Finite Group Databasebeta

← #7987202

Subgroups — #7987202

Order 512.

4559 conjugacy classes of subgroups.

The subgroup lattice has 1062 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59870C211yesmaximal, characteristic, complemented
2#59443C212yesmaximal, complemented
3#59436C212yesmaximal
4#59262C212yesmaximal, complemented
5#51488C218yesmaximal, complemented
6#45611C214yesmaximal, complemented
7#45083C214yesmaximal
8#45080C214yesmaximal, complemented
9#42610C214yesmaximal, complemented
10#42527C214yesmaximal, complemented
11#39855C214yesmaximal, complemented
12#39753C212yesmaximal, complemented
13#39642C212yesmaximal, complemented
14#39617C212yesmaximal
15#38933C212yesmaximal, complemented
16#36593C211yesmaximal, characteristic, complemented
17Q8×C4⋊Q8C211yesmaximal, characteristic, complemented
18#36194C211yesmaximal, characteristic
19#36134C212yesmaximal
20#36133C212yesmaximal, complemented
21#35239C212yesmaximal, complemented
22#35206C212yesmaximal
23#34951C211yesmaximal, characteristic, complemented
24#34945C211yesmaximal, characteristic
25#34491C212yesmaximal, complemented
26C4×#554C211yesmaximal, characteristic
27C2×Q82C2212yes—
28C2×#557C2212yes—
29C2×#554C2211yescharacteristic
30C2×#533C2214yes—
31#2868C2212yes—
32#2868C2211yescharacteristic
33#2868C2212yes—
34#2857C2212yes—
35#2857C2214yes—
36#2855C2214yes—
37#2851C2214yes—
38#2833C2218yes—
39#2805C2214yes—
40#2791C2218yes—
41#2776C2218yes—
42#2776C2218yes—
43#2769C2218yes—
44#2766C2218yes—
45#2745C2218yes—
46#2738C2218yes—
47#2738C2218yes—
48#2719C2218yes—
49#2713C2218yes—
50#2713C2218yes—
51#2713C2218yes—
52#2690C2218yes—
53#2690C2218yes—
54#2677C2218yes—
55#2677C2218yes—
56#2666C2218yes—
57#2660C2214yes—
58#2652C2218yes—
59#2647C2214yes—
60#2634C2218yes—
61#2611C2218yes—
62#2611C2218yes—
63#2599C2218yes—
64#2585C2214yes—
65#2582C2211yescharacteristic
66#2581C2214yes—
67#2573C2214yes—
68#2571C2212yes—
69#2571C2211yescharacteristic
70#2571C2212yes—
71#2570C2214yes—
72#2570C2214yes—
73#2568C2211yescharacteristic
74#2568C2211yescharacteristic
75#2568C2212yes—
76#2567C2214yes—
77#2567C2212yes—
78#2567C2212yes—
79#2565C2214yes—
80#2565C2214yes—
81#2563C2212yes—
82#2552C2212yes—
83#2552C2214yes—
84#2552C2214yes—
85#2552C2214yes—
86#2552C2214yes—
87#2552C2212yes—
88#2552C2211yescharacteristic
89#2551C2214yes—
90#2551C2212yes—
91#2551C2214yes—
92#2551C2212yes—
93#2550C2214yes—
94#2547C2211yescharacteristic
95#2546C2214yes—
96#2546C2211yescharacteristic
97#2546C2212yes—
98#2542C2214yes—
99#2538C2211yescharacteristic
100#2538C2212yes—
101#2533C2218yes—
102#2515C2218yes—
103#2514C2214yes—
104#2514C2212yes—
105#2514C2214yes—
106#2511C2214yes—
107#2511C2214yes—
108#2511C2214yes—
109#2511C2212yes—
110#2509C2214yes—
111#2509C2212yes—
112#2506C2214yes—
113#2506C2214yes—
114#2506C2214yes—
115#2497C2214yes—
116#2495C2214yes—
117#2495C2214yes—
118#2494C2214yes—
119#2494C2212yes—
120#2492C2214yes—
121#2489C2214yes—
122#2462C2218yes—
123#2453C2212yes—
124#2451C2214yes—
125#2447C2212yes—
126#2447C2214yes—
127#2446C2214yes—
128#2446C2212yes—
129#2442C2214yes—
130#2441C2218yes—
131#2440C2214yes—
132#2440C2214yes—
133#2439C2214yes—
134#2438C2218yes—
135#2438C2218yes—
136#2429C2218yes—
137#2423C2214yes—
138#2423C2214yes—
139#2423C2214yes—
140#2423C2214yes—
141#2421C2212yes—
142#2402C2214yes—
143#2401C2214yes—
144#2381C2218yes—
145#2370C2212yes—
146#2369C2212yes—
147#2369C2211yescharacteristic
148#2368C2214yes—
149#2365C2212yes—
150#2365C2214yes—
151#2365C2214yes—
152#2360C2212yes—
153#2356C2214yes—
154#2356C2214yes—
155#2356C2214yes—
156#2355C2212yes—
157#2355C2212yes—
158#2355C2211yescharacteristic
159#2354C2212yes—
160#2354C2214yes—
161Q8×C4⋊C4C2212yes—
162Q8×C4⋊C4C2212yes—
163Q8×C4⋊C4C2212yes—
164Q8×C4⋊C4C2212yes—
165Q8×C4⋊C4C2212yes—
166#2349C2212yes—
167D4×C4⋊C4C2211yescharacteristic
168#2345C2212yes—
169#2344C2214yes—
170#2331C2214yes—
171#2331C2214yes—
172#2330C2214yes—
173#2327C2218yes—
174#2326C2214yes—
175#2320C2214yes—
176#2320C2214yes—
177C4×C4⋊Q8C2212yes—
178C4×C4⋊Q8C2212yes—
179C4×C4⋊Q8C2212yes—
180C4×C4⋊Q8C2211yescharacteristic
181C4×C4⋊Q8C2211yescharacteristic
182C4×C4⋊Q8C2211yescharacteristic
183C4×#125C2212yes—
184C4×#125C2212yes—
185C4×#124C2212yes—
186C4×C22⋊Q8C2212yes—
187C4×C22⋊Q8C2212yes—
188C4×C22⋊Q8C2214yes—
189#2295C2212yes—
190#2295C2212yes—
191#2295C2212yes—
192#2285C2212yes—
193#2283C2212yes—
194C42×Q8C2211yescharacteristic
195C42×Q8C2211yescharacteristic
196C42×D4C2212yes—
197C42×D4C2211yescharacteristic
198C2×C4×C4⋊C4C2212yes—
199Q82—216no—
200#557—48no—
201#554—28no—
202#533—416no—
203C2×C4⋊Q8C2311yescharacteristic
204C2×C4⋊Q8C2312yes—
205C2×C4⋊Q8C2311yescharacteristic
206C2×C4⋊Q8C2311yescharacteristic
207C2×C4⋊Q8C2312yes—
208C2×C4⋊Q8C2314yes—
209C2×C4⋊Q8C2318yes—
210C2×C4⋊Q8C2314yes—
211C2×C4⋊Q8C2314yes—
212C2×C4⋊Q8C2314yes—
213C2×C4⋊Q8C2312yes—
214C2×C4⋊Q8C2314yes—
215C2×C4⋊Q8C2314yes—
216C2×C4⋊Q8C2312yes—
217C2×#125C2312yes—
218C2×#125C2312yes—
219C2×#125C2314yes—
220C2×#125C2318yes—
221C2×#125C2318yes—
222C2×#125C2318yes—
223C2×#124C2312yes—
224C2×C22⋊Q8C2312yes—
225C2×C22⋊Q8C2314yes—
226C2×C22⋊Q8C2312yes—
227C2×C22⋊Q8C2314yes—
228C2×C22⋊Q8C2318yes—
229C2×C22⋊Q8C2318yes—
230C2×C4×Q8C2311yescharacteristic
231C2×C4×Q8C2312yes—
232C2×C4×Q8C2314yes—
233C2×C4×Q8C2312yes—
234C2×C4×Q8C2311yescharacteristic
235C2×C4×Q8C2314yes—
236C2×C4×Q8C2311yescharacteristic
237C2×C4×Q8C2314yes—
238C2×C4×Q8C2311yescharacteristic
239C2×C4×Q8C2311yescharacteristic
240C2×C4×Q8C2312yes—
241C2×C4×Q8C2314yes—
242C2×C4×Q8C2314yes—
243C2×C4×Q8C2318yes—
244C2×C4×Q8C2311yescharacteristic
245C2×C4×D4C2311yescharacteristic
246C2×C4×D4C2312yes—
247C2×C4×D4C2312yes—
248C2×C4×D4C2311yescharacteristic
249C2×C4×D4C2311yescharacteristic
250C2×#117C2318yes—
251C2×#117C2314yes—
252C22×C4⋊C4C2312yes—
253C22×C4⋊C4C2312yes—
254C22×C42C2312yes—
255C22×C42C2314yes—
256#401C2314yes—
257#401C2318yes—
258#400C2314yes—
259#400C2314yes—
260#400C2318yes—
261#400C2318yes—
262#400C2318yes—
263#400C2314yes—
264#400C2318yes—
265#400C2318yes—
266#400C2314yes—
267#400C2318yes—
268#400C2318yes—
269#400C2318yes—
270#400C2314yes—
271#400C2314yes—
272#400C2318yes—
273#400C2318yes—
274#400C2314yes—
275#399C2318yes—
276#399C2318yes—
277#398C2318yes—
278#398C2318yes—
279#398C2318yes—
280#398C2318yes—
281#398C2318yes—
282#398C2318yes—
283#398C2318yes—
284#398C2314yes—
285#398C2314yes—
286#398C2314yes—
287#398C2314yes—
288#398C2318yes—
289#398C2318yes—
290#398C2318yes—
291#398C2318yes—
292#398C2318yes—
293#397C2314yes—
294#397C2318yes—
295#397C2314yes—
296#397C2318yes—
297#397C2314yes—
298#396C2314yes—
299#396C2318yes—
300#395C2318yes—
301#395C2318yes—
302#395C2318yes—
303#395C2318yes—
304#395C2318yes—
305#395C2318yes—
306#393C2318yes—
307#391C2312yes—
308#391C2314yes—
309#391C2312yes—
310#391C2312yes—
311#391C2312yes—
312#391C2312yes—
313#391C2314yes—
314#391C2312yes—
315#391C2312yes—
316#391C2314yes—
317#391C2314yes—
318#391C2312yes—
319#391C2314yes—
320#391C2314yes—
321#391C2312yes—
322#391C2312yes—
323#391C2312yes—
324#391C2312yes—
325#391C2318yes—
326#391C2312yes—
327#391C2318yes—
328#391C2318yes—
329#391C2318yes—
330#391C2312yes—
331#391C2314yes—
332#390C2314yes—
333#390C2312yes—
334#389C2312yes—
335#389C2312yes—
336#389C2312yes—
337#389C2312yes—
338#389C2314yes—
339#389C2314yes—
340#389C2312yes—
341#389C2314yes—
342#389C2312yes—
343#389C2312yes—
344#389C2314yes—
345#389C2314yes—
346#389C2312yes—
347#389C2312yes—
348#389C2314yes—
349#389C2312yes—
350#389C2314yes—
351#389C2314yes—
352#389C2318yes—
353#389C2318yes—
354#389C2314yes—
355#389C2314yes—
356#389C2314yes—
357#389C2314yes—
358#389C2314yes—
359#389C2312yes—
360#389C2314yes—
361#389C2312yes—
362#389C2314yes—
363#389C2312yes—
364#389C2318yes—
365#389C2318yes—
366#389C2312yes—
367#389C2312yes—
368#389C2314yes—
369#389C2312yes—
370#389C2318yes—
371#389C2318yes—
372#389C2318yes—
373#389C2314yes—
374#389C2312yes—
375#389C2312yes—
376#388C2314yes—
377#388C2314yes—
378#388C2318yes—
379#388C2318yes—
380#388C2318yes—
381#388C2318yes—
382#388C2318yes—
383#387C2314yes—
384#387C2314yes—
385#387C2314yes—
386#387C2314yes—
387#387C2318yes—
388#387C2318yes—
389#387C2318yes—
390#387C2318yes—
391#387C2318yes—
392#387C2318yes—
393#387C2318yes—
394#387C2314yes—
395#387C2314yes—
396#387C2314yes—
397#387C2318yes—
398#387C2318yes—
399#387C2318yes—
400#387C2314yes—
401#387C2318yes—
402#387C2318yes—
403#387C2314yes—
404#387C2314yes—
405#387C2318yes—
406#387C2318yes—
407#387C2314yes—
408#387C2314yes—
409#387C2314yes—
410#387C2318yes—
411#387C2318yes—
412#387C2318yes—
413#387C2318yes—
414#387C2318yes—
415#387C2318yes—
416#387C2318yes—
417#387C2314yes—
418#385C2314yes—
419#385C2318yes—
420#385C2318yes—
421#385C2318yes—
422#385C2314yes—
423#385C2314yes—
424#385C2314yes—
425#384C2311yescharacteristic
426#384C2312yes—
427#384C2311yescharacteristic
428#384C2311yescharacteristic
429#384C2312yes—
430#384C2314yes—
431#384C2314yes—
432#384C2314yes—
433#384C2312yes—
434#384C2314yes—
435#384C2314yes—
436#384C2314yes—
437#384C2312yes—
438#384C2314yes—
439#384C2314yes—
440#384C2312yes—
441#383C2314yes—
442#383C2318yes—
443#383C2318yes—
444#383C2318yes—
445#382C2312yes—
446#382C2312yes—
447#382C2314yes—
448#382C2312yes—
449#382C2312yes—
450#382C2314yes—
451#382C2312yes—
452#382C2314yes—
453#382C2314yes—
454#382C2318yes—
455#381C2314yes—
456#381C2318yes—
457#380C2314yes—
458#380C2314yes—
459#380C2312yes—
460#380C2314yes—
461#380C2312yes—
462#380C2312yes—
463#380C2314yes—
464#380C2312yes—
465#380C2314yes—
466#380C2318yes—
467C4×C4⋊C4C2311yescharacteristic
468C4×C4⋊C4C2311yescharacteristic
469C4×C4⋊C4C2312yes—
470C4×C4⋊C4C2312yes—
471C4×C4⋊C4C2314yes—
472C4×C4⋊C4C2314yes—
473C4×C4⋊C4C2314yes—
474C4×C4⋊C4C2314yes—
475C4×C4⋊C4C2314yes—
476C4×C4⋊C4C2312yes—
477C4×C4⋊C4C2312yes—
478C4×C4⋊C4C2312yes—
479C4×C4⋊C4C2314yes—
480C4×C4⋊C4C2314yes—
481C4×C4⋊C4C2314yes—
482C4×C4⋊C4C2312yes—
483C4×C4⋊C4C2314yes—
484C4×C4⋊C4C2312yes—
485C4×C4⋊C4C2311yescharacteristic
486C4×C4⋊C4C2314yes—
487C4×C4⋊C4C2314yes—
488C4×C4⋊C4C2311yescharacteristic
489C4×C4⋊C4C2311yescharacteristic
490C4×C4⋊C4C2312yes—
491C4×C4⋊C4C2312yes—
492C4×C4⋊C4C2314yes—
493C4×C4⋊C4C2312yes—
494C4×C4⋊C4C2312yes—
495C4×C4⋊C4C2314yes—
496C4×C4⋊C4C2312yes—
497C4×C4⋊C4C2314yes—
498C4×C4⋊C4C2311yescharacteristic
499C4×C4⋊C4C2311yescharacteristic
500C4×C4⋊C4C2314yes—
501C4×C4⋊C4C2314yes—
502C4×C4⋊C4C2312yes—
503C4×C4⋊C4C2312yes—
504C4×C4⋊C4C2312yes—
505C4×C4⋊C4C2312yes—
506C4×C4⋊C4C2311yescharacteristic
507C4×C4⋊C4C2311yescharacteristic
508C4×C22⋊C4C2312yes—
509C4×C22⋊C4C2314yes—
510C4×C22⋊C4C2312yes—
511C4×C22⋊C4C2314yes—
512C4×C22⋊C4C2314yes—
513C4×C22⋊C4C2314yes—
514C4×C22⋊C4C2312yes—
515C4×C22⋊C4C2314yes—
516#376C2314yes—
517#376C2314yes—
518#376C2318yes—
519C2×#95C2314yes—
520C43C2312yes—
521C43C2312yes—
522C43C2311yescharacteristic
523C22×Q8C2412yes—
524C22×Q8C2412yes—
525C22×Q8C2411yescharacteristic
526C22×Q8C2411yescharacteristic
527C22×Q8C2418yes—
528C22×Q8C2412yes—
529C22×Q8C2414yes—
530C22×D4C2411yescharacteristic
531C23×C4C2412yes—
532C23×C4C2412yes—
533C23×C4C2414yes—
534C23×C4C2412yes—
535C23×C4C2414yes—
536C4⋊Q8—28no—
537C4⋊Q8—216no—
538C4⋊Q8—232no—
539C4⋊Q8—24no—
540C4⋊Q8—216no—
541C4⋊Q8—28no—
542C4⋊Q8—24no—
543C4⋊Q8—24no—
544C4⋊Q8—48no—
545C4⋊Q8—48no—
546C4⋊Q8—44no—
547C4⋊Q8—82no—
548C4⋊Q8—84no—
549C4⋊Q8—84no—
550#125—28no—
551#125—28no—
552#125—48no—
553#125—416no—
554#125—416no—
555#125—88no—
556#124—28no—
557C22⋊Q8—28no—
558C22⋊Q8—28no—
559C22⋊Q8—216no—
560C22⋊Q8—416no—
561C22⋊Q8—48no—
562C22⋊Q8—88no—
563C4×Q8—216no—
564C4×Q8—216no—
565C4×Q8—24no—
566C4×Q8—24no—
567C4×Q8—216no—
568C4×Q8—28no—
569C4×Q8—24no—
570C4×Q8—24no—
571C4×Q8—24no—
572C4×Q8—28no—
573C4×Q8—44no—
574C4×Q8—48no—
575C4×Q8—416no—
576C4×Q8—48no—
577C4×Q8#4118yes—
578C4×D4—28no—
579C4×D4—24no—
580C4×D4—28no—
581C4×D4—24no—
582C4×D4—24no—
583#117—416no—
584#117—84no—
585C2×C4⋊C4—28no—
586C2×C4⋊C4—28no—
587C2×C4⋊C4C2414yes—
588C2×C4⋊C4C2412yes—
589C2×C4⋊C4C2412yes—
590C2×C4⋊C4C2414yes—
591C2×C4⋊C4C2414yes—
592C2×C4⋊C4C2411yescharacteristic
593C2×C4⋊C4C2412yes—
594C2×C4⋊C4C2411yescharacteristic
595C2×C4⋊C4C2412yes—
596C2×C4⋊C4C2411yescharacteristic
597C2×C4⋊C4C2414yes—
598C2×C4⋊C4C2414yes—
599C2×C4⋊C4C2412yes—
600C2×C4⋊C4C2418yes—
601C2×C4⋊C4C2414yes—
602C2×C4⋊C4C2411yescharacteristic
603C2×C4⋊C4C2412yes—
604C2×C4⋊C4C2414yes—
605C2×C4⋊C4C2414yes—
606C2×C4⋊C4C2412yes—
607C2×C4⋊C4C2418yes—
608C2×C4⋊C4C2418yes—
609C2×C4⋊C4C2414yes—
610C2×C4⋊C4C2411yescharacteristic
611C2×C4⋊C4C2412yes—
612C2×C4⋊C4C2411yescharacteristic
613C2×C4⋊C4C2411yescharacteristic
614C2×C4⋊C4C2412yes—
615C2×C4⋊C4C2412yes—
616C2×C4⋊C4C2412yes—
617C2×C4⋊C4C2412yes—
618C2×C4⋊C4C2414yes—
619C2×C4⋊C4C2414yes—
620C2×C4⋊C4C2412yes—
621C2×C4⋊C4C2414yes—
622C2×C4⋊C4C2414yes—
623C2×C4⋊C4C2412yes—
624C2×C4⋊C4C2412yes—
625C2×C4⋊C4C2412yes—
626C2×C4⋊C4C2412yes—
627C2×C4⋊C4C2412yes—
628C2×C4⋊C4C2418yes—
629C2×C4⋊C4C2414yes—
630C2×C4⋊C4C2412yes—
631C2×C4⋊C4C2418yes—
632C2×C4⋊C4C2418yes—
633C2×C4⋊C4C2414yes—
634C2×C4⋊C4C2418yes—
635C2×C4⋊C4C2414yes—
636C2×C4⋊C4C2418yes—
637C2×C4⋊C4C2418yes—
638C2×C4⋊C4C2418yes—
639C2×C4⋊C4C2414yes—
640C2×C4⋊C4C2414yes—
641C2×C4⋊C4C2414yes—
642C2×C4⋊C4C2414yes—
643C2×C4⋊C4C2418yes—
644C2×C4⋊C4C2418yes—
645C2×C4⋊C4C2414yes—
646C2×C4⋊C4C2412yes—
647C2×C4⋊C4C2411yescharacteristic
648C2×C4⋊C4C2412yes—
649C2×C4⋊C4C2411yescharacteristic
650C2×C22⋊C4C2414yes—
651C2×C22⋊C4C2412yes—
652C2×C22⋊C4C2414yes—
653C2×C22⋊C4C2412yes—
654C2×C22⋊C4C2412yes—
655C2×C22⋊C4C2414yes—
656C2×C22⋊C4C2414yes—
657C2×C22⋊C4C2414yes—
658C2×C22⋊C4C2418yes—
659C2×C22⋊C4C2418yes—
660C2×C22⋊C4C2414yes—
661C2×C42—28no—
662C2×C42—48no—
663C2×C42C2418yes—
664C2×C42C2412yes—
665C2×C42C2411yescharacteristic
666C2×C42C2414yes—
667C2×C42C2411yescharacteristic
668C2×C42C2412yes—
669C2×C42C2414yes—
670C2×C42C2418yes—
671C2×C42C2411yescharacteristic
672C2×C42C2412yes—
673C2×C42C2412yes—
674C2×C42C2412yes—
675C2×C42C2412yes—
676C2×C42C2414yes—
677C2×C42C2412yes—
678C2×C42C2412yes—
679C2×C42C2412yes—
680C2×C42C2412yes—
681C2×C42C2412yes—
682C2×C42C2412yes—
683C2×C42C2418yes—
684C2×C42C2418yes—
685C2×C42C2414yes—
686C2×C42C2414yes—
687C2×C42C2411yescharacteristic
688C2×C42C2412yes—
689C2×C42C2412yes—
690C2×C42C2412yes—
691C2×C42C2411yescharacteristic
692C2×C42C2411yescharacteristic
693C2×C42C2411yescharacteristic
694#95C2412yes—
695#95C2414yes—
696#95C2414yes—
697#95C2414yes—
698#95C2414yes—
699#95C2414yes—
700#95C2414yes—
701#95C2414yes—
702#95C2414yes—
703#95C2414yes—
704#95C2414yes—
705#95C2418yes—
706#95C2414yes—
707#95C2414yes—
708#95C2414yes—
709#95C2414yes—
710#95C2414yes—
711#95C2412yes—
712#95C2412yes—
713#95C2414yes—
714#95C2412yes—
715#95C2414yes—
716#95C2414yes—
717#95C2414yes—
718#95C2414yes—
719#95C2414yes—
720#95C2412yes—
721#95C2412yes—
722#95C2412yes—
723#95C2412yes—
724#95C2412yes—
725#95C2418yes—
726#95C2418yes—
727#95C2418yes—
728#95C2414yes—
729#95C2414yes—
730#95C2418yes—
731#95C2418yes—
732#95C2414yes—
733#95C2418yes—
734#95C2414yes—
735#95C2418yes—
736#95C2418yes—
737#95C2414yes—
738#95C2414yes—
739#95C2414yes—
740#95C2414yes—
741#95C2418yes—
742#95C2414yes—
743#95C2414yes—
744#95C2414yes—
745#95C2418yes—
746#95C2418yes—
747#95C2418yes—
748C24C2512yes—
749C2×Q8—24no—
750C2×Q8—24no—
751C2×Q8—28no—
752C2×Q8—216no—
753C2×Q8—24no—
754C2×Q8—22no—
755C2×Q8—22no—
756C2×Q8—22no—
757C2×Q8—22no—
758C2×Q8—24no—
759C2×Q8—24no—
760C2×Q8—24no—
761C2×Q8—24no—
762C2×Q8—48no—
763C2×Q8—42no—
764C2×Q8—44no—
765C2×Q8—48no—
766C2×Q8—44no—
767C2×Q8—42no—
768C2×Q8C2×#4114yes—
769C2×Q8H(5,𝔽2)14yes—
770C2×D4—22no—
771C2×D4—22no—
772C2×D42−1+414yes—
773C22×C4—28no—
774C22×C4—24no—
775C22×C4—24no—
776C22×C4—24no—
777C22×C4—24no—
778C22×C4—24no—
779C22×C4—24no—
780C22×C4—28no—
781C22×C4—24no—
782C22×C4—24no—
783C22×C4—28no—
784C22×C4—44no—
785C22×C4—42no—
786C22×C4—44no—
787C22×C4—44no—
788C22×C4C2514yes—
789C22×C4C2512yes—
790C22×C4C2512yes—
791C22×C4C2514yes—
792C22×C4C2512yes—
793C22×C4C2512yes—
794C22×C4C2512yes—
795C22×C4C2512yes—
796C22×C4C2514yes—
797C22×C4C2514yes—
798C22×C4C2512yes—
799C22×C4C2511yescharacteristic
800C22×C4C2518yes—
801C22×C4C2514yes—
802C22×C4C2514yes—
803C22×C4C2512yes—
804C22×C4C2511yescharacteristic
805C22×C4C2512yes—
806C22×C4C2512yes—
807C22×C4C2511yescharacteristic
808C22×C4C2512yes—
809C22×C4C2511yescharacteristic
810C22×C4C2511yescharacteristic
811C22×C4C2511yescharacteristic
812C22×C4C2511yescharacteristic
813C4⋊C4—28no—
814C4⋊C4—24no—
815C4⋊C4—22no—
816C4⋊C4—24no—
817C4⋊C4—28no—
818C4⋊C4—216no—
819C4⋊C4—216no—
820C4⋊C4—28no—
821C4⋊C4—28no—
822C4⋊C4—24no—
823C4⋊C4—28no—
824C4⋊C4—28no—
825C4⋊C4—216no—
826C4⋊C4—28no—
827C4⋊C4—24no—
828C4⋊C4—22no—
829C4⋊C4—28no—
830C4⋊C4—24no—
831C4⋊C4—28no—
832C4⋊C4—28no—
833C4⋊C4—24no—
834C4⋊C4—22no—
835C4⋊C4—22no—
836C4⋊C4—24no—
837C4⋊C4—24no—
838C4⋊C4—24no—
839C4⋊C4—24no—
840C4⋊C4—24no—
841C4⋊C4—22no—
842C4⋊C4—22no—
843C4⋊C4—22no—
844C4⋊C4—24no—
845C4⋊C4—28no—
846C4⋊C4—28no—
847C4⋊C4—28no—
848C4⋊C4—24no—
849C4⋊C4—24no—
850C4⋊C4—24no—
851C4⋊C4—24no—
852C4⋊C4—24no—
853C4⋊C4—48no—
854C4⋊C4—42no—
855C4⋊C4—44no—
856C4⋊C4—42no—
857C4⋊C4—48no—
858C4⋊C4—48no—
859C4⋊C4—44no—
860C4⋊C4—48no—
861C4⋊C4—44no—
862C4⋊C4—48no—
863C4⋊C4—48no—
864C4⋊C4—48no—
865C4⋊C4—44no—
866C4⋊C4—44no—
867C4⋊C4—44no—
868C4⋊C4—44no—
869C4⋊C4—48no—
870C4⋊C4—48no—
871C4⋊C4—44no—
872C4⋊C4—42no—
873C4⋊C4C2×#4114yes—
874C4⋊C4C2×#4118yes—
875C4⋊C42−1+414yes—
876C22⋊C4—24no—
877C22⋊C4—28no—
878C22⋊C4—28no—
879C22⋊C4—28no—
880C22⋊C4—24no—
881C22⋊C4—28no—
882C22⋊C4—28no—
883C22⋊C4—24no—
884C22⋊C4—48no—
885C22⋊C4—48no—
886C22⋊C4—44no—
887C42—216no—
888C42—28no—
889C42—24no—
890C42—28no—
891C42—216no—
892C42—24no—
893C42—22no—
894C42—24no—
895C42—24no—
896C42—24no—
897C42—24no—
898C42—22no—
899C42—24no—
900C42—22no—
901C42—24no—
902C42—24no—
903C42—24no—
904C42—28no—
905C42—24no—
906C42—24no—
907C42—44no—
908C42—44no—
909C42—48no—
910C42—48no—
911C42—41no—
912C42—42no—
913C42—42no—
914C42C2×#4118yes—
915C42C2×#4114yes—
916C422−1+414yes—
917C422−1+414yes—
918C23—22no—
919C23—22no—
920C23—22no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23C2×2−1+414yes—
925C23C2611yescharacteristic
926Q8—28no—
927Q8—28no—
928Q8—48no—
929Q8—48no—
930Q8—816no—
931Q8—84no—
932Q8—88no—
933D4—28no—
934C2×C4—21no—
935C2×C4—22no—
936C2×C4—22no—
937C2×C4—21no—
938C2×C4—22no—
939C2×C4—22no—
940C2×C4—22no—
941C2×C4—22no—
942C2×C4—22no—
943C2×C4—21no—
944C2×C4—21no—
945C2×C4—21no—
946C2×C4—21no—
947C2×C4—22no—
948C2×C4—24no—
949C2×C4—28no—
950C2×C4—24no—
951C2×C4—22no—
952C2×C4—24no—
953C2×C4—24no—
954C2×C4—24no—
955C2×C4—28no—
956C2×C4—22no—
957C2×C4—21no—
958C2×C4—22no—
959C2×C4—24no—
960C2×C4—24no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—22no—
964C2×C4—21no—
965C2×C4—22no—
966C2×C4—22no—
967C2×C4—22no—
968C2×C4—21no—
969C2×C4—22no—
970C2×C4—22no—
971C2×C4—24no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—24no—
976C2×C4—24no—
977C2×C4—22no—
978C2×C4—24no—
979C2×C4—22no—
980C2×C4—24no—
981C2×C4—24no—
982C2×C4—22no—
983C2×C4—24no—
984C2×C4—24no—
985C2×C4—22no—
986C2×C4—24no—
987C2×C4—22no—
988C2×C4—28no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—24no—
992C2×C4—24no—
993C2×C4—416no—
994C2×C4—48no—
995C2×C4—48no—
996C2×C4—48no—
997C2×C4—88no—
998C2×C4C22×#4114yes—
999C2×C4C22×#4112yes—
1000C2×C4C22×#4114yes—
1001C2×C4C22×#4112yes—
1002C2×C4C22×#4112yes—
1003C2×C4C2×H(5,𝔽2)14yes—
1004C2×C4C2×H(5,𝔽2)12yes—
1005C2×C4C2×2−1+412yes—
1006C2×C4C2×2−1+414yes—
1007C2×C4C2×2−1+412yes—
1008C2×C4C2×2−1+412yes—
1009C2×C4C2×2−1+412yes—
1010C2×C4C2×2−1+412yes—
1011C2×C4C2×2−1+412yes—
1012C2×C4C2×2−1+412yes—
1013C2×C4C2×2−1+412yes—
1014C22—24no—
1015C22—24no—
1016C22—24no—
1017C22—42no—
1018C22—42no—
1019C22—42no—
1020C22—42no—
1021C22C23×#4111yescharacteristic
1022C22C22×H(5,𝔽2)11yescharacteristic
1023C22C22×2−1+411yescharacteristic
1024C22C22×2−1+411yescharacteristic
1025C22C22×2−1+411yescharacteristic
1026C22C22×2−1+411yescharacteristic
1027C22H(7,𝔽2)11yescharacteristic
1028C4—24no—
1029C4—22no—
1030C4—24no—
1031C4—24no—
1032C4—24no—
1033C4—22no—
1034C4—22no—
1035C4—44no—
1036C4—48no—
1037C4—44no—
1038C4—42no—
1039C4—44no—
1040C4—41no—
1041C4—42no—
1042C4—44no—
1043C4—44no—
1044C4—42no—
1045C4—42no—
1046C4—44no—
1047C4—42no—
1048C4—42no—
1049C4—42no—
1050C4#350914yes—
1051C4#352314yes—
1052C4#354414yes—
1053C2—44no—
1054C2C2×#354411yescharacteristic
1055C2C2×#352311yescharacteristic
1056C2C2×#350911yescharacteristic
1057C2#6294311yescharacteristic
1058C2#6294511yescharacteristic
1059C2#6298611yescharacteristic
1060C2#6301611yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC22×D4C24
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59870C2semidirect
2. #59443C2semidirect
4. #59262C2semidirect
5. #51488C2semidirect
6. #45611C2semidirect
8. #45080C2semidirect
9. #42610C2semidirect
10. #42527C2semidirect
11. #39855C2semidirect
12. #39753C2semidirect
13. #39642C2semidirect
15. #38933C2semidirect
16. #36593C2semidirect
17. Q8×C4⋊Q8C2semidirect
20. #36133C2semidirect
21. #35239C2semidirect
23. #34951C2semidirect
25. #34491C2semidirect

Maximal subgroups

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

subgroupindex
#598702
#594432
#594362
#592622
#514882
#456112
#450832
#450802
#426102
#425272
#398552
#397532
#396422
#396172
#389332
#365932
Q8×C4⋊Q82
#361942
#361342
#361332
#352392
#352062
#349512
#349452
#344912
C4×#5542