Subgroups — C₂×Q₈×D₁₁ #67038

Order 352.

156 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	Q₈×D₁₁	C₂	1	8	yes	maximal, direct product factor
3	C₂×C₄×D₁₁	C₂	1	3	yes	maximal
4	C₂×Dic₂₂	C₂	1	3	yes	maximal, complemented
5	C₂²×D₁₁	C₂²	1	1	yes	characteristic
6	Q₈×C₁₁	C₂²	1	4	yes	complemented
7	C₂×C₄×C₁₁	C₂²	1	3	yes	—
8	C₂×Dic₁₁	C₂²	1	3	yes	—
9	C₄×D₁₁	C₂²	1	12	yes	—
10	Dic₂₂	C₂²	1	12	yes	complemented
11	C₂²×C₁₁	C₂³	1	1	yes	characteristic
12	C₂×D₁₁	Q₈	1	4	yes	direct product factor
13	C₂×D₁₁	C₂³	1	2	yes	—
14	C₄×C₁₁	C₂³	1	6	yes	—
15	Dic₁₁	C₂³	1	6	yes	—
16	C₂²×Q₈	—	11	1	no	maximal, Sylow
17	C₂×C₁₁	C₂×Q₈	1	2	yes	complemented
18	C₂×C₁₁	C₂⁴	1	1	yes	characteristic
19	D₁₁	C₂×Q₈	1	4	yes	direct product factor
20	C₂×Q₈	—	11	8	no	—
21	C₂×Q₈	—	11	3	no	—
22	C₂×Q₈	D₁₁	1	1	yes	characteristic, direct product factor
23	C₂²×C₄	—	11	3	no	—
24	C₁₁	C₂²×Q₈	1	1	yes	characteristic, complemented, Sylow
25	C₂³	—	11	1	no	—
26	Q₈	—	11	12	no	—
27	Q₈	C₂×D₁₁	1	4	yes	direct product factor
28	C₂×C₄	—	11	3	no	—
29	C₂×C₄	—	11	12	no	—
30	C₂×C₄	C₂×D₁₁	1	3	yes	—
31	C₂²	—	11	4	no	—
32	C₂²	—	11	2	no	—
33	C₂²	C₂²×D₁₁	1	1	yes	characteristic
34	C₄	—	11	6	no	—
35	C₄	C₂²×D₁₁	1	6	yes	—
36	C₂	—	11	4	no	—
37	C₂	Q₈×D₁₁	1	2	yes	direct product factor
38	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.