Subgroups — #41×D₆₆₁ #35232574

Order 21152.

164 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#24902373	C₂	1	1	yes	maximal, characteristic, complemented
2	#24902372	C₂	1	3	yes	maximal, complemented
3	#24902371	C₂	1	3	yes	maximal, complemented
4	Q₈×D₆₆₁	C₂	1	1	yes	maximal, characteristic, complemented
5	D₄×D₆₆₁	C₂	1	3	yes	maximal, complemented
6	C₂×C₄×D₆₆₁	C₂	1	3	yes	maximal, complemented
7	#41×C₆₆₁	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×D₆₆₁	C₂²	1	3	yes	—
9	Dic₁₃₂₂	C₂²	1	3	yes	complemented
10	D₂₆₄₄	C₂²	1	3	yes	complemented
11	C₂²⋊D₆₆₁	C₂²	1	6	yes	complemented
12	C₂×Dic₆₆₁	C₂²	1	3	yes	complemented
13	C₄×D₆₆₁	C₂²	1	1	yes	characteristic
14	C₄×D₆₆₁	C₂²	1	3	yes	—
15	C₄×D₆₆₁	C₂²	1	3	yes	complemented
16	C₄×D₆₆₁	C₂²	1	3	yes	complemented
17	Q₈×C₆₆₁	C₂²	1	1	yes	characteristic, complemented
18	D₄×C₆₆₁	C₂²	1	3	yes	complemented
19	C₂×C₄×C₆₆₁	C₂²	1	3	yes	complemented
20	C₂²×C₆₆₁	C₂³	1	3	yes	—
21	C₂×D₆₆₁	—	2	6	no	—
22	C₂×D₆₆₁	C₂³	1	3	yes	—
23	C₂×D₆₆₁	C₂³	1	1	yes	characteristic
24	C₄×C₆₆₁	C₂³	1	3	yes	—
25	C₄×C₆₆₁	C₂³	1	1	yes	characteristic
26	Dic₆₆₁	C₂³	1	1	yes	characteristic
27	Dic₆₆₁	C₂³	1	3	yes	—
28	C₂×C₆₆₁	—	2	3	no	—
29	C₂×C₆₆₁	C₂⁴	1	1	yes	characteristic
30	D₆₆₁	—	2	3	no	—
31	D₆₆₁	#41	1	2	yes	direct product factor
32	C₆₆₁	C₂×#41	1	1	yes	characteristic, complemented, Sylow
33	C₂×#41	—	661	1	no	maximal, Sylow
34	#41	—	661	1	no	—
35	#41	—	661	3	no	—
36	#41	—	661	3	no	—
37	#41	D₆₆₁	1	1	yes	characteristic, direct product factor
38	C₂×Q₈	—	661	1	no	—
39	C₂×D₄	—	661	3	no	—
40	C₂²×C₄	—	661	3	no	—
41	C₂³	—	661	3	no	—
42	Q₈	—	661	3	no	—
43	Q₈	C₂×D₆₆₁	1	1	yes	characteristic, complemented
44	D₄	—	661	6	no	—
45	D₄	—	661	3	no	—
46	D₄	C₂×D₆₆₁	1	3	yes	complemented
47	C₂×C₄	—	661	3	no	—
48	C₂×C₄	—	661	3	no	—
49	C₂×C₄	—	661	3	no	—
50	C₂×C₄	—	661	1	no	—
51	C₂×C₄	—	661	3	no	—
52	C₂×C₄	C₂×D₆₆₁	1	3	yes	complemented
53	C₂²	—	1322	6	no	—
54	C₂²	—	661	3	no	—
55	C₂²	—	661	1	no	—
56	C₂²	C₂²×D₆₆₁	1	3	yes	—
57	C₄	—	661	1	no	—
58	C₄	—	661	3	no	—
59	C₄	C₂²×D₆₆₁	1	3	yes	—
60	C₄	C₂²×D₆₆₁	1	1	yes	characteristic
61	C₂	—	2	3	no	—
62	C₂	—	1322	3	no	—
63	C₂	—	661	2	no	—
64	C₂	C₂³×D₆₆₁	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂²×D₆₆₁
commutator, socle, cosocle	C₂×C₆₆₁	C₂⁴
Frattini	C₂	C₂³×D₆₆₁
Fitting	#41×C₆₆₁	C₂
hypercenter	#41	D₆₆₁
hypocenter	C₆₆₁	C₂×#41
LCS	G ▷ C₂×C₆₆₁ ▷ C₆₆₁
UCS	C₁ ◁ C₄ ◁ #41

Complements

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

N	H ≅ G/N	type
1. #24902373	C₂	semidirect
2. #24902372	C₂	semidirect
3. #24902371	C₂	semidirect
4. Q₈×D₆₆₁	C₂	semidirect
5. D₄×D₆₆₁	C₂	semidirect
6. C₂×C₄×D₆₆₁	C₂	semidirect
7. #41×C₆₆₁	C₂	semidirect
9. Dic₁₃₂₂	C₂²	semidirect
10. D₂₆₄₄	C₂²	semidirect
11. C₂²⋊D₆₆₁	C₂²	semidirect
12. C₂×Dic₆₆₁	C₂²	semidirect
15. C₄×D₆₆₁	C₂²	semidirect
16. C₄×D₆₆₁	C₂²	semidirect
17. Q₈×C₆₆₁	C₂²	semidirect
18. D₄×C₆₆₁	C₂²	semidirect
19. C₂×C₄×C₆₆₁	C₂²	semidirect
31. D₆₆₁	#41	direct (N × H)
32. C₆₆₁	C₂×#41	semidirect
37. #41	D₆₆₁	direct (N × H)
43. Q₈	C₂×D₆₆₁	semidirect
46. D₄	C₂×D₆₆₁	semidirect
52. C₂×C₄	C₂×D₆₆₁	semidirect

Maximal subgroups

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

subgroup	index
#24902373	2
#24902372	2
#24902371	2
Q₈×D₆₆₁	2
D₄×D₆₆₁	2
C₂×C₄×D₆₆₁	2
#41×C₆₆₁	2
C₂×#41	661

Subgroups — #41×D661 #35232574

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #41×D₆₆₁ #35232574