Finite Group Databasebeta

← #8174410

Subgroups — #8174410

Order 512.

3841 conjugacy classes of subgroups.

The subgroup lattice has 1501 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59262C211yesmaximal, characteristic
2#59259C211yesmaximal, characteristic
3#59249C211yesmaximal, characteristic
4#59242C211yesmaximal, characteristic
5#58672C214yesmaximal
6#58563C214yesmaximal, complemented
7#56689C214yesmaximal
8#55142C214yesmaximal, complemented
9#53131C212yesmaximal, complemented
10#53107C212yesmaximal
11#53086C212yesmaximal
12#53028C212yesmaximal
13#45339C212yesmaximal
14#45154C212yesmaximal, complemented
15#42854C212yesmaximal
16#42824C212yesmaximal, complemented
17#42774C212yesmaximal, complemented
18#42710C212yesmaximal, complemented
19#42562C212yesmaximal
20#42553C212yesmaximal, complemented
21#39802C212yesmaximal, complemented
22#39754C211yesmaximal, characteristic, complemented
23#39753C211yesmaximal, characteristic, complemented
24#39637C212yesmaximal, complemented
25#39635C211yesmaximal, characteristic, complemented
26#39635C211yesmaximal, characteristic, complemented
27#39180C211yesmaximal, characteristic, complemented
28#38976C211yesmaximal, characteristic, complemented
29#37592C212yesmaximal
30#37397C212yesmaximal
31#36598C211yesmaximal, characteristic, complemented
32Q8×#125C211yesmaximal, characteristic, complemented
33#35294C211yesmaximal, characteristic
34#34916C211yesmaximal, characteristic
35#34629C211yesmaximal, characteristic
36#2868C2211yescharacteristic
37#2862C2212yes—
38#2859C2211yescharacteristic
39#2859C2212yes—
40#2859C2211yescharacteristic
41#2859C2211yescharacteristic
42#2843C2214yes—
43#2839C2214yes—
44#2839C2214yes—
45#2839C2214yes—
46#2839C2214yes—
47#2839C2214yes—
48#2838C2214yes—
49#2836C2214yes—
50#2836C2214yes—
51#2836C2214yes—
52#2831C2214yes—
53#2822C2214yes—
54#2809C2214yes—
55#2806C2214yes—
56#2805C2214yes—
57#2802C2214yes—
58#2802C2214yes—
59#2802C2214yes—
60#2802C2214yes—
61#2802C2214yes—
62#2802C2214yes—
63#2798C2214yes—
64#2798C2214yes—
65#2794C2214yes—
66#2794C2214yes—
67#2793C2214yes—
68#2791C2214yes—
69#2791C2214yes—
70#2789C2214yes—
71#2787C2214yes—
72#2777C2214yes—
73#2776C2214yes—
74#2774C2214yes—
75#2774C2214yes—
76#2773C2214yes—
77#2773C2214yes—
78#2769C2214yes—
79#2769C2214yes—
80#2769C2214yes—
81#2768C2214yes—
82#2767C2214yes—
83#2767C2214yes—
84#2767C2214yes—
85#2767C2214yes—
86#2766C2214yes—
87#2766C2214yes—
88#2766C2214yes—
89#2762C2214yes—
90#2758C2214yes—
91#2755C2214yes—
92#2755C2214yes—
93#2755C2214yes—
94#2726C2214yes—
95#2726C2214yes—
96#2725C2214yes—
97#2721C2214yes—
98#2719C2214yes—
99#2719C2214yes—
100#2719C2214yes—
101#2713C2214yes—
102#2666C2214yes—
103#2660C2212yes—
104#2660C2212yes—
105#2655C2214yes—
106#2655C2214yes—
107#2655C2212yes—
108#2655C2212yes—
109#2655C2214yes—
110#2652C2212yes—
111#2652C2212yes—
112#2650C2214yes—
113#2647C2212yes—
114#2647C2214yes—
115#2647C2212yes—
116#2647C2211yescharacteristic
117#2647C2212yes—
118#2645C2211yescharacteristic
119#2645C2212yes—
120#2645C2211yescharacteristic
121#2642C2211yescharacteristic
122#2637C2214yes—
123#2634C2214yes—
124#2629C2212yes—
125#2629C2211yescharacteristic
126#2628C2212yes—
127#2625C2211yescharacteristic
128#2625C2211yescharacteristic
129#2621C2211yescharacteristic
130#2611C2214yes—
131#2605C2214yes—
132#2590C2212yes—
133#2589C2212yes—
134#2588C2212yes—
135#2588C2214yes—
136#2587C2212yes—
137#2585C2214yes—
138#2585C2214yes—
139#2585C2214yes—
140#2584C2212yes—
141#2584C2212yes—
142#2582C2212yes—
143#2582C2211yescharacteristic
144#2582C2211yescharacteristic
145#2582C2211yescharacteristic
146#2582C2211yescharacteristic
147#2581C2212yes—
148#2571C2212yes—
149#2571C2212yes—
150#2571C2211yescharacteristic
151#2571C2212yes—
152#2570C2212yes—
153#2570C2214yes—
154#2570C2212yes—
155#2570C2212yes—
156#2570C2212yes—
157#2568C2212yes—
158#2565C2212yes—
159#2565C2212yes—
160#2552C2212yes—
161#2552C2211yescharacteristic
162#2552C2211yescharacteristic
163#2552C2212yes—
164#2552C2212yes—
165#2552C2211yescharacteristic
166#2552C2212yes—
167#2550C2212yes—
168#2550C2212yes—
169#2550C2212yes—
170#2550C2212yes—
171#2528C2214yes—
172#2528C2214yes—
173#2524C2214yes—
174#2524C2214yes—
175#2524C2214yes—
176#2519C2214yes—
177#2514C2212yes—
178#2514C2212yes—
179#2514C2212yes—
180#2511C2212yes—
181#2511C2212yes—
182#2511C2212yes—
183#2511C2212yes—
184#2511C2211yescharacteristic
185#2511C2212yes—
186#2511C2212yes—
187#2511C2212yes—
188#2511C2212yes—
189#2509C2212yes—
190#2508C2212yes—
191#2508C2212yes—
192#2508C2212yes—
193#2507C2212yes—
194#2507C2212yes—
195#2507C2212yes—
196#2507C2214yes—
197#2507C2212yes—
198#2507C2212yes—
199#2507C2212yes—
200#2507C2211yescharacteristic
201#2507C2214yes—
202#2507C2212yes—
203#2506C2212yes—
204#2506C2212yes—
205#2506C2214yes—
206#2506C2212yes—
207#2506C2212yes—
208#2506C2212yes—
209#2506C2212yes—
210#2499C2212yes—
211#2497C2211yescharacteristic
212#2497C2212yes—
213#2496C2212yes—
214#2496C2212yes—
215#2495C2212yes—
216#2495C2212yes—
217#2495C2212yes—
218#2492C2211yescharacteristic
219#2489C2212yes—
220#2489C2212yes—
221#2478C2214yes—
222#2453C2212yes—
223#2453C2212yes—
224#2453C2212yes—
225#2453C2212yes—
226#2453C2212yes—
227#2453C2212yes—
228#2453C2214yes—
229#2453C2214yes—
230#2451C2212yes—
231#2451C2211yescharacteristic
232#2446C2212yes—
233#2446C2211yescharacteristic
234#2446C2214yes—
235#2441C2212yes—
236#2441C2212yes—
237#2441C2212yes—
238#2439C2212yes—
239#2439C2212yes—
240#2429C2211yescharacteristic
241#2423C2212yes—
242#2423C2212yes—
243#2423C2211yescharacteristic
244#2423C2212yes—
245#2421C2212yes—
246#2402C2212yes—
247#2402C2212yes—
248#2402C2212yes—
249#2401C2212yes—
250#2401C2212yes—
251#2396C2212yes—
252#2370C2212yes—
253#2370C2212yes—
254#2365C2212yes—
255#2362C2212yes—
256#2356C2212yes—
257#2356C2212yes—
258#2355C2211yescharacteristic
259#2355C2212yes—
260#2355C2212yes—
261#2355C2211yescharacteristic
262#2355C2211yescharacteristic
263#2355C2212yes—
264Q8×C4⋊C4C2211yescharacteristic
265Q8×C4⋊C4C2212yes—
266Q8×C4⋊C4C2211yescharacteristic
267Q8×C4⋊C4C2212yes—
268Q8×C4⋊C4C2211yescharacteristic
269Q8×C4⋊C4C2211yescharacteristic
270Q8×C4⋊C4C2211yescharacteristic
271#2347C2212yes—
272#2331C2212yes—
273#2331C2212yes—
274#2330C2212yes—
275#2330C2212yes—
276#2330C2212yes—
277#2327C2212yes—
278#2327C2212yes—
279#2320C2212yes—
280C4×C4⋊Q8C2211yescharacteristic
281C4×C4⋊Q8C2211yescharacteristic
282C4×C4⋊Q8C2211yescharacteristic
283C4×C4⋊Q8C2212yes—
284C4×#125C2211yescharacteristic
285C4×#125C2212yes—
286C4×C22⋊Q8C2211yescharacteristic
287C4×C22⋊Q8C2211yescharacteristic
288C4×C22⋊Q8C2211yescharacteristic
289C4×C22⋊Q8C2211yescharacteristic
290#2298C2212yes—
291#2295C2211yescharacteristic
292#2295C2211yescharacteristic
293#2295C2211yescharacteristic
294#2295C2212yes—
295#2285C2211yescharacteristic
296#2285C2211yescharacteristic
297C42×Q8C2211yescharacteristic
298C4×#117C2211yescharacteristic
299C2×C4⋊Q8C2311yescharacteristic
300C2×C4⋊Q8C2311yescharacteristic
301C2×C4⋊Q8C2312yes—
302C2×C4⋊Q8C2311yescharacteristic
303C2×C4⋊Q8C2312yes—
304C2×C4⋊Q8C2312yes—
305C2×#126C2314yes—
306C2×#125C2311yescharacteristic
307C2×#125C2312yes—
308C2×#125C2312yes—
309C2×#125C2312yes—
310C2×#125C2312yes—
311C2×#125C2312yes—
312C2×#125C2314yes—
313C2×#125C2314yes—
314C2×#125C2312yes—
315C2×#125C2314yes—
316C2×#125C2314yes—
317C2×C22⋊Q8C2311yescharacteristic
318C2×C22⋊Q8C2311yescharacteristic
319C2×C22⋊Q8C2311yescharacteristic
320C2×C22⋊Q8C2311yescharacteristic
321C2×C4×Q8C2311yescharacteristic
322C2×C4×Q8C2311yescharacteristic
323C2×C4×Q8C2311yescharacteristic
324C2×C4×Q8C2311yescharacteristic
325C2×C4×Q8C2312yes—
326C2×C4×Q8C2311yescharacteristic
327C2×C4×Q8C2312yes—
328C2×C4×Q8C2312yes—
329C2×C4×Q8C2312yes—
330C2×C4×Q8C2311yescharacteristic
331C2×C4×Q8C2312yes—
332C2×C4×Q8C2312yes—
333C2×C4×Q8C2314yes—
334C2×#117C2311yescharacteristic
335C2×#117C2312yes—
336C2×#117C2311yescharacteristic
337C2×#117C2312yes—
338C22×C42C2311yescharacteristic
339#401C2314yes—
340#401C2312yes—
341#401C2312yes—
342#401C2314yes—
343#400C2314yes—
344#400C2314yes—
345#400C2314yes—
346#400C2314yes—
347#400C2314yes—
348#400C2314yes—
349#400C2314yes—
350#400C2314yes—
351#400C2314yes—
352#400C2314yes—
353#400C2314yes—
354#400C2314yes—
355#400C2314yes—
356#400C2314yes—
357#400C2314yes—
358#400C2314yes—
359#400C2314yes—
360#400C2314yes—
361#400C2314yes—
362#400C2314yes—
363#400C2314yes—
364#400C2314yes—
365#400C2312yes—
366#400C2312yes—
367#400C2312yes—
368#400C2312yes—
369#400C2314yes—
370#400C2312yes—
371#400C2312yes—
372#400C2314yes—
373#400C2314yes—
374#400C2314yes—
375#400C2314yes—
376#400C2314yes—
377#400C2314yes—
378#400C2314yes—
379#400C2314yes—
380#400C2312yes—
381#400C2312yes—
382#400C2312yes—
383#400C2312yes—
384#400C2312yes—
385#400C2312yes—
386#400C2314yes—
387#400C2312yes—
388#400C2312yes—
389#400C2312yes—
390#400C2312yes—
391#400C2312yes—
392#400C2312yes—
393#400C2312yes—
394#400C2314yes—
395#400C2314yes—
396#400C2314yes—
397#399C2314yes—
398#399C2314yes—
399#399C2314yes—
400#399C2312yes—
401#398C2314yes—
402#398C2314yes—
403#398C2314yes—
404#398C2314yes—
405#398C2312yes—
406#398C2312yes—
407#398C2314yes—
408#398C2314yes—
409#398C2314yes—
410#398C2314yes—
411#398C2314yes—
412#398C2314yes—
413#398C2314yes—
414#398C2314yes—
415#398C2314yes—
416#398C2314yes—
417#398C2314yes—
418#398C2314yes—
419#398C2314yes—
420#398C2314yes—
421#398C2314yes—
422#398C2314yes—
423#398C2314yes—
424#398C2314yes—
425#398C2314yes—
426#398C2314yes—
427#398C2314yes—
428#398C2314yes—
429#398C2312yes—
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#398C2312yes—
445#398C2312yes—
446#398C2312yes—
447#398C2312yes—
448#398C2312yes—
449#398C2312yes—
450#398C2312yes—
451#398C2314yes—
452#398C2312yes—
453#398C2314yes—
454#398C2314yes—
455#398C2314yes—
456#397C2312yes—
457#397C2314yes—
458#397C2314yes—
459#397C2314yes—
460#397C2312yes—
461#397C2312yes—
462#397C2314yes—
463#397C2314yes—
464#397C2312yes—
465#397C2312yes—
466#397C2312yes—
467#396C2314yes—
468#396C2314yes—
469#396C2312yes—
470#396C2312yes—
471#396C2312yes—
472#396C2314yes—
473#396C2312yes—
474#395C2314yes—
475#395C2314yes—
476#395C2314yes—
477#395C2312yes—
478#395C2314yes—
479#395C2314yes—
480#395C2314yes—
481#393C2312yes—
482#393C2314yes—
483#391C2314yes—
484#391C2311yescharacteristic
485#391C2312yes—
486#391C2311yescharacteristic
487#391C2311yescharacteristic
488#391C2311yescharacteristic
489#391C2311yescharacteristic
490#391C2311yescharacteristic
491#391C2312yes—
492#391C2312yes—
493#391C2312yes—
494#391C2314yes—
495#391C2314yes—
496#391C2311yescharacteristic
497#391C2312yes—
498#391C2311yescharacteristic
499#391C2312yes—
500#391C2312yes—
501#391C2312yes—
502#391C2312yes—
503#391C2312yes—
504#391C2312yes—
505#391C2312yes—
506#391C2314yes—
507#391C2314yes—
508#391C2314yes—
509#391C2314yes—
510#391C2312yes—
511#391C2312yes—
512#391C2314yes—
513#391C2311yescharacteristic
514#391C2311yescharacteristic
515#391C2311yescharacteristic
516#391C2311yescharacteristic
517#391C2311yescharacteristic
518#391C2311yescharacteristic
519#389C2311yescharacteristic
520#389C2312yes—
521#389C2312yes—
522#389C2311yescharacteristic
523#389C2311yescharacteristic
524#389C2312yes—
525#389C2314yes—
526#389C2311yescharacteristic
527#389C2312yes—
528#389C2312yes—
529#389C2312yes—
530#389C2312yes—
531#389C2312yes—
532#389C2312yes—
533#389C2312yes—
534#389C2312yes—
535#389C2312yes—
536#389C2312yes—
537#389C2312yes—
538#389C2312yes—
539#389C2311yescharacteristic
540#389C2312yes—
541#389C2312yes—
542#389C2312yes—
543#389C2314yes—
544#389C2312yes—
545#389C2312yes—
546#389C2314yes—
547#389C2312yes—
548#389C2312yes—
549#389C2314yes—
550#389C2314yes—
551#389C2312yes—
552#389C2312yes—
553#389C2314yes—
554#389C2312yes—
555#389C2312yes—
556#389C2314yes—
557#389C2314yes—
558#389C2314yes—
559#389C2314yes—
560#389C2314yes—
561#389C2311yescharacteristic
562#389C2311yescharacteristic
563#389C2314yes—
564#389C2312yes—
565#389C2312yes—
566#389C2314yes—
567#389C2314yes—
568#389C2314yes—
569#389C2314yes—
570#389C2312yes—
571#389C2312yes—
572#389C2314yes—
573#389C2314yes—
574#389C2312yes—
575#389C2312yes—
576#389C2312yes—
577#389C2314yes—
578#389C2312yes—
579#389C2312yes—
580#389C2314yes—
581#389C2314yes—
582#389C2314yes—
583#389C2314yes—
584#389C2312yes—
585#389C2312yes—
586#389C2312yes—
587#389C2312yes—
588#389C2314yes—
589#389C2314yes—
590#389C2312yes—
591#389C2311yescharacteristic
592#389C2311yescharacteristic
593#389C2311yescharacteristic
594#389C2311yescharacteristic
595#389C2314yes—
596#389C2314yes—
597#389C2314yes—
598#389C2314yes—
599#389C2311yescharacteristic
600#389C2311yescharacteristic
601#389C2311yescharacteristic
602#388C2314yes—
603#388C2312yes—
604#388C2314yes—
605#388C2314yes—
606#388C2314yes—
607#388C2312yes—
608#388C2312yes—
609#388C2312yes—
610#388C2314yes—
611#388C2314yes—
612#388C2314yes—
613#387C2314yes—
614#387C2314yes—
615#387C2312yes—
616#387C2312yes—
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#387C2312yes—
645#387C2314yes—
646#387C2314yes—
647#387C2314yes—
648#387C2314yes—
649#387C2314yes—
650#387C2312yes—
651#387C2312yes—
652#387C2312yes—
653#387C2314yes—
654#387C2312yes—
655#387C2314yes—
656#387C2314yes—
657#387C2314yes—
658#387C2314yes—
659#387C2314yes—
660#387C2314yes—
661#387C2314yes—
662#387C2312yes—
663#387C2312yes—
664#387C2314yes—
665#387C2314yes—
666#387C2312yes—
667#387C2314yes—
668#387C2312yes—
669#387C2312yes—
670#387C2312yes—
671#387C2312yes—
672#387C2312yes—
673#387C2314yes—
674#387C2314yes—
675#387C2314yes—
676#387C2314yes—
677#387C2314yes—
678#387C2314yes—
679#387C2314yes—
680#387C2314yes—
681#387C2314yes—
682#387C2312yes—
683#387C2312yes—
684#387C2312yes—
685#387C2312yes—
686#387C2312yes—
687#387C2314yes—
688#387C2314yes—
689#387C2314yes—
690#385C2312yes—
691#385C2312yes—
692#385C2312yes—
693#385C2312yes—
694#384C2311yescharacteristic
695#384C2311yescharacteristic
696#384C2311yescharacteristic
697#384C2312yes—
698#384C2312yes—
699#384C2312yes—
700#384C2312yes—
701#384C2312yes—
702#384C2311yescharacteristic
703#384C2311yescharacteristic
704#384C2311yescharacteristic
705#384C2311yescharacteristic
706#384C2312yes—
707#384C2312yes—
708#384C2314yes—
709#384C2312yes—
710#384C2312yes—
711#384C2312yes—
712#384C2312yes—
713#384C2314yes—
714#383C2314yes—
715#383C2314yes—
716#383C2314yes—
717#383C2314yes—
718#383C2314yes—
719#382C2312yes—
720#382C2311yescharacteristic
721#382C2312yes—
722#382C2312yes—
723#382C2314yes—
724#382C2312yes—
725#382C2312yes—
726#382C2312yes—
727#382C2312yes—
728#382C2314yes—
729#382C2312yes—
730#382C2314yes—
731#382C2312yes—
732#382C2312yes—
733#382C2314yes—
734#382C2314yes—
735#382C2314yes—
736#382C2314yes—
737#380C2311yescharacteristic
738#380C2311yescharacteristic
739#380C2311yescharacteristic
740#380C2312yes—
741#380C2312yes—
742#380C2312yes—
743#380C2312yes—
744#380C2311yescharacteristic
745C4×C4⋊C4C2312yes—
746C4×C4⋊C4C2311yescharacteristic
747C4×C4⋊C4C2314yes—
748C4×C4⋊C4C2311yescharacteristic
749C4×C4⋊C4C2312yes—
750C4×C4⋊C4C2312yes—
751C4×C4⋊C4C2312yes—
752C4×C4⋊C4C2314yes—
753C4×C4⋊C4C2312yes—
754C4×C4⋊C4C2314yes—
755C4×C4⋊C4C2311yescharacteristic
756C4×C4⋊C4C2312yes—
757C4×C4⋊C4C2312yes—
758C4×C4⋊C4C2312yes—
759C4×C4⋊C4C2311yescharacteristic
760C4×C4⋊C4C2312yes—
761C4×C4⋊C4C2312yes—
762C4×C4⋊C4C2312yes—
763C4×C4⋊C4C2312yes—
764C4×C4⋊C4C2312yes—
765C4×C4⋊C4C2311yescharacteristic
766C4×C4⋊C4C2311yescharacteristic
767C4×C4⋊C4C2312yes—
768C4×C4⋊C4C2312yes—
769C4×C4⋊C4C2312yes—
770C4×C4⋊C4C2312yes—
771C4×C4⋊C4C2312yes—
772C4×C4⋊C4C2312yes—
773C4×C4⋊C4C2311yescharacteristic
774C4×C4⋊C4C2312yes—
775C4×C4⋊C4C2312yes—
776C4×C4⋊C4C2312yes—
777C4×C4⋊C4C2314yes—
778C4×C4⋊C4C2314yes—
779C4×C4⋊C4C2314yes—
780C4×C4⋊C4C2312yes—
781C4×C4⋊C4C2312yes—
782C4×C4⋊C4C2312yes—
783C4×C4⋊C4C2312yes—
784C4×C4⋊C4C2312yes—
785C4×C4⋊C4C2312yes—
786C4×C4⋊C4C2311yescharacteristic
787C4×C4⋊C4C2312yes—
788C4×C4⋊C4C2311yescharacteristic
789C4×C4⋊C4C2312yes—
790C4×C4⋊C4C2312yes—
791C4×C4⋊C4C2312yes—
792C4×C4⋊C4C2311yescharacteristic
793C4×C22⋊C4C2311yescharacteristic
794C4×C22⋊C4C2311yescharacteristic
795C4×C22⋊C4C2312yes—
796C4×C22⋊C4C2312yes—
797C4×C22⋊C4C2312yes—
798C4×C22⋊C4C2312yes—
799C4×C22⋊C4C2311yescharacteristic
800C4×C22⋊C4C2311yescharacteristic
801#376C2312yes—
802#376C2312yes—
803#376C2312yes—
804#376C2311yescharacteristic
805#376C2311yescharacteristic
806#376C2314yes—
807C43C2312yes—
808C43C2311yescharacteristic
809C43C2311yescharacteristic
810C22×Q8C2411yescharacteristic
811C22×Q8C2411yescharacteristic
812C22×Q8C2411yescharacteristic
813C22×Q8C2411yescharacteristic
814C22×Q8C2414yes—
815C22×Q8C2412yes—
816C23×C4C2411yescharacteristic
817C23×C4C2411yescharacteristic
818C23×C4C2411yescharacteristic
819C4⋊Q8—24no—
820C4⋊Q8—24no—
821C4⋊Q8—28no—
822C4⋊Q8—44no—
823C4⋊Q8—42no—
824C4⋊Q8—82no—
825#126—84no—
826#125—24no—
827#125—44no—
828#125—44no—
829#125—44no—
830#125—44no—
831#125—44no—
832#125—84no—
833#125—84no—
834#125—82no—
835#125—84no—
836#125—84no—
837C22⋊Q8—24no—
838C22⋊Q8—42no—
839C22⋊Q8—42no—
840C22⋊Q8—42no—
841C4×Q8—28no—
842C4×Q8—24no—
843C4×Q8—24no—
844C4×Q8—24no—
845C4×Q8—24no—
846C4×Q8—24no—
847C4×Q8—44no—
848C4×Q8—44no—
849C4×Q8—44no—
850C4×Q8—44no—
851C4×Q8—44no—
852C4×Q8—42no—
853C4×Q8—84no—
854#117—24no—
855#117—42no—
856#117—44no—
857#117—82no—
858C2×C4⋊C4C2412yes—
859C2×C4⋊C4C2412yes—
860C2×C4⋊C4C2411yescharacteristic
861C2×C4⋊C4C2411yescharacteristic
862C2×C4⋊C4C2411yescharacteristic
863C2×C4⋊C4C2412yes—
864C2×C4⋊C4C2412yes—
865C2×C4⋊C4C2412yes—
866C2×C4⋊C4C2411yescharacteristic
867C2×C4⋊C4C2412yes—
868C2×C4⋊C4C2411yescharacteristic
869C2×C4⋊C4C2411yescharacteristic
870C2×C4⋊C4C2411yescharacteristic
871C2×C4⋊C4C2411yescharacteristic
872C2×C4⋊C4C2412yes—
873C2×C4⋊C4C2412yes—
874C2×C4⋊C4C2414yes—
875C2×C4⋊C4C2412yes—
876C2×C4⋊C4C2412yes—
877C2×C4⋊C4C2412yes—
878C2×C4⋊C4C2411yescharacteristic
879C2×C4⋊C4C2411yescharacteristic
880C2×C4⋊C4C2411yescharacteristic
881C2×C4⋊C4C2412yes—
882C2×C4⋊C4C2411yescharacteristic
883C2×C4⋊C4C2411yescharacteristic
884C2×C4⋊C4C2411yescharacteristic
885C2×C4⋊C4C2412yes—
886C2×C4⋊C4C2412yes—
887C2×C4⋊C4C2412yes—
888C2×C4⋊C4C2412yes—
889C2×C4⋊C4C2412yes—
890C2×C4⋊C4C2414yes—
891C2×C4⋊C4C2412yes—
892C2×C4⋊C4C2412yes—
893C2×C4⋊C4C2412yes—
894C2×C4⋊C4C2412yes—
895C2×C4⋊C4C2412yes—
896C2×C4⋊C4C2411yescharacteristic
897C2×C4⋊C4C2411yescharacteristic
898C2×C4⋊C4C2412yes—
899C2×C4⋊C4C2414yes—
900C2×C4⋊C4C2414yes—
901C2×C4⋊C4C2412yes—
902C2×C4⋊C4C2414yes—
903C2×C4⋊C4C2412yes—
904C2×C4⋊C4C2414yes—
905C2×C4⋊C4C2414yes—
906C2×C4⋊C4C2414yes—
907C2×C4⋊C4C2412yes—
908C2×C4⋊C4C2412yes—
909C2×C4⋊C4C2412yes—
910C2×C4⋊C4C2412yes—
911C2×C4⋊C4C2412yes—
912C2×C4⋊C4C2412yes—
913C2×C4⋊C4C2414yes—
914C2×C4⋊C4C2412yes—
915C2×C4⋊C4C2412yes—
916C2×C4⋊C4C2412yes—
917C2×C4⋊C4C2412yes—
918C2×C4⋊C4C2412yes—
919C2×C4⋊C4C2412yes—
920C2×C4⋊C4C2412yes—
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⋊C4C2412yes—
930C2×C4⋊C4C2414yes—
931C2×C4⋊C4C2414yes—
932C2×C4⋊C4C2414yes—
933C2×C4⋊C4C2414yes—
934C2×C4⋊C4C2414yes—
935C2×C4⋊C4C2414yes—
936C2×C4⋊C4C2414yes—
937C2×C4⋊C4C2414yes—
938C2×C4⋊C4C2414yes—
939C2×C4⋊C4C2414yes—
940C2×C4⋊C4C2414yes—
941C2×C4⋊C4C2412yes—
942C2×C4⋊C4C2414yes—
943C2×C4⋊C4C2412yes—
944C2×C4⋊C4C2412yes—
945C2×C4⋊C4C2412yes—
946C2×C4⋊C4C2412yes—
947C2×C4⋊C4C2414yes—
948C2×C4⋊C4C2412yes—
949C2×C4⋊C4C2412yes—
950C2×C4⋊C4C2412yes—
951C2×C4⋊C4C2412yes—
952C2×C4⋊C4C2412yes—
953C2×C4⋊C4C2414yes—
954C2×C4⋊C4C2414yes—
955C2×C4⋊C4C2414yes—
956C2×C22⋊C4C2411yescharacteristic
957C2×C22⋊C4C2411yescharacteristic
958C2×C22⋊C4C2412yes—
959C2×C22⋊C4C2414yes—
960C2×C22⋊C4C2411yescharacteristic
961C2×C22⋊C4C2411yescharacteristic
962C2×C22⋊C4C2414yes—
963C2×C22⋊C4C2412yes—
964C2×C22⋊C4C2412yes—
965C2×C22⋊C4C2412yes—
966C2×C22⋊C4C2412yes—
967C2×C22⋊C4C2412yes—
968C2×C22⋊C4C2412yes—
969C2×C22⋊C4C2412yes—
970C2×C42—24no—
971C2×C42C2411yescharacteristic
972C2×C42C2411yescharacteristic
973C2×C42C2411yescharacteristic
974C2×C42C2412yes—
975C2×C42C2412yes—
976C2×C42C2412yes—
977C2×C42C2411yescharacteristic
978C2×C42C2411yescharacteristic
979C2×C42C2412yes—
980C2×C42C2412yes—
981C2×C42C2412yes—
982C2×C42C2412yes—
983C2×C42C2412yes—
984C2×C42C2412yes—
985C2×C42C2414yes—
986C2×C42C2411yescharacteristic
987C2×C42C2411yescharacteristic
988C2×C42C2411yescharacteristic
989C2×C42C2411yescharacteristic
990C2×C42C2411yescharacteristic
991C2×C42C2414yes—
992C2×C42C2414yes—
993C2×C42C2412yes—
994C2×C42C2414yes—
995C2×C42C2414yes—
996C2×C42C2412yes—
997C2×C42C2414yes—
998C2×C42C2414yes—
999C2×C42C2414yes—
1000C2×C42C2414yes—
1001C2×C42C2411yescharacteristic
1002C2×C42C2414yes—
1003C2×C42C2411yescharacteristic
1004C2×C42C2411yescharacteristic
1005C2×C42C2411yescharacteristic
1006C2×C42C2412yes—
1007C2×C42C2411yescharacteristic
1008C2×C42C2411yescharacteristic
1009#95C2412yes—
1010#95C2412yes—
1011#95C2411yescharacteristic
1012#95C2411yescharacteristic
1013#95C2411yescharacteristic
1014#95C2411yescharacteristic
1015#95C2411yescharacteristic
1016#95C2411yescharacteristic
1017#95C2411yescharacteristic
1018#95C2411yescharacteristic
1019#95C2414yes—
1020#95C2412yes—
1021#95C2414yes—
1022#95C2412yes—
1023#95C2412yes—
1024#95C2412yes—
1025#95C2412yes—
1026#95C2412yes—
1027#95C2412yes—
1028#95C2412yes—
1029#95C2412yes—
1030#95C2412yes—
1031#95C2412yes—
1032#95C2412yes—
1033#95C2412yes—
1034#95C2412yes—
1035#95C2412yes—
1036#95C2412yes—
1037#95C2412yes—
1038#95C2412yes—
1039#95C2412yes—
1040#95C2412yes—
1041#95C2412yes—
1042#95C2412yes—
1043#95C2412yes—
1044#95C2412yes—
1045#95C2412yes—
1046#95C2414yes—
1047#95C2414yes—
1048#95C2414yes—
1049#95C2414yes—
1050#95C2412yes—
1051#95C2412yes—
1052#95C2412yes—
1053#95C2414yes—
1054#95C2412yes—
1055#95C2412yes—
1056#95C2414yes—
1057#95C2412yes—
1058#95C2414yes—
1059#95C2414yes—
1060#95C2414yes—
1061#95C2414yes—
1062#95C2412yes—
1063#95C2414yes—
1064#95C2414yes—
1065#95C2414yes—
1066#95C2414yes—
1067#95C2414yes—
1068#95C2412yes—
1069#95C2412yes—
1070#95C2414yes—
1071#95C2414yes—
1072#95C2414yes—
1073#95C2412yes—
1074#95C2412yes—
1075#95C2412yes—
1076#95C2412yes—
1077#95C2412yes—
1078#95C2412yes—
1079#95C2412yes—
1080#95C2412yes—
1081#95C2412yes—
1082#95C2414yes—
1083#95C2414yes—
1084#95C2412yes—
1085#95C2412yes—
1086#95C2412yes—
1087#95C2412yes—
1088#95C2412yes—
1089#95C2414yes—
1090#95C2414yes—
1091#95C2414yes—
1092#95C2412yes—
1093#95C2412yes—
1094#95C2412yes—
1095#95C2412yes—
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—
1113C24C2511yescharacteristic
1114C2×Q8—22no—
1115C2×Q8—22no—
1116C2×Q8—22no—
1117C2×Q8—22no—
1118C2×Q8—22no—
1119C2×Q8—22no—
1120C2×Q8—22no—
1121C2×Q8—28no—
1122C2×Q8—22no—
1123C2×Q8—22no—
1124C2×Q8—22no—
1125C2×Q8—22no—
1126C2×Q8—42no—
1127C2×Q8—44no—
1128C2×Q8—44no—
1129C2×Q8—42no—
1130C2×Q8—42no—
1131C2×Q82−1+414yes—
1132C22×C4—22no—
1133C22×C4—22no—
1134C22×C4—22no—
1135C22×C4—22no—
1136C22×C4—22no—
1137C22×C4—22no—
1138C22×C4—22no—
1139C22×C4—41no—
1140C22×C4—41no—
1141C22×C4C2511yescharacteristic
1142C22×C4C2512yes—
1143C22×C4C2511yescharacteristic
1144C22×C4C2512yes—
1145C22×C4C2512yes—
1146C22×C4C2512yes—
1147C22×C4C2511yescharacteristic
1148C22×C4C2511yescharacteristic
1149C22×C4C2511yescharacteristic
1150C22×C4C2512yes—
1151C22×C4C2512yes—
1152C22×C4C2512yes—
1153C22×C4C2512yes—
1154C22×C4C2514yes—
1155C22×C4C2514yes—
1156C22×C4C2512yes—
1157C22×C4C2512yes—
1158C22×C4C2512yes—
1159C22×C4C2511yescharacteristic
1160C22×C4C2511yescharacteristic
1161C22×C4C2511yescharacteristic
1162C22×C4C2514yes—
1163C22×C4C2512yes—
1164C22×C4C2512yes—
1165C22×C4C2512yes—
1166C22×C4C2512yes—
1167C22×C4C2511yescharacteristic
1168C22×C4C2514yes—
1169C22×C4C2511yescharacteristic
1170C22×C4C2512yes—
1171C22×C4C2511yescharacteristic
1172C22×C4C2511yescharacteristic
1173C22×C4C2511yescharacteristic
1174C22×C4C2511yescharacteristic
1175C4⋊C4—22no—
1176C4⋊C4—22no—
1177C4⋊C4—24no—
1178C4⋊C4—24no—
1179C4⋊C4—28no—
1180C4⋊C4—22no—
1181C4⋊C4—22no—
1182C4⋊C4—22no—
1183C4⋊C4—22no—
1184C4⋊C4—22no—
1185C4⋊C4—24no—
1186C4⋊C4—24no—
1187C4⋊C4—24no—
1188C4⋊C4—24no—
1189C4⋊C4—22no—
1190C4⋊C4—24no—
1191C4⋊C4—24no—
1192C4⋊C4—24no—
1193C4⋊C4—22no—
1194C4⋊C4—22no—
1195C4⋊C4—24no—
1196C4⋊C4—24no—
1197C4⋊C4—24no—
1198C4⋊C4—28no—
1199C4⋊C4—24no—
1200C4⋊C4—24no—
1201C4⋊C4—24no—
1202C4⋊C4—24no—
1203C4⋊C4—24no—
1204C4⋊C4—22no—
1205C4⋊C4—24no—
1206C4⋊C4—24no—
1207C4⋊C4—24no—
1208C4⋊C4—22no—
1209C4⋊C4—22no—
1210C4⋊C4—22no—
1211C4⋊C4—42no—
1212C4⋊C4—42no—
1213C4⋊C4—42no—
1214C4⋊C4—44no—
1215C4⋊C4—42no—
1216C4⋊C4—42no—
1217C4⋊C4—42no—
1218C4⋊C4—44no—
1219C4⋊C4—42no—
1220C4⋊C4—42no—
1221C4⋊C4—44no—
1222C4⋊C4—44no—
1223C4⋊C4—42no—
1224C4⋊C4—41no—
1225C4⋊C4—41no—
1226C4⋊C4—42no—
1227C4⋊C4—42no—
1228C4⋊C4—44no—
1229C4⋊C4—42no—
1230C4⋊C4—42no—
1231C4⋊C4—42no—
1232C4⋊C4—44no—
1233C4⋊C4—44no—
1234C4⋊C4—42no—
1235C4⋊C4—44no—
1236C4⋊C4—42no—
1237C4⋊C4—44no—
1238C4⋊C4—44no—
1239C4⋊C4—42no—
1240C4⋊C4—42no—
1241C4⋊C4—42no—
1242C4⋊C4—44no—
1243C4⋊C4—44no—
1244C4⋊C4—44no—
1245C4⋊C4—44no—
1246C4⋊C4—44no—
1247C4⋊C4—44no—
1248C4⋊C4—44no—
1249C4⋊C4—44no—
1250C4⋊C4—44no—
1251C4⋊C4—44no—
1252C4⋊C4—42no—
1253C4⋊C4—42no—
1254C4⋊C4—42no—
1255C4⋊C4—42no—
1256C4⋊C4—42no—
1257C4⋊C4—42no—
1258C4⋊C4—44no—
1259C4⋊C4—44no—
1260C4⋊C4—44no—
1261C4⋊C4—42no—
1262C4⋊C4—42no—
1263C4⋊C4—44no—
1264C4⋊C4—44no—
1265C4⋊C4—44no—
1266C4⋊C4—44no—
1267C4⋊C4—44no—
1268C4⋊C4—44no—
1269C4⋊C4—42no—
1270C4⋊C4—44no—
1271C4⋊C4—44no—
1272C4⋊C4—42no—
1273C22⋊C4—22no—
1274C22⋊C4—22no—
1275C22⋊C4—24no—
1276C22⋊C4—42no—
1277C22⋊C4—42no—
1278C22⋊C4—41no—
1279C22⋊C4—41no—
1280C22⋊C4—44no—
1281C22⋊C4—44no—
1282C22⋊C4—42no—
1283C22⋊C4—42no—
1284C22⋊C4—42no—
1285C22⋊C4—42no—
1286C22⋊C4—42no—
1287C42—22no—
1288C42—22no—
1289C42—22no—
1290C42—22no—
1291C42—24no—
1292C42—22no—
1293C42—24no—
1294C42—28no—
1295C42—24no—
1296C42—24no—
1297C42—24no—
1298C42—24no—
1299C42—22no—
1300C42—22no—
1301C42—22no—
1302C42—24no—
1303C42—24no—
1304C42—24no—
1305C42—22no—
1306C42—22no—
1307C42—41no—
1308C42—42no—
1309C42—41no—
1310C42—44no—
1311C42—44no—
1312C42—42no—
1313C42—44no—
1314C42—44no—
1315C42—44no—
1316C42—44no—
1317C42—42no—
1318C42—44no—
1319C42—44no—
1320C42—41no—
1321C42—44no—
1322C42—41no—
1323C422−1+414yes—
1324C422−1+414yes—
1325C23—21no—
1326C23—21no—
1327C23—21no—
1328C23—21no—
1329C23—21no—
1330C23—21no—
1331C23—21no—
1332C23C2611yescharacteristic
1333Q8—28no—
1334Q8—44no—
1335Q8—44no—
1336Q8—44no—
1337Q8—88no—
1338Q8—84no—
1339C2×C4—21no—
1340C2×C4—22no—
1341C2×C4—21no—
1342C2×C4—22no—
1343C2×C4—21no—
1344C2×C4—21no—
1345C2×C4—21no—
1346C2×C4—21no—
1347C2×C4—22no—
1348C2×C4—21no—
1349C2×C4—21no—
1350C2×C4—21no—
1351C2×C4—21no—
1352C2×C4—21no—
1353C2×C4—22no—
1354C2×C4—22no—
1355C2×C4—22no—
1356C2×C4—22no—
1357C2×C4—21no—
1358C2×C4—22no—
1359C2×C4—21no—
1360C2×C4—24no—
1361C2×C4—22no—
1362C2×C4—21no—
1363C2×C4—22no—
1364C2×C4—22no—
1365C2×C4—22no—
1366C2×C4—22no—
1367C2×C4—22no—
1368C2×C4—22no—
1369C2×C4—21no—
1370C2×C4—21no—
1371C2×C4—22no—
1372C2×C4—22no—
1373C2×C4—22no—
1374C2×C4—24no—
1375C2×C4—24no—
1376C2×C4—22no—
1377C2×C4—22no—
1378C2×C4—22no—
1379C2×C4—22no—
1380C2×C4—21no—
1381C2×C4—21no—
1382C2×C4—21no—
1383C2×C4—21no—
1384C2×C4—22no—
1385C2×C4—21no—
1386C2×C4—21no—
1387C2×C4—22no—
1388C2×C4—21no—
1389C2×C4—21no—
1390C2×C4—24no—
1391C2×C4—22no—
1392C2×C4—22no—
1393C2×C4—22no—
1394C2×C4—24no—
1395C2×C4—22no—
1396C2×C4—24no—
1397C2×C4—24no—
1398C2×C4—24no—
1399C2×C4—22no—
1400C2×C4—22no—
1401C2×C4—22no—
1402C2×C4—21no—
1403C2×C4—22no—
1404C2×C4—21no—
1405C2×C4—22no—
1406C2×C4—22no—
1407C2×C4—24no—
1408C2×C4—22no—
1409C2×C4—22no—
1410C2×C4—24no—
1411C2×C4—24no—
1412C2×C4—22no—
1413C2×C4—21no—
1414C2×C4—21no—
1415C2×C4—21no—
1416C2×C4—22no—
1417C2×C4—22no—
1418C2×C4—22no—
1419C2×C4—21no—
1420C2×C4—21no—
1421C2×C4—22no—
1422C2×C4—21no—
1423C2×C4—22no—
1424C2×C4—22no—
1425C2×C4—22no—
1426C2×C4—22no—
1427C2×C4—22no—
1428C2×C4—22no—
1429C2×C4—24no—
1430C2×C4—21no—
1431C2×C4—44no—
1432C2×C4—44no—
1433C2×C4—44no—
1434C2×C4C2×2−1+414yes—
1435C2×C4C2×2−1+412yes—
1436C2×C4C2×2−1+412yes—
1437C2×C4C2×2−1+412yes—
1438C2×C4C2×2−1+412yes—
1439C2×C4C2×2−1+412yes—
1440C2×C4C2×2−1+412yes—
1441C2×C4C2×2−1+412yes—
1442C2×C4#58512yes—
1443C2×C4#58512yes—
1444C22—41no—
1445C22—41no—
1446C22—41no—
1447C22—41no—
1448C22—41no—
1449C22—41no—
1450C22—41no—
1451C22C22×2−1+411yescharacteristic
1452C22C22×2−1+411yescharacteristic
1453C22C22×2−1+411yescharacteristic
1454C22C2×#58511yescharacteristic
1455C22C2×#58511yescharacteristic
1456C22H(7,𝔽2)11yescharacteristic
1457C222−1+611yescharacteristic
1458C4—24no—
1459C4—22no—
1460C4—22no—
1461C4—22no—
1462C4—41no—
1463C4—42no—
1464C4—41no—
1465C4—42no—
1466C4—42no—
1467C4—42no—
1468C4—42no—
1469C4—42no—
1470C4—42no—
1471C4—41no—
1472C4—42no—
1473C4—41no—
1474C4—41no—
1475C4—41no—
1476C4—42no—
1477C4—44no—
1478C4—42no—
1479C4—42no—
1480C4—41no—
1481C4—42no—
1482C4—44no—
1483C4—44no—
1484C4—42no—
1485C4—41no—
1486C4—44no—
1487C4—42no—
1488C4—42no—
1489C4—41no—
1490C4#355514yes—
1491C4#356314yes—
1492C2—81no—
1493C2C2×#356311yescharacteristic
1494C2C2×#355511yescharacteristic
1495C2#6287711yescharacteristic
1496C2#6294711yescharacteristic
1497C2#6295211yescharacteristic
1498C2#6296211yescharacteristic
1499C2#6296711yescharacteristic
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
6. #58563C2semidirect
8. #55142C2semidirect
9. #53131C2semidirect
14. #45154C2semidirect
16. #42824C2semidirect
17. #42774C2semidirect
18. #42710C2semidirect
20. #42553C2semidirect
21. #39802C2semidirect
22. #39754C2semidirect
23. #39753C2semidirect
24. #39637C2semidirect
25. #39635C2semidirect
26. #39635C2semidirect
27. #39180C2semidirect
28. #38976C2semidirect
31. #36598C2semidirect
32. Q8×#125C2semidirect

Maximal subgroups

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

subgroupindex
#592622
#592592
#592492
#592422
#586722
#585632
#566892
#551422
#531312
#531072
#530862
#530282
#453392
#451542
#428542
#428242
#427742
#427102
#425622
#425532
#398022
#397542
#397532
#396372
#396352
#391802
#389762
#375922
#373972
#365982
Q8×#1252
#352942
#349162
#346292