Finite Group Databasebeta

← #7646472

Subgroups — #7646472

Order 512.

4574 conjugacy classes of subgroups.

The subgroup lattice has 989 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42955C214yesmaximal, complemented
2#42933C214yesmaximal, complemented
3#42932C214yesmaximal, complemented
4#42932C214yesmaximal, complemented
5#39987C214yesmaximal, complemented
6#39986C214yesmaximal, complemented
7#39983C214yesmaximal, complemented
8#39982C214yesmaximal, complemented
9#37562C214yesmaximal, complemented
10#36750C214yesmaximal
11#36749C214yesmaximal
12#35585C212yesmaximal, complemented
13#35566C212yesmaximal, complemented
14#35253C212yesmaximal
15#35239C214yesmaximal, complemented
16#35173C211yesmaximal, characteristic, complemented
17#35167C211yesmaximal, characteristic, complemented
18#35159C211yesmaximal, characteristic, complemented
19#35159C211yesmaximal, characteristic, complemented
20#34739C212yesmaximal
21#34179C211yesmaximal, characteristic
22C2×#2347C211yesmaximal, characteristic
23#34052C211yesmaximal, characteristic
24C2×#544C2212yes—
25C2×#533C2212yes—
26C22×#117C2212yes—
27C22×#117C2211yescharacteristic
28#2857C2214yes—
29#2857C2214yes—
30#2857C2214yes—
31#2851C2214yes—
32#2851C2214yes—
33#2851C2214yes—
34#2843C2218yescomplemented
35#2843C2218yescomplemented
36#2807C2218yes—
37#2790C2218yes—
38#2790C2218yes—
39#2788C2218yes—
40#2788C2218yes—
41#2768C2218yes—
42#2768C2218yes—
43#2763C2218yes—
44#2742C2218yes—
45#2729C2218yes—
46#2729C2218yes—
47#2720C2218yes—
48#2720C2218yes—
49#2704C2218yes—
50#2704C2218yes—
51#2677C2218yes—
52#2666C2218yescomplemented
53#2666C2218yescomplemented
54#2666C2218yescomplemented
55#2666C2218yescomplemented
56#2666C2218yescomplemented
57#2666C2218yescomplemented
58#2659C2214yes—
59#2659C2214yes—
60#2646C2214yes—
61#2646C2214yes—
62#2629C2214yes—
63#2628C2214yes—
64#2606C2218yescomplemented
65#2605C2218yescomplemented
66#2584C2214yescomplemented
67#2584C2214yescomplemented
68#2584C2214yescomplemented
69#2584C2214yescomplemented
70#2571C2214yescomplemented
71#2570C2214yescomplemented
72#2570C2214yescomplemented
73#2569C2218yes—
74#2567C2214yescomplemented
75#2567C2214yescomplemented
76#2552C2214yescomplemented
77#2552C2214yescomplemented
78#2552C2214yescomplemented
79#2552C2214yescomplemented
80#2551C2214yescomplemented
81#2551C2214yescomplemented
82#2551C2214yescomplemented
83#2550C2214yescomplemented
84#2550C2214yescomplemented
85#2550C2214yescomplemented
86#2550C2214yescomplemented
87#2550C2214yescomplemented
88#2550C2214yescomplemented
89#2549C2218yes—
90#2546C2214yescomplemented
91#2546C2214yescomplemented
92#2509C2214yescomplemented
93#2509C2214yescomplemented
94#2509C2214yescomplemented
95#2509C2214yescomplemented
96#2508C2214yescomplemented
97#2508C2214yescomplemented
98#2508C2214yescomplemented
99#2508C2214yescomplemented
100#2507C2214yescomplemented
101#2507C2214yescomplemented
102#2507C2214yescomplemented
103#2507C2214yescomplemented
104#2506C2214yescomplemented
105#2506C2214yescomplemented
106#2506C2214yescomplemented
107#2506C2214yescomplemented
108#2442C2218yes—
109#2442C2212yes—
110#2442C2212yes—
111#2442C2214yes—
112#2441C2214yes—
113#2441C2212yes—
114#2441C2212yes—
115#2440C2218yes—
116#2440C2212yes—
117#2440C2212yes—
118#2440C2214yes—
119#2439C2212yes—
120#2439C2214yes—
121#2439C2212yes—
122#2438C2214yes—
123#2438C2218yes—
124#2438C2214yes—
125#2437C2214yes—
126#2437C2218yes—
127#2437C2214yes—
128#2396C2214yes—
129#2396C2214yes—
130#2347C2214yes—
131#2347C2214yes—
132#2347C2214yes—
133#2347C2214yes—
134#2347C2214yes—
135#2347C2214yes—
136#2346C2214yes—
137#2346C2214yes—
138#2331C2218yescomplemented
139#2330C2218yescomplemented
140#2317C2212yes—
141#2317C2214yes—
142#2317C2214yes—
143#2317C2212yes—
144#2316C2212yes—
145#2316C2212yes—
146#2316C2211yescharacteristic
147#2316C2211yescharacteristic
148#2316C2211yescharacteristic
149#2316C2211yescharacteristic
150#2315C2214yes—
151#2312C2214yes—
152C4×C22⋊Q8C2214yes—
153C4×C22⋊Q8C2214yes—
154#2296C2212yes—
155#2296C2214yes—
156#2296C2214yes—
157#2296C2212yes—
158C2×#389C2211yescharacteristic
159C2×#389C2211yescharacteristic
160C2×#388C2212yes—
161C2×#388C2212yes—
162#2285C2212yes—
163#2285C2214yes—
164#2283C2214yes—
165C2×#383C2212yes—
166#2280C2212yes—
167C2×#380C2211yescharacteristic
168#2274C2212yes—
169C2×C4×C4⋊C4C2211yescharacteristic
170C2×C4×C4⋊C4C2211yescharacteristic
171C2×C4×C4⋊C4C2212yes—
172C2×C4×C22⋊C4C2211yescharacteristic
173C24×C4C2311yescharacteristic
174#544—48no—
175#533—48no—
176C2×C4⋊Q8C2312yes—
177C2×C4⋊Q8C2314yes—
178C2×C4⋊Q8C2318yes—
179C2×C4⋊Q8C2314yes—
180C2×C4⋊Q8C2312yes—
181C2×C4⋊Q8C2314yes—
182C2×C4⋊Q8C2314yes—
183C2×#125C2312yes—
184C2×#125C2312yes—
185C2×#125C2314yes—
186C2×#125C2318yes—
187C2×#125C2314yes—
188C2×#125C2314yes—
189C2×#125C2314yes—
190C2×C22⋊Q8C2314yes—
191C2×C22⋊Q8C2318yes—
192C2×C22⋊Q8C2314yes—
193C2×C22⋊Q8C2314yes—
194C2×C22⋊Q8C2314yes—
195C2×C22⋊Q8C2318yes—
196C2×C4×Q8C2314yes—
197C2×C4×Q8C2314yes—
198C2×#117—48no—
199C2×#117Q8116yescomplemented
200C2×#117C2312yes—
201C2×#117C2312yes—
202C2×#117C2312yes—
203C2×#117C2312yes—
204C2×#117C2314yes—
205C2×#117C2314yes—
206C2×#117C2312yes—
207C2×#117C2312yes—
208C2×#117C2314yes—
209C2×#117C2314yes—
210C22×C4⋊C4C2311yescharacteristic
211C22×C4⋊C4C2311yescharacteristic
212C22×C4⋊C4C2312yes—
213C22×C4⋊C4C2312yes—
214C22×C4⋊C4C2312yes—
215C22×C4⋊C4C2312yes—
216C22×C4⋊C4C2311yescharacteristic
217C22×C4⋊C4C2311yescharacteristic
218C22×C22⋊C4C2314yes—
219C22×C22⋊C4C2311yescharacteristic
220C22×C22⋊C4C2311yescharacteristic
221C22×C22⋊C4C2312yes—
222C22×C22⋊C4C2312yes—
223C22×C42C2311yescharacteristic
224C22×C42C2311yescharacteristic
225C22×C42C2314yes—
226C22×C42C2312yes—
227C22×C42C2312yes—
228C22×C42C2312yes—
229#400C2318yes—
230#400C2318yes—
231#400C2318yes—
232#400C2318yes—
233#400C2314yes—
234#400C2318yes—
235#400C2314yes—
236#400C2318yes—
237#400C2318yes—
238#400C2318yes—
239#400C2318yes—
240#399C2318yes—
241#399C2314yes—
242#399C2314yes—
243#398C2318yes—
244#398C2318yes—
245#398C2318yes—
246#398C2318yes—
247#398C2318yes—
248#398C2318yes—
249#398C2318yes—
250#398C2314yes—
251#398C2314yes—
252#398C2318yes—
253#398C2318yes—
254#398C2318yes—
255#398C2318yes—
256#398C2318yes—
257#398C2318yes—
258#398C2318yes—
259#398C2318yes—
260#398C2314yes—
261#398C2314yes—
262#398C2318yes—
263#398C2318yes—
264#398C2318yes—
265#396C2318yes—
266#396C2318yes—
267#396C2314yes—
268#396C2314yes—
269#396C2314yes—
270#396C2314yes—
271#395C2318yes—
272#395C2318yes—
273#395C2318yes—
274#395C2318yes—
275#395C2318yes—
276#395C2318yes—
277#395C2314yes—
278#395C2318yes—
279#395C2318yes—
280#395C2314yes—
281#395C2318yes—
282#393C2318yes—
283#393C2314yes—
284#393C2314yes—
285#391C2318yes—
286#391C2318yes—
287#391C2314yes—
288#391C2318yes—
289#391C2318yes—
290#391C2314yes—
291#391C2318yes—
292#389C2312yes—
293#389C2314yes—
294#389C2314yes—
295#389C2314yes—
296#389C2314yes—
297#389C2314yes—
298#389C2314yes—
299#389C2314yes—
300#389C2314yes—
301#389C2314yes—
302#389C2314yes—
303#389C2314yes—
304#389C2314yes—
305#389C2318yes—
306#389C2314yes—
307#389C2314yes—
308#389C2314yes—
309#389C2314yes—
310#389C2314yes—
311#389C2314yes—
312#389C2314yes—
313#389C2314yes—
314#389C2314yes—
315#389C2314yes—
316#389C2314yes—
317#389C2314yes—
318#389C2314yes—
319#389C2314yes—
320#389C2314yes—
321#389C2318yes—
322#389C2312yes—
323#389C2312yes—
324#389C2318yes—
325#389C2314yes—
326#389C2318yes—
327#389C2318yes—
328#389C2314yes—
329#389C2318yes—
330#389C2318yes—
331#389C2318yes—
332#389C2318yes—
333#389C2314yes—
334#389C2314yes—
335#389C2314yes—
336#389C2314yes—
337#389C2314yes—
338#389C2312yes—
339#389C2312yes—
340#389C2312yes—
341#389C2312yes—
342#389C2312yes—
343#388C2318yes—
344#388C2318yes—
345#388C2318yes—
346#388C2318yes—
347#388C2318yes—
348#388C2318yes—
349#388C2318yes—
350#388C2318yes—
351#387C2318yes—
352#387C2318yes—
353#387C2318yes—
354#387C2318yes—
355#387C2314yes—
356#387C2314yes—
357#387C2318yes—
358#387C2318yes—
359#387C2318yes—
360#387C2318yes—
361#387C2318yes—
362#387C2318yes—
363#387C2314yes—
364#387C2314yes—
365#385C2314yes—
366#385C2318yes—
367#385C2318yes—
368#385C2318yes—
369#385C2318yes—
370#385C2318yes—
371#385C2318yes—
372#385C2314yes—
373#385C2314yes—
374#385C2318yes—
375#385C2318yes—
376#385C2314yes—
377#385C2314yes—
378#385C2314yes—
379#385C2314yes—
380#385C2314yes—
381#384C2314yes—
382#384C2318yes—
383#384C2314yes—
384#384C2314yes—
385#384C2314yes—
386#384C2314yes—
387#384C2314yes—
388#384C2312yes—
389#384C2312yes—
390#383C2318yes—
391#383C2318yes—
392#383C2318yes—
393#382C2314yes—
394#382C2314yes—
395#382C2314yes—
396#382C2318yes—
397#382C2318yes—
398#382C2314yes—
399#382C2314yes—
400#382C2314yes—
401#382C2312yes—
402#382C2312yes—
403#381C2314yes—
404#380C2314yes—
405#380C2314yes—
406#380C2314yes—
407#380C2318yes—
408#380C2318yes—
409#380C2314yes—
410#380C2314yes—
411#380C2312yes—
412#380C2314yes—
413#380C2312yes—
414#380C2314yes—
415#380C2318yes—
416#380C2312yes—
417#380C2314yes—
418#380C2312yes—
419#380C2314yes—
420#380C2314yes—
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⋊C4C2314yes—
430C4×C4⋊C4C2314yes—
431C4×C4⋊C4C2314yes—
432C4×C4⋊C4C2318yes—
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×C22⋊C4C2318yes—
446C4×C22⋊C4C2314yes—
447C4×C22⋊C4C2312yes—
448C4×C22⋊C4C2314yes—
449C4×C22⋊C4C2312yes—
450C4×C22⋊C4C2312yes—
451C4×C22⋊C4C2312yes—
452#376C2318yes—
453C2×#95C2312yes—
454C2×#95C2312yes—
455C2×#95C2312yes—
456C2×#95C2311yescharacteristic
457C2×#95C2311yescharacteristic
458C2×#95C2312yes—
459C2×#95C2312yes—
460C25C2411yescharacteristic
461C22×Q8C2414yes—
462C22×Q8C2414yes—
463C22×Q8C2418yes—
464C23×C4—24no—
465C23×C4—24no—
466C23×C4C2×Q818yes—
467C23×C4C2411yescharacteristic
468C23×C4C2411yescharacteristic
469C23×C4C2412yes—
470C23×C4C2411yescharacteristic
471C23×C4C2412yes—
472C23×C4C2412yes—
473C23×C4C2412yes—
474C23×C4C2411yescharacteristic
475C23×C4C2411yescharacteristic
476C23×C4C2414yes—
477C23×C4C2414yes—
478C23×C4C2412yes—
479C23×C4C2412yes—
480C23×C4C2411yescharacteristic
481C4⋊Q8—44no—
482C4⋊Q8—44no—
483C4⋊Q8—48no—
484C4⋊Q8—48no—
485C4⋊Q8—416no—
486C4⋊Q8—84no—
487C4⋊Q8—84no—
488#125—44no—
489#125—44no—
490#125—48no—
491#125—48no—
492#125—416no—
493#125—84no—
494#125—84no—
495C22⋊Q8—48no—
496C22⋊Q8—48no—
497C22⋊Q8—416no—
498C22⋊Q8—48no—
499C22⋊Q8—48no—
500C22⋊Q8—88no—
501C4×Q8—48no—
502C4×Q8—48no—
503#117—28no—
504#117—28no—
505#117—28no—
506#117—28no—
507#117—48no—
508#117—48no—
509#117—44no—
510#117—44no—
511#117C2×Q8132yes—
512#117C2×Q8132yes—
513C2×C4⋊C4—24no—
514C2×C4⋊C4—24no—
515C2×C4⋊C4—44no—
516C2×C4⋊C4—44no—
517C2×C4⋊C4—44no—
518C2×C4⋊C4—44no—
519C2×C4⋊C4C2×Q818yes—
520C2×C4⋊C4C2×Q818yes—
521C2×C4⋊C4C2412yes—
522C2×C4⋊C4C2412yes—
523C2×C4⋊C4C2412yes—
524C2×C4⋊C4C2412yes—
525C2×C4⋊C4C2414yes—
526C2×C4⋊C4C2414yes—
527C2×C4⋊C4C2414yes—
528C2×C4⋊C4C2414yes—
529C2×C4⋊C4C2412yes—
530C2×C4⋊C4C2412yes—
531C2×C4⋊C4C2412yes—
532C2×C4⋊C4C2412yes—
533C2×C4⋊C4C2414yes—
534C2×C4⋊C4C2414yes—
535C2×C4⋊C4C2414yes—
536C2×C4⋊C4C2414yes—
537C2×C4⋊C4C2414yes—
538C2×C4⋊C4C2414yes—
539C2×C4⋊C4C2414yes—
540C2×C4⋊C4C2414yes—
541C2×C4⋊C4C2414yes—
542C2×C4⋊C4C2414yes—
543C2×C4⋊C4C2414yes—
544C2×C4⋊C4C2414yes—
545C2×C4⋊C4C2414yes—
546C2×C4⋊C4C2418yes—
547C2×C4⋊C4C2418yes—
548C2×C4⋊C4C2418yes—
549C2×C4⋊C4C2418yes—
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⋊C4C2418yes—
561C2×C4⋊C4C2418yes—
562C2×C4⋊C4C2418yes—
563C2×C4⋊C4C2414yes—
564C2×C4⋊C4C2414yes—
565C2×C4⋊C4C2418yes—
566C2×C4⋊C4C2418yes—
567C2×C4⋊C4C2414yes—
568C2×C4⋊C4C2414yes—
569C2×C4⋊C4C2414yes—
570C2×C4⋊C4C2414yes—
571C2×C4⋊C4C2414yes—
572C2×C4⋊C4C2414yes—
573C2×C4⋊C4C2414yes—
574C2×C4⋊C4C2414yes—
575C2×C4⋊C4C2414yes—
576C2×C22⋊C4—42no—
577C2×C22⋊C4—42no—
578C2×C22⋊C4—48no—
579C2×C22⋊C4—82no—
580C2×C22⋊C4C2×Q8116yes—
581C2×C22⋊C4C2414yes—
582C2×C22⋊C4C2414yes—
583C2×C22⋊C4C2412yes—
584C2×C22⋊C4C2412yes—
585C2×C22⋊C4C2414yes—
586C2×C22⋊C4C2414yes—
587C2×C22⋊C4C2414yes—
588C2×C22⋊C4C2414yes—
589C2×C22⋊C4C2418yes—
590C2×C22⋊C4C2412yes—
591C2×C22⋊C4C2412yes—
592C2×C22⋊C4C2414yes—
593C2×C22⋊C4C2414yes—
594C2×C22⋊C4C2414yes—
595C2×C22⋊C4C2414yes—
596C2×C22⋊C4C2418yes—
597C2×C42—24no—
598C2×C42—24no—
599C2×C42—48no—
600C2×C42—82no—
601C2×C42—82no—
602C2×C42C2×Q8116yes—
603C2×C42C2414yes—
604C2×C42C2414yes—
605C2×C42C2414yes—
606C2×C42C2414yes—
607C2×C42C2412yes—
608C2×C42C2412yes—
609C2×C42C2412yes—
610C2×C42C2412yes—
611C2×C42C2414yes—
612C2×C42C2414yes—
613C2×C42C2418yes—
614C2×C42C2414yes—
615C2×C42C2414yes—
616C2×C42C2418yes—
617C2×C42C2414yes—
618C2×C42C2414yes—
619C2×C42C2414yes—
620C2×C42C2414yes—
621#95C2411yescharacteristic
622#95C2411yescharacteristic
623#95C2411yescharacteristic
624#95C2411yescharacteristic
625#95C2412yes—
626#95C2412yes—
627#95C2414yes—
628#95C2414yes—
629#95C2418yes—
630#95C2418yes—
631#95C2418yes—
632#95C2418yes—
633#95C2414yes—
634#95C2414yes—
635#95C2418yes—
636#95C2418yes—
637#95C2414yes—
638#95C2414yes—
639#95C2418yes—
640#95C2418yes—
641#95C2414yes—
642#95C2414yes—
643#95C2414yes—
644#95C2414yes—
645#95C2418yes—
646#95C2418yes—
647#95C2418yes—
648#95C2418yes—
649#95C2414yes—
650#95C2414yes—
651#95C2414yes—
652#95C2414yes—
653#95C2414yes—
654#95C2414yes—
655#95C2414yes—
656#95C2414yes—
657#95C2418yes—
658#95C2418yes—
659#95C2418yes—
660#95C2418yes—
661#95C2418yes—
662#95C2418yes—
663C24—22no—
664C24—22no—
665C24—41no—
666C24—41no—
667C24—41no—
668C24—41no—
669C24C22×Q814yes—
670C24C2512yes—
671C24C2511yescharacteristic
672C2×Q8—28no—
673C2×Q8—44no—
674C2×Q8—44no—
675C2×Q8—44no—
676C2×Q8—44no—
677C2×Q8—44no—
678C2×Q8—48no—
679C2×Q8—48no—
680C2×Q8—48no—
681C22×C4—22no—
682C22×C4—22no—
683C22×C4—232no—
684C22×C4—24no—
685C22×C4—24no—
686C22×C4—24no—
687C22×C4—24no—
688C22×C4—22no—
689C22×C4—22no—
690C22×C4—22no—
691C22×C4—24no—
692C22×C4—22no—
693C22×C4—24no—
694C22×C4—22no—
695C22×C4—22no—
696C22×C4—42no—
697C22×C4—41no—
698C22×C4—41no—
699C22×C4—42no—
700C22×C4—42no—
701C22×C4—42no—
702C22×C4—44no—
703C22×C4—44no—
704C22×C4—42no—
705C22×C4—42no—
706C22×C4—41no—
707C22×C4—41no—
708C22×C4—42no—
709C22×C4—42no—
710C22×C4—44no—
711C22×C4—44no—
712C22×C4—44no—
713C22×C4—41no—
714C22×C4—44no—
715C22×C4—41no—
716C22×C4C22×Q814yes—
717C22×C4C22×Q818yes—
718C22×C4C22×Q818yes—
719C22×C4C22×Q818yes—
720C22×C4C22×Q818yes—
721C22×C4C22×Q814yes—
722C22×C4H(5,𝔽2)14yes—
723C22×C42−1+414yes—
724C22×C4C2512yes—
725C22×C4C2514yes—
726C22×C4C2511yescharacteristic
727C22×C4C2514yes—
728C22×C4C2512yes—
729C22×C4C2514yes—
730C22×C4C2514yes—
731C22×C4C2514yes—
732C22×C4C2514yes—
733C22×C4C2514yes—
734C22×C4C2514yes—
735C22×C4C2514yes—
736C22×C4C2514yes—
737C22×C4C2511yescharacteristic
738C22×C4C2511yescharacteristic
739C22×C4C2511yescharacteristic
740C22×C4C2514yes—
741C22×C4C2514yes—
742C22×C4C2511yescharacteristic
743C22×C4C2511yescharacteristic
744C22×C4C2512yes—
745C4⋊C4—28no—
746C4⋊C4—24no—
747C4⋊C4—24no—
748C4⋊C4—24no—
749C4⋊C4—24no—
750C4⋊C4—24no—
751C4⋊C4—24no—
752C4⋊C4—28no—
753C4⋊C4—24no—
754C4⋊C4—24no—
755C4⋊C4—28no—
756C4⋊C4—28no—
757C4⋊C4—28no—
758C4⋊C4—28no—
759C4⋊C4—28no—
760C4⋊C4—44no—
761C4⋊C4—44no—
762C4⋊C4—44no—
763C4⋊C4—44no—
764C4⋊C4—44no—
765C4⋊C4—44no—
766C4⋊C4—44no—
767C4⋊C4—44no—
768C4⋊C4—44no—
769C4⋊C4—44no—
770C4⋊C4—44no—
771C4⋊C4—44no—
772C4⋊C4—44no—
773C4⋊C4—44no—
774C4⋊C4—44no—
775C4⋊C4—44no—
776C4⋊C4—44no—
777C4⋊C4—44no—
778C4⋊C4—44no—
779C4⋊C4—44no—
780C4⋊C4—48no—
781C4⋊C4—48no—
782C4⋊C4—48no—
783C4⋊C4—48no—
784C4⋊C4—48no—
785C4⋊C4—48no—
786C4⋊C4—48no—
787C4⋊C4—48no—
788C4⋊C4—48no—
789C4⋊C4—44no—
790C4⋊C4—44no—
791C4⋊C4—44no—
792C4⋊C4—44no—
793C4⋊C4—44no—
794C4⋊C4—48no—
795C4⋊C4—48no—
796C4⋊C4—44no—
797C4⋊C4—44no—
798C4⋊C4C22×Q8116yes—
799C4⋊C4C22×Q8116yes—
800C22⋊C4—28no—
801C22⋊C4—28no—
802C22⋊C4—28no—
803C22⋊C4—28no—
804C22⋊C4—24no—
805C22⋊C4—24no—
806C22⋊C4—42no—
807C22⋊C4—42no—
808C22⋊C4—44no—
809C22⋊C4—44no—
810C22⋊C4—48no—
811C22⋊C4—44no—
812C22⋊C4—44no—
813C22⋊C4—44no—
814C22⋊C4—44no—
815C22⋊C4C22×Q8132yes—
816C42—24no—
817C42—24no—
818C42—28no—
819C42—28no—
820C42—28no—
821C42—24no—
822C42—24no—
823C42—28no—
824C42—44no—
825C42—44no—
826C42—44no—
827C42—44no—
828C42—44no—
829C42—44no—
830C42—48no—
831C42—48no—
832C42C22×Q8116yes—
833C42C22×Q8116yes—
834C23—21no—
835C23—21no—
836C23—21no—
837C23—21no—
838C23—22no—
839C23—22no—
840C23—22no—
841C23—22no—
842C23—22no—
843C23—22no—
844C23—28no—
845C23—44no—
846C23—44no—
847C23—82no—
848C23—82no—
849C23—82no—
850C23—82no—
851C23C23×Q814yes—
852C23C23×Q812yes—
853C23C2×H(5,𝔽2)12yes—
854C23C2×2−1+412yes—
855C23C2611yescharacteristic
856Q8—88no—
857Q8—88no—
858Q8—168no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—21no—
862C2×C4—21no—
863C2×C4—21no—
864C2×C4—21no—
865C2×C4—24no—
866C2×C4—24no—
867C2×C4—24no—
868C2×C4—21no—
869C2×C4—21no—
870C2×C4—24no—
871C2×C4—28no—
872C2×C4—216no—
873C2×C4—216no—
874C2×C4—21no—
875C2×C4—22no—
876C2×C4—24no—
877C2×C4—24no—
878C2×C4—24no—
879C2×C4—24no—
880C2×C4—24no—
881C2×C4—24no—
882C2×C4—24no—
883C2×C4—21no—
884C2×C4—22no—
885C2×C4—24no—
886C2×C4—24no—
887C2×C4—24no—
888C2×C4—24no—
889C2×C4—24no—
890C2×C4—24no—
891C2×C4—24no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—21no—
895C2×C4—21no—
896C2×C4—24no—
897C2×C4—24no—
898C2×C4—24no—
899C2×C4—24no—
900C2×C4—24no—
901C2×C4—24no—
902C2×C4—21no—
903C2×C4—21no—
904C2×C4—24no—
905C2×C4—24no—
906C2×C4—24no—
907C2×C4—24no—
908C2×C4—24no—
909C2×C4—24no—
910C2×C4—24no—
911C2×C4—24no—
912C2×C4—22no—
913C2×C4—24no—
914C2×C4—24no—
915C2×C4—22no—
916C2×C4—48no—
917C2×C4—48no—
918C2×C4—44no—
919C2×C4—44no—
920C2×C4—84no—
921C2×C4—84no—
922C2×C4—82no—
923C2×C4—82no—
924C2×C4—88no—
925C2×C4—88no—
926C2×C4#544116yes—
927C2×C4C23×Q812yes—
928C2×C4C23×Q812yes—
929C2×C4C23×Q818yes—
930C2×C4C23×Q818yes—
931C2×C4C23×Q814yes—
932C2×C4C2×H(5,𝔽2)14yes—
933C2×C4C2×2−1+414yes—
934C2×C4#58512yes—
935C2×C4#58512yes—
936C22—22no—
937C22—22no—
938C22—22no—
939C22—22no—
940C22—22no—
941C22—22no—
942C22—24no—
943C22—24no—
944C22—24no—
945C22—42no—
946C22—42no—
947C22—42no—
948C22—42no—
949C22—88no—
950C22C2×#54414yes—
951C22C24×Q811yescharacteristic
952C22C22×H(5,𝔽2)11yescharacteristic
953C22C22×2−1+411yescharacteristic
954C22C2×#58511yescharacteristic
955C22C2×#58511yescharacteristic
956C22H(7,𝔽2)11yescharacteristic
957C222−1+611yescharacteristic
958C4—28no—
959C4—28no—
960C4—22no—
961C4—22no—
962C4—22no—
963C4—22no—
964C4—41no—
965C4—44no—
966C4—44no—
967C4—44no—
968C4—44no—
969C4—44no—
970C4—41no—
971C4—44no—
972C4—44no—
973C4—42no—
974C4—44no—
975C4—44no—
976C4—42no—
977C4—44no—
978C4C2×#54418yes—
979C2—24no—
980C2—44no—
981C2C22×#54411yescharacteristic
982C2#6281311yescharacteristic
983C2#6285411yescharacteristic
984C2#6295711yescharacteristic
985C2#6295811yescharacteristic
986C2#6295911yescharacteristic
987C2#6296011yescharacteristic
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. #42955C2semidirect
2. #42933C2semidirect
3. #42932C2semidirect
4. #42932C2semidirect
5. #39987C2semidirect
6. #39986C2semidirect
7. #39983C2semidirect
8. #39982C2semidirect
9. #37562C2semidirect
12. #35585C2semidirect
13. #35566C2semidirect
15. #35239C2semidirect
16. #35173C2semidirect
17. #35167C2semidirect
18. #35159C2semidirect
19. #35159C2semidirect
34. #2843C22semidirect
35. #2843C22semidirect
52. #2666C22semidirect
53. #2666C22semidirect
54. #2666C22semidirect
55. #2666C22semidirect
56. #2666C22semidirect
57. #2666C22semidirect
64. #2606C22semidirect
65. #2605C22semidirect
66. #2584C22semidirect
67. #2584C22semidirect
68. #2584C22semidirect
69. #2584C22semidirect
70. #2571C22semidirect
71. #2570C22semidirect
72. #2570C22semidirect
74. #2567C22semidirect
75. #2567C22semidirect
76. #2552C22semidirect
77. #2552C22semidirect
78. #2552C22semidirect
79. #2552C22semidirect
80. #2551C22semidirect
81. #2551C22semidirect
82. #2551C22semidirect
83. #2550C22semidirect
84. #2550C22semidirect
85. #2550C22semidirect
86. #2550C22semidirect
87. #2550C22semidirect
88. #2550C22semidirect
90. #2546C22semidirect
91. #2546C22semidirect
92. #2509C22semidirect
93. #2509C22semidirect
94. #2509C22semidirect
95. #2509C22semidirect
96. #2508C22semidirect
97. #2508C22semidirect
98. #2508C22semidirect
99. #2508C22semidirect
100. #2507C22semidirect
101. #2507C22semidirect
102. #2507C22semidirect
103. #2507C22semidirect
104. #2506C22semidirect
105. #2506C22semidirect
106. #2506C22semidirect
107. #2506C22semidirect
138. #2331C22semidirect
139. #2330C22semidirect
199. C2×#117Q8semidirect

Maximal subgroups

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

subgroupindex
#429552
#429332
#429322
#399872
#399862
#399832
#399822
#375622
#367502
#367492
#355852
#355662
#352532
#352392
#351732
#351672
#351592
#347392
#341792
C2×#23472
#340522