Subgroups — C₂×#22549702 #30640507

Order 16256.

168 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16861143	C₂	1	2	yes	maximal
2	#22549702	C₂	1	4	yes	maximal, direct product factor
3	C₂²×C₁₆×C₁₂₇	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄⋊Dic₁₂₇	—	2	2	no	—
5	#16861143	—	2	2	no	—
6	#16861143	C₂²	1	4	yes	—
7	C₂²×C₈×C₁₂₇	C₂²	1	1	yes	characteristic
8	C₂×C₁₆×C₁₂₇	C₄	1	4	yes	complemented
9	C₂×C₁₆×C₁₂₇	C₂²	1	2	yes	—
10	C₂²×Dic₁₂₇	—	4	2	no	—
11	C₄⋊Dic₁₂₇	—	2	4	no	—
12	C₄⋊Dic₁₂₇	—	4	2	no	—
13	C₂²×C₄×C₁₂₇	D₄	1	1	yes	characteristic
14	C₂×C₈×C₁₂₇	C₂×C₄	1	2	yes	—
15	C₂×C₈×C₁₂₇	D₄	1	1	yes	characteristic
16	C₂×C₈×C₁₂₇	Q₈	1	2	yes	—
17	C₂×C₈×C₁₂₇	C₂³	1	1	yes	characteristic
18	C₁₆×C₁₂₇	C₂×C₄	1	4	yes	complemented
19	C₂×Dic₁₂₇	—	4	4	no	—
20	C₂×Dic₁₂₇	—	8	4	no	—
21	C₂³×C₁₂₇	D₈	1	1	yes	characteristic
22	C₂×C₄×C₁₂₇	C₄⋊C₄	1	2	yes	—
23	C₂×C₄×C₁₂₇	D₈	1	1	yes	characteristic
24	C₂×C₄×C₁₂₇	Q₁₆	1	2	yes	—
25	C₂×C₄×C₁₂₇	C₂×D₄	1	1	yes	characteristic
26	C₈×C₁₂₇	C₄⋊C₄	1	2	yes	—
27	C₈×C₁₂₇	C₂²×C₄	1	1	yes	characteristic
28	C₈×C₁₂₇	C₂×Q₈	1	1	yes	characteristic
29	C₂²×C₁₂₇	#107	1	2	yes	—
30	C₂²×C₁₂₇	D₁₆	1	2	yes	—
31	C₂²×C₁₂₇	Q₃₂	1	2	yes	—
32	C₂²×C₁₂₇	C₂×D₈	1	1	yes	characteristic
33	C₄×C₁₂₇	#107	1	2	yes	—
34	C₄×C₁₂₇	C₂×C₄⋊C₄	1	1	yes	characteristic
35	C₄×C₁₂₇	C₂×Q₁₆	1	1	yes	characteristic
36	Dic₁₂₇	—	8	4	no	—
37	C₂×C₁₂₇	#366	1	4	yes	complemented
38	C₂×C₁₂₇	C₂×#107	1	1	yes	characteristic
39	C₂×C₁₂₇	C₂×D₁₆	1	1	yes	characteristic
40	C₂×C₁₂₇	C₂×Q₃₂	1	1	yes	characteristic
41	C₂×#366	—	127	1	no	maximal, Sylow
42	C₁₂₇	C₂×#366	1	1	yes	characteristic, complemented, Sylow
43	C₂²×C₁₆	D₁₂₇	1	1	yes	characteristic
44	C₂×#107	—	127	2	no	—
45	#366	—	127	4	no	—
46	C₂²×C₈	C₂×D₁₂₇	1	1	yes	characteristic
47	C₂×C₄⋊C₄	—	254	2	no	—
48	C₂×C₁₆	Dic₁₂₇	1	4	yes	complemented
49	C₂×C₁₆	C₂×D₁₂₇	1	2	yes	—
50	#107	—	127	4	no	—
51	#107	—	254	2	no	—
52	C₂²×C₄	—	508	2	no	—
53	C₂²×C₄	D₅₀₈	1	1	yes	characteristic
54	C₂×C₈	C₂×Dic₁₂₇	1	2	yes	—
55	C₂×C₈	D₅₀₈	1	1	yes	characteristic
56	C₂×C₈	Dic₂₅₄	1	2	yes	—
57	C₂×C₈	C₂²×D₁₂₇	1	1	yes	characteristic
58	C₄⋊C₄	—	508	2	no	—
59	C₄⋊C₄	—	254	4	no	—
60	C₁₆	C₂×Dic₁₂₇	1	4	yes	complemented
61	C₂³	D₁₀₁₆	1	1	yes	characteristic
62	C₂×C₄	—	1016	4	no	—
63	C₂×C₄	—	508	4	no	—
64	C₂×C₄	C₄⋊Dic₁₂₇	1	2	yes	—
65	C₂×C₄	D₁₀₁₆	1	1	yes	characteristic
66	C₂×C₄	Dic₅₀₈	1	2	yes	—
67	C₂×C₄	C₂×D₅₀₈	1	1	yes	characteristic
68	C₈	C₄⋊Dic₁₂₇	1	2	yes	—
69	C₈	C₂²×Dic₁₂₇	1	1	yes	characteristic
70	C₈	C₂×Dic₂₅₄	1	1	yes	characteristic
71	C₂²	#16861143	1	2	yes	—
72	C₂²	D₂₀₃₂	1	2	yes	—
73	C₂²	Dic₁₀₁₆	1	2	yes	—
74	C₂²	C₂×D₁₀₁₆	1	1	yes	characteristic
75	C₄	—	1016	4	no	—
76	C₄	#16861143	1	2	yes	—
77	C₄	C₂×C₄⋊Dic₁₂₇	1	1	yes	characteristic
78	C₄	C₂×Dic₅₀₈	1	1	yes	characteristic
79	C₂	#22549702	1	4	yes	direct product factor
80	C₂	C₂×#16861143	1	1	yes	characteristic
81	C₂	C₂×D₂₀₃₂	1	1	yes	characteristic
82	C₂	C₂×Dic₁₀₁₆	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	D₁₀₁₆
commutator	C₈×C₁₂₇	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₁₂₇
Fitting	C₂²×C₁₆×C₁₂₇	C₂
socle, prime radical	C₂³×C₁₂₇	D₈
cosocle	C₂×C₈×C₁₂₇	C₂³
hypercenter	C₂²×C₁₆	D₁₂₇
hypocenter	C₁₂₇	C₂×#366
LCS	G ▷ C₈×C₁₂₇ ▷ C₄×C₁₂₇ ▷ C₂×C₁₂₇ ▷ C₁₂₇
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×C₁₆

Complements

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

N	H ≅ G/N	type
2. #22549702	C₂	direct (N × H)
8. C₂×C₁₆×C₁₂₇	C₄	semidirect
18. C₁₆×C₁₂₇	C₂×C₄	semidirect
37. C₂×C₁₂₇	#366	semidirect
42. C₁₂₇	C₂×#366	semidirect
48. C₂×C₁₆	Dic₁₂₇	semidirect
60. C₁₆	C₂×Dic₁₂₇	semidirect
79. C₂	#22549702	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×#16861143	2
#22549702	2
C₂²×C₁₆×C₁₂₇	2
C₂×#366	127

Subgroups — C2×#22549702 #30640507

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#22549702 #30640507