Finite Group Databasebeta

← #7681495

Subgroups — #7681495

Order 512.

6668 conjugacy classes of subgroups.

The subgroup lattice has 1131 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3502C211yesmaximal, characteristic, complemented
2C2×Q8×#41C211yesmaximal, characteristic
3#59833C214yesmaximal, complemented
4#59667C214yesmaximal, complemented
5#59149C218yesmaximal, complemented
6#45389C212yesmaximal, complemented
7#45389C212yesmaximal, complemented
8#45139C212yesmaximal, complemented
9#44934C212yesmaximal, complemented
10#44449C214yesmaximal, complemented
11#43891C214yesmaximal, complemented
12#39597C214yesmaximal, complemented
13#39591C214yesmaximal, complemented
14#39591C214yesmaximal, complemented
15#36545C214yesmaximal, complemented
16#35662C212yesmaximal, complemented
17#35566C212yesmaximal, complemented
18#35334C211yesmaximal, characteristic
19#35257C212yesmaximal
20#34953C211yesmaximal, characteristic, complemented
21C2×#2581C211yesmaximal, characteristic, complemented
22#34268C212yesmaximal
23#34215C211yesmaximal, characteristic, complemented
24C4×#536C211yesmaximal, characteristic
25#3502—216no—
26Q8×#41—216no—
27C2×Q82C2212yes—
28C2×Q82C2212yes—
29C2×Q82C2211yescharacteristic
30C2×#557C2212yes—
31C2×#557C2214yes—
32C2×#557C2212yes—
33C2×#557C2212yes—
34C2×#557C2214yes—
35C2×#557C2211yescharacteristic
36C2×#554C2214yes—
37C2×#554C2211yescharacteristic
38C2×#554C2212yes—
39C2×#554C2212yes—
40C2×D4×Q8C2212yes—
41C2×D4×Q8C2211yescharacteristic
42C2×#544C2214yes—
43C2×#544C2212yes—
44C2×#536C2211yescharacteristic
45C2×#533C2211yescharacteristic
46C2×#533C2214yes—
47C2×#533C2212yes—
48C2×#533C2212yes—
49C2×#533C2214yes—
50C2×#533C2211yescharacteristic
51C2×#519C2212yes—
52C2×C4×#41C2211yescharacteristic
53C2×C4×#41C2212yes—
54C22×C4×Q8C2211yescharacteristic
55C22×C4×Q8C2211yescharacteristic
56C22×C4×Q8C2212yes—
57#2857C2214yes—
58#2851C2214yes—
59#2851C2214yes—
60#2734C2218yes—
61#2734C2218yes—
62#2729C2218yes—
63#2729C2218yes—
64#2720C2218yes—
65#2720C2218yes—
66#2713C2218yes—
67#2713C2218yes—
68#2713C2218yes—
69#2713C2218yes—
70#2677C2218yes—
71#2677C2218yes—
72#2629C2214yes—
73#2628C2212yes—
74#2628C2212yes—
75#2628C2214yes—
76#2584C2212yes—
77#2584C2212yes—
78#2584C2214yes—
79#2584C2214yes—
80#2583C2214yes—
81#2582C2214yes—
82#2582C2214yes—
83#2581C2212yes—
84#2581C2212yes—
85#2581C2214yes—
86#2581C2212yes—
87#2581C2212yes—
88#2581C2214yes—
89#2581C2214yes—
90#2581C2212yes—
91#2581C2214yes—
92#2581C2212yes—
93#2580C2212yes—
94#2580C2212yes—
95#2567C2212yes—
96#2567C2214yes—
97#2564C2214yes—
98#2564C2214yes—
99#2556C2218yes—
100#2556C2218yes—
101#2552C2214yes—
102#2551C2218yes—
103#2551C2214yes—
104#2550C2214yes—
105#2550C2214yes—
106#2549C2218yes—
107#2546C2212yes—
108#2546C2214yes—
109#2506C2218yes—
110#2506C2218yes—
111#2502C2212yes—
112#2492C2218yes—
113#2473C2218yes—
114#2473C2218yes—
115#2465C2218yes—
116#2465C2218yes—
117#2462C2218yes—
118#2462C2218yes—
119#2462C2218yes—
120#2462C2218yes—
121#2454C2214yes—
122#2453C2214yes—
123#2453C2214yes—
124#2453C2214yes—
125#2452C2214yes—
126#2451C2214yes—
127#2451C2214yes—
128#2451C2214yes—
129#2450C2218yes—
130#2449C2218yes—
131#2446C2218yes—
132#2446C2218yes—
133#2440C2218yes—
134#2438C2218yes—
135#2438C2218yes—
136#2434C2212yes—
137#2434C2218yes—
138#2423C2218yes—
139#2399C2212yes—
140#2399C2212yes—
141C2×#400C2212yes—
142C2×#395C2212yes—
143#2368C2214yes—
144#2368C2214yes—
145#2367C2214yes—
146#2367C2214yes—
147#2365C2218yes—
148#2365C2214yes—
149#2365C2214yes—
150#2360C2218yes—
151#2359C2218yes—
152#2359C2218yes—
153#2355C2214yes—
154#2355C2214yes—
155#2331C2212yes—
156#2331C2212yes—
157#2327C2212yes—
158#2326C2212yes—
159#2323C2214yes—
160#2323C2214yes—
161#2323C2214yes—
162#2322C2214yes—
163#2317C2211yescharacteristic
164#2317C2212yes—
165#2316C2212yes—
166#2311C2212yes—
167#2311C2211yescharacteristic
168#2310C2211yescharacteristic
169C4×C4⋊Q8C2212yes—
170C4×C4⋊Q8C2214yes—
171C4×#125C2214yes—
172C4×#124C2212yes—
173C4×C22⋊Q8C2214yes—
174C4×C22⋊Q8C2214yes—
175C4×C22⋊Q8C2214yes—
176C4×#123C2214yes—
177#2296C2212yes—
178#2296C2212yes—
179C2×#391C2212yes—
180C2×#389C2212yes—
181C2×#387C2214yes—
182C2×#382C2211yescharacteristic
183#2274C2212yes—
184C4×#117C2211yescharacteristic
185C22×#41C2311yescharacteristic
186C23×Q8C2311yescharacteristic
187C23×Q8C2311yescharacteristic
188C23×Q8C2312yes—
189Q82—28no—
190Q82—216no—
191Q82—216no—
192#557—28no—
193#557—216no—
194#557—216no—
195#557—232no—
196#557—232no—
197#557—216no—
198#554—28no—
199#554—216no—
200#554—216no—
201#554—232no—
202D4×Q8—28no—
203D4×Q8—216no—
204#544—232no—
205#544—216no—
206#536Q8116yescomplemented
207#533—232no—
208#533—232no—
209#533—216no—
210#533—216no—
211#533—28no—
212#533D4116yes—
213C2×C4⋊Q8C2311yescharacteristic
214C2×C4⋊Q8C2314yes—
215C2×C4⋊Q8C2311yescharacteristic
216C2×C4⋊Q8C2314yes—
217C2×C4⋊Q8C2312yes—
218C2×C4⋊Q8C2314yes—
219C2×C4⋊Q8C2312yes—
220C2×C4⋊Q8C2314yes—
221C2×C4⋊Q8C2312yes—
222C2×C4⋊Q8C2312yes—
223C2×C4⋊Q8C2314yes—
224C2×C4⋊Q8C2318yes—
225C2×C4⋊Q8C2318yes—
226C2×C4⋊Q8C2314yes—
227C2×C4⋊Q8C2314yes—
228C2×C4⋊Q8C2318yes—
229C2×C4⋊Q8C2311yescharacteristic
230C2×C4⋊Q8C2311yescharacteristic
231C2×C4⋊Q8C2312yes—
232C2×#125C2312yes—
233C2×#125C2314yes—
234C2×#125C2312yes—
235C2×#125C2312yes—
236C2×#125C2314yes—
237C2×#125C2314yes—
238C2×#125C2314yes—
239C2×#125C2318yes—
240C2×#125C2314yes—
241C2×#125C2318yes—
242C2×#125C2318yes—
243C2×#125C2312yes—
244C2×#124C2312yes—
245C2×#123C2314yes—
246C2×C22⋊Q8C2312yes—
247C2×C22⋊Q8C2312yes—
248C2×C22⋊Q8C2314yes—
249C2×C22⋊Q8C2314yes—
250C2×C22⋊Q8C2314yes—
251C2×C22⋊Q8C2318yes—
252C2×C22⋊Q8C2314yes—
253C2×C22⋊Q8C2314yes—
254C2×C22⋊Q8C2312yes—
255C2×C22⋊Q8C2312yes—
256C2×C22⋊Q8C2314yes—
257C2×C22⋊Q8C2314yes—
258C2×C22⋊Q8C2318yes—
259C2×C22⋊Q8C2312yes—
260C2×C22⋊Q8C2312yes—
261C2×C22⋊Q8C2314yes—
262#519—216no—
263C4×#41—216no—
264C4×#41—28no—
265C2×C4×Q8—216no—
266C2×C4×Q8—28no—
267C2×C4×Q8—28no—
268C2×C4×Q8C2312yes—
269C2×C4×Q8C2312yes—
270C2×C4×Q8C2311yescharacteristic
271C2×C4×Q8C2312yes—
272C2×C4×Q8C2312yes—
273C2×C4×Q8C2314yes—
274C2×C4×Q8C2312yes—
275C2×C4×Q8C2314yes—
276C2×C4×Q8C2314yes—
277C2×C4×Q8C2312yes—
278C2×C4×Q8C2312yes—
279C2×C4×Q8C2311yescharacteristic
280C2×C4×Q8C2311yescharacteristic
281C2×C4×Q8C2311yescharacteristic
282C2×C4×Q8C2311yescharacteristic
283C2×C4×Q8C2311yescharacteristic
284C2×C4×Q8C2312yes—
285C2×C4×Q8C2314yes—
286C2×C4×Q8C2318yes—
287C2×C4×Q8C2314yes—
288C2×C4×Q8C2312yes—
289C2×C4×Q8C2312yes—
290C2×C4×Q8C2314yes—
291C2×C4×Q8C2314yes—
292C2×C4×Q8C2312yes—
293C2×C4×Q8C2312yes—
294C2×C4×Q8C2314yes—
295C2×C4×Q8C2314yes—
296C2×C4×Q8C2312yes—
297C2×C4×Q8C2312yes—
298C2×C4×D4C2312yes—
299C2×C4×D4C2312yes—
300C2×C4×D4C2311yescharacteristic
301C2×C4×D4C2311yescharacteristic
302C2×C4×D4C2314yes—
303C2×C4×D4C2314yes—
304C2×C4×D4C2312yes—
305C2×C4×D4C2312yes—
306C2×#117C2311yescharacteristic
307C2×#117C2311yescharacteristic
308C2×#117C2312yes—
309C2×#117C2312yes—
310C2×#117C2314yes—
311C2×#117C2318yes—
312C2×#117C2312yes—
313C2×#117C2311yescharacteristic
314C22×C4⋊C4C2312yes—
315C22×C4⋊C4C2311yescharacteristic
316C22×C4⋊C4C2312yes—
317C22×C4⋊C4C2312yes—
318C22×C4⋊C4C2314yes—
319C22×C4⋊C4C2311yescharacteristic
320C22×C4⋊C4C2312yes—
321C22×C4⋊C4C2314yes—
322C22×C42C2312yes—
323C22×C42C2314yes—
324C22×C42C2312yes—
325C22×C42C2312yes—
326C22×C42C2311yescharacteristic
327#400C2314yes—
328#400C2314yes—
329#400C2314yes—
330#400C2314yes—
331#400C2318yes—
332#400C2318yes—
333#400C2318yes—
334#400C2318yes—
335#399C2314yes—
336#399C2314yes—
337#399C2318yes—
338#398C2318yes—
339#398C2318yes—
340#398C2318yes—
341#398C2318yes—
342#398C2314yes—
343#398C2314yes—
344#398C2314yes—
345#398C2314yes—
346#398C2318yes—
347#398C2318yes—
348#398C2318yes—
349#398C2318yes—
350#398C2318yes—
351#398C2318yes—
352#396C2318yes—
353#396C2318yes—
354#395C2314yes—
355#395C2314yes—
356#395C2314yes—
357#395C2314yes—
358#395C2318yes—
359#395C2318yes—
360#395C2318yes—
361#395C2314yes—
362#395C2314yes—
363#395C2318yes—
364#395C2318yes—
365#395C2314yes—
366#395C2314yes—
367#395C2318yes—
368#395C2318yes—
369#395C2318yes—
370#393C2314yes—
371#393C2314yes—
372#393C2318yes—
373#391C2312yes—
374#391C2312yes—
375#391C2314yes—
376#391C2314yes—
377#391C2314yes—
378#391C2312yes—
379#391C2314yes—
380#391C2318yes—
381#391C2314yes—
382#391C2314yes—
383#391C2314yes—
384#391C2314yes—
385#391C2318yes—
386#391C2318yes—
387#391C2318yes—
388#391C2318yes—
389#391C2318yes—
390#391C2318yes—
391#390C2314yes—
392#390C2312yes—
393#389C2314yes—
394#389C2314yes—
395#389C2318yes—
396#389C2314yes—
397#389C2314yes—
398#389C2314yes—
399#389C2314yes—
400#389C2312yes—
401#389C2314yes—
402#389C2314yes—
403#389C2312yes—
404#389C2314yes—
405#389C2312yes—
406#389C2312yes—
407#389C2312yes—
408#389C2314yes—
409#389C2314yes—
410#389C2314yes—
411#389C2318yes—
412#389C2318yes—
413#389C2314yes—
414#389C2312yes—
415#389C2314yes—
416#389C2314yes—
417#389C2312yes—
418#389C2318yes—
419#389C2318yes—
420#389C2318yes—
421#389C2318yes—
422#389C2318yes—
423#389C2318yes—
424#389C2312yes—
425#389C2318yes—
426#388C2318yes—
427#388C2318yes—
428#388C2318yes—
429#388C2318yes—
430#388C2318yes—
431#388C2318yes—
432#387C2318yes—
433#387C2318yes—
434#387C2318yes—
435#387C2318yes—
436#387C2318yes—
437#387C2318yes—
438#387C2318yes—
439#387C2318yes—
440#387C2318yes—
441#387C2318yes—
442#387C2318yes—
443#387C2318yes—
444#387C2318yes—
445#387C2318yes—
446#387C2318yes—
447#387C2318yes—
448#387C2318yes—
449#387C2318yes—
450#387C2318yes—
451#387C2318yes—
452#387C2318yes—
453#387C2318yes—
454#386C2318yes—
455#386C2314yes—
456#385C2318yes—
457#385C2318yes—
458#385C2314yes—
459#385C2318yes—
460#385C2318yes—
461#385C2314yes—
462#385C2314yes—
463#385C2314yes—
464#385C2314yes—
465#385C2318yes—
466#385C2318yes—
467#385C2318yes—
468#385C2318yes—
469#384C2314yes—
470#384C2312yes—
471#384C2318yes—
472#384C2314yes—
473#382C2312yes—
474#382C2314yes—
475#382C2312yes—
476#382C2312yes—
477#382C2312yes—
478#382C2312yes—
479#381C2314yes—
480#380C2318yes—
481#380C2314yes—
482#380C2314yes—
483#380C2314yes—
484#380C2318yes—
485C4×C4⋊C4C2314yes—
486C4×C4⋊C4C2314yes—
487C4×C4⋊C4C2318yes—
488C4×C4⋊C4C2318yes—
489C4×C4⋊C4C2314yes—
490C4×C4⋊C4C2314yes—
491C4×C4⋊C4C2318yes—
492C4×C4⋊C4C2314yes—
493C4×C4⋊C4C2314yes—
494C4×C4⋊C4C2312yes—
495C4×C4⋊C4C2314yes—
496C4×C4⋊C4C2314yes—
497C4×C4⋊C4C2312yes—
498C4×C4⋊C4C2318yes—
499C4×C4⋊C4C2318yes—
500C4×C22⋊C4C2312yes—
501C4×C22⋊C4C2312yes—
502C4×C22⋊C4C2318yes—
503C4×C22⋊C4C2318yes—
504C4×C22⋊C4C2318yes—
505C4×C22⋊C4C2318yes—
506#376C2312yes—
507C2×#95C2312yes—
508C2×#95C2312yes—
509C2×#95C2314yes—
510C2×#95C2314yes—
511C2×#95C2314yes—
512C43C2312yes—
513C2×#41—24no—
514C2×#41—24no—
515C2×#41C2×Q818yes—
516C22×Q8—28no—
517C22×Q8—24no—
518C22×Q8—24no—
519C22×Q8—24no—
520C22×Q8—44no—
521C22×Q8—48no—
522C22×Q8C2×Q818yescomplemented
523C22×Q8C2411yescharacteristic
524C22×Q8C2412yes—
525C22×Q8C2414yes—
526C22×Q8C2412yes—
527C22×Q8C2412yes—
528C22×Q8C2411yescharacteristic
529C22×Q8C2412yes—
530C22×Q8C2411yescharacteristic
531C22×Q8C2414yes—
532C22×Q8C2418yes—
533C22×Q8C2412yes—
534C22×Q8C2412yes—
535C22×Q8C2412yes—
536C22×D4C2412yes—
537C22×D4C2411yescharacteristic
538C23×C4C2412yes—
539C23×C4C2414yes—
540C23×C4C2412yes—
541C23×C4C2412yes—
542C23×C4C2412yes—
543C23×C4C2412yes—
544C23×C4C2412yes—
545C23×C4C2414yes—
546C23×C4C2414yes—
547C23×C4C2412yes—
548C23×C4C2411yescharacteristic
549C23×C4C2411yescharacteristic
550C23×C4C2411yescharacteristic
551C4⋊Q8—28no—
552C4⋊Q8—216no—
553C4⋊Q8—216no—
554C4⋊Q8—232no—
555C4⋊Q8—216no—
556C4⋊Q8—28no—
557C4⋊Q8—28no—
558C4⋊Q8—28no—
559C4⋊Q8—216no—
560C4⋊Q8—232no—
561C4⋊Q8—216no—
562C4⋊Q8—24no—
563C4⋊Q8—24no—
564C4⋊Q8—216no—
565C4⋊Q8—416no—
566C4⋊Q8—48no—
567C4⋊Q8C2×D418yes—
568C4⋊Q8C2×D418yes—
569C4⋊Q8C2×Q8116yescomplemented
570#125—216no—
571#125—216no—
572#125—28no—
573#125—28no—
574#125—216no—
575#125—232no—
576#125—232no—
577#125—232no—
578#125—216no—
579#125—28no—
580#125—216no—
581#125C2×D4116yes—
582#124C2×Q8116yescomplemented
583#123C2×Q8132yescomplemented
584C22⋊Q8—28no—
585C22⋊Q8—216no—
586C22⋊Q8—28no—
587C22⋊Q8—28no—
588C22⋊Q8—216no—
589C22⋊Q8—216no—
590C22⋊Q8—28no—
591C22⋊Q8—216no—
592C22⋊Q8—216no—
593C22⋊Q8—232no—
594C22⋊Q8—216no—
595C22⋊Q8—216no—
596C22⋊Q8—416no—
597C22⋊Q8C2×D4116yes—
598C22⋊Q8C2×D4116yes—
599C22⋊Q8C2×Q8132yescomplemented
600C4×Q8—28no—
601C4×Q8—216no—
602C4×Q8—28no—
603C4×Q8—216no—
604C4×Q8—28no—
605C4×Q8—28no—
606C4×Q8—216no—
607C4×Q8—216no—
608C4×Q8—232no—
609C4×Q8—216no—
610C4×Q8—24no—
611C4×Q8—216no—
612C4×Q8—28no—
613C4×Q8—24no—
614C4×Q8—24no—
615C4×Q8—24no—
616C4×Q8—28no—
617C4×Q8—28no—
618C4×Q8—28no—
619C4×Q8—28no—
620C4×Q8—28no—
621C4×Q8—24no—
622C4×Q8—24no—
623C4×Q8—216no—
624C4×Q8—216no—
625C4×Q8—216no—
626C4×Q8—28no—
627C4×Q8—28no—
628C4×Q8C2×D4116yes—
629C4×Q8C2×D4116yes—
630C4×D4—28no—
631C4×D4—28no—
632C4×D4—28no—
633C4×D4—28no—
634C4×D4—216no—
635C4×D4—216no—
636C4×D4—24no—
637C4×D4—24no—
638#117—24no—
639#117—28no—
640#117—24no—
641#117—232no—
642#117—216no—
643#117—28no—
644#117C2×D4116yes—
645#117C2×Q818yescomplemented
646C2×C4⋊C4—28no—
647C2×C4⋊C4—24no—
648C2×C4⋊C4—28no—
649C2×C4⋊C4—24no—
650C2×C4⋊C4—28no—
651C2×C4⋊C4—28no—
652C2×C4⋊C4—216no—
653C2×C4⋊C4—48no—
654C2×C4⋊C4C2412yes—
655C2×C4⋊C4C2411yescharacteristic
656C2×C4⋊C4C2412yes—
657C2×C4⋊C4C2412yes—
658C2×C4⋊C4C2412yes—
659C2×C4⋊C4C2414yes—
660C2×C4⋊C4C2414yes—
661C2×C4⋊C4C2412yes—
662C2×C4⋊C4C2414yes—
663C2×C4⋊C4C2411yescharacteristic
664C2×C4⋊C4C2412yes—
665C2×C4⋊C4C2412yes—
666C2×C4⋊C4C2414yes—
667C2×C4⋊C4C2414yes—
668C2×C4⋊C4C2418yes—
669C2×C4⋊C4C2414yes—
670C2×C4⋊C4C2414yes—
671C2×C4⋊C4C2411yescharacteristic
672C2×C4⋊C4C2411yescharacteristic
673C2×C4⋊C4C2412yes—
674C2×C4⋊C4C2414yes—
675C2×C4⋊C4C2414yes—
676C2×C4⋊C4C2412yes—
677C2×C4⋊C4C2412yes—
678C2×C4⋊C4C2418yes—
679C2×C4⋊C4C2412yes—
680C2×C4⋊C4C2418yes—
681C2×C4⋊C4C2412yes—
682C2×C4⋊C4C2414yes—
683C2×C4⋊C4C2412yes—
684C2×C4⋊C4C2414yes—
685C2×C4⋊C4C2414yes—
686C2×C4⋊C4C2414yes—
687C2×C4⋊C4C2412yes—
688C2×C4⋊C4C2418yes—
689C2×C4⋊C4C2418yes—
690C2×C4⋊C4C2414yes—
691C2×C4⋊C4C2418yes—
692C2×C4⋊C4C2414yes—
693C2×C4⋊C4C2414yes—
694C2×C4⋊C4C2418yes—
695C2×C4⋊C4C2418yes—
696C2×C4⋊C4C2418yes—
697C2×C4⋊C4C2414yes—
698C2×C4⋊C4C2414yes—
699C2×C4⋊C4C2418yes—
700C2×C4⋊C4C2414yes—
701C2×C4⋊C4C2418yes—
702C2×C4⋊C4C2414yes—
703C2×C4⋊C4C2414yes—
704C2×C4⋊C4C2414yes—
705C2×C4⋊C4C2418yes—
706C2×C4⋊C4C2414yes—
707C2×C4⋊C4C2412yes—
708C2×C4⋊C4C2412yes—
709C2×C4⋊C4C2412yes—
710C2×C4⋊C4C2412yes—
711C2×C4⋊C4C2414yes—
712C2×C4⋊C4C2412yes—
713C2×C4⋊C4C2418yes—
714C2×C22⋊C4C2414yes—
715C2×C22⋊C4C2412yes—
716C2×C22⋊C4C2414yes—
717C2×C22⋊C4C2412yes—
718C2×C22⋊C4C2412yes—
719C2×C22⋊C4C2414yes—
720C2×C22⋊C4C2412yes—
721C2×C22⋊C4C2418yes—
722C2×C22⋊C4C2418yes—
723C2×C22⋊C4C2418yes—
724C2×C22⋊C4C2414yes—
725C2×C22⋊C4C2412yes—
726C2×C22⋊C4C2418yes—
727C2×C42—28no—
728C2×C42—28no—
729C2×C42—216no—
730C2×C42—28no—
731C2×C42C2×D418yes—
732C2×C42C2412yes—
733C2×C42C2412yes—
734C2×C42C2418yes—
735C2×C42C2418yes—
736C2×C42C2414yes—
737C2×C42C2412yes—
738C2×C42C2412yes—
739C2×C42C2412yes—
740C2×C42C2414yes—
741C2×C42C2412yes—
742C2×C42C2414yes—
743C2×C42C2412yes—
744C2×C42C2414yes—
745C2×C42C2414yes—
746C2×C42C2412yes—
747C2×C42C2414yes—
748C2×C42C2418yes—
749C2×C42C2414yes—
750C2×C42C2418yes—
751C2×C42C2414yes—
752C2×C42C2411yescharacteristic
753C2×C42C2411yescharacteristic
754C2×C42C2411yescharacteristic
755C2×C42C2411yescharacteristic
756C2×C42C2412yes—
757#95C2418yes—
758#95C2418yes—
759#95C2414yes—
760#95C2414yes—
761#95C2418yes—
762#95C2414yes—
763#95C2414yes—
764#95C2418yes—
765#95C2418yes—
766#95C2418yes—
767#95C2414yes—
768#95C2414yes—
769#95C2414yes—
770#95C2414yes—
771#95C2418yes—
772#95C2418yes—
773#95C2418yes—
774#95C2418yes—
775#95C2414yes—
776#95C2418yes—
777#95C2418yes—
778#95C2418yes—
779#95C2418yes—
780#95C2418yes—
781#95C2418yes—
782#95C2414yes—
783#95C2414yes—
784#95C2414yes—
785#95C2414yes—
786#95C2414yes—
787#95C2418yes—
788#95C2418yes—
789C24C2512yes—
790C24C2511yescharacteristic
791#41—232no—
792C2×Q8—232no—
793C2×Q8—24no—
794C2×Q8—24no—
795C2×Q8—22no—
796C2×Q8—22no—
797C2×Q8—24no—
798C2×Q8—28no—
799C2×Q8—24no—
800C2×Q8—22no—
801C2×Q8—28no—
802C2×Q8—24no—
803C2×Q8—216no—
804C2×Q8—24no—
805C2×Q8—24no—
806C2×Q8—22no—
807C2×Q8—24no—
808C2×Q8—28no—
809C2×Q8—24no—
810C2×Q8—44no—
811C2×Q8—42no—
812C2×Q8—44no—
813C2×Q8—42no—
814C2×Q8—44no—
815C2×Q8—44no—
816C2×Q8—48no—
817C2×Q8—44no—
818C2×Q8—48no—
819C2×Q8—44no—
820C2×Q8—44no—
821C2×Q8—416no—
822C2×Q8—432no—
823C2×Q8C22×D418yes—
824C2×Q8C22×D418yes—
825C2×Q8C22×Q818yes—
826C2×Q8C22×Q818yes—
827C2×Q8C22×Q814yes—
828C2×D4—24no—
829C2×D4—24no—
830C2×D4—22no—
831C2×D4—22no—
832C2×D4C22×Q818yes—
833C2×D4C22×Q814yes—
834C22×C4—24no—
835C22×C4—24no—
836C22×C4—24no—
837C22×C4—24no—
838C22×C4—24no—
839C22×C4—24no—
840C22×C4—24no—
841C22×C4—28no—
842C22×C4—28no—
843C22×C4—24no—
844C22×C4—24no—
845C22×C4—28no—
846C22×C4—28no—
847C22×C4—24no—
848C22×C4—42no—
849C22×C4—42no—
850C22×C4—44no—
851C22×C4—42no—
852C22×C4—44no—
853C22×C4—44no—
854C22×C4—44no—
855C22×C4—44no—
856C22×C4—44no—
857C22×C4—44no—
858C22×C4—44no—
859C22×C4—42no—
860C22×C4—42no—
861C22×C4C22×D414yes—
862C22×C4C22×D414yes—
863C22×C4C22×D414yes—
864C22×C4C22×Q818yes—
865C22×C4C22×Q818yes—
866C22×C4C22×Q814yes—
867C22×C42−1+414yes—
868C22×C4C2518yes—
869C22×C4C2514yes—
870C22×C4C2512yes—
871C22×C4C2512yes—
872C22×C4C2512yes—
873C22×C4C2514yes—
874C22×C4C2514yes—
875C22×C4C2512yes—
876C22×C4C2512yes—
877C22×C4C2514yes—
878C22×C4C2511yescharacteristic
879C22×C4C2511yescharacteristic
880C22×C4C2511yescharacteristic
881C22×C4C2514yes—
882C22×C4C2511yescharacteristic
883C22×C4C2514yes—
884C22×C4C2514yes—
885C22×C4C2514yes—
886C22×C4C2512yes—
887C22×C4C2512yes—
888C22×C4C2511yescharacteristic
889C22×C4C2511yescharacteristic
890C4⋊C4—24no—
891C4⋊C4—22no—
892C4⋊C4—24no—
893C4⋊C4—28no—
894C4⋊C4—28no—
895C4⋊C4—24no—
896C4⋊C4—24no—
897C4⋊C4—24no—
898C4⋊C4—28no—
899C4⋊C4—22no—
900C4⋊C4—28no—
901C4⋊C4—28no—
902C4⋊C4—24no—
903C4⋊C4—24no—
904C4⋊C4—24no—
905C4⋊C4—28no—
906C4⋊C4—28no—
907C4⋊C4—24no—
908C4⋊C4—22no—
909C4⋊C4—22no—
910C4⋊C4—216no—
911C4⋊C4—24no—
912C4⋊C4—216no—
913C4⋊C4—24no—
914C4⋊C4—28no—
915C4⋊C4—24no—
916C4⋊C4—28no—
917C4⋊C4—28no—
918C4⋊C4—28no—
919C4⋊C4—24no—
920C4⋊C4—216no—
921C4⋊C4—28no—
922C4⋊C4—216no—
923C4⋊C4—216no—
924C4⋊C4—28no—
925C4⋊C4—28no—
926C4⋊C4—24no—
927C4⋊C4—216no—
928C4⋊C4—28no—
929C4⋊C4—28no—
930C4⋊C4—48no—
931C4⋊C4—44no—
932C4⋊C4—44no—
933C4⋊C4—48no—
934C4⋊C4—48no—
935C4⋊C4—44no—
936C4⋊C4—44no—
937C4⋊C4—48no—
938C4⋊C4—44no—
939C4⋊C4—48no—
940C4⋊C4—44no—
941C4⋊C4—48no—
942C4⋊C4C22×D4116yes—
943C4⋊C4C22×D418yes—
944C4⋊C4C22×D418yes—
945C4⋊C4C22×D418yes—
946C4⋊C4C22×D418yes—
947C4⋊C4C22×D4116yes—
948C4⋊C4C22×Q818yes—
949C4⋊C4C22×Q8132yes—
950C22⋊C4—28no—
951C22⋊C4—24no—
952C22⋊C4—24no—
953C22⋊C4—24no—
954C22⋊C4—28no—
955C22⋊C4—28no—
956C22⋊C4—24no—
957C22⋊C4—48no—
958C22⋊C4—48no—
959C22⋊C4—48no—
960C22⋊C4C22×D4116yes—
961C22⋊C4C22×Q818yes—
962C22⋊C4C22×Q8132yes—
963C42—24no—
964C42—24no—
965C42—24no—
966C42—28no—
967C42—24no—
968C42—24no—
969C42—28no—
970C42—24no—
971C42—24no—
972C42—28no—
973C42—28no—
974C42—216no—
975C42—216no—
976C42—28no—
977C42—24no—
978C42—44no—
979C42—48no—
980C42—44no—
981C42—48no—
982C42C22×D414yes—
983C42C22×D4116yes—
984C42C22×D414yes—
985C42C22×D414yes—
986C42C22×D414yes—
987C42C22×Q818yes—
988C23—22no—
989C23—22no—
990C23—22no—
991C23—22no—
992C23—24no—
993C23—24no—
994C23C23×D412yes—
995C23C23×Q814yes—
996C23C23×Q812yes—
997C23C2×2−1+412yes—
998C23C2611yescharacteristic
999Q8—28no—
1000Q8—216no—
1001Q8—216no—
1002Q8—28no—
1003Q8—48no—
1004Q8—48no—
1005Q8—48no—
1006Q8—416no—
1007Q8—48no—
1008Q8—44no—
1009Q8—816no—
1010Q8—84no—
1011Q8—88no—
1012D4—216no—
1013D4—28no—
1014C2×C4—22no—
1015C2×C4—24no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—24no—
1019C2×C4—24no—
1020C2×C4—22no—
1021C2×C4—24no—
1022C2×C4—24no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—24no—
1026C2×C4—22no—
1027C2×C4—24no—
1028C2×C4—24no—
1029C2×C4—22no—
1030C2×C4—216no—
1031C2×C4—216no—
1032C2×C4—22no—
1033C2×C4—24no—
1034C2×C4—24no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—22no—
1039C2×C4—24no—
1040C2×C4—24no—
1041C2×C4—28no—
1042C2×C4—24no—
1043C2×C4—28no—
1044C2×C4—24no—
1045C2×C4—28no—
1046C2×C4—24no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—24no—
1050C2×C4—28no—
1051C2×C4—24no—
1052C2×C4—24no—
1053C2×C4—24no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—24no—
1057C2×C4—22no—
1058C2×C4—22no—
1059C2×C4—44no—
1060C2×C4—44no—
1061C2×C4—416no—
1062C2×C4—48no—
1063C2×C4—48no—
1064C2×C4—84no—
1065C2×C4—88no—
1066C2×C4—84no—
1067C2×C4—84no—
1068C2×C4—88no—
1069C2×C4D4×Q8116yes—
1070C2×C4C23×D412yes—
1071C2×C4C23×D412yes—
1072C2×C4C23×D418yes—
1073C2×C4C23×D418yes—
1074C2×C4C23×D412yes—
1075C2×C4C23×D412yes—
1076C2×C4C23×D412yes—
1077C2×C4C23×D412yes—
1078C2×C4C23×Q818yes—
1079C2×C4C23×Q818yes—
1080C2×C4C23×Q814yes—
1081C2×C4C23×Q812yes—
1082C2×C4C23×Q812yes—
1083C2×C4C2×2−1+412yes—
1084C2×C4C2×2−1+412yes—
1085C2×C4#58514yes—
1086C22—24no—
1087C22—22no—
1088C22—22no—
1089C22—24no—
1090C22—28no—
1091C22—24no—
1092C22—42no—
1093C22—42no—
1094C22—44no—
1095C22C2×D4×Q814yes—
1096C22C24×D411yescharacteristic
1097C22C24×Q811yescharacteristic
1098C22C22×2−1+411yescharacteristic
1099C22C2×#58512yes—
1100C222−1+612yes—
1101C4—28no—
1102C4—22no—
1103C4—24no—
1104C4—22no—
1105C4—28no—
1106C4—22no—
1107C4—22no—
1108C4—28no—
1109C4—24no—
1110C4—28no—
1111C4—42no—
1112C4—42no—
1113C4—44no—
1114C4—44no—
1115C4—42no—
1116C4—42no—
1117C4—42no—
1118C4—44no—
1119C4—44no—
1120C4—48no—
1121C4C2×D4×Q814yes—
1122C4C2×D4×Q814yes—
1123C2—24no—
1124C2—44no—
1125C2C22×D4×Q811yescharacteristic
1126C2#6281111yescharacteristic
1127C2#6285911yescharacteristic
1128C2#6293212yes—
1129C2#6300412yes—
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. C2×#3502C2semidirect
3. #59833C2semidirect
4. #59667C2semidirect
5. #59149C2semidirect
6. #45389C2semidirect
7. #45389C2semidirect
8. #45139C2semidirect
9. #44934C2semidirect
10. #44449C2semidirect
11. #43891C2semidirect
12. #39597C2semidirect
13. #39591C2semidirect
14. #39591C2semidirect
15. #36545C2semidirect
16. #35662C2semidirect
17. #35566C2semidirect
20. #34953C2semidirect
21. C2×#2581C2semidirect
23. #34215C2semidirect
206. #536Q8semidirect
522. C22×Q8C2×Q8semidirect
569. C4⋊Q8C2×Q8semidirect
582. #124C2×Q8semidirect
583. #123C2×Q8semidirect
599. C22⋊Q8C2×Q8semidirect
645. #117C2×Q8semidirect

Maximal subgroups

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

subgroupindex
C2×#35022
C2×Q8×#412
#598332
#596672
#591492
#453892
#451392
#449342
#444492
#438912
#395972
#395912
#365452
#356622
#355662
#353342
#352572
#349532
C2×#25812
#342682
#342152
C4×#5362