Subgroups — C₂×D₁₆₂₁₉ #72302136

Order 64876.

30 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₆₂₁₉	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₄₉×C₃₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₉×C₃₃₁	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×D₂₃₁₇	—	7	1	no	maximal
5	C₂×C₇×C₃₃₁	D₇	1	1	yes	characteristic
6	D₂₃₁₇	—	7	2	no	—
7	C₇×C₃₃₁	C₂×D₇	1	1	yes	characteristic
8	C₂×D₃₃₁	—	49	1	no	Hall
9	C₂×C₃₃₁	D₄₉	1	1	yes	characteristic, complemented
10	D₃₃₁	—	49	2	no	—
11	C₃₃₁	C₂×D₄₉	1	1	yes	characteristic, complemented, Sylow
12	C₂×D₄₉	—	331	1	no	maximal, Hall
13	C₂×C₄₉	D₃₃₁	1	1	yes	characteristic, complemented
14	D₄₉	—	331	2	no	—
15	C₄₉	C₂×D₃₃₁	1	1	yes	characteristic, complemented, Sylow
16	C₂×D₇	—	2317	1	no	—
17	C₂×C₇	D₂₃₁₇	1	1	yes	characteristic
18	D₇	—	2317	2	no	—
19	C₇	C₂×D₂₃₁₇	1	1	yes	characteristic
20	C₂²	—	16219	1	no	Sylow
21	C₂	—	16219	2	no	—
22	C₂	D₁₆₂₁₉	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	D₁₆₂₁₉
commutator, cosocle, hypocenter	C₄₉×C₃₃₁	C₂²
Frattini	C₇	C₂×D₂₃₁₇
Fitting	C₂×C₄₉×C₃₃₁	C₂
socle	C₂×C₇×C₃₃₁	D₇
LCS	G ▷ C₄₉×C₃₃₁
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.