Finite Group Databasebeta

← #7893245

Subgroups — #7893245

Order 512.

5331 conjugacy classes of subgroups.

The subgroup lattice has 1570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59815C211yesmaximal, characteristic, complemented
2#59684C212yesmaximal, complemented
3#52274C211yesmaximal, characteristic, complemented
4#50097C214yesmaximal, complemented
5#49848C214yesmaximal, complemented
6#48168C214yesmaximal, complemented
7#46521C214yesmaximal, complemented
8#46318C212yesmaximal, complemented
9#45421C212yesmaximal, complemented
10#45041C212yesmaximal, complemented
11#44970C212yesmaximal, complemented
12#43897C214yesmaximal, complemented
13#42529C212yesmaximal, complemented
14#42528C212yesmaximal, complemented
15#41240C214yesmaximal, complemented
16#39745C212yesmaximal, complemented
17#39745C212yesmaximal, complemented
18#39739C211yesmaximal, characteristic, complemented
19#39739C211yesmaximal, characteristic, complemented
20#39454C212yesmaximal, complemented
21#39386C212yesmaximal, complemented
22#38822C212yesmaximal, complemented
23#37217C212yesmaximal, complemented
24#36469C211yesmaximal, characteristic, complemented
25#35930C212yesmaximal, complemented
26#35615C212yesmaximal, complemented
27#35197C211yesmaximal, characteristic, complemented
28#34500C212yesmaximal, complemented
29#34330C211yesmaximal, characteristic, complemented
30C2×#559C2212yes—
31C2×#559C2212yes—
32C2×#559C2212yes—
33C2×#550C2211yescharacteristic
34C2×#550C2212yes—
35C2×#547C2212yes—
36C2×#540C2214yes—
37#2867C2212yes—
38#2858C2211yescharacteristic
39#2854C2212yes—
40#2854C2212yes—
41#2850C2212yes—
42#2829C2214yes—
43#2828C2214yes—
44#2809C2211yescharacteristic
45#2806C2211yescharacteristic
46#2805C2211yescharacteristic
47#2802C2212yes—
48#2801C2214yes—
49#2800C2214yes—
50#2799C2212yes—
51#2791C2212yes—
52#2778C2214yes—
53#2778C2214yes—
54#2774C2212yes—
55#2756C2214yes—
56#2756C2214yes—
57#2755C2212yes—
58#2753C2214yes—
59#2749C2214yes—
60#2733C2212yes—
61#2733C2212yes—
62#2733C2212yes—
63#2733C2212yes—
64#2726C2211yescharacteristic
65#2713C2212yes—
66#2708C2214yes—
67#2706C2214yes—
68#2706C2214yes—
69#2706C2214yes—
70#2703C2214yes—
71#2703C2214yes—
72#2703C2214yes—
73#2699C2214yes—
74#2688C2214yes—
75#2688C2214yes—
76#2688C2214yes—
77#2682C2212yes—
78#2682C2212yes—
79#2682C2212yes—
80#2682C2212yes—
81#2682C2212yes—
82#2682C2212yes—
83#2673C2214yes—
84#2673C2214yes—
85#2673C2214yes—
86#2673C2214yes—
87#2673C2214yes—
88#2673C2214yes—
89#2673C2214yes—
90#2673C2214yes—
91#2673C2214yes—
92#2673C2214yes—
93#2673C2214yes—
94#2673C2214yes—
95#2672C2214yes—
96#2672C2214yes—
97#2671C2214yes—
98#2661C2214yes—
99#2661C2214yes—
100#2657C2212yes—
101#2657C2212yes—
102#2657C2212yes—
103#2648C2214yes—
104#2648C2214yes—
105#2635C2214yes—
106#2630C2214yes—
107#2619C2214yes—
108#2602C2214yes—
109#2598C2214yes—
110#2592C2212yes—
111#2591C2214yes—
112#2578C2214yes—
113#2576C2214yes—
114#2576C2214yes—
115#2571C2211yescharacteristic
116#2558C2214yes—
117#2557C2214yes—
118#2555C2214yes—
119#2555C2214yes—
120#2548C2212yes—
121#2548C2212yes—
122#2548C2211yescharacteristic
123#2547C2211yescharacteristic
124#2545C2212yes—
125#2545C2212yes—
126#2544C2212yes—
127#2544C2212yes—
128#2544C2212yes—
129#2544C2212yes—
130#2544C2212yes—
131#2544C2212yes—
132#2543C2214yes—
133#2543C2214yes—
134#2543C2214yes—
135#2541C2212yes—
136#2541C2212yes—
137#2541C2212yes—
138#2541C2212yes—
139#2541C2212yes—
140#2541C2211yescharacteristic
141#2541C2212yes—
142#2541C2212yes—
143#2541C2212yes—
144#2541C2211yescharacteristic
145#2538C2212yes—
146#2538C2211yescharacteristic
147#2537C2212yes—
148#2518C2214yes—
149#2518C2214yes—
150#2518C2214yes—
151#2518C2214yes—
152#2516C2214yes—
153#2514C2212yes—
154#2513C2212yes—
155#2513C2212yes—
156#2510C2214yes—
157#2491C2212yes—
158#2488C2214yes—
159#2477C2214yes—
160#2476C2214yes—
161#2470C2214yes—
162#2464C2214yes—
163#2464C2214yes—
164#2464C2214yes—
165#2464C2214yes—
166#2464C2214yes—
167#2461C2214yes—
168#2461C2214yes—
169#2457C2214yes—
170#2457C2214yes—
171#2456C2214yes—
172#2456C2214yes—
173#2456C2214yes—
174#2456C2214yes—
175#2448C2212yes—
176#2448C2212yes—
177#2447C2212yes—
178#2445C2212yes—
179#2445C2212yes—
180#2445C2212yes—
181#2445C2212yes—
182#2445C2212yes—
183#2445C2212yes—
184#2443C2214yes—
185#2431C2214yes—
186#2431C2214yes—
187#2431C2214yes—
188#2431C2214yes—
189#2430C2214yes—
190#2428C2214yes—
191#2428C2214yes—
192#2428C2214yes—
193#2428C2214yes—
194#2428C2214yes—
195#2428C2214yes—
196#2427C2212yes—
197#2425C2214yes—
198#2425C2214yes—
199#2422C2212yes—
200#2420C2212yes—
201#2416C2214yes—
202#2407C2214yes—
203#2402C2212yes—
204#2402C2212yes—
205#2399C2212yes—
206#2388C2214yes—
207#2379C2214yes—
208#2376C2214yes—
209#2374C2214yes—
210#2367C2212yes—
211#2367C2212yes—
212#2367C2212yes—
213#2366C2212yes—
214#2366C2211yescharacteristic
215#2366C2212yes—
216#2366C2212yes—
217#2366C2211yescharacteristic
218#2365C2211yescharacteristic
219#2364C2214yes—
220#2363C2212yes—
221#2359C2214yes—
222#2357C2212yes—
223#2355C2211yescharacteristic
224#2354C2211yescharacteristic
225#2352C2214yes—
226#2351C2212yes—
227#2349C2212yes—
228D4×C4⋊C4C2212yes—
229#2339C2212yes—
230#2337C2214yes—
231#2335C2214yes—
232#2333C2214yes—
233#2328C2212yes—
234#2328C2212yes—
235#2328C2212yes—
236#2328C2212yes—
237#2326C2212yes—
238#2326C2212yes—
239#2322C2214yes—
240#2320C2212yes—
241#2319C2212yes—
242#2318C2214yes—
243C4×C4⋊Q8C2211yescharacteristic
244C4×#127C2211yescharacteristic
245C4×#127C2211yescharacteristic
246C4×#125C2212yes—
247C4×#124C2212yes—
248C4×#124C2212yes—
249C4×#121C2212yes—
250C4×#121C2212yes—
251#2297C2212yes—
252#2295C2211yescharacteristic
253#2295C2212yes—
254#2295C2211yescharacteristic
255#2295C2212yes—
256#2293C2212yes—
257#2275C2212yes—
258C42×D4C2211yescharacteristic
259C22×#41C2312yes—
260C22×#41C2314yes—
261#559—216no—
262#559—48no—
263#559—48no—
264#550—28no—
265#550—48no—
266#547—48no—
267#540—416no—
268C2×C4⋊Q8C2311yescharacteristic
269C2×C4⋊Q8C2311yescharacteristic
270C2×#127C2311yescharacteristic
271C2×#127C2311yescharacteristic
272C2×#127C2312yes—
273C2×#127C2312yes—
274C2×#127C2312yes—
275C2×#127C2312yes—
276C2×#127C2311yescharacteristic
277C2×#127C2314yes—
278C2×#127C2312yes—
279C2×#127C2312yes—
280C2×#127C2312yes—
281C2×#127C2312yes—
282C2×#127C2312yes—
283C2×#127C2314yes—
284C2×#127C2314yes—
285C2×#127C2314yes—
286C2×#125C2312yes—
287C2×#124C2312yes—
288C2×#124C2312yes—
289C2×#124C2314yes—
290C2×#124C2312yes—
291C2×#124C2312yes—
292C2×#124C2312yes—
293C2×#124C2312yes—
294C2×#124C2312yes—
295C2×#124C2314yes—
296C2×#124C2314yes—
297C2×#124C2312yes—
298C2×#123C2314yes—
299C2×#123C2314yes—
300C2×#123C2314yes—
301C2×#123C2314yes—
302C2×#123C2314yes—
303C2×#123C2314yes—
304C2×#123C2314yes—
305C2×#123C2314yes—
306C2×#123C2314yes—
307C2×#123C2314yes—
308C2×#123C2314yes—
309C2×#123C2314yes—
310C2×C22⋊Q8C2314yes—
311C2×C22⋊Q8C2312yes—
312C2×#121C2314yes—
313C2×#121C2312yes—
314C2×#121C2312yes—
315C2×#121C2314yes—
316C2×#121C2314yes—
317C2×#121C2314yes—
318C2×#121C2314yes—
319C2×#121C2314yes—
320C2×#121C2314yes—
321C2×#121C2314yes—
322C2×#121C2314yes—
323C2×#121C2314yes—
324C2×#121C2312yes—
325C2×#121C2312yes—
326C2×#121C2312yes—
327C2×#121C2314yes—
328C2×#121C2314yes—
329C2×#121C2314yes—
330C2×#121C2314yes—
331C2×#121C2314yes—
332C2×#121C2314yes—
333C2×#121C2314yes—
334C2×#121C2314yes—
335C2×#121C2314yes—
336C2×#121C2314yes—
337C2×C4×Q8C2312yes—
338C2×C4×Q8C2312yes—
339C2×C4×Q8C2311yescharacteristic
340C2×C4×Q8C2312yes—
341C2×C4×Q8C2312yes—
342C2×C4×Q8C2311yescharacteristic
343C2×C4×D4C2312yes—
344C2×C4×D4C2312yes—
345C2×C4×D4C2314yes—
346C2×C4×D4C2312yes—
347C2×C4×D4C2311yescharacteristic
348C2×C4×D4C2311yescharacteristic
349C2×C4×D4C2312yes—
350C2×C4×D4C2312yes—
351C2×C4×D4C2312yes—
352C2×C4×D4C2314yes—
353C2×C4×D4C2312yes—
354C2×C4×D4C2312yes—
355C2×C4×D4C2312yes—
356C2×C4×D4C2314yes—
357C2×C4×D4C2312yes—
358C2×C4×D4C2314yes—
359C2×C4×D4C2311yescharacteristic
360C2×C4×D4C2312yes—
361C2×C4×D4C2314yes—
362C2×C4×D4C2312yes—
363C2×C4×D4C2312yes—
364C2×C4×D4C2312yes—
365C2×C4×D4C2314yes—
366C2×C4×D4C2312yes—
367C2×#117C2314yes—
368C2×#117C2312yes—
369C22×C4⋊C4C2314yes—
370C22×C42C2312yes—
371#401C2314yes—
372#400C2314yes—
373#400C2312yes—
374#400C2312yes—
375#400C2314yes—
376#400C2312yes—
377#400C2312yes—
378#400C2312yes—
379#400C2312yes—
380#400C2312yes—
381#400C2312yes—
382#399C2314yes—
383#399C2314yes—
384#398C2312yes—
385#398C2312yes—
386#398C2312yes—
387#398C2312yes—
388#398C2312yes—
389#398C2312yes—
390#398C2312yes—
391#398C2312yes—
392#398C2312yes—
393#398C2312yes—
394#398C2312yes—
395#398C2312yes—
396#397C2314yes—
397#397C2314yes—
398#397C2314yes—
399#397C2314yes—
400#397C2314yes—
401#397C2314yes—
402#397C2314yes—
403#397C2314yes—
404#397C2314yes—
405#397C2314yes—
406#396C2314yes—
407#396C2314yes—
408#396C2314yes—
409#396C2314yes—
410#396C2314yes—
411#396C2314yes—
412#396C2314yes—
413#395C2312yes—
414#395C2312yes—
415#395C2312yes—
416#395C2312yes—
417#394C2314yes—
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#394C2314yes—
444#394C2314yes—
445#394C2314yes—
446#393C2314yes—
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#392C2314yes—
469#392C2314yes—
470#392C2314yes—
471#392C2314yes—
472#392C2314yes—
473#392C2314yes—
474#392C2314yes—
475#392C2314yes—
476#392C2314yes—
477#391C2312yes—
478#391C2312yes—
479#391C2312yes—
480#391C2312yes—
481#391C2312yes—
482#391C2312yes—
483#391C2312yes—
484#391C2311yescharacteristic
485#391C2311yescharacteristic
486#391C2312yes—
487#391C2311yescharacteristic
488#391C2312yes—
489#391C2312yes—
490#391C2311yescharacteristic
491#390C2312yes—
492#390C2312yes—
493#390C2312yes—
494#390C2312yes—
495#390C2312yes—
496#390C2312yes—
497#390C2312yes—
498#390C2314yes—
499#390C2312yes—
500#390C2312yes—
501#390C2312yes—
502#390C2312yes—
503#390C2312yes—
504#390C2312yes—
505#390C2312yes—
506#390C2312yes—
507#390C2312yes—
508#390C2312yes—
509#390C2314yes—
510#390C2312yes—
511#390C2312yes—
512#390C2312yes—
513#390C2312yes—
514#390C2312yes—
515#390C2312yes—
516#390C2312yes—
517#390C2314yes—
518#390C2314yes—
519#390C2314yes—
520#390C2314yes—
521#390C2314yes—
522#390C2312yes—
523#389C2312yes—
524#389C2312yes—
525#389C2311yescharacteristic
526#389C2312yes—
527#389C2311yescharacteristic
528#389C2312yes—
529#389C2312yes—
530#389C2312yes—
531#389C2312yes—
532#389C2312yes—
533#389C2314yes—
534#389C2314yes—
535#389C2311yescharacteristic
536#389C2312yes—
537#389C2312yes—
538#389C2311yescharacteristic
539#389C2312yes—
540#389C2311yescharacteristic
541#389C2311yescharacteristic
542#389C2312yes—
543#389C2312yes—
544#388C2314yes—
545#388C2314yes—
546#388C2314yes—
547#388C2314yes—
548#388C2314yes—
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#387C2312yes—
580#387C2312yes—
581#387C2312yes—
582#387C2312yes—
583#387C2314yes—
584#387C2312yes—
585#387C2314yes—
586#387C2314yes—
587#387C2312yes—
588#387C2314yes—
589#387C2312yes—
590#387C2312yes—
591#387C2312yes—
592#387C2312yes—
593#387C2312yes—
594#387C2312yes—
595#387C2314yes—
596#387C2312yes—
597#387C2312yes—
598#387C2312yes—
599#387C2312yes—
600#386C2314yes—
601#386C2314yes—
602#386C2314yes—
603#386C2314yes—
604#386C2314yes—
605#386C2314yes—
606#386C2314yes—
607#386C2314yes—
608#386C2314yes—
609#386C2314yes—
610#386C2314yes—
611#386C2314yes—
612#386C2314yes—
613#386C2314yes—
614#386C2314yes—
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#386C2314yes—
638#386C2314yes—
639#386C2314yes—
640#386C2314yes—
641#386C2314yes—
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#384C2311yescharacteristic
655#384C2311yescharacteristic
656#384C2311yescharacteristic
657#383C2314yes—
658#383C2314yes—
659#382C2312yes—
660#382C2312yes—
661#382C2312yes—
662#382C2314yes—
663#382C2314yes—
664#382C2312yes—
665#381C2314yes—
666#381C2314yes—
667#381C2314yes—
668#380C2314yes—
669#380C2314yes—
670#380C2314yes—
671#380C2314yes—
672#380C2312yes—
673#380C2312yes—
674#380C2312yes—
675#380C2312yes—
676C4×C4⋊C4C2311yescharacteristic
677C4×C4⋊C4C2312yes—
678C4×C4⋊C4C2312yes—
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2312yes—
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2311yescharacteristic
684C4×C4⋊C4C2311yescharacteristic
685C4×C4⋊C4C2311yescharacteristic
686C4×C4⋊C4C2311yescharacteristic
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2314yes—
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2312yes—
692C4×C4⋊C4C2311yescharacteristic
693C4×C4⋊C4C2311yescharacteristic
694C4×C4⋊C4C2312yes—
695C4×C4⋊C4C2312yes—
696C4×C4⋊C4C2312yes—
697C4×C22⋊C4C2314yes—
698C4×C22⋊C4C2314yes—
699C4×C22⋊C4C2314yes—
700C4×C22⋊C4C2314yes—
701C4×C22⋊C4C2314yes—
702C4×C22⋊C4C2312yes—
703C4×C22⋊C4C2314yes—
704C4×C22⋊C4C2314yes—
705C4×C22⋊C4C2314yes—
706C4×C22⋊C4C2314yes—
707C4×C22⋊C4C2312yes—
708C4×C22⋊C4C2314yes—
709C4×C22⋊C4C2314yes—
710C4×C22⋊C4C2312yes—
711C4×C22⋊C4C2314yes—
712#376C2312yes—
713#376C2312yes—
714#376C2312yes—
715C2×#95C2314yes—
716C2×#95C2314yes—
717C43C2312yes—
718C43C2311yescharacteristic
719C2×#41—28no—
720C2×#41—48no—
721C2×#41—48no—
722C2×#41—82no—
723C2×#41—82no—
724C2×#41—84no—
725C22×Q8C2412yes—
726C22×Q8C2412yes—
727C22×Q8C2411yescharacteristic
728C22×Q8C2411yescharacteristic
729C22×D4C2412yes—
730C22×D4C2412yes—
731C22×D4C2411yescharacteristic
732C22×D4C2412yes—
733C22×D4C2412yes—
734C22×D4C2412yes—
735C22×D4C2412yes—
736C22×D4C2412yes—
737C22×D4C2414yes—
738C22×D4C2414yes—
739C22×D4C2414yes—
740C22×D4C2414yes—
741C22×D4C2412yes—
742C22×D4C2414yes—
743C22×D4C2414yes—
744C22×D4C2414yes—
745C22×D4C2414yes—
746C22×D4C2414yes—
747C22×D4C2414yes—
748C22×D4C2414yes—
749C22×D4C2414yes—
750C22×D4C2412yes—
751C22×D4C2414yes—
752C22×D4C2414yes—
753C22×D4C2414yes—
754C22×D4C2414yes—
755C22×D4C2414yes—
756C22×D4C2414yes—
757C23×C4C2414yes—
758C23×C4C2414yes—
759C23×C4C2414yes—
760C23×C4C2412yes—
761C23×C4C2414yes—
762C23×C4C2412yes—
763C23×C4C2412yes—
764C23×C4C2414yes—
765C23×C4C2414yes—
766C23×C4C2414yes—
767C23×C4C2414yes—
768C23×C4C2414yes—
769C4⋊Q8—24no—
770C4⋊Q8—42no—
771#127—24no—
772#127—28no—
773#127—28no—
774#127—24no—
775#127—44no—
776#127—42no—
777#127—44no—
778#127—44no—
779#127—48no—
780#127—44no—
781#127—44no—
782#127—44no—
783#127—44no—
784#127—84no—
785#127—84no—
786#127—84no—
787#125—28no—
788#124—216no—
789#124—28no—
790#124—28no—
791#124—28no—
792#124—44no—
793#124—44no—
794#124—44no—
795#124—44no—
796#124—48no—
797#124—48no—
798#124—82no—
799#123—216no—
800#123—216no—
801#123—216no—
802#123—48no—
803#123—48no—
804#123—48no—
805#123—48no—
806#123—48no—
807#123—48no—
808#123—48no—
809#123—48no—
810#123—84no—
811C22⋊Q8—48no—
812C22⋊Q8—82no—
813#121—216no—
814#121—28no—
815#121—28no—
816#121—48no—
817#121—48no—
818#121—48no—
819#121—48no—
820#121—48no—
821#121—48no—
822#121—48no—
823#121—48no—
824#121—48no—
825#121—84no—
826#121—84no—
827#121—84no—
828#121—84no—
829#121—84no—
830#121—84no—
831#121—82no—
832#121—82no—
833#121—82no—
834#121—84no—
835#121—84no—
836#121—84no—
837#121—84no—
838C4×Q8—28no—
839C4×Q8—28no—
840C4×Q8—24no—
841C4×Q8—44no—
842C4×Q8—44no—
843C4×Q8#4118yescomplemented
844C4×D4—216no—
845C4×D4—24no—
846C4×D4—28no—
847C4×D4—28no—
848C4×D4—28no—
849C4×D4—28no—
850C4×D4—24no—
851C4×D4—44no—
852C4×D4—44no—
853C4×D4—44no—
854C4×D4—42no—
855C4×D4—44no—
856C4×D4—44no—
857C4×D4—44no—
858C4×D4—44no—
859C4×D4—48no—
860C4×D4—48no—
861C4×D4—48no—
862C4×D4—48no—
863C4×D4—82no—
864C4×D4—82no—
865C4×D4—84no—
866C4×D4—82no—
867C4×D4—82no—
868#117—48no—
869#117—82no—
870C2×C4⋊C4—48no—
871C2×C4⋊C4C2412yes—
872C2×C4⋊C4C2414yes—
873C2×C4⋊C4C2412yes—
874C2×C4⋊C4C2411yescharacteristic
875C2×C4⋊C4C2411yescharacteristic
876C2×C4⋊C4C2411yescharacteristic
877C2×C4⋊C4C2412yes—
878C2×C4⋊C4C2412yes—
879C2×C4⋊C4C2412yes—
880C2×C4⋊C4C2412yes—
881C2×C4⋊C4C2412yes—
882C2×C4⋊C4C2412yes—
883C2×C4⋊C4C2412yes—
884C2×C4⋊C4C2411yescharacteristic
885C2×C4⋊C4C2414yes—
886C2×C4⋊C4C2412yes—
887C2×C4⋊C4C2412yes—
888C2×C4⋊C4C2412yes—
889C2×C4⋊C4C2411yescharacteristic
890C2×C4⋊C4C2412yes—
891C2×C4⋊C4C2414yes—
892C2×C4⋊C4C2411yescharacteristic
893C2×C4⋊C4C2412yes—
894C2×C4⋊C4C2414yes—
895C2×C4⋊C4C2411yescharacteristic
896C2×C4⋊C4C2411yescharacteristic
897C2×C4⋊C4C2412yes—
898C2×C4⋊C4C2412yes—
899C2×C4⋊C4C2412yes—
900C2×C4⋊C4C2414yes—
901C2×C4⋊C4C2414yes—
902C2×C4⋊C4C2412yes—
903C2×C4⋊C4C2411yescharacteristic
904C2×C4⋊C4C2412yes—
905C2×C4⋊C4C2412yes—
906C2×C4⋊C4C2411yescharacteristic
907C2×C4⋊C4C2412yes—
908C2×C4⋊C4C2412yes—
909C2×C4⋊C4C2412yes—
910C2×C4⋊C4C2412yes—
911C2×C4⋊C4C2411yescharacteristic
912C2×C4⋊C4C2412yes—
913C2×C4⋊C4C2412yes—
914C2×C4⋊C4C2412yes—
915C2×C4⋊C4C2414yes—
916C2×C4⋊C4C2412yes—
917C2×C4⋊C4C2412yes—
918C2×C4⋊C4C2412yes—
919C2×C4⋊C4C2412yes—
920C2×C4⋊C4C2411yescharacteristic
921C2×C4⋊C4C2411yescharacteristic
922C2×C22⋊C4C2414yes—
923C2×C22⋊C4C2414yes—
924C2×C22⋊C4C2414yes—
925C2×C22⋊C4C2412yes—
926C2×C22⋊C4C2414yes—
927C2×C22⋊C4C2414yes—
928C2×C22⋊C4C2412yes—
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⋊C4C2412yes—
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×C22⋊C4C2414yes—
964C2×C22⋊C4C2414yes—
965C2×C22⋊C4C2414yes—
966C2×C22⋊C4C2414yes—
967C2×C22⋊C4C2414yes—
968C2×C22⋊C4C2414yes—
969C2×C22⋊C4C2414yes—
970C2×C22⋊C4C2414yes—
971C2×C22⋊C4C2414yes—
972C2×C22⋊C4C2414yes—
973C2×C22⋊C4C2414yes—
974C2×C22⋊C4C2414yes—
975C2×C22⋊C4C2414yes—
976C2×C42—82no—
977C2×C42C2412yes—
978C2×C42C2411yescharacteristic
979C2×C42C2412yes—
980C2×C42C2412yes—
981C2×C42C2412yes—
982C2×C42C2414yes—
983C2×C42C2412yes—
984C2×C42C2411yescharacteristic
985C2×C42C2412yes—
986C2×C42C2414yes—
987C2×C42C2414yes—
988C2×C42C2411yescharacteristic
989C2×C42C2411yescharacteristic
990C2×C42C2414yes—
991C2×C42C2414yes—
992C2×C42C2412yes—
993C2×C42C2412yes—
994C2×C42C2412yes—
995C2×C42C2412yes—
996C2×C42C2412yes—
997C2×C42C2412yes—
998C2×C42C2411yescharacteristic
999C2×C42C2411yescharacteristic
1000C2×C42C2412yes—
1001C2×C42C2411yescharacteristic
1002#95C2412yes—
1003#95C2412yes—
1004#95C2412yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2414yes—
1008#95C2414yes—
1009#95C2414yes—
1010#95C2412yes—
1011#95C2412yes—
1012#95C2412yes—
1013#95C2412yes—
1014#95C2412yes—
1015#95C2412yes—
1016#95C2412yes—
1017#95C2412yes—
1018#95C2412yes—
1019#95C2412yes—
1020#95C2412yes—
1021#95C2412yes—
1022#95C2412yes—
1023#95C2412yes—
1024#95C2414yes—
1025#95C2412yes—
1026#95C2412yes—
1027#95C2414yes—
1028#95C2412yes—
1029#95C2414yes—
1030#95C2414yes—
1031#95C2414yes—
1032#95C2414yes—
1033#95C2414yes—
1034#95C2414yes—
1035#95C2414yes—
1036#95C2414yes—
1037#95C2414yes—
1038#95C2412yes—
1039#95C2412yes—
1040#95C2412yes—
1041#95C2412yes—
1042#95C2412yes—
1043#95C2412yes—
1044#95C2412yes—
1045#95C2412yes—
1046#95C2412yes—
1047#95C2412yes—
1048#95C2412yes—
1049#95C2412yes—
1050#95C2412yes—
1051#95C2412yes—
1052#95C2412yes—
1053#95C2412yes—
1054#95C2412yes—
1055#95C2414yes—
1056#95C2414yes—
1057C24C2514yes—
1058C24C2514yes—
1059C24C2514yes—
1060C24C2512yes—
1061#41—816no—
1062#41—832no—
1063C2×Q8—24no—
1064C2×Q8—24no—
1065C2×Q8—24no—
1066C2×Q8—24no—
1067C2×Q8—22no—
1068C2×Q8—24no—
1069C2×Q8—41no—
1070C2×Q8—41no—
1071C2×Q8—42no—
1072C2×Q8—41no—
1073C2×Q8—41no—
1074C2×Q8C2×#4114yes—
1075C2×D4—24no—
1076C2×D4—24no—
1077C2×D4—22no—
1078C2×D4—24no—
1079C2×D4—24no—
1080C2×D4—28no—
1081C2×D4—24no—
1082C2×D4—28no—
1083C2×D4—28no—
1084C2×D4—28no—
1085C2×D4—22no—
1086C2×D4—24no—
1087C2×D4—24no—
1088C2×D4—24no—
1089C2×D4—24no—
1090C2×D4—24no—
1091C2×D4—28no—
1092C2×D4—24no—
1093C2×D4—28no—
1094C2×D4—24no—
1095C2×D4—22no—
1096C2×D4—24no—
1097C2×D4—24no—
1098C2×D4—42no—
1099C2×D4—42no—
1100C2×D4—42no—
1101C2×D4—42no—
1102C2×D4—42no—
1103C2×D4—44no—
1104C2×D4—44no—
1105C2×D4—44no—
1106C2×D4—44no—
1107C2×D4—42no—
1108C2×D4—42no—
1109C2×D4—44no—
1110C2×D4—44no—
1111C2×D4—44no—
1112C2×D4—44no—
1113C2×D4—42no—
1114C2×D4—44no—
1115C2×D4—44no—
1116C2×D4—44no—
1117C2×D4—42no—
1118C2×D4—44no—
1119C2×D4—44no—
1120C2×D4—44no—
1121C2×D4—44no—
1122C2×D4—44no—
1123C2×D4—44no—
1124C2×D4—42no—
1125C2×D4—44no—
1126C2×D4—44no—
1127C2×D4—44no—
1128C2×D4—44no—
1129C2×D4—44no—
1130C2×D4—44no—
1131C2×D4—44no—
1132C2×D4—44no—
1133C2×D4—44no—
1134C2×D4—44no—
1135C2×D4—42no—
1136C2×D4—42no—
1137C2×D4—44no—
1138C2×D4—44no—
1139C2×D4—44no—
1140C2×D4—44no—
1141C2×D4—44no—
1142C2×D4—44no—
1143C2×D4—44no—
1144C2×D4—44no—
1145C2×D4—44no—
1146C2×D4—44no—
1147C2×D4—44no—
1148C2×D4—44no—
1149C2×D4—44no—
1150C2×D4—44no—
1151C2×D4—44no—
1152C2×D4—44no—
1153C2×D4—42no—
1154C2×D4—44no—
1155C2×D4—44no—
1156C2×D4—44no—
1157C2×D4—44no—
1158C2×D4—44no—
1159C22×C4—24no—
1160C22×C4—28no—
1161C22×C4—28no—
1162C22×C4—28no—
1163C22×C4—28no—
1164C22×C4—24no—
1165C22×C4—28no—
1166C22×C4—24no—
1167C22×C4—42no—
1168C22×C4—42no—
1169C22×C4—42no—
1170C22×C4—42no—
1171C22×C4—44no—
1172C22×C4—44no—
1173C22×C4—44no—
1174C22×C4—44no—
1175C22×C4—44no—
1176C22×C4—44no—
1177C22×C4—42no—
1178C22×C4—44no—
1179C22×C4—44no—
1180C22×C4—44no—
1181C22×C4—44no—
1182C22×C4—42no—
1183C22×C4—44no—
1184C22×C4—44no—
1185C22×C4—44no—
1186C22×C4—44no—
1187C22×C4—44no—
1188C22×C4—44no—
1189C22×C4—44no—
1190C22×C4—44no—
1191C22×C4—44no—
1192C22×C4—44no—
1193C22×C4—44no—
1194C22×C4—44no—
1195C22×C4C2512yes—
1196C22×C4C2512yes—
1197C22×C4C2512yes—
1198C22×C4C2512yes—
1199C22×C4C2512yes—
1200C22×C4C2512yes—
1201C22×C4C2511yescharacteristic
1202C22×C4C2512yes—
1203C22×C4C2512yes—
1204C22×C4C2512yes—
1205C22×C4C2512yes—
1206C22×C4C2514yes—
1207C22×C4C2512yes—
1208C22×C4C2514yes—
1209C22×C4C2514yes—
1210C22×C4C2512yes—
1211C22×C4C2512yes—
1212C22×C4C2511yescharacteristic
1213C22×C4C2512yes—
1214C22×C4C2511yescharacteristic
1215C22×C4C2511yescharacteristic
1216C22×C4C2512yes—
1217C22×C4C2511yescharacteristic
1218C22×C4C2511yescharacteristic
1219C22×C4C2511yescharacteristic
1220C4⋊C4—22no—
1221C4⋊C4—24no—
1222C4⋊C4—28no—
1223C4⋊C4—24no—
1224C4⋊C4—28no—
1225C4⋊C4—24no—
1226C4⋊C4—22no—
1227C4⋊C4—24no—
1228C4⋊C4—24no—
1229C4⋊C4—24no—
1230C4⋊C4—24no—
1231C4⋊C4—24no—
1232C4⋊C4—24no—
1233C4⋊C4—22no—
1234C4⋊C4—24no—
1235C4⋊C4—24no—
1236C4⋊C4—24no—
1237C4⋊C4—22no—
1238C4⋊C4—22no—
1239C4⋊C4—42no—
1240C4⋊C4—44no—
1241C4⋊C4—44no—
1242C4⋊C4—41no—
1243C4⋊C4—42no—
1244C4⋊C4—42no—
1245C4⋊C4—41no—
1246C4⋊C4—41no—
1247C4⋊C4—42no—
1248C4⋊C4—42no—
1249C4⋊C4—44no—
1250C4⋊C4—44no—
1251C4⋊C4—41no—
1252C4⋊C4—41no—
1253C4⋊C4—41no—
1254C4⋊C4—42no—
1255C4⋊C4—42no—
1256C4⋊C4—42no—
1257C4⋊C4—42no—
1258C4⋊C4—42no—
1259C4⋊C4—42no—
1260C4⋊C4—42no—
1261C4⋊C4—42no—
1262C4⋊C4—42no—
1263C4⋊C4—42no—
1264C4⋊C4—44no—
1265C4⋊C4—42no—
1266C4⋊C4—42no—
1267C4⋊C4—42no—
1268C4⋊C4C2×#4118yes—
1269C4⋊C4C2×#4114yes—
1270C4⋊C4H(5,𝔽2)14yes—
1271C22⋊C4—24no—
1272C22⋊C4—28no—
1273C22⋊C4—28no—
1274C22⋊C4—28no—
1275C22⋊C4—28no—
1276C22⋊C4—28no—
1277C22⋊C4—28no—
1278C22⋊C4—28no—
1279C22⋊C4—28no—
1280C22⋊C4—28no—
1281C22⋊C4—24no—
1282C22⋊C4—28no—
1283C22⋊C4—28no—
1284C22⋊C4—28no—
1285C22⋊C4—28no—
1286C22⋊C4—28no—
1287C22⋊C4—44no—
1288C22⋊C4—44no—
1289C22⋊C4—44no—
1290C22⋊C4—42no—
1291C22⋊C4—44no—
1292C22⋊C4—44no—
1293C22⋊C4—44no—
1294C22⋊C4—44no—
1295C22⋊C4—44no—
1296C22⋊C4—44no—
1297C22⋊C4—44no—
1298C22⋊C4—44no—
1299C22⋊C4—44no—
1300C22⋊C4—44no—
1301C22⋊C4—44no—
1302C22⋊C4—44no—
1303C22⋊C4—44no—
1304C22⋊C4—44no—
1305C22⋊C4—44no—
1306C22⋊C4—44no—
1307C22⋊C4—44no—
1308C22⋊C4—44no—
1309C22⋊C4—44no—
1310C22⋊C4—44no—
1311C22⋊C4—44no—
1312C22⋊C4—44no—
1313C22⋊C4—44no—
1314C22⋊C4—44no—
1315C22⋊C4—44no—
1316C22⋊C4—44no—
1317C22⋊C4—44no—
1318C22⋊C4—44no—
1319C22⋊C4—44no—
1320C22⋊C4—44no—
1321C22⋊C4—44no—
1322C22⋊C4—44no—
1323C22⋊C4—44no—
1324C22⋊C4—44no—
1325C42—28no—
1326C42—24no—
1327C42—22no—
1328C42—24no—
1329C42—24no—
1330C42—24no—
1331C42—24no—
1332C42—22no—
1333C42—24no—
1334C42—41no—
1335C42—42no—
1336C42—42no—
1337C42—42no—
1338C42—44no—
1339C42—44no—
1340C42—44no—
1341C42—44no—
1342C42—41no—
1343C42—41no—
1344C42—42no—
1345C42—42no—
1346C42—42no—
1347C42C2×#4114yes—
1348C42C2×#4118yes—
1349C42H(5,𝔽2)14yes—
1350C23—24no—
1351C23—24no—
1352C23—22no—
1353C23—24no—
1354C23—24no—
1355C23—24no—
1356C23—22no—
1357C23—24no—
1358C23—24no—
1359C23—24no—
1360C23—22no—
1361C23—24no—
1362C23—24no—
1363C23—24no—
1364C23—22no—
1365C23—24no—
1366C23—24no—
1367C23—24no—
1368C23—24no—
1369C23—22no—
1370C23—24no—
1371C23—22no—
1372C23—24no—
1373C23—24no—
1374C23—24no—
1375C23—24no—
1376C23—24no—
1377C23—22no—
1378C23C2611yescharacteristic
1379Q8—44no—
1380Q8—48no—
1381Q8—48no—
1382Q8—82no—
1383D4—48no—
1384D4—48no—
1385D4—48no—
1386D4—48no—
1387D4—44no—
1388D4—48no—
1389D4—84no—
1390D4—88no—
1391D4—88no—
1392D4—88no—
1393D4—84no—
1394D4—88no—
1395D4—84no—
1396D4—88no—
1397D4—88no—
1398D4—88no—
1399D4—88no—
1400D4—88no—
1401D4—162no—
1402D4—164no—
1403D4—164no—
1404D4—164no—
1405D4—164no—
1406D4—164no—
1407D4—164no—
1408D4—164no—
1409D4—164no—
1410D4—164no—
1411C2×C4—22no—
1412C2×C4—22no—
1413C2×C4—21no—
1414C2×C4—21no—
1415C2×C4—21no—
1416C2×C4—21no—
1417C2×C4—21no—
1418C2×C4—21no—
1419C2×C4—21no—
1420C2×C4—21no—
1421C2×C4—21no—
1422C2×C4—22no—
1423C2×C4—22no—
1424C2×C4—22no—
1425C2×C4—22no—
1426C2×C4—21no—
1427C2×C4—24no—
1428C2×C4—24no—
1429C2×C4—22no—
1430C2×C4—22no—
1431C2×C4—22no—
1432C2×C4—22no—
1433C2×C4—22no—
1434C2×C4—22no—
1435C2×C4—22no—
1436C2×C4—24no—
1437C2×C4—22no—
1438C2×C4—22no—
1439C2×C4—24no—
1440C2×C4—24no—
1441C2×C4—24no—
1442C2×C4—22no—
1443C2×C4—22no—
1444C2×C4—22no—
1445C2×C4—22no—
1446C2×C4—21no—
1447C2×C4—22no—
1448C2×C4—22no—
1449C2×C4—22no—
1450C2×C4—24no—
1451C2×C4—22no—
1452C2×C4—22no—
1453C2×C4—22no—
1454C2×C4—22no—
1455C2×C4—22no—
1456C2×C4—22no—
1457C2×C4—21no—
1458C2×C4—21no—
1459C2×C4—24no—
1460C2×C4—22no—
1461C2×C4—22no—
1462C2×C4—22no—
1463C2×C4—22no—
1464C2×C4—22no—
1465C2×C4—24no—
1466C2×C4—22no—
1467C2×C4—22no—
1468C2×C4—22no—
1469C2×C4—22no—
1470C2×C4—22no—
1471C2×C4—22no—
1472C2×C4—22no—
1473C2×C4—22no—
1474C2×C4—22no—
1475C2×C4—48no—
1476C2×C4—88no—
1477C2×C4—88no—
1478C2×C4—84no—
1479C2×C4—84no—
1480C2×C4—88no—
1481C2×C4—88no—
1482C2×C4—88no—
1483C2×C4—88no—
1484C2×C4—164no—
1485C2×C4—164no—
1486C2×C4—164no—
1487C2×C4C22×#4114yes—
1488C2×C4C22×#4112yes—
1489C2×C4C22×#4112yes—
1490C2×C4C22×#4114yes—
1491C2×C4C22×#4112yes—
1492C2×C4C2×H(5,𝔽2)12yes—
1493C2×C4C2×H(5,𝔽2)14yes—
1494C2×C4C2×H(5,𝔽2)12yes—
1495C2×C4C2×H(5,𝔽2)12yes—
1496C2×C4C2×H(5,𝔽2)12yes—
1497C2×C4#58512yes—
1498C22—44no—
1499C22—44no—
1500C22—44no—
1501C22—42no—
1502C22—44no—
1503C22—44no—
1504C22—42no—
1505C22—44no—
1506C22—44no—
1507C22—44no—
1508C22—42no—
1509C22—44no—
1510C22—42no—
1511C22—44no—
1512C22—44no—
1513C22—44no—
1514C22—42no—
1515C22—44no—
1516C22—44no—
1517C22—44no—
1518C22—44no—
1519C22—44no—
1520C22—44no—
1521C22—42no—
1522C22—42no—
1523C22—44no—
1524C22—44no—
1525C22—44no—
1526C22C23×#4111yescharacteristic
1527C22C22×H(5,𝔽2)11yescharacteristic
1528C22C22×H(5,𝔽2)11yescharacteristic
1529C22C2×#58511yescharacteristic
1530C22H(7,𝔽2)11yescharacteristic
1531C22H(7,𝔽2)11yescharacteristic
1532C22H(7,𝔽2)11yescharacteristic
1533C4—22no—
1534C4—24no—
1535C4—22no—
1536C4—24no—
1537C4—22no—
1538C4—22no—
1539C4—24no—
1540C4—22no—
1541C4—44no—
1542C4—44no—
1543C4—42no—
1544C4—41no—
1545C4—42no—
1546C4—42no—
1547C4—42no—
1548C4—42no—
1549C4—42no—
1550C4—42no—
1551C4—44no—
1552C4—42no—
1553C4—42no—
1554C4—42no—
1555C4—42no—
1556C4—42no—
1557C4#351714yes—
1558C2—84no—
1559C2—84no—
1560C2—82no—
1561C2—84no—
1562C2C2×#351711yescharacteristic
1563C2#6285511yescharacteristic
1564C2#6288011yescharacteristic
1565C2#6291211yescharacteristic
1566C2#6296111yescharacteristic
1567C2#6298611yescharacteristic
1568C2#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. #59684C2semidirect
3. #52274C2semidirect
4. #50097C2semidirect
5. #49848C2semidirect
6. #48168C2semidirect
7. #46521C2semidirect
8. #46318C2semidirect
9. #45421C2semidirect
10. #45041C2semidirect
11. #44970C2semidirect
12. #43897C2semidirect
13. #42529C2semidirect
14. #42528C2semidirect
15. #41240C2semidirect
16. #39745C2semidirect
17. #39745C2semidirect
18. #39739C2semidirect
19. #39739C2semidirect
20. #39454C2semidirect
21. #39386C2semidirect
22. #38822C2semidirect
23. #37217C2semidirect
24. #36469C2semidirect
25. #35930C2semidirect
26. #35615C2semidirect
27. #35197C2semidirect
28. #34500C2semidirect
29. #34330C2semidirect
843. C4×Q8#41semidirect

Maximal subgroups

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

subgroupindex
#598152
#596842
#522742
#500972
#498482
#481682
#465212
#463182
#454212
#450412
#449702
#438972
#425292
#425282
#412402
#397452
#397392
#394542
#393862
#388222
#372172
#364692
#359302
#356152
#351972
#345002
#343302