Subgroups — C₂×#21460989 #30608593

Order 15616.

134 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21460989	C₂	1	4	yes	maximal, direct product factor
2	C₂×#16840601	C₂	1	2	yes	maximal, complemented
3	C₂×C₃₂×D₆₁	C₂	1	1	yes	maximal, characteristic
4	#16840601	C₂²	1	4	yes	complemented
5	C₂×C₁₆×D₆₁	C₄	1	1	yes	characteristic
6	C₂×#14519683	C₂²	1	1	yes	characteristic
7	C₃₂×D₆₁	C₄	1	2	yes	—
8	C₃₂×D₆₁	C₂²	1	2	yes	—
9	C₂×C₃₂×C₆₁	C₄	1	1	yes	characteristic
10	C₂×C₈×D₆₁	C₈	1	1	yes	characteristic
11	C₂×#11758185	C₈	1	1	yes	characteristic
12	C₁₆×D₆₁	C₈	1	2	yes	—
13	C₁₆×D₆₁	C₂×C₄	1	2	yes	—
14	#14519683	C₂×C₄	1	1	yes	characteristic
15	#14519683	C₂³	1	1	yes	characteristic
16	C₂×C₁₆×C₆₁	C₂×C₄	1	1	yes	characteristic
17	C₃₂×C₆₁	C₂×C₄	1	2	yes	—
18	C₂×C₄×D₆₁	C₁₆	1	1	yes	characteristic
19	C₂×C₈×C₆₁	C₂×C₈	1	1	yes	characteristic
20	C₂×#92418	C₁₆	1	1	yes	characteristic
21	C₈×D₆₁	C₁₆	1	2	yes	—
22	C₈×D₆₁	C₂×C₈	1	2	yes	—
23	C₁₆×C₆₁	C₂×C₈	1	1	yes	characteristic
24	C₁₆×C₆₁	C₂²×C₄	1	1	yes	characteristic
25	#11758185	C₂×C₈	1	2	yes	—
26	C₂²×D₆₁	C₃₂	1	1	yes	characteristic
27	C₂×C₄×C₆₁	C₂×C₁₆	1	1	yes	characteristic
28	C₂×Dic₆₁	C₃₂	1	1	yes	characteristic
29	C₄×D₆₁	C₃₂	1	2	yes	—
30	C₄×D₆₁	C₂×C₁₆	1	2	yes	—
31	C₈×C₆₁	C₂×C₁₆	1	1	yes	characteristic
32	C₈×C₆₁	C₂²×C₈	1	1	yes	characteristic
33	#92418	C₂×C₁₆	1	2	yes	—
34	C₂×M₁₂₈	—	61	1	no	maximal, Sylow
35	C₂²×C₆₁	C₂×C₃₂	1	1	yes	characteristic
36	C₂×D₆₁	—	2	2	no	—
37	C₂×D₆₁	C₂×C₃₂	1	2	yes	—
38	C₄×C₆₁	C₂×C₃₂	1	1	yes	characteristic
39	C₄×C₆₁	C₂²×C₁₆	1	1	yes	characteristic
40	Dic₆₁	C₂×C₃₂	1	2	yes	—
41	C₂²×C₃₂	—	61	1	no	—
42	M₁₂₈	—	61	4	no	—
43	C₂×C₆₄	—	61	2	no	—
44	C₂×C₆₁	M₁₂₈	1	2	yes	complemented
45	C₂×C₆₁	C₂²×C₃₂	1	1	yes	characteristic
46	D₆₁	—	2	2	no	—
47	C₂²×C₁₆	—	61	1	no	—
48	C₂×C₃₂	—	61	1	no	—
49	C₂×C₃₂	—	61	2	no	—
50	C₂×C₃₂	—	61	2	no	—
51	C₂×C₃₂	#6923	1	1	yes	characteristic
52	C₆₄	—	61	4	no	—
53	C₆₁	C₂×M₁₂₈	1	1	yes	characteristic, complemented, Sylow
54	C₂²×C₈	—	61	1	no	—
55	C₂×C₁₆	—	61	1	no	—
56	C₂×C₁₆	—	61	2	no	—
57	C₂×C₁₆	—	61	2	no	—
58	C₂×C₁₆	C₂×#6923	1	1	yes	characteristic
59	C₃₂	—	61	1	no	—
60	C₃₂	—	61	1	no	—
61	C₃₂	C₂×#6923	1	2	yes	—
62	C₂²×C₄	—	61	1	no	—
63	C₂×C₈	—	61	1	no	—
64	C₂×C₈	—	61	2	no	—
65	C₂×C₈	—	61	2	no	—
66	C₂×C₈	D₆₁⋊C₈	1	1	yes	characteristic
67	C₁₆	—	61	2	no	—
68	C₁₆	D₆₁⋊C₈	1	1	yes	characteristic
69	C₁₆	C₂²×#6923	1	1	yes	characteristic
70	C₂³	—	61	1	no	—
71	C₂×C₄	—	61	1	no	—
72	C₂×C₄	—	61	2	no	—
73	C₂×C₄	—	61	2	no	—
74	C₂×C₄	D₆₁⋊C₁₆	1	1	yes	characteristic
75	C₈	—	61	2	no	—
76	C₈	D₆₁⋊C₁₆	1	1	yes	characteristic
77	C₈	C₂×D₆₁⋊C₈	1	1	yes	characteristic
78	C₂²	—	61	2	no	—
79	C₂²	—	122	2	no	—
80	C₂²	D₆₁⋊C₃₂	1	1	yes	characteristic
81	C₄	—	61	2	no	—
82	C₄	D₆₁⋊C₃₂	1	1	yes	characteristic
83	C₄	C₂×D₆₁⋊C₁₆	1	1	yes	characteristic
84	C₂	—	122	2	no	—
85	C₂	#21460989	1	2	yes	direct product factor
86	C₂	C₂×D₆₁⋊C₃₂	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₁₆	C₂×#6923
commutator	C₂×C₆₁	C₂²×C₃₂
Frattini	C₁₆	C₂²×#6923
Fitting	C₂×C₃₂×C₆₁	C₄
socle	C₂²×C₆₁	C₂×C₃₂
prime radical	C₂²×D₆₁	C₃₂
cosocle	#14519683	C₂³
hypercenter	C₂×C₃₂	#6923
hypocenter	C₆₁	C₂×M₁₂₈
LCS	G ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₁₆ ◁ C₂×C₃₂

Complements

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

N	H ≅ G/N	type
1. #21460989	C₂	direct (N × H)
2. C₂×#16840601	C₂	semidirect
4. #16840601	C₂²	semidirect
44. C₂×C₆₁	M₁₂₈	semidirect
53. C₆₁	C₂×M₁₂₈	semidirect
85. C₂	#21460989	direct (N × H)

Maximal subgroups

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

subgroup	index
#21460989	2
C₂×#16840601	2
C₂×C₃₂×D₆₁	2
C₂×M₁₂₈	61

Subgroups — C2×#21460989 #30608593

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#21460989 #30608593