Group #32921082 — subgroups

Subgroups — C₇₃×#11678 #32921082

Order 18688.

362 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 122 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×#3169	C₂	1	1	yes	maximal, characteristic
2	C₂×#346×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₃×#1568	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₃×#1333	C₂	1	4	yes	maximal, complemented
5	#532×C₇₃	—	2	1	no	—
6	C₂²×C₁₆×C₇₃	—	2	1	no	—
7	#500×C₇₃	C₄	1	1	yes	characteristic
8	#493×C₇₃	C₄	1	1	yes	characteristic
9	#486×C₇₃	—	2	1	no	—
10	#466×C₇₃	—	2	1	no	—
11	#466×C₇₃	C₄	1	2	yes	—
12	C₄×D₈×C₇₃	—	2	1	no	—
13	C₄×D₈×C₇₃	C₂²	1	2	yes	—
14	#432×C₇₃	—	2	1	no	—
15	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
16	#346×C₇₃	—	2	1	no	—
17	#346×C₇₃	C₂²	1	2	yes	—
18	#335×C₇₃	—	2	1	no	—
19	#334×C₇₃	C₂²	1	2	yes	—
20	C₂×#41×C₇₃	—	4	1	no	—
21	C₂×D₈×C₇₃	—	2	1	no	—
22	C₂×D₈×C₇₃	C₂×C₄	1	2	yes	—
23	C₂²×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
24	C₂²×C₈×C₇₃	D₄	1	1	yes	characteristic
25	C₄⋊Q₈×C₇₃	—	2	1	no	—
26	#127×C₇₃	—	2	1	no	—
27	#124×C₇₃	—	4	1	no	—
28	#121×C₇₃	—	2	2	no	—
29	#121×C₇₃	—	4	1	no	—
30	C₄×D₄×C₇₃	—	2	2	no	—
31	C₄×D₄×C₇₃	—	4	1	no	—
32	C₂×C₄²×C₇₃	D₄	1	1	yes	characteristic
33	C₂×C₁₆×C₇₃	—	2	4	no	—
34	C₂×C₁₆×C₇₃	—	2	2	no	—
35	#107×C₇₃	—	2	1	no	—
36	#107×C₇₃	C₂×C₄	1	2	yes	—
37	C₄⋊C₈×C₇₃	—	2	2	no	—
38	#102×C₇₃	—	2	2	no	—
39	#102×C₇₃	—	2	2	no	—
40	C₂²⋊C₈×C₇₃	—	4	1	no	—
41	#97×C₇₃	—	4	1	no	—
42	C₄×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
43	C₄×C₈×C₇₃	D₄	1	1	yes	characteristic
44	C₄×C₈×C₇₃	D₄	1	1	yes	characteristic
45	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
46	#41×C₇₃	—	8	4	no	—
47	C₂×Q₈×C₇₃	—	4	1	no	—
48	C₂×D₄×C₇₃	—	2	2	no	—
49	C₂×D₄×C₇₃	—	4	2	no	—
50	C₂×D₄×C₇₃	—	4	1	no	—
51	C₂×D₄×C₇₃	—	4	1	no	—
52	C₂²×C₄×C₇₃	—	4	2	no	—
53	C₂²×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
54	C₂²×C₄×C₇₃	D₈	1	1	yes	characteristic
55	C₂²×C₄×C₇₃	SD₁₆	1	1	yes	characteristic
56	D₈×C₇₃	—	2	4	no	—
57	D₈×C₇₃	—	4	2	no	—
58	C₂×C₈×C₇₃	—	2	2	no	—
59	C₂×C₈×C₇₃	—	2	2	no	—
60	C₂×C₈×C₇₃	—	4	2	no	—
61	C₂×C₈×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
62	C₂×C₈×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
63	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
64	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
65	C₄⋊C₄×C₇₃	—	2	2	no	—
66	C₄⋊C₄×C₇₃	—	4	1	no	—
67	C₂²⋊C₄×C₇₃	—	4	2	no	—
68	C₂²⋊C₄×C₇₃	—	4	2	no	—
69	C₄²×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
70	C₄²×C₇₃	D₈	1	1	yes	characteristic
71	C₄²×C₇₃	SD₁₆	1	1	yes	characteristic
72	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
73	C₁₆×C₇₃	—	2	4	no	—
74	C₂³×C₇₃	—	4	2	no	—
75	C₂³×C₇₃	#102	1	1	yes	characteristic
76	Q₈×C₇₃	—	8	2	no	—
77	D₄×C₇₃	—	4	2	no	—
78	D₄×C₇₃	—	4	2	no	—
79	D₄×C₇₃	—	8	2	no	—
80	D₄×C₇₃	—	8	2	no	—
81	D₄×C₇₃	—	8	4	no	—
82	C₂×C₄×C₇₃	—	2	2	no	—
83	C₂×C₄×C₇₃	—	2	1	no	—
84	C₂×C₄×C₇₃	—	2	1	no	—
85	C₂×C₄×C₇₃	—	4	1	no	—
86	C₂×C₄×C₇₃	—	4	2	no	—
87	C₂×C₄×C₇₃	—	8	4	no	—
88	C₂×C₄×C₇₃	#102	1	1	yes	characteristic
89	C₂×C₄×C₇₃	#102	1	1	yes	characteristic
90	C₂×C₄×C₇₃	#102	1	1	yes	characteristic
91	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
92	C₂×C₄×C₇₃	C₂×D₈	1	1	yes	characteristic
93	C₂×C₄×C₇₃	C₂×SD₁₆	1	1	yes	characteristic
94	C₈×C₇₃	—	2	1	no	—
95	C₈×C₇₃	—	2	1	no	—
96	C₈×C₇₃	—	8	2	no	—
97	C₈×C₇₃	#104	1	2	yes	—
98	C₈×C₇₃	#131	1	2	yes	—
99	C₂²×C₇₃	—	2	1	no	—
100	C₂²×C₇₃	—	2	1	no	—
101	C₂²×C₇₃	—	8	2	no	—
102	C₂²×C₇₃	—	8	2	no	—
103	C₂²×C₇₃	—	8	2	no	—
104	C₂²×C₇₃	#361	1	2	yes	—
105	C₂²×C₇₃	C₂×#102	1	1	yes	characteristic
106	C₄×C₇₃	—	2	1	no	—
107	C₄×C₇₃	—	2	1	no	—
108	C₄×C₇₃	—	2	1	no	—
109	C₄×C₇₃	—	2	1	no	—
110	C₄×C₇₃	—	2	1	no	—
111	C₄×C₇₃	—	8	2	no	—
112	C₄×C₇₃	#408	1	1	yes	characteristic
113	C₄×C₇₃	C₂×#104	1	1	yes	characteristic
114	#11678	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
115	C₂×C₇₃	—	2	2	no	—
116	C₂×C₇₃	—	16	2	no	—
117	C₂×C₇₃	#1492	1	1	yes	characteristic
118	C₂×C₇₃	#2145	1	1	yes	characteristic
119	C₂×C₇₃	C₂×#361	1	1	yes	characteristic
120	#3169	C₂×C₇₃	1	1	yes	characteristic
121	C₂×#346	C₂×C₇₃	1	1	yes	characteristic, complemented
122	#1568	C₂×C₇₃	1	1	yes	characteristic, complemented
123	#1333	C₂×C₇₃	1	4	yes	complemented
124	C₇₃	#11678	1	1	yes	characteristic, direct product factor, Sylow
125	#532	—	2	1	no	—
126	C₂²×C₁₆	—	2	1	no	—
127	#500	C₄×C₇₃	1	1	yes	characteristic
128	#493	C₄×C₇₃	1	1	yes	characteristic
129	#486	—	2	1	no	—
130	#466	—	2	1	no	—
131	#466	C₄×C₇₃	1	2	yes	—
132	C₄×D₈	—	2	1	no	—
133	C₄×D₈	C₂²×C₇₃	1	2	yes	—
134	#432	—	2	1	no	—
135	C₂×C₄×C₈	C₂²×C₇₃	1	1	yes	characteristic
136	#346	—	2	1	no	—
137	#346	C₂²×C₇₃	1	2	yes	—
138	#335	—	2	1	no	—
139	#334	C₂²×C₇₃	1	2	yes	—
140	C₂×#41	—	4	1	no	—
141	C₂×D₈	—	2	1	no	—
142	C₂×D₈	C₂×C₄×C₇₃	1	2	yes	—
143	C₂²×C₈	C₂×C₄×C₇₃	1	1	yes	characteristic
144	C₂²×C₈	D₄×C₇₃	1	1	yes	characteristic
145	C₄⋊Q₈	—	2	1	no	—
146	#127	—	2	1	no	—
147	#124	—	4	1	no	—
148	#121	—	2	2	no	—
149	#121	—	4	1	no	—
150	C₄×D₄	—	2	2	no	—
151	C₄×D₄	—	4	1	no	—
152	C₂×C₄²	D₄×C₇₃	1	1	yes	characteristic
153	C₂×C₁₆	—	2	4	no	—
154	C₂×C₁₆	—	2	2	no	—
155	#107	—	2	1	no	—
156	#107	C₂×C₄×C₇₃	1	2	yes	—
157	C₄⋊C₈	—	2	2	no	—
158	#102	—	2	2	no	—
159	#102	—	2	2	no	—
160	C₂²⋊C₈	—	4	1	no	—
161	#97	—	4	1	no	—
162	C₄×C₈	C₂×C₄×C₇₃	1	1	yes	characteristic
163	C₄×C₈	D₄×C₇₃	1	1	yes	characteristic
164	C₄×C₈	D₄×C₇₃	1	1	yes	characteristic
165	C₄×C₈	C₂³×C₇₃	1	1	yes	characteristic
166	#41	—	8	4	no	—
167	C₂×Q₈	—	4	1	no	—
168	C₂×D₄	—	2	2	no	—
169	C₂×D₄	—	4	2	no	—
170	C₂×D₄	—	4	1	no	—
171	C₂×D₄	—	4	1	no	—
172	C₂²×C₄	—	4	2	no	—
173	C₂²×C₄	C₂²⋊C₄×C₇₃	1	1	yes	characteristic
174	C₂²×C₄	D₈×C₇₃	1	1	yes	characteristic
175	C₂²×C₄	SD₁₆×C₇₃	1	1	yes	characteristic
176	D₈	—	2	4	no	—
177	D₈	—	4	2	no	—
178	C₂×C₈	—	2	2	no	—
179	C₂×C₈	—	2	2	no	—
180	C₂×C₈	—	4	2	no	—
181	C₂×C₈	C₂²⋊C₄×C₇₃	1	1	yes	characteristic
182	C₂×C₈	C₂²⋊C₄×C₇₃	1	1	yes	characteristic
183	C₂×C₈	C₂²×C₄×C₇₃	1	1	yes	characteristic
184	C₂×C₈	C₂×D₄×C₇₃	1	1	yes	characteristic
185	C₄⋊C₄	—	2	2	no	—
186	C₄⋊C₄	—	4	1	no	—
187	C₂²⋊C₄	—	4	2	no	—
188	C₂²⋊C₄	—	4	2	no	—
189	C₄²	C₂²⋊C₄×C₇₃	1	1	yes	characteristic
190	C₄²	D₈×C₇₃	1	1	yes	characteristic
191	C₄²	SD₁₆×C₇₃	1	1	yes	characteristic
192	C₄²	C₂×D₄×C₇₃	1	1	yes	characteristic
193	C₁₆	—	2	4	no	—
194	C₂³	—	4	2	no	—
195	C₂³	#102×C₇₃	1	1	yes	characteristic
196	Q₈	—	8	2	no	—
197	D₄	—	4	2	no	—
198	D₄	—	4	2	no	—
199	D₄	—	8	2	no	—
200	D₄	—	8	2	no	—
201	D₄	—	8	4	no	—
202	C₂×C₄	—	2	2	no	—
203	C₂×C₄	—	2	1	no	—
204	C₂×C₄	—	2	1	no	—
205	C₂×C₄	—	4	1	no	—
206	C₂×C₄	—	4	2	no	—
207	C₂×C₄	—	8	4	no	—
208	C₂×C₄	#102×C₇₃	1	1	yes	characteristic
209	C₂×C₄	#102×C₇₃	1	1	yes	characteristic
210	C₂×C₄	#102×C₇₃	1	1	yes	characteristic
211	C₂×C₄	C₂×C₂²⋊C₄×C₇₃	1	1	yes	characteristic
212	C₂×C₄	C₂×D₈×C₇₃	1	1	yes	characteristic
213	C₂×C₄	C₂×SD₁₆×C₇₃	1	1	yes	characteristic
214	C₈	—	2	1	no	—
215	C₈	—	2	1	no	—
216	C₈	—	8	2	no	—
217	C₈	#104×C₇₃	1	2	yes	—
218	C₈	#131×C₇₃	1	2	yes	—
219	C₂²	—	2	1	no	—
220	C₂²	—	2	1	no	—
221	C₂²	—	8	2	no	—
222	C₂²	—	8	2	no	—
223	C₂²	—	8	2	no	—
224	C₂²	#361×C₇₃	1	2	yes	—
225	C₂²	C₂×#102×C₇₃	1	1	yes	characteristic
226	C₄	—	2	1	no	—
227	C₄	—	2	1	no	—
228	C₄	—	2	1	no	—
229	C₄	—	2	1	no	—
230	C₄	—	2	1	no	—
231	C₄	—	8	2	no	—
232	C₄	#408×C₇₃	1	1	yes	characteristic
233	C₄	C₂×#104×C₇₃	1	1	yes	characteristic
234	C₂	—	2	2	no	—
235	C₂	—	16	2	no	—
236	C₂	C₇₃×#1492	1	1	yes	characteristic
237	C₂	C₇₃×#2145	1	1	yes	characteristic
238	C₂	C₂×#361×C₇₃	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₇₃×#3169

C₂

yes

maximal, characteristic

C₂×#346×C₇₃

C₂

yes

maximal, characteristic, complemented

C₇₃×#1568

C₂

yes

maximal, characteristic, complemented

C₇₃×#1333

C₂

yes

maximal, complemented

#532×C₇₃

—

C₂²×C₁₆×C₇₃

—

#500×C₇₃

C₄

yes

characteristic

#493×C₇₃

C₄

yes

characteristic

#486×C₇₃

—

#466×C₇₃

—

#466×C₇₃

C₄

yes

—

C₄×D₈×C₇₃

—

C₄×D₈×C₇₃

C₂²

yes

—

#432×C₇₃

—

C₂×C₄×C₈×C₇₃

C₂²

yes

characteristic

#346×C₇₃

—

#346×C₇₃

C₂²

yes

—

#335×C₇₃

—

#334×C₇₃

C₂²

yes

—

C₂×#41×C₇₃

—

C₂×D₈×C₇₃

—

C₂×D₈×C₇₃

C₂×C₄

yes

—

C₂²×C₈×C₇₃

C₂×C₄

yes

characteristic

C₂²×C₈×C₇₃

D₄

yes

characteristic

C₄⋊Q₈×C₇₃

—

#127×C₇₃

—

#124×C₇₃

—

#121×C₇₃

—

#121×C₇₃

—

C₄×D₄×C₇₃

—

C₄×D₄×C₇₃

—

C₂×C₄²×C₇₃

D₄

yes

characteristic

C₂×C₁₆×C₇₃

—

C₂×C₁₆×C₇₃

—

#107×C₇₃

—

#107×C₇₃

C₂×C₄

yes

—

C₄⋊C₈×C₇₃

—

#102×C₇₃

—

#102×C₇₃

—

C₂²⋊C₈×C₇₃

—

#97×C₇₃

—

C₄×C₈×C₇₃

C₂×C₄

yes

characteristic

C₄×C₈×C₇₃

D₄

yes

characteristic

C₄×C₈×C₇₃

D₄

yes

characteristic

C₄×C₈×C₇₃

C₂³

yes

characteristic

#41×C₇₃

—

C₂×Q₈×C₇₃

—

C₂×D₄×C₇₃

—

C₂×D₄×C₇₃

—

C₂×D₄×C₇₃

—

C₂×D₄×C₇₃

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₇₃

D₈

yes

characteristic

C₂²×C₄×C₇₃

SD₁₆

yes

characteristic

D₈×C₇₃

—

D₈×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₇₃

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₇₃

C₂²×C₄

yes

characteristic

C₂×C₈×C₇₃

C₂×D₄

yes

characteristic

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

—

C₂²⋊C₄×C₇₃

—

C₂²⋊C₄×C₇₃

—

C₄²×C₇₃

C₂²⋊C₄

yes

characteristic

C₄²×C₇₃

D₈

yes

characteristic

C₄²×C₇₃

SD₁₆

yes

characteristic

C₄²×C₇₃

C₂×D₄

yes

characteristic

C₁₆×C₇₃

—

C₂³×C₇₃

—

C₂³×C₇₃

#102

yes

characteristic

Q₈×C₇₃

—

D₄×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

—

C₂×C₄×C₇₃

yes

C₂×C₄×C₇₃

yes

C₂×C₄×C₇₃

yes

C₂×C₄×C₇₃

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₇₃

C₂×D₈

yes

characteristic

C₂×C₄×C₇₃

C₂×SD₁₆

yes

characteristic

C₈×C₇₃

—

C₈×C₇₃

—

C₈×C₇₃

—

C₈×C₇₃

#104

yes

—

C₈×C₇₃

#131

yes

—

C₂²×C₇₃

—

100

C₂²×C₇₃

—

101

C₂²×C₇₃

—

102

C₂²×C₇₃

—

103

C₂²×C₇₃

—

104

C₂²×C₇₃

#361

yes

—

105

C₂²×C₇₃

C₂×#102

yes

characteristic

106

C₄×C₇₃

—

107

C₄×C₇₃

—

108

C₄×C₇₃

—

109

C₄×C₇₃

—

110

C₄×C₇₃

—

111

C₄×C₇₃

—

112

C₄×C₇₃

#408

yes

characteristic

113

C₄×C₇₃

C₂×#104

yes

characteristic

114

#11678

C₇₃

yes

maximal, characteristic, direct product factor, Sylow

115

C₂×C₇₃

—

116

C₂×C₇₃

—

117

C₂×C₇₃

#1492

yes

characteristic

118

C₂×C₇₃

#2145

yes

characteristic

119

C₂×C₇₃

C₂×#361

yes

characteristic

120

#3169

C₂×C₇₃

yes

characteristic

121

C₂×#346

C₂×C₇₃

yes

characteristic, complemented

122

#1568

C₂×C₇₃

yes

characteristic, complemented

123

#1333

C₂×C₇₃

yes

complemented

124

C₇₃

#11678

yes

characteristic, direct product factor, Sylow

125

#532

—

126

C₂²×C₁₆

—

127

#500

C₄×C₇₃

yes

characteristic

128

#493

C₄×C₇₃

yes

characteristic

129

#486

—

130

#466

—

131

#466

C₄×C₇₃

yes

—

132

C₄×D₈

—

133

C₄×D₈

C₂²×C₇₃

yes

—

134

#432

—

135

C₂×C₄×C₈

C₂²×C₇₃

yes

characteristic

136

#346

—

137

#346

C₂²×C₇₃

yes

—

138

#335

—

139

#334

C₂²×C₇₃

yes

—

140

C₂×#41

—

141

C₂×D₈

—

142

C₂×D₈

C₂×C₄×C₇₃

yes

—

143

C₂²×C₈

C₂×C₄×C₇₃

yes

characteristic

144

C₂²×C₈

D₄×C₇₃

yes

characteristic

145

C₄⋊Q₈

—

146

#127

—

147

#124

—

148

#121

—

149

#121

—

150

C₄×D₄

—

151

C₄×D₄

—

152

C₂×C₄²

D₄×C₇₃

yes

characteristic

153

C₂×C₁₆

—

154

C₂×C₁₆

—

155

#107

—

156

#107

C₂×C₄×C₇₃

yes

—

157

C₄⋊C₈

—

158

#102

—

159

#102

—

160

C₂²⋊C₈

—

161

#97

—

162

C₄×C₈

C₂×C₄×C₇₃

yes

characteristic

163

C₄×C₈

D₄×C₇₃

yes

characteristic

164

C₄×C₈

D₄×C₇₃

yes

characteristic

165

C₄×C₈

C₂³×C₇₃

yes

characteristic

166

#41

—

167

C₂×Q₈

—

168

C₂×D₄

—

169

C₂×D₄

—

170

C₂×D₄

—

171

C₂×D₄

—

172

C₂²×C₄

—

173

C₂²×C₄

C₂²⋊C₄×C₇₃

yes

characteristic

174

C₂²×C₄

D₈×C₇₃

yes

characteristic

175

C₂²×C₄

SD₁₆×C₇₃

yes

characteristic

176

D₈

—

177

D₈

—

178

C₂×C₈

—

179

C₂×C₈

—

180

C₂×C₈

—

181

C₂×C₈

C₂²⋊C₄×C₇₃

yes

characteristic

182

C₂×C₈

C₂²⋊C₄×C₇₃

yes

characteristic

183

C₂×C₈

C₂²×C₄×C₇₃

yes

characteristic

184

C₂×C₈

C₂×D₄×C₇₃

yes

characteristic

185

C₄⋊C₄

—

186

C₄⋊C₄

—

187

C₂²⋊C₄

—

188

C₂²⋊C₄

—

189

C₄²

C₂²⋊C₄×C₇₃

yes

characteristic

190

C₄²

D₈×C₇₃

yes

characteristic

191

C₄²

SD₁₆×C₇₃

yes

characteristic

192

C₄²

C₂×D₄×C₇₃

yes

characteristic

193

C₁₆

—

194

C₂³

—

195

C₂³

#102×C₇₃

yes

characteristic

196

Q₈

—

197

D₄

—

198

D₄

—

199

D₄

—

200

D₄

—

201

D₄

—

202

C₂×C₄

—

203

C₂×C₄

—

204

C₂×C₄

—

205

C₂×C₄

—

206

C₂×C₄

—

207

C₂×C₄

—

208

C₂×C₄

#102×C₇₃

yes

characteristic

209

C₂×C₄

#102×C₇₃

yes

characteristic

210

C₂×C₄

#102×C₇₃

yes

characteristic

211

C₂×C₄

C₂×C₂²⋊C₄×C₇₃

yes

characteristic

212

C₂×C₄

C₂×D₈×C₇₃

yes

characteristic

213

C₂×C₄

C₂×SD₁₆×C₇₃

yes

characteristic

214

C₈

—

215

C₈

—

216

C₈

—

217

C₈

#104×C₇₃

yes

—

218

C₈

#131×C₇₃

yes

—

219

C₂²

—

220

C₂²

—

221

C₂²

—

222

C₂²

—

223

C₂²

—

224

C₂²

#361×C₇₃

yes

—

225

C₂²

C₂×#102×C₇₃

yes

characteristic

226

C₄

—

227

C₄

—

228

C₄

—

229

C₄

—

230

C₄

—

231

C₄

—

232

C₄

#408×C₇₃

yes

characteristic

233

C₄

C₂×#104×C₇₃

yes

characteristic

234

C₂

—

235

C₂

—

236

C₂

C₇₃×#1492

yes

characteristic

237

C₂

C₇₃×#2145

yes

characteristic

238

C₂

C₂×#361×C₇₃

yes

characteristic

	subgroup	G/H
center, socle	C₂²×C₇₃	C₂×#102
commutator	C₂×C₈	C₂²×C₄×C₇₃
Frattini, cosocle	C₄×C₈	C₂³×C₇₃
prime radical	C₇₃×#3169	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇₃ ◁ C₂×C₄²×C₇₃ ◁ C₂×C₄×C₈×C₇₃ ◁ G

subgroup

G/H

center, socle

C₂²×C₇₃

C₂×#102

commutator

C₂×C₈

C₂²×C₄×C₇₃

Frattini, cosocle

C₄×C₈

C₂³×C₇₃

prime radical

C₇₃×#3169

C₂

LCS

G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂²×C₇₃ ◁ C₂×C₄²×C₇₃ ◁ C₂×C₄×C₈×C₇₃ ◁ G

N	H ≅ G/N	type
2. C₂×#346×C₇₃	C₂	semidirect
3. C₇₃×#1568	C₂	semidirect
4. C₇₃×#1333	C₂	semidirect
114. #11678	C₇₃	direct (N × H)
121. C₂×#346	C₂×C₇₃	semidirect
122. #1568	C₂×C₇₃	semidirect
123. #1333	C₂×C₇₃	semidirect
124. C₇₃	#11678	direct (N × H)

H ≅ G/N

type

2. C₂×#346×C₇₃

C₂

semidirect

3. C₇₃×#1568

C₂

semidirect

4. C₇₃×#1333

C₂

semidirect

114. #11678

C₇₃

direct (N × H)

121. C₂×#346

C₂×C₇₃

semidirect

122. #1568

C₂×C₇₃

semidirect

123. #1333

C₂×C₇₃

semidirect

124. C₇₃

#11678

direct (N × H)

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

subgroup	index
C₇₃×#3169	2
C₂×#346×C₇₃	2
C₇₃×#1568	2
C₇₃×#1333	2
#11678	73

subgroup

index

C₇₃×#3169

C₂×#346×C₇₃

C₇₃×#1568

C₇₃×#1333

#11678

Subgroups — C₇₃×#11678 #32921082

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C73×#11678 #32921082

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#11678 #32921082