Subgroups — #44569739

Order 32416.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#30633824	C₂	1	1	yes	maximal, characteristic, complemented
2	#30633823	C₂	1	2	yes	maximal, complemented
3	D₁₀₁₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#22549208	C₂	1	2	yes	maximal, complemented
5	#30633813	C₂	1	1	yes	maximal, characteristic
6	#22549208	C₂²	1	1	yes	characteristic
7	#22549208	C₂²	1	2	yes	—
8	#22549208	C₂²	1	1	yes	characteristic
9	Dic₂₀₂₆	C₄	1	1	yes	characteristic
10	C₂²⋊D₁₀₁₃	C₄	1	2	yes	—
11	C₂×Dic₁₀₁₃	C₂²	1	2	yes	—
12	C₄×D₁₀₁₃	C₂²	1	1	yes	characteristic
13	D₄×C₁₀₁₃	C₄	1	1	yes	characteristic
14	C₂²×C₁₀₁₃	C₂×C₄	1	2	yes	—
15	C₂×D₁₀₁₃	C₂×C₄	1	1	yes	characteristic
16	C₄×C₁₀₁₃	C₂×C₄	1	1	yes	characteristic
17	Dic₁₀₁₃	C₂×C₄	1	2	yes	—
18	Dic₁₀₁₃	C₂³	1	1	yes	characteristic
19	C₂×C₁₀₁₃	—	2	2	no	—
20	C₂×C₁₀₁₃	C₂²×C₄	1	1	yes	characteristic
21	D₁₀₁₃	—	2	1	no	—
22	C₁₀₁₃	#131	1	1	yes	characteristic, complemented, Sylow
23	#131	—	1013	1	no	maximal, Sylow
24	#41	—	1013	1	no	—
25	M₁₆	—	1013	2	no	—
26	M₁₆	—	1013	1	no	—
27	C₂×C₈	—	1013	2	no	—
28	C₂×C₈	—	1013	1	no	—
29	Q₈	—	1013	1	no	—
30	D₄	—	1013	2	no	—
31	D₄	#16860990	1	1	yes	characteristic
32	C₂×C₄	—	1013	2	no	—
33	C₂×C₄	—	1013	1	no	—
34	C₈	—	1013	1	no	—
35	C₈	—	1013	2	no	—
36	C₈	—	1013	1	no	—
37	C₂²	—	1013	1	no	—
38	C₂²	C₂×#16860990	1	2	yes	—
39	C₄	—	1013	1	no	—
40	C₄	—	1013	2	no	—
41	C₄	C₂×#16860990	1	1	yes	characteristic
42	C₂	—	2	2	no	—
43	C₂	—	2026	1	no	—
44	C₂	C₂²×#16860990	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂	C₂²×#16860990
commutator, socle	C₂×C₁₀₁₃	C₂²×C₄
Fitting	D₄×C₁₀₁₃	C₄
prime radical	#30633813	C₂
cosocle	Dic₁₀₁₃	C₂³
hypercenter	D₄	#16860990
hypocenter	C₁₀₁₃	#131
LCS	G ▷ C₂×C₁₀₁₃ ▷ C₁₀₁₃
UCS	C₁ ◁ C₂ ◁ D₄

Complements

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

N	H ≅ G/N	type
1. #30633824	C₂	semidirect
2. #30633823	C₂	semidirect
3. D₁₀₁₃⋊C₈	C₂	semidirect
4. C₂×#22549208	C₂	semidirect
22. C₁₀₁₃	#131	semidirect

Maximal subgroups

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

subgroup	index
#30633824	2
#30633823	2
D₁₀₁₃⋊C₈	2
C₂×#22549208	2
#30633813	2
#131	1013