Subgroups — C₂×Q₈×D₆₆₁ #35232572

Order 21152.

156 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₁₃₂₂	C₂	1	3	yes	maximal, complemented
2	Q₈×D₆₆₁	C₂	1	8	yes	maximal, direct product factor
3	C₂×C₄×D₆₆₁	C₂	1	3	yes	maximal
4	C₂×Q₈×C₆₆₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×D₆₆₁	C₂²	1	1	yes	characteristic
6	Dic₁₃₂₂	C₂²	1	12	yes	complemented
7	C₂×Dic₆₆₁	C₂²	1	3	yes	—
8	C₄×D₆₆₁	C₂²	1	12	yes	—
9	Q₈×C₆₆₁	C₂²	1	4	yes	complemented
10	C₂×C₄×C₆₆₁	C₂²	1	3	yes	—
11	C₂²×C₆₆₁	C₂³	1	1	yes	characteristic
12	C₂×D₆₆₁	Q₈	1	4	yes	direct product factor
13	C₂×D₆₆₁	C₂³	1	2	yes	—
14	C₄×C₆₆₁	C₂³	1	6	yes	—
15	Dic₆₆₁	C₂³	1	6	yes	—
16	C₂×C₆₆₁	C₂×Q₈	1	2	yes	complemented
17	C₂×C₆₆₁	C₂⁴	1	1	yes	characteristic
18	D₆₆₁	C₂×Q₈	1	4	yes	direct product factor
19	C₆₆₁	C₂²×Q₈	1	1	yes	characteristic, complemented, Sylow
20	C₂²×Q₈	—	661	1	no	maximal, Sylow
21	C₂×Q₈	—	661	8	no	—
22	C₂×Q₈	—	661	3	no	—
23	C₂×Q₈	D₆₆₁	1	1	yes	characteristic, direct product factor
24	C₂²×C₄	—	661	3	no	—
25	C₂³	—	661	1	no	—
26	Q₈	—	661	12	no	—
27	Q₈	C₂×D₆₆₁	1	4	yes	direct product factor
28	C₂×C₄	—	661	3	no	—
29	C₂×C₄	—	661	12	no	—
30	C₂×C₄	C₂×D₆₆₁	1	3	yes	—
31	C₂²	—	661	4	no	—
32	C₂²	—	661	2	no	—
33	C₂²	C₂²×D₆₆₁	1	1	yes	characteristic
34	C₄	—	661	6	no	—
35	C₄	C₂²×D₆₆₁	1	6	yes	—
36	C₂	—	661	4	no	—
37	C₂	Q₈×D₆₆₁	1	2	yes	direct product factor
38	C₂	C₂³×D₆₆₁	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.