Subgroups — C₂×D₈₉₉₃ #49112608

Order 35972.

30 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₈₉₉₃	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₁₇×C₅₂₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₇×C₅₂₉	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×D₅₂₉	—	17	1	no	maximal, Hall
5	C₂×D₃₉₁	—	23	1	no	maximal
6	C₂×C₅₂₉	D₁₇	1	1	yes	characteristic, complemented
7	D₅₂₉	—	17	2	no	—
8	C₂×C₁₇×C₂₃	D₂₃	1	1	yes	characteristic
9	D₃₉₁	—	23	2	no	—
10	C₅₂₉	C₂×D₁₇	1	1	yes	characteristic, complemented, Sylow
11	C₁₇×C₂₃	C₂×D₂₃	1	1	yes	characteristic
12	C₂×D₂₃	—	391	1	no	—
13	C₂×D₁₇	—	529	1	no	Hall
14	C₂×C₂₃	D₃₉₁	1	1	yes	characteristic
15	D₂₃	—	391	2	no	—
16	C₂×C₁₇	D₅₂₉	1	1	yes	characteristic, complemented
17	D₁₇	—	529	2	no	—
18	C₂₃	C₂×D₃₉₁	1	1	yes	characteristic
19	C₁₇	C₂×D₅₂₉	1	1	yes	characteristic, complemented, Sylow
20	C₂²	—	8993	1	no	Sylow
21	C₂	—	8993	2	no	—
22	C₂	D₈₉₉₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	D₈₉₉₃
commutator, cosocle, hypocenter	C₁₇×C₅₂₉	C₂²
Frattini	C₂₃	C₂×D₃₉₁
Fitting	C₂×C₁₇×C₅₂₉	C₂
socle	C₂×C₁₇×C₂₃	D₂₃
LCS	G ▷ C₁₇×C₅₂₉
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.