Finite Group Databasebeta

← #7898079

Subgroups — #7898079

Order 512.

5171 conjugacy classes of subgroups.

The subgroup lattice has 1520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59815C211yesmaximal, characteristic, complemented
2#59680C212yesmaximal, complemented
3#52274C211yesmaximal, characteristic, complemented
4#51936C214yesmaximal, complemented
5#50135C214yesmaximal, complemented
6#48723C214yesmaximal, complemented
7#47328C214yesmaximal, complemented
8#45962C212yesmaximal, complemented
9#45155C212yesmaximal, complemented
10#44969C212yesmaximal, complemented
11#44964C212yesmaximal, complemented
12#43112C214yesmaximal, complemented
13#42529C212yesmaximal, complemented
14#42529C212yesmaximal, complemented
15#42136C214yesmaximal, complemented
16#40025C212yesmaximal, complemented
17#39747C212yesmaximal, complemented
18#39739C211yesmaximal, characteristic, complemented
19#39739C212yesmaximal, complemented
20#39739C211yesmaximal, characteristic, complemented
21#38831C212yesmaximal, complemented
22#38433C212yesmaximal, complemented
23#37216C212yesmaximal, complemented
24#36271C211yesmaximal, characteristic, complemented
25#35930C212yesmaximal, complemented
26#35561C212yesmaximal, complemented
27#35186C211yesmaximal, characteristic, complemented
28#34498C212yesmaximal, complemented
29#34331C211yesmaximal, characteristic, complemented
30C2×#559C2211yescharacteristic
31C2×#559C2212yes—
32C2×#559C2212yes—
33C2×#556C2212yes—
34C2×#553C2214yes—
35C2×#550C2212yes—
36C2×#547C2212yes—
37#2861C2212yes—
38#2860C2212yes—
39#2860C2212yes—
40#2858C2211yescharacteristic
41#2858C2212yes—
42#2828C2214yes—
43#2828C2214yes—
44#2809C2211yescharacteristic
45#2806C2211yescharacteristic
46#2805C2211yescharacteristic
47#2802C2212yes—
48#2800C2214yes—
49#2799C2212yes—
50#2795C2214yes—
51#2791C2212yes—
52#2786C2214yes—
53#2782C2214yes—
54#2781C2214yes—
55#2780C2214yes—
56#2780C2214yes—
57#2779C2214yes—
58#2774C2212yes—
59#2761C2214yes—
60#2755C2212yes—
61#2750C2214yes—
62#2733C2214yes—
63#2733C2212yes—
64#2733C2212yes—
65#2733C2212yes—
66#2733C2214yes—
67#2733C2212yes—
68#2726C2211yescharacteristic
69#2718C2214yes—
70#2718C2214yes—
71#2715C2214yes—
72#2714C2214yes—
73#2714C2214yes—
74#2714C2214yes—
75#2714C2214yes—
76#2714C2214yes—
77#2714C2214yes—
78#2713C2212yes—
79#2707C2214yes—
80#2703C2214yes—
81#2703C2214yes—
82#2699C2214yes—
83#2699C2214yes—
84#2695C2214yes—
85#2688C2214yes—
86#2688C2214yes—
87#2682C2212yes—
88#2682C2212yes—
89#2682C2212yes—
90#2682C2212yes—
91#2682C2214yes—
92#2682C2212yes—
93#2682C2214yes—
94#2682C2212yes—
95#2680C2214yes—
96#2671C2214yes—
97#2671C2214yes—
98#2661C2214yes—
99#2661C2214yes—
100#2661C2214yes—
101#2657C2212yes—
102#2657C2212yes—
103#2657C2212yes—
104#2651C2214yes—
105#2651C2214yes—
106#2635C2214yes—
107#2635C2214yes—
108#2601C2214yes—
109#2601C2214yes—
110#2595C2214yes—
111#2595C2214yes—
112#2593C2214yes—
113#2592C2212yes—
114#2582C2211yescharacteristic
115#2579C2214yes—
116#2560C2214yes—
117#2560C2214yes—
118#2558C2214yes—
119#2555C2214yes—
120#2555C2214yes—
121#2552C2211yescharacteristic
122#2548C2211yescharacteristic
123#2548C2212yes—
124#2548C2211yescharacteristic
125#2548C2211yescharacteristic
126#2547C2212yes—
127#2546C2211yescharacteristic
128#2545C2212yes—
129#2545C2212yes—
130#2545C2212yes—
131#2545C2212yes—
132#2544C2212yes—
133#2544C2212yes—
134#2544C2212yes—
135#2544C2212yes—
136#2544C2212yes—
137#2544C2212yes—
138#2543C2214yes—
139#2541C2212yes—
140#2541C2212yes—
141#2541C2212yes—
142#2541C2212yes—
143#2541C2212yes—
144#2541C2212yes—
145#2538C2212yes—
146#2537C2212yes—
147#2535C2214yes—
148#2531C2214yes—
149#2531C2214yes—
150#2526C2214yes—
151#2526C2214yes—
152#2512C2212yes—
153#2512C2212yes—
154#2512C2212yes—
155#2511C2212yes—
156#2481C2214yes—
157#2474C2214yes—
158#2470C2214yes—
159#2468C2214yes—
160#2468C2214yes—
161#2468C2214yes—
162#2466C2214yes—
163#2464C2214yes—
164#2464C2214yes—
165#2464C2214yes—
166#2464C2214yes—
167#2460C2214yes—
168#2456C2214yes—
169#2456C2214yes—
170#2456C2214yes—
171#2456C2214yes—
172#2456C2214yes—
173#2456C2214yes—
174#2456C2214yes—
175#2456C2214yes—
176#2456C2214yes—
177#2456C2214yes—
178#2454C2212yes—
179#2452C2212yes—
180#2450C2214yes—
181#2449C2214yes—
182#2448C2212yes—
183#2448C2212yes—
184#2447C2212yes—
185#2447C2212yes—
186#2447C2212yes—
187#2446C2212yes—
188#2445C2212yes—
189#2445C2212yes—
190#2445C2212yes—
191#2445C2212yes—
192#2430C2214yes—
193#2419C2214yes—
194#2416C2214yes—
195#2416C2214yes—
196#2414C2214yes—
197#2414C2214yes—
198#2414C2214yes—
199#2413C2214yes—
200#2407C2214yes—
201#2407C2214yes—
202#2407C2214yes—
203#2402C2212yes—
204#2402C2212yes—
205#2399C2212yes—
206#2388C2214yes—
207#2376C2214yes—
208#2376C2214yes—
209#2367C2212yes—
210#2367C2212yes—
211#2367C2212yes—
212#2367C2212yes—
213#2367C2212yes—
214#2367C2214yes—
215#2366C2211yescharacteristic
216#2366C2211yescharacteristic
217#2366C2212yes—
218#2366C2212yes—
219#2365C2211yescharacteristic
220#2359C2214yes—
221#2355C2211yescharacteristic
222#2354C2212yes—
223Q8×C4⋊C4C2211yescharacteristic
224Q8×C4⋊C4C2212yes—
225#2349C2212yes—
226D4×C4⋊C4C2212yes—
227D4×C4⋊C4C2212yes—
228D4×C4⋊C4C2214yes—
229#2335C2214yes—
230#2335C2214yes—
231#2326C2212yes—
232#2326C2212yes—
233#2326C2212yes—
234#2326C2212yes—
235#2326C2212yes—
236#2326C2212yes—
237#2326C2214yes—
238#2322C2214yes—
239#2322C2214yes—
240#2319C2212yes—
241#2319C2212yes—
242#2319C2214yes—
243C4×C4⋊Q8C2211yescharacteristic
244C4×#127C2211yescharacteristic
245C4×#127C2212yes—
246C4×#127C2212yes—
247C4×#127C2211yescharacteristic
248C4×#125C2212yes—
249C4×#124C2212yes—
250#2295C2211yescharacteristic
251#2295C2211yescharacteristic
252#2295C2212yes—
253#2295C2212yes—
254#2295C2212yes—
255#2293C2212yes—
256#2293C2212yes—
257#2275C2212yes—
258C42×Q8C2211yescharacteristic
259C22×#41C2314yes—
260#559—28no—
261#559—216no—
262#559—48no—
263#556—48no—
264#553—416no—
265#550—48no—
266#547—48no—
267C2×C4⋊Q8C2311yescharacteristic
268C2×C4⋊Q8C2311yescharacteristic
269C2×C4⋊Q8C2312yes—
270C2×#127C2311yescharacteristic
271C2×#127C2312yes—
272C2×#127C2311yescharacteristic
273C2×#127C2312yes—
274C2×#127C2311yescharacteristic
275C2×#127C2312yes—
276C2×#127C2312yes—
277C2×#127C2312yes—
278C2×#127C2312yes—
279C2×#126C2314yes—
280C2×#126C2314yes—
281C2×#126C2314yes—
282C2×#126C2314yes—
283C2×#125C2312yes—
284C2×#125C2312yes—
285C2×#124C2312yes—
286C2×#124C2312yes—
287C2×#124C2312yes—
288C2×#124C2312yes—
289C2×#124C2314yes—
290C2×#124C2312yes—
291C2×#124C2312yes—
292C2×#124C2312yes—
293C2×#124C2312yes—
294C2×#124C2312yes—
295C2×#124C2312yes—
296C2×#124C2314yes—
297C2×#124C2312yes—
298C2×#123C2314yes—
299C2×#123C2314yes—
300C2×#123C2314yes—
301C2×#123C2314yes—
302C2×#123C2314yes—
303C2×#123C2314yes—
304C2×#123C2314yes—
305C2×#123C2314yes—
306C2×#123C2314yes—
307C2×C22⋊Q8C2314yes—
308C2×C22⋊Q8C2314yes—
309C2×#121C2314yes—
310C2×#121C2314yes—
311C2×#121C2314yes—
312C2×#121C2314yes—
313C2×#121C2314yes—
314C2×#121C2314yes—
315C2×#121C2314yes—
316C2×#121C2314yes—
317C2×#121C2314yes—
318C2×#121C2314yes—
319C2×#121C2314yes—
320C2×#121C2314yes—
321C2×#121C2314yes—
322C2×#121C2314yes—
323C2×#121C2314yes—
324C2×C4×Q8C2312yes—
325C2×C4×Q8C2311yescharacteristic
326C2×C4×Q8C2312yes—
327C2×C4×Q8C2311yescharacteristic
328C2×C4×Q8C2311yescharacteristic
329C2×C4×Q8C2312yes—
330C2×C4×Q8C2312yes—
331C2×C4×Q8C2311yescharacteristic
332C2×C4×Q8C2312yes—
333C2×C4×Q8C2311yescharacteristic
334C2×C4×D4C2312yes—
335C2×C4×D4C2312yes—
336C2×C4×D4C2312yes—
337C2×C4×D4C2312yes—
338C2×C4×D4C2314yes—
339C2×C4×D4C2312yes—
340C2×C4×D4C2312yes—
341C2×C4×D4C2314yes—
342C2×C4×D4C2312yes—
343C2×C4×D4C2312yes—
344C2×C4×D4C2312yes—
345C2×C4×D4C2312yes—
346C2×C4×D4C2314yes—
347C2×C4×D4C2314yes—
348C2×C4×D4C2312yes—
349C2×C4×D4C2312yes—
350C2×C4×D4C2312yes—
351C2×C4×D4C2314yes—
352C2×C4×D4C2314yes—
353C2×C4×D4C2312yes—
354C2×C4×D4C2314yes—
355C2×C4×D4C2312yes—
356C2×C4×D4C2314yes—
357C2×C4×D4C2312yes—
358C2×#117C2314yes—
359C2×#117C2314yes—
360C22×C4⋊C4C2314yes—
361C22×C4⋊C4C2314yes—
362#400C2312yes—
363#400C2312yes—
364#400C2314yes—
365#400C2312yes—
366#400C2312yes—
367#400C2312yes—
368#400C2312yes—
369#400C2312yes—
370#400C2312yes—
371#400C2314yes—
372#400C2314yes—
373#399C2314yes—
374#399C2314yes—
375#398C2314yes—
376#398C2314yes—
377#398C2312yes—
378#398C2314yes—
379#398C2314yes—
380#398C2312yes—
381#398C2312yes—
382#398C2312yes—
383#398C2312yes—
384#398C2312yes—
385#398C2312yes—
386#398C2312yes—
387#398C2312yes—
388#398C2312yes—
389#398C2312yes—
390#398C2312yes—
391#397C2314yes—
392#397C2314yes—
393#397C2314yes—
394#397C2314yes—
395#397C2314yes—
396#397C2314yes—
397#397C2314yes—
398#397C2314yes—
399#397C2314yes—
400#397C2314yes—
401#397C2314yes—
402#396C2314yes—
403#396C2314yes—
404#396C2314yes—
405#396C2314yes—
406#396C2314yes—
407#396C2314yes—
408#396C2314yes—
409#396C2314yes—
410#396C2314yes—
411#396C2314yes—
412#396C2314yes—
413#396C2314yes—
414#395C2312yes—
415#395C2312yes—
416#395C2312yes—
417#395C2312yes—
418#394C2314yes—
419#394C2314yes—
420#394C2314yes—
421#394C2314yes—
422#394C2314yes—
423#394C2314yes—
424#394C2314yes—
425#394C2314yes—
426#394C2314yes—
427#394C2314yes—
428#394C2314yes—
429#394C2314yes—
430#394C2314yes—
431#394C2314yes—
432#394C2314yes—
433#394C2314yes—
434#394C2314yes—
435#394C2314yes—
436#394C2314yes—
437#394C2314yes—
438#394C2314yes—
439#394C2314yes—
440#394C2314yes—
441#394C2314yes—
442#394C2314yes—
443#393C2314yes—
444#392C2314yes—
445#392C2314yes—
446#392C2314yes—
447#392C2314yes—
448#392C2314yes—
449#392C2314yes—
450#392C2314yes—
451#392C2314yes—
452#392C2314yes—
453#392C2314yes—
454#392C2314yes—
455#392C2314yes—
456#392C2314yes—
457#392C2314yes—
458#392C2314yes—
459#392C2314yes—
460#392C2314yes—
461#392C2314yes—
462#392C2314yes—
463#392C2314yes—
464#392C2314yes—
465#392C2314yes—
466#392C2314yes—
467#392C2314yes—
468#391C2312yes—
469#391C2312yes—
470#391C2312yes—
471#391C2312yes—
472#391C2312yes—
473#391C2312yes—
474#391C2312yes—
475#391C2312yes—
476#391C2312yes—
477#391C2312yes—
478#391C2311yescharacteristic
479#391C2311yescharacteristic
480#391C2312yes—
481#391C2312yes—
482#391C2311yescharacteristic
483#391C2311yescharacteristic
484#390C2312yes—
485#390C2314yes—
486#390C2314yes—
487#390C2312yes—
488#390C2312yes—
489#390C2312yes—
490#390C2312yes—
491#390C2312yes—
492#390C2312yes—
493#390C2314yes—
494#390C2312yes—
495#390C2312yes—
496#390C2314yes—
497#390C2312yes—
498#390C2312yes—
499#390C2312yes—
500#390C2314yes—
501#390C2312yes—
502#390C2312yes—
503#390C2312yes—
504#390C2312yes—
505#390C2312yes—
506#390C2312yes—
507#390C2314yes—
508#390C2314yes—
509#390C2314yes—
510#390C2314yes—
511#390C2312yes—
512#390C2312yes—
513#390C2314yes—
514#390C2314yes—
515#390C2312yes—
516#390C2314yes—
517#390C2312yes—
518#390C2312yes—
519#390C2312yes—
520#390C2312yes—
521#390C2312yes—
522#390C2312yes—
523#389C2312yes—
524#389C2312yes—
525#389C2312yes—
526#389C2311yescharacteristic
527#389C2311yescharacteristic
528#389C2312yes—
529#389C2312yes—
530#389C2314yes—
531#389C2312yes—
532#389C2312yes—
533#389C2312yes—
534#389C2314yes—
535#389C2314yes—
536#389C2312yes—
537#389C2312yes—
538#389C2312yes—
539#389C2312yes—
540#389C2311yescharacteristic
541#389C2312yes—
542#389C2312yes—
543#389C2312yes—
544#389C2311yescharacteristic
545#389C2312yes—
546#389C2312yes—
547#389C2311yescharacteristic
548#389C2311yescharacteristic
549#388C2314yes—
550#388C2314yes—
551#388C2314yes—
552#388C2314yes—
553#388C2314yes—
554#388C2314yes—
555#388C2314yes—
556#388C2314yes—
557#388C2314yes—
558#388C2314yes—
559#388C2314yes—
560#388C2314yes—
561#388C2314yes—
562#388C2314yes—
563#388C2314yes—
564#388C2314yes—
565#388C2314yes—
566#388C2314yes—
567#388C2314yes—
568#388C2314yes—
569#388C2314yes—
570#388C2314yes—
571#388C2314yes—
572#388C2314yes—
573#388C2314yes—
574#388C2314yes—
575#388C2314yes—
576#388C2314yes—
577#388C2314yes—
578#388C2314yes—
579#388C2314yes—
580#388C2314yes—
581#388C2314yes—
582#388C2314yes—
583#388C2314yes—
584#388C2314yes—
585#388C2314yes—
586#388C2314yes—
587#388C2314yes—
588#388C2314yes—
589#388C2314yes—
590#388C2314yes—
591#387C2314yes—
592#387C2314yes—
593#387C2312yes—
594#387C2312yes—
595#387C2312yes—
596#387C2312yes—
597#387C2314yes—
598#387C2312yes—
599#387C2312yes—
600#387C2314yes—
601#387C2312yes—
602#387C2314yes—
603#387C2314yes—
604#387C2314yes—
605#387C2312yes—
606#387C2314yes—
607#387C2312yes—
608#387C2312yes—
609#387C2312yes—
610#387C2312yes—
611#387C2312yes—
612#387C2312yes—
613#387C2312yes—
614#387C2312yes—
615#386C2314yes—
616#386C2314yes—
617#386C2314yes—
618#386C2314yes—
619#386C2314yes—
620#386C2314yes—
621#386C2314yes—
622#386C2314yes—
623#386C2314yes—
624#386C2314yes—
625#386C2314yes—
626#386C2314yes—
627#386C2314yes—
628#386C2314yes—
629#386C2314yes—
630#386C2314yes—
631#386C2314yes—
632#386C2314yes—
633#386C2314yes—
634#386C2314yes—
635#386C2314yes—
636#386C2314yes—
637#385C2314yes—
638#385C2314yes—
639#385C2314yes—
640#385C2314yes—
641#385C2314yes—
642#385C2314yes—
643#385C2314yes—
644#385C2314yes—
645#385C2314yes—
646#385C2314yes—
647#385C2314yes—
648#385C2314yes—
649#385C2314yes—
650#385C2314yes—
651#385C2314yes—
652#385C2314yes—
653#385C2314yes—
654#385C2314yes—
655#385C2314yes—
656#385C2314yes—
657#385C2314yes—
658#385C2314yes—
659#384C2311yescharacteristic
660#384C2311yescharacteristic
661#384C2312yes—
662#384C2312yes—
663#384C2311yescharacteristic
664#384C2314yes—
665#382C2312yes—
666#382C2312yes—
667#381C2314yes—
668#381C2314yes—
669#381C2314yes—
670#381C2314yes—
671#380C2314yes—
672#380C2314yes—
673#380C2314yes—
674#380C2314yes—
675#380C2314yes—
676#380C2314yes—
677#380C2314yes—
678#380C2314yes—
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2314yes—
681C4×C4⋊C4C2311yescharacteristic
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2311yescharacteristic
689C4×C4⋊C4C2311yescharacteristic
690C4×C4⋊C4C2314yes—
691C4×C4⋊C4C2312yes—
692C4×C4⋊C4C2312yes—
693C4×C4⋊C4C2311yescharacteristic
694C4×C4⋊C4C2312yes—
695C4×C4⋊C4C2312yes—
696C4×C4⋊C4C2312yes—
697C4×C4⋊C4C2311yescharacteristic
698C4×C4⋊C4C2312yes—
699C4×C4⋊C4C2311yescharacteristic
700C4×C4⋊C4C2312yes—
701C4×C4⋊C4C2312yes—
702C4×C4⋊C4C2312yes—
703C4×C4⋊C4C2311yescharacteristic
704C4×C22⋊C4C2314yes—
705C4×C22⋊C4C2314yes—
706C4×C22⋊C4C2314yes—
707C4×C22⋊C4C2314yes—
708C4×C22⋊C4C2314yes—
709C4×C22⋊C4C2314yes—
710C4×C22⋊C4C2314yes—
711#376C2312yes—
712#376C2312yes—
713#376C2314yes—
714#376C2312yes—
715C2×#95C2314yes—
716C43C2312yes—
717C43C2311yescharacteristic
718C43C2312yes—
719C2×#41—48no—
720C2×#41—48no—
721C2×#41—84no—
722C22×Q8C2411yescharacteristic
723C22×Q8C2412yes—
724C22×Q8C2412yes—
725C22×Q8C2411yescharacteristic
726C22×Q8C2411yescharacteristic
727C22×D4C2412yes—
728C22×D4C2412yes—
729C22×D4C2412yes—
730C22×D4C2414yes—
731C22×D4C2412yes—
732C22×D4C2414yes—
733C22×D4C2412yes—
734C22×D4C2412yes—
735C22×D4C2412yes—
736C22×D4C2412yes—
737C22×D4C2414yes—
738C22×D4C2414yes—
739C22×D4C2414yes—
740C22×D4C2414yes—
741C22×D4C2414yes—
742C22×D4C2414yes—
743C22×D4C2414yes—
744C22×D4C2414yes—
745C22×D4C2414yes—
746C22×D4C2412yes—
747C22×D4C2414yes—
748C23×C4C2414yes—
749C23×C4C2414yes—
750C23×C4C2414yes—
751C23×C4C2414yes—
752C23×C4C2414yes—
753C23×C4C2414yes—
754C23×C4C2414yes—
755C23×C4C2414yes—
756C23×C4C2414yes—
757C4⋊Q8—24no—
758C4⋊Q8—42no—
759C4⋊Q8—44no—
760#127—24no—
761#127—28no—
762#127—24no—
763#127—44no—
764#127—42no—
765#127—44no—
766#127—44no—
767#127—44no—
768#127—44no—
769#126—48no—
770#126—48no—
771#126—48no—
772#126—48no—
773#125—28no—
774#125—82no—
775#124—216no—
776#124—28no—
777#124—28no—
778#124—28no—
779#124—28no—
780#124—28no—
781#124—44no—
782#124—44no—
783#124—44no—
784#124—44no—
785#124—44no—
786#124—48no—
787#124—82no—
788#123—216no—
789#123—216no—
790#123—216no—
791#123—216no—
792#123—48no—
793#123—48no—
794#123—48no—
795#123—48no—
796#123—84no—
797C22⋊Q8—48no—
798C22⋊Q8—48no—
799#121—48no—
800#121—48no—
801#121—48no—
802#121—48no—
803#121—48no—
804#121—48no—
805#121—48no—
806#121—48no—
807#121—84no—
808#121—84no—
809#121—84no—
810#121—84no—
811#121—84no—
812#121—84no—
813#121—84no—
814C4×Q8—28no—
815C4×Q8—24no—
816C4×Q8—28no—
817C4×Q8—24no—
818C4×Q8—24no—
819C4×Q8—42no—
820C4×Q8—44no—
821C4×Q8—44no—
822C4×Q8—82no—
823C4×Q8#4118yescomplemented
824C4×D4—216no—
825C4×D4—28no—
826C4×D4—28no—
827C4×D4—28no—
828C4×D4—28no—
829C4×D4—28no—
830C4×D4—28no—
831C4×D4—44no—
832C4×D4—44no—
833C4×D4—48no—
834C4×D4—44no—
835C4×D4—44no—
836C4×D4—44no—
837C4×D4—44no—
838C4×D4—44no—
839C4×D4—48no—
840C4×D4—48no—
841C4×D4—48no—
842C4×D4—84no—
843C4×D4—82no—
844C4×D4—84no—
845C4×D4—82no—
846C4×D4—84no—
847C4×D4—82no—
848#117—48no—
849#117—48no—
850C2×C4⋊C4—48no—
851C2×C4⋊C4—48no—
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2412yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2412yes—
856C2×C4⋊C4C2412yes—
857C2×C4⋊C4C2412yes—
858C2×C4⋊C4C2411yescharacteristic
859C2×C4⋊C4C2412yes—
860C2×C4⋊C4C2411yescharacteristic
861C2×C4⋊C4C2411yescharacteristic
862C2×C4⋊C4C2412yes—
863C2×C4⋊C4C2412yes—
864C2×C4⋊C4C2412yes—
865C2×C4⋊C4C2412yes—
866C2×C4⋊C4C2412yes—
867C2×C4⋊C4C2411yescharacteristic
868C2×C4⋊C4C2412yes—
869C2×C4⋊C4C2414yes—
870C2×C4⋊C4C2412yes—
871C2×C4⋊C4C2412yes—
872C2×C4⋊C4C2411yescharacteristic
873C2×C4⋊C4C2412yes—
874C2×C4⋊C4C2414yes—
875C2×C4⋊C4C2414yes—
876C2×C4⋊C4C2414yes—
877C2×C4⋊C4C2414yes—
878C2×C4⋊C4C2411yescharacteristic
879C2×C4⋊C4C2412yes—
880C2×C4⋊C4C2412yes—
881C2×C4⋊C4C2414yes—
882C2×C4⋊C4C2412yes—
883C2×C4⋊C4C2414yes—
884C2×C4⋊C4C2412yes—
885C2×C4⋊C4C2414yes—
886C2×C4⋊C4C2414yes—
887C2×C4⋊C4C2414yes—
888C2×C4⋊C4C2412yes—
889C2×C4⋊C4C2412yes—
890C2×C4⋊C4C2412yes—
891C2×C4⋊C4C2412yes—
892C2×C4⋊C4C2412yes—
893C2×C4⋊C4C2412yes—
894C2×C4⋊C4C2412yes—
895C2×C4⋊C4C2412yes—
896C2×C4⋊C4C2412yes—
897C2×C4⋊C4C2414yes—
898C2×C4⋊C4C2411yescharacteristic
899C2×C4⋊C4C2414yes—
900C2×C4⋊C4C2412yes—
901C2×C4⋊C4C2412yes—
902C2×C4⋊C4C2411yescharacteristic
903C2×C4⋊C4C2412yes—
904C2×C4⋊C4C2411yescharacteristic
905C2×C4⋊C4C2411yescharacteristic
906C2×C4⋊C4C2412yes—
907C2×C4⋊C4C2412yes—
908C2×C4⋊C4C2411yescharacteristic
909C2×C4⋊C4C2412yes—
910C2×C4⋊C4C2411yescharacteristic
911C2×C4⋊C4C2411yescharacteristic
912C2×C22⋊C4C2414yes—
913C2×C22⋊C4C2414yes—
914C2×C22⋊C4C2414yes—
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⋊C4C2414yes—
926C2×C22⋊C4C2414yes—
927C2×C22⋊C4C2414yes—
928C2×C22⋊C4C2414yes—
929C2×C22⋊C4C2414yes—
930C2×C22⋊C4C2414yes—
931C2×C22⋊C4C2414yes—
932C2×C22⋊C4C2414yes—
933C2×C22⋊C4C2414yes—
934C2×C22⋊C4C2414yes—
935C2×C22⋊C4C2414yes—
936C2×C22⋊C4C2414yes—
937C2×C22⋊C4C2414yes—
938C2×C22⋊C4C2414yes—
939C2×C22⋊C4C2414yes—
940C2×C22⋊C4C2414yes—
941C2×C22⋊C4C2414yes—
942C2×C22⋊C4C2414yes—
943C2×C22⋊C4C2414yes—
944C2×C22⋊C4C2414yes—
945C2×C22⋊C4C2414yes—
946C2×C22⋊C4C2414yes—
947C2×C22⋊C4C2414yes—
948C2×C22⋊C4C2414yes—
949C2×C22⋊C4C2414yes—
950C2×C22⋊C4C2414yes—
951C2×C22⋊C4C2414yes—
952C2×C22⋊C4C2414yes—
953C2×C22⋊C4C2414yes—
954C2×C22⋊C4C2414yes—
955C2×C22⋊C4C2414yes—
956C2×C22⋊C4C2414yes—
957C2×C22⋊C4C2414yes—
958C2×C22⋊C4C2414yes—
959C2×C22⋊C4C2414yes—
960C2×C22⋊C4C2414yes—
961C2×C22⋊C4C2414yes—
962C2×C22⋊C4C2414yes—
963C2×C42C2412yes—
964C2×C42C2412yes—
965C2×C42C2412yes—
966C2×C42C2411yescharacteristic
967C2×C42C2412yes—
968C2×C42C2412yes—
969C2×C42C2412yes—
970C2×C42C2412yes—
971C2×C42C2414yes—
972C2×C42C2412yes—
973C2×C42C2411yescharacteristic
974C2×C42C2412yes—
975C2×C42C2414yes—
976C2×C42C2414yes—
977C2×C42C2411yescharacteristic
978C2×C42C2412yes—
979C2×C42C2411yescharacteristic
980C2×C42C2412yes—
981C2×C42C2414yes—
982C2×C42C2412yes—
983C2×C42C2414yes—
984C2×C42C2412yes—
985C2×C42C2412yes—
986C2×C42C2411yescharacteristic
987C2×C42C2412yes—
988C2×C42C2411yescharacteristic
989C2×C42C2412yes—
990C2×C42C2411yescharacteristic
991#95C2412yes—
992#95C2412yes—
993#95C2414yes—
994#95C2414yes—
995#95C2412yes—
996#95C2412yes—
997#95C2412yes—
998#95C2414yes—
999#95C2412yes—
1000#95C2412yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2412yes—
1004#95C2412yes—
1005#95C2414yes—
1006#95C2412yes—
1007#95C2412yes—
1008#95C2412yes—
1009#95C2412yes—
1010#95C2414yes—
1011#95C2412yes—
1012#95C2412yes—
1013#95C2412yes—
1014#95C2412yes—
1015#95C2414yes—
1016#95C2414yes—
1017#95C2412yes—
1018#95C2412yes—
1019#95C2414yes—
1020#95C2414yes—
1021#95C2414yes—
1022#95C2414yes—
1023#95C2412yes—
1024#95C2412yes—
1025#95C2412yes—
1026#95C2412yes—
1027#95C2412yes—
1028#95C2412yes—
1029#95C2412yes—
1030#95C2414yes—
1031#95C2412yes—
1032#95C2412yes—
1033#95C2412yes—
1034#95C2412yes—
1035#95C2412yes—
1036#95C2412yes—
1037#95C2412yes—
1038#95C2412yes—
1039#95C2412yes—
1040#95C2412yes—
1041#95C2412yes—
1042#95C2414yes—
1043#95C2414yes—
1044#95C2414yes—
1045#95C2414yes—
1046C24C2514yes—
1047C24C2514yes—
1048C24C2514yes—
1049#41—832no—
1050C2×Q8—22no—
1051C2×Q8—24no—
1052C2×Q8—24no—
1053C2×Q8—22no—
1054C2×Q8—24no—
1055C2×Q8—24no—
1056C2×Q8—22no—
1057C2×Q8—22no—
1058C2×Q8—24no—
1059C2×Q8—41no—
1060C2×Q8—41no—
1061C2×Q8—42no—
1062C2×Q8—41no—
1063C2×Q8—41no—
1064C2×Q8C2×#4114yes—
1065C2×D4—28no—
1066C2×D4—24no—
1067C2×D4—24no—
1068C2×D4—24no—
1069C2×D4—24no—
1070C2×D4—28no—
1071C2×D4—24no—
1072C2×D4—24no—
1073C2×D4—24no—
1074C2×D4—24no—
1075C2×D4—24no—
1076C2×D4—24no—
1077C2×D4—24no—
1078C2×D4—28no—
1079C2×D4—24no—
1080C2×D4—24no—
1081C2×D4—24no—
1082C2×D4—42no—
1083C2×D4—42no—
1084C2×D4—44no—
1085C2×D4—42no—
1086C2×D4—44no—
1087C2×D4—42no—
1088C2×D4—42no—
1089C2×D4—44no—
1090C2×D4—44no—
1091C2×D4—44no—
1092C2×D4—44no—
1093C2×D4—44no—
1094C2×D4—42no—
1095C2×D4—44no—
1096C2×D4—44no—
1097C2×D4—44no—
1098C2×D4—44no—
1099C2×D4—42no—
1100C2×D4—44no—
1101C2×D4—44no—
1102C2×D4—44no—
1103C2×D4—44no—
1104C2×D4—42no—
1105C2×D4—44no—
1106C2×D4—44no—
1107C2×D4—44no—
1108C2×D4—42no—
1109C2×D4—42no—
1110C2×D4—44no—
1111C2×D4—44no—
1112C2×D4—44no—
1113C2×D4—44no—
1114C2×D4—44no—
1115C2×D4—44no—
1116C2×D4—42no—
1117C2×D4—44no—
1118C2×D4—42no—
1119C2×D4—44no—
1120C2×D4—44no—
1121C2×D4—44no—
1122C2×D4—44no—
1123C2×D4—44no—
1124C2×D4—44no—
1125C2×D4—42no—
1126C2×D4—44no—
1127C2×D4—44no—
1128C22×C4—28no—
1129C22×C4—28no—
1130C22×C4—28no—
1131C22×C4—28no—
1132C22×C4—28no—
1133C22×C4—28no—
1134C22×C4—44no—
1135C22×C4—44no—
1136C22×C4—44no—
1137C22×C4—44no—
1138C22×C4—44no—
1139C22×C4—44no—
1140C22×C4—44no—
1141C22×C4—44no—
1142C22×C4—44no—
1143C22×C4—44no—
1144C22×C4—44no—
1145C22×C4—44no—
1146C22×C4—44no—
1147C22×C4—44no—
1148C22×C4—44no—
1149C22×C4—44no—
1150C22×C4—44no—
1151C22×C4—44no—
1152C22×C4—44no—
1153C22×C4—44no—
1154C22×C4—44no—
1155C22×C4C2512yes—
1156C22×C4C2512yes—
1157C22×C4C2512yes—
1158C22×C4C2512yes—
1159C22×C4C2512yes—
1160C22×C4C2512yes—
1161C22×C4C2512yes—
1162C22×C4C2512yes—
1163C22×C4C2511yescharacteristic
1164C22×C4C2512yes—
1165C22×C4C2512yes—
1166C22×C4C2512yes—
1167C22×C4C2514yes—
1168C22×C4C2514yes—
1169C22×C4C2514yes—
1170C22×C4C2512yes—
1171C22×C4C2512yes—
1172C22×C4C2512yes—
1173C22×C4C2511yescharacteristic
1174C22×C4C2512yes—
1175C22×C4C2511yescharacteristic
1176C22×C4C2511yescharacteristic
1177C22×C4C2512yes—
1178C22×C4C2511yescharacteristic
1179C22×C4C2511yescharacteristic
1180C22×C4C2511yescharacteristic
1181C4⋊C4—22no—
1182C4⋊C4—24no—
1183C4⋊C4—24no—
1184C4⋊C4—28no—
1185C4⋊C4—24no—
1186C4⋊C4—24no—
1187C4⋊C4—28no—
1188C4⋊C4—24no—
1189C4⋊C4—24no—
1190C4⋊C4—24no—
1191C4⋊C4—22no—
1192C4⋊C4—24no—
1193C4⋊C4—24no—
1194C4⋊C4—24no—
1195C4⋊C4—24no—
1196C4⋊C4—24no—
1197C4⋊C4—22no—
1198C4⋊C4—24no—
1199C4⋊C4—24no—
1200C4⋊C4—22no—
1201C4⋊C4—22no—
1202C4⋊C4—42no—
1203C4⋊C4—44no—
1204C4⋊C4—44no—
1205C4⋊C4—44no—
1206C4⋊C4—41no—
1207C4⋊C4—41no—
1208C4⋊C4—41no—
1209C4⋊C4—41no—
1210C4⋊C4—42no—
1211C4⋊C4—42no—
1212C4⋊C4—42no—
1213C4⋊C4—44no—
1214C4⋊C4—42no—
1215C4⋊C4—44no—
1216C4⋊C4—41no—
1217C4⋊C4—42no—
1218C4⋊C4—44no—
1219C4⋊C4—42no—
1220C4⋊C4—42no—
1221C4⋊C4—44no—
1222C4⋊C4—42no—
1223C4⋊C4—44no—
1224C4⋊C4—44no—
1225C4⋊C4—42no—
1226C4⋊C4—42no—
1227C4⋊C4—42no—
1228C4⋊C4—42no—
1229C4⋊C4—42no—
1230C4⋊C4—42no—
1231C4⋊C4—42no—
1232C4⋊C4—42no—
1233C4⋊C4—44no—
1234C4⋊C4—41no—
1235C4⋊C4—44no—
1236C4⋊C4—42no—
1237C4⋊C4—42no—
1238C4⋊C4C2×#4118yes—
1239C4⋊C4C2×#4114yes—
1240C4⋊C4H(5,𝔽2)14yes—
1241C22⋊C4—28no—
1242C22⋊C4—28no—
1243C22⋊C4—28no—
1244C22⋊C4—28no—
1245C22⋊C4—28no—
1246C22⋊C4—28no—
1247C22⋊C4—28no—
1248C22⋊C4—28no—
1249C22⋊C4—28no—
1250C22⋊C4—28no—
1251C22⋊C4—28no—
1252C22⋊C4—28no—
1253C22⋊C4—28no—
1254C22⋊C4—28no—
1255C22⋊C4—28no—
1256C22⋊C4—28no—
1257C22⋊C4—44no—
1258C22⋊C4—44no—
1259C22⋊C4—44no—
1260C22⋊C4—44no—
1261C22⋊C4—44no—
1262C22⋊C4—44no—
1263C22⋊C4—44no—
1264C22⋊C4—44no—
1265C22⋊C4—44no—
1266C22⋊C4—44no—
1267C22⋊C4—44no—
1268C22⋊C4—44no—
1269C22⋊C4—44no—
1270C22⋊C4—44no—
1271C22⋊C4—44no—
1272C22⋊C4—44no—
1273C22⋊C4—44no—
1274C22⋊C4—44no—
1275C22⋊C4—44no—
1276C22⋊C4—44no—
1277C22⋊C4—44no—
1278C22⋊C4—44no—
1279C22⋊C4—44no—
1280C22⋊C4—44no—
1281C22⋊C4—44no—
1282C22⋊C4—44no—
1283C22⋊C4—44no—
1284C22⋊C4—44no—
1285C22⋊C4—44no—
1286C22⋊C4—44no—
1287C22⋊C4—44no—
1288C22⋊C4—44no—
1289C22⋊C4—44no—
1290C22⋊C4—44no—
1291C22⋊C4—44no—
1292C42—24no—
1293C42—28no—
1294C42—24no—
1295C42—24no—
1296C42—24no—
1297C42—22no—
1298C42—24no—
1299C42—24no—
1300C42—24no—
1301C42—24no—
1302C42—22no—
1303C42—24no—
1304C42—41no—
1305C42—42no—
1306C42—44no—
1307C42—44no—
1308C42—44no—
1309C42—41no—
1310C42—42no—
1311C42—41no—
1312C42—42no—
1313C42—42no—
1314C42—44no—
1315C42—42no—
1316C42—42no—
1317C42C2×#4114yes—
1318C42C2×#4118yes—
1319C42H(5,𝔽2)14yes—
1320C23—24no—
1321C23—24no—
1322C23—24no—
1323C23—24no—
1324C23—24no—
1325C23—24no—
1326C23—24no—
1327C23—24no—
1328C23—24no—
1329C23—24no—
1330C23—24no—
1331C23—24no—
1332C23—24no—
1333C23—24no—
1334C23—24no—
1335C23—24no—
1336C23—24no—
1337C23—24no—
1338C23—24no—
1339C23—24no—
1340C23—24no—
1341C23C2611yescharacteristic
1342Q8—44no—
1343Q8—48no—
1344Q8—44no—
1345Q8—48no—
1346Q8—82no—
1347D4—48no—
1348D4—416no—
1349D4—48no—
1350D4—48no—
1351D4—48no—
1352D4—48no—
1353D4—84no—
1354D4—88no—
1355D4—84no—
1356D4—84no—
1357D4—88no—
1358D4—88no—
1359D4—88no—
1360D4—88no—
1361D4—88no—
1362D4—88no—
1363D4—164no—
1364D4—162no—
1365D4—164no—
1366D4—164no—
1367D4—164no—
1368C2×C4—22no—
1369C2×C4—21no—
1370C2×C4—22no—
1371C2×C4—21no—
1372C2×C4—21no—
1373C2×C4—22no—
1374C2×C4—21no—
1375C2×C4—21no—
1376C2×C4—21no—
1377C2×C4—22no—
1378C2×C4—22no—
1379C2×C4—21no—
1380C2×C4—21no—
1381C2×C4—21no—
1382C2×C4—22no—
1383C2×C4—21no—
1384C2×C4—22no—
1385C2×C4—24no—
1386C2×C4—22no—
1387C2×C4—24no—
1388C2×C4—22no—
1389C2×C4—22no—
1390C2×C4—22no—
1391C2×C4—22no—
1392C2×C4—22no—
1393C2×C4—22no—
1394C2×C4—22no—
1395C2×C4—22no—
1396C2×C4—22no—
1397C2×C4—22no—
1398C2×C4—24no—
1399C2×C4—22no—
1400C2×C4—24no—
1401C2×C4—24no—
1402C2×C4—24no—
1403C2×C4—22no—
1404C2×C4—22no—
1405C2×C4—22no—
1406C2×C4—22no—
1407C2×C4—22no—
1408C2×C4—22no—
1409C2×C4—21no—
1410C2×C4—22no—
1411C2×C4—22no—
1412C2×C4—24no—
1413C2×C4—22no—
1414C2×C4—22no—
1415C2×C4—22no—
1416C2×C4—22no—
1417C2×C4—22no—
1418C2×C4—21no—
1419C2×C4—21no—
1420C2×C4—22no—
1421C2×C4—24no—
1422C2×C4—22no—
1423C2×C4—24no—
1424C2×C4—22no—
1425C2×C4—22no—
1426C2×C4—22no—
1427C2×C4—22no—
1428C2×C4—22no—
1429C2×C4—22no—
1430C2×C4—22no—
1431C2×C4—22no—
1432C2×C4—22no—
1433C2×C4—22no—
1434C2×C4—22no—
1435C2×C4—88no—
1436C2×C4—88no—
1437C2×C4—88no—
1438C2×C4—88no—
1439C2×C4—88no—
1440C2×C4—88no—
1441C2×C4—88no—
1442C2×C4—164no—
1443C2×C4—164no—
1444C2×C4C22×#4112yes—
1445C2×C4C22×#4114yes—
1446C2×C4C22×#4112yes—
1447C2×C4C22×#4114yes—
1448C2×C4C22×#4112yes—
1449C2×C4C2×H(5,𝔽2)12yes—
1450C2×C4C2×H(5,𝔽2)12yes—
1451C2×C4C2×H(5,𝔽2)14yes—
1452C2×C4C2×H(5,𝔽2)12yes—
1453C2×C4C2×H(5,𝔽2)12yes—
1454C2×C4#58512yes—
1455C22—44no—
1456C22—44no—
1457C22—44no—
1458C22—44no—
1459C22—44no—
1460C22—44no—
1461C22—44no—
1462C22—44no—
1463C22—44no—
1464C22—44no—
1465C22—44no—
1466C22—44no—
1467C22—44no—
1468C22—44no—
1469C22—44no—
1470C22—44no—
1471C22—44no—
1472C22—44no—
1473C22—44no—
1474C22—44no—
1475C22—44no—
1476C22C23×#4111yescharacteristic
1477C22C22×H(5,𝔽2)11yescharacteristic
1478C22C22×H(5,𝔽2)11yescharacteristic
1479C22C2×#58511yescharacteristic
1480C22H(7,𝔽2)11yescharacteristic
1481C22H(7,𝔽2)11yescharacteristic
1482C222−1+611yescharacteristic
1483C4—24no—
1484C4—22no—
1485C4—24no—
1486C4—22no—
1487C4—22no—
1488C4—22no—
1489C4—24no—
1490C4—22no—
1491C4—42no—
1492C4—44no—
1493C4—42no—
1494C4—44no—
1495C4—42no—
1496C4—42no—
1497C4—42no—
1498C4—41no—
1499C4—42no—
1500C4—42no—
1501C4—42no—
1502C4—42no—
1503C4—44no—
1504C4—42no—
1505C4—42no—
1506C4—42no—
1507C4—42no—
1508C4#351714yes—
1509C2—84no—
1510C2—84no—
1511C2—84no—
1512C2C2×#351711yescharacteristic
1513C2#6284511yescharacteristic
1514C2#6287811yescharacteristic
1515C2#6291211yescharacteristic
1516C2#6296011yescharacteristic
1517C2#6298611yescharacteristic
1518C2#6306011yescharacteristic
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. #59815C2semidirect
2. #59680C2semidirect
3. #52274C2semidirect
4. #51936C2semidirect
5. #50135C2semidirect
6. #48723C2semidirect
7. #47328C2semidirect
8. #45962C2semidirect
9. #45155C2semidirect
10. #44969C2semidirect
11. #44964C2semidirect
12. #43112C2semidirect
13. #42529C2semidirect
14. #42529C2semidirect
15. #42136C2semidirect
16. #40025C2semidirect
17. #39747C2semidirect
18. #39739C2semidirect
19. #39739C2semidirect
20. #39739C2semidirect
21. #38831C2semidirect
22. #38433C2semidirect
23. #37216C2semidirect
24. #36271C2semidirect
25. #35930C2semidirect
26. #35561C2semidirect
27. #35186C2semidirect
28. #34498C2semidirect
29. #34331C2semidirect
823. C4×Q8#41semidirect

Maximal subgroups

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

subgroupindex
#598152
#596802
#522742
#519362
#501352
#487232
#473282
#459622
#451552
#449692
#449642
#431122
#425292
#421362
#400252
#397472
#397392
#388312
#384332
#372162
#362712
#359302
#355612
#351862
#344982
#343312