Subgroups — C₂×C₇×D₇₁⋊C₇ #28358166

Order 13916.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×C₇₁⋊C₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×D₇₁⋊C₇	C₂	1	2	yes	maximal, direct product factor
3	C₇×C₇₁⋊C₇	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×C₇×D₇₁	C₇	1	1	yes	maximal, characteristic, complemented
5	C₂×D₇₁⋊C₇	C₇	1	7	yes	maximal, direct product factor
6	C₂×C₇×C₇₁	C₂×C₇	1	1	yes	characteristic, complemented
7	C₇×D₇₁	C₂×C₇	1	2	yes	complemented
8	C₂×C₇₁⋊C₇	C₂×C₇	1	7	yes	complemented
9	D₇₁⋊C₇	C₂×C₇	1	14	yes	direct product factor
10	C₇×C₇₁	C₂²×C₇	1	1	yes	characteristic, complemented
11	C₇₁⋊C₇	C₂²×C₇	1	7	yes	complemented
12	C₂×D₇₁	C₇²	1	1	yes	characteristic, complemented, Hall
13	C₂²×C₇²	—	71	1	no	maximal, Hall
14	C₂×C₇₁	C₂×C₇²	1	1	yes	characteristic, complemented
15	D₇₁	C₂×C₇²	1	2	yes	complemented
16	C₂×C₇²	—	71	2	no	—
17	C₂×C₇²	—	71	1	no	—
18	C₇₁	C₂²×C₇²	1	1	yes	characteristic, complemented, Sylow
19	C₇²	—	71	1	no	Sylow
20	C₂²×C₇	—	71	7	no	—
21	C₂²×C₇	—	497	1	no	—
22	C₂×C₇	—	71	14	no	—
23	C₂×C₇	—	71	7	no	—
24	C₂×C₇	—	497	2	no	—
25	C₂×C₇	D₇₁⋊C₇	1	1	yes	characteristic, direct product factor
26	C₇	—	71	7	no	—
27	C₇	C₂×D₇₁⋊C₇	1	1	yes	characteristic, direct product factor
28	C₂²	—	497	1	no	Sylow
29	C₂	—	497	2	no	—
30	C₂	C₇×D₇₁⋊C₇	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₇	D₇₁⋊C₇
commutator, cosocle, hypocenter	C₇₁	C₂²×C₇²
Frattini	C₁	G
Fitting, socle	C₂×C₇×C₇₁	C₂×C₇
LCS	G ▷ C₇₁
UCS	C₁ ◁ C₂×C₇

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.