Subgroups — C₇×SD₃₂ #6429

Order 224.

26 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×D₈	C₂	1	1	yes	maximal, characteristic
3	C₇×C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×Q₈	—	2	1	no	—
5	C₇×D₄	—	2	1	no	—
6	C₇×C₈	C₂²	1	1	yes	characteristic
7	SD₃₂	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
8	C₂²×C₇	—	4	1	no	—
9	C₄×C₇	—	4	1	no	—
10	C₄×C₇	D₄	1	1	yes	characteristic
11	Q₁₆	C₂×C₇	1	1	yes	characteristic, complemented
12	D₈	C₂×C₇	1	1	yes	characteristic
13	C₁₆	C₂×C₇	1	1	yes	characteristic, complemented
14	C₂×C₇	—	8	1	no	—
15	C₂×C₇	D₈	1	1	yes	characteristic
16	Q₈	—	2	1	no	—
17	D₄	—	2	1	no	—
18	C₈	C₂²×C₇	1	1	yes	characteristic
19	C₇	SD₃₂	1	1	yes	characteristic, direct product factor, Sylow
20	C₂²	—	4	1	no	—
21	C₄	—	4	1	no	—
22	C₄	C₇×D₄	1	1	yes	characteristic
23	C₂	—	8	1	no	—
24	C₂	C₇×D₈	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₇	D₈
commutator, Frattini, cosocle	C₈	C₂²×C₇
prime radical	C₇×D₈	C₂
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₇ ◁ C₄×C₇ ◁ C₇×C₈ ◁ 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.