Finite Group Databasebeta

← #7698454

Subgroups — #7698454

Order 512.

7303 conjugacy classes of subgroups.

The subgroup lattice has 1476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3517C211yesmaximal, characteristic, complemented
2C2×#3517C211yesmaximal, characteristic, complemented
3#59318C213yesmaximal, complemented
4#59110C213yesmaximal, complemented
5#59039C213yesmaximal, complemented
6#52147C213yesmaximal, complemented
7#45135C213yesmaximal, complemented
8#45106C213yesmaximal, complemented
9#45004C213yesmaximal, complemented
10#44931C213yesmaximal, complemented
11#44880C213yesmaximal, complemented
12#44873C213yesmaximal, complemented
13#39352C213yesmaximal, complemented
14#38914C213yesmaximal, complemented
15#38041C213yesmaximal, complemented
16#37864C213yesmaximal, complemented
17#37792C213yesmaximal, complemented
18#37764C213yesmaximal, complemented
19#36455C211yesmaximal, characteristic, complemented
20#36433C211yesmaximal, characteristic, complemented
21#36431C211yesmaximal, characteristic, complemented
22#36076C211yesmaximal, characteristic, complemented
23#36076C211yesmaximal, characteristic, complemented
24#36040C211yesmaximal, characteristic, complemented
25#36029C211yesmaximal, characteristic, complemented
26#36005C211yesmaximal, characteristic, complemented
27#35957C211yesmaximal, characteristic, complemented
28#34295C211yesmaximal, characteristic, complemented
29#34295C211yesmaximal, characteristic, complemented
30#34250C211yesmaximal, characteristic, complemented
31#34184C211yesmaximal, characteristic, complemented
32#3517—216no—
33#3517—216no—
34C2×#557C2211yescharacteristic
35C2×#557C2211yescharacteristic
36C2×#553C2213yes—
37C2×#553C2213yes—
38C2×#553C2213yes—
39C2×#553C2213yes—
40C2×#550C2213yes—
41C2×#550C2211yescharacteristic
42C2×#550C2211yescharacteristic
43C2×#550C2211yescharacteristic
44C2×#550C2213yes—
45C2×#550C2211yescharacteristic
46C2×#550C2211yescharacteristic
47C2×#550C2211yescharacteristic
48C2×#547C2213yes—
49C2×#547C2213yes—
50C2×#540C2213yes—
51C2×#540C2213yes—
52C2×#540C2213yes—
53C2×#540C2213yes—
54C2×#532C2213yes—
55C2×#532C2213yes—
56C2×#529C2213yes—
57C2×#529C2213yes—
58C2×#520C2211yescharacteristic
59C2×#520C2211yescharacteristic
60C2×#520C2211yescharacteristic
61C2×#520C2211yescharacteristic
62C2×#520C2211yescharacteristic
63C2×C4×#41C2211yescharacteristic
64C2×C4×#41C2211yescharacteristic
65C2×C4×#41C2211yescharacteristic
66#2856C2213yes—
67#2854C2213yes—
68#2851C2213yes—
69#2723C2216yes—
70#2723C2213yes—
71#2722C2213yes—
72#2721C2213yes—
73#2720C2213yes—
74#2719C2211yescharacteristic
75#2718C2216yes—
76#2718C2213yes—
77#2717C2213yes—
78#2715C2213yes—
79#2710C2216yes—
80#2708C2216yes—
81#2708C2213yes—
82#2706C2216yes—
83#2706C2213yes—
84#2706C2216yes—
85#2701C2216yes—
86#2698C2213yes—
87#2695C2213yes—
88#2686C2216yes—
89#2686C2213yes—
90#2682C2216yes—
91#2680C2213yes—
92#2672C2213yes—
93#2671C2216yes—
94#2671C2216yes—
95#2671C2216yes—
96#2671C2213yes—
97#2671C2216yes—
98#2660C2213yes—
99#2628C2213yes—
100#2624C2213yes—
101#2624C2213yes—
102#2624C2213yes—
103#2619C2213yes—
104#2584C2213yes—
105#2580C2213yes—
106#2580C2213yes—
107#2567C2213yes—
108#2566C2213yes—
109#2563C2213yes—
110#2553C2216yes—
111#2552C2213yes—
112#2552C2213yes—
113#2550C2213yes—
114#2550C2213yes—
115#2541C2213yes—
116#2541C2213yes—
117#2537C2216yes—
118#2537C2213yes—
119#2535C2213yes—
120#2504C2213yes—
121#2504C2213yes—
122#2501C2216yes—
123#2501C2213yes—
124#2500C2213yes—
125#2488C2216yes—
126#2487C2213yes—
127#2486C2213yes—
128#2486C2213yes—
129#2485C2213yes—
130#2466C2216yes—
131#2455C2216yes—
132#2454C2213yes—
133#2454C2213yes—
134#2454C2213yes—
135#2452C2213yes—
136#2445C2213yes—
137#2445C2213yes—
138#2445C2213yes—
139#2445C2213yes—
140#2445C2213yes—
141#2445C2213yes—
142#2445C2213yes—
143#2445C2213yes—
144#2443C2216yes—
145#2442C2213yes—
146#2442C2213yes—
147#2441C2213yes—
148#2439C2213yes—
149#2430C2216yes—
150#2430C2216yes—
151#2430C2216yes—
152#2430C2216yes—
153#2430C2216yes—
154#2428C2213yes—
155#2428C2213yes—
156#2428C2213yes—
157#2428C2213yes—
158#2425C2216yes—
159#2425C2216yes—
160#2425C2216yes—
161#2422C2216yes—
162#2422C2213yes—
163#2422C2213yes—
164#2422C2216yes—
165#2422C2213yes—
166#2420C2213yes—
167#2420C2213yes—
168#2420C2213yes—
169#2420C2213yes—
170#2420C2213yes—
171#2419C2216yes—
172#2416C2213yes—
173#2416C2213yes—
174#2416C2216yes—
175#2414C2213yes—
176#2414C2213yes—
177#2407C2216yes—
178#2406C2216yes—
179#2399C2213yes—
180#2396C2213yes—
181#2395C2213yes—
182#2395C2213yes—
183#2395C2213yes—
184#2392C2213yes—
185#2366C2213yes—
186#2366C2213yes—
187#2363C2213yes—
188#2363C2213yes—
189#2361C2213yes—
190#2361C2213yes—
191#2352C2213yes—
192#2352C2213yes—
193#2351C2211yescharacteristic
194#2351C2211yescharacteristic
195#2351C2211yescharacteristic
196#2351C2211yescharacteristic
197#2351C2211yescharacteristic
198#2351C2211yescharacteristic
199#2351C2211yescharacteristic
200Q8×C4⋊C4C2211yescharacteristic
201Q8×C4⋊C4C2211yescharacteristic
202Q8×C4⋊C4C2211yescharacteristic
203#2349C2213yes—
204#2349C2213yes—
205#2349C2213yes—
206#2349C2213yes—
207#2349C2213yes—
208#2349C2213yes—
209D4×C4⋊C4C2213yes—
210D4×C4⋊C4C2213yes—
211#2341C2211yescharacteristic
212#2341C2211yescharacteristic
213#2341C2211yescharacteristic
214#2341C2211yescharacteristic
215#2341C2211yescharacteristic
216#2341C2211yescharacteristic
217#2341C2211yescharacteristic
218#2341C2211yescharacteristic
219#2339C2216yes—
220#2328C2213yes—
221#2328C2213yes—
222#2324C2213yes—
223#2324C2213yes—
224#2317C2213yes—
225#2317C2213yes—
226#2317C2213yes—
227#2316C2213yes—
228C4×C22⋊Q8C2213yes—
229C4×#123C2213yes—
230C4×#121C2213yes—
231C4×#121C2213yes—
232C4×#121C2213yes—
233#2296C2213yes—
234C2×#389C2213yes—
235#2290C2213yes—
236#2290C2213yes—
237#2285C2213yes—
238C2×#382C2213yes—
239#2276C2211yescharacteristic
240C22×#41C2311yescharacteristic
241C22×#41C2311yescharacteristic
242C22×#41C2311yescharacteristic
243C22×#41C2311yescharacteristic
244C22×#41C2316yes—
245C22×#41C2316yes—
246#557—28no—
247#557—28no—
248#553—224no—
249#553—224no—
250#553—224no—
251#553—224no—
252#550—28no—
253#550—28no—
254#550—28no—
255#550—28no—
256#550—224no—
257#550—224no—
258#550—28no—
259#550D4116yescomplemented
260#547—224no—
261#547—224no—
262#540—224no—
263#540—224no—
264#540—224no—
265#540—224no—
266#532—224no—
267#532—224no—
268C2×C4⋊Q8C2313yes—
269C2×C4⋊Q8C2313yes—
270C2×#127C2313yes—
271C2×#127C2313yes—
272C2×#127C2313yes—
273C2×#127C2313yes—
274C2×#127C2313yes—
275C2×#127C2313yes—
276#529—224no—
277#529—224no—
278C2×#126C2313yes—
279C2×#126C2313yes—
280C2×#126C2313yes—
281C2×#126C2313yes—
282C2×#125C2313yes—
283C2×#125C2311yescharacteristic
284C2×#125C2311yescharacteristic
285C2×#125C2313yes—
286C2×#125C2313yes—
287C2×#125C2313yes—
288C2×#124C2313yes—
289C2×#124C2313yes—
290C2×#123C2313yes—
291C2×#123C2313yes—
292C2×#123C2313yes—
293C2×#123C2313yes—
294C2×#123C2316yes—
295C2×#123C2316yes—
296C2×#123C2316yes—
297C2×#123C2316yes—
298C2×#123C2313yes—
299C2×#123C2316yes—
300C2×#123C2316yes—
301C2×#123C2316yes—
302C2×#123C2316yes—
303C2×#123C2316yes—
304C2×C22⋊Q8C2313yes—
305C2×C22⋊Q8C2313yes—
306C2×C22⋊Q8C2313yes—
307C2×#121C2313yes—
308C2×#121C2313yes—
309C2×#121C2313yes—
310C2×#121C2313yes—
311C2×#121C2313yes—
312C2×#121C2313yes—
313C2×#121C2316yes—
314C2×#121C2313yes—
315C2×#121C2316yes—
316C2×#121C2313yes—
317C2×#121C2316yes—
318C2×#121C2316yes—
319C2×#121C2316yes—
320C2×#121C2316yes—
321C2×#121C2313yes—
322C2×#121C2313yes—
323C2×#121C2313yes—
324C2×#121C2313yes—
325C2×#121C2313yes—
326C2×#121C2316yes—
327C2×#121C2316yes—
328C2×#121C2316yes—
329C2×#121C2316yes—
330C2×#121C2313yes—
331C2×#121C2313yes—
332#520—28no—
333#520—28no—
334#520—28no—
335#520—28no—
336#520—28no—
337C4×#41—28no—
338C4×#41—28no—
339C4×#41—28no—
340C2×C4×Q8C2313yes—
341C2×C4×Q8C2313yes—
342C2×C4×Q8C2311yescharacteristic
343C2×C4×Q8C2311yescharacteristic
344C2×C4×Q8C2311yescharacteristic
345C2×C4×Q8C2311yescharacteristic
346C2×C4×Q8C2311yescharacteristic
347C2×C4×Q8C2311yescharacteristic
348C2×C4×Q8C2311yescharacteristic
349C2×C4×Q8C2311yescharacteristic
350C2×C4×Q8C2311yescharacteristic
351C2×C4×Q8C2311yescharacteristic
352C2×C4×Q8C2311yescharacteristic
353C2×C4×D4C2313yes—
354C2×C4×D4C2313yes—
355C2×C4×D4C2313yes—
356C2×C4×D4C2313yes—
357C2×C4×D4C2316yes—
358C2×C4×D4C2313yes—
359C2×C4×D4C2313yes—
360C2×C4×D4C2313yes—
361C2×C4×D4C2313yes—
362C2×C4×D4C2313yes—
363C2×C4×D4C2313yes—
364C2×C4×D4C2313yes—
365C2×C4×D4C2313yes—
366C2×C4×D4C2313yes—
367C2×C4×D4C2313yes—
368C2×C4×D4C2313yes—
369C2×C4×D4C2313yes—
370C2×C4×D4C2313yes—
371C2×C4×D4C2313yes—
372C2×C4×D4C2313yes—
373C2×C4×D4C2313yes—
374C2×C4×D4C2313yes—
375C2×C4×D4C2316yes—
376C2×C4×D4C2316yes—
377C2×C4×D4C2316yes—
378C2×C4×D4C2313yes—
379C2×#117C2313yes—
380C2×#117C2313yes—
381C2×#117C2313yes—
382C2×#117C2313yes—
383C2×#117C2313yes—
384C2×#117C2313yes—
385C2×#117C2313yes—
386C2×#117C2313yes—
387C22×C4⋊C4C2313yes—
388C22×C4⋊C4C2313yes—
389C22×C4⋊C4C2313yes—
390C22×C4⋊C4C2313yes—
391C22×C4⋊C4C2313yes—
392C22×C4⋊C4C2316yes—
393C22×C42C2313yes—
394C22×C42C2313yes—
395C22×C42C2313yes—
396#400C2316yes—
397#400C2311yescharacteristic
398#400C2311yescharacteristic
399#400C2313yes—
400#400C2311yescharacteristic
401#399C2313yes—
402#399C2316yes—
403#399C2313yes—
404#399C2313yes—
405#399C2316yes—
406#399C2316yes—
407#399C2313yes—
408#398C2313yes—
409#398C2311yescharacteristic
410#398C2311yescharacteristic
411#398C2313yes—
412#398C2313yes—
413#398C2313yes—
414#398C2313yes—
415#398C2311yescharacteristic
416#398C2313yes—
417#398C2313yes—
418#398C2316yes—
419#398C2316yes—
420#397C2313yes—
421#397C2316yes—
422#397C2316yes—
423#397C2313yes—
424#397C2313yes—
425#397C2313yes—
426#397C2313yes—
427#397C2313yes—
428#397C2313yes—
429#397C2313yes—
430#397C2313yes—
431#397C2313yes—
432#397C2316yes—
433#396C2316yes—
434#396C2316yes—
435#396C2313yes—
436#396C2313yes—
437#396C2313yes—
438#396C2313yes—
439#395C2313yes—
440#395C2316yes—
441#395C2313yes—
442#395C2313yes—
443#395C2313yes—
444#395C2313yes—
445#394C2313yes—
446#394C2316yes—
447#394C2316yes—
448#394C2316yes—
449#394C2316yes—
450#394C2316yes—
451#394C2316yes—
452#394C2316yes—
453#394C2313yes—
454#394C2313yes—
455#394C2313yes—
456#394C2313yes—
457#394C2313yes—
458#394C2313yes—
459#394C2313yes—
460#394C2313yes—
461#394C2316yes—
462#394C2316yes—
463#394C2316yes—
464#394C2316yes—
465#394C2316yes—
466#393C2313yes—
467#393C2316yes—
468#393C2316yes—
469#392C2316yes—
470#392C2316yes—
471#392C2313yes—
472#392C2316yes—
473#392C2316yes—
474#391C2316yes—
475#391C2313yes—
476#390C2313yes—
477#390C2313yes—
478#390C2313yes—
479#390C2313yes—
480#390C2313yes—
481#390C2313yes—
482#390C2316yes—
483#390C2316yes—
484#390C2313yes—
485#390C2313yes—
486#390C2313yes—
487#390C2313yes—
488#390C2313yes—
489#390C2313yes—
490#390C2313yes—
491#390C2313yes—
492#390C2313yes—
493#390C2313yes—
494#390C2313yes—
495#390C2316yes—
496#389C2313yes—
497#389C2313yes—
498#389C2313yes—
499#389C2313yes—
500#389C2313yes—
501#389C2313yes—
502#389C2316yes—
503#389C2313yes—
504#389C2313yes—
505#389C2313yes—
506#389C2313yes—
507#389C2313yes—
508#389C2313yes—
509#389C2313yes—
510#389C2313yes—
511#389C2313yes—
512#389C2313yes—
513#389C2313yes—
514#389C2313yes—
515#389C2313yes—
516#389C2313yes—
517#389C2316yes—
518#389C2316yes—
519#389C2313yes—
520#389C2313yes—
521#389C2311yescharacteristic
522#389C2313yes—
523#389C2311yescharacteristic
524#389C2313yes—
525#388C2316yes—
526#388C2316yes—
527#388C2313yes—
528#388C2316yes—
529#388C2313yes—
530#388C2313yes—
531#388C2313yes—
532#388C2313yes—
533#388C2313yes—
534#388C2313yes—
535#388C2313yes—
536#387C2313yes—
537#387C2316yes—
538#387C2313yes—
539#387C2313yes—
540#387C2311yescharacteristic
541#387C2311yescharacteristic
542#387C2311yescharacteristic
543#387C2311yescharacteristic
544#387C2313yes—
545#386C2316yes—
546#386C2316yes—
547#386C2313yes—
548#386C2313yes—
549#386C2316yes—
550#386C2316yes—
551#386C2316yes—
552#386C2316yes—
553#386C2313yes—
554#386C2316yes—
555#386C2316yes—
556#386C2316yes—
557#386C2316yes—
558#386C2313yes—
559#386C2313yes—
560#386C2316yes—
561#386C2316yes—
562#386C2313yes—
563#386C2316yes—
564#386C2316yes—
565#386C2313yes—
566#385C2313yes—
567#385C2316yes—
568#385C2316yes—
569#385C2316yes—
570#385C2316yes—
571#385C2316yes—
572#385C2316yes—
573#385C2316yes—
574#385C2313yes—
575#385C2313yes—
576#385C2313yes—
577#385C2316yes—
578#385C2316yes—
579#385C2316yes—
580#385C2313yes—
581#385C2313yes—
582#385C2313yes—
583#385C2313yes—
584#385C2313yes—
585#385C2313yes—
586#385C2316yes—
587#385C2313yes—
588#384C2313yes—
589#384C2316yes—
590#384C2313yes—
591#384C2313yes—
592#384C2313yes—
593#384C2313yes—
594#382C2313yes—
595#382C2313yes—
596#382C2313yes—
597#382C2316yes—
598#382C2313yes—
599#382C2313yes—
600#382C2313yes—
601#382C2313yes—
602#382C2313yes—
603#382C2311yescharacteristic
604#381C2313yes—
605#381C2316yes—
606#381C2316yes—
607#380C2316yes—
608#380C2316yes—
609#380C2316yes—
610#380C2316yes—
611#380C2313yes—
612#380C2313yes—
613#380C2313yes—
614#380C2313yes—
615#380C2313yes—
616#380C2313yes—
617#380C2313yes—
618#380C2313yes—
619#380C2313yes—
620#380C2313yes—
621#380C2313yes—
622#380C2313yes—
623#380C2313yes—
624#380C2313yes—
625C4×C4⋊C4C2313yes—
626C4×C4⋊C4C2313yes—
627C4×C4⋊C4C2313yes—
628C4×C4⋊C4C2313yes—
629C4×C4⋊C4C2313yes—
630C4×C4⋊C4C2313yes—
631C4×C4⋊C4C2313yes—
632C4×C4⋊C4C2313yes—
633C4×C4⋊C4C2313yes—
634C4×C4⋊C4C2313yes—
635C4×C4⋊C4C2313yes—
636C4×C4⋊C4C2313yes—
637C4×C4⋊C4C2313yes—
638C4×C22⋊C4C2316yes—
639C4×C22⋊C4C2313yes—
640C4×C22⋊C4C2313yes—
641C4×C22⋊C4C2313yes—
642C4×C22⋊C4C2313yes—
643C4×C22⋊C4C2313yes—
644C4×C22⋊C4C2313yes—
645C4×C22⋊C4C2313yes—
646C4×C22⋊C4C2313yes—
647C4×C22⋊C4C2316yes—
648#376C2313yes—
649C2×#95C2316yes—
650C2×#95C2316yes—
651C2×#95C2316yes—
652C2×#41—24no—
653C2×#41—24no—
654C2×#41—24no—
655C2×#41—24no—
656C2×#41—24no—
657C2×#41—24no—
658C2×#41—24no—
659C2×#41—24no—
660C2×#41—24no—
661C2×#41—24no—
662C2×#41—224no—
663C2×#41—224no—
664C2×#41—412no—
665C2×#41—86no—
666C2×#41—86no—
667C2×#41—86no—
668C2×#41C2×D418yes—
669C2×#41C2×D418yes—
670C22×Q8C2413yes—
671C22×Q8C2413yes—
672C22×Q8C2411yescharacteristic
673C22×D4C2413yes—
674C22×D4C2413yes—
675C22×D4C2413yes—
676C22×D4C2413yes—
677C22×D4C2413yes—
678C22×D4C2416yes—
679C22×D4C2413yes—
680C22×D4C2413yes—
681C22×D4C2416yes—
682C22×D4C2413yes—
683C22×D4C2413yes—
684C22×D4C2416yes—
685C22×D4C2416yes—
686C22×D4C2416yes—
687C22×D4C2416yes—
688C22×D4C2413yes—
689C23×C4C2413yes—
690C23×C4C2413yes—
691C23×C4C2413yes—
692C23×C4C2413yes—
693C23×C4C2413yes—
694C23×C4C2416yes—
695C23×C4C2416yes—
696C23×C4C2413yes—
697C23×C4C2416yes—
698C23×C4C2416yes—
699C23×C4C2416yes—
700C23×C4C2413yes—
701C23×C4C2413yes—
702C23×C4C2413yes—
703C23×C4C2413yes—
704C4⋊Q8—212no—
705C4⋊Q8—212no—
706#127—212no—
707#127—212no—
708#127—212no—
709#127—212no—
710#127—212no—
711#127C2×D4124yes—
712#126—212no—
713#126—212no—
714#126—212no—
715#126—212no—
716#125—24no—
717#125—24no—
718#125—212no—
719#125—212no—
720#125—212no—
721#125—212no—
722#124—212no—
723#124—212no—
724#123—212no—
725#123—224no—
726#123—212no—
727#123—212no—
728#123—212no—
729#123—224no—
730#123—224no—
731#123—224no—
732#123—46no—
733#123—86no—
734#123—86no—
735#123—86no—
736#123—86no—
737#123—86no—
738C22⋊Q8—212no—
739C22⋊Q8—212no—
740C22⋊Q8—46no—
741#121—212no—
742#121—212no—
743#121—224no—
744#121—224no—
745#121—212no—
746#121—212no—
747#121—212no—
748#121—224no—
749#121—224no—
750#121—224no—
751#121—224no—
752#121—212no—
753#121—212no—
754#121—212no—
755#121—212no—
756#121—212no—
757#121—212no—
758#121—212no—
759#121—46no—
760#121—86no—
761#121—86no—
762#121—86no—
763#121—86no—
764#121C2×D4124yes—
765#121C2×D4124yes—
766C4×Q8—24no—
767C4×Q8—24no—
768C4×Q8—24no—
769C4×Q8—24no—
770C4×Q8—24no—
771C4×Q8—24no—
772C4×Q8—24no—
773C4×Q8—24no—
774C4×Q8—24no—
775C4×Q8—212no—
776C4×Q8—212no—
777C4×Q8C2×D418yes—
778C4×Q8#4118yescomplemented
779C4×D4—212no—
780C4×D4—212no—
781C4×D4—212no—
782C4×D4—212no—
783C4×D4—212no—
784C4×D4—212no—
785C4×D4—212no—
786C4×D4—212no—
787C4×D4—224no—
788C4×D4—212no—
789C4×D4—212no—
790C4×D4—212no—
791C4×D4—212no—
792C4×D4—212no—
793C4×D4—212no—
794C4×D4—212no—
795C4×D4—212no—
796C4×D4—224no—
797C4×D4—212no—
798C4×D4—212no—
799C4×D4—212no—
800C4×D4—212no—
801C4×D4—212no—
802C4×D4—86no—
803C4×D4—86no—
804C4×D4C2×D4124yes—
805#117—212no—
806#117—212no—
807#117—212no—
808#117—212no—
809#117—212no—
810#117—212no—
811#117—212no—
812#117—212no—
813C2×C4⋊C4—212no—
814C2×C4⋊C4—212no—
815C2×C4⋊C4—212no—
816C2×C4⋊C4—212no—
817C2×C4⋊C4—212no—
818C2×C4⋊C4—86no—
819C2×C4⋊C4C2413yes—
820C2×C4⋊C4C2413yes—
821C2×C4⋊C4C2413yes—
822C2×C4⋊C4C2413yes—
823C2×C4⋊C4C2413yes—
824C2×C4⋊C4C2413yes—
825C2×C4⋊C4C2413yes—
826C2×C4⋊C4C2413yes—
827C2×C4⋊C4C2413yes—
828C2×C4⋊C4C2413yes—
829C2×C4⋊C4C2413yes—
830C2×C4⋊C4C2411yescharacteristic
831C2×C4⋊C4C2411yescharacteristic
832C2×C4⋊C4C2411yescharacteristic
833C2×C4⋊C4C2411yescharacteristic
834C2×C4⋊C4C2411yescharacteristic
835C2×C4⋊C4C2413yes—
836C2×C4⋊C4C2413yes—
837C2×C4⋊C4C2411yescharacteristic
838C2×C4⋊C4C2411yescharacteristic
839C2×C4⋊C4C2411yescharacteristic
840C2×C4⋊C4C2411yescharacteristic
841C2×C4⋊C4C2411yescharacteristic
842C2×C4⋊C4C2416yes—
843C2×C4⋊C4C2416yes—
844C2×C4⋊C4C2411yescharacteristic
845C2×C4⋊C4C2411yescharacteristic
846C2×C4⋊C4C2413yes—
847C2×C4⋊C4C2413yes—
848C2×C4⋊C4C2413yes—
849C2×C4⋊C4C2413yes—
850C2×C4⋊C4C2413yes—
851C2×C4⋊C4C2411yescharacteristic
852C2×C4⋊C4C2411yescharacteristic
853C2×C4⋊C4C2411yescharacteristic
854C2×C4⋊C4C2413yes—
855C2×C4⋊C4C2413yes—
856C2×C4⋊C4C2416yes—
857C2×C4⋊C4C2416yes—
858C2×C4⋊C4C2413yes—
859C2×C4⋊C4C2413yes—
860C2×C4⋊C4C2413yes—
861C2×C4⋊C4C2413yes—
862C2×C4⋊C4C2413yes—
863C2×C4⋊C4C2413yes—
864C2×C4⋊C4C2413yes—
865C2×C4⋊C4C2413yes—
866C2×C4⋊C4C2413yes—
867C2×C4⋊C4C2413yes—
868C2×C4⋊C4C2413yes—
869C2×C4⋊C4C2413yes—
870C2×C4⋊C4C2413yes—
871C2×C4⋊C4C2413yes—
872C2×C4⋊C4C2416yes—
873C2×C4⋊C4C2413yes—
874C2×C4⋊C4C2413yes—
875C2×C4⋊C4C2411yescharacteristic
876C2×C4⋊C4C2413yes—
877C2×C22⋊C4C2413yes—
878C2×C22⋊C4C2413yes—
879C2×C22⋊C4C2413yes—
880C2×C22⋊C4C2413yes—
881C2×C22⋊C4C2416yes—
882C2×C22⋊C4C2416yes—
883C2×C22⋊C4C2413yes—
884C2×C22⋊C4C2413yes—
885C2×C22⋊C4C2413yes—
886C2×C22⋊C4C2413yes—
887C2×C22⋊C4C2413yes—
888C2×C22⋊C4C2416yes—
889C2×C22⋊C4C2413yes—
890C2×C22⋊C4C2413yes—
891C2×C22⋊C4C2413yes—
892C2×C22⋊C4C2413yes—
893C2×C22⋊C4C2413yes—
894C2×C22⋊C4C2413yes—
895C2×C22⋊C4C2413yes—
896C2×C22⋊C4C2413yes—
897C2×C22⋊C4C2413yes—
898C2×C22⋊C4C2413yes—
899C2×C22⋊C4C2413yes—
900C2×C22⋊C4C2413yes—
901C2×C22⋊C4C2413yes—
902C2×C22⋊C4C2413yes—
903C2×C22⋊C4C2416yes—
904C2×C22⋊C4C2416yes—
905C2×C22⋊C4C2413yes—
906C2×C22⋊C4C2413yes—
907C2×C22⋊C4C2413yes—
908C2×C22⋊C4C2413yes—
909C2×C22⋊C4C2416yes—
910C2×C22⋊C4C2416yes—
911C2×C22⋊C4C2416yes—
912C2×C22⋊C4C2416yes—
913C2×C22⋊C4C2413yes—
914C2×C22⋊C4C2413yes—
915C2×C22⋊C4C2413yes—
916C2×C22⋊C4C2416yes—
917C2×C22⋊C4C2416yes—
918C2×C22⋊C4C2413yes—
919C2×C22⋊C4C2413yes—
920C2×C22⋊C4C2413yes—
921C2×C22⋊C4C2413yes—
922C2×C22⋊C4C2413yes—
923C2×C22⋊C4C2413yes—
924C2×C22⋊C4C2413yes—
925C2×C22⋊C4C2413yes—
926C2×C42—212no—
927C2×C42—212no—
928C2×C42—212no—
929C2×C42C2413yes—
930C2×C42C2413yes—
931C2×C42C2413yes—
932C2×C42C2413yes—
933C2×C42C2413yes—
934C2×C42C2413yes—
935C2×C42C2413yes—
936C2×C42C2413yes—
937C2×C42C2413yes—
938C2×C42C2413yes—
939C2×C42C2413yes—
940C2×C42C2413yes—
941C2×C42C2411yescharacteristic
942C2×C42C2411yescharacteristic
943C2×C42C2411yescharacteristic
944C2×C42C2416yes—
945C2×C42C2413yes—
946C2×C42C2413yes—
947#95C2416yes—
948#95C2413yes—
949#95C2413yes—
950#95C2413yes—
951#95C2413yes—
952#95C2413yes—
953#95C2413yes—
954#95C2416yes—
955#95C2416yes—
956#95C2416yes—
957#95C2416yes—
958#95C2411yescharacteristic
959#95C2413yes—
960#95C2413yes—
961#95C2413yes—
962#95C2413yes—
963#95C2413yes—
964#95C2411yescharacteristic
965#95C2411yescharacteristic
966#95C2411yescharacteristic
967#95C2411yescharacteristic
968#95C2411yescharacteristic
969#95C2411yescharacteristic
970#95C2411yescharacteristic
971#95C2411yescharacteristic
972#95C2413yes—
973#95C2413yes—
974#95C2413yes—
975#95C2413yes—
976#95C2413yes—
977#95C2413yes—
978#95C2416yes—
979#95C2411yescharacteristic
980#95C2411yescharacteristic
981#95C2411yescharacteristic
982#95C2411yescharacteristic
983#95C2411yescharacteristic
984#95C2411yescharacteristic
985#95C2411yescharacteristic
986#95C2413yes—
987#95C2413yes—
988#95C2413yes—
989#95C2413yes—
990#95C2413yes—
991#95C2413yes—
992#95C2413yes—
993#95C2416yes—
994C24C2513yes—
995C24C2513yes—
996C24C2513yes—
997C24C2513yes—
998#41—232no—
999#41—232no—
1000#41—416no—
1001#41—416no—
1002#41—848no—
1003#41—848no—
1004C2×Q8—26no—
1005C2×Q8—26no—
1006C2×Q8—26no—
1007C2×Q8—43no—
1008C2×Q8—43no—
1009C2×Q8—43no—
1010C2×Q8C22×D414yes—
1011C2×Q8C2×#4114yes—
1012C2×Q82−1+414yes—
1013C2×D4—26no—
1014C2×D4—212no—
1015C2×D4—26no—
1016C2×D4—26no—
1017C2×D4—26no—
1018C2×D4—212no—
1019C2×D4—212no—
1020C2×D4—212no—
1021C2×D4—26no—
1022C2×D4—26no—
1023C2×D4—26no—
1024C2×D4—26no—
1025C2×D4—26no—
1026C2×D4—26no—
1027C2×D4—26no—
1028C2×D4—212no—
1029C2×D4—26no—
1030C2×D4—26no—
1031C2×D4—26no—
1032C2×D4—26no—
1033C2×D4—26no—
1034C2×D4—46no—
1035C2×D4—46no—
1036C2×D4—43no—
1037C2×D4—43no—
1038C2×D4—43no—
1039C2×D4—46no—
1040C2×D4—43no—
1041C2×D4—43no—
1042C2×D4—46no—
1043C2×D4—43no—
1044C2×D4—43no—
1045C2×D4—43no—
1046C2×D4—46no—
1047C2×D4—46no—
1048C2×D4—46no—
1049C2×D4—46no—
1050C2×D4—46no—
1051C2×D4—46no—
1052C2×D4—43no—
1053C2×D4—43no—
1054C2×D4—43no—
1055C2×D4—46no—
1056C2×D4—46no—
1057C2×D4C22×D4112yes—
1058C2×D4C22×D4112yes—
1059C2×D4C22×D4124yes—
1060C2×D4C22×D4112yes—
1061C22×C4—26no—
1062C22×C4—26no—
1063C22×C4—26no—
1064C22×C4—26no—
1065C22×C4—26no—
1066C22×C4—26no—
1067C22×C4—212no—
1068C22×C4—212no—
1069C22×C4—212no—
1070C22×C4—26no—
1071C22×C4—26no—
1072C22×C4—26no—
1073C22×C4—26no—
1074C22×C4—26no—
1075C22×C4—26no—
1076C22×C4—26no—
1077C22×C4—26no—
1078C22×C4—26no—
1079C22×C4—212no—
1080C22×C4—26no—
1081C22×C4—26no—
1082C22×C4—212no—
1083C22×C4—43no—
1084C22×C4—43no—
1085C22×C4—43no—
1086C22×C4—43no—
1087C22×C4—46no—
1088C22×C4—46no—
1089C22×C4—43no—
1090C22×C4—43no—
1091C22×C4—46no—
1092C22×C4—46no—
1093C22×C4—43no—
1094C22×C4—43no—
1095C22×C4—43no—
1096C22×C4—43no—
1097C22×C4—43no—
1098C22×C4—46no—
1099C22×C4—46no—
1100C22×C4—46no—
1101C22×C4—46no—
1102C22×C4—46no—
1103C22×C4—46no—
1104C22×C4C22×D4112yes—
1105C22×C4C22×D4112yes—
1106C22×C4C2511yescharacteristic
1107C22×C4C2511yescharacteristic
1108C22×C4C2511yescharacteristic
1109C22×C4C2511yescharacteristic
1110C22×C4C2513yes—
1111C22×C4C2513yes—
1112C22×C4C2513yes—
1113C22×C4C2513yes—
1114C22×C4C2513yes—
1115C22×C4C2511yescharacteristic
1116C22×C4C2513yes—
1117C22×C4C2513yes—
1118C22×C4C2513yes—
1119C22×C4C2511yescharacteristic
1120C22×C4C2511yescharacteristic
1121C22×C4C2511yescharacteristic
1122C22×C4C2511yescharacteristic
1123C22×C4C2511yescharacteristic
1124C22×C4C2513yes—
1125C22×C4C2511yescharacteristic
1126C22×C4C2511yescharacteristic
1127C22×C4C2511yescharacteristic
1128C22×C4C2513yes—
1129C22×C4C2511yescharacteristic
1130C22×C4C2513yes—
1131C22×C4C2511yescharacteristic
1132C22×C4C2513yes—
1133C4⋊C4—26no—
1134C4⋊C4—26no—
1135C4⋊C4—26no—
1136C4⋊C4—26no—
1137C4⋊C4—26no—
1138C4⋊C4—26no—
1139C4⋊C4—26no—
1140C4⋊C4—26no—
1141C4⋊C4—26no—
1142C4⋊C4—22no—
1143C4⋊C4—22no—
1144C4⋊C4—22no—
1145C4⋊C4—22no—
1146C4⋊C4—26no—
1147C4⋊C4—22no—
1148C4⋊C4—22no—
1149C4⋊C4—22no—
1150C4⋊C4—22no—
1151C4⋊C4—212no—
1152C4⋊C4—212no—
1153C4⋊C4—22no—
1154C4⋊C4—22no—
1155C4⋊C4—26no—
1156C4⋊C4—26no—
1157C4⋊C4—26no—
1158C4⋊C4—26no—
1159C4⋊C4—26no—
1160C4⋊C4—26no—
1161C4⋊C4—22no—
1162C4⋊C4—26no—
1163C4⋊C4—22no—
1164C4⋊C4—26no—
1165C4⋊C4—22no—
1166C4⋊C4—22no—
1167C4⋊C4—22no—
1168C4⋊C4—43no—
1169C4⋊C4—43no—
1170C4⋊C4—46no—
1171C4⋊C4—46no—
1172C4⋊C4—43no—
1173C4⋊C4—43no—
1174C4⋊C4—43no—
1175C4⋊C4—43no—
1176C4⋊C4—43no—
1177C4⋊C4—43no—
1178C4⋊C4—43no—
1179C4⋊C4—43no—
1180C4⋊C4—43no—
1181C4⋊C4—43no—
1182C4⋊C4—46no—
1183C4⋊C4—43no—
1184C4⋊C4—43no—
1185C4⋊C4—43no—
1186C4⋊C4—43no—
1187C4⋊C4—43no—
1188C4⋊C4C22×D4112yes—
1189C4⋊C4C22×D414yes—
1190C4⋊C4C2×#41112yes—
1191C22⋊C4—26no—
1192C22⋊C4—26no—
1193C22⋊C4—26no—
1194C22⋊C4—212no—
1195C22⋊C4—26no—
1196C22⋊C4—26no—
1197C22⋊C4—26no—
1198C22⋊C4—26no—
1199C22⋊C4—26no—
1200C22⋊C4—26no—
1201C22⋊C4—26no—
1202C22⋊C4—26no—
1203C22⋊C4—212no—
1204C22⋊C4—26no—
1205C22⋊C4—26no—
1206C22⋊C4—26no—
1207C22⋊C4—26no—
1208C22⋊C4—26no—
1209C22⋊C4—26no—
1210C22⋊C4—212no—
1211C22⋊C4—26no—
1212C22⋊C4—26no—
1213C22⋊C4—26no—
1214C22⋊C4—26no—
1215C22⋊C4—43no—
1216C22⋊C4—43no—
1217C22⋊C4—46no—
1218C22⋊C4—46no—
1219C22⋊C4—43no—
1220C22⋊C4—43no—
1221C22⋊C4—43no—
1222C22⋊C4—43no—
1223C22⋊C4—43no—
1224C22⋊C4—46no—
1225C22⋊C4—46no—
1226C22⋊C4—46no—
1227C22⋊C4—46no—
1228C22⋊C4—43no—
1229C22⋊C4—43no—
1230C22⋊C4—43no—
1231C22⋊C4—43no—
1232C22⋊C4—46no—
1233C22⋊C4—43no—
1234C22⋊C4—43no—
1235C22⋊C4—46no—
1236C22⋊C4—43no—
1237C22⋊C4—43no—
1238C22⋊C4C22×D4112yes—
1239C22⋊C4C22×D4112yes—
1240C42—22no—
1241C42—22no—
1242C42—26no—
1243C42—26no—
1244C42—26no—
1245C42—26no—
1246C42—26no—
1247C42—26no—
1248C42—26no—
1249C42—26no—
1250C42—22no—
1251C42—26no—
1252C42—26no—
1253C42—26no—
1254C42—26no—
1255C42—46no—
1256C42C22×D4112yes—
1257C42C2×#41112yes—
1258C23—23no—
1259C23—23no—
1260C23—23no—
1261C23—23no—
1262C23—23no—
1263C23—23no—
1264C23—23no—
1265C23—23no—
1266C23—23no—
1267C23—23no—
1268C23—23no—
1269C23—23no—
1270C23—23no—
1271C23—23no—
1272C23—23no—
1273C23—23no—
1274C23—23no—
1275C23—23no—
1276C23—23no—
1277C23—23no—
1278C23—23no—
1279C23—23no—
1280C23—23no—
1281C23—23no—
1282C23—23no—
1283C23—23no—
1284C23C23×D416yes—
1285C23C23×D416yes—
1286C23C2611yescharacteristic
1287Q8—412no—
1288Q8—412no—
1289Q8#547116yes—
1290D4—224no—
1291D4—224no—
1292D4—424no—
1293D4—412no—
1294D4—412no—
1295D4—412no—
1296D4—412no—
1297D4—86no—
1298D4—812no—
1299D4—86no—
1300D4—86no—
1301D4—812no—
1302D4—86no—
1303D4—812no—
1304D4—812no—
1305D4—812no—
1306C2×C4—21no—
1307C2×C4—21no—
1308C2×C4—21no—
1309C2×C4—21no—
1310C2×C4—21no—
1311C2×C4—21no—
1312C2×C4—23no—
1313C2×C4—23no—
1314C2×C4—23no—
1315C2×C4—23no—
1316C2×C4—21no—
1317C2×C4—21no—
1318C2×C4—21no—
1319C2×C4—21no—
1320C2×C4—224no—
1321C2×C4—224no—
1322C2×C4—21no—
1323C2×C4—21no—
1324C2×C4—21no—
1325C2×C4—21no—
1326C2×C4—21no—
1327C2×C4—21no—
1328C2×C4—23no—
1329C2×C4—23no—
1330C2×C4—23no—
1331C2×C4—23no—
1332C2×C4—23no—
1333C2×C4—23no—
1334C2×C4—21no—
1335C2×C4—21no—
1336C2×C4—21no—
1337C2×C4—23no—
1338C2×C4—23no—
1339C2×C4—21no—
1340C2×C4—21no—
1341C2×C4—21no—
1342C2×C4—23no—
1343C2×C4—21no—
1344C2×C4—21no—
1345C2×C4—23no—
1346C2×C4—21no—
1347C2×C4—21no—
1348C2×C4—21no—
1349C2×C4—23no—
1350C2×C4—23no—
1351C2×C4—21no—
1352C2×C4—21no—
1353C2×C4—23no—
1354C2×C4—21no—
1355C2×C4—23no—
1356C2×C4—21no—
1357C2×C4—23no—
1358C2×C4—21no—
1359C2×C4—23no—
1360C2×C4—23no—
1361C2×C4—21no—
1362C2×C4—21no—
1363C2×C4—21no—
1364C2×C4—21no—
1365C2×C4—21no—
1366C2×C4—23no—
1367C2×C4—23no—
1368C2×C4—23no—
1369C2×C4—23no—
1370C2×C4—23no—
1371C2×C4—23no—
1372C2×C4—23no—
1373C2×C4—23no—
1374C2×C4—23no—
1375C2×C4—23no—
1376C2×C4—21no—
1377C2×C4—21no—
1378C2×C4—21no—
1379C2×C4—412no—
1380C2×C4—412no—
1381C2×C4—412no—
1382C2×C4—412no—
1383C2×C4—86no—
1384C2×C4—86no—
1385C2×C4—812no—
1386C2×C4—86no—
1387C2×C4—812no—
1388C2×C4—86no—
1389C2×C4—812no—
1390C2×C4—812no—
1391C2×C4—812no—
1392C2×C4C23×D412yes—
1393C2×C4C23×D412yes—
1394C2×C4C23×D416yes—
1395C2×C4C23×D412yes—
1396C2×C4C23×D416yes—
1397C2×C4C22×#4112yes—
1398C2×C4C22×#4116yes—
1399C2×C4C22×#4116yes—
1400C2×C4C2×2−1+416yes—
1401C2×C4#58512yes—
1402C22—26no—
1403C22—26no—
1404C22—26no—
1405C22—26no—
1406C22—26no—
1407C22—26no—
1408C22—43no—
1409C22—43no—
1410C22—43no—
1411C22—43no—
1412C22—43no—
1413C22—43no—
1414C22—43no—
1415C22—43no—
1416C22—43no—
1417C22—43no—
1418C22—43no—
1419C22—43no—
1420C22—43no—
1421C22—43no—
1422C22—43no—
1423C22—43no—
1424C22—43no—
1425C22—43no—
1426C22—43no—
1427C22—43no—
1428C22—43no—
1429C22—43no—
1430C22C24×D411yescharacteristic
1431C22C23×#4111yescharacteristic
1432C22C22×2−1+411yescharacteristic
1433C22C2×#58511yescharacteristic
1434C22H(7,𝔽2)11yescharacteristic
1435C22H(7,𝔽2)11yescharacteristic
1436C22H(7,𝔽2)11yescharacteristic
1437C4—22no—
1438C4—26no—
1439C4—22no—
1440C4—22no—
1441C4—26no—
1442C4—22no—
1443C4—22no—
1444C4—43no—
1445C4—41no—
1446C4—43no—
1447C4—41no—
1448C4—41no—
1449C4—41no—
1450C4—43no—
1451C4—43no—
1452C4—43no—
1453C4—41no—
1454C4—43no—
1455C4—43no—
1456C4—43no—
1457C4—41no—
1458C4—43no—
1459C4—41no—
1460C4—41no—
1461C4—41no—
1462C4—41no—
1463C4C2×#547112yes—
1464C2—46no—
1465C2—46no—
1466C2—83no—
1467C2—83no—
1468C2C22×#54711yescharacteristic
1469C2#6285211yescharacteristic
1470C2#6285811yescharacteristic
1471C2#6295211yescharacteristic
1472C2#6298711yescharacteristic
1473C2#6300611yescharacteristic
1474C2#6307011yescharacteristic
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. C2×#3517C2semidirect
2. C2×#3517C2semidirect
3. #59318C2semidirect
4. #59110C2semidirect
5. #59039C2semidirect
6. #52147C2semidirect
7. #45135C2semidirect
8. #45106C2semidirect
9. #45004C2semidirect
10. #44931C2semidirect
11. #44880C2semidirect
12. #44873C2semidirect
13. #39352C2semidirect
14. #38914C2semidirect
15. #38041C2semidirect
16. #37864C2semidirect
17. #37792C2semidirect
18. #37764C2semidirect
19. #36455C2semidirect
20. #36433C2semidirect
21. #36431C2semidirect
22. #36076C2semidirect
23. #36076C2semidirect
24. #36040C2semidirect
25. #36029C2semidirect
26. #36005C2semidirect
27. #35957C2semidirect
28. #34295C2semidirect
29. #34295C2semidirect
30. #34250C2semidirect
31. #34184C2semidirect
259. #550D4semidirect
778. C4×Q8#41semidirect

Maximal subgroups

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

subgroupindex
C2×#35172
#593182
#591102
#590392
#521472
#451352
#451062
#450042
#449312
#448802
#448732
#393522
#389142
#380412
#378642
#377922
#377642
#364552
#364332
#364312
#360762
#360402
#360292
#360052
#359572
#342952
#342502
#341842