Subgroups — C₂×#22549711 #30641027

Order 16256.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₂₀₃₂	C₂	1	1	yes	maximal, characteristic, complemented
2	#22549711	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₁₂₇⋊C₃₂	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₁₆×C₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×D₁₀₁₆	—	2	1	no	—
6	D₂₀₃₂	—	2	1	no	—
7	D₂₀₃₂	C₂²	1	2	yes	complemented
8	C₁₂₇⋊C₃₂	C₂²	1	2	yes	complemented
9	C₂×D₈×C₁₂₇	—	2	1	no	—
10	D₁₆×C₁₂₇	—	2	1	no	—
11	D₁₆×C₁₂₇	C₂²	1	2	yes	complemented
12	C₂×C₁₆×C₁₂₇	C₂²	1	1	yes	characteristic
13	C₂×D₅₀₈	—	4	1	no	—
14	D₁₀₁₆	—	2	2	no	—
15	D₁₀₁₆	—	4	1	no	—
16	C₂×D₄×C₁₂₇	—	4	1	no	—
17	D₈×C₁₂₇	—	2	2	no	—
18	D₈×C₁₂₇	—	4	1	no	—
19	C₂×C₈×C₁₂₇	D₄	1	1	yes	characteristic
20	C₁₆×C₁₂₇	D₄	1	1	yes	characteristic
21	C₁₆×C₁₂₇	C₂³	1	1	yes	characteristic
22	C₂²×D₁₂₇	—	8	1	no	—
23	D₅₀₈	—	4	2	no	—
24	D₅₀₈	—	8	1	no	—
25	C₂³×C₁₂₇	—	8	1	no	—
26	D₄×C₁₂₇	—	4	2	no	—
27	D₄×C₁₂₇	—	8	1	no	—
28	C₂×C₄×C₁₂₇	D₈	1	1	yes	characteristic
29	C₈×C₁₂₇	D₈	1	1	yes	characteristic
30	C₈×C₁₂₇	C₂×D₄	1	1	yes	characteristic
31	C₂²×C₁₂₇	—	8	2	no	—
32	C₂²×C₁₂₇	—	16	2	no	—
33	C₂²×C₁₂₇	D₁₆	1	1	yes	characteristic
34	C₂×D₁₂₇	—	8	2	no	—
35	C₂×D₁₂₇	—	16	2	no	—
36	C₄×C₁₂₇	D₁₆	1	1	yes	characteristic
37	C₄×C₁₂₇	C₂×D₈	1	1	yes	characteristic
38	C₂×C₁₂₇	—	16	2	no	—
39	C₂×C₁₂₇	D₃₂	1	2	yes	complemented
40	C₂×C₁₂₇	C₂×D₁₆	1	1	yes	characteristic
41	D₁₂₇	—	16	2	no	—
42	C₂×D₃₂	—	127	1	no	maximal, Sylow
43	C₁₂₇	C₂×D₃₂	1	1	yes	characteristic, complemented, Sylow
44	C₂×D₁₆	—	127	1	no	—
45	C₂×D₁₆	D₁₂₇	1	1	yes	characteristic, complemented
46	D₃₂	—	127	4	no	—
47	C₂×C₃₂	—	127	1	no	—
48	C₂×D₈	—	2	1	no	—
49	C₂×D₈	—	254	1	no	—
50	D₁₆	—	2	1	no	—
51	D₁₆	—	127	2	no	—
52	D₁₆	—	254	1	no	—
53	D₁₆	C₂×D₁₂₇	1	2	yes	complemented
54	C₂×C₁₆	C₂×D₁₂₇	1	1	yes	characteristic
55	C₃₂	—	127	2	no	—
56	C₂×D₄	—	4	1	no	—
57	C₂×D₄	—	508	1	no	—
58	D₈	—	2	2	no	—
59	D₈	—	4	1	no	—
60	D₈	—	508	1	no	—
61	D₈	—	254	2	no	—
62	C₂×C₈	C₂²⋊D₁₂₇	1	1	yes	characteristic
63	C₁₆	C₂²⋊D₁₂₇	1	1	yes	characteristic
64	C₁₆	C₂²×D₁₂₇	1	1	yes	characteristic
65	C₂³	—	8	1	no	—
66	C₂³	—	1016	1	no	—
67	D₄	—	4	2	no	—
68	D₄	—	8	1	no	—
69	D₄	—	1016	1	no	—
70	D₄	—	508	2	no	—
71	C₂×C₄	#14523233	1	1	yes	characteristic
72	C₈	#14523233	1	1	yes	characteristic
73	C₈	C₂×C₂²⋊D₁₂₇	1	1	yes	characteristic
74	C₂²	—	8	2	no	—
75	C₂²	—	16	2	no	—
76	C₂²	—	2032	2	no	—
77	C₂²	—	1016	2	no	—
78	C₂²	#16861150	1	1	yes	characteristic
79	C₄	#16861150	1	1	yes	characteristic
80	C₄	C₂×#14523233	1	1	yes	characteristic
81	C₂	—	16	2	no	—
82	C₂	—	2032	2	no	—
83	C₂	#22549711	1	2	yes	direct product factor
84	C₂	C₂×#16861150	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#16861150
commutator, cosocle	C₁₆×C₁₂₇	C₂³
Frattini	C₁₆	C₂²×D₁₂₇
Fitting	C₂×D₁₆×C₁₂₇	C₂
socle	C₂²×C₁₂₇	D₁₆
hypercenter	C₂×D₁₆	D₁₂₇
hypocenter	C₁₂₇	C₂×D₃₂
LCS	G ▷ C₁₆×C₁₂₇ ▷ C₈×C₁₂₇ ▷ C₄×C₁₂₇ ▷ C₂×C₁₂₇ ▷ C₁₂₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×D₁₆

Complements

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

N	H ≅ G/N	type
1. C₂×D₂₀₃₂	C₂	semidirect
2. #22549711	C₂	direct (N × H)
3. C₂×C₁₂₇⋊C₃₂	C₂	semidirect
4. C₂×D₁₆×C₁₂₇	C₂	semidirect
7. D₂₀₃₂	C₂²	semidirect
8. C₁₂₇⋊C₃₂	C₂²	semidirect
11. D₁₆×C₁₂₇	C₂²	semidirect
39. C₂×C₁₂₇	D₃₂	semidirect
43. C₁₂₇	C₂×D₃₂	semidirect
45. C₂×D₁₆	D₁₂₇	semidirect
53. D₁₆	C₂×D₁₂₇	semidirect
83. C₂	#22549711	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×D₂₀₃₂	2
#22549711	2
C₂×C₁₂₇⋊C₃₂	2
C₂×D₁₆×C₁₂₇	2
C₂×D₃₂	127

Subgroups — C2×#22549711 #30641027

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#22549711 #30641027