Group #32922771 — subgroups

Subgroups — C₇₃×#13367 #32922771

Order 18688.

406 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 114 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×#3162	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇₃×#2140	C₂	1	2	yes	maximal
3	C₇₃×#1972	C₂	1	1	yes	maximal, characteristic
4	C₇₃×#1386	C₂	1	2	yes	maximal, complemented
5	C₇₃×#1377	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×D₈×C₇₃	C₂²	1	1	yes	characteristic
7	#533×C₇₃	—	2	1	no	—
8	C₂×M₃₂×C₇₃	C₂²	1	2	yes	—
9	#501×C₇₃	—	2	4	no	—
10	#427×C₇₃	—	2	1	no	—
11	#427×C₇₃	C₂²	1	2	yes	—
12	C₂×#106×C₇₃	C₂²	1	1	yes	characteristic
13	C₂×#102×C₇₃	—	2	1	no	—
14	C₂×#97×C₇₃	C₂²	1	1	yes	characteristic
15	#390×C₇₃	—	2	1	no	—
16	#357×C₇₃	—	2	4	no	—
17	C₂²×D₄×C₇₃	—	2	1	no	—
18	C₂×D₈×C₇₃	—	2	2	no	—
19	C₂×D₈×C₇₃	—	2	2	no	—
20	C₂×D₈×C₇₃	—	2	1	no	—
21	C₂×D₈×C₇₃	Q₈	1	2	yes	complemented
22	C₂²×C₈×C₇₃	D₄	1	1	yes	characteristic
23	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
24	C₄⋊Q₈×C₇₃	—	2	2	no	—
25	#125×C₇₃	—	2	2	no	—
26	C₂²⋊Q₈×C₇₃	—	4	2	no	—
27	C₄×Q₈×C₇₃	—	4	2	no	—
28	#117×C₇₃	—	2	2	no	—
29	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
30	C₂×C₂²⋊C₄×C₇₃	—	4	2	no	—
31	C₂×C₄²×C₇₃	D₄	1	1	yes	characteristic
32	M₃₂×C₇₃	—	2	2	no	—
33	M₃₂×C₇₃	—	2	2	no	—
34	C₂×C₁₆×C₇₃	—	2	2	no	—
35	#107×C₇₃	—	2	2	no	—
36	#107×C₇₃	D₄	1	4	yes	—
37	#106×C₇₃	—	2	2	no	—
38	#106×C₇₃	—	2	2	no	—
39	#106×C₇₃	—	2	2	no	—
40	#102×C₇₃	—	4	2	no	—
41	#97×C₇₃	—	2	2	no	—
42	C₂⁴×C₇₃	—	4	1	no	—
43	C₂×Q₈×C₇₃	—	4	2	no	—
44	C₂×D₄×C₇₃	—	2	2	no	—
45	C₂×D₄×C₇₃	—	4	1	no	—
46	C₂×D₄×C₇₃	—	4	1	no	—
47	C₂×D₄×C₇₃	—	4	1	no	—
48	C₂×D₄×C₇₃	—	4	1	no	—
49	C₂×D₄×C₇₃	—	4	1	no	—
50	C₂²×C₄×C₇₃	—	4	1	no	—
51	C₂²×C₄×C₇₃	D₈	1	2	yes	—
52	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
53	D₈×C₇₃	—	2	4	no	—
54	D₈×C₇₃	—	4	2	no	—
55	C₂×C₈×C₇₃	—	2	1	no	—
56	C₂×C₈×C₇₃	—	2	1	no	—
57	C₂×C₈×C₇₃	SD₁₆	1	2	yes	—
58	C₂×C₈×C₇₃	C₂×D₄	1	2	yes	—
59	C₂×C₈×C₇₃	C₂×Q₈	1	1	yes	characteristic
60	C₂×C₈×C₇₃	#41	1	2	yes	—
61	C₂×C₈×C₇₃	#41	1	1	yes	characteristic
62	C₄⋊C₄×C₇₃	—	2	4	no	—
63	C₄⋊C₄×C₇₃	—	4	4	no	—
64	C₄⋊C₄×C₇₃	—	4	2	no	—
65	C₄⋊C₄×C₇₃	—	4	1	no	—
66	C₄⋊C₄×C₇₃	—	4	1	no	—
67	C₂²⋊C₄×C₇₃	—	4	2	no	—
68	C₂²⋊C₄×C₇₃	—	8	4	no	—
69	C₄²×C₇₃	—	2	1	no	—
70	C₄²×C₇₃	—	2	1	no	—
71	C₄²×C₇₃	—	4	2	no	—
72	C₁₆×C₇₃	—	4	2	no	—
73	C₂³×C₇₃	—	4	2	no	—
74	C₂³×C₇₃	—	8	2	no	—
75	C₂³×C₇₃	—	8	2	no	—
76	C₂³×C₇₃	—	8	1	no	—
77	C₂³×C₇₃	—	8	1	no	—
78	C₂³×C₇₃	C₂×D₈	1	1	yes	characteristic
79	Q₈×C₇₃	—	8	4	no	—
80	D₄×C₇₃	—	4	2	no	—
81	D₄×C₇₃	—	4	2	no	—
82	D₄×C₇₃	—	8	1	no	—
83	D₄×C₇₃	—	8	1	no	—
84	C₂×C₄×C₇₃	—	2	2	no	—
85	C₂×C₄×C₇₃	—	4	2	no	—
86	C₂×C₄×C₇₃	—	4	4	no	—
87	C₂×C₄×C₇₃	—	8	2	no	—
88	C₂×C₄×C₇₃	—	8	1	no	—
89	C₂×C₄×C₇₃	#120	1	1	yes	characteristic
90	C₂×C₄×C₇₃	C₂²⋊Q₈	1	1	yes	characteristic
91	C₂×C₄×C₇₃	#124	1	1	yes	characteristic
92	C₂×C₄×C₇₃	C₂×SD₁₆	1	1	yes	characteristic
93	C₂×C₄×C₇₃	AGL(1,ℤ/8)	1	1	yes	characteristic
94	C₂×C₄×C₇₃	#137	1	1	yes	characteristic
95	C₈×C₇₃	—	2	2	no	—
96	C₈×C₇₃	C₂²⋊Q₈	1	2	yes	—
97	C₈×C₇₃	#124	1	2	yes	—
98	C₂²×C₇₃	—	2	2	no	—
99	C₂²×C₇₃	—	8	4	no	—
100	C₂²×C₇₃	—	8	2	no	—
101	C₂²×C₇₃	—	16	1	no	—
102	C₂²×C₇₃	—	16	1	no	—
103	C₂²×C₇₃	—	16	2	no	—
104	C₂²×C₇₃	#447	1	1	yes	characteristic
105	C₂²×C₇₃	#474	1	1	yes	characteristic
106	C₂²×C₇₃	#486	1	1	yes	characteristic
107	C₄×C₇₃	—	4	2	no	—
108	C₄×C₇₃	—	8	4	no	—
109	C₄×C₇₃	—	16	1	no	—
110	C₄×C₇₃	#393	1	1	yes	characteristic
111	C₄×C₇₃	#448	1	1	yes	characteristic
112	C₄×C₇₃	#476	1	1	yes	characteristic
113	C₄×C₇₃	#489	1	1	yes	characteristic
114	#13367	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
115	C₂×C₇₃	—	2	1	no	—
116	C₂×C₇₃	—	2	1	no	—
117	C₂×C₇₃	—	16	2	no	—
118	C₂×C₇₃	#2023	1	1	yes	characteristic
119	C₂×C₇₃	#2190	1	2	yes	—
120	#3162	C₂×C₇₃	1	1	yes	characteristic, complemented
121	#2140	C₂×C₇₃	1	2	yes	—
122	#1972	C₂×C₇₃	1	1	yes	characteristic
123	#1386	C₂×C₇₃	1	2	yes	complemented
124	#1377	C₂×C₇₃	1	1	yes	characteristic, complemented
125	C₇₃	#13367	1	1	yes	characteristic, direct product factor, Sylow
126	C₂²×D₈	C₂²×C₇₃	1	1	yes	characteristic
127	#533	—	2	1	no	—
128	C₂×M₃₂	C₂²×C₇₃	1	2	yes	—
129	#501	—	2	4	no	—
130	#427	—	2	1	no	—
131	#427	C₂²×C₇₃	1	2	yes	—
132	C₂×#106	C₂²×C₇₃	1	1	yes	characteristic
133	C₂×#102	—	2	1	no	—
134	C₂×#97	C₂²×C₇₃	1	1	yes	characteristic
135	#390	—	2	1	no	—
136	#357	—	2	4	no	—
137	C₂²×D₄	—	2	1	no	—
138	C₂×D₈	—	2	2	no	—
139	C₂×D₈	—	2	2	no	—
140	C₂×D₈	—	2	1	no	—
141	C₂×D₈	Q₈×C₇₃	1	2	yes	complemented
142	C₂²×C₈	D₄×C₇₃	1	1	yes	characteristic
143	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
144	C₄⋊Q₈	—	2	2	no	—
145	#125	—	2	2	no	—
146	C₂²⋊Q₈	—	4	2	no	—
147	C₄×Q₈	—	4	2	no	—
148	#117	—	2	2	no	—
149	C₂×C₄⋊C₄	—	2	1	no	—
150	C₂×C₂²⋊C₄	—	4	2	no	—
151	C₂×C₄²	D₄×C₇₃	1	1	yes	characteristic
152	M₃₂	—	2	2	no	—
153	M₃₂	—	2	2	no	—
154	C₂×C₁₆	—	2	2	no	—
155	#107	—	2	2	no	—
156	#107	D₄×C₇₃	1	4	yes	—
157	#106	—	2	2	no	—
158	#106	—	2	2	no	—
159	#106	—	2	2	no	—
160	#102	—	4	2	no	—
161	#97	—	2	2	no	—
162	C₂⁴	—	4	1	no	—
163	C₂×Q₈	—	4	2	no	—
164	C₂×D₄	—	2	2	no	—
165	C₂×D₄	—	4	1	no	—
166	C₂×D₄	—	4	1	no	—
167	C₂×D₄	—	4	1	no	—
168	C₂×D₄	—	4	1	no	—
169	C₂×D₄	—	4	1	no	—
170	C₂²×C₄	—	4	1	no	—
171	C₂²×C₄	D₈×C₇₃	1	2	yes	—
172	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
173	D₈	—	2	4	no	—
174	D₈	—	4	2	no	—
175	C₂×C₈	—	2	1	no	—
176	C₂×C₈	—	2	1	no	—
177	C₂×C₈	SD₁₆×C₇₃	1	2	yes	—
178	C₂×C₈	C₂×D₄×C₇₃	1	2	yes	—
179	C₂×C₈	C₂×Q₈×C₇₃	1	1	yes	characteristic
180	C₂×C₈	#41×C₇₃	1	2	yes	—
181	C₂×C₈	#41×C₇₃	1	1	yes	characteristic
182	C₄⋊C₄	—	2	4	no	—
183	C₄⋊C₄	—	4	4	no	—
184	C₄⋊C₄	—	4	2	no	—
185	C₄⋊C₄	—	4	1	no	—
186	C₄⋊C₄	—	4	1	no	—
187	C₂²⋊C₄	—	4	2	no	—
188	C₂²⋊C₄	—	8	4	no	—
189	C₄²	—	2	1	no	—
190	C₄²	—	2	1	no	—
191	C₄²	—	4	2	no	—
192	C₁₆	—	4	2	no	—
193	C₂³	—	4	2	no	—
194	C₂³	—	8	2	no	—
195	C₂³	—	8	2	no	—
196	C₂³	—	8	1	no	—
197	C₂³	—	8	1	no	—
198	C₂³	C₂×D₈×C₇₃	1	1	yes	characteristic
199	Q₈	—	8	4	no	—
200	D₄	—	4	2	no	—
201	D₄	—	4	2	no	—
202	D₄	—	8	1	no	—
203	D₄	—	8	1	no	—
204	C₂×C₄	—	2	2	no	—
205	C₂×C₄	—	4	2	no	—
206	C₂×C₄	—	4	4	no	—
207	C₂×C₄	—	8	2	no	—
208	C₂×C₄	—	8	1	no	—
209	C₂×C₄	#120×C₇₃	1	1	yes	characteristic
210	C₂×C₄	C₂²⋊Q₈×C₇₃	1	1	yes	characteristic
211	C₂×C₄	#124×C₇₃	1	1	yes	characteristic
212	C₂×C₄	C₂×SD₁₆×C₇₃	1	1	yes	characteristic
213	C₂×C₄	AGL(1,ℤ/8)×C₇₃	1	1	yes	characteristic
214	C₂×C₄	#137×C₇₃	1	1	yes	characteristic
215	C₈	—	2	2	no	—
216	C₈	C₂²⋊Q₈×C₇₃	1	2	yes	—
217	C₈	#124×C₇₃	1	2	yes	—
218	C₂²	—	2	2	no	—
219	C₂²	—	8	4	no	—
220	C₂²	—	8	2	no	—
221	C₂²	—	16	1	no	—
222	C₂²	—	16	1	no	—
223	C₂²	—	16	2	no	—
224	C₂²	#447×C₇₃	1	1	yes	characteristic
225	C₂²	#474×C₇₃	1	1	yes	characteristic
226	C₂²	#486×C₇₃	1	1	yes	characteristic
227	C₄	—	4	2	no	—
228	C₄	—	8	4	no	—
229	C₄	—	16	1	no	—
230	C₄	#393×C₇₃	1	1	yes	characteristic
231	C₄	#448×C₇₃	1	1	yes	characteristic
232	C₄	#476×C₇₃	1	1	yes	characteristic
233	C₄	#489×C₇₃	1	1	yes	characteristic
234	C₂	—	2	1	no	—
235	C₂	—	2	1	no	—
236	C₂	—	16	2	no	—
237	C₂	C₇₃×#2023	1	1	yes	characteristic
238	C₂	C₇₃×#2190	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₇₃×#3162

C₂

yes

maximal, characteristic, complemented

C₇₃×#2140

C₂

yes

maximal

C₇₃×#1972

C₂

yes

maximal, characteristic

C₇₃×#1386

C₂

yes

maximal, complemented

C₇₃×#1377

C₂

yes

maximal, characteristic, complemented

C₂²×D₈×C₇₃

C₂²

yes

characteristic

#533×C₇₃

—

C₂×M₃₂×C₇₃

C₂²

yes

—

#501×C₇₃

—

#427×C₇₃

—

#427×C₇₃

C₂²

yes

—

C₂×#106×C₇₃

C₂²

yes

characteristic

C₂×#102×C₇₃

—

C₂×#97×C₇₃

C₂²

yes

characteristic

#390×C₇₃

—

#357×C₇₃

—

C₂²×D₄×C₇₃

—

C₂×D₈×C₇₃

—

C₂×D₈×C₇₃

—

C₂×D₈×C₇₃

—

C₂×D₈×C₇₃

Q₈

yes

complemented

C₂²×C₈×C₇₃

D₄

yes

characteristic

C₂²×C₈×C₇₃

C₂³

yes

characteristic

C₄⋊Q₈×C₇₃

—

#125×C₇₃

—

C₂²⋊Q₈×C₇₃

—

C₄×Q₈×C₇₃

—

#117×C₇₃

—

C₂×C₄⋊C₄×C₇₃

—

C₂×C₂²⋊C₄×C₇₃

—

C₂×C₄²×C₇₃

D₄

yes

characteristic

M₃₂×C₇₃

—

M₃₂×C₇₃

—

C₂×C₁₆×C₇₃

—

#107×C₇₃

—

#107×C₇₃

D₄

yes

—

#106×C₇₃

—

#106×C₇₃

—

#106×C₇₃

—

#102×C₇₃

—

#97×C₇₃

—

C₂⁴×C₇₃

—

C₂×Q₈×C₇₃

—

C₂×D₄×C₇₃

—

C₂×D₄×C₇₃

—

C₂×D₄×C₇₃

—

C₂×D₄×C₇₃

—

C₂×D₄×C₇₃

—

C₂×D₄×C₇₃

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

D₈

yes

—

C₂²×C₄×C₇₃

C₂×D₄

yes

characteristic

D₈×C₇₃

—

D₈×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

SD₁₆

yes

—

C₂×C₈×C₇₃

C₂×D₄

yes

—

C₂×C₈×C₇₃

C₂×Q₈

yes

characteristic

C₂×C₈×C₇₃

#41

yes

—

C₂×C₈×C₇₃

#41

yes

characteristic

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

—

C₁₆×C₇₃

—

C₂³×C₇₃

—

C₂³×C₇₃

—

C₂³×C₇₃

—

C₂³×C₇₃

—

C₂³×C₇₃

—

C₂³×C₇₃

C₂×D₈

yes

characteristic

Q₈×C₇₃

—

D₄×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

#120

yes

characteristic

C₂×C₄×C₇₃

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₇₃

#124

yes

characteristic

C₂×C₄×C₇₃

C₂×SD₁₆

yes

C₂×C₄×C₇₃

yes

C₂×C₄×C₇₃

yes

C₈×C₇₃

—

C₈×C₇₃

C₂²⋊Q₈

yes

—

C₈×C₇₃

#124

yes

—

C₂²×C₇₃

—

C₂²×C₇₃

—

100

C₂²×C₇₃

—

101

C₂²×C₇₃

—

102

C₂²×C₇₃

—

103

C₂²×C₇₃

—

104

C₂²×C₇₃

#447

yes

characteristic

105

C₂²×C₇₃

#474

yes

characteristic

106

C₂²×C₇₃

#486

yes

characteristic

107

C₄×C₇₃

—

108

C₄×C₇₃

—

109

C₄×C₇₃

—

110

C₄×C₇₃

#393

yes

characteristic

111

C₄×C₇₃

#448

yes

characteristic

112

C₄×C₇₃

#476

yes

characteristic

113

C₄×C₇₃

#489

yes

characteristic

114

#13367

C₇₃

yes

maximal, characteristic, direct product factor, Sylow

115

C₂×C₇₃

—

116

C₂×C₇₃

—

117

C₂×C₇₃

—

118

C₂×C₇₃

#2023

yes

characteristic

119

C₂×C₇₃

#2190

yes

—

120

#3162

C₂×C₇₃

yes

characteristic, complemented

121

#2140

C₂×C₇₃

yes

—

122

#1972

C₂×C₇₃

yes

characteristic

123

#1386

C₂×C₇₃

yes

complemented

124

#1377

C₂×C₇₃

yes

characteristic, complemented

125

C₇₃

#13367

yes

characteristic, direct product factor, Sylow

126

C₂²×D₈

C₂²×C₇₃

yes

characteristic

127

#533

—

128

C₂×M₃₂

C₂²×C₇₃

yes

—

129

#501

—

130

#427

—

131

#427

C₂²×C₇₃

yes

—

132

C₂×#106

C₂²×C₇₃

yes

characteristic

133

C₂×#102

—

134

C₂×#97

C₂²×C₇₃

yes

characteristic

135

#390

—

136

#357

—

137

C₂²×D₄

—

138

C₂×D₈

—

139

C₂×D₈

—

140

C₂×D₈

—

141

C₂×D₈

Q₈×C₇₃

yes

complemented

142

C₂²×C₈

D₄×C₇₃

yes

characteristic

143

C₂²×C₈

C₂³×C₇₃

yes

characteristic

144

C₄⋊Q₈

—

145

#125

—

146

C₂²⋊Q₈

—

147

C₄×Q₈

—

148

#117

—

149

C₂×C₄⋊C₄

—

150

C₂×C₂²⋊C₄

—

151

C₂×C₄²

D₄×C₇₃

yes

characteristic

152

M₃₂

—

153

M₃₂

—

154

C₂×C₁₆

—

155

#107

—

156

#107

D₄×C₇₃

yes

—

157

#106

—

158

#106

—

159

#106

—

160

#102

—

161

#97

—

162

C₂⁴

—

163

C₂×Q₈

—

164

C₂×D₄

—

165

C₂×D₄

—

166

C₂×D₄

—

167

C₂×D₄

—

168

C₂×D₄

—

169

C₂×D₄

—

170

C₂²×C₄

—

171

C₂²×C₄

D₈×C₇₃

yes

—

172

C₂²×C₄

C₂×D₄×C₇₃

yes

characteristic

173

D₈

—

174

D₈

—

175

C₂×C₈

—

176

C₂×C₈

—

177

C₂×C₈

SD₁₆×C₇₃

yes

—

178

C₂×C₈

C₂×D₄×C₇₃

yes

—

179

C₂×C₈

C₂×Q₈×C₇₃

yes

characteristic

180

C₂×C₈

#41×C₇₃

yes

—

181

C₂×C₈

#41×C₇₃

yes

characteristic

182

C₄⋊C₄

—

183

C₄⋊C₄

—

184

C₄⋊C₄

—

185

C₄⋊C₄

—

186

C₄⋊C₄

—

187

C₂²⋊C₄

—

188

C₂²⋊C₄

—

189

C₄²

—

190

C₄²

—

191

C₄²

—

192

C₁₆

—

193

C₂³

—

194

C₂³

—

195

C₂³

—

196

C₂³

—

197

C₂³

—

198

C₂³

C₂×D₈×C₇₃

yes

characteristic

199

Q₈

—

200

D₄

—

201

D₄

—

202

D₄

—

203

D₄

—

204

C₂×C₄

—

205

C₂×C₄

—

206

C₂×C₄

—

207

C₂×C₄

—

208

C₂×C₄

—

209

C₂×C₄

#120×C₇₃

yes

characteristic

210

C₂×C₄

C₂²⋊Q₈×C₇₃

yes

characteristic

211

C₂×C₄

#124×C₇₃

yes

characteristic

212

C₂×C₄

C₂×SD₁₆×C₇₃

yes

characteristic

213

C₂×C₄

AGL(1,ℤ/8)×C₇₃

yes

characteristic

214

C₂×C₄

#137×C₇₃

yes

characteristic

215

C₈

—

216

C₈

C₂²⋊Q₈×C₇₃

yes

—

217

C₈

#124×C₇₃

yes

—

218

C₂²

—

219

C₂²

—

220

C₂²

—

221

C₂²

—

222

C₂²

—

223

C₂²

—

224

C₂²

#447×C₇₃

yes

characteristic

225

C₂²

#474×C₇₃

yes

characteristic

226

C₂²

#486×C₇₃

yes

characteristic

227

C₄

—

228

C₄

—

229

C₄

—

230

C₄

#393×C₇₃

yes

characteristic

231

C₄

#448×C₇₃

yes

characteristic

232

C₄

#476×C₇₃

yes

characteristic

233

C₄

#489×C₇₃

yes

characteristic

234

C₂

—

235

C₂

—

236

C₂

—

237

C₂

C₇₃×#2023

yes

characteristic

238

C₂

C₇₃×#2190

yes

—

	subgroup	G/H
center, socle	C₂²×C₇₃	#447
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₇₃
prime radical	C₂²×D₈×C₇₃	C₂²
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇₃ ◁ C₂²×C₄×C₇₃ ◁ C₂×#97×C₇₃ ◁ G

subgroup

G/H

center, socle

C₂²×C₇₃

#447

commutator, Frattini, cosocle

C₂²×C₈

C₂³×C₇₃

prime radical

C₂²×D₈×C₇₃

C₂²

LCS

G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂²×C₇₃ ◁ C₂²×C₄×C₇₃ ◁ C₂×#97×C₇₃ ◁ G

N	H ≅ G/N	type
1. C₇₃×#3162	C₂	semidirect
4. C₇₃×#1386	C₂	semidirect
5. C₇₃×#1377	C₂	semidirect
21. C₂×D₈×C₇₃	Q₈	semidirect
114. #13367	C₇₃	direct (N × H)
120. #3162	C₂×C₇₃	semidirect
123. #1386	C₂×C₇₃	semidirect
124. #1377	C₂×C₇₃	semidirect
125. C₇₃	#13367	direct (N × H)
141. C₂×D₈	Q₈×C₇₃	semidirect

H ≅ G/N

type

1. C₇₃×#3162

C₂

semidirect

4. C₇₃×#1386

C₂

semidirect

5. C₇₃×#1377

C₂

semidirect

21. C₂×D₈×C₇₃

Q₈

semidirect

114. #13367

C₇₃

direct (N × H)

120. #3162

C₂×C₇₃

semidirect

123. #1386

C₂×C₇₃

semidirect

124. #1377

C₂×C₇₃

semidirect

125. C₇₃

#13367

direct (N × H)

141. C₂×D₈

Q₈×C₇₃

semidirect

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

subgroup	index
C₇₃×#3162	2
C₇₃×#2140	2
C₇₃×#1972	2
C₇₃×#1386	2
C₇₃×#1377	2
#13367	73

subgroup

index

C₇₃×#3162

C₇₃×#2140

C₇₃×#1972

C₇₃×#1386

C₇₃×#1377

#13367

Subgroups — C₇₃×#13367 #32922771

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C73×#13367 #32922771

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#13367 #32922771