Finite Group Databasebeta

← #7659787

Subgroups — #7659787

Order 512.

5618 conjugacy classes of subgroups.

The subgroup lattice has 1430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#52277C213yesmaximal, complemented
2#42989C213yesmaximal, complemented
3#42923C213yesmaximal, complemented
4#42894C213yesmaximal, complemented
5#42874C213yesmaximal, complemented
6#42872C213yesmaximal, complemented
7#42838C213yesmaximal, complemented
8#40125C213yesmaximal, complemented
9#40122C213yesmaximal, complemented
10#40030C213yesmaximal, complemented
11#40007C213yesmaximal, complemented
12#39666C213yesmaximal, complemented
13#39242C213yesmaximal, complemented
14#37346C213yesmaximal, complemented
15#37343C213yesmaximal, complemented
16#37316C213yesmaximal, complemented
17#36576C211yesmaximal, characteristic, complemented
18Q8×#126C211yesmaximal, characteristic, complemented
19Q8×C22⋊Q8C211yesmaximal, characteristic, complemented
20#36457C211yesmaximal, characteristic, complemented
21#36455C211yesmaximal, characteristic, complemented
22#36432C211yesmaximal, characteristic, complemented
23#36005C211yesmaximal, characteristic, complemented
24#35948C211yesmaximal, characteristic, complemented
25#35898C211yesmaximal, characteristic, complemented
26#35831C211yesmaximal, characteristic, complemented
27#35757C211yesmaximal, characteristic, complemented
28#35757C211yesmaximal, characteristic, complemented
29#34312C211yesmaximal, characteristic, complemented
30#34293C211yesmaximal, characteristic, complemented
31#34257C211yesmaximal, characteristic, complemented
32C22×2−1+4C2211yescharacteristic
33C2×Q82C2211yescharacteristic
34C2×#550C2211yescharacteristic
35C2×#550C2211yescharacteristic
36C2×#550C2211yescharacteristic
37C2×#548C2211yescharacteristic
38C2×#548C2211yescharacteristic
39C2×#548C2211yescharacteristic
40C2×#548C2211yescharacteristic
41C2×#520C2211yescharacteristic
42C2×#519C2211yescharacteristic
43C2×C4×#41C2211yescharacteristic
44C22×C4×Q8C2211yescharacteristic
45#2863C2213yes—
46#2858C2213yes—
47#2857C2213yes—
48#2856C2213yes—
49#2856C2213yes—
50#2855C2213yes—
51#2832C2216yes—
52#2829C2216yes—
53#2808C2216yes—
54#2804C2216yes—
55#2803C2213yes—
56#2800C2213yes—
57#2797C2213yes—
58#2788C2213yes—
59#2786C2216yes—
60#2784C2216yes—
61#2780C2216yes—
62#2778C2213yes—
63#2774C2213yes—
64#2759C2213yes—
65#2756C2216yes—
66#2753C2213yes—
67#2751C2213yes—
68#2749C2213yes—
69#2741C2213yes—
70#2733C2216yes—
71#2730C2216yes—
72#2715C2216yes—
73#2714C2213yes—
74#2714C2216yes—
75#2710C2213yes—
76#2708C2216yes—
77#2703C2213yes—
78#2703C2216yes—
79#2702C2211yescharacteristic
80#2696C2216yes—
81#2688C2216yes—
82#2686C2216yes—
83#2686C2216yes—
84#2682C2216yes—
85#2676C2213yes—
86#2676C2216yes—
87#2676C2216yes—
88#2665C2216yes—
89#2662C2216yes—
90#2661C2216yes—
91#2653C2216yes—
92#2649C2216yes—
93#2648C2216yes—
94#2644C2213yes—
95#2640C2213yes—
96#2624C2213yes—
97#2620C2213yes—
98#2615C2213yes—
99#2615C2213yes—
100#2592C2213yes—
101#2589C2216yes—
102#2582C2213yes—
103#2574C2216yes—
104#2567C2213yes—
105#2563C2213yes—
106#2559C2216yes—
107#2557C2216yes—
108#2557C2216yes—
109#2555C2216yes—
110#2548C2213yes—
111#2548C2213yes—
112#2547C2213yes—
113#2544C2213yes—
114#2541C2213yes—
115#2538C2213yes—
116#2537C2213yes—
117#2537C2213yes—
118#2513C2213yes—
119#2512C2213yes—
120#2512C2213yes—
121#2511C2213yes—
122#2511C2213yes—
123#2511C2213yes—
124#2501C2213yes—
125#2499C2213yes—
126#2497C2213yes—
127#2497C2213yes—
128#2497C2213yes—
129#2497C2213yes—
130#2496C2213yes—
131#2494C2213yes—
132#2492C2213yes—
133#2492C2213yes—
134#2491C2213yes—
135#2491C2213yes—
136#2491C2213yes—
137#2491C2213yes—
138#2491C2213yes—
139#2491C2213yes—
140#2487C2213yes—
141#2485C2213yes—
142#2451C2213yes—
143#2451C2213yes—
144#2447C2213yes—
145#2447C2213yes—
146#2445C2213yes—
147#2445C2213yes—
148#2440C2213yes—
149#2440C2213yes—
150#2436C2213yes—
151#2436C2213yes—
152#2431C2213yes—
153#2431C2213yes—
154#2431C2213yes—
155#2431C2213yes—
156#2428C2213yes—
157#2428C2213yes—
158#2428C2213yes—
159#2427C2213yes—
160#2426C2213yes—
161#2426C2213yes—
162#2422C2213yes—
163#2422C2213yes—
164#2422C2213yes—
165#2420C2213yes—
166#2417C2213yes—
167#2416C2213yes—
168#2416C2213yes—
169#2416C2213yes—
170#2414C2213yes—
171#2414C2213yes—
172#2409C2213yes—
173#2409C2213yes—
174#2407C2213yes—
175#2407C2213yes—
176#2407C2213yes—
177#2407C2213yes—
178#2401C2213yes—
179#2398C2213yes—
180#2395C2213yes—
181#2392C2213yes—
182#2388C2213yes—
183#2388C2213yes—
184#2367C2213yes—
185#2367C2213yes—
186#2363C2213yes—
187#2363C2213yes—
188#2362C2213yes—
189#2360C2213yes—
190#2354C2213yes—
191#2352C2213yes—
192#2351C2211yescharacteristic
193Q8×C4⋊C4C2211yescharacteristic
194Q8×C4⋊C4C2211yescharacteristic
195Q8×C4⋊C4C2211yescharacteristic
196Q8×C4⋊C4C2211yescharacteristic
197Q8×C4⋊C4C2211yescharacteristic
198#2341C2211yescharacteristic
199#2341C2211yescharacteristic
200#2341C2211yescharacteristic
201#2341C2211yescharacteristic
202#2341C2211yescharacteristic
203#2341C2213yes—
204#2341C2211yescharacteristic
205#2341C2211yescharacteristic
206#2341C2211yescharacteristic
207#2341C2213yes—
208Q8×C22⋊C4C2211yescharacteristic
209Q8×C22⋊C4C2213yes—
210Q8×C22⋊C4C2211yescharacteristic
211Q8×C22⋊C4C2211yescharacteristic
212Q8×C22⋊C4C2211yescharacteristic
213Q8×C22⋊C4C2213yes—
214Q8×C22⋊C4C2211yescharacteristic
215Q8×C22⋊C4C2211yescharacteristic
216#2335C2216yes—
217#2333C2216yes—
218#2326C2213yes—
219#2324C2213yes—
220#2324C2213yes—
221#2323C2213yes—
222#2311C2213yes—
223#2311C2213yes—
224C4×#126C2213yes—
225C4×#124C2213yes—
226C4×#124C2213yes—
227C4×C22⋊Q8C2213yes—
228C4×C22⋊Q8C2213yes—
229C4×#123C2213yes—
230C4×#121C2213yes—
231C4×#121C2213yes—
232#2297C2213yes—
233#2297C2213yes—
234#2293C2213yes—
235#2290C2213yes—
236#2276C2211yescharacteristic
237C42×Q8C2211yescharacteristic
238C2×2−1+4—28no—
239C2×2−1+4—44no—
240C2×2−1+4—44no—
241C22×#41C2311yescharacteristic
242C22×#41C2311yescharacteristic
243C22×#41C2311yescharacteristic
244C22×#41C2313yes—
245C22×#41C2313yes—
246C22×#41C2313yes—
247C23×Q8C2311yescharacteristic
248C23×Q8C2311yescharacteristic
249C23×Q8C2313yes—
250Q82—44no—
251#550—44no—
252#550—44no—
253#550—44no—
254#548—28no—
255#548—28no—
256#548—44no—
257#548—44no—
258C2×C4⋊Q8C2313yes—
259C2×C4⋊Q8C2313yes—
260C2×C4⋊Q8C2313yes—
261C2×#127C2313yes—
262C2×#127C2313yes—
263C2×#127C2313yes—
264C2×#126C2311yescharacteristic
265C2×#126C2316yes—
266C2×#124C2313yes—
267C2×#124C2313yes—
268C2×#124C2313yes—
269C2×#124C2313yes—
270C2×#124C2313yes—
271C2×#124C2316yes—
272C2×#124C2316yes—
273C2×#124C2316yes—
274C2×#123C2316yes—
275C2×#123C2313yes—
276C2×#123C2316yes—
277C2×C22⋊Q8C2313yes—
278C2×C22⋊Q8C2313yes—
279C2×C22⋊Q8C2311yescharacteristic
280C2×C22⋊Q8C2313yes—
281C2×C22⋊Q8C2313yes—
282C2×C22⋊Q8C2316yes—
283C2×#121C2313yes—
284C2×#121C2313yes—
285C2×#121C2313yes—
286C2×#121C2313yes—
287C2×#121C2313yes—
288C2×#121C2313yes—
289C2×#121C2313yes—
290C2×#121C2313yes—
291C2×#121C2313yes—
292C2×#121C2313yes—
293C2×#121C2313yes—
294C2×#121C2313yes—
295C2×#121C2316yes—
296C2×#121C2316yes—
297C2×#121C2316yes—
298C2×#121C2316yes—
299#520—44no—
300#519—44no—
301C4×#41—44no—
302C2×C4×Q8—44no—
303C2×C4×Q8C2311yescharacteristic
304C2×C4×Q8C2311yescharacteristic
305C2×C4×Q8C2311yescharacteristic
306C2×C4×Q8C2311yescharacteristic
307C2×C4×Q8C2311yescharacteristic
308C2×C4×Q8C2311yescharacteristic
309C2×C4×Q8C2311yescharacteristic
310C2×C4×Q8C2311yescharacteristic
311C2×C4×Q8C2311yescharacteristic
312C2×C4×Q8C2311yescharacteristic
313C2×C4×Q8C2313yes—
314C2×C4×Q8C2313yes—
315C2×C4×Q8C2313yes—
316C2×C4×Q8C2313yes—
317C2×C4×Q8C2313yes—
318C2×C4×D4C2313yes—
319C2×C4×D4C2313yes—
320C2×C4×D4C2313yes—
321C2×C4×D4C2313yes—
322C2×C4×D4C2313yes—
323C2×C4×D4C2313yes—
324C2×C4×D4C2313yes—
325C2×C4×D4C2313yes—
326C2×C4×D4C2313yes—
327C2×C4×D4C2313yes—
328C2×C4×D4C2313yes—
329C2×#117C2313yes—
330C2×#117C2313yes—
331C2×#117C2313yes—
332C2×#117C2313yes—
333C22×C4⋊C4C2313yes—
334C22×C4⋊C4C2313yes—
335C22×C42C2313yes—
336C22×C42C2313yes—
337#401C2313yes—
338#400C2313yes—
339#400C2316yes—
340#400C2316yes—
341#400C2313yes—
342#400C2313yes—
343#400C2313yes—
344#400C2311yescharacteristic
345#400C2313yes—
346#400C2316yes—
347#399C2316yes—
348#399C2313yes—
349#398C2316yes—
350#398C2316yes—
351#398C2313yes—
352#398C2311yescharacteristic
353#397C2313yes—
354#397C2316yes—
355#397C2313yes—
356#397C2316yes—
357#397C2316yes—
358#397C2313yes—
359#397C2313yes—
360#397C2313yes—
361#397C2316yes—
362#397C2313yes—
363#397C2316yes—
364#397C2313yes—
365#397C2316yes—
366#397C2313yes—
367#397C2313yes—
368#396C2316yes—
369#396C2316yes—
370#396C2316yes—
371#396C2313yes—
372#396C2316yes—
373#396C2316yes—
374#396C2311yescharacteristic
375#396C2313yes—
376#395C2316yes—
377#395C2316yes—
378#395C2313yes—
379#395C2313yes—
380#394C2313yes—
381#394C2313yes—
382#394C2316yes—
383#394C2316yes—
384#394C2316yes—
385#394C2316yes—
386#394C2316yes—
387#394C2316yes—
388#394C2316yes—
389#394C2316yes—
390#394C2316yes—
391#394C2311yescharacteristic
392#394C2311yescharacteristic
393#394C2313yes—
394#394C2313yes—
395#394C2313yes—
396#394C2313yes—
397#394C2313yes—
398#394C2316yes—
399#394C2313yes—
400#394C2313yes—
401#394C2316yes—
402#394C2313yes—
403#394C2313yes—
404#393C2316yes—
405#393C2316yes—
406#393C2316yes—
407#393C2313yes—
408#393C2316yes—
409#393C2313yes—
410#393C2316yes—
411#393C2316yes—
412#393C2313yes—
413#393C2311yescharacteristic
414#392C2316yes—
415#392C2313yes—
416#392C2313yes—
417#392C2316yes—
418#392C2316yes—
419#392C2316yes—
420#392C2313yes—
421#392C2313yes—
422#392C2313yes—
423#392C2313yes—
424#392C2313yes—
425#392C2316yes—
426#392C2316yes—
427#391C2316yes—
428#391C2313yes—
429#391C2313yes—
430#391C2313yes—
431#391C2313yes—
432#391C2313yes—
433#391C2313yes—
434#391C2313yes—
435#391C2316yes—
436#391C2316yes—
437#391C2313yes—
438#391C2313yes—
439#391C2313yes—
440#391C2313yes—
441#391C2313yes—
442#391C2313yes—
443#391C2313yes—
444#391C2313yes—
445#391C2311yescharacteristic
446#390C2316yes—
447#390C2316yes—
448#390C2313yes—
449#390C2313yes—
450#390C2313yes—
451#390C2313yes—
452#390C2313yes—
453#390C2316yes—
454#390C2313yes—
455#390C2316yes—
456#390C2316yes—
457#390C2313yes—
458#390C2313yes—
459#390C2313yes—
460#390C2313yes—
461#390C2313yes—
462#390C2313yes—
463#390C2313yes—
464#390C2313yes—
465#390C2313yes—
466#390C2313yes—
467#390C2313yes—
468#390C2313yes—
469#390C2313yes—
470#390C2313yes—
471#390C2316yes—
472#390C2313yes—
473#390C2313yes—
474#390C2313yes—
475#389C2313yes—
476#389C2316yes—
477#389C2313yes—
478#389C2313yes—
479#389C2313yes—
480#389C2313yes—
481#389C2313yes—
482#389C2313yes—
483#389C2313yes—
484#389C2313yes—
485#389C2313yes—
486#389C2313yes—
487#389C2313yes—
488#389C2313yes—
489#389C2313yes—
490#389C2313yes—
491#389C2313yes—
492#389C2311yescharacteristic
493#388C2313yes—
494#388C2313yes—
495#388C2313yes—
496#388C2316yes—
497#388C2313yes—
498#388C2316yes—
499#388C2316yes—
500#388C2316yes—
501#388C2316yes—
502#388C2316yes—
503#388C2316yes—
504#388C2313yes—
505#388C2313yes—
506#388C2313yes—
507#388C2316yes—
508#388C2316yes—
509#388C2313yes—
510#388C2313yes—
511#388C2313yes—
512#388C2313yes—
513#388C2313yes—
514#388C2313yes—
515#388C2311yescharacteristic
516#388C2311yescharacteristic
517#388C2311yescharacteristic
518#388C2313yes—
519#388C2313yes—
520#388C2313yes—
521#387C2313yes—
522#387C2313yes—
523#387C2313yes—
524#387C2316yes—
525#387C2316yes—
526#387C2316yes—
527#387C2316yes—
528#387C2313yes—
529#387C2313yes—
530#387C2316yes—
531#387C2313yes—
532#387C2316yes—
533#387C2313yes—
534#387C2313yes—
535#387C2313yes—
536#386C2313yes—
537#386C2313yes—
538#386C2316yes—
539#386C2313yes—
540#386C2316yes—
541#386C2316yes—
542#386C2316yes—
543#386C2316yes—
544#386C2316yes—
545#386C2316yes—
546#386C2313yes—
547#386C2316yes—
548#386C2316yes—
549#386C2316yes—
550#386C2316yes—
551#386C2313yes—
552#386C2313yes—
553#386C2313yes—
554#386C2313yes—
555#386C2313yes—
556#386C2313yes—
557#386C2311yescharacteristic
558#385C2316yes—
559#385C2316yes—
560#385C2316yes—
561#385C2313yes—
562#385C2316yes—
563#385C2316yes—
564#385C2316yes—
565#385C2313yes—
566#385C2313yes—
567#385C2313yes—
568#385C2313yes—
569#384C2313yes—
570#384C2313yes—
571#384C2313yes—
572#384C2313yes—
573#384C2313yes—
574#383C2313yes—
575#382C2313yes—
576#382C2313yes—
577#381C2316yes—
578#381C2313yes—
579#380C2313yes—
580#380C2313yes—
581#380C2313yes—
582#380C2313yes—
583#380C2313yes—
584#380C2313yes—
585#380C2313yes—
586#380C2316yes—
587#380C2316yes—
588#380C2316yes—
589#380C2313yes—
590#380C2313yes—
591#380C2313yes—
592#380C2313yes—
593#380C2313yes—
594#380C2313yes—
595#380C2313yes—
596#380C2313yes—
597#380C2313yes—
598#380C2311yescharacteristic
599C4×C4⋊C4C2313yes—
600C4×C4⋊C4C2313yes—
601C4×C4⋊C4C2313yes—
602C4×C4⋊C4C2313yes—
603C4×C4⋊C4C2313yes—
604C4×C4⋊C4C2316yes—
605C4×C4⋊C4C2313yes—
606C4×C4⋊C4C2313yes—
607C4×C4⋊C4C2313yes—
608C4×C4⋊C4C2313yes—
609C4×C4⋊C4C2313yes—
610C4×C4⋊C4C2313yes—
611C4×C4⋊C4C2313yes—
612C4×C22⋊C4C2313yes—
613C4×C22⋊C4C2313yes—
614C4×C22⋊C4C2313yes—
615C4×C22⋊C4C2316yes—
616C4×C22⋊C4C2316yes—
617C4×C22⋊C4C2316yes—
618C4×C22⋊C4C2316yes—
619C4×C22⋊C4C2316yes—
620C4×C22⋊C4C2313yes—
621C4×C22⋊C4C2313yes—
622C4×C22⋊C4C2313yes—
623C4×C22⋊C4C2313yes—
624C4×C22⋊C4C2313yes—
625C4×C22⋊C4C2313yes—
626C4×C22⋊C4C2313yes—
627C4×C22⋊C4C2313yes—
628C4×C22⋊C4C2313yes—
629C4×C22⋊C4C2313yes—
630C4×C22⋊C4C2313yes—
631#376C2313yes—
632C43C2313yes—
6332−1+4—464no—
634C2×#41—24no—
635C2×#41—24no—
636C2×#41—212no—
637C2×#41—24no—
638C2×#41—24no—
639C2×#41—24no—
640C2×#41—24no—
641C2×#41—24no—
642C2×#41—24no—
643C2×#41—24no—
644C2×#41—212no—
645C2×#41—212no—
646C2×#41—46no—
647C2×#41—46no—
648C2×#41—46no—
649C2×#41—46no—
650C2×#41—46no—
651C2×#41—46no—
652C22×Q8—24no—
653C22×Q8—24no—
654C22×Q8—212no—
655C22×Q8—24no—
656C22×Q8—24no—
657C22×Q8—24no—
658C22×Q8—46no—
659C22×Q8—46no—
660C22×Q8#4118yes—
661C22×Q8C2413yes—
662C22×Q8C2411yescharacteristic
663C22×Q8C2413yes—
664C22×Q8C2413yes—
665C22×Q8C2416yes—
666C22×Q8C2411yescharacteristic
667C22×D4C2413yes—
668C22×D4C2413yes—
669C22×D4C2413yes—
670C22×D4C2413yes—
671C22×D4C2413yes—
672C22×D4C2413yes—
673C22×D4C2413yes—
674C22×D4C2413yes—
675C22×D4C2411yescharacteristic
676C22×D4C2413yes—
677C22×D4C2413yes—
678C22×D4C2413yes—
679C22×D4C2413yes—
680C22×D4C2416yes—
681C22×D4C2416yes—
682C22×D4C2416yes—
683C23×C4C2413yes—
684C23×C4C2413yes—
685C23×C4C2413yes—
686C23×C4C2413yes—
687C23×C4C2411yescharacteristic
688C23×C4C2413yes—
689C23×C4C2413yes—
690C23×C4C2416yes—
691C23×C4C2413yes—
692C23×C4C2416yes—
693C23×C4C2413yes—
694C4⋊Q8—46no—
695C4⋊Q8—46no—
696C4⋊Q8—46no—
697#127—46no—
698#127—46no—
699#127—46no—
700#126—24no—
701#126—86no—
702#124—212no—
703#124—212no—
704#124—46no—
705#124—46no—
706#124—46no—
707#124—86no—
708#124—86no—
709#124—86no—
710#123—412no—
711#123—46no—
712#123—86no—
713C22⋊Q8—212no—
714C22⋊Q8—212no—
715C22⋊Q8—24no—
716C22⋊Q8—46no—
717C22⋊Q8—46no—
718C22⋊Q8—86no—
719#121—212no—
720#121—212no—
721#121—212no—
722#121—46no—
723#121—46no—
724#121—46no—
725#121—46no—
726#121—46no—
727#121—46no—
728#121—46no—
729#121—46no—
730#121—46no—
731#121—86no—
732#121—86no—
733#121—86no—
734#121—86no—
735C4×Q8—24no—
736C4×Q8—24no—
737C4×Q8—24no—
738C4×Q8—24no—
739C4×Q8—24no—
740C4×Q8—24no—
741C4×Q8—24no—
742C4×Q8—24no—
743C4×Q8—24no—
744C4×Q8—24no—
745C4×Q8—46no—
746C4×Q8—46no—
747C4×Q8—46no—
748C4×Q8—46no—
749C4×Q8—46no—
750C4×D4—212no—
751C4×D4—212no—
752C4×D4—46no—
753C4×D4—46no—
754C4×D4—46no—
755C4×D4—46no—
756C4×D4—46no—
757C4×D4—46no—
758C4×D4—46no—
759C4×D4—46no—
760C4×D4—46no—
761#117—46no—
762#117—46no—
763#117—46no—
764#117—46no—
765C2×C4⋊C4—46no—
766C2×C4⋊C4—46no—
767C2×C4⋊C4C2413yes—
768C2×C4⋊C4C2413yes—
769C2×C4⋊C4C2413yes—
770C2×C4⋊C4C2413yes—
771C2×C4⋊C4C2413yes—
772C2×C4⋊C4C2413yes—
773C2×C4⋊C4C2413yes—
774C2×C4⋊C4C2413yes—
775C2×C4⋊C4C2413yes—
776C2×C4⋊C4C2413yes—
777C2×C4⋊C4C2413yes—
778C2×C4⋊C4C2413yes—
779C2×C4⋊C4C2411yescharacteristic
780C2×C4⋊C4C2411yescharacteristic
781C2×C4⋊C4C2413yes—
782C2×C4⋊C4C2411yescharacteristic
783C2×C4⋊C4C2411yescharacteristic
784C2×C4⋊C4C2413yes—
785C2×C4⋊C4C2416yes—
786C2×C4⋊C4C2411yescharacteristic
787C2×C4⋊C4C2413yes—
788C2×C4⋊C4C2413yes—
789C2×C4⋊C4C2411yescharacteristic
790C2×C4⋊C4C2411yescharacteristic
791C2×C4⋊C4C2411yescharacteristic
792C2×C4⋊C4C2413yes—
793C2×C4⋊C4C2413yes—
794C2×C4⋊C4C2413yes—
795C2×C4⋊C4C2413yes—
796C2×C4⋊C4C2413yes—
797C2×C4⋊C4C2413yes—
798C2×C4⋊C4C2416yes—
799C2×C4⋊C4C2416yes—
800C2×C4⋊C4C2416yes—
801C2×C4⋊C4C2413yes—
802C2×C4⋊C4C2416yes—
803C2×C4⋊C4C2413yes—
804C2×C4⋊C4C2416yes—
805C2×C4⋊C4C2413yes—
806C2×C4⋊C4C2413yes—
807C2×C4⋊C4C2413yes—
808C2×C4⋊C4C2411yescharacteristic
809C2×C22⋊C4C2411yescharacteristic
810C2×C22⋊C4C2411yescharacteristic
811C2×C22⋊C4C2413yes—
812C2×C22⋊C4C2413yes—
813C2×C22⋊C4C2416yes—
814C2×C22⋊C4C2416yes—
815C2×C22⋊C4C2413yes—
816C2×C22⋊C4C2413yes—
817C2×C22⋊C4C2413yes—
818C2×C22⋊C4C2413yes—
819C2×C22⋊C4C2411yescharacteristic
820C2×C22⋊C4C2411yescharacteristic
821C2×C22⋊C4C2411yescharacteristic
822C2×C22⋊C4C2413yes—
823C2×C22⋊C4C2411yescharacteristic
824C2×C22⋊C4C2411yescharacteristic
825C2×C22⋊C4C2411yescharacteristic
826C2×C22⋊C4C2413yes—
827C2×C22⋊C4C2411yescharacteristic
828C2×C22⋊C4C2416yes—
829C2×C22⋊C4C2413yes—
830C2×C22⋊C4C2413yes—
831C2×C22⋊C4C2411yescharacteristic
832C2×C22⋊C4C2411yescharacteristic
833C2×C22⋊C4C2413yes—
834C2×C22⋊C4C2413yes—
835C2×C22⋊C4C2413yes—
836C2×C22⋊C4C2413yes—
837C2×C22⋊C4C2413yes—
838C2×C22⋊C4C2413yes—
839C2×C22⋊C4C2413yes—
840C2×C22⋊C4C2413yes—
841C2×C22⋊C4C2413yes—
842C2×C22⋊C4C2413yes—
843C2×C22⋊C4C2413yes—
844C2×C22⋊C4C2416yes—
845C2×C22⋊C4C2416yes—
846C2×C22⋊C4C2416yes—
847C2×C22⋊C4C2416yes—
848C2×C22⋊C4C2416yes—
849C2×C22⋊C4C2416yes—
850C2×C22⋊C4C2416yes—
851C2×C22⋊C4C2413yes—
852C2×C22⋊C4C2413yes—
853C2×C22⋊C4C2413yes—
854C2×C22⋊C4C2413yes—
855C2×C22⋊C4C2416yes—
856C2×C22⋊C4C2413yes—
857C2×C22⋊C4C2416yes—
858C2×C22⋊C4C2413yes—
859C2×C22⋊C4C2413yes—
860C2×C22⋊C4C2413yes—
861C2×C22⋊C4C2413yes—
862C2×C22⋊C4C2413yes—
863C2×C22⋊C4C2413yes—
864C2×C22⋊C4C2416yes—
865C2×C22⋊C4C2413yes—
866C2×C22⋊C4C2413yes—
867C2×C22⋊C4C2413yes—
868C2×C42—46no—
869C2×C42—46no—
870C2×C42C2413yes—
871C2×C42C2413yes—
872C2×C42C2413yes—
873C2×C42C2413yes—
874C2×C42C2413yes—
875C2×C42C2413yes—
876C2×C42C2413yes—
877C2×C42C2413yes—
878C2×C42C2413yes—
879C2×C42C2413yes—
880C2×C42C2411yescharacteristic
881C2×C42C2413yes—
882C2×C42C2416yes—
883C2×C42C2413yes—
884C2×C42C2413yes—
885C2×C42C2413yes—
886C2×C42C2413yes—
887C2×C42C2416yes—
888C2×C42C2413yes—
889C2×C42C2411yescharacteristic
890#95C2411yescharacteristic
891#95C2413yes—
892#95C2413yes—
893#95C2413yes—
894#95C2411yescharacteristic
895#95C2411yescharacteristic
896#95C2413yes—
897#95C2413yes—
898#95C2411yescharacteristic
899#95C2413yes—
900#95C2411yescharacteristic
901#95C2413yes—
902#95C2411yescharacteristic
903#95C2411yescharacteristic
904#95C2411yescharacteristic
905#95C2411yescharacteristic
906#95C2413yes—
907#95C2413yes—
908#95C2413yes—
909#95C2416yes—
910#95C2413yes—
911#95C2413yes—
912#95C2413yes—
913#95C2416yes—
914#95C2413yes—
915#95C2413yes—
916#95C2413yes—
917#95C2413yes—
918#95C2413yes—
919#95C2413yes—
920#95C2416yes—
921#95C2413yes—
922#95C2416yes—
923#95C2413yes—
924#95C2413yes—
925#95C2413yes—
926#95C2413yes—
927#95C2413yes—
928#95C2411yescharacteristic
929#95C2416yes—
930#95C2416yes—
931#95C2413yes—
932#95C2413yes—
933#95C2413yes—
934#95C2413yes—
935#95C2413yes—
936#95C2413yes—
937#95C2413yes—
938#95C2413yes—
939#95C2413yes—
940#95C2416yes—
941#95C2416yes—
942C24C2513yes—
943C24C2513yes—
944C24C2511yescharacteristic
945C24C2513yes—
946C24C2511yescharacteristic
947#41—448no—
948#41—448no—
949#41—448no—
950#41—416no—
951#41—416no—
952#41—416no—
953C2×Q8—232no—
954C2×Q8—26no—
955C2×Q8—26no—
956C2×Q8—26no—
957C2×Q8—26no—
958C2×Q8—26no—
959C2×Q8—26no—
960C2×Q8—22no—
961C2×Q8—22no—
962C2×Q8—41no—
963C2×Q8—43no—
964C2×Q8—43no—
965C2×Q8—46no—
966C2×Q8—46no—
967C2×Q8—46no—
968C2×Q8—448no—
969C2×Q8—416no—
970C2×Q8C2×#41112yes—
971C2×Q8C2×#4114yes—
972C2×Q8H(5,𝔽2)14yes—
973C2×Q8H(5,𝔽2)14yes—
974C2×D4—22no—
975C2×D4—26no—
976C2×D4—26no—
977C2×D4—26no—
978C2×D4—26no—
979C2×D4—26no—
980C2×D4—26no—
981C2×D4—26no—
982C2×D4—26no—
983C2×D4—26no—
984C2×D4—26no—
985C2×D4—26no—
986C2×D4—26no—
987C2×D4—26no—
988C2×D4—26no—
989C2×D4—26no—
990C2×D4—26no—
991C2×D4—43no—
992C2×D4—43no—
993C2×D4—41no—
994C2×D4—41no—
995C2×D4—43no—
996C2×D4—43no—
997C2×D4—43no—
998C2×D4—43no—
999C2×D4—43no—
1000C2×D4—43no—
1001C2×D4—43no—
1002C2×D4—43no—
1003C2×D4—43no—
1004C2×D4—43no—
1005C2×D4—43no—
1006C2×D4—43no—
1007C2×D4—43no—
1008C2×D4—43no—
1009C2×D4—43no—
1010C2×D4—43no—
1011C2×D4—43no—
1012C2×D4—43no—
1013C2×D4—46no—
1014C2×D4—46no—
1015C2×D4—46no—
1016C2×D4—46no—
1017C2×D4—46no—
1018C2×D4—46no—
1019C2×D4—46no—
1020C2×D4—46no—
1021C2×D4—46no—
1022C22×C4—26no—
1023C22×C4—26no—
1024C22×C4—26no—
1025C22×C4—26no—
1026C22×C4—212no—
1027C22×C4—26no—
1028C22×C4—26no—
1029C22×C4—26no—
1030C22×C4—26no—
1031C22×C4—26no—
1032C22×C4—26no—
1033C22×C4—26no—
1034C22×C4—26no—
1035C22×C4—26no—
1036C22×C4—26no—
1037C22×C4—22no—
1038C22×C4—22no—
1039C22×C4—26no—
1040C22×C4—41no—
1041C22×C4—46no—
1042C22×C4—46no—
1043C22×C4—43no—
1044C22×C4—43no—
1045C22×C4—43no—
1046C22×C4—43no—
1047C22×C4—43no—
1048C22×C4—43no—
1049C22×C4—43no—
1050C22×C4—43no—
1051C22×C4—46no—
1052C22×C4—46no—
1053C22×C4—46no—
1054C22×C4C2×#41112yes—
1055C22×C4C2511yescharacteristic
1056C22×C4C2513yes—
1057C22×C4C2511yescharacteristic
1058C22×C4C2511yescharacteristic
1059C22×C4C2511yescharacteristic
1060C22×C4C2513yes—
1061C22×C4C2511yescharacteristic
1062C22×C4C2513yes—
1063C22×C4C2513yes—
1064C22×C4C2513yes—
1065C22×C4C2513yes—
1066C22×C4C2513yes—
1067C22×C4C2511yescharacteristic
1068C22×C4C2513yes—
1069C22×C4C2511yescharacteristic
1070C22×C4C2511yescharacteristic
1071C22×C4C2513yes—
1072C22×C4C2513yes—
1073C22×C4C2513yes—
1074C22×C4C2511yescharacteristic
1075C22×C4C2513yes—
1076C22×C4C2511yescharacteristic
1077C22×C4C2511yescharacteristic
1078C22×C4C2511yescharacteristic
1079C22×C4C2511yescharacteristic
1080C22×C4C2513yes—
1081C4⋊C4—26no—
1082C4⋊C4—26no—
1083C4⋊C4—26no—
1084C4⋊C4—26no—
1085C4⋊C4—26no—
1086C4⋊C4—26no—
1087C4⋊C4—26no—
1088C4⋊C4—26no—
1089C4⋊C4—26no—
1090C4⋊C4—26no—
1091C4⋊C4—26no—
1092C4⋊C4—26no—
1093C4⋊C4—22no—
1094C4⋊C4—22no—
1095C4⋊C4—22no—
1096C4⋊C4—22no—
1097C4⋊C4—26no—
1098C4⋊C4—43no—
1099C4⋊C4—46no—
1100C4⋊C4—41no—
1101C4⋊C4—43no—
1102C4⋊C4—43no—
1103C4⋊C4—41no—
1104C4⋊C4—41no—
1105C4⋊C4—41no—
1106C4⋊C4—43no—
1107C4⋊C4—43no—
1108C4⋊C4—43no—
1109C4⋊C4—43no—
1110C4⋊C4—43no—
1111C4⋊C4—43no—
1112C4⋊C4—43no—
1113C4⋊C4—46no—
1114C4⋊C4—46no—
1115C4⋊C4—46no—
1116C4⋊C4—46no—
1117C4⋊C4—43no—
1118C4⋊C4—46no—
1119C4⋊C4—43no—
1120C4⋊C4—43no—
1121C4⋊C4—43no—
1122C4⋊C42−1+414yescomplemented
1123C22⋊C4—22no—
1124C22⋊C4—22no—
1125C22⋊C4—26no—
1126C22⋊C4—26no—
1127C22⋊C4—212no—
1128C22⋊C4—212no—
1129C22⋊C4—26no—
1130C22⋊C4—26no—
1131C22⋊C4—22no—
1132C22⋊C4—22no—
1133C22⋊C4—22no—
1134C22⋊C4—22no—
1135C22⋊C4—22no—
1136C22⋊C4—26no—
1137C22⋊C4—26no—
1138C22⋊C4—22no—
1139C22⋊C4—26no—
1140C22⋊C4—41no—
1141C22⋊C4—43no—
1142C22⋊C4—43no—
1143C22⋊C4—43no—
1144C22⋊C4—46no—
1145C22⋊C4—41no—
1146C22⋊C4—41no—
1147C22⋊C4—43no—
1148C22⋊C4—43no—
1149C22⋊C4—43no—
1150C22⋊C4—43no—
1151C22⋊C4—43no—
1152C22⋊C4—43no—
1153C22⋊C4—43no—
1154C22⋊C4—43no—
1155C22⋊C4—46no—
1156C22⋊C4—46no—
1157C22⋊C4—43no—
1158C22⋊C4—43no—
1159C22⋊C4—43no—
1160C22⋊C4—46no—
1161C22⋊C4—46no—
1162C22⋊C4—46no—
1163C22⋊C4—46no—
1164C22⋊C4—46no—
1165C22⋊C4—43no—
1166C22⋊C4—43no—
1167C22⋊C4—43no—
1168C22⋊C4—46no—
1169C22⋊C4—43no—
1170C22⋊C4—43no—
1171C22⋊C4—46no—
1172C22⋊C4—43no—
1173C22⋊C4—43no—
1174C22⋊C4—43no—
1175C22⋊C4—43no—
1176C22⋊C4—43no—
1177C22⋊C4—43no—
1178C22⋊C4—43no—
1179C22⋊C4—43no—
1180C22⋊C4—46no—
1181C22⋊C4—43no—
1182C42—26no—
1183C42—26no—
1184C42—26no—
1185C42—26no—
1186C42—26no—
1187C42—26no—
1188C42—26no—
1189C42—26no—
1190C42—26no—
1191C42—26no—
1192C42—22no—
1193C42—41no—
1194C42—43no—
1195C42—43no—
1196C42—43no—
1197C42—46no—
1198C42—43no—
1199C42—43no—
1200C42—43no—
1201C42—46no—
1202C23—21no—
1203C23—21no—
1204C23—21no—
1205C23—21no—
1206C23—21no—
1207C23—21no—
1208C23—23no—
1209C23—23no—
1210C23—21no—
1211C23—23no—
1212C23—23no—
1213C23—23no—
1214C23—23no—
1215C23—23no—
1216C23—21no—
1217C23—21no—
1218C23—23no—
1219C23—23no—
1220C23—21no—
1221C23—23no—
1222C23—23no—
1223C23—23no—
1224C23—23no—
1225C23—21no—
1226C23—23no—
1227C23—23no—
1228C23—21no—
1229C23—23no—
1230C23—23no—
1231C23—23no—
1232C23—23no—
1233C23—23no—
1234C23—21no—
1235C23—23no—
1236C23C22×#4112yes—
1237C23C2611yescharacteristic
1238Q8—224no—
1239Q8—44no—
1240Q8—412no—
1241Q8—412no—
1242Q8—166no—
1243Q8#538116yes—
1244D4—412no—
1245D4—44no—
1246D4—412no—
1247D4—412no—
1248D4—412no—
1249D4—412no—
1250D4—86no—
1251D4—86no—
1252D4—86no—
1253D4—86no—
1254D4—86no—
1255D4—86no—
1256D4—86no—
1257D4—166no—
1258D4—166no—
1259D4—166no—
1260C2×C4—21no—
1261C2×C4—21no—
1262C2×C4—21no—
1263C2×C4—21no—
1264C2×C4—23no—
1265C2×C4—23no—
1266C2×C4—21no—
1267C2×C4—21no—
1268C2×C4—21no—
1269C2×C4—21no—
1270C2×C4—224no—
1271C2×C4—21no—
1272C2×C4—21no—
1273C2×C4—23no—
1274C2×C4—23no—
1275C2×C4—21no—
1276C2×C4—21no—
1277C2×C4—21no—
1278C2×C4—23no—
1279C2×C4—21no—
1280C2×C4—21no—
1281C2×C4—21no—
1282C2×C4—21no—
1283C2×C4—23no—
1284C2×C4—23no—
1285C2×C4—23no—
1286C2×C4—23no—
1287C2×C4—23no—
1288C2×C4—23no—
1289C2×C4—23no—
1290C2×C4—23no—
1291C2×C4—21no—
1292C2×C4—21no—
1293C2×C4—21no—
1294C2×C4—21no—
1295C2×C4—21no—
1296C2×C4—21no—
1297C2×C4—23no—
1298C2×C4—23no—
1299C2×C4—21no—
1300C2×C4—21no—
1301C2×C4—23no—
1302C2×C4—21no—
1303C2×C4—21no—
1304C2×C4—21no—
1305C2×C4—23no—
1306C2×C4—23no—
1307C2×C4—23no—
1308C2×C4—21no—
1309C2×C4—21no—
1310C2×C4—23no—
1311C2×C4—23no—
1312C2×C4—21no—
1313C2×C4—21no—
1314C2×C4—23no—
1315C2×C4—23no—
1316C2×C4—23no—
1317C2×C4—23no—
1318C2×C4—23no—
1319C2×C4—23no—
1320C2×C4—23no—
1321C2×C4—21no—
1322C2×C4—21no—
1323C2×C4—23no—
1324C2×C4—23no—
1325C2×C4—23no—
1326C2×C4—21no—
1327C2×C4—23no—
1328C2×C4—23no—
1329C2×C4—23no—
1330C2×C4—23no—
1331C2×C4—44no—
1332C2×C4—424no—
1333C2×C4—412no—
1334C2×C4—412no—
1335C2×C4—412no—
1336C2×C4—412no—
1337C2×C4—86no—
1338C2×C4—86no—
1339C2×C4—86no—
1340C2×C4—166no—
1341C2×C4C22×#4116yes—
1342C2×C4C22×#4116yes—
1343C2×C4C2×H(5,𝔽2)16yes—
1344C2×C4C2×H(5,𝔽2)16yes—
1345C2×C4C2×2−1+412yes—
1346C2×C4C2×2−1+412yes—
1347C2×C4C2×2−1+412yes—
1348C2×C4#58512yes—
1349C22—22no—
1350C22—22no—
1351C22—22no—
1352C22—41no—
1353C22—41no—
1354C22—41no—
1355C22—41no—
1356C22—43no—
1357C22—43no—
1358C22—41no—
1359C22—43no—
1360C22—43no—
1361C22—43no—
1362C22—43no—
1363C22—41no—
1364C22—43no—
1365C22—43no—
1366C22—43no—
1367C22—41no—
1368C22—41no—
1369C22—43no—
1370C22—43no—
1371C22—43no—
1372C22—43no—
1373C22—43no—
1374C22—43no—
1375C22—41no—
1376C22—43no—
1377C22—43no—
1378C22—41no—
1379C22—43no—
1380C22—43no—
1381C22—41no—
1382C22—43no—
1383C22—43no—
1384C22C23×#4111yescharacteristic
1385C22C22×H(5,𝔽2)11yescharacteristic
1386C22C22×H(5,𝔽2)11yescharacteristic
1387C22C22×2−1+411yescharacteristic
1388C22C2×#58511yescharacteristic
1389C22H(7,𝔽2)11yescharacteristic
1390C22H(7,𝔽2)11yescharacteristic
1391C4—22no—
1392C4—22no—
1393C4—22no—
1394C4—22no—
1395C4—26no—
1396C4—41no—
1397C4—41no—
1398C4—43no—
1399C4—43no—
1400C4—41no—
1401C4—43no—
1402C4—43no—
1403C4—43no—
1404C4—43no—
1405C4—41no—
1406C4—41no—
1407C4—43no—
1408C4—41no—
1409C4—43no—
1410C4—43no—
1411C4—43no—
1412C4—41no—
1413C4—41no—
1414C4—41no—
1415C4—43no—
1416C4C2×#538112yes—
1417C2—42no—
1418C2—83no—
1419C2—83no—
1420C2—83no—
1421C2—81no—
1422C2C22×#53811yescharacteristic
1423C2#6291711yescharacteristic
1424C2#6292311yescharacteristic
1425C2#6299911yescharacteristic
1426C2#6300611yescharacteristic
1427C2#6301511yescharacteristic
1428C2#6306611yescharacteristic
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. #52277C2semidirect
2. #42989C2semidirect
3. #42923C2semidirect
4. #42894C2semidirect
5. #42874C2semidirect
6. #42872C2semidirect
7. #42838C2semidirect
8. #40125C2semidirect
9. #40122C2semidirect
10. #40030C2semidirect
11. #40007C2semidirect
12. #39666C2semidirect
13. #39242C2semidirect
14. #37346C2semidirect
15. #37343C2semidirect
16. #37316C2semidirect
17. #36576C2semidirect
18. Q8×#126C2semidirect
19. Q8×C22⋊Q8C2semidirect
20. #36457C2semidirect
21. #36455C2semidirect
22. #36432C2semidirect
23. #36005C2semidirect
24. #35948C2semidirect
25. #35898C2semidirect
26. #35831C2semidirect
27. #35757C2semidirect
28. #35757C2semidirect
29. #34312C2semidirect
30. #34293C2semidirect
31. #34257C2semidirect
1122. C4⋊C42−1+4semidirect

Maximal subgroups

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

subgroupindex
#522772
#429892
#429232
#428942
#428742
#428722
#428382
#401252
#401222
#400302
#400072
#396662
#392422
#373462
#373432
#373162
#365762
Q8×#1262
Q8×C22⋊Q82
#364572
#364552
#364322
#360052
#359482
#358982
#358312
#357572
#343122
#342932
#342572