Subgroups — #22549620

Order 8128.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊(C₁₂₇⋊C₈)	C₂	1	2	yes	maximal, complemented
2	#127×C₁₂₇	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₂₇⋊C₈	—	2	2	no	—
4	C₂×D₄×C₁₂₇	—	2	2	no	—
5	C₂×D₄×C₁₂₇	C₄	1	2	yes	—
6	C₄²×C₁₂₇	C₂²	1	1	yes	characteristic
7	C₁₂₇⋊C₈	—	4	2	no	—
8	C₂³×C₁₂₇	—	2	2	no	—
9	D₄×C₁₂₇	—	4	2	no	—
10	D₄×C₁₂₇	—	4	2	no	—
11	D₄×C₁₂₇	—	4	2	no	—
12	C₂×C₄×C₁₂₇	C₂×C₄	1	1	yes	characteristic
13	C₂×C₄×C₁₂₇	D₄	1	2	yes	—
14	C₂²×C₁₂₇	—	4	2	no	—
15	C₂²×C₁₂₇	—	4	4	no	—
16	C₂²×C₁₂₇	C₂²⋊C₄	1	1	yes	characteristic
17	C₄×C₁₂₇	—	2	1	no	—
18	C₄×C₁₂₇	D₈	1	2	yes	—
19	C₄×C₁₂₇	SD₁₆	1	2	yes	—
20	C₂×C₁₂₇	—	8	2	no	—
21	C₂×C₁₂₇	#100	1	1	yes	characteristic
22	C₂×C₁₂₇	#102	1	2	yes	—
23	C₁₂₇	#331	1	1	yes	characteristic, complemented, Sylow
24	#331	—	127	1	no	maximal, Sylow
25	#127	D₁₂₇	1	1	yes	characteristic
26	C₄⋊C₈	—	127	2	no	—
27	C₂×D₄	—	2	2	no	—
28	C₂×D₄	Dic₁₂₇	1	2	yes	—
29	C₂×C₈	—	254	2	no	—
30	C₄²	C₂×D₁₂₇	1	1	yes	characteristic
31	C₂³	—	2	2	no	—
32	D₄	—	4	2	no	—
33	D₄	—	4	2	no	—
34	D₄	—	4	2	no	—
35	C₂×C₄	C₂×Dic₁₂₇	1	1	yes	characteristic
36	C₂×C₄	C₂²⋊D₁₂₇	1	2	yes	—
37	C₈	—	508	2	no	—
38	C₂²	—	4	2	no	—
39	C₂²	—	4	4	no	—
40	C₂²	C₂²⋊Dic₁₂₇	1	1	yes	characteristic
41	C₄	—	2	1	no	—
42	C₄	#14523233	1	2	yes	—
43	C₄	#14523236	1	2	yes	—
44	C₂	—	8	2	no	—
45	C₂	#16861126	1	1	yes	characteristic
46	C₂	#16861130	1	2	yes	—

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

N	H ≅ G/N	type
1. C₄⋊(C₁₂₇⋊C₈)	C₂	semidirect
23. C₁₂₇	#331	semidirect