Subgroups — Q₈×#87938 #15692336

Order 3232.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#87938	C₂	1	3	yes	maximal
2	C₄×#87938	C₂	1	3	yes	maximal
3	Q₈×D₁₀₁	C₂	1	1	yes	maximal, characteristic
4	C₂×#87938	C₂²	1	3	yes	—
5	C₂×#87938	C₂²	1	1	yes	characteristic
6	Q₈×C₁₀₁	C₄	1	1	yes	characteristic, complemented
7	C₄×D₁₀₁	C₂²	1	3	yes	—
8	Dic₂₀₂	C₄	1	3	yes	complemented
9	C₂×D₁₀₁	C₂³	1	1	yes	characteristic
10	#87938	—	2	3	no	—
11	#87938	Q₈	1	2	yes	direct product factor
12	C₄×C₁₀₁	C₂×C₄	1	3	yes	—
13	Dic₁₀₁	C₂×C₄	1	3	yes	—
14	C₂×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
15	D₁₀₁	C₂×Q₈	1	1	yes	characteristic
16	D₁₀₁	#41	1	1	yes	characteristic
17	C₁₀₁	C₄×Q₈	1	1	yes	characteristic, complemented, Sylow
18	C₄×Q₈	—	101	1	no	maximal, Sylow
19	C₂×Q₈	—	101	1	no	—
20	C₄⋊C₄	—	101	3	no	—
21	C₄²	—	101	3	no	—
22	Q₈	—	101	3	no	—
23	Q₈	#87938	1	1	yes	characteristic, direct product factor
24	C₂×C₄	—	101	1	no	—
25	C₂×C₄	—	101	3	no	—
26	C₂×C₄	—	101	3	no	—
27	C₂²	—	101	1	no	—
28	C₄	—	101	2	no	—
29	C₄	—	101	3	no	—
30	C₄	—	202	3	no	—
31	C₄	C₂×#87938	1	3	yes	—
32	C₂	—	101	1	no	—
33	C₂	—	101	1	no	—
34	C₂	C₂²×#87938	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.