Subgroups — C₂×C₇×D₈ #6535

Order 224.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×D₄	C₂	1	2	yes	maximal, complemented
2	C₇×D₈	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₇×C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂³×C₇	—	2	2	no	—
5	C₇×D₄	—	2	2	no	—
6	C₇×D₄	C₂²	1	4	yes	complemented
7	C₂×C₄×C₇	C₂²	1	1	yes	characteristic
8	C₇×C₈	C₂²	1	2	yes	complemented
9	C₂×D₈	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
10	C₂²×C₇	—	2	4	no	—
11	C₂²×C₇	—	4	4	no	—
12	C₂²×C₇	D₄	1	1	yes	characteristic
13	C₄×C₇	D₄	1	1	yes	characteristic
14	C₄×C₇	C₂³	1	1	yes	characteristic
15	C₂×D₄	C₂×C₇	1	2	yes	complemented
16	D₈	C₂×C₇	1	4	yes	direct product factor
17	C₂×C₈	C₂×C₇	1	1	yes	characteristic, complemented
18	C₂×C₇	—	4	4	no	—
19	C₂×C₇	D₈	1	2	yes	direct product factor
20	C₂×C₇	C₂×D₄	1	1	yes	characteristic
21	C₂³	—	2	2	no	—
22	D₄	—	2	2	no	—
23	D₄	C₂²×C₇	1	4	yes	complemented
24	C₂×C₄	C₂²×C₇	1	1	yes	characteristic
25	C₈	C₂²×C₇	1	2	yes	complemented
26	C₇	C₂×D₈	1	1	yes	characteristic, direct product factor, Sylow
27	C₂²	—	2	4	no	—
28	C₂²	—	4	4	no	—
29	C₂²	C₇×D₄	1	1	yes	characteristic
30	C₄	C₇×D₄	1	1	yes	characteristic
31	C₄	C₂³×C₇	1	1	yes	characteristic
32	C₂	—	4	4	no	—
33	C₂	C₇×D₈	1	2	yes	direct product factor
34	C₂	C₂×C₇×D₄	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇	D₄
commutator, Frattini, cosocle	C₄	C₂³×C₇
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇ ◁ C₂×C₄×C₇ ◁ 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.