Subgroups — C₂×C₄×Dic₁₁ #66975

Order 352.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×C₁₁	C₂	1	1	yes	maximal, characteristic
2	C₂²×Dic₁₁	C₂	1	2	yes	maximal
3	C₄×Dic₁₁	C₂	1	4	yes	maximal, direct product factor
4	C₂³×C₁₁	C₂²	1	1	yes	characteristic
5	C₂×C₄×C₁₁	C₄	1	4	yes	complemented
6	C₂×C₄×C₁₁	C₂²	1	2	yes	—
7	C₂×Dic₁₁	C₄	1	8	yes	direct product factor
8	C₂×Dic₁₁	C₂²	1	4	yes	—
9	C₂²×C₁₁	C₂×C₄	1	4	yes	—
10	C₂²×C₁₁	C₂×C₄	1	2	yes	—
11	C₂²×C₁₁	C₂³	1	1	yes	characteristic
12	C₄×C₁₁	C₂×C₄	1	4	yes	complemented
13	Dic₁₁	C₂×C₄	1	8	yes	direct product factor
14	C₂×C₄²	—	11	1	no	maximal, Sylow
15	C₂×C₁₁	C₄²	1	4	yes	complemented
16	C₂×C₁₁	C₂²×C₄	1	2	yes	—
17	C₂×C₁₁	C₂²×C₄	1	1	yes	characteristic
18	C₂²×C₄	—	11	2	no	—
19	C₂²×C₄	D₁₁	1	1	yes	characteristic
20	C₄²	—	11	4	no	—
21	C₁₁	C₂×C₄²	1	1	yes	characteristic, complemented, Sylow
22	C₂³	C₂×D₁₁	1	1	yes	characteristic
23	C₂×C₄	—	11	4	no	—
24	C₂×C₄	—	11	8	no	—
25	C₂×C₄	Dic₁₁	1	4	yes	direct product factor
26	C₂×C₄	C₂×D₁₁	1	2	yes	—
27	C₂²	C₄×D₁₁	1	4	yes	—
28	C₂²	C₂×Dic₁₁	1	2	yes	—
29	C₂²	C₂²×D₁₁	1	1	yes	characteristic
30	C₄	—	11	8	no	—
31	C₄	C₂×Dic₁₁	1	4	yes	direct product factor
32	C₂	C₄×Dic₁₁	1	4	yes	direct product factor
33	C₂	C₂×C₄×D₁₁	1	2	yes	—
34	C₂	C₂²×Dic₁₁	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.