Finite Group Databasebeta

← #7646815

Subgroups — #7646815

Order 512.

4886 conjugacy classes of subgroups.

The subgroup lattice has 1022 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42492C214yesmaximal, complemented
2#42491C214yesmaximal, complemented
3#42489C214yesmaximal, complemented
4#42488C214yesmaximal, complemented
5#39496C214yesmaximal, complemented
6#39368C214yesmaximal, complemented
7#38963C214yesmaximal, complemented
8#38963C214yesmaximal, complemented
9#37478C214yesmaximal
10#36752C214yesmaximal, complemented
11#36751C214yesmaximal, complemented
12#35585C212yesmaximal, complemented
13#35566C212yesmaximal, complemented
14#35253C212yesmaximal
15#35253C214yesmaximal
16#35173C211yesmaximal, characteristic, complemented
17#35167C211yesmaximal, characteristic, complemented
18#35159C211yesmaximal, characteristic, complemented
19#35159C211yesmaximal, characteristic, complemented
20#34739C212yesmaximal
21#34178C211yesmaximal, characteristic
22C2×#2344C211yesmaximal, characteristic
23C2×#2316C211yesmaximal, characteristic
24C2×#544C2212yes—
25C2×#544C2214yes—
26C2×#533C2212yes—
27C22×#117C2212yes—
28C22×#117C2212yes—
29C23×C4⋊C4C2211yescharacteristic
30#2857C2214yes—
31#2857C2214yes—
32#2857C2214yes—
33#2851C2214yes—
34#2851C2214yes—
35#2851C2214yes—
36#2841C2218yes—
37#2841C2218yes—
38#2806C2218yescomplemented
39#2805C2218yescomplemented
40#2802C2218yescomplemented
41#2802C2218yescomplemented
42#2792C2218yescomplemented
43#2792C2218yescomplemented
44#2791C2218yescomplemented
45#2791C2218yescomplemented
46#2774C2218yescomplemented
47#2774C2218yescomplemented
48#2755C2218yescomplemented
49#2755C2218yescomplemented
50#2734C2218yescomplemented
51#2726C2218yescomplemented
52#2713C2218yescomplemented
53#2713C2218yescomplemented
54#2667C2218yes—
55#2665C2218yes—
56#2659C2214yes—
57#2659C2214yes—
58#2646C2214yes—
59#2646C2214yes—
60#2629C2214yes—
61#2629C2214yes—
62#2629C2214yes—
63#2628C2214yes—
64#2628C2214yes—
65#2628C2214yes—
66#2627C2218yes—
67#2627C2218yes—
68#2584C2214yescomplemented
69#2584C2214yescomplemented
70#2584C2214yescomplemented
71#2584C2214yescomplemented
72#2569C2218yes—
73#2567C2214yescomplemented
74#2567C2214yescomplemented
75#2552C2214yescomplemented
76#2552C2214yescomplemented
77#2551C2214yescomplemented
78#2551C2214yescomplemented
79#2550C2214yescomplemented
80#2550C2214yescomplemented
81#2550C2214yescomplemented
82#2550C2214yescomplemented
83#2549C2218yes—
84#2546C2214yescomplemented
85#2546C2214yescomplemented
86#2509C2214yescomplemented
87#2509C2214yescomplemented
88#2509C2214yescomplemented
89#2509C2214yescomplemented
90#2508C2214yescomplemented
91#2508C2214yescomplemented
92#2508C2214yescomplemented
93#2508C2214yescomplemented
94#2507C2214yescomplemented
95#2507C2214yescomplemented
96#2507C2214yescomplemented
97#2507C2214yescomplemented
98#2506C2214yescomplemented
99#2506C2214yescomplemented
100#2506C2214yescomplemented
101#2506C2214yescomplemented
102#2442C2218yes—
103#2442C2212yes—
104#2442C2214yes—
105#2442C2212yes—
106#2441C2212yes—
107#2441C2212yes—
108#2441C2214yes—
109#2441C2218yes—
110#2440C2212yes—
111#2440C2214yes—
112#2440C2218yes—
113#2440C2212yes—
114#2439C2212yes—
115#2439C2212yes—
116#2439C2218yes—
117#2439C2214yes—
118#2438C2218yes—
119#2438C2218yes—
120#2438C2218yes—
121#2438C2218yes—
122#2438C2214yes—
123#2438C2218yes—
124#2438C2214yes—
125#2437C2214yes—
126#2437C2218yes—
127#2437C2214yes—
128#2396C2214yes—
129#2396C2214yes—
130#2345C2214yes—
131#2345C2214yes—
132#2344C2214yes—
133#2344C2214yes—
134#2344C2214yes—
135#2344C2214yes—
136#2344C2214yes—
137#2344C2214yes—
138#2317C2212yes—
139#2317C2214yes—
140#2317C2214yes—
141#2317C2212yes—
142#2316C2212yes—
143#2316C2212yes—
144#2316C2211yescharacteristic
145#2316C2211yescharacteristic
146#2316C2214yes—
147#2316C2214yes—
148#2316C2214yes—
149#2316C2214yes—
150#2316C2211yescharacteristic
151#2316C2211yescharacteristic
152#2313C2214yes—
153C4×C22⋊Q8C2214yes—
154C4×C22⋊Q8C2214yes—
155#2296C2212yes—
156#2296C2212yes—
157C2×#389C2211yescharacteristic
158C2×#389C2214yes—
159C2×#389C2214yes—
160C2×#389C2211yescharacteristic
161C2×#387C2212yes—
162C2×#387C2212yes—
163#2285C2212yes—
164#2280C2214yes—
165#2280C2212yes—
166C2×#381C2212yes—
167C2×#380C2214yes—
168C2×#380C2211yescharacteristic
169#2274C2212yes—
170C2×C4×C4⋊C4C2211yescharacteristic
171C2×C4×C4⋊C4C2211yescharacteristic
172C2×C4×C22⋊C4C2211yescharacteristic
173C24×C4C2311yescharacteristic
174C24×C4C2312yes—
175#544—48no—
176#544—416no—
177#533—48no—
178C2×C4⋊Q8C2312yes—
179C2×C4⋊Q8C2314yes—
180C2×C4⋊Q8C2314yes—
181C2×C4⋊Q8C2314yes—
182C2×C4⋊Q8C2314yes—
183C2×C4⋊Q8C2312yes—
184C2×C4⋊Q8C2318yes—
185C2×#125C2312yes—
186C2×#125C2312yes—
187C2×#125C2314yes—
188C2×#125C2314yes—
189C2×#125C2314yes—
190C2×#125C2314yes—
191C2×#125C2318yes—
192C2×C22⋊Q8C2314yes—
193C2×C22⋊Q8C2314yes—
194C2×C22⋊Q8C2318yes—
195C2×C22⋊Q8C2318yes—
196C2×C22⋊Q8C2314yes—
197C2×C22⋊Q8C2314yes—
198C2×C4×Q8C2314yes—
199C2×C4×Q8C2314yes—
200C2×#117—48no—
201C2×#117—48no—
202C2×#117C2312yes—
203C2×#117C2312yes—
204C2×#117C2312yes—
205C2×#117C2312yes—
206C2×#117C2314yes—
207C2×#117C2314yes—
208C2×#117C2314yes—
209C2×#117C2312yes—
210C2×#117C2312yes—
211C2×#117C2314yes—
212C2×#117C2314yes—
213C2×#117C2314yes—
214C2×#117C2314yes—
215C2×#117C2314yes—
216C22×C4⋊C4Q8116yescomplemented
217C22×C4⋊C4C2311yescharacteristic
218C22×C4⋊C4C2311yescharacteristic
219C22×C4⋊C4C2314yes—
220C22×C4⋊C4C2314yes—
221C22×C4⋊C4C2312yes—
222C22×C4⋊C4C2312yes—
223C22×C4⋊C4C2312yes—
224C22×C4⋊C4C2312yes—
225C22×C4⋊C4C2312yes—
226C22×C4⋊C4C2311yescharacteristic
227C22×C4⋊C4C2314yes—
228C22×C4⋊C4C2311yescharacteristic
229C22×C4⋊C4C2314yes—
230C22×C22⋊C4C2311yescharacteristic
231C22×C22⋊C4C2314yes—
232C22×C22⋊C4C2312yes—
233C22×C22⋊C4C2311yescharacteristic
234C22×C42C2311yescharacteristic
235C22×C42C2311yescharacteristic
236C22×C42C2312yes—
237C22×C42C2312yes—
238C22×C42C2314yes—
239#400C2318yes—
240#400C2318yes—
241#400C2318yes—
242#400C2318yes—
243#400C2318yes—
244#400C2318yes—
245#400C2318yes—
246#400C2318yes—
247#400C2318yes—
248#400C2314yes—
249#400C2314yes—
250#399C2314yes—
251#399C2318yes—
252#399C2314yes—
253#398C2318yes—
254#398C2318yes—
255#398C2318yes—
256#398C2318yes—
257#398C2318yes—
258#398C2318yes—
259#398C2318yes—
260#398C2318yes—
261#398C2318yes—
262#398C2318yes—
263#398C2318yes—
264#398C2318yes—
265#398C2318yes—
266#398C2318yes—
267#398C2318yes—
268#398C2318yes—
269#398C2318yes—
270#398C2318yes—
271#398C2314yes—
272#398C2314yes—
273#398C2314yes—
274#398C2314yes—
275#396C2314yes—
276#396C2314yes—
277#396C2318yes—
278#396C2318yes—
279#396C2314yes—
280#396C2314yes—
281#395C2318yes—
282#395C2318yes—
283#395C2318yes—
284#395C2318yes—
285#395C2318yes—
286#395C2318yes—
287#395C2318yes—
288#395C2318yes—
289#395C2318yes—
290#395C2314yes—
291#395C2314yes—
292#393C2314yes—
293#393C2318yes—
294#393C2314yes—
295#391C2318yes—
296#391C2318yes—
297#391C2318yes—
298#391C2318yes—
299#391C2318yes—
300#391C2314yes—
301#391C2314yes—
302#389C2312yes—
303#389C2314yes—
304#389C2314yes—
305#389C2314yes—
306#389C2314yes—
307#389C2314yes—
308#389C2314yes—
309#389C2314yes—
310#389C2314yes—
311#389C2314yes—
312#389C2318yes—
313#389C2318yes—
314#389C2318yes—
315#389C2314yes—
316#389C2314yes—
317#389C2314yes—
318#389C2314yes—
319#389C2318yes—
320#389C2314yes—
321#389C2314yes—
322#389C2314yes—
323#389C2314yes—
324#389C2318yes—
325#389C2314yes—
326#389C2314yes—
327#389C2314yes—
328#389C2314yes—
329#389C2314yes—
330#389C2318yes—
331#389C2314yes—
332#389C2314yes—
333#389C2318yes—
334#389C2314yes—
335#389C2314yes—
336#389C2314yes—
337#389C2314yes—
338#389C2314yes—
339#389C2318yes—
340#389C2318yes—
341#389C2312yes—
342#389C2312yes—
343#389C2314yes—
344#389C2318yes—
345#389C2318yes—
346#389C2314yes—
347#389C2314yes—
348#389C2318yes—
349#389C2318yes—
350#389C2314yes—
351#389C2314yes—
352#389C2312yes—
353#389C2312yes—
354#389C2312yes—
355#389C2312yes—
356#389C2312yes—
357#387C2318yes—
358#387C2318yes—
359#387C2318yes—
360#387C2318yes—
361#387C2318yes—
362#387C2318yes—
363#387C2318yes—
364#387C2318yes—
365#387C2318yes—
366#387C2318yes—
367#387C2318yes—
368#387C2318yes—
369#387C2318yes—
370#387C2318yes—
371#387C2318yes—
372#387C2318yes—
373#387C2318yes—
374#387C2318yes—
375#387C2314yes—
376#387C2314yes—
377#387C2314yes—
378#387C2314yes—
379#385C2314yes—
380#385C2318yes—
381#385C2314yes—
382#385C2314yes—
383#385C2318yes—
384#385C2318yes—
385#385C2318yes—
386#385C2314yes—
387#385C2314yes—
388#385C2314yes—
389#385C2314yes—
390#385C2314yes—
391#384C2314yes—
392#384C2318yes—
393#384C2314yes—
394#384C2314yes—
395#384C2314yes—
396#384C2312yes—
397#384C2312yes—
398#382C2314yes—
399#382C2314yes—
400#382C2314yes—
401#382C2318yes—
402#382C2314yes—
403#382C2312yes—
404#382C2312yes—
405#381C2314yes—
406#381C2318yes—
407#381C2318yes—
408#381C2318yes—
409#380C2314yes—
410#380C2314yes—
411#380C2314yes—
412#380C2318yes—
413#380C2318yes—
414#380C2318yes—
415#380C2314yes—
416#380C2314yes—
417#380C2314yes—
418#380C2314yes—
419#380C2314yes—
420#380C2318yes—
421#380C2314yes—
422#380C2314yes—
423#380C2312yes—
424#380C2314yes—
425#380C2312yes—
426#380C2314yes—
427#380C2312yes—
428#380C2312yes—
429#380C2314yes—
430#380C2314yes—
431#379C2314yes—
432C4×C4⋊C4C2314yes—
433C4×C4⋊C4C2314yes—
434C4×C4⋊C4C2314yes—
435C4×C4⋊C4C2314yes—
436C4×C4⋊C4C2314yes—
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×C22⋊C4C2318yes—
447C4×C22⋊C4C2312yes—
448C4×C22⋊C4C2312yes—
449C4×C22⋊C4C2312yes—
450C4×C22⋊C4C2314yes—
451C4×C22⋊C4C2312yes—
452C4×C22⋊C4C2314yes—
453C4×C22⋊C4C2318yes—
454C2×#95C2312yes—
455C2×#95C2312yes—
456C2×#95C2312yes—
457C2×#95C2311yescharacteristic
458C2×#95C2311yescharacteristic
459C2×#95C2312yes—
460C2×#95C2318yes—
461C2×#95C2312yes—
462C25C2411yescharacteristic
463C22×Q8C2414yes—
464C22×Q8C2414yes—
465C22×Q8C2418yes—
466C23×C4—24no—
467C23×C4—24no—
468C23×C4—44no—
469C23×C4—44no—
470C23×C4C2×Q818yes—
471C23×C4C2×Q8116yes—
472C23×C4C2411yescharacteristic
473C23×C4C2411yescharacteristic
474C23×C4C2414yes—
475C23×C4C2412yes—
476C23×C4C2411yescharacteristic
477C23×C4C2412yes—
478C23×C4C2414yes—
479C23×C4C2414yes—
480C23×C4C2412yes—
481C23×C4C2412yes—
482C23×C4C2411yescharacteristic
483C23×C4C2411yescharacteristic
484C23×C4C2412yes—
485C23×C4C2414yes—
486C23×C4C2412yes—
487C23×C4C2411yescharacteristic
488C4⋊Q8—44no—
489C4⋊Q8—44no—
490C4⋊Q8—48no—
491C4⋊Q8—48no—
492C4⋊Q8—48no—
493C4⋊Q8—48no—
494C4⋊Q8—416no—
495#125—44no—
496#125—44no—
497#125—48no—
498#125—48no—
499#125—48no—
500#125—48no—
501#125—416no—
502C22⋊Q8—216no—
503C22⋊Q8—48no—
504C22⋊Q8—48no—
505C22⋊Q8—48no—
506C22⋊Q8—416no—
507C22⋊Q8—416no—
508C4×Q8—48no—
509C4×Q8—48no—
510#117—28no—
511#117—28no—
512#117—28no—
513#117—28no—
514#117—216no—
515#117—48no—
516#117—48no—
517#117—48no—
518#117—48no—
519#117—48no—
520#117—48no—
521#117—48no—
522#117—44no—
523#117—44no—
524C2×C4⋊C4—24no—
525C2×C4⋊C4—24no—
526C2×C4⋊C4—44no—
527C2×C4⋊C4—44no—
528C2×C4⋊C4—44no—
529C2×C4⋊C4—44no—
530C2×C4⋊C4—48no—
531C2×C4⋊C4—48no—
532C2×C4⋊C4C2×Q8132yes—
533C2×C4⋊C4C2×Q8116yes—
534C2×C4⋊C4C2×Q8132yes—
535C2×C4⋊C4C2×Q818yes—
536C2×C4⋊C4C2×Q818yes—
537C2×C4⋊C4C2412yes—
538C2×C4⋊C4C2414yes—
539C2×C4⋊C4C2412yes—
540C2×C4⋊C4C2412yes—
541C2×C4⋊C4C2412yes—
542C2×C4⋊C4C2414yes—
543C2×C4⋊C4C2414yes—
544C2×C4⋊C4C2414yes—
545C2×C4⋊C4C2412yes—
546C2×C4⋊C4C2412yes—
547C2×C4⋊C4C2412yes—
548C2×C4⋊C4C2412yes—
549C2×C4⋊C4C2414yes—
550C2×C4⋊C4C2414yes—
551C2×C4⋊C4C2414yes—
552C2×C4⋊C4C2414yes—
553C2×C4⋊C4C2414yes—
554C2×C4⋊C4C2414yes—
555C2×C4⋊C4C2414yes—
556C2×C4⋊C4C2418yes—
557C2×C4⋊C4C2414yes—
558C2×C4⋊C4C2414yes—
559C2×C4⋊C4C2414yes—
560C2×C4⋊C4C2414yes—
561C2×C4⋊C4C2418yes—
562C2×C4⋊C4C2414yes—
563C2×C4⋊C4C2414yes—
564C2×C4⋊C4C2414yes—
565C2×C4⋊C4C2414yes—
566C2×C4⋊C4C2414yes—
567C2×C4⋊C4C2414yes—
568C2×C4⋊C4C2414yes—
569C2×C4⋊C4C2414yes—
570C2×C4⋊C4C2414yes—
571C2×C4⋊C4C2414yes—
572C2×C4⋊C4C2418yes—
573C2×C4⋊C4C2418yes—
574C2×C4⋊C4C2418yes—
575C2×C4⋊C4C2418yes—
576C2×C4⋊C4C2418yes—
577C2×C4⋊C4C2418yes—
578C2×C4⋊C4C2414yes—
579C2×C4⋊C4C2414yes—
580C2×C4⋊C4C2414yes—
581C2×C4⋊C4C2414yes—
582C2×C4⋊C4C2414yes—
583C2×C4⋊C4C2414yes—
584C2×C4⋊C4C2414yes—
585C2×C4⋊C4C2414yes—
586C2×C4⋊C4C2414yes—
587C2×C4⋊C4C2418yes—
588C2×C4⋊C4C2418yes—
589C2×C4⋊C4C2418yes—
590C2×C4⋊C4C2414yes—
591C2×C4⋊C4C2414yes—
592C2×C4⋊C4C2418yes—
593C2×C22⋊C4—24no—
594C2×C22⋊C4—42no—
595C2×C22⋊C4—44no—
596C2×C22⋊C4—48no—
597C2×C22⋊C4C2411yescharacteristic
598C2×C22⋊C4C2411yescharacteristic
599C2×C22⋊C4C2411yescharacteristic
600C2×C22⋊C4C2414yes—
601C2×C22⋊C4C2414yes—
602C2×C22⋊C4C2414yes—
603C2×C22⋊C4C2412yes—
604C2×C22⋊C4C2414yes—
605C2×C22⋊C4C2414yes—
606C2×C22⋊C4C2414yes—
607C2×C22⋊C4C2414yes—
608C2×C22⋊C4C2414yes—
609C2×C22⋊C4C2414yes—
610C2×C22⋊C4C2414yes—
611C2×C22⋊C4C2412yes—
612C2×C22⋊C4C2414yes—
613C2×C22⋊C4C2414yes—
614C2×C22⋊C4C2411yescharacteristic
615C2×C42—24no—
616C2×C42—24no—
617C2×C42—48no—
618C2×C42—44no—
619C2×C42—44no—
620C2×C42C2414yes—
621C2×C42C2414yes—
622C2×C42C2414yes—
623C2×C42C2414yes—
624C2×C42C2414yes—
625C2×C42C2414yes—
626C2×C42C2412yes—
627C2×C42C2412yes—
628C2×C42C2412yes—
629C2×C42C2412yes—
630C2×C42C2414yes—
631C2×C42C2414yes—
632C2×C42C2414yes—
633C2×C42C2414yes—
634C2×C42C2418yes—
635C2×C42C2418yes—
636#95C2412yes—
637#95C2412yes—
638#95C2412yes—
639#95C2412yes—
640#95C2418yes—
641#95C2418yes—
642#95C2418yes—
643#95C2418yes—
644#95C2418yes—
645#95C2418yes—
646#95C2418yes—
647#95C2418yes—
648#95C2418yes—
649#95C2418yes—
650#95C2418yes—
651#95C2414yes—
652#95C2418yes—
653#95C2414yes—
654#95C2414yes—
655#95C2414yes—
656#95C2418yes—
657#95C2414yes—
658#95C2414yes—
659#95C2414yes—
660#95C2414yes—
661#95C2414yes—
662#95C2414yes—
663#95C2414yes—
664#95C2414yes—
665#95C2414yes—
666#95C2414yes—
667#95C2414yes—
668#95C2414yes—
669#95C2418yes—
670#95C2418yes—
671#95C2418yes—
672#95C2418yes—
673#95C2418yes—
674#95C2418yes—
675C24—22no—
676C24—22no—
677C24—22no—
678C24—22no—
679C24—41no—
680C24—41no—
681C24C22×Q814yes—
682C24C2511yescharacteristic
683C24C2511yescharacteristic
684C24C2511yescharacteristic
685C2×Q8—28no—
686C2×Q8—44no—
687C2×Q8—44no—
688C2×Q8—44no—
689C2×Q8—44no—
690C2×Q8—44no—
691C2×Q8—48no—
692C2×Q8—48no—
693C2×Q8—48no—
694C22×C4—28no—
695C22×C4—22no—
696C22×C4—22no—
697C22×C4—28no—
698C22×C4—232no—
699C22×C4—24no—
700C22×C4—24no—
701C22×C4—24no—
702C22×C4—24no—
703C22×C4—22no—
704C22×C4—22no—
705C22×C4—22no—
706C22×C4—24no—
707C22×C4—28no—
708C22×C4—22no—
709C22×C4—24no—
710C22×C4—28no—
711C22×C4—22no—
712C22×C4—22no—
713C22×C4—42no—
714C22×C4—42no—
715C22×C4—44no—
716C22×C4—432no—
717C22×C4—42no—
718C22×C4—44no—
719C22×C4—42no—
720C22×C4—41no—
721C22×C4—41no—
722C22×C4—42no—
723C22×C4—44no—
724C22×C4—44no—
725C22×C4—42no—
726C22×C4—41no—
727C22×C4—41no—
728C22×C4—42no—
729C22×C4—41no—
730C22×C4—44no—
731C22×C4—44no—
732C22×C4—42no—
733C22×C4—41no—
734C22×C4C22×Q814yes—
735C22×C4C22×Q8116yes—
736C22×C4C22×Q818yes—
737C22×C4C22×Q818yes—
738C22×C4C22×Q8116yes—
739C22×C4C22×Q818yes—
740C22×C4C22×Q818yes—
741C22×C4C22×Q814yes—
742C22×C4H(5,𝔽2)14yes—
743C22×C42−1+414yes—
744C22×C4C2512yes—
745C22×C4C2514yes—
746C22×C4C2511yescharacteristic
747C22×C4C2514yes—
748C22×C4C2512yes—
749C22×C4C2514yes—
750C22×C4C2514yes—
751C22×C4C2514yes—
752C22×C4C2514yes—
753C22×C4C2514yes—
754C22×C4C2514yes—
755C22×C4C2514yes—
756C22×C4C2514yes—
757C22×C4C2511yescharacteristic
758C22×C4C2512yes—
759C22×C4C2514yes—
760C22×C4C2514yes—
761C22×C4C2511yescharacteristic
762C22×C4C2511yescharacteristic
763C22×C4C2512yes—
764C4⋊C4—28no—
765C4⋊C4—28no—
766C4⋊C4—24no—
767C4⋊C4—24no—
768C4⋊C4—24no—
769C4⋊C4—28no—
770C4⋊C4—24no—
771C4⋊C4—24no—
772C4⋊C4—24no—
773C4⋊C4—28no—
774C4⋊C4—28no—
775C4⋊C4—28no—
776C4⋊C4—28no—
777C4⋊C4—24no—
778C4⋊C4—24no—
779C4⋊C4—48no—
780C4⋊C4—44no—
781C4⋊C4—44no—
782C4⋊C4—44no—
783C4⋊C4—44no—
784C4⋊C4—44no—
785C4⋊C4—44no—
786C4⋊C4—44no—
787C4⋊C4—44no—
788C4⋊C4—48no—
789C4⋊C4—44no—
790C4⋊C4—48no—
791C4⋊C4—44no—
792C4⋊C4—44no—
793C4⋊C4—44no—
794C4⋊C4—44no—
795C4⋊C4—48no—
796C4⋊C4—48no—
797C4⋊C4—44no—
798C4⋊C4—44no—
799C4⋊C4—44no—
800C4⋊C4—44no—
801C4⋊C4—44no—
802C4⋊C4—44no—
803C4⋊C4—44no—
804C4⋊C4—44no—
805C4⋊C4—44no—
806C4⋊C4—44no—
807C4⋊C4—44no—
808C4⋊C4—44no—
809C4⋊C4—44no—
810C4⋊C4—44no—
811C4⋊C4—48no—
812C4⋊C4—48no—
813C4⋊C4—48no—
814C4⋊C4—48no—
815C4⋊C4—48no—
816C4⋊C4—48no—
817C4⋊C4C22×Q8132yes—
818C4⋊C4C22×Q8116yes—
819C4⋊C4C22×Q8116yes—
820C22⋊C4—22no—
821C22⋊C4—28no—
822C22⋊C4—28no—
823C22⋊C4—28no—
824C22⋊C4—28no—
825C22⋊C4—28no—
826C22⋊C4—28no—
827C22⋊C4—24no—
828C22⋊C4—28no—
829C22⋊C4—22no—
830C22⋊C4—22no—
831C22⋊C4—42no—
832C22⋊C4—44no—
833C22⋊C4—44no—
834C22⋊C4—44no—
835C22⋊C4—44no—
836C22⋊C4—44no—
837C22⋊C4H(5,𝔽2)14yes—
838C42—24no—
839C42—24no—
840C42—28no—
841C42—28no—
842C42—28no—
843C42—28no—
844C42—28no—
845C42—24no—
846C42—24no—
847C42—28no—
848C42—44no—
849C42—44no—
850C42—44no—
851C42—44no—
852C42—48no—
853C42—48no—
854C23—21no—
855C23—21no—
856C23—21no—
857C23—21no—
858C23—21no—
859C23—21no—
860C23—21no—
861C23—21no—
862C23—21no—
863C23—21no—
864C23—21no—
865C23—21no—
866C23—21no—
867C23—21no—
868C23—28no—
869C23—28no—
870C23—44no—
871C23—44no—
872C23—44no—
873C23—44no—
874C23—44no—
875C23C23×Q812yes—
876C23C23×Q812yes—
877C23C23×Q812yes—
878C23C2×H(5,𝔽2)12yes—
879C23C2×H(5,𝔽2)12yes—
880C23C2×2−1+412yes—
881C23#58512yes—
882C23C2611yescharacteristic
883Q8—88no—
884Q8—88no—
885Q8—168no—
886C2×C4—24no—
887C2×C4—21no—
888C2×C4—22no—
889C2×C4—24no—
890C2×C4—21no—
891C2×C4—22no—
892C2×C4—24no—
893C2×C4—24no—
894C2×C4—21no—
895C2×C4—21no—
896C2×C4—28no—
897C2×C4—232no—
898C2×C4—216no—
899C2×C4—216no—
900C2×C4—21no—
901C2×C4—22no—
902C2×C4—24no—
903C2×C4—24no—
904C2×C4—24no—
905C2×C4—24no—
906C2×C4—24no—
907C2×C4—24no—
908C2×C4—24no—
909C2×C4—24no—
910C2×C4—21no—
911C2×C4—21no—
912C2×C4—24no—
913C2×C4—24no—
914C2×C4—24no—
915C2×C4—24no—
916C2×C4—24no—
917C2×C4—21no—
918C2×C4—22no—
919C2×C4—24no—
920C2×C4—24no—
921C2×C4—24no—
922C2×C4—24no—
923C2×C4—24no—
924C2×C4—22no—
925C2×C4—22no—
926C2×C4—24no—
927C2×C4—24no—
928C2×C4—24no—
929C2×C4—24no—
930C2×C4—24no—
931C2×C4—24no—
932C2×C4—21no—
933C2×C4—21no—
934C2×C4—24no—
935C2×C4—24no—
936C2×C4—22no—
937C2×C4—24no—
938C2×C4—24no—
939C2×C4—24no—
940C2×C4—24no—
941C2×C4—22no—
942C2×C4—48no—
943C2×C4—48no—
944C2×C4—416no—
945C2×C4—44no—
946C2×C4—44no—
947C2×C4—88no—
948C2×C4—84no—
949C2×C4—84no—
950C2×C4—88no—
951C2×C4—82no—
952C2×C4—82no—
953C2×C4#544116yescomplemented
954C2×C4C23×Q818yes—
955C2×C4C23×Q818yes—
956C2×C4C23×Q814yes—
957C2×C4C23×Q814yes—
958C2×C4C2×H(5,𝔽2)12yes—
959C2×C4C2×H(5,𝔽2)12yes—
960C2×C4C2×H(5,𝔽2)14yes—
961C2×C4C2×2−1+414yes—
962C22—22no—
963C22—22no—
964C22—22no—
965C22—22no—
966C22—22no—
967C22—22no—
968C22—22no—
969C22—22no—
970C22—22no—
971C22—22no—
972C22—22no—
973C22—22no—
974C22—22no—
975C22—22no—
976C22—22no—
977C22—416no—
978C22—41no—
979C22—41no—
980C22—41no—
981C22—41no—
982C22C2×#54414yes—
983C22#350114yes—
984C22C24×Q811yescharacteristic
985C22C22×H(5,𝔽2)11yescharacteristic
986C22C22×H(5,𝔽2)11yescharacteristic
987C22C22×2−1+411yescharacteristic
988C22C2×#58511yescharacteristic
989C222−1+611yescharacteristic
990C222−1+611yescharacteristic
991C4—28no—
992C4—28no—
993C4—22no—
994C4—22no—
995C4—24no—
996C4—41no—
997C4—44no—
998C4—44no—
999C4—44no—
1000C4—44no—
1001C4—44no—
1002C4—41no—
1003C4—44no—
1004C4—44no—
1005C4—44no—
1006C4—42no—
1007C4—44no—
1008C4—44no—
1009C4—42no—
1010C4C2×#54418yes—
1011C2—24no—
1012C2—24no—
1013C2—42no—
1014C2C22×#54411yescharacteristic
1015C2C2×#350111yescharacteristic
1016C2#6284911yescharacteristic
1017C2#6291411yescharacteristic
1018C2#6291511yescharacteristic
1019C2#6292711yescharacteristic
1020C2#6292811yescharacteristic
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. #42492C2semidirect
2. #42491C2semidirect
3. #42489C2semidirect
4. #42488C2semidirect
5. #39496C2semidirect
6. #39368C2semidirect
7. #38963C2semidirect
8. #38963C2semidirect
10. #36752C2semidirect
11. #36751C2semidirect
12. #35585C2semidirect
13. #35566C2semidirect
16. #35173C2semidirect
17. #35167C2semidirect
18. #35159C2semidirect
19. #35159C2semidirect
38. #2806C22semidirect
39. #2805C22semidirect
40. #2802C22semidirect
41. #2802C22semidirect
42. #2792C22semidirect
43. #2792C22semidirect
44. #2791C22semidirect
45. #2791C22semidirect
46. #2774C22semidirect
47. #2774C22semidirect
48. #2755C22semidirect
49. #2755C22semidirect
50. #2734C22semidirect
51. #2726C22semidirect
52. #2713C22semidirect
53. #2713C22semidirect
68. #2584C22semidirect
69. #2584C22semidirect
70. #2584C22semidirect
71. #2584C22semidirect
73. #2567C22semidirect
74. #2567C22semidirect
75. #2552C22semidirect
76. #2552C22semidirect
77. #2551C22semidirect
78. #2551C22semidirect
79. #2550C22semidirect
80. #2550C22semidirect
81. #2550C22semidirect
82. #2550C22semidirect
84. #2546C22semidirect
85. #2546C22semidirect
86. #2509C22semidirect
87. #2509C22semidirect
88. #2509C22semidirect
89. #2509C22semidirect
90. #2508C22semidirect
91. #2508C22semidirect
92. #2508C22semidirect
93. #2508C22semidirect
94. #2507C22semidirect
95. #2507C22semidirect
96. #2507C22semidirect
97. #2507C22semidirect
98. #2506C22semidirect
99. #2506C22semidirect
100. #2506C22semidirect
101. #2506C22semidirect
216. C22×C4⋊C4Q8semidirect
953. C2×C4#544semidirect

Maximal subgroups

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

subgroupindex
#424922
#424912
#424892
#424882
#394962
#393682
#389632
#374782
#367522
#367512
#355852
#355662
#352532
#351732
#351672
#351592
#347392
#341782
C2×#23442
C2×#23162