Finite Group Databasebeta

← #7646512

Subgroups — #7646512

Order 512.

7588 conjugacy classes of subgroups.

The subgroup lattice has 1373 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3517C211yesmaximal, characteristic, complemented
2C2×#3460C211yesmaximal, characteristic, complemented
3#42986C212yesmaximal, complemented
4#42969C212yesmaximal, complemented
5#42914C212yesmaximal, complemented
6#42909C212yesmaximal, complemented
7#41961C214yesmaximal, complemented
8#41959C214yesmaximal, complemented
9#39341C212yesmaximal, complemented
10#39340C212yesmaximal, complemented
11#39139C212yesmaximal, complemented
12#39138C212yesmaximal, complemented
13#37657C214yesmaximal, complemented
14#37656C214yesmaximal, complemented
15#37559C212yesmaximal, complemented
16#37550C212yesmaximal, complemented
17#36744C218yesmaximal, complemented
18#35539C214yesmaximal, complemented
19#35292C211yesmaximal, characteristic, complemented
20#35236C211yesmaximal, characteristic, complemented
21#35234C212yesmaximal, complemented
22#35171C214yesmaximal, complemented
23#35166C212yesmaximal, complemented
24#34936C211yesmaximal, characteristic, complemented
25#34911C211yesmaximal, characteristic, complemented
26#34127C211yesmaximal, characteristic, complemented
27#3517—216no—
28C2×#557C2211yescharacteristic, complemented
29C2×#553C2212yes—
30C2×#553C2214yescomplemented
31C2×#550C2212yes—
32C2×#550C2212yes—
33C2×#550C2211yescharacteristic, complemented
34C2×#550C2211yescharacteristic, complemented
35C2×#547C2212yes—
36C2×#547C2211yescharacteristic, complemented
37#3460—216no—
38C2×#544C2211yescharacteristic
39C2×#542C2212yes—
40C2×#542C2212yes—
41C2×#540C2214yes—
42C2×#540C2212yes—
43C2×#540C2212yes—
44C2×#540C2212yescomplemented
45C2×#538C2214yes—
46C2×#537C2211yescharacteristic
47C2×#537C2214yescomplemented
48C2×#537C2214yescomplemented
49C2×#535C2211yescharacteristic
50C2×#535C2211yescharacteristic
51C2×#532C2211yescharacteristic
52C2×#532C2212yes—
53C2×#532C2212yes—
54C2×#532C2212yescomplemented
55C2×#529C2211yescharacteristic
56C2×#529C2212yes—
57C2×#529C2212yes—
58C2×#529C2212yescomplemented
59C2×#525C2214yes—
60C2×#525C2214yes—
61C2×#520C2212yescomplemented
62C2×C4×#41C2211yescharacteristic
63C2×C4×#41C2211yescharacteristic
64C22×C4×D4C2211yescharacteristic
65#2857C2212yescomplemented
66#2856C2218yescomplemented
67#2856C2212yescomplemented
68#2854C2218yescomplemented
69#2848C2212yes—
70#2847C2212yes—
71#2821C2214yescomplemented
72#2818C2214yes—
73#2816C2214yescomplemented
74#2815C2214yes—
75#2721C2218yescomplemented
76#2714C2218yescomplemented
77#2694C2218yescomplemented
78#2681C2218yes—
79#2680C2218yes—
80#2678C2218yes—
81#2676C2218yescomplemented
82#2675C2218yescomplemented
83#2673C2218yes—
84#2673C2218yescomplemented
85#2672C2218yescomplemented
86#2671C2218yes—
87#2671C2218yescomplemented
88#2669C2218yes—
89#2669C2218yes—
90#2668C2218yes—
91#2664C2214yescomplemented
92#2662C2214yes—
93#2661C2218yescomplemented
94#2661C2218yescomplemented
95#2656C2214yes—
96#2656C2214yescomplemented
97#2636C2214yes—
98#2635C2214yes—
99#2635C2214yescomplemented
100#2633C2214yescomplemented
101#2631C2214yes—
102#2624C2212yes—
103#2621C2214yescomplemented
104#2619C2214yescomplemented
105#2616C2214yescomplemented
106#2615C2212yes—
107#2615C2214yescomplemented
108#2610C2218yescomplemented
109#2604C2212yescomplemented
110#2603C2212yescomplemented
111#2603C2218yescomplemented
112#2602C2214yes—
113#2601C2218yescomplemented
114#2592C2211yescharacteristic, complemented
115#2592C2212yescomplemented
116#2584C2211yescharacteristic, complemented
117#2580C2212yescomplemented
118#2564C2214yescomplemented
119#2562C2212yes—
120#2562C2211yescharacteristic, complemented
121#2552C2214yescomplemented
122#2543C2214yes—
123#2542C2212yes—
124#2542C2214yescomplemented
125#2542C2214yescomplemented
126#2541C2214yes—
127#2541C2214yes—
128#2541C2214yes—
129#2541C2212yes—
130#2541C2214yescomplemented
131#2540C2212yes—
132#2540C2212yes—
133#2540C2212yes—
134#2540C2211yescharacteristic, complemented
135#2540C2218yescomplemented
136#2540C2212yescomplemented
137#2539C2214yes—
138#2538C2212yes—
139#2537C2212yes—
140#2537C2214yescomplemented
141#2536C2214yescomplemented
142#2535C2214yescomplemented
143#2535C2212yescomplemented
144#2501C2212yes—
145#2490C2214yes—
146#2490C2214yescomplemented
147#2487C2212yes—
148#2464C2218yescomplemented
149#2464C2218yescomplemented
150#2463C2218yescomplemented
151#2456C2218yescomplemented
152#2452C2214yescomplemented
153#2449C2218yescomplemented
154#2448C2214yes—
155#2443C2218yescomplemented
156#2440C2214yescomplemented
157#2433C2212yes—
158#2431C2214yes—
159#2428C2214yes—
160#2428C2214yes—
161#2428C2218yescomplemented
162#2428C2214yescomplemented
163#2423C2214yescomplemented
164#2422C2218yescomplemented
165#2417C2214yescomplemented
166#2416C2214yes—
167#2416C2214yescomplemented
168#2415C2212yes—
169#2414C2212yes—
170#2414C2214yes—
171#2411C2214yes—
172#2408C2212yes—
173#2407C2214yes—
174#2407C2214yescomplemented
175#2407C2214yescomplemented
176#2407C2214yescomplemented
177#2397C2214yes—
178#2395C2212yes—
179#2388C2212yes—
180#2355C2212yescomplemented
181#2352C2214yes—
182D4×C4⋊C4C2212yescomplemented
183#2347C2212yes—
184#2343C2214yescomplemented
185#2339C2212yes—
186#2324C2214yes—
187#2324C2214yescomplemented
188#2324C2214yescomplemented
189#2323C2214yescomplemented
190C4×#127C2214yes—
191C4×C22⋊Q8C2212yescomplemented
192C4×#121C2212yescomplemented
193#2295C2212yescomplemented
194#2293C2214yescomplemented
195#2290C2214yes—
196#2285C2211yescharacteristic
197#2283C2212yescomplemented
198C42×D4C2212yescomplemented
199C4×#117C2211yescharacteristic
200C2×C4×C4⋊C4C2212yescomplemented
201C22×#41C2311yescharacteristic
202C22×#41C2314yes—
203C22×#41C2312yes—
204C22×#41C2312yes—
205C22×#41C2312yes—
206C22×#41C2312yes—
207C22×#41C2311yescharacteristic
208C23×D4C2311yescharacteristic
209C24×C4C2312yes—
210#557—28no—
211#553—216no—
212#553—232no—
213#550—216no—
214#550—28no—
215#550—216no—
216#550—28no—
217#547—216no—
218#547—28no—
219#544—28no—
220#542—216no—
221#542—216no—
222#540—216no—
223#540—232no—
224#540—216no—
225#540—216no—
226#538—232no—
227#537—28no—
228#537—416no—
229#537—416no—
230#535—28no—
231#535—28no—
232#532—216no—
233#532—216no—
234#532—28no—
235#532—216no—
236C2×C4⋊Q8C2312yes—
237C2×C4⋊Q8C2311yescharacteristic
238C2×C4⋊Q8C2312yes—
239C2×C4⋊Q8C2312yes—
240C2×#127C2312yes—
241C2×#127C2311yescharacteristic
242C2×#127C2312yes—
243C2×#127C2314yes—
244C2×#127C2312yes—
245C2×#127C2312yes—
246C2×#127C2314yes—
247C2×#127C2318yes—
248#529—216no—
249#529—216no—
250#529—28no—
251#529—216no—
252C2×#126C2314yes—
253C2×#126C2314yes—
254C2×#126C2312yes—
255C2×#126C2314yes—
256C2×#125C2311yescharacteristic
257C2×#125C2312yes—
258C2×#125C2312yes—
259C2×#125C2314yes—
260C2×#125C2312yes—
261C2×#124C2311yescharacteristic
262C2×#124C2312yes—
263C2×#124C2314yes—
264C2×#124C2312yes—
265C2×#124C2312yes—
266C2×#124C2314yes—
267#525—232no—
268#525—416no—
269C2×#123C2314yes—
270C2×#123C2314yes—
271C2×#123C2312yes—
272C2×#123C2314yes—
273C2×#123C2314yes—
274C2×#123C2314yes—
275C2×#123C2314yes—
276C2×#123C2314yes—
277C2×#123C2314yes—
278C2×#123C2318yes—
279C2×C22⋊Q8C2312yes—
280C2×C22⋊Q8C2314yes—
281C2×C22⋊Q8C2311yescharacteristic
282C2×C22⋊Q8C2312yes—
283C2×C22⋊Q8C2312yes—
284C2×C22⋊Q8C2314yes—
285C2×C22⋊Q8C2314yes—
286C2×C22⋊Q8C2312yes—
287C2×C22⋊Q8C2314yes—
288C2×C22⋊Q8C2314yes—
289C2×C22⋊Q8C2314yes—
290C2×C22⋊Q8C2318yes—
291C2×C22⋊Q8C2318yes—
292C2×#121C2314yes—
293C2×#121C2314yes—
294C2×#121C2311yescharacteristic
295C2×#121C2314yes—
296C2×#121C2314yes—
297C2×#121C2312yes—
298C2×#121C2312yes—
299C2×#121C2312yes—
300C2×#121C2312yes—
301C2×#121C2314yes—
302C2×#121C2314yes—
303C2×#121C2314yes—
304C2×#121C2314yes—
305C2×#121C2312yes—
306C2×#121C2312yes—
307C2×#121C2314yes—
308C2×#121C2312yes—
309C2×#121C2312yes—
310C2×#121C2312yes—
311C2×#121C2314yes—
312C2×#121C2312yes—
313C2×#121C2314yes—
314C2×#121C2312yes—
315C2×#121C2314yes—
316C2×#121C2312yes—
317C2×#121C2314yes—
318C2×#121C2314yes—
319C2×#121C2314yes—
320C2×#121C2314yes—
321C2×#121C2318yes—
322C2×#121C2318yes—
323C2×#121C2318yes—
324C2×#121C2318yes—
325C2×#121C2314yes—
326C2×#121C2318yes—
327C2×#121C2318yes—
328C2×#121C2318yes—
329C2×#121C2314yes—
330C2×#120C2314yes—
331C2×#120C2314yes—
332C2×#120C2318yes—
333C2×#120C2314yes—
334#520—216no—
335C4×#41—28no—
336C4×#41D4116yescomplemented
337C2×C4×Q8C2312yes—
338C2×C4×Q8C2311yescharacteristic
339C2×C4×Q8C2311yescharacteristic
340C2×C4×Q8C2312yes—
341C2×C4×Q8C2311yescharacteristic
342C2×C4×Q8C2311yescharacteristic
343C2×C4×Q8C2311yescharacteristic
344C2×C4×D4—28no—
345C2×C4×D4C2312yes—
346C2×C4×D4C2312yes—
347C2×C4×D4C2312yes—
348C2×C4×D4C2311yescharacteristic
349C2×C4×D4C2314yes—
350C2×C4×D4C2312yes—
351C2×C4×D4C2312yes—
352C2×C4×D4C2312yes—
353C2×C4×D4C2311yescharacteristic
354C2×C4×D4C2314yes—
355C2×C4×D4C2314yes—
356C2×C4×D4C2312yes—
357C2×C4×D4C2312yes—
358C2×C4×D4C2312yes—
359C2×C4×D4C2312yes—
360C2×C4×D4C2312yes—
361C2×C4×D4C2314yes—
362C2×C4×D4C2314yes—
363C2×C4×D4C2314yes—
364C2×C4×D4C2311yescharacteristic
365C2×C4×D4C2318yes—
366C2×C4×D4C2318yes—
367C2×C4×D4C2314yes—
368C2×C4×D4C2314yes—
369C2×C4×D4C2311yescharacteristic
370C2×C4×D4C2312yes—
371C2×C4×D4C2312yes—
372C2×C4×D4C2311yescharacteristic
373C2×#117C2314yes—
374C2×#117C2312yes—
375C2×#117C2312yes—
376C2×#117C2314yes—
377C2×#117C2312yes—
378C2×#117C2311yescharacteristic
379C2×#117C2312yes—
380C2×#117C2312yes—
381C2×#117C2311yescharacteristic
382C22×C4⋊C4C2314yes—
383C22×C4⋊C4C2311yescharacteristic
384C22×C4⋊C4C2312yes—
385C22×C4⋊C4C2314yes—
386C22×C22⋊C4C2312yes—
387C22×C42C2312yes—
388C22×C42C2314yes—
389C22×C42C2311yescharacteristic
390C22×C42C2312yes—
391#400C2314yes—
392#400C2312yes—
393#399C2314yes—
394#399C2314yes—
395#399C2314yes—
396#399C2314yes—
397#399C2312yes—
398#399C2318yes—
399#399C2318yes—
400#399C2318yes—
401#398C2318yes—
402#398C2318yes—
403#398C2312yes—
404#398C2318yes—
405#398C2318yes—
406#397C2318yes—
407#397C2312yes—
408#397C2314yes—
409#397C2314yes—
410#397C2318yes—
411#397C2318yes—
412#396C2318yes—
413#396C2318yes—
414#396C2318yes—
415#395C2312yes—
416#395C2318yes—
417#394C2318yes—
418#394C2318yes—
419#394C2318yes—
420#394C2314yes—
421#394C2312yes—
422#394C2318yes—
423#394C2318yes—
424#394C2318yes—
425#394C2314yes—
426#394C2314yes—
427#394C2318yes—
428#394C2318yes—
429#394C2318yes—
430#394C2318yes—
431#394C2318yes—
432#393C2312yes—
433#393C2314yes—
434#393C2318yes—
435#392C2318yes—
436#392C2314yes—
437#392C2314yes—
438#392C2318yes—
439#392C2314yes—
440#392C2318yes—
441#392C2312yes—
442#392C2318yes—
443#392C2318yes—
444#392C2318yes—
445#392C2318yes—
446#392C2314yes—
447#392C2314yes—
448#392C2318yes—
449#392C2318yes—
450#392C2318yes—
451#392C2318yes—
452#392C2318yes—
453#391C2314yes—
454#391C2312yes—
455#391C2314yes—
456#390C2318yes—
457#390C2318yes—
458#390C2314yes—
459#390C2314yes—
460#390C2318yes—
461#390C2314yes—
462#390C2314yes—
463#390C2318yes—
464#390C2318yes—
465#390C2314yes—
466#390C2314yes—
467#390C2312yes—
468#390C2314yes—
469#390C2318yes—
470#390C2318yes—
471#390C2314yes—
472#389C2312yes—
473#389C2318yes—
474#389C2314yes—
475#389C2312yes—
476#389C2314yes—
477#389C2314yes—
478#389C2314yes—
479#389C2314yes—
480#389C2314yes—
481#388C2318yes—
482#388C2314yes—
483#388C2318yes—
484#388C2318yes—
485#388C2318yes—
486#388C2318yes—
487#388C2314yes—
488#388C2314yes—
489#388C2318yes—
490#388C2314yes—
491#388C2314yes—
492#388C2318yes—
493#388C2318yes—
494#387C2318yes—
495#387C2318yes—
496#387C2318yes—
497#387C2314yes—
498#386C2318yes—
499#386C2318yes—
500#386C2318yes—
501#386C2318yes—
502#386C2314yes—
503#386C2318yes—
504#386C2318yes—
505#386C2314yes—
506#386C2318yes—
507#386C2318yes—
508#386C2318yes—
509#386C2318yes—
510#385C2318yes—
511#385C2318yes—
512#385C2318yes—
513#385C2314yes—
514#385C2318yes—
515#385C2314yes—
516#385C2318yes—
517#385C2318yes—
518#384C2314yes—
519#384C2312yes—
520#384C2318yes—
521#383C2314yes—
522#382C2312yes—
523#382C2314yes—
524#381C2314yes—
525#380C2314yes—
526#380C2314yes—
527#380C2312yes—
528#380C2312yes—
529#380C2318yes—
530#380C2314yes—
531#380C2314yes—
532#380C2312yes—
533#380C2312yes—
534#380C2314yes—
535#380C2314yes—
536#379C2314yes—
537C4×C4⋊C4C2312yes—
538C4×C4⋊C4C2311yescharacteristic
539C4×C4⋊C4C2314yes—
540C4×C4⋊C4C2312yes—
541C4×C4⋊C4C2311yescharacteristic
542C4×C4⋊C4C2314yes—
543C4×C4⋊C4C2314yes—
544C4×C4⋊C4C2314yes—
545C4×C4⋊C4C2312yes—
546C4×C4⋊C4C2314yes—
547C4×C22⋊C4C2312yes—
548C4×C22⋊C4C2318yes—
549C4×C22⋊C4C2312yes—
550C4×C22⋊C4C2314yes—
551C4×C22⋊C4C2314yes—
552C4×C22⋊C4C2314yes—
553#376C2312yes—
554#376C2314yes—
555C2×#95C2314yes—
556C43C2312yes—
557C25C2412yes—
558C2×#41—28no—
559C2×#41—24no—
560C2×#41—216no—
561C2×#41—28no—
562C2×#41—28no—
563C2×#41—28no—
564C2×#41—44no—
565C2×#41—48no—
566C2×#41—48no—
567C2×#41—44no—
568C2×#41—48no—
569C2×#41—48no—
570C2×#41—48no—
571C2×#41—48no—
572C2×#41C2×D418yes—
573C22×Q8C2412yes—
574C22×Q8C2411yescharacteristic
575C22×Q8C2411yescharacteristic
576C22×Q8C2411yescharacteristic
577C22×Q8C2414yes—
578C22×D4—24no—
579C22×D4—44no—
580C22×D4C2412yes—
581C22×D4C2412yes—
582C22×D4C2412yes—
583C22×D4C2411yescharacteristic
584C22×D4C2411yescharacteristic
585C22×D4C2412yes—
586C22×D4C2412yes—
587C22×D4C2411yescharacteristic
588C22×D4C2414yes—
589C22×D4C2412yes—
590C22×D4C2414yes—
591C22×D4C2418yes—
592C22×D4C2414yes—
593C22×D4C2412yes—
594C22×D4C2414yes—
595C22×D4C2414yes—
596C22×D4C2414yes—
597C22×D4C2414yes—
598C22×D4C2414yes—
599C22×D4C2414yes—
600C22×D4C2414yes—
601C22×D4C2414yes—
602C22×D4C2414yes—
603C22×D4C2418yes—
604C22×D4C2418yes—
605C22×D4C2418yes—
606C22×D4C2412yes—
607C23×C4—28no—
608C23×C4—48no—
609C23×C4C2412yes—
610C23×C4C2414yes—
611C23×C4C2412yes—
612C23×C4C2412yes—
613C23×C4C2412yes—
614C23×C4C2411yescharacteristic
615C23×C4C2411yescharacteristic
616C23×C4C2412yes—
617C23×C4C2414yes—
618C23×C4C2414yes—
619C23×C4C2414yes—
620C23×C4C2414yes—
621C23×C4C2418yes—
622C23×C4C2414yes—
623C23×C4C2412yes—
624C23×C4C2411yescharacteristic
625C23×C4C2412yes—
626C23×C4C2412yes—
627C4⋊Q8—28no—
628C4⋊Q8—28no—
629C4⋊Q8—24no—
630C4⋊Q8—28no—
631#127—28no—
632#127—28no—
633#127—216no—
634#127—28no—
635#127—24no—
636#127—28no—
637#127—48no—
638#127—88no—
639#126—216no—
640#126—216no—
641#126—28no—
642#126—216no—
643#125—28no—
644#125—28no—
645#125—216no—
646#125—24no—
647#125—28no—
648#124—28no—
649#124—216no—
650#124—24no—
651#124—28no—
652#124—28no—
653#124—216no—
654#123—216no—
655#123—28no—
656#123—216no—
657#123—216no—
658#123—216no—
659#123—216no—
660#123—216no—
661#123—216no—
662#123—216no—
663#123—416no—
664C22⋊Q8—28no—
665C22⋊Q8—28no—
666C22⋊Q8—24no—
667C22⋊Q8—28no—
668C22⋊Q8—216no—
669C22⋊Q8—216no—
670C22⋊Q8—28no—
671C22⋊Q8—216no—
672C22⋊Q8—416no—
673C22⋊Q8—416no—
674C22⋊Q8—48no—
675C22⋊Q8—48no—
676C22⋊Q8—48no—
677#121—216no—
678#121—28no—
679#121—28no—
680#121—216no—
681#121—28no—
682#121—24no—
683#121—28no—
684#121—28no—
685#121—28no—
686#121—216no—
687#121—28no—
688#121—216no—
689#121—28no—
690#121—216no—
691#121—28no—
692#121—28no—
693#121—28no—
694#121—216no—
695#121—216no—
696#121—28no—
697#121—216no—
698#121—216no—
699#121—216no—
700#121—216no—
701#121—216no—
702#121—416no—
703#121—416no—
704#121—416no—
705#121—416no—
706#121—48no—
707#121—48no—
708#121—48no—
709#121—48no—
710#121—48no—
711#121—416no—
712#121—416no—
713#121—88no—
714#121—84no—
715#120—216no—
716#120—216no—
717#120—416no—
718#120—84no—
719C4×Q8—28no—
720C4×Q8—24no—
721C4×Q8—24no—
722C4×Q8—24no—
723C4×Q8—28no—
724C4×Q8C2×D418yes—
725C4×Q8C2×D418yes—
726C4×D4—28no—
727C4×D4—28no—
728C4×D4—216no—
729C4×D4—28no—
730C4×D4—216no—
731C4×D4—28no—
732C4×D4—216no—
733C4×D4—28no—
734C4×D4—28no—
735C4×D4—28no—
736C4×D4—28no—
737C4×D4—24no—
738C4×D4—24no—
739C4×D4—28no—
740C4×D4—216no—
741C4×D4—216no—
742C4×D4—24no—
743C4×D4—28no—
744C4×D4—28no—
745C4×D4—216no—
746C4×D4—416no—
747C4×D4—48no—
748C4×D4—416no—
749C4×D4—48no—
750C4×D4C2×D4116yes—
751C4×D4C2×D418yes—
752C4×D4C2×D4116yes—
753C4×D4C2×D418yes—
754#117—24no—
755#117—28no—
756#117—28no—
757#117—28no—
758#117—216no—
759#117—216no—
760#117—82no—
761#117C2×D418yes—
762#117C2×D4116yes—
763C2×C4⋊C4—24no—
764C2×C4⋊C4—28no—
765C2×C4⋊C4—216no—
766C2×C4⋊C4—216no—
767C2×C4⋊C4C2412yes—
768C2×C4⋊C4C2414yes—
769C2×C4⋊C4C2412yes—
770C2×C4⋊C4C2412yes—
771C2×C4⋊C4C2412yes—
772C2×C4⋊C4C2414yes—
773C2×C4⋊C4C2414yes—
774C2×C4⋊C4C2418yes—
775C2×C4⋊C4C2412yes—
776C2×C4⋊C4C2411yescharacteristic
777C2×C4⋊C4C2411yescharacteristic
778C2×C4⋊C4C2412yes—
779C2×C4⋊C4C2412yes—
780C2×C4⋊C4C2412yes—
781C2×C4⋊C4C2414yes—
782C2×C4⋊C4C2414yes—
783C2×C4⋊C4C2411yescharacteristic
784C2×C4⋊C4C2412yes—
785C2×C4⋊C4C2414yes—
786C2×C4⋊C4C2418yes—
787C2×C4⋊C4C2414yes—
788C2×C4⋊C4C2414yes—
789C2×C4⋊C4C2412yes—
790C2×C4⋊C4C2414yes—
791C2×C4⋊C4C2411yescharacteristic
792C2×C4⋊C4C2412yes—
793C2×C4⋊C4C2414yes—
794C2×C4⋊C4C2414yes—
795C2×C4⋊C4C2414yes—
796C2×C4⋊C4C2418yes—
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2414yes—
799C2×C4⋊C4C2418yes—
800C2×C4⋊C4C2418yes—
801C2×C4⋊C4C2411yescharacteristic
802C2×C4⋊C4C2412yes—
803C2×C4⋊C4C2411yescharacteristic
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2412yes—
806C2×C22⋊C4—28no—
807C2×C22⋊C4C2414yes—
808C2×C22⋊C4C2414yes—
809C2×C22⋊C4C2412yes—
810C2×C22⋊C4C2412yes—
811C2×C22⋊C4C2414yes—
812C2×C22⋊C4C2412yes—
813C2×C22⋊C4C2412yes—
814C2×C22⋊C4C2414yes—
815C2×C22⋊C4C2412yes—
816C2×C22⋊C4C2414yes—
817C2×C22⋊C4C2414yes—
818C2×C22⋊C4C2414yes—
819C2×C22⋊C4C2414yes—
820C2×C22⋊C4C2412yes—
821C2×C22⋊C4C2418yes—
822C2×C22⋊C4C2414yes—
823C2×C22⋊C4C2414yes—
824C2×C22⋊C4C2412yes—
825C2×C22⋊C4C2414yes—
826C2×C22⋊C4C2414yes—
827C2×C22⋊C4C2414yes—
828C2×C22⋊C4C2418yes—
829C2×C22⋊C4C2412yes—
830C2×C22⋊C4C2414yes—
831C2×C22⋊C4C2414yes—
832C2×C22⋊C4C2414yes—
833C2×C22⋊C4C2414yes—
834C2×C22⋊C4C2418yes—
835C2×C22⋊C4C2418yes—
836C2×C22⋊C4C2418yes—
837C2×C22⋊C4C2414yes—
838C2×C22⋊C4C2414yes—
839C2×C22⋊C4C2418yes—
840C2×C22⋊C4C2418yes—
841C2×C22⋊C4C2418yes—
842C2×C22⋊C4C2418yes—
843C2×C22⋊C4C2418yes—
844C2×C22⋊C4C2418yes—
845C2×C22⋊C4C2418yes—
846C2×C22⋊C4C2418yes—
847C2×C22⋊C4C2414yes—
848C2×C22⋊C4C2414yes—
849C2×C22⋊C4C2412yes—
850C2×C22⋊C4C2412yes—
851C2×C22⋊C4C2412yes—
852C2×C42—28no—
853C2×C42—84no—
854C2×C42C2×D418yes—
855C2×C42C2×D4116yes—
856C2×C42C2412yes—
857C2×C42C2412yes—
858C2×C42C2414yes—
859C2×C42C2412yes—
860C2×C42C2414yes—
861C2×C42C2414yes—
862C2×C42C2412yes—
863C2×C42C2414yes—
864C2×C42C2418yes—
865C2×C42C2412yes—
866C2×C42C2412yes—
867C2×C42C2411yescharacteristic
868C2×C42C2411yescharacteristic
869C2×C42C2412yes—
870C2×C42C2412yes—
871C2×C42C2412yes—
872C2×C42C2411yescharacteristic
873C2×C42C2411yescharacteristic
874#95C2412yes—
875#95C2414yes—
876#95C2418yes—
877#95C2412yes—
878#95C2414yes—
879#95C2418yes—
880#95C2418yes—
881#95C2414yes—
882#95C2418yes—
883#95C2414yes—
884#95C2414yes—
885#95C2414yes—
886#95C2414yes—
887#95C2414yes—
888#95C2414yes—
889#95C2418yes—
890#95C2418yes—
891#95C2418yes—
892#95C2418yes—
893C24—24no—
894C24—44no—
895C24—44no—
896C24—42no—
897C24—42no—
898C24C2514yes—
899C24C2512yes—
900C24C2512yes—
901C24C2514yes—
902C24C2511yescharacteristic
903C24C2512yes—
904#41—416no—
905#41—416no—
906#41—432no—
907#41—832no—
908#41—816no—
909#41—816no—
910#41—816no—
911C2×Q8—22no—
912C2×Q8—22no—
913C2×Q8—24no—
914C2×Q8—28no—
915C2×Q8—28no—
916C2×Q8—24no—
917C2×Q8—24no—
918C2×Q8—42no—
919C2×Q8—44no—
920C2×Q8—44no—
921C2×Q8C22×D414yes—
922C2×D4—24no—
923C2×D4—28no—
924C2×D4—24no—
925C2×D4—28no—
926C2×D4—28no—
927C2×D4—28no—
928C2×D4—28no—
929C2×D4—28no—
930C2×D4—28no—
931C2×D4—24no—
932C2×D4—24no—
933C2×D4—28no—
934C2×D4—22no—
935C2×D4—24no—
936C2×D4—22no—
937C2×D4—24no—
938C2×D4—28no—
939C2×D4—24no—
940C2×D4—28no—
941C2×D4—28no—
942C2×D4—28no—
943C2×D4—24no—
944C2×D4—216no—
945C2×D4—28no—
946C2×D4—24no—
947C2×D4—24no—
948C2×D4—28no—
949C2×D4—24no—
950C2×D4—44no—
951C2×D4—42no—
952C2×D4—44no—
953C2×D4—48no—
954C2×D4—42no—
955C2×D4—42no—
956C2×D4—416no—
957C2×D4—48no—
958C2×D4—44no—
959C2×D4—48no—
960C2×D4—42no—
961C2×D4—44no—
962C2×D4—44no—
963C2×D4—44no—
964C2×D4—44no—
965C2×D4—48no—
966C2×D4—48no—
967C2×D4—44no—
968C2×D4—44no—
969C2×D4—42no—
970C2×D4—44no—
971C2×D4—44no—
972C2×D4—48no—
973C2×D4—48no—
974C2×D4—48no—
975C2×D4—44no—
976C2×D4—44no—
977C2×D4—44no—
978C2×D4—42no—
979C2×D4—44no—
980C2×D4—44no—
981C2×D4—48no—
982C2×D4—44no—
983C2×D4—44no—
984C2×D4—42no—
985C2×D4—48no—
986C2×D4—48no—
987C2×D4—48no—
988C2×D4—48no—
989C2×D4—48no—
990C2×D4—48no—
991C2×D4C22×D414yes—
992C2×D4C22×D418yes—
993C22×C4—28no—
994C22×C4—24no—
995C22×C4—24no—
996C22×C4—24no—
997C22×C4—24no—
998C22×C4—24no—
999C22×C4—28no—
1000C22×C4—24no—
1001C22×C4—28no—
1002C22×C4—28no—
1003C22×C4—24no—
1004C22×C4—28no—
1005C22×C4—24no—
1006C22×C4—24no—
1007C22×C4—28no—
1008C22×C4—24no—
1009C22×C4—24no—
1010C22×C4—28no—
1011C22×C4—28no—
1012C22×C4—28no—
1013C22×C4—28no—
1014C22×C4—216no—
1015C22×C4—42no—
1016C22×C4—41no—
1017C22×C4—41no—
1018C22×C4—42no—
1019C22×C4—44no—
1020C22×C4—48no—
1021C22×C4—48no—
1022C22×C4—44no—
1023C22×C4—44no—
1024C22×C4—48no—
1025C22×C4—48no—
1026C22×C4—48no—
1027C22×C4—48no—
1028C22×C4—42no—
1029C22×C4—44no—
1030C22×C4—42no—
1031C22×C4—816no—
1032C22×C4C22×D414yes—
1033C22×C4C22×D414yes—
1034C22×C4C22×D418yes—
1035C22×C4C22×D414yes—
1036C22×C4C22×D418yes—
1037C22×C4C22×D418yes—
1038C22×C4C2514yes—
1039C22×C4C2518yes—
1040C22×C4C2512yes—
1041C22×C4C2512yes—
1042C22×C4C2512yes—
1043C22×C4C2512yes—
1044C22×C4C2512yes—
1045C22×C4C2512yes—
1046C22×C4C2514yes—
1047C22×C4C2514yes—
1048C22×C4C2511yescharacteristic
1049C22×C4C2512yes—
1050C22×C4C2512yes—
1051C22×C4C2511yescharacteristic
1052C22×C4C2511yescharacteristic
1053C22×C4C2512yes—
1054C22×C4C2511yescharacteristic
1055C22×C4C2514yes—
1056C22×C4C2511yescharacteristic
1057C22×C4C2511yescharacteristic
1058C4⋊C4—24no—
1059C4⋊C4—28no—
1060C4⋊C4—24no—
1061C4⋊C4—24no—
1062C4⋊C4—28no—
1063C4⋊C4—24no—
1064C4⋊C4—24no—
1065C4⋊C4—22no—
1066C4⋊C4—22no—
1067C4⋊C4—24no—
1068C4⋊C4—24no—
1069C4⋊C4—28no—
1070C4⋊C4—28no—
1071C4⋊C4—22no—
1072C4⋊C4—24no—
1073C4⋊C4—28no—
1074C4⋊C4—28no—
1075C4⋊C4—24no—
1076C4⋊C4—28no—
1077C4⋊C4—22no—
1078C4⋊C4—24no—
1079C4⋊C4—28no—
1080C4⋊C4—216no—
1081C4⋊C4—28no—
1082C4⋊C4—24no—
1083C4⋊C4—216no—
1084C4⋊C4—28no—
1085C4⋊C4—28no—
1086C4⋊C4—44no—
1087C4⋊C4—44no—
1088C4⋊C4—48no—
1089C4⋊C4—48no—
1090C4⋊C4—48no—
1091C4⋊C4—44no—
1092C4⋊C4C22×D414yes—
1093C4⋊C4C22×D418yes—
1094C4⋊C4C22×D414yes—
1095C4⋊C4C22×D418yes—
1096C4⋊C4H(5,𝔽2)18yes—
1097C22⋊C4—24no—
1098C22⋊C4—24no—
1099C22⋊C4—28no—
1100C22⋊C4—28no—
1101C22⋊C4—28no—
1102C22⋊C4—28no—
1103C22⋊C4—24no—
1104C22⋊C4—28no—
1105C22⋊C4—24no—
1106C22⋊C4—24no—
1107C22⋊C4—28no—
1108C22⋊C4—24no—
1109C22⋊C4—28no—
1110C22⋊C4—28no—
1111C22⋊C4—28no—
1112C22⋊C4—24no—
1113C22⋊C4—28no—
1114C22⋊C4—28no—
1115C22⋊C4—28no—
1116C22⋊C4—24no—
1117C22⋊C4—28no—
1118C22⋊C4—28no—
1119C22⋊C4—216no—
1120C22⋊C4—216no—
1121C22⋊C4—28no—
1122C22⋊C4—28no—
1123C22⋊C4—44no—
1124C22⋊C4—44no—
1125C22⋊C4—44no—
1126C22⋊C4—48no—
1127C22⋊C4—44no—
1128C22⋊C4—44no—
1129C22⋊C4—48no—
1130C22⋊C4—48no—
1131C22⋊C4—48no—
1132C22⋊C4—48no—
1133C22⋊C4—48no—
1134C22⋊C4—48no—
1135C22⋊C4—48no—
1136C22⋊C4—48no—
1137C22⋊C4—48no—
1138C22⋊C4—48no—
1139C22⋊C4C22×D418yes—
1140C22⋊C4C22×D418yes—
1141C22⋊C4C22×D418yes—
1142C42—24no—
1143C42—24no—
1144C42—24no—
1145C42—28no—
1146C42—24no—
1147C42—28no—
1148C42—28no—
1149C42—42no—
1150C42—44no—
1151C42—48no—
1152C42—42no—
1153C42C22×D414yes—
1154C42C22×D414yes—
1155C42C22×D414yes—
1156C42C22×D418yes—
1157C42C22×D418yes—
1158C42C22×D414yes—
1159C42C22×D418yes—
1160C23—22no—
1161C23—24no—
1162C23—24no—
1163C23—22no—
1164C23—21no—
1165C23—22no—
1166C23—22no—
1167C23—21no—
1168C23—24no—
1169C23—22no—
1170C23—24no—
1171C23—22no—
1172C23—24no—
1173C23—22no—
1174C23—24no—
1175C23—28no—
1176C23—24no—
1177C23—22no—
1178C23—22no—
1179C23—24no—
1180C23—24no—
1181C23—28no—
1182C23—22no—
1183C23—24no—
1184C23—24no—
1185C23—24no—
1186C23—22no—
1187C23—22no—
1188C23—22no—
1189C23—22no—
1190C23—24no—
1191C23—24no—
1192C23—48no—
1193C23—84no—
1194C23—84no—
1195C23—88no—
1196C23—88no—
1197C23C23×D412yes—
1198C23C23×D414yes—
1199C23C2611yescharacteristic
1200Q8—28no—
1201Q8—44no—
1202Q8—48no—
1203Q8—44no—
1204Q8—88no—
1205D4—28no—
1206D4—48no—
1207D4—48no—
1208D4—44no—
1209D4—416no—
1210D4—48no—
1211D4—48no—
1212D4—48no—
1213D4—48no—
1214D4—44no—
1215D4—84no—
1216D4—88no—
1217D4—88no—
1218D4—88no—
1219D4—816no—
1220D4—88no—
1221D4—88no—
1222D4—88no—
1223D4—84no—
1224D4—88no—
1225D4—88no—
1226D4—88no—
1227D4—88no—
1228D4—88no—
1229D4—816no—
1230D4—168no—
1231D4—168no—
1232C2×C4—22no—
1233C2×C4—24no—
1234C2×C4—24no—
1235C2×C4—22no—
1236C2×C4—24no—
1237C2×C4—21no—
1238C2×C4—22no—
1239C2×C4—24no—
1240C2×C4—21no—
1241C2×C4—21no—
1242C2×C4—21no—
1243C2×C4—22no—
1244C2×C4—28no—
1245C2×C4—28no—
1246C2×C4—216no—
1247C2×C4—22no—
1248C2×C4—22no—
1249C2×C4—22no—
1250C2×C4—22no—
1251C2×C4—24no—
1252C2×C4—22no—
1253C2×C4—22no—
1254C2×C4—24no—
1255C2×C4—24no—
1256C2×C4—24no—
1257C2×C4—22no—
1258C2×C4—28no—
1259C2×C4—24no—
1260C2×C4—28no—
1261C2×C4—24no—
1262C2×C4—22no—
1263C2×C4—24no—
1264C2×C4—22no—
1265C2×C4—28no—
1266C2×C4—24no—
1267C2×C4—22no—
1268C2×C4—28no—
1269C2×C4—22no—
1270C2×C4—22no—
1271C2×C4—24no—
1272C2×C4—22no—
1273C2×C4—22no—
1274C2×C4—44no—
1275C2×C4—48no—
1276C2×C4—48no—
1277C2×C4—416no—
1278C2×C4—48no—
1279C2×C4—48no—
1280C2×C4—416no—
1281C2×C4—48no—
1282C2×C4—84no—
1283C2×C4—816no—
1284C2×C4—88no—
1285C2×C4—88no—
1286C2×C4—88no—
1287C2×C4—88no—
1288C2×C4—84no—
1289C2×C4C23×D412yes—
1290C2×C4C23×D414yes—
1291C2×C4C23×D412yes—
1292C2×C4C23×D412yes—
1293C2×C4C23×D414yes—
1294C2×C4C23×D412yes—
1295C2×C4C23×D414yes—
1296C2×C4C23×D412yes—
1297C2×C4C23×D412yes—
1298C2×C4C2×H(5,𝔽2)18yes—
1299C2×C4C2×H(5,𝔽2)14yes—
1300C2×C4#58514yes—
1301C22—22no—
1302C22—24no—
1303C22—24no—
1304C22—22no—
1305C22—22no—
1306C22—24no—
1307C22—44no—
1308C22—42no—
1309C22—44no—
1310C22—42no—
1311C22—44no—
1312C22—42no—
1313C22—42no—
1314C22—44no—
1315C22—42no—
1316C22—44no—
1317C22—42no—
1318C22—44no—
1319C22—42no—
1320C22—44no—
1321C22—44no—
1322C22—48no—
1323C22—42no—
1324C22—44no—
1325C22—44no—
1326C22—48no—
1327C22—42no—
1328C22—44no—
1329C22—42no—
1330C22—44no—
1331C22—44no—
1332C22—42no—
1333C22—42no—
1334C22—44no—
1335C22—816no—
1336C22C24×D411yescharacteristic
1337C22C22×H(5,𝔽2)12yes—
1338C22C2×#58512yes—
1339C22H(7,𝔽2)11yescharacteristic
1340C222−1+611yescharacteristic
1341C4—22no—
1342C4—24no—
1343C4—22no—
1344C4—22no—
1345C4—24no—
1346C4—28no—
1347C4—22no—
1348C4—24no—
1349C4—44no—
1350C4—42no—
1351C4—44no—
1352C4—42no—
1353C4—42no—
1354C4—42no—
1355C4—48no—
1356C4—44no—
1357C4—42no—
1358C4—42no—
1359C4#344914yes—
1360C4#349814yes—
1361C2—44no—
1362C2—42no—
1363C2—82no—
1364C2—82no—
1365C2—84no—
1366C2—84no—
1367C2C2×#344911yescharacteristic
1368C2C2×#349811yescharacteristic
1369C2#6285311yescharacteristic
1370C2#6292012yes—
1371C2#6292212yes—
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×#3460C2semidirect
3. #42986C2semidirect
4. #42969C2semidirect
5. #42914C2semidirect
6. #42909C2semidirect
7. #41961C2semidirect
8. #41959C2semidirect
9. #39341C2semidirect
10. #39340C2semidirect
11. #39139C2semidirect
12. #39138C2semidirect
13. #37657C2semidirect
14. #37656C2semidirect
15. #37559C2semidirect
16. #37550C2semidirect
17. #36744C2semidirect
18. #35539C2semidirect
19. #35292C2semidirect
20. #35236C2semidirect
21. #35234C2semidirect
22. #35171C2semidirect
23. #35166C2semidirect
24. #34936C2semidirect
25. #34911C2semidirect
26. #34127C2semidirect
28. C2×#557C22semidirect
30. C2×#553C22semidirect
33. C2×#550C22semidirect
34. C2×#550C22semidirect
36. C2×#547C22semidirect
44. C2×#540C22semidirect
47. C2×#537C22semidirect
48. C2×#537C22semidirect
54. C2×#532C22semidirect
58. C2×#529C22semidirect
61. C2×#520C22semidirect
65. #2857C22semidirect
66. #2856C22semidirect
67. #2856C22semidirect
68. #2854C22semidirect
71. #2821C22semidirect
73. #2816C22semidirect
75. #2721C22semidirect
76. #2714C22semidirect
77. #2694C22semidirect
81. #2676C22semidirect
82. #2675C22semidirect
84. #2673C22semidirect
85. #2672C22semidirect
87. #2671C22semidirect
91. #2664C22semidirect
93. #2661C22semidirect
94. #2661C22semidirect
96. #2656C22semidirect
99. #2635C22semidirect
100. #2633C22semidirect
103. #2621C22semidirect
104. #2619C22semidirect
105. #2616C22semidirect
107. #2615C22semidirect
108. #2610C22semidirect
109. #2604C22semidirect
110. #2603C22semidirect
111. #2603C22semidirect
113. #2601C22semidirect
114. #2592C22semidirect
115. #2592C22semidirect
116. #2584C22semidirect
117. #2580C22semidirect
118. #2564C22semidirect
120. #2562C22semidirect
121. #2552C22semidirect
124. #2542C22semidirect
125. #2542C22semidirect
130. #2541C22semidirect
134. #2540C22semidirect
135. #2540C22semidirect
136. #2540C22semidirect
140. #2537C22semidirect
141. #2536C22semidirect
142. #2535C22semidirect
143. #2535C22semidirect
146. #2490C22semidirect
148. #2464C22semidirect
149. #2464C22semidirect
150. #2463C22semidirect
151. #2456C22semidirect
152. #2452C22semidirect
153. #2449C22semidirect
155. #2443C22semidirect
156. #2440C22semidirect
161. #2428C22semidirect
162. #2428C22semidirect
163. #2423C22semidirect
164. #2422C22semidirect
165. #2417C22semidirect
167. #2416C22semidirect
174. #2407C22semidirect
175. #2407C22semidirect
176. #2407C22semidirect
180. #2355C22semidirect
182. D4×C4⋊C4C22semidirect
184. #2343C22semidirect
187. #2324C22semidirect
188. #2324C22semidirect
189. #2323C22semidirect
191. C4×C22⋊Q8C22semidirect
192. C4×#121C22semidirect
193. #2295C22semidirect
194. #2293C22semidirect
197. #2283C22semidirect
198. C42×D4C22semidirect
200. C2×C4×C4⋊C4C22semidirect
336. C4×#41D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35172
C2×#34602
#429862
#429692
#429142
#429092
#419612
#419592
#393412
#393402
#391392
#391382
#376572
#376562
#375592
#375502
#367442
#355392
#352922
#352362
#352342
#351712
#351662
#349362
#349112
#341272