Subgroups — #22549711

Order 8128.

34 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₂₀₃₂	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₂₇⋊C₃₂	C₂	1	1	yes	maximal, characteristic, complemented
3	D₁₆×C₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
4	D₁₀₁₆	—	2	1	no	—
5	D₈×C₁₂₇	—	2	1	no	—
6	C₁₆×C₁₂₇	C₂²	1	1	yes	characteristic
7	D₅₀₈	—	4	1	no	—
8	D₄×C₁₂₇	—	4	1	no	—
9	C₈×C₁₂₇	D₄	1	1	yes	characteristic
10	C₂²×C₁₂₇	—	8	1	no	—
11	C₂×D₁₂₇	—	8	1	no	—
12	C₄×C₁₂₇	D₈	1	1	yes	characteristic
13	C₂×C₁₂₇	—	16	1	no	—
14	C₂×C₁₂₇	D₁₆	1	1	yes	characteristic
15	D₁₂₇	—	16	1	no	—
16	C₁₂₇	D₃₂	1	1	yes	characteristic, complemented, Sylow
17	D₃₂	—	127	1	no	maximal, Sylow
18	D₁₆	—	127	1	no	—
19	D₁₆	D₁₂₇	1	1	yes	characteristic, complemented
20	C₃₂	—	127	1	no	—
21	D₈	—	2	1	no	—
22	D₈	—	254	1	no	—
23	C₁₆	C₂×D₁₂₇	1	1	yes	characteristic
24	D₄	—	4	1	no	—
25	D₄	—	508	1	no	—
26	C₈	C₂²⋊D₁₂₇	1	1	yes	characteristic
27	C₂²	—	8	1	no	—
28	C₂²	—	1016	1	no	—
29	C₄	#14523233	1	1	yes	characteristic
30	C₂	—	16	1	no	—
31	C₂	—	2032	1	no	—
32	C₂	#16861150	1	1	yes	characteristic

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