Finite Group Databasebeta

← #7661824

Subgroups — #7661824

Order 512.

6480 conjugacy classes of subgroups.

The subgroup lattice has 1398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3524C211yesmaximal, characteristic
2C2×#3502C211yesmaximal, characteristic, complemented
3#52166C213yesmaximal, complemented
4#42968C213yesmaximal, complemented
5#42944C213yesmaximal, complemented
6#42888C213yesmaximal, complemented
7#42886C213yesmaximal, complemented
8#42804C213yesmaximal, complemented
9#42789C213yesmaximal, complemented
10#39955C213yesmaximal, complemented
11#39891C213yesmaximal, complemented
12#39866C213yesmaximal, complemented
13#39859C213yesmaximal, complemented
14#39746C213yesmaximal, complemented
15#39125C213yesmaximal, complemented
16#37304C213yesmaximal, complemented
17#37279C213yesmaximal, complemented
18#37274C213yesmaximal, complemented
19#36578C211yesmaximal, characteristic, complemented
20#36483C211yesmaximal, characteristic, complemented
21#36466C211yesmaximal, characteristic, complemented
22#36457C211yesmaximal, characteristic, complemented
23#36445C211yesmaximal, characteristic, complemented
24#36431C211yesmaximal, characteristic, complemented
25#36049C211yesmaximal, characteristic, complemented
26#36040C211yesmaximal, characteristic, complemented
27#35937C211yesmaximal, characteristic, complemented
28#35816C211yesmaximal, characteristic, complemented
29#35801C211yesmaximal, characteristic, complemented
30#35801C211yesmaximal, characteristic, complemented
31#34262C211yesmaximal, characteristic, complemented
32#3524—216no—
33#3502—216no—
34C2×#559C2213yes—
35C2×Q82C2213yes—
36C2×Q82C2211yescharacteristic
37C2×#557C2213yes—
38C2×#557C2213yes—
39C2×#557C2213yes—
40C2×#557C2211yescharacteristic
41C2×#557C2211yescharacteristic
42C2×#557C2211yescharacteristic
43C2×#557C2211yescharacteristic
44C2×#555C2213yes—
45C2×#553C2213yes—
46C2×#552C2213yes—
47C2×#550C2211yescharacteristic
48C2×#548C2211yescharacteristic
49C2×#548C2211yescharacteristic
50C2×#544C2213yes—
51C2×#544C2213yes—
52C2×#542C2213yes—
53C2×#540C2213yes—
54C2×#533C2213yes—
55C2×#533C2213yes—
56C2×#529C2213yes—
57C2×#529C2213yes—
58C2×#520C2211yescharacteristic
59C2×#519C2211yescharacteristic
60C2×#519C2211yescharacteristic
61C2×C4×#41C2211yescharacteristic
62C22×C4×Q8C2211yescharacteristic
63#2859C2213yes—
64#2858C2213yes—
65#2857C2213yes—
66#2854C2213yes—
67#2854C2213yes—
68#2851C2213yes—
69#2821C2216yes—
70#2820C2216yes—
71#2721C2213yes—
72#2719C2216yes—
73#2719C2213yes—
74#2716C2216yes—
75#2716C2213yes—
76#2713C2213yes—
77#2700C2213yes—
78#2698C2213yes—
79#2694C2216yes—
80#2694C2216yes—
81#2694C2213yes—
82#2694C2216yes—
83#2694C2216yes—
84#2694C2216yes—
85#2690C2213yes—
86#2689C2211yescharacteristic
87#2687C2216yes—
88#2687C2213yes—
89#2681C2216yes—
90#2681C2216yes—
91#2681C2213yes—
92#2680C2213yes—
93#2677C2213yes—
94#2677C2216yes—
95#2674C2216yes—
96#2674C2216yes—
97#2674C2216yes—
98#2674C2216yes—
99#2674C2213yes—
100#2674C2216yes—
101#2674C2213yes—
102#2672C2213yes—
103#2672C2216yes—
104#2672C2216yes—
105#2672C2216yes—
106#2664C2216yes—
107#2660C2213yes—
108#2658C2216yes—
109#2641C2213yes—
110#2637C2216yes—
111#2633C2216yes—
112#2632C2216yes—
113#2629C2213yes—
114#2628C2213yes—
115#2628C2216yes—
116#2624C2213yes—
117#2624C2213yes—
118#2611C2216yes—
119#2604C2216yes—
120#2599C2216yes—
121#2584C2213yes—
122#2584C2213yes—
123#2584C2213yes—
124#2580C2213yes—
125#2580C2213yes—
126#2566C2213yes—
127#2566C2213yes—
128#2563C2213yes—
129#2563C2213yes—
130#2562C2213yes—
131#2552C2213yes—
132#2551C2213yes—
133#2551C2213yes—
134#2551C2213yes—
135#2550C2213yes—
136#2550C2213yes—
137#2550C2213yes—
138#2550C2213yes—
139#2548C2213yes—
140#2548C2213yes—
141#2547C2216yes—
142#2546C2213yes—
143#2545C2216yes—
144#2542C2213yes—
145#2538C2213yes—
146#2538C2213yes—
147#2536C2216yes—
148#2504C2213yes—
149#2501C2213yes—
150#2500C2213yes—
151#2500C2213yes—
152#2491C2213yes—
153#2491C2213yes—
154#2491C2213yes—
155#2491C2213yes—
156#2491C2213yes—
157#2491C2213yes—
158#2490C2213yes—
159#2490C2213yes—
160#2487C2213yes—
161#2486C2213yes—
162#2485C2213yes—
163#2485C2213yes—
164#2454C2213yes—
165#2454C2213yes—
166#2454C2213yes—
167#2454C2213yes—
168#2454C2213yes—
169#2454C2213yes—
170#2452C2213yes—
171#2452C2213yes—
172#2448C2213yes—
173#2448C2213yes—
174#2448C2213yes—
175#2448C2213yes—
176#2448C2213yes—
177#2448C2213yes—
178#2448C2213yes—
179#2448C2213yes—
180#2442C2213yes—
181#2442C2213yes—
182#2442C2213yes—
183#2441C2213yes—
184#2441C2213yes—
185#2441C2213yes—
186#2440C2213yes—
187#2439C2213yes—
188#2423C2213yes—
189#2423C2213yes—
190#2423C2213yes—
191#2423C2213yes—
192#2421C2213yes—
193#2421C2213yes—
194#2421C2213yes—
195#2421C2213yes—
196#2399C2213yes—
197#2398C2213yes—
198#2396C2213yes—
199#2396C2213yes—
200#2395C2213yes—
201#2395C2213yes—
202#2356C2213yes—
203#2355C2213yes—
204#2351C2211yescharacteristic
205#2351C2211yescharacteristic
206#2351C2211yescharacteristic
207#2351C2211yescharacteristic
208#2351C2211yescharacteristic
209Q8×C4⋊C4C2211yescharacteristic
210Q8×C4⋊C4C2211yescharacteristic
211Q8×C4⋊C4C2211yescharacteristic
212Q8×C4⋊C4C2211yescharacteristic
213Q8×C4⋊C4C2211yescharacteristic
214#2347C2213yes—
215#2346C2213yes—
216#2341C2211yescharacteristic
217#2341C2211yescharacteristic
218#2341C2211yescharacteristic
219#2341C2211yescharacteristic
220#2341C2211yescharacteristic
221#2341C2211yescharacteristic
222#2341C2211yescharacteristic
223#2341C2211yescharacteristic
224Q8×C22⋊C4C2211yescharacteristic
225Q8×C22⋊C4C2211yescharacteristic
226#2326C2216yes—
227#2323C2216yes—
228#2320C2213yes—
229#2314C2213yes—
230C4×C4⋊Q8C2213yes—
231C4×#124C2213yes—
232C4×C22⋊Q8C2213yes—
233C4×C22⋊Q8C2213yes—
234C4×#123C2213yes—
235C4×#123C2213yes—
236#2298C2213yes—
237#2295C2213yes—
238#2276C2211yescharacteristic
239C42×Q8C2211yescharacteristic
240C22×#41C2311yescharacteristic
241C22×#41C2311yescharacteristic
242C23×Q8C2311yescharacteristic
243#559—224no—
244Q82—224no—
245Q82—28no—
246#557—224no—
247#557—28no—
248#557—28no—
249#557—224no—
250#557—28no—
251#557—224no—
252#557—28no—
253#555—224no—
254#553—224no—
255#552—224no—
256#550—28no—
257#548—28no—
258#548—28no—
259#544—224no—
260#544—224no—
261#542—224no—
262#540—224no—
263#533—224no—
264#533—224no—
265C2×C4⋊Q8C2313yes—
266C2×C4⋊Q8C2313yes—
267C2×C4⋊Q8C2316yes—
268C2×C4⋊Q8C2313yes—
269C2×C4⋊Q8C2313yes—
270C2×C4⋊Q8C2316yes—
271C2×C4⋊Q8C2313yes—
272C2×C4⋊Q8C2313yes—
273C2×C4⋊Q8C2313yes—
274C2×C4⋊Q8C2313yes—
275C2×C4⋊Q8C2313yes—
276C2×C4⋊Q8C2313yes—
277C2×C4⋊Q8C2316yes—
278C2×#127C2313yes—
279#529—224no—
280#529—224no—
281C2×#126C2316yes—
282C2×#126C2311yescharacteristic
283C2×#126C2313yes—
284C2×#125C2313yes—
285C2×#125C2316yes—
286C2×#125C2313yes—
287C2×#125C2313yes—
288C2×#125C2313yes—
289C2×#125C2313yes—
290C2×#125C2313yes—
291C2×#125C2313yes—
292C2×#125C2313yes—
293C2×#125C2313yes—
294C2×#125C2316yes—
295C2×#125C2313yes—
296C2×#125C2313yes—
297C2×#124C2316yes—
298C2×#124C2313yes—
299C2×#124C2313yes—
300C2×#124C2313yes—
301C2×#124C2316yes—
302C2×#124C2313yes—
303C2×#124C2316yes—
304C2×#124C2316yes—
305C2×#123C2316yes—
306C2×#123C2313yes—
307C2×#123C2313yes—
308C2×#123C2316yes—
309C2×#123C2313yes—
310C2×#123C2313yes—
311C2×#123C2316yes—
312C2×C22⋊Q8C2313yes—
313C2×C22⋊Q8C2313yes—
314C2×C22⋊Q8C2311yescharacteristic
315C2×C22⋊Q8C2313yes—
316C2×C22⋊Q8C2316yes—
317C2×C22⋊Q8C2313yes—
318C2×C22⋊Q8C2313yes—
319C2×C22⋊Q8C2313yes—
320C2×C22⋊Q8C2316yes—
321C2×C22⋊Q8C2313yes—
322C2×C22⋊Q8C2313yes—
323C2×C22⋊Q8C2316yes—
324C2×#121C2313yes—
325C2×#121C2313yes—
326C2×#121C2313yes—
327C2×#121C2313yes—
328C2×#121C2316yes—
329C2×#121C2313yes—
330#520—28no—
331#519—28no—
332#519D4116yes—
333C4×#41—28no—
334C2×C4×Q8—28no—
335C2×C4×Q8C2313yes—
336C2×C4×Q8C2313yes—
337C2×C4×Q8C2316yes—
338C2×C4×Q8C2313yes—
339C2×C4×Q8C2313yes—
340C2×C4×Q8C2316yes—
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×Q8C2313yes—
353C2×C4×Q8C2313yes—
354C2×C4×Q8C2313yes—
355C2×C4×Q8C2313yes—
356C2×C4×Q8C2313yes—
357C2×C4×Q8C2311yescharacteristic
358C2×C4×Q8C2313yes—
359C2×C4×Q8C2311yescharacteristic
360C2×C4×D4C2313yes—
361C2×C4×D4C2313yes—
362C2×C4×D4C2313yes—
363C2×C4×D4C2316yes—
364C2×C4×D4C2313yes—
365C2×C4×D4C2313yes—
366C2×C4×D4C2313yes—
367C2×C4×D4C2313yes—
368C2×#117C2316yes—
369C2×#117C2313yes—
370C2×#117C2313yes—
371C2×#117C2313yes—
372C2×#117C2313yes—
373C2×#117C2313yes—
374C2×#117C2313yes—
375C22×C4⋊C4C2313yes—
376C22×C4⋊C4C2313yes—
377C22×C42C2313yes—
378C22×C42C2313yes—
379#400C2313yes—
380#400C2313yes—
381#400C2316yes—
382#400C2316yes—
383#400C2313yes—
384#400C2313yes—
385#400C2311yescharacteristic
386#400C2311yescharacteristic
387#399C2316yes—
388#399C2316yes—
389#399C2316yes—
390#399C2316yes—
391#399C2313yes—
392#399C2316yes—
393#399C2316yes—
394#399C2316yes—
395#399C2316yes—
396#399C2316yes—
397#399C2313yes—
398#399C2313yes—
399#399C2313yes—
400#398C2313yes—
401#398C2316yes—
402#398C2316yes—
403#398C2316yes—
404#398C2316yes—
405#398C2313yes—
406#398C2313yes—
407#398C2316yes—
408#398C2313yes—
409#398C2313yes—
410#398C2311yescharacteristic
411#398C2313yes—
412#398C2313yes—
413#398C2313yes—
414#398C2313yes—
415#397C2313yes—
416#397C2316yes—
417#397C2316yes—
418#397C2316yes—
419#397C2313yes—
420#397C2316yes—
421#397C2313yes—
422#397C2311yescharacteristic
423#397C2311yescharacteristic
424#397C2313yes—
425#397C2313yes—
426#397C2313yes—
427#397C2316yes—
428#396C2313yes—
429#396C2316yes—
430#396C2316yes—
431#396C2316yes—
432#396C2313yes—
433#396C2316yes—
434#396C2316yes—
435#396C2316yes—
436#396C2313yes—
437#396C2313yes—
438#395C2313yes—
439#395C2316yes—
440#395C2316yes—
441#395C2316yes—
442#395C2313yes—
443#395C2313yes—
444#395C2313yes—
445#395C2316yes—
446#395C2313yes—
447#395C2311yescharacteristic
448#394C2316yes—
449#394C2316yes—
450#394C2316yes—
451#394C2313yes—
452#394C2313yes—
453#394C2316yes—
454#394C2316yes—
455#394C2316yes—
456#394C2316yes—
457#394C2313yes—
458#394C2313yes—
459#394C2313yes—
460#394C2313yes—
461#393C2313yes—
462#393C2316yes—
463#393C2316yes—
464#393C2316yes—
465#393C2313yes—
466#393C2316yes—
467#393C2313yes—
468#393C2313yes—
469#391C2313yes—
470#391C2313yes—
471#391C2313yes—
472#391C2313yes—
473#391C2313yes—
474#391C2316yes—
475#391C2313yes—
476#391C2313yes—
477#391C2313yes—
478#391C2311yescharacteristic
479#390C2313yes—
480#390C2313yes—
481#390C2316yes—
482#390C2313yes—
483#390C2313yes—
484#390C2313yes—
485#390C2313yes—
486#390C2313yes—
487#390C2313yes—
488#390C2313yes—
489#390C2313yes—
490#390C2316yes—
491#390C2313yes—
492#390C2313yes—
493#390C2313yes—
494#390C2313yes—
495#390C2313yes—
496#390C2313yes—
497#390C2313yes—
498#389C2311yescharacteristic
499#389C2313yes—
500#389C2313yes—
501#389C2313yes—
502#389C2313yes—
503#389C2313yes—
504#389C2316yes—
505#389C2316yes—
506#389C2316yes—
507#389C2313yes—
508#389C2313yes—
509#389C2313yes—
510#389C2313yes—
511#389C2316yes—
512#389C2313yes—
513#389C2313yes—
514#389C2313yes—
515#389C2313yes—
516#389C2313yes—
517#389C2313yes—
518#389C2313yes—
519#389C2313yes—
520#389C2316yes—
521#389C2313yes—
522#389C2313yes—
523#389C2313yes—
524#389C2313yes—
525#389C2316yes—
526#389C2313yes—
527#389C2313yes—
528#389C2313yes—
529#389C2311yescharacteristic
530#388C2316yes—
531#388C2316yes—
532#388C2313yes—
533#388C2316yes—
534#388C2313yes—
535#388C2316yes—
536#388C2316yes—
537#388C2313yes—
538#388C2316yes—
539#388C2316yes—
540#388C2316yes—
541#388C2316yes—
542#388C2316yes—
543#388C2316yes—
544#388C2313yes—
545#388C2313yes—
546#388C2313yes—
547#388C2313yes—
548#388C2313yes—
549#388C2316yes—
550#388C2316yes—
551#388C2313yes—
552#388C2313yes—
553#388C2311yescharacteristic
554#388C2313yes—
555#387C2316yes—
556#387C2316yes—
557#387C2313yes—
558#387C2313yes—
559#387C2316yes—
560#387C2313yes—
561#387C2316yes—
562#387C2313yes—
563#387C2313yes—
564#387C2313yes—
565#387C2316yes—
566#387C2313yes—
567#387C2313yes—
568#387C2313yes—
569#387C2313yes—
570#387C2311yescharacteristic
571#387C2313yes—
572#386C2313yes—
573#386C2316yes—
574#386C2313yes—
575#385C2313yes—
576#385C2316yes—
577#385C2316yes—
578#385C2316yes—
579#385C2313yes—
580#385C2316yes—
581#385C2316yes—
582#385C2313yes—
583#385C2316yes—
584#385C2313yes—
585#385C2313yes—
586#385C2311yescharacteristic
587#384C2313yes—
588#384C2313yes—
589#384C2313yes—
590#384C2313yes—
591#384C2313yes—
592#384C2313yes—
593#383C2316yes—
594#382C2313yes—
595#382C2313yes—
596#382C2313yes—
597#382C2316yes—
598#382C2313yes—
599#382C2313yes—
600#382C2313yes—
601#381C2313yes—
602#381C2311yescharacteristic
603#380C2313yes—
604#380C2313yes—
605#380C2313yes—
606#380C2313yes—
607#380C2316yes—
608#380C2313yes—
609#380C2313yes—
610#380C2313yes—
611#380C2313yes—
612#380C2316yes—
613#380C2313yes—
614#380C2313yes—
615#380C2316yes—
616#380C2316yes—
617#380C2313yes—
618#380C2313yes—
619C4×C4⋊C4C2313yes—
620C4×C4⋊C4C2313yes—
621C4×C4⋊C4C2313yes—
622C4×C4⋊C4C2313yes—
623C4×C4⋊C4C2313yes—
624C4×C4⋊C4C2313yes—
625C4×C4⋊C4C2313yes—
626C4×C4⋊C4C2313yes—
627C4×C4⋊C4C2316yes—
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×C22⋊C4C2313yes—
637C4×C22⋊C4C2313yes—
638C4×C22⋊C4C2313yes—
639C4×C22⋊C4C2313yes—
640C4×C22⋊C4C2313yes—
641C4×C22⋊C4C2313yes—
642C4×C22⋊C4C2313yes—
643C4×C22⋊C4C2313yes—
644C4×C22⋊C4C2313yes—
645C4×C22⋊C4C2313yes—
646#376C2313yes—
647#376C2316yes—
648C43C2313yes—
649C2×#41—24no—
650C2×#41—24no—
651C2×#41—24no—
652C2×#41—24no—
653C2×#41—24no—
654C2×#41—24no—
655C22×Q8—24no—
656C22×Q8—24no—
657C22×Q8C2×D418yes—
658C22×Q8C2413yes—
659C22×Q8C2411yescharacteristic
660C22×Q8C2413yes—
661C22×Q8C2413yes—
662C22×Q8C2413yes—
663C22×Q8C2416yes—
664C22×Q8C2413yes—
665C22×Q8C2411yescharacteristic
666C22×D4C2413yes—
667C22×D4C2413yes—
668C22×D4C2413yes—
669C22×D4C2413yes—
670C22×D4C2416yes—
671C22×D4C2413yes—
672C23×C4C2413yes—
673C23×C4C2413yes—
674C23×C4C2411yescharacteristic
675C23×C4C2413yes—
676C23×C4C2413yes—
677C23×C4C2416yes—
678C23×C4C2413yes—
679C23×C4C2413yes—
680C4⋊Q8—212no—
681C4⋊Q8—212no—
682C4⋊Q8—212no—
683C4⋊Q8—212no—
684C4⋊Q8—212no—
685C4⋊Q8—212no—
686C4⋊Q8—212no—
687C4⋊Q8—224no—
688C4⋊Q8—212no—
689C4⋊Q8—224no—
690C4⋊Q8—212no—
691C4⋊Q8—46no—
692C4⋊Q8—86no—
693#127—212no—
694#126—212no—
695#126—24no—
696#126—224no—
697#125—212no—
698#125—212no—
699#125—212no—
700#125—212no—
701#125—212no—
702#125—212no—
703#125—212no—
704#125—212no—
705#125—224no—
706#125—212no—
707#125—212no—
708#125—224no—
709#125—212no—
710#124—212no—
711#124—212no—
712#124—212no—
713#124—224no—
714#124—412no—
715#124—46no—
716#124—86no—
717#124—86no—
718#123—224no—
719#123—212no—
720#123—224no—
721#123—212no—
722#123—46no—
723#123—46no—
724#123—86no—
725C22⋊Q8—212no—
726C22⋊Q8—212no—
727C22⋊Q8—212no—
728C22⋊Q8—24no—
729C22⋊Q8—212no—
730C22⋊Q8—212no—
731C22⋊Q8—212no—
732C22⋊Q8—224no—
733C22⋊Q8—46no—
734C22⋊Q8—412no—
735C22⋊Q8—46no—
736C22⋊Q8—86no—
737#121—212no—
738#121—212no—
739#121—212no—
740#121—212no—
741#121—212no—
742#121—224no—
743C4×Q8—212no—
744C4×Q8—24no—
745C4×Q8—212no—
746C4×Q8—24no—
747C4×Q8—24no—
748C4×Q8—212no—
749C4×Q8—24no—
750C4×Q8—212no—
751C4×Q8—24no—
752C4×Q8—24no—
753C4×Q8—24no—
754C4×Q8—24no—
755C4×Q8—24no—
756C4×Q8—24no—
757C4×Q8—212no—
758C4×Q8—212no—
759C4×Q8—224no—
760C4×Q8—212no—
761C4×Q8—212no—
762C4×Q8—224no—
763C4×Q8—212no—
764C4×Q8C2×D418yes—
765C4×Q8C2×D4124yes—
766C4×Q8C2×D418yes—
767C4×Q8C2×D4124yes—
768C4×D4—212no—
769C4×D4—212no—
770C4×D4—212no—
771C4×D4—212no—
772C4×D4—212no—
773C4×D4—212no—
774C4×D4—212no—
775C4×D4—224no—
776#117—212no—
777#117—212no—
778#117—212no—
779#117—212no—
780#117—224no—
781#117C2×D4124yes—
782#117C2×D4124yes—
783C2×C4⋊C4—212no—
784C2×C4⋊C4—212no—
785C2×C4⋊C4C2413yes—
786C2×C4⋊C4C2413yes—
787C2×C4⋊C4C2413yes—
788C2×C4⋊C4C2413yes—
789C2×C4⋊C4C2416yes—
790C2×C4⋊C4C2411yescharacteristic
791C2×C4⋊C4C2413yes—
792C2×C4⋊C4C2413yes—
793C2×C4⋊C4C2413yes—
794C2×C4⋊C4C2413yes—
795C2×C4⋊C4C2413yes—
796C2×C4⋊C4C2413yes—
797C2×C4⋊C4C2416yes—
798C2×C4⋊C4C2411yescharacteristic
799C2×C4⋊C4C2413yes—
800C2×C4⋊C4C2413yes—
801C2×C4⋊C4C2411yescharacteristic
802C2×C4⋊C4C2413yes—
803C2×C4⋊C4C2413yes—
804C2×C4⋊C4C2411yescharacteristic
805C2×C4⋊C4C2411yescharacteristic
806C2×C4⋊C4C2413yes—
807C2×C4⋊C4C2411yescharacteristic
808C2×C4⋊C4C2413yes—
809C2×C4⋊C4C2413yes—
810C2×C4⋊C4C2416yes—
811C2×C4⋊C4C2413yes—
812C2×C4⋊C4C2416yes—
813C2×C4⋊C4C2413yes—
814C2×C4⋊C4C2413yes—
815C2×C4⋊C4C2413yes—
816C2×C4⋊C4C2416yes—
817C2×C4⋊C4C2413yes—
818C2×C4⋊C4C2413yes—
819C2×C4⋊C4C2413yes—
820C2×C4⋊C4C2413yes—
821C2×C4⋊C4C2413yes—
822C2×C4⋊C4C2411yescharacteristic
823C2×C4⋊C4C2411yescharacteristic
824C2×C4⋊C4C2413yes—
825C2×C4⋊C4C2413yes—
826C2×C4⋊C4C2411yescharacteristic
827C2×C4⋊C4C2413yes—
828C2×C4⋊C4C2416yes—
829C2×C4⋊C4C2416yes—
830C2×C4⋊C4C2413yes—
831C2×C4⋊C4C2416yes—
832C2×C4⋊C4C2413yes—
833C2×C4⋊C4C2413yes—
834C2×C4⋊C4C2416yes—
835C2×C4⋊C4C2416yes—
836C2×C4⋊C4C2413yes—
837C2×C4⋊C4C2413yes—
838C2×C4⋊C4C2413yes—
839C2×C4⋊C4C2413yes—
840C2×C4⋊C4C2413yes—
841C2×C4⋊C4C2413yes—
842C2×C4⋊C4C2413yes—
843C2×C4⋊C4C2411yescharacteristic
844C2×C4⋊C4C2411yescharacteristic
845C2×C4⋊C4C2413yes—
846C2×C4⋊C4C2413yes—
847C2×C4⋊C4C2413yes—
848C2×C4⋊C4C2413yes—
849C2×C4⋊C4C2413yes—
850C2×C4⋊C4C2413yes—
851C2×C22⋊C4C2411yescharacteristic
852C2×C22⋊C4C2413yes—
853C2×C22⋊C4C2413yes—
854C2×C22⋊C4C2413yes—
855C2×C22⋊C4C2416yes—
856C2×C22⋊C4C2413yes—
857C2×C22⋊C4C2416yes—
858C2×C22⋊C4C2411yescharacteristic
859C2×C22⋊C4C2413yes—
860C2×C22⋊C4C2411yescharacteristic
861C2×C22⋊C4C2413yes—
862C2×C22⋊C4C2416yes—
863C2×C22⋊C4C2413yes—
864C2×C22⋊C4C2413yes—
865C2×C22⋊C4C2413yes—
866C2×C22⋊C4C2413yes—
867C2×C22⋊C4C2411yescharacteristic
868C2×C22⋊C4C2413yes—
869C2×C22⋊C4C2416yes—
870C2×C22⋊C4C2416yes—
871C2×C22⋊C4C2413yes—
872C2×C22⋊C4C2413yes—
873C2×C22⋊C4C2416yes—
874C2×C22⋊C4C2413yes—
875C2×C22⋊C4C2416yes—
876C2×C22⋊C4C2416yes—
877C2×C22⋊C4C2413yes—
878C2×C22⋊C4C2413yes—
879C2×C22⋊C4C2413yes—
880C2×C22⋊C4C2413yes—
881C2×C22⋊C4C2413yes—
882C2×C22⋊C4C2413yes—
883C2×C22⋊C4C2413yes—
884C2×C22⋊C4C2413yes—
885C2×C22⋊C4C2413yes—
886C2×C22⋊C4C2416yes—
887C2×C22⋊C4C2416yes—
888C2×C22⋊C4C2411yescharacteristic
889C2×C22⋊C4C2413yes—
890C2×C22⋊C4C2413yes—
891C2×C22⋊C4C2416yes—
892C2×C22⋊C4C2411yescharacteristic
893C2×C22⋊C4C2413yes—
894C2×C42—212no—
895C2×C42—212no—
896C2×C42C2413yes—
897C2×C42C2413yes—
898C2×C42C2413yes—
899C2×C42C2413yes—
900C2×C42C2416yes—
901C2×C42C2413yes—
902C2×C42C2413yes—
903C2×C42C2413yes—
904C2×C42C2413yes—
905C2×C42C2413yes—
906C2×C42C2413yes—
907C2×C42C2413yes—
908C2×C42C2413yes—
909C2×C42C2413yes—
910C2×C42C2413yes—
911C2×C42C2411yescharacteristic
912C2×C42C2413yes—
913C2×C42C2416yes—
914C2×C42C2413yes—
915C2×C42C2411yescharacteristic
916C2×C42C2413yes—
917C2×C42C2416yes—
918C2×C42C2413yes—
919#95C2411yescharacteristic
920#95C2413yes—
921#95C2413yes—
922#95C2413yes—
923#95C2413yes—
924#95C2413yes—
925#95C2416yes—
926#95C2416yes—
927#95C2411yescharacteristic
928#95C2411yescharacteristic
929#95C2411yescharacteristic
930#95C2411yescharacteristic
931#95C2411yescharacteristic
932#95C2411yescharacteristic
933#95C2411yescharacteristic
934#95C2411yescharacteristic
935#95C2413yes—
936#95C2413yes—
937#95C2413yes—
938#95C2413yes—
939#95C2413yes—
940#95C2413yes—
941#95C2413yes—
942#95C2413yes—
943#95C2413yes—
944#95C2413yes—
945#95C2413yes—
946#95C2411yescharacteristic
947#95C2411yescharacteristic
948#95C2411yescharacteristic
949#95C2416yes—
950#95C2411yescharacteristic
951#95C2411yescharacteristic
952#95C2413yes—
953#95C2413yes—
954#95C2413yes—
955#95C2413yes—
956#95C2413yes—
957#95C2413yes—
958#95C2416yes—
959#95C2413yes—
960#95C2413yes—
961#95C2413yes—
962#95C2413yes—
963#95C2413yes—
964#95C2413yes—
965#95C2413yes—
966#95C2413yes—
967#95C2416yes—
968#95C2416yes—
969#95C2416yes—
970#95C2416yes—
971C24C2513yes—
972C24C2513yes—
973C24C2511yescharacteristic
974#41—416no—
975#41—416no—
976C2×Q8—232no—
977C2×Q8—26no—
978C2×Q8—22no—
979C2×Q8—26no—
980C2×Q8—26no—
981C2×Q8—212no—
982C2×Q8—26no—
983C2×Q8—26no—
984C2×Q8—26no—
985C2×Q8—26no—
986C2×Q8—22no—
987C2×Q8—41no—
988C2×Q8—43no—
989C2×Q8—43no—
990C2×Q8—43no—
991C2×Q8—46no—
992C2×Q8—43no—
993C2×Q8—46no—
994C2×Q8—43no—
995C2×Q8—43no—
996C2×Q8—43no—
997C2×Q8C22×D4112yes—
998C2×Q8C22×D414yes—
999C2×Q82−1+414yes—
1000C2×Q82−1+414yes—
1001C2×D4—26no—
1002C2×D4—26no—
1003C2×D4—26no—
1004C2×D4—26no—
1005C2×D4—212no—
1006C2×D4—26no—
1007C2×D4—26no—
1008C2×D4—26no—
1009C2×D4—26no—
1010C2×D4—26no—
1011C2×D4—43no—
1012C2×D4—43no—
1013C2×D4—43no—
1014C2×D4—46no—
1015C2×D4—43no—
1016C2×D4—46no—
1017C2×D4—43no—
1018C2×D4—43no—
1019C22×C4—26no—
1020C22×C4—26no—
1021C22×C4—22no—
1022C22×C4—26no—
1023C22×C4—26no—
1024C22×C4—26no—
1025C22×C4—26no—
1026C22×C4—26no—
1027C22×C4—26no—
1028C22×C4—26no—
1029C22×C4—22no—
1030C22×C4—26no—
1031C22×C4—26no—
1032C22×C4—212no—
1033C22×C4—41no—
1034C22×C4—43no—
1035C22×C4—43no—
1036C22×C4—46no—
1037C22×C4—43no—
1038C22×C4—43no—
1039C22×C4—43no—
1040C22×C4—43no—
1041C22×C4—46no—
1042C22×C4C22×D4112yes—
1043C22×C4C2511yescharacteristic
1044C22×C4C2511yescharacteristic
1045C22×C4C2511yescharacteristic
1046C22×C4C2511yescharacteristic
1047C22×C4C2511yescharacteristic
1048C22×C4C2513yes—
1049C22×C4C2513yes—
1050C22×C4C2513yes—
1051C22×C4C2513yes—
1052C22×C4C2511yescharacteristic
1053C22×C4C2513yes—
1054C22×C4C2511yescharacteristic
1055C22×C4C2511yescharacteristic
1056C22×C4C2513yes—
1057C22×C4C2511yescharacteristic
1058C22×C4C2513yes—
1059C22×C4C2511yescharacteristic
1060C22×C4C2513yes—
1061C22×C4C2513yes—
1062C22×C4C2513yes—
1063C22×C4C2513yes—
1064C22×C4C2513yes—
1065C22×C4C2511yescharacteristic
1066C22×C4C2513yes—
1067C22×C4C2511yescharacteristic
1068C22×C4C2511yescharacteristic
1069C22×C4C2511yescharacteristic
1070C22×C4C2513yes—
1071C4⋊C4—26no—
1072C4⋊C4—26no—
1073C4⋊C4—212no—
1074C4⋊C4—26no—
1075C4⋊C4—26no—
1076C4⋊C4—22no—
1077C4⋊C4—26no—
1078C4⋊C4—26no—
1079C4⋊C4—26no—
1080C4⋊C4—26no—
1081C4⋊C4—26no—
1082C4⋊C4—26no—
1083C4⋊C4—212no—
1084C4⋊C4—22no—
1085C4⋊C4—26no—
1086C4⋊C4—26no—
1087C4⋊C4—22no—
1088C4⋊C4—26no—
1089C4⋊C4—26no—
1090C4⋊C4—22no—
1091C4⋊C4—22no—
1092C4⋊C4—26no—
1093C4⋊C4—22no—
1094C4⋊C4—26no—
1095C4⋊C4—26no—
1096C4⋊C4—212no—
1097C4⋊C4—26no—
1098C4⋊C4—26no—
1099C4⋊C4—212no—
1100C4⋊C4—26no—
1101C4⋊C4—212no—
1102C4⋊C4—26no—
1103C4⋊C4—26no—
1104C4⋊C4—26no—
1105C4⋊C4—26no—
1106C4⋊C4—26no—
1107C4⋊C4—26no—
1108C4⋊C4—22no—
1109C4⋊C4—22no—
1110C4⋊C4—26no—
1111C4⋊C4—26no—
1112C4⋊C4—22no—
1113C4⋊C4—41no—
1114C4⋊C4—43no—
1115C4⋊C4—43no—
1116C4⋊C4—41no—
1117C4⋊C4—43no—
1118C4⋊C4—43no—
1119C4⋊C4—46no—
1120C4⋊C4—43no—
1121C4⋊C4—46no—
1122C4⋊C4—43no—
1123C4⋊C4—43no—
1124C4⋊C4—46no—
1125C4⋊C4—46no—
1126C4⋊C4—43no—
1127C4⋊C4—43no—
1128C4⋊C4—46no—
1129C4⋊C4—43no—
1130C4⋊C4—43no—
1131C4⋊C4—43no—
1132C4⋊C4—43no—
1133C4⋊C4C22×D4112yes—
1134C4⋊C4C22×D4112yes—
1135C4⋊C4C22×D4112yes—
1136C4⋊C4C22×D4112yes—
1137C22⋊C4—22no—
1138C22⋊C4—26no—
1139C22⋊C4—22no—
1140C22⋊C4—22no—
1141C22⋊C4—26no—
1142C22⋊C4—26no—
1143C22⋊C4—212no—
1144C22⋊C4—26no—
1145C22⋊C4—212no—
1146C22⋊C4—26no—
1147C22⋊C4—26no—
1148C22⋊C4—212no—
1149C22⋊C4—26no—
1150C22⋊C4—26no—
1151C22⋊C4—26no—
1152C22⋊C4—26no—
1153C22⋊C4—22no—
1154C22⋊C4—26no—
1155C22⋊C4—41no—
1156C22⋊C4—43no—
1157C22⋊C4—43no—
1158C22⋊C4—46no—
1159C22⋊C4—46no—
1160C22⋊C4—43no—
1161C22⋊C4—43no—
1162C22⋊C4—46no—
1163C22⋊C4—46no—
1164C22⋊C4—43no—
1165C22⋊C4—43no—
1166C22⋊C4—43no—
1167C22⋊C4—43no—
1168C22⋊C4—46no—
1169C22⋊C4—46no—
1170C22⋊C4—46no—
1171C22⋊C4—46no—
1172C22⋊C4—43no—
1173C22⋊C4—43no—
1174C22⋊C4—43no—
1175C22⋊C4—43no—
1176C22⋊C4—43no—
1177C22⋊C4—43no—
1178C22⋊C4C22×D414yes—
1179C22⋊C4C22×D4112yes—
1180C42—22no—
1181C42—26no—
1182C42—26no—
1183C42—26no—
1184C42—26no—
1185C42—26no—
1186C42—26no—
1187C42—26no—
1188C42—212no—
1189C42—26no—
1190C42—26no—
1191C42—26no—
1192C42—26no—
1193C42—26no—
1194C42—26no—
1195C42—26no—
1196C42—41no—
1197C42—43no—
1198C42—43no—
1199C42—46no—
1200C42C22×D4112yes—
1201C42C22×D4124yes—
1202C42C22×D4112yes—
1203C23—21no—
1204C23—21no—
1205C23—21no—
1206C23—21no—
1207C23—21no—
1208C23—21no—
1209C23—23no—
1210C23—23no—
1211C23—23no—
1212C23—23no—
1213C23—23no—
1214C23—23no—
1215C23—23no—
1216C23—23no—
1217C23—23no—
1218C23—23no—
1219C23—23no—
1220C23—23no—
1221C23—23no—
1222C23—23no—
1223C23C23×D412yes—
1224C23C2611yescharacteristic
1225Q8—224no—
1226Q8—412no—
1227Q8—44no—
1228Q8—86no—
1229Q8—86no—
1230Q8—812no—
1231Q8—86no—
1232Q8#536116yes—
1233D4—412no—
1234D4—412no—
1235D4—86no—
1236D4—812no—
1237D4—86no—
1238D4—86no—
1239C2×C4—21no—
1240C2×C4—21no—
1241C2×C4—23no—
1242C2×C4—23no—
1243C2×C4—23no—
1244C2×C4—21no—
1245C2×C4—21no—
1246C2×C4—23no—
1247C2×C4—23no—
1248C2×C4—21no—
1249C2×C4—21no—
1250C2×C4—21no—
1251C2×C4—23no—
1252C2×C4—21no—
1253C2×C4—224no—
1254C2×C4—21no—
1255C2×C4—21no—
1256C2×C4—21no—
1257C2×C4—21no—
1258C2×C4—21no—
1259C2×C4—23no—
1260C2×C4—23no—
1261C2×C4—21no—
1262C2×C4—23no—
1263C2×C4—23no—
1264C2×C4—23no—
1265C2×C4—23no—
1266C2×C4—21no—
1267C2×C4—21no—
1268C2×C4—21no—
1269C2×C4—21no—
1270C2×C4—23no—
1271C2×C4—23no—
1272C2×C4—23no—
1273C2×C4—23no—
1274C2×C4—21no—
1275C2×C4—21no—
1276C2×C4—21no—
1277C2×C4—21no—
1278C2×C4—23no—
1279C2×C4—23no—
1280C2×C4—23no—
1281C2×C4—21no—
1282C2×C4—23no—
1283C2×C4—23no—
1284C2×C4—21no—
1285C2×C4—23no—
1286C2×C4—21no—
1287C2×C4—21no—
1288C2×C4—21no—
1289C2×C4—23no—
1290C2×C4—23no—
1291C2×C4—21no—
1292C2×C4—23no—
1293C2×C4—23no—
1294C2×C4—21no—
1295C2×C4—21no—
1296C2×C4—21no—
1297C2×C4—23no—
1298C2×C4—23no—
1299C2×C4—23no—
1300C2×C4—21no—
1301C2×C4—23no—
1302C2×C4—23no—
1303C2×C4—23no—
1304C2×C4—23no—
1305C2×C4—21no—
1306C2×C4—21no—
1307C2×C4—21no—
1308C2×C4—23no—
1309C2×C4—21no—
1310C2×C4—23no—
1311C2×C4—21no—
1312C2×C4—21no—
1313C2×C4—23no—
1314C2×C4—44no—
1315C2×C4—412no—
1316C2×C4—412no—
1317C2×C4—86no—
1318C2×C4—812no—
1319C2×C4—86no—
1320C2×C4—86no—
1321C2×C4C23×D416yes—
1322C2×C4C23×D416yes—
1323C2×C4C23×D412yes—
1324C2×C4C23×D416yes—
1325C2×C4C23×D412yes—
1326C2×C4C23×D416yes—
1327C2×C4C2×2−1+416yes—
1328C2×C4C2×2−1+416yes—
1329C2×C4#58512yes—
1330C2×C4#58512yes—
1331C22—22no—
1332C22—22no—
1333C22—22no—
1334C22—41no—
1335C22—41no—
1336C22—41no—
1337C22—41no—
1338C22—43no—
1339C22—43no—
1340C22—43no—
1341C22—43no—
1342C22—43no—
1343C22—43no—
1344C22—43no—
1345C22—43no—
1346C22—43no—
1347C22—43no—
1348C22—43no—
1349C22—43no—
1350C22—43no—
1351C22—43no—
1352C22C24×D411yescharacteristic
1353C22C22×2−1+411yescharacteristic
1354C22C22×2−1+411yescharacteristic
1355C22C2×#58511yescharacteristic
1356C22C2×#58511yescharacteristic
1357C22H(7,𝔽2)11yescharacteristic
1358C222−1+611yescharacteristic
1359C4—22no—
1360C4—26no—
1361C4—22no—
1362C4—22no—
1363C4—26no—
1364C4—26no—
1365C4—22no—
1366C4—41no—
1367C4—41no—
1368C4—43no—
1369C4—41no—
1370C4—43no—
1371C4—43no—
1372C4—43no—
1373C4—43no—
1374C4—41no—
1375C4—43no—
1376C4—41no—
1377C4—41no—
1378C4—43no—
1379C4—41no—
1380C4—43no—
1381C4—41no—
1382C4—41no—
1383C4—41no—
1384C4—43no—
1385C4—43no—
1386C4C2×#536112yes—
1387C2—42no—
1388C2—83no—
1389C2—83no—
1390C2C22×#53611yescharacteristic
1391C2#6294911yescharacteristic
1392C2#6295211yescharacteristic
1393C2#6300211yescharacteristic
1394C2#6300311yescharacteristic
1395C2#6303411yescharacteristic
1396C2#6306111yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#3524C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×#3502C2semidirect
3. #52166C2semidirect
4. #42968C2semidirect
5. #42944C2semidirect
6. #42888C2semidirect
7. #42886C2semidirect
8. #42804C2semidirect
9. #42789C2semidirect
10. #39955C2semidirect
11. #39891C2semidirect
12. #39866C2semidirect
13. #39859C2semidirect
14. #39746C2semidirect
15. #39125C2semidirect
16. #37304C2semidirect
17. #37279C2semidirect
18. #37274C2semidirect
19. #36578C2semidirect
20. #36483C2semidirect
21. #36466C2semidirect
22. #36457C2semidirect
23. #36445C2semidirect
24. #36431C2semidirect
25. #36049C2semidirect
26. #36040C2semidirect
27. #35937C2semidirect
28. #35816C2semidirect
29. #35801C2semidirect
30. #35801C2semidirect
31. #34262C2semidirect

Maximal subgroups

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

subgroupindex
C2×#35242
C2×#35022
#521662
#429682
#429442
#428882
#428862
#428042
#427892
#399552
#398912
#398662
#398592
#397462
#391252
#373042
#372792
#372742
#365782
#364832
#364662
#364572
#364452
#364312
#360492
#360402
#359372
#358162
#358012
#342622