Subgroups — C₂×D₂₇₃₇ #24926517

Order 10948.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₂₇₃₇	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₇×C₁₇×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×C₁₇×C₂₃	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×D₃₉₁	—	7	1	no	maximal, Hall
5	C₂×C₁₇×C₂₃	D₇	1	1	yes	characteristic, complemented
6	D₃₉₁	—	7	2	no	—
7	C₂×D₁₆₁	—	17	1	no	maximal, Hall
8	C₂×D₁₁₉	—	23	1	no	maximal, Hall
9	C₁₇×C₂₃	C₂×D₇	1	1	yes	characteristic, complemented, Hall
10	C₂×C₇×C₂₃	D₁₇	1	1	yes	characteristic, complemented
11	D₁₆₁	—	17	2	no	—
12	C₂×C₇×C₁₇	D₂₃	1	1	yes	characteristic, complemented
13	D₁₁₉	—	23	2	no	—
14	C₇×C₂₃	C₂×D₁₇	1	1	yes	characteristic, complemented, Hall
15	C₇×C₁₇	C₂×D₂₃	1	1	yes	characteristic, complemented, Hall
16	C₂×D₂₃	—	119	1	no	Hall
17	C₂×D₁₇	—	161	1	no	Hall
18	C₂×C₂₃	D₁₁₉	1	1	yes	characteristic, complemented
19	D₂₃	—	119	2	no	—
20	C₂×C₁₇	D₁₆₁	1	1	yes	characteristic, complemented
21	D₁₇	—	161	2	no	—
22	C₂×D₇	—	391	1	no	Hall
23	C₂₃	C₂×D₁₁₉	1	1	yes	characteristic, complemented, Sylow
24	C₁₇	C₂×D₁₆₁	1	1	yes	characteristic, complemented, Sylow
25	C₂×C₇	D₃₉₁	1	1	yes	characteristic, complemented
26	D₇	—	391	2	no	—
27	C₇	C₂×D₃₉₁	1	1	yes	characteristic, complemented, Sylow
28	C₂²	—	2737	1	no	Sylow
29	C₂	—	2737	2	no	—
30	C₂	D₂₇₃₇	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	D₂₇₃₇
commutator, cosocle, hypocenter	C₇×C₁₇×C₂₃	C₂²
Frattini	C₁	G
Fitting, socle	C₂×C₇×C₁₇×C₂₃	C₂
LCS	G ▷ C₇×C₁₇×C₂₃
UCS	C₁ ◁ C₂

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.