Subgroups — C₂×#16861155 #22550303

Order 8128.

82 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₅₀₈	C₂	1	1	yes	maximal, characteristic
2	#16861155	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₁₂₇⋊C₁₆	C₂	1	1	yes	maximal, characteristic
4	C₂×Q₁₆×C₁₂₇	C₂	1	1	yes	maximal, characteristic
5	C₂×Dic₂₅₄	—	2	1	no	—
6	Dic₅₀₈	—	2	1	no	—
7	Dic₅₀₈	C₂²	1	2	yes	—
8	C₁₂₇⋊C₁₆	C₂²	1	2	yes	—
9	C₂×Q₈×C₁₂₇	—	2	1	no	—
10	Q₁₆×C₁₂₇	—	2	1	no	—
11	Q₁₆×C₁₂₇	C₂²	1	2	yes	—
12	C₂×C₈×C₁₂₇	C₂²	1	1	yes	characteristic
13	Dic₂₅₄	—	2	2	no	—
14	Dic₂₅₄	—	4	1	no	—
15	C₂×Dic₁₂₇	—	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	C₄×C₁₂₇	—	4	2	no	—
24	C₄×C₁₂₇	D₈	1	1	yes	characteristic
25	C₄×C₁₂₇	C₂×D₄	1	1	yes	characteristic
26	Dic₁₂₇	—	4	2	no	—
27	C₂×C₁₂₇	Q₃₂	1	2	yes	complemented
28	C₂×C₁₂₇	C₂×D₈	1	1	yes	characteristic
29	C₁₂₇	C₂×Q₃₂	1	1	yes	characteristic, complemented, Sylow
30	C₂×Q₃₂	—	127	1	no	maximal, Sylow
31	C₂×Q₁₆	—	127	1	no	—
32	C₂×Q₁₆	D₁₂₇	1	1	yes	characteristic
33	Q₃₂	—	127	4	no	—
34	C₂×C₁₆	—	127	1	no	—
35	C₂×Q₈	—	2	1	no	—
36	C₂×Q₈	—	254	1	no	—
37	Q₁₆	—	2	1	no	—
38	Q₁₆	—	127	2	no	—
39	Q₁₆	—	254	1	no	—
40	Q₁₆	C₂×D₁₂₇	1	2	yes	—
41	C₂×C₈	C₂×D₁₂₇	1	1	yes	characteristic
42	C₁₆	—	127	2	no	—
43	Q₈	—	2	2	no	—
44	Q₈	—	4	1	no	—
45	Q₈	—	508	1	no	—
46	Q₈	—	254	2	no	—
47	C₂×C₄	—	4	1	no	—
48	C₂×C₄	—	508	1	no	—
49	C₂×C₄	C₂²⋊D₁₂₇	1	1	yes	characteristic
50	C₈	C₂²⋊D₁₂₇	1	1	yes	characteristic
51	C₈	C₂²×D₁₂₇	1	1	yes	characteristic
52	C₂²	#14523233	1	1	yes	characteristic
53	C₄	—	4	2	no	—
54	C₄	—	508	2	no	—
55	C₄	#14523233	1	1	yes	characteristic
56	C₄	C₂×C₂²⋊D₁₂₇	1	1	yes	characteristic
57	C₂	#16861155	1	2	yes	direct product factor
58	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×Q₃₂
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. #16861155	C₂	direct (N × H)
27. C₂×C₁₂₇	Q₃₂	semidirect
29. C₁₂₇	C₂×Q₃₂	semidirect
57. C₂	#16861155	direct (N × H)

Subgroups — C2×#16861155 #22550303

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#16861155 #22550303