Subgroups — #41×D₇₆₉ #37589940

Order 24608.

164 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#27134382	C₂	1	1	yes	maximal, characteristic, complemented
2	#27134381	C₂	1	3	yes	maximal, complemented
3	#27134380	C₂	1	3	yes	maximal, complemented
4	Q₈×D₇₆₉	C₂	1	1	yes	maximal, characteristic, complemented
5	D₄×D₇₆₉	C₂	1	3	yes	maximal, complemented
6	C₂×C₄×D₇₆₉	C₂	1	3	yes	maximal, complemented
7	#41×C₇₆₉	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×D₇₆₉	C₂²	1	3	yes	—
9	Dic₁₅₃₈	C₂²	1	3	yes	complemented
10	D₃₀₇₆	C₂²	1	3	yes	complemented
11	C₂²⋊D₇₆₉	C₂²	1	6	yes	complemented
12	C₂×Dic₇₆₉	C₂²	1	3	yes	complemented
13	C₄×D₇₆₉	C₂²	1	1	yes	characteristic
14	C₄×D₇₆₉	C₂²	1	3	yes	—
15	C₄×D₇₆₉	C₂²	1	3	yes	complemented
16	C₄×D₇₆₉	C₂²	1	3	yes	complemented
17	Q₈×C₇₆₉	C₂²	1	1	yes	characteristic, complemented
18	D₄×C₇₆₉	C₂²	1	3	yes	complemented
19	C₂×C₄×C₇₆₉	C₂²	1	3	yes	complemented
20	C₂²×C₇₆₉	C₂³	1	3	yes	—
21	C₂×D₇₆₉	—	2	6	no	—
22	C₂×D₇₆₉	C₂³	1	3	yes	—
23	C₂×D₇₆₉	C₂³	1	1	yes	characteristic
24	C₄×C₇₆₉	C₂³	1	3	yes	—
25	C₄×C₇₆₉	C₂³	1	1	yes	characteristic
26	Dic₇₆₉	C₂³	1	1	yes	characteristic
27	Dic₇₆₉	C₂³	1	3	yes	—
28	C₂×C₇₆₉	—	2	3	no	—
29	C₂×C₇₆₉	C₂⁴	1	1	yes	characteristic
30	D₇₆₉	—	2	3	no	—
31	D₇₆₉	#41	1	2	yes	direct product factor
32	C₇₆₉	C₂×#41	1	1	yes	characteristic, complemented, Sylow
33	C₂×#41	—	769	1	no	maximal, Sylow
34	#41	—	769	1	no	—
35	#41	—	769	3	no	—
36	#41	—	769	3	no	—
37	#41	D₇₆₉	1	1	yes	characteristic, direct product factor
38	C₂×Q₈	—	769	1	no	—
39	C₂×D₄	—	769	3	no	—
40	C₂²×C₄	—	769	3	no	—
41	C₂³	—	769	3	no	—
42	Q₈	—	769	3	no	—
43	Q₈	C₂×D₇₆₉	1	1	yes	characteristic, complemented
44	D₄	—	769	6	no	—
45	D₄	—	769	3	no	—
46	D₄	C₂×D₇₆₉	1	3	yes	complemented
47	C₂×C₄	—	769	3	no	—
48	C₂×C₄	—	769	3	no	—
49	C₂×C₄	—	769	3	no	—
50	C₂×C₄	—	769	1	no	—
51	C₂×C₄	—	769	3	no	—
52	C₂×C₄	C₂×D₇₆₉	1	3	yes	complemented
53	C₂²	—	769	1	no	—
54	C₂²	—	769	3	no	—
55	C₂²	—	1538	6	no	—
56	C₂²	C₂²×D₇₆₉	1	3	yes	—
57	C₄	—	769	1	no	—
58	C₄	—	769	3	no	—
59	C₄	C₂²×D₇₆₉	1	3	yes	—
60	C₄	C₂²×D₇₆₉	1	1	yes	characteristic
61	C₂	—	769	2	no	—
62	C₂	—	2	3	no	—
63	C₂	—	1538	3	no	—
64	C₂	C₂³×D₇₆₉	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂²×D₇₆₉
commutator, socle, cosocle	C₂×C₇₆₉	C₂⁴
Frattini	C₂	C₂³×D₇₆₉
Fitting	#41×C₇₆₉	C₂
hypercenter	#41	D₇₆₉
hypocenter	C₇₆₉	C₂×#41
LCS	G ▷ C₂×C₇₆₉ ▷ C₇₆₉
UCS	C₁ ◁ C₄ ◁ #41

Complements

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

N	H ≅ G/N	type
1. #27134382	C₂	semidirect
2. #27134381	C₂	semidirect
3. #27134380	C₂	semidirect
4. Q₈×D₇₆₉	C₂	semidirect
5. D₄×D₇₆₉	C₂	semidirect
6. C₂×C₄×D₇₆₉	C₂	semidirect
7. #41×C₇₆₉	C₂	semidirect
9. Dic₁₅₃₈	C₂²	semidirect
10. D₃₀₇₆	C₂²	semidirect
11. C₂²⋊D₇₆₉	C₂²	semidirect
12. C₂×Dic₇₆₉	C₂²	semidirect
15. C₄×D₇₆₉	C₂²	semidirect
16. C₄×D₇₆₉	C₂²	semidirect
17. Q₈×C₇₆₉	C₂²	semidirect
18. D₄×C₇₆₉	C₂²	semidirect
19. C₂×C₄×C₇₆₉	C₂²	semidirect
31. D₇₆₉	#41	direct (N × H)
32. C₇₆₉	C₂×#41	semidirect
37. #41	D₇₆₉	direct (N × H)
43. Q₈	C₂×D₇₆₉	semidirect
46. D₄	C₂×D₇₆₉	semidirect
52. C₂×C₄	C₂×D₇₆₉	semidirect

Maximal subgroups

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

subgroup	index
#27134382	2
#27134381	2
#27134380	2
Q₈×D₇₆₉	2
D₄×D₇₆₉	2
C₂×C₄×D₇₆₉	2
#41×C₇₆₉	2
C₂×#41	769

Subgroups — #41×D769 #37589940

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #41×D₇₆₉ #37589940