Finite Group Databasebeta

← #7695612

Subgroups — #7695612

Order 512.

6695 conjugacy classes of subgroups.

The subgroup lattice has 1380 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#59413C213yesmaximal, complemented
4#59144C213yesmaximal, complemented
5#59036C213yesmaximal, complemented
6#52162C213yesmaximal, complemented
7#45139C213yesmaximal, complemented
8#45110C213yesmaximal, complemented
9#45099C213yesmaximal, complemented
10#44934C213yesmaximal, complemented
11#44894C213yesmaximal, complemented
12#44879C213yesmaximal, complemented
13#39613C213yesmaximal, complemented
14#39591C213yesmaximal, complemented
15#39590C213yesmaximal, complemented
16#39370C213yesmaximal, complemented
17#37691C213yesmaximal, complemented
18#37686C213yesmaximal, complemented
19#36466C211yesmaximal, characteristic, complemented
20#36435C211yesmaximal, characteristic, complemented
21#36431C211yesmaximal, characteristic, complemented
22#36040C211yesmaximal, characteristic, complemented
23#35957C211yesmaximal, characteristic, complemented
24#35937C211yesmaximal, characteristic, complemented
25#35816C211yesmaximal, characteristic, complemented
26#35786C211yesmaximal, characteristic, complemented
27#35711C211yesmaximal, characteristic, complemented
28#34335C211yesmaximal, characteristic, complemented
29#34312C211yesmaximal, characteristic
30#34294C211yesmaximal, characteristic
31#34293C211yesmaximal, characteristic
32#3503—216no—
33#3502—216no—
34C2×Q82C2213yes—
35C2×Q82C2211yescharacteristic
36C2×Q82C2211yescharacteristic
37C2×#557C2213yes—
38C2×#557C2213yes—
39C2×#557C2211yescharacteristic
40C2×#557C2211yescharacteristic
41C2×#557C2211yescharacteristic
42C2×#557C2213yes—
43C2×#557C2211yescharacteristic
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#2859C2213yes—
65#2851C2213yes—
66#2851C2213yes—
67#2734C2216yes—
68#2734C2213yes—
69#2732C2216yes—
70#2732C2213yes—
71#2729C2216yes—
72#2729C2216yes—
73#2729C2216yes—
74#2729C2216yes—
75#2729C2216yes—
76#2729C2213yes—
77#2729C2211yescharacteristic
78#2726C2213yes—
79#2720C2216yes—
80#2720C2213yes—
81#2720C2213yes—
82#2713C2213yes—
83#2713C2216yes—
84#2713C2213yes—
85#2704C2213yes—
86#2704C2216yes—
87#2704C2216yes—
88#2704C2213yes—
89#2692C2213yes—
90#2692C2216yes—
91#2692C2213yes—
92#2683C2213yes—
93#2677C2213yes—
94#2677C2216yes—
95#2677C2213yes—
96#2660C2213yes—
97#2660C2213yes—
98#2629C2213yes—
99#2629C2213yes—
100#2628C2213yes—
101#2628C2213yes—
102#2584C2213yes—
103#2584C2213yes—
104#2584C2213yes—
105#2584C2213yes—
106#2582C2213yes—
107#2581C2213yes—
108#2581C2213yes—
109#2580C2213yes—
110#2580C2213yes—
111#2568C2213yes—
112#2567C2213yes—
113#2566C2213yes—
114#2566C2213yes—
115#2565C2213yes—
116#2565C2213yes—
117#2563C2213yes—
118#2556C2216yes—
119#2556C2216yes—
120#2552C2213yes—
121#2552C2213yes—
122#2552C2213yes—
123#2551C2213yes—
124#2551C2213yes—
125#2551C2213yes—
126#2550C2213yes—
127#2550C2213yes—
128#2550C2213yes—
129#2550C2213yes—
130#2550C2213yes—
131#2550C2213yes—
132#2546C2216yes—
133#2546C2213yes—
134#2538C2213yes—
135#2538C2216yes—
136#2506C2216yes—
137#2473C2216yes—
138#2473C2216yes—
139#2473C2216yes—
140#2465C2216yes—
141#2465C2216yes—
142#2465C2216yes—
143#2462C2216yes—
144#2454C2213yes—
145#2454C2213yes—
146#2454C2213yes—
147#2454C2213yes—
148#2453C2213yes—
149#2453C2213yes—
150#2452C2213yes—
151#2452C2213yes—
152#2452C2216yes—
153#2451C2213yes—
154#2451C2213yes—
155#2451C2213yes—
156#2451C2213yes—
157#2449C2216yes—
158#2446C2216yes—
159#2442C2213yes—
160#2442C2213yes—
161#2442C2213yes—
162#2442C2213yes—
163#2441C2213yes—
164#2441C2213yes—
165#2440C2213yes—
166#2440C2213yes—
167#2439C2213yes—
168#2439C2213yes—
169#2439C2213yes—
170#2439C2213yes—
171#2434C2216yes—
172#2434C2216yes—
173#2429C2216yes—
174#2423C2216yes—
175#2423C2216yes—
176#2409C2216yes—
177#2399C2213yes—
178#2399C2213yes—
179#2396C2213yes—
180#2396C2213yes—
181#2396C2213yes—
182#2396C2213yes—
183#2369C2213yes—
184#2367C2213yes—
185#2367C2213yes—
186#2367C2213yes—
187#2365C2213yes—
188#2365C2213yes—
189#2363C2213yes—
190#2363C2213yes—
191#2362C2213yes—
192#2361C2213yes—
193#2360C2213yes—
194#2360C2213yes—
195#2355C2213yes—
196#2354C2213yes—
197#2352C2213yes—
198#2351C2211yescharacteristic
199#2351C2211yescharacteristic
200#2351C2211yescharacteristic
201#2351C2211yescharacteristic
202#2351C2211yescharacteristic
203#2351C2211yescharacteristic
204#2351C2211yescharacteristic
205Q8×C4⋊C4C2211yescharacteristic
206Q8×C4⋊C4C2211yescharacteristic
207Q8×C4⋊C4C2211yescharacteristic
208Q8×C4⋊C4C2211yescharacteristic
209Q8×C4⋊C4C2211yescharacteristic
210D4×C4⋊C4C2213yes—
211#2341C2211yescharacteristic
212#2341C2211yescharacteristic
213#2341C2211yescharacteristic
214Q8×C22⋊C4C2211yescharacteristic
215Q8×C22⋊C4C2216yes—
216Q8×C22⋊C4C2211yescharacteristic
217Q8×C22⋊C4C2211yescharacteristic
218#2331C2213yes—
219#2331C2213yes—
220#2326C2213yes—
221#2326C2213yes—
222#2324C2213yes—
223#2324C2213yes—
224#2323C2213yes—
225#2323C2213yes—
226C4×C4⋊Q8C2213yes—
227C4×C4⋊Q8C2213yes—
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—
245Q82D4116yescomplemented
246#557—224no—
247#557—224no—
248#557—28no—
249#557—28no—
250#557—28no—
251#557—224no—
252#557—28no—
253#557—28no—
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⋊Q8C2313yes—
268C2×C4⋊Q8C2313yes—
269C2×C4⋊Q8C2313yes—
270C2×C4⋊Q8C2316yes—
271C2×C4⋊Q8C2313yes—
272C2×C4⋊Q8C2313yes—
273C2×C4⋊Q8C2311yescharacteristic
274C2×C4⋊Q8C2313yes—
275C2×C4⋊Q8C2313yes—
276C2×C4⋊Q8C2316yes—
277C2×C4⋊Q8C2316yes—
278C2×C4⋊Q8C2313yes—
279C2×C4⋊Q8C2313yes—
280C2×C4⋊Q8C2313yes—
281C2×C4⋊Q8C2313yes—
282C2×C4⋊Q8C2313yes—
283C2×C4⋊Q8C2316yes—
284C2×C4⋊Q8C2313yes—
285C2×C4⋊Q8C2313yes—
286C2×C4⋊Q8C2313yes—
287C2×#125C2313yes—
288C2×#125C2313yes—
289C2×#125C2313yes—
290C2×#125C2313yes—
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×#124C2313yes—
304C2×C22⋊Q8C2316yes—
305C2×C22⋊Q8C2313yes—
306C2×C22⋊Q8C2311yescharacteristic
307C2×C22⋊Q8C2313yes—
308C2×C22⋊Q8C2313yes—
309C2×C22⋊Q8C2313yes—
310C2×C22⋊Q8C2313yes—
311C2×C22⋊Q8C2313yes—
312C2×C22⋊Q8C2313yes—
313C2×C22⋊Q8C2316yes—
314C2×C22⋊Q8C2316yes—
315C2×C22⋊Q8C2316yes—
316C2×C22⋊Q8C2316yes—
317C2×C22⋊Q8C2313yes—
318C2×C22⋊Q8C2313yes—
319C2×C22⋊Q8C2316yes—
320C2×C22⋊Q8C2313yes—
321C2×#121C2313yes—
322#520—28no—
323#520—28no—
324#519—28no—
325#519—28no—
326C4×#41—28no—
327C2×C4×Q8—28no—
328C2×C4×Q8C2313yes—
329C2×C4×Q8C2313yes—
330C2×C4×Q8C2313yes—
331C2×C4×Q8C2313yes—
332C2×C4×Q8C2313yes—
333C2×C4×Q8C2313yes—
334C2×C4×Q8C2313yes—
335C2×C4×Q8C2313yes—
336C2×C4×Q8C2313yes—
337C2×C4×Q8C2311yescharacteristic
338C2×C4×Q8C2311yescharacteristic
339C2×C4×Q8C2311yescharacteristic
340C2×C4×Q8C2311yescharacteristic
341C2×C4×Q8C2311yescharacteristic
342C2×C4×Q8C2311yescharacteristic
343C2×C4×Q8C2316yes—
344C2×C4×Q8C2311yescharacteristic
345C2×C4×Q8C2311yescharacteristic
346C2×C4×Q8C2311yescharacteristic
347C2×C4×Q8C2313yes—
348C2×C4×Q8C2313yes—
349C2×C4×Q8C2313yes—
350C2×C4×Q8C2316yes—
351C2×C4×Q8C2316yes—
352C2×C4×Q8C2311yescharacteristic
353C2×C4×Q8C2311yescharacteristic
354C2×C4×Q8C2311yescharacteristic
355C2×C4×Q8C2313yes—
356C2×C4×Q8C2311yescharacteristic
357C2×C4×D4C2313yes—
358C2×C4×D4C2313yes—
359C2×C4×D4C2313yes—
360C2×C4×D4C2313yes—
361C2×C4×D4C2313yes—
362C2×C4×D4C2313yes—
363C2×C4×D4C2316yes—
364C2×C4×D4C2313yes—
365C2×#117C2313yes—
366C2×#117C2313yes—
367C2×#117C2313yes—
368C2×#117C2313yes—
369C2×#117C2313yes—
370C2×#117C2313yes—
371C2×#117C2313yes—
372C22×C4⋊C4C2313yes—
373C22×C4⋊C4C2313yes—
374C22×C4⋊C4C2313yes—
375C22×C4⋊C4C2316yes—
376C22×C42C2313yes—
377C22×C42C2313yes—
378#400C2313yes—
379#400C2316yes—
380#400C2316yes—
381#400C2316yes—
382#400C2311yescharacteristic
383#400C2313yes—
384#400C2313yes—
385#399C2313yes—
386#399C2316yes—
387#399C2313yes—
388#399C2316yes—
389#399C2313yes—
390#399C2313yes—
391#398C2313yes—
392#398C2316yes—
393#398C2316yes—
394#398C2316yes—
395#398C2313yes—
396#398C2313yes—
397#398C2316yes—
398#398C2316yes—
399#398C2316yes—
400#398C2313yes—
401#398C2316yes—
402#398C2316yes—
403#398C2311yescharacteristic
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#396C2313yes—
422#396C2316yes—
423#396C2316yes—
424#396C2311yescharacteristic
425#396C2313yes—
426#396C2313yes—
427#396C2313yes—
428#396C2313yes—
429#396C2313yes—
430#395C2313yes—
431#395C2316yes—
432#395C2313yes—
433#395C2316yes—
434#395C2313yes—
435#395C2316yes—
436#395C2316yes—
437#395C2313yes—
438#395C2316yes—
439#395C2313yes—
440#395C2313yes—
441#395C2311yescharacteristic
442#395C2313yes—
443#395C2313yes—
444#395C2313yes—
445#395C2313yes—
446#395C2313yes—
447#395C2316yes—
448#395C2316yes—
449#393C2313yes—
450#393C2316yes—
451#393C2316yes—
452#393C2316yes—
453#393C2311yescharacteristic
454#393C2313yes—
455#393C2313yes—
456#391C2316yes—
457#391C2313yes—
458#391C2313yes—
459#391C2313yes—
460#391C2313yes—
461#391C2313yes—
462#391C2316yes—
463#391C2316yes—
464#391C2316yes—
465#391C2313yes—
466#391C2313yes—
467#391C2313yes—
468#391C2316yes—
469#391C2316yes—
470#391C2316yes—
471#391C2313yes—
472#391C2316yes—
473#391C2313yes—
474#391C2313yes—
475#391C2311yescharacteristic
476#390C2313yes—
477#390C2313yes—
478#390C2313yes—
479#390C2313yes—
480#390C2313yes—
481#390C2313yes—
482#390C2316yes—
483#390C2313yes—
484#390C2313yes—
485#389C2311yescharacteristic
486#389C2313yes—
487#389C2313yes—
488#389C2313yes—
489#389C2313yes—
490#389C2313yes—
491#389C2313yes—
492#389C2313yes—
493#389C2313yes—
494#389C2313yes—
495#389C2313yes—
496#389C2313yes—
497#389C2313yes—
498#389C2316yes—
499#389C2313yes—
500#389C2313yes—
501#389C2313yes—
502#389C2313yes—
503#389C2313yes—
504#389C2313yes—
505#389C2313yes—
506#389C2313yes—
507#389C2313yes—
508#389C2313yes—
509#389C2316yes—
510#389C2316yes—
511#389C2313yes—
512#389C2313yes—
513#389C2316yes—
514#389C2316yes—
515#389C2316yes—
516#389C2316yes—
517#389C2313yes—
518#389C2313yes—
519#389C2313yes—
520#389C2313yes—
521#389C2313yes—
522#389C2316yes—
523#389C2316yes—
524#389C2313yes—
525#389C2313yes—
526#389C2313yes—
527#389C2313yes—
528#388C2316yes—
529#388C2316yes—
530#388C2316yes—
531#388C2316yes—
532#388C2316yes—
533#388C2313yes—
534#388C2316yes—
535#388C2316yes—
536#388C2313yes—
537#388C2313yes—
538#388C2313yes—
539#388C2313yes—
540#388C2311yescharacteristic
541#388C2311yescharacteristic
542#388C2313yes—
543#387C2313yes—
544#387C2316yes—
545#387C2316yes—
546#387C2316yes—
547#387C2313yes—
548#387C2316yes—
549#387C2313yes—
550#387C2316yes—
551#387C2316yes—
552#387C2313yes—
553#387C2313yes—
554#387C2316yes—
555#387C2316yes—
556#387C2313yes—
557#387C2316yes—
558#387C2316yes—
559#387C2313yes—
560#387C2313yes—
561#387C2313yes—
562#387C2313yes—
563#387C2311yescharacteristic
564#387C2313yes—
565#386C2313yes—
566#386C2316yes—
567#386C2313yes—
568#386C2313yes—
569#386C2313yes—
570#385C2313yes—
571#385C2316yes—
572#385C2316yes—
573#385C2316yes—
574#385C2316yes—
575#385C2316yes—
576#385C2313yes—
577#385C2316yes—
578#385C2316yes—
579#385C2313yes—
580#385C2316yes—
581#385C2316yes—
582#385C2313yes—
583#385C2316yes—
584#385C2316yes—
585#385C2313yes—
586#385C2313yes—
587#385C2311yescharacteristic
588#385C2311yescharacteristic
589#384C2313yes—
590#384C2313yes—
591#384C2313yes—
592#384C2313yes—
593#384C2316yes—
594#384C2313yes—
595#384C2313yes—
596#382C2313yes—
597#382C2313yes—
598#382C2313yes—
599#382C2313yes—
600#382C2313yes—
601#382C2313yes—
602#382C2313yes—
603#380C2316yes—
604#380C2316yes—
605#380C2313yes—
606#380C2313yes—
607#380C2313yes—
608#380C2313yes—
609#380C2313yes—
610#380C2313yes—
611#380C2316yes—
612#380C2313yes—
613#380C2313yes—
614C4×C4⋊C4C2313yes—
615C4×C4⋊C4C2313yes—
616C4×C4⋊C4C2313yes—
617C4×C4⋊C4C2313yes—
618C4×C4⋊C4C2313yes—
619C4×C4⋊C4C2313yes—
620C4×C4⋊C4C2316yes—
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⋊C4C2316yes—
638C4×C22⋊C4C2316yes—
639C4×C22⋊C4C2313yes—
640C4×C22⋊C4C2316yes—
641C4×C22⋊C4C2313yes—
642C4×C22⋊C4C2313yes—
643C4×C22⋊C4C2313yes—
644C4×C22⋊C4C2313yes—
645C4×C22⋊C4C2313yes—
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—412no—
657C22×Q8—86no—
658C22×Q8C2×Q818yescomplemented
659C22×Q8C2413yes—
660C22×Q8C2413yes—
661C22×Q8C2413yes—
662C22×Q8C2411yescharacteristic
663C22×Q8C2413yes—
664C22×Q8C2413yes—
665C22×Q8C2413yes—
666C22×Q8C2416yes—
667C22×Q8C2411yescharacteristic
668C22×Q8C2416yes—
669C22×Q8C2411yescharacteristic
670C22×D4C2413yes—
671C22×D4C2413yes—
672C23×C4C2413yes—
673C23×C4C2413yes—
674C23×C4C2413yes—
675C23×C4C2416yes—
676C23×C4C2413yes—
677C23×C4C2416yes—
678C23×C4C2413yes—
679C23×C4C2411yescharacteristic
680C4⋊Q8—224no—
681C4⋊Q8—24no—
682C4⋊Q8—212no—
683C4⋊Q8—224no—
684C4⋊Q8—224no—
685C4⋊Q8—212no—
686C4⋊Q8—212no—
687C4⋊Q8—212no—
688C4⋊Q8—212no—
689C4⋊Q8—212no—
690C4⋊Q8—212no—
691C4⋊Q8—212no—
692C4⋊Q8—212no—
693C4⋊Q8—212no—
694C4⋊Q8—212no—
695C4⋊Q8—46no—
696C4⋊Q8—86no—
697C4⋊Q8C2×D4124yes—
698C4⋊Q8C2×D4124yes—
699C4⋊Q8C2×D4124yes—
700#125—212no—
701#125—212no—
702#125—212no—
703#125—212no—
704#125—212no—
705#125—212no—
706#125—212no—
707#125—212no—
708#125—224no—
709#125—224no—
710#125—212no—
711#125—212no—
712#125—212no—
713#125—212no—
714#125—212no—
715#125—212no—
716#124C2×Q8124yescomplemented
717C22⋊Q8—24no—
718C22⋊Q8—224no—
719C22⋊Q8—212no—
720C22⋊Q8—224no—
721C22⋊Q8—224no—
722C22⋊Q8—212no—
723C22⋊Q8—212no—
724C22⋊Q8—212no—
725C22⋊Q8—212no—
726C22⋊Q8—212no—
727C22⋊Q8—212no—
728C22⋊Q8—224no—
729C22⋊Q8—224no—
730C22⋊Q8—46no—
731C22⋊Q8—46no—
732C22⋊Q8—86no—
733C22⋊Q8C2×Q8124yescomplemented
734#121C2×Q8124yescomplemented
735C4×Q8—24no—
736C4×Q8—24no—
737C4×Q8—24no—
738C4×Q8—24no—
739C4×Q8—24no—
740C4×Q8—24no—
741C4×Q8—224no—
742C4×Q8—24no—
743C4×Q8—24no—
744C4×Q8—24no—
745C4×Q8—212no—
746C4×Q8—212no—
747C4×Q8—212no—
748C4×Q8—224no—
749C4×Q8—212no—
750C4×Q8—212no—
751C4×Q8—212no—
752C4×Q8—212no—
753C4×Q8—212no—
754C4×Q8—212no—
755C4×Q8—212no—
756C4×Q8—212no—
757C4×Q8—212no—
758C4×Q8—86no—
759C4×Q8C2×D418yes—
760C4×Q8C2×D418yes—
761C4×Q8C2×D418yes—
762C4×Q8C2×D4124yes—
763C4×Q8C2×Q818yescomplemented
764C4×D4—212no—
765C4×D4—212no—
766C4×D4—212no—
767C4×D4—212no—
768C4×D4—212no—
769C4×D4—212no—
770C4×D4—86no—
771C4×D4C2×Q8124yescomplemented
772#117—212no—
773#117—212no—
774#117—212no—
775#117—212no—
776#117—212no—
777#117—212no—
778#117—212no—
779C2×C4⋊C4—212no—
780C2×C4⋊C4—212no—
781C2×C4⋊C4—212no—
782C2×C4⋊C4—224no—
783C2×C4⋊C4C2413yes—
784C2×C4⋊C4C2413yes—
785C2×C4⋊C4C2413yes—
786C2×C4⋊C4C2413yes—
787C2×C4⋊C4C2413yes—
788C2×C4⋊C4C2413yes—
789C2×C4⋊C4C2416yes—
790C2×C4⋊C4C2416yes—
791C2×C4⋊C4C2416yes—
792C2×C4⋊C4C2411yescharacteristic
793C2×C4⋊C4C2411yescharacteristic
794C2×C4⋊C4C2413yes—
795C2×C4⋊C4C2413yes—
796C2×C4⋊C4C2413yes—
797C2×C4⋊C4C2413yes—
798C2×C4⋊C4C2413yes—
799C2×C4⋊C4C2413yes—
800C2×C4⋊C4C2413yes—
801C2×C4⋊C4C2411yescharacteristic
802C2×C4⋊C4C2411yescharacteristic
803C2×C4⋊C4C2413yes—
804C2×C4⋊C4C2413yes—
805C2×C4⋊C4C2411yescharacteristic
806C2×C4⋊C4C2411yescharacteristic
807C2×C4⋊C4C2411yescharacteristic
808C2×C4⋊C4C2413yes—
809C2×C4⋊C4C2413yes—
810C2×C4⋊C4C2413yes—
811C2×C4⋊C4C2413yes—
812C2×C4⋊C4C2413yes—
813C2×C4⋊C4C2413yes—
814C2×C4⋊C4C2416yes—
815C2×C4⋊C4C2413yes—
816C2×C4⋊C4C2413yes—
817C2×C4⋊C4C2413yes—
818C2×C4⋊C4C2413yes—
819C2×C4⋊C4C2416yes—
820C2×C4⋊C4C2416yes—
821C2×C4⋊C4C2413yes—
822C2×C4⋊C4C2413yes—
823C2×C4⋊C4C2413yes—
824C2×C4⋊C4C2411yescharacteristic
825C2×C4⋊C4C2413yes—
826C2×C4⋊C4C2411yescharacteristic
827C2×C4⋊C4C2416yes—
828C2×C4⋊C4C2413yes—
829C2×C4⋊C4C2413yes—
830C2×C4⋊C4C2416yes—
831C2×C4⋊C4C2413yes—
832C2×C4⋊C4C2416yes—
833C2×C4⋊C4C2413yes—
834C2×C4⋊C4C2413yes—
835C2×C4⋊C4C2413yes—
836C2×C4⋊C4C2413yes—
837C2×C4⋊C4C2413yes—
838C2×C4⋊C4C2413yes—
839C2×C4⋊C4C2413yes—
840C2×C4⋊C4C2411yescharacteristic
841C2×C4⋊C4C2413yes—
842C2×C4⋊C4C2411yescharacteristic
843C2×C4⋊C4C2411yescharacteristic
844C2×C4⋊C4C2413yes—
845C2×C4⋊C4C2413yes—
846C2×C4⋊C4C2416yes—
847C2×C4⋊C4C2413yes—
848C2×C4⋊C4C2413yes—
849C2×C4⋊C4C2413yes—
850C2×C4⋊C4C2413yes—
851C2×C4⋊C4C2413yes—
852C2×C4⋊C4C2416yes—
853C2×C4⋊C4C2413yes—
854C2×C4⋊C4C2413yes—
855C2×C4⋊C4C2413yes—
856C2×C4⋊C4C2413yes—
857C2×C4⋊C4C2413yes—
858C2×C4⋊C4C2413yes—
859C2×C4⋊C4C2413yes—
860C2×C4⋊C4C2413yes—
861C2×C22⋊C4C2411yescharacteristic
862C2×C22⋊C4C2413yes—
863C2×C22⋊C4C2413yes—
864C2×C22⋊C4C2411yescharacteristic
865C2×C22⋊C4C2413yes—
866C2×C22⋊C4C2413yes—
867C2×C22⋊C4C2413yes—
868C2×C22⋊C4C2416yes—
869C2×C22⋊C4C2413yes—
870C2×C22⋊C4C2411yescharacteristic
871C2×C22⋊C4C2413yes—
872C2×C22⋊C4C2416yes—
873C2×C22⋊C4C2413yes—
874C2×C22⋊C4C2413yes—
875C2×C22⋊C4C2413yes—
876C2×C22⋊C4C2413yes—
877C2×C22⋊C4C2413yes—
878C2×C22⋊C4C2413yes—
879C2×C22⋊C4C2411yescharacteristic
880C2×C22⋊C4C2411yescharacteristic
881C2×C22⋊C4C2413yes—
882C2×C22⋊C4C2416yes—
883C2×C22⋊C4C2413yes—
884C2×C22⋊C4C2416yes—
885C2×C22⋊C4C2411yescharacteristic
886C2×C22⋊C4C2413yes—
887C2×C22⋊C4C2416yes—
888C2×C42—212no—
889C2×C42—212no—
890C2×C42C2413yes—
891C2×C42C2413yes—
892C2×C42C2413yes—
893C2×C42C2416yes—
894C2×C42C2413yes—
895C2×C42C2413yes—
896C2×C42C2416yes—
897C2×C42C2413yes—
898C2×C42C2413yes—
899C2×C42C2413yes—
900C2×C42C2413yes—
901C2×C42C2413yes—
902C2×C42C2413yes—
903C2×C42C2413yes—
904C2×C42C2411yescharacteristic
905C2×C42C2416yes—
906C2×C42C2413yes—
907C2×C42C2416yes—
908C2×C42C2413yes—
909C2×C42C2411yescharacteristic
910C2×C42C2413yes—
911C2×C42C2413yes—
912C2×C42C2413yes—
913C2×C42C2413yes—
914C2×C42C2413yes—
915#95C2411yescharacteristic
916#95C2411yescharacteristic
917#95C2413yes—
918#95C2413yes—
919#95C2413yes—
920#95C2413yes—
921#95C2413yes—
922#95C2413yes—
923#95C2411yescharacteristic
924#95C2413yes—
925#95C2411yescharacteristic
926#95C2411yescharacteristic
927#95C2413yes—
928#95C2413yes—
929#95C2413yes—
930#95C2413yes—
931#95C2413yes—
932#95C2413yes—
933#95C2413yes—
934#95C2416yes—
935#95C2416yes—
936#95C2416yes—
937#95C2413yes—
938#95C2413yes—
939#95C2413yes—
940#95C2413yes—
941#95C2411yescharacteristic
942#95C2411yescharacteristic
943#95C2416yes—
944#95C2411yescharacteristic
945#95C2411yescharacteristic
946#95C2411yescharacteristic
947#95C2411yescharacteristic
948#95C2411yescharacteristic
949#95C2413yes—
950#95C2413yes—
951#95C2413yes—
952#95C2413yes—
953#95C2413yes—
954#95C2416yes—
955#95C2413yes—
956#95C2413yes—
957#95C2413yes—
958#95C2413yes—
959#95C2416yes—
960#95C2416yes—
961#95C2413yes—
962#95C2413yes—
963#95C2413yes—
964#95C2413yes—
965#95C2413yes—
966#95C2416yes—
967#95C2416yes—
968#95C2416yes—
969#95C2416yes—
970C24C2511yescharacteristic
971C24C2513yes—
972#41—232no—
973C2×Q8—232no—
974C2×Q8—26no—
975C2×Q8—22no—
976C2×Q8—26no—
977C2×Q8—26no—
978C2×Q8—26no—
979C2×Q8—26no—
980C2×Q8—26no—
981C2×Q8—212no—
982C2×Q8—26no—
983C2×Q8—26no—
984C2×Q8—26no—
985C2×Q8—46no—
986C2×Q8—46no—
987C2×Q8—43no—
988C2×Q8—43no—
989C2×Q8—41no—
990C2×Q8—41no—
991C2×Q8—41no—
992C2×Q8—41no—
993C2×Q8—43no—
994C2×Q8—43no—
995C2×Q8—43no—
996C2×Q8—43no—
997C2×Q8—43no—
998C2×Q8—43no—
999C2×Q8—46no—
1000C2×Q8—46no—
1001C2×Q8—848no—
1002C2×Q8C22×D4124yes—
1003C2×Q8C22×D414yes—
1004C2×Q8C22×D414yes—
1005C2×Q8C22×Q8112yes—
1006C2×Q8C22×Q814yes—
1007C2×Q82−1+414yes—
1008C2×D4—26no—
1009C2×D4—26no—
1010C2×D4—43no—
1011C2×D4—43no—
1012C2×D4C22×Q8112yes—
1013C2×D4C22×Q8112yes—
1014C22×C4—26no—
1015C22×C4—26no—
1016C22×C4—26no—
1017C22×C4—26no—
1018C22×C4—22no—
1019C22×C4—26no—
1020C22×C4—26no—
1021C22×C4—26no—
1022C22×C4—26no—
1023C22×C4—212no—
1024C22×C4—212no—
1025C22×C4—43no—
1026C22×C4—43no—
1027C22×C4—41no—
1028C22×C4—41no—
1029C22×C4—43no—
1030C22×C4—43no—
1031C22×C4—46no—
1032C22×C4—43no—
1033C22×C4—46no—
1034C22×C4—46no—
1035C22×C4—46no—
1036C22×C4C22×Q8112yes—
1037C22×C4C22×Q8112yes—
1038C22×C4C2511yescharacteristic
1039C22×C4C2511yescharacteristic
1040C22×C4C2513yes—
1041C22×C4C2511yescharacteristic
1042C22×C4C2513yes—
1043C22×C4C2513yes—
1044C22×C4C2513yes—
1045C22×C4C2513yes—
1046C22×C4C2511yescharacteristic
1047C22×C4C2511yescharacteristic
1048C22×C4C2511yescharacteristic
1049C22×C4C2513yes—
1050C22×C4C2513yes—
1051C22×C4C2513yes—
1052C22×C4C2511yescharacteristic
1053C22×C4C2511yescharacteristic
1054C22×C4C2513yes—
1055C22×C4C2511yescharacteristic
1056C22×C4C2511yescharacteristic
1057C22×C4C2513yes—
1058C22×C4C2513yes—
1059C22×C4C2513yes—
1060C22×C4C2511yescharacteristic
1061C22×C4C2511yescharacteristic
1062C22×C4C2513yes—
1063C22×C4C2513yes—
1064C22×C4C2511yescharacteristic
1065C22×C4C2511yescharacteristic
1066C22×C4C2513yes—
1067C4⋊C4—26no—
1068C4⋊C4—26no—
1069C4⋊C4—26no—
1070C4⋊C4—26no—
1071C4⋊C4—26no—
1072C4⋊C4—212no—
1073C4⋊C4—26no—
1074C4⋊C4—212no—
1075C4⋊C4—212no—
1076C4⋊C4—22no—
1077C4⋊C4—22no—
1078C4⋊C4—26no—
1079C4⋊C4—26no—
1080C4⋊C4—26no—
1081C4⋊C4—26no—
1082C4⋊C4—26no—
1083C4⋊C4—26no—
1084C4⋊C4—26no—
1085C4⋊C4—22no—
1086C4⋊C4—22no—
1087C4⋊C4—26no—
1088C4⋊C4—26no—
1089C4⋊C4—22no—
1090C4⋊C4—22no—
1091C4⋊C4—22no—
1092C4⋊C4—26no—
1093C4⋊C4—26no—
1094C4⋊C4—26no—
1095C4⋊C4—26no—
1096C4⋊C4—26no—
1097C4⋊C4—26no—
1098C4⋊C4—212no—
1099C4⋊C4—26no—
1100C4⋊C4—26no—
1101C4⋊C4—26no—
1102C4⋊C4—26no—
1103C4⋊C4—212no—
1104C4⋊C4—212no—
1105C4⋊C4—26no—
1106C4⋊C4—26no—
1107C4⋊C4—26no—
1108C4⋊C4—22no—
1109C4⋊C4—26no—
1110C4⋊C4—22no—
1111C4⋊C4—41no—
1112C4⋊C4—41no—
1113C4⋊C4—43no—
1114C4⋊C4—43no—
1115C4⋊C4—46no—
1116C4⋊C4—43no—
1117C4⋊C4—43no—
1118C4⋊C4—43no—
1119C4⋊C4—43no—
1120C4⋊C4—41no—
1121C4⋊C4—43no—
1122C4⋊C4—43no—
1123C4⋊C4—46no—
1124C4⋊C4—46no—
1125C4⋊C4—43no—
1126C4⋊C4—43no—
1127C4⋊C4—46no—
1128C4⋊C4—43no—
1129C4⋊C4—43no—
1130C4⋊C4—43no—
1131C4⋊C4—43no—
1132C4⋊C4—46no—
1133C4⋊C4—43no—
1134C4⋊C4—43no—
1135C4⋊C4—43no—
1136C4⋊C4—43no—
1137C4⋊C4C22×D4112yes—
1138C4⋊C4C22×D4112yes—
1139C4⋊C4C22×D4112yes—
1140C4⋊C4C22×D4112yes—
1141C4⋊C4C22×D4112yes—
1142C4⋊C4C22×D4112yes—
1143C4⋊C4C22×Q8112yes—
1144C4⋊C4C22×Q8112yes—
1145C22⋊C4—26no—
1146C22⋊C4—26no—
1147C22⋊C4—22no—
1148C22⋊C4—22no—
1149C22⋊C4—26no—
1150C22⋊C4—26no—
1151C22⋊C4—212no—
1152C22⋊C4—26no—
1153C22⋊C4—26no—
1154C22⋊C4—22no—
1155C22⋊C4—43no—
1156C22⋊C4—41no—
1157C22⋊C4—46no—
1158C22⋊C4—46no—
1159C22⋊C4—43no—
1160C22⋊C4—43no—
1161C22⋊C4—43no—
1162C22⋊C4—41no—
1163C22⋊C4—43no—
1164C22⋊C4—46no—
1165C22⋊C4—43no—
1166C22⋊C4—43no—
1167C22⋊C4—43no—
1168C22⋊C4—43no—
1169C22⋊C4C22×Q814yes—
1170C22⋊C4C22×Q8112yes—
1171C22⋊C4C22×Q8124yes—
1172C42—22no—
1173C42—26no—
1174C42—26no—
1175C42—26no—
1176C42—26no—
1177C42—26no—
1178C42—26no—
1179C42—26no—
1180C42—212no—
1181C42—212no—
1182C42—26no—
1183C42—26no—
1184C42—26no—
1185C42—26no—
1186C42—26no—
1187C42—43no—
1188C42—41no—
1189C42—46no—
1190C42—43no—
1191C42—46no—
1192C42—43no—
1193C42C22×D4112yes—
1194C42C22×D4112yes—
1195C42C22×D4112yes—
1196C42C22×Q8112yes—
1197C23—21no—
1198C23—23no—
1199C23—21no—
1200C23—23no—
1201C23—21no—
1202C23—23no—
1203C23—23no—
1204C23—21no—
1205C23—21no—
1206C23—23no—
1207C23—23no—
1208C23—21no—
1209C23C23×Q816yes—
1210C23C23×Q812yes—
1211C23C2611yescharacteristic
1212Q8—224no—
1213Q8—424no—
1214Q8—44no—
1215Q8—412no—
1216Q8—412no—
1217Q8—44no—
1218Q8—412no—
1219Q8—86no—
1220Q8—86no—
1221Q8—812no—
1222Q8D4×Q8116yes—
1223D4—224no—
1224D4—412no—
1225C2×C4—23no—
1226C2×C4—21no—
1227C2×C4—21no—
1228C2×C4—21no—
1229C2×C4—23no—
1230C2×C4—21no—
1231C2×C4—23no—
1232C2×C4—23no—
1233C2×C4—23no—
1234C2×C4—23no—
1235C2×C4—23no—
1236C2×C4—23no—
1237C2×C4—23no—
1238C2×C4—21no—
1239C2×C4—21no—
1240C2×C4—21no—
1241C2×C4—23no—
1242C2×C4—21no—
1243C2×C4—21no—
1244C2×C4—21no—
1245C2×C4—21no—
1246C2×C4—21no—
1247C2×C4—224no—
1248C2×C4—224no—
1249C2×C4—21no—
1250C2×C4—21no—
1251C2×C4—21no—
1252C2×C4—23no—
1253C2×C4—23no—
1254C2×C4—21no—
1255C2×C4—21no—
1256C2×C4—23no—
1257C2×C4—23no—
1258C2×C4—23no—
1259C2×C4—23no—
1260C2×C4—21no—
1261C2×C4—21no—
1262C2×C4—21no—
1263C2×C4—23no—
1264C2×C4—23no—
1265C2×C4—23no—
1266C2×C4—23no—
1267C2×C4—21no—
1268C2×C4—21no—
1269C2×C4—21no—
1270C2×C4—23no—
1271C2×C4—23no—
1272C2×C4—21no—
1273C2×C4—23no—
1274C2×C4—21no—
1275C2×C4—23no—
1276C2×C4—23no—
1277C2×C4—21no—
1278C2×C4—23no—
1279C2×C4—23no—
1280C2×C4—21no—
1281C2×C4—23no—
1282C2×C4—21no—
1283C2×C4—23no—
1284C2×C4—23no—
1285C2×C4—21no—
1286C2×C4—21no—
1287C2×C4—23no—
1288C2×C4—23no—
1289C2×C4—23no—
1290C2×C4—21no—
1291C2×C4—23no—
1292C2×C4—21no—
1293C2×C4—23no—
1294C2×C4—21no—
1295C2×C4—23no—
1296C2×C4—21no—
1297C2×C4—23no—
1298C2×C4—21no—
1299C2×C4—21no—
1300C2×C4—412no—
1301C2×C4—412no—
1302C2×C4—44no—
1303C2×C4—86no—
1304C2×C4—812no—
1305C2×C4—812no—
1306C2×C4C23×D412yes—
1307C2×C4C23×D416yes—
1308C2×C4C23×D416yes—
1309C2×C4C23×D412yes—
1310C2×C4C23×D416yes—
1311C2×C4C23×D412yes—
1312C2×C4C23×D416yes—
1313C2×C4C23×Q812yes—
1314C2×C4C23×Q816yes—
1315C2×C4C23×Q816yes—
1316C2×C4C23×Q812yes—
1317C2×C4C23×Q816yes—
1318C2×C4C2×2−1+416yes—
1319C2×C4#58512yes—
1320C22—22no—
1321C22—26no—
1322C22—22no—
1323C22—26no—
1324C22—22no—
1325C22—26no—
1326C22—43no—
1327C22—41no—
1328C22—41no—
1329C22—43no—
1330C22—41no—
1331C22—43no—
1332C22—41no—
1333C22—43no—
1334C22C24×D411yescharacteristic
1335C22C24×Q811yescharacteristic
1336C22C22×2−1+411yescharacteristic
1337C22C2×#58511yescharacteristic
1338C22H(7,𝔽2)11yescharacteristic
1339C222−1+611yescharacteristic
1340C222−1+611yescharacteristic
1341C4—22no—
1342C4—26no—
1343C4—26no—
1344C4—26no—
1345C4—22no—
1346C4—22no—
1347C4—22no—
1348C4—22no—
1349C4—26no—
1350C4—22no—
1351C4—26no—
1352C4—43no—
1353C4—43no—
1354C4—43no—
1355C4—41no—
1356C4—41no—
1357C4—41no—
1358C4—43no—
1359C4—43no—
1360C4—41no—
1361C4—43no—
1362C4—41no—
1363C4—41no—
1364C4—43no—
1365C4—43no—
1366C4—41no—
1367C4—41no—
1368C4—43no—
1369C4C2×D4×Q8112yes—
1370C2—42no—
1371C2—46no—
1372C2C22×D4×Q811yescharacteristic
1373C2#6284811yescharacteristic
1374C2#6285411yescharacteristic
1375C2#6295311yescharacteristic
1376C2#6298711yescharacteristic
1377C2#6300411yescharacteristic
1378C2#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. #59413C2semidirect
4. #59144C2semidirect
5. #59036C2semidirect
6. #52162C2semidirect
7. #45139C2semidirect
8. #45110C2semidirect
9. #45099C2semidirect
10. #44934C2semidirect
11. #44894C2semidirect
12. #44879C2semidirect
13. #39613C2semidirect
14. #39591C2semidirect
15. #39590C2semidirect
16. #39370C2semidirect
17. #37691C2semidirect
18. #37686C2semidirect
19. #36466C2semidirect
20. #36435C2semidirect
21. #36431C2semidirect
22. #36040C2semidirect
23. #35957C2semidirect
24. #35937C2semidirect
25. #35816C2semidirect
26. #35786C2semidirect
27. #35711C2semidirect
28. #34335C2semidirect
245. Q82D4semidirect
258. #548Q8semidirect
658. C22×Q8C2×Q8semidirect
716. #124C2×Q8semidirect
733. C22⋊Q8C2×Q8semidirect
734. #121C2×Q8semidirect
763. C4×Q8C2×Q8semidirect
771. 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
#594132
#591442
#590362
#521622
#451392
#451102
#450992
#449342
#448942
#448792
#396132
#395912
#395902
#393702
#376912
#376862
#364662
#364352
#364312
#360402
#359572
#359372
#358162
#357862
#357112
#343352
#343122
#342942
#342932