Finite Group Databasebeta

← #7630962

Subgroups — #7630962

Order 512.

5778 conjugacy classes of subgroups.

The subgroup lattice has 1097 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36626C212yesmaximal, complemented
2#36621C214yesmaximal, complemented
3#36588C214yesmaximal, complemented
4#36553C214yesmaximal, complemented
5#36489C214yesmaximal, complemented
6#36488C214yesmaximal, complemented
7#36257C214yesmaximal, complemented
8#36256C214yesmaximal, complemented
9#36178C214yesmaximal, complemented
10#36118C214yesmaximal, complemented
11#35224C211yesmaximal, characteristic, complemented
12#35223C211yesmaximal, characteristic
13#35160C212yesmaximal, complemented
14#35159C211yesmaximal, characteristic, complemented
15#35158C211yesmaximal, characteristic, complemented
16#35035C214yesmaximal, complemented
17#35021C214yesmaximal, complemented
18#34997C214yesmaximal, complemented
19#34274C211yesmaximal, characteristic, complemented
20#34271C211yesmaximal, characteristic, complemented
21#34252C212yesmaximal, complemented
22#34200C212yesmaximal, complemented
23C22×C4×C4⋊C4C211yesmaximal, characteristic, complemented
24C2×#544C2211yescharacteristic
25C2×#537C2211yescharacteristic
26C2×#529C2214yes—
27C2×#525C2212yes—
28C2×#520C2212yes—
29C23×C4⋊C4C2211yescharacteristic
30C23×C4⋊C4C2211yescharacteristic
31C23×C42C2211yescharacteristic
32C23×C42C2212yes—
33#2855C2214yes—
34#2855C2212yes—
35#2855C2212yes—
36#2855C2212yes—
37#2855C2212yes—
38#2854C2214yes—
39#2854C2212yes—
40#2854C2212yes—
41#2854C2212yes—
42#2854C2212yes—
43#2853C2218yes—
44#2853C2214yes—
45#2853C2214yes—
46#2852C2218yes—
47#2852C2218yes—
48#2851C2214yes—
49#2851C2214yes—
50#2850C2214yes—
51#2850C2214yes—
52#2849C2214yes—
53#2849C2214yes—
54#2848C2214yes—
55#2847C2214yes—
56#2646C2214yes—
57#2643C2218yes—
58#2639C2214yes—
59#2627C2214yes—
60#2618C2214yes—
61#2595C2218yescomplemented
62#2594C2218yescomplemented
63#2593C2218yescomplemented
64#2588C2218yescomplemented
65#2587C2218yescomplemented
66#2585C2218yescomplemented
67#2574C2218yescomplemented
68#2573C2218yescomplemented
69#2529C2218yescomplemented
70#2528C2218yescomplemented
71#2525C2218yescomplemented
72#2524C2218yescomplemented
73#2514C2214yescomplemented
74#2513C2214yescomplemented
75#2512C2214yescomplemented
76#2511C2214yescomplemented
77#2510C2218yes—
78#2509C2214yescomplemented
79#2508C2214yescomplemented
80#2507C2214yescomplemented
81#2506C2214yescomplemented
82#2505C2218yes—
83#2497C2214yescomplemented
84#2496C2214yescomplemented
85#2495C2214yescomplemented
86#2494C2214yescomplemented
87#2493C2218yes—
88#2492C2214yescomplemented
89#2491C2214yescomplemented
90#2490C2214yescomplemented
91#2489C2214yescomplemented
92#2488C2218yes—
93#2475C2218yescomplemented
94#2474C2218yescomplemented
95#2469C2218yescomplemented
96#2468C2218yescomplemented
97#2450C2218yes—
98#2444C2218yes—
99#2442C2214yes—
100#2442C2214yes—
101#2440C2214yes—
102#2440C2214yes—
103#2425C2218yes—
104#2419C2218yes—
105#2417C2214yes—
106#2417C2214yes—
107#2416C2214yes—
108#2416C2214yes—
109#2370C2214yescomplemented
110#2370C2214yescomplemented
111#2369C2214yescomplemented
112#2365C2214yescomplemented
113#2363C2214yescomplemented
114#2362C2214yescomplemented
115#2361C2214yes—
116#2361C2214yes—
117#2361C2214yescomplemented
118#2360C2214yes—
119#2360C2214yes—
120#2360C2214yescomplemented
121#2357C2214yescomplemented
122#2356C2214yescomplemented
123#2355C2214yescomplemented
124#2354C2214yescomplemented
125#2352C2214yes—
126#2352C2214yes—
127D4×C4⋊C4C2214yes—
128D4×C4⋊C4C2214yes—
129#2347C2214yescomplemented
130#2346C2214yescomplemented
131#2345C2214yescomplemented
132#2344C2214yescomplemented
133#2329C2214yes—
134#2325C2214yes—
135#2322C2218yes—
136#2318C2218yes—
137#2317C2212yes—
138#2317C2212yes—
139#2316C2211yescharacteristic
140#2316C2211yescharacteristic
141#2311C2212yes—
142#2311C2212yes—
143C4×C22⋊Q8C2214yes—
144C4×C22⋊Q8C2214yes—
145C4×#123C2218yes—
146C4×#123C2214yes—
147C4×#123C2214yes—
148C4×#123C2214yes—
149C4×#123C2214yes—
150C4×#121C2214yes—
151C4×#121C2214yes—
152C4×#120C2218yes—
153#2297C2212yes—
154#2297C2212yes—
155#2296C2212yes—
156#2296C2212yes—
157#2290C2218yes—
158#2290C2218yes—
159#2283C2214yes—
160#2280C2212yes—
161#2274C2212yes—
162C2×C4×C4⋊C4C2214yes—
163C2×C4×C4⋊C4C2211yescharacteristic
164C2×C4×C4⋊C4C2211yescharacteristic
165C2×C4×C4⋊C4C2214yes—
166C2×C4×C4⋊C4C2214yes—
167C2×C4×C4⋊C4C2214yes—
168C2×C4×C4⋊C4C2211yescharacteristic
169C2×C4×C4⋊C4C2212yes—
170C2×C4×C4⋊C4C2212yes—
171C2×C4×C4⋊C4C2211yescharacteristic
172C22×#95C2212yes—
173C22×#41C2312yes—
174C24×C4C2311yescharacteristic
175C24×C4C2311yescharacteristic
176C24×C4C2312yes—
177C24×C4C2311yescharacteristic
178C24×C4C2312yes—
179#544—28no—
180#537—28no—
181C2×C4⋊Q8C2314yes—
182#529—416no—
183C2×#126C2318yes—
184C2×#125C2314yes—
185C2×#125C2314yes—
186C2×#124C2314yes—
187#525—216no—
188C2×#123C2314yes—
189C2×#123C2314yes—
190C2×#123C2314yes—
191C2×#123C2314yes—
192C2×#123C2314yes—
193C2×C22⋊Q8C2314yes—
194C2×C22⋊Q8C2312yes—
195C2×C22⋊Q8C2312yes—
196C2×C22⋊Q8C2314yes—
197C2×C22⋊Q8C2314yes—
198C2×C22⋊Q8C2314yes—
199C2×#121C2314yes—
200C2×#121C2312yes—
201C2×#121C2312yes—
202C2×#121C2314yes—
203C2×#121C2314yes—
204C2×#121C2314yes—
205C2×#120C2314yes—
206#520—216no—
207C2×C4×Q8C2314yes—
208C2×C4×Q8C2314yes—
209C2×C4×D4C2318yes—
210C2×C4×D4C2314yes—
211C2×C4×D4C2314yes—
212C2×C4×D4C2314yes—
213C2×C4×D4C2318yes—
214C2×C4×D4C2318yes—
215C2×C4×D4C2314yes—
216C2×#117C2312yes—
217C2×#117C2312yes—
218C2×#117C2312yes—
219C2×#117C2314yes—
220C2×#117C2318yes—
221C22×C4⋊C4—28no—
222C22×C4⋊C4—28no—
223C22×C4⋊C4C2311yescharacteristic
224C22×C4⋊C4C2311yescharacteristic
225C22×C4⋊C4C2312yes—
226C22×C4⋊C4C2314yes—
227C22×C4⋊C4C2314yes—
228C22×C4⋊C4C2314yes—
229C22×C4⋊C4C2312yes—
230C22×C4⋊C4C2314yes—
231C22×C4⋊C4C2314yes—
232C22×C4⋊C4C2311yescharacteristic
233C22×C4⋊C4C2311yescharacteristic
234C22×C42—28no—
235C22×C42—48no—
236C22×C42C2311yescharacteristic
237C22×C42C2311yescharacteristic
238C22×C42C2314yes—
239C22×C42C2312yes—
240C22×C42C2312yes—
241C22×C42C2312yes—
242C22×C42C2312yes—
243C22×C42C2311yescharacteristic
244C22×C42C2311yescharacteristic
245C22×C42C2312yes—
246C22×C42C2314yes—
247C22×C42C2312yes—
248C22×C42C2314yes—
249C22×C42C2314yes—
250C22×C42C2312yes—
251C22×C42C2312yes—
252#401C2318yes—
253#400C2318yes—
254#400C2318yes—
255#400C2318yes—
256#400C2318yes—
257#400C2318yes—
258#400C2318yes—
259#400C2318yes—
260#398C2318yes—
261#398C2318yes—
262#398C2318yes—
263#398C2318yes—
264#398C2318yes—
265#397C2318yes—
266#397C2318yes—
267#397C2318yes—
268#397C2318yes—
269#396C2318yes—
270#396C2318yes—
271#396C2318yes—
272#395C2318yes—
273#394C2318yes—
274#394C2318yes—
275#393C2318yes—
276#391C2314yes—
277#391C2314yes—
278#391C2314yes—
279#391C2318yes—
280#391C2314yes—
281#391C2312yes—
282#391C2312yes—
283#391C2312yes—
284#391C2312yes—
285#390C2314yes—
286#390C2314yes—
287#390C2314yes—
288#390C2314yes—
289#390C2312yes—
290#390C2312yes—
291#390C2312yes—
292#390C2312yes—
293#389C2314yes—
294#389C2314yes—
295#389C2314yes—
296#389C2314yes—
297#389C2314yes—
298#389C2314yes—
299#389C2314yes—
300#389C2314yes—
301#389C2314yes—
302#389C2318yes—
303#389C2318yes—
304#389C2318yes—
305#389C2314yes—
306#389C2314yes—
307#389C2314yes—
308#389C2312yes—
309#389C2312yes—
310#389C2312yes—
311#389C2312yes—
312#389C2312yes—
313#389C2312yes—
314#389C2312yes—
315#389C2312yes—
316#388C2314yes—
317#388C2318yes—
318#388C2318yes—
319#388C2318yes—
320#388C2314yes—
321#388C2318yes—
322#388C2318yes—
323#388C2318yes—
324#388C2318yes—
325#388C2314yes—
326#388C2318yes—
327#388C2314yes—
328#388C2318yes—
329#388C2318yes—
330#388C2318yes—
331#388C2318yes—
332#388C2318yes—
333#388C2314yes—
334#388C2314yes—
335#388C2314yes—
336#388C2314yes—
337#387C2314yes—
338#387C2318yes—
339#387C2318yes—
340#387C2318yes—
341#387C2318yes—
342#387C2314yes—
343#387C2318yes—
344#387C2318yes—
345#387C2318yes—
346#387C2318yes—
347#387C2318yes—
348#387C2314yes—
349#387C2318yes—
350#387C2314yes—
351#387C2318yes—
352#387C2318yes—
353#387C2318yes—
354#387C2318yes—
355#387C2318yes—
356#387C2314yes—
357#387C2314yes—
358#387C2314yes—
359#387C2314yes—
360#386C2318yes—
361#386C2318yes—
362#386C2314yes—
363#386C2314yes—
364#386C2318yes—
365#386C2318yes—
366#386C2318yes—
367#386C2314yes—
368#386C2314yes—
369#386C2314yes—
370#386C2314yes—
371#386C2314yes—
372#386C2314yes—
373#386C2318yes—
374#386C2318yes—
375#385C2318yes—
376#385C2318yes—
377#385C2318yes—
378#385C2314yes—
379#385C2318yes—
380#385C2318yes—
381#385C2314yes—
382#385C2318yes—
383#385C2318yes—
384#385C2314yes—
385#385C2314yes—
386#385C2314yes—
387#385C2314yes—
388#385C2314yes—
389#385C2314yes—
390#385C2318yes—
391#385C2318yes—
392#384C2314yes—
393#384C2314yes—
394#383C2318yes—
395#383C2318yes—
396#382C2314yes—
397#382C2314yes—
398#382C2318yes—
399#382C2314yes—
400#382C2314yes—
401#381C2318yes—
402#381C2314yes—
403#381C2314yes—
404#381C2314yes—
405#381C2314yes—
406#381C2314yes—
407#380C2314yes—
408#380C2314yes—
409#380C2314yes—
410#380C2314yes—
411#380C2314yes—
412#380C2314yes—
413#380C2318yes—
414#380C2314yes—
415#380C2314yes—
416#380C2314yes—
417#380C2314yes—
418#380C2312yes—
419#380C2312yes—
420#380C2312yes—
421#380C2312yes—
422#379C2314yes—
423C4×C4⋊C4C2318yes—
424C4×C4⋊C4C2318yes—
425C4×C4⋊C4C2318yes—
426C4×C4⋊C4C2318yes—
427C4×C4⋊C4C2314yes—
428C4×C4⋊C4C2314yes—
429C4×C4⋊C4C2314yes—
430C4×C4⋊C4C2314yes—
431C4×C4⋊C4C2314yes—
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⋊C4C2318yes—
442C4×C4⋊C4C2318yes—
443C4×C4⋊C4C2314yes—
444C4×C4⋊C4C2314yes—
445C4×C4⋊C4C2314yes—
446C4×C4⋊C4C2314yes—
447C4×C22⋊C4C2318yes—
448C4×C22⋊C4C2318yes—
449C4×C22⋊C4C2318yes—
450C4×C22⋊C4C2314yes—
451C4×C22⋊C4C2314yes—
452C4×C22⋊C4C2318yes—
453C4×C22⋊C4C2318yes—
454C4×C22⋊C4C2314yes—
455C4×C22⋊C4C2314yes—
456C4×C22⋊C4C2314yes—
457C4×C22⋊C4C2314yes—
458#376C2318yes—
459C2×#95C2312yes—
460C2×#95C2312yes—
461C2×#95C2312yes—
462C2×#95C2312yes—
463C2×#95C2318yes—
464C2×#95C2318yes—
465C25C2411yescharacteristic
466C2×#41—28no—
467C2×#41—28no—
468C2×#41—28no—
469C22×Q8C2412yes—
470C22×Q8C2414yes—
471C22×D4C2414yes—
472C22×D4C2414yes—
473C22×D4C2414yes—
474C22×D4C2412yes—
475C22×D4C2414yes—
476C23×C4—24no—
477C23×C4—24no—
478C23×C4—24no—
479C23×C4—24no—
480C23×C4—24no—
481C23×C4—24no—
482C23×C4—28no—
483C23×C4—28no—
484C23×C4—44no—
485C23×C4—44no—
486C23×C4—42no—
487C23×C4—42no—
488C23×C4—44no—
489C23×C4—44no—
490C23×C4#4118yes—
491C23×C4C2414yes—
492C23×C4C2412yes—
493C23×C4C2411yescharacteristic
494C23×C4C2411yescharacteristic
495C23×C4C2411yescharacteristic
496C23×C4C2411yescharacteristic
497C23×C4C2414yes—
498C23×C4C2414yes—
499C23×C4C2414yes—
500C23×C4C2414yes—
501C23×C4C2412yes—
502C23×C4C2412yes—
503C23×C4C2411yescharacteristic
504C23×C4C2411yescharacteristic
505C23×C4C2411yescharacteristic
506C23×C4C2412yes—
507C23×C4C2412yes—
508C23×C4C2418yes—
509C23×C4C2411yescharacteristic
510C23×C4C2411yescharacteristic
511C23×C4C2412yes—
512C23×C4C2412yes—
513C23×C4C2412yes—
514C23×C4C2411yescharacteristic
515C4⋊Q8—216no—
516#126—416no—
517#125—216no—
518#125—48no—
519#124—48no—
520#123—216no—
521#123—216no—
522#123—216no—
523#123—48no—
524#123—48no—
525C22⋊Q8—28no—
526C22⋊Q8—28no—
527C22⋊Q8—216no—
528C22⋊Q8—216no—
529C22⋊Q8—48no—
530C22⋊Q8—48no—
531#121—28no—
532#121—28no—
533#121—216no—
534#121—216no—
535#121—48no—
536#121—48no—
537#120—216no—
538C4×Q8—216no—
539C4×Q8—48no—
540C4×D4—232no—
541C4×D4—216no—
542C4×D4—216no—
543C4×D4—216no—
544C4×D4—48no—
545C4×D4—416no—
546C4×D4—416no—
547#117—28no—
548#117—28no—
549#117—28no—
550#117—216no—
551#117—416no—
552C2×C4⋊C4—28no—
553C2×C4⋊C4—28no—
554C2×C4⋊C4—24no—
555C2×C4⋊C4—24no—
556C2×C4⋊C4—216no—
557C2×C4⋊C4—216no—
558C2×C4⋊C4—216no—
559C2×C4⋊C4—216no—
560C2×C4⋊C4—216no—
561C2×C4⋊C4#4118yes—
562C2×C4⋊C4#4118yes—
563C2×C4⋊C4C2414yes—
564C2×C4⋊C4C2414yes—
565C2×C4⋊C4C2418yes—
566C2×C4⋊C4C2418yes—
567C2×C4⋊C4C2412yes—
568C2×C4⋊C4C2418yes—
569C2×C4⋊C4C2412yes—
570C2×C4⋊C4C2414yes—
571C2×C4⋊C4C2412yes—
572C2×C4⋊C4C2412yes—
573C2×C4⋊C4C2412yes—
574C2×C4⋊C4C2412yes—
575C2×C4⋊C4C2414yes—
576C2×C4⋊C4C2414yes—
577C2×C4⋊C4C2414yes—
578C2×C4⋊C4C2414yes—
579C2×C4⋊C4C2414yes—
580C2×C4⋊C4C2418yes—
581C2×C4⋊C4C2414yes—
582C2×C4⋊C4C2414yes—
583C2×C4⋊C4C2418yes—
584C2×C4⋊C4C2414yes—
585C2×C4⋊C4C2418yes—
586C2×C4⋊C4C2418yes—
587C2×C4⋊C4C2414yes—
588C2×C4⋊C4C2414yes—
589C2×C4⋊C4C2414yes—
590C2×C4⋊C4C2418yes—
591C2×C4⋊C4C2414yes—
592C2×C4⋊C4C2414yes—
593C2×C4⋊C4C2414yes—
594C2×C4⋊C4C2414yes—
595C2×C4⋊C4C2414yes—
596C2×C4⋊C4C2414yes—
597C2×C22⋊C4C2414yes—
598C2×C22⋊C4C2414yes—
599C2×C22⋊C4C2418yes—
600C2×C22⋊C4C2414yes—
601C2×C22⋊C4C2414yes—
602C2×C22⋊C4C2414yes—
603C2×C22⋊C4C2414yes—
604C2×C22⋊C4C2414yes—
605C2×C22⋊C4C2414yes—
606C2×C22⋊C4C2414yes—
607C2×C22⋊C4C2414yes—
608C2×C22⋊C4C2414yes—
609C2×C22⋊C4C2418yes—
610C2×C22⋊C4C2414yes—
611C2×C22⋊C4C2414yes—
612C2×C22⋊C4C2414yes—
613C2×C22⋊C4C2414yes—
614C2×C22⋊C4C2418yes—
615C2×C22⋊C4C2418yes—
616C2×C22⋊C4C2418yes—
617C2×C22⋊C4C2418yes—
618C2×C22⋊C4C2414yes—
619C2×C22⋊C4C2414yes—
620C2×C22⋊C4C2414yes—
621C2×C22⋊C4C2414yes—
622C2×C42—28no—
623C2×C42—28no—
624C2×C42—28no—
625C2×C42—28no—
626C2×C42—24no—
627C2×C42—24no—
628C2×C42—24no—
629C2×C42—24no—
630C2×C42—216no—
631C2×C42—44no—
632C2×C42—48no—
633C2×C42—44no—
634C2×C42—48no—
635C2×C42—44no—
636C2×C42—44no—
637C2×C42—48no—
638C2×C42C2414yes—
639C2×C42C2414yes—
640C2×C42C2418yes—
641C2×C42C2414yes—
642C2×C42C2414yes—
643C2×C42C2414yes—
644C2×C42C2414yes—
645C2×C42C2414yes—
646C2×C42C2412yes—
647C2×C42C2412yes—
648C2×C42C2412yes—
649C2×C42C2412yes—
650C2×C42C2412yes—
651C2×C42C2412yes—
652C2×C42C2412yes—
653C2×C42C2412yes—
654C2×C42C2418yes—
655C2×C42C2418yes—
656C2×C42C2414yes—
657C2×C42C2414yes—
658C2×C42C2414yes—
659C2×C42C2414yes—
660#95C2418yes—
661#95C2418yes—
662#95C2418yes—
663#95C2418yes—
664#95C2414yes—
665#95C2414yes—
666#95C2418yes—
667#95C2418yes—
668#95C2414yes—
669#95C2414yes—
670#95C2418yes—
671#95C2414yes—
672#95C2418yes—
673#95C2414yes—
674#95C2418yes—
675#95C2414yes—
676#95C2414yes—
677#95C2414yes—
678#95C2414yes—
679#95C2418yes—
680#95C2418yes—
681#95C2418yes—
682#95C2414yes—
683#95C2414yes—
684#95C2414yes—
685#95C2414yes—
686#95C2418yes—
687#95C2418yes—
688#95C2414yes—
689#95C2414yes—
690#95C2418yes—
691#95C2418yes—
692#95C2414yes—
693#95C2414yes—
694#95C2414yes—
695#95C2414yes—
696C24—22no—
697C24—22no—
698C24—22no—
699C24—22no—
700C24—22no—
701C24—22no—
702C24C2×#4114yes—
703C24C2514yes—
704C24C2511yescharacteristic
705C24C2511yescharacteristic
706C24C2511yescharacteristic
707#41—432no—
708C2×Q8—24no—
709C2×Q8—24no—
710C2×Q8—24no—
711C2×Q8—28no—
712C2×Q8—44no—
713C2×Q8—44no—
714C2×D4—28no—
715C2×D4—28no—
716C2×D4—28no—
717C2×D4—28no—
718C2×D4—28no—
719C2×D4—28no—
720C2×D4—28no—
721C2×D4—28no—
722C2×D4—28no—
723C2×D4—24no—
724C2×D4—24no—
725C2×D4—24no—
726C2×D4—28no—
727C2×D4—44no—
728C2×D4—44no—
729C22×C4—232no—
730C22×C4—22no—
731C22×C4—22no—
732C22×C4—22no—
733C22×C4—22no—
734C22×C4—22no—
735C22×C4—22no—
736C22×C4—22no—
737C22×C4—22no—
738C22×C4—22no—
739C22×C4—22no—
740C22×C4—232no—
741C22×C4—24no—
742C22×C4—24no—
743C22×C4—24no—
744C22×C4—24no—
745C22×C4—22no—
746C22×C4—22no—
747C22×C4—22no—
748C22×C4—22no—
749C22×C4—22no—
750C22×C4—22no—
751C22×C4—22no—
752C22×C4—22no—
753C22×C4—22no—
754C22×C4—22no—
755C22×C4—24no—
756C22×C4—24no—
757C22×C4—24no—
758C22×C4—24no—
759C22×C4—28no—
760C22×C4—28no—
761C22×C4—28no—
762C22×C4—28no—
763C22×C4—24no—
764C22×C4—24no—
765C22×C4—28no—
766C22×C4—28no—
767C22×C4—28no—
768C22×C4—28no—
769C22×C4—28no—
770C22×C4—28no—
771C22×C4—28no—
772C22×C4—216no—
773C22×C4—42no—
774C22×C4—44no—
775C22×C4—42no—
776C22×C4—44no—
777C22×C4—42no—
778C22×C4—42no—
779C22×C4—42no—
780C22×C4—44no—
781C22×C4—42no—
782C22×C4—44no—
783C22×C4—42no—
784C22×C4—42no—
785C22×C4—41no—
786C22×C4—41no—
787C22×C4—41no—
788C22×C4—41no—
789C22×C4—42no—
790C22×C4—42no—
791C22×C4—48no—
792C22×C4—48no—
793C22×C4—432no—
794C22×C4—432no—
795C22×C4—416no—
796C22×C4C2×#4118yes—
797C22×C4C2×#4118yes—
798C22×C4C2×#4114yes—
799C22×C4C2×#4118yes—
800C22×C4C2×#4118yes—
801C22×C4C2×#4114yes—
802C22×C4C2×#4114yes—
803C22×C4C2×#4114yes—
804C22×C4H(5,𝔽2)14yes—
805C22×C42−1+414yes—
806C22×C4C2512yes—
807C22×C4C2512yes—
808C22×C4C2514yes—
809C22×C4C2514yes—
810C22×C4C2514yes—
811C22×C4C2514yes—
812C22×C4C2514yes—
813C22×C4C2514yes—
814C22×C4C2514yes—
815C22×C4C2514yes—
816C22×C4C2514yes—
817C22×C4C2514yes—
818C22×C4C2512yes—
819C22×C4C2514yes—
820C22×C4C2511yescharacteristic
821C22×C4C2511yescharacteristic
822C22×C4C2511yescharacteristic
823C22×C4C2511yescharacteristic
824C22×C4C2512yes—
825C4⋊C4—216no—
826C4⋊C4—216no—
827C4⋊C4—28no—
828C4⋊C4—28no—
829C4⋊C4—24no—
830C4⋊C4—216no—
831C4⋊C4—24no—
832C4⋊C4—24no—
833C4⋊C4—24no—
834C4⋊C4—24no—
835C4⋊C4—24no—
836C4⋊C4—28no—
837C4⋊C4—28no—
838C4⋊C4—28no—
839C4⋊C4—28no—
840C4⋊C4—216no—
841C4⋊C4—28no—
842C4⋊C4—28no—
843C4⋊C4—28no—
844C4⋊C4—28no—
845C4⋊C4—48no—
846C4⋊C4—48no—
847C4⋊C4—44no—
848C4⋊C4—48no—
849C4⋊C4—44no—
850C4⋊C4—44no—
851C4⋊C4—44no—
852C4⋊C4—48no—
853C4⋊C4—44no—
854C4⋊C4—44no—
855C4⋊C4—44no—
856C4⋊C4—44no—
857C4⋊C4C2×#41116yes—
858C4⋊C4C2×#41116yes—
859C22⋊C4—28no—
860C22⋊C4—28no—
861C22⋊C4—28no—
862C22⋊C4—28no—
863C22⋊C4—28no—
864C22⋊C4—28no—
865C22⋊C4—28no—
866C22⋊C4—28no—
867C22⋊C4—28no—
868C22⋊C4—216no—
869C22⋊C4—28no—
870C22⋊C4—28no—
871C22⋊C4—216no—
872C22⋊C4—28no—
873C22⋊C4—28no—
874C22⋊C4—28no—
875C22⋊C4—28no—
876C22⋊C4—48no—
877C22⋊C4—48no—
878C22⋊C4—48no—
879C22⋊C4—48no—
880C22⋊C4—44no—
881C22⋊C4—44no—
882C22⋊C4—44no—
883C22⋊C4—44no—
884C42—24no—
885C42—24no—
886C42—24no—
887C42—24no—
888C42—24no—
889C42—24no—
890C42—24no—
891C42—24no—
892C42—28no—
893C42—216no—
894C42—28no—
895C42—28no—
896C42—28no—
897C42—28no—
898C42—28no—
899C42—28no—
900C42—44no—
901C42—44no—
902C42—44no—
903C42—44no—
904C42—48no—
905C42—48no—
906C23—28no—
907C23—28no—
908C23—28no—
909C23—28no—
910C23—21no—
911C23—21no—
912C23—21no—
913C23—21no—
914C23—21no—
915C23—21no—
916C23—21no—
917C23—21no—
918C23—21no—
919C23—21no—
920C23—21no—
921C23—21no—
922C23—28no—
923C23—28no—
924C23—28no—
925C23—24no—
926C23—24no—
927C23—24no—
928C23—24no—
929C23—24no—
930C23—24no—
931C23—24no—
932C23C22×#4112yes—
933C23C22×#4112yes—
934C23C22×#4112yes—
935C23C22×#4112yes—
936C23C22×#4112yes—
937C23C2×H(5,𝔽2)12yes—
938C23C2×2−1+412yes—
939C23#58512yes—
940C23#58512yes—
941C23C2611yescharacteristic
942Q8—48no—
943Q8—88no—
944D4—416no—
945D4—416no—
946D4—416no—
947D4—48no—
948D4—88no—
949C2×C4—28no—
950C2×C4—28no—
951C2×C4—28no—
952C2×C4—28no—
953C2×C4—21no—
954C2×C4—21no—
955C2×C4—21no—
956C2×C4—21no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—24no—
960C2×C4—24no—
961C2×C4—21no—
962C2×C4—21no—
963C2×C4—21no—
964C2×C4—21no—
965C2×C4—24no—
966C2×C4—24no—
967C2×C4—28no—
968C2×C4—28no—
969C2×C4—28no—
970C2×C4—216no—
971C2×C4—216no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—24no—
975C2×C4—24no—
976C2×C4—24no—
977C2×C4—24no—
978C2×C4—24no—
979C2×C4—24no—
980C2×C4—24no—
981C2×C4—24no—
982C2×C4—24no—
983C2×C4—24no—
984C2×C4—24no—
985C2×C4—24no—
986C2×C4—24no—
987C2×C4—24no—
988C2×C4—24no—
989C2×C4—24no—
990C2×C4—24no—
991C2×C4—24no—
992C2×C4—24no—
993C2×C4—24no—
994C2×C4—24no—
995C2×C4—24no—
996C2×C4—24no—
997C2×C4—24no—
998C2×C4—24no—
999C2×C4—24no—
1000C2×C4—24no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—48no—
1006C2×C4—48no—
1007C2×C4—416no—
1008C2×C4—416no—
1009C2×C4—416no—
1010C2×C4—416no—
1011C2×C4—48no—
1012C2×C4—48no—
1013C2×C4—44no—
1014C2×C4—44no—
1015C2×C4—48no—
1016C2×C4—48no—
1017C2×C4—416no—
1018C2×C4—816no—
1019C2×C4#529116yescomplemented
1020C2×C4C22×#4114yes—
1021C2×C4C22×#4118yes—
1022C2×C4C22×#4118yes—
1023C2×C4C22×#4114yes—
1024C2×C4C22×#4114yes—
1025C2×C4C22×#4114yes—
1026C2×C4C2×H(5,𝔽2)12yes—
1027C2×C4C2×H(5,𝔽2)12yes—
1028C2×C4C2×2−1+412yes—
1029C2×C4C2×2−1+412yes—
1030C22—232no—
1031C22—22no—
1032C22—22no—
1033C22—22no—
1034C22—22no—
1035C22—22no—
1036C22—22no—
1037C22—22no—
1038C22—22no—
1039C22—22no—
1040C22—22no—
1041C22—22no—
1042C22—22no—
1043C22—22no—
1044C22—22no—
1045C22—22no—
1046C22—22no—
1047C22—22no—
1048C22—22no—
1049C22—44no—
1050C22—44no—
1051C22—44no—
1052C22—44no—
1053C22—44no—
1054C22—44no—
1055C22—44no—
1056C22C2×#52914yes—
1057C22#349214yes—
1058C22#349314yes—
1059C22C23×#4111yescharacteristic
1060C22C23×#4111yescharacteristic
1061C22C23×#4111yescharacteristic
1062C22C22×H(5,𝔽2)11yescharacteristic
1063C22C22×2−1+411yescharacteristic
1064C22C2×#58511yescharacteristic
1065C22C2×#58511yescharacteristic
1066C4—22no—
1067C4—22no—
1068C4—22no—
1069C4—22no—
1070C4—28no—
1071C4—28no—
1072C4—24no—
1073C4—44no—
1074C4—44no—
1075C4—44no—
1076C4—44no—
1077C4—44no—
1078C4—42no—
1079C4—42no—
1080C4—44no—
1081C4—44no—
1082C4—44no—
1083C4—44no—
1084C4C2×#52918yes—
1085C2—24no—
1086C2—24no—
1087C2—24no—
1088C2—84no—
1089C2C22×#52911yescharacteristic
1090C2C2×#349211yescharacteristic
1091C2#6277311yescharacteristic
1092C2#6277311yescharacteristic
1093C2C2×#349311yescharacteristic
1094C2#6278811yescharacteristic
1095C2#6278811yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35223C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #36626C2semidirect
2. #36621C2semidirect
3. #36588C2semidirect
4. #36553C2semidirect
5. #36489C2semidirect
6. #36488C2semidirect
7. #36257C2semidirect
8. #36256C2semidirect
9. #36178C2semidirect
10. #36118C2semidirect
11. #35224C2semidirect
13. #35160C2semidirect
14. #35159C2semidirect
15. #35158C2semidirect
16. #35035C2semidirect
17. #35021C2semidirect
18. #34997C2semidirect
19. #34274C2semidirect
20. #34271C2semidirect
21. #34252C2semidirect
22. #34200C2semidirect
23. C22×C4×C4⋊C4C2semidirect
61. #2595C22semidirect
62. #2594C22semidirect
63. #2593C22semidirect
64. #2588C22semidirect
65. #2587C22semidirect
66. #2585C22semidirect
67. #2574C22semidirect
68. #2573C22semidirect
69. #2529C22semidirect
70. #2528C22semidirect
71. #2525C22semidirect
72. #2524C22semidirect
73. #2514C22semidirect
74. #2513C22semidirect
75. #2512C22semidirect
76. #2511C22semidirect
78. #2509C22semidirect
79. #2508C22semidirect
80. #2507C22semidirect
81. #2506C22semidirect
83. #2497C22semidirect
84. #2496C22semidirect
85. #2495C22semidirect
86. #2494C22semidirect
88. #2492C22semidirect
89. #2491C22semidirect
90. #2490C22semidirect
91. #2489C22semidirect
93. #2475C22semidirect
94. #2474C22semidirect
95. #2469C22semidirect
96. #2468C22semidirect
109. #2370C22semidirect
110. #2370C22semidirect
111. #2369C22semidirect
112. #2365C22semidirect
113. #2363C22semidirect
114. #2362C22semidirect
117. #2361C22semidirect
120. #2360C22semidirect
121. #2357C22semidirect
122. #2356C22semidirect
123. #2355C22semidirect
124. #2354C22semidirect
129. #2347C22semidirect
130. #2346C22semidirect
131. #2345C22semidirect
132. #2344C22semidirect
1019. C2×C4#529semidirect

Maximal subgroups

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

subgroupindex
#366262
#366212
#365882
#365532
#364892
#364882
#362572
#362562
#361782
#361182
#352242
#352232
#351602
#351592
#351582
#350352
#350212
#349972
#342742
#342712
#342522
#342002
C22×C4×C4⋊C42