Finite Group Databasebeta

← #7697411

Subgroups — #7697411

Order 512.

4417 conjugacy classes of subgroups.

The subgroup lattice has 1358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59879C212yesmaximal, complemented
2#59875C211yesmaximal, characteristic, complemented
3#59788C214yesmaximal, complemented
4#59684C212yesmaximal
5#52274C211yesmaximal, characteristic, complemented
6#52272C212yesmaximal, complemented
7#45344C212yesmaximal, complemented
8#45163C212yesmaximal, complemented
9#45156C212yesmaximal, complemented
10#44752C214yesmaximal, complemented
11#44389C214yesmaximal, complemented
12#43718C214yesmaximal, complemented
13#39829C212yesmaximal, complemented
14#39811C212yesmaximal, complemented
15#39765C211yesmaximal, characteristic
16#39740C211yesmaximal, characteristic
17#39329C214yesmaximal, complemented
18#39172C212yesmaximal, complemented
19#38667C214yesmaximal, complemented
20#38492C212yesmaximal, complemented
21#36313C212yesmaximal, complemented
22#36271C211yesmaximal, characteristic
23#35974C212yesmaximal, complemented
24#35970C212yesmaximal
25#35938C212yesmaximal, complemented
26#34335C211yesmaximal, characteristic, complemented
27#34328C211yesmaximal, characteristic, complemented
28#34326C212yesmaximal, complemented
29#34326C212yesmaximal, complemented
30C2×Q82C2211yescharacteristic
31C2×#557C2211yescharacteristic
32C2×#556C2212yes—
33C2×#556C2212yes—
34#2863C2214yes—
35#2862C2212yes—
36#2860C2212yes—
37#2858C2211yescharacteristic
38#2810C2212yes—
39#2810C2212yes—
40#2809C2211yescharacteristic
41#2808C2212yes—
42#2808C2212yes—
43#2806C2211yescharacteristic
44#2805C2211yescharacteristic
45#2804C2212yes—
46#2802C2212yes—
47#2801C2214yes—
48#2800C2214yes—
49#2799C2212yes—
50#2798C2214yes—
51#2793C2214yes—
52#2791C2212yes—
53#2790C2214yes—
54#2783C2214yes—
55#2776C2214yes—
56#2776C2214yes—
57#2774C2212yes—
58#2773C2214yes—
59#2766C2214yes—
60#2766C2214yes—
61#2765C2214yes—
62#2759C2214yes—
63#2759C2214yes—
64#2755C2212yes—
65#2754C2214yes—
66#2754C2214yes—
67#2745C2214yes—
68#2745C2214yes—
69#2732C2212yes—
70#2732C2212yes—
71#2727C2212yes—
72#2727C2212yes—
73#2726C2211yescharacteristic
74#2724C2212yes—
75#2716C2214yes—
76#2716C2214yes—
77#2716C2214yes—
78#2716C2214yes—
79#2713C2212yes—
80#2664C2214yes—
81#2658C2212yes—
82#2654C2214yes—
83#2653C2214yes—
84#2640C2212yes—
85#2640C2212yes—
86#2611C2214yes—
87#2607C2214yes—
88#2606C2214yes—
89#2606C2214yes—
90#2604C2214yes—
91#2601C2214yes—
92#2597C2214yes—
93#2594C2214yes—
94#2592C2212yes—
95#2592C2212yes—
96#2589C2214yes—
97#2589C2214yes—
98#2587C2214yes—
99#2585C2214yes—
100#2585C2214yes—
101#2578C2214yes—
102#2577C2214yes—
103#2577C2214yes—
104#2576C2214yes—
105#2575C2214yes—
106#2573C2214yes—
107#2573C2214yes—
108#2572C2214yes—
109#2568C2212yes—
110#2568C2212yes—
111#2568C2212yes—
112#2568C2212yes—
113#2563C2212yes—
114#2560C2214yes—
115#2558C2214yes—
116#2556C2214yes—
117#2556C2214yes—
118#2548C2211yescharacteristic
119#2546C2212yes—
120#2546C2211yescharacteristic
121#2546C2212yes—
122#2546C2212yes—
123#2545C2212yes—
124#2545C2212yes—
125#2545C2212yes—
126#2545C2212yes—
127#2544C2212yes—
128#2532C2214yes—
129#2532C2214yes—
130#2532C2214yes—
131#2532C2214yes—
132#2531C2214yes—
133#2528C2214yes—
134#2528C2214yes—
135#2527C2214yes—
136#2525C2214yes—
137#2525C2214yes—
138#2524C2214yes—
139#2524C2214yes—
140#2519C2214yes—
141#2519C2214yes—
142#2518C2214yes—
143#2518C2214yes—
144#2517C2214yes—
145#2516C2214yes—
146#2514C2214yes—
147#2514C2212yes—
148#2514C2212yes—
149#2514C2212yes—
150#2514C2212yes—
151#2514C2214yes—
152#2514C2214yes—
153#2513C2212yes—
154#2513C2212yes—
155#2512C2212yes—
156#2510C2214yes—
157#2479C2214yes—
158#2479C2214yes—
159#2458C2214yes—
160#2458C2214yes—
161#2453C2214yes—
162#2452C2212yes—
163#2448C2212yes—
164#2447C2212yes—
165#2446C2212yes—
166#2446C2212yes—
167#2446C2212yes—
168#2445C2212yes—
169#2439C2214yes—
170#2439C2214yes—
171#2421C2214yes—
172#2421C2214yes—
173#2419C2214yes—
174#2402C2212yes—
175#2402C2212yes—
176#2401C2214yes—
177#2399C2212yes—
178#2398C2214yes—
179#2396C2214yes—
180#2374C2214yes—
181#2373C2214yes—
182#2373C2214yes—
183#2373C2214yes—
184#2373C2214yes—
185#2371C2214yes—
186#2370C2212yes—
187#2369C2211yescharacteristic
188#2369C2212yes—
189#2368C2214yes—
190#2368C2214yes—
191#2367C2212yes—
192#2367C2212yes—
193#2367C2212yes—
194#2367C2212yes—
195#2367C2212yes—
196#2366C2211yescharacteristic
197#2365C2212yes—
198#2365C2212yes—
199#2365C2212yes—
200#2365C2211yescharacteristic
201#2365C2214yes—
202#2365C2212yes—
203#2365C2212yes—
204#2365C2211yescharacteristic
205#2357C2212yes—
206#2357C2212yes—
207#2356C2212yes—
208#2356C2212yes—
209#2356C2212yes—
210#2356C2212yes—
211#2355C2211yescharacteristic
212#2355C2211yescharacteristic
213#2355C2212yes—
214#2355C2212yes—
215#2355C2211yescharacteristic
216#2355C2212yes—
217#2355C2212yes—
218#2351C2212yes—
219Q8×C4⋊C4C2211yescharacteristic
220#2343C2214yes—
221#2343C2214yes—
222#2336C2214yes—
223#2334C2214yes—
224#2334C2214yes—
225#2332C2214yes—
226#2332C2214yes—
227#2331C2214yes—
228#2331C2212yes—
229#2327C2212yes—
230#2327C2212yes—
231#2327C2212yes—
232#2326C2212yes—
233#2326C2212yes—
234C4×C4⋊Q8C2211yescharacteristic
235C4×C4⋊Q8C2212yes—
236C4×C4⋊Q8C2211yescharacteristic
237C4×C4⋊Q8C2211yescharacteristic
238C4×#125C2212yes—
239C4×#125C2212yes—
240C4×#126C2214yes—
241C4×#126C2214yes—
242C4×#124C2212yes—
243C4×#124C2212yes—
244#2298C2214yes—
245#2298C2214yes—
246#2295C2212yes—
247#2295C2212yes—
248#2295C2212yes—
249#2295C2211yescharacteristic
250#2295C2211yescharacteristic
251#2295C2212yes—
252#2295C2214yes—
253#2293C2212yes—
254#2276C2212yes—
255#2276C2212yes—
256#2275C2212yes—
257C42×Q8C2212yes—
258C42×Q8C2211yescharacteristic
259Q82—28no—
260#557—28no—
261#556—216no—
262#556—216no—
263C2×C4⋊Q8C2311yescharacteristic
264C2×C4⋊Q8C2311yescharacteristic
265C2×C4⋊Q8C2312yes—
266C2×C4⋊Q8C2312yes—
267C2×C4⋊Q8C2312yes—
268C2×C4⋊Q8C2312yes—
269C2×C4⋊Q8C2312yes—
270C2×C4⋊Q8C2314yes—
271C2×C4⋊Q8C2311yescharacteristic
272C2×C4⋊Q8C2311yescharacteristic
273C2×C4⋊Q8C2312yes—
274C2×#127C2311yescharacteristic
275C2×#126C2314yes—
276C2×#126C2314yes—
277C2×#126C2314yes—
278C2×#126C2314yes—
279C2×#125C2312yes—
280C2×#125C2314yes—
281C2×#125C2312yes—
282C2×#124C2312yes—
283C2×#124C2312yes—
284C2×#124C2312yes—
285C2×#124C2312yes—
286C2×#124C2312yes—
287C2×#123C2314yes—
288C2×C22⋊Q8C2314yes—
289C2×C22⋊Q8C2314yes—
290C2×C4×Q8C2312yes—
291C2×C4×Q8C2312yes—
292C2×C4×Q8C2312yes—
293C2×C4×Q8C2311yescharacteristic
294C2×C4×Q8C2312yes—
295C2×C4×Q8C2311yescharacteristic
296C2×C4×Q8C2312yes—
297C2×C4×Q8C2312yes—
298C2×C4×Q8C2312yes—
299C2×C4×Q8C2312yes—
300C2×C4×Q8C2312yes—
301C2×C4×Q8C2314yes—
302C2×C4×Q8C2312yes—
303C2×C4×Q8C2312yes—
304C2×C4×Q8C2312yes—
305C2×C4×Q8C2311yescharacteristic
306C2×C4×Q8C2311yescharacteristic
307C2×C4×Q8C2311yescharacteristic
308C2×C4×D4C2312yes—
309C2×C4×D4C2312yes—
310C2×C4×D4C2312yes—
311C2×C4×D4C2312yes—
312C2×#117C2314yes—
313C2×#117C2314yes—
314#401C2314yes—
315#401C2314yes—
316#401C2314yes—
317#401C2314yes—
318#400C2314yes—
319#400C2314yes—
320#400C2314yes—
321#400C2314yes—
322#400C2314yes—
323#400C2314yes—
324#400C2314yes—
325#400C2314yes—
326#400C2312yes—
327#400C2312yes—
328#400C2314yes—
329#400C2312yes—
330#400C2314yes—
331#400C2314yes—
332#400C2314yes—
333#400C2312yes—
334#400C2312yes—
335#400C2312yes—
336#400C2312yes—
337#400C2312yes—
338#400C2314yes—
339#399C2314yes—
340#399C2314yes—
341#399C2314yes—
342#399C2314yes—
343#399C2314yes—
344#398C2314yes—
345#398C2312yes—
346#398C2312yes—
347#398C2312yes—
348#398C2312yes—
349#398C2314yes—
350#398C2314yes—
351#398C2314yes—
352#398C2312yes—
353#398C2312yes—
354#398C2314yes—
355#398C2312yes—
356#398C2312yes—
357#398C2312yes—
358#398C2314yes—
359#398C2314yes—
360#398C2314yes—
361#398C2314yes—
362#398C2312yes—
363#398C2312yes—
364#398C2312yes—
365#398C2314yes—
366#397C2314yes—
367#397C2314yes—
368#397C2314yes—
369#397C2314yes—
370#397C2314yes—
371#397C2314yes—
372#397C2314yes—
373#397C2314yes—
374#397C2314yes—
375#397C2314yes—
376#397C2314yes—
377#397C2314yes—
378#397C2314yes—
379#396C2314yes—
380#396C2314yes—
381#396C2314yes—
382#396C2314yes—
383#396C2314yes—
384#396C2314yes—
385#396C2314yes—
386#396C2314yes—
387#395C2312yes—
388#395C2312yes—
389#395C2312yes—
390#395C2312yes—
391#394C2314yes—
392#394C2314yes—
393#394C2314yes—
394#394C2314yes—
395#394C2314yes—
396#393C2314yes—
397#393C2314yes—
398#393C2314yes—
399#393C2314yes—
400#393C2314yes—
401#393C2314yes—
402#393C2314yes—
403#393C2314yes—
404#391C2312yes—
405#391C2314yes—
406#391C2312yes—
407#391C2312yes—
408#391C2314yes—
409#391C2312yes—
410#391C2314yes—
411#391C2312yes—
412#391C2312yes—
413#391C2314yes—
414#391C2312yes—
415#391C2312yes—
416#391C2314yes—
417#391C2312yes—
418#391C2314yes—
419#391C2314yes—
420#391C2314yes—
421#391C2312yes—
422#391C2312yes—
423#391C2312yes—
424#391C2312yes—
425#391C2312yes—
426#391C2312yes—
427#391C2314yes—
428#391C2314yes—
429#391C2312yes—
430#391C2312yes—
431#391C2312yes—
432#391C2314yes—
433#391C2314yes—
434#391C2311yescharacteristic
435#391C2312yes—
436#391C2311yescharacteristic
437#391C2312yes—
438#391C2312yes—
439#391C2311yescharacteristic
440#391C2311yescharacteristic
441#390C2312yes—
442#390C2312yes—
443#390C2312yes—
444#390C2312yes—
445#390C2312yes—
446#390C2312yes—
447#390C2312yes—
448#390C2312yes—
449#390C2312yes—
450#390C2312yes—
451#390C2312yes—
452#390C2312yes—
453#390C2312yes—
454#389C2311yescharacteristic
455#389C2312yes—
456#389C2312yes—
457#389C2312yes—
458#389C2312yes—
459#389C2311yescharacteristic
460#389C2312yes—
461#389C2312yes—
462#389C2311yescharacteristic
463#389C2314yes—
464#389C2312yes—
465#389C2311yescharacteristic
466#389C2312yes—
467#389C2314yes—
468#389C2312yes—
469#389C2312yes—
470#389C2314yes—
471#389C2314yes—
472#389C2314yes—
473#389C2314yes—
474#389C2312yes—
475#389C2314yes—
476#389C2312yes—
477#389C2314yes—
478#389C2312yes—
479#389C2314yes—
480#389C2312yes—
481#389C2314yes—
482#389C2314yes—
483#389C2312yes—
484#389C2314yes—
485#389C2314yes—
486#389C2312yes—
487#389C2311yescharacteristic
488#389C2311yescharacteristic
489#389C2312yes—
490#389C2312yes—
491#388C2314yes—
492#388C2314yes—
493#388C2314yes—
494#388C2314yes—
495#388C2314yes—
496#388C2314yes—
497#388C2314yes—
498#388C2314yes—
499#388C2314yes—
500#388C2314yes—
501#388C2314yes—
502#388C2314yes—
503#388C2314yes—
504#388C2314yes—
505#388C2314yes—
506#388C2314yes—
507#388C2314yes—
508#388C2314yes—
509#388C2314yes—
510#388C2314yes—
511#388C2314yes—
512#388C2314yes—
513#388C2314yes—
514#388C2314yes—
515#388C2314yes—
516#388C2314yes—
517#388C2314yes—
518#388C2314yes—
519#388C2314yes—
520#388C2314yes—
521#388C2314yes—
522#388C2314yes—
523#388C2314yes—
524#388C2314yes—
525#388C2314yes—
526#388C2314yes—
527#388C2314yes—
528#388C2314yes—
529#388C2314yes—
530#388C2314yes—
531#387C2312yes—
532#387C2312yes—
533#387C2314yes—
534#387C2314yes—
535#387C2314yes—
536#387C2314yes—
537#387C2314yes—
538#387C2314yes—
539#387C2312yes—
540#387C2314yes—
541#387C2312yes—
542#387C2312yes—
543#387C2312yes—
544#387C2314yes—
545#387C2314yes—
546#387C2314yes—
547#387C2314yes—
548#387C2312yes—
549#387C2314yes—
550#387C2314yes—
551#387C2314yes—
552#387C2314yes—
553#387C2314yes—
554#387C2314yes—
555#387C2314yes—
556#387C2314yes—
557#387C2314yes—
558#387C2314yes—
559#387C2314yes—
560#387C2314yes—
561#387C2314yes—
562#387C2314yes—
563#387C2314yes—
564#387C2314yes—
565#387C2314yes—
566#387C2314yes—
567#387C2314yes—
568#387C2314yes—
569#387C2314yes—
570#387C2314yes—
571#387C2312yes—
572#387C2314yes—
573#387C2314yes—
574#387C2314yes—
575#387C2314yes—
576#387C2314yes—
577#387C2314yes—
578#387C2314yes—
579#387C2312yes—
580#387C2314yes—
581#387C2314yes—
582#387C2314yes—
583#387C2312yes—
584#387C2314yes—
585#387C2314yes—
586#387C2314yes—
587#387C2314yes—
588#387C2312yes—
589#387C2314yes—
590#387C2312yes—
591#387C2312yes—
592#387C2312yes—
593#387C2314yes—
594#387C2312yes—
595#387C2312yes—
596#386C2314yes—
597#386C2314yes—
598#386C2314yes—
599#386C2314yes—
600#385C2314yes—
601#385C2314yes—
602#385C2314yes—
603#385C2314yes—
604#385C2314yes—
605#385C2314yes—
606#385C2314yes—
607#385C2314yes—
608#385C2314yes—
609#385C2314yes—
610#384C2311yescharacteristic
611#384C2311yescharacteristic
612#384C2312yes—
613#384C2311yescharacteristic
614#383C2314yes—
615#383C2314yes—
616#383C2314yes—
617#383C2314yes—
618#383C2314yes—
619#383C2314yes—
620#383C2314yes—
621#382C2312yes—
622#382C2312yes—
623#382C2312yes—
624#382C2312yes—
625#382C2312yes—
626#382C2314yes—
627#382C2314yes—
628#382C2314yes—
629#382C2314yes—
630#382C2312yes—
631#382C2314yes—
632#381C2314yes—
633#381C2314yes—
634#381C2314yes—
635#380C2314yes—
636#380C2314yes—
637C4×C4⋊C4C2312yes—
638C4×C4⋊C4C2314yes—
639C4×C4⋊C4C2314yes—
640C4×C4⋊C4C2314yes—
641C4×C4⋊C4C2314yes—
642C4×C4⋊C4C2314yes—
643C4×C4⋊C4C2312yes—
644C4×C4⋊C4C2311yescharacteristic
645C4×C4⋊C4C2312yes—
646C4×C4⋊C4C2314yes—
647C4×C4⋊C4C2312yes—
648C4×C4⋊C4C2312yes—
649C4×C4⋊C4C2314yes—
650C4×C4⋊C4C2312yes—
651C4×C4⋊C4C2312yes—
652C4×C4⋊C4C2312yes—
653C4×C4⋊C4C2312yes—
654C4×C4⋊C4C2312yes—
655C4×C4⋊C4C2312yes—
656C4×C4⋊C4C2312yes—
657C4×C4⋊C4C2314yes—
658C4×C4⋊C4C2312yes—
659C4×C4⋊C4C2312yes—
660C4×C4⋊C4C2312yes—
661C4×C4⋊C4C2311yescharacteristic
662C4×C4⋊C4C2312yes—
663C4×C4⋊C4C2312yes—
664C4×C4⋊C4C2314yes—
665C4×C4⋊C4C2311yescharacteristic
666C4×C4⋊C4C2312yes—
667C4×C4⋊C4C2314yes—
668C4×C4⋊C4C2314yes—
669C4×C4⋊C4C2314yes—
670C4×C4⋊C4C2314yes—
671C4×C4⋊C4C2314yes—
672C4×C4⋊C4C2311yescharacteristic
673C4×C4⋊C4C2312yes—
674C4×C4⋊C4C2312yes—
675C4×C4⋊C4C2312yes—
676C4×C4⋊C4C2312yes—
677C4×C4⋊C4C2312yes—
678C4×C4⋊C4C2311yescharacteristic
679C4×C4⋊C4C2314yes—
680C4×C4⋊C4C2311yescharacteristic
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2311yescharacteristic
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2314yes—
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2312yes—
689C4×C22⋊C4C2314yes—
690C4×C22⋊C4C2314yes—
691C4×C22⋊C4C2314yes—
692C4×C22⋊C4C2314yes—
693C4×C22⋊C4C2314yes—
694C4×C22⋊C4C2314yes—
695C4×C22⋊C4C2314yes—
696C4×C22⋊C4C2314yes—
697C4×C22⋊C4C2314yes—
698C4×C22⋊C4C2314yes—
699C4×C22⋊C4C2314yes—
700C4×C22⋊C4C2314yes—
701C4×C22⋊C4C2314yes—
702C4×C22⋊C4C2314yes—
703#376C2312yes—
704#376C2312yes—
705#376C2312yes—
706#376C2314yes—
707#376C2314yes—
708#376C2314yes—
709#376C2314yes—
710#376C2314yes—
711C2×#95C2314yes—
712C43C2314yes—
713C43C2312yes—
714C43C2312yes—
715C43C2311yescharacteristic
716C22×Q8C2412yes—
717C22×Q8C2412yes—
718C22×Q8C2411yescharacteristic
719C22×Q8C2411yescharacteristic
720C22×Q8C2412yes—
721C22×Q8C2412yes—
722C22×Q8C2414yes—
723C22×Q8C2411yescharacteristic
724C22×D4C2412yes—
725C22×D4C2412yes—
726C22×D4C2412yes—
727C23×C4C2414yes—
728C23×C4C2414yes—
729C23×C4C2414yes—
730C4⋊Q8—28no—
731C4⋊Q8—28no—
732C4⋊Q8—216no—
733C4⋊Q8—28no—
734C4⋊Q8—28no—
735C4⋊Q8—24no—
736C4⋊Q8—28no—
737C4⋊Q8—24no—
738C4⋊Q8—42no—
739C4⋊Q8—44no—
740C4⋊Q8—42no—
741#127—42no—
742#126—216no—
743#126—216no—
744#126—216no—
745#126—216no—
746#125—216no—
747#125—28no—
748#125—44no—
749#124—28no—
750#124—28no—
751#124—28no—
752#124—28no—
753#124—44no—
754#123—48no—
755C22⋊Q8—216no—
756C22⋊Q8—216no—
757C4×Q8—28no—
758C4×Q8—28no—
759C4×Q8—28no—
760C4×Q8—28no—
761C4×Q8—28no—
762C4×Q8—28no—
763C4×Q8—28no—
764C4×Q8—24no—
765C4×Q8—28no—
766C4×Q8—24no—
767C4×Q8—48no—
768C4×Q8—44no—
769C4×Q8—44no—
770C4×Q8—44no—
771C4×Q8—44no—
772C4×Q8—42no—
773C4×Q8#4118yes—
774C4×Q8#4118yes—
775C4×D4—28no—
776C4×D4—28no—
777C4×D4—44no—
778C4×D4—44no—
779#117—216no—
780#117—216no—
781C2×C4⋊C4C2412yes—
782C2×C4⋊C4C2414yes—
783C2×C4⋊C4C2414yes—
784C2×C4⋊C4C2411yescharacteristic
785C2×C4⋊C4C2412yes—
786C2×C4⋊C4C2412yes—
787C2×C4⋊C4C2411yescharacteristic
788C2×C4⋊C4C2414yes—
789C2×C4⋊C4C2412yes—
790C2×C4⋊C4C2414yes—
791C2×C4⋊C4C2414yes—
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2414yes—
794C2×C4⋊C4C2411yescharacteristic
795C2×C4⋊C4C2412yes—
796C2×C4⋊C4C2412yes—
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2412yes—
799C2×C4⋊C4C2412yes—
800C2×C4⋊C4C2411yescharacteristic
801C2×C4⋊C4C2412yes—
802C2×C4⋊C4C2412yes—
803C2×C4⋊C4C2414yes—
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2414yes—
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2411yescharacteristic
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2414yes—
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2414yes—
815C2×C4⋊C4C2414yes—
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2412yes—
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2414yes—
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2411yescharacteristic
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2411yescharacteristic
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2411yescharacteristic
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2411yescharacteristic
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2411yescharacteristic
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2411yescharacteristic
842C2×C4⋊C4C2412yes—
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2412yes—
845C2×C4⋊C4C2412yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2412yes—
849C2×C4⋊C4C2411yescharacteristic
850C2×C4⋊C4C2412yes—
851C2×C4⋊C4C2411yescharacteristic
852C2×C22⋊C4C2414yes—
853C2×C22⋊C4C2414yes—
854C2×C22⋊C4C2414yes—
855C2×C22⋊C4C2414yes—
856C2×C22⋊C4C2414yes—
857C2×C22⋊C4C2414yes—
858C2×C22⋊C4C2414yes—
859C2×C22⋊C4C2414yes—
860C2×C22⋊C4C2414yes—
861C2×C22⋊C4C2414yes—
862C2×C22⋊C4C2414yes—
863C2×C22⋊C4C2414yes—
864C2×C22⋊C4C2414yes—
865C2×C22⋊C4C2414yes—
866C2×C22⋊C4C2414yes—
867C2×C22⋊C4C2414yes—
868C2×C22⋊C4C2414yes—
869C2×C22⋊C4C2414yes—
870C2×C22⋊C4C2414yes—
871C2×C22⋊C4C2414yes—
872C2×C22⋊C4C2414yes—
873C2×C22⋊C4C2414yes—
874C2×C22⋊C4C2414yes—
875C2×C22⋊C4C2414yes—
876C2×C22⋊C4C2414yes—
877C2×C42C2414yes—
878C2×C42C2414yes—
879C2×C42C2414yes—
880C2×C42C2412yes—
881C2×C42C2412yes—
882C2×C42C2412yes—
883C2×C42C2412yes—
884C2×C42C2414yes—
885C2×C42C2411yescharacteristic
886C2×C42C2412yes—
887C2×C42C2414yes—
888C2×C42C2412yes—
889C2×C42C2412yes—
890C2×C42C2411yescharacteristic
891C2×C42C2414yes—
892C2×C42C2414yes—
893C2×C42C2412yes—
894C2×C42C2414yes—
895C2×C42C2414yes—
896C2×C42C2414yes—
897C2×C42C2414yes—
898C2×C42C2412yes—
899C2×C42C2412yes—
900C2×C42C2411yescharacteristic
901C2×C42C2414yes—
902C2×C42C2412yes—
903C2×C42C2412yes—
904C2×C42C2414yes—
905C2×C42C2412yes—
906C2×C42C2412yes—
907C2×C42C2411yescharacteristic
908C2×C42C2411yescharacteristic
909C2×C42C2414yes—
910C2×C42C2414yes—
911C2×C42C2412yes—
912C2×C42C2412yes—
913C2×C42C2411yescharacteristic
914C2×C42C2411yescharacteristic
915#95C2412yes—
916#95C2414yes—
917#95C2414yes—
918#95C2414yes—
919#95C2412yes—
920#95C2412yes—
921#95C2412yes—
922#95C2412yes—
923#95C2412yes—
924#95C2412yes—
925#95C2412yes—
926#95C2412yes—
927#95C2412yes—
928#95C2414yes—
929#95C2414yes—
930#95C2414yes—
931#95C2414yes—
932#95C2412yes—
933#95C2412yes—
934#95C2414yes—
935#95C2414yes—
936#95C2412yes—
937#95C2412yes—
938#95C2412yes—
939#95C2412yes—
940#95C2414yes—
941#95C2414yes—
942#95C2414yes—
943#95C2414yes—
944#95C2414yes—
945#95C2414yes—
946#95C2414yes—
947#95C2412yes—
948#95C2414yes—
949#95C2412yes—
950#95C2412yes—
951#95C2412yes—
952#95C2412yes—
953#95C2412yes—
954#95C2412yes—
955#95C2414yes—
956#95C2414yes—
957#95C2414yes—
958#95C2414yes—
959#95C2414yes—
960#95C2414yes—
961#95C2414yes—
962#95C2414yes—
963#95C2414yes—
964#95C2414yes—
965#95C2412yes—
966#95C2412yes—
967#95C2412yes—
968#95C2414yes—
969#95C2414yes—
970#95C2412yes—
971#95C2412yes—
972#95C2414yes—
973#95C2414yes—
974#95C2414yes—
975#95C2412yes—
976#95C2412yes—
977#95C2414yes—
978#95C2412yes—
979#95C2414yes—
980#95C2414yes—
981#95C2414yes—
982#95C2412yes—
983#95C2414yes—
984#95C2414yes—
985#95C2412yes—
986#95C2412yes—
987#95C2412yes—
988#95C2414yes—
989#95C2412yes—
990#95C2412yes—
991#95C2414yes—
992#95C2414yes—
993#95C2414yes—
994#95C2414yes—
995#95C2414yes—
996C24C2514yes—
997C2×Q8—22no—
998C2×Q8—22no—
999C2×Q8—24no—
1000C2×Q8—24no—
1001C2×Q8—24no—
1002C2×Q8—24no—
1003C2×Q8—24no—
1004C2×Q8—24no—
1005C2×Q8—28no—
1006C2×Q8—22no—
1007C2×Q8—24no—
1008C2×Q8—24no—
1009C2×Q8—41no—
1010C2×Q8—41no—
1011C2×Q8—41no—
1012C2×Q8—41no—
1013C2×Q8—42no—
1014C2×Q8—44no—
1015C2×Q8—42no—
1016C2×Q8—42no—
1017C2×Q8—44no—
1018C2×Q8—42no—
1019C2×Q8C2×#4114yes—
1020C2×Q8C2×#4114yes—
1021C2×D4—24no—
1022C2×D4—24no—
1023C2×D4—24no—
1024C2×D4—24no—
1025C2×D4—42no—
1026C2×D4—42no—
1027C2×D4—42no—
1028C2×D4—42no—
1029C2×D4—42no—
1030C22×C4—28no—
1031C22×C4—28no—
1032C22×C4—44no—
1033C22×C4—44no—
1034C22×C4—44no—
1035C22×C4—44no—
1036C22×C4—44no—
1037C22×C4—44no—
1038C22×C4—44no—
1039C22×C4C2511yescharacteristic
1040C22×C4C2512yes—
1041C22×C4C2514yes—
1042C22×C4C2512yes—
1043C22×C4C2512yes—
1044C22×C4C2512yes—
1045C22×C4C2514yes—
1046C22×C4C2512yes—
1047C22×C4C2512yes—
1048C22×C4C2512yes—
1049C22×C4C2514yes—
1050C22×C4C2512yes—
1051C22×C4C2512yes—
1052C22×C4C2512yes—
1053C22×C4C2512yes—
1054C22×C4C2512yes—
1055C22×C4C2514yes—
1056C22×C4C2514yes—
1057C22×C4C2512yes—
1058C22×C4C2512yes—
1059C22×C4C2511yescharacteristic
1060C22×C4C2511yescharacteristic
1061C22×C4C2511yescharacteristic
1062C22×C4C2511yescharacteristic
1063C22×C4C2512yes—
1064C22×C4C2512yes—
1065C22×C4C2511yescharacteristic
1066C22×C4C2511yescharacteristic
1067C4⋊C4—24no—
1068C4⋊C4—28no—
1069C4⋊C4—28no—
1070C4⋊C4—24no—
1071C4⋊C4—28no—
1072C4⋊C4—28no—
1073C4⋊C4—28no—
1074C4⋊C4—24no—
1075C4⋊C4—22no—
1076C4⋊C4—28no—
1077C4⋊C4—28no—
1078C4⋊C4—24no—
1079C4⋊C4—24no—
1080C4⋊C4—24no—
1081C4⋊C4—24no—
1082C4⋊C4—28no—
1083C4⋊C4—24no—
1084C4⋊C4—28no—
1085C4⋊C4—22no—
1086C4⋊C4—24no—
1087C4⋊C4—28no—
1088C4⋊C4—24no—
1089C4⋊C4—28no—
1090C4⋊C4—28no—
1091C4⋊C4—22no—
1092C4⋊C4—24no—
1093C4⋊C4—22no—
1094C4⋊C4—28no—
1095C4⋊C4—24no—
1096C4⋊C4—24no—
1097C4⋊C4—22no—
1098C4⋊C4—41no—
1099C4⋊C4—41no—
1100C4⋊C4—42no—
1101C4⋊C4—42no—
1102C4⋊C4—41no—
1103C4⋊C4—41no—
1104C4⋊C4—41no—
1105C4⋊C4—41no—
1106C4⋊C4—42no—
1107C4⋊C4—42no—
1108C4⋊C4—42no—
1109C4⋊C4—42no—
1110C4⋊C4—42no—
1111C4⋊C4—42no—
1112C4⋊C4—42no—
1113C4⋊C4—42no—
1114C4⋊C4—42no—
1115C4⋊C4—42no—
1116C4⋊C4—42no—
1117C4⋊C4—42no—
1118C4⋊C4—44no—
1119C4⋊C4—42no—
1120C4⋊C4—42no—
1121C4⋊C4—44no—
1122C4⋊C4—42no—
1123C4⋊C4—44no—
1124C4⋊C4—44no—
1125C4⋊C4—44no—
1126C4⋊C4—42no—
1127C4⋊C4—42no—
1128C4⋊C4—42no—
1129C4⋊C4—42no—
1130C4⋊C4—42no—
1131C4⋊C4—44no—
1132C4⋊C4—44no—
1133C4⋊C4—42no—
1134C4⋊C4C2×#4118yes—
1135C4⋊C4C2×#4114yes—
1136C4⋊C4C2×#4118yes—
1137C4⋊C4C2×#4114yes—
1138C22⋊C4—28no—
1139C22⋊C4—28no—
1140C22⋊C4—28no—
1141C22⋊C4—28no—
1142C22⋊C4—28no—
1143C22⋊C4—28no—
1144C22⋊C4—28no—
1145C22⋊C4—28no—
1146C22⋊C4—28no—
1147C22⋊C4—28no—
1148C22⋊C4—44no—
1149C22⋊C4—44no—
1150C22⋊C4—44no—
1151C22⋊C4—44no—
1152C22⋊C4—44no—
1153C22⋊C4—44no—
1154C22⋊C4—44no—
1155C22⋊C4—44no—
1156C22⋊C4—44no—
1157C22⋊C4—44no—
1158C22⋊C4—44no—
1159C22⋊C4—44no—
1160C22⋊C4—44no—
1161C22⋊C4—44no—
1162C22⋊C4—44no—
1163C42—28no—
1164C42—28no—
1165C42—28no—
1166C42—24no—
1167C42—24no—
1168C42—28no—
1169C42—24no—
1170C42—28no—
1171C42—24no—
1172C42—24no—
1173C42—24no—
1174C42—22no—
1175C42—24no—
1176C42—22no—
1177C42—42no—
1178C42—41no—
1179C42—41no—
1180C42—42no—
1181C42—44no—
1182C42—41no—
1183C42—42no—
1184C42—42no—
1185C42—42no—
1186C42—44no—
1187C42—44no—
1188C42—44no—
1189C42—44no—
1190C42—44no—
1191C42—44no—
1192C42—42no—
1193C42—44no—
1194C42—44no—
1195C42—44no—
1196C42—42no—
1197C42C2×#4118yes—
1198C42C2×#4118yes—
1199C42C2×#4114yes—
1200C42C2×#4114yes—
1201C23—24no—
1202C23—24no—
1203C23—24no—
1204C23—24no—
1205C23—24no—
1206C23—24no—
1207C23—24no—
1208C23C2611yescharacteristic
1209Q8—28no—
1210Q8—44no—
1211Q8—44no—
1212Q8—48no—
1213Q8—48no—
1214Q8—84no—
1215Q8—88no—
1216Q8—84no—
1217D4—48no—
1218D4—84no—
1219D4—162no—
1220C2×C4—22no—
1221C2×C4—22no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—21no—
1225C2×C4—22no—
1226C2×C4—22no—
1227C2×C4—21no—
1228C2×C4—21no—
1229C2×C4—22no—
1230C2×C4—21no—
1231C2×C4—21no—
1232C2×C4—21no—
1233C2×C4—21no—
1234C2×C4—22no—
1235C2×C4—21no—
1236C2×C4—22no—
1237C2×C4—22no—
1238C2×C4—22no—
1239C2×C4—22no—
1240C2×C4—24no—
1241C2×C4—22no—
1242C2×C4—22no—
1243C2×C4—24no—
1244C2×C4—24no—
1245C2×C4—24no—
1246C2×C4—22no—
1247C2×C4—24no—
1248C2×C4—22no—
1249C2×C4—24no—
1250C2×C4—22no—
1251C2×C4—22no—
1252C2×C4—22no—
1253C2×C4—22no—
1254C2×C4—22no—
1255C2×C4—22no—
1256C2×C4—21no—
1257C2×C4—22no—
1258C2×C4—24no—
1259C2×C4—24no—
1260C2×C4—24no—
1261C2×C4—22no—
1262C2×C4—22no—
1263C2×C4—24no—
1264C2×C4—22no—
1265C2×C4—24no—
1266C2×C4—22no—
1267C2×C4—22no—
1268C2×C4—22no—
1269C2×C4—22no—
1270C2×C4—22no—
1271C2×C4—24no—
1272C2×C4—24no—
1273C2×C4—24no—
1274C2×C4—22no—
1275C2×C4—22no—
1276C2×C4—22no—
1277C2×C4—22no—
1278C2×C4—22no—
1279C2×C4—22no—
1280C2×C4—22no—
1281C2×C4—22no—
1282C2×C4—21no—
1283C2×C4—21no—
1284C2×C4—22no—
1285C2×C4—22no—
1286C2×C4—22no—
1287C2×C4—22no—
1288C2×C4—22no—
1289C2×C4—24no—
1290C2×C4—22no—
1291C2×C4—22no—
1292C2×C4—88no—
1293C2×C4—88no—
1294C2×C4—164no—
1295C2×C4C22×#4112yes—
1296C2×C4C22×#4114yes—
1297C2×C4C22×#4112yes—
1298C2×C4C22×#4114yes—
1299C2×C4C22×#4114yes—
1300C2×C4C22×#4112yes—
1301C2×C4C22×#4114yes—
1302C2×C4C22×#4112yes—
1303C2×C4C22×#4112yes—
1304C2×C4C22×#4112yes—
1305C2×C4#58512yes—
1306C2×C4#58512yes—
1307C22—44no—
1308C22—44no—
1309C22—44no—
1310C22—44no—
1311C22—44no—
1312C22—44no—
1313C22—44no—
1314C22C23×#4111yescharacteristic
1315C22C23×#4111yescharacteristic
1316C22C2×#58511yescharacteristic
1317C22C2×#58511yescharacteristic
1318C222−1+611yescharacteristic
1319C222−1+611yescharacteristic
1320C222−1+611yescharacteristic
1321C4—22no—
1322C4—24no—
1323C4—24no—
1324C4—22no—
1325C4—22no—
1326C4—24no—
1327C4—22no—
1328C4—22no—
1329C4—24no—
1330C4—42no—
1331C4—44no—
1332C4—42no—
1333C4—42no—
1334C4—42no—
1335C4—42no—
1336C4—42no—
1337C4—42no—
1338C4—41no—
1339C4—42no—
1340C4—42no—
1341C4—42no—
1342C4—44no—
1343C4—42no—
1344C4—44no—
1345C4—42no—
1346C4—44no—
1347C4—44no—
1348C4#348014yes—
1349C2—84no—
1350C2C2×#348011yescharacteristic
1351C2#6285011yescharacteristic
1352C2#6286011yescharacteristic
1353C2#6296411yescharacteristic
1354C2#6299511yescharacteristic
1355C2#6300911yescharacteristic
1356C2#6306211yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#127C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59879C2semidirect
2. #59875C2semidirect
3. #59788C2semidirect
5. #52274C2semidirect
6. #52272C2semidirect
7. #45344C2semidirect
8. #45163C2semidirect
9. #45156C2semidirect
10. #44752C2semidirect
11. #44389C2semidirect
12. #43718C2semidirect
13. #39829C2semidirect
14. #39811C2semidirect
17. #39329C2semidirect
18. #39172C2semidirect
19. #38667C2semidirect
20. #38492C2semidirect
21. #36313C2semidirect
23. #35974C2semidirect
25. #35938C2semidirect
26. #34335C2semidirect
27. #34328C2semidirect
28. #34326C2semidirect
29. #34326C2semidirect

Maximal subgroups

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

subgroupindex
#598792
#598752
#597882
#596842
#522742
#522722
#453442
#451632
#451562
#447522
#443892
#437182
#398292
#398112
#397652
#397402
#393292
#391722
#386672
#384922
#363132
#362712
#359742
#359702
#359382
#343352
#343282
#343262