Subgroups — #28334672

Order 13696.

38 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₀₇⋊C₆₄	C₂	1	2	yes	maximal, complemented
2	C₂×C₃₂×C₁₀₇	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₆×C₁₀₇	C₄	1	1	yes	characteristic
4	C₃₂×C₁₀₇	C₄	1	1	yes	characteristic
5	C₃₂×C₁₀₇	C₂²	1	1	yes	characteristic
6	C₂×C₈×C₁₀₇	C₈	1	1	yes	characteristic
7	C₁₆×C₁₀₇	C₈	1	1	yes	characteristic
8	C₁₆×C₁₀₇	C₂×C₄	1	1	yes	characteristic
9	C₂×C₄×C₁₀₇	C₁₆	1	1	yes	characteristic
10	C₈×C₁₀₇	C₁₆	1	1	yes	characteristic
11	C₈×C₁₀₇	C₂×C₈	1	1	yes	characteristic
12	C₂²×C₁₀₇	C₃₂	1	1	yes	characteristic
13	C₄×C₁₀₇	C₃₂	1	1	yes	characteristic
14	C₄×C₁₀₇	C₂×C₁₆	1	1	yes	characteristic
15	C₂×C₁₀₇	—	2	1	no	—
16	C₂×C₁₀₇	C₂×C₃₂	1	1	yes	characteristic
17	M₁₂₈	—	107	1	no	maximal, Sylow
18	C₁₀₇	M₁₂₈	1	1	yes	characteristic, complemented, Sylow
19	C₂×C₃₂	D₁₀₇	1	1	yes	characteristic
20	C₆₄	—	107	2	no	—
21	C₂×C₁₆	Dic₁₀₇	1	1	yes	characteristic
22	C₃₂	Dic₁₀₇	1	1	yes	characteristic
23	C₃₂	C₂×D₁₀₇	1	1	yes	characteristic
24	C₂×C₈	C₁₀₇⋊C₈	1	1	yes	characteristic
25	C₁₆	C₁₀₇⋊C₈	1	1	yes	characteristic
26	C₁₆	C₂×Dic₁₀₇	1	1	yes	characteristic
27	C₂×C₄	C₁₀₇⋊C₁₆	1	1	yes	characteristic
28	C₈	C₁₀₇⋊C₁₆	1	1	yes	characteristic
29	C₈	C₂×C₁₀₇⋊C₈	1	1	yes	characteristic
30	C₂²	C₁₀₇⋊C₃₂	1	1	yes	characteristic
31	C₄	C₁₀₇⋊C₃₂	1	1	yes	characteristic
32	C₄	C₂×C₁₀₇⋊C₁₆	1	1	yes	characteristic
33	C₂	—	2	1	no	—
34	C₂	C₂×C₁₀₇⋊C₃₂	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₃₂	C₂×D₁₀₇
commutator, socle	C₂×C₁₀₇	C₂×C₃₂
Fitting	C₂×C₃₂×C₁₀₇	C₂
prime radical	C₂²×C₁₀₇	C₃₂
cosocle	C₃₂×C₁₀₇	C₂²
hypercenter	C₂×C₃₂	D₁₀₇
hypocenter	C₁₀₇	M₁₂₈
LCS	G ▷ C₂×C₁₀₇ ▷ C₁₀₇
UCS	C₁ ◁ C₃₂ ◁ C₂×C₃₂

Complements

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

N	H ≅ G/N	type
1. C₁₀₇⋊C₆₄	C₂	semidirect
18. C₁₀₇	M₁₂₈	semidirect

Maximal subgroups

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

subgroup	index
C₁₀₇⋊C₆₄	2
C₂×C₃₂×C₁₀₇	2
M₁₂₈	107