Finite Group Databasebeta

← #8429416

Subgroups — #8429416

Order 512.

4299 conjugacy classes of subgroups.

The subgroup lattice has 1059 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59821C211yesmaximal, characteristic
2#59679C212yesmaximal
3#59655C212yesmaximal, complemented
4#59450C212yesmaximal, complemented
5#53725C218yesmaximal, complemented
6#53050C214yesmaximal, complemented
7#52998C214yesmaximal, complemented
8#52998C214yesmaximal, complemented
9#42845C214yesmaximal, complemented
10#42614C214yesmaximal, complemented
11#42452C214yesmaximal, complemented
12#39761C212yesmaximal, complemented
13#39635C212yesmaximal, complemented
14#39497C212yesmaximal, complemented
15#39490C212yesmaximal, complemented
16#39182C212yesmaximal, complemented
17#39172C212yesmaximal, complemented
18#37637C212yesmaximal, complemented
19#37629C212yesmaximal
20#37628C212yesmaximal, complemented
21#36598C211yesmaximal, characteristic, complemented
22#36559C211yesmaximal, characteristic
23Q8×C4⋊Q8C211yesmaximal, characteristic, complemented
24#34954C211yesmaximal, characteristic
25#34951C211yesmaximal, characteristic, complemented
26#34951C211yesmaximal, characteristic, complemented
27C2×Q82C2212yes—
28C2×#556C2212yes—
29C2×#554C2212yes—
30#2868C2212yes—
31#2868C2211yescharacteristic
32#2862C2212yes—
33#2859C2212yes—
34#2836C2218yes—
35#2836C2218yes—
36#2835C2218yes—
37#2831C2218yes—
38#2831C2218yes—
39#2831C2218yes—
40#2830C2218yes—
41#2805C2218yes—
42#2802C2218yes—
43#2802C2218yes—
44#2800C2218yes—
45#2793C2218yes—
46#2790C2218yes—
47#2783C2218yes—
48#2771C2218yes—
49#2771C2218yes—
50#2755C2218yes—
51#2729C2218yes—
52#2729C2218yes—
53#2727C2214yes—
54#2716C2218yes—
55#2716C2218yes—
56#2716C2218yes—
57#2689C2218yes—
58#2689C2218yes—
59#2689C2218yes—
60#2654C2218yes—
61#2652C2218yes—
62#2647C2214yes—
63#2647C2214yes—
64#2644C2214yes—
65#2644C2214yes—
66#2640C2214yes—
67#2640C2214yes—
68#2638C2218yes—
69#2637C2218yes—
70#2629C2214yes—
71#2625C2214yes—
72#2621C2214yes—
73#2593C2214yes—
74#2585C2214yes—
75#2585C2214yes—
76#2582C2211yescharacteristic
77#2582C2211yescharacteristic
78#2582C2211yescharacteristic
79#2582C2212yes—
80#2575C2218yes—
81#2571C2211yescharacteristic
82#2571C2214yes—
83#2571C2212yes—
84#2570C2214yes—
85#2568C2214yes—
86#2568C2212yes—
87#2568C2211yescharacteristic
88#2568C2211yescharacteristic
89#2567C2212yes—
90#2567C2214yes—
91#2566C2214yes—
92#2566C2214yes—
93#2563C2212yes—
94#2552C2211yescharacteristic
95#2552C2211yescharacteristic
96#2551C2212yes—
97#2551C2214yes—
98#2551C2212yes—
99#2551C2214yes—
100#2550C2214yes—
101#2550C2214yes—
102#2548C2211yescharacteristic
103#2548C2212yes—
104#2548C2211yescharacteristic
105#2546C2211yescharacteristic
106#2546C2211yescharacteristic
107#2545C2214yes—
108#2542C2212yes—
109#2538C2212yes—
110#2538C2212yes—
111#2538C2212yes—
112#2513C2212yes—
113#2513C2214yes—
114#2513C2212yes—
115#2512C2214yes—
116#2512C2214yes—
117#2512C2214yes—
118#2511C2212yes—
119#2511C2214yes—
120#2511C2214yes—
121#2511C2214yes—
122#2511C2212yes—
123#2509C2212yes—
124#2509C2212yes—
125#2508C2214yes—
126#2507C2214yes—
127#2507C2214yes—
128#2503C2214yes—
129#2499C2214yes—
130#2496C2214yes—
131#2492C2214yes—
132#2489C2214yes—
133#2466C2218yes—
134#2453C2212yes—
135#2453C2214yes—
136#2453C2214yes—
137#2453C2214yes—
138#2453C2212yes—
139#2452C2214yes—
140#2452C2214yes—
141#2452C2214yes—
142#2452C2214yes—
143#2448C2212yes—
144#2448C2214yes—
145#2448C2212yes—
146#2447C2214yes—
147#2447C2214yes—
148#2447C2214yes—
149#2446C2212yes—
150#2446C2212yes—
151#2446C2214yes—
152#2440C2214yes—
153#2439C2214yes—
154#2439C2214yes—
155#2429C2214yes—
156#2429C2218yes—
157#2421C2214yes—
158#2421C2214yes—
159#2415C2214yes—
160#2402C2214yes—
161#2402C2214yes—
162#2395C2214yes—
163#2367C2214yes—
164#2365C2212yes—
165#2360C2214yes—
166#2357C2214yes—
167#2355C2212yes—
168#2355C2212yes—
169#2354C2212yes—
170Q8×C4⋊C4C2212yes—
171Q8×C4⋊C4C2212yes—
172Q8×C4⋊C4C2212yes—
173D4×C4⋊C4C2212yes—
174D4×C4⋊C4C2212yes—
175#2331C2214yes—
176#2327C2214yes—
177#2317C2214yes—
178C4×C4⋊Q8C2212yes—
179C4×C4⋊Q8C2212yes—
180C4×C4⋊Q8C2212yes—
181C4×C4⋊Q8C2212yes—
182C4×C4⋊Q8C2211yescharacteristic
183C4×C4⋊Q8C2211yescharacteristic
184C4×#127C2212yes—
185C4×#127C2211yescharacteristic
186C4×#125C2212yes—
187C4×#125C2212yes—
188C4×#124C2212yes—
189C4×#124C2212yes—
190#2295C2212yes—
191#2295C2212yes—
192#2295C2212yes—
193#2295C2212yes—
194#2293C2212yes—
195#2293C2212yes—
196C42×Q8C2211yescharacteristic
197C42×Q8C2211yescharacteristic
198C42×Q8C2211yescharacteristic
199Q82—48no—
200#556—48no—
201#554—48no—
202C2×C4⋊Q8C2311yescharacteristic
203C2×C4⋊Q8C2312yes—
204C2×C4⋊Q8C2311yescharacteristic
205C2×C4⋊Q8C2312yes—
206C2×C4⋊Q8C2312yes—
207C2×C4⋊Q8C2314yes—
208C2×C4⋊Q8C2312yes—
209C2×C4⋊Q8C2314yes—
210C2×C4⋊Q8C2314yes—
211C2×C4⋊Q8C2318yes—
212C2×C4⋊Q8C2312yes—
213C2×C4⋊Q8C2314yes—
214C2×#127C2311yescharacteristic
215C2×#126C2318yes—
216C2×#126C2318yes—
217C2×#125C2312yes—
218C2×#125C2312yes—
219C2×#125C2314yes—
220C2×#124C2312yes—
221C2×#124C2312yes—
222C2×#124C2314yes—
223C2×C22⋊Q8C2314yes—
224C2×C22⋊Q8C2314yes—
225C2×C22⋊Q8C2314yes—
226C2×C22⋊Q8C2318yes—
227C2×C22⋊Q8C2318yes—
228C2×C4×Q8C2312yes—
229C2×C4×Q8C2311yescharacteristic
230C2×C4×Q8C2311yescharacteristic
231C2×C4×Q8C2312yes—
232C2×C4×Q8C2311yescharacteristic
233C2×C4×Q8C2311yescharacteristic
234C2×C4×Q8C2311yescharacteristic
235C2×C4×Q8C2311yescharacteristic
236C2×C4×Q8C2311yescharacteristic
237C2×C4×Q8C2314yes—
238C2×C4×Q8C2311yescharacteristic
239C2×C4×Q8C2314yes—
240C2×C4×Q8C2314yes—
241C2×C4×Q8C2311yescharacteristic
242C2×C4×Q8C2314yes—
243C2×C4×D4C2312yes—
244C2×C4×D4C2312yes—
245C2×C4×D4C2314yes—
246C2×C4×D4C2314yes—
247C2×C4×D4C2312yes—
248C2×C4×D4C2314yes—
249C2×#117C2314yes—
250C2×#117C2314yes—
251C22×C4⋊C4C2314yes—
252#400C2318yes—
253#400C2318yes—
254#400C2314yes—
255#400C2318yes—
256#400C2314yes—
257#400C2318yes—
258#400C2318yes—
259#400C2314yes—
260#400C2314yes—
261#400C2318yes—
262#400C2314yes—
263#400C2318yes—
264#400C2318yes—
265#400C2314yes—
266#400C2314yes—
267#400C2318yes—
268#400C2318yes—
269#400C2314yes—
270#400C2314yes—
271#399C2318yes—
272#399C2314yes—
273#398C2318yes—
274#398C2314yes—
275#398C2314yes—
276#398C2318yes—
277#398C2318yes—
278#398C2318yes—
279#398C2318yes—
280#398C2314yes—
281#398C2314yes—
282#398C2318yes—
283#398C2318yes—
284#398C2314yes—
285#398C2314yes—
286#398C2314yes—
287#398C2314yes—
288#398C2314yes—
289#398C2318yes—
290#397C2318yes—
291#397C2318yes—
292#397C2318yes—
293#397C2318yes—
294#397C2314yes—
295#397C2314yes—
296#397C2318yes—
297#397C2318yes—
298#397C2318yes—
299#397C2318yes—
300#397C2318yes—
301#397C2318yes—
302#397C2318yes—
303#397C2314yes—
304#396C2318yes—
305#396C2318yes—
306#396C2318yes—
307#396C2318yes—
308#396C2318yes—
309#396C2318yes—
310#396C2318yes—
311#396C2318yes—
312#395C2318yes—
313#395C2318yes—
314#395C2318yes—
315#395C2318yes—
316#394C2314yes—
317#394C2318yes—
318#394C2314yes—
319#393C2318yes—
320#393C2318yes—
321#393C2318yes—
322#393C2318yes—
323#391C2314yes—
324#391C2312yes—
325#391C2314yes—
326#391C2312yes—
327#391C2312yes—
328#391C2312yes—
329#391C2312yes—
330#391C2312yes—
331#391C2312yes—
332#391C2318yes—
333#391C2314yes—
334#391C2318yes—
335#391C2314yes—
336#391C2314yes—
337#391C2312yes—
338#391C2312yes—
339#391C2312yes—
340#391C2312yes—
341#391C2318yes—
342#391C2312yes—
343#391C2314yes—
344#391C2312yes—
345#391C2312yes—
346#391C2312yes—
347#391C2314yes—
348#391C2312yes—
349#390C2314yes—
350#390C2312yes—
351#390C2314yes—
352#390C2312yes—
353#390C2314yes—
354#390C2312yes—
355#390C2312yes—
356#390C2314yes—
357#390C2312yes—
358#390C2314yes—
359#390C2314yes—
360#390C2312yes—
361#390C2312yes—
362#390C2312yes—
363#390C2312yes—
364#389C2312yes—
365#389C2312yes—
366#389C2312yes—
367#389C2312yes—
368#389C2312yes—
369#389C2314yes—
370#389C2314yes—
371#389C2314yes—
372#389C2314yes—
373#389C2312yes—
374#389C2312yes—
375#389C2314yes—
376#389C2314yes—
377#389C2314yes—
378#389C2314yes—
379#389C2312yes—
380#389C2318yes—
381#389C2314yes—
382#389C2314yes—
383#389C2318yes—
384#389C2314yes—
385#389C2314yes—
386#389C2318yes—
387#389C2312yes—
388#389C2312yes—
389#389C2318yes—
390#389C2318yes—
391#389C2312yes—
392#389C2312yes—
393#389C2312yes—
394#389C2312yes—
395#389C2314yes—
396#389C2314yes—
397#389C2314yes—
398#389C2314yes—
399#389C2318yes—
400#389C2312yes—
401#389C2312yes—
402#389C2312yes—
403#389C2312yes—
404#389C2318yes—
405#389C2312yes—
406#389C2312yes—
407#388C2314yes—
408#388C2318yes—
409#388C2314yes—
410#388C2318yes—
411#388C2318yes—
412#388C2314yes—
413#388C2318yes—
414#388C2314yes—
415#388C2314yes—
416#388C2314yes—
417#388C2314yes—
418#388C2314yes—
419#388C2318yes—
420#388C2318yes—
421#388C2318yes—
422#387C2314yes—
423#387C2314yes—
424#387C2314yes—
425#387C2314yes—
426#387C2318yes—
427#387C2318yes—
428#387C2314yes—
429#387C2314yes—
430#387C2318yes—
431#387C2318yes—
432#387C2318yes—
433#387C2314yes—
434#387C2318yes—
435#387C2314yes—
436#387C2318yes—
437#387C2318yes—
438#387C2318yes—
439#387C2314yes—
440#387C2314yes—
441#387C2314yes—
442#387C2314yes—
443#387C2318yes—
444#387C2318yes—
445#385C2318yes—
446#385C2318yes—
447#385C2318yes—
448#385C2318yes—
449#385C2318yes—
450#385C2318yes—
451#384C2311yescharacteristic
452#384C2312yes—
453#384C2311yescharacteristic
454#384C2312yes—
455#384C2312yes—
456#384C2311yescharacteristic
457#384C2312yes—
458#384C2312yes—
459#384C2314yes—
460#384C2312yes—
461#384C2314yes—
462#384C2314yes—
463#384C2314yes—
464#382C2312yes—
465#382C2312yes—
466#382C2314yes—
467#382C2314yes—
468#382C2312yes—
469#382C2314yes—
470#382C2314yes—
471#382C2312yes—
472#382C2318yes—
473#381C2318yes—
474#381C2318yes—
475#380C2314yes—
476#380C2314yes—
477#380C2314yes—
478C4×C4⋊C4C2311yescharacteristic
479C4×C4⋊C4C2311yescharacteristic
480C4×C4⋊C4C2314yes—
481C4×C4⋊C4C2312yes—
482C4×C4⋊C4C2312yes—
483C4×C4⋊C4C2314yes—
484C4×C4⋊C4C2314yes—
485C4×C4⋊C4C2314yes—
486C4×C4⋊C4C2312yes—
487C4×C4⋊C4C2314yes—
488C4×C4⋊C4C2314yes—
489C4×C4⋊C4C2314yes—
490C4×C4⋊C4C2312yes—
491C4×C4⋊C4C2314yes—
492C4×C4⋊C4C2314yes—
493C4×C4⋊C4C2314yes—
494C4×C4⋊C4C2311yescharacteristic
495C4×C4⋊C4C2312yes—
496C4×C4⋊C4C2311yescharacteristic
497C4×C4⋊C4C2312yes—
498C4×C4⋊C4C2312yes—
499C4×C4⋊C4C2311yescharacteristic
500C4×C4⋊C4C2314yes—
501C4×C4⋊C4C2311yescharacteristic
502C4×C4⋊C4C2312yes—
503C4×C4⋊C4C2312yes—
504C4×C4⋊C4C2312yes—
505C4×C4⋊C4C2314yes—
506C4×C4⋊C4C2311yescharacteristic
507C4×C4⋊C4C2311yescharacteristic
508C4×C4⋊C4C2312yes—
509C4×C4⋊C4C2312yes—
510C4×C4⋊C4C2312yes—
511C4×C4⋊C4C2311yescharacteristic
512C4×C22⋊C4C2318yes—
513C4×C22⋊C4C2314yes—
514C4×C22⋊C4C2314yes—
515C4×C22⋊C4C2314yes—
516#376C2314yes—
517#376C2314yes—
518C43C2312yes—
519C43C2312yes—
520C43C2311yescharacteristic
521C43C2312yes—
522C22×Q8C2412yes—
523C22×Q8C2411yescharacteristic
524C22×Q8C2412yes—
525C22×Q8C2411yescharacteristic
526C22×Q8C2411yescharacteristic
527C22×Q8C2414yes—
528C22×Q8C2418yes—
529C22×D4C2412yes—
530C22×D4C2412yes—
531C22×D4C2412yes—
532C23×C4C2414yes—
533C23×C4C2418yes—
534C4⋊Q8—28no—
535C4⋊Q8—28no—
536C4⋊Q8—24no—
537C4⋊Q8—24no—
538C4⋊Q8—44no—
539C4⋊Q8—48no—
540C4⋊Q8—48no—
541C4⋊Q8—48no—
542C4⋊Q8—44no—
543C4⋊Q8—416no—
544C4⋊Q8—82no—
545C4⋊Q8—84no—
546#127—24no—
547#126—416no—
548#126—88no—
549#125—44no—
550#125—44no—
551#125—48no—
552#124—28no—
553#124—44no—
554#124—48no—
555C22⋊Q8—416no—
556C22⋊Q8—48no—
557C22⋊Q8—48no—
558C22⋊Q8—48no—
559C22⋊Q8—88no—
560C4×Q8—24no—
561C4×Q8—24no—
562C4×Q8—28no—
563C4×Q8—24no—
564C4×Q8—24no—
565C4×Q8—24no—
566C4×Q8—24no—
567C4×Q8—28no—
568C4×Q8—24no—
569C4×Q8—42no—
570C4×Q8—42no—
571C4×Q8—48no—
572C4×Q8—48no—
573C4×Q8—48no—
574C4×Q8—84no—
575C4×D4—28no—
576C4×D4—28no—
577C4×D4—48no—
578C4×D4—48no—
579C4×D4—44no—
580C4×D4—84no—
581#117—48no—
582#117—48no—
583C2×C4⋊C4—48no—
584C2×C4⋊C4C2411yescharacteristic
585C2×C4⋊C4C2414yes—
586C2×C4⋊C4C2412yes—
587C2×C4⋊C4C2412yes—
588C2×C4⋊C4C2412yes—
589C2×C4⋊C4C2414yes—
590C2×C4⋊C4C2414yes—
591C2×C4⋊C4C2412yes—
592C2×C4⋊C4C2412yes—
593C2×C4⋊C4C2411yescharacteristic
594C2×C4⋊C4C2411yescharacteristic
595C2×C4⋊C4C2414yes—
596C2×C4⋊C4C2411yescharacteristic
597C2×C4⋊C4C2412yes—
598C2×C4⋊C4C2411yescharacteristic
599C2×C4⋊C4C2411yescharacteristic
600C2×C4⋊C4C2411yescharacteristic
601C2×C4⋊C4C2412yes—
602C2×C4⋊C4C2412yes—
603C2×C4⋊C4C2412yes—
604C2×C4⋊C4C2412yes—
605C2×C4⋊C4C2411yescharacteristic
606C2×C4⋊C4C2411yescharacteristic
607C2×C4⋊C4C2412yes—
608C2×C4⋊C4C2412yes—
609C2×C4⋊C4C2414yes—
610C2×C4⋊C4C2412yes—
611C2×C4⋊C4C2412yes—
612C2×C4⋊C4C2412yes—
613C2×C4⋊C4C2412yes—
614C2×C4⋊C4C2412yes—
615C2×C4⋊C4C2414yes—
616C2×C4⋊C4C2414yes—
617C2×C4⋊C4C2418yes—
618C2×C4⋊C4C2414yes—
619C2×C4⋊C4C2414yes—
620C2×C4⋊C4C2414yes—
621C2×C4⋊C4C2412yes—
622C2×C4⋊C4C2412yes—
623C2×C4⋊C4C2418yes—
624C2×C4⋊C4C2418yes—
625C2×C4⋊C4C2418yes—
626C2×C4⋊C4C2418yes—
627C2×C4⋊C4C2412yes—
628C2×C4⋊C4C2412yes—
629C2×C4⋊C4C2418yes—
630C2×C4⋊C4C2414yes—
631C2×C4⋊C4C2414yes—
632C2×C4⋊C4C2418yes—
633C2×C4⋊C4C2414yes—
634C2×C4⋊C4C2414yes—
635C2×C4⋊C4C2414yes—
636C2×C4⋊C4C2414yes—
637C2×C4⋊C4C2414yes—
638C2×C4⋊C4C2414yes—
639C2×C4⋊C4C2418yes—
640C2×C4⋊C4C2414yes—
641C2×C4⋊C4C2412yes—
642C2×C4⋊C4C2414yes—
643C2×C4⋊C4C2414yes—
644C2×C4⋊C4C2414yes—
645C2×C4⋊C4C2418yes—
646C2×C22⋊C4C2414yes—
647C2×C22⋊C4C2414yes—
648C2×C22⋊C4C2414yes—
649C2×C22⋊C4C2414yes—
650C2×C22⋊C4C2418yes—
651C2×C22⋊C4C2414yes—
652C2×C22⋊C4C2414yes—
653C2×C22⋊C4C2418yes—
654C2×C22⋊C4C2418yes—
655C2×C22⋊C4C2418yes—
656C2×C22⋊C4C2414yes—
657C2×C22⋊C4C2414yes—
658C2×C22⋊C4C2418yes—
659C2×C22⋊C4C2418yes—
660C2×C22⋊C4C2418yes—
661C2×C22⋊C4C2414yes—
662C2×C22⋊C4C2414yes—
663C2×C22⋊C4C2414yes—
664C2×C42C2412yes—
665C2×C42C2412yes—
666C2×C42C2412yes—
667C2×C42C2411yescharacteristic
668C2×C42C2412yes—
669C2×C42C2414yes—
670C2×C42C2412yes—
671C2×C42C2411yescharacteristic
672C2×C42C2412yes—
673C2×C42C2412yes—
674C2×C42C2412yes—
675C2×C42C2412yes—
676C2×C42C2411yescharacteristic
677C2×C42C2412yes—
678C2×C42C2414yes—
679C2×C42C2412yes—
680C2×C42C2412yes—
681C2×C42C2412yes—
682C2×C42C2418yes—
683C2×C42C2412yes—
684C2×C42C2418yes—
685C2×C42C2412yes—
686C2×C42C2418yes—
687C2×C42C2412yes—
688C2×C42C2412yes—
689C2×C42C2411yescharacteristic
690C2×C42C2412yes—
691C2×C42C2411yescharacteristic
692C2×C42C2411yescharacteristic
693C2×C42C2411yescharacteristic
694#95C2414yes—
695#95C2414yes—
696#95C2414yes—
697#95C2414yes—
698#95C2414yes—
699#95C2414yes—
700#95C2414yes—
701#95C2414yes—
702#95C2414yes—
703#95C2414yes—
704#95C2414yes—
705#95C2414yes—
706#95C2414yes—
707#95C2414yes—
708#95C2414yes—
709#95C2414yes—
710#95C2412yes—
711#95C2412yes—
712#95C2412yes—
713#95C2412yes—
714#95C2412yes—
715#95C2412yes—
716#95C2412yes—
717#95C2412yes—
718#95C2412yes—
719#95C2418yes—
720#95C2414yes—
721#95C2414yes—
722#95C2414yes—
723#95C2418yes—
724#95C2418yes—
725#95C2418yes—
726#95C2414yes—
727#95C2418yes—
728#95C2418yes—
729#95C2414yes—
730#95C2414yes—
731#95C2414yes—
732#95C2414yes—
733#95C2414yes—
734#95C2414yes—
735#95C2414yes—
736#95C2414yes—
737#95C2414yes—
738#95C2414yes—
739#95C2418yes—
740#95C2418yes—
741#95C2418yes—
742#95C2418yes—
743#95C2418yes—
744C24C2514yes—
745C2×Q8—22no—
746C2×Q8—24no—
747C2×Q8—22no—
748C2×Q8—24no—
749C2×Q8—28no—
750C2×Q8—22no—
751C2×Q8—24no—
752C2×Q8—22no—
753C2×Q8—22no—
754C2×Q8—22no—
755C2×Q8—24no—
756C2×Q8—24no—
757C2×Q8—22no—
758C2×Q8—22no—
759C2×Q8—24no—
760C2×Q8—44no—
761C2×Q8—44no—
762C2×Q8—48no—
763C2×Q8—48no—
764C2×Q8—48no—
765C2×Q82−1+414yes—
766C2×D4—24no—
767C2×D4—24no—
768C2×D4—24no—
769C2×D4—24no—
770C2×D4—24no—
771C2×D4—24no—
772C2×D4—24no—
773C2×D4—42no—
774C2×D4—42no—
775C22×C4—28no—
776C22×C4—28no—
777C22×C4—28no—
778C22×C4—48no—
779C22×C4—48no—
780C22×C4—48no—
781C22×C4C2512yes—
782C22×C4C2512yes—
783C22×C4C2512yes—
784C22×C4C2514yes—
785C22×C4C2512yes—
786C22×C4C2511yescharacteristic
787C22×C4C2512yes—
788C22×C4C2512yes—
789C22×C4C2512yes—
790C22×C4C2512yes—
791C22×C4C2514yes—
792C22×C4C2514yes—
793C22×C4C2512yes—
794C22×C4C2512yes—
795C22×C4C2512yes—
796C22×C4C2514yes—
797C22×C4C2518yes—
798C22×C4C2514yes—
799C22×C4C2511yescharacteristic
800C22×C4C2511yescharacteristic
801C22×C4C2512yes—
802C22×C4C2511yescharacteristic
803C22×C4C2511yescharacteristic
804C22×C4C2511yescharacteristic
805C22×C4C2511yescharacteristic
806C4⋊C4—22no—
807C4⋊C4—28no—
808C4⋊C4—24no—
809C4⋊C4—24no—
810C4⋊C4—24no—
811C4⋊C4—28no—
812C4⋊C4—24no—
813C4⋊C4—28no—
814C4⋊C4—24no—
815C4⋊C4—22no—
816C4⋊C4—24no—
817C4⋊C4—24no—
818C4⋊C4—24no—
819C4⋊C4—24no—
820C4⋊C4—22no—
821C4⋊C4—22no—
822C4⋊C4—24no—
823C4⋊C4—22no—
824C4⋊C4—22no—
825C4⋊C4—22no—
826C4⋊C4—24no—
827C4⋊C4—24no—
828C4⋊C4—24no—
829C4⋊C4—28no—
830C4⋊C4—28no—
831C4⋊C4—28no—
832C4⋊C4—24no—
833C4⋊C4—24no—
834C4⋊C4—28no—
835C4⋊C4—22no—
836C4⋊C4—22no—
837C4⋊C4—24no—
838C4⋊C4—24no—
839C4⋊C4—48no—
840C4⋊C4—44no—
841C4⋊C4—44no—
842C4⋊C4—42no—
843C4⋊C4—44no—
844C4⋊C4—42no—
845C4⋊C4—42no—
846C4⋊C4—48no—
847C4⋊C4—48no—
848C4⋊C4—48no—
849C4⋊C4—42no—
850C4⋊C4—48no—
851C4⋊C4—48no—
852C4⋊C4—48no—
853C4⋊C4—44no—
854C4⋊C4—44no—
855C4⋊C4—44no—
856C4⋊C4—44no—
857C4⋊C4—44no—
858C4⋊C4—44no—
859C4⋊C4—44no—
860C4⋊C4—44no—
861C4⋊C4—48no—
862C4⋊C4—44no—
863C4⋊C4—44no—
864C4⋊C4—48no—
865C4⋊C4—44no—
866C4⋊C4—44no—
867C4⋊C4—42no—
868C22⋊C4—28no—
869C22⋊C4—28no—
870C22⋊C4—28no—
871C22⋊C4—28no—
872C22⋊C4—44no—
873C22⋊C4—44no—
874C22⋊C4—48no—
875C22⋊C4—48no—
876C22⋊C4—44no—
877C22⋊C4—48no—
878C22⋊C4—48no—
879C22⋊C4—48no—
880C22⋊C4—48no—
881C22⋊C4—44no—
882C22⋊C4—48no—
883C22⋊C4—44no—
884C22⋊C4—44no—
885C22⋊C4—44no—
886C42—24no—
887C42—28no—
888C42—24no—
889C42—24no—
890C42—22no—
891C42—24no—
892C42—24no—
893C42—24no—
894C42—28no—
895C42—24no—
896C42—24no—
897C42—24no—
898C42—24no—
899C42—24no—
900C42—22no—
901C42—24no—
902C42—22no—
903C42—24no—
904C42—48no—
905C42—42no—
906C42—42no—
907C42—42no—
908C42—48no—
909C42—42no—
910C42—48no—
911C42—41no—
912C42—42no—
913C42H(5,𝔽2)14yes—
914C422−1+414yes—
915C422−1+414yes—
916C23—24no—
917C23—24no—
918C23—24no—
919C23—24no—
920C23—24no—
921C23—24no—
922C23—24no—
923C23C2611yescharacteristic
924Q8—28no—
925Q8—48no—
926Q8—48no—
927Q8—44no—
928Q8—44no—
929Q8—88no—
930Q8—168no—
931D4—48no—
932D4—48no—
933D4—48no—
934C2×C4—22no—
935C2×C4—21no—
936C2×C4—22no—
937C2×C4—21no—
938C2×C4—21no—
939C2×C4—21no—
940C2×C4—21no—
941C2×C4—21no—
942C2×C4—24no—
943C2×C4—24no—
944C2×C4—22no—
945C2×C4—22no—
946C2×C4—22no—
947C2×C4—24no—
948C2×C4—24no—
949C2×C4—28no—
950C2×C4—22no—
951C2×C4—22no—
952C2×C4—21no—
953C2×C4—22no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—24no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—24no—
962C2×C4—22no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—24no—
966C2×C4—24no—
967C2×C4—24no—
968C2×C4—21no—
969C2×C4—22no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—21no—
977C2×C4—22no—
978C2×C4—22no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—24no—
983C2×C4—24no—
984C2×C4—28no—
985C2×C4—24no—
986C2×C4—24no—
987C2×C4—22no—
988C2×C4—24no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—28no—
994C2×C4—22no—
995C2×C4—24no—
996C2×C4—416no—
997C2×C4—168no—
998C2×C4C2×H(5,𝔽2)12yes—
999C2×C4C2×H(5,𝔽2)12yes—
1000C2×C4C2×H(5,𝔽2)12yes—
1001C2×C4C2×2−1+414yes—
1002C2×C4C2×2−1+412yes—
1003C2×C4C2×2−1+412yes—
1004C2×C4C2×2−1+412yes—
1005C2×C4C2×2−1+412yes—
1006C2×C4C2×2−1+412yes—
1007C2×C4C2×2−1+412yes—
1008C2×C4C2×2−1+412yes—
1009C2×C4#58512yes—
1010C2×C4#58512yes—
1011C22—44no—
1012C22—44no—
1013C22—44no—
1014C22—44no—
1015C22—44no—
1016C22—44no—
1017C22—44no—
1018C22C22×H(5,𝔽2)11yescharacteristic
1019C22C22×2−1+411yescharacteristic
1020C22C22×2−1+411yescharacteristic
1021C22C22×2−1+411yescharacteristic
1022C22C2×#58511yescharacteristic
1023C22C2×#58511yescharacteristic
1024C22H(7,𝔽2)11yescharacteristic
1025C4—24no—
1026C4—22no—
1027C4—22no—
1028C4—22no—
1029C4—44no—
1030C4—44no—
1031C4—44no—
1032C4—42no—
1033C4—42no—
1034C4—42no—
1035C4—41no—
1036C4—42no—
1037C4—42no—
1038C4—42no—
1039C4—42no—
1040C4—44no—
1041C4—42no—
1042C4—42no—
1043C4—42no—
1044C4—48no—
1045C4—44no—
1046C4—42no—
1047C4#355214yes—
1048C4#355414yes—
1049C4#355514yes—
1050C2—84no—
1051C2C2×#355211yescharacteristic
1052C2C2×#355411yescharacteristic
1053C2C2×#355511yescharacteristic
1054C2#6292611yescharacteristic
1055C2#6294311yescharacteristic
1056C2#6296111yescharacteristic
1057C2#6303411yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#127C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
3. #59655C2semidirect
4. #59450C2semidirect
5. #53725C2semidirect
6. #53050C2semidirect
7. #52998C2semidirect
8. #52998C2semidirect
9. #42845C2semidirect
10. #42614C2semidirect
11. #42452C2semidirect
12. #39761C2semidirect
13. #39635C2semidirect
14. #39497C2semidirect
15. #39490C2semidirect
16. #39182C2semidirect
17. #39172C2semidirect
18. #37637C2semidirect
20. #37628C2semidirect
21. #36598C2semidirect
23. Q8×C4⋊Q8C2semidirect
25. #34951C2semidirect
26. #34951C2semidirect

Maximal subgroups

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

subgroupindex
#598212
#596792
#596552
#594502
#537252
#530502
#529982
#428452
#426142
#424522
#397612
#396352
#394972
#394902
#391822
#391722
#376372
#376292
#376282
#365982
#365592
Q8×C4⋊Q82
#349542
#349512