Finite Group Databasebeta

← #8096662

Subgroups — #8096662

Order 512.

4510 conjugacy classes of subgroups.

The subgroup lattice has 1471 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53077C212yesmaximal, complemented
2#53044C212yesmaximal, complemented
3#53007C211yesmaximal, characteristic, complemented
4#52991C211yesmaximal, characteristic, complemented
5#52751C212yesmaximal, complemented
6#52728C214yesmaximal, complemented
7#52673C212yesmaximal, complemented
8#52626C214yesmaximal, complemented
9#52294C211yesmaximal, characteristic, complemented
10#52275C212yesmaximal, complemented
11#46158C212yesmaximal, complemented
12#46104C212yesmaximal, complemented
13#46104C212yesmaximal, complemented
14#46095C214yesmaximal, complemented
15#45896C214yesmaximal, complemented
16#45857C214yesmaximal, complemented
17#45646C212yesmaximal, complemented
18#45582C214yesmaximal, complemented
19#45504C212yesmaximal, complemented
20#45493C211yesmaximal, characteristic, complemented
21#36555C212yesmaximal, complemented
22#36517C211yesmaximal, characteristic, complemented
23#36312C212yesmaximal, complemented
24#36268C212yesmaximal, complemented
25#36234C212yesmaximal, complemented
26#35947C212yesmaximal, complemented
27#35856C211yesmaximal, characteristic, complemented
28#35758C212yesmaximal, complemented
29#35689C211yesmaximal, characteristic, complemented
30C2×#556C2211yescharacteristic, complemented
31C2×#553C2211yescharacteristic
32C2×#552C2212yes—
33C2×#520C2211yescharacteristic, complemented
34C22×#117C2211yescharacteristic
35#2864C2214yescomplemented
36#2861C2212yescomplemented
37#2860C2214yes—
38#2860C2214yes—
39#2859C2212yescomplemented
40#2859C2212yescomplemented
41#2854C2212yes—
42#2851C2214yes—
43#2848C2212yes—
44#2847C2211yescharacteristic
45#2842C2212yes—
46#2841C2212yes—
47#2841C2212yes—
48#2839C2214yescomplemented
49#2837C2214yes—
50#2837C2214yes—
51#2837C2214yes—
52#2837C2214yescomplemented
53#2837C2214yescomplemented
54#2836C2214yes—
55#2836C2214yescomplemented
56#2835C2212yescomplemented
57#2830C2214yes—
58#2829C2214yescomplemented
59#2828C2214yes—
60#2826C2214yes—
61#2823C2212yescomplemented
62#2820C2214yes—
63#2813C2214yes—
64#2807C2212yes—
65#2805C2214yescomplemented
66#2803C2214yescomplemented
67#2802C2214yescomplemented
68#2802C2214yescomplemented
69#2798C2214yes—
70#2798C2214yescomplemented
71#2797C2214yes—
72#2796C2214yes—
73#2792C2212yescomplemented
74#2790C2214yes—
75#2780C2214yes—
76#2780C2214yes—
77#2773C2214yes—
78#2773C2214yescomplemented
79#2771C2212yes—
80#2768C2214yescomplemented
81#2768C2214yescomplemented
82#2763C2212yes—
83#2763C2211yescharacteristic
84#2754C2214yescomplemented
85#2754C2214yescomplemented
86#2753C2212yes—
87#2753C2212yes—
88#2753C2212yes—
89#2752C2212yes—
90#2748C2212yes—
91#2742C2214yescomplemented
92#2736C2211yescharacteristic
93#2727C2214yes—
94#2725C2214yes—
95#2725C2214yescomplemented
96#2722C2212yescomplemented
97#2714C2214yes—
98#2712C2211yescharacteristic
99#2712C2212yes—
100#2710C2214yes—
101#2710C2214yes—
102#2706C2214yes—
103#2706C2214yes—
104#2705C2214yes—
105#2705C2214yescomplemented
106#2695C2214yes—
107#2694C2214yes—
108#2694C2214yes—
109#2694C2214yescomplemented
110#2694C2214yescomplemented
111#2691C2214yes—
112#2685C2214yes—
113#2678C2214yes—
114#2670C2212yes—
115#2670C2211yescharacteristic
116#2663C2212yescomplemented
117#2649C2214yes—
118#2647C2212yescomplemented
119#2642C2211yescharacteristic, complemented
120#2636C2212yescomplemented
121#2630C2214yes—
122#2616C2212yescomplemented
123#2615C2211yescharacteristic, complemented
124#2611C2214yes—
125#2609C2214yes—
126#2604C2212yescomplemented
127#2602C2214yes—
128#2601C2214yes—
129#2601C2214yescomplemented
130#2587C2214yes—
131#2587C2214yescomplemented
132#2584C2211yescharacteristic, complemented
133#2584C2212yescomplemented
134#2582C2212yescomplemented
135#2582C2212yescomplemented
136#2580C2212yes—
137#2580C2212yescomplemented
138#2564C2212yes—
139#2559C2214yes—
140#2559C2214yes—
141#2556C2214yescomplemented
142#2554C2214yes—
143#2553C2214yescomplemented
144#2542C2211yescharacteristic
145#2540C2212yes—
146#2539C2212yes—
147#2538C2212yes—
148#2538C2212yes—
149#2537C2212yes—
150#2534C2212yes—
151#2530C2214yescomplemented
152#2529C2214yes—
153#2529C2214yescomplemented
154#2522C2214yes—
155#2522C2214yescomplemented
156#2519C2214yes—
157#2519C2214yescomplemented
158#2519C2214yescomplemented
159#2508C2214yescomplemented
160#2505C2214yescomplemented
161#2501C2211yescharacteristic
162#2501C2211yescharacteristic, complemented
163#2499C2212yes—
164#2499C2212yescomplemented
165#2498C2212yescomplemented
166#2497C2212yes—
167#2497C2212yes—
168#2497C2212yescomplemented
169#2496C2212yes—
170#2496C2214yescomplemented
171#2496C2212yescomplemented
172#2496C2212yescomplemented
173#2487C2211yescharacteristic
174#2486C2211yescharacteristic
175#2485C2212yes—
176#2485C2212yes—
177#2485C2214yescomplemented
178#2480C2214yes—
179#2479C2214yes—
180#2478C2214yes—
181#2471C2214yes—
182#2470C2214yes—
183#2469C2214yes—
184#2467C2214yes—
185#2462C2214yescomplemented
186#2461C2214yes—
187#2460C2214yescomplemented
188#2458C2214yes—
189#2456C2214yes—
190#2455C2214yescomplemented
191#2454C2214yes—
192#2453C2214yescomplemented
193#2448C2214yes—
194#2442C2212yes—
195#2442C2212yescomplemented
196#2441C2212yes—
197#2441C2212yes—
198#2441C2212yescomplemented
199#2441C2212yescomplemented
200#2429C2212yes—
201#2429C2212yescomplemented
202#2427C2212yes—
203#2427C2212yescomplemented
204#2426C2212yes—
205#2426C2212yescomplemented
206#2425C2214yes—
207#2423C2212yes—
208#2423C2212yes—
209#2423C2212yescomplemented
210#2423C2212yescomplemented
211#2422C2212yes—
212#2422C2212yescomplemented
213#2418C2214yes—
214#2417C2212yes—
215#2417C2212yes—
216#2415C2212yes—
217#2415C2212yes—
218#2414C2212yes—
219#2414C2212yes—
220#2398C2211yescharacteristic
221#2398C2212yes—
222#2398C2214yescomplemented
223#2397C2212yes—
224#2395C2212yes—
225#2395C2214yescomplemented
226#2388C2211yescharacteristic
227#2388C2212yes—
228#2382C2214yescomplemented
229#2376C2214yes—
230#2376C2214yes—
231#2376C2214yescomplemented
232#2375C2212yes—
233#2363C2212yes—
234#2362C2212yes—
235#2362C2212yescomplemented
236#2361C2212yescomplemented
237#2360C2212yes—
238#2360C2212yescomplemented
239#2354C2212yes—
240#2352C2212yes—
241Q8×C4⋊C4C2212yescomplemented
242D4×C4⋊C4C2212yes—
243#2346C2212yes—
244#2346C2211yescharacteristic, complemented
245#2345C2211yescharacteristic
246#2345C2212yescomplemented
247C4×#124C2212yes—
248C4×#124C2212yes—
249C4×#124C2214yes—
250C4×#124C2212yes—
251C4×#123C2212yes—
252C4×#120C2212yes—
253C4×#120C2211yescharacteristic
254#2295C2214yescomplemented
255#2293C2214yescomplemented
256#2290C2214yes—
257#2275C2211yescharacteristic, complemented
258C42×Q8C2212yescomplemented
259C22×#41C2311yescharacteristic
260C24×C4C2311yescharacteristic
261#556—44no—
262#553—44no—
263#552—48no—
264C2×C4⋊Q8C2311yescharacteristic
265C2×#126C2314yes—
266C2×#126C2314yes—
267C2×#126C2312yes—
268C2×#126C2314yes—
269C2×#126C2314yes—
270C2×#126C2314yes—
271C2×#125C2314yes—
272C2×#125C2312yes—
273C2×#125C2311yescharacteristic
274C2×#125C2314yes—
275C2×#125C2314yes—
276C2×#124C2312yes—
277C2×#124C2312yes—
278C2×#124C2312yes—
279C2×#124C2312yes—
280C2×#123C2312yes—
281C2×#123C2314yes—
282C2×#123C2314yes—
283C2×#123C2314yes—
284C2×#123C2312yes—
285C2×#123C2312yes—
286C2×#123C2312yes—
287C2×#123C2314yes—
288C2×C22⋊Q8C2312yes—
289C2×C22⋊Q8C2312yes—
290C2×C22⋊Q8C2312yes—
291C2×C22⋊Q8C2312yes—
292C2×C22⋊Q8C2312yes—
293C2×C22⋊Q8C2312yes—
294C2×C22⋊Q8C2312yes—
295C2×#121C2312yes—
296C2×#121C2311yescharacteristic
297C2×#121C2312yes—
298C2×#121C2312yes—
299C2×#121C2311yescharacteristic
300C2×#121C2314yes—
301C2×#120C2311yescharacteristic
302C2×#120C2312yes—
303C2×#120C2312yes—
304#520—44no—
305C2×C4×Q8C2312yes—
306C2×C4×Q8C2312yes—
307C2×C4×Q8C2312yes—
308C2×C4×Q8C2312yes—
309C2×C4×Q8C2312yes—
310C2×C4×Q8C2311yescharacteristic
311C2×C4×Q8C2314yes—
312C2×C4×D4C2311yescharacteristic
313C2×C4×D4C2312yes—
314C2×C4×D4C2312yes—
315C2×C4×D4C2314yes—
316C2×C4×D4C2312yes—
317C2×C4×D4C2314yes—
318C2×C4×D4C2312yes—
319C2×C4×D4C2312yes—
320C2×C4×D4C2314yes—
321C2×C4×D4C2312yes—
322C2×C4×D4C2311yescharacteristic
323C2×C4×D4C2312yes—
324C2×#117—44no—
325C2×#117C2312yes—
326C2×#117C2311yescharacteristic
327C2×#117C2312yes—
328C2×#117C2314yes—
329C2×#117C2314yes—
330C2×#117C2312yes—
331C2×#117C2312yes—
332C22×C4⋊C4C2311yescharacteristic
333C22×C4⋊C4C2312yes—
334C22×C4⋊C4C2311yescharacteristic
335C22×C4⋊C4C2311yescharacteristic
336C22×C22⋊C4C2312yes—
337C22×C42C2312yes—
338#400C2312yes—
339#400C2314yes—
340#400C2314yes—
341#400C2314yes—
342#400C2314yes—
343#400C2314yes—
344#400C2312yes—
345#400C2314yes—
346#400C2314yes—
347#400C2314yes—
348#400C2314yes—
349#400C2312yes—
350#400C2312yes—
351#400C2314yes—
352#400C2312yes—
353#400C2312yes—
354#400C2314yes—
355#399C2312yes—
356#399C2314yes—
357#399C2314yes—
358#399C2314yes—
359#399C2314yes—
360#399C2312yes—
361#399C2312yes—
362#399C2314yes—
363#399C2314yes—
364#399C2314yes—
365#399C2312yes—
366#399C2314yes—
367#399C2314yes—
368#399C2314yes—
369#399C2312yes—
370#399C2314yes—
371#398C2314yes—
372#398C2312yes—
373#398C2314yes—
374#398C2314yes—
375#398C2314yes—
376#398C2314yes—
377#398C2314yes—
378#398C2314yes—
379#398C2314yes—
380#398C2314yes—
381#398C2314yes—
382#398C2314yes—
383#398C2314yes—
384#398C2314yes—
385#398C2314yes—
386#398C2314yes—
387#398C2314yes—
388#398C2312yes—
389#398C2314yes—
390#397C2314yes—
391#397C2314yes—
392#397C2314yes—
393#397C2314yes—
394#397C2314yes—
395#397C2314yes—
396#397C2314yes—
397#397C2314yes—
398#397C2314yes—
399#397C2312yes—
400#397C2312yes—
401#397C2314yes—
402#397C2312yes—
403#397C2314yes—
404#397C2314yes—
405#397C2314yes—
406#397C2311yescharacteristic
407#397C2314yes—
408#397C2311yescharacteristic
409#397C2314yes—
410#396C2314yes—
411#396C2314yes—
412#396C2314yes—
413#396C2314yes—
414#396C2314yes—
415#396C2314yes—
416#396C2314yes—
417#396C2314yes—
418#396C2314yes—
419#396C2314yes—
420#396C2314yes—
421#396C2314yes—
422#396C2314yes—
423#396C2314yes—
424#396C2314yes—
425#396C2314yes—
426#396C2314yes—
427#395C2312yes—
428#395C2314yes—
429#395C2314yes—
430#395C2311yescharacteristic
431#395C2312yes—
432#394C2314yes—
433#394C2314yes—
434#394C2311yescharacteristic
435#394C2314yes—
436#394C2314yes—
437#394C2314yes—
438#394C2314yes—
439#394C2314yes—
440#394C2314yes—
441#394C2314yes—
442#394C2314yes—
443#394C2312yes—
444#394C2314yes—
445#394C2314yes—
446#394C2314yes—
447#394C2314yes—
448#394C2314yes—
449#394C2312yes—
450#394C2312yes—
451#394C2314yes—
452#394C2312yes—
453#394C2312yes—
454#394C2312yes—
455#394C2314yes—
456#394C2312yes—
457#393C2311yescharacteristic
458#393C2312yes—
459#393C2312yes—
460#393C2311yescharacteristic
461#393C2311yescharacteristic
462#393C2314yes—
463#393C2312yes—
464#393C2312yes—
465#392C2314yes—
466#392C2312yes—
467#392C2314yes—
468#392C2314yes—
469#392C2312yes—
470#392C2312yes—
471#392C2311yescharacteristic
472#392C2312yes—
473#392C2312yes—
474#392C2314yes—
475#391C2312yes—
476#391C2312yes—
477#391C2312yes—
478#391C2312yes—
479#391C2314yes—
480#391C2314yes—
481#391C2312yes—
482#391C2312yes—
483#391C2312yes—
484#390C2314yes—
485#390C2314yes—
486#390C2314yes—
487#390C2314yes—
488#390C2312yes—
489#390C2312yes—
490#390C2314yes—
491#390C2314yes—
492#390C2312yes—
493#390C2314yes—
494#390C2314yes—
495#390C2312yes—
496#390C2312yes—
497#390C2312yes—
498#390C2314yes—
499#390C2314yes—
500#389C2314yes—
501#389C2312yes—
502#389C2312yes—
503#389C2314yes—
504#389C2314yes—
505#389C2314yes—
506#389C2314yes—
507#389C2314yes—
508#389C2314yes—
509#389C2312yes—
510#389C2312yes—
511#389C2312yes—
512#389C2312yes—
513#389C2314yes—
514#389C2314yes—
515#389C2312yes—
516#389C2312yes—
517#389C2312yes—
518#389C2312yes—
519#389C2312yes—
520#389C2312yes—
521#389C2314yes—
522#389C2314yes—
523#389C2314yes—
524#389C2314yes—
525#389C2314yes—
526#389C2314yes—
527#389C2314yes—
528#389C2314yes—
529#389C2314yes—
530#389C2314yes—
531#389C2314yes—
532#389C2314yes—
533#389C2314yes—
534#389C2314yes—
535#389C2314yes—
536#389C2314yes—
537#388C2314yes—
538#388C2314yes—
539#388C2314yes—
540#388C2314yes—
541#388C2312yes—
542#388C2314yes—
543#388C2314yes—
544#388C2314yes—
545#388C2314yes—
546#388C2312yes—
547#388C2314yes—
548#388C2314yes—
549#388C2312yes—
550#388C2314yes—
551#388C2314yes—
552#388C2314yes—
553#388C2312yes—
554#388C2314yes—
555#388C2312yes—
556#388C2314yes—
557#388C2314yes—
558#388C2314yes—
559#388C2314yes—
560#388C2314yes—
561#388C2314yes—
562#388C2314yes—
563#388C2312yes—
564#388C2314yes—
565#388C2314yes—
566#388C2314yes—
567#388C2314yes—
568#388C2314yes—
569#388C2314yes—
570#388C2314yes—
571#388C2314yes—
572#388C2314yes—
573#388C2312yes—
574#388C2314yes—
575#388C2312yes—
576#388C2314yes—
577#388C2312yes—
578#388C2312yes—
579#388C2312yes—
580#388C2312yes—
581#388C2314yes—
582#387C2314yes—
583#387C2314yes—
584#387C2314yes—
585#387C2314yes—
586#387C2314yes—
587#387C2314yes—
588#387C2314yes—
589#387C2314yes—
590#387C2314yes—
591#387C2314yes—
592#387C2314yes—
593#387C2314yes—
594#387C2314yes—
595#387C2314yes—
596#387C2314yes—
597#387C2314yes—
598#387C2314yes—
599#387C2314yes—
600#387C2314yes—
601#387C2314yes—
602#387C2314yes—
603#387C2314yes—
604#387C2314yes—
605#387C2314yes—
606#387C2314yes—
607#387C2314yes—
608#387C2314yes—
609#387C2314yes—
610#386C2314yes—
611#386C2312yes—
612#386C2314yes—
613#386C2312yes—
614#386C2311yescharacteristic
615#386C2314yes—
616#386C2314yes—
617#386C2314yes—
618#386C2314yes—
619#386C2312yes—
620#386C2312yes—
621#386C2314yes—
622#386C2314yes—
623#386C2312yes—
624#386C2312yes—
625#385C2314yes—
626#385C2314yes—
627#385C2314yes—
628#385C2312yes—
629#385C2314yes—
630#385C2314yes—
631#385C2314yes—
632#385C2314yes—
633#385C2314yes—
634#385C2314yes—
635#385C2314yes—
636#385C2314yes—
637#385C2312yes—
638#385C2312yes—
639#385C2312yes—
640#385C2314yes—
641#385C2314yes—
642#385C2314yes—
643#385C2311yescharacteristic
644#385C2312yes—
645#384C2312yes—
646#384C2312yes—
647#384C2312yes—
648#384C2312yes—
649#384C2312yes—
650#384C2312yes—
651#382C2314yes—
652#382C2312yes—
653#382C2312yes—
654#382C2314yes—
655#382C2314yes—
656#382C2312yes—
657#382C2312yes—
658#382C2312yes—
659#381C2312yes—
660#380C2314yes—
661#380C2314yes—
662#380C2314yes—
663#380C2311yescharacteristic
664#380C2312yes—
665#380C2312yes—
666#380C2312yes—
667#380C2312yes—
668#380C2312yes—
669#380C2312yes—
670#380C2314yes—
671#380C2311yescharacteristic
672#380C2312yes—
673#380C2312yes—
674#380C2312yes—
675#380C2314yes—
676#380C2314yes—
677#380C2314yes—
678#380C2314yes—
679#379C2311yescharacteristic
680#379C2314yes—
681#379C2312yes—
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2311yescharacteristic
684C4×C4⋊C4C2314yes—
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2314yes—
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2314yes—
690C4×C4⋊C4C2314yes—
691C4×C4⋊C4C2314yes—
692C4×C4⋊C4C2314yes—
693C4×C22⋊C4C2312yes—
694C4×C22⋊C4C2314yes—
695C4×C22⋊C4C2311yescharacteristic
696C4×C22⋊C4C2312yes—
697C4×C22⋊C4C2312yes—
698C4×C22⋊C4C2311yescharacteristic
699C4×C22⋊C4C2314yes—
700C4×C22⋊C4C2314yes—
701C4×C22⋊C4C2312yes—
702C4×C22⋊C4C2312yes—
703C4×C22⋊C4C2314yes—
704C4×C22⋊C4C2312yes—
705C4×C22⋊C4C2312yes—
706C4×C22⋊C4C2312yes—
707C4×C22⋊C4C2312yes—
708C4×C22⋊C4C2314yes—
709C4×C22⋊C4C2312yes—
710C4×C22⋊C4C2314yes—
711#376C2314yes—
712#376C2312yes—
713#376C2311yescharacteristic
714C2×#95C2312yes—
715C43C2312yes—
716C43C2314yes—
717C25C2411yescharacteristic
718C2×#41—42no—
719C2×#41—44no—
720C22×Q8C2412yes—
721C22×Q8C2412yes—
722C22×Q8C2411yescharacteristic
723C22×Q8C2411yescharacteristic
724C22×D4C2411yescharacteristic
725C22×D4C2412yes—
726C22×D4C2411yescharacteristic
727C22×D4C2412yes—
728C22×D4C2412yes—
729C22×D4C2412yes—
730C22×D4C2411yescharacteristic
731C22×D4C2412yes—
732C22×D4C2412yes—
733C22×D4C2414yes—
734C22×D4C2414yes—
735C22×D4C2412yes—
736C23×C4—42no—
737C23×C4—44no—
738C23×C4C2411yescharacteristic
739C23×C4C2412yes—
740C23×C4C2411yescharacteristic
741C23×C4C2412yes—
742C23×C4C2412yes—
743C23×C4C2412yes—
744C23×C4C2414yes—
745C23×C4C2412yes—
746C23×C4C2412yes—
747C23×C4C2412yes—
748C23×C4C2414yes—
749C23×C4C2411yescharacteristic
750C4⋊Q8—42no—
751#126—48no—
752#126—44no—
753#126—48no—
754#126—84no—
755#126—84no—
756#126—84no—
757#125—48no—
758#125—48no—
759#125—44no—
760#125—42no—
761#125—84no—
762#124—28no—
763#124—44no—
764#124—44no—
765#124—44no—
766#123—28no—
767#123—48no—
768#123—48no—
769#123—48no—
770#123—44no—
771#123—82no—
772#123—82no—
773#123—84no—
774C22⋊Q8—44no—
775C22⋊Q8—44no—
776C22⋊Q8—44no—
777C22⋊Q8—44no—
778C22⋊Q8—44no—
779C22⋊Q8—44no—
780C22⋊Q8—44no—
781#121—44no—
782#121—44no—
783#121—44no—
784#121—42no—
785#121—42no—
786#121—84no—
787#120—24no—
788#120—44no—
789#120—82no—
790C4×Q8—28no—
791C4×Q8—44no—
792C4×Q8—42no—
793C4×Q8—44no—
794C4×Q8—48no—
795C4×Q8—44no—
796C4×Q8—44no—
797C4×D4—24no—
798C4×D4—48no—
799C4×D4—44no—
800C4×D4—48no—
801C4×D4—44no—
802C4×D4—44no—
803C4×D4—44no—
804C4×D4—44no—
805C4×D4—44no—
806C4×D4—44no—
807C4×D4—42no—
808C4×D4—48no—
809#117—28no—
810#117—24no—
811#117—48no—
812#117—44no—
813#117—48no—
814#117—44no—
815#117—44no—
816C2×C4⋊C4—24no—
817C2×C4⋊C4—28no—
818C2×C4⋊C4—42no—
819C2×C4⋊C4—42no—
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2411yescharacteristic
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2411yescharacteristic
826C2×C4⋊C4C2412yes—
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2411yescharacteristic
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2412yes—
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2411yescharacteristic
842C2×C4⋊C4C2412yes—
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2412yes—
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2412yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2412yes—
850C2×C4⋊C4C2412yes—
851C2×C4⋊C4C2414yes—
852C2×C4⋊C4C2414yes—
853C2×C4⋊C4C2412yes—
854C2×C4⋊C4C2412yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2414yes—
864C2×C4⋊C4C2414yes—
865C2×C4⋊C4C2414yes—
866C2×C4⋊C4C2414yes—
867C2×C4⋊C4C2414yes—
868C2×C4⋊C4C2414yes—
869C2×C4⋊C4C2414yes—
870C2×C4⋊C4C2414yes—
871C2×C4⋊C4C2414yes—
872C2×C4⋊C4C2414yes—
873C2×C4⋊C4C2414yes—
874C2×C4⋊C4C2414yes—
875C2×C4⋊C4C2414yes—
876C2×C4⋊C4C2412yes—
877C2×C4⋊C4C2414yes—
878C2×C4⋊C4C2411yescharacteristic
879C2×C22⋊C4—44no—
880C2×C22⋊C4C2414yes—
881C2×C22⋊C4C2412yes—
882C2×C22⋊C4C2412yes—
883C2×C22⋊C4C2412yes—
884C2×C22⋊C4C2414yes—
885C2×C22⋊C4C2412yes—
886C2×C22⋊C4C2412yes—
887C2×C22⋊C4C2412yes—
888C2×C22⋊C4C2412yes—
889C2×C22⋊C4C2414yes—
890C2×C22⋊C4C2412yes—
891C2×C22⋊C4C2412yes—
892C2×C22⋊C4C2412yes—
893C2×C22⋊C4C2414yes—
894C2×C22⋊C4C2412yes—
895C2×C22⋊C4C2414yes—
896C2×C22⋊C4C2414yes—
897C2×C22⋊C4C2414yes—
898C2×C22⋊C4C2411yescharacteristic
899C2×C22⋊C4C2412yes—
900C2×C22⋊C4C2411yescharacteristic
901C2×C22⋊C4C2412yes—
902C2×C22⋊C4C2412yes—
903C2×C22⋊C4C2414yes—
904C2×C22⋊C4C2414yes—
905C2×C22⋊C4C2412yes—
906C2×C22⋊C4C2412yes—
907C2×C22⋊C4C2412yes—
908C2×C22⋊C4C2412yes—
909C2×C22⋊C4C2414yes—
910C2×C22⋊C4C2412yes—
911C2×C22⋊C4C2412yes—
912C2×C22⋊C4C2414yes—
913C2×C22⋊C4C2412yes—
914C2×C22⋊C4C2412yes—
915C2×C22⋊C4C2414yes—
916C2×C22⋊C4C2414yes—
917C2×C22⋊C4C2414yes—
918C2×C22⋊C4C2414yes—
919C2×C22⋊C4C2414yes—
920C2×C22⋊C4C2414yes—
921C2×C22⋊C4C2414yes—
922C2×C22⋊C4C2414yes—
923C2×C22⋊C4C2414yes—
924C2×C22⋊C4C2414yes—
925C2×C22⋊C4C2411yescharacteristic
926C2×C22⋊C4C2412yes—
927C2×C22⋊C4C2414yes—
928C2×C22⋊C4C2414yes—
929C2×C22⋊C4C2414yes—
930C2×C22⋊C4C2414yes—
931C2×C22⋊C4C2414yes—
932C2×C22⋊C4C2412yes—
933C2×C22⋊C4C2412yes—
934C2×C22⋊C4C2412yes—
935C2×C22⋊C4C2412yes—
936C2×C22⋊C4C2412yes—
937C2×C22⋊C4C2412yes—
938C2×C22⋊C4C2412yes—
939C2×C22⋊C4C2412yes—
940C2×C22⋊C4C2411yescharacteristic
941C2×C42—44no—
942C2×C42C2414yes—
943C2×C42C2414yes—
944C2×C42C2412yes—
945C2×C42C2411yescharacteristic
946C2×C42C2414yes—
947C2×C42C2412yes—
948C2×C42C2412yes—
949C2×C42C2412yes—
950C2×C42C2412yes—
951C2×C42C2412yes—
952C2×C42C2412yes—
953C2×C42C2414yes—
954C2×C42C2414yes—
955C2×C42C2414yes—
956C2×C42C2414yes—
957C2×C42C2414yes—
958C2×C42C2414yes—
959C2×C42C2412yes—
960C2×C42C2412yes—
961C2×C42C2414yes—
962C2×C42C2412yes—
963#95C2411yescharacteristic
964#95C2414yes—
965#95C2412yes—
966#95C2412yes—
967#95C2411yescharacteristic
968#95C2411yescharacteristic
969#95C2412yes—
970#95C2414yes—
971#95C2412yes—
972#95C2414yes—
973#95C2414yes—
974#95C2414yes—
975#95C2412yes—
976#95C2412yes—
977#95C2412yes—
978#95C2412yes—
979#95C2412yes—
980#95C2414yes—
981#95C2414yes—
982#95C2414yes—
983#95C2411yescharacteristic
984#95C2412yes—
985#95C2412yes—
986#95C2412yes—
987#95C2414yes—
988#95C2412yes—
989#95C2414yes—
990#95C2412yes—
991#95C2412yes—
992#95C2414yes—
993#95C2412yes—
994#95C2414yes—
995#95C2412yes—
996#95C2412yes—
997#95C2414yes—
998#95C2414yes—
999#95C2412yes—
1000#95C2412yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2414yes—
1004#95C2414yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2414yes—
1008#95C2414yes—
1009#95C2414yes—
1010#95C2414yes—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2414yes—
1014#95C2414yes—
1015#95C2414yes—
1016#95C2414yes—
1017#95C2412yes—
1018#95C2414yes—
1019#95C2414yes—
1020#95C2414yes—
1021#95C2414yes—
1022C24—22no—
1023C24—41no—
1024C24—42no—
1025C24—42no—
1026C24—41no—
1027C24C2512yes—
1028C24C2511yescharacteristic
1029C24C2512yes—
1030C24C2512yes—
1031C24C2511yescharacteristic
1032#41—416no—
1033C2×Q8—24no—
1034C2×Q8—24no—
1035C2×Q8—24no—
1036C2×Q8—24no—
1037C2×Q8—24no—
1038C2×Q8—41no—
1039C2×Q8—42no—
1040C2×Q8—42no—
1041C2×Q8—41no—
1042C2×Q8—42no—
1043C2×D4—24no—
1044C2×D4—22no—
1045C2×D4—24no—
1046C2×D4—22no—
1047C2×D4—24no—
1048C2×D4—24no—
1049C2×D4—24no—
1050C2×D4—41no—
1051C2×D4—42no—
1052C2×D4—42no—
1053C2×D4—42no—
1054C2×D4—42no—
1055C2×D4—42no—
1056C2×D4—42no—
1057C2×D4—41no—
1058C2×D4—42no—
1059C2×D4—42no—
1060C2×D4—44no—
1061C2×D4—42no—
1062C2×D4—42no—
1063C2×D4—42no—
1064C2×D4—42no—
1065C2×D4—44no—
1066C2×D4—42no—
1067C2×D4—44no—
1068C2×D4—41no—
1069C2×D4—42no—
1070C2×D4—42no—
1071C2×D4—44no—
1072C2×D4—42no—
1073C2×D4—44no—
1074C2×D4—44no—
1075C2×D4—44no—
1076C22×C4—24no—
1077C22×C4—22no—
1078C22×C4—24no—
1079C22×C4—22no—
1080C22×C4—24no—
1081C22×C4—24no—
1082C22×C4—24no—
1083C22×C4—24no—
1084C22×C4—24no—
1085C22×C4—24no—
1086C22×C4—24no—
1087C22×C4—24no—
1088C22×C4—28no—
1089C22×C4—24no—
1090C22×C4—41no—
1091C22×C4—42no—
1092C22×C4—42no—
1093C22×C4—42no—
1094C22×C4—42no—
1095C22×C4—42no—
1096C22×C4—44no—
1097C22×C4—44no—
1098C22×C4—44no—
1099C22×C4—44no—
1100C22×C4—42no—
1101C22×C4—42no—
1102C22×C4—44no—
1103C22×C4—44no—
1104C22×C4—44no—
1105C22×C4—44no—
1106C22×C4—416no—
1107C22×C4C2512yes—
1108C22×C4C2512yes—
1109C22×C4C2512yes—
1110C22×C4C2511yescharacteristic
1111C22×C4C2512yes—
1112C22×C4C2511yescharacteristic
1113C22×C4C2511yescharacteristic
1114C22×C4C2512yes—
1115C22×C4C2511yescharacteristic
1116C22×C4C2514yes—
1117C22×C4C2514yes—
1118C22×C4C2512yes—
1119C22×C4C2514yes—
1120C22×C4C2514yes—
1121C22×C4C2512yes—
1122C22×C4C2514yes—
1123C22×C4C2512yes—
1124C22×C4C2512yes—
1125C22×C4C2512yes—
1126C22×C4C2514yes—
1127C22×C4C2512yes—
1128C22×C4C2512yes—
1129C22×C4C2512yes—
1130C22×C4C2511yescharacteristic
1131C4⋊C4—24no—
1132C4⋊C4—22no—
1133C4⋊C4—24no—
1134C4⋊C4—28no—
1135C4⋊C4—24no—
1136C4⋊C4—22no—
1137C4⋊C4—28no—
1138C4⋊C4—28no—
1139C4⋊C4—24no—
1140C4⋊C4—28no—
1141C4⋊C4—24no—
1142C4⋊C4—24no—
1143C4⋊C4—28no—
1144C4⋊C4—42no—
1145C4⋊C4—42no—
1146C4⋊C4—41no—
1147C4⋊C4—44no—
1148C4⋊C4—42no—
1149C4⋊C4—44no—
1150C4⋊C4—42no—
1151C4⋊C4—42no—
1152C4⋊C4—44no—
1153C4⋊C4—42no—
1154C4⋊C4—42no—
1155C4⋊C4—42no—
1156C4⋊C4—41no—
1157C4⋊C4—42no—
1158C4⋊C4—42no—
1159C4⋊C4—44no—
1160C4⋊C4—42no—
1161C4⋊C4—44no—
1162C4⋊C4—44no—
1163C4⋊C4—44no—
1164C4⋊C4—42no—
1165C4⋊C4—42no—
1166C4⋊C4—44no—
1167C4⋊C4—44no—
1168C4⋊C4—44no—
1169C4⋊C4—44no—
1170C4⋊C4—44no—
1171C4⋊C4—44no—
1172C4⋊C4—44no—
1173C4⋊C4—44no—
1174C4⋊C4—44no—
1175C4⋊C4—44no—
1176C4⋊C4—44no—
1177C4⋊C4—44no—
1178C4⋊C4—44no—
1179C4⋊C4—44no—
1180C4⋊C4—44no—
1181C4⋊C4—44no—
1182C4⋊C4—44no—
1183C4⋊C4—44no—
1184C4⋊C4—44no—
1185C4⋊C4—44no—
1186C4⋊C4—44no—
1187C4⋊C4—42no—
1188C4⋊C4—44no—
1189C4⋊C4H(5,𝔽2)14yes—
1190C22⋊C4—24no—
1191C22⋊C4—28no—
1192C22⋊C4—24no—
1193C22⋊C4—24no—
1194C22⋊C4—24no—
1195C22⋊C4—28no—
1196C22⋊C4—24no—
1197C22⋊C4—24no—
1198C22⋊C4—24no—
1199C22⋊C4—28no—
1200C22⋊C4—24no—
1201C22⋊C4—24no—
1202C22⋊C4—24no—
1203C22⋊C4—44no—
1204C22⋊C4—42no—
1205C22⋊C4—44no—
1206C22⋊C4—44no—
1207C22⋊C4—44no—
1208C22⋊C4—44no—
1209C22⋊C4—42no—
1210C22⋊C4—42no—
1211C22⋊C4—42no—
1212C22⋊C4—42no—
1213C22⋊C4—42no—
1214C22⋊C4—42no—
1215C22⋊C4—44no—
1216C22⋊C4—44no—
1217C22⋊C4—41no—
1218C22⋊C4—42no—
1219C22⋊C4—41no—
1220C22⋊C4—42no—
1221C22⋊C4—42no—
1222C22⋊C4—42no—
1223C22⋊C4—44no—
1224C22⋊C4—44no—
1225C22⋊C4—44no—
1226C22⋊C4—42no—
1227C22⋊C4—44no—
1228C22⋊C4—44no—
1229C22⋊C4—44no—
1230C22⋊C4—44no—
1231C22⋊C4—44no—
1232C22⋊C4—44no—
1233C22⋊C4—44no—
1234C22⋊C4—44no—
1235C22⋊C4—44no—
1236C22⋊C4—44no—
1237C22⋊C4—41no—
1238C22⋊C4—44no—
1239C22⋊C4—42no—
1240C22⋊C4—44no—
1241C22⋊C4—44no—
1242C22⋊C4—42no—
1243C22⋊C4—42no—
1244C22⋊C4—42no—
1245C22⋊C4—42no—
1246C22⋊C4—42no—
1247C22⋊C4—42no—
1248C22⋊C4—42no—
1249C22⋊C4—42no—
1250C22⋊C42−1+414yes—
1251C42—28no—
1252C42—24no—
1253C42—28no—
1254C42—22no—
1255C42—24no—
1256C42—24no—
1257C42—28no—
1258C42—24no—
1259C42—24no—
1260C42—24no—
1261C42—24no—
1262C42—44no—
1263C42—44no—
1264C42—44no—
1265C42—44no—
1266C42—44no—
1267C42—44no—
1268C42—42no—
1269C42—42no—
1270C42—44no—
1271C42—42no—
1272C23—21no—
1273C23—22no—
1274C23—22no—
1275C23—21no—
1276C23—22no—
1277C23—21no—
1278C23—22no—
1279C23—22no—
1280C23—22no—
1281C23—22no—
1282C23—22no—
1283C23—21no—
1284C23—22no—
1285C23—22no—
1286C23—22no—
1287C23—24no—
1288C23—22no—
1289C23—22no—
1290C23—22no—
1291C23—22no—
1292C23—24no—
1293C23—22no—
1294C23—22no—
1295C23—22no—
1296C23—21no—
1297C23—22no—
1298C23—22no—
1299C23—22no—
1300C23—44no—
1301C23—84no—
1302C23—82no—
1303C23—82no—
1304C23—84no—
1305C23C2×2−1+412yes—
1306C23C2611yescharacteristic
1307Q8—48no—
1308Q8—44no—
1309Q8—48no—
1310Q8—82no—
1311D4—48no—
1312D4—44no—
1313D4—48no—
1314D4—44no—
1315D4—84no—
1316D4—82no—
1317D4—84no—
1318D4—84no—
1319D4—84no—
1320D4—88no—
1321D4—162no—
1322D4—164no—
1323C2×C4—22no—
1324C2×C4—22no—
1325C2×C4—22no—
1326C2×C4—24no—
1327C2×C4—22no—
1328C2×C4—22no—
1329C2×C4—22no—
1330C2×C4—21no—
1331C2×C4—22no—
1332C2×C4—24no—
1333C2×C4—21no—
1334C2×C4—24no—
1335C2×C4—22no—
1336C2×C4—21no—
1337C2×C4—22no—
1338C2×C4—22no—
1339C2×C4—24no—
1340C2×C4—21no—
1341C2×C4—22no—
1342C2×C4—21no—
1343C2×C4—22no—
1344C2×C4—24no—
1345C2×C4—22no—
1346C2×C4—22no—
1347C2×C4—22no—
1348C2×C4—22no—
1349C2×C4—22no—
1350C2×C4—24no—
1351C2×C4—22no—
1352C2×C4—22no—
1353C2×C4—22no—
1354C2×C4—22no—
1355C2×C4—22no—
1356C2×C4—24no—
1357C2×C4—24no—
1358C2×C4—24no—
1359C2×C4—24no—
1360C2×C4—24no—
1361C2×C4—24no—
1362C2×C4—24no—
1363C2×C4—22no—
1364C2×C4—22no—
1365C2×C4—24no—
1366C2×C4—22no—
1367C2×C4—22no—
1368C2×C4—24no—
1369C2×C4—24no—
1370C2×C4—22no—
1371C2×C4—22no—
1372C2×C4—22no—
1373C2×C4—22no—
1374C2×C4—22no—
1375C2×C4—21no—
1376C2×C4—22no—
1377C2×C4—24no—
1378C2×C4—24no—
1379C2×C4—22no—
1380C2×C4—24no—
1381C2×C4—24no—
1382C2×C4—22no—
1383C2×C4—22no—
1384C2×C4—44no—
1385C2×C4—48no—
1386C2×C4—44no—
1387C2×C4—48no—
1388C2×C4—48no—
1389C2×C4—44no—
1390C2×C4—84no—
1391C2×C4—88no—
1392C2×C4—84no—
1393C2×C4—84no—
1394C2×C4—162no—
1395C2×C4—164no—
1396C2×C4C2×H(5,𝔽2)14yes—
1397C2×C4C2×H(5,𝔽2)12yes—
1398C2×C4C2×2−1+414yes—
1399C2×C4#58514yes—
1400C2×C4#58514yes—
1401C22—24no—
1402C22—22no—
1403C22—41no—
1404C22—42no—
1405C22—41no—
1406C22—42no—
1407C22—42no—
1408C22—41no—
1409C22—42no—
1410C22—42no—
1411C22—42no—
1412C22—42no—
1413C22—42no—
1414C22—44no—
1415C22—42no—
1416C22—41no—
1417C22—42no—
1418C22—42no—
1419C22—42no—
1420C22—44no—
1421C22—42no—
1422C22—42no—
1423C22—42no—
1424C22—42no—
1425C22—42no—
1426C22—42no—
1427C22—41no—
1428C22—42no—
1429C22—42no—
1430C22—88no—
1431C22C22×H(5,𝔽2)11yescharacteristic
1432C22C22×2−1+411yescharacteristic
1433C22C2×#58512yes—
1434C22C2×#58512yes—
1435C22H(7,𝔽2)11yescharacteristic
1436C4—24no—
1437C4—24no—
1438C4—24no—
1439C4—41no—
1440C4—44no—
1441C4—42no—
1442C4—42no—
1443C4—42no—
1444C4—42no—
1445C4—44no—
1446C4—42no—
1447C4—41no—
1448C4—42no—
1449C4—42no—
1450C4—44no—
1451C4—42no—
1452C4—44no—
1453C4—44no—
1454C4—42no—
1455C4—41no—
1456C4—41no—
1457C4—42no—
1458C4—44no—
1459C4#352914yes—
1460C2—42no—
1461C2—82no—
1462C2—82no—
1463C2—81no—
1464C2—82no—
1465C2C2×#352911yescharacteristic
1466C2#6291711yescharacteristic
1467C2#6293712yes—
1468C2#6302111yescharacteristic
1469C2#6302312yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #53077C2semidirect
2. #53044C2semidirect
3. #53007C2semidirect
4. #52991C2semidirect
5. #52751C2semidirect
6. #52728C2semidirect
7. #52673C2semidirect
8. #52626C2semidirect
9. #52294C2semidirect
10. #52275C2semidirect
11. #46158C2semidirect
12. #46104C2semidirect
13. #46104C2semidirect
14. #46095C2semidirect
15. #45896C2semidirect
16. #45857C2semidirect
17. #45646C2semidirect
18. #45582C2semidirect
19. #45504C2semidirect
20. #45493C2semidirect
21. #36555C2semidirect
22. #36517C2semidirect
23. #36312C2semidirect
24. #36268C2semidirect
25. #36234C2semidirect
26. #35947C2semidirect
27. #35856C2semidirect
28. #35758C2semidirect
29. #35689C2semidirect
30. C2×#556C22semidirect
33. C2×#520C22semidirect
35. #2864C22semidirect
36. #2861C22semidirect
39. #2859C22semidirect
40. #2859C22semidirect
48. #2839C22semidirect
52. #2837C22semidirect
53. #2837C22semidirect
55. #2836C22semidirect
56. #2835C22semidirect
58. #2829C22semidirect
61. #2823C22semidirect
65. #2805C22semidirect
66. #2803C22semidirect
67. #2802C22semidirect
68. #2802C22semidirect
70. #2798C22semidirect
73. #2792C22semidirect
78. #2773C22semidirect
80. #2768C22semidirect
81. #2768C22semidirect
84. #2754C22semidirect
85. #2754C22semidirect
91. #2742C22semidirect
95. #2725C22semidirect
96. #2722C22semidirect
105. #2705C22semidirect
109. #2694C22semidirect
110. #2694C22semidirect
116. #2663C22semidirect
118. #2647C22semidirect
119. #2642C22semidirect
120. #2636C22semidirect
122. #2616C22semidirect
123. #2615C22semidirect
126. #2604C22semidirect
129. #2601C22semidirect
131. #2587C22semidirect
132. #2584C22semidirect
133. #2584C22semidirect
134. #2582C22semidirect
135. #2582C22semidirect
137. #2580C22semidirect
141. #2556C22semidirect
143. #2553C22semidirect
151. #2530C22semidirect
153. #2529C22semidirect
155. #2522C22semidirect
157. #2519C22semidirect
158. #2519C22semidirect
159. #2508C22semidirect
160. #2505C22semidirect
162. #2501C22semidirect
164. #2499C22semidirect
165. #2498C22semidirect
168. #2497C22semidirect
170. #2496C22semidirect
171. #2496C22semidirect
172. #2496C22semidirect
177. #2485C22semidirect
185. #2462C22semidirect
187. #2460C22semidirect
190. #2455C22semidirect
192. #2453C22semidirect
195. #2442C22semidirect
198. #2441C22semidirect
199. #2441C22semidirect
201. #2429C22semidirect
203. #2427C22semidirect
205. #2426C22semidirect
209. #2423C22semidirect
210. #2423C22semidirect
212. #2422C22semidirect
222. #2398C22semidirect
225. #2395C22semidirect
228. #2382C22semidirect
231. #2376C22semidirect
235. #2362C22semidirect
236. #2361C22semidirect
238. #2360C22semidirect
241. Q8×C4⋊C4C22semidirect
244. #2346C22semidirect
246. #2345C22semidirect
254. #2295C22semidirect
255. #2293C22semidirect
257. #2275C22semidirect
258. C42×Q8C22semidirect

Maximal subgroups

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

subgroupindex
#530772
#530442
#530072
#529912
#527512
#527282
#526732
#526262
#522942
#522752
#461582
#461042
#460952
#458962
#458572
#456462
#455822
#455042
#454932
#365552
#365172
#363122
#362682
#362342
#359472
#358562
#357582
#356892