Finite Group Databasebeta

← #7681115

Subgroups — #7681115

Order 512.

10704 conjugacy classes of subgroups.

The subgroup lattice has 1091 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3499C212yesmaximal, complemented
2C2×#3499C211yesmaximal, characteristic, complemented
3C2×#3497C211yesmaximal, characteristic, complemented
4#59127C214yesmaximal, complemented
5#59112C218yesmaximal, complemented
6#59066C214yesmaximal, complemented
7#45332C218yesmaximal, complemented
8#44447C218yesmaximal, complemented
9#39363C212yesmaximal, complemented
10#39360C212yesmaximal, complemented
11#37680C214yesmaximal, complemented
12#37675C214yesmaximal, complemented
13#36125C212yesmaximal, complemented
14D4×C4⋊Q8C212yesmaximal, complemented
15#35666C212yesmaximal, complemented
16#35660C212yesmaximal, complemented
17#35317C211yesmaximal, characteristic, complemented
18#35308C212yesmaximal, complemented
19#34937C211yesmaximal, characteristic, complemented
20C2×#2546C211yesmaximal, characteristic, complemented
21#34141C211yesmaximal, characteristic, complemented
22C4×#536C211yesmaximal, characteristic, complemented
23C22×2−1+4C2212yes—
24C22×2−1+4C2212yes—
25#3499—232no—
26#3499—216no—
27#3497—216no—
28C2×#550C2212yes—
29C2×#550C2212yes—
30C2×D4×Q8C2218yes—
31C2×D4×Q8C2212yes—
32C2×D4×Q8C2212yes—
33C2×D4×Q8C2212yes—
34C2×D4×Q8C2212yes—
35C2×#548C2214yes—
36C2×#548C2214yes—
37C2×#547C2218yes—
38C2×#547C2212yes—
39C2×#547C2212yes—
40C2×#547C2214yes—
41C2×#547C22116yes—
42C2×#547C2214yes—
43C2×#537C2212yes—
44C2×#537C2214yes—
45C2×#536C2214yes—
46C2×#536C2214yes—
47C2×#536C2214yes—
48C2×#536C2212yes—
49C2×#536C2212yes—
50C2×#536C2212yes—
51C2×#536C2211yescharacteristic
52C2×#532C2214yes—
53C2×#532C2211yescharacteristic
54C2×#532C2214yes—
55C2×#532C2212yes—
56C2×#532C2212yes—
57C2×#532C2211yescharacteristic
58C22×C4⋊Q8C2214yes—
59C22×C4⋊Q8C2212yes—
60C22×C4⋊Q8C2211yescharacteristic
61C22×C4⋊Q8C2212yes—
62C2×C4×#41C2211yescharacteristic
63C2×C4×#41C2212yes—
64C22×C4×Q8C2211yescharacteristic
65#2868C2212yes—
66#2858C2212yes—
67#2857C2214yes—
68#2850C2214yes—
69#2681C22116yes—
70#2680C22116yes—
71#2677C22116yes—
72#2674C22116yes—
73#2672C22116yes—
74#2671C22116yes—
75#2658C2214yes—
76#2621C2214yes—
77#2620C2214yes—
78#2551C2218yes—
79#2548C2211yescharacteristic
80#2547C2211yescharacteristic
81#2546C2214yes—
82#2546C2211yescharacteristic
83#2546C2212yes—
84#2546C2214yes—
85#2546C2214yes—
86#2546C2212yes—
87#2545C2212yes—
88#2544C2212yes—
89#2543C2214yes—
90#2542C2214yes—
91#2542C2214yes—
92#2541C2211yescharacteristic
93#2501C2214yes—
94#2501C2214yes—
95#2464C22116yes—
96#2455C22116yes—
97#2452C2218yes—
98#2449C22116yes—
99#2449C22116yes—
100#2445C2218yes—
101#2443C22116yes—
102#2440C22116yes—
103#2440C2218yes—
104#2436C2214yes—
105#2434C2218yes—
106#2434C2214yes—
107#2434C2214yes—
108#2434C2214yes—
109#2432C2218yes—
110#2432C2214yes—
111#2432C2214yes—
112#2432C2214yes—
113#2431C2214yes—
114#2430C22116yes—
115#2429C2218yes—
116#2428C2218yes—
117#2427C2218yes—
118#2425C22116yes—
119#2422C2218yes—
120#2416C2214yes—
121#2409C2218yes—
122#2407C2218yes—
123#2406C22116yes—
124#2392C2214yes—
125C2×#398C2214yes—
126#2367C2214yes—
127#2366C2212yes—
128#2365C2212yes—
129#2364C2214yes—
130#2361C2218yes—
131#2361C2214yes—
132D4×C4⋊C4C2218yes—
133#2327C2212yes—
134#2326C2212yes—
135#2323C2214yes—
136#2322C2214yes—
137#2317C2211yescharacteristic
138#2311C2211yescharacteristic
139#2310C2211yescharacteristic
140C4×C4⋊Q8C2212yes—
141C4×#124C2212yes—
142C4×C22⋊Q8C2214yes—
143C4×#123C2214yes—
144C4×#121C2214yes—
145#2297C2212yes—
146#2297C2212yes—
147C2×#391C2212yes—
148#2293C2212yes—
149C2×#389C2214yes—
150#2290C2214yes—
151C42×D4C2212yes—
152C4×#117C2211yescharacteristic
153C2×C4×C4⋊C4C2211yescharacteristic
154C2×2−1+4—216no—
155C2×2−1+4—216no—
156C2×2−1+4—216no—
157C2×2−1+4—216no—
158C2×2−1+4—48no—
159C2×2−1+4—48no—
160C22×#41C2312yes—
161C22×#41C2318yes—
162C22×#41C2314yes—
163C22×#41C2314yes—
164C22×#41C2314yes—
165C22×#41C2318yes—
166C22×#41C2314yes—
167C22×#41C2311yescharacteristic
168C22×#41C2312yes—
169C23×Q8C2312yes—
170C23×Q8C2314yes—
171C23×Q8C2314yes—
172C23×Q8C2314yes—
173C23×Q8C2314yes—
174C23×Q8C2311yescharacteristic
175#550—216no—
176#550—216no—
177D4×Q8—216no—
178D4×Q8—264no—
179D4×Q8—216no—
180D4×Q8—216no—
181D4×Q8—216no—
182#548—232no—
183#548—232no—
184#547—2128no—
185#547—264no—
186#547—232no—
187#547—232no—
188#547—216no—
189#547—216no—
190#537—216no—
191#537—232no—
192#536—216no—
193#536—232no—
194#536—232no—
195#536—232no—
196#536—216no—
197#536—48no—
198#536D4116yescomplemented
199#532—216no—
200#532—216no—
201#532—232no—
202#532—232no—
203#532—28no—
204#532D4116yescomplemented
205C2×C4⋊Q8—216no—
206C2×C4⋊Q8—232no—
207C2×C4⋊Q8—216no—
208C2×C4⋊Q8—28no—
209C2×C4⋊Q8C2314yes—
210C2×C4⋊Q8C2312yes—
211C2×C4⋊Q8C2311yescharacteristic
212C2×C4⋊Q8C2312yes—
213C2×C4⋊Q8C2314yes—
214C2×C4⋊Q8C2312yes—
215C2×C4⋊Q8C2312yes—
216C2×C4⋊Q8C23116yes—
217C2×C4⋊Q8C2314yes—
218C2×C4⋊Q8C2314yes—
219C2×C4⋊Q8C2314yes—
220C2×C4⋊Q8C2312yes—
221C2×C4⋊Q8C2318yes—
222C2×C4⋊Q8C2314yes—
223C2×C4⋊Q8C2314yes—
224C2×C4⋊Q8C2314yes—
225C2×C4⋊Q8C2312yes—
226C2×C4⋊Q8C2311yescharacteristic
227C2×#127C2311yescharacteristic
228C2×#127C2312yes—
229C2×#127C2314yes—
230C2×#127C2311yescharacteristic
231C2×#124C2314yes—
232C2×#124C2312yes—
233C2×#124C2318yes—
234C2×#124C2314yes—
235C2×#124C2312yes—
236C2×#124C2312yes—
237C2×#124C2314yes—
238C2×#124C2312yes—
239C2×#124C2312yes—
240C2×#123C2318yes—
241C2×#123C23116yes—
242C2×#123C2318yes—
243C2×#123C23116yes—
244C2×#123C2318yes—
245C2×#123C2318yes—
246C2×#123C2318yes—
247C2×#123C2314yes—
248C2×C22⋊Q8C2314yes—
249C2×C22⋊Q8C2314yes—
250C2×C22⋊Q8C2314yes—
251C2×C22⋊Q8C2314yes—
252C2×C22⋊Q8C23116yes—
253C2×C22⋊Q8C2318yes—
254C2×C22⋊Q8C2318yes—
255C2×C22⋊Q8C23116yes—
256C2×C22⋊Q8C2318yes—
257C2×C22⋊Q8C2318yes—
258C2×C22⋊Q8C2318yes—
259C2×C22⋊Q8C2318yes—
260C2×C22⋊Q8C2314yes—
261C2×#121C2314yes—
262C2×#121C2314yes—
263C2×#121C2314yes—
264C2×#121C2314yes—
265C2×#121C2318yes—
266C2×#121C23116yes—
267C2×#121C2312yes—
268C2×#121C2318yes—
269C2×#121C2314yes—
270C2×#121C2318yes—
271C2×#121C2312yes—
272C2×#121C2318yes—
273C2×#121C2312yes—
274C2×#121C2312yes—
275C4×#41—216no—
276C4×#41—28no—
277C2×C4×Q8—28no—
278C2×C4×Q8C2311yescharacteristic
279C2×C4×Q8C2312yes—
280C2×C4×Q8C2312yes—
281C2×C4×Q8C2312yes—
282C2×C4×Q8C2311yescharacteristic
283C2×C4×Q8C2314yes—
284C2×C4×Q8C2312yes—
285C2×C4×D4C2312yes—
286C2×C4×D4C2311yescharacteristic
287C2×C4×D4C2314yes—
288C2×C4×D4C2314yes—
289C2×C4×D4C2314yes—
290C2×C4×D4C2314yes—
291C2×C4×D4C2318yes—
292C2×C4×D4C23116yes—
293C2×C4×D4C2314yes—
294C2×C4×D4C2312yes—
295C2×C4×D4C2318yes—
296C2×C4×D4C2312yes—
297C2×C4×D4C2311yescharacteristic
298C2×C4×D4C2314yes—
299C2×C4×D4C2318yes—
300C2×C4×D4C2312yes—
301C2×C4×D4C2312yes—
302C2×C4×D4C2312yes—
303C2×#117C2311yescharacteristic
304C2×#117C2311yescharacteristic
305C2×#117C2312yes—
306C2×#117C2314yes—
307C2×#117C2311yescharacteristic
308C22×C4⋊C4C2311yescharacteristic
309C22×C4⋊C4C2312yes—
310C22×C4⋊C4C23116yes—
311C22×C4⋊C4C2312yes—
312C22×C4⋊C4C2314yes—
313C22×C4⋊C4C2312yes—
314C22×C4⋊C4C2318yes—
315C22×C4⋊C4C2314yes—
316C22×C4⋊C4C2312yes—
317C22×C42C2314yes—
318C22×C42C2312yes—
319C22×C42C2312yes—
320C22×C42C2312yes—
321C22×C42C2311yescharacteristic
322#399C23116yes—
323#399C23116yes—
324#398C23116yes—
325#398C23116yes—
326#398C2318yes—
327#398C2318yes—
328#398C2314yes—
329#397C23116yes—
330#397C2314yes—
331#396C23116yes—
332#396C2318yes—
333#395C23116yes—
334#395C23116yes—
335#395C23116yes—
336#394C23116yes—
337#394C2318yes—
338#394C2314yes—
339#394C23116yes—
340#394C23116yes—
341#394C23116yes—
342#393C23116yes—
343#392C2314yes—
344#392C23116yes—
345#391C2312yes—
346#391C2312yes—
347#391C2314yes—
348#391C2312yes—
349#391C2314yes—
350#391C2312yes—
351#391C2314yes—
352#391C2314yes—
353#391C2312yes—
354#391C2318yes—
355#390C2312yes—
356#390C2312yes—
357#390C2318yes—
358#390C2318yes—
359#390C2314yes—
360#390C2312yes—
361#390C2314yes—
362#390C2314yes—
363#389C2318yes—
364#389C2314yes—
365#389C23116yes—
366#389C2314yes—
367#389C2318yes—
368#389C2314yes—
369#389C23116yes—
370#389C2318yes—
371#388C2318yes—
372#388C2318yes—
373#388C23116yes—
374#388C2318yes—
375#388C2318yes—
376#388C2318yes—
377#387C2318yes—
378#387C2318yes—
379#387C2318yes—
380#386C2314yes—
381#386C23116yes—
382#386C2318yes—
383#386C23116yes—
384#386C2318yes—
385#386C2318yes—
386#386C23116yes—
387#386C2318yes—
388#385C2314yes—
389#385C2318yes—
390#385C23116yes—
391#385C23116yes—
392#385C2318yes—
393#385C23116yes—
394#385C23116yes—
395#385C23116yes—
396#385C23116yes—
397#384C2312yes—
398#384C2318yes—
399#384C2318yes—
400#382C2312yes—
401#381C2314yes—
402#380C2314yes—
403#380C23116yes—
404#380C2314yes—
405C4×C4⋊C4C2318yes—
406C4×C4⋊C4C2312yes—
407C4×C4⋊C4C2314yes—
408C4×C4⋊C4C2312yes—
409C4×C4⋊C4C2312yes—
410C4×C4⋊C4C2312yes—
411C4×C4⋊C4C2311yescharacteristic
412C4×C4⋊C4C2312yes—
413C4×C4⋊C4C2311yescharacteristic
414C4×C22⋊C4C2312yes—
415C4×C22⋊C4C2312yes—
416C4×C22⋊C4C2318yes—
417C4×C22⋊C4C2318yes—
418C4×C22⋊C4C2318yes—
419C4×C22⋊C4C2314yes—
420C4×C22⋊C4C2314yes—
421#376C2312yes—
422C2×#95C2312yes—
423C2×#95C2318yes—
424C43C2312yes—
4252−1+4—4128no—
4262−1+4—4128no—
427C2×#41—216no—
428C2×#41—216no—
429C2×#41—216no—
430C2×#41—216no—
431C2×#41—232no—
432C2×#41—232no—
433C2×#41—232no—
434C2×#41—216no—
435C2×#41—28no—
436C2×#41—24no—
437C2×#41—28no—
438C2×#41—28no—
439C2×#41—216no—
440C2×#41—216no—
441C2×#41—232no—
442C2×#41—216no—
443C2×#41—24no—
444C2×#41—28no—
445C2×#41—28no—
446C2×#41—416no—
447C2×#41—416no—
448C2×#41—48no—
449C2×#41—48no—
450C2×#41—48no—
451C2×#41—48no—
452C2×#41C2×D418yes—
453C2×#41C2×D4116yes—
454C22×Q8—216no—
455C22×Q8—216no—
456C22×Q8—216no—
457C22×Q8—216no—
458C22×Q8—216no—
459C22×Q8—24no—
460C22×Q8—28no—
461C22×Q8—28no—
462C22×Q8—216no—
463C22×Q8—216no—
464C22×Q8—216no—
465C22×Q8—24no—
466C22×Q8—28no—
467C22×Q8—48no—
468C22×Q8—48no—
469C22×Q8—48no—
470C22×Q8—48no—
471C22×Q8C2×D418yes—
472C22×Q8C2414yes—
473C22×Q8C2412yes—
474C22×Q8C2414yes—
475C22×Q8C2418yes—
476C22×Q8C2418yes—
477C22×Q8C2412yes—
478C22×Q8C2412yes—
479C22×Q8C2411yescharacteristic
480C22×Q8C2412yes—
481C22×D4C2412yes—
482C22×D4C2414yes—
483C22×D4C2412yes—
484C22×D4C2418yes—
485C22×D4C2418yes—
486C22×D4C2418yes—
487C22×D4C2412yes—
488C22×D4C2412yes—
489C22×D4C2414yes—
490C22×D4C2412yes—
491C22×D4C2411yescharacteristic
492C22×D4C2418yes—
493C22×D4C2412yes—
494C22×D4C2412yes—
495C23×C4C2414yes—
496C23×C4C2412yes—
497C23×C4C2414yes—
498C23×C4C2414yes—
499C23×C4C2418yes—
500C23×C4C2418yes—
501C23×C4C2418yes—
502C23×C4C2418yes—
503C23×C4C2418yes—
504C23×C4C2412yes—
505C23×C4C2411yescharacteristic
506C23×C4C2412yes—
507C23×C4C2414yes—
508C23×C4C2412yes—
509C23×C4C2412yes—
510C23×C4C2411yescharacteristic
511C23×C4C2411yescharacteristic
512C4⋊Q8—28no—
513C4⋊Q8—216no—
514C4⋊Q8—216no—
515C4⋊Q8—216no—
516C4⋊Q8—232no—
517C4⋊Q8—264no—
518C4⋊Q8—216no—
519C4⋊Q8—216no—
520C4⋊Q8—216no—
521C4⋊Q8—28no—
522C4⋊Q8—216no—
523C4⋊Q8—28no—
524C4⋊Q8—28no—
525C4⋊Q8—28no—
526C4⋊Q8—24no—
527C4⋊Q8—48no—
528C4⋊Q8C2×D418yes—
529C4⋊Q8C2×D4116yes—
530#127—28no—
531#127—216no—
532#127—24no—
533#127C2×D418yes—
534#124—28no—
535#124—216no—
536#124—28no—
537#124—232no—
538#124—216no—
539#124—28no—
540#124—48no—
541#124C2×D4116yes—
542#124C2×D4116yes—
543#123—232no—
544#123—264no—
545#123—232no—
546#123—264no—
547#123—232no—
548#123—232no—
549#123—416no—
550#123C2×D4132yes—
551C22⋊Q8—216no—
552C22⋊Q8—216no—
553C22⋊Q8—216no—
554C22⋊Q8—216no—
555C22⋊Q8—232no—
556C22⋊Q8—264no—
557C22⋊Q8—232no—
558C22⋊Q8—232no—
559C22⋊Q8—264no—
560C22⋊Q8—232no—
561C22⋊Q8—232no—
562C22⋊Q8—416no—
563C22⋊Q8C2×D4132yes—
564#121—232no—
565#121—216no—
566#121—216no—
567#121—232no—
568#121—216no—
569#121—232no—
570#121—28no—
571#121—28no—
572#121—216no—
573#121—216no—
574#121—264no—
575#121—232no—
576#121C2×D4116yes—
577#121C2×D4116yes—
578C4×Q8—216no—
579C4×Q8—28no—
580C4×Q8—28no—
581C4×Q8—28no—
582C4×Q8—28no—
583C4×Q8—24no—
584C4×Q8—24no—
585C4×D4—216no—
586C4×D4—216no—
587C4×D4—216no—
588C4×D4—28no—
589C4×D4—28no—
590C4×D4—232no—
591C4×D4—216no—
592C4×D4—216no—
593C4×D4—216no—
594C4×D4—232no—
595C4×D4—264no—
596C4×D4—232no—
597C4×D4—24no—
598C4×D4—24no—
599C4×D4—28no—
600C4×D4—28no—
601C4×D4C2×D4116yes—
602C4×D4C2×D4116yes—
603#117—24no—
604#117—24no—
605#117—216no—
606#117—28no—
607#117C2×D418yes—
608C2×C4⋊C4—28no—
609C2×C4⋊C4—24no—
610C2×C4⋊C4—232no—
611C2×C4⋊C4—28no—
612C2×C4⋊C4—28no—
613C2×C4⋊C4—264no—
614C2×C4⋊C4—216no—
615C2×C4⋊C4—216no—
616C2×C4⋊C4—28no—
617C2×C4⋊C4C2414yes—
618C2×C4⋊C4C2418yes—
619C2×C4⋊C4C24116yes—
620C2×C4⋊C4C2414yes—
621C2×C4⋊C4C2412yes—
622C2×C4⋊C4C2412yes—
623C2×C4⋊C4C2414yes—
624C2×C4⋊C4C2414yes—
625C2×C4⋊C4C24116yes—
626C2×C4⋊C4C2414yes—
627C2×C4⋊C4C2418yes—
628C2×C4⋊C4C24116yes—
629C2×C4⋊C4C2418yes—
630C2×C4⋊C4C2414yes—
631C2×C4⋊C4C2412yes—
632C2×C4⋊C4C2414yes—
633C2×C4⋊C4C2411yescharacteristic
634C2×C4⋊C4C2411yescharacteristic
635C2×C4⋊C4C2418yes—
636C2×C4⋊C4C2412yes—
637C2×C4⋊C4C2412yes—
638C2×C4⋊C4C2412yes—
639C2×C4⋊C4C2412yes—
640C2×C4⋊C4C2412yes—
641C2×C4⋊C4C2418yes—
642C2×C4⋊C4C24116yes—
643C2×C4⋊C4C2418yes—
644C2×C4⋊C4C2412yes—
645C2×C4⋊C4C2412yes—
646C2×C4⋊C4C2418yes—
647C2×C4⋊C4C2412yes—
648C2×C4⋊C4C2412yes—
649C2×C22⋊C4C2412yes—
650C2×C22⋊C4C2418yes—
651C2×C22⋊C4C2412yes—
652C2×C22⋊C4C2412yes—
653C2×C22⋊C4C2412yes—
654C2×C22⋊C4C2414yes—
655C2×C22⋊C4C2418yes—
656C2×C22⋊C4C2418yes—
657C2×C22⋊C4C2414yes—
658C2×C22⋊C4C2418yes—
659C2×C22⋊C4C2418yes—
660C2×C22⋊C4C2418yes—
661C2×C22⋊C4C2418yes—
662C2×C22⋊C4C24116yes—
663C2×C22⋊C4C2418yes—
664C2×C22⋊C4C2418yes—
665C2×C22⋊C4C24116yes—
666C2×C22⋊C4C2418yes—
667C2×C22⋊C4C2418yes—
668C2×C22⋊C4C2418yes—
669C2×C22⋊C4C2412yes—
670C2×C22⋊C4C2414yes—
671C2×C22⋊C4C2418yes—
672C2×C22⋊C4C2414yes—
673C2×C42—28no—
674C2×C42—28no—
675C2×C42—216no—
676C2×C42—28no—
677C2×C42C2×D418yes—
678C2×C42C2412yes—
679C2×C42C2412yes—
680C2×C42C2412yes—
681C2×C42C2414yes—
682C2×C42C2418yes—
683C2×C42C2412yes—
684C2×C42C2412yes—
685C2×C42C2414yes—
686C2×C42C2414yes—
687C2×C42C2414yes—
688C2×C42C2412yes—
689C2×C42C2414yes—
690C2×C42C2412yes—
691C2×C42C2411yescharacteristic
692C2×C42C2411yescharacteristic
693C2×C42C2411yescharacteristic
694C2×C42C2411yescharacteristic
695#95C2412yes—
696#95C2414yes—
697#95C2412yes—
698#95C24116yes—
699#95C24116yes—
700#95C2414yes—
701#95C2414yes—
702#95C2418yes—
703#95C2418yes—
704#95C2418yes—
705#95C2418yes—
706#95C2418yes—
707#95C2418yes—
708#95C2418yes—
709#95C2418yes—
710C24C2514yes—
711C24C2514yes—
712C24C2512yes—
713C24C2511yescharacteristic
714#41—232no—
715#41—264no—
716#41—4128no—
717#41—464no—
718#41—464no—
719#41—464no—
720#41—4128no—
721#41—464no—
722#41—432no—
723C2×Q8—232no—
724C2×Q8—24no—
725C2×Q8—22no—
726C2×Q8—24no—
727C2×Q8—24no—
728C2×Q8—216no—
729C2×Q8—24no—
730C2×Q8—216no—
731C2×Q8—216no—
732C2×Q8—216no—
733C2×Q8—28no—
734C2×Q8—28no—
735C2×Q8—24no—
736C2×Q8—28no—
737C2×Q8—28no—
738C2×Q8—24no—
739C2×Q8—24no—
740C2×Q8—22no—
741C2×Q8—24no—
742C2×Q8—28no—
743C2×Q8—28no—
744C2×Q8—24no—
745C2×Q8—48no—
746C2×Q8—48no—
747C2×Q8—464no—
748C2×Q8—464no—
749C2×Q8—464no—
750C2×Q8—464no—
751C2×Q8—432no—
752C2×Q8C22×D418yes—
753C2×Q8C22×D418yes—
754C2×Q8C22×D414yes—
755C2×Q8C22×D418yes—
756C2×D4—24no—
757C2×D4—28no—
758C2×D4—24no—
759C2×D4—28no—
760C2×D4—216no—
761C2×D4—28no—
762C2×D4—216no—
763C2×D4—216no—
764C2×D4—28no—
765C2×D4—216no—
766C2×D4—28no—
767C2×D4—216no—
768C2×D4—24no—
769C2×D4—22no—
770C2×D4—24no—
771C2×D4—216no—
772C2×D4—24no—
773C2×D4—24no—
774C2×D4—24no—
775C2×D4—22no—
776C2×D4—24no—
777C2×D4—24no—
778C2×D4—28no—
779C2×D4—216no—
780C2×D4—28no—
781C2×D4—44no—
782C2×D4—48no—
783C2×D4—48no—
784C2×D4—48no—
785C2×D4—44no—
786C2×D4—416no—
787C2×D4C22×D418yes—
788C2×D4C22×D418yes—
789C2×D4C22×D4116yes—
790C2×D4C22×D418yes—
791C2×D4C22×D414yes—
792C2×D4C22×D418yes—
793C22×C4—24no—
794C22×C4—24no—
795C22×C4—28no—
796C22×C4—24no—
797C22×C4—28no—
798C22×C4—24no—
799C22×C4—24no—
800C22×C4—28no—
801C22×C4—28no—
802C22×C4—28no—
803C22×C4—216no—
804C22×C4—216no—
805C22×C4—216no—
806C22×C4—28no—
807C22×C4—24no—
808C22×C4—216no—
809C22×C4—24no—
810C22×C4—24no—
811C22×C4—216no—
812C22×C4—216no—
813C22×C4—216no—
814C22×C4—216no—
815C22×C4—28no—
816C22×C4—216no—
817C22×C4—28no—
818C22×C4—28no—
819C22×C4—28no—
820C22×C4—216no—
821C22×C4—28no—
822C22×C4—42no—
823C22×C4—48no—
824C22×C4—44no—
825C22×C4—44no—
826C22×C4—48no—
827C22×C4—48no—
828C22×C4—48no—
829C22×C4—48no—
830C22×C4—44no—
831C22×C4C22×D414yes—
832C22×C4C22×D418yes—
833C22×C4C22×D418yes—
834C22×C4C22×D4116yes—
835C22×C4C22×D414yes—
836C22×C4C22×D414yes—
837C22×C4C22×D414yes—
838C22×C4H(5,𝔽2)14yes—
839C22×C4C2514yes—
840C22×C4C2512yes—
841C22×C4C2514yes—
842C22×C4C2514yes—
843C22×C4C2512yes—
844C22×C4C2514yes—
845C22×C4C2518yes—
846C22×C4C2511yescharacteristic
847C22×C4C2511yescharacteristic
848C22×C4C2511yescharacteristic
849C22×C4C2514yes—
850C22×C4C2512yes—
851C22×C4C2514yes—
852C22×C4C2514yes—
853C22×C4C2514yes—
854C22×C4C2511yescharacteristic
855C22×C4C2511yescharacteristic
856C22×C4C2511yescharacteristic
857C4⋊C4—216no—
858C4⋊C4—232no—
859C4⋊C4—28no—
860C4⋊C4—28no—
861C4⋊C4—28no—
862C4⋊C4—28no—
863C4⋊C4—24no—
864C4⋊C4—24no—
865C4⋊C4—216no—
866C4⋊C4—216no—
867C4⋊C4—232no—
868C4⋊C4—28no—
869C4⋊C4—232no—
870C4⋊C4—28no—
871C4⋊C4—24no—
872C4⋊C4—216no—
873C4⋊C4—24no—
874C4⋊C4—22no—
875C4⋊C4—22no—
876C4⋊C4—24no—
877C4⋊C4—216no—
878C4⋊C4—24no—
879C4⋊C4—24no—
880C4⋊C4—28no—
881C4⋊C4—24no—
882C4⋊C4—48no—
883C4⋊C4—416no—
884C4⋊C4C22×D418yes—
885C4⋊C4C22×D418yes—
886C4⋊C4C22×D4132yes—
887C4⋊C4C22×D418yes—
888C4⋊C42−1+418yescomplemented
889C22⋊C4—24no—
890C22⋊C4—216no—
891C22⋊C4—216no—
892C22⋊C4—216no—
893C22⋊C4—216no—
894C22⋊C4—24no—
895C22⋊C4—24no—
896C22⋊C4—216no—
897C22⋊C4—24no—
898C22⋊C4—28no—
899C22⋊C4—216no—
900C22⋊C4—28no—
901C22⋊C4—216no—
902C22⋊C4—232no—
903C22⋊C4—216no—
904C22⋊C4—216no—
905C22⋊C4—48no—
906C22⋊C4—48no—
907C22⋊C4—48no—
908C22⋊C4—416no—
909C22⋊C4C22×D418yes—
910C22⋊C4C22×D4116yes—
911C22⋊C4C22×D4132yes—
912C22⋊C4C22×D4116yes—
913C42—24no—
914C42—24no—
915C42—24no—
916C42—216no—
917C42—28no—
918C42—24no—
919C42—24no—
920C42—28no—
921C42—28no—
922C42—24no—
923C42—28no—
924C42—44no—
925C42C22×D414yes—
926C42C22×D418yes—
927C42C22×D414yes—
928C42C22×D414yes—
929C42C22×D414yes—
930C23—22no—
931C23—22no—
932C23—24no—
933C23—22no—
934C23—24no—
935C23—22no—
936C23—28no—
937C23—24no—
938C23—24no—
939C23—28no—
940C23—24no—
941C23—24no—
942C23—24no—
943C23—28no—
944C23—28no—
945C23C23×D418yes—
946C23C23×D414yes—
947C23C23×D412yes—
948C23C23×D412yes—
949C23C2×H(5,𝔽2)12yes—
950C23C2611yescharacteristic
951Q8—216no—
952Q8—216no—
953Q8—28no—
954Q8—216no—
955Q8—432no—
956Q8—432no—
957Q8—48no—
958Q8—416no—
959Q8—416no—
960D4—216no—
961D4—232no—
962D4—28no—
963D4—216no—
964D4—216no—
965D4—48no—
966D4—432no—
967D4—432no—
968D4—432no—
969D4—416no—
970D4—48no—
971D4—48no—
972D4—84no—
973D4—816no—
974C2×C4—24no—
975C2×C4—24no—
976C2×C4—24no—
977C2×C4—22no—
978C2×C4—24no—
979C2×C4—22no—
980C2×C4—24no—
981C2×C4—24no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—24no—
985C2×C4—24no—
986C2×C4—22no—
987C2×C4—216no—
988C2×C4—232no—
989C2×C4—216no—
990C2×C4—28no—
991C2×C4—24no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—24no—
995C2×C4—24no—
996C2×C4—24no—
997C2×C4—28no—
998C2×C4—28no—
999C2×C4—24no—
1000C2×C4—28no—
1001C2×C4—24no—
1002C2×C4—24no—
1003C2×C4—24no—
1004C2×C4—24no—
1005C2×C4—24no—
1006C2×C4—24no—
1007C2×C4—24no—
1008C2×C4—28no—
1009C2×C4—44no—
1010C2×C4—432no—
1011C2×C4—432no—
1012C2×C4—416no—
1013C2×C4—432no—
1014C2×C4—432no—
1015C2×C4—432no—
1016C2×C4—48no—
1017C2×C4—416no—
1018C2×C4—416no—
1019C2×C4—48no—
1020C2×C4—84no—
1021C2×C4D42116yes—
1022C2×C4C23×D412yes—
1023C2×C4C23×D412yes—
1024C2×C4C23×D418yes—
1025C2×C4C23×D412yes—
1026C2×C4C23×D414yes—
1027C2×C4C23×D418yes—
1028C2×C4C23×D418yes—
1029C2×C4C23×D412yes—
1030C2×C4C23×D412yes—
1031C2×C4C23×D412yes—
1032C2×C4C23×D412yes—
1033C2×C4C23×D412yes—
1034C2×C4C2×H(5,𝔽2)12yes—
1035C2×C4C2×H(5,𝔽2)12yes—
1036C2×C4C2×2−1+418yes—
1037C2×C4C2×2−1+414yes—
1038C22—24no—
1039C22—22no—
1040C22—22no—
1041C22—24no—
1042C22—28no—
1043C22—28no—
1044C22—28no—
1045C22—28no—
1046C22—24no—
1047C22—48no—
1048C22—42no—
1049C22—42no—
1050C22—48no—
1051C22—44no—
1052C22—48no—
1053C22—44no—
1054C22—44no—
1055C22—48no—
1056C22—44no—
1057C22C2×D4214yes—
1058C22C24×D411yescharacteristic
1059C22C24×D411yescharacteristic
1060C22C22×H(5,𝔽2)11yescharacteristic
1061C22C22×2−1+412yes—
1062C222−1+612yes—
1063C4—28no—
1064C4—28no—
1065C4—22no—
1066C4—22no—
1067C4—22no—
1068C4—28no—
1069C4—24no—
1070C4—28no—
1071C4—44no—
1072C4—42no—
1073C4—42no—
1074C4—44no—
1075C4—44no—
1076C4—44no—
1077C4—48no—
1078C4C2×D4214yes—
1079C4C2×D4214yes—
1080C4#349914yescomplemented
1081C2—24no—
1082C2—44no—
1083C2—48no—
1084C2—84no—
1085C2C22×D4211yescharacteristic
1086C2C2×#349911yescharacteristic
1087C2#6285911yescharacteristic
1088C2#6294612yes—
1089C2D4×2−1+412yes—
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×#3499C2semidirect
2. C2×#3499C2semidirect
3. C2×#3497C2semidirect
4. #59127C2semidirect
5. #59112C2semidirect
6. #59066C2semidirect
7. #45332C2semidirect
8. #44447C2semidirect
9. #39363C2semidirect
10. #39360C2semidirect
11. #37680C2semidirect
12. #37675C2semidirect
13. #36125C2semidirect
14. D4×C4⋊Q8C2semidirect
15. #35666C2semidirect
16. #35660C2semidirect
17. #35317C2semidirect
18. #35308C2semidirect
19. #34937C2semidirect
20. C2×#2546C2semidirect
21. #34141C2semidirect
22. C4×#536C2semidirect
198. #536D4semidirect
204. #532D4semidirect
888. C4⋊C42−1+4semidirect
1080. C4#3499semidirect

Maximal subgroups

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

subgroupindex
C2×#34992
C2×#34972
#591272
#591122
#590662
#453322
#444472
#393632
#393602
#376802
#376752
#361252
D4×C4⋊Q82
#356662
#356602
#353172
#353082
#349372
C2×#25462
#341412
C4×#5362