Finite Group Databasebeta

← #7986025

Subgroups — #7986025

Order 512.

5549 conjugacy classes of subgroups.

The subgroup lattice has 990 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59817C211yesmaximal, characteristic, complemented
2#59569C214yesmaximal, complemented
3#59466C211yesmaximal, characteristic, complemented
4#59466C211yesmaximal, characteristic, complemented
5#48839C214yesmaximal, complemented
6#47960C214yesmaximal, complemented
7#45492C214yesmaximal, complemented
8#44943C214yesmaximal, complemented
9#44879C214yesmaximal, complemented
10#42490C214yesmaximal, complemented
11#42486C214yesmaximal, complemented
12#39688C214yesmaximal, complemented
13#39588C214yesmaximal, complemented
14#39369C212yesmaximal, complemented
15#38965C212yesmaximal, complemented
16#36559C211yesmaximal, characteristic, complemented
17#36407C212yesmaximal, complemented
18D4×C22⋊Q8C214yesmaximal, complemented
19#35174C214yesmaximal, complemented
20#34893C212yesmaximal, complemented
21#34493C211yesmaximal, characteristic
22#34493C211yesmaximal, characteristic
23C4×D42C211yesmaximal, characteristic
24C2×#554C2212yescomplemented
25C2×D4×Q8C2214yescomplemented
26C2×D42C2211yescharacteristic
27C2×#544C2214yescomplemented
28C22×C22⋊Q8C2214yescomplemented
29C22×C4×D4C2214yes—
30#2868C2211yescharacteristic, complemented
31#2859C2211yescharacteristic, complemented
32#2859C2211yescharacteristic, complemented
33#2857C2214yescomplemented
34#2848C2214yescomplemented
35#2848C2218yescomplemented
36#2842C2218yescomplemented
37#2788C2218yescomplemented
38#2784C2218yescomplemented
39#2780C2218yescomplemented
40#2780C2218yescomplemented
41#2780C2218yescomplemented
42#2768C2218yescomplemented
43#2748C2214yescomplemented
44#2748C2214yescomplemented
45#2748C2218yescomplemented
46#2732C2218yescomplemented
47#2729C2218yescomplemented
48#2720C2218yescomplemented
49#2704C2218yescomplemented
50#2704C2218yescomplemented
51#2692C2218yescomplemented
52#2683C2218yescomplemented
53#2683C2214yescomplemented
54#2677C2218yescomplemented
55#2629C2214yescomplemented
56#2628C2214yescomplemented
57#2626C2218yescomplemented
58#2626C2218yescomplemented
59#2626C2214yescomplemented
60#2626C2214yescomplemented
61#2589C2214yescomplemented
62#2587C2218yescomplemented
63#2587C2214yescomplemented
64#2584C2214yescomplemented
65#2584C2212yescomplemented
66#2583C2214yescomplemented
67#2583C2214yescomplemented
68#2580C2212yes—
69#2579C2214yescomplemented
70#2579C2214yescomplemented
71#2574C2218yescomplemented
72#2566C2212yes—
73#2566C2214yescomplemented
74#2566C2214yescomplemented
75#2566C2212yescomplemented
76#2566C2212yescomplemented
77#2563C2212yescomplemented
78#2556C2218yescomplemented
79#2556C2218yescomplemented
80#2552C2212yescomplemented
81#2552C2212yescomplemented
82#2551C2214yescomplemented
83#2551C2212yescomplemented
84#2550C2212yescomplemented
85#2542C2214yes—
86#2538C2214yes—
87#2538C2214yescomplemented
88#2538C2214yescomplemented
89#2522C2214yescomplemented
90#2522C2218yescomplemented
91#2509C2212yescomplemented
92#2507C2214yescomplemented
93#2507C2212yescomplemented
94#2506C2214yescomplemented
95#2465C2214yescomplemented
96#2454C2214yes—
97#2454C2214yes—
98#2454C2212yes—
99#2454C2214yescomplemented
100#2454C2214yescomplemented
101#2454C2214yescomplemented
102#2454C2214yescomplemented
103#2454C2218yescomplemented
104#2454C2218yescomplemented
105#2452C2214yes—
106#2452C2212yes—
107#2452C2214yes—
108#2452C2218yescomplemented
109#2452C2214yescomplemented
110#2452C2214yescomplemented
111#2452C2218yescomplemented
112#2452C2214yescomplemented
113#2452C2214yescomplemented
114#2449C2218yescomplemented
115#2449C2218yescomplemented
116#2441C2214yescomplemented
117#2441C2214yescomplemented
118#2441C2214yescomplemented
119#2440C2214yescomplemented
120#2440C2214yescomplemented
121#2439C2214yescomplemented
122#2437C2218yescomplemented
123#2437C2218yescomplemented
124#2434C2214yescomplemented
125#2417C2218yescomplemented
126#2409C2218yescomplemented
127#2409C2214yescomplemented
128#2396C2214yescomplemented
129#2396C2214yescomplemented
130#2375C2214yes—
131#2375C2214yes—
132#2370C2214yescomplemented
133#2369C2214yescomplemented
134#2366C2211yescharacteristic
135#2366C2211yescharacteristic
136#2366C2211yescharacteristic
137#2363C2214yes—
138#2363C2214yes—
139#2361C2214yes—
140#2358C2214yes—
141#2354C2212yes—
142#2354C2212yes—
143D4×C4⋊C4C2212yes—
144D4×C4⋊C4C2214yescomplemented
145D4×C4⋊C4C2214yescomplemented
146D4×C4⋊C4C2214yescomplemented
147#2345C2214yescomplemented
148D4×C22⋊C4C2214yes—
149D4×C22⋊C4C2214yes—
150D4×C22⋊C4C2214yes—
151#2324C2214yes—
152#2324C2214yes—
153#2321C2214yes—
154#2321C2214yes—
155#2316C2214yescomplemented
156#2309C2214yes—
157#2309C2214yes—
158C4×C4⋊Q8C2212yescomplemented
159C4×#127C2211yescharacteristic
160C4×#127C2211yescharacteristic
161C4×#127C2211yescharacteristic
162C4×#125C2212yescomplemented
163C4×#125C2212yescomplemented
164C4×C22⋊Q8C2214yescomplemented
165C4×#121C2214yes—
166C4×#120C2214yes—
167#2296C2214yescomplemented
168#2296C2214yescomplemented
169#2293C2212yes—
170#2293C2212yes—
171C42×Q8C2211yescharacteristic, complemented
172C42×D4C2212yes—
173C23×Q8C2314yes—
174C23×D4C2314yes—
175C24×C4C2314yes—
176#554—48no—
177D4×Q8—416no—
178D42Q8116yescomplemented
179#544—416no—
180C2×C4⋊Q8C2312yes—
181C2×C4⋊Q8C2314yes—
182C2×C4⋊Q8C2312yes—
183C2×C4⋊Q8C2314yes—
184C2×C4⋊Q8C2314yes—
185C2×C4⋊Q8C2318yes—
186C2×#127C2311yescharacteristic
187C2×#125C2312yes—
188C2×#125C2312yes—
189C2×#125C2314yes—
190C2×#125C2312yes—
191C2×#125C2312yes—
192C2×#125C2314yes—
193C2×#125C2318yes—
194C2×C22⋊Q8—416no—
195C2×C22⋊Q8C2314yes—
196C2×C22⋊Q8C2314yes—
197C2×C22⋊Q8C2314yes—
198C2×C22⋊Q8C2318yes—
199C2×C22⋊Q8C2318yes—
200C2×C22⋊Q8C2318yes—
201C2×C22⋊Q8C2318yes—
202C2×C22⋊Q8C2314yes—
203C2×C22⋊Q8C2318yes—
204C2×C22⋊Q8C2318yes—
205C2×C22⋊Q8C2318yes—
206C2×C22⋊Q8C2318yes—
207C2×#121C2314yes—
208C2×#120C2314yes—
209C2×C4×Q8C2311yescharacteristic
210C2×C4×Q8C2314yes—
211C2×C4×Q8C2312yes—
212C2×C4×D4—416no—
213C2×C4×D4C2314yes—
214C2×C4×D4C2312yes—
215C2×C4×D4C2312yes—
216C2×C4×D4C2312yes—
217C2×C4×D4C2312yes—
218C2×C4×D4C2314yes—
219C2×C4×D4C2314yes—
220C2×C4×D4C2314yes—
221C2×C4×D4C2312yes—
222C2×C4×D4C2314yes—
223C2×C4×D4C2314yes—
224C2×C4×D4C2314yes—
225C2×C4×D4C2318yes—
226C2×C4×D4C2318yes—
227C2×C4×D4C2312yes—
228C2×#117C2314yes—
229C2×#117C2314yes—
230C2×#117C2314yes—
231C2×#117C2314yes—
232C22×C4⋊C4C2314yes—
233C22×C4⋊C4C2314yes—
234C22×C4⋊C4C2314yes—
235C22×C4⋊C4C2314yes—
236C22×C22⋊C4C2314yes—
237C22×C22⋊C4C2314yes—
238C22×C22⋊C4C2318yes—
239C22×C42C2314yes—
240#400C2318yes—
241#400C2314yes—
242#400C2314yes—
243#399C2314yes—
244#399C2318yes—
245#399C2318yes—
246#399C2318yes—
247#399C2314yes—
248#399C2318yes—
249#399C2318yes—
250#399C2318yes—
251#398C2318yes—
252#398C2318yes—
253#398C2318yes—
254#398C2318yes—
255#398C2318yes—
256#398C2314yes—
257#398C2314yes—
258#398C2314yes—
259#398C2314yes—
260#398C2318yes—
261#396C2314yes—
262#396C2314yes—
263#396C2318yes—
264#396C2318yes—
265#396C2318yes—
266#396C2318yes—
267#396C2318yes—
268#396C2318yes—
269#396C2318yes—
270#396C2318yes—
271#396C2318yes—
272#396C2318yes—
273#396C2318yes—
274#396C2314yes—
275#396C2314yes—
276#396C2318yes—
277#396C2318yes—
278#396C2318yes—
279#395C2318yes—
280#395C2314yes—
281#395C2318yes—
282#395C2318yes—
283#395C2314yes—
284#395C2318yes—
285#393C2318yes—
286#393C2318yes—
287#393C2314yes—
288#393C2314yes—
289#393C2318yes—
290#393C2318yes—
291#391C2314yes—
292#391C2318yes—
293#391C2314yes—
294#391C2318yes—
295#390C2312yes—
296#390C2312yes—
297#390C2314yes—
298#390C2314yes—
299#390C2312yes—
300#390C2314yes—
301#390C2312yes—
302#390C2312yes—
303#390C2314yes—
304#390C2318yes—
305#390C2318yes—
306#390C2314yes—
307#390C2314yes—
308#390C2314yes—
309#390C2318yes—
310#390C2318yes—
311#390C2312yes—
312#390C2314yes—
313#390C2312yes—
314#389C2312yes—
315#389C2312yes—
316#389C2312yes—
317#389C2312yes—
318#389C2312yes—
319#389C2312yes—
320#389C2314yes—
321#389C2318yes—
322#389C2318yes—
323#389C2314yes—
324#389C2314yes—
325#389C2314yes—
326#389C2312yes—
327#389C2312yes—
328#389C2314yes—
329#389C2318yes—
330#389C2318yes—
331#389C2312yes—
332#389C2314yes—
333#389C2314yes—
334#389C2318yes—
335#389C2314yes—
336#389C2314yes—
337#389C2312yes—
338#389C2314yes—
339#389C2314yes—
340#389C2318yes—
341#389C2314yes—
342#389C2314yes—
343#389C2314yes—
344#389C2314yes—
345#389C2314yes—
346#389C2314yes—
347#388C2318yes—
348#388C2318yes—
349#388C2314yes—
350#388C2314yes—
351#388C2318yes—
352#388C2318yes—
353#388C2314yes—
354#388C2314yes—
355#388C2318yes—
356#387C2314yes—
357#387C2314yes—
358#387C2314yes—
359#387C2314yes—
360#387C2318yes—
361#387C2318yes—
362#387C2314yes—
363#387C2318yes—
364#387C2314yes—
365#387C2318yes—
366#386C2314yes—
367#386C2314yes—
368#386C2318yes—
369#386C2318yes—
370#386C2314yes—
371#386C2318yes—
372#386C2318yes—
373#386C2318yes—
374#386C2318yes—
375#385C2314yes—
376#385C2314yes—
377#385C2314yes—
378#385C2314yes—
379#385C2318yes—
380#385C2318yes—
381#385C2318yes—
382#385C2318yes—
383#385C2318yes—
384#385C2314yes—
385#385C2314yes—
386#385C2314yes—
387#385C2318yes—
388#385C2314yes—
389#385C2318yes—
390#385C2314yes—
391#385C2314yes—
392#385C2314yes—
393#385C2314yes—
394#385C2314yes—
395#385C2314yes—
396#385C2318yes—
397#385C2314yes—
398#385C2318yes—
399#385C2318yes—
400#385C2318yes—
401#384C2311yescharacteristic
402#384C2311yescharacteristic
403#384C2311yescharacteristic
404#384C2312yes—
405#384C2312yes—
406#384C2314yes—
407#384C2314yes—
408#384C2314yes—
409#382C2312yes—
410#382C2312yes—
411#382C2312yes—
412#382C2312yes—
413#380C2318yes—
414#380C2318yes—
415#380C2318yes—
416#380C2318yes—
417#380C2314yes—
418#380C2314yes—
419#380C2314yes—
420#380C2314yes—
421#380C2314yes—
422#380C2318yes—
423#380C2314yes—
424#380C2314yes—
425#380C2318yes—
426#379C2314yes—
427#379C2314yes—
428#379C2318yes—
429#379C2318yes—
430#379C2314yes—
431C4×C4⋊C4C2312yes—
432C4×C4⋊C4C2312yes—
433C4×C4⋊C4C2312yes—
434C4×C4⋊C4C2314yes—
435C4×C4⋊C4C2314yes—
436C4×C4⋊C4C2314yes—
437C4×C4⋊C4C2314yes—
438C4×C4⋊C4C2314yes—
439C4×C4⋊C4C2311yescharacteristic
440C4×C4⋊C4C2312yes—
441C4×C4⋊C4C2311yescharacteristic
442C4×C4⋊C4C2311yescharacteristic
443C4×C4⋊C4C2318yes—
444C4×C4⋊C4C2314yes—
445C4×C4⋊C4C2314yes—
446C4×C4⋊C4C2312yes—
447C4×C4⋊C4C2318yes—
448C4×C4⋊C4C2312yes—
449C4×C4⋊C4C2312yes—
450C4×C4⋊C4C2312yes—
451C4×C22⋊C4C2314yes—
452C4×C22⋊C4C2314yes—
453C4×C22⋊C4C2314yes—
454C4×C22⋊C4C2314yes—
455C4×C22⋊C4C2314yes—
456C4×C22⋊C4C2314yes—
457C4×C22⋊C4C2314yes—
458C4×C22⋊C4C2314yes—
459C43C2311yescharacteristic
460C43C2311yescharacteristic
461C43C2311yescharacteristic
462C25C2414yes—
463C22×Q8—48no—
464C22×Q8—416no—
465C22×Q8C2414yes—
466C22×Q8C2411yescharacteristic
467C22×Q8C2418yes—
468C22×Q8C2414yes—
469C22×D4—48no—
470C22×D4—48no—
471C22×D4C2×Q8132yescomplemented
472C22×D4C2414yes—
473C22×D4C2412yes—
474C22×D4C2412yes—
475C22×D4C2418yes—
476C23×C4—416no—
477C23×C4—48no—
478C23×C4C2414yes—
479C23×C4C2414yes—
480C23×C4C2414yes—
481C23×C4C2414yes—
482C23×C4C2414yes—
483C23×C4C2418yes—
484C23×C4C2414yes—
485C23×C4C2414yes—
486C23×C4C2414yes—
487C23×C4C2414yes—
488C4⋊Q8—216no—
489C4⋊Q8—28no—
490C4⋊Q8—48no—
491C4⋊Q8—48no—
492C4⋊Q8—44no—
493C4⋊Q8—416no—
494#127C2×Q818yes—
495#125—28no—
496#125—48no—
497#125—44no—
498#125—48no—
499#125—44no—
500#125—44no—
501#125—416no—
502C22⋊Q8—216no—
503C22⋊Q8—416no—
504C22⋊Q8—416no—
505C22⋊Q8—416no—
506C22⋊Q8—416no—
507C22⋊Q8—416no—
508C22⋊Q8—416no—
509C22⋊Q8—416no—
510C22⋊Q8—48no—
511C22⋊Q8—48no—
512C22⋊Q8—416no—
513C22⋊Q8—48no—
514#121C2×Q8132yescomplemented
515#120C2×Q8132yescomplemented
516C4×Q8—24no—
517C4×Q8—44no—
518C4×Q8—48no—
519C4×D4—28no—
520C4×D4—216no—
521C4×D4—48no—
522C4×D4—48no—
523C4×D4—48no—
524C4×D4—48no—
525C4×D4—44no—
526C4×D4—48no—
527C4×D4—48no—
528C4×D4—44no—
529C4×D4—44no—
530C4×D4—44no—
531C4×D4—416no—
532C4×D4—416no—
533C4×D4C2×Q8116yescomplemented
534#117—48no—
535#117—48no—
536#117—48no—
537#117—48no—
538C2×C4⋊C4—216no—
539C2×C4⋊C4—216no—
540C2×C4⋊C4—48no—
541C2×C4⋊C4—48no—
542C2×C4⋊C4C2414yes—
543C2×C4⋊C4C2414yes—
544C2×C4⋊C4C2414yes—
545C2×C4⋊C4C2418yes—
546C2×C4⋊C4C2414yes—
547C2×C4⋊C4C2414yes—
548C2×C4⋊C4C2414yes—
549C2×C4⋊C4C2412yes—
550C2×C4⋊C4C2412yes—
551C2×C4⋊C4C2414yes—
552C2×C4⋊C4C2414yes—
553C2×C4⋊C4C2412yes—
554C2×C4⋊C4C2412yes—
555C2×C4⋊C4C2412yes—
556C2×C4⋊C4C2411yescharacteristic
557C2×C4⋊C4C2411yescharacteristic
558C2×C4⋊C4C2414yes—
559C2×C4⋊C4C2418yes—
560C2×C4⋊C4C2414yes—
561C2×C4⋊C4C2414yes—
562C2×C4⋊C4C2418yes—
563C2×C4⋊C4C2418yes—
564C2×C4⋊C4C2414yes—
565C2×C4⋊C4C2414yes—
566C2×C4⋊C4C2414yes—
567C2×C4⋊C4C2414yes—
568C2×C4⋊C4C2412yes—
569C2×C4⋊C4C2412yes—
570C2×C4⋊C4C2412yes—
571C2×C4⋊C4C2414yes—
572C2×C4⋊C4C2414yes—
573C2×C4⋊C4C2414yes—
574C2×C4⋊C4C2412yes—
575C2×C4⋊C4C2412yes—
576C2×C4⋊C4C2412yes—
577C2×C4⋊C4C2414yes—
578C2×C4⋊C4C2414yes—
579C2×C4⋊C4C2418yes—
580C2×C4⋊C4C2418yes—
581C2×C4⋊C4C2418yes—
582C2×C4⋊C4C2418yes—
583C2×C4⋊C4C2414yes—
584C2×C4⋊C4C2418yes—
585C2×C4⋊C4C2414yes—
586C2×C4⋊C4C2418yes—
587C2×C4⋊C4C2414yes—
588C2×C4⋊C4C2414yes—
589C2×C4⋊C4C2414yes—
590C2×C4⋊C4C2412yes—
591C2×C4⋊C4C2411yescharacteristic
592C2×C4⋊C4C2412yes—
593C2×C22⋊C4—416no—
594C2×C22⋊C4—48no—
595C2×C22⋊C4—48no—
596C2×C22⋊C4C2414yes—
597C2×C22⋊C4C2414yes—
598C2×C22⋊C4C2414yes—
599C2×C22⋊C4C2418yes—
600C2×C22⋊C4C2418yes—
601C2×C22⋊C4C2418yes—
602C2×C22⋊C4C2418yes—
603C2×C22⋊C4C2418yes—
604C2×C22⋊C4C2414yes—
605C2×C22⋊C4C2418yes—
606C2×C22⋊C4C2414yes—
607C2×C22⋊C4C2414yes—
608C2×C22⋊C4C2418yes—
609C2×C22⋊C4C2414yes—
610C2×C22⋊C4C2418yes—
611C2×C22⋊C4C2418yes—
612C2×C22⋊C4C2414yes—
613C2×C22⋊C4C2414yes—
614C2×C22⋊C4C2414yes—
615C2×C22⋊C4C2414yes—
616C2×C22⋊C4C2418yes—
617C2×C22⋊C4C2418yes—
618C2×C22⋊C4C2414yes—
619C2×C22⋊C4C2414yes—
620C2×C22⋊C4C2414yes—
621C2×C22⋊C4C2414yes—
622C2×C22⋊C4C2414yes—
623C2×C22⋊C4C2414yes—
624C2×C22⋊C4C2414yes—
625C2×C42—48no—
626C2×C42C2412yes—
627C2×C42C2412yes—
628C2×C42C2414yes—
629C2×C42C2414yes—
630C2×C42C2412yes—
631C2×C42C2412yes—
632C2×C42C2411yescharacteristic
633C2×C42C2411yescharacteristic
634C2×C42C2411yescharacteristic
635C2×C42C2414yes—
636C2×C42C2412yes—
637C2×C42C2412yes—
638C2×C42C2418yes—
639C2×C42C2418yes—
640C2×C42C2414yes—
641C2×C42C2414yes—
642C2×C42C2411yescharacteristic
643C2×C42C2411yescharacteristic
644C2×C42C2411yescharacteristic
645C2×C42C2411yescharacteristic
646#95C2414yes—
647#95C2414yes—
648#95C2414yes—
649#95C2414yes—
650#95C2414yes—
651#95C2418yes—
652#95C2414yes—
653#95C2414yes—
654#95C2414yes—
655#95C2412yes—
656#95C2412yes—
657#95C2412yes—
658#95C2414yes—
659#95C2418yes—
660#95C2414yes—
661#95C2418yes—
662#95C2414yes—
663#95C2414yes—
664#95C2418yes—
665#95C2418yes—
666#95C2418yes—
667#95C2414yes—
668#95C2414yes—
669#95C2414yes—
670#95C2414yes—
671#95C2414yes—
672#95C2414yes—
673#95C2414yes—
674#95C2418yes—
675#95C2418yes—
676C24—44no—
677C24—48no—
678C24—48no—
679C24—44no—
680C24C22×Q8116yes—
681C24C2514yes—
682C24C2514yes—
683C2×Q8—22no—
684C2×Q8—28no—
685C2×Q8—28no—
686C2×Q8—216no—
687C2×Q8—44no—
688C2×Q8—42no—
689C2×Q8—48no—
690C2×Q8—48no—
691C2×Q8—44no—
692C2×Q8—48no—
693C2×Q8—832no—
694C2×D4—28no—
695C2×D4—24no—
696C2×D4—28no—
697C2×D4—24no—
698C2×D4—464no—
699C2×D4—42no—
700C2×D4—48no—
701C2×D4—48no—
702C2×D4—42no—
703C2×D4C22×Q818yes—
704C2×D4C22×Q8116yes—
705C2×D4C22×Q818yes—
706C2×D4C22×Q8132yes—
707C22×C4—28no—
708C22×C4—28no—
709C22×C4—28no—
710C22×C4—216no—
711C22×C4—28no—
712C22×C4—28no—
713C22×C4—28no—
714C22×C4—216no—
715C22×C4—28no—
716C22×C4—44no—
717C22×C4—44no—
718C22×C4—44no—
719C22×C4—44no—
720C22×C4—44no—
721C22×C4—48no—
722C22×C4—48no—
723C22×C4—48no—
724C22×C4—48no—
725C22×C4—48no—
726C22×C4—48no—
727C22×C4—44no—
728C22×C4—48no—
729C22×C4—44no—
730C22×C4—832no—
731C22×C4C22×Q8116yes—
732C22×C4C2512yes—
733C22×C4C2514yes—
734C22×C4C2514yes—
735C22×C4C2512yes—
736C22×C4C2514yes—
737C22×C4C2512yes—
738C22×C4C2514yes—
739C22×C4C2511yescharacteristic
740C22×C4C2511yescharacteristic
741C22×C4C2514yes—
742C22×C4C2514yes—
743C22×C4C2511yescharacteristic
744C22×C4C2514yes—
745C22×C4C2514yes—
746C22×C4C2511yescharacteristic
747C22×C4C2514yes—
748C22×C4C2511yescharacteristic
749C22×C4C2511yescharacteristic
750C22×C4C2511yescharacteristic
751C22×C4C2514yes—
752C22×C4C2512yes—
753C4⋊C4—216no—
754C4⋊C4—28no—
755C4⋊C4—28no—
756C4⋊C4—28no—
757C4⋊C4—28no—
758C4⋊C4—28no—
759C4⋊C4—28no—
760C4⋊C4—24no—
761C4⋊C4—28no—
762C4⋊C4—24no—
763C4⋊C4—22no—
764C4⋊C4—22no—
765C4⋊C4—28no—
766C4⋊C4—216no—
767C4⋊C4—28no—
768C4⋊C4—28no—
769C4⋊C4—24no—
770C4⋊C4—28no—
771C4⋊C4—24no—
772C4⋊C4—24no—
773C4⋊C4—48no—
774C4⋊C4—48no—
775C4⋊C4—44no—
776C4⋊C4—44no—
777C4⋊C4—44no—
778C4⋊C4—44no—
779C4⋊C4—44no—
780C4⋊C4—44no—
781C4⋊C4—44no—
782C4⋊C4—42no—
783C4⋊C4—42no—
784C4⋊C4—42no—
785C4⋊C4—42no—
786C4⋊C4—42no—
787C4⋊C4—42no—
788C4⋊C4—44no—
789C4⋊C4—44no—
790C4⋊C4—44no—
791C4⋊C4—44no—
792C4⋊C4—44no—
793C4⋊C4—48no—
794C4⋊C4—48no—
795C4⋊C4—48no—
796C4⋊C4—48no—
797C4⋊C4—48no—
798C4⋊C4—44no—
799C4⋊C4—48no—
800C4⋊C4—44no—
801C4⋊C4C22×Q818yes—
802C4⋊C4H(5,𝔽2)14yes—
803C4⋊C4H(5,𝔽2)18yes—
804C22⋊C4—28no—
805C22⋊C4—28no—
806C22⋊C4—28no—
807C22⋊C4—216no—
808C22⋊C4—48no—
809C22⋊C4—48no—
810C22⋊C4—48no—
811C22⋊C4—48no—
812C22⋊C4—44no—
813C22⋊C4—44no—
814C22⋊C4—44no—
815C22⋊C4—44no—
816C22⋊C4—44no—
817C22⋊C4—44no—
818C22⋊C4—44no—
819C22⋊C4—48no—
820C22⋊C4—44no—
821C22⋊C4—44no—
822C22⋊C4—48no—
823C22⋊C4—48no—
824C22⋊C4—48no—
825C22⋊C4—44no—
826C22⋊C4—48no—
827C22⋊C4—44no—
828C22⋊C4—44no—
829C22⋊C4—44no—
830C22⋊C4—48no—
831C22⋊C4C22×Q8116yes—
832C22⋊C4C22×Q8116yes—
833C42—24no—
834C42—28no—
835C42—24no—
836C42—28no—
837C42—22no—
838C42—22no—
839C42—22no—
840C42—24no—
841C42—24no—
842C42—28no—
843C42—24no—
844C42—24no—
845C42—44no—
846C42—44no—
847C42—41no—
848C42—41no—
849C42—41no—
850C42—48no—
851C42—48no—
852C42C22×Q814yes—
853C23—24no—
854C23—28no—
855C23—24no—
856C23—24no—
857C23—24no—
858C23—24no—
859C23—28no—
860C23—24no—
861C23—24no—
862C23—24no—
863C23—432no—
864C23—416no—
865C23—88no—
866C23—88no—
867C23—816no—
868C23C23×Q818yes—
869C23C23×Q818yes—
870C23C2611yescharacteristic
871Q8—416no—
872Q8—44no—
873Q8—816no—
874Q8—164no—
875D4—216no—
876D4—232no—
877D4—432no—
878D4—48no—
879C2×C4—21no—
880C2×C4—22no—
881C2×C4—24no—
882C2×C4—22no—
883C2×C4—24no—
884C2×C4—24no—
885C2×C4—22no—
886C2×C4—24no—
887C2×C4—21no—
888C2×C4—232no—
889C2×C4—22no—
890C2×C4—24no—
891C2×C4—22no—
892C2×C4—21no—
893C2×C4—21no—
894C2×C4—21no—
895C2×C4—24no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—24no—
899C2×C4—24no—
900C2×C4—28no—
901C2×C4—24no—
902C2×C4—24no—
903C2×C4—24no—
904C2×C4—24no—
905C2×C4—28no—
906C2×C4—24no—
907C2×C4—24no—
908C2×C4—22no—
909C2×C4—24no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—22no—
913C2×C4—24no—
914C2×C4—22no—
915C2×C4—24no—
916C2×C4—28no—
917C2×C4—24no—
918C2×C4—24no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—24no—
923C2×C4—24no—
924C2×C4—24no—
925C2×C4—416no—
926C2×C4—416no—
927C2×C4—88no—
928C2×C4—88no—
929C2×C4—816no—
930C2×C4—88no—
931C2×C4—88no—
932C2×C4—88no—
933C2×C4—88no—
934C2×C4C23×Q812yes—
935C2×C4C23×Q818yes—
936C2×C4C23×Q814yes—
937C2×C4C2×H(5,𝔽2)12yes—
938C2×C4C2×H(5,𝔽2)12yes—
939C2×C4C2×H(5,𝔽2)12yes—
940C2×C4C2×H(5,𝔽2)18yes—
941C2×C4C2×H(5,𝔽2)14yes—
942C2×C4#58514yes—
943C22—28no—
944C22—28no—
945C22—28no—
946C22—28no—
947C22—216no—
948C22—44no—
949C22—44no—
950C22—44no—
951C22—44no—
952C22—44no—
953C22—48no—
954C22—44no—
955C22—832no—
956C22C24×Q811yescharacteristic
957C22C22×H(5,𝔽2)11yescharacteristic
958C22C22×H(5,𝔽2)12yes—
959C22C2×#58512yes—
960C222−1+611yescharacteristic
961C4—22no—
962C4—22no—
963C4—28no—
964C4—22no—
965C4—22no—
966C4—28no—
967C4—44no—
968C4—44no—
969C4—44no—
970C4—41no—
971C4—44no—
972C4—44no—
973C4—41no—
974C4—41no—
975C4—42no—
976C4—44no—
977C4—42no—
978C4—44no—
979C4—44no—
980C4—42no—
981C4#350118yes—
982C2—48no—
983C2—48no—
984C2#6275911yescharacteristic
985C2C2×#350112yes—
986C2#6292212yes—
987C2Q8×H(5,𝔽2)11yescharacteristic
988C2#6301111yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×D42C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59817C2semidirect
2. #59569C2semidirect
3. #59466C2semidirect
4. #59466C2semidirect
5. #48839C2semidirect
6. #47960C2semidirect
7. #45492C2semidirect
8. #44943C2semidirect
9. #44879C2semidirect
10. #42490C2semidirect
11. #42486C2semidirect
12. #39688C2semidirect
13. #39588C2semidirect
14. #39369C2semidirect
15. #38965C2semidirect
16. #36559C2semidirect
17. #36407C2semidirect
18. D4×C22⋊Q8C2semidirect
19. #35174C2semidirect
20. #34893C2semidirect
24. C2×#554C22semidirect
25. C2×D4×Q8C22semidirect
27. C2×#544C22semidirect
28. C22×C22⋊Q8C22semidirect
30. #2868C22semidirect
31. #2859C22semidirect
32. #2859C22semidirect
33. #2857C22semidirect
34. #2848C22semidirect
35. #2848C22semidirect
36. #2842C22semidirect
37. #2788C22semidirect
38. #2784C22semidirect
39. #2780C22semidirect
40. #2780C22semidirect
41. #2780C22semidirect
42. #2768C22semidirect
43. #2748C22semidirect
44. #2748C22semidirect
45. #2748C22semidirect
46. #2732C22semidirect
47. #2729C22semidirect
48. #2720C22semidirect
49. #2704C22semidirect
50. #2704C22semidirect
51. #2692C22semidirect
52. #2683C22semidirect
53. #2683C22semidirect
54. #2677C22semidirect
55. #2629C22semidirect
56. #2628C22semidirect
57. #2626C22semidirect
58. #2626C22semidirect
59. #2626C22semidirect
60. #2626C22semidirect
61. #2589C22semidirect
62. #2587C22semidirect
63. #2587C22semidirect
64. #2584C22semidirect
65. #2584C22semidirect
66. #2583C22semidirect
67. #2583C22semidirect
69. #2579C22semidirect
70. #2579C22semidirect
71. #2574C22semidirect
73. #2566C22semidirect
74. #2566C22semidirect
75. #2566C22semidirect
76. #2566C22semidirect
77. #2563C22semidirect
78. #2556C22semidirect
79. #2556C22semidirect
80. #2552C22semidirect
81. #2552C22semidirect
82. #2551C22semidirect
83. #2551C22semidirect
84. #2550C22semidirect
87. #2538C22semidirect
88. #2538C22semidirect
89. #2522C22semidirect
90. #2522C22semidirect
91. #2509C22semidirect
92. #2507C22semidirect
93. #2507C22semidirect
94. #2506C22semidirect
95. #2465C22semidirect
99. #2454C22semidirect
100. #2454C22semidirect
101. #2454C22semidirect
102. #2454C22semidirect
103. #2454C22semidirect
104. #2454C22semidirect
108. #2452C22semidirect
109. #2452C22semidirect
110. #2452C22semidirect
111. #2452C22semidirect
112. #2452C22semidirect
113. #2452C22semidirect
114. #2449C22semidirect
115. #2449C22semidirect
116. #2441C22semidirect
117. #2441C22semidirect
118. #2441C22semidirect
119. #2440C22semidirect
120. #2440C22semidirect
121. #2439C22semidirect
122. #2437C22semidirect
123. #2437C22semidirect
124. #2434C22semidirect
125. #2417C22semidirect
126. #2409C22semidirect
127. #2409C22semidirect
128. #2396C22semidirect
129. #2396C22semidirect
132. #2370C22semidirect
133. #2369C22semidirect
144. D4×C4⋊C4C22semidirect
145. D4×C4⋊C4C22semidirect
146. D4×C4⋊C4C22semidirect
147. #2345C22semidirect
155. #2316C22semidirect
158. C4×C4⋊Q8C22semidirect
162. C4×#125C22semidirect
163. C4×#125C22semidirect
164. C4×C22⋊Q8C22semidirect
167. #2296C22semidirect
168. #2296C22semidirect
171. C42×Q8C22semidirect
178. D42Q8semidirect
471. C22×D4C2×Q8semidirect
514. #121C2×Q8semidirect
515. #120C2×Q8semidirect
533. C4×D4C2×Q8semidirect

Maximal subgroups

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

subgroupindex
#598172
#595692
#594662
#488392
#479602
#454922
#449432
#448792
#424902
#424862
#396882
#395882
#393692
#389652
#365592
#364072
D4×C22⋊Q82
#351742
#348932
#344932
C4×D422