Finite Group Databasebeta

← #7680353

Subgroups — #7680353

Order 512.

5930 conjugacy classes of subgroups.

The subgroup lattice has 1257 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59862C214yesmaximal, complemented
2#59647C212yesmaximal, complemented
3#59646C212yesmaximal, complemented
4#59641C212yesmaximal, complemented
5#59640C212yesmaximal, complemented
6#59143C214yesmaximal, complemented
7#45072C214yesmaximal, complemented
8#45043C214yesmaximal, complemented
9#43175C218yesmaximal, complemented
10#39275C214yesmaximal, complemented
11#39270C214yesmaximal, complemented
12#39202C212yesmaximal, complemented
13#39201C212yesmaximal, complemented
14#36469C212yesmaximal, complemented
15#36463C212yesmaximal, complemented
16#35584C212yesmaximal, complemented
17#35540C212yesmaximal, complemented
18#35285C211yesmaximal, characteristic, complemented
19#35262C212yesmaximal, complemented
20#34946C211yesmaximal, characteristic, complemented
21C2×#2541C211yesmaximal, characteristic
22#34213C211yesmaximal, characteristic, complemented
23#34210C211yesmaximal, characteristic, complemented
24#34204C212yesmaximal, complemented
25D4×#117C211yesmaximal, characteristic, complemented
26C4×#544C211yesmaximal, characteristic, complemented
27C2×#559C2214yescomplemented
28C2×#544C2211yescharacteristic
29C2×#533C2211yescharacteristic
30C22×#127C2211yescharacteristic
31C22×#127C2212yes—
32C22×#121C2212yes—
33C22×#121C2212yes—
34C2×#518C2212yes—
35C22×C4×D4C2211yescharacteristic
36C22×#117C2212yes—
37#2858C2212yescomplemented
38#2858C2212yescomplemented
39#2854C2214yescomplemented
40#2854C2214yescomplemented
41#2803C2218yescomplemented
42#2803C2218yescomplemented
43#2797C2218yescomplemented
44#2797C2218yescomplemented
45#2796C2218yescomplemented
46#2752C2218yescomplemented
47#2751C2218yescomplemented
48#2712C2218yescomplemented
49#2710C2218yescomplemented
50#2710C2218yescomplemented
51#2709C2218yescomplemented
52#2709C2218yescomplemented
53#2641C2214yescomplemented
54#2624C2214yescomplemented
55#2624C2214yescomplemented
56#2602C2218yescomplemented
57#2602C2218yescomplemented
58#2600C2218yescomplemented
59#2595C2218yescomplemented
60#2592C2214yescomplemented
61#2580C2214yescomplemented
62#2563C2211yescharacteristic, complemented
63#2563C2211yescharacteristic, complemented
64#2562C2212yescomplemented
65#2562C2212yescomplemented
66#2561C2218yes—
67#2561C2214yes—
68#2557C2218yescomplemented
69#2557C2218yescomplemented
70#2548C2214yescomplemented
71#2548C2214yescomplemented
72#2548C2212yescomplemented
73#2548C2212yescomplemented
74#2548C2212yescomplemented
75#2548C2212yescomplemented
76#2547C2211yescharacteristic, complemented
77#2547C2211yescharacteristic, complemented
78#2544C2214yescomplemented
79#2544C2218yescomplemented
80#2544C2214yescomplemented
81#2541C2214yes—
82#2541C2212yes—
83#2541C2214yes—
84#2541C2212yes—
85#2541C2212yes—
86#2541C2212yes—
87#2516C2218yescomplemented
88#2513C2214yescomplemented
89#2513C2214yescomplemented
90#2504C2214yescomplemented
91#2503C2212yes—
92#2501C2214yescomplemented
93#2500C2214yescomplemented
94#2500C2214yescomplemented
95#2491C2214yescomplemented
96#2491C2214yescomplemented
97#2491C2214yescomplemented
98#2491C2214yescomplemented
99#2490C2214yescomplemented
100#2490C2214yescomplemented
101#2490C2214yescomplemented
102#2490C2214yescomplemented
103#2483C2218yes—
104#2482C2218yes—
105#2459C2218yescomplemented
106#2459C2218yescomplemented
107#2455C2218yescomplemented
108#2448C2214yescomplemented
109#2447C2214yescomplemented
110#2445C2218yescomplemented
111#2445C2214yescomplemented
112#2445C2214yescomplemented
113#2435C2218yes—
114#2435C2212yes—
115#2435C2214yes—
116#2435C2214yes—
117#2422C2214yescomplemented
118#2422C2214yescomplemented
119#2422C2214yescomplemented
120#2422C2214yescomplemented
121#2420C2214yescomplemented
122#2420C2214yescomplemented
123#2420C2214yescomplemented
124#2420C2214yescomplemented
125#2405C2218yes—
126#2405C2218yes—
127#2398C2214yescomplemented
128C2×#392C2214yes—
129#2370C2214yescomplemented
130#2369C2212yescomplemented
131#2367C2214yescomplemented
132#2366C2214yescomplemented
133#2366C2212yescomplemented
134#2366C2212yescomplemented
135#2366C2212yescomplemented
136#2366C2212yescomplemented
137#2365C2212yescomplemented
138#2363C2214yescomplemented
139#2363C2214yescomplemented
140#2361C2214yescomplemented
141#2361C2214yescomplemented
142#2357C2214yescomplemented
143#2355C2214yescomplemented
144#2355C2212yescomplemented
145#2354C2211yescharacteristic, complemented
146#2354C2211yescharacteristic, complemented
147#2352C2212yescomplemented
148#2352C2212yescomplemented
149Q8×C4⋊C4C2212yescomplemented
150D4×C4⋊C4C2211yescharacteristic, complemented
151D4×C4⋊C4C2211yescharacteristic, complemented
152#2344C2212yes—
153#2342C2214yes—
154#2342C2218yes—
155D4×C22⋊C4C2212yes—
156D4×C22⋊C4C2218yes—
157D4×C22⋊C4C2214yes—
158D4×C22⋊C4C2214yes—
159#2331C2212yescomplemented
160#2331C2212yescomplemented
161#2330C2212yescomplemented
162#2330C2212yescomplemented
163#2329C2214yes—
164#2329C2214yes—
165#2328C2214yescomplemented
166#2324C2214yescomplemented
167#2324C2214yescomplemented
168#2317C2211yescharacteristic
169#2317C2211yescharacteristic
170#2317C2212yes—
171#2316C2211yescharacteristic
172#2309C2212yes—
173#2309C2212yes—
174#2309C2212yes—
175C4×C4⋊Q8C2212yescomplemented
176C4×C4⋊Q8C2212yescomplemented
177C4×#127C2212yescomplemented
178C4×#127C2212yescomplemented
179C4×#125C2212yescomplemented
180C4×#125C2212yescomplemented
181C4×#124C2212yescomplemented
182C4×#124C2212yescomplemented
183C4×C22⋊Q8C2214yes—
184C4×C22⋊Q8C2214yes—
185C4×#121C2214yescomplemented
186C4×#121C2214yescomplemented
187#2293C2212yescomplemented
188C2×#390C2212yes—
189#2290C2214yescomplemented
190#2285C2211yescharacteristic
191#2280C2212yes—
192#2280C2212yes—
193#2280C2212yes—
194#2274C2212yes—
195C42×D4C2212yescomplemented
196C4×#117C2211yescharacteristic
197C4×#117C2211yescharacteristic
198C2×C4×C4⋊C4C2211yescharacteristic
199C23×D4C2312yes—
200C23×D4C2311yescharacteristic
201C23×D4C2312yes—
202C23×D4C2314yes—
203C23×D4C2312yes—
204C23×D4C2314yes—
205C24×C4C2312yes—
206#559—416no—
207#544—28no—
208#533—28no—
209C2×C4⋊Q8C2312yes—
210C2×C4⋊Q8C2312yes—
211C2×C4⋊Q8C2311yescharacteristic
212C2×C4⋊Q8C2311yescharacteristic
213C2×#127—28no—
214C2×#127—48no—
215C2×#127C2312yes—
216C2×#127C2312yes—
217C2×#127C2312yes—
218C2×#127C2312yes—
219C2×#127C2314yes—
220C2×#127C2318yes—
221C2×#127C2314yes—
222C2×#125C2312yes—
223C2×#125C2312yes—
224C2×#125C2312yes—
225C2×#124C2312yes—
226C2×#124C2314yes—
227C2×#124C2314yes—
228C2×#124C2318yes—
229C2×#124C2312yes—
230C2×#124C2314yes—
231C2×#124C2314yes—
232C2×#124C2318yes—
233C2×#123C2318yes—
234C2×#123C2318yes—
235C2×#123C2318yes—
236C2×#123C2318yes—
237C2×C22⋊Q8C2312yes—
238C2×C22⋊Q8C2314yes—
239C2×C22⋊Q8C2312yes—
240C2×#121—216no—
241C2×#121—48no—
242C2×#121C2314yes—
243C2×#121C2314yes—
244C2×#121C2314yes—
245C2×#121C2314yes—
246C2×#121C2314yes—
247C2×#121C2314yes—
248C2×#121C2314yes—
249C2×#121C2314yes—
250#518—48no—
251C2×C4×Q8C2312yes—
252C2×C4×Q8C2312yes—
253C2×C4×Q8C2314yes—
254C2×C4×Q8C2314yes—
255C2×C4×D4—28no—
256C2×C4×D4C2312yes—
257C2×C4×D4C2311yescharacteristic
258C2×C4×D4C2311yescharacteristic
259C2×C4×D4C2312yes—
260C2×C4×D4C2311yescharacteristic
261C2×C4×D4C2312yes—
262C2×C4×D4C2311yescharacteristic
263C2×C4×D4C2314yes—
264C2×C4×D4C2314yes—
265C2×C4×D4C2314yes—
266C2×C4×D4C2314yes—
267C2×C4×D4C2314yes—
268C2×C4×D4C2314yes—
269C2×C4×D4C2318yes—
270C2×C4×D4C2312yes—
271C2×C4×D4C2314yes—
272C2×C4×D4C2314yes—
273C2×C4×D4C2318yes—
274C2×#117—48no—
275C2×#117C2311yescharacteristic
276C2×#117C2312yes—
277C2×#117C2311yescharacteristic
278C2×#117C2311yescharacteristic
279C2×#117C2312yes—
280C2×#117C2311yescharacteristic
281C2×#117C2314yes—
282C2×#117C2314yes—
283C2×#117C2312yes—
284C2×#117C2312yes—
285C22×C4⋊C4C2311yescharacteristic
286C22×C4⋊C4C2311yescharacteristic
287C22×C4⋊C4C2312yes—
288C22×C4⋊C4C2312yes—
289C22×C4⋊C4C2311yescharacteristic
290C22×C22⋊C4C2312yes—
291C22×C22⋊C4C2314yes—
292C22×C22⋊C4C2314yes—
293C22×C22⋊C4C2318yes—
294C22×C22⋊C4C2314yes—
295C22×C42C2314yes—
296C22×C42C2312yes—
297C22×C42C2311yescharacteristic
298#400C2314yes—
299#400C2314yes—
300#399C2318yes—
301#399C2318yes—
302#397C2314yes—
303#397C2318yes—
304#397C2314yes—
305#397C2318yes—
306#397C2318yes—
307#397C2318yes—
308#397C2318yes—
309#397C2318yes—
310#397C2318yes—
311#397C2318yes—
312#394C2314yes—
313#394C2314yes—
314#394C2318yes—
315#394C2318yes—
316#394C2318yes—
317#394C2318yes—
318#394C2318yes—
319#394C2318yes—
320#394C2318yes—
321#394C2318yes—
322#394C2318yes—
323#394C2318yes—
324#394C2318yes—
325#394C2318yes—
326#394C2318yes—
327#394C2318yes—
328#394C2318yes—
329#394C2318yes—
330#393C2314yes—
331#393C2314yes—
332#393C2318yes—
333#393C2318yes—
334#392C2318yes—
335#392C2318yes—
336#392C2318yes—
337#392C2318yes—
338#391C2314yes—
339#391C2314yes—
340#391C2318yes—
341#391C2314yes—
342#391C2312yes—
343#391C2314yes—
344#391C2312yes—
345#390C2314yes—
346#390C2314yes—
347#390C2314yes—
348#390C2314yes—
349#390C2314yes—
350#390C2314yes—
351#390C2312yes—
352#390C2312yes—
353#390C2314yes—
354#390C2314yes—
355#390C2314yes—
356#390C2314yes—
357#390C2314yes—
358#390C2314yes—
359#390C2314yes—
360#390C2314yes—
361#390C2314yes—
362#390C2314yes—
363#390C2318yes—
364#390C2318yes—
365#390C2314yes—
366#390C2314yes—
367#390C2314yes—
368#390C2312yes—
369#390C2312yes—
370#390C2318yes—
371#390C2314yes—
372#390C2318yes—
373#390C2314yes—
374#390C2314yes—
375#390C2318yes—
376#389C2312yes—
377#389C2312yes—
378#389C2312yes—
379#389C2312yes—
380#389C2312yes—
381#389C2312yes—
382#389C2312yes—
383#389C2312yes—
384#389C2314yes—
385#389C2314yes—
386#389C2314yes—
387#389C2314yes—
388#389C2312yes—
389#389C2314yes—
390#389C2318yes—
391#389C2314yes—
392#389C2312yes—
393#388C2314yes—
394#388C2314yes—
395#388C2314yes—
396#388C2314yes—
397#388C2318yes—
398#388C2318yes—
399#388C2318yes—
400#388C2318yes—
401#388C2318yes—
402#388C2318yes—
403#388C2318yes—
404#388C2318yes—
405#388C2318yes—
406#388C2314yes—
407#388C2314yes—
408#388C2314yes—
409#388C2314yes—
410#388C2318yes—
411#388C2318yes—
412#388C2318yes—
413#387C2314yes—
414#387C2314yes—
415#387C2314yes—
416#387C2314yes—
417#387C2318yes—
418#387C2318yes—
419#387C2314yes—
420#387C2314yes—
421#387C2314yes—
422#387C2314yes—
423#387C2318yes—
424#386C2318yes—
425#386C2318yes—
426#386C2318yes—
427#386C2318yes—
428#386C2318yes—
429#386C2318yes—
430#386C2314yes—
431#386C2314yes—
432#386C2318yes—
433#386C2318yes—
434#386C2318yes—
435#386C2318yes—
436#386C2318yes—
437#386C2318yes—
438#385C2314yes—
439#385C2318yes—
440#385C2314yes—
441#385C2318yes—
442#385C2318yes—
443#385C2318yes—
444#385C2314yes—
445#385C2314yes—
446#385C2318yes—
447#384C2311yescharacteristic
448#384C2311yescharacteristic
449#384C2312yes—
450#384C2312yes—
451#384C2314yes—
452#382C2312yes—
453#382C2312yes—
454#382C2312yes—
455#382C2312yes—
456#382C2314yes—
457#382C2312yes—
458#381C2314yes—
459#381C2314yes—
460#381C2314yes—
461#381C2318yes—
462#381C2318yes—
463#380C2312yes—
464#380C2312yes—
465#380C2312yes—
466#380C2312yes—
467#380C2312yes—
468#380C2312yes—
469#380C2312yes—
470#380C2312yes—
471#380C2314yes—
472#380C2312yes—
473#380C2312yes—
474#380C2312yes—
475#380C2312yes—
476#380C2312yes—
477#380C2312yes—
478#379C2318yes—
479#379C2318yes—
480#379C2314yes—
481#379C2314yes—
482#379C2318yes—
483#379C2314yes—
484C4×C4⋊C4C2311yescharacteristic
485C4×C4⋊C4C2311yescharacteristic
486C4×C4⋊C4C2314yes—
487C4×C4⋊C4C2312yes—
488C4×C4⋊C4C2314yes—
489C4×C4⋊C4C2312yes—
490C4×C4⋊C4C2314yes—
491C4×C4⋊C4C2311yescharacteristic
492C4×C4⋊C4C2311yescharacteristic
493C4×C4⋊C4C2311yescharacteristic
494C4×C4⋊C4C2311yescharacteristic
495C4×C4⋊C4C2314yes—
496C4×C4⋊C4C2314yes—
497C4×C4⋊C4C2311yescharacteristic
498C4×C4⋊C4C2312yes—
499C4×C4⋊C4C2312yes—
500C4×C4⋊C4C2311yescharacteristic
501C4×C4⋊C4C2312yes—
502C4×C4⋊C4C2318yes—
503C4×C4⋊C4C2312yes—
504C4×C4⋊C4C2314yes—
505C4×C4⋊C4C2314yes—
506C4×C4⋊C4C2314yes—
507C4×C4⋊C4C2312yes—
508C4×C4⋊C4C2312yes—
509C4×C22⋊C4C2312yes—
510C4×C22⋊C4C2318yes—
511C4×C22⋊C4C2312yes—
512C4×C22⋊C4C2312yes—
513C4×C22⋊C4C2312yes—
514C4×C22⋊C4C2318yes—
515C4×C22⋊C4C2314yes—
516C4×C22⋊C4C2314yes—
517C4×C22⋊C4C2318yes—
518C4×C22⋊C4C2314yes—
519C4×C22⋊C4C2314yes—
520C4×C22⋊C4C2314yes—
521C4×C22⋊C4C2314yes—
522C4×C22⋊C4C2314yes—
523C4×C22⋊C4C2314yes—
524#376C2312yes—
525#376C2312yes—
526C2×#95C2312yes—
527C43C2312yes—
528C43C2312yes—
529C25C2412yes—
530C25C2414yes—
531C22×Q8C2412yes—
532C22×Q8C2414yes—
533C22×Q8C2412yes—
534C22×D4—24no—
535C22×D4—24no—
536C22×D4—28no—
537C22×D4—28no—
538C22×D4—216no—
539C22×D4—28no—
540C22×D4—28no—
541C22×D4—28no—
542C22×D4—42no—
543C22×D4—44no—
544C22×D4—44no—
545C22×D4—48no—
546C22×D4—48no—
547C22×D4—48no—
548C22×D4—84no—
549C22×D4—82no—
550C22×D4—82no—
551C22×D4—84no—
552C22×D4C2414yes—
553C22×D4C2414yes—
554C22×D4C2411yescharacteristic
555C22×D4C2414yes—
556C22×D4C2418yes—
557C22×D4C2412yes—
558C22×D4C2411yescharacteristic
559C22×D4C2414yes—
560C22×D4C2418yes—
561C22×D4C2418yes—
562C22×D4C2414yes—
563C22×D4C2414yes—
564C22×D4C2418yes—
565C23×C4—28no—
566C23×C4—28no—
567C23×C4—28no—
568C23×C4C2412yes—
569C23×C4C2412yes—
570C23×C4C2412yes—
571C23×C4C2412yes—
572C23×C4C2412yes—
573C23×C4C2411yescharacteristic
574C23×C4C2412yes—
575C23×C4C2414yes—
576C23×C4C2414yes—
577C23×C4C2418yes—
578C23×C4C2418yes—
579C23×C4C2412yes—
580C23×C4C2411yescharacteristic
581C23×C4C2411yescharacteristic
582C4⋊Q8—28no—
583C4⋊Q8—28no—
584C4⋊Q8—24no—
585C4⋊Q8—24no—
586#127—216no—
587#127—28no—
588#127—28no—
589#127—28no—
590#127—28no—
591#127—48no—
592#127—416no—
593#125—28no—
594#125—28no—
595#125—28no—
596#124—28no—
597#124—44no—
598#124—48no—
599#124—48no—
600#124—416no—
601#124—88no—
602#124—84no—
603#124—84no—
604#123—416no—
605#123—416no—
606#123—88no—
607#123—88no—
608C22⋊Q8—28no—
609C22⋊Q8—28no—
610C22⋊Q8—216no—
611#121—216no—
612#121—216no—
613#121—216no—
614#121—216no—
615#121—48no—
616#121—48no—
617#121—48no—
618#121—48no—
619C4×Q8—28no—
620C4×Q8—28no—
621C4×Q8—48no—
622C4×Q8—48no—
623C4×D4—28no—
624C4×D4—24no—
625C4×D4—28no—
626C4×D4—24no—
627C4×D4—28no—
628C4×D4—24no—
629C4×D4—24no—
630C4×D4—48no—
631C4×D4—44no—
632C4×D4—48no—
633C4×D4—48no—
634C4×D4—48no—
635C4×D4—48no—
636C4×D4—48no—
637C4×D4—416no—
638C4×D4—84no—
639C4×D4—84no—
640C4×D4—88no—
641#117—28no—
642#117—24no—
643#117—24no—
644#117—24no—
645#117—28no—
646#117—24no—
647#117—48no—
648#117—48no—
649#117—44no—
650#117—44no—
651C2×C4⋊C4—24no—
652C2×C4⋊C4—24no—
653C2×C4⋊C4—44no—
654C2×C4⋊C4—44no—
655C2×C4⋊C4#4118yes—
656C2×C4⋊C4C2411yescharacteristic
657C2×C4⋊C4C2411yescharacteristic
658C2×C4⋊C4C2412yes—
659C2×C4⋊C4C2412yes—
660C2×C4⋊C4C2411yescharacteristic
661C2×C4⋊C4C2411yescharacteristic
662C2×C4⋊C4C2412yes—
663C2×C4⋊C4C2412yes—
664C2×C4⋊C4C2412yes—
665C2×C4⋊C4C2411yescharacteristic
666C2×C4⋊C4C2411yescharacteristic
667C2×C4⋊C4C2411yescharacteristic
668C2×C4⋊C4C2411yescharacteristic
669C2×C4⋊C4C2412yes—
670C2×C4⋊C4C2412yes—
671C2×C4⋊C4C2411yescharacteristic
672C2×C4⋊C4C2411yescharacteristic
673C2×C4⋊C4C2412yes—
674C2×C4⋊C4C2412yes—
675C2×C4⋊C4C2414yes—
676C2×C4⋊C4C2414yes—
677C2×C4⋊C4C2412yes—
678C2×C4⋊C4C2412yes—
679C2×C4⋊C4C2414yes—
680C2×C4⋊C4C2414yes—
681C2×C4⋊C4C2414yes—
682C2×C4⋊C4C2414yes—
683C2×C4⋊C4C2414yes—
684C2×C4⋊C4C2414yes—
685C2×C4⋊C4C2412yes—
686C2×C4⋊C4C2412yes—
687C2×C4⋊C4C2414yes—
688C2×C4⋊C4C2414yes—
689C2×C4⋊C4C2418yes—
690C2×C4⋊C4C2414yes—
691C2×C4⋊C4C2414yes—
692C2×C4⋊C4C2418yes—
693C2×C4⋊C4C2414yes—
694C2×C4⋊C4C2412yes—
695C2×C4⋊C4C2412yes—
696C2×C22⋊C4—28no—
697C2×C22⋊C4—216no—
698C2×C22⋊C4—48no—
699C2×C22⋊C4—416no—
700C2×C22⋊C4—48no—
701C2×C22⋊C4C2412yes—
702C2×C22⋊C4C2414yes—
703C2×C22⋊C4C2412yes—
704C2×C22⋊C4C2412yes—
705C2×C22⋊C4C2412yes—
706C2×C22⋊C4C2412yes—
707C2×C22⋊C4C2412yes—
708C2×C22⋊C4C2418yes—
709C2×C22⋊C4C2418yes—
710C2×C22⋊C4C2412yes—
711C2×C22⋊C4C2412yes—
712C2×C22⋊C4C2414yes—
713C2×C22⋊C4C2414yes—
714C2×C22⋊C4C2414yes—
715C2×C22⋊C4C2414yes—
716C2×C22⋊C4C2414yes—
717C2×C22⋊C4C2414yes—
718C2×C22⋊C4C2418yes—
719C2×C22⋊C4C2418yes—
720C2×C22⋊C4C2418yes—
721C2×C22⋊C4C2418yes—
722C2×C22⋊C4C2414yes—
723C2×C22⋊C4C2418yes—
724C2×C22⋊C4C2418yes—
725C2×C22⋊C4C2418yes—
726C2×C22⋊C4C2418yes—
727C2×C22⋊C4C2418yes—
728C2×C22⋊C4C2414yes—
729C2×C22⋊C4C2418yes—
730C2×C22⋊C4C2414yes—
731C2×C22⋊C4C2414yes—
732C2×C22⋊C4C2414yes—
733C2×C22⋊C4C2418yes—
734C2×C22⋊C4C2418yes—
735C2×C22⋊C4C2418yes—
736C2×C22⋊C4C2414yes—
737C2×C22⋊C4C2414yes—
738C2×C22⋊C4C2418yes—
739C2×C22⋊C4C2414yes—
740C2×C22⋊C4C2414yes—
741C2×C22⋊C4C2418yes—
742C2×C22⋊C4C2418yes—
743C2×C42—48no—
744C2×C42—44no—
745C2×C42#4118yes—
746C2×C42C2412yes—
747C2×C42C2414yes—
748C2×C42C2412yes—
749C2×C42C2414yes—
750C2×C42C2412yes—
751C2×C42C2412yes—
752C2×C42C2412yes—
753C2×C42C2412yes—
754C2×C42C2412yes—
755C2×C42C2412yes—
756C2×C42C2414yes—
757C2×C42C2414yes—
758C2×C42C2414yes—
759C2×C42C2412yes—
760C2×C42C2412yes—
761C2×C42C2418yes—
762C2×C42C2418yes—
763C2×C42C2412yes—
764C2×C42C2412yes—
765C2×C42C2414yes—
766C2×C42C2411yescharacteristic
767C2×C42C2411yescharacteristic
768C2×C42C2411yescharacteristic
769C2×C42C2411yescharacteristic
770#95C2414yes—
771#95C2414yes—
772#95C2412yes—
773#95C2412yes—
774#95C2412yes—
775#95C2412yes—
776#95C2412yes—
777#95C2412yes—
778#95C2412yes—
779#95C2412yes—
780#95C2414yes—
781#95C2414yes—
782#95C2414yes—
783#95C2414yes—
784#95C2414yes—
785#95C2414yes—
786#95C2414yes—
787#95C2418yes—
788#95C2418yes—
789#95C2414yes—
790#95C2414yes—
791#95C2414yes—
792#95C2414yes—
793#95C2414yes—
794#95C2414yes—
795#95C2414yes—
796#95C2414yes—
797#95C2414yes—
798#95C2414yes—
799#95C2414yes—
800#95C2418yes—
801#95C2418yes—
802#95C2414yes—
803#95C2414yes—
804C24—24no—
805C24—24no—
806C24—24no—
807C24—24no—
808C24—28no—
809C24—28no—
810C24—28no—
811C24—42no—
812C24—42no—
813C24—42no—
814C24—44no—
815C24—44no—
816C24—44no—
817C24—44no—
818C24C2512yes—
819C24C2518yes—
820C24C2512yes—
821C24C2511yescharacteristic
822C2×Q8—24no—
823C2×Q8—24no—
824C2×Q8—28no—
825C2×Q8—24no—
826C2×Q8—24no—
827C2×Q8—44no—
828C2×Q8—44no—
829C2×Q8—42no—
830C2×Q8—42no—
831C2×D4—216no—
832C2×D4—24no—
833C2×D4—216no—
834C2×D4—22no—
835C2×D4—24no—
836C2×D4—22no—
837C2×D4—216no—
838C2×D4—28no—
839C2×D4—28no—
840C2×D4—28no—
841C2×D4—28no—
842C2×D4—28no—
843C2×D4—28no—
844C2×D4—216no—
845C2×D4—28no—
846C2×D4—28no—
847C2×D4—28no—
848C2×D4—28no—
849C2×D4—28no—
850C2×D4—22no—
851C2×D4—22no—
852C2×D4—28no—
853C2×D4—22no—
854C2×D4—416no—
855C2×D4—44no—
856C2×D4—44no—
857C2×D4—48no—
858C2×D4—42no—
859C2×D4—48no—
860C2×D4—48no—
861C2×D4—48no—
862C2×D4—48no—
863C2×D4—48no—
864C2×D4—44no—
865C2×D4—44no—
866C2×D4—48no—
867C2×D4—44no—
868C2×D4—48no—
869C2×D4—44no—
870C2×D4—432no—
871C2×D4—816no—
872C2×D4—832no—
873C2×D4—816no—
874C2×D4—832no—
875C2×D4H(5,𝔽2)14yes—
876C22×C4—22no—
877C22×C4—22no—
878C22×C4—24no—
879C22×C4—24no—
880C22×C4—24no—
881C22×C4—24no—
882C22×C4—28no—
883C22×C4—24no—
884C22×C4—24no—
885C22×C4—24no—
886C22×C4—24no—
887C22×C4—24no—
888C22×C4—24no—
889C22×C4—24no—
890C22×C4—24no—
891C22×C4—24no—
892C22×C4—24no—
893C22×C4—24no—
894C22×C4—24no—
895C22×C4—42no—
896C22×C4—42no—
897C22×C4—41no—
898C22×C4—41no—
899C22×C4—42no—
900C22×C4—42no—
901C22×C4—44no—
902C22×C4—44no—
903C22×C4—44no—
904C22×C4—44no—
905C22×C4—44no—
906C22×C4—48no—
907C22×C4—48no—
908C22×C4—48no—
909C22×C4—48no—
910C22×C4—48no—
911C22×C4—48no—
912C22×C4—432no—
913C22×C4C2×#4114yes—
914C22×C4C2×#4114yes—
915C22×C4C2×#4118yes—
916C22×C4C2×#4114yes—
917C22×C4C2×#4114yes—
918C22×C4H(5,𝔽2)14yes—
919C22×C4C2512yes—
920C22×C4C2512yes—
921C22×C4C2512yes—
922C22×C4C2514yes—
923C22×C4C2514yes—
924C22×C4C2512yes—
925C22×C4C2512yes—
926C22×C4C2512yes—
927C22×C4C2514yes—
928C22×C4C2514yes—
929C22×C4C2512yes—
930C22×C4C2512yes—
931C22×C4C2512yes—
932C22×C4C2514yes—
933C22×C4C2512yes—
934C22×C4C2511yescharacteristic
935C22×C4C2511yescharacteristic
936C22×C4C2511yescharacteristic
937C22×C4C2514yes—
938C22×C4C2511yescharacteristic
939C22×C4C2511yescharacteristic
940C22×C4C2511yescharacteristic
941C4⋊C4—24no—
942C4⋊C4—22no—
943C4⋊C4—22no—
944C4⋊C4—22no—
945C4⋊C4—22no—
946C4⋊C4—24no—
947C4⋊C4—24no—
948C4⋊C4—22no—
949C4⋊C4—22no—
950C4⋊C4—28no—
951C4⋊C4—28no—
952C4⋊C4—24no—
953C4⋊C4—24no—
954C4⋊C4—28no—
955C4⋊C4—28no—
956C4⋊C4—28no—
957C4⋊C4—24no—
958C4⋊C4—24no—
959C4⋊C4—22no—
960C4⋊C4—22no—
961C4⋊C4—24no—
962C4⋊C4—24no—
963C4⋊C4—22no—
964C4⋊C4—22no—
965C4⋊C4—24no—
966C4⋊C4—24no—
967C4⋊C4—44no—
968C4⋊C4—44no—
969C4⋊C4—44no—
970C4⋊C4—42no—
971C4⋊C4—42no—
972C4⋊C4—44no—
973C4⋊C4—44no—
974C4⋊C4—44no—
975C4⋊C4—48no—
976C4⋊C4—44no—
977C4⋊C4—44no—
978C4⋊C4—48no—
979C4⋊C4C2×#4118yes—
980C4⋊C4C2×#4118yes—
981C22⋊C4—24no—
982C22⋊C4—24no—
983C22⋊C4—28no—
984C22⋊C4—24no—
985C22⋊C4—28no—
986C22⋊C4—24no—
987C22⋊C4—28no—
988C22⋊C4—28no—
989C22⋊C4—28no—
990C22⋊C4—24no—
991C22⋊C4—24no—
992C22⋊C4—24no—
993C22⋊C4—24no—
994C22⋊C4—216no—
995C22⋊C4—216no—
996C22⋊C4—44no—
997C22⋊C4—44no—
998C22⋊C4—48no—
999C22⋊C4—48no—
1000C22⋊C4—48no—
1001C22⋊C4—48no—
1002C22⋊C4—44no—
1003C22⋊C4—48no—
1004C22⋊C4—48no—
1005C22⋊C4—48no—
1006C22⋊C4—44no—
1007C22⋊C4—48no—
1008C22⋊C4—48no—
1009C22⋊C4—48no—
1010C22⋊C4—48no—
1011C22⋊C4—44no—
1012C22⋊C4—44no—
1013C22⋊C4—44no—
1014C22⋊C4—48no—
1015C22⋊C4—48no—
1016C22⋊C4—44no—
1017C22⋊C4—48no—
1018C22⋊C4—48no—
1019C22⋊C4—44no—
1020C22⋊C4—44no—
1021C22⋊C4—48no—
1022C22⋊C4—44no—
1023C42—28no—
1024C42—24no—
1025C42—24no—
1026C42—24no—
1027C42—28no—
1028C42—28no—
1029C42—24no—
1030C42—24no—
1031C42—24no—
1032C42—24no—
1033C42—24no—
1034C42—44no—
1035C42—44no—
1036C42—44no—
1037C42—48no—
1038C42—42no—
1039C42—42no—
1040C42—48no—
1041C42—42no—
1042C42—42no—
1043C42C2×#4114yes—
1044C42C2×#4114yes—
1045C42C2×#4114yes—
1046C42C2×#4114yes—
1047C23—21no—
1048C23—21no—
1049C23—21no—
1050C23—21no—
1051C23—22no—
1052C23—22no—
1053C23—22no—
1054C23—22no—
1055C23—22no—
1056C23—22no—
1057C23—22no—
1058C23—28no—
1059C23—22no—
1060C23—28no—
1061C23—22no—
1062C23—28no—
1063C23—28no—
1064C23—22no—
1065C23—22no—
1066C23—28no—
1067C23—22no—
1068C23—22no—
1069C23—28no—
1070C23—28no—
1071C23—48no—
1072C23—48no—
1073C23—48no—
1074C23—48no—
1075C23—416no—
1076C23—84no—
1077C23—84no—
1078C23—84no—
1079C23—88no—
1080C23—88no—
1081C23—88no—
1082C23—88no—
1083C23—88no—
1084C23—88no—
1085C23C22×#4112yes—
1086C23C22×#4112yes—
1087C23C2×H(5,𝔽2)14yes—
1088C23C2×H(5,𝔽2)12yes—
1089C23C2611yescharacteristic
1090Q8—48no—
1091Q8—88no—
1092Q8—84no—
1093D4—28no—
1094D4—48no—
1095D4—432no—
1096D4—416no—
1097D4—416no—
1098D4—416no—
1099D4—44no—
1100D4—416no—
1101D4—816no—
1102D4—88no—
1103D4—88no—
1104D4—816no—
1105D4—816no—
1106C2×C4—24no—
1107C2×C4—21no—
1108C2×C4—21no—
1109C2×C4—21no—
1110C2×C4—21no—
1111C2×C4—24no—
1112C2×C4—21no—
1113C2×C4—21no—
1114C2×C4—28no—
1115C2×C4—22no—
1116C2×C4—22no—
1117C2×C4—24no—
1118C2×C4—24no—
1119C2×C4—22no—
1120C2×C4—22no—
1121C2×C4—22no—
1122C2×C4—22no—
1123C2×C4—22no—
1124C2×C4—22no—
1125C2×C4—22no—
1126C2×C4—22no—
1127C2×C4—24no—
1128C2×C4—24no—
1129C2×C4—24no—
1130C2×C4—22no—
1131C2×C4—22no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—24no—
1138C2×C4—24no—
1139C2×C4—24no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—22no—
1145C2×C4—24no—
1146C2×C4—24no—
1147C2×C4—24no—
1148C2×C4—24no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—22no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—22no—
1155C2×C4—22no—
1156C2×C4—22no—
1157C2×C4—24no—
1158C2×C4—24no—
1159C2×C4—24no—
1160C2×C4—48no—
1161C2×C4—44no—
1162C2×C4—48no—
1163C2×C4—48no—
1164C2×C4—48no—
1165C2×C4—48no—
1166C2×C4—48no—
1167C2×C4—48no—
1168C2×C4—88no—
1169C2×C4—88no—
1170C2×C4—168no—
1171C2×C4—168no—
1172C2×C4#559116yescomplemented
1173C2×C4C22×#4112yes—
1174C2×C4C22×#4112yes—
1175C2×C4C22×#4112yes—
1176C2×C4C22×#4118yes—
1177C2×C4C22×#4112yes—
1178C2×C4C22×#4112yes—
1179C2×C4C22×#4112yes—
1180C2×C4C22×#4112yes—
1181C2×C4C22×#4112yes—
1182C2×C4C2×H(5,𝔽2)12yes—
1183C2×C4C2×H(5,𝔽2)12yes—
1184C2×C4C2×H(5,𝔽2)12yes—
1185C2×C4#58512yes—
1186C22—22no—
1187C22—22no—
1188C22—22no—
1189C22—22no—
1190C22—22no—
1191C22—22no—
1192C22—24no—
1193C22—24no—
1194C22—24no—
1195C22—42no—
1196C22—42no—
1197C22—42no—
1198C22—42no—
1199C22—48no—
1200C22—42no—
1201C22—42no—
1202C22—48no—
1203C22—42no—
1204C22—48no—
1205C22—48no—
1206C22—42no—
1207C22—48no—
1208C22—42no—
1209C22—48no—
1210C22—42no—
1211C22—42no—
1212C22—48no—
1213C22—816no—
1214C22—1616no—
1215C22C2×#55914yes—
1216C22C23×#4111yescharacteristic
1217C22C23×#4111yescharacteristic
1218C22C22×H(5,𝔽2)11yescharacteristic
1219C22C22×H(5,𝔽2)11yescharacteristic
1220C22C2×#58511yescharacteristic
1221C22H(7,𝔽2)11yescharacteristic
1222C22H(7,𝔽2)11yescharacteristic
1223C4—28no—
1224C4—22no—
1225C4—22no—
1226C4—22no—
1227C4—42no—
1228C4—42no—
1229C4—42no—
1230C4—42no—
1231C4—44no—
1232C4—44no—
1233C4—44no—
1234C4—42no—
1235C4—44no—
1236C4—42no—
1237C4—42no—
1238C4—44no—
1239C4—42no—
1240C4—42no—
1241C4—42no—
1242C4C2×#55914yes—
1243C4C2×#55914yes—
1244C4#349414yes—
1245C2—24no—
1246C2—44no—
1247C2—82no—
1248C2—88no—
1249C2C22×#55911yescharacteristic
1250C2C2×#349411yescharacteristic
1251C2#6285511yescharacteristic
1252C2#6291211yescharacteristic
1253C2#6295511yescharacteristic
1254C2#6298311yescharacteristic
1255C2#6300611yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#2541C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59862C2semidirect
2. #59647C2semidirect
3. #59646C2semidirect
4. #59641C2semidirect
5. #59640C2semidirect
6. #59143C2semidirect
7. #45072C2semidirect
8. #45043C2semidirect
9. #43175C2semidirect
10. #39275C2semidirect
11. #39270C2semidirect
12. #39202C2semidirect
13. #39201C2semidirect
14. #36469C2semidirect
15. #36463C2semidirect
16. #35584C2semidirect
17. #35540C2semidirect
18. #35285C2semidirect
19. #35262C2semidirect
20. #34946C2semidirect
22. #34213C2semidirect
23. #34210C2semidirect
24. #34204C2semidirect
25. D4×#117C2semidirect
26. C4×#544C2semidirect
27. C2×#559C22semidirect
37. #2858C22semidirect
38. #2858C22semidirect
39. #2854C22semidirect
40. #2854C22semidirect
41. #2803C22semidirect
42. #2803C22semidirect
43. #2797C22semidirect
44. #2797C22semidirect
45. #2796C22semidirect
46. #2752C22semidirect
47. #2751C22semidirect
48. #2712C22semidirect
49. #2710C22semidirect
50. #2710C22semidirect
51. #2709C22semidirect
52. #2709C22semidirect
53. #2641C22semidirect
54. #2624C22semidirect
55. #2624C22semidirect
56. #2602C22semidirect
57. #2602C22semidirect
58. #2600C22semidirect
59. #2595C22semidirect
60. #2592C22semidirect
61. #2580C22semidirect
62. #2563C22semidirect
63. #2563C22semidirect
64. #2562C22semidirect
65. #2562C22semidirect
68. #2557C22semidirect
69. #2557C22semidirect
70. #2548C22semidirect
71. #2548C22semidirect
72. #2548C22semidirect
73. #2548C22semidirect
74. #2548C22semidirect
75. #2548C22semidirect
76. #2547C22semidirect
77. #2547C22semidirect
78. #2544C22semidirect
79. #2544C22semidirect
80. #2544C22semidirect
87. #2516C22semidirect
88. #2513C22semidirect
89. #2513C22semidirect
90. #2504C22semidirect
92. #2501C22semidirect
93. #2500C22semidirect
94. #2500C22semidirect
95. #2491C22semidirect
96. #2491C22semidirect
97. #2491C22semidirect
98. #2491C22semidirect
99. #2490C22semidirect
100. #2490C22semidirect
101. #2490C22semidirect
102. #2490C22semidirect
105. #2459C22semidirect
106. #2459C22semidirect
107. #2455C22semidirect
108. #2448C22semidirect
109. #2447C22semidirect
110. #2445C22semidirect
111. #2445C22semidirect
112. #2445C22semidirect
117. #2422C22semidirect
118. #2422C22semidirect
119. #2422C22semidirect
120. #2422C22semidirect
121. #2420C22semidirect
122. #2420C22semidirect
123. #2420C22semidirect
124. #2420C22semidirect
127. #2398C22semidirect
129. #2370C22semidirect
130. #2369C22semidirect
131. #2367C22semidirect
132. #2366C22semidirect
133. #2366C22semidirect
134. #2366C22semidirect
135. #2366C22semidirect
136. #2366C22semidirect
137. #2365C22semidirect
138. #2363C22semidirect
139. #2363C22semidirect
140. #2361C22semidirect
141. #2361C22semidirect
142. #2357C22semidirect
143. #2355C22semidirect
144. #2355C22semidirect
145. #2354C22semidirect
146. #2354C22semidirect
147. #2352C22semidirect
148. #2352C22semidirect
149. Q8×C4⋊C4C22semidirect
150. D4×C4⋊C4C22semidirect
151. D4×C4⋊C4C22semidirect
159. #2331C22semidirect
160. #2331C22semidirect
161. #2330C22semidirect
162. #2330C22semidirect
165. #2328C22semidirect
166. #2324C22semidirect
167. #2324C22semidirect
175. C4×C4⋊Q8C22semidirect
176. C4×C4⋊Q8C22semidirect
177. C4×#127C22semidirect
178. C4×#127C22semidirect
179. C4×#125C22semidirect
180. C4×#125C22semidirect
181. C4×#124C22semidirect
182. C4×#124C22semidirect
185. C4×#121C22semidirect
186. C4×#121C22semidirect
187. #2293C22semidirect
189. #2290C22semidirect
195. C42×D4C22semidirect
1172. C2×C4#559semidirect

Maximal subgroups

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

subgroupindex
#598622
#596472
#596462
#596412
#596402
#591432
#450722
#450432
#431752
#392752
#392702
#392022
#392012
#364692
#364632
#355842
#355402
#352852
#352622
#349462
C2×#25412
#342132
#342102
#342042
D4×#1172
C4×#5442