Subgroups — Q₈×D₁₂₁ #14515439

Order 1936.

57 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×C₁₂₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×D₁₂₁	C₂	1	3	yes	maximal
3	Dic₂₄₂	C₂	1	3	yes	maximal, complemented
4	C₂×D₁₂₁	C₂²	1	1	yes	characteristic
5	C₄×C₁₂₁	C₂²	1	3	yes	—
6	Dic₁₂₁	C₂²	1	3	yes	—
7	C₂×C₁₂₁	C₂³	1	1	yes	characteristic
8	D₁₂₁	Q₈	1	2	yes	direct product factor
9	Q₈×D₁₁	—	11	1	no	maximal
10	C₁₂₁	C₂×Q₈	1	1	yes	characteristic, complemented, Sylow
11	Q₈×C₁₁	D₁₁	1	1	yes	characteristic
12	C₄×D₁₁	—	11	3	no	—
13	Dic₂₂	—	11	3	no	—
14	C₂×D₁₁	—	11	1	no	—
15	C₄×C₁₁	C₂×D₁₁	1	3	yes	—
16	Dic₁₁	—	11	3	no	—
17	C₂×C₁₁	C₂²×D₁₁	1	1	yes	characteristic
18	D₁₁	—	11	2	no	—
19	C₂×Q₈	—	121	1	no	Sylow
20	C₁₁	Q₈×D₁₁	1	1	yes	characteristic
21	Q₈	—	121	3	no	—
22	Q₈	D₁₂₁	1	1	yes	characteristic, direct product factor
23	C₂×C₄	—	121	3	no	—
24	C₂²	—	121	1	no	—
25	C₄	—	121	3	no	—
26	C₄	C₂×D₁₂₁	1	3	yes	—
27	C₂	—	121	2	no	—
28	C₂	C₂²×D₁₂₁	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.