Subgroups — (C₁₁⋊D₁₁)⋊D₆₇ #44569846

Order 32428.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×D₇₃₇	C₂	1	2	yes	maximal, complemented
2	C₆₇×C₁₁⋊D₁₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁²×C₆₇	C₂²	1	1	yes	characteristic, complemented, Hall
4	D₁₁×D₆₇	—	11	2	no	maximal
5	D₇₃₇	D₁₁	1	2	yes	complemented
6	C₁₁×D₆₇	—	11	2	no	—
7	D₁₁×C₆₇	—	11	2	no	—
8	D₁₁×C₆₇	—	22	5	no	—
9	C₁₁×C₆₇	—	2	5	no	—
10	C₁₁×C₆₇	C₂×D₁₁	1	2	yes	complemented
11	D₁₁²	—	67	1	no	maximal, Hall
12	C₂×D₆₇	—	121	1	no	Hall
13	C₁₁⋊D₁₁	D₆₇	1	1	yes	characteristic, complemented
14	C₁₁×D₁₁	—	67	2	no	—
15	C₂×C₆₇	—	121	1	no	—
16	D₆₇	—	11	2	no	—
17	C₁₁²	C₂×D₆₇	1	1	yes	characteristic, complemented, Sylow
18	C₆₇	D₁₁²	1	1	yes	characteristic, complemented, Sylow
19	C₂×D₁₁	—	737	2	no	—
20	C₂×C₁₁	—	737	2	no	—
21	D₁₁	—	11	2	no	—
22	D₁₁	—	22	5	no	—
23	D₁₁	—	67	2	no	—
24	C₁₁	—	2	5	no	—
25	C₁₁	D₁₁×D₆₇	1	2	yes	complemented
26	C₂²	—	8107	1	no	Sylow
27	C₂	—	121	1	no	—
28	C₂	—	737	2	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₁₁²×C₆₇	C₂²
LCS	G ▷ C₁₁²×C₆₇
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.