Subgroups — #66927

Order 352.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄₄	C₂	1	6	yes	maximal, complemented
2	C₄²×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×D₁₁	C₂²	1	4	yes	—
4	C₂×C₄×C₁₁	C₂²	1	3	yes	—
5	D₄₄	—	2	12	no	—
6	C₂²×C₁₁	C₂³	1	1	yes	characteristic
7	C₂×D₁₁	—	2	12	no	—
8	C₄×C₁₁	D₄	1	6	yes	complemented
9	#127	—	11	1	no	maximal, Sylow
10	C₂×C₁₁	C₂×D₄	1	3	yes	—
11	D₁₁	—	4	4	no	—
12	C₂×D₄	—	11	6	no	—
13	C₄²	D₁₁	1	1	yes	characteristic, complemented
14	C₁₁	#127	1	1	yes	characteristic, complemented, Sylow
15	C₂³	—	11	4	no	—
16	D₄	—	22	12	no	—
17	C₂×C₄	C₂×D₁₁	1	3	yes	—
18	C₂²	—	22	12	no	—
19	C₂²	C₂²×D₁₁	1	1	yes	characteristic
20	C₄	D₄₄	1	6	yes	complemented
21	C₂	—	44	4	no	—
22	C₂	C₂×D₄₄	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.