Subgroups — #27186302

Order 12928.

38 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20266016	C₂	1	2	yes	maximal, complemented
2	C₃₂×D₁₀₁	C₂	1	1	yes	maximal, characteristic
3	C₁₆×D₁₀₁	C₄	1	1	yes	characteristic
4	#15692161	C₂²	1	1	yes	characteristic
5	C₃₂×C₁₀₁	C₄	1	1	yes	characteristic
6	C₈×D₁₀₁	C₈	1	1	yes	characteristic
7	#13108049	C₈	1	1	yes	characteristic
8	C₁₆×C₁₀₁	C₂×C₄	1	1	yes	characteristic
9	C₄×D₁₀₁	C₁₆	1	1	yes	characteristic
10	C₈×C₁₀₁	C₂×C₈	1	1	yes	characteristic
11	#11717579	C₁₆	1	1	yes	characteristic
12	C₂×D₁₀₁	C₃₂	1	1	yes	characteristic
13	C₄×C₁₀₁	C₂×C₁₆	1	1	yes	characteristic
14	Dic₁₀₁	C₃₂	1	1	yes	characteristic
15	C₂×C₁₀₁	C₂×C₃₂	1	1	yes	characteristic
16	D₁₀₁	—	2	1	no	—
17	M₁₂₈	—	101	1	no	maximal, Sylow
18	C₁₀₁	M₁₂₈	1	1	yes	characteristic, complemented, Sylow
19	C₂×C₃₂	—	101	1	no	—
20	C₆₄	—	101	2	no	—
21	C₂×C₁₆	—	101	1	no	—
22	C₃₂	—	101	1	no	—
23	C₃₂	#87938	1	1	yes	characteristic
24	C₂×C₈	—	101	1	no	—
25	C₁₆	—	101	1	no	—
26	C₁₆	C₂×#87938	1	1	yes	characteristic
27	C₂×C₄	—	101	1	no	—
28	C₈	—	101	1	no	—
29	C₈	D₁₀₁⋊C₈	1	1	yes	characteristic
30	C₂²	—	101	1	no	—
31	C₄	—	101	1	no	—
32	C₄	D₁₀₁⋊C₁₆	1	1	yes	characteristic
33	C₂	—	202	1	no	—
34	C₂	D₁₀₁⋊C₃₂	1	1	yes	characteristic

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. #20266016	C₂	semidirect
18. C₁₀₁	M₁₂₈	semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.