Subgroups — (C₁₁⋊D₁₁)⋊D₅₉ #43270010

Order 28556.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×D₆₄₉	C₂	1	2	yes	maximal, complemented
2	C₅₉×C₁₁⋊D₁₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁²×C₅₉	C₂²	1	1	yes	characteristic, complemented, Hall
4	D₁₁×D₅₉	—	11	2	no	maximal
5	D₆₄₉	D₁₁	1	2	yes	complemented
6	C₁₁×D₅₉	—	11	2	no	—
7	D₁₁×C₅₉	—	11	2	no	—
8	D₁₁×C₅₉	—	22	5	no	—
9	C₁₁×C₅₉	—	2	5	no	—
10	C₁₁×C₅₉	C₂×D₁₁	1	2	yes	complemented
11	D₁₁²	—	59	1	no	maximal, Hall
12	C₁₁⋊D₁₁	D₅₉	1	1	yes	characteristic, complemented
13	C₁₁×D₁₁	—	59	2	no	—
14	C₂×D₅₉	—	121	1	no	Hall
15	C₁₁²	C₂×D₅₉	1	1	yes	characteristic, complemented, Sylow
16	C₂×C₅₉	—	121	1	no	—
17	D₅₉	—	11	2	no	—
18	C₅₉	D₁₁²	1	1	yes	characteristic, complemented, Sylow
19	C₂×D₁₁	—	649	2	no	—
20	C₂×C₁₁	—	649	2	no	—
21	D₁₁	—	11	2	no	—
22	D₁₁	—	22	5	no	—
23	D₁₁	—	59	2	no	—
24	C₁₁	—	2	5	no	—
25	C₁₁	D₁₁×D₅₉	1	2	yes	complemented
26	C₂²	—	7139	1	no	Sylow
27	C₂	—	121	1	no	—
28	C₂	—	649	2	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₁₁²×C₅₉	C₂²
LCS	G ▷ C₁₁²×C₅₉
UCS	C₁

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.