Group #21460638 — subgroups

Subgroups — #21460638

Order 7808.

158 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 158 conjugacy classes of subgroups — too many to draw. Only its 54 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	#16840628	C₂	1	1	yes	maximal, characteristic
2	#16840628	C₂	1	1	yes	maximal, characteristic
3	#16839658	C₂	1	1	yes	maximal, characteristic
4	C₂²×#92420	—	2	1	no	—
5	C₂²×#92420	—	2	1	no	—
6	C₂×C₄⋊Dic₆₁	C₄	1	1	yes	characteristic
7	C₂×#11758196	—	2	1	no	—
8	C₂×C₄×Dic₆₁	C₂²	1	1	yes	characteristic
9	#14519684	—	2	1	no	—
10	C₂×C₄⋊C₄×C₆₁	C₄	1	1	yes	characteristic
11	C₂²×C₄×C₆₁	—	2	1	no	—
12	C₂²×C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
13	C₂²×Dic₆₁	—	2	1	no	—
14	C₂²×Dic₆₁	D₄	1	1	yes	characteristic
15	C₂²×Dic₆₁	D₄	1	1	yes	characteristic
16	C₂×#92420	—	2	2	no	—
17	C₂×#92420	—	2	2	no	—
18	C₂×#92420	—	4	1	no	—
19	C₂×#92420	—	4	1	no	—
20	C₂×#92420	—	4	1	no	—
21	C₂×#92420	—	4	1	no	—
22	C₄⋊C₄×C₆₁	—	4	1	no	—
23	C₄⋊Dic₆₁	—	2	1	no	—
24	C₄⋊Dic₆₁	C₈	1	2	yes	complemented
25	#11758196	—	4	1	no	—
26	#11758196	—	4	1	no	—
27	C₄×Dic₆₁	—	4	1	no	—
28	C₂³×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
29	C₂×C₄×C₆₁	—	2	1	no	—
30	C₂×C₄×C₆₁	—	2	1	no	—
31	C₂×C₄×C₆₁	—	4	1	no	—
32	C₂×C₄×C₆₁	—	4	1	no	—
33	C₂×C₄×C₆₁	—	4	1	no	—
34	C₂×C₄×C₆₁	C₂×C₈	1	1	yes	characteristic
35	C₂×C₄×C₆₁	M₁₆	1	1	yes	characteristic
36	C₂×Dic₆₁	—	2	1	no	—
37	C₂×Dic₆₁	—	2	1	no	—
38	C₂×Dic₆₁	—	2	1	no	—
39	C₂×Dic₆₁	—	2	1	no	—
40	C₂×Dic₆₁	—	2	2	no	—
41	C₂×Dic₆₁	—	4	1	no	—
42	C₂×Dic₆₁	—	4	1	no	—
43	C₂×Dic₆₁	D₈	1	1	yes	characteristic
44	C₂×Dic₆₁	SD₁₆	1	1	yes	characteristic
45	C₂×Dic₆₁	SD₁₆	1	1	yes	characteristic
46	C₂×Dic₆₁	Q₁₆	1	1	yes	characteristic
47	#92420	—	4	2	no	—
48	#92420	—	4	2	no	—
49	C₂²×C₆₁	C₂²⋊C₈	1	1	yes	characteristic
50	C₂²×C₆₁	#99	1	1	yes	characteristic
51	C₂²×C₆₁	#101	1	1	yes	characteristic
52	C₂²×C₆₁	#102	1	1	yes	characteristic
53	C₂²×C₆₁	#103	1	1	yes	characteristic
54	C₂²×C₆₁	#104	1	1	yes	characteristic
55	C₂²×C₆₁	#104	1	1	yes	characteristic
56	C₄×C₆₁	—	2	1	no	—
57	C₄×C₆₁	—	2	1	no	—
58	C₄×C₆₁	—	8	1	no	—
59	Dic₆₁	—	2	1	no	—
60	Dic₆₁	—	2	1	no	—
61	Dic₆₁	—	2	1	no	—
62	Dic₆₁	—	2	1	no	—
63	Dic₆₁	—	4	2	no	—
64	#1271	—	61	1	no	maximal, Sylow
65	C₂×C₆₁	#324	1	1	yes	characteristic
66	C₂×C₆₁	D₄⋊C₈	1	1	yes	characteristic
67	C₂×C₆₁	Q₈⋊C₈	1	1	yes	characteristic
68	C₂×C₆₁	#327	1	1	yes	characteristic
69	C₂×C₆₁	#328	1	1	yes	characteristic
70	C₂×C₆₁	#330	1	1	yes	characteristic
71	C₂×C₆₁	#332	1	1	yes	characteristic
72	#389	—	61	1	no	—
73	#336	—	61	1	no	—
74	#336	—	61	1	no	—
75	C₆₁	#1271	1	1	yes	characteristic, complemented, Sylow
76	C₂²×C₈	—	122	1	no	—
77	C₂²×C₈	—	122	1	no	—
78	C₂×C₄⋊C₄	—	61	1	no	—
79	C₂×C₄⋊C₄	—	122	1	no	—
80	C₂×C₄⋊C₄	#6923	1	1	yes	characteristic
81	C₂×C₄²	—	61	1	no	—
82	#95	—	122	1	no	—
83	C₂²×C₄	—	2	1	no	—
84	C₂²×C₄	—	61	1	no	—
85	C₂²×C₄	—	61	1	no	—
86	C₂²×C₄	—	122	1	no	—
87	C₂²×C₄	C₂×#6923	1	1	yes	characteristic
88	C₂×C₈	—	122	2	no	—
89	C₂×C₈	—	122	2	no	—
90	C₂×C₈	—	244	1	no	—
91	C₂×C₈	—	244	1	no	—
92	C₂×C₈	—	244	1	no	—
93	C₂×C₈	—	244	1	no	—
94	C₄⋊C₄	—	4	1	no	—
95	C₄⋊C₄	—	61	2	no	—
96	C₄⋊C₄	—	122	1	no	—
97	C₄⋊C₄	—	244	1	no	—
98	C₄⋊C₄	—	244	1	no	—
99	C₄²	—	244	1	no	—
100	C₂³	C₂²⋊#6923	1	1	yes	characteristic
101	C₂×C₄	—	2	1	no	—
102	C₂×C₄	—	2	1	no	—
103	C₂×C₄	—	4	1	no	—
104	C₂×C₄	—	4	1	no	—
105	C₂×C₄	—	4	1	no	—
106	C₂×C₄	—	61	1	no	—
107	C₂×C₄	—	61	1	no	—
108	C₂×C₄	—	61	1	no	—
109	C₂×C₄	—	61	1	no	—
110	C₂×C₄	—	122	1	no	—
111	C₂×C₄	—	122	1	no	—
112	C₂×C₄	—	122	1	no	—
113	C₂×C₄	—	122	1	no	—
114	C₂×C₄	—	122	2	no	—
115	C₂×C₄	—	244	1	no	—
116	C₂×C₄	—	244	1	no	—
117	C₂×C₄	D₆₁⋊C₈	1	1	yes	characteristic
118	C₂×C₄	#11758213	1	1	yes	characteristic
119	C₈	—	244	2	no	—
120	C₈	—	244	2	no	—
121	C₂²	#14519834	1	1	yes	characteristic
122	C₂²	#14519835	1	1	yes	characteristic
123	C₂²	#14519838	1	1	yes	characteristic
124	C₂²	#14519839	1	1	yes	characteristic
125	C₂²	#14519840	1	1	yes	characteristic
126	C₂²	#14519841	1	1	yes	characteristic
127	C₂²	#14519842	1	1	yes	characteristic
128	C₄	—	2	1	no	—
129	C₄	—	2	1	no	—
130	C₄	—	8	1	no	—
131	C₄	—	122	1	no	—
132	C₄	—	122	1	no	—
133	C₄	—	122	1	no	—
134	C₄	—	122	1	no	—
135	C₄	—	244	2	no	—
136	C₂	#16840608	1	1	yes	characteristic
137	C₂	#16840610	1	1	yes	characteristic
138	C₂	#16840612	1	1	yes	characteristic
139	C₂	#16840613	1	1	yes	characteristic
140	C₂	#16840616	1	1	yes	characteristic
141	C₂	#16840619	1	1	yes	characteristic
142	C₂	#16840621	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#16840628

C₂

yes

maximal, characteristic

#16840628

C₂

yes

maximal, characteristic

#16839658

C₂

yes

maximal, characteristic

C₂²×#92420

—

C₂²×#92420

—

C₂×C₄⋊Dic₆₁

C₄

yes

characteristic

C₂×#11758196

—

C₂×C₄×Dic₆₁

C₂²

yes

characteristic

#14519684

—

C₂×C₄⋊C₄×C₆₁

C₄

yes

characteristic

C₂²×C₄×C₆₁

—

C₂²×C₄×C₆₁

C₂×C₄

yes

characteristic

C₂²×Dic₆₁

—

C₂²×Dic₆₁

D₄

yes

characteristic

C₂²×Dic₆₁

D₄

yes

—

—

—

—

—

—

C₄⋊C₄×C₆₁

—

C₄⋊Dic₆₁

—

C₄⋊Dic₆₁

C₈

yes

complemented

#11758196

—

#11758196

—

C₄×Dic₆₁

—

C₂³×C₆₁

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

C₂×C₈

yes

characteristic

C₂×C₄×C₆₁

M₁₆

yes

characteristic

C₂×Dic₆₁

—

C₂×Dic₆₁

—

C₂×Dic₆₁

—

C₂×Dic₆₁

—

C₂×Dic₆₁

—

C₂×Dic₆₁

—

C₂×Dic₆₁

—

C₂×Dic₆₁

D₈

yes

characteristic

C₂×Dic₆₁

SD₁₆

yes

characteristic

C₂×Dic₆₁

SD₁₆

yes

characteristic

C₂×Dic₆₁

Q₁₆

yes

characteristic

#92420

—

#92420

—

C₂²×C₆₁

C₂²⋊C₈

yes

C₂²×C₆₁

yes

C₂²×C₆₁

yes

C₂²×C₆₁

yes

C₂²×C₆₁

yes

C₂²×C₆₁

yes

C₂²×C₆₁

yes

C₄×C₆₁

—

C₄×C₆₁

—

C₄×C₆₁

—

Dic₆₁

—

Dic₆₁

—

Dic₆₁

—

Dic₆₁

—

Dic₆₁

—

—

C₂×C₆₁

yes

C₂×C₆₁

D₄⋊C₈

yes

characteristic

C₂×C₆₁

Q₈⋊C₈

yes

C₂×C₆₁

yes

C₂×C₆₁

yes

C₂×C₆₁

yes

C₂×C₆₁

yes

—

—

—

C₆₁

#1271

yes

characteristic, complemented, Sylow

C₂²×C₈

—

122

—

C₂²×C₈

—

122

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

122

—

C₂×C₄⋊C₄

#6923

yes

characteristic

C₂×C₄²

—

#95

—

122

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

122

—

C₂²×C₄

C₂×#6923

yes

characteristic

C₂×C₈

—

122

—

C₂×C₈

—

122

—

C₂×C₈

—

244

—

C₂×C₈

—

244

—

C₂×C₈

—

244

—

C₂×C₈

—

244

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

122

—

C₄⋊C₄

—

244

—

C₄⋊C₄

—

244

—

C₄²

—

244

—

100

C₂³

C₂²⋊#6923

yes

characteristic

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

—

122

—

111

C₂×C₄

—

122

—

112

C₂×C₄

—

122

—

113

C₂×C₄

—

122

—

114

C₂×C₄

—

122

—

115

C₂×C₄

—

244

—

116

C₂×C₄

—

244

—

117

C₂×C₄

D₆₁⋊C₈

yes

characteristic

118

C₂×C₄

#11758213

yes

characteristic

119

C₈

—

244

—

120

C₈

—

244

—

121

C₂²

#14519834

yes

characteristic

122

C₂²

#14519835

yes

characteristic

123

C₂²

#14519838

yes

characteristic

124

C₂²

#14519839

yes

characteristic

125

C₂²

#14519840

yes

characteristic

126

C₂²

#14519841

yes

characteristic

127

C₂²

#14519842

yes

characteristic

128

C₄

—

129

C₄

—

130

C₄

—

131

C₄

—

122

—

132

C₄

—

122

—

133

C₄

—

122

—

134

C₄

—

122

—

135

C₄

—

244

—

136

C₂

#16840608

yes

characteristic

137

C₂

#16840610

yes

characteristic

138

C₂

#16840612

yes

characteristic

139

C₂

#16840613

yes

characteristic

140

C₂

#16840616

yes

characteristic

141

C₂

#16840619

yes

characteristic

142

C₂

#16840621

yes

characteristic

	subgroup	G/H
center	C₂³	C₂²⋊#6923
commutator	C₂×C₄×C₆₁	C₂×C₈
Frattini	C₂²×C₄	C₂×#6923
Fitting	C₂×C₄⋊C₄×C₆₁	C₄
socle	C₂³×C₆₁	C₂²⋊C₄
hypercenter	C₂×C₄⋊C₄	#6923
hypocenter	C₆₁	#1271
LCS	G ▷ C₂×C₄×C₆₁ ▷ C₂²×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×C₄⋊C₄

subgroup

G/H

center

C₂³

C₂²⋊#6923

commutator

C₂×C₄×C₆₁

C₂×C₈

Frattini

C₂²×C₄

C₂×#6923

Fitting

C₂×C₄⋊C₄×C₆₁

C₄

socle

C₂³×C₆₁

C₂²⋊C₄

C₂×C₄⋊C₄

C₆₁

G ▷ C₂×C₄×C₆₁ ▷ C₂²×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×C₄⋊C₄

N	H ≅ G/N	type
24. C₄⋊Dic₆₁	C₈	semidirect
75. C₆₁	#1271	semidirect

H ≅ G/N

type

24. C₄⋊Dic₆₁

C₈

semidirect

75. C₆₁

#1271

semidirect

Subgroups — #21460638

Conjugacy classes of subgroups

Complements