Group #16835251 — subgroups

Subgroups — #16835251

Order 3712.

284 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 86 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×#11745348	C₂	1	1	yes	maximal, characteristic
2	#14272144	C₂	1	1	yes	maximal, characteristic
3	#14272129	C₂	1	2	yes	maximal, complemented
4	#14272046	C₂	1	2	yes	maximal, complemented
5	#14271146	C₂	1	1	yes	maximal, characteristic
6	C₂×#90809	C₂²	1	1	yes	characteristic
7	#11745348	—	2	2	no	—
8	#11745348	—	2	2	no	—
9	#11745345	C₂²	1	2	yes	—
10	C₂×#90796	C₄	1	2	yes	complemented
11	C₂×#90796	C₂²	1	1	yes	characteristic
12	C₂×D₂₉⋊C₈	C₄	1	2	yes	complemented
13	C₂×D₂₉⋊C₈	C₂²	1	1	yes	characteristic
14	M₁₆×D₂₉	C₂²	1	2	yes	—
15	#11745215	C₄	1	4	yes	—
16	#11745208	—	2	2	no	—
17	C₈×#1181	—	2	2	no	—
18	C₂₉×#101	C₄	1	1	yes	characteristic, complemented
19	#11745184	C₄	1	1	yes	characteristic, complemented
20	#11745171	C₄	1	2	yes	complemented
21	C₂×Q₈×C₂₉	C₂×C₄	1	1	yes	characteristic
22	#90809	—	2	2	no	—
23	#90809	—	2	2	no	—
24	C₂×D₁₁₆	C₂×C₄	1	2	yes	—
25	C₂×D₁₁₆	C₂×C₄	1	1	yes	characteristic
26	C₂×C₄×D₂₉	C₂×C₄	1	2	yes	—
27	C₂×C₄×D₂₉	C₂³	1	1	yes	characteristic
28	C₂²⋊#1181	C₂×C₄	1	4	yes	—
29	C₂×#6599	C₂×C₄	1	2	yes	—
30	C₂×#6599	C₂×C₄	1	1	yes	characteristic
31	C₂×#6599	C₂×C₄	1	1	yes	characteristic
32	C₄⋊#1181	—	2	2	no	—
33	C₄×#1181	—	2	2	no	—
34	#90796	—	2	2	no	—
35	#90796	—	2	4	no	—
36	D₂₉⋊C₈	—	2	2	no	—
37	D₂₉⋊C₈	—	2	2	no	—
38	D₂₉⋊C₈	D₄	1	2	yes	—
39	D₂₉⋊C₈	D₄	1	2	yes	—
40	M₁₆×C₂₉	C₂×C₄	1	2	yes	—
41	#90777	C₂×C₄	1	2	yes	—
42	#90772	—	2	2	no	—
43	C₈×D₂₉	—	2	2	no	—
44	C₂²×D₂₉	C₄²	1	2	yes	—
45	C₂²×D₂₉	C₂²×C₄	1	1	yes	characteristic
46	C₂×#1181	—	2	4	no	—
47	Q₈×C₂₉	—	2	2	no	—
48	C₂×C₄×C₂₉	C₄²	1	2	yes	—
49	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
50	C₂×Dic₂₉	C₂²×C₄	1	1	yes	characteristic
51	D₁₁₆	—	2	4	no	—
52	D₁₁₆	—	2	2	no	—
53	C₄×D₂₉	—	2	2	no	—
54	C₄×D₂₉	—	2	2	no	—
55	C₄×D₂₉	C₂×D₄	1	2	yes	—
56	C₄×D₂₉	#41	1	2	yes	—
57	#6599	—	2	2	no	—
58	#6599	C₂²⋊C₄	1	1	yes	characteristic
59	#6599	C₂²⋊C₄	1	1	yes	characteristic
60	#6599	C₂²⋊C₄	1	2	yes	—
61	C₈×C₂₉	—	2	2	no	—
62	#6597	—	2	2	no	—
63	#1757	—	29	1	no	maximal, Sylow
64	C₂²×C₂₉	C₂×C₄²	1	1	yes	characteristic
65	C₂×D₂₉	—	2	2	no	—
66	C₂×D₂₉	—	4	1	no	—
67	C₂×D₂₉	—	4	2	no	—
68	C₂×D₂₉	C₄×D₄	1	2	yes	—
69	#1181	—	4	4	no	—
70	C₄×C₂₉	—	2	2	no	—
71	C₄×C₂₉	C₄×D₄	1	2	yes	—
72	Dic₂₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
73	Dic₂₉	#117	1	1	yes	characteristic
74	C₂×#131	—	29	1	no	—
75	#413	—	29	1	no	—
76	#410	—	29	1	no	—
77	#405	—	29	2	no	—
78	#344	—	29	2	no	—
79	C₂×C₂₉	—	2	1	no	—
80	C₂×C₂₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
81	D₂₉	—	2	2	no	—
82	D₂₉	—	4	2	no	—
83	C₂×#41	—	29	1	no	—
84	#131	—	58	2	no	—
85	#131	—	58	2	no	—
86	C₂×M₁₆	—	29	2	no	—
87	C₂×M₁₆	—	29	1	no	—
88	C₂×M₁₆	—	29	2	no	—
89	C₂²×C₈	—	29	1	no	—
90	C₂²×C₈	—	29	2	no	—
91	#117	—	29	2	no	—
92	#101	—	29	1	no	—
93	#101	#1181	1	1	yes	characteristic, complemented
94	#100	—	29	2	no	—
95	#99	—	29	4	no	—
96	#97	—	58	2	no	—
97	C₄×C₈	—	58	2	no	—
98	C₂₉	#1757	1	1	yes	characteristic, complemented, Sylow
99	#41	—	58	2	no	—
100	#41	—	58	2	no	—
101	C₂×Q₈	C₂×#1181	1	1	yes	characteristic
102	C₂×D₄	—	29	2	no	—
103	C₂×D₄	—	29	1	no	—
104	C₂²×C₄	—	29	1	no	—
105	C₂²×C₄	—	29	2	no	—
106	M₁₆	—	29	2	no	—
107	M₁₆	—	58	2	no	—
108	M₁₆	—	58	4	no	—
109	M₁₆	—	58	2	no	—
110	M₁₆	C₂×#1181	1	2	yes	—
111	C₂×C₈	—	29	2	no	—
112	C₂×C₈	—	29	2	no	—
113	C₂×C₈	—	29	1	no	—
114	C₂×C₈	—	29	1	no	—
115	C₂×C₈	—	29	2	no	—
116	C₂×C₈	—	58	2	no	—
117	C₂×C₈	—	58	2	no	—
118	C₂×C₈	—	58	2	no	—
119	C₄⋊C₄	—	58	2	no	—
120	C₂²⋊C₄	—	29	4	no	—
121	C₄²	—	58	2	no	—
122	C₂³	—	29	1	no	—
123	C₂³	—	29	2	no	—
124	Q₈	—	2	2	no	—
125	D₄	—	58	4	no	—
126	D₄	—	58	2	no	—
127	C₂×C₄	—	29	1	no	—
128	C₂×C₄	—	29	2	no	—
129	C₂×C₄	—	29	2	no	—
130	C₂×C₄	—	58	2	no	—
131	C₂×C₄	—	58	2	no	—
132	C₂×C₄	—	58	4	no	—
133	C₂×C₄	C₄×#1181	1	2	yes	—
134	C₂×C₄	C₂²×#1181	1	1	yes	characteristic
135	C₈	—	2	2	no	—
136	C₈	—	29	1	no	—
137	C₈	—	29	1	no	—
138	C₈	—	29	2	no	—
139	C₈	—	58	2	no	—
140	C₈	—	58	2	no	—
141	C₂²	—	29	2	no	—
142	C₂²	—	58	2	no	—
143	C₂²	—	116	1	no	—
144	C₂²	—	116	2	no	—
145	C₂²	C₂×C₄×#1181	1	1	yes	characteristic
146	C₄	—	2	2	no	—
147	C₄	—	29	1	no	—
148	C₄	—	29	1	no	—
149	C₄	—	116	4	no	—
150	C₄	D₄×#1181	1	2	yes	—
151	C₂	—	2	1	no	—
152	C₂	—	58	2	no	—
153	C₂	—	116	2	no	—
154	C₂	C₂²⋊C₄×#1181	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11745348

C₂

yes

maximal, characteristic

#14272144

C₂

yes

maximal, characteristic

#14272129

C₂

yes

maximal, complemented

#14272046

C₂

yes

maximal, complemented

#14271146

C₂

yes

maximal, characteristic

C₂×#90809

C₂²

yes

—

—

C₂²

yes

—

C₂×#90796

C₄

yes

complemented

C₂×#90796

C₂²

yes

characteristic

C₂×D₂₉⋊C₈

C₄

yes

complemented

C₂×D₂₉⋊C₈

C₂²

yes

characteristic

M₁₆×D₂₉

C₂²

yes

—

#11745215

C₄

yes

—

#11745208

—

C₈×#1181

—

C₂₉×#101

C₄

yes

characteristic, complemented

#11745184

C₄

yes

characteristic, complemented

#11745171

C₄

yes

complemented

C₂×Q₈×C₂₉

C₂×C₄

yes

characteristic

#90809

—

#90809

—

C₂×D₁₁₆

C₂×C₄

yes

—

C₂×D₁₁₆

C₂×C₄

yes

characteristic

C₂×C₄×D₂₉

C₂×C₄

yes

—

C₂×C₄×D₂₉

C₂³

yes

characteristic

C₂²⋊#1181

C₂×C₄

yes

—

C₂×#6599

C₂×C₄

yes

—

C₂×#6599

C₂×C₄

yes

characteristic

C₂×#6599

C₂×C₄

yes

—

—

—

—

D₂₉⋊C₈

—

D₂₉⋊C₈

—

D₂₉⋊C₈

D₄

yes

—

D₂₉⋊C₈

D₄

yes

—

M₁₆×C₂₉

C₂×C₄

yes

—

#90777

C₂×C₄

yes

—

#90772

—

C₈×D₂₉

—

C₂²×D₂₉

C₄²

yes

—

C₂²×D₂₉

C₂²×C₄

yes

characteristic

C₂×#1181

—

Q₈×C₂₉

—

C₂×C₄×C₂₉

C₄²

yes

—

C₂×C₄×C₂₉

C₂²×C₄

yes

characteristic

C₂×Dic₂₉

C₂²×C₄

yes

characteristic

D₁₁₆

—

D₁₁₆

—

C₄×D₂₉

—

C₄×D₂₉

—

C₄×D₂₉

C₂×D₄

yes

—

C₄×D₂₉

#41

yes

—

#6599

—

#6599

C₂²⋊C₄

yes

characteristic

#6599

C₂²⋊C₄

yes

characteristic

#6599

C₂²⋊C₄

yes

—

C₈×C₂₉

—

#6597

—

#1757

—

maximal, Sylow

C₂²×C₂₉

C₂×C₄²

yes

characteristic

C₂×D₂₉

—

C₂×D₂₉

—

C₂×D₂₉

—

C₂×D₂₉

C₄×D₄

yes

—

#1181

—

C₄×C₂₉

—

C₄×C₂₉

C₄×D₄

yes

—

Dic₂₉

C₂×C₂²⋊C₄

yes

Dic₂₉

yes

—

—

—

—

—

C₂×C₂₉

—

C₂×C₂₉

C₄×C₂²⋊C₄

yes

characteristic

D₂₉

—

D₂₉

—

C₂×#41

—

#131

—

#131

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂²×C₈

—

C₂²×C₈

—

—

—

yes

characteristic, complemented

#100

—

#99

—

#97

—

C₄×C₈

—

C₂₉

#1757

yes

characteristic, complemented, Sylow

#41

—

100

#41

—

101

C₂×Q₈

C₂×#1181

yes

characteristic

102

C₂×D₄

—

103

C₂×D₄

—

104

C₂²×C₄

—

105

C₂²×C₄

—

106

M₁₆

—

107

M₁₆

—

108

M₁₆

—

109

M₁₆

—

110

M₁₆

C₂×#1181

yes

—

111

C₂×C₈

—

112

C₂×C₈

—

113

C₂×C₈

—

114

C₂×C₈

—

115

C₂×C₈

—

116

C₂×C₈

—

117

C₂×C₈

—

118

C₂×C₈

—

119

C₄⋊C₄

—

120

C₂²⋊C₄

—

121

C₄²

—

122

C₂³

—

123

C₂³

—

124

Q₈

—

125

D₄

—

126

D₄

—

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

—

130

C₂×C₄

—

131

C₂×C₄

—

132

C₂×C₄

—

133

C₂×C₄

C₄×#1181

yes

—

134

C₂×C₄

C₂²×#1181

yes

characteristic

135

C₈

—

136

C₈

—

137

C₈

—

138

C₈

—

139

C₈

—

140

C₈

—

141

C₂²

—

142

C₂²

—

143

C₂²

—

116

—

144

C₂²

—

116

—

145

C₂²

C₂×C₄×#1181

yes

characteristic

146

C₄

—

147

C₄

—

148

C₄

—

149

C₄

—

116

—

150

C₄

D₄×#1181

yes

—

151

C₂

—

152

C₂

—

153

C₂

—

116

—

154

C₂

C₂²⋊C₄×#1181

yes

characteristic

	subgroup	G/H
center	C₂	C₂²⋊C₄×#1181
commutator	C₂²×C₂₉	C₂×C₄²
Frattini	C₂×C₄	C₂²×#1181
Fitting	C₂₉×#101	C₄
socle	C₂×C₂₉	C₄×C₂²⋊C₄
prime radical	C₂×#90809	C₂²
cosocle	C₂×C₄×D₂₉	C₂³
hypercenter	#101	#1181
hypocenter	C₂₉	#1757
LCS	G ▷ C₂²×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ #101

subgroup

G/H

center

C₂

C₂²⋊C₄×#1181

commutator

C₂²×C₂₉

C₂×C₄²

Frattini

C₂×C₄

C₂²×#1181

Fitting

C₂₉×#101

C₄

socle

C₂×C₂₉

C₄×C₂²⋊C₄

prime radical

C₂×#90809

C₂²

cosocle

C₂×C₄×D₂₉

C₂³

C₂₉

G ▷ C₂²×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ #101

N	H ≅ G/N	type
3. #14272129	C₂	semidirect
4. #14272046	C₂	semidirect
10. C₂×#90796	C₄	semidirect
12. C₂×D₂₉⋊C₈	C₄	semidirect
18. C₂₉×#101	C₄	semidirect
19. #11745184	C₄	semidirect
20. #11745171	C₄	semidirect
93. #101	#1181	semidirect
98. C₂₉	#1757	semidirect

H ≅ G/N

type

3. #14272129

C₂

semidirect

4. #14272046

C₂

semidirect

10. C₂×#90796

C₄

semidirect

12. C₂×D₂₉⋊C₈

C₄

semidirect

18. C₂₉×#101

C₄

semidirect

19. #11745184

C₄

semidirect

20. #11745171

C₄

semidirect

93. #101

#1181

semidirect

98. C₂₉

#1757

semidirect

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

subgroup	index
C₂×#11745348	2
#14272144	2
#14272129	2
#14272046	2
#14271146	2
#1757	29

subgroup

index

Subgroups — #16835251

Conjugacy classes of subgroups

Complements

Maximal subgroups