45400C2semidirect
11. #45396C2semidirect
12. #45152C2semidirect
13. #44982C2semidirect
14. #44977C2semidirect
15. #44556C2semidirect
16. #44550C2semidirect
17. #44121C2semidirect
18. #44108C2semidirect
19. #35652C2semidirect
20. #35635C2semidirect
21. #35609C2semidirect
23. #34793C2semidirect
24. #34300C2semidirect
25. #34281C2semidirect
26. #34242C2semidirect
27. #34217C2semidirect

Maximal subgroups

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

subgroupindex
#597962
#597472
#597252
#594512
#594332
#592432
#591402
#454322
#454002
#453962
#451522
#449822
#449772
#445562
#445502
#441212
#441082
#356522
#356352
#356092
#348802
#347932
#343002
#342812
#342422
#342172