Subgroups — C₂×C₇⋊D₃₇₁ #23780751

Order 10388.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇⋊D₃₇₁	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₇²×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇²×C₅₃	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×D₃₇₁	—	7	8	no	maximal
5	C₂×C₇×C₅₃	D₇	1	8	yes	complemented
6	D₃₇₁	—	7	16	no	—
7	C₇×C₅₃	C₂×D₇	1	8	yes	complemented
8	C₂×D₅₃	—	49	1	no	Hall
9	C₂×C₇⋊D₇	—	53	1	no	maximal, Hall
10	C₂×C₅₃	C₇⋊D₇	1	1	yes	characteristic, complemented
11	D₅₃	—	49	2	no	—
12	C₂×C₇²	D₅₃	1	1	yes	characteristic, complemented
13	C₇⋊D₇	—	53	2	no	—
14	C₅₃	C₂×C₇⋊D₇	1	1	yes	characteristic, complemented, Sylow
15	C₇²	C₂×D₅₃	1	1	yes	characteristic, complemented, Sylow
16	C₂×D₇	—	371	8	no	—
17	C₂×C₇	D₃₇₁	1	8	yes	complemented
18	D₇	—	371	16	no	—
19	C₇	C₂×D₃₇₁	1	8	yes	complemented
20	C₂²	—	2597	1	no	Sylow
21	C₂	—	2597	2	no	—
22	C₂	C₇⋊D₃₇₁	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	C₇⋊D₃₇₁
commutator, cosocle, hypocenter	C₇²×C₅₃	C₂²
Frattini	C₁	G
Fitting, socle	C₂×C₇²×C₅₃	C₂
LCS	G ▷ C₇²×C₅₃
UCS	C₁ ◁ C₂

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