Subgroups — #66960

Order 352.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#4339	C₂	1	1	yes	maximal, characteristic
2	C₁₁×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₁⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	#4313	C₂	1	2	yes	maximal, complemented
5	C₈×D₁₁	C₂	1	2	yes	maximal, complemented
6	C₂×C₄×C₁₁	C₂²	1	1	yes	characteristic
7	C₂²⋊D₁₁	C₄	1	2	yes	—
8	D₄₄	C₄	1	1	yes	characteristic
9	C₄×D₁₁	C₂²	1	2	yes	—
10	Dic₂₂	C₄	1	1	yes	characteristic
11	C₈×C₁₁	C₂²	1	2	yes	—
12	C₁₁⋊C₈	C₂²	1	1	yes	characteristic
13	C₁₁⋊C₈	C₂²	1	1	yes	characteristic
14	C₂²×C₁₁	C₂×C₄	1	1	yes	characteristic
15	C₂×D₁₁	C₂×C₄	1	2	yes	—
16	C₄×C₁₁	C₂×C₄	1	1	yes	characteristic
17	C₄×C₁₁	C₂³	1	1	yes	characteristic
18	Dic₁₁	C₂×C₄	1	2	yes	—
19	#131	—	11	1	no	maximal, Sylow
20	C₂×C₁₁	—	2	1	no	—
21	C₂×C₁₁	C₂²×C₄	1	1	yes	characteristic
22	D₁₁	—	2	2	no	—
23	#41	—	11	1	no	—
24	M₁₆	—	11	2	no	—
25	M₁₆	D₁₁	1	1	yes	characteristic, complemented
26	C₂×C₈	—	11	1	no	—
27	C₂×C₈	—	11	2	no	—
28	C₁₁	#131	1	1	yes	characteristic, complemented, Sylow
29	Q₈	—	11	1	no	—
30	D₄	—	11	2	no	—
31	D₄	—	11	1	no	—
32	C₂×C₄	—	11	2	no	—
33	C₂×C₄	C₂×D₁₁	1	1	yes	characteristic
34	C₈	—	11	1	no	—
35	C₈	—	11	1	no	—
36	C₈	C₂×D₁₁	1	2	yes	—
37	C₂²	—	11	2	no	—
38	C₂²	C₄×D₁₁	1	1	yes	characteristic
39	C₄	—	11	2	no	—
40	C₄	C₄×D₁₁	1	1	yes	characteristic
41	C₄	C₂²×D₁₁	1	1	yes	characteristic
42	C₂	—	2	1	no	—
43	C₂	—	22	2	no	—
44	C₂	C₂×C₄×D₁₁	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.