Subgroups — #67043

Order 352.

146 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#41	C₂	1	1	yes	maximal, characteristic, complemented
2	Q₈×D₁₁	C₂	1	2	yes	maximal, complemented
3	#4341	C₂	1	6	yes	maximal, complemented
4	#4339	C₂	1	3	yes	maximal, complemented
5	C₂×Dic₂₂	C₂	1	3	yes	maximal, complemented
6	Q₈×C₁₁	C₂²	1	1	yes	characteristic
7	D₄×C₁₁	C₂²	1	3	yes	—
8	C₂×C₄×C₁₁	C₂²	1	3	yes	—
9	C₂²⋊D₁₁	C₂²	1	6	yes	—
10	C₂×Dic₁₁	C₂²	1	6	yes	—
11	D₄₄	C₂²	1	1	yes	characteristic
12	C₄×D₁₁	C₂²	1	6	yes	—
13	Dic₂₂	C₂²	1	3	yes	—
14	Dic₂₂	C₂²	1	6	yes	—
15	C₂²×C₁₁	C₂³	1	3	yes	—
16	C₂×D₁₁	C₂³	1	2	yes	—
17	C₄×C₁₁	C₂³	1	1	yes	characteristic
18	C₄×C₁₁	C₂³	1	3	yes	—
19	Dic₁₁	C₂³	1	6	yes	—
20	2₋¹⁺⁴	—	11	1	no	maximal, Sylow
21	C₂×C₁₁	—	2	3	no	—
22	C₂×C₁₁	C₂⁴	1	1	yes	characteristic
23	D₁₁	—	2	2	no	—
24	#41	—	11	6	no	—
25	#41	—	11	3	no	—
26	#41	D₁₁	1	1	yes	characteristic, complemented
27	C₂×Q₈	—	11	2	no	—
28	C₂×Q₈	—	11	3	no	—
29	C₁₁	2₋¹⁺⁴	1	1	yes	characteristic, complemented, Sylow
30	Q₈	—	11	6	no	—
31	Q₈	—	11	3	no	—
32	Q₈	C₂×D₁₁	1	1	yes	characteristic
33	D₄	—	11	6	no	—
34	D₄	—	11	1	no	—
35	D₄	C₂×D₁₁	1	3	yes	—
36	C₂×C₄	—	11	6	no	—
37	C₂×C₄	—	11	6	no	—
38	C₂×C₄	C₂×D₁₁	1	3	yes	—
39	C₂²	—	11	2	no	—
40	C₂²	C₂²×D₁₁	1	3	yes	—
41	C₄	—	11	6	no	—
42	C₄	C₂²×D₁₁	1	3	yes	—
43	C₄	C₂²×D₁₁	1	1	yes	characteristic
44	C₂	—	2	3	no	—
45	C₂	—	22	2	no	—
46	C₂	C₂³×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.