Finite Group Databasebeta

← #7653797

Subgroups — #7653797

Order 512.

7624 conjugacy classes of subgroups.

The subgroup lattice has 1038 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3522C211yesmaximal, characteristic, complemented
2C22×#554C211yesmaximal, characteristic, complemented
3#42794C214yesmaximal, complemented
4#41957C218yesmaximal, complemented
5#39617C212yesmaximal, complemented
6#39611C214yesmaximal, complemented
7#39169C212yesmaximal, complemented
8#39161C214yesmaximal, complemented
9#39133C214yesmaximal, complemented
10#37653C218yesmaximal, complemented
11#37632C211yesmaximal, characteristic, complemented
12#37539C212yesmaximal, complemented
13#36559C212yesmaximal, complemented
14#36496C212yesmaximal, complemented
15#36103C214yesmaximal, complemented
16#35701C214yesmaximal, complemented
17#35317C211yesmaximal, characteristic, complemented
18#35237C211yesmaximal, characteristic, complemented
19#35233C212yesmaximal, complemented
20#35139C212yesmaximal, complemented
21#34965C211yesmaximal, characteristic, complemented
22#34936C212yesmaximal, complemented
23#34128C211yesmaximal, characteristic, complemented
24#3522—216no—
25C2×#559C2211yescharacteristic, complemented
26C2×#559C2212yescomplemented
27C2×Q82C2211yescharacteristic, complemented
28C2×#554—216no—
29C2×#554C2212yes—
30C2×#554C2212yes—
31C2×#554C2212yes—
32C2×#554C2212yes—
33C2×#554C2214yes—
34C2×#554C2214yes—
35C2×#554C2212yescomplemented
36C2×#554C2211yescharacteristic, complemented
37C2×#550C2211yescharacteristic, complemented
38C2×#548C2212yes—
39C2×#547C2212yes—
40C2×#547C2214yes—
41C2×#542C2212yescomplemented
42C2×#542C2214yescomplemented
43C2×#536C2214yes—
44C2×#532C2212yes—
45C2×#532C2211yescharacteristic
46C22×C4⋊Q8C2211yescharacteristic
47C2×#529C2211yescharacteristic
48C2×#529C2212yes—
49C22×#125C2212yes—
50C2×#525C2218yes—
51C22×C22⋊Q8C2214yes—
52C22×C22⋊Q8C2212yes—
53C2×#520C2212yescomplemented
54C22×C4×Q8C2211yescharacteristic
55C22×C4×D4C2212yes—
56C22×C4×D4C2211yescharacteristic
57C23×C4⋊C4C2212yes—
58#2868C2212yescomplemented
59#2861C2214yescomplemented
60#2859C2214yescomplemented
61#2858C2212yescomplemented
62#2849C2218yes—
63#2847C2214yes—
64#2821C2214yescomplemented
65#2820C2218yescomplemented
66#2732C22116yescomplemented
67#2730C22116yescomplemented
68#2683C22116yescomplemented
69#2681C22116yescomplemented
70#2677C22116yescomplemented
71#2676C22116yescomplemented
72#2664C2218yescomplemented
73#2660C2212yescomplemented
74#2660C2214yescomplemented
75#2658C2214yescomplemented
76#2641C2214yescomplemented
77#2640C2212yescomplemented
78#2636C2218yes—
79#2633C2218yescomplemented
80#2631C2214yes—
81#2628C2214yescomplemented
82#2618C2218yes—
83#2614C2214yes—
84#2611C2218yescomplemented
85#2603C2214yes—
86#2598C2218yes—
87#2567C2212yescomplemented
88#2566C2212yes—
89#2566C2214yes—
90#2566C2214yescomplemented
91#2566C2214yescomplemented
92#2566C2214yescomplemented
93#2565C2214yescomplemented
94#2563C2212yes—
95#2563C2212yescomplemented
96#2544C2214yes—
97#2544C2212yes—
98#2542C2214yes—
99#2542C2214yescomplemented
100#2542C2214yescomplemented
101#2541C2214yes—
102#2541C2212yes—
103#2540C2218yes—
104#2539C2218yes—
105#2538C2218yescomplemented
106#2535C2214yes—
107#2534C2218yes—
108#2504C2212yes—
109#2504C2211yescharacteristic
110#2503C2212yes—
111#2502C2211yescharacteristic
112#2501C2212yes—
113#2501C2214yes—
114#2501C2212yes—
115#2501C2212yes—
116#2486C2214yes—
117#2463C22116yescomplemented
118#2461C22116yescomplemented
119#2452C22116yescomplemented
120#2449C22116yescomplemented
121#2449C22116yescomplemented
122#2443C22116yescomplemented
123#2440C2218yescomplemented
124#2435C2211yescharacteristic
125#2433C2211yescharacteristic
126#2433C2212yes—
127#2426C2218yescomplemented
128#2423C2218yescomplemented
129#2416C2218yescomplemented
130#2413C2218yes—
131#2411C2214yes—
132#2407C2218yescomplemented
133#2406C2218yes—
134#2404C2214yes—
135#2397C2218yes—
136#2392C2214yes—
137#2361C2218yescomplemented
138#2356C2212yescomplemented
139#2356C2214yescomplemented
140#2351C2212yescomplemented
141D4×C4⋊C4C2218yescomplemented
142#2344C2212yes—
143#2344C2214yes—
144Q8×C22⋊C4C2212yes—
145#2328C2214yes—
146#2328C2214yes—
147#2326C2214yes—
148#2322C2218yes—
149C4×#127C2212yes—
150C4×#127C2214yes—
151C4×#127C2214yes—
152C4×#124C2212yes—
153C4×#120C2214yes—
154#2295C2212yescomplemented
155#2295C2214yescomplemented
156#2283C2211yescharacteristic
157#2283C2212yes—
158C42×Q8C2212yescomplemented
159C4×#117C2212yes—
160C4×#117C2211yescharacteristic
161C22×#41C2312yes—
162C22×#41C2312yes—
163C22×#41C2314yes—
164C23×Q8C2312yes—
165C23×Q8C2311yescharacteristic
166C23×D4C2311yescharacteristic
167C24×C4C2312yes—
168C24×C4C2314yes—
169#559—28no—
170#559—216no—
171Q82—28no—
172#554—216no—
173#554—216no—
174#554—232no—
175#554—216no—
176#554—216no—
177#554—232no—
178#554—216no—
179#554—28no—
180#550—28no—
181#548—216no—
182#547—216no—
183#547—232no—
184#542—216no—
185#542—232no—
186#536—416no—
187#532—216no—
188#532—28no—
189C2×C4⋊Q8—28no—
190C2×C4⋊Q8C2311yescharacteristic
191C2×C4⋊Q8C2312yes—
192C2×C4⋊Q8C2312yes—
193C2×C4⋊Q8C2312yes—
194C2×C4⋊Q8C2312yes—
195C2×C4⋊Q8C2312yes—
196C2×C4⋊Q8C2314yes—
197C2×C4⋊Q8C2312yes—
198C2×C4⋊Q8C2318yes—
199C2×#127C2312yes—
200C2×#127C2314yes—
201C2×#127C2311yescharacteristic
202C2×#127C2312yes—
203#529—216no—
204#529—28no—
205C2×#126C2312yes—
206C2×#126C2314yes—
207C2×#125—216no—
208C2×#125C2314yes—
209C2×#125C2314yes—
210C2×#125C2312yes—
211C2×#125C2311yescharacteristic
212C2×#125C2314yes—
213C2×#125C2314yes—
214C2×#124C2314yes—
215C2×#124C2312yes—
216C2×#124C2312yes—
217C2×#124C2312yes—
218C2×#124C2311yescharacteristic
219C2×#124C2312yes—
220C2×#124C2314yes—
221C2×#124C2318yes—
222#525—432no—
223C2×#123C2318yes—
224C2×#123C2314yes—
225C2×#123C2312yes—
226C2×#123C2314yes—
227C2×#123C2314yes—
228C2×#123C2314yes—
229C2×#123C2318yes—
230C2×#123C2318yes—
231C2×C22⋊Q8—216no—
232C2×C22⋊Q8—232no—
233C2×C22⋊Q8C2314yes—
234C2×C22⋊Q8C2318yes—
235C2×C22⋊Q8C2318yes—
236C2×C22⋊Q8C2314yes—
237C2×C22⋊Q8C2318yes—
238C2×C22⋊Q8C2318yes—
239C2×C22⋊Q8C2318yes—
240C2×C22⋊Q8C2311yescharacteristic
241C2×C22⋊Q8C2314yes—
242C2×C22⋊Q8C2314yes—
243C2×C22⋊Q8C2314yes—
244C2×C22⋊Q8C2314yes—
245C2×C22⋊Q8C2312yes—
246C2×C22⋊Q8C23116yes—
247C2×C22⋊Q8C23116yes—
248C2×#121C2312yes—
249C2×#121C2314yes—
250C2×#121C2311yescharacteristic
251C2×#121C2312yes—
252C2×#121C2312yes—
253C2×#121C2314yes—
254C2×#121C2318yes—
255C2×#121C23116yes—
256C2×#120C2314yes—
257C2×#120C2318yes—
258#520—216no—
259C2×C4×Q8D4116yescomplemented
260C2×C4×Q8C2312yes—
261C2×C4×Q8C2311yescharacteristic
262C2×C4×Q8C2312yes—
263C2×C4×Q8C2314yes—
264C2×C4×Q8C2311yescharacteristic
265C2×C4×Q8C2311yescharacteristic
266C2×C4×Q8C2312yes—
267C2×C4×Q8C2311yescharacteristic
268C2×C4×Q8C2311yescharacteristic
269C2×C4×Q8C2312yes—
270C2×C4×D4—216no—
271C2×C4×D4—28no—
272C2×C4×D4C2311yescharacteristic
273C2×C4×D4C2314yes—
274C2×C4×D4C2312yes—
275C2×C4×D4C2312yes—
276C2×C4×D4C2312yes—
277C2×C4×D4C2312yes—
278C2×C4×D4C2312yes—
279C2×C4×D4C2314yes—
280C2×C4×D4C2314yes—
281C2×C4×D4C2312yes—
282C2×C4×D4C2314yes—
283C2×C4×D4C2312yes—
284C2×C4×D4C2312yes—
285C2×C4×D4C2314yes—
286C2×C4×D4C2314yes—
287C2×C4×D4C2312yes—
288C2×C4×D4C2312yes—
289C2×C4×D4C2314yes—
290C2×C4×D4C2312yes—
291C2×C4×D4C2318yes—
292C2×C4×D4C23116yes—
293C2×C4×D4C23116yes—
294C2×#117C2314yes—
295C2×#117C2312yes—
296C2×#117C2314yes—
297C2×#117C2312yes—
298C22×C4⋊C4—216no—
299C22×C4⋊C4C2314yes—
300C22×C4⋊C4C2312yes—
301C22×C4⋊C4C2314yes—
302C22×C4⋊C4C2314yes—
303C22×C4⋊C4C2312yes—
304C22×C4⋊C4C2314yes—
305C22×C4⋊C4C2318yes—
306C22×C4⋊C4C2311yescharacteristic
307C22×C4⋊C4C2312yes—
308C22×C4⋊C4C2314yes—
309C22×C4⋊C4C2311yescharacteristic
310C22×C4⋊C4C2312yes—
311C22×C22⋊C4C2312yes—
312C22×C22⋊C4C2314yes—
313C22×C42C2312yes—
314C22×C42C2311yescharacteristic
315#400C2318yes—
316#399C2318yes—
317#399C2318yes—
318#399C2318yes—
319#399C23116yes—
320#399C23116yes—
321#398C23116yes—
322#398C2318yes—
323#398C2314yes—
324#398C23116yes—
325#397C2314yes—
326#397C2318yes—
327#397C2318yes—
328#396C23116yes—
329#396C23116yes—
330#396C23116yes—
331#396C2318yes—
332#396C23116yes—
333#395C23116yes—
334#395C2318yes—
335#395C2318yes—
336#394C23116yes—
337#394C2314yes—
338#394C23116yes—
339#394C23116yes—
340#394C2318yes—
341#393C2318yes—
342#393C2318yes—
343#393C2318yes—
344#392C2318yes—
345#392C2314yes—
346#392C2318yes—
347#392C23116yes—
348#391C2312yes—
349#391C2314yes—
350#391C2314yes—
351#391C2318yes—
352#390C2312yes—
353#390C2314yes—
354#390C2314yes—
355#390C2312yes—
356#390C2312yes—
357#390C2314yes—
358#390C2318yes—
359#390C23116yes—
360#390C23116yes—
361#390C2314yes—
362#390C2314yes—
363#390C2318yes—
364#389C2318yes—
365#389C23116yes—
366#389C2314yes—
367#389C2318yes—
368#389C23116yes—
369#388C23116yes—
370#388C23116yes—
371#388C2318yes—
372#388C23116yes—
373#387C23116yes—
374#387C2318yes—
375#387C2318yes—
376#387C2318yes—
377#386C2318yes—
378#386C23116yes—
379#386C23116yes—
380#386C23116yes—
381#386C23116yes—
382#386C23116yes—
383#386C2318yes—
384#386C2314yes—
385#385C23116yes—
386#385C2318yes—
387#385C23116yes—
388#385C23116yes—
389#385C23116yes—
390#385C2314yes—
391#385C23116yes—
392#384C2314yes—
393#384C2312yes—
394#384C2314yes—
395#384C2314yes—
396#384C2318yes—
397#383C2312yes—
398#383C2314yes—
399#382C2314yes—
400#382C2314yes—
401#382C2314yes—
402#382C2312yes—
403#382C2312yes—
404#381C2318yes—
405#381C2314yes—
406#381C2312yes—
407#380C2318yes—
408#380C2318yes—
409#380C2312yes—
410#380C2314yes—
411#379C2314yes—
412C4×C4⋊C4C2312yes—
413C4×C4⋊C4C2314yes—
414C4×C4⋊C4C2314yes—
415C4×C4⋊C4C2312yes—
416C4×C4⋊C4C2314yes—
417C4×C4⋊C4C2318yes—
418C4×C4⋊C4C2312yes—
419C4×C4⋊C4C2314yes—
420C4×C22⋊C4C2314yes—
421C4×C22⋊C4C2312yes—
422C4×C22⋊C4C2318yes—
423C4×C22⋊C4C2311yescharacteristic
424C4×C22⋊C4C2312yes—
425C4×C22⋊C4C2311yescharacteristic
426#376C2314yes—
427#376C2312yes—
428#376C2312yes—
429#376C2314yes—
430C43C2314yes—
431C43C2312yes—
432C25C2412yes—
433C2×#41—28no—
434C2×#41—28no—
435C2×#41—216no—
436C2×#41—416no—
437C2×#41—48no—
438C2×#41—48no—
439C22×Q8—28no—
440C22×Q8—48no—
441C22×Q8—44no—
442C22×Q8C2×D418yes—
443C22×Q8C2411yescharacteristic
444C22×Q8C2411yescharacteristic
445C22×Q8C2411yescharacteristic
446C22×Q8C2414yes—
447C22×Q8C2414yes—
448C22×Q8C2414yes—
449C22×Q8C2412yes—
450C22×Q8C2412yes—
451C22×D4—28no—
452C22×D4—24no—
453C22×D4C2412yes—
454C22×D4C2411yescharacteristic
455C22×D4C2412yes—
456C22×D4C2412yes—
457C22×D4C2412yes—
458C22×D4C2414yes—
459C22×D4C2418yes—
460C22×D4C2412yes—
461C22×D4C2414yes—
462C22×D4C24116yes—
463C22×D4C2414yes—
464C22×D4C2412yes—
465C23×C4—28no—
466C23×C4—216no—
467C23×C4—48no—
468C23×C4—416no—
469C23×C4C2414yes—
470C23×C4C2414yes—
471C23×C4C2412yes—
472C23×C4C2411yescharacteristic
473C23×C4C2412yes—
474C23×C4C2411yescharacteristic
475C23×C4C2411yescharacteristic
476C23×C4C2412yes—
477C23×C4C2418yes—
478C23×C4C2418yes—
479C23×C4C2414yes—
480C23×C4C2414yes—
481C23×C4C2414yes—
482C23×C4C2414yes—
483C23×C4C2414yes—
484C23×C4C2412yes—
485C4⋊Q8—28no—
486C4⋊Q8—216no—
487C4⋊Q8—28no—
488C4⋊Q8—28no—
489C4⋊Q8—28no—
490C4⋊Q8—28no—
491C4⋊Q8—28no—
492C4⋊Q8—24no—
493C4⋊Q8—416no—
494#127—28no—
495#127—216no—
496#127—28no—
497#127—24no—
498#126—216no—
499#126—28no—
500#125—216no—
501#125—216no—
502#125—216no—
503#125—216no—
504#125—28no—
505#125—24no—
506#124—28no—
507#124—216no—
508#124—28no—
509#124—28no—
510#124—24no—
511#124—216no—
512#124—28no—
513#124—416no—
514#123—28no—
515#123—216no—
516#123—216no—
517#123—216no—
518#123—216no—
519#123—232no—
520#123—416no—
521#123—416no—
522C22⋊Q8—216no—
523C22⋊Q8—216no—
524C22⋊Q8—232no—
525C22⋊Q8—28no—
526C22⋊Q8—216no—
527C22⋊Q8—24no—
528C22⋊Q8—232no—
529C22⋊Q8—232no—
530C22⋊Q8—232no—
531C22⋊Q8—232no—
532C22⋊Q8—216no—
533C22⋊Q8—216no—
534C22⋊Q8—216no—
535C22⋊Q8—432no—
536C22⋊Q8—432no—
537#121—24no—
538#121—28no—
539#121—28no—
540#121—216no—
541#121—28no—
542#121—216no—
543#121—432no—
544#121—416no—
545#120—216no—
546#120—416no—
547C4×Q8—28no—
548C4×Q8—28no—
549C4×Q8—24no—
550C4×Q8—48no—
551C4×Q8C2×D418yes—
552C4×Q8C2×D4116yes—
553C4×Q8C2×D418yes—
554C4×Q8C2×D418yes—
555C4×Q8C2×D418yes—
556C4×Q8C2×D4116yes—
557C4×D4—28no—
558C4×D4—216no—
559C4×D4—28no—
560C4×D4—216no—
561C4×D4—216no—
562C4×D4—28no—
563C4×D4—216no—
564C4×D4—28no—
565C4×D4—216no—
566C4×D4—28no—
567C4×D4—216no—
568C4×D4—28no—
569C4×D4—216no—
570C4×D4—28no—
571C4×D4—28no—
572C4×D4—24no—
573C4×D4—28no—
574C4×D4—28no—
575C4×D4—28no—
576C4×D4—432no—
577C4×D4—432no—
578C4×D4—416no—
579#117—216no—
580#117—28no—
581#117—216no—
582#117—28no—
583C2×C4⋊C4—216no—
584C2×C4⋊C4—28no—
585C2×C4⋊C4—24no—
586C2×C4⋊C4—28no—
587C2×C4⋊C4—216no—
588C2×C4⋊C4—216no—
589C2×C4⋊C4—216no—
590C2×C4⋊C4—232no—
591C2×C4⋊C4—28no—
592C2×C4⋊C4—216no—
593C2×C4⋊C4C2×D418yes—
594C2×C4⋊C4C2×D4116yes—
595C2×C4⋊C4C2418yes—
596C2×C4⋊C4C2418yes—
597C2×C4⋊C4C2414yes—
598C2×C4⋊C4C2414yes—
599C2×C4⋊C4C2414yes—
600C2×C4⋊C4C2412yes—
601C2×C4⋊C4C2412yes—
602C2×C4⋊C4C2412yes—
603C2×C4⋊C4C2414yes—
604C2×C4⋊C4C2414yes—
605C2×C4⋊C4C2412yes—
606C2×C4⋊C4C2414yes—
607C2×C4⋊C4C2418yes—
608C2×C4⋊C4C2418yes—
609C2×C4⋊C4C2412yes—
610C2×C4⋊C4C2418yes—
611C2×C4⋊C4C2414yes—
612C2×C4⋊C4C2411yescharacteristic
613C2×C4⋊C4C2411yescharacteristic
614C2×C4⋊C4C2412yes—
615C2×C4⋊C4C2412yes—
616C2×C4⋊C4C2414yes—
617C2×C4⋊C4C24116yes—
618C2×C4⋊C4C2414yes—
619C2×C4⋊C4C2414yes—
620C2×C4⋊C4C2412yes—
621C2×C4⋊C4C24116yes—
622C2×C4⋊C4C2418yes—
623C2×C4⋊C4C2418yes—
624C2×C4⋊C4C24116yes—
625C2×C4⋊C4C2411yescharacteristic
626C2×C4⋊C4C2411yescharacteristic
627C2×C4⋊C4C2412yes—
628C2×C4⋊C4C2412yes—
629C2×C4⋊C4C2412yes—
630C2×C4⋊C4C2412yes—
631C2×C4⋊C4C2412yes—
632C2×C22⋊C4—28no—
633C2×C22⋊C4—216no—
634C2×C22⋊C4C2414yes—
635C2×C22⋊C4C2418yes—
636C2×C22⋊C4C2414yes—
637C2×C22⋊C4C2418yes—
638C2×C22⋊C4C2414yes—
639C2×C22⋊C4C2412yes—
640C2×C22⋊C4C2414yes—
641C2×C22⋊C4C2412yes—
642C2×C22⋊C4C2414yes—
643C2×C22⋊C4C2412yes—
644C2×C22⋊C4C2412yes—
645C2×C22⋊C4C2418yes—
646C2×C22⋊C4C2414yes—
647C2×C22⋊C4C2412yes—
648C2×C22⋊C4C2414yes—
649C2×C22⋊C4C2414yes—
650C2×C22⋊C4C2414yes—
651C2×C22⋊C4C24116yes—
652C2×C22⋊C4C2412yes—
653C2×C22⋊C4C2414yes—
654C2×C22⋊C4C2418yes—
655C2×C22⋊C4C24116yes—
656C2×C22⋊C4C24116yes—
657C2×C22⋊C4C2418yes—
658C2×C22⋊C4C2418yes—
659C2×C22⋊C4C24116yes—
660C2×C22⋊C4C24116yes—
661C2×C22⋊C4C2412yes—
662C2×C42C2×D4116yes—
663C2×C42C2×D418yes—
664C2×C42C2418yes—
665C2×C42C2412yes—
666C2×C42C2414yes—
667C2×C42C2414yes—
668C2×C42C2414yes—
669C2×C42C2412yes—
670C2×C42C2412yes—
671C2×C42C2414yes—
672C2×C42C2418yes—
673C2×C42C2412yes—
674C2×C42C2411yescharacteristic
675C2×C42C2412yes—
676C2×C42C2411yescharacteristic
677C2×C42C2412yes—
678C2×C42C2411yescharacteristic
679C2×C42C2412yes—
680C2×C42C2411yescharacteristic
681#95C2412yes—
682#95C2414yes—
683#95C2412yes—
684#95C2414yes—
685#95C2418yes—
686#95C2414yes—
687#95C2418yes—
688#95C2418yes—
689#95C2414yes—
690#95C2418yes—
691#95C2418yes—
692#95C2418yes—
693#95C2414yes—
694#95C24116yes—
695#95C24116yes—
696#95C24116yes—
697C24—24no—
698C24—28no—
699C24—28no—
700C24—44no—
701C24C2514yes—
702C24C2512yes—
703C24C2514yes—
704C24C2511yescharacteristic
705#41—432no—
706#41—832no—
707#41—816no—
708C2×Q8—22no—
709C2×Q8—28no—
710C2×Q8—28no—
711C2×Q8—24no—
712C2×Q8—28no—
713C2×Q8—24no—
714C2×Q8—24no—
715C2×Q8—24no—
716C2×Q8—44no—
717C2×Q8—48no—
718C2×Q8—48no—
719C2×Q8—48no—
720C2×Q8—44no—
721C2×Q8—416no—
722C2×Q8—816no—
723C2×Q8C22×D414yes—
724C2×Q8C22×D414yes—
725C2×Q8C22×D418yes—
726C2×D4—232no—
727C2×D4—28no—
728C2×D4—24no—
729C2×D4—28no—
730C2×D4—28no—
731C2×D4—216no—
732C2×D4—216no—
733C2×D4—232no—
734C2×D4—24no—
735C2×D4—24no—
736C2×D4—24no—
737C2×D4—22no—
738C2×D4—28no—
739C2×D4—24no—
740C2×D4—24no—
741C2×D4—28no—
742C2×D4—216no—
743C2×D4—24no—
744C2×D4—24no—
745C2×D4—28no—
746C2×D4—28no—
747C2×D4—48no—
748C2×D4—48no—
749C2×D4—416no—
750C2×D4—48no—
751C2×D4—416no—
752C2×D4—44no—
753C2×D42−1+418yes—
754C22×C4—28no—
755C22×C4—24no—
756C22×C4—24no—
757C22×C4—24no—
758C22×C4—24no—
759C22×C4—28no—
760C22×C4—216no—
761C22×C4—28no—
762C22×C4—28no—
763C22×C4—28no—
764C22×C4—24no—
765C22×C4—28no—
766C22×C4—216no—
767C22×C4—216no—
768C22×C4—216no—
769C22×C4—28no—
770C22×C4—28no—
771C22×C4—28no—
772C22×C4—48no—
773C22×C4—44no—
774C22×C4—44no—
775C22×C4—48no—
776C22×C4—416no—
777C22×C4—48no—
778C22×C4—48no—
779C22×C4—416no—
780C22×C4—48no—
781C22×C4—432no—
782C22×C4—832no—
783C22×C4C22×D414yes—
784C22×C4C22×D414yes—
785C22×C4C22×D418yes—
786C22×C4C22×D414yes—
787C22×C4C22×D418yes—
788C22×C4C2518yes—
789C22×C4C2512yes—
790C22×C4C2514yes—
791C22×C4C2512yes—
792C22×C4C2514yes—
793C22×C4C2512yes—
794C22×C4C2514yes—
795C22×C4C2518yes—
796C22×C4C2511yescharacteristic
797C22×C4C2512yes—
798C22×C4C2511yescharacteristic
799C22×C4C2511yescharacteristic
800C22×C4C2512yes—
801C22×C4C2511yescharacteristic
802C22×C4C2512yes—
803C22×C4C2512yes—
804C22×C4C2514yes—
805C22×C4C2511yescharacteristic
806C22×C4C2511yescharacteristic
807C4⋊C4—216no—
808C4⋊C4—216no—
809C4⋊C4—28no—
810C4⋊C4—28no—
811C4⋊C4—24no—
812C4⋊C4—28no—
813C4⋊C4—24no—
814C4⋊C4—24no—
815C4⋊C4—28no—
816C4⋊C4—28no—
817C4⋊C4—28no—
818C4⋊C4—24no—
819C4⋊C4—216no—
820C4⋊C4—216no—
821C4⋊C4—24no—
822C4⋊C4—22no—
823C4⋊C4—22no—
824C4⋊C4—24no—
825C4⋊C4—28no—
826C4⋊C4—24no—
827C4⋊C4—24no—
828C4⋊C4—28no—
829C4⋊C4—216no—
830C4⋊C4—28no—
831C4⋊C4—232no—
832C4⋊C4—28no—
833C4⋊C4—48no—
834C4⋊C4—416no—
835C4⋊C4—48no—
836C4⋊C4—416no—
837C4⋊C4C22×D414yes—
838C4⋊C4C22×D414yes—
839C4⋊C4C22×D418yes—
840C4⋊C4C22×D418yes—
841C4⋊C4C22×D418yes—
842C4⋊C4C22×D418yes—
843C4⋊C4C22×D418yes—
844C22⋊C4—24no—
845C22⋊C4—28no—
846C22⋊C4—24no—
847C22⋊C4—216no—
848C22⋊C4—28no—
849C22⋊C4—28no—
850C22⋊C4—216no—
851C22⋊C4—216no—
852C22⋊C4—28no—
853C22⋊C4—24no—
854C22⋊C4—24no—
855C22⋊C4—28no—
856C22⋊C4—24no—
857C22⋊C4—28no—
858C22⋊C4—28no—
859C22⋊C4—28no—
860C22⋊C4—28no—
861C22⋊C4—28no—
862C22⋊C4—24no—
863C22⋊C4—216no—
864C22⋊C4—232no—
865C22⋊C4—48no—
866C22⋊C4—48no—
867C22⋊C4—416no—
868C22⋊C4—416no—
869C22⋊C4—416no—
870C22⋊C4—416no—
871C22⋊C4H(5,𝔽2)18yes—
872C42—28no—
873C42—24no—
874C42—216no—
875C42—28no—
876C42—24no—
877C42—24no—
878C42—28no—
879C42—28no—
880C42—48no—
881C42C22×D418yes—
882C42C22×D414yes—
883C42C22×D418yes—
884C42C22×D414yes—
885C42C22×D418yes—
886C42C22×D414yes—
887C42C22×D418yes—
888C42C22×D414yes—
889C23—22no—
890C23—22no—
891C23—216no—
892C23—24no—
893C23—28no—
894C23—24no—
895C23—28no—
896C23—24no—
897C23—22no—
898C23—28no—
899C23—24no—
900C23—24no—
901C23—28no—
902C23—24no—
903C23—28no—
904C23—432no—
905C23—48no—
906C23—48no—
907C23C23×D412yes—
908C23C2×H(5,𝔽2)14yes—
909C23C2×2−1+418yes—
910C23C2611yescharacteristic
911Q8—28no—
912Q8—28no—
913Q8—48no—
914Q8—44no—
915Q8—88no—
916Q8—88no—
917Q8—88no—
918Q8—84no—
919D4—216no—
920D4—216no—
921D4—432no—
922D4—416no—
923D4—48no—
924D4—416no—
925D4—48no—
926D4—44no—
927D4—48no—
928D4—88no—
929D4—84no—
930D4—832no—
931C2×C4—24no—
932C2×C4—22no—
933C2×C4—24no—
934C2×C4—22no—
935C2×C4—24no—
936C2×C4—22no—
937C2×C4—24no—
938C2×C4—24no—
939C2×C4—22no—
940C2×C4—24no—
941C2×C4—216no—
942C2×C4—28no—
943C2×C4—28no—
944C2×C4—28no—
945C2×C4—22no—
946C2×C4—22no—
947C2×C4—24no—
948C2×C4—22no—
949C2×C4—24no—
950C2×C4—28no—
951C2×C4—24no—
952C2×C4—28no—
953C2×C4—24no—
954C2×C4—216no—
955C2×C4—28no—
956C2×C4—24no—
957C2×C4—28no—
958C2×C4—24no—
959C2×C4—24no—
960C2×C4—28no—
961C2×C4—28no—
962C2×C4—24no—
963C2×C4—48no—
964C2×C4—416no—
965C2×C4—416no—
966C2×C4—48no—
967C2×C4—416no—
968C2×C4—416no—
969C2×C4—48no—
970C2×C4—816no—
971C2×C4—816no—
972C2×C4—88no—
973C2×C4—88no—
974C2×C4—88no—
975C2×C4C23×D414yes—
976C2×C4C23×D412yes—
977C2×C4C23×D414yes—
978C2×C4C23×D412yes—
979C2×C4C23×D412yes—
980C2×C4C23×D412yes—
981C2×C4C23×D414yes—
982C2×C4C23×D414yes—
983C2×C4C23×D412yes—
984C2×C4C23×D412yes—
985C2×C4C2×H(5,𝔽2)18yes—
986C2×C4C2×2−1+414yes—
987C2×C4#58514yes—
988C22—28no—
989C22—22no—
990C22—22no—
991C22—216no—
992C22—28no—
993C22—432no—
994C22—48no—
995C22—44no—
996C22—44no—
997C22—48no—
998C22—416no—
999C22—42no—
1000C22—44no—
1001C22—44no—
1002C22—42no—
1003C22—44no—
1004C22—42no—
1005C22#349814yes—
1006C22C24×D411yescharacteristic
1007C22C22×H(5,𝔽2)12yes—
1008C22C22×2−1+412yes—
1009C22C2×#58512yes—
1010C4—28no—
1011C4—22no—
1012C4—24no—
1013C4—24no—
1014C4—22no—
1015C4—22no—
1016C4—22no—
1017C4—24no—
1018C4—24no—
1019C4—44no—
1020C4—48no—
1021C4—42no—
1022C4—48no—
1023C4—42no—
1024C4—44no—
1025C4—42no—
1026C4—44no—
1027C4#344914yes—
1028C4#348614yes—
1029C2—24no—
1030C2—48no—
1031C2—82no—
1032C2—84no—
1033C2C2×#344911yescharacteristic
1034C2C2×#348611yescharacteristic
1035C2C2×#349811yescharacteristic
1036C2#6301314yes—
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×#3522C2semidirect
2. C22×#554C2semidirect
3. #42794C2semidirect
4. #41957C2semidirect
5. #39617C2semidirect
6. #39611C2semidirect
7. #39169C2semidirect
8. #39161C2semidirect
9. #39133C2semidirect
10. #37653C2semidirect
11. #37632C2semidirect
12. #37539C2semidirect
13. #36559C2semidirect
14. #36496C2semidirect
15. #36103C2semidirect
16. #35701C2semidirect
17. #35317C2semidirect
18. #35237C2semidirect
19. #35233C2semidirect
20. #35139C2semidirect
21. #34965C2semidirect
22. #34936C2semidirect
23. #34128C2semidirect
25. C2×#559C22semidirect
26. C2×#559C22semidirect
27. C2×Q82C22semidirect
35. C2×#554C22semidirect
36. C2×#554C22semidirect
37. C2×#550C22semidirect
41. C2×#542C22semidirect
42. C2×#542C22semidirect
53. C2×#520C22semidirect
58. #2868C22semidirect
59. #2861C22semidirect
60. #2859C22semidirect
61. #2858C22semidirect
64. #2821C22semidirect
65. #2820C22semidirect
66. #2732C22semidirect
67. #2730C22semidirect
68. #2683C22semidirect
69. #2681C22semidirect
70. #2677C22semidirect
71. #2676C22semidirect
72. #2664C22semidirect
73. #2660C22semidirect
74. #2660C22semidirect
75. #2658C22semidirect
76. #2641C22semidirect
77. #2640C22semidirect
79. #2633C22semidirect
81. #2628C22semidirect
84. #2611C22semidirect
87. #2567C22semidirect
90. #2566C22semidirect
91. #2566C22semidirect
92. #2566C22semidirect
93. #2565C22semidirect
95. #2563C22semidirect
99. #2542C22semidirect
100. #2542C22semidirect
105. #2538C22semidirect
117. #2463C22semidirect
118. #2461C22semidirect
119. #2452C22semidirect
120. #2449C22semidirect
121. #2449C22semidirect
122. #2443C22semidirect
123. #2440C22semidirect
127. #2426C22semidirect
128. #2423C22semidirect
129. #2416C22semidirect
132. #2407C22semidirect
137. #2361C22semidirect
138. #2356C22semidirect
139. #2356C22semidirect
140. #2351C22semidirect
141. D4×C4⋊C4C22semidirect
154. #2295C22semidirect
155. #2295C22semidirect
158. C42×Q8C22semidirect
259. C2×C4×Q8D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35222
C22×#5542
#427942
#419572
#396172
#396112
#391692
#391612
#391332
#376532
#376322
#375392
#365592
#364962
#361032
#357012
#353172
#352372
#352332
#351392
#349652
#349362
#341282