Subgroups — C₂×#16861206 #22550416

Order 8128.

498 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×D₅₀₈	C₂	1	6	yes	maximal, complemented
2	#16861206	C₂	1	8	yes	maximal, direct product factor
3	C₂×C₄²×C₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂³×D₁₂₇	C₂²	1	4	yes	—
5	C₂×D₅₀₈	—	2	24	no	—
6	C₂×D₅₀₈	C₂²	1	24	yes	complemented
7	C₂²×C₄×C₁₂₇	C₂²	1	3	yes	—
8	C₄²×C₁₂₇	C₂²	1	4	yes	complemented
9	C₂²×D₁₂₇	—	2	24	no	—
10	C₂²×D₁₂₇	C₂³	1	8	yes	—
11	D₅₀₈	—	2	48	no	—
12	C₂³×C₁₂₇	C₂³	1	1	yes	characteristic
13	C₂×C₄×C₁₂₇	D₄	1	12	yes	complemented
14	C₂×C₄×C₁₂₇	C₂³	1	6	yes	—
15	C₂²×C₁₂₇	C₂×D₄	1	6	yes	—
16	C₂²×C₁₂₇	C₂⁴	1	1	yes	characteristic
17	C₂×D₁₂₇	—	2	24	no	—
18	C₂×D₁₂₇	—	4	16	no	—
19	C₄×C₁₂₇	C₂×D₄	1	12	yes	complemented
20	C₂×C₁₂₇	#127	1	4	yes	complemented
21	C₂×C₁₂₇	C₂²×D₄	1	3	yes	—
22	D₁₂₇	—	4	8	no	—
23	C₁₂₇	C₂×#127	1	1	yes	characteristic, complemented, Sylow
24	C₂×#127	—	127	1	no	maximal, Sylow
25	C₂²×D₄	—	127	6	no	—
26	#127	—	127	8	no	—
27	C₂×C₄²	D₁₂₇	1	1	yes	characteristic, complemented
28	C₂⁴	—	127	4	no	—
29	C₂×D₄	—	127	24	no	—
30	C₂×D₄	—	254	24	no	—
31	C₂²×C₄	C₂×D₁₂₇	1	3	yes	—
32	C₄²	C₂×D₁₂₇	1	4	yes	complemented
33	C₂³	—	127	8	no	—
34	C₂³	—	254	24	no	—
35	C₂³	C₂²×D₁₂₇	1	1	yes	characteristic
36	D₄	—	254	48	no	—
37	C₂×C₄	D₅₀₈	1	12	yes	complemented
38	C₂×C₄	C₂²×D₁₂₇	1	6	yes	—
39	C₂²	—	508	16	no	—
40	C₂²	—	254	24	no	—
41	C₂²	C₂×D₅₀₈	1	6	yes	—
42	C₂²	C₂³×D₁₂₇	1	1	yes	characteristic
43	C₄	C₂×D₅₀₈	1	12	yes	complemented
44	C₂	—	508	8	no	—
45	C₂	#16861206	1	4	yes	direct product factor
46	C₂	C₂²×D₅₀₈	1	3	yes	—

	subgroup	G/H
center	C₂³	C₂²×D₁₂₇
commutator	C₂²×C₁₂₇	C₂⁴
Frattini	C₂²	C₂³×D₁₂₇
Fitting	C₂×C₄²×C₁₂₇	C₂
socle	C₂³×C₁₂₇	C₂³
hypercenter	C₂×C₄²	D₁₂₇
hypocenter	C₁₂₇	C₂×#127
LCS	G ▷ C₂²×C₁₂₇ ▷ C₁₂₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
1. C₂²×D₅₀₈	C₂	semidirect
2. #16861206	C₂	direct (N × H)
3. C₂×C₄²×C₁₂₇	C₂	semidirect
6. C₂×D₅₀₈	C₂²	semidirect
8. C₄²×C₁₂₇	C₂²	semidirect
13. C₂×C₄×C₁₂₇	D₄	semidirect
19. C₄×C₁₂₇	C₂×D₄	semidirect
20. C₂×C₁₂₇	#127	semidirect
23. C₁₂₇	C₂×#127	semidirect
27. C₂×C₄²	D₁₂₇	semidirect
32. C₄²	C₂×D₁₂₇	semidirect
37. C₂×C₄	D₅₀₈	semidirect
43. C₄	C₂×D₅₀₈	semidirect
45. C₂	#16861206	direct (N × H)

Subgroups — C2×#16861206 #22550416

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#16861206 #22550416