Subgroups — C₆₇×D₁₂₈ #30686802

Order 17152.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×D₆₄	C₂	1	2	yes	maximal, complemented
2	C₆₇×C₁₂₈	C₂	1	1	yes	maximal, characteristic, complemented
3	D₃₂×C₆₇	—	2	2	no	—
4	C₆₄×C₆₇	C₂²	1	1	yes	characteristic
5	D₁₆×C₆₇	—	4	2	no	—
6	C₃₂×C₆₇	D₄	1	1	yes	characteristic
7	D₈×C₆₇	—	8	2	no	—
8	C₁₆×C₆₇	D₈	1	1	yes	characteristic
9	D₄×C₆₇	—	16	2	no	—
10	C₈×C₆₇	D₁₆	1	1	yes	characteristic
11	C₂²×C₆₇	—	32	2	no	—
12	C₄×C₆₇	D₃₂	1	1	yes	characteristic
13	D₁₂₈	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
14	C₂×C₆₇	—	64	2	no	—
15	C₂×C₆₇	D₆₄	1	1	yes	characteristic
16	D₆₄	C₂×C₆₇	1	2	yes	complemented
17	C₁₂₈	C₂×C₆₇	1	1	yes	characteristic, complemented
18	C₆₇	D₁₂₈	1	1	yes	characteristic, direct product factor, Sylow
19	D₃₂	—	2	2	no	—
20	C₆₄	C₂²×C₆₇	1	1	yes	characteristic
21	D₁₆	—	4	2	no	—
22	C₃₂	D₄×C₆₇	1	1	yes	characteristic
23	D₈	—	8	2	no	—
24	C₁₆	D₈×C₆₇	1	1	yes	characteristic
25	D₄	—	16	2	no	—
26	C₈	D₁₆×C₆₇	1	1	yes	characteristic
27	C₂²	—	32	2	no	—
28	C₄	D₃₂×C₆₇	1	1	yes	characteristic
29	C₂	—	64	2	no	—
30	C₂	C₆₇×D₆₄	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₆₇	D₆₄
commutator, Frattini, cosocle	C₆₄	C₂²×C₆₇
LCS	G ▷ C₆₄ ▷ C₃₂ ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₆₇ ◁ C₄×C₆₇ ◁ C₈×C₆₇ ◁ C₁₆×C₆₇ ◁ C₃₂×C₆₇ ◁ C₆₄×C₆₇ ◁ 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.