Group #32919620 — subgroups

Subgroups — C₇₃×#10216 #32919620

Order 18688.

468 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 98 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	C₇₃×#3255	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇₃×#3235	C₂	1	2	yes	maximal
3	C₇₃×#1963	C₂	1	1	yes	maximal, characteristic
4	C₇₃×#1506	C₂	1	2	yes	maximal, complemented
5	C₇₃×#1307	C₂	1	1	yes	maximal, characteristic, complemented
6	#533×C₇₃	C₂²	1	2	yes	—
7	#532×C₇₃	C₂²	1	1	yes	characteristic
8	#501×C₇₃	—	2	2	no	—
9	#490×C₇₃	—	2	2	no	—
10	#482×C₇₃	—	2	4	no	—
11	#476×C₇₃	—	2	2	no	—
12	#475×C₇₃	—	2	2	no	—
13	#474×C₇₃	—	2	2	no	—
14	#470×C₇₃	—	2	2	no	—
15	#462×C₇₃	—	2	2	no	—
16	#432×C₇₃	C₂²	1	2	yes	—
17	#423×C₇₃	C₂²	1	1	yes	characteristic
18	C₂×#104×C₇₃	—	2	2	no	—
19	#376×C₇₃	C₂²	1	1	yes	characteristic
20	#328×C₇₃	—	2	4	no	—
21	C₂×#41×C₇₃	—	2	1	no	—
22	C₂×Q₁₆×C₇₃	—	2	2	no	—
23	C₂×M₁₆×C₇₃	D₄	1	2	yes	—
24	C₄⋊Q₈×C₇₃	D₄	1	2	yes	—
25	C₄⋊Q₈×C₇₃	D₄	1	2	yes	—
26	C₄⋊Q₈×C₇₃	D₄	1	1	yes	characteristic
27	#127×C₇₃	D₄	1	1	yes	characteristic
28	#125×C₇₃	—	2	2	no	—
29	#124×C₇₃	—	2	1	no	—
30	C₂²⋊Q₈×C₇₃	—	2	2	no	—
31	C₂²⋊Q₈×C₇₃	—	2	2	no	—
32	#121×C₇₃	—	2	2	no	—
33	C₄×Q₈×C₇₃	—	2	2	no	—
34	C₄×Q₈×C₇₃	—	2	2	no	—
35	C₄×D₄×C₇₃	—	2	2	no	—
36	#117×C₇₃	—	2	2	no	—
37	C₂×C₄²×C₇₃	—	2	1	no	—
38	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
39	#107×C₇₃	—	2	4	no	—
40	#106×C₇₃	—	2	2	no	—
41	#106×C₇₃	—	2	4	no	—
42	C₄⋊C₈×C₇₃	—	2	2	no	—
43	C₄⋊C₈×C₇₃	—	2	2	no	—
44	#104×C₇₃	—	4	4	no	—
45	#103×C₇₃	—	2	4	no	—
46	#102×C₇₃	—	2	4	no	—
47	#102×C₇₃	—	2	4	no	—
48	C₂²⋊C₈×C₇₃	D₄	1	4	yes	—
49	#97×C₇₃	—	2	2	no	—
50	#95×C₇₃	—	2	2	no	—
51	#41×C₇₃	—	4	2	no	—
52	#41×C₇₃	—	4	2	no	—
53	C₂×Q₈×C₇₃	—	2	2	no	—
54	C₂×Q₈×C₇₃	—	2	1	no	—
55	C₂×Q₈×C₇₃	—	2	2	no	—
56	C₂×D₄×C₇₃	—	2	2	no	—
57	C₂×D₄×C₇₃	—	2	1	no	—
58	C₂×D₄×C₇₃	—	4	1	no	—
59	C₂²×C₄×C₇₃	—	4	1	no	—
60	C₂²×C₄×C₇₃	—	4	1	no	—
61	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
62	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
63	Q₁₆×C₇₃	—	8	2	no	—
64	M₁₆×C₇₃	—	4	2	no	—
65	C₂×C₈×C₇₃	—	2	4	no	—
66	C₂×C₈×C₇₃	—	2	2	no	—
67	C₄⋊C₄×C₇₃	—	2	2	no	—
68	C₄⋊C₄×C₇₃	—	2	2	no	—
69	C₄⋊C₄×C₇₃	—	2	2	no	—
70	C₄⋊C₄×C₇₃	—	2	2	no	—
71	C₄⋊C₄×C₇₃	—	2	2	no	—
72	C₄⋊C₄×C₇₃	—	4	2	no	—
73	C₄⋊C₄×C₇₃	—	4	2	no	—
74	C₂²⋊C₄×C₇₃	—	4	2	no	—
75	C₂²⋊C₄×C₇₃	—	4	2	no	—
76	C₄²×C₇₃	—	2	2	no	—
77	C₄²×C₇₃	—	4	1	no	—
78	C₄²×C₇₃	—	4	2	no	—
79	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
80	C₄²×C₇₃	C₂×D₄	1	2	yes	—
81	C₄²×C₇₃	#41	1	1	yes	characteristic
82	C₂³×C₇₃	—	4	1	no	—
83	C₂³×C₇₃	#127	1	1	yes	characteristic
84	Q₈×C₇₃	—	4	2	no	—
85	Q₈×C₇₃	—	4	2	no	—
86	Q₈×C₇₃	—	4	2	no	—
87	Q₈×C₇₃	—	8	2	no	—
88	D₄×C₇₃	—	4	4	no	—
89	D₄×C₇₃	—	4	2	no	—
90	D₄×C₇₃	—	8	2	no	—
91	C₂×C₄×C₇₃	—	2	1	no	—
92	C₂×C₄×C₇₃	—	2	1	no	—
93	C₂×C₄×C₇₃	—	4	2	no	—
94	C₂×C₄×C₇₃	—	4	2	no	—
95	C₂×C₄×C₇₃	—	4	2	no	—
96	C₂×C₄×C₇₃	—	4	2	no	—
97	C₂×C₄×C₇₃	—	4	1	no	—
98	C₂×C₄×C₇₃	—	8	2	no	—
99	C₂×C₄×C₇₃	—	8	1	no	—
100	C₂×C₄×C₇₃	—	8	1	no	—
101	C₂×C₄×C₇₃	#120	1	2	yes	—
102	C₂×C₄×C₇₃	#120	1	1	yes	characteristic
103	C₂×C₄×C₇₃	#121	1	2	yes	—
104	C₂×C₄×C₇₃	#121	1	1	yes	characteristic
105	C₈×C₇₃	—	4	4	no	—
106	C₈×C₇₃	—	4	2	no	—
107	C₂²×C₇₃	—	2	1	no	—
108	C₂²×C₇₃	—	2	2	no	—
109	C₂²×C₇₃	—	8	1	no	—
110	C₂²×C₇₃	—	8	2	no	—
111	C₂²×C₇₃	#392	1	1	yes	characteristic
112	C₄×C₇₃	—	2	1	no	—
113	C₄×C₇₃	—	2	2	no	—
114	C₄×C₇₃	—	2	2	no	—
115	C₄×C₇₃	—	8	2	no	—
116	C₄×C₇₃	—	8	1	no	—
117	C₄×C₇₃	—	8	2	no	—
118	C₄×C₇₃	—	8	2	no	—
119	C₄×C₇₃	#453	1	1	yes	characteristic
120	C₄×C₇₃	#454	1	1	yes	characteristic
121	#10216	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
122	C₂×C₇₃	—	4	1	no	—
123	C₂×C₇₃	—	16	1	no	—
124	C₂×C₇₃	#2006	1	1	yes	characteristic
125	C₂×C₇₃	#2009	1	2	yes	—
126	#3255	C₂×C₇₃	1	1	yes	characteristic, complemented
127	#3235	C₂×C₇₃	1	2	yes	—
128	#1963	C₂×C₇₃	1	1	yes	characteristic
129	#1506	C₂×C₇₃	1	2	yes	complemented
130	#1307	C₂×C₇₃	1	1	yes	characteristic, complemented
131	C₇₃	#10216	1	1	yes	characteristic, direct product factor, Sylow
132	#533	C₂²×C₇₃	1	2	yes	—
133	#532	C₂²×C₇₃	1	1	yes	characteristic
134	#501	—	2	2	no	—
135	#490	—	2	2	no	—
136	#482	—	2	4	no	—
137	#476	—	2	2	no	—
138	#475	—	2	2	no	—
139	#474	—	2	2	no	—
140	#470	—	2	2	no	—
141	#462	—	2	2	no	—
142	#432	C₂²×C₇₃	1	2	yes	—
143	#423	C₂²×C₇₃	1	1	yes	characteristic
144	C₂×#104	—	2	2	no	—
145	#376	C₂²×C₇₃	1	1	yes	characteristic
146	#328	—	2	4	no	—
147	C₂×#41	—	2	1	no	—
148	C₂×Q₁₆	—	2	2	no	—
149	C₂×M₁₆	D₄×C₇₃	1	2	yes	—
150	C₄⋊Q₈	D₄×C₇₃	1	1	yes	characteristic
151	C₄⋊Q₈	D₄×C₇₃	1	2	yes	—
152	C₄⋊Q₈	D₄×C₇₃	1	2	yes	—
153	#127	D₄×C₇₃	1	1	yes	characteristic
154	#125	—	2	2	no	—
155	#124	—	2	1	no	—
156	C₂²⋊Q₈	—	2	2	no	—
157	C₂²⋊Q₈	—	2	2	no	—
158	#121	—	2	2	no	—
159	C₄×Q₈	—	2	2	no	—
160	C₄×Q₈	—	2	2	no	—
161	C₄×D₄	—	2	2	no	—
162	#117	—	2	2	no	—
163	C₂×C₄²	—	2	1	no	—
164	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
165	#107	—	2	4	no	—
166	#106	—	2	2	no	—
167	#106	—	2	4	no	—
168	C₄⋊C₈	—	2	2	no	—
169	C₄⋊C₈	—	2	2	no	—
170	#104	—	4	4	no	—
171	#103	—	2	4	no	—
172	#102	—	2	4	no	—
173	#102	—	2	4	no	—
174	C₂²⋊C₈	D₄×C₇₃	1	4	yes	—
175	#97	—	2	2	no	—
176	#95	—	2	2	no	—
177	#41	—	4	2	no	—
178	#41	—	4	2	no	—
179	C₂×Q₈	—	2	2	no	—
180	C₂×Q₈	—	2	1	no	—
181	C₂×Q₈	—	2	2	no	—
182	C₂×D₄	—	2	2	no	—
183	C₂×D₄	—	2	1	no	—
184	C₂×D₄	—	4	1	no	—
185	C₂²×C₄	—	4	1	no	—
186	C₂²×C₄	—	4	1	no	—
187	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
188	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
189	Q₁₆	—	8	2	no	—
190	M₁₆	—	4	2	no	—
191	C₂×C₈	—	2	4	no	—
192	C₂×C₈	—	2	2	no	—
193	C₄⋊C₄	—	2	2	no	—
194	C₄⋊C₄	—	2	2	no	—
195	C₄⋊C₄	—	2	2	no	—
196	C₄⋊C₄	—	2	2	no	—
197	C₄⋊C₄	—	2	2	no	—
198	C₄⋊C₄	—	4	2	no	—
199	C₄⋊C₄	—	4	2	no	—
200	C₂²⋊C₄	—	4	2	no	—
201	C₂²⋊C₄	—	4	2	no	—
202	C₄²	—	2	2	no	—
203	C₄²	—	4	1	no	—
204	C₄²	—	4	2	no	—
205	C₄²	C₂×D₄×C₇₃	1	1	yes	characteristic
206	C₄²	C₂×D₄×C₇₃	1	2	yes	—
207	C₄²	#41×C₇₃	1	1	yes	characteristic
208	C₂³	—	4	1	no	—
209	C₂³	#127×C₇₃	1	1	yes	characteristic
210	Q₈	—	4	2	no	—
211	Q₈	—	4	2	no	—
212	Q₈	—	4	2	no	—
213	Q₈	—	8	2	no	—
214	D₄	—	4	2	no	—
215	D₄	—	4	4	no	—
216	D₄	—	8	2	no	—
217	C₂×C₄	—	2	1	no	—
218	C₂×C₄	—	2	1	no	—
219	C₂×C₄	—	4	2	no	—
220	C₂×C₄	—	4	2	no	—
221	C₂×C₄	—	4	2	no	—
222	C₂×C₄	—	4	2	no	—
223	C₂×C₄	—	4	1	no	—
224	C₂×C₄	—	8	2	no	—
225	C₂×C₄	—	8	1	no	—
226	C₂×C₄	—	8	1	no	—
227	C₂×C₄	#120×C₇₃	1	2	yes	—
228	C₂×C₄	#120×C₇₃	1	1	yes	characteristic
229	C₂×C₄	#121×C₇₃	1	2	yes	—
230	C₂×C₄	#121×C₇₃	1	1	yes	characteristic
231	C₈	—	4	4	no	—
232	C₈	—	4	2	no	—
233	C₂²	—	2	1	no	—
234	C₂²	—	2	2	no	—
235	C₂²	—	8	1	no	—
236	C₂²	—	8	2	no	—
237	C₂²	#392×C₇₃	1	1	yes	characteristic
238	C₄	—	2	1	no	—
239	C₄	—	2	2	no	—
240	C₄	—	2	2	no	—
241	C₄	—	8	2	no	—
242	C₄	—	8	1	no	—
243	C₄	—	8	2	no	—
244	C₄	—	8	2	no	—
245	C₄	#453×C₇₃	1	1	yes	characteristic
246	C₄	#454×C₇₃	1	1	yes	characteristic
247	C₂	—	4	1	no	—
248	C₂	—	16	1	no	—
249	C₂	C₇₃×#2006	1	1	yes	characteristic
250	C₂	C₇₃×#2009	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₇₃×#3255

C₂

yes

maximal, characteristic, complemented

C₇₃×#3235

C₂

yes

maximal

C₇₃×#1963

C₂

yes

maximal, characteristic

C₇₃×#1506

C₂

yes

maximal, complemented

C₇₃×#1307

C₂

yes

maximal, characteristic, complemented

#533×C₇₃

C₂²

yes

—

#532×C₇₃

C₂²

yes

characteristic

#501×C₇₃

—

#490×C₇₃

—

#482×C₇₃

—

#476×C₇₃

—

#475×C₇₃

—

#474×C₇₃

—

#470×C₇₃

—

#462×C₇₃

—

#432×C₇₃

C₂²

yes

—

#423×C₇₃

C₂²

yes

characteristic

C₂×#104×C₇₃

—

#376×C₇₃

C₂²

yes

characteristic

#328×C₇₃

—

C₂×#41×C₇₃

—

C₂×Q₁₆×C₇₃

—

C₂×M₁₆×C₇₃

D₄

yes

—

C₄⋊Q₈×C₇₃

D₄

yes

—

C₄⋊Q₈×C₇₃

D₄

yes

—

C₄⋊Q₈×C₇₃

D₄

yes

characteristic

#127×C₇₃

D₄

yes

characteristic

#125×C₇₃

—

#124×C₇₃

—

C₂²⋊Q₈×C₇₃

—

C₂²⋊Q₈×C₇₃

—

#121×C₇₃

—

C₄×Q₈×C₇₃

—

C₄×Q₈×C₇₃

—

C₄×D₄×C₇₃

—

#117×C₇₃

—

C₂×C₄²×C₇₃

—

C₂×C₄²×C₇₃

C₂³

yes

characteristic

#107×C₇₃

—

#106×C₇₃

—

#106×C₇₃

—

C₄⋊C₈×C₇₃

—

C₄⋊C₈×C₇₃

—

#104×C₇₃

—

#103×C₇₃

—

#102×C₇₃

—

#102×C₇₃

—

C₂²⋊C₈×C₇₃

D₄

yes

—

#97×C₇₃

—

#95×C₇₃

—

#41×C₇₃

—

#41×C₇₃

—

C₂×Q₈×C₇₃

—

C₂×Q₈×C₇₃

—

C₂×Q₈×C₇₃

—

C₂×D₄×C₇₃

—

C₂×D₄×C₇₃

—

C₂×D₄×C₇₃

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂²×C₄×C₇₃

C₂×D₄

yes

—

Q₁₆×C₇₃

—

M₁₆×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

—

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

—

C₂²⋊C₄×C₇₃

—

C₂²⋊C₄×C₇₃

—

C₄²×C₇₃

—

C₄²×C₇₃

—

C₄²×C₇₃

—

C₄²×C₇₃

C₂×D₄

yes

characteristic

C₄²×C₇₃

C₂×D₄

yes

—

C₄²×C₇₃

#41

yes

characteristic

C₂³×C₇₃

—

C₂³×C₇₃

#127

yes

characteristic

Q₈×C₇₃

—

Q₈×C₇₃

—

Q₈×C₇₃

—

Q₈×C₇₃

—

D₄×C₇₃

—

D₄×C₇₃

—

D₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

100

C₂×C₄×C₇₃

—

101

C₂×C₄×C₇₃

#120

yes

—

102

C₂×C₄×C₇₃

#120

yes

characteristic

103

C₂×C₄×C₇₃

#121

yes

—

104

C₂×C₄×C₇₃

#121

yes

characteristic

105

C₈×C₇₃

—

106

C₈×C₇₃

—

107

C₂²×C₇₃

—

108

C₂²×C₇₃

—

109

C₂²×C₇₃

—

110

C₂²×C₇₃

—

111

C₂²×C₇₃

#392

yes

characteristic

112

C₄×C₇₃

—

113

C₄×C₇₃

—

114

C₄×C₇₃

—

115

C₄×C₇₃

—

116

C₄×C₇₃

—

117

C₄×C₇₃

—

118

C₄×C₇₃

—

119

C₄×C₇₃

#453

yes

characteristic

120

C₄×C₇₃

#454

yes

characteristic

121

#10216

C₇₃

yes

maximal, characteristic, direct product factor, Sylow

122

C₂×C₇₃

—

123

C₂×C₇₃

—

124

C₂×C₇₃

#2006

yes

characteristic

125

C₂×C₇₃

#2009

yes

—

126

#3255

C₂×C₇₃

yes

characteristic, complemented

127

#3235

C₂×C₇₃

yes

—

128

#1963

C₂×C₇₃

yes

characteristic

129

#1506

C₂×C₇₃

yes

complemented

130

#1307

C₂×C₇₃

yes

characteristic, complemented

131

C₇₃

#10216

yes

characteristic, direct product factor, Sylow

132

#533

C₂²×C₇₃

yes

—

133

#532

C₂²×C₇₃

yes

characteristic

134

#501

—

135

#490

—

136

#482

—

137

#476

—

138

#475

—

139

#474

—

140

#470

—

141

#462

—

142

#432

C₂²×C₇₃

yes

—

143

#423

C₂²×C₇₃

yes

characteristic

144

C₂×#104

—

145

#376

C₂²×C₇₃

yes

characteristic

146

#328

—

147

C₂×#41

—

148

C₂×Q₁₆

—

149

C₂×M₁₆

D₄×C₇₃

yes

—

150

C₄⋊Q₈

D₄×C₇₃

yes

characteristic

151

C₄⋊Q₈

D₄×C₇₃

yes

—

152

C₄⋊Q₈

D₄×C₇₃

yes

—

153

#127

D₄×C₇₃

yes

characteristic

154

#125

—

155

#124

—

156

C₂²⋊Q₈

—

157

C₂²⋊Q₈

—

158

#121

—

159

C₄×Q₈

—

160

C₄×Q₈

—

161

C₄×D₄

—

162

#117

—

163

C₂×C₄²

—

164

C₂×C₄²

C₂³×C₇₃

yes

characteristic

165

#107

—

166

#106

—

167

#106

—

168

C₄⋊C₈

—

169

C₄⋊C₈

—

170

#104

—

171

#103

—

172

#102

—

173

#102

—

174

C₂²⋊C₈

D₄×C₇₃

yes

—

175

#97

—

176

#95

—

177

#41

—

178

#41

—

179

C₂×Q₈

—

180

C₂×Q₈

—

181

C₂×Q₈

—

182

C₂×D₄

—

183

C₂×D₄

—

184

C₂×D₄

—

185

C₂²×C₄

—

186

C₂²×C₄

—

187

C₂²×C₄

C₂×D₄×C₇₃

yes

characteristic

188

C₂²×C₄

C₂×D₄×C₇₃

yes

—

189

Q₁₆

—

190

M₁₆

—

191

C₂×C₈

—

192

C₂×C₈

—

193

C₄⋊C₄

—

194

C₄⋊C₄

—

195

C₄⋊C₄

—

196

C₄⋊C₄

—

197

C₄⋊C₄

—

198

C₄⋊C₄

—

199

C₄⋊C₄

—

200

C₂²⋊C₄

—

201

C₂²⋊C₄

—

202

C₄²

—

203

C₄²

—

204

C₄²

—

205

C₄²

C₂×D₄×C₇₃

yes

characteristic

206

C₄²

C₂×D₄×C₇₃

yes

—

207

C₄²

#41×C₇₃

yes

characteristic

208

C₂³

—

209

C₂³

#127×C₇₃

yes

characteristic

210

Q₈

—

211

Q₈

—

212

Q₈

—

213

Q₈

—

214

D₄

—

215

D₄

—

216

D₄

—

217

C₂×C₄

—

218

C₂×C₄

—

219

C₂×C₄

—

220

C₂×C₄

—

221

C₂×C₄

—

222

C₂×C₄

—

223

C₂×C₄

—

224

C₂×C₄

—

225

C₂×C₄

—

226

C₂×C₄

—

227

C₂×C₄

#120×C₇₃

yes

—

228

C₂×C₄

#120×C₇₃

yes

characteristic

229

C₂×C₄

#121×C₇₃

yes

—

230

C₂×C₄

#121×C₇₃

yes

characteristic

231

C₈

—

232

C₈

—

233

C₂²

—

234

C₂²

—

235

C₂²

—

236

C₂²

—

237

C₂²

#392×C₇₃

yes

characteristic

238

C₄

—

239

C₄

—

240

C₄

—

241

C₄

—

242

C₄

—

243

C₄

—

244

C₄

—

245

C₄

#453×C₇₃

yes

characteristic

246

C₄

#454×C₇₃

yes

characteristic

247

C₂

—

248

C₂

—

249

C₂

C₇₃×#2006

yes

characteristic

250

C₂

C₇₃×#2009

yes

—

	subgroup	G/H
center, socle	C₂²×C₇₃	#392
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₇₃
prime radical	#532×C₇₃	C₂²
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₇₃ ◁ C₂×C₄²×C₇₃ ◁ G

subgroup

G/H

center, socle

C₂²×C₇₃

#392

commutator, Frattini, cosocle

C₂×C₄²

C₂³×C₇₃

prime radical

#532×C₇₃

C₂²

LCS

G ▷ C₂×C₄² ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂²×C₇₃ ◁ C₂×C₄²×C₇₃ ◁ G

N	H ≅ G/N	type
1. C₇₃×#3255	C₂	semidirect
4. C₇₃×#1506	C₂	semidirect
5. C₇₃×#1307	C₂	semidirect
121. #10216	C₇₃	direct (N × H)
126. #3255	C₂×C₇₃	semidirect
129. #1506	C₂×C₇₃	semidirect
130. #1307	C₂×C₇₃	semidirect
131. C₇₃	#10216	direct (N × H)

H ≅ G/N

type

1. C₇₃×#3255

C₂

semidirect

4. C₇₃×#1506

C₂

semidirect

5. C₇₃×#1307

C₂

semidirect

121. #10216

C₇₃

direct (N × H)

126. #3255

C₂×C₇₃

semidirect

129. #1506

C₂×C₇₃

semidirect

130. #1307

C₂×C₇₃

semidirect

131. C₇₃

#10216

direct (N × H)

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

subgroup	index
C₇₃×#3255	2
C₇₃×#3235	2
C₇₃×#1963	2
C₇₃×#1506	2
C₇₃×#1307	2
#10216	73

subgroup

index

C₇₃×#3255

C₇₃×#3235

C₇₃×#1963

C₇₃×#1506

C₇₃×#1307

#10216

Subgroups — C₇₃×#10216 #32919620

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C73×#10216 #32919620

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#10216 #32919620