Group #16835595 — subgroups

Subgroups — #16835595

Order 3712.

248 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 82 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×#11745209	C₂	1	1	yes	maximal, characteristic
2	C₂×C₈×#1181	C₂	1	1	yes	maximal, characteristic
3	#14272114	C₂	1	2	yes	maximal
4	#14272036	C₂	1	2	yes	maximal
5	#106×D₂₉	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄⋊#1181	—	2	2	no	—
7	C₂×C₄⋊#1181	C₂²	1	2	yes	—
8	C₂×C₄×#1181	C₂²	1	1	yes	characteristic
9	C₂×D₂₉⋊C₈	C₂²	1	1	yes	characteristic
10	C₂×C₈×D₂₉	C₂²	1	1	yes	characteristic
11	C₄⋊C₄×D₂₉	C₂²	1	2	yes	—
12	(C₂×#1181)⋊C₄	—	2	2	no	—
13	#11745209	—	2	2	no	—
14	C₈×#1181	—	2	2	no	—
15	C₂₉×#106	C₄	1	1	yes	characteristic, complemented
16	#11745165	C₄	1	1	yes	characteristic, complemented
17	#11745156	C₄	1	2	yes	complemented
18	C₂²×#1181	—	2	2	no	—
19	C₂²×#1181	D₄	1	2	yes	—
20	C₂×C₄×D₂₉	—	2	2	no	—
21	C₂×C₄×D₂₉	C₂³	1	1	yes	characteristic
22	C₂×#6599	—	2	1	no	—
23	C₄⋊#1181	—	2	2	no	—
24	C₄⋊#1181	—	2	2	no	—
25	C₄⋊#1181	—	4	4	no	—
26	C₄×#1181	—	2	1	no	—
27	C₄×#1181	—	2	1	no	—
28	D₂₉⋊C₈	—	2	1	no	—
29	D₂₉⋊C₈	Q₈	1	2	yes	—
30	C₂×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
31	C₄⋊C₄×C₂₉	C₂×C₄	1	2	yes	—
32	C₄⋊Dic₂₉	C₂×C₄	1	2	yes	—
33	#90779	—	2	2	no	—
34	C₂×#6597	C₂×C₄	1	1	yes	characteristic
35	C₈×D₂₉	D₄	1	2	yes	—
36	C₈×D₂₉	Q₈	1	2	yes	—
37	C₂²×D₂₉	C₂×D₄	1	1	yes	characteristic
38	C₂×#1181	—	2	2	no	—
39	C₂×#1181	—	2	2	no	—
40	C₂×#1181	—	4	2	no	—
41	C₂×#1181	—	4	2	no	—
42	C₂×#1181	—	4	2	no	—
43	C₂×#1181	SD₁₆	1	4	yes	—
44	C₂×C₄×C₂₉	—	2	2	no	—
45	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
46	C₂×Dic₂₉	—	2	2	no	—
47	C₂×Dic₂₉	#41	1	1	yes	characteristic
48	C₄×D₂₉	—	4	2	no	—
49	C₄×D₂₉	—	4	2	no	—
50	C₄×D₂₉	C₂×D₄	1	1	yes	characteristic
51	C₄×D₂₉	C₂×Q₈	1	1	yes	characteristic
52	C₄×D₂₉	C₂×Q₈	1	1	yes	characteristic
53	C₄×D₂₉	#41	1	1	yes	characteristic
54	#6599	—	2	2	no	—
55	C₈×C₂₉	C₄⋊C₄	1	2	yes	complemented
56	#6597	C₄⋊C₄	1	2	yes	complemented
57	#1941	—	29	1	no	maximal, Sylow
58	C₂²×C₂₉	C₄×D₄	1	1	yes	characteristic
59	C₂×D₂₉	#121	1	1	yes	characteristic
60	C₂×D₂₉	C₄⋊Q₈	1	1	yes	characteristic
61	C₂×D₂₉	C₂×SD₁₆	1	2	yes	—
62	C₂×D₂₉	#135	1	2	yes	—
63	#1181	—	2	4	no	—
64	#1181	—	8	2	no	—
65	C₄×C₂₉	—	4	2	no	—
66	C₄×C₂₉	C₂×C₄⋊C₄	1	1	yes	characteristic
67	C₄×C₂₉	C₄×Q₈	1	1	yes	characteristic
68	Dic₂₉	—	4	2	no	—
69	Dic₂₉	C₂²⋊Q₈	1	1	yes	characteristic
70	Dic₂₉	#125	1	1	yes	characteristic
71	C₂×#106	—	29	1	no	—
72	C₂×#106	—	29	1	no	—
73	C₂×C₄×C₈	—	29	1	no	—
74	#389	—	29	2	no	—
75	#340	—	29	2	no	—
76	C₂×C₂₉	#389	1	1	yes	characteristic
77	C₂×C₂₉	C₄×SD₁₆	1	2	yes	—
78	D₂₉	#465	1	2	yes	—
79	D₂₉	#498	1	1	yes	characteristic
80	D₂₉	#499	1	1	yes	characteristic
81	C₂²×C₈	—	29	1	no	—
82	C₂²×C₈	—	29	1	no	—
83	C₂×C₄⋊C₄	—	29	2	no	—
84	C₂×C₄⋊C₄	—	29	2	no	—
85	C₂×C₄⋊C₄	—	58	2	no	—
86	C₂×C₄²	—	29	1	no	—
87	#106	—	29	1	no	—
88	#106	—	29	2	no	—
89	#106	—	58	2	no	—
90	#106	#1181	1	1	yes	characteristic, complemented
91	C₄×C₈	—	58	2	no	—
92	#95	—	58	2	no	—
93	C₂₉	#1941	1	1	yes	characteristic, complemented, Sylow
94	C₂²×C₄	—	29	1	no	—
95	C₂²×C₄	—	29	2	no	—
96	C₂²×C₄	—	58	2	no	—
97	C₂²×C₄	—	58	2	no	—
98	C₂×C₈	—	29	1	no	—
99	C₂×C₈	—	29	2	no	—
100	C₂×C₈	—	29	2	no	—
101	C₂×C₈	—	29	2	no	—
102	C₂×C₈	—	58	1	no	—
103	C₂×C₈	—	58	1	no	—
104	C₂×C₈	C₂×#1181	1	1	yes	characteristic
105	C₄⋊C₄	—	29	2	no	—
106	C₄⋊C₄	—	58	2	no	—
107	C₄⋊C₄	—	58	2	no	—
108	C₄⋊C₄	—	58	2	no	—
109	C₄⋊C₄	—	116	4	no	—
110	C₄⋊C₄	C₂×#1181	1	2	yes	—
111	C₄²	—	58	1	no	—
112	C₄²	—	58	1	no	—
113	C₂³	—	29	1	no	—
114	C₂×C₄	—	2	2	no	—
115	C₂×C₄	—	29	1	no	—
116	C₂×C₄	—	29	1	no	—
117	C₂×C₄	—	29	1	no	—
118	C₂×C₄	—	29	1	no	—
119	C₂×C₄	—	29	1	no	—
120	C₂×C₄	—	29	4	no	—
121	C₂×C₄	—	58	2	no	—
122	C₂×C₄	—	58	2	no	—
123	C₂×C₄	—	58	2	no	—
124	C₂×C₄	—	116	2	no	—
125	C₂×C₄	—	116	2	no	—
126	C₂×C₄	—	116	2	no	—
127	C₂×C₄	—	116	2	no	—
128	C₂×C₄	—	116	2	no	—
129	C₂×C₄	C₂²×#1181	1	1	yes	characteristic
130	C₈	—	29	2	no	—
131	C₈	—	58	2	no	—
132	C₈	C₄⋊#1181	1	2	yes	complemented
133	C₂²	—	29	1	no	—
134	C₂²	—	29	1	no	—
135	C₂²	—	29	2	no	—
136	C₂²	—	29	2	no	—
137	C₂²	D₄×#1181	1	1	yes	characteristic
138	C₄	—	4	2	no	—
139	C₄	—	29	1	no	—
140	C₄	—	29	1	no	—
141	C₄	—	58	4	no	—
142	C₄	—	116	2	no	—
143	C₄	—	232	2	no	—
144	C₄	C₂×C₄⋊#1181	1	1	yes	characteristic
145	C₄	Q₈×#1181	1	1	yes	characteristic
146	C₂	—	29	2	no	—
147	C₂	—	29	1	no	—
148	C₂	—	29	1	no	—
149	C₂	#14272114	1	1	yes	characteristic
150	C₂	SD₁₆×#1181	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11745209

C₂

yes

maximal, characteristic

C₂×C₈×#1181

C₂

yes

maximal, characteristic

#14272114

C₂

yes

maximal

#14272036

C₂

yes

maximal

#106×D₂₉

C₂

yes

maximal, characteristic

C₂×C₄⋊#1181

—

C₂×C₄⋊#1181

C₂²

yes

—

C₂×C₄×#1181

C₂²

yes

characteristic

C₂×D₂₉⋊C₈

C₂²

yes

characteristic

C₂×C₈×D₂₉

C₂²

yes

characteristic

C₄⋊C₄×D₂₉

C₂²

yes

—

(C₂×#1181)⋊C₄

—

#11745209

—

C₈×#1181

—

C₂₉×#106

C₄

yes

characteristic, complemented

#11745165

C₄

yes

characteristic, complemented

#11745156

C₄

yes

complemented

C₂²×#1181

—

C₂²×#1181

D₄

yes

—

C₂×C₄×D₂₉

—

C₂×C₄×D₂₉

C₂³

yes

—

—

—

—

—

—

D₂₉⋊C₈

—

D₂₉⋊C₈

Q₈

yes

—

C₂×C₈×C₂₉

C₂×C₄

yes

characteristic

C₄⋊C₄×C₂₉

C₂×C₄

yes

—

C₄⋊Dic₂₉

C₂×C₄

yes

—

#90779

—

C₂×#6597

C₂×C₄

yes

characteristic

C₈×D₂₉

D₄

yes

—

C₈×D₂₉

Q₈

yes

—

C₂²×D₂₉

C₂×D₄

yes

—

—

—

—

—

SD₁₆

yes

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

C₂²×C₄

yes

characteristic

C₂×Dic₂₉

—

C₂×Dic₂₉

#41

yes

characteristic

C₄×D₂₉

—

C₄×D₂₉

—

C₄×D₂₉

C₂×D₄

yes

characteristic

C₄×D₂₉

C₂×Q₈

yes

characteristic

C₄×D₂₉

C₂×Q₈

yes

C₄×D₂₉

yes

—

C₈×C₂₉

C₄⋊C₄

yes

complemented

#6597

C₄⋊C₄

yes

complemented

#1941

—

maximal, Sylow

C₂²×C₂₉

C₄×D₄

yes

characteristic

C₂×D₂₉

#121

yes

characteristic

C₂×D₂₉

C₄⋊Q₈

yes

characteristic

C₂×D₂₉

C₂×SD₁₆

yes

—

C₂×D₂₉

#135

yes

—

#1181

—

#1181

—

C₄×C₂₉

—

C₄×C₂₉

C₂×C₄⋊C₄

yes

characteristic

C₄×C₂₉

C₄×Q₈

yes

characteristic

Dic₂₉

—

Dic₂₉

C₂²⋊Q₈

yes

Dic₂₉

yes

—

—

C₂×C₄×C₈

—

#389

—

#340

—

C₂×C₂₉

#389

yes

characteristic

C₂×C₂₉

C₄×SD₁₆

yes

—

D₂₉

#465

yes

—

D₂₉

yes

D₂₉

yes

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

—

—

—

—

yes

characteristic, complemented

C₄×C₈

—

#95

—

C₂₉

#1941

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂×C₈

—

C₂×C₈

—

100

C₂×C₈

—

101

C₂×C₈

—

102

C₂×C₈

—

103

C₂×C₈

—

104

C₂×C₈

C₂×#1181

yes

characteristic

105

C₄⋊C₄

—

106

C₄⋊C₄

—

107

C₄⋊C₄

—

108

C₄⋊C₄

—

109

C₄⋊C₄

—

116

—

110

C₄⋊C₄

C₂×#1181

yes

—

111

C₄²

—

112

C₄²

—

113

C₂³

—

114

C₂×C₄

—

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

—

124

C₂×C₄

—

116

—

125

C₂×C₄

—

116

—

126

C₂×C₄

—

116

—

127

C₂×C₄

—

116

—

128

C₂×C₄

—

116

—

129

C₂×C₄

C₂²×#1181

yes

characteristic

130

C₈

—

131

C₈

—

132

C₈

C₄⋊#1181

yes

complemented

133

C₂²

—

134

C₂²

—

135

C₂²

—

136

C₂²

—

137

C₂²

D₄×#1181

yes

characteristic

138

C₄

—

139

C₄

—

140

C₄

—

141

C₄

—

142

C₄

—

116

—

143

C₄

—

232

—

144

C₄

C₂×C₄⋊#1181

yes

characteristic

145

C₄

Q₈×#1181

yes

characteristic

146

C₂

—

147

C₂

—

148

C₂

—

149

C₂

#14272114

yes

characteristic

150

C₂

SD₁₆×#1181

yes

—

	subgroup	G/H
center	C₂²	D₄×#1181
commutator	C₂×C₄×C₂₉	C₂²×C₄
Frattini	C₂×C₄	C₂²×#1181
Fitting	C₂₉×#106	C₄
socle	C₂²×C₂₉	C₄×D₄
prime radical	C₂²×D₂₉	C₂×D₄
cosocle	C₂×C₄×D₂₉	C₂³
hypercenter	#106	#1181
hypocenter	C₂₉	#1941
LCS	G ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #106

subgroup

G/H

center

C₂²

D₄×#1181

commutator

C₂×C₄×C₂₉

C₂²×C₄

Frattini

C₂×C₄

C₂²×#1181

Fitting

C₂₉×#106

C₄

socle

C₂²×C₂₉

C₄×D₄

prime radical

C₂²×D₂₉

C₂×D₄

cosocle

C₂×C₄×D₂₉

C₂³

C₂₉

G ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ #106

N	H ≅ G/N	type
15. C₂₉×#106	C₄	semidirect
16. #11745165	C₄	semidirect
17. #11745156	C₄	semidirect
55. C₈×C₂₉	C₄⋊C₄	semidirect
56. #6597	C₄⋊C₄	semidirect
90. #106	#1181	semidirect
93. C₂₉	#1941	semidirect
132. C₈	C₄⋊#1181	semidirect

H ≅ G/N

type

15. C₂₉×#106

C₄

semidirect

16. #11745165

C₄

semidirect

17. #11745156

C₄

semidirect

55. C₈×C₂₉

C₄⋊C₄

semidirect

56. #6597

C₄⋊C₄

semidirect

90. #106

#1181

semidirect

93. C₂₉

#1941

semidirect

132. C₈

C₄⋊#1181

semidirect

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

subgroup	index
C₂×#11745209	2
C₂×C₈×#1181	2
#14272114	2
#14272036	2
#106×D₂₉	2
#1941	29

subgroup

index

C₂×C₈×#1181

#106×D₂₉

Subgroups — #16835595

Conjugacy classes of subgroups

Complements

Maximal subgroups