Finite Group Databasebeta

← #7658294

Subgroups — #7658294

Order 512.

5498 conjugacy classes of subgroups.

The subgroup lattice has 1413 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42895C213yesmaximal, complemented
2#42892C213yesmaximal, complemented
3#42872C213yesmaximal, complemented
4#42843C213yesmaximal, complemented
5#42839C213yesmaximal, complemented
6#42838C213yesmaximal, complemented
7#42831C213yesmaximal, complemented
8#42829C213yesmaximal, complemented
9#42518C213yesmaximal, complemented
10#42504C213yesmaximal, complemented
11#42448C213yesmaximal, complemented
12#42447C213yesmaximal, complemented
13#37515C213yesmaximal, complemented
14#37501C213yesmaximal, complemented
15#37498C213yesmaximal, complemented
16#36670C213yesmaximal, complemented
17#36049C211yesmaximal, characteristic, complemented
18#36029C211yesmaximal, characteristic, complemented
19#36018C211yesmaximal, characteristic, complemented
20#36005C211yesmaximal, characteristic, complemented
21#35996C211yesmaximal, characteristic, complemented
22#35898C211yesmaximal, characteristic, complemented
23#35883C211yesmaximal, characteristic, complemented
24#35854C211yesmaximal, characteristic, complemented
25#35831C211yesmaximal, characteristic, complemented
26#35786C211yesmaximal, characteristic, complemented
27#35757C211yesmaximal, characteristic, complemented
28#35757C211yesmaximal, characteristic, complemented
29#34294C211yesmaximal, characteristic, complemented
30#34294C211yesmaximal, characteristic, complemented
31#34257C211yesmaximal, characteristic, complemented
32C22×2−1+4C2211yescharacteristic
33C2×#557C2211yescharacteristic
34C2×#550C2211yescharacteristic
35C2×#550C2211yescharacteristic
36C2×#550C2211yescharacteristic
37C2×#548C2211yescharacteristic
38C2×#548C2211yescharacteristic
39C2×#548C2211yescharacteristic
40C2×#548C2211yescharacteristic
41C2×#520C2211yescharacteristic
42C2×#520C2211yescharacteristic
43C2×#519C2211yescharacteristic
44C22×C4×Q8C2211yescharacteristic
45#2833C2213yes—
46#2832C2213yes—
47#2831C2213yes—
48#2831C2213yes—
49#2830C2213yes—
50#2829C2213yes—
51#2829C2213yes—
52#2828C2213yes—
53#2827C2213yes—
54#2827C2211yescharacteristic
55#2826C2213yes—
56#2826C2213yes—
57#2825C2213yes—
58#2825C2213yes—
59#2825C2216yes—
60#2824C2213yes—
61#2824C2213yes—
62#2804C2216yes—
63#2803C2216yes—
64#2788C2216yes—
65#2780C2216yes—
66#2778C2216yes—
67#2775C2216yes—
68#2768C2216yes—
69#2756C2216yes—
70#2751C2216yes—
71#2714C2216yes—
72#2710C2216yes—
73#2708C2216yes—
74#2708C2216yes—
75#2695C2216yes—
76#2686C2216yes—
77#2682C2216yes—
78#2661C2216yes—
79#2661C2216yes—
80#2653C2216yes—
81#2653C2216yes—
82#2653C2216yes—
83#2649C2216yes—
84#2648C2216yes—
85#2648C2216yes—
86#2645C2213yes—
87#2644C2213yes—
88#2641C2213yes—
89#2640C2213yes—
90#2636C2216yes—
91#2635C2216yes—
92#2631C2216yes—
93#2630C2216yes—
94#2629C2213yes—
95#2625C2213yes—
96#2624C2213yes—
97#2620C2213yes—
98#2619C2213yes—
99#2619C2213yes—
100#2615C2213yes—
101#2615C2213yes—
102#2592C2213yes—
103#2582C2213yes—
104#2578C2216yes—
105#2576C2216yes—
106#2565C2213yes—
107#2563C2213yes—
108#2562C2213yes—
109#2559C2216yes—
110#2557C2216yes—
111#2548C2213yes—
112#2548C2213yes—
113#2544C2213yes—
114#2541C2213yes—
115#2537C2213yes—
116#2536C2213yes—
117#2535C2213yes—
118#2514C2213yes—
119#2514C2213yes—
120#2513C2213yes—
121#2512C2213yes—
122#2512C2213yes—
123#2511C2213yes—
124#2502C2213yes—
125#2501C2213yes—
126#2497C2213yes—
127#2497C2213yes—
128#2496C2213yes—
129#2495C2213yes—
130#2494C2213yes—
131#2494C2213yes—
132#2491C2213yes—
133#2491C2213yes—
134#2490C2213yes—
135#2490C2213yes—
136#2490C2213yes—
137#2490C2213yes—
138#2489C2213yes—
139#2489C2213yes—
140#2487C2213yes—
141#2486C2213yes—
142#2456C2216yes—
143#2456C2216yes—
144#2453C2213yes—
145#2451C2213yes—
146#2447C2213yes—
147#2447C2213yes—
148#2445C2213yes—
149#2445C2213yes—
150#2441C2213yes—
151#2439C2213yes—
152#2436C2213yes—
153#2436C2213yes—
154#2431C2213yes—
155#2431C2213yes—
156#2431C2213yes—
157#2431C2213yes—
158#2428C2213yes—
159#2428C2213yes—
160#2428C2213yes—
161#2427C2213yes—
162#2426C2213yes—
163#2426C2213yes—
164#2422C2213yes—
165#2422C2213yes—
166#2422C2213yes—
167#2422C2213yes—
168#2417C2213yes—
169#2416C2213yes—
170#2416C2213yes—
171#2416C2213yes—
172#2414C2213yes—
173#2414C2213yes—
174#2409C2213yes—
175#2409C2213yes—
176#2407C2213yes—
177#2407C2213yes—
178#2407C2213yes—
179#2407C2213yes—
180#2401C2213yes—
181#2401C2213yes—
182#2398C2213yes—
183#2398C2213yes—
184#2396C2213yes—
185#2395C2213yes—
186#2395C2213yes—
187#2392C2213yes—
188#2392C2213yes—
189#2392C2213yes—
190#2388C2213yes—
191#2388C2213yes—
192#2367C2213yes—
193#2367C2213yes—
194#2361C2213yes—
195#2361C2213yes—
196#2360C2213yes—
197#2360C2213yes—
198#2351C2211yescharacteristic
199#2351C2211yescharacteristic
200Q8×C4⋊C4C2211yescharacteristic
201Q8×C4⋊C4C2211yescharacteristic
202Q8×C4⋊C4C2211yescharacteristic
203Q8×C4⋊C4C2211yescharacteristic
204D4×C4⋊C4C2213yes—
205D4×C4⋊C4C2213yes—
206#2341C2211yescharacteristic
207#2341C2211yescharacteristic
208#2341C2211yescharacteristic
209#2341C2211yescharacteristic
210#2341C2211yescharacteristic
211#2341C2213yes—
212#2341C2213yes—
213#2341C2211yescharacteristic
214#2341C2211yescharacteristic
215#2341C2211yescharacteristic
216Q8×C22⋊C4C2211yescharacteristic
217Q8×C22⋊C4C2211yescharacteristic
218Q8×C22⋊C4C2211yescharacteristic
219Q8×C22⋊C4C2211yescharacteristic
220Q8×C22⋊C4C2213yes—
221Q8×C22⋊C4C2213yes—
222Q8×C22⋊C4C2211yescharacteristic
223Q8×C22⋊C4C2211yescharacteristic
224#2326C2213yes—
225#2326C2213yes—
226#2323C2213yes—
227#2323C2213yes—
228#2311C2213yes—
229#2311C2213yes—
230C4×#121C2213yes—
231C4×#121C2213yes—
232#2297C2213yes—
233#2297C2213yes—
234#2290C2213yes—
235#2290C2213yes—
236#2276C2211yescharacteristic
237#2276C2211yescharacteristic
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—
250#557—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×#127C2313yes—
260C2×#127C2313yes—
261C2×#127C2313yes—
262C2×#126C2316yes—
263C2×#125C2313yes—
264C2×#125C2313yes—
265C2×#124C2313yes—
266C2×#124C2313yes—
267C2×#124C2313yes—
268C2×#124C2313yes—
269C2×#124C2316yes—
270C2×#123C2316yes—
271C2×#123C2316yes—
272C2×#123C2316yes—
273C2×C22⋊Q8C2313yes—
274C2×C22⋊Q8C2313yes—
275C2×C22⋊Q8C2313yes—
276C2×C22⋊Q8C2313yes—
277C2×#121C2313yes—
278C2×#121C2313yes—
279C2×#121C2313yes—
280C2×#121C2313yes—
281C2×#121C2313yes—
282C2×#121C2313yes—
283C2×#121C2313yes—
284C2×#121C2313yes—
285C2×#121C2313yes—
286C2×#121C2313yes—
287C2×#121C2316yes—
288C2×#121C2316yes—
289C2×#121C2316yes—
290#520—44no—
291#520—44no—
292#519—44no—
293C2×C4×Q8—44no—
294C2×C4×Q8C2311yescharacteristic
295C2×C4×Q8C2311yescharacteristic
296C2×C4×Q8C2311yescharacteristic
297C2×C4×Q8C2311yescharacteristic
298C2×C4×Q8C2311yescharacteristic
299C2×C4×Q8C2311yescharacteristic
300C2×C4×Q8C2311yescharacteristic
301C2×C4×Q8C2311yescharacteristic
302C2×C4×Q8C2311yescharacteristic
303C2×C4×Q8C2311yescharacteristic
304C2×C4×Q8C2313yes—
305C2×C4×Q8C2313yes—
306C2×C4×Q8C2313yes—
307C2×C4×Q8C2313yes—
308C2×C4×Q8C2313yes—
309C2×C4×D4C2313yes—
310C2×C4×D4C2313yes—
311C2×C4×D4C2313yes—
312C2×C4×D4C2313yes—
313C2×C4×D4C2313yes—
314C2×C4×D4C2313yes—
315C2×C4×D4C2313yes—
316C2×C4×D4C2313yes—
317C2×C4×D4C2313yes—
318C2×C4×D4C2313yes—
319C2×C4×D4C2313yes—
320C2×C4×D4C2316yes—
321C2×C4×D4C2316yes—
322C2×#117C2313yes—
323C2×#117C2313yes—
324C2×#117C2313yes—
325C2×#117C2313yes—
326C22×C4⋊C4C2313yes—
327C22×C4⋊C4C2313yes—
328C22×C4⋊C4C2313yes—
329C22×C42C2313yes—
330#401C2316yes—
331#401C2313yes—
332#401C2313yes—
333#400C2313yes—
334#400C2313yes—
335#400C2313yes—
336#400C2313yes—
337#400C2313yes—
338#400C2313yes—
339#400C2313yes—
340#400C2313yes—
341#400C2311yescharacteristic
342#400C2313yes—
343#400C2311yescharacteristic
344#400C2313yes—
345#400C2313yes—
346#400C2316yes—
347#400C2316yes—
348#399C2313yes—
349#399C2311yescharacteristic
350#399C2313yes—
351#399C2316yes—
352#398C2313yes—
353#398C2316yes—
354#398C2311yescharacteristic
355#398C2313yes—
356#398C2311yescharacteristic
357#398C2313yes—
358#398C2313yes—
359#398C2313yes—
360#398C2316yes—
361#398C2316yes—
362#397C2313yes—
363#397C2313yes—
364#397C2313yes—
365#397C2313yes—
366#397C2313yes—
367#397C2313yes—
368#397C2313yes—
369#397C2313yes—
370#397C2313yes—
371#397C2313yes—
372#397C2316yes—
373#397C2316yes—
374#397C2316yes—
375#397C2313yes—
376#397C2313yes—
377#397C2313yes—
378#397C2313yes—
379#397C2311yescharacteristic
380#397C2311yescharacteristic
381#397C2313yes—
382#397C2311yescharacteristic
383#397C2313yes—
384#397C2316yes—
385#397C2316yes—
386#397C2316yes—
387#396C2311yescharacteristic
388#396C2313yes—
389#396C2316yes—
390#396C2313yes—
391#396C2313yes—
392#396C2313yes—
393#396C2313yes—
394#396C2311yescharacteristic
395#396C2313yes—
396#396C2313yes—
397#396C2313yes—
398#396C2316yes—
399#396C2316yes—
400#395C2313yes—
401#395C2313yes—
402#395C2313yes—
403#394C2316yes—
404#394C2311yescharacteristic
405#394C2313yes—
406#394C2313yes—
407#394C2313yes—
408#394C2313yes—
409#394C2313yes—
410#394C2313yes—
411#394C2313yes—
412#394C2313yes—
413#394C2313yes—
414#394C2313yes—
415#394C2313yes—
416#394C2316yes—
417#394C2313yes—
418#394C2313yes—
419#394C2316yes—
420#394C2316yes—
421#394C2311yescharacteristic
422#394C2313yes—
423#394C2313yes—
424#394C2313yes—
425#394C2313yes—
426#394C2313yes—
427#394C2313yes—
428#394C2313yes—
429#394C2313yes—
430#394C2316yes—
431#394C2316yes—
432#394C2316yes—
433#394C2316yes—
434#394C2316yes—
435#394C2316yes—
436#393C2313yes—
437#393C2316yes—
438#393C2313yes—
439#393C2313yes—
440#393C2313yes—
441#393C2313yes—
442#393C2313yes—
443#393C2313yes—
444#393C2316yes—
445#393C2316yes—
446#392C2313yes—
447#392C2313yes—
448#392C2313yes—
449#392C2313yes—
450#392C2313yes—
451#392C2313yes—
452#392C2313yes—
453#392C2316yes—
454#392C2316yes—
455#392C2316yes—
456#392C2316yes—
457#392C2313yes—
458#392C2313yes—
459#392C2316yes—
460#392C2316yes—
461#392C2316yes—
462#391C2313yes—
463#391C2313yes—
464#391C2313yes—
465#391C2313yes—
466#391C2316yes—
467#391C2313yes—
468#391C2313yes—
469#391C2313yes—
470#391C2313yes—
471#391C2316yes—
472#391C2313yes—
473#391C2313yes—
474#391C2313yes—
475#391C2313yes—
476#391C2313yes—
477#391C2313yes—
478#390C2316yes—
479#390C2313yes—
480#390C2316yes—
481#390C2313yes—
482#390C2313yes—
483#390C2313yes—
484#390C2313yes—
485#390C2313yes—
486#390C2313yes—
487#390C2313yes—
488#390C2313yes—
489#390C2313yes—
490#390C2313yes—
491#390C2313yes—
492#390C2313yes—
493#390C2313yes—
494#390C2313yes—
495#390C2313yes—
496#390C2313yes—
497#390C2313yes—
498#390C2316yes—
499#390C2316yes—
500#390C2316yes—
501#389C2316yes—
502#389C2316yes—
503#389C2313yes—
504#389C2313yes—
505#389C2313yes—
506#389C2313yes—
507#389C2316yes—
508#389C2313yes—
509#389C2313yes—
510#389C2313yes—
511#389C2313yes—
512#389C2313yes—
513#389C2313yes—
514#389C2313yes—
515#389C2313yes—
516#388C2316yes—
517#388C2316yes—
518#388C2313yes—
519#388C2313yes—
520#388C2313yes—
521#388C2313yes—
522#388C2316yes—
523#388C2316yes—
524#388C2316yes—
525#388C2316yes—
526#388C2316yes—
527#388C2316yes—
528#388C2316yes—
529#388C2316yes—
530#388C2316yes—
531#388C2316yes—
532#388C2316yes—
533#387C2316yes—
534#387C2316yes—
535#387C2313yes—
536#387C2313yes—
537#387C2313yes—
538#387C2313yes—
539#387C2316yes—
540#387C2316yes—
541#387C2316yes—
542#386C2313yes—
543#386C2313yes—
544#386C2316yes—
545#386C2313yes—
546#386C2313yes—
547#386C2313yes—
548#386C2313yes—
549#386C2311yescharacteristic
550#386C2313yes—
551#386C2316yes—
552#386C2316yes—
553#386C2316yes—
554#386C2316yes—
555#386C2316yes—
556#386C2316yes—
557#386C2316yes—
558#386C2316yes—
559#386C2316yes—
560#386C2316yes—
561#386C2316yes—
562#385C2311yescharacteristic
563#385C2313yes—
564#385C2311yescharacteristic
565#385C2313yes—
566#385C2316yes—
567#385C2316yes—
568#385C2316yes—
569#385C2316yes—
570#385C2316yes—
571#385C2316yes—
572#385C2316yes—
573#385C2316yes—
574#385C2316yes—
575#384C2313yes—
576#384C2313yes—
577#384C2313yes—
578#384C2313yes—
579#383C2316yes—
580#382C2316yes—
581#382C2313yes—
582#382C2313yes—
583#381C2316yes—
584#380C2313yes—
585#380C2313yes—
586#380C2313yes—
587#380C2313yes—
588#380C2313yes—
589#380C2313yes—
590#380C2313yes—
591#380C2313yes—
592#380C2313yes—
593#380C2313yes—
594#380C2316yes—
595#380C2316yes—
596#380C2316yes—
597#380C2313yes—
598#380C2313yes—
599#380C2313yes—
600#380C2313yes—
601C4×C4⋊C4C2313yes—
602C4×C4⋊C4C2313yes—
603C4×C4⋊C4C2313yes—
604C4×C4⋊C4C2313yes—
605C4×C4⋊C4C2313yes—
606C4×C4⋊C4C2313yes—
607C4×C4⋊C4C2313yes—
608C4×C4⋊C4C2313yes—
609C4×C4⋊C4C2313yes—
610C4×C4⋊C4C2313yes—
611C4×C4⋊C4C2313yes—
612C4×C4⋊C4C2313yes—
613C4×C22⋊C4C2316yes—
614C4×C22⋊C4C2316yes—
615C4×C22⋊C4C2316yes—
616C4×C22⋊C4C2316yes—
617C4×C22⋊C4C2313yes—
618C4×C22⋊C4C2313yes—
619C4×C22⋊C4C2313yes—
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—
632#376C2313yes—
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×Q8C2413yes—
663C22×Q8C2413yes—
664C22×Q8C2413yes—
665C22×Q8C2411yescharacteristic
666C22×D4C2413yes—
667C22×D4C2413yes—
668C22×D4C2413yes—
669C22×D4C2413yes—
670C22×D4C2413yes—
671C22×D4C2411yescharacteristic
672C22×D4C2413yes—
673C22×D4C2413yes—
674C22×D4C2413yes—
675C22×D4C2413yes—
676C22×D4C2413yes—
677C22×D4C2413yes—
678C22×D4C2413yes—
679C22×D4C2416yes—
680C22×D4C2416yes—
681C22×D4C2416yes—
682C23×C4C2413yes—
683C23×C4C2413yes—
684C23×C4C2413yes—
685C23×C4C2413yes—
686C23×C4C2413yes—
687C23×C4C2416yes—
688C23×C4C2413yes—
689C23×C4C2416yes—
690C23×C4C2416yes—
691C23×C4C2411yescharacteristic
692C4⋊Q8—46no—
693#127—46no—
694#127—46no—
695#127—46no—
696#126—86no—
697#125—46no—
698#125—46no—
699#124—212no—
700#124—212no—
701#124—46no—
702#124—46no—
703#124—86no—
704#123—86no—
705#123—86no—
706#123—86no—
707C22⋊Q8—212no—
708C22⋊Q8—212no—
709C22⋊Q8—46no—
710C22⋊Q8—46no—
711#121—212no—
712#121—212no—
713#121—46no—
714#121—46no—
715#121—46no—
716#121—46no—
717#121—46no—
718#121—46no—
719#121—46no—
720#121—46no—
721#121—86no—
722#121—86no—
723#121—86no—
724C4×Q8—24no—
725C4×Q8—24no—
726C4×Q8—24no—
727C4×Q8—24no—
728C4×Q8—24no—
729C4×Q8—24no—
730C4×Q8—24no—
731C4×Q8—24no—
732C4×Q8—24no—
733C4×Q8—24no—
734C4×Q8—46no—
735C4×Q8—46no—
736C4×Q8—46no—
737C4×Q8—46no—
738C4×Q8—46no—
739C4×D4—212no—
740C4×D4—212no—
741C4×D4—46no—
742C4×D4—46no—
743C4×D4—46no—
744C4×D4—46no—
745C4×D4—46no—
746C4×D4—46no—
747C4×D4—46no—
748C4×D4—46no—
749C4×D4—46no—
750C4×D4—86no—
751C4×D4—86no—
752#117—46no—
753#117—46no—
754#117—46no—
755#117—46no—
756C2×C4⋊C4—46no—
757C2×C4⋊C4—46no—
758C2×C4⋊C4—46no—
759C2×C4⋊C4C2413yes—
760C2×C4⋊C4C2413yes—
761C2×C4⋊C4C2413yes—
762C2×C4⋊C4C2413yes—
763C2×C4⋊C4C2413yes—
764C2×C4⋊C4C2413yes—
765C2×C4⋊C4C2413yes—
766C2×C4⋊C4C2413yes—
767C2×C4⋊C4C2413yes—
768C2×C4⋊C4C2413yes—
769C2×C4⋊C4C2413yes—
770C2×C4⋊C4C2413yes—
771C2×C4⋊C4C2413yes—
772C2×C4⋊C4C2413yes—
773C2×C4⋊C4C2416yes—
774C2×C4⋊C4C2411yescharacteristic
775C2×C4⋊C4C2411yescharacteristic
776C2×C4⋊C4C2413yes—
777C2×C4⋊C4C2413yes—
778C2×C4⋊C4C2411yescharacteristic
779C2×C4⋊C4C2411yescharacteristic
780C2×C4⋊C4C2411yescharacteristic
781C2×C4⋊C4C2413yes—
782C2×C4⋊C4C2413yes—
783C2×C4⋊C4C2416yes—
784C2×C4⋊C4C2416yes—
785C2×C4⋊C4C2411yescharacteristic
786C2×C4⋊C4C2413yes—
787C2×C4⋊C4C2413yes—
788C2×C4⋊C4C2413yes—
789C2×C4⋊C4C2413yes—
790C2×C4⋊C4C2416yes—
791C2×C4⋊C4C2413yes—
792C2×C4⋊C4C2413yes—
793C2×C4⋊C4C2416yes—
794C2×C4⋊C4C2416yes—
795C2×C4⋊C4C2413yes—
796C2×C4⋊C4C2413yes—
797C2×C4⋊C4C2411yescharacteristic
798C2×C4⋊C4C2411yescharacteristic
799C2×C4⋊C4C2411yescharacteristic
800C2×C4⋊C4C2411yescharacteristic
801C2×C4⋊C4C2413yes—
802C2×C4⋊C4C2413yes—
803C2×C22⋊C4C2411yescharacteristic
804C2×C22⋊C4C2411yescharacteristic
805C2×C22⋊C4C2413yes—
806C2×C22⋊C4C2413yes—
807C2×C22⋊C4C2416yes—
808C2×C22⋊C4C2416yes—
809C2×C22⋊C4C2411yescharacteristic
810C2×C22⋊C4C2413yes—
811C2×C22⋊C4C2413yes—
812C2×C22⋊C4C2413yes—
813C2×C22⋊C4C2413yes—
814C2×C22⋊C4C2413yes—
815C2×C22⋊C4C2411yescharacteristic
816C2×C22⋊C4C2411yescharacteristic
817C2×C22⋊C4C2413yes—
818C2×C22⋊C4C2413yes—
819C2×C22⋊C4C2413yes—
820C2×C22⋊C4C2413yes—
821C2×C22⋊C4C2413yes—
822C2×C22⋊C4C2413yes—
823C2×C22⋊C4C2413yes—
824C2×C22⋊C4C2413yes—
825C2×C22⋊C4C2416yes—
826C2×C22⋊C4C2416yes—
827C2×C22⋊C4C2413yes—
828C2×C22⋊C4C2413yes—
829C2×C22⋊C4C2413yes—
830C2×C22⋊C4C2413yes—
831C2×C22⋊C4C2413yes—
832C2×C22⋊C4C2416yes—
833C2×C22⋊C4C2416yes—
834C2×C22⋊C4C2416yes—
835C2×C22⋊C4C2413yes—
836C2×C22⋊C4C2413yes—
837C2×C22⋊C4C2413yes—
838C2×C22⋊C4C2413yes—
839C2×C22⋊C4C2413yes—
840C2×C22⋊C4C2413yes—
841C2×C22⋊C4C2416yes—
842C2×C22⋊C4C2416yes—
843C2×C22⋊C4C2416yes—
844C2×C22⋊C4C2413yes—
845C2×C22⋊C4C2413yes—
846C2×C22⋊C4C2413yes—
847C2×C22⋊C4C2411yescharacteristic
848C2×C22⋊C4C2411yescharacteristic
849C2×C22⋊C4C2413yes—
850C2×C22⋊C4C2413yes—
851C2×C22⋊C4C2411yescharacteristic
852C2×C22⋊C4C2413yes—
853C2×C22⋊C4C2413yes—
854C2×C22⋊C4C2411yescharacteristic
855C2×C22⋊C4C2411yescharacteristic
856C2×C22⋊C4C2411yescharacteristic
857C2×C22⋊C4C2413yes—
858C2×C22⋊C4C2413yes—
859C2×C22⋊C4C2413yes—
860C2×C22⋊C4C2413yes—
861C2×C22⋊C4C2416yes—
862C2×C22⋊C4C2416yes—
863C2×C42—46no—
864C2×C42C2413yes—
865C2×C42C2413yes—
866C2×C42C2413yes—
867C2×C42C2413yes—
868C2×C42C2413yes—
869C2×C42C2413yes—
870C2×C42C2413yes—
871C2×C42C2413yes—
872C2×C42C2413yes—
873C2×C42C2413yes—
874C2×C42C2416yes—
875C2×C42C2416yes—
876C2×C42C2416yes—
877C2×C42C2413yes—
878C2×C42C2413yes—
879#95C2411yescharacteristic
880#95C2411yescharacteristic
881#95C2413yes—
882#95C2413yes—
883#95C2413yes—
884#95C2413yes—
885#95C2413yes—
886#95C2413yes—
887#95C2411yescharacteristic
888#95C2411yescharacteristic
889#95C2413yes—
890#95C2411yescharacteristic
891#95C2413yes—
892#95C2411yescharacteristic
893#95C2411yescharacteristic
894#95C2411yescharacteristic
895#95C2411yescharacteristic
896#95C2411yescharacteristic
897#95C2413yes—
898#95C2413yes—
899#95C2413yes—
900#95C2416yes—
901#95C2416yes—
902#95C2413yes—
903#95C2413yes—
904#95C2413yes—
905#95C2413yes—
906#95C2413yes—
907#95C2413yes—
908#95C2413yes—
909#95C2413yes—
910#95C2413yes—
911#95C2416yes—
912#95C2416yes—
913#95C2413yes—
914#95C2413yes—
915#95C2413yes—
916#95C2413yes—
917#95C2413yes—
918#95C2413yes—
919#95C2413yes—
920#95C2413yes—
921#95C2411yescharacteristic
922#95C2411yescharacteristic
923#95C2413yes—
924#95C2413yes—
925#95C2413yes—
926#95C2413yes—
927#95C2413yes—
928#95C2413yes—
929#95C2413yes—
930#95C2413yes—
931#95C2416yes—
932#95C2416yes—
933#95C2416yes—
934#95C2416yes—
935C24C2513yes—
936C24C2513yes—
937C24C2511yescharacteristic
938C24C2513yes—
939C24C2511yescharacteristic
940#41—448no—
941#41—448no—
942#41—448no—
943#41—416no—
944#41—416no—
945#41—416no—
946C2×Q8—232no—
947C2×Q8—26no—
948C2×Q8—26no—
949C2×Q8—26no—
950C2×Q8—26no—
951C2×Q8—26no—
952C2×Q8—26no—
953C2×Q8—43no—
954C2×Q8—43no—
955C2×Q8—43no—
956C2×Q8—43no—
957C2×Q8—43no—
958C2×Q8—448no—
959C2×Q8—416no—
960C2×Q8C2×#41112yes—
961C2×Q8C2×#4114yes—
962C2×Q8H(5,𝔽2)14yes—
963C2×Q8H(5,𝔽2)14yes—
964C2×D4—26no—
965C2×D4—26no—
966C2×D4—22no—
967C2×D4—26no—
968C2×D4—26no—
969C2×D4—26no—
970C2×D4—26no—
971C2×D4—26no—
972C2×D4—26no—
973C2×D4—26no—
974C2×D4—26no—
975C2×D4—26no—
976C2×D4—26no—
977C2×D4—26no—
978C2×D4—43no—
979C2×D4—43no—
980C2×D4—43no—
981C2×D4—43no—
982C2×D4—43no—
983C2×D4—43no—
984C2×D4—41no—
985C2×D4—41no—
986C2×D4—43no—
987C2×D4—43no—
988C2×D4—43no—
989C2×D4—43no—
990C2×D4—43no—
991C2×D4—43no—
992C2×D4—43no—
993C2×D4—43no—
994C2×D4—43no—
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—46no—
1004C2×D4—46no—
1005C2×D4—46no—
1006C2×D4—46no—
1007C2×D4—46no—
1008C2×D4—46no—
1009C2×D4—46no—
1010C2×D4—46no—
1011C2×D4—46no—
1012C22×C4—26no—
1013C22×C4—26no—
1014C22×C4—26no—
1015C22×C4—26no—
1016C22×C4—212no—
1017C22×C4—26no—
1018C22×C4—26no—
1019C22×C4—26no—
1020C22×C4—26no—
1021C22×C4—26no—
1022C22×C4—26no—
1023C22×C4—26no—
1024C22×C4—26no—
1025C22×C4—26no—
1026C22×C4—26no—
1027C22×C4—41no—
1028C22×C4—41no—
1029C22×C4—41no—
1030C22×C4—46no—
1031C22×C4—46no—
1032C22×C4—43no—
1033C22×C4—43no—
1034C22×C4—43no—
1035C22×C4—46no—
1036C22×C4—46no—
1037C22×C4—46no—
1038C22×C4—46no—
1039C22×C4—46no—
1040C22×C4—46no—
1041C22×C4C2×#41112yes—
1042C22×C4C2511yescharacteristic
1043C22×C4C2511yescharacteristic
1044C22×C4C2513yes—
1045C22×C4C2511yescharacteristic
1046C22×C4C2511yescharacteristic
1047C22×C4C2511yescharacteristic
1048C22×C4C2513yes—
1049C22×C4C2513yes—
1050C22×C4C2513yes—
1051C22×C4C2511yescharacteristic
1052C22×C4C2511yescharacteristic
1053C22×C4C2511yescharacteristic
1054C22×C4C2511yescharacteristic
1055C22×C4C2511yescharacteristic
1056C22×C4C2513yes—
1057C22×C4C2513yes—
1058C22×C4C2513yes—
1059C22×C4C2513yes—
1060C22×C4C2513yes—
1061C22×C4C2513yes—
1062C22×C4C2513yes—
1063C22×C4C2511yescharacteristic
1064C22×C4C2511yescharacteristic
1065C22×C4C2511yescharacteristic
1066C22×C4C2513yes—
1067C22×C4C2513yes—
1068C4⋊C4—26no—
1069C4⋊C4—26no—
1070C4⋊C4—26no—
1071C4⋊C4—26no—
1072C4⋊C4—26no—
1073C4⋊C4—26no—
1074C4⋊C4—26no—
1075C4⋊C4—26no—
1076C4⋊C4—26no—
1077C4⋊C4—26no—
1078C4⋊C4—26no—
1079C4⋊C4—26no—
1080C4⋊C4—43no—
1081C4⋊C4—43no—
1082C4⋊C4—46no—
1083C4⋊C4—41no—
1084C4⋊C4—41no—
1085C4⋊C4—41no—
1086C4⋊C4—41no—
1087C4⋊C4—43no—
1088C4⋊C4—43no—
1089C4⋊C4—41no—
1090C4⋊C4—41no—
1091C4⋊C4—43no—
1092C4⋊C4—43no—
1093C4⋊C4—41no—
1094C4⋊C4—41no—
1095C4⋊C4—41no—
1096C4⋊C4—43no—
1097C4⋊C4—43no—
1098C4⋊C4—46no—
1099C4⋊C4—46no—
1100C4⋊C4—41no—
1101C4⋊C4—43no—
1102C4⋊C4—43no—
1103C4⋊C4—43no—
1104C4⋊C4—43no—
1105C4⋊C4—46no—
1106C4⋊C4—43no—
1107C4⋊C4—43no—
1108C4⋊C4—46no—
1109C4⋊C4—46no—
1110C4⋊C4—43no—
1111C4⋊C4—43no—
1112C22⋊C4—22no—
1113C22⋊C4—22no—
1114C22⋊C4—26no—
1115C22⋊C4—26no—
1116C22⋊C4—212no—
1117C22⋊C4—212no—
1118C22⋊C4—41no—
1119C22⋊C4—43no—
1120C22⋊C4—43no—
1121C22⋊C4—41no—
1122C22⋊C4—43no—
1123C22⋊C4—43no—
1124C22⋊C4—41no—
1125C22⋊C4—46no—
1126C22⋊C4—43no—
1127C22⋊C4—43no—
1128C22⋊C4—43no—
1129C22⋊C4—43no—
1130C22⋊C4—46no—
1131C22⋊C4—41no—
1132C22⋊C4—41no—
1133C22⋊C4—41no—
1134C22⋊C4—41no—
1135C22⋊C4—43no—
1136C22⋊C4—43no—
1137C22⋊C4—43no—
1138C22⋊C4—43no—
1139C22⋊C4—43no—
1140C22⋊C4—41no—
1141C22⋊C4—41no—
1142C22⋊C4—43no—
1143C22⋊C4—43no—
1144C22⋊C4—43no—
1145C22⋊C4—43no—
1146C22⋊C4—43no—
1147C22⋊C4—43no—
1148C22⋊C4—43no—
1149C22⋊C4—43no—
1150C22⋊C4—43no—
1151C22⋊C4—43no—
1152C22⋊C4—46no—
1153C22⋊C4—46no—
1154C22⋊C4—46no—
1155C22⋊C4—46no—
1156C22⋊C4—43no—
1157C22⋊C4—43no—
1158C22⋊C4—43no—
1159C22⋊C4—46no—
1160C22⋊C4—43no—
1161C22⋊C4—43no—
1162C22⋊C4—43no—
1163C22⋊C4—43no—
1164C22⋊C4—43no—
1165C22⋊C4—43no—
1166C22⋊C4—46no—
1167C22⋊C4—46no—
1168C22⋊C4—46no—
1169C22⋊C4—43no—
1170C22⋊C4—43no—
1171C22⋊C4—43no—
1172C42—26no—
1173C42—26no—
1174C42—26no—
1175C42—26no—
1176C42—26no—
1177C42—26no—
1178C42—26no—
1179C42—26no—
1180C42—26no—
1181C42—26no—
1182C42—43no—
1183C42—43no—
1184C42—46no—
1185C42—46no—
1186C42—46no—
1187C23—21no—
1188C23—21no—
1189C23—21no—
1190C23—21no—
1191C23—21no—
1192C23—21no—
1193C23—23no—
1194C23—23no—
1195C23—23no—
1196C23—21no—
1197C23—23no—
1198C23—23no—
1199C23—23no—
1200C23—23no—
1201C23—21no—
1202C23—21no—
1203C23—23no—
1204C23—23no—
1205C23—23no—
1206C23—21no—
1207C23—23no—
1208C23—23no—
1209C23—23no—
1210C23—21no—
1211C23—23no—
1212C23—23no—
1213C23—21no—
1214C23—23no—
1215C23—23no—
1216C23—23no—
1217C23—21no—
1218C23—23no—
1219C23—23no—
1220C23—23no—
1221C23C22×#4112yes—
1222C23C2611yescharacteristic
1223Q8—224no—
1224Q8—412no—
1225Q8—412no—
1226Q8—86no—
1227Q8#538116yes—
1228D4—412no—
1229D4—412no—
1230D4—412no—
1231D4—44no—
1232D4—412no—
1233D4—412no—
1234D4—412no—
1235D4—412no—
1236D4—86no—
1237D4—86no—
1238D4—86no—
1239D4—86no—
1240D4—86no—
1241D4—166no—
1242D4—166no—
1243D4—166no—
1244C2×C4—23no—
1245C2×C4—23no—
1246C2×C4—224no—
1247C2×C4—21no—
1248C2×C4—21no—
1249C2×C4—23no—
1250C2×C4—23no—
1251C2×C4—21no—
1252C2×C4—21no—
1253C2×C4—21no—
1254C2×C4—23no—
1255C2×C4—21no—
1256C2×C4—21no—
1257C2×C4—21no—
1258C2×C4—21no—
1259C2×C4—21no—
1260C2×C4—21no—
1261C2×C4—21no—
1262C2×C4—21no—
1263C2×C4—23no—
1264C2×C4—23no—
1265C2×C4—23no—
1266C2×C4—23no—
1267C2×C4—23no—
1268C2×C4—23no—
1269C2×C4—23no—
1270C2×C4—23no—
1271C2×C4—21no—
1272C2×C4—21no—
1273C2×C4—21no—
1274C2×C4—21no—
1275C2×C4—21no—
1276C2×C4—23no—
1277C2×C4—23no—
1278C2×C4—21no—
1279C2×C4—23no—
1280C2×C4—23no—
1281C2×C4—23no—
1282C2×C4—23no—
1283C2×C4—23no—
1284C2×C4—23no—
1285C2×C4—21no—
1286C2×C4—21no—
1287C2×C4—23no—
1288C2×C4—21no—
1289C2×C4—23no—
1290C2×C4—23no—
1291C2×C4—21no—
1292C2×C4—23no—
1293C2×C4—21no—
1294C2×C4—21no—
1295C2×C4—23no—
1296C2×C4—23no—
1297C2×C4—23no—
1298C2×C4—23no—
1299C2×C4—21no—
1300C2×C4—21no—
1301C2×C4—21no—
1302C2×C4—21no—
1303C2×C4—23no—
1304C2×C4—23no—
1305C2×C4—21no—
1306C2×C4—21no—
1307C2×C4—21no—
1308C2×C4—23no—
1309C2×C4—23no—
1310C2×C4—21no—
1311C2×C4—21no—
1312C2×C4—23no—
1313C2×C4—21no—
1314C2×C4—21no—
1315C2×C4—23no—
1316C2×C4—21no—
1317C2×C4—21no—
1318C2×C4—21no—
1319C2×C4—424no—
1320C2×C4—44no—
1321C2×C4—412no—
1322C2×C4—412no—
1323C2×C4—412no—
1324C2×C4—412no—
1325C2×C4—86no—
1326C2×C4—166no—
1327C2×C4—166no—
1328C2×C4C22×#4116yes—
1329C2×C4C22×#4116yes—
1330C2×C4C2×H(5,𝔽2)16yes—
1331C2×C4C2×H(5,𝔽2)16yes—
1332C22—22no—
1333C22—22no—
1334C22—22no—
1335C22—41no—
1336C22—41no—
1337C22—41no—
1338C22—41no—
1339C22—43no—
1340C22—43no—
1341C22—43no—
1342C22—41no—
1343C22—41no—
1344C22—43no—
1345C22—43no—
1346C22—43no—
1347C22—43no—
1348C22—43no—
1349C22—43no—
1350C22—41no—
1351C22—43no—
1352C22—43no—
1353C22—41no—
1354C22—43no—
1355C22—43no—
1356C22—43no—
1357C22—43no—
1358C22—43no—
1359C22—43no—
1360C22—41no—
1361C22—43no—
1362C22—41no—
1363C22—43no—
1364C22—41no—
1365C22—43no—
1366C22—43no—
1367C22C23×#4111yescharacteristic
1368C22C22×H(5,𝔽2)11yescharacteristic
1369C22C22×H(5,𝔽2)11yescharacteristic
1370C22H(7,𝔽2)11yescharacteristic
1371C22H(7,𝔽2)11yescharacteristic
1372C222−1+611yescharacteristic
1373C222−1+611yescharacteristic
1374C4—26no—
1375C4—41no—
1376C4—41no—
1377C4—41no—
1378C4—41no—
1379C4—41no—
1380C4—43no—
1381C4—41no—
1382C4—41no—
1383C4—43no—
1384C4—43no—
1385C4—43no—
1386C4—41no—
1387C4—43no—
1388C4—43no—
1389C4—43no—
1390C4—43no—
1391C4—41no—
1392C4—41no—
1393C4—43no—
1394C4—43no—
1395C4—41no—
1396C4—41no—
1397C4—41no—
1398C4—43no—
1399C4C2×#538112yes—
1400C2—42no—
1401C2—83no—
1402C2—83no—
1403C2—81no—
1404C2—83no—
1405C2C22×#53811yescharacteristic
1406C2#6285111yescharacteristic
1407C2#6285111yescharacteristic
1408C2#6304411yescharacteristic
1409C2#6305211yescharacteristic
1410C2#6305211yescharacteristic
1411C2#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. #42895C2semidirect
2. #42892C2semidirect
3. #42872C2semidirect
4. #42843C2semidirect
5. #42839C2semidirect
6. #42838C2semidirect
7. #42831C2semidirect
8. #42829C2semidirect
9. #42518C2semidirect
10. #42504C2semidirect
11. #42448C2semidirect
12. #42447C2semidirect
13. #37515C2semidirect
14. #37501C2semidirect
15. #37498C2semidirect
16. #36670C2semidirect
17. #36049C2semidirect
18. #36029C2semidirect
19. #36018C2semidirect
20. #36005C2semidirect
21. #35996C2semidirect
22. #35898C2semidirect
23. #35883C2semidirect
24. #35854C2semidirect
25. #35831C2semidirect
26. #35786C2semidirect
27. #35757C2semidirect
28. #35757C2semidirect
29. #34294C2semidirect
30. #34294C2semidirect
31. #34257C2semidirect

Maximal subgroups

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

subgroupindex
#428952
#428922
#428722
#428432
#428392
#428382
#428312
#428292
#425182
#425042
#424482
#424472
#375152
#375012
#374982
#366702
#360492
#360292
#360182
#360052
#359962
#358982
#358832
#358542
#358312
#357862
#357572
#342942
#342572