Finite Group Databasebeta

← #7683812

Subgroups — #7683812

Order 512.

4876 conjugacy classes of subgroups.

The subgroup lattice has 1050 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59912C218yesmaximal, complemented
2#59464C214yesmaximal, complemented
3#59463C214yesmaximal, complemented
4#59325C214yesmaximal, complemented
5#59245C214yesmaximal, complemented
6#45279C214yesmaximal, complemented
7#45275C214yesmaximal, complemented
8#45213C214yesmaximal, complemented
9#45121C214yesmaximal, complemented
10#44477C218yesmaximal, complemented
11#35668C211yesmaximal, characteristic, complemented
12#35662C211yesmaximal, characteristic, complemented
13#35627C211yesmaximal, characteristic, complemented
14#35620C211yesmaximal, characteristic
15#35576C211yesmaximal, characteristic, complemented
16#35574C211yesmaximal, characteristic
17C2×#2568C211yesmaximal, characteristic, complemented
18#34815C211yesmaximal, characteristic, complemented
19#34745C211yesmaximal, characteristic
20#34276C211yesmaximal, characteristic
21#34268C211yesmaximal, characteristic
22#34266C211yesmaximal, characteristic
23#34249C211yesmaximal, characteristic, complemented
24#34215C211yesmaximal, characteristic, complemented
25#34184C211yesmaximal, characteristic
26C2×#544C2211yescharacteristic
27C2×#536C2211yescharacteristic
28C2×#533C2211yescharacteristic
29C22×C4⋊Q8C2211yescharacteristic
30C2×#520C2211yescharacteristic
31C2×#520C2211yescharacteristic
32C2×#519C2211yescharacteristic
33C2×#519C2211yescharacteristic
34C2×C4×#41C2211yescharacteristic
35C22×C4×Q8C2211yescharacteristic
36#2806C2218yes—
37#2802C2218yes—
38#2791C2218yes—
39#2790C2218yes—
40#2788C2218yes—
41#2788C2218yes—
42#2788C2218yes—
43#2774C2218yes—
44#2774C2218yes—
45#2763C2218yes—
46#2755C2218yes—
47#2729C2218yes—
48#2589C2218yes—
49#2588C2218yes—
50#2588C2218yes—
51#2588C2218yes—
52#2587C2218yes—
53#2586C2218yes—
54#2583C2214yes—
55#2582C2214yes—
56#2581C2214yes—
57#2579C2214yes—
58#2574C2218yes—
59#2571C2214yes—
60#2570C2214yes—
61#2568C2212yes—
62#2568C2214yes—
63#2568C2214yes—
64#2568C2212yes—
65#2568C2214yes—
66#2568C2214yes—
67#2567C2212yes—
68#2566C2212yes—
69#2565C2212yes—
70#2565C2212yes—
71#2565C2212yes—
72#2563C2212yes—
73#2556C2218yes—
74#2551C2214yes—
75#2551C2214yes—
76#2550C2218yes—
77#2550C2214yes—
78#2550C2214yes—
79#2549C2218yes—
80#2520C2218yes—
81#2511C2218yes—
82#2509C2214yes—
83#2509C2218yes—
84#2509C2212yes—
85#2508C2214yes—
86#2508C2218yes—
87#2508C2212yes—
88#2507C2212yes—
89#2506C2212yes—
90#2505C2218yes—
91#2505C2218yes—
92#2505C2218yes—
93#2505C2214yes—
94#2497C2218yes—
95#2492C2218yes—
96#2473C2214yes—
97#2454C2212yes—
98#2453C2214yes—
99#2453C2214yes—
100#2453C2212yes—
101#2452C2214yes—
102#2452C2212yes—
103#2451C2214yes—
104#2451C2214yes—
105#2451C2214yes—
106#2451C2212yes—
107#2450C2218yes—
108#2450C2214yes—
109#2449C2214yes—
110#2442C2214yes—
111#2440C2214yes—
112#2439C2214yes—
113#2439C2214yes—
114#2438C2218yes—
115#2438C2218yes—
116#2434C2214yes—
117#2409C2214yes—
118#2402C2214yes—
119#2396C2214yes—
120C2×#400C2214yes—
121#2369C2218yes—
122#2368C2218yes—
123#2368C2218yes—
124#2367C2214yes—
125#2367C2214yes—
126#2365C2214yes—
127#2365C2214yes—
128#2362C2214yes—
129#2362C2214yes—
130#2360C2214yes—
131#2360C2214yes—
132#2359C2218yes—
133#2359C2218yes—
134#2355C2214yes—
135#2355C2214yes—
136#2351C2214yes—
137#2351C2214yes—
138#2351C2214yes—
139Q8×C4⋊C4C2214yes—
140Q8×C4⋊C4C2214yes—
141#2349C2218yes—
142#2349C2214yes—
143#2331C2214yes—
144#2327C2212yes—
145#2326C2212yes—
146#2323C2214yes—
147#2322C2214yes—
148#2317C2211yescharacteristic
149#2317C2211yescharacteristic
150#2317C2212yes—
151#2317C2211yescharacteristic
152#2317C2211yescharacteristic
153#2317C2211yescharacteristic
154#2317C2212yes—
155#2317C2214yes—
156#2316C2211yescharacteristic
157#2311C2211yescharacteristic
158#2310C2211yescharacteristic
159C4×C4⋊Q8C2212yes—
160C4×#125C2214yes—
161C4×#125C2214yes—
162C4×#124C2212yes—
163C4×C22⋊Q8C2214yes—
164C4×C22⋊Q8C2214yes—
165C4×#123C2214yes—
166#2297C2211yescharacteristic
167#2297C2211yescharacteristic
168#2296C2214yes—
169#2296C2211yescharacteristic
170#2296C2211yescharacteristic
171#2296C2211yescharacteristic
172#2296C2211yescharacteristic
173#2296C2211yescharacteristic
174#2296C2211yescharacteristic
175C2×#391C2214yes—
176C2×#391C2211yescharacteristic
177C2×#391C2211yescharacteristic
178#2285C2211yescharacteristic
179#2285C2212yes—
180C2×#382C2211yescharacteristic
181C2×#382C2211yescharacteristic
182C2×#382C2212yes—
183#2274C2211yescharacteristic
184#2274C2211yescharacteristic
185C4×#117C2211yescharacteristic
186C2×C4×C4⋊C4C2211yescharacteristic
187C22×#41C2311yescharacteristic
188C23×Q8C2311yescharacteristic
189C23×Q8C2312yes—
190#544—44no—
191#536Q8116yescomplemented
192#533—28no—
193C2×C4⋊Q8—44no—
194C2×C4⋊Q8C2312yes—
195C2×C4⋊Q8C2312yes—
196C2×C4⋊Q8C2312yes—
197C2×C4⋊Q8C2314yes—
198C2×C4⋊Q8C2314yes—
199C2×C4⋊Q8C2318yes—
200C2×C4⋊Q8C2312yes—
201C2×#125C2312yes—
202C2×#125C2314yes—
203C2×#125C2312yes—
204C2×#125C2312yes—
205C2×#124C2312yes—
206C2×#123C2314yes—
207C2×C22⋊Q8C2314yes—
208C2×C22⋊Q8C2314yes—
209C2×C22⋊Q8C2318yes—
210C2×C22⋊Q8C2314yes—
211C2×C22⋊Q8C2314yes—
212#520—44no—
213#520—44no—
214#519—28no—
215#519—44no—
216C4×#41—28no—
217C2×C4×Q8—44no—
218C2×C4×Q8C2314yes—
219C2×C4×Q8C2314yes—
220C2×C4×Q8C2314yes—
221C2×C4×Q8C2312yes—
222C2×C4×Q8C2312yes—
223C2×C4×Q8C2312yes—
224C2×C4×Q8C2312yes—
225C2×C4×Q8C2312yes—
226C2×C4×Q8C2312yes—
227C2×C4×Q8C2314yes—
228C2×C4×Q8C2314yes—
229C2×C4×Q8C2312yes—
230C2×C4×D4C2314yes—
231C2×C4×D4C2312yes—
232C2×C4×D4C2312yes—
233C2×C4×D4C2314yes—
234C2×C4×D4C2314yes—
235C2×C4×D4C2312yes—
236C2×#117C2311yescharacteristic
237C2×#117C2311yescharacteristic
238C2×#117C2311yescharacteristic
239C2×#117C2312yes—
240C2×#117C2311yescharacteristic
241C2×#117C2311yescharacteristic
242C2×#117C2314yes—
243C2×#117C2314yes—
244C2×#117C2312yes—
245C2×#117C2312yes—
246C2×#117C2311yescharacteristic
247C2×#117C2311yescharacteristic
248C22×C4⋊C4C2311yescharacteristic
249C22×C4⋊C4C2311yescharacteristic
250C22×C4⋊C4C2311yescharacteristic
251C22×C4⋊C4C2312yes—
252C22×C4⋊C4C2312yes—
253C22×C4⋊C4C2312yes—
254C22×C4⋊C4C2312yes—
255C22×C4⋊C4C2312yes—
256C22×C42C2311yescharacteristic
257C22×C42C2311yescharacteristic
258C22×C42C2312yes—
259C22×C42C2311yescharacteristic
260C22×C42C2312yes—
261#400C2318yes—
262#400C2318yes—
263#400C2318yes—
264#400C2318yes—
265#400C2318yes—
266#400C2318yes—
267#400C2318yes—
268#400C2318yes—
269#400C2318yes—
270#400C2318yes—
271#400C2314yes—
272#400C2314yes—
273#400C2314yes—
274#400C2314yes—
275#400C2314yes—
276#399C2314yes—
277#398C2318yes—
278#398C2318yes—
279#398C2318yes—
280#398C2318yes—
281#398C2314yes—
282#398C2318yes—
283#398C2318yes—
284#398C2318yes—
285#398C2318yes—
286#398C2314yes—
287#398C2314yes—
288#398C2314yes—
289#398C2314yes—
290#398C2314yes—
291#396C2318yes—
292#396C2314yes—
293#396C2318yes—
294#396C2314yes—
295#395C2318yes—
296#395C2318yes—
297#395C2318yes—
298#395C2318yes—
299#395C2314yes—
300#395C2318yes—
301#395C2318yes—
302#393C2318yes—
303#393C2318yes—
304#393C2314yes—
305#391C2311yescharacteristic
306#391C2312yes—
307#391C2312yes—
308#391C2311yescharacteristic
309#391C2312yes—
310#391C2312yes—
311#391C2312yes—
312#391C2312yes—
313#391C2314yes—
314#391C2318yes—
315#391C2314yes—
316#391C2312yes—
317#391C2318yes—
318#391C2318yes—
319#391C2314yes—
320#391C2318yes—
321#391C2318yes—
322#391C2318yes—
323#391C2318yes—
324#391C2318yes—
325#391C2318yes—
326#391C2318yes—
327#391C2318yes—
328#391C2312yes—
329#391C2314yes—
330#390C2311yescharacteristic
331#390C2312yes—
332#390C2311yescharacteristic
333#390C2312yes—
334#389C2314yes—
335#389C2314yes—
336#389C2314yes—
337#389C2314yes—
338#389C2318yes—
339#389C2318yes—
340#389C2312yes—
341#389C2314yes—
342#389C2312yes—
343#389C2318yes—
344#389C2314yes—
345#389C2318yes—
346#389C2318yes—
347#389C2318yes—
348#389C2318yes—
349#389C2314yes—
350#389C2314yes—
351#389C2314yes—
352#389C2318yes—
353#389C2312yes—
354#389C2318yes—
355#389C2312yes—
356#389C2312yes—
357#389C2318yes—
358#389C2318yes—
359#389C2318yes—
360#389C2318yes—
361#389C2312yes—
362#389C2312yes—
363#389C2312yes—
364#389C2312yes—
365#389C2318yes—
366#389C2312yes—
367#389C2312yes—
368#389C2314yes—
369#389C2312yes—
370#388C2318yes—
371#388C2318yes—
372#388C2318yes—
373#388C2318yes—
374#388C2318yes—
375#388C2318yes—
376#387C2314yes—
377#387C2314yes—
378#387C2318yes—
379#387C2314yes—
380#387C2318yes—
381#387C2314yes—
382#387C2318yes—
383#387C2318yes—
384#387C2318yes—
385#387C2318yes—
386#387C2318yes—
387#387C2318yes—
388#387C2318yes—
389#387C2318yes—
390#387C2318yes—
391#387C2318yes—
392#387C2318yes—
393#387C2318yes—
394#387C2318yes—
395#387C2318yes—
396#387C2318yes—
397#387C2314yes—
398#387C2314yes—
399#387C2318yes—
400#386C2314yes—
401#386C2312yes—
402#386C2314yes—
403#386C2312yes—
404#385C2318yes—
405#385C2312yes—
406#385C2312yes—
407#385C2314yes—
408#385C2314yes—
409#385C2318yes—
410#385C2314yes—
411#385C2314yes—
412#385C2314yes—
413#385C2318yes—
414#385C2312yes—
415#385C2318yes—
416#385C2318yes—
417#385C2318yes—
418#385C2314yes—
419#385C2318yes—
420#385C2314yes—
421#385C2312yes—
422#385C2312yes—
423#385C2312yes—
424#385C2314yes—
425#385C2314yes—
426#385C2314yes—
427#384C2312yes—
428#384C2311yescharacteristic
429#384C2312yes—
430#384C2312yes—
431#384C2311yescharacteristic
432#384C2312yes—
433#384C2312yes—
434#384C2318yes—
435#382C2312yes—
436#382C2314yes—
437#382C2312yes—
438#382C2312yes—
439#382C2311yescharacteristic
440#382C2312yes—
441#382C2314yes—
442#382C2312yes—
443#382C2314yes—
444#382C2312yes—
445#382C2311yescharacteristic
446#382C2312yes—
447#382C2318yes—
448#382C2312yes—
449#382C2312yes—
450#382C2318yes—
451#382C2318yes—
452#381C2314yes—
453#380C2318yes—
454#380C2314yes—
455#380C2314yes—
456#380C2314yes—
457#380C2318yes—
458#380C2314yes—
459C4×C4⋊C4C2312yes—
460C4×C4⋊C4C2312yes—
461C4×C4⋊C4C2314yes—
462C4×C4⋊C4C2314yes—
463C4×C4⋊C4C2314yes—
464C4×C4⋊C4C2318yes—
465C4×C4⋊C4C2318yes—
466C4×C4⋊C4C2314yes—
467C4×C4⋊C4C2314yes—
468C4×C4⋊C4C2314yes—
469C4×C4⋊C4C2318yes—
470C4×C4⋊C4C2312yes—
471C4×C4⋊C4C2312yes—
472C4×C4⋊C4C2312yes—
473C4×C4⋊C4C2312yes—
474C4×C4⋊C4C2312yes—
475C4×C4⋊C4C2312yes—
476C4×C4⋊C4C2318yes—
477C4×C4⋊C4C2314yes—
478C4×C4⋊C4C2318yes—
479C4×C4⋊C4C2318yes—
480C4×C4⋊C4C2318yes—
481C4×C4⋊C4C2314yes—
482C4×C4⋊C4C2312yes—
483C4×C4⋊C4C2314yes—
484C4×C4⋊C4C2312yes—
485C4×C4⋊C4C2318yes—
486C4×C22⋊C4C2318yes—
487C4×C22⋊C4C2314yes—
488C4×C22⋊C4C2314yes—
489C4×C22⋊C4C2318yes—
490C4×C22⋊C4C2314yes—
491C4×C22⋊C4C2318yes—
492C4×C22⋊C4C2314yes—
493C4×C22⋊C4C2314yes—
494#376C2312yes—
495C2×#95C2318yes—
496C2×#95C2314yes—
497C2×#95C2314yes—
498C2×#95C2314yes—
499C2×#95C2314yes—
500C2×#95C2312yes—
501C43C2312yes—
502C2×#41—24no—
503C2×#41—24no—
504C2×#41C2×Q818yes—
505C22×Q8—24no—
506C22×Q8—24no—
507C22×Q8—44no—
508C22×Q8—48no—
509C22×Q8C2×Q818yes—
510C22×Q8C2412yes—
511C22×Q8C2412yes—
512C22×Q8C2411yescharacteristic
513C22×Q8C2414yes—
514C22×Q8C2418yes—
515C22×Q8C2414yes—
516C22×D4C2412yes—
517C22×D4C2411yescharacteristic
518C23×C4C2411yescharacteristic
519C23×C4C2412yes—
520C23×C4C2412yes—
521C23×C4C2411yescharacteristic
522C23×C4C2412yes—
523C23×C4C2412yes—
524C23×C4C2412yes—
525C23×C4C2412yes—
526C23×C4C2412yes—
527C23×C4C2414yes—
528C23×C4C2414yes—
529C23×C4C2414yes—
530C23×C4C2411yescharacteristic
531C4⋊Q8—28no—
532C4⋊Q8—48no—
533C4⋊Q8—48no—
534C4⋊Q8—44no—
535C4⋊Q8—44no—
536C4⋊Q8—416no—
537C4⋊Q8C2×Q8116yescomplemented
538#125—28no—
539#125—44no—
540#125—44no—
541#125—48no—
542#124C2×Q8116yescomplemented
543#123C2×Q8132yes—
544C22⋊Q8—216no—
545C22⋊Q8—48no—
546C22⋊Q8—48no—
547C22⋊Q8—416no—
548C22⋊Q8C2×Q8132yescomplemented
549C4×Q8—28no—
550C4×Q8—216no—
551C4×Q8—216no—
552C4×Q8—216no—
553C4×Q8—48no—
554C4×Q8—48no—
555C4×Q8—44no—
556C4×Q8—44no—
557C4×Q8—44no—
558C4×Q8—44no—
559C4×Q8—44no—
560C4×Q8—44no—
561C4×D4—28no—
562C4×D4—216no—
563C4×D4—44no—
564C4×D4—44no—
565C4×D4—48no—
566C4×D4—48no—
567#117—24no—
568#117—24no—
569#117—24no—
570#117—24no—
571#117—24no—
572#117—216no—
573#117—28no—
574#117—48no—
575#117—44no—
576#117—44no—
577#117C2×Q818yes—
578#117#4118yes—
579C2×C4⋊C4—24no—
580C2×C4⋊C4—24no—
581C2×C4⋊C4—24no—
582C2×C4⋊C4—44no—
583C2×C4⋊C4—44no—
584C2×C4⋊C4—44no—
585C2×C4⋊C4—44no—
586C2×C4⋊C4—44no—
587C2×C4⋊C4C2412yes—
588C2×C4⋊C4C2411yescharacteristic
589C2×C4⋊C4C2411yescharacteristic
590C2×C4⋊C4C2412yes—
591C2×C4⋊C4C2412yes—
592C2×C4⋊C4C2412yes—
593C2×C4⋊C4C2412yes—
594C2×C4⋊C4C2412yes—
595C2×C4⋊C4C2412yes—
596C2×C4⋊C4C2412yes—
597C2×C4⋊C4C2411yescharacteristic
598C2×C4⋊C4C2411yescharacteristic
599C2×C4⋊C4C2414yes—
600C2×C4⋊C4C2411yescharacteristic
601C2×C4⋊C4C2411yescharacteristic
602C2×C4⋊C4C2412yes—
603C2×C4⋊C4C2418yes—
604C2×C4⋊C4C2412yes—
605C2×C4⋊C4C2414yes—
606C2×C4⋊C4C2414yes—
607C2×C4⋊C4C2414yes—
608C2×C4⋊C4C2414yes—
609C2×C4⋊C4C2414yes—
610C2×C4⋊C4C2414yes—
611C2×C4⋊C4C2414yes—
612C2×C4⋊C4C2414yes—
613C2×C4⋊C4C2418yes—
614C2×C4⋊C4C2418yes—
615C2×C4⋊C4C2412yes—
616C2×C4⋊C4C2412yes—
617C2×C4⋊C4C2414yes—
618C2×C4⋊C4C2414yes—
619C2×C4⋊C4C2414yes—
620C2×C4⋊C4C2414yes—
621C2×C4⋊C4C2414yes—
622C2×C4⋊C4C2418yes—
623C2×C4⋊C4C2414yes—
624C2×C4⋊C4C2418yes—
625C2×C4⋊C4C2414yes—
626C2×C4⋊C4C2414yes—
627C2×C4⋊C4C2414yes—
628C2×C4⋊C4C2418yes—
629C2×C4⋊C4C2418yes—
630C2×C4⋊C4C2418yes—
631C2×C4⋊C4C2414yes—
632C2×C4⋊C4C2414yes—
633C2×C4⋊C4C2414yes—
634C2×C4⋊C4C2414yes—
635C2×C4⋊C4C2414yes—
636C2×C4⋊C4C2418yes—
637C2×C4⋊C4C2414yes—
638C2×C4⋊C4C2414yes—
639C2×C4⋊C4C2412yes—
640C2×C4⋊C4C2418yes—
641C2×C4⋊C4C2412yes—
642C2×C22⋊C4C2412yes—
643C2×C22⋊C4C2412yes—
644C2×C22⋊C4C2412yes—
645C2×C22⋊C4C2412yes—
646C2×C22⋊C4C2414yes—
647C2×C22⋊C4C2412yes—
648C2×C22⋊C4C2414yes—
649C2×C22⋊C4C2414yes—
650C2×C22⋊C4C2414yes—
651C2×C22⋊C4C2414yes—
652C2×C22⋊C4C2418yes—
653C2×C22⋊C4C2414yes—
654C2×C22⋊C4C2414yes—
655C2×C22⋊C4C2412yes—
656C2×C22⋊C4C2418yes—
657C2×C22⋊C4C2412yes—
658C2×C42—24no—
659C2×C42—24no—
660C2×C42—24no—
661C2×C42—28no—
662C2×C42—44no—
663C2×C42C2411yescharacteristic
664C2×C42C2412yes—
665C2×C42C2412yes—
666C2×C42C2412yes—
667C2×C42C2412yes—
668C2×C42C2418yes—
669C2×C42C2412yes—
670C2×C42C2412yes—
671C2×C42C2414yes—
672C2×C42C2412yes—
673C2×C42C2412yes—
674C2×C42C2412yes—
675C2×C42C2411yescharacteristic
676C2×C42C2411yescharacteristic
677C2×C42C2411yescharacteristic
678C2×C42C2414yes—
679C2×C42C2414yes—
680C2×C42C2414yes—
681C2×C42C2414yes—
682C2×C42C2418yes—
683C2×C42C2414yes—
684C2×C42C2418yes—
685C2×C42C2414yes—
686C2×C42C2418yes—
687C2×C42C2412yes—
688C2×C42C2412yes—
689#95C2414yes—
690#95C2418yes—
691#95C2418yes—
692#95C2418yes—
693#95C2412yes—
694#95C2418yes—
695#95C2418yes—
696#95C2412yes—
697#95C2412yes—
698#95C2412yes—
699#95C2418yes—
700#95C2418yes—
701#95C2418yes—
702#95C2418yes—
703#95C2418yes—
704#95C2414yes—
705#95C2414yes—
706#95C2414yes—
707#95C2414yes—
708#95C2418yes—
709#95C2418yes—
710#95C2414yes—
711#95C2414yes—
712#95C2418yes—
713#95C2418yes—
714#95C2414yes—
715#95C2414yes—
716#95C2414yes—
717#95C2414yes—
718#95C2414yes—
719#95C2418yes—
720#95C2414yes—
721#95C2418yes—
722#95C2418yes—
723#95C2414yes—
724#95C2414yes—
725#95C2414yes—
726#95C2414yes—
727#95C2418yes—
728#95C2414yes—
729#95C2414yes—
730#95C2414yes—
731#95C2418yes—
732C24C2512yes—
733C24C2511yescharacteristic
734#41—232no—
735C2×Q8—232no—
736C2×Q8—24no—
737C2×Q8—24no—
738C2×Q8—22no—
739C2×Q8—28no—
740C2×Q8—24no—
741C2×Q8—24no—
742C2×Q8—22no—
743C2×Q8—216no—
744C2×Q8—44no—
745C2×Q8—48no—
746C2×Q8—48no—
747C2×Q8—44no—
748C2×Q8—44no—
749C2×Q8—48no—
750C2×Q8—816no—
751C2×Q8C22×Q818yes—
752C2×Q8C22×Q818yes—
753C2×Q8C22×Q814yes—
754C2×D4—24no—
755C2×D4—24no—
756C2×D4—22no—
757C2×D4—22no—
758C2×D4C22×Q818yes—
759C2×D4C22×Q814yes—
760C22×C4—24no—
761C22×C4—22no—
762C22×C4—24no—
763C22×C4—24no—
764C22×C4—24no—
765C22×C4—24no—
766C22×C4—22no—
767C22×C4—24no—
768C22×C4—24no—
769C22×C4—24no—
770C22×C4—24no—
771C22×C4—24no—
772C22×C4—28no—
773C22×C4—42no—
774C22×C4—42no—
775C22×C4—42no—
776C22×C4—44no—
777C22×C4—44no—
778C22×C4—42no—
779C22×C4—44no—
780C22×C4—42no—
781C22×C4—44no—
782C22×C4—44no—
783C22×C4—44no—
784C22×C4—44no—
785C22×C4—48no—
786C22×C4—48no—
787C22×C4C22×Q818yes—
788C22×C4C22×Q818yes—
789C22×C4C22×Q814yes—
790C22×C4C2×#4114yes—
791C22×C4H(5,𝔽2)14yes—
792C22×C4C2512yes—
793C22×C4C2512yes—
794C22×C4C2512yes—
795C22×C4C2514yes—
796C22×C4C2514yes—
797C22×C4C2512yes—
798C22×C4C2514yes—
799C22×C4C2512yes—
800C22×C4C2514yes—
801C22×C4C2514yes—
802C22×C4C2512yes—
803C22×C4C2512yes—
804C22×C4C2512yes—
805C22×C4C2512yes—
806C22×C4C2512yes—
807C22×C4C2512yes—
808C22×C4C2514yes—
809C22×C4C2514yes—
810C22×C4C2512yes—
811C22×C4C2514yes—
812C22×C4C2512yes—
813C22×C4C2511yescharacteristic
814C22×C4C2511yescharacteristic
815C4⋊C4—28no—
816C4⋊C4—216no—
817C4⋊C4—24no—
818C4⋊C4—24no—
819C4⋊C4—28no—
820C4⋊C4—28no—
821C4⋊C4—28no—
822C4⋊C4—24no—
823C4⋊C4—24no—
824C4⋊C4—24no—
825C4⋊C4—24no—
826C4⋊C4—24no—
827C4⋊C4—24no—
828C4⋊C4—22no—
829C4⋊C4—22no—
830C4⋊C4—22no—
831C4⋊C4—22no—
832C4⋊C4—22no—
833C4⋊C4—22no—
834C4⋊C4—24no—
835C4⋊C4—24no—
836C4⋊C4—28no—
837C4⋊C4—28no—
838C4⋊C4—28no—
839C4⋊C4—42no—
840C4⋊C4—42no—
841C4⋊C4—44no—
842C4⋊C4—44no—
843C4⋊C4—48no—
844C4⋊C4—48no—
845C4⋊C4—44no—
846C4⋊C4—44no—
847C4⋊C4—48no—
848C4⋊C4—44no—
849C4⋊C4—44no—
850C4⋊C4—44no—
851C4⋊C4—44no—
852C4⋊C4—48no—
853C4⋊C4—44no—
854C4⋊C4—44no—
855C4⋊C4—44no—
856C4⋊C4—48no—
857C4⋊C4—48no—
858C4⋊C4—44no—
859C4⋊C4—44no—
860C4⋊C4—44no—
861C4⋊C4—44no—
862C4⋊C4—44no—
863C4⋊C4—44no—
864C4⋊C4—44no—
865C4⋊C4—48no—
866C4⋊C4—48no—
867C4⋊C4C22×Q818yes—
868C4⋊C4C22×Q8132yes—
869C4⋊C4C2×#4118yes—
870C22⋊C4—24no—
871C22⋊C4—24no—
872C22⋊C4—24no—
873C22⋊C4—24no—
874C22⋊C4—24no—
875C22⋊C4—28no—
876C22⋊C4—28no—
877C22⋊C4—44no—
878C22⋊C4—44no—
879C22⋊C4—44no—
880C22⋊C4—44no—
881C22⋊C4—48no—
882C22⋊C4—44no—
883C22⋊C4C22×Q818yes—
884C22⋊C4C22×Q8132yes—
885C22⋊C4C2×#4118yes—
886C42—22no—
887C42—22no—
888C42—28no—
889C42—24no—
890C42—24no—
891C42—22no—
892C42—22no—
893C42—216no—
894C42—24no—
895C42—24no—
896C42—24no—
897C42—24no—
898C42—24no—
899C42—24no—
900C42—24no—
901C42—48no—
902C42—44no—
903C42—48no—
904C42—44no—
905C42—44no—
906C42—44no—
907C42—44no—
908C42—44no—
909C42—48no—
910C42C22×Q818yes—
911C42C2×#4118yes—
912C23—22no—
913C23—22no—
914C23—22no—
915C23—22no—
916C23—24no—
917C23—24no—
918C23C23×Q814yes—
919C23C23×Q812yes—
920C23C22×#4112yes—
921C23C2×H(5,𝔽2)12yes—
922C23C2611yescharacteristic
923Q8—216no—
924Q8—216no—
925Q8—28no—
926Q8—88no—
927Q8—816no—
928Q8—164no—
929D4—216no—
930D4—28no—
931C2×C4—28no—
932C2×C4—22no—
933C2×C4—24no—
934C2×C4—22no—
935C2×C4—22no—
936C2×C4—24no—
937C2×C4—24no—
938C2×C4—24no—
939C2×C4—22no—
940C2×C4—24no—
941C2×C4—24no—
942C2×C4—216no—
943C2×C4—216no—
944C2×C4—22no—
945C2×C4—24no—
946C2×C4—22no—
947C2×C4—22no—
948C2×C4—22no—
949C2×C4—24no—
950C2×C4—22no—
951C2×C4—22no—
952C2×C4—22no—
953C2×C4—22no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—24no—
958C2×C4—24no—
959C2×C4—24no—
960C2×C4—22no—
961C2×C4—28no—
962C2×C4—24no—
963C2×C4—24no—
964C2×C4—24no—
965C2×C4—22no—
966C2×C4—24no—
967C2×C4—22no—
968C2×C4—24no—
969C2×C4—22no—
970C2×C4—28no—
971C2×C4—22no—
972C2×C4—24no—
973C2×C4—24no—
974C2×C4—28no—
975C2×C4—22no—
976C2×C4—24no—
977C2×C4—24no—
978C2×C4—22no—
979C2×C4—22no—
980C2×C4—24no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—44no—
984C2×C4—88no—
985C2×C4—84no—
986C2×C4—84no—
987C2×C4—84no—
988C2×C4—84no—
989C2×C4—84no—
990C2×C4—164no—
991C2×C4—164no—
992C2×C4#554116yes—
993C2×C4C23×Q818yes—
994C2×C4C23×Q818yes—
995C2×C4C23×Q814yes—
996C2×C4C23×Q812yes—
997C2×C4C23×Q812yes—
998C2×C4C22×#4118yes—
999C2×C4C22×#4112yes—
1000C2×C4C22×#4112yes—
1001C2×C4C2×H(5,𝔽2)12yes—
1002C2×C4C2×H(5,𝔽2)12yes—
1003C2×C4#58514yes—
1004C22—24no—
1005C22—24no—
1006C22—22no—
1007C22—22no—
1008C22—28no—
1009C22—24no—
1010C22—44no—
1011C22—42no—
1012C22—42no—
1013C22C2×#55414yes—
1014C22C24×Q811yescharacteristic
1015C22C23×#4111yescharacteristic
1016C22C22×H(5,𝔽2)11yescharacteristic
1017C22C2×#58512yes—
1018C222−1+612yes—
1019C4—28no—
1020C4—28no—
1021C4—24no—
1022C4—24no—
1023C4—28no—
1024C4—44no—
1025C4—42no—
1026C4—42no—
1027C4—42no—
1028C4—42no—
1029C4—44no—
1030C4—44no—
1031C4—44no—
1032C4—42no—
1033C4—42no—
1034C4—42no—
1035C4—42no—
1036C4—42no—
1037C4—42no—
1038C4—44no—
1039C4—42no—
1040C4C2×#55414yes—
1041C4C2×#55414yes—
1042C2—24no—
1043C2—44no—
1044C2C22×#55411yescharacteristic
1045C2#6282411yescharacteristic
1046C2#6288711yescharacteristic
1047C2#6300412yes—
1048C2#6300912yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC22×#41C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59912C2semidirect
2. #59464C2semidirect
3. #59463C2semidirect
4. #59325C2semidirect
5. #59245C2semidirect
6. #45279C2semidirect
7. #45275C2semidirect
8. #45213C2semidirect
9. #45121C2semidirect
10. #44477C2semidirect
11. #35668C2semidirect
12. #35662C2semidirect
13. #35627C2semidirect
15. #35576C2semidirect
17. C2×#2568C2semidirect
18. #34815C2semidirect
23. #34249C2semidirect
24. #34215C2semidirect
191. #536Q8semidirect
537. C4⋊Q8C2×Q8semidirect
542. #124C2×Q8semidirect
548. C22⋊Q8C2×Q8semidirect

Maximal subgroups

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

subgroupindex
#599122
#594642
#594632
#593252
#592452
#452792
#452752
#452132
#451212
#444772
#356682
#356622
#356272
#356202
#355762
#355742
C2×#25682
#348152
#347452
#342762
#342682
#342662
#342492
#342152
#341842