Subgroups — #22549702

Order 8128.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16861143	C₂	1	2	yes	maximal
2	C₂×C₁₆×C₁₂₇	C₂	1	1	yes	maximal, characteristic
3	C₄⋊Dic₁₂₇	—	2	2	no	—
4	C₂×C₈×C₁₂₇	C₂²	1	1	yes	characteristic
5	C₁₆×C₁₂₇	C₄	1	2	yes	complemented
6	C₂×Dic₁₂₇	—	4	2	no	—
7	C₂×C₄×C₁₂₇	D₄	1	1	yes	characteristic
8	C₈×C₁₂₇	C₂×C₄	1	1	yes	characteristic
9	C₈×C₁₂₇	Q₈	1	1	yes	characteristic
10	C₂²×C₁₂₇	D₈	1	1	yes	characteristic
11	C₄×C₁₂₇	C₄⋊C₄	1	1	yes	characteristic
12	C₄×C₁₂₇	Q₁₆	1	1	yes	characteristic
13	Dic₁₂₇	—	8	2	no	—
14	C₂×C₁₂₇	#107	1	1	yes	characteristic
15	C₂×C₁₂₇	D₁₆	1	1	yes	characteristic
16	C₂×C₁₂₇	Q₃₂	1	1	yes	characteristic
17	C₁₂₇	#366	1	1	yes	characteristic, complemented, Sylow
18	#366	—	127	1	no	maximal, Sylow
19	C₂×C₁₆	D₁₂₇	1	1	yes	characteristic
20	#107	—	127	2	no	—
21	C₂×C₈	C₂×D₁₂₇	1	1	yes	characteristic
22	C₄⋊C₄	—	254	2	no	—
23	C₁₆	Dic₁₂₇	1	2	yes	complemented
24	C₂×C₄	—	508	2	no	—
25	C₂×C₄	D₅₀₈	1	1	yes	characteristic
26	C₈	C₂×Dic₁₂₇	1	1	yes	characteristic
27	C₈	Dic₂₅₄	1	1	yes	characteristic
28	C₂²	D₁₀₁₆	1	1	yes	characteristic
29	C₄	—	1016	2	no	—
30	C₄	C₄⋊Dic₁₂₇	1	1	yes	characteristic
31	C₄	Dic₅₀₈	1	1	yes	characteristic
32	C₂	#16861143	1	1	yes	characteristic
33	C₂	D₂₀₃₂	1	1	yes	characteristic
34	C₂	Dic₁₀₁₆	1	1	yes	characteristic

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