Subgroups — C₂×D₈₃₈₁ #45692829

Order 33524.

30 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₈₃₈₁	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₂₉×C₂₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₉×C₂₈₉	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×D₄₉₃	—	17	1	no	maximal
5	C₂×D₂₈₉	—	29	1	no	maximal, Hall
6	C₂×C₁₇×C₂₉	D₁₇	1	1	yes	characteristic
7	D₄₉₃	—	17	2	no	—
8	C₂×C₂₈₉	D₂₉	1	1	yes	characteristic, complemented
9	D₂₈₉	—	29	2	no	—
10	C₁₇×C₂₉	C₂×D₁₇	1	1	yes	characteristic
11	C₂₈₉	C₂×D₂₉	1	1	yes	characteristic, complemented, Sylow
12	C₂×D₂₉	—	289	1	no	Hall
13	C₂×D₁₇	—	493	1	no	—
14	C₂×C₂₉	D₂₈₉	1	1	yes	characteristic, complemented
15	D₂₉	—	289	2	no	—
16	C₂×C₁₇	D₄₉₃	1	1	yes	characteristic
17	D₁₇	—	493	2	no	—
18	C₂₉	C₂×D₂₈₉	1	1	yes	characteristic, complemented, Sylow
19	C₁₇	C₂×D₄₉₃	1	1	yes	characteristic
20	C₂²	—	8381	1	no	Sylow
21	C₂	—	8381	2	no	—
22	C₂	D₈₃₈₁	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	D₈₃₈₁
commutator, cosocle, hypocenter	C₂₉×C₂₈₉	C₂²
Frattini	C₁₇	C₂×D₄₉₃
Fitting	C₂×C₂₉×C₂₈₉	C₂
socle	C₂×C₁₇×C₂₉	D₁₇
LCS	G ▷ C₂₉×C₂₈₉
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.