Finite Group Databasebeta

← #8115490

Subgroups — #8115490

Order 512.

3835 conjugacy classes of subgroups.

The subgroup lattice has 1242 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#58720C214yesmaximal
2#58672C214yesmaximal, complemented
3#58018C214yesmaximal, complemented
4#57021C214yesmaximal, complemented
5#56713C214yesmaximal, complemented
6#55849C214yesmaximal, complemented
7#54319C214yesmaximal, complemented
8#54286C214yesmaximal, complemented
9#53067C212yesmaximal, complemented
10#52961C212yesmaximal, complemented
11#45085C212yesmaximal, complemented
12#44953C212yesmaximal, complemented
13#42773C212yesmaximal, complemented
14#42670C212yesmaximal, complemented
15#42623C212yesmaximal, complemented
16#42466C212yesmaximal
17#39641C211yesmaximal, characteristic, complemented
18#39622C211yesmaximal, characteristic, complemented
19#39514C211yesmaximal, characteristic, complemented
20#39494C211yesmaximal, characteristic, complemented
21#37960C212yesmaximal, complemented
22#37937C212yesmaximal, complemented
23#37328C212yesmaximal, complemented
24#37313C212yesmaximal, complemented
25#35336C211yesmaximal, characteristic, complemented
26#35294C211yesmaximal, characteristic, complemented
27#34640C211yesmaximal, characteristic
28#2868C2211yescharacteristic
29#2859C2211yescharacteristic
30#2859C2211yescharacteristic
31#2859C2211yescharacteristic
32#2859C2212yes—
33#2851C2211yescharacteristic
34#2851C2211yescharacteristic
35#2839C2214yes—
36#2837C2214yes—
37#2836C2214yes—
38#2836C2214yes—
39#2836C2214yes—
40#2836C2214yes—
41#2836C2214yes—
42#2834C2214yes—
43#2833C2214yes—
44#2833C2214yes—
45#2831C2214yes—
46#2823C2214yes—
47#2809C2214yes—
48#2807C2214yes—
49#2806C2214yes—
50#2806C2214yes—
51#2802C2214yes—
52#2802C2214yes—
53#2802C2214yes—
54#2802C2214yes—
55#2799C2214yes—
56#2798C2214yes—
57#2798C2214yes—
58#2796C2214yes—
59#2793C2214yes—
60#2792C2214yes—
61#2792C2214yes—
62#2791C2214yes—
63#2791C2214yes—
64#2791C2214yes—
65#2789C2214yes—
66#2789C2214yes—
67#2789C2214yes—
68#2787C2214yes—
69#2783C2214yes—
70#2783C2214yes—
71#2780C2214yes—
72#2776C2214yes—
73#2774C2214yes—
74#2773C2214yes—
75#2772C2214yes—
76#2772C2214yes—
77#2768C2214yes—
78#2768C2214yes—
79#2767C2214yes—
80#2767C2214yes—
81#2766C2214yes—
82#2766C2214yes—
83#2765C2214yes—
84#2762C2214yes—
85#2755C2214yes—
86#2750C2214yes—
87#2740C2214yes—
88#2739C2214yes—
89#2730C2214yes—
90#2726C2214yes—
91#2726C2214yes—
92#2725C2214yes—
93#2725C2214yes—
94#2725C2214yes—
95#2722C2214yes—
96#2721C2214yes—
97#2721C2214yes—
98#2720C2214yes—
99#2719C2214yes—
100#2719C2214yes—
101#2716C2214yes—
102#2716C2214yes—
103#2716C2214yes—
104#2716C2214yes—
105#2715C2214yes—
106#2715C2214yes—
107#2715C2214yes—
108#2713C2214yes—
109#2704C2214yes—
110#2698C2214yes—
111#2664C2214yes—
112#2660C2212yes—
113#2655C2214yes—
114#2655C2212yes—
115#2655C2214yes—
116#2655C2214yes—
117#2654C2212yes—
118#2653C2212yes—
119#2653C2214yes—
120#2652C2212yes—
121#2651C2212yes—
122#2650C2212yes—
123#2649C2212yes—
124#2648C2212yes—
125#2647C2212yes—
126#2647C2214yes—
127#2647C2212yes—
128#2632C2214yes—
129#2629C2212yes—
130#2629C2212yes—
131#2629C2212yes—
132#2629C2211yescharacteristic
133#2629C2211yescharacteristic
134#2628C2212yes—
135#2625C2214yes—
136#2611C2214yes—
137#2609C2214yes—
138#2601C2214yes—
139#2594C2214yes—
140#2590C2214yes—
141#2590C2214yes—
142#2588C2214yes—
143#2587C2214yes—
144#2587C2214yes—
145#2587C2214yes—
146#2586C2214yes—
147#2585C2214yes—
148#2570C2214yes—
149#2570C2214yes—
150#2570C2212yes—
151#2570C2212yes—
152#2565C2214yes—
153#2563C2212yes—
154#2562C2212yes—
155#2552C2212yes—
156#2552C2212yes—
157#2552C2212yes—
158#2550C2214yes—
159#2550C2212yes—
160#2550C2212yes—
161#2550C2212yes—
162#2547C2212yes—
163#2546C2212yes—
164#2546C2214yes—
165#2533C2214yes—
166#2528C2214yes—
167#2528C2214yes—
168#2527C2214yes—
169#2522C2214yes—
170#2519C2214yes—
171#2512C2214yes—
172#2511C2214yes—
173#2509C2212yes—
174#2508C2212yes—
175#2508C2212yes—
176#2507C2212yes—
177#2507C2214yes—
178#2507C2212yes—
179#2507C2212yes—
180#2506C2212yes—
181#2506C2212yes—
182#2497C2212yes—
183#2497C2212yes—
184#2497C2212yes—
185#2496C2212yes—
186#2496C2212yes—
187#2496C2212yes—
188#2496C2212yes—
189#2495C2212yes—
190#2494C2212yes—
191#2494C2212yes—
192#2494C2212yes—
193#2494C2212yes—
194#2487C2212yes—
195#2485C2212yes—
196#2478C2214yes—
197#2478C2214yes—
198#2475C2214yes—
199#2474C2214yes—
200#2465C2214yes—
201#2453C2214yes—
202#2446C2214yes—
203#2442C2212yes—
204#2442C2212yes—
205#2441C2212yes—
206#2441C2212yes—
207#2441C2212yes—
208#2441C2214yes—
209#2440C2212yes—
210#2439C2214yes—
211#2439C2214yes—
212#2402C2211yescharacteristic
213#2401C2212yes—
214#2398C2211yescharacteristic
215#2396C2211yescharacteristic
216#2395C2212yes—
217#2392C2211yescharacteristic
218#2370C2212yes—
219#2369C2212yes—
220#2369C2212yes—
221#2365C2212yes—
222#2355C2212yes—
223#2352C2212yes—
224#2346C2212yes—
225#2344C2212yes—
226#2331C2212yes—
227#2330C2212yes—
228#2330C2211yescharacteristic
229#2330C2212yes—
230#2330C2212yes—
231#2330C2211yescharacteristic
232#2317C2212yes—
233#2314C2212yes—
234#2314C2212yes—
235C4×#125C2211yescharacteristic
236C4×#125C2211yescharacteristic
237#2298C2212yes—
238#2295C2211yescharacteristic
239#2293C2211yescharacteristic
240#2290C2212yes—
241#2285C2212yes—
242C4×#117C2211yescharacteristic
243C2×C4⋊Q8C2312yes—
244C2×C4⋊Q8C2312yes—
245C2×C4⋊Q8C2314yes—
246C2×C4⋊Q8C2314yes—
247C2×#126C2314yes—
248C2×#126C2314yes—
249C2×#126C2314yes—
250C2×#126C2314yes—
251C2×#125C2311yescharacteristic
252C2×#125C2311yescharacteristic
253C2×#125C2312yes—
254C2×#125C2311yescharacteristic
255C2×#125C2312yes—
256C2×#125C2311yescharacteristic
257C2×#125C2314yes—
258C2×#125C2314yes—
259C2×#125C2314yes—
260C2×#125C2314yes—
261C2×#124C2314yes—
262C2×C22⋊Q8C2314yes—
263C2×C4×Q8C2311yescharacteristic
264C2×C4×Q8C2314yes—
265C2×C4×D4C2311yescharacteristic
266C2×C4×D4C2312yes—
267C2×#117C2311yescharacteristic
268C2×#117C2312yes—
269C2×#117C2312yes—
270C2×#117C2311yescharacteristic
271C2×#117C2314yes—
272C2×#117C2314yes—
273C22×C4⋊C4C2312yes—
274C22×C42C2311yescharacteristic
275#401C2314yes—
276#401C2314yes—
277#401C2314yes—
278#401C2314yes—
279#401C2312yes—
280#400C2314yes—
281#400C2314yes—
282#400C2314yes—
283#400C2314yes—
284#400C2314yes—
285#400C2314yes—
286#400C2314yes—
287#400C2314yes—
288#400C2312yes—
289#400C2314yes—
290#400C2314yes—
291#400C2314yes—
292#400C2314yes—
293#400C2314yes—
294#400C2314yes—
295#400C2314yes—
296#400C2314yes—
297#400C2314yes—
298#400C2314yes—
299#400C2314yes—
300#400C2312yes—
301#400C2314yes—
302#400C2314yes—
303#400C2314yes—
304#400C2312yes—
305#400C2314yes—
306#400C2314yes—
307#400C2312yes—
308#400C2312yes—
309#400C2312yes—
310#400C2311yescharacteristic
311#400C2312yes—
312#400C2314yes—
313#399C2312yes—
314#399C2314yes—
315#399C2314yes—
316#399C2314yes—
317#399C2314yes—
318#399C2314yes—
319#399C2311yescharacteristic
320#398C2312yes—
321#398C2314yes—
322#398C2314yes—
323#398C2314yes—
324#398C2314yes—
325#398C2314yes—
326#398C2314yes—
327#398C2314yes—
328#398C2314yes—
329#398C2314yes—
330#398C2314yes—
331#398C2314yes—
332#398C2314yes—
333#398C2314yes—
334#398C2312yes—
335#398C2314yes—
336#398C2314yes—
337#398C2314yes—
338#398C2314yes—
339#398C2314yes—
340#398C2314yes—
341#398C2314yes—
342#398C2314yes—
343#398C2314yes—
344#398C2314yes—
345#398C2314yes—
346#398C2314yes—
347#398C2314yes—
348#398C2314yes—
349#398C2314yes—
350#398C2314yes—
351#398C2314yes—
352#398C2314yes—
353#398C2312yes—
354#398C2314yes—
355#398C2314yes—
356#398C2314yes—
357#398C2314yes—
358#398C2314yes—
359#398C2314yes—
360#398C2311yescharacteristic
361#398C2312yes—
362#398C2314yes—
363#398C2314yes—
364#398C2314yes—
365#397C2314yes—
366#397C2314yes—
367#397C2314yes—
368#397C2314yes—
369#397C2314yes—
370#397C2314yes—
371#397C2312yes—
372#397C2312yes—
373#397C2312yes—
374#397C2312yes—
375#397C2314yes—
376#397C2314yes—
377#397C2314yes—
378#397C2314yes—
379#397C2314yes—
380#397C2312yes—
381#397C2314yes—
382#397C2311yescharacteristic
383#397C2312yes—
384#397C2312yes—
385#396C2314yes—
386#396C2314yes—
387#396C2314yes—
388#396C2314yes—
389#396C2314yes—
390#396C2314yes—
391#396C2312yes—
392#396C2314yes—
393#396C2314yes—
394#396C2312yes—
395#396C2314yes—
396#396C2314yes—
397#396C2314yes—
398#396C2314yes—
399#396C2314yes—
400#396C2314yes—
401#396C2312yes—
402#395C2314yes—
403#395C2314yes—
404#395C2314yes—
405#395C2314yes—
406#395C2314yes—
407#395C2314yes—
408#395C2314yes—
409#395C2311yescharacteristic
410#394C2314yes—
411#394C2312yes—
412#394C2314yes—
413#394C2312yes—
414#394C2312yes—
415#394C2312yes—
416#394C2311yescharacteristic
417#393C2314yes—
418#393C2314yes—
419#393C2314yes—
420#393C2312yes—
421#393C2311yescharacteristic
422#392C2311yescharacteristic
423#391C2314yes—
424#391C2314yes—
425#391C2314yes—
426#391C2314yes—
427#391C2314yes—
428#391C2314yes—
429#391C2314yes—
430#391C2314yes—
431#391C2314yes—
432#391C2314yes—
433#391C2314yes—
434#391C2312yes—
435#391C2314yes—
436#391C2314yes—
437#390C2314yes—
438#390C2312yes—
439#389C2312yes—
440#389C2312yes—
441#389C2312yes—
442#389C2314yes—
443#389C2312yes—
444#389C2314yes—
445#389C2312yes—
446#389C2314yes—
447#389C2312yes—
448#389C2312yes—
449#389C2314yes—
450#389C2314yes—
451#389C2314yes—
452#389C2314yes—
453#389C2314yes—
454#389C2314yes—
455#389C2314yes—
456#389C2314yes—
457#389C2314yes—
458#389C2314yes—
459#389C2314yes—
460#389C2314yes—
461#389C2314yes—
462#389C2312yes—
463#389C2312yes—
464#389C2312yes—
465#389C2314yes—
466#389C2314yes—
467#389C2314yes—
468#389C2314yes—
469#389C2314yes—
470#389C2312yes—
471#389C2312yes—
472#389C2312yes—
473#389C2312yes—
474#389C2312yes—
475#389C2312yes—
476#389C2314yes—
477#389C2314yes—
478#389C2314yes—
479#389C2314yes—
480#389C2314yes—
481#389C2314yes—
482#389C2312yes—
483#389C2314yes—
484#389C2312yes—
485#389C2312yes—
486#389C2312yes—
487#389C2312yes—
488#389C2314yes—
489#389C2314yes—
490#389C2314yes—
491#389C2312yes—
492#389C2314yes—
493#389C2314yes—
494#389C2314yes—
495#388C2314yes—
496#388C2314yes—
497#388C2314yes—
498#388C2314yes—
499#388C2314yes—
500#388C2314yes—
501#388C2314yes—
502#388C2314yes—
503#388C2314yes—
504#388C2314yes—
505#388C2314yes—
506#388C2314yes—
507#388C2312yes—
508#388C2312yes—
509#388C2314yes—
510#388C2314yes—
511#388C2314yes—
512#388C2314yes—
513#388C2314yes—
514#388C2312yes—
515#388C2312yes—
516#388C2312yes—
517#388C2312yes—
518#388C2312yes—
519#388C2312yes—
520#388C2314yes—
521#387C2314yes—
522#387C2314yes—
523#387C2314yes—
524#387C2314yes—
525#387C2314yes—
526#387C2314yes—
527#387C2314yes—
528#387C2314yes—
529#387C2314yes—
530#387C2314yes—
531#387C2314yes—
532#387C2314yes—
533#387C2314yes—
534#387C2314yes—
535#387C2314yes—
536#387C2314yes—
537#387C2314yes—
538#387C2314yes—
539#387C2314yes—
540#387C2314yes—
541#387C2314yes—
542#387C2314yes—
543#387C2314yes—
544#387C2314yes—
545#387C2314yes—
546#387C2314yes—
547#387C2314yes—
548#387C2314yes—
549#387C2314yes—
550#387C2314yes—
551#387C2314yes—
552#387C2314yes—
553#387C2314yes—
554#387C2314yes—
555#387C2312yes—
556#387C2312yes—
557#387C2314yes—
558#387C2314yes—
559#387C2314yes—
560#387C2314yes—
561#387C2314yes—
562#387C2314yes—
563#387C2314yes—
564#387C2314yes—
565#387C2314yes—
566#387C2314yes—
567#387C2314yes—
568#387C2312yes—
569#387C2312yes—
570#387C2312yes—
571#387C2312yes—
572#387C2312yes—
573#387C2314yes—
574#387C2312yes—
575#387C2314yes—
576#387C2314yes—
577#387C2314yes—
578#387C2314yes—
579#387C2314yes—
580#387C2314yes—
581#387C2314yes—
582#387C2314yes—
583#386C2314yes—
584#386C2312yes—
585#386C2314yes—
586#386C2312yes—
587#385C2314yes—
588#385C2314yes—
589#385C2314yes—
590#385C2314yes—
591#385C2314yes—
592#385C2314yes—
593#385C2314yes—
594#385C2312yes—
595#385C2312yes—
596#385C2314yes—
597#384C2314yes—
598#384C2312yes—
599#384C2312yes—
600#384C2314yes—
601#384C2312yes—
602#384C2312yes—
603#384C2312yes—
604#384C2311yescharacteristic
605#384C2311yescharacteristic
606#384C2312yes—
607#384C2314yes—
608#383C2314yes—
609#382C2311yescharacteristic
610#382C2311yescharacteristic
611#382C2314yes—
612#382C2314yes—
613#382C2312yes—
614#382C2312yes—
615#382C2312yes—
616#382C2314yes—
617#382C2312yes—
618#382C2314yes—
619#382C2314yes—
620#382C2314yes—
621#381C2314yes—
622#380C2312yes—
623#380C2312yes—
624#380C2312yes—
625#380C2312yes—
626#380C2312yes—
627#380C2312yes—
628#380C2312yes—
629#380C2312yes—
630#380C2312yes—
631#380C2314yes—
632#380C2312yes—
633#380C2314yes—
634#380C2314yes—
635C4×C4⋊C4C2312yes—
636C4×C4⋊C4C2312yes—
637C4×C4⋊C4C2314yes—
638C4×C4⋊C4C2314yes—
639C4×C4⋊C4C2312yes—
640C4×C4⋊C4C2314yes—
641C4×C4⋊C4C2312yes—
642C4×C4⋊C4C2312yes—
643C4×C4⋊C4C2312yes—
644C4×C4⋊C4C2311yescharacteristic
645C4×C4⋊C4C2314yes—
646C4×C4⋊C4C2314yes—
647C4×C4⋊C4C2312yes—
648C4×C4⋊C4C2312yes—
649C4×C4⋊C4C2312yes—
650C4×C4⋊C4C2312yes—
651C4×C4⋊C4C2312yes—
652C4×C4⋊C4C2312yes—
653C4×C4⋊C4C2314yes—
654C4×C4⋊C4C2314yes—
655C4×C4⋊C4C2312yes—
656C4×C4⋊C4C2311yescharacteristic
657C4×C4⋊C4C2312yes—
658C4×C4⋊C4C2312yes—
659C4×C4⋊C4C2312yes—
660C4×C22⋊C4C2312yes—
661C4×C22⋊C4C2312yes—
662C4×C22⋊C4C2314yes—
663C4×C22⋊C4C2312yes—
664C4×C22⋊C4C2312yes—
665C4×C22⋊C4C2312yes—
666C4×C22⋊C4C2312yes—
667C4×C22⋊C4C2312yes—
668#376C2311yescharacteristic
669#376C2311yescharacteristic
670#376C2312yes—
671#376C2314yes—
672C43C2311yescharacteristic
673C43C2311yescharacteristic
674C22×Q8C2411yescharacteristic
675C22×Q8C2414yes—
676C22×Q8C2414yes—
677C22×D4C2411yescharacteristic
678C22×D4C2412yes—
679C23×C4C2412yes—
680C23×C4C2411yescharacteristic
681C23×C4C2412yes—
682C23×C4C2414yes—
683C4⋊Q8—28no—
684C4⋊Q8—44no—
685C4⋊Q8—84no—
686C4⋊Q8—84no—
687#126—84no—
688#126—84no—
689#126—84no—
690#126—84no—
691#125—24no—
692#125—24no—
693#125—44no—
694#125—42no—
695#125—42no—
696#125—44no—
697#125—84no—
698#125—84no—
699#125—84no—
700#125—84no—
701#124—84no—
702C22⋊Q8—84no—
703C4×Q8—24no—
704C4×Q8—84no—
705C4×D4—24no—
706C4×D4—44no—
707#117—28no—
708#117—24no—
709#117—42no—
710#117—44no—
711#117—84no—
712#117—84no—
713C2×C4⋊C4—44no—
714C2×C4⋊C4C2412yes—
715C2×C4⋊C4C2412yes—
716C2×C4⋊C4C2412yes—
717C2×C4⋊C4C2411yescharacteristic
718C2×C4⋊C4C2411yescharacteristic
719C2×C4⋊C4C2412yes—
720C2×C4⋊C4C2412yes—
721C2×C4⋊C4C2411yescharacteristic
722C2×C4⋊C4C2412yes—
723C2×C4⋊C4C2411yescharacteristic
724C2×C4⋊C4C2412yes—
725C2×C4⋊C4C2412yes—
726C2×C4⋊C4C2412yes—
727C2×C4⋊C4C2414yes—
728C2×C4⋊C4C2414yes—
729C2×C4⋊C4C2412yes—
730C2×C4⋊C4C2412yes—
731C2×C4⋊C4C2414yes—
732C2×C4⋊C4C2414yes—
733C2×C4⋊C4C2414yes—
734C2×C4⋊C4C2414yes—
735C2×C4⋊C4C2414yes—
736C2×C4⋊C4C2414yes—
737C2×C4⋊C4C2412yes—
738C2×C4⋊C4C2412yes—
739C2×C4⋊C4C2412yes—
740C2×C4⋊C4C2414yes—
741C2×C4⋊C4C2414yes—
742C2×C4⋊C4C2414yes—
743C2×C4⋊C4C2414yes—
744C2×C4⋊C4C2412yes—
745C2×C4⋊C4C2412yes—
746C2×C4⋊C4C2412yes—
747C2×C4⋊C4C2414yes—
748C2×C4⋊C4C2414yes—
749C2×C4⋊C4C2414yes—
750C2×C4⋊C4C2414yes—
751C2×C4⋊C4C2414yes—
752C2×C4⋊C4C2414yes—
753C2×C4⋊C4C2414yes—
754C2×C4⋊C4C2414yes—
755C2×C4⋊C4C2414yes—
756C2×C4⋊C4C2414yes—
757C2×C4⋊C4C2414yes—
758C2×C4⋊C4C2414yes—
759C2×C4⋊C4C2414yes—
760C2×C4⋊C4C2414yes—
761C2×C4⋊C4C2414yes—
762C2×C4⋊C4C2414yes—
763C2×C4⋊C4C2414yes—
764C2×C4⋊C4C2414yes—
765C2×C4⋊C4C2414yes—
766C2×C4⋊C4C2414yes—
767C2×C4⋊C4C2414yes—
768C2×C4⋊C4C2414yes—
769C2×C4⋊C4C2414yes—
770C2×C4⋊C4C2414yes—
771C2×C4⋊C4C2412yes—
772C2×C4⋊C4C2412yes—
773C2×C4⋊C4C2414yes—
774C2×C4⋊C4C2412yes—
775C2×C4⋊C4C2412yes—
776C2×C4⋊C4C2414yes—
777C2×C4⋊C4C2414yes—
778C2×C4⋊C4C2412yes—
779C2×C4⋊C4C2412yes—
780C2×C4⋊C4C2414yes—
781C2×C4⋊C4C2414yes—
782C2×C4⋊C4C2414yes—
783C2×C4⋊C4C2414yes—
784C2×C4⋊C4C2414yes—
785C2×C4⋊C4C2414yes—
786C2×C22⋊C4C2411yescharacteristic
787C2×C22⋊C4C2411yescharacteristic
788C2×C22⋊C4C2412yes—
789C2×C22⋊C4C2412yes—
790C2×C22⋊C4C2412yes—
791C2×C22⋊C4C2412yes—
792C2×C22⋊C4C2414yes—
793C2×C22⋊C4C2414yes—
794C2×C22⋊C4C2414yes—
795C2×C22⋊C4C2412yes—
796C2×C22⋊C4C2414yes—
797C2×C22⋊C4C2412yes—
798C2×C22⋊C4C2412yes—
799C2×C22⋊C4C2412yes—
800C2×C22⋊C4C2414yes—
801C2×C22⋊C4C2414yes—
802C2×C22⋊C4C2414yes—
803C2×C22⋊C4C2414yes—
804C2×C22⋊C4C2412yes—
805C2×C22⋊C4C2412yes—
806C2×C22⋊C4C2412yes—
807C2×C22⋊C4C2412yes—
808C2×C22⋊C4C2414yes—
809C2×C22⋊C4C2414yes—
810C2×C22⋊C4C2412yes—
811C2×C22⋊C4C2412yes—
812C2×C22⋊C4C2412yes—
813C2×C22⋊C4C2412yes—
814C2×C22⋊C4C2414yes—
815C2×C42—24no—
816C2×C42C2411yescharacteristic
817C2×C42C2411yescharacteristic
818C2×C42C2411yescharacteristic
819C2×C42C2412yes—
820C2×C42C2412yes—
821C2×C42C2412yes—
822C2×C42C2411yescharacteristic
823C2×C42C2412yes—
824C2×C42C2414yes—
825C2×C42C2414yes—
826C2×C42C2414yes—
827C2×C42C2414yes—
828C2×C42C2414yes—
829C2×C42C2414yes—
830C2×C42C2414yes—
831C2×C42C2412yes—
832C2×C42C2414yes—
833C2×C42C2414yes—
834C2×C42C2412yes—
835C2×C42C2412yes—
836C2×C42C2412yes—
837C2×C42C2414yes—
838C2×C42C2414yes—
839C2×C42C2411yescharacteristic
840C2×C42C2411yescharacteristic
841#95C2412yes—
842#95C2412yes—
843#95C2412yes—
844#95C2412yes—
845#95C2412yes—
846#95C2414yes—
847#95C2414yes—
848#95C2412yes—
849#95C2412yes—
850#95C2414yes—
851#95C2412yes—
852#95C2412yes—
853#95C2414yes—
854#95C2412yes—
855#95C2414yes—
856#95C2412yes—
857#95C2412yes—
858#95C2412yes—
859#95C2412yes—
860#95C2412yes—
861#95C2412yes—
862#95C2412yes—
863#95C2412yes—
864#95C2412yes—
865#95C2414yes—
866#95C2414yes—
867#95C2414yes—
868#95C2414yes—
869#95C2414yes—
870#95C2414yes—
871#95C2412yes—
872#95C2412yes—
873#95C2414yes—
874#95C2414yes—
875#95C2414yes—
876#95C2414yes—
877#95C2414yes—
878#95C2414yes—
879#95C2414yes—
880#95C2414yes—
881#95C2414yes—
882#95C2411yescharacteristic
883#95C2411yescharacteristic
884#95C2414yes—
885#95C2412yes—
886#95C2414yes—
887#95C2411yescharacteristic
888#95C2411yescharacteristic
889#95C2412yes—
890#95C2414yes—
891#95C2414yes—
892#95C2414yes—
893#95C2414yes—
894#95C2414yes—
895#95C2412yes—
896#95C2414yes—
897#95C2412yes—
898#95C2412yes—
899#95C2414yes—
900#95C2414yes—
901#95C2414yes—
902#95C2414yes—
903#95C2414yes—
904#95C2414yes—
905#95C2414yes—
906#95C2414yes—
907#95C2414yes—
908#95C2414yes—
909#95C2414yes—
910#95C2414yes—
911#95C2414yes—
912#95C2414yes—
913#95C2414yes—
914#95C2414yes—
915#95C2414yes—
916#95C2414yes—
917#95C2414yes—
918#95C2414yes—
919#95C2414yes—
920#95C2414yes—
921C24C2512yes—
922C24C2511yescharacteristic
923C2×Q8—22no—
924C2×Q8—28no—
925C2×Q8—44no—
926C2×Q8—44no—
927C2×Q8—42no—
928C2×Q8—44no—
929C2×Q8—44no—
930C2×Q8—44no—
931C2×D4—22no—
932C2×D4—42no—
933C2×D4—42no—
934C2×D4—42no—
935C2×D4—42no—
936C22×C4—24no—
937C22×C4—22no—
938C22×C4—24no—
939C22×C4—22no—
940C22×C4—24no—
941C22×C4—24no—
942C22×C4—22no—
943C22×C4—42no—
944C22×C4—42no—
945C22×C4—44no—
946C22×C4—44no—
947C22×C4—44no—
948C22×C4C2511yescharacteristic
949C22×C4C2512yes—
950C22×C4C2511yescharacteristic
951C22×C4C2512yes—
952C22×C4C2512yes—
953C22×C4C2512yes—
954C22×C4C2512yes—
955C22×C4C2512yes—
956C22×C4C2514yes—
957C22×C4C2514yes—
958C22×C4C2514yes—
959C22×C4C2512yes—
960C22×C4C2514yes—
961C22×C4C2514yes—
962C22×C4C2514yes—
963C22×C4C2514yes—
964C22×C4C2511yescharacteristic
965C22×C4C2512yes—
966C22×C4C2512yes—
967C22×C4C2512yes—
968C22×C4C2514yes—
969C22×C4C2511yescharacteristic
970C22×C4C2511yescharacteristic
971C22×C4C2512yes—
972C22×C4C2511yescharacteristic
973C4⋊C4—24no—
974C4⋊C4—24no—
975C4⋊C4—22no—
976C4⋊C4—22no—
977C4⋊C4—22no—
978C4⋊C4—22no—
979C4⋊C4—24no—
980C4⋊C4—28no—
981C4⋊C4—28no—
982C4⋊C4—24no—
983C4⋊C4—24no—
984C4⋊C4—28no—
985C4⋊C4—24no—
986C4⋊C4—24no—
987C4⋊C4—24no—
988C4⋊C4—24no—
989C4⋊C4—24no—
990C4⋊C4—24no—
991C4⋊C4—44no—
992C4⋊C4—42no—
993C4⋊C4—44no—
994C4⋊C4—42no—
995C4⋊C4—44no—
996C4⋊C4—42no—
997C4⋊C4—44no—
998C4⋊C4—44no—
999C4⋊C4—44no—
1000C4⋊C4—44no—
1001C4⋊C4—42no—
1002C4⋊C4—42no—
1003C4⋊C4—44no—
1004C4⋊C4—44no—
1005C4⋊C4—44no—
1006C4⋊C4—42no—
1007C4⋊C4—42no—
1008C4⋊C4—44no—
1009C4⋊C4—44no—
1010C4⋊C4—44no—
1011C4⋊C4—44no—
1012C4⋊C4—42no—
1013C4⋊C4—42no—
1014C4⋊C4—44no—
1015C4⋊C4—44no—
1016C4⋊C4—44no—
1017C4⋊C4—44no—
1018C4⋊C4—44no—
1019C4⋊C4—44no—
1020C4⋊C4—44no—
1021C4⋊C4—44no—
1022C4⋊C4—44no—
1023C4⋊C4—44no—
1024C4⋊C4—42no—
1025C4⋊C4—42no—
1026C4⋊C4—44no—
1027C4⋊C4—42no—
1028C4⋊C4—44no—
1029C4⋊C4—44no—
1030C4⋊C4—44no—
1031C4⋊C4—44no—
1032C4⋊C4—44no—
1033C4⋊C4—44no—
1034C4⋊C4—44no—
1035C4⋊C4—44no—
1036C4⋊C4—44no—
1037C4⋊C4—44no—
1038C4⋊C4—44no—
1039C4⋊C4—44no—
1040C4⋊C4—44no—
1041C4⋊C4—44no—
1042C4⋊C4—44no—
1043C4⋊C4—44no—
1044C4⋊C4—44no—
1045C22⋊C4—24no—
1046C22⋊C4—24no—
1047C22⋊C4—22no—
1048C22⋊C4—22no—
1049C22⋊C4—24no—
1050C22⋊C4—44no—
1051C22⋊C4—42no—
1052C22⋊C4—42no—
1053C22⋊C4—44no—
1054C22⋊C4—42no—
1055C22⋊C4—42no—
1056C22⋊C4—42no—
1057C22⋊C4—44no—
1058C22⋊C4—42no—
1059C22⋊C4—44no—
1060C22⋊C4—44no—
1061C22⋊C4—44no—
1062C22⋊C4—42no—
1063C22⋊C4—42no—
1064C22⋊C4—42no—
1065C22⋊C4—44no—
1066C22⋊C4—44no—
1067C22⋊C4—44no—
1068C22⋊C4—44no—
1069C22⋊C4—42no—
1070C22⋊C4—42no—
1071C22⋊C4—42no—
1072C22⋊C4—42no—
1073C22⋊C4—44no—
1074C42—24no—
1075C42—22no—
1076C42—22no—
1077C42—24no—
1078C42—24no—
1079C42—22no—
1080C42—22no—
1081C42—24no—
1082C42—42no—
1083C42—44no—
1084C42—42no—
1085C42—44no—
1086C42—44no—
1087C42—44no—
1088C42—44no—
1089C42—44no—
1090C42—44no—
1091C42—44no—
1092C42—44no—
1093C42—42no—
1094C42—44no—
1095C42—44no—
1096C42—42no—
1097C422−1+414yes—
1098C422−1+414yes—
1099C23—22no—
1100C23—21no—
1101C23—22no—
1102C23—21no—
1103C23—21no—
1104C23—22no—
1105C23—22no—
1106C23—22no—
1107C23—22no—
1108C23—22no—
1109C23—22no—
1110C23—22no—
1111C23C2611yescharacteristic
1112Q8—82no—
1113Q8—88no—
1114Q8—164no—
1115D4—82no—
1116D4—84no—
1117C2×C4—22no—
1118C2×C4—22no—
1119C2×C4—22no—
1120C2×C4—22no—
1121C2×C4—21no—
1122C2×C4—22no—
1123C2×C4—22no—
1124C2×C4—22no—
1125C2×C4—21no—
1126C2×C4—21no—
1127C2×C4—22no—
1128C2×C4—22no—
1129C2×C4—22no—
1130C2×C4—24no—
1131C2×C4—24no—
1132C2×C4—22no—
1133C2×C4—21no—
1134C2×C4—24no—
1135C2×C4—24no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—24no—
1142C2×C4—24no—
1143C2×C4—21no—
1144C2×C4—24no—
1145C2×C4—24no—
1146C2×C4—22no—
1147C2×C4—24no—
1148C2×C4—24no—
1149C2×C4—22no—
1150C2×C4—24no—
1151C2×C4—24no—
1152C2×C4—22no—
1153C2×C4—24no—
1154C2×C4—22no—
1155C2×C4—22no—
1156C2×C4—22no—
1157C2×C4—24no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—24no—
1161C2×C4—22no—
1162C2×C4—24no—
1163C2×C4—24no—
1164C2×C4—24no—
1165C2×C4—22no—
1166C2×C4—24no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—24no—
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—24no—
1173C2×C4—22no—
1174C2×C4—22no—
1175C2×C4—24no—
1176C2×C4—22no—
1177C2×C4—22no—
1178C2×C4—24no—
1179C2×C4—22no—
1180C2×C4—24no—
1181C2×C4—22no—
1182C2×C4—48no—
1183C2×C4—44no—
1184C2×C4—48no—
1185C2×C4—88no—
1186C2×C4C2×2−1+414yes—
1187C2×C4C2×2−1+412yes—
1188C2×C4C2×2−1+412yes—
1189C2×C4C2×2−1+412yes—
1190C2×C4C2×2−1+412yes—
1191C2×C4#58512yes—
1192C22—42no—
1193C22—41no—
1194C22—42no—
1195C22—42no—
1196C22—42no—
1197C22—41no—
1198C22—42no—
1199C22—42no—
1200C22—42no—
1201C22—42no—
1202C22—42no—
1203C22—41no—
1204C22C22×2−1+411yescharacteristic
1205C22C22×2−1+411yescharacteristic
1206C22C2×#58511yescharacteristic
1207C22H(7,𝔽2)12yes—
1208C222−1+612yes—
1209C4—24no—
1210C4—22no—
1211C4—22no—
1212C4—41no—
1213C4—42no—
1214C4—42no—
1215C4—42no—
1216C4—44no—
1217C4—44no—
1218C4—42no—
1219C4—41no—
1220C4—42no—
1221C4—44no—
1222C4—44no—
1223C4—42no—
1224C4—42no—
1225C4—42no—
1226C4—44no—
1227C4—44no—
1228C4—44no—
1229C4—42no—
1230C4—44no—
1231C4—41no—
1232C4—42no—
1233C4#355514yes—
1234C2—81no—
1235C2—82no—
1236C2C2×#355511yescharacteristic
1237C2#6287712yes—
1238C2#6288111yescharacteristic
1239C2#6288412yes—
1240C2#6288911yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#392C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #58672C2semidirect
3. #58018C2semidirect
4. #57021C2semidirect
5. #56713C2semidirect
6. #55849C2semidirect
7. #54319C2semidirect
8. #54286C2semidirect
9. #53067C2semidirect
10. #52961C2semidirect
11. #45085C2semidirect
12. #44953C2semidirect
13. #42773C2semidirect
14. #42670C2semidirect
15. #42623C2semidirect
17. #39641C2semidirect
18. #39622C2semidirect
19. #39514C2semidirect
20. #39494C2semidirect
21. #37960C2semidirect
22. #37937C2semidirect
23. #37328C2semidirect
24. #37313C2semidirect
25. #35336C2semidirect
26. #35294C2semidirect

Maximal subgroups

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

subgroupindex
#587202
#586722
#580182
#570212
#567132
#558492
#543192
#542862
#530672
#529612
#450852
#449532
#427732
#426702
#426232
#424662
#396412
#396222
#395142
#394942
#379602
#379372
#373282
#373132
#353362
#352942
#346402