Subgroups — C₂×#16861152 #22550299

Order 8128.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₁₀₁₆	C₂	1	1	yes	maximal, characteristic
2	#16861152	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₁₂₇⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×Q₁₆×C₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×D₅₀₈	—	2	1	no	—
6	D₁₀₁₆	—	2	1	no	—
7	D₁₀₁₆	C₂²	1	2	yes	—
8	C₁₂₇⋊C₁₆	C₂²	1	2	yes	complemented
9	C₂×Q₈×C₁₂₇	—	2	1	no	—
10	Q₁₆×C₁₂₇	—	2	1	no	—
11	Q₁₆×C₁₂₇	C₂²	1	2	yes	complemented
12	C₂×C₈×C₁₂₇	C₂²	1	1	yes	characteristic
13	C₂²×D₁₂₇	—	4	1	no	—
14	D₅₀₈	—	2	2	no	—
15	D₅₀₈	—	4	1	no	—
16	Q₈×C₁₂₇	—	2	2	no	—
17	Q₈×C₁₂₇	—	4	1	no	—
18	C₂×C₄×C₁₂₇	—	4	1	no	—
19	C₂×C₄×C₁₂₇	D₄	1	1	yes	characteristic
20	C₈×C₁₂₇	D₄	1	1	yes	characteristic
21	C₈×C₁₂₇	C₂³	1	1	yes	characteristic
22	C₂²×C₁₂₇	D₈	1	1	yes	characteristic
23	C₂×D₁₂₇	—	4	2	no	—
24	C₂×D₁₂₇	—	8	2	no	—
25	C₄×C₁₂₇	—	4	2	no	—
26	C₄×C₁₂₇	D₈	1	1	yes	characteristic
27	C₄×C₁₂₇	C₂×D₄	1	1	yes	characteristic
28	C₂×C₁₂₇	SD₃₂	1	2	yes	complemented
29	C₂×C₁₂₇	C₂×D₈	1	1	yes	characteristic
30	D₁₂₇	—	8	2	no	—
31	C₁₂₇	C₂×SD₃₂	1	1	yes	characteristic, complemented, Sylow
32	C₂×SD₃₂	—	127	1	no	maximal, Sylow
33	C₂×Q₁₆	D₁₂₇	1	1	yes	characteristic, complemented
34	C₂×D₈	—	127	1	no	—
35	SD₃₂	—	127	4	no	—
36	C₂×C₁₆	—	127	1	no	—
37	C₂×Q₈	—	2	1	no	—
38	C₂×D₄	—	254	1	no	—
39	Q₁₆	—	2	1	no	—
40	Q₁₆	C₂×D₁₂₇	1	2	yes	complemented
41	D₈	—	127	2	no	—
42	D₈	—	254	1	no	—
43	C₂×C₈	C₂×D₁₂₇	1	1	yes	characteristic
44	C₁₆	—	127	2	no	—
45	C₂³	—	508	1	no	—
46	Q₈	—	2	2	no	—
47	Q₈	—	4	1	no	—
48	D₄	—	508	1	no	—
49	D₄	—	254	2	no	—
50	C₂×C₄	—	4	1	no	—
51	C₂×C₄	C₂²⋊D₁₂₇	1	1	yes	characteristic
52	C₈	C₂²⋊D₁₂₇	1	1	yes	characteristic
53	C₈	C₂²×D₁₂₇	1	1	yes	characteristic
54	C₂²	—	1016	2	no	—
55	C₂²	—	508	2	no	—
56	C₂²	#14523233	1	1	yes	characteristic
57	C₄	—	4	2	no	—
58	C₄	#14523233	1	1	yes	characteristic
59	C₄	C₂×C₂²⋊D₁₂₇	1	1	yes	characteristic
60	C₂	—	1016	2	no	—
61	C₂	#16861152	1	2	yes	direct product factor
62	C₂	C₂×#14523233	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#14523233
commutator	C₈×C₁₂₇	C₂³
Frattini	C₈	C₂²×D₁₂₇
Fitting	C₂×Q₁₆×C₁₂₇	C₂
socle	C₂²×C₁₂₇	D₈
hypercenter	C₂×Q₁₆	D₁₂₇
hypocenter	C₁₂₇	C₂×SD₃₂
LCS	G ▷ C₈×C₁₂₇ ▷ C₄×C₁₂₇ ▷ C₂×C₁₂₇ ▷ C₁₂₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×Q₁₆

Complements

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

N	H ≅ G/N	type
2. #16861152	C₂	direct (N × H)
3. C₂×C₁₂₇⋊C₁₆	C₂	semidirect
4. C₂×Q₁₆×C₁₂₇	C₂	semidirect
8. C₁₂₇⋊C₁₆	C₂²	semidirect
11. Q₁₆×C₁₂₇	C₂²	semidirect
28. C₂×C₁₂₇	SD₃₂	semidirect
31. C₁₂₇	C₂×SD₃₂	semidirect
33. C₂×Q₁₆	D₁₂₇	semidirect
40. Q₁₆	C₂×D₁₂₇	semidirect
61. C₂	#16861152	direct (N × H)

Subgroups — C2×#16861152 #22550299

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#16861152 #22550299