Subgroups — Q₈×D₁₃₂₇ #35234776

Order 21232.

38 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₂₆₅₄	C₂	1	3	yes	maximal, complemented
2	C₄×D₁₃₂₇	C₂	1	3	yes	maximal
3	Q₈×C₁₃₂₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₁₃₂₇	C₂²	1	1	yes	characteristic
5	C₄×C₁₃₂₇	C₂²	1	3	yes	—
6	Dic₁₃₂₇	C₂²	1	3	yes	—
7	C₂×C₁₃₂₇	C₂³	1	1	yes	characteristic
8	D₁₃₂₇	Q₈	1	2	yes	direct product factor
9	C₁₃₂₇	C₂×Q₈	1	1	yes	characteristic, complemented, Sylow
10	C₂×Q₈	—	1327	1	no	maximal, Sylow
11	Q₈	—	1327	3	no	—
12	Q₈	D₁₃₂₇	1	1	yes	characteristic, direct product factor
13	C₂×C₄	—	1327	3	no	—
14	C₂²	—	1327	1	no	—
15	C₄	—	1327	3	no	—
16	C₄	C₂×D₁₃₂₇	1	3	yes	—
17	C₂	—	1327	2	no	—
18	C₂	C₂²×D₁₃₂₇	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.