Finite Group Databasebeta

← #7987071

Subgroups — #7987071

Order 512.

4623 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#59832C211yesmaximal, characteristic, complemented
2#59421C212yesmaximal
3#59230C212yesmaximal, complemented
4#59134C212yesmaximal, complemented
5#48984C218yesmaximal, complemented
6#46051C214yesmaximal, complemented
7#45305C214yesmaximal, complemented
8#45212C214yesmaximal, complemented
9#42847C214yesmaximal, complemented
10#42756C214yesmaximal, complemented
11#39172C212yesmaximal, complemented
12#39159C212yesmaximal, complemented
13#39159C212yesmaximal, complemented
14#39035C214yesmaximal, complemented
15#38940C212yesmaximal, complemented
16#36598C211yesmaximal, characteristic, complemented
17Q8×#124C212yesmaximal, complemented
18#36449C212yesmaximal, complemented
19#36188C211yesmaximal, characteristic, complemented
20D4×C4⋊Q8C211yesmaximal, characteristic, complemented
21#35192C212yesmaximal, complemented
22#35187C212yesmaximal, complemented
23#34945C211yesmaximal, characteristic, complemented
24#34943C211yesmaximal, characteristic
25#34371C212yesmaximal, complemented
26C4×#556C211yesmaximal, characteristic, complemented
27C2×Q82C2212yes—
28C2×#556C2211yescharacteristic
29C2×#556C2212yes—
30C2×D4×Q8C2212yes—
31C22×C4⋊Q8C2212yes—
32#2868C2211yescharacteristic
33#2864C2214yes—
34#2863C2214yes—
35#2862C2212yes—
36#2862C2214yes—
37#2857C2212yes—
38#2857C2212yes—
39#2831C2218yes—
40#2799C2218yes—
41#2786C2218yes—
42#2784C2218yes—
43#2775C2218yes—
44#2762C2218yes—
45#2759C2218yes—
46#2758C2218yes—
47#2758C2218yes—
48#2747C2218yes—
49#2745C2218yes—
50#2745C2218yes—
51#2737C2218yes—
52#2734C2214yes—
53#2716C2218yes—
54#2716C2218yes—
55#2716C2218yes—
56#2702C2218yes—
57#2665C2218yes—
58#2655C2218yes—
59#2653C2218yes—
60#2645C2214yes—
61#2640C2214yes—
62#2605C2218yes—
63#2582C2212yes—
64#2582C2212yes—
65#2578C2218yes—
66#2574C2218yes—
67#2573C2214yes—
68#2572C2214yes—
69#2571C2212yes—
70#2571C2211yescharacteristic
71#2571C2211yescharacteristic
72#2570C2214yes—
73#2568C2214yes—
74#2568C2212yes—
75#2568C2211yescharacteristic
76#2568C2214yes—
77#2568C2212yes—
78#2563C2211yescharacteristic
79#2563C2214yes—
80#2563C2214yes—
81#2563C2211yescharacteristic
82#2560C2218yes—
83#2551C2212yes—
84#2551C2212yes—
85#2551C2212yes—
86#2551C2212yes—
87#2547C2212yes—
88#2547C2212yes—
89#2547C2211yescharacteristic
90#2546C2212yes—
91#2546C2214yes—
92#2545C2214yes—
93#2538C2211yescharacteristic
94#2537C2211yescharacteristic
95#2530C2218yes—
96#2524C2218yes—
97#2523C2218yes—
98#2514C2214yes—
99#2514C2214yes—
100#2514C2212yes—
101#2511C2214yes—
102#2508C2214yes—
103#2499C2214yes—
104#2496C2214yes—
105#2496C2214yes—
106#2495C2214yes—
107#2495C2214yes—
108#2495C2212yes—
109#2495C2212yes—
110#2494C2212yes—
111#2492C2218yes—
112#2492C2214yes—
113#2492C2214yes—
114#2492C2214yes—
115#2492C2214yes—
116#2492C2218yes—
117#2492C2214yes—
118#2485C2214yes—
119#2481C2218yes—
120#2451C2214yes—
121#2451C2214yes—
122#2447C2212yes—
123#2446C2214yes—
124#2446C2214yes—
125#2440C2214yes—
126#2440C2214yes—
127#2439C2214yes—
128#2439C2214yes—
129#2439C2214yes—
130#2439C2214yes—
131#2439C2214yes—
132#2436C2214yes—
133#2434C2214yes—
134#2427C2214yes—
135#2426C2214yes—
136#2421C2214yes—
137#2421C2214yes—
138#2421C2212yes—
139#2421C2214yes—
140#2420C2212yes—
141#2420C2212yes—
142#2417C2214yes—
143#2401C2214yes—
144#2398C2214yes—
145#2381C2218yes—
146#2373C2214yes—
147#2367C2212yes—
148#2365C2212yes—
149#2365C2211yescharacteristic
150#2365C2212yes—
151#2365C2212yes—
152#2365C2212yes—
153#2365C2212yes—
154#2363C2214yes—
155#2362C2212yes—
156#2356C2212yes—
157#2355C2212yes—
158#2355C2211yescharacteristic
159#2355C2212yes—
160#2354C2211yescharacteristic
161#2352C2214yes—
162D4×C4⋊C4C2212yes—
163D4×C4⋊C4C2212yes—
164#2347C2212yes—
165#2345C2214yes—
166#2345C2214yes—
167Q8×C22⋊C4C2214yes—
168Q8×C22⋊C4C2214yes—
169Q8×C22⋊C4C2214yes—
170#2331C2214yes—
171#2331C2214yes—
172#2331C2214yes—
173#2327C2214yes—
174#2327C2214yes—
175#2320C2214yes—
176#2313C2218yes—
177C4×C4⋊Q8C2211yescharacteristic
178C4×C4⋊Q8C2212yes—
179C4×C4⋊Q8C2211yescharacteristic
180C4×C4⋊Q8C2211yescharacteristic
181C4×#126C2214yes—
182C4×#124C2212yes—
183C4×#124C2212yes—
184C4×#124C2214yes—
185C4×C22⋊Q8C2212yes—
186C4×C22⋊Q8C2212yes—
187C4×#121C2212yes—
188C4×#121C2212yes—
189#2295C2212yes—
190#2285C2212yes—
191#2283C2212yes—
192#2283C2212yes—
193#2283C2212yes—
194C42×Q8C2212yes—
195C42×Q8C2211yescharacteristic
196C42×D4C2211yescharacteristic
197C42×D4C2211yescharacteristic
198C4×#117C2212yes—
199C23×Q8C2314yes—
200Q82—48no—
201#556—28no—
202#556—48no—
203D4×Q8—48no—
204C2×C4⋊Q8—216no—
205C2×C4⋊Q8C2311yescharacteristic
206C2×C4⋊Q8C2311yescharacteristic
207C2×C4⋊Q8C2312yes—
208C2×C4⋊Q8C2312yes—
209C2×C4⋊Q8C2314yes—
210C2×C4⋊Q8C2314yes—
211C2×C4⋊Q8C2314yes—
212C2×C4⋊Q8C2314yes—
213C2×C4⋊Q8C2314yes—
214C2×C4⋊Q8C2314yes—
215C2×C4⋊Q8C2314yes—
216C2×C4⋊Q8C2312yes—
217C2×C4⋊Q8C2318yes—
218C2×C4⋊Q8C2311yescharacteristic
219C2×#126C2314yes—
220C2×#126C2318yes—
221C2×#124C2312yes—
222C2×#124C2312yes—
223C2×#124C2314yes—
224C2×C22⋊Q8C2312yes—
225C2×C22⋊Q8C2318yes—
226C2×C22⋊Q8C2314yes—
227C2×C22⋊Q8C2314yes—
228C2×C22⋊Q8C2312yes—
229C2×#121C2312yes—
230C2×#121C2312yes—
231C2×C4×Q8C2312yes—
232C2×C4×Q8C2312yes—
233C2×C4×Q8C2311yescharacteristic
234C2×C4×Q8C2311yescharacteristic
235C2×C4×Q8C2312yes—
236C2×C4×Q8C2314yes—
237C2×C4×Q8C2312yes—
238C2×C4×Q8C2314yes—
239C2×C4×Q8C2314yes—
240C2×C4×Q8C2311yescharacteristic
241C2×C4×Q8C2312yes—
242C2×C4×Q8C2314yes—
243C2×C4×D4C2311yescharacteristic
244C2×C4×D4C2311yescharacteristic
245C2×C4×D4C2311yescharacteristic
246C2×C4×D4C2311yescharacteristic
247C2×C4×D4C2311yescharacteristic
248C2×C4×D4C2314yes—
249C2×C4×D4C2314yes—
250C2×C4×D4C2311yescharacteristic
251C2×#117C2312yes—
252C2×#117C2312yes—
253C2×#117C2314yes—
254C22×C4⋊C4C2314yes—
255C22×C4⋊C4C2314yes—
256C22×C42C2312yes—
257C22×C42C2312yes—
258#401C2318yes—
259#401C2314yes—
260#400C2318yes—
261#400C2314yes—
262#400C2318yes—
263#400C2318yes—
264#400C2318yes—
265#400C2318yes—
266#400C2318yes—
267#400C2314yes—
268#400C2314yes—
269#400C2318yes—
270#400C2314yes—
271#400C2318yes—
272#400C2318yes—
273#400C2314yes—
274#400C2318yes—
275#398C2318yes—
276#398C2318yes—
277#398C2318yes—
278#398C2318yes—
279#398C2318yes—
280#397C2318yes—
281#397C2314yes—
282#397C2314yes—
283#397C2318yes—
284#397C2318yes—
285#397C2318yes—
286#397C2314yes—
287#397C2314yes—
288#397C2314yes—
289#397C2318yes—
290#396C2314yes—
291#396C2318yes—
292#396C2318yes—
293#396C2318yes—
294#395C2318yes—
295#395C2318yes—
296#395C2318yes—
297#395C2318yes—
298#394C2314yes—
299#394C2318yes—
300#394C2314yes—
301#393C2318yes—
302#393C2318yes—
303#393C2314yes—
304#393C2314yes—
305#393C2318yes—
306#393C2318yes—
307#393C2318yes—
308#393C2318yes—
309#391C2318yes—
310#391C2314yes—
311#391C2312yes—
312#391C2312yes—
313#391C2312yes—
314#391C2312yes—
315#391C2314yes—
316#391C2314yes—
317#391C2318yes—
318#391C2314yes—
319#391C2314yes—
320#391C2314yes—
321#391C2314yes—
322#391C2318yes—
323#391C2318yes—
324#391C2318yes—
325#391C2312yes—
326#391C2312yes—
327#391C2318yes—
328#391C2314yes—
329#391C2314yes—
330#391C2314yes—
331#391C2312yes—
332#391C2314yes—
333#391C2318yes—
334#391C2318yes—
335#391C2318yes—
336#391C2318yes—
337#391C2314yes—
338#391C2312yes—
339#391C2312yes—
340#391C2318yes—
341#390C2318yes—
342#390C2312yes—
343#390C2312yes—
344#390C2312yes—
345#390C2312yes—
346#389C2312yes—
347#389C2314yes—
348#389C2312yes—
349#389C2314yes—
350#389C2312yes—
351#389C2312yes—
352#389C2312yes—
353#389C2312yes—
354#389C2312yes—
355#389C2314yes—
356#389C2312yes—
357#389C2312yes—
358#389C2312yes—
359#389C2314yes—
360#389C2314yes—
361#389C2312yes—
362#389C2314yes—
363#389C2314yes—
364#389C2314yes—
365#389C2314yes—
366#389C2314yes—
367#389C2314yes—
368#389C2314yes—
369#389C2314yes—
370#389C2312yes—
371#388C2314yes—
372#388C2314yes—
373#388C2314yes—
374#388C2314yes—
375#388C2314yes—
376#388C2318yes—
377#388C2314yes—
378#388C2314yes—
379#388C2314yes—
380#388C2318yes—
381#388C2318yes—
382#388C2318yes—
383#388C2314yes—
384#388C2318yes—
385#388C2318yes—
386#387C2314yes—
387#387C2314yes—
388#387C2314yes—
389#387C2318yes—
390#387C2318yes—
391#387C2318yes—
392#387C2318yes—
393#387C2318yes—
394#387C2318yes—
395#387C2318yes—
396#387C2318yes—
397#387C2318yes—
398#387C2314yes—
399#387C2314yes—
400#387C2314yes—
401#387C2314yes—
402#387C2318yes—
403#387C2318yes—
404#387C2318yes—
405#387C2318yes—
406#387C2318yes—
407#387C2318yes—
408#387C2318yes—
409#387C2318yes—
410#387C2318yes—
411#387C2318yes—
412#387C2318yes—
413#387C2318yes—
414#386C2318yes—
415#386C2314yes—
416#386C2314yes—
417#386C2318yes—
418#385C2314yes—
419#385C2318yes—
420#385C2318yes—
421#385C2314yes—
422#384C2311yescharacteristic
423#384C2311yescharacteristic
424#384C2311yescharacteristic
425#384C2312yes—
426#384C2312yes—
427#384C2312yes—
428#384C2312yes—
429#383C2314yes—
430#383C2314yes—
431#383C2314yes—
432#383C2314yes—
433#383C2318yes—
434#383C2318yes—
435#382C2312yes—
436#382C2312yes—
437#382C2314yes—
438#382C2314yes—
439#382C2318yes—
440#382C2312yes—
441#382C2314yes—
442#382C2312yes—
443#382C2314yes—
444#382C2312yes—
445#382C2312yes—
446#382C2312yes—
447#382C2312yes—
448#381C2314yes—
449#381C2314yes—
450#381C2314yes—
451#380C2312yes—
452#380C2312yes—
453#380C2318yes—
454#380C2318yes—
455#380C2312yes—
456#380C2312yes—
457#380C2314yes—
458#380C2314yes—
459#380C2312yes—
460#380C2312yes—
461#380C2318yes—
462#380C2314yes—
463#380C2312yes—
464#380C2312yes—
465#380C2314yes—
466#380C2314yes—
467#380C2312yes—
468#380C2314yes—
469#380C2312yes—
470C4×C4⋊C4C2312yes—
471C4×C4⋊C4C2312yes—
472C4×C4⋊C4C2314yes—
473C4×C4⋊C4C2314yes—
474C4×C4⋊C4C2312yes—
475C4×C4⋊C4C2314yes—
476C4×C4⋊C4C2312yes—
477C4×C4⋊C4C2312yes—
478C4×C4⋊C4C2312yes—
479C4×C4⋊C4C2312yes—
480C4×C4⋊C4C2311yescharacteristic
481C4×C4⋊C4C2311yescharacteristic
482C4×C4⋊C4C2314yes—
483C4×C4⋊C4C2311yescharacteristic
484C4×C4⋊C4C2314yes—
485C4×C4⋊C4C2311yescharacteristic
486C4×C4⋊C4C2312yes—
487C4×C4⋊C4C2314yes—
488C4×C4⋊C4C2312yes—
489C4×C4⋊C4C2312yes—
490C4×C4⋊C4C2314yes—
491C4×C4⋊C4C2312yes—
492C4×C4⋊C4C2314yes—
493C4×C4⋊C4C2311yescharacteristic
494C4×C4⋊C4C2314yes—
495C4×C4⋊C4C2311yescharacteristic
496C4×C4⋊C4C2311yescharacteristic
497C4×C4⋊C4C2312yes—
498C4×C4⋊C4C2311yescharacteristic
499C4×C4⋊C4C2312yes—
500C4×C4⋊C4C2314yes—
501C4×C4⋊C4C2311yescharacteristic
502C4×C22⋊C4C2312yes—
503C4×C22⋊C4C2314yes—
504C4×C22⋊C4C2314yes—
505C4×C22⋊C4C2318yes—
506C4×C22⋊C4C2318yes—
507C4×C22⋊C4C2312yes—
508C4×C22⋊C4C2312yes—
509C4×C22⋊C4C2314yes—
510C4×C22⋊C4C2314yes—
511C4×C22⋊C4C2318yes—
512C4×C22⋊C4C2314yes—
513C4×C22⋊C4C2314yes—
514C4×C22⋊C4C2312yes—
515C4×C22⋊C4C2312yes—
516C4×C22⋊C4C2314yes—
517C4×C22⋊C4C2312yes—
518#376C2314yes—
519#376C2314yes—
520#376C2314yes—
521C43C2314yes—
522C43C2311yescharacteristic
523C43C2312yes—
524C22×Q8—216no—
525C22×Q8—48no—
526C22×Q8—48no—
527C22×Q8C2411yescharacteristic
528C22×Q8C2412yes—
529C22×Q8C2414yes—
530C22×Q8C2412yes—
531C22×Q8C2412yes—
532C22×Q8C2418yes—
533C22×Q8C2418yes—
534C22×D4C2411yescharacteristic
535C22×D4C2411yescharacteristic
536C22×D4C2414yes—
537C23×C4C2412yes—
538C23×C4C2412yes—
539C23×C4C2412yes—
540C23×C4C2412yes—
541C23×C4C2412yes—
542C23×C4C2418yes—
543C23×C4C2412yes—
544C4⋊Q8—216no—
545C4⋊Q8—216no—
546C4⋊Q8—216no—
547C4⋊Q8—28no—
548C4⋊Q8—28no—
549C4⋊Q8—24no—
550C4⋊Q8—24no—
551C4⋊Q8—48no—
552C4⋊Q8—48no—
553C4⋊Q8—48no—
554C4⋊Q8—48no—
555C4⋊Q8—44no—
556C4⋊Q8—416no—
557C4⋊Q8#4118yes—
558#126—216no—
559#126—416no—
560#124—28no—
561#124—28no—
562#124—48no—
563C22⋊Q8—28no—
564C22⋊Q8—416no—
565C22⋊Q8—44no—
566C22⋊Q8—48no—
567C22⋊Q8—48no—
568#121—28no—
569#121—44no—
570C4×Q8—28no—
571C4×Q8—24no—
572C4×Q8—28no—
573C4×Q8—28no—
574C4×Q8—24no—
575C4×Q8—44no—
576C4×Q8—42no—
577C4×Q8—44no—
578C4×Q8—48no—
579C4×Q8—48no—
580C4×Q8—48no—
581C4×Q8—48no—
582C4×D4—24no—
583C4×D4—24no—
584C4×D4—24no—
585C4×D4—24no—
586C4×D4—24no—
587C4×D4—42no—
588C4×D4—48no—
589C4×D4—48no—
590#117—28no—
591#117—44no—
592#117—48no—
593C2×C4⋊C4—216no—
594C2×C4⋊C4—216no—
595C2×C4⋊C4C2414yes—
596C2×C4⋊C4C2414yes—
597C2×C4⋊C4C2418yes—
598C2×C4⋊C4C2418yes—
599C2×C4⋊C4C2412yes—
600C2×C4⋊C4C2411yescharacteristic
601C2×C4⋊C4C2411yescharacteristic
602C2×C4⋊C4C2414yes—
603C2×C4⋊C4C2412yes—
604C2×C4⋊C4C2411yescharacteristic
605C2×C4⋊C4C2411yescharacteristic
606C2×C4⋊C4C2411yescharacteristic
607C2×C4⋊C4C2411yescharacteristic
608C2×C4⋊C4C2411yescharacteristic
609C2×C4⋊C4C2411yescharacteristic
610C2×C4⋊C4C2412yes—
611C2×C4⋊C4C2412yes—
612C2×C4⋊C4C2412yes—
613C2×C4⋊C4C2412yes—
614C2×C4⋊C4C2414yes—
615C2×C4⋊C4C2414yes—
616C2×C4⋊C4C2414yes—
617C2×C4⋊C4C2412yes—
618C2×C4⋊C4C2411yescharacteristic
619C2×C4⋊C4C2412yes—
620C2×C4⋊C4C2412yes—
621C2×C4⋊C4C2414yes—
622C2×C4⋊C4C2412yes—
623C2×C4⋊C4C2412yes—
624C2×C4⋊C4C2412yes—
625C2×C4⋊C4C2414yes—
626C2×C4⋊C4C2418yes—
627C2×C4⋊C4C2418yes—
628C2×C4⋊C4C2418yes—
629C2×C4⋊C4C2414yes—
630C2×C4⋊C4C2412yes—
631C2×C4⋊C4C2412yes—
632C2×C4⋊C4C2418yes—
633C2×C4⋊C4C2414yes—
634C2×C4⋊C4C2418yes—
635C2×C4⋊C4C2414yes—
636C2×C4⋊C4C2414yes—
637C2×C4⋊C4C2418yes—
638C2×C4⋊C4C2414yes—
639C2×C4⋊C4C2412yes—
640C2×C4⋊C4C2412yes—
641C2×C4⋊C4C2414yes—
642C2×C4⋊C4C2412yes—
643C2×C4⋊C4C2412yes—
644C2×C22⋊C4C2414yes—
645C2×C22⋊C4C2412yes—
646C2×C22⋊C4C2412yes—
647C2×C22⋊C4C2412yes—
648C2×C22⋊C4C2412yes—
649C2×C22⋊C4C2412yes—
650C2×C22⋊C4C2414yes—
651C2×C22⋊C4C2414yes—
652C2×C22⋊C4C2414yes—
653C2×C22⋊C4C2414yes—
654C2×C22⋊C4C2418yes—
655C2×C22⋊C4C2414yes—
656C2×C22⋊C4C2418yes—
657C2×C22⋊C4C2414yes—
658C2×C22⋊C4C2412yes—
659C2×C22⋊C4C2414yes—
660C2×C22⋊C4C2414yes—
661C2×C22⋊C4C2418yes—
662C2×C22⋊C4C2414yes—
663C2×C22⋊C4C2414yes—
664C2×C22⋊C4C2414yes—
665C2×C22⋊C4C2414yes—
666C2×C22⋊C4C2414yes—
667C2×C42—28no—
668C2×C42—28no—
669C2×C42C2414yes—
670C2×C42C2414yes—
671C2×C42C2414yes—
672C2×C42C2411yescharacteristic
673C2×C42C2411yescharacteristic
674C2×C42C2414yes—
675C2×C42C2412yes—
676C2×C42C2411yescharacteristic
677C2×C42C2412yes—
678C2×C42C2412yes—
679C2×C42C2412yes—
680C2×C42C2412yes—
681C2×C42C2412yes—
682C2×C42C2412yes—
683C2×C42C2412yes—
684C2×C42C2412yes—
685C2×C42C2412yes—
686C2×C42C2418yes—
687C2×C42C2414yes—
688C2×C42C2418yes—
689C2×C42C2414yes—
690C2×C42C2412yes—
691C2×C42C2418yes—
692C2×C42C2411yescharacteristic
693C2×C42C2414yes—
694C2×C42C2412yes—
695C2×C42C2411yescharacteristic
696C2×C42C2411yescharacteristic
697C2×C42C2411yescharacteristic
698#95C2412yes—
699#95C2414yes—
700#95C2414yes—
701#95C2414yes—
702#95C2414yes—
703#95C2414yes—
704#95C2414yes—
705#95C2414yes—
706#95C2414yes—
707#95C2414yes—
708#95C2414yes—
709#95C2414yes—
710#95C2414yes—
711#95C2412yes—
712#95C2412yes—
713#95C2412yes—
714#95C2412yes—
715#95C2412yes—
716#95C2412yes—
717#95C2414yes—
718#95C2414yes—
719#95C2418yes—
720#95C2418yes—
721#95C2414yes—
722#95C2418yes—
723#95C2414yes—
724#95C2414yes—
725#95C2414yes—
726#95C2414yes—
727#95C2414yes—
728#95C2418yes—
729#95C2418yes—
730#95C2414yes—
731#95C2414yes—
732#95C2412yes—
733#95C2412yes—
734#95C2414yes—
735#95C2418yes—
736#95C2418yes—
737#95C2418yes—
738#95C2414yes—
739#95C2418yes—
740#95C2414yes—
741#95C2414yes—
742#95C2414yes—
743#95C2418yes—
744#95C2414yes—
745#95C2414yes—
746#95C2418yes—
747#95C2414yes—
748#95C2418yes—
749#95C2418yes—
750#95C2418yes—
751#95C2418yes—
752C24C2512yes—
753C24C2512yes—
754C2×Q8—22no—
755C2×Q8—28no—
756C2×Q8—216no—
757C2×Q8—24no—
758C2×Q8—24no—
759C2×Q8—28no—
760C2×Q8—24no—
761C2×Q8—22no—
762C2×Q8—24no—
763C2×Q8—24no—
764C2×Q8—24no—
765C2×Q8—22no—
766C2×Q8—28no—
767C2×Q8—42no—
768C2×Q8—48no—
769C2×Q8—48no—
770C2×Q8—42no—
771C2×Q8—48no—
772C2×Q8—48no—
773C2×Q8—48no—
774C2×Q8—832no—
775C2×Q8C2×#4118yes—
776C2×D4—28no—
777C2×D4—22no—
778C2×D4—22no—
779C2×D4—22no—
780C2×D4—22no—
781C2×D4—22no—
782C2×D4—44no—
783C2×D4—44no—
784C2×D42−1+414yes—
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—24no—
795C22×C4—24no—
796C22×C4—24no—
797C22×C4—24no—
798C22×C4—24no—
799C22×C4—216no—
800C22×C4—24no—
801C22×C4—42no—
802C22×C4—48no—
803C22×C4—42no—
804C22×C4—42no—
805C22×C4—48no—
806C22×C4C2512yes—
807C22×C4C2512yes—
808C22×C4C2512yes—
809C22×C4C2512yes—
810C22×C4C2512yes—
811C22×C4C2512yes—
812C22×C4C2512yes—
813C22×C4C2514yes—
814C22×C4C2514yes—
815C22×C4C2512yes—
816C22×C4C2512yes—
817C22×C4C2512yes—
818C22×C4C2511yescharacteristic
819C22×C4C2514yes—
820C22×C4C2514yes—
821C22×C4C2514yes—
822C22×C4C2518yes—
823C22×C4C2511yescharacteristic
824C22×C4C2514yes—
825C22×C4C2511yescharacteristic
826C22×C4C2511yescharacteristic
827C22×C4C2511yescharacteristic
828C22×C4C2511yescharacteristic
829C22×C4C2511yescharacteristic
830C4⋊C4—216no—
831C4⋊C4—216no—
832C4⋊C4—28no—
833C4⋊C4—28no—
834C4⋊C4—22no—
835C4⋊C4—22no—
836C4⋊C4—28no—
837C4⋊C4—24no—
838C4⋊C4—24no—
839C4⋊C4—28no—
840C4⋊C4—22no—
841C4⋊C4—22no—
842C4⋊C4—28no—
843C4⋊C4—24no—
844C4⋊C4—28no—
845C4⋊C4—24no—
846C4⋊C4—24no—
847C4⋊C4—28no—
848C4⋊C4—22no—
849C4⋊C4—22no—
850C4⋊C4—22no—
851C4⋊C4—24no—
852C4⋊C4—24no—
853C4⋊C4—24no—
854C4⋊C4—24no—
855C4⋊C4—22no—
856C4⋊C4—24no—
857C4⋊C4—22no—
858C4⋊C4—24no—
859C4⋊C4—24no—
860C4⋊C4—42no—
861C4⋊C4—42no—
862C4⋊C4—44no—
863C4⋊C4—44no—
864C4⋊C4—42no—
865C4⋊C4—44no—
866C4⋊C4—48no—
867C4⋊C4—44no—
868C4⋊C4—42no—
869C4⋊C4—48no—
870C4⋊C4—48no—
871C4⋊C4—48no—
872C4⋊C4—44no—
873C4⋊C4—48no—
874C4⋊C4—44no—
875C4⋊C4—44no—
876C4⋊C4—48no—
877C4⋊C4C2×#4118yes—
878C4⋊C4C2×#4118yes—
879C22⋊C4—24no—
880C22⋊C4—28no—
881C22⋊C4—28no—
882C22⋊C4—28no—
883C22⋊C4—28no—
884C22⋊C4—24no—
885C22⋊C4—28no—
886C22⋊C4—24no—
887C22⋊C4—24no—
888C22⋊C4—24no—
889C22⋊C4—44no—
890C22⋊C4—44no—
891C22⋊C4—44no—
892C22⋊C4—44no—
893C22⋊C4—44no—
894C22⋊C4—48no—
895C22⋊C4—42no—
896C22⋊C4—44no—
897C22⋊C4—44no—
898C22⋊C4—48no—
899C22⋊C4—44no—
900C22⋊C4—44no—
901C22⋊C4—48no—
902C42—24no—
903C42—24no—
904C42—24no—
905C42—28no—
906C42—24no—
907C42—28no—
908C42—28no—
909C42—24no—
910C42—24no—
911C42—24no—
912C42—22no—
913C42—24no—
914C42—24no—
915C42—28no—
916C42—22no—
917C42—22no—
918C42—24no—
919C42—41no—
920C42—42no—
921C42—44no—
922C42—44no—
923C42—48no—
924C42—42no—
925C42—44no—
926C42—48no—
927C42—48no—
928C42C2×#4114yes—
929C42H(5,𝔽2)14yes—
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—
944C23C2×2−1+414yes—
945C23C2611yescharacteristic
946Q8—216no—
947Q8—416no—
948Q8—44no—
949Q8—48no—
950Q8—84no—
951Q8—816no—
952Q8—168no—
953D4—28no—
954D4—44no—
955D4—88no—
956C2×C4—24no—
957C2×C4—21no—
958C2×C4—21no—
959C2×C4—21no—
960C2×C4—24no—
961C2×C4—21no—
962C2×C4—21no—
963C2×C4—21no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—22no—
967C2×C4—22no—
968C2×C4—22no—
969C2×C4—22no—
970C2×C4—28no—
971C2×C4—24no—
972C2×C4—24no—
973C2×C4—24no—
974C2×C4—22no—
975C2×C4—24no—
976C2×C4—28no—
977C2×C4—22no—
978C2×C4—22no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—21no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—24no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—24no—
991C2×C4—24no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—21no—
995C2×C4—24no—
996C2×C4—21no—
997C2×C4—24no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—24no—
1002C2×C4—22no—
1003C2×C4—24no—
1004C2×C4—28no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—24no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—24no—
1012C2×C4—22no—
1013C2×C4—24no—
1014C2×C4—24no—
1015C2×C4—48no—
1016C2×C4—48no—
1017C2×C4—48no—
1018C2×C4—48no—
1019C2×C4—48no—
1020C2×C4—84no—
1021C2×C4—816no—
1022C2×C4C22×#4112yes—
1023C2×C4C22×#4118yes—
1024C2×C4C22×#4112yes—
1025C2×C4C22×#4112yes—
1026C2×C4C2×H(5,𝔽2)12yes—
1027C2×C4C2×H(5,𝔽2)12yes—
1028C2×C4C2×H(5,𝔽2)12yes—
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—44no—
1064C4—42no—
1065C4—41no—
1066C4—44no—
1067C4—42no—
1068C4—48no—
1069C4—42no—
1070C4—42no—
1071C4—42no—
1072C4—44no—
1073C4—44no—
1074C4—44no—
1075C4—42no—
1076C4—42no—
1077C4#351414yes—
1078C4#351814yes—
1079C4#355214yes—
1080C2—44no—
1081C2—82no—
1082C2C2×#355211yescharacteristic
1083C2C2×#351411yescharacteristic
1084C2C2×#351811yescharacteristic
1085C2#6293111yescharacteristic
1086C2#6295911yescharacteristic
1087C2#6299811yescharacteristic
1088C2#6302511yescharacteristic
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. #59832C2semidirect
3. #59230C2semidirect
4. #59134C2semidirect
5. #48984C2semidirect
6. #46051C2semidirect
7. #45305C2semidirect
8. #45212C2semidirect
9. #42847C2semidirect
10. #42756C2semidirect
11. #39172C2semidirect
12. #39159C2semidirect
13. #39159C2semidirect
14. #39035C2semidirect
15. #38940C2semidirect
16. #36598C2semidirect
17. Q8×#124C2semidirect
18. #36449C2semidirect
19. #36188C2semidirect
20. D4×C4⋊Q8C2semidirect
21. #35192C2semidirect
22. #35187C2semidirect
23. #34945C2semidirect
25. #34371C2semidirect
26. C4×#556C2semidirect

Maximal subgroups

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

subgroupindex
#598322
#594212
#592302
#591342
#489842
#460512
#453052
#452122
#428472
#427562
#391722
#391592
#390352
#389402
#365982
Q8×#1242
#364492
#361882
D4×C4⋊Q82
#351922
#351872
#349452
#349432
#343712
C4×#5562