Group #33085097 — subgroups

Subgroups — #33085097

Order 18688.

3958 conjugacy classes of subgroups; only the 571 normal subgroups are shown.

normal subgroups only

This group has 3958 conjugacy classes of subgroups — too many to draw. Only its 571 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×#17988551	C₂	1	6	yes	maximal, complemented
2	#22609843	C₂	1	8	yes	maximal, complemented
3	C₂³×#41×C₇₃	C₂	1	1	yes	maximal, characteristic
4	C₂²×#11924012	C₂²	1	4	yes	—
5	#17988551	—	2	24	no	—
6	C₂×C₂²⋊#10596831	C₂²	1	24	yes	complemented
7	C₂²×#41×C₇₃	—	2	24	no	—
8	C₂²×#41×C₇₃	C₄	1	4	yes	—
9	C₂²×#41×C₇₃	C₂²	1	4	yes	—
10	C₂³×Q₈×C₇₃	C₄	1	1	yes	characteristic
11	C₂³×D₄×C₇₃	C₄	1	3	yes	—
12	C₂⁴×C₄×C₇₃	C₂²	1	3	yes	—
13	C₂×#11924012	—	2	24	no	—
14	C₂²×#10596831	C₂³	1	8	yes	—
15	C₂²⋊#10596831	—	2	48	no	—
16	C₂⁵×C₇₃	C₂×C₄	1	3	yes	—
17	C₂×#41×C₇₃	—	2	128	no	—
18	C₂×#41×C₇₃	—	2	48	no	—
19	C₂×#41×C₇₃	—	2	48	no	—
20	C₂²×Q₈×C₇₃	—	2	12	no	—
21	C₂²×Q₈×C₇₃	C₂×C₄	1	4	yes	—
22	C₂²×D₄×C₇₃	—	2	24	no	—
23	C₂²×D₄×C₇₃	—	2	12	no	—
24	C₂²×D₄×C₇₃	C₂×C₄	1	12	yes	—
25	C₂³×C₄×C₇₃	—	2	24	no	—
26	C₂³×C₄×C₇₃	C₂×C₄	1	3	yes	—
27	C₂³×C₄×C₇₃	C₂×C₄	1	6	yes	—
28	C₂³×C₄×C₇₃	D₄	1	24	yes	—
29	C₂³×C₄×C₇₃	C₂³	1	6	yes	—
30	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
31	#11924012	—	4	16	no	—
32	C₂×#10596831	—	2	24	no	—
33	C₂⁴×C₇₃	—	2	12	no	—
34	C₂⁴×C₇₃	—	4	12	no	—
35	C₂⁴×C₇₃	C₂²⋊C₄	1	12	yes	—
36	C₂⁴×C₇₃	C₂²×C₄	1	6	yes	—
37	C₂⁴×C₇₃	C₂²×C₄	1	1	yes	characteristic
38	#41×C₇₃	—	2	128	no	—
39	#41×C₇₃	—	2	128	no	—
40	C₂×Q₈×C₇₃	—	2	32	no	—
41	C₂×Q₈×C₇₃	—	2	24	no	—
42	C₂×D₄×C₇₃	—	2	96	no	—
43	C₂×D₄×C₇₃	—	2	48	no	—
44	C₂×D₄×C₇₃	—	2	24	no	—
45	C₂²×C₄×C₇₃	—	2	12	no	—
46	C₂²×C₄×C₇₃	—	2	24	no	—
47	C₂²×C₄×C₇₃	—	2	96	no	—
48	C₂²×C₄×C₇₃	—	2	24	no	—
49	C₂²×C₄×C₇₃	C₂²⋊C₄	1	12	yes	—
50	C₂²×C₄×C₇₃	C₂²⋊C₄	1	24	yes	—
51	C₂²×C₄×C₇₃	C₂²×C₄	1	6	yes	—
52	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
53	C₂²×C₄×C₇₃	C₂×D₄	1	24	yes	—
54	C₂²×C₄×C₇₃	C₂×D₄	1	12	yes	—
55	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
56	C₂³×C₇₃	—	2	4	no	—
57	C₂³×C₇₃	—	2	12	no	—
58	C₂³×C₇₃	—	2	24	no	—
59	C₂³×C₇₃	—	2	24	no	—
60	C₂³×C₇₃	—	4	24	no	—
61	C₂³×C₇₃	—	4	48	no	—
62	C₂³×C₇₃	C₂×C₂²⋊C₄	1	12	yes	—
63	C₂³×C₇₃	C₂×C₂²⋊C₄	1	6	yes	—
64	C₂³×C₇₃	C₂³×C₄	1	1	yes	characteristic
65	Q₈×C₇₃	—	2	32	no	—
66	D₄×C₇₃	—	2	96	no	—
67	C₂×C₄×C₇₃	—	2	12	no	—
68	C₂×C₄×C₇₃	—	2	24	no	—
69	C₂×C₄×C₇₃	—	2	48	no	—
70	C₂×C₄×C₇₃	—	2	48	no	—
71	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	12	yes	—
72	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	6	yes	—
73	C₂×C₄×C₇₃	#120	1	16	yes	—
74	C₂×C₄×C₇₃	C₂²×D₄	1	6	yes	—
75	#10596831	—	4	8	no	—
76	C₂²×C₇₃	—	2	12	no	—
77	C₂²×C₇₃	—	2	24	no	—
78	C₂²×C₇₃	—	2	12	no	—
79	C₂²×C₇₃	—	4	48	no	—
80	C₂²×C₇₃	—	4	24	no	—
81	C₂²×C₇₃	#379	1	4	yes	—
82	C₂²×C₇₃	C₂²×C₂²⋊C₄	1	3	yes	—
83	C₂²×C₇₃	#568	1	4	yes	—
84	C₄×C₇₃	—	2	12	no	—
85	C₄×C₇₃	#379	1	4	yes	—
86	C₄×C₇₃	C₂×#120	1	4	yes	—
87	#20580	—	73	1	no	maximal, Sylow
88	C₂×C₇₃	—	2	4	no	—
89	C₂×C₇₃	—	4	12	no	—
90	C₂×C₇₃	C₂×#379	1	1	yes	characteristic
91	C₂×C₇₃	#2879	1	6	yes	—
92	C₂³×#41	D₇₃	1	1	yes	characteristic
93	C₂×#407	—	73	6	no	—
94	#1780	—	73	8	no	—
95	C₇₃	#20580	1	1	yes	characteristic, complemented, Sylow
96	C₂²×#41	—	2	24	no	—
97	C₂²×#41	Dic₇₃	1	4	yes	—
98	C₂²×#41	C₂×D₇₃	1	4	yes	—
99	C₂³×Q₈	Dic₇₃	1	1	yes	characteristic
100	C₂³×D₄	Dic₇₃	1	3	yes	—
101	C₂⁴×C₄	C₂×D₇₃	1	3	yes	—
102	C₂²×M₁₆	—	73	4	no	—
103	#407	—	146	24	no	—
104	C₂×C₂²⋊C₈	—	73	24	no	—
105	C₂⁵	C₂×Dic₇₃	1	3	yes	—
106	C₂×#41	—	2	128	no	—
107	C₂×#41	—	2	48	no	—
108	C₂×#41	—	2	48	no	—
109	C₂²×Q₈	—	2	12	no	—
110	C₂²×Q₈	C₂×Dic₇₃	1	4	yes	—
111	C₂²×D₄	—	2	24	no	—
112	C₂²×D₄	—	2	12	no	—
113	C₂²×D₄	C₂×Dic₇₃	1	12	yes	—
114	C₂³×C₄	—	2	24	no	—
115	C₂³×C₄	C₂×Dic₇₃	1	3	yes	—
116	C₂³×C₄	C₂×Dic₇₃	1	6	yes	—
117	C₂³×C₄	C₂²⋊D₇₃	1	24	yes	—
118	C₂³×C₄	C₂²×D₇₃	1	6	yes	—
119	C₂³×C₄	C₂²×D₇₃	1	1	yes	characteristic
120	C₂×M₁₆	—	146	24	no	—
121	C₂²×C₈	—	73	8	no	—
122	C₂²⋊C₈	—	146	48	no	—
123	C₂⁴	—	2	12	no	—
124	C₂⁴	—	4	12	no	—
125	C₂⁴	C₂²⋊Dic₇₃	1	12	yes	—
126	C₂⁴	C₂²×Dic₇₃	1	6	yes	—
127	C₂⁴	C₂²×Dic₇₃	1	1	yes	characteristic
128	#41	—	2	128	no	—
129	#41	—	2	128	no	—
130	C₂×Q₈	—	2	32	no	—
131	C₂×Q₈	—	2	24	no	—
132	C₂×D₄	—	2	96	no	—
133	C₂×D₄	—	2	48	no	—
134	C₂×D₄	—	2	24	no	—
135	C₂²×C₄	—	2	12	no	—
136	C₂²×C₄	—	2	24	no	—
137	C₂²×C₄	—	2	96	no	—
138	C₂²×C₄	—	2	24	no	—
139	C₂²×C₄	C₂²⋊Dic₇₃	1	12	yes	—
140	C₂²×C₄	C₂²⋊Dic₇₃	1	24	yes	—
141	C₂²×C₄	C₂²×Dic₇₃	1	6	yes	—
142	C₂²×C₄	C₂²×Dic₇₃	1	1	yes	characteristic
143	C₂²×C₄	C₂×C₂²⋊D₇₃	1	24	yes	—
144	C₂²×C₄	C₂×C₂²⋊D₇₃	1	12	yes	—
145	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
146	M₁₆	—	292	16	no	—
147	C₂×C₈	—	146	24	no	—
148	C₂³	—	2	4	no	—
149	C₂³	—	2	24	no	—
150	C₂³	—	2	12	no	—
151	C₂³	—	2	24	no	—
152	C₂³	—	4	24	no	—
153	C₂³	—	4	48	no	—
154	C₂³	C₂×C₂²⋊Dic₇₃	1	12	yes	—
155	C₂³	C₂×C₂²⋊Dic₇₃	1	6	yes	—
156	C₂³	C₂³×Dic₇₃	1	1	yes	characteristic
157	Q₈	—	2	32	no	—
158	D₄	—	2	96	no	—
159	C₂×C₄	—	2	24	no	—
160	C₂×C₄	—	2	12	no	—
161	C₂×C₄	—	2	48	no	—
162	C₂×C₄	—	2	48	no	—
163	C₂×C₄	C₂×C₂²⋊Dic₇₃	1	12	yes	—
164	C₂×C₄	C₂×C₂²⋊Dic₇₃	1	6	yes	—
165	C₂×C₄	#14556560	1	16	yes	—
166	C₂×C₄	C₂²×C₂²⋊D₇₃	1	6	yes	—
167	C₈	—	292	8	no	—
168	C₂²	—	2	12	no	—
169	C₂²	—	2	24	no	—
170	C₂²	—	2	12	no	—
171	C₂²	—	4	48	no	—
172	C₂²	—	4	24	no	—
173	C₂²	#17988443	1	4	yes	—
174	C₂²	C₂²×C₂²⋊Dic₇₃	1	3	yes	—
175	C₂²	#17989354	1	4	yes	—
176	C₄	—	2	12	no	—
177	C₄	#17988443	1	4	yes	—
178	C₄	C₂×#14556560	1	4	yes	—
179	C₂	—	2	4	no	—
180	C₂	—	4	12	no	—
181	C₂	C₂×#17988443	1	1	yes	characteristic
182	C₂	#22618376	1	6	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#17988551

C₂

yes

maximal, complemented

#22609843

C₂

yes

maximal, complemented

C₂³×#41×C₇₃

C₂

yes

maximal, characteristic

C₂²×#11924012

C₂²

yes

—

#17988551

—

C₂×C₂²⋊#10596831

C₂²

yes

complemented

C₂²×#41×C₇₃

—

C₂²×#41×C₇₃

C₄

yes

—

C₂²×#41×C₇₃

C₂²

yes

—

C₂³×Q₈×C₇₃

C₄

yes

characteristic

C₂³×D₄×C₇₃

C₄

yes

—

C₂⁴×C₄×C₇₃

C₂²

yes

—

C₂×#11924012

—

C₂²×#10596831

C₂³

yes

—

C₂²⋊#10596831

—

C₂⁵×C₇₃

C₂×C₄

yes

—

C₂×#41×C₇₃

—

128

—

C₂×#41×C₇₃

—

C₂×#41×C₇₃

—

C₂²×Q₈×C₇₃

—

C₂²×Q₈×C₇₃

C₂×C₄

yes

—

C₂²×D₄×C₇₃

—

C₂²×D₄×C₇₃

—

C₂²×D₄×C₇₃

C₂×C₄

yes

—

C₂³×C₄×C₇₃

—

C₂³×C₄×C₇₃

C₂×C₄

yes

—

C₂³×C₄×C₇₃

C₂×C₄

yes

—

C₂³×C₄×C₇₃

D₄

yes

—

C₂³×C₄×C₇₃

C₂³

yes

—

C₂³×C₄×C₇₃

C₂³

yes

characteristic

#11924012

—

C₂×#10596831

—

C₂⁴×C₇₃

—

C₂⁴×C₇₃

—

C₂⁴×C₇₃

C₂²⋊C₄

yes

—

C₂⁴×C₇₃

C₂²×C₄

yes

—

C₂⁴×C₇₃

C₂²×C₄

yes

characteristic

#41×C₇₃

—

128

—

#41×C₇₃

—

128

—

C₂×Q₈×C₇₃

—

C₂×Q₈×C₇₃

—

C₂×D₄×C₇₃

—

C₂×D₄×C₇₃

—

C₂×D₄×C₇₃

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

C₂²⋊C₄

yes

—

C₂²×C₄×C₇₃

C₂²⋊C₄

yes

—

C₂²×C₄×C₇₃

C₂²×C₄

yes

—

C₂²×C₄×C₇₃

C₂²×C₄

yes

characteristic

C₂²×C₄×C₇₃

C₂×D₄

yes

—

C₂²×C₄×C₇₃

C₂×D₄

yes

—

C₂²×C₄×C₇₃

C₂⁴

yes

characteristic

C₂³×C₇₃

—

C₂³×C₇₃

—

C₂³×C₇₃

—

C₂³×C₇₃

—

C₂³×C₇₃

—

C₂³×C₇₃

—

C₂³×C₇₃

C₂×C₂²⋊C₄

yes

—

C₂³×C₇₃

C₂×C₂²⋊C₄

yes

—

C₂³×C₇₃

C₂³×C₄

yes

characteristic

Q₈×C₇₃

—

D₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂×C₂²⋊C₄

yes

—

C₂×C₄×C₇₃

C₂×C₂²⋊C₄

yes

—

C₂×C₄×C₇₃

#120

yes

—

C₂×C₄×C₇₃

C₂²×D₄

yes

—

#10596831

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

#379

yes

—

C₂²×C₇₃

C₂²×C₂²⋊C₄

yes

—

C₂²×C₇₃

#568

yes

—

C₄×C₇₃

—

C₄×C₇₃

#379

yes

—

C₄×C₇₃

C₂×#120

yes

—

#20580

—

maximal, Sylow

C₂×C₇₃

—

C₂×C₇₃

—

C₂×C₇₃

C₂×#379

yes

characteristic

C₂×C₇₃

#2879

yes

—

C₂³×#41

D₇₃

yes

characteristic

C₂×#407

—

#1780

—

C₇₃

#20580

yes

characteristic, complemented, Sylow

C₂²×#41

—

C₂²×#41

Dic₇₃

yes

—

C₂²×#41

C₂×D₇₃

yes

—

C₂³×Q₈

Dic₇₃

yes

characteristic

100

C₂³×D₄

Dic₇₃

yes

—

101

C₂⁴×C₄

C₂×D₇₃

yes

—

102

C₂²×M₁₆

—

103

#407

—

146

—

104

C₂×C₂²⋊C₈

—

105

C₂⁵

C₂×Dic₇₃

yes

—

106

C₂×#41

—

128

—

107

C₂×#41

—

108

C₂×#41

—

109

C₂²×Q₈

—

110

C₂²×Q₈

C₂×Dic₇₃

yes

—

111

C₂²×D₄

—

112

C₂²×D₄

—

113

C₂²×D₄

C₂×Dic₇₃

yes

—

114

C₂³×C₄

—

115

C₂³×C₄

C₂×Dic₇₃

yes

—

116

C₂³×C₄

C₂×Dic₇₃

yes

—

117

C₂³×C₄

C₂²⋊D₇₃

yes

—

118

C₂³×C₄

C₂²×D₇₃

yes

—

119

C₂³×C₄

C₂²×D₇₃

yes

characteristic

120

C₂×M₁₆

—

146

—

121

C₂²×C₈

—

122

C₂²⋊C₈

—

146

—

123

C₂⁴

—

124

C₂⁴

—

125

C₂⁴

C₂²⋊Dic₇₃

yes

—

126

C₂⁴

C₂²×Dic₇₃

yes

—

127

C₂⁴

C₂²×Dic₇₃

yes

characteristic

128

#41

—

128

—

129

#41

—

128

—

130

C₂×Q₈

—

131

C₂×Q₈

—

132

C₂×D₄

—

133

C₂×D₄

—

134

C₂×D₄

—

135

C₂²×C₄

—

136

C₂²×C₄

—

137

C₂²×C₄

—

138

C₂²×C₄

—

139

C₂²×C₄

C₂²⋊Dic₇₃

yes

—

140

C₂²×C₄

C₂²⋊Dic₇₃

yes

—

141

C₂²×C₄

C₂²×Dic₇₃

yes

—

142

C₂²×C₄

C₂²×Dic₇₃

yes

characteristic

143

C₂²×C₄

C₂×C₂²⋊D₇₃

yes

—

144

C₂²×C₄

C₂×C₂²⋊D₇₃

yes

—

145

C₂²×C₄

C₂³×D₇₃

yes

characteristic

146

M₁₆

—

292

—

147

C₂×C₈

—

146

—

148

C₂³

—

149

C₂³

—

150

C₂³

—

151

C₂³

—

152

C₂³

—

153

C₂³

—

154

C₂³

C₂×C₂²⋊Dic₇₃

yes

—

155

C₂³

C₂×C₂²⋊Dic₇₃

yes

—

156

C₂³

C₂³×Dic₇₃

yes

characteristic

157

Q₈

—

158

D₄

—

159

C₂×C₄

—

160

C₂×C₄

—

161

C₂×C₄

—

162

C₂×C₄

—

163

C₂×C₄

C₂×C₂²⋊Dic₇₃

yes

—

164

C₂×C₄

C₂×C₂²⋊Dic₇₃

yes

—

165

C₂×C₄

#14556560

yes

—

166

C₂×C₄

C₂²×C₂²⋊D₇₃

yes

—

167

C₈

—

292

—

168

C₂²

—

169

C₂²

—

170

C₂²

—

171

C₂²

—

172

C₂²

—

173

C₂²

#17988443

yes

—

174

C₂²

C₂²×C₂²⋊Dic₇₃

yes

—

175

C₂²

#17989354

yes

—

176

C₄

—

177

C₄

#17988443

yes

—

178

C₄

C₂×#14556560

yes

—

179

C₂

—

180

C₂

—

181

C₂

C₂×#17988443

yes

characteristic

182

C₂

#22618376

yes

—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₇₃
commutator, socle	C₂³×C₇₃	C₂³×C₄
Fitting, prime radical	C₂³×#41×C₇₃	C₂
cosocle	C₂²×C₄×C₇₃	C₂⁴
hypercenter	C₂³×#41	D₇₃
hypocenter	C₇₃	#20580
LCS	G ▷ C₂³×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂³×#41

subgroup

G/H

center, Frattini

C₂²×C₄

C₂³×D₇₃

commutator, socle

C₂³×C₇₃

C₂³×C₄

Fitting, prime radical

C₂³×#41×C₇₃

C₂

cosocle

C₂²×C₄×C₇₃

C₂⁴

hypercenter

C₂³×#41

D₇₃

C₇₃

G ▷ C₂³×C₇₃ ▷ C₇₃

C₁ ◁ C₂²×C₄ ◁ C₂³×#41

N	H ≅ G/N	type
1. C₂×#17988551	C₂	semidirect
2. #22609843	C₂	semidirect
6. C₂×C₂²⋊#10596831	C₂²	semidirect
95. C₇₃	#20580	semidirect

H ≅ G/N

type

1. C₂×#17988551

C₂

semidirect

2. #22609843

C₂

semidirect

6. C₂×C₂²⋊#10596831

C₂²

semidirect

95. C₇₃

#20580

semidirect

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

subgroup	index
C₂×#17988551	2
#22609843	2
C₂³×#41×C₇₃	2
#20580	73

subgroup

index

C₂×#17988551

#22609843

C₂³×#41×C₇₃

#20580

Subgroups — #33085097

Conjugacy classes of subgroups

Complements

Maximal subgroups