Subgroups — #45685229

Order 33248.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#30659027	C₂	1	2	yes	maximal, complemented
2	Dic₄₁₅₆	C₂	1	1	yes	maximal, characteristic, complemented
3	#30659016	C₂	1	2	yes	maximal, complemented
4	D₈₃₁₂	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₈×C₁₀₃₉	C₂	1	1	yes	maximal, characteristic, complemented
6	Dic₂₀₇₈	C₂²	1	2	yes	—
7	D₄₁₅₆	C₂²	1	2	yes	—
8	C₂²⋊D₁₀₃₉	—	2	2	no	—
9	C₄×D₁₀₃₉	—	2	2	no	—
10	C₂×C₄×C₁₀₃₉	C₂²	1	1	yes	characteristic
11	C₈×C₁₀₃₉	C₂²	1	1	yes	characteristic
12	C₈×C₁₀₃₉	C₂²	1	1	yes	characteristic
13	C₂²×C₁₀₃₉	D₄	1	1	yes	characteristic
14	C₂×D₁₀₃₉	—	2	2	no	—
15	C₄×C₁₀₃₉	D₄	1	1	yes	characteristic
16	C₄×C₁₀₃₉	C₂³	1	1	yes	characteristic
17	Dic₁₀₃₉	—	2	2	no	—
18	C₂×C₁₀₃₉	—	2	1	no	—
19	C₂×C₁₀₃₉	C₂×D₄	1	1	yes	characteristic
20	D₁₀₃₉	—	4	2	no	—
21	C₁₀₃₉	#135	1	1	yes	characteristic, complemented, Sylow
22	#135	—	1039	1	no	maximal, Sylow
23	#41	—	1039	2	no	—
24	Q₁₆	—	1039	1	no	—
25	SD₁₆	—	1039	2	no	—
26	D₈	—	1039	1	no	—
27	C₂×C₈	D₁₀₃₉	1	1	yes	characteristic, complemented
28	Q₈	—	1039	2	no	—
29	D₄	—	1039	2	no	—
30	D₄	—	2078	2	no	—
31	C₂×C₄	—	2078	2	no	—
32	C₂×C₄	C₂×D₁₀₃₉	1	1	yes	characteristic
33	C₈	C₂×D₁₀₃₉	1	1	yes	characteristic
34	C₈	C₂×D₁₀₃₉	1	1	yes	characteristic
35	C₂²	—	2078	2	no	—
36	C₂²	D₄₁₅₆	1	1	yes	characteristic
37	C₄	—	2078	2	no	—
38	C₄	D₄₁₅₆	1	1	yes	characteristic
39	C₄	C₂²×D₁₀₃₉	1	1	yes	characteristic
40	C₂	—	2	1	no	—
41	C₂	—	4156	2	no	—
42	C₂	C₂×D₄₁₅₆	1	1	yes	characteristic

	subgroup	G/H
center	C₄	D₄₁₅₆
commutator, cosocle	C₄×C₁₀₃₉	C₂³
Frattini	C₄	C₂²×D₁₀₃₉
Fitting	C₂×C₈×C₁₀₃₉	C₂
socle	C₂×C₁₀₃₉	C₂×D₄
hypercenter	C₂×C₈	D₁₀₃₉
hypocenter	C₁₀₃₉	#135
LCS	G ▷ C₄×C₁₀₃₉ ▷ C₂×C₁₀₃₉ ▷ C₁₀₃₉
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
1. #30659027	C₂	semidirect
2. Dic₄₁₅₆	C₂	semidirect
3. #30659016	C₂	semidirect
4. D₈₃₁₂	C₂	semidirect
5. C₂×C₈×C₁₀₃₉	C₂	semidirect
21. C₁₀₃₉	#135	semidirect
27. C₂×C₈	D₁₀₃₉	semidirect

Maximal subgroups

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

subgroup	index
#30659027	2
Dic₄₁₅₆	2
#30659016	2
D₈₃₁₂	2
C₂×C₈×C₁₀₃₉	2
#135	1039