Finite Group Databasebeta

← #8157202

Subgroups — #8157202

Order 512.

4032 conjugacy classes of subgroups.

The subgroup lattice has 1392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59868C212yesmaximal, complemented
2#59321C212yesmaximal, complemented
3#58230C214yesmaximal, complemented
4#55672C214yesmaximal, complemented
5#54742C214yesmaximal, complemented
6#54106C214yesmaximal, complemented
7#53107C212yesmaximal, complemented
8#52965C212yesmaximal, complemented
9#52452C214yesmaximal, complemented
10#45346C212yesmaximal, complemented
11#45329C212yesmaximal, complemented
12#42832C212yesmaximal, complemented
13#42713C212yesmaximal, complemented
14#42455C212yesmaximal, complemented
15#42455C212yesmaximal, complemented
16#40563C214yesmaximal
17#39751C211yesmaximal, characteristic, complemented
18#39748C212yesmaximal, complemented
19#39679C212yesmaximal, complemented
20#39639C211yesmaximal, characteristic, complemented
21#37850C212yesmaximal
22#37850C212yesmaximal
23#37460C212yesmaximal
24#36760C212yesmaximal
25#36599C211yesmaximal, characteristic, complemented
26#36552C211yesmaximal, characteristic, complemented
27#35014C211yesmaximal, characteristic
28C2×#2497C211yesmaximal, characteristic
29#34578C211yesmaximal, characteristic
30#2857C2212yes—
31#2857C2211yescharacteristic
32#2857C2211yescharacteristic
33#2851C2212yes—
34#2848C2212yes—
35#2839C2214yescomplemented
36#2839C2214yescomplemented
37#2839C2214yescomplemented
38#2839C2214yescomplemented
39#2839C2214yescomplemented
40#2839C2214yescomplemented
41#2839C2214yescomplemented
42#2836C2214yes—
43#2836C2214yes—
44#2831C2214yes—
45#2831C2214yes—
46#2822C2214yescomplemented
47#2810C2214yescomplemented
48#2809C2214yescomplemented
49#2809C2212yescomplemented
50#2805C2212yescomplemented
51#2805C2214yescomplemented
52#2802C2214yescomplemented
53#2802C2214yescomplemented
54#2802C2214yescomplemented
55#2802C2214yescomplemented
56#2798C2214yes—
57#2791C2214yescomplemented
58#2791C2214yescomplemented
59#2791C2214yescomplemented
60#2783C2214yes—
61#2783C2214yes—
62#2783C2214yes—
63#2774C2214yescomplemented
64#2774C2214yescomplemented
65#2774C2214yescomplemented
66#2772C2214yes—
67#2772C2214yes—
68#2772C2214yes—
69#2767C2214yescomplemented
70#2767C2214yescomplemented
71#2767C2214yescomplemented
72#2767C2214yescomplemented
73#2755C2214yescomplemented
74#2754C2214yes—
75#2747C2214yes—
76#2747C2214yes—
77#2744C2214yes—
78#2744C2214yes—
79#2739C2214yes—
80#2739C2214yes—
81#2726C2212yescomplemented
82#2726C2212yescomplemented
83#2725C2214yes—
84#2725C2214yes—
85#2725C2214yes—
86#2725C2214yes—
87#2725C2214yes—
88#2725C2214yes—
89#2722C2214yes—
90#2722C2214yes—
91#2721C2214yes—
92#2719C2214yescomplemented
93#2719C2214yescomplemented
94#2719C2214yescomplemented
95#2716C2214yes—
96#2713C2214yescomplemented
97#2667C2212yes—
98#2667C2212yes—
99#2665C2212yes—
100#2665C2212yes—
101#2664C2214yes—
102#2664C2214yes—
103#2659C2211yescharacteristic
104#2659C2211yescharacteristic
105#2659C2212yes—
106#2654C2214yes—
107#2654C2214yes—
108#2650C2214yes—
109#2650C2214yes—
110#2646C2212yes—
111#2646C2212yes—
112#2646C2212yes—
113#2637C2214yes—
114#2637C2214yes—
115#2629C2212yes—
116#2629C2212yes—
117#2626C2211yescharacteristic
118#2626C2212yes—
119#2626C2211yescharacteristic
120#2626C2212yes—
121#2625C2212yes—
122#2625C2212yes—
123#2590C2214yescomplemented
124#2590C2214yescomplemented
125#2590C2214yescomplemented
126#2589C2214yes—
127#2588C2214yescomplemented
128#2587C2214yes—
129#2585C2214yescomplemented
130#2585C2214yescomplemented
131#2584C2212yescomplemented
132#2584C2212yescomplemented
133#2583C2214yes—
134#2582C2212yescomplemented
135#2582C2212yescomplemented
136#2581C2212yescomplemented
137#2581C2214yescomplemented
138#2569C2214yes—
139#2569C2214yes—
140#2569C2214yes—
141#2568C2211yescharacteristic, complemented
142#2565C2214yescomplemented
143#2552C2212yescomplemented
144#2552C2211yescharacteristic, complemented
145#2552C2212yescomplemented
146#2552C2212yescomplemented
147#2552C2211yescharacteristic, complemented
148#2552C2212yescomplemented
149#2550C2212yescomplemented
150#2546C2211yescharacteristic, complemented
151#2520C2214yescomplemented
152#2519C2214yes—
153#2519C2214yes—
154#2511C2212yescomplemented
155#2511C2212yescomplemented
156#2511C2212yescomplemented
157#2511C2212yescomplemented
158#2511C2212yescomplemented
159#2509C2212yescomplemented
160#2509C2214yescomplemented
161#2509C2212yescomplemented
162#2508C2212yescomplemented
163#2508C2212yescomplemented
164#2508C2212yescomplemented
165#2508C2214yescomplemented
166#2506C2212yescomplemented
167#2506C2214yescomplemented
168#2505C2214yes—
169#2505C2214yes—
170#2505C2214yes—
171#2505C2214yes—
172#2505C2214yes—
173#2502C2212yes—
174#2502C2212yes—
175#2497C2212yes—
176#2497C2212yes—
177#2497C2214yes—
178#2497C2212yes—
179#2497C2214yes—
180#2497C2212yes—
181#2497C2212yes—
182#2496C2212yes—
183#2496C2212yes—
184#2496C2212yes—
185#2496C2212yes—
186#2492C2212yes—
187#2489C2212yes—
188#2489C2212yes—
189#2480C2214yes—
190#2480C2214yes—
191#2480C2214yes—
192#2480C2214yes—
193#2473C2214yes—
194#2473C2214yes—
195#2473C2214yes—
196#2469C2214yes—
197#2469C2214yes—
198#2462C2214yescomplemented
199#2462C2214yescomplemented
200#2453C2212yescomplemented
201#2453C2212yescomplemented
202#2453C2212yescomplemented
203#2446C2212yescomplemented
204#2446C2212yescomplemented
205#2442C2214yes—
206#2442C2214yes—
207#2442C2212yes—
208#2442C2212yes—
209#2429C2212yes—
210#2423C2212yes—
211#2421C2212yes—
212#2421C2212yes—
213#2396C2212yes—
214#2396C2212yes—
215#2396C2212yes—
216#2396C2212yes—
217C2×#400C2212yes—
218C2×#396C2212yes—
219#2370C2212yescomplemented
220#2370C2212yescomplemented
221#2365C2211yescharacteristic, complemented
222#2365C2211yescharacteristic, complemented
223#2360C2214yes—
224#2360C2212yes—
225#2360C2212yes—
226#2355C2212yescomplemented
227#2355C2211yescharacteristic, complemented
228#2355C2212yescomplemented
229#2351C2212yescomplemented
230Q8×C4⋊C4C2212yescomplemented
231Q8×C4⋊C4C2211yescharacteristic, complemented
232#2345C2214yes—
233#2345C2212yes—
234#2345C2212yes—
235#2329C2212yes—
236#2329C2212yes—
237#2329C2212yes—
238#2323C2212yes—
239#2323C2212yes—
240#2314C2212yes—
241#2314C2212yes—
242#2312C2212yes—
243C4×C22⋊Q8C2211yescharacteristic
244C4×C22⋊Q8C2212yes—
245C4×C22⋊Q8C2211yescharacteristic
246C4×C22⋊Q8C2212yes—
247C4×C22⋊Q8C2212yes—
248C4×C22⋊Q8C2212yes—
249C2×#389C2211yescharacteristic
250C2×#389C2211yescharacteristic
251C2×#388C2212yes—
252C2×#387C2212yes—
253C2×#384C2211yescharacteristic
254#2280C2212yes—
255C2×#380C2211yescharacteristic
256C2×#380C2211yescharacteristic
257C2×C4×C4⋊C4C2211yescharacteristic
258C2×C4×C22⋊C4C2211yescharacteristic
259C24×C4C2311yescharacteristic
260C2×C4⋊Q8C2311yescharacteristic
261C2×C4⋊Q8C2311yescharacteristic
262C2×C4⋊Q8C2312yes—
263C2×#126C2314yes—
264C2×#126C2314yes—
265C2×#126C2314yes—
266C2×#126C2314yes—
267C2×#125C2312yes—
268C2×#125C2312yes—
269C2×#125C2314yes—
270C2×#125C2314yes—
271C2×#125C2314yes—
272C2×#125C2312yes—
273C2×#125C2314yes—
274C2×#125C2314yes—
275C2×C22⋊Q8C2312yes—
276C2×C22⋊Q8C2311yescharacteristic
277C2×C22⋊Q8C2312yes—
278C2×C22⋊Q8C2312yes—
279C2×C22⋊Q8C2311yescharacteristic
280C2×C22⋊Q8C2312yes—
281C2×C22⋊Q8C2312yes—
282C2×C4×Q8C2311yescharacteristic
283C2×C4×Q8C2312yes—
284C2×C4×Q8C2312yes—
285C2×C4×Q8C2312yes—
286C2×C4×Q8C2311yescharacteristic
287C2×C4×Q8C2312yes—
288C2×C4×Q8C2314yes—
289C2×C4×Q8C2312yes—
290C2×C4×Q8C2312yes—
291C2×#117C2312yes—
292C2×#117C2312yes—
293C22×C4⋊C4C2312yes—
294C22×C4⋊C4C2311yescharacteristic
295C22×C4⋊C4C2311yescharacteristic
296C22×C4⋊C4C2311yescharacteristic
297C22×C4⋊C4C2311yescharacteristic
298C22×C4⋊C4C2312yes—
299C22×C4⋊C4C2312yes—
300C22×C4⋊C4C2312yes—
301C22×C22⋊C4C2311yescharacteristic
302C22×C22⋊C4C2311yescharacteristic
303C22×C22⋊C4C2312yes—
304C22×C22⋊C4C2312yes—
305C22×C42C2311yescharacteristic
306C22×C42C2311yescharacteristic
307C22×C42C2312yes—
308#400C2314yes—
309#400C2314yes—
310#400C2314yes—
311#400C2314yes—
312#400C2314yes—
313#400C2314yes—
314#400C2314yes—
315#400C2314yes—
316#400C2314yes—
317#400C2314yes—
318#400C2314yes—
319#400C2314yes—
320#400C2314yes—
321#400C2314yes—
322#400C2314yes—
323#400C2314yes—
324#400C2314yes—
325#400C2314yes—
326#400C2314yes—
327#400C2314yes—
328#400C2314yes—
329#400C2314yes—
330#400C2314yes—
331#400C2314yes—
332#400C2312yes—
333#400C2312yes—
334#400C2312yes—
335#400C2312yes—
336#400C2314yes—
337#400C2314yes—
338#400C2314yes—
339#400C2314yes—
340#400C2314yes—
341#400C2314yes—
342#400C2314yes—
343#400C2314yes—
344#400C2314yes—
345#400C2314yes—
346#400C2314yes—
347#400C2314yes—
348#400C2314yes—
349#400C2314yes—
350#399C2312yes—
351#399C2314yes—
352#399C2312yes—
353#399C2312yes—
354#399C2312yes—
355#398C2314yes—
356#398C2314yes—
357#398C2314yes—
358#398C2314yes—
359#398C2312yes—
360#398C2314yes—
361#398C2314yes—
362#398C2314yes—
363#398C2314yes—
364#398C2314yes—
365#398C2314yes—
366#398C2314yes—
367#398C2314yes—
368#398C2314yes—
369#398C2314yes—
370#398C2314yes—
371#398C2314yes—
372#398C2314yes—
373#398C2314yes—
374#398C2314yes—
375#398C2314yes—
376#398C2314yes—
377#398C2314yes—
378#398C2314yes—
379#398C2314yes—
380#398C2314yes—
381#398C2314yes—
382#398C2314yes—
383#398C2312yes—
384#398C2312yes—
385#398C2312yes—
386#398C2314yes—
387#398C2314yes—
388#398C2314yes—
389#398C2314yes—
390#398C2314yes—
391#398C2314yes—
392#398C2312yes—
393#398C2312yes—
394#398C2312yes—
395#398C2314yes—
396#398C2314yes—
397#398C2314yes—
398#398C2314yes—
399#398C2312yes—
400#398C2314yes—
401#397C2314yes—
402#397C2314yes—
403#397C2314yes—
404#397C2314yes—
405#397C2314yes—
406#397C2314yes—
407#397C2314yes—
408#397C2314yes—
409#397C2314yes—
410#397C2314yes—
411#397C2314yes—
412#397C2314yes—
413#396C2312yes—
414#396C2314yes—
415#396C2314yes—
416#396C2314yes—
417#396C2312yes—
418#396C2314yes—
419#396C2314yes—
420#396C2314yes—
421#396C2314yes—
422#396C2312yes—
423#396C2312yes—
424#396C2312yes—
425#396C2312yes—
426#396C2312yes—
427#396C2312yes—
428#396C2314yes—
429#396C2314yes—
430#396C2314yes—
431#395C2314yes—
432#395C2314yes—
433#395C2314yes—
434#395C2312yes—
435#395C2314yes—
436#395C2312yes—
437#395C2312yes—
438#395C2312yes—
439#393C2312yes—
440#393C2314yes—
441#393C2312yes—
442#393C2312yes—
443#393C2312yes—
444#391C2312yes—
445#391C2314yes—
446#391C2312yes—
447#391C2312yes—
448#391C2312yes—
449#391C2312yes—
450#391C2312yes—
451#391C2314yes—
452#391C2314yes—
453#391C2312yes—
454#391C2312yes—
455#391C2314yes—
456#391C2312yes—
457#391C2312yes—
458#391C2312yes—
459#391C2312yes—
460#391C2312yes—
461#391C2312yes—
462#391C2311yescharacteristic
463#391C2311yescharacteristic
464#389C2312yes—
465#389C2314yes—
466#389C2314yes—
467#389C2312yes—
468#389C2312yes—
469#389C2314yes—
470#389C2314yes—
471#389C2312yes—
472#389C2314yes—
473#389C2314yes—
474#389C2312yes—
475#389C2312yes—
476#389C2312yes—
477#389C2312yes—
478#389C2314yes—
479#389C2314yes—
480#389C2314yes—
481#389C2314yes—
482#389C2314yes—
483#389C2314yes—
484#389C2314yes—
485#389C2314yes—
486#389C2314yes—
487#389C2312yes—
488#389C2314yes—
489#389C2312yes—
490#389C2312yes—
491#389C2312yes—
492#389C2314yes—
493#389C2312yes—
494#389C2312yes—
495#389C2312yes—
496#389C2314yes—
497#389C2314yes—
498#389C2312yes—
499#389C2314yes—
500#389C2314yes—
501#389C2314yes—
502#389C2312yes—
503#389C2314yes—
504#389C2312yes—
505#389C2314yes—
506#389C2314yes—
507#389C2312yes—
508#389C2312yes—
509#389C2312yes—
510#389C2314yes—
511#389C2314yes—
512#389C2314yes—
513#389C2314yes—
514#389C2312yes—
515#389C2312yes—
516#389C2311yescharacteristic
517#389C2311yescharacteristic
518#389C2312yes—
519#389C2312yes—
520#389C2312yes—
521#388C2314yes—
522#388C2314yes—
523#388C2314yes—
524#388C2314yes—
525#388C2314yes—
526#388C2314yes—
527#388C2314yes—
528#388C2314yes—
529#388C2314yes—
530#388C2314yes—
531#388C2314yes—
532#388C2314yes—
533#388C2314yes—
534#388C2314yes—
535#388C2314yes—
536#388C2314yes—
537#388C2314yes—
538#388C2314yes—
539#388C2314yes—
540#388C2314yes—
541#387C2314yes—
542#387C2314yes—
543#387C2314yes—
544#387C2314yes—
545#387C2314yes—
546#387C2314yes—
547#387C2314yes—
548#387C2314yes—
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#387C2314yes—
572#387C2314yes—
573#387C2314yes—
574#387C2314yes—
575#387C2314yes—
576#387C2314yes—
577#387C2314yes—
578#387C2314yes—
579#387C2312yes—
580#387C2312yes—
581#387C2314yes—
582#387C2314yes—
583#387C2314yes—
584#387C2314yes—
585#387C2314yes—
586#387C2312yes—
587#387C2314yes—
588#387C2314yes—
589#387C2314yes—
590#387C2314yes—
591#387C2314yes—
592#387C2314yes—
593#387C2314yes—
594#387C2314yes—
595#387C2314yes—
596#387C2314yes—
597#387C2312yes—
598#387C2314yes—
599#387C2314yes—
600#385C2314yes—
601#385C2312yes—
602#385C2314yes—
603#385C2314yes—
604#385C2314yes—
605#385C2314yes—
606#385C2314yes—
607#385C2314yes—
608#385C2314yes—
609#385C2314yes—
610#385C2314yes—
611#385C2314yes—
612#385C2312yes—
613#385C2312yes—
614#385C2312yes—
615#385C2314yes—
616#384C2314yes—
617#384C2312yes—
618#384C2312yes—
619#384C2312yes—
620#384C2311yescharacteristic
621#384C2311yescharacteristic
622#384C2312yes—
623#384C2312yes—
624#384C2312yes—
625#384C2312yes—
626#382C2314yes—
627#382C2314yes—
628#382C2312yes—
629#382C2312yes—
630#382C2312yes—
631#382C2314yes—
632#382C2314yes—
633#382C2314yes—
634#382C2314yes—
635#382C2314yes—
636#381C2312yes—
637#381C2312yes—
638#380C2312yes—
639#380C2312yes—
640#380C2312yes—
641#380C2314yes—
642#380C2314yes—
643#380C2314yes—
644#380C2314yes—
645#380C2312yes—
646#380C2312yes—
647#380C2312yes—
648#380C2312yes—
649#380C2311yescharacteristic
650#380C2312yes—
651#380C2312yes—
652#380C2312yes—
653#380C2312yes—
654#380C2312yes—
655#380C2311yescharacteristic
656#380C2312yes—
657#380C2312yes—
658#380C2312yes—
659#380C2314yes—
660#380C2314yes—
661#379C2314yes—
662#379C2312yes—
663#379C2312yes—
664C4×C4⋊C4C2314yes—
665C4×C4⋊C4C2311yescharacteristic
666C4×C4⋊C4C2312yes—
667C4×C4⋊C4C2312yes—
668C4×C4⋊C4C2312yes—
669C4×C4⋊C4C2312yes—
670C4×C4⋊C4C2312yes—
671C4×C4⋊C4C2312yes—
672C4×C4⋊C4C2312yes—
673C4×C4⋊C4C2314yes—
674C4×C4⋊C4C2314yes—
675C4×C4⋊C4C2314yes—
676C4×C4⋊C4C2314yes—
677C4×C4⋊C4C2312yes—
678C4×C4⋊C4C2312yes—
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2314yes—
681C4×C4⋊C4C2311yescharacteristic
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2311yescharacteristic
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2311yescharacteristic
688C4×C4⋊C4C2311yescharacteristic
689C4×C4⋊C4C2312yes—
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2311yescharacteristic
692C4×C22⋊C4C2314yes—
693C4×C22⋊C4C2314yes—
694C4×C22⋊C4C2314yes—
695C4×C22⋊C4C2314yes—
696C4×C22⋊C4C2314yes—
697C4×C22⋊C4C2312yes—
698C4×C22⋊C4C2312yes—
699C4×C22⋊C4C2312yes—
700C4×C22⋊C4C2312yes—
701C4×C22⋊C4C2312yes—
702C4×C22⋊C4C2312yes—
703C4×C22⋊C4C2312yes—
704C4×C22⋊C4C2312yes—
705C2×#95C2312yes—
706C2×#95C2312yes—
707C2×#95C2312yes—
708C2×#95C2312yes—
709C2×#95C2311yescharacteristic
710C2×#95C2311yescharacteristic
711C2×#95C2312yes—
712C25C2411yescharacteristic
713C22×Q8C2412yes—
714C22×Q8C2411yescharacteristic
715C22×Q8C2412yes—
716C22×Q8C2411yescharacteristic
717C22×Q8C2412yes—
718C23×C4—24no—
719C23×C4—42no—
720C23×C4—42no—
721C23×C4C2412yes—
722C23×C4C2411yescharacteristic
723C23×C4C2412yes—
724C23×C4C2412yes—
725C23×C4C2412yes—
726C23×C4C2412yes—
727C23×C4C2411yescharacteristic
728C23×C4C2411yescharacteristic
729C23×C4C2411yescharacteristic
730C23×C4C2412yes—
731C23×C4C2411yescharacteristic
732C23×C4C2411yescharacteristic
733C4⋊Q8—42no—
734C4⋊Q8—42no—
735C4⋊Q8—82no—
736#126—84no—
737#126—84no—
738#126—84no—
739#126—84no—
740#125—44no—
741#125—44no—
742#125—82no—
743#125—84no—
744#125—84no—
745#125—84no—
746#125—84no—
747#125—84no—
748C22⋊Q8—28no—
749C22⋊Q8—28no—
750C22⋊Q8—24no—
751C22⋊Q8—24no—
752C22⋊Q8—28no—
753C22⋊Q8—44no—
754C22⋊Q8—44no—
755C4×Q8—44no—
756C4×Q8—42no—
757C4×Q8—42no—
758C4×Q8—44no—
759C4×Q8—44no—
760C4×Q8—44no—
761C4×Q8—82no—
762C4×Q8—82no—
763C4×Q8—84no—
764#117—44no—
765#117—44no—
766C2×C4⋊C4—24no—
767C2×C4⋊C4—24no—
768C2×C4⋊C4—28no—
769C2×C4⋊C4—42no—
770C2×C4⋊C4—42no—
771C2×C4⋊C4—82no—
772C2×C4⋊C4—82no—
773C2×C4⋊C4—82no—
774C2×C4⋊C4C2411yescharacteristic
775C2×C4⋊C4C2412yes—
776C2×C4⋊C4C2411yescharacteristic
777C2×C4⋊C4C2411yescharacteristic
778C2×C4⋊C4C2411yescharacteristic
779C2×C4⋊C4C2412yes—
780C2×C4⋊C4C2412yes—
781C2×C4⋊C4C2414yes—
782C2×C4⋊C4C2412yes—
783C2×C4⋊C4C2414yes—
784C2×C4⋊C4C2412yes—
785C2×C4⋊C4C2412yes—
786C2×C4⋊C4C2412yes—
787C2×C4⋊C4C2412yes—
788C2×C4⋊C4C2412yes—
789C2×C4⋊C4C2411yescharacteristic
790C2×C4⋊C4C2412yes—
791C2×C4⋊C4C2411yescharacteristic
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2412yes—
794C2×C4⋊C4C2412yes—
795C2×C4⋊C4C2414yes—
796C2×C4⋊C4C2412yes—
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2414yes—
799C2×C4⋊C4C2414yes—
800C2×C4⋊C4C2414yes—
801C2×C4⋊C4C2414yes—
802C2×C4⋊C4C2414yes—
803C2×C4⋊C4C2412yes—
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2412yes—
809C2×C4⋊C4C2411yescharacteristic
810C2×C4⋊C4C2412yes—
811C2×C4⋊C4C2414yes—
812C2×C4⋊C4C2414yes—
813C2×C4⋊C4C2414yes—
814C2×C4⋊C4C2414yes—
815C2×C4⋊C4C2411yescharacteristic
816C2×C4⋊C4C2411yescharacteristic
817C2×C4⋊C4C2412yes—
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2411yescharacteristic
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2412yes—
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2414yes—
852C2×C4⋊C4C2414yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2412yes—
855C2×C4⋊C4C2412yes—
856C2×C4⋊C4C2412yes—
857C2×C22⋊C4—24no—
858C2×C22⋊C4—24no—
859C2×C22⋊C4—82no—
860C2×C22⋊C4—82no—
861C2×C22⋊C4C2412yes—
862C2×C22⋊C4C2412yes—
863C2×C22⋊C4C2412yes—
864C2×C22⋊C4C2412yes—
865C2×C22⋊C4C2414yes—
866C2×C22⋊C4C2412yes—
867C2×C22⋊C4C2412yes—
868C2×C22⋊C4C2414yes—
869C2×C22⋊C4C2412yes—
870C2×C22⋊C4C2412yes—
871C2×C22⋊C4C2414yes—
872C2×C22⋊C4C2414yes—
873C2×C22⋊C4C2414yes—
874C2×C22⋊C4C2414yes—
875C2×C22⋊C4C2412yes—
876C2×C22⋊C4C2412yes—
877C2×C22⋊C4C2412yes—
878C2×C22⋊C4C2412yes—
879C2×C22⋊C4C2414yes—
880C2×C22⋊C4C2414yes—
881C2×C22⋊C4C2412yes—
882C2×C22⋊C4C2412yes—
883C2×C22⋊C4C2412yes—
884C2×C22⋊C4C2412yes—
885C2×C22⋊C4C2414yes—
886C2×C22⋊C4C2414yes—
887C2×C42—42no—
888C2×C42—42no—
889C2×C42—82no—
890C2×C42C2412yes—
891C2×C42C2412yes—
892C2×C42C2412yes—
893C2×C42C2412yes—
894C2×C42C2412yes—
895C2×C42C2411yescharacteristic
896C2×C42C2411yescharacteristic
897C2×C42C2414yes—
898C2×C42C2414yes—
899C2×C42C2414yes—
900C2×C42C2414yes—
901C2×C42C2414yes—
902C2×C42C2414yes—
903C2×C42C2414yes—
904C2×C42C2412yes—
905C2×C42C2412yes—
906C2×C42C2414yes—
907C2×C42C2414yes—
908C2×C42C2414yes—
909C2×C42C2412yes—
910C2×C42C2412yes—
911C2×C42C2412yes—
912C2×C42C2411yescharacteristic
913C2×C42C2411yescharacteristic
914#95C2412yes—
915#95C2412yes—
916#95C2412yes—
917#95C2412yes—
918#95C2412yes—
919#95C2412yes—
920#95C2412yes—
921#95C2412yes—
922#95C2414yes—
923#95C2414yes—
924#95C2414yes—
925#95C2414yes—
926#95C2414yes—
927#95C2414yes—
928#95C2414yes—
929#95C2414yes—
930#95C2412yes—
931#95C2412yes—
932#95C2412yes—
933#95C2412yes—
934#95C2412yes—
935#95C2412yes—
936#95C2412yes—
937#95C2412yes—
938#95C2414yes—
939#95C2414yes—
940#95C2414yes—
941#95C2414yes—
942#95C2414yes—
943#95C2414yes—
944#95C2414yes—
945#95C2414yes—
946#95C2414yes—
947#95C2414yes—
948#95C2412yes—
949#95C2412yes—
950#95C2412yes—
951#95C2414yes—
952#95C2414yes—
953#95C2414yes—
954#95C2414yes—
955#95C2412yes—
956#95C2414yes—
957#95C2414yes—
958#95C2414yes—
959#95C2414yes—
960#95C2414yes—
961#95C2414yes—
962#95C2412yes—
963#95C2412yes—
964#95C2412yes—
965#95C2414yes—
966#95C2414yes—
967#95C2412yes—
968#95C2412yes—
969#95C2412yes—
970#95C2412yes—
971#95C2414yes—
972#95C2414yes—
973#95C2414yes—
974#95C2414yes—
975#95C2414yes—
976#95C2412yes—
977#95C2414yes—
978#95C2414yes—
979#95C2414yes—
980#95C2414yes—
981#95C2414yes—
982#95C2414yes—
983#95C2414yes—
984#95C2414yes—
985#95C2414yes—
986#95C2414yes—
987#95C2414yes—
988#95C2414yes—
989#95C2414yes—
990#95C2414yes—
991#95C2414yes—
992C24—22no—
993C24—22no—
994C24—22no—
995C24—41no—
996C24—41no—
997C24—41no—
998C24—41no—
999C24C2512yes—
1000C24C2511yescharacteristic
1001C2×Q8—22no—
1002C2×Q8—24no—
1003C2×Q8—24no—
1004C2×Q8—22no—
1005C2×Q8—24no—
1006C2×Q8—24no—
1007C2×Q8—24no—
1008C2×Q8—42no—
1009C2×Q8—41no—
1010C2×Q8—41no—
1011C2×Q8—42no—
1012C2×Q8—41no—
1013C2×Q8—42no—
1014C2×Q8—42no—
1015C2×Q8—41no—
1016C22×C4—22no—
1017C22×C4—22no—
1018C22×C4—22no—
1019C22×C4—22no—
1020C22×C4—24no—
1021C22×C4—24no—
1022C22×C4—24no—
1023C22×C4—24no—
1024C22×C4—22no—
1025C22×C4—24no—
1026C22×C4—24no—
1027C22×C4—24no—
1028C22×C4—24no—
1029C22×C4—41no—
1030C22×C4—41no—
1031C22×C4—41no—
1032C22×C4—41no—
1033C22×C4—41no—
1034C22×C4—41no—
1035C22×C4—41no—
1036C22×C4—42no—
1037C22×C4—42no—
1038C22×C4—42no—
1039C22×C4—42no—
1040C22×C4—42no—
1041C22×C4—42no—
1042C22×C4—42no—
1043C22×C4—42no—
1044C22×C4—41no—
1045C22×C4—42no—
1046C22×C4—42no—
1047C22×C4—41no—
1048C22×C4—41no—
1049C22×C4—88no—
1050C22×C42−1+414yes—
1051C22×C42−1+414yes—
1052C22×C42−1+414yes—
1053C22×C4C2512yes—
1054C22×C4C2514yes—
1055C22×C4C2512yes—
1056C22×C4C2512yes—
1057C22×C4C2512yes—
1058C22×C4C2512yes—
1059C22×C4C2512yes—
1060C22×C4C2514yes—
1061C22×C4C2511yescharacteristic
1062C22×C4C2511yescharacteristic
1063C22×C4C2512yes—
1064C22×C4C2514yes—
1065C22×C4C2512yes—
1066C22×C4C2512yes—
1067C22×C4C2512yes—
1068C22×C4C2512yes—
1069C22×C4C2512yes—
1070C22×C4C2512yes—
1071C22×C4C2514yes—
1072C22×C4C2512yes—
1073C22×C4C2514yes—
1074C22×C4C2514yes—
1075C22×C4C2511yescharacteristic
1076C22×C4C2511yescharacteristic
1077C22×C4C2512yes—
1078C22×C4C2511yescharacteristic
1079C22×C4C2511yescharacteristic
1080C4⋊C4—28no—
1081C4⋊C4—28no—
1082C4⋊C4—24no—
1083C4⋊C4—24no—
1084C4⋊C4—22no—
1085C4⋊C4—22no—
1086C4⋊C4—24no—
1087C4⋊C4—22no—
1088C4⋊C4—24no—
1089C4⋊C4—24no—
1090C4⋊C4—22no—
1091C4⋊C4—24no—
1092C4⋊C4—28no—
1093C4⋊C4—24no—
1094C4⋊C4—24no—
1095C4⋊C4—24no—
1096C4⋊C4—24no—
1097C4⋊C4—28no—
1098C4⋊C4—22no—
1099C4⋊C4—24no—
1100C4⋊C4—22no—
1101C4⋊C4—24no—
1102C4⋊C4—24no—
1103C4⋊C4—42no—
1104C4⋊C4—42no—
1105C4⋊C4—44no—
1106C4⋊C4—44no—
1107C4⋊C4—44no—
1108C4⋊C4—44no—
1109C4⋊C4—44no—
1110C4⋊C4—44no—
1111C4⋊C4—42no—
1112C4⋊C4—42no—
1113C4⋊C4—42no—
1114C4⋊C4—42no—
1115C4⋊C4—42no—
1116C4⋊C4—41no—
1117C4⋊C4—41no—
1118C4⋊C4—42no—
1119C4⋊C4—42no—
1120C4⋊C4—42no—
1121C4⋊C4—42no—
1122C4⋊C4—44no—
1123C4⋊C4—44no—
1124C4⋊C4—44no—
1125C4⋊C4—41no—
1126C4⋊C4—42no—
1127C4⋊C4—44no—
1128C4⋊C4—44no—
1129C4⋊C4—44no—
1130C4⋊C4—44no—
1131C4⋊C4—44no—
1132C4⋊C4—44no—
1133C4⋊C4—44no—
1134C4⋊C4—44no—
1135C4⋊C4—44no—
1136C4⋊C4—44no—
1137C4⋊C4—41no—
1138C4⋊C4—42no—
1139C4⋊C4—42no—
1140C4⋊C4—42no—
1141C4⋊C4—42no—
1142C4⋊C4—44no—
1143C4⋊C4—44no—
1144C4⋊C4—44no—
1145C4⋊C4—44no—
1146C4⋊C4—42no—
1147C4⋊C4—42no—
1148C4⋊C4—42no—
1149C4⋊C4—44no—
1150C4⋊C4—44no—
1151C4⋊C4—44no—
1152C4⋊C4—44no—
1153C4⋊C4—44no—
1154C4⋊C4—44no—
1155C4⋊C4—44no—
1156C4⋊C4—44no—
1157C4⋊C4—44no—
1158C4⋊C4—44no—
1159C4⋊C4—44no—
1160C4⋊C4—42no—
1161C4⋊C4—42no—
1162C4⋊C4—42no—
1163C22⋊C4—24no—
1164C22⋊C4—28no—
1165C22⋊C4—24no—
1166C22⋊C4—28no—
1167C22⋊C4—24no—
1168C22⋊C4—24no—
1169C22⋊C4—24no—
1170C22⋊C4—24no—
1171C22⋊C4—24no—
1172C22⋊C4—24no—
1173C22⋊C4—44no—
1174C22⋊C4—44no—
1175C22⋊C4—44no—
1176C22⋊C4—44no—
1177C22⋊C4—42no—
1178C22⋊C4—42no—
1179C22⋊C4—42no—
1180C22⋊C4—42no—
1181C22⋊C4—44no—
1182C22⋊C4—44no—
1183C22⋊C4—44no—
1184C22⋊C4—42no—
1185C22⋊C4—44no—
1186C22⋊C4—42no—
1187C22⋊C4—42no—
1188C22⋊C4—42no—
1189C42—24no—
1190C42—22no—
1191C42—22no—
1192C42—24no—
1193C42—24no—
1194C42—24no—
1195C42—24no—
1196C42—42no—
1197C42—41no—
1198C42—41no—
1199C42—42no—
1200C42—42no—
1201C42—42no—
1202C42—42no—
1203C42—44no—
1204C42—44no—
1205C42—44no—
1206C42—44no—
1207C42—44no—
1208C42—44no—
1209C42—44no—
1210C42—44no—
1211C42—44no—
1212C42—44no—
1213C23—21no—
1214C23—21no—
1215C23—21no—
1216C23—21no—
1217C23—22no—
1218C23—22no—
1219C23—22no—
1220C23—22no—
1221C23—22no—
1222C23—22no—
1223C23—22no—
1224C23—44no—
1225C23—44no—
1226C23—44no—
1227C23—82no—
1228C23—82no—
1229C23—82no—
1230C23—82no—
1231C23C2×2−1+412yes—
1232C23C2×2−1+412yes—
1233C23C2×2−1+412yes—
1234C23C2611yescharacteristic
1235Q8—48no—
1236Q8—44no—
1237Q8—48no—
1238Q8—82no—
1239Q8—84no—
1240C2×C4—22no—
1241C2×C4—21no—
1242C2×C4—21no—
1243C2×C4—21no—
1244C2×C4—21no—
1245C2×C4—21no—
1246C2×C4—21no—
1247C2×C4—22no—
1248C2×C4—28no—
1249C2×C4—22no—
1250C2×C4—21no—
1251C2×C4—21no—
1252C2×C4—24no—
1253C2×C4—22no—
1254C2×C4—22no—
1255C2×C4—24no—
1256C2×C4—22no—
1257C2×C4—22no—
1258C2×C4—24no—
1259C2×C4—22no—
1260C2×C4—22no—
1261C2×C4—22no—
1262C2×C4—22no—
1263C2×C4—24no—
1264C2×C4—22no—
1265C2×C4—22no—
1266C2×C4—24no—
1267C2×C4—22no—
1268C2×C4—22no—
1269C2×C4—24no—
1270C2×C4—22no—
1271C2×C4—22no—
1272C2×C4—22no—
1273C2×C4—22no—
1274C2×C4—21no—
1275C2×C4—21no—
1276C2×C4—22no—
1277C2×C4—22no—
1278C2×C4—22no—
1279C2×C4—22no—
1280C2×C4—22no—
1281C2×C4—22no—
1282C2×C4—24no—
1283C2×C4—22no—
1284C2×C4—24no—
1285C2×C4—24no—
1286C2×C4—24no—
1287C2×C4—24no—
1288C2×C4—22no—
1289C2×C4—22no—
1290C2×C4—22no—
1291C2×C4—22no—
1292C2×C4—22no—
1293C2×C4—24no—
1294C2×C4—22no—
1295C2×C4—22no—
1296C2×C4—24no—
1297C2×C4—24no—
1298C2×C4—22no—
1299C2×C4—22no—
1300C2×C4—22no—
1301C2×C4—22no—
1302C2×C4—22no—
1303C2×C4—22no—
1304C2×C4—22no—
1305C2×C4—24no—
1306C2×C4—24no—
1307C2×C4—24no—
1308C2×C4—24no—
1309C2×C4—22no—
1310C2×C4—22no—
1311C2×C4—22no—
1312C2×C4—22no—
1313C2×C4—21no—
1314C2×C4—21no—
1315C2×C4—44no—
1316C2×C4—44no—
1317C2×C4—44no—
1318C2×C4—48no—
1319C2×C4—84no—
1320C2×C4—84no—
1321C2×C4—84no—
1322C2×C4—84no—
1323C2×C4—82no—
1324C2×C4—84no—
1325C2×C4—82no—
1326C2×C4C2×2−1+412yes—
1327C2×C4C2×2−1+414yes—
1328C2×C4C2×2−1+412yes—
1329C2×C4C2×2−1+412yes—
1330C2×C4C2×2−1+412yes—
1331C2×C4#58512yes—
1332C2×C4#58512yes—
1333C22—22no—
1334C22—22no—
1335C22—22no—
1336C22—22no—
1337C22—22no—
1338C22—22no—
1339C22—42no—
1340C22—42no—
1341C22—42no—
1342C22—42no—
1343C22—42no—
1344C22—42no—
1345C22—42no—
1346C22—88no—
1347C22#355614yes—
1348C22C22×2−1+411yescharacteristic
1349C22C22×2−1+411yescharacteristic
1350C22C22×2−1+411yescharacteristic
1351C22C2×#58511yescharacteristic
1352C22C2×#58511yescharacteristic
1353C22H(7,𝔽2)11yescharacteristic
1354C22H(7,𝔽2)11yescharacteristic
1355C4—22no—
1356C4—24no—
1357C4—22no—
1358C4—22no—
1359C4—42no—
1360C4—44no—
1361C4—44no—
1362C4—42no—
1363C4—42no—
1364C4—44no—
1365C4—42no—
1366C4—42no—
1367C4—42no—
1368C4—42no—
1369C4—42no—
1370C4—42no—
1371C4—44no—
1372C4—42no—
1373C4—42no—
1374C4—44no—
1375C4—42no—
1376C4—42no—
1377C4—42no—
1378C4—41no—
1379C4—41no—
1380C4—44no—
1381C4#356414yes—
1382C2—24no—
1383C2—82no—
1384C2C2×#356411yescharacteristic
1385C2C2×#355611yescharacteristic
1386C2#6288111yescharacteristic
1387C2#6290211yescharacteristic
1388C2#6290211yescharacteristic
1389C2#6292611yescharacteristic
1390C2#6292911yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC25C24
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59868C2semidirect
2. #59321C2semidirect
3. #58230C2semidirect
4. #55672C2semidirect
5. #54742C2semidirect
6. #54106C2semidirect
7. #53107C2semidirect
8. #52965C2semidirect
9. #52452C2semidirect
10. #45346C2semidirect
11. #45329C2semidirect
12. #42832C2semidirect
13. #42713C2semidirect
14. #42455C2semidirect
15. #42455C2semidirect
17. #39751C2semidirect
18. #39748C2semidirect
19. #39679C2semidirect
20. #39639C2semidirect
25. #36599C2semidirect
26. #36552C2semidirect
35. #2839C22semidirect
36. #2839C22semidirect
37. #2839C22semidirect
38. #2839C22semidirect
39. #2839C22semidirect
40. #2839C22semidirect
41. #2839C22semidirect
46. #2822C22semidirect
47. #2810C22semidirect
48. #2809C22semidirect
49. #2809C22semidirect
50. #2805C22semidirect
51. #2805C22semidirect
52. #2802C22semidirect
53. #2802C22semidirect
54. #2802C22semidirect
55. #2802C22semidirect
57. #2791C22semidirect
58. #2791C22semidirect
59. #2791C22semidirect
63. #2774C22semidirect
64. #2774C22semidirect
65. #2774C22semidirect
69. #2767C22semidirect
70. #2767C22semidirect
71. #2767C22semidirect
72. #2767C22semidirect
73. #2755C22semidirect
81. #2726C22semidirect
82. #2726C22semidirect
92. #2719C22semidirect
93. #2719C22semidirect
94. #2719C22semidirect
96. #2713C22semidirect
123. #2590C22semidirect
124. #2590C22semidirect
125. #2590C22semidirect
127. #2588C22semidirect
129. #2585C22semidirect
130. #2585C22semidirect
131. #2584C22semidirect
132. #2584C22semidirect
134. #2582C22semidirect
135. #2582C22semidirect
136. #2581C22semidirect
137. #2581C22semidirect
141. #2568C22semidirect
142. #2565C22semidirect
143. #2552C22semidirect
144. #2552C22semidirect
145. #2552C22semidirect
146. #2552C22semidirect
147. #2552C22semidirect
148. #2552C22semidirect
149. #2550C22semidirect
150. #2546C22semidirect
151. #2520C22semidirect
154. #2511C22semidirect
155. #2511C22semidirect
156. #2511C22semidirect
157. #2511C22semidirect
158. #2511C22semidirect
159. #2509C22semidirect
160. #2509C22semidirect
161. #2509C22semidirect
162. #2508C22semidirect
163. #2508C22semidirect
164. #2508C22semidirect
165. #2508C22semidirect
166. #2506C22semidirect
167. #2506C22semidirect
198. #2462C22semidirect
199. #2462C22semidirect
200. #2453C22semidirect
201. #2453C22semidirect
202. #2453C22semidirect
203. #2446C22semidirect
204. #2446C22semidirect
219. #2370C22semidirect
220. #2370C22semidirect
221. #2365C22semidirect
222. #2365C22semidirect
226. #2355C22semidirect
227. #2355C22semidirect
228. #2355C22semidirect
229. #2351C22semidirect
230. Q8×C4⋊C4C22semidirect
231. Q8×C4⋊C4C22semidirect

Maximal subgroups

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

subgroupindex
#598682
#593212
#582302
#556722
#547422
#541062
#531072
#529652
#524522
#453462
#453292
#428322
#427132
#424552
#405632
#397512
#397482
#396792
#396392
#378502
#374602
#367602
#365992
#365522
#350142
C2×#24972
#345782