Finite Group Databasebeta

← #7716046

Subgroups — #7716046

Order 512.

7852 conjugacy classes of subgroups.

The subgroup lattice has 1139 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3536C212yesmaximal, complemented
2#49572C218yesmaximal, complemented
3#47856C218yesmaximal, complemented
4#45018C214yesmaximal, complemented
5#44989C214yesmaximal, complemented
6#44915C214yesmaximal, complemented
7#44886C214yesmaximal, complemented
8#39743C212yesmaximal, complemented
9#39359C212yesmaximal, complemented
10#39354C214yesmaximal, complemented
11#37678C214yesmaximal, complemented
12#36741C214yesmaximal, complemented
13#36576C212yesmaximal, complemented
14#36126C212yesmaximal, complemented
15#35252C212yesmaximal, complemented
16#35166C212yesmaximal, complemented
17#35004C212yesmaximal, complemented
18#35001C211yesmaximal, characteristic, complemented
19#34575C211yesmaximal, characteristic, complemented
20C2×#2362C211yesmaximal, characteristic, complemented
21#3536—232no—
22C2×#562C2218yes—
23C2×#554C2214yescomplemented
24C2×#550C2212yescomplemented
25C2×#548C2214yescomplemented
26C2×#547C2214yescomplemented
27C2×#546C2218yes—
28C2×#546C2214yescomplemented
29C2×#543C2214yescomplemented
30C2×#542C2214yes—
31C2×#539C2214yescomplemented
32C2×#538C2214yescomplemented
33C2×#537C2214yes—
34C2×#537C2214yescomplemented
35C2×#537C2214yescomplemented
36C2×#535C2212yescomplemented
37C2×#534C2212yes—
38C2×#534C2212yes—
39C2×#532C2214yescomplemented
40C2×#525C2212yes—
41C22×C22⋊Q8C2211yescharacteristic
42C22×#121C2212yes—
43C22×C4×Q8C2211yescharacteristic, complemented
44C22×#117C2211yescharacteristic
45#2856C2212yes—
46#2856C2212yes—
47#2856C2214yescomplemented
48#2856C2214yescomplemented
49#2854C2214yescomplemented
50#2850C2214yescomplemented
51#2733C2214yescomplemented
52#2732C2214yescomplemented
53#2730C2218yescomplemented
54#2723C2218yescomplemented
55#2720C2218yescomplemented
56#2714C2218yescomplemented
57#2711C2218yescomplemented
58#2696C2218yescomplemented
59#2692C2218yescomplemented
60#2683C2214yescomplemented
61#2682C2214yescomplemented
62#2681C2218yescomplemented
63#2681C2218yescomplemented
64#2680C2218yescomplemented
65#2678C2218yescomplemented
66#2676C2218yescomplemented
67#2674C2218yescomplemented
68#2673C2218yescomplemented
69#2672C2218yescomplemented
70#2670C2218yescomplemented
71#2669C2218yescomplemented
72#2669C2218yescomplemented
73#2663C2214yescomplemented
74#2661C2214yescomplemented
75#2659C2211yescharacteristic, complemented
76#2656C2212yes—
77#2656C2212yes—
78#2656C2211yescharacteristic, complemented
79#2656C2214yescomplemented
80#2639C2212yescomplemented
81#2620C2214yes—
82#2619C2214yes—
83#2618C2214yescomplemented
84#2617C2212yes—
85#2617C2212yes—
86#2556C2218yescomplemented
87#2554C2218yescomplemented
88#2551C2212yescomplemented
89#2548C2214yescomplemented
90#2548C2212yescomplemented
91#2543C2218yescomplemented
92#2542C2218yescomplemented
93#2541C2212yescomplemented
94#2541C2218yescomplemented
95#2540C2218yescomplemented
96#2540C2218yescomplemented
97#2539C2218yes—
98#2538C2212yescomplemented
99#2538C2214yescomplemented
100#2519C2218yescomplemented
101#2501C2214yes—
102#2491C2214yescomplemented
103#2472C2218yescomplemented
104#2464C2218yescomplemented
105#2461C2218yescomplemented
106#2461C2218yescomplemented
107#2461C2218yescomplemented
108#2456C2218yescomplemented
109#2455C2218yescomplemented
110#2452C2214yescomplemented
111#2452C2214yescomplemented
112#2448C2214yescomplemented
113#2445C2214yescomplemented
114#2440C2214yescomplemented
115#2433C2214yes—
116#2431C2214yescomplemented
117#2430C2218yescomplemented
118#2430C2218yescomplemented
119#2428C2214yescomplemented
120#2426C2214yescomplemented
121#2426C2218yescomplemented
122#2424C2218yescomplemented
123#2424C2218yescomplemented
124#2423C2214yescomplemented
125#2418C2218yescomplemented
126#2416C2214yescomplemented
127#2416C2218yescomplemented
128#2416C2214yescomplemented
129#2416C2214yescomplemented
130#2414C2214yes—
131#2414C2214yes—
132#2411C2218yescomplemented
133#2410C2218yes—
134#2407C2214yescomplemented
135#2395C2214yescomplemented
136#2388C2214yescomplemented
137#2366C2212yescomplemented
138#2362C2214yescomplemented
139#2362C2214yescomplemented
140#2362C2218yescomplemented
141#2361C2214yescomplemented
142Q8×C4⋊C4C2212yescomplemented
143D4×C4⋊C4C2212yescomplemented
144#2341C2214yescomplemented
145#2325C2214yescomplemented
146#2317C2212yescomplemented
147#2311C2212yescomplemented
148#2309C2212yescomplemented
149C4×#121C2212yescomplemented
150C4×#121C2212yescomplemented
151C4×#121C2214yescomplemented
152C2×#391C2211yescharacteristic, complemented
153C2×#389C2211yescharacteristic, complemented
154C2×#388C2212yes—
155C2×#388C2212yes—
156C2×#387C2212yescomplemented
157C2×C4×C4⋊C4C2211yescharacteristic, complemented
158C2×C4×C4⋊C4C2212yescomplemented
159C2×C4×C22⋊C4C2211yescharacteristic
160C22×#41C2312yes—
161C22×#41C2314yes—
162C22×#41C2318yes—
163C23×Q8C2311yescharacteristic
164C23×D4C2312yes—
165C23×D4C2314yes—
166C24×C4C2311yescharacteristic
167#562—264no—
168#554—232no—
169#550—48no—
170#548—232no—
171#547—232no—
172#546—232no—
173#546—264no—
174#543—232no—
175#542—232no—
176#539—232no—
177#538—232no—
178#537—232no—
179#537—232no—
180#537—416no—
181#535—48no—
182#534—48no—
183#534—48no—
184#532—416no—
185C2×C4⋊Q8C2314yes—
186C2×C4⋊Q8C2314yes—
187C2×#127C2312yes—
188C2×#127C2312yes—
189C2×#127C2314yes—
190C2×#127C2314yes—
191C2×#127C2314yes—
192C2×#126C2318yes—
193C2×#125C2318yes—
194C2×#124C2318yes—
195C2×#124C2318yes—
196C2×#124C2314yes—
197C2×#124C2314yes—
198C2×#124C2318yes—
199#525—216no—
200C2×#123C2318yes—
201C2×#123C2314yes—
202C2×#123C2318yes—
203C2×#123C2318yes—
204C2×#123C2318yes—
205C2×#123C2318yes—
206C2×#123C2318yes—
207C2×C22⋊Q8D4116yescomplemented
208C2×C22⋊Q8C2312yes—
209C2×C22⋊Q8C2312yes—
210C2×C22⋊Q8C2314yes—
211C2×C22⋊Q8C2318yes—
212C2×C22⋊Q8C2318yes—
213C2×C22⋊Q8C2318yes—
214C2×C22⋊Q8C2318yes—
215C2×C22⋊Q8C2318yes—
216C2×C22⋊Q8C2318yes—
217C2×C22⋊Q8C2318yes—
218C2×C22⋊Q8C2318yes—
219C2×C22⋊Q8C2314yes—
220C2×C22⋊Q8C2314yes—
221C2×#121—216no—
222C2×#121C2314yes—
223C2×#121C2314yes—
224C2×#121C2314yes—
225C2×#121C2314yes—
226C2×#121C2312yes—
227C2×#121C2312yes—
228C2×#121C2318yes—
229C2×#121C2314yes—
230C2×#121C2312yes—
231C2×#121C2312yes—
232C2×#121C2314yes—
233C2×#121C2314yes—
234C2×#121C2318yes—
235C2×#121C2318yes—
236C2×#121C2314yes—
237C2×#121C2318yes—
238C2×#121C2318yes—
239C2×#121C2314yes—
240C2×#121C2314yes—
241C2×#121C2318yes—
242C2×#121C2318yes—
243C2×#121C2314yes—
244C2×#121C2318yes—
245C2×#121C2318yes—
246C2×#121C2318yes—
247C2×#120C2314yes—
248C2×#120C2318yes—
249C2×#120C2318yes—
250C2×#120C2318yes—
251C2×#120C2318yes—
252C2×C4×Q8—44no—
253C2×C4×Q8C2314yes—
254C2×C4×Q8C2312yes—
255C2×C4×Q8C2312yes—
256C2×C4×Q8C2314yes—
257C2×C4×D4C2318yes—
258C2×C4×D4C2314yes—
259C2×C4×D4C2314yes—
260C2×C4×D4C2314yes—
261C2×C4×D4C2318yes—
262C2×C4×D4C2312yes—
263C2×C4×D4C2314yes—
264C2×C4×D4C2318yes—
265C2×C4×D4C2314yes—
266C2×C4×D4C2312yes—
267C2×C4×D4C2314yes—
268C2×#117—44no—
269C2×#117C2312yes—
270C2×#117C2312yes—
271C2×#117C2312yes—
272C2×#117C2314yes—
273C22×C4⋊C4C2312yes—
274C22×C4⋊C4C2314yes—
275C22×C4⋊C4C2312yes—
276C22×C4⋊C4C2311yescharacteristic
277C22×C4⋊C4C2311yescharacteristic
278C22×C4⋊C4C2312yes—
279C22×C4⋊C4C2312yes—
280C22×C4⋊C4C2311yescharacteristic
281C22×C22⋊C4C2311yescharacteristic
282C22×C22⋊C4C2311yescharacteristic
283C22×C22⋊C4C2314yes—
284C22×C22⋊C4C2318yes—
285C22×C22⋊C4C2312yes—
286C22×C22⋊C4C2312yes—
287C22×C42C2312yes—
288C22×C42C2312yes—
289C22×C42C2311yescharacteristic
290C22×C42C2311yescharacteristic
291C22×C42C2312yes—
292#400C2314yes—
293#399C2314yes—
294#399C2318yes—
295#399C2318yes—
296#399C2318yes—
297#399C2318yes—
298#398C2318yes—
299#398C2314yes—
300#398C2318yes—
301#397C2314yes—
302#397C2314yes—
303#397C2314yes—
304#397C2318yes—
305#396C2318yes—
306#396C2318yes—
307#396C2318yes—
308#396C2318yes—
309#396C2318yes—
310#396C2318yes—
311#395C2314yes—
312#395C2318yes—
313#395C2318yes—
314#394C2314yes—
315#394C2314yes—
316#394C2314yes—
317#394C2314yes—
318#394C2318yes—
319#394C2318yes—
320#394C2318yes—
321#394C2318yes—
322#394C2318yes—
323#394C2314yes—
324#394C2318yes—
325#394C2318yes—
326#394C2318yes—
327#394C2318yes—
328#394C2318yes—
329#393C2314yes—
330#393C2318yes—
331#393C2318yes—
332#392C2314yes—
333#392C2314yes—
334#392C2318yes—
335#392C2318yes—
336#392C2314yes—
337#392C2318yes—
338#392C2318yes—
339#392C2318yes—
340#392C2318yes—
341#392C2318yes—
342#392C2318yes—
343#392C2318yes—
344#391C2314yes—
345#391C2314yes—
346#391C2314yes—
347#390C2314yes—
348#390C2314yes—
349#390C2314yes—
350#390C2314yes—
351#390C2314yes—
352#390C2314yes—
353#390C2318yes—
354#390C2318yes—
355#390C2314yes—
356#390C2314yes—
357#390C2314yes—
358#390C2314yes—
359#390C2314yes—
360#390C2314yes—
361#390C2314yes—
362#390C2318yes—
363#390C2318yes—
364#390C2318yes—
365#390C2314yes—
366#390C2314yes—
367#390C2312yes—
368#390C2312yes—
369#390C2314yes—
370#389C2314yes—
371#389C2314yes—
372#389C2314yes—
373#389C2314yes—
374#389C2318yes—
375#389C2314yes—
376#389C2314yes—
377#389C2312yes—
378#389C2312yes—
379#389C2314yes—
380#388C2318yes—
381#388C2318yes—
382#388C2318yes—
383#388C2318yes—
384#388C2318yes—
385#388C2318yes—
386#388C2318yes—
387#388C2318yes—
388#388C2318yes—
389#388C2314yes—
390#388C2314yes—
391#388C2318yes—
392#388C2318yes—
393#388C2318yes—
394#387C2318yes—
395#387C2318yes—
396#387C2318yes—
397#386C2318yes—
398#386C2318yes—
399#386C2318yes—
400#386C2318yes—
401#386C2318yes—
402#386C2314yes—
403#386C2314yes—
404#386C2318yes—
405#386C2318yes—
406#386C2318yes—
407#386C2318yes—
408#386C2318yes—
409#385C2318yes—
410#385C2318yes—
411#385C2318yes—
412#385C2318yes—
413#385C2318yes—
414#385C2318yes—
415#384C2314yes—
416#384C2312yes—
417#384C2312yes—
418#384C2314yes—
419#382C2314yes—
420#380C2314yes—
421#380C2314yes—
422#380C2312yes—
423#380C2318yes—
424#380C2312yes—
425#379C2318yes—
426C4×C4⋊C4C2312yes—
427C4×C4⋊C4C2312yes—
428C4×C4⋊C4C2314yes—
429C4×C4⋊C4C2312yes—
430C4×C4⋊C4C2314yes—
431C4×C4⋊C4C2318yes—
432C4×C4⋊C4C2318yes—
433C4×C4⋊C4C2312yes—
434C4×C22⋊C4C2314yes—
435C4×C22⋊C4C2318yes—
436C4×C22⋊C4C2314yes—
437C4×C22⋊C4C2314yes—
438C4×C22⋊C4C2314yes—
439C2×#95C2312yes—
440C2×#95C2311yescharacteristic
441C2×#95C2311yescharacteristic
442C2×#95C2312yes—
443C2×#95C2312yes—
444C2×#95C2312yes—
445C25C2411yescharacteristic
446C25C2414yes—
447C2×#41—216no—
448C2×#41—28no—
449C2×#41—232no—
450C2×#41—44no—
451C2×#41—44no—
452C2×#41—416no—
453C2×#41—416no—
454C2×#41—48no—
455C2×#41—48no—
456C22×Q8—42no—
457C22×Q8—42no—
458C22×Q8C2×D418yes—
459C22×Q8C2412yes—
460C22×Q8C2418yes—
461C22×Q8C2412yes—
462C22×Q8C2412yes—
463C22×D4—216no—
464C22×D4—28no—
465C22×D4—44no—
466C22×D4—44no—
467C22×D4—48no—
468C22×D4—48no—
469C22×D4C2414yes—
470C22×D4C2418yes—
471C22×D4C2414yes—
472C22×D4C2414yes—
473C22×D4C2412yes—
474C22×D4C2414yes—
475C22×D4C2414yes—
476C22×D4C2418yes—
477C22×D4C2412yes—
478C22×D4C2414yes—
479C22×D4C2418yes—
480C22×D4C2418yes—
481C22×D4C2418yes—
482C22×D4C2412yes—
483C22×D4C2414yes—
484C22×D4C2414yes—
485C22×D4C2414yes—
486C22×D4C2418yes—
487C23×C4—42no—
488C23×C4—42no—
489C23×C4C2×D418yes—
490C23×C4C2414yes—
491C23×C4C2412yes—
492C23×C4C2412yes—
493C23×C4C2411yescharacteristic
494C23×C4C2412yes—
495C23×C4C2411yescharacteristic
496C23×C4C2412yes—
497C23×C4C2414yes—
498C23×C4C2418yes—
499C23×C4C2418yes—
500C23×C4C2411yescharacteristic
501C23×C4C2418yes—
502C23×C4C2412yes—
503C23×C4C2412yes—
504C23×C4C2411yescharacteristic
505C23×C4C2411yescharacteristic
506C23×C4C2411yescharacteristic
507C4⋊Q8—216no—
508C4⋊Q8—48no—
509#127—44no—
510#127—48no—
511#127—48no—
512#127—44no—
513#127—48no—
514#126—232no—
515#125—232no—
516#124—232no—
517#124—216no—
518#124—232no—
519#124—416no—
520#124—48no—
521#123—216no—
522#123—232no—
523#123—232no—
524#123—232no—
525#123—232no—
526#123—416no—
527#123—416no—
528C22⋊Q8—216no—
529C22⋊Q8—232no—
530C22⋊Q8—28no—
531C22⋊Q8—28no—
532C22⋊Q8—232no—
533C22⋊Q8—232no—
534C22⋊Q8—232no—
535C22⋊Q8—232no—
536C22⋊Q8—232no—
537C22⋊Q8—416no—
538C22⋊Q8—416no—
539C22⋊Q8C2×D4132yes—
540C22⋊Q8C2×D4132yes—
541#121—216no—
542#121—216no—
543#121—216no—
544#121—216no—
545#121—28no—
546#121—28no—
547#121—232no—
548#121—28no—
549#121—216no—
550#121—216no—
551#121—28no—
552#121—232no—
553#121—216no—
554#121—232no—
555#121—216no—
556#121—232no—
557#121—232no—
558#121—416no—
559#121—416no—
560#121—416no—
561#121—48no—
562#121—416no—
563#121—48no—
564#121—48no—
565#121—416no—
566#120—216no—
567#120—232no—
568#120—416no—
569#120—416no—
570#120—416no—
571C4×Q8—216no—
572C4×Q8—28no—
573C4×Q8—48no—
574C4×Q8—44no—
575C4×D4—216no—
576C4×D4—216no—
577C4×D4—232no—
578C4×D4—216no—
579C4×D4—232no—
580C4×D4—416no—
581C4×D4—48no—
582C4×D4—48no—
583C4×D4—48no—
584C4×D4—44no—
585C4×D4—44no—
586#117—28no—
587#117—28no—
588#117—48no—
589#117—44no—
590C2×C4⋊C4—28no—
591C2×C4⋊C4—28no—
592C2×C4⋊C4—216no—
593C2×C4⋊C4—24no—
594C2×C4⋊C4—42no—
595C2×C4⋊C4—44no—
596C2×C4⋊C4C2×D4116yes—
597C2×C4⋊C4C2×D418yes—
598C2×C4⋊C4C2414yes—
599C2×C4⋊C4C2411yescharacteristic
600C2×C4⋊C4C2412yes—
601C2×C4⋊C4C2412yes—
602C2×C4⋊C4C2414yes—
603C2×C4⋊C4C2414yes—
604C2×C4⋊C4C2418yes—
605C2×C4⋊C4C2418yes—
606C2×C4⋊C4C2412yes—
607C2×C4⋊C4C2412yes—
608C2×C4⋊C4C2412yes—
609C2×C4⋊C4C2418yes—
610C2×C4⋊C4C2414yes—
611C2×C4⋊C4C2414yes—
612C2×C4⋊C4C2414yes—
613C2×C4⋊C4C2418yes—
614C2×C4⋊C4C2418yes—
615C2×C4⋊C4C2412yes—
616C2×C4⋊C4C2414yes—
617C2×C4⋊C4C2412yes—
618C2×C4⋊C4C2414yes—
619C2×C4⋊C4C2412yes—
620C2×C4⋊C4C2418yes—
621C2×C4⋊C4C2412yes—
622C2×C4⋊C4C2418yes—
623C2×C4⋊C4C2414yes—
624C2×C4⋊C4C2414yes—
625C2×C4⋊C4C2412yes—
626C2×C4⋊C4C2412yes—
627C2×C4⋊C4C2412yes—
628C2×C4⋊C4C2418yes—
629C2×C4⋊C4C2412yes—
630C2×C4⋊C4C2411yescharacteristic
631C2×C22⋊C4—216no—
632C2×C22⋊C4—24no—
633C2×C22⋊C4—24no—
634C2×C22⋊C4—232no—
635C2×C22⋊C4—44no—
636C2×C22⋊C4C2×D4116yes—
637C2×C22⋊C4C2414yes—
638C2×C22⋊C4C2414yes—
639C2×C22⋊C4C2414yes—
640C2×C22⋊C4C2414yes—
641C2×C22⋊C4C2418yes—
642C2×C22⋊C4C2418yes—
643C2×C22⋊C4C2418yes—
644C2×C22⋊C4C2418yes—
645C2×C22⋊C4C2414yes—
646C2×C22⋊C4C2414yes—
647C2×C22⋊C4C2414yes—
648C2×C22⋊C4C2418yes—
649C2×C22⋊C4C2418yes—
650C2×C22⋊C4C2418yes—
651C2×C22⋊C4C2418yes—
652C2×C22⋊C4C2414yes—
653C2×C22⋊C4C2418yes—
654C2×C22⋊C4C2414yes—
655C2×C22⋊C4C2418yes—
656C2×C22⋊C4C2414yes—
657C2×C22⋊C4C2414yes—
658C2×C22⋊C4C2414yes—
659C2×C22⋊C4C2418yes—
660C2×C22⋊C4C2418yes—
661C2×C22⋊C4C2414yes—
662C2×C22⋊C4C2418yes—
663C2×C22⋊C4C2418yes—
664C2×C22⋊C4C2418yes—
665C2×C22⋊C4C2418yes—
666C2×C22⋊C4C2418yes—
667C2×C22⋊C4C2418yes—
668C2×C22⋊C4C2414yes—
669C2×C22⋊C4C2414yes—
670C2×C22⋊C4C2418yes—
671C2×C22⋊C4C2418yes—
672C2×C42—28no—
673C2×C42—44no—
674C2×C42—42no—
675C2×C42—44no—
676C2×C42—42no—
677C2×C42C2414yes—
678C2×C42C2414yes—
679C2×C42C2418yes—
680C2×C42C2414yes—
681C2×C42C2414yes—
682C2×C42C2412yes—
683C2×C42C2414yes—
684C2×C42C2412yes—
685C2×C42C2414yes—
686C2×C42C2414yes—
687C2×C42C2412yes—
688C2×C42C2412yes—
689#95C2414yes—
690#95C2414yes—
691#95C2414yes—
692#95C2414yes—
693#95C2418yes—
694#95C2418yes—
695#95C2418yes—
696#95C2414yes—
697#95C2418yes—
698#95C2414yes—
699#95C2414yes—
700#95C2414yes—
701#95C2418yes—
702#95C2414yes—
703#95C2414yes—
704#95C2418yes—
705#95C2418yes—
706C24—22no—
707C24—22no—
708C24—28no—
709C24—41no—
710C24—41no—
711C24—41no—
712C24—41no—
713C24—44no—
714C24—44no—
715C24—44no—
716C24—44no—
717C24—44no—
718C24—44no—
719C24C22×D414yes—
720C24C2518yes—
721C24C2514yes—
722C24C2512yes—
723C24C2511yescharacteristic
724#41—816no—
725#41—864no—
726#41—832no—
727C2×Q8—24no—
728C2×Q8—216no—
729C2×Q8—24no—
730C2×Q8—24no—
731C2×Q8—42no—
732C2×Q8—42no—
733C2×Q8—48no—
734C2×Q8—42no—
735C2×Q8—48no—
736C2×Q8—42no—
737C2×Q8—416no—
738C2×Q8C22×D418yes—
739C2×Q8C22×D418yes—
740C2×D4—28no—
741C2×D4—28no—
742C2×D4—216no—
743C2×D4—216no—
744C2×D4—216no—
745C2×D4—28no—
746C2×D4—28no—
747C2×D4—28no—
748C2×D4—216no—
749C2×D4—28no—
750C2×D4—216no—
751C2×D4—216no—
752C2×D4—24no—
753C2×D4—28no—
754C2×D4—24no—
755C2×D4—28no—
756C2×D4—28no—
757C2×D4—28no—
758C2×D4—216no—
759C2×D4—24no—
760C2×D4—28no—
761C2×D4—42no—
762C2×D4—42no—
763C2×D4—44no—
764C2×D4—44no—
765C2×D4—48no—
766C2×D4—44no—
767C2×D4—42no—
768C2×D4—44no—
769C2×D4—48no—
770C2×D4—48no—
771C2×D4—48no—
772C2×D4—48no—
773C2×D4—44no—
774C2×D4—48no—
775C2×D4—42no—
776C2×D4—44no—
777C2×D4—44no—
778C2×D4—44no—
779C2×D4—44no—
780C2×D4—42no—
781C2×D4—48no—
782C2×D4—42no—
783C2×D4—48no—
784C2×D4—44no—
785C2×D4—44no—
786C2×D4—44no—
787C2×D4—48no—
788C2×D4—48no—
789C2×D4—44no—
790C2×D4—44no—
791C2×D4—44no—
792C2×D4—44no—
793C2×D4—48no—
794C2×D4—816no—
795C2×D4—832no—
796C22×C4—24no—
797C22×C4—24no—
798C22×C4—22no—
799C22×C4—24no—
800C22×C4—22no—
801C22×C4—24no—
802C22×C4—24no—
803C22×C4—28no—
804C22×C4—22no—
805C22×C4—22no—
806C22×C4—24no—
807C22×C4—28no—
808C22×C4—24no—
809C22×C4—28no—
810C22×C4—28no—
811C22×C4—216no—
812C22×C4—216no—
813C22×C4—216no—
814C22×C4—416no—
815C22×C4—41no—
816C22×C4—41no—
817C22×C4—42no—
818C22×C4—41no—
819C22×C4—42no—
820C22×C4—42no—
821C22×C4—41no—
822C22×C4—41no—
823C22×C4—41no—
824C22×C4—42no—
825C22×C4—42no—
826C22×C4—42no—
827C22×C4—41no—
828C22×C4—41no—
829C22×C4—48no—
830C22×C4—48no—
831C22×C4—48no—
832C22×C4—48no—
833C22×C4—48no—
834C22×C4—44no—
835C22×C4—44no—
836C22×C4—42no—
837C22×C4—41no—
838C22×C4—41no—
839C22×C4—48no—
840C22×C4C22×D418yes—
841C22×C4C22×D418yes—
842C22×C4C22×D414yes—
843C22×C4C22×D418yes—
844C22×C4C22×D418yes—
845C22×C4C22×D414yes—
846C22×C4H(5,𝔽2)14yes—
847C22×C4H(5,𝔽2)14yes—
848C22×C4C2512yes—
849C22×C4C2514yes—
850C22×C4C2512yes—
851C22×C4C2514yes—
852C22×C4C2514yes—
853C22×C4C2512yes—
854C22×C4C2514yes—
855C22×C4C2518yes—
856C22×C4C2514yes—
857C22×C4C2512yes—
858C22×C4C2514yes—
859C22×C4C2511yescharacteristic
860C22×C4C2512yes—
861C22×C4C2512yes—
862C22×C4C2512yes—
863C22×C4C2511yescharacteristic
864C4⋊C4—28no—
865C4⋊C4—28no—
866C4⋊C4—216no—
867C4⋊C4—24no—
868C4⋊C4—24no—
869C4⋊C4—216no—
870C4⋊C4—28no—
871C4⋊C4—28no—
872C4⋊C4—216no—
873C4⋊C4—216no—
874C4⋊C4—24no—
875C4⋊C4—22no—
876C4⋊C4—216no—
877C4⋊C4—24no—
878C4⋊C4—28no—
879C4⋊C4—24no—
880C4⋊C4—28no—
881C4⋊C4—24no—
882C4⋊C4—28no—
883C4⋊C4—42no—
884C4⋊C4—44no—
885C4⋊C4—42no—
886C4⋊C4—42no—
887C4⋊C4—42no—
888C4⋊C4—42no—
889C4⋊C4—48no—
890C4⋊C4—48no—
891C4⋊C4—44no—
892C4⋊C4—44no—
893C4⋊C4C22×D418yes—
894C4⋊C4C22×D4132yes—
895C4⋊C4C22×D418yes—
896C4⋊C4H(5,𝔽2)14yes—
897C22⋊C4—28no—
898C22⋊C4—28no—
899C22⋊C4—28no—
900C22⋊C4—216no—
901C22⋊C4—216no—
902C22⋊C4—216no—
903C22⋊C4—216no—
904C22⋊C4—216no—
905C22⋊C4—216no—
906C22⋊C4—28no—
907C22⋊C4—216no—
908C22⋊C4—28no—
909C22⋊C4—28no—
910C22⋊C4—28no—
911C22⋊C4—28no—
912C22⋊C4—28no—
913C22⋊C4—216no—
914C22⋊C4—216no—
915C22⋊C4—216no—
916C22⋊C4—28no—
917C22⋊C4—44no—
918C22⋊C4—48no—
919C22⋊C4—44no—
920C22⋊C4—44no—
921C22⋊C4—48no—
922C22⋊C4—44no—
923C22⋊C4—44no—
924C22⋊C4—48no—
925C22⋊C4—48no—
926C22⋊C4—48no—
927C22⋊C4—48no—
928C22⋊C4—48no—
929C22⋊C4—48no—
930C22⋊C4—48no—
931C22⋊C4C22×D4132yes—
932C42—28no—
933C42—216no—
934C42—28no—
935C42—28no—
936C42—28no—
937C42—28no—
938C42—24no—
939C42—24no—
940C42—42no—
941C42—44no—
942C42—44no—
943C42—42no—
944C23—21no—
945C23—21no—
946C23—21no—
947C23—21no—
948C23—22no—
949C23—22no—
950C23—22no—
951C23—22no—
952C23—22no—
953C23—22no—
954C23—28no—
955C23—28no—
956C23—24no—
957C23—24no—
958C23—24no—
959C23—28no—
960C23—28no—
961C23—28no—
962C23—24no—
963C23—24no—
964C23—28no—
965C23—24no—
966C23—28no—
967C23—28no—
968C23—24no—
969C23—44no—
970C23—44no—
971C23—416no—
972C23—82no—
973C23—82no—
974C23—82no—
975C23—82no—
976C23—88no—
977C23—88no—
978C23—164no—
979C23—164no—
980C23—164no—
981C23—164no—
982C23C23×D414yes—
983C23C23×D412yes—
984C23C2×H(5,𝔽2)12yes—
985C23C2×H(5,𝔽2)12yes—
986C23C2611yescharacteristic
987Q8—216no—
988Q8—48no—
989Q8—84no—
990Q8—816no—
991D4—48no—
992D4—416no—
993D4—432no—
994D4—416no—
995D4—416no—
996D4—84no—
997D4—88no—
998D4—88no—
999D4—816no—
1000D4—88no—
1001D4—84no—
1002D4—816no—
1003D4—816no—
1004D4—816no—
1005D4—88no—
1006D4—168no—
1007D4—164no—
1008D4—164no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—24no—
1013C2×C4—24no—
1014C2×C4—21no—
1015C2×C4—24no—
1016C2×C4—22no—
1017C2×C4—21no—
1018C2×C4—22no—
1019C2×C4—24no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—216no—
1024C2×C4—216no—
1025C2×C4—28no—
1026C2×C4—24no—
1027C2×C4—24no—
1028C2×C4—28no—
1029C2×C4—24no—
1030C2×C4—22no—
1031C2×C4—24no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—24no—
1037C2×C4—28no—
1038C2×C4—28no—
1039C2×C4—24no—
1040C2×C4—24no—
1041C2×C4—24no—
1042C2×C4—22no—
1043C2×C4—24no—
1044C2×C4—22no—
1045C2×C4—24no—
1046C2×C4—24no—
1047C2×C4—24no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—44no—
1051C2×C4—48no—
1052C2×C4—48no—
1053C2×C4—44no—
1054C2×C4—44no—
1055C2×C4—48no—
1056C2×C4—416no—
1057C2×C4—816no—
1058C2×C4—816no—
1059C2×C4—816no—
1060C2×C4—84no—
1061C2×C4—82no—
1062C2×C4—82no—
1063C2×C4—88no—
1064C2×C4C23×D418yes—
1065C2×C4C23×D412yes—
1066C2×C4C23×D414yes—
1067C2×C4C23×D418yes—
1068C2×C4C23×D412yes—
1069C2×C4C2×H(5,𝔽2)14yes—
1070C2×C4C2×H(5,𝔽2)14yes—
1071C2×C4C2×H(5,𝔽2)14yes—
1072C2×C4C2×H(5,𝔽2)12yes—
1073C2×C4#58512yes—
1074C22—22no—
1075C22—22no—
1076C22—22no—
1077C22—22no—
1078C22—22no—
1079C22—22no—
1080C22—24no—
1081C22—24no—
1082C22—24no—
1083C22—42no—
1084C22—42no—
1085C22—42no—
1086C22—42no—
1087C22—44no—
1088C22—48no—
1089C22—44no—
1090C22—48no—
1091C22—44no—
1092C22—48no—
1093C22—44no—
1094C22—48no—
1095C22—44no—
1096C22—48no—
1097C22—44no—
1098C22—48no—
1099C22—48no—
1100C22—44no—
1101C22—88no—
1102C22—1616no—
1103C22#349814yes—
1104C22C24×D411yescharacteristic
1105C22C22×H(5,𝔽2)11yescharacteristic
1106C22C22×H(5,𝔽2)11yescharacteristic
1107C22C22×H(5,𝔽2)11yescharacteristic
1108C22C2×#58511yescharacteristic
1109C222−1+611yescharacteristic
1110C222−1+611yescharacteristic
1111C4—24no—
1112C4—22no—
1113C4—28no—
1114C4—28no—
1115C4—24no—
1116C4—24no—
1117C4—24no—
1118C4—44no—
1119C4—48no—
1120C4—44no—
1121C4—44no—
1122C4—44no—
1123C4—42no—
1124C4—42no—
1125C4—42no—
1126C4#349614yes—
1127C2—24no—
1128C2—44no—
1129C2—84no—
1130C2—88no—
1131C2C2×#349611yescharacteristic
1132C2C2×#349811yescharacteristic
1133C2#6284811yescharacteristic
1134C2#6289511yescharacteristic
1135C2#6290111yescharacteristic
1136C2#6291411yescharacteristic
1137C2#6293111yescharacteristic
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×#3536C2semidirect
2. #49572C2semidirect
3. #47856C2semidirect
4. #45018C2semidirect
5. #44989C2semidirect
6. #44915C2semidirect
7. #44886C2semidirect
8. #39743C2semidirect
9. #39359C2semidirect
10. #39354C2semidirect
11. #37678C2semidirect
12. #36741C2semidirect
13. #36576C2semidirect
14. #36126C2semidirect
15. #35252C2semidirect
16. #35166C2semidirect
17. #35004C2semidirect
18. #35001C2semidirect
19. #34575C2semidirect
20. C2×#2362C2semidirect
23. C2×#554C22semidirect
24. C2×#550C22semidirect
25. C2×#548C22semidirect
26. C2×#547C22semidirect
28. C2×#546C22semidirect
29. C2×#543C22semidirect
31. C2×#539C22semidirect
32. C2×#538C22semidirect
34. C2×#537C22semidirect
35. C2×#537C22semidirect
36. C2×#535C22semidirect
39. C2×#532C22semidirect
43. C22×C4×Q8C22semidirect
47. #2856C22semidirect
48. #2856C22semidirect
49. #2854C22semidirect
50. #2850C22semidirect
51. #2733C22semidirect
52. #2732C22semidirect
53. #2730C22semidirect
54. #2723C22semidirect
55. #2720C22semidirect
56. #2714C22semidirect
57. #2711C22semidirect
58. #2696C22semidirect
59. #2692C22semidirect
60. #2683C22semidirect
61. #2682C22semidirect
62. #2681C22semidirect
63. #2681C22semidirect
64. #2680C22semidirect
65. #2678C22semidirect
66. #2676C22semidirect
67. #2674C22semidirect
68. #2673C22semidirect
69. #2672C22semidirect
70. #2670C22semidirect
71. #2669C22semidirect
72. #2669C22semidirect
73. #2663C22semidirect
74. #2661C22semidirect
75. #2659C22semidirect
78. #2656C22semidirect
79. #2656C22semidirect
80. #2639C22semidirect
83. #2618C22semidirect
86. #2556C22semidirect
87. #2554C22semidirect
88. #2551C22semidirect
89. #2548C22semidirect
90. #2548C22semidirect
91. #2543C22semidirect
92. #2542C22semidirect
93. #2541C22semidirect
94. #2541C22semidirect
95. #2540C22semidirect
96. #2540C22semidirect
98. #2538C22semidirect
99. #2538C22semidirect
100. #2519C22semidirect
102. #2491C22semidirect
103. #2472C22semidirect
104. #2464C22semidirect
105. #2461C22semidirect
106. #2461C22semidirect
107. #2461C22semidirect
108. #2456C22semidirect
109. #2455C22semidirect
110. #2452C22semidirect
111. #2452C22semidirect
112. #2448C22semidirect
113. #2445C22semidirect
114. #2440C22semidirect
116. #2431C22semidirect
117. #2430C22semidirect
118. #2430C22semidirect
119. #2428C22semidirect
120. #2426C22semidirect
121. #2426C22semidirect
122. #2424C22semidirect
123. #2424C22semidirect
124. #2423C22semidirect
125. #2418C22semidirect
126. #2416C22semidirect
127. #2416C22semidirect
128. #2416C22semidirect
129. #2416C22semidirect
132. #2411C22semidirect
134. #2407C22semidirect
135. #2395C22semidirect
136. #2388C22semidirect
137. #2366C22semidirect
138. #2362C22semidirect
139. #2362C22semidirect
140. #2362C22semidirect
141. #2361C22semidirect
142. Q8×C4⋊C4C22semidirect
143. D4×C4⋊C4C22semidirect
144. #2341C22semidirect
145. #2325C22semidirect
146. #2317C22semidirect
147. #2311C22semidirect
148. #2309C22semidirect
149. C4×#121C22semidirect
150. C4×#121C22semidirect
151. C4×#121C22semidirect
152. C2×#391C22semidirect
153. C2×#389C22semidirect
156. C2×#387C22semidirect
157. C2×C4×C4⋊C4C22semidirect
158. C2×C4×C4⋊C4C22semidirect
207. C2×C22⋊Q8D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35362
#495722
#478562
#450182
#449892
#449152
#448862
#397432
#393592
#393542
#376782
#367412
#365762
#361262
#352522
#351662
#350042
#350012
#345752
C2×#23622