Finite Group Databasebeta

← #7987593

Subgroups — #7987593

Order 512.

7200 conjugacy classes of subgroups.

The subgroup lattice has 1115 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3544C211yesmaximal, characteristic, complemented
2C2×#3483C211yesmaximal, characteristic, complemented
3#59832C211yesmaximal, characteristic, complemented
4#59151C211yesmaximal, characteristic, complemented
5#59112C214yesmaximal, complemented
6#59084C211yesmaximal, characteristic, complemented
7#51586C214yesmaximal, complemented
8#51531C214yesmaximal, complemented
9#46228C214yesmaximal, complemented
10#44930C214yesmaximal, complemented
11#44891C214yesmaximal, complemented
12#42970C214yesmaximal, complemented
13#42968C214yesmaximal, complemented
14#38952C212yesmaximal, complemented
15#38909C212yesmaximal, complemented
16#37794C214yesmaximal, complemented
17#37680C214yesmaximal, complemented
18#36275C212yesmaximal, complemented
19#36230C214yesmaximal, complemented
20#36122C211yesmaximal, characteristic, complemented
21#35257C214yesmaximal, complemented
22#34724C212yesmaximal, complemented
23#34485C211yesmaximal, characteristic, complemented
24#3544—216no—
25C2×#563C2214yes—
26#3483—216no—
27C2×Q82C2211yescharacteristic
28C2×Q82C2211yescharacteristic
29C2×#555C2214yes—
30C2×#555C2214yes—
31C2×#555C2211yescharacteristic
32C2×#554C2212yes—
33C2×#552C2214yes—
34C2×#550C2212yes—
35C2×#550C2214yes—
36C2×#548C2212yes—
37C2×#547C2214yes—
38C2×#547C2214yes—
39C2×#544C2214yes—
40C2×#542C2214yes—
41C2×#536C2214yes—
42C2×#532C2211yescharacteristic
43C2×#532C2214yes—
44C2×#532C2214yes—
45C22×C4⋊Q8C2211yescharacteristic
46C2×#529C2212yes—
47C2×C4×#41C2214yes—
48C2×C4×#41C2212yes—
49#2858C2211yescharacteristic
50#2857C2211yescharacteristic
51#2857C2214yes—
52#2856C2211yescharacteristic
53#2855C2214yes—
54#2851C2218yes—
55#2820C2218yes—
56#2734C2214yes—
57#2734C2214yes—
58#2731C2214yes—
59#2715C2218yes—
60#2709C2218yes—
61#2701C2218yes—
62#2691C2218yes—
63#2691C2218yes—
64#2686C2218yes—
65#2674C2218yes—
66#2674C2218yes—
67#2672C2218yes—
68#2672C2218yes—
69#2672C2218yes—
70#2672C2218yes—
71#2672C2218yes—
72#2671C2218yes—
73#2671C2218yes—
74#2658C2214yes—
75#2629C2218yes—
76#2628C2218yes—
77#2624C2214yes—
78#2620C2214yes—
79#2620C2214yes—
80#2611C2218yes—
81#2609C2218yes—
82#2582C2212yes—
83#2567C2212yes—
84#2551C2214yes—
85#2551C2214yes—
86#2548C2212yes—
87#2546C2214yes—
88#2545C2212yes—
89#2544C2214yes—
90#2544C2214yes—
91#2501C2214yes—
92#2491C2214yes—
93#2491C2214yes—
94#2487C2214yes—
95#2478C2214yes—
96#2470C2214yes—
97#2468C2218yes—
98#2466C2218yes—
99#2466C2214yes—
100#2457C2218yes—
101#2455C2214yes—
102#2455C2218yes—
103#2454C2214yes—
104#2454C2214yes—
105#2454C2214yes—
106#2453C2214yes—
107#2453C2212yes—
108#2452C2214yes—
109#2452C2214yes—
110#2451C2214yes—
111#2451C2214yes—
112#2451C2214yes—
113#2450C2218yes—
114#2450C2218yes—
115#2449C2218yes—
116#2449C2218yes—
117#2449C2218yes—
118#2447C2212yes—
119#2445C2214yes—
120#2445C2214yes—
121#2441C2212yes—
122#2441C2214yes—
123#2440C2214yes—
124#2438C2218yes—
125#2436C2212yes—
126#2434C2214yes—
127#2432C2212yes—
128#2432C2214yes—
129#2432C2214yes—
130#2432C2214yes—
131#2432C2212yes—
132#2431C2214yes—
133#2430C2218yes—
134#2429C2212yes—
135#2428C2214yes—
136#2427C2214yes—
137#2426C2214yes—
138#2425C2218yes—
139#2422C2212yes—
140#2417C2214yes—
141#2416C2214yes—
142#2416C2214yes—
143#2415C2212yes—
144#2407C2212yes—
145#2407C2214yes—
146#2406C2218yes—
147#2395C2214yes—
148#2392C2214yes—
149#2379C2214yes—
150#2369C2211yescharacteristic
151#2367C2214yes—
152#2365C2214yes—
153#2361C2214yes—
154#2361C2214yes—
155#2360C2214yes—
156D4×C4⋊C4C2214yes—
157D4×C4⋊C4C2212yes—
158#2346C2214yes—
159#2339C2214yes—
160#2326C2214yes—
161#2324C2214yes—
162#2317C2214yes—
163#2311C2214yes—
164#2311C2214yes—
165C4×C4⋊Q8C2211yescharacteristic
166C4×C4⋊Q8C2212yes—
167C4×C22⋊Q8C2212yes—
168C4×C22⋊Q8C2212yes—
169C4×#123C2214yes—
170#2296C2214yes—
171#2293C2212yes—
172C2×#389C2214yes—
173#2290C2214yes—
174C42×D4C2211yescharacteristic
175C22×#41C2314yes—
176C22×#41C2312yes—
177C22×#41C2314yes—
178C22×#41C2312yes—
179C22×#41C2314yes—
180C23×Q8C2312yes—
181#563—232no—
182Q82—28no—
183Q82—28no—
184#555—232no—
185#555—232no—
186#555D4116yescomplemented
187#554—216no—
188#552—232no—
189#550—232no—
190#550—216no—
191#548—48no—
192#547—232no—
193#547—416no—
194#544—232no—
195#542—232no—
196#536—232no—
197#532—28no—
198#532—232no—
199#532—232no—
200C2×C4⋊Q8—28no—
201C2×C4⋊Q8C2312yes—
202C2×C4⋊Q8C2311yescharacteristic
203C2×C4⋊Q8C2314yes—
204C2×C4⋊Q8C2314yes—
205C2×C4⋊Q8C2312yes—
206C2×C4⋊Q8C2314yes—
207C2×C4⋊Q8C2314yes—
208C2×C4⋊Q8C2314yes—
209C2×C4⋊Q8C2314yes—
210C2×C4⋊Q8C2314yes—
211C2×C4⋊Q8C2314yes—
212C2×C4⋊Q8C2311yescharacteristic
213C2×#127C2311yescharacteristic
214C2×#127C2314yes—
215C2×#127C2314yes—
216#529—216no—
217C2×#126C2314yes—
218C2×#126C2318yes—
219C2×#125C2318yes—
220C2×#125C2312yes—
221C2×#125C2314yes—
222C2×#124C2314yes—
223C2×#124C2312yes—
224C2×#124C2318yes—
225C2×#124C2312yes—
226C2×#124C2314yes—
227C2×#124C2312yes—
228C2×#124C2314yes—
229C2×#124C2314yes—
230C2×#124C2312yes—
231C2×#124C2314yes—
232C2×#124C2314yes—
233C2×#123C2318yes—
234C2×#123C2314yes—
235C2×#123C2318yes—
236C2×#123C2314yes—
237C2×#123C2318yes—
238C2×#123C2318yes—
239C2×C22⋊Q8C2314yes—
240C2×C22⋊Q8C2312yes—
241C2×C22⋊Q8C2312yes—
242C2×C22⋊Q8C2318yes—
243C2×C22⋊Q8C2318yes—
244C2×C22⋊Q8C2318yes—
245C2×C22⋊Q8C2314yes—
246C2×C22⋊Q8C2312yes—
247C2×C22⋊Q8C2314yes—
248C2×C22⋊Q8C2314yes—
249C2×C22⋊Q8C2312yes—
250C2×#121C2314yes—
251C2×#121C2312yes—
252C2×#121C2318yes—
253C2×#121C2318yes—
254C2×#121C2314yes—
255C2×#121C2318yes—
256C2×#121C2314yes—
257C2×#121C2312yes—
258C2×#121C2314yes—
259C2×#121C2318yes—
260C2×#121C2314yes—
261C4×#41—216no—
262C4×#41—232no—
263C2×C4×Q8C2312yes—
264C2×C4×Q8C2312yes—
265C2×C4×Q8C2314yes—
266C2×C4×Q8C2314yes—
267C2×C4×Q8C2312yes—
268C2×C4×Q8C2312yes—
269C2×C4×D4C2314yes—
270C2×C4×D4C2312yes—
271C2×C4×D4C2314yes—
272C2×C4×D4C2314yes—
273C2×C4×D4C2314yes—
274C2×C4×D4C2314yes—
275C2×C4×D4C2318yes—
276C2×C4×D4C2314yes—
277C2×C4×D4C2314yes—
278C2×C4×D4C2318yes—
279C2×C4×D4C2311yescharacteristic
280C2×C4×D4C2314yes—
281C2×C4×D4C2314yes—
282C2×C4×D4C2312yes—
283C2×C4×D4C2312yes—
284C2×#117C2314yes—
285C2×#117C2314yes—
286C2×#117C2318yes—
287C2×#117C2312yes—
288C2×#117C2314yes—
289C2×#117C2314yes—
290C2×#117C2314yes—
291C22×C4⋊C4C2314yes—
292C22×C4⋊C4C2314yes—
293C22×C4⋊C4C2314yes—
294C22×C4⋊C4C2318yes—
295C22×C42C2314yes—
296C22×C42C2314yes—
297C22×C42C2311yescharacteristic
298C22×C42C2311yescharacteristic
299#400C2318yes—
300#400C2314yes—
301#399C2318yes—
302#399C2318yes—
303#399C2318yes—
304#399C2318yes—
305#399C2314yes—
306#398C2318yes—
307#398C2318yes—
308#398C2314yes—
309#398C2314yes—
310#398C2318yes—
311#398C2318yes—
312#397C2314yes—
313#397C2318yes—
314#397C2314yes—
315#397C2314yes—
316#397C2314yes—
317#396C2314yes—
318#396C2318yes—
319#396C2318yes—
320#396C2318yes—
321#396C2314yes—
322#396C2318yes—
323#396C2318yes—
324#396C2318yes—
325#395C2318yes—
326#395C2318yes—
327#395C2318yes—
328#395C2318yes—
329#395C2318yes—
330#394C2318yes—
331#394C2318yes—
332#394C2318yes—
333#394C2314yes—
334#394C2318yes—
335#394C2318yes—
336#394C2318yes—
337#394C2318yes—
338#394C2314yes—
339#394C2314yes—
340#394C2314yes—
341#394C2314yes—
342#394C2318yes—
343#394C2318yes—
344#394C2318yes—
345#394C2318yes—
346#393C2318yes—
347#393C2318yes—
348#392C2314yes—
349#392C2318yes—
350#391C2312yes—
351#391C2312yes—
352#391C2312yes—
353#391C2312yes—
354#391C2314yes—
355#391C2314yes—
356#391C2314yes—
357#391C2314yes—
358#391C2312yes—
359#391C2314yes—
360#391C2314yes—
361#391C2312yes—
362#391C2314yes—
363#390C2314yes—
364#390C2314yes—
365#390C2314yes—
366#390C2314yes—
367#390C2314yes—
368#390C2312yes—
369#390C2312yes—
370#390C2314yes—
371#390C2312yes—
372#390C2314yes—
373#390C2314yes—
374#389C2314yes—
375#389C2314yes—
376#389C2314yes—
377#389C2314yes—
378#389C2314yes—
379#389C2312yes—
380#389C2314yes—
381#389C2314yes—
382#389C2314yes—
383#389C2314yes—
384#389C2314yes—
385#389C2318yes—
386#389C2314yes—
387#389C2314yes—
388#389C2312yes—
389#389C2318yes—
390#389C2318yes—
391#389C2312yes—
392#389C2314yes—
393#389C2318yes—
394#389C2314yes—
395#389C2312yes—
396#388C2318yes—
397#388C2314yes—
398#388C2318yes—
399#388C2314yes—
400#388C2318yes—
401#388C2318yes—
402#388C2318yes—
403#388C2314yes—
404#388C2314yes—
405#387C2314yes—
406#387C2318yes—
407#387C2318yes—
408#387C2318yes—
409#387C2318yes—
410#387C2318yes—
411#387C2314yes—
412#387C2314yes—
413#387C2314yes—
414#386C2318yes—
415#386C2318yes—
416#386C2318yes—
417#386C2318yes—
418#386C2318yes—
419#386C2318yes—
420#386C2318yes—
421#386C2318yes—
422#386C2318yes—
423#386C2318yes—
424#386C2314yes—
425#385C2318yes—
426#385C2318yes—
427#385C2318yes—
428#385C2318yes—
429#385C2318yes—
430#385C2318yes—
431#385C2318yes—
432#385C2318yes—
433#385C2318yes—
434#385C2318yes—
435#385C2318yes—
436#385C2314yes—
437#385C2314yes—
438#385C2314yes—
439#385C2314yes—
440#385C2314yes—
441#385C2314yes—
442#385C2314yes—
443#384C2311yescharacteristic
444#384C2312yes—
445#384C2314yes—
446#384C2314yes—
447#382C2318yes—
448#381C2318yes—
449#381C2314yes—
450#380C2318yes—
451#380C2318yes—
452#380C2318yes—
453#380C2318yes—
454#380C2314yes—
455#380C2314yes—
456#380C2318yes—
457#380C2312yes—
458#380C2312yes—
459C4×C4⋊C4C2314yes—
460C4×C4⋊C4C2314yes—
461C4×C4⋊C4C2314yes—
462C4×C4⋊C4C2312yes—
463C4×C4⋊C4C2314yes—
464C4×C4⋊C4C2314yes—
465C4×C4⋊C4C2314yes—
466C4×C4⋊C4C2314yes—
467C4×C4⋊C4C2312yes—
468C4×C4⋊C4C2311yescharacteristic
469C4×C22⋊C4C2314yes—
470C4×C22⋊C4C2314yes—
471C4×C22⋊C4C2314yes—
472C4×C22⋊C4C2314yes—
473C4×C22⋊C4C2312yes—
474C4×C22⋊C4C2314yes—
475C4×C22⋊C4C2312yes—
476C4×C22⋊C4C2311yescharacteristic
477C4×C22⋊C4C2311yescharacteristic
478#376C2314yes—
479C2×#95C2318yes—
480C43C2311yescharacteristic
481C2×#41—28no—
482C2×#41—216no—
483C2×#41—28no—
484C2×#41—28no—
485C2×#41—216no—
486C2×#41—216no—
487C2×#41—216no—
488C2×#41—48no—
489C2×#41—44no—
490C2×#41—48no—
491C2×#41—48no—
492C2×#41—44no—
493C2×#41—84no—
494C2×#41—84no—
495C2×#41—82no—
496C22×Q8—28no—
497C22×Q8—44no—
498C22×Q8—82no—
499C22×Q8C2412yes—
500C22×Q8C2412yes—
501C22×Q8C2412yes—
502C22×Q8C2414yes—
503C22×Q8C2414yes—
504C22×Q8C2414yes—
505C22×Q8C2412yes—
506C22×D4C2414yes—
507C22×D4C2414yes—
508C22×D4C2418yes—
509C22×D4C2414yes—
510C22×D4C2412yes—
511C22×D4C2411yescharacteristic
512C22×D4C2414yes—
513C22×D4C2418yes—
514C22×D4C2412yes—
515C22×D4C2414yes—
516C22×D4C2414yes—
517C23×C4C2412yes—
518C23×C4C2412yes—
519C23×C4C2414yes—
520C23×C4C2414yes—
521C23×C4C2414yes—
522C23×C4C2418yes—
523C23×C4C2414yes—
524C23×C4C2411yescharacteristic
525C23×C4C2411yescharacteristic
526C23×C4C2414yes—
527C23×C4C2418yes—
528C23×C4C2418yes—
529C4⋊Q8—28no—
530C4⋊Q8—216no—
531C4⋊Q8—216no—
532C4⋊Q8—28no—
533C4⋊Q8—216no—
534C4⋊Q8—216no—
535C4⋊Q8—216no—
536C4⋊Q8—24no—
537C4⋊Q8—216no—
538C4⋊Q8—48no—
539C4⋊Q8—84no—
540C4⋊Q8C2×D418yes—
541#127—216no—
542#127—216no—
543#127—24no—
544#126—216no—
545#126—232no—
546#125—28no—
547#125—216no—
548#125—232no—
549#124—28no—
550#124—28no—
551#124—216no—
552#124—232no—
553#124—216no—
554#124—48no—
555#124—44no—
556#124—48no—
557#124—82no—
558#124—84no—
559#124C2×D4132yes—
560#123—232no—
561#123—216no—
562#123—232no—
563#123—216no—
564#123—416no—
565#123—88no—
566C22⋊Q8—28no—
567C22⋊Q8—216no—
568C22⋊Q8—28no—
569C22⋊Q8—232no—
570C22⋊Q8—232no—
571C22⋊Q8—232no—
572C22⋊Q8—48no—
573C22⋊Q8—48no—
574C22⋊Q8—44no—
575C22⋊Q8—48no—
576C22⋊Q8—44no—
577#121—28no—
578#121—232no—
579#121—216no—
580#121—216no—
581#121—232no—
582#121—232no—
583#121—416no—
584#121—48no—
585#121—44no—
586#121—48no—
587#121C2×D4132yes—
588C4×Q8—28no—
589C4×Q8—216no—
590C4×Q8—216no—
591C4×Q8—28no—
592C4×Q8—28no—
593C4×Q8—44no—
594C4×D4—28no—
595C4×D4—216no—
596C4×D4—216no—
597C4×D4—216no—
598C4×D4—216no—
599C4×D4—216no—
600C4×D4—216no—
601C4×D4—232no—
602C4×D4—232no—
603C4×D4—216no—
604C4×D4—24no—
605C4×D4—48no—
606C4×D4—48no—
607C4×D4—44no—
608C4×D4C2×D4116yes—
609#117—216no—
610#117—28no—
611#117—216no—
612#117—232no—
613#117—216no—
614#117—48no—
615#117C2×D4132yes—
616C2×C4⋊C4—216no—
617C2×C4⋊C4—216no—
618C2×C4⋊C4—48no—
619C2×C4⋊C4—416no—
620C2×C4⋊C4C2414yes—
621C2×C4⋊C4C2414yes—
622C2×C4⋊C4C2412yes—
623C2×C4⋊C4C2414yes—
624C2×C4⋊C4C2412yes—
625C2×C4⋊C4C2414yes—
626C2×C4⋊C4C2418yes—
627C2×C4⋊C4C2418yes—
628C2×C4⋊C4C2414yes—
629C2×C4⋊C4C2412yes—
630C2×C4⋊C4C2418yes—
631C2×C4⋊C4C2414yes—
632C2×C4⋊C4C2418yes—
633C2×C4⋊C4C2414yes—
634C2×C4⋊C4C2414yes—
635C2×C4⋊C4C2411yescharacteristic
636C2×C4⋊C4C2414yes—
637C2×C4⋊C4C2414yes—
638C2×C4⋊C4C2418yes—
639C2×C4⋊C4C2412yes—
640C2×C4⋊C4C2414yes—
641C2×C4⋊C4C2414yes—
642C2×C4⋊C4C2414yes—
643C2×C4⋊C4C2414yes—
644C2×C4⋊C4C2418yes—
645C2×C4⋊C4C2418yes—
646C2×C4⋊C4C2418yes—
647C2×C4⋊C4C2414yes—
648C2×C4⋊C4C2414yes—
649C2×C4⋊C4C2414yes—
650C2×C4⋊C4C2412yes—
651C2×C4⋊C4C2412yes—
652C2×C4⋊C4C2414yes—
653C2×C4⋊C4C2414yes—
654C2×C4⋊C4C2414yes—
655C2×C4⋊C4C2418yes—
656C2×C4⋊C4C2414yes—
657C2×C4⋊C4C2414yes—
658C2×C4⋊C4C2412yes—
659C2×C22⋊C4C2414yes—
660C2×C22⋊C4C2414yes—
661C2×C22⋊C4C2418yes—
662C2×C22⋊C4C2418yes—
663C2×C22⋊C4C2414yes—
664C2×C22⋊C4C2414yes—
665C2×C22⋊C4C2414yes—
666C2×C22⋊C4C2414yes—
667C2×C22⋊C4C2418yes—
668C2×C22⋊C4C2414yes—
669C2×C22⋊C4C2414yes—
670C2×C22⋊C4C2411yescharacteristic
671C2×C22⋊C4C2414yes—
672C2×C22⋊C4C2414yes—
673C2×C22⋊C4C2414yes—
674C2×C22⋊C4C2414yes—
675C2×C22⋊C4C2412yes—
676C2×C22⋊C4C2412yes—
677C2×C22⋊C4C2418yes—
678C2×C22⋊C4C2418yes—
679C2×C22⋊C4C2414yes—
680C2×C22⋊C4C2414yes—
681C2×C22⋊C4C2414yes—
682C2×C22⋊C4C2418yes—
683C2×C22⋊C4C2414yes—
684C2×C22⋊C4C2414yes—
685C2×C22⋊C4C2418yes—
686C2×C22⋊C4C2418yes—
687C2×C22⋊C4C2414yes—
688C2×C22⋊C4C2418yes—
689C2×C22⋊C4C2418yes—
690C2×C22⋊C4C2414yes—
691C2×C22⋊C4C2418yes—
692C2×C22⋊C4C2411yescharacteristic
693C2×C42—216no—
694C2×C42—24no—
695C2×C42—216no—
696C2×C42—24no—
697C2×C42C2411yescharacteristic
698C2×C42C2414yes—
699C2×C42C2412yes—
700C2×C42C2412yes—
701C2×C42C2414yes—
702C2×C42C2414yes—
703C2×C42C2414yes—
704C2×C42C2412yes—
705C2×C42C2414yes—
706C2×C42C2414yes—
707C2×C42C2414yes—
708C2×C42C2414yes—
709C2×C42C2411yescharacteristic
710C2×C42C2411yescharacteristic
711C2×C42C2412yes—
712C2×C42C2411yescharacteristic
713C2×C42C2414yes—
714C2×C42C2414yes—
715C2×C42C2411yescharacteristic
716#95C2414yes—
717#95C2418yes—
718#95C2418yes—
719#95C2418yes—
720#95C2414yes—
721#95C2418yes—
722#95C2412yes—
723#95C2414yes—
724#95C2412yes—
725#95C2412yes—
726#95C2414yes—
727#95C2418yes—
728#95C2414yes—
729#95C2414yes—
730#95C2414yes—
731#95C2414yes—
732#95C2414yes—
733#95C2414yes—
734#95C2418yes—
735#95C2414yes—
736#95C2414yes—
737#95C2414yes—
738#95C2418yes—
739#95C2418yes—
740#95C2414yes—
741#95C2414yes—
742#95C2418yes—
743C24C2511yescharacteristic
744C24C2514yes—
745C24C2514yes—
746C24C2511yescharacteristic
747#41—464no—
748#41—432no—
749#41—832no—
750#41—816no—
751#41—832no—
752C2×Q8—24no—
753C2×Q8—24no—
754C2×Q8—24no—
755C2×Q8—28no—
756C2×Q8—28no—
757C2×Q8—28no—
758C2×Q8—24no—
759C2×Q8—24no—
760C2×Q8—24no—
761C2×Q8—42no—
762C2×Q8—42no—
763C2×Q8—44no—
764C2×Q8—42no—
765C2×Q8—44no—
766C2×Q8—44no—
767C2×Q8—42no—
768C2×Q8—44no—
769C2×Q8—44no—
770C2×Q8—44no—
771C2×Q8—816no—
772C2×Q8C22×D418yes—
773C2×Q82−1+418yes—
774C2×D4—28no—
775C2×D4—216no—
776C2×D4—28no—
777C2×D4—22no—
778C2×D4—28no—
779C2×D4—216no—
780C2×D4—28no—
781C2×D4—28no—
782C2×D4—28no—
783C2×D4—24no—
784C2×D4—24no—
785C2×D4—216no—
786C2×D4—28no—
787C2×D4—28no—
788C2×D4—24no—
789C2×D4—28no—
790C2×D4—42no—
791C2×D4—44no—
792C2×D4—48no—
793C2×D4—44no—
794C2×D4—44no—
795C2×D4—44no—
796C2×D4—48no—
797C2×D4—44no—
798C2×D4—42no—
799C2×D4—48no—
800C2×D4—48no—
801C2×D4—44no—
802C2×D4—42no—
803C2×D4C22×D418yes—
804C2×D4C22×D4116yes—
805C22×C4—28no—
806C22×C4—28no—
807C22×C4—28no—
808C22×C4—28no—
809C22×C4—22no—
810C22×C4—28no—
811C22×C4—216no—
812C22×C4—24no—
813C22×C4—216no—
814C22×C4—24no—
815C22×C4—28no—
816C22×C4—22no—
817C22×C4—22no—
818C22×C4—28no—
819C22×C4—28no—
820C22×C4—28no—
821C22×C4—22no—
822C22×C4—24no—
823C22×C4—216no—
824C22×C4—28no—
825C22×C4—24no—
826C22×C4—24no—
827C22×C4—24no—
828C22×C4—41no—
829C22×C4—44no—
830C22×C4—48no—
831C22×C4—44no—
832C22×C4—44no—
833C22×C4—41no—
834C22×C4—44no—
835C22×C4—48no—
836C22×C4—48no—
837C22×C4—48no—
838C22×C4—48no—
839C22×C4—48no—
840C22×C4C22×D4116yes—
841C22×C4C2512yes—
842C22×C4C2512yes—
843C22×C4C2514yes—
844C22×C4C2514yes—
845C22×C4C2514yes—
846C22×C4C2514yes—
847C22×C4C2511yescharacteristic
848C22×C4C2512yes—
849C22×C4C2511yescharacteristic
850C22×C4C2514yes—
851C22×C4C2514yes—
852C22×C4C2514yes—
853C22×C4C2514yes—
854C22×C4C2511yescharacteristic
855C22×C4C2514yes—
856C22×C4C2511yescharacteristic
857C22×C4C2511yescharacteristic
858C22×C4C2514yes—
859C22×C4C2512yes—
860C4⋊C4—28no—
861C4⋊C4—24no—
862C4⋊C4—216no—
863C4⋊C4—216no—
864C4⋊C4—28no—
865C4⋊C4—216no—
866C4⋊C4—28no—
867C4⋊C4—24no—
868C4⋊C4—216no—
869C4⋊C4—28no—
870C4⋊C4—28no—
871C4⋊C4—28no—
872C4⋊C4—28no—
873C4⋊C4—216no—
874C4⋊C4—28no—
875C4⋊C4—28no—
876C4⋊C4—22no—
877C4⋊C4—28no—
878C4⋊C4—24no—
879C4⋊C4—28no—
880C4⋊C4—28no—
881C4⋊C4—28no—
882C4⋊C4—24no—
883C4⋊C4—28no—
884C4⋊C4—48no—
885C4⋊C4—48no—
886C4⋊C4—48no—
887C4⋊C4—44no—
888C4⋊C4—44no—
889C4⋊C4—42no—
890C4⋊C4—44no—
891C4⋊C4—44no—
892C4⋊C4—42no—
893C4⋊C4—44no—
894C4⋊C4—44no—
895C4⋊C4—48no—
896C4⋊C4—44no—
897C4⋊C4C22×D4116yes—
898C4⋊C4C22×D418yes—
899C22⋊C4—28no—
900C22⋊C4—28no—
901C22⋊C4—28no—
902C22⋊C4—216no—
903C22⋊C4—28no—
904C22⋊C4—28no—
905C22⋊C4—28no—
906C22⋊C4—216no—
907C22⋊C4—28no—
908C22⋊C4—216no—
909C22⋊C4—28no—
910C22⋊C4—22no—
911C22⋊C4—28no—
912C22⋊C4—28no—
913C22⋊C4—44no—
914C22⋊C4—44no—
915C22⋊C4—48no—
916C22⋊C4—42no—
917C22⋊C4—42no—
918C22⋊C4—48no—
919C22⋊C4—48no—
920C22⋊C4—44no—
921C22⋊C4—44no—
922C22⋊C4—44no—
923C22⋊C4—44no—
924C22⋊C4—44no—
925C22⋊C4—48no—
926C22⋊C4—48no—
927C22⋊C4—48no—
928C22⋊C4—48no—
929C22⋊C4—44no—
930C22⋊C4C22×D4116yes—
931C22⋊C4C22×D4132yes—
932C22⋊C4H(5,𝔽2)14yes—
933C42—28no—
934C42—24no—
935C42—22no—
936C42—28no—
937C42—24no—
938C42—28no—
939C42—28no—
940C42—22no—
941C42—28no—
942C42—28no—
943C42—28no—
944C42—22no—
945C42—24no—
946C42—24no—
947C42—28no—
948C42—41no—
949C42—44no—
950C42C22×D414yes—
951C42C22×D4116yes—
952C23—21no—
953C23—24no—
954C23—22no—
955C23—24no—
956C23—24no—
957C23—24no—
958C23—24no—
959C23—22no—
960C23—24no—
961C23—21no—
962C23—21no—
963C23—24no—
964C23—21no—
965C23—24no—
966C23—28no—
967C23—22no—
968C23—22no—
969C23—28no—
970C23—24no—
971C23—21no—
972C23C23×D418yes—
973C23C2×H(5,𝔽2)12yes—
974C23C2611yescharacteristic
975Q8—216no—
976Q8—48no—
977Q8—48no—
978Q8—88no—
979Q8—84no—
980Q8—88no—
981Q8—88no—
982D4—216no—
983D4—416no—
984D4—432no—
985D4—416no—
986D4—416no—
987D4—44no—
988D4—416no—
989D4—88no—
990D4—84no—
991D4—88no—
992D4—816no—
993C2×C4—21no—
994C2×C4—24no—
995C2×C4—24no—
996C2×C4—21no—
997C2×C4—22no—
998C2×C4—24no—
999C2×C4—24no—
1000C2×C4—24no—
1001C2×C4—24no—
1002C2×C4—21no—
1003C2×C4—21no—
1004C2×C4—232no—
1005C2×C4—22no—
1006C2×C4—24no—
1007C2×C4—22no—
1008C2×C4—24no—
1009C2×C4—21no—
1010C2×C4—24no—
1011C2×C4—24no—
1012C2×C4—21no—
1013C2×C4—24no—
1014C2×C4—24no—
1015C2×C4—21no—
1016C2×C4—24no—
1017C2×C4—24no—
1018C2×C4—24no—
1019C2×C4—22no—
1020C2×C4—24no—
1021C2×C4—22no—
1022C2×C4—24no—
1023C2×C4—22no—
1024C2×C4—24no—
1025C2×C4—22no—
1026C2×C4—24no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—24no—
1030C2×C4—28no—
1031C2×C4—24no—
1032C2×C4—22no—
1033C2×C4—24no—
1034C2×C4—22no—
1035C2×C4—24no—
1036C2×C4—24no—
1037C2×C4—24no—
1038C2×C4—21no—
1039C2×C4—432no—
1040C2×C4—416no—
1041C2×C4—44no—
1042C2×C4—44no—
1043C2×C4—416no—
1044C2×C4—416no—
1045C2×C4—416no—
1046C2×C4—48no—
1047C2×C4—48no—
1048C2×C4—816no—
1049C2×C4—816no—
1050C2×C4C23×D418yes—
1051C2×C4C23×D418yes—
1052C2×C4C23×D412yes—
1053C2×C4C23×D414yes—
1054C2×C4C2×H(5,𝔽2)12yes—
1055C2×C4C2×H(5,𝔽2)12yes—
1056C2×C4C2×2−1+418yes—
1057C2×C4C2×2−1+414yes—
1058C2×C4#58514yes—
1059C22—22no—
1060C22—28no—
1061C22—22no—
1062C22—22no—
1063C22—28no—
1064C22—28no—
1065C22—44no—
1066C22—44no—
1067C22—42no—
1068C22—42no—
1069C22—44no—
1070C22—44no—
1071C22—41no—
1072C22—44no—
1073C22—41no—
1074C22—44no—
1075C22—41no—
1076C22—44no—
1077C22—48no—
1078C22—42no—
1079C22—42no—
1080C22—48no—
1081C22C24×D411yescharacteristic
1082C22C22×H(5,𝔽2)11yescharacteristic
1083C22C22×2−1+412yes—
1084C22C2×#58512yes—
1085C22H(7,𝔽2)11yescharacteristic
1086C4—22no—
1087C4—28no—
1088C4—22no—
1089C4—22no—
1090C4—28no—
1091C4—28no—
1092C4—44no—
1093C4—44no—
1094C4—41no—
1095C4—44no—
1096C4—44no—
1097C4—44no—
1098C4—41no—
1099C4—42no—
1100C4—42no—
1101C4—44no—
1102C4—42no—
1103C4—44no—
1104C4#348918yes—
1105C2—42no—
1106C2—48no—
1107C2—81no—
1108C2—84no—
1109C2#6275911yescharacteristic
1110C2C2×#348912yes—
1111C2#6295212yes—
1112C2D4×H(5,𝔽2)11yescharacteristic
1113C2#6303711yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
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×#3544C2semidirect
2. C2×#3483C2semidirect
3. #59832C2semidirect
4. #59151C2semidirect
5. #59112C2semidirect
6. #59084C2semidirect
7. #51586C2semidirect
8. #51531C2semidirect
9. #46228C2semidirect
10. #44930C2semidirect
11. #44891C2semidirect
12. #42970C2semidirect
13. #42968C2semidirect
14. #38952C2semidirect
15. #38909C2semidirect
16. #37794C2semidirect
17. #37680C2semidirect
18. #36275C2semidirect
19. #36230C2semidirect
20. #36122C2semidirect
21. #35257C2semidirect
22. #34724C2semidirect
23. #34485C2semidirect
186. #555D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35442
C2×#34832
#598322
#591512
#591122
#590842
#515862
#515312
#462282
#449302
#448912
#429702
#429682
#389522
#389092
#377942
#376802
#362752
#362302
#361222
#352572
#347242
#344852