Group #14271857 — subgroups

Subgroups — #14271857

Order 1856.

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

normal subgroups only

This group has 238 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	C₂₉×#117	C₂	1	1	yes	maximal, characteristic, complemented
2	#11745292	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₂²⋊D₂₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#11745257	C₂	1	1	yes	maximal, characteristic, complemented
5	#11745255	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄⋊C₄×D₂₉	C₂	1	1	yes	maximal, characteristic, complemented
7	#11745252	C₂	1	1	yes	maximal, characteristic, complemented
8	#11745246	C₂	1	2	yes	maximal, complemented
9	#11745245	C₂	1	2	yes	maximal, complemented
10	#11745238	C₂	1	2	yes	maximal, complemented
11	C₄×D₁₁₆	C₂	1	2	yes	maximal, complemented
12	C₂²×C₄×C₂₉	C₂²	1	1	yes	characteristic
13	C₂×C₂²⋊D₂₉	C₂²	1	1	yes	characteristic
14	C₂×C₂²⋊D₂₉	C₂²	1	2	yes	—
15	C₂×D₁₁₆	C₂²	1	1	yes	characteristic
16	C₂×D₁₁₆	C₂²	1	2	yes	—
17	C₂×C₄×D₂₉	C₂²	1	1	yes	characteristic
18	C₂×C₄×D₂₉	C₂²	1	2	yes	—
19	C₂×C₄×D₂₉	C₂²	1	2	yes	—
20	C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
21	C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
22	C₂²⋊C₄×C₂₉	C₂²	1	2	yes	—
23	C₄²×C₂₉	C₂²	1	2	yes	—
24	C₂²⋊Dic₂₉	C₂²	1	1	yes	characteristic
25	#90781	C₂²	1	1	yes	characteristic
26	#90781	C₂²	1	2	yes	—
27	#90781	C₂²	1	2	yes	—
28	#90781	C₂²	1	2	yes	—
29	C₄⋊Dic₂₉	C₂²	1	1	yes	characteristic
30	C₄⋊Dic₂₉	C₂²	1	2	yes	—
31	#90779	C₂²	1	1	yes	characteristic
32	#90779	C₂²	1	2	yes	—
33	#90779	C₂²	1	2	yes	—
34	C₄×Dic₂₉	C₂²	1	1	yes	characteristic
35	C₂³×C₂₉	C₂³	1	1	yes	characteristic
36	C₂²×D₂₉	C₂³	1	2	yes	—
37	C₂²×D₂₉	C₂³	1	1	yes	characteristic
38	C₂×C₄×C₂₉	—	2	2	no	—
39	C₂×C₄×C₂₉	C₂³	1	2	yes	—
40	C₂×C₄×C₂₉	C₂³	1	1	yes	characteristic
41	C₂×C₄×C₂₉	C₂³	1	2	yes	—
42	C₂×C₄×C₂₉	C₂³	1	1	yes	characteristic
43	C₂²⋊D₂₉	—	2	2	no	—
44	C₂²⋊D₂₉	—	4	2	no	—
45	C₂×Dic₂₉	C₂³	1	1	yes	characteristic
46	C₂×Dic₂₉	C₂³	1	1	yes	characteristic
47	C₂×Dic₂₉	C₂³	1	1	yes	characteristic
48	C₂×Dic₂₉	C₂³	1	2	yes	—
49	D₁₁₆	—	2	4	no	—
50	D₁₁₆	—	2	2	no	—
51	C₄×D₂₉	—	2	2	no	—
52	C₄×D₂₉	—	4	2	no	—
53	C₄×D₂₉	—	4	2	no	—
54	C₂²×C₂₉	—	2	1	no	—
55	C₂²×C₂₉	—	2	1	no	—
56	C₂²×C₂₉	—	2	1	no	—
57	C₂²×C₂₉	C₂⁴	1	1	yes	characteristic
58	C₂×D₂₉	—	2	1	no	—
59	C₂×D₂₉	—	2	1	no	—
60	C₂×D₂₉	—	2	2	no	—
61	C₂×D₂₉	—	2	2	no	—
62	C₂×D₂₉	—	2	2	no	—
63	C₂×D₂₉	#41	1	2	yes	—
64	C₄×C₂₉	—	2	2	no	—
65	C₄×C₂₉	—	2	1	no	—
66	C₄×C₂₉	—	2	2	no	—
67	C₄×C₂₉	#41	1	2	yes	—
68	Dic₂₉	—	2	1	no	—
69	Dic₂₉	—	2	1	no	—
70	Dic₂₉	—	2	1	no	—
71	Dic₂₉	—	2	2	no	—
72	#553	—	29	1	no	maximal, Sylow
73	C₂×C₂₉	—	4	1	no	—
74	C₂×C₂₉	C₂×#41	1	1	yes	characteristic
75	C₂×C₂₉	C₂×#41	1	1	yes	characteristic
76	C₂×C₂₉	H(5,𝔽₂)	1	1	yes	characteristic
77	D₂₉	—	2	2	no	—
78	D₂₉	—	4	2	no	—
79	#126	—	29	2	no	—
80	#125	—	29	1	no	—
81	#123	—	29	2	no	—
82	#121	—	29	1	no	—
83	#121	—	29	1	no	—
84	#121	—	29	2	no	—
85	C₄×D₄	—	29	1	no	—
86	C₄×D₄	—	29	1	no	—
87	C₄×D₄	—	29	2	no	—
88	#117	D₂₉	1	1	yes	characteristic, complemented
89	C₂×C₄⋊C₄	—	29	1	no	—
90	C₂₉	#553	1	1	yes	characteristic, complemented, Sylow
91	C₂×D₄	—	29	1	no	—
92	C₂×D₄	—	29	2	no	—
93	C₂×D₄	—	29	2	no	—
94	C₂×D₄	—	29	1	no	—
95	C₂²×C₄	—	29	1	no	—
96	C₂²×C₄	—	29	2	no	—
97	C₂²×C₄	—	29	2	no	—
98	C₂²×C₄	C₂×D₂₉	1	1	yes	characteristic
99	C₄⋊C₄	—	29	1	no	—
100	C₄⋊C₄	—	29	2	no	—
101	C₄⋊C₄	—	29	2	no	—
102	C₄⋊C₄	—	29	1	no	—
103	C₄⋊C₄	—	29	2	no	—
104	C₄⋊C₄	C₂×D₂₉	1	1	yes	characteristic
105	C₄⋊C₄	C₂×D₂₉	1	1	yes	characteristic
106	C₂²⋊C₄	—	29	1	no	—
107	C₂²⋊C₄	—	29	1	no	—
108	C₂²⋊C₄	—	29	2	no	—
109	C₂²⋊C₄	—	29	2	no	—
110	C₂²⋊C₄	—	29	2	no	—
111	C₂²⋊C₄	C₂×D₂₉	1	2	yes	—
112	C₄²	—	29	1	no	—
113	C₄²	C₂×D₂₉	1	2	yes	—
114	C₂³	—	29	1	no	—
115	C₂³	—	29	2	no	—
116	C₂³	C₂²×D₂₉	1	1	yes	characteristic
117	D₄	—	58	4	no	—
118	D₄	—	58	2	no	—
119	D₄	—	58	2	no	—
120	D₄	—	116	2	no	—
121	C₂×C₄	—	2	2	no	—
122	C₂×C₄	—	29	1	no	—
123	C₂×C₄	—	29	1	no	—
124	C₂×C₄	—	29	1	no	—
125	C₂×C₄	—	29	2	no	—
126	C₂×C₄	—	58	2	no	—
127	C₂×C₄	—	116	2	no	—
128	C₂×C₄	—	116	2	no	—
129	C₂×C₄	C₂²×D₂₉	1	1	yes	characteristic
130	C₂×C₄	C₂²×D₂₉	1	2	yes	—
131	C₂×C₄	C₂²×D₂₉	1	2	yes	—
132	C₂×C₄	C₂²×D₂₉	1	1	yes	characteristic
133	C₂²	—	2	1	no	—
134	C₂²	—	2	1	no	—
135	C₂²	—	2	1	no	—
136	C₂²	—	29	2	no	—
137	C₂²	—	58	1	no	—
138	C₂²	—	58	1	no	—
139	C₂²	—	58	2	no	—
140	C₂²	—	58	2	no	—
141	C₂²	—	58	2	no	—
142	C₂²	C₂³×D₂₉	1	1	yes	characteristic
143	C₄	—	2	1	no	—
144	C₄	—	2	2	no	—
145	C₄	—	2	2	no	—
146	C₄	—	58	1	no	—
147	C₄	—	58	1	no	—
148	C₄	—	58	1	no	—
149	C₄	—	58	2	no	—
150	C₄	#90805	1	2	yes	—
151	C₂	—	4	1	no	—
152	C₂	—	58	2	no	—
153	C₂	—	116	2	no	—
154	C₂	C₂×#90805	1	1	yes	characteristic
155	C₂	#41×D₂₉	1	1	yes	characteristic
156	C₂	#11745364	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂₉×#117

C₂

yes

maximal, characteristic, complemented

#11745292

C₂

yes

maximal, characteristic, complemented

C₄×C₂²⋊D₂₉

C₂

yes

maximal, characteristic, complemented

#11745257

C₂

yes

maximal, characteristic, complemented

#11745255

C₂

yes

maximal, characteristic, complemented

C₄⋊C₄×D₂₉

C₂

yes

maximal, characteristic, complemented

#11745252

C₂

yes

maximal, characteristic, complemented

#11745246

C₂

yes

maximal, complemented

#11745245

C₂

yes

maximal, complemented

#11745238

C₂

yes

maximal, complemented

C₄×D₁₁₆

C₂

yes

maximal, complemented

C₂²×C₄×C₂₉

C₂²

yes

characteristic

C₂×C₂²⋊D₂₉

C₂²

yes

characteristic

C₂×C₂²⋊D₂₉

C₂²

yes

—

C₂×D₁₁₆

C₂²

yes

characteristic

C₂×D₁₁₆

C₂²

yes

—

C₂×C₄×D₂₉

C₂²

yes

characteristic

C₂×C₄×D₂₉

C₂²

yes

—

C₂×C₄×D₂₉

C₂²

yes

—

C₄⋊C₄×C₂₉

C₂²

yes

characteristic

C₄⋊C₄×C₂₉

C₂²

yes

characteristic

C₂²⋊C₄×C₂₉

C₂²

yes

—

C₄²×C₂₉

C₂²

yes

—

C₂²⋊Dic₂₉

C₂²

yes

characteristic

#90781

C₂²

yes

characteristic

#90781

C₂²

yes

—

#90781

C₂²

yes

—

#90781

C₂²

yes

—

C₄⋊Dic₂₉

C₂²

yes

characteristic

C₄⋊Dic₂₉

C₂²

yes

—

#90779

C₂²

yes

characteristic

#90779

C₂²

yes

—

#90779

C₂²

yes

—

C₄×Dic₂₉

C₂²

yes

characteristic

C₂³×C₂₉

C₂³

yes

characteristic

C₂²×D₂₉

C₂³

yes

—

C₂²×D₂₉

C₂³

yes

characteristic

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

C₂³

yes

—

C₂×C₄×C₂₉

C₂³

yes

characteristic

C₂×C₄×C₂₉

C₂³

yes

—

C₂×C₄×C₂₉

C₂³

yes

characteristic

C₂²⋊D₂₉

—

C₂²⋊D₂₉

—

C₂×Dic₂₉

C₂³

yes

characteristic

C₂×Dic₂₉

C₂³

yes

characteristic

C₂×Dic₂₉

C₂³

yes

characteristic

C₂×Dic₂₉

C₂³

yes

—

D₁₁₆

—

D₁₁₆

—

C₄×D₂₉

—

C₄×D₂₉

—

C₄×D₂₉

—

C₂²×C₂₉

—

C₂²×C₂₉

—

C₂²×C₂₉

—

C₂²×C₂₉

C₂⁴

yes

characteristic

C₂×D₂₉

—

C₂×D₂₉

—

C₂×D₂₉

—

C₂×D₂₉

—

C₂×D₂₉

—

C₂×D₂₉

#41

yes

—

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

#41

yes

—

Dic₂₉

—

Dic₂₉

—

Dic₂₉

—

Dic₂₉

—

#553

—

maximal, Sylow

C₂×C₂₉

—

C₂×C₂₉

C₂×#41

yes

characteristic

C₂×C₂₉

C₂×#41

yes

characteristic

C₂×C₂₉

H(5,𝔽₂)

yes

characteristic

D₂₉

—

D₂₉

—

—

—

—

—

—

—

C₄×D₄

—

C₄×D₄

—

C₄×D₄

—

#117

D₂₉

yes

characteristic, complemented

C₂×C₄⋊C₄

—

C₂₉

#553

yes

characteristic, complemented, Sylow

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂×D₂₉

yes

characteristic

C₄⋊C₄

—

100

C₄⋊C₄

—

101

C₄⋊C₄

—

102

C₄⋊C₄

—

103

C₄⋊C₄

—

104

C₄⋊C₄

C₂×D₂₉

yes

characteristic

105

C₄⋊C₄

C₂×D₂₉

yes

characteristic

106

C₂²⋊C₄

—

107

C₂²⋊C₄

—

108

C₂²⋊C₄

—

109

C₂²⋊C₄

—

110

C₂²⋊C₄

—

111

C₂²⋊C₄

C₂×D₂₉

yes

—

112

C₄²

—

113

C₄²

C₂×D₂₉

yes

—

114

C₂³

—

115

C₂³

—

116

C₂³

C₂²×D₂₉

yes

characteristic

117

D₄

—

118

D₄

—

119

D₄

—

120

D₄

—

116

—

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

—

127

C₂×C₄

—

116

—

128

C₂×C₄

—

116

—

129

C₂×C₄

C₂²×D₂₉

yes

characteristic

130

C₂×C₄

C₂²×D₂₉

yes

—

131

C₂×C₄

C₂²×D₂₉

yes

—

132

C₂×C₄

C₂²×D₂₉

yes

characteristic

133

C₂²

—

134

C₂²

—

135

C₂²

—

136

C₂²

—

137

C₂²

—

138

C₂²

—

139

C₂²

—

140

C₂²

—

141

C₂²

—

142

C₂²

C₂³×D₂₉

yes

characteristic

143

C₄

—

144

C₄

—

145

C₄

—

146

C₄

—

147

C₄

—

148

C₄

—

149

C₄

—

150

C₄

#90805

yes

—

151

C₂

—

152

C₂

—

153

C₂

—

116

—

154

C₂

C₂×#90805

yes

characteristic

155

C₂

#41×D₂₉

yes

characteristic

156

C₂

#11745364

yes

characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂³×D₂₉
commutator, socle, cosocle	C₂²×C₂₉	C₂⁴
Fitting	C₂₉×#117	C₂
hypercenter	#117	D₂₉
hypocenter	C₂₉	#553
LCS	G ▷ C₂²×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ #117

subgroup

G/H

center, Frattini

C₂²

C₂³×D₂₉

commutator, socle, cosocle

C₂²×C₂₉

C₂⁴

Fitting

C₂₉×#117

C₂

D₂₉

C₂₉

G ▷ C₂²×C₂₉ ▷ C₂₉

C₁ ◁ C₂² ◁ #117

N	H ≅ G/N	type
1. C₂₉×#117	C₂	semidirect
2. #11745292	C₂	semidirect
3. C₄×C₂²⋊D₂₉	C₂	semidirect
4. #11745257	C₂	semidirect
5. #11745255	C₂	semidirect
6. C₄⋊C₄×D₂₉	C₂	semidirect
7. #11745252	C₂	semidirect
8. #11745246	C₂	semidirect
9. #11745245	C₂	semidirect
10. #11745238	C₂	semidirect
11. C₄×D₁₁₆	C₂	semidirect
88. #117	D₂₉	semidirect
90. C₂₉	#553	semidirect

H ≅ G/N

type

1. C₂₉×#117

C₂

semidirect

2. #11745292

C₂

semidirect

3. C₄×C₂²⋊D₂₉

C₂

semidirect

4. #11745257

C₂

semidirect

5. #11745255

C₂

semidirect

6. C₄⋊C₄×D₂₉

C₂

semidirect

7. #11745252

C₂

semidirect

8. #11745246

C₂

semidirect

9. #11745245

C₂

semidirect

10. #11745238

C₂

semidirect

11. C₄×D₁₁₆

C₂

semidirect

88. #117

D₂₉

semidirect

90. C₂₉

#553

semidirect

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

subgroup	index
C₂₉×#117	2
#11745292	2
C₄×C₂²⋊D₂₉	2
#11745257	2
#11745255	2
C₄⋊C₄×D₂₉	2
#11745252	2
#11745246	2
#11745245	2
#11745238	2
C₄×D₁₁₆	2
#553	29

subgroup

index

C₂₉×#117

C₄×C₂²⋊D₂₉

C₄⋊C₄×D₂₉

C₄×D₁₁₆

Subgroups — #14271857

Conjugacy classes of subgroups

Complements

Maximal subgroups