Finite Group Databasebeta

← #7674816

Subgroups — #7674816

Order 512.

8110 conjugacy classes of subgroups.

The subgroup lattice has 1163 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3505C212yesmaximal, complemented
2#59047C214yesmaximal, complemented
3#59046C214yesmaximal, complemented
4#59022C214yesmaximal, complemented
5#59003C214yesmaximal, complemented
6#43913C218yesmaximal, complemented
7#43029C218yesmaximal, complemented
8#39743C212yesmaximal, complemented
9#39742C214yesmaximal, complemented
10#39742C212yesmaximal, complemented
11#39738C214yesmaximal, complemented
12#36596C212yesmaximal, complemented
13#36576C212yesmaximal, complemented
14#35358C214yesmaximal, complemented
15#35001C212yesmaximal, complemented
16#35001C211yesmaximal, characteristic, complemented
17C2×#2416C212yesmaximal, complemented
18#34273C212yesmaximal, complemented
19C2×#2360C211yesmaximal, characteristic, complemented
20C4×#534C211yesmaximal, characteristic, complemented
21#3505—232no—
22C2×#553C2218yescomplemented
23C2×#553C2214yescomplemented
24C2×#552C2214yescomplemented
25C2×#551C2218yescomplemented
26C2×#550C2212yescomplemented
27C2×#548C2214yescomplemented
28C2×#546C2214yescomplemented
29C2×#539C2214yescomplemented
30C2×#538C2214yescomplemented
31C2×#534C2214yes—
32C2×#534C2211yescharacteristic
33C2×#534C2212yes—
34C2×#534C2212yes—
35C2×#529C2214yescomplemented
36C2×#525C2214yescomplemented
37C22×C22⋊Q8C2211yescharacteristic
38C22×#121C2212yes—
39C22×#121C2214yes—
40C22×#121C2212yescomplemented
41C2×#518C2214yes—
42C22×C4×Q8C2211yescharacteristic, complemented
43C22×C4×D4C2212yes—
44C23×C4⋊C4C2211yescharacteristic
45#2856C2214yescomplemented
46#2856C2212yescomplemented
47#2856C2214yescomplemented
48#2856C2212yescomplemented
49#2733C2214yescomplemented
50#2732C2214yescomplemented
51#2730C2218yescomplemented
52#2727C2214yescomplemented
53#2727C2218yescomplemented
54#2721C2218yescomplemented
55#2714C2218yescomplemented
56#2705C2218yescomplemented
57#2705C2218yescomplemented
58#2705C2218yescomplemented
59#2694C2218yescomplemented
60#2682C2218yescomplemented
61#2682C2214yescomplemented
62#2673C2218yescomplemented
63#2656C2212yescomplemented
64#2656C2214yescomplemented
65#2656C2212yescomplemented
66#2656C2214yescomplemented
67#2554C2218yescomplemented
68#2552C2212yescomplemented
69#2548C2214yescomplemented
70#2548C2212yescomplemented
71#2543C2218yescomplemented
72#2543C2218yescomplemented
73#2541C2212yescomplemented
74#2539C2218yescomplemented
75#2539C2218yescomplemented
76#2539C2218yescomplemented
77#2538C2214yescomplemented
78#2538C2212yescomplemented
79#2512C2214yescomplemented
80#2501C2218yescomplemented
81#2501C2214yescomplemented
82#2490C2214yescomplemented
83#2479C2218yescomplemented
84#2471C2218yescomplemented
85#2467C2218yescomplemented
86#2456C2218yescomplemented
87#2454C2218yescomplemented
88#2454C2214yescomplemented
89#2448C2214yescomplemented
90#2445C2214yescomplemented
91#2441C2218yescomplemented
92#2441C2214yescomplemented
93#2433C2218yescomplemented
94#2433C2214yescomplemented
95#2431C2214yescomplemented
96#2428C2218yescomplemented
97#2428C2214yescomplemented
98#2426C2218yescomplemented
99#2426C2214yescomplemented
100#2425C2218yescomplemented
101#2425C2218yescomplemented
102#2424C2218yescomplemented
103#2424C2218yescomplemented
104#2423C2214yescomplemented
105#2416C2218yes—
106#2416C2214yes—
107#2416C2214yes—
108#2416C2218yescomplemented
109#2416C2218yescomplemented
110#2416C2218yescomplemented
111#2416C2214yescomplemented
112#2416C2214yescomplemented
113#2414C2214yescomplemented
114#2414C2218yescomplemented
115#2413C2218yescomplemented
116#2412C2218yescomplemented
117#2411C2218yescomplemented
118#2410C2218yescomplemented
119#2407C2214yescomplemented
120C2×#396C2214yescomplemented
121C2×#394C2214yescomplemented
122#2366C2212yescomplemented
123#2363C2214yescomplemented
124#2360C2218yescomplemented
125#2360C2214yescomplemented
126#2360C2214yescomplemented
127#2359C2218yescomplemented
128#2359C2218yescomplemented
129#2358C2218yescomplemented
130#2358C2218yescomplemented
131#2354C2212yescomplemented
132Q8×C4⋊C4C2212yescomplemented
133#2341C2214yescomplemented
134#2325C2212yescomplemented
135#2325C2212yescomplemented
136#2325C2214yescomplemented
137#2325C2214yescomplemented
138#2322C2214yescomplemented
139#2321C2214yescomplemented
140#2315C2211yescharacteristic
141#2308C2212yes—
142C4×#123C2214yescomplemented
143C4×#121C2212yescomplemented
144C4×#121C2212yescomplemented
145C4×#121C2214yescomplemented
146C4×#121C2214yescomplemented
147C4×#120C2214yescomplemented
148C2×#391C2211yescharacteristic, complemented
149C2×#390C2212yescomplemented
150C2×#389C2212yescomplemented
151C2×#389C2211yescharacteristic, complemented
152C2×#389C2212yescomplemented
153C2×#387C2212yescomplemented
154C2×#386C2214yes—
155C2×#385C2212yes—
156C2×#380C2212yescomplemented
157C2×C4×C4⋊C4C2211yescharacteristic, complemented
158C2×C4×C22⋊C4C2211yescharacteristic
159C2×C4×C22⋊C4C2212yes—
160C22×#41C2314yes—
161C23×Q8C2311yescharacteristic
162C23×D4C2312yes—
163C23×D4C2314yes—
164C23×D4C2312yes—
165C23×D4C2314yes—
166C24×C4C2312yes—
167C24×C4C2312yes—
168C24×C4C2311yescharacteristic
169#553—232no—
170#553—264no—
171#552—232no—
172#551—264no—
173#550—48no—
174#548—232no—
175#546—232no—
176#539—232no—
177#538—232no—
178#534—232no—
179#534—28no—
180#534—216no—
181#534—48no—
182C2×#127C2312yes—
183C2×#127C2314yes—
184C2×#127C2312yes—
185C2×#127C2314yes—
186#529—232no—
187C2×#126C2318yes—
188C2×#126C2318yes—
189C2×#126C2318yes—
190C2×#125C2314yes—
191C2×#125C2318yes—
192C2×#124C2314yes—
193C2×#124C2318yes—
194#525—232no—
195C2×#123C2314yes—
196C2×#123C2318yes—
197C2×#123C2318yes—
198C2×#123C2318yes—
199C2×#123C2318yes—
200C2×#123C2318yes—
201C2×#123C2318yes—
202C2×#123C2318yes—
203C2×C22⋊Q8D4116yescomplemented
204C2×C22⋊Q8C2314yes—
205C2×C22⋊Q8C2318yes—
206C2×C22⋊Q8C2314yes—
207C2×C22⋊Q8C2314yes—
208C2×#121—216no—
209C2×#121—48no—
210C2×#121—416no—
211C2×#121C2312yes—
212C2×#121C2312yes—
213C2×#121C2314yes—
214C2×#121C2314yes—
215C2×#121C2314yes—
216C2×#121C2318yes—
217C2×#121C2318yes—
218C2×#121C2314yes—
219C2×#121C2314yes—
220C2×#121C2314yes—
221C2×#121C2314yes—
222C2×#121C2314yes—
223C2×#121C2318yes—
224C2×#121C2318yes—
225C2×#121C2314yes—
226C2×#121C2314yes—
227C2×#121C2318yes—
228C2×#121C2314yes—
229C2×#121C2318yes—
230C2×#121C2318yes—
231C2×#121C2318yes—
232C2×#121C2318yes—
233C2×#121C2318yes—
234C2×#120C2314yes—
235C2×#120C2318yes—
236C2×#120C2318yes—
237C2×#120C2318yes—
238C2×#120C2318yes—
239#518—232no—
240C2×C4×Q8—44no—
241C2×C4×Q8C2314yes—
242C2×C4×Q8C2312yes—
243C2×C4×Q8C2312yes—
244C2×C4×Q8C2314yes—
245C2×C4×D4—216no—
246C2×C4×D4C2314yes—
247C2×C4×D4C2314yes—
248C2×C4×D4C2318yes—
249C2×C4×D4C2318yes—
250C2×C4×D4C2318yes—
251C2×C4×D4C2318yes—
252C2×C4×D4C2314yes—
253C2×C4×D4C2314yes—
254C2×C4×D4C2314yes—
255C2×C4×D4C2318yes—
256C2×C4×D4C2312yes—
257C2×C4×D4C2314yes—
258C2×C4×D4C2312yes—
259C2×C4×D4C2314yes—
260C2×#117C2314yes—
261C2×#117C2318yes—
262C2×#117C2318yes—
263C22×C4⋊C4—44no—
264C22×C4⋊C4C2312yes—
265C22×C4⋊C4C2312yes—
266C22×C4⋊C4C2311yescharacteristic
267C22×C4⋊C4C2312yes—
268C22×C4⋊C4C2314yes—
269C22×C4⋊C4C2312yes—
270C22×C4⋊C4C2314yes—
271C22×C4⋊C4C2312yes—
272C22×C4⋊C4C2311yescharacteristic
273C22×C4⋊C4C2312yes—
274C22×C4⋊C4C2312yes—
275C22×C4⋊C4C2311yescharacteristic
276C22×C4⋊C4C2312yes—
277C22×C22⋊C4C2311yescharacteristic
278C22×C22⋊C4C2312yes—
279C22×C22⋊C4C2312yes—
280C22×C22⋊C4C2318yes—
281C22×C22⋊C4C2314yes—
282C22×C22⋊C4C2314yes—
283C22×C22⋊C4C2314yes—
284C22×C22⋊C4C2314yes—
285C22×C22⋊C4C2314yes—
286C22×C22⋊C4C2312yes—
287C22×C22⋊C4C2311yescharacteristic
288C22×C42C2312yes—
289C22×C42C2312yes—
290C22×C42C2311yescharacteristic
291C22×C42C2311yescharacteristic
292C22×C42C2312yes—
293#399C2318yes—
294#399C2318yes—
295#399C2318yes—
296#399C2318yes—
297#399C2318yes—
298#399C2318yes—
299#398C2318yes—
300#398C2318yes—
301#397C2318yes—
302#397C2318yes—
303#396C2318yes—
304#396C2318yes—
305#396C2318yes—
306#396C2318yes—
307#396C2318yes—
308#396C2318yes—
309#396C2318yes—
310#396C2318yes—
311#394C2318yes—
312#394C2318yes—
313#394C2318yes—
314#394C2318yes—
315#394C2318yes—
316#394C2318yes—
317#394C2318yes—
318#394C2318yes—
319#394C2318yes—
320#394C2318yes—
321#392C2318yes—
322#392C2318yes—
323#392C2318yes—
324#392C2318yes—
325#392C2318yes—
326#392C2318yes—
327#392C2318yes—
328#392C2318yes—
329#391C2314yes—
330#391C2314yes—
331#390C2312yes—
332#390C2312yes—
333#390C2314yes—
334#390C2318yes—
335#390C2314yes—
336#390C2318yes—
337#390C2314yes—
338#390C2314yes—
339#390C2318yes—
340#390C2314yes—
341#390C2318yes—
342#390C2314yes—
343#390C2318yes—
344#390C2314yes—
345#390C2314yes—
346#390C2314yes—
347#390C2314yes—
348#390C2314yes—
349#390C2314yes—
350#390C2314yes—
351#390C2318yes—
352#390C2318yes—
353#390C2314yes—
354#389C2312yes—
355#389C2312yes—
356#389C2314yes—
357#389C2318yes—
358#389C2314yes—
359#389C2314yes—
360#389C2314yes—
361#389C2318yes—
362#389C2318yes—
363#389C2314yes—
364#389C2318yes—
365#389C2314yes—
366#389C2318yes—
367#388C2314yes—
368#388C2314yes—
369#388C2314yes—
370#388C2314yes—
371#388C2318yes—
372#388C2318yes—
373#388C2318yes—
374#388C2318yes—
375#388C2318yes—
376#388C2318yes—
377#388C2318yes—
378#388C2318yes—
379#387C2314yes—
380#387C2314yes—
381#387C2318yes—
382#387C2318yes—
383#387C2318yes—
384#387C2318yes—
385#386C2314yes—
386#386C2314yes—
387#386C2314yes—
388#386C2314yes—
389#386C2314yes—
390#386C2314yes—
391#386C2318yes—
392#386C2318yes—
393#386C2318yes—
394#386C2318yes—
395#386C2318yes—
396#386C2318yes—
397#386C2318yes—
398#386C2318yes—
399#386C2318yes—
400#386C2318yes—
401#385C2314yes—
402#385C2314yes—
403#385C2314yes—
404#385C2314yes—
405#385C2318yes—
406#385C2318yes—
407#385C2318yes—
408#385C2318yes—
409#384C2312yes—
410#384C2314yes—
411#384C2312yes—
412#384C2314yes—
413#381C2314yes—
414#380C2312yes—
415#380C2312yes—
416#380C2314yes—
417#380C2318yes—
418#380C2314yes—
419#380C2318yes—
420#380C2318yes—
421#379C2314yes—
422C4×C4⋊C4C2314yes—
423C4×C4⋊C4C2312yes—
424C4×C4⋊C4C2314yes—
425C4×C4⋊C4C2312yes—
426C4×C4⋊C4C2312yes—
427C4×C4⋊C4C2314yes—
428C4×C4⋊C4C2312yes—
429C4×C22⋊C4C2314yes—
430C4×C22⋊C4C2318yes—
431C4×C22⋊C4C2314yes—
432C4×C22⋊C4C2318yes—
433C4×C22⋊C4C2318yes—
434C4×C22⋊C4C2318yes—
435C4×C22⋊C4C2314yes—
436C4×C22⋊C4C2314yes—
437C2×#95C2311yescharacteristic
438C2×#95C2312yes—
439C2×#95C2311yescharacteristic
440C2×#95C2312yes—
441C2×#95C2314yes—
442C2×#95C2314yes—
443C2×#95C2312yes—
444C2×#95C2312yes—
445C25C2414yes—
446C25C2412yes—
447C25C2411yescharacteristic
448C2×#41—216no—
449C2×#41—48no—
450C2×#41—48no—
451C22×Q8—42no—
452C22×Q8—42no—
453C22×Q8C2×D418yescomplemented
454C22×Q8C2412yes—
455C22×Q8C2412yes—
456C22×D4—28no—
457C22×D4—216no—
458C22×D4—28no—
459C22×D4—216no—
460C22×D4—28no—
461C22×D4—216no—
462C22×D4—28no—
463C22×D4—44no—
464C22×D4—48no—
465C22×D4—44no—
466C22×D4—48no—
467C22×D4—84no—
468C22×D4C2414yes—
469C22×D4C2418yes—
470C22×D4C2414yes—
471C22×D4C2418yes—
472C22×D4C2414yes—
473C22×D4C2418yes—
474C22×D4C2414yes—
475C22×D4C2412yes—
476C22×D4C2412yes—
477C22×D4C2414yes—
478C22×D4C2418yes—
479C22×D4C2414yes—
480C22×D4C2418yes—
481C22×D4C2414yes—
482C22×D4C2414yes—
483C22×D4C2418yes—
484C23×C4—28no—
485C23×C4—28no—
486C23×C4—42no—
487C23×C4—42no—
488C23×C4—44no—
489C23×C4—44no—
490C23×C4—44no—
491C23×C4—82no—
492C23×C4C2×D418yes—
493C23×C4C2412yes—
494C23×C4C2414yes—
495C23×C4C2414yes—
496C23×C4C2414yes—
497C23×C4C2412yes—
498C23×C4C2411yescharacteristic
499C23×C4C2412yes—
500C23×C4C2412yes—
501C23×C4C2414yes—
502C23×C4C2412yes—
503C23×C4C2411yescharacteristic
504C23×C4C2418yes—
505C23×C4C2418yes—
506C23×C4C2411yescharacteristic
507C23×C4C2412yes—
508C23×C4C2414yes—
509C23×C4C2412yes—
510C23×C4C2412yes—
511C23×C4C2412yes—
512C23×C4C2411yescharacteristic
513C23×C4C2411yescharacteristic
514C23×C4C2411yescharacteristic
515#127—44no—
516#127—44no—
517#127—48no—
518#127—84no—
519#126—232no—
520#126—232no—
521#126—232no—
522#125—216no—
523#125—232no—
524#124—216no—
525#124—232no—
526#123—232no—
527#123—232no—
528#123—232no—
529#123—232no—
530#123—232no—
531#123—216no—
532#123—232no—
533#123—416no—
534C22⋊Q8—216no—
535C22⋊Q8—232no—
536C22⋊Q8C2×D4132yescomplemented
537C22⋊Q8C2×D4132yescomplemented
538#121—216no—
539#121—216no—
540#121—216no—
541#121—216no—
542#121—232no—
543#121—232no—
544#121—28no—
545#121—28no—
546#121—216no—
547#121—216no—
548#121—216no—
549#121—232no—
550#121—216no—
551#121—416no—
552#121—416no—
553#121—48no—
554#121—416no—
555#121—416no—
556#121—416no—
557#121—416no—
558#121—48no—
559#121—48no—
560#121—88no—
561#120—232no—
562#120—232no—
563#120—216no—
564#120—232no—
565#120—416no—
566C4×Q8—216no—
567C4×Q8—28no—
568C4×Q8—48no—
569C4×Q8—44no—
570C4×D4—216no—
571C4×D4—216no—
572C4×D4—216no—
573C4×D4—216no—
574C4×D4—232no—
575C4×D4—232no—
576C4×D4—232no—
577C4×D4—216no—
578C4×D4—232no—
579C4×D4—232no—
580C4×D4—48no—
581C4×D4—44no—
582C4×D4—44no—
583C4×D4—84no—
584#117—216no—
585#117—232no—
586#117—232no—
587C2×C4⋊C4—28no—
588C2×C4⋊C4—28no—
589C2×C4⋊C4—24no—
590C2×C4⋊C4—28no—
591C2×C4⋊C4—44no—
592C2×C4⋊C4—48no—
593C2×C4⋊C4—42no—
594C2×C4⋊C4—44no—
595C2×C4⋊C4—44no—
596C2×C4⋊C4—48no—
597C2×C4⋊C4—82no—
598C2×C4⋊C4C2×D418yescomplemented
599C2×C4⋊C4C2×D4116yescomplemented
600C2×C4⋊C4C2411yescharacteristic
601C2×C4⋊C4C2412yes—
602C2×C4⋊C4C2412yes—
603C2×C4⋊C4C2414yes—
604C2×C4⋊C4C2414yes—
605C2×C4⋊C4C2414yes—
606C2×C4⋊C4C2414yes—
607C2×C4⋊C4C2414yes—
608C2×C4⋊C4C2414yes—
609C2×C4⋊C4C2418yes—
610C2×C4⋊C4C2418yes—
611C2×C4⋊C4C2418yes—
612C2×C4⋊C4C2418yes—
613C2×C4⋊C4C2412yes—
614C2×C4⋊C4C2412yes—
615C2×C4⋊C4C2414yes—
616C2×C4⋊C4C2414yes—
617C2×C4⋊C4C2414yes—
618C2×C4⋊C4C2412yes—
619C2×C4⋊C4C2414yes—
620C2×C4⋊C4C2418yes—
621C2×C4⋊C4C2418yes—
622C2×C4⋊C4C2418yes—
623C2×C4⋊C4C2412yes—
624C2×C4⋊C4C2412yes—
625C2×C4⋊C4C2412yes—
626C2×C4⋊C4C2414yes—
627C2×C4⋊C4C2414yes—
628C2×C4⋊C4C2412yes—
629C2×C4⋊C4C2412yes—
630C2×C4⋊C4C2418yes—
631C2×C4⋊C4C2412yes—
632C2×C4⋊C4C2411yescharacteristic
633C2×C22⋊C4—28no—
634C2×C22⋊C4—24no—
635C2×C22⋊C4—28no—
636C2×C22⋊C4—216no—
637C2×C22⋊C4—232no—
638C2×C22⋊C4—48no—
639C2×C22⋊C4—48no—
640C2×C22⋊C4—48no—
641C2×C22⋊C4—84no—
642C2×C22⋊C4C2×D4116yes—
643C2×C22⋊C4#4118yescomplemented
644C2×C22⋊C4C2414yes—
645C2×C22⋊C4C2418yes—
646C2×C22⋊C4C2414yes—
647C2×C22⋊C4C2414yes—
648C2×C22⋊C4C2418yes—
649C2×C22⋊C4C2418yes—
650C2×C22⋊C4C2414yes—
651C2×C22⋊C4C2418yes—
652C2×C22⋊C4C2414yes—
653C2×C22⋊C4C2418yes—
654C2×C22⋊C4C2418yes—
655C2×C22⋊C4C2418yes—
656C2×C22⋊C4C2418yes—
657C2×C22⋊C4C2418yes—
658C2×C22⋊C4C2414yes—
659C2×C22⋊C4C2414yes—
660C2×C22⋊C4C2418yes—
661C2×C22⋊C4C2418yes—
662C2×C22⋊C4C2418yes—
663C2×C22⋊C4C2418yes—
664C2×C22⋊C4C2418yes—
665C2×C22⋊C4C2418yes—
666C2×C22⋊C4C2418yes—
667C2×C22⋊C4C2418yes—
668C2×C22⋊C4C2418yes—
669C2×C22⋊C4C2414yes—
670C2×C22⋊C4C2414yes—
671C2×C22⋊C4C2418yes—
672C2×C22⋊C4C2418yes—
673C2×C22⋊C4C2414yes—
674C2×C22⋊C4C2414yes—
675C2×C22⋊C4C2418yes—
676C2×C22⋊C4C2414yes—
677C2×C42—28no—
678C2×C42—42no—
679C2×C42—44no—
680C2×C42—42no—
681C2×C42—82no—
682C2×C42C2418yes—
683C2×C42C2418yes—
684C2×C42C2414yes—
685C2×C42C2414yes—
686C2×C42C2412yes—
687C2×C42C2414yes—
688C2×C42C2412yes—
689C2×C42C2414yes—
690C2×C42C2414yes—
691C2×C42C2412yes—
692C2×C42C2414yes—
693C2×C42C2412yes—
694#95C2414yes—
695#95C2418yes—
696#95C2414yes—
697#95C2418yes—
698#95C2418yes—
699#95C2418yes—
700#95C2414yes—
701#95C2414yes—
702#95C2418yes—
703#95C2418yes—
704#95C2418yes—
705#95C2414yes—
706#95C2414yes—
707#95C2414yes—
708#95C2414yes—
709#95C2414yes—
710#95C2414yes—
711C24—24no—
712C24—28no—
713C24—24no—
714C24—24no—
715C24—28no—
716C24—28no—
717C24—41no—
718C24—41no—
719C24—41no—
720C24—41no—
721C24—42no—
722C24—42no—
723C24—42no—
724C24—42no—
725C24—44no—
726C24—44no—
727C24—44no—
728C24—44no—
729C24C22×D414yes—
730C24C2×#4114yes—
731C24H(5,𝔽2)14yes—
732C24C2518yes—
733C24C2514yes—
734C24C2512yes—
735C24C2511yescharacteristic
736#41—832no—
737C2×Q8—24no—
738C2×Q8—24no—
739C2×Q8—42no—
740C2×Q8—42no—
741C2×Q8—416no—
742C2×Q8C22×D418yes—
743C2×Q8C22×D418yes—
744C2×D4—28no—
745C2×D4—216no—
746C2×D4—28no—
747C2×D4—216no—
748C2×D4—28no—
749C2×D4—216no—
750C2×D4—28no—
751C2×D4—216no—
752C2×D4—216no—
753C2×D4—28no—
754C2×D4—28no—
755C2×D4—216no—
756C2×D4—28no—
757C2×D4—216no—
758C2×D4—216no—
759C2×D4—28no—
760C2×D4—24no—
761C2×D4—28no—
762C2×D4—24no—
763C2×D4—28no—
764C2×D4—28no—
765C2×D4—216no—
766C2×D4—28no—
767C2×D4—44no—
768C2×D4—42no—
769C2×D4—42no—
770C2×D4—44no—
771C2×D4—44no—
772C2×D4—48no—
773C2×D4—48no—
774C2×D4—48no—
775C2×D4—48no—
776C2×D4—48no—
777C2×D4—48no—
778C2×D4—44no—
779C2×D4—42no—
780C2×D4—48no—
781C2×D4—44no—
782C2×D4—42no—
783C2×D4—44no—
784C2×D4—48no—
785C2×D4—48no—
786C2×D4—44no—
787C2×D4—44no—
788C2×D4—44no—
789C2×D4—44no—
790C2×D4—44no—
791C2×D4—44no—
792C2×D4—432no—
793C2×D4—464no—
794C2×D4—816no—
795C2×D4—832no—
796C22×C4—22no—
797C22×C4—24no—
798C22×C4—22no—
799C22×C4—24no—
800C22×C4—24no—
801C22×C4—28no—
802C22×C4—24no—
803C22×C4—28no—
804C22×C4—24no—
805C22×C4—28no—
806C22×C4—28no—
807C22×C4—24no—
808C22×C4—24no—
809C22×C4—24no—
810C22×C4—22no—
811C22×C4—22no—
812C22×C4—28no—
813C22×C4—24no—
814C22×C4—28no—
815C22×C4—24no—
816C22×C4—28no—
817C22×C4—28no—
818C22×C4—28no—
819C22×C4—216no—
820C22×C4—216no—
821C22×C4—28no—
822C22×C4—416no—
823C22×C4—41no—
824C22×C4—42no—
825C22×C4—41no—
826C22×C4—41no—
827C22×C4—42no—
828C22×C4—42no—
829C22×C4—42no—
830C22×C4—41no—
831C22×C4—42no—
832C22×C4—41no—
833C22×C4—44no—
834C22×C4—41no—
835C22×C4—42no—
836C22×C4—42no—
837C22×C4—41no—
838C22×C4—41no—
839C22×C4—42no—
840C22×C4—42no—
841C22×C4—44no—
842C22×C4—44no—
843C22×C4—42no—
844C22×C4—41no—
845C22×C4—42no—
846C22×C4—48no—
847C22×C4—48no—
848C22×C4—44no—
849C22×C4—44no—
850C22×C4—42no—
851C22×C4—48no—
852C22×C4—41no—
853C22×C4—42no—
854C22×C4—48no—
855C22×C4—816no—
856C22×C4—816no—
857C22×C4C22×D418yes—
858C22×C4C22×D414yes—
859C22×C4C22×D418yes—
860C22×C4C22×D418yes—
861C22×C4C22×D418yes—
862C22×C4C22×D414yes—
863C22×C4C2×#4114yes—
864C22×C4C2×#4114yes—
865C22×C4C2512yes—
866C22×C4C2514yes—
867C22×C4C2514yes—
868C22×C4C2514yes—
869C22×C4C2512yes—
870C22×C4C2512yes—
871C22×C4C2518yes—
872C22×C4C2514yes—
873C22×C4C2514yes—
874C22×C4C2514yes—
875C22×C4C2512yes—
876C22×C4C2511yescharacteristic
877C22×C4C2512yes—
878C22×C4C2512yes—
879C22×C4C2512yes—
880C22×C4C2511yescharacteristic
881C4⋊C4—28no—
882C4⋊C4—28no—
883C4⋊C4—28no—
884C4⋊C4—28no—
885C4⋊C4—216no—
886C4⋊C4—216no—
887C4⋊C4—216no—
888C4⋊C4—216no—
889C4⋊C4—24no—
890C4⋊C4—28no—
891C4⋊C4—24no—
892C4⋊C4—28no—
893C4⋊C4—24no—
894C4⋊C4—22no—
895C4⋊C4—28no—
896C4⋊C4—24no—
897C4⋊C4—28no—
898C4⋊C4—42no—
899C4⋊C4—44no—
900C4⋊C4—44no—
901C4⋊C4—48no—
902C4⋊C4—48no—
903C4⋊C4—48no—
904C4⋊C4—42no—
905C4⋊C4—42no—
906C4⋊C4—42no—
907C4⋊C4—42no—
908C4⋊C4—44no—
909C4⋊C4—44no—
910C4⋊C4C22×D418yes—
911C4⋊C4C22×D4132yes—
912C4⋊C4C22×D418yes—
913C4⋊C4H(5,𝔽2)14yes—
914C22⋊C4—28no—
915C22⋊C4—28no—
916C22⋊C4—28no—
917C22⋊C4—216no—
918C22⋊C4—28no—
919C22⋊C4—216no—
920C22⋊C4—216no—
921C22⋊C4—28no—
922C22⋊C4—216no—
923C22⋊C4—216no—
924C22⋊C4—216no—
925C22⋊C4—216no—
926C22⋊C4—216no—
927C22⋊C4—28no—
928C22⋊C4—216no—
929C22⋊C4—28no—
930C22⋊C4—216no—
931C22⋊C4—216no—
932C22⋊C4—48no—
933C22⋊C4—48no—
934C22⋊C4—48no—
935C22⋊C4—48no—
936C22⋊C4—48no—
937C22⋊C4—48no—
938C22⋊C4—48no—
939C22⋊C4—44no—
940C22⋊C4—44no—
941C22⋊C4—44no—
942C22⋊C4—48no—
943C22⋊C4—48no—
944C22⋊C4—44no—
945C22⋊C4C22×D4132yes—
946C22⋊C4C2×#41116yes—
947C42—28no—
948C42—28no—
949C42—216no—
950C42—216no—
951C42—28no—
952C42—24no—
953C42—24no—
954C42—42no—
955C42—44no—
956C42—42no—
957C42—44no—
958C42—44no—
959C23—21no—
960C23—22no—
961C23—21no—
962C23—22no—
963C23—21no—
964C23—22no—
965C23—21no—
966C23—22no—
967C23—24no—
968C23—28no—
969C23—24no—
970C23—28no—
971C23—28no—
972C23—24no—
973C23—28no—
974C23—24no—
975C23—24no—
976C23—28no—
977C23—28no—
978C23—24no—
979C23—24no—
980C23—28no—
981C23—44no—
982C23—44no—
983C23—44no—
984C23—44no—
985C23—44no—
986C23—44no—
987C23—48no—
988C23—48no—
989C23—48no—
990C23—416no—
991C23—84no—
992C23—84no—
993C23—84no—
994C23—84no—
995C23—88no—
996C23—88no—
997C23—88no—
998C23—88no—
999C23—88no—
1000C23—88no—
1001C23#550116yescomplemented
1002C23C23×D412yes—
1003C23C23×D414yes—
1004C23C22×#4114yes—
1005C23C22×#4112yes—
1006C23C2×H(5,𝔽2)14yes—
1007C23C2×H(5,𝔽2)12yes—
1008C23C2611yescharacteristic
1009Q8—216no—
1010Q8—48no—
1011D4—416no—
1012D4—432no—
1013D4—416no—
1014D4—432no—
1015D4—416no—
1016D4—84no—
1017D4—88no—
1018D4—84no—
1019D4—88no—
1020D4—816no—
1021D4—88no—
1022D4—816no—
1023D4—816no—
1024D4—816no—
1025D4—164no—
1026D4—164no—
1027C2×C4—22no—
1028C2×C4—24no—
1029C2×C4—21no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—21no—
1034C2×C4—22no—
1035C2×C4—24no—
1036C2×C4—22no—
1037C2×C4—24no—
1038C2×C4—22no—
1039C2×C4—22no—
1040C2×C4—24no—
1041C2×C4—216no—
1042C2×C4—28no—
1043C2×C4—24no—
1044C2×C4—24no—
1045C2×C4—28no—
1046C2×C4—24no—
1047C2×C4—24no—
1048C2×C4—28no—
1049C2×C4—22no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—24no—
1054C2×C4—22no—
1055C2×C4—24no—
1056C2×C4—28no—
1057C2×C4—24no—
1058C2×C4—24no—
1059C2×C4—22no—
1060C2×C4—24no—
1061C2×C4—22no—
1062C2×C4—24no—
1063C2×C4—22no—
1064C2×C4—24no—
1065C2×C4—22no—
1066C2×C4—24no—
1067C2×C4—44no—
1068C2×C4—48no—
1069C2×C4—48no—
1070C2×C4—48no—
1071C2×C4—44no—
1072C2×C4—44no—
1073C2×C4—48no—
1074C2×C4—416no—
1075C2×C4—48no—
1076C2×C4—416no—
1077C2×C4—416no—
1078C2×C4—816no—
1079C2×C4—88no—
1080C2×C4—816no—
1081C2×C4—84no—
1082C2×C4—82no—
1083C2×C4—82no—
1084C2×C4—84no—
1085C2×C4—88no—
1086C2×C4—84no—
1087C2×C4C23×D418yes—
1088C2×C4C23×D418yes—
1089C2×C4C23×D414yes—
1090C2×C4C23×D412yes—
1091C2×C4C23×D412yes—
1092C2×C4C22×#4114yes—
1093C2×C4C22×#4114yes—
1094C2×C4C2×H(5,𝔽2)14yes—
1095C2×C4C2×H(5,𝔽2)12yes—
1096C2×C4#58512yes—
1097C22—22no—
1098C22—24no—
1099C22—22no—
1100C22—24no—
1101C22—22no—
1102C22—24no—
1103C22—22no—
1104C22—24no—
1105C22—22no—
1106C22—24no—
1107C22—22no—
1108C22—24no—
1109C22—416no—
1110C22—44no—
1111C22—48no—
1112C22—44no—
1113C22—48no—
1114C22—44no—
1115C22—48no—
1116C22—48no—
1117C22—44no—
1118C22—44no—
1119C22—48no—
1120C22—48no—
1121C22—44no—
1122C22—44no—
1123C22—48no—
1124C22—816no—
1125C22—1616no—
1126C22C2×#55018yes—
1127C22C2×#55014yes—
1128C22C24×D411yescharacteristic
1129C22C23×#4111yescharacteristic
1130C22C22×H(5,𝔽2)11yescharacteristic
1131C22C22×H(5,𝔽2)11yescharacteristic
1132C22C2×#58511yescharacteristic
1133C22H(7,𝔽2)11yescharacteristic
1134C222−1+611yescharacteristic
1135C4—24no—
1136C4—24no—
1137C4—24no—
1138C4—22no—
1139C4—28no—
1140C4—28no—
1141C4—24no—
1142C4—44no—
1143C4—44no—
1144C4—42no—
1145C4—44no—
1146C4—42no—
1147C4—42no—
1148C4—44no—
1149C4—48no—
1150C4#349614yes—
1151C2—28no—
1152C2—24no—
1153C2—84no—
1154C2—88no—
1155C2C22×#55011yescharacteristic
1156C2C2×#349611yescharacteristic
1157C2#6285311yescharacteristic
1158C2#6289211yescharacteristic
1159C2#6290111yescharacteristic
1160C2#6298411yescharacteristic
1161C2#6299211yescharacteristic
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×#3505C2semidirect
2. #59047C2semidirect
3. #59046C2semidirect
4. #59022C2semidirect
5. #59003C2semidirect
6. #43913C2semidirect
7. #43029C2semidirect
8. #39743C2semidirect
9. #39742C2semidirect
10. #39742C2semidirect
11. #39738C2semidirect
12. #36596C2semidirect
13. #36576C2semidirect
14. #35358C2semidirect
15. #35001C2semidirect
16. #35001C2semidirect
17. C2×#2416C2semidirect
18. #34273C2semidirect
19. C2×#2360C2semidirect
20. C4×#534C2semidirect
22. C2×#553C22semidirect
23. C2×#553C22semidirect
24. C2×#552C22semidirect
25. C2×#551C22semidirect
26. C2×#550C22semidirect
27. C2×#548C22semidirect
28. C2×#546C22semidirect
29. C2×#539C22semidirect
30. C2×#538C22semidirect
35. C2×#529C22semidirect
36. C2×#525C22semidirect
40. C22×#121C22semidirect
42. C22×C4×Q8C22semidirect
45. #2856C22semidirect
46. #2856C22semidirect
47. #2856C22semidirect
48. #2856C22semidirect
49. #2733C22semidirect
50. #2732C22semidirect
51. #2730C22semidirect
52. #2727C22semidirect
53. #2727C22semidirect
54. #2721C22semidirect
55. #2714C22semidirect
56. #2705C22semidirect
57. #2705C22semidirect
58. #2705C22semidirect
59. #2694C22semidirect
60. #2682C22semidirect
61. #2682C22semidirect
62. #2673C22semidirect
63. #2656C22semidirect
64. #2656C22semidirect
65. #2656C22semidirect
66. #2656C22semidirect
67. #2554C22semidirect
68. #2552C22semidirect
69. #2548C22semidirect
70. #2548C22semidirect
71. #2543C22semidirect
72. #2543C22semidirect
73. #2541C22semidirect
74. #2539C22semidirect
75. #2539C22semidirect
76. #2539C22semidirect
77. #2538C22semidirect
78. #2538C22semidirect
79. #2512C22semidirect
80. #2501C22semidirect
81. #2501C22semidirect
82. #2490C22semidirect
83. #2479C22semidirect
84. #2471C22semidirect
85. #2467C22semidirect
86. #2456C22semidirect
87. #2454C22semidirect
88. #2454C22semidirect
89. #2448C22semidirect
90. #2445C22semidirect
91. #2441C22semidirect
92. #2441C22semidirect
93. #2433C22semidirect
94. #2433C22semidirect
95. #2431C22semidirect
96. #2428C22semidirect
97. #2428C22semidirect
98. #2426C22semidirect
99. #2426C22semidirect
100. #2425C22semidirect
101. #2425C22semidirect
102. #2424C22semidirect
103. #2424C22semidirect
104. #2423C22semidirect
108. #2416C22semidirect
109. #2416C22semidirect
110. #2416C22semidirect
111. #2416C22semidirect
112. #2416C22semidirect
113. #2414C22semidirect
114. #2414C22semidirect
115. #2413C22semidirect
116. #2412C22semidirect
117. #2411C22semidirect
118. #2410C22semidirect
119. #2407C22semidirect
120. C2×#396C22semidirect
121. C2×#394C22semidirect
122. #2366C22semidirect
123. #2363C22semidirect
124. #2360C22semidirect
125. #2360C22semidirect
126. #2360C22semidirect
127. #2359C22semidirect
128. #2359C22semidirect
129. #2358C22semidirect
130. #2358C22semidirect
131. #2354C22semidirect
132. Q8×C4⋊C4C22semidirect
133. #2341C22semidirect
134. #2325C22semidirect
135. #2325C22semidirect
136. #2325C22semidirect
137. #2325C22semidirect
138. #2322C22semidirect
139. #2321C22semidirect
142. C4×#123C22semidirect
143. C4×#121C22semidirect
144. C4×#121C22semidirect
145. C4×#121C22semidirect
146. C4×#121C22semidirect
147. C4×#120C22semidirect
148. C2×#391C22semidirect
149. C2×#390C22semidirect
150. C2×#389C22semidirect
151. C2×#389C22semidirect
152. C2×#389C22semidirect
153. C2×#387C22semidirect
156. C2×#380C22semidirect
157. C2×C4×C4⋊C4C22semidirect
203. C2×C22⋊Q8D4semidirect
453. C22×Q8C2×D4semidirect
536. C22⋊Q8C2×D4semidirect
537. C22⋊Q8C2×D4semidirect
598. C2×C4⋊C4C2×D4semidirect
599. C2×C4⋊C4C2×D4semidirect
643. C2×C22⋊C4#41semidirect
1001. C23#550semidirect

Maximal subgroups

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

subgroupindex
C2×#35052
#590472
#590462
#590222
#590032
#439132
#430292
#397432
#397422
#397382
#365962
#365762
#353582
#350012
C2×#24162
#342732
C2×#23602
C4×#5342