Finite Group Databasebeta

← #7732532

Subgroups — #7732532

Order 512.

7892 conjugacy classes of subgroups.

The subgroup lattice has 1393 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3494C211yesmaximal, characteristic, complemented
2C2×#3537C211yesmaximal, characteristic, complemented
3#48830C218yesmaximal, complemented
4#47212C214yesmaximal, complemented
5#46813C214yesmaximal, complemented
6#43023C218yesmaximal, complemented
7#39483C212yesmaximal, complemented
8#38953C212yesmaximal, complemented
9#38080C212yesmaximal, complemented
10#38080C212yesmaximal, complemented
11#37869C212yesmaximal, complemented
12#37864C212yesmaximal, complemented
13#37770C214yesmaximal, complemented
14#37678C214yesmaximal, complemented
15#37450C211yesmaximal, characteristic, complemented
16#37304C212yesmaximal, complemented
17#37297C212yesmaximal, complemented
18#36260C212yesmaximal, complemented
19#36182C212yesmaximal, complemented
20#35537C212yesmaximal, complemented
21#35531C212yesmaximal, complemented
22#35262C211yesmaximal, characteristic, complemented
23#35001C211yesmaximal, characteristic, complemented
24C2×#2500C211yesmaximal, characteristic, complemented
25#34082C211yesmaximal, characteristic, complemented
26#3537—216no—
27C2×#560C2214yes—
28#3494—216no—
29C2×#555C2212yescomplemented
30C2×#553C2212yescomplemented
31C2×#553C2212yescomplemented
32C2×#553C2212yescomplemented
33C2×#553C2212yescomplemented
34C2×#551C2214yescomplemented
35C2×#547C2212yescomplemented
36C2×#546C2214yescomplemented
37C2×#546C2218yescomplemented
38C2×D42C2214yes—
39C2×D42C2212yescomplemented
40C2×D42C2212yescomplemented
41C2×#544C2211yescharacteristic, complemented
42C2×#542C2212yescomplemented
43C2×#540C2212yes—
44C2×#540C2212yescomplemented
45C2×#538C2212yescomplemented
46C2×#538C2212yescomplemented
47C2×#535C2212yes—
48C2×#535C2211yescharacteristic, complemented
49C2×#534C2212yescomplemented
50C2×#534C2212yescomplemented
51C2×#534C2214yescomplemented
52C2×#532C2212yescomplemented
53C2×#529C2212yescomplemented
54C2×#525C2211yescharacteristic
55C22×#121C2211yescharacteristic
56C22×#121C2211yescharacteristic
57C22×#121C2211yescharacteristic, complemented
58C2×#520C2211yescharacteristic, complemented
59C2×#518C2211yescharacteristic, complemented
60C22×#117C2211yescharacteristic, complemented
61#2859C2212yescomplemented
62#2858C2212yescomplemented
63#2856C2212yescomplemented
64#2856C2212yescomplemented
65#2856C2212yescomplemented
66#2856C2212yescomplemented
67#2854C2214yescomplemented
68#2815C2214yescomplemented
69#2733C2218yescomplemented
70#2727C2218yescomplemented
71#2723C2218yescomplemented
72#2714C2218yescomplemented
73#2714C2218yescomplemented
74#2706C2218yescomplemented
75#2694C2218yescomplemented
76#2682C2218yescomplemented
77#2681C2218yescomplemented
78#2679C2218yescomplemented
79#2678C2218yescomplemented
80#2678C2218yescomplemented
81#2674C2218yescomplemented
82#2672C2218yescomplemented
83#2672C2218yescomplemented
84#2671C2218yescomplemented
85#2670C2218yescomplemented
86#2670C2218yescomplemented
87#2669C2218yescomplemented
88#2669C2218yescomplemented
89#2660C2212yescomplemented
90#2656C2214yescomplemented
91#2641C2212yescomplemented
92#2624C2214yescomplemented
93#2619C2212yescomplemented
94#2619C2212yescomplemented
95#2619C2212yescomplemented
96#2619C2212yescomplemented
97#2617C2214yescomplemented
98#2617C2214yescomplemented
99#2566C2212yescomplemented
100#2566C2212yescomplemented
101#2566C2212yescomplemented
102#2566C2212yescomplemented
103#2563C2212yescomplemented
104#2542C2212yescomplemented
105#2541C2212yescomplemented
106#2541C2212yescomplemented
107#2540C2218yescomplemented
108#2539C2218yescomplemented
109#2539C2214yescomplemented
110#2539C2218yescomplemented
111#2539C2214yescomplemented
112#2512C2218yescomplemented
113#2504C2212yescomplemented
114#2504C2212yescomplemented
115#2504C2212yescomplemented
116#2504C2212yescomplemented
117#2501C2212yescomplemented
118#2501C2212yescomplemented
119#2501C2212yescomplemented
120#2501C2212yescomplemented
121#2500C2212yescomplemented
122#2500C2212yescomplemented
123#2500C2212yescomplemented
124#2500C2212yescomplemented
125#2500C2214yescomplemented
126#2500C2212yescomplemented
127#2500C2212yescomplemented
128#2500C2212yescomplemented
129#2500C2212yescomplemented
130#2500C2214yescomplemented
131#2500C2212yescomplemented
132#2500C2212yescomplemented
133#2482C2214yescomplemented
134#2479C2218yescomplemented
135#2461C2218yescomplemented
136#2456C2218yescomplemented
137#2456C2218yescomplemented
138#2455C2218yescomplemented
139#2455C2218yescomplemented
140#2448C2218yescomplemented
141#2445C2218yescomplemented
142#2433C2212yescomplemented
143#2433C2212yescomplemented
144#2433C2212yescomplemented
145#2433C2212yescomplemented
146#2433C2212yescomplemented
147#2433C2212yescomplemented
148#2430C2218yescomplemented
149#2425C2218yescomplemented
150#2424C2218yescomplemented
151#2424C2218yescomplemented
152#2424C2218yescomplemented
153#2424C2218yescomplemented
154#2422C2218yescomplemented
155#2418C2218yescomplemented
156#2418C2218yescomplemented
157#2416C2218yescomplemented
158#2414C2218yescomplemented
159#2410C2218yescomplemented
160#2410C2218yescomplemented
161#2408C2218yescomplemented
162#2405C2214yescomplemented
163#2403C2214yescomplemented
164C2×#394C2214yescomplemented
165#2361C2218yescomplemented
166#2335C2214yescomplemented
167#2333C2212yescomplemented
168#2332C2212yescomplemented
169#2329C2212yescomplemented
170#2328C2212yescomplemented
171#2328C2212yescomplemented
172#2325C2212yescomplemented
173#2321C2214yescomplemented
174#2317C2211yescharacteristic, complemented
175#2317C2212yescomplemented
176#2317C2211yescharacteristic, complemented
177#2309C2211yescharacteristic, complemented
178#2309C2212yescomplemented
179#2309C2211yescharacteristic, complemented
180C4×#127C2212yescomplemented
181C4×#127C2212yescomplemented
182#2298C2212yescomplemented
183#2297C2212yescomplemented
184#2293C2212yescomplemented
185C2×#390C2211yescharacteristic, complemented
186C2×#390C2212yescomplemented
187C2×#390C2211yescharacteristic, complemented
188#2290C2212yescomplemented
189#2290C2212yescomplemented
190C2×#388C2214yescomplemented
191#2285C2212yescomplemented
192C2×#384C2211yescharacteristic, complemented
193C2×#382C2211yescharacteristic, complemented
194#2280C2211yescharacteristic, complemented
195C42×D4C2212yescomplemented
196C2×C4×C22⋊C4C2211yescharacteristic, complemented
197C22×#41C2314yes—
198C22×#41C2311yescharacteristic
199C23×D4C2311yescharacteristic
200C23×D4C2312yes—
201C23×D4C2311yescharacteristic
202C23×D4C2312yes—
203C23×D4C2312yes—
204C23×D4C2311yescharacteristic
205C23×D4C2314yes—
206C23×D4C2312yes—
207C23×D4C2314yes—
208C24×C4C2311yescharacteristic
209#560—232no—
210#555—216no—
211#553—216no—
212#553—216no—
213#553—216no—
214#553—216no—
215#551—232no—
216#547—216no—
217#546—232no—
218#546—432no—
219D42—232no—
220D42—216no—
221D42—216no—
222#544—28no—
223#542—216no—
224#540—216no—
225#540—216no—
226#538—216no—
227#538—216no—
228#535—216no—
229#535—28no—
230#534—216no—
231#534—216no—
232#534—416no—
233#532—216no—
234C2×C4⋊Q8C2312yes—
235C2×C4⋊Q8C2312yes—
236C2×#127C2312yes—
237C2×#127C2312yes—
238C2×#127C2314yes—
239C2×#127C2312yes—
240C2×#127C2312yes—
241C2×#127C2312yes—
242C2×#127C2312yes—
243#529—216no—
244C2×#126C2314yes—
245C2×#126C2314yes—
246C2×#126C2314yes—
247C2×#126C2314yes—
248C2×#125C2312yes—
249C2×#125C2312yes—
250C2×#125C2312yes—
251C2×#124C2314yes—
252C2×#124C2314yes—
253C2×#124C2312yes—
254C2×#124C2314yes—
255C2×#124C2318yes—
256#525D4116yescomplemented
257C2×#123C2314yes—
258C2×#123C2314yes—
259C2×#123C2314yes—
260C2×#123C2314yes—
261C2×#123C2314yes—
262C2×#123C2314yes—
263C2×#123C2314yes—
264C2×#123C2314yes—
265C2×#123C2318yes—
266C2×#123C2318yes—
267C2×#123C2318yes—
268C2×#123C2318yes—
269C2×#123C2312yes—
270C2×C22⋊Q8C2314yes—
271C2×C22⋊Q8C2314yes—
272C2×C22⋊Q8C2318yes—
273C2×C22⋊Q8C2311yescharacteristic
274C2×C22⋊Q8C2311yescharacteristic
275C2×#121—28no—
276C2×#121—28no—
277C2×#121—28no—
278C2×#121C2312yes—
279C2×#121C2312yes—
280C2×#121C2312yes—
281C2×#121C2318yes—
282C2×#121C2312yes—
283C2×#121C2312yes—
284C2×#121C2312yes—
285C2×#121C2312yes—
286C2×#121C2312yes—
287C2×#121C2312yes—
288C2×#121C2312yes—
289C2×#121C2312yes—
290C2×#121C2312yes—
291C2×#121C2314yes—
292C2×#121C2312yes—
293C2×#121C2312yes—
294C2×#121C2312yes—
295C2×#121C2312yes—
296C2×#121C2314yes—
297C2×#121C2314yes—
298C2×#121C2314yes—
299C2×#121C2314yes—
300C2×#121C2314yes—
301C2×#121C2314yes—
302C2×#121C2314yes—
303C2×#121C2314yes—
304C2×#121C2318yes—
305C2×#121C2318yes—
306C2×#121C2318yes—
307C2×#121C2318yes—
308C2×#121C2318yes—
309C2×#121C2311yescharacteristic
310C2×#121C2311yescharacteristic
311C2×#120C2314yes—
312C2×#120C2314yes—
313C2×#120C2314yes—
314C2×#120C2314yes—
315C2×#120C2314yes—
316C2×#120C2314yes—
317C2×#120C2314yes—
318C2×#120C2318yes—
319C2×#120C2318yes—
320C2×#120C2318yes—
321C2×#120C2318yes—
322C2×#120C2318yes—
323C2×#120C2318yes—
324C2×#120C2312yes—
325#520—28no—
326#518—28no—
327C2×C4×Q8C2312yes—
328C2×C4×D4C2312yes—
329C2×C4×D4C2312yes—
330C2×C4×D4C2312yes—
331C2×C4×D4C2312yes—
332C2×C4×D4C2314yes—
333C2×C4×D4C2314yes—
334C2×C4×D4C2314yes—
335C2×C4×D4C2312yes—
336C2×C4×D4C2312yes—
337C2×C4×D4C2312yes—
338C2×C4×D4C2314yes—
339C2×C4×D4C2314yes—
340C2×C4×D4C2314yes—
341C2×C4×D4C2318yes—
342C2×C4×D4C2318yes—
343C2×C4×D4C2312yes—
344C2×C4×D4C2312yes—
345C2×#117—28no—
346C2×#117C2311yescharacteristic
347C2×#117C2311yescharacteristic
348C2×#117C2312yes—
349C2×#117C2312yes—
350C2×#117C2312yes—
351C2×#117C2311yescharacteristic
352C2×#117C2311yescharacteristic
353C2×#117C2312yes—
354C2×#117C2314yes—
355C2×#117C2311yescharacteristic
356C2×#117C2311yescharacteristic
357C2×#117C2312yes—
358C2×#117C2311yescharacteristic
359C22×C4⋊C4C2311yescharacteristic
360C22×C4⋊C4C2312yes—
361C22×C4⋊C4C2311yescharacteristic
362C22×C4⋊C4C2311yescharacteristic
363C22×C4⋊C4C2311yescharacteristic
364C22×C4⋊C4C2311yescharacteristic
365C22×C4⋊C4C2314yes—
366C22×C22⋊C4C2312yes—
367C22×C22⋊C4C2312yes—
368C22×C22⋊C4C2312yes—
369C22×C22⋊C4C2312yes—
370C22×C22⋊C4C2314yes—
371C22×C22⋊C4C2314yes—
372C22×C22⋊C4C2312yes—
373C22×C22⋊C4C2318yes—
374C22×C22⋊C4C2314yes—
375C22×C42C2312yes—
376C22×C42C2311yescharacteristic
377C22×C42C2311yescharacteristic
378C22×C42C2312yes—
379#399C2318yes—
380#399C2318yes—
381#399C2318yes—
382#399C2318yes—
383#399C2318yes—
384#398C2318yes—
385#397C2318yes—
386#397C2318yes—
387#397C2318yes—
388#397C2318yes—
389#396C2318yes—
390#396C2318yes—
391#396C2318yes—
392#396C2318yes—
393#395C2318yes—
394#394C2318yes—
395#394C2318yes—
396#394C2318yes—
397#394C2318yes—
398#394C2318yes—
399#394C2318yes—
400#394C2318yes—
401#394C2318yes—
402#394C2318yes—
403#394C2318yes—
404#394C2318yes—
405#394C2318yes—
406#394C2318yes—
407#394C2318yes—
408#394C2318yes—
409#394C2318yes—
410#393C2318yes—
411#392C2318yes—
412#392C2318yes—
413#392C2318yes—
414#392C2318yes—
415#392C2318yes—
416#392C2318yes—
417#392C2318yes—
418#392C2318yes—
419#392C2318yes—
420#392C2318yes—
421#392C2318yes—
422#392C2318yes—
423#391C2314yes—
424#390C2312yes—
425#390C2312yes—
426#390C2312yes—
427#390C2318yes—
428#390C2318yes—
429#390C2312yes—
430#390C2312yes—
431#390C2312yes—
432#390C2312yes—
433#390C2312yes—
434#390C2312yes—
435#390C2312yes—
436#390C2314yes—
437#390C2314yes—
438#390C2318yes—
439#390C2312yes—
440#390C2312yes—
441#390C2312yes—
442#390C2312yes—
443#390C2314yes—
444#390C2314yes—
445#390C2312yes—
446#390C2318yes—
447#390C2318yes—
448#390C2318yes—
449#390C2318yes—
450#390C2318yes—
451#390C2312yes—
452#390C2314yes—
453#390C2318yes—
454#390C2314yes—
455#389C2314yes—
456#389C2314yes—
457#389C2318yes—
458#389C2314yes—
459#389C2318yes—
460#389C2318yes—
461#388C2314yes—
462#388C2314yes—
463#388C2314yes—
464#388C2314yes—
465#388C2314yes—
466#388C2314yes—
467#388C2318yes—
468#388C2318yes—
469#388C2318yes—
470#388C2318yes—
471#388C2318yes—
472#388C2318yes—
473#388C2318yes—
474#388C2318yes—
475#388C2318yes—
476#388C2318yes—
477#387C2314yes—
478#387C2314yes—
479#387C2314yes—
480#387C2314yes—
481#386C2314yes—
482#386C2314yes—
483#386C2314yes—
484#386C2314yes—
485#386C2318yes—
486#386C2318yes—
487#386C2318yes—
488#386C2318yes—
489#386C2318yes—
490#386C2318yes—
491#386C2318yes—
492#386C2318yes—
493#385C2318yes—
494#385C2318yes—
495#385C2318yes—
496#385C2318yes—
497#385C2314yes—
498#385C2314yes—
499#385C2318yes—
500#385C2314yes—
501#385C2314yes—
502#384C2312yes—
503#384C2312yes—
504#384C2312yes—
505#384C2312yes—
506#384C2312yes—
507#384C2312yes—
508#384C2314yes—
509#382C2312yes—
510#382C2312yes—
511#382C2312yes—
512#382C2312yes—
513#382C2312yes—
514#382C2312yes—
515#382C2314yes—
516#381C2312yes—
517#380C2318yes—
518#380C2312yes—
519#380C2312yes—
520#380C2318yes—
521#379C2314yes—
522#379C2314yes—
523#379C2318yes—
524#379C2312yes—
525C4×C4⋊C4C2312yes—
526C4×C4⋊C4C2312yes—
527C4×C4⋊C4C2314yes—
528C4×C4⋊C4C2318yes—
529C4×C22⋊C4C2314yes—
530C4×C22⋊C4C2312yes—
531C4×C22⋊C4C2314yes—
532C4×C22⋊C4C2312yes—
533C4×C22⋊C4C2312yes—
534C4×C22⋊C4C2312yes—
535C4×C22⋊C4C2312yes—
536C4×C22⋊C4C2312yes—
537C4×C22⋊C4C2312yes—
538C4×C22⋊C4C2312yes—
539#376C2312yes—
540C2×#95C2312yes—
541C2×#95C2314yes—
542C43C2312yes—
543C25C2412yes—
544C25C2411yescharacteristic
545C25C2412yes—
546C25C2414yes—
547C25C2412yes—
548C2×#41—216no—
549C2×#41—42no—
550C2×#41—42no—
551C2×#41—416no—
552C2×#41C2×D418yes—
553C22×Q8C2414yes—
554C22×Q8C2411yescharacteristic
555C22×D4—28no—
556C22×D4—28no—
557C22×D4—28no—
558C22×D4—216no—
559C22×D4—216no—
560C22×D4—24no—
561C22×D4—24no—
562C22×D4—24no—
563C22×D4—28no—
564C22×D4—42no—
565C22×D4—42no—
566C22×D4—42no—
567C22×D4—42no—
568C22×D4—44no—
569C22×D4—42no—
570C22×D4—42no—
571C22×D4—44no—
572C22×D4—48no—
573C22×D4—48no—
574C22×D4—416no—
575C22×D4—84no—
576C22×D4—88no—
577C22×D4C2412yes—
578C22×D4C2414yes—
579C22×D4C2414yes—
580C22×D4C2412yes—
581C22×D4C2412yes—
582C22×D4C2412yes—
583C22×D4C2412yes—
584C22×D4C2414yes—
585C22×D4C2418yes—
586C22×D4C2414yes—
587C22×D4C2414yes—
588C22×D4C2414yes—
589C22×D4C2414yes—
590C22×D4C2414yes—
591C22×D4C2414yes—
592C22×D4C2414yes—
593C22×D4C2414yes—
594C22×D4C2414yes—
595C22×D4C2412yes—
596C22×D4C2412yes—
597C22×D4C2414yes—
598C22×D4C2418yes—
599C22×D4C2418yes—
600C22×D4C2418yes—
601C22×D4C2412yes—
602C22×D4C2411yescharacteristic
603C22×D4C2412yes—
604C23×C4—42no—
605C23×C4—42no—
606C23×C4C2×D418yes—
607C23×C4C2412yes—
608C23×C4C2411yescharacteristic
609C23×C4C2411yescharacteristic
610C23×C4C2412yes—
611C23×C4C2411yescharacteristic
612C23×C4C2412yes—
613C23×C4C2412yes—
614C23×C4C2414yes—
615C23×C4C2414yes—
616C23×C4C2412yes—
617C23×C4C2412yes—
618C23×C4C2412yes—
619C23×C4C2414yes—
620C23×C4C2414yes—
621C23×C4C2414yes—
622C23×C4C2414yes—
623C23×C4C2411yescharacteristic
624C23×C4C2411yescharacteristic
625C23×C4C2411yescharacteristic
626C23×C4C2412yes—
627C4⋊Q8—28no—
628C4⋊Q8—28no—
629#127—28no—
630#127—216no—
631#127—28no—
632#127—44no—
633#127—44no—
634#127—44no—
635#127—44no—
636#126—216no—
637#126—216no—
638#126—216no—
639#126—216no—
640#125—28no—
641#125—28no—
642#125—28no—
643#124—28no—
644#124—216no—
645#124—216no—
646#124—216no—
647#124—416no—
648#123—216no—
649#123—216no—
650#123—216no—
651#123—216no—
652#123—216no—
653#123—216no—
654#123—216no—
655#123—216no—
656#123—416no—
657#123—416no—
658#123—416no—
659#123—416no—
660#123C2×D4116yes—
661C22⋊Q8—216no—
662C22⋊Q8—216no—
663C22⋊Q8—416no—
664C22⋊Q8C2×D418yes—
665C22⋊Q8C2×D418yes—
666#121—216no—
667#121—216no—
668#121—216no—
669#121—216no—
670#121—216no—
671#121—28no—
672#121—28no—
673#121—28no—
674#121—28no—
675#121—28no—
676#121—28no—
677#121—28no—
678#121—28no—
679#121—28no—
680#121—28no—
681#121—28no—
682#121—28no—
683#121—28no—
684#121—28no—
685#121—28no—
686#121—28no—
687#121—232no—
688#121—216no—
689#121—216no—
690#121—216no—
691#121—216no—
692#121—416no—
693#121—416no—
694#121—416no—
695#121—88no—
696#121—88no—
697#121C2×D418yes—
698#121C2×D418yes—
699#120—216no—
700#120—216no—
701#120—216no—
702#120—216no—
703#120—216no—
704#120—216no—
705#120—216no—
706#120—416no—
707#120—416no—
708#120—416no—
709#120—416no—
710#120—88no—
711#120—88no—
712#120C2×D4116yes—
713C4×Q8—28no—
714C4×D4—28no—
715C4×D4—216no—
716C4×D4—216no—
717C4×D4—28no—
718C4×D4—28no—
719C4×D4—216no—
720C4×D4—216no—
721C4×D4—216no—
722C4×D4—216no—
723C4×D4—28no—
724C4×D4—28no—
725C4×D4—28no—
726C4×D4—28no—
727C4×D4—416no—
728C4×D4—88no—
729C4×D4C2×D4116yes—
730C4×D4C2×D4116yes—
731#117—24no—
732#117—24no—
733#117—28no—
734#117—28no—
735#117—24no—
736#117—24no—
737#117—28no—
738#117—28no—
739#117—216no—
740#117—42no—
741#117—44no—
742#117—42no—
743#117C2×D418yes—
744C2×C4⋊C4—24no—
745C2×C4⋊C4—24no—
746C2×C4⋊C4—24no—
747C2×C4⋊C4—28no—
748C2×C4⋊C4—24no—
749C2×C4⋊C4—24no—
750C2×C4⋊C4—84no—
751C2×C4⋊C4C2411yescharacteristic
752C2×C4⋊C4C2412yes—
753C2×C4⋊C4C2411yescharacteristic
754C2×C4⋊C4C2411yescharacteristic
755C2×C4⋊C4C2411yescharacteristic
756C2×C4⋊C4C2412yes—
757C2×C4⋊C4C2412yes—
758C2×C4⋊C4C2412yes—
759C2×C4⋊C4C2412yes—
760C2×C4⋊C4C2412yes—
761C2×C4⋊C4C2414yes—
762C2×C4⋊C4C2412yes—
763C2×C4⋊C4C2412yes—
764C2×C4⋊C4C2414yes—
765C2×C4⋊C4C2414yes—
766C2×C4⋊C4C2414yes—
767C2×C4⋊C4C2414yes—
768C2×C4⋊C4C2414yes—
769C2×C4⋊C4C2414yes—
770C2×C4⋊C4C2418yes—
771C2×C4⋊C4C2418yes—
772C2×C4⋊C4C2418yes—
773C2×C4⋊C4C2412yes—
774C2×C4⋊C4C2412yes—
775C2×C4⋊C4C2414yes—
776C2×C4⋊C4C2418yes—
777C2×C4⋊C4C2414yes—
778C2×C4⋊C4C2418yes—
779C2×C4⋊C4C2418yes—
780C2×C4⋊C4C2412yes—
781C2×C4⋊C4C2411yescharacteristic
782C2×C4⋊C4C2411yescharacteristic
783C2×C4⋊C4C2412yes—
784C2×C22⋊C4—28no—
785C2×C22⋊C4—28no—
786C2×C22⋊C4—28no—
787C2×C22⋊C4—28no—
788C2×C22⋊C4—28no—
789C2×C22⋊C4—216no—
790C2×C22⋊C4—216no—
791C2×C22⋊C4—416no—
792C2×C22⋊C4—84no—
793C2×C22⋊C4C2412yes—
794C2×C22⋊C4C2418yes—
795C2×C22⋊C4C2412yes—
796C2×C22⋊C4C2412yes—
797C2×C22⋊C4C2412yes—
798C2×C22⋊C4C2414yes—
799C2×C22⋊C4C2414yes—
800C2×C22⋊C4C2414yes—
801C2×C22⋊C4C2414yes—
802C2×C22⋊C4C2414yes—
803C2×C22⋊C4C2414yes—
804C2×C22⋊C4C2414yes—
805C2×C22⋊C4C2414yes—
806C2×C22⋊C4C2414yes—
807C2×C22⋊C4C2418yes—
808C2×C22⋊C4C2418yes—
809C2×C22⋊C4C2414yes—
810C2×C22⋊C4C2414yes—
811C2×C22⋊C4C2414yes—
812C2×C22⋊C4C2414yes—
813C2×C22⋊C4C2414yes—
814C2×C22⋊C4C2414yes—
815C2×C22⋊C4C2414yes—
816C2×C22⋊C4C2414yes—
817C2×C22⋊C4C2414yes—
818C2×C22⋊C4C2414yes—
819C2×C22⋊C4C2418yes—
820C2×C22⋊C4C2414yes—
821C2×C22⋊C4C2418yes—
822C2×C22⋊C4C2418yes—
823C2×C22⋊C4C2418yes—
824C2×C22⋊C4C2418yes—
825C2×C22⋊C4C2412yes—
826C2×C22⋊C4C2412yes—
827C2×C22⋊C4C2414yes—
828C2×C22⋊C4C2418yes—
829C2×C22⋊C4C2418yes—
830C2×C22⋊C4C2414yes—
831C2×C22⋊C4C2414yes—
832C2×C22⋊C4C2418yes—
833C2×C22⋊C4C2418yes—
834C2×C22⋊C4C2418yes—
835C2×C22⋊C4C2418yes—
836C2×C22⋊C4C2418yes—
837C2×C22⋊C4C2418yes—
838C2×C22⋊C4C2412yes—
839C2×C22⋊C4C2412yes—
840C2×C22⋊C4C2412yes—
841C2×C22⋊C4C2412yes—
842C2×C22⋊C4C2412yes—
843C2×C42—28no—
844C2×C42—42no—
845C2×C42—44no—
846C2×C42—42no—
847C2×C42C2412yes—
848C2×C42C2412yes—
849C2×C42C2414yes—
850C2×C42C2412yes—
851C2×C42C2412yes—
852C2×C42C2412yes—
853C2×C42C2414yes—
854C2×C42C2412yes—
855C2×C42C2412yes—
856C2×C42C2414yes—
857C2×C42C2412yes—
858C2×C42C2414yes—
859C2×C42C2412yes—
860C2×C42C2412yes—
861C2×C42C2414yes—
862C2×C42C2412yes—
863#95C2414yes—
864#95C2414yes—
865#95C2418yes—
866#95C2418yes—
867#95C2414yes—
868#95C2414yes—
869#95C2414yes—
870#95C2414yes—
871#95C2414yes—
872#95C2414yes—
873#95C2414yes—
874#95C2418yes—
875#95C2418yes—
876#95C2414yes—
877#95C2418yes—
878#95C2418yes—
879C24—24no—
880C24—24no—
881C24—24no—
882C24—24no—
883C24—28no—
884C24—28no—
885C24—41no—
886C24—41no—
887C24—42no—
888C24—42no—
889C24—42no—
890C24—44no—
891C24—44no—
892C24—42no—
893C24—42no—
894C24—44no—
895C24—48no—
896C24—48no—
897C24—44no—
898C24—44no—
899C24—44no—
900C24—42no—
901C24—42no—
902C24—44no—
903C24C22×D414yes—
904C24C2514yes—
905C24C2514yes—
906C24C2514yes—
907C24C2511yescharacteristic
908C24C2511yescharacteristic
909C24C2512yes—
910C24C2511yescharacteristic
911#41—416no—
912#41—832no—
913C2×Q8—28no—
914C2×Q8—41no—
915C2×Q8—41no—
916C2×Q8—48no—
917C2×Q8C22×D414yes—
918C2×D4—28no—
919C2×D4—28no—
920C2×D4—28no—
921C2×D4—28no—
922C2×D4—216no—
923C2×D4—216no—
924C2×D4—28no—
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—24no—
934C2×D4—24no—
935C2×D4—24no—
936C2×D4—24no—
937C2×D4—28no—
938C2×D4—28no—
939C2×D4—28no—
940C2×D4—216no—
941C2×D4—24no—
942C2×D4—24no—
943C2×D4—24no—
944C2×D4—24no—
945C2×D4—24no—
946C2×D4—24no—
947C2×D4—42no—
948C2×D4—42no—
949C2×D4—44no—
950C2×D4—48no—
951C2×D4—42no—
952C2×D4—42no—
953C2×D4—41no—
954C2×D4—41no—
955C2×D4—416no—
956C2×D4—48no—
957C2×D4—48no—
958C2×D4—48no—
959C2×D4—48no—
960C2×D4—48no—
961C2×D4—48no—
962C2×D4—48no—
963C2×D4—48no—
964C2×D4—48no—
965C2×D4—48no—
966C2×D4—48no—
967C2×D4—48no—
968C2×D4—48no—
969C2×D4—48no—
970C2×D4—42no—
971C2×D4—42no—
972C2×D4—44no—
973C2×D4—42no—
974C2×D4—42no—
975C2×D4—44no—
976C2×D4—48no—
977C2×D4—48no—
978C2×D4—48no—
979C2×D4—48no—
980C2×D4—48no—
981C2×D4—48no—
982C2×D4—88no—
983C2×D4—88no—
984C2×D4—816no—
985C2×D4—832no—
986C2×D4—816no—
987C2×D4—816no—
988C2×D4—832no—
989C2×D4—816no—
990C2×D4C22×D418yes—
991C2×D4C22×D418yes—
992C2×D4C22×D414yes—
993C2×D4C22×D418yes—
994C22×C4—22no—
995C22×C4—22no—
996C22×C4—24no—
997C22×C4—22no—
998C22×C4—22no—
999C22×C4—24no—
1000C22×C4—22no—
1001C22×C4—22no—
1002C22×C4—24no—
1003C22×C4—28no—
1004C22×C4—24no—
1005C22×C4—24no—
1006C22×C4—24no—
1007C22×C4—24no—
1008C22×C4—28no—
1009C22×C4—24no—
1010C22×C4—28no—
1011C22×C4—28no—
1012C22×C4—28no—
1013C22×C4—28no—
1014C22×C4—28no—
1015C22×C4—416no—
1016C22×C4—42no—
1017C22×C4—42no—
1018C22×C4—41no—
1019C22×C4—41no—
1020C22×C4—41no—
1021C22×C4—41no—
1022C22×C4—41no—
1023C22×C4—41no—
1024C22×C4—44no—
1025C22×C4—42no—
1026C22×C4—48no—
1027C22×C4—42no—
1028C22×C4—44no—
1029C22×C4—44no—
1030C22×C4—48no—
1031C22×C4—48no—
1032C22×C4—48no—
1033C22×C4—48no—
1034C22×C4—44no—
1035C22×C4—44no—
1036C22×C4—44no—
1037C22×C4C22×D414yes—
1038C22×C4C22×D414yes—
1039C22×C4C22×D414yes—
1040C22×C4C22×D418yes—
1041C22×C4C22×D414yes—
1042C22×C4C22×D414yes—
1043C22×C4C22×D414yes—
1044C22×C4H(5,𝔽2)18yes—
1045C22×C4C2514yes—
1046C22×C4C2514yes—
1047C22×C4C2514yes—
1048C22×C4C2514yes—
1049C22×C4C2512yes—
1050C22×C4C2512yes—
1051C22×C4C2512yes—
1052C22×C4C2512yes—
1053C22×C4C2514yes—
1054C22×C4C2514yes—
1055C22×C4C2511yescharacteristic
1056C22×C4C2512yes—
1057C22×C4C2511yescharacteristic
1058C22×C4C2511yescharacteristic
1059C22×C4C2512yes—
1060C22×C4C2512yes—
1061C22×C4C2514yes—
1062C22×C4C2511yescharacteristic
1063C4⋊C4—22no—
1064C4⋊C4—24no—
1065C4⋊C4—22no—
1066C4⋊C4—22no—
1067C4⋊C4—22no—
1068C4⋊C4—24no—
1069C4⋊C4—24no—
1070C4⋊C4—24no—
1071C4⋊C4—24no—
1072C4⋊C4—24no—
1073C4⋊C4—28no—
1074C4⋊C4—24no—
1075C4⋊C4—24no—
1076C4⋊C4—28no—
1077C4⋊C4—28no—
1078C4⋊C4—28no—
1079C4⋊C4—28no—
1080C4⋊C4—28no—
1081C4⋊C4—28no—
1082C4⋊C4—216no—
1083C4⋊C4—48no—
1084C4⋊C4—48no—
1085C4⋊C4—42no—
1086C4⋊C4—42no—
1087C4⋊C4—44no—
1088C4⋊C4—48no—
1089C4⋊C4—48no—
1090C4⋊C4—48no—
1091C4⋊C4—44no—
1092C4⋊C4C22×D418yes—
1093C4⋊C4C22×D414yes—
1094C4⋊C4C22×D414yes—
1095C4⋊C4C22×D418yes—
1096C22⋊C4—24no—
1097C22⋊C4—24no—
1098C22⋊C4—24no—
1099C22⋊C4—24no—
1100C22⋊C4—28no—
1101C22⋊C4—28no—
1102C22⋊C4—28no—
1103C22⋊C4—28no—
1104C22⋊C4—28no—
1105C22⋊C4—28no—
1106C22⋊C4—28no—
1107C22⋊C4—28no—
1108C22⋊C4—28no—
1109C22⋊C4—28no—
1110C22⋊C4—28no—
1111C22⋊C4—28no—
1112C22⋊C4—28no—
1113C22⋊C4—28no—
1114C22⋊C4—28no—
1115C22⋊C4—28no—
1116C22⋊C4—28no—
1117C22⋊C4—216no—
1118C22⋊C4—28no—
1119C22⋊C4—28no—
1120C22⋊C4—216no—
1121C22⋊C4—216no—
1122C22⋊C4—28no—
1123C22⋊C4—216no—
1124C22⋊C4—48no—
1125C22⋊C4—48no—
1126C22⋊C4—48no—
1127C22⋊C4—48no—
1128C22⋊C4—42no—
1129C22⋊C4—44no—
1130C22⋊C4—42no—
1131C22⋊C4—48no—
1132C22⋊C4—48no—
1133C22⋊C4—48no—
1134C22⋊C4—48no—
1135C22⋊C4—48no—
1136C22⋊C4—48no—
1137C22⋊C4—44no—
1138C22⋊C4—44no—
1139C22⋊C4—48no—
1140C22⋊C4—48no—
1141C22⋊C4C22×D418yes—
1142C22⋊C4C22×D418yes—
1143C22⋊C4C22×D418yes—
1144C22⋊C4C22×D418yes—
1145C22⋊C4C22×D418yes—
1146C42—24no—
1147C42—24no—
1148C42—24no—
1149C42—24no—
1150C42—28no—
1151C42—28no—
1152C42—28no—
1153C42—24no—
1154C42—24no—
1155C42—24no—
1156C42—24no—
1157C42—42no—
1158C42—44no—
1159C42—42no—
1160C42—44no—
1161C42C22×D418yes—
1162C23—21no—
1163C23—21no—
1164C23—22no—
1165C23—22no—
1166C23—22no—
1167C23—24no—
1168C23—21no—
1169C23—21no—
1170C23—22no—
1171C23—22no—
1172C23—21no—
1173C23—21no—
1174C23—22no—
1175C23—24no—
1176C23—22no—
1177C23—28no—
1178C23—24no—
1179C23—24no—
1180C23—24no—
1181C23—28no—
1182C23—28no—
1183C23—28no—
1184C23—24no—
1185C23—24no—
1186C23—24no—
1187C23—24no—
1188C23—24no—
1189C23—24no—
1190C23—28no—
1191C23—28no—
1192C23—28no—
1193C23—44no—
1194C23—44no—
1195C23—48no—
1196C23—48no—
1197C23—48no—
1198C23—84no—
1199C23—84no—
1200C23—84no—
1201C23—84no—
1202C23—84no—
1203C23—88no—
1204C23—88no—
1205C23—84no—
1206C23—84no—
1207C23—88no—
1208C23—88no—
1209C23—88no—
1210C23—84no—
1211C23—816no—
1212C23—168no—
1213C23—164no—
1214C23—164no—
1215C23—164no—
1216C23—164no—
1217C23C23×D412yes—
1218C23C23×D412yes—
1219C23C23×D414yes—
1220C23C23×D412yes—
1221C23C2×H(5,𝔽2)14yes—
1222C23C2611yescharacteristic
1223Q8—44no—
1224Q8—88no—
1225D4—216no—
1226D4—48no—
1227D4—44no—
1228D4—48no—
1229D4—48no—
1230D4—416no—
1231D4—416no—
1232D4—416no—
1233D4—48no—
1234D4—48no—
1235D4—48no—
1236D4—816no—
1237D4—84no—
1238D4—84no—
1239D4—88no—
1240D4—88no—
1241D4—88no—
1242D4—88no—
1243D4—88no—
1244D4—88no—
1245D4—88no—
1246D4—88no—
1247D4—88no—
1248D4—88no—
1249D4—816no—
1250D4—168no—
1251D4—168no—
1252C2×C4—24no—
1253C2×C4—24no—
1254C2×C4—21no—
1255C2×C4—21no—
1256C2×C4—22no—
1257C2×C4—21no—
1258C2×C4—21no—
1259C2×C4—22no—
1260C2×C4—21no—
1261C2×C4—21no—
1262C2×C4—24no—
1263C2×C4—24no—
1264C2×C4—28no—
1265C2×C4—28no—
1266C2×C4—28no—
1267C2×C4—216no—
1268C2×C4—22no—
1269C2×C4—22no—
1270C2×C4—22no—
1271C2×C4—22no—
1272C2×C4—24no—
1273C2×C4—24no—
1274C2×C4—24no—
1275C2×C4—24no—
1276C2×C4—24no—
1277C2×C4—24no—
1278C2×C4—24no—
1279C2×C4—24no—
1280C2×C4—28no—
1281C2×C4—28no—
1282C2×C4—24no—
1283C2×C4—24no—
1284C2×C4—24no—
1285C2×C4—24no—
1286C2×C4—24no—
1287C2×C4—24no—
1288C2×C4—24no—
1289C2×C4—24no—
1290C2×C4—28no—
1291C2×C4—44no—
1292C2×C4—44no—
1293C2×C4—44no—
1294C2×C4—48no—
1295C2×C4—48no—
1296C2×C4—88no—
1297C2×C4—88no—
1298C2×C4—88no—
1299C2×C4—88no—
1300C2×C4—88no—
1301C2×C4—84no—
1302C2×C4—84no—
1303C2×C4—84no—
1304C2×C4—84no—
1305C2×C4—84no—
1306C2×C4—88no—
1307C2×C4C23×D412yes—
1308C2×C4C23×D414yes—
1309C2×C4C23×D412yes—
1310C2×C4C23×D414yes—
1311C2×C4C23×D414yes—
1312C2×C4C23×D412yes—
1313C2×C4C23×D412yes—
1314C2×C4C2×H(5,𝔽2)18yes—
1315C2×C4#58512yes—
1316C2×C4#58512yes—
1317C22—22no—
1318C22—22no—
1319C22—24no—
1320C22—24no—
1321C22—22no—
1322C22—22no—
1323C22—24no—
1324C22—24no—
1325C22—22no—
1326C22—22no—
1327C22—22no—
1328C22—24no—
1329C22—22no—
1330C22—44no—
1331C22—42no—
1332C22—42no—
1333C22—44no—
1334C22—42no—
1335C22—42no—
1336C22—44no—
1337C22—44no—
1338C22—44no—
1339C22—44no—
1340C22—44no—
1341C22—44no—
1342C22—44no—
1343C22—44no—
1344C22—44no—
1345C22—48no—
1346C22—48no—
1347C22—48no—
1348C22—48no—
1349C22—48no—
1350C22—48no—
1351C22—88no—
1352C22—168no—
1353C22—168no—
1354C22—168no—
1355C22—1616no—
1356C22#349814yes—
1357C22C24×D411yescharacteristic
1358C22C22×H(5,𝔽2)12yes—
1359C22C2×#58511yescharacteristic
1360C22C2×#58511yescharacteristic
1361C22H(7,𝔽2)12yes—
1362C4—22no—
1363C4—22no—
1364C4—22no—
1365C4—24no—
1366C4—24no—
1367C4—24no—
1368C4—28no—
1369C4—42no—
1370C4—42no—
1371C4—44no—
1372C4—44no—
1373C4—42no—
1374C4—44no—
1375C4—42no—
1376C4—44no—
1377C4—44no—
1378C4—44no—
1379C4#348514yes—
1380C2—24no—
1381C2—42no—
1382C2—42no—
1383C2—44no—
1384C2—84no—
1385C2—84no—
1386C2—84no—
1387C2C2×#348511yescharacteristic
1388C2C2×#349811yescharacteristic
1389C2#6285211yescharacteristic
1390C2#6290512yes—
1391C2#6293012yes—
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×#3494C2semidirect
2. C2×#3537C2semidirect
3. #48830C2semidirect
4. #47212C2semidirect
5. #46813C2semidirect
6. #43023C2semidirect
7. #39483C2semidirect
8. #38953C2semidirect
9. #38080C2semidirect
10. #38080C2semidirect
11. #37869C2semidirect
12. #37864C2semidirect
13. #37770C2semidirect
14. #37678C2semidirect
15. #37450C2semidirect
16. #37304C2semidirect
17. #37297C2semidirect
18. #36260C2semidirect
19. #36182C2semidirect
20. #35537C2semidirect
21. #35531C2semidirect
22. #35262C2semidirect
23. #35001C2semidirect
24. C2×#2500C2semidirect
25. #34082C2semidirect
29. C2×#555C22semidirect
30. C2×#553C22semidirect
31. C2×#553C22semidirect
32. C2×#553C22semidirect
33. C2×#553C22semidirect
34. C2×#551C22semidirect
35. C2×#547C22semidirect
36. C2×#546C22semidirect
37. C2×#546C22semidirect
39. C2×D42C22semidirect
40. C2×D42C22semidirect
41. C2×#544C22semidirect
42. C2×#542C22semidirect
44. C2×#540C22semidirect
45. C2×#538C22semidirect
46. C2×#538C22semidirect
48. C2×#535C22semidirect
49. C2×#534C22semidirect
50. C2×#534C22semidirect
51. C2×#534C22semidirect
52. C2×#532C22semidirect
53. C2×#529C22semidirect
57. C22×#121C22semidirect
58. C2×#520C22semidirect
59. C2×#518C22semidirect
60. C22×#117C22semidirect
61. #2859C22semidirect
62. #2858C22semidirect
63. #2856C22semidirect
64. #2856C22semidirect
65. #2856C22semidirect
66. #2856C22semidirect
67. #2854C22semidirect
68. #2815C22semidirect
69. #2733C22semidirect
70. #2727C22semidirect
71. #2723C22semidirect
72. #2714C22semidirect
73. #2714C22semidirect
74. #2706C22semidirect
75. #2694C22semidirect
76. #2682C22semidirect
77. #2681C22semidirect
78. #2679C22semidirect
79. #2678C22semidirect
80. #2678C22semidirect
81. #2674C22semidirect
82. #2672C22semidirect
83. #2672C22semidirect
84. #2671C22semidirect
85. #2670C22semidirect
86. #2670C22semidirect
87. #2669C22semidirect
88. #2669C22semidirect
89. #2660C22semidirect
90. #2656C22semidirect
91. #2641C22semidirect
92. #2624C22semidirect
93. #2619C22semidirect
94. #2619C22semidirect
95. #2619C22semidirect
96. #2619C22semidirect
97. #2617C22semidirect
98. #2617C22semidirect
99. #2566C22semidirect
100. #2566C22semidirect
101. #2566C22semidirect
102. #2566C22semidirect
103. #2563C22semidirect
104. #2542C22semidirect
105. #2541C22semidirect
106. #2541C22semidirect
107. #2540C22semidirect
108. #2539C22semidirect
109. #2539C22semidirect
110. #2539C22semidirect
111. #2539C22semidirect
112. #2512C22semidirect
113. #2504C22semidirect
114. #2504C22semidirect
115. #2504C22semidirect
116. #2504C22semidirect
117. #2501C22semidirect
118. #2501C22semidirect
119. #2501C22semidirect
120. #2501C22semidirect
121. #2500C22semidirect
122. #2500C22semidirect
123. #2500C22semidirect
124. #2500C22semidirect
125. #2500C22semidirect
126. #2500C22semidirect
127. #2500C22semidirect
128. #2500C22semidirect
129. #2500C22semidirect
130. #2500C22semidirect
131. #2500C22semidirect
132. #2500C22semidirect
133. #2482C22semidirect
134. #2479C22semidirect
135. #2461C22semidirect
136. #2456C22semidirect
137. #2456C22semidirect
138. #2455C22semidirect
139. #2455C22semidirect
140. #2448C22semidirect
141. #2445C22semidirect
142. #2433C22semidirect
143. #2433C22semidirect
144. #2433C22semidirect
145. #2433C22semidirect
146. #2433C22semidirect
147. #2433C22semidirect
148. #2430C22semidirect
149. #2425C22semidirect
150. #2424C22semidirect
151. #2424C22semidirect
152. #2424C22semidirect
153. #2424C22semidirect
154. #2422C22semidirect
155. #2418C22semidirect
156. #2418C22semidirect
157. #2416C22semidirect
158. #2414C22semidirect
159. #2410C22semidirect
160. #2410C22semidirect
161. #2408C22semidirect
162. #2405C22semidirect
163. #2403C22semidirect
164. C2×#394C22semidirect
165. #2361C22semidirect
166. #2335C22semidirect
167. #2333C22semidirect
168. #2332C22semidirect
169. #2329C22semidirect
170. #2328C22semidirect
171. #2328C22semidirect
172. #2325C22semidirect
173. #2321C22semidirect
174. #2317C22semidirect
175. #2317C22semidirect
176. #2317C22semidirect
177. #2309C22semidirect
178. #2309C22semidirect
179. #2309C22semidirect
180. C4×#127C22semidirect
181. C4×#127C22semidirect
182. #2298C22semidirect
183. #2297C22semidirect
184. #2293C22semidirect
185. C2×#390C22semidirect
186. C2×#390C22semidirect
187. C2×#390C22semidirect
188. #2290C22semidirect
189. #2290C22semidirect
190. C2×#388C22semidirect
191. #2285C22semidirect
192. C2×#384C22semidirect
193. C2×#382C22semidirect
194. #2280C22semidirect
195. C42×D4C22semidirect
196. C2×C4×C22⋊C4C22semidirect
256. #525D4semidirect

Maximal subgroups

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

subgroupindex
C2×#34942
C2×#35372
#488302
#472122
#468132
#430232
#394832
#389532
#380802
#378692
#378642
#377702
#376782
#374502
#373042
#372972
#362602
#361822
#355372
#355312
#352622
#350012
C2×#25002
#340822