Subgroups — #66890

Order 352.

28 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×D₈	C₂	1	1	yes	maximal, characteristic, complemented
2	D₈₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	D₄×C₁₁	—	2	1	no	—
5	D₄₄	—	2	1	no	—
6	C₈×C₁₁	C₂²	1	1	yes	characteristic
7	C₂²×C₁₁	—	4	1	no	—
8	C₂×D₁₁	—	4	1	no	—
9	C₄×C₁₁	D₄	1	1	yes	characteristic
10	D₁₆	—	11	1	no	maximal, Sylow
11	C₂×C₁₁	—	8	1	no	—
12	C₂×C₁₁	D₈	1	1	yes	characteristic
13	D₁₁	—	8	1	no	—
14	D₈	—	11	1	no	—
15	D₈	D₁₁	1	1	yes	characteristic, complemented
16	C₁₆	—	11	1	no	—
17	C₁₁	D₁₆	1	1	yes	characteristic, complemented, Sylow
18	D₄	—	2	1	no	—
19	D₄	—	22	1	no	—
20	C₈	C₂×D₁₁	1	1	yes	characteristic
21	C₂²	—	4	1	no	—
22	C₂²	—	44	1	no	—
23	C₄	C₂²⋊D₁₁	1	1	yes	characteristic
24	C₂	—	8	1	no	—
25	C₂	—	88	1	no	—
26	C₂	#4323	1	1	yes	characteristic

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.