Subgroups — C₂×D₈×C₃₃₇ #24924852

Order 10784.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄×C₃₃₇	C₂	1	2	yes	maximal, complemented
2	D₈×C₃₃₇	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₈×C₃₃₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂³×C₃₃₇	—	2	2	no	—
5	D₄×C₃₃₇	—	2	2	no	—
6	D₄×C₃₃₇	C₂²	1	4	yes	complemented
7	C₂×C₄×C₃₃₇	C₂²	1	1	yes	characteristic
8	C₈×C₃₃₇	C₂²	1	2	yes	complemented
9	C₂²×C₃₃₇	—	2	4	no	—
10	C₂²×C₃₃₇	—	4	4	no	—
11	C₂²×C₃₃₇	D₄	1	1	yes	characteristic
12	C₄×C₃₃₇	D₄	1	1	yes	characteristic
13	C₄×C₃₃₇	C₂³	1	1	yes	characteristic
14	C₂×C₃₃₇	—	4	4	no	—
15	C₂×C₃₃₇	D₈	1	2	yes	direct product factor
16	C₂×C₃₃₇	C₂×D₄	1	1	yes	characteristic
17	C₃₃₇	C₂×D₈	1	1	yes	characteristic, direct product factor, Sylow
18	C₂×D₈	C₃₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
19	C₂×D₄	C₂×C₃₃₇	1	2	yes	complemented
20	D₈	C₂×C₃₃₇	1	4	yes	direct product factor
21	C₂×C₈	C₂×C₃₃₇	1	1	yes	characteristic, complemented
22	C₂³	—	2	2	no	—
23	D₄	—	2	2	no	—
24	D₄	C₂²×C₃₃₇	1	4	yes	complemented
25	C₂×C₄	C₂²×C₃₃₇	1	1	yes	characteristic
26	C₈	C₂²×C₃₃₇	1	2	yes	complemented
27	C₂²	—	2	4	no	—
28	C₂²	—	4	4	no	—
29	C₂²	D₄×C₃₃₇	1	1	yes	characteristic
30	C₄	D₄×C₃₃₇	1	1	yes	characteristic
31	C₄	C₂³×C₃₃₇	1	1	yes	characteristic
32	C₂	—	4	4	no	—
33	C₂	D₈×C₃₃₇	1	2	yes	direct product factor
34	C₂	C₂×D₄×C₃₃₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₃₇	D₄
commutator, Frattini, cosocle	C₄	C₂³×C₃₃₇
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₃₇ ◁ C₂×C₄×C₃₃₇ ◁ 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.