Group #21446602 — subgroups

Subgroups — #21446602

Order 7808.

196 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 89 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×#14519713	C₂	1	1	yes	maximal, characteristic
2	#16839802	C₂	1	2	yes	maximal
3	#16839717	C₂	1	1	yes	maximal, characteristic
4	#16839531	C₂	1	2	yes	maximal
5	C₂×#107×C₆₁	C₂	1	1	yes	maximal, characteristic
6	C₂×#11758194	C₂²	1	2	yes	—
7	C₂×#11758194	C₂²	1	1	yes	characteristic
8	#14519736	C₂²	1	1	yes	characteristic
9	#14519713	C₄	1	4	yes	complemented
10	#14519710	—	2	2	no	—
11	#14519708	—	2	2	no	—
12	#14519687	—	2	1	no	—
13	C₈×Dic₆₁	—	2	1	no	—
14	C₂²×C₈×C₆₁	C₂²	1	1	yes	characteristic
15	C₂×C₄⋊C₄×C₆₁	C₂²	1	2	yes	—
16	#107×C₆₁	—	2	1	no	—
17	#107×C₆₁	—	2	1	no	—
18	C₂²×C₄×C₆₁	—	2	2	no	—
19	C₂²×C₄×C₆₁	C₂³	1	1	yes	characteristic
20	C₂×C₈×C₆₁	C₂×C₄	1	2	yes	—
21	C₂×C₈×C₆₁	D₄	1	1	yes	characteristic
22	C₂×C₈×C₆₁	D₄	1	1	yes	characteristic
23	C₂×C₈×C₆₁	Q₈	1	2	yes	—
24	C₄⋊C₄×C₆₁	—	2	2	no	—
25	C₄⋊C₄×C₆₁	—	2	2	no	—
26	C₂²⋊Dic₆₁	—	2	1	no	—
27	C₄⋊Dic₆₁	D₄	1	1	yes	characteristic
28	C₄⋊Dic₆₁	D₄	1	1	yes	characteristic
29	C₄×Dic₆₁	—	2	1	no	—
30	#11758194	—	2	2	no	—
31	#11758194	—	2	1	no	—
32	#11758194	C₂×C₄	1	4	yes	—
33	#11758194	Q₈	1	2	yes	—
34	C₂×#92418	—	2	1	no	—
35	C₂×#92418	—	2	2	no	—
36	C₂³×C₆₁	#41	1	1	yes	characteristic
37	C₂×C₄×C₆₁	—	4	2	no	—
38	C₂×C₄×C₆₁	—	8	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×D₄	1	1	yes	characteristic
42	C₂×C₄×C₆₁	C₂×Q₈	1	1	yes	characteristic
43	C₂×C₄×C₆₁	C₂×Q₈	1	1	yes	characteristic
44	C₂×C₄×C₆₁	#41	1	1	yes	characteristic
45	C₂×Dic₆₁	—	2	1	no	—
46	C₂×Dic₆₁	—	2	1	no	—
47	C₈×C₆₁	C₄⋊C₄	1	2	yes	—
48	C₈×C₆₁	C₄⋊C₄	1	2	yes	—
49	#92418	—	2	4	no	—
50	#92418	—	2	2	no	—
51	C₂²×C₆₁	—	2	1	no	—
52	C₂²×C₆₁	—	2	1	no	—
53	C₂²×C₆₁	C₄×Q₈	1	1	yes	characteristic
54	C₂²×C₆₁	#121	1	1	yes	characteristic
55	C₂²×C₆₁	#125	1	1	yes	characteristic
56	C₄×C₆₁	—	8	2	no	—
57	C₄×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
58	C₄×C₆₁	C₄×D₄	1	1	yes	characteristic
59	C₄×C₆₁	C₂²⋊Q₈	1	1	yes	characteristic
60	C₄×C₆₁	C₄⋊Q₈	1	1	yes	characteristic
61	Dic₆₁	—	4	1	no	—
62	Dic₆₁	—	4	1	no	—
63	#1952	—	61	1	no	maximal, Sylow
64	C₂×C₆₁	—	2	1	no	—
65	C₂×C₆₁	—	2	1	no	—
66	C₂×C₆₁	#389	1	1	yes	characteristic
67	C₂×C₆₁	#472	1	1	yes	characteristic
68	C₂×C₆₁	#473	1	1	yes	characteristic
69	C₂×#108	—	61	1	no	—
70	#428	—	61	2	no	—
71	C₂×#107	D₆₁	1	1	yes	characteristic
72	#405	—	61	1	no	—
73	#343	—	61	2	no	—
74	C₆₁	#1952	1	1	yes	characteristic, complemented, Sylow
75	C₂×M₁₆	—	61	1	no	—
76	C₂×M₁₆	—	61	2	no	—
77	C₂²×C₈	C₂×D₆₁	1	1	yes	characteristic
78	#117	—	61	1	no	—
79	C₂×C₄⋊C₄	C₂×D₆₁	1	2	yes	—
80	#108	—	61	4	no	—
81	#107	—	2	1	no	—
82	#107	—	2	1	no	—
83	#107	—	122	2	no	—
84	#106	—	122	2	no	—
85	#97	—	122	1	no	—
86	C₄×C₈	—	122	1	no	—
87	C₂²×C₄	—	2	2	no	—
88	C₂²×C₄	C₂²×D₆₁	1	1	yes	characteristic
89	M₁₆	—	61	4	no	—
90	M₁₆	—	61	2	no	—
91	M₁₆	—	122	2	no	—
92	M₁₆	—	122	1	no	—
93	C₂×C₈	—	122	2	no	—
94	C₂×C₈	—	122	1	no	—
95	C₂×C₈	Dic₁₂₂	1	2	yes	—
96	C₂×C₈	C₄×D₆₁	1	2	yes	—
97	C₂×C₈	C₂²⋊D₆₁	1	1	yes	characteristic
98	C₂×C₈	C₂²⋊D₆₁	1	1	yes	characteristic
99	C₄⋊C₄	—	2	2	no	—
100	C₄⋊C₄	—	2	2	no	—
101	C₄⋊C₄	—	61	1	no	—
102	C₄⋊C₄	—	61	1	no	—
103	C₂²⋊C₄	—	122	1	no	—
104	C₄²	—	122	1	no	—
105	C₂³	#11758224	1	1	yes	characteristic
106	C₂×C₄	—	4	2	no	—
107	C₂×C₄	—	8	2	no	—
108	C₂×C₄	—	122	1	no	—
109	C₂×C₄	—	122	1	no	—
110	C₂×C₄	C₂×Dic₁₂₂	1	1	yes	characteristic
111	C₂×C₄	C₂×C₄×D₆₁	1	1	yes	characteristic
112	C₂×C₄	D₄×D₆₁	1	1	yes	characteristic
113	C₂×C₄	Q₈×D₆₁	1	1	yes	characteristic
114	C₂×C₄	#11758226	1	1	yes	characteristic
115	C₂×C₄	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
116	C₈	—	122	4	no	—
117	C₈	—	122	2	no	—
118	C₈	#11758196	1	2	yes	—
119	C₈	#11758196	1	2	yes	—
120	C₂²	—	2	1	no	—
121	C₂²	—	2	1	no	—
122	C₂²	#14519742	1	1	yes	characteristic
123	C₂²	#14519748	1	1	yes	characteristic
124	C₂²	#14519768	1	1	yes	characteristic
125	C₄	—	8	2	no	—
126	C₄	—	244	1	no	—
127	C₄	—	244	1	no	—
128	C₄	C₂×#11758196	1	1	yes	characteristic
129	C₄	#14519739	1	1	yes	characteristic
130	C₄	#14519753	1	1	yes	characteristic
131	C₄	#14519776	1	1	yes	characteristic
132	C₂	—	2	1	no	—
133	C₂	—	2	1	no	—
134	C₂	#16839658	1	1	yes	characteristic
135	C₂	#16840029	1	1	yes	characteristic
136	C₂	#16840034	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14519713

C₂

yes

maximal, characteristic

#16839802

C₂

yes

maximal

#16839717

C₂

yes

maximal, characteristic

#16839531

C₂

yes

maximal

C₂×#107×C₆₁

C₂

yes

maximal, characteristic

C₂×#11758194

C₂²

yes

—

C₂×#11758194

C₂²

yes

characteristic

#14519736

C₂²

yes

characteristic

#14519713

C₄

yes

—

—

—

C₈×Dic₆₁

—

C₂²×C₈×C₆₁

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₆₁

C₂²

yes

—

#107×C₆₁

—

#107×C₆₁

—

C₂²×C₄×C₆₁

—

C₂²×C₄×C₆₁

C₂³

yes

characteristic

C₂×C₈×C₆₁

C₂×C₄

yes

—

C₂×C₈×C₆₁

D₄

yes

characteristic

C₂×C₈×C₆₁

D₄

yes

characteristic

C₂×C₈×C₆₁

Q₈

yes

—

C₄⋊C₄×C₆₁

—

C₄⋊C₄×C₆₁

—

C₂²⋊Dic₆₁

—

C₄⋊Dic₆₁

D₄

yes

characteristic

C₄⋊Dic₆₁

D₄

yes

characteristic

C₄×Dic₆₁

—

#11758194

—

#11758194

—

#11758194

C₂×C₄

yes

—

#11758194

Q₈

yes

—

C₂×#92418

—

C₂×#92418

—

C₂³×C₆₁

#41

yes

characteristic

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

C₂²×C₄

yes

characteristic

C₂×C₄×C₆₁

C₂×D₄

yes

characteristic

C₂×C₄×C₆₁

C₂×D₄

yes

characteristic

C₂×C₄×C₆₁

C₂×Q₈

yes

characteristic

C₂×C₄×C₆₁

C₂×Q₈

yes

characteristic

C₂×C₄×C₆₁

#41

yes

characteristic

C₂×Dic₆₁

—

C₂×Dic₆₁

—

C₈×C₆₁

C₄⋊C₄

yes

—

C₈×C₆₁

C₄⋊C₄

yes

—

#92418

—

#92418

—

C₂²×C₆₁

—

C₂²×C₆₁

—

C₂²×C₆₁

C₄×Q₈

yes

C₂²×C₆₁

yes

C₂²×C₆₁

yes

C₄×C₆₁

—

C₄×C₆₁

C₂×C₄⋊C₄

yes

characteristic

C₄×C₆₁

C₄×D₄

yes

characteristic

C₄×C₆₁

C₂²⋊Q₈

yes

characteristic

C₄×C₆₁

C₄⋊Q₈

yes

characteristic

Dic₆₁

—

Dic₆₁

—

#1952

—

maximal, Sylow

C₂×C₆₁

—

C₂×C₆₁

—

C₂×C₆₁

yes

C₂×C₆₁

yes

C₂×C₆₁

yes

—

—

D₆₁

yes

characteristic

#405

—

#343

—

C₆₁

#1952

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₂×M₁₆

—

C₂²×C₈

C₂×D₆₁

yes

characteristic

#117

—

C₂×C₄⋊C₄

C₂×D₆₁

yes

—

—

—

—

—

122

—

#106

—

122

—

#97

—

122

—

C₄×C₈

—

122

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₆₁

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

122

—

M₁₆

—

122

—

C₂×C₈

—

122

—

C₂×C₈

—

122

—

C₂×C₈

Dic₁₂₂

yes

—

C₂×C₈

C₄×D₆₁

yes

—

C₂×C₈

C₂²⋊D₆₁

yes

characteristic

C₂×C₈

C₂²⋊D₆₁

yes

characteristic

C₄⋊C₄

—

100

C₄⋊C₄

—

101

C₄⋊C₄

—

102

C₄⋊C₄

—

103

C₂²⋊C₄

—

122

—

104

C₄²

—

122

—

105

C₂³

#11758224

yes

characteristic

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

—

122

—

109

C₂×C₄

—

122

—

110

C₂×C₄

C₂×Dic₁₂₂

yes

characteristic

111

C₂×C₄

C₂×C₄×D₆₁

yes

characteristic

112

C₂×C₄

D₄×D₆₁

yes

characteristic

113

C₂×C₄

Q₈×D₆₁

yes

characteristic

114

C₂×C₄

#11758226

yes

characteristic

115

C₂×C₄

C₂×C₂²⋊D₆₁

yes

characteristic

116

C₈

—

122

—

117

C₈

—

122

—

118

C₈

#11758196

yes

—

119

C₈

#11758196

yes

—

120

C₂²

—

121

C₂²

—

122

C₂²

#14519742

yes

characteristic

123

C₂²

#14519748

yes

characteristic

124

C₂²

#14519768

yes

characteristic

125

C₄

—

126

C₄

—

244

—

127

C₄

—

244

—

128

C₄

C₂×#11758196

yes

characteristic

129

C₄

#14519739

yes

characteristic

130

C₄

#14519753

yes

characteristic

131

C₄

#14519776

yes

characteristic

132

C₂

—

133

C₂

—

134

C₂

#16839658

yes

characteristic

135

C₂

#16840029

yes

characteristic

136

C₂

#16840034

yes

characteristic

	subgroup	G/H
center	C₂²	#14519748
commutator	C₂×C₄×C₆₁	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₆₁
Fitting	C₂×#107×C₆₁	C₂
socle	C₂²×C₆₁	#121
hypercenter	C₂×#107	D₆₁
hypocenter	C₆₁	#1952
LCS	G ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#107

subgroup

G/H

center

C₂²

#14519748

commutator

C₂×C₄×C₆₁

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₆₁

Fitting

C₂×#107×C₆₁

C₂

C₂²×C₆₁

D₆₁

C₆₁

G ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#107

N	H ≅ G/N	type
9. #14519713	C₄	semidirect
74. C₆₁	#1952	semidirect

H ≅ G/N

type

9. #14519713

C₄

semidirect

74. C₆₁

#1952

semidirect

Subgroups — #21446602

Conjugacy classes of subgroups

Complements