Subgroups — #21460988

Order 7808.

38 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16840601	C₂	1	2	yes	maximal, complemented
2	C₂×#14519683	C₂	1	1	yes	maximal, characteristic
3	#14519683	C₄	1	1	yes	characteristic
4	#14519683	C₂²	1	1	yes	characteristic
5	C₂×C₁₆×C₆₁	C₄	1	1	yes	characteristic
6	C₂×C₈×C₆₁	C₈	1	1	yes	characteristic
7	C₁₆×C₆₁	C₈	1	1	yes	characteristic
8	C₁₆×C₆₁	C₂×C₄	1	1	yes	characteristic
9	C₂×C₄×C₆₁	C₁₆	1	1	yes	characteristic
10	C₈×C₆₁	C₁₆	1	1	yes	characteristic
11	C₈×C₆₁	C₂×C₈	1	1	yes	characteristic
12	C₂²×C₆₁	C₃₂	1	1	yes	characteristic
13	C₄×C₆₁	C₃₂	1	1	yes	characteristic
14	C₄×C₆₁	C₂×C₁₆	1	1	yes	characteristic
15	M₁₂₈	—	61	1	no	maximal, Sylow
16	C₂×C₆₁	—	2	1	no	—
17	C₂×C₆₁	C₂×C₃₂	1	1	yes	characteristic
18	C₂×C₃₂	—	61	1	no	—
19	C₆₄	—	61	2	no	—
20	C₆₁	M₁₂₈	1	1	yes	characteristic, complemented, Sylow
21	C₂×C₁₆	#6923	1	1	yes	characteristic
22	C₃₂	—	61	1	no	—
23	C₃₂	—	61	1	no	—
24	C₂×C₈	#92420	1	1	yes	characteristic
25	C₁₆	#92420	1	1	yes	characteristic
26	C₁₆	C₂×#6923	1	1	yes	characteristic
27	C₂×C₄	#11758187	1	1	yes	characteristic
28	C₈	#11758187	1	1	yes	characteristic
29	C₈	C₂×#92420	1	1	yes	characteristic
30	C₂²	#14519827	1	1	yes	characteristic
31	C₄	#14519827	1	1	yes	characteristic
32	C₄	C₂×#11758187	1	1	yes	characteristic
33	C₂	—	2	1	no	—
34	C₂	C₂×#14519827	1	1	yes	characteristic

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

N	H ≅ G/N	type
1. #16840601	C₂	semidirect
20. C₆₁	M₁₂₈	semidirect