Subgroups — #87641

Order 392.

47 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇⋊D₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₇×D₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×Dic₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₇²	C₂²	1	1	yes	characteristic
5	C₇⋊D₇	—	2	1	no	—
6	C₇×D₇	—	2	1	no	—
7	C₂²⋊D₇	—	7	1	no	maximal
8	D₂₈	—	7	1	no	maximal
9	C₇²	D₄	1	1	yes	characteristic, complemented, Sylow
10	C₂²×C₇	—	7	1	no	—
11	C₂×D₇	—	7	1	no	—
12	C₂×D₇	—	7	1	no	—
13	C₂×D₇	—	14	3	no	—
14	C₂×D₇	D₇	1	1	yes	characteristic, complemented
15	C₄×C₇	—	7	1	no	—
16	Dic₇	D₇	1	1	yes	characteristic, complemented
17	C₂×C₇	—	2	3	no	—
18	C₂×C₇	—	14	1	no	—
19	C₂×C₇	C₂×D₇	1	1	yes	characteristic
20	C₂×C₇	C₂×D₇	1	1	yes	characteristic
21	D₇	—	2	1	no	—
22	D₇	—	14	6	no	—
23	D₇	—	14	1	no	—
24	D₇	—	14	1	no	—
25	D₄	—	49	1	no	Sylow
26	C₇	—	2	3	no	—
27	C₇	D₂₈	1	1	yes	characteristic, complemented
28	C₇	C₂²⋊D₇	1	1	yes	characteristic, complemented
29	C₂²	—	7	1	no	—
30	C₂²	—	49	1	no	—
31	C₄	—	7	1	no	—
32	C₂	—	14	1	no	—
33	C₂	—	98	1	no	—
34	C₂	D₇²	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₇²
commutator, Fitting, socle, cosocle	C₂×C₇²	C₂²
hypocenter	C₇²	D₄
LCS	G ▷ C₂×C₇² ▷ C₇²
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.