Group #16820325 — subgroups

Subgroups — #16820325

Order 3712.

320 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 97 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	#14271187	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#11745185	C₂	1	4	yes	maximal, complemented
3	#14271009	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₉×#532	C₂	1	1	yes	maximal, characteristic
5	C₂×#41×C₂₉	C₂²	1	2	yes	—
6	C₂₉×C₄⋊Q₈	C₄	1	1	yes	characteristic, complemented
7	C₂₉×#127	C₄	1	1	yes	characteristic, complemented
8	C₂₉×#124	C₄	1	2	yes	complemented
9	C₂₉×#121	—	2	2	no	—
10	C₄×D₄×C₂₉	—	2	2	no	—
11	C₂×C₄²×C₂₉	C₂²	1	1	yes	characteristic
12	C₂×C₄×Dic₂₉	C₂²	1	2	yes	—
13	C₂×#90777	C₂²	1	2	yes	—
14	#11745185	—	2	8	no	—
15	#11745179	—	2	2	no	—
16	C₄⋊#6597	—	2	2	no	—
17	#41×C₂₉	—	2	4	no	—
18	#41×C₂₉	—	2	4	no	—
19	C₂×Q₈×C₂₉	C₂×C₄	1	2	yes	—
20	C₂×D₄×C₂₉	—	2	2	no	—
21	C₂×D₄×C₂₉	—	2	2	no	—
22	C₂×D₄×C₂₉	C₂×C₄	1	2	yes	—
23	C₂²×C₄×C₂₉	—	2	2	no	—
24	C₂²×C₄×C₂₉	D₄	1	2	yes	—
25	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
26	C₂²×Dic₂₉	—	2	2	no	—
27	C₄⋊C₄×C₂₉	—	2	2	no	—
28	C₂²⋊C₄×C₂₉	—	2	4	no	—
29	C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
30	C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
31	C₄²×C₂₉	D₄	1	2	yes	—
32	C₄×Dic₂₉	—	2	2	no	—
33	C₄×Dic₂₉	D₄	1	4	yes	complemented
34	#90777	—	2	4	no	—
35	C₂×#6597	—	2	2	no	—
36	C₂³×C₂₉	—	2	2	no	—
37	C₂³×C₂₉	C₂×D₄	1	1	yes	characteristic
38	Q₈×C₂₉	—	2	4	no	—
39	D₄×C₂₉	—	2	4	no	—
40	D₄×C₂₉	—	4	4	no	—
41	D₄×C₂₉	—	4	4	no	—
42	C₂×C₄×C₂₉	—	2	2	no	—
43	C₂×C₄×C₂₉	—	4	2	no	—
44	C₂×C₄×C₂₉	—	4	2	no	—
45	C₂×C₄×C₂₉	—	4	2	no	—
46	C₂×C₄×C₂₉	C₂²⋊C₄	1	2	yes	—
47	C₂×C₄×C₂₉	C₂²⋊C₄	1	2	yes	—
48	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
49	C₂×C₄×C₂₉	C₂×D₄	1	2	yes	—
50	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
51	C₂×C₄×C₂₉	#41	1	2	yes	—
52	C₂×Dic₂₉	—	2	4	no	—
53	C₂×Dic₂₉	—	4	4	no	—
54	#6597	—	4	2	no	—
55	#1963	—	29	1	no	maximal, Sylow
56	C₂²×C₂₉	—	2	2	no	—
57	C₂²×C₂₉	—	4	2	no	—
58	C₂²×C₂₉	—	4	4	no	—
59	C₂²×C₂₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
60	C₂²×C₂₉	#121	1	2	yes	—
61	C₄×C₂₉	—	2	2	no	—
62	C₄×C₂₉	—	2	2	no	—
63	C₄×C₂₉	—	4	2	no	—
64	C₄×C₂₉	C₄×D₄	1	2	yes	—
65	C₄×C₂₉	#124	1	1	yes	characteristic
66	C₄×C₂₉	#127	1	1	yes	characteristic
67	Dic₂₉	—	4	4	no	—
68	#532	D₂₉	1	1	yes	characteristic
69	#423	—	29	1	no	—
70	C₂×#104	—	29	4	no	—
71	#376	—	29	1	no	—
72	C₂×C₂₉	—	2	2	no	—
73	C₂×C₂₉	—	8	2	no	—
74	C₂×C₂₉	#390	1	1	yes	characteristic
75	C₂×C₂₉	#421	1	2	yes	—
76	C₂×#41	C₂×D₂₉	1	2	yes	—
77	C₂×M₁₆	—	29	2	no	—
78	C₄⋊Q₈	Dic₂₉	1	1	yes	characteristic, complemented
79	#127	Dic₂₉	1	1	yes	characteristic, complemented
80	#124	Dic₂₉	1	2	yes	complemented
81	#121	—	2	2	no	—
82	C₄×D₄	—	2	2	no	—
83	C₂×C₄²	—	29	2	no	—
84	C₂×C₄²	C₂×D₂₉	1	1	yes	characteristic
85	C₄⋊C₈	—	58	2	no	—
86	#104	—	58	8	no	—
87	#95	—	58	2	no	—
88	C₂₉	#1963	1	1	yes	characteristic, complemented, Sylow
89	#41	—	2	4	no	—
90	#41	—	2	4	no	—
91	C₂×Q₈	C₂×Dic₂₉	1	2	yes	—
92	C₂×D₄	—	2	2	no	—
93	C₂×D₄	—	2	2	no	—
94	C₂×D₄	C₂×Dic₂₉	1	2	yes	—
95	C₂²×C₄	—	2	2	no	—
96	C₂²×C₄	—	58	2	no	—
97	C₂²×C₄	C₂²⋊D₂₉	1	2	yes	—
98	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
99	M₁₆	—	58	4	no	—
100	C₂×C₈	—	58	2	no	—
101	C₄⋊C₄	—	2	2	no	—
102	C₂²⋊C₄	—	2	4	no	—
103	C₄²	—	29	4	no	—
104	C₄²	—	58	2	no	—
105	C₄²	C₂×Dic₂₉	1	1	yes	characteristic
106	C₄²	C₂×Dic₂₉	1	1	yes	characteristic
107	C₄²	C₂²⋊D₂₉	1	2	yes	—
108	C₂³	—	2	2	no	—
109	C₂³	C₂×C₂²⋊D₂₉	1	1	yes	characteristic
110	Q₈	—	2	4	no	—
111	D₄	—	2	4	no	—
112	D₄	—	4	4	no	—
113	D₄	—	4	4	no	—
114	C₂×C₄	—	2	2	no	—
115	C₂×C₄	—	4	2	no	—
116	C₂×C₄	—	4	2	no	—
117	C₂×C₄	—	4	2	no	—
118	C₂×C₄	—	58	4	no	—
119	C₂×C₄	—	116	4	no	—
120	C₂×C₄	C₂²⋊Dic₂₉	1	2	yes	—
121	C₂×C₄	C₂²⋊Dic₂₉	1	2	yes	—
122	C₂×C₄	D₄×D₂₉	1	2	yes	—
123	C₂×C₄	#90807	1	2	yes	—
124	C₂×C₄	C₂²×Dic₂₉	1	1	yes	characteristic
125	C₂×C₄	C₂×C₂²⋊D₂₉	1	1	yes	characteristic
126	C₈	—	116	2	no	—
127	C₂²	—	2	2	no	—
128	C₂²	—	4	2	no	—
129	C₂²	—	4	4	no	—
130	C₂²	#11745300	1	2	yes	—
131	C₂²	C₂×C₂²⋊Dic₂₉	1	1	yes	characteristic
132	C₄	—	2	2	no	—
133	C₄	—	2	2	no	—
134	C₄	—	4	2	no	—
135	C₄	—	116	4	no	—
136	C₄	D₄×Dic₂₉	1	2	yes	—
137	C₄	#11745298	1	1	yes	characteristic
138	C₄	#11745302	1	1	yes	characteristic
139	C₂	—	2	2	no	—
140	C₂	—	8	2	no	—
141	C₂	#14271066	1	1	yes	characteristic
142	C₂	#14271180	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14271187

C₂

yes

maximal, characteristic, complemented

C₂×#11745185

C₂

yes

maximal, complemented

#14271009

C₂

yes

maximal, characteristic, complemented

C₂₉×#532

C₂

yes

maximal, characteristic

C₂×#41×C₂₉

C₂²

yes

—

C₂₉×C₄⋊Q₈

C₄

yes

characteristic, complemented

C₂₉×#127

C₄

yes

characteristic, complemented

C₂₉×#124

C₄

yes

complemented

C₂₉×#121

—

C₄×D₄×C₂₉

—

C₂×C₄²×C₂₉

C₂²

yes

characteristic

C₂×C₄×Dic₂₉

C₂²

yes

—

C₂×#90777

C₂²

yes

—

#11745185

—

#11745179

—

C₄⋊#6597

—

#41×C₂₉

—

#41×C₂₉

—

C₂×Q₈×C₂₉

C₂×C₄

yes

—

C₂×D₄×C₂₉

—

C₂×D₄×C₂₉

—

C₂×D₄×C₂₉

C₂×C₄

yes

—

C₂²×C₄×C₂₉

—

C₂²×C₄×C₂₉

D₄

yes

—

C₂²×C₄×C₂₉

C₂³

yes

characteristic

C₂²×Dic₂₉

—

C₄⋊C₄×C₂₉

—

C₂²⋊C₄×C₂₉

—

C₄²×C₂₉

C₂×C₄

yes

characteristic

C₄²×C₂₉

C₂×C₄

yes

characteristic

C₄²×C₂₉

D₄

yes

—

C₄×Dic₂₉

—

C₄×Dic₂₉

D₄

yes

complemented

#90777

—

C₂×#6597

—

C₂³×C₂₉

—

C₂³×C₂₉

C₂×D₄

yes

characteristic

Q₈×C₂₉

—

D₄×C₂₉

—

D₄×C₂₉

—

D₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

C₂²⋊C₄

yes

—

C₂×C₄×C₂₉

C₂²⋊C₄

yes

—

C₂×C₄×C₂₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₂₉

C₂×D₄

yes

—

C₂×C₄×C₂₉

C₂×D₄

yes

characteristic

C₂×C₄×C₂₉

#41

yes

—

C₂×Dic₂₉

—

C₂×Dic₂₉

—

#6597

—

#1963

—

maximal, Sylow

C₂²×C₂₉

—

C₂²×C₂₉

—

C₂²×C₂₉

—

C₂²×C₂₉

C₂×C₂²⋊C₄

yes

characteristic

C₂²×C₂₉

#121

yes

—

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

C₄×D₄

yes

—

C₄×C₂₉

yes

C₄×C₂₉

yes

Dic₂₉

—

#532

D₂₉

yes

—

—

—

C₂×C₂₉

—

C₂×C₂₉

—

C₂×C₂₉

#390

yes

characteristic

C₂×C₂₉

#421

yes

—

C₂×#41

C₂×D₂₉

yes

—

C₂×M₁₆

—

C₄⋊Q₈

Dic₂₉

yes

characteristic, complemented

#127

Dic₂₉

yes

characteristic, complemented

#124

Dic₂₉

yes

complemented

#121

—

C₄×D₄

—

C₂×C₄²

—

C₂×C₄²

C₂×D₂₉

yes

characteristic

C₄⋊C₈

—

#104

—

#95

—

C₂₉

#1963

yes

characteristic, complemented, Sylow

#41

—

#41

—

C₂×Q₈

C₂×Dic₂₉

yes

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

C₂×Dic₂₉

yes

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²⋊D₂₉

yes

—

C₂²×C₄

C₂²×D₂₉

yes

characteristic

M₁₆

—

100

C₂×C₈

—

101

C₄⋊C₄

—

102

C₂²⋊C₄

—

103

C₄²

—

104

C₄²

—

105

C₄²

C₂×Dic₂₉

yes

characteristic

106

C₄²

C₂×Dic₂₉

yes

characteristic

107

C₄²

C₂²⋊D₂₉

yes

—

108

C₂³

—

109

C₂³

C₂×C₂²⋊D₂₉

yes

characteristic

110

Q₈

—

111

D₄

—

112

D₄

—

113

D₄

—

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

—

116

—

120

C₂×C₄

C₂²⋊Dic₂₉

yes

—

121

C₂×C₄

C₂²⋊Dic₂₉

yes

—

122

C₂×C₄

D₄×D₂₉

yes

—

123

C₂×C₄

#90807

yes

—

124

C₂×C₄

C₂²×Dic₂₉

yes

characteristic

125

C₂×C₄

C₂×C₂²⋊D₂₉

yes

characteristic

126

C₈

—

116

—

127

C₂²

—

128

C₂²

—

129

C₂²

—

130

C₂²

#11745300

yes

—

131

C₂²

C₂×C₂²⋊Dic₂₉

yes

characteristic

132

C₄

—

133

C₄

—

134

C₄

—

135

C₄

—

116

—

136

C₄

D₄×Dic₂₉

yes

—

137

C₄

#11745298

yes

characteristic

138

C₄

#11745302

yes

characteristic

139

C₂

—

140

C₂

—

141

C₂

#14271066

yes

characteristic

142

C₂

#14271180

yes

—

	subgroup	G/H
center	C₂×C₄	C₂×C₂²⋊D₂₉
commutator	C₂×C₄×C₂₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₂₉
Fitting, prime radical	C₂₉×#532	C₂
socle	C₂²×C₂₉	C₂×C₂²⋊C₄
cosocle	C₂²×C₄×C₂₉	C₂³
hypercenter	#532	D₂₉
hypocenter	C₂₉	#1963
LCS	G ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #532

subgroup

G/H

center

C₂×C₄

C₂×C₂²⋊D₂₉

commutator

C₂×C₄×C₂₉

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₂₉

Fitting, prime radical

C₂₉×#532

C₂

socle

C₂²×C₂₉

C₂×C₂²⋊C₄

cosocle

C₂²×C₄×C₂₉

C₂³

D₂₉

C₂₉

G ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #532

N	H ≅ G/N	type
1. #14271187	C₂	semidirect
2. C₂×#11745185	C₂	semidirect
3. #14271009	C₂	semidirect
6. C₂₉×C₄⋊Q₈	C₄	semidirect
7. C₂₉×#127	C₄	semidirect
8. C₂₉×#124	C₄	semidirect
33. C₄×Dic₂₉	D₄	semidirect
78. C₄⋊Q₈	Dic₂₉	semidirect
79. #127	Dic₂₉	semidirect
80. #124	Dic₂₉	semidirect
88. C₂₉	#1963	semidirect

H ≅ G/N

type

1. #14271187

C₂

semidirect

2. C₂×#11745185

C₂

semidirect

3. #14271009

C₂

semidirect

6. C₂₉×C₄⋊Q₈

C₄

semidirect

7. C₂₉×#127

C₄

semidirect

8. C₂₉×#124

C₄

semidirect

33. C₄×Dic₂₉

D₄

semidirect

78. C₄⋊Q₈

Dic₂₉

semidirect

79. #127

Dic₂₉

semidirect

80. #124

Dic₂₉

semidirect

88. C₂₉

#1963

semidirect

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

subgroup	index
#14271187	2
C₂×#11745185	2
#14271009	2
C₂₉×#532	2
#1963	29

subgroup

index

C₂₉×#532

Subgroups — #16820325

Conjugacy classes of subgroups

Complements

Maximal subgroups