Finite Group Databasebeta

← #7651280

Subgroups — #7651280

Order 512.

4132 conjugacy classes of subgroups.

The subgroup lattice has 1524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42782C212yesmaximal, complemented
2#42774C212yesmaximal, complemented
3#42774C212yesmaximal, complemented
4#42765C212yesmaximal, complemented
5#42744C212yesmaximal, complemented
6#42710C212yesmaximal, complemented
7#42710C212yesmaximal, complemented
8#42553C212yesmaximal, complemented
9#41394C214yesmaximal
10#40564C214yesmaximal
11#40189C212yesmaximal, complemented
12#40107C212yesmaximal, complemented
13#40082C212yesmaximal, complemented
14#40082C212yesmaximal, complemented
15#39526C212yesmaximal, complemented
16#39241C212yesmaximal, complemented
17#39241C212yesmaximal, complemented
18#39003C212yesmaximal, complemented
19#38395C214yesmaximal
20#38066C214yesmaximal
21#35640C211yesmaximal, characteristic
22#35630C211yesmaximal, characteristic
23#35630C211yesmaximal, characteristic
24#35585C211yesmaximal, characteristic
25#35585C211yesmaximal, characteristic
26#35543C211yesmaximal, characteristic
27#35313C211yesmaximal, characteristic
28#35313C211yesmaximal, characteristic
29#35154C211yesmaximal, characteristic
30#34948C211yesmaximal, characteristic
31#34815C211yesmaximal, characteristic
32C2×#2453C211yesmaximal, characteristic
33#34272C211yesmaximal, characteristic
34#34217C211yesmaximal, characteristic
35#34187C211yesmaximal, characteristic
36C2×#544C2211yescharacteristic
37C22×#125C2211yescharacteristic
38C22×C4×Q8C2211yescharacteristic
39#2863C2212yes—
40#2863C2212yes—
41#2863C2212yes—
42#2863C2212yes—
43#2855C2214yes—
44#2839C2214yes—
45#2839C2214yes—
46#2839C2214yes—
47#2833C2214yes—
48#2802C2214yes—
49#2802C2214yes—
50#2794C2214yes—
51#2794C2214yes—
52#2794C2214yes—
53#2794C2214yes—
54#2789C2214yes—
55#2789C2214yes—
56#2776C2214yes—
57#2776C2214yes—
58#2776C2214yes—
59#2776C2214yes—
60#2776C2214yes—
61#2769C2214yes—
62#2769C2214yes—
63#2769C2214yes—
64#2766C2214yes—
65#2766C2214yes—
66#2766C2214yes—
67#2766C2214yes—
68#2766C2214yes—
69#2762C2214yes—
70#2762C2214yes—
71#2758C2214yes—
72#2758C2214yes—
73#2758C2214yes—
74#2755C2214yes—
75#2719C2214yes—
76#2719C2214yes—
77#2719C2214yes—
78#2719C2214yes—
79#2719C2214yes—
80#2666C2214yes—
81#2655C2214yes—
82#2655C2214yes—
83#2655C2214yes—
84#2655C2214yes—
85#2655C2214yes—
86#2655C2214yes—
87#2655C2214yes—
88#2655C2214yes—
89#2647C2214yes—
90#2645C2212yes—
91#2645C2212yes—
92#2645C2212yes—
93#2645C2214yes—
94#2645C2212yes—
95#2634C2214yes—
96#2627C2214yes—
97#2583C2214yes—
98#2571C2211yescharacteristic
99#2571C2211yescharacteristic
100#2571C2212yes—
101#2570C2212yes—
102#2570C2211yescharacteristic
103#2570C2212yes—
104#2570C2211yescharacteristic
105#2570C2211yescharacteristic
106#2570C2211yescharacteristic
107#2569C2214yes—
108#2569C2214yes—
109#2569C2212yes—
110#2569C2212yes—
111#2552C2212yes—
112#2552C2212yes—
113#2552C2212yes—
114#2552C2212yes—
115#2552C2211yescharacteristic
116#2552C2211yescharacteristic
117#2552C2212yes—
118#2550C2212yes—
119#2550C2212yes—
120#2550C2212yes—
121#2550C2212yes—
122#2533C2214yes—
123#2533C2214yes—
124#2528C2214yes—
125#2528C2214yes—
126#2524C2214yes—
127#2524C2214yes—
128#2524C2214yes—
129#2514C2212yes—
130#2514C2212yes—
131#2514C2212yes—
132#2514C2214yes—
133#2514C2212yes—
134#2514C2212yes—
135#2514C2212yes—
136#2514C2212yes—
137#2514C2212yes—
138#2514C2212yes—
139#2514C2212yes—
140#2514C2212yes—
141#2514C2212yes—
142#2511C2212yes—
143#2511C2212yes—
144#2511C2212yes—
145#2511C2212yes—
146#2511C2212yes—
147#2511C2212yes—
148#2511C2212yes—
149#2511C2212yes—
150#2511C2212yes—
151#2511C2212yes—
152#2511C2212yes—
153#2511C2212yes—
154#2509C2212yes—
155#2509C2212yes—
156#2509C2212yes—
157#2509C2212yes—
158#2509C2212yes—
159#2509C2211yescharacteristic
160#2509C2211yescharacteristic
161#2508C2212yes—
162#2508C2212yes—
163#2508C2212yes—
164#2508C2212yes—
165#2508C2211yescharacteristic
166#2508C2212yes—
167#2508C2211yescharacteristic
168#2507C2212yes—
169#2507C2212yes—
170#2507C2212yes—
171#2507C2212yes—
172#2507C2211yescharacteristic
173#2507C2212yes—
174#2507C2211yescharacteristic
175#2506C2212yes—
176#2506C2212yes—
177#2506C2212yes—
178#2506C2212yes—
179#2506C2214yes—
180#2506C2214yes—
181#2506C2212yes—
182#2506C2211yescharacteristic
183#2506C2211yescharacteristic
184#2505C2214yes—
185#2505C2212yes—
186#2505C2212yes—
187#2502C2214yes—
188#2493C2214yes—
189#2493C2214yes—
190#2493C2214yes—
191#2493C2214yes—
192#2493C2214yes—
193#2493C2214yes—
194#2493C2214yes—
195#2493C2214yes—
196#2473C2212yes—
197#2473C2212yes—
198#2473C2214yes—
199#2462C2214yes—
200#2453C2212yes—
201#2453C2212yes—
202#2453C2212yes—
203#2453C2212yes—
204#2453C2212yes—
205#2453C2212yes—
206#2453C2214yes—
207#2453C2212yes—
208#2453C2212yes—
209#2453C2212yes—
210#2453C2212yes—
211#2453C2212yes—
212#2453C2212yes—
213#2451C2212yes—
214#2451C2212yes—
215#2451C2212yes—
216#2451C2212yes—
217#2442C2214yes—
218#2442C2214yes—
219#2442C2212yes—
220#2442C2212yes—
221#2402C2212yes—
222#2402C2212yes—
223#2402C2212yes—
224#2402C2212yes—
225C2×#400C2212yes—
226C2×#398C2212yes—
227#2370C2212yes—
228#2370C2212yes—
229#2370C2212yes—
230#2370C2212yes—
231#2370C2212yes—
232#2370C2212yes—
233#2369C2212yes—
234#2368C2214yes—
235#2365C2212yes—
236#2360C2214yes—
237#2356C2212yes—
238#2356C2212yes—
239#2356C2212yes—
240#2356C2212yes—
241#2355C2212yes—
242#2355C2212yes—
243#2355C2212yes—
244#2355C2212yes—
245#2345C2214yes—
246#2345C2214yes—
247#2336C2214yes—
248#2336C2214yes—
249#2331C2212yes—
250#2330C2212yes—
251#2330C2212yes—
252#2330C2212yes—
253#2330C2214yes—
254#2320C2214yes—
255#2317C2211yescharacteristic
256#2317C2211yescharacteristic
257#2317C2211yescharacteristic
258#2317C2211yescharacteristic
259#2316C2211yescharacteristic
260#2316C2211yescharacteristic
261#2316C2211yescharacteristic
262#2313C2214yes—
263#2310C2211yescharacteristic
264#2310C2211yescharacteristic
265#2310C2211yescharacteristic
266#2310C2211yescharacteristic
267C4×C4⋊Q8C2212yes—
268C4×#125C2212yes—
269C4×#125C2212yes—
270C4×#125C2212yes—
271C4×#125C2212yes—
272C4×#125C2212yes—
273C4×#125C2212yes—
274C4×#125C2212yes—
275#2296C2211yescharacteristic
276#2296C2211yescharacteristic
277#2296C2211yescharacteristic
278#2296C2211yescharacteristic
279#2296C2211yescharacteristic
280#2296C2211yescharacteristic
281C2×#391C2211yescharacteristic
282C2×#391C2211yescharacteristic
283C2×#389C2211yescharacteristic
284C2×#389C2211yescharacteristic
285C2×#389C2212yes—
286C2×#387C2212yes—
287#2285C2211yescharacteristic
288#2285C2211yescharacteristic
289#2285C2211yescharacteristic
290#2285C2211yescharacteristic
291#2283C2214yes—
292#2274C2211yescharacteristic
293#2274C2211yescharacteristic
294#2274C2211yescharacteristic
295#2274C2211yescharacteristic
296C4×#117C2211yescharacteristic
297C4×#117C2211yescharacteristic
298C2×C4×C4⋊C4C2211yescharacteristic
299C23×Q8C2311yescharacteristic
300#544—28no—
301C2×C4⋊Q8C2312yes—
302C2×C4⋊Q8C2312yes—
303C2×#125—28no—
304C2×#125C2312yes—
305C2×#125C2312yes—
306C2×#125C2312yes—
307C2×#125C2312yes—
308C2×#125C2312yes—
309C2×#125C2312yes—
310C2×#125C2312yes—
311C2×#125C2312yes—
312C2×#125C2312yes—
313C2×#125C2312yes—
314C2×#125C2314yes—
315C2×#125C2314yes—
316C2×#125C2314yes—
317C2×C22⋊Q8C2314yes—
318C2×C4×Q8—28no—
319C2×C4×Q8C2312yes—
320C2×C4×Q8C2312yes—
321C2×C4×Q8C2312yes—
322C2×C4×Q8C2312yes—
323C2×C4×Q8C2314yes—
324C2×#117C2311yescharacteristic
325C2×#117C2311yescharacteristic
326C2×#117C2311yescharacteristic
327C2×#117C2311yescharacteristic
328C2×#117C2311yescharacteristic
329C2×#117C2311yescharacteristic
330C2×#117C2311yescharacteristic
331C2×#117C2311yescharacteristic
332C22×C4⋊C4C2312yes—
333C22×C4⋊C4C2311yescharacteristic
334C22×C4⋊C4C2311yescharacteristic
335C22×C4⋊C4C2312yes—
336C22×C4⋊C4C2312yes—
337C22×C4⋊C4C2312yes—
338C22×C4⋊C4C2311yescharacteristic
339C22×C4⋊C4C2311yescharacteristic
340C22×C4⋊C4C2312yes—
341C22×C4⋊C4C2311yescharacteristic
342C22×C42C2312yes—
343C22×C42C2311yescharacteristic
344C22×C42C2311yescharacteristic
345C22×C42C2311yescharacteristic
346#401C2314yes—
347#401C2314yes—
348#401C2314yes—
349#401C2314yes—
350#401C2314yes—
351#401C2314yes—
352#401C2314yes—
353#401C2314yes—
354#400C2312yes—
355#400C2312yes—
356#400C2312yes—
357#400C2312yes—
358#400C2314yes—
359#400C2314yes—
360#400C2314yes—
361#400C2314yes—
362#400C2314yes—
363#400C2312yes—
364#400C2314yes—
365#400C2312yes—
366#400C2312yes—
367#400C2312yes—
368#400C2314yes—
369#400C2314yes—
370#400C2314yes—
371#400C2314yes—
372#400C2314yes—
373#400C2314yes—
374#400C2312yes—
375#400C2312yes—
376#400C2314yes—
377#400C2314yes—
378#400C2314yes—
379#400C2314yes—
380#400C2314yes—
381#400C2314yes—
382#400C2314yes—
383#400C2314yes—
384#400C2314yes—
385#400C2314yes—
386#400C2314yes—
387#400C2314yes—
388#400C2314yes—
389#400C2314yes—
390#400C2314yes—
391#400C2314yes—
392#400C2314yes—
393#400C2312yes—
394#400C2314yes—
395#400C2314yes—
396#400C2314yes—
397#400C2314yes—
398#400C2314yes—
399#400C2314yes—
400#400C2314yes—
401#400C2314yes—
402#400C2312yes—
403#400C2312yes—
404#400C2312yes—
405#400C2314yes—
406#400C2314yes—
407#400C2314yes—
408#400C2314yes—
409#400C2312yes—
410#400C2312yes—
411#400C2314yes—
412#398C2312yes—
413#398C2312yes—
414#398C2314yes—
415#398C2314yes—
416#398C2314yes—
417#398C2314yes—
418#398C2312yes—
419#398C2312yes—
420#398C2312yes—
421#398C2312yes—
422#398C2314yes—
423#398C2314yes—
424#398C2312yes—
425#398C2312yes—
426#398C2312yes—
427#398C2314yes—
428#398C2314yes—
429#398C2314yes—
430#398C2312yes—
431#398C2314yes—
432#398C2314yes—
433#398C2314yes—
434#398C2314yes—
435#398C2314yes—
436#398C2314yes—
437#398C2314yes—
438#398C2314yes—
439#398C2312yes—
440#398C2314yes—
441#398C2314yes—
442#398C2314yes—
443#398C2312yes—
444#398C2314yes—
445#398C2312yes—
446#398C2312yes—
447#398C2314yes—
448#398C2314yes—
449#398C2314yes—
450#398C2314yes—
451#398C2314yes—
452#398C2312yes—
453#398C2312yes—
454#395C2314yes—
455#395C2314yes—
456#395C2314yes—
457#395C2314yes—
458#391C2314yes—
459#391C2312yes—
460#391C2312yes—
461#391C2312yes—
462#391C2312yes—
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#391C2314yes—
476#391C2314yes—
477#391C2314yes—
478#391C2314yes—
479#391C2314yes—
480#391C2312yes—
481#391C2312yes—
482#391C2312yes—
483#391C2312yes—
484#391C2314yes—
485#391C2312yes—
486#391C2312yes—
487#391C2312yes—
488#391C2312yes—
489#389C2311yescharacteristic
490#389C2312yes—
491#389C2312yes—
492#389C2312yes—
493#389C2312yes—
494#389C2312yes—
495#389C2312yes—
496#389C2312yes—
497#389C2312yes—
498#389C2312yes—
499#389C2312yes—
500#389C2312yes—
501#389C2312yes—
502#389C2312yes—
503#389C2311yescharacteristic
504#389C2314yes—
505#389C2312yes—
506#389C2311yescharacteristic
507#389C2311yescharacteristic
508#389C2311yescharacteristic
509#389C2311yescharacteristic
510#389C2312yes—
511#389C2311yescharacteristic
512#389C2311yescharacteristic
513#389C2311yescharacteristic
514#389C2311yescharacteristic
515#389C2312yes—
516#389C2312yes—
517#389C2314yes—
518#389C2312yes—
519#389C2312yes—
520#389C2312yes—
521#389C2312yes—
522#389C2312yes—
523#389C2312yes—
524#389C2312yes—
525#389C2312yes—
526#389C2312yes—
527#389C2312yes—
528#389C2312yes—
529#389C2312yes—
530#389C2312yes—
531#389C2312yes—
532#389C2314yes—
533#389C2314yes—
534#389C2314yes—
535#389C2314yes—
536#389C2314yes—
537#389C2314yes—
538#389C2314yes—
539#389C2314yes—
540#389C2314yes—
541#389C2311yescharacteristic
542#389C2312yes—
543#389C2314yes—
544#389C2314yes—
545#389C2314yes—
546#389C2314yes—
547#389C2314yes—
548#389C2311yescharacteristic
549#389C2314yes—
550#389C2314yes—
551#389C2311yescharacteristic
552#389C2311yescharacteristic
553#389C2312yes—
554#389C2312yes—
555#389C2311yescharacteristic
556#389C2311yescharacteristic
557#389C2314yes—
558#389C2314yes—
559#389C2314yes—
560#389C2311yescharacteristic
561#389C2311yescharacteristic
562#389C2314yes—
563#389C2314yes—
564#389C2311yescharacteristic
565#389C2312yes—
566#389C2311yescharacteristic
567#389C2312yes—
568#389C2311yescharacteristic
569#389C2311yescharacteristic
570#389C2311yescharacteristic
571#389C2311yescharacteristic
572#387C2312yes—
573#387C2312yes—
574#387C2312yes—
575#387C2312yes—
576#387C2312yes—
577#387C2312yes—
578#387C2312yes—
579#387C2312yes—
580#387C2312yes—
581#387C2312yes—
582#387C2314yes—
583#387C2314yes—
584#387C2314yes—
585#387C2314yes—
586#387C2314yes—
587#387C2314yes—
588#387C2312yes—
589#387C2312yes—
590#387C2312yes—
591#387C2312yes—
592#387C2312yes—
593#387C2312yes—
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#387C2314yes—
651#387C2314yes—
652#387C2314yes—
653#387C2314yes—
654#385C2312yes—
655#385C2312yes—
656#385C2314yes—
657#385C2314yes—
658#385C2312yes—
659#385C2312yes—
660#385C2312yes—
661#385C2312yes—
662#385C2314yes—
663#385C2314yes—
664#385C2312yes—
665#385C2312yes—
666#385C2312yes—
667#385C2312yes—
668#385C2312yes—
669#385C2312yes—
670#384C2312yes—
671#384C2311yescharacteristic
672#384C2311yescharacteristic
673#384C2311yescharacteristic
674#384C2311yescharacteristic
675#384C2311yescharacteristic
676#384C2312yes—
677#384C2311yescharacteristic
678#384C2311yescharacteristic
679#384C2312yes—
680#384C2312yes—
681#384C2314yes—
682#384C2311yescharacteristic
683#384C2314yes—
684#383C2314yes—
685#383C2314yes—
686#383C2314yes—
687#383C2314yes—
688#383C2314yes—
689#383C2314yes—
690#383C2314yes—
691#383C2314yes—
692#383C2314yes—
693#383C2314yes—
694#382C2311yescharacteristic
695#382C2311yescharacteristic
696#382C2312yes—
697#382C2312yes—
698#382C2312yes—
699#382C2312yes—
700#382C2312yes—
701#382C2312yes—
702#382C2311yescharacteristic
703#382C2311yescharacteristic
704#382C2311yescharacteristic
705#382C2311yescharacteristic
706#382C2311yescharacteristic
707#382C2311yescharacteristic
708#382C2314yes—
709#382C2312yes—
710#382C2312yes—
711#382C2314yes—
712#382C2314yes—
713#382C2314yes—
714#382C2314yes—
715#381C2314yes—
716#381C2314yes—
717#381C2314yes—
718#381C2314yes—
719#380C2312yes—
720#380C2312yes—
721#380C2312yes—
722#380C2314yes—
723#380C2314yes—
724#380C2314yes—
725#380C2312yes—
726#380C2312yes—
727#380C2312yes—
728#380C2312yes—
729#380C2312yes—
730C4×C4⋊C4C2311yescharacteristic
731C4×C4⋊C4C2311yescharacteristic
732C4×C4⋊C4C2311yescharacteristic
733C4×C4⋊C4C2311yescharacteristic
734C4×C4⋊C4C2312yes—
735C4×C4⋊C4C2312yes—
736C4×C4⋊C4C2312yes—
737C4×C4⋊C4C2312yes—
738C4×C4⋊C4C2314yes—
739C4×C4⋊C4C2314yes—
740C4×C4⋊C4C2312yes—
741C4×C4⋊C4C2312yes—
742C4×C4⋊C4C2314yes—
743C4×C4⋊C4C2312yes—
744C4×C4⋊C4C2312yes—
745C4×C4⋊C4C2312yes—
746C4×C4⋊C4C2312yes—
747C4×C4⋊C4C2314yes—
748C4×C4⋊C4C2314yes—
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⋊C4C2312yes—
759C4×C4⋊C4C2312yes—
760C4×C4⋊C4C2312yes—
761C4×C4⋊C4C2312yes—
762C4×C4⋊C4C2312yes—
763C4×C4⋊C4C2312yes—
764C4×C4⋊C4C2312yes—
765C4×C4⋊C4C2312yes—
766C4×C4⋊C4C2314yes—
767C4×C4⋊C4C2311yescharacteristic
768C4×C4⋊C4C2311yescharacteristic
769C4×C4⋊C4C2311yescharacteristic
770C4×C4⋊C4C2312yes—
771C4×C4⋊C4C2312yes—
772C4×C4⋊C4C2311yescharacteristic
773C4×C4⋊C4C2311yescharacteristic
774C4×C4⋊C4C2314yes—
775C4×C4⋊C4C2314yes—
776C4×C4⋊C4C2312yes—
777C4×C4⋊C4C2312yes—
778C4×C4⋊C4C2312yes—
779C4×C4⋊C4C2312yes—
780C4×C4⋊C4C2312yes—
781C4×C4⋊C4C2312yes—
782C4×C4⋊C4C2311yescharacteristic
783C4×C4⋊C4C2311yescharacteristic
784C4×C4⋊C4C2311yescharacteristic
785C4×C4⋊C4C2311yescharacteristic
786C4×C4⋊C4C2311yescharacteristic
787C4×C4⋊C4C2311yescharacteristic
788C4×C4⋊C4C2311yescharacteristic
789C4×C4⋊C4C2312yes—
790C4×C4⋊C4C2312yes—
791C4×C22⋊C4C2314yes—
792C4×C22⋊C4C2314yes—
793C4×C22⋊C4C2312yes—
794C4×C22⋊C4C2314yes—
795C4×C22⋊C4C2312yes—
796C4×C22⋊C4C2312yes—
797C4×C22⋊C4C2314yes—
798C4×C22⋊C4C2312yes—
799#376C2314yes—
800#376C2312yes—
801#376C2312yes—
802#376C2314yes—
803C2×#95C2312yes—
804C2×#95C2312yes—
805C2×#95C2311yescharacteristic
806C2×#95C2311yescharacteristic
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—
819C23×C4C2412yes—
820C23×C4C2411yescharacteristic
821C23×C4C2411yescharacteristic
822C23×C4C2412yes—
823C23×C4C2412yes—
824C23×C4C2411yescharacteristic
825C23×C4C2411yescharacteristic
826C23×C4C2411yescharacteristic
827C23×C4C2411yescharacteristic
828C23×C4C2412yes—
829C23×C4C2411yescharacteristic
830C4⋊Q8—28no—
831C4⋊Q8—28no—
832#125—28no—
833#125—28no—
834#125—28no—
835#125—28no—
836#125—28no—
837#125—28no—
838#125—44no—
839#125—48no—
840#125—44no—
841#125—44no—
842#125—44no—
843#125—48no—
844#125—48no—
845C22⋊Q8—216no—
846C4×Q8—28no—
847C4×Q8—28no—
848C4×Q8—28no—
849C4×Q8—28no—
850C4×Q8—48no—
851#117—24no—
852#117—24no—
853#117—24no—
854#117—24no—
855#117—24no—
856#117—24no—
857#117—24no—
858#117—24no—
859C2×C4⋊C4—28no—
860C2×C4⋊C4—28no—
861C2×C4⋊C4—28no—
862C2×C4⋊C4—24no—
863C2×C4⋊C4—24no—
864C2×C4⋊C4—44no—
865C2×C4⋊C4—42no—
866C2×C4⋊C4—42no—
867C2×C4⋊C4—44no—
868C2×C4⋊C4#4118yes—
869C2×C4⋊C4C2414yes—
870C2×C4⋊C4C2414yes—
871C2×C4⋊C4C2414yes—
872C2×C4⋊C4C2411yescharacteristic
873C2×C4⋊C4C2412yes—
874C2×C4⋊C4C2412yes—
875C2×C4⋊C4C2414yes—
876C2×C4⋊C4C2414yes—
877C2×C4⋊C4C2411yescharacteristic
878C2×C4⋊C4C2411yescharacteristic
879C2×C4⋊C4C2411yescharacteristic
880C2×C4⋊C4C2414yes—
881C2×C4⋊C4C2414yes—
882C2×C4⋊C4C2414yes—
883C2×C4⋊C4C2412yes—
884C2×C4⋊C4C2412yes—
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⋊C4C2411yescharacteristic
901C2×C4⋊C4C2412yes—
902C2×C4⋊C4C2414yes—
903C2×C4⋊C4C2414yes—
904C2×C4⋊C4C2414yes—
905C2×C4⋊C4C2412yes—
906C2×C4⋊C4C2412yes—
907C2×C4⋊C4C2412yes—
908C2×C4⋊C4C2412yes—
909C2×C4⋊C4C2412yes—
910C2×C4⋊C4C2412yes—
911C2×C4⋊C4C2411yescharacteristic
912C2×C4⋊C4C2411yescharacteristic
913C2×C4⋊C4C2411yescharacteristic
914C2×C4⋊C4C2411yescharacteristic
915C2×C4⋊C4C2414yes—
916C2×C4⋊C4C2414yes—
917C2×C4⋊C4C2414yes—
918C2×C4⋊C4C2412yes—
919C2×C4⋊C4C2414yes—
920C2×C4⋊C4C2412yes—
921C2×C4⋊C4C2412yes—
922C2×C4⋊C4C2412yes—
923C2×C4⋊C4C2412yes—
924C2×C4⋊C4C2414yes—
925C2×C4⋊C4C2412yes—
926C2×C4⋊C4C2412yes—
927C2×C4⋊C4C2412yes—
928C2×C4⋊C4C2414yes—
929C2×C4⋊C4C2412yes—
930C2×C4⋊C4C2412yes—
931C2×C4⋊C4C2412yes—
932C2×C4⋊C4C2412yes—
933C2×C4⋊C4C2412yes—
934C2×C4⋊C4C2414yes—
935C2×C4⋊C4C2414yes—
936C2×C4⋊C4C2414yes—
937C2×C4⋊C4C2414yes—
938C2×C4⋊C4C2414yes—
939C2×C4⋊C4C2414yes—
940C2×C4⋊C4C2412yes—
941C2×C4⋊C4C2412yes—
942C2×C4⋊C4C2412yes—
943C2×C4⋊C4C2412yes—
944C2×C4⋊C4C2412yes—
945C2×C4⋊C4C2412yes—
946C2×C4⋊C4C2412yes—
947C2×C4⋊C4C2412yes—
948C2×C4⋊C4C2412yes—
949C2×C4⋊C4C2414yes—
950C2×C4⋊C4C2414yes—
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⋊C4C2414yes—
963C2×C4⋊C4C2414yes—
964C2×C4⋊C4C2412yes—
965C2×C4⋊C4C2412yes—
966C2×C22⋊C4C2412yes—
967C2×C22⋊C4C2412yes—
968C2×C22⋊C4C2412yes—
969C2×C22⋊C4C2412yes—
970C2×C22⋊C4C2412yes—
971C2×C22⋊C4C2412yes—
972C2×C22⋊C4C2412yes—
973C2×C22⋊C4C2412yes—
974C2×C42—28no—
975C2×C42—24no—
976C2×C42—24no—
977C2×C42—24no—
978C2×C42C2412yes—
979C2×C42C2412yes—
980C2×C42C2412yes—
981C2×C42C2412yes—
982C2×C42C2412yes—
983C2×C42C2412yes—
984C2×C42C2412yes—
985C2×C42C2412yes—
986C2×C42C2412yes—
987C2×C42C2414yes—
988C2×C42C2411yescharacteristic
989C2×C42C2411yescharacteristic
990C2×C42C2411yescharacteristic
991C2×C42C2411yescharacteristic
992C2×C42C2414yes—
993C2×C42C2411yescharacteristic
994C2×C42C2411yescharacteristic
995C2×C42C2411yescharacteristic
996C2×C42C2411yescharacteristic
997C2×C42C2411yescharacteristic
998C2×C42C2411yescharacteristic
999C2×C42C2411yescharacteristic
1000C2×C42C2411yescharacteristic
1001C2×C42C2414yes—
1002C2×C42C2414yes—
1003C2×C42C2412yes—
1004C2×C42C2412yes—
1005C2×C42C2412yes—
1006C2×C42C2414yes—
1007C2×C42C2414yes—
1008C2×C42C2414yes—
1009C2×C42C2412yes—
1010C2×C42C2412yes—
1011C2×C42C2412yes—
1012C2×C42C2412yes—
1013C2×C42C2414yes—
1014C2×C42C2414yes—
1015C2×C42C2414yes—
1016#95C2411yescharacteristic
1017#95C2411yescharacteristic
1018#95C2411yescharacteristic
1019#95C2411yescharacteristic
1020#95C2414yes—
1021#95C2411yescharacteristic
1022#95C2411yescharacteristic
1023#95C2411yescharacteristic
1024#95C2411yescharacteristic
1025#95C2414yes—
1026#95C2414yes—
1027#95C2414yes—
1028#95C2414yes—
1029#95C2414yes—
1030#95C2414yes—
1031#95C2414yes—
1032#95C2414yes—
1033#95C2414yes—
1034#95C2414yes—
1035#95C2414yes—
1036#95C2412yes—
1037#95C2412yes—
1038#95C2412yes—
1039#95C2412yes—
1040#95C2412yes—
1041#95C2412yes—
1042#95C2412yes—
1043#95C2412yes—
1044#95C2412yes—
1045#95C2412yes—
1046#95C2412yes—
1047#95C2412yes—
1048#95C2414yes—
1049#95C2414yes—
1050#95C2414yes—
1051#95C2414yes—
1052#95C2414yes—
1053#95C2414yes—
1054#95C2414yes—
1055#95C2414yes—
1056#95C2414yes—
1057#95C2414yes—
1058#95C2414yes—
1059#95C2414yes—
1060#95C2412yes—
1061#95C2412yes—
1062#95C2412yes—
1063#95C2412yes—
1064#95C2412yes—
1065#95C2412yes—
1066#95C2412yes—
1067#95C2412yes—
1068#95C2412yes—
1069#95C2412yes—
1070#95C2412yes—
1071#95C2414yes—
1072#95C2412yes—
1073#95C2412yes—
1074#95C2412yes—
1075#95C2414yes—
1076#95C2414yes—
1077#95C2414yes—
1078#95C2414yes—
1079#95C2414yes—
1080#95C2414yes—
1081#95C2414yes—
1082#95C2414yes—
1083#95C2412yes—
1084#95C2412yes—
1085#95C2412yes—
1086#95C2412yes—
1087#95C2412yes—
1088#95C2412yes—
1089#95C2414yes—
1090#95C2412yes—
1091#95C2412yes—
1092#95C2412yes—
1093#95C2412yes—
1094#95C2412yes—
1095#95C2412yes—
1096#95C2412yes—
1097#95C2412yes—
1098#95C2412yes—
1099#95C2412yes—
1100#95C2412yes—
1101#95C2412yes—
1102#95C2412yes—
1103#95C2412yes—
1104#95C2412yes—
1105#95C2412yes—
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—
1121#95C2414yes—
1122C24C2511yescharacteristic
1123C2×Q8—24no—
1124C2×Q8—24no—
1125C2×Q8—28no—
1126C2×Q8—24no—
1127C2×Q8—24no—
1128C2×Q8—24no—
1129C2×Q8—24no—
1130C2×Q8—44no—
1131C2×Q8—44no—
1132C2×Q8—416no—
1133C22×C4—22no—
1134C22×C4—24no—
1135C22×C4—22no—
1136C22×C4—24no—
1137C22×C4—24no—
1138C22×C4—22no—
1139C22×C4—22no—
1140C22×C4—22no—
1141C22×C4—24no—
1142C22×C4—22no—
1143C22×C4—24no—
1144C22×C4—22no—
1145C22×C4—22no—
1146C22×C4—41no—
1147C22×C4—42no—
1148C22×C4—42no—
1149C22×C4—41no—
1150C22×C4—41no—
1151C22×C4—41no—
1152C22×C4—42no—
1153C22×C4—42no—
1154C22×C4—42no—
1155C22×C4—41no—
1156C22×C4—41no—
1157C22×C4—41no—
1158C22×C4—41no—
1159C22×C4—41no—
1160C22×C4—42no—
1161C22×C4—41no—
1162C22×C4C2×#4118yes—
1163C22×C4C2×#4114yes—
1164C22×C42−1+414yes—
1165C22×C42−1+414yes—
1166C22×C4C2514yes—
1167C22×C4C2511yescharacteristic
1168C22×C4C2511yescharacteristic
1169C22×C4C2512yes—
1170C22×C4C2512yes—
1171C22×C4C2512yes—
1172C22×C4C2512yes—
1173C22×C4C2512yes—
1174C22×C4C2512yes—
1175C22×C4C2512yes—
1176C22×C4C2512yes—
1177C22×C4C2512yes—
1178C22×C4C2512yes—
1179C22×C4C2512yes—
1180C22×C4C2512yes—
1181C22×C4C2511yescharacteristic
1182C22×C4C2514yes—
1183C22×C4C2512yes—
1184C22×C4C2511yescharacteristic
1185C22×C4C2511yescharacteristic
1186C22×C4C2511yescharacteristic
1187C22×C4C2512yes—
1188C22×C4C2511yescharacteristic
1189C22×C4C2511yescharacteristic
1190C22×C4C2511yescharacteristic
1191C22×C4C2511yescharacteristic
1192C22×C4C2514yes—
1193C22×C4C2512yes—
1194C22×C4C2512yes—
1195C22×C4C2514yes—
1196C22×C4C2511yescharacteristic
1197C22×C4C2511yescharacteristic
1198C22×C4C2511yescharacteristic
1199C22×C4C2511yescharacteristic
1200C4⋊C4—28no—
1201C4⋊C4—28no—
1202C4⋊C4—28no—
1203C4⋊C4—28no—
1204C4⋊C4—28no—
1205C4⋊C4—28no—
1206C4⋊C4—24no—
1207C4⋊C4—24no—
1208C4⋊C4—22no—
1209C4⋊C4—22no—
1210C4⋊C4—22no—
1211C4⋊C4—22no—
1212C4⋊C4—28no—
1213C4⋊C4—28no—
1214C4⋊C4—28no—
1215C4⋊C4—24no—
1216C4⋊C4—24no—
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—28no—
1230C4⋊C4—22no—
1231C4⋊C4—22no—
1232C4⋊C4—22no—
1233C4⋊C4—28no—
1234C4⋊C4—22no—
1235C4⋊C4—24no—
1236C4⋊C4—24no—
1237C4⋊C4—24no—
1238C4⋊C4—24no—
1239C4⋊C4—24no—
1240C4⋊C4—24no—
1241C4⋊C4—24no—
1242C4⋊C4—41no—
1243C4⋊C4—44no—
1244C4⋊C4—41no—
1245C4⋊C4—44no—
1246C4⋊C4—41no—
1247C4⋊C4—41no—
1248C4⋊C4—44no—
1249C4⋊C4—42no—
1250C4⋊C4—42no—
1251C4⋊C4—42no—
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—42no—
1262C4⋊C4—42no—
1263C4⋊C4—42no—
1264C4⋊C4—44no—
1265C4⋊C4—44no—
1266C4⋊C4—42no—
1267C4⋊C4—42no—
1268C4⋊C4—42no—
1269C4⋊C4—44no—
1270C4⋊C4—42no—
1271C4⋊C4—42no—
1272C4⋊C4—44no—
1273C4⋊C4—42no—
1274C4⋊C4—44no—
1275C4⋊C4—42no—
1276C4⋊C4—42no—
1277C4⋊C4—42no—
1278C4⋊C4—42no—
1279C4⋊C4—42no—
1280C4⋊C4—42no—
1281C4⋊C4—42no—
1282C4⋊C4—44no—
1283C4⋊C4—44no—
1284C4⋊C4—42no—
1285C4⋊C4—42no—
1286C4⋊C4—44no—
1287C4⋊C4—44no—
1288C4⋊C4—44no—
1289C4⋊C4—44no—
1290C4⋊C4—42no—
1291C4⋊C4—44no—
1292C4⋊C4—44no—
1293C4⋊C4—42no—
1294C4⋊C4—42no—
1295C4⋊C4C2×#4118yes—
1296C4⋊C4C2×#4118yes—
1297C22⋊C4—24no—
1298C22⋊C4—24no—
1299C22⋊C4—24no—
1300C22⋊C4—24no—
1301C22⋊C4—24no—
1302C22⋊C4—24no—
1303C22⋊C4—24no—
1304C22⋊C4—24no—
1305C42—22no—
1306C42—22no—
1307C42—28no—
1308C42—22no—
1309C42—22no—
1310C42—28no—
1311C42—22no—
1312C42—22no—
1313C42—22no—
1314C42—22no—
1315C42—24no—
1316C42—24no—
1317C42—22no—
1318C42—22no—
1319C42—22no—
1320C42—22no—
1321C42—24no—
1322C42—24no—
1323C42—24no—
1324C42—24no—
1325C42—24no—
1326C42—24no—
1327C42—24no—
1328C42—44no—
1329C42—44no—
1330C42—44no—
1331C42—42no—
1332C42—42no—
1333C42—42no—
1334C42—42no—
1335C42—44no—
1336C42—44no—
1337C42—42no—
1338C42—44no—
1339C42—44no—
1340C42—44no—
1341C42—42no—
1342C42—42no—
1343C23—21no—
1344C23—21no—
1345C23—21no—
1346C23—21no—
1347C23C22×#4112yes—
1348C23C2×2−1+412yes—
1349C23C2×2−1+412yes—
1350C23C2611yescharacteristic
1351Q8—48no—
1352Q8—48no—
1353Q8—88no—
1354C2×C4—21no—
1355C2×C4—21no—
1356C2×C4—21no—
1357C2×C4—24no—
1358C2×C4—24no—
1359C2×C4—21no—
1360C2×C4—21no—
1361C2×C4—21no—
1362C2×C4—21no—
1363C2×C4—21no—
1364C2×C4—21no—
1365C2×C4—21no—
1366C2×C4—21no—
1367C2×C4—24no—
1368C2×C4—22no—
1369C2×C4—22no—
1370C2×C4—22no—
1371C2×C4—22no—
1372C2×C4—24no—
1373C2×C4—21no—
1374C2×C4—21no—
1375C2×C4—21no—
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—22no—
1386C2×C4—22no—
1387C2×C4—22no—
1388C2×C4—24no—
1389C2×C4—24no—
1390C2×C4—24no—
1391C2×C4—22no—
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—21no—
1401C2×C4—21no—
1402C2×C4—22no—
1403C2×C4—22no—
1404C2×C4—22no—
1405C2×C4—22no—
1406C2×C4—24no—
1407C2×C4—24no—
1408C2×C4—24no—
1409C2×C4—22no—
1410C2×C4—22no—
1411C2×C4—22no—
1412C2×C4—21no—
1413C2×C4—21no—
1414C2×C4—21no—
1415C2×C4—21no—
1416C2×C4—21no—
1417C2×C4—21no—
1418C2×C4—21no—
1419C2×C4—22no—
1420C2×C4—22no—
1421C2×C4—22no—
1422C2×C4—22no—
1423C2×C4—22no—
1424C2×C4—22no—
1425C2×C4—21no—
1426C2×C4—21no—
1427C2×C4—21no—
1428C2×C4—21no—
1429C2×C4—22no—
1430C2×C4—22no—
1431C2×C4—22no—
1432C2×C4—22no—
1433C2×C4—24no—
1434C2×C4—22no—
1435C2×C4—22no—
1436C2×C4—22no—
1437C2×C4—22no—
1438C2×C4—22no—
1439C2×C4—21no—
1440C2×C4—21no—
1441C2×C4—21no—
1442C2×C4—21no—
1443C2×C4—21no—
1444C2×C4—21no—
1445C2×C4—21no—
1446C2×C4—22no—
1447C2×C4—48no—
1448C2×C4—44no—
1449C2×C4—44no—
1450C2×C4—48no—
1451C2×C4—82no—
1452C2×C4—82no—
1453C2×C4—82no—
1454C2×C4—84no—
1455C2×C4—84no—
1456C2×C4—82no—
1457C2×C4#541116yes—
1458C2×C4C22×#4118yes—
1459C2×C4C22×#4112yes—
1460C2×C4C22×#4112yes—
1461C2×C4C2×2−1+412yes—
1462C2×C4C2×2−1+412yes—
1463C2×C4C2×2−1+412yes—
1464C2×C4C2×2−1+412yes—
1465C2×C4#58512yes—
1466C2×C4#58512yes—
1467C22—22no—
1468C22—22no—
1469C22—22no—
1470C22—22no—
1471C22—22no—
1472C22—22no—
1473C22C2×#54114yes—
1474C22C23×#4111yescharacteristic
1475C22C22×2−1+411yescharacteristic
1476C22C22×2−1+411yescharacteristic
1477C22C2×#58511yescharacteristic
1478C22C2×#58511yescharacteristic
1479C222−1+611yescharacteristic
1480C222−1+611yescharacteristic
1481C4—28no—
1482C4—22no—
1483C4—22no—
1484C4—41no—
1485C4—41no—
1486C4—41no—
1487C4—41no—
1488C4—42no—
1489C4—42no—
1490C4—42no—
1491C4—42no—
1492C4—41no—
1493C4—41no—
1494C4—41no—
1495C4—44no—
1496C4—42no—
1497C4—42no—
1498C4—41no—
1499C4—44no—
1500C4—42no—
1501C4—42no—
1502C4—41no—
1503C4—41no—
1504C4—44no—
1505C4—42no—
1506C4—42no—
1507C4—42no—
1508C4—42no—
1509C4—42no—
1510C4—42no—
1511C4—42no—
1512C4—42no—
1513C4C2×#54114yes—
1514C4C2×#54114yes—
1515C2—24no—
1516C2C22×#54111yescharacteristic
1517C2#6283111yescharacteristic
1518C2#6288911yescharacteristic
1519C2#6295611yescharacteristic
1520C2#6295611yescharacteristic
1521C2#6299111yescharacteristic
1522C2#6300511yescharacteristic
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. #42782C2semidirect
2. #42774C2semidirect
3. #42774C2semidirect
4. #42765C2semidirect
5. #42744C2semidirect
6. #42710C2semidirect
7. #42710C2semidirect
8. #42553C2semidirect
11. #40189C2semidirect
12. #40107C2semidirect
13. #40082C2semidirect
14. #40082C2semidirect
15. #39526C2semidirect
16. #39241C2semidirect
17. #39241C2semidirect
18. #39003C2semidirect

Maximal subgroups

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

subgroupindex
#427822
#427742
#427652
#427442
#427102
#425532
#413942
#405642
#401892
#401072
#400822
#395262
#392412
#390032
#383952
#380662
#356402
#356302
#355852
#355432
#353132
#351542
#349482
#348152
C2×#24532
#342722
#342172
#341872