Finite Group Databasebeta

← #7695639

Subgroups — #7695639

Order 512.

4779 conjugacy classes of subgroups.

The subgroup lattice has 1440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59886C212yesmaximal, complemented
2#59864C211yesmaximal, characteristic, complemented
3#59457C212yesmaximal, complemented
4#59452C214yesmaximal, complemented
5#52288C212yesmaximal, complemented
6#52287C211yesmaximal, characteristic, complemented
7#45362C212yesmaximal, complemented
8#44947C212yesmaximal, complemented
9#44947C212yesmaximal, complemented
10#43567C214yesmaximal, complemented
11#43144C214yesmaximal, complemented
12#43140C214yesmaximal, complemented
13#39750C212yesmaximal, complemented
14#39749C211yesmaximal, characteristic, complemented
15#39708C212yesmaximal, complemented
16#39696C214yesmaximal, complemented
17#39618C212yesmaximal, complemented
18#39611C211yesmaximal, characteristic, complemented
19#38448C214yesmaximal, complemented
20#38444C212yesmaximal, complemented
21#36477C211yesmaximal, characteristic, complemented
22#36476C212yesmaximal, complemented
23#35952C212yesmaximal, complemented
24#35952C212yesmaximal, complemented
25#35934C212yesmaximal, complemented
26#34334C211yesmaximal, characteristic, complemented
27#34333C212yesmaximal, complemented
28#34330C212yesmaximal
29#34330C211yesmaximal, characteristic
30C2×#554C2212yes—
31C2×#550C2211yescharacteristic
32C2×D4×Q8C2211yescharacteristic
33#2862C2212yes—
34#2859C2211yescharacteristic
35#2855C2214yes—
36#2855C2212yes—
37#2811C2211yescharacteristic
38#2809C2212yes—
39#2806C2212yes—
40#2806C2212yes—
41#2806C2211yescharacteristic
42#2806C2212yes—
43#2806C2211yescharacteristic
44#2805C2212yes—
45#2804C2212yes—
46#2804C2212yes—
47#2799C2214yes—
48#2799C2214yes—
49#2792C2212yes—
50#2792C2212yes—
51#2792C2212yes—
52#2784C2214yes—
53#2784C2214yes—
54#2780C2214yes—
55#2780C2214yes—
56#2780C2214yes—
57#2780C2214yes—
58#2755C2214yes—
59#2755C2214yes—
60#2748C2214yes—
61#2748C2214yes—
62#2748C2214yes—
63#2748C2214yes—
64#2734C2211yescharacteristic
65#2734C2212yes—
66#2732C2212yes—
67#2732C2212yes—
68#2726C2212yes—
69#2692C2214yes—
70#2692C2214yes—
71#2692C2214yes—
72#2692C2214yes—
73#2692C2214yes—
74#2692C2214yes—
75#2692C2214yes—
76#2692C2214yes—
77#2683C2212yes—
78#2683C2212yes—
79#2667C2214yes—
80#2665C2214yes—
81#2665C2214yes—
82#2660C2212yes—
83#2660C2212yes—
84#2660C2212yes—
85#2608C2214yes—
86#2607C2214yes—
87#2607C2214yes—
88#2590C2214yes—
89#2589C2214yes—
90#2589C2214yes—
91#2588C2214yes—
92#2588C2214yes—
93#2587C2214yes—
94#2580C2214yes—
95#2580C2212yes—
96#2580C2212yes—
97#2580C2212yes—
98#2580C2212yes—
99#2580C2212yes—
100#2579C2214yes—
101#2579C2214yes—
102#2574C2214yes—
103#2574C2214yes—
104#2574C2214yes—
105#2574C2214yes—
106#2571C2212yes—
107#2571C2212yes—
108#2570C2212yes—
109#2570C2212yes—
110#2570C2212yes—
111#2570C2212yes—
112#2570C2212yes—
113#2570C2212yes—
114#2569C2214yes—
115#2569C2214yes—
116#2566C2214yes—
117#2566C2212yes—
118#2566C2212yes—
119#2566C2212yes—
120#2566C2212yes—
121#2564C2214yes—
122#2564C2214yes—
123#2564C2214yes—
124#2564C2214yes—
125#2563C2212yes—
126#2563C2212yes—
127#2563C2212yes—
128#2563C2212yes—
129#2556C2214yes—
130#2556C2214yes—
131#2552C2212yes—
132#2549C2214yes—
133#2542C2212yes—
134#2542C2212yes—
135#2538C2212yes—
136#2538C2212yes—
137#2538C2211yescharacteristic
138#2538C2212yes—
139#2538C2211yescharacteristic
140#2522C2214yes—
141#2522C2214yes—
142#2522C2214yes—
143#2520C2214yes—
144#2520C2214yes—
145#2497C2212yes—
146#2492C2214yes—
147#2487C2214yes—
148#2465C2214yes—
149#2465C2214yes—
150#2465C2214yes—
151#2462C2214yes—
152#2454C2214yes—
153#2452C2214yes—
154#2450C2214yes—
155#2450C2214yes—
156#2450C2214yes—
157#2450C2214yes—
158#2450C2214yes—
159#2450C2214yes—
160#2449C2214yes—
161#2449C2214yes—
162#2449C2214yes—
163#2449C2214yes—
164#2438C2214yes—
165#2438C2214yes—
166#2438C2214yes—
167#2429C2212yes—
168#2423C2214yes—
169#2417C2214yes—
170#2417C2214yes—
171#2409C2214yes—
172#2409C2214yes—
173#2399C2212yes—
174#2399C2212yes—
175#2399C2212yes—
176#2396C2214yes—
177#2396C2214yes—
178#2396C2214yes—
179#2370C2212yes—
180#2370C2212yes—
181#2369C2212yes—
182#2368C2214yes—
183#2368C2214yes—
184#2368C2214yes—
185#2366C2212yes—
186#2366C2212yes—
187#2366C2212yes—
188#2366C2211yescharacteristic
189#2366C2212yes—
190#2365C2212yes—
191#2365C2211yescharacteristic
192#2364C2214yes—
193#2364C2214yes—
194#2364C2214yes—
195#2363C2214yes—
196#2363C2212yes—
197#2360C2212yes—
198#2360C2214yes—
199#2357C2212yes—
200#2357C2212yes—
201#2357C2212yes—
202#2355C2212yes—
203#2355C2211yescharacteristic
204#2355C2211yescharacteristic
205#2355C2212yes—
206#2355C2212yes—
207#2355C2211yescharacteristic
208#2354C2212yes—
209#2354C2211yescharacteristic
210Q8×C4⋊C4C2211yescharacteristic
211#2349C2212yes—
212#2349C2212yes—
213#2349C2212yes—
214#2349C2214yes—
215D4×C4⋊C4C2212yes—
216D4×C4⋊C4C2211yescharacteristic
217D4×C4⋊C4C2212yes—
218#2345C2214yes—
219Q8×C22⋊C4C2212yes—
220#2339C2214yes—
221#2339C2212yes—
222#2333C2214yes—
223#2333C2214yes—
224#2333C2214yes—
225#2331C2212yes—
226#2331C2212yes—
227#2330C2212yes—
228#2329C2214yes—
229#2329C2214yes—
230#2329C2214yes—
231#2328C2212yes—
232#2328C2212yes—
233#2328C2212yes—
234C4×C4⋊Q8C2211yescharacteristic
235C4×C4⋊Q8C2212yes—
236C4×C4⋊Q8C2211yescharacteristic
237C4×#127C2212yes—
238C4×#127C2211yescharacteristic
239C4×#125C2212yes—
240C4×C22⋊Q8C2214yes—
241C4×C22⋊Q8C2212yes—
242C4×C22⋊Q8C2214yes—
243C4×C22⋊Q8C2212yes—
244C4×#121C2214yes—
245C4×#121C2212yes—
246#2297C2212yes—
247#2297C2214yes—
248#2295C2211yescharacteristic
249#2295C2212yes—
250#2295C2212yes—
251#2295C2211yescharacteristic
252C2×#391C2212yes—
253C2×#387C2214yes—
254#2275C2212yes—
255#2275C2212yes—
256#2275C2212yes—
257C42×D4C2212yes—
258C42×D4C2211yescharacteristic
259C22×#41C2312yes—
260C23×Q8C2312yes—
261#554—216no—
262#550Q8116yescomplemented
263D4×Q8—28no—
264C2×C4⋊Q8C2311yescharacteristic
265C2×C4⋊Q8C2312yes—
266C2×C4⋊Q8C2312yes—
267C2×C4⋊Q8C2311yescharacteristic
268C2×C4⋊Q8C2312yes—
269C2×#127C2312yes—
270C2×#127C2311yescharacteristic
271C2×#125C2312yes—
272C2×#125C2312yes—
273C2×#125C2314yes—
274C2×C22⋊Q8C2314yes—
275C2×C22⋊Q8C2314yes—
276C2×C22⋊Q8C2314yes—
277C2×C22⋊Q8C2312yes—
278C2×C22⋊Q8C2314yes—
279C2×C22⋊Q8C2312yes—
280C2×C22⋊Q8C2314yes—
281C2×C22⋊Q8C2314yes—
282C2×C22⋊Q8C2314yes—
283C2×C22⋊Q8C2314yes—
284C2×C22⋊Q8C2314yes—
285C2×C22⋊Q8C2312yes—
286C2×C22⋊Q8C2314yes—
287C2×C22⋊Q8C2314yes—
288C2×#121C2314yes—
289C2×#121C2312yes—
290C2×C4×Q8C2311yescharacteristic
291C2×C4×Q8C2311yescharacteristic
292C2×C4×Q8C2312yes—
293C2×C4×Q8C2312yes—
294C2×C4×Q8C2312yes—
295C2×C4×Q8C2312yes—
296C2×C4×Q8C2312yes—
297C2×C4×Q8C2314yes—
298C2×C4×Q8C2311yescharacteristic
299C2×C4×Q8C2311yescharacteristic
300C2×C4×D4C2312yes—
301C2×C4×D4C2312yes—
302C2×C4×D4C2312yes—
303C2×C4×D4C2312yes—
304C2×C4×D4C2311yescharacteristic
305C2×C4×D4C2312yes—
306C2×C4×D4C2314yes—
307C2×C4×D4C2312yes—
308C2×C4×D4C2312yes—
309C2×C4×D4C2312yes—
310C2×C4×D4C2312yes—
311C2×C4×D4C2311yescharacteristic
312C2×C4×D4C2314yes—
313C2×C4×D4C2312yes—
314C2×C4×D4C2314yes—
315C2×C4×D4C2312yes—
316C2×C4×D4C2314yes—
317C2×C4×D4C2314yes—
318C2×C4×D4C2314yes—
319C2×C4×D4C2311yescharacteristic
320C2×C4×D4C2312yes—
321C2×#117C2314yes—
322C2×#117C2312yes—
323C22×C4⋊C4C2314yes—
324C22×C4⋊C4C2312yes—
325C22×C4⋊C4C2314yes—
326C22×C42C2314yes—
327C22×C42C2312yes—
328#400C2314yes—
329#400C2314yes—
330#400C2314yes—
331#400C2314yes—
332#400C2314yes—
333#400C2314yes—
334#400C2314yes—
335#400C2314yes—
336#400C2314yes—
337#400C2314yes—
338#399C2314yes—
339#399C2314yes—
340#399C2314yes—
341#399C2314yes—
342#399C2314yes—
343#399C2314yes—
344#399C2314yes—
345#399C2314yes—
346#399C2314yes—
347#398C2312yes—
348#398C2312yes—
349#398C2314yes—
350#398C2314yes—
351#398C2314yes—
352#398C2314yes—
353#398C2314yes—
354#398C2314yes—
355#398C2314yes—
356#398C2314yes—
357#398C2312yes—
358#398C2312yes—
359#398C2314yes—
360#398C2314yes—
361#398C2314yes—
362#398C2314yes—
363#398C2312yes—
364#398C2312yes—
365#398C2314yes—
366#398C2312yes—
367#398C2312yes—
368#398C2312yes—
369#398C2312yes—
370#398C2312yes—
371#398C2312yes—
372#398C2314yes—
373#396C2314yes—
374#396C2314yes—
375#396C2314yes—
376#396C2314yes—
377#396C2314yes—
378#396C2314yes—
379#396C2314yes—
380#396C2314yes—
381#396C2314yes—
382#396C2314yes—
383#396C2314yes—
384#396C2314yes—
385#396C2314yes—
386#396C2314yes—
387#396C2314yes—
388#396C2314yes—
389#395C2312yes—
390#395C2312yes—
391#395C2312yes—
392#395C2312yes—
393#395C2312yes—
394#395C2312yes—
395#395C2314yes—
396#395C2314yes—
397#395C2314yes—
398#395C2314yes—
399#395C2312yes—
400#395C2314yes—
401#395C2312yes—
402#395C2312yes—
403#395C2312yes—
404#395C2312yes—
405#395C2312yes—
406#395C2314yes—
407#393C2314yes—
408#393C2314yes—
409#393C2314yes—
410#393C2314yes—
411#393C2314yes—
412#393C2314yes—
413#393C2314yes—
414#393C2314yes—
415#393C2314yes—
416#393C2314yes—
417#393C2314yes—
418#391C2311yescharacteristic
419#391C2312yes—
420#391C2312yes—
421#391C2312yes—
422#391C2311yescharacteristic
423#391C2312yes—
424#391C2314yes—
425#391C2314yes—
426#391C2314yes—
427#391C2312yes—
428#391C2312yes—
429#391C2314yes—
430#391C2314yes—
431#391C2314yes—
432#391C2314yes—
433#391C2314yes—
434#391C2314yes—
435#391C2314yes—
436#391C2314yes—
437#391C2312yes—
438#391C2311yescharacteristic
439#391C2312yes—
440#391C2314yes—
441#391C2311yescharacteristic
442#391C2314yes—
443#391C2312yes—
444#391C2314yes—
445#391C2312yes—
446#391C2311yescharacteristic
447#391C2312yes—
448#391C2311yescharacteristic
449#390C2312yes—
450#390C2312yes—
451#390C2312yes—
452#390C2314yes—
453#390C2312yes—
454#390C2312yes—
455#390C2314yes—
456#390C2312yes—
457#390C2312yes—
458#390C2312yes—
459#390C2312yes—
460#390C2314yes—
461#390C2312yes—
462#390C2312yes—
463#390C2314yes—
464#390C2314yes—
465#390C2312yes—
466#390C2314yes—
467#389C2312yes—
468#389C2312yes—
469#389C2312yes—
470#389C2312yes—
471#389C2312yes—
472#389C2312yes—
473#389C2312yes—
474#389C2312yes—
475#389C2312yes—
476#389C2312yes—
477#389C2312yes—
478#389C2312yes—
479#389C2312yes—
480#389C2312yes—
481#389C2312yes—
482#389C2312yes—
483#389C2314yes—
484#389C2314yes—
485#389C2312yes—
486#389C2314yes—
487#389C2314yes—
488#389C2314yes—
489#389C2314yes—
490#389C2314yes—
491#389C2312yes—
492#389C2314yes—
493#389C2312yes—
494#389C2314yes—
495#389C2312yes—
496#389C2312yes—
497#389C2312yes—
498#389C2312yes—
499#389C2311yescharacteristic
500#389C2311yescharacteristic
501#389C2312yes—
502#389C2311yescharacteristic
503#389C2311yescharacteristic
504#389C2312yes—
505#388C2314yes—
506#388C2314yes—
507#388C2314yes—
508#388C2314yes—
509#388C2314yes—
510#388C2314yes—
511#388C2314yes—
512#388C2314yes—
513#388C2314yes—
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#387C2314yes—
534#387C2314yes—
535#387C2314yes—
536#387C2314yes—
537#387C2314yes—
538#387C2314yes—
539#387C2314yes—
540#387C2314yes—
541#387C2314yes—
542#387C2314yes—
543#387C2314yes—
544#387C2312yes—
545#387C2314yes—
546#387C2314yes—
547#387C2312yes—
548#387C2312yes—
549#387C2314yes—
550#387C2314yes—
551#387C2312yes—
552#387C2312yes—
553#387C2314yes—
554#387C2312yes—
555#387C2312yes—
556#387C2312yes—
557#387C2312yes—
558#387C2312yes—
559#387C2314yes—
560#387C2312yes—
561#387C2312yes—
562#386C2314yes—
563#386C2314yes—
564#386C2314yes—
565#386C2314yes—
566#386C2314yes—
567#386C2314yes—
568#386C2314yes—
569#386C2314yes—
570#386C2314yes—
571#386C2314yes—
572#386C2314yes—
573#386C2314yes—
574#386C2314yes—
575#386C2314yes—
576#386C2314yes—
577#386C2314yes—
578#386C2314yes—
579#386C2314yes—
580#386C2314yes—
581#386C2314yes—
582#386C2314yes—
583#385C2314yes—
584#385C2314yes—
585#385C2314yes—
586#385C2314yes—
587#385C2314yes—
588#385C2314yes—
589#385C2314yes—
590#385C2314yes—
591#385C2314yes—
592#385C2314yes—
593#385C2314yes—
594#385C2314yes—
595#385C2314yes—
596#385C2314yes—
597#385C2314yes—
598#385C2314yes—
599#385C2314yes—
600#385C2314yes—
601#385C2314yes—
602#385C2314yes—
603#385C2314yes—
604#385C2314yes—
605#385C2314yes—
606#385C2314yes—
607#385C2314yes—
608#385C2314yes—
609#385C2314yes—
610#384C2311yescharacteristic
611#384C2312yes—
612#384C2312yes—
613#384C2311yescharacteristic
614#384C2311yescharacteristic
615#384C2311yescharacteristic
616#384C2312yes—
617#384C2312yes—
618#384C2312yes—
619#384C2311yescharacteristic
620#382C2312yes—
621#382C2312yes—
622#382C2312yes—
623#382C2312yes—
624#382C2312yes—
625#382C2314yes—
626#382C2312yes—
627#382C2314yes—
628#382C2312yes—
629#382C2312yes—
630#382C2312yes—
631#381C2314yes—
632#381C2314yes—
633#381C2314yes—
634#380C2314yes—
635#380C2314yes—
636#380C2314yes—
637#380C2314yes—
638#380C2314yes—
639#380C2314yes—
640#380C2314yes—
641#380C2312yes—
642#380C2314yes—
643#380C2314yes—
644#380C2314yes—
645#380C2312yes—
646#380C2314yes—
647#380C2314yes—
648#380C2314yes—
649#380C2312yes—
650#380C2314yes—
651#380C2312yes—
652C4×C4⋊C4C2314yes—
653C4×C4⋊C4C2312yes—
654C4×C4⋊C4C2312yes—
655C4×C4⋊C4C2314yes—
656C4×C4⋊C4C2312yes—
657C4×C4⋊C4C2312yes—
658C4×C4⋊C4C2312yes—
659C4×C4⋊C4C2312yes—
660C4×C4⋊C4C2312yes—
661C4×C4⋊C4C2312yes—
662C4×C4⋊C4C2312yes—
663C4×C4⋊C4C2312yes—
664C4×C4⋊C4C2312yes—
665C4×C4⋊C4C2311yescharacteristic
666C4×C4⋊C4C2312yes—
667C4×C4⋊C4C2311yescharacteristic
668C4×C4⋊C4C2311yescharacteristic
669C4×C4⋊C4C2312yes—
670C4×C4⋊C4C2314yes—
671C4×C4⋊C4C2314yes—
672C4×C4⋊C4C2314yes—
673C4×C4⋊C4C2314yes—
674C4×C4⋊C4C2312yes—
675C4×C4⋊C4C2314yes—
676C4×C4⋊C4C2312yes—
677C4×C4⋊C4C2312yes—
678C4×C4⋊C4C2311yescharacteristic
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2312yes—
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2311yescharacteristic
685C4×C4⋊C4C2314yes—
686C4×C22⋊C4C2314yes—
687C4×C22⋊C4C2314yes—
688C4×C22⋊C4C2314yes—
689C4×C22⋊C4C2314yes—
690C4×C22⋊C4C2314yes—
691C4×C22⋊C4C2314yes—
692C4×C22⋊C4C2314yes—
693C4×C22⋊C4C2312yes—
694C4×C22⋊C4C2314yes—
695C4×C22⋊C4C2314yes—
696C4×C22⋊C4C2314yes—
697C4×C22⋊C4C2312yes—
698C4×C22⋊C4C2314yes—
699C4×C22⋊C4C2314yes—
700C4×C22⋊C4C2314yes—
701C4×C22⋊C4C2314yes—
702C4×C22⋊C4C2314yes—
703C4×C22⋊C4C2312yes—
704#376C2312yes—
705#376C2312yes—
706#376C2312yes—
707C2×#95C2314yes—
708C2×#95C2314yes—
709C2×#95C2314yes—
710C2×#95C2314yes—
711C2×#95C2314yes—
712C2×#95C2314yes—
713C43C2312yes—
714C43C2311yescharacteristic
715C2×#41—82no—
716C2×#41—82no—
717C2×#41C2×Q8116yescomplemented
718C22×Q8—28no—
719C22×Q8—82no—
720C22×Q8—82no—
721C22×Q8C2411yescharacteristic
722C22×Q8C2412yes—
723C22×Q8C2414yes—
724C22×Q8C2411yescharacteristic
725C22×Q8C2414yes—
726C22×Q8C2412yes—
727C22×Q8C2412yes—
728C22×Q8C2411yescharacteristic
729C22×Q8C2411yescharacteristic
730C22×D4C2411yescharacteristic
731C22×D4C2412yes—
732C22×D4C2414yes—
733C22×D4C2412yes—
734C22×D4C2414yes—
735C22×D4C2412yes—
736C23×C4C2414yes—
737C23×C4C2414yes—
738C23×C4C2414yes—
739C23×C4C2412yes—
740C23×C4C2412yes—
741C23×C4C2414yes—
742C23×C4C2414yes—
743C23×C4C2414yes—
744C23×C4C2414yes—
745C23×C4C2414yes—
746C23×C4C2412yes—
747C23×C4C2414yes—
748C4⋊Q8—24no—
749C4⋊Q8—28no—
750C4⋊Q8—28no—
751C4⋊Q8—42no—
752C4⋊Q8—44no—
753#127C2×Q8116yes—
754#127C2×Q818yescomplemented
755#125—28no—
756#125—28no—
757#125—84no—
758C22⋊Q8—216no—
759C22⋊Q8—216no—
760C22⋊Q8—28no—
761C22⋊Q8—216no—
762C22⋊Q8—216no—
763C22⋊Q8—48no—
764C22⋊Q8—44no—
765C22⋊Q8—84no—
766C22⋊Q8—84no—
767C22⋊Q8—84no—
768C22⋊Q8—82no—
769C22⋊Q8—84no—
770C22⋊Q8—84no—
771C22⋊Q8—84no—
772#121C2×Q8132yescomplemented
773#121C2×Q8116yescomplemented
774C4×Q8—42no—
775C4×Q8—42no—
776C4×Q8—44no—
777C4×Q8—44no—
778C4×Q8—84no—
779C4×Q8—82no—
780C4×Q8—82no—
781C4×Q8—82no—
782C4×Q8C2×Q818yescomplemented
783C4×Q8#4118yescomplemented
784C4×D4—24no—
785C4×D4—28no—
786C4×D4—28no—
787C4×D4—28no—
788C4×D4—28no—
789C4×D4—44no—
790C4×D4—44no—
791C4×D4—42no—
792C4×D4—44no—
793C4×D4—44no—
794C4×D4—44no—
795C4×D4—48no—
796C4×D4—84no—
797C4×D4—82no—
798C4×D4—84no—
799C4×D4—82no—
800C4×D4—84no—
801C4×D4—84no—
802C4×D4—84no—
803C4×D4C2×Q818yes—
804C4×D4C2×Q8116yescomplemented
805#117—84no—
806#117—82no—
807C2×C4⋊C4—216no—
808C2×C4⋊C4—84no—
809C2×C4⋊C4—82no—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2414yes—
812C2×C4⋊C4C2414yes—
813C2×C4⋊C4C2411yescharacteristic
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2412yes—
817C2×C4⋊C4C2412yes—
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2412yes—
820C2×C4⋊C4C2411yescharacteristic
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2414yes—
823C2×C4⋊C4C2414yes—
824C2×C4⋊C4C2412yes—
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2411yescharacteristic
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2411yescharacteristic
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2412yes—
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2411yescharacteristic
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2412yes—
845C2×C4⋊C4C2411yescharacteristic
846C2×C4⋊C4C2412yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2411yescharacteristic
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2412yes—
854C2×C4⋊C4C2411yescharacteristic
855C2×C4⋊C4C2412yes—
856C2×C4⋊C4C2412yes—
857C2×C4⋊C4C2412yes—
858C2×C4⋊C4C2412yes—
859C2×C4⋊C4C2412yes—
860C2×C4⋊C4C2412yes—
861C2×C4⋊C4C2412yes—
862C2×C4⋊C4C2412yes—
863C2×C4⋊C4C2414yes—
864C2×C4⋊C4C2412yes—
865C2×C4⋊C4C2414yes—
866C2×C4⋊C4C2414yes—
867C2×C4⋊C4C2414yes—
868C2×C4⋊C4C2412yes—
869C2×C4⋊C4C2414yes—
870C2×C4⋊C4C2414yes—
871C2×C4⋊C4C2414yes—
872C2×C4⋊C4C2414yes—
873C2×C4⋊C4C2412yes—
874C2×C4⋊C4C2412yes—
875C2×C4⋊C4C2412yes—
876C2×C4⋊C4C2412yes—
877C2×C4⋊C4C2412yes—
878C2×C4⋊C4C2412yes—
879C2×C4⋊C4C2411yescharacteristic
880C2×C4⋊C4C2411yescharacteristic
881C2×C4⋊C4C2412yes—
882C2×C4⋊C4C2412yes—
883C2×C4⋊C4C2411yescharacteristic
884C2×C22⋊C4C2414yes—
885C2×C22⋊C4C2414yes—
886C2×C22⋊C4C2412yes—
887C2×C22⋊C4C2414yes—
888C2×C22⋊C4C2414yes—
889C2×C22⋊C4C2414yes—
890C2×C22⋊C4C2414yes—
891C2×C22⋊C4C2414yes—
892C2×C22⋊C4C2414yes—
893C2×C22⋊C4C2414yes—
894C2×C22⋊C4C2414yes—
895C2×C22⋊C4C2414yes—
896C2×C22⋊C4C2414yes—
897C2×C22⋊C4C2414yes—
898C2×C22⋊C4C2414yes—
899C2×C22⋊C4C2414yes—
900C2×C22⋊C4C2414yes—
901C2×C22⋊C4C2414yes—
902C2×C22⋊C4C2414yes—
903C2×C22⋊C4C2414yes—
904C2×C22⋊C4C2414yes—
905C2×C22⋊C4C2414yes—
906C2×C22⋊C4C2414yes—
907C2×C22⋊C4C2412yes—
908C2×C22⋊C4C2414yes—
909C2×C22⋊C4C2414yes—
910C2×C22⋊C4C2414yes—
911C2×C22⋊C4C2414yes—
912C2×C22⋊C4C2412yes—
913C2×C22⋊C4C2414yes—
914C2×C42—82no—
915C2×C42—84no—
916C2×C42C2411yescharacteristic
917C2×C42C2412yes—
918C2×C42C2411yescharacteristic
919C2×C42C2412yes—
920C2×C42C2412yes—
921C2×C42C2412yes—
922C2×C42C2414yes—
923C2×C42C2414yes—
924C2×C42C2414yes—
925C2×C42C2412yes—
926C2×C42C2411yescharacteristic
927C2×C42C2412yes—
928C2×C42C2414yes—
929C2×C42C2414yes—
930C2×C42C2414yes—
931C2×C42C2414yes—
932C2×C42C2412yes—
933C2×C42C2411yescharacteristic
934C2×C42C2414yes—
935C2×C42C2412yes—
936C2×C42C2414yes—
937C2×C42C2412yes—
938C2×C42C2412yes—
939C2×C42C2412yes—
940C2×C42C2411yescharacteristic
941C2×C42C2411yescharacteristic
942C2×C42C2412yes—
943C2×C42C2411yescharacteristic
944C2×C42C2412yes—
945#95C2412yes—
946#95C2412yes—
947#95C2412yes—
948#95C2412yes—
949#95C2414yes—
950#95C2414yes—
951#95C2412yes—
952#95C2412yes—
953#95C2412yes—
954#95C2414yes—
955#95C2414yes—
956#95C2414yes—
957#95C2414yes—
958#95C2414yes—
959#95C2414yes—
960#95C2414yes—
961#95C2414yes—
962#95C2414yes—
963#95C2414yes—
964#95C2414yes—
965#95C2414yes—
966#95C2414yes—
967#95C2412yes—
968#95C2412yes—
969#95C2412yes—
970#95C2412yes—
971#95C2412yes—
972#95C2412yes—
973#95C2412yes—
974#95C2412yes—
975#95C2412yes—
976#95C2414yes—
977#95C2412yes—
978#95C2414yes—
979#95C2412yes—
980#95C2412yes—
981#95C2412yes—
982#95C2412yes—
983#95C2414yes—
984#95C2414yes—
985#95C2414yes—
986#95C2412yes—
987#95C2412yes—
988#95C2414yes—
989#95C2414yes—
990#95C2414yes—
991#95C2412yes—
992#95C2414yes—
993#95C2412yes—
994#95C2414yes—
995#95C2414yes—
996#95C2414yes—
997#95C2412yes—
998#95C2412yes—
999#95C2412yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2414yes—
1004#95C2412yes—
1005#95C2412yes—
1006#95C2412yes—
1007#95C2412yes—
1008#95C2412yes—
1009#95C2414yes—
1010#95C2414yes—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2414yes—
1014C24C2514yes—
1015C24C2512yes—
1016#41—816no—
1017C2×Q8—24no—
1018C2×Q8—28no—
1019C2×Q8—28no—
1020C2×Q8—22no—
1021C2×Q8—22no—
1022C2×Q8—41no—
1023C2×Q8—41no—
1024C2×Q8—42no—
1025C2×Q8—42no—
1026C2×Q8—41no—
1027C2×Q8—41no—
1028C2×Q8—41no—
1029C2×Q8—41no—
1030C2×Q8—41no—
1031C2×Q8—42no—
1032C2×Q8—42no—
1033C2×Q8—44no—
1034C2×Q8—44no—
1035C2×Q8—41no—
1036C2×Q8—42no—
1037C2×Q8—42no—
1038C2×Q8—42no—
1039C2×Q8—44no—
1040C2×Q8—44no—
1041C2×Q8—42no—
1042C2×Q8—816no—
1043C2×Q8C22×Q814yes—
1044C2×Q8C2×#4114yes—
1045C2×D4—22no—
1046C2×D4—24no—
1047C2×D4—22no—
1048C2×D4—24no—
1049C2×D4—42no—
1050C2×D4—44no—
1051C2×D4—42no—
1052C2×D4—44no—
1053C2×D4—42no—
1054C2×D4—44no—
1055C2×D4—44no—
1056C2×D4—42no—
1057C2×D4C22×Q814yes—
1058C2×D4C22×Q818yes—
1059C2×D4C22×Q8116yes—
1060C2×D4C22×Q818yes—
1061C2×D4C22×Q8116yes—
1062C2×D4C22×Q818yes—
1063C22×C4—24no—
1064C22×C4—28no—
1065C22×C4—28no—
1066C22×C4—28no—
1067C22×C4—28no—
1068C22×C4—24no—
1069C22×C4—42no—
1070C22×C4—44no—
1071C22×C4—42no—
1072C22×C4—42no—
1073C22×C4—42no—
1074C22×C4—44no—
1075C22×C4—44no—
1076C22×C4—44no—
1077C22×C4—42no—
1078C22×C4—44no—
1079C22×C4—44no—
1080C22×C4—42no—
1081C22×C4—44no—
1082C22×C4—44no—
1083C22×C4—44no—
1084C22×C4—44no—
1085C22×C4—44no—
1086C22×C4—44no—
1087C22×C4—44no—
1088C22×C4—44no—
1089C22×C4—44no—
1090C22×C4—44no—
1091C22×C4—44no—
1092C22×C4—44no—
1093C22×C4—44no—
1094C22×C4—44no—
1095C22×C4—44no—
1096C22×C4—44no—
1097C22×C4C22×Q818yes—
1098C22×C4C22×Q8116yes—
1099C22×C4C2512yes—
1100C22×C4C2512yes—
1101C22×C4C2514yes—
1102C22×C4C2512yes—
1103C22×C4C2514yes—
1104C22×C4C2514yes—
1105C22×C4C2512yes—
1106C22×C4C2514yes—
1107C22×C4C2512yes—
1108C22×C4C2512yes—
1109C22×C4C2512yes—
1110C22×C4C2512yes—
1111C22×C4C2512yes—
1112C22×C4C2512yes—
1113C22×C4C2514yes—
1114C22×C4C2511yescharacteristic
1115C22×C4C2512yes—
1116C22×C4C2511yescharacteristic
1117C22×C4C2512yes—
1118C22×C4C2511yescharacteristic
1119C22×C4C2512yes—
1120C22×C4C2512yes—
1121C22×C4C2512yes—
1122C22×C4C2511yescharacteristic
1123C22×C4C2511yescharacteristic
1124C22×C4C2511yescharacteristic
1125C22×C4C2511yescharacteristic
1126C4⋊C4—28no—
1127C4⋊C4—28no—
1128C4⋊C4—28no—
1129C4⋊C4—24no—
1130C4⋊C4—24no—
1131C4⋊C4—24no—
1132C4⋊C4—22no—
1133C4⋊C4—24no—
1134C4⋊C4—28no—
1135C4⋊C4—28no—
1136C4⋊C4—28no—
1137C4⋊C4—24no—
1138C4⋊C4—22no—
1139C4⋊C4—24no—
1140C4⋊C4—24no—
1141C4⋊C4—24no—
1142C4⋊C4—24no—
1143C4⋊C4—42no—
1144C4⋊C4—42no—
1145C4⋊C4—41no—
1146C4⋊C4—42no—
1147C4⋊C4—44no—
1148C4⋊C4—44no—
1149C4⋊C4—44no—
1150C4⋊C4—41no—
1151C4⋊C4—42no—
1152C4⋊C4—44no—
1153C4⋊C4—42no—
1154C4⋊C4—42no—
1155C4⋊C4—42no—
1156C4⋊C4—42no—
1157C4⋊C4—42no—
1158C4⋊C4—41no—
1159C4⋊C4—44no—
1160C4⋊C4—41no—
1161C4⋊C4—41no—
1162C4⋊C4—42no—
1163C4⋊C4—42no—
1164C4⋊C4—42no—
1165C4⋊C4—42no—
1166C4⋊C4—42no—
1167C4⋊C4—42no—
1168C4⋊C4—42no—
1169C4⋊C4—42no—
1170C4⋊C4—42no—
1171C4⋊C4—41no—
1172C4⋊C4—42no—
1173C4⋊C4—44no—
1174C4⋊C4—44no—
1175C4⋊C4—44no—
1176C4⋊C4—44no—
1177C4⋊C4—44no—
1178C4⋊C4—44no—
1179C4⋊C4—42no—
1180C4⋊C4—42no—
1181C4⋊C4—42no—
1182C4⋊C4—42no—
1183C4⋊C4—44no—
1184C4⋊C4—44no—
1185C4⋊C4—44no—
1186C4⋊C4—44no—
1187C4⋊C4—44no—
1188C4⋊C4—44no—
1189C4⋊C4—42no—
1190C4⋊C4—42no—
1191C4⋊C4—42no—
1192C4⋊C4—42no—
1193C4⋊C4—42no—
1194C4⋊C4—42no—
1195C4⋊C4C22×Q814yes—
1196C4⋊C4C22×Q818yes—
1197C4⋊C4C22×Q814yes—
1198C4⋊C4C2×#4118yes—
1199C4⋊C4C2×#4114yes—
1200C22⋊C4—28no—
1201C22⋊C4—28no—
1202C22⋊C4—28no—
1203C22⋊C4—28no—
1204C22⋊C4—24no—
1205C22⋊C4—28no—
1206C22⋊C4—44no—
1207C22⋊C4—44no—
1208C22⋊C4—44no—
1209C22⋊C4—42no—
1210C22⋊C4—44no—
1211C22⋊C4—44no—
1212C22⋊C4—44no—
1213C22⋊C4—44no—
1214C22⋊C4—44no—
1215C22⋊C4—44no—
1216C22⋊C4—44no—
1217C22⋊C4—44no—
1218C22⋊C4—44no—
1219C22⋊C4—44no—
1220C22⋊C4—44no—
1221C22⋊C4—44no—
1222C22⋊C4—44no—
1223C22⋊C4—44no—
1224C22⋊C4—44no—
1225C22⋊C4—44no—
1226C22⋊C4—44no—
1227C22⋊C4—44no—
1228C22⋊C4C22×Q818yes—
1229C22⋊C4C22×Q8116yes—
1230C42—22no—
1231C42—22no—
1232C42—24no—
1233C42—24no—
1234C42—24no—
1235C42—24no—
1236C42—41no—
1237C42—42no—
1238C42—44no—
1239C42—42no—
1240C42—42no—
1241C42—44no—
1242C42—42no—
1243C42—44no—
1244C42—44no—
1245C42—44no—
1246C42—44no—
1247C42—44no—
1248C42—42no—
1249C42—41no—
1250C42—42no—
1251C42—44no—
1252C42—44no—
1253C42—41no—
1254C42—42no—
1255C42C22×Q814yes—
1256C42C22×Q818yes—
1257C42C2×#4114yes—
1258C42C2×#4118yes—
1259C23—24no—
1260C23—22no—
1261C23—24no—
1262C23—22no—
1263C23—24no—
1264C23—22no—
1265C23—24no—
1266C23—22no—
1267C23—24no—
1268C23—22no—
1269C23—24no—
1270C23—22no—
1271C23C23×Q814yes—
1272C23C23×Q818yes—
1273C23C2611yescharacteristic
1274Q8—44no—
1275Q8—44no—
1276Q8—44no—
1277Q8—48no—
1278Q8—88no—
1279Q8—82no—
1280Q8—88no—
1281Q8—84no—
1282Q8—84no—
1283D4—28no—
1284D4—216no—
1285D4—416no—
1286D4—48no—
1287D4—416no—
1288D4—48no—
1289C2×C4—21no—
1290C2×C4—21no—
1291C2×C4—21no—
1292C2×C4—22no—
1293C2×C4—22no—
1294C2×C4—22no—
1295C2×C4—22no—
1296C2×C4—21no—
1297C2×C4—22no—
1298C2×C4—22no—
1299C2×C4—21no—
1300C2×C4—22no—
1301C2×C4—21no—
1302C2×C4—21no—
1303C2×C4—21no—
1304C2×C4—21no—
1305C2×C4—22no—
1306C2×C4—21no—
1307C2×C4—22no—
1308C2×C4—22no—
1309C2×C4—24no—
1310C2×C4—24no—
1311C2×C4—24no—
1312C2×C4—22no—
1313C2×C4—24no—
1314C2×C4—21no—
1315C2×C4—22no—
1316C2×C4—22no—
1317C2×C4—22no—
1318C2×C4—22no—
1319C2×C4—22no—
1320C2×C4—22no—
1321C2×C4—22no—
1322C2×C4—22no—
1323C2×C4—22no—
1324C2×C4—24no—
1325C2×C4—22no—
1326C2×C4—24no—
1327C2×C4—22no—
1328C2×C4—22no—
1329C2×C4—24no—
1330C2×C4—22no—
1331C2×C4—22no—
1332C2×C4—22no—
1333C2×C4—22no—
1334C2×C4—22no—
1335C2×C4—22no—
1336C2×C4—24no—
1337C2×C4—22no—
1338C2×C4—24no—
1339C2×C4—24no—
1340C2×C4—22no—
1341C2×C4—21no—
1342C2×C4—22no—
1343C2×C4—22no—
1344C2×C4—24no—
1345C2×C4—24no—
1346C2×C4—24no—
1347C2×C4—24no—
1348C2×C4—24no—
1349C2×C4—21no—
1350C2×C4—22no—
1351C2×C4—22no—
1352C2×C4—22no—
1353C2×C4—22no—
1354C2×C4—22no—
1355C2×C4—22no—
1356C2×C4—22no—
1357C2×C4—48no—
1358C2×C4—416no—
1359C2×C4—48no—
1360C2×C4—88no—
1361C2×C4—88no—
1362C2×C4—88no—
1363C2×C4—84no—
1364C2×C4—88no—
1365C2×C4—88no—
1366C2×C4—164no—
1367C2×C4—164no—
1368C2×C4—164no—
1369C2×C4C23×Q812yes—
1370C2×C4C23×Q814yes—
1371C2×C4C23×Q812yes—
1372C2×C4C23×Q814yes—
1373C2×C4C23×Q814yes—
1374C2×C4C23×Q812yes—
1375C2×C4C22×#4114yes—
1376C2×C4C22×#4112yes—
1377C2×C4C22×#4112yes—
1378C2×C4C22×#4114yes—
1379C2×C4C22×#4112yes—
1380C2×C4#58512yes—
1381C2×C4#58512yes—
1382C22—28no—
1383C22—24no—
1384C22—28no—
1385C22—24no—
1386C22—28no—
1387C22—24no—
1388C22—44no—
1389C22—42no—
1390C22—44no—
1391C22—42no—
1392C22—42no—
1393C22—44no—
1394C22—42no—
1395C22—44no—
1396C22C24×Q811yescharacteristic
1397C22C23×#4111yescharacteristic
1398C22C2×#58511yescharacteristic
1399C22C2×#58511yescharacteristic
1400C22H(7,𝔽2)11yescharacteristic
1401C22H(7,𝔽2)11yescharacteristic
1402C22H(7,𝔽2)11yescharacteristic
1403C4—22no—
1404C4—24no—
1405C4—22no—
1406C4—24no—
1407C4—24no—
1408C4—24no—
1409C4—22no—
1410C4—22no—
1411C4—24no—
1412C4—22no—
1413C4—44no—
1414C4—44no—
1415C4—41no—
1416C4—42no—
1417C4—44no—
1418C4—42no—
1419C4—42no—
1420C4—42no—
1421C4—42no—
1422C4—44no—
1423C4—44no—
1424C4—42no—
1425C4—42no—
1426C4—42no—
1427C4—42no—
1428C4—42no—
1429C4Q8×#4114yes—
1430C2—48no—
1431C2—44no—
1432C2C2×Q8×#4111yescharacteristic
1433C2#6284311yescharacteristic
1434C2#6285511yescharacteristic
1435C2#6290811yescharacteristic
1436C2#6298911yescharacteristic
1437C2#6301011yescharacteristic
1438C2#6305111yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#550C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59886C2semidirect
2. #59864C2semidirect
3. #59457C2semidirect
4. #59452C2semidirect
5. #52288C2semidirect
6. #52287C2semidirect
7. #45362C2semidirect
8. #44947C2semidirect
9. #44947C2semidirect
10. #43567C2semidirect
11. #43144C2semidirect
12. #43140C2semidirect
13. #39750C2semidirect
14. #39749C2semidirect
15. #39708C2semidirect
16. #39696C2semidirect
17. #39618C2semidirect
18. #39611C2semidirect
19. #38448C2semidirect
20. #38444C2semidirect
21. #36477C2semidirect
22. #36476C2semidirect
23. #35952C2semidirect
24. #35952C2semidirect
25. #35934C2semidirect
26. #34334C2semidirect
27. #34333C2semidirect
262. #550Q8semidirect
717. C2×#41C2×Q8semidirect
754. #127C2×Q8semidirect
772. #121C2×Q8semidirect
773. #121C2×Q8semidirect
782. C4×Q8C2×Q8semidirect
783. C4×Q8#41semidirect
804. C4×D4C2×Q8semidirect

Maximal subgroups

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

subgroupindex
#598862
#598642
#594572
#594522
#522882
#522872
#453622
#449472
#435672
#431442
#431402
#397502
#397492
#397082
#396962
#396182
#396112
#384482
#384442
#364772
#364762
#359522
#359342
#343342
#343332
#343302