Subgroups — #66929

Order 352.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄²×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
2	(C₂×D₁₁)⋊C₄	C₂	1	3	yes	maximal
3	Dic₁₁⋊C₄	C₂	1	3	yes	maximal, complemented
4	C₂²×D₁₁	C₂²	1	1	yes	characteristic
5	C₂×C₄×C₁₁	C₂²	1	3	yes	—
6	C₂×Dic₁₁	C₂²	1	3	yes	—
7	C₂²×C₁₁	C₂³	1	1	yes	characteristic
8	C₂×D₁₁	—	2	3	no	—
9	C₄×C₁₁	—	2	3	no	—
10	Dic₁₁	—	2	3	no	—
11	#126	—	11	1	no	maximal, Sylow
12	C₂×C₁₁	#41	1	3	yes	—
13	D₁₁	—	4	1	no	—
14	C₄⋊C₄	—	11	3	no	—
15	C₂²⋊C₄	—	11	3	no	—
16	C₄²	D₁₁	1	1	yes	characteristic, complemented
17	C₁₁	#126	1	1	yes	characteristic, complemented, Sylow
18	C₂³	—	11	1	no	—
19	C₂×C₄	—	11	3	no	—
20	C₂×C₄	C₂×D₁₁	1	3	yes	—
21	C₂²	—	22	3	no	—
22	C₂²	C₂²×D₁₁	1	1	yes	characteristic
23	C₄	—	2	3	no	—
24	C₄	—	22	3	no	—
25	C₂	—	44	1	no	—
26	C₂	#4339	1	3	yes	—

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.