Finite Group Databasebeta

← #8174394

Subgroups — #8174394

Order 512.

3907 conjugacy classes of subgroups.

The subgroup lattice has 1534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59249C211yesmaximal, characteristic, complemented
2#59242C211yesmaximal, characteristic, complemented
3#59230C211yesmaximal, characteristic
4#59218C211yesmaximal, characteristic
5#57617C214yesmaximal, complemented
6#56801C214yesmaximal, complemented
7#55196C214yesmaximal, complemented
8#54576C214yesmaximal, complemented
9#53092C212yesmaximal, complemented
10#53058C212yesmaximal, complemented
11#53035C212yesmaximal, complemented
12#53010C212yesmaximal, complemented
13#45202C212yesmaximal, complemented
14#45193C212yesmaximal
15#42781C212yesmaximal
16#42774C212yesmaximal, complemented
17#42728C212yesmaximal, complemented
18#42717C212yesmaximal, complemented
19#42597C212yesmaximal, complemented
20#42530C212yesmaximal, complemented
21#39761C211yesmaximal, characteristic, complemented
22#39625C211yesmaximal, characteristic, complemented
23#39294C212yesmaximal, complemented
24#39192C211yesmaximal, characteristic, complemented
25#39183C211yesmaximal, characteristic, complemented
26#38977C211yesmaximal, characteristic, complemented
27#38966C211yesmaximal, characteristic, complemented
28#38265C212yesmaximal, complemented
29#37637C212yesmaximal, complemented
30#37403C212yesmaximal, complemented
31#36497C211yesmaximal, characteristic, complemented
32#36285C211yesmaximal, characteristic, complemented
33#35294C211yesmaximal, characteristic, complemented
34#34915C211yesmaximal, characteristic
35#34629C211yesmaximal, characteristic, complemented
36#2868C2211yescharacteristic
37#2864C2212yes—
38#2863C2212yes—
39#2859C2211yescharacteristic
40#2859C2211yescharacteristic
41#2859C2211yescharacteristic
42#2841C2214yes—
43#2839C2214yes—
44#2839C2214yes—
45#2838C2214yes—
46#2838C2214yes—
47#2836C2214yes—
48#2831C2214yes—
49#2831C2214yes—
50#2831C2214yes—
51#2831C2214yes—
52#2830C2214yes—
53#2821C2214yes—
54#2802C2214yes—
55#2802C2214yes—
56#2794C2214yes—
57#2794C2214yes—
58#2793C2214yes—
59#2793C2214yes—
60#2792C2214yes—
61#2791C2214yes—
62#2791C2214yes—
63#2790C2214yes—
64#2789C2214yes—
65#2787C2214yes—
66#2786C2214yes—
67#2784C2214yes—
68#2783C2214yes—
69#2783C2214yes—
70#2777C2214yes—
71#2776C2214yes—
72#2775C2214yes—
73#2774C2214yes—
74#2774C2214yes—
75#2772C2214yes—
76#2772C2214yes—
77#2770C2214yes—
78#2769C2214yes—
79#2768C2214yes—
80#2767C2214yes—
81#2766C2214yes—
82#2765C2214yes—
83#2762C2214yes—
84#2762C2214yes—
85#2757C2214yes—
86#2755C2214yes—
87#2751C2214yes—
88#2747C2214yes—
89#2745C2214yes—
90#2744C2214yes—
91#2740C2214yes—
92#2739C2214yes—
93#2739C2214yes—
94#2734C2214yes—
95#2727C2214yes—
96#2725C2214yes—
97#2722C2214yes—
98#2722C2214yes—
99#2716C2214yes—
100#2716C2214yes—
101#2716C2214yes—
102#2660C2212yes—
103#2655C2214yes—
104#2655C2212yes—
105#2655C2214yes—
106#2655C2212yes—
107#2652C2212yes—
108#2652C2214yes—
109#2652C2212yes—
110#2650C2214yes—
111#2647C2214yes—
112#2647C2212yes—
113#2647C2211yescharacteristic
114#2645C2212yes—
115#2645C2211yescharacteristic
116#2645C2211yescharacteristic
117#2644C2214yes—
118#2642C2211yescharacteristic
119#2640C2212yes—
120#2637C2214yes—
121#2637C2214yes—
122#2629C2212yes—
123#2629C2212yes—
124#2629C2211yescharacteristic
125#2628C2212yes—
126#2625C2211yescharacteristic
127#2625C2212yes—
128#2625C2211yescharacteristic
129#2621C2211yescharacteristic
130#2606C2214yes—
131#2601C2214yes—
132#2597C2212yes—
133#2596C2212yes—
134#2595C2212yes—
135#2594C2212yes—
136#2594C2214yes—
137#2590C2214yes—
138#2588C2214yes—
139#2582C2211yescharacteristic
140#2582C2211yescharacteristic
141#2574C2214yes—
142#2573C2214yes—
143#2571C2212yes—
144#2570C2212yes—
145#2570C2212yes—
146#2570C2212yes—
147#2570C2212yes—
148#2570C2212yes—
149#2567C2212yes—
150#2566C2212yes—
151#2565C2212yes—
152#2565C2212yes—
153#2563C2212yes—
154#2563C2212yes—
155#2552C2212yes—
156#2552C2212yes—
157#2552C2211yescharacteristic
158#2552C2211yescharacteristic
159#2552C2212yes—
160#2552C2211yescharacteristic
161#2551C2212yes—
162#2551C2212yes—
163#2551C2211yescharacteristic
164#2550C2212yes—
165#2550C2212yes—
166#2550C2212yes—
167#2550C2212yes—
168#2538C2212yes—
169#2538C2211yescharacteristic
170#2538C2211yescharacteristic
171#2528C2214yes—
172#2527C2214yes—
173#2524C2214yes—
174#2520C2214yes—
175#2514C2212yes—
176#2514C2212yes—
177#2513C2212yes—
178#2513C2211yescharacteristic
179#2512C2214yes—
180#2512C2212yes—
181#2512C2212yes—
182#2512C2212yes—
183#2511C2212yes—
184#2511C2212yes—
185#2511C2214yes—
186#2509C2212yes—
187#2509C2214yes—
188#2509C2212yes—
189#2509C2211yescharacteristic
190#2509C2212yes—
191#2508C2214yes—
192#2508C2212yes—
193#2508C2212yes—
194#2508C2212yes—
195#2507C2212yes—
196#2507C2212yes—
197#2507C2212yes—
198#2503C2212yes—
199#2499C2212yes—
200#2499C2212yes—
201#2497C2212yes—
202#2496C2212yes—
203#2496C2212yes—
204#2496C2212yes—
205#2496C2212yes—
206#2496C2212yes—
207#2496C2214yes—
208#2495C2212yes—
209#2494C2212yes—
210#2494C2211yescharacteristic
211#2492C2212yes—
212#2492C2212yes—
213#2490C2212yes—
214#2490C2211yescharacteristic
215#2489C2212yes—
216#2489C2212yes—
217#2489C2212yes—
218#2485C2212yes—
219#2478C2214yes—
220#2469C2214yes—
221#2462C2214yes—
222#2454C2212yes—
223#2453C2212yes—
224#2453C2211yescharacteristic
225#2453C2212yes—
226#2451C2212yes—
227#2451C2212yes—
228#2448C2211yescharacteristic
229#2447C2212yes—
230#2446C2212yes—
231#2446C2214yes—
232#2442C2212yes—
233#2442C2212yes—
234#2441C2212yes—
235#2441C2212yes—
236#2441C2212yes—
237#2439C2212yes—
238#2439C2212yes—
239#2439C2212yes—
240#2439C2212yes—
241#2429C2212yes—
242#2426C2211yescharacteristic
243#2421C2212yes—
244#2421C2211yescharacteristic
245#2417C2212yes—
246#2402C2212yes—
247#2402C2212yes—
248#2401C2212yes—
249#2401C2212yes—
250#2401C2212yes—
251#2395C2212yes—
252#2370C2212yes—
253#2370C2212yes—
254#2370C2212yes—
255#2370C2212yes—
256#2370C2212yes—
257#2365C2212yes—
258#2363C2212yes—
259#2362C2212yes—
260#2356C2212yes—
261#2355C2211yescharacteristic
262#2355C2211yescharacteristic
263#2355C2211yescharacteristic
264#2355C2211yescharacteristic
265#2355C2212yes—
266#2354C2211yescharacteristic
267Q8×C4⋊C4C2211yescharacteristic
268Q8×C4⋊C4C2211yescharacteristic
269D4×C4⋊C4C2211yescharacteristic
270#2347C2212yes—
271#2345C2212yes—
272#2331C2212yes—
273#2331C2212yes—
274#2330C2212yes—
275#2330C2212yes—
276#2330C2212yes—
277#2323C2212yes—
278#2319C2212yes—
279#2317C2212yes—
280C4×C4⋊Q8C2212yes—
281C4×C4⋊Q8C2211yescharacteristic
282C4×#125C2211yescharacteristic
283C4×#125C2211yescharacteristic
284C4×#124C2211yescharacteristic
285C4×C22⋊Q8C2211yescharacteristic
286C4×C22⋊Q8C2211yescharacteristic
287C4×C22⋊Q8C2211yescharacteristic
288C4×#121C2211yescharacteristic
289#2298C2212yes—
290#2295C2212yes—
291#2295C2211yescharacteristic
292#2295C2211yescharacteristic
293#2293C2212yes—
294#2293C2211yescharacteristic
295#2285C2211yescharacteristic
296#2285C2211yescharacteristic
297C42×Q8C2211yescharacteristic
298C4×#117C2211yescharacteristic
299C2×C4⋊Q8C2312yes—
300C2×C4⋊Q8C2311yescharacteristic
301C2×C4⋊Q8C2312yes—
302C2×C4⋊Q8C2312yes—
303C2×C4⋊Q8C2312yes—
304C2×C4⋊Q8C2314yes—
305C2×C4⋊Q8C2312yes—
306C2×#126C2314yes—
307C2×#126C2314yes—
308C2×#126C2314yes—
309C2×#126C2314yes—
310C2×#125C2311yescharacteristic
311C2×#125C2312yes—
312C2×#125C2311yescharacteristic
313C2×#125C2312yes—
314C2×#125C2312yes—
315C2×#125C2312yes—
316C2×#125C2312yes—
317C2×#125C2312yes—
318C2×#124C2311yescharacteristic
319C2×C22⋊Q8C2312yes—
320C2×C22⋊Q8C2312yes—
321C2×C22⋊Q8C2311yescharacteristic
322C2×C22⋊Q8C2311yescharacteristic
323C2×C22⋊Q8C2311yescharacteristic
324C2×#121C2311yescharacteristic
325C2×C4×Q8C2311yescharacteristic
326C2×C4×Q8C2311yescharacteristic
327C2×C4×Q8C2311yescharacteristic
328C2×C4×Q8C2311yescharacteristic
329C2×C4×Q8C2311yescharacteristic
330C2×C4×Q8C2312yes—
331C2×C4×Q8C2312yes—
332C2×C4×Q8C2314yes—
333C2×C4×D4C2311yescharacteristic
334C2×C4×D4C2312yes—
335C2×C4×D4C2312yes—
336C2×#117C2312yes—
337C2×#117C2312yes—
338C2×#117C2312yes—
339C2×#117C2311yescharacteristic
340C2×#117C2311yescharacteristic
341C2×#117C2312yes—
342C22×C4⋊C4C2312yes—
343C22×C42C2311yescharacteristic
344#401C2314yes—
345#401C2314yes—
346#401C2312yes—
347#401C2312yes—
348#401C2312yes—
349#400C2314yes—
350#400C2314yes—
351#400C2314yes—
352#400C2314yes—
353#400C2314yes—
354#400C2314yes—
355#400C2314yes—
356#400C2314yes—
357#400C2312yes—
358#400C2314yes—
359#400C2312yes—
360#400C2314yes—
361#400C2314yes—
362#400C2314yes—
363#400C2314yes—
364#400C2314yes—
365#400C2314yes—
366#400C2314yes—
367#400C2314yes—
368#400C2312yes—
369#400C2314yes—
370#400C2314yes—
371#400C2312yes—
372#400C2312yes—
373#400C2314yes—
374#400C2314yes—
375#400C2314yes—
376#400C2314yes—
377#400C2312yes—
378#400C2314yes—
379#400C2312yes—
380#400C2312yes—
381#400C2312yes—
382#400C2312yes—
383#400C2312yes—
384#400C2312yes—
385#400C2312yes—
386#400C2312yes—
387#400C2312yes—
388#400C2312yes—
389#400C2312yes—
390#400C2312yes—
391#399C2312yes—
392#399C2314yes—
393#399C2314yes—
394#398C2314yes—
395#398C2314yes—
396#398C2314yes—
397#398C2314yes—
398#398C2312yes—
399#398C2314yes—
400#398C2314yes—
401#398C2314yes—
402#398C2314yes—
403#398C2314yes—
404#398C2314yes—
405#398C2314yes—
406#398C2312yes—
407#398C2314yes—
408#398C2314yes—
409#398C2314yes—
410#398C2314yes—
411#398C2314yes—
412#398C2314yes—
413#398C2314yes—
414#398C2312yes—
415#398C2312yes—
416#398C2314yes—
417#398C2312yes—
418#398C2314yes—
419#398C2312yes—
420#398C2314yes—
421#398C2312yes—
422#398C2314yes—
423#398C2312yes—
424#398C2312yes—
425#398C2314yes—
426#398C2314yes—
427#398C2314yes—
428#398C2314yes—
429#398C2314yes—
430#397C2314yes—
431#397C2314yes—
432#397C2314yes—
433#397C2314yes—
434#397C2314yes—
435#397C2314yes—
436#397C2312yes—
437#397C2312yes—
438#397C2312yes—
439#397C2312yes—
440#397C2314yes—
441#397C2314yes—
442#397C2314yes—
443#397C2314yes—
444#397C2312yes—
445#397C2312yes—
446#397C2312yes—
447#397C2314yes—
448#397C2314yes—
449#397C2312yes—
450#397C2312yes—
451#397C2312yes—
452#397C2314yes—
453#397C2312yes—
454#397C2312yes—
455#397C2314yes—
456#396C2314yes—
457#396C2314yes—
458#396C2314yes—
459#396C2314yes—
460#396C2312yes—
461#396C2314yes—
462#396C2314yes—
463#396C2314yes—
464#396C2314yes—
465#396C2314yes—
466#396C2312yes—
467#396C2314yes—
468#396C2312yes—
469#396C2314yes—
470#396C2314yes—
471#395C2314yes—
472#395C2314yes—
473#395C2314yes—
474#395C2314yes—
475#395C2314yes—
476#395C2314yes—
477#395C2314yes—
478#395C2314yes—
479#394C2312yes—
480#394C2314yes—
481#394C2312yes—
482#393C2314yes—
483#393C2314yes—
484#393C2314yes—
485#393C2314yes—
486#393C2314yes—
487#393C2314yes—
488#391C2314yes—
489#391C2311yescharacteristic
490#391C2311yescharacteristic
491#391C2311yescharacteristic
492#391C2312yes—
493#391C2312yes—
494#391C2312yes—
495#391C2311yescharacteristic
496#391C2312yes—
497#391C2314yes—
498#391C2314yes—
499#391C2314yes—
500#391C2312yes—
501#391C2312yes—
502#391C2314yes—
503#391C2314yes—
504#391C2314yes—
505#391C2311yescharacteristic
506#391C2312yes—
507#391C2312yes—
508#391C2311yescharacteristic
509#391C2311yescharacteristic
510#391C2311yescharacteristic
511#391C2311yescharacteristic
512#391C2311yescharacteristic
513#391C2314yes—
514#390C2311yescharacteristic
515#390C2314yes—
516#390C2312yes—
517#390C2311yescharacteristic
518#390C2312yes—
519#390C2311yescharacteristic
520#390C2312yes—
521#390C2312yes—
522#390C2312yes—
523#390C2314yes—
524#390C2311yescharacteristic
525#389C2311yescharacteristic
526#389C2311yescharacteristic
527#389C2311yescharacteristic
528#389C2311yescharacteristic
529#389C2312yes—
530#389C2312yes—
531#389C2312yes—
532#389C2314yes—
533#389C2314yes—
534#389C2314yes—
535#389C2312yes—
536#389C2312yes—
537#389C2312yes—
538#389C2312yes—
539#389C2312yes—
540#389C2312yes—
541#389C2312yes—
542#389C2312yes—
543#389C2312yes—
544#389C2311yescharacteristic
545#389C2314yes—
546#389C2312yes—
547#389C2312yes—
548#389C2312yes—
549#389C2314yes—
550#389C2314yes—
551#389C2314yes—
552#389C2312yes—
553#389C2312yes—
554#389C2314yes—
555#389C2314yes—
556#389C2314yes—
557#389C2314yes—
558#389C2314yes—
559#389C2312yes—
560#389C2312yes—
561#389C2312yes—
562#389C2314yes—
563#389C2314yes—
564#389C2312yes—
565#389C2312yes—
566#389C2314yes—
567#389C2312yes—
568#389C2312yes—
569#389C2311yescharacteristic
570#389C2312yes—
571#389C2312yes—
572#389C2312yes—
573#389C2312yes—
574#389C2312yes—
575#389C2312yes—
576#389C2312yes—
577#389C2314yes—
578#389C2314yes—
579#389C2312yes—
580#389C2311yescharacteristic
581#389C2311yescharacteristic
582#389C2311yescharacteristic
583#389C2311yescharacteristic
584#389C2312yes—
585#389C2314yes—
586#389C2314yes—
587#389C2311yescharacteristic
588#389C2311yescharacteristic
589#389C2314yes—
590#389C2311yescharacteristic
591#389C2311yescharacteristic
592#388C2312yes—
593#388C2314yes—
594#388C2312yes—
595#388C2314yes—
596#388C2314yes—
597#388C2314yes—
598#388C2312yes—
599#388C2312yes—
600#388C2314yes—
601#388C2314yes—
602#388C2314yes—
603#388C2314yes—
604#388C2314yes—
605#388C2314yes—
606#388C2312yes—
607#388C2312yes—
608#388C2314yes—
609#388C2312yes—
610#388C2312yes—
611#388C2312yes—
612#388C2312yes—
613#388C2312yes—
614#388C2312yes—
615#388C2312yes—
616#388C2314yes—
617#388C2314yes—
618#388C2314yes—
619#387C2312yes—
620#387C2312yes—
621#387C2312yes—
622#387C2312yes—
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#387C2312yes—
639#387C2314yes—
640#387C2314yes—
641#387C2314yes—
642#387C2314yes—
643#387C2314yes—
644#387C2314yes—
645#387C2314yes—
646#387C2314yes—
647#387C2314yes—
648#387C2314yes—
649#387C2314yes—
650#387C2314yes—
651#387C2314yes—
652#387C2312yes—
653#387C2314yes—
654#387C2314yes—
655#387C2314yes—
656#387C2312yes—
657#387C2314yes—
658#387C2312yes—
659#387C2312yes—
660#387C2312yes—
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#387C2312yes—
674#387C2312yes—
675#387C2312yes—
676#387C2312yes—
677#387C2312yes—
678#387C2314yes—
679#387C2314yes—
680#387C2314yes—
681#387C2314yes—
682#387C2314yes—
683#386C2312yes—
684#386C2314yes—
685#385C2314yes—
686#385C2314yes—
687#385C2314yes—
688#385C2314yes—
689#385C2312yes—
690#385C2312yes—
691#385C2312yes—
692#385C2314yes—
693#384C2312yes—
694#384C2311yescharacteristic
695#384C2312yes—
696#384C2312yes—
697#384C2312yes—
698#384C2312yes—
699#384C2312yes—
700#384C2312yes—
701#384C2314yes—
702#384C2311yescharacteristic
703#384C2311yescharacteristic
704#384C2311yescharacteristic
705#384C2311yescharacteristic
706#384C2312yes—
707#384C2314yes—
708#383C2314yes—
709#383C2314yes—
710#383C2314yes—
711#382C2311yescharacteristic
712#382C2311yescharacteristic
713#382C2312yes—
714#382C2312yes—
715#382C2314yes—
716#382C2312yes—
717#382C2312yes—
718#382C2312yes—
719#382C2312yes—
720#382C2312yes—
721#382C2312yes—
722#382C2314yes—
723#382C2314yes—
724#382C2311yescharacteristic
725#382C2312yes—
726#382C2314yes—
727#382C2314yes—
728#381C2314yes—
729#381C2314yes—
730#380C2311yescharacteristic
731#380C2314yes—
732#380C2312yes—
733#380C2314yes—
734#380C2312yes—
735#380C2312yes—
736#380C2314yes—
737#380C2312yes—
738#380C2314yes—
739#380C2311yescharacteristic
740#380C2312yes—
741#380C2311yescharacteristic
742#380C2312yes—
743#380C2311yescharacteristic
744#380C2312yes—
745#380C2312yes—
746C4×C4⋊C4C2312yes—
747C4×C4⋊C4C2312yes—
748C4×C4⋊C4C2312yes—
749C4×C4⋊C4C2311yescharacteristic
750C4×C4⋊C4C2311yescharacteristic
751C4×C4⋊C4C2311yescharacteristic
752C4×C4⋊C4C2311yescharacteristic
753C4×C4⋊C4C2312yes—
754C4×C4⋊C4C2312yes—
755C4×C4⋊C4C2312yes—
756C4×C4⋊C4C2312yes—
757C4×C4⋊C4C2314yes—
758C4×C4⋊C4C2312yes—
759C4×C4⋊C4C2312yes—
760C4×C4⋊C4C2312yes—
761C4×C4⋊C4C2311yescharacteristic
762C4×C4⋊C4C2311yescharacteristic
763C4×C4⋊C4C2311yescharacteristic
764C4×C4⋊C4C2312yes—
765C4×C4⋊C4C2312yes—
766C4×C4⋊C4C2312yes—
767C4×C4⋊C4C2312yes—
768C4×C4⋊C4C2312yes—
769C4×C4⋊C4C2312yes—
770C4×C4⋊C4C2312yes—
771C4×C4⋊C4C2314yes—
772C4×C4⋊C4C2312yes—
773C4×C4⋊C4C2312yes—
774C4×C4⋊C4C2312yes—
775C4×C4⋊C4C2312yes—
776C4×C4⋊C4C2312yes—
777C4×C4⋊C4C2312yes—
778C4×C4⋊C4C2312yes—
779C4×C4⋊C4C2312yes—
780C4×C4⋊C4C2314yes—
781C4×C4⋊C4C2312yes—
782C4×C4⋊C4C2314yes—
783C4×C4⋊C4C2311yescharacteristic
784C4×C4⋊C4C2312yes—
785C4×C4⋊C4C2314yes—
786C4×C4⋊C4C2312yes—
787C4×C4⋊C4C2311yescharacteristic
788C4×C4⋊C4C2312yes—
789C4×C4⋊C4C2311yescharacteristic
790C4×C22⋊C4C2314yes—
791C4×C22⋊C4C2311yescharacteristic
792C4×C22⋊C4C2311yescharacteristic
793C4×C22⋊C4C2312yes—
794C4×C22⋊C4C2312yes—
795C4×C22⋊C4C2312yes—
796C4×C22⋊C4C2312yes—
797C4×C22⋊C4C2312yes—
798C4×C22⋊C4C2312yes—
799C4×C22⋊C4C2311yescharacteristic
800C4×C22⋊C4C2311yescharacteristic
801C4×C22⋊C4C2312yes—
802#376C2312yes—
803#376C2311yescharacteristic
804#376C2312yes—
805#376C2311yescharacteristic
806#376C2314yes—
807C43C2311yescharacteristic
808C43C2311yescharacteristic
809C43C2312yes—
810C22×Q8C2411yescharacteristic
811C22×Q8C2411yescharacteristic
812C22×Q8C2411yescharacteristic
813C22×Q8C2414yes—
814C22×Q8C2414yes—
815C22×D4C2411yescharacteristic
816C22×D4C2412yes—
817C23×C4C2412yes—
818C23×C4C2411yescharacteristic
819C23×C4C2411yescharacteristic
820C23×C4C2411yescharacteristic
821C23×C4C2414yes—
822C4⋊Q8—44no—
823C4⋊Q8—44no—
824C4⋊Q8—44no—
825C4⋊Q8—44no—
826C4⋊Q8—42no—
827C4⋊Q8—84no—
828C4⋊Q8—82no—
829#126—84no—
830#126—84no—
831#126—84no—
832#126—84no—
833#125—24no—
834#125—28no—
835#125—44no—
836#125—44no—
837#125—42no—
838#125—44no—
839#125—44no—
840#125—82no—
841#124—42no—
842C22⋊Q8—42no—
843C22⋊Q8—44no—
844C22⋊Q8—42no—
845C22⋊Q8—42no—
846C22⋊Q8—44no—
847#121—24no—
848C4×Q8—24no—
849C4×Q8—24no—
850C4×Q8—24no—
851C4×Q8—24no—
852C4×Q8—44no—
853C4×Q8—44no—
854C4×Q8—42no—
855C4×Q8—84no—
856C4×D4—24no—
857C4×D4—44no—
858C4×D4—44no—
859#117—44no—
860#117—42no—
861#117—42no—
862#117—44no—
863#117—44no—
864#117—82no—
865C2×C4⋊C4—44no—
866C2×C4⋊C4C2411yescharacteristic
867C2×C4⋊C4C2412yes—
868C2×C4⋊C4C2411yescharacteristic
869C2×C4⋊C4C2412yes—
870C2×C4⋊C4C2412yes—
871C2×C4⋊C4C2412yes—
872C2×C4⋊C4C2411yescharacteristic
873C2×C4⋊C4C2412yes—
874C2×C4⋊C4C2411yescharacteristic
875C2×C4⋊C4C2411yescharacteristic
876C2×C4⋊C4C2411yescharacteristic
877C2×C4⋊C4C2411yescharacteristic
878C2×C4⋊C4C2412yes—
879C2×C4⋊C4C2412yes—
880C2×C4⋊C4C2412yes—
881C2×C4⋊C4C2412yes—
882C2×C4⋊C4C2411yescharacteristic
883C2×C4⋊C4C2411yescharacteristic
884C2×C4⋊C4C2412yes—
885C2×C4⋊C4C2412yes—
886C2×C4⋊C4C2411yescharacteristic
887C2×C4⋊C4C2411yescharacteristic
888C2×C4⋊C4C2412yes—
889C2×C4⋊C4C2412yes—
890C2×C4⋊C4C2414yes—
891C2×C4⋊C4C2412yes—
892C2×C4⋊C4C2414yes—
893C2×C4⋊C4C2414yes—
894C2×C4⋊C4C2412yes—
895C2×C4⋊C4C2412yes—
896C2×C4⋊C4C2411yescharacteristic
897C2×C4⋊C4C2411yescharacteristic
898C2×C4⋊C4C2411yescharacteristic
899C2×C4⋊C4C2411yescharacteristic
900C2×C4⋊C4C2412yes—
901C2×C4⋊C4C2412yes—
902C2×C4⋊C4C2412yes—
903C2×C4⋊C4C2412yes—
904C2×C4⋊C4C2414yes—
905C2×C4⋊C4C2414yes—
906C2×C4⋊C4C2412yes—
907C2×C4⋊C4C2414yes—
908C2×C4⋊C4C2414yes—
909C2×C4⋊C4C2412yes—
910C2×C4⋊C4C2412yes—
911C2×C4⋊C4C2412yes—
912C2×C4⋊C4C2414yes—
913C2×C4⋊C4C2414yes—
914C2×C4⋊C4C2414yes—
915C2×C4⋊C4C2412yes—
916C2×C4⋊C4C2414yes—
917C2×C4⋊C4C2414yes—
918C2×C4⋊C4C2414yes—
919C2×C4⋊C4C2412yes—
920C2×C4⋊C4C2412yes—
921C2×C4⋊C4C2414yes—
922C2×C4⋊C4C2414yes—
923C2×C4⋊C4C2414yes—
924C2×C4⋊C4C2414yes—
925C2×C4⋊C4C2414yes—
926C2×C4⋊C4C2412yes—
927C2×C4⋊C4C2412yes—
928C2×C4⋊C4C2412yes—
929C2×C4⋊C4C2414yes—
930C2×C4⋊C4C2414yes—
931C2×C4⋊C4C2414yes—
932C2×C4⋊C4C2414yes—
933C2×C4⋊C4C2414yes—
934C2×C4⋊C4C2412yes—
935C2×C4⋊C4C2412yes—
936C2×C4⋊C4C2414yes—
937C2×C4⋊C4C2412yes—
938C2×C4⋊C4C2412yes—
939C2×C4⋊C4C2414yes—
940C2×C4⋊C4C2414yes—
941C2×C4⋊C4C2414yes—
942C2×C4⋊C4C2412yes—
943C2×C4⋊C4C2412yes—
944C2×C4⋊C4C2412yes—
945C2×C4⋊C4C2414yes—
946C2×C4⋊C4C2412yes—
947C2×C4⋊C4C2412yes—
948C2×C4⋊C4C2412yes—
949C2×C4⋊C4C2412yes—
950C2×C4⋊C4C2412yes—
951C2×C4⋊C4C2414yes—
952C2×C4⋊C4C2411yescharacteristic
953C2×C22⋊C4C2412yes—
954C2×C22⋊C4C2412yes—
955C2×C22⋊C4C2414yes—
956C2×C22⋊C4C2411yescharacteristic
957C2×C22⋊C4C2411yescharacteristic
958C2×C22⋊C4C2411yescharacteristic
959C2×C22⋊C4C2411yescharacteristic
960C2×C22⋊C4C2414yes—
961C2×C22⋊C4C2412yes—
962C2×C22⋊C4C2412yes—
963C2×C22⋊C4C2414yes—
964C2×C22⋊C4C2412yes—
965C2×C22⋊C4C2414yes—
966C2×C22⋊C4C2412yes—
967C2×C22⋊C4C2412yes—
968C2×C22⋊C4C2412yes—
969C2×C22⋊C4C2412yes—
970C2×C22⋊C4C2414yes—
971C2×C22⋊C4C2414yes—
972C2×C22⋊C4C2412yes—
973C2×C22⋊C4C2412yes—
974C2×C22⋊C4C2412yes—
975C2×C22⋊C4C2412yes—
976C2×C22⋊C4C2412yes—
977C2×C22⋊C4C2414yes—
978C2×C22⋊C4C2412yes—
979C2×C22⋊C4C2412yes—
980C2×C22⋊C4C2414yes—
981C2×C22⋊C4C2414yes—
982C2×C22⋊C4C2412yes—
983C2×C22⋊C4C2412yes—
984C2×C22⋊C4C2412yes—
985C2×C42—24no—
986C2×C42C2411yescharacteristic
987C2×C42C2412yes—
988C2×C42C2411yescharacteristic
989C2×C42C2411yescharacteristic
990C2×C42C2411yescharacteristic
991C2×C42C2412yes—
992C2×C42C2412yes—
993C2×C42C2411yescharacteristic
994C2×C42C2412yes—
995C2×C42C2412yes—
996C2×C42C2411yescharacteristic
997C2×C42C2412yes—
998C2×C42C2412yes—
999C2×C42C2411yescharacteristic
1000C2×C42C2411yescharacteristic
1001C2×C42C2412yes—
1002C2×C42C2411yescharacteristic
1003C2×C42C2411yescharacteristic
1004C2×C42C2411yescharacteristic
1005C2×C42C2414yes—
1006C2×C42C2414yes—
1007C2×C42C2414yes—
1008C2×C42C2412yes—
1009C2×C42C2414yes—
1010C2×C42C2414yes—
1011C2×C42C2412yes—
1012C2×C42C2414yes—
1013C2×C42C2414yes—
1014C2×C42C2411yescharacteristic
1015C2×C42C2414yes—
1016C2×C42C2411yescharacteristic
1017C2×C42C2411yescharacteristic
1018C2×C42C2411yescharacteristic
1019C2×C42C2412yes—
1020C2×C42C2414yes—
1021C2×C42C2411yescharacteristic
1022#95C2412yes—
1023#95C2411yescharacteristic
1024#95C2411yescharacteristic
1025#95C2411yescharacteristic
1026#95C2411yescharacteristic
1027#95C2411yescharacteristic
1028#95C2411yescharacteristic
1029#95C2411yescharacteristic
1030#95C2411yescharacteristic
1031#95C2412yes—
1032#95C2412yes—
1033#95C2414yes—
1034#95C2414yes—
1035#95C2414yes—
1036#95C2412yes—
1037#95C2412yes—
1038#95C2412yes—
1039#95C2412yes—
1040#95C2412yes—
1041#95C2412yes—
1042#95C2412yes—
1043#95C2412yes—
1044#95C2412yes—
1045#95C2412yes—
1046#95C2412yes—
1047#95C2412yes—
1048#95C2412yes—
1049#95C2412yes—
1050#95C2412yes—
1051#95C2412yes—
1052#95C2414yes—
1053#95C2412yes—
1054#95C2412yes—
1055#95C2412yes—
1056#95C2412yes—
1057#95C2412yes—
1058#95C2412yes—
1059#95C2412yes—
1060#95C2412yes—
1061#95C2412yes—
1062#95C2412yes—
1063#95C2412yes—
1064#95C2412yes—
1065#95C2414yes—
1066#95C2414yes—
1067#95C2412yes—
1068#95C2414yes—
1069#95C2414yes—
1070#95C2412yes—
1071#95C2414yes—
1072#95C2414yes—
1073#95C2412yes—
1074#95C2414yes—
1075#95C2412yes—
1076#95C2414yes—
1077#95C2412yes—
1078#95C2412yes—
1079#95C2414yes—
1080#95C2412yes—
1081#95C2414yes—
1082#95C2412yes—
1083#95C2412yes—
1084#95C2414yes—
1085#95C2414yes—
1086#95C2412yes—
1087#95C2414yes—
1088#95C2414yes—
1089#95C2414yes—
1090#95C2412yes—
1091#95C2412yes—
1092#95C2412yes—
1093#95C2412yes—
1094#95C2412yes—
1095#95C2412yes—
1096#95C2414yes—
1097#95C2412yes—
1098#95C2412yes—
1099#95C2414yes—
1100#95C2414yes—
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—
1118C24C2512yes—
1119C24C2511yescharacteristic
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—22no—
1136C2×D4—22no—
1137C2×D4—24no—
1138C2×D4—22no—
1139C2×D4—42no—
1140C2×D4—42no—
1141C22×C4—22no—
1142C22×C4—22no—
1143C22×C4—22no—
1144C22×C4—24no—
1145C22×C4—22no—
1146C22×C4—24no—
1147C22×C4—22no—
1148C22×C4—22no—
1149C22×C4—24no—
1150C22×C4—22no—
1151C22×C4—41no—
1152C22×C4—41no—
1153C22×C4—44no—
1154C22×C4—44no—
1155C22×C4—44no—
1156C22×C4C2511yescharacteristic
1157C22×C4C2512yes—
1158C22×C4C2511yescharacteristic
1159C22×C4C2511yescharacteristic
1160C22×C4C2511yescharacteristic
1161C22×C4C2512yes—
1162C22×C4C2512yes—
1163C22×C4C2512yes—
1164C22×C4C2511yescharacteristic
1165C22×C4C2511yescharacteristic
1166C22×C4C2512yes—
1167C22×C4C2512yes—
1168C22×C4C2512yes—
1169C22×C4C2512yes—
1170C22×C4C2512yes—
1171C22×C4C2514yes—
1172C22×C4C2511yescharacteristic
1173C22×C4C2511yescharacteristic
1174C22×C4C2511yescharacteristic
1175C22×C4C2512yes—
1176C22×C4C2512yes—
1177C22×C4C2514yes—
1178C22×C4C2512yes—
1179C22×C4C2511yescharacteristic
1180C22×C4C2512yes—
1181C22×C4C2512yes—
1182C22×C4C2514yes—
1183C22×C4C2514yes—
1184C22×C4C2511yescharacteristic
1185C22×C4C2512yes—
1186C22×C4C2511yescharacteristic
1187C22×C4C2511yescharacteristic
1188C22×C4C2511yescharacteristic
1189C4⋊C4—22no—
1190C4⋊C4—22no—
1191C4⋊C4—22no—
1192C4⋊C4—22no—
1193C4⋊C4—24no—
1194C4⋊C4—24no—
1195C4⋊C4—24no—
1196C4⋊C4—24no—
1197C4⋊C4—24no—
1198C4⋊C4—28no—
1199C4⋊C4—24no—
1200C4⋊C4—28no—
1201C4⋊C4—22no—
1202C4⋊C4—24no—
1203C4⋊C4—22no—
1204C4⋊C4—24no—
1205C4⋊C4—22no—
1206C4⋊C4—24no—
1207C4⋊C4—24no—
1208C4⋊C4—24no—
1209C4⋊C4—24no—
1210C4⋊C4—22no—
1211C4⋊C4—22no—
1212C4⋊C4—22no—
1213C4⋊C4—24no—
1214C4⋊C4—24no—
1215C4⋊C4—22no—
1216C4⋊C4—44no—
1217C4⋊C4—42no—
1218C4⋊C4—42no—
1219C4⋊C4—42no—
1220C4⋊C4—42no—
1221C4⋊C4—42no—
1222C4⋊C4—42no—
1223C4⋊C4—44no—
1224C4⋊C4—42no—
1225C4⋊C4—42no—
1226C4⋊C4—44no—
1227C4⋊C4—42no—
1228C4⋊C4—41no—
1229C4⋊C4—41no—
1230C4⋊C4—42no—
1231C4⋊C4—41no—
1232C4⋊C4—41no—
1233C4⋊C4—42no—
1234C4⋊C4—42no—
1235C4⋊C4—42no—
1236C4⋊C4—44no—
1237C4⋊C4—44no—
1238C4⋊C4—42no—
1239C4⋊C4—42no—
1240C4⋊C4—44no—
1241C4⋊C4—44no—
1242C4⋊C4—42no—
1243C4⋊C4—44no—
1244C4⋊C4—42no—
1245C4⋊C4—44no—
1246C4⋊C4—42no—
1247C4⋊C4—44no—
1248C4⋊C4—44no—
1249C4⋊C4—44no—
1250C4⋊C4—42no—
1251C4⋊C4—42no—
1252C4⋊C4—44no—
1253C4⋊C4—44no—
1254C4⋊C4—44no—
1255C4⋊C4—44no—
1256C4⋊C4—44no—
1257C4⋊C4—44no—
1258C4⋊C4—42no—
1259C4⋊C4—44no—
1260C4⋊C4—42no—
1261C4⋊C4—44no—
1262C4⋊C4—42no—
1263C4⋊C4—42no—
1264C4⋊C4—44no—
1265C4⋊C4—44no—
1266C4⋊C4—44no—
1267C4⋊C4—44no—
1268C4⋊C4—44no—
1269C4⋊C4—44no—
1270C4⋊C4—42no—
1271C4⋊C4—42no—
1272C4⋊C4—44no—
1273C4⋊C4—42no—
1274C4⋊C4—42no—
1275C4⋊C42−1+414yes—
1276C22⋊C4—24no—
1277C22⋊C4—24no—
1278C22⋊C4—42no—
1279C22⋊C4—42no—
1280C22⋊C4—42no—
1281C22⋊C4—42no—
1282C22⋊C4—41no—
1283C22⋊C4—41no—
1284C22⋊C4—42no—
1285C22⋊C4—41no—
1286C22⋊C4—41no—
1287C22⋊C4—44no—
1288C22⋊C4—44no—
1289C22⋊C4—44no—
1290C22⋊C4—42no—
1291C22⋊C4—44no—
1292C22⋊C4—42no—
1293C22⋊C4—42no—
1294C22⋊C4—42no—
1295C22⋊C4—44no—
1296C22⋊C4—42no—
1297C22⋊C4—44no—
1298C22⋊C4—42no—
1299C22⋊C4—42no—
1300C22⋊C4—42no—
1301C22⋊C4—42no—
1302C22⋊C4—42no—
1303C22⋊C4—44no—
1304C22⋊C4—42no—
1305C22⋊C4—44no—
1306C22⋊C4—44no—
1307C22⋊C4—42no—
1308C42—22no—
1309C42—22no—
1310C42—22no—
1311C42—22no—
1312C42—24no—
1313C42—24no—
1314C42—24no—
1315C42—24no—
1316C42—22no—
1317C42—24no—
1318C42—22no—
1319C42—24no—
1320C42—22no—
1321C42—22no—
1322C42—22no—
1323C42—24no—
1324C42—24no—
1325C42—22no—
1326C42—22no—
1327C42—42no—
1328C42—44no—
1329C42—41no—
1330C42—41no—
1331C42—44no—
1332C42—44no—
1333C42—44no—
1334C42—44no—
1335C42—44no—
1336C42—42no—
1337C42—42no—
1338C42—44no—
1339C42—44no—
1340C42—41no—
1341C42—44no—
1342C42—41no—
1343C422−1+414yes—
1344C23—22no—
1345C23—22no—
1346C23—21no—
1347C23—21no—
1348C23—21no—
1349C23—21no—
1350C23—22no—
1351C23—22no—
1352C23—21no—
1353C23—22no—
1354C23—22no—
1355C23—21no—
1356C23—22no—
1357C23—21no—
1358C23C2611yescharacteristic
1359Q8—44no—
1360Q8—44no—
1361Q8—44no—
1362Q8—88no—
1363Q8—164no—
1364D4—44no—
1365D4—84no—
1366C2×C4—22no—
1367C2×C4—21no—
1368C2×C4—22no—
1369C2×C4—21no—
1370C2×C4—21no—
1371C2×C4—21no—
1372C2×C4—21no—
1373C2×C4—21no—
1374C2×C4—22no—
1375C2×C4—22no—
1376C2×C4—22no—
1377C2×C4—21no—
1378C2×C4—21no—
1379C2×C4—22no—
1380C2×C4—21no—
1381C2×C4—22no—
1382C2×C4—22no—
1383C2×C4—22no—
1384C2×C4—22no—
1385C2×C4—22no—
1386C2×C4—21no—
1387C2×C4—22no—
1388C2×C4—22no—
1389C2×C4—24no—
1390C2×C4—22no—
1391C2×C4—21no—
1392C2×C4—21no—
1393C2×C4—21no—
1394C2×C4—21no—
1395C2×C4—22no—
1396C2×C4—22no—
1397C2×C4—21no—
1398C2×C4—21no—
1399C2×C4—21no—
1400C2×C4—22no—
1401C2×C4—21no—
1402C2×C4—21no—
1403C2×C4—21no—
1404C2×C4—21no—
1405C2×C4—21no—
1406C2×C4—22no—
1407C2×C4—21no—
1408C2×C4—22no—
1409C2×C4—24no—
1410C2×C4—22no—
1411C2×C4—22no—
1412C2×C4—22no—
1413C2×C4—22no—
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—22no—
1423C2×C4—22no—
1424C2×C4—24no—
1425C2×C4—24no—
1426C2×C4—24no—
1427C2×C4—22no—
1428C2×C4—22no—
1429C2×C4—21no—
1430C2×C4—22no—
1431C2×C4—21no—
1432C2×C4—21no—
1433C2×C4—22no—
1434C2×C4—24no—
1435C2×C4—22no—
1436C2×C4—22no—
1437C2×C4—22no—
1438C2×C4—24no—
1439C2×C4—21no—
1440C2×C4—21no—
1441C2×C4—24no—
1442C2×C4—22no—
1443C2×C4—21no—
1444C2×C4—22no—
1445C2×C4—21no—
1446C2×C4—22no—
1447C2×C4—21no—
1448C2×C4—21no—
1449C2×C4—22no—
1450C2×C4—21no—
1451C2×C4—24no—
1452C2×C4—22no—
1453C2×C4—22no—
1454C2×C4—22no—
1455C2×C4—21no—
1456C2×C4—22no—
1457C2×C4—44no—
1458C2×C4—44no—
1459C2×C4—44no—
1460C2×C4—48no—
1461C2×C4—164no—
1462C2×C4C2×2−1+412yes—
1463C2×C4C2×2−1+414yes—
1464C2×C4C2×2−1+412yes—
1465C2×C4C2×2−1+412yes—
1466C2×C4C2×2−1+412yes—
1467C2×C4#58512yes—
1468C2×C4#58512yes—
1469C2×C4#58512yes—
1470C22—42no—
1471C22—41no—
1472C22—41no—
1473C22—42no—
1474C22—41no—
1475C22—42no—
1476C22—41no—
1477C22—42no—
1478C22—42no—
1479C22—41no—
1480C22—42no—
1481C22—41no—
1482C22—41no—
1483C22—42no—
1484C22C22×2−1+411yescharacteristic
1485C22C22×2−1+411yescharacteristic
1486C22C2×#58511yescharacteristic
1487C22C2×#58511yescharacteristic
1488C22C2×#58511yescharacteristic
1489C22H(7,𝔽2)11yescharacteristic
1490C222−1+611yescharacteristic
1491C4—22no—
1492C4—24no—
1493C4—41no—
1494C4—42no—
1495C4—42no—
1496C4—42no—
1497C4—41no—
1498C4—42no—
1499C4—42no—
1500C4—42no—
1501C4—42no—
1502C4—41no—
1503C4—41no—
1504C4—41no—
1505C4—42no—
1506C4—41no—
1507C4—41no—
1508C4—42no—
1509C4—42no—
1510C4—44no—
1511C4—42no—
1512C4—41no—
1513C4—41no—
1514C4—44no—
1515C4—42no—
1516C4—41no—
1517C4—42no—
1518C4—42no—
1519C4—44no—
1520C4—44no—
1521C4—41no—
1522C4#355514yes—
1523C4#356514yes—
1524C2—81no—
1525C2—82no—
1526C2C2×#356511yescharacteristic
1527C2C2×#355511yescharacteristic
1528C2#6287711yescharacteristic
1529C2#6295011yescharacteristic
1530C2#6295211yescharacteristic
1531C2#6296811yescharacteristic
1532C2#6296911yescharacteristic
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. #59249C2semidirect
2. #59242C2semidirect
5. #57617C2semidirect
6. #56801C2semidirect
7. #55196C2semidirect
8. #54576C2semidirect
9. #53092C2semidirect
10. #53058C2semidirect
11. #53035C2semidirect
12. #53010C2semidirect
13. #45202C2semidirect
16. #42774C2semidirect
17. #42728C2semidirect
18. #42717C2semidirect
19. #42597C2semidirect
20. #42530C2semidirect
21. #39761C2semidirect
22. #39625C2semidirect
23. #39294C2semidirect
24. #39192C2semidirect
25. #39183C2semidirect
26. #38977C2semidirect
27. #38966C2semidirect
28. #38265C2semidirect
29. #37637C2semidirect
30. #37403C2semidirect
31. #36497C2semidirect
32. #36285C2semidirect
33. #35294C2semidirect
35. #34629C2semidirect

Maximal subgroups

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

subgroupindex
#592492
#592422
#592302
#592182
#576172
#568012
#551962
#545762
#530922
#530582
#530352
#530102
#452022
#451932
#427812
#427742
#427282
#427172
#425972
#425302
#397612
#396252
#392942
#391922
#391832
#389772
#389662
#382652
#376372
#374032
#364972
#362852
#352942
#349152
#346292