Group #21446562 — subgroups

Subgroups — #21446562

Order 7808.

240 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 109 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×#14519711	C₂	1	1	yes	maximal, characteristic
2	C₂×#14519709	C₂	1	1	yes	maximal, characteristic
3	#16839660	C₂	1	2	yes	maximal
4	#16839525	C₂	1	2	yes	maximal
5	C₂×#97×C₆₁	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄⋊Dic₆₁	C₂²	1	2	yes	—
7	C₂×C₄⋊Dic₆₁	C₂²	1	2	yes	—
8	C₂×#11758196	—	2	2	no	—
9	#14519711	—	2	2	no	—
10	#14519709	C₄	1	4	yes	complemented
11	#14519684	—	2	2	no	—
12	C₂²×C₈×C₆₁	C₂²	1	1	yes	characteristic
13	C₂²×C₈×C₆₁	C₂²	1	1	yes	characteristic
14	C₂×C₄²×C₆₁	C₂²	1	1	yes	characteristic
15	#97×C₆₁	—	2	2	no	—
16	C₂²×C₄×C₆₁	D₄	1	1	yes	characteristic
17	C₂²×C₄×C₆₁	D₄	1	1	yes	characteristic
18	C₂²×C₄×C₆₁	C₂³	1	1	yes	characteristic
19	C₂²×Dic₆₁	—	2	2	no	—
20	C₂²×Dic₆₁	—	2	2	no	—
21	C₂×C₈×C₆₁	—	2	1	no	—
22	C₂×C₈×C₆₁	—	2	1	no	—
23	C₂×C₈×C₆₁	C₂×C₄	1	2	yes	—
24	C₂×C₈×C₆₁	D₄	1	2	yes	—
25	C₂×C₈×C₆₁	Q₈	1	2	yes	—
26	C₂×C₈×C₆₁	Q₈	1	2	yes	—
27	C₄²×C₆₁	—	2	1	no	—
28	C₄²×C₆₁	—	2	1	no	—
29	C₄⋊Dic₆₁	—	2	2	no	—
30	C₄⋊Dic₆₁	—	2	2	no	—
31	C₄⋊Dic₆₁	—	2	2	no	—
32	C₄⋊Dic₆₁	C₂×C₄	1	4	yes	—
33	#11758196	—	4	4	no	—
34	C₂³×C₆₁	C₂×D₄	1	1	yes	characteristic
35	C₂×C₄×C₆₁	—	2	1	no	—
36	C₂×C₄×C₆₁	—	2	1	no	—
37	C₂×C₄×C₆₁	—	2	2	no	—
38	C₂×C₄×C₆₁	—	2	2	no	—
39	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
40	C₂×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
41	C₂×C₄×C₆₁	C₂×Q₈	1	1	yes	characteristic
42	C₂×C₄×C₆₁	C₂×Q₈	1	1	yes	characteristic
43	C₂×C₄×C₆₁	#41	1	1	yes	characteristic
44	C₂×C₄×C₆₁	#41	1	1	yes	characteristic
45	C₂×Dic₆₁	—	2	4	no	—
46	C₂×Dic₆₁	—	4	2	no	—
47	C₂×Dic₆₁	—	4	2	no	—
48	C₂×Dic₆₁	—	4	2	no	—
49	C₂×Dic₆₁	—	4	2	no	—
50	C₂×Dic₆₁	—	4	2	no	—
51	C₈×C₆₁	—	2	2	no	—
52	C₈×C₆₁	C₄⋊C₄	1	4	yes	complemented
53	C₂²×C₆₁	C₄×D₄	1	1	yes	characteristic
54	C₂²×C₆₁	#121	1	1	yes	characteristic
55	C₂²×C₆₁	C₄⋊Q₈	1	1	yes	characteristic
56	C₂²×C₆₁	AGL(1,ℤ/8)	1	2	yes	—
57	C₂²×C₆₁	#137	1	2	yes	—
58	C₄×C₆₁	—	4	1	no	—
59	C₄×C₆₁	—	4	1	no	—
60	C₄×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
61	C₄×C₆₁	C₄×Q₈	1	1	yes	characteristic
62	C₄×C₆₁	C₂²⋊Q₈	1	1	yes	characteristic
63	C₄×C₆₁	#125	1	1	yes	characteristic
64	Dic₆₁	—	4	4	no	—
65	Dic₆₁	—	8	2	no	—
66	#1944	—	61	1	no	maximal, Sylow
67	C₂×C₆₁	#389	1	1	yes	characteristic
68	C₂×C₆₁	#440	1	2	yes	—
69	C₂×C₆₁	#469	1	1	yes	characteristic
70	C₂×C₆₁	#470	1	1	yes	characteristic
71	C₂×C₆₁	#501	1	2	yes	—
72	C₂×#107	—	61	1	no	—
73	C₂×#106	—	61	1	no	—
74	C₂×#97	D₆₁	1	1	yes	characteristic
75	#389	—	61	2	no	—
76	#340	—	61	2	no	—
77	C₆₁	#1944	1	1	yes	characteristic, complemented, Sylow
78	C₂²×C₈	C₂×D₆₁	1	1	yes	characteristic
79	C₂²×C₈	C₂×D₆₁	1	1	yes	characteristic
80	C₂×C₄⋊C₄	—	61	2	no	—
81	C₂×C₄⋊C₄	—	61	2	no	—
82	C₂×C₄⋊C₄	—	122	2	no	—
83	C₂×C₄²	C₂×D₆₁	1	1	yes	characteristic
84	#107	—	122	2	no	—
85	#106	—	61	4	no	—
86	#97	—	2	2	no	—
87	#95	—	122	2	no	—
88	C₂²×C₄	—	122	2	no	—
89	C₂²×C₄	—	122	2	no	—
90	C₂²×C₄	D₂₄₄	1	1	yes	characteristic
91	C₂²×C₄	D₂₄₄	1	1	yes	characteristic
92	C₂²×C₄	C₂²×D₆₁	1	1	yes	characteristic
93	C₂×C₈	—	2	1	no	—
94	C₂×C₈	—	2	1	no	—
95	C₂×C₈	Dic₁₂₂	1	2	yes	—
96	C₂×C₈	Dic₁₂₂	1	2	yes	—
97	C₂×C₈	C₄×D₆₁	1	2	yes	—
98	C₂×C₈	C₂²⋊D₆₁	1	2	yes	—
99	C₄⋊C₄	—	61	4	no	—
100	C₄⋊C₄	—	122	2	no	—
101	C₄⋊C₄	—	122	2	no	—
102	C₄⋊C₄	—	122	2	no	—
103	C₄⋊C₄	—	244	4	no	—
104	C₄²	—	2	1	no	—
105	C₄²	—	2	1	no	—
106	C₂³	C₂×D₂₄₄	1	1	yes	characteristic
107	C₂×C₄	—	2	2	no	—
108	C₂×C₄	—	2	1	no	—
109	C₂×C₄	—	2	1	no	—
110	C₂×C₄	—	2	2	no	—
111	C₂×C₄	—	122	4	no	—
112	C₂×C₄	—	244	2	no	—
113	C₂×C₄	—	244	2	no	—
114	C₂×C₄	—	244	2	no	—
115	C₂×C₄	—	244	2	no	—
116	C₂×C₄	—	244	2	no	—
117	C₂×C₄	C₂×Dic₁₂₂	1	1	yes	characteristic
118	C₂×C₄	C₂×Dic₁₂₂	1	1	yes	characteristic
119	C₂×C₄	C₂×C₄×D₆₁	1	1	yes	characteristic
120	C₂×C₄	#11758222	1	1	yes	characteristic
121	C₂×C₄	#11758222	1	1	yes	characteristic
122	C₂×C₄	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
123	C₈	—	2	2	no	—
124	C₈	#11758196	1	4	yes	complemented
125	C₂²	C₄×D₂₄₄	1	1	yes	characteristic
126	C₂²	#14519751	1	1	yes	characteristic
127	C₂²	#14519777	1	1	yes	characteristic
128	C₂²	#14519805	1	2	yes	—
129	C₂²	#14519810	1	2	yes	—
130	C₄	—	4	1	no	—
131	C₄	—	4	1	no	—
132	C₄	—	488	2	no	—
133	C₄	—	244	4	no	—
134	C₄	C₂×#11758196	1	1	yes	characteristic
135	C₄	C₄×Dic₁₂₂	1	1	yes	characteristic
136	C₄	#14519756	1	1	yes	characteristic
137	C₄	#14519769	1	1	yes	characteristic
138	C₂	#16839660	1	1	yes	characteristic
139	C₂	#16839864	1	2	yes	—
140	C₂	#16840015	1	1	yes	characteristic
141	C₂	#16840020	1	1	yes	characteristic
142	C₂	#16840171	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14519711

C₂

yes

maximal, characteristic

C₂×#14519709

C₂

yes

maximal, characteristic

#16839660

C₂

yes

maximal

#16839525

C₂

yes

maximal

C₂×#97×C₆₁

C₂

yes

maximal, characteristic

C₂×C₄⋊Dic₆₁

C₂²

yes

—

C₂×C₄⋊Dic₆₁

C₂²

yes

—

C₂×#11758196

—

#14519711

—

#14519709

C₄

yes

complemented

#14519684

—

C₂²×C₈×C₆₁

C₂²

yes

characteristic

C₂²×C₈×C₆₁

C₂²

yes

characteristic

C₂×C₄²×C₆₁

C₂²

yes

characteristic

#97×C₆₁

—

C₂²×C₄×C₆₁

D₄

yes

characteristic

C₂²×C₄×C₆₁

D₄

yes

characteristic

C₂²×C₄×C₆₁

C₂³

yes

characteristic

C₂²×Dic₆₁

—

C₂²×Dic₆₁

—

C₂×C₈×C₆₁

—

C₂×C₈×C₆₁

—

C₂×C₈×C₆₁

C₂×C₄

yes

—

C₂×C₈×C₆₁

D₄

yes

—

C₂×C₈×C₆₁

Q₈

yes

—

C₂×C₈×C₆₁

Q₈

yes

—

C₄²×C₆₁

—

C₄²×C₆₁

—

C₄⋊Dic₆₁

—

C₄⋊Dic₆₁

—

C₄⋊Dic₆₁

—

C₄⋊Dic₆₁

C₂×C₄

yes

—

#11758196

—

C₂³×C₆₁

C₂×D₄

yes

characteristic

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

C₂²×C₄

yes

characteristic

C₂×C₄×C₆₁

C₂×D₄

yes

characteristic

C₂×C₄×C₆₁

C₂×Q₈

yes

characteristic

C₂×C₄×C₆₁

C₂×Q₈

yes

C₂×C₄×C₆₁

yes

C₂×C₄×C₆₁

yes

C₂×Dic₆₁

—

C₂×Dic₆₁

—

C₂×Dic₆₁

—

C₂×Dic₆₁

—

C₂×Dic₆₁

—

C₂×Dic₆₁

—

C₈×C₆₁

—

C₈×C₆₁

C₄⋊C₄

yes

complemented

C₂²×C₆₁

C₄×D₄

yes

characteristic

C₂²×C₆₁

#121

yes

characteristic

C₂²×C₆₁

C₄⋊Q₈

yes

characteristic

C₂²×C₆₁

AGL(1,ℤ/8)

yes

—

C₂²×C₆₁

#137

yes

—

C₄×C₆₁

—

C₄×C₆₁

—

C₄×C₆₁

C₂×C₄⋊C₄

yes

characteristic

C₄×C₆₁

C₄×Q₈

yes

characteristic

C₄×C₆₁

C₂²⋊Q₈

yes

characteristic

C₄×C₆₁

#125

yes

characteristic

Dic₆₁

—

Dic₆₁

—

—

C₂×C₆₁

yes

C₂×C₆₁

yes

—

C₂×C₆₁

yes

C₂×C₆₁

yes

C₂×C₆₁

yes

—

C₂×#107

—

C₂×#106

—

C₂×#97

D₆₁

yes

characteristic

#389

—

#340

—

C₆₁

#1944

yes

characteristic, complemented, Sylow

C₂²×C₈

C₂×D₆₁

yes

characteristic

C₂²×C₈

C₂×D₆₁

yes

characteristic

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

122

—

C₂×C₄²

C₂×D₆₁

yes

characteristic

#107

—

122

—

#106

—

#97

—

#95

—

122

—

C₂²×C₄

—

122

—

C₂²×C₄

—

122

—

C₂²×C₄

D₂₄₄

yes

characteristic

C₂²×C₄

D₂₄₄

yes

characteristic

C₂²×C₄

C₂²×D₆₁

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

Dic₁₂₂

yes

—

C₂×C₈

Dic₁₂₂

yes

—

C₂×C₈

C₄×D₆₁

yes

—

C₂×C₈

C₂²⋊D₆₁

yes

—

C₄⋊C₄

—

100

C₄⋊C₄

—

122

—

101

C₄⋊C₄

—

122

—

102

C₄⋊C₄

—

122

—

103

C₄⋊C₄

—

244

—

104

C₄²

—

105

C₄²

—

106

C₂³

C₂×D₂₄₄

yes

characteristic

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

—

122

—

112

C₂×C₄

—

244

—

113

C₂×C₄

—

244

—

114

C₂×C₄

—

244

—

115

C₂×C₄

—

244

—

116

C₂×C₄

—

244

—

117

C₂×C₄

C₂×Dic₁₂₂

yes

characteristic

118

C₂×C₄

C₂×Dic₁₂₂

yes

characteristic

119

C₂×C₄

C₂×C₄×D₆₁

yes

characteristic

120

C₂×C₄

#11758222

yes

characteristic

121

C₂×C₄

#11758222

yes

characteristic

122

C₂×C₄

C₂×C₂²⋊D₆₁

yes

characteristic

123

C₈

—

124

C₈

#11758196

yes

complemented

125

C₂²

C₄×D₂₄₄

yes

characteristic

126

C₂²

#14519751

yes

characteristic

127

C₂²

#14519777

yes

characteristic

128

C₂²

#14519805

yes

—

129

C₂²

#14519810

yes

—

130

C₄

—

131

C₄

—

132

C₄

—

488

—

133

C₄

—

244

—

134

C₄

C₂×#11758196

yes

characteristic

135

C₄

C₄×Dic₁₂₂

yes

characteristic

136

C₄

#14519756

yes

characteristic

137

C₄

#14519769

yes

characteristic

138

C₂

#16839660

yes

characteristic

139

C₂

#16839864

yes

—

140

C₂

#16840015

yes

characteristic

141

C₂

#16840020

yes

characteristic

142

C₂

#16840171

yes

—

	subgroup	G/H
center	C₂³	C₂×D₂₄₄
commutator	C₂×C₄×C₆₁	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₆₁
Fitting	C₂×#97×C₆₁	C₂
socle	C₂³×C₆₁	C₂×D₄
hypercenter	C₂×#97	D₆₁
hypocenter	C₆₁	#1944
LCS	G ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#97

subgroup

G/H

center

C₂³

C₂×D₂₄₄

commutator

C₂×C₄×C₆₁

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₆₁

Fitting

C₂×#97×C₆₁

C₂

socle

C₂³×C₆₁

C₂×D₄

hypercenter

C₂×#97

D₆₁

hypocenter

C₆₁

#1944

LCS

G ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#97

N	H ≅ G/N	type
10. #14519709	C₄	semidirect
52. C₈×C₆₁	C₄⋊C₄	semidirect
77. C₆₁	#1944	semidirect
124. C₈	#11758196	semidirect

H ≅ G/N

type

10. #14519709

C₄

semidirect

52. C₈×C₆₁

C₄⋊C₄

semidirect

77. C₆₁

#1944

semidirect

124. C₈

#11758196

semidirect

Subgroups — #21446562

Conjugacy classes of subgroups

Complements