Subgroups — D₄₁×C₇⋊D₇ #22548813

Order 8036.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇⋊D₂₈₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄₁×C₇⋊D₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇²×D₄₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇²×C₄₁	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₇×D₄₁	—	7	8	no	maximal
6	D₂₈₇	—	7	8	no	—
7	C₇×D₄₁	D₇	1	8	yes	complemented
8	D₇×C₄₁	—	7	8	no	—
9	C₇×C₄₁	C₂×D₇	1	8	yes	complemented
10	C₂×C₇⋊D₇	—	41	1	no	maximal, Hall
11	C₂×D₄₁	—	49	1	no	Hall
12	C₂×C₇²	—	41	1	no	—
13	C₇⋊D₇	—	41	1	no	—
14	C₇⋊D₇	D₄₁	1	1	yes	characteristic, direct product factor
15	C₂×C₄₁	—	49	1	no	—
16	D₄₁	—	49	1	no	—
17	D₄₁	C₇⋊D₇	1	1	yes	characteristic, direct product factor
18	C₇²	C₂×D₄₁	1	1	yes	characteristic, complemented, Sylow
19	C₄₁	C₂×C₇⋊D₇	1	1	yes	characteristic, complemented, Sylow
20	C₂×D₇	—	287	8	no	—
21	C₂×C₇	—	41	8	no	—
22	D₇	—	7	8	no	—
23	D₇	—	287	8	no	—
24	C₇	D₇×D₄₁	1	8	yes	complemented
25	C₂²	—	2009	1	no	Sylow
26	C₂	—	41	1	no	—
27	C₂	—	49	1	no	—
28	C₂	—	2009	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₇²×C₄₁	C₂²
LCS	G ▷ C₇²×C₄₁
UCS	C₁

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