Finite Group Databasebeta

← #7678680

Subgroups — #7678680

Order 512.

4880 conjugacy classes of subgroups.

The subgroup lattice has 1002 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59922C214yesmaximal, complemented
2#59920C214yesmaximal, complemented
3#59756C214yesmaximal, complemented
4#59551C214yesmaximal, complemented
5#45415C214yesmaximal, complemented
6#45413C214yesmaximal, complemented
7#45180C214yesmaximal, complemented
8#44997C214yesmaximal, complemented
9#39492C214yesmaximal
10#37877C214yesmaximal, complemented
11#37876C214yesmaximal
12#36193C214yesmaximal, complemented
13#35662C212yesmaximal, complemented
14#35585C212yesmaximal, complemented
15#35173C211yesmaximal, characteristic, complemented
16#35154C211yesmaximal, characteristic, complemented
17#35151C211yesmaximal, characteristic
18#34739C212yesmaximal
19#34271C211yesmaximal, characteristic, complemented
20#34203C212yesmaximal
21#34182C211yesmaximal, characteristic, complemented
22C2×#2362C211yesmaximal, characteristic
23#34052C211yesmaximal, characteristic
24C2×#544C2211yescharacteristic
25C2×#533C2212yes—
26C22×C22⋊Q8C2211yescharacteristic
27C2×#519C2212yes—
28C22×C4×Q8C2211yescharacteristic
29C22×#117C2211yescharacteristic
30C22×#117C2212yes—
31#2857C2214yes—
32#2855C2214yes—
33#2855C2214yes—
34#2807C2218yes—
35#2792C2218yescomplemented
36#2791C2218yescomplemented
37#2790C2218yes—
38#2790C2218yes—
39#2788C2218yes—
40#2774C2218yescomplemented
41#2768C2218yes—
42#2763C2218yes—
43#2755C2218yescomplemented
44#2729C2218yes—
45#2720C2218yes—
46#2659C2214yes—
47#2627C2214yes—
48#2626C2214yes—
49#2590C2218yescomplemented
50#2589C2218yes—
51#2589C2218yes—
52#2588C2218yescomplemented
53#2587C2218yes—
54#2587C2218yes—
55#2586C2218yescomplemented
56#2585C2218yescomplemented
57#2584C2214yescomplemented
58#2584C2214yescomplemented
59#2582C2214yescomplemented
60#2582C2214yescomplemented
61#2581C2214yescomplemented
62#2581C2214yescomplemented
63#2574C2218yes—
64#2569C2218yes—
65#2567C2214yescomplemented
66#2567C2214yescomplemented
67#2556C2218yes—
68#2552C2214yescomplemented
69#2546C2214yescomplemented
70#2522C2218yes—
71#2520C2218yescomplemented
72#2520C2218yescomplemented
73#2511C2214yescomplemented
74#2511C2214yescomplemented
75#2509C2214yescomplemented
76#2509C2214yescomplemented
77#2508C2214yescomplemented
78#2508C2214yescomplemented
79#2508C2218yescomplemented
80#2507C2214yescomplemented
81#2507C2214yescomplemented
82#2507C2214yescomplemented
83#2507C2214yescomplemented
84#2506C2214yescomplemented
85#2506C2214yescomplemented
86#2465C2218yes—
87#2453C2214yescomplemented
88#2453C2214yescomplemented
89#2453C2214yescomplemented
90#2453C2214yescomplemented
91#2451C2214yescomplemented
92#2451C2214yescomplemented
93#2451C2214yescomplemented
94#2451C2214yescomplemented
95#2442C2218yes—
96#2442C2212yes—
97#2442C2212yes—
98#2441C2212yes—
99#2441C2214yes—
100#2441C2214yes—
101#2441C2212yes—
102#2440C2212yes—
103#2440C2212yes—
104#2439C2214yes—
105#2439C2212yes—
106#2439C2214yes—
107#2439C2212yes—
108#2438C2218yes—
109#2438C2218yes—
110#2438C2214yes—
111#2438C2214yes—
112#2437C2214yes—
113#2437C2214yes—
114#2396C2214yes—
115#2396C2214yes—
116#2370C2218yescomplemented
117#2370C2214yescomplemented
118#2370C2214yescomplemented
119#2369C2214yescomplemented
120#2369C2214yescomplemented
121#2365C2214yescomplemented
122#2362C2214yes—
123#2362C2214yes—
124#2362C2214yes—
125#2362C2214yes—
126#2362C2214yes—
127#2362C2214yes—
128#2360C2214yes—
129#2360C2214yes—
130#2355C2214yescomplemented
131#2351C2214yescomplemented
132#2351C2214yescomplemented
133Q8×C4⋊C4C2214yescomplemented
134Q8×C4⋊C4C2214yescomplemented
135#2344C2218yes—
136#2342C2218yes—
137#2329C2214yes—
138#2323C2214yes—
139#2323C2214yes—
140#2317C2212yes—
141#2317C2214yes—
142#2317C2214yes—
143#2316C2212yes—
144#2316C2212yes—
145#2316C2211yescharacteristic
146#2316C2211yescharacteristic
147#2316C2214yes—
148#2316C2211yescharacteristic
149#2315C2214yes—
150#2310C2212yes—
151C4×C22⋊Q8C2214yes—
152C4×C22⋊Q8C2214yes—
153C4×C22⋊Q8C2214yes—
154C4×C22⋊Q8C2214yes—
155C4×C22⋊Q8C2214yes—
156#2296C2212yes—
157#2296C2214yes—
158#2296C2214yes—
159#2296C2212yes—
160C2×#391C2211yescharacteristic
161C2×#389C2211yescharacteristic
162C2×#388C2212yes—
163C2×#388C2212yes—
164C2×#387C2212yes—
165#2285C2212yes—
166#2285C2214yes—
167#2285C2214yes—
168#2280C2212yes—
169#2274C2212yes—
170C2×C4×C4⋊C4C2212yes—
171C2×C4×C4⋊C4C2211yescharacteristic
172C2×C4×C22⋊C4C2211yescharacteristic
173C23×Q8C2311yescharacteristic
174C24×C4C2311yescharacteristic
175#544—28no—
176#533—48no—
177C2×C4⋊Q8C2314yes—
178C2×C4⋊Q8C2312yes—
179C2×C4⋊Q8C2314yes—
180C2×C4⋊Q8C2312yes—
181C2×#125C2314yes—
182C2×#125C2312yes—
183C2×#125C2312yes—
184C2×#125C2318yes—
185C2×C22⋊Q8Q8116yescomplemented
186C2×C22⋊Q8C2314yes—
187C2×C22⋊Q8C2314yes—
188C2×C22⋊Q8C2314yes—
189C2×C22⋊Q8C2314yes—
190C2×C22⋊Q8C2314yes—
191C2×C22⋊Q8C2314yes—
192C2×C22⋊Q8C2314yes—
193#519—48no—
194C2×C4×Q8—28no—
195C2×C4×Q8C2314yes—
196C2×C4×Q8C2314yes—
197C2×C4×Q8C2314yes—
198C2×C4×Q8C2314yes—
199C2×C4×Q8C2314yes—
200C2×C4×Q8C2314yes—
201C2×C4×Q8C2314yes—
202C2×C4×Q8C2314yes—
203C2×C4×Q8C2314yes—
204C2×#117—28no—
205C2×#117—48no—
206C2×#117C2312yes—
207C2×#117C2312yes—
208C2×#117C2312yes—
209C2×#117C2312yes—
210C2×#117C2314yes—
211C2×#117C2314yes—
212C2×#117C2318yes—
213C2×#117C2314yes—
214C2×#117C2314yes—
215C2×#117C2312yes—
216C2×#117C2312yes—
217C22×C4⋊C4C2311yescharacteristic
218C22×C4⋊C4C2312yes—
219C22×C4⋊C4C2312yes—
220C22×C4⋊C4C2312yes—
221C22×C4⋊C4C2312yes—
222C22×C4⋊C4C2311yescharacteristic
223C22×C4⋊C4C2312yes—
224C22×C4⋊C4C2311yescharacteristic
225C22×C22⋊C4C2312yes—
226C22×C22⋊C4C2314yes—
227C22×C22⋊C4C2311yescharacteristic
228C22×C22⋊C4C2311yescharacteristic
229C22×C22⋊C4C2312yes—
230C22×C42C2312yes—
231C22×C42C2312yes—
232C22×C42C2311yescharacteristic
233C22×C42C2311yescharacteristic
234C22×C42C2312yes—
235C22×C42C2314yes—
236#400C2318yes—
237#400C2318yes—
238#400C2318yes—
239#400C2318yes—
240#400C2318yes—
241#400C2318yes—
242#400C2318yes—
243#400C2314yes—
244#400C2314yes—
245#399C2314yes—
246#399C2318yes—
247#399C2314yes—
248#398C2318yes—
249#398C2318yes—
250#398C2318yes—
251#398C2318yes—
252#398C2318yes—
253#398C2318yes—
254#398C2318yes—
255#398C2318yes—
256#398C2318yes—
257#398C2318yes—
258#398C2318yes—
259#398C2314yes—
260#398C2314yes—
261#398C2314yes—
262#398C2314yes—
263#398C2318yes—
264#396C2318yes—
265#396C2314yes—
266#396C2314yes—
267#396C2318yes—
268#396C2314yes—
269#396C2314yes—
270#395C2314yes—
271#395C2318yes—
272#395C2318yes—
273#395C2318yes—
274#395C2318yes—
275#395C2318yes—
276#395C2314yes—
277#393C2314yes—
278#393C2314yes—
279#393C2318yes—
280#391C2314yes—
281#391C2314yes—
282#391C2314yes—
283#391C2314yes—
284#391C2314yes—
285#391C2318yes—
286#391C2314yes—
287#391C2318yes—
288#391C2314yes—
289#391C2314yes—
290#391C2318yes—
291#391C2318yes—
292#391C2314yes—
293#391C2314yes—
294#391C2314yes—
295#391C2314yes—
296#391C2314yes—
297#389C2314yes—
298#389C2314yes—
299#389C2314yes—
300#389C2314yes—
301#389C2318yes—
302#389C2318yes—
303#389C2314yes—
304#389C2314yes—
305#389C2314yes—
306#389C2314yes—
307#389C2314yes—
308#389C2314yes—
309#389C2314yes—
310#389C2314yes—
311#389C2314yes—
312#389C2314yes—
313#389C2318yes—
314#389C2318yes—
315#389C2318yes—
316#389C2318yes—
317#389C2314yes—
318#389C2314yes—
319#389C2318yes—
320#389C2312yes—
321#389C2312yes—
322#389C2312yes—
323#389C2312yes—
324#389C2318yes—
325#389C2318yes—
326#389C2314yes—
327#389C2318yes—
328#389C2314yes—
329#389C2318yes—
330#389C2314yes—
331#389C2318yes—
332#389C2314yes—
333#389C2314yes—
334#389C2314yes—
335#389C2314yes—
336#389C2314yes—
337#389C2314yes—
338#389C2314yes—
339#389C2314yes—
340#389C2312yes—
341#389C2312yes—
342#389C2312yes—
343#389C2312yes—
344#388C2318yes—
345#388C2318yes—
346#388C2318yes—
347#388C2318yes—
348#388C2318yes—
349#388C2318yes—
350#388C2318yes—
351#388C2318yes—
352#387C2318yes—
353#387C2318yes—
354#387C2318yes—
355#387C2318yes—
356#387C2318yes—
357#387C2318yes—
358#387C2318yes—
359#387C2318yes—
360#387C2318yes—
361#387C2318yes—
362#387C2318yes—
363#387C2318yes—
364#387C2318yes—
365#387C2314yes—
366#387C2318yes—
367#387C2318yes—
368#387C2318yes—
369#387C2314yes—
370#387C2318yes—
371#387C2318yes—
372#387C2318yes—
373#387C2314yes—
374#387C2318yes—
375#387C2318yes—
376#387C2314yes—
377#385C2314yes—
378#385C2318yes—
379#385C2318yes—
380#385C2318yes—
381#385C2318yes—
382#385C2318yes—
383#385C2314yes—
384#385C2314yes—
385#385C2314yes—
386#385C2314yes—
387#385C2314yes—
388#385C2318yes—
389#385C2318yes—
390#385C2314yes—
391#385C2314yes—
392#384C2314yes—
393#384C2314yes—
394#384C2314yes—
395#384C2314yes—
396#384C2314yes—
397#384C2312yes—
398#384C2312yes—
399#384C2314yes—
400#382C2318yes—
401#382C2314yes—
402#382C2318yes—
403#382C2312yes—
404#382C2312yes—
405#382C2318yes—
406#381C2318yes—
407#381C2314yes—
408#380C2314yes—
409#380C2318yes—
410#380C2318yes—
411#380C2314yes—
412#380C2314yes—
413#380C2314yes—
414#380C2314yes—
415#380C2312yes—
416#380C2312yes—
417#380C2314yes—
418#380C2314yes—
419#380C2312yes—
420#380C2312yes—
421#379C2314yes—
422C4×C4⋊C4C2314yes—
423C4×C4⋊C4C2314yes—
424C4×C4⋊C4C2314yes—
425C4×C4⋊C4C2314yes—
426C4×C4⋊C4C2314yes—
427C4×C4⋊C4C2314yes—
428C4×C4⋊C4C2314yes—
429C4×C4⋊C4C2318yes—
430C4×C4⋊C4C2318yes—
431C4×C4⋊C4C2318yes—
432C4×C4⋊C4C2314yes—
433C4×C4⋊C4C2318yes—
434C4×C4⋊C4C2314yes—
435C4×C4⋊C4C2314yes—
436C4×C4⋊C4C2318yes—
437C4×C4⋊C4C2314yes—
438C4×C4⋊C4C2314yes—
439C4×C4⋊C4C2314yes—
440C4×C4⋊C4C2314yes—
441C4×C4⋊C4C2314yes—
442C4×C4⋊C4C2314yes—
443C4×C4⋊C4C2314yes—
444C4×C4⋊C4C2314yes—
445C4×C4⋊C4C2314yes—
446C4×C4⋊C4C2314yes—
447C4×C4⋊C4C2314yes—
448C4×C22⋊C4C2318yes—
449C4×C22⋊C4C2318yes—
450C4×C22⋊C4C2318yes—
451C4×C22⋊C4C2314yes—
452C4×C22⋊C4C2312yes—
453C4×C22⋊C4C2312yes—
454C4×C22⋊C4C2312yes—
455C4×C22⋊C4C2314yes—
456C4×C22⋊C4C2312yes—
457C2×#95C2312yes—
458C2×#95C2312yes—
459C2×#95C2311yescharacteristic
460C2×#95C2311yescharacteristic
461C2×#95C2312yes—
462C2×#95C2312yes—
463C25C2411yescharacteristic
464C22×Q8—24no—
465C22×Q8—24no—
466C22×Q8C2×Q818yes—
467C22×Q8C2414yes—
468C22×Q8C2414yes—
469C22×Q8C2414yes—
470C22×Q8C2414yes—
471C23×C4—24no—
472C23×C4—24no—
473C23×C4C2×Q818yes—
474C23×C4C2411yescharacteristic
475C23×C4C2411yescharacteristic
476C23×C4C2412yes—
477C23×C4C2412yes—
478C23×C4C2411yescharacteristic
479C23×C4C2412yes—
480C23×C4C2412yes—
481C23×C4C2411yescharacteristic
482C23×C4C2411yescharacteristic
483C23×C4C2414yes—
484C23×C4C2414yes—
485C23×C4C2412yes—
486C23×C4C2412yes—
487C23×C4C2411yescharacteristic
488C4⋊Q8—216no—
489C4⋊Q8—44no—
490C4⋊Q8—44no—
491C4⋊Q8—48no—
492#125—216no—
493#125—44no—
494#125—44no—
495#125—416no—
496C22⋊Q8—216no—
497C22⋊Q8—48no—
498C22⋊Q8—48no—
499C22⋊Q8—48no—
500C22⋊Q8—48no—
501C22⋊Q8C2×Q8132yes—
502C22⋊Q8C2×Q8132yes—
503C4×Q8—216no—
504C4×Q8—216no—
505C4×Q8—48no—
506C4×Q8—48no—
507C4×Q8—48no—
508C4×Q8—48no—
509C4×Q8—48no—
510C4×Q8—48no—
511C4×Q8—48no—
512#117—28no—
513#117—28no—
514#117—28no—
515#117—28no—
516#117—216no—
517#117—216no—
518#117—48no—
519#117—48no—
520#117—416no—
521#117—44no—
522#117—44no—
523C2×C4⋊C4—24no—
524C2×C4⋊C4—28no—
525C2×C4⋊C4—44no—
526C2×C4⋊C4—44no—
527C2×C4⋊C4—44no—
528C2×C4⋊C4C2×Q8116yes—
529C2×C4⋊C4C2×Q818yes—
530C2×C4⋊C4#4118yes—
531C2×C4⋊C4C2412yes—
532C2×C4⋊C4C2412yes—
533C2×C4⋊C4C2412yes—
534C2×C4⋊C4C2412yes—
535C2×C4⋊C4C2414yes—
536C2×C4⋊C4C2418yes—
537C2×C4⋊C4C2414yes—
538C2×C4⋊C4C2412yes—
539C2×C4⋊C4C2412yes—
540C2×C4⋊C4C2412yes—
541C2×C4⋊C4C2412yes—
542C2×C4⋊C4C2414yes—
543C2×C4⋊C4C2414yes—
544C2×C4⋊C4C2414yes—
545C2×C4⋊C4C2414yes—
546C2×C4⋊C4C2418yes—
547C2×C4⋊C4C2414yes—
548C2×C4⋊C4C2414yes—
549C2×C4⋊C4C2414yes—
550C2×C4⋊C4C2418yes—
551C2×C4⋊C4C2418yes—
552C2×C4⋊C4C2414yes—
553C2×C4⋊C4C2414yes—
554C2×C4⋊C4C2414yes—
555C2×C4⋊C4C2414yes—
556C2×C4⋊C4C2414yes—
557C2×C4⋊C4C2414yes—
558C2×C4⋊C4C2414yes—
559C2×C4⋊C4C2414yes—
560C2×C4⋊C4C2414yes—
561C2×C4⋊C4C2414yes—
562C2×C4⋊C4C2418yes—
563C2×C4⋊C4C2418yes—
564C2×C4⋊C4C2418yes—
565C2×C4⋊C4C2414yes—
566C2×C4⋊C4C2414yes—
567C2×C4⋊C4C2418yes—
568C2×C4⋊C4C2414yes—
569C2×C4⋊C4C2414yes—
570C2×C4⋊C4C2414yes—
571C2×C4⋊C4C2414yes—
572C2×C4⋊C4C2414yes—
573C2×C4⋊C4C2418yes—
574C2×C4⋊C4C2414yes—
575C2×C4⋊C4C2414yes—
576C2×C4⋊C4C2414yes—
577C2×C4⋊C4C2414yes—
578C2×C4⋊C4C2418yes—
579C2×C4⋊C4C2414yes—
580C2×C4⋊C4C2414yes—
581C2×C4⋊C4C2414yes—
582C2×C4⋊C4C2414yes—
583C2×C22⋊C4—28no—
584C2×C22⋊C4—42no—
585C2×C22⋊C4—42no—
586C2×C22⋊C4—48no—
587C2×C22⋊C4C2×Q8116yes—
588C2×C22⋊C4C2414yes—
589C2×C22⋊C4C2414yes—
590C2×C22⋊C4C2418yes—
591C2×C22⋊C4C2412yes—
592C2×C22⋊C4C2412yes—
593C2×C22⋊C4C2414yes—
594C2×C22⋊C4C2414yes—
595C2×C22⋊C4C2414yes—
596C2×C22⋊C4C2414yes—
597C2×C22⋊C4C2412yes—
598C2×C22⋊C4C2412yes—
599C2×C22⋊C4C2414yes—
600C2×C22⋊C4C2414yes—
601C2×C22⋊C4C2414yes—
602C2×C22⋊C4C2414yes—
603C2×C22⋊C4C2418yes—
604C2×C42—28no—
605C2×C42—28no—
606C2×C42—24no—
607C2×C42—24no—
608C2×C42—48no—
609C2×C42—44no—
610C2×C42C2414yes—
611C2×C42C2414yes—
612C2×C42C2414yes—
613C2×C42C2414yes—
614C2×C42C2414yes—
615C2×C42C2414yes—
616C2×C42C2412yes—
617C2×C42C2412yes—
618C2×C42C2412yes—
619C2×C42C2412yes—
620C2×C42C2414yes—
621C2×C42C2414yes—
622C2×C42C2414yes—
623C2×C42C2414yes—
624C2×C42C2414yes—
625C2×C42C2418yes—
626C2×C42C2418yes—
627C2×C42C2418yes—
628C2×C42C2418yes—
629C2×C42C2414yes—
630#95C2411yescharacteristic
631#95C2411yescharacteristic
632#95C2411yescharacteristic
633#95C2411yescharacteristic
634#95C2412yes—
635#95C2412yes—
636#95C2418yes—
637#95C2414yes—
638#95C2414yes—
639#95C2418yes—
640#95C2418yes—
641#95C2414yes—
642#95C2414yes—
643#95C2418yes—
644#95C2418yes—
645#95C2414yes—
646#95C2414yes—
647#95C2418yes—
648#95C2418yes—
649#95C2418yes—
650#95C2418yes—
651#95C2414yes—
652#95C2414yes—
653#95C2418yes—
654#95C2414yes—
655#95C2414yes—
656#95C2414yes—
657#95C2418yes—
658#95C2418yes—
659#95C2418yes—
660#95C2414yes—
661#95C2418yes—
662#95C2414yes—
663#95C2418yes—
664#95C2418yes—
665#95C2414yes—
666#95C2414yes—
667#95C2414yes—
668#95C2414yes—
669#95C2414yes—
670#95C2418yes—
671#95C2418yes—
672C24—22no—
673C24—22no—
674C24—41no—
675C24—41no—
676C24—41no—
677C24—41no—
678C24C22×Q814yes—
679C24C2512yes—
680C24C2511yescharacteristic
681C2×Q8—232no—
682C2×Q8—28no—
683C2×Q8—28no—
684C2×Q8—28no—
685C2×Q8—28no—
686C2×Q8—44no—
687C2×Q8—44no—
688C2×Q8—44no—
689C2×Q8—44no—
690C2×Q8—44no—
691C2×Q8—44no—
692C2×Q8—44no—
693C2×Q8C22×Q8116yes—
694C22×C4—22no—
695C22×C4—24no—
696C22×C4—22no—
697C22×C4—24no—
698C22×C4—232no—
699C22×C4—24no—
700C22×C4—24no—
701C22×C4—24no—
702C22×C4—24no—
703C22×C4—22no—
704C22×C4—22no—
705C22×C4—24no—
706C22×C4—22no—
707C22×C4—22no—
708C22×C4—22no—
709C22×C4—22no—
710C22×C4—42no—
711C22×C4—42no—
712C22×C4—42no—
713C22×C4—41no—
714C22×C4—42no—
715C22×C4—41no—
716C22×C4—44no—
717C22×C4—44no—
718C22×C4—41no—
719C22×C4—41no—
720C22×C4—42no—
721C22×C4—44no—
722C22×C4—44no—
723C22×C4—41no—
724C22×C4—42no—
725C22×C4—44no—
726C22×C4—44no—
727C22×C4—41no—
728C22×C4C22×Q818yes—
729C22×C4C22×Q814yes—
730C22×C4C22×Q818yes—
731C22×C4C22×Q818yes—
732C22×C4C22×Q818yes—
733C22×C4C22×Q814yes—
734C22×C4C2×#4118yes—
735C22×C4C2×#4114yes—
736C22×C4H(5,𝔽2)14yes—
737C22×C4C2514yes—
738C22×C4C2511yescharacteristic
739C22×C4C2514yes—
740C22×C4C2512yes—
741C22×C4C2512yes—
742C22×C4C2514yes—
743C22×C4C2514yes—
744C22×C4C2514yes—
745C22×C4C2511yescharacteristic
746C22×C4C2514yes—
747C22×C4C2514yes—
748C22×C4C2514yes—
749C22×C4C2514yes—
750C22×C4C2511yescharacteristic
751C22×C4C2514yes—
752C22×C4C2514yes—
753C22×C4C2511yescharacteristic
754C22×C4C2514yes—
755C22×C4C2511yescharacteristic
756C22×C4C2511yescharacteristic
757C22×C4C2512yes—
758C4⋊C4—28no—
759C4⋊C4—216no—
760C4⋊C4—24no—
761C4⋊C4—24no—
762C4⋊C4—28no—
763C4⋊C4—216no—
764C4⋊C4—24no—
765C4⋊C4—24no—
766C4⋊C4—24no—
767C4⋊C4—24no—
768C4⋊C4—24no—
769C4⋊C4—24no—
770C4⋊C4—28no—
771C4⋊C4—28no—
772C4⋊C4—28no—
773C4⋊C4—28no—
774C4⋊C4—44no—
775C4⋊C4—44no—
776C4⋊C4—44no—
777C4⋊C4—44no—
778C4⋊C4—44no—
779C4⋊C4—44no—
780C4⋊C4—44no—
781C4⋊C4—48no—
782C4⋊C4—44no—
783C4⋊C4—44no—
784C4⋊C4—44no—
785C4⋊C4—44no—
786C4⋊C4—44no—
787C4⋊C4—48no—
788C4⋊C4—48no—
789C4⋊C4—48no—
790C4⋊C4—44no—
791C4⋊C4—44no—
792C4⋊C4—44no—
793C4⋊C4—44no—
794C4⋊C4—44no—
795C4⋊C4—44no—
796C4⋊C4—44no—
797C4⋊C4—44no—
798C4⋊C4—44no—
799C4⋊C4—44no—
800C4⋊C4—48no—
801C4⋊C4—48no—
802C4⋊C4—48no—
803C4⋊C4—48no—
804C4⋊C4—44no—
805C4⋊C4—44no—
806C4⋊C4C22×Q8116yes—
807C4⋊C4C22×Q8116yes—
808C4⋊C4C22×Q8116yes—
809C4⋊C4C2×#41116yes—
810C22⋊C4—28no—
811C22⋊C4—28no—
812C22⋊C4—28no—
813C22⋊C4—28no—
814C22⋊C4—216no—
815C22⋊C4—24no—
816C22⋊C4—24no—
817C22⋊C4—42no—
818C22⋊C4—42no—
819C22⋊C4—44no—
820C22⋊C4—44no—
821C22⋊C4—44no—
822C22⋊C4—44no—
823C22⋊C4—44no—
824C22⋊C4—44no—
825C22⋊C4C22×Q8132yes—
826C42—28no—
827C42—28no—
828C42—28no—
829C42—24no—
830C42—28no—
831C42—24no—
832C42—28no—
833C42—24no—
834C42—24no—
835C42—28no—
836C42—28no—
837C42—28no—
838C42—28no—
839C42—44no—
840C42—44no—
841C42—44no—
842C42—48no—
843C42—48no—
844C42—48no—
845C42—48no—
846C23—21no—
847C23—21no—
848C23—21no—
849C23—21no—
850C23—22no—
851C23—22no—
852C23—22no—
853C23—22no—
854C23—22no—
855C23—22no—
856C23—28no—
857C23—44no—
858C23—44no—
859C23—82no—
860C23—82no—
861C23—82no—
862C23—82no—
863C23C23×Q814yes—
864C23C23×Q812yes—
865C23C22×#4112yes—
866C23C2×H(5,𝔽2)12yes—
867C23C2611yescharacteristic
868Q8—232no—
869Q8—88no—
870Q8—88no—
871Q8—88no—
872C2×C4—21no—
873C2×C4—21no—
874C2×C4—21no—
875C2×C4—24no—
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—24no—
879C2×C4—21no—
880C2×C4—24no—
881C2×C4—24no—
882C2×C4—24no—
883C2×C4—21no—
884C2×C4—24no—
885C2×C4—21no—
886C2×C4—28no—
887C2×C4—216no—
888C2×C4—216no—
889C2×C4—216no—
890C2×C4—21no—
891C2×C4—24no—
892C2×C4—22no—
893C2×C4—24no—
894C2×C4—24no—
895C2×C4—21no—
896C2×C4—22no—
897C2×C4—24no—
898C2×C4—24no—
899C2×C4—24no—
900C2×C4—24no—
901C2×C4—24no—
902C2×C4—24no—
903C2×C4—21no—
904C2×C4—24no—
905C2×C4—24no—
906C2×C4—24no—
907C2×C4—24no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—21no—
911C2×C4—24no—
912C2×C4—24no—
913C2×C4—24no—
914C2×C4—24no—
915C2×C4—24no—
916C2×C4—24no—
917C2×C4—24no—
918C2×C4—24no—
919C2×C4—24no—
920C2×C4—22no—
921C2×C4—21no—
922C2×C4—24no—
923C2×C4—21no—
924C2×C4—24no—
925C2×C4—24no—
926C2×C4—24no—
927C2×C4—24no—
928C2×C4—22no—
929C2×C4—48no—
930C2×C4—48no—
931C2×C4—44no—
932C2×C4—44no—
933C2×C4—82no—
934C2×C4—84no—
935C2×C4—82no—
936C2×C4—88no—
937C2×C4—88no—
938C2×C4#554116yes—
939C2×C4C23×Q818yes—
940C2×C4C23×Q818yes—
941C2×C4C23×Q812yes—
942C2×C4C23×Q812yes—
943C2×C4C23×Q814yes—
944C2×C4C22×#4118yes—
945C2×C4C22×#4114yes—
946C2×C4C2×H(5,𝔽2)14yes—
947C2×C4#58512yes—
948C2×C4#58512yes—
949C22—22no—
950C22—22no—
951C22—22no—
952C22—22no—
953C22—22no—
954C22—22no—
955C22—24no—
956C22—24no—
957C22—24no—
958C22—42no—
959C22—42no—
960C22—42no—
961C22—42no—
962C22—88no—
963C22C2×#55414yes—
964C22C24×Q811yescharacteristic
965C22C23×#4111yescharacteristic
966C22C22×H(5,𝔽2)11yescharacteristic
967C22C2×#58511yescharacteristic
968C22C2×#58511yescharacteristic
969C222−1+611yescharacteristic
970C222−1+611yescharacteristic
971C4—28no—
972C4—22no—
973C4—28no—
974C4—22no—
975C4—22no—
976C4—22no—
977C4—28no—
978C4—42no—
979C4—44no—
980C4—44no—
981C4—41no—
982C4—44no—
983C4—41no—
984C4—44no—
985C4—44no—
986C4—44no—
987C4—44no—
988C4—44no—
989C4—42no—
990C4—44no—
991C4C2×#55418yes—
992C2—24no—
993C2—44no—
994C2C22×#55411yescharacteristic
995C2#6281311yescharacteristic
996C2#6284911yescharacteristic
997C2#6292711yescharacteristic
998C2#6296011yescharacteristic
999C2#6299111yescharacteristic
1000C2#6300511yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC25C24
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59922C2semidirect
2. #59920C2semidirect
3. #59756C2semidirect
4. #59551C2semidirect
5. #45415C2semidirect
6. #45413C2semidirect
7. #45180C2semidirect
8. #44997C2semidirect
10. #37877C2semidirect
12. #36193C2semidirect
13. #35662C2semidirect
14. #35585C2semidirect
15. #35173C2semidirect
16. #35154C2semidirect
19. #34271C2semidirect
21. #34182C2semidirect
35. #2792C22semidirect
36. #2791C22semidirect
40. #2774C22semidirect
43. #2755C22semidirect
49. #2590C22semidirect
52. #2588C22semidirect
55. #2586C22semidirect
56. #2585C22semidirect
57. #2584C22semidirect
58. #2584C22semidirect
59. #2582C22semidirect
60. #2582C22semidirect
61. #2581C22semidirect
62. #2581C22semidirect
65. #2567C22semidirect
66. #2567C22semidirect
68. #2552C22semidirect
69. #2546C22semidirect
71. #2520C22semidirect
72. #2520C22semidirect
73. #2511C22semidirect
74. #2511C22semidirect
75. #2509C22semidirect
76. #2509C22semidirect
77. #2508C22semidirect
78. #2508C22semidirect
79. #2508C22semidirect
80. #2507C22semidirect
81. #2507C22semidirect
82. #2507C22semidirect
83. #2507C22semidirect
84. #2506C22semidirect
85. #2506C22semidirect
87. #2453C22semidirect
88. #2453C22semidirect
89. #2453C22semidirect
90. #2453C22semidirect
91. #2451C22semidirect
92. #2451C22semidirect
93. #2451C22semidirect
94. #2451C22semidirect
116. #2370C22semidirect
117. #2370C22semidirect
118. #2370C22semidirect
119. #2369C22semidirect
120. #2369C22semidirect
121. #2365C22semidirect
130. #2355C22semidirect
131. #2351C22semidirect
132. #2351C22semidirect
133. Q8×C4⋊C4C22semidirect
134. Q8×C4⋊C4C22semidirect
185. C2×C22⋊Q8Q8semidirect

Maximal subgroups

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

subgroupindex
#599222
#599202
#597562
#595512
#454152
#454132
#451802
#449972
#394922
#378772
#378762
#361932
#356622
#355852
#351732
#351542
#351512
#347392
#342712
#342032
#341822
C2×#23622
#340522