Group #32922769 — subgroups

Subgroups — C₇₃×#13365 #32922769

Order 18688.

418 conjugacy classes of subgroups; only the 130 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 130 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×#499×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#357×C₇₃	C₂	1	2	yes	maximal
3	C₇₃×#1970	C₂	1	1	yes	maximal, characteristic
4	C₇₃×#1380	C₂	1	2	yes	maximal, complemented
5	C₇₃×#1374	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×D₈×C₇₃	C₂²	1	1	yes	characteristic
7	C₂×#125×C₇₃	—	2	1	no	—
8	C₂²×C₁₆×C₇₃	C₂²	1	2	yes	—
9	#499×C₇₃	—	2	4	no	—
10	C₂×#107×C₇₃	C₂²	1	1	yes	characteristic
11	C₂×#107×C₇₃	C₂²	1	2	yes	—
12	C₂×#106×C₇₃	—	2	1	no	—
13	C₂×#102×C₇₃	—	2	1	no	—
14	C₂×C₄×C₈×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	—
22	C₂²×C₈×C₇₃	D₄	1	1	yes	characteristic
23	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
24	#125×C₇₃	—	2	4	no	—
25	#125×C₇₃	—	4	2	no	—
26	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
27	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
28	C₂×C₄⋊C₄×C₇₃	—	4	2	no	—
29	C₂×C₂²⋊C₄×C₇₃	—	4	2	no	—
30	C₂×C₄²×C₇₃	D₄	1	1	yes	characteristic
31	C₂×C₁₆×C₇₃	—	2	2	no	—
32	C₂×C₁₆×C₇₃	—	2	2	no	—
33	C₂×C₁₆×C₇₃	—	2	2	no	—
34	#107×C₇₃	—	2	2	no	—
35	#107×C₇₃	—	2	2	no	—
36	#107×C₇₃	D₄	1	4	yes	—
37	#106×C₇₃	—	2	4	no	—
38	#102×C₇₃	—	4	2	no	—
39	C₄×C₈×C₇₃	—	2	2	no	—
40	C₂⁴×C₇₃	—	4	1	no	—
41	C₂×D₄×C₇₃	—	2	2	no	—
42	C₂×D₄×C₇₃	—	4	1	no	—
43	C₂×D₄×C₇₃	—	4	1	no	—
44	C₂×D₄×C₇₃	—	4	1	no	—
45	C₂×D₄×C₇₃	—	4	1	no	—
46	C₂×D₄×C₇₃	—	4	1	no	—
47	C₂²×C₄×C₇₃	—	4	2	no	—
48	C₂²×C₄×C₇₃	—	4	1	no	—
49	C₂²×C₄×C₇₃	D₈	1	2	yes	—
50	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
51	D₈×C₇₃	—	2	4	no	—
52	D₈×C₇₃	—	4	2	no	—
53	C₂×C₈×C₇₃	—	2	1	no	—
54	C₂×C₈×C₇₃	—	2	1	no	—
55	C₂×C₈×C₇₃	SD₁₆	1	2	yes	—
56	C₂×C₈×C₇₃	C₂×D₄	1	2	yes	—
57	C₂×C₈×C₇₃	C₂×Q₈	1	1	yes	characteristic
58	C₂×C₈×C₇₃	#41	1	2	yes	—
59	C₂×C₈×C₇₃	#41	1	1	yes	characteristic
60	C₄⋊C₄×C₇₃	—	2	4	no	—
61	C₄⋊C₄×C₇₃	—	4	8	no	—
62	C₄⋊C₄×C₇₃	—	4	2	no	—
63	C₄⋊C₄×C₇₃	—	4	1	no	—
64	C₄⋊C₄×C₇₃	—	4	1	no	—
65	C₂²⋊C₄×C₇₃	—	8	4	no	—
66	C₄²×C₇₃	—	2	1	no	—
67	C₄²×C₇₃	—	2	1	no	—
68	C₁₆×C₇₃	—	4	2	no	—
69	C₂³×C₇₃	—	4	2	no	—
70	C₂³×C₇₃	—	8	1	no	—
71	C₂³×C₇₃	—	8	1	no	—
72	C₂³×C₇₃	—	8	2	no	—
73	C₂³×C₇₃	—	8	2	no	—
74	C₂³×C₇₃	C₂×D₈	1	1	yes	characteristic
75	D₄×C₇₃	—	4	2	no	—
76	D₄×C₇₃	—	4	2	no	—
77	D₄×C₇₃	—	8	1	no	—
78	D₄×C₇₃	—	8	1	no	—
79	C₂×C₄×C₇₃	—	2	2	no	—
80	C₂×C₄×C₇₃	—	2	2	no	—
81	C₂×C₄×C₇₃	—	2	2	no	—
82	C₂×C₄×C₇₃	—	4	4	no	—
83	C₂×C₄×C₇₃	—	8	2	no	—
84	C₂×C₄×C₇₃	—	8	2	no	—
85	C₂×C₄×C₇₃	—	8	1	no	—
86	C₂×C₄×C₇₃	—	8	2	no	—
87	C₂×C₄×C₇₃	#120	1	1	yes	characteristic
88	C₂×C₄×C₇₃	C₂²⋊Q₈	1	1	yes	characteristic
89	C₂×C₄×C₇₃	#124	1	1	yes	characteristic
90	C₂×C₄×C₇₃	C₂×SD₁₆	1	1	yes	characteristic
91	C₂×C₄×C₇₃	AGL(1,ℤ/8)	1	1	yes	characteristic
92	C₂×C₄×C₇₃	#137	1	1	yes	characteristic
93	C₈×C₇₃	—	2	2	no	—
94	C₈×C₇₃	C₂²⋊Q₈	1	2	yes	—
95	C₈×C₇₃	#124	1	2	yes	—
96	C₂²×C₇₃	—	8	4	no	—
97	C₂²×C₇₃	—	8	2	no	—
98	C₂²×C₇₃	—	16	2	no	—
99	C₂²×C₇₃	—	16	1	no	—
100	C₂²×C₇₃	—	16	1	no	—
101	C₂²×C₇₃	#447	1	1	yes	characteristic
102	C₂²×C₇₃	#474	1	1	yes	characteristic
103	C₂²×C₇₃	#486	1	1	yes	characteristic
104	C₂²×C₇₃	#508	1	2	yes	—
105	C₂²×C₇₃	#509	1	2	yes	—
106	C₄×C₇₃	—	4	2	no	—
107	C₄×C₇₃	—	8	4	no	—
108	C₄×C₇₃	—	16	1	no	—
109	C₄×C₇₃	#393	1	1	yes	characteristic
110	C₄×C₇₃	#448	1	1	yes	characteristic
111	C₄×C₇₃	#476	1	1	yes	characteristic
112	C₄×C₇₃	#489	1	1	yes	characteristic
113	#13365	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
114	C₂×C₇₃	—	16	2	no	—
115	C₂×C₇₃	#2023	1	1	yes	characteristic
116	C₂×C₇₃	#2186	1	2	yes	—
117	C₂×C₇₃	#2228	1	2	yes	—
118	C₂×C₇₃	#2242	1	1	yes	characteristic
119	C₂×C₇₃	#2244	1	1	yes	characteristic
120	C₂×#499	C₂×C₇₃	1	1	yes	characteristic, complemented
121	C₂×#357	C₂×C₇₃	1	2	yes	—
122	#1970	C₂×C₇₃	1	1	yes	characteristic
123	#1380	C₂×C₇₃	1	2	yes	complemented
124	#1374	C₂×C₇₃	1	1	yes	characteristic, complemented
125	C₇₃	#13365	1	1	yes	characteristic, direct product factor, Sylow
126	C₂²×D₈	C₂²×C₇₃	1	1	yes	characteristic
127	C₂×#125	—	2	1	no	—
128	C₂²×C₁₆	C₂²×C₇₃	1	2	yes	—
129	#499	—	2	4	no	—
130	C₂×#107	C₂²×C₇₃	1	1	yes	characteristic
131	C₂×#107	C₂²×C₇₃	1	2	yes	—
132	C₂×#106	—	2	1	no	—
133	C₂×#102	—	2	1	no	—
134	C₂×C₄×C₈	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	—
142	C₂²×C₈	D₄×C₇₃	1	1	yes	characteristic
143	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
144	#125	—	2	4	no	—
145	#125	—	4	2	no	—
146	C₂×C₄⋊C₄	—	2	2	no	—
147	C₂×C₄⋊C₄	—	2	1	no	—
148	C₂×C₄⋊C₄	—	4	2	no	—
149	C₂×C₂²⋊C₄	—	4	2	no	—
150	C₂×C₄²	D₄×C₇₃	1	1	yes	characteristic
151	C₂×C₁₆	—	2	2	no	—
152	C₂×C₁₆	—	2	2	no	—
153	C₂×C₁₆	—	2	2	no	—
154	#107	—	2	2	no	—
155	#107	—	2	2	no	—
156	#107	D₄×C₇₃	1	4	yes	—
157	#106	—	2	4	no	—
158	#102	—	4	2	no	—
159	C₄×C₈	—	2	2	no	—
160	C₂⁴	—	4	1	no	—
161	C₂×D₄	—	2	2	no	—
162	C₂×D₄	—	4	1	no	—
163	C₂×D₄	—	4	1	no	—
164	C₂×D₄	—	4	1	no	—
165	C₂×D₄	—	4	1	no	—
166	C₂×D₄	—	4	1	no	—
167	C₂²×C₄	—	4	2	no	—
168	C₂²×C₄	—	4	1	no	—
169	C₂²×C₄	D₈×C₇₃	1	2	yes	—
170	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
171	D₈	—	2	4	no	—
172	D₈	—	4	2	no	—
173	C₂×C₈	—	2	1	no	—
174	C₂×C₈	—	2	1	no	—
175	C₂×C₈	SD₁₆×C₇₃	1	2	yes	—
176	C₂×C₈	C₂×D₄×C₇₃	1	2	yes	—
177	C₂×C₈	C₂×Q₈×C₇₃	1	1	yes	characteristic
178	C₂×C₈	#41×C₇₃	1	2	yes	—
179	C₂×C₈	#41×C₇₃	1	1	yes	characteristic
180	C₄⋊C₄	—	2	4	no	—
181	C₄⋊C₄	—	4	8	no	—
182	C₄⋊C₄	—	4	2	no	—
183	C₄⋊C₄	—	4	1	no	—
184	C₄⋊C₄	—	4	1	no	—
185	C₂²⋊C₄	—	8	4	no	—
186	C₄²	—	2	1	no	—
187	C₄²	—	2	1	no	—
188	C₁₆	—	4	2	no	—
189	C₂³	—	4	2	no	—
190	C₂³	—	8	1	no	—
191	C₂³	—	8	1	no	—
192	C₂³	—	8	2	no	—
193	C₂³	—	8	2	no	—
194	C₂³	C₂×D₈×C₇₃	1	1	yes	characteristic
195	D₄	—	4	2	no	—
196	D₄	—	4	2	no	—
197	D₄	—	8	1	no	—
198	D₄	—	8	1	no	—
199	C₂×C₄	—	2	2	no	—
200	C₂×C₄	—	2	2	no	—
201	C₂×C₄	—	2	2	no	—
202	C₂×C₄	—	4	4	no	—
203	C₂×C₄	—	8	2	no	—
204	C₂×C₄	—	8	2	no	—
205	C₂×C₄	—	8	1	no	—
206	C₂×C₄	—	8	2	no	—
207	C₂×C₄	#120×C₇₃	1	1	yes	characteristic
208	C₂×C₄	C₂²⋊Q₈×C₇₃	1	1	yes	characteristic
209	C₂×C₄	#124×C₇₃	1	1	yes	characteristic
210	C₂×C₄	C₂×SD₁₆×C₇₃	1	1	yes	characteristic
211	C₂×C₄	AGL(1,ℤ/8)×C₇₃	1	1	yes	characteristic
212	C₂×C₄	#137×C₇₃	1	1	yes	characteristic
213	C₈	—	2	2	no	—
214	C₈	C₂²⋊Q₈×C₇₃	1	2	yes	—
215	C₈	#124×C₇₃	1	2	yes	—
216	C₂²	—	8	4	no	—
217	C₂²	—	8	2	no	—
218	C₂²	—	16	2	no	—
219	C₂²	—	16	1	no	—
220	C₂²	—	16	1	no	—
221	C₂²	#447×C₇₃	1	1	yes	characteristic
222	C₂²	#474×C₇₃	1	1	yes	characteristic
223	C₂²	#486×C₇₃	1	1	yes	characteristic
224	C₂²	#508×C₇₃	1	2	yes	—
225	C₂²	#509×C₇₃	1	2	yes	—
226	C₄	—	4	2	no	—
227	C₄	—	8	4	no	—
228	C₄	—	16	1	no	—
229	C₄	#393×C₇₃	1	1	yes	characteristic
230	C₄	#448×C₇₃	1	1	yes	characteristic
231	C₄	#476×C₇₃	1	1	yes	characteristic
232	C₄	#489×C₇₃	1	1	yes	characteristic
233	C₂	—	16	2	no	—
234	C₂	C₇₃×#2023	1	1	yes	characteristic
235	C₂	C₇₃×#2186	1	2	yes	—
236	C₂	C₇₃×#2228	1	2	yes	—
237	C₂	C₇₃×#2242	1	1	yes	characteristic
238	C₂	C₇₃×#2244	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#499×C₇₃

C₂

yes

maximal, characteristic, complemented

C₂×#357×C₇₃

C₂

yes

maximal

C₇₃×#1970

C₂

yes

maximal, characteristic

C₇₃×#1380

C₂

yes

maximal, complemented

C₇₃×#1374

C₂

yes

maximal, characteristic, complemented

C₂²×D₈×C₇₃

C₂²

yes

characteristic

C₂×#125×C₇₃

—

C₂²×C₁₆×C₇₃

C₂²

yes

—

#499×C₇₃

—

C₂×#107×C₇₃

C₂²

yes

characteristic

C₂×#107×C₇₃

C₂²

yes

—

C₂×#106×C₇₃

—

C₂×#102×C₇₃

—

C₂×C₄×C₈×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

—

C₂²×C₈×C₇₃

D₄

yes

characteristic

C₂²×C₈×C₇₃

C₂³

yes

characteristic

#125×C₇₃

—

#125×C₇₃

—

C₂×C₄⋊C₄×C₇₃

—

C₂×C₄⋊C₄×C₇₃

—

C₂×C₄⋊C₄×C₇₃

—

C₂×C₂²⋊C₄×C₇₃

—

C₂×C₄²×C₇₃

D₄

yes

characteristic

C₂×C₁₆×C₇₃

—

C₂×C₁₆×C₇₃

—

C₂×C₁₆×C₇₃

—

#107×C₇₃

—

#107×C₇₃

—

#107×C₇₃

D₄

yes

—

#106×C₇₃

—

#102×C₇₃

—

C₄×C₈×C₇₃

—

C₂⁴×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

—

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

—

C₄²×C₇₃

—

C₄²×C₇₃

—

C₁₆×C₇₃

—

C₂³×C₇₃

—

C₂³×C₇₃

—

C₂³×C₇₃

—

C₂³×C₇₃

—

C₂³×C₇₃

—

C₂³×C₇₃

C₂×D₈

yes

characteristic

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

—

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

—

C₂²×C₇₃

—

C₂²×C₇₃

—

100

C₂²×C₇₃

—

101

C₂²×C₇₃

#447

yes

characteristic

102

C₂²×C₇₃

#474

yes

characteristic

103

C₂²×C₇₃

#486

yes

characteristic

104

C₂²×C₇₃

#508

yes

—

105

C₂²×C₇₃

#509

yes

—

106

C₄×C₇₃

—

107

C₄×C₇₃

—

108

C₄×C₇₃

—

109

C₄×C₇₃

#393

yes

characteristic

110

C₄×C₇₃

#448

yes

characteristic

111

C₄×C₇₃

#476

yes

characteristic

112

C₄×C₇₃

#489

yes

characteristic

113

#13365

C₇₃

yes

maximal, characteristic, direct product factor, Sylow

114

C₂×C₇₃

—

115

C₂×C₇₃

#2023

yes

characteristic

116

C₂×C₇₃

#2186

yes

—

117

C₂×C₇₃

#2228

yes

—

118

C₂×C₇₃

#2242

yes

characteristic

119

C₂×C₇₃

#2244

yes

characteristic

120

C₂×#499

C₂×C₇₃

yes

characteristic, complemented

121

C₂×#357

C₂×C₇₃

yes

—

122

#1970

C₂×C₇₃

yes

characteristic

123

#1380

C₂×C₇₃

yes

complemented

124

#1374

C₂×C₇₃

yes

characteristic, complemented

125

C₇₃

#13365

yes

characteristic, direct product factor, Sylow

126

C₂²×D₈

C₂²×C₇₃

yes

characteristic

127

C₂×#125

—

128

C₂²×C₁₆

C₂²×C₇₃

yes

—

129

#499

—

130

C₂×#107

C₂²×C₇₃

yes

characteristic

131

C₂×#107

C₂²×C₇₃

yes

—

132

C₂×#106

—

133

C₂×#102

—

134

C₂×C₄×C₈

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

—

142

C₂²×C₈

D₄×C₇₃

yes

characteristic

143

C₂²×C₈

C₂³×C₇₃

yes

characteristic

144

#125

—

145

#125

—

146

C₂×C₄⋊C₄

—

147

C₂×C₄⋊C₄

—

148

C₂×C₄⋊C₄

—

149

C₂×C₂²⋊C₄

—

150

C₂×C₄²

D₄×C₇₃

yes

characteristic

151

C₂×C₁₆

—

152

C₂×C₁₆

—

153

C₂×C₁₆

—

154

#107

—

155

#107

—

156

#107

D₄×C₇₃

yes

—

157

#106

—

158

#102

—

159

C₄×C₈

—

160

C₂⁴

—

161

C₂×D₄

—

162

C₂×D₄

—

163

C₂×D₄

—

164

C₂×D₄

—

165

C₂×D₄

—

166

C₂×D₄

—

167

C₂²×C₄

—

168

C₂²×C₄

—

169

C₂²×C₄

D₈×C₇₃

yes

—

170

C₂²×C₄

C₂×D₄×C₇₃

yes

characteristic

171

D₈

—

172

D₈

—

173

C₂×C₈

—

174

C₂×C₈

—

175

C₂×C₈

SD₁₆×C₇₃

yes

—

176

C₂×C₈

C₂×D₄×C₇₃

yes

—

177

C₂×C₈

C₂×Q₈×C₇₃

yes

characteristic

178

C₂×C₈

#41×C₇₃

yes

—

179

C₂×C₈

#41×C₇₃

yes

characteristic

180

C₄⋊C₄

—

181

C₄⋊C₄

—

182

C₄⋊C₄

—

183

C₄⋊C₄

—

184

C₄⋊C₄

—

185

C₂²⋊C₄

—

186

C₄²

—

187

C₄²

—

188

C₁₆

—

189

C₂³

—

190

C₂³

—

191

C₂³

—

192

C₂³

—

193

C₂³

—

194

C₂³

C₂×D₈×C₇₃

yes

characteristic

195

D₄

—

196

D₄

—

197

D₄

—

198

D₄

—

199

C₂×C₄

—

200

C₂×C₄

—

201

C₂×C₄

—

202

C₂×C₄

—

203

C₂×C₄

—

204

C₂×C₄

—

205

C₂×C₄

—

206

C₂×C₄

—

207

C₂×C₄

#120×C₇₃

yes

characteristic

208

C₂×C₄

C₂²⋊Q₈×C₇₃

yes

characteristic

209

C₂×C₄

#124×C₇₃

yes

characteristic

210

C₂×C₄

C₂×SD₁₆×C₇₃

yes

characteristic

211

C₂×C₄

AGL(1,ℤ/8)×C₇₃

yes

characteristic

212

C₂×C₄

#137×C₇₃

yes

characteristic

213

C₈

—

214

C₈

C₂²⋊Q₈×C₇₃

yes

—

215

C₈

#124×C₇₃

yes

—

216

C₂²

—

217

C₂²

—

218

C₂²

—

219

C₂²

—

220

C₂²

—

221

C₂²

#447×C₇₃

yes

characteristic

222

C₂²

#474×C₇₃

yes

characteristic

223

C₂²

#486×C₇₃

yes

characteristic

224

C₂²

#508×C₇₃

yes

—

225

C₂²

#509×C₇₃

yes

—

226

C₄

—

227

C₄

—

228

C₄

—

229

C₄

#393×C₇₃

yes

characteristic

230

C₄

#448×C₇₃

yes

characteristic

231

C₄

#476×C₇₃

yes

characteristic

232

C₄

#489×C₇₃

yes

characteristic

233

C₂

—

234

C₂

C₇₃×#2023

yes

characteristic

235

C₂

C₇₃×#2186

yes

—

236

C₂

C₇₃×#2228

yes

—

237

C₂

C₇₃×#2242

yes

characteristic

238

C₂

C₇₃×#2244

yes

characteristic

	subgroup	G/H
center, socle	C₂³×C₇₃	C₂×D₈
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₇₃
prime radical	C₂²×D₈×C₇₃	C₂²
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇₃ ◁ C₂×C₄²×C₇₃ ◁ C₂×C₄×C₈×C₇₃ ◁ G

subgroup

G/H

center, socle

C₂³×C₇₃

C₂×D₈

commutator, Frattini, cosocle

C₂²×C₈

C₂³×C₇₃

prime radical

C₂²×D₈×C₇₃

C₂²

LCS

G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂³×C₇₃ ◁ C₂×C₄²×C₇₃ ◁ C₂×C₄×C₈×C₇₃ ◁ G

N	H ≅ G/N	type
1. C₂×#499×C₇₃	C₂	semidirect
4. C₇₃×#1380	C₂	semidirect
5. C₇₃×#1374	C₂	semidirect
113. #13365	C₇₃	direct (N × H)
120. C₂×#499	C₂×C₇₃	semidirect
123. #1380	C₂×C₇₃	semidirect
124. #1374	C₂×C₇₃	semidirect
125. C₇₃	#13365	direct (N × H)

H ≅ G/N

type

1. C₂×#499×C₇₃

C₂

semidirect

4. C₇₃×#1380

C₂

semidirect

5. C₇₃×#1374

C₂

semidirect

113. #13365

C₇₃

direct (N × H)

120. C₂×#499

C₂×C₇₃

semidirect

123. #1380

C₂×C₇₃

semidirect

124. #1374

C₂×C₇₃

semidirect

125. C₇₃

#13365

direct (N × H)

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

subgroup	index
C₂×#499×C₇₃	2
C₂×#357×C₇₃	2
C₇₃×#1970	2
C₇₃×#1380	2
C₇₃×#1374	2
#13365	73

subgroup

index

C₂×#499×C₇₃

C₂×#357×C₇₃

C₇₃×#1970

C₇₃×#1380

C₇₃×#1374

#13365

Subgroups — C₇₃×#13365 #32922769

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C73×#13365 #32922769

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#13365 #32922769