Finite Group Databasebeta

← #8467009

Subgroups — #8467009

Order 512.

3941 conjugacy classes of subgroups.

The subgroup lattice has 1523 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59672C211yesmaximal, characteristic, complemented
2#59665C211yesmaximal, characteristic, complemented
3#59456C211yesmaximal, characteristic, complemented
4#58097C214yesmaximal, complemented
5#54911C214yesmaximal, complemented
6#54288C214yesmaximal, complemented
7#53131C212yesmaximal, complemented
8#53107C212yesmaximal, complemented
9#49715C214yesmaximal, complemented
10#46191C212yesmaximal, complemented
11#45674C212yesmaximal, complemented
12#45346C212yesmaximal, complemented
13#45164C212yesmaximal, complemented
14#42832C212yesmaximal, complemented
15#42713C212yesmaximal, complemented
16#42687C212yesmaximal
17#42569C212yesmaximal
18#39643C211yesmaximal, characteristic, complemented
19#39642C211yesmaximal, characteristic, complemented
20#39478C212yesmaximal, complemented
21#39203C211yesmaximal, characteristic
22#39203C211yesmaximal, characteristic
23#39177C212yesmaximal, complemented
24#39027C212yesmaximal
25#37982C212yesmaximal, complemented
26#37637C211yesmaximal, characteristic
27#37367C212yesmaximal
28#37323C212yesmaximal, complemented
29#36598C211yesmaximal, characteristic, complemented
30#36556C211yesmaximal, characteristic, complemented
31#36194C211yesmaximal, characteristic
32#35185C211yesmaximal, characteristic
33#35176C211yesmaximal, characteristic
34#34920C211yesmaximal, characteristic, complemented
35#34893C211yesmaximal, characteristic
36#2868C2211yescharacteristic
37#2864C2212yes—
38#2864C2212yes—
39#2862C2211yescharacteristic
40#2862C2211yescharacteristic
41#2860C2212yes—
42#2857C2212yes—
43#2857C2212yes—
44#2855C2212yes—
45#2839C2214yes—
46#2839C2214yes—
47#2839C2214yes—
48#2839C2214yes—
49#2836C2214yes—
50#2831C2214yes—
51#2831C2214yes—
52#2822C2214yes—
53#2810C2214yes—
54#2809C2214yes—
55#2809C2214yes—
56#2805C2214yes—
57#2805C2214yes—
58#2799C2214yes—
59#2799C2214yes—
60#2799C2214yes—
61#2798C2214yes—
62#2798C2214yes—
63#2791C2214yes—
64#2783C2214yes—
65#2783C2214yes—
66#2774C2214yes—
67#2774C2214yes—
68#2774C2214yes—
69#2772C2214yes—
70#2772C2214yes—
71#2772C2214yes—
72#2767C2214yes—
73#2767C2214yes—
74#2767C2214yes—
75#2767C2214yes—
76#2767C2214yes—
77#2767C2214yes—
78#2755C2214yes—
79#2755C2214yes—
80#2754C2214yes—
81#2754C2214yes—
82#2754C2214yes—
83#2747C2214yes—
84#2747C2214yes—
85#2747C2214yes—
86#2747C2214yes—
87#2744C2214yes—
88#2739C2214yes—
89#2726C2214yes—
90#2725C2214yes—
91#2722C2214yes—
92#2721C2214yes—
93#2719C2214yes—
94#2719C2214yes—
95#2713C2214yes—
96#2713C2214yes—
97#2698C2214yes—
98#2690C2214yes—
99#2690C2214yes—
100#2690C2214yes—
101#2689C2214yes—
102#2667C2214yes—
103#2654C2214yes—
104#2654C2214yes—
105#2650C2214yes—
106#2650C2214yes—
107#2650C2214yes—
108#2647C2212yes—
109#2647C2212yes—
110#2647C2212yes—
111#2644C2212yes—
112#2637C2214yes—
113#2629C2212yes—
114#2625C2212yes—
115#2625C2212yes—
116#2625C2212yes—
117#2625C2214yes—
118#2590C2214yes—
119#2590C2214yes—
120#2590C2214yes—
121#2590C2212yes—
122#2589C2212yes—
123#2588C2212yes—
124#2588C2214yes—
125#2587C2212yes—
126#2585C2214yes—
127#2585C2214yes—
128#2584C2212yes—
129#2584C2212yes—
130#2584C2211yescharacteristic
131#2584C2211yescharacteristic
132#2582C2212yes—
133#2582C2212yes—
134#2581C2211yescharacteristic
135#2580C2211yescharacteristic
136#2571C2212yes—
137#2571C2211yescharacteristic
138#2571C2212yes—
139#2571C2212yes—
140#2571C2212yes—
141#2570C2212yes—
142#2570C2212yes—
143#2570C2212yes—
144#2570C2212yes—
145#2568C2212yes—
146#2568C2212yes—
147#2567C2211yescharacteristic
148#2567C2211yescharacteristic
149#2566C2211yescharacteristic
150#2565C2214yes—
151#2565C2211yescharacteristic
152#2565C2212yes—
153#2563C2211yescharacteristic
154#2563C2211yescharacteristic
155#2552C2211yescharacteristic
156#2552C2212yes—
157#2552C2211yescharacteristic
158#2552C2212yes—
159#2552C2212yes—
160#2552C2212yes—
161#2550C2211yescharacteristic
162#2550C2212yes—
163#2550C2211yescharacteristic
164#2546C2211yescharacteristic
165#2542C2211yescharacteristic
166#2538C2211yescharacteristic
167#2538C2212yes—
168#2522C2212yes—
169#2522C2214yes—
170#2520C2214yes—
171#2520C2214yes—
172#2520C2212yes—
173#2519C2214yes—
174#2519C2214yes—
175#2513C2212yes—
176#2513C2212yes—
177#2513C2212yes—
178#2513C2212yes—
179#2513C2212yes—
180#2512C2212yes—
181#2511C2214yes—
182#2511C2212yes—
183#2511C2212yes—
184#2511C2212yes—
185#2511C2212yes—
186#2511C2212yes—
187#2511C2212yes—
188#2509C2212yes—
189#2509C2212yes—
190#2509C2212yes—
191#2509C2211yescharacteristic
192#2509C2212yes—
193#2509C2212yes—
194#2508C2212yes—
195#2508C2212yes—
196#2508C2212yes—
197#2508C2211yescharacteristic
198#2508C2214yes—
199#2508C2214yes—
200#2508C2212yes—
201#2508C2212yes—
202#2508C2212yes—
203#2507C2212yes—
204#2507C2211yescharacteristic
205#2507C2212yes—
206#2506C2212yes—
207#2506C2212yes—
208#2506C2212yes—
209#2506C2212yes—
210#2506C2212yes—
211#2506C2211yescharacteristic
212#2506C2212yes—
213#2497C2212yes—
214#2497C2212yes—
215#2496C2212yes—
216#2496C2212yes—
217#2492C2214yes—
218#2489C2212yes—
219#2489C2212yes—
220#2489C2212yes—
221#2475C2214yes—
222#2475C2214yes—
223#2469C2214yes—
224#2465C2212yes—
225#2462C2212yes—
226#2454C2212yes—
227#2454C2211yescharacteristic
228#2453C2214yes—
229#2453C2212yes—
230#2453C2211yescharacteristic
231#2452C2211yescharacteristic
232#2451C2212yes—
233#2451C2211yescharacteristic
234#2446C2212yes—
235#2446C2212yes—
236#2446C2212yes—
237#2446C2212yes—
238#2439C2214yes—
239#2429C2212yes—
240#2423C2212yes—
241#2421C2212yes—
242#2421C2212yes—
243#2421C2212yes—
244#2402C2212yes—
245#2399C2212yes—
246#2396C2212yes—
247#2396C2212yes—
248#2382C2214yes—
249#2370C2212yes—
250#2370C2212yes—
251#2370C2212yes—
252#2369C2211yescharacteristic
253#2369C2211yescharacteristic
254#2369C2211yescharacteristic
255#2369C2211yescharacteristic
256#2365C2211yescharacteristic
257#2365C2211yescharacteristic
258#2365C2212yes—
259#2365C2212yes—
260#2355C2212yes—
261#2355C2212yes—
262#2355C2212yes—
263#2355C2212yes—
264#2355C2212yes—
265#2355C2212yes—
266#2354C2212yes—
267#2351C2212yes—
268#2331C2212yes—
269#2330C2212yes—
270#2330C2212yes—
271#2323C2212yes—
272#2323C2212yes—
273#2323C2212yes—
274#2319C2212yes—
275#2314C2212yes—
276#2314C2214yes—
277C4×C4⋊Q8C2211yescharacteristic
278C4×C4⋊Q8C2211yescharacteristic
279C4×C4⋊Q8C2211yescharacteristic
280C4×C4⋊Q8C2211yescharacteristic
281C4×C4⋊Q8C2211yescharacteristic
282C4×#125C2212yes—
283C4×#125C2211yescharacteristic
284C4×#125C2211yescharacteristic
285C4×#125C2211yescharacteristic
286C4×#125C2211yescharacteristic
287C4×#125C2212yes—
288C4×C22⋊Q8C2212yes—
289#2296C2212yes—
290#2295C2211yescharacteristic
291#2295C2212yes—
292#2295C2211yescharacteristic
293#2293C2211yescharacteristic
294#2293C2211yescharacteristic
295#2285C2212yes—
296C42×Q8C2211yescharacteristic
297C42×Q8C2211yescharacteristic
298C42×D4C2211yescharacteristic
299C2×C4⋊Q8C2311yescharacteristic
300C2×C4⋊Q8C2311yescharacteristic
301C2×C4⋊Q8C2311yescharacteristic
302C2×C4⋊Q8C2311yescharacteristic
303C2×C4⋊Q8C2311yescharacteristic
304C2×C4⋊Q8C2312yes—
305C2×C4⋊Q8C2312yes—
306C2×C4⋊Q8C2312yes—
307C2×#126C2314yes—
308C2×#126C2314yes—
309C2×#125C2311yescharacteristic
310C2×#125C2311yescharacteristic
311C2×#125C2312yes—
312C2×#125C2311yescharacteristic
313C2×#125C2311yescharacteristic
314C2×#125C2312yes—
315C2×#125C2312yes—
316C2×#125C2314yes—
317C2×#125C2314yes—
318C2×#125C2314yes—
319C2×#125C2314yes—
320C2×C22⋊Q8C2312yes—
321C2×C22⋊Q8C2312yes—
322C2×C22⋊Q8C2312yes—
323C2×C22⋊Q8C2312yes—
324C2×C22⋊Q8C2314yes—
325C2×C4×Q8C2312yes—
326C2×C4×Q8C2311yescharacteristic
327C2×C4×Q8C2311yescharacteristic
328C2×C4×Q8C2312yes—
329C2×C4×Q8C2312yes—
330C2×C4×Q8C2312yes—
331C2×C4×Q8C2311yescharacteristic
332C2×C4×Q8C2311yescharacteristic
333C2×C4×Q8C2311yescharacteristic
334C2×C4×Q8C2312yes—
335C2×C4×Q8C2311yescharacteristic
336C2×C4×Q8C2312yes—
337C2×C4×Q8C2312yes—
338C2×C4×D4C2311yescharacteristic
339C2×C4×D4C2311yescharacteristic
340C2×C4×D4C2311yescharacteristic
341C2×#117C2312yes—
342C2×#117C2314yes—
343C2×#117C2312yes—
344C22×C42C2312yes—
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#400C2314yes—
366#400C2314yes—
367#400C2314yes—
368#400C2314yes—
369#400C2314yes—
370#400C2312yes—
371#400C2312yes—
372#400C2312yes—
373#400C2314yes—
374#400C2314yes—
375#400C2314yes—
376#400C2314yes—
377#400C2312yes—
378#400C2312yes—
379#400C2314yes—
380#400C2312yes—
381#400C2314yes—
382#400C2314yes—
383#400C2314yes—
384#400C2314yes—
385#400C2314yes—
386#400C2314yes—
387#399C2312yes—
388#399C2314yes—
389#399C2312yes—
390#399C2314yes—
391#398C2314yes—
392#398C2314yes—
393#398C2314yes—
394#398C2314yes—
395#398C2314yes—
396#398C2312yes—
397#398C2312yes—
398#398C2314yes—
399#398C2312yes—
400#398C2312yes—
401#398C2314yes—
402#398C2314yes—
403#398C2314yes—
404#398C2314yes—
405#398C2314yes—
406#398C2314yes—
407#398C2314yes—
408#398C2314yes—
409#398C2314yes—
410#398C2314yes—
411#398C2314yes—
412#398C2314yes—
413#398C2314yes—
414#398C2314yes—
415#398C2314yes—
416#398C2312yes—
417#398C2312yes—
418#398C2314yes—
419#398C2314yes—
420#398C2314yes—
421#398C2314yes—
422#398C2314yes—
423#398C2314yes—
424#398C2312yes—
425#398C2314yes—
426#398C2312yes—
427#398C2314yes—
428#398C2312yes—
429#398C2312yes—
430#398C2312yes—
431#398C2312yes—
432#398C2314yes—
433#397C2314yes—
434#397C2314yes—
435#397C2314yes—
436#397C2314yes—
437#397C2314yes—
438#397C2314yes—
439#397C2314yes—
440#397C2314yes—
441#397C2314yes—
442#397C2314yes—
443#397C2314yes—
444#397C2314yes—
445#397C2314yes—
446#397C2314yes—
447#396C2312yes—
448#396C2312yes—
449#396C2314yes—
450#396C2314yes—
451#396C2314yes—
452#396C2312yes—
453#396C2314yes—
454#396C2312yes—
455#396C2314yes—
456#396C2314yes—
457#395C2314yes—
458#395C2314yes—
459#395C2312yes—
460#395C2312yes—
461#395C2314yes—
462#395C2312yes—
463#395C2314yes—
464#395C2312yes—
465#395C2312yes—
466#395C2312yes—
467#393C2314yes—
468#393C2314yes—
469#393C2312yes—
470#393C2312yes—
471#391C2312yes—
472#391C2312yes—
473#391C2312yes—
474#391C2312yes—
475#391C2312yes—
476#391C2311yescharacteristic
477#391C2312yes—
478#391C2311yescharacteristic
479#391C2314yes—
480#391C2314yes—
481#391C2312yes—
482#391C2312yes—
483#391C2314yes—
484#391C2312yes—
485#391C2314yes—
486#391C2312yes—
487#391C2312yes—
488#391C2312yes—
489#391C2312yes—
490#391C2311yescharacteristic
491#391C2311yescharacteristic
492#391C2314yes—
493#391C2312yes—
494#391C2312yes—
495#391C2314yes—
496#391C2312yes—
497#391C2312yes—
498#391C2314yes—
499#391C2312yes—
500#391C2312yes—
501#391C2314yes—
502#391C2314yes—
503#391C2312yes—
504#391C2314yes—
505#391C2312yes—
506#390C2312yes—
507#390C2312yes—
508#390C2311yescharacteristic
509#390C2311yescharacteristic
510#390C2312yes—
511#390C2312yes—
512#390C2311yescharacteristic
513#390C2311yescharacteristic
514#389C2312yes—
515#389C2311yescharacteristic
516#389C2311yescharacteristic
517#389C2311yescharacteristic
518#389C2312yes—
519#389C2311yescharacteristic
520#389C2311yescharacteristic
521#389C2312yes—
522#389C2312yes—
523#389C2311yescharacteristic
524#389C2311yescharacteristic
525#389C2311yescharacteristic
526#389C2312yes—
527#389C2312yes—
528#389C2312yes—
529#389C2311yescharacteristic
530#389C2311yescharacteristic
531#389C2312yes—
532#389C2312yes—
533#389C2311yescharacteristic
534#389C2311yescharacteristic
535#389C2312yes—
536#389C2312yes—
537#389C2312yes—
538#389C2312yes—
539#389C2312yes—
540#389C2312yes—
541#389C2311yescharacteristic
542#389C2311yescharacteristic
543#389C2312yes—
544#389C2312yes—
545#389C2311yescharacteristic
546#389C2311yescharacteristic
547#389C2312yes—
548#389C2314yes—
549#389C2314yes—
550#389C2314yes—
551#389C2314yes—
552#389C2312yes—
553#389C2312yes—
554#389C2312yes—
555#389C2312yes—
556#389C2312yes—
557#389C2312yes—
558#389C2312yes—
559#389C2314yes—
560#389C2314yes—
561#389C2311yescharacteristic
562#389C2312yes—
563#389C2314yes—
564#389C2314yes—
565#389C2314yes—
566#389C2314yes—
567#389C2312yes—
568#389C2312yes—
569#389C2312yes—
570#389C2312yes—
571#389C2312yes—
572#389C2312yes—
573#389C2312yes—
574#389C2314yes—
575#389C2311yescharacteristic
576#389C2314yes—
577#389C2311yescharacteristic
578#389C2312yes—
579#389C2314yes—
580#389C2314yes—
581#389C2314yes—
582#389C2314yes—
583#389C2314yes—
584#389C2314yes—
585#389C2312yes—
586#389C2314yes—
587#389C2311yescharacteristic
588#389C2314yes—
589#389C2312yes—
590#389C2312yes—
591#389C2312yes—
592#389C2312yes—
593#389C2312yes—
594#388C2314yes—
595#388C2314yes—
596#388C2314yes—
597#388C2314yes—
598#388C2314yes—
599#388C2314yes—
600#388C2314yes—
601#388C2314yes—
602#388C2312yes—
603#388C2314yes—
604#388C2314yes—
605#388C2314yes—
606#388C2314yes—
607#388C2314yes—
608#388C2314yes—
609#388C2314yes—
610#388C2312yes—
611#388C2312yes—
612#388C2312yes—
613#388C2314yes—
614#388C2314yes—
615#388C2314yes—
616#387C2312yes—
617#387C2312yes—
618#387C2312yes—
619#387C2312yes—
620#387C2312yes—
621#387C2312yes—
622#387C2312yes—
623#387C2314yes—
624#387C2312yes—
625#387C2312yes—
626#387C2312yes—
627#387C2312yes—
628#387C2312yes—
629#387C2314yes—
630#387C2314yes—
631#387C2314yes—
632#387C2314yes—
633#387C2312yes—
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#387C2312yes—
647#387C2314yes—
648#387C2314yes—
649#387C2314yes—
650#387C2312yes—
651#387C2312yes—
652#387C2314yes—
653#387C2314yes—
654#387C2314yes—
655#387C2314yes—
656#387C2312yes—
657#387C2314yes—
658#387C2314yes—
659#387C2314yes—
660#387C2314yes—
661#387C2314yes—
662#387C2314yes—
663#387C2314yes—
664#387C2314yes—
665#387C2314yes—
666#387C2314yes—
667#387C2312yes—
668#387C2314yes—
669#387C2314yes—
670#387C2314yes—
671#387C2314yes—
672#387C2314yes—
673#387C2312yes—
674#387C2314yes—
675#387C2312yes—
676#387C2314yes—
677#387C2314yes—
678#387C2314yes—
679#387C2314yes—
680#387C2314yes—
681#387C2314yes—
682#387C2314yes—
683#387C2314yes—
684#387C2314yes—
685#387C2312yes—
686#387C2314yes—
687#387C2314yes—
688#387C2312yes—
689#385C2312yes—
690#385C2312yes—
691#385C2312yes—
692#385C2312yes—
693#385C2314yes—
694#385C2312yes—
695#385C2312yes—
696#384C2311yescharacteristic
697#384C2311yescharacteristic
698#384C2311yescharacteristic
699#384C2314yes—
700#384C2312yes—
701#384C2312yes—
702#384C2312yes—
703#384C2312yes—
704#384C2312yes—
705#384C2312yes—
706#384C2312yes—
707#384C2312yes—
708#384C2312yes—
709#382C2311yescharacteristic
710#382C2311yescharacteristic
711#382C2312yes—
712#382C2311yescharacteristic
713#382C2311yescharacteristic
714#382C2312yes—
715#382C2312yes—
716#382C2312yes—
717#382C2312yes—
718#382C2314yes—
719#382C2314yes—
720#382C2314yes—
721#382C2314yes—
722#382C2312yes—
723#382C2312yes—
724#382C2312yes—
725#382C2312yes—
726#382C2314yes—
727#382C2314yes—
728#382C2314yes—
729#382C2314yes—
730#382C2314yes—
731#381C2314yes—
732#380C2312yes—
733#380C2312yes—
734#380C2312yes—
735#380C2312yes—
736#380C2312yes—
737#380C2312yes—
738#380C2314yes—
739#380C2314yes—
740#380C2314yes—
741#380C2314yes—
742C4×C4⋊C4C2311yescharacteristic
743C4×C4⋊C4C2311yescharacteristic
744C4×C4⋊C4C2312yes—
745C4×C4⋊C4C2312yes—
746C4×C4⋊C4C2311yescharacteristic
747C4×C4⋊C4C2311yescharacteristic
748C4×C4⋊C4C2311yescharacteristic
749C4×C4⋊C4C2311yescharacteristic
750C4×C4⋊C4C2312yes—
751C4×C4⋊C4C2311yescharacteristic
752C4×C4⋊C4C2312yes—
753C4×C4⋊C4C2314yes—
754C4×C4⋊C4C2312yes—
755C4×C4⋊C4C2312yes—
756C4×C4⋊C4C2312yes—
757C4×C4⋊C4C2314yes—
758C4×C4⋊C4C2312yes—
759C4×C4⋊C4C2312yes—
760C4×C4⋊C4C2312yes—
761C4×C4⋊C4C2312yes—
762C4×C4⋊C4C2312yes—
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⋊C4C2314yes—
772C4×C4⋊C4C2311yescharacteristic
773C4×C4⋊C4C2311yescharacteristic
774C4×C4⋊C4C2312yes—
775C4×C4⋊C4C2311yescharacteristic
776C4×C4⋊C4C2314yes—
777C4×C4⋊C4C2311yescharacteristic
778C4×C4⋊C4C2312yes—
779C4×C4⋊C4C2311yescharacteristic
780C4×C4⋊C4C2312yes—
781C4×C4⋊C4C2312yes—
782C4×C4⋊C4C2312yes—
783C4×C4⋊C4C2312yes—
784C4×C4⋊C4C2311yescharacteristic
785C4×C4⋊C4C2311yescharacteristic
786C4×C4⋊C4C2314yes—
787C4×C4⋊C4C2314yes—
788C4×C4⋊C4C2312yes—
789C4×C4⋊C4C2311yescharacteristic
790C4×C4⋊C4C2311yescharacteristic
791C4×C4⋊C4C2312yes—
792C4×C4⋊C4C2312yes—
793C4×C4⋊C4C2311yescharacteristic
794C4×C4⋊C4C2314yes—
795C4×C4⋊C4C2312yes—
796C4×C4⋊C4C2311yescharacteristic
797C4×C4⋊C4C2312yes—
798C4×C4⋊C4C2311yescharacteristic
799C4×C22⋊C4C2312yes—
800C4×C22⋊C4C2312yes—
801C4×C22⋊C4C2312yes—
802C4×C22⋊C4C2312yes—
803C4×C22⋊C4C2312yes—
804#376C2312yes—
805#376C2312yes—
806C43C2311yescharacteristic
807C43C2312yes—
808C43C2311yescharacteristic
809C43C2311yescharacteristic
810C22×Q8C2411yescharacteristic
811C22×Q8C2412yes—
812C22×Q8C2411yescharacteristic
813C22×Q8C2412yes—
814C22×Q8C2412yes—
815C22×Q8C2412yes—
816C22×Q8C2412yes—
817C22×D4C2411yescharacteristic
818C23×C4C2412yes—
819C23×C4C2412yes—
820C23×C4C2412yes—
821C4⋊Q8—24no—
822C4⋊Q8—24no—
823C4⋊Q8—24no—
824C4⋊Q8—24no—
825C4⋊Q8—42no—
826C4⋊Q8—44no—
827C4⋊Q8—44no—
828C4⋊Q8—82no—
829#126—84no—
830#126—84no—
831#125—24no—
832#125—28no—
833#125—24no—
834#125—44no—
835#125—42no—
836#125—42no—
837#125—44no—
838#125—48no—
839#125—84no—
840#125—84no—
841#125—84no—
842C22⋊Q8—44no—
843C22⋊Q8—44no—
844C22⋊Q8—44no—
845C22⋊Q8—44no—
846C22⋊Q8—84no—
847C4×Q8—24no—
848C4×Q8—28no—
849C4×Q8—24no—
850C4×Q8—44no—
851C4×Q8—42no—
852C4×Q8—42no—
853C4×Q8—42no—
854C4×Q8—44no—
855C4×Q8—44no—
856C4×Q8—44no—
857C4×Q8—42no—
858C4×Q8—82no—
859C4×Q8—82no—
860C4×D4—24no—
861C4×D4—24no—
862C4×D4—24no—
863#117—44no—
864#117—44no—
865#117—48no—
866C2×C4⋊C4C2412yes—
867C2×C4⋊C4C2414yes—
868C2×C4⋊C4C2411yescharacteristic
869C2×C4⋊C4C2411yescharacteristic
870C2×C4⋊C4C2411yescharacteristic
871C2×C4⋊C4C2411yescharacteristic
872C2×C4⋊C4C2411yescharacteristic
873C2×C4⋊C4C2412yes—
874C2×C4⋊C4C2411yescharacteristic
875C2×C4⋊C4C2411yescharacteristic
876C2×C4⋊C4C2411yescharacteristic
877C2×C4⋊C4C2411yescharacteristic
878C2×C4⋊C4C2412yes—
879C2×C4⋊C4C2411yescharacteristic
880C2×C4⋊C4C2411yescharacteristic
881C2×C4⋊C4C2412yes—
882C2×C4⋊C4C2412yes—
883C2×C4⋊C4C2412yes—
884C2×C4⋊C4C2411yescharacteristic
885C2×C4⋊C4C2411yescharacteristic
886C2×C4⋊C4C2412yes—
887C2×C4⋊C4C2411yescharacteristic
888C2×C4⋊C4C2412yes—
889C2×C4⋊C4C2412yes—
890C2×C4⋊C4C2411yescharacteristic
891C2×C4⋊C4C2412yes—
892C2×C4⋊C4C2411yescharacteristic
893C2×C4⋊C4C2411yescharacteristic
894C2×C4⋊C4C2412yes—
895C2×C4⋊C4C2414yes—
896C2×C4⋊C4C2412yes—
897C2×C4⋊C4C2414yes—
898C2×C4⋊C4C2412yes—
899C2×C4⋊C4C2412yes—
900C2×C4⋊C4C2412yes—
901C2×C4⋊C4C2412yes—
902C2×C4⋊C4C2412yes—
903C2×C4⋊C4C2412yes—
904C2×C4⋊C4C2411yescharacteristic
905C2×C4⋊C4C2412yes—
906C2×C4⋊C4C2412yes—
907C2×C4⋊C4C2412yes—
908C2×C4⋊C4C2412yes—
909C2×C4⋊C4C2412yes—
910C2×C4⋊C4C2412yes—
911C2×C4⋊C4C2412yes—
912C2×C4⋊C4C2414yes—
913C2×C4⋊C4C2414yes—
914C2×C4⋊C4C2412yes—
915C2×C4⋊C4C2411yescharacteristic
916C2×C4⋊C4C2411yescharacteristic
917C2×C4⋊C4C2412yes—
918C2×C4⋊C4C2411yescharacteristic
919C2×C4⋊C4C2412yes—
920C2×C4⋊C4C2411yescharacteristic
921C2×C4⋊C4C2414yes—
922C2×C4⋊C4C2414yes—
923C2×C4⋊C4C2412yes—
924C2×C4⋊C4C2412yes—
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⋊C4C2412yes—
934C2×C4⋊C4C2412yes—
935C2×C4⋊C4C2412yes—
936C2×C4⋊C4C2412yes—
937C2×C4⋊C4C2412yes—
938C2×C4⋊C4C2412yes—
939C2×C4⋊C4C2414yes—
940C2×C4⋊C4C2414yes—
941C2×C4⋊C4C2414yes—
942C2×C4⋊C4C2414yes—
943C2×C4⋊C4C2414yes—
944C2×C4⋊C4C2414yes—
945C2×C4⋊C4C2414yes—
946C2×C4⋊C4C2412yes—
947C2×C4⋊C4C2412yes—
948C2×C4⋊C4C2414yes—
949C2×C4⋊C4C2412yes—
950C2×C4⋊C4C2412yes—
951C2×C4⋊C4C2412yes—
952C2×C4⋊C4C2412yes—
953C2×C4⋊C4C2412yes—
954C2×C4⋊C4C2414yes—
955C2×C4⋊C4C2414yes—
956C2×C4⋊C4C2414yes—
957C2×C4⋊C4C2414yes—
958C2×C4⋊C4C2412yes—
959C2×C4⋊C4C2412yes—
960C2×C4⋊C4C2414yes—
961C2×C4⋊C4C2414yes—
962C2×C4⋊C4C2414yes—
963C2×C4⋊C4C2411yescharacteristic
964C2×C22⋊C4C2412yes—
965C2×C22⋊C4C2412yes—
966C2×C22⋊C4C2412yes—
967C2×C22⋊C4C2414yes—
968C2×C22⋊C4C2414yes—
969C2×C22⋊C4C2412yes—
970C2×C22⋊C4C2412yes—
971C2×C22⋊C4C2412yes—
972C2×C22⋊C4C2412yes—
973C2×C22⋊C4C2414yes—
974C2×C22⋊C4C2414yes—
975C2×C22⋊C4C2412yes—
976C2×C22⋊C4C2412yes—
977C2×C22⋊C4C2414yes—
978C2×C22⋊C4C2414yes—
979C2×C22⋊C4C2414yes—
980C2×C22⋊C4C2412yes—
981C2×C22⋊C4C2412yes—
982C2×C22⋊C4C2414yes—
983C2×C42—44no—
984C2×C42C2411yescharacteristic
985C2×C42C2411yescharacteristic
986C2×C42C2412yes—
987C2×C42C2412yes—
988C2×C42C2411yescharacteristic
989C2×C42C2411yescharacteristic
990C2×C42C2411yescharacteristic
991C2×C42C2411yescharacteristic
992C2×C42C2411yescharacteristic
993C2×C42C2412yes—
994C2×C42C2412yes—
995C2×C42C2411yescharacteristic
996C2×C42C2411yescharacteristic
997C2×C42C2412yes—
998C2×C42C2412yes—
999C2×C42C2411yescharacteristic
1000C2×C42C2412yes—
1001C2×C42C2411yescharacteristic
1002C2×C42C2411yescharacteristic
1003C2×C42C2414yes—
1004C2×C42C2414yes—
1005C2×C42C2411yescharacteristic
1006C2×C42C2411yescharacteristic
1007C2×C42C2414yes—
1008C2×C42C2414yes—
1009C2×C42C2412yes—
1010C2×C42C2411yescharacteristic
1011C2×C42C2412yes—
1012C2×C42C2411yescharacteristic
1013C2×C42C2414yes—
1014C2×C42C2414yes—
1015C2×C42C2414yes—
1016C2×C42C2414yes—
1017C2×C42C2412yes—
1018C2×C42C2414yes—
1019C2×C42C2412yes—
1020C2×C42C2411yescharacteristic
1021C2×C42C2412yes—
1022C2×C42C2412yes—
1023C2×C42C2411yescharacteristic
1024C2×C42C2411yescharacteristic
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#95C2411yescharacteristic
1041#95C2411yescharacteristic
1042#95C2412yes—
1043#95C2412yes—
1044#95C2412yes—
1045#95C2411yescharacteristic
1046#95C2411yescharacteristic
1047#95C2411yescharacteristic
1048#95C2412yes—
1049#95C2412yes—
1050#95C2411yescharacteristic
1051#95C2412yes—
1052#95C2412yes—
1053#95C2412yes—
1054#95C2414yes—
1055#95C2414yes—
1056#95C2414yes—
1057#95C2414yes—
1058#95C2414yes—
1059#95C2412yes—
1060#95C2414yes—
1061#95C2414yes—
1062#95C2414yes—
1063#95C2412yes—
1064#95C2412yes—
1065#95C2412yes—
1066#95C2414yes—
1067#95C2414yes—
1068#95C2412yes—
1069#95C2414yes—
1070#95C2414yes—
1071#95C2412yes—
1072#95C2412yes—
1073#95C2412yes—
1074#95C2412yes—
1075#95C2412yes—
1076#95C2414yes—
1077#95C2414yes—
1078#95C2414yes—
1079#95C2412yes—
1080#95C2414yes—
1081#95C2412yes—
1082#95C2414yes—
1083#95C2412yes—
1084#95C2412yes—
1085#95C2412yes—
1086#95C2412yes—
1087#95C2412yes—
1088#95C2412yes—
1089#95C2412yes—
1090#95C2412yes—
1091#95C2412yes—
1092#95C2412yes—
1093#95C2414yes—
1094#95C2414yes—
1095#95C2414yes—
1096#95C2414yes—
1097#95C2414yes—
1098#95C2414yes—
1099#95C2414yes—
1100#95C2414yes—
1101#95C2414yes—
1102#95C2412yes—
1103#95C2414yes—
1104#95C2414yes—
1105#95C2414yes—
1106#95C2414yes—
1107#95C2414yes—
1108#95C2414yes—
1109#95C2414yes—
1110#95C2414yes—
1111#95C2414yes—
1112#95C2414yes—
1113#95C2414yes—
1114#95C2414yes—
1115#95C2414yes—
1116#95C2414yes—
1117#95C2414yes—
1118#95C2414yes—
1119C24C2512yes—
1120C2×Q8—22no—
1121C2×Q8—22no—
1122C2×Q8—24no—
1123C2×Q8—24no—
1124C2×Q8—24no—
1125C2×Q8—24no—
1126C2×Q8—24no—
1127C2×Q8—24no—
1128C2×Q8—22no—
1129C2×Q8—24no—
1130C2×Q8—22no—
1131C2×Q8—41no—
1132C2×Q8—41no—
1133C2×Q8—42no—
1134C2×Q8—42no—
1135C2×Q8—42no—
1136C2×Q8—42no—
1137C2×Q8—42no—
1138C2×Q8—42no—
1139C2×Q8—42no—
1140C2×Q8—42no—
1141C2×D4—22no—
1142C2×D4—22no—
1143C2×D4—22no—
1144C22×C4—24no—
1145C22×C4—24no—
1146C22×C4—24no—
1147C22×C4—24no—
1148C22×C4—24no—
1149C22×C4—24no—
1150C22×C4—42no—
1151C22×C4—42no—
1152C22×C4—42no—
1153C22×C4C2511yescharacteristic
1154C22×C4C2511yescharacteristic
1155C22×C4C2511yescharacteristic
1156C22×C4C2512yes—
1157C22×C4C2512yes—
1158C22×C4C2514yes—
1159C22×C4C2512yes—
1160C22×C4C2511yescharacteristic
1161C22×C4C2512yes—
1162C22×C4C2512yes—
1163C22×C4C2512yes—
1164C22×C4C2512yes—
1165C22×C4C2512yes—
1166C22×C4C2512yes—
1167C22×C4C2514yes—
1168C22×C4C2514yes—
1169C22×C4C2512yes—
1170C22×C4C2511yescharacteristic
1171C22×C4C2511yescharacteristic
1172C22×C4C2511yescharacteristic
1173C22×C4C2511yescharacteristic
1174C22×C4C2511yescharacteristic
1175C22×C4C2512yes—
1176C22×C4C2512yes—
1177C22×C4C2512yes—
1178C22×C4C2512yes—
1179C22×C4C2514yes—
1180C22×C4C2511yescharacteristic
1181C22×C4C2511yescharacteristic
1182C22×C4C2512yes—
1183C22×C4C2511yescharacteristic
1184C22×C4C2511yescharacteristic
1185C22×C4C2511yescharacteristic
1186C22×C4C2511yescharacteristic
1187C4⋊C4—22no—
1188C4⋊C4—22no—
1189C4⋊C4—22no—
1190C4⋊C4—24no—
1191C4⋊C4—22no—
1192C4⋊C4—24no—
1193C4⋊C4—24no—
1194C4⋊C4—24no—
1195C4⋊C4—22no—
1196C4⋊C4—22no—
1197C4⋊C4—24no—
1198C4⋊C4—24no—
1199C4⋊C4—28no—
1200C4⋊C4—28no—
1201C4⋊C4—24no—
1202C4⋊C4—24no—
1203C4⋊C4—22no—
1204C4⋊C4—22no—
1205C4⋊C4—22no—
1206C4⋊C4—24no—
1207C4⋊C4—24no—
1208C4⋊C4—24no—
1209C4⋊C4—22no—
1210C4⋊C4—24no—
1211C4⋊C4—24no—
1212C4⋊C4—24no—
1213C4⋊C4—24no—
1214C4⋊C4—24no—
1215C4⋊C4—24no—
1216C4⋊C4—28no—
1217C4⋊C4—22no—
1218C4⋊C4—22no—
1219C4⋊C4—22no—
1220C4⋊C4—24no—
1221C4⋊C4—22no—
1222C4⋊C4—22no—
1223C4⋊C4—22no—
1224C4⋊C4—22no—
1225C4⋊C4—24no—
1226C4⋊C4—24no—
1227C4⋊C4—22no—
1228C4⋊C4—42no—
1229C4⋊C4—42no—
1230C4⋊C4—42no—
1231C4⋊C4—42no—
1232C4⋊C4—41no—
1233C4⋊C4—42no—
1234C4⋊C4—41no—
1235C4⋊C4—42no—
1236C4⋊C4—41no—
1237C4⋊C4—42no—
1238C4⋊C4—41no—
1239C4⋊C4—42no—
1240C4⋊C4—44no—
1241C4⋊C4—44no—
1242C4⋊C4—44no—
1243C4⋊C4—42no—
1244C4⋊C4—42no—
1245C4⋊C4—44no—
1246C4⋊C4—44no—
1247C4⋊C4—42no—
1248C4⋊C4—44no—
1249C4⋊C4—44no—
1250C4⋊C4—44no—
1251C4⋊C4—44no—
1252C4⋊C4—44no—
1253C4⋊C4—44no—
1254C4⋊C4—44no—
1255C4⋊C4—42no—
1256C4⋊C4—44no—
1257C4⋊C4—42no—
1258C4⋊C4—42no—
1259C4⋊C4—42no—
1260C4⋊C4—42no—
1261C4⋊C4—42no—
1262C4⋊C4—42no—
1263C4⋊C4—44no—
1264C4⋊C4—44no—
1265C4⋊C4—44no—
1266C4⋊C4—42no—
1267C4⋊C4—42no—
1268C4⋊C4—44no—
1269C4⋊C4—42no—
1270C4⋊C4—42no—
1271C4⋊C4—42no—
1272C4⋊C4—42no—
1273C4⋊C4—44no—
1274C4⋊C4—44no—
1275C4⋊C4—44no—
1276C4⋊C4—44no—
1277C4⋊C4—44no—
1278C4⋊C4—44no—
1279C4⋊C4—42no—
1280C4⋊C4—42no—
1281C4⋊C4—44no—
1282C4⋊C4—44no—
1283C4⋊C4—44no—
1284C4⋊C42−1+414yes—
1285C22⋊C4—24no—
1286C22⋊C4—24no—
1287C22⋊C4—24no—
1288C22⋊C4—42no—
1289C22⋊C4—42no—
1290C22⋊C4—42no—
1291C22⋊C4—42no—
1292C22⋊C4—44no—
1293C22⋊C4—44no—
1294C22⋊C4—42no—
1295C22⋊C4—44no—
1296C22⋊C4—42no—
1297C22⋊C4—44no—
1298C22⋊C4—44no—
1299C22⋊C4—44no—
1300C22⋊C4—44no—
1301C22⋊C4—42no—
1302C22⋊C4—42no—
1303C22⋊C4—44no—
1304C42—22no—
1305C42—24no—
1306C42—22no—
1307C42—22no—
1308C42—24no—
1309C42—24no—
1310C42—22no—
1311C42—24no—
1312C42—22no—
1313C42—22no—
1314C42—24no—
1315C42—22no—
1316C42—22no—
1317C42—24no—
1318C42—24no—
1319C42—22no—
1320C42—22no—
1321C42—22no—
1322C42—22no—
1323C42—42no—
1324C42—42no—
1325C42—44no—
1326C42—44no—
1327C42—44no—
1328C42—41no—
1329C42—41no—
1330C42—42no—
1331C42—44no—
1332C42—44no—
1333C42—42no—
1334C42—41no—
1335C42—41no—
1336C42—44no—
1337C42—44no—
1338C42—42no—
1339C42—44no—
1340C42—44no—
1341C42—42no—
1342C42—41no—
1343C422−1+414yes—
1344C422−1+414yes—
1345C23—22no—
1346C23—22no—
1347C23—22no—
1348C23—22no—
1349C23—22no—
1350C23—22no—
1351C23—22no—
1352C23C2611yescharacteristic
1353Q8—44no—
1354Q8—44no—
1355Q8—48no—
1356Q8—84no—
1357Q8—84no—
1358Q8—84no—
1359Q8—84no—
1360D4—44no—
1361C2×C4—21no—
1362C2×C4—21no—
1363C2×C4—21no—
1364C2×C4—21no—
1365C2×C4—21no—
1366C2×C4—22no—
1367C2×C4—21no—
1368C2×C4—22no—
1369C2×C4—21no—
1370C2×C4—21no—
1371C2×C4—21no—
1372C2×C4—21no—
1373C2×C4—22no—
1374C2×C4—22no—
1375C2×C4—22no—
1376C2×C4—21no—
1377C2×C4—21no—
1378C2×C4—21no—
1379C2×C4—22no—
1380C2×C4—21no—
1381C2×C4—22no—
1382C2×C4—22no—
1383C2×C4—21no—
1384C2×C4—21no—
1385C2×C4—22no—
1386C2×C4—22no—
1387C2×C4—21no—
1388C2×C4—22no—
1389C2×C4—22no—
1390C2×C4—22no—
1391C2×C4—22no—
1392C2×C4—22no—
1393C2×C4—24no—
1394C2×C4—24no—
1395C2×C4—22no—
1396C2×C4—24no—
1397C2×C4—24no—
1398C2×C4—21no—
1399C2×C4—22no—
1400C2×C4—22no—
1401C2×C4—21no—
1402C2×C4—22no—
1403C2×C4—21no—
1404C2×C4—21no—
1405C2×C4—21no—
1406C2×C4—22no—
1407C2×C4—22no—
1408C2×C4—21no—
1409C2×C4—21no—
1410C2×C4—21no—
1411C2×C4—21no—
1412C2×C4—22no—
1413C2×C4—21no—
1414C2×C4—22no—
1415C2×C4—22no—
1416C2×C4—22no—
1417C2×C4—24no—
1418C2×C4—24no—
1419C2×C4—22no—
1420C2×C4—22no—
1421C2×C4—22no—
1422C2×C4—21no—
1423C2×C4—21no—
1424C2×C4—22no—
1425C2×C4—24no—
1426C2×C4—24no—
1427C2×C4—24no—
1428C2×C4—22no—
1429C2×C4—21no—
1430C2×C4—22no—
1431C2×C4—22no—
1432C2×C4—22no—
1433C2×C4—22no—
1434C2×C4—22no—
1435C2×C4—22no—
1436C2×C4—22no—
1437C2×C4—21no—
1438C2×C4—21no—
1439C2×C4—21no—
1440C2×C4—22no—
1441C2×C4—24no—
1442C2×C4—24no—
1443C2×C4—22no—
1444C2×C4—22no—
1445C2×C4—22no—
1446C2×C4—24no—
1447C2×C4—21no—
1448C2×C4—21no—
1449C2×C4—22no—
1450C2×C4—22no—
1451C2×C4—22no—
1452C2×C4—48no—
1453C2×C4—48no—
1454C2×C4—84no—
1455C2×C4C2×2−1+412yes—
1456C2×C4C2×2−1+412yes—
1457C2×C4C2×2−1+412yes—
1458C2×C4C2×2−1+414yes—
1459C2×C4C2×2−1+412yes—
1460C2×C4C2×2−1+412yes—
1461C2×C4C2×2−1+412yes—
1462C2×C4C2×2−1+412yes—
1463C2×C4#58512yes—
1464C2×C4#58512yes—
1465C2×C4#58512yes—
1466C22—42no—
1467C22—42no—
1468C22—42no—
1469C22—42no—
1470C22—42no—
1471C22—42no—
1472C22—42no—
1473C22C22×2−1+411yescharacteristic
1474C22C22×2−1+411yescharacteristic
1475C22C22×2−1+411yescharacteristic
1476C22C2×#58511yescharacteristic
1477C22C2×#58511yescharacteristic
1478C22C2×#58511yescharacteristic
1479C22H(7,𝔽2)11yescharacteristic
1480C4—22no—
1481C4—24no—
1482C4—22no—
1483C4—22no—
1484C4—22no—
1485C4—42no—
1486C4—42no—
1487C4—44no—
1488C4—41no—
1489C4—42no—
1490C4—42no—
1491C4—41no—
1492C4—42no—
1493C4—42no—
1494C4—42no—
1495C4—41no—
1496C4—41no—
1497C4—41no—
1498C4—41no—
1499C4—42no—
1500C4—42no—
1501C4—42no—
1502C4—42no—
1503C4—41no—
1504C4—41no—
1505C4—41no—
1506C4—42no—
1507C4—42no—
1508C4—44no—
1509C4—42no—
1510C4—44no—
1511C4—44no—
1512C4#355614yes—
1513C4#355714yes—
1514C2—82no—
1515C2C2×#355711yescharacteristic
1516C2C2×#355611yescharacteristic
1517C2#6283811yescharacteristic
1518C2#6292911yescharacteristic
1519C2#6295211yescharacteristic
1520C2#6296211yescharacteristic
1521C2#6302311yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC22×D4C24
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59672C2semidirect
2. #59665C2semidirect
3. #59456C2semidirect
4. #58097C2semidirect
5. #54911C2semidirect
6. #54288C2semidirect
7. #53131C2semidirect
8. #53107C2semidirect
9. #49715C2semidirect
10. #46191C2semidirect
11. #45674C2semidirect
12. #45346C2semidirect
13. #45164C2semidirect
14. #42832C2semidirect
15. #42713C2semidirect
18. #39643C2semidirect
19. #39642C2semidirect
20. #39478C2semidirect
23. #39177C2semidirect
25. #37982C2semidirect
28. #37323C2semidirect
29. #36598C2semidirect
30. #36556C2semidirect
34. #34920C2semidirect

Maximal subgroups

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

subgroupindex
#596722
#596652
#594562
#580972
#549112
#542882
#531312
#531072
#497152
#461912
#456742
#453462
#451642
#428322
#427132
#426872
#425692
#396432
#396422
#394782
#392032
#391772
#390272
#379822
#376372
#373672
#373232
#365982
#365562
#361942
#351852
#351762
#349202
#348932