Group #21446644 — subgroups

Subgroups — #21446644

Order 7808.

412 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 113 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14519698	C₂	1	4	yes	maximal, complemented
2	C₂×#14519688	C₂	1	1	yes	maximal, characteristic, complemented
3	#16839628	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#127×C₆₁	C₂	1	1	yes	maximal, characteristic
5	C₂²×#92418	C₂²	1	2	yes	—
6	C₂×C₄⋊Dic₆₁	C₂²	1	2	yes	—
7	#14519698	—	2	8	no	—
8	#14519688	—	2	2	no	—
9	#14519684	—	2	2	no	—
10	C₂²×D₄×C₆₁	—	2	2	no	—
11	C₂²×D₄×C₆₁	C₂²	1	2	yes	—
12	#127×C₆₁	—	2	2	no	—
13	#127×C₆₁	C₄	1	4	yes	complemented
14	C₂×C₄²×C₆₁	C₂²	1	1	yes	characteristic
15	C₂⁴×C₆₁	—	2	2	no	—
16	C₂×D₄×C₆₁	—	2	8	no	—
17	C₂×D₄×C₆₁	—	2	4	no	—
18	C₂×D₄×C₆₁	—	2	2	no	—
19	C₂×D₄×C₆₁	—	2	4	no	—
20	C₂×D₄×C₆₁	—	4	8	no	—
21	C₂×D₄×C₆₁	C₂×C₄	1	4	yes	—
22	C₂²×C₄×C₆₁	D₄	1	2	yes	—
23	C₂²×C₄×C₆₁	C₂³	1	1	yes	characteristic
24	C₂²×Dic₆₁	—	2	2	no	—
25	C₄²×C₆₁	C₂×C₄	1	2	yes	—
26	C₄²×C₆₁	D₄	1	2	yes	—
27	C₄⋊Dic₆₁	—	2	4	no	—
28	C₂×#92418	—	2	2	no	—
29	C₂×#92418	—	2	2	no	—
30	C₂×#92418	D₄	1	4	yes	complemented
31	C₂³×C₆₁	—	2	4	no	—
32	C₂³×C₆₁	—	4	2	no	—
33	C₂³×C₆₁	—	4	2	no	—
34	C₂³×C₆₁	—	4	8	no	—
35	C₂³×C₆₁	C₂×D₄	1	1	yes	characteristic
36	D₄×C₆₁	—	2	8	no	—
37	D₄×C₆₁	—	4	16	no	—
38	D₄×C₆₁	—	4	4	no	—
39	C₂×C₄×C₆₁	—	2	4	no	—
40	C₂×C₄×C₆₁	C₂²⋊C₄	1	4	yes	—
41	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
42	C₂×C₄×C₆₁	C₂×D₄	1	2	yes	—
43	C₂×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
44	C₂×C₄×C₆₁	#41	1	2	yes	—
45	C₂×Dic₆₁	—	4	2	no	—
46	C₂×Dic₆₁	—	4	4	no	—
47	#92418	—	2	4	no	—
48	C₂²×C₆₁	—	4	4	no	—
49	C₂²×C₆₁	—	4	8	no	—
50	C₂²×C₆₁	—	8	4	no	—
51	C₂²×C₆₁	—	8	4	no	—
52	C₂²×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
53	C₂²×C₆₁	#124	1	1	yes	characteristic
54	C₂²×C₆₁	#127	1	1	yes	characteristic
55	C₂²×C₆₁	AGL(1,ℤ/8)	1	4	yes	—
56	C₄×C₆₁	—	2	4	no	—
57	C₄×C₆₁	C₄×D₄	1	2	yes	—
58	C₄×C₆₁	#121	1	2	yes	—
59	Dic₆₁	—	8	2	no	—
60	#1961	—	61	1	no	maximal, Sylow
61	C₂×C₆₁	—	8	4	no	—
62	C₂×C₆₁	#390	1	1	yes	characteristic
63	C₂×C₆₁	#418	1	2	yes	—
64	C₂×C₆₁	#490	1	2	yes	—
65	C₂×C₆₁	#496	1	2	yes	—
66	C₂×#127	D₆₁	1	1	yes	characteristic
67	C₂×#102	—	61	4	no	—
68	C₂×#97	—	61	1	no	—
69	#382	—	61	1	no	—
70	C₆₁	#1961	1	1	yes	characteristic, complemented, Sylow
71	C₂²×D₄	—	2	2	no	—
72	C₂²×D₄	C₂×D₆₁	1	2	yes	—
73	C₂²×C₈	—	61	2	no	—
74	#127	—	2	2	no	—
75	#127	Dic₆₁	1	4	yes	complemented
76	C₂×C₄⋊C₄	—	61	2	no	—
77	C₂×C₄²	C₂×D₆₁	1	1	yes	characteristic
78	#102	—	122	8	no	—
79	#97	—	122	2	no	—
80	#95	—	122	2	no	—
81	C₂⁴	—	2	2	no	—
82	C₂×D₄	—	2	8	no	—
83	C₂×D₄	—	2	4	no	—
84	C₂×D₄	—	2	4	no	—
85	C₂×D₄	—	2	2	no	—
86	C₂×D₄	—	4	8	no	—
87	C₂×D₄	C₂×Dic₆₁	1	4	yes	—
88	C₂²×C₄	—	122	2	no	—
89	C₂²×C₄	C₂²⋊D₆₁	1	2	yes	—
90	C₂²×C₄	C₂²×D₆₁	1	1	yes	characteristic
91	C₂×C₈	—	61	4	no	—
92	C₂×C₈	—	122	2	no	—
93	C₂×C₈	—	122	2	no	—
94	C₄⋊C₄	—	122	4	no	—
95	C₄²	C₂×Dic₆₁	1	2	yes	—
96	C₄²	C₂²⋊D₆₁	1	2	yes	—
97	C₂³	—	2	4	no	—
98	C₂³	—	4	2	no	—
99	C₂³	—	4	2	no	—
100	C₂³	—	4	8	no	—
101	C₂³	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
102	D₄	—	2	8	no	—
103	D₄	—	4	16	no	—
104	D₄	—	4	4	no	—
105	C₂×C₄	—	2	4	no	—
106	C₂×C₄	—	244	2	no	—
107	C₂×C₄	—	244	4	no	—
108	C₂×C₄	C₂²⋊Dic₆₁	1	4	yes	—
109	C₂×C₄	D₄×D₆₁	1	2	yes	—
110	C₂×C₄	#11758224	1	2	yes	—
111	C₂×C₄	C₂²×Dic₆₁	1	1	yes	characteristic
112	C₂×C₄	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
113	C₈	—	122	4	no	—
114	C₂²	—	4	8	no	—
115	C₂²	—	4	4	no	—
116	C₂²	—	8	4	no	—
117	C₂²	—	8	4	no	—
118	C₂²	C₂×C₂²⋊Dic₆₁	1	1	yes	characteristic
119	C₂²	#14519764	1	1	yes	characteristic
120	C₂²	#14519773	1	1	yes	characteristic
121	C₂²	#14519803	1	4	yes	—
122	C₄	—	2	4	no	—
123	C₄	—	488	2	no	—
124	C₄	D₄×Dic₆₁	1	2	yes	—
125	C₄	#14519748	1	2	yes	—
126	C₂	—	8	4	no	—
127	C₂	#16839665	1	1	yes	characteristic
128	C₂	#16839767	1	2	yes	—
129	C₂	#16840126	1	2	yes	—
130	C₂	#16840149	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14519698

C₂

yes

maximal, complemented

C₂×#14519688

C₂

yes

maximal, characteristic, complemented

#16839628

C₂

yes

maximal, characteristic, complemented

C₂×#127×C₆₁

C₂

yes

maximal, characteristic

C₂²×#92418

C₂²

yes

—

C₂×C₄⋊Dic₆₁

C₂²

yes

—

#14519698

—

#14519688

—

#14519684

—

C₂²×D₄×C₆₁

—

C₂²×D₄×C₆₁

C₂²

yes

—

#127×C₆₁

—

#127×C₆₁

C₄

yes

complemented

C₂×C₄²×C₆₁

C₂²

yes

characteristic

C₂⁴×C₆₁

—

C₂×D₄×C₆₁

—

C₂×D₄×C₆₁

—

C₂×D₄×C₆₁

—

C₂×D₄×C₆₁

—

C₂×D₄×C₆₁

—

C₂×D₄×C₆₁

C₂×C₄

yes

—

C₂²×C₄×C₆₁

D₄

yes

—

C₂²×C₄×C₆₁

C₂³

yes

characteristic

C₂²×Dic₆₁

—

C₄²×C₆₁

C₂×C₄

yes

—

C₄²×C₆₁

D₄

yes

—

C₄⋊Dic₆₁

—

C₂×#92418

—

C₂×#92418

—

C₂×#92418

D₄

yes

complemented

C₂³×C₆₁

—

C₂³×C₆₁

—

C₂³×C₆₁

—

C₂³×C₆₁

—

C₂³×C₆₁

C₂×D₄

yes

characteristic

D₄×C₆₁

—

D₄×C₆₁

—

D₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

C₂²⋊C₄

yes

—

C₂×C₄×C₆₁

C₂²×C₄

yes

characteristic

C₂×C₄×C₆₁

C₂×D₄

yes

—

C₂×C₄×C₆₁

C₂×D₄

yes

characteristic

C₂×C₄×C₆₁

#41

yes

—

C₂×Dic₆₁

—

C₂×Dic₆₁

—

#92418

—

C₂²×C₆₁

—

C₂²×C₆₁

—

C₂²×C₆₁

—

C₂²×C₆₁

—

C₂²×C₆₁

C₂×C₂²⋊C₄

yes

C₂²×C₆₁

yes

C₂²×C₆₁

yes

C₂²×C₆₁

yes

—

C₄×C₆₁

—

C₄×C₆₁

C₄×D₄

yes

—

C₄×C₆₁

#121

yes

—

Dic₆₁

—

#1961

—

maximal, Sylow

C₂×C₆₁

—

C₂×C₆₁

#390

yes

characteristic

C₂×C₆₁

#418

yes

—

C₂×C₆₁

#490

yes

—

C₂×C₆₁

#496

yes

—

C₂×#127

D₆₁

yes

characteristic

C₂×#102

—

C₂×#97

—

#382

—

C₆₁

#1961

yes

characteristic, complemented, Sylow

C₂²×D₄

—

C₂²×D₄

C₂×D₆₁

yes

—

C₂²×C₈

—

#127

—

#127

Dic₆₁

yes

complemented

C₂×C₄⋊C₄

—

C₂×C₄²

C₂×D₆₁

yes

characteristic

#102

—

122

—

#97

—

122

—

#95

—

122

—

C₂⁴

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

C₂×Dic₆₁

yes

—

C₂²×C₄

—

122

—

C₂²×C₄

C₂²⋊D₆₁

yes

—

C₂²×C₄

C₂²×D₆₁

yes

characteristic

C₂×C₈

—

C₂×C₈

—

122

—

C₂×C₈

—

122

—

C₄⋊C₄

—

122

—

C₄²

C₂×Dic₆₁

yes

—

C₄²

C₂²⋊D₆₁

yes

—

C₂³

—

C₂³

—

C₂³

—

100

C₂³

—

101

C₂³

C₂×C₂²⋊D₆₁

yes

characteristic

102

D₄

—

103

D₄

—

104

D₄

—

105

C₂×C₄

—

106

C₂×C₄

—

244

—

107

C₂×C₄

—

244

—

108

C₂×C₄

C₂²⋊Dic₆₁

yes

—

109

C₂×C₄

D₄×D₆₁

yes

—

110

C₂×C₄

#11758224

yes

—

111

C₂×C₄

C₂²×Dic₆₁

yes

characteristic

112

C₂×C₄

C₂×C₂²⋊D₆₁

yes

characteristic

113

C₈

—

122

—

114

C₂²

—

115

C₂²

—

116

C₂²

—

117

C₂²

—

118

C₂²

C₂×C₂²⋊Dic₆₁

yes

characteristic

119

C₂²

#14519764

yes

characteristic

120

C₂²

#14519773

yes

characteristic

121

C₂²

#14519803

yes

—

122

C₄

—

123

C₄

—

488

—

124

C₄

D₄×Dic₆₁

yes

—

125

C₄

#14519748

yes

—

126

C₂

—

127

C₂

#16839665

yes

characteristic

128

C₂

#16839767

yes

—

129

C₂

#16840126

yes

—

130

C₂

#16840149

yes

—

	subgroup	G/H
center	C₂³	C₂×C₂²⋊D₆₁
commutator	C₂×C₄×C₆₁	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₆₁
Fitting	C₂×#127×C₆₁	C₂
socle	C₂³×C₆₁	C₂×D₄
hypercenter	C₂×#127	D₆₁
hypocenter	C₆₁	#1961
LCS	G ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#127

subgroup

G/H

center

C₂³

C₂×C₂²⋊D₆₁

commutator

C₂×C₄×C₆₁

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₆₁

Fitting

C₂×#127×C₆₁

C₂

socle

C₂³×C₆₁

C₂×D₄

D₆₁

C₆₁

G ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#127

N	H ≅ G/N	type
1. C₂×#14519698	C₂	semidirect
2. C₂×#14519688	C₂	semidirect
3. #16839628	C₂	semidirect
13. #127×C₆₁	C₄	semidirect
30. C₂×#92418	D₄	semidirect
70. C₆₁	#1961	semidirect
75. #127	Dic₆₁	semidirect

H ≅ G/N

type

1. C₂×#14519698

C₂

semidirect

2. C₂×#14519688

C₂

semidirect

3. #16839628

C₂

semidirect

13. #127×C₆₁

C₄

semidirect

30. C₂×#92418

D₄

semidirect

70. C₆₁

#1961

semidirect

75. #127

Dic₆₁

semidirect

Subgroups — #21446644

Conjugacy classes of subgroups

Complements