Subgroups — D₇²×C₄₇ #22604255

Order 9212.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₇×C₇⋊D₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×D₇×C₄₇	C₂	1	2	yes	maximal, complemented
3	C₇²×C₄₇	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×D₇×C₄₇	—	7	2	no	maximal
5	C₂×C₇×C₄₇	—	7	2	no	—
6	D₇×C₄₇	—	7	2	no	—
7	D₇×C₄₇	—	14	3	no	—
8	D₇×C₄₇	D₇	1	2	yes	direct product factor
9	C₇×C₄₇	—	2	3	no	—
10	C₇×C₄₇	C₂×D₇	1	2	yes	complemented
11	D₇²	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₂²×C₄₇	—	49	1	no	Hall
13	C₇⋊D₇	C₂×C₄₇	1	1	yes	characteristic, complemented
14	C₇×D₇	C₂×C₄₇	1	2	yes	complemented
15	C₂×C₄₇	—	7	2	no	—
16	C₂×C₄₇	—	49	1	no	—
17	C₇²	C₂²×C₄₇	1	1	yes	characteristic, complemented, Sylow
18	C₄₇	D₇²	1	1	yes	characteristic, direct product factor, Sylow
19	C₂×D₇	—	7	2	no	—
20	C₂×C₇	—	7	2	no	—
21	D₇	—	7	2	no	—
22	D₇	—	14	3	no	—
23	D₇	D₇×C₄₇	1	2	yes	direct product factor
24	C₇	—	2	3	no	—
25	C₇	C₂×D₇×C₄₇	1	2	yes	complemented
26	C₂²	—	49	1	no	Sylow
27	C₂	—	7	2	no	—
28	C₂	—	49	1	no	—

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