Finite Group Databasebeta

← #8095296

Subgroups — #8095296

Order 512.

3920 conjugacy classes of subgroups.

The subgroup lattice has 1515 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53131C212yesmaximal, complemented
2#53131C212yesmaximal, complemented
3#53131C212yesmaximal, complemented
4#53121C212yesmaximal, complemented
5#53036C212yesmaximal, complemented
6#53036C212yesmaximal, complemented
7#52996C212yesmaximal, complemented
8#52996C212yesmaximal, complemented
9#52428C214yesmaximal
10#52428C214yesmaximal
11#46200C214yesmaximal
12#46191C212yesmaximal, complemented
13#46181C212yesmaximal, complemented
14#46181C212yesmaximal, complemented
15#46175C212yesmaximal, complemented
16#46175C212yesmaximal, complemented
17#46169C214yesmaximal
18#46157C212yesmaximal, complemented
19#46153C212yesmaximal, complemented
20#46153C212yesmaximal, complemented
21#35585C211yesmaximal, characteristic
22#35585C211yesmaximal, characteristic
23#35555C211yesmaximal, characteristic
24#35543C211yesmaximal, characteristic
25#35543C211yesmaximal, characteristic
26#35543C211yesmaximal, characteristic
27#35286C211yesmaximal, characteristic
28#35265C211yesmaximal, characteristic
29#35265C211yesmaximal, characteristic
30#35265C211yesmaximal, characteristic
31#35181C211yesmaximal, characteristic
32#35159C211yesmaximal, characteristic
33#34948C211yesmaximal, characteristic
34#34815C211yesmaximal, characteristic
35C2×#2507C211yesmaximal, characteristic
36#2864C2212yes—
37#2864C2212yes—
38#2864C2212yes—
39#2859C2212yes—
40#2859C2212yes—
41#2859C2212yes—
42#2859C2212yes—
43#2859C2212yes—
44#2851C2214yes—
45#2851C2214yes—
46#2845C2214yes—
47#2845C2214yes—
48#2839C2214yes—
49#2839C2214yes—
50#2839C2214yes—
51#2839C2214yes—
52#2839C2214yes—
53#2839C2214yes—
54#2839C2214yes—
55#2839C2214yes—
56#2839C2214yes—
57#2839C2214yes—
58#2839C2214yes—
59#2839C2214yes—
60#2839C2214yes—
61#2839C2214yes—
62#2822C2214yes—
63#2822C2214yes—
64#2822C2214yes—
65#2822C2214yes—
66#2810C2214yes—
67#2810C2214yes—
68#2767C2214yes—
69#2767C2214yes—
70#2767C2214yes—
71#2767C2214yes—
72#2767C2214yes—
73#2767C2214yes—
74#2767C2214yes—
75#2767C2214yes—
76#2767C2214yes—
77#2767C2214yes—
78#2767C2214yes—
79#2767C2214yes—
80#2726C2214yes—
81#2726C2214yes—
82#2726C2214yes—
83#2726C2214yes—
84#2726C2214yes—
85#2726C2214yes—
86#2726C2214yes—
87#2726C2214yes—
88#2726C2214yes—
89#2726C2214yes—
90#2726C2214yes—
91#2726C2214yes—
92#2719C2214yes—
93#2719C2214yes—
94#2719C2214yes—
95#2719C2214yes—
96#2719C2214yes—
97#2719C2214yes—
98#2719C2214yes—
99#2719C2214yes—
100#2719C2214yes—
101#2719C2214yes—
102#2719C2214yes—
103#2719C2214yes—
104#2719C2214yes—
105#2719C2214yes—
106#2647C2212yes—
107#2647C2212yes—
108#2647C2212yes—
109#2647C2212yes—
110#2647C2212yes—
111#2647C2212yes—
112#2647C2212yes—
113#2647C2212yes—
114#2646C2214yes—
115#2646C2214yes—
116#2571C2212yes—
117#2571C2212yes—
118#2571C2211yescharacteristic
119#2571C2212yes—
120#2571C2212yes—
121#2571C2212yes—
122#2571C2212yes—
123#2571C2212yes—
124#2571C2211yescharacteristic
125#2570C2211yescharacteristic
126#2570C2212yes—
127#2570C2212yes—
128#2570C2212yes—
129#2570C2212yes—
130#2570C2212yes—
131#2570C2212yes—
132#2570C2212yes—
133#2570C2211yescharacteristic
134#2570C2212yes—
135#2570C2211yescharacteristic
136#2570C2212yes—
137#2570C2212yes—
138#2570C2212yes—
139#2570C2212yes—
140#2570C2211yescharacteristic
141#2569C2214yes—
142#2569C2214yes—
143#2569C2212yes—
144#2569C2212yes—
145#2552C2212yes—
146#2552C2212yes—
147#2552C2212yes—
148#2552C2212yes—
149#2552C2211yescharacteristic
150#2552C2212yes—
151#2552C2212yes—
152#2552C2212yes—
153#2552C2211yescharacteristic
154#2552C2212yes—
155#2552C2212yes—
156#2509C2212yes—
157#2509C2212yes—
158#2509C2212yes—
159#2509C2212yes—
160#2509C2211yescharacteristic
161#2509C2212yes—
162#2509C2212yes—
163#2509C2212yes—
164#2509C2212yes—
165#2509C2212yes—
166#2509C2212yes—
167#2509C2211yescharacteristic
168#2509C2212yes—
169#2509C2212yes—
170#2508C2212yes—
171#2508C2212yes—
172#2508C2212yes—
173#2508C2212yes—
174#2508C2211yescharacteristic
175#2508C2212yes—
176#2508C2212yes—
177#2508C2212yes—
178#2508C2212yes—
179#2508C2212yes—
180#2508C2212yes—
181#2508C2212yes—
182#2508C2211yescharacteristic
183#2508C2212yes—
184#2507C2212yes—
185#2507C2212yes—
186#2507C2212yes—
187#2507C2212yes—
188#2507C2212yes—
189#2507C2212yes—
190#2507C2212yes—
191#2507C2212yes—
192#2507C2212yes—
193#2507C2211yescharacteristic
194#2507C2212yes—
195#2507C2212yes—
196#2507C2212yes—
197#2507C2212yes—
198#2507C2212yes—
199#2507C2212yes—
200#2507C2212yes—
201#2507C2212yes—
202#2507C2212yes—
203#2507C2212yes—
204#2507C2212yes—
205#2507C2212yes—
206#2507C2211yescharacteristic
207#2507C2212yes—
208#2506C2212yes—
209#2506C2212yes—
210#2506C2212yes—
211#2506C2212yes—
212#2506C2212yes—
213#2506C2212yes—
214#2506C2212yes—
215#2506C2212yes—
216#2506C2212yes—
217#2506C2212yes—
218#2506C2212yes—
219#2506C2212yes—
220#2506C2212yes—
221#2506C2211yescharacteristic
222#2506C2212yes—
223#2506C2211yescharacteristic
224#2505C2214yes—
225#2505C2214yes—
226#2505C2214yes—
227#2505C2214yes—
228#2505C2214yes—
229#2505C2214yes—
230#2505C2212yes—
231#2505C2212yes—
232#2473C2212yes—
233#2473C2214yes—
234#2473C2214yes—
235#2473C2214yes—
236#2473C2214yes—
237#2473C2214yes—
238#2473C2214yes—
239#2473C2214yes—
240#2473C2214yes—
241#2473C2212yes—
242#2442C2214yes—
243#2442C2214yes—
244#2442C2212yes—
245#2442C2214yes—
246#2442C2214yes—
247#2442C2212yes—
248#2402C2212yes—
249#2402C2212yes—
250#2402C2212yes—
251#2402C2212yes—
252C2×#398C2212yes—
253C2×#398C2212yes—
254#2382C2214yes—
255#2382C2214yes—
256#2382C2214yes—
257#2382C2214yes—
258#2317C2211yescharacteristic
259#2317C2211yescharacteristic
260#2317C2211yescharacteristic
261#2317C2211yescharacteristic
262#2317C2211yescharacteristic
263#2317C2211yescharacteristic
264#2317C2211yescharacteristic
265#2317C2211yescharacteristic
266#2317C2211yescharacteristic
267#2317C2211yescharacteristic
268#2316C2211yescharacteristic
269#2316C2211yescharacteristic
270#2316C2211yescharacteristic
271#2316C2211yescharacteristic
272C4×#125C2212yes—
273C4×#125C2212yes—
274C4×#125C2212yes—
275C4×#125C2212yes—
276#2296C2211yescharacteristic
277#2296C2211yescharacteristic
278#2296C2211yescharacteristic
279#2296C2211yescharacteristic
280#2296C2211yescharacteristic
281#2296C2211yescharacteristic
282C2×#389C2211yescharacteristic
283C2×#389C2211yescharacteristic
284C2×#389C2212yes—
285C2×#389C2211yescharacteristic
286C2×#389C2211yescharacteristic
287C2×#387C2212yes—
288#2285C2211yescharacteristic
289#2285C2211yescharacteristic
290#2285C2211yescharacteristic
291#2285C2211yescharacteristic
292C2×#384C2211yescharacteristic
293#2274C2211yescharacteristic
294#2274C2211yescharacteristic
295C4×#117C2211yescharacteristic
296C4×#117C2211yescharacteristic
297C2×C4×C4⋊C4C2211yescharacteristic
298C2×C4×C4⋊C4C2211yescharacteristic
299C2×#125C2312yes—
300C2×#125C2312yes—
301C2×#125C2312yes—
302C2×#125C2312yes—
303C2×#125C2314yes—
304C2×#125C2314yes—
305C2×#125C2314yes—
306C2×#125C2314yes—
307C2×#125C2314yes—
308C2×#125C2314yes—
309C2×#125C2314yes—
310C2×#125C2314yes—
311C2×#125C2314yes—
312C2×#125C2314yes—
313C2×#125C2314yes—
314C2×#125C2314yes—
315C2×#125C2314yes—
316C2×#125C2314yes—
317C2×#117C2311yescharacteristic
318C2×#117C2311yescharacteristic
319C2×#117C2311yescharacteristic
320C2×#117C2311yescharacteristic
321C2×#117C2311yescharacteristic
322C2×#117C2311yescharacteristic
323C2×#117C2311yescharacteristic
324C2×#117C2311yescharacteristic
325C22×C4⋊C4C2311yescharacteristic
326C22×C4⋊C4C2311yescharacteristic
327C22×C4⋊C4C2311yescharacteristic
328C22×C4⋊C4C2311yescharacteristic
329C22×C4⋊C4C2311yescharacteristic
330C22×C4⋊C4C2311yescharacteristic
331C22×C4⋊C4C2312yes—
332C22×C4⋊C4C2312yes—
333C22×C4⋊C4C2312yes—
334C22×C4⋊C4C2312yes—
335C22×C4⋊C4C2312yes—
336C22×C4⋊C4C2312yes—
337C22×C42C2311yescharacteristic
338C22×C42C2311yescharacteristic
339C22×C42C2311yescharacteristic
340C22×C42C2312yes—
341#400C2312yes—
342#400C2312yes—
343#400C2314yes—
344#400C2314yes—
345#400C2314yes—
346#400C2314yes—
347#400C2314yes—
348#400C2314yes—
349#400C2314yes—
350#400C2314yes—
351#400C2314yes—
352#400C2314yes—
353#400C2314yes—
354#400C2314yes—
355#400C2314yes—
356#400C2314yes—
357#400C2312yes—
358#400C2312yes—
359#400C2314yes—
360#400C2314yes—
361#400C2314yes—
362#400C2314yes—
363#400C2312yes—
364#400C2314yes—
365#400C2314yes—
366#400C2312yes—
367#400C2312yes—
368#400C2314yes—
369#400C2314yes—
370#400C2314yes—
371#400C2314yes—
372#400C2312yes—
373#400C2314yes—
374#400C2314yes—
375#400C2314yes—
376#400C2314yes—
377#400C2314yes—
378#400C2314yes—
379#400C2314yes—
380#400C2314yes—
381#400C2314yes—
382#400C2312yes—
383#400C2312yes—
384#400C2314yes—
385#400C2314yes—
386#400C2314yes—
387#400C2314yes—
388#400C2314yes—
389#400C2314yes—
390#400C2314yes—
391#400C2314yes—
392#400C2314yes—
393#400C2314yes—
394#400C2314yes—
395#400C2314yes—
396#400C2312yes—
397#400C2312yes—
398#400C2312yes—
399#400C2312yes—
400#400C2314yes—
401#400C2312yes—
402#400C2312yes—
403#398C2312yes—
404#398C2312yes—
405#398C2312yes—
406#398C2314yes—
407#398C2312yes—
408#398C2314yes—
409#398C2314yes—
410#398C2314yes—
411#398C2314yes—
412#398C2314yes—
413#398C2314yes—
414#398C2314yes—
415#398C2314yes—
416#398C2314yes—
417#398C2314yes—
418#398C2314yes—
419#398C2314yes—
420#398C2314yes—
421#398C2314yes—
422#398C2314yes—
423#398C2314yes—
424#398C2314yes—
425#398C2314yes—
426#398C2314yes—
427#398C2314yes—
428#398C2314yes—
429#398C2314yes—
430#398C2314yes—
431#398C2314yes—
432#398C2312yes—
433#398C2314yes—
434#398C2314yes—
435#398C2314yes—
436#398C2312yes—
437#398C2314yes—
438#398C2312yes—
439#398C2312yes—
440#398C2314yes—
441#398C2312yes—
442#398C2314yes—
443#398C2314yes—
444#398C2314yes—
445#398C2312yes—
446#398C2314yes—
447#398C2314yes—
448#398C2314yes—
449#398C2314yes—
450#398C2314yes—
451#398C2314yes—
452#398C2314yes—
453#398C2314yes—
454#398C2314yes—
455#398C2314yes—
456#398C2312yes—
457#398C2312yes—
458#398C2312yes—
459#398C2314yes—
460#398C2314yes—
461#398C2314yes—
462#398C2314yes—
463#398C2314yes—
464#398C2314yes—
465#398C2314yes—
466#398C2314yes—
467#398C2314yes—
468#398C2314yes—
469#398C2312yes—
470#398C2314yes—
471#398C2314yes—
472#398C2314yes—
473#398C2314yes—
474#398C2314yes—
475#398C2312yes—
476#398C2312yes—
477#389C2312yes—
478#389C2312yes—
479#389C2312yes—
480#389C2312yes—
481#389C2312yes—
482#389C2312yes—
483#389C2312yes—
484#389C2312yes—
485#389C2312yes—
486#389C2312yes—
487#389C2312yes—
488#389C2311yescharacteristic
489#389C2311yescharacteristic
490#389C2312yes—
491#389C2312yes—
492#389C2312yes—
493#389C2312yes—
494#389C2311yescharacteristic
495#389C2311yescharacteristic
496#389C2312yes—
497#389C2311yescharacteristic
498#389C2311yescharacteristic
499#389C2312yes—
500#389C2312yes—
501#389C2312yes—
502#389C2312yes—
503#389C2312yes—
504#389C2312yes—
505#389C2312yes—
506#389C2312yes—
507#389C2311yescharacteristic
508#389C2312yes—
509#389C2311yescharacteristic
510#389C2311yescharacteristic
511#389C2312yes—
512#389C2312yes—
513#389C2311yescharacteristic
514#389C2312yes—
515#389C2312yes—
516#389C2312yes—
517#389C2312yes—
518#389C2312yes—
519#389C2312yes—
520#389C2312yes—
521#389C2314yes—
522#389C2314yes—
523#389C2314yes—
524#389C2314yes—
525#389C2314yes—
526#389C2314yes—
527#389C2314yes—
528#389C2312yes—
529#389C2312yes—
530#389C2312yes—
531#389C2312yes—
532#389C2312yes—
533#389C2312yes—
534#389C2312yes—
535#389C2312yes—
536#389C2312yes—
537#389C2312yes—
538#389C2312yes—
539#389C2312yes—
540#389C2312yes—
541#389C2312yes—
542#389C2312yes—
543#389C2312yes—
544#389C2314yes—
545#389C2314yes—
546#389C2314yes—
547#389C2314yes—
548#389C2314yes—
549#389C2314yes—
550#389C2314yes—
551#389C2314yes—
552#389C2314yes—
553#389C2314yes—
554#389C2311yescharacteristic
555#389C2311yescharacteristic
556#389C2312yes—
557#389C2312yes—
558#389C2314yes—
559#389C2314yes—
560#389C2314yes—
561#389C2314yes—
562#389C2311yescharacteristic
563#389C2311yescharacteristic
564#389C2314yes—
565#389C2314yes—
566#389C2314yes—
567#389C2314yes—
568#389C2314yes—
569#389C2314yes—
570#389C2314yes—
571#389C2311yescharacteristic
572#389C2311yescharacteristic
573#389C2312yes—
574#389C2312yes—
575#389C2311yescharacteristic
576#389C2311yescharacteristic
577#389C2314yes—
578#389C2314yes—
579#389C2312yes—
580#389C2311yescharacteristic
581#389C2311yescharacteristic
582#389C2311yescharacteristic
583#389C2312yes—
584#389C2312yes—
585#389C2312yes—
586#389C2312yes—
587#389C2311yescharacteristic
588#389C2312yes—
589#389C2311yescharacteristic
590#389C2311yescharacteristic
591#387C2312yes—
592#387C2312yes—
593#387C2312yes—
594#387C2312yes—
595#387C2312yes—
596#387C2312yes—
597#387C2312yes—
598#387C2312yes—
599#387C2312yes—
600#387C2312yes—
601#387C2312yes—
602#387C2312yes—
603#387C2312yes—
604#387C2312yes—
605#387C2312yes—
606#387C2312yes—
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#387C2314yes—
651#387C2314yes—
652#387C2314yes—
653#387C2314yes—
654#387C2314yes—
655#385C2312yes—
656#385C2312yes—
657#385C2314yes—
658#385C2314yes—
659#385C2312yes—
660#385C2312yes—
661#385C2312yes—
662#385C2312yes—
663#385C2314yes—
664#385C2314yes—
665#385C2314yes—
666#385C2314yes—
667#385C2314yes—
668#385C2314yes—
669#385C2314yes—
670#385C2314yes—
671#385C2312yes—
672#385C2312yes—
673#385C2312yes—
674#385C2312yes—
675#385C2312yes—
676#385C2312yes—
677#384C2311yescharacteristic
678#384C2311yescharacteristic
679#384C2311yescharacteristic
680#384C2312yes—
681#384C2311yescharacteristic
682#384C2312yes—
683#384C2312yes—
684#384C2312yes—
685#384C2312yes—
686#384C2312yes—
687#384C2312yes—
688#384C2312yes—
689#384C2311yescharacteristic
690#384C2311yescharacteristic
691#384C2312yes—
692#384C2311yescharacteristic
693#384C2312yes—
694#384C2312yes—
695#384C2312yes—
696#384C2312yes—
697#384C2312yes—
698#384C2311yescharacteristic
699#382C2312yes—
700#382C2312yes—
701#382C2312yes—
702#382C2312yes—
703#382C2314yes—
704#382C2314yes—
705#382C2314yes—
706#382C2314yes—
707#382C2311yescharacteristic
708#382C2311yescharacteristic
709#382C2312yes—
710#382C2312yes—
711#382C2312yes—
712#382C2312yes—
713#382C2311yescharacteristic
714#382C2311yescharacteristic
715#382C2311yescharacteristic
716#382C2312yes—
717#382C2312yes—
718#382C2311yescharacteristic
719#382C2311yescharacteristic
720#382C2312yes—
721#382C2311yescharacteristic
722#382C2314yes—
723#382C2314yes—
724#382C2314yes—
725#382C2312yes—
726#382C2312yes—
727#382C2312yes—
728#382C2314yes—
729#382C2314yes—
730#382C2314yes—
731#382C2314yes—
732#382C2314yes—
733#380C2312yes—
734#380C2314yes—
735#380C2312yes—
736#380C2312yes—
737#380C2314yes—
738#380C2314yes—
739#380C2312yes—
740#380C2312yes—
741#380C2312yes—
742#380C2314yes—
743#380C2312yes—
744#380C2312yes—
745C4×C4⋊C4C2311yescharacteristic
746C4×C4⋊C4C2312yes—
747C4×C4⋊C4C2311yescharacteristic
748C4×C4⋊C4C2311yescharacteristic
749C4×C4⋊C4C2312yes—
750C4×C4⋊C4C2311yescharacteristic
751C4×C4⋊C4C2312yes—
752C4×C4⋊C4C2312yes—
753C4×C4⋊C4C2312yes—
754C4×C4⋊C4C2312yes—
755C4×C4⋊C4C2312yes—
756C4×C4⋊C4C2312yes—
757C4×C4⋊C4C2312yes—
758C4×C4⋊C4C2312yes—
759C4×C4⋊C4C2312yes—
760C4×C4⋊C4C2312yes—
761C4×C4⋊C4C2312yes—
762C4×C4⋊C4C2312yes—
763C4×C4⋊C4C2312yes—
764C4×C4⋊C4C2312yes—
765C4×C4⋊C4C2312yes—
766C4×C4⋊C4C2312yes—
767C4×C4⋊C4C2311yescharacteristic
768C4×C4⋊C4C2311yescharacteristic
769C4×C4⋊C4C2311yescharacteristic
770C4×C4⋊C4C2312yes—
771C4×C4⋊C4C2312yes—
772C4×C4⋊C4C2312yes—
773C4×C4⋊C4C2312yes—
774C4×C4⋊C4C2312yes—
775C4×C4⋊C4C2312yes—
776C4×C4⋊C4C2312yes—
777C4×C4⋊C4C2312yes—
778C4×C4⋊C4C2312yes—
779C4×C4⋊C4C2312yes—
780C4×C4⋊C4C2312yes—
781C4×C4⋊C4C2311yescharacteristic
782C4×C4⋊C4C2311yescharacteristic
783C4×C4⋊C4C2311yescharacteristic
784C4×C4⋊C4C2311yescharacteristic
785C4×C4⋊C4C2312yes—
786C4×C4⋊C4C2312yes—
787C4×C4⋊C4C2311yescharacteristic
788C4×C4⋊C4C2312yes—
789C4×C4⋊C4C2311yescharacteristic
790C4×C4⋊C4C2311yescharacteristic
791C4×C4⋊C4C2311yescharacteristic
792C4×C4⋊C4C2311yescharacteristic
793C4×C22⋊C4C2312yes—
794C4×C22⋊C4C2314yes—
795C4×C22⋊C4C2314yes—
796C4×C22⋊C4C2312yes—
797C4×C22⋊C4C2312yes—
798C4×C22⋊C4C2312yes—
799#376C2312yes—
800#376C2312yes—
801C2×#95C2311yescharacteristic
802C2×#95C2312yes—
803C2×#95C2311yescharacteristic
804C2×#95C2312yes—
805C2×#95C2312yes—
806C2×#95C2312yes—
807C2×#95C2312yes—
808C43C2312yes—
809C43C2312yes—
810C23×C4C2411yescharacteristic
811C23×C4C2411yescharacteristic
812C23×C4C2411yescharacteristic
813C23×C4C2411yescharacteristic
814C23×C4C2412yes—
815C23×C4C2412yes—
816C23×C4C2411yescharacteristic
817C23×C4C2412yes—
818C23×C4C2411yescharacteristic
819C23×C4C2412yes—
820C23×C4C2411yescharacteristic
821#125—28no—
822#125—28no—
823#125—44no—
824#125—48no—
825#125—44no—
826#125—48no—
827#125—84no—
828#125—84no—
829#125—84no—
830#125—84no—
831#125—84no—
832#125—84no—
833#125—84no—
834#125—84no—
835#125—84no—
836#125—84no—
837#125—84no—
838#125—84no—
839#117—24no—
840#117—24no—
841#117—24no—
842#117—24no—
843#117—24no—
844#117—24no—
845#117—24no—
846#117—24no—
847C2×C4⋊C4—24no—
848C2×C4⋊C4—24no—
849C2×C4⋊C4—24no—
850C2×C4⋊C4—24no—
851C2×C4⋊C4—24no—
852C2×C4⋊C4—42no—
853C2×C4⋊C4—44no—
854C2×C4⋊C4—82no—
855C2×C4⋊C4—82no—
856C2×C4⋊C4—82no—
857C2×C4⋊C4—82no—
858C2×C4⋊C4—82no—
859C2×C4⋊C4C2411yescharacteristic
860C2×C4⋊C4C2411yescharacteristic
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2412yes—
863C2×C4⋊C4C2412yes—
864C2×C4⋊C4C2412yes—
865C2×C4⋊C4C2411yescharacteristic
866C2×C4⋊C4C2412yes—
867C2×C4⋊C4C2412yes—
868C2×C4⋊C4C2412yes—
869C2×C4⋊C4C2412yes—
870C2×C4⋊C4C2412yes—
871C2×C4⋊C4C2411yescharacteristic
872C2×C4⋊C4C2411yescharacteristic
873C2×C4⋊C4C2411yescharacteristic
874C2×C4⋊C4C2411yescharacteristic
875C2×C4⋊C4C2411yescharacteristic
876C2×C4⋊C4C2411yescharacteristic
877C2×C4⋊C4C2411yescharacteristic
878C2×C4⋊C4C2411yescharacteristic
879C2×C4⋊C4C2411yescharacteristic
880C2×C4⋊C4C2411yescharacteristic
881C2×C4⋊C4C2411yescharacteristic
882C2×C4⋊C4C2411yescharacteristic
883C2×C4⋊C4C2411yescharacteristic
884C2×C4⋊C4C2411yescharacteristic
885C2×C4⋊C4C2411yescharacteristic
886C2×C4⋊C4C2411yescharacteristic
887C2×C4⋊C4C2411yescharacteristic
888C2×C4⋊C4C2411yescharacteristic
889C2×C4⋊C4C2412yes—
890C2×C4⋊C4C2412yes—
891C2×C4⋊C4C2412yes—
892C2×C4⋊C4C2412yes—
893C2×C4⋊C4C2412yes—
894C2×C4⋊C4C2412yes—
895C2×C4⋊C4C2412yes—
896C2×C4⋊C4C2412yes—
897C2×C4⋊C4C2412yes—
898C2×C4⋊C4C2412yes—
899C2×C4⋊C4C2412yes—
900C2×C4⋊C4C2412yes—
901C2×C4⋊C4C2412yes—
902C2×C4⋊C4C2414yes—
903C2×C4⋊C4C2414yes—
904C2×C4⋊C4C2414yes—
905C2×C4⋊C4C2414yes—
906C2×C4⋊C4C2414yes—
907C2×C4⋊C4C2414yes—
908C2×C4⋊C4C2414yes—
909C2×C4⋊C4C2414yes—
910C2×C4⋊C4C2414yes—
911C2×C4⋊C4C2414yes—
912C2×C4⋊C4C2411yescharacteristic
913C2×C4⋊C4C2411yescharacteristic
914C2×C4⋊C4C2414yes—
915C2×C4⋊C4C2412yes—
916C2×C4⋊C4C2412yes—
917C2×C4⋊C4C2412yes—
918C2×C4⋊C4C2412yes—
919C2×C4⋊C4C2412yes—
920C2×C4⋊C4C2412yes—
921C2×C4⋊C4C2412yes—
922C2×C4⋊C4C2412yes—
923C2×C4⋊C4C2412yes—
924C2×C4⋊C4C2412yes—
925C2×C4⋊C4C2412yes—
926C2×C4⋊C4C2412yes—
927C2×C4⋊C4C2412yes—
928C2×C4⋊C4C2412yes—
929C2×C4⋊C4C2412yes—
930C2×C4⋊C4C2412yes—
931C2×C4⋊C4C2412yes—
932C2×C4⋊C4C2412yes—
933C2×C4⋊C4C2412yes—
934C2×C4⋊C4C2412yes—
935C2×C4⋊C4C2414yes—
936C2×C4⋊C4C2414yes—
937C2×C4⋊C4C2414yes—
938C2×C4⋊C4C2414yes—
939C2×C4⋊C4C2414yes—
940C2×C4⋊C4C2414yes—
941C2×C4⋊C4C2414yes—
942C2×C4⋊C4C2414yes—
943C2×C4⋊C4C2414yes—
944C2×C4⋊C4C2414yes—
945C2×C4⋊C4C2414yes—
946C2×C4⋊C4C2414yes—
947C2×C4⋊C4C2414yes—
948C2×C4⋊C4C2414yes—
949C2×C4⋊C4C2414yes—
950C2×C4⋊C4C2414yes—
951C2×C4⋊C4C2414yes—
952C2×C4⋊C4C2414yes—
953C2×C4⋊C4C2414yes—
954C2×C4⋊C4C2414yes—
955C2×C4⋊C4C2414yes—
956C2×C4⋊C4C2412yes—
957C2×C4⋊C4C2412yes—
958C2×C4⋊C4C2412yes—
959C2×C4⋊C4C2412yes—
960C2×C4⋊C4C2412yes—
961C2×C4⋊C4C2412yes—
962C2×C4⋊C4C2412yes—
963C2×C4⋊C4C2414yes—
964C2×C4⋊C4C2414yes—
965C2×C4⋊C4C2414yes—
966C2×C4⋊C4C2414yes—
967C2×C4⋊C4C2414yes—
968C2×C4⋊C4C2414yes—
969C2×C4⋊C4C2414yes—
970C2×C4⋊C4C2411yescharacteristic
971C2×C22⋊C4C2412yes—
972C2×C22⋊C4C2412yes—
973C2×C22⋊C4C2412yes—
974C2×C22⋊C4C2412yes—
975C2×C22⋊C4C2412yes—
976C2×C22⋊C4C2412yes—
977C2×C22⋊C4C2412yes—
978C2×C22⋊C4C2412yes—
979C2×C42—24no—
980C2×C42—24no—
981C2×C42—24no—
982C2×C42—82no—
983C2×C42C2412yes—
984C2×C42C2412yes—
985C2×C42C2412yes—
986C2×C42C2412yes—
987C2×C42C2412yes—
988C2×C42C2412yes—
989C2×C42C2412yes—
990C2×C42C2412yes—
991C2×C42C2412yes—
992C2×C42C2412yes—
993C2×C42C2412yes—
994C2×C42C2411yescharacteristic
995C2×C42C2411yescharacteristic
996C2×C42C2411yescharacteristic
997C2×C42C2411yescharacteristic
998C2×C42C2411yescharacteristic
999C2×C42C2411yescharacteristic
1000C2×C42C2411yescharacteristic
1001C2×C42C2411yescharacteristic
1002C2×C42C2411yescharacteristic
1003C2×C42C2411yescharacteristic
1004C2×C42C2411yescharacteristic
1005C2×C42C2411yescharacteristic
1006C2×C42C2412yes—
1007C2×C42C2412yes—
1008C2×C42C2412yes—
1009C2×C42C2412yes—
1010C2×C42C2414yes—
1011C2×C42C2414yes—
1012C2×C42C2414yes—
1013C2×C42C2412yes—
1014C2×C42C2414yes—
1015C2×C42C2414yes—
1016C2×C42C2414yes—
1017#95C2411yescharacteristic
1018#95C2411yescharacteristic
1019#95C2411yescharacteristic
1020#95C2411yescharacteristic
1021#95C2411yescharacteristic
1022#95C2411yescharacteristic
1023#95C2411yescharacteristic
1024#95C2414yes—
1025#95C2414yes—
1026#95C2411yescharacteristic
1027#95C2414yes—
1028#95C2414yes—
1029#95C2414yes—
1030#95C2414yes—
1031#95C2414yes—
1032#95C2414yes—
1033#95C2414yes—
1034#95C2414yes—
1035#95C2412yes—
1036#95C2412yes—
1037#95C2412yes—
1038#95C2412yes—
1039#95C2412yes—
1040#95C2412yes—
1041#95C2412yes—
1042#95C2412yes—
1043#95C2414yes—
1044#95C2414yes—
1045#95C2414yes—
1046#95C2414yes—
1047#95C2412yes—
1048#95C2412yes—
1049#95C2412yes—
1050#95C2412yes—
1051#95C2412yes—
1052#95C2412yes—
1053#95C2412yes—
1054#95C2412yes—
1055#95C2412yes—
1056#95C2412yes—
1057#95C2412yes—
1058#95C2412yes—
1059#95C2412yes—
1060#95C2412yes—
1061#95C2412yes—
1062#95C2412yes—
1063#95C2412yes—
1064#95C2412yes—
1065#95C2412yes—
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#95C2414yes—
1088#95C2414yes—
1089#95C2414yes—
1090#95C2414yes—
1091#95C2414yes—
1092#95C2414yes—
1093#95C2414yes—
1094#95C2414yes—
1095#95C2414yes—
1096#95C2414yes—
1097#95C2414yes—
1098#95C2414yes—
1099#95C2414yes—
1100#95C2414yes—
1101#95C2414yes—
1102#95C2414yes—
1103#95C2414yes—
1104#95C2414yes—
1105#95C2414yes—
1106#95C2414yes—
1107#95C2414yes—
1108#95C2414yes—
1109#95C2414yes—
1110#95C2414yes—
1111#95C2414yes—
1112#95C2414yes—
1113#95C2414yes—
1114#95C2414yes—
1115C24C2511yescharacteristic
1116C22×C4—22no—
1117C22×C4—22no—
1118C22×C4—22no—
1119C22×C4—22no—
1120C22×C4—24no—
1121C22×C4—22no—
1122C22×C4—22no—
1123C22×C4—24no—
1124C22×C4—24no—
1125C22×C4—24no—
1126C22×C4—22no—
1127C22×C4—22no—
1128C22×C4—22no—
1129C22×C4—22no—
1130C22×C4—41no—
1131C22×C4—42no—
1132C22×C4—41no—
1133C22×C4—42no—
1134C22×C4—41no—
1135C22×C4—41no—
1136C22×C4—42no—
1137C22×C4—42no—
1138C22×C4—41no—
1139C22×C4—41no—
1140C22×C4—41no—
1141C22×C4—42no—
1142C22×C4—42no—
1143C22×C4—42no—
1144C22×C4—42no—
1145C22×C4—41no—
1146C22×C42−1+414yes—
1147C22×C42−1+414yes—
1148C22×C42−1+414yes—
1149C22×C4C2511yescharacteristic
1150C22×C4C2511yescharacteristic
1151C22×C4C2512yes—
1152C22×C4C2512yes—
1153C22×C4C2511yescharacteristic
1154C22×C4C2512yes—
1155C22×C4C2512yes—
1156C22×C4C2512yes—
1157C22×C4C2512yes—
1158C22×C4C2512yes—
1159C22×C4C2512yes—
1160C22×C4C2511yescharacteristic
1161C22×C4C2511yescharacteristic
1162C22×C4C2511yescharacteristic
1163C22×C4C2514yes—
1164C22×C4C2514yes—
1165C22×C4C2511yescharacteristic
1166C22×C4C2512yes—
1167C22×C4C2512yes—
1168C22×C4C2512yes—
1169C22×C4C2512yes—
1170C22×C4C2512yes—
1171C22×C4C2512yes—
1172C22×C4C2511yescharacteristic
1173C22×C4C2514yes—
1174C22×C4C2514yes—
1175C22×C4C2512yes—
1176C22×C4C2512yes—
1177C22×C4C2511yescharacteristic
1178C22×C4C2511yescharacteristic
1179C22×C4C2511yescharacteristic
1180C22×C4C2511yescharacteristic
1181C22×C4C2511yescharacteristic
1182C22×C4C2511yescharacteristic
1183C4⋊C4—22no—
1184C4⋊C4—22no—
1185C4⋊C4—22no—
1186C4⋊C4—24no—
1187C4⋊C4—24no—
1188C4⋊C4—24no—
1189C4⋊C4—24no—
1190C4⋊C4—24no—
1191C4⋊C4—24no—
1192C4⋊C4—24no—
1193C4⋊C4—24no—
1194C4⋊C4—22no—
1195C4⋊C4—22no—
1196C4⋊C4—22no—
1197C4⋊C4—22no—
1198C4⋊C4—22no—
1199C4⋊C4—22no—
1200C4⋊C4—22no—
1201C4⋊C4—22no—
1202C4⋊C4—22no—
1203C4⋊C4—22no—
1204C4⋊C4—22no—
1205C4⋊C4—22no—
1206C4⋊C4—22no—
1207C4⋊C4—22no—
1208C4⋊C4—22no—
1209C4⋊C4—22no—
1210C4⋊C4—24no—
1211C4⋊C4—24no—
1212C4⋊C4—24no—
1213C4⋊C4—24no—
1214C4⋊C4—24no—
1215C4⋊C4—24no—
1216C4⋊C4—24no—
1217C4⋊C4—24no—
1218C4⋊C4—24no—
1219C4⋊C4—24no—
1220C4⋊C4—22no—
1221C4⋊C4—28no—
1222C4⋊C4—22no—
1223C4⋊C4—24no—
1224C4⋊C4—24no—
1225C4⋊C4—24no—
1226C4⋊C4—41no—
1227C4⋊C4—44no—
1228C4⋊C4—41no—
1229C4⋊C4—44no—
1230C4⋊C4—44no—
1231C4⋊C4—44no—
1232C4⋊C4—44no—
1233C4⋊C4—44no—
1234C4⋊C4—44no—
1235C4⋊C4—44no—
1236C4⋊C4—44no—
1237C4⋊C4—44no—
1238C4⋊C4—44no—
1239C4⋊C4—42no—
1240C4⋊C4—42no—
1241C4⋊C4—42no—
1242C4⋊C4—44no—
1243C4⋊C4—44no—
1244C4⋊C4—44no—
1245C4⋊C4—42no—
1246C4⋊C4—42no—
1247C4⋊C4—44no—
1248C4⋊C4—42no—
1249C4⋊C4—44no—
1250C4⋊C4—44no—
1251C4⋊C4—44no—
1252C4⋊C4—42no—
1253C4⋊C4—42no—
1254C4⋊C4—42no—
1255C4⋊C4—42no—
1256C4⋊C4—42no—
1257C4⋊C4—42no—
1258C4⋊C4—42no—
1259C4⋊C4—42no—
1260C4⋊C4—42no—
1261C4⋊C4—44no—
1262C4⋊C4—42no—
1263C4⋊C4—44no—
1264C4⋊C4—44no—
1265C4⋊C4—44no—
1266C4⋊C4—44no—
1267C4⋊C4—44no—
1268C4⋊C4—44no—
1269C4⋊C4—44no—
1270C4⋊C4—44no—
1271C4⋊C4—42no—
1272C4⋊C4—42no—
1273C4⋊C4—42no—
1274C4⋊C4—42no—
1275C4⋊C4—42no—
1276C4⋊C4—42no—
1277C4⋊C4—42no—
1278C4⋊C4—42no—
1279C4⋊C4—44no—
1280C4⋊C4—44no—
1281C4⋊C4—42no—
1282C4⋊C4—42no—
1283C4⋊C4—44no—
1284C4⋊C4—44no—
1285C4⋊C4—42no—
1286C4⋊C4—44no—
1287C4⋊C4—44no—
1288C4⋊C4—44no—
1289C4⋊C4—44no—
1290C4⋊C4—44no—
1291C4⋊C4—44no—
1292C4⋊C4—44no—
1293C4⋊C4—44no—
1294C4⋊C42−1+414yes—
1295C22⋊C4—24no—
1296C22⋊C4—24no—
1297C22⋊C4—24no—
1298C22⋊C4—24no—
1299C22⋊C4—24no—
1300C22⋊C4—24no—
1301C22⋊C4—24no—
1302C22⋊C4—24no—
1303C42—22no—
1304C42—22no—
1305C42—22no—
1306C42—22no—
1307C42—22no—
1308C42—22no—
1309C42—22no—
1310C42—22no—
1311C42—22no—
1312C42—22no—
1313C42—22no—
1314C42—22no—
1315C42—24no—
1316C42—24no—
1317C42—24no—
1318C42—24no—
1319C42—24no—
1320C42—24no—
1321C42—24no—
1322C42—24no—
1323C42—24no—
1324C42—24no—
1325C42—24no—
1326C42—44no—
1327C42—44no—
1328C42—42no—
1329C42—44no—
1330C42—42no—
1331C42—42no—
1332C42—44no—
1333C42—44no—
1334C42—44no—
1335C42—42no—
1336C42—42no—
1337C23—21no—
1338C23—21no—
1339C23—21no—
1340C23—21no—
1341C23C2×2−1+412yes—
1342C23C2×2−1+412yes—
1343C23C2×2−1+412yes—
1344C23C2611yescharacteristic
1345C2×C4—21no—
1346C2×C4—21no—
1347C2×C4—21no—
1348C2×C4—21no—
1349C2×C4—21no—
1350C2×C4—21no—
1351C2×C4—21no—
1352C2×C4—21no—
1353C2×C4—21no—
1354C2×C4—21no—
1355C2×C4—21no—
1356C2×C4—21no—
1357C2×C4—21no—
1358C2×C4—21no—
1359C2×C4—21no—
1360C2×C4—21no—
1361C2×C4—22no—
1362C2×C4—22no—
1363C2×C4—22no—
1364C2×C4—22no—
1365C2×C4—22no—
1366C2×C4—22no—
1367C2×C4—22no—
1368C2×C4—22no—
1369C2×C4—22no—
1370C2×C4—22no—
1371C2×C4—22no—
1372C2×C4—22no—
1373C2×C4—22no—
1374C2×C4—22no—
1375C2×C4—22no—
1376C2×C4—22no—
1377C2×C4—22no—
1378C2×C4—22no—
1379C2×C4—22no—
1380C2×C4—22no—
1381C2×C4—22no—
1382C2×C4—22no—
1383C2×C4—22no—
1384C2×C4—22no—
1385C2×C4—21no—
1386C2×C4—24no—
1387C2×C4—24no—
1388C2×C4—24no—
1389C2×C4—21no—
1390C2×C4—21no—
1391C2×C4—24no—
1392C2×C4—22no—
1393C2×C4—22no—
1394C2×C4—22no—
1395C2×C4—22no—
1396C2×C4—22no—
1397C2×C4—22no—
1398C2×C4—24no—
1399C2×C4—22no—
1400C2×C4—22no—
1401C2×C4—21no—
1402C2×C4—24no—
1403C2×C4—21no—
1404C2×C4—21no—
1405C2×C4—21no—
1406C2×C4—21no—
1407C2×C4—22no—
1408C2×C4—22no—
1409C2×C4—22no—
1410C2×C4—22no—
1411C2×C4—22no—
1412C2×C4—22no—
1413C2×C4—24no—
1414C2×C4—21no—
1415C2×C4—21no—
1416C2×C4—24no—
1417C2×C4—22no—
1418C2×C4—22no—
1419C2×C4—22no—
1420C2×C4—22no—
1421C2×C4—22no—
1422C2×C4—22no—
1423C2×C4—22no—
1424C2×C4—22no—
1425C2×C4—24no—
1426C2×C4—24no—
1427C2×C4—24no—
1428C2×C4—22no—
1429C2×C4—22no—
1430C2×C4—21no—
1431C2×C4—21no—
1432C2×C4—24no—
1433C2×C4—21no—
1434C2×C4—21no—
1435C2×C4—21no—
1436C2×C4—21no—
1437C2×C4—44no—
1438C2×C4—44no—
1439C2×C4—44no—
1440C2×C4—44no—
1441C2×C4—48no—
1442C2×C4—82no—
1443C2×C4—84no—
1444C2×C4—84no—
1445C2×C4—82no—
1446C2×C4—84no—
1447C2×C4#564116yes—
1448C2×C4C2×2−1+412yes—
1449C2×C4C2×2−1+412yes—
1450C2×C4C2×2−1+412yes—
1451C2×C4C2×2−1+412yes—
1452C2×C4C2×2−1+412yes—
1453C2×C4C2×2−1+412yes—
1454C2×C4C2×2−1+412yes—
1455C2×C4C2×2−1+412yes—
1456C2×C4C2×2−1+412yes—
1457C2×C4#58512yes—
1458C22—22no—
1459C22—22no—
1460C22—22no—
1461C22—22no—
1462C22—22no—
1463C22—22no—
1464C22C2×#56414yes—
1465C22C22×2−1+411yescharacteristic
1466C22C22×2−1+411yescharacteristic
1467C22C22×2−1+411yescharacteristic
1468C22C22×2−1+411yescharacteristic
1469C22C2×#58511yescharacteristic
1470C22H(7,𝔽2)11yescharacteristic
1471C22H(7,𝔽2)11yescharacteristic
1472C4—22no—
1473C4—22no—
1474C4—22no—
1475C4—22no—
1476C4—42no—
1477C4—42no—
1478C4—41no—
1479C4—42no—
1480C4—42no—
1481C4—41no—
1482C4—41no—
1483C4—44no—
1484C4—44no—
1485C4—42no—
1486C4—42no—
1487C4—42no—
1488C4—42no—
1489C4—44no—
1490C4—42no—
1491C4—42no—
1492C4—42no—
1493C4—42no—
1494C4—42no—
1495C4—42no—
1496C4—41no—
1497C4—41no—
1498C4—42no—
1499C4—42no—
1500C4—41no—
1501C4—41no—
1502C4—41no—
1503C4—44no—
1504C4C2×#56414yes—
1505C4C2×#56414yes—
1506C2—24no—
1507C2C22×#56411yescharacteristic
1508C2#6283711yescharacteristic
1509C2#6288111yescharacteristic
1510C2#6292611yescharacteristic
1511C2#6294311yescharacteristic
1512C2#6294511yescharacteristic
1513C2#6295811yescharacteristic
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. #53131C2semidirect
2. #53131C2semidirect
3. #53131C2semidirect
4. #53121C2semidirect
5. #53036C2semidirect
6. #53036C2semidirect
7. #52996C2semidirect
8. #52996C2semidirect
12. #46191C2semidirect
13. #46181C2semidirect
14. #46181C2semidirect
15. #46175C2semidirect
16. #46175C2semidirect
18. #46157C2semidirect
19. #46153C2semidirect
20. #46153C2semidirect

Maximal subgroups

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

subgroupindex
#531312
#531212
#530362
#529962
#524282
#462002
#461912
#461812
#461752
#461692
#461572
#461532
#355852
#355552
#355432
#352862
#352652
#351812
#351592
#349482
#348152
C2×#25072