Subgroups — C₇×D₃₂ #89413

Order 448.

34 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×D₁₆	C₂	1	2	yes	maximal, complemented
2	C₇×C₃₂	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×D₈	—	2	2	no	—
4	C₇×C₁₆	C₂²	1	1	yes	characteristic
5	D₃₂	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
6	C₇×D₄	—	4	2	no	—
7	C₇×C₈	D₄	1	1	yes	characteristic
8	D₁₆	C₂×C₇	1	2	yes	complemented
9	C₃₂	C₂×C₇	1	1	yes	characteristic, complemented
10	C₂²×C₇	—	8	2	no	—
11	C₄×C₇	D₈	1	1	yes	characteristic
12	D₈	—	2	2	no	—
13	C₁₆	C₂²×C₇	1	1	yes	characteristic
14	C₂×C₇	—	16	2	no	—
15	C₂×C₇	D₁₆	1	1	yes	characteristic
16	D₄	—	4	2	no	—
17	C₈	C₇×D₄	1	1	yes	characteristic
18	C₇	D₃₂	1	1	yes	characteristic, direct product factor, Sylow
19	C₂²	—	8	2	no	—
20	C₄	C₇×D₈	1	1	yes	characteristic
21	C₂	—	16	2	no	—
22	C₂	C₇×D₁₆	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₇	D₁₆
commutator, Frattini, cosocle	C₁₆	C₂²×C₇
LCS	G ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₇ ◁ C₄×C₇ ◁ C₇×C₈ ◁ C₇×C₁₆ ◁ G

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.