Finite Group Databasebeta

← #7688927

Subgroups — #7688927

Order 512.

5221 conjugacy classes of subgroups.

The subgroup lattice has 1503 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#60048C212yesmaximal, complemented
2#59952C211yesmaximal, characteristic, complemented
3#59903C214yesmaximal, complemented
4#59894C212yesmaximal, complemented
5#59878C214yesmaximal, complemented
6#59049C212yesmaximal, complemented
7#45408C211yesmaximal, characteristic, complemented
8#45364C211yesmaximal, characteristic, complemented
9#45101C212yesmaximal, complemented
10#44265C214yesmaximal, complemented
11#43788C212yesmaximal, complemented
12#43400C212yesmaximal, complemented
13#38835C214yesmaximal, complemented
14#38816C214yesmaximal, complemented
15#38290C212yesmaximal, complemented
16#37772C212yesmaximal, complemented
17#36471C212yesmaximal, complemented
18#36470C212yesmaximal, complemented
19#36406C211yesmaximal, characteristic, complemented
20#36385C212yesmaximal, complemented
21#36381C214yesmaximal, complemented
22#36048C211yesmaximal, characteristic, complemented
23#35956C211yesmaximal, characteristic, complemented
24#35768C212yesmaximal, complemented
25#34962C212yesmaximal, complemented
26#34874C211yesmaximal, characteristic, complemented
27#34307C212yesmaximal, complemented
28#34284C212yesmaximal, complemented
29#34155C212yesmaximal, complemented
30C2×#559C2211yescharacteristic
31C2×#556C2212yes—
32C2×#556C2211yescharacteristic
33C2×#556C2211yescharacteristic
34C2×#553C2212yes—
35C2×#547C2211yescharacteristic
36C2×#542C2212yes—
37C2×#532C2212yes—
38#2862C2211yescharacteristic
39#2861C2212yes—
40#2860C2214yes—
41#2857C2212yes—
42#2854C2214yes—
43#2850C2212yes—
44#2811C2212yes—
45#2808C2214yes—
46#2806C2214yes—
47#2803C2214yes—
48#2803C2214yes—
49#2792C2212yes—
50#2785C2212yes—
51#2775C2214yes—
52#2756C2214yes—
53#2756C2214yes—
54#2737C2214yes—
55#2733C2214yes—
56#2733C2212yes—
57#2733C2212yes—
58#2733C2214yes—
59#2730C2214yes—
60#2730C2214yes—
61#2727C2214yes—
62#2714C2214yes—
63#2714C2214yes—
64#2714C2214yes—
65#2705C2214yes—
66#2699C2212yes—
67#2673C2214yes—
68#2662C2212yes—
69#2662C2212yes—
70#2661C2214yes—
71#2657C2211yescharacteristic
72#2640C2211yescharacteristic
73#2619C2212yes—
74#2612C2211yescharacteristic
75#2610C2212yes—
76#2610C2214yes—
77#2610C2212yes—
78#2610C2212yes—
79#2610C2214yes—
80#2610C2214yes—
81#2609C2214yes—
82#2609C2211yescharacteristic
83#2604C2214yes—
84#2604C2212yes—
85#2603C2212yes—
86#2603C2214yes—
87#2602C2214yes—
88#2602C2214yes—
89#2602C2214yes—
90#2593C2211yescharacteristic
91#2593C2212yes—
92#2593C2214yes—
93#2592C2211yescharacteristic
94#2586C2212yes—
95#2584C2212yes—
96#2582C2212yes—
97#2574C2212yes—
98#2574C2214yes—
99#2572C2212yes—
100#2567C2211yescharacteristic
101#2560C2214yes—
102#2560C2214yes—
103#2559C2214yes—
104#2557C2214yes—
105#2555C2212yes—
106#2555C2211yescharacteristic
107#2555C2214yes—
108#2555C2214yes—
109#2554C2214yes—
110#2554C2214yes—
111#2554C2214yes—
112#2553C2214yes—
113#2553C2214yes—
114#2553C2214yes—
115#2553C2214yes—
116#2550C2212yes—
117#2550C2212yes—
118#2548C2211yescharacteristic
119#2548C2212yes—
120#2548C2214yes—
121#2546C2211yescharacteristic
122#2545C2212yes—
123#2542C2211yescharacteristic
124#2541C2212yes—
125#2540C2212yes—
126#2540C2212yes—
127#2540C2211yescharacteristic
128#2532C2214yes—
129#2531C2214yes—
130#2531C2214yes—
131#2531C2212yes—
132#2529C2214yes—
133#2529C2212yes—
134#2521C2214yes—
135#2518C2214yes—
136#2518C2214yes—
137#2513C2214yes—
138#2512C2214yes—
139#2512C2214yes—
140#2500C2214yes—
141#2499C2212yes—
142#2491C2214yes—
143#2491C2212yes—
144#2491C2212yes—
145#2490C2212yes—
146#2489C2212yes—
147#2485C2214yes—
148#2476C2212yes—
149#2474C2214yes—
150#2474C2212yes—
151#2467C2214yes—
152#2467C2214yes—
153#2467C2214yes—
154#2464C2214yes—
155#2461C2214yes—
156#2461C2214yes—
157#2459C2214yes—
158#2456C2214yes—
159#2451C2214yes—
160#2448C2214yes—
161#2448C2214yes—
162#2445C2214yes—
163#2432C2212yes—
164#2431C2214yes—
165#2431C2214yes—
166#2431C2214yes—
167#2429C2212yes—
168#2428C2212yes—
169#2428C2212yes—
170#2427C2212yes—
171#2427C2212yes—
172#2427C2212yes—
173#2427C2212yes—
174#2426C2212yes—
175#2423C2214yes—
176#2415C2212yes—
177#2414C2212yes—
178#2414C2212yes—
179#2414C2212yes—
180#2407C2214yes—
181#2399C2211yescharacteristic
182#2398C2211yescharacteristic
183#2396C2212yes—
184#2392C2212yes—
185#2392C2212yes—
186#2388C2214yes—
187#2373C2214yes—
188#2373C2214yes—
189#2373C2214yes—
190#2373C2214yes—
191#2372C2214yes—
192#2372C2214yes—
193#2372C2212yes—
194#2372C2214yes—
195#2372C2214yes—
196#2372C2214yes—
197#2369C2212yes—
198#2369C2212yes—
199#2367C2212yes—
200#2367C2212yes—
201#2367C2214yes—
202#2366C2212yes—
203#2366C2212yes—
204#2365C2212yes—
205#2363C2212yes—
206#2363C2212yes—
207#2363C2212yes—
208#2363C2214yes—
209#2363C2214yes—
210#2363C2212yes—
211#2363C2212yes—
212#2362C2212yes—
213#2362C2212yes—
214#2361C2212yes—
215#2360C2212yes—
216#2360C2212yes—
217#2356C2214yes—
218#2356C2212yes—
219#2352C2212yes—
220#2347C2212yes—
221#2346C2212yes—
222#2346C2214yes—
223#2346C2214yes—
224#2341C2214yes—
225#2337C2214yes—
226#2335C2214yes—
227#2334C2214yes—
228#2332C2214yes—
229#2331C2212yes—
230#2323C2212yes—
231#2319C2212yes—
232C4×#126C2214yes—
233C4×#124C2211yescharacteristic
234C4×#124C2212yes—
235C4×#124C2214yes—
236C4×C22⋊Q8C2212yes—
237C4×C22⋊Q8C2214yes—
238C4×#123C2214yes—
239C4×#121C2212yes—
240C4×#121C2214yes—
241#2298C2212yes—
242#2297C2214yes—
243#2297C2212yes—
244#2297C2214yes—
245#2295C2214yes—
246#2295C2212yes—
247#2293C2212yes—
248#2293C2212yes—
249#2293C2214yes—
250#2290C2212yes—
251#2276C2211yescharacteristic
252#2276C2211yescharacteristic
253#2274C2212yes—
254C42×D4C2214yes—
255C42×D4C2211yescharacteristic
256C42×D4C2212yes—
257C4×#117C2212yes—
258C4×#117C2212yes—
259C22×#41C2314yes—
260C22×#41C2312yes—
261#559—44no—
262#556—216no—
263#556—44no—
264#556—44no—
265#553—48no—
266#547—44no—
267#542—216no—
268#532—216no—
269C2×C4⋊Q8C2311yescharacteristic
270C2×C4⋊Q8C2311yescharacteristic
271C2×C4⋊Q8C2311yescharacteristic
272C2×C4⋊Q8C2312yes—
273C2×C4⋊Q8C2312yes—
274C2×#127C2312yes—
275C2×#127C2311yescharacteristic
276C2×#127C2314yes—
277C2×#126C2314yes—
278C2×#126C2314yes—
279C2×#126C2314yes—
280C2×#126C2314yes—
281C2×#126C2314yes—
282C2×#126C2312yes—
283C2×#126C2312yes—
284C2×#125C2312yes—
285C2×#124C2314yes—
286C2×#124C2312yes—
287C2×#124C2314yes—
288C2×#124C2314yes—
289C2×#124C2311yescharacteristic
290C2×#124C2312yes—
291C2×#124C2311yescharacteristic
292C2×#124C2314yes—
293C2×#124C2312yes—
294C2×#124C2312yes—
295C2×#124C2312yes—
296C2×#124C2314yes—
297C2×#124C2312yes—
298C2×#124C2311yescharacteristic
299C2×#123C2314yes—
300C2×#123C2314yes—
301C2×#123C2314yes—
302C2×#123C2314yes—
303C2×C22⋊Q8C2312yes—
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×#121C2312yes—
315C2×#121C2312yes—
316C2×#121C2312yes—
317C2×#121C2314yes—
318C2×#121C2314yes—
319C2×#121C2312yes—
320C2×#121C2314yes—
321C2×C4×Q8C2312yes—
322C2×C4×Q8C2314yes—
323C2×C4×Q8C2311yescharacteristic
324C2×C4×Q8C2311yescharacteristic
325C2×C4×Q8C2312yes—
326C2×C4×Q8C2311yescharacteristic
327C2×C4×Q8C2311yescharacteristic
328C2×C4×Q8C2312yes—
329C2×C4×Q8C2314yes—
330C2×C4×D4C2312yes—
331C2×C4×D4C2312yes—
332C2×C4×D4C2312yes—
333C2×C4×D4C2311yescharacteristic
334C2×C4×D4C2312yes—
335C2×C4×D4C2312yes—
336C2×C4×D4C2314yes—
337C2×C4×D4C2314yes—
338C2×C4×D4C2312yes—
339C2×C4×D4C2314yes—
340C2×C4×D4C2314yes—
341C2×C4×D4C2311yescharacteristic
342C2×C4×D4C2312yes—
343C2×C4×D4C2311yescharacteristic
344C2×C4×D4C2314yes—
345C2×#117C2312yes—
346C2×#117C2312yes—
347C2×#117C2312yes—
348C2×#117C2312yes—
349C2×#117C2314yes—
350C2×#117C2314yes—
351C2×#117C2312yes—
352C2×#117C2312yes—
353C2×#117C2312yes—
354C22×C4⋊C4C2312yes—
355C22×C42C2312yes—
356C22×C42C2314yes—
357C22×C42C2312yes—
358#400C2311yescharacteristic
359#400C2311yescharacteristic
360#400C2314yes—
361#399C2312yes—
362#399C2314yes—
363#399C2314yes—
364#399C2314yes—
365#398C2312yes—
366#398C2314yes—
367#398C2311yescharacteristic
368#398C2314yes—
369#398C2312yes—
370#398C2314yes—
371#398C2311yescharacteristic
372#398C2312yes—
373#398C2314yes—
374#398C2312yes—
375#397C2314yes—
376#397C2314yes—
377#397C2312yes—
378#397C2312yes—
379#397C2314yes—
380#397C2314yes—
381#397C2314yes—
382#397C2312yes—
383#397C2314yes—
384#397C2314yes—
385#397C2314yes—
386#396C2312yes—
387#396C2314yes—
388#396C2314yes—
389#396C2314yes—
390#396C2312yes—
391#396C2314yes—
392#395C2312yes—
393#395C2312yes—
394#395C2314yes—
395#395C2312yes—
396#395C2314yes—
397#395C2314yes—
398#395C2311yescharacteristic
399#395C2311yescharacteristic
400#394C2314yes—
401#394C2314yes—
402#394C2312yes—
403#394C2314yes—
404#394C2314yes—
405#394C2312yes—
406#394C2314yes—
407#394C2314yes—
408#394C2314yes—
409#394C2314yes—
410#394C2314yes—
411#394C2312yes—
412#394C2314yes—
413#394C2311yescharacteristic
414#394C2314yes—
415#394C2314yes—
416#394C2314yes—
417#394C2314yes—
418#394C2312yes—
419#394C2312yes—
420#394C2314yes—
421#394C2311yescharacteristic
422#394C2314yes—
423#394C2314yes—
424#394C2314yes—
425#393C2312yes—
426#393C2314yes—
427#393C2312yes—
428#393C2312yes—
429#393C2314yes—
430#393C2312yes—
431#392C2314yes—
432#392C2314yes—
433#392C2314yes—
434#392C2312yes—
435#392C2314yes—
436#392C2312yes—
437#392C2314yes—
438#392C2312yes—
439#392C2314yes—
440#392C2314yes—
441#392C2314yes—
442#392C2312yes—
443#392C2314yes—
444#392C2314yes—
445#392C2314yes—
446#392C2314yes—
447#391C2312yes—
448#391C2314yes—
449#391C2312yes—
450#391C2311yescharacteristic
451#391C2312yes—
452#391C2312yes—
453#391C2314yes—
454#391C2314yes—
455#391C2314yes—
456#391C2314yes—
457#391C2314yes—
458#391C2314yes—
459#391C2312yes—
460#391C2312yes—
461#391C2312yes—
462#391C2312yes—
463#391C2312yes—
464#391C2314yes—
465#391C2314yes—
466#390C2314yes—
467#390C2314yes—
468#390C2312yes—
469#390C2312yes—
470#390C2314yes—
471#390C2312yes—
472#390C2314yes—
473#390C2312yes—
474#390C2311yescharacteristic
475#390C2312yes—
476#390C2314yes—
477#390C2314yes—
478#390C2314yes—
479#390C2314yes—
480#390C2314yes—
481#390C2314yes—
482#390C2312yes—
483#390C2314yes—
484#390C2314yes—
485#390C2314yes—
486#390C2314yes—
487#390C2312yes—
488#390C2314yes—
489#390C2314yes—
490#390C2314yes—
491#390C2312yes—
492#390C2314yes—
493#390C2312yes—
494#390C2314yes—
495#390C2312yes—
496#390C2314yes—
497#389C2312yes—
498#389C2312yes—
499#389C2312yes—
500#389C2312yes—
501#389C2314yes—
502#389C2314yes—
503#389C2314yes—
504#389C2312yes—
505#389C2314yes—
506#389C2312yes—
507#389C2312yes—
508#389C2314yes—
509#389C2314yes—
510#389C2314yes—
511#389C2314yes—
512#389C2314yes—
513#389C2312yes—
514#389C2312yes—
515#389C2314yes—
516#389C2314yes—
517#388C2312yes—
518#388C2314yes—
519#388C2314yes—
520#388C2314yes—
521#388C2314yes—
522#388C2314yes—
523#388C2314yes—
524#388C2314yes—
525#388C2314yes—
526#388C2314yes—
527#388C2314yes—
528#388C2312yes—
529#388C2314yes—
530#388C2312yes—
531#388C2314yes—
532#388C2314yes—
533#388C2314yes—
534#388C2314yes—
535#388C2314yes—
536#388C2314yes—
537#388C2314yes—
538#388C2314yes—
539#388C2314yes—
540#388C2312yes—
541#388C2314yes—
542#388C2314yes—
543#388C2314yes—
544#388C2314yes—
545#388C2314yes—
546#388C2314yes—
547#388C2312yes—
548#388C2314yes—
549#388C2314yes—
550#388C2314yes—
551#388C2314yes—
552#388C2314yes—
553#388C2312yes—
554#388C2312yes—
555#388C2312yes—
556#388C2314yes—
557#388C2314yes—
558#388C2314yes—
559#388C2314yes—
560#388C2312yes—
561#388C2314yes—
562#388C2314yes—
563#388C2314yes—
564#388C2314yes—
565#388C2314yes—
566#388C2314yes—
567#388C2312yes—
568#388C2312yes—
569#388C2314yes—
570#388C2312yes—
571#388C2314yes—
572#388C2312yes—
573#388C2314yes—
574#388C2314yes—
575#388C2314yes—
576#388C2312yes—
577#387C2314yes—
578#387C2314yes—
579#387C2314yes—
580#387C2314yes—
581#387C2314yes—
582#387C2312yes—
583#387C2312yes—
584#387C2314yes—
585#387C2312yes—
586#387C2314yes—
587#387C2314yes—
588#387C2314yes—
589#387C2312yes—
590#387C2314yes—
591#387C2314yes—
592#387C2314yes—
593#387C2314yes—
594#387C2314yes—
595#387C2314yes—
596#387C2312yes—
597#387C2312yes—
598#386C2314yes—
599#386C2314yes—
600#386C2314yes—
601#386C2314yes—
602#386C2312yes—
603#386C2314yes—
604#386C2314yes—
605#386C2314yes—
606#386C2314yes—
607#386C2314yes—
608#386C2314yes—
609#386C2314yes—
610#386C2312yes—
611#386C2314yes—
612#386C2314yes—
613#386C2314yes—
614#386C2314yes—
615#386C2314yes—
616#386C2312yes—
617#386C2314yes—
618#386C2314yes—
619#386C2312yes—
620#386C2314yes—
621#385C2314yes—
622#385C2312yes—
623#385C2312yes—
624#385C2314yes—
625#385C2314yes—
626#385C2314yes—
627#385C2314yes—
628#385C2314yes—
629#384C2312yes—
630#384C2312yes—
631#383C2314yes—
632#383C2314yes—
633#382C2314yes—
634#382C2312yes—
635#382C2312yes—
636#382C2314yes—
637#382C2314yes—
638#382C2311yescharacteristic
639#381C2314yes—
640#380C2312yes—
641#380C2314yes—
642#380C2314yes—
643#380C2312yes—
644#380C2314yes—
645#380C2314yes—
646#380C2314yes—
647#380C2312yes—
648C4×C4⋊C4C2312yes—
649C4×C4⋊C4C2314yes—
650C4×C4⋊C4C2314yes—
651C4×C4⋊C4C2314yes—
652C4×C4⋊C4C2314yes—
653C4×C4⋊C4C2311yescharacteristic
654C4×C4⋊C4C2312yes—
655C4×C4⋊C4C2312yes—
656C4×C4⋊C4C2312yes—
657C4×C4⋊C4C2312yes—
658C4×C4⋊C4C2314yes—
659C4×C4⋊C4C2312yes—
660C4×C4⋊C4C2312yes—
661C4×C4⋊C4C2314yes—
662C4×C4⋊C4C2311yescharacteristic
663C4×C4⋊C4C2314yes—
664C4×C4⋊C4C2314yes—
665C4×C4⋊C4C2314yes—
666C4×C4⋊C4C2314yes—
667C4×C4⋊C4C2312yes—
668C4×C4⋊C4C2314yes—
669C4×C4⋊C4C2312yes—
670C4×C4⋊C4C2312yes—
671C4×C4⋊C4C2312yes—
672C4×C4⋊C4C2312yes—
673C4×C4⋊C4C2311yescharacteristic
674C4×C4⋊C4C2312yes—
675C4×C4⋊C4C2312yes—
676C4×C4⋊C4C2312yes—
677C4×C22⋊C4C2314yes—
678C4×C22⋊C4C2314yes—
679C4×C22⋊C4C2314yes—
680C4×C22⋊C4C2314yes—
681C4×C22⋊C4C2314yes—
682C4×C22⋊C4C2312yes—
683C4×C22⋊C4C2314yes—
684C4×C22⋊C4C2314yes—
685C4×C22⋊C4C2314yes—
686C4×C22⋊C4C2314yes—
687C4×C22⋊C4C2314yes—
688C4×C22⋊C4C2314yes—
689C4×C22⋊C4C2312yes—
690C4×C22⋊C4C2314yes—
691C4×C22⋊C4C2314yes—
692C4×C22⋊C4C2314yes—
693C4×C22⋊C4C2312yes—
694C4×C22⋊C4C2312yes—
695C4×C22⋊C4C2314yes—
696C4×C22⋊C4C2312yes—
697C4×C22⋊C4C2312yes—
698C4×C22⋊C4C2312yes—
699C4×C22⋊C4C2312yes—
700C4×C22⋊C4C2314yes—
701C4×C22⋊C4C2314yes—
702C4×C22⋊C4C2314yes—
703C4×C22⋊C4C2314yes—
704C4×C22⋊C4C2314yes—
705C4×C22⋊C4C2314yes—
706C4×C22⋊C4C2312yes—
707#376C2311yescharacteristic
708#376C2311yescharacteristic
709#376C2314yes—
710#376C2312yes—
711#376C2314yes—
712#376C2314yes—
713#376C2314yes—
714#376C2312yes—
715#376C2312yes—
716#376C2312yes—
717C43C2314yes—
718C43C2312yes—
719C43C2311yescharacteristic
720C2×#41—216no—
721C2×#41—44no—
722C2×#41—48no—
723C2×#41—44no—
724C2×#41—84no—
725C2×#41—82no—
726C22×Q8C2411yescharacteristic
727C22×Q8C2411yescharacteristic
728C22×Q8C2411yescharacteristic
729C22×Q8C2412yes—
730C22×Q8C2411yescharacteristic
731C22×Q8C2412yes—
732C22×Q8C2414yes—
733C22×D4C2412yes—
734C22×D4C2411yescharacteristic
735C22×D4C2414yes—
736C22×D4C2414yes—
737C22×D4C2412yes—
738C22×D4C2411yescharacteristic
739C22×D4C2414yes—
740C22×D4C2414yes—
741C22×D4C2414yes—
742C22×D4C2414yes—
743C22×D4C2412yes—
744C22×D4C2411yescharacteristic
745C22×D4C2412yes—
746C22×D4C2414yes—
747C22×D4C2412yes—
748C22×D4C2414yes—
749C23×C4C2412yes—
750C23×C4C2412yes—
751C23×C4C2412yes—
752C23×C4C2414yes—
753C23×C4C2414yes—
754C23×C4C2412yes—
755C23×C4C2414yes—
756C23×C4C2412yes—
757C23×C4C2414yes—
758C23×C4C2414yes—
759C4⋊Q8—42no—
760C4⋊Q8—42no—
761C4⋊Q8—42no—
762C4⋊Q8—82no—
763C4⋊Q8#41116yescomplemented
764#127—28no—
765#127—42no—
766#127—84no—
767#126—216no—
768#126—216no—
769#126—216no—
770#126—48no—
771#126—48no—
772#126—44no—
773#126—44no—
774#125—44no—
775#124—216no—
776#124—216no—
777#124—216no—
778#124—28no—
779#124—44no—
780#124—48no—
781#124—44no—
782#124—44no—
783#124—42no—
784#124—42no—
785#124—42no—
786#124—44no—
787#124—48no—
788#124—44no—
789#123—216no—
790#123—48no—
791#123—48no—
792#123—48no—
793C22⋊Q8—216no—
794C22⋊Q8—28no—
795C22⋊Q8—28no—
796C22⋊Q8—28no—
797C22⋊Q8—44no—
798C22⋊Q8—44no—
799C22⋊Q8—44no—
800#121—28no—
801#121—28no—
802#121—216no—
803#121—28no—
804#121—44no—
805#121—48no—
806#121—48no—
807#121—44no—
808#121—44no—
809#121—44no—
810#121—84no—
811C4×Q8—216no—
812C4×Q8—28no—
813C4×Q8—24no—
814C4×Q8—24no—
815C4×Q8—28no—
816C4×Q8—44no—
817C4×Q8—42no—
818C4×Q8—42no—
819C4×Q8—84no—
820C4×D4—28no—
821C4×D4—28no—
822C4×D4—216no—
823C4×D4—28no—
824C4×D4—24no—
825C4×D4—28no—
826C4×D4—28no—
827C4×D4—42no—
828C4×D4—48no—
829C4×D4—44no—
830C4×D4—42no—
831C4×D4—44no—
832C4×D4—48no—
833C4×D4—48no—
834C4×D4—84no—
835#117—28no—
836#117—28no—
837#117—28no—
838#117—28no—
839#117—48no—
840#117—48no—
841#117—44no—
842#117—44no—
843#117—44no—
844C2×C4⋊C4—28no—
845C2×C4⋊C4C2412yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2412yes—
849C2×C4⋊C4C2412yes—
850C2×C4⋊C4C2412yes—
851C2×C4⋊C4C2412yes—
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2412yes—
854C2×C4⋊C4C2412yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2412yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2411yescharacteristic
862C2×C4⋊C4C2412yes—
863C2×C4⋊C4C2414yes—
864C2×C4⋊C4C2414yes—
865C2×C4⋊C4C2412yes—
866C2×C4⋊C4C2412yes—
867C2×C4⋊C4C2414yes—
868C2×C4⋊C4C2414yes—
869C2×C4⋊C4C2411yescharacteristic
870C2×C4⋊C4C2411yescharacteristic
871C2×C4⋊C4C2414yes—
872C2×C4⋊C4C2411yescharacteristic
873C2×C4⋊C4C2414yes—
874C2×C4⋊C4C2412yes—
875C2×C4⋊C4C2412yes—
876C2×C4⋊C4C2414yes—
877C2×C4⋊C4C2412yes—
878C2×C4⋊C4C2411yescharacteristic
879C2×C4⋊C4C2411yescharacteristic
880C2×C4⋊C4C2414yes—
881C2×C4⋊C4C2414yes—
882C2×C4⋊C4C2414yes—
883C2×C4⋊C4C2414yes—
884C2×C4⋊C4C2412yes—
885C2×C4⋊C4C2412yes—
886C2×C4⋊C4C2412yes—
887C2×C4⋊C4C2412yes—
888C2×C4⋊C4C2412yes—
889C2×C4⋊C4C2412yes—
890C2×C4⋊C4C2414yes—
891C2×C4⋊C4C2411yescharacteristic
892C2×C22⋊C4C2414yes—
893C2×C22⋊C4C2412yes—
894C2×C22⋊C4C2412yes—
895C2×C22⋊C4C2412yes—
896C2×C22⋊C4C2412yes—
897C2×C22⋊C4C2414yes—
898C2×C22⋊C4C2414yes—
899C2×C22⋊C4C2414yes—
900C2×C22⋊C4C2414yes—
901C2×C22⋊C4C2414yes—
902C2×C22⋊C4C2414yes—
903C2×C22⋊C4C2414yes—
904C2×C22⋊C4C2414yes—
905C2×C22⋊C4C2412yes—
906C2×C22⋊C4C2414yes—
907C2×C22⋊C4C2414yes—
908C2×C22⋊C4C2412yes—
909C2×C22⋊C4C2412yes—
910C2×C22⋊C4C2412yes—
911C2×C22⋊C4C2414yes—
912C2×C22⋊C4C2412yes—
913C2×C22⋊C4C2414yes—
914C2×C22⋊C4C2414yes—
915C2×C22⋊C4C2414yes—
916C2×C22⋊C4C2414yes—
917C2×C22⋊C4C2414yes—
918C2×C22⋊C4C2412yes—
919C2×C22⋊C4C2412yes—
920C2×C22⋊C4C2412yes—
921C2×C22⋊C4C2412yes—
922C2×C22⋊C4C2414yes—
923C2×C22⋊C4C2414yes—
924C2×C22⋊C4C2414yes—
925C2×C22⋊C4C2414yes—
926C2×C22⋊C4C2412yes—
927C2×C22⋊C4C2412yes—
928C2×C22⋊C4C2414yes—
929C2×C22⋊C4C2414yes—
930C2×C22⋊C4C2412yes—
931C2×C22⋊C4C2412yes—
932C2×C22⋊C4C2414yes—
933C2×C22⋊C4C2412yes—
934C2×C22⋊C4C2414yes—
935C2×C22⋊C4C2414yes—
936C2×C22⋊C4C2412yes—
937C2×C22⋊C4C2414yes—
938C2×C22⋊C4C2414yes—
939C2×C22⋊C4C2412yes—
940C2×C22⋊C4C2412yes—
941C2×C22⋊C4C2414yes—
942C2×C22⋊C4C2414yes—
943C2×C22⋊C4C2414yes—
944C2×C22⋊C4C2414yes—
945C2×C22⋊C4C2414yes—
946C2×C22⋊C4C2414yes—
947C2×C22⋊C4C2414yes—
948C2×C22⋊C4C2412yes—
949C2×C22⋊C4C2412yes—
950C2×C22⋊C4C2412yes—
951C2×C22⋊C4C2412yes—
952C2×C42—28no—
953C2×C42—82no—
954C2×C42—84no—
955C2×C42C2412yes—
956C2×C42C2414yes—
957C2×C42C2412yes—
958C2×C42C2411yescharacteristic
959C2×C42C2412yes—
960C2×C42C2414yes—
961C2×C42C2412yes—
962C2×C42C2412yes—
963C2×C42C2414yes—
964C2×C42C2414yes—
965C2×C42C2412yes—
966C2×C42C2411yescharacteristic
967C2×C42C2412yes—
968C2×C42C2412yes—
969C2×C42C2411yescharacteristic
970C2×C42C2411yescharacteristic
971C2×C42C2414yes—
972C2×C42C2414yes—
973C2×C42C2412yes—
974C2×C42C2412yes—
975C2×C42C2412yes—
976C2×C42C2414yes—
977C2×C42C2414yes—
978C2×C42C2414yes—
979C2×C42C2412yes—
980C2×C42C2414yes—
981C2×C42C2414yes—
982C2×C42C2414yes—
983C2×C42C2412yes—
984C2×C42C2412yes—
985C2×C42C2414yes—
986C2×C42C2411yescharacteristic
987C2×C42C2412yes—
988C2×C42C2412yes—
989#95C2412yes—
990#95C2411yescharacteristic
991#95C2411yescharacteristic
992#95C2414yes—
993#95C2414yes—
994#95C2412yes—
995#95C2412yes—
996#95C2414yes—
997#95C2412yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2412yes—
1003#95C2414yes—
1004#95C2412yes—
1005#95C2412yes—
1006#95C2412yes—
1007#95C2412yes—
1008#95C2412yes—
1009#95C2411yescharacteristic
1010#95C2412yes—
1011#95C2411yescharacteristic
1012#95C2412yes—
1013#95C2412yes—
1014#95C2414yes—
1015#95C2414yes—
1016#95C2414yes—
1017#95C2414yes—
1018#95C2414yes—
1019#95C2414yes—
1020#95C2412yes—
1021#95C2414yes—
1022#95C2414yes—
1023#95C2412yes—
1024#95C2412yes—
1025#95C2414yes—
1026#95C2414yes—
1027#95C2414yes—
1028#95C2414yes—
1029#95C2412yes—
1030#95C2414yes—
1031#95C2412yes—
1032#95C2412yes—
1033#95C2414yes—
1034#95C2412yes—
1035#95C2414yes—
1036#95C2412yes—
1037#95C2412yes—
1038#95C2414yes—
1039#95C2414yes—
1040#95C2414yes—
1041#95C2414yes—
1042#95C2414yes—
1043#95C2412yes—
1044C24C2512yes—
1045C24C2512yes—
1046C24C2514yes—
1047C24C2512yes—
1048#41—832no—
1049#41—816no—
1050C2×Q8—24no—
1051C2×Q8—24no—
1052C2×Q8—22no—
1053C2×Q8—22no—
1054C2×Q8—22no—
1055C2×Q8—24no—
1056C2×Q8—44no—
1057C2×Q8—44no—
1058C2×Q8—41no—
1059C2×Q8—41no—
1060C2×Q8—42no—
1061C2×Q8—42no—
1062C2×Q8—44no—
1063C2×Q8—42no—
1064C2×Q8—41no—
1065C2×Q8—42no—
1066C2×Q8C2×#41116yes—
1067C2×D4—24no—
1068C2×D4—28no—
1069C2×D4—24no—
1070C2×D4—24no—
1071C2×D4—24no—
1072C2×D4—28no—
1073C2×D4—28no—
1074C2×D4—28no—
1075C2×D4—28no—
1076C2×D4—22no—
1077C2×D4—24no—
1078C2×D4—22no—
1079C2×D4—44no—
1080C2×D4—44no—
1081C2×D4—41no—
1082C2×D4—41no—
1083C2×D4—42no—
1084C2×D4—44no—
1085C2×D4—41no—
1086C2×D4—42no—
1087C2×D4—44no—
1088C2×D4—44no—
1089C2×D4—44no—
1090C2×D4—42no—
1091C2×D4—44no—
1092C2×D4—42no—
1093C2×D4—42no—
1094C2×D4—44no—
1095C2×D4—44no—
1096C2×D4—42no—
1097C2×D4—44no—
1098C2×D4—42no—
1099C2×D4—44no—
1100C2×D4—44no—
1101C2×D4—44no—
1102C2×D4—44no—
1103C2×D4—44no—
1104C2×D4—44no—
1105C2×D4—44no—
1106C2×D4—44no—
1107C2×D4—42no—
1108C2×D4—44no—
1109C2×D4—42no—
1110C2×D4—42no—
1111C2×D4—44no—
1112C22×C4—24no—
1113C22×C4—24no—
1114C22×C4—24no—
1115C22×C4—24no—
1116C22×C4—24no—
1117C22×C4—24no—
1118C22×C4—28no—
1119C22×C4—28no—
1120C22×C4—24no—
1121C22×C4—24no—
1122C22×C4—24no—
1123C22×C4—28no—
1124C22×C4—28no—
1125C22×C4—24no—
1126C22×C4—24no—
1127C22×C4—28no—
1128C22×C4—28no—
1129C22×C4—28no—
1130C22×C4—44no—
1131C22×C4—44no—
1132C22×C4—42no—
1133C22×C4—42no—
1134C22×C4—42no—
1135C22×C4—42no—
1136C22×C4—44no—
1137C22×C4—44no—
1138C22×C4—44no—
1139C22×C4—44no—
1140C22×C4—44no—
1141C22×C4—44no—
1142C22×C4C2512yes—
1143C22×C4C2512yes—
1144C22×C4C2511yescharacteristic
1145C22×C4C2511yescharacteristic
1146C22×C4C2514yes—
1147C22×C4C2512yes—
1148C22×C4C2514yes—
1149C22×C4C2512yes—
1150C22×C4C2514yes—
1151C22×C4C2511yescharacteristic
1152C22×C4C2512yes—
1153C22×C4C2512yes—
1154C22×C4C2512yes—
1155C22×C4C2512yes—
1156C22×C4C2512yes—
1157C22×C4C2511yescharacteristic
1158C22×C4C2511yescharacteristic
1159C22×C4C2512yes—
1160C22×C4C2512yes—
1161C22×C4C2514yes—
1162C22×C4C2514yes—
1163C22×C4C2512yes—
1164C22×C4C2512yes—
1165C22×C4C2511yescharacteristic
1166C22×C4C2511yescharacteristic
1167C4⋊C4—24no—
1168C4⋊C4—24no—
1169C4⋊C4—24no—
1170C4⋊C4—24no—
1171C4⋊C4—28no—
1172C4⋊C4—28no—
1173C4⋊C4—28no—
1174C4⋊C4—28no—
1175C4⋊C4—28no—
1176C4⋊C4—24no—
1177C4⋊C4—28no—
1178C4⋊C4—24no—
1179C4⋊C4—24no—
1180C4⋊C4—24no—
1181C4⋊C4—24no—
1182C4⋊C4—24no—
1183C4⋊C4—42no—
1184C4⋊C4—42no—
1185C4⋊C4—44no—
1186C4⋊C4—44no—
1187C4⋊C4—44no—
1188C4⋊C4—44no—
1189C4⋊C4—41no—
1190C4⋊C4—42no—
1191C4⋊C4—41no—
1192C4⋊C4—41no—
1193C4⋊C4—41no—
1194C4⋊C4—44no—
1195C4⋊C4—42no—
1196C4⋊C4—44no—
1197C4⋊C4—44no—
1198C4⋊C4—42no—
1199C4⋊C4—41no—
1200C4⋊C4—41no—
1201C4⋊C4—42no—
1202C4⋊C4—44no—
1203C4⋊C4—44no—
1204C4⋊C4—42no—
1205C4⋊C4—44no—
1206C4⋊C4—44no—
1207C4⋊C4—42no—
1208C4⋊C4—42no—
1209C4⋊C4—42no—
1210C4⋊C4C2×#4118yes—
1211C4⋊C4C2×#4118yes—
1212C4⋊C4C2×#41116yes—
1213C4⋊C4H(5,𝔽2)14yes—
1214C22⋊C4—24no—
1215C22⋊C4—24no—
1216C22⋊C4—28no—
1217C22⋊C4—28no—
1218C22⋊C4—28no—
1219C22⋊C4—28no—
1220C22⋊C4—28no—
1221C22⋊C4—28no—
1222C22⋊C4—28no—
1223C22⋊C4—24no—
1224C22⋊C4—24no—
1225C22⋊C4—28no—
1226C22⋊C4—28no—
1227C22⋊C4—28no—
1228C22⋊C4—28no—
1229C22⋊C4—28no—
1230C22⋊C4—28no—
1231C22⋊C4—28no—
1232C22⋊C4—28no—
1233C22⋊C4—24no—
1234C22⋊C4—24no—
1235C22⋊C4—24no—
1236C22⋊C4—28no—
1237C22⋊C4—28no—
1238C22⋊C4—24no—
1239C22⋊C4—24no—
1240C22⋊C4—42no—
1241C22⋊C4—44no—
1242C22⋊C4—44no—
1243C22⋊C4—44no—
1244C22⋊C4—44no—
1245C22⋊C4—42no—
1246C22⋊C4—42no—
1247C22⋊C4—42no—
1248C22⋊C4—44no—
1249C22⋊C4—44no—
1250C22⋊C4—42no—
1251C22⋊C4—44no—
1252C22⋊C4—42no—
1253C22⋊C4—42no—
1254C22⋊C4—44no—
1255C22⋊C4—42no—
1256C22⋊C4—42no—
1257C22⋊C4—44no—
1258C22⋊C4—44no—
1259C22⋊C4—44no—
1260C22⋊C4—42no—
1261C22⋊C4—44no—
1262C22⋊C4—42no—
1263C22⋊C4—42no—
1264C22⋊C4—44no—
1265C22⋊C4—42no—
1266C22⋊C4—42no—
1267C22⋊C4—44no—
1268C22⋊C4—42no—
1269C22⋊C4—44no—
1270C22⋊C4—42no—
1271C22⋊C4—44no—
1272C22⋊C4—44no—
1273C22⋊C4—44no—
1274C42—24no—
1275C42—24no—
1276C42—24no—
1277C42—24no—
1278C42—28no—
1279C42—28no—
1280C42—28no—
1281C42—28no—
1282C42—28no—
1283C42—24no—
1284C42—24no—
1285C42—24no—
1286C42—22no—
1287C42—22no—
1288C42—22no—
1289C42—24no—
1290C42—22no—
1291C42—28no—
1292C42—24no—
1293C42—44no—
1294C42—41no—
1295C42—42no—
1296C42—44no—
1297C42—44no—
1298C42—42no—
1299C42—42no—
1300C42—42no—
1301C42—44no—
1302C42—44no—
1303C42—42no—
1304C42—44no—
1305C42—42no—
1306C42—44no—
1307C42C2×#4118yes—
1308C23—22no—
1309C23—22no—
1310C23—24no—
1311C23—22no—
1312C23—24no—
1313C23—24no—
1314C23—22no—
1315C23—22no—
1316C23—22no—
1317C23—24no—
1318C23—22no—
1319C23—22no—
1320C23—22no—
1321C23—24no—
1322C23—22no—
1323C23—24no—
1324C23—22no—
1325C23—24no—
1326C23—24no—
1327C23—22no—
1328C23—22no—
1329C23—22no—
1330C23—24no—
1331C23—22no—
1332C23—22no—
1333C23—22no—
1334C23C2611yescharacteristic
1335Q8—416no—
1336Q8—44no—
1337Q8—44no—
1338Q8—82no—
1339Q8—84no—
1340Q8—82no—
1341Q8—84no—
1342D4—416no—
1343D4—44no—
1344D4—48no—
1345D4—44no—
1346D4—84no—
1347D4—88no—
1348D4—88no—
1349D4—88no—
1350D4—88no—
1351D4—84no—
1352D4—84no—
1353D4—88no—
1354D4—82no—
1355D4—88no—
1356D4—164no—
1357D4—162no—
1358C2×C4—22no—
1359C2×C4—21no—
1360C2×C4—22no—
1361C2×C4—22no—
1362C2×C4—22no—
1363C2×C4—24no—
1364C2×C4—24no—
1365C2×C4—22no—
1366C2×C4—24no—
1367C2×C4—22no—
1368C2×C4—22no—
1369C2×C4—24no—
1370C2×C4—21no—
1371C2×C4—22no—
1372C2×C4—22no—
1373C2×C4—24no—
1374C2×C4—22no—
1375C2×C4—22no—
1376C2×C4—22no—
1377C2×C4—22no—
1378C2×C4—24no—
1379C2×C4—24no—
1380C2×C4—22no—
1381C2×C4—22no—
1382C2×C4—21no—
1383C2×C4—21no—
1384C2×C4—22no—
1385C2×C4—21no—
1386C2×C4—22no—
1387C2×C4—24no—
1388C2×C4—22no—
1389C2×C4—21no—
1390C2×C4—22no—
1391C2×C4—22no—
1392C2×C4—21no—
1393C2×C4—22no—
1394C2×C4—24no—
1395C2×C4—22no—
1396C2×C4—22no—
1397C2×C4—22no—
1398C2×C4—24no—
1399C2×C4—22no—
1400C2×C4—22no—
1401C2×C4—24no—
1402C2×C4—24no—
1403C2×C4—22no—
1404C2×C4—21no—
1405C2×C4—24no—
1406C2×C4—22no—
1407C2×C4—22no—
1408C2×C4—22no—
1409C2×C4—24no—
1410C2×C4—22no—
1411C2×C4—22no—
1412C2×C4—21no—
1413C2×C4—22no—
1414C2×C4—22no—
1415C2×C4—21no—
1416C2×C4—24no—
1417C2×C4—21no—
1418C2×C4—416no—
1419C2×C4—416no—
1420C2×C4—48no—
1421C2×C4—48no—
1422C2×C4—48no—
1423C2×C4—48no—
1424C2×C4—48no—
1425C2×C4—88no—
1426C2×C4—88no—
1427C2×C4—88no—
1428C2×C4C22×#4114yes—
1429C2×C4C22×#4118yes—
1430C2×C4C22×#4114yes—
1431C2×C4C22×#4118yes—
1432C2×C4C22×#4114yes—
1433C2×C4C2×H(5,𝔽2)14yes—
1434C2×C4C2×H(5,𝔽2)12yes—
1435C2×C4#58514yes—
1436C2×C4#58512yes—
1437C22—42no—
1438C22—44no—
1439C22—44no—
1440C22—44no—
1441C22—42no—
1442C22—42no—
1443C22—42no—
1444C22—42no—
1445C22—42no—
1446C22—44no—
1447C22—42no—
1448C22—42no—
1449C22—44no—
1450C22—44no—
1451C22—42no—
1452C22—42no—
1453C22—44no—
1454C22—42no—
1455C22—42no—
1456C22—42no—
1457C22—44no—
1458C22—42no—
1459C22—42no—
1460C22—42no—
1461C22—44no—
1462C22—42no—
1463C22C23×#4112yes—
1464C22C22×H(5,𝔽2)11yescharacteristic
1465C22C2×#58512yes—
1466C22C2×#58511yescharacteristic
1467C22H(7,𝔽2)11yescharacteristic
1468C4—24no—
1469C4—28no—
1470C4—24no—
1471C4—28no—
1472C4—24no—
1473C4—22no—
1474C4—24no—
1475C4—42no—
1476C4—41no—
1477C4—41no—
1478C4—42no—
1479C4—44no—
1480C4—41no—
1481C4—42no—
1482C4—44no—
1483C4—42no—
1484C4—42no—
1485C4—44no—
1486C4—41no—
1487C4—41no—
1488C4—42no—
1489C4—42no—
1490C4—42no—
1491C4—42no—
1492C4#348314yes—
1493C2—82no—
1494C2—82no—
1495C2—84no—
1496C2—82no—
1497C2C2×#348311yescharacteristic
1498C2#6279312yes—
1499C2#6291811yescharacteristic
1500C2#6299012yes—
1501C2#6302211yescharacteristic
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. #60048C2semidirect
2. #59952C2semidirect
3. #59903C2semidirect
4. #59894C2semidirect
5. #59878C2semidirect
6. #59049C2semidirect
7. #45408C2semidirect
8. #45364C2semidirect
9. #45101C2semidirect
10. #44265C2semidirect
11. #43788C2semidirect
12. #43400C2semidirect
13. #38835C2semidirect
14. #38816C2semidirect
15. #38290C2semidirect
16. #37772C2semidirect
17. #36471C2semidirect
18. #36470C2semidirect
19. #36406C2semidirect
20. #36385C2semidirect
21. #36381C2semidirect
22. #36048C2semidirect
23. #35956C2semidirect
24. #35768C2semidirect
25. #34962C2semidirect
26. #34874C2semidirect
27. #34307C2semidirect
28. #34284C2semidirect
29. #34155C2semidirect
763. C4⋊Q8#41semidirect

Maximal subgroups

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

subgroupindex
#600482
#599522
#599032
#598942
#598782
#590492
#454082
#453642
#451012
#442652
#437882
#434002
#388352
#388162
#382902
#377722
#364712
#364702
#364062
#363852
#363812
#360482
#359562
#357682
#349622
#348742
#343072
#342842
#341552