Finite Group Databasebeta

← #7716089

Subgroups — #7716089

Order 512.

4520 conjugacy classes of subgroups.

The subgroup lattice has 1458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#48847C214yesmaximal, complemented
2#48843C214yesmaximal, complemented
3#47971C214yesmaximal, complemented
4#47967C214yesmaximal, complemented
5#45415C212yesmaximal, complemented
6#45405C212yesmaximal, complemented
7#45274C212yesmaximal, complemented
8#45273C212yesmaximal, complemented
9#45190C212yesmaximal, complemented
10#45180C212yesmaximal, complemented
11#45121C212yesmaximal, complemented
12#45099C212yesmaximal, complemented
13#39179C212yesmaximal, complemented
14#38963C212yesmaximal, complemented
15#38959C214yesmaximal
16#38102C214yesmaximal
17#36752C212yesmaximal, complemented
18#36751C212yesmaximal, complemented
19#36435C212yesmaximal, complemented
20#36425C212yesmaximal, complemented
21#35253C211yesmaximal, characteristic
22#35253C211yesmaximal, characteristic
23#35159C212yesmaximal, complemented
24#35020C211yesmaximal, characteristic
25#35015C212yesmaximal, complemented
26#34578C211yesmaximal, characteristic
27#34380C211yesmaximal, characteristic
28#34380C211yesmaximal, characteristic
29C2×#2362C211yesmaximal, characteristic
30C2×#557C2212yescomplemented
31C2×#544C2211yescharacteristic
32C2×#544C2211yescharacteristic
33C22×C22⋊Q8C2211yescharacteristic
34C22×C4×Q8C2211yescharacteristic
35C22×#117C2211yescharacteristic
36#2857C2212yes—
37#2857C2212yes—
38#2855C2214yes—
39#2851C2212yes—
40#2851C2214yes—
41#2851C2212yes—
42#2851C2212yes—
43#2851C2212yes—
44#2809C2214yescomplemented
45#2807C2214yes—
46#2806C2214yescomplemented
47#2806C2214yescomplemented
48#2805C2214yescomplemented
49#2802C2214yescomplemented
50#2802C2214yescomplemented
51#2799C2214yescomplemented
52#2799C2214yescomplemented
53#2792C2214yescomplemented
54#2792C2214yescomplemented
55#2792C2214yescomplemented
56#2791C2214yescomplemented
57#2791C2214yescomplemented
58#2791C2214yescomplemented
59#2790C2214yes—
60#2790C2214yes—
61#2788C2214yes—
62#2788C2214yes—
63#2788C2214yes—
64#2774C2214yescomplemented
65#2774C2214yescomplemented
66#2774C2214yescomplemented
67#2768C2214yes—
68#2768C2214yes—
69#2768C2214yes—
70#2763C2214yes—
71#2755C2214yescomplemented
72#2755C2214yescomplemented
73#2755C2214yescomplemented
74#2742C2214yes—
75#2742C2214yes—
76#2734C2214yescomplemented
77#2729C2214yes—
78#2726C2214yescomplemented
79#2720C2214yes—
80#2713C2214yescomplemented
81#2713C2214yescomplemented
82#2704C2214yes—
83#2704C2214yes—
84#2667C2212yes—
85#2667C2212yes—
86#2665C2212yes—
87#2665C2212yes—
88#2659C2211yescharacteristic
89#2659C2211yescharacteristic
90#2646C2214yes—
91#2646C2211yescharacteristic
92#2646C2211yescharacteristic
93#2646C2212yes—
94#2646C2212yes—
95#2629C2212yes—
96#2629C2212yes—
97#2628C2212yes—
98#2628C2212yes—
99#2627C2214yes—
100#2626C2212yes—
101#2626C2212yes—
102#2590C2214yescomplemented
103#2590C2214yescomplemented
104#2590C2214yescomplemented
105#2589C2214yes—
106#2589C2214yes—
107#2588C2214yescomplemented
108#2588C2214yescomplemented
109#2588C2214yescomplemented
110#2587C2214yes—
111#2587C2214yes—
112#2586C2214yescomplemented
113#2585C2214yescomplemented
114#2584C2212yescomplemented
115#2584C2212yescomplemented
116#2582C2212yescomplemented
117#2581C2212yescomplemented
118#2581C2212yescomplemented
119#2581C2214yescomplemented
120#2574C2214yes—
121#2574C2214yes—
122#2574C2214yes—
123#2569C2214yes—
124#2569C2214yes—
125#2569C2214yes—
126#2568C2212yescomplemented
127#2567C2212yescomplemented
128#2565C2212yescomplemented
129#2565C2212yescomplemented
130#2565C2214yescomplemented
131#2556C2214yes—
132#2552C2212yescomplemented
133#2550C2212yescomplemented
134#2550C2212yescomplemented
135#2549C2214yes—
136#2522C2214yes—
137#2522C2214yes—
138#2522C2214yes—
139#2511C2214yescomplemented
140#2509C2212yescomplemented
141#2509C2214yescomplemented
142#2509C2212yescomplemented
143#2509C2214yescomplemented
144#2508C2212yescomplemented
145#2508C2212yescomplemented
146#2508C2214yescomplemented
147#2508C2214yescomplemented
148#2507C2212yescomplemented
149#2507C2212yescomplemented
150#2507C2214yescomplemented
151#2507C2214yescomplemented
152#2507C2214yescomplemented
153#2506C2214yescomplemented
154#2506C2214yescomplemented
155#2497C2214yes—
156#2497C2214yes—
157#2492C2214yes—
158#2465C2214yes—
159#2453C2212yescomplemented
160#2453C2212yescomplemented
161#2453C2212yescomplemented
162#2453C2214yescomplemented
163#2453C2212yescomplemented
164#2451C2212yescomplemented
165#2451C2212yescomplemented
166#2451C2214yescomplemented
167#2451C2214yescomplemented
168#2446C2214yescomplemented
169#2442C2212yes—
170#2442C2212yes—
171#2442C2212yes—
172#2442C2214yes—
173#2442C2212yes—
174#2442C2212yes—
175#2442C2212yes—
176#2441C2212yes—
177#2441C2212yes—
178#2440C2212yes—
179#2440C2212yes—
180#2440C2214yes—
181#2439C2212yes—
182#2439C2212yes—
183#2438C2214yes—
184#2438C2214yes—
185#2438C2214yes—
186#2438C2214yes—
187#2438C2214yes—
188#2438C2214yes—
189#2437C2214yes—
190#2437C2214yes—
191#2423C2214yes—
192#2396C2212yes—
193#2396C2212yes—
194#2396C2212yes—
195#2396C2212yes—
196#2378C2214yes—
197#2378C2214yes—
198#2370C2212yescomplemented
199#2370C2212yescomplemented
200#2369C2212yescomplemented
201#2362C2212yes—
202#2362C2212yes—
203#2362C2212yes—
204#2362C2214yes—
205#2362C2214yes—
206#2362C2212yes—
207#2360C2212yes—
208#2360C2212yes—
209#2360C2212yes—
210#2360C2212yes—
211#2355C2212yescomplemented
212#2351C2212yescomplemented
213#2351C2212yescomplemented
214Q8×C4⋊C4C2212yescomplemented
215#2344C2212yes—
216#2344C2212yes—
217#2342C2214yes—
218#2342C2214yes—
219Q8×C22⋊C4C2212yes—
220Q8×C22⋊C4C2212yes—
221#2329C2214yes—
222#2329C2212yes—
223#2329C2212yes—
224#2329C2212yes—
225#2329C2212yes—
226#2323C2212yes—
227#2323C2212yes—
228#2323C2212yes—
229#2323C2212yes—
230#2317C2214yes—
231#2317C2211yescharacteristic
232#2317C2211yescharacteristic
233#2317C2211yescharacteristic
234#2317C2211yescharacteristic
235#2316C2212yes—
236#2316C2212yes—
237#2316C2211yescharacteristic
238#2316C2211yescharacteristic
239#2315C2212yes—
240#2315C2212yes—
241#2313C2212yes—
242#2313C2212yes—
243C4×C22⋊Q8C2212yes—
244C4×C22⋊Q8C2212yes—
245C4×C22⋊Q8C2214yes—
246#2296C2214yes—
247C2×#391C2211yescharacteristic
248C2×#389C2211yescharacteristic
249C2×#388C2212yes—
250C2×#388C2212yes—
251C2×#387C2212yes—
252#2280C2211yescharacteristic
253#2280C2211yescharacteristic
254C2×#380C2211yescharacteristic
255C2×#380C2211yescharacteristic
256C2×C4×C4⋊C4C2211yescharacteristic
257C2×C4×C4⋊C4C2212yes—
258C2×C4×C22⋊C4C2211yescharacteristic
259C23×Q8C2311yescharacteristic
260C24×C4C2311yescharacteristic
261#557—48no—
262#544—44no—
263#544—44no—
264C2×C4⋊Q8C2312yes—
265C2×C4⋊Q8C2312yes—
266C2×C4⋊Q8C2312yes—
267C2×C4⋊Q8C2312yes—
268C2×C4⋊Q8C2314yes—
269C2×#125C2312yes—
270C2×#125C2312yes—
271C2×#125C2312yes—
272C2×#125C2314yes—
273C2×#125C2312yes—
274C2×#125C2312yes—
275C2×#125C2312yes—
276C2×#125C2314yes—
277C2×C22⋊Q8Q8116yescomplemented
278C2×C22⋊Q8C2314yes—
279C2×C22⋊Q8C2314yes—
280C2×C22⋊Q8C2312yes—
281C2×C22⋊Q8C2312yes—
282C2×C22⋊Q8C2314yes—
283C2×C22⋊Q8C2314yes—
284C2×C22⋊Q8C2312yes—
285C2×C22⋊Q8C2312yes—
286C2×C22⋊Q8C2312yes—
287C2×C22⋊Q8C2312yes—
288C2×C4×Q8—44no—
289C2×C4×Q8C2312yes—
290C2×C4×Q8C2312yes—
291C2×C4×Q8C2312yes—
292C2×C4×Q8C2314yes—
293C2×C4×Q8C2312yes—
294C2×C4×Q8C2312yes—
295C2×C4×Q8C2312yes—
296C2×C4×Q8C2312yes—
297C2×C4×Q8C2312yes—
298C2×C4×Q8C2314yes—
299C2×#117—44no—
300C2×#117C2311yescharacteristic
301C2×#117C2311yescharacteristic
302C2×#117C2314yes—
303C2×#117C2314yes—
304C2×#117C2311yescharacteristic
305C2×#117C2311yescharacteristic
306C2×#117C2311yescharacteristic
307C2×#117C2311yescharacteristic
308C2×#117C2311yescharacteristic
309C2×#117C2311yescharacteristic
310C2×#117C2312yes—
311C2×#117C2312yes—
312C22×C4⋊C4C2311yescharacteristic
313C22×C4⋊C4C2311yescharacteristic
314C22×C4⋊C4C2311yescharacteristic
315C22×C4⋊C4C2312yes—
316C22×C4⋊C4C2311yescharacteristic
317C22×C4⋊C4C2311yescharacteristic
318C22×C4⋊C4C2311yescharacteristic
319C22×C4⋊C4C2312yes—
320C22×C4⋊C4C2312yes—
321C22×C4⋊C4C2311yescharacteristic
322C22×C22⋊C4C2312yes—
323C22×C22⋊C4C2312yes—
324C22×C22⋊C4C2311yescharacteristic
325C22×C22⋊C4C2311yescharacteristic
326C22×C22⋊C4C2312yes—
327C22×C22⋊C4C2312yes—
328C22×C42C2312yes—
329C22×C42C2311yescharacteristic
330C22×C42C2312yes—
331C22×C42C2311yescharacteristic
332C22×C42C2312yes—
333#400C2314yes—
334#400C2314yes—
335#400C2314yes—
336#400C2314yes—
337#400C2314yes—
338#400C2314yes—
339#400C2314yes—
340#400C2314yes—
341#400C2314yes—
342#400C2314yes—
343#400C2314yes—
344#400C2314yes—
345#400C2314yes—
346#400C2312yes—
347#400C2314yes—
348#400C2314yes—
349#400C2312yes—
350#400C2314yes—
351#400C2314yes—
352#400C2312yes—
353#400C2312yes—
354#400C2314yes—
355#400C2314yes—
356#400C2314yes—
357#399C2312yes—
358#399C2314yes—
359#399C2312yes—
360#399C2312yes—
361#399C2312yes—
362#399C2314yes—
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#398C2314yes—
384#398C2312yes—
385#398C2314yes—
386#398C2312yes—
387#398C2314yes—
388#398C2314yes—
389#398C2314yes—
390#398C2314yes—
391#398C2312yes—
392#398C2312yes—
393#398C2314yes—
394#398C2312yes—
395#398C2312yes—
396#398C2312yes—
397#398C2312yes—
398#398C2314yes—
399#398C2314yes—
400#398C2314yes—
401#398C2314yes—
402#398C2314yes—
403#396C2312yes—
404#396C2314yes—
405#396C2314yes—
406#396C2312yes—
407#396C2312yes—
408#396C2314yes—
409#396C2312yes—
410#396C2312yes—
411#396C2312yes—
412#396C2312yes—
413#396C2312yes—
414#396C2314yes—
415#395C2314yes—
416#395C2314yes—
417#395C2314yes—
418#395C2314yes—
419#395C2314yes—
420#395C2314yes—
421#395C2314yes—
422#395C2314yes—
423#395C2314yes—
424#395C2314yes—
425#395C2314yes—
426#395C2312yes—
427#395C2312yes—
428#395C2312yes—
429#395C2312yes—
430#395C2314yes—
431#393C2312yes—
432#393C2312yes—
433#393C2314yes—
434#393C2312yes—
435#393C2312yes—
436#393C2314yes—
437#391C2312yes—
438#391C2312yes—
439#391C2312yes—
440#391C2314yes—
441#391C2314yes—
442#391C2314yes—
443#391C2314yes—
444#391C2312yes—
445#391C2314yes—
446#391C2314yes—
447#391C2312yes—
448#391C2312yes—
449#391C2314yes—
450#391C2314yes—
451#391C2314yes—
452#391C2312yes—
453#391C2314yes—
454#391C2314yes—
455#391C2314yes—
456#391C2314yes—
457#391C2314yes—
458#391C2314yes—
459#391C2314yes—
460#391C2314yes—
461#391C2312yes—
462#391C2314yes—
463#389C2312yes—
464#389C2312yes—
465#389C2312yes—
466#389C2312yes—
467#389C2314yes—
468#389C2314yes—
469#389C2314yes—
470#389C2314yes—
471#389C2312yes—
472#389C2312yes—
473#389C2312yes—
474#389C2312yes—
475#389C2312yes—
476#389C2312yes—
477#389C2312yes—
478#389C2314yes—
479#389C2314yes—
480#389C2314yes—
481#389C2314yes—
482#389C2312yes—
483#389C2312yes—
484#389C2312yes—
485#389C2312yes—
486#389C2314yes—
487#389C2314yes—
488#389C2312yes—
489#389C2314yes—
490#389C2312yes—
491#389C2312yes—
492#389C2312yes—
493#389C2314yes—
494#389C2312yes—
495#389C2312yes—
496#389C2312yes—
497#389C2314yes—
498#389C2312yes—
499#389C2314yes—
500#389C2314yes—
501#389C2312yes—
502#389C2314yes—
503#389C2314yes—
504#389C2312yes—
505#389C2312yes—
506#389C2314yes—
507#389C2314yes—
508#389C2312yes—
509#389C2314yes—
510#389C2314yes—
511#389C2314yes—
512#389C2314yes—
513#389C2314yes—
514#389C2314yes—
515#389C2314yes—
516#389C2314yes—
517#389C2314yes—
518#389C2314yes—
519#389C2314yes—
520#389C2314yes—
521#389C2314yes—
522#389C2314yes—
523#389C2312yes—
524#389C2314yes—
525#389C2314yes—
526#389C2314yes—
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#388C2314yes—
542#388C2314yes—
543#387C2314yes—
544#387C2312yes—
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#387C2312yes—
572#387C2314yes—
573#387C2314yes—
574#387C2314yes—
575#387C2314yes—
576#387C2314yes—
577#387C2314yes—
578#387C2314yes—
579#387C2314yes—
580#387C2314yes—
581#387C2314yes—
582#387C2314yes—
583#387C2314yes—
584#387C2312yes—
585#387C2314yes—
586#387C2314yes—
587#387C2314yes—
588#387C2312yes—
589#387C2314yes—
590#387C2314yes—
591#387C2314yes—
592#387C2314yes—
593#387C2314yes—
594#387C2314yes—
595#387C2314yes—
596#387C2314yes—
597#385C2314yes—
598#385C2314yes—
599#385C2314yes—
600#385C2314yes—
601#385C2314yes—
602#385C2314yes—
603#385C2314yes—
604#385C2314yes—
605#385C2314yes—
606#385C2312yes—
607#385C2314yes—
608#385C2314yes—
609#385C2314yes—
610#385C2314yes—
611#385C2314yes—
612#385C2312yes—
613#385C2314yes—
614#385C2314yes—
615#385C2314yes—
616#385C2314yes—
617#385C2314yes—
618#385C2314yes—
619#385C2312yes—
620#385C2312yes—
621#384C2312yes—
622#384C2312yes—
623#384C2314yes—
624#384C2314yes—
625#384C2312yes—
626#384C2312yes—
627#384C2314yes—
628#382C2312yes—
629#382C2312yes—
630#382C2314yes—
631#382C2312yes—
632#382C2314yes—
633#382C2314yes—
634#382C2312yes—
635#382C2312yes—
636#382C2312yes—
637#382C2314yes—
638#381C2314yes—
639#381C2314yes—
640#381C2312yes—
641#381C2312yes—
642#380C2311yescharacteristic
643#380C2311yescharacteristic
644#380C2312yes—
645#380C2312yes—
646#380C2312yes—
647#380C2312yes—
648#380C2312yes—
649#380C2314yes—
650#380C2314yes—
651#380C2314yes—
652#380C2314yes—
653#380C2314yes—
654#380C2314yes—
655#380C2311yescharacteristic
656#380C2311yescharacteristic
657#380C2314yes—
658#380C2314yes—
659#380C2314yes—
660#380C2312yes—
661#380C2312yes—
662#380C2311yescharacteristic
663#380C2311yescharacteristic
664#380C2311yescharacteristic
665#380C2311yescharacteristic
666#380C2312yes—
667#380C2312yes—
668#380C2314yes—
669#380C2312yes—
670#379C2312yes—
671#379C2312yes—
672C4×C4⋊C4C2314yes—
673C4×C4⋊C4C2312yes—
674C4×C4⋊C4C2312yes—
675C4×C4⋊C4C2312yes—
676C4×C4⋊C4C2312yes—
677C4×C4⋊C4C2314yes—
678C4×C4⋊C4C2314yes—
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2312yes—
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2314yes—
684C4×C4⋊C4C2314yes—
685C4×C4⋊C4C2314yes—
686C4×C4⋊C4C2314yes—
687C4×C4⋊C4C2314yes—
688C4×C4⋊C4C2314yes—
689C4×C4⋊C4C2314yes—
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2312yes—
692C4×C4⋊C4C2312yes—
693C4×C4⋊C4C2314yes—
694C4×C4⋊C4C2314yes—
695C4×C4⋊C4C2312yes—
696C4×C22⋊C4C2314yes—
697C4×C22⋊C4C2314yes—
698C4×C22⋊C4C2312yes—
699C4×C22⋊C4C2312yes—
700C4×C22⋊C4C2314yes—
701C4×C22⋊C4C2314yes—
702C4×C22⋊C4C2314yes—
703C4×C22⋊C4C2314yes—
704C4×C22⋊C4C2312yes—
705C4×C22⋊C4C2312yes—
706C4×C22⋊C4C2312yes—
707C4×C22⋊C4C2312yes—
708C4×C22⋊C4C2312yes—
709C4×C22⋊C4C2312yes—
710C2×#95C2312yes—
711C2×#95C2312yes—
712C2×#95C2312yes—
713C2×#95C2312yes—
714C2×#95C2311yescharacteristic
715C2×#95C2311yescharacteristic
716C2×#95C2312yes—
717C2×#95C2312yes—
718C25C2411yescharacteristic
719C22×Q8—42no—
720C22×Q8—42no—
721C22×Q8C2×Q818yes—
722C22×Q8C2412yes—
723C22×Q8C2414yes—
724C22×Q8C2412yes—
725C22×Q8C2412yes—
726C22×Q8C2414yes—
727C22×Q8C2412yes—
728C23×C4—42no—
729C23×C4—42no—
730C23×C4C2×Q818yes—
731C23×C4C2412yes—
732C23×C4C2412yes—
733C23×C4C2411yescharacteristic
734C23×C4C2411yescharacteristic
735C23×C4C2411yescharacteristic
736C23×C4C2411yescharacteristic
737C23×C4C2412yes—
738C23×C4C2411yescharacteristic
739C23×C4C2411yescharacteristic
740C23×C4C2411yescharacteristic
741C23×C4C2412yes—
742C23×C4C2412yes—
743C23×C4C2412yes—
744C23×C4C2412yes—
745C23×C4C2412yes—
746C23×C4C2411yescharacteristic
747C23×C4C2411yescharacteristic
748C23×C4C2411yescharacteristic
749C4⋊Q8—28no—
750C4⋊Q8—44no—
751C4⋊Q8—44no—
752C4⋊Q8—44no—
753C4⋊Q8—48no—
754#125—28no—
755#125—44no—
756#125—44no—
757#125—44no—
758#125—44no—
759#125—44no—
760#125—48no—
761#125—48no—
762C22⋊Q8—48no—
763C22⋊Q8—48no—
764C22⋊Q8—44no—
765C22⋊Q8—44no—
766C22⋊Q8—48no—
767C22⋊Q8—48no—
768C22⋊Q8C2×Q8116yes—
769C22⋊Q8C2×Q8116yes—
770C22⋊Q8C2×Q8116yes—
771C22⋊Q8C2×Q8116yes—
772C4×Q8—28no—
773C4×Q8—44no—
774C4×Q8—44no—
775C4×Q8—48no—
776C4×Q8—44no—
777C4×Q8—44no—
778C4×Q8—44no—
779C4×Q8—48no—
780C4×Q8—44no—
781C4×Q8—44no—
782#117—24no—
783#117—24no—
784#117—42no—
785#117—42no—
786#117—42no—
787#117—42no—
788#117—44no—
789#117—44no—
790#117—48no—
791#117—48no—
792#117—42no—
793#117—42no—
794C2×C4⋊C4—24no—
795C2×C4⋊C4—42no—
796C2×C4⋊C4—42no—
797C2×C4⋊C4—42no—
798C2×C4⋊C4—44no—
799C2×C4⋊C4—42no—
800C2×C4⋊C4—42no—
801C2×C4⋊C4—44no—
802C2×C4⋊C4C2×Q818yes—
803C2×C4⋊C4C2×Q8116yes—
804C2×C4⋊C4C2411yescharacteristic
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2411yescharacteristic
807C2×C4⋊C4C2411yescharacteristic
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2412yes—
810C2×C4⋊C4C2412yes—
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2414yes—
814C2×C4⋊C4C2414yes—
815C2×C4⋊C4C2414yes—
816C2×C4⋊C4C2412yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2412yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2414yes—
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2411yescharacteristic
825C2×C4⋊C4C2411yescharacteristic
826C2×C4⋊C4C2411yescharacteristic
827C2×C4⋊C4C2411yescharacteristic
828C2×C4⋊C4C2411yescharacteristic
829C2×C4⋊C4C2411yescharacteristic
830C2×C4⋊C4C2411yescharacteristic
831C2×C4⋊C4C2411yescharacteristic
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2412yes—
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2412yes—
846C2×C4⋊C4C2412yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2414yes—
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2412yes—
855C2×C4⋊C4C2412yes—
856C2×C4⋊C4C2412yes—
857C2×C4⋊C4C2412yes—
858C2×C4⋊C4C2412yes—
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2414yes—
864C2×C4⋊C4C2414yes—
865C2×C4⋊C4C2412yes—
866C2×C4⋊C4C2412yes—
867C2×C4⋊C4C2414yes—
868C2×C4⋊C4C2414yes—
869C2×C4⋊C4C2414yes—
870C2×C4⋊C4C2414yes—
871C2×C4⋊C4C2412yes—
872C2×C4⋊C4C2412yes—
873C2×C4⋊C4C2412yes—
874C2×C4⋊C4C2414yes—
875C2×C4⋊C4C2412yes—
876C2×C4⋊C4C2414yes—
877C2×C4⋊C4C2414yes—
878C2×C4⋊C4C2414yes—
879C2×C4⋊C4C2414yes—
880C2×C4⋊C4C2414yes—
881C2×C4⋊C4C2412yes—
882C2×C4⋊C4C2412yes—
883C2×C4⋊C4C2414yes—
884C2×C4⋊C4C2414yes—
885C2×C4⋊C4C2411yescharacteristic
886C2×C22⋊C4—44no—
887C2×C22⋊C4—44no—
888C2×C22⋊C4—44no—
889C2×C22⋊C4—42no—
890C2×C22⋊C4—42no—
891C2×C22⋊C4C2×Q8116yes—
892C2×C22⋊C4C2412yes—
893C2×C22⋊C4C2412yes—
894C2×C22⋊C4C2414yes—
895C2×C22⋊C4C2414yes—
896C2×C22⋊C4C2412yes—
897C2×C22⋊C4C2412yes—
898C2×C22⋊C4C2412yes—
899C2×C22⋊C4C2412yes—
900C2×C22⋊C4C2412yes—
901C2×C22⋊C4C2412yes—
902C2×C22⋊C4C2412yes—
903C2×C22⋊C4C2412yes—
904C2×C22⋊C4C2412yes—
905C2×C22⋊C4C2412yes—
906C2×C22⋊C4C2414yes—
907C2×C22⋊C4C2414yes—
908C2×C22⋊C4C2412yes—
909C2×C22⋊C4C2412yes—
910C2×C22⋊C4C2412yes—
911C2×C22⋊C4C2412yes—
912C2×C22⋊C4C2412yes—
913C2×C22⋊C4C2412yes—
914C2×C22⋊C4C2412yes—
915C2×C22⋊C4C2412yes—
916C2×C22⋊C4C2414yes—
917C2×C22⋊C4C2414yes—
918C2×C42—44no—
919C2×C42—42no—
920C2×C42—44no—
921C2×C42—42no—
922C2×C42—44no—
923C2×C42C2412yes—
924C2×C42C2412yes—
925C2×C42C2412yes—
926C2×C42C2412yes—
927C2×C42C2412yes—
928C2×C42C2412yes—
929C2×C42C2412yes—
930C2×C42C2414yes—
931C2×C42C2412yes—
932C2×C42C2412yes—
933C2×C42C2412yes—
934C2×C42C2414yes—
935C2×C42C2414yes—
936C2×C42C2414yes—
937C2×C42C2414yes—
938C2×C42C2414yes—
939C2×C42C2414yes—
940C2×C42C2412yes—
941C2×C42C2414yes—
942C2×C42C2414yes—
943C2×C42C2414yes—
944C2×C42C2412yes—
945C2×C42C2414yes—
946C2×C42C2414yes—
947#95C2412yes—
948#95C2412yes—
949#95C2412yes—
950#95C2412yes—
951#95C2414yes—
952#95C2414yes—
953#95C2414yes—
954#95C2414yes—
955#95C2414yes—
956#95C2414yes—
957#95C2414yes—
958#95C2414yes—
959#95C2414yes—
960#95C2414yes—
961#95C2414yes—
962#95C2414yes—
963#95C2412yes—
964#95C2412yes—
965#95C2412yes—
966#95C2412yes—
967#95C2412yes—
968#95C2412yes—
969#95C2412yes—
970#95C2412yes—
971#95C2414yes—
972#95C2414yes—
973#95C2414yes—
974#95C2414yes—
975#95C2414yes—
976#95C2414yes—
977#95C2414yes—
978#95C2414yes—
979#95C2414yes—
980#95C2414yes—
981#95C2414yes—
982#95C2414yes—
983#95C2412yes—
984#95C2412yes—
985#95C2412yes—
986#95C2412yes—
987#95C2414yes—
988#95C2414yes—
989#95C2414yes—
990#95C2412yes—
991#95C2414yes—
992#95C2414yes—
993#95C2414yes—
994#95C2414yes—
995#95C2412yes—
996#95C2412yes—
997#95C2412yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2412yes—
1003#95C2414yes—
1004#95C2414yes—
1005#95C2412yes—
1006#95C2414yes—
1007#95C2412yes—
1008#95C2412yes—
1009#95C2414yes—
1010#95C2414yes—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2414yes—
1014#95C2414yes—
1015#95C2414yes—
1016#95C2414yes—
1017#95C2414yes—
1018#95C2414yes—
1019C24—22no—
1020C24—22no—
1021C24—41no—
1022C24—41no—
1023C24—41no—
1024C24—41no—
1025C24C22×Q814yes—
1026C24C2511yescharacteristic
1027C24C2511yescharacteristic
1028C24C2511yescharacteristic
1029C2×Q8—24no—
1030C2×Q8—28no—
1031C2×Q8—24no—
1032C2×Q8—42no—
1033C2×Q8—42no—
1034C2×Q8—42no—
1035C2×Q8—42no—
1036C2×Q8—44no—
1037C2×Q8—42no—
1038C2×Q8—42no—
1039C2×Q8—44no—
1040C2×Q8—42no—
1041C2×Q8—42no—
1042C2×Q8—44no—
1043C2×Q8—44no—
1044C2×Q8—44no—
1045C2×Q8—416no—
1046C2×Q8C22×Q818yes—
1047C2×Q8C22×Q818yes—
1048C22×C4—24no—
1049C22×C4—24no—
1050C22×C4—22no—
1051C22×C4—22no—
1052C22×C4—22no—
1053C22×C4—22no—
1054C22×C4—22no—
1055C22×C4—22no—
1056C22×C4—22no—
1057C22×C4—24no—
1058C22×C4—22no—
1059C22×C4—22no—
1060C22×C4—22no—
1061C22×C4—24no—
1062C22×C4—24no—
1063C22×C4—416no—
1064C22×C4—41no—
1065C22×C4—41no—
1066C22×C4—42no—
1067C22×C4—41no—
1068C22×C4—41no—
1069C22×C4—41no—
1070C22×C4—41no—
1071C22×C4—41no—
1072C22×C4—41no—
1073C22×C4—42no—
1074C22×C4—41no—
1075C22×C4—41no—
1076C22×C4—42no—
1077C22×C4—42no—
1078C22×C4—41no—
1079C22×C4—41no—
1080C22×C4—42no—
1081C22×C4—41no—
1082C22×C4—41no—
1083C22×C4—42no—
1084C22×C4—42no—
1085C22×C4—42no—
1086C22×C4—42no—
1087C22×C4—42no—
1088C22×C4—42no—
1089C22×C4—42no—
1090C22×C4—42no—
1091C22×C4—42no—
1092C22×C4—42no—
1093C22×C4—42no—
1094C22×C4—42no—
1095C22×C4C22×Q818yes—
1096C22×C4C22×Q814yes—
1097C22×C4C22×Q814yes—
1098C22×C4C22×Q814yes—
1099C22×C4C22×Q818yes—
1100C22×C4C22×Q814yes—
1101C22×C4C22×Q814yes—
1102C22×C4C22×Q814yes—
1103C22×C4C2512yes—
1104C22×C4C2512yes—
1105C22×C4C2512yes—
1106C22×C4C2512yes—
1107C22×C4C2512yes—
1108C22×C4C2514yes—
1109C22×C4C2514yes—
1110C22×C4C2512yes—
1111C22×C4C2512yes—
1112C22×C4C2512yes—
1113C22×C4C2512yes—
1114C22×C4C2512yes—
1115C22×C4C2514yes—
1116C22×C4C2514yes—
1117C22×C4C2512yes—
1118C22×C4C2512yes—
1119C22×C4C2512yes—
1120C22×C4C2512yes—
1121C22×C4C2512yes—
1122C22×C4C2511yescharacteristic
1123C22×C4C2514yes—
1124C22×C4C2514yes—
1125C22×C4C2511yescharacteristic
1126C22×C4C2511yescharacteristic
1127C22×C4C2512yes—
1128C22×C4C2511yescharacteristic
1129C4⋊C4—24no—
1130C4⋊C4—22no—
1131C4⋊C4—22no—
1132C4⋊C4—22no—
1133C4⋊C4—28no—
1134C4⋊C4—24no—
1135C4⋊C4—24no—
1136C4⋊C4—28no—
1137C4⋊C4—28no—
1138C4⋊C4—28no—
1139C4⋊C4—24no—
1140C4⋊C4—24no—
1141C4⋊C4—44no—
1142C4⋊C4—44no—
1143C4⋊C4—42no—
1144C4⋊C4—42no—
1145C4⋊C4—42no—
1146C4⋊C4—44no—
1147C4⋊C4—42no—
1148C4⋊C4—42no—
1149C4⋊C4—44no—
1150C4⋊C4—42no—
1151C4⋊C4—42no—
1152C4⋊C4—42no—
1153C4⋊C4—42no—
1154C4⋊C4—44no—
1155C4⋊C4—44no—
1156C4⋊C4—44no—
1157C4⋊C4—42no—
1158C4⋊C4—42no—
1159C4⋊C4—44no—
1160C4⋊C4—44no—
1161C4⋊C4—44no—
1162C4⋊C4—44no—
1163C4⋊C4—44no—
1164C4⋊C4—44no—
1165C4⋊C4—44no—
1166C4⋊C4—44no—
1167C4⋊C4—44no—
1168C4⋊C4—44no—
1169C4⋊C4—41no—
1170C4⋊C4—41no—
1171C4⋊C4—41no—
1172C4⋊C4—41no—
1173C4⋊C4—41no—
1174C4⋊C4—41no—
1175C4⋊C4—41no—
1176C4⋊C4—41no—
1177C4⋊C4—44no—
1178C4⋊C4—44no—
1179C4⋊C4—42no—
1180C4⋊C4—42no—
1181C4⋊C4—42no—
1182C4⋊C4—42no—
1183C4⋊C4—44no—
1184C4⋊C4—42no—
1185C4⋊C4—44no—
1186C4⋊C4—42no—
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⋊C4—44no—
1196C4⋊C4—44no—
1197C4⋊C4—44no—
1198C4⋊C4—44no—
1199C4⋊C4—44no—
1200C4⋊C4—44no—
1201C4⋊C4—44no—
1202C4⋊C4—44no—
1203C4⋊C4—44no—
1204C4⋊C4—44no—
1205C4⋊C4—44no—
1206C4⋊C4C22×Q818yes—
1207C4⋊C4C22×Q818yes—
1208C4⋊C4C22×Q8116yes—
1209C4⋊C4C22×Q8116yes—
1210C4⋊C4H(5,𝔽2)14yes—
1211C22⋊C4—28no—
1212C22⋊C4—28no—
1213C22⋊C4—24no—
1214C22⋊C4—24no—
1215C22⋊C4—24no—
1216C22⋊C4—24no—
1217C22⋊C4—24no—
1218C22⋊C4—24no—
1219C22⋊C4—42no—
1220C22⋊C4—42no—
1221C22⋊C4—44no—
1222C22⋊C4—44no—
1223C22⋊C4—42no—
1224C22⋊C4—42no—
1225C22⋊C4—42no—
1226C22⋊C4—42no—
1227C22⋊C4—42no—
1228C22⋊C4—42no—
1229C22⋊C4—42no—
1230C22⋊C4—42no—
1231C22⋊C4—42no—
1232C22⋊C4—42no—
1233C22⋊C4—42no—
1234C22⋊C4—42no—
1235C22⋊C4C22×Q8116yes—
1236C22⋊C4C22×Q8116yes—
1237C42—24no—
1238C42—24no—
1239C42—28no—
1240C42—24no—
1241C42—24no—
1242C42—24no—
1243C42—24no—
1244C42—24no—
1245C42—24no—
1246C42—44no—
1247C42—44no—
1248C42—42no—
1249C42—42no—
1250C42—42no—
1251C42—44no—
1252C42—42no—
1253C42—44no—
1254C42—44no—
1255C42—44no—
1256C42—44no—
1257C42—44no—
1258C42—44no—
1259C42—44no—
1260C42—44no—
1261C23—21no—
1262C23—21no—
1263C23—21no—
1264C23—21no—
1265C23—21no—
1266C23—21no—
1267C23—21no—
1268C23—21no—
1269C23—21no—
1270C23—21no—
1271C23—21no—
1272C23—21no—
1273C23—21no—
1274C23—21no—
1275C23—21no—
1276C23—21no—
1277C23—28no—
1278C23—44no—
1279C23—44no—
1280C23—82no—
1281C23—82no—
1282C23—82no—
1283C23—82no—
1284C23C23×Q812yes—
1285C23C23×Q812yes—
1286C23C23×Q812yes—
1287C23#58512yes—
1288C23#58512yes—
1289C23C2611yescharacteristic
1290Q8—216no—
1291Q8—48no—
1292Q8—88no—
1293Q8—84no—
1294Q8—84no—
1295Q8—164no—
1296C2×C4—21no—
1297C2×C4—21no—
1298C2×C4—24no—
1299C2×C4—21no—
1300C2×C4—24no—
1301C2×C4—24no—
1302C2×C4—22no—
1303C2×C4—24no—
1304C2×C4—21no—
1305C2×C4—21no—
1306C2×C4—21no—
1307C2×C4—22no—
1308C2×C4—216no—
1309C2×C4—28no—
1310C2×C4—28no—
1311C2×C4—28no—
1312C2×C4—22no—
1313C2×C4—22no—
1314C2×C4—22no—
1315C2×C4—22no—
1316C2×C4—22no—
1317C2×C4—22no—
1318C2×C4—22no—
1319C2×C4—22no—
1320C2×C4—22no—
1321C2×C4—24no—
1322C2×C4—24no—
1323C2×C4—22no—
1324C2×C4—22no—
1325C2×C4—22no—
1326C2×C4—22no—
1327C2×C4—22no—
1328C2×C4—22no—
1329C2×C4—22no—
1330C2×C4—22no—
1331C2×C4—22no—
1332C2×C4—22no—
1333C2×C4—22no—
1334C2×C4—22no—
1335C2×C4—24no—
1336C2×C4—24no—
1337C2×C4—24no—
1338C2×C4—24no—
1339C2×C4—24no—
1340C2×C4—24no—
1341C2×C4—22no—
1342C2×C4—22no—
1343C2×C4—22no—
1344C2×C4—22no—
1345C2×C4—22no—
1346C2×C4—22no—
1347C2×C4—22no—
1348C2×C4—22no—
1349C2×C4—22no—
1350C2×C4—22no—
1351C2×C4—22no—
1352C2×C4—22no—
1353C2×C4—22no—
1354C2×C4—22no—
1355C2×C4—22no—
1356C2×C4—22no—
1357C2×C4—22no—
1358C2×C4—22no—
1359C2×C4—24no—
1360C2×C4—22no—
1361C2×C4—22no—
1362C2×C4—22no—
1363C2×C4—24no—
1364C2×C4—22no—
1365C2×C4—24no—
1366C2×C4—22no—
1367C2×C4—24no—
1368C2×C4—22no—
1369C2×C4—44no—
1370C2×C4—44no—
1371C2×C4—44no—
1372C2×C4—48no—
1373C2×C4—48no—
1374C2×C4—44no—
1375C2×C4—44no—
1376C2×C4—82no—
1377C2×C4—82no—
1378C2×C4—84no—
1379C2×C4—162no—
1380C2×C4—162no—
1381C2×C4—162no—
1382C2×C4—162no—
1383C2×C4C23×Q818yes—
1384C2×C4C23×Q818yes—
1385C2×C4C23×Q812yes—
1386C2×C4C23×Q812yes—
1387C2×C4C23×Q812yes—
1388C2×C4C23×Q812yes—
1389C2×C4C2×H(5,𝔽2)14yes—
1390C2×C4C2×H(5,𝔽2)12yes—
1391C2×C4#58512yes—
1392C22—22no—
1393C22—22no—
1394C22—22no—
1395C22—22no—
1396C22—22no—
1397C22—22no—
1398C22—22no—
1399C22—22no—
1400C22—22no—
1401C22—22no—
1402C22—22no—
1403C22—22no—
1404C22—41no—
1405C22—41no—
1406C22—41no—
1407C22—41no—
1408C22—41no—
1409C22—41no—
1410C22—41no—
1411C22—41no—
1412C22—88no—
1413C22#350414yes—
1414C22C24×Q811yescharacteristic
1415C22C22×H(5,𝔽2)11yescharacteristic
1416C22C2×#58511yescharacteristic
1417C22C2×#58511yescharacteristic
1418C22C2×#58511yescharacteristic
1419C222−1+611yescharacteristic
1420C222−1+611yescharacteristic
1421C4—22no—
1422C4—22no—
1423C4—22no—
1424C4—28no—
1425C4—28no—
1426C4—24no—
1427C4—42no—
1428C4—42no—
1429C4—44no—
1430C4—42no—
1431C4—42no—
1432C4—42no—
1433C4—44no—
1434C4—42no—
1435C4—42no—
1436C4—42no—
1437C4—42no—
1438C4—42no—
1439C4—42no—
1440C4—44no—
1441C4—42no—
1442C4—42no—
1443C4—42no—
1444C4—42no—
1445C4—44no—
1446C4#350114yes—
1447C2—24no—
1448C2—42no—
1449C2—42no—
1450C2C2×#350111yescharacteristic
1451C2C2×#350411yescharacteristic
1452C2#6284911yescharacteristic
1453C2#6289811yescharacteristic
1454C2#6291111yescharacteristic
1455C2#6291911yescharacteristic
1456C2#6293411yescharacteristic
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. #48847C2semidirect
2. #48843C2semidirect
3. #47971C2semidirect
4. #47967C2semidirect
5. #45415C2semidirect
6. #45405C2semidirect
7. #45274C2semidirect
8. #45273C2semidirect
9. #45190C2semidirect
10. #45180C2semidirect
11. #45121C2semidirect
12. #45099C2semidirect
13. #39179C2semidirect
14. #38963C2semidirect
17. #36752C2semidirect
18. #36751C2semidirect
19. #36435C2semidirect
20. #36425C2semidirect
23. #35159C2semidirect
25. #35015C2semidirect
30. C2×#557C22semidirect
44. #2809C22semidirect
46. #2806C22semidirect
47. #2806C22semidirect
48. #2805C22semidirect
49. #2802C22semidirect
50. #2802C22semidirect
51. #2799C22semidirect
52. #2799C22semidirect
53. #2792C22semidirect
54. #2792C22semidirect
55. #2792C22semidirect
56. #2791C22semidirect
57. #2791C22semidirect
58. #2791C22semidirect
64. #2774C22semidirect
65. #2774C22semidirect
66. #2774C22semidirect
71. #2755C22semidirect
72. #2755C22semidirect
73. #2755C22semidirect
76. #2734C22semidirect
78. #2726C22semidirect
80. #2713C22semidirect
81. #2713C22semidirect
102. #2590C22semidirect
103. #2590C22semidirect
104. #2590C22semidirect
107. #2588C22semidirect
108. #2588C22semidirect
109. #2588C22semidirect
112. #2586C22semidirect
113. #2585C22semidirect
114. #2584C22semidirect
115. #2584C22semidirect
116. #2582C22semidirect
117. #2581C22semidirect
118. #2581C22semidirect
119. #2581C22semidirect
126. #2568C22semidirect
127. #2567C22semidirect
128. #2565C22semidirect
129. #2565C22semidirect
130. #2565C22semidirect
132. #2552C22semidirect
133. #2550C22semidirect
134. #2550C22semidirect
139. #2511C22semidirect
140. #2509C22semidirect
141. #2509C22semidirect
142. #2509C22semidirect
143. #2509C22semidirect
144. #2508C22semidirect
145. #2508C22semidirect
146. #2508C22semidirect
147. #2508C22semidirect
148. #2507C22semidirect
149. #2507C22semidirect
150. #2507C22semidirect
151. #2507C22semidirect
152. #2507C22semidirect
153. #2506C22semidirect
154. #2506C22semidirect
159. #2453C22semidirect
160. #2453C22semidirect
161. #2453C22semidirect
162. #2453C22semidirect
163. #2453C22semidirect
164. #2451C22semidirect
165. #2451C22semidirect
166. #2451C22semidirect
167. #2451C22semidirect
168. #2446C22semidirect
198. #2370C22semidirect
199. #2370C22semidirect
200. #2369C22semidirect
211. #2355C22semidirect
212. #2351C22semidirect
213. #2351C22semidirect
214. Q8×C4⋊C4C22semidirect
277. C2×C22⋊Q8Q8semidirect

Maximal subgroups

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

subgroupindex
#488472
#488432
#479712
#479672
#454152
#454052
#452742
#452732
#451902
#451802
#451212
#450992
#391792
#389632
#389592
#381022
#367522
#367512
#364352
#364252
#352532
#351592
#350202
#350152
#345782
#343802
C2×#23622