Subgroups — C₂×D₈₃₃ #16809708

Order 3332.

30 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₇×C₄₉	C₂	1	1	yes	maximal, characteristic, complemented
2	D₈₃₃	C₂	1	2	yes	maximal, direct product factor
3	C₁₇×C₄₉	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×D₁₁₉	—	7	1	no	maximal
5	C₂×C₇×C₁₇	D₇	1	1	yes	characteristic
6	D₁₁₉	—	7	2	no	—
7	C₂×D₄₉	—	17	1	no	maximal, Hall
8	C₇×C₁₇	C₂×D₇	1	1	yes	characteristic
9	C₂×C₄₉	D₁₇	1	1	yes	characteristic, complemented
10	D₄₉	—	17	2	no	—
11	C₂×D₁₇	—	49	1	no	Hall
12	C₄₉	C₂×D₁₇	1	1	yes	characteristic, complemented, Sylow
13	C₂×C₁₇	D₄₉	1	1	yes	characteristic, complemented
14	D₁₇	—	49	2	no	—
15	C₂×D₇	—	119	1	no	—
16	C₁₇	C₂×D₄₉	1	1	yes	characteristic, complemented, Sylow
17	C₂×C₇	D₁₁₉	1	1	yes	characteristic
18	D₇	—	119	2	no	—
19	C₇	C₂×D₁₁₉	1	1	yes	characteristic
20	C₂²	—	833	1	no	Sylow
21	C₂	—	833	2	no	—
22	C₂	D₈₃₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	D₈₃₃
commutator, cosocle, hypocenter	C₁₇×C₄₉	C₂²
Frattini	C₇	C₂×D₁₁₉
Fitting	C₂×C₁₇×C₄₉	C₂
socle	C₂×C₇×C₁₇	D₇
LCS	G ▷ C₁₇×C₄₉
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.