Subgroups — #10622158

Order 704.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×D₁₆	C₂	1	1	yes	maximal, characteristic
2	Dic₈₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁⋊C₃₂	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁×D₈	—	2	1	no	—
5	Dic₄₄	—	2	1	no	—
6	C₁₁×C₁₆	C₂²	1	1	yes	characteristic
7	D₄×C₁₁	—	4	1	no	—
8	Dic₂₂	—	4	1	no	—
9	C₈×C₁₁	D₄	1	1	yes	characteristic
10	SD₆₄	—	11	1	no	maximal, Sylow
11	C₂²×C₁₁	—	8	1	no	—
12	C₄×C₁₁	D₈	1	1	yes	characteristic
13	Dic₁₁	—	8	1	no	—
14	Q₃₂	—	11	1	no	—
15	D₁₆	D₁₁	1	1	yes	characteristic
16	C₃₂	—	11	1	no	—
17	C₂×C₁₁	—	16	1	no	—
18	C₂×C₁₁	D₁₆	1	1	yes	characteristic
19	Q₁₆	—	22	1	no	—
20	D₈	—	2	1	no	—
21	C₁₆	C₂×D₁₁	1	1	yes	characteristic
22	C₁₁	SD₆₄	1	1	yes	characteristic, complemented, Sylow
23	Q₈	—	44	1	no	—
24	D₄	—	4	1	no	—
25	C₈	C₂²⋊D₁₁	1	1	yes	characteristic
26	C₂²	—	8	1	no	—
27	C₄	—	88	1	no	—
28	C₄	#4323	1	1	yes	characteristic
29	C₂	—	16	1	no	—
30	C₂	#66890	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.