Finite Group Databasebeta

← #7674584

Subgroups — #7674584

Order 512.

4986 conjugacy classes of subgroups.

The subgroup lattice has 1036 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#44463C214yesmaximal, complemented
2#43961C214yesmaximal, complemented
3#43512C214yesmaximal, complemented
4#43081C214yesmaximal, complemented
5#39695C214yesmaximal, complemented
6#39694C214yesmaximal, complemented
7#39691C214yesmaximal, complemented
8#39690C214yesmaximal, complemented
9#39498C214yesmaximal, complemented
10#39493C214yesmaximal, complemented
11#37878C214yesmaximal, complemented
12#37875C214yesmaximal, complemented
13#35575C212yesmaximal, complemented
14#35543C212yesmaximal, complemented
15#35330C211yesmaximal, characteristic, complemented
16#35279C211yesmaximal, characteristic, complemented
17#35253C212yesmaximal, complemented
18C2×#2628C211yesmaximal, characteristic, complemented
19#34216C211yesmaximal, characteristic, complemented
20#34202C212yesmaximal
21#34184C211yesmaximal, characteristic, complemented
22#34065C211yesmaximal, characteristic
23#34052C211yesmaximal, characteristic, complemented
24C2×#544C2212yes—
25C22×C4⋊Q8C2211yescharacteristic
26C2×#525C2211yescharacteristic
27C2×#520C2212yes—
28C2×C4×#41C2211yescharacteristic
29C22×#117C2211yescharacteristic
30C22×#117C2212yes—
31#2862C2212yescomplemented
32#2859C2212yescomplemented
33#2857C2214yes—
34#2857C2214yescomplemented
35#2851C2214yes—
36#2807C2218yes—
37#2807C2218yescomplemented
38#2806C2218yescomplemented
39#2805C2218yescomplemented
40#2804C2218yes—
41#2788C2218yes—
42#2788C2218yescomplemented
43#2774C2218yescomplemented
44#2768C2218yes—
45#2763C2218yes—
46#2755C2218yescomplemented
47#2748C2218yes—
48#2742C2218yescomplemented
49#2732C2218yes—
50#2704C2218yescomplemented
51#2692C2218yes—
52#2660C2214yescomplemented
53#2629C2214yes—
54#2628C2214yes—
55#2628C2214yes—
56#2628C2214yes—
57#2628C2214yes—
58#2628C2214yes—
59#2628C2212yescomplemented
60#2628C2212yescomplemented
61#2590C2218yescomplemented
62#2589C2218yes—
63#2589C2218yes—
64#2589C2218yescomplemented
65#2586C2218yescomplemented
66#2584C2218yescomplemented
67#2580C2218yes—
68#2571C2214yescomplemented
69#2570C2214yescomplemented
70#2570C2214yescomplemented
71#2568C2212yescomplemented
72#2567C2212yescomplemented
73#2564C2218yes—
74#2564C2218yes—
75#2563C2212yescomplemented
76#2556C2218yes—
77#2552C2214yescomplemented
78#2550C2214yescomplemented
79#2550C2214yescomplemented
80#2549C2214yes—
81#2549C2214yes—
82#2549C2218yescomplemented
83#2542C2212yescomplemented
84#2509C2214yescomplemented
85#2509C2218yescomplemented
86#2508C2214yescomplemented
87#2507C2214yescomplemented
88#2506C2214yescomplemented
89#2505C2218yes—
90#2505C2218yescomplemented
91#2487C2214yes—
92#2473C2218yes—
93#2465C2218yes—
94#2465C2218yescomplemented
95#2454C2218yes—
96#2454C2214yescomplemented
97#2453C2214yescomplemented
98#2452C2214yescomplemented
99#2451C2214yescomplemented
100#2450C2218yes—
101#2442C2214yes—
102#2442C2214yescomplemented
103#2441C2214yes—
104#2441C2214yescomplemented
105#2440C2214yes—
106#2440C2214yescomplemented
107#2439C2214yes—
108#2439C2214yescomplemented
109#2438C2218yes—
110#2437C2218yes—
111#2417C2218yes—
112#2409C2214yes—
113C2×#400C2212yes—
114C2×#399C2212yes—
115C2×#395C2212yes—
116C2×#393C2212yes—
117#2369C2214yescomplemented
118#2365C2214yescomplemented
119#2359C2218yes—
120#2358C2218yes—
121#2354C2214yes—
122#2352C2214yes—
123#2352C2214yes—
124#2351C2212yescomplemented
125#2351C2212yescomplemented
126#2349C2214yes—
127#2349C2214yes—
128#2349C2212yescomplemented
129#2349C2212yescomplemented
130D4×C4⋊C4C2214yes—
131#2345C2214yes—
132Q8×C22⋊C4C2214yes—
133#2331C2212yescomplemented
134#2331C2212yescomplemented
135#2324C2212yes—
136#2324C2214yes—
137#2324C2212yes—
138#2323C2212yes—
139#2323C2214yes—
140#2323C2212yes—
141#2322C2212yes—
142#2322C2212yes—
143#2321C2212yes—
144#2321C2212yes—
145#2317C2212yes—
146#2317C2212yes—
147#2317C2212yes—
148#2317C2212yes—
149#2317C2212yes—
150#2317C2212yes—
151#2317C2212yes—
152#2317C2214yescomplemented
153#2316C2212yes—
154#2316C2212yes—
155#2316C2212yes—
156#2315C2212yes—
157#2315C2212yes—
158#2311C2212yes—
159C4×C4⋊Q8C2214yescomplemented
160C4×C22⋊Q8C2214yes—
161C4×#121C2214yes—
162#2297C2211yescharacteristic
163#2296C2214yes—
164#2296C2214yes—
165#2296C2211yescharacteristic
166#2293C2214yes—
167C2×#389C2212yes—
168#2290C2214yes—
169#2285C2211yescharacteristic
170#2285C2211yescharacteristic
171#2285C2212yes—
172#2285C2212yescomplemented
173C2×#382C2211yescharacteristic
174C2×#382C2212yescomplemented
175#2280C2211yescharacteristic
176C2×#380C2212yes—
177#2274C2212yes—
178C4×#117C2211yescharacteristic
179C22×#41C2311yescharacteristic
180C23×Q8C2312yes—
181C24×C4C2311yescharacteristic
182#544—48no—
183C2×C4⋊Q8—28no—
184C2×C4⋊Q8C2312yes—
185C2×C4⋊Q8C2312yes—
186C2×C4⋊Q8C2312yes—
187C2×C4⋊Q8C2312yes—
188C2×C4⋊Q8C2314yes—
189C2×C4⋊Q8C2314yes—
190C2×#125C2314yes—
191C2×#125C2314yes—
192C2×#125C2318yes—
193#525Q8116yescomplemented
194C2×#123C2312yes—
195C2×C22⋊Q8C2318yes—
196C2×C22⋊Q8C2318yes—
197C2×C22⋊Q8C2318yes—
198C2×C22⋊Q8C2318yes—
199C2×C22⋊Q8C2312yes—
200C2×#121C2312yes—
201C2×#120C2312yes—
202#520—48no—
203C4×#41—28no—
204C2×C4×Q8C2311yescharacteristic
205C2×C4×Q8C2311yescharacteristic
206C2×C4×Q8C2314yes—
207C2×C4×Q8C2318yes—
208C2×C4×D4C2311yescharacteristic
209C2×C4×D4C2312yes—
210C2×C4×D4C2312yes—
211C2×C4×D4C2311yescharacteristic
212C2×C4×D4C2318yes—
213C2×C4×D4C2314yes—
214C2×C4×D4C2318yes—
215C2×C4×D4C2314yes—
216C2×#117—28no—
217C2×#117—48no—
218C2×#117C2312yes—
219C2×#117C2311yescharacteristic
220C2×#117C2312yes—
221C2×#117C2311yescharacteristic
222C2×#117C2312yes—
223C2×#117C2312yes—
224C2×#117C2312yes—
225C2×#117C2312yes—
226C2×#117C2312yes—
227C2×#117C2314yes—
228C2×#117C2312yes—
229C2×#117C2312yes—
230C2×#117C2314yes—
231C2×#117C2314yes—
232C2×#117C2311yescharacteristic
233C22×C4⋊C4C2312yes—
234C22×C4⋊C4C2311yescharacteristic
235C22×C4⋊C4C2311yescharacteristic
236C22×C4⋊C4C2312yes—
237C22×C4⋊C4C2312yes—
238C22×C4⋊C4C2312yes—
239C22×C4⋊C4C2312yes—
240C22×C4⋊C4C2314yes—
241C22×C4⋊C4C2314yes—
242C22×C22⋊C4C2311yescharacteristic
243C22×C22⋊C4C2311yescharacteristic
244C22×C22⋊C4C2314yes—
245C22×C22⋊C4C2314yes—
246C22×C42C2312yes—
247C22×C42C2311yescharacteristic
248C22×C42C2314yes—
249C22×C42C2311yescharacteristic
250#400C2318yes—
251#400C2318yes—
252#400C2314yes—
253#400C2314yes—
254#400C2318yes—
255#400C2318yes—
256#400C2318yes—
257#400C2318yes—
258#400C2318yes—
259#400C2318yes—
260#399C2318yes—
261#399C2318yes—
262#399C2318yes—
263#399C2318yes—
264#399C2314yes—
265#399C2314yes—
266#398C2318yes—
267#398C2318yes—
268#398C2318yes—
269#398C2318yes—
270#398C2318yes—
271#398C2318yes—
272#398C2318yes—
273#398C2318yes—
274#398C2318yes—
275#398C2318yes—
276#396C2318yes—
277#396C2318yes—
278#396C2318yes—
279#396C2318yes—
280#395C2318yes—
281#395C2318yes—
282#395C2314yes—
283#395C2314yes—
284#395C2318yes—
285#395C2318yes—
286#395C2318yes—
287#395C2318yes—
288#393C2314yes—
289#393C2314yes—
290#393C2318yes—
291#393C2318yes—
292#393C2318yes—
293#393C2318yes—
294#391C2318yes—
295#391C2314yes—
296#391C2318yes—
297#391C2312yes—
298#391C2318yes—
299#391C2318yes—
300#391C2318yes—
301#391C2318yes—
302#391C2318yes—
303#391C2318yes—
304#390C2314yes—
305#390C2314yes—
306#390C2314yes—
307#390C2312yes—
308#390C2318yes—
309#389C2314yes—
310#389C2314yes—
311#389C2318yes—
312#389C2318yes—
313#389C2314yes—
314#389C2314yes—
315#389C2314yes—
316#389C2314yes—
317#389C2318yes—
318#389C2314yes—
319#389C2314yes—
320#389C2314yes—
321#389C2314yes—
322#389C2314yes—
323#389C2314yes—
324#389C2314yes—
325#389C2314yes—
326#389C2314yes—
327#389C2314yes—
328#389C2314yes—
329#389C2314yes—
330#389C2314yes—
331#389C2314yes—
332#389C2318yes—
333#389C2318yes—
334#389C2314yes—
335#389C2314yes—
336#389C2312yes—
337#389C2312yes—
338#389C2318yes—
339#389C2318yes—
340#389C2318yes—
341#389C2318yes—
342#389C2318yes—
343#389C2318yes—
344#389C2314yes—
345#389C2314yes—
346#388C2314yes—
347#388C2314yes—
348#388C2314yes—
349#388C2314yes—
350#388C2314yes—
351#388C2314yes—
352#388C2318yes—
353#388C2318yes—
354#388C2318yes—
355#388C2318yes—
356#387C2318yes—
357#387C2318yes—
358#387C2318yes—
359#387C2318yes—
360#387C2318yes—
361#387C2318yes—
362#387C2318yes—
363#387C2314yes—
364#387C2314yes—
365#387C2318yes—
366#387C2318yes—
367#387C2318yes—
368#387C2318yes—
369#387C2318yes—
370#386C2312yes—
371#386C2314yes—
372#386C2318yes—
373#386C2318yes—
374#386C2312yes—
375#386C2314yes—
376#386C2318yes—
377#385C2314yes—
378#385C2318yes—
379#385C2318yes—
380#385C2318yes—
381#385C2314yes—
382#385C2314yes—
383#385C2314yes—
384#385C2314yes—
385#385C2314yes—
386#385C2314yes—
387#385C2314yes—
388#385C2318yes—
389#385C2318yes—
390#385C2318yes—
391#385C2318yes—
392#385C2318yes—
393#385C2312yes—
394#385C2312yes—
395#385C2314yes—
396#385C2314yes—
397#385C2318yes—
398#385C2318yes—
399#385C2318yes—
400#384C2312yes—
401#384C2314yes—
402#384C2312yes—
403#384C2314yes—
404#384C2314yes—
405#384C2312yes—
406#384C2312yes—
407#382C2314yes—
408#382C2312yes—
409#382C2314yes—
410#382C2314yes—
411#382C2312yes—
412#382C2318yes—
413#382C2311yescharacteristic
414#382C2311yescharacteristic
415#382C2311yescharacteristic
416#382C2311yescharacteristic
417#382C2312yes—
418#382C2314yes—
419#382C2314yes—
420#382C2312yes—
421#382C2312yes—
422#382C2312yes—
423#381C2312yes—
424#380C2318yes—
425#380C2314yes—
426#380C2318yes—
427#380C2318yes—
428#380C2314yes—
429#380C2314yes—
430#380C2312yes—
431#380C2312yes—
432#380C2312yes—
433#380C2314yes—
434#380C2312yes—
435#380C2312yes—
436#380C2314yes—
437#380C2312yes—
438#380C2318yes—
439#380C2314yes—
440#380C2314yes—
441#380C2314yes—
442#380C2314yes—
443#380C2314yes—
444#379C2312yes—
445C4×C4⋊C4C2314yes—
446C4×C4⋊C4C2314yes—
447C4×C4⋊C4C2318yes—
448C4×C4⋊C4C2312yes—
449C4×C4⋊C4C2312yes—
450C4×C4⋊C4C2314yes—
451C4×C4⋊C4C2312yes—
452C4×C4⋊C4C2312yes—
453C4×C4⋊C4C2314yes—
454C4×C4⋊C4C2314yes—
455C4×C4⋊C4C2318yes—
456C4×C4⋊C4C2314yes—
457C4×C4⋊C4C2314yes—
458C4×C4⋊C4C2312yes—
459C4×C4⋊C4C2312yes—
460C4×C4⋊C4C2314yes—
461C4×C4⋊C4C2314yes—
462C4×C22⋊C4C2312yes—
463C4×C22⋊C4C2312yes—
464C4×C22⋊C4C2318yes—
465C4×C22⋊C4C2318yes—
466C4×C22⋊C4C2318yes—
467C4×C22⋊C4C2314yes—
468C4×C22⋊C4C2314yes—
469#376C2312yes—
470C2×#95C2314yes—
471C2×#95C2314yes—
472C2×#95C2312yes—
473C2×#95C2312yes—
474C2×#95C2314yes—
475C2×#95C2314yes—
476C43C2312yes—
477C25C2411yescharacteristic
478C2×#41—24no—
479C2×#41—24no—
480C2×#41C2×Q818yes—
481C22×Q8—28no—
482C22×Q8—84no—
483C22×Q8C2411yescharacteristic
484C22×Q8C2414yes—
485C22×Q8C2414yes—
486C22×Q8C2418yes—
487C22×D4C2412yes—
488C22×D4C2411yescharacteristic
489C22×D4C2414yes—
490C23×C4—24no—
491C23×C4—24no—
492C23×C4C2×Q818yes—
493C23×C4C2412yes—
494C23×C4C2411yescharacteristic
495C23×C4C2412yes—
496C23×C4C2412yes—
497C23×C4C2411yescharacteristic
498C23×C4C2414yes—
499C23×C4C2414yes—
500C23×C4C2411yescharacteristic
501C23×C4C2412yes—
502C23×C4C2412yes—
503C23×C4C2414yes—
504C23×C4C2414yes—
505C23×C4C2418yes—
506C23×C4C2411yescharacteristic
507C23×C4C2411yescharacteristic
508C23×C4C2411yescharacteristic
509C4⋊Q8—28no—
510C4⋊Q8—28no—
511C4⋊Q8—28no—
512C4⋊Q8—28no—
513C4⋊Q8—48no—
514C4⋊Q8—48no—
515#125—48no—
516#125—48no—
517#125—88no—
518#123C2×Q8116yes—
519C22⋊Q8—416no—
520C22⋊Q8—88no—
521C22⋊Q8—88no—
522C22⋊Q8—88no—
523C22⋊Q8C2×Q8116yescomplemented
524#121C2×Q8116yescomplemented
525#120C2×Q8116yes—
526C4×Q8—24no—
527C4×Q8—24no—
528C4×Q8—48no—
529C4×Q8—88no—
530C4×D4—28no—
531C4×D4—28no—
532C4×D4—24no—
533C4×D4—24no—
534C4×D4—48no—
535C4×D4—416no—
536C4×D4—88no—
537C4×D4C2×Q8132yescomplemented
538#117—24no—
539#117—28no—
540#117—28no—
541#117—24no—
542#117—28no—
543#117—28no—
544#117—28no—
545#117—28no—
546#117—28no—
547#117—48no—
548#117—48no—
549#117—44no—
550#117—44no—
551#117—48no—
552#117C2×Q818yes—
553C2×C4⋊C4—24no—
554C2×C4⋊C4—24no—
555C2×C4⋊C4—28no—
556C2×C4⋊C4—28no—
557C2×C4⋊C4—28no—
558C2×C4⋊C4—44no—
559C2×C4⋊C4—44no—
560C2×C4⋊C4—48no—
561C2×C4⋊C4—84no—
562C2×C4⋊C4C2412yes—
563C2×C4⋊C4C2414yes—
564C2×C4⋊C4C2412yes—
565C2×C4⋊C4C2412yes—
566C2×C4⋊C4C2412yes—
567C2×C4⋊C4C2412yes—
568C2×C4⋊C4C2412yes—
569C2×C4⋊C4C2412yes—
570C2×C4⋊C4C2412yes—
571C2×C4⋊C4C2414yes—
572C2×C4⋊C4C2414yes—
573C2×C4⋊C4C2414yes—
574C2×C4⋊C4C2414yes—
575C2×C4⋊C4C2414yes—
576C2×C4⋊C4C2411yescharacteristic
577C2×C4⋊C4C2411yescharacteristic
578C2×C4⋊C4C2412yes—
579C2×C4⋊C4C2412yes—
580C2×C4⋊C4C2412yes—
581C2×C4⋊C4C2414yes—
582C2×C4⋊C4C2414yes—
583C2×C4⋊C4C2418yes—
584C2×C4⋊C4C2418yes—
585C2×C4⋊C4C2418yes—
586C2×C4⋊C4C2418yes—
587C2×C4⋊C4C2414yes—
588C2×C4⋊C4C2418yes—
589C2×C4⋊C4C2418yes—
590C2×C4⋊C4C2414yes—
591C2×C4⋊C4C2414yes—
592C2×C4⋊C4C2418yes—
593C2×C4⋊C4C2418yes—
594C2×C4⋊C4C2418yes—
595C2×C4⋊C4C2418yes—
596C2×C4⋊C4C2418yes—
597C2×C4⋊C4C2418yes—
598C2×C4⋊C4C2414yes—
599C2×C4⋊C4C2414yes—
600C2×C4⋊C4C2414yes—
601C2×C4⋊C4C2414yes—
602C2×C4⋊C4C2414yes—
603C2×C4⋊C4C2418yes—
604C2×C4⋊C4C2414yes—
605C2×C4⋊C4C2414yes—
606C2×C4⋊C4C2418yes—
607C2×C4⋊C4C2412yes—
608C2×C4⋊C4C2414yes—
609C2×C22⋊C4—24no—
610C2×C22⋊C4—24no—
611C2×C22⋊C4—48no—
612C2×C22⋊C4—84no—
613C2×C22⋊C4C2414yes—
614C2×C22⋊C4C2414yes—
615C2×C22⋊C4C2412yes—
616C2×C22⋊C4C2412yes—
617C2×C22⋊C4C2412yes—
618C2×C22⋊C4C2412yes—
619C2×C22⋊C4C2412yes—
620C2×C22⋊C4C2412yes—
621C2×C22⋊C4C2412yes—
622C2×C22⋊C4C2412yes—
623C2×C22⋊C4C2414yes—
624C2×C22⋊C4C2414yes—
625C2×C22⋊C4C2418yes—
626C2×C22⋊C4C2418yes—
627C2×C22⋊C4C2418yes—
628C2×C22⋊C4C2418yes—
629C2×C22⋊C4C2414yes—
630C2×C22⋊C4C2418yes—
631C2×C22⋊C4C2414yes—
632C2×C22⋊C4C2414yes—
633C2×C22⋊C4C2414yes—
634C2×C22⋊C4C2412yes—
635C2×C22⋊C4C2414yes—
636C2×C22⋊C4C2414yes—
637C2×C42—24no—
638C2×C42—28no—
639C2×C42—48no—
640C2×C42#4118yes—
641C2×C42C2414yes—
642C2×C42C2414yes—
643C2×C42C2412yes—
644C2×C42C2412yes—
645C2×C42C2412yes—
646C2×C42C2412yes—
647C2×C42C2412yes—
648C2×C42C2412yes—
649C2×C42C2414yes—
650C2×C42C2414yes—
651C2×C42C2418yes—
652C2×C42C2418yes—
653C2×C42C2414yes—
654C2×C42C2418yes—
655C2×C42C2414yes—
656C2×C42C2412yes—
657C2×C42C2411yescharacteristic
658C2×C42C2411yescharacteristic
659C2×C42C2411yescharacteristic
660C2×C42C2411yescharacteristic
661#95C2412yes—
662#95C2412yes—
663#95C2414yes—
664#95C2414yes—
665#95C2418yes—
666#95C2418yes—
667#95C2418yes—
668#95C2418yes—
669#95C2414yes—
670#95C2414yes—
671#95C2418yes—
672#95C2418yes—
673#95C2414yes—
674#95C2414yes—
675#95C2418yes—
676#95C2418yes—
677#95C2414yes—
678#95C2414yes—
679#95C2418yes—
680#95C2418yes—
681#95C2418yes—
682#95C2414yes—
683#95C2414yes—
684#95C2412yes—
685#95C2412yes—
686#95C2414yes—
687#95C2418yes—
688#95C2414yes—
689#95C2414yes—
690#95C2414yes—
691#95C2412yes—
692#95C2412yes—
693#95C2412yes—
694#95C2412yes—
695#95C2418yes—
696#95C2418yes—
697#95C2414yes—
698#95C2414yes—
699#95C2418yes—
700#95C2418yes—
701C24—22no—
702C24—22no—
703C24—42no—
704C24—42no—
705C24C22×Q814yes—
706C24C2512yes—
707C24C2512yes—
708C24C2511yescharacteristic
709#41—232no—
710C2×Q8—22no—
711C2×Q8—28no—
712C2×Q8—28no—
713C2×Q8—22no—
714C2×Q8—48no—
715C2×Q8—48no—
716C2×Q8—48no—
717C2×Q8—48no—
718C2×Q8—48no—
719C2×Q8—816no—
720C2×Q8C22×Q814yes—
721C2×D4—24no—
722C2×D4—24no—
723C2×D4—22no—
724C2×D4—22no—
725C2×D4—44no—
726C2×D4—44no—
727C2×D4C22×Q818yes—
728C2×D4C22×Q814yes—
729C2×D4C22×Q8116yes—
730C22×C4—22no—
731C22×C4—22no—
732C22×C4—232no—
733C22×C4—24no—
734C22×C4—24no—
735C22×C4—24no—
736C22×C4—24no—
737C22×C4—24no—
738C22×C4—24no—
739C22×C4—22no—
740C22×C4—22no—
741C22×C4—28no—
742C22×C4—28no—
743C22×C4—24no—
744C22×C4—24no—
745C22×C4—42no—
746C22×C4—42no—
747C22×C4—44no—
748C22×C4—44no—
749C22×C4—44no—
750C22×C4—44no—
751C22×C4—42no—
752C22×C4—44no—
753C22×C4—44no—
754C22×C4—44no—
755C22×C4—44no—
756C22×C4—44no—
757C22×C4—42no—
758C22×C4—44no—
759C22×C4—44no—
760C22×C4—44no—
761C22×C4—48no—
762C22×C4—48no—
763C22×C4—48no—
764C22×C4C22×Q818yes—
765C22×C4C22×Q818yes—
766C22×C4C22×Q818yes—
767C22×C4C22×Q814yes—
768C22×C4C22×Q814yes—
769C22×C4C2×#4114yes—
770C22×C4C2×#4114yes—
771C22×C4C2×#4114yes—
772C22×C4H(5,𝔽2)14yes—
773C22×C4C2512yes—
774C22×C4C2512yes—
775C22×C4C2514yes—
776C22×C4C2518yes—
777C22×C4C2514yes—
778C22×C4C2518yes—
779C22×C4C2514yes—
780C22×C4C2514yes—
781C22×C4C2512yes—
782C22×C4C2512yes—
783C22×C4C2514yes—
784C22×C4C2514yes—
785C22×C4C2512yes—
786C22×C4C2512yes—
787C22×C4C2511yescharacteristic
788C22×C4C2511yescharacteristic
789C22×C4C2511yescharacteristic
790C22×C4C2511yescharacteristic
791C22×C4C2511yescharacteristic
792C22×C4C2511yescharacteristic
793C4⋊C4—24no—
794C4⋊C4—24no—
795C4⋊C4—24no—
796C4⋊C4—24no—
797C4⋊C4—28no—
798C4⋊C4—28no—
799C4⋊C4—28no—
800C4⋊C4—28no—
801C4⋊C4—24no—
802C4⋊C4—24no—
803C4⋊C4—22no—
804C4⋊C4—22no—
805C4⋊C4—28no—
806C4⋊C4—28no—
807C4⋊C4—24no—
808C4⋊C4—24no—
809C4⋊C4—24no—
810C4⋊C4—24no—
811C4⋊C4—24no—
812C4⋊C4—44no—
813C4⋊C4—44no—
814C4⋊C4—48no—
815C4⋊C4—48no—
816C4⋊C4—48no—
817C4⋊C4—44no—
818C4⋊C4—44no—
819C4⋊C4—48no—
820C4⋊C4—44no—
821C4⋊C4—44no—
822C4⋊C4—48no—
823C4⋊C4—44no—
824C4⋊C4—48no—
825C4⋊C4—44no—
826C4⋊C4—48no—
827C4⋊C4—48no—
828C4⋊C4—48no—
829C4⋊C4—48no—
830C4⋊C4—48no—
831C4⋊C4—44no—
832C4⋊C4—44no—
833C4⋊C4—48no—
834C4⋊C4—48no—
835C4⋊C4—48no—
836C4⋊C4—44no—
837C4⋊C4—44no—
838C4⋊C4C22×Q818yes—
839C4⋊C4C22×Q8116yes—
840C22⋊C4—24no—
841C22⋊C4—28no—
842C22⋊C4—28no—
843C22⋊C4—24no—
844C22⋊C4—24no—
845C22⋊C4—24no—
846C22⋊C4—24no—
847C22⋊C4—24no—
848C22⋊C4—24no—
849C22⋊C4—24no—
850C22⋊C4—44no—
851C22⋊C4—44no—
852C22⋊C4—48no—
853C22⋊C4—48no—
854C22⋊C4—44no—
855C22⋊C4—44no—
856C22⋊C4—48no—
857C22⋊C4—48no—
858C22⋊C4—44no—
859C22⋊C4—44no—
860C22⋊C4—48no—
861C22⋊C4C22×Q818yes—
862C22⋊C4C22×Q8116yes—
863C22⋊C4C22×Q8116yes—
864C42—24no—
865C42—24no—
866C42—24no—
867C42—24no—
868C42—24no—
869C42—28no—
870C42—28no—
871C42—24no—
872C42—44no—
873C42—44no—
874C42—44no—
875C42—48no—
876C42—48no—
877C42—44no—
878C42—48no—
879C42C22×Q818yes—
880C42C2×#4114yes—
881C42C2×#4114yes—
882C42C2×#4114yes—
883C42C2×#4114yes—
884C23—22no—
885C23—22no—
886C23—22no—
887C23—22no—
888C23—22no—
889C23—22no—
890C23—22no—
891C23—24no—
892C23—22no—
893C23—22no—
894C23—24no—
895C23—22no—
896C23—28no—
897C23—48no—
898C23—82no—
899C23—82no—
900C23—84no—
901C23C23×Q814yes—
902C23C23×Q814yes—
903C23C23×Q812yes—
904C23C22×#4112yes—
905C23C2×H(5,𝔽2)12yes—
906C23C2611yescharacteristic
907Q8—28no—
908Q8—416no—
909Q8—88no—
910Q8—168no—
911D4—216no—
912D4—28no—
913D4—416no—
914C2×C4—22no—
915C2×C4—22no—
916C2×C4—22no—
917C2×C4—22no—
918C2×C4—24no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—24no—
923C2×C4—22no—
924C2×C4—28no—
925C2×C4—216no—
926C2×C4—216no—
927C2×C4—216no—
928C2×C4—22no—
929C2×C4—22no—
930C2×C4—22no—
931C2×C4—22no—
932C2×C4—28no—
933C2×C4—24no—
934C2×C4—24no—
935C2×C4—24no—
936C2×C4—24no—
937C2×C4—24no—
938C2×C4—28no—
939C2×C4—24no—
940C2×C4—24no—
941C2×C4—28no—
942C2×C4—24no—
943C2×C4—28no—
944C2×C4—22no—
945C2×C4—24no—
946C2×C4—28no—
947C2×C4—24no—
948C2×C4—24no—
949C2×C4—22no—
950C2×C4—24no—
951C2×C4—22no—
952C2×C4—24no—
953C2×C4—22no—
954C2×C4—24no—
955C2×C4—24no—
956C2×C4—24no—
957C2×C4—28no—
958C2×C4—24no—
959C2×C4—44no—
960C2×C4—44no—
961C2×C4—84no—
962C2×C4—84no—
963C2×C4—82no—
964C2×C4—82no—
965C2×C4—88no—
966C2×C4—88no—
967C2×C4—88no—
968C2×C4—88no—
969C2×C4—168no—
970C2×C4#554116yes—
971C2×C4C23×Q818yes—
972C2×C4C23×Q814yes—
973C2×C4C23×Q814yes—
974C2×C4C23×Q812yes—
975C2×C4C23×Q812yes—
976C2×C4C22×#4112yes—
977C2×C4C22×#4112yes—
978C2×C4C22×#4112yes—
979C2×C4C22×#4112yes—
980C2×C4C22×#4112yes—
981C2×C4C22×#4112yes—
982C2×C4C2×H(5,𝔽2)12yes—
983C2×C4C2×H(5,𝔽2)12yes—
984C22—24no—
985C22—22no—
986C22—22no—
987C22—24no—
988C22—24no—
989C22—28no—
990C22—24no—
991C22—24no—
992C22—24no—
993C22—42no—
994C22—42no—
995C22—42no—
996C22—42no—
997C22—42no—
998C22—42no—
999C22—44no—
1000C22—88no—
1001C22C2×#55414yes—
1002C22C24×Q811yescharacteristic
1003C22C23×#4111yescharacteristic
1004C22C22×H(5,𝔽2)11yescharacteristic
1005C22H(7,𝔽2)12yes—
1006C222−1+612yes—
1007C4—28no—
1008C4—22no—
1009C4—22no—
1010C4—22no—
1011C4—22no—
1012C4—24no—
1013C4—24no—
1014C4—42no—
1015C4—42no—
1016C4—48no—
1017C4—42no—
1018C4—42no—
1019C4—44no—
1020C4—44no—
1021C4—44no—
1022C4—48no—
1023C4—44no—
1024C4—44no—
1025C4C2×#55414yes—
1026C4C2×#55414yes—
1027C2—24no—
1028C2—44no—
1029C2—44no—
1030C2C22×#55411yescharacteristic
1031C2#6285412yes—
1032C2#6285511yescharacteristic
1033C2#6286011yescharacteristic
1034C2#6287812yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#525C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #44463C2semidirect
2. #43961C2semidirect
3. #43512C2semidirect
4. #43081C2semidirect
5. #39695C2semidirect
6. #39694C2semidirect
7. #39691C2semidirect
8. #39690C2semidirect
9. #39498C2semidirect
10. #39493C2semidirect
11. #37878C2semidirect
12. #37875C2semidirect
13. #35575C2semidirect
14. #35543C2semidirect
15. #35330C2semidirect
16. #35279C2semidirect
17. #35253C2semidirect
18. C2×#2628C2semidirect
19. #34216C2semidirect
21. #34184C2semidirect
23. #34052C2semidirect
31. #2862C22semidirect
32. #2859C22semidirect
34. #2857C22semidirect
37. #2807C22semidirect
38. #2806C22semidirect
39. #2805C22semidirect
42. #2788C22semidirect
43. #2774C22semidirect
46. #2755C22semidirect
48. #2742C22semidirect
50. #2704C22semidirect
52. #2660C22semidirect
59. #2628C22semidirect
60. #2628C22semidirect
61. #2590C22semidirect
64. #2589C22semidirect
65. #2586C22semidirect
66. #2584C22semidirect
68. #2571C22semidirect
69. #2570C22semidirect
70. #2570C22semidirect
71. #2568C22semidirect
72. #2567C22semidirect
75. #2563C22semidirect
77. #2552C22semidirect
78. #2550C22semidirect
79. #2550C22semidirect
82. #2549C22semidirect
83. #2542C22semidirect
84. #2509C22semidirect
85. #2509C22semidirect
86. #2508C22semidirect
87. #2507C22semidirect
88. #2506C22semidirect
90. #2505C22semidirect
94. #2465C22semidirect
96. #2454C22semidirect
97. #2453C22semidirect
98. #2452C22semidirect
99. #2451C22semidirect
102. #2442C22semidirect
104. #2441C22semidirect
106. #2440C22semidirect
108. #2439C22semidirect
117. #2369C22semidirect
118. #2365C22semidirect
124. #2351C22semidirect
125. #2351C22semidirect
128. #2349C22semidirect
129. #2349C22semidirect
133. #2331C22semidirect
134. #2331C22semidirect
152. #2317C22semidirect
159. C4×C4⋊Q8C22semidirect
172. #2285C22semidirect
174. C2×#382C22semidirect
193. #525Q8semidirect
523. C22⋊Q8C2×Q8semidirect
524. #121C2×Q8semidirect
537. C4×D4C2×Q8semidirect

Maximal subgroups

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

subgroupindex
#444632
#439612
#435122
#430812
#396952
#396942
#396912
#396902
#394982
#394932
#378782
#378752
#355752
#355432
#353302
#352792
#352532
C2×#26282
#342162
#342022
#341842
#340652
#340522