Finite Group Databasebeta

← #7696296

Subgroups — #7696296

Order 512.

5585 conjugacy classes of subgroups.

The subgroup lattice has 1554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59841C211yesmaximal, characteristic, complemented
2#59810C214yesmaximal, complemented
3#59419C212yesmaximal, complemented
4#59051C212yesmaximal, complemented
5#52297C212yesmaximal, complemented
6#52228C211yesmaximal, characteristic, complemented
7#45382C212yesmaximal, complemented
8#45378C211yesmaximal, characteristic, complemented
9#45364C211yesmaximal, characteristic, complemented
10#44882C212yesmaximal, complemented
11#44657C212yesmaximal, complemented
12#44305C212yesmaximal, complemented
13#44242C214yesmaximal, complemented
14#43373C214yesmaximal, complemented
15#40112C214yesmaximal, complemented
16#40111C214yesmaximal, complemented
17#38936C212yesmaximal, complemented
18#38822C214yesmaximal, complemented
19#38286C212yesmaximal, complemented
20#37772C212yesmaximal, complemented
21#36518C212yesmaximal, complemented
22#36496C211yesmaximal, characteristic, complemented
23#36051C211yesmaximal, characteristic, complemented
24#35941C212yesmaximal, complemented
25#35930C211yesmaximal, characteristic, complemented
26#35830C212yesmaximal, complemented
27#34298C212yesmaximal, complemented
28#34285C212yesmaximal, complemented
29#34236C212yesmaximal, complemented
30C2×#559C2211yescharacteristic
31C2×#555C2212yes—
32C2×#555C2211yescharacteristic
33C2×#554C2211yescharacteristic
34C2×#553C2212yes—
35C2×#550C2214yes—
36C2×#550C2211yescharacteristic
37C2×#547C2212yes—
38C2×#542C2212yes—
39C2×#532C2212yes—
40#2861C2212yes—
41#2858C2211yescharacteristic
42#2850C2212yes—
43#2850C2214yes—
44#2811C2212yes—
45#2806C2214yes—
46#2803C2214yes—
47#2795C2212yes—
48#2792C2212yes—
49#2785C2211yescharacteristic
50#2785C2214yes—
51#2784C2211yescharacteristic
52#2784C2214yes—
53#2784C2212yes—
54#2783C2214yes—
55#2781C2212yes—
56#2781C2214yes—
57#2775C2212yes—
58#2769C2211yescharacteristic
59#2756C2212yes—
60#2756C2214yes—
61#2744C2212yes—
62#2744C2214yes—
63#2737C2212yes—
64#2737C2214yes—
65#2733C2214yes—
66#2733C2214yes—
67#2732C2214yes—
68#2731C2212yes—
69#2730C2214yes—
70#2730C2214yes—
71#2714C2214yes—
72#2705C2214yes—
73#2699C2211yescharacteristic
74#2699C2212yes—
75#2699C2214yes—
76#2686C2212yes—
77#2686C2214yes—
78#2686C2214yes—
79#2686C2214yes—
80#2682C2214yes—
81#2673C2214yes—
82#2673C2214yes—
83#2673C2214yes—
84#2662C2214yes—
85#2661C2212yes—
86#2661C2214yes—
87#2661C2212yes—
88#2657C2211yescharacteristic
89#2641C2212yes—
90#2640C2211yescharacteristic
91#2619C2212yes—
92#2609C2212yes—
93#2601C2214yes—
94#2592C2211yescharacteristic
95#2586C2212yes—
96#2584C2212yes—
97#2582C2212yes—
98#2572C2214yes—
99#2567C2211yescharacteristic
100#2566C2212yes—
101#2564C2214yes—
102#2560C2214yes—
103#2559C2214yes—
104#2559C2214yes—
105#2558C2214yes—
106#2557C2214yes—
107#2557C2214yes—
108#2555C2212yes—
109#2555C2214yes—
110#2555C2214yes—
111#2555C2214yes—
112#2554C2214yes—
113#2550C2212yes—
114#2550C2212yes—
115#2548C2211yescharacteristic
116#2546C2211yescharacteristic
117#2544C2212yes—
118#2544C2212yes—
119#2544C2214yes—
120#2543C2212yes—
121#2543C2212yes—
122#2543C2214yes—
123#2543C2214yes—
124#2541C2212yes—
125#2541C2212yes—
126#2541C2212yes—
127#2541C2211yescharacteristic
128#2540C2211yescharacteristic
129#2540C2212yes—
130#2537C2212yes—
131#2519C2214yes—
132#2518C2214yes—
133#2518C2214yes—
134#2498C2212yes—
135#2491C2212yes—
136#2491C2212yes—
137#2491C2214yes—
138#2490C2212yes—
139#2489C2212yes—
140#2485C2214yes—
141#2476C2214yes—
142#2476C2214yes—
143#2476C2214yes—
144#2467C2214yes—
145#2464C2214yes—
146#2464C2214yes—
147#2461C2214yes—
148#2461C2214yes—
149#2461C2214yes—
150#2459C2214yes—
151#2459C2214yes—
152#2459C2214yes—
153#2459C2214yes—
154#2456C2214yes—
155#2456C2214yes—
156#2456C2214yes—
157#2451C2214yes—
158#2445C2214yes—
159#2431C2214yes—
160#2431C2214yes—
161#2431C2214yes—
162#2430C2214yes—
163#2430C2212yes—
164#2428C2212yes—
165#2428C2214yes—
166#2428C2214yes—
167#2428C2212yes—
168#2428C2212yes—
169#2428C2212yes—
170#2428C2214yes—
171#2428C2212yes—
172#2427C2212yes—
173#2426C2212yes—
174#2426C2212yes—
175#2426C2214yes—
176#2420C2214yes—
177#2420C2214yes—
178#2417C2212yes—
179#2416C2212yes—
180#2416C2212yes—
181#2416C2212yes—
182#2414C2214yes—
183#2407C2214yes—
184#2407C2214yes—
185#2407C2214yes—
186#2399C2211yescharacteristic
187#2398C2211yescharacteristic
188#2398C2212yes—
189#2395C2212yes—
190#2392C2212yes—
191#2392C2214yes—
192#2388C2212yes—
193#2388C2214yes—
194#2374C2214yes—
195#2374C2214yes—
196#2369C2212yes—
197#2369C2212yes—
198#2368C2214yes—
199#2368C2214yes—
200#2367C2212yes—
201#2367C2212yes—
202#2366C2212yes—
203#2366C2212yes—
204#2365C2212yes—
205#2363C2212yes—
206#2363C2212yes—
207#2362C2214yes—
208#2362C2212yes—
209#2361C2212yes—
210#2361C2212yes—
211#2361C2212yes—
212#2361C2212yes—
213#2361C2212yes—
214#2361C2212yes—
215#2360C2212yes—
216#2359C2214yes—
217#2359C2214yes—
218#2357C2212yes—
219#2357C2214yes—
220#2352C2212yes—
221#2349C2214yes—
222#2345C2212yes—
223#2344C2212yes—
224#2339C2214yes—
225#2339C2214yes—
226#2339C2214yes—
227#2337C2214yes—
228#2337C2214yes—
229#2337C2214yes—
230#2335C2214yes—
231#2334C2214yes—
232#2332C2214yes—
233#2331C2212yes—
234#2324C2212yes—
235#2320C2212yes—
236#2319C2212yes—
237#2319C2212yes—
238C4×#127C2212yes—
239C4×#126C2214yes—
240C4×#124C2211yescharacteristic
241C4×#124C2214yes—
242C4×#123C2214yes—
243C4×#121C2212yes—
244C4×#121C2212yes—
245C4×#121C2214yes—
246C4×#121C2214yes—
247C4×#121C2214yes—
248#2298C2212yes—
249#2297C2214yes—
250#2293C2212yes—
251#2290C2212yes—
252#2283C2212yes—
253#2275C2211yescharacteristic
254#2275C2212yes—
255#2275C2211yescharacteristic
256#2274C2212yes—
257C42×Q8C2211yescharacteristic
258C2×C4×C4⋊C4C2212yes—
259C22×#41C2314yes—
260C22×#41C2314yes—
261C22×#41C2312yes—
262#559—44no—
263#555—44no—
264#555—48no—
265#554—44no—
266#553—48no—
267#550—44no—
268#550—416no—
269#547—216no—
270#542—216no—
271#532—216no—
272C2×C4⋊Q8C2311yescharacteristic
273C2×C4⋊Q8C2311yescharacteristic
274C2×C4⋊Q8C2312yes—
275C2×C4⋊Q8C2312yes—
276C2×#127C2312yes—
277C2×#127C2312yes—
278C2×#127C2311yescharacteristic
279C2×#127C2312yes—
280C2×#127C2311yescharacteristic
281C2×#127C2314yes—
282C2×#127C2314yes—
283C2×#126C2314yes—
284C2×#126C2314yes—
285C2×#125C2312yes—
286C2×#125C2312yes—
287C2×#124C2314yes—
288C2×#124C2314yes—
289C2×#124C2312yes—
290C2×#124C2311yescharacteristic
291C2×#124C2311yescharacteristic
292C2×#124C2312yes—
293C2×#124C2311yescharacteristic
294C2×#124C2314yes—
295C2×#124C2314yes—
296C2×#124C2312yes—
297C2×#124C2314yes—
298C2×#124C2314yes—
299C2×#123C2314yes—
300C2×#123C2314yes—
301C2×#123C2314yes—
302C2×#123C2314yes—
303C2×#123C2312yes—
304C2×#123C2312yes—
305C2×C22⋊Q8C2314yes—
306C2×C22⋊Q8C2312yes—
307C2×C22⋊Q8C2314yes—
308C2×C22⋊Q8C2314yes—
309C2×C22⋊Q8C2312yes—
310C2×#121C2312yes—
311C2×#121C2312yes—
312C2×#121C2312yes—
313C2×#121C2312yes—
314C2×#121C2312yes—
315C2×#121C2314yes—
316C2×#121C2314yes—
317C2×#121C2312yes—
318C2×#121C2312yes—
319C2×#121C2314yes—
320C2×#121C2312yes—
321C2×#121C2312yes—
322C2×#121C2312yes—
323C2×#121C2312yes—
324C2×#121C2314yes—
325C2×#121C2314yes—
326C2×#121C2314yes—
327C2×#121C2314yes—
328C2×#121C2314yes—
329C2×#121C2314yes—
330C2×#121C2314yes—
331C2×#121C2314yes—
332C2×#121C2314yes—
333C2×#121C2314yes—
334C2×C4×Q8C2312yes—
335C2×C4×Q8C2311yescharacteristic
336C2×C4×Q8C2311yescharacteristic
337C2×C4×Q8C2314yes—
338C2×C4×Q8C2311yescharacteristic
339C2×C4×D4C2312yes—
340C2×C4×D4C2312yes—
341C2×C4×D4C2312yes—
342C2×C4×D4C2314yes—
343C2×C4×D4C2312yes—
344C2×C4×D4C2311yescharacteristic
345C2×C4×D4C2311yescharacteristic
346C2×C4×D4C2312yes—
347C2×C4×D4C2312yes—
348C2×C4×D4C2312yes—
349C2×C4×D4C2312yes—
350C2×C4×D4C2314yes—
351C2×C4×D4C2314yes—
352C2×C4×D4C2314yes—
353C2×C4×D4C2314yes—
354C2×C4×D4C2314yes—
355C2×C4×D4C2311yescharacteristic
356C2×C4×D4C2312yes—
357C2×C4×D4C2311yescharacteristic
358C2×C4×D4C2314yes—
359C2×C4×D4C2314yes—
360C2×C4×D4C2314yes—
361C2×C4×D4C2314yes—
362C2×C4×D4C2314yes—
363C2×#117C2312yes—
364C2×#117C2312yes—
365C2×#117C2314yes—
366C2×#117C2312yes—
367C2×#117C2314yes—
368C22×C4⋊C4C2312yes—
369C22×C4⋊C4C2312yes—
370C22×C4⋊C4C2312yes—
371C22×C42C2312yes—
372C22×C42C2314yes—
373#400C2314yes—
374#400C2311yescharacteristic
375#400C2312yes—
376#400C2311yescharacteristic
377#400C2312yes—
378#399C2314yes—
379#399C2312yes—
380#398C2314yes—
381#398C2311yescharacteristic
382#398C2312yes—
383#398C2314yes—
384#398C2314yes—
385#398C2311yescharacteristic
386#398C2312yes—
387#398C2314yes—
388#398C2312yes—
389#398C2312yes—
390#397C2314yes—
391#397C2312yes—
392#397C2312yes—
393#397C2312yes—
394#397C2314yes—
395#397C2312yes—
396#397C2314yes—
397#397C2312yes—
398#397C2312yes—
399#397C2312yes—
400#396C2314yes—
401#396C2314yes—
402#396C2314yes—
403#396C2314yes—
404#396C2314yes—
405#396C2312yes—
406#396C2312yes—
407#396C2314yes—
408#395C2314yes—
409#395C2312yes—
410#395C2312yes—
411#395C2314yes—
412#395C2314yes—
413#395C2311yescharacteristic
414#395C2311yescharacteristic
415#395C2312yes—
416#394C2314yes—
417#394C2314yes—
418#394C2314yes—
419#394C2312yes—
420#394C2314yes—
421#394C2314yes—
422#394C2314yes—
423#394C2314yes—
424#394C2314yes—
425#394C2314yes—
426#394C2314yes—
427#394C2312yes—
428#394C2314yes—
429#394C2314yes—
430#394C2312yes—
431#394C2312yes—
432#394C2314yes—
433#394C2311yescharacteristic
434#394C2312yes—
435#394C2312yes—
436#394C2311yescharacteristic
437#394C2314yes—
438#394C2314yes—
439#394C2314yes—
440#394C2312yes—
441#394C2314yes—
442#394C2314yes—
443#394C2314yes—
444#394C2314yes—
445#394C2314yes—
446#394C2314yes—
447#393C2314yes—
448#393C2314yes—
449#393C2314yes—
450#393C2312yes—
451#393C2312yes—
452#393C2312yes—
453#393C2312yes—
454#392C2314yes—
455#392C2314yes—
456#392C2312yes—
457#392C2314yes—
458#392C2314yes—
459#392C2314yes—
460#392C2314yes—
461#392C2314yes—
462#392C2312yes—
463#392C2314yes—
464#392C2312yes—
465#392C2314yes—
466#392C2314yes—
467#392C2314yes—
468#392C2312yes—
469#392C2314yes—
470#392C2314yes—
471#392C2314yes—
472#392C2314yes—
473#392C2314yes—
474#391C2314yes—
475#391C2312yes—
476#391C2314yes—
477#391C2312yes—
478#391C2312yes—
479#391C2314yes—
480#391C2314yes—
481#391C2312yes—
482#391C2314yes—
483#391C2314yes—
484#391C2314yes—
485#391C2314yes—
486#391C2314yes—
487#391C2311yescharacteristic
488#390C2314yes—
489#390C2311yescharacteristic
490#390C2312yes—
491#390C2314yes—
492#390C2314yes—
493#390C2312yes—
494#390C2312yes—
495#390C2312yes—
496#390C2312yes—
497#390C2312yes—
498#390C2312yes—
499#390C2314yes—
500#390C2312yes—
501#390C2314yes—
502#390C2314yes—
503#390C2312yes—
504#390C2314yes—
505#390C2314yes—
506#390C2312yes—
507#390C2312yes—
508#390C2314yes—
509#390C2314yes—
510#390C2314yes—
511#390C2314yes—
512#390C2314yes—
513#390C2312yes—
514#390C2312yes—
515#389C2312yes—
516#389C2312yes—
517#389C2312yes—
518#389C2312yes—
519#389C2312yes—
520#389C2312yes—
521#389C2314yes—
522#389C2314yes—
523#389C2312yes—
524#389C2314yes—
525#389C2314yes—
526#389C2314yes—
527#389C2314yes—
528#389C2312yes—
529#389C2314yes—
530#389C2312yes—
531#388C2314yes—
532#388C2314yes—
533#388C2314yes—
534#388C2312yes—
535#388C2314yes—
536#388C2314yes—
537#388C2314yes—
538#388C2314yes—
539#388C2314yes—
540#388C2314yes—
541#388C2314yes—
542#388C2314yes—
543#388C2314yes—
544#388C2314yes—
545#388C2314yes—
546#388C2314yes—
547#388C2314yes—
548#388C2314yes—
549#388C2312yes—
550#388C2314yes—
551#388C2314yes—
552#388C2314yes—
553#388C2312yes—
554#388C2314yes—
555#388C2314yes—
556#388C2314yes—
557#388C2314yes—
558#388C2314yes—
559#388C2314yes—
560#388C2314yes—
561#388C2314yes—
562#388C2314yes—
563#388C2314yes—
564#388C2312yes—
565#388C2314yes—
566#388C2314yes—
567#388C2312yes—
568#388C2312yes—
569#388C2312yes—
570#388C2312yes—
571#388C2312yes—
572#388C2314yes—
573#388C2314yes—
574#388C2312yes—
575#387C2312yes—
576#387C2314yes—
577#387C2314yes—
578#387C2314yes—
579#387C2314yes—
580#387C2314yes—
581#387C2314yes—
582#387C2314yes—
583#387C2314yes—
584#387C2314yes—
585#387C2312yes—
586#387C2314yes—
587#387C2314yes—
588#387C2312yes—
589#387C2314yes—
590#387C2314yes—
591#387C2312yes—
592#387C2312yes—
593#387C2312yes—
594#386C2314yes—
595#386C2314yes—
596#386C2314yes—
597#386C2314yes—
598#386C2314yes—
599#386C2314yes—
600#386C2314yes—
601#386C2314yes—
602#386C2314yes—
603#386C2314yes—
604#386C2314yes—
605#386C2314yes—
606#386C2314yes—
607#386C2312yes—
608#386C2314yes—
609#386C2314yes—
610#386C2312yes—
611#386C2314yes—
612#386C2314yes—
613#386C2314yes—
614#386C2314yes—
615#386C2314yes—
616#386C2314yes—
617#386C2314yes—
618#386C2314yes—
619#386C2314yes—
620#386C2314yes—
621#386C2312yes—
622#386C2314yes—
623#386C2312yes—
624#386C2314yes—
625#386C2314yes—
626#386C2314yes—
627#385C2314yes—
628#385C2314yes—
629#385C2314yes—
630#385C2314yes—
631#385C2314yes—
632#385C2314yes—
633#385C2314yes—
634#385C2314yes—
635#385C2314yes—
636#385C2314yes—
637#385C2312yes—
638#385C2312yes—
639#384C2312yes—
640#383C2314yes—
641#383C2312yes—
642#383C2312yes—
643#382C2311yescharacteristic
644#382C2314yes—
645#382C2312yes—
646#382C2314yes—
647#382C2312yes—
648#382C2312yes—
649#381C2314yes—
650#381C2314yes—
651#381C2314yes—
652#381C2312yes—
653#381C2312yes—
654#381C2314yes—
655#380C2312yes—
656#380C2314yes—
657#380C2314yes—
658#380C2314yes—
659#380C2312yes—
660#380C2314yes—
661#380C2312yes—
662#380C2314yes—
663#380C2312yes—
664#380C2312yes—
665C4×C4⋊C4C2314yes—
666C4×C4⋊C4C2314yes—
667C4×C4⋊C4C2314yes—
668C4×C4⋊C4C2314yes—
669C4×C4⋊C4C2312yes—
670C4×C4⋊C4C2311yescharacteristic
671C4×C4⋊C4C2312yes—
672C4×C4⋊C4C2312yes—
673C4×C4⋊C4C2312yes—
674C4×C4⋊C4C2312yes—
675C4×C4⋊C4C2314yes—
676C4×C4⋊C4C2312yes—
677C4×C4⋊C4C2314yes—
678C4×C4⋊C4C2311yescharacteristic
679C4×C4⋊C4C2314yes—
680C4×C4⋊C4C2314yes—
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2311yescharacteristic
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2312yes—
688C4×C22⋊C4C2314yes—
689C4×C22⋊C4C2314yes—
690C4×C22⋊C4C2314yes—
691C4×C22⋊C4C2314yes—
692C4×C22⋊C4C2314yes—
693C4×C22⋊C4C2314yes—
694C4×C22⋊C4C2314yes—
695C4×C22⋊C4C2314yes—
696C4×C22⋊C4C2312yes—
697C4×C22⋊C4C2314yes—
698C4×C22⋊C4C2312yes—
699C4×C22⋊C4C2314yes—
700C4×C22⋊C4C2314yes—
701C4×C22⋊C4C2314yes—
702C4×C22⋊C4C2312yes—
703C4×C22⋊C4C2312yes—
704C4×C22⋊C4C2314yes—
705C4×C22⋊C4C2314yes—
706C4×C22⋊C4C2312yes—
707C4×C22⋊C4C2314yes—
708C4×C22⋊C4C2312yes—
709C4×C22⋊C4C2312yes—
710C4×C22⋊C4C2312yes—
711C4×C22⋊C4C2314yes—
712C4×C22⋊C4C2314yes—
713#376C2311yescharacteristic
714#376C2312yes—
715#376C2311yescharacteristic
716C2×#95C2314yes—
717C2×#95C2312yes—
718C2×#95C2312yes—
719C2×#95C2314yes—
720C43C2312yes—
721C43C2311yescharacteristic
722C2×#41—216no—
723C2×#41—216no—
724C2×#41—44no—
725C2×#41—48no—
726C2×#41—48no—
727C2×#41—84no—
728C2×#41—84no—
729C2×#41—84no—
730C22×Q8C2411yescharacteristic
731C22×Q8C2411yescharacteristic
732C22×Q8C2411yescharacteristic
733C22×Q8C2412yes—
734C22×Q8C2412yes—
735C22×Q8C2414yes—
736C22×D4C2411yescharacteristic
737C22×D4C2412yes—
738C22×D4C2411yescharacteristic
739C22×D4C2414yes—
740C22×D4C2414yes—
741C22×D4C2414yes—
742C22×D4C2412yes—
743C22×D4C2414yes—
744C22×D4C2414yes—
745C22×D4C2412yes—
746C22×D4C2412yes—
747C22×D4C2414yes—
748C22×D4C2414yes—
749C22×D4C2414yes—
750C22×D4C2411yescharacteristic
751C22×D4C2414yes—
752C22×D4C2414yes—
753C22×D4C2412yes—
754C22×D4C2414yes—
755C22×D4C2412yes—
756C22×D4C2414yes—
757C22×D4C2412yes—
758C22×D4C2411yescharacteristic
759C23×C4C2412yes—
760C23×C4C2412yes—
761C23×C4C2414yes—
762C23×C4C2412yes—
763C23×C4C2414yes—
764C23×C4C2414yes—
765C23×C4C2412yes—
766C23×C4C2414yes—
767C23×C4C2412yes—
768C23×C4C2414yes—
769C23×C4C2414yes—
770C23×C4C2414yes—
771C23×C4C2414yes—
772C23×C4C2412yes—
773C4⋊Q8—42no—
774C4⋊Q8—42no—
775C4⋊Q8—44no—
776C4⋊Q8#41116yescomplemented
777#127—28no—
778#127—28no—
779#127—44no—
780#127—42no—
781#127—42no—
782#127—48no—
783#127—48no—
784#126—216no—
785#126—48no—
786#125—44no—
787#125—44no—
788#124—216no—
789#124—216no—
790#124—24no—
791#124—28no—
792#124—48no—
793#124—44no—
794#124—42no—
795#124—42no—
796#124—48no—
797#124—44no—
798#124—84no—
799#124—84no—
800#123—216no—
801#123—216no—
802#123—216no—
803#123—48no—
804#123—44no—
805#123—44no—
806C22⋊Q8—216no—
807C22⋊Q8—216no—
808C22⋊Q8—28no—
809C22⋊Q8—48no—
810C22⋊Q8—44no—
811#121—28no—
812#121—216no—
813#121—28no—
814#121—28no—
815#121—216no—
816#121—28no—
817#121—28no—
818#121—28no—
819#121—44no—
820#121—48no—
821#121—48no—
822#121—44no—
823#121—48no—
824#121—48no—
825#121—48no—
826#121—48no—
827#121—48no—
828#121—44no—
829#121—44no—
830#121—44no—
831#121—84no—
832#121—84no—
833#121—84no—
834#121—84no—
835C4×Q8—28no—
836C4×Q8—24no—
837C4×Q8—42no—
838C4×Q8—42no—
839C4×Q8—48no—
840C4×D4—28no—
841C4×D4—28no—
842C4×D4—216no—
843C4×D4—28no—
844C4×D4—28no—
845C4×D4—24no—
846C4×D4—24no—
847C4×D4—28no—
848C4×D4—28no—
849C4×D4—48no—
850C4×D4—48no—
851C4×D4—44no—
852C4×D4—44no—
853C4×D4—42no—
854C4×D4—42no—
855C4×D4—44no—
856C4×D4—48no—
857C4×D4—48no—
858C4×D4—48no—
859C4×D4—84no—
860C4×D4—84no—
861C4×D4—84no—
862C4×D4—84no—
863C4×D4—84no—
864#117—28no—
865#117—28no—
866#117—44no—
867#117—48no—
868#117—48no—
869C2×C4⋊C4—28no—
870C2×C4⋊C4—28no—
871C2×C4⋊C4—28no—
872C2×C4⋊C4C2412yes—
873C2×C4⋊C4C2412yes—
874C2×C4⋊C4C2414yes—
875C2×C4⋊C4C2414yes—
876C2×C4⋊C4C2414yes—
877C2×C4⋊C4C2414yes—
878C2×C4⋊C4C2412yes—
879C2×C4⋊C4C2412yes—
880C2×C4⋊C4C2412yes—
881C2×C4⋊C4C2412yes—
882C2×C4⋊C4C2412yes—
883C2×C4⋊C4C2412yes—
884C2×C4⋊C4C2414yes—
885C2×C4⋊C4C2414yes—
886C2×C4⋊C4C2414yes—
887C2×C4⋊C4C2411yescharacteristic
888C2×C4⋊C4C2414yes—
889C2×C4⋊C4C2412yes—
890C2×C4⋊C4C2414yes—
891C2×C4⋊C4C2411yescharacteristic
892C2×C4⋊C4C2412yes—
893C2×C4⋊C4C2412yes—
894C2×C4⋊C4C2414yes—
895C2×C4⋊C4C2414yes—
896C2×C4⋊C4C2414yes—
897C2×C4⋊C4C2414yes—
898C2×C4⋊C4C2411yescharacteristic
899C2×C4⋊C4C2412yes—
900C2×C4⋊C4C2412yes—
901C2×C4⋊C4C2414yes—
902C2×C4⋊C4C2412yes—
903C2×C4⋊C4C2411yescharacteristic
904C2×C4⋊C4C2411yescharacteristic
905C2×C4⋊C4C2411yescharacteristic
906C2×C4⋊C4C2412yes—
907C2×C4⋊C4C2414yes—
908C2×C4⋊C4C2414yes—
909C2×C4⋊C4C2412yes—
910C2×C4⋊C4C2412yes—
911C2×C4⋊C4C2412yes—
912C2×C4⋊C4C2412yes—
913C2×C4⋊C4C2414yes—
914C2×C4⋊C4C2411yescharacteristic
915C2×C22⋊C4C2412yes—
916C2×C22⋊C4C2414yes—
917C2×C22⋊C4C2414yes—
918C2×C22⋊C4C2414yes—
919C2×C22⋊C4C2412yes—
920C2×C22⋊C4C2412yes—
921C2×C22⋊C4C2412yes—
922C2×C22⋊C4C2412yes—
923C2×C22⋊C4C2412yes—
924C2×C22⋊C4C2414yes—
925C2×C22⋊C4C2412yes—
926C2×C22⋊C4C2414yes—
927C2×C22⋊C4C2414yes—
928C2×C22⋊C4C2414yes—
929C2×C22⋊C4C2414yes—
930C2×C22⋊C4C2412yes—
931C2×C22⋊C4C2414yes—
932C2×C22⋊C4C2412yes—
933C2×C22⋊C4C2412yes—
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⋊C4C2412yes—
944C2×C22⋊C4C2412yes—
945C2×C22⋊C4C2412yes—
946C2×C22⋊C4C2412yes—
947C2×C22⋊C4C2414yes—
948C2×C22⋊C4C2414yes—
949C2×C22⋊C4C2414yes—
950C2×C22⋊C4C2414yes—
951C2×C22⋊C4C2414yes—
952C2×C22⋊C4C2414yes—
953C2×C22⋊C4C2412yes—
954C2×C22⋊C4C2414yes—
955C2×C22⋊C4C2412yes—
956C2×C22⋊C4C2412yes—
957C2×C22⋊C4C2412yes—
958C2×C22⋊C4C2414yes—
959C2×C22⋊C4C2412yes—
960C2×C22⋊C4C2414yes—
961C2×C22⋊C4C2414yes—
962C2×C22⋊C4C2414yes—
963C2×C22⋊C4C2414yes—
964C2×C22⋊C4C2412yes—
965C2×C22⋊C4C2412yes—
966C2×C22⋊C4C2414yes—
967C2×C22⋊C4C2414yes—
968C2×C22⋊C4C2414yes—
969C2×C22⋊C4C2414yes—
970C2×C22⋊C4C2412yes—
971C2×C22⋊C4C2412yes—
972C2×C22⋊C4C2412yes—
973C2×C22⋊C4C2414yes—
974C2×C22⋊C4C2412yes—
975C2×C22⋊C4C2412yes—
976C2×C22⋊C4C2414yes—
977C2×C42—28no—
978C2×C42—84no—
979C2×C42C2411yescharacteristic
980C2×C42C2414yes—
981C2×C42C2412yes—
982C2×C42C2412yes—
983C2×C42C2412yes—
984C2×C42C2411yescharacteristic
985C2×C42C2412yes—
986C2×C42C2412yes—
987C2×C42C2412yes—
988C2×C42C2411yescharacteristic
989C2×C42C2411yescharacteristic
990C2×C42C2414yes—
991C2×C42C2412yes—
992C2×C42C2412yes—
993C2×C42C2414yes—
994C2×C42C2412yes—
995C2×C42C2414yes—
996C2×C42C2414yes—
997C2×C42C2414yes—
998C2×C42C2414yes—
999C2×C42C2414yes—
1000C2×C42C2414yes—
1001C2×C42C2412yes—
1002C2×C42C2414yes—
1003C2×C42C2411yescharacteristic
1004C2×C42C2412yes—
1005#95C2414yes—
1006#95C2411yescharacteristic
1007#95C2412yes—
1008#95C2411yescharacteristic
1009#95C2414yes—
1010#95C2414yes—
1011#95C2412yes—
1012#95C2412yes—
1013#95C2414yes—
1014#95C2414yes—
1015#95C2414yes—
1016#95C2411yescharacteristic
1017#95C2412yes—
1018#95C2412yes—
1019#95C2412yes—
1020#95C2412yes—
1021#95C2411yescharacteristic
1022#95C2412yes—
1023#95C2412yes—
1024#95C2412yes—
1025#95C2412yes—
1026#95C2414yes—
1027#95C2414yes—
1028#95C2412yes—
1029#95C2412yes—
1030#95C2414yes—
1031#95C2414yes—
1032#95C2412yes—
1033#95C2412yes—
1034#95C2414yes—
1035#95C2412yes—
1036#95C2414yes—
1037#95C2414yes—
1038#95C2414yes—
1039#95C2412yes—
1040#95C2414yes—
1041#95C2414yes—
1042#95C2412yes—
1043#95C2412yes—
1044#95C2414yes—
1045#95C2412yes—
1046#95C2412yes—
1047#95C2414yes—
1048#95C2414yes—
1049#95C2412yes—
1050#95C2414yes—
1051#95C2414yes—
1052#95C2412yes—
1053#95C2412yes—
1054#95C2412yes—
1055#95C2412yes—
1056#95C2414yes—
1057#95C2414yes—
1058#95C2414yes—
1059#95C2412yes—
1060C24C2514yes—
1061C24C2512yes—
1062C24C2512yes—
1063C24C2512yes—
1064C24C2512yes—
1065#41—832no—
1066#41—832no—
1067#41—816no—
1068C2×Q8—24no—
1069C2×Q8—22no—
1070C2×Q8—22no—
1071C2×Q8—44no—
1072C2×Q8—41no—
1073C2×Q8—44no—
1074C2×Q8—42no—
1075C2×Q8—41no—
1076C2×Q8—41no—
1077C2×Q8—42no—
1078C2×Q8—42no—
1079C2×Q8—42no—
1080C2×Q8—44no—
1081C2×Q8—42no—
1082C2×Q8C2×#41116yes—
1083C2×D4—28no—
1084C2×D4—28no—
1085C2×D4—28no—
1086C2×D4—24no—
1087C2×D4—28no—
1088C2×D4—24no—
1089C2×D4—24no—
1090C2×D4—24no—
1091C2×D4—28no—
1092C2×D4—24no—
1093C2×D4—24no—
1094C2×D4—24no—
1095C2×D4—28no—
1096C2×D4—28no—
1097C2×D4—28no—
1098C2×D4—28no—
1099C2×D4—28no—
1100C2×D4—28no—
1101C2×D4—22no—
1102C2×D4—24no—
1103C2×D4—22no—
1104C2×D4—24no—
1105C2×D4—41no—
1106C2×D4—44no—
1107C2×D4—44no—
1108C2×D4—44no—
1109C2×D4—44no—
1110C2×D4—41no—
1111C2×D4—44no—
1112C2×D4—42no—
1113C2×D4—42no—
1114C2×D4—44no—
1115C2×D4—41no—
1116C2×D4—42no—
1117C2×D4—44no—
1118C2×D4—44no—
1119C2×D4—44no—
1120C2×D4—44no—
1121C2×D4—42no—
1122C2×D4—44no—
1123C2×D4—42no—
1124C2×D4—44no—
1125C2×D4—44no—
1126C2×D4—44no—
1127C2×D4—44no—
1128C2×D4—44no—
1129C2×D4—42no—
1130C2×D4—44no—
1131C2×D4—42no—
1132C2×D4—44no—
1133C2×D4—44no—
1134C2×D4—42no—
1135C2×D4—42no—
1136C2×D4—44no—
1137C2×D4—44no—
1138C2×D4—44no—
1139C2×D4—44no—
1140C2×D4—44no—
1141C2×D4—44no—
1142C2×D4—42no—
1143C2×D4—44no—
1144C2×D4—42no—
1145C2×D4—44no—
1146C2×D4H(5,𝔽2)14yes—
1147C22×C4—28no—
1148C22×C4—24no—
1149C22×C4—24no—
1150C22×C4—24no—
1151C22×C4—24no—
1152C22×C4—24no—
1153C22×C4—24no—
1154C22×C4—28no—
1155C22×C4—24no—
1156C22×C4—24no—
1157C22×C4—24no—
1158C22×C4—28no—
1159C22×C4—28no—
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—44no—
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—44no—
1178C22×C4—44no—
1179C22×C4—44no—
1180C22×C4—44no—
1181C22×C4—44no—
1182C22×C4—44no—
1183C22×C4—44no—
1184C22×C4—44no—
1185C22×C4—44no—
1186C22×C4—44no—
1187C22×C4C2512yes—
1188C22×C4C2512yes—
1189C22×C4C2512yes—
1190C22×C4C2511yescharacteristic
1191C22×C4C2512yes—
1192C22×C4C2514yes—
1193C22×C4C2511yescharacteristic
1194C22×C4C2511yescharacteristic
1195C22×C4C2514yes—
1196C22×C4C2511yescharacteristic
1197C22×C4C2512yes—
1198C22×C4C2512yes—
1199C22×C4C2512yes—
1200C22×C4C2512yes—
1201C22×C4C2512yes—
1202C22×C4C2514yes—
1203C22×C4C2511yescharacteristic
1204C22×C4C2512yes—
1205C22×C4C2512yes—
1206C22×C4C2514yes—
1207C22×C4C2514yes—
1208C22×C4C2512yes—
1209C22×C4C2511yescharacteristic
1210C22×C4C2511yescharacteristic
1211C4⋊C4—24no—
1212C4⋊C4—28no—
1213C4⋊C4—28no—
1214C4⋊C4—24no—
1215C4⋊C4—24no—
1216C4⋊C4—24no—
1217C4⋊C4—28no—
1218C4⋊C4—28no—
1219C4⋊C4—24no—
1220C4⋊C4—28no—
1221C4⋊C4—24no—
1222C4⋊C4—28no—
1223C4⋊C4—24no—
1224C4⋊C4—24no—
1225C4⋊C4—42no—
1226C4⋊C4—42no—
1227C4⋊C4—44no—
1228C4⋊C4—41no—
1229C4⋊C4—44no—
1230C4⋊C4—42no—
1231C4⋊C4—44no—
1232C4⋊C4—41no—
1233C4⋊C4—44no—
1234C4⋊C4—41no—
1235C4⋊C4—42no—
1236C4⋊C4—42no—
1237C4⋊C4—42no—
1238C4⋊C4—42no—
1239C4⋊C4—44no—
1240C4⋊C4—44no—
1241C4⋊C4—44no—
1242C4⋊C4—44no—
1243C4⋊C4—42no—
1244C4⋊C4—41no—
1245C4⋊C4—41no—
1246C4⋊C4—41no—
1247C4⋊C4—44no—
1248C4⋊C4—42no—
1249C4⋊C4—44no—
1250C4⋊C4C2×#4118yes—
1251C4⋊C4C2×#4118yes—
1252C4⋊C4C2×#41116yes—
1253C4⋊C4H(5,𝔽2)14yes—
1254C22⋊C4—24no—
1255C22⋊C4—28no—
1256C22⋊C4—24no—
1257C22⋊C4—24no—
1258C22⋊C4—24no—
1259C22⋊C4—24no—
1260C22⋊C4—28no—
1261C22⋊C4—28no—
1262C22⋊C4—28no—
1263C22⋊C4—28no—
1264C22⋊C4—24no—
1265C22⋊C4—24no—
1266C22⋊C4—28no—
1267C22⋊C4—28no—
1268C22⋊C4—28no—
1269C22⋊C4—28no—
1270C22⋊C4—28no—
1271C22⋊C4—28no—
1272C22⋊C4—28no—
1273C22⋊C4—28no—
1274C22⋊C4—28no—
1275C22⋊C4—28no—
1276C22⋊C4—28no—
1277C22⋊C4—24no—
1278C22⋊C4—24no—
1279C22⋊C4—24no—
1280C22⋊C4—44no—
1281C22⋊C4—42no—
1282C22⋊C4—44no—
1283C22⋊C4—42no—
1284C22⋊C4—44no—
1285C22⋊C4—44no—
1286C22⋊C4—42no—
1287C22⋊C4—44no—
1288C22⋊C4—44no—
1289C22⋊C4—44no—
1290C22⋊C4—44no—
1291C22⋊C4—42no—
1292C22⋊C4—42no—
1293C22⋊C4—42no—
1294C22⋊C4—42no—
1295C22⋊C4—42no—
1296C22⋊C4—44no—
1297C22⋊C4—42no—
1298C22⋊C4—42no—
1299C22⋊C4—42no—
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—42no—
1309C22⋊C4—42no—
1310C22⋊C4—44no—
1311C22⋊C4—44no—
1312C22⋊C4—44no—
1313C22⋊C4—42no—
1314C22⋊C4—42no—
1315C22⋊C4—42no—
1316C42—24no—
1317C42—24no—
1318C42—24no—
1319C42—24no—
1320C42—28no—
1321C42—28no—
1322C42—22no—
1323C42—22no—
1324C42—24no—
1325C42—22no—
1326C42—24no—
1327C42—24no—
1328C42—22no—
1329C42—44no—
1330C42—44no—
1331C42—44no—
1332C42—44no—
1333C42—41no—
1334C42—44no—
1335C42—42no—
1336C42—42no—
1337C42—44no—
1338C42—44no—
1339C42—44no—
1340C42—42no—
1341C42C2×#4118yes—
1342C23—22no—
1343C23—22no—
1344C23—22no—
1345C23—22no—
1346C23—22no—
1347C23—22no—
1348C23—24no—
1349C23—22no—
1350C23—24no—
1351C23—24no—
1352C23—24no—
1353C23—22no—
1354C23—22no—
1355C23—22no—
1356C23—24no—
1357C23—22no—
1358C23—24no—
1359C23—22no—
1360C23—22no—
1361C23—22no—
1362C23—22no—
1363C23—24no—
1364C23—24no—
1365C23—24no—
1366C23—24no—
1367C23—22no—
1368C23—22no—
1369C23—22no—
1370C23—24no—
1371C23—22no—
1372C23C2×H(5,𝔽2)14yes—
1373C23C2611yescharacteristic
1374Q8—416no—
1375Q8—44no—
1376Q8—44no—
1377Q8—82no—
1378Q8—162no—
1379Q8—162no—
1380D4—44no—
1381D4—416no—
1382D4—416no—
1383D4—416no—
1384D4—48no—
1385D4—416no—
1386D4—44no—
1387D4—48no—
1388D4—44no—
1389D4—88no—
1390D4—84no—
1391D4—88no—
1392D4—88no—
1393D4—84no—
1394D4—88no—
1395D4—82no—
1396D4—88no—
1397D4—84no—
1398D4—164no—
1399D4—162no—
1400D4—164no—
1401D4—164no—
1402D4—162no—
1403C2×C4—21no—
1404C2×C4—24no—
1405C2×C4—24no—
1406C2×C4—22no—
1407C2×C4—22no—
1408C2×C4—24no—
1409C2×C4—24no—
1410C2×C4—24no—
1411C2×C4—22no—
1412C2×C4—21no—
1413C2×C4—22no—
1414C2×C4—22no—
1415C2×C4—22no—
1416C2×C4—22no—
1417C2×C4—22no—
1418C2×C4—24no—
1419C2×C4—22no—
1420C2×C4—22no—
1421C2×C4—22no—
1422C2×C4—22no—
1423C2×C4—24no—
1424C2×C4—22no—
1425C2×C4—22no—
1426C2×C4—21no—
1427C2×C4—21no—
1428C2×C4—22no—
1429C2×C4—24no—
1430C2×C4—22no—
1431C2×C4—21no—
1432C2×C4—21no—
1433C2×C4—22no—
1434C2×C4—21no—
1435C2×C4—21no—
1436C2×C4—24no—
1437C2×C4—21no—
1438C2×C4—22no—
1439C2×C4—24no—
1440C2×C4—22no—
1441C2×C4—22no—
1442C2×C4—24no—
1443C2×C4—22no—
1444C2×C4—22no—
1445C2×C4—24no—
1446C2×C4—24no—
1447C2×C4—22no—
1448C2×C4—22no—
1449C2×C4—24no—
1450C2×C4—22no—
1451C2×C4—22no—
1452C2×C4—22no—
1453C2×C4—22no—
1454C2×C4—22no—
1455C2×C4—22no—
1456C2×C4—22no—
1457C2×C4—24no—
1458C2×C4—21no—
1459C2×C4—22no—
1460C2×C4—21no—
1461C2×C4—416no—
1462C2×C4—48no—
1463C2×C4—48no—
1464C2×C4—48no—
1465C2×C4—48no—
1466C2×C4—88no—
1467C2×C4—84no—
1468C2×C4—88no—
1469C2×C4—88no—
1470C2×C4—88no—
1471C2×C4—88no—
1472C2×C4—88no—
1473C2×C4—88no—
1474C2×C4—84no—
1475C2×C4C22×#4114yes—
1476C2×C4C22×#4114yes—
1477C2×C4C22×#4118yes—
1478C2×C4C22×#4118yes—
1479C2×C4C22×#4114yes—
1480C2×C4C2×H(5,𝔽2)12yes—
1481C2×C4C2×H(5,𝔽2)14yes—
1482C2×C4C2×H(5,𝔽2)12yes—
1483C22—24no—
1484C22—24no—
1485C22—24no—
1486C22—42no—
1487C22—42no—
1488C22—42no—
1489C22—42no—
1490C22—42no—
1491C22—44no—
1492C22—44no—
1493C22—44no—
1494C22—44no—
1495C22—42no—
1496C22—42no—
1497C22—44no—
1498C22—42no—
1499C22—42no—
1500C22—44no—
1501C22—44no—
1502C22—44no—
1503C22—42no—
1504C22—44no—
1505C22—42no—
1506C22—42no—
1507C22—42no—
1508C22—42no—
1509C22—44no—
1510C22—42no—
1511C22—44no—
1512C22—42no—
1513C22—42no—
1514C22C23×#4112yes—
1515C22C22×H(5,𝔽2)11yescharacteristic
1516C22C22×H(5,𝔽2)11yescharacteristic
1517C22H(7,𝔽2)12yes—
1518C222−1+611yescharacteristic
1519C4—24no—
1520C4—28no—
1521C4—28no—
1522C4—24no—
1523C4—24no—
1524C4—22no—
1525C4—44no—
1526C4—42no—
1527C4—42no—
1528C4—41no—
1529C4—42no—
1530C4—41no—
1531C4—44no—
1532C4—41no—
1533C4—42no—
1534C4—42no—
1535C4—42no—
1536C4—44no—
1537C4—41no—
1538C4—41no—
1539C4—42no—
1540C4—42no—
1541C4—42no—
1542C4#348314yes—
1543C2—44no—
1544C2—82no—
1545C2—82no—
1546C2—82no—
1547C2—84no—
1548C2C2×#348311yescharacteristic
1549C2#6285112yes—
1550C2#6289511yescharacteristic
1551C2#6298312yes—
1552C2#6304111yescharacteristic
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. #59841C2semidirect
2. #59810C2semidirect
3. #59419C2semidirect
4. #59051C2semidirect
5. #52297C2semidirect
6. #52228C2semidirect
7. #45382C2semidirect
8. #45378C2semidirect
9. #45364C2semidirect
10. #44882C2semidirect
11. #44657C2semidirect
12. #44305C2semidirect
13. #44242C2semidirect
14. #43373C2semidirect
15. #40112C2semidirect
16. #40111C2semidirect
17. #38936C2semidirect
18. #38822C2semidirect
19. #38286C2semidirect
20. #37772C2semidirect
21. #36518C2semidirect
22. #36496C2semidirect
23. #36051C2semidirect
24. #35941C2semidirect
25. #35930C2semidirect
26. #35830C2semidirect
27. #34298C2semidirect
28. #34285C2semidirect
29. #34236C2semidirect
776. C4⋊Q8#41semidirect

Maximal subgroups

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

subgroupindex
#598412
#598102
#594192
#590512
#522972
#522282
#453822
#453782
#453642
#448822
#446572
#443052
#442422
#433732
#401122
#401112
#389362
#388222
#382862
#377722
#365182
#364962
#360512
#359412
#359302
#358302
#342982
#342852
#342362