Finite Group Databasebeta

← #7987172

Subgroups — #7987172

Order 512.

7277 conjugacy classes of subgroups.

The subgroup lattice has 1132 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3544C211yesmaximal, characteristic, complemented
2C22×#555C211yesmaximal, characteristic, complemented
3#59659C211yesmaximal, characteristic, complemented
4#59151C211yesmaximal, characteristic, complemented
5#59135C211yesmaximal, characteristic, complemented
6#59015C214yesmaximal, complemented
7#51586C214yesmaximal, complemented
8#51531C214yesmaximal, complemented
9#46136C214yesmaximal, complemented
10#44928C214yesmaximal, complemented
11#44890C214yesmaximal, complemented
12#42970C214yesmaximal, complemented
13#42968C214yesmaximal, complemented
14#39489C212yesmaximal, complemented
15#38922C212yesmaximal, complemented
16#37676C214yesmaximal, complemented
17#37664C214yesmaximal, complemented
18#36234C214yesmaximal, complemented
19#36154C212yesmaximal, complemented
20D4×C4⋊Q8C211yesmaximal, characteristic, complemented
21#35253C214yesmaximal, complemented
22#34700C212yesmaximal, complemented
23#34485C211yesmaximal, characteristic, complemented
24#3544—216no—
25C2×#563C2214yescomplemented
26C2×Q82C2211yescharacteristic, complemented
27C2×#555—216no—
28C2×#555C2212yes—
29C2×#555C2211yescharacteristic
30C2×#555C2214yes—
31C2×#555C2214yes—
32C2×#555C2214yes—
33C2×#555C2211yescharacteristic
34C2×#554C2212yescomplemented
35C2×#552C2214yescomplemented
36C2×D4×Q8C2212yes—
37C2×#547C2214yescomplemented
38C2×#546C2214yes—
39C2×#544C2214yescomplemented
40C2×#542C2214yescomplemented
41C2×#536C2214yescomplemented
42C22×C4⋊Q8C2211yescharacteristic
43C22×C4⋊Q8C2211yescharacteristic, complemented
44C2×#529C2212yescomplemented
45C22×#124C2214yes—
46C22×#121C2214yes—
47C22×C4×D4C2212yes—
48C22×#117C2214yes—
49#2868C2211yescharacteristic, complemented
50#2857C2211yescharacteristic
51#2857C2214yes—
52#2857C2211yescharacteristic, complemented
53#2851C2218yes—
54#2848C2214yes—
55#2820C2218yescomplemented
56#2734C2214yescomplemented
57#2731C2214yescomplemented
58#2731C2214yescomplemented
59#2717C2218yescomplemented
60#2715C2218yescomplemented
61#2715C2218yescomplemented
62#2701C2218yescomplemented
63#2691C2218yescomplemented
64#2686C2218yescomplemented
65#2674C2218yescomplemented
66#2674C2218yescomplemented
67#2674C2218yescomplemented
68#2674C2218yescomplemented
69#2672C2218yescomplemented
70#2672C2218yescomplemented
71#2672C2218yescomplemented
72#2672C2218yescomplemented
73#2671C2218yescomplemented
74#2658C2214yescomplemented
75#2629C2218yescomplemented
76#2628C2218yescomplemented
77#2624C2214yescomplemented
78#2620C2214yescomplemented
79#2620C2214yescomplemented
80#2611C2218yescomplemented
81#2609C2218yescomplemented
82#2567C2212yescomplemented
83#2563C2212yescomplemented
84#2551C2214yescomplemented
85#2551C2214yescomplemented
86#2547C2214yescomplemented
87#2546C2212yescomplemented
88#2545C2214yescomplemented
89#2538C2212yescomplemented
90#2537C2214yescomplemented
91#2501C2214yescomplemented
92#2499C2214yescomplemented
93#2491C2214yescomplemented
94#2491C2214yescomplemented
95#2487C2214yescomplemented
96#2485C2214yescomplemented
97#2480C2218yes—
98#2480C2214yes—
99#2478C2218yescomplemented
100#2470C2218yescomplemented
101#2468C2214yescomplemented
102#2457C2214yescomplemented
103#2454C2214yescomplemented
104#2454C2212yescomplemented
105#2451C2214yescomplemented
106#2450C2218yescomplemented
107#2447C2212yescomplemented
108#2442C2214yes—
109#2442C2212yes—
110#2441C2214yescomplemented
111#2441C2214yescomplemented
112#2441C2214yescomplemented
113#2440C2214yes—
114#2440C2214yes—
115#2440C2214yescomplemented
116#2439C2214yescomplemented
117#2439C2214yescomplemented
118#2438C2218yescomplemented
119#2438C2218yescomplemented
120#2437C2218yes—
121#2437C2218yes—
122#2437C2218yes—
123#2436C2214yescomplemented
124#2435C2214yes—
125#2435C2212yes—
126#2434C2214yes—
127#2434C2212yes—
128#2434C2212yescomplemented
129#2432C2214yescomplemented
130#2430C2218yescomplemented
131#2427C2214yescomplemented
132#2427C2212yescomplemented
133#2426C2214yescomplemented
134#2425C2218yescomplemented
135#2422C2214yescomplemented
136#2422C2214yescomplemented
137#2420C2212yescomplemented
138#2418C2214yes—
139#2418C2218yes—
140#2417C2212yes—
141#2417C2214yescomplemented
142#2416C2214yescomplemented
143#2416C2214yescomplemented
144#2415C2214yescomplemented
145#2408C2212yes—
146#2405C2218yes—
147#2395C2214yescomplemented
148#2392C2214yescomplemented
149#2379C2214yescomplemented
150#2369C2211yescharacteristic, complemented
151#2362C2214yescomplemented
152#2361C2214yescomplemented
153#2360C2214yes—
154#2352C2214yescomplemented
155#2349C2214yescomplemented
156D4×C4⋊C4C2214yes—
157D4×C4⋊C4C2212yescomplemented
158#2346C2214yescomplemented
159D4×C22⋊C4C2214yes—
160#2326C2214yescomplemented
161#2324C2214yescomplemented
162#2317C2214yescomplemented
163#2317C2214yescomplemented
164#2316C2214yescomplemented
165C4×C4⋊Q8C2211yescharacteristic, complemented
166C4×#124C2212yescomplemented
167C4×C22⋊Q8C2212yes—
168C4×#121C2212yescomplemented
169C4×#120C2214yes—
170#2293C2212yescomplemented
171#2290C2214yes—
172#2280C2214yes—
173C2×#380C2214yes—
174C42×D4C2211yescharacteristic
175C22×#41C2314yes—
176C23×Q8C2312yes—
177C23×Q8C2312yes—
178C23×D4C2312yes—
179C23×D4C2314yes—
180C24×C4C2314yes—
181#563—232no—
182Q82—28no—
183#555—28no—
184#555—232no—
185#555—232no—
186#555—216no—
187#555—232no—
188#555D4116yescomplemented
189#554—216no—
190#552—232no—
191D4×Q8—48no—
192#547—232no—
193#546—416no—
194#544—232no—
195#542—232no—
196#536—232no—
197C2×C4⋊Q8—28no—
198C2×C4⋊Q8—28no—
199C2×C4⋊Q8C2311yescharacteristic
200C2×C4⋊Q8C2311yescharacteristic
201C2×C4⋊Q8C2314yes—
202C2×C4⋊Q8C2312yes—
203C2×C4⋊Q8C2314yes—
204C2×C4⋊Q8C2314yes—
205C2×C4⋊Q8C2312yes—
206C2×C4⋊Q8C2314yes—
207C2×C4⋊Q8C2314yes—
208C2×C4⋊Q8C2312yes—
209C2×C4⋊Q8C2314yes—
210C2×C4⋊Q8C2312yes—
211C2×C4⋊Q8C2314yes—
212C2×C4⋊Q8C2311yescharacteristic
213#529—216no—
214C2×#126C2314yes—
215C2×#126C2318yes—
216C2×#125C2318yes—
217C2×#125C2312yes—
218C2×#125C2314yes—
219C2×#124—232no—
220C2×#124C2314yes—
221C2×#124C2318yes—
222C2×#124C2318yes—
223C2×#124C2314yes—
224C2×#124C2314yes—
225C2×#124C2312yes—
226C2×#124C2314yes—
227C2×#124C2312yes—
228C2×#124C2314yes—
229C2×#124C2314yes—
230C2×#124C2314yes—
231C2×#123C2318yes—
232C2×#123C2318yes—
233C2×#123C2314yes—
234C2×#123C2318yes—
235C2×#123C2318yes—
236C2×C22⋊Q8C2312yes—
237C2×C22⋊Q8C2314yes—
238C2×C22⋊Q8C2312yes—
239C2×C22⋊Q8C2318yes—
240C2×C22⋊Q8C2318yes—
241C2×C22⋊Q8C2318yes—
242C2×C22⋊Q8C2314yes—
243C2×C22⋊Q8C2312yes—
244C2×C22⋊Q8C2314yes—
245C2×C22⋊Q8C2314yes—
246C2×C22⋊Q8C2312yes—
247C2×C22⋊Q8C2314yes—
248C2×#121—232no—
249C2×#121C2314yes—
250C2×#121C2312yes—
251C2×#121C2318yes—
252C2×#121C2314yes—
253C2×#121C2314yes—
254C2×#121C2318yes—
255C2×#121C2314yes—
256C2×#121C2312yes—
257C2×#121C2318yes—
258C2×#121C2314yes—
259C2×#120C2314yes—
260C2×C4×Q8C2312yes—
261C2×C4×Q8C2314yes—
262C2×C4×Q8C2312yes—
263C2×C4×D4—216no—
264C2×C4×D4C2312yes—
265C2×C4×D4C2314yes—
266C2×C4×D4C2312yes—
267C2×C4×D4C2314yes—
268C2×C4×D4C2312yes—
269C2×C4×D4C2314yes—
270C2×C4×D4C2314yes—
271C2×C4×D4C2312yes—
272C2×C4×D4C2314yes—
273C2×C4×D4C2311yescharacteristic
274C2×C4×D4C2314yes—
275C2×C4×D4C2314yes—
276C2×C4×D4C2314yes—
277C2×C4×D4C2312yes—
278C2×#117—232no—
279C2×#117C2314yes—
280C2×#117C2314yes—
281C2×#117C2314yes—
282C2×#117C2314yes—
283C2×#117C2318yes—
284C2×#117C2314yes—
285C2×#117C2318yes—
286C2×#117C2314yes—
287C2×#117C2314yes—
288C22×C4⋊C4C2314yes—
289C22×C4⋊C4C2314yes—
290C22×C4⋊C4C2314yes—
291C22×C4⋊C4C2312yes—
292C22×C4⋊C4C2314yes—
293C22×C22⋊C4C2318yes—
294C22×C22⋊C4C2314yes—
295C22×C22⋊C4C2318yes—
296C22×C42C2314yes—
297C22×C42C2311yescharacteristic
298C22×C42C2311yescharacteristic
299#400C2318yes—
300#400C2314yes—
301#399C2318yes—
302#399C2318yes—
303#399C2318yes—
304#399C2318yes—
305#399C2314yes—
306#398C2318yes—
307#398C2314yes—
308#398C2314yes—
309#398C2318yes—
310#398C2318yes—
311#397C2314yes—
312#397C2318yes—
313#397C2314yes—
314#397C2314yes—
315#397C2314yes—
316#397C2318yes—
317#397C2318yes—
318#397C2318yes—
319#396C2314yes—
320#396C2318yes—
321#396C2318yes—
322#396C2318yes—
323#396C2314yes—
324#396C2318yes—
325#396C2318yes—
326#396C2318yes—
327#396C2318yes—
328#395C2318yes—
329#395C2318yes—
330#395C2318yes—
331#395C2318yes—
332#395C2318yes—
333#394C2318yes—
334#394C2318yes—
335#394C2318yes—
336#394C2314yes—
337#394C2318yes—
338#394C2318yes—
339#394C2318yes—
340#394C2318yes—
341#394C2314yes—
342#394C2314yes—
343#394C2314yes—
344#394C2314yes—
345#394C2318yes—
346#393C2318yes—
347#393C2318yes—
348#393C2318yes—
349#392C2314yes—
350#391C2312yes—
351#391C2314yes—
352#391C2314yes—
353#391C2314yes—
354#391C2312yes—
355#391C2314yes—
356#391C2312yes—
357#391C2312yes—
358#391C2314yes—
359#391C2312yes—
360#390C2314yes—
361#390C2314yes—
362#390C2312yes—
363#390C2314yes—
364#390C2312yes—
365#390C2314yes—
366#390C2312yes—
367#390C2312yes—
368#389C2314yes—
369#389C2314yes—
370#389C2314yes—
371#389C2312yes—
372#389C2318yes—
373#389C2318yes—
374#389C2314yes—
375#389C2314yes—
376#389C2312yes—
377#389C2318yes—
378#389C2318yes—
379#389C2314yes—
380#389C2314yes—
381#389C2314yes—
382#389C2312yes—
383#389C2318yes—
384#389C2318yes—
385#389C2312yes—
386#388C2318yes—
387#388C2314yes—
388#388C2318yes—
389#388C2318yes—
390#388C2318yes—
391#388C2318yes—
392#388C2318yes—
393#388C2314yes—
394#388C2314yes—
395#388C2314yes—
396#388C2314yes—
397#387C2318yes—
398#387C2318yes—
399#387C2318yes—
400#387C2318yes—
401#387C2318yes—
402#387C2318yes—
403#387C2314yes—
404#386C2318yes—
405#386C2318yes—
406#386C2318yes—
407#386C2318yes—
408#386C2314yes—
409#386C2318yes—
410#386C2314yes—
411#386C2314yes—
412#386C2314yes—
413#385C2318yes—
414#385C2318yes—
415#385C2318yes—
416#385C2318yes—
417#385C2318yes—
418#385C2318yes—
419#385C2318yes—
420#385C2318yes—
421#385C2314yes—
422#385C2318yes—
423#385C2318yes—
424#385C2318yes—
425#385C2318yes—
426#385C2314yes—
427#385C2314yes—
428#385C2314yes—
429#384C2311yescharacteristic
430#384C2314yes—
431#384C2314yes—
432#384C2314yes—
433#384C2314yes—
434#382C2314yes—
435#382C2318yes—
436#382C2312yes—
437#381C2314yes—
438#381C2314yes—
439#380C2314yes—
440#380C2314yes—
441#380C2318yes—
442#380C2318yes—
443#380C2314yes—
444#380C2314yes—
445#380C2314yes—
446#380C2318yes—
447#380C2314yes—
448#380C2314yes—
449#380C2318yes—
450#380C2312yes—
451#380C2314yes—
452#380C2318yes—
453#380C2314yes—
454#380C2312yes—
455#380C2314yes—
456#379C2318yes—
457#379C2314yes—
458#379C2314yes—
459#379C2314yes—
460C4×C4⋊C4C2314yes—
461C4×C4⋊C4C2312yes—
462C4×C4⋊C4C2314yes—
463C4×C4⋊C4C2314yes—
464C4×C4⋊C4C2314yes—
465C4×C4⋊C4C2312yes—
466C4×C4⋊C4C2311yescharacteristic
467C4×C22⋊C4C2314yes—
468C4×C22⋊C4C2314yes—
469C4×C22⋊C4C2314yes—
470C4×C22⋊C4C2314yes—
471C4×C22⋊C4C2314yes—
472C4×C22⋊C4C2312yes—
473C4×C22⋊C4C2314yes—
474C4×C22⋊C4C2314yes—
475C4×C22⋊C4C2311yescharacteristic
476C4×C22⋊C4C2311yescharacteristic
477C4×C22⋊C4C2312yes—
478#376C2314yes—
479C2×#95C2318yes—
480C43C2311yescharacteristic
481C25C2414yes—
482C2×#41—216no—
483C2×#41—48no—
484C2×#41—84no—
485C22×Q8—28no—
486C22×Q8—28no—
487C22×Q8—44no—
488C22×Q8—44no—
489C22×Q8—82no—
490C22×Q8—82no—
491C22×Q8C2412yes—
492C22×Q8C2412yes—
493C22×Q8C2414yes—
494C22×Q8C2414yes—
495C22×Q8C2414yes—
496C22×Q8C2412yes—
497C22×Q8C2412yes—
498C22×D4—28no—
499C22×D4—216no—
500C22×D4—28no—
501C22×D4—44no—
502C22×D4—48no—
503C22×D4—84no—
504C22×D4C2412yes—
505C22×D4C2414yes—
506C22×D4C2414yes—
507C22×D4C2412yes—
508C22×D4C2411yescharacteristic
509C22×D4C2414yes—
510C22×D4C2418yes—
511C22×D4C2414yes—
512C22×D4C2414yes—
513C23×C4—216no—
514C23×C4—216no—
515C23×C4—48no—
516C23×C4C2412yes—
517C23×C4C2414yes—
518C23×C4C2411yescharacteristic
519C23×C4C2414yes—
520C23×C4C2414yes—
521C23×C4C2414yes—
522C23×C4C2414yes—
523C23×C4C2414yes—
524C23×C4C2411yescharacteristic
525C23×C4C2414yes—
526C23×C4C2412yes—
527C23×C4C2418yes—
528C23×C4C2418yes—
529C4⋊Q8—28no—
530C4⋊Q8—28no—
531C4⋊Q8—216no—
532C4⋊Q8—216no—
533C4⋊Q8—216no—
534C4⋊Q8—216no—
535C4⋊Q8—24no—
536C4⋊Q8—24no—
537C4⋊Q8—216no—
538C4⋊Q8—48no—
539C4⋊Q8—44no—
540C4⋊Q8—84no—
541C4⋊Q8—82no—
542C4⋊Q8C2×D418yes—
543#126—216no—
544#126—232no—
545#125—28no—
546#125—216no—
547#125—232no—
548#124—216no—
549#124—216no—
550#124—28no—
551#124—216no—
552#124—232no—
553#124—232no—
554#124—216no—
555#124—48no—
556#124—44no—
557#124—84no—
558#124C2×D4132yes—
559#123—232no—
560#123—216no—
561#123—232no—
562#123—416no—
563#123—88no—
564C22⋊Q8—216no—
565C22⋊Q8—28no—
566C22⋊Q8—28no—
567C22⋊Q8—232no—
568C22⋊Q8—232no—
569C22⋊Q8—232no—
570C22⋊Q8—48no—
571C22⋊Q8—44no—
572C22⋊Q8—48no—
573C22⋊Q8—44no—
574C22⋊Q8—48no—
575C22⋊Q8—48no—
576#121—216no—
577#121—232no—
578#121—28no—
579#121—216no—
580#121—216no—
581#121—232no—
582#121—416no—
583#121—44no—
584#121—48no—
585#121C2×D4132yes—
586#120—216no—
587C4×Q8—216no—
588C4×Q8—28no—
589C4×Q8—44no—
590C4×D4—28no—
591C4×D4—216no—
592C4×D4—216no—
593C4×D4—24no—
594C4×D4—216no—
595C4×D4—216no—
596C4×D4—28no—
597C4×D4—28no—
598C4×D4—216no—
599C4×D4—28no—
600C4×D4—48no—
601C4×D4—48no—
602C4×D4—48no—
603C4×D4C2×D4116yes—
604#117—216no—
605#117—216no—
606#117—216no—
607#117—216no—
608#117—232no—
609#117—232no—
610#117—216no—
611#117—48no—
612#117C2×D4132yes—
613C2×C4⋊C4—216no—
614C2×C4⋊C4—28no—
615C2×C4⋊C4—216no—
616C2×C4⋊C4—216no—
617C2×C4⋊C4—48no—
618C2×C4⋊C4C2414yes—
619C2×C4⋊C4C2412yes—
620C2×C4⋊C4C2412yes—
621C2×C4⋊C4C2412yes—
622C2×C4⋊C4C2414yes—
623C2×C4⋊C4C2414yes—
624C2×C4⋊C4C2418yes—
625C2×C4⋊C4C2414yes—
626C2×C4⋊C4C2418yes—
627C2×C4⋊C4C2418yes—
628C2×C4⋊C4C2418yes—
629C2×C4⋊C4C2414yes—
630C2×C4⋊C4C2414yes—
631C2×C4⋊C4C2414yes—
632C2×C4⋊C4C2414yes—
633C2×C4⋊C4C2411yescharacteristic
634C2×C4⋊C4C2412yes—
635C2×C4⋊C4C2414yes—
636C2×C4⋊C4C2418yes—
637C2×C4⋊C4C2412yes—
638C2×C4⋊C4C2414yes—
639C2×C4⋊C4C2418yes—
640C2×C4⋊C4C2414yes—
641C2×C4⋊C4C2414yes—
642C2×C4⋊C4C2414yes—
643C2×C4⋊C4C2414yes—
644C2×C4⋊C4C2412yes—
645C2×C4⋊C4C2414yes—
646C2×C4⋊C4C2418yes—
647C2×C4⋊C4C2414yes—
648C2×C4⋊C4C2414yes—
649C2×C4⋊C4C2414yes—
650C2×C4⋊C4C2418yes—
651C2×C4⋊C4C2418yes—
652C2×C4⋊C4C2418yes—
653C2×C4⋊C4C2414yes—
654C2×C4⋊C4C2414yes—
655C2×C4⋊C4C2412yes—
656C2×C22⋊C4—232no—
657C2×C22⋊C4—216no—
658C2×C22⋊C4—416no—
659C2×C22⋊C4C2414yes—
660C2×C22⋊C4C2414yes—
661C2×C22⋊C4C2418yes—
662C2×C22⋊C4C2418yes—
663C2×C22⋊C4C2418yes—
664C2×C22⋊C4C2414yes—
665C2×C22⋊C4C2414yes—
666C2×C22⋊C4C2414yes—
667C2×C22⋊C4C2414yes—
668C2×C22⋊C4C2414yes—
669C2×C22⋊C4C2414yes—
670C2×C22⋊C4C2414yes—
671C2×C22⋊C4C2414yes—
672C2×C22⋊C4C2411yescharacteristic
673C2×C22⋊C4C2411yescharacteristic
674C2×C22⋊C4C2418yes—
675C2×C22⋊C4C2414yes—
676C2×C22⋊C4C2412yes—
677C2×C22⋊C4C2412yes—
678C2×C22⋊C4C2414yes—
679C2×C22⋊C4C2414yes—
680C2×C22⋊C4C2418yes—
681C2×C22⋊C4C2418yes—
682C2×C22⋊C4C2414yes—
683C2×C22⋊C4C2414yes—
684C2×C22⋊C4C2414yes—
685C2×C22⋊C4C2418yes—
686C2×C22⋊C4C2414yes—
687C2×C22⋊C4C2414yes—
688C2×C22⋊C4C2418yes—
689C2×C22⋊C4C2414yes—
690C2×C22⋊C4C2414yes—
691C2×C22⋊C4C2418yes—
692C2×C22⋊C4C2414yes—
693C2×C22⋊C4C2414yes—
694C2×C22⋊C4C2414yes—
695C2×C22⋊C4C2418yes—
696C2×C22⋊C4C2414yes—
697C2×C42—216no—
698C2×C42—24no—
699C2×C42—24no—
700C2×C42C2414yes—
701C2×C42C2418yes—
702C2×C42C2412yes—
703C2×C42C2412yes—
704C2×C42C2414yes—
705C2×C42C2414yes—
706C2×C42C2414yes—
707C2×C42C2412yes—
708C2×C42C2411yescharacteristic
709C2×C42C2414yes—
710C2×C42C2411yescharacteristic
711C2×C42C2412yes—
712C2×C42C2411yescharacteristic
713C2×C42C2414yes—
714C2×C42C2411yescharacteristic
715C2×C42C2414yes—
716C2×C42C2411yescharacteristic
717#95C2414yes—
718#95C2418yes—
719#95C2418yes—
720#95C2418yes—
721#95C2414yes—
722#95C2418yes—
723#95C2412yes—
724#95C2412yes—
725#95C2412yes—
726#95C2414yes—
727#95C2414yes—
728#95C2414yes—
729#95C2414yes—
730#95C2414yes—
731#95C2414yes—
732#95C2414yes—
733#95C2418yes—
734#95C2414yes—
735#95C2414yes—
736#95C2418yes—
737#95C2414yes—
738#95C2418yes—
739#95C2418yes—
740#95C2414yes—
741#95C2418yes—
742#95C2418yes—
743C24—28no—
744C24—28no—
745C24—28no—
746C24—28no—
747C24—44no—
748C24—44no—
749C24—44no—
750C24C2514yes—
751C24C2514yes—
752C24C2511yescharacteristic
753C24C2511yescharacteristic
754#41—832no—
755C2×Q8—24no—
756C2×Q8—24no—
757C2×Q8—28no—
758C2×Q8—28no—
759C2×Q8—28no—
760C2×Q8—24no—
761C2×Q8—24no—
762C2×Q8—24no—
763C2×Q8—42no—
764C2×Q8—42no—
765C2×Q8—44no—
766C2×Q8—44no—
767C2×Q8—44no—
768C2×Q8—42no—
769C2×Q8—42no—
770C2×Q8—44no—
771C2×Q8—44no—
772C2×Q8—42no—
773C2×Q8—42no—
774C2×Q8—44no—
775C2×Q8—816no—
776C2×Q8—816no—
777C2×Q8C22×D418yes—
778C2×D4—24no—
779C2×D4—28no—
780C2×D4—28no—
781C2×D4—28no—
782C2×D4—216no—
783C2×D4—28no—
784C2×D4—24no—
785C2×D4—28no—
786C2×D4—24no—
787C2×D4—28no—
788C2×D4—24no—
789C2×D4—24no—
790C2×D4—24no—
791C2×D4—432no—
792C2×D4—44no—
793C2×D4—44no—
794C2×D4—44no—
795C2×D4—44no—
796C2×D4—44no—
797C2×D4—48no—
798C2×D4—44no—
799C2×D4—44no—
800C2×D4—48no—
801C2×D4—44no—
802C2×D4—832no—
803C2×D4C22×D418yes—
804C2×D4C22×D4116yes—
805C2×D4H(5,𝔽2)14yes—
806C22×C4—24no—
807C22×C4—28no—
808C22×C4—28no—
809C22×C4—24no—
810C22×C4—28no—
811C22×C4—28no—
812C22×C4—28no—
813C22×C4—22no—
814C22×C4—22no—
815C22×C4—28no—
816C22×C4—216no—
817C22×C4—28no—
818C22×C4—22no—
819C22×C4—28no—
820C22×C4—24no—
821C22×C4—22no—
822C22×C4—28no—
823C22×C4—28no—
824C22×C4—28no—
825C22×C4—24no—
826C22×C4—28no—
827C22×C4—28no—
828C22×C4—28no—
829C22×C4—24no—
830C22×C4—28no—
831C22×C4—44no—
832C22×C4—44no—
833C22×C4—44no—
834C22×C4—44no—
835C22×C4—41no—
836C22×C4—41no—
837C22×C4—44no—
838C22×C4—464no—
839C22×C4—48no—
840C22×C4—48no—
841C22×C4—48no—
842C22×C4—48no—
843C22×C4—48no—
844C22×C4C22×D4116yes—
845C22×C42−1+418yes—
846C22×C4C2514yes—
847C22×C4C2512yes—
848C22×C4C2514yes—
849C22×C4C2514yes—
850C22×C4C2514yes—
851C22×C4C2514yes—
852C22×C4C2512yes—
853C22×C4C2511yescharacteristic
854C22×C4C2511yescharacteristic
855C22×C4C2511yescharacteristic
856C22×C4C2514yes—
857C22×C4C2514yes—
858C22×C4C2514yes—
859C22×C4C2511yescharacteristic
860C22×C4C2514yes—
861C22×C4C2514yes—
862C22×C4C2511yescharacteristic
863C22×C4C2512yes—
864C22×C4C2512yes—
865C4⋊C4—28no—
866C4⋊C4—24no—
867C4⋊C4—28no—
868C4⋊C4—24no—
869C4⋊C4—216no—
870C4⋊C4—28no—
871C4⋊C4—216no—
872C4⋊C4—216no—
873C4⋊C4—216no—
874C4⋊C4—28no—
875C4⋊C4—28no—
876C4⋊C4—28no—
877C4⋊C4—28no—
878C4⋊C4—216no—
879C4⋊C4—28no—
880C4⋊C4—22no—
881C4⋊C4—24no—
882C4⋊C4—24no—
883C4⋊C4—28no—
884C4⋊C4—24no—
885C4⋊C4—28no—
886C4⋊C4—48no—
887C4⋊C4—44no—
888C4⋊C4—44no—
889C4⋊C4—44no—
890C4⋊C4—44no—
891C4⋊C4—44no—
892C4⋊C4—42no—
893C4⋊C4—48no—
894C4⋊C4—48no—
895C4⋊C4—44no—
896C4⋊C4—44no—
897C4⋊C4—44no—
898C4⋊C4—48no—
899C4⋊C4—48no—
900C4⋊C4—44no—
901C4⋊C4C22×D4116yes—
902C4⋊C4C22×D418yes—
903C22⋊C4—216no—
904C22⋊C4—28no—
905C22⋊C4—28no—
906C22⋊C4—28no—
907C22⋊C4—216no—
908C22⋊C4—28no—
909C22⋊C4—28no—
910C22⋊C4—28no—
911C22⋊C4—28no—
912C22⋊C4—22no—
913C22⋊C4—22no—
914C22⋊C4—24no—
915C22⋊C4—28no—
916C22⋊C4—216no—
917C22⋊C4—216no—
918C22⋊C4—28no—
919C22⋊C4—28no—
920C22⋊C4—28no—
921C22⋊C4—28no—
922C22⋊C4—28no—
923C22⋊C4—24no—
924C22⋊C4—48no—
925C22⋊C4—48no—
926C22⋊C4—44no—
927C22⋊C4—44no—
928C22⋊C4—44no—
929C22⋊C4—48no—
930C22⋊C4—44no—
931C22⋊C4—44no—
932C22⋊C4—48no—
933C22⋊C4—44no—
934C22⋊C4—44no—
935C22⋊C4—48no—
936C22⋊C4—44no—
937C22⋊C4—44no—
938C22⋊C4—44no—
939C22⋊C4C22×D4132yes—
940C22⋊C4C22×D4116yes—
941C42—28no—
942C42—216no—
943C42—24no—
944C42—22no—
945C42—24no—
946C42—22no—
947C42—28no—
948C42—28no—
949C42—28no—
950C42—22no—
951C42—24no—
952C42—24no—
953C42—28no—
954C42—44no—
955C42—41no—
956C42C22×D414yes—
957C42C22×D4116yes—
958C23—21no—
959C23—22no—
960C23—21no—
961C23—21no—
962C23—24no—
963C23—22no—
964C23—24no—
965C23—24no—
966C23—24no—
967C23—22no—
968C23—24no—
969C23—24no—
970C23—21no—
971C23—24no—
972C23—24no—
973C23—24no—
974C23—24no—
975C23—24no—
976C23—24no—
977C23—24no—
978C23—416no—
979C23—416no—
980C23—416no—
981C23—416no—
982C23—88no—
983C23—88no—
984C23—88no—
985C23C23×D418yes—
986C23C2×H(5,𝔽2)12yes—
987C23C2×H(5,𝔽2)12yes—
988C23C2×2−1+414yes—
989C23C2611yescharacteristic
990Q8—48no—
991Q8—48no—
992Q8—88no—
993Q8—88no—
994Q8—84no—
995Q8—84no—
996Q8—88no—
997D4—28no—
998D4—216no—
999D4—416no—
1000D4—416no—
1001D4—416no—
1002D4—48no—
1003D4—88no—
1004D4—88no—
1005D4—816no—
1006C2×C4—22no—
1007C2×C4—24no—
1008C2×C4—21no—
1009C2×C4—22no—
1010C2×C4—24no—
1011C2×C4—24no—
1012C2×C4—22no—
1013C2×C4—24no—
1014C2×C4—21no—
1015C2×C4—216no—
1016C2×C4—232no—
1017C2×C4—24no—
1018C2×C4—24no—
1019C2×C4—21no—
1020C2×C4—22no—
1021C2×C4—24no—
1022C2×C4—21no—
1023C2×C4—24no—
1024C2×C4—24no—
1025C2×C4—24no—
1026C2×C4—21no—
1027C2×C4—24no—
1028C2×C4—24no—
1029C2×C4—24no—
1030C2×C4—24no—
1031C2×C4—21no—
1032C2×C4—21no—
1033C2×C4—22no—
1034C2×C4—24no—
1035C2×C4—22no—
1036C2×C4—24no—
1037C2×C4—24no—
1038C2×C4—24no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—24no—
1042C2×C4—22no—
1043C2×C4—24no—
1044C2×C4—28no—
1045C2×C4—24no—
1046C2×C4—24no—
1047C2×C4—24no—
1048C2×C4—22no—
1049C2×C4—21no—
1050C2×C4—24no—
1051C2×C4—24no—
1052C2×C4—24no—
1053C2×C4—21no—
1054C2×C4—416no—
1055C2×C4—416no—
1056C2×C4—416no—
1057C2×C4—416no—
1058C2×C4—44no—
1059C2×C4—44no—
1060C2×C4—416no—
1061C2×C4—48no—
1062C2×C4—416no—
1063C2×C4—816no—
1064C2×C4—168no—
1065C2×C4C23×D418yes—
1066C2×C4C23×D412yes—
1067C2×C4C23×D418yes—
1068C2×C4C23×D414yes—
1069C2×C4C2×H(5,𝔽2)12yes—
1070C2×C4C2×2−1+414yes—
1071C2×C4C2×2−1+414yes—
1072C2×C4#58514yes—
1073C22—22no—
1074C22—22no—
1075C22—24no—
1076C22—24no—
1077C22—22no—
1078C22—28no—
1079C22—22no—
1080C22—22no—
1081C22—28no—
1082C22—28no—
1083C22—44no—
1084C22—44no—
1085C22—42no—
1086C22—42no—
1087C22—44no—
1088C22—44no—
1089C22—44no—
1090C22—44no—
1091C22—44no—
1092C22—44no—
1093C22—44no—
1094C22—44no—
1095C22—44no—
1096C22—832no—
1097C22#354414yescomplemented
1098C22C24×D411yescharacteristic
1099C22C22×H(5,𝔽2)11yescharacteristic
1100C22C22×2−1+412yes—
1101C22C2×#58512yes—
1102C22H(7,𝔽2)11yescharacteristic
1103C4—28no—
1104C4—22no—
1105C4—22no—
1106C4—24no—
1107C4—28no—
1108C4—44no—
1109C4—44no—
1110C4—41no—
1111C4—41no—
1112C4—44no—
1113C4—41no—
1114C4—44no—
1115C4—44no—
1116C4—42no—
1117C4—44no—
1118C4—44no—
1119C4—42no—
1120C4—44no—
1121C4#348918yes—
1122C2—24no—
1123C2—42no—
1124C2—48no—
1125C2—84no—
1126C2C2×#354411yescharacteristic
1127C2C2×#348912yes—
1128C2#6292912yes—
1129C2D4×H(5,𝔽2)11yescharacteristic
1130C2#6302411yescharacteristic
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. C22×#555C2semidirect
3. #59659C2semidirect
4. #59151C2semidirect
5. #59135C2semidirect
6. #59015C2semidirect
7. #51586C2semidirect
8. #51531C2semidirect
9. #46136C2semidirect
10. #44928C2semidirect
11. #44890C2semidirect
12. #42970C2semidirect
13. #42968C2semidirect
14. #39489C2semidirect
15. #38922C2semidirect
16. #37676C2semidirect
17. #37664C2semidirect
18. #36234C2semidirect
19. #36154C2semidirect
20. D4×C4⋊Q8C2semidirect
21. #35253C2semidirect
22. #34700C2semidirect
23. #34485C2semidirect
25. C2×#563C22semidirect
26. C2×Q82C22semidirect
34. C2×#554C22semidirect
35. C2×#552C22semidirect
37. C2×#547C22semidirect
39. C2×#544C22semidirect
40. C2×#542C22semidirect
41. C2×#536C22semidirect
43. C22×C4⋊Q8C22semidirect
44. C2×#529C22semidirect
49. #2868C22semidirect
52. #2857C22semidirect
55. #2820C22semidirect
56. #2734C22semidirect
57. #2731C22semidirect
58. #2731C22semidirect
59. #2717C22semidirect
60. #2715C22semidirect
61. #2715C22semidirect
62. #2701C22semidirect
63. #2691C22semidirect
64. #2686C22semidirect
65. #2674C22semidirect
66. #2674C22semidirect
67. #2674C22semidirect
68. #2674C22semidirect
69. #2672C22semidirect
70. #2672C22semidirect
71. #2672C22semidirect
72. #2672C22semidirect
73. #2671C22semidirect
74. #2658C22semidirect
75. #2629C22semidirect
76. #2628C22semidirect
77. #2624C22semidirect
78. #2620C22semidirect
79. #2620C22semidirect
80. #2611C22semidirect
81. #2609C22semidirect
82. #2567C22semidirect
83. #2563C22semidirect
84. #2551C22semidirect
85. #2551C22semidirect
86. #2547C22semidirect
87. #2546C22semidirect
88. #2545C22semidirect
89. #2538C22semidirect
90. #2537C22semidirect
91. #2501C22semidirect
92. #2499C22semidirect
93. #2491C22semidirect
94. #2491C22semidirect
95. #2487C22semidirect
96. #2485C22semidirect
99. #2478C22semidirect
100. #2470C22semidirect
101. #2468C22semidirect
102. #2457C22semidirect
103. #2454C22semidirect
104. #2454C22semidirect
105. #2451C22semidirect
106. #2450C22semidirect
107. #2447C22semidirect
110. #2441C22semidirect
111. #2441C22semidirect
112. #2441C22semidirect
115. #2440C22semidirect
116. #2439C22semidirect
117. #2439C22semidirect
118. #2438C22semidirect
119. #2438C22semidirect
123. #2436C22semidirect
128. #2434C22semidirect
129. #2432C22semidirect
130. #2430C22semidirect
131. #2427C22semidirect
132. #2427C22semidirect
133. #2426C22semidirect
134. #2425C22semidirect
135. #2422C22semidirect
136. #2422C22semidirect
137. #2420C22semidirect
141. #2417C22semidirect
142. #2416C22semidirect
143. #2416C22semidirect
144. #2415C22semidirect
147. #2395C22semidirect
148. #2392C22semidirect
149. #2379C22semidirect
150. #2369C22semidirect
151. #2362C22semidirect
152. #2361C22semidirect
154. #2352C22semidirect
155. #2349C22semidirect
157. D4×C4⋊C4C22semidirect
158. #2346C22semidirect
160. #2326C22semidirect
161. #2324C22semidirect
162. #2317C22semidirect
163. #2317C22semidirect
164. #2316C22semidirect
165. C4×C4⋊Q8C22semidirect
166. C4×#124C22semidirect
168. C4×#121C22semidirect
170. #2293C22semidirect
188. #555D4semidirect
1097. C22#3544semidirect

Maximal subgroups

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

subgroupindex
C2×#35442
C22×#5552
#596592
#591512
#591352
#590152
#515862
#515312
#461362
#449282
#448902
#429702
#429682
#394892
#389222
#376762
#376642
#362342
#361542
D4×C4⋊Q82
#352532
#347002
#344852