Subgroups — C₂×D₂₈₉₁ #26040586

Order 11564.

30 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₂₈₉₁	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₄₉×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₉×C₅₉	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×D₄₁₃	—	7	1	no	maximal
5	C₂×C₇×C₅₉	D₇	1	1	yes	characteristic
6	D₄₁₃	—	7	2	no	—
7	C₇×C₅₉	C₂×D₇	1	1	yes	characteristic
8	C₂×D₅₉	—	49	1	no	Hall
9	C₂×D₄₉	—	59	1	no	maximal, Hall
10	C₂×C₅₉	D₄₉	1	1	yes	characteristic, complemented
11	D₅₉	—	49	2	no	—
12	C₂×C₄₉	D₅₉	1	1	yes	characteristic, complemented
13	D₄₉	—	59	2	no	—
14	C₅₉	C₂×D₄₉	1	1	yes	characteristic, complemented, Sylow
15	C₄₉	C₂×D₅₉	1	1	yes	characteristic, complemented, Sylow
16	C₂×D₇	—	413	1	no	—
17	C₂×C₇	D₄₁₃	1	1	yes	characteristic
18	D₇	—	413	2	no	—
19	C₇	C₂×D₄₁₃	1	1	yes	characteristic
20	C₂²	—	2891	1	no	Sylow
21	C₂	—	2891	2	no	—
22	C₂	D₂₈₉₁	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	D₂₈₉₁
commutator, cosocle, hypocenter	C₄₉×C₅₉	C₂²
Frattini	C₇	C₂×D₄₁₃
Fitting	C₂×C₄₉×C₅₉	C₂
socle	C₂×C₇×C₅₉	D₇
LCS	G ▷ C₄₉×C₅₉
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.