Finite Group Databasebeta

← #7696293

Subgroups — #7696293

Order 512.

4897 conjugacy classes of subgroups.

The subgroup lattice has 1441 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59991C214yesmaximal, complemented
2#59935C211yesmaximal, characteristic, complemented
3#59620C212yesmaximal, complemented
4#59052C212yesmaximal, complemented
5#52291C212yesmaximal, complemented
6#52228C211yesmaximal, characteristic, complemented
7#45384C211yesmaximal, characteristic, complemented
8#45382C212yesmaximal, complemented
9#45364C211yesmaximal, characteristic, complemented
10#45112C212yesmaximal, complemented
11#43883C212yesmaximal, complemented
12#43878C214yesmaximal, complemented
13#43832C214yesmaximal, complemented
14#43788C212yesmaximal, complemented
15#40124C214yesmaximal, complemented
16#40119C214yesmaximal, complemented
17#38937C212yesmaximal, complemented
18#38827C214yesmaximal, complemented
19#38287C212yesmaximal, complemented
20#37773C212yesmaximal, complemented
21#36424C212yesmaximal, complemented
22#36406C211yesmaximal, characteristic, complemented
23#36048C211yesmaximal, characteristic, complemented
24#35949C212yesmaximal, complemented
25#35938C211yesmaximal, characteristic, complemented
26#35834C212yesmaximal, complemented
27#34299C212yesmaximal, complemented
28#34284C212yesmaximal, complemented
29#34235C212yesmaximal, complemented
30C2×#557C2211yescharacteristic
31C2×#556C2211yescharacteristic
32C2×#556C2211yescharacteristic
33C2×#554C2212yes—
34C2×#552C2212yes—
35C2×#547C2211yescharacteristic
36C2×#542C2212yes—
37C2×#533C2212yes—
38#2862C2211yescharacteristic
39#2857C2212yes—
40#2854C2214yes—
41#2850C2212yes—
42#2811C2212yes—
43#2809C2212yes—
44#2809C2212yes—
45#2809C2214yes—
46#2806C2214yes—
47#2792C2212yes—
48#2785C2211yescharacteristic
49#2784C2211yescharacteristic
50#2784C2214yes—
51#2784C2212yes—
52#2784C2214yes—
53#2783C2214yes—
54#2783C2214yes—
55#2781C2212yes—
56#2781C2214yes—
57#2775C2212yes—
58#2775C2214yes—
59#2775C2214yes—
60#2769C2211yescharacteristic
61#2769C2212yes—
62#2769C2214yes—
63#2756C2212yes—
64#2744C2212yes—
65#2744C2214yes—
66#2744C2214yes—
67#2744C2214yes—
68#2737C2212yes—
69#2737C2214yes—
70#2732C2214yes—
71#2732C2214yes—
72#2732C2214yes—
73#2732C2214yes—
74#2730C2214yes—
75#2730C2214yes—
76#2721C2214yes—
77#2721C2214yes—
78#2699C2211yescharacteristic
79#2694C2214yes—
80#2694C2214yes—
81#2686C2212yes—
82#2664C2212yes—
83#2664C2214yes—
84#2664C2214yes—
85#2662C2212yes—
86#2658C2211yescharacteristic
87#2642C2212yes—
88#2640C2211yescharacteristic
89#2621C2212yes—
90#2612C2212yes—
91#2612C2214yes—
92#2611C2214yes—
93#2611C2212yes—
94#2610C2212yes—
95#2609C2212yes—
96#2604C2214yes—
97#2604C2212yes—
98#2604C2212yes—
99#2601C2214yes—
100#2592C2211yescharacteristic
101#2586C2212yes—
102#2584C2212yes—
103#2582C2212yes—
104#2574C2214yes—
105#2572C2212yes—
106#2572C2214yes—
107#2568C2211yescharacteristic
108#2567C2211yescharacteristic
109#2565C2214yes—
110#2560C2214yes—
111#2560C2214yes—
112#2558C2214yes—
113#2558C2214yes—
114#2558C2214yes—
115#2557C2214yes—
116#2556C2214yes—
117#2556C2214yes—
118#2554C2214yes—
119#2553C2214yes—
120#2553C2214yes—
121#2553C2214yes—
122#2552C2214yes—
123#2550C2212yes—
124#2550C2212yes—
125#2546C2211yescharacteristic
126#2546C2212yes—
127#2545C2212yes—
128#2542C2211yescharacteristic
129#2542C2212yes—
130#2542C2212yes—
131#2540C2211yescharacteristic
132#2540C2212yes—
133#2538C2214yes—
134#2532C2214yes—
135#2532C2214yes—
136#2529C2214yes—
137#2526C2214yes—
138#2521C2214yes—
139#2519C2214yes—
140#2518C2214yes—
141#2512C2214yes—
142#2508C2214yes—
143#2506C2214yes—
144#2506C2214yes—
145#2499C2212yes—
146#2498C2214yes—
147#2497C2214yes—
148#2496C2214yes—
149#2495C2214yes—
150#2492C2212yes—
151#2492C2212yes—
152#2490C2212yes—
153#2489C2212yes—
154#2485C2214yes—
155#2479C2214yes—
156#2476C2214yes—
157#2471C2214yes—
158#2467C2214yes—
159#2456C2214yes—
160#2454C2214yes—
161#2451C2214yes—
162#2448C2214yes—
163#2441C2214yes—
164#2439C2214yes—
165#2432C2212yes—
166#2430C2214yes—
167#2429C2212yes—
168#2429C2212yes—
169#2429C2212yes—
170#2429C2212yes—
171#2429C2212yes—
172#2427C2212yes—
173#2427C2212yes—
174#2426C2214yes—
175#2426C2212yes—
176#2423C2214yes—
177#2423C2214yes—
178#2423C2214yes—
179#2420C2214yes—
180#2417C2212yes—
181#2417C2212yes—
182#2417C2212yes—
183#2416C2212yes—
184#2399C2211yescharacteristic
185#2398C2212yes—
186#2398C2211yescharacteristic
187#2396C2212yes—
188#2396C2214yes—
189#2396C2214yes—
190#2396C2212yes—
191#2392C2212yes—
192#2373C2214yes—
193#2373C2214yes—
194#2372C2214yes—
195#2372C2212yes—
196#2371C2214yes—
197#2369C2212yes—
198#2368C2214yes—
199#2367C2212yes—
200#2367C2212yes—
201#2367C2214yes—
202#2365C2212yes—
203#2365C2212yes—
204#2365C2212yes—
205#2365C2212yes—
206#2363C2212yes—
207#2363C2214yes—
208#2362C2212yes—
209#2362C2212yes—
210#2362C2214yes—
211#2361C2212yes—
212#2360C2212yes—
213#2360C2212yes—
214#2360C2212yes—
215#2360C2212yes—
216#2360C2212yes—
217#2360C2212yes—
218#2356C2214yes—
219#2356C2212yes—
220#2353C2214yes—
221#2352C2212yes—
222#2351C2214yes—
223#2345C2212yes—
224#2344C2212yes—
225#2343C2214yes—
226#2343C2214yes—
227#2336C2214yes—
228#2336C2214yes—
229#2336C2214yes—
230#2335C2214yes—
231#2332C2214yes—
232#2332C2214yes—
233#2331C2212yes—
234#2323C2212yes—
235#2320C2212yes—
236#2320C2212yes—
237#2319C2212yes—
238C4×#124C2211yescharacteristic
239C4×C22⋊Q8C2212yes—
240C4×C22⋊Q8C2214yes—
241C4×C22⋊Q8C2214yes—
242C4×C22⋊Q8C2214yes—
243C4×C22⋊Q8C2214yes—
244C4×#123C2214yes—
245C4×#121C2212yes—
246#2298C2212yes—
247#2297C2212yes—
248#2297C2214yes—
249#2295C2212yes—
250#2290C2212yes—
251#2290C2214yes—
252#2283C2212yes—
253#2276C2211yescharacteristic
254#2276C2212yes—
255#2276C2211yescharacteristic
256#2274C2212yes—
257C42×D4C2211yescharacteristic
258C2×C4×C4⋊C4C2212yes—
259C22×#41C2312yes—
260#557—44no—
261#556—44no—
262#556—44no—
263#554—216no—
264#552—48no—
265#547—44no—
266#542—216no—
267#533—216no—
268C2×C4⋊Q8C2312yes—
269C2×C4⋊Q8C2311yescharacteristic
270C2×C4⋊Q8C2311yescharacteristic
271C2×C4⋊Q8C2311yescharacteristic
272C2×C4⋊Q8C2311yescharacteristic
273C2×C4⋊Q8C2312yes—
274C2×C4⋊Q8C2312yes—
275C2×C4⋊Q8C2312yes—
276C2×#126C2314yes—
277C2×#126C2314yes—
278C2×#126C2314yes—
279C2×#126C2312yes—
280C2×#126C2312yes—
281C2×#125C2314yes—
282C2×#125C2314yes—
283C2×#125C2314yes—
284C2×#125C2312yes—
285C2×#125C2312yes—
286C2×#125C2314yes—
287C2×#124C2312yes—
288C2×#124C2314yes—
289C2×#124C2311yescharacteristic
290C2×#124C2311yescharacteristic
291C2×#124C2312yes—
292C2×#124C2311yescharacteristic
293C2×#123C2314yes—
294C2×#123C2314yes—
295C2×#123C2314yes—
296C2×C22⋊Q8C2312yes—
297C2×C22⋊Q8C2314yes—
298C2×C22⋊Q8C2314yes—
299C2×C22⋊Q8C2312yes—
300C2×C22⋊Q8C2312yes—
301C2×C22⋊Q8C2312yes—
302C2×C22⋊Q8C2312yes—
303C2×C22⋊Q8C2314yes—
304C2×C22⋊Q8C2314yes—
305C2×C22⋊Q8C2312yes—
306C2×C22⋊Q8C2312yes—
307C2×C22⋊Q8C2312yes—
308C2×C22⋊Q8C2312yes—
309C2×C22⋊Q8C2312yes—
310C2×#121C2312yes—
311C2×#121C2312yes—
312C2×#121C2312yes—
313C2×#121C2314yes—
314C2×C4×Q8C2312yes—
315C2×C4×Q8C2312yes—
316C2×C4×Q8C2312yes—
317C2×C4×Q8C2314yes—
318C2×C4×Q8C2311yescharacteristic
319C2×C4×Q8C2311yescharacteristic
320C2×C4×Q8C2312yes—
321C2×C4×Q8C2312yes—
322C2×C4×Q8C2312yes—
323C2×C4×Q8C2311yescharacteristic
324C2×C4×Q8C2311yescharacteristic
325C2×C4×Q8C2312yes—
326C2×C4×Q8C2314yes—
327C2×C4×Q8C2314yes—
328C2×C4×D4C2312yes—
329C2×C4×D4C2312yes—
330C2×C4×D4C2314yes—
331C2×C4×D4C2311yescharacteristic
332C2×C4×D4C2311yescharacteristic
333C2×C4×D4C2312yes—
334C2×C4×D4C2311yescharacteristic
335C2×C4×D4C2314yes—
336C2×#117C2312yes—
337C2×#117C2314yes—
338C2×#117C2312yes—
339C2×#117C2314yes—
340C2×#117C2312yes—
341C2×#117C2314yes—
342C22×C4⋊C4C2312yes—
343C22×C4⋊C4C2312yes—
344C22×C4⋊C4C2312yes—
345C22×C42C2312yes—
346C22×C42C2314yes—
347C22×C42C2312yes—
348#400C2312yes—
349#400C2312yes—
350#400C2314yes—
351#400C2311yescharacteristic
352#400C2314yes—
353#400C2314yes—
354#400C2314yes—
355#400C2311yescharacteristic
356#400C2314yes—
357#400C2312yes—
358#400C2312yes—
359#400C2314yes—
360#400C2314yes—
361#399C2312yes—
362#399C2312yes—
363#399C2314yes—
364#399C2314yes—
365#399C2312yes—
366#399C2314yes—
367#399C2314yes—
368#399C2314yes—
369#399C2314yes—
370#399C2314yes—
371#398C2314yes—
372#398C2314yes—
373#398C2312yes—
374#398C2314yes—
375#398C2314yes—
376#398C2314yes—
377#398C2314yes—
378#398C2311yescharacteristic
379#398C2314yes—
380#398C2312yes—
381#398C2314yes—
382#398C2311yescharacteristic
383#398C2312yes—
384#398C2314yes—
385#398C2314yes—
386#398C2314yes—
387#398C2314yes—
388#398C2312yes—
389#398C2314yes—
390#398C2314yes—
391#398C2314yes—
392#397C2314yes—
393#397C2314yes—
394#397C2312yes—
395#397C2312yes—
396#397C2314yes—
397#397C2314yes—
398#397C2312yes—
399#397C2312yes—
400#397C2312yes—
401#397C2314yes—
402#397C2314yes—
403#397C2314yes—
404#396C2314yes—
405#396C2314yes—
406#396C2314yes—
407#396C2314yes—
408#396C2312yes—
409#396C2312yes—
410#396C2314yes—
411#396C2314yes—
412#396C2314yes—
413#396C2314yes—
414#396C2314yes—
415#396C2314yes—
416#396C2314yes—
417#396C2314yes—
418#395C2312yes—
419#395C2312yes—
420#395C2314yes—
421#395C2314yes—
422#395C2311yescharacteristic
423#395C2311yescharacteristic
424#395C2314yes—
425#395C2312yes—
426#394C2314yes—
427#394C2314yes—
428#394C2311yescharacteristic
429#394C2314yes—
430#394C2312yes—
431#394C2311yescharacteristic
432#394C2312yes—
433#394C2312yes—
434#394C2312yes—
435#394C2312yes—
436#394C2314yes—
437#394C2314yes—
438#393C2312yes—
439#393C2314yes—
440#393C2312yes—
441#393C2314yes—
442#393C2312yes—
443#393C2312yes—
444#393C2312yes—
445#393C2312yes—
446#392C2312yes—
447#392C2312yes—
448#392C2314yes—
449#391C2312yes—
450#391C2314yes—
451#391C2314yes—
452#391C2314yes—
453#391C2312yes—
454#391C2312yes—
455#391C2312yes—
456#391C2312yes—
457#391C2312yes—
458#391C2312yes—
459#391C2312yes—
460#391C2312yes—
461#391C2314yes—
462#391C2314yes—
463#391C2314yes—
464#391C2314yes—
465#391C2311yescharacteristic
466#391C2312yes—
467#391C2312yes—
468#391C2312yes—
469#391C2314yes—
470#391C2314yes—
471#391C2312yes—
472#391C2314yes—
473#390C2314yes—
474#390C2314yes—
475#390C2312yes—
476#390C2312yes—
477#390C2314yes—
478#390C2314yes—
479#390C2314yes—
480#390C2312yes—
481#390C2314yes—
482#390C2314yes—
483#390C2311yescharacteristic
484#390C2312yes—
485#390C2314yes—
486#389C2312yes—
487#389C2312yes—
488#389C2312yes—
489#389C2312yes—
490#389C2312yes—
491#389C2312yes—
492#389C2312yes—
493#389C2314yes—
494#389C2314yes—
495#389C2314yes—
496#389C2312yes—
497#389C2314yes—
498#389C2314yes—
499#389C2314yes—
500#389C2314yes—
501#389C2314yes—
502#389C2314yes—
503#389C2314yes—
504#389C2314yes—
505#389C2314yes—
506#389C2314yes—
507#389C2314yes—
508#389C2314yes—
509#389C2314yes—
510#389C2314yes—
511#389C2314yes—
512#389C2314yes—
513#389C2314yes—
514#389C2314yes—
515#389C2312yes—
516#388C2312yes—
517#388C2314yes—
518#388C2314yes—
519#388C2314yes—
520#388C2314yes—
521#388C2314yes—
522#388C2314yes—
523#388C2314yes—
524#388C2314yes—
525#388C2312yes—
526#388C2314yes—
527#388C2314yes—
528#388C2314yes—
529#388C2314yes—
530#388C2314yes—
531#388C2312yes—
532#388C2314yes—
533#388C2314yes—
534#388C2314yes—
535#388C2314yes—
536#388C2314yes—
537#388C2312yes—
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#388C2312yes—
552#388C2312yes—
553#388C2312yes—
554#388C2312yes—
555#388C2312yes—
556#387C2314yes—
557#387C2314yes—
558#387C2314yes—
559#387C2314yes—
560#387C2314yes—
561#387C2314yes—
562#387C2314yes—
563#387C2314yes—
564#387C2314yes—
565#387C2314yes—
566#387C2314yes—
567#387C2314yes—
568#387C2314yes—
569#387C2314yes—
570#387C2314yes—
571#387C2314yes—
572#387C2314yes—
573#387C2312yes—
574#387C2314yes—
575#387C2314yes—
576#387C2314yes—
577#387C2314yes—
578#387C2314yes—
579#387C2314yes—
580#387C2314yes—
581#387C2312yes—
582#387C2314yes—
583#387C2314yes—
584#387C2314yes—
585#387C2314yes—
586#387C2314yes—
587#387C2314yes—
588#387C2314yes—
589#387C2314yes—
590#387C2312yes—
591#387C2312yes—
592#387C2312yes—
593#387C2314yes—
594#387C2312yes—
595#386C2314yes—
596#386C2314yes—
597#386C2314yes—
598#386C2314yes—
599#386C2314yes—
600#386C2314yes—
601#386C2312yes—
602#386C2314yes—
603#386C2312yes—
604#386C2314yes—
605#386C2314yes—
606#386C2314yes—
607#386C2314yes—
608#386C2312yes—
609#386C2312yes—
610#385C2314yes—
611#385C2314yes—
612#385C2314yes—
613#385C2314yes—
614#385C2314yes—
615#385C2314yes—
616#385C2314yes—
617#385C2314yes—
618#385C2314yes—
619#385C2312yes—
620#385C2312yes—
621#385C2314yes—
622#384C2314yes—
623#384C2312yes—
624#384C2312yes—
625#384C2314yes—
626#383C2314yes—
627#383C2314yes—
628#383C2314yes—
629#383C2312yes—
630#383C2312yes—
631#382C2314yes—
632#382C2312yes—
633#382C2314yes—
634#382C2314yes—
635#382C2312yes—
636#382C2314yes—
637#382C2312yes—
638#382C2312yes—
639#382C2311yescharacteristic
640#381C2312yes—
641#381C2314yes—
642#381C2314yes—
643#381C2312yes—
644#380C2314yes—
645#380C2314yes—
646#380C2312yes—
647#380C2312yes—
648#380C2314yes—
649#380C2314yes—
650#380C2314yes—
651#380C2314yes—
652#380C2314yes—
653#380C2312yes—
654#380C2312yes—
655#380C2312yes—
656C4×C4⋊C4C2314yes—
657C4×C4⋊C4C2314yes—
658C4×C4⋊C4C2314yes—
659C4×C4⋊C4C2311yescharacteristic
660C4×C4⋊C4C2311yescharacteristic
661C4×C4⋊C4C2314yes—
662C4×C4⋊C4C2312yes—
663C4×C4⋊C4C2312yes—
664C4×C4⋊C4C2312yes—
665C4×C4⋊C4C2312yes—
666C4×C4⋊C4C2314yes—
667C4×C4⋊C4C2312yes—
668C4×C4⋊C4C2312yes—
669C4×C4⋊C4C2314yes—
670C4×C4⋊C4C2314yes—
671C4×C4⋊C4C2314yes—
672C4×C4⋊C4C2314yes—
673C4×C4⋊C4C2312yes—
674C4×C4⋊C4C2314yes—
675C4×C4⋊C4C2314yes—
676C4×C4⋊C4C2312yes—
677C4×C4⋊C4C2312yes—
678C4×C4⋊C4C2314yes—
679C4×C4⋊C4C2314yes—
680C4×C4⋊C4C2312yes—
681C4×C4⋊C4C2311yescharacteristic
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2314yes—
684C4×C4⋊C4C2314yes—
685C4×C4⋊C4C2314yes—
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⋊C4C2314yes—
697C4×C22⋊C4C2314yes—
698C4×C22⋊C4C2314yes—
699C4×C22⋊C4C2314yes—
700C4×C22⋊C4C2314yes—
701C4×C22⋊C4C2312yes—
702C4×C22⋊C4C2312yes—
703C4×C22⋊C4C2314yes—
704C4×C22⋊C4C2314yes—
705C4×C22⋊C4C2312yes—
706C4×C22⋊C4C2312yes—
707C4×C22⋊C4C2312yes—
708C4×C22⋊C4C2312yes—
709C4×C22⋊C4C2312yes—
710#376C2312yes—
711#376C2311yescharacteristic
712#376C2311yescharacteristic
713#376C2312yes—
714#376C2314yes—
715#376C2312yes—
716#376C2314yes—
717#376C2314yes—
718C2×#95C2314yes—
719C43C2311yescharacteristic
720C2×#41—28no—
721C2×#41—44no—
722C2×#41—82no—
723C22×Q8C2411yescharacteristic
724C22×Q8C2412yes—
725C22×Q8C2411yescharacteristic
726C22×Q8C2411yescharacteristic
727C22×Q8C2412yes—
728C22×Q8C2411yescharacteristic
729C22×Q8C2412yes—
730C22×Q8C2414yes—
731C22×D4C2411yescharacteristic
732C22×D4C2412yes—
733C22×D4C2412yes—
734C22×D4C2414yes—
735C22×D4C2414yes—
736C22×D4C2411yescharacteristic
737C22×D4C2411yescharacteristic
738C23×C4C2412yes—
739C23×C4C2412yes—
740C23×C4C2414yes—
741C23×C4C2412yes—
742C23×C4C2412yes—
743C23×C4C2414yes—
744C23×C4C2414yes—
745C23×C4C2414yes—
746C23×C4C2412yes—
747C4⋊Q8—28no—
748C4⋊Q8—42no—
749C4⋊Q8—42no—
750C4⋊Q8—42no—
751C4⋊Q8—44no—
752C4⋊Q8—42no—
753C4⋊Q8—82no—
754C4⋊Q8#41116yescomplemented
755#126—216no—
756#126—48no—
757#126—48no—
758#126—44no—
759#126—44no—
760#125—216no—
761#125—216no—
762#125—48no—
763#125—44no—
764#125—48no—
765#125—44no—
766#124—216no—
767#124—24no—
768#124—28no—
769#124—44no—
770#124—42no—
771#124—42no—
772#123—216no—
773#123—48no—
774#123—48no—
775C22⋊Q8—216no—
776C22⋊Q8—216no—
777C22⋊Q8—216no—
778C22⋊Q8—216no—
779C22⋊Q8—28no—
780C22⋊Q8—28no—
781C22⋊Q8—28no—
782C22⋊Q8—28no—
783C22⋊Q8—28no—
784C22⋊Q8—44no—
785C22⋊Q8—44no—
786C22⋊Q8—44no—
787C22⋊Q8—44no—
788C22⋊Q8—44no—
789#121—28no—
790#121—28no—
791#121—44no—
792#121—84no—
793C4×Q8—216no—
794C4×Q8—28no—
795C4×Q8—28no—
796C4×Q8—28no—
797C4×Q8—28no—
798C4×Q8—24no—
799C4×Q8—24no—
800C4×Q8—28no—
801C4×Q8—44no—
802C4×Q8—42no—
803C4×Q8—44no—
804C4×Q8—42no—
805C4×Q8—84no—
806C4×Q8—84no—
807C4×D4—28no—
808C4×D4—216no—
809C4×D4—24no—
810C4×D4—28no—
811C4×D4—42no—
812C4×D4—44no—
813C4×D4—42no—
814C4×D4—84no—
815#117—216no—
816#117—28no—
817#117—28no—
818#117—48no—
819#117—44no—
820#117—84no—
821C2×C4⋊C4—28no—
822C2×C4⋊C4—28no—
823C2×C4⋊C4—28no—
824C2×C4⋊C4C2412yes—
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2412yes—
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2412yes—
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2411yescharacteristic
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2412yes—
852C2×C4⋊C4C2414yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2411yescharacteristic
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2411yescharacteristic
857C2×C4⋊C4C2412yes—
858C2×C4⋊C4C2412yes—
859C2×C4⋊C4C2412yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2412yes—
863C2×C4⋊C4C2411yescharacteristic
864C2×C4⋊C4C2412yes—
865C2×C4⋊C4C2414yes—
866C2×C4⋊C4C2411yescharacteristic
867C2×C4⋊C4C2411yescharacteristic
868C2×C4⋊C4C2414yes—
869C2×C4⋊C4C2414yes—
870C2×C4⋊C4C2412yes—
871C2×C4⋊C4C2414yes—
872C2×C4⋊C4C2412yes—
873C2×C4⋊C4C2414yes—
874C2×C4⋊C4C2412yes—
875C2×C4⋊C4C2412yes—
876C2×C4⋊C4C2412yes—
877C2×C4⋊C4C2412yes—
878C2×C4⋊C4C2414yes—
879C2×C4⋊C4C2414yes—
880C2×C4⋊C4C2414yes—
881C2×C4⋊C4C2412yes—
882C2×C4⋊C4C2412yes—
883C2×C4⋊C4C2412yes—
884C2×C4⋊C4C2414yes—
885C2×C4⋊C4C2411yescharacteristic
886C2×C22⋊C4C2414yes—
887C2×C22⋊C4C2414yes—
888C2×C22⋊C4C2412yes—
889C2×C22⋊C4C2414yes—
890C2×C22⋊C4C2412yes—
891C2×C22⋊C4C2414yes—
892C2×C22⋊C4C2412yes—
893C2×C22⋊C4C2412yes—
894C2×C22⋊C4C2414yes—
895C2×C22⋊C4C2412yes—
896C2×C22⋊C4C2414yes—
897C2×C22⋊C4C2414yes—
898C2×C22⋊C4C2412yes—
899C2×C22⋊C4C2412yes—
900C2×C22⋊C4C2414yes—
901C2×C22⋊C4C2414yes—
902C2×C22⋊C4C2414yes—
903C2×C22⋊C4C2412yes—
904C2×C22⋊C4C2412yes—
905C2×C22⋊C4C2412yes—
906C2×C22⋊C4C2412yes—
907C2×C22⋊C4C2414yes—
908C2×C22⋊C4C2414yes—
909C2×C22⋊C4C2412yes—
910C2×C22⋊C4C2412yes—
911C2×C22⋊C4C2412yes—
912C2×C22⋊C4C2414yes—
913C2×C22⋊C4C2412yes—
914C2×C22⋊C4C2412yes—
915C2×C22⋊C4C2412yes—
916C2×C22⋊C4C2414yes—
917C2×C22⋊C4C2414yes—
918C2×C22⋊C4C2412yes—
919C2×C22⋊C4C2412yes—
920C2×C22⋊C4C2414yes—
921C2×C22⋊C4C2414yes—
922C2×C22⋊C4C2412yes—
923C2×C22⋊C4C2412yes—
924C2×C22⋊C4C2412yes—
925C2×C22⋊C4C2414yes—
926C2×C22⋊C4C2414yes—
927C2×C22⋊C4C2412yes—
928C2×C22⋊C4C2414yes—
929C2×C22⋊C4C2412yes—
930C2×C22⋊C4C2412yes—
931C2×C42—28no—
932C2×C42—82no—
933C2×C42—84no—
934C2×C42C2414yes—
935C2×C42C2412yes—
936C2×C42C2412yes—
937C2×C42C2414yes—
938C2×C42C2412yes—
939C2×C42C2414yes—
940C2×C42C2414yes—
941C2×C42C2411yescharacteristic
942C2×C42C2411yescharacteristic
943C2×C42C2412yes—
944C2×C42C2414yes—
945C2×C42C2411yescharacteristic
946C2×C42C2412yes—
947C2×C42C2412yes—
948C2×C42C2414yes—
949C2×C42C2411yescharacteristic
950C2×C42C2412yes—
951C2×C42C2412yes—
952C2×C42C2414yes—
953C2×C42C2414yes—
954C2×C42C2412yes—
955C2×C42C2414yes—
956C2×C42C2414yes—
957C2×C42C2414yes—
958C2×C42C2414yes—
959C2×C42C2412yes—
960C2×C42C2412yes—
961C2×C42C2411yescharacteristic
962C2×C42C2414yes—
963C2×C42C2414yes—
964C2×C42C2412yes—
965#95C2414yes—
966#95C2414yes—
967#95C2414yes—
968#95C2414yes—
969#95C2411yescharacteristic
970#95C2412yes—
971#95C2411yescharacteristic
972#95C2412yes—
973#95C2414yes—
974#95C2414yes—
975#95C2414yes—
976#95C2414yes—
977#95C2412yes—
978#95C2412yes—
979#95C2411yescharacteristic
980#95C2412yes—
981#95C2412yes—
982#95C2412yes—
983#95C2414yes—
984#95C2412yes—
985#95C2411yescharacteristic
986#95C2412yes—
987#95C2414yes—
988#95C2414yes—
989#95C2414yes—
990#95C2414yes—
991#95C2414yes—
992#95C2412yes—
993#95C2412yes—
994#95C2412yes—
995#95C2412yes—
996#95C2414yes—
997#95C2414yes—
998#95C2412yes—
999#95C2412yes—
1000#95C2414yes—
1001#95C2412yes—
1002#95C2414yes—
1003#95C2412yes—
1004#95C2414yes—
1005#95C2414yes—
1006#95C2412yes—
1007#95C2414yes—
1008#95C2412yes—
1009#95C2414yes—
1010#95C2412yes—
1011#95C2414yes—
1012#95C2412yes—
1013#95C2412yes—
1014#95C2414yes—
1015#95C2414yes—
1016#95C2412yes—
1017#95C2414yes—
1018#95C2414yes—
1019#95C2414yes—
1020#95C2412yes—
1021#95C2414yes—
1022#95C2414yes—
1023#95C2414yes—
1024#95C2414yes—
1025#95C2412yes—
1026#95C2412yes—
1027#95C2414yes—
1028#95C2414yes—
1029#95C2414yes—
1030#95C2414yes—
1031#95C2412yes—
1032C24C2512yes—
1033C24C2512yes—
1034C24C2512yes—
1035#41—816no—
1036C2×Q8—24no—
1037C2×Q8—24no—
1038C2×Q8—24no—
1039C2×Q8—24no—
1040C2×Q8—22no—
1041C2×Q8—24no—
1042C2×Q8—22no—
1043C2×Q8—22no—
1044C2×Q8—24no—
1045C2×Q8—41no—
1046C2×Q8—44no—
1047C2×Q8—44no—
1048C2×Q8—42no—
1049C2×Q8—41no—
1050C2×Q8—42no—
1051C2×Q8—42no—
1052C2×Q8—41no—
1053C2×Q8—42no—
1054C2×Q8—44no—
1055C2×Q8C2×#41116yes—
1056C2×D4—24no—
1057C2×D4—24no—
1058C2×D4—28no—
1059C2×D4—24no—
1060C2×D4—24no—
1061C2×D4—28no—
1062C2×D4—22no—
1063C2×D4—41no—
1064C2×D4—42no—
1065C2×D4—41no—
1066C2×D4—42no—
1067C2×D4—41no—
1068C2×D4—44no—
1069C2×D4—44no—
1070C2×D4—42no—
1071C2×D4—44no—
1072C2×D4—44no—
1073C2×D4—42no—
1074C2×D42−1+414yes—
1075C22×C4—24no—
1076C22×C4—28no—
1077C22×C4—24no—
1078C22×C4—24no—
1079C22×C4—24no—
1080C22×C4—24no—
1081C22×C4—24no—
1082C22×C4—24no—
1083C22×C4—28no—
1084C22×C4—24no—
1085C22×C4—24no—
1086C22×C4—24no—
1087C22×C4—24no—
1088C22×C4—28no—
1089C22×C4—28no—
1090C22×C4—28no—
1091C22×C4—42no—
1092C22×C4—42no—
1093C22×C4—44no—
1094C22×C4—42no—
1095C22×C4—42no—
1096C22×C4—44no—
1097C22×C4—44no—
1098C22×C4—44no—
1099C22×C4—44no—
1100C22×C4—44no—
1101C22×C4—44no—
1102C22×C4C2512yes—
1103C22×C4C2512yes—
1104C22×C4C2511yescharacteristic
1105C22×C4C2512yes—
1106C22×C4C2514yes—
1107C22×C4C2514yes—
1108C22×C4C2512yes—
1109C22×C4C2512yes—
1110C22×C4C2511yescharacteristic
1111C22×C4C2514yes—
1112C22×C4C2511yescharacteristic
1113C22×C4C2511yescharacteristic
1114C22×C4C2511yescharacteristic
1115C22×C4C2512yes—
1116C22×C4C2514yes—
1117C22×C4C2512yes—
1118C22×C4C2512yes—
1119C22×C4C2512yes—
1120C22×C4C2512yes—
1121C22×C4C2512yes—
1122C22×C4C2512yes—
1123C22×C4C2514yes—
1124C22×C4C2514yes—
1125C22×C4C2512yes—
1126C22×C4C2511yescharacteristic
1127C22×C4C2511yescharacteristic
1128C4⋊C4—24no—
1129C4⋊C4—28no—
1130C4⋊C4—28no—
1131C4⋊C4—24no—
1132C4⋊C4—28no—
1133C4⋊C4—24no—
1134C4⋊C4—24no—
1135C4⋊C4—28no—
1136C4⋊C4—28no—
1137C4⋊C4—28no—
1138C4⋊C4—28no—
1139C4⋊C4—28no—
1140C4⋊C4—28no—
1141C4⋊C4—28no—
1142C4⋊C4—28no—
1143C4⋊C4—28no—
1144C4⋊C4—28no—
1145C4⋊C4—24no—
1146C4⋊C4—28no—
1147C4⋊C4—24no—
1148C4⋊C4—24no—
1149C4⋊C4—24no—
1150C4⋊C4—28no—
1151C4⋊C4—24no—
1152C4⋊C4—42no—
1153C4⋊C4—44no—
1154C4⋊C4—44no—
1155C4⋊C4—44no—
1156C4⋊C4—42no—
1157C4⋊C4—42no—
1158C4⋊C4—41no—
1159C4⋊C4—44no—
1160C4⋊C4—42no—
1161C4⋊C4—44no—
1162C4⋊C4—44no—
1163C4⋊C4—44no—
1164C4⋊C4—41no—
1165C4⋊C4—41no—
1166C4⋊C4—42no—
1167C4⋊C4—44no—
1168C4⋊C4—44no—
1169C4⋊C4—42no—
1170C4⋊C4—41no—
1171C4⋊C4—44no—
1172C4⋊C4—42no—
1173C4⋊C4—41no—
1174C4⋊C4—41no—
1175C4⋊C4—42no—
1176C4⋊C4—42no—
1177C4⋊C4—44no—
1178C4⋊C4—44no—
1179C4⋊C4—44no—
1180C4⋊C4—42no—
1181C4⋊C4—44no—
1182C4⋊C4—42no—
1183C4⋊C4—44no—
1184C4⋊C4—42no—
1185C4⋊C4—42no—
1186C4⋊C4C2×#4118yes—
1187C4⋊C4C2×#4118yes—
1188C4⋊C4C2×#41116yes—
1189C4⋊C4H(5,𝔽2)14yes—
1190C22⋊C4—24no—
1191C22⋊C4—24no—
1192C22⋊C4—24no—
1193C22⋊C4—28no—
1194C22⋊C4—28no—
1195C22⋊C4—24no—
1196C22⋊C4—24no—
1197C22⋊C4—28no—
1198C22⋊C4—28no—
1199C22⋊C4—24no—
1200C22⋊C4—24no—
1201C22⋊C4—28no—
1202C22⋊C4—28no—
1203C22⋊C4—28no—
1204C22⋊C4—28no—
1205C22⋊C4—28no—
1206C22⋊C4—28no—
1207C22⋊C4—24no—
1208C22⋊C4—24no—
1209C22⋊C4—42no—
1210C22⋊C4—44no—
1211C22⋊C4—42no—
1212C22⋊C4—44no—
1213C22⋊C4—44no—
1214C22⋊C4—42no—
1215C22⋊C4—42no—
1216C22⋊C4—42no—
1217C22⋊C4—44no—
1218C22⋊C4—42no—
1219C22⋊C4—42no—
1220C22⋊C4—44no—
1221C22⋊C4—42no—
1222C22⋊C4—42no—
1223C22⋊C4—42no—
1224C22⋊C4—44no—
1225C22⋊C4—42no—
1226C22⋊C4—42no—
1227C22⋊C4—42no—
1228C22⋊C4—42no—
1229C22⋊C4—44no—
1230C22⋊C4—44no—
1231C22⋊C4—44no—
1232C22⋊C4—44no—
1233C22⋊C4—42no—
1234C22⋊C4—42no—
1235C42—24no—
1236C42—24no—
1237C42—24no—
1238C42—24no—
1239C42—28no—
1240C42—28no—
1241C42—28no—
1242C42—28no—
1243C42—28no—
1244C42—24no—
1245C42—28no—
1246C42—24no—
1247C42—22no—
1248C42—22no—
1249C42—24no—
1250C42—22no—
1251C42—22no—
1252C42—41no—
1253C42—44no—
1254C42—44no—
1255C42—44no—
1256C42—44no—
1257C42—44no—
1258C42—42no—
1259C42—44no—
1260C42—44no—
1261C42—42no—
1262C42—42no—
1263C42—44no—
1264C42—42no—
1265C42C2×#4118yes—
1266C23—22no—
1267C23—22no—
1268C23—22no—
1269C23—22no—
1270C23—22no—
1271C23—22no—
1272C23—24no—
1273C23—22no—
1274C23—22no—
1275C23—22no—
1276C23—22no—
1277C23—22no—
1278C23—22no—
1279C23—22no—
1280C23—22no—
1281C23—24no—
1282C23—22no—
1283C23—22no—
1284C23C2×2−1+414yes—
1285C23C2611yescharacteristic
1286Q8—416no—
1287Q8—44no—
1288Q8—44no—
1289Q8—48no—
1290Q8—44no—
1291Q8—82no—
1292Q8—84no—
1293Q8—84no—
1294D4—44no—
1295D4—48no—
1296D4—44no—
1297D4—88no—
1298D4—84no—
1299D4—88no—
1300D4—82no—
1301C2×C4—21no—
1302C2×C4—22no—
1303C2×C4—22no—
1304C2×C4—22no—
1305C2×C4—24no—
1306C2×C4—22no—
1307C2×C4—24no—
1308C2×C4—21no—
1309C2×C4—22no—
1310C2×C4—24no—
1311C2×C4—24no—
1312C2×C4—22no—
1313C2×C4—22no—
1314C2×C4—22no—
1315C2×C4—22no—
1316C2×C4—22no—
1317C2×C4—24no—
1318C2×C4—24no—
1319C2×C4—24no—
1320C2×C4—24no—
1321C2×C4—22no—
1322C2×C4—24no—
1323C2×C4—22no—
1324C2×C4—22no—
1325C2×C4—22no—
1326C2×C4—22no—
1327C2×C4—21no—
1328C2×C4—21no—
1329C2×C4—22no—
1330C2×C4—21no—
1331C2×C4—24no—
1332C2×C4—21no—
1333C2×C4—22no—
1334C2×C4—21no—
1335C2×C4—24no—
1336C2×C4—22no—
1337C2×C4—22no—
1338C2×C4—22no—
1339C2×C4—24no—
1340C2×C4—22no—
1341C2×C4—22no—
1342C2×C4—21no—
1343C2×C4—21no—
1344C2×C4—22no—
1345C2×C4—24no—
1346C2×C4—22no—
1347C2×C4—24no—
1348C2×C4—22no—
1349C2×C4—22no—
1350C2×C4—21no—
1351C2×C4—24no—
1352C2×C4—21no—
1353C2×C4—22no—
1354C2×C4—24no—
1355C2×C4—22no—
1356C2×C4—24no—
1357C2×C4—22no—
1358C2×C4—22no—
1359C2×C4—22no—
1360C2×C4—22no—
1361C2×C4—22no—
1362C2×C4—22no—
1363C2×C4—24no—
1364C2×C4—22no—
1365C2×C4—48no—
1366C2×C4—48no—
1367C2×C4—416no—
1368C2×C4—48no—
1369C2×C4—48no—
1370C2×C4—48no—
1371C2×C4—88no—
1372C2×C4—88no—
1373C2×C4—88no—
1374C2×C4C22×#4114yes—
1375C2×C4C22×#4118yes—
1376C2×C4C22×#4114yes—
1377C2×C4C22×#4118yes—
1378C2×C4C22×#4114yes—
1379C2×C4C2×H(5,𝔽2)14yes—
1380C2×C4C2×H(5,𝔽2)12yes—
1381C2×C4C2×2−1+412yes—
1382C22—24no—
1383C22—24no—
1384C22—24no—
1385C22—42no—
1386C22—42no—
1387C22—42no—
1388C22—42no—
1389C22—42no—
1390C22—42no—
1391C22—44no—
1392C22—42no—
1393C22—42no—
1394C22—42no—
1395C22—44no—
1396C22—42no—
1397C22—42no—
1398C22—42no—
1399C22—42no—
1400C22—42no—
1401C22C23×#4112yes—
1402C22C22×H(5,𝔽2)11yescharacteristic
1403C22C22×2−1+411yescharacteristic
1404C22H(7,𝔽2)11yescharacteristic
1405C222−1+612yes—
1406C4—24no—
1407C4—24no—
1408C4—28no—
1409C4—28no—
1410C4—24no—
1411C4—22no—
1412C4—42no—
1413C4—42no—
1414C4—41no—
1415C4—41no—
1416C4—42no—
1417C4—41no—
1418C4—44no—
1419C4—42no—
1420C4—42no—
1421C4—44no—
1422C4—44no—
1423C4—42no—
1424C4—41no—
1425C4—41no—
1426C4—42no—
1427C4—42no—
1428C4—44no—
1429C4—42no—
1430C4—42no—
1431C4#348314yes—
1432C2—44no—
1433C2—82no—
1434C2—82no—
1435C2C2×#348311yescharacteristic
1436C2#6284712yes—
1437C2#6289411yescharacteristic
1438C2#6299812yes—
1439C2#6304411yescharacteristic
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. #59991C2semidirect
2. #59935C2semidirect
3. #59620C2semidirect
4. #59052C2semidirect
5. #52291C2semidirect
6. #52228C2semidirect
7. #45384C2semidirect
8. #45382C2semidirect
9. #45364C2semidirect
10. #45112C2semidirect
11. #43883C2semidirect
12. #43878C2semidirect
13. #43832C2semidirect
14. #43788C2semidirect
15. #40124C2semidirect
16. #40119C2semidirect
17. #38937C2semidirect
18. #38827C2semidirect
19. #38287C2semidirect
20. #37773C2semidirect
21. #36424C2semidirect
22. #36406C2semidirect
23. #36048C2semidirect
24. #35949C2semidirect
25. #35938C2semidirect
26. #35834C2semidirect
27. #34299C2semidirect
28. #34284C2semidirect
29. #34235C2semidirect
754. C4⋊Q8#41semidirect

Maximal subgroups

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

subgroupindex
#599912
#599352
#596202
#590522
#522912
#522282
#453842
#453822
#453642
#451122
#438832
#438782
#438322
#437882
#401242
#401192
#389372
#388272
#382872
#377732
#364242
#364062
#360482
#359492
#359382
#358342
#342992
#342842
#342352