Finite Group Databasebeta

← #7698379

Subgroups — #7698379

Order 512.

6751 conjugacy classes of subgroups.

The subgroup lattice has 1389 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3503C211yesmaximal, characteristic, complemented
2C2×#3502C211yesmaximal, characteristic, complemented
3#59833C213yesmaximal, complemented
4#59153C213yesmaximal, complemented
5#59151C213yesmaximal, complemented
6#52162C213yesmaximal, complemented
7#45424C213yesmaximal, complemented
8#45274C213yesmaximal, complemented
9#45272C213yesmaximal, complemented
10#44941C213yesmaximal, complemented
11#44934C213yesmaximal, complemented
12#44879C213yesmaximal, complemented
13#39616C213yesmaximal, complemented
14#39596C213yesmaximal, complemented
15#39591C213yesmaximal, complemented
16#39369C213yesmaximal, complemented
17#37690C213yesmaximal, complemented
18#37686C213yesmaximal, complemented
19Q8×C4⋊Q8C211yesmaximal, characteristic, complemented
20Q8×C22⋊Q8C211yesmaximal, characteristic, complemented
21#36431C211yesmaximal, characteristic, complemented
22#35957C211yesmaximal, characteristic, complemented
23#35937C211yesmaximal, characteristic, complemented
24#35845C211yesmaximal, characteristic, complemented
25#35816C211yesmaximal, characteristic, complemented
26#35748C211yesmaximal, characteristic, complemented
27#35711C211yesmaximal, characteristic, complemented
28#34336C211yesmaximal, characteristic, complemented
29#34312C211yesmaximal, characteristic
30#34294C211yesmaximal, characteristic
31#34293C211yesmaximal, characteristic
32#3503—216no—
33#3502—216no—
34C2×Q82C2213yes—
35C2×Q82C2211yescharacteristic
36C2×Q82C2211yescharacteristic
37C2×Q82C2211yescharacteristic
38C2×#557C2211yescharacteristic
39C2×#557C2211yescharacteristic
40C2×#557C2211yescharacteristic
41C2×#557C2213yes—
42C2×#557C2213yes—
43C2×#557C2213yes—
44C2×#557C2211yescharacteristic
45C2×#554C2213yes—
46C2×#554C2213yes—
47C2×D4×Q8C2213yes—
48C2×D4×Q8C2213yes—
49C2×#548C2211yescharacteristic
50C2×#544C2213yes—
51C2×#544C2213yes—
52C2×#544C2213yes—
53C2×#544C2213yes—
54C2×#533C2213yes—
55C2×#533C2213yes—
56C2×#533C2213yes—
57C22×C4⋊Q8C2213yes—
58C2×#520C2211yescharacteristic
59C2×#520C2211yescharacteristic
60C2×#519C2211yescharacteristic
61C2×#519C2211yescharacteristic
62C2×C4×#41C2211yescharacteristic
63C22×C4×Q8C2211yescharacteristic
64#2868C2213yes—
65#2857C2213yes—
66#2851C2213yes—
67#2734C2213yes—
68#2734C2216yes—
69#2732C2213yes—
70#2729C2213yes—
71#2729C2216yes—
72#2729C2213yes—
73#2726C2213yes—
74#2720C2216yes—
75#2720C2216yes—
76#2720C2216yes—
77#2720C2216yes—
78#2720C2213yes—
79#2720C2213yes—
80#2713C2216yes—
81#2713C2213yes—
82#2713C2213yes—
83#2704C2213yes—
84#2704C2216yes—
85#2704C2213yes—
86#2692C2216yes—
87#2692C2213yes—
88#2692C2213yes—
89#2683C2213yes—
90#2683C2216yes—
91#2677C2216yes—
92#2677C2216yes—
93#2677C2216yes—
94#2677C2213yes—
95#2677C2211yescharacteristic
96#2660C2213yes—
97#2660C2213yes—
98#2629C2213yes—
99#2628C2213yes—
100#2628C2213yes—
101#2628C2213yes—
102#2584C2213yes—
103#2584C2213yes—
104#2582C2213yes—
105#2581C2213yes—
106#2581C2213yes—
107#2580C2213yes—
108#2580C2213yes—
109#2568C2213yes—
110#2567C2213yes—
111#2567C2213yes—
112#2567C2213yes—
113#2567C2213yes—
114#2567C2213yes—
115#2566C2213yes—
116#2566C2213yes—
117#2556C2216yes—
118#2556C2216yes—
119#2552C2213yes—
120#2552C2213yes—
121#2551C2213yes—
122#2551C2213yes—
123#2551C2216yes—
124#2551C2213yes—
125#2551C2213yes—
126#2551C2213yes—
127#2551C2213yes—
128#2550C2213yes—
129#2550C2213yes—
130#2550C2213yes—
131#2550C2213yes—
132#2546C2213yes—
133#2542C2213yes—
134#2542C2216yes—
135#2538C2213yes—
136#2506C2216yes—
137#2492C2216yes—
138#2473C2216yes—
139#2465C2216yes—
140#2465C2216yes—
141#2465C2216yes—
142#2462C2216yes—
143#2454C2213yes—
144#2454C2213yes—
145#2453C2213yes—
146#2453C2213yes—
147#2452C2213yes—
148#2452C2216yes—
149#2452C2213yes—
150#2452C2213yes—
151#2452C2213yes—
152#2451C2216yes—
153#2451C2213yes—
154#2451C2213yes—
155#2451C2213yes—
156#2451C2213yes—
157#2449C2216yes—
158#2442C2213yes—
159#2441C2213yes—
160#2441C2213yes—
161#2441C2213yes—
162#2440C2213yes—
163#2440C2216yes—
164#2440C2213yes—
165#2440C2213yes—
166#2440C2213yes—
167#2440C2213yes—
168#2439C2213yes—
169#2439C2213yes—
170#2439C2213yes—
171#2434C2216yes—
172#2434C2216yes—
173#2434C2216yes—
174#2429C2216yes—
175#2429C2216yes—
176#2409C2216yes—
177#2399C2213yes—
178#2399C2213yes—
179#2396C2213yes—
180#2396C2213yes—
181#2396C2213yes—
182#2396C2213yes—
183#2370C2213yes—
184#2370C2213yes—
185#2369C2213yes—
186#2367C2213yes—
187#2367C2213yes—
188#2367C2213yes—
189#2363C2213yes—
190#2363C2213yes—
191#2362C2213yes—
192#2361C2213yes—
193#2360C2213yes—
194#2360C2216yes—
195#2360C2213yes—
196#2355C2213yes—
197#2354C2213yes—
198#2352C2213yes—
199#2351C2211yescharacteristic
200#2351C2211yescharacteristic
201#2351C2211yescharacteristic
202#2351C2211yescharacteristic
203#2351C2211yescharacteristic
204Q8×C4⋊C4C2211yescharacteristic
205Q8×C4⋊C4C2211yescharacteristic
206Q8×C4⋊C4C2211yescharacteristic
207Q8×C4⋊C4C2211yescharacteristic
208Q8×C4⋊C4C2211yescharacteristic
209Q8×C4⋊C4C2211yescharacteristic
210Q8×C4⋊C4C2211yescharacteristic
211D4×C4⋊C4C2213yes—
212#2341C2211yescharacteristic
213#2341C2211yescharacteristic
214#2341C2211yescharacteristic
215Q8×C22⋊C4C2211yescharacteristic
216Q8×C22⋊C4C2211yescharacteristic
217Q8×C22⋊C4C2211yescharacteristic
218#2331C2213yes—
219#2330C2213yes—
220#2326C2213yes—
221#2326C2213yes—
222#2324C2213yes—
223#2324C2213yes—
224#2323C2213yes—
225#2323C2213yes—
226C4×C4⋊Q8C2213yes—
227C4×#125C2213yes—
228C4×#124C2213yes—
229C4×C22⋊Q8C2213yes—
230C4×C22⋊Q8C2213yes—
231C4×C22⋊Q8C2213yes—
232C4×#121C2213yes—
233#2295C2213yes—
234#2293C2213yes—
235#2290C2213yes—
236#2290C2213yes—
237#2276C2211yescharacteristic
238#2276C2211yescharacteristic
239C42×Q8C2211yescharacteristic
240C22×#41C2311yescharacteristic
241C23×Q8C2311yescharacteristic
242C23×Q8C2316yes—
243Q82—224no—
244Q82—28no—
245Q82—28no—
246Q82—28no—
247#557—224no—
248#557—224no—
249#557—28no—
250#557—28no—
251#557—224no—
252#557—28no—
253#557D4116yescomplemented
254#554—224no—
255#554—224no—
256D4×Q8—224no—
257D4×Q8—224no—
258#548Q8116yescomplemented
259#544—224no—
260#544—224no—
261#544—224no—
262#544—224no—
263#533—224no—
264#533—224no—
265#533—224no—
266C2×C4⋊Q8—224no—
267C2×C4⋊Q8C2311yescharacteristic
268C2×C4⋊Q8C2313yes—
269C2×C4⋊Q8C2313yes—
270C2×C4⋊Q8C2313yes—
271C2×C4⋊Q8C2313yes—
272C2×C4⋊Q8C2313yes—
273C2×C4⋊Q8C2316yes—
274C2×C4⋊Q8C2313yes—
275C2×C4⋊Q8C2313yes—
276C2×C4⋊Q8C2311yescharacteristic
277C2×C4⋊Q8C2313yes—
278C2×C4⋊Q8C2313yes—
279C2×C4⋊Q8C2313yes—
280C2×C4⋊Q8C2313yes—
281C2×C4⋊Q8C2316yes—
282C2×C4⋊Q8C2316yes—
283C2×C4⋊Q8C2313yes—
284C2×C4⋊Q8C2313yes—
285C2×C4⋊Q8C2313yes—
286C2×C4⋊Q8C2313yes—
287C2×C4⋊Q8C2316yes—
288C2×C4⋊Q8C2316yes—
289C2×C4⋊Q8C2316yes—
290C2×C4⋊Q8C2313yes—
291C2×#125C2313yes—
292C2×#125C2313yes—
293C2×#125C2313yes—
294C2×#125C2313yes—
295C2×#125C2313yes—
296C2×#125C2313yes—
297C2×#125C2313yes—
298C2×#125C2313yes—
299C2×#125C2313yes—
300C2×#125C2313yes—
301C2×#125C2316yes—
302C2×#125C2316yes—
303C2×#125C2313yes—
304C2×#125C2313yes—
305C2×#124C2313yes—
306C2×C22⋊Q8C2313yes—
307C2×C22⋊Q8C2313yes—
308C2×C22⋊Q8C2311yescharacteristic
309C2×C22⋊Q8C2313yes—
310C2×C22⋊Q8C2316yes—
311C2×C22⋊Q8C2313yes—
312C2×C22⋊Q8C2313yes—
313C2×C22⋊Q8C2313yes—
314C2×C22⋊Q8C2313yes—
315C2×C22⋊Q8C2313yes—
316C2×C22⋊Q8C2311yescharacteristic
317C2×C22⋊Q8C2316yes—
318C2×C22⋊Q8C2316yes—
319C2×C22⋊Q8C2316yes—
320C2×C22⋊Q8C2316yes—
321C2×C22⋊Q8C2316yes—
322C2×C22⋊Q8C2316yes—
323C2×C22⋊Q8C2316yes—
324C2×C22⋊Q8C2316yes—
325C2×C22⋊Q8C2313yes—
326C2×#121C2313yes—
327#520—28no—
328#520—28no—
329#519—28no—
330#519—28no—
331C4×#41—28no—
332C2×C4×Q8—28no—
333C2×C4×Q8C2313yes—
334C2×C4×Q8C2313yes—
335C2×C4×Q8C2313yes—
336C2×C4×Q8C2313yes—
337C2×C4×Q8C2313yes—
338C2×C4×Q8C2313yes—
339C2×C4×Q8C2313yes—
340C2×C4×Q8C2313yes—
341C2×C4×Q8C2311yescharacteristic
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×Q8C2313yes—
351C2×C4×Q8C2313yes—
352C2×C4×Q8C2316yes—
353C2×C4×Q8C2313yes—
354C2×C4×Q8C2313yes—
355C2×C4×Q8C2316yes—
356C2×C4×Q8C2311yescharacteristic
357C2×C4×Q8C2311yescharacteristic
358C2×C4×Q8C2311yescharacteristic
359C2×C4×Q8C2313yes—
360C2×C4×Q8C2311yescharacteristic
361C2×C4×D4C2313yes—
362C2×C4×D4C2313yes—
363C2×C4×D4C2313yes—
364C2×C4×D4C2313yes—
365C2×C4×D4C2313yes—
366C2×C4×D4C2313yes—
367C2×C4×D4C2316yes—
368C2×C4×D4C2313yes—
369C2×#117C2313yes—
370C2×#117C2313yes—
371C2×#117C2313yes—
372C2×#117C2313yes—
373C2×#117C2313yes—
374C2×#117C2313yes—
375C2×#117C2313yes—
376C22×C4⋊C4C2313yes—
377C22×C4⋊C4C2313yes—
378C22×C4⋊C4C2313yes—
379C22×C4⋊C4C2316yes—
380C22×C42C2313yes—
381C22×C42C2313yes—
382#400C2313yes—
383#400C2316yes—
384#400C2313yes—
385#400C2313yes—
386#400C2316yes—
387#400C2313yes—
388#399C2316yes—
389#399C2316yes—
390#399C2313yes—
391#399C2316yes—
392#399C2311yescharacteristic
393#399C2313yes—
394#399C2313yes—
395#398C2316yes—
396#398C2316yes—
397#398C2313yes—
398#398C2316yes—
399#398C2313yes—
400#398C2316yes—
401#398C2311yescharacteristic
402#398C2313yes—
403#398C2313yes—
404#398C2313yes—
405#398C2313yes—
406#398C2313yes—
407#398C2313yes—
408#398C2311yescharacteristic
409#398C2313yes—
410#398C2313yes—
411#398C2313yes—
412#398C2313yes—
413#398C2313yes—
414#398C2313yes—
415#398C2316yes—
416#398C2316yes—
417#396C2313yes—
418#396C2316yes—
419#396C2316yes—
420#396C2316yes—
421#396C2316yes—
422#396C2313yes—
423#396C2313yes—
424#396C2313yes—
425#396C2313yes—
426#396C2313yes—
427#396C2313yes—
428#396C2313yes—
429#395C2313yes—
430#395C2313yes—
431#395C2316yes—
432#395C2316yes—
433#395C2316yes—
434#395C2316yes—
435#395C2316yes—
436#395C2316yes—
437#395C2316yes—
438#395C2316yes—
439#395C2313yes—
440#395C2313yes—
441#395C2316yes—
442#395C2316yes—
443#395C2311yescharacteristic
444#395C2313yes—
445#395C2311yescharacteristic
446#395C2313yes—
447#395C2313yes—
448#395C2313yes—
449#395C2313yes—
450#395C2313yes—
451#395C2316yes—
452#395C2316yes—
453#393C2313yes—
454#393C2316yes—
455#393C2313yes—
456#393C2316yes—
457#393C2316yes—
458#393C2311yescharacteristic
459#393C2313yes—
460#391C2313yes—
461#391C2313yes—
462#391C2313yes—
463#391C2313yes—
464#391C2313yes—
465#391C2316yes—
466#391C2316yes—
467#391C2316yes—
468#391C2313yes—
469#391C2313yes—
470#391C2313yes—
471#391C2313yes—
472#391C2313yes—
473#391C2316yes—
474#391C2316yes—
475#391C2313yes—
476#391C2316yes—
477#391C2313yes—
478#390C2313yes—
479#390C2313yes—
480#390C2313yes—
481#390C2313yes—
482#390C2313yes—
483#390C2313yes—
484#390C2316yes—
485#390C2313yes—
486#390C2313yes—
487#389C2313yes—
488#389C2313yes—
489#389C2313yes—
490#389C2313yes—
491#389C2313yes—
492#389C2313yes—
493#389C2313yes—
494#389C2313yes—
495#389C2313yes—
496#389C2313yes—
497#389C2313yes—
498#389C2313yes—
499#389C2313yes—
500#389C2313yes—
501#389C2313yes—
502#389C2316yes—
503#389C2313yes—
504#389C2313yes—
505#389C2313yes—
506#389C2316yes—
507#389C2316yes—
508#389C2313yes—
509#389C2313yes—
510#389C2316yes—
511#389C2313yes—
512#389C2313yes—
513#389C2313yes—
514#389C2313yes—
515#389C2313yes—
516#389C2313yes—
517#389C2316yes—
518#389C2316yes—
519#389C2316yes—
520#389C2316yes—
521#389C2313yes—
522#389C2313yes—
523#389C2313yes—
524#389C2316yes—
525#389C2313yes—
526#389C2313yes—
527#389C2313yes—
528#389C2313yes—
529#389C2313yes—
530#388C2316yes—
531#388C2316yes—
532#388C2316yes—
533#388C2316yes—
534#388C2316yes—
535#388C2313yes—
536#388C2316yes—
537#388C2316yes—
538#388C2313yes—
539#388C2313yes—
540#388C2313yes—
541#388C2313yes—
542#388C2311yescharacteristic
543#388C2313yes—
544#388C2311yescharacteristic
545#387C2313yes—
546#387C2316yes—
547#387C2313yes—
548#387C2316yes—
549#387C2316yes—
550#387C2316yes—
551#387C2316yes—
552#387C2316yes—
553#387C2316yes—
554#387C2316yes—
555#387C2313yes—
556#387C2316yes—
557#387C2313yes—
558#387C2313yes—
559#387C2313yes—
560#387C2313yes—
561#387C2313yes—
562#387C2311yescharacteristic
563#387C2311yescharacteristic
564#387C2313yes—
565#387C2313yes—
566#386C2313yes—
567#386C2316yes—
568#386C2313yes—
569#386C2313yes—
570#386C2313yes—
571#385C2313yes—
572#385C2316yes—
573#385C2316yes—
574#385C2316yes—
575#385C2316yes—
576#385C2316yes—
577#385C2313yes—
578#385C2316yes—
579#385C2316yes—
580#385C2313yes—
581#385C2316yes—
582#385C2316yes—
583#385C2316yes—
584#385C2313yes—
585#385C2313yes—
586#385C2311yescharacteristic
587#385C2313yes—
588#385C2313yes—
589#384C2313yes—
590#384C2313yes—
591#384C2313yes—
592#384C2316yes—
593#384C2313yes—
594#384C2313yes—
595#384C2316yes—
596#384C2313yes—
597#384C2313yes—
598#384C2313yes—
599#382C2313yes—
600#382C2313yes—
601#382C2313yes—
602#382C2313yes—
603#382C2313yes—
604#380C2313yes—
605#380C2313yes—
606#380C2313yes—
607#380C2313yes—
608#380C2313yes—
609#380C2313yes—
610#380C2313yes—
611#380C2316yes—
612#380C2313yes—
613C4×C4⋊C4C2313yes—
614C4×C4⋊C4C2313yes—
615C4×C4⋊C4C2316yes—
616C4×C4⋊C4C2316yes—
617C4×C4⋊C4C2313yes—
618C4×C4⋊C4C2313yes—
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⋊C4C2313yes—
628C4×C4⋊C4C2313yes—
629C4×C4⋊C4C2313yes—
630C4×C4⋊C4C2313yes—
631C4×C4⋊C4C2313yes—
632C4×C4⋊C4C2313yes—
633C4×C4⋊C4C2316yes—
634C4×C4⋊C4C2313yes—
635C4×C4⋊C4C2313yes—
636C4×C4⋊C4C2313yes—
637C4×C22⋊C4C2313yes—
638C4×C22⋊C4C2313yes—
639C4×C22⋊C4C2313yes—
640C4×C22⋊C4C2313yes—
641C4×C22⋊C4C2313yes—
642C4×C22⋊C4C2313yes—
643C4×C22⋊C4C2316yes—
644C4×C22⋊C4C2316yes—
645C4×C22⋊C4C2316yes—
646C4×C22⋊C4C2316yes—
647#376C2313yes—
648#376C2313yes—
649C43C2313yes—
650C2×#41—24no—
651C2×#41—24no—
652C2×#41C2×Q818yes—
653C22×Q8—24no—
654C22×Q8—24no—
655C22×Q8—224no—
656C22×Q8—86no—
657C22×Q8—86no—
658C22×Q8C2×Q818yescomplemented
659C22×Q8C2411yescharacteristic
660C22×Q8C2411yescharacteristic
661C22×Q8C2413yes—
662C22×Q8C2411yescharacteristic
663C22×Q8C2413yes—
664C22×Q8C2413yes—
665C22×Q8C2416yes—
666C22×Q8C2413yes—
667C22×Q8C2416yes—
668C22×Q8C2416yes—
669C22×Q8C2413yes—
670C22×Q8C2411yescharacteristic
671C22×D4C2413yes—
672C22×D4C2413yes—
673C23×C4C2413yes—
674C23×C4C2411yescharacteristic
675C23×C4C2413yes—
676C23×C4C2413yes—
677C23×C4C2416yes—
678C23×C4C2413yes—
679C23×C4C2416yes—
680C23×C4C2413yes—
681C4⋊Q8—212no—
682C4⋊Q8—212no—
683C4⋊Q8—224no—
684C4⋊Q8—224no—
685C4⋊Q8—212no—
686C4⋊Q8—212no—
687C4⋊Q8—24no—
688C4⋊Q8—212no—
689C4⋊Q8—212no—
690C4⋊Q8—212no—
691C4⋊Q8—212no—
692C4⋊Q8—212no—
693C4⋊Q8—224no—
694C4⋊Q8—212no—
695C4⋊Q8—212no—
696C4⋊Q8—24no—
697C4⋊Q8—212no—
698C4⋊Q8—212no—
699C4⋊Q8—212no—
700C4⋊Q8—212no—
701C4⋊Q8—86no—
702C4⋊Q8—86no—
703C4⋊Q8—86no—
704C4⋊Q8C2×D4124yes—
705#125—212no—
706#125—212no—
707#125—212no—
708#125—212no—
709#125—212no—
710#125—212no—
711#125—224no—
712#125—224no—
713#125—212no—
714#125—212no—
715#125—212no—
716#125—212no—
717#125C2×D4124yes—
718#125C2×D4124yes—
719#124C2×Q8124yescomplemented
720C22⋊Q8—212no—
721C22⋊Q8—212no—
722C22⋊Q8—212no—
723C22⋊Q8—24no—
724C22⋊Q8—224no—
725C22⋊Q8—212no—
726C22⋊Q8—212no—
727C22⋊Q8—212no—
728C22⋊Q8—212no—
729C22⋊Q8—224no—
730C22⋊Q8—224no—
731C22⋊Q8—224no—
732C22⋊Q8—224no—
733C22⋊Q8—212no—
734C22⋊Q8—24no—
735C22⋊Q8—86no—
736C22⋊Q8—86no—
737C22⋊Q8—86no—
738C22⋊Q8—86no—
739C22⋊Q8C2×Q8124yescomplemented
740#121C2×Q8124yescomplemented
741C4×Q8—24no—
742C4×Q8—24no—
743C4×Q8—24no—
744C4×Q8—24no—
745C4×Q8—24no—
746C4×Q8—24no—
747C4×Q8—24no—
748C4×Q8—24no—
749C4×Q8—24no—
750C4×Q8—212no—
751C4×Q8—212no—
752C4×Q8—212no—
753C4×Q8—224no—
754C4×Q8—224no—
755C4×Q8—212no—
756C4×Q8—212no—
757C4×Q8—212no—
758C4×Q8—212no—
759C4×Q8—212no—
760C4×Q8—212no—
761C4×Q8—212no—
762C4×Q8—212no—
763C4×Q8—212no—
764C4×Q8C2×D418yes—
765C4×Q8C2×D418yes—
766C4×Q8C2×D418yes—
767C4×Q8C2×D4124yes—
768C4×Q8C2×Q818yescomplemented
769C4×D4—212no—
770C4×D4—212no—
771C4×D4—212no—
772C4×D4—212no—
773C4×D4—212no—
774C4×D4—212no—
775C4×D4—86no—
776C4×D4C2×Q8124yescomplemented
777#117—212no—
778#117—212no—
779#117—212no—
780#117—212no—
781#117—212no—
782#117—212no—
783#117—212no—
784C2×C4⋊C4—212no—
785C2×C4⋊C4—212no—
786C2×C4⋊C4—212no—
787C2×C4⋊C4—224no—
788C2×C4⋊C4C2413yes—
789C2×C4⋊C4C2413yes—
790C2×C4⋊C4C2413yes—
791C2×C4⋊C4C2413yes—
792C2×C4⋊C4C2413yes—
793C2×C4⋊C4C2413yes—
794C2×C4⋊C4C2413yes—
795C2×C4⋊C4C2416yes—
796C2×C4⋊C4C2416yes—
797C2×C4⋊C4C2411yescharacteristic
798C2×C4⋊C4C2411yescharacteristic
799C2×C4⋊C4C2413yes—
800C2×C4⋊C4C2413yes—
801C2×C4⋊C4C2413yes—
802C2×C4⋊C4C2413yes—
803C2×C4⋊C4C2413yes—
804C2×C4⋊C4C2413yes—
805C2×C4⋊C4C2413yes—
806C2×C4⋊C4C2411yescharacteristic
807C2×C4⋊C4C2411yescharacteristic
808C2×C4⋊C4C2413yes—
809C2×C4⋊C4C2411yescharacteristic
810C2×C4⋊C4C2413yes—
811C2×C4⋊C4C2413yes—
812C2×C4⋊C4C2413yes—
813C2×C4⋊C4C2413yes—
814C2×C4⋊C4C2413yes—
815C2×C4⋊C4C2413yes—
816C2×C4⋊C4C2413yes—
817C2×C4⋊C4C2413yes—
818C2×C4⋊C4C2416yes—
819C2×C4⋊C4C2413yes—
820C2×C4⋊C4C2413yes—
821C2×C4⋊C4C2413yes—
822C2×C4⋊C4C2416yes—
823C2×C4⋊C4C2413yes—
824C2×C4⋊C4C2413yes—
825C2×C4⋊C4C2413yes—
826C2×C4⋊C4C2413yes—
827C2×C4⋊C4C2411yescharacteristic
828C2×C4⋊C4C2413yes—
829C2×C4⋊C4C2411yescharacteristic
830C2×C4⋊C4C2413yes—
831C2×C4⋊C4C2411yescharacteristic
832C2×C4⋊C4C2411yescharacteristic
833C2×C4⋊C4C2411yescharacteristic
834C2×C4⋊C4C2416yes—
835C2×C4⋊C4C2416yes—
836C2×C4⋊C4C2413yes—
837C2×C4⋊C4C2413yes—
838C2×C4⋊C4C2413yes—
839C2×C4⋊C4C2413yes—
840C2×C4⋊C4C2413yes—
841C2×C4⋊C4C2416yes—
842C2×C4⋊C4C2416yes—
843C2×C4⋊C4C2416yes—
844C2×C4⋊C4C2416yes—
845C2×C4⋊C4C2413yes—
846C2×C4⋊C4C2413yes—
847C2×C4⋊C4C2413yes—
848C2×C4⋊C4C2413yes—
849C2×C4⋊C4C2413yes—
850C2×C4⋊C4C2416yes—
851C2×C4⋊C4C2413yes—
852C2×C4⋊C4C2411yescharacteristic
853C2×C4⋊C4C2413yes—
854C2×C4⋊C4C2413yes—
855C2×C4⋊C4C2413yes—
856C2×C4⋊C4C2413yes—
857C2×C4⋊C4C2413yes—
858C2×C4⋊C4C2413yes—
859C2×C4⋊C4C2416yes—
860C2×C4⋊C4C2413yes—
861C2×C4⋊C4C2413yes—
862C2×C4⋊C4C2411yescharacteristic
863C2×C4⋊C4C2413yes—
864C2×C4⋊C4C2413yes—
865C2×C4⋊C4C2413yes—
866C2×C4⋊C4C2411yescharacteristic
867C2×C22⋊C4C2411yescharacteristic
868C2×C22⋊C4C2413yes—
869C2×C22⋊C4C2413yes—
870C2×C22⋊C4C2411yescharacteristic
871C2×C22⋊C4C2413yes—
872C2×C22⋊C4C2413yes—
873C2×C22⋊C4C2413yes—
874C2×C22⋊C4C2416yes—
875C2×C22⋊C4C2413yes—
876C2×C22⋊C4C2411yescharacteristic
877C2×C22⋊C4C2413yes—
878C2×C22⋊C4C2413yes—
879C2×C22⋊C4C2411yescharacteristic
880C2×C22⋊C4C2413yes—
881C2×C22⋊C4C2416yes—
882C2×C22⋊C4C2413yes—
883C2×C22⋊C4C2413yes—
884C2×C22⋊C4C2413yes—
885C2×C22⋊C4C2416yes—
886C2×C22⋊C4C2413yes—
887C2×C22⋊C4C2413yes—
888C2×C22⋊C4C2411yescharacteristic
889C2×C22⋊C4C2416yes—
890C2×C22⋊C4C2413yes—
891C2×C22⋊C4C2411yescharacteristic
892C2×C22⋊C4C2413yes—
893C2×C22⋊C4C2416yes—
894C2×C42—212no—
895C2×C42—212no—
896C2×C42C2413yes—
897C2×C42C2413yes—
898C2×C42C2413yes—
899C2×C42C2416yes—
900C2×C42C2413yes—
901C2×C42C2413yes—
902C2×C42C2416yes—
903C2×C42C2413yes—
904C2×C42C2413yes—
905C2×C42C2413yes—
906C2×C42C2413yes—
907C2×C42C2413yes—
908C2×C42C2413yes—
909C2×C42C2413yes—
910C2×C42C2411yescharacteristic
911C2×C42C2411yescharacteristic
912C2×C42C2416yes—
913C2×C42C2413yes—
914C2×C42C2413yes—
915C2×C42C2413yes—
916C2×C42C2416yes—
917C2×C42C2413yes—
918C2×C42C2413yes—
919C2×C42C2413yes—
920C2×C42C2413yes—
921#95C2411yescharacteristic
922#95C2411yescharacteristic
923#95C2413yes—
924#95C2413yes—
925#95C2413yes—
926#95C2413yes—
927#95C2413yes—
928#95C2413yes—
929#95C2413yes—
930#95C2411yescharacteristic
931#95C2411yescharacteristic
932#95C2411yescharacteristic
933#95C2413yes—
934#95C2413yes—
935#95C2413yes—
936#95C2413yes—
937#95C2413yes—
938#95C2413yes—
939#95C2413yes—
940#95C2416yes—
941#95C2416yes—
942#95C2416yes—
943#95C2413yes—
944#95C2413yes—
945#95C2413yes—
946#95C2413yes—
947#95C2411yescharacteristic
948#95C2413yes—
949#95C2413yes—
950#95C2411yescharacteristic
951#95C2416yes—
952#95C2411yescharacteristic
953#95C2411yescharacteristic
954#95C2411yescharacteristic
955#95C2413yes—
956#95C2413yes—
957#95C2413yes—
958#95C2416yes—
959#95C2413yes—
960#95C2413yes—
961#95C2413yes—
962#95C2413yes—
963#95C2416yes—
964#95C2416yes—
965#95C2413yes—
966#95C2413yes—
967#95C2413yes—
968#95C2413yes—
969#95C2413yes—
970#95C2413yes—
971#95C2413yes—
972#95C2416yes—
973#95C2416yes—
974C24C2511yescharacteristic
975C24C2513yes—
976#41—232no—
977C2×Q8—232no—
978C2×Q8—26no—
979C2×Q8—22no—
980C2×Q8—22no—
981C2×Q8—26no—
982C2×Q8—22no—
983C2×Q8—26no—
984C2×Q8—26no—
985C2×Q8—212no—
986C2×Q8—212no—
987C2×Q8—212no—
988C2×Q8—26no—
989C2×Q8—26no—
990C2×Q8—22no—
991C2×Q8—22no—
992C2×Q8—22no—
993C2×Q8—43no—
994C2×Q8—43no—
995C2×Q8—43no—
996C2×Q8—43no—
997C2×Q8—41no—
998C2×Q8—41no—
999C2×Q8—43no—
1000C2×Q8—41no—
1001C2×Q8—43no—
1002C2×Q8—46no—
1003C2×Q8—46no—
1004C2×Q8—46no—
1005C2×Q8—43no—
1006C2×Q8—46no—
1007C2×Q8—46no—
1008C2×Q8—46no—
1009C2×Q8—848no—
1010C2×Q8C22×D4112yes—
1011C2×Q8C22×D414yes—
1012C2×Q8C22×Q8112yes—
1013C2×Q8C22×Q814yes—
1014C2×Q82−1+414yes—
1015C2×D4—26no—
1016C2×D4—26no—
1017C2×D4—43no—
1018C2×D4—43no—
1019C2×D4C22×Q8112yes—
1020C2×D4C22×Q8112yes—
1021C22×C4—26no—
1022C22×C4—26no—
1023C22×C4—26no—
1024C22×C4—26no—
1025C22×C4—22no—
1026C22×C4—26no—
1027C22×C4—26no—
1028C22×C4—22no—
1029C22×C4—26no—
1030C22×C4—26no—
1031C22×C4—212no—
1032C22×C4—212no—
1033C22×C4—43no—
1034C22×C4—41no—
1035C22×C4—43no—
1036C22×C4—43no—
1037C22×C4—43no—
1038C22×C4—46no—
1039C22×C4—43no—
1040C22×C4—46no—
1041C22×C4—46no—
1042C22×C4—46no—
1043C22×C4C22×Q8112yes—
1044C22×C4C22×Q8112yes—
1045C22×C4C2511yescharacteristic
1046C22×C4C2513yes—
1047C22×C4C2511yescharacteristic
1048C22×C4C2513yes—
1049C22×C4C2513yes—
1050C22×C4C2511yescharacteristic
1051C22×C4C2511yescharacteristic
1052C22×C4C2513yes—
1053C22×C4C2511yescharacteristic
1054C22×C4C2513yes—
1055C22×C4C2513yes—
1056C22×C4C2513yes—
1057C22×C4C2511yescharacteristic
1058C22×C4C2513yes—
1059C22×C4C2513yes—
1060C22×C4C2511yescharacteristic
1061C22×C4C2511yescharacteristic
1062C22×C4C2513yes—
1063C22×C4C2511yescharacteristic
1064C22×C4C2513yes—
1065C22×C4C2513yes—
1066C22×C4C2511yescharacteristic
1067C22×C4C2513yes—
1068C22×C4C2513yes—
1069C22×C4C2511yescharacteristic
1070C22×C4C2511yescharacteristic
1071C22×C4C2511yescharacteristic
1072C22×C4C2511yescharacteristic
1073C22×C4C2513yes—
1074C4⋊C4—26no—
1075C4⋊C4—26no—
1076C4⋊C4—26no—
1077C4⋊C4—26no—
1078C4⋊C4—26no—
1079C4⋊C4—26no—
1080C4⋊C4—212no—
1081C4⋊C4—26no—
1082C4⋊C4—212no—
1083C4⋊C4—22no—
1084C4⋊C4—22no—
1085C4⋊C4—26no—
1086C4⋊C4—26no—
1087C4⋊C4—26no—
1088C4⋊C4—26no—
1089C4⋊C4—26no—
1090C4⋊C4—26no—
1091C4⋊C4—26no—
1092C4⋊C4—22no—
1093C4⋊C4—26no—
1094C4⋊C4—22no—
1095C4⋊C4—26no—
1096C4⋊C4—22no—
1097C4⋊C4—26no—
1098C4⋊C4—26no—
1099C4⋊C4—26no—
1100C4⋊C4—26no—
1101C4⋊C4—26no—
1102C4⋊C4—26no—
1103C4⋊C4—26no—
1104C4⋊C4—212no—
1105C4⋊C4—212no—
1106C4⋊C4—26no—
1107C4⋊C4—26no—
1108C4⋊C4—26no—
1109C4⋊C4—26no—
1110C4⋊C4—26no—
1111C4⋊C4—26no—
1112C4⋊C4—26no—
1113C4⋊C4—26no—
1114C4⋊C4—22no—
1115C4⋊C4—22no—
1116C4⋊C4—26no—
1117C4⋊C4—22no—
1118C4⋊C4—22no—
1119C4⋊C4—22no—
1120C4⋊C4—43no—
1121C4⋊C4—43no—
1122C4⋊C4—43no—
1123C4⋊C4—43no—
1124C4⋊C4—41no—
1125C4⋊C4—46no—
1126C4⋊C4—43no—
1127C4⋊C4—43no—
1128C4⋊C4—46no—
1129C4⋊C4—43no—
1130C4⋊C4—43no—
1131C4⋊C4—43no—
1132C4⋊C4—46no—
1133C4⋊C4—46no—
1134C4⋊C4—46no—
1135C4⋊C4—46no—
1136C4⋊C4—43no—
1137C4⋊C4—43no—
1138C4⋊C4—43no—
1139C4⋊C4—43no—
1140C4⋊C4—46no—
1141C4⋊C4—43no—
1142C4⋊C4—43no—
1143C4⋊C4C22×D4112yes—
1144C4⋊C4C22×D4112yes—
1145C4⋊C4C22×D4124yes—
1146C4⋊C4C22×D4112yes—
1147C4⋊C4C22×D4112yes—
1148C4⋊C4C22×D414yes—
1149C4⋊C4C22×D4112yes—
1150C4⋊C4C22×Q8112yes—
1151C4⋊C4C22×Q8112yes—
1152C4⋊C42−1+414yes—
1153C22⋊C4—26no—
1154C22⋊C4—22no—
1155C22⋊C4—26no—
1156C22⋊C4—22no—
1157C22⋊C4—26no—
1158C22⋊C4—26no—
1159C22⋊C4—212no—
1160C22⋊C4—26no—
1161C22⋊C4—26no—
1162C22⋊C4—26no—
1163C22⋊C4—22no—
1164C22⋊C4—26no—
1165C22⋊C4—22no—
1166C22⋊C4—43no—
1167C22⋊C4—46no—
1168C22⋊C4—41no—
1169C22⋊C4—43no—
1170C22⋊C4—46no—
1171C22⋊C4—43no—
1172C22⋊C4—43no—
1173C22⋊C4—46no—
1174C22⋊C4—43no—
1175C22⋊C4—43no—
1176C22⋊C4—43no—
1177C22⋊C4C22×Q814yes—
1178C22⋊C4C22×Q8112yes—
1179C22⋊C4C22×Q8124yes—
1180C42—22no—
1181C42—26no—
1182C42—26no—
1183C42—26no—
1184C42—26no—
1185C42—26no—
1186C42—26no—
1187C42—26no—
1188C42—212no—
1189C42—212no—
1190C42—26no—
1191C42—26no—
1192C42—26no—
1193C42—26no—
1194C42—26no—
1195C42—22no—
1196C42—43no—
1197C42—46no—
1198C42—46no—
1199C42—43no—
1200C42—43no—
1201C42C22×D4112yes—
1202C42C22×D4112yes—
1203C42C22×D4112yes—
1204C42C22×Q8112yes—
1205C23—21no—
1206C23—23no—
1207C23—21no—
1208C23—23no—
1209C23—21no—
1210C23—23no—
1211C23—21no—
1212C23—23no—
1213C23—23no—
1214C23—21no—
1215C23—23no—
1216C23—21no—
1217C23C23×Q816yes—
1218C23C23×Q812yes—
1219C23C2611yescharacteristic
1220Q8—224no—
1221Q8—412no—
1222Q8—44no—
1223Q8—44no—
1224Q8—412no—
1225Q8—44no—
1226Q8—412no—
1227Q8—86no—
1228Q8—812no—
1229Q8—812no—
1230Q8—812no—
1231Q8D4×Q8116yes—
1232D4—224no—
1233D4—412no—
1234C2×C4—23no—
1235C2×C4—21no—
1236C2×C4—21no—
1237C2×C4—21no—
1238C2×C4—21no—
1239C2×C4—21no—
1240C2×C4—21no—
1241C2×C4—23no—
1242C2×C4—21no—
1243C2×C4—21no—
1244C2×C4—23no—
1245C2×C4—21no—
1246C2×C4—21no—
1247C2×C4—23no—
1248C2×C4—23no—
1249C2×C4—23no—
1250C2×C4—23no—
1251C2×C4—23no—
1252C2×C4—21no—
1253C2×C4—21no—
1254C2×C4—23no—
1255C2×C4—21no—
1256C2×C4—23no—
1257C2×C4—21no—
1258C2×C4—21no—
1259C2×C4—21no—
1260C2×C4—224no—
1261C2×C4—224no—
1262C2×C4—21no—
1263C2×C4—21no—
1264C2×C4—23no—
1265C2×C4—21no—
1266C2×C4—21no—
1267C2×C4—23no—
1268C2×C4—23no—
1269C2×C4—23no—
1270C2×C4—23no—
1271C2×C4—23no—
1272C2×C4—21no—
1273C2×C4—21no—
1274C2×C4—23no—
1275C2×C4—23no—
1276C2×C4—23no—
1277C2×C4—21no—
1278C2×C4—23no—
1279C2×C4—21no—
1280C2×C4—23no—
1281C2×C4—21no—
1282C2×C4—21no—
1283C2×C4—23no—
1284C2×C4—23no—
1285C2×C4—21no—
1286C2×C4—23no—
1287C2×C4—21no—
1288C2×C4—21no—
1289C2×C4—23no—
1290C2×C4—23no—
1291C2×C4—23no—
1292C2×C4—23no—
1293C2×C4—23no—
1294C2×C4—23no—
1295C2×C4—23no—
1296C2×C4—21no—
1297C2×C4—23no—
1298C2×C4—23no—
1299C2×C4—23no—
1300C2×C4—23no—
1301C2×C4—23no—
1302C2×C4—21no—
1303C2×C4—23no—
1304C2×C4—21no—
1305C2×C4—21no—
1306C2×C4—21no—
1307C2×C4—412no—
1308C2×C4—44no—
1309C2×C4—412no—
1310C2×C4—86no—
1311C2×C4—812no—
1312C2×C4—812no—
1313C2×C4C23×D412yes—
1314C2×C4C23×D416yes—
1315C2×C4C23×D416yes—
1316C2×C4C23×D412yes—
1317C2×C4C23×D416yes—
1318C2×C4C23×D412yes—
1319C2×C4C23×D416yes—
1320C2×C4C23×Q812yes—
1321C2×C4C23×Q816yes—
1322C2×C4C23×Q816yes—
1323C2×C4C23×Q812yes—
1324C2×C4C23×Q816yes—
1325C2×C4C2×2−1+412yes—
1326C2×C4C2×2−1+412yes—
1327C2×C4C2×2−1+412yes—
1328C2×C4C2×2−1+416yes—
1329C22—22no—
1330C22—26no—
1331C22—22no—
1332C22—26no—
1333C22—22no—
1334C22—26no—
1335C22—41no—
1336C22—43no—
1337C22—41no—
1338C22—43no—
1339C22—43no—
1340C22—41no—
1341C22—41no—
1342C22—43no—
1343C22C24×D411yescharacteristic
1344C22C24×Q811yescharacteristic
1345C22C22×2−1+411yescharacteristic
1346C22C22×2−1+411yescharacteristic
1347C22H(7,𝔽2)11yescharacteristic
1348C22H(7,𝔽2)11yescharacteristic
1349C222−1+611yescharacteristic
1350C4—22no—
1351C4—26no—
1352C4—22no—
1353C4—22no—
1354C4—22no—
1355C4—22no—
1356C4—22no—
1357C4—26no—
1358C4—26no—
1359C4—26no—
1360C4—22no—
1361C4—22no—
1362C4—26no—
1363C4—41no—
1364C4—41no—
1365C4—43no—
1366C4—41no—
1367C4—41no—
1368C4—43no—
1369C4—43no—
1370C4—43no—
1371C4—43no—
1372C4—43no—
1373C4—43no—
1374C4—41no—
1375C4—43no—
1376C4—41no—
1377C4—43no—
1378C4C2×D4×Q8112yes—
1379C2—42no—
1380C2—46no—
1381C2C22×D4×Q811yescharacteristic
1382C2#6285211yescharacteristic
1383C2#6285411yescharacteristic
1384C2#6294311yescharacteristic
1385C2D4×2−1+411yescharacteristic
1386C2Q8×2−1+411yescharacteristic
1387C2#6306111yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#548C22
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×#3503C2semidirect
2. C2×#3502C2semidirect
3. #59833C2semidirect
4. #59153C2semidirect
5. #59151C2semidirect
6. #52162C2semidirect
7. #45424C2semidirect
8. #45274C2semidirect
9. #45272C2semidirect
10. #44941C2semidirect
11. #44934C2semidirect
12. #44879C2semidirect
13. #39616C2semidirect
14. #39596C2semidirect
15. #39591C2semidirect
16. #39369C2semidirect
17. #37690C2semidirect
18. #37686C2semidirect
19. Q8×C4⋊Q8C2semidirect
20. Q8×C22⋊Q8C2semidirect
21. #36431C2semidirect
22. #35957C2semidirect
23. #35937C2semidirect
24. #35845C2semidirect
25. #35816C2semidirect
26. #35748C2semidirect
27. #35711C2semidirect
28. #34336C2semidirect
253. #557D4semidirect
258. #548Q8semidirect
658. C22×Q8C2×Q8semidirect
719. #124C2×Q8semidirect
739. C22⋊Q8C2×Q8semidirect
740. #121C2×Q8semidirect
768. C4×Q8C2×Q8semidirect
776. C4×D4C2×Q8semidirect

Maximal subgroups

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

subgroupindex
C2×#35032
C2×#35022
#598332
#591532
#591512
#521622
#454242
#452742
#452722
#449412
#449342
#448792
#396162
#395962
#395912
#393692
#376902
#376862
Q8×C4⋊Q82
Q8×C22⋊Q82
#364312
#359572
#359372
#358452
#358162
#357482
#357112
#343362
#343122
#342942
#342932