Finite Group Databasebeta

← #7655116

Subgroups — #7655116

Order 512.

8070 conjugacy classes of subgroups.

The subgroup lattice has 1058 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3499C211yesmaximal, characteristic, complemented
2C2×#3482C211yesmaximal, characteristic, complemented
3#42911C214yesmaximal, complemented
4#42297C218yesmaximal, complemented
5#39616C212yesmaximal, complemented
6#39596C214yesmaximal, complemented
7#39167C212yesmaximal, complemented
8#38079C214yesmaximal, complemented
9#38041C218yesmaximal, complemented
10#37863C214yesmaximal, complemented
11#37640C211yesmaximal, characteristic, complemented
12#37632C212yesmaximal, complemented
13#36303C212yesmaximal, complemented
14#36259C214yesmaximal, complemented
15#36179C212yesmaximal, complemented
16#36085C214yesmaximal, complemented
17#35281C211yesmaximal, characteristic, complemented
18#35279C211yesmaximal, characteristic, complemented
19#35249C212yesmaximal, complemented
20#35238C212yesmaximal, complemented
21#34977C211yesmaximal, characteristic, complemented
22C2×#2567C212yesmaximal, complemented
23#34127C211yesmaximal, characteristic, complemented
24C22×2−1+4C2212yes—
25#3499—216no—
26#3482—216no—
27C2×#557C2211yescharacteristic
28C2×#556C2212yes—
29C2×#556C2211yescharacteristic
30C2×#552C2214yes—
31C2×#552C2212yes—
32C2×D4×Q8C2212yes—
33C2×D4×Q8C2212yes—
34C2×D4×Q8C2211yescharacteristic
35C2×#548C2212yes—
36C2×#547C2212yes—
37C2×#547C2214yes—
38C2×#547C2212yes—
39C2×#547C2214yes—
40C2×#547C2211yescharacteristic
41C2×#547C2212yes—
42C2×#547C2218yes—
43C2×#536C2214yes—
44C2×#536C2212yes—
45C2×#533C2211yescharacteristic
46C2×#533C2212yes—
47C2×#532C2211yescharacteristic
48C2×#532C2212yes—
49C22×C4⋊Q8C2212yes—
50C22×C4⋊Q8C2211yescharacteristic
51C2×#529C2212yes—
52C2×#529C2214yes—
53C2×C4×#41C2211yescharacteristic
54C2×C4×#41C2212yes—
55C2×C4×#41C2211yescharacteristic
56C22×C4×Q8C2212yes—
57#2868C2212yes—
58#2862C2212yes—
59#2857C2214yes—
60#2856C2214yes—
61#2854C2218yes—
62#2850C2214yes—
63#2821C2218yes—
64#2820C2214yes—
65#2723C22116yes—
66#2720C22116yes—
67#2720C22116yes—
68#2718C22116yes—
69#2710C22116yes—
70#2692C22116yes—
71#2662C2218yes—
72#2660C2214yes—
73#2660C2214yes—
74#2640C2214yes—
75#2632C2218yes—
76#2628C2218yes—
77#2628C2214yes—
78#2624C2214yes—
79#2620C2214yes—
80#2616C2214yes—
81#2614C2218yes—
82#2610C2214yes—
83#2580C2218yes—
84#2568C2212yes—
85#2567C2212yes—
86#2567C2212yes—
87#2567C2218yes—
88#2567C2211yescharacteristic
89#2567C2218yes—
90#2567C2212yes—
91#2567C2212yes—
92#2567C2214yes—
93#2567C2214yes—
94#2566C2214yes—
95#2563C2211yescharacteristic
96#2563C2212yes—
97#2548C2212yes—
98#2548C2211yescharacteristic
99#2547C2212yes—
100#2546C2214yes—
101#2544C2214yes—
102#2542C2212yes—
103#2542C2218yes—
104#2542C2212yes—
105#2541C2211yescharacteristic
106#2538C2214yes—
107#2503C2214yes—
108#2502C2214yes—
109#2501C2214yes—
110#2501C22116yes—
111#2501C2214yes—
112#2500C2212yes—
113#2492C2218yes—
114#2488C22116yes—
115#2487C2214yes—
116#2486C2218yes—
117#2436C2214yes—
118#2434C2214yes—
119#2434C2218yes—
120#2431C2212yes—
121#2430C2218yes—
122#2430C22116yes—
123#2429C2218yes—
124#2425C22116yes—
125#2416C2218yes—
126#2415C2218yes—
127#2414C2214yes—
128#2413C22116yes—
129#2409C2214yes—
130#2409C2218yes—
131#2406C2218yes—
132#2406C22116yes—
133#2388C2214yes—
134C2×#395C2218yes—
135#2355C2212yes—
136#2352C2214yes—
137D4×C4⋊C4C2212yes—
138#2347C2212yes—
139#2343C2214yes—
140#2339C2212yes—
141#2339C2218yes—
142#2326C2214yes—
143#2326C2214yes—
144#2324C2218yes—
145#2317C2214yes—
146#2317C2212yes—
147#2311C2212yes—
148C4×#127C2212yes—
149C4×#124C2212yes—
150C4×#121C2214yes—
151#2295C2212yes—
152C2×#391C2214yes—
153C2×#389C2218yes—
154#2290C2214yes—
155#2285C2211yescharacteristic
156C2×#384C2214yes—
157#2283C2212yes—
158C42×D4C2212yes—
159C4×#117C2211yescharacteristic
160C2×C4×C4⋊C4C2212yes—
161C2×2−1+4—216no—
162C2×2−1+4—416no—
163C22×#41C2314yes—
164C22×#41C2312yes—
165C22×#41C2311yescharacteristic
166C22×#41C2311yescharacteristic
167C22×#41C2312yes—
168C22×#41C2314yes—
169C22×#41C2318yes—
170C23×Q8C2312yes—
171C23×Q8C2314yes—
172C23×Q8C2312yes—
173C23×Q8C2314yes—
174#557—28no—
175#556—28no—
176#556—216no—
177#552—216no—
178#552—232no—
179D4×Q8—216no—
180D4×Q8—216no—
181D4×Q8—28no—
182#548—216no—
183#547—216no—
184#547—28no—
185#547—216no—
186#547—232no—
187#547—216no—
188#547—232no—
189#547—432no—
190#536—232no—
191#536—216no—
192#533—216no—
193#533—28no—
194#532—216no—
195#532—28no—
196C2×C4⋊Q8—216no—
197C2×C4⋊Q8—28no—
198C2×C4⋊Q8C2311yescharacteristic
199C2×C4⋊Q8C2312yes—
200C2×C4⋊Q8C2314yes—
201C2×C4⋊Q8C2314yes—
202C2×C4⋊Q8C2314yes—
203C2×C4⋊Q8C2312yes—
204C2×C4⋊Q8C2312yes—
205C2×C4⋊Q8C2311yescharacteristic
206C2×C4⋊Q8C2311yescharacteristic
207C2×C4⋊Q8C2312yes—
208C2×C4⋊Q8C2312yes—
209C2×C4⋊Q8C2312yes—
210C2×C4⋊Q8C2318yes—
211C2×#127C2311yescharacteristic
212C2×#127C2312yes—
213#529—232no—
214#529—216no—
215C2×#126C2314yes—
216C2×#126C2314yes—
217C2×#126C2314yes—
218C2×#125C2312yes—
219C2×#125C2312yes—
220C2×#125C2314yes—
221C2×#125C2314yes—
222C2×#124C2312yes—
223C2×#124C2312yes—
224C2×#124C2314yes—
225C2×#124C2312yes—
226C2×#124C2314yes—
227C2×#124C2314yes—
228C2×#123C2314yes—
229C2×#123C2314yes—
230C2×#123C2318yes—
231C2×#123C2314yes—
232C2×#123C2318yes—
233C2×#123C2318yes—
234C2×#123C23116yes—
235C2×#123C23116yes—
236C2×C22⋊Q8C2312yes—
237C2×C22⋊Q8C2312yes—
238C2×C22⋊Q8C2312yes—
239C2×C22⋊Q8C2312yes—
240C2×C22⋊Q8C2314yes—
241C2×C22⋊Q8C2314yes—
242C2×C22⋊Q8C2314yes—
243C2×C22⋊Q8C2312yes—
244C2×C22⋊Q8C2318yes—
245C2×C22⋊Q8C2318yes—
246C2×C22⋊Q8C2314yes—
247C2×C22⋊Q8C2318yes—
248C2×C22⋊Q8C2318yes—
249C2×#121C2314yes—
250C2×#121C2314yes—
251C2×#121C2314yes—
252C2×#121C2312yes—
253C2×#121C2312yes—
254C2×#121C2312yes—
255C2×#121C2314yes—
256C2×#121C23116yes—
257C4×#41—216no—
258C4×#41—28no—
259C4×#41D4116yescomplemented
260C2×C4×Q8—216no—
261C2×C4×Q8C2311yescharacteristic
262C2×C4×Q8C2312yes—
263C2×C4×Q8C2314yes—
264C2×C4×Q8C2312yes—
265C2×C4×Q8C2312yes—
266C2×C4×Q8C2314yes—
267C2×C4×Q8C2311yescharacteristic
268C2×C4×Q8C2312yes—
269C2×C4×Q8C2312yes—
270C2×C4×Q8C2311yescharacteristic
271C2×C4×Q8C2311yescharacteristic
272C2×C4×D4C2311yescharacteristic
273C2×C4×D4C2312yes—
274C2×C4×D4C2311yescharacteristic
275C2×C4×D4C2314yes—
276C2×C4×D4C2314yes—
277C2×C4×D4C2312yes—
278C2×C4×D4C2314yes—
279C2×C4×D4C2312yes—
280C2×C4×D4C2312yes—
281C2×C4×D4C2314yes—
282C2×C4×D4C2314yes—
283C2×C4×D4C2312yes—
284C2×C4×D4C2318yes—
285C2×C4×D4C2311yescharacteristic
286C2×C4×D4C2312yes—
287C2×C4×D4C2311yescharacteristic
288C2×C4×D4C2312yes—
289C2×#117C2312yes—
290C2×#117C2312yes—
291C2×#117C2311yescharacteristic
292C2×#117C2314yes—
293C2×#117C2312yes—
294C2×#117C2314yes—
295C2×#117C2312yes—
296C2×#117C2312yes—
297C2×#117C2312yes—
298C2×#117C2311yescharacteristic
299C22×C4⋊C4C2312yes—
300C22×C4⋊C4C2312yes—
301C22×C4⋊C4C2314yes—
302C22×C4⋊C4C2314yes—
303C22×C4⋊C4C2312yes—
304C22×C4⋊C4C2314yes—
305C22×C4⋊C4C2314yes—
306C22×C4⋊C4C23116yes—
307C22×C42C2314yes—
308C22×C42C2312yes—
309C22×C42C2314yes—
310C22×C42C2312yes—
311C22×C42C2311yescharacteristic
312#400C23116yes—
313#400C2318yes—
314#399C2318yes—
315#399C23116yes—
316#399C23116yes—
317#399C2318yes—
318#398C23116yes—
319#398C23116yes—
320#397C2318yes—
321#397C23116yes—
322#396C23116yes—
323#396C23116yes—
324#395C2318yes—
325#395C2318yes—
326#395C2314yes—
327#395C2318yes—
328#395C2318yes—
329#395C23116yes—
330#395C23116yes—
331#395C23116yes—
332#394C2318yes—
333#394C2314yes—
334#394C23116yes—
335#394C2318yes—
336#394C23116yes—
337#393C2314yes—
338#393C2318yes—
339#393C23116yes—
340#393C23116yes—
341#392C2314yes—
342#392C2318yes—
343#391C2314yes—
344#391C2312yes—
345#391C2314yes—
346#391C2314yes—
347#391C23116yes—
348#391C2314yes—
349#391C2318yes—
350#391C2318yes—
351#391C2314yes—
352#390C2312yes—
353#390C2312yes—
354#390C2318yes—
355#390C2314yes—
356#390C2312yes—
357#390C2314yes—
358#390C2318yes—
359#390C23116yes—
360#390C2314yes—
361#389C2314yes—
362#389C2318yes—
363#389C2318yes—
364#389C2318yes—
365#389C23116yes—
366#389C23116yes—
367#389C2318yes—
368#389C2318yes—
369#389C2314yes—
370#388C23116yes—
371#388C23116yes—
372#388C23116yes—
373#388C2318yes—
374#388C2318yes—
375#388C2318yes—
376#387C2318yes—
377#387C2318yes—
378#386C2318yes—
379#386C23116yes—
380#386C23116yes—
381#386C23116yes—
382#386C2318yes—
383#386C2318yes—
384#385C23116yes—
385#385C2318yes—
386#385C23116yes—
387#385C23116yes—
388#385C23116yes—
389#385C2318yes—
390#384C2312yes—
391#384C2314yes—
392#384C2314yes—
393#384C2314yes—
394#384C23116yes—
395#384C2314yes—
396#384C2318yes—
397#384C2312yes—
398#383C2314yes—
399#382C2314yes—
400#382C2312yes—
401#382C2312yes—
402#382C2318yes—
403#382C2314yes—
404#381C2314yes—
405#381C23116yes—
406#380C2318yes—
407#380C2314yes—
408#380C2318yes—
409#380C2312yes—
410#380C2318yes—
411#380C2314yes—
412#380C2312yes—
413C4×C4⋊C4C2312yes—
414C4×C4⋊C4C2311yescharacteristic
415C4×C4⋊C4C2314yes—
416C4×C4⋊C4C2311yescharacteristic
417C4×C4⋊C4C2314yes—
418C4×C4⋊C4C2314yes—
419C4×C4⋊C4C2312yes—
420C4×C4⋊C4C2314yes—
421C4×C4⋊C4C2312yes—
422C4×C22⋊C4C2312yes—
423C4×C22⋊C4C2318yes—
424C4×C22⋊C4C2318yes—
425C4×C22⋊C4C2312yes—
426C4×C22⋊C4C2314yes—
427#376C2314yes—
428#376C2312yes—
429C2×#95C2314yes—
430C2×#95C23116yes—
431C43C2312yes—
4322−1+4—4128no—
433C2×#41—24no—
434C2×#41—28no—
435C2×#41—232no—
436C2×#41—216no—
437C2×#41—28no—
438C2×#41—216no—
439C2×#41—232no—
440C2×#41—24no—
441C2×#41—216no—
442C2×#41—28no—
443C2×#41—48no—
444C2×#41—416no—
445C2×#41—432no—
446C2×#41—42no—
447C2×#41C2×D418yes—
448C22×Q8—216no—
449C22×Q8—28no—
450C22×Q8—28no—
451C22×Q8—216no—
452C22×Q8—28no—
453C22×Q8—416no—
454C22×Q8—44no—
455C22×Q8—48no—
456C22×Q8—416no—
457C22×Q8C2412yes—
458C22×Q8C2412yes—
459C22×Q8C2414yes—
460C22×Q8C2414yes—
461C22×Q8C2411yescharacteristic
462C22×Q8C2411yescharacteristic
463C22×Q8C2418yes—
464C22×Q8C2412yes—
465C22×Q8C2414yes—
466C22×D4C2412yes—
467C22×D4C2412yes—
468C22×D4C2414yes—
469C22×D4C2411yescharacteristic
470C22×D4C2418yes—
471C22×D4C2412yes—
472C22×D4C2412yes—
473C22×D4C2418yes—
474C22×D4C2414yes—
475C22×D4C2412yes—
476C22×D4C2411yescharacteristic
477C23×C4C2414yes—
478C23×C4C2418yes—
479C23×C4C2412yes—
480C23×C4C2412yes—
481C23×C4C2414yes—
482C23×C4C2418yes—
483C23×C4C2414yes—
484C23×C4C2412yes—
485C23×C4C2412yes—
486C23×C4C2412yes—
487C23×C4C2411yescharacteristic
488C23×C4C2411yescharacteristic
489C23×C4C2412yes—
490C23×C4C2411yescharacteristic
491C23×C4C2414yes—
492C23×C4C2418yes—
493C4⋊Q8—28no—
494C4⋊Q8—28no—
495C4⋊Q8—24no—
496C4⋊Q8—28no—
497C4⋊Q8—28no—
498C4⋊Q8—216no—
499C4⋊Q8—28no—
500C4⋊Q8—216no—
501C4⋊Q8—28no—
502C4⋊Q8—216no—
503C4⋊Q8—24no—
504C4⋊Q8—24no—
505C4⋊Q8—416no—
506#127—24no—
507#127—44no—
508#126—216no—
509#126—216no—
510#126—216no—
511#125—216no—
512#125—216no—
513#125—28no—
514#125—28no—
515#124—28no—
516#124—216no—
517#124—28no—
518#124—28no—
519#124—216no—
520#124—48no—
521#123—216no—
522#123—216no—
523#123—216no—
524#123—232no—
525#123—232no—
526#123—232no—
527#123—432no—
528#123—432no—
529C22⋊Q8—28no—
530C22⋊Q8—28no—
531C22⋊Q8—28no—
532C22⋊Q8—28no—
533C22⋊Q8—28no—
534C22⋊Q8—216no—
535C22⋊Q8—216no—
536C22⋊Q8—232no—
537C22⋊Q8—216no—
538C22⋊Q8—232no—
539C22⋊Q8—216no—
540C22⋊Q8—416no—
541C22⋊Q8—416no—
542#121—216no—
543#121—28no—
544#121—216no—
545#121—216no—
546#121—28no—
547#121—28no—
548#121—216no—
549#121—432no—
550C4×Q8—28no—
551C4×Q8—24no—
552C4×Q8—216no—
553C4×Q8—28no—
554C4×Q8—28no—
555C4×Q8—28no—
556C4×Q8—216no—
557C4×Q8—28no—
558C4×Q8—24no—
559C4×Q8C2×D418yes—
560C4×Q8C2×D418yes—
561C4×D4—28no—
562C4×D4—216no—
563C4×D4—28no—
564C4×D4—216no—
565C4×D4—28no—
566C4×D4—216no—
567C4×D4—24no—
568C4×D4—24no—
569C4×D4—28no—
570C4×D4—216no—
571C4×D4—28no—
572C4×D4—216no—
573C4×D4—416no—
574C4×D4C2×D418yes—
575C4×D4C2×D4116yes—
576C4×D4C2×D418yes—
577C4×D4C2×D4116yes—
578#117—24no—
579#117—28no—
580#117—28no—
581#117—28no—
582#117—216no—
583#117—28no—
584#117—216no—
585#117—44no—
586#117C2×D4116yes—
587#117C2×D418yes—
588C2×C4⋊C4—28no—
589C2×C4⋊C4—216no—
590C2×C4⋊C4—216no—
591C2×C4⋊C4—216no—
592C2×C4⋊C4—28no—
593C2×C4⋊C4—28no—
594C2×C4⋊C4—216no—
595C2×C4⋊C4—432no—
596C2×C4⋊C4C2411yescharacteristic
597C2×C4⋊C4C2412yes—
598C2×C4⋊C4C2414yes—
599C2×C4⋊C4C2412yes—
600C2×C4⋊C4C2414yes—
601C2×C4⋊C4C2412yes—
602C2×C4⋊C4C2412yes—
603C2×C4⋊C4C2414yes—
604C2×C4⋊C4C2414yes—
605C2×C4⋊C4C2414yes—
606C2×C4⋊C4C2414yes—
607C2×C4⋊C4C2414yes—
608C2×C4⋊C4C2414yes—
609C2×C4⋊C4C2418yes—
610C2×C4⋊C4C2418yes—
611C2×C4⋊C4C2414yes—
612C2×C4⋊C4C2418yes—
613C2×C4⋊C4C2411yescharacteristic
614C2×C4⋊C4C2412yes—
615C2×C4⋊C4C2414yes—
616C2×C4⋊C4C2412yes—
617C2×C4⋊C4C2414yes—
618C2×C4⋊C4C2412yes—
619C2×C4⋊C4C2414yes—
620C2×C4⋊C4C2412yes—
621C2×C4⋊C4C2414yes—
622C2×C4⋊C4C2412yes—
623C2×C4⋊C4C2414yes—
624C2×C4⋊C4C2418yes—
625C2×C4⋊C4C24116yes—
626C2×C4⋊C4C24116yes—
627C2×C4⋊C4C24116yes—
628C2×C4⋊C4C2414yes—
629C2×C4⋊C4C24116yes—
630C2×C4⋊C4C2411yescharacteristic
631C2×C4⋊C4C2412yes—
632C2×C4⋊C4C2411yescharacteristic
633C2×C4⋊C4C2412yes—
634C2×C4⋊C4C2412yes—
635C2×C22⋊C4C2414yes—
636C2×C22⋊C4C2412yes—
637C2×C22⋊C4C2412yes—
638C2×C22⋊C4C2412yes—
639C2×C22⋊C4C2414yes—
640C2×C22⋊C4C2414yes—
641C2×C22⋊C4C2414yes—
642C2×C22⋊C4C2414yes—
643C2×C22⋊C4C2414yes—
644C2×C22⋊C4C2414yes—
645C2×C22⋊C4C2418yes—
646C2×C22⋊C4C2418yes—
647C2×C22⋊C4C2414yes—
648C2×C22⋊C4C2418yes—
649C2×C22⋊C4C2418yes—
650C2×C22⋊C4C2418yes—
651C2×C22⋊C4C2414yes—
652C2×C22⋊C4C2418yes—
653C2×C22⋊C4C2418yes—
654C2×C22⋊C4C24116yes—
655C2×C22⋊C4C24116yes—
656C2×C22⋊C4C24116yes—
657C2×C22⋊C4C2412yes—
658C2×C22⋊C4C2412yes—
659C2×C22⋊C4C2412yes—
660C2×C42—216no—
661C2×C42—28no—
662C2×C42—48no—
663C2×C42C2×D4116yes—
664C2×C42C2×D418yes—
665C2×C42C2412yes—
666C2×C42C2414yes—
667C2×C42C2414yes—
668C2×C42C2414yes—
669C2×C42C2414yes—
670C2×C42C2414yes—
671C2×C42C2412yes—
672C2×C42C2414yes—
673C2×C42C2412yes—
674C2×C42C2412yes—
675C2×C42C2412yes—
676C2×C42C2418yes—
677C2×C42C2411yescharacteristic
678C2×C42C2412yes—
679C2×C42C2412yes—
680C2×C42C2411yescharacteristic
681C2×C42C2412yes—
682C2×C42C2411yescharacteristic
683C2×C42C2411yescharacteristic
684#95C2412yes—
685#95C2418yes—
686#95C2414yes—
687#95C2418yes—
688#95C24116yes—
689#95C24116yes—
690#95C24116yes—
691#95C2412yes—
692#95C2414yes—
693#95C2418yes—
694#95C2418yes—
695#95C2414yes—
696#95C2418yes—
697#95C2418yes—
698#95C24116yes—
699#95C24116yes—
700C24C2512yes—
701C24C2514yes—
702C24C2511yescharacteristic
703C24C2512yes—
704#41—232no—
705#41—416no—
706#41—464no—
707#41—432no—
708#41—4128no—
709#41—432no—
710#41—464no—
711C2×Q8—22no—
712C2×Q8—28no—
713C2×Q8—24no—
714C2×Q8—24no—
715C2×Q8—216no—
716C2×Q8—28no—
717C2×Q8—24no—
718C2×Q8—28no—
719C2×Q8—24no—
720C2×Q8—28no—
721C2×Q8—216no—
722C2×Q8—28no—
723C2×Q8—24no—
724C2×Q8—22no—
725C2×Q8—24no—
726C2×Q8—44no—
727C2×Q8—48no—
728C2×Q8—416no—
729C2×Q8—44no—
730C2×Q8—432no—
731C2×Q8—464no—
732C2×Q8—432no—
733C2×Q8—464no—
734C2×Q8C22×D414yes—
735C2×Q82−1+414yescomplemented
736C2×D4—28no—
737C2×D4—28no—
738C2×D4—24no—
739C2×D4—28no—
740C2×D4—216no—
741C2×D4—216no—
742C2×D4—232no—
743C2×D4—24no—
744C2×D4—24no—
745C2×D4—22no—
746C2×D4—24no—
747C2×D4—28no—
748C2×D4—24no—
749C2×D4—24no—
750C2×D4—22no—
751C2×D4—216no—
752C2×D4—24no—
753C2×D4—22no—
754C2×D4—42no—
755C2×D4—44no—
756C2×D4—48no—
757C2×D4—48no—
758C2×D4—48no—
759C2×D4C22×D418yes—
760C2×D4C22×D414yes—
761C2×D4H(5,𝔽2)18yes—
762C22×C4—28no—
763C22×C4—24no—
764C22×C4—28no—
765C22×C4—24no—
766C22×C4—24no—
767C22×C4—22no—
768C22×C4—24no—
769C22×C4—22no—
770C22×C4—28no—
771C22×C4—28no—
772C22×C4—28no—
773C22×C4—216no—
774C22×C4—216no—
775C22×C4—216no—
776C22×C4—232no—
777C22×C4—24no—
778C22×C4—24no—
779C22×C4—24no—
780C22×C4—216no—
781C22×C4—28no—
782C22×C4—28no—
783C22×C4—216no—
784C22×C4—216no—
785C22×C4—28no—
786C22×C4—28no—
787C22×C4—24no—
788C22×C4—48no—
789C22×C4—44no—
790C22×C4—416no—
791C22×C4—48no—
792C22×C4—42no—
793C22×C4C22×D418yes—
794C22×C4C22×D418yes—
795C22×C4C22×D414yes—
796C22×C4C22×D414yes—
797C22×C4C22×D418yes—
798C22×C4C22×D414yes—
799C22×C4C2514yes—
800C22×C4C2512yes—
801C22×C4C2518yes—
802C22×C4C2514yes—
803C22×C4C2514yes—
804C22×C4C2518yes—
805C22×C4C2512yes—
806C22×C4C2514yes—
807C22×C4C2511yescharacteristic
808C22×C4C2512yes—
809C22×C4C2511yescharacteristic
810C22×C4C2512yes—
811C22×C4C2512yes—
812C22×C4C2511yescharacteristic
813C22×C4C2512yes—
814C22×C4C2514yes—
815C22×C4C2511yescharacteristic
816C22×C4C2511yescharacteristic
817C22×C4C2511yescharacteristic
818C4⋊C4—24no—
819C4⋊C4—22no—
820C4⋊C4—24no—
821C4⋊C4—28no—
822C4⋊C4—24no—
823C4⋊C4—28no—
824C4⋊C4—28no—
825C4⋊C4—24no—
826C4⋊C4—28no—
827C4⋊C4—28no—
828C4⋊C4—28no—
829C4⋊C4—216no—
830C4⋊C4—28no—
831C4⋊C4—28no—
832C4⋊C4—216no—
833C4⋊C4—24no—
834C4⋊C4—22no—
835C4⋊C4—28no—
836C4⋊C4—24no—
837C4⋊C4—28no—
838C4⋊C4—28no—
839C4⋊C4—24no—
840C4⋊C4—28no—
841C4⋊C4—24no—
842C4⋊C4—28no—
843C4⋊C4—216no—
844C4⋊C4—28no—
845C4⋊C4—24no—
846C4⋊C4—48no—
847C4⋊C4—416no—
848C4⋊C4—416no—
849C4⋊C4—416no—
850C4⋊C4—44no—
851C4⋊C4—416no—
852C4⋊C4C22×D414yes—
853C4⋊C4C22×D418yes—
854C4⋊C4C22×D414yes—
855C4⋊C4C22×D418yes—
856C4⋊C42−1+418yescomplemented
857C22⋊C4—28no—
858C22⋊C4—24no—
859C22⋊C4—28no—
860C22⋊C4—216no—
861C22⋊C4—24no—
862C22⋊C4—24no—
863C22⋊C4—28no—
864C22⋊C4—28no—
865C22⋊C4—28no—
866C22⋊C4—216no—
867C22⋊C4—28no—
868C22⋊C4—28no—
869C22⋊C4—216no—
870C22⋊C4—28no—
871C22⋊C4—216no—
872C22⋊C4—216no—
873C22⋊C4—44no—
874C22⋊C4—48no—
875C22⋊C4—48no—
876C22⋊C4—416no—
877C22⋊C4—416no—
878C22⋊C4—416no—
879C22⋊C4C22×D418yes—
880C22⋊C4C22×D418yes—
881C22⋊C4C22×D418yes—
882C42—24no—
883C42—24no—
884C42—28no—
885C42—28no—
886C42—24no—
887C42—28no—
888C42—28no—
889C42—28no—
890C42—24no—
891C42—24no—
892C42—28no—
893C42—48no—
894C42C22×D414yes—
895C42C22×D414yes—
896C42C22×D414yes—
897C42C22×D418yes—
898C42C22×D418yes—
899C42C22×D414yes—
900C42C22×D418yes—
901C23—24no—
902C23—22no—
903C23—22no—
904C23—22no—
905C23—22no—
906C23—21no—
907C23—21no—
908C23—22no—
909C23—24no—
910C23—24no—
911C23—28no—
912C23—24no—
913C23—28no—
914C23—24no—
915C23—22no—
916C23—24no—
917C23—22no—
918C23C23×D412yes—
919C23C23×D414yes—
920C23C2×H(5,𝔽2)18yes—
921C23C2611yescharacteristic
922Q8—28no—
923Q8—28no—
924Q8—416no—
925Q8—48no—
926Q8—416no—
927Q8—432no—
928Q8—416no—
929Q8—48no—
930Q8—48no—
931D4—216no—
932D4—48no—
933D4—48no—
934D4—416no—
935D4—416no—
936D4—432no—
937D4—48no—
938D4—44no—
939D4—48no—
940D4—816no—
941D4#535116yes—
942C2×C4—22no—
943C2×C4—24no—
944C2×C4—22no—
945C2×C4—24no—
946C2×C4—22no—
947C2×C4—24no—
948C2×C4—21no—
949C2×C4—22no—
950C2×C4—24no—
951C2×C4—22no—
952C2×C4—21no—
953C2×C4—22no—
954C2×C4—216no—
955C2×C4—28no—
956C2×C4—216no—
957C2×C4—28no—
958C2×C4—216no—
959C2×C4—28no—
960C2×C4—22no—
961C2×C4—22no—
962C2×C4—24no—
963C2×C4—24no—
964C2×C4—24no—
965C2×C4—28no—
966C2×C4—24no—
967C2×C4—28no—
968C2×C4—24no—
969C2×C4—28no—
970C2×C4—28no—
971C2×C4—216no—
972C2×C4—24no—
973C2×C4—24no—
974C2×C4—24no—
975C2×C4—28no—
976C2×C4—24no—
977C2×C4—28no—
978C2×C4—24no—
979C2×C4—48no—
980C2×C4—432no—
981C2×C4—416no—
982C2×C4—432no—
983C2×C4—416no—
984C2×C4—432no—
985C2×C4—416no—
986C2×C4—416no—
987C2×C4—48no—
988C2×C4—48no—
989C2×C4C23×D414yes—
990C2×C4C23×D412yes—
991C2×C4C23×D412yes—
992C2×C4C23×D412yes—
993C2×C4C23×D414yes—
994C2×C4C23×D414yes—
995C2×C4C23×D412yes—
996C2×C4C23×D412yes—
997C2×C4C23×D412yes—
998C2×C4C2×H(5,𝔽2)14yes—
999C2×C4C2×2−1+418yes—
1000C2×C4C2×2−1+414yes—
1001C2×C4C2×2−1+412yes—
1002C2×C4C2×2−1+414yes—
1003C2×C4#58512yes—
1004C22—28no—
1005C22—28no—
1006C22—24no—
1007C22—24no—
1008C22—22no—
1009C22—22no—
1010C22—22no—
1011C22—42no—
1012C22—42no—
1013C22—44no—
1014C22—48no—
1015C22—44no—
1016C22—48no—
1017C22—42no—
1018C22—44no—
1019C22—42no—
1020C22—44no—
1021C22—44no—
1022C22—42no—
1023C22C2×#53518yes—
1024C22C24×D411yescharacteristic
1025C22C22×H(5,𝔽2)12yes—
1026C22C22×2−1+412yes—
1027C22C22×2−1+411yescharacteristic
1028C22C2×#58511yescharacteristic
1029C4—28no—
1030C4—22no—
1031C4—24no—
1032C4—24no—
1033C4—22no—
1034C4—24no—
1035C4—22no—
1036C4—24no—
1037C4—48no—
1038C4—44no—
1039C4—44no—
1040C4—42no—
1041C4—42no—
1042C4—44no—
1043C4—48no—
1044C4—44no—
1045C4C2×#53514yes—
1046C4#348914yes—
1047C4#349914yes—
1048C2—28no—
1049C2—42no—
1050C2—82no—
1051C2—84no—
1052C2C22×#53511yescharacteristic
1053C2C2×#348911yescharacteristic
1054C2C2×#349911yescharacteristic
1055C2#6301312yes—
1056C2#6303712yes—
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×#3482C2semidirect
3. #42911C2semidirect
4. #42297C2semidirect
5. #39616C2semidirect
6. #39596C2semidirect
7. #39167C2semidirect
8. #38079C2semidirect
9. #38041C2semidirect
10. #37863C2semidirect
11. #37640C2semidirect
12. #37632C2semidirect
13. #36303C2semidirect
14. #36259C2semidirect
15. #36179C2semidirect
16. #36085C2semidirect
17. #35281C2semidirect
18. #35279C2semidirect
19. #35249C2semidirect
20. #35238C2semidirect
21. #34977C2semidirect
22. C2×#2567C2semidirect
23. #34127C2semidirect
259. C4×#41D4semidirect
735. C2×Q82−1+4semidirect
856. C4⋊C42−1+4semidirect

Maximal subgroups

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

subgroupindex
C2×#34992
C2×#34822
#429112
#422972
#396162
#395962
#391672
#380792
#380412
#378632
#376402
#376322
#363032
#362592
#361792
#360852
#352812
#352792
#352492
#352382
#349772
C2×#25672
#341272