Subgroups — #22550274

Order 8128.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16861209	C₂	1	2	yes	maximal
2	#16861141	C₂	1	4	yes	maximal
3	C₄×C₈×C₁₂₇	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₂₅₄	—	2	2	no	—
5	C₄⋊Dic₁₂₇	—	2	2	no	—
6	C₄⋊Dic₁₂₇	C₂²	1	4	yes	—
7	C₂×C₈×C₁₂₇	C₂²	1	2	yes	—
8	C₄²×C₁₂₇	C₂²	1	1	yes	characteristic
9	Dic₂₅₄	—	4	4	no	—
10	C₂×Dic₁₂₇	—	2	4	no	—
11	C₂×C₄×C₁₂₇	D₄	1	2	yes	—
12	C₂×C₄×C₁₂₇	C₂³	1	1	yes	characteristic
13	C₈×C₁₂₇	Q₈	1	4	yes	complemented
14	C₂²×C₁₂₇	C₂×D₄	1	1	yes	characteristic
15	C₄×C₁₂₇	SD₁₆	1	4	yes	—
16	C₄×C₁₂₇	C₂×Q₈	1	2	yes	—
17	Dic₁₂₇	—	4	4	no	—
18	C₂×C₁₂₇	C₄⋊Q₈	1	1	yes	characteristic
19	C₂×C₁₂₇	C₂×SD₁₆	1	2	yes	—
20	C₁₂₇	#498	1	1	yes	characteristic, complemented, Sylow
21	#498	—	127	1	no	maximal, Sylow
22	C₄⋊Q₈	—	127	2	no	—
23	#106	—	127	4	no	—
24	C₄×C₈	D₁₂₇	1	1	yes	characteristic
25	C₂×Q₈	—	254	2	no	—
26	C₂×C₈	C₂×D₁₂₇	1	2	yes	—
27	C₄⋊C₄	—	127	4	no	—
28	C₄⋊C₄	—	254	2	no	—
29	C₄²	C₂×D₁₂₇	1	1	yes	characteristic
30	Q₈	—	508	4	no	—
31	C₂×C₄	—	254	4	no	—
32	C₂×C₄	D₅₀₈	1	2	yes	—
33	C₂×C₄	C₂²×D₁₂₇	1	1	yes	characteristic
34	C₈	Dic₂₅₄	1	4	yes	complemented
35	C₂²	C₂×D₅₀₈	1	1	yes	characteristic
36	C₄	—	508	4	no	—
37	C₄	#14523237	1	4	yes	—
38	C₄	C₂×Dic₂₅₄	1	2	yes	—
39	C₂	#16861209	1	1	yes	characteristic
40	C₂	C₂×#14523237	1	2	yes	—

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