Finite Group Databasebeta

← #8174396

Subgroups — #8174396

Order 512.

3929 conjugacy classes of subgroups.

The subgroup lattice has 1537 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59262C211yesmaximal, characteristic, complemented
2#59242C211yesmaximal, characteristic, complemented
3#59230C211yesmaximal, characteristic
4#59219C211yesmaximal, characteristic
5#58513C214yesmaximal, complemented
6#56952C214yesmaximal, complemented
7#55842C214yesmaximal, complemented
8#55197C214yesmaximal, complemented
9#53093C212yesmaximal, complemented
10#53036C212yesmaximal, complemented
11#53024C212yesmaximal, complemented
12#53017C212yesmaximal, complemented
13#45231C212yesmaximal, complemented
14#45172C212yesmaximal
15#42764C212yesmaximal, complemented
16#42753C212yesmaximal, complemented
17#42747C212yesmaximal, complemented
18#42744C212yesmaximal, complemented
19#42622C212yesmaximal
20#42500C212yesmaximal, complemented
21#39753C211yesmaximal, characteristic, complemented
22#39633C211yesmaximal, characteristic, complemented
23#39182C211yesmaximal, characteristic, complemented
24#39182C211yesmaximal, characteristic, complemented
25#39153C212yesmaximal, complemented
26#38977C211yesmaximal, characteristic, complemented
27#38976C211yesmaximal, characteristic, complemented
28#38066C212yesmaximal, complemented
29#37503C212yesmaximal, complemented
30#37408C212yesmaximal, complemented
31#36477C211yesmaximal, characteristic, complemented
32#36290C211yesmaximal, characteristic, complemented
33#35294C211yesmaximal, characteristic, complemented
34#34913C211yesmaximal, characteristic
35#34629C211yesmaximal, characteristic, complemented
36#2868C2211yescharacteristic
37#2859C2211yescharacteristic
38#2859C2211yescharacteristic
39#2859C2211yescharacteristic
40#2855C2212yes—
41#2851C2212yes—
42#2845C2214yes—
43#2841C2214yes—
44#2839C2214yes—
45#2839C2214yes—
46#2839C2214yes—
47#2838C2214yes—
48#2836C2214yes—
49#2833C2214yes—
50#2831C2214yes—
51#2831C2214yes—
52#2827C2214yes—
53#2822C2214yes—
54#2805C2214yes—
55#2805C2214yes—
56#2799C2214yes—
57#2796C2214yes—
58#2791C2214yes—
59#2790C2214yes—
60#2789C2214yes—
61#2789C2214yes—
62#2788C2214yes—
63#2787C2214yes—
64#2787C2214yes—
65#2784C2214yes—
66#2781C2214yes—
67#2776C2214yes—
68#2772C2214yes—
69#2769C2214yes—
70#2769C2214yes—
71#2769C2214yes—
72#2768C2214yes—
73#2767C2214yes—
74#2767C2214yes—
75#2766C2214yes—
76#2766C2214yes—
77#2765C2214yes—
78#2765C2214yes—
79#2764C2214yes—
80#2764C2214yes—
81#2764C2214yes—
82#2763C2214yes—
83#2762C2214yes—
84#2759C2214yes—
85#2758C2214yes—
86#2755C2214yes—
87#2755C2214yes—
88#2754C2214yes—
89#2751C2214yes—
90#2747C2214yes—
91#2747C2214yes—
92#2739C2214yes—
93#2739C2214yes—
94#2729C2214yes—
95#2719C2214yes—
96#2719C2214yes—
97#2719C2214yes—
98#2713C2214yes—
99#2707C2214yes—
100#2707C2214yes—
101#2704C2214yes—
102#2666C2214yes—
103#2665C2214yes—
104#2660C2212yes—
105#2655C2214yes—
106#2655C2212yes—
107#2655C2212yes—
108#2654C2214yes—
109#2652C2214yes—
110#2652C2212yes—
111#2652C2212yes—
112#2647C2211yescharacteristic
113#2647C2212yes—
114#2647C2212yes—
115#2647C2212yes—
116#2645C2212yes—
117#2645C2212yes—
118#2645C2211yescharacteristic
119#2645C2211yescharacteristic
120#2645C2214yes—
121#2642C2211yescharacteristic
122#2629C2211yescharacteristic
123#2629C2212yes—
124#2628C2212yes—
125#2627C2214yes—
126#2625C2211yescharacteristic
127#2625C2211yescharacteristic
128#2623C2214yes—
129#2621C2211yescharacteristic
130#2611C2214yes—
131#2608C2214yes—
132#2587C2214yes—
133#2582C2211yescharacteristic
134#2582C2211yescharacteristic
135#2578C2212yes—
136#2577C2212yes—
137#2576C2212yes—
138#2575C2212yes—
139#2574C2214yes—
140#2573C2214yes—
141#2571C2212yes—
142#2571C2212yes—
143#2571C2211yescharacteristic
144#2571C2212yes—
145#2571C2211yescharacteristic
146#2570C2212yes—
147#2570C2212yes—
148#2570C2212yes—
149#2570C2212yes—
150#2568C2212yes—
151#2568C2212yes—
152#2566C2212yes—
153#2565C2212yes—
154#2563C2212yes—
155#2563C2212yes—
156#2552C2212yes—
157#2552C2211yescharacteristic
158#2551C2211yescharacteristic
159#2550C2212yes—
160#2550C2212yes—
161#2550C2212yes—
162#2550C2212yes—
163#2550C2212yes—
164#2550C2212yes—
165#2550C2212yes—
166#2538C2211yescharacteristic
167#2538C2211yescharacteristic
168#2536C2212yes—
169#2533C2214yes—
170#2527C2214yes—
171#2527C2214yes—
172#2524C2214yes—
173#2514C2214yes—
174#2514C2212yes—
175#2514C2211yescharacteristic
176#2514C2212yes—
177#2514C2212yes—
178#2511C2212yes—
179#2509C2212yes—
180#2508C2212yes—
181#2508C2212yes—
182#2508C2212yes—
183#2508C2212yes—
184#2508C2211yescharacteristic
185#2508C2212yes—
186#2507C2212yes—
187#2507C2212yes—
188#2506C2212yes—
189#2506C2212yes—
190#2506C2212yes—
191#2506C2212yes—
192#2506C2212yes—
193#2505C2214yes—
194#2503C2212yes—
195#2502C2212yes—
196#2499C2212yes—
197#2497C2212yes—
198#2497C2212yes—
199#2495C2211yescharacteristic
200#2495C2212yes—
201#2495C2212yes—
202#2495C2212yes—
203#2494C2212yes—
204#2494C2212yes—
205#2494C2212yes—
206#2493C2214yes—
207#2493C2214yes—
208#2493C2214yes—
209#2492C2212yes—
210#2492C2212yes—
211#2489C2214yes—
212#2489C2212yes—
213#2489C2212yes—
214#2489C2211yescharacteristic
215#2488C2214yes—
216#2486C2212yes—
217#2473C2214yes—
218#2473C2214yes—
219#2470C2214yes—
220#2454C2211yescharacteristic
221#2453C2212yes—
222#2453C2212yes—
223#2452C2212yes—
224#2451C2212yes—
225#2451C2212yes—
226#2447C2212yes—
227#2447C2211yescharacteristic
228#2446C2212yes—
229#2442C2212yes—
230#2442C2214yes—
231#2442C2212yes—
232#2442C2212yes—
233#2441C2212yes—
234#2441C2212yes—
235#2440C2212yes—
236#2439C2212yes—
237#2439C2212yes—
238#2439C2212yes—
239#2429C2212yes—
240#2427C2211yescharacteristic
241#2423C2212yes—
242#2423C2212yes—
243#2422C2212yes—
244#2420C2211yescharacteristic
245#2417C2212yes—
246#2402C2212yes—
247#2402C2212yes—
248#2401C2212yes—
249#2401C2212yes—
250#2401C2212yes—
251#2395C2212yes—
252#2370C2212yes—
253#2370C2212yes—
254#2363C2212yes—
255#2360C2212yes—
256#2357C2212yes—
257#2357C2212yes—
258#2356C2212yes—
259#2356C2212yes—
260#2355C2211yescharacteristic
261#2355C2211yescharacteristic
262#2355C2211yescharacteristic
263Q8×C4⋊C4C2211yescharacteristic
264Q8×C4⋊C4C2211yescharacteristic
265Q8×C4⋊C4C2211yescharacteristic
266#2349C2212yes—
267D4×C4⋊C4C2212yes—
268D4×C4⋊C4C2211yescharacteristic
269D4×C4⋊C4C2211yescharacteristic
270#2347C2212yes—
271#2345C2212yes—
272#2331C2212yes—
273#2331C2212yes—
274#2331C2212yes—
275#2331C2212yes—
276#2330C2212yes—
277#2326C2212yes—
278#2320C2212yes—
279#2319C2212yes—
280C4×C4⋊Q8C2211yescharacteristic
281C4×#125C2211yescharacteristic
282C4×#125C2211yescharacteristic
283C4×#124C2211yescharacteristic
284C4×C22⋊Q8C2211yescharacteristic
285C4×C22⋊Q8C2211yescharacteristic
286C4×C22⋊Q8C2211yescharacteristic
287C4×C22⋊Q8C2212yes—
288C4×#121C2211yescharacteristic
289#2295C2211yescharacteristic
290#2295C2211yescharacteristic
291#2295C2211yescharacteristic
292C2×#389C2212yes—
293#2290C2212yes—
294#2285C2211yescharacteristic
295#2285C2211yescharacteristic
296#2283C2212yes—
297C42×D4C2211yescharacteristic
298C4×#117C2211yescharacteristic
299C2×C4⋊Q8C2311yescharacteristic
300C2×C4⋊Q8C2312yes—
301C2×C4⋊Q8C2312yes—
302C2×C4⋊Q8C2312yes—
303C2×C4⋊Q8C2312yes—
304C2×C4⋊Q8C2312yes—
305C2×#125C2311yescharacteristic
306C2×#125C2311yescharacteristic
307C2×#125C2312yes—
308C2×#125C2312yes—
309C2×#125C2312yes—
310C2×#125C2314yes—
311C2×#125C2314yes—
312C2×#125C2312yes—
313C2×#125C2314yes—
314C2×#124C2311yescharacteristic
315C2×#123C2314yes—
316C2×C22⋊Q8C2312yes—
317C2×C22⋊Q8C2311yescharacteristic
318C2×C22⋊Q8C2311yescharacteristic
319C2×C22⋊Q8C2312yes—
320C2×C22⋊Q8C2311yescharacteristic
321C2×C22⋊Q8C2314yes—
322C2×#121C2311yescharacteristic
323C2×C4×Q8C2311yescharacteristic
324C2×C4×Q8C2311yescharacteristic
325C2×C4×Q8C2311yescharacteristic
326C2×C4×Q8C2312yes—
327C2×C4×Q8C2312yes—
328C2×C4×Q8C2312yes—
329C2×C4×D4C2312yes—
330C2×C4×D4C2311yescharacteristic
331C2×C4×D4C2311yescharacteristic
332C2×C4×D4C2312yes—
333C2×C4×D4C2312yes—
334C2×C4×D4C2311yescharacteristic
335C2×#117C2312yes—
336C2×#117C2311yescharacteristic
337C2×#117C2311yescharacteristic
338C2×#117C2312yes—
339C22×C4⋊C4C2312yes—
340C22×C4⋊C4C2312yes—
341C22×C4⋊C4C2314yes—
342C22×C42C2311yescharacteristic
343C22×C42C2312yes—
344#401C2312yes—
345#401C2314yes—
346#401C2314yes—
347#401C2314yes—
348#401C2312yes—
349#401C2312yes—
350#401C2314yes—
351#400C2314yes—
352#400C2314yes—
353#400C2314yes—
354#400C2314yes—
355#400C2314yes—
356#400C2314yes—
357#400C2314yes—
358#400C2314yes—
359#400C2314yes—
360#400C2314yes—
361#400C2314yes—
362#400C2314yes—
363#400C2314yes—
364#400C2314yes—
365#400C2314yes—
366#400C2314yes—
367#400C2312yes—
368#400C2314yes—
369#400C2312yes—
370#400C2312yes—
371#400C2314yes—
372#400C2314yes—
373#400C2314yes—
374#400C2312yes—
375#400C2312yes—
376#400C2312yes—
377#400C2314yes—
378#400C2314yes—
379#400C2312yes—
380#400C2312yes—
381#400C2314yes—
382#400C2314yes—
383#400C2314yes—
384#400C2314yes—
385#400C2314yes—
386#400C2314yes—
387#400C2314yes—
388#400C2314yes—
389#400C2312yes—
390#400C2314yes—
391#400C2312yes—
392#400C2312yes—
393#400C2312yes—
394#400C2312yes—
395#400C2312yes—
396#400C2312yes—
397#400C2312yes—
398#400C2312yes—
399#400C2312yes—
400#400C2314yes—
401#399C2314yes—
402#399C2312yes—
403#399C2314yes—
404#398C2314yes—
405#398C2314yes—
406#398C2312yes—
407#398C2312yes—
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#398C2312yes—
428#398C2314yes—
429#398C2314yes—
430#398C2314yes—
431#398C2314yes—
432#398C2314yes—
433#398C2312yes—
434#398C2312yes—
435#398C2314yes—
436#398C2314yes—
437#398C2312yes—
438#398C2312yes—
439#398C2314yes—
440#398C2312yes—
441#398C2312yes—
442#398C2314yes—
443#397C2312yes—
444#397C2314yes—
445#397C2314yes—
446#397C2314yes—
447#397C2312yes—
448#397C2312yes—
449#397C2312yes—
450#397C2314yes—
451#397C2314yes—
452#397C2314yes—
453#397C2312yes—
454#397C2312yes—
455#397C2312yes—
456#397C2312yes—
457#397C2312yes—
458#397C2312yes—
459#397C2312yes—
460#397C2312yes—
461#397C2314yes—
462#396C2314yes—
463#396C2314yes—
464#396C2314yes—
465#396C2314yes—
466#396C2314yes—
467#396C2312yes—
468#396C2312yes—
469#396C2314yes—
470#396C2312yes—
471#396C2314yes—
472#396C2314yes—
473#395C2314yes—
474#395C2314yes—
475#395C2314yes—
476#395C2314yes—
477#395C2314yes—
478#395C2314yes—
479#395C2314yes—
480#394C2312yes—
481#394C2314yes—
482#394C2312yes—
483#393C2314yes—
484#393C2314yes—
485#393C2314yes—
486#393C2314yes—
487#393C2314yes—
488#391C2311yescharacteristic
489#391C2311yescharacteristic
490#391C2311yescharacteristic
491#391C2312yes—
492#391C2311yescharacteristic
493#391C2311yescharacteristic
494#391C2314yes—
495#391C2314yes—
496#391C2314yes—
497#391C2312yes—
498#391C2312yes—
499#391C2314yes—
500#391C2314yes—
501#391C2314yes—
502#391C2312yes—
503#391C2314yes—
504#391C2312yes—
505#391C2312yes—
506#391C2312yes—
507#391C2314yes—
508#391C2314yes—
509#391C2314yes—
510#391C2314yes—
511#391C2311yescharacteristic
512#391C2311yescharacteristic
513#391C2311yescharacteristic
514#391C2311yescharacteristic
515#391C2311yescharacteristic
516#391C2311yescharacteristic
517#391C2314yes—
518#391C2311yescharacteristic
519#390C2311yescharacteristic
520#390C2312yes—
521#390C2314yes—
522#390C2312yes—
523#390C2311yescharacteristic
524#389C2311yescharacteristic
525#389C2311yescharacteristic
526#389C2311yescharacteristic
527#389C2311yescharacteristic
528#389C2312yes—
529#389C2312yes—
530#389C2312yes—
531#389C2312yes—
532#389C2312yes—
533#389C2312yes—
534#389C2312yes—
535#389C2312yes—
536#389C2312yes—
537#389C2311yescharacteristic
538#389C2314yes—
539#389C2312yes—
540#389C2312yes—
541#389C2312yes—
542#389C2312yes—
543#389C2312yes—
544#389C2312yes—
545#389C2312yes—
546#389C2312yes—
547#389C2314yes—
548#389C2314yes—
549#389C2312yes—
550#389C2312yes—
551#389C2312yes—
552#389C2312yes—
553#389C2314yes—
554#389C2312yes—
555#389C2314yes—
556#389C2314yes—
557#389C2314yes—
558#389C2312yes—
559#389C2314yes—
560#389C2314yes—
561#389C2312yes—
562#389C2312yes—
563#389C2314yes—
564#389C2312yes—
565#389C2311yescharacteristic
566#389C2312yes—
567#389C2312yes—
568#389C2312yes—
569#389C2312yes—
570#389C2314yes—
571#389C2312yes—
572#389C2312yes—
573#389C2314yes—
574#389C2311yescharacteristic
575#389C2311yescharacteristic
576#389C2311yescharacteristic
577#389C2311yescharacteristic
578#389C2311yescharacteristic
579#389C2314yes—
580#389C2314yes—
581#389C2314yes—
582#389C2311yescharacteristic
583#389C2312yes—
584#389C2311yescharacteristic
585#389C2311yescharacteristic
586#388C2314yes—
587#388C2314yes—
588#388C2312yes—
589#388C2314yes—
590#388C2312yes—
591#388C2314yes—
592#388C2314yes—
593#388C2312yes—
594#388C2312yes—
595#388C2312yes—
596#388C2314yes—
597#388C2314yes—
598#388C2314yes—
599#388C2314yes—
600#388C2314yes—
601#388C2314yes—
602#388C2314yes—
603#388C2314yes—
604#388C2314yes—
605#387C2312yes—
606#387C2312yes—
607#387C2312yes—
608#387C2312yes—
609#387C2314yes—
610#387C2314yes—
611#387C2314yes—
612#387C2314yes—
613#387C2314yes—
614#387C2314yes—
615#387C2314yes—
616#387C2314yes—
617#387C2314yes—
618#387C2314yes—
619#387C2312yes—
620#387C2314yes—
621#387C2314yes—
622#387C2312yes—
623#387C2312yes—
624#387C2312yes—
625#387C2314yes—
626#387C2314yes—
627#387C2314yes—
628#387C2314yes—
629#387C2312yes—
630#387C2312yes—
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#387C2312yes—
650#387C2312yes—
651#387C2312yes—
652#387C2312yes—
653#387C2314yes—
654#387C2312yes—
655#387C2314yes—
656#387C2314yes—
657#387C2314yes—
658#387C2314yes—
659#386C2314yes—
660#386C2312yes—
661#386C2312yes—
662#386C2312yes—
663#385C2314yes—
664#385C2314yes—
665#385C2314yes—
666#385C2314yes—
667#385C2314yes—
668#385C2314yes—
669#385C2312yes—
670#385C2312yes—
671#385C2312yes—
672#385C2314yes—
673#385C2314yes—
674#385C2314yes—
675#385C2314yes—
676#385C2312yes—
677#385C2314yes—
678#385C2312yes—
679#385C2314yes—
680#385C2314yes—
681#384C2311yescharacteristic
682#384C2312yes—
683#384C2312yes—
684#384C2312yes—
685#384C2312yes—
686#384C2311yescharacteristic
687#384C2311yescharacteristic
688#384C2312yes—
689#384C2312yes—
690#384C2312yes—
691#384C2311yescharacteristic
692#384C2311yescharacteristic
693#383C2314yes—
694#383C2314yes—
695#383C2312yes—
696#383C2312yes—
697#383C2314yes—
698#383C2314yes—
699#383C2314yes—
700#382C2311yescharacteristic
701#382C2311yescharacteristic
702#382C2314yes—
703#382C2312yes—
704#382C2312yes—
705#382C2312yes—
706#382C2312yes—
707#382C2312yes—
708#382C2312yes—
709#382C2312yes—
710#382C2312yes—
711#382C2312yes—
712#382C2312yes—
713#382C2312yes—
714#382C2314yes—
715#382C2314yes—
716#382C2314yes—
717#382C2312yes—
718#382C2314yes—
719#382C2312yes—
720#382C2314yes—
721#382C2312yes—
722#382C2311yescharacteristic
723#381C2312yes—
724#381C2314yes—
725#381C2312yes—
726#381C2314yes—
727#381C2314yes—
728#381C2314yes—
729#380C2311yescharacteristic
730#380C2314yes—
731#380C2312yes—
732#380C2312yes—
733#380C2314yes—
734#380C2312yes—
735#380C2314yes—
736#380C2312yes—
737#380C2312yes—
738#380C2314yes—
739#380C2312yes—
740#380C2311yescharacteristic
741#380C2314yes—
742#380C2311yescharacteristic
743#380C2312yes—
744#380C2312yes—
745#380C2311yescharacteristic
746#380C2312yes—
747#380C2312yes—
748C4×C4⋊C4C2312yes—
749C4×C4⋊C4C2312yes—
750C4×C4⋊C4C2312yes—
751C4×C4⋊C4C2311yescharacteristic
752C4×C4⋊C4C2311yescharacteristic
753C4×C4⋊C4C2311yescharacteristic
754C4×C4⋊C4C2311yescharacteristic
755C4×C4⋊C4C2312yes—
756C4×C4⋊C4C2312yes—
757C4×C4⋊C4C2312yes—
758C4×C4⋊C4C2312yes—
759C4×C4⋊C4C2312yes—
760C4×C4⋊C4C2311yescharacteristic
761C4×C4⋊C4C2311yescharacteristic
762C4×C4⋊C4C2311yescharacteristic
763C4×C4⋊C4C2312yes—
764C4×C4⋊C4C2312yes—
765C4×C4⋊C4C2312yes—
766C4×C4⋊C4C2312yes—
767C4×C4⋊C4C2312yes—
768C4×C4⋊C4C2312yes—
769C4×C4⋊C4C2312yes—
770C4×C4⋊C4C2312yes—
771C4×C4⋊C4C2312yes—
772C4×C4⋊C4C2312yes—
773C4×C4⋊C4C2314yes—
774C4×C4⋊C4C2311yescharacteristic
775C4×C4⋊C4C2312yes—
776C4×C4⋊C4C2312yes—
777C4×C4⋊C4C2312yes—
778C4×C4⋊C4C2312yes—
779C4×C4⋊C4C2312yes—
780C4×C4⋊C4C2314yes—
781C4×C4⋊C4C2312yes—
782C4×C4⋊C4C2312yes—
783C4×C4⋊C4C2311yescharacteristic
784C4×C4⋊C4C2311yescharacteristic
785C4×C22⋊C4C2314yes—
786C4×C22⋊C4C2314yes—
787C4×C22⋊C4C2312yes—
788C4×C22⋊C4C2311yescharacteristic
789C4×C22⋊C4C2312yes—
790C4×C22⋊C4C2311yescharacteristic
791C4×C22⋊C4C2312yes—
792C4×C22⋊C4C2312yes—
793C4×C22⋊C4C2314yes—
794C4×C22⋊C4C2312yes—
795C4×C22⋊C4C2312yes—
796C4×C22⋊C4C2312yes—
797C4×C22⋊C4C2312yes—
798C4×C22⋊C4C2311yescharacteristic
799C4×C22⋊C4C2311yescharacteristic
800C4×C22⋊C4C2312yes—
801#376C2312yes—
802#376C2312yes—
803#376C2312yes—
804#376C2311yescharacteristic
805#376C2311yescharacteristic
806#376C2314yes—
807C2×#95C2314yes—
808C43C2311yescharacteristic
809C43C2311yescharacteristic
810C22×Q8C2411yescharacteristic
811C22×Q8C2411yescharacteristic
812C22×Q8C2411yescharacteristic
813C22×Q8C2414yes—
814C22×Q8C2414yes—
815C22×D4C2411yescharacteristic
816C22×D4C2412yes—
817C23×C4C2412yes—
818C23×C4C2411yescharacteristic
819C23×C4C2411yescharacteristic
820C23×C4C2414yes—
821C23×C4C2411yescharacteristic
822C23×C4C2412yes—
823C23×C4C2414yes—
824C23×C4C2412yes—
825C4⋊Q8—44no—
826C4⋊Q8—44no—
827C4⋊Q8—44no—
828C4⋊Q8—44no—
829C4⋊Q8—42no—
830C4⋊Q8—82no—
831#125—44no—
832#125—44no—
833#125—42no—
834#125—44no—
835#125—42no—
836#125—84no—
837#125—82no—
838#125—84no—
839#125—84no—
840#124—24no—
841#123—84no—
842C22⋊Q8—42no—
843C22⋊Q8—42no—
844C22⋊Q8—44no—
845C22⋊Q8—42no—
846C22⋊Q8—44no—
847C22⋊Q8—84no—
848#121—24no—
849C4×Q8—24no—
850C4×Q8—24no—
851C4×Q8—24no—
852C4×Q8—44no—
853C4×Q8—44no—
854C4×Q8—44no—
855C4×D4—28no—
856C4×D4—24no—
857C4×D4—24no—
858C4×D4—44no—
859C4×D4—42no—
860C4×D4—44no—
861#117—42no—
862#117—42no—
863#117—44no—
864#117—82no—
865C2×C4⋊C4—44no—
866C2×C4⋊C4—44no—
867C2×C4⋊C4—84no—
868C2×C4⋊C4C2411yescharacteristic
869C2×C4⋊C4C2411yescharacteristic
870C2×C4⋊C4C2412yes—
871C2×C4⋊C4C2412yes—
872C2×C4⋊C4C2412yes—
873C2×C4⋊C4C2412yes—
874C2×C4⋊C4C2411yescharacteristic
875C2×C4⋊C4C2411yescharacteristic
876C2×C4⋊C4C2412yes—
877C2×C4⋊C4C2411yescharacteristic
878C2×C4⋊C4C2412yes—
879C2×C4⋊C4C2412yes—
880C2×C4⋊C4C2411yescharacteristic
881C2×C4⋊C4C2411yescharacteristic
882C2×C4⋊C4C2411yescharacteristic
883C2×C4⋊C4C2412yes—
884C2×C4⋊C4C2412yes—
885C2×C4⋊C4C2412yes—
886C2×C4⋊C4C2411yescharacteristic
887C2×C4⋊C4C2411yescharacteristic
888C2×C4⋊C4C2412yes—
889C2×C4⋊C4C2411yescharacteristic
890C2×C4⋊C4C2411yescharacteristic
891C2×C4⋊C4C2412yes—
892C2×C4⋊C4C2414yes—
893C2×C4⋊C4C2414yes—
894C2×C4⋊C4C2414yes—
895C2×C4⋊C4C2414yes—
896C2×C4⋊C4C2414yes—
897C2×C4⋊C4C2412yes—
898C2×C4⋊C4C2412yes—
899C2×C4⋊C4C2411yescharacteristic
900C2×C4⋊C4C2411yescharacteristic
901C2×C4⋊C4C2411yescharacteristic
902C2×C4⋊C4C2411yescharacteristic
903C2×C4⋊C4C2412yes—
904C2×C4⋊C4C2414yes—
905C2×C4⋊C4C2414yes—
906C2×C4⋊C4C2414yes—
907C2×C4⋊C4C2412yes—
908C2×C4⋊C4C2414yes—
909C2×C4⋊C4C2414yes—
910C2×C4⋊C4C2412yes—
911C2×C4⋊C4C2412yes—
912C2×C4⋊C4C2412yes—
913C2×C4⋊C4C2414yes—
914C2×C4⋊C4C2414yes—
915C2×C4⋊C4C2414yes—
916C2×C4⋊C4C2414yes—
917C2×C4⋊C4C2412yes—
918C2×C4⋊C4C2412yes—
919C2×C4⋊C4C2412yes—
920C2×C4⋊C4C2412yes—
921C2×C4⋊C4C2412yes—
922C2×C4⋊C4C2412yes—
923C2×C4⋊C4C2414yes—
924C2×C4⋊C4C2414yes—
925C2×C4⋊C4C2414yes—
926C2×C4⋊C4C2412yes—
927C2×C4⋊C4C2414yes—
928C2×C4⋊C4C2412yes—
929C2×C4⋊C4C2412yes—
930C2×C4⋊C4C2414yes—
931C2×C4⋊C4C2414yes—
932C2×C4⋊C4C2412yes—
933C2×C4⋊C4C2412yes—
934C2×C4⋊C4C2414yes—
935C2×C4⋊C4C2414yes—
936C2×C4⋊C4C2414yes—
937C2×C4⋊C4C2414yes—
938C2×C4⋊C4C2412yes—
939C2×C4⋊C4C2412yes—
940C2×C4⋊C4C2414yes—
941C2×C4⋊C4C2414yes—
942C2×C4⋊C4C2414yes—
943C2×C4⋊C4C2414yes—
944C2×C4⋊C4C2412yes—
945C2×C4⋊C4C2412yes—
946C2×C4⋊C4C2412yes—
947C2×C4⋊C4C2412yes—
948C2×C4⋊C4C2412yes—
949C2×C4⋊C4C2412yes—
950C2×C4⋊C4C2412yes—
951C2×C4⋊C4C2412yes—
952C2×C22⋊C4C2412yes—
953C2×C22⋊C4C2412yes—
954C2×C22⋊C4C2414yes—
955C2×C22⋊C4C2412yes—
956C2×C22⋊C4C2412yes—
957C2×C22⋊C4C2412yes—
958C2×C22⋊C4C2414yes—
959C2×C22⋊C4C2411yescharacteristic
960C2×C22⋊C4C2411yescharacteristic
961C2×C22⋊C4C2411yescharacteristic
962C2×C22⋊C4C2411yescharacteristic
963C2×C22⋊C4C2414yes—
964C2×C22⋊C4C2412yes—
965C2×C22⋊C4C2412yes—
966C2×C22⋊C4C2414yes—
967C2×C22⋊C4C2412yes—
968C2×C22⋊C4C2412yes—
969C2×C22⋊C4C2414yes—
970C2×C22⋊C4C2414yes—
971C2×C22⋊C4C2414yes—
972C2×C22⋊C4C2412yes—
973C2×C22⋊C4C2412yes—
974C2×C22⋊C4C2412yes—
975C2×C22⋊C4C2412yes—
976C2×C22⋊C4C2412yes—
977C2×C22⋊C4C2412yes—
978C2×C22⋊C4C2414yes—
979C2×C22⋊C4C2412yes—
980C2×C22⋊C4C2412yes—
981C2×C42—24no—
982C2×C42—44no—
983C2×C42C2411yescharacteristic
984C2×C42C2411yescharacteristic
985C2×C42C2411yescharacteristic
986C2×C42C2411yescharacteristic
987C2×C42C2412yes—
988C2×C42C2412yes—
989C2×C42C2411yescharacteristic
990C2×C42C2411yescharacteristic
991C2×C42C2412yes—
992C2×C42C2412yes—
993C2×C42C2412yes—
994C2×C42C2412yes—
995C2×C42C2412yes—
996C2×C42C2411yescharacteristic
997C2×C42C2411yescharacteristic
998C2×C42C2411yescharacteristic
999C2×C42C2411yescharacteristic
1000C2×C42C2411yescharacteristic
1001C2×C42C2414yes—
1002C2×C42C2414yes—
1003C2×C42C2414yes—
1004C2×C42C2414yes—
1005C2×C42C2414yes—
1006C2×C42C2411yescharacteristic
1007C2×C42C2414yes—
1008C2×C42C2411yescharacteristic
1009C2×C42C2411yescharacteristic
1010C2×C42C2411yescharacteristic
1011C2×C42C2414yes—
1012C2×C42C2412yes—
1013C2×C42C2412yes—
1014C2×C42C2414yes—
1015C2×C42C2411yescharacteristic
1016#95C2412yes—
1017#95C2414yes—
1018#95C2414yes—
1019#95C2414yes—
1020#95C2412yes—
1021#95C2412yes—
1022#95C2411yescharacteristic
1023#95C2411yescharacteristic
1024#95C2411yescharacteristic
1025#95C2411yescharacteristic
1026#95C2411yescharacteristic
1027#95C2411yescharacteristic
1028#95C2411yescharacteristic
1029#95C2411yescharacteristic
1030#95C2412yes—
1031#95C2412yes—
1032#95C2412yes—
1033#95C2412yes—
1034#95C2412yes—
1035#95C2412yes—
1036#95C2414yes—
1037#95C2414yes—
1038#95C2412yes—
1039#95C2412yes—
1040#95C2412yes—
1041#95C2412yes—
1042#95C2412yes—
1043#95C2412yes—
1044#95C2412yes—
1045#95C2412yes—
1046#95C2412yes—
1047#95C2412yes—
1048#95C2412yes—
1049#95C2412yes—
1050#95C2412yes—
1051#95C2412yes—
1052#95C2414yes—
1053#95C2414yes—
1054#95C2412yes—
1055#95C2412yes—
1056#95C2414yes—
1057#95C2412yes—
1058#95C2412yes—
1059#95C2412yes—
1060#95C2412yes—
1061#95C2412yes—
1062#95C2412yes—
1063#95C2412yes—
1064#95C2412yes—
1065#95C2412yes—
1066#95C2414yes—
1067#95C2412yes—
1068#95C2414yes—
1069#95C2412yes—
1070#95C2414yes—
1071#95C2414yes—
1072#95C2412yes—
1073#95C2414yes—
1074#95C2414yes—
1075#95C2414yes—
1076#95C2412yes—
1077#95C2412yes—
1078#95C2412yes—
1079#95C2412yes—
1080#95C2414yes—
1081#95C2414yes—
1082#95C2414yes—
1083#95C2412yes—
1084#95C2412yes—
1085#95C2412yes—
1086#95C2412yes—
1087#95C2414yes—
1088#95C2414yes—
1089#95C2412yes—
1090#95C2412yes—
1091#95C2412yes—
1092#95C2412yes—
1093#95C2412yes—
1094#95C2414yes—
1095#95C2412yes—
1096#95C2414yes—
1097#95C2412yes—
1098#95C2412yes—
1099#95C2412yes—
1100#95C2414yes—
1101#95C2414yes—
1102#95C2414yes—
1103#95C2414yes—
1104#95C2414yes—
1105#95C2414yes—
1106#95C2414yes—
1107#95C2414yes—
1108#95C2414yes—
1109#95C2414yes—
1110#95C2414yes—
1111#95C2414yes—
1112#95C2414yes—
1113#95C2414yes—
1114#95C2414yes—
1115#95C2414yes—
1116#95C2414yes—
1117#95C2414yes—
1118C24C2511yescharacteristic
1119C24C2512yes—
1120C2×Q8—22no—
1121C2×Q8—22no—
1122C2×Q8—22no—
1123C2×Q8—22no—
1124C2×Q8—22no—
1125C2×Q8—22no—
1126C2×Q8—22no—
1127C2×Q8—22no—
1128C2×Q8—22no—
1129C2×Q8—44no—
1130C2×Q8—44no—
1131C2×Q8—44no—
1132C2×Q8—44no—
1133C2×Q8—44no—
1134C2×Q8—44no—
1135C2×D4—24no—
1136C2×D4—22no—
1137C2×D4—22no—
1138C2×D4—42no—
1139C2×D4—42no—
1140C2×D42−1+414yes—
1141C22×C4—28no—
1142C22×C4—24no—
1143C22×C4—22no—
1144C22×C4—22no—
1145C22×C4—22no—
1146C22×C4—24no—
1147C22×C4—22no—
1148C22×C4—24no—
1149C22×C4—24no—
1150C22×C4—22no—
1151C22×C4—22no—
1152C22×C4—22no—
1153C22×C4—41no—
1154C22×C4—41no—
1155C22×C4—42no—
1156C22×C4—42no—
1157C22×C4—44no—
1158C22×C4—42no—
1159C22×C4—44no—
1160C22×C4—42no—
1161C22×C4—42no—
1162C22×C4—44no—
1163C22×C4—44no—
1164C22×C4—44no—
1165C22×C4C2511yescharacteristic
1166C22×C4C2511yescharacteristic
1167C22×C4C2512yes—
1168C22×C4C2512yes—
1169C22×C4C2511yescharacteristic
1170C22×C4C2511yescharacteristic
1171C22×C4C2512yes—
1172C22×C4C2512yes—
1173C22×C4C2512yes—
1174C22×C4C2512yes—
1175C22×C4C2512yes—
1176C22×C4C2511yescharacteristic
1177C22×C4C2511yescharacteristic
1178C22×C4C2512yes—
1179C22×C4C2512yes—
1180C22×C4C2512yes—
1181C22×C4C2512yes—
1182C22×C4C2512yes—
1183C22×C4C2514yes—
1184C22×C4C2512yes—
1185C22×C4C2514yes—
1186C22×C4C2511yescharacteristic
1187C22×C4C2511yescharacteristic
1188C22×C4C2511yescharacteristic
1189C22×C4C2511yescharacteristic
1190C22×C4C2511yescharacteristic
1191C22×C4C2514yes—
1192C22×C4C2512yes—
1193C22×C4C2514yes—
1194C22×C4C2512yes—
1195C22×C4C2511yescharacteristic
1196C22×C4C2511yescharacteristic
1197C22×C4C2511yescharacteristic
1198C4⋊C4—22no—
1199C4⋊C4—22no—
1200C4⋊C4—24no—
1201C4⋊C4—22no—
1202C4⋊C4—22no—
1203C4⋊C4—22no—
1204C4⋊C4—24no—
1205C4⋊C4—24no—
1206C4⋊C4—24no—
1207C4⋊C4—22no—
1208C4⋊C4—22no—
1209C4⋊C4—22no—
1210C4⋊C4—24no—
1211C4⋊C4—24no—
1212C4⋊C4—24no—
1213C4⋊C4—24no—
1214C4⋊C4—22no—
1215C4⋊C4—24no—
1216C4⋊C4—24no—
1217C4⋊C4—22no—
1218C4⋊C4—24no—
1219C4⋊C4—22no—
1220C4⋊C4—22no—
1221C4⋊C4—44no—
1222C4⋊C4—44no—
1223C4⋊C4—42no—
1224C4⋊C4—44no—
1225C4⋊C4—44no—
1226C4⋊C4—44no—
1227C4⋊C4—42no—
1228C4⋊C4—42no—
1229C4⋊C4—42no—
1230C4⋊C4—42no—
1231C4⋊C4—42no—
1232C4⋊C4—42no—
1233C4⋊C4—42no—
1234C4⋊C4—42no—
1235C4⋊C4—41no—
1236C4⋊C4—41no—
1237C4⋊C4—41no—
1238C4⋊C4—41no—
1239C4⋊C4—42no—
1240C4⋊C4—42no—
1241C4⋊C4—42no—
1242C4⋊C4—44no—
1243C4⋊C4—44no—
1244C4⋊C4—44no—
1245C4⋊C4—42no—
1246C4⋊C4—42no—
1247C4⋊C4—44no—
1248C4⋊C4—42no—
1249C4⋊C4—44no—
1250C4⋊C4—42no—
1251C4⋊C4—44no—
1252C4⋊C4—44no—
1253C4⋊C4—44no—
1254C4⋊C4—44no—
1255C4⋊C4—44no—
1256C4⋊C4—44no—
1257C4⋊C4—44no—
1258C4⋊C4—44no—
1259C4⋊C4—44no—
1260C4⋊C4—42no—
1261C4⋊C4—42no—
1262C4⋊C4—42no—
1263C4⋊C4—44no—
1264C4⋊C4—42no—
1265C4⋊C4—42no—
1266C4⋊C4—42no—
1267C4⋊C4—44no—
1268C4⋊C4—44no—
1269C4⋊C4—42no—
1270C4⋊C4—42no—
1271C4⋊C4—42no—
1272C4⋊C4—42no—
1273C4⋊C4—44no—
1274C4⋊C4—42no—
1275C4⋊C4—44no—
1276C4⋊C4—42no—
1277C4⋊C4—42no—
1278C4⋊C4—44no—
1279C4⋊C4—44no—
1280C4⋊C4—44no—
1281C4⋊C4—44no—
1282C22⋊C4—24no—
1283C22⋊C4—28no—
1284C22⋊C4—24no—
1285C22⋊C4—24no—
1286C22⋊C4—24no—
1287C22⋊C4—24no—
1288C22⋊C4—42no—
1289C22⋊C4—42no—
1290C22⋊C4—44no—
1291C22⋊C4—42no—
1292C22⋊C4—42no—
1293C22⋊C4—41no—
1294C22⋊C4—41no—
1295C22⋊C4—41no—
1296C22⋊C4—41no—
1297C22⋊C4—44no—
1298C22⋊C4—44no—
1299C22⋊C4—44no—
1300C22⋊C4—42no—
1301C22⋊C4—42no—
1302C22⋊C4—42no—
1303C22⋊C4—42no—
1304C22⋊C4—42no—
1305C22⋊C4—44no—
1306C22⋊C4—42no—
1307C22⋊C4—44no—
1308C22⋊C4—42no—
1309C22⋊C4—44no—
1310C22⋊C4—42no—
1311C42—22no—
1312C42—22no—
1313C42—22no—
1314C42—22no—
1315C42—24no—
1316C42—24no—
1317C42—24no—
1318C42—24no—
1319C42—22no—
1320C42—22no—
1321C42—24no—
1322C42—22no—
1323C42—22no—
1324C42—22no—
1325C42—24no—
1326C42—24no—
1327C42—22no—
1328C42—22no—
1329C42—42no—
1330C42—42no—
1331C42—41no—
1332C42—41no—
1333C42—44no—
1334C42—44no—
1335C42—44no—
1336C42—44no—
1337C42—44no—
1338C42—44no—
1339C42—44no—
1340C42—41no—
1341C42—44no—
1342C42—41no—
1343C422−1+414yes—
1344C23—22no—
1345C23—22no—
1346C23—22no—
1347C23—22no—
1348C23—22no—
1349C23—22no—
1350C23—21no—
1351C23—21no—
1352C23—21no—
1353C23—21no—
1354C23—21no—
1355C23—21no—
1356C23—21no—
1357C23C2×2−1+414yes—
1358C23C2611yescharacteristic
1359Q8—44no—
1360Q8—44no—
1361Q8—44no—
1362Q8—164no—
1363Q8—164no—
1364D4—28no—
1365D4—84no—
1366C2×C4—21no—
1367C2×C4—21no—
1368C2×C4—21no—
1369C2×C4—21no—
1370C2×C4—21no—
1371C2×C4—22no—
1372C2×C4—21no—
1373C2×C4—21no—
1374C2×C4—21no—
1375C2×C4—22no—
1376C2×C4—22no—
1377C2×C4—22no—
1378C2×C4—22no—
1379C2×C4—22no—
1380C2×C4—22no—
1381C2×C4—21no—
1382C2×C4—22no—
1383C2×C4—21no—
1384C2×C4—22no—
1385C2×C4—22no—
1386C2×C4—22no—
1387C2×C4—24no—
1388C2×C4—22no—
1389C2×C4—22no—
1390C2×C4—22no—
1391C2×C4—22no—
1392C2×C4—21no—
1393C2×C4—21no—
1394C2×C4—22no—
1395C2×C4—21no—
1396C2×C4—21no—
1397C2×C4—21no—
1398C2×C4—21no—
1399C2×C4—21no—
1400C2×C4—21no—
1401C2×C4—21no—
1402C2×C4—21no—
1403C2×C4—22no—
1404C2×C4—21no—
1405C2×C4—22no—
1406C2×C4—21no—
1407C2×C4—21no—
1408C2×C4—22no—
1409C2×C4—22no—
1410C2×C4—22no—
1411C2×C4—22no—
1412C2×C4—24no—
1413C2×C4—24no—
1414C2×C4—24no—
1415C2×C4—24no—
1416C2×C4—24no—
1417C2×C4—22no—
1418C2×C4—22no—
1419C2×C4—21no—
1420C2×C4—22no—
1421C2×C4—22no—
1422C2×C4—24no—
1423C2×C4—22no—
1424C2×C4—22no—
1425C2×C4—22no—
1426C2×C4—24no—
1427C2×C4—22no—
1428C2×C4—22no—
1429C2×C4—21no—
1430C2×C4—21no—
1431C2×C4—22no—
1432C2×C4—22no—
1433C2×C4—24no—
1434C2×C4—21no—
1435C2×C4—24no—
1436C2×C4—21no—
1437C2×C4—21no—
1438C2×C4—21no—
1439C2×C4—24no—
1440C2×C4—22no—
1441C2×C4—22no—
1442C2×C4—22no—
1443C2×C4—22no—
1444C2×C4—22no—
1445C2×C4—22no—
1446C2×C4—22no—
1447C2×C4—24no—
1448C2×C4—22no—
1449C2×C4—22no—
1450C2×C4—21no—
1451C2×C4—21no—
1452C2×C4—21no—
1453C2×C4—21no—
1454C2×C4—22no—
1455C2×C4—21no—
1456C2×C4—22no—
1457C2×C4—22no—
1458C2×C4—44no—
1459C2×C4—44no—
1460C2×C4—48no—
1461C2×C4—44no—
1462C2×C4—84no—
1463C2×C4—88no—
1464C2×C4—84no—
1465C2×C4—164no—
1466C2×C4C2×2−1+412yes—
1467C2×C4C2×2−1+412yes—
1468C2×C4C2×2−1+412yes—
1469C2×C4C2×2−1+412yes—
1470C2×C4#58512yes—
1471C2×C4#58512yes—
1472C2×C4#58512yes—
1473C22—24no—
1474C22—24no—
1475C22—24no—
1476C22—42no—
1477C22—42no—
1478C22—42no—
1479C22—42no—
1480C22—41no—
1481C22—41no—
1482C22—41no—
1483C22—41no—
1484C22—41no—
1485C22—41no—
1486C22—41no—
1487C22C22×2−1+411yescharacteristic
1488C22C22×2−1+411yescharacteristic
1489C22C2×#58511yescharacteristic
1490C22C2×#58511yescharacteristic
1491C22C2×#58511yescharacteristic
1492C22H(7,𝔽2)11yescharacteristic
1493C222−1+611yescharacteristic
1494C4—22no—
1495C4—41no—
1496C4—42no—
1497C4—41no—
1498C4—42no—
1499C4—42no—
1500C4—42no—
1501C4—42no—
1502C4—42no—
1503C4—42no—
1504C4—41no—
1505C4—41no—
1506C4—42no—
1507C4—42no—
1508C4—41no—
1509C4—41no—
1510C4—41no—
1511C4—44no—
1512C4—42no—
1513C4—42no—
1514C4—42no—
1515C4—41no—
1516C4—42no—
1517C4—44no—
1518C4—44no—
1519C4—41no—
1520C4—41no—
1521C4—41no—
1522C4—44no—
1523C4—42no—
1524C4—42no—
1525C4#356314yes—
1526C4#356514yes—
1527C2—44no—
1528C2—81no—
1529C2C2×#356311yescharacteristic
1530C2C2×#356511yescharacteristic
1531C2#6287711yescharacteristic
1532C2#6295011yescharacteristic
1533C2#6295111yescharacteristic
1534C2#6296611yescharacteristic
1535C2#6296811yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#121C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59262C2semidirect
2. #59242C2semidirect
5. #58513C2semidirect
6. #56952C2semidirect
7. #55842C2semidirect
8. #55197C2semidirect
9. #53093C2semidirect
10. #53036C2semidirect
11. #53024C2semidirect
12. #53017C2semidirect
13. #45231C2semidirect
15. #42764C2semidirect
16. #42753C2semidirect
17. #42747C2semidirect
18. #42744C2semidirect
20. #42500C2semidirect
21. #39753C2semidirect
22. #39633C2semidirect
23. #39182C2semidirect
24. #39182C2semidirect
25. #39153C2semidirect
26. #38977C2semidirect
27. #38976C2semidirect
28. #38066C2semidirect
29. #37503C2semidirect
30. #37408C2semidirect
31. #36477C2semidirect
32. #36290C2semidirect
33. #35294C2semidirect
35. #34629C2semidirect

Maximal subgroups

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

subgroupindex
#592622
#592422
#592302
#592192
#585132
#569522
#558422
#551972
#530932
#530362
#530242
#530172
#452312
#451722
#427642
#427532
#427472
#427442
#426222
#425002
#397532
#396332
#391822
#391532
#389772
#389762
#380662
#375032
#374082
#364772
#362902
#352942
#349132
#346292