Finite Group Databasebeta

← #7987156

Subgroups — #7987156

Order 512.

4563 conjugacy classes of subgroups.

The subgroup lattice has 1090 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59924C211yesmaximal, characteristic, complemented
2#59464C212yesmaximal, complemented
3#59234C212yesmaximal, complemented
4#59079C212yesmaximal, complemented
5#51679C218yesmaximal, complemented
6#45702C214yesmaximal, complemented
7#45232C214yesmaximal, complemented
8#45227C214yesmaximal, complemented
9#42775C214yesmaximal, complemented
10#42770C214yesmaximal, complemented
11#39350C212yesmaximal, complemented
12#39203C212yesmaximal, complemented
13#39159C212yesmaximal, complemented
14#39157C212yesmaximal, complemented
15#38931C214yesmaximal, complemented
16#36598C211yesmaximal, characteristic, complemented
17#36188C211yesmaximal, characteristic, complemented
18#36176C212yesmaximal, complemented
19#36175C212yesmaximal, complemented
20#36134C211yesmaximal, characteristic, complemented
21#35239C212yesmaximal, complemented
22#35170C212yesmaximal
23#34943C211yesmaximal, characteristic
24#34941C211yesmaximal, characteristic, complemented
25#34394C212yesmaximal, complemented
26C4×#554C211yesmaximal, characteristic, complemented
27C2×#556C2212yes—
28C2×#554C2211yescharacteristic
29C2×#542C2214yes—
30C2×#533C2212yes—
31#2868C2211yescharacteristic
32#2862C2212yes—
33#2857C2214yes—
34#2857C2212yes—
35#2857C2212yes—
36#2854C2214yes—
37#2851C2214yes—
38#2838C2218yes—
39#2811C2214yes—
40#2798C2218yes—
41#2793C2218yes—
42#2775C2218yes—
43#2774C2218yes—
44#2762C2218yes—
45#2758C2218yes—
46#2758C2218yes—
47#2754C2218yes—
48#2745C2218yes—
49#2728C2218yes—
50#2718C2218yes—
51#2717C2218yes—
52#2715C2218yes—
53#2698C2218yes—
54#2698C2218yes—
55#2689C2218yes—
56#2666C2218yes—
57#2663C2218yes—
58#2647C2218yes—
59#2645C2214yes—
60#2625C2214yes—
61#2588C2218yes—
62#2582C2212yes—
63#2574C2214yes—
64#2572C2214yes—
65#2571C2214yes—
66#2571C2211yescharacteristic
67#2571C2212yes—
68#2570C2214yes—
69#2570C2214yes—
70#2568C2212yes—
71#2568C2214yes—
72#2568C2212yes—
73#2567C2214yes—
74#2567C2214yes—
75#2567C2214yes—
76#2567C2211yescharacteristic
77#2563C2211yescharacteristic
78#2563C2211yescharacteristic
79#2563C2211yescharacteristic
80#2552C2212yes—
81#2552C2211yescharacteristic
82#2551C2212yes—
83#2551C2212yes—
84#2551C2212yes—
85#2550C2214yes—
86#2547C2212yes—
87#2547C2212yes—
88#2547C2214yes—
89#2542C2212yes—
90#2538C2212yes—
91#2538C2211yescharacteristic
92#2537C2211yescharacteristic
93#2532C2218yes—
94#2527C2218yes—
95#2523C2218yes—
96#2521C2218yes—
97#2514C2214yes—
98#2513C2214yes—
99#2513C2214yes—
100#2511C2214yes—
101#2509C2214yes—
102#2508C2212yes—
103#2508C2214yes—
104#2499C2214yes—
105#2497C2212yes—
106#2496C2214yes—
107#2496C2214yes—
108#2496C2218yes—
109#2496C2214yes—
110#2496C2214yes—
111#2495C2212yes—
112#2495C2212yes—
113#2495C2214yes—
114#2495C2214yes—
115#2494C2214yes—
116#2492C2214yes—
117#2492C2214yes—
118#2491C2214yes—
119#2489C2214yes—
120#2489C2214yes—
121#2488C2218yes—
122#2486C2214yes—
123#2474C2218yes—
124#2454C2212yes—
125#2453C2214yes—
126#2451C2214yes—
127#2447C2214yes—
128#2446C2214yes—
129#2442C2214yes—
130#2441C2214yes—
131#2440C2214yes—
132#2438C2218yes—
133#2429C2214yes—
134#2427C2214yes—
135#2423C2212yes—
136#2423C2214yes—
137#2421C2218yes—
138#2421C2214yes—
139#2420C2212yes—
140#2420C2212yes—
141#2415C2214yes—
142#2398C2214yes—
143#2396C2214yes—
144#2378C2218yes—
145#2370C2212yes—
146#2369C2214yes—
147#2369C2212yes—
148#2369C2212yes—
149#2369C2212yes—
150#2369C2211yescharacteristic
151#2368C2214yes—
152#2367C2214yes—
153#2365C2212yes—
154#2365C2212yes—
155#2365C2212yes—
156#2365C2212yes—
157#2360C2212yes—
158#2356C2214yes—
159#2355C2212yes—
160#2355C2211yescharacteristic
161#2355C2212yes—
162#2354C2212yes—
163#2352C2214yes—
164#2351C2214yes—
165Q8×C4⋊C4C2212yes—
166#2349C2212yes—
167D4×C4⋊C4C2211yescharacteristic
168#2347C2214yes—
169#2346C2214yes—
170#2345C2212yes—
171#2331C2214yes—
172#2330C2214yes—
173#2330C2214yes—
174#2323C2214yes—
175#2323C2214yes—
176#2320C2218yes—
177C4×C4⋊Q8C2211yescharacteristic
178C4×C4⋊Q8C2211yescharacteristic
179C4×C4⋊Q8C2211yescharacteristic
180C4×C4⋊Q8C2212yes—
181C4×#125C2212yes—
182C4×#125C2212yes—
183C4×C22⋊Q8C2214yes—
184C4×C22⋊Q8C2212yes—
185C4×C22⋊Q8C2212yes—
186C4×#121C2212yes—
187C4×#121C2212yes—
188#2293C2212yes—
189#2285C2212yes—
190#2285C2212yes—
191#2283C2214yes—
192#2283C2212yes—
193#2283C2212yes—
194C42×Q8C2211yescharacteristic
195C42×D4C2211yescharacteristic
196C42×D4C2212yes—
197C42×D4C2211yescharacteristic
198C2×C4×C4⋊C4C2212yes—
199#556—48no—
200#554—28no—
201#542—416no—
202#533—216no—
203C2×C4⋊Q8C2311yescharacteristic
204C2×C4⋊Q8C2311yescharacteristic
205C2×C4⋊Q8C2312yes—
206C2×C4⋊Q8C2312yes—
207C2×C4⋊Q8C2314yes—
208C2×C4⋊Q8C2314yes—
209C2×C4⋊Q8C2314yes—
210C2×C4⋊Q8C2312yes—
211C2×C4⋊Q8C2311yescharacteristic
212C2×#126C2318yes—
213C2×#126C2318yes—
214C2×#125C2312yes—
215C2×#125C2314yes—
216C2×#125C2312yes—
217C2×#124C2314yes—
218C2×#124C2318yes—
219C2×#123C2318yes—
220C2×C22⋊Q8C2314yes—
221C2×C22⋊Q8C2312yes—
222C2×C22⋊Q8C2314yes—
223C2×C22⋊Q8C2314yes—
224C2×C22⋊Q8C2314yes—
225C2×C22⋊Q8C2318yes—
226C2×C22⋊Q8C2314yes—
227C2×C22⋊Q8C2312yes—
228C2×#121C2312yes—
229C2×#121C2312yes—
230C2×C4×Q8C2311yescharacteristic
231C2×C4×Q8C2311yescharacteristic
232C2×C4×Q8C2314yes—
233C2×C4×Q8C2314yes—
234C2×C4×Q8C2312yes—
235C2×C4×Q8C2312yes—
236C2×C4×Q8C2312yes—
237C2×C4×Q8C2314yes—
238C2×C4×Q8C2314yes—
239C2×C4×Q8C2311yescharacteristic
240C2×C4×D4C2311yescharacteristic
241C2×C4×D4C2311yescharacteristic
242C2×C4×D4C2311yescharacteristic
243C2×C4×D4C2312yes—
244C2×C4×D4C2311yescharacteristic
245C2×C4×D4C2311yescharacteristic
246C2×C4×D4C2312yes—
247C2×C4×D4C2314yes—
248C2×C4×D4C2311yescharacteristic
249C2×#117C2314yes—
250C2×#117C2314yes—
251C2×#117C2314yes—
252C22×C4⋊C4C2312yes—
253C22×C4⋊C4C2312yes—
254C22×C42C2312yes—
255C22×C42C2312yes—
256C22×C42C2314yes—
257#401C2318yes—
258#400C2318yes—
259#400C2318yes—
260#400C2318yes—
261#400C2318yes—
262#400C2318yes—
263#400C2314yes—
264#400C2318yes—
265#400C2318yes—
266#400C2318yes—
267#400C2318yes—
268#400C2318yes—
269#400C2314yes—
270#400C2318yes—
271#400C2314yes—
272#399C2314yes—
273#399C2318yes—
274#398C2318yes—
275#398C2318yes—
276#398C2314yes—
277#398C2318yes—
278#398C2314yes—
279#398C2318yes—
280#398C2318yes—
281#397C2314yes—
282#397C2318yes—
283#397C2318yes—
284#397C2318yes—
285#397C2314yes—
286#397C2318yes—
287#397C2318yes—
288#397C2318yes—
289#397C2318yes—
290#397C2318yes—
291#397C2318yes—
292#396C2314yes—
293#396C2318yes—
294#396C2314yes—
295#395C2318yes—
296#395C2314yes—
297#395C2318yes—
298#395C2318yes—
299#395C2318yes—
300#395C2318yes—
301#394C2314yes—
302#394C2314yes—
303#394C2318yes—
304#393C2314yes—
305#393C2314yes—
306#393C2314yes—
307#393C2318yes—
308#391C2314yes—
309#391C2312yes—
310#391C2312yes—
311#391C2312yes—
312#391C2318yes—
313#391C2318yes—
314#391C2318yes—
315#391C2312yes—
316#391C2314yes—
317#391C2314yes—
318#391C2318yes—
319#391C2314yes—
320#391C2314yes—
321#391C2314yes—
322#391C2314yes—
323#391C2318yes—
324#391C2314yes—
325#391C2314yes—
326#391C2314yes—
327#391C2318yes—
328#391C2318yes—
329#391C2314yes—
330#391C2312yes—
331#390C2312yes—
332#390C2312yes—
333#390C2312yes—
334#390C2314yes—
335#390C2312yes—
336#389C2312yes—
337#389C2312yes—
338#389C2312yes—
339#389C2312yes—
340#389C2312yes—
341#389C2312yes—
342#389C2312yes—
343#389C2312yes—
344#389C2312yes—
345#389C2312yes—
346#389C2314yes—
347#389C2314yes—
348#389C2314yes—
349#389C2312yes—
350#389C2314yes—
351#389C2314yes—
352#389C2314yes—
353#389C2314yes—
354#389C2314yes—
355#389C2312yes—
356#389C2318yes—
357#389C2314yes—
358#389C2314yes—
359#389C2312yes—
360#389C2312yes—
361#389C2318yes—
362#389C2314yes—
363#389C2312yes—
364#389C2318yes—
365#389C2314yes—
366#389C2318yes—
367#389C2312yes—
368#389C2314yes—
369#389C2314yes—
370#389C2314yes—
371#389C2318yes—
372#389C2318yes—
373#388C2314yes—
374#388C2314yes—
375#388C2314yes—
376#388C2314yes—
377#388C2318yes—
378#388C2318yes—
379#388C2318yes—
380#388C2318yes—
381#388C2318yes—
382#388C2318yes—
383#388C2318yes—
384#388C2318yes—
385#388C2318yes—
386#388C2318yes—
387#387C2314yes—
388#387C2314yes—
389#387C2314yes—
390#387C2314yes—
391#387C2318yes—
392#387C2318yes—
393#387C2318yes—
394#387C2318yes—
395#387C2314yes—
396#387C2318yes—
397#387C2318yes—
398#387C2318yes—
399#387C2318yes—
400#387C2318yes—
401#387C2318yes—
402#387C2318yes—
403#387C2318yes—
404#387C2318yes—
405#387C2314yes—
406#387C2314yes—
407#387C2318yes—
408#387C2314yes—
409#386C2314yes—
410#386C2314yes—
411#386C2318yes—
412#385C2314yes—
413#385C2318yes—
414#385C2318yes—
415#385C2314yes—
416#385C2314yes—
417#385C2314yes—
418#384C2311yescharacteristic
419#384C2311yescharacteristic
420#384C2311yescharacteristic
421#384C2318yes—
422#384C2312yes—
423#384C2312yes—
424#384C2314yes—
425#384C2312yes—
426#384C2312yes—
427#384C2312yes—
428#384C2312yes—
429#383C2314yes—
430#383C2314yes—
431#383C2318yes—
432#383C2318yes—
433#382C2312yes—
434#382C2312yes—
435#382C2312yes—
436#382C2312yes—
437#382C2312yes—
438#382C2314yes—
439#382C2314yes—
440#382C2314yes—
441#382C2314yes—
442#382C2318yes—
443#382C2312yes—
444#382C2314yes—
445#382C2318yes—
446#381C2314yes—
447#381C2314yes—
448#381C2318yes—
449#380C2312yes—
450#380C2312yes—
451#380C2312yes—
452#380C2312yes—
453#380C2312yes—
454#380C2312yes—
455#380C2314yes—
456#380C2312yes—
457#380C2314yes—
458#380C2314yes—
459#380C2312yes—
460#380C2314yes—
461#380C2312yes—
462#380C2314yes—
463#380C2314yes—
464#380C2318yes—
465#380C2314yes—
466#380C2312yes—
467#380C2314yes—
468C4×C4⋊C4C2311yescharacteristic
469C4×C4⋊C4C2311yescharacteristic
470C4×C4⋊C4C2312yes—
471C4×C4⋊C4C2312yes—
472C4×C4⋊C4C2314yes—
473C4×C4⋊C4C2314yes—
474C4×C4⋊C4C2314yes—
475C4×C4⋊C4C2314yes—
476C4×C4⋊C4C2312yes—
477C4×C4⋊C4C2314yes—
478C4×C4⋊C4C2312yes—
479C4×C4⋊C4C2314yes—
480C4×C4⋊C4C2312yes—
481C4×C4⋊C4C2312yes—
482C4×C4⋊C4C2311yescharacteristic
483C4×C4⋊C4C2314yes—
484C4×C4⋊C4C2314yes—
485C4×C4⋊C4C2314yes—
486C4×C4⋊C4C2311yescharacteristic
487C4×C4⋊C4C2311yescharacteristic
488C4×C4⋊C4C2312yes—
489C4×C4⋊C4C2314yes—
490C4×C4⋊C4C2312yes—
491C4×C4⋊C4C2318yes—
492C4×C4⋊C4C2312yes—
493C4×C4⋊C4C2312yes—
494C4×C4⋊C4C2314yes—
495C4×C4⋊C4C2314yes—
496C4×C4⋊C4C2312yes—
497C4×C4⋊C4C2311yescharacteristic
498C4×C4⋊C4C2311yescharacteristic
499C4×C4⋊C4C2312yes—
500C4×C4⋊C4C2311yescharacteristic
501C4×C4⋊C4C2314yes—
502C4×C4⋊C4C2311yescharacteristic
503C4×C4⋊C4C2312yes—
504C4×C4⋊C4C2314yes—
505C4×C22⋊C4C2312yes—
506C4×C22⋊C4C2312yes—
507C4×C22⋊C4C2312yes—
508C4×C22⋊C4C2314yes—
509C4×C22⋊C4C2314yes—
510C4×C22⋊C4C2318yes—
511C4×C22⋊C4C2314yes—
512C4×C22⋊C4C2312yes—
513C4×C22⋊C4C2314yes—
514C4×C22⋊C4C2312yes—
515C4×C22⋊C4C2314yes—
516C4×C22⋊C4C2312yes—
517C4×C22⋊C4C2314yes—
518#376C2318yes—
519#376C2314yes—
520C2×#95C2314yes—
521C43C2312yes—
522C43C2311yescharacteristic
523C22×Q8C2411yescharacteristic
524C22×Q8C2414yes—
525C22×Q8C2412yes—
526C22×Q8C2412yes—
527C22×Q8C2418yes—
528C22×Q8C2412yes—
529C22×D4C2411yescharacteristic
530C22×D4C2411yescharacteristic
531C22×D4C2414yes—
532C23×C4C2412yes—
533C23×C4C2412yes—
534C23×C4C2412yes—
535C23×C4C2412yes—
536C23×C4C2412yes—
537C23×C4C2414yes—
538C23×C4C2414yes—
539C23×C4C2412yes—
540C4⋊Q8—28no—
541C4⋊Q8—24no—
542C4⋊Q8—28no—
543C4⋊Q8—24no—
544C4⋊Q8—48no—
545C4⋊Q8—48no—
546C4⋊Q8—48no—
547C4⋊Q8—44no—
548C4⋊Q8#4118yes—
549#126—416no—
550#126—416no—
551#125—216no—
552#125—28no—
553#125—44no—
554#124—216no—
555#124—416no—
556#123—416no—
557C22⋊Q8—216no—
558C22⋊Q8—216no—
559C22⋊Q8—216no—
560C22⋊Q8—28no—
561C22⋊Q8—416no—
562C22⋊Q8—48no—
563C22⋊Q8—44no—
564C22⋊Q8—48no—
565#121—28no—
566#121—44no—
567C4×Q8—216no—
568C4×Q8—216no—
569C4×Q8—24no—
570C4×Q8—24no—
571C4×Q8—44no—
572C4×Q8—44no—
573C4×Q8—44no—
574C4×Q8—42no—
575C4×Q8—48no—
576C4×Q8—48no—
577C4×D4—28no—
578C4×D4—24no—
579C4×D4—28no—
580C4×D4—24no—
581C4×D4—24no—
582C4×D4—24no—
583C4×D4—24no—
584C4×D4—42no—
585C4×D4—48no—
586#117—216no—
587#117—48no—
588#117—48no—
589C2×C4⋊C4—28no—
590C2×C4⋊C4—44no—
591C2×C4⋊C4C2411yescharacteristic
592C2×C4⋊C4C2411yescharacteristic
593C2×C4⋊C4C2414yes—
594C2×C4⋊C4C2412yes—
595C2×C4⋊C4C2414yes—
596C2×C4⋊C4C2411yescharacteristic
597C2×C4⋊C4C2412yes—
598C2×C4⋊C4C2411yescharacteristic
599C2×C4⋊C4C2411yescharacteristic
600C2×C4⋊C4C2411yescharacteristic
601C2×C4⋊C4C2411yescharacteristic
602C2×C4⋊C4C2411yescharacteristic
603C2×C4⋊C4C2412yes—
604C2×C4⋊C4C2412yes—
605C2×C4⋊C4C2418yes—
606C2×C4⋊C4C2418yes—
607C2×C4⋊C4C2414yes—
608C2×C4⋊C4C2411yescharacteristic
609C2×C4⋊C4C2412yes—
610C2×C4⋊C4C2412yes—
611C2×C4⋊C4C2414yes—
612C2×C4⋊C4C2412yes—
613C2×C4⋊C4C2412yes—
614C2×C4⋊C4C2412yes—
615C2×C4⋊C4C2412yes—
616C2×C4⋊C4C2414yes—
617C2×C4⋊C4C2412yes—
618C2×C4⋊C4C2412yes—
619C2×C4⋊C4C2414yes—
620C2×C4⋊C4C2414yes—
621C2×C4⋊C4C2412yes—
622C2×C4⋊C4C2414yes—
623C2×C4⋊C4C2414yes—
624C2×C4⋊C4C2414yes—
625C2×C4⋊C4C2414yes—
626C2×C4⋊C4C2418yes—
627C2×C4⋊C4C2418yes—
628C2×C4⋊C4C2414yes—
629C2×C4⋊C4C2412yes—
630C2×C4⋊C4C2412yes—
631C2×C4⋊C4C2412yes—
632C2×C4⋊C4C2414yes—
633C2×C4⋊C4C2414yes—
634C2×C4⋊C4C2418yes—
635C2×C4⋊C4C2414yes—
636C2×C4⋊C4C2418yes—
637C2×C4⋊C4C2414yes—
638C2×C4⋊C4C2414yes—
639C2×C4⋊C4C2414yes—
640C2×C4⋊C4C2418yes—
641C2×C4⋊C4C2418yes—
642C2×C4⋊C4C2414yes—
643C2×C4⋊C4C2414yes—
644C2×C4⋊C4C2412yes—
645C2×C4⋊C4C2412yes—
646C2×C22⋊C4C2418yes—
647C2×C22⋊C4C2418yes—
648C2×C22⋊C4C2412yes—
649C2×C22⋊C4C2414yes—
650C2×C22⋊C4C2414yes—
651C2×C22⋊C4C2412yes—
652C2×C22⋊C4C2412yes—
653C2×C22⋊C4C2412yes—
654C2×C22⋊C4C2412yes—
655C2×C22⋊C4C2414yes—
656C2×C22⋊C4C2418yes—
657C2×C22⋊C4C2414yes—
658C2×C22⋊C4C2414yes—
659C2×C22⋊C4C2414yes—
660C2×C22⋊C4C2412yes—
661C2×C22⋊C4C2414yes—
662C2×C22⋊C4C2414yes—
663C2×C22⋊C4C2418yes—
664C2×C22⋊C4C2414yes—
665C2×C22⋊C4C2414yes—
666C2×C22⋊C4C2414yes—
667C2×C22⋊C4C2414yes—
668C2×C42—28no—
669C2×C42—28no—
670C2×C42—48no—
671C2×C42C2412yes—
672C2×C42C2414yes—
673C2×C42C2418yes—
674C2×C42C2411yescharacteristic
675C2×C42C2411yescharacteristic
676C2×C42C2412yes—
677C2×C42C2414yes—
678C2×C42C2411yescharacteristic
679C2×C42C2412yes—
680C2×C42C2412yes—
681C2×C42C2414yes—
682C2×C42C2412yes—
683C2×C42C2412yes—
684C2×C42C2412yes—
685C2×C42C2412yes—
686C2×C42C2412yes—
687C2×C42C2412yes—
688C2×C42C2418yes—
689C2×C42C2418yes—
690C2×C42C2412yes—
691C2×C42C2411yescharacteristic
692C2×C42C2412yes—
693C2×C42C2414yes—
694C2×C42C2418yes—
695C2×C42C2414yes—
696C2×C42C2411yescharacteristic
697C2×C42C2411yescharacteristic
698C2×C42C2411yescharacteristic
699#95C2412yes—
700#95C2414yes—
701#95C2414yes—
702#95C2414yes—
703#95C2414yes—
704#95C2414yes—
705#95C2414yes—
706#95C2414yes—
707#95C2414yes—
708#95C2418yes—
709#95C2414yes—
710#95C2418yes—
711#95C2414yes—
712#95C2412yes—
713#95C2412yes—
714#95C2414yes—
715#95C2412yes—
716#95C2412yes—
717#95C2414yes—
718#95C2412yes—
719#95C2414yes—
720#95C2412yes—
721#95C2414yes—
722#95C2414yes—
723#95C2414yes—
724#95C2418yes—
725#95C2414yes—
726#95C2414yes—
727#95C2412yes—
728#95C2412yes—
729#95C2414yes—
730#95C2418yes—
731#95C2418yes—
732#95C2414yes—
733#95C2418yes—
734#95C2418yes—
735#95C2414yes—
736#95C2414yes—
737#95C2414yes—
738#95C2418yes—
739#95C2418yes—
740#95C2414yes—
741#95C2418yes—
742#95C2418yes—
743#95C2414yes—
744#95C2414yes—
745#95C2418yes—
746#95C2418yes—
747#95C2418yes—
748#95C2418yes—
749C24C2512yes—
750C24C2512yes—
751C2×Q8—22no—
752C2×Q8—28no—
753C2×Q8—28no—
754C2×Q8—22no—
755C2×Q8—28no—
756C2×Q8—24no—
757C2×Q8—24no—
758C2×Q8—22no—
759C2×Q8—42no—
760C2×Q8—42no—
761C2×Q8—42no—
762C2×Q8—42no—
763C2×Q8—42no—
764C2×Q8—42no—
765C2×Q8—48no—
766C2×Q8—48no—
767C2×Q8—48no—
768C2×Q8C2×#4118yes—
769C2×D4—28no—
770C2×D4—22no—
771C2×D4—22no—
772C2×D4—22no—
773C2×D4—22no—
774C2×D4—22no—
775C2×D4—44no—
776C2×D4—44no—
777C2×D4H(5,𝔽2)14yes—
778C22×C4—24no—
779C22×C4—28no—
780C22×C4—24no—
781C22×C4—24no—
782C22×C4—24no—
783C22×C4—24no—
784C22×C4—24no—
785C22×C4—24no—
786C22×C4—24no—
787C22×C4—24no—
788C22×C4—24no—
789C22×C4—24no—
790C22×C4—24no—
791C22×C4—24no—
792C22×C4—24no—
793C22×C4—24no—
794C22×C4—28no—
795C22×C4—42no—
796C22×C4—44no—
797C22×C4—44no—
798C22×C4—44no—
799C22×C4—42no—
800C22×C4—44no—
801C22×C4—42no—
802C22×C4C2512yes—
803C22×C4C2514yes—
804C22×C4C2512yes—
805C22×C4C2512yes—
806C22×C4C2512yes—
807C22×C4C2512yes—
808C22×C4C2512yes—
809C22×C4C2514yes—
810C22×C4C2512yes—
811C22×C4C2512yes—
812C22×C4C2518yes—
813C22×C4C2514yes—
814C22×C4C2512yes—
815C22×C4C2514yes—
816C22×C4C2512yes—
817C22×C4C2514yes—
818C22×C4C2511yescharacteristic
819C22×C4C2511yescharacteristic
820C22×C4C2514yes—
821C22×C4C2511yescharacteristic
822C22×C4C2511yescharacteristic
823C22×C4C2511yescharacteristic
824C22×C4C2511yescharacteristic
825C22×C4C2511yescharacteristic
826C4⋊C4—22no—
827C4⋊C4—28no—
828C4⋊C4—28no—
829C4⋊C4—22no—
830C4⋊C4—24no—
831C4⋊C4—216no—
832C4⋊C4—216no—
833C4⋊C4—28no—
834C4⋊C4—28no—
835C4⋊C4—22no—
836C4⋊C4—24no—
837C4⋊C4—24no—
838C4⋊C4—22no—
839C4⋊C4—22no—
840C4⋊C4—22no—
841C4⋊C4—22no—
842C4⋊C4—24no—
843C4⋊C4—28no—
844C4⋊C4—24no—
845C4⋊C4—24no—
846C4⋊C4—24no—
847C4⋊C4—24no—
848C4⋊C4—28no—
849C4⋊C4—22no—
850C4⋊C4—24no—
851C4⋊C4—22no—
852C4⋊C4—24no—
853C4⋊C4—24no—
854C4⋊C4—24no—
855C4⋊C4—44no—
856C4⋊C4—44no—
857C4⋊C4—44no—
858C4⋊C4—42no—
859C4⋊C4—44no—
860C4⋊C4—44no—
861C4⋊C4—44no—
862C4⋊C4—44no—
863C4⋊C4—42no—
864C4⋊C4—44no—
865C4⋊C4—42no—
866C4⋊C4—44no—
867C4⋊C4—42no—
868C4⋊C4—48no—
869C4⋊C4—48no—
870C4⋊C4—44no—
871C4⋊C4—44no—
872C4⋊C4—48no—
873C4⋊C4—48no—
874C4⋊C4—44no—
875C4⋊C4—44no—
876C4⋊C4—44no—
877C4⋊C4—48no—
878C4⋊C4—48no—
879C4⋊C4C2×#4118yes—
880C4⋊C4C2×#4118yes—
881C22⋊C4—216no—
882C22⋊C4—28no—
883C22⋊C4—24no—
884C22⋊C4—28no—
885C22⋊C4—216no—
886C22⋊C4—216no—
887C22⋊C4—28no—
888C22⋊C4—24no—
889C22⋊C4—24no—
890C22⋊C4—24no—
891C22⋊C4—24no—
892C22⋊C4—44no—
893C22⋊C4—44no—
894C22⋊C4—44no—
895C22⋊C4—44no—
896C22⋊C4—44no—
897C22⋊C4—42no—
898C22⋊C4—44no—
899C22⋊C4—44no—
900C22⋊C4—44no—
901C22⋊C4—44no—
902C22⋊C4—48no—
903C42—24no—
904C42—24no—
905C42—24no—
906C42—216no—
907C42—24no—
908C42—24no—
909C42—28no—
910C42—22no—
911C42—24no—
912C42—24no—
913C42—24no—
914C42—24no—
915C42—24no—
916C42—28no—
917C42—22no—
918C42—28no—
919C42—22no—
920C42—44no—
921C42—44no—
922C42—41no—
923C42—42no—
924C42—48no—
925C42—48no—
926C42—42no—
927C42—48no—
928C42C2×#4114yes—
929C422−1+414yes—
930C422−1+414yes—
931C23—22no—
932C23—22no—
933C23—22no—
934C23—22no—
935C23—22no—
936C23—22no—
937C23—22no—
938C23—22no—
939C23—22no—
940C23—22no—
941C23—22no—
942C23—22no—
943C23—22no—
944C23C2×H(5,𝔽2)14yes—
945C23C2611yescharacteristic
946Q8—48no—
947Q8—44no—
948Q8—416no—
949Q8—84no—
950Q8—84no—
951Q8—168no—
952D4—28no—
953D4—44no—
954D4—88no—
955C2×C4—21no—
956C2×C4—21no—
957C2×C4—24no—
958C2×C4—21no—
959C2×C4—21no—
960C2×C4—24no—
961C2×C4—21no—
962C2×C4—21no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—22no—
967C2×C4—28no—
968C2×C4—22no—
969C2×C4—22no—
970C2×C4—22no—
971C2×C4—24no—
972C2×C4—24no—
973C2×C4—21no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—28no—
977C2×C4—24no—
978C2×C4—22no—
979C2×C4—24no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—28no—
989C2×C4—24no—
990C2×C4—24no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—24no—
994C2×C4—21no—
995C2×C4—24no—
996C2×C4—21no—
997C2×C4—24no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—24no—
1005C2×C4—24no—
1006C2×C4—24no—
1007C2×C4—24no—
1008C2×C4—24no—
1009C2×C4—24no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—48no—
1015C2×C4—48no—
1016C2×C4—48no—
1017C2×C4—48no—
1018C2×C4—48no—
1019C2×C4—84no—
1020C2×C4—88no—
1021C2×C4—88no—
1022C2×C4C22×#4112yes—
1023C2×C4C22×#4118yes—
1024C2×C4C22×#4112yes—
1025C2×C4C22×#4112yes—
1026C2×C4C2×H(5,𝔽2)12yes—
1027C2×C4C2×2−1+412yes—
1028C2×C4C2×2−1+412yes—
1029C2×C4C2×2−1+412yes—
1030C2×C4C2×2−1+412yes—
1031C2×C4C2×2−1+412yes—
1032C2×C4C2×2−1+412yes—
1033C2×C4#58512yes—
1034C2×C4#58512yes—
1035C22—24no—
1036C22—24no—
1037C22—24no—
1038C22—42no—
1039C22—42no—
1040C22—42no—
1041C22—42no—
1042C22—42no—
1043C22—42no—
1044C22—42no—
1045C22—42no—
1046C22—42no—
1047C22—42no—
1048C22—42no—
1049C22C23×#4111yescharacteristic
1050C22C22×H(5,𝔽2)11yescharacteristic
1051C22C22×2−1+411yescharacteristic
1052C22C22×2−1+411yescharacteristic
1053C22C2×#58511yescharacteristic
1054C22C2×#58511yescharacteristic
1055C222−1+611yescharacteristic
1056C4—22no—
1057C4—28no—
1058C4—22no—
1059C4—22no—
1060C4—42no—
1061C4—42no—
1062C4—42no—
1063C4—41no—
1064C4—42no—
1065C4—44no—
1066C4—44no—
1067C4—44no—
1068C4—42no—
1069C4—48no—
1070C4—42no—
1071C4—42no—
1072C4—42no—
1073C4—42no—
1074C4—42no—
1075C4—44no—
1076C4—44no—
1077C4#351814yes—
1078C4#352214yes—
1079C4#355514yes—
1080C2—44no—
1081C2—82no—
1082C2C2×#355511yescharacteristic
1083C2C2×#352211yescharacteristic
1084C2C2×#351811yescharacteristic
1085C2#6291511yescharacteristic
1086C2#6293211yescharacteristic
1087C2#6299111yescharacteristic
1088C2#6302411yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#2537C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59924C2semidirect
2. #59464C2semidirect
3. #59234C2semidirect
4. #59079C2semidirect
5. #51679C2semidirect
6. #45702C2semidirect
7. #45232C2semidirect
8. #45227C2semidirect
9. #42775C2semidirect
10. #42770C2semidirect
11. #39350C2semidirect
12. #39203C2semidirect
13. #39159C2semidirect
14. #39157C2semidirect
15. #38931C2semidirect
16. #36598C2semidirect
17. #36188C2semidirect
18. #36176C2semidirect
19. #36175C2semidirect
20. #36134C2semidirect
21. #35239C2semidirect
24. #34941C2semidirect
25. #34394C2semidirect
26. C4×#554C2semidirect

Maximal subgroups

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

subgroupindex
#599242
#594642
#592342
#590792
#516792
#457022
#452322
#452272
#427752
#427702
#393502
#392032
#391592
#391572
#389312
#365982
#361882
#361762
#361752
#361342
#352392
#351702
#349432
#349412
#343942
C4×#5542