Finite Group Databasebeta

← #7987106

Subgroups — #7987106

Order 512.

4459 conjugacy classes of subgroups.

The subgroup lattice has 1055 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59828C211yesmaximal, characteristic, complemented
2#59653C212yesmaximal
3#59434C212yesmaximal
4#59259C212yesmaximal, complemented
5#50788C218yesmaximal, complemented
6#46079C214yesmaximal, complemented
7#45344C214yesmaximal, complemented
8#45339C214yesmaximal, complemented
9#42716C214yesmaximal, complemented
10#42702C214yesmaximal
11#40201C214yesmaximal, complemented
12#39744C212yesmaximal
13#39744C212yesmaximal
14#39641C212yesmaximal, complemented
15#38933C212yesmaximal, complemented
16#36593C211yesmaximal, characteristic, complemented
17#36593C211yesmaximal, characteristic, complemented
18#36560C212yesmaximal, complemented
19#36481C212yesmaximal, complemented
20#36188C211yesmaximal, characteristic
21#35202C212yesmaximal, complemented
22#35187C212yesmaximal, complemented
23#34951C211yesmaximal, characteristic, complemented
24#34945C211yesmaximal, characteristic
25#34488C212yesmaximal, complemented
26C4×#556C211yesmaximal, characteristic
27C2×#557C2212yes—
28C2×#557C2212yes—
29C2×#557C2212yes—
30C2×#556C2211yescharacteristic
31C2×#556C2212yes—
32#2868C2212yes—
33#2868C2212yes—
34#2868C2211yescharacteristic
35#2864C2214yes—
36#2863C2214yes—
37#2859C2214yes—
38#2857C2212yes—
39#2836C2218yes—
40#2791C2218yes—
41#2791C2218yes—
42#2777C2218yes—
43#2777C2218yes—
44#2776C2218yes—
45#2776C2218yes—
46#2773C2218yes—
47#2768C2218yes—
48#2766C2218yes—
49#2766C2218yes—
50#2738C2218yes—
51#2726C2214yes—
52#2725C2218yes—
53#2721C2218yes—
54#2721C2218yes—
55#2721C2218yes—
56#2721C2218yes—
57#2667C2218yes—
58#2658C2214yes—
59#2655C2218yes—
60#2654C2218yes—
61#2647C2214yes—
62#2606C2218yes—
63#2606C2218yes—
64#2594C2218yes—
65#2585C2218yes—
66#2585C2218yes—
67#2585C2214yes—
68#2582C2212yes—
69#2582C2211yescharacteristic
70#2573C2214yes—
71#2571C2211yescharacteristic
72#2568C2211yescharacteristic
73#2568C2212yes—
74#2568C2211yescharacteristic
75#2565C2214yes—
76#2565C2214yes—
77#2552C2214yes—
78#2552C2212yes—
79#2552C2214yes—
80#2552C2214yes—
81#2552C2214yes—
82#2552C2212yes—
83#2552C2212yes—
84#2552C2211yescharacteristic
85#2552C2212yes—
86#2552C2212yes—
87#2547C2212yes—
88#2547C2211yescharacteristic
89#2547C2212yes—
90#2546C2214yes—
91#2546C2214yes—
92#2546C2214yes—
93#2546C2214yes—
94#2546C2212yes—
95#2546C2212yes—
96#2546C2212yes—
97#2546C2211yescharacteristic
98#2546C2214yes—
99#2545C2214yes—
100#2545C2214yes—
101#2538C2211yescharacteristic
102#2524C2218yes—
103#2522C2218yes—
104#2519C2218yes—
105#2514C2214yes—
106#2514C2212yes—
107#2514C2214yes—
108#2511C2212yes—
109#2509C2212yes—
110#2508C2214yes—
111#2507C2214yes—
112#2507C2214yes—
113#2506C2218yes—
114#2506C2214yes—
115#2506C2218yes—
116#2499C2214yes—
117#2497C2214yes—
118#2496C2214yes—
119#2496C2214yes—
120#2494C2214yes—
121#2494C2212yes—
122#2489C2214yes—
123#2453C2214yes—
124#2453C2212yes—
125#2448C2214yes—
126#2447C2212yes—
127#2446C2214yes—
128#2446C2212yes—
129#2446C2214yes—
130#2446C2214yes—
131#2441C2214yes—
132#2441C2214yes—
133#2441C2214yes—
134#2441C2214yes—
135#2441C2214yes—
136#2441C2214yes—
137#2429C2214yes—
138#2423C2214yes—
139#2423C2214yes—
140#2423C2214yes—
141#2423C2214yes—
142#2421C2212yes—
143#2402C2214yes—
144#2401C2214yes—
145#2382C2218yes—
146#2373C2214yes—
147#2370C2214yes—
148#2367C2212yes—
149#2365C2212yes—
150#2365C2212yes—
151#2365C2214yes—
152#2365C2212yes—
153#2365C2211yescharacteristic
154#2365C2214yes—
155#2362C2214yes—
156#2362C2212yes—
157#2356C2212yes—
158#2355C2214yes—
159#2355C2211yescharacteristic
160#2354C2211yescharacteristic
161#2351C2214yes—
162Q8×C4⋊C4C2212yes—
163Q8×C4⋊C4C2212yes—
164Q8×C4⋊C4C2212yes—
165Q8×C4⋊C4C2212yes—
166Q8×C4⋊C4C2212yes—
167#2347C2214yes—
168#2347C2212yes—
169#2336C2218yes—
170#2330C2214yes—
171#2330C2214yes—
172#2327C2214yes—
173#2327C2214yes—
174#2320C2214yes—
175#2320C2214yes—
176C4×C4⋊Q8C2212yes—
177C4×C4⋊Q8C2212yes—
178C4×C4⋊Q8C2214yes—
179C4×C4⋊Q8C2212yes—
180C4×C4⋊Q8C2211yescharacteristic
181C4×C4⋊Q8C2211yescharacteristic
182C4×C4⋊Q8C2211yescharacteristic
183C4×#125C2212yes—
184C4×#126C2214yes—
185C4×#124C2212yes—
186C4×#124C2212yes—
187C4×C22⋊Q8C2212yes—
188C4×C22⋊Q8C2212yes—
189#2295C2212yes—
190#2295C2212yes—
191#2295C2212yes—
192#2285C2212yes—
193#2283C2212yes—
194C42×Q8C2212yes—
195C42×Q8C2211yescharacteristic
196C42×Q8C2211yescharacteristic
197C42×D4C2211yescharacteristic
198C4×#117C2212yes—
199#557—216no—
200#557—48no—
201#557—48no—
202#556—28no—
203#556—48no—
204C2×C4⋊Q8C2312yes—
205C2×C4⋊Q8C2311yescharacteristic
206C2×C4⋊Q8C2312yes—
207C2×C4⋊Q8C2311yescharacteristic
208C2×C4⋊Q8C2311yescharacteristic
209C2×C4⋊Q8C2312yes—
210C2×C4⋊Q8C2314yes—
211C2×C4⋊Q8C2314yes—
212C2×C4⋊Q8C2314yes—
213C2×C4⋊Q8C2312yes—
214C2×C4⋊Q8C2314yes—
215C2×C4⋊Q8C2314yes—
216C2×#126C2314yes—
217C2×#126C2318yes—
218C2×#125C2312yes—
219C2×#125C2314yes—
220C2×#125C2318yes—
221C2×#125C2314yes—
222C2×#125C2314yes—
223C2×#125C2318yes—
224C2×#125C2318yes—
225C2×#124C2312yes—
226C2×#124C2312yes—
227C2×#124C2314yes—
228C2×C22⋊Q8C2312yes—
229C2×C22⋊Q8C2312yes—
230C2×C22⋊Q8C2314yes—
231C2×C4×Q8C2312yes—
232C2×C4×Q8C2311yescharacteristic
233C2×C4×Q8C2314yes—
234C2×C4×Q8C2312yes—
235C2×C4×Q8C2312yes—
236C2×C4×Q8C2311yescharacteristic
237C2×C4×Q8C2314yes—
238C2×C4×Q8C2311yescharacteristic
239C2×C4×Q8C2312yes—
240C2×C4×Q8C2311yescharacteristic
241C2×C4×Q8C2311yescharacteristic
242C2×C4×Q8C2314yes—
243C2×C4×Q8C2314yes—
244C2×C4×Q8C2314yes—
245C2×C4×Q8C2314yes—
246C2×C4×Q8C2314yes—
247C2×C4×Q8C2312yes—
248C2×C4×Q8C2311yescharacteristic
249C2×C4×D4C2311yescharacteristic
250C2×C4×D4C2311yescharacteristic
251C2×C4×D4C2311yescharacteristic
252C2×#117C2312yes—
253C2×#117C2312yes—
254C2×#117C2314yes—
255C22×C42C2312yes—
256#401C2318yes—
257#401C2314yes—
258#400C2314yes—
259#400C2314yes—
260#400C2318yes—
261#400C2314yes—
262#400C2314yes—
263#400C2318yes—
264#400C2314yes—
265#400C2318yes—
266#400C2318yes—
267#400C2318yes—
268#400C2314yes—
269#400C2314yes—
270#399C2318yes—
271#399C2318yes—
272#399C2318yes—
273#399C2318yes—
274#399C2318yes—
275#398C2318yes—
276#398C2318yes—
277#398C2318yes—
278#398C2318yes—
279#398C2318yes—
280#398C2318yes—
281#398C2318yes—
282#398C2314yes—
283#398C2318yes—
284#398C2314yes—
285#398C2314yes—
286#398C2314yes—
287#398C2318yes—
288#398C2318yes—
289#398C2318yes—
290#398C2318yes—
291#398C2318yes—
292#398C2318yes—
293#398C2318yes—
294#398C2318yes—
295#398C2318yes—
296#397C2314yes—
297#397C2314yes—
298#397C2318yes—
299#397C2318yes—
300#397C2318yes—
301#397C2314yes—
302#396C2314yes—
303#396C2318yes—
304#396C2318yes—
305#396C2318yes—
306#396C2318yes—
307#391C2312yes—
308#391C2312yes—
309#391C2312yes—
310#391C2314yes—
311#391C2314yes—
312#391C2312yes—
313#391C2312yes—
314#391C2314yes—
315#391C2312yes—
316#391C2312yes—
317#391C2314yes—
318#391C2314yes—
319#391C2312yes—
320#391C2312yes—
321#391C2312yes—
322#391C2312yes—
323#391C2314yes—
324#391C2314yes—
325#391C2312yes—
326#391C2312yes—
327#391C2312yes—
328#391C2312yes—
329#390C2312yes—
330#390C2312yes—
331#389C2312yes—
332#389C2312yes—
333#389C2312yes—
334#389C2314yes—
335#389C2312yes—
336#389C2314yes—
337#389C2314yes—
338#389C2312yes—
339#389C2318yes—
340#389C2314yes—
341#389C2312yes—
342#389C2314yes—
343#389C2314yes—
344#389C2312yes—
345#389C2312yes—
346#389C2318yes—
347#389C2312yes—
348#389C2312yes—
349#389C2314yes—
350#389C2314yes—
351#389C2318yes—
352#389C2314yes—
353#389C2312yes—
354#389C2318yes—
355#389C2318yes—
356#389C2318yes—
357#389C2318yes—
358#389C2318yes—
359#389C2318yes—
360#389C2312yes—
361#389C2314yes—
362#389C2318yes—
363#389C2318yes—
364#389C2314yes—
365#389C2318yes—
366#389C2318yes—
367#389C2314yes—
368#389C2312yes—
369#389C2318yes—
370#389C2318yes—
371#389C2314yes—
372#389C2314yes—
373#389C2314yes—
374#389C2312yes—
375#389C2312yes—
376#389C2314yes—
377#389C2312yes—
378#388C2314yes—
379#388C2314yes—
380#388C2314yes—
381#388C2314yes—
382#388C2314yes—
383#388C2318yes—
384#388C2318yes—
385#388C2318yes—
386#388C2314yes—
387#388C2318yes—
388#388C2314yes—
389#388C2318yes—
390#388C2318yes—
391#387C2314yes—
392#387C2314yes—
393#387C2314yes—
394#387C2314yes—
395#387C2314yes—
396#387C2318yes—
397#387C2318yes—
398#387C2318yes—
399#387C2318yes—
400#387C2314yes—
401#387C2314yes—
402#387C2314yes—
403#387C2318yes—
404#387C2318yes—
405#387C2318yes—
406#387C2318yes—
407#387C2318yes—
408#387C2318yes—
409#387C2318yes—
410#387C2318yes—
411#387C2318yes—
412#387C2318yes—
413#387C2314yes—
414#387C2314yes—
415#387C2318yes—
416#387C2318yes—
417#387C2318yes—
418#387C2314yes—
419#387C2318yes—
420#387C2314yes—
421#387C2314yes—
422#387C2318yes—
423#387C2318yes—
424#387C2318yes—
425#387C2318yes—
426#387C2318yes—
427#385C2314yes—
428#385C2314yes—
429#384C2311yescharacteristic
430#384C2311yescharacteristic
431#384C2311yescharacteristic
432#384C2312yes—
433#384C2314yes—
434#384C2314yes—
435#384C2314yes—
436#384C2314yes—
437#384C2312yes—
438#384C2314yes—
439#384C2314yes—
440#384C2314yes—
441#384C2312yes—
442#384C2312yes—
443#384C2314yes—
444#384C2314yes—
445#384C2312yes—
446#383C2314yes—
447#383C2314yes—
448#383C2318yes—
449#383C2318yes—
450#382C2312yes—
451#382C2312yes—
452#382C2314yes—
453#382C2312yes—
454#382C2312yes—
455#382C2318yes—
456#382C2318yes—
457#382C2312yes—
458#381C2314yes—
459#380C2314yes—
460#380C2314yes—
461#380C2312yes—
462#380C2314yes—
463#380C2312yes—
464#380C2312yes—
465#380C2314yes—
466#380C2312yes—
467C4×C4⋊C4C2312yes—
468C4×C4⋊C4C2312yes—
469C4×C4⋊C4C2314yes—
470C4×C4⋊C4C2311yescharacteristic
471C4×C4⋊C4C2312yes—
472C4×C4⋊C4C2314yes—
473C4×C4⋊C4C2314yes—
474C4×C4⋊C4C2318yes—
475C4×C4⋊C4C2314yes—
476C4×C4⋊C4C2318yes—
477C4×C4⋊C4C2314yes—
478C4×C4⋊C4C2314yes—
479C4×C4⋊C4C2312yes—
480C4×C4⋊C4C2312yes—
481C4×C4⋊C4C2312yes—
482C4×C4⋊C4C2314yes—
483C4×C4⋊C4C2314yes—
484C4×C4⋊C4C2312yes—
485C4×C4⋊C4C2311yescharacteristic
486C4×C4⋊C4C2311yescharacteristic
487C4×C4⋊C4C2311yescharacteristic
488C4×C4⋊C4C2312yes—
489C4×C4⋊C4C2312yes—
490C4×C4⋊C4C2314yes—
491C4×C4⋊C4C2318yes—
492C4×C4⋊C4C2314yes—
493C4×C4⋊C4C2312yes—
494C4×C4⋊C4C2312yes—
495C4×C4⋊C4C2314yes—
496C4×C4⋊C4C2312yes—
497C4×C4⋊C4C2311yescharacteristic
498C4×C4⋊C4C2314yes—
499C4×C4⋊C4C2312yes—
500C4×C4⋊C4C2311yescharacteristic
501C4×C4⋊C4C2314yes—
502C4×C4⋊C4C2311yescharacteristic
503C4×C4⋊C4C2312yes—
504C4×C4⋊C4C2314yes—
505C4×C4⋊C4C2312yes—
506C4×C4⋊C4C2312yes—
507C4×C4⋊C4C2311yescharacteristic
508C4×C4⋊C4C2311yescharacteristic
509C4×C22⋊C4C2312yes—
510C4×C22⋊C4C2314yes—
511C4×C22⋊C4C2314yes—
512C4×C22⋊C4C2312yes—
513C4×C22⋊C4C2312yes—
514C4×C22⋊C4C2314yes—
515C4×C22⋊C4C2314yes—
516C4×C22⋊C4C2314yes—
517#376C2314yes—
518#376C2314yes—
519#376C2314yes—
520C43C2314yes—
521C43C2312yes—
522C43C2311yescharacteristic
523C43C2312yes—
524C22×Q8C2412yes—
525C22×Q8C2412yes—
526C22×Q8C2414yes—
527C22×Q8C2412yes—
528C22×Q8C2411yescharacteristic
529C22×Q8C2411yescharacteristic
530C22×D4C2411yescharacteristic
531C23×C4C2412yes—
532C23×C4C2412yes—
533C23×C4C2412yes—
534C4⋊Q8—28no—
535C4⋊Q8—24no—
536C4⋊Q8—28no—
537C4⋊Q8—216no—
538C4⋊Q8—28no—
539C4⋊Q8—24no—
540C4⋊Q8—24no—
541C4⋊Q8—44no—
542C4⋊Q8—48no—
543C4⋊Q8—48no—
544C4⋊Q8—48no—
545C4⋊Q8—48no—
546#126—216no—
547#126—416no—
548#125—216no—
549#125—232no—
550#125—28no—
551#125—48no—
552#125—48no—
553#125—416no—
554#125—416no—
555#124—28no—
556#124—44no—
557#124—48no—
558C22⋊Q8—28no—
559C22⋊Q8—28no—
560C22⋊Q8—48no—
561C4×Q8—216no—
562C4×Q8—24no—
563C4×Q8—24no—
564C4×Q8—28no—
565C4×Q8—28no—
566C4×Q8—216no—
567C4×Q8—28no—
568C4×Q8—28no—
569C4×Q8—24no—
570C4×Q8—24no—
571C4×Q8—24no—
572C4×Q8—44no—
573C4×Q8—48no—
574C4×Q8—48no—
575C4×Q8—48no—
576C4×Q8—48no—
577C4×Q8—48no—
578C4×Q8#4118yes—
579C4×D4—24no—
580C4×D4—24no—
581C4×D4—42no—
582#117—28no—
583#117—28no—
584#117—48no—
585C2×C4⋊C4C2412yes—
586C2×C4⋊C4C2414yes—
587C2×C4⋊C4C2412yes—
588C2×C4⋊C4C2412yes—
589C2×C4⋊C4C2411yescharacteristic
590C2×C4⋊C4C2411yescharacteristic
591C2×C4⋊C4C2411yescharacteristic
592C2×C4⋊C4C2412yes—
593C2×C4⋊C4C2412yes—
594C2×C4⋊C4C2412yes—
595C2×C4⋊C4C2414yes—
596C2×C4⋊C4C2411yescharacteristic
597C2×C4⋊C4C2414yes—
598C2×C4⋊C4C2412yes—
599C2×C4⋊C4C2414yes—
600C2×C4⋊C4C2418yes—
601C2×C4⋊C4C2414yes—
602C2×C4⋊C4C2414yes—
603C2×C4⋊C4C2418yes—
604C2×C4⋊C4C2411yescharacteristic
605C2×C4⋊C4C2411yescharacteristic
606C2×C4⋊C4C2411yescharacteristic
607C2×C4⋊C4C2412yes—
608C2×C4⋊C4C2412yes—
609C2×C4⋊C4C2412yes—
610C2×C4⋊C4C2412yes—
611C2×C4⋊C4C2412yes—
612C2×C4⋊C4C2414yes—
613C2×C4⋊C4C2412yes—
614C2×C4⋊C4C2414yes—
615C2×C4⋊C4C2414yes—
616C2×C4⋊C4C2418yes—
617C2×C4⋊C4C2412yes—
618C2×C4⋊C4C2414yes—
619C2×C4⋊C4C2414yes—
620C2×C4⋊C4C2412yes—
621C2×C4⋊C4C2412yes—
622C2×C4⋊C4C2414yes—
623C2×C4⋊C4C2414yes—
624C2×C4⋊C4C2412yes—
625C2×C4⋊C4C2418yes—
626C2×C4⋊C4C2418yes—
627C2×C4⋊C4C2418yes—
628C2×C4⋊C4C2418yes—
629C2×C4⋊C4C2418yes—
630C2×C4⋊C4C2414yes—
631C2×C4⋊C4C2418yes—
632C2×C4⋊C4C2418yes—
633C2×C4⋊C4C2414yes—
634C2×C4⋊C4C2418yes—
635C2×C4⋊C4C2418yes—
636C2×C4⋊C4C2418yes—
637C2×C4⋊C4C2418yes—
638C2×C4⋊C4C2414yes—
639C2×C4⋊C4C2412yes—
640C2×C4⋊C4C2412yes—
641C2×C4⋊C4C2412yes—
642C2×C4⋊C4C2414yes—
643C2×C4⋊C4C2418yes—
644C2×C4⋊C4C2414yes—
645C2×C4⋊C4C2414yes—
646C2×C4⋊C4C2411yescharacteristic
647C2×C4⋊C4C2412yes—
648C2×C4⋊C4C2411yescharacteristic
649C2×C22⋊C4C2414yes—
650C2×C22⋊C4C2414yes—
651C2×C22⋊C4C2412yes—
652C2×C22⋊C4C2412yes—
653C2×C22⋊C4C2414yes—
654C2×C22⋊C4C2414yes—
655C2×C22⋊C4C2418yes—
656C2×C22⋊C4C2412yes—
657C2×C22⋊C4C2418yes—
658C2×C22⋊C4C2414yes—
659C2×C22⋊C4C2414yes—
660C2×C22⋊C4C2414yes—
661C2×C22⋊C4C2414yes—
662C2×C42—28no—
663C2×C42C2414yes—
664C2×C42C2414yes—
665C2×C42C2411yescharacteristic
666C2×C42C2414yes—
667C2×C42C2414yes—
668C2×C42C2412yes—
669C2×C42C2414yes—
670C2×C42C2418yes—
671C2×C42C2412yes—
672C2×C42C2411yescharacteristic
673C2×C42C2412yes—
674C2×C42C2411yescharacteristic
675C2×C42C2412yes—
676C2×C42C2412yes—
677C2×C42C2412yes—
678C2×C42C2412yes—
679C2×C42C2412yes—
680C2×C42C2412yes—
681C2×C42C2412yes—
682C2×C42C2412yes—
683C2×C42C2412yes—
684C2×C42C2418yes—
685C2×C42C2418yes—
686C2×C42C2418yes—
687C2×C42C2414yes—
688C2×C42C2411yescharacteristic
689C2×C42C2414yes—
690C2×C42C2412yes—
691C2×C42C2412yes—
692C2×C42C2411yescharacteristic
693C2×C42C2412yes—
694C2×C42C2411yescharacteristic
695C2×C42C2411yescharacteristic
696#95C2412yes—
697#95C2414yes—
698#95C2414yes—
699#95C2414yes—
700#95C2414yes—
701#95C2414yes—
702#95C2414yes—
703#95C2414yes—
704#95C2414yes—
705#95C2414yes—
706#95C2414yes—
707#95C2414yes—
708#95C2412yes—
709#95C2412yes—
710#95C2412yes—
711#95C2414yes—
712#95C2414yes—
713#95C2414yes—
714#95C2414yes—
715#95C2414yes—
716#95C2414yes—
717#95C2414yes—
718#95C2412yes—
719#95C2414yes—
720#95C2412yes—
721#95C2414yes—
722#95C2412yes—
723#95C2412yes—
724#95C2414yes—
725#95C2412yes—
726#95C2418yes—
727#95C2418yes—
728#95C2418yes—
729#95C2418yes—
730#95C2414yes—
731#95C2414yes—
732#95C2414yes—
733#95C2418yes—
734#95C2418yes—
735#95C2414yes—
736#95C2414yes—
737#95C2414yes—
738#95C2418yes—
739#95C2418yes—
740#95C2414yes—
741#95C2414yes—
742#95C2414yes—
743#95C2414yes—
744#95C2414yes—
745#95C2418yes—
746#95C2418yes—
747#95C2418yes—
748C24C2512yes—
749C2×Q8—24no—
750C2×Q8—28no—
751C2×Q8—24no—
752C2×Q8—22no—
753C2×Q8—24no—
754C2×Q8—24no—
755C2×Q8—28no—
756C2×Q8—24no—
757C2×Q8—22no—
758C2×Q8—22no—
759C2×Q8—22no—
760C2×Q8—24no—
761C2×Q8—24no—
762C2×Q8—24no—
763C2×Q8—24no—
764C2×Q8—28no—
765C2×Q8C2×#4114yes—
766C2×Q82−1+414yes—
767C2×D4—22no—
768C2×D4—22no—
769C2×D4—22no—
770C22×C4—24no—
771C22×C4—24no—
772C22×C4—24no—
773C22×C4—24no—
774C22×C4—24no—
775C22×C4—24no—
776C22×C4—24no—
777C22×C4—42no—
778C22×C4—42no—
779C22×C4C2512yes—
780C22×C4C2512yes—
781C22×C4C2512yes—
782C22×C4C2511yescharacteristic
783C22×C4C2512yes—
784C22×C4C2514yes—
785C22×C4C2512yes—
786C22×C4C2512yes—
787C22×C4C2514yes—
788C22×C4C2514yes—
789C22×C4C2514yes—
790C22×C4C2512yes—
791C22×C4C2514yes—
792C22×C4C2518yes—
793C22×C4C2514yes—
794C22×C4C2512yes—
795C22×C4C2511yescharacteristic
796C22×C4C2512yes—
797C22×C4C2511yescharacteristic
798C22×C4C2511yescharacteristic
799C22×C4C2512yes—
800C22×C4C2512yes—
801C22×C4C2511yescharacteristic
802C22×C4C2511yescharacteristic
803C22×C4C2511yescharacteristic
804C4⋊C4—24no—
805C4⋊C4—22no—
806C4⋊C4—24no—
807C4⋊C4—28no—
808C4⋊C4—216no—
809C4⋊C4—28no—
810C4⋊C4—216no—
811C4⋊C4—28no—
812C4⋊C4—216no—
813C4⋊C4—28no—
814C4⋊C4—24no—
815C4⋊C4—24no—
816C4⋊C4—28no—
817C4⋊C4—22no—
818C4⋊C4—24no—
819C4⋊C4—24no—
820C4⋊C4—28no—
821C4⋊C4—22no—
822C4⋊C4—28no—
823C4⋊C4—24no—
824C4⋊C4—24no—
825C4⋊C4—28no—
826C4⋊C4—24no—
827C4⋊C4—24no—
828C4⋊C4—24no—
829C4⋊C4—24no—
830C4⋊C4—24no—
831C4⋊C4—22no—
832C4⋊C4—22no—
833C4⋊C4—22no—
834C4⋊C4—24no—
835C4⋊C4—28no—
836C4⋊C4—28no—
837C4⋊C4—28no—
838C4⋊C4—24no—
839C4⋊C4—28no—
840C4⋊C4—28no—
841C4⋊C4—24no—
842C4⋊C4—24no—
843C4⋊C4—22no—
844C4⋊C4—44no—
845C4⋊C4—42no—
846C4⋊C4—42no—
847C4⋊C4—42no—
848C4⋊C4—44no—
849C4⋊C4—44no—
850C4⋊C4—48no—
851C4⋊C4—44no—
852C4⋊C4—48no—
853C4⋊C4—48no—
854C4⋊C4—48no—
855C4⋊C4—48no—
856C4⋊C4—48no—
857C4⋊C4—48no—
858C4⋊C4—48no—
859C4⋊C4—48no—
860C4⋊C4—44no—
861C4⋊C4—48no—
862C4⋊C4—48no—
863C4⋊C4—44no—
864C4⋊C4—48no—
865C4⋊C4C2×#4114yes—
866C4⋊C4C2×#4118yes—
867C4⋊C42−1+414yes—
868C22⋊C4—28no—
869C22⋊C4—24no—
870C22⋊C4—28no—
871C22⋊C4—24no—
872C22⋊C4—28no—
873C22⋊C4—28no—
874C22⋊C4—44no—
875C22⋊C4—44no—
876C22⋊C4—48no—
877C22⋊C4—42no—
878C22⋊C4—48no—
879C22⋊C4—44no—
880C22⋊C4—44no—
881C42—28no—
882C42—216no—
883C42—28no—
884C42—28no—
885C42—28no—
886C42—24no—
887C42—24no—
888C42—24no—
889C42—24no—
890C42—28no—
891C42—24no—
892C42—24no—
893C42—22no—
894C42—22no—
895C42—24no—
896C42—24no—
897C42—24no—
898C42—24no—
899C42—22no—
900C42—24no—
901C42—24no—
902C42—41no—
903C42—42no—
904C42—44no—
905C42—42no—
906C42—48no—
907C42—44no—
908C42—48no—
909C42—48no—
910C42C2×#4114yes—
911C42C2×#4118yes—
912C42H(5,𝔽2)14yes—
913C422−1+414yes—
914C23—22no—
915C23—22no—
916C23—22no—
917C23—22no—
918C23—22no—
919C23—22no—
920C23—22no—
921C23C2611yescharacteristic
922Q8—28no—
923Q8—28no—
924Q8—48no—
925Q8—416no—
926Q8—48no—
927Q8—48no—
928D4—44no—
929C2×C4—22no—
930C2×C4—21no—
931C2×C4—21no—
932C2×C4—22no—
933C2×C4—22no—
934C2×C4—22no—
935C2×C4—22no—
936C2×C4—22no—
937C2×C4—22no—
938C2×C4—21no—
939C2×C4—21no—
940C2×C4—22no—
941C2×C4—21no—
942C2×C4—21no—
943C2×C4—24no—
944C2×C4—22no—
945C2×C4—24no—
946C2×C4—28no—
947C2×C4—24no—
948C2×C4—24no—
949C2×C4—24no—
950C2×C4—24no—
951C2×C4—22no—
952C2×C4—24no—
953C2×C4—22no—
954C2×C4—28no—
955C2×C4—24no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—24no—
961C2×C4—22no—
962C2×C4—21no—
963C2×C4—21no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—22no—
967C2×C4—22no—
968C2×C4—24no—
969C2×C4—24no—
970C2×C4—22no—
971C2×C4—24no—
972C2×C4—24no—
973C2×C4—21no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—22no—
977C2×C4—22no—
978C2×C4—24no—
979C2×C4—24no—
980C2×C4—28no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—24no—
985C2×C4—22no—
986C2×C4—24no—
987C2×C4—24no—
988C2×C4—48no—
989C2×C4—48no—
990C2×C4—84no—
991C2×C4C22×#4114yes—
992C2×C4C22×#4114yes—
993C2×C4C22×#4112yes—
994C2×C4C22×#4112yes—
995C2×C4C22×#4112yes—
996C2×C4C2×H(5,𝔽2)12yes—
997C2×C4C2×H(5,𝔽2)12yes—
998C2×C4C2×H(5,𝔽2)12yes—
999C2×C4C2×2−1+414yes—
1000C2×C4C2×2−1+412yes—
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×C4#58512yes—
1007C22—42no—
1008C22—42no—
1009C22—42no—
1010C22—42no—
1011C22—42no—
1012C22—42no—
1013C22—42no—
1014C22C23×#4111yescharacteristic
1015C22C22×H(5,𝔽2)11yescharacteristic
1016C22C22×2−1+411yescharacteristic
1017C22C22×2−1+411yescharacteristic
1018C22C22×2−1+411yescharacteristic
1019C22C2×#58511yescharacteristic
1020C222−1+611yescharacteristic
1021C4—24no—
1022C4—22no—
1023C4—24no—
1024C4—24no—
1025C4—24no—
1026C4—22no—
1027C4—22no—
1028C4—42no—
1029C4—44no—
1030C4—44no—
1031C4—41no—
1032C4—42no—
1033C4—44no—
1034C4—48no—
1035C4—44no—
1036C4—42no—
1037C4—44no—
1038C4—44no—
1039C4—42no—
1040C4—42no—
1041C4—42no—
1042C4—42no—
1043C4#350914yes—
1044C4#351714yes—
1045C4#355214yes—
1046C2—82no—
1047C2C2×#355211yescharacteristic
1048C2C2×#351711yescharacteristic
1049C2C2×#350911yescharacteristic
1050C2#6294611yescharacteristic
1051C2#6295911yescharacteristic
1052C2#6300111yescharacteristic
1053C2#6303211yescharacteristic
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. #59828C2semidirect
4. #59259C2semidirect
5. #50788C2semidirect
6. #46079C2semidirect
7. #45344C2semidirect
8. #45339C2semidirect
9. #42716C2semidirect
11. #40201C2semidirect
14. #39641C2semidirect
15. #38933C2semidirect
16. #36593C2semidirect
17. #36593C2semidirect
18. #36560C2semidirect
19. #36481C2semidirect
21. #35202C2semidirect
22. #35187C2semidirect
23. #34951C2semidirect
25. #34488C2semidirect

Maximal subgroups

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

subgroupindex
#598282
#596532
#594342
#592592
#507882
#460792
#453442
#453392
#427162
#427022
#402012
#397442
#396412
#389332
#365932
#365602
#364812
#361882
#352022
#351872
#349512
#349452
#344882
C4×#5562