Finite Group Databasebeta

← #8094832

Subgroups — #8094832

Order 512.

4068 conjugacy classes of subgroups.

The subgroup lattice has 1521 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#52452C214yesmaximal
10#52428C214yesmaximal
11#46191C212yesmaximal, complemented
12#46181C212yesmaximal, complemented
13#46181C212yesmaximal, complemented
14#46175C212yesmaximal, complemented
15#46175C212yesmaximal, complemented
16#46169C214yesmaximal
17#46157C212yesmaximal, complemented
18C4⋊#564C212yesmaximal, complemented
19C4⋊#564C212yesmaximal, complemented
20C22⋊#564C214yesmaximal
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×#2506C211yesmaximal, characteristic
36C2×#564C2214yes—
37C22×#125C2212yes—
38#2864C2212yes—
39#2864C2212yes—
40#2864C2212yes—
41#2859C2212yes—
42#2859C2212yes—
43#2859C2212yes—
44#2859C2212yes—
45#2859C2212yes—
46#2851C2214yes—
47#2851C2214yes—
48#2845C2214yes—
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#2839C2214yes—
63#2822C2214yes—
64#2822C2214yes—
65#2822C2214yes—
66#2822C2214yes—
67#2822C2214yes—
68#2810C2214yes—
69#2810C2214yes—
70#2767C2214yes—
71#2767C2214yes—
72#2767C2214yes—
73#2767C2214yes—
74#2767C2214yes—
75#2767C2214yes—
76#2767C2214yes—
77#2767C2214yes—
78#2767C2214yes—
79#2767C2214yes—
80#2767C2214yes—
81#2767C2214yes—
82#2726C2214yes—
83#2726C2214yes—
84#2726C2214yes—
85#2726C2214yes—
86#2726C2214yes—
87#2726C2214yes—
88#2726C2214yes—
89#2726C2214yes—
90#2719C2214yes—
91#2719C2214yes—
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#2719C2214yes—
107#2719C2214yes—
108#2647C2212yes—
109#2647C2212yes—
110#2647C2212yes—
111#2647C2212yes—
112#2647C2212yes—
113#2647C2212yes—
114#2647C2212yes—
115#2647C2212yes—
116#2646C2214yes—
117#2646C2214yes—
118#2571C2211yescharacteristic
119#2571C2212yes—
120#2571C2212yes—
121#2571C2212yes—
122#2571C2212yes—
123#2571C2212yes—
124#2571C2212yes—
125#2571C2212yes—
126#2571C2211yescharacteristic
127#2570C2212yes—
128#2570C2212yes—
129#2570C2212yes—
130#2570C2212yes—
131#2570C2211yescharacteristic
132#2570C2212yes—
133#2570C2212yes—
134#2570C2212yes—
135#2570C2211yescharacteristic
136#2570C2212yes—
137#2570C2212yes—
138#2570C2211yescharacteristic
139#2570C2212yes—
140#2570C2212yes—
141#2570C2212yes—
142#2570C2211yescharacteristic
143#2569C2214yes—
144#2569C2214yes—
145#2569C2212yes—
146#2569C2212yes—
147#2552C2212yes—
148#2552C2212yes—
149#2552C2212yes—
150#2552C2212yes—
151#2552C2211yescharacteristic
152#2552C2212yes—
153#2552C2212yes—
154#2552C2212yes—
155#2552C2212yes—
156#2552C2212yes—
157#2552C2211yescharacteristic
158#2509C2212yes—
159#2509C2212yes—
160#2509C2212yes—
161#2509C2212yes—
162#2509C2211yescharacteristic
163#2509C2212yes—
164#2509C2212yes—
165#2509C2212yes—
166#2509C2212yes—
167#2509C2212yes—
168#2509C2212yes—
169#2509C2212yes—
170#2509C2211yescharacteristic
171#2509C2212yes—
172#2508C2212yes—
173#2508C2212yes—
174#2508C2212yes—
175#2508C2212yes—
176#2508C2211yescharacteristic
177#2508C2212yes—
178#2508C2212yes—
179#2508C2212yes—
180#2508C2212yes—
181#2508C2212yes—
182#2508C2212yes—
183#2508C2211yescharacteristic
184#2508C2212yes—
185#2508C2212yes—
186#2507C2212yes—
187#2507C2212yes—
188#2507C2212yes—
189#2507C2212yes—
190#2507C2212yes—
191#2507C2212yes—
192#2507C2212yes—
193#2507C2212yes—
194#2507C2212yes—
195#2507C2212yes—
196#2507C2212yes—
197#2507C2212yes—
198#2507C2212yes—
199#2507C2211yescharacteristic
200#2507C2212yes—
201#2507C2211yescharacteristic
202#2506C2212yes—
203#2506C2212yes—
204#2506C2212yes—
205#2506C2212yes—
206#2506C2212yes—
207#2506C2212yes—
208#2506C2212yes—
209#2506C2212yes—
210#2506C2212yes—
211#2506C2211yescharacteristic
212#2506C2212yes—
213#2506C2212yes—
214#2506C2212yes—
215#2506C2212yes—
216#2506C2212yes—
217#2506C2212yes—
218#2506C2212yes—
219#2506C2212yes—
220#2506C2212yes—
221#2506C2212yes—
222#2506C2212yes—
223#2506C2212yes—
224#2506C2211yescharacteristic
225#2506C2212yes—
226#2505C2212yes—
227#2505C2214yes—
228#2505C2214yes—
229#2505C2214yes—
230#2505C2214yes—
231#2505C2214yes—
232#2505C2214yes—
233#2505C2212yes—
234#2473C2212yes—
235#2473C2214yes—
236#2473C2214yes—
237#2473C2214yes—
238#2473C2214yes—
239#2473C2214yes—
240#2473C2214yes—
241#2473C2214yes—
242#2473C2214yes—
243#2473C2212yes—
244#2442C2214yes—
245#2442C2214yes—
246#2442C2212yes—
247#2442C2214yes—
248#2442C2214yes—
249#2442C2212yes—
250#2402C2212yes—
251#2402C2212yes—
252#2402C2212yes—
253#2402C2212yes—
254C2×#400C2212yes—
255C2×#398C2212yes—
256#2382C2214yes—
257#2382C2214yes—
258#2382C2214yes—
259#2317C2211yescharacteristic
260#2317C2211yescharacteristic
261#2317C2211yescharacteristic
262#2317C2211yescharacteristic
263#2317C2211yescharacteristic
264#2317C2211yescharacteristic
265#2317C2211yescharacteristic
266#2317C2211yescharacteristic
267#2317C2211yescharacteristic
268#2317C2211yescharacteristic
269#2316C2211yescharacteristic
270#2316C2211yescharacteristic
271#2316C2211yescharacteristic
272#2316C2211yescharacteristic
273C4×#125C2212yes—
274C4×#125C2212yes—
275C4×#125C2212yes—
276C4×#125C2212yes—
277#2296C2211yescharacteristic
278#2296C2211yescharacteristic
279#2296C2211yescharacteristic
280#2296C2211yescharacteristic
281#2296C2211yescharacteristic
282#2296C2211yescharacteristic
283C2×#389C2211yescharacteristic
284C2×#389C2211yescharacteristic
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
299#564—416no—
300C2×#125—48no—
301C2×#125C2312yes—
302C2×#125C2312yes—
303C2×#125C2314yes—
304C2×#125C2312yes—
305C2×#125C2312yes—
306C2×#125C2314yes—
307C2×#125C2314yes—
308C2×#125C2314yes—
309C2×#125C2314yes—
310C2×#125C2314yes—
311C2×#125C2314yes—
312C2×#125C2314yes—
313C2×#125C2314yes—
314C2×#125C2314yes—
315C2×#125C2314yes—
316C2×#125C2314yes—
317C2×#125C2314yes—
318C2×#125C2314yes—
319C2×#125C2314yes—
320C2×#125C2314yes—
321C2×#125C2314yes—
322C2×#125C2314yes—
323C2×#117C2311yescharacteristic
324C2×#117C2311yescharacteristic
325C2×#117C2311yescharacteristic
326C2×#117C2311yescharacteristic
327C2×#117C2311yescharacteristic
328C2×#117C2311yescharacteristic
329C2×#117C2311yescharacteristic
330C2×#117C2311yescharacteristic
331C22×C4⋊C4C2311yescharacteristic
332C22×C4⋊C4C2311yescharacteristic
333C22×C4⋊C4C2311yescharacteristic
334C22×C4⋊C4C2311yescharacteristic
335C22×C4⋊C4C2311yescharacteristic
336C22×C4⋊C4C2311yescharacteristic
337C22×C4⋊C4C2312yes—
338C22×C4⋊C4C2312yes—
339C22×C4⋊C4C2312yes—
340C22×C4⋊C4C2312yes—
341C22×C4⋊C4C2312yes—
342C22×C4⋊C4C2312yes—
343C22×C42C2311yescharacteristic
344C22×C42C2311yescharacteristic
345C22×C42C2311yescharacteristic
346C22×C42C2312yes—
347#400C2312yes—
348#400C2312yes—
349#400C2314yes—
350#400C2314yes—
351#400C2314yes—
352#400C2314yes—
353#400C2314yes—
354#400C2314yes—
355#400C2314yes—
356#400C2314yes—
357#400C2314yes—
358#400C2314yes—
359#400C2314yes—
360#400C2314yes—
361#400C2314yes—
362#400C2314yes—
363#400C2314yes—
364#400C2314yes—
365#400C2314yes—
366#400C2314yes—
367#400C2312yes—
368#400C2312yes—
369#400C2312yes—
370#400C2312yes—
371#400C2314yes—
372#400C2314yes—
373#400C2314yes—
374#400C2314yes—
375#400C2314yes—
376#400C2314yes—
377#400C2312yes—
378#400C2314yes—
379#400C2314yes—
380#400C2314yes—
381#400C2314yes—
382#400C2314yes—
383#400C2314yes—
384#400C2312yes—
385#400C2314yes—
386#400C2314yes—
387#400C2314yes—
388#400C2314yes—
389#400C2314yes—
390#400C2314yes—
391#400C2312yes—
392#400C2312yes—
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#400C2312yes—
407#400C2312yes—
408#400C2314yes—
409#400C2314yes—
410#400C2314yes—
411#400C2312yes—
412#400C2312yes—
413#398C2312yes—
414#398C2314yes—
415#398C2312yes—
416#398C2314yes—
417#398C2314yes—
418#398C2312yes—
419#398C2312yes—
420#398C2312yes—
421#398C2314yes—
422#398C2314yes—
423#398C2314yes—
424#398C2314yes—
425#398C2314yes—
426#398C2314yes—
427#398C2314yes—
428#398C2314yes—
429#398C2314yes—
430#398C2314yes—
431#398C2314yes—
432#398C2314yes—
433#398C2314yes—
434#398C2314yes—
435#398C2314yes—
436#398C2314yes—
437#398C2314yes—
438#398C2314yes—
439#398C2314yes—
440#398C2314yes—
441#398C2314yes—
442#398C2314yes—
443#398C2314yes—
444#398C2314yes—
445#398C2314yes—
446#398C2314yes—
447#398C2314yes—
448#398C2314yes—
449#398C2314yes—
450#398C2314yes—
451#398C2314yes—
452#398C2312yes—
453#398C2312yes—
454#398C2312yes—
455#398C2312yes—
456#398C2314yes—
457#398C2314yes—
458#398C2312yes—
459#398C2314yes—
460#398C2314yes—
461#398C2312yes—
462#398C2312yes—
463#398C2314yes—
464#398C2312yes—
465#398C2314yes—
466#398C2314yes—
467#398C2314yes—
468#398C2314yes—
469#398C2314yes—
470#398C2314yes—
471#398C2314yes—
472#398C2312yes—
473#398C2314yes—
474#398C2314yes—
475#398C2314yes—
476#398C2314yes—
477#398C2314yes—
478#398C2314yes—
479#398C2314yes—
480#398C2314yes—
481#398C2312yes—
482#398C2312yes—
483#389C2312yes—
484#389C2312yes—
485#389C2312yes—
486#389C2312yes—
487#389C2312yes—
488#389C2312yes—
489#389C2312yes—
490#389C2312yes—
491#389C2312yes—
492#389C2312yes—
493#389C2312yes—
494#389C2311yescharacteristic
495#389C2311yescharacteristic
496#389C2312yes—
497#389C2312yes—
498#389C2312yes—
499#389C2312yes—
500#389C2312yes—
501#389C2311yescharacteristic
502#389C2311yescharacteristic
503#389C2312yes—
504#389C2312yes—
505#389C2311yescharacteristic
506#389C2311yescharacteristic
507#389C2312yes—
508#389C2312yes—
509#389C2312yes—
510#389C2312yes—
511#389C2312yes—
512#389C2312yes—
513#389C2311yescharacteristic
514#389C2312yes—
515#389C2311yescharacteristic
516#389C2311yescharacteristic
517#389C2312yes—
518#389C2312yes—
519#389C2311yescharacteristic
520#389C2312yes—
521#389C2312yes—
522#389C2312yes—
523#389C2312yes—
524#389C2312yes—
525#389C2312yes—
526#389C2312yes—
527#389C2314yes—
528#389C2314yes—
529#389C2314yes—
530#389C2314yes—
531#389C2314yes—
532#389C2314yes—
533#389C2314yes—
534#389C2312yes—
535#389C2312yes—
536#389C2312yes—
537#389C2312yes—
538#389C2312yes—
539#389C2312yes—
540#389C2312yes—
541#389C2312yes—
542#389C2312yes—
543#389C2312yes—
544#389C2312yes—
545#389C2312yes—
546#389C2312yes—
547#389C2312yes—
548#389C2312yes—
549#389C2312yes—
550#389C2314yes—
551#389C2314yes—
552#389C2314yes—
553#389C2314yes—
554#389C2314yes—
555#389C2314yes—
556#389C2314yes—
557#389C2314yes—
558#389C2314yes—
559#389C2311yescharacteristic
560#389C2311yescharacteristic
561#389C2312yes—
562#389C2312yes—
563#389C2314yes—
564#389C2314yes—
565#389C2314yes—
566#389C2314yes—
567#389C2314yes—
568#389C2314yes—
569#389C2311yescharacteristic
570#389C2311yescharacteristic
571#389C2314yes—
572#389C2314yes—
573#389C2314yes—
574#389C2314yes—
575#389C2312yes—
576#389C2312yes—
577#389C2311yescharacteristic
578#389C2311yescharacteristic
579#389C2311yescharacteristic
580#389C2311yescharacteristic
581#389C2311yescharacteristic
582#389C2312yes—
583#389C2312yes—
584#389C2312yes—
585#389C2311yescharacteristic
586#389C2312yes—
587#389C2312yes—
588#389C2312yes—
589#389C2311yescharacteristic
590#389C2311yescharacteristic
591#389C2311yescharacteristic
592#389C2311yescharacteristic
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#387C2312yes—
608#387C2312yes—
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#387C2314yes—
656#387C2314yes—
657#385C2312yes—
658#385C2312yes—
659#385C2314yes—
660#385C2314yes—
661#385C2312yes—
662#385C2312yes—
663#385C2312yes—
664#385C2312yes—
665#385C2314yes—
666#385C2314yes—
667#385C2314yes—
668#385C2314yes—
669#385C2314yes—
670#385C2314yes—
671#385C2314yes—
672#385C2314yes—
673#385C2312yes—
674#385C2312yes—
675#385C2312yes—
676#385C2312yes—
677#385C2312yes—
678#385C2312yes—
679#384C2311yescharacteristic
680#384C2311yescharacteristic
681#384C2311yescharacteristic
682#384C2312yes—
683#384C2311yescharacteristic
684#384C2312yes—
685#384C2312yes—
686#384C2312yes—
687#384C2312yes—
688#384C2312yes—
689#384C2312yes—
690#384C2312yes—
691#384C2311yescharacteristic
692#384C2311yescharacteristic
693#384C2312yes—
694#384C2311yescharacteristic
695#384C2312yes—
696#384C2312yes—
697#384C2312yes—
698#384C2312yes—
699#384C2312yes—
700#384C2311yescharacteristic
701#382C2312yes—
702#382C2312yes—
703#382C2312yes—
704#382C2312yes—
705#382C2314yes—
706#382C2314yes—
707#382C2314yes—
708#382C2311yescharacteristic
709#382C2311yescharacteristic
710#382C2312yes—
711#382C2312yes—
712#382C2312yes—
713#382C2312yes—
714#382C2311yescharacteristic
715#382C2311yescharacteristic
716#382C2311yescharacteristic
717#382C2312yes—
718#382C2312yes—
719#382C2311yescharacteristic
720#382C2311yescharacteristic
721#382C2312yes—
722#382C2311yescharacteristic
723#382C2314yes—
724#382C2314yes—
725#382C2314yes—
726#382C2314yes—
727#382C2314yes—
728#382C2312yes—
729#382C2312yes—
730#382C2312yes—
731#382C2314yes—
732#382C2314yes—
733#382C2314yes—
734#382C2314yes—
735#380C2312yes—
736#380C2312yes—
737#380C2314yes—
738#380C2314yes—
739#380C2314yes—
740#380C2312yes—
741#380C2312yes—
742#380C2312yes—
743#380C2314yes—
744#380C2312yes—
745#380C2312yes—
746#380C2312yes—
747C4×C4⋊C4C2311yescharacteristic
748C4×C4⋊C4C2312yes—
749C4×C4⋊C4C2311yescharacteristic
750C4×C4⋊C4C2311yescharacteristic
751C4×C4⋊C4C2312yes—
752C4×C4⋊C4C2311yescharacteristic
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⋊C4C2312yes—
768C4×C4⋊C4C2312yes—
769C4×C4⋊C4C2311yescharacteristic
770C4×C4⋊C4C2312yes—
771C4×C4⋊C4C2312yes—
772C4×C4⋊C4C2311yescharacteristic
773C4×C4⋊C4C2311yescharacteristic
774C4×C4⋊C4C2312yes—
775C4×C4⋊C4C2312yes—
776C4×C4⋊C4C2312yes—
777C4×C4⋊C4C2312yes—
778C4×C4⋊C4C2312yes—
779C4×C4⋊C4C2312yes—
780C4×C4⋊C4C2312yes—
781C4×C4⋊C4C2312yes—
782C4×C4⋊C4C2312yes—
783C4×C4⋊C4C2311yescharacteristic
784C4×C4⋊C4C2311yescharacteristic
785C4×C4⋊C4C2311yescharacteristic
786C4×C4⋊C4C2311yescharacteristic
787C4×C4⋊C4C2312yes—
788C4×C4⋊C4C2312yes—
789C4×C4⋊C4C2311yescharacteristic
790C4×C4⋊C4C2311yescharacteristic
791C4×C4⋊C4C2311yescharacteristic
792C4×C4⋊C4C2312yes—
793C4×C4⋊C4C2311yescharacteristic
794C4×C4⋊C4C2311yescharacteristic
795C4×C22⋊C4C2312yes—
796C4×C22⋊C4C2314yes—
797C4×C22⋊C4C2314yes—
798C4×C22⋊C4C2312yes—
799C4×C22⋊C4C2312yes—
800C4×C22⋊C4C2312yes—
801#376C2312yes—
802#376C2312yes—
803C2×#95C2312yes—
804C2×#95C2311yescharacteristic
805C2×#95C2312yes—
806C2×#95C2311yescharacteristic
807C2×#95C2312yes—
808C2×#95C2312yes—
809C2×#95C2312yes—
810C43C2312yes—
811C43C2312yes—
812C23×C4C2411yescharacteristic
813C23×C4C2411yescharacteristic
814C23×C4C2411yescharacteristic
815C23×C4C2411yescharacteristic
816C23×C4C2412yes—
817C23×C4C2412yes—
818C23×C4C2412yes—
819C23×C4C2412yes—
820C23×C4C2411yescharacteristic
821C23×C4C2411yescharacteristic
822C23×C4C2411yescharacteristic
823#125—216no—
824#125—28no—
825#125—28no—
826#125—48no—
827#125—44no—
828#125—48no—
829#125—48no—
830#125—48no—
831#125—48no—
832#125—48no—
833#125—48no—
834#125—48no—
835#125—48no—
836#125—48no—
837#125—44no—
838#125—48no—
839#125—48no—
840#125—48no—
841#125—48no—
842#125—48no—
843#125—48no—
844#125—48no—
845#117—24no—
846#117—24no—
847#117—24no—
848#117—24no—
849#117—24no—
850#117—24no—
851#117—24no—
852#117—24no—
853C2×C4⋊C4—24no—
854C2×C4⋊C4—24no—
855C2×C4⋊C4—24no—
856C2×C4⋊C4—24no—
857C2×C4⋊C4—24no—
858C2×C4⋊C4—42no—
859C2×C4⋊C4—44no—
860C2×C4⋊C4—44no—
861C2×C4⋊C4—44no—
862C2×C4⋊C4—44no—
863C2×C4⋊C4—44no—
864C2×C4⋊C4—44no—
865C2×C4⋊C4C2411yescharacteristic
866C2×C4⋊C4C2411yescharacteristic
867C2×C4⋊C4C2411yescharacteristic
868C2×C4⋊C4C2414yes—
869C2×C4⋊C4C2414yes—
870C2×C4⋊C4C2414yes—
871C2×C4⋊C4C2414yes—
872C2×C4⋊C4C2414yes—
873C2×C4⋊C4C2411yescharacteristic
874C2×C4⋊C4C2411yescharacteristic
875C2×C4⋊C4C2414yes—
876C2×C4⋊C4C2412yes—
877C2×C4⋊C4C2412yes—
878C2×C4⋊C4C2412yes—
879C2×C4⋊C4C2412yes—
880C2×C4⋊C4C2412yes—
881C2×C4⋊C4C2412yes—
882C2×C4⋊C4C2412yes—
883C2×C4⋊C4C2412yes—
884C2×C4⋊C4C2411yescharacteristic
885C2×C4⋊C4C2411yescharacteristic
886C2×C4⋊C4C2411yescharacteristic
887C2×C4⋊C4C2411yescharacteristic
888C2×C4⋊C4C2411yescharacteristic
889C2×C4⋊C4C2411yescharacteristic
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⋊C4C2412yes—
901C2×C4⋊C4C2412yes—
902C2×C4⋊C4C2412yes—
903C2×C4⋊C4C2412yes—
904C2×C4⋊C4C2412yes—
905C2×C4⋊C4C2412yes—
906C2×C4⋊C4C2412yes—
907C2×C4⋊C4C2412yes—
908C2×C4⋊C4C2412yes—
909C2×C4⋊C4C2412yes—
910C2×C4⋊C4C2412yes—
911C2×C4⋊C4C2412yes—
912C2×C4⋊C4C2412yes—
913C2×C4⋊C4C2414yes—
914C2×C4⋊C4C2414yes—
915C2×C4⋊C4C2414yes—
916C2×C4⋊C4C2414yes—
917C2×C4⋊C4C2414yes—
918C2×C4⋊C4C2411yescharacteristic
919C2×C4⋊C4C2411yescharacteristic
920C2×C4⋊C4C2414yes—
921C2×C4⋊C4C2414yes—
922C2×C4⋊C4C2414yes—
923C2×C4⋊C4C2414yes—
924C2×C4⋊C4C2414yes—
925C2×C4⋊C4C2414yes—
926C2×C4⋊C4C2414yes—
927C2×C4⋊C4C2414yes—
928C2×C4⋊C4C2414yes—
929C2×C4⋊C4C2414yes—
930C2×C4⋊C4C2414yes—
931C2×C4⋊C4C2414yes—
932C2×C4⋊C4C2414yes—
933C2×C4⋊C4C2414yes—
934C2×C4⋊C4C2414yes—
935C2×C4⋊C4C2412yes—
936C2×C4⋊C4C2412yes—
937C2×C4⋊C4C2412yes—
938C2×C4⋊C4C2412yes—
939C2×C4⋊C4C2412yes—
940C2×C4⋊C4C2412yes—
941C2×C4⋊C4C2412yes—
942C2×C4⋊C4C2414yes—
943C2×C4⋊C4C2414yes—
944C2×C4⋊C4C2414yes—
945C2×C4⋊C4C2414yes—
946C2×C4⋊C4C2414yes—
947C2×C4⋊C4C2414yes—
948C2×C4⋊C4C2414yes—
949C2×C4⋊C4C2412yes—
950C2×C4⋊C4C2412yes—
951C2×C4⋊C4C2412yes—
952C2×C4⋊C4C2412yes—
953C2×C4⋊C4C2412yes—
954C2×C4⋊C4C2412yes—
955C2×C4⋊C4C2412yes—
956C2×C4⋊C4C2412yes—
957C2×C4⋊C4C2412yes—
958C2×C4⋊C4C2412yes—
959C2×C4⋊C4C2412yes—
960C2×C4⋊C4C2412yes—
961C2×C4⋊C4C2412yes—
962C2×C4⋊C4C2412yes—
963C2×C4⋊C4C2412yes—
964C2×C4⋊C4C2412yes—
965C2×C4⋊C4C2412yes—
966C2×C4⋊C4C2412yes—
967C2×C4⋊C4C2412yes—
968C2×C4⋊C4C2412yes—
969C2×C4⋊C4C2414yes—
970C2×C4⋊C4C2414yes—
971C2×C4⋊C4C2414yes—
972C2×C4⋊C4C2414yes—
973C2×C4⋊C4C2414yes—
974C2×C4⋊C4C2414yes—
975C2×C4⋊C4C2414yes—
976C2×C4⋊C4C2411yescharacteristic
977C2×C22⋊C4C2412yes—
978C2×C22⋊C4C2412yes—
979C2×C22⋊C4C2412yes—
980C2×C22⋊C4C2412yes—
981C2×C22⋊C4C2412yes—
982C2×C22⋊C4C2412yes—
983C2×C22⋊C4C2412yes—
984C2×C22⋊C4C2412yes—
985C2×C42—24no—
986C2×C42—24no—
987C2×C42—24no—
988C2×C42—44no—
989C2×C42C2412yes—
990C2×C42C2412yes—
991C2×C42C2412yes—
992C2×C42C2412yes—
993C2×C42C2412yes—
994C2×C42C2412yes—
995C2×C42C2412yes—
996C2×C42C2412yes—
997C2×C42C2412yes—
998C2×C42C2412yes—
999C2×C42C2414yes—
1000C2×C42C2412yes—
1001C2×C42C2411yescharacteristic
1002C2×C42C2411yescharacteristic
1003C2×C42C2411yescharacteristic
1004C2×C42C2411yescharacteristic
1005C2×C42C2411yescharacteristic
1006C2×C42C2411yescharacteristic
1007C2×C42C2411yescharacteristic
1008C2×C42C2411yescharacteristic
1009C2×C42C2411yescharacteristic
1010C2×C42C2411yescharacteristic
1011C2×C42C2411yescharacteristic
1012C2×C42C2411yescharacteristic
1013C2×C42C2414yes—
1014C2×C42C2414yes—
1015C2×C42C2414yes—
1016C2×C42C2412yes—
1017C2×C42C2414yes—
1018C2×C42C2412yes—
1019C2×C42C2412yes—
1020C2×C42C2412yes—
1021C2×C42C2412yes—
1022C2×C42C2414yes—
1023#95C2411yescharacteristic
1024#95C2411yescharacteristic
1025#95C2411yescharacteristic
1026#95C2411yescharacteristic
1027#95C2411yescharacteristic
1028#95C2411yescharacteristic
1029#95C2411yescharacteristic
1030#95C2414yes—
1031#95C2414yes—
1032#95C2411yescharacteristic
1033#95C2414yes—
1034#95C2414yes—
1035#95C2414yes—
1036#95C2414yes—
1037#95C2414yes—
1038#95C2414yes—
1039#95C2414yes—
1040#95C2414yes—
1041#95C2412yes—
1042#95C2412yes—
1043#95C2412yes—
1044#95C2412yes—
1045#95C2412yes—
1046#95C2412yes—
1047#95C2412yes—
1048#95C2412yes—
1049#95C2414yes—
1050#95C2414yes—
1051#95C2414yes—
1052#95C2414yes—
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#95C2412yes—
1088#95C2412yes—
1089#95C2412yes—
1090#95C2412yes—
1091#95C2412yes—
1092#95C2412yes—
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—
1115#95C2414yes—
1116#95C2414yes—
1117#95C2414yes—
1118#95C2414yes—
1119#95C2414yes—
1120#95C2414yes—
1121C24C2511yescharacteristic
1122C22×C4—22no—
1123C22×C4—22no—
1124C22×C4—22no—
1125C22×C4—22no—
1126C22×C4—24no—
1127C22×C4—22no—
1128C22×C4—22no—
1129C22×C4—24no—
1130C22×C4—24no—
1131C22×C4—24no—
1132C22×C4—22no—
1133C22×C4—22no—
1134C22×C4—22no—
1135C22×C4—22no—
1136C22×C4—42no—
1137C22×C4—41no—
1138C22×C4—41no—
1139C22×C4—41no—
1140C22×C4—41no—
1141C22×C4—42no—
1142C22×C4—42no—
1143C22×C4—42no—
1144C22×C4—42no—
1145C22×C4—42no—
1146C22×C4—42no—
1147C22×C4—41no—
1148C22×C4—41no—
1149C22×C4—41no—
1150C22×C4—42no—
1151C22×C4—41no—
1152C22×C42−1+414yes—
1153C22×C42−1+414yes—
1154C22×C42−1+414yes—
1155C22×C4C2511yescharacteristic
1156C22×C4C2511yescharacteristic
1157C22×C4C2512yes—
1158C22×C4C2512yes—
1159C22×C4C2511yescharacteristic
1160C22×C4C2511yescharacteristic
1161C22×C4C2511yescharacteristic
1162C22×C4C2512yes—
1163C22×C4C2512yes—
1164C22×C4C2512yes—
1165C22×C4C2512yes—
1166C22×C4C2512yes—
1167C22×C4C2512yes—
1168C22×C4C2511yescharacteristic
1169C22×C4C2514yes—
1170C22×C4C2514yes—
1171C22×C4C2511yescharacteristic
1172C22×C4C2512yes—
1173C22×C4C2512yes—
1174C22×C4C2512yes—
1175C22×C4C2512yes—
1176C22×C4C2512yes—
1177C22×C4C2512yes—
1178C22×C4C2514yes—
1179C22×C4C2514yes—
1180C22×C4C2511yescharacteristic
1181C22×C4C2512yes—
1182C22×C4C2512yes—
1183C22×C4C2511yescharacteristic
1184C22×C4C2511yescharacteristic
1185C22×C4C2511yescharacteristic
1186C22×C4C2511yescharacteristic
1187C22×C4C2511yescharacteristic
1188C22×C4C2511yescharacteristic
1189C4⋊C4—22no—
1190C4⋊C4—22no—
1191C4⋊C4—22no—
1192C4⋊C4—28no—
1193C4⋊C4—28no—
1194C4⋊C4—28no—
1195C4⋊C4—28no—
1196C4⋊C4—28no—
1197C4⋊C4—24no—
1198C4⋊C4—24no—
1199C4⋊C4—24no—
1200C4⋊C4—24no—
1201C4⋊C4—24no—
1202C4⋊C4—24no—
1203C4⋊C4—24no—
1204C4⋊C4—24no—
1205C4⋊C4—24no—
1206C4⋊C4—24no—
1207C4⋊C4—24no—
1208C4⋊C4—24no—
1209C4⋊C4—24no—
1210C4⋊C4—24no—
1211C4⋊C4—24no—
1212C4⋊C4—24no—
1213C4⋊C4—24no—
1214C4⋊C4—24no—
1215C4⋊C4—22no—
1216C4⋊C4—22no—
1217C4⋊C4—22no—
1218C4⋊C4—22no—
1219C4⋊C4—22no—
1220C4⋊C4—22no—
1221C4⋊C4—22no—
1222C4⋊C4—22no—
1223C4⋊C4—22no—
1224C4⋊C4—22no—
1225C4⋊C4—22no—
1226C4⋊C4—22no—
1227C4⋊C4—22no—
1228C4⋊C4—22no—
1229C4⋊C4—22no—
1230C4⋊C4—22no—
1231C4⋊C4—22no—
1232C4⋊C4—28no—
1233C4⋊C4—22no—
1234C4⋊C4—24no—
1235C4⋊C4—24no—
1236C4⋊C4—24no—
1237C4⋊C4—41no—
1238C4⋊C4—44no—
1239C4⋊C4—41no—
1240C4⋊C4—44no—
1241C4⋊C4—44no—
1242C4⋊C4—44no—
1243C4⋊C4—44no—
1244C4⋊C4—44no—
1245C4⋊C4—42no—
1246C4⋊C4—42no—
1247C4⋊C4—42no—
1248C4⋊C4—42no—
1249C4⋊C4—42no—
1250C4⋊C4—42no—
1251C4⋊C4—42no—
1252C4⋊C4—42no—
1253C4⋊C4—42no—
1254C4⋊C4—44no—
1255C4⋊C4—44no—
1256C4⋊C4—44no—
1257C4⋊C4—44no—
1258C4⋊C4—42no—
1259C4⋊C4—42no—
1260C4⋊C4—42no—
1261C4⋊C4—42no—
1262C4⋊C4—42no—
1263C4⋊C4—42no—
1264C4⋊C4—42no—
1265C4⋊C4—42no—
1266C4⋊C4—42no—
1267C4⋊C4—44no—
1268C4⋊C4—44no—
1269C4⋊C4—42no—
1270C4⋊C4—42no—
1271C4⋊C4—44no—
1272C4⋊C4—42no—
1273C4⋊C4—42no—
1274C4⋊C4—42no—
1275C4⋊C4—44no—
1276C4⋊C4—44no—
1277C4⋊C4—44no—
1278C4⋊C4—42no—
1279C4⋊C4—42no—
1280C4⋊C4—44no—
1281C4⋊C4—42no—
1282C4⋊C4—44no—
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⋊C4—44no—
1295C4⋊C4—44no—
1296C4⋊C4—44no—
1297C4⋊C4—44no—
1298C4⋊C4—44no—
1299C4⋊C4—44no—
1300C4⋊C4H(5,𝔽2)14yes—
1301C22⋊C4—24no—
1302C22⋊C4—24no—
1303C22⋊C4—24no—
1304C22⋊C4—24no—
1305C22⋊C4—24no—
1306C22⋊C4—24no—
1307C22⋊C4—24no—
1308C22⋊C4—24no—
1309C42—28no—
1310C42—24no—
1311C42—24no—
1312C42—22no—
1313C42—22no—
1314C42—22no—
1315C42—22no—
1316C42—22no—
1317C42—22no—
1318C42—22no—
1319C42—22no—
1320C42—22no—
1321C42—22no—
1322C42—22no—
1323C42—22no—
1324C42—24no—
1325C42—24no—
1326C42—24no—
1327C42—24no—
1328C42—24no—
1329C42—24no—
1330C42—24no—
1331C42—24no—
1332C42—24no—
1333C42—44no—
1334C42—42no—
1335C42—42no—
1336C42—44no—
1337C42—42no—
1338C42—42no—
1339C42—42no—
1340C42—44no—
1341C42—44no—
1342C42—44no—
1343C23—21no—
1344C23—21no—
1345C23—21no—
1346C23—21no—
1347C23C2×2−1+412yes—
1348C23C2×2−1+412yes—
1349C23C2×2−1+412yes—
1350C23C2611yescharacteristic
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—24no—
1360C2×C4—24no—
1361C2×C4—22no—
1362C2×C4—22no—
1363C2×C4—22no—
1364C2×C4—22no—
1365C2×C4—21no—
1366C2×C4—22no—
1367C2×C4—22no—
1368C2×C4—22no—
1369C2×C4—22no—
1370C2×C4—24no—
1371C2×C4—24no—
1372C2×C4—21no—
1373C2×C4—21no—
1374C2×C4—21no—
1375C2×C4—21no—
1376C2×C4—21no—
1377C2×C4—21no—
1378C2×C4—21no—
1379C2×C4—21no—
1380C2×C4—21no—
1381C2×C4—21no—
1382C2×C4—22no—
1383C2×C4—22no—
1384C2×C4—22no—
1385C2×C4—22no—
1386C2×C4—22no—
1387C2×C4—22no—
1388C2×C4—22no—
1389C2×C4—22no—
1390C2×C4—22no—
1391C2×C4—22no—
1392C2×C4—22no—
1393C2×C4—22no—
1394C2×C4—22no—
1395C2×C4—22no—
1396C2×C4—22no—
1397C2×C4—22no—
1398C2×C4—24no—
1399C2×C4—24no—
1400C2×C4—24no—
1401C2×C4—24no—
1402C2×C4—22no—
1403C2×C4—22no—
1404C2×C4—22no—
1405C2×C4—22no—
1406C2×C4—22no—
1407C2×C4—22no—
1408C2×C4—24no—
1409C2×C4—22no—
1410C2×C4—22no—
1411C2×C4—21no—
1412C2×C4—24no—
1413C2×C4—21no—
1414C2×C4—21no—
1415C2×C4—21no—
1416C2×C4—22no—
1417C2×C4—22no—
1418C2×C4—21no—
1419C2×C4—21no—
1420C2×C4—22no—
1421C2×C4—22no—
1422C2×C4—22no—
1423C2×C4—22no—
1424C2×C4—22no—
1425C2×C4—22no—
1426C2×C4—22no—
1427C2×C4—22no—
1428C2×C4—24no—
1429C2×C4—22no—
1430C2×C4—22no—
1431C2×C4—22no—
1432C2×C4—22no—
1433C2×C4—22no—
1434C2×C4—22no—
1435C2×C4—21no—
1436C2×C4—21no—
1437C2×C4—24no—
1438C2×C4—21no—
1439C2×C4—21no—
1440C2×C4—21no—
1441C2×C4—21no—
1442C2×C4—21no—
1443C2×C4—44no—
1444C2×C4—44no—
1445C2×C4—44no—
1446C2×C4—44no—
1447C2×C4—48no—
1448C2×C4—84no—
1449C2×C4—84no—
1450C2×C4—82no—
1451C2×C4—84no—
1452C2×C4—82no—
1453C2×C4#564116yescomplemented
1454C2×C4C2×H(5,𝔽2)12yes—
1455C2×C4C2×H(5,𝔽2)12yes—
1456C2×C4C2×H(5,𝔽2)12yes—
1457C2×C4C2×2−1+412yes—
1458C2×C4C2×2−1+412yes—
1459C2×C4C2×2−1+412yes—
1460C2×C4C2×2−1+412yes—
1461C2×C4C2×2−1+412yes—
1462C2×C4C2×2−1+412yes—
1463C2×C4#58512yes—
1464C22—22no—
1465C22—22no—
1466C22—22no—
1467C22—22no—
1468C22—22no—
1469C22—22no—
1470C22C2×#56414yes—
1471C22C22×H(5,𝔽2)11yescharacteristic
1472C22C22×2−1+411yescharacteristic
1473C22C22×2−1+411yescharacteristic
1474C22C22×2−1+411yescharacteristic
1475C22C2×#58511yescharacteristic
1476C222−1+611yescharacteristic
1477C222−1+611yescharacteristic
1478C4—22no—
1479C4—22no—
1480C4—22no—
1481C4—22no—
1482C4—42no—
1483C4—42no—
1484C4—41no—
1485C4—44no—
1486C4—44no—
1487C4—42no—
1488C4—42no—
1489C4—41no—
1490C4—41no—
1491C4—42no—
1492C4—42no—
1493C4—42no—
1494C4—42no—
1495C4—44no—
1496C4—42no—
1497C4—42no—
1498C4—41no—
1499C4—41no—
1500C4—44no—
1501C4—42no—
1502C4—42no—
1503C4—41no—
1504C4—41no—
1505C4—41no—
1506C4—42no—
1507C4—42no—
1508C4—42no—
1509C4—42no—
1510C4C2×#56414yes—
1511C4C2×#56414yes—
1512C2—24no—
1513C2C22×#56411yescharacteristic
1514C2#6283511yescharacteristic
1515C2#6288911yescharacteristic
1516C2#6291311yescharacteristic
1517C2#6291511yescharacteristic
1518C2#6292811yescharacteristic
1519C2#6295611yescharacteristic
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
11. #46191C2semidirect
12. #46181C2semidirect
13. #46181C2semidirect
14. #46175C2semidirect
15. #46175C2semidirect
17. #46157C2semidirect
18. C4⋊#564C2semidirect
19. C4⋊#564C2semidirect
1453. C2×C4#564semidirect

Maximal subgroups

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

subgroupindex
#531312
#531212
#530362
#529962
#524522
#524282
#461912
#461812
#461752
#461692
#461572
C4⋊#5642
C22⋊#5642
#355852
#355552
#355432
#352862
#352652
#351812
#351592
#349482
#348152
C2×#25062