Group #16836154 — subgroups

Subgroups — #16836154

Order 3712.

440 conjugacy classes of subgroups; only the 198 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 198 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	#14272242	C₂	1	2	yes	maximal
2	#14272178	C₂	1	6	yes	maximal, complemented
3	C₂×#11745212	C₂	1	3	yes	maximal, complemented
4	D₂₉⋊#108	C₂	1	3	yes	maximal, complemented
5	#131×D₂₉	C₂	1	1	yes	maximal, characteristic
6	#41×D₂₉	C₂²	1	1	yes	characteristic
7	#11745348	—	2	2	no	—
8	#11745346	—	2	6	no	—
9	D₂₉⋊M₁₆	C₂²	1	6	yes	—
10	C₂×#90796	C₂²	1	6	yes	—
11	C₂₉×#131	C₄	1	1	yes	characteristic
12	#11745310	C₄	1	1	yes	characteristic
13	#11745269	C₄	1	3	yes	—
14	M₁₆×D₂₉	C₂²	1	3	yes	—
15	#11745263	C₄	1	3	yes	—
16	C₂×C₈×D₂₉	C₂²	1	3	yes	—
17	#11745212	C₂²	1	1	yes	characteristic
18	#11745212	C₂²	1	3	yes	—
19	#11745212	C₂²	1	6	yes	—
20	#11745211	C₂²	1	6	yes	—
21	#41×C₂₉	C₂×C₄	1	1	yes	characteristic
22	#90809	D₄	1	1	yes	characteristic
23	Q₈×D₂₉	Q₈	1	1	yes	characteristic
24	#90807	D₄	1	3	yes	—
25	D₄×D₂₉	Q₈	1	3	yes	—
26	#90805	C₂×C₄	1	3	yes	—
27	C₂×C₄×D₂₉	C₂³	1	3	yes	—
28	#90800	—	2	6	no	—
29	C₂×#6599	—	2	6	no	—
30	#90796	—	2	6	no	—
31	#90796	C₂³	1	6	yes	—
32	#90796	C₂³	1	2	yes	—
33	D₂₉⋊C₈	—	2	6	no	—
34	M₁₆×C₂₉	C₂×C₄	1	3	yes	—
35	C₂×C₈×C₂₉	C₂×C₄	1	3	yes	—
36	#90777	C₂×C₄	1	3	yes	—
37	C₂×#6597	C₂×C₄	1	3	yes	—
38	#90772	C₂×C₄	1	6	yes	—
39	C₈×D₂₉	C₂×C₄	1	3	yes	—
40	C₈×D₂₉	C₂×C₄	1	3	yes	—
41	C₈×D₂₉	C₂³	1	3	yes	—
42	C₈×D₂₉	C₂³	1	1	yes	characteristic
43	C₂²×D₂₉	C₂×Q₈	1	3	yes	—
44	Q₈×C₂₉	C₄⋊C₄	1	1	yes	characteristic
45	D₄×C₂₉	C₄⋊C₄	1	3	yes	—
46	C₂×C₄×C₂₉	C₂²×C₄	1	3	yes	—
47	C₂²⋊D₂₉	C₄⋊C₄	1	6	yes	—
48	C₂×Dic₂₉	C₂×D₄	1	3	yes	—
49	D₁₁₆	C₄⋊C₄	1	3	yes	—
50	C₄×D₂₉	C₂²×C₄	1	3	yes	—
51	C₄×D₂₉	C₂×D₄	1	3	yes	—
52	C₄×D₂₉	C₂×Q₈	1	3	yes	—
53	C₄×D₂₉	C₂⁴	1	1	yes	characteristic
54	Dic₅₈	C₄⋊C₄	1	3	yes	—
55	#6599	—	2	2	no	—
56	#6599	—	2	6	no	—
57	C₈×C₂₉	C₂²×C₄	1	1	yes	characteristic
58	C₈×C₂₉	C₂²×C₄	1	3	yes	—
59	#6597	C₂²×C₄	1	1	yes	characteristic
60	#6597	C₂²×C₄	1	3	yes	—
61	#2916	—	29	1	no	maximal, Sylow
62	C₂²×C₂₉	C₂×C₄⋊C₄	1	3	yes	—
63	C₂×D₂₉	—	4	3	no	—
64	C₂×D₂₉	C₂×C₄⋊C₄	1	3	yes	—
65	C₂×D₂₉	C₂²×Q₈	1	1	yes	characteristic
66	C₄×C₂₉	C₂×C₄⋊C₄	1	3	yes	—
67	C₄×C₂₉	C₂³×C₄	1	1	yes	characteristic
68	Dic₂₉	C₂×C₄⋊C₄	1	3	yes	—
69	Dic₂₉	C₂²×D₄	1	1	yes	characteristic
70	#568	—	29	2	no	—
71	C₂×#131	—	29	1	no	—
72	#430	—	29	6	no	—
73	C₂×#108	—	29	3	no	—
74	C₂×#108	—	29	3	no	—
75	C₂×C₂₉	—	2	3	no	—
76	C₂×C₂₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
77	D₂₉	—	2	1	no	—
78	D₂₉	—	2	3	no	—
79	C₂×#41	—	29	1	no	—
80	#131	—	29	1	no	—
81	#131	—	29	3	no	—
82	#131	—	29	3	no	—
83	#131	—	58	6	no	—
84	#131	—	58	2	no	—
85	#131	#1181	1	1	yes	characteristic
86	C₂×M₁₆	—	29	3	no	—
87	C₂×M₁₆	—	29	6	no	—
88	C₂×M₁₆	—	29	6	no	—
89	C₂²×C₈	—	29	3	no	—
90	#108	—	29	1	no	—
91	#108	—	29	3	no	—
92	#108	—	29	6	no	—
93	#108	—	29	6	no	—
94	C₂₉	#2916	1	1	yes	characteristic, complemented, Sylow
95	#41	—	29	1	no	—
96	#41	—	29	3	no	—
97	#41	—	29	3	no	—
98	#41	C₂×#1181	1	1	yes	characteristic
99	C₂×Q₈	—	29	1	no	—
100	C₂×D₄	—	29	3	no	—
101	C₂²×C₄	—	29	3	no	—
102	M₁₆	—	29	3	no	—
103	M₁₆	—	29	6	no	—
104	M₁₆	—	29	2	no	—
105	M₁₆	—	29	6	no	—
106	M₁₆	—	58	6	no	—
107	M₁₆	—	58	6	no	—
108	M₁₆	C₂×#1181	1	3	yes	—
109	C₂×C₈	—	29	3	no	—
110	C₂×C₈	—	29	1	no	—
111	C₂×C₈	—	29	3	no	—
112	C₂×C₈	—	29	3	no	—
113	C₂×C₈	—	29	3	no	—
114	C₂×C₈	—	58	6	no	—
115	C₂×C₈	—	58	6	no	—
116	C₂×C₈	C₂×#1181	1	3	yes	—
117	C₂³	—	29	3	no	—
118	Q₈	—	29	3	no	—
119	Q₈	C₄⋊#1181	1	1	yes	characteristic
120	D₄	—	29	6	no	—
121	D₄	—	29	3	no	—
122	D₄	C₄⋊#1181	1	3	yes	—
123	C₂×C₄	—	29	3	no	—
124	C₂×C₄	—	29	3	no	—
125	C₂×C₄	—	29	3	no	—
126	C₂×C₄	—	29	1	no	—
127	C₂×C₄	—	29	3	no	—
128	C₂×C₄	C₂²×#1181	1	3	yes	—
129	C₈	—	29	1	no	—
130	C₈	—	29	3	no	—
131	C₈	—	58	2	no	—
132	C₈	—	58	6	no	—
133	C₈	C₂²×#1181	1	1	yes	characteristic
134	C₈	C₂²×#1181	1	3	yes	—
135	C₂²	—	29	1	no	—
136	C₂²	—	29	3	no	—
137	C₂²	—	116	3	no	—
138	C₂²	C₂×C₄⋊#1181	1	3	yes	—
139	C₄	—	29	1	no	—
140	C₄	—	29	3	no	—
141	C₄	C₂×C₄⋊#1181	1	3	yes	—
142	C₄	C₂³×#1181	1	1	yes	characteristic
143	C₂	—	2	3	no	—
144	C₂	—	58	1	no	—
145	C₂	—	58	3	no	—
146	C₂	C₂²×C₄⋊#1181	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14272242

C₂

yes

maximal

#14272178

C₂

yes

maximal, complemented

C₂×#11745212

C₂

yes

maximal, complemented

D₂₉⋊#108

C₂

yes

maximal, complemented

#131×D₂₉

C₂

yes

maximal, characteristic

#41×D₂₉

C₂²

yes

characteristic

#11745348

—

#11745346

—

D₂₉⋊M₁₆

C₂²

yes

—

C₂×#90796

C₂²

yes

—

C₂₉×#131

C₄

yes

characteristic

#11745310

C₄

yes

characteristic

#11745269

C₄

yes

—

M₁₆×D₂₉

C₂²

yes

—

#11745263

C₄

yes

—

C₂×C₈×D₂₉

C₂²

yes

—

#11745212

C₂²

yes

characteristic

#11745212

C₂²

yes

—

#11745212

C₂²

yes

—

#11745211

C₂²

yes

—

#41×C₂₉

C₂×C₄

yes

characteristic

#90809

D₄

yes

characteristic

Q₈×D₂₉

Q₈

yes

characteristic

#90807

D₄

yes

—

D₄×D₂₉

Q₈

yes

—

#90805

C₂×C₄

yes

—

C₂×C₄×D₂₉

C₂³

yes

—

—

—

—

C₂³

yes

—

#90796

C₂³

yes

—

D₂₉⋊C₈

—

M₁₆×C₂₉

C₂×C₄

yes

—

C₂×C₈×C₂₉

C₂×C₄

yes

—

#90777

C₂×C₄

yes

—

C₂×#6597

C₂×C₄

yes

—

#90772

C₂×C₄

yes

—

C₈×D₂₉

C₂×C₄

yes

—

C₈×D₂₉

C₂×C₄

yes

—

C₈×D₂₉

C₂³

yes

—

C₈×D₂₉

C₂³

yes

characteristic

C₂²×D₂₉

C₂×Q₈

yes

—

Q₈×C₂₉

C₄⋊C₄

yes

characteristic

D₄×C₂₉

C₄⋊C₄

yes

—

C₂×C₄×C₂₉

C₂²×C₄

yes

—

C₂²⋊D₂₉

C₄⋊C₄

yes

—

C₂×Dic₂₉

C₂×D₄

yes

—

D₁₁₆

C₄⋊C₄

yes

—

C₄×D₂₉

C₂²×C₄

yes

—

C₄×D₂₉

C₂×D₄

yes

—

C₄×D₂₉

C₂×Q₈

yes

—

C₄×D₂₉

C₂⁴

yes

characteristic

Dic₅₈

C₄⋊C₄

yes

—

#6599

—

#6599

—

C₈×C₂₉

C₂²×C₄

yes

characteristic

C₈×C₂₉

C₂²×C₄

yes

—

#6597

C₂²×C₄

yes

characteristic

#6597

C₂²×C₄

yes

—

#2916

—

maximal, Sylow

C₂²×C₂₉

C₂×C₄⋊C₄

yes

—

C₂×D₂₉

—

C₂×D₂₉

C₂×C₄⋊C₄

yes

—

C₂×D₂₉

C₂²×Q₈

yes

characteristic

C₄×C₂₉

C₂×C₄⋊C₄

yes

—

C₄×C₂₉

C₂³×C₄

yes

characteristic

Dic₂₉

C₂×C₄⋊C₄

yes

—

Dic₂₉

C₂²×D₄

yes

—

—

—

—

—

C₂×C₂₉

—

C₂×C₂₉

C₂²×C₄⋊C₄

yes

characteristic

D₂₉

—

D₂₉

—

C₂×#41

—

—

—

—

—

—

yes

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂²×C₈

—

—

—

—

—

C₂₉

#2916

yes

characteristic, complemented, Sylow

—

—

—

yes

C₂×Q₈

—

100

C₂×D₄

—

101

C₂²×C₄

—

102

M₁₆

—

103

M₁₆

—

104

M₁₆

—

105

M₁₆

—

106

M₁₆

—

107

M₁₆

—

108

M₁₆

C₂×#1181

yes

—

109

C₂×C₈

—

110

C₂×C₈

—

111

C₂×C₈

—

112

C₂×C₈

—

113

C₂×C₈

—

114

C₂×C₈

—

115

C₂×C₈

—

116

C₂×C₈

C₂×#1181

yes

—

117

C₂³

—

118

Q₈

—

119

Q₈

C₄⋊#1181

yes

characteristic

120

D₄

—

121

D₄

—

122

D₄

C₄⋊#1181

yes

—

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

C₂²×#1181

yes

—

129

C₈

—

130

C₈

—

131

C₈

—

132

C₈

—

133

C₈

C₂²×#1181

yes

characteristic

134

C₈

C₂²×#1181

yes

—

135

C₂²

—

136

C₂²

—

137

C₂²

—

116

—

138

C₂²

C₂×C₄⋊#1181

yes

—

139

C₄

—

140

C₄

—

141

C₄

C₂×C₄⋊#1181

yes

—

142

C₄

C₂³×#1181

yes

characteristic

143

C₂

—

144

C₂

—

145

C₂

—

146

C₂

C₂²×C₄⋊#1181

yes

characteristic

	subgroup	G/H
center	C₂	C₂²×C₄⋊#1181
commutator	C₄×C₂₉	C₂³×C₄
Frattini	C₄	C₂³×#1181
Fitting	C₂₉×#131	C₄
socle	C₂×C₂₉	C₂²×C₄⋊C₄
prime radical	#41×D₂₉	C₂²
cosocle	C₄×D₂₉	C₂⁴
hypercenter	#131	#1181
hypocenter	C₂₉	#2916
LCS	G ▷ C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂ ◁ #41 ◁ #131

subgroup

G/H

center

C₂

C₂²×C₄⋊#1181

commutator

C₄×C₂₉

C₂³×C₄

Frattini

C₄

C₂³×#1181

Fitting

C₂₉×#131

C₄

socle

C₂×C₂₉

C₂²×C₄⋊C₄

prime radical

#41×D₂₉

C₂²

cosocle

C₄×D₂₉

C₂⁴

C₂₉

G ▷ C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉

UCS

C₁ ◁ C₂ ◁ #41 ◁ #131

N	H ≅ G/N	type
2. #14272178	C₂	semidirect
3. C₂×#11745212	C₂	semidirect
4. D₂₉⋊#108	C₂	semidirect
94. C₂₉	#2916	semidirect

H ≅ G/N

type

2. #14272178

C₂

semidirect

3. C₂×#11745212

C₂

semidirect

4. D₂₉⋊#108

C₂

semidirect

94. C₂₉

#2916

semidirect

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

subgroup	index
#14272242	2
#14272178	2
C₂×#11745212	2
D₂₉⋊#108	2
#131×D₂₉	2
#2916	29

subgroup

index

#14272242

#14272178

C₂×#11745212

D₂₉⋊#108

#131×D₂₉

#2916

Subgroups — #16836154

Conjugacy classes of subgroups

Complements

Maximal subgroups