Subgroups — C₂×C₄⋊Dic₁₁ #66978

Order 352.

92 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	—	2	4	no	—
8	C₂×Dic₁₁	C₂²	1	4	yes	—
9	C₂²×C₁₁	C₂×C₄	1	2	yes	—
10	C₂²×C₁₁	D₄	1	2	yes	—
11	C₂²×C₁₁	Q₈	1	2	yes	—
12	C₂²×C₁₁	C₂³	1	1	yes	characteristic
13	C₄×C₁₁	C₂×C₄	1	4	yes	complemented
14	Dic₁₁	—	2	4	no	—
15	C₂×C₄⋊C₄	—	11	1	no	maximal, Sylow
16	C₂×C₁₁	C₄⋊C₄	1	4	yes	complemented
17	C₂×C₁₁	C₂²×C₄	1	1	yes	characteristic
18	C₂×C₁₁	C₂×D₄	1	1	yes	characteristic
19	C₂×C₁₁	C₂×Q₈	1	1	yes	characteristic
20	C₂²×C₄	—	11	2	no	—
21	C₂²×C₄	D₁₁	1	1	yes	characteristic
22	C₄⋊C₄	—	11	4	no	—
23	C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic, complemented, Sylow
24	C₂³	C₂×D₁₁	1	1	yes	characteristic
25	C₂×C₄	—	11	4	no	—
26	C₂×C₄	—	22	4	no	—
27	C₂×C₄	Dic₁₁	1	4	yes	complemented
28	C₂×C₄	C₂×D₁₁	1	2	yes	—
29	C₂²	Dic₂₂	1	2	yes	—
30	C₂²	D₄₄	1	2	yes	—
31	C₂²	C₂×Dic₁₁	1	2	yes	—
32	C₂²	C₂²×D₁₁	1	1	yes	characteristic
33	C₄	—	22	4	no	—
34	C₄	C₂×Dic₁₁	1	4	yes	complemented
35	C₂	C₄⋊Dic₁₁	1	4	yes	direct product factor
36	C₂	C₂×Dic₂₂	1	1	yes	characteristic
37	C₂	C₂×D₄₄	1	1	yes	characteristic
38	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.