Subgroups — C₇×SD₆₄ #89414

Order 448.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×Q₃₂	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×D₁₆	C₂	1	1	yes	maximal, characteristic
3	C₇×C₃₂	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×Q₁₆	—	2	1	no	—
5	C₇×D₈	—	2	1	no	—
6	C₇×C₁₆	C₂²	1	1	yes	characteristic
7	SD₆₄	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
8	C₇×Q₈	—	4	1	no	—
9	C₇×D₄	—	4	1	no	—
10	C₇×C₈	D₄	1	1	yes	characteristic
11	Q₃₂	C₂×C₇	1	1	yes	characteristic, complemented
12	D₁₆	C₂×C₇	1	1	yes	characteristic
13	C₃₂	C₂×C₇	1	1	yes	characteristic, complemented
14	C₂²×C₇	—	8	1	no	—
15	C₄×C₇	—	8	1	no	—
16	C₄×C₇	D₈	1	1	yes	characteristic
17	Q₁₆	—	2	1	no	—
18	D₈	—	2	1	no	—
19	C₁₆	C₂²×C₇	1	1	yes	characteristic
20	C₂×C₇	—	16	1	no	—
21	C₂×C₇	D₁₆	1	1	yes	characteristic
22	Q₈	—	4	1	no	—
23	D₄	—	4	1	no	—
24	C₈	C₇×D₄	1	1	yes	characteristic
25	C₇	SD₆₄	1	1	yes	characteristic, direct product factor, Sylow
26	C₂²	—	8	1	no	—
27	C₄	—	8	1	no	—
28	C₄	C₇×D₈	1	1	yes	characteristic
29	C₂	—	16	1	no	—
30	C₂	C₇×D₁₆	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₇	D₁₆
commutator, Frattini, cosocle	C₁₆	C₂²×C₇
prime radical	C₇×D₁₆	C₂
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.