Finite Group Databasebeta

← #7697247

Subgroups — #7697247

Order 512.

10951 conjugacy classes of subgroups.

The subgroup lattice has 1130 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3489C214yesmaximal, complemented
2#59817C211yesmaximal, characteristic, complemented
3#59814C212yesmaximal, complemented
4#58998C212yesmaximal, complemented
5#58992C214yesmaximal, complemented
6#52103C211yesmaximal, characteristic, complemented
7C2×#2683C212yesmaximal, complemented
8#45248C214yesmaximal, complemented
9#45244C212yesmaximal, complemented
10#44758C214yesmaximal, complemented
11#43907C218yesmaximal, complemented
12#39359C214yesmaximal, complemented
13#39356C212yesmaximal, complemented
14#37653C218yesmaximal, complemented
15#37649C214yesmaximal, complemented
16#36260C211yesmaximal, characteristic, complemented
17#36212C212yesmaximal, complemented
18#36085C212yesmaximal, complemented
19#35821C214yesmaximal, complemented
20#34308C212yesmaximal, complemented
21C22×2−1+4C2212yes—
22C23×#41C2212yescomplemented
23#3489—264no—
24C2×D4×Q8C2214yescomplemented
25C2×D4×Q8C2214yescomplemented
26C2×#548C2214yescomplemented
27C2×#548C2214yescomplemented
28C2×#547C2212yes—
29C2×#547C2218yescomplemented
30C2×#547C2218yescomplemented
31C2×#547C2214yescomplemented
32C2×#547C2211yescharacteristic, complemented
33C2×#546C2214yes—
34C2×#546C2218yescomplemented
35C2×#546C2218yescomplemented
36C2×#546C2214yescomplemented
37C2×D42C2211yescharacteristic
38C2×#537C2214yescomplemented
39C2×#537C2218yescomplemented
40C2×#536C2218yescomplemented
41C2×#536C2214yescomplemented
42C2×#525C2214yescomplemented
43C2×#525C2218yescomplemented
44C22×C22⋊Q8C2214yescomplemented
45C22×C22⋊Q8C2218yescomplemented
46C2×#520C2214yescomplemented
47#2858C2211yescharacteristic, complemented
48#2856C2212yescomplemented
49#2849C2214yescomplemented
50#2847C2212yescomplemented
51#2683C2214yes—
52#2683C2211yescharacteristic
53#2683C2212yes—
54#2683C2218yescomplemented
55#2683C2214yescomplemented
56#2683C2218yescomplemented
57#2683C2214yescomplemented
58#2683C2214yescomplemented
59#2683C2212yescomplemented
60#2682C2214yescomplemented
61#2682C2212yescomplemented
62#2682C2214yescomplemented
63#2681C2218yescomplemented
64#2681C2214yescomplemented
65#2681C2218yescomplemented
66#2680C2212yescomplemented
67#2679C2211yescharacteristic
68#2678C2214yescomplemented
69#2677C2214yescomplemented
70#2677C2218yescomplemented
71#2676C2218yescomplemented
72#2676C2218yescomplemented
73#2675C2214yescomplemented
74#2674C2218yescomplemented
75#2672C2218yescomplemented
76#2669C2212yes—
77#2620C2214yescomplemented
78#2618C2218yescomplemented
79#2616C2212yescomplemented
80#2614C2214yescomplemented
81#2555C2214yescomplemented
82#2551C2212yescomplemented
83#2545C2214yescomplemented
84#2542C2211yescharacteristic
85#2541C2211yescharacteristic, complemented
86#2540C2214yescomplemented
87#2539C2218yescomplemented
88#2538C2214yescomplemented
89#2534C2218yescomplemented
90#2501C2212yescomplemented
91#2463C2214yescomplemented
92#2463C2218yescomplemented
93#2461C2218yescomplemented
94#2461C2218yescomplemented
95#2461C2218yescomplemented
96#2456C2218yescomplemented
97#2452C2218yescomplemented
98#2452C2218yescomplemented
99#2449C2218yescomplemented
100#2449C2218yescomplemented
101#2440C2218yescomplemented
102#2437C2214yescomplemented
103#2436C2212yescomplemented
104#2434C2214yescomplemented
105#2434C2212yescomplemented
106#2433C2212yes—
107#2431C2214yescomplemented
108#2430C2218yescomplemented
109#2430C2218yescomplemented
110#2430C2214yescomplemented
111#2429C2214yescomplemented
112#2428C2218yescomplemented
113#2426C2214yescomplemented
114#2425C2218yescomplemented
115#2424C2218yescomplemented
116#2424C2218yescomplemented
117#2424C2218yescomplemented
118#2417C2214yescomplemented
119#2416C2218yescomplemented
120#2416C2214yescomplemented
121#2416C2218yescomplemented
122#2413C2218yescomplemented
123#2411C2218yescomplemented
124#2410C2214yescomplemented
125#2409C2212yes—
126#2409C2214yescomplemented
127#2409C2212yescomplemented
128#2407C2214yes—
129#2406C2218yescomplemented
130#2406C2214yescomplemented
131#2404C2218yes—
132#2403C2214yes—
133#2392C2214yescomplemented
134C2×#396C2218yescomplemented
135#2388C2212yescomplemented
136C2×#395C2214yescomplemented
137#2366C2212yes—
138#2365C2212yescomplemented
139#2361C2214yescomplemented
140#2360C2214yescomplemented
141#2359C2218yescomplemented
142#2358C2214yes—
143D4×C4⋊C4C2212yescomplemented
144D4×C4⋊C4C2212yescomplemented
145#2344C2214yescomplemented
146#2339C2214yescomplemented
147#2339C2212yescomplemented
148D4×C22⋊C4C2212yescomplemented
149#2323C2214yescomplemented
150#2322C2218yescomplemented
151C4×C4⋊Q8C2212yescomplemented
152C4×#127C2211yescharacteristic
153C4×#121C2214yescomplemented
154C4×#120C2212yes—
155#2293C2212yescomplemented
156C2×#390C2212yes—
157C2×#389C2214yescomplemented
158C2×#386C2214yes—
159C42×D4C2211yescharacteristic, complemented
160C2×2−1+4—232no—
161C2×2−1+4—48no—
162C22×#41—232no—
163C22×#41—48no—
164C22×#41C2312yes—
165C22×#41C2318yes—
166C22×#41C2314yes—
167C22×#41C2312yes—
168C22×#41C2318yes—
169C22×#41C2314yes—
170C22×#41C2314yes—
171C23×Q8C2312yes—
172C23×Q8C2314yes—
173C23×Q8C2314yes—
174C23×Q8C2312yes—
175C23×D4C2312yes—
176C23×D4C2314yes—
177C23×D4C2312yes—
178C24×C4C2312yes—
179C24×C4C2314yes—
180D4×Q8—232no—
181D4×Q8—232no—
182#548—232no—
183#548—232no—
184#547—232no—
185#547—264no—
186#547—264no—
187#547—44no—
188#547D4132yescomplemented
189#546—232no—
190#546—264no—
191#546—264no—
192#546—232no—
193D42—44no—
194#537—232no—
195#537—264no—
196#536—232no—
197#536—264no—
198C2×C4⋊Q8C2318yes—
199C2×C4⋊Q8C2318yes—
200C2×C4⋊Q8C2314yes—
201C2×C4⋊Q8C2311yescharacteristic
202C2×C4⋊Q8C2312yes—
203C2×#127C2311yescharacteristic
204C2×#127C2311yescharacteristic
205C2×#127C2312yes—
206C2×#124C2314yes—
207C2×#124C2318yes—
208C2×#124C2318yes—
209C2×#124C2314yes—
210#525—264no—
211#525—232no—
212C2×#123C2318yes—
213C2×#123C2318yes—
214C2×#123C2318yes—
215C2×#123C2314yes—
216C2×#123C2314yes—
217C2×#123C2318yes—
218C2×#123C2318yes—
219C2×#123C2318yes—
220C2×#123C2314yes—
221C2×#123C2318yes—
222C2×C22⋊Q8—232no—
223C2×C22⋊Q8—264no—
224C2×C22⋊Q8C2314yes—
225C2×C22⋊Q8C2314yes—
226C2×C22⋊Q8C2314yes—
227C2×C22⋊Q8C2318yes—
228C2×C22⋊Q8C2314yes—
229C2×C22⋊Q8C2318yes—
230C2×C22⋊Q8C2314yes—
231C2×C22⋊Q8C2318yes—
232C2×C22⋊Q8C2318yes—
233C2×C22⋊Q8C2318yes—
234C2×C22⋊Q8C2318yes—
235C2×C22⋊Q8C2318yes—
236C2×C22⋊Q8C2318yes—
237C2×C22⋊Q8C2318yes—
238C2×C22⋊Q8C2314yes—
239C2×C22⋊Q8C2318yes—
240C2×C22⋊Q8C2318yes—
241C2×C22⋊Q8C2312yes—
242C2×C22⋊Q8C2314yes—
243C2×#121C2314yes—
244C2×#121C2318yes—
245C2×#121C2318yes—
246C2×#121C2314yes—
247C2×#121C2314yes—
248C2×#121C2318yes—
249C2×#121C2318yes—
250C2×#121C2318yes—
251C2×#121C2318yes—
252C2×#121C2314yes—
253C2×#121C2318yes—
254C2×#121C2318yes—
255C2×#121C2312yes—
256C2×#121C2312yes—
257C2×#121C2312yes—
258C2×#121C2318yes—
259C2×#121C2314yes—
260C2×#120C2312yes—
261C2×#120C2318yes—
262C2×#120C2318yes—
263C2×#120C2314yes—
264C2×#120C2314yes—
265C2×#120C2314yes—
266C2×#120C2314yes—
267#520—232no—
268C2×C4×Q8C2314yes—
269C2×C4×Q8C2314yes—
270C2×C4×D4C2314yes—
271C2×C4×D4C2318yes—
272C2×C4×D4C2314yes—
273C2×C4×D4C2311yescharacteristic
274C2×C4×D4C2318yes—
275C2×C4×D4C2318yes—
276C2×C4×D4C2318yes—
277C2×C4×D4C2314yes—
278C2×C4×D4C2314yes—
279C2×C4×D4C2318yes—
280C2×C4×D4C2318yes—
281C2×C4×D4C2311yescharacteristic
282C2×C4×D4C2311yescharacteristic
283C2×C4×D4C2314yes—
284C2×C4×D4C2312yes—
285C2×C4×D4C2312yes—
286C2×#117C2314yes—
287C2×#117C2318yes—
288C22×C4⋊C4C2318yes—
289C22×C4⋊C4C2314yes—
290C22×C4⋊C4C2318yes—
291C22×C4⋊C4C2318yes—
292C22×C4⋊C4C2312yes—
293C22×C4⋊C4C2314yes—
294C22×C4⋊C4C2314yes—
295C22×C22⋊C4C2318yes—
296C22×C22⋊C4C2318yes—
297C22×C22⋊C4C2318yes—
298C22×C22⋊C4C2314yes—
299C22×C42C2312yes—
300#399C2318yes—
301#399C2314yes—
302#398C2318yes—
303#398C2318yes—
304#398C2314yes—
305#397C2314yes—
306#396C2314yes—
307#396C2318yes—
308#396C2318yes—
309#396C2318yes—
310#396C2318yes—
311#396C2314yes—
312#396C2318yes—
313#396C2318yes—
314#396C2318yes—
315#396C2318yes—
316#396C2318yes—
317#396C2318yes—
318#395C2314yes—
319#395C2314yes—
320#395C2318yes—
321#395C2312yes—
322#395C2318yes—
323#395C2314yes—
324#395C2314yes—
325#395C2318yes—
326#395C2314yes—
327#394C2318yes—
328#394C2314yes—
329#394C2318yes—
330#394C2318yes—
331#394C2318yes—
332#394C2318yes—
333#394C2314yes—
334#394C2312yes—
335#394C2314yes—
336#394C2314yes—
337#394C2314yes—
338#394C2318yes—
339#393C2312yes—
340#393C2314yes—
341#393C2318yes—
342#393C2314yes—
343#393C2318yes—
344#392C2314yes—
345#392C2312yes—
346#392C2314yes—
347#392C2318yes—
348#392C2318yes—
349#392C2318yes—
350#392C2314yes—
351#392C2318yes—
352#391C2314yes—
353#391C2314yes—
354#391C2314yes—
355#390C2311yescharacteristic
356#390C2314yes—
357#390C2311yescharacteristic
358#390C2314yes—
359#390C2312yes—
360#390C2318yes—
361#390C2314yes—
362#390C2312yes—
363#390C2312yes—
364#390C2312yes—
365#390C2318yes—
366#390C2318yes—
367#390C2312yes—
368#390C2318yes—
369#390C2312yes—
370#389C2314yes—
371#389C2314yes—
372#389C2318yes—
373#389C2314yes—
374#389C2312yes—
375#389C2314yes—
376#389C2318yes—
377#389C2314yes—
378#389C2318yes—
379#389C2318yes—
380#389C2312yes—
381#388C2314yes—
382#388C2318yes—
383#388C2318yes—
384#388C2318yes—
385#388C2314yes—
386#388C2318yes—
387#388C2318yes—
388#388C2318yes—
389#387C2318yes—
390#387C2318yes—
391#387C2318yes—
392#386C2318yes—
393#386C2314yes—
394#386C2318yes—
395#386C2314yes—
396#386C2318yes—
397#386C2318yes—
398#386C2318yes—
399#386C2318yes—
400#386C2314yes—
401#386C2318yes—
402#386C2314yes—
403#386C2314yes—
404#386C2318yes—
405#386C2318yes—
406#386C2314yes—
407#386C2312yes—
408#386C2318yes—
409#386C2318yes—
410#385C2318yes—
411#385C2318yes—
412#385C2318yes—
413#385C2312yes—
414#385C2318yes—
415#385C2314yes—
416#385C2318yes—
417#385C2318yes—
418#385C2314yes—
419#385C2318yes—
420#385C2318yes—
421#385C2314yes—
422#384C2311yescharacteristic
423#384C2312yes—
424#384C2312yes—
425#381C2318yes—
426#381C2314yes—
427#380C2314yes—
428#380C2312yes—
429#380C2312yes—
430#380C2314yes—
431#380C2318yes—
432#379C2314yes—
433#379C2312yes—
434C4×C4⋊C4C2314yes—
435C4×C4⋊C4C2314yes—
436C4×C4⋊C4C2312yes—
437C4×C4⋊C4C2314yes—
438C4×C4⋊C4C2312yes—
439C4×C4⋊C4C2311yescharacteristic
440C4×C22⋊C4C2314yes—
441C4×C22⋊C4C2312yes—
442C4×C22⋊C4C2314yes—
443C4×C22⋊C4C2312yes—
444C4×C22⋊C4C2318yes—
445C4×C22⋊C4C2312yes—
446C2×#95C2318yes—
447C2×#95C2314yes—
448C43C2311yescharacteristic
449C25C2414yes—
450C25C2412yes—
4512−1+4—4128no—
452C2×#41—216no—
453C2×#41—216no—
454C2×#41—232no—
455C2×#41—232no—
456C2×#41—216no—
457C2×#41—232no—
458C2×#41—216no—
459C2×#41—28no—
460C2×#41—216no—
461C2×#41—232no—
462C2×#41—232no—
463C2×#41—216no—
464C2×#41—44no—
465C2×#41—416no—
466C2×#41—416no—
467C2×#41—48no—
468C2×#41—48no—
469C2×#41—4128no—
470C2×#41C2×D4132yes—
471C22×Q8—216no—
472C22×Q8—216no—
473C22×Q8—216no—
474C22×Q8—232no—
475C22×Q8—216no—
476C22×Q8—48no—
477C22×Q8—44no—
478C22×Q8—48no—
479C22×Q8—44no—
480C22×Q8C2412yes—
481C22×Q8C2412yes—
482C22×Q8C2418yes—
483C22×Q8C2414yes—
484C22×Q8C2414yes—
485C22×Q8C2414yes—
486C22×D4—232no—
487C22×D4—216no—
488C22×D4—28no—
489C22×D4—28no—
490C22×D4—44no—
491C22×D4—48no—
492C22×D4—82no—
493C22×D4C2414yes—
494C22×D4C2414yes—
495C22×D4C2412yes—
496C22×D4C2414yes—
497C22×D4C2414yes—
498C22×D4C2412yes—
499C22×D4C2414yes—
500C22×D4C2418yes—
501C22×D4C2418yes—
502C22×D4C2418yes—
503C22×D4C2414yes—
504C22×D4C2418yes—
505C22×D4C2411yescharacteristic
506C22×D4C2414yes—
507C22×D4C2412yes—
508C22×D4C2412yes—
509C22×D4C2412yes—
510C22×D4C2411yescharacteristic
511C22×D4C2411yescharacteristic
512C23×C4—232no—
513C23×C4—216no—
514C23×C4—44no—
515C23×C4—48no—
516C23×C4C2414yes—
517C23×C4C2412yes—
518C23×C4C2412yes—
519C23×C4C2418yes—
520C23×C4C2414yes—
521C23×C4C2412yes—
522C23×C4C2414yes—
523C23×C4C2414yes—
524C23×C4C2418yes—
525C23×C4C2412yes—
526C23×C4C2418yes—
527C23×C4C2414yes—
528C23×C4C2418yes—
529C23×C4C2418yes—
530C23×C4C2414yes—
531C4⋊Q8—216no—
532C4⋊Q8—232no—
533C4⋊Q8—232no—
534C4⋊Q8—42no—
535C4⋊Q8C2×D4116yescomplemented
536#127—24no—
537#127—42no—
538#127—82no—
539#124—216no—
540#124—232no—
541#124—232no—
542#124—216no—
543#123—232no—
544#123—232no—
545#123—232no—
546#123—216no—
547#123—232no—
548#123—232no—
549#123—216no—
550#123—232no—
551#123—48no—
552#123C2×D4164yescomplemented
553C22⋊Q8—216no—
554C22⋊Q8—216no—
555C22⋊Q8—216no—
556C22⋊Q8—232no—
557C22⋊Q8—216no—
558C22⋊Q8—232no—
559C22⋊Q8—232no—
560C22⋊Q8—232no—
561C22⋊Q8—232no—
562C22⋊Q8—216no—
563C22⋊Q8—232no—
564C22⋊Q8—232no—
565C22⋊Q8—232no—
566C22⋊Q8—232no—
567C22⋊Q8—232no—
568C22⋊Q8—216no—
569C22⋊Q8—232no—
570C22⋊Q8—44no—
571C22⋊Q8C2×D4132yescomplemented
572#121—216no—
573#121—232no—
574#121—232no—
575#121—232no—
576#121—232no—
577#121—216no—
578#121—232no—
579#121—216no—
580#121—216no—
581#121—232no—
582#121—232no—
583#121—232no—
584#121—44no—
585#121—44no—
586#121—44no—
587#121—88no—
588#121C2×D4132yescomplemented
589#120—232no—
590#120—216no—
591#120—28no—
592#120—216no—
593#120—232no—
594#120—48no—
595#120—84no—
596C4×Q8—216no—
597C4×Q8—216no—
598C4×D4—216no—
599C4×D4—24no—
600C4×D4—232no—
601C4×D4—216no—
602C4×D4—216no—
603C4×D4—232no—
604C4×D4—232no—
605C4×D4—232no—
606C4×D4—232no—
607C4×D4—232no—
608C4×D4—216no—
609C4×D4—42no—
610C4×D4—42no—
611C4×D4—84no—
612C4×D4C2×D4116yes—
613C4×D4C2×D4116yescomplemented
614#117—232no—
615#117—216no—
616C2×C4⋊C4—232no—
617C2×C4⋊C4—232no—
618C2×C4⋊C4—216no—
619C2×C4⋊C4—232no—
620C2×C4⋊C4—44no—
621C2×C4⋊C4—84no—
622C2×C4⋊C4C2×D4132yescomplemented
623C2×C4⋊C4C2418yes—
624C2×C4⋊C4C2414yes—
625C2×C4⋊C4C2414yes—
626C2×C4⋊C4C2418yes—
627C2×C4⋊C4C2414yes—
628C2×C4⋊C4C2418yes—
629C2×C4⋊C4C2418yes—
630C2×C4⋊C4C2418yes—
631C2×C4⋊C4C2418yes—
632C2×C4⋊C4C2418yes—
633C2×C4⋊C4C2418yes—
634C2×C4⋊C4C2414yes—
635C2×C4⋊C4C2411yescharacteristic
636C2×C4⋊C4C2414yes—
637C2×C4⋊C4C2414yes—
638C2×C4⋊C4C2418yes—
639C2×C4⋊C4C2411yescharacteristic
640C2×C4⋊C4C2412yes—
641C2×C4⋊C4C2414yes—
642C2×C4⋊C4C2412yes—
643C2×C4⋊C4C2418yes—
644C2×C4⋊C4C2414yes—
645C2×C4⋊C4C2411yescharacteristic
646C2×C4⋊C4C2412yes—
647C2×C4⋊C4C2412yes—
648C2×C4⋊C4C2414yes—
649C2×C4⋊C4C2412yes—
650C2×C4⋊C4C2418yes—
651C2×C4⋊C4C2412yes—
652C2×C4⋊C4C2414yes—
653C2×C4⋊C4C2414yes—
654C2×C22⋊C4—232no—
655C2×C22⋊C4—232no—
656C2×C22⋊C4—232no—
657C2×C22⋊C4—84no—
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⋊C4C2414yes—
671C2×C22⋊C4C2412yes—
672C2×C22⋊C4C2414yes—
673C2×C22⋊C4C2418yes—
674C2×C22⋊C4C2418yes—
675C2×C22⋊C4C2414yes—
676C2×C22⋊C4C2418yes—
677C2×C22⋊C4C2414yes—
678C2×C22⋊C4C2414yes—
679C2×C22⋊C4C2412yes—
680C2×C22⋊C4C2412yes—
681C2×C22⋊C4C2414yes—
682C2×C22⋊C4C2418yes—
683C2×C22⋊C4C2412yes—
684C2×C22⋊C4C2418yes—
685C2×C22⋊C4C2412yes—
686C2×C22⋊C4C2414yes—
687C2×C22⋊C4C2414yes—
688C2×C22⋊C4C2414yes—
689C2×C22⋊C4C2414yes—
690C2×C22⋊C4C2414yes—
691C2×C22⋊C4C2418yes—
692C2×C22⋊C4C2418yes—
693C2×C22⋊C4C2414yes—
694C2×C22⋊C4C2414yes—
695C2×C42—82no—
696C2×C42C2414yes—
697C2×C42C2418yes—
698C2×C42C2418yes—
699C2×C42C2411yescharacteristic
700C2×C42C2411yescharacteristic
701C2×C42C2414yes—
702C2×C42C2412yes—
703C2×C42C2412yes—
704C2×C42C2411yescharacteristic
705C2×C42C2412yes—
706#95C2414yes—
707#95C2412yes—
708#95C2418yes—
709#95C2418yes—
710#95C2414yes—
711#95C2418yes—
712#95C2418yes—
713#95C2412yes—
714#95C2414yes—
715#95C2418yes—
716#95C2414yes—
717#95C2412yes—
718#95C2414yes—
719#95C2418yes—
720#95C2418yes—
721#95C2414yes—
722#95C2414yes—
723#95C2418yes—
724C24—28no—
725C24—28no—
726C24—216no—
727C24—28no—
728C24—24no—
729C24—44no—
730C24—42no—
731C24—48no—
732C24—44no—
733C24—42no—
734C24C2514yes—
735C24C2512yes—
736C24C2514yes—
737C24C2512yes—
738C24C2512yes—
739#41—2128no—
740#41—432no—
741#41—4128no—
742#41—4128no—
743#41—464no—
744#41—464no—
745#41—432no—
746C2×Q8—28no—
747C2×Q8—28no—
748C2×Q8—216no—
749C2×Q8—216no—
750C2×Q8—216no—
751C2×Q8—28no—
752C2×Q8—216no—
753C2×Q8—28no—
754C2×Q8—24no—
755C2×Q8—42no—
756C2×Q8—48no—
757C2×Q8—44no—
758C2×Q8—44no—
759C2×Q8—464no—
760C2×Q8—464no—
761C2×Q8—432no—
762C2×Q8—432no—
763C2×Q8C22×D4116yes—
764C2×D4—216no—
765C2×D4—216no—
766C2×D4—28no—
767C2×D4—28no—
768C2×D4—216no—
769C2×D4—28no—
770C2×D4—216no—
771C2×D4—216no—
772C2×D4—28no—
773C2×D4—28no—
774C2×D4—28no—
775C2×D4—28no—
776C2×D4—216no—
777C2×D4—28no—
778C2×D4—28no—
779C2×D4—28no—
780C2×D4—28no—
781C2×D4—216no—
782C2×D4—28no—
783C2×D4—216no—
784C2×D4—24no—
785C2×D4—22no—
786C2×D4—24no—
787C2×D4—41no—
788C2×D4—42no—
789C2×D4—48no—
790C2×D4—41no—
791C2×D4—44no—
792C2×D4—42no—
793C2×D4—44no—
794C2×D4—44no—
795C2×D4—42no—
796C2×D4—41no—
797C2×D4—44no—
798C2×D4—48no—
799C2×D4—44no—
800C2×D4—42no—
801C2×D4—44no—
802C2×D4—48no—
803C2×D4—41no—
804C2×D4—42no—
805C2×D4—48no—
806C2×D4—44no—
807C2×D4—48no—
808C2×D4—42no—
809C2×D4—44no—
810C2×D4—464no—
811C2×D4—432no—
812C2×D4—816no—
813C2×D4C22×D4132yes—
814C2×D4C22×D418yes—
815C2×D4C22×D418yes—
816C2×D4H(5,𝔽2)14yes—
817C2×D42−1+414yescomplemented
818C22×C4—216no—
819C22×C4—216no—
820C22×C4—28no—
821C22×C4—28no—
822C22×C4—216no—
823C22×C4—216no—
824C22×C4—28no—
825C22×C4—24no—
826C22×C4—28no—
827C22×C4—216no—
828C22×C4—216no—
829C22×C4—28no—
830C22×C4—216no—
831C22×C4—28no—
832C22×C4—216no—
833C22×C4—28no—
834C22×C4—216no—
835C22×C4—28no—
836C22×C4—216no—
837C22×C4—24no—
838C22×C4—24no—
839C22×C4—24no—
840C22×C4—216no—
841C22×C4—44no—
842C22×C4—42no—
843C22×C4—42no—
844C22×C4—44no—
845C22×C4—48no—
846C22×C4—44no—
847C22×C4—44no—
848C22×C4—44no—
849C22×C4—48no—
850C22×C4—464no—
851C22×C4—432no—
852C22×C4—48no—
853C22×C4—48no—
854C22×C4—48no—
855C22×C4—48no—
856C22×C4C22×D4132yes—
857C22×C4C22×D4116yes—
858C22×C4C22×D4116yes—
859C22×C4C2511yescharacteristic
860C22×C4C2512yes—
861C22×C4C2514yes—
862C22×C4C2518yes—
863C22×C4C2514yes—
864C22×C4C2512yes—
865C22×C4C2514yes—
866C22×C4C2512yes—
867C22×C4C2512yes—
868C22×C4C2514yes—
869C22×C4C2518yes—
870C22×C4C2514yes—
871C22×C4C2512yes—
872C22×C4C2511yescharacteristic
873C22×C4C2511yescharacteristic
874C4⋊C4—216no—
875C4⋊C4—28no—
876C4⋊C4—28no—
877C4⋊C4—216no—
878C4⋊C4—216no—
879C4⋊C4—216no—
880C4⋊C4—28no—
881C4⋊C4—216no—
882C4⋊C4—216no—
883C4⋊C4—216no—
884C4⋊C4—216no—
885C4⋊C4—28no—
886C4⋊C4—216no—
887C4⋊C4—28no—
888C4⋊C4—28no—
889C4⋊C4—22no—
890C4⋊C4—41no—
891C4⋊C4—42no—
892C4⋊C4—44no—
893C4⋊C4—42no—
894C4⋊C4—44no—
895C4⋊C4—48no—
896C4⋊C4—44no—
897C4⋊C4—42no—
898C4⋊C4—41no—
899C4⋊C4—42no—
900C4⋊C4C22×D418yes—
901C4⋊C4C22×D4132yes—
902C4⋊C4C22×D418yes—
903C4⋊C4C22×D4116yes—
904C4⋊C4C22×D4116yes—
905C22⋊C4—216no—
906C22⋊C4—216no—
907C22⋊C4—28no—
908C22⋊C4—28no—
909C22⋊C4—24no—
910C22⋊C4—24no—
911C22⋊C4—28no—
912C22⋊C4—216no—
913C22⋊C4—216no—
914C22⋊C4—28no—
915C22⋊C4—216no—
916C22⋊C4—216no—
917C22⋊C4—216no—
918C22⋊C4—216no—
919C22⋊C4—28no—
920C22⋊C4—28no—
921C22⋊C4—28no—
922C22⋊C4—216no—
923C22⋊C4—216no—
924C22⋊C4—216no—
925C22⋊C4—28no—
926C22⋊C4—28no—
927C22⋊C4—42no—
928C22⋊C4—44no—
929C22⋊C4—48no—
930C22⋊C4—44no—
931C22⋊C4—44no—
932C22⋊C4—48no—
933C22⋊C4—42no—
934C22⋊C4—42no—
935C22⋊C4—48no—
936C22⋊C4—44no—
937C22⋊C4—44no—
938C22⋊C4—44no—
939C22⋊C4C22×D4132yes—
940C22⋊C4C22×D4116yes—
941C22⋊C4C22×D4116yes—
942C42—216no—
943C42—216no—
944C42—28no—
945C42—22no—
946C42—22no—
947C42—41no—
948C42—44no—
949C42—42no—
950C42—42no—
951C42C22×D418yes—
952C23—22no—
953C23—22no—
954C23—24no—
955C23—24no—
956C23—24no—
957C23—22no—
958C23—24no—
959C23—24no—
960C23—22no—
961C23—24no—
962C23—24no—
963C23—24no—
964C23—24no—
965C23—28no—
966C23—24no—
967C23—22no—
968C23—24no—
969C23—22no—
970C23—24no—
971C23—22no—
972C23—24no—
973C23—24no—
974C23—28no—
975C23—48no—
976C23—416no—
977C23—432no—
978C23—416no—
979C23—416no—
980C23—88no—
981C23—816no—
982C23—88no—
983C23—84no—
984C23—84no—
985C23C23×D418yes—
986C23C23×D418yes—
987C23C2×H(5,𝔽2)14yes—
988C23C2×2−1+414yes—
989C23C2611yescharacteristic
990Q8—232no—
991Q8—48no—
992Q8—432no—
993Q8—416no—
994Q8—416no—
995Q8—48no—
996D4—264no—
997D4—44no—
998D4—48no—
999D4—416no—
1000D4—432no—
1001D4—416no—
1002D4—416no—
1003D4—48no—
1004D4—416no—
1005D4—416no—
1006D4—48no—
1007D4—816no—
1008D4—82no—
1009D4—84no—
1010D4—88no—
1011D4—816no—
1012D4—88no—
1013D4—162no—
1014D4D42116yes—
1015C2×C4—28no—
1016C2×C4—24no—
1017C2×C4—21no—
1018C2×C4—24no—
1019C2×C4—28no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—21no—
1023C2×C4—24no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—24no—
1027C2×C4—264no—
1028C2×C4—232no—
1029C2×C4—24no—
1030C2×C4—28no—
1031C2×C4—24no—
1032C2×C4—28no—
1033C2×C4—24no—
1034C2×C4—24no—
1035C2×C4—21no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—22no—
1039C2×C4—24no—
1040C2×C4—24no—
1041C2×C4—22no—
1042C2×C4—22no—
1043C2×C4—28no—
1044C2×C4—24no—
1045C2×C4—22no—
1046C2×C4—24no—
1047C2×C4—24no—
1048C2×C4—28no—
1049C2×C4—416no—
1050C2×C4—48no—
1051C2×C4—416no—
1052C2×C4—432no—
1053C2×C4—416no—
1054C2×C4—416no—
1055C2×C4—48no—
1056C2×C4—432no—
1057C2×C4—416no—
1058C2×C4—48no—
1059C2×C4—48no—
1060C2×C4—816no—
1061C2×C4—816no—
1062C2×C4C23×D414yes—
1063C2×C4C23×D418yes—
1064C2×C4C23×D414yes—
1065C2×C4C23×D418yes—
1066C2×C4C23×D4116yes—
1067C2×C4C23×D414yes—
1068C2×C4C2×H(5,𝔽2)12yes—
1069C2×C4C2×2−1+412yes—
1070C22—28no—
1071C22—24no—
1072C22—28no—
1073C22—24no—
1074C22—28no—
1075C22—28no—
1076C22—28no—
1077C22—24no—
1078C22—28no—
1079C22—44no—
1080C22—44no—
1081C22—42no—
1082C22—44no—
1083C22—44no—
1084C22—44no—
1085C22—42no—
1086C22—44no—
1087C22—48no—
1088C22—44no—
1089C22—42no—
1090C22—44no—
1091C22—48no—
1092C22—44no—
1093C22—42no—
1094C22—42no—
1095C22—44no—
1096C22—832no—
1097C22—816no—
1098C22C2×D4218yes—
1099C22C24×D412yes—
1100C22C22×H(5,𝔽2)11yescharacteristic
1101C22C22×2−1+411yescharacteristic
1102C22H(7,𝔽2)11yescharacteristic
1103C222−1+612yes—
1104C4—24no—
1105C4—24no—
1106C4—28no—
1107C4—22no—
1108C4—28no—
1109C4—216no—
1110C4—44no—
1111C4—41no—
1112C4—48no—
1113C4—44no—
1114C4—42no—
1115C4—42no—
1116C4—42no—
1117C4—44no—
1118C4C2×D4214yes—
1119C2—28no—
1120C2—48no—
1121C2—44no—
1122C2—82no—
1123C2—84no—
1124C2C22×D4211yescharacteristic
1125C2#6285312yes—
1126C2#6289411yescharacteristic
1127C2D4×2−1+412yes—
1128C2#6306311yescharacteristic
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×#3489C2semidirect
2. #59817C2semidirect
3. #59814C2semidirect
4. #58998C2semidirect
5. #58992C2semidirect
6. #52103C2semidirect
7. C2×#2683C2semidirect
8. #45248C2semidirect
9. #45244C2semidirect
10. #44758C2semidirect
11. #43907C2semidirect
12. #39359C2semidirect
13. #39356C2semidirect
14. #37653C2semidirect
15. #37649C2semidirect
16. #36260C2semidirect
17. #36212C2semidirect
18. #36085C2semidirect
19. #35821C2semidirect
20. #34308C2semidirect
22. C23×#41C22semidirect
24. C2×D4×Q8C22semidirect
25. C2×D4×Q8C22semidirect
26. C2×#548C22semidirect
27. C2×#548C22semidirect
29. C2×#547C22semidirect
30. C2×#547C22semidirect
31. C2×#547C22semidirect
32. C2×#547C22semidirect
34. C2×#546C22semidirect
35. C2×#546C22semidirect
36. C2×#546C22semidirect
38. C2×#537C22semidirect
39. C2×#537C22semidirect
40. C2×#536C22semidirect
41. C2×#536C22semidirect
42. C2×#525C22semidirect
43. C2×#525C22semidirect
44. C22×C22⋊Q8C22semidirect
45. C22×C22⋊Q8C22semidirect
46. C2×#520C22semidirect
47. #2858C22semidirect
48. #2856C22semidirect
49. #2849C22semidirect
50. #2847C22semidirect
54. #2683C22semidirect
55. #2683C22semidirect
56. #2683C22semidirect
57. #2683C22semidirect
58. #2683C22semidirect
59. #2683C22semidirect
60. #2682C22semidirect
61. #2682C22semidirect
62. #2682C22semidirect
63. #2681C22semidirect
64. #2681C22semidirect
65. #2681C22semidirect
66. #2680C22semidirect
68. #2678C22semidirect
69. #2677C22semidirect
70. #2677C22semidirect
71. #2676C22semidirect
72. #2676C22semidirect
73. #2675C22semidirect
74. #2674C22semidirect
75. #2672C22semidirect
77. #2620C22semidirect
78. #2618C22semidirect
79. #2616C22semidirect
80. #2614C22semidirect
81. #2555C22semidirect
82. #2551C22semidirect
83. #2545C22semidirect
85. #2541C22semidirect
86. #2540C22semidirect
87. #2539C22semidirect
88. #2538C22semidirect
89. #2534C22semidirect
90. #2501C22semidirect
91. #2463C22semidirect
92. #2463C22semidirect
93. #2461C22semidirect
94. #2461C22semidirect
95. #2461C22semidirect
96. #2456C22semidirect
97. #2452C22semidirect
98. #2452C22semidirect
99. #2449C22semidirect
100. #2449C22semidirect
101. #2440C22semidirect
102. #2437C22semidirect
103. #2436C22semidirect
104. #2434C22semidirect
105. #2434C22semidirect
107. #2431C22semidirect
108. #2430C22semidirect
109. #2430C22semidirect
110. #2430C22semidirect
111. #2429C22semidirect
112. #2428C22semidirect
113. #2426C22semidirect
114. #2425C22semidirect
115. #2424C22semidirect
116. #2424C22semidirect
117. #2424C22semidirect
118. #2417C22semidirect
119. #2416C22semidirect
120. #2416C22semidirect
121. #2416C22semidirect
122. #2413C22semidirect
123. #2411C22semidirect
124. #2410C22semidirect
126. #2409C22semidirect
127. #2409C22semidirect
129. #2406C22semidirect
130. #2406C22semidirect
133. #2392C22semidirect
134. C2×#396C22semidirect
135. #2388C22semidirect
136. C2×#395C22semidirect
138. #2365C22semidirect
139. #2361C22semidirect
140. #2360C22semidirect
141. #2359C22semidirect
143. D4×C4⋊C4C22semidirect
144. D4×C4⋊C4C22semidirect
145. #2344C22semidirect
146. #2339C22semidirect
147. #2339C22semidirect
148. D4×C22⋊C4C22semidirect
149. #2323C22semidirect
150. #2322C22semidirect
151. C4×C4⋊Q8C22semidirect
153. C4×#121C22semidirect
155. #2293C22semidirect
157. C2×#389C22semidirect
159. C42×D4C22semidirect
188. #547D4semidirect
535. C4⋊Q8C2×D4semidirect
552. #123C2×D4semidirect
571. C22⋊Q8C2×D4semidirect
588. #121C2×D4semidirect
613. C4×D4C2×D4semidirect
622. C2×C4⋊C4C2×D4semidirect
817. C2×D42−1+4semidirect

Maximal subgroups

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

subgroupindex
C2×#34892
#598172
#598142
#589982
#589922
#521032
C2×#26832
#452482
#452442
#447582
#439072
#393592
#393562
#376532
#376492
#362602
#362122
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