Finite Group Databasebeta

← #7652172

Subgroups — #7652172

Order 512.

4198 conjugacy classes of subgroups.

The subgroup lattice has 1533 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42774C212yesmaximal, complemented
2#42733C212yesmaximal, complemented
3#42710C212yesmaximal, complemented
4#42703C212yesmaximal, complemented
5#42703C212yesmaximal, complemented
6#42600C212yesmaximal, complemented
7#42527C212yesmaximal, complemented
8#42527C212yesmaximal, complemented
9#41494C214yesmaximal
10#40703C214yesmaximal
11#40143C212yesmaximal, complemented
12#40082C212yesmaximal, complemented
13#40024C212yesmaximal, complemented
14#40024C212yesmaximal, complemented
15#39769C212yesmaximal, complemented
16#39653C212yesmaximal, complemented
17#39642C212yesmaximal, complemented
18#39241C212yesmaximal, complemented
19#38610C214yesmaximal
20#38507C214yesmaximal
21#35668C211yesmaximal, characteristic
22#35668C211yesmaximal, characteristic
23#35630C211yesmaximal, characteristic
24#35630C211yesmaximal, characteristic
25#35555C211yesmaximal, characteristic
26#35543C211yesmaximal, characteristic
27#35313C211yesmaximal, characteristic
28#35275C211yesmaximal, characteristic
29#35181C211yesmaximal, characteristic
30#34948C211yesmaximal, characteristic
31#34815C211yesmaximal, characteristic
32C2×#2511C211yesmaximal, characteristic
33#34272C211yesmaximal, characteristic
34#34271C211yesmaximal, characteristic
35#34254C211yesmaximal, characteristic
36C2×#544C2211yescharacteristic
37C2×#544C2211yescharacteristic
38C2×#519C2211yescharacteristic
39#2868C2212yes—
40#2863C2212yes—
41#2863C2212yes—
42#2859C2212yes—
43#2851C2214yes—
44#2839C2214yes—
45#2839C2214yes—
46#2833C2214yes—
47#2833C2214yes—
48#2802C2214yes—
49#2802C2214yes—
50#2794C2214yes—
51#2794C2214yes—
52#2794C2214yes—
53#2794C2214yes—
54#2776C2214yes—
55#2776C2214yes—
56#2776C2214yes—
57#2776C2214yes—
58#2769C2214yes—
59#2769C2214yes—
60#2766C2214yes—
61#2766C2214yes—
62#2766C2214yes—
63#2766C2214yes—
64#2762C2214yes—
65#2762C2214yes—
66#2762C2214yes—
67#2762C2214yes—
68#2758C2214yes—
69#2758C2214yes—
70#2755C2214yes—
71#2755C2214yes—
72#2719C2214yes—
73#2719C2214yes—
74#2719C2214yes—
75#2719C2214yes—
76#2713C2214yes—
77#2713C2214yes—
78#2713C2214yes—
79#2713C2214yes—
80#2666C2214yes—
81#2666C2214yes—
82#2660C2212yes—
83#2660C2212yes—
84#2655C2214yes—
85#2655C2214yes—
86#2655C2214yes—
87#2655C2214yes—
88#2655C2214yes—
89#2655C2214yes—
90#2647C2214yes—
91#2646C2214yes—
92#2645C2212yes—
93#2645C2212yes—
94#2642C2214yes—
95#2634C2214yes—
96#2634C2214yes—
97#2571C2211yescharacteristic
98#2571C2212yes—
99#2571C2212yes—
100#2571C2212yes—
101#2571C2211yescharacteristic
102#2570C2212yes—
103#2570C2211yescharacteristic
104#2570C2212yes—
105#2570C2212yes—
106#2570C2211yescharacteristic
107#2570C2212yes—
108#2570C2212yes—
109#2570C2211yescharacteristic
110#2570C2212yes—
111#2570C2212yes—
112#2570C2211yescharacteristic
113#2570C2212yes—
114#2569C2212yes—
115#2569C2212yes—
116#2568C2212yes—
117#2568C2212yes—
118#2567C2212yes—
119#2567C2212yes—
120#2565C2212yes—
121#2565C2212yes—
122#2565C2212yes—
123#2565C2212yes—
124#2552C2212yes—
125#2552C2212yes—
126#2552C2212yes—
127#2552C2212yes—
128#2552C2212yes—
129#2552C2211yescharacteristic
130#2552C2212yes—
131#2552C2212yes—
132#2552C2211yescharacteristic
133#2551C2212yes—
134#2551C2212yes—
135#2533C2214yes—
136#2533C2214yes—
137#2528C2214yes—
138#2528C2214yes—
139#2524C2214yes—
140#2524C2214yes—
141#2514C2212yes—
142#2514C2212yes—
143#2514C2212yes—
144#2514C2212yes—
145#2514C2212yes—
146#2514C2212yes—
147#2514C2212yes—
148#2514C2212yes—
149#2514C2212yes—
150#2514C2212yes—
151#2511C2212yes—
152#2511C2212yes—
153#2511C2212yes—
154#2511C2212yes—
155#2511C2212yes—
156#2511C2212yes—
157#2511C2212yes—
158#2511C2212yes—
159#2511C2212yes—
160#2511C2212yes—
161#2511C2212yes—
162#2511C2212yes—
163#2511C2212yes—
164#2511C2212yes—
165#2511C2212yes—
166#2511C2212yes—
167#2511C2212yes—
168#2511C2212yes—
169#2509C2211yescharacteristic
170#2509C2211yescharacteristic
171#2509C2212yes—
172#2508C2211yescharacteristic
173#2508C2212yes—
174#2508C2211yescharacteristic
175#2507C2212yes—
176#2507C2212yes—
177#2507C2212yes—
178#2507C2211yescharacteristic
179#2507C2211yescharacteristic
180#2506C2214yes—
181#2506C2212yes—
182#2506C2212yes—
183#2506C2214yes—
184#2506C2211yescharacteristic
185#2506C2212yes—
186#2506C2211yescharacteristic
187#2505C2214yes—
188#2505C2212yes—
189#2505C2212yes—
190#2493C2214yes—
191#2493C2214yes—
192#2493C2214yes—
193#2493C2214yes—
194#2493C2214yes—
195#2493C2214yes—
196#2473C2212yes—
197#2473C2214yes—
198#2473C2214yes—
199#2473C2212yes—
200#2473C2214yes—
201#2462C2214yes—
202#2462C2214yes—
203#2453C2212yes—
204#2453C2212yes—
205#2453C2212yes—
206#2453C2212yes—
207#2451C2212yes—
208#2451C2212yes—
209#2451C2212yes—
210#2451C2212yes—
211#2446C2214yes—
212#2446C2214yes—
213#2442C2212yes—
214#2442C2212yes—
215#2440C2214yes—
216#2440C2214yes—
217#2438C2214yes—
218#2438C2214yes—
219#2438C2214yes—
220#2438C2214yes—
221#2402C2212yes—
222#2402C2212yes—
223#2402C2212yes—
224#2402C2212yes—
225C2×#400C2212yes—
226C2×#400C2212yes—
227#2370C2212yes—
228#2370C2212yes—
229#2370C2212yes—
230#2370C2212yes—
231#2370C2212yes—
232#2370C2212yes—
233#2369C2212yes—
234#2369C2212yes—
235#2369C2212yes—
236#2368C2214yes—
237#2365C2212yes—
238#2365C2212yes—
239#2365C2212yes—
240#2360C2214yes—
241#2356C2212yes—
242#2356C2212yes—
243#2355C2212yes—
244#2355C2212yes—
245#2343C2214yes—
246#2343C2214yes—
247#2336C2214yes—
248#2336C2214yes—
249#2331C2212yes—
250#2330C2212yes—
251#2330C2214yes—
252#2329C2214yes—
253#2327C2214yes—
254#2320C2212yes—
255#2320C2212yes—
256#2317C2211yescharacteristic
257#2317C2211yescharacteristic
258#2317C2211yescharacteristic
259#2317C2211yescharacteristic
260#2317C2211yescharacteristic
261#2317C2211yescharacteristic
262#2316C2211yescharacteristic
263#2310C2211yescharacteristic
264#2310C2211yescharacteristic
265#2310C2211yescharacteristic
266C4×C4⋊Q8C2212yes—
267C4×#125C2212yes—
268C4×#125C2212yes—
269C4×#125C2212yes—
270C4×#125C2212yes—
271C4×#125C2212yes—
272C4×C22⋊Q8C2214yes—
273#2296C2211yescharacteristic
274#2296C2211yescharacteristic
275#2296C2211yescharacteristic
276#2296C2211yescharacteristic
277#2296C2211yescharacteristic
278#2296C2211yescharacteristic
279#2295C2212yes—
280#2295C2212yes—
281C2×#391C2211yescharacteristic
282C2×#391C2211yescharacteristic
283C2×#391C2211yescharacteristic
284C2×#389C2211yescharacteristic
285C2×#387C2212yes—
286C2×#387C2212yes—
287#2285C2211yescharacteristic
288#2285C2211yescharacteristic
289#2285C2211yescharacteristic
290#2285C2211yescharacteristic
291C2×#384C2211yescharacteristic
292#2274C2211yescharacteristic
293#2274C2211yescharacteristic
294#2274C2211yescharacteristic
295C4×#117C2211yescharacteristic
296C4×#117C2211yescharacteristic
297C2×C4×C4⋊C4C2211yescharacteristic
298C2×C4×C4⋊C4C2211yescharacteristic
299C23×Q8C2311yescharacteristic
300#544—28no—
301#544—28no—
302C2×C4⋊Q8C2312yes—
303C2×C4⋊Q8C2312yes—
304C2×C4⋊Q8C2312yes—
305C2×C4⋊Q8C2312yes—
306C2×C4⋊Q8C2314yes—
307C2×C4⋊Q8C2314yes—
308C2×#125C2312yes—
309C2×#125C2312yes—
310C2×#125C2312yes—
311C2×#125C2312yes—
312C2×#125C2312yes—
313C2×#125C2312yes—
314C2×#125C2312yes—
315C2×#125C2312yes—
316C2×#125C2314yes—
317C2×#125C2314yes—
318C2×#125C2314yes—
319C2×#125C2314yes—
320C2×C22⋊Q8C2314yes—
321C2×C22⋊Q8C2314yes—
322#519—28no—
323C2×C4×Q8C2312yes—
324C2×C4×Q8C2312yes—
325C2×C4×Q8C2312yes—
326C2×C4×Q8C2312yes—
327C2×C4×Q8C2314yes—
328C2×C4×Q8C2314yes—
329C2×#117C2311yescharacteristic
330C2×#117C2311yescharacteristic
331C2×#117C2311yescharacteristic
332C2×#117C2311yescharacteristic
333C2×#117C2311yescharacteristic
334C2×#117C2311yescharacteristic
335C2×#117C2311yescharacteristic
336C2×#117C2314yes—
337C2×#117C2311yescharacteristic
338C22×C4⋊C4C2311yescharacteristic
339C22×C4⋊C4C2311yescharacteristic
340C22×C4⋊C4C2311yescharacteristic
341C22×C4⋊C4C2311yescharacteristic
342C22×C4⋊C4C2311yescharacteristic
343C22×C4⋊C4C2312yes—
344C22×C4⋊C4C2312yes—
345C22×C4⋊C4C2312yes—
346C22×C42C2311yescharacteristic
347C22×C42C2311yescharacteristic
348C22×C42C2311yescharacteristic
349C22×C42C2312yes—
350#401C2314yes—
351#401C2314yes—
352#401C2314yes—
353#401C2314yes—
354#401C2314yes—
355#401C2314yes—
356#400C2314yes—
357#400C2314yes—
358#400C2314yes—
359#400C2314yes—
360#400C2312yes—
361#400C2312yes—
362#400C2312yes—
363#400C2312yes—
364#400C2314yes—
365#400C2314yes—
366#400C2314yes—
367#400C2314yes—
368#400C2312yes—
369#400C2314yes—
370#400C2314yes—
371#400C2312yes—
372#400C2314yes—
373#400C2312yes—
374#400C2314yes—
375#400C2312yes—
376#400C2314yes—
377#400C2314yes—
378#400C2312yes—
379#400C2312yes—
380#400C2314yes—
381#400C2314yes—
382#400C2314yes—
383#400C2314yes—
384#400C2314yes—
385#400C2314yes—
386#400C2314yes—
387#400C2314yes—
388#400C2314yes—
389#400C2314yes—
390#400C2312yes—
391#400C2312yes—
392#400C2314yes—
393#400C2314yes—
394#400C2314yes—
395#400C2314yes—
396#400C2314yes—
397#400C2314yes—
398#400C2314yes—
399#400C2314yes—
400#400C2314yes—
401#400C2314yes—
402#400C2314yes—
403#400C2314yes—
404#400C2312yes—
405#400C2312yes—
406#400C2314yes—
407#400C2314yes—
408#400C2314yes—
409#400C2312yes—
410#400C2312yes—
411#400C2314yes—
412#398C2314yes—
413#398C2314yes—
414#398C2314yes—
415#398C2314yes—
416#398C2314yes—
417#398C2314yes—
418#398C2314yes—
419#398C2314yes—
420#398C2312yes—
421#398C2312yes—
422#398C2312yes—
423#398C2312yes—
424#398C2314yes—
425#398C2312yes—
426#398C2314yes—
427#398C2314yes—
428#398C2314yes—
429#398C2314yes—
430#398C2314yes—
431#398C2312yes—
432#398C2314yes—
433#398C2314yes—
434#398C2312yes—
435#398C2312yes—
436#398C2314yes—
437#398C2314yes—
438#398C2314yes—
439#398C2312yes—
440#398C2312yes—
441#398C2314yes—
442#398C2314yes—
443#398C2314yes—
444#398C2312yes—
445#398C2312yes—
446#398C2314yes—
447#398C2314yes—
448#398C2314yes—
449#398C2312yes—
450#398C2312yes—
451#398C2312yes—
452#398C2312yes—
453#398C2314yes—
454#395C2314yes—
455#395C2314yes—
456#395C2314yes—
457#395C2314yes—
458#395C2314yes—
459#395C2314yes—
460#395C2314yes—
461#395C2314yes—
462#391C2314yes—
463#391C2312yes—
464#391C2312yes—
465#391C2312yes—
466#391C2312yes—
467#391C2312yes—
468#391C2312yes—
469#391C2312yes—
470#391C2312yes—
471#391C2312yes—
472#391C2312yes—
473#391C2312yes—
474#391C2312yes—
475#391C2312yes—
476#391C2312yes—
477#391C2312yes—
478#391C2312yes—
479#391C2314yes—
480#391C2314yes—
481#391C2314yes—
482#391C2314yes—
483#391C2312yes—
484#391C2314yes—
485#391C2314yes—
486#391C2314yes—
487#391C2314yes—
488#391C2312yes—
489#391C2312yes—
490#391C2312yes—
491#391C2314yes—
492#391C2312yes—
493#391C2312yes—
494#391C2312yes—
495#391C2312yes—
496#389C2311yescharacteristic
497#389C2312yes—
498#389C2312yes—
499#389C2312yes—
500#389C2312yes—
501#389C2312yes—
502#389C2312yes—
503#389C2312yes—
504#389C2312yes—
505#389C2312yes—
506#389C2311yescharacteristic
507#389C2314yes—
508#389C2314yes—
509#389C2314yes—
510#389C2314yes—
511#389C2314yes—
512#389C2312yes—
513#389C2311yescharacteristic
514#389C2311yescharacteristic
515#389C2312yes—
516#389C2312yes—
517#389C2312yes—
518#389C2312yes—
519#389C2311yescharacteristic
520#389C2311yescharacteristic
521#389C2312yes—
522#389C2311yescharacteristic
523#389C2312yes—
524#389C2312yes—
525#389C2312yes—
526#389C2312yes—
527#389C2312yes—
528#389C2311yescharacteristic
529#389C2312yes—
530#389C2311yescharacteristic
531#389C2311yescharacteristic
532#389C2314yes—
533#389C2314yes—
534#389C2314yes—
535#389C2312yes—
536#389C2312yes—
537#389C2312yes—
538#389C2312yes—
539#389C2312yes—
540#389C2312yes—
541#389C2314yes—
542#389C2314yes—
543#389C2314yes—
544#389C2311yescharacteristic
545#389C2312yes—
546#389C2314yes—
547#389C2314yes—
548#389C2314yes—
549#389C2311yescharacteristic
550#389C2314yes—
551#389C2314yes—
552#389C2314yes—
553#389C2314yes—
554#389C2311yescharacteristic
555#389C2311yescharacteristic
556#389C2311yescharacteristic
557#389C2311yescharacteristic
558#389C2311yescharacteristic
559#389C2311yescharacteristic
560#389C2314yes—
561#389C2311yescharacteristic
562#389C2311yescharacteristic
563#389C2314yes—
564#389C2311yescharacteristic
565#389C2311yescharacteristic
566#389C2311yescharacteristic
567#389C2311yescharacteristic
568#387C2312yes—
569#387C2312yes—
570#387C2312yes—
571#387C2312yes—
572#387C2312yes—
573#387C2312yes—
574#387C2312yes—
575#387C2312yes—
576#387C2312yes—
577#387C2312yes—
578#387C2314yes—
579#387C2314yes—
580#387C2312yes—
581#387C2312yes—
582#387C2312yes—
583#387C2312yes—
584#387C2312yes—
585#387C2312yes—
586#387C2314yes—
587#387C2314yes—
588#387C2314yes—
589#387C2314yes—
590#387C2314yes—
591#387C2314yes—
592#387C2314yes—
593#387C2314yes—
594#387C2314yes—
595#387C2314yes—
596#387C2314yes—
597#387C2314yes—
598#387C2314yes—
599#387C2314yes—
600#387C2314yes—
601#387C2314yes—
602#387C2314yes—
603#387C2314yes—
604#387C2314yes—
605#387C2314yes—
606#387C2314yes—
607#387C2314yes—
608#387C2314yes—
609#387C2314yes—
610#387C2314yes—
611#387C2314yes—
612#387C2314yes—
613#387C2314yes—
614#387C2314yes—
615#387C2314yes—
616#387C2314yes—
617#387C2314yes—
618#387C2314yes—
619#387C2314yes—
620#387C2314yes—
621#387C2314yes—
622#387C2314yes—
623#387C2314yes—
624#387C2314yes—
625#387C2314yes—
626#387C2314yes—
627#387C2314yes—
628#387C2314yes—
629#387C2314yes—
630#387C2314yes—
631#387C2314yes—
632#387C2314yes—
633#387C2314yes—
634#387C2314yes—
635#387C2314yes—
636#387C2314yes—
637#387C2314yes—
638#387C2314yes—
639#387C2314yes—
640#387C2314yes—
641#387C2314yes—
642#387C2314yes—
643#387C2314yes—
644#387C2314yes—
645#387C2314yes—
646#387C2314yes—
647#387C2314yes—
648#387C2314yes—
649#387C2314yes—
650#385C2312yes—
651#385C2312yes—
652#385C2312yes—
653#385C2312yes—
654#385C2314yes—
655#385C2314yes—
656#385C2314yes—
657#385C2314yes—
658#385C2314yes—
659#385C2314yes—
660#385C2312yes—
661#385C2312yes—
662#385C2312yes—
663#385C2312yes—
664#385C2312yes—
665#385C2312yes—
666#385C2312yes—
667#385C2312yes—
668#384C2312yes—
669#384C2311yescharacteristic
670#384C2311yescharacteristic
671#384C2312yes—
672#384C2312yes—
673#384C2311yescharacteristic
674#384C2311yescharacteristic
675#384C2312yes—
676#384C2312yes—
677#384C2312yes—
678#384C2311yescharacteristic
679#384C2312yes—
680#384C2311yescharacteristic
681#384C2312yes—
682#384C2311yescharacteristic
683#384C2314yes—
684#384C2314yes—
685#384C2312yes—
686#384C2312yes—
687#384C2311yescharacteristic
688#383C2314yes—
689#383C2314yes—
690#383C2314yes—
691#383C2314yes—
692#383C2314yes—
693#383C2314yes—
694#383C2314yes—
695#383C2314yes—
696#382C2312yes—
697#382C2312yes—
698#382C2312yes—
699#382C2312yes—
700#382C2312yes—
701#382C2311yescharacteristic
702#382C2311yescharacteristic
703#382C2312yes—
704#382C2312yes—
705#382C2311yescharacteristic
706#382C2311yescharacteristic
707#382C2311yescharacteristic
708#382C2311yescharacteristic
709#382C2312yes—
710#382C2312yes—
711#382C2312yes—
712#382C2311yescharacteristic
713#382C2311yescharacteristic
714#382C2314yes—
715#382C2314yes—
716#382C2314yes—
717#382C2314yes—
718#381C2314yes—
719#381C2314yes—
720#381C2314yes—
721#380C2312yes—
722#380C2312yes—
723#380C2312yes—
724#380C2312yes—
725#380C2312yes—
726#380C2314yes—
727#380C2312yes—
728#380C2312yes—
729#380C2312yes—
730C4×C4⋊C4C2311yescharacteristic
731C4×C4⋊C4C2312yes—
732C4×C4⋊C4C2312yes—
733C4×C4⋊C4C2311yescharacteristic
734C4×C4⋊C4C2311yescharacteristic
735C4×C4⋊C4C2311yescharacteristic
736C4×C4⋊C4C2312yes—
737C4×C4⋊C4C2312yes—
738C4×C4⋊C4C2312yes—
739C4×C4⋊C4C2312yes—
740C4×C4⋊C4C2312yes—
741C4×C4⋊C4C2312yes—
742C4×C4⋊C4C2312yes—
743C4×C4⋊C4C2312yes—
744C4×C4⋊C4C2312yes—
745C4×C4⋊C4C2312yes—
746C4×C4⋊C4C2312yes—
747C4×C4⋊C4C2314yes—
748C4×C4⋊C4C2312yes—
749C4×C4⋊C4C2314yes—
750C4×C4⋊C4C2312yes—
751C4×C4⋊C4C2312yes—
752C4×C4⋊C4C2312yes—
753C4×C4⋊C4C2312yes—
754C4×C4⋊C4C2312yes—
755C4×C4⋊C4C2312yes—
756C4×C4⋊C4C2312yes—
757C4×C4⋊C4C2312yes—
758C4×C4⋊C4C2314yes—
759C4×C4⋊C4C2311yescharacteristic
760C4×C4⋊C4C2312yes—
761C4×C4⋊C4C2312yes—
762C4×C4⋊C4C2311yescharacteristic
763C4×C4⋊C4C2311yescharacteristic
764C4×C4⋊C4C2312yes—
765C4×C4⋊C4C2312yes—
766C4×C4⋊C4C2312yes—
767C4×C4⋊C4C2312yes—
768C4×C4⋊C4C2312yes—
769C4×C4⋊C4C2311yescharacteristic
770C4×C4⋊C4C2311yescharacteristic
771C4×C4⋊C4C2312yes—
772C4×C4⋊C4C2312yes—
773C4×C4⋊C4C2311yescharacteristic
774C4×C4⋊C4C2312yes—
775C4×C4⋊C4C2312yes—
776C4×C4⋊C4C2314yes—
777C4×C4⋊C4C2314yes—
778C4×C4⋊C4C2314yes—
779C4×C4⋊C4C2314yes—
780C4×C4⋊C4C2314yes—
781C4×C4⋊C4C2311yescharacteristic
782C4×C4⋊C4C2311yescharacteristic
783C4×C4⋊C4C2311yescharacteristic
784C4×C4⋊C4C2311yescharacteristic
785C4×C4⋊C4C2312yes—
786C4×C4⋊C4C2312yes—
787C4×C4⋊C4C2312yes—
788C4×C4⋊C4C2311yescharacteristic
789C4×C4⋊C4C2311yescharacteristic
790C4×C22⋊C4C2312yes—
791C4×C22⋊C4C2314yes—
792C4×C22⋊C4C2314yes—
793C4×C22⋊C4C2312yes—
794C4×C22⋊C4C2312yes—
795C4×C22⋊C4C2314yes—
796C4×C22⋊C4C2312yes—
797#376C2312yes—
798#376C2314yes—
799#376C2312yes—
800#376C2314yes—
801C2×#95C2311yescharacteristic
802C2×#95C2311yescharacteristic
803C2×#95C2312yes—
804C2×#95C2312yes—
805C2×#95C2312yes—
806C2×#95C2312yes—
807C2×#95C2312yes—
808C2×#95C2312yes—
809C2×#95C2312yes—
810C2×#95C2312yes—
811C43C2312yes—
812C43C2312yes—
813C22×Q8—24no—
814C22×Q8—24no—
815C22×Q8—24no—
816C22×Q8C2412yes—
817C22×Q8C2412yes—
818C22×Q8C2414yes—
819C22×Q8C2414yes—
820C23×C4C2412yes—
821C23×C4C2411yescharacteristic
822C23×C4C2411yescharacteristic
823C23×C4C2411yescharacteristic
824C23×C4C2411yescharacteristic
825C23×C4C2412yes—
826C23×C4C2412yes—
827C23×C4C2412yes—
828C23×C4C2411yescharacteristic
829C23×C4C2411yescharacteristic
830C23×C4C2411yescharacteristic
831C4⋊Q8—28no—
832C4⋊Q8—28no—
833C4⋊Q8—28no—
834C4⋊Q8—28no—
835C4⋊Q8—48no—
836C4⋊Q8—84no—
837#125—28no—
838#125—28no—
839#125—28no—
840#125—28no—
841#125—28no—
842#125—28no—
843#125—44no—
844#125—44no—
845#125—48no—
846#125—84no—
847#125—84no—
848#125—84no—
849C22⋊Q8—216no—
850C22⋊Q8—216no—
851C4×Q8—28no—
852C4×Q8—28no—
853C4×Q8—28no—
854C4×Q8—28no—
855C4×Q8—84no—
856C4×Q8—84no—
857#117—24no—
858#117—24no—
859#117—24no—
860#117—24no—
861#117—24no—
862#117—24no—
863#117—24no—
864#117—216no—
865#117#4118yes—
866C2×C4⋊C4—24no—
867C2×C4⋊C4—24no—
868C2×C4⋊C4—24no—
869C2×C4⋊C4—24no—
870C2×C4⋊C4—42no—
871C2×C4⋊C4—44no—
872C2×C4⋊C4—82no—
873C2×C4⋊C4—82no—
874C2×C4⋊C4C2411yescharacteristic
875C2×C4⋊C4C2411yescharacteristic
876C2×C4⋊C4C2412yes—
877C2×C4⋊C4C2412yes—
878C2×C4⋊C4C2412yes—
879C2×C4⋊C4C2412yes—
880C2×C4⋊C4C2414yes—
881C2×C4⋊C4C2412yes—
882C2×C4⋊C4C2412yes—
883C2×C4⋊C4C2411yescharacteristic
884C2×C4⋊C4C2411yescharacteristic
885C2×C4⋊C4C2411yescharacteristic
886C2×C4⋊C4C2411yescharacteristic
887C2×C4⋊C4C2411yescharacteristic
888C2×C4⋊C4C2414yes—
889C2×C4⋊C4C2414yes—
890C2×C4⋊C4C2411yescharacteristic
891C2×C4⋊C4C2411yescharacteristic
892C2×C4⋊C4C2411yescharacteristic
893C2×C4⋊C4C2411yescharacteristic
894C2×C4⋊C4C2411yescharacteristic
895C2×C4⋊C4C2411yescharacteristic
896C2×C4⋊C4C2411yescharacteristic
897C2×C4⋊C4C2411yescharacteristic
898C2×C4⋊C4C2411yescharacteristic
899C2×C4⋊C4C2411yescharacteristic
900C2×C4⋊C4C2411yescharacteristic
901C2×C4⋊C4C2411yescharacteristic
902C2×C4⋊C4C2414yes—
903C2×C4⋊C4C2414yes—
904C2×C4⋊C4C2414yes—
905C2×C4⋊C4C2414yes—
906C2×C4⋊C4C2414yes—
907C2×C4⋊C4C2414yes—
908C2×C4⋊C4C2412yes—
909C2×C4⋊C4C2412yes—
910C2×C4⋊C4C2412yes—
911C2×C4⋊C4C2412yes—
912C2×C4⋊C4C2412yes—
913C2×C4⋊C4C2412yes—
914C2×C4⋊C4C2412yes—
915C2×C4⋊C4C2412yes—
916C2×C4⋊C4C2412yes—
917C2×C4⋊C4C2412yes—
918C2×C4⋊C4C2412yes—
919C2×C4⋊C4C2412yes—
920C2×C4⋊C4C2412yes—
921C2×C4⋊C4C2414yes—
922C2×C4⋊C4C2414yes—
923C2×C4⋊C4C2414yes—
924C2×C4⋊C4C2414yes—
925C2×C4⋊C4C2411yescharacteristic
926C2×C4⋊C4C2411yescharacteristic
927C2×C4⋊C4C2414yes—
928C2×C4⋊C4C2412yes—
929C2×C4⋊C4C2412yes—
930C2×C4⋊C4C2412yes—
931C2×C4⋊C4C2414yes—
932C2×C4⋊C4C2414yes—
933C2×C4⋊C4C2412yes—
934C2×C4⋊C4C2412yes—
935C2×C4⋊C4C2412yes—
936C2×C4⋊C4C2412yes—
937C2×C4⋊C4C2414yes—
938C2×C4⋊C4C2412yes—
939C2×C4⋊C4C2412yes—
940C2×C4⋊C4C2414yes—
941C2×C4⋊C4C2414yes—
942C2×C4⋊C4C2414yes—
943C2×C4⋊C4C2414yes—
944C2×C4⋊C4C2412yes—
945C2×C4⋊C4C2412yes—
946C2×C4⋊C4C2412yes—
947C2×C4⋊C4C2414yes—
948C2×C4⋊C4C2412yes—
949C2×C4⋊C4C2412yes—
950C2×C4⋊C4C2412yes—
951C2×C4⋊C4C2412yes—
952C2×C4⋊C4C2414yes—
953C2×C4⋊C4C2414yes—
954C2×C4⋊C4C2412yes—
955C2×C4⋊C4C2414yes—
956C2×C4⋊C4C2414yes—
957C2×C4⋊C4C2412yes—
958C2×C4⋊C4C2412yes—
959C2×C4⋊C4C2412yes—
960C2×C4⋊C4C2412yes—
961C2×C4⋊C4C2412yes—
962C2×C4⋊C4C2414yes—
963C2×C4⋊C4C2412yes—
964C2×C4⋊C4C2412yes—
965C2×C4⋊C4C2414yes—
966C2×C4⋊C4C2412yes—
967C2×C4⋊C4C2412yes—
968C2×C4⋊C4C2412yes—
969C2×C4⋊C4C2411yescharacteristic
970C2×C4⋊C4C2411yescharacteristic
971C2×C4⋊C4C2411yescharacteristic
972C2×C22⋊C4C2412yes—
973C2×C22⋊C4C2412yes—
974C2×C22⋊C4C2412yes—
975C2×C22⋊C4C2412yes—
976C2×C22⋊C4C2412yes—
977C2×C22⋊C4C2412yes—
978C2×C22⋊C4C2412yes—
979C2×C22⋊C4C2412yes—
980C2×C42—24no—
981C2×C42—24no—
982C2×C42—24no—
983C2×C42—82no—
984C2×C42C2414yes—
985C2×C42C2414yes—
986C2×C42C2412yes—
987C2×C42C2412yes—
988C2×C42C2412yes—
989C2×C42C2412yes—
990C2×C42C2412yes—
991C2×C42C2412yes—
992C2×C42C2412yes—
993C2×C42C2412yes—
994C2×C42C2412yes—
995C2×C42C2412yes—
996C2×C42C2411yescharacteristic
997C2×C42C2411yescharacteristic
998C2×C42C2411yescharacteristic
999C2×C42C2411yescharacteristic
1000C2×C42C2411yescharacteristic
1001C2×C42C2411yescharacteristic
1002C2×C42C2411yescharacteristic
1003C2×C42C2411yescharacteristic
1004C2×C42C2411yescharacteristic
1005C2×C42C2411yescharacteristic
1006C2×C42C2411yescharacteristic
1007C2×C42C2411yescharacteristic
1008C2×C42C2412yes—
1009C2×C42C2414yes—
1010C2×C42C2414yes—
1011C2×C42C2414yes—
1012C2×C42C2414yes—
1013C2×C42C2412yes—
1014C2×C42C2414yes—
1015C2×C42C2414yes—
1016C2×C42C2412yes—
1017C2×C42C2412yes—
1018C2×C42C2412yes—
1019C2×C42C2414yes—
1020C2×C42C2414yes—
1021C2×C42C2412yes—
1022#95C2414yes—
1023#95C2414yes—
1024#95C2411yescharacteristic
1025#95C2411yescharacteristic
1026#95C2411yescharacteristic
1027#95C2411yescharacteristic
1028#95C2411yescharacteristic
1029#95C2414yes—
1030#95C2411yescharacteristic
1031#95C2411yescharacteristic
1032#95C2414yes—
1033#95C2414yes—
1034#95C2411yescharacteristic
1035#95C2414yes—
1036#95C2414yes—
1037#95C2414yes—
1038#95C2414yes—
1039#95C2414yes—
1040#95C2414yes—
1041#95C2414yes—
1042#95C2414yes—
1043#95C2414yes—
1044#95C2414yes—
1045#95C2414yes—
1046#95C2412yes—
1047#95C2412yes—
1048#95C2412yes—
1049#95C2412yes—
1050#95C2412yes—
1051#95C2412yes—
1052#95C2412yes—
1053#95C2412yes—
1054#95C2412yes—
1055#95C2412yes—
1056#95C2414yes—
1057#95C2414yes—
1058#95C2414yes—
1059#95C2414yes—
1060#95C2414yes—
1061#95C2414yes—
1062#95C2414yes—
1063#95C2414yes—
1064#95C2414yes—
1065#95C2414yes—
1066#95C2412yes—
1067#95C2412yes—
1068#95C2412yes—
1069#95C2412yes—
1070#95C2412yes—
1071#95C2412yes—
1072#95C2412yes—
1073#95C2412yes—
1074#95C2412yes—
1075#95C2412yes—
1076#95C2412yes—
1077#95C2412yes—
1078#95C2412yes—
1079#95C2412yes—
1080#95C2412yes—
1081#95C2412yes—
1082#95C2412yes—
1083#95C2412yes—
1084#95C2412yes—
1085#95C2412yes—
1086#95C2412yes—
1087#95C2412yes—
1088#95C2414yes—
1089#95C2414yes—
1090#95C2414yes—
1091#95C2414yes—
1092#95C2414yes—
1093#95C2412yes—
1094#95C2412yes—
1095#95C2412yes—
1096#95C2414yes—
1097#95C2412yes—
1098#95C2412yes—
1099#95C2412yes—
1100#95C2412yes—
1101#95C2412yes—
1102#95C2412yes—
1103#95C2412yes—
1104#95C2412yes—
1105#95C2412yes—
1106#95C2412yes—
1107#95C2412yes—
1108#95C2412yes—
1109#95C2412yes—
1110#95C2414yes—
1111#95C2414yes—
1112#95C2414yes—
1113#95C2414yes—
1114#95C2414yes—
1115#95C2414yes—
1116#95C2414yes—
1117#95C2414yes—
1118#95C2414yes—
1119#95C2414yes—
1120#95C2414yes—
1121#95C2414yes—
1122#95C2414yes—
1123#95C2414yes—
1124#95C2414yes—
1125#95C2414yes—
1126C24C2511yescharacteristic
1127C2×Q8—24no—
1128C2×Q8—24no—
1129C2×Q8—28no—
1130C2×Q8—28no—
1131C2×Q8—24no—
1132C2×Q8—24no—
1133C2×Q8—24no—
1134C2×Q8—24no—
1135C2×Q8—44no—
1136C2×Q8—44no—
1137C2×Q8—44no—
1138C2×Q8—44no—
1139C2×Q8—416no—
1140C22×C4—24no—
1141C22×C4—22no—
1142C22×C4—22no—
1143C22×C4—22no—
1144C22×C4—22no—
1145C22×C4—24no—
1146C22×C4—24no—
1147C22×C4—24no—
1148C22×C4—24no—
1149C22×C4—22no—
1150C22×C4—22no—
1151C22×C4—24no—
1152C22×C4—22no—
1153C22×C4—22no—
1154C22×C4—22no—
1155C22×C4—22no—
1156C22×C4—41no—
1157C22×C4—41no—
1158C22×C4—41no—
1159C22×C4—41no—
1160C22×C4—42no—
1161C22×C4—42no—
1162C22×C4—42no—
1163C22×C4—41no—
1164C22×C4—42no—
1165C22×C4—41no—
1166C22×C4—42no—
1167C22×C4—42no—
1168C22×C4—41no—
1169C22×C4—41no—
1170C22×C4C2×#4114yes—
1171C22×C42−1+414yes—
1172C22×C42−1+414yes—
1173C22×C4C2514yes—
1174C22×C4C2511yescharacteristic
1175C22×C4C2511yescharacteristic
1176C22×C4C2512yes—
1177C22×C4C2512yes—
1178C22×C4C2511yescharacteristic
1179C22×C4C2511yescharacteristic
1180C22×C4C2511yescharacteristic
1181C22×C4C2511yescharacteristic
1182C22×C4C2512yes—
1183C22×C4C2512yes—
1184C22×C4C2511yescharacteristic
1185C22×C4C2514yes—
1186C22×C4C2512yes—
1187C22×C4C2512yes—
1188C22×C4C2512yes—
1189C22×C4C2512yes—
1190C22×C4C2512yes—
1191C22×C4C2511yescharacteristic
1192C22×C4C2512yes—
1193C22×C4C2512yes—
1194C22×C4C2512yes—
1195C22×C4C2512yes—
1196C22×C4C2514yes—
1197C22×C4C2514yes—
1198C22×C4C2512yes—
1199C22×C4C2512yes—
1200C22×C4C2512yes—
1201C22×C4C2511yescharacteristic
1202C22×C4C2511yescharacteristic
1203C22×C4C2511yescharacteristic
1204C22×C4C2511yescharacteristic
1205C22×C4C2511yescharacteristic
1206C22×C4C2511yescharacteristic
1207C4⋊C4—24no—
1208C4⋊C4—24no—
1209C4⋊C4—24no—
1210C4⋊C4—24no—
1211C4⋊C4—22no—
1212C4⋊C4—22no—
1213C4⋊C4—28no—
1214C4⋊C4—28no—
1215C4⋊C4—22no—
1216C4⋊C4—22no—
1217C4⋊C4—22no—
1218C4⋊C4—22no—
1219C4⋊C4—28no—
1220C4⋊C4—28no—
1221C4⋊C4—28no—
1222C4⋊C4—28no—
1223C4⋊C4—28no—
1224C4⋊C4—28no—
1225C4⋊C4—22no—
1226C4⋊C4—22no—
1227C4⋊C4—22no—
1228C4⋊C4—24no—
1229C4⋊C4—24no—
1230C4⋊C4—22no—
1231C4⋊C4—22no—
1232C4⋊C4—22no—
1233C4⋊C4—22no—
1234C4⋊C4—22no—
1235C4⋊C4—22no—
1236C4⋊C4—22no—
1237C4⋊C4—22no—
1238C4⋊C4—24no—
1239C4⋊C4—24no—
1240C4⋊C4—24no—
1241C4⋊C4—24no—
1242C4⋊C4—24no—
1243C4⋊C4—24no—
1244C4⋊C4—24no—
1245C4⋊C4—24no—
1246C4⋊C4—24no—
1247C4⋊C4—24no—
1248C4⋊C4—22no—
1249C4⋊C4—22no—
1250C4⋊C4—28no—
1251C4⋊C4—24no—
1252C4⋊C4—24no—
1253C4⋊C4—24no—
1254C4⋊C4—41no—
1255C4⋊C4—44no—
1256C4⋊C4—41no—
1257C4⋊C4—44no—
1258C4⋊C4—44no—
1259C4⋊C4—44no—
1260C4⋊C4—44no—
1261C4⋊C4—42no—
1262C4⋊C4—42no—
1263C4⋊C4—42no—
1264C4⋊C4—42no—
1265C4⋊C4—42no—
1266C4⋊C4—42no—
1267C4⋊C4—42no—
1268C4⋊C4—42no—
1269C4⋊C4—44no—
1270C4⋊C4—44no—
1271C4⋊C4—42no—
1272C4⋊C4—42no—
1273C4⋊C4—42no—
1274C4⋊C4—42no—
1275C4⋊C4—42no—
1276C4⋊C4—44no—
1277C4⋊C4—44no—
1278C4⋊C4—42no—
1279C4⋊C4—42no—
1280C4⋊C4—42no—
1281C4⋊C4—42no—
1282C4⋊C4—42no—
1283C4⋊C4—44no—
1284C4⋊C4—42no—
1285C4⋊C4—44no—
1286C4⋊C4—44no—
1287C4⋊C4—42no—
1288C4⋊C4—42no—
1289C4⋊C4—42no—
1290C4⋊C4—42no—
1291C4⋊C4—44no—
1292C4⋊C4—42no—
1293C4⋊C4—44no—
1294C4⋊C4—42no—
1295C4⋊C4—44no—
1296C4⋊C4—42no—
1297C4⋊C4—44no—
1298C4⋊C4—44no—
1299C4⋊C4—44no—
1300C4⋊C4—44no—
1301C4⋊C4—42no—
1302C4⋊C4C2×#4114yes—
1303C4⋊C4C2×#4114yes—
1304C4⋊C42−1+414yes—
1305C22⋊C4—24no—
1306C22⋊C4—24no—
1307C22⋊C4—24no—
1308C22⋊C4—24no—
1309C22⋊C4—24no—
1310C22⋊C4—24no—
1311C22⋊C4—24no—
1312C22⋊C4C2×#4118yes—
1313C42—24no—
1314C42—28no—
1315C42—28no—
1316C42—24no—
1317C42—24no—
1318C42—22no—
1319C42—22no—
1320C42—22no—
1321C42—22no—
1322C42—22no—
1323C42—22no—
1324C42—22no—
1325C42—22no—
1326C42—22no—
1327C42—22no—
1328C42—22no—
1329C42—22no—
1330C42—24no—
1331C42—24no—
1332C42—24no—
1333C42—24no—
1334C42—24no—
1335C42—24no—
1336C42—24no—
1337C42—44no—
1338C42—44no—
1339C42—42no—
1340C42—44no—
1341C42—42no—
1342C42—44no—
1343C42—44no—
1344C42—42no—
1345C42—44no—
1346C42—44no—
1347C42—42no—
1348C42—44no—
1349C42—42no—
1350C42C2×#4118yes—
1351C23—21no—
1352C23—21no—
1353C23—21no—
1354C23—21no—
1355C23C22×#4112yes—
1356C23C2×2−1+412yes—
1357C23C2×2−1+412yes—
1358C23C2611yescharacteristic
1359Q8—48no—
1360Q8—48no—
1361Q8—88no—
1362Q8—88no—
1363C2×C4—21no—
1364C2×C4—21no—
1365C2×C4—21no—
1366C2×C4—21no—
1367C2×C4—22no—
1368C2×C4—22no—
1369C2×C4—21no—
1370C2×C4—21no—
1371C2×C4—22no—
1372C2×C4—21no—
1373C2×C4—22no—
1374C2×C4—21no—
1375C2×C4—22no—
1376C2×C4—22no—
1377C2×C4—24no—
1378C2×C4—22no—
1379C2×C4—22no—
1380C2×C4—22no—
1381C2×C4—22no—
1382C2×C4—24no—
1383C2×C4—24no—
1384C2×C4—21no—
1385C2×C4—21no—
1386C2×C4—21no—
1387C2×C4—21no—
1388C2×C4—21no—
1389C2×C4—21no—
1390C2×C4—21no—
1391C2×C4—21no—
1392C2×C4—22no—
1393C2×C4—22no—
1394C2×C4—22no—
1395C2×C4—22no—
1396C2×C4—22no—
1397C2×C4—22no—
1398C2×C4—22no—
1399C2×C4—22no—
1400C2×C4—22no—
1401C2×C4—22no—
1402C2×C4—22no—
1403C2×C4—22no—
1404C2×C4—22no—
1405C2×C4—22no—
1406C2×C4—22no—
1407C2×C4—21no—
1408C2×C4—24no—
1409C2×C4—21no—
1410C2×C4—21no—
1411C2×C4—24no—
1412C2×C4—24no—
1413C2×C4—22no—
1414C2×C4—22no—
1415C2×C4—22no—
1416C2×C4—24no—
1417C2×C4—22no—
1418C2×C4—22no—
1419C2×C4—22no—
1420C2×C4—21no—
1421C2×C4—21no—
1422C2×C4—21no—
1423C2×C4—24no—
1424C2×C4—22no—
1425C2×C4—21no—
1426C2×C4—22no—
1427C2×C4—24no—
1428C2×C4—21no—
1429C2×C4—22no—
1430C2×C4—22no—
1431C2×C4—21no—
1432C2×C4—24no—
1433C2×C4—22no—
1434C2×C4—22no—
1435C2×C4—24no—
1436C2×C4—22no—
1437C2×C4—22no—
1438C2×C4—21no—
1439C2×C4—21no—
1440C2×C4—22no—
1441C2×C4—22no—
1442C2×C4—22no—
1443C2×C4—21no—
1444C2×C4—24no—
1445C2×C4—22no—
1446C2×C4—22no—
1447C2×C4—22no—
1448C2×C4—22no—
1449C2×C4—21no—
1450C2×C4—21no—
1451C2×C4—21no—
1452C2×C4—21no—
1453C2×C4—44no—
1454C2×C4—44no—
1455C2×C4—44no—
1456C2×C4—44no—
1457C2×C4—48no—
1458C2×C4—84no—
1459C2×C4—84no—
1460C2×C4—82no—
1461C2×C4—84no—
1462C2×C4—82no—
1463C2×C4#541116yes—
1464C2×C4C22×#4114yes—
1465C2×C4C22×#4114yes—
1466C2×C4C22×#4112yes—
1467C2×C4C22×#4112yes—
1468C2×C4C2×2−1+412yes—
1469C2×C4C2×2−1+412yes—
1470C2×C4C2×2−1+412yes—
1471C2×C4C2×2−1+412yes—
1472C2×C4C2×2−1+412yes—
1473C2×C4C2×2−1+412yes—
1474C2×C4C2×2−1+412yes—
1475C2×C4#58512yes—
1476C22—22no—
1477C22—22no—
1478C22—22no—
1479C22—22no—
1480C22—22no—
1481C22—22no—
1482C22C2×#54114yes—
1483C22C23×#4111yescharacteristic
1484C22C22×2−1+411yescharacteristic
1485C22C22×2−1+411yescharacteristic
1486C22C22×2−1+411yescharacteristic
1487C22C2×#58511yescharacteristic
1488C22H(7,𝔽2)11yescharacteristic
1489C222−1+611yescharacteristic
1490C4—24no—
1491C4—24no—
1492C4—22no—
1493C4—22no—
1494C4—22no—
1495C4—22no—
1496C4—42no—
1497C4—42no—
1498C4—42no—
1499C4—42no—
1500C4—44no—
1501C4—44no—
1502C4—42no—
1503C4—42no—
1504C4—42no—
1505C4—42no—
1506C4—41no—
1507C4—42no—
1508C4—42no—
1509C4—41no—
1510C4—41no—
1511C4—44no—
1512C4—42no—
1513C4—42no—
1514C4—41no—
1515C4—41no—
1516C4—41no—
1517C4—44no—
1518C4—42no—
1519C4—42no—
1520C4—41no—
1521C4—41no—
1522C4C2×#54114yes—
1523C4C2×#54114yes—
1524C2—24no—
1525C2C22×#54111yescharacteristic
1526C2#6283711yescharacteristic
1527C2#6287911yescharacteristic
1528C2#6292811yescharacteristic
1529C2#6294511yescharacteristic
1530C2#6300111yescharacteristic
1531C2#6301011yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC24C25
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42774C2semidirect
2. #42733C2semidirect
3. #42710C2semidirect
4. #42703C2semidirect
5. #42703C2semidirect
6. #42600C2semidirect
7. #42527C2semidirect
8. #42527C2semidirect
11. #40143C2semidirect
12. #40082C2semidirect
13. #40024C2semidirect
14. #40024C2semidirect
15. #39769C2semidirect
16. #39653C2semidirect
17. #39642C2semidirect
18. #39241C2semidirect

Maximal subgroups

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

subgroupindex
#427742
#427332
#427102
#427032
#426002
#425272
#414942
#407032
#401432
#400822
#400242
#397692
#396532
#396422
#392412
#386102
#385072
#356682
#356302
#355552
#355432
#353132
#352752
#351812
#349482
#348152
C2×#25112
#342722
#342712
#342542