Finite Group Databasebeta

← #7711003

Subgroups — #7711003

Order 512.

5126 conjugacy classes of subgroups.

The subgroup lattice has 1105 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59326C214yesmaximal, complemented
2#59136C212yesmaximal, complemented
3#59127C212yesmaximal, complemented
4#46154C214yesmaximal, complemented
5#46005C212yesmaximal, complemented
6#46004C212yesmaximal, complemented
7#39977C214yesmaximal, complemented
8#39668C214yesmaximal, complemented
9#39643C212yesmaximal, complemented
10#39632C212yesmaximal, complemented
11#39628C212yesmaximal, complemented
12#39621C212yesmaximal, complemented
13#39618C212yesmaximal, complemented
14#39615C212yesmaximal, complemented
15#38444C214yesmaximal, complemented
16#37561C212yesmaximal, complemented
17#37136C214yesmaximal, complemented
18#36635C211yesmaximal, characteristic, complemented
19C2×#2862C211yesmaximal, characteristic, complemented
20#36476C212yesmaximal, complemented
21#36276C212yesmaximal, complemented
22#36274C214yesmaximal, complemented
23#35016C214yesmaximal, complemented
24#34398C212yesmaximal
25C4×#532C211yesmaximal, characteristic
26C2×#554C2212yes—
27C2×D4×Q8C2214yes—
28C2×D4×Q8C2212yes—
29C2×#532C2211yescharacteristic
30C22×C4⋊Q8C2211yescharacteristic
31C22×C4⋊Q8C2211yescharacteristic
32C2×C4×#41C2212yes—
33#2864C2212yes—
34#2863C2212yes—
35#2863C2212yes—
36#2862C2212yes—
37#2862C2212yes—
38#2862C2212yes—
39#2862C2212yes—
40#2862C2212yes—
41#2862C2212yes—
42#2862C2212yes—
43#2862C2212yes—
44#2862C2211yescharacteristic
45#2859C2211yescharacteristic
46#2857C2211yescharacteristic
47#2857C2211yescharacteristic
48#2857C2214yes—
49#2855C2212yes—
50#2855C2212yes—
51#2855C2214yes—
52#2851C2212yes—
53#2845C2214yes—
54#2844C2214yes—
55#2811C2214yes—
56#2806C2214yes—
57#2806C2214yes—
58#2804C2214yes—
59#2804C2214yes—
60#2799C2218yes—
61#2788C2218yes—
62#2768C2218yes—
63#2763C2218yes—
64#2763C2218yes—
65#2755C2218yes—
66#2734C2214yes—
67#2732C2214yes—
68#2732C2214yes—
69#2729C2218yes—
70#2729C2218yes—
71#2704C2218yes—
72#2692C2218yes—
73#2692C2218yes—
74#2677C2218yes—
75#2666C2218yes—
76#2665C2218yes—
77#2660C2214yes—
78#2659C2214yes—
79#2647C2214yes—
80#2646C2214yes—
81#2607C2218yes—
82#2589C2218yes—
83#2586C2218yes—
84#2582C2214yes—
85#2580C2214yes—
86#2574C2218yes—
87#2570C2214yes—
88#2568C2214yes—
89#2567C2212yes—
90#2566C2214yes—
91#2564C2218yes—
92#2563C2212yes—
93#2563C2214yes—
94#2551C2214yes—
95#2550C2214yes—
96#2550C2214yes—
97#2550C2214yes—
98#2549C2218yes—
99#2549C2218yes—
100#2546C2212yes—
101#2542C2212yes—
102#2511C2214yes—
103#2509C2214yes—
104#2508C2214yes—
105#2505C2218yes—
106#2502C2214yes—
107#2492C2214yes—
108#2492C2214yes—
109#2452C2214yes—
110#2452C2214yes—
111#2451C2218yes—
112#2450C2218yes—
113#2450C2218yes—
114#2450C2218yes—
115#2450C2218yes—
116#2449C2218yes—
117#2446C2214yes—
118#2442C2214yes—
119#2440C2214yes—
120#2440C2214yes—
121#2439C2218yes—
122#2438C2218yes—
123#2438C2218yes—
124#2434C2214yes—
125#2434C2214yes—
126#2429C2214yes—
127#2423C2214yes—
128#2417C2214yes—
129#2417C2214yes—
130#2417C2214yes—
131#2409C2218yes—
132#2409C2214yes—
133#2409C2214yes—
134#2409C2214yes—
135#2379C2214yes—
136#2379C2214yes—
137#2369C2212yes—
138#2365C2212yes—
139#2361C2214yes—
140#2361C2214yes—
141#2357C2214yes—
142#2355C2214yes—
143#2349C2214yes—
144#2349C2218yes—
145#2349C2214yes—
146D4×C4⋊C4C2214yes—
147#2339C2218yes—
148#2331C2214yes—
149#2329C2218yes—
150#2328C2214yes—
151#2325C2214yes—
152#2325C2214yes—
153#2318C2218yes—
154C4×C4⋊Q8C2211yescharacteristic
155C4×C4⋊Q8C2211yescharacteristic
156C4×C4⋊Q8C2211yescharacteristic
157C4×C4⋊Q8C2211yescharacteristic
158C4×#127C2211yescharacteristic
159C4×#127C2211yescharacteristic
160C4×#125C2212yes—
161C4×#124C2212yes—
162C4×#124C2212yes—
163C4×C22⋊Q8C2212yes—
164C4×C22⋊Q8C2212yes—
165C4×C22⋊Q8C2214yes—
166C4×#121C2212yes—
167C4×#121C2212yes—
168C4×#121C2212yes—
169C4×#121C2212yes—
170#2297C2212yes—
171#2295C2212yes—
172#2295C2212yes—
173C2×#391C2212yes—
174C2×#391C2212yes—
175C2×#391C2212yes—
176C2×#391C2212yes—
177C2×#391C2214yes—
178#2293C2212yes—
179#2293C2212yes—
180#2285C2211yescharacteristic
181#2283C2212yes—
182C2×#382C2212yes—
183C2×#382C2212yes—
184C42×D4C2212yes—
185C42×D4C2212yes—
186C2×C43C2211yescharacteristic
187C22×#41C2312yes—
188C23×Q8C2312yes—
189C23×Q8C2312yes—
190C23×Q8C2314yes—
191#554—48no—
192D4×Q8—48no—
193D4×Q8—416no—
194#532Q8116yescomplemented
195C2×C4⋊Q8—44no—
196C2×C4⋊Q8—44no—
197C2×C4⋊Q8C2312yes—
198C2×C4⋊Q8C2312yes—
199C2×C4⋊Q8C2311yescharacteristic
200C2×C4⋊Q8C2311yescharacteristic
201C2×C4⋊Q8C2314yes—
202C2×C4⋊Q8C2314yes—
203C2×C4⋊Q8C2312yes—
204C2×C4⋊Q8C2312yes—
205C2×C4⋊Q8C2312yes—
206C2×C4⋊Q8C2312yes—
207C2×C4⋊Q8C2312yes—
208C2×C4⋊Q8C2312yes—
209C2×C4⋊Q8C2318yes—
210C2×C4⋊Q8C2311yescharacteristic
211C2×#127C2311yescharacteristic
212C2×#125C2312yes—
213C2×#125C2314yes—
214C2×#124C2312yes—
215C2×C22⋊Q8C2312yes—
216C2×C22⋊Q8C2318yes—
217C2×C22⋊Q8C2318yes—
218C2×C22⋊Q8C2312yes—
219C2×C22⋊Q8C2314yes—
220C2×C22⋊Q8C2314yes—
221C2×C22⋊Q8C2314yes—
222C2×C22⋊Q8C2314yes—
223C2×C22⋊Q8C2318yes—
224C2×C22⋊Q8C2318yes—
225C2×C22⋊Q8C2318yes—
226C2×#121C2312yes—
227C2×#121C2312yes—
228C4×#41—48no—
229C2×C4×Q8C2312yes—
230C2×C4×Q8C2312yes—
231C2×C4×Q8C2312yes—
232C2×C4×Q8C2312yes—
233C2×C4×Q8C2314yes—
234C2×C4×D4C2312yes—
235C2×C4×D4C2312yes—
236C2×C4×D4C2314yes—
237C2×C4×D4C2312yes—
238C2×C4×D4C2312yes—
239C2×C4×D4C2312yes—
240C2×C4×D4C2312yes—
241C2×C4×D4C2314yes—
242C2×C4×D4C2318yes—
243C2×C4×D4C2314yes—
244C2×C4×D4C2318yes—
245C2×C4×D4C2314yes—
246C2×C4×D4C2312yes—
247C2×C4×D4C2312yes—
248C2×#117C2312yes—
249C2×#117C2314yes—
250C22×C4⋊C4C2312yes—
251C22×C4⋊C4C2314yes—
252C22×C4⋊C4C2312yes—
253C22×C4⋊C4C2312yes—
254C22×C4⋊C4C2312yes—
255C22×C42C2311yescharacteristic
256C22×C42C2311yescharacteristic
257C22×C42C2311yescharacteristic
258C22×C42C2311yescharacteristic
259C22×C42C2311yescharacteristic
260C22×C42C2314yes—
261C22×C42C2311yescharacteristic
262C22×C42C2311yescharacteristic
263#400C2318yes—
264#400C2318yes—
265#400C2318yes—
266#400C2318yes—
267#400C2318yes—
268#400C2318yes—
269#400C2318yes—
270#399C2318yes—
271#399C2318yes—
272#398C2318yes—
273#398C2318yes—
274#398C2318yes—
275#398C2318yes—
276#398C2318yes—
277#398C2318yes—
278#398C2318yes—
279#398C2318yes—
280#398C2318yes—
281#398C2318yes—
282#398C2318yes—
283#398C2318yes—
284#396C2318yes—
285#396C2318yes—
286#396C2318yes—
287#396C2318yes—
288#395C2318yes—
289#395C2318yes—
290#395C2318yes—
291#395C2318yes—
292#395C2318yes—
293#395C2318yes—
294#395C2318yes—
295#395C2318yes—
296#395C2318yes—
297#393C2318yes—
298#393C2318yes—
299#393C2318yes—
300#393C2318yes—
301#393C2318yes—
302#393C2318yes—
303#391C2312yes—
304#391C2312yes—
305#391C2312yes—
306#391C2312yes—
307#391C2314yes—
308#391C2312yes—
309#391C2314yes—
310#391C2318yes—
311#391C2314yes—
312#391C2318yes—
313#391C2318yes—
314#391C2314yes—
315#391C2314yes—
316#391C2318yes—
317#391C2314yes—
318#391C2314yes—
319#391C2318yes—
320#391C2314yes—
321#391C2312yes—
322#391C2312yes—
323#391C2312yes—
324#391C2314yes—
325#391C2314yes—
326#391C2314yes—
327#391C2314yes—
328#391C2314yes—
329#391C2314yes—
330#391C2314yes—
331#391C2314yes—
332#391C2314yes—
333#391C2314yes—
334#391C2314yes—
335#391C2312yes—
336#391C2312yes—
337#391C2318yes—
338#391C2318yes—
339#390C2312yes—
340#390C2312yes—
341#390C2312yes—
342#390C2312yes—
343#390C2312yes—
344#390C2312yes—
345#390C2314yes—
346#390C2314yes—
347#389C2312yes—
348#389C2312yes—
349#389C2312yes—
350#389C2312yes—
351#389C2312yes—
352#389C2312yes—
353#389C2312yes—
354#389C2312yes—
355#389C2312yes—
356#389C2312yes—
357#389C2314yes—
358#389C2314yes—
359#389C2314yes—
360#389C2314yes—
361#389C2312yes—
362#389C2314yes—
363#389C2318yes—
364#389C2318yes—
365#389C2318yes—
366#389C2318yes—
367#389C2314yes—
368#389C2312yes—
369#389C2312yes—
370#389C2312yes—
371#389C2312yes—
372#389C2312yes—
373#389C2318yes—
374#389C2314yes—
375#388C2318yes—
376#388C2318yes—
377#388C2318yes—
378#388C2318yes—
379#388C2314yes—
380#388C2314yes—
381#388C2314yes—
382#388C2314yes—
383#387C2314yes—
384#387C2314yes—
385#387C2318yes—
386#387C2318yes—
387#387C2318yes—
388#387C2318yes—
389#387C2318yes—
390#387C2318yes—
391#387C2314yes—
392#387C2318yes—
393#387C2314yes—
394#387C2318yes—
395#387C2318yes—
396#387C2314yes—
397#387C2314yes—
398#387C2314yes—
399#387C2314yes—
400#386C2314yes—
401#386C2318yes—
402#386C2318yes—
403#386C2318yes—
404#386C2318yes—
405#386C2318yes—
406#386C2318yes—
407#386C2314yes—
408#385C2318yes—
409#385C2318yes—
410#385C2318yes—
411#385C2318yes—
412#385C2318yes—
413#385C2318yes—
414#385C2318yes—
415#385C2318yes—
416#385C2318yes—
417#385C2318yes—
418#385C2314yes—
419#385C2314yes—
420#385C2318yes—
421#385C2318yes—
422#385C2318yes—
423#385C2318yes—
424#384C2311yescharacteristic
425#384C2311yescharacteristic
426#384C2311yescharacteristic
427#384C2311yescharacteristic
428#384C2314yes—
429#384C2314yes—
430#383C2314yes—
431#382C2312yes—
432#382C2314yes—
433#382C2314yes—
434#382C2318yes—
435#382C2314yes—
436#382C2314yes—
437#382C2314yes—
438#382C2314yes—
439#382C2314yes—
440#382C2312yes—
441#382C2312yes—
442#382C2314yes—
443#382C2312yes—
444#382C2314yes—
445#381C2318yes—
446#381C2314yes—
447#380C2318yes—
448#380C2314yes—
449#380C2318yes—
450#380C2314yes—
451#380C2312yes—
452#380C2318yes—
453#380C2318yes—
454#380C2318yes—
455#380C2312yes—
456#380C2312yes—
457#380C2312yes—
458#380C2312yes—
459#380C2312yes—
460C4×C4⋊C4C2312yes—
461C4×C4⋊C4C2312yes—
462C4×C4⋊C4C2314yes—
463C4×C4⋊C4C2314yes—
464C4×C4⋊C4C2312yes—
465C4×C4⋊C4C2312yes—
466C4×C4⋊C4C2312yes—
467C4×C4⋊C4C2312yes—
468C4×C4⋊C4C2312yes—
469C4×C4⋊C4C2312yes—
470C4×C4⋊C4C2314yes—
471C4×C4⋊C4C2312yes—
472C4×C4⋊C4C2318yes—
473C4×C4⋊C4C2314yes—
474C4×C4⋊C4C2314yes—
475C4×C4⋊C4C2312yes—
476C4×C22⋊C4C2318yes—
477C4×C22⋊C4C2314yes—
478C4×C22⋊C4C2314yes—
479C4×C22⋊C4C2314yes—
480C4×C22⋊C4C2314yes—
481C4×C22⋊C4C2314yes—
482C4×C22⋊C4C2314yes—
483C4×C22⋊C4C2314yes—
484#376C2314yes—
485C2×#95C2314yes—
486C2×#95C2318yes—
487C2×#95C2314yes—
488C2×#95C2314yes—
489C2×#95C2318yes—
490C2×#95C2314yes—
491C43C2311yescharacteristic
492C43C2311yescharacteristic
493C43C2311yescharacteristic
494C43C2311yescharacteristic
495C43C2311yescharacteristic
496C43C2311yescharacteristic
497C43C2311yescharacteristic
498C43C2311yescharacteristic
499C2×#41—44no—
500C2×#41—44no—
501C2×#41C2×Q8116yescomplemented
502C22×Q8—28no—
503C22×Q8—44no—
504C22×Q8—44no—
505C22×Q8—44no—
506C22×Q8—48no—
507C22×Q8—48no—
508C22×Q8—44no—
509C22×Q8—44no—
510C22×Q8—48no—
511C22×Q8C2412yes—
512C22×Q8C2414yes—
513C22×Q8C2412yes—
514C22×Q8C2414yes—
515C22×Q8C2414yes—
516C22×Q8C2414yes—
517C22×Q8C2418yes—
518C22×Q8C2412yes—
519C22×D4C2412yes—
520C22×D4C2414yes—
521C22×D4C2412yes—
522C22×D4C2412yes—
523C23×C4C2411yescharacteristic
524C23×C4C2414yes—
525C23×C4C2411yescharacteristic
526C23×C4C2411yescharacteristic
527C23×C4C2411yescharacteristic
528C23×C4C2411yescharacteristic
529C23×C4C2411yescharacteristic
530C23×C4C2414yes—
531C23×C4C2414yes—
532C23×C4C2414yes—
533C23×C4C2418yes—
534C23×C4C2418yes—
535C23×C4C2414yes—
536C23×C4C2411yescharacteristic
537C4⋊Q8—28no—
538C4⋊Q8—28no—
539C4⋊Q8—44no—
540C4⋊Q8—44no—
541C4⋊Q8—44no—
542C4⋊Q8—44no—
543C4⋊Q8—42no—
544C4⋊Q8—48no—
545C4⋊Q8—44no—
546C4⋊Q8—44no—
547C4⋊Q8—42no—
548C4⋊Q8—48no—
549C4⋊Q8—416no—
550C4⋊Q8C2×Q818yescomplemented
551#127C2×Q818yescomplemented
552#125—44no—
553#125—48no—
554#124C2×Q8116yescomplemented
555C22⋊Q8—28no—
556C22⋊Q8—44no—
557C22⋊Q8—416no—
558C22⋊Q8—416no—
559C22⋊Q8—416no—
560C22⋊Q8—416no—
561C22⋊Q8—416no—
562C22⋊Q8—48no—
563C22⋊Q8—48no—
564C22⋊Q8—48no—
565C22⋊Q8—48no—
566#121C2×Q8116yescomplemented
567#121C2×Q8116yescomplemented
568C4×Q8—28no—
569C4×Q8—28no—
570C4×Q8—44no—
571C4×Q8—44no—
572C4×Q8—48no—
573C4×D4—216no—
574C4×D4—28no—
575C4×D4—28no—
576C4×D4—44no—
577C4×D4—44no—
578C4×D4—48no—
579C4×D4—48no—
580C4×D4—44no—
581C4×D4—44no—
582C4×D4—416no—
583C4×D4—48no—
584C4×D4—416no—
585C4×D4C2×Q8116yescomplemented
586C4×D4C2×Q8116yescomplemented
587#117—48no—
588#117—44no—
589C2×C4⋊C4—44no—
590C2×C4⋊C4—44no—
591C2×C4⋊C4—44no—
592C2×C4⋊C4—44no—
593C2×C4⋊C4—48no—
594C2×C4⋊C4C2412yes—
595C2×C4⋊C4C2414yes—
596C2×C4⋊C4C2414yes—
597C2×C4⋊C4C2414yes—
598C2×C4⋊C4C2414yes—
599C2×C4⋊C4C2414yes—
600C2×C4⋊C4C2412yes—
601C2×C4⋊C4C2412yes—
602C2×C4⋊C4C2412yes—
603C2×C4⋊C4C2414yes—
604C2×C4⋊C4C2414yes—
605C2×C4⋊C4C2412yes—
606C2×C4⋊C4C2414yes—
607C2×C4⋊C4C2414yes—
608C2×C4⋊C4C2412yes—
609C2×C4⋊C4C2418yes—
610C2×C4⋊C4C2414yes—
611C2×C4⋊C4C2414yes—
612C2×C4⋊C4C2414yes—
613C2×C4⋊C4C2414yes—
614C2×C4⋊C4C2414yes—
615C2×C4⋊C4C2412yes—
616C2×C4⋊C4C2412yes—
617C2×C4⋊C4C2418yes—
618C2×C4⋊C4C2412yes—
619C2×C4⋊C4C2412yes—
620C2×C4⋊C4C2418yes—
621C2×C4⋊C4C2418yes—
622C2×C4⋊C4C2418yes—
623C2×C4⋊C4C2418yes—
624C2×C4⋊C4C2418yes—
625C2×C4⋊C4C2418yes—
626C2×C4⋊C4C2414yes—
627C2×C4⋊C4C2412yes—
628C2×C4⋊C4C2418yes—
629C2×C4⋊C4C2418yes—
630C2×C4⋊C4C2418yes—
631C2×C4⋊C4C2414yes—
632C2×C4⋊C4C2412yes—
633C2×C4⋊C4C2412yes—
634C2×C4⋊C4C2412yes—
635C2×C4⋊C4C2412yes—
636C2×C4⋊C4C2412yes—
637C2×C4⋊C4C2412yes—
638C2×C4⋊C4C2412yes—
639C2×C22⋊C4C2414yes—
640C2×C22⋊C4C2414yes—
641C2×C22⋊C4C2414yes—
642C2×C22⋊C4C2414yes—
643C2×C22⋊C4C2414yes—
644C2×C22⋊C4C2414yes—
645C2×C22⋊C4C2414yes—
646C2×C22⋊C4C2414yes—
647C2×C22⋊C4C2418yes—
648C2×C22⋊C4C2418yes—
649C2×C22⋊C4C2418yes—
650C2×C22⋊C4C2414yes—
651C2×C22⋊C4C2418yes—
652C2×C22⋊C4C2418yes—
653C2×C22⋊C4C2418yes—
654C2×C22⋊C4C2414yes—
655C2×C22⋊C4C2414yes—
656C2×C42—24no—
657C2×C42—24no—
658C2×C42—24no—
659C2×C42—48no—
660C2×C42—42no—
661C2×C42—42no—
662C2×C42—42no—
663C2×C42C2×Q818yescomplemented
664C2×C42C2411yescharacteristic
665C2×C42C2411yescharacteristic
666C2×C42C2411yescharacteristic
667C2×C42C2414yes—
668C2×C42C2411yescharacteristic
669C2×C42C2411yescharacteristic
670C2×C42C2414yes—
671C2×C42C2414yes—
672C2×C42C2411yescharacteristic
673C2×C42C2411yescharacteristic
674C2×C42C2411yescharacteristic
675C2×C42C2411yescharacteristic
676C2×C42C2411yescharacteristic
677C2×C42C2411yescharacteristic
678C2×C42C2411yescharacteristic
679C2×C42C2411yescharacteristic
680C2×C42C2411yescharacteristic
681C2×C42C2414yes—
682C2×C42C2418yes—
683C2×C42C2414yes—
684C2×C42C2418yes—
685C2×C42C2411yescharacteristic
686C2×C42C2411yescharacteristic
687C2×C42C2411yescharacteristic
688C2×C42C2411yescharacteristic
689C2×C42C2411yescharacteristic
690C2×C42C2411yescharacteristic
691C2×C42C2411yescharacteristic
692C2×C42C2411yescharacteristic
693C2×C42C2411yescharacteristic
694C2×C42C2411yescharacteristic
695C2×C42C2411yescharacteristic
696C2×C42C2411yescharacteristic
697C2×C42C2411yescharacteristic
698C2×C42C2411yescharacteristic
699#95C2418yes—
700#95C2414yes—
701#95C2414yes—
702#95C2418yes—
703#95C2418yes—
704#95C2418yes—
705#95C2418yes—
706#95C2418yes—
707#95C2418yes—
708#95C2418yes—
709#95C2418yes—
710#95C2418yes—
711#95C2418yes—
712#95C2418yes—
713#95C2414yes—
714#95C2414yes—
715#95C2414yes—
716#95C2414yes—
717#95C2414yes—
718#95C2414yes—
719#95C2414yes—
720#95C2414yes—
721#95C2414yes—
722#95C2414yes—
723#95C2414yes—
724#95C2414yes—
725#95C2414yes—
726#95C2418yes—
727#95C2414yes—
728#95C2414yes—
729#95C2418yes—
730#95C2418yes—
731#95C2414yes—
732#95C2414yes—
733#95C2418yes—
734#95C2414yes—
735#95C2418yes—
736#95C2418yes—
737C24C2514yes—
738C24C2511yescharacteristic
739#41—432no—
740C2×Q8—24no—
741C2×Q8—28no—
742C2×Q8—24no—
743C2×Q8—28no—
744C2×Q8—28no—
745C2×Q8—28no—
746C2×Q8—24no—
747C2×Q8—28no—
748C2×Q8—24no—
749C2×Q8—28no—
750C2×Q8—42no—
751C2×Q8—42no—
752C2×Q8—48no—
753C2×Q8—48no—
754C2×Q8—42no—
755C2×Q8—44no—
756C2×Q8—44no—
757C2×Q8—42no—
758C2×Q8—44no—
759C2×Q8—44no—
760C2×Q8—44no—
761C2×Q8—44no—
762C2×Q8—48no—
763C2×Q8—816no—
764C2×Q8—816no—
765C2×Q8—832no—
766C2×Q8C22×Q818yes—
767C2×D4—28no—
768C2×D4—28no—
769C2×D4—24no—
770C2×D4—24no—
771C2×D4—42no—
772C2×D4—42no—
773C2×D4—42no—
774C2×D4—42no—
775C2×D4C22×Q818yes—
776C2×D4C22×Q8116yes—
777C2×D4C22×Q818yes—
778C2×D4C22×Q818yes—
779C22×C4—22no—
780C22×C4—22no—
781C22×C4—22no—
782C22×C4—22no—
783C22×C4—22no—
784C22×C4—22no—
785C22×C4—22no—
786C22×C4—22no—
787C22×C4—22no—
788C22×C4—22no—
789C22×C4—22no—
790C22×C4—28no—
791C22×C4—28no—
792C22×C4—28no—
793C22×C4—28no—
794C22×C4—22no—
795C22×C4—22no—
796C22×C4—28no—
797C22×C4—28no—
798C22×C4—44no—
799C22×C4—41no—
800C22×C4—41no—
801C22×C4—41no—
802C22×C4—41no—
803C22×C4—44no—
804C22×C4—44no—
805C22×C4—44no—
806C22×C4—44no—
807C22×C4—48no—
808C22×C4—48no—
809C22×C4—44no—
810C22×C4—44no—
811C22×C4—44no—
812C22×C4—48no—
813C22×C4—48no—
814C22×C4—48no—
815C22×C4—48no—
816C22×C4C22×Q814yes—
817C22×C4C22×Q814yes—
818C22×C4C22×Q814yes—
819C22×C4C22×Q8116yes—
820C22×C4H(5,𝔽2)14yes—
821C22×C4C2511yescharacteristic
822C22×C4C2514yes—
823C22×C4C2518yes—
824C22×C4C2511yescharacteristic
825C22×C4C2514yes—
826C22×C4C2514yes—
827C22×C4C2518yes—
828C22×C4C2514yes—
829C22×C4C2514yes—
830C22×C4C2514yes—
831C22×C4C2511yescharacteristic
832C22×C4C2511yescharacteristic
833C22×C4C2511yescharacteristic
834C22×C4C2511yescharacteristic
835C22×C4C2511yescharacteristic
836C22×C4C2514yes—
837C22×C4C2511yescharacteristic
838C22×C4C2511yescharacteristic
839C22×C4C2511yescharacteristic
840C22×C4C2511yescharacteristic
841C22×C4C2511yescharacteristic
842C22×C4C2511yescharacteristic
843C22×C4C2511yescharacteristic
844C4⋊C4—24no—
845C4⋊C4—28no—
846C4⋊C4—28no—
847C4⋊C4—28no—
848C4⋊C4—28no—
849C4⋊C4—28no—
850C4⋊C4—24no—
851C4⋊C4—28no—
852C4⋊C4—24no—
853C4⋊C4—28no—
854C4⋊C4—24no—
855C4⋊C4—24no—
856C4⋊C4—28no—
857C4⋊C4—28no—
858C4⋊C4—24no—
859C4⋊C4—48no—
860C4⋊C4—44no—
861C4⋊C4—44no—
862C4⋊C4—44no—
863C4⋊C4—44no—
864C4⋊C4—42no—
865C4⋊C4—42no—
866C4⋊C4—44no—
867C4⋊C4—42no—
868C4⋊C4—42no—
869C4⋊C4—48no—
870C4⋊C4—48no—
871C4⋊C4—48no—
872C4⋊C4—42no—
873C4⋊C4—44no—
874C4⋊C4—48no—
875C4⋊C4—48no—
876C4⋊C4—48no—
877C4⋊C4—48no—
878C4⋊C4—48no—
879C4⋊C4—48no—
880C4⋊C4—48no—
881C4⋊C4—42no—
882C4⋊C4—42no—
883C4⋊C4—44no—
884C4⋊C4—42no—
885C4⋊C4—42no—
886C4⋊C4—42no—
887C4⋊C4C22×Q818yes—
888C4⋊C4C22×Q818yes—
889C22⋊C4—28no—
890C22⋊C4—28no—
891C22⋊C4—28no—
892C22⋊C4—28no—
893C22⋊C4—28no—
894C22⋊C4—28no—
895C22⋊C4—28no—
896C22⋊C4—44no—
897C22⋊C4—44no—
898C22⋊C4—48no—
899C22⋊C4—48no—
900C22⋊C4—48no—
901C22⋊C4—48no—
902C22⋊C4—48no—
903C22⋊C4—48no—
904C22⋊C4C22×Q8116yes—
905C22⋊C4C22×Q8116yes—
906C42—22no—
907C42—22no—
908C42—22no—
909C42—22no—
910C42—22no—
911C42—22no—
912C42—22no—
913C42—28no—
914C42—28no—
915C42—22no—
916C42—22no—
917C42—22no—
918C42—28no—
919C42—22no—
920C42—22no—
921C42—22no—
922C42—22no—
923C42—41no—
924C42—41no—
925C42—41no—
926C42—41no—
927C42—41no—
928C42—41no—
929C42—41no—
930C42—41no—
931C42—44no—
932C42—44no—
933C42—48no—
934C42—48no—
935C42C22×Q814yes—
936C42C22×Q814yes—
937C42C22×Q814yes—
938C42C22×Q814yes—
939C42H(5,𝔽2)14yes—
940C422−1+414yes—
941C23—21no—
942C23—21no—
943C23—21no—
944C23—21no—
945C23—24no—
946C23—24no—
947C23—24no—
948C23—24no—
949C23—24no—
950C23—24no—
951C23C23×Q818yes—
952C23C23×Q812yes—
953C23C2×H(5,𝔽2)12yes—
954C23#58512yes—
955C23C2611yescharacteristic
956Q8—48no—
957Q8—48no—
958Q8—416no—
959Q8—84no—
960Q8—88no—
961Q8—88no—
962Q8—88no—
963Q8—816no—
964D4—232no—
965D4—216no—
966D4—48no—
967D4—48no—
968C2×C4—28no—
969C2×C4—21no—
970C2×C4—21no—
971C2×C4—21no—
972C2×C4—21no—
973C2×C4—21no—
974C2×C4—21no—
975C2×C4—24no—
976C2×C4—21no—
977C2×C4—21no—
978C2×C4—21no—
979C2×C4—21no—
980C2×C4—21no—
981C2×C4—21no—
982C2×C4—21no—
983C2×C4—21no—
984C2×C4—24no—
985C2×C4—21no—
986C2×C4—21no—
987C2×C4—21no—
988C2×C4—21no—
989C2×C4—21no—
990C2×C4—21no—
991C2×C4—28no—
992C2×C4—28no—
993C2×C4—28no—
994C2×C4—21no—
995C2×C4—24no—
996C2×C4—24no—
997C2×C4—24no—
998C2×C4—24no—
999C2×C4—24no—
1000C2×C4—28no—
1001C2×C4—24no—
1002C2×C4—24no—
1003C2×C4—28no—
1004C2×C4—28no—
1005C2×C4—21no—
1006C2×C4—21no—
1007C2×C4—24no—
1008C2×C4—24no—
1009C2×C4—24no—
1010C2×C4—21no—
1011C2×C4—21no—
1012C2×C4—24no—
1013C2×C4—21no—
1014C2×C4—28no—
1015C2×C4—24no—
1016C2×C4—24no—
1017C2×C4—24no—
1018C2×C4—24no—
1019C2×C4—24no—
1020C2×C4—28no—
1021C2×C4—28no—
1022C2×C4—24no—
1023C2×C4—24no—
1024C2×C4—44no—
1025C2×C4—416no—
1026C2×C4—44no—
1027C2×C4—44no—
1028C2×C4—416no—
1029C2×C4—88no—
1030C2×C4—88no—
1031C2×C4—88no—
1032C2×C4—816no—
1033C2×C4—168no—
1034C2×C4C23×Q812yes—
1035C2×C4C23×Q812yes—
1036C2×C4C23×Q812yes—
1037C2×C4C23×Q812yes—
1038C2×C4C23×Q812yes—
1039C2×C4C23×Q818yes—
1040C2×C4C23×Q812yes—
1041C2×C4C2×H(5,𝔽2)12yes—
1042C2×C4C2×H(5,𝔽2)12yes—
1043C2×C4C2×H(5,𝔽2)12yes—
1044C2×C4C2×H(5,𝔽2)12yes—
1045C2×C4C2×H(5,𝔽2)12yes—
1046C2×C4C2×2−1+412yes—
1047C2×C4C2×2−1+412yes—
1048C2×C4C2×2−1+412yes—
1049C2×C4#58512yes—
1050C2×C4#58512yes—
1051C22—22no—
1052C22—22no—
1053C22—22no—
1054C22—22no—
1055C22—22no—
1056C22—22no—
1057C22—28no—
1058C22—28no—
1059C22—28no—
1060C22—44no—
1061C22—44no—
1062C22—44no—
1063C22—44no—
1064C22#350114yes—
1065C22C24×Q811yescharacteristic
1066C22C22×H(5,𝔽2)11yescharacteristic
1067C22C22×H(5,𝔽2)11yescharacteristic
1068C22C22×2−1+411yescharacteristic
1069C22C2×#58511yescharacteristic
1070C22C2×#58511yescharacteristic
1071C22C2×#58511yescharacteristic
1072C4—22no—
1073C4—22no—
1074C4—22no—
1075C4—22no—
1076C4—28no—
1077C4—22no—
1078C4—22no—
1079C4—22no—
1080C4—22no—
1081C4—22no—
1082C4—22no—
1083C4—44no—
1084C4—44no—
1085C4—48no—
1086C4—41no—
1087C4—44no—
1088C4—48no—
1089C4—44no—
1090C4—44no—
1091C4—41no—
1092C4—44no—
1093C4#350314yes—
1094C4#355814yes—
1095C2—24no—
1096C2—48no—
1097C2C2×#355811yescharacteristic
1098C2#6275211yescharacteristic
1099C2C2×#350111yescharacteristic
1100C2C2×#350311yescharacteristic
1101C2#6281311yescharacteristic
1102C2#6282411yescharacteristic
1103C2#6283511yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#532C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59326C2semidirect
2. #59136C2semidirect
3. #59127C2semidirect
4. #46154C2semidirect
5. #46005C2semidirect
6. #46004C2semidirect
7. #39977C2semidirect
8. #39668C2semidirect
9. #39643C2semidirect
10. #39632C2semidirect
11. #39628C2semidirect
12. #39621C2semidirect
13. #39618C2semidirect
14. #39615C2semidirect
15. #38444C2semidirect
16. #37561C2semidirect
17. #37136C2semidirect
18. #36635C2semidirect
19. C2×#2862C2semidirect
20. #36476C2semidirect
21. #36276C2semidirect
22. #36274C2semidirect
23. #35016C2semidirect
194. #532Q8semidirect
501. C2×#41C2×Q8semidirect
550. C4⋊Q8C2×Q8semidirect
551. #127C2×Q8semidirect
554. #124C2×Q8semidirect
566. #121C2×Q8semidirect
567. #121C2×Q8semidirect
585. C4×D4C2×Q8semidirect
586. C4×D4C2×Q8semidirect
663. C2×C42C2×Q8semidirect

Maximal subgroups

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

subgroupindex
#593262
#591362
#591272
#461542
#460052
#460042
#399772
#396682
#396432
#396322
#396282
#396212
#396182
#396152
#384442
#375612
#371362
#366352
C2×#28622
#364762
#362762
#362742
#350162
#343982
C4×#5322