Group #14271698 — subgroups

Subgroups — #14271698

Order 1856.

234 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 99 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×#125	C₂	1	1	yes	maximal, characteristic, complemented
2	#11745260	C₂	1	2	yes	maximal, complemented
3	#11745259	C₂	1	1	yes	maximal, characteristic, complemented
4	#11745257	C₂	1	1	yes	maximal, characteristic
5	#11745256	C₂	1	2	yes	maximal, complemented
6	#11745255	C₂	1	1	yes	maximal, characteristic, complemented
7	#11745255	C₂	1	2	yes	maximal, complemented
8	#11745254	C₂	1	2	yes	maximal, complemented
9	#11745249	C₂	1	1	yes	maximal, characteristic, complemented
10	#11745237	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄²×D₂₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×D₁₁₆	C₂²	1	1	yes	characteristic
13	C₂×D₁₁₆	C₂²	1	2	yes	—
14	C₂×C₄×D₂₉	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₂₉	C₂²	1	1	yes	characteristic
16	C₂×C₄×D₂₉	C₂²	1	1	yes	characteristic
17	C₂×C₄×D₂₉	C₂²	1	2	yes	—
18	C₂×Dic₅₈	C₂²	1	1	yes	characteristic
19	C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
20	C₄⋊C₄×C₂₉	C₂²	1	2	yes	—
21	C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
22	C₄⋊C₄×C₂₉	C₂²	1	2	yes	—
23	C₄²×C₂₉	C₂²	1	1	yes	characteristic
24	#90781	C₂²	1	2	yes	—
25	#90781	C₂²	1	2	yes	—
26	#90781	C₂²	1	2	yes	—
27	#90781	C₂²	1	2	yes	—
28	#90781	C₂²	1	2	yes	—
29	C₄⋊Dic₂₉	C₂²	1	2	yes	—
30	#90779	C₂²	1	2	yes	—
31	C₄×Dic₂₉	C₂²	1	1	yes	characteristic
32	C₄×Dic₂₉	C₂²	1	1	yes	characteristic
33	C₄×Dic₂₉	C₂²	1	1	yes	characteristic
34	C₄×Dic₂₉	C₂²	1	2	yes	—
35	C₂²×D₂₉	C₂³	1	2	yes	—
36	C₂²×D₂₉	C₂³	1	1	yes	characteristic
37	C₂×C₄×C₂₉	C₂³	1	2	yes	—
38	C₂×C₄×C₂₉	C₂³	1	1	yes	characteristic
39	C₂×C₄×C₂₉	C₂³	1	1	yes	characteristic
40	C₂×C₄×C₂₉	C₂³	1	2	yes	—
41	C₂×C₄×C₂₉	C₂³	1	1	yes	characteristic
42	C₂×Dic₂₉	C₂³	1	1	yes	characteristic
43	C₂×Dic₂₉	C₂³	1	1	yes	characteristic
44	C₂×Dic₂₉	C₂³	1	2	yes	—
45	C₂×Dic₂₉	C₂³	1	1	yes	characteristic
46	D₁₁₆	—	2	4	no	—
47	D₁₁₆	—	2	2	no	—
48	C₄×D₂₉	—	2	2	no	—
49	C₄×D₂₉	—	2	2	no	—
50	C₄×D₂₉	—	2	2	no	—
51	C₄×D₂₉	—	2	4	no	—
52	Dic₅₈	—	2	2	no	—
53	C₂²×C₂₉	C₂⁴	1	1	yes	characteristic
54	C₂×D₂₉	—	2	1	no	—
55	C₂×D₂₉	—	2	1	no	—
56	C₂×D₂₉	—	2	2	no	—
57	C₂×D₂₉	—	2	2	no	—
58	C₂×D₂₉	—	2	2	no	—
59	C₂×D₂₉	#41	1	2	yes	—
60	C₄×C₂₉	—	2	1	no	—
61	C₄×C₂₉	—	2	1	no	—
62	C₄×C₂₉	—	2	2	no	—
63	C₄×C₂₉	—	2	2	no	—
64	C₄×C₂₉	#41	1	2	yes	—
65	Dic₂₉	—	2	2	no	—
66	Dic₂₉	—	2	1	no	—
67	Dic₂₉	—	2	1	no	—
68	Dic₂₉	#41	1	2	yes	—
69	#529	—	29	1	no	maximal, Sylow
70	C₂×C₂₉	C₂×#41	1	1	yes	characteristic
71	C₂×C₂₉	C₂×#41	1	1	yes	characteristic
72	C₂×C₂₉	C₂×#41	1	1	yes	characteristic
73	D₂₉	—	2	2	no	—
74	D₂₉	—	4	2	no	—
75	#126	—	29	2	no	—
76	#125	D₂₉	1	1	yes	characteristic, complemented
77	#124	—	29	1	no	—
78	#123	—	29	2	no	—
79	C₂²⋊Q₈	—	29	1	no	—
80	#121	—	29	1	no	—
81	C₄×Q₈	—	29	1	no	—
82	C₄×D₄	—	29	1	no	—
83	C₄×D₄	—	29	2	no	—
84	#117	—	29	2	no	—
85	C₂×C₄²	—	29	1	no	—
86	C₂₉	#529	1	1	yes	characteristic, complemented, Sylow
87	C₂×Q₈	—	29	1	no	—
88	C₂×D₄	—	29	2	no	—
89	C₂×D₄	—	29	1	no	—
90	C₂²×C₄	—	29	1	no	—
91	C₂²×C₄	—	29	1	no	—
92	C₂²×C₄	—	29	1	no	—
93	C₂²×C₄	—	29	2	no	—
94	C₄⋊C₄	—	29	2	no	—
95	C₄⋊C₄	—	29	2	no	—
96	C₄⋊C₄	C₂×D₂₉	1	2	yes	—
97	C₄⋊C₄	C₂×D₂₉	1	1	yes	characteristic
98	C₄⋊C₄	C₂×D₂₉	1	2	yes	—
99	C₄⋊C₄	C₂×D₂₉	1	1	yes	characteristic
100	C₂²⋊C₄	—	29	2	no	—
101	C₂²⋊C₄	—	29	2	no	—
102	C₂²⋊C₄	—	29	2	no	—
103	C₂²⋊C₄	—	29	2	no	—
104	C₂²⋊C₄	—	29	2	no	—
105	C₄²	—	29	1	no	—
106	C₄²	—	29	1	no	—
107	C₄²	—	29	1	no	—
108	C₄²	—	29	2	no	—
109	C₄²	C₂×D₂₉	1	1	yes	characteristic
110	C₂³	—	29	1	no	—
111	C₂³	—	29	2	no	—
112	Q₈	—	58	2	no	—
113	D₄	—	58	4	no	—
114	D₄	—	58	2	no	—
115	C₂×C₄	—	29	1	no	—
116	C₂×C₄	—	29	1	no	—
117	C₂×C₄	—	29	1	no	—
118	C₂×C₄	—	29	2	no	—
119	C₂×C₄	—	58	2	no	—
120	C₂×C₄	—	58	4	no	—
121	C₂×C₄	—	58	2	no	—
122	C₂×C₄	—	58	2	no	—
123	C₂×C₄	C₂²×D₂₉	1	1	yes	characteristic
124	C₂×C₄	C₂²×D₂₉	1	1	yes	characteristic
125	C₂×C₄	C₂²×D₂₉	1	2	yes	—
126	C₂×C₄	C₂²×D₂₉	1	2	yes	—
127	C₂×C₄	C₂²×D₂₉	1	1	yes	characteristic
128	C₂²	—	29	2	no	—
129	C₂²	—	58	1	no	—
130	C₂²	—	58	1	no	—
131	C₂²	—	58	2	no	—
132	C₂²	—	58	2	no	—
133	C₂²	—	58	2	no	—
134	C₂²	C₂³×D₂₉	1	1	yes	characteristic
135	C₄	—	2	1	no	—
136	C₄	—	2	2	no	—
137	C₄	—	2	1	no	—
138	C₄	—	2	2	no	—
139	C₄	—	29	2	no	—
140	C₄	—	58	1	no	—
141	C₄	—	58	2	no	—
142	C₄	—	58	1	no	—
143	C₄	#90809	1	2	yes	—
144	C₂	—	58	2	no	—
145	C₂	—	116	2	no	—
146	C₂	C₂×#90809	1	1	yes	characteristic
147	C₂	#41×D₂₉	1	1	yes	characteristic
148	C₂	#41×D₂₉	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂₉×#125

C₂

yes

maximal, characteristic, complemented

#11745260

C₂

yes

maximal, complemented

#11745259

C₂

yes

maximal, characteristic, complemented

#11745257

C₂

yes

maximal, characteristic

#11745256

C₂

yes

maximal, complemented

#11745255

C₂

yes

maximal, characteristic, complemented

#11745255

C₂

yes

maximal, complemented

#11745254

C₂

yes

maximal, complemented

#11745249

C₂

yes

maximal, characteristic, complemented

#11745237

C₂

yes

maximal, characteristic, complemented

C₄²×D₂₉

C₂

yes

maximal, characteristic, complemented

C₂×D₁₁₆

C₂²

yes

characteristic

C₂×D₁₁₆

C₂²

yes

—

C₂×C₄×D₂₉

C₂²

yes

characteristic

C₂×C₄×D₂₉

C₂²

yes

characteristic

C₂×C₄×D₂₉

C₂²

yes

characteristic

C₂×C₄×D₂₉

C₂²

yes

—

C₂×Dic₅₈

C₂²

yes

characteristic

C₄⋊C₄×C₂₉

C₂²

yes

characteristic

C₄⋊C₄×C₂₉

C₂²

yes

—

C₄⋊C₄×C₂₉

C₂²

yes

characteristic

C₄⋊C₄×C₂₉

C₂²

yes

—

C₄²×C₂₉

C₂²

yes

characteristic

#90781

C₂²

yes

—

#90781

C₂²

yes

—

#90781

C₂²

yes

—

#90781

C₂²

yes

—

#90781

C₂²

yes

—

C₄⋊Dic₂₉

C₂²

yes

—

#90779

C₂²

yes

—

C₄×Dic₂₉

C₂²

yes

characteristic

C₄×Dic₂₉

C₂²

yes

characteristic

C₄×Dic₂₉

C₂²

yes

characteristic

C₄×Dic₂₉

C₂²

yes

—

C₂²×D₂₉

C₂³

yes

—

C₂²×D₂₉

C₂³

yes

characteristic

C₂×C₄×C₂₉

C₂³

yes

—

C₂×C₄×C₂₉

C₂³

yes

characteristic

C₂×C₄×C₂₉

C₂³

yes

characteristic

C₂×C₄×C₂₉

C₂³

yes

—

C₂×C₄×C₂₉

C₂³

yes

characteristic

C₂×Dic₂₉

C₂³

yes

characteristic

C₂×Dic₂₉

C₂³

yes

characteristic

C₂×Dic₂₉

C₂³

yes

—

C₂×Dic₂₉

C₂³

yes

characteristic

D₁₁₆

—

D₁₁₆

—

C₄×D₂₉

—

C₄×D₂₉

—

C₄×D₂₉

—

C₄×D₂₉

—

Dic₅₈

—

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

—

C₄×C₂₉

#41

yes

—

Dic₂₉

—

Dic₂₉

—

Dic₂₉

—

Dic₂₉

#41

yes

—

#529

—

maximal, Sylow

C₂×C₂₉

C₂×#41

yes

characteristic

C₂×C₂₉

C₂×#41

yes

characteristic

C₂×C₂₉

C₂×#41

yes

characteristic

D₂₉

—

D₂₉

—

#126

—

#125

D₂₉

yes

characteristic, complemented

#124

—

#123

—

C₂²⋊Q₈

—

#121

—

C₄×Q₈

—

C₄×D₄

—

C₄×D₄

—

#117

—

C₂×C₄²

—

C₂₉

#529

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×D₄

—

C₂×D₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

C₂×D₂₉

yes

—

C₄⋊C₄

C₂×D₂₉

yes

characteristic

C₄⋊C₄

C₂×D₂₉

yes

—

C₄⋊C₄

C₂×D₂₉

yes

characteristic

100

C₂²⋊C₄

—

101

C₂²⋊C₄

—

102

C₂²⋊C₄

—

103

C₂²⋊C₄

—

104

C₂²⋊C₄

—

105

C₄²

—

106

C₄²

—

107

C₄²

—

108

C₄²

—

109

C₄²

C₂×D₂₉

yes

characteristic

110

C₂³

—

111

C₂³

—

112

Q₈

—

113

D₄

—

114

D₄

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

C₂²×D₂₉

yes

characteristic

124

C₂×C₄

C₂²×D₂₉

yes

characteristic

125

C₂×C₄

C₂²×D₂₉

yes

—

126

C₂×C₄

C₂²×D₂₉

yes

—

127

C₂×C₄

C₂²×D₂₉

yes

characteristic

128

C₂²

—

129

C₂²

—

130

C₂²

—

131

C₂²

—

132

C₂²

—

133

C₂²

—

134

C₂²

C₂³×D₂₉

yes

characteristic

135

C₄

—

136

C₄

—

137

C₄

—

138

C₄

—

139

C₄

—

140

C₄

—

141

C₄

—

142

C₄

—

143

C₄

#90809

yes

—

144

C₂

—

145

C₂

—

116

—

146

C₂

C₂×#90809

yes

characteristic

147

C₂

#41×D₂₉

yes

characteristic

148

C₂

#41×D₂₉

yes

characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂³×D₂₉
commutator, socle, cosocle	C₂²×C₂₉	C₂⁴
Fitting	C₂₉×#125	C₂
prime radical	#11745257	C₂
hypercenter	#125	D₂₉
hypocenter	C₂₉	#529
LCS	G ▷ C₂²×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ #125

subgroup

G/H

center, Frattini

C₂²

C₂³×D₂₉

commutator, socle, cosocle

C₂²×C₂₉

C₂⁴

Fitting

C₂₉×#125

C₂

C₂

D₂₉

C₂₉

G ▷ C₂²×C₂₉ ▷ C₂₉

C₁ ◁ C₂² ◁ #125

N	H ≅ G/N	type
1. C₂₉×#125	C₂	semidirect
2. #11745260	C₂	semidirect
3. #11745259	C₂	semidirect
5. #11745256	C₂	semidirect
6. #11745255	C₂	semidirect
7. #11745255	C₂	semidirect
8. #11745254	C₂	semidirect
9. #11745249	C₂	semidirect
10. #11745237	C₂	semidirect
11. C₄²×D₂₉	C₂	semidirect
76. #125	D₂₉	semidirect
86. C₂₉	#529	semidirect

H ≅ G/N

type

1. C₂₉×#125

C₂

semidirect

2. #11745260

C₂

semidirect

3. #11745259

C₂

semidirect

5. #11745256

C₂

semidirect

6. #11745255

C₂

semidirect

7. #11745255

C₂

semidirect

8. #11745254

C₂

semidirect

9. #11745249

C₂

semidirect

10. #11745237

C₂

semidirect

11. C₄²×D₂₉

C₂

semidirect

76. #125

D₂₉

semidirect

86. C₂₉

#529

semidirect

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

subgroup	index
C₂₉×#125	2
#11745260	2
#11745259	2
#11745257	2
#11745256	2
#11745255	2
#11745254	2
#11745249	2
#11745237	2
C₄²×D₂₉	2
#529	29

subgroup

index

C₂₉×#125

C₄²×D₂₉

Subgroups — #14271698

Conjugacy classes of subgroups

Complements

Maximal subgroups