Subgroups — #121×C₇₆₉ #37589781

Order 24608.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄×C₇₆₉	C₂	1	2	yes	maximal, complemented
2	C₂×D₄×C₇₆₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₄×C₇₆₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄⋊C₄×C₇₆₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²⋊C₄×C₇₆₉	C₂	1	2	yes	maximal, complemented
6	C₂³×C₇₆₉	C₂²	1	2	yes	—
7	C₂³×C₇₆₉	C₂²	1	1	yes	characteristic
8	D₄×C₇₆₉	—	2	4	no	—
9	D₄×C₇₆₉	—	2	2	no	—
10	C₂×C₄×C₇₆₉	—	2	2	no	—
11	C₂×C₄×C₇₆₉	C₂²	1	1	yes	characteristic
12	C₂×C₄×C₇₆₉	C₂²	1	2	yes	—
13	C₂×C₄×C₇₆₉	C₂²	1	1	yes	characteristic
14	C₂²×C₇₆₉	—	2	1	no	—
15	C₂²×C₇₆₉	—	2	1	no	—
16	C₂²×C₇₆₉	—	2	2	no	—
17	C₂²×C₇₆₉	—	2	2	no	—
18	C₂²×C₇₆₉	—	2	2	no	—
19	C₂²×C₇₆₉	D₄	1	2	yes	complemented
20	C₂²×C₇₆₉	C₂³	1	1	yes	characteristic
21	C₄×C₇₆₉	—	2	1	no	—
22	C₄×C₇₆₉	—	2	2	no	—
23	C₄×C₇₆₉	D₄	1	2	yes	complemented
24	C₂×C₇₆₉	—	2	2	no	—
25	C₂×C₇₆₉	—	4	2	no	—
26	C₂×C₇₆₉	C₂×D₄	1	1	yes	characteristic
27	C₂×C₇₆₉	C₂×D₄	1	1	yes	characteristic
28	C₂×C₇₆₉	#41	1	1	yes	characteristic
29	C₇₆₉	#121	1	1	yes	characteristic, direct product factor, Sylow
30	#121	C₇₆₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
31	C₂×D₄	C₂×C₇₆₉	1	2	yes	complemented
32	C₂×D₄	C₂×C₇₆₉	1	1	yes	characteristic, complemented
33	C₂²×C₄	C₂×C₇₆₉	1	1	yes	characteristic, complemented
34	C₄⋊C₄	C₂×C₇₆₉	1	1	yes	characteristic, complemented
35	C₂²⋊C₄	C₂×C₇₆₉	1	2	yes	complemented
36	C₂³	C₂²×C₇₆₉	1	2	yes	—
37	C₂³	C₂²×C₇₆₉	1	1	yes	characteristic
38	D₄	—	2	4	no	—
39	D₄	—	2	2	no	—
40	C₂×C₄	—	2	2	no	—
41	C₂×C₄	C₂²×C₇₆₉	1	1	yes	characteristic
42	C₂×C₄	C₂²×C₇₆₉	1	2	yes	—
43	C₂×C₄	C₂²×C₇₆₉	1	1	yes	characteristic
44	C₂²	—	2	1	no	—
45	C₂²	—	2	1	no	—
46	C₂²	—	2	2	no	—
47	C₂²	—	2	2	no	—
48	C₂²	—	2	2	no	—
49	C₂²	D₄×C₇₆₉	1	2	yes	complemented
50	C₂²	C₂³×C₇₆₉	1	1	yes	characteristic
51	C₄	—	2	1	no	—
52	C₄	—	2	2	no	—
53	C₄	D₄×C₇₆₉	1	2	yes	complemented
54	C₂	—	2	2	no	—
55	C₂	—	4	2	no	—
56	C₂	C₂×D₄×C₇₆₉	1	1	yes	characteristic
57	C₂	C₂×D₄×C₇₆₉	1	1	yes	characteristic
58	C₂	#41×C₇₆₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇₆₉	C₂³
commutator, Frattini, cosocle	C₂²	C₂³×C₇₆₉
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₇₆₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×D₄×C₇₆₉	C₂	semidirect
2. C₂×D₄×C₇₆₉	C₂	semidirect
3. C₂²×C₄×C₇₆₉	C₂	semidirect
4. C₄⋊C₄×C₇₆₉	C₂	semidirect
5. C₂²⋊C₄×C₇₆₉	C₂	semidirect
19. C₂²×C₇₆₉	D₄	semidirect
23. C₄×C₇₆₉	D₄	semidirect
29. C₇₆₉	#121	direct (N × H)
30. #121	C₇₆₉	direct (N × H)
31. C₂×D₄	C₂×C₇₆₉	semidirect
32. C₂×D₄	C₂×C₇₆₉	semidirect
33. C₂²×C₄	C₂×C₇₆₉	semidirect
34. C₄⋊C₄	C₂×C₇₆₉	semidirect
35. C₂²⋊C₄	C₂×C₇₆₉	semidirect
49. C₂²	D₄×C₇₆₉	semidirect
53. C₄	D₄×C₇₆₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₄×C₇₆₉	2
C₂²×C₄×C₇₆₉	2
C₄⋊C₄×C₇₆₉	2
C₂²⋊C₄×C₇₆₉	2
#121	769

Subgroups — #121×C769 #37589781

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #121×C₇₆₉ #37589781