Subgroups — C₂×C₂²⋊Dic₁₁ #67005

Order 352.

132 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

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.