Subgroups — #67000

Order 352.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₈×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₄₄	C₂	1	1	yes	maximal, characteristic
3	(C₂×D₁₁)⋊C₄	C₂	1	4	yes	maximal, complemented
4	C₄×Dic₁₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×D₁₁	C₂²	1	2	yes	—
6	Q₈×C₁₁	—	2	2	no	—
7	C₂×C₄×C₁₁	C₂²	1	2	yes	—
8	C₂×C₄×C₁₁	C₂²	1	1	yes	characteristic
9	C₂×Dic₁₁	C₂²	1	2	yes	—
10	D₄₄	—	2	2	no	—
11	C₂²×C₁₁	C₂³	1	1	yes	characteristic
12	C₂×D₁₁	—	2	2	no	—
13	C₂×D₁₁	—	2	4	no	—
14	C₄×C₁₁	—	2	2	no	—
15	C₄×C₁₁	D₄	1	2	yes	—
16	Dic₁₁	—	2	2	no	—
17	#124	—	11	1	no	maximal, Sylow
18	C₂×C₁₁	C₂×D₄	1	1	yes	characteristic
19	C₂×C₁₁	#41	1	2	yes	—
20	D₁₁	—	4	2	no	—
21	C₂×Q₈	D₁₁	1	1	yes	characteristic, complemented
22	C₂×D₄	—	11	1	no	—
23	C₂²⋊C₄	—	11	4	no	—
24	C₄²	—	11	1	no	—
25	C₁₁	#124	1	1	yes	characteristic, complemented, Sylow
26	C₂³	—	11	2	no	—
27	Q₈	—	2	2	no	—
28	D₄	—	22	2	no	—
29	C₂×C₄	—	11	2	no	—
30	C₂×C₄	C₂×D₁₁	1	2	yes	—
31	C₂×C₄	C₂×D₁₁	1	1	yes	characteristic
32	C₂²	—	22	4	no	—
33	C₂²	—	22	2	no	—
34	C₂²	C₂²×D₁₁	1	1	yes	characteristic
35	C₄	—	2	2	no	—
36	C₄	—	22	2	no	—
37	C₄	C₂²⋊D₁₁	1	2	yes	—
38	C₂	—	44	2	no	—
39	C₂	#4343	1	2	yes	—
40	C₂	C₂×C₂²⋊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.