Group #32990790 — subgroups

Subgroups — #32990790

Order 18688.

346 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 85 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	#22610755	C₂	1	1	yes	maximal, characteristic
2	#22608600	C₂	1	2	yes	maximal
3	#22607791	C₂	1	2	yes	maximal, complemented
4	#22607776	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₃×#1838	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#14556588	C₂²	1	1	yes	characteristic
7	#17988640	C₂²	1	2	yes	—
8	C₂×#14556513	—	2	2	no	—
9	#17988453	C₂²	1	1	yes	characteristic
10	#17988330	—	2	4	no	—
11	#423×C₇₃	C₂²	1	2	yes	—
12	C₂×#97×C₇₃	C₂²	1	1	yes	characteristic
13	#341×C₇₃	—	2	2	no	—
14	C₂²×D₂₉₂	—	2	1	no	—
15	C₂²×D₂₉₂	—	2	2	no	—
16	#14556588	—	2	1	no	—
17	#14556588	—	2	2	no	—
18	#14556588	D₄	1	2	yes	—
19	C₂×C₄⋊Dic₇₃	—	2	1	no	—
20	C₄⋊#10596831	—	2	2	no	—
21	#14556513	—	4	4	no	—
22	C₂²⋊#10596831	—	2	2	no	—
23	C₄×#10596831	—	2	2	no	—
24	#14556498	—	2	2	no	—
25	C₂×M₁₆×C₇₃	—	2	2	no	—
26	C₂²×C₈×C₇₃	D₄	1	2	yes	—
27	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
28	C₄⋊C₈×C₇₃	—	2	2	no	—
29	C₄⋊C₈×C₇₃	—	2	2	no	—
30	#97×C₇₃	—	2	2	no	—
31	C₂³×D₇₃	—	4	1	no	—
32	C₂×D₂₉₂	—	2	2	no	—
33	C₂×D₂₉₂	—	2	4	no	—
34	C₂×D₂₉₂	—	4	2	no	—
35	C₂×D₂₉₂	—	4	2	no	—
36	C₂×D₂₉₂	—	4	1	no	—
37	C₂×D₂₉₂	—	4	2	no	—
38	C₂×D₂₉₂	—	8	4	no	—
39	C₂²×Dic₇₃	—	4	1	no	—
40	C₂×#10596831	—	4	2	no	—
41	C₄⋊Dic₇₃	—	4	2	no	—
42	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
43	C₂²×C₄×C₇₃	#41	1	2	yes	—
44	M₁₆×C₇₃	—	4	2	no	—
45	M₁₆×C₇₃	—	4	2	no	—
46	C₂×C₈×C₇₃	—	2	2	no	—
47	C₂×C₈×C₇₃	—	2	2	no	—
48	C₂×C₈×C₇₃	—	2	2	no	—
49	C₂×C₈×C₇₃	—	4	2	no	—
50	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
51	C₄²×C₇₃	#41	1	1	yes	characteristic
52	C₄²×C₇₃	#41	1	2	yes	—
53	C₂³×C₇₃	#124	1	1	yes	characteristic
54	C₂²×D₇₃	—	4	2	no	—
55	C₂²×D₇₃	—	8	4	no	—
56	C₂²×D₇₃	—	8	1	no	—
57	C₂²×D₇₃	—	8	1	no	—
58	C₂×C₄×C₇₃	—	4	2	no	—
59	C₂×C₄×C₇₃	#121	1	1	yes	characteristic
60	C₂×C₄×C₇₃	#123	1	1	yes	characteristic
61	C₂×C₄×C₇₃	#123	1	2	yes	—
62	C₂×C₄×C₇₃	#126	1	2	yes	—
63	C₂×C₄×C₇₃	#135	1	2	yes	—
64	C₂×C₄×C₇₃	AGL(1,ℤ/8)	1	2	yes	—
65	C₂×Dic₇₃	—	8	2	no	—
66	C₂×Dic₇₃	—	8	1	no	—
67	D₂₉₂	—	4	4	no	—
68	D₂₉₂	—	8	4	no	—
69	D₂₉₂	—	8	4	no	—
70	D₂₉₂	—	8	2	no	—
71	C₈×C₇₃	—	4	2	no	—
72	C₈×C₇₃	—	8	2	no	—
73	#10596831	—	8	2	no	—
74	C₂²×C₇₃	—	2	2	no	—
75	C₂²×C₇₃	#397	1	1	yes	characteristic
76	C₂²×C₇₃	#488	1	1	yes	characteristic
77	C₂²×C₇₃	#490	1	1	yes	characteristic
78	C₂×D₇₃	—	8	2	no	—
79	C₂×D₇₃	—	8	4	no	—
80	C₂×D₇₃	—	16	2	no	—
81	C₂×D₇₃	—	16	2	no	—
82	C₄×C₇₃	—	2	2	no	—
83	C₄×C₇₃	—	2	2	no	—
84	C₄×C₇₃	#463	1	2	yes	—
85	C₄×C₇₃	#482	1	2	yes	—
86	Dic₇₃	—	16	1	no	—
87	#10634	—	73	1	no	maximal, Sylow
88	C₂×C₇₃	—	2	1	no	—
89	C₂×C₇₃	—	2	1	no	—
90	C₂×C₇₃	#2073	1	1	yes	characteristic
91	C₂×C₇₃	#2081	1	2	yes	—
92	D₇₃	—	16	2	no	—
93	#1961	—	73	1	no	—
94	#1838	D₇₃	1	1	yes	characteristic, complemented
95	#1545	—	73	2	no	—
96	#1286	—	73	2	no	—
97	#1281	—	73	1	no	—
98	C₇₃	#10634	1	1	yes	characteristic, complemented, Sylow
99	C₂×#127	—	73	1	no	—
100	#431	—	73	2	no	—
101	#423	C₂×D₇₃	1	2	yes	—
102	C₂×#102	—	146	2	no	—
103	C₂×#97	C₂×D₇₃	1	1	yes	characteristic
104	#382	—	73	1	no	—
105	#341	—	2	2	no	—
106	#331	—	146	4	no	—
107	C₂²×D₄	—	146	1	no	—
108	C₂²×D₄	—	146	2	no	—
109	C₂×M₁₆	—	2	2	no	—
110	C₂²×C₈	C₂²⋊D₇₃	1	2	yes	—
111	#127	—	73	2	no	—
112	#127	—	146	1	no	—
113	#127	—	146	2	no	—
114	C₂×C₄⋊C₄	—	146	1	no	—
115	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
116	C₄⋊C₈	—	2	2	no	—
117	C₄⋊C₈	—	2	2	no	—
118	C₄⋊C₈	—	146	2	no	—
119	#102	—	292	4	no	—
120	C₂²⋊C₈	—	146	2	no	—
121	#97	—	2	2	no	—
122	C₄×C₈	—	146	2	no	—
123	#95	—	146	2	no	—
124	C₂⁴	—	292	1	no	—
125	C₂×D₄	—	292	1	no	—
126	C₂×D₄	—	292	2	no	—
127	C₂×D₄	—	292	2	no	—
128	C₂×D₄	—	292	2	no	—
129	C₂×D₄	—	584	4	no	—
130	C₂×D₄	—	146	2	no	—
131	C₂×D₄	—	146	4	no	—
132	C₂²×C₄	—	292	1	no	—
133	C₂²×C₄	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
134	C₂²×C₄	#11924029	1	2	yes	—
135	M₁₆	—	4	2	no	—
136	M₁₆	—	4	2	no	—
137	C₂×C₈	—	2	2	no	—
138	C₂×C₈	—	2	2	no	—
139	C₂×C₈	—	2	2	no	—
140	C₂×C₈	—	4	2	no	—
141	C₂×C₈	—	292	2	no	—
142	C₄⋊C₄	—	292	2	no	—
143	C₄²	D₄×D₇₃	1	1	yes	characteristic
144	C₄²	#11924027	1	1	yes	characteristic
145	C₄²	#11924028	1	2	yes	—
146	C₂³	—	292	2	no	—
147	C₂³	—	584	4	no	—
148	C₂³	—	584	1	no	—
149	C₂³	—	584	1	no	—
150	C₂³	#14556580	1	1	yes	characteristic
151	D₄	—	292	4	no	—
152	D₄	—	584	4	no	—
153	D₄	—	584	4	no	—
154	D₄	—	584	2	no	—
155	C₂×C₄	—	4	2	no	—
156	C₂×C₄	—	584	2	no	—
157	C₂×C₄	—	584	1	no	—
158	C₂×C₄	#14556562	1	1	yes	characteristic
159	C₂×C₄	#14556574	1	1	yes	characteristic
160	C₂×C₄	#14556576	1	2	yes	—
161	C₂×C₄	#14556586	1	2	yes	—
162	C₂×C₄	#14556611	1	2	yes	—
163	C₂×C₄	#14556616	1	2	yes	—
164	C₈	—	4	2	no	—
165	C₈	—	8	2	no	—
166	C₈	—	584	2	no	—
167	C₂²	—	2	2	no	—
168	C₂²	—	584	2	no	—
169	C₂²	—	584	4	no	—
170	C₂²	—	1168	2	no	—
171	C₂²	—	1168	2	no	—
172	C₂²	#17988513	1	1	yes	characteristic
173	C₂²	#17988944	1	1	yes	characteristic
174	C₂²	#17988953	1	1	yes	characteristic
175	C₄	—	2	2	no	—
176	C₄	—	2	2	no	—
177	C₄	—	1168	1	no	—
178	C₄	#17988799	1	2	yes	—
179	C₄	#17988911	1	2	yes	—
180	C₂	—	2	1	no	—
181	C₂	—	2	1	no	—
182	C₂	—	1168	2	no	—
183	C₂	#22611345	1	1	yes	characteristic
184	C₂	#22611389	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#22610755

C₂

yes

maximal, characteristic

#22608600

C₂

yes

maximal

#22607791

C₂

yes

maximal, complemented

#22607776

C₂

yes

maximal, characteristic, complemented

C₇₃×#1838

C₂

yes

maximal, characteristic, complemented

C₂×#14556588

C₂²

yes

characteristic

#17988640

C₂²

yes

—

C₂×#14556513

—

#17988453

C₂²

yes

characteristic

#17988330

—

#423×C₇₃

C₂²

yes

—

C₂×#97×C₇₃

C₂²

yes

characteristic

#341×C₇₃

—

C₂²×D₂₉₂

—

C₂²×D₂₉₂

—

#14556588

—

#14556588

—

#14556588

D₄

yes

—

C₂×C₄⋊Dic₇₃

—

—

—

—

—

—

C₂×M₁₆×C₇₃

—

C₂²×C₈×C₇₃

D₄

yes

—

C₂×C₄²×C₇₃

C₂³

yes

characteristic

C₄⋊C₈×C₇₃

—

C₄⋊C₈×C₇₃

—

#97×C₇₃

—

C₂³×D₇₃

—

C₂×D₂₉₂

—

C₂×D₂₉₂

—

C₂×D₂₉₂

—

C₂×D₂₉₂

—

C₂×D₂₉₂

—

C₂×D₂₉₂

—

C₂×D₂₉₂

—

C₂²×Dic₇₃

—

C₂×#10596831

—

C₄⋊Dic₇₃

—

C₂²×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂²×C₄×C₇₃

#41

yes

—

M₁₆×C₇₃

—

M₁₆×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

—

C₄²×C₇₃

C₂×D₄

yes

C₄²×C₇₃

yes

C₄²×C₇₃

yes

—

C₂³×C₇₃

#124

yes

characteristic

C₂²×D₇₃

—

C₂²×D₇₃

—

C₂²×D₇₃

—

C₂²×D₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

yes

C₂×C₄×C₇₃

yes

C₂×C₄×C₇₃

yes

—

C₂×C₄×C₇₃

#126

yes

—

C₂×C₄×C₇₃

#135

yes

—

C₂×C₄×C₇₃

AGL(1,ℤ/8)

yes

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

D₂₉₂

—

D₂₉₂

—

D₂₉₂

—

D₂₉₂

—

C₈×C₇₃

—

C₈×C₇₃

—

#10596831

—

C₂²×C₇₃

—

C₂²×C₇₃

yes

C₂²×C₇₃

yes

C₂²×C₇₃

yes

C₂×D₇₃

—

C₂×D₇₃

—

C₂×D₇₃

—

C₂×D₇₃

—

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

#463

yes

—

C₄×C₇₃

#482

yes

—

Dic₇₃

—

#10634

—

maximal, Sylow

C₂×C₇₃

—

C₂×C₇₃

—

C₂×C₇₃

#2073

yes

characteristic

C₂×C₇₃

#2081

yes

—

D₇₃

—

#1961

—

#1838

D₇₃

yes

characteristic, complemented

#1545

—

#1286

—

#1281

—

C₇₃

#10634

yes

characteristic, complemented, Sylow

C₂×#127

—

100

#431

—

101

#423

C₂×D₇₃

yes

—

102

C₂×#102

—

146

—

103

C₂×#97

C₂×D₇₃

yes

characteristic

104

#382

—

105

#341

—

106

#331

—

146

—

107

C₂²×D₄

—

146

—

108

C₂²×D₄

—

146

—

109

C₂×M₁₆

—

110

C₂²×C₈

C₂²⋊D₇₃

yes

—

111

#127

—

112

#127

—

146

—

113

#127

—

146

—

114

C₂×C₄⋊C₄

—

146

—

115

C₂×C₄²

C₂²×D₇₃

yes

characteristic

116

C₄⋊C₈

—

117

C₄⋊C₈

—

118

C₄⋊C₈

—

146

—

119

#102

—

292

—

120

C₂²⋊C₈

—

146

—

121

#97

—

122

C₄×C₈

—

146

—

123

#95

—

146

—

124

C₂⁴

—

292

—

125

C₂×D₄

—

292

—

126

C₂×D₄

—

292

—

127

C₂×D₄

—

292

—

128

C₂×D₄

—

292

—

129

C₂×D₄

—

584

—

130

C₂×D₄

—

146

—

131

C₂×D₄

—

146

—

132

C₂²×C₄

—

292

—

133

C₂²×C₄

C₂×C₂²⋊D₇₃

yes

characteristic

134

C₂²×C₄

#11924029

yes

—

135

M₁₆

—

136

M₁₆

—

137

C₂×C₈

—

138

C₂×C₈

—

139

C₂×C₈

—

140

C₂×C₈

—

141

C₂×C₈

—

292

—

142

C₄⋊C₄

—

292

—

143

C₄²

D₄×D₇₃

yes

characteristic

144

C₄²

#11924027

yes

characteristic

145

C₄²

#11924028

yes

—

146

C₂³

—

292

—

147

C₂³

—

584

—

148

C₂³

—

584

—

149

C₂³

—

584

—

150

C₂³

#14556580

yes

characteristic

151

D₄

—

292

—

152

D₄

—

584

—

153

D₄

—

584

—

154

D₄

—

584

—

155

C₂×C₄

—

156

C₂×C₄

—

584

—

157

C₂×C₄

—

584

—

158

C₂×C₄

#14556562

yes

characteristic

159

C₂×C₄

#14556574

yes

characteristic

160

C₂×C₄

#14556576

yes

—

161

C₂×C₄

#14556586

yes

—

162

C₂×C₄

#14556611

yes

—

163

C₂×C₄

#14556616

yes

—

164

C₈

—

165

C₈

—

166

C₈

—

584

—

167

C₂²

—

168

C₂²

—

584

—

169

C₂²

—

584

—

170

C₂²

—

1168

—

171

C₂²

—

1168

—

172

C₂²

#17988513

yes

characteristic

173

C₂²

#17988944

yes

characteristic

174

C₂²

#17988953

yes

characteristic

175

C₄

—

176

C₄

—

177

C₄

—

1168

—

178

C₄

#17988799

yes

—

179

C₄

#17988911

yes

—

180

C₂

—

181

C₂

—

182

C₂

—

1168

—

183

C₂

#22611345

yes

characteristic

184

C₂

#22611389

yes

—

	subgroup	G/H
center	C₂²	#17988513
commutator, cosocle	C₂×C₄²×C₇₃	C₂³
Frattini	C₂×C₄²	C₂²×D₇₃
Fitting	C₇₃×#1838	C₂
socle	C₂²×C₇₃	#397
prime radical	C₂×#14556588	C₂²
hypercenter	#1838	D₇₃
hypocenter	C₇₃	#10634
LCS	G ▷ C₂×C₄²×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1838

subgroup

G/H

center

C₂²

#17988513

commutator, cosocle

C₂×C₄²×C₇₃

C₂³

Frattini

C₂×C₄²

C₂²×D₇₃

Fitting

C₇₃×#1838

C₂

C₂²×C₇₃

C₂²

D₇₃

C₇₃

G ▷ C₂×C₄²×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1838

N	H ≅ G/N	type
3. #22607791	C₂	semidirect
4. #22607776	C₂	semidirect
5. C₇₃×#1838	C₂	semidirect
94. #1838	D₇₃	semidirect
98. C₇₃	#10634	semidirect

H ≅ G/N

type

3. #22607791

C₂

semidirect

4. #22607776

C₂

semidirect

5. C₇₃×#1838

C₂

semidirect

94. #1838

D₇₃

semidirect

98. C₇₃

#10634

semidirect

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

subgroup	index
#22610755	2
#22608600	2
#22607791	2
#22607776	2
C₇₃×#1838	2
#10634	73

subgroup

index

C₇₃×#1838

Subgroups — #32990790

Conjugacy classes of subgroups

Complements

Maximal subgroups