Subgroups — Dic₇×C₁₉₇⋊C₇ #50311013

Order 38612.

36 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, complemented, Hall
3	Dic₇×C₁₉₇	C₇	1	1	yes	maximal, characteristic, complemented
4	C₄×C₁₉₇⋊C₇	—	7	1	no	maximal
5	C₂×C₇×C₁₉₇	C₂×C₇	1	1	yes	characteristic
6	C₂×C₁₉₇⋊C₇	—	2	3	no	—
7	C₂×C₁₉₇⋊C₇	D₇	1	1	yes	characteristic
8	C₇×C₁₉₇	C₄×C₇	1	1	yes	characteristic, complemented
9	C₁₉₇⋊C₇	—	2	3	no	—
10	C₁₉₇⋊C₇	Dic₇	1	1	yes	characteristic, direct product factor
11	C₄×C₁₉₇	—	7	1	no	Hall
12	C₂×C₁₉₇	C₇×D₇	1	1	yes	characteristic
13	C₁₉₇	C₇×Dic₇	1	1	yes	characteristic, complemented, Sylow
14	C₇×Dic₇	—	197	1	no	maximal, Hall
15	C₂×C₇²	—	197	1	no	—
16	C₇²	—	197	1	no	Sylow
17	C₄×C₇	—	1379	1	no	—
18	Dic₇	C₁₉₇⋊C₇	1	1	yes	characteristic, direct product factor
19	C₂×C₇	—	394	3	no	—
20	C₂×C₇	—	197	1	no	—
21	C₂×C₇	C₂×C₁₉₇⋊C₇	1	1	yes	characteristic
22	C₇	—	394	3	no	—
23	C₇	—	197	1	no	—
24	C₇	C₄×C₁₉₇⋊C₇	1	1	yes	characteristic, complemented
25	C₄	—	7	1	no	Sylow
26	C₂	D₇×C₁₉₇⋊C₇	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₇×C₁₉₇⋊C₇
commutator, hypocenter	C₇×C₁₉₇	C₄×C₇
Fitting, socle, cosocle	C₂×C₇×C₁₉₇	C₂×C₇
prime radical	C₂×C₇×C₁₉₇⋊C₇	C₂
LCS	G ▷ C₇×C₁₉₇
UCS	C₁ ◁ C₂

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.