Subgroups — #15692320

Order 3232.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13108084	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×#87938	C₂	1	1	yes	maximal, characteristic, complemented
3	#13108075	C₂	1	1	yes	maximal, characteristic
4	C₂×#87938	—	2	1	no	—
5	Q₈×C₁₀₁	C₄	1	1	yes	characteristic, complemented
6	D₄₀₄	—	2	1	no	—
7	D₄₀₄	C₄	1	1	yes	characteristic, complemented
8	C₄×D₁₀₁	—	2	1	no	—
9	C₄×D₁₀₁	C₂²	1	1	yes	characteristic
10	#11717581	—	2	1	no	—
11	C₂×D₁₀₁	—	2	1	no	—
12	C₂×D₁₀₁	D₄	1	1	yes	characteristic
13	#87938	—	2	2	no	—
14	C₄×C₁₀₁	—	2	1	no	—
15	C₄×C₁₀₁	C₂×C₄	1	1	yes	characteristic
16	Dic₁₀₁	D₄	1	1	yes	characteristic
17	C₂×C₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
18	D₁₀₁	—	2	1	no	—
19	D₁₀₁	—	4	1	no	—
20	C₁₀₁	#104	1	1	yes	characteristic, complemented, Sylow
21	#104	—	101	1	no	maximal, Sylow
22	#41	—	101	1	no	—
23	M₁₆	—	101	1	no	—
24	C₄²	—	101	1	no	—
25	Q₈	#87938	1	1	yes	characteristic, complemented
26	D₄	—	101	1	no	—
27	D₄	—	202	1	no	—
28	C₂×C₄	—	101	1	no	—
29	C₂×C₄	—	202	1	no	—
30	C₂×C₄	—	202	1	no	—
31	C₈	—	202	1	no	—
32	C₂²	—	101	1	no	—
33	C₂²	—	202	1	no	—
34	C₄	—	2	1	no	—
35	C₄	—	101	1	no	—
36	C₄	—	202	2	no	—
37	C₄	C₂×#87938	1	1	yes	characteristic
38	C₂	—	404	1	no	—
39	C₂	—	202	1	no	—
40	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.