Finite Group Databasebeta

← #8467154

Subgroups — #8467154

Order 512.

3945 conjugacy classes of subgroups.

The subgroup lattice has 1525 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59871C211yesmaximal, characteristic, complemented
2#59426C211yesmaximal, characteristic
3#59426C211yesmaximal, characteristic
4#58690C214yesmaximal, complemented
5#55412C214yesmaximal, complemented
6#54069C214yesmaximal, complemented
7#53114C212yesmaximal
8#53091C212yesmaximal, complemented
9#50050C214yesmaximal, complemented
10#46343C212yesmaximal
11#45661C212yesmaximal, complemented
12#45426C212yesmaximal, complemented
13#45199C212yesmaximal, complemented
14#42738C212yesmaximal, complemented
15#42716C212yesmaximal, complemented
16#42698C212yesmaximal
17#42689C212yesmaximal, complemented
18#39983C212yesmaximal, complemented
19#39762C212yesmaximal, complemented
20#39762C211yesmaximal, characteristic, complemented
21#39626C211yesmaximal, characteristic, complemented
22#39181C211yesmaximal, characteristic, complemented
23#38978C211yesmaximal, characteristic
24#38239C212yesmaximal, complemented
25#38075C212yesmaximal, complemented
26#37638C211yesmaximal, characteristic, complemented
27#37353C212yesmaximal
28#37295C212yesmaximal, complemented
29#36574C211yesmaximal, characteristic, complemented
30#36416C211yesmaximal, characteristic
31#36312C211yesmaximal, characteristic
32#35208C211yesmaximal, characteristic, complemented
33#35177C211yesmaximal, characteristic
34#34950C211yesmaximal, characteristic, complemented
35#34945C211yesmaximal, characteristic
36#2863C2212yes—
37#2860C2212yes—
38#2859C2211yescharacteristic
39#2859C2211yescharacteristic
40#2859C2211yescharacteristic
41#2859C2212yes—
42#2857C2212yes—
43#2855C2212yes—
44#2851C2212yes—
45#2838C2214yes—
46#2838C2214yes—
47#2836C2214yes—
48#2834C2214yes—
49#2833C2214yes—
50#2833C2214yes—
51#2831C2214yes—
52#2821C2214yes—
53#2806C2214yes—
54#2806C2214yes—
55#2805C2214yes—
56#2792C2214yes—
57#2791C2214yes—
58#2789C2214yes—
59#2783C2214yes—
60#2777C2214yes—
61#2776C2214yes—
62#2776C2214yes—
63#2776C2214yes—
64#2776C2214yes—
65#2776C2214yes—
66#2776C2214yes—
67#2776C2214yes—
68#2774C2214yes—
69#2772C2214yes—
70#2769C2214yes—
71#2766C2214yes—
72#2765C2214yes—
73#2764C2214yes—
74#2762C2214yes—
75#2762C2214yes—
76#2762C2214yes—
77#2759C2214yes—
78#2759C2214yes—
79#2759C2214yes—
80#2759C2214yes—
81#2755C2214yes—
82#2755C2214yes—
83#2747C2214yes—
84#2745C2214yes—
85#2744C2214yes—
86#2742C2214yes—
87#2738C2214yes—
88#2729C2214yes—
89#2725C2214yes—
90#2725C2214yes—
91#2725C2214yes—
92#2722C2214yes—
93#2721C2214yes—
94#2720C2214yes—
95#2716C2214yes—
96#2713C2214yes—
97#2713C2214yes—
98#2704C2214yes—
99#2698C2214yes—
100#2689C2214yes—
101#2689C2214yes—
102#2666C2214yes—
103#2666C2214yes—
104#2665C2214yes—
105#2660C2212yes—
106#2655C2214yes—
107#2654C2214yes—
108#2650C2214yes—
109#2647C2212yes—
110#2647C2212yes—
111#2647C2212yes—
112#2645C2212yes—
113#2645C2212yes—
114#2644C2212yes—
115#2642C2214yes—
116#2642C2212yes—
117#2634C2214yes—
118#2605C2214yes—
119#2592C2212yes—
120#2592C2212yes—
121#2589C2214yes—
122#2588C2214yes—
123#2587C2214yes—
124#2586C2212yes—
125#2586C2212yes—
126#2584C2212yes—
127#2584C2214yes—
128#2584C2212yes—
129#2582C2211yescharacteristic
130#2582C2212yes—
131#2582C2211yescharacteristic
132#2582C2212yes—
133#2582C2212yes—
134#2582C2211yescharacteristic
135#2581C2212yes—
136#2581C2212yes—
137#2580C2212yes—
138#2573C2212yes—
139#2573C2212yes—
140#2571C2211yescharacteristic
141#2571C2211yescharacteristic
142#2570C2212yes—
143#2568C2211yescharacteristic
144#2567C2211yescharacteristic
145#2567C2211yescharacteristic
146#2567C2212yes—
147#2567C2211yescharacteristic
148#2567C2211yescharacteristic
149#2567C2211yescharacteristic
150#2566C2212yes—
151#2563C2211yescharacteristic
152#2552C2211yescharacteristic
153#2552C2212yes—
154#2552C2212yes—
155#2552C2212yes—
156#2551C2212yes—
157#2551C2211yescharacteristic
158#2551C2211yescharacteristic
159#2550C2214yes—
160#2550C2212yes—
161#2547C2211yescharacteristic
162#2546C2212yes—
163#2538C2211yescharacteristic
164#2538C2211yescharacteristic
165#2533C2214yes—
166#2529C2214yes—
167#2525C2214yes—
168#2524C2214yes—
169#2524C2214yes—
170#2520C2214yes—
171#2519C2214yes—
172#2514C2212yes—
173#2514C2212yes—
174#2514C2212yes—
175#2514C2212yes—
176#2514C2212yes—
177#2514C2214yes—
178#2514C2214yes—
179#2514C2212yes—
180#2514C2211yescharacteristic
181#2514C2212yes—
182#2514C2212yes—
183#2514C2214yes—
184#2514C2211yescharacteristic
185#2512C2212yes—
186#2512C2212yes—
187#2511C2212yes—
188#2509C2212yes—
189#2509C2212yes—
190#2509C2212yes—
191#2509C2212yes—
192#2509C2212yes—
193#2509C2212yes—
194#2509C2212yes—
195#2508C2212yes—
196#2508C2212yes—
197#2508C2212yes—
198#2507C2212yes—
199#2507C2212yes—
200#2507C2212yes—
201#2507C2212yes—
202#2507C2211yescharacteristic
203#2507C2211yescharacteristic
204#2507C2212yes—
205#2506C2212yes—
206#2506C2212yes—
207#2506C2212yes—
208#2506C2214yes—
209#2499C2212yes—
210#2497C2212yes—
211#2496C2212yes—
212#2496C2212yes—
213#2496C2212yes—
214#2495C2212yes—
215#2494C2212yes—
216#2494C2212yes—
217#2494C2212yes—
218#2492C2212yes—
219#2489C2212yes—
220#2469C2214yes—
221#2469C2214yes—
222#2465C2214yes—
223#2462C2214yes—
224#2453C2212yes—
225#2453C2212yes—
226#2453C2212yes—
227#2452C2212yes—
228#2451C2212yes—
229#2451C2212yes—
230#2451C2212yes—
231#2451C2211yescharacteristic
232#2451C2211yescharacteristic
233#2448C2212yes—
234#2448C2212yes—
235#2447C2211yescharacteristic
236#2447C2211yescharacteristic
237#2441C2212yes—
238#2441C2212yes—
239#2439C2212yes—
240#2439C2212yes—
241#2439C2212yes—
242#2423C2212yes—
243#2421C2212yes—
244#2401C2212yes—
245#2401C2212yes—
246#2399C2212yes—
247#2399C2212yes—
248#2383C2214yes—
249#2370C2212yes—
250#2370C2212yes—
251#2370C2212yes—
252#2369C2212yes—
253#2365C2212yes—
254#2362C2212yes—
255#2355C2211yescharacteristic
256#2355C2212yes—
257#2355C2211yescharacteristic
258#2355C2212yes—
259#2355C2212yes—
260#2354C2211yescharacteristic
261#2354C2211yescharacteristic
262#2351C2212yes—
263Q8×C4⋊C4C2211yescharacteristic
264Q8×C4⋊C4C2211yescharacteristic
265#2347C2212yes—
266#2347C2212yes—
267#2346C2212yes—
268#2331C2212yes—
269#2331C2212yes—
270#2331C2212yes—
271#2330C2214yes—
272#2330C2212yes—
273#2330C2212yes—
274#2320C2212yes—
275#2320C2212yes—
276#2319C2212yes—
277C4×C4⋊Q8C2211yescharacteristic
278C4×C4⋊Q8C2212yes—
279C4×C4⋊Q8C2211yescharacteristic
280C4×C4⋊Q8C2211yescharacteristic
281C4×C4⋊Q8C2211yescharacteristic
282C4×C4⋊Q8C2211yescharacteristic
283C4×C4⋊Q8C2211yescharacteristic
284C4×C4⋊Q8C2211yescharacteristic
285C4×#124C2211yescharacteristic
286C4×#124C2211yescharacteristic
287C4×C22⋊Q8C2212yes—
288#2296C2212yes—
289#2295C2211yescharacteristic
290#2295C2211yescharacteristic
291#2295C2211yescharacteristic
292#2295C2212yes—
293#2295C2211yescharacteristic
294#2295C2212yes—
295#2283C2212yes—
296C42×Q8C2211yescharacteristic
297C42×Q8C2211yescharacteristic
298C42×D4C2211yescharacteristic
299C2×C4⋊Q8C2311yescharacteristic
300C2×C4⋊Q8C2311yescharacteristic
301C2×C4⋊Q8C2311yescharacteristic
302C2×C4⋊Q8C2311yescharacteristic
303C2×C4⋊Q8C2311yescharacteristic
304C2×C4⋊Q8C2312yes—
305C2×C4⋊Q8C2312yes—
306C2×C4⋊Q8C2312yes—
307C2×C4⋊Q8C2314yes—
308C2×#126C2314yes—
309C2×#126C2314yes—
310C2×#126C2314yes—
311C2×#125C2312yes—
312C2×#125C2312yes—
313C2×#125C2312yes—
314C2×#125C2314yes—
315C2×#125C2314yes—
316C2×#125C2312yes—
317C2×#125C2314yes—
318C2×#124C2311yescharacteristic
319C2×#124C2311yescharacteristic
320C2×C22⋊Q8C2312yes—
321C2×C22⋊Q8C2312yes—
322C2×C22⋊Q8C2314yes—
323C2×C4×Q8C2311yescharacteristic
324C2×C4×Q8C2311yescharacteristic
325C2×C4×Q8C2311yescharacteristic
326C2×C4×Q8C2311yescharacteristic
327C2×C4×Q8C2311yescharacteristic
328C2×C4×Q8C2312yes—
329C2×C4×Q8C2312yes—
330C2×C4×Q8C2312yes—
331C2×C4×Q8C2312yes—
332C2×C4×Q8C2311yescharacteristic
333C2×C4×Q8C2311yescharacteristic
334C2×C4×Q8C2312yes—
335C2×C4×Q8C2311yescharacteristic
336C2×C4×Q8C2312yes—
337C2×C4×Q8C2312yes—
338C2×C4×Q8C2312yes—
339C2×C4×D4C2311yescharacteristic
340C2×C4×D4C2311yescharacteristic
341C2×C4×D4C2311yescharacteristic
342C2×#117C2312yes—
343C2×#117C2312yes—
344C22×C42C2312yes—
345#401C2312yes—
346#401C2314yes—
347#401C2314yes—
348#401C2314yes—
349#401C2314yes—
350#401C2314yes—
351#401C2312yes—
352#401C2314yes—
353#400C2314yes—
354#400C2314yes—
355#400C2312yes—
356#400C2312yes—
357#400C2314yes—
358#400C2312yes—
359#400C2312yes—
360#400C2314yes—
361#400C2314yes—
362#400C2314yes—
363#400C2314yes—
364#400C2314yes—
365#400C2314yes—
366#400C2314yes—
367#400C2314yes—
368#400C2314yes—
369#400C2314yes—
370#400C2314yes—
371#400C2314yes—
372#400C2314yes—
373#400C2314yes—
374#400C2314yes—
375#400C2314yes—
376#400C2312yes—
377#400C2314yes—
378#400C2314yes—
379#400C2314yes—
380#400C2314yes—
381#400C2314yes—
382#400C2314yes—
383#400C2314yes—
384#400C2312yes—
385#400C2314yes—
386#400C2314yes—
387#400C2314yes—
388#399C2314yes—
389#399C2314yes—
390#399C2314yes—
391#398C2314yes—
392#398C2314yes—
393#398C2314yes—
394#398C2314yes—
395#398C2314yes—
396#398C2314yes—
397#398C2314yes—
398#398C2314yes—
399#398C2314yes—
400#398C2314yes—
401#398C2312yes—
402#398C2314yes—
403#398C2314yes—
404#398C2314yes—
405#398C2312yes—
406#398C2314yes—
407#398C2314yes—
408#398C2314yes—
409#398C2312yes—
410#398C2314yes—
411#398C2314yes—
412#398C2314yes—
413#398C2314yes—
414#398C2312yes—
415#398C2314yes—
416#398C2314yes—
417#398C2312yes—
418#398C2312yes—
419#398C2312yes—
420#398C2312yes—
421#398C2314yes—
422#398C2314yes—
423#398C2314yes—
424#397C2312yes—
425#397C2314yes—
426#397C2312yes—
427#397C2312yes—
428#397C2314yes—
429#397C2314yes—
430#397C2314yes—
431#397C2314yes—
432#397C2312yes—
433#397C2314yes—
434#397C2314yes—
435#397C2312yes—
436#397C2314yes—
437#397C2312yes—
438#397C2314yes—
439#396C2314yes—
440#396C2314yes—
441#396C2312yes—
442#396C2312yes—
443#396C2314yes—
444#396C2314yes—
445#396C2314yes—
446#396C2314yes—
447#396C2314yes—
448#395C2312yes—
449#395C2314yes—
450#395C2314yes—
451#395C2314yes—
452#395C2312yes—
453#395C2314yes—
454#395C2314yes—
455#395C2312yes—
456#395C2312yes—
457#395C2314yes—
458#395C2312yes—
459#395C2314yes—
460#395C2314yes—
461#395C2314yes—
462#395C2312yes—
463#395C2312yes—
464#395C2312yes—
465#395C2314yes—
466#393C2314yes—
467#393C2314yes—
468#393C2314yes—
469#393C2314yes—
470#393C2314yes—
471#391C2312yes—
472#391C2312yes—
473#391C2311yescharacteristic
474#391C2311yescharacteristic
475#391C2312yes—
476#391C2312yes—
477#391C2312yes—
478#391C2312yes—
479#391C2312yes—
480#391C2312yes—
481#391C2312yes—
482#391C2312yes—
483#391C2312yes—
484#391C2314yes—
485#391C2312yes—
486#391C2311yescharacteristic
487#391C2311yescharacteristic
488#391C2311yescharacteristic
489#391C2312yes—
490#391C2311yescharacteristic
491#391C2311yescharacteristic
492#391C2311yescharacteristic
493#391C2314yes—
494#391C2312yes—
495#391C2312yes—
496#391C2314yes—
497#391C2311yescharacteristic
498#391C2312yes—
499#391C2311yescharacteristic
500#391C2314yes—
501#391C2312yes—
502#391C2311yescharacteristic
503#391C2312yes—
504#391C2314yes—
505#391C2312yes—
506#391C2312yes—
507#391C2311yescharacteristic
508#391C2314yes—
509#391C2314yes—
510#391C2314yes—
511#391C2314yes—
512#391C2314yes—
513#391C2314yes—
514#391C2314yes—
515#390C2312yes—
516#390C2312yes—
517#390C2312yes—
518#390C2312yes—
519#390C2311yescharacteristic
520#390C2311yescharacteristic
521#389C2312yes—
522#389C2311yescharacteristic
523#389C2311yescharacteristic
524#389C2312yes—
525#389C2312yes—
526#389C2311yescharacteristic
527#389C2312yes—
528#389C2311yescharacteristic
529#389C2312yes—
530#389C2312yes—
531#389C2312yes—
532#389C2312yes—
533#389C2312yes—
534#389C2312yes—
535#389C2312yes—
536#389C2312yes—
537#389C2311yescharacteristic
538#389C2311yescharacteristic
539#389C2312yes—
540#389C2312yes—
541#389C2312yes—
542#389C2311yescharacteristic
543#389C2312yes—
544#389C2312yes—
545#389C2312yes—
546#389C2312yes—
547#389C2312yes—
548#389C2312yes—
549#389C2312yes—
550#389C2311yescharacteristic
551#389C2312yes—
552#389C2312yes—
553#389C2311yescharacteristic
554#389C2312yes—
555#389C2312yes—
556#389C2312yes—
557#389C2312yes—
558#389C2312yes—
559#389C2311yescharacteristic
560#389C2312yes—
561#389C2312yes—
562#389C2312yes—
563#389C2312yes—
564#389C2312yes—
565#389C2314yes—
566#389C2312yes—
567#389C2312yes—
568#389C2312yes—
569#389C2314yes—
570#389C2314yes—
571#389C2312yes—
572#389C2312yes—
573#389C2312yes—
574#389C2314yes—
575#389C2312yes—
576#389C2312yes—
577#389C2314yes—
578#389C2314yes—
579#389C2314yes—
580#389C2312yes—
581#389C2312yes—
582#389C2314yes—
583#389C2314yes—
584#389C2314yes—
585#389C2314yes—
586#389C2314yes—
587#389C2314yes—
588#389C2314yes—
589#389C2314yes—
590#389C2314yes—
591#389C2314yes—
592#389C2314yes—
593#389C2312yes—
594#389C2312yes—
595#389C2314yes—
596#389C2311yescharacteristic
597#389C2312yes—
598#389C2312yes—
599#389C2314yes—
600#389C2311yescharacteristic
601#389C2311yescharacteristic
602#389C2314yes—
603#389C2312yes—
604#389C2311yescharacteristic
605#388C2312yes—
606#388C2312yes—
607#388C2312yes—
608#388C2312yes—
609#388C2314yes—
610#388C2314yes—
611#388C2314yes—
612#388C2314yes—
613#388C2314yes—
614#388C2314yes—
615#388C2314yes—
616#388C2314yes—
617#388C2314yes—
618#388C2314yes—
619#388C2314yes—
620#388C2314yes—
621#388C2314yes—
622#388C2314yes—
623#388C2314yes—
624#388C2314yes—
625#388C2314yes—
626#387C2314yes—
627#387C2314yes—
628#387C2312yes—
629#387C2312yes—
630#387C2312yes—
631#387C2312yes—
632#387C2312yes—
633#387C2312yes—
634#387C2314yes—
635#387C2314yes—
636#387C2314yes—
637#387C2314yes—
638#387C2314yes—
639#387C2312yes—
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#387C2312yes—
654#387C2312yes—
655#387C2312yes—
656#387C2312yes—
657#387C2312yes—
658#387C2312yes—
659#387C2312yes—
660#387C2314yes—
661#387C2314yes—
662#387C2314yes—
663#387C2314yes—
664#387C2314yes—
665#387C2314yes—
666#387C2314yes—
667#387C2314yes—
668#387C2314yes—
669#387C2314yes—
670#387C2314yes—
671#387C2314yes—
672#387C2314yes—
673#387C2314yes—
674#387C2314yes—
675#387C2314yes—
676#387C2314yes—
677#387C2314yes—
678#387C2314yes—
679#387C2314yes—
680#387C2314yes—
681#387C2314yes—
682#387C2314yes—
683#387C2314yes—
684#387C2314yes—
685#385C2314yes—
686#385C2314yes—
687#385C2312yes—
688#385C2312yes—
689#385C2314yes—
690#385C2314yes—
691#385C2314yes—
692#384C2312yes—
693#384C2311yescharacteristic
694#384C2311yescharacteristic
695#384C2311yescharacteristic
696#384C2311yescharacteristic
697#384C2311yescharacteristic
698#384C2311yescharacteristic
699#384C2311yescharacteristic
700#384C2312yes—
701#384C2312yes—
702#384C2312yes—
703#384C2312yes—
704#384C2314yes—
705#384C2312yes—
706#384C2312yes—
707#383C2314yes—
708#383C2312yes—
709#383C2312yes—
710#383C2314yes—
711#383C2314yes—
712#383C2314yes—
713#383C2314yes—
714#383C2314yes—
715#383C2314yes—
716#382C2312yes—
717#382C2312yes—
718#382C2312yes—
719#382C2312yes—
720#382C2312yes—
721#382C2311yescharacteristic
722#382C2311yescharacteristic
723#382C2312yes—
724#382C2314yes—
725#382C2314yes—
726#382C2312yes—
727#382C2312yes—
728#382C2312yes—
729#382C2314yes—
730#382C2314yes—
731#382C2312yes—
732#381C2312yes—
733#381C2312yes—
734#381C2314yes—
735#380C2312yes—
736#380C2312yes—
737#380C2314yes—
738#380C2312yes—
739#380C2312yes—
740#380C2312yes—
741#380C2312yes—
742#380C2312yes—
743#380C2312yes—
744C4×C4⋊C4C2311yescharacteristic
745C4×C4⋊C4C2311yescharacteristic
746C4×C4⋊C4C2311yescharacteristic
747C4×C4⋊C4C2311yescharacteristic
748C4×C4⋊C4C2312yes—
749C4×C4⋊C4C2312yes—
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⋊C4C2311yescharacteristic
762C4×C4⋊C4C2312yes—
763C4×C4⋊C4C2311yescharacteristic
764C4×C4⋊C4C2311yescharacteristic
765C4×C4⋊C4C2311yescharacteristic
766C4×C4⋊C4C2312yes—
767C4×C4⋊C4C2312yes—
768C4×C4⋊C4C2311yescharacteristic
769C4×C4⋊C4C2311yescharacteristic
770C4×C4⋊C4C2311yescharacteristic
771C4×C4⋊C4C2312yes—
772C4×C4⋊C4C2314yes—
773C4×C4⋊C4C2311yescharacteristic
774C4×C4⋊C4C2314yes—
775C4×C4⋊C4C2314yes—
776C4×C4⋊C4C2312yes—
777C4×C4⋊C4C2312yes—
778C4×C4⋊C4C2311yescharacteristic
779C4×C4⋊C4C2312yes—
780C4×C4⋊C4C2312yes—
781C4×C4⋊C4C2312yes—
782C4×C4⋊C4C2314yes—
783C4×C4⋊C4C2314yes—
784C4×C4⋊C4C2314yes—
785C4×C4⋊C4C2312yes—
786C4×C4⋊C4C2311yescharacteristic
787C4×C4⋊C4C2314yes—
788C4×C4⋊C4C2311yescharacteristic
789C4×C4⋊C4C2311yescharacteristic
790C4×C4⋊C4C2312yes—
791C4×C4⋊C4C2312yes—
792C4×C4⋊C4C2312yes—
793C4×C4⋊C4C2311yescharacteristic
794C4×C22⋊C4C2312yes—
795C4×C22⋊C4C2312yes—
796C4×C22⋊C4C2312yes—
797C4×C22⋊C4C2312yes—
798C4×C22⋊C4C2312yes—
799C4×C22⋊C4C2312yes—
800C4×C22⋊C4C2312yes—
801#376C2312yes—
802#376C2312yes—
803#376C2312yes—
804#376C2314yes—
805#376C2312yes—
806C43C2311yescharacteristic
807C43C2311yescharacteristic
808C43C2311yescharacteristic
809C43C2312yes—
810C22×Q8C2411yescharacteristic
811C22×Q8C2411yescharacteristic
812C22×Q8C2411yescharacteristic
813C22×Q8C2411yescharacteristic
814C22×Q8C2412yes—
815C22×Q8C2412yes—
816C22×Q8C2412yes—
817C22×Q8C2412yes—
818C22×Q8C2414yes—
819C22×D4C2411yescharacteristic
820C23×C4C2412yes—
821C23×C4C2412yes—
822C23×C4C2412yes—
823C4⋊Q8—24no—
824C4⋊Q8—24no—
825C4⋊Q8—24no—
826C4⋊Q8—24no—
827C4⋊Q8—44no—
828C4⋊Q8—42no—
829C4⋊Q8—44no—
830C4⋊Q8—44no—
831C4⋊Q8—84no—
832#126—48no—
833#126—84no—
834#126—84no—
835#125—28no—
836#125—44no—
837#125—44no—
838#125—48no—
839#125—84no—
840#125—84no—
841#125—82no—
842#124—42no—
843#124—42no—
844C22⋊Q8—44no—
845C22⋊Q8—44no—
846C22⋊Q8—84no—
847C4×Q8—24no—
848C4×Q8—24no—
849C4×Q8—24no—
850C4×Q8—24no—
851C4×Q8—24no—
852C4×Q8—42no—
853C4×Q8—44no—
854C4×Q8—44no—
855C4×Q8—44no—
856C4×Q8—44no—
857C4×Q8—44no—
858C4×Q8—44no—
859C4×Q8—42no—
860C4×Q8—42no—
861C4×Q8—82no—
862C4×Q8—82no—
863C4×D4—24no—
864C4×D4—24no—
865C4×D4—42no—
866#117—28no—
867#117—44no—
868C2×C4⋊C4C2411yescharacteristic
869C2×C4⋊C4C2412yes—
870C2×C4⋊C4C2412yes—
871C2×C4⋊C4C2411yescharacteristic
872C2×C4⋊C4C2411yescharacteristic
873C2×C4⋊C4C2411yescharacteristic
874C2×C4⋊C4C2412yes—
875C2×C4⋊C4C2411yescharacteristic
876C2×C4⋊C4C2414yes—
877C2×C4⋊C4C2411yescharacteristic
878C2×C4⋊C4C2411yescharacteristic
879C2×C4⋊C4C2411yescharacteristic
880C2×C4⋊C4C2411yescharacteristic
881C2×C4⋊C4C2411yescharacteristic
882C2×C4⋊C4C2412yes—
883C2×C4⋊C4C2411yescharacteristic
884C2×C4⋊C4C2412yes—
885C2×C4⋊C4C2411yescharacteristic
886C2×C4⋊C4C2412yes—
887C2×C4⋊C4C2412yes—
888C2×C4⋊C4C2412yes—
889C2×C4⋊C4C2412yes—
890C2×C4⋊C4C2412yes—
891C2×C4⋊C4C2412yes—
892C2×C4⋊C4C2414yes—
893C2×C4⋊C4C2414yes—
894C2×C4⋊C4C2412yes—
895C2×C4⋊C4C2411yescharacteristic
896C2×C4⋊C4C2411yescharacteristic
897C2×C4⋊C4C2411yescharacteristic
898C2×C4⋊C4C2412yes—
899C2×C4⋊C4C2412yes—
900C2×C4⋊C4C2412yes—
901C2×C4⋊C4C2412yes—
902C2×C4⋊C4C2412yes—
903C2×C4⋊C4C2412yes—
904C2×C4⋊C4C2414yes—
905C2×C4⋊C4C2412yes—
906C2×C4⋊C4C2412yes—
907C2×C4⋊C4C2414yes—
908C2×C4⋊C4C2411yescharacteristic
909C2×C4⋊C4C2411yescharacteristic
910C2×C4⋊C4C2411yescharacteristic
911C2×C4⋊C4C2412yes—
912C2×C4⋊C4C2412yes—
913C2×C4⋊C4C2411yescharacteristic
914C2×C4⋊C4C2411yescharacteristic
915C2×C4⋊C4C2412yes—
916C2×C4⋊C4C2412yes—
917C2×C4⋊C4C2412yes—
918C2×C4⋊C4C2412yes—
919C2×C4⋊C4C2414yes—
920C2×C4⋊C4C2414yes—
921C2×C4⋊C4C2412yes—
922C2×C4⋊C4C2412yes—
923C2×C4⋊C4C2412yes—
924C2×C4⋊C4C2412yes—
925C2×C4⋊C4C2412yes—
926C2×C4⋊C4C2412yes—
927C2×C4⋊C4C2414yes—
928C2×C4⋊C4C2412yes—
929C2×C4⋊C4C2414yes—
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⋊C4C2412yes—
952C2×C4⋊C4C2414yes—
953C2×C4⋊C4C2412yes—
954C2×C4⋊C4C2412yes—
955C2×C4⋊C4C2412yes—
956C2×C4⋊C4C2412yes—
957C2×C4⋊C4C2414yes—
958C2×C4⋊C4C2414yes—
959C2×C4⋊C4C2411yescharacteristic
960C2×C22⋊C4C2414yes—
961C2×C22⋊C4C2412yes—
962C2×C22⋊C4C2412yes—
963C2×C22⋊C4C2412yes—
964C2×C22⋊C4C2414yes—
965C2×C22⋊C4C2412yes—
966C2×C22⋊C4C2414yes—
967C2×C22⋊C4C2414yes—
968C2×C22⋊C4C2412yes—
969C2×C22⋊C4C2414yes—
970C2×C22⋊C4C2412yes—
971C2×C22⋊C4C2412yes—
972C2×C22⋊C4C2412yes—
973C2×C22⋊C4C2412yes—
974C2×C22⋊C4C2412yes—
975C2×C22⋊C4C2412yes—
976C2×C22⋊C4C2414yes—
977C2×C22⋊C4C2414yes—
978C2×C22⋊C4C2414yes—
979C2×C42—44no—
980C2×C42C2414yes—
981C2×C42C2411yescharacteristic
982C2×C42C2412yes—
983C2×C42C2411yescharacteristic
984C2×C42C2412yes—
985C2×C42C2411yescharacteristic
986C2×C42C2411yescharacteristic
987C2×C42C2411yescharacteristic
988C2×C42C2412yes—
989C2×C42C2411yescharacteristic
990C2×C42C2411yescharacteristic
991C2×C42C2411yescharacteristic
992C2×C42C2412yes—
993C2×C42C2411yescharacteristic
994C2×C42C2412yes—
995C2×C42C2411yescharacteristic
996C2×C42C2412yes—
997C2×C42C2412yes—
998C2×C42C2412yes—
999C2×C42C2412yes—
1000C2×C42C2411yescharacteristic
1001C2×C42C2411yescharacteristic
1002C2×C42C2414yes—
1003C2×C42C2411yescharacteristic
1004C2×C42C2411yescharacteristic
1005C2×C42C2414yes—
1006C2×C42C2414yes—
1007C2×C42C2411yescharacteristic
1008C2×C42C2412yes—
1009C2×C42C2411yescharacteristic
1010C2×C42C2414yes—
1011C2×C42C2414yes—
1012C2×C42C2414yes—
1013C2×C42C2411yescharacteristic
1014C2×C42C2412yes—
1015C2×C42C2414yes—
1016C2×C42C2414yes—
1017C2×C42C2412yes—
1018C2×C42C2412yes—
1019C2×C42C2411yescharacteristic
1020C2×C42C2411yescharacteristic
1021#95C2412yes—
1022#95C2412yes—
1023#95C2412yes—
1024#95C2414yes—
1025#95C2412yes—
1026#95C2412yes—
1027#95C2412yes—
1028#95C2412yes—
1029#95C2412yes—
1030#95C2412yes—
1031#95C2412yes—
1032#95C2412yes—
1033#95C2412yes—
1034#95C2414yes—
1035#95C2412yes—
1036#95C2412yes—
1037#95C2412yes—
1038#95C2412yes—
1039#95C2412yes—
1040#95C2414yes—
1041#95C2412yes—
1042#95C2412yes—
1043#95C2412yes—
1044#95C2412yes—
1045#95C2412yes—
1046#95C2412yes—
1047#95C2412yes—
1048#95C2412yes—
1049#95C2412yes—
1050#95C2412yes—
1051#95C2411yescharacteristic
1052#95C2411yescharacteristic
1053#95C2411yescharacteristic
1054#95C2412yes—
1055#95C2412yes—
1056#95C2411yescharacteristic
1057#95C2411yescharacteristic
1058#95C2412yes—
1059#95C2412yes—
1060#95C2411yescharacteristic
1061#95C2414yes—
1062#95C2414yes—
1063#95C2414yes—
1064#95C2414yes—
1065#95C2412yes—
1066#95C2414yes—
1067#95C2412yes—
1068#95C2412yes—
1069#95C2412yes—
1070#95C2414yes—
1071#95C2414yes—
1072#95C2414yes—
1073#95C2414yes—
1074#95C2414yes—
1075#95C2414yes—
1076#95C2414yes—
1077#95C2412yes—
1078#95C2414yes—
1079#95C2412yes—
1080#95C2412yes—
1081#95C2412yes—
1082#95C2414yes—
1083#95C2412yes—
1084#95C2412yes—
1085#95C2414yes—
1086#95C2414yes—
1087#95C2414yes—
1088#95C2414yes—
1089#95C2414yes—
1090#95C2412yes—
1091#95C2412yes—
1092#95C2412yes—
1093#95C2412yes—
1094#95C2412yes—
1095#95C2414yes—
1096#95C2412yes—
1097#95C2412yes—
1098#95C2414yes—
1099#95C2414yes—
1100#95C2412yes—
1101#95C2412yes—
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—
1119C24C2512yes—
1120C2×Q8—22no—
1121C2×Q8—22no—
1122C2×Q8—22no—
1123C2×Q8—22no—
1124C2×Q8—22no—
1125C2×Q8—24no—
1126C2×Q8—22no—
1127C2×Q8—22no—
1128C2×Q8—24no—
1129C2×Q8—24no—
1130C2×Q8—22no—
1131C2×Q8—22no—
1132C2×Q8—22no—
1133C2×Q8—22no—
1134C2×Q8—41no—
1135C2×Q8—42no—
1136C2×Q8—42no—
1137C2×Q8—42no—
1138C2×Q8—42no—
1139C2×Q8—42no—
1140C2×Q8—42no—
1141C2×Q8—42no—
1142C2×Q8—42no—
1143C2×Q8—42no—
1144C2×Q8—44no—
1145C2×Q8—44no—
1146C2×Q8—44no—
1147C2×D4—22no—
1148C2×D4—22no—
1149C2×D4—22no—
1150C22×C4—24no—
1151C22×C4—24no—
1152C22×C4—24no—
1153C22×C4—24no—
1154C22×C4—42no—
1155C22×C4—42no—
1156C22×C4—42no—
1157C22×C4—42no—
1158C22×C4—42no—
1159C22×C4C2512yes—
1160C22×C4C2512yes—
1161C22×C4C2512yes—
1162C22×C4C2512yes—
1163C22×C4C2511yescharacteristic
1164C22×C4C2511yescharacteristic
1165C22×C4C2511yescharacteristic
1166C22×C4C2514yes—
1167C22×C4C2511yescharacteristic
1168C22×C4C2511yescharacteristic
1169C22×C4C2512yes—
1170C22×C4C2512yes—
1171C22×C4C2512yes—
1172C22×C4C2511yescharacteristic
1173C22×C4C2514yes—
1174C22×C4C2514yes—
1175C22×C4C2512yes—
1176C22×C4C2512yes—
1177C22×C4C2511yescharacteristic
1178C22×C4C2512yes—
1179C22×C4C2512yes—
1180C22×C4C2512yes—
1181C22×C4C2511yescharacteristic
1182C22×C4C2512yes—
1183C22×C4C2514yes—
1184C22×C4C2511yescharacteristic
1185C22×C4C2512yes—
1186C22×C4C2511yescharacteristic
1187C22×C4C2512yes—
1188C22×C4C2511yescharacteristic
1189C22×C4C2511yescharacteristic
1190C22×C4C2511yescharacteristic
1191C22×C4C2511yescharacteristic
1192C22×C4C2511yescharacteristic
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—24no—
1202C4⋊C4—22no—
1203C4⋊C4—24no—
1204C4⋊C4—24no—
1205C4⋊C4—24no—
1206C4⋊C4—28no—
1207C4⋊C4—28no—
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—24no—
1218C4⋊C4—22no—
1219C4⋊C4—24no—
1220C4⋊C4—22no—
1221C4⋊C4—24no—
1222C4⋊C4—22no—
1223C4⋊C4—28no—
1224C4⋊C4—22no—
1225C4⋊C4—24no—
1226C4⋊C4—24no—
1227C4⋊C4—24no—
1228C4⋊C4—22no—
1229C4⋊C4—41no—
1230C4⋊C4—42no—
1231C4⋊C4—42no—
1232C4⋊C4—42no—
1233C4⋊C4—41no—
1234C4⋊C4—41no—
1235C4⋊C4—41no—
1236C4⋊C4—42no—
1237C4⋊C4—42no—
1238C4⋊C4—42no—
1239C4⋊C4—41no—
1240C4⋊C4—42no—
1241C4⋊C4—42no—
1242C4⋊C4—42no—
1243C4⋊C4—42no—
1244C4⋊C4—44no—
1245C4⋊C4—44no—
1246C4⋊C4—42no—
1247C4⋊C4—44no—
1248C4⋊C4—42no—
1249C4⋊C4—42no—
1250C4⋊C4—44no—
1251C4⋊C4—42no—
1252C4⋊C4—44no—
1253C4⋊C4—42no—
1254C4⋊C4—42no—
1255C4⋊C4—44no—
1256C4⋊C4—44no—
1257C4⋊C4—44no—
1258C4⋊C4—44no—
1259C4⋊C4—44no—
1260C4⋊C4—44no—
1261C4⋊C4—44no—
1262C4⋊C4—44no—
1263C4⋊C4—44no—
1264C4⋊C4—42no—
1265C4⋊C4—42no—
1266C4⋊C4—42no—
1267C4⋊C4—42no—
1268C4⋊C4—44no—
1269C4⋊C4—44no—
1270C4⋊C4—44no—
1271C4⋊C4—44no—
1272C4⋊C4—44no—
1273C4⋊C4—44no—
1274C4⋊C4—44no—
1275C4⋊C4—44no—
1276C4⋊C4—44no—
1277C4⋊C4—42no—
1278C4⋊C4—42no—
1279C4⋊C4—44no—
1280C4⋊C4—42no—
1281C4⋊C4—42no—
1282C4⋊C4—44no—
1283C4⋊C4—42no—
1284C4⋊C42−1+414yes—
1285C22⋊C4—28no—
1286C22⋊C4—24no—
1287C22⋊C4—24no—
1288C22⋊C4—24no—
1289C22⋊C4—44no—
1290C22⋊C4—42no—
1291C22⋊C4—42no—
1292C22⋊C4—44no—
1293C22⋊C4—44no—
1294C22⋊C4—44no—
1295C22⋊C4—42no—
1296C22⋊C4—42no—
1297C22⋊C4—42no—
1298C22⋊C4—42no—
1299C22⋊C4—44no—
1300C22⋊C4—44no—
1301C22⋊C4—42no—
1302C22⋊C4—42no—
1303C22⋊C4—44no—
1304C42—28no—
1305C42—22no—
1306C42—22no—
1307C42—24no—
1308C42—24no—
1309C42—24no—
1310C42—24no—
1311C42—22no—
1312C42—22no—
1313C42—22no—
1314C42—22no—
1315C42—24no—
1316C42—22no—
1317C42—22no—
1318C42—24no—
1319C42—24no—
1320C42—22no—
1321C42—22no—
1322C42—22no—
1323C42—24no—
1324C42—22no—
1325C42—24no—
1326C42—42no—
1327C42—42no—
1328C42—44no—
1329C42—42no—
1330C42—41no—
1331C42—44no—
1332C42—41no—
1333C42—44no—
1334C42—44no—
1335C42—41no—
1336C42—41no—
1337C42—44no—
1338C42—44no—
1339C42—41no—
1340C42—44no—
1341C42—42no—
1342C42—44no—
1343C422−1+414yes—
1344C422−1+414yes—
1345C23—22no—
1346C23—22no—
1347C23—22no—
1348C23—22no—
1349C23—22no—
1350C23—22no—
1351C23—22no—
1352C23C2611yescharacteristic
1353Q8—44no—
1354Q8—48no—
1355Q8—44no—
1356Q8—44no—
1357Q8—44no—
1358Q8—84no—
1359Q8—84no—
1360Q8—84no—
1361Q8—164no—
1362D4—44no—
1363C2×C4—21no—
1364C2×C4—21no—
1365C2×C4—21no—
1366C2×C4—22no—
1367C2×C4—21no—
1368C2×C4—21no—
1369C2×C4—22no—
1370C2×C4—21no—
1371C2×C4—21no—
1372C2×C4—21no—
1373C2×C4—21no—
1374C2×C4—22no—
1375C2×C4—24no—
1376C2×C4—21no—
1377C2×C4—22no—
1378C2×C4—22no—
1379C2×C4—22no—
1380C2×C4—21no—
1381C2×C4—21no—
1382C2×C4—21no—
1383C2×C4—22no—
1384C2×C4—22no—
1385C2×C4—22no—
1386C2×C4—22no—
1387C2×C4—21no—
1388C2×C4—21no—
1389C2×C4—21no—
1390C2×C4—22no—
1391C2×C4—22no—
1392C2×C4—24no—
1393C2×C4—24no—
1394C2×C4—22no—
1395C2×C4—22no—
1396C2×C4—22no—
1397C2×C4—22no—
1398C2×C4—24no—
1399C2×C4—21no—
1400C2×C4—22no—
1401C2×C4—21no—
1402C2×C4—22no—
1403C2×C4—22no—
1404C2×C4—21no—
1405C2×C4—21no—
1406C2×C4—21no—
1407C2×C4—21no—
1408C2×C4—21no—
1409C2×C4—22no—
1410C2×C4—22no—
1411C2×C4—21no—
1412C2×C4—22no—
1413C2×C4—21no—
1414C2×C4—22no—
1415C2×C4—21no—
1416C2×C4—21no—
1417C2×C4—22no—
1418C2×C4—22no—
1419C2×C4—22no—
1420C2×C4—22no—
1421C2×C4—22no—
1422C2×C4—22no—
1423C2×C4—22no—
1424C2×C4—24no—
1425C2×C4—24no—
1426C2×C4—22no—
1427C2×C4—21no—
1428C2×C4—24no—
1429C2×C4—24no—
1430C2×C4—22no—
1431C2×C4—21no—
1432C2×C4—21no—
1433C2×C4—22no—
1434C2×C4—22no—
1435C2×C4—24no—
1436C2×C4—22no—
1437C2×C4—22no—
1438C2×C4—22no—
1439C2×C4—21no—
1440C2×C4—21no—
1441C2×C4—22no—
1442C2×C4—22no—
1443C2×C4—24no—
1444C2×C4—24no—
1445C2×C4—22no—
1446C2×C4—22no—
1447C2×C4—21no—
1448C2×C4—24no—
1449C2×C4—21no—
1450C2×C4—21no—
1451C2×C4—22no—
1452C2×C4—22no—
1453C2×C4—22no—
1454C2×C4—48no—
1455C2×C4—84no—
1456C2×C4—84no—
1457C2×C4C2×2−1+414yes—
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×C4C2×2−1+412yes—
1464C2×C4C2×2−1+412yes—
1465C2×C4#58512yes—
1466C2×C4#58512yes—
1467C2×C4#58512yes—
1468C22—42no—
1469C22—42no—
1470C22—42no—
1471C22—42no—
1472C22—42no—
1473C22—42no—
1474C22—42no—
1475C22C22×2−1+411yescharacteristic
1476C22C22×2−1+411yescharacteristic
1477C22C22×2−1+411yescharacteristic
1478C22C2×#58511yescharacteristic
1479C22C2×#58511yescharacteristic
1480C22C2×#58511yescharacteristic
1481C22H(7,𝔽2)11yescharacteristic
1482C4—24no—
1483C4—22no—
1484C4—22no—
1485C4—22no—
1486C4—22no—
1487C4—42no—
1488C4—42no—
1489C4—42no—
1490C4—42no—
1491C4—41no—
1492C4—42no—
1493C4—42no—
1494C4—41no—
1495C4—41no—
1496C4—44no—
1497C4—42no—
1498C4—41no—
1499C4—42no—
1500C4—42no—
1501C4—42no—
1502C4—44no—
1503C4—41no—
1504C4—42no—
1505C4—41no—
1506C4—42no—
1507C4—42no—
1508C4—41no—
1509C4—42no—
1510C4—44no—
1511C4—41no—
1512C4—44no—
1513C4—41no—
1514C4#355514yes—
1515C4#355514yes—
1516C2—82no—
1517C2C2×#355511yescharacteristic
1518C2C2×#355511yescharacteristic
1519C2#6283111yescharacteristic
1520C2#6292611yescharacteristic
1521C2#6293711yescharacteristic
1522C2#6294311yescharacteristic
1523C2#6302511yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC22×D4C24
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59871C2semidirect
4. #58690C2semidirect
5. #55412C2semidirect
6. #54069C2semidirect
8. #53091C2semidirect
9. #50050C2semidirect
11. #45661C2semidirect
12. #45426C2semidirect
13. #45199C2semidirect
14. #42738C2semidirect
15. #42716C2semidirect
17. #42689C2semidirect
18. #39983C2semidirect
19. #39762C2semidirect
20. #39762C2semidirect
21. #39626C2semidirect
22. #39181C2semidirect
24. #38239C2semidirect
25. #38075C2semidirect
26. #37638C2semidirect
28. #37295C2semidirect
29. #36574C2semidirect
32. #35208C2semidirect
34. #34950C2semidirect

Maximal subgroups

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

subgroupindex
#598712
#594262
#586902
#554122
#540692
#531142
#530912
#500502
#463432
#456612
#454262
#451992
#427382
#427162
#426982
#426892
#399832
#397622
#396262
#391812
#389782
#382392
#380752
#376382
#373532
#372952
#365742
#364162
#363122
#352082
#351772
#349502
#349452