Subgroups — #27186301

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	C₂×#15692161	C₂	1	1	yes	maximal, characteristic
3	#15692161	C₄	1	1	yes	characteristic
4	#15692161	C₂²	1	1	yes	characteristic
5	C₂×C₁₆×C₁₀₁	C₄	1	1	yes	characteristic
6	C₂×C₈×C₁₀₁	C₈	1	1	yes	characteristic
7	C₁₆×C₁₀₁	C₈	1	1	yes	characteristic
8	C₁₆×C₁₀₁	C₂×C₄	1	1	yes	characteristic
9	C₂×C₄×C₁₀₁	C₁₆	1	1	yes	characteristic
10	C₈×C₁₀₁	C₁₆	1	1	yes	characteristic
11	C₈×C₁₀₁	C₂×C₈	1	1	yes	characteristic
12	C₂²×C₁₀₁	C₃₂	1	1	yes	characteristic
13	C₄×C₁₀₁	C₃₂	1	1	yes	characteristic
14	C₄×C₁₀₁	C₂×C₁₆	1	1	yes	characteristic
15	C₂×C₁₀₁	—	2	1	no	—
16	C₂×C₁₀₁	C₂×C₃₂	1	1	yes	characteristic
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	#87938	1	1	yes	characteristic
22	C₃₂	—	101	1	no	—
23	C₃₂	—	101	1	no	—
24	C₂×C₈	#11717581	1	1	yes	characteristic
25	C₁₆	#11717581	1	1	yes	characteristic
26	C₁₆	C₂×#87938	1	1	yes	characteristic
27	C₂×C₄	#13108077	1	1	yes	characteristic
28	C₈	#13108077	1	1	yes	characteristic
29	C₈	C₂×#11717581	1	1	yes	characteristic
30	C₂²	#15692305	1	1	yes	characteristic
31	C₄	#15692305	1	1	yes	characteristic
32	C₄	C₂×#13108077	1	1	yes	characteristic
33	C₂	—	2	1	no	—
34	C₂	C₂×#15692305	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.