Subgroups — #45657028

Order 32608.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#30654504	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₄₀₇₆	C₂	1	1	yes	maximal, characteristic, complemented
3	#30654493	C₂	1	2	yes	maximal, complemented
4	D₈₁₅₂	C₂	1	2	yes	maximal, complemented
5	M₁₆×C₁₀₁₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×D₁₀₁₉	—	2	1	no	—
7	Dic₂₀₃₈	C₂²	1	1	yes	characteristic, complemented
8	D₄₀₇₆	—	2	1	no	—
9	D₄₀₇₆	C₂²	1	2	yes	—
10	D₄₀₇₆	C₂²	1	1	yes	characteristic, complemented
11	C₂²⋊D₁₀₁₉	—	2	1	no	—
12	C₄×D₁₀₁₉	—	2	1	no	—
13	C₂×C₄×C₁₀₁₉	C₂²	1	1	yes	characteristic
14	C₈×C₁₀₁₉	C₂²	1	2	yes	complemented
15	C₂²×C₁₀₁₉	D₄	1	1	yes	characteristic
16	C₂×D₁₀₁₉	—	2	1	no	—
17	C₂×D₁₀₁₉	—	2	2	no	—
18	C₂×D₁₀₁₉	—	4	2	no	—
19	C₄×C₁₀₁₉	D₄	1	1	yes	characteristic
20	C₄×C₁₀₁₉	C₂³	1	1	yes	characteristic
21	Dic₁₀₁₉	—	2	1	no	—
22	C₂×C₁₀₁₉	—	2	1	no	—
23	C₂×C₁₀₁₉	C₂×D₄	1	1	yes	characteristic
24	D₁₀₁₉	—	4	1	no	—
25	D₁₀₁₉	—	4	2	no	—
26	C₁₀₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic, complemented, Sylow
27	AGL(1,ℤ/8)	—	1019	1	no	maximal, Sylow
28	#41	—	1019	1	no	—
29	C₂×D₄	—	1019	1	no	—
30	SD₁₆	—	1019	2	no	—
31	D₈	—	1019	2	no	—
32	M₁₆	D₁₀₁₉	1	1	yes	characteristic, complemented
33	C₂³	—	2038	1	no	—
34	Q₈	—	1019	1	no	—
35	D₄	—	2038	1	no	—
36	D₄	—	2038	1	no	—
37	D₄	—	1019	1	no	—
38	D₄	—	1019	2	no	—
39	C₂×C₄	—	2038	1	no	—
40	C₂×C₄	C₂×D₁₀₁₉	1	1	yes	characteristic
41	C₈	C₂×D₁₀₁₉	1	2	yes	complemented
42	C₂²	—	4076	2	no	—
43	C₂²	—	2038	1	no	—
44	C₂²	—	2038	2	no	—
45	C₂²	D₄₀₇₆	1	1	yes	characteristic
46	C₄	—	2038	1	no	—
47	C₄	D₄₀₇₆	1	1	yes	characteristic
48	C₄	C₂²×D₁₀₁₉	1	1	yes	characteristic
49	C₂	—	2	1	no	—
50	C₂	—	4076	2	no	—
51	C₂	—	4076	1	no	—
52	C₂	C₂×D₄₀₇₆	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂×D₄₀₇₆
commutator, cosocle	C₄×C₁₀₁₉	C₂³
Frattini	C₄	C₂²×D₁₀₁₉
Fitting	M₁₆×C₁₀₁₉	C₂
socle	C₂×C₁₀₁₉	C₂×D₄
hypercenter	M₁₆	D₁₀₁₉
hypocenter	C₁₀₁₉	AGL(1,ℤ/8)
LCS	G ▷ C₄×C₁₀₁₉ ▷ C₂×C₁₀₁₉ ▷ C₁₀₁₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ M₁₆

Complements

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

N	H ≅ G/N	type
1. #30654504	C₂	semidirect
2. C₂×D₄₀₇₆	C₂	semidirect
3. #30654493	C₂	semidirect
4. D₈₁₅₂	C₂	semidirect
5. M₁₆×C₁₀₁₉	C₂	semidirect
7. Dic₂₀₃₈	C₂²	semidirect
10. D₄₀₇₆	C₂²	semidirect
14. C₈×C₁₀₁₉	C₂²	semidirect
26. C₁₀₁₉	AGL(1,ℤ/8)	semidirect
32. M₁₆	D₁₀₁₉	semidirect
41. C₈	C₂×D₁₀₁₉	semidirect

Maximal subgroups

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

subgroup	index
#30654504	2
C₂×D₄₀₇₆	2
#30654493	2
D₈₁₅₂	2
M₁₆×C₁₀₁₉	2
AGL(1,ℤ/8)	1019