Subgroups — C₄×C₇×C₁₉₇⋊C₇ #50311014

Order 38612.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×C₁₉₇⋊C₇	C₂	1	1	yes	maximal, characteristic
2	C₇×C₁₉₇⋊C₇	C₄	1	1	yes	characteristic, direct product factor, Hall
3	C₄×C₁₉₇⋊C₇	C₇	1	7	yes	maximal, direct product factor
4	C₄×C₇×C₁₉₇	C₇	1	1	yes	maximal, characteristic, complemented
5	C₂×C₇×C₁₉₇	C₂×C₇	1	1	yes	characteristic
6	C₂×C₁₉₇⋊C₇	C₂×C₇	1	7	yes	—
7	C₇×C₁₉₇	C₄×C₇	1	1	yes	characteristic, complemented
8	C₁₉₇⋊C₇	C₄×C₇	1	7	yes	direct product factor
9	C₄×C₁₉₇	C₇²	1	1	yes	characteristic, complemented, Hall
10	C₂×C₁₉₇	C₂×C₇²	1	1	yes	characteristic
11	C₁₉₇	C₄×C₇²	1	1	yes	characteristic, complemented, Sylow
12	C₄×C₇²	—	197	1	no	maximal, Hall
13	C₂×C₇²	—	197	1	no	—
14	C₇²	—	197	1	no	Sylow
15	C₄×C₇	—	197	7	no	—
16	C₄×C₇	C₁₉₇⋊C₇	1	1	yes	characteristic, direct product factor
17	C₂×C₇	—	197	7	no	—
18	C₂×C₇	C₂×C₁₉₇⋊C₇	1	1	yes	characteristic
19	C₇	—	197	7	no	—
20	C₇	C₄×C₁₉₇⋊C₇	1	1	yes	characteristic, direct product factor
21	C₄	C₇×C₁₉₇⋊C₇	1	1	yes	characteristic, direct product factor, Sylow
22	C₂	C₂×C₇×C₁₉₇⋊C₇	1	1	yes	characteristic

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

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