Subgroups — C₂×C₄₇×C₇⋊D₇ #22604261

Order 9212.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₇×C₇⋊D₇	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₇²×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇²×C₄₇	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×D₇×C₄₇	—	7	8	no	maximal
5	C₂×C₇×C₄₇	D₇	1	8	yes	complemented
6	D₇×C₄₇	—	7	16	no	—
7	C₇×C₄₇	C₂×D₇	1	8	yes	complemented
8	C₂×C₇⋊D₇	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂²×C₄₇	—	49	1	no	Hall
10	C₂×C₇²	C₂×C₄₇	1	1	yes	characteristic, complemented
11	C₇⋊D₇	C₂×C₄₇	1	2	yes	direct product factor
12	C₂×C₄₇	—	49	2	no	—
13	C₂×C₄₇	C₇⋊D₇	1	1	yes	characteristic, direct product factor
14	C₇²	C₂²×C₄₇	1	1	yes	characteristic, complemented, Sylow
15	C₄₇	C₂×C₇⋊D₇	1	1	yes	characteristic, direct product factor, Sylow
16	C₂×D₇	—	7	8	no	—
17	C₂×C₇	D₇×C₄₇	1	8	yes	complemented
18	D₇	—	7	16	no	—
19	C₇	C₂×D₇×C₄₇	1	8	yes	complemented
20	C₂²	—	49	1	no	Sylow
21	C₂	—	49	2	no	—
22	C₂	C₄₇×C₇⋊D₇	1	1	yes	characteristic, direct product factor

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