Subgroups — C₇₃×#21426 #32930830

Order 18688.

1132 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#529×C₇₃	C₂	1	1	yes	maximal, characteristic
2	C₇₃×#2920	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×M₁₆×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₃×#1998	C₂	1	2	yes	maximal, complemented
5	C₇₃×#1967	C₂	1	2	yes	maximal, complemented
6	C₇₃×#1901	C₂	1	2	yes	maximal, complemented
7	C₇₃×#1900	C₂	1	2	yes	maximal
8	C₄×#101×C₇₃	C₂	1	2	yes	maximal, complemented
9	C₄×#100×C₇₃	C₂	1	2	yes	maximal, complemented
10	C₂²×M₁₆×C₇₃	C₂²	1	2	yes	—
11	#529×C₇₃	—	2	1	no	—
12	#529×C₇₃	—	2	1	no	—
13	#529×C₇₃	—	2	1	no	—
14	#529×C₇₃	—	2	1	no	—
15	#529×C₇₃	—	2	1	no	—
16	#529×C₇₃	—	2	1	no	—
17	#529×C₇₃	—	2	1	no	—
18	#529×C₇₃	—	2	1	no	—
19	C₂×#126×C₇₃	C₄	1	2	yes	—
20	C₂×#125×C₇₃	C₂²	1	1	yes	characteristic
21	C₂×#124×C₇₃	C₂²	1	1	yes	characteristic
22	C₂×#123×C₇₃	C₄	1	2	yes	—
23	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
24	C₂×#121×C₇₃	C₂²	1	1	yes	characteristic
25	C₂×C₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic
26	C₂×C₄×D₄×C₇₃	C₄	1	2	yes	—
27	C₂×C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
28	C₂×#117×C₇₃	C₄	1	2	yes	—
29	C₂²×C₄²×C₇₃	C₂²	1	1	yes	characteristic
30	#432×C₇₃	—	2	1	no	—
31	#432×C₇₃	—	2	1	no	—
32	#431×C₇₃	—	2	1	no	—
33	#431×C₇₃	—	2	1	no	—
34	#423×C₇₃	C₂²	1	2	yes	—
35	C₂×#101×C₇₃	C₂²	1	4	yes	—
36	C₂×#100×C₇₃	C₂²	1	4	yes	—
37	#407×C₇₃	C₂²	1	2	yes	—
38	C₄×M₁₆×C₇₃	—	2	1	no	—
39	C₄×M₁₆×C₇₃	—	2	1	no	—
40	C₄×M₁₆×C₇₃	C₂²	1	2	yes	—
41	C₄×M₁₆×C₇₃	C₂²	1	2	yes	—
42	C₄×M₁₆×C₇₃	C₂²	1	2	yes	—
43	C₂×#97×C₇₃	—	2	1	no	—
44	C₂×C₄×C₈×C₇₃	—	2	1	no	—
45	#343×C₇₃	C₂²	1	4	yes	—
46	#343×C₇₃	C₂²	1	4	yes	—
47	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
48	C₂²×D₄×C₇₃	C₂×C₄	1	2	yes	—
49	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
50	C₂³×C₄×C₇₃	C₂×C₄	1	2	yes	—
51	C₂³×C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
52	C₂³×C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
53	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
54	C₂×M₁₆×C₇₃	—	2	2	no	—
55	C₂×M₁₆×C₇₃	—	2	8	no	—
56	C₂×M₁₆×C₇₃	C₂³	1	4	yes	—
57	C₂×M₁₆×C₇₃	C₂³	1	4	yes	—
58	C₂²×C₈×C₇₃	—	2	2	no	—
59	#126×C₇₃	—	2	2	no	—
60	#126×C₇₃	—	2	2	no	—
61	#126×C₇₃	—	2	2	no	—
62	#126×C₇₃	—	2	2	no	—
63	#125×C₇₃	—	2	1	no	—
64	#125×C₇₃	—	2	1	no	—
65	#125×C₇₃	—	2	1	no	—
66	#125×C₇₃	—	2	1	no	—
67	#124×C₇₃	—	2	1	no	—
68	#124×C₇₃	—	2	1	no	—
69	#124×C₇₃	—	2	1	no	—
70	#124×C₇₃	—	2	1	no	—
71	#123×C₇₃	—	2	2	no	—
72	#123×C₇₃	—	2	2	no	—
73	#123×C₇₃	—	2	2	no	—
74	#123×C₇₃	—	2	2	no	—
75	C₂²⋊Q₈×C₇₃	—	2	1	no	—
76	C₂²⋊Q₈×C₇₃	—	2	1	no	—
77	C₂²⋊Q₈×C₇₃	—	2	1	no	—
78	C₂²⋊Q₈×C₇₃	—	2	1	no	—
79	#121×C₇₃	—	2	1	no	—
80	#121×C₇₃	—	2	1	no	—
81	#121×C₇₃	—	2	1	no	—
82	#121×C₇₃	—	2	1	no	—
83	C₄×Q₈×C₇₃	—	2	1	no	—
84	C₄×Q₈×C₇₃	—	2	1	no	—
85	C₄×Q₈×C₇₃	—	2	1	no	—
86	C₄×Q₈×C₇₃	—	2	1	no	—
87	C₄×D₄×C₇₃	—	2	2	no	—
88	C₄×D₄×C₇₃	—	2	2	no	—
89	C₄×D₄×C₇₃	—	2	2	no	—
90	C₄×D₄×C₇₃	—	2	2	no	—
91	C₄×D₄×C₇₃	—	2	1	no	—
92	C₄×D₄×C₇₃	—	2	1	no	—
93	C₄×D₄×C₇₃	—	2	1	no	—
94	C₄×D₄×C₇₃	—	2	1	no	—
95	#117×C₇₃	—	2	2	no	—
96	#117×C₇₃	—	2	2	no	—
97	#117×C₇₃	—	2	2	no	—
98	#117×C₇₃	—	2	2	no	—
99	C₂×C₄⋊C₄×C₇₃	C₂×C₄	1	2	yes	—
100	C₂×C₄⋊C₄×C₇₃	C₂×C₄	1	2	yes	—
101	C₂×C₄⋊C₄×C₇₃	C₂×C₄	1	2	yes	—
102	C₂×C₄⋊C₄×C₇₃	C₂×C₄	1	2	yes	—
103	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
104	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
105	C₂×C₂²⋊C₄×C₇₃	C₂×C₄	1	2	yes	—
106	C₂×C₂²⋊C₄×C₇₃	C₂×C₄	1	2	yes	—
107	C₂×C₂²⋊C₄×C₇₃	C₂×C₄	1	2	yes	—
108	C₂×C₂²⋊C₄×C₇₃	C₂×C₄	1	2	yes	—
109	C₂×C₂²⋊C₄×C₇₃	C₂×C₄	1	2	yes	—
110	C₂×C₄²×C₇₃	C₂×C₄	1	2	yes	—
111	C₂×C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
112	C₂×C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
113	C₂×C₄²×C₇₃	D₄	1	1	yes	characteristic
114	C₂×C₄²×C₇₃	D₄	1	1	yes	characteristic
115	C₂×C₄²×C₇₃	D₄	1	1	yes	characteristic
116	C₂×C₄²×C₇₃	D₄	1	1	yes	characteristic
117	C₂×C₄²×C₇₃	D₄	1	1	yes	characteristic
118	C₂×C₄²×C₇₃	D₄	1	1	yes	characteristic
119	C₂×C₄²×C₇₃	D₄	1	1	yes	characteristic
120	C₂×C₄²×C₇₃	D₄	1	1	yes	characteristic
121	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
122	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
123	C₄⋊C₈×C₇₃	—	2	2	no	—
124	C₄⋊C₈×C₇₃	—	2	2	no	—
125	#101×C₇₃	—	2	8	no	—
126	#100×C₇₃	—	2	8	no	—
127	C₂²⋊C₈×C₇₃	—	2	2	no	—
128	C₂²⋊C₈×C₇₃	—	2	2	no	—
129	#97×C₇₃	—	2	2	no	—
130	#97×C₇₃	—	2	2	no	—
131	#97×C₇₃	—	2	2	no	—
132	C₄×C₈×C₇₃	—	2	2	no	—
133	C₄×C₈×C₇₃	—	2	2	no	—
134	C₄×C₈×C₇₃	—	2	2	no	—
135	C₂⁴×C₇₃	C₂²×C₄	1	1	yes	characteristic
136	C₂⁴×C₇₃	C₂²×C₄	1	2	yes	—
137	C₂×Q₈×C₇₃	—	2	1	no	—
138	C₂×Q₈×C₇₃	—	2	1	no	—
139	C₂×Q₈×C₇₃	—	2	4	no	—
140	C₂×D₄×C₇₃	—	2	2	no	—
141	C₂×D₄×C₇₃	—	2	2	no	—
142	C₂×D₄×C₇₃	—	2	1	no	—
143	C₂×D₄×C₇₃	—	2	1	no	—
144	C₂×D₄×C₇₃	—	2	4	no	—
145	C₂×D₄×C₇₃	—	4	4	no	—
146	C₂²×C₄×C₇₃	—	2	4	no	—
147	C₂²×C₄×C₇₃	—	2	2	no	—
148	C₂²×C₄×C₇₃	—	2	2	no	—
149	C₂²×C₄×C₇₃	—	4	2	no	—
150	C₂²×C₄×C₇₃	—	4	2	no	—
151	C₂²×C₄×C₇₃	—	4	4	no	—
152	C₂²×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
153	C₂²×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
154	C₂²×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
155	C₂²×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
156	C₂²×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
157	C₂²×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
158	C₂²×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
159	C₂²×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
160	C₂²×C₄×C₇₃	C₂²×C₄	1	2	yes	—
161	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
162	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
163	C₂²×C₄×C₇₃	C₂²×C₄	1	2	yes	—
164	C₂²×C₄×C₇₃	C₂²×C₄	1	2	yes	—
165	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
166	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
167	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
168	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
169	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
170	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
171	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
172	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
173	M₁₆×C₇₃	—	2	8	no	—
174	M₁₆×C₇₃	—	2	4	no	—
175	M₁₆×C₇₃	—	2	4	no	—
176	M₁₆×C₇₃	—	2	4	no	—
177	M₁₆×C₇₃	#41	1	8	yes	—
178	C₂×C₈×C₇₃	—	2	8	no	—
179	C₂×C₈×C₇₃	—	2	4	no	—
180	C₂×C₈×C₇₃	—	2	4	no	—
181	C₄⋊C₄×C₇₃	—	2	2	no	—
182	C₄⋊C₄×C₇₃	—	2	2	no	—
183	C₄⋊C₄×C₇₃	—	2	2	no	—
184	C₄⋊C₄×C₇₃	—	2	2	no	—
185	C₄⋊C₄×C₇₃	—	2	2	no	—
186	C₄⋊C₄×C₇₃	—	2	2	no	—
187	C₄⋊C₄×C₇₃	—	2	2	no	—
188	C₄⋊C₄×C₇₃	—	2	2	no	—
189	C₄⋊C₄×C₇₃	—	2	1	no	—
190	C₄⋊C₄×C₇₃	—	2	1	no	—
191	C₄⋊C₄×C₇₃	—	2	1	no	—
192	C₄⋊C₄×C₇₃	—	2	1	no	—
193	C₂²⋊C₄×C₇₃	—	2	2	no	—
194	C₂²⋊C₄×C₇₃	—	2	2	no	—
195	C₂²⋊C₄×C₇₃	—	2	2	no	—
196	C₂²⋊C₄×C₇₃	—	2	2	no	—
197	C₂²⋊C₄×C₇₃	—	2	2	no	—
198	C₂²⋊C₄×C₇₃	—	2	2	no	—
199	C₂²⋊C₄×C₇₃	—	2	2	no	—
200	C₂²⋊C₄×C₇₃	—	2	2	no	—
201	C₂²⋊C₄×C₇₃	—	2	2	no	—
202	C₂²⋊C₄×C₇₃	—	2	2	no	—
203	C₄²×C₇₃	—	2	2	no	—
204	C₄²×C₇₃	—	2	2	no	—
205	C₄²×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
206	C₄²×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
207	C₄²×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
208	C₄²×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
209	C₄²×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
210	C₄²×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
211	C₄²×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
212	C₄²×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
213	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
214	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
215	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
216	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
217	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
218	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
219	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
220	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
221	C₂³×C₇₃	—	2	2	no	—
222	C₂³×C₇₃	—	2	2	no	—
223	C₂³×C₇₃	—	2	2	no	—
224	C₂³×C₇₃	—	2	4	no	—
225	C₂³×C₇₃	—	4	1	no	—
226	C₂³×C₇₃	—	4	2	no	—
227	C₂³×C₇₃	—	4	2	no	—
228	C₂³×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
229	C₂³×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
230	C₂³×C₇₃	C₂³×C₄	1	1	yes	characteristic
231	Q₈×C₇₃	—	4	2	no	—
232	Q₈×C₇₃	—	4	2	no	—
233	D₄×C₇₃	—	4	4	no	—
234	D₄×C₇₃	—	4	4	no	—
235	D₄×C₇₃	—	4	2	no	—
236	D₄×C₇₃	—	4	2	no	—
237	C₂×C₄×C₇₃	—	2	2	no	—
238	C₂×C₄×C₇₃	—	2	2	no	—
239	C₂×C₄×C₇₃	—	2	2	no	—
240	C₂×C₄×C₇₃	—	2	2	no	—
241	C₂×C₄×C₇₃	—	2	2	no	—
242	C₂×C₄×C₇₃	—	2	2	no	—
243	C₂×C₄×C₇₃	—	2	2	no	—
244	C₂×C₄×C₇₃	—	2	2	no	—
245	C₂×C₄×C₇₃	—	2	2	no	—
246	C₂×C₄×C₇₃	—	2	2	no	—
247	C₂×C₄×C₇₃	—	2	2	no	—
248	C₂×C₄×C₇₃	—	2	2	no	—
249	C₂×C₄×C₇₃	—	2	2	no	—
250	C₂×C₄×C₇₃	—	2	4	no	—
251	C₂×C₄×C₇₃	—	4	1	no	—
252	C₂×C₄×C₇₃	—	4	1	no	—
253	C₂×C₄×C₇₃	—	4	1	no	—
254	C₂×C₄×C₇₃	—	4	1	no	—
255	C₂×C₄×C₇₃	—	4	1	no	—
256	C₂×C₄×C₇₃	—	4	1	no	—
257	C₂×C₄×C₇₃	—	4	1	no	—
258	C₂×C₄×C₇₃	—	4	4	no	—
259	C₂×C₄×C₇₃	—	4	4	no	—
260	C₂×C₄×C₇₃	—	4	2	no	—
261	C₂×C₄×C₇₃	—	4	2	no	—
262	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
263	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
264	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
265	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
266	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
267	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
268	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
269	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
270	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
271	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
272	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
273	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
274	C₂×C₄×C₇₃	C₂×#41	1	4	yes	—
275	C₈×C₇₃	—	2	8	no	—
276	C₈×C₇₃	—	4	4	no	—
277	C₂²×C₇₃	—	2	1	no	—
278	C₂²×C₇₃	—	2	1	no	—
279	C₂²×C₇₃	—	2	1	no	—
280	C₂²×C₇₃	—	2	1	no	—
281	C₂²×C₇₃	—	2	1	no	—
282	C₂²×C₇₃	—	2	1	no	—
283	C₂²×C₇₃	—	2	1	no	—
284	C₂²×C₇₃	—	4	4	no	—
285	C₂²×C₇₃	—	4	2	no	—
286	C₂²×C₇₃	—	4	2	no	—
287	C₂²×C₇₃	—	4	2	no	—
288	C₂²×C₇₃	—	8	4	no	—
289	C₂²×C₇₃	#413	1	2	yes	—
290	C₂²×C₇₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
291	C₂²×C₇₃	C₄×#41	1	2	yes	—
292	C₄×C₇₃	—	2	1	no	—
293	C₄×C₇₃	—	2	1	no	—
294	C₄×C₇₃	—	2	1	no	—
295	C₄×C₇₃	—	2	1	no	—
296	C₄×C₇₃	—	2	1	no	—
297	C₄×C₇₃	—	2	1	no	—
298	C₄×C₇₃	—	2	1	no	—
299	C₄×C₇₃	—	2	1	no	—
300	C₄×C₇₃	—	2	1	no	—
301	C₄×C₇₃	—	4	2	no	—
302	C₄×C₇₃	—	4	2	no	—
303	C₄×C₇₃	—	4	2	no	—
304	C₄×C₇₃	#413	1	2	yes	—
305	C₄×C₇₃	#525	1	2	yes	—
306	C₄×C₇₃	#532	1	2	yes	—
307	#21426	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
308	C₂×C₇₃	—	2	2	no	—
309	C₂×C₇₃	—	2	2	no	—
310	C₂×C₇₃	—	4	1	no	—
311	C₂×C₇₃	—	8	2	no	—
312	C₂×C₇₃	#2297	1	1	yes	characteristic
313	C₂×C₇₃	C₂×#413	1	1	yes	characteristic
314	C₂×C₇₃	C₂×#413	1	1	yes	characteristic
315	C₂×#529	C₂×C₇₃	1	1	yes	characteristic
316	#2920	C₂×C₇₃	1	1	yes	characteristic, complemented
317	C₂×C₄×M₁₆	C₂×C₇₃	1	1	yes	characteristic, complemented
318	#1998	C₂×C₇₃	1	2	yes	complemented
319	#1967	C₂×C₇₃	1	2	yes	complemented
320	#1901	C₂×C₇₃	1	2	yes	complemented
321	#1900	C₂×C₇₃	1	2	yes	—
322	C₄×#101	C₂×C₇₃	1	2	yes	complemented
323	C₄×#100	C₂×C₇₃	1	2	yes	complemented
324	C₇₃	#21426	1	1	yes	characteristic, direct product factor, Sylow
325	C₂²×M₁₆	C₂²×C₇₃	1	2	yes	—
326	#529	—	2	1	no	—
327	#529	—	2	1	no	—
328	#529	—	2	1	no	—
329	#529	—	2	1	no	—
330	#529	—	2	1	no	—
331	#529	—	2	1	no	—
332	#529	—	2	1	no	—
333	#529	—	2	1	no	—
334	C₂×#126	C₄×C₇₃	1	2	yes	—
335	C₂×#125	C₂²×C₇₃	1	1	yes	characteristic
336	C₂×#124	C₂²×C₇₃	1	1	yes	characteristic
337	C₂×#123	C₄×C₇₃	1	2	yes	—
338	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
339	C₂×#121	C₂²×C₇₃	1	1	yes	characteristic
340	C₂×C₄×Q₈	C₂²×C₇₃	1	1	yes	characteristic
341	C₂×C₄×D₄	C₄×C₇₃	1	2	yes	—
342	C₂×C₄×D₄	C₂²×C₇₃	1	1	yes	characteristic
343	C₂×#117	C₄×C₇₃	1	2	yes	—
344	C₂²×C₄²	C₂²×C₇₃	1	1	yes	characteristic
345	#432	—	2	1	no	—
346	#432	—	2	1	no	—
347	#431	—	2	1	no	—
348	#431	—	2	1	no	—
349	#423	C₂²×C₇₃	1	2	yes	—
350	C₂×#101	C₂²×C₇₃	1	4	yes	—
351	C₂×#100	C₂²×C₇₃	1	4	yes	—
352	#407	C₂²×C₇₃	1	2	yes	—
353	C₄×M₁₆	—	2	1	no	—
354	C₄×M₁₆	—	2	1	no	—
355	C₄×M₁₆	C₂²×C₇₃	1	2	yes	—
356	C₄×M₁₆	C₂²×C₇₃	1	2	yes	—
357	C₄×M₁₆	C₂²×C₇₃	1	2	yes	—
358	C₂×#97	—	2	1	no	—
359	C₂×C₄×C₈	—	2	1	no	—
360	#343	C₂²×C₇₃	1	4	yes	—
361	#343	C₂²×C₇₃	1	4	yes	—
362	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
363	C₂²×D₄	C₂×C₄×C₇₃	1	2	yes	—
364	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
365	C₂³×C₄	C₂×C₄×C₇₃	1	2	yes	—
366	C₂³×C₄	C₂×C₄×C₇₃	1	1	yes	characteristic
367	C₂³×C₄	C₂×C₄×C₇₃	1	1	yes	characteristic
368	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
369	C₂×M₁₆	—	2	2	no	—
370	C₂×M₁₆	—	2	8	no	—
371	C₂×M₁₆	C₂³×C₇₃	1	4	yes	—
372	C₂×M₁₆	C₂³×C₇₃	1	4	yes	—
373	C₂²×C₈	—	2	2	no	—
374	#126	—	2	2	no	—
375	#126	—	2	2	no	—
376	#126	—	2	2	no	—
377	#126	—	2	2	no	—
378	#125	—	2	1	no	—
379	#125	—	2	1	no	—
380	#125	—	2	1	no	—
381	#125	—	2	1	no	—
382	#124	—	2	1	no	—
383	#124	—	2	1	no	—
384	#124	—	2	1	no	—
385	#124	—	2	1	no	—
386	#123	—	2	2	no	—
387	#123	—	2	2	no	—
388	#123	—	2	2	no	—
389	#123	—	2	2	no	—
390	C₂²⋊Q₈	—	2	1	no	—
391	C₂²⋊Q₈	—	2	1	no	—
392	C₂²⋊Q₈	—	2	1	no	—
393	C₂²⋊Q₈	—	2	1	no	—
394	#121	—	2	1	no	—
395	#121	—	2	1	no	—
396	#121	—	2	1	no	—
397	#121	—	2	1	no	—
398	C₄×Q₈	—	2	1	no	—
399	C₄×Q₈	—	2	1	no	—
400	C₄×Q₈	—	2	1	no	—
401	C₄×Q₈	—	2	1	no	—
402	C₄×D₄	—	2	2	no	—
403	C₄×D₄	—	2	2	no	—
404	C₄×D₄	—	2	2	no	—
405	C₄×D₄	—	2	2	no	—
406	C₄×D₄	—	2	1	no	—
407	C₄×D₄	—	2	1	no	—
408	C₄×D₄	—	2	1	no	—
409	C₄×D₄	—	2	1	no	—
410	#117	—	2	2	no	—
411	#117	—	2	2	no	—
412	#117	—	2	2	no	—
413	#117	—	2	2	no	—
414	C₂×C₄⋊C₄	C₂×C₄×C₇₃	1	2	yes	—
415	C₂×C₄⋊C₄	C₂×C₄×C₇₃	1	2	yes	—
416	C₂×C₄⋊C₄	C₂×C₄×C₇₃	1	2	yes	—
417	C₂×C₄⋊C₄	C₂×C₄×C₇₃	1	2	yes	—
418	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
419	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
420	C₂×C₂²⋊C₄	C₂×C₄×C₇₃	1	2	yes	—
421	C₂×C₂²⋊C₄	C₂×C₄×C₇₃	1	2	yes	—
422	C₂×C₂²⋊C₄	C₂×C₄×C₇₃	1	2	yes	—
423	C₂×C₂²⋊C₄	C₂×C₄×C₇₃	1	2	yes	—
424	C₂×C₂²⋊C₄	C₂×C₄×C₇₃	1	2	yes	—
425	C₂×C₄²	C₂×C₄×C₇₃	1	2	yes	—
426	C₂×C₄²	C₂×C₄×C₇₃	1	1	yes	characteristic
427	C₂×C₄²	C₂×C₄×C₇₃	1	1	yes	characteristic
428	C₂×C₄²	D₄×C₇₃	1	1	yes	characteristic
429	C₂×C₄²	D₄×C₇₃	1	1	yes	characteristic
430	C₂×C₄²	D₄×C₇₃	1	1	yes	characteristic
431	C₂×C₄²	D₄×C₇₃	1	1	yes	characteristic
432	C₂×C₄²	D₄×C₇₃	1	1	yes	characteristic
433	C₂×C₄²	D₄×C₇₃	1	1	yes	characteristic
434	C₂×C₄²	D₄×C₇₃	1	1	yes	characteristic
435	C₂×C₄²	D₄×C₇₃	1	1	yes	characteristic
436	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
437	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
438	C₄⋊C₈	—	2	2	no	—
439	C₄⋊C₈	—	2	2	no	—
440	#101	—	2	8	no	—
441	#100	—	2	8	no	—
442	C₂²⋊C₈	—	2	2	no	—
443	C₂²⋊C₈	—	2	2	no	—
444	#97	—	2	2	no	—
445	#97	—	2	2	no	—
446	#97	—	2	2	no	—
447	C₄×C₈	—	2	2	no	—
448	C₄×C₈	—	2	2	no	—
449	C₄×C₈	—	2	2	no	—
450	C₂⁴	C₂²×C₄×C₇₃	1	1	yes	characteristic
451	C₂⁴	C₂²×C₄×C₇₃	1	2	yes	—
452	C₂×Q₈	—	2	1	no	—
453	C₂×Q₈	—	2	1	no	—
454	C₂×Q₈	—	2	4	no	—
455	C₂×D₄	—	2	2	no	—
456	C₂×D₄	—	2	2	no	—
457	C₂×D₄	—	2	1	no	—
458	C₂×D₄	—	2	1	no	—
459	C₂×D₄	—	2	4	no	—
460	C₂×D₄	—	4	4	no	—
461	C₂²×C₄	—	2	4	no	—
462	C₂²×C₄	—	2	2	no	—
463	C₂²×C₄	—	2	2	no	—
464	C₂²×C₄	—	4	2	no	—
465	C₂²×C₄	—	4	2	no	—
466	C₂²×C₄	—	4	4	no	—
467	C₂²×C₄	C₂²⋊C₄×C₇₃	1	1	yes	characteristic
468	C₂²×C₄	C₂²⋊C₄×C₇₃	1	1	yes	characteristic
469	C₂²×C₄	C₂²⋊C₄×C₇₃	1	1	yes	characteristic
470	C₂²×C₄	C₂²⋊C₄×C₇₃	1	1	yes	characteristic
471	C₂²×C₄	C₂²⋊C₄×C₇₃	1	1	yes	characteristic
472	C₂²×C₄	C₂²⋊C₄×C₇₃	1	1	yes	characteristic
473	C₂²×C₄	C₂²⋊C₄×C₇₃	1	1	yes	characteristic
474	C₂²×C₄	C₂²⋊C₄×C₇₃	1	1	yes	characteristic
475	C₂²×C₄	C₂²×C₄×C₇₃	1	2	yes	—
476	C₂²×C₄	C₂²×C₄×C₇₃	1	1	yes	characteristic
477	C₂²×C₄	C₂²×C₄×C₇₃	1	1	yes	characteristic
478	C₂²×C₄	C₂²×C₄×C₇₃	1	2	yes	—
479	C₂²×C₄	C₂²×C₄×C₇₃	1	2	yes	—
480	C₂²×C₄	C₂²×C₄×C₇₃	1	1	yes	characteristic
481	C₂²×C₄	C₂²×C₄×C₇₃	1	1	yes	characteristic
482	C₂²×C₄	C₂²×C₄×C₇₃	1	1	yes	characteristic
483	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
484	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
485	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
486	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
487	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
488	M₁₆	—	2	8	no	—
489	M₁₆	—	2	4	no	—
490	M₁₆	—	2	4	no	—
491	M₁₆	—	2	4	no	—
492	M₁₆	#41×C₇₃	1	8	yes	—
493	C₂×C₈	—	2	8	no	—
494	C₂×C₈	—	2	4	no	—
495	C₂×C₈	—	2	4	no	—
496	C₄⋊C₄	—	2	2	no	—
497	C₄⋊C₄	—	2	2	no	—
498	C₄⋊C₄	—	2	2	no	—
499	C₄⋊C₄	—	2	2	no	—
500	C₄⋊C₄	—	2	2	no	—
501	C₄⋊C₄	—	2	2	no	—
502	C₄⋊C₄	—	2	2	no	—
503	C₄⋊C₄	—	2	2	no	—
504	C₄⋊C₄	—	2	1	no	—
505	C₄⋊C₄	—	2	1	no	—
506	C₄⋊C₄	—	2	1	no	—
507	C₄⋊C₄	—	2	1	no	—
508	C₂²⋊C₄	—	2	2	no	—
509	C₂²⋊C₄	—	2	2	no	—
510	C₂²⋊C₄	—	2	2	no	—
511	C₂²⋊C₄	—	2	2	no	—
512	C₂²⋊C₄	—	2	2	no	—
513	C₂²⋊C₄	—	2	2	no	—
514	C₂²⋊C₄	—	2	2	no	—
515	C₂²⋊C₄	—	2	2	no	—
516	C₂²⋊C₄	—	2	2	no	—
517	C₂²⋊C₄	—	2	2	no	—
518	C₄²	—	2	2	no	—
519	C₄²	—	2	2	no	—
520	C₄²	C₂²⋊C₄×C₇₃	1	1	yes	characteristic
521	C₄²	C₂²⋊C₄×C₇₃	1	1	yes	characteristic
522	C₄²	C₂²⋊C₄×C₇₃	1	1	yes	characteristic
523	C₄²	C₂²⋊C₄×C₇₃	1	1	yes	characteristic
524	C₄²	C₂²⋊C₄×C₇₃	1	1	yes	characteristic
525	C₄²	C₂²⋊C₄×C₇₃	1	1	yes	characteristic
526	C₄²	C₂²⋊C₄×C₇₃	1	1	yes	characteristic
527	C₄²	C₂²⋊C₄×C₇₃	1	1	yes	characteristic
528	C₄²	C₂×D₄×C₇₃	1	1	yes	characteristic
529	C₄²	C₂×D₄×C₇₃	1	1	yes	characteristic
530	C₄²	C₂×D₄×C₇₃	1	1	yes	characteristic
531	C₄²	C₂×D₄×C₇₃	1	1	yes	characteristic
532	C₄²	C₂×D₄×C₇₃	1	1	yes	characteristic
533	C₄²	C₂×D₄×C₇₃	1	1	yes	characteristic
534	C₄²	C₂×D₄×C₇₃	1	1	yes	characteristic
535	C₄²	C₂×D₄×C₇₃	1	1	yes	characteristic
536	C₂³	—	2	2	no	—
537	C₂³	—	2	2	no	—
538	C₂³	—	2	2	no	—
539	C₂³	—	2	4	no	—
540	C₂³	—	4	1	no	—
541	C₂³	—	4	2	no	—
542	C₂³	—	4	2	no	—
543	C₂³	C₂×C₂²⋊C₄×C₇₃	1	1	yes	characteristic
544	C₂³	C₂×C₂²⋊C₄×C₇₃	1	1	yes	characteristic
545	C₂³	C₂³×C₄×C₇₃	1	1	yes	characteristic
546	Q₈	—	4	2	no	—
547	Q₈	—	4	2	no	—
548	D₄	—	4	4	no	—
549	D₄	—	4	4	no	—
550	D₄	—	4	2	no	—
551	D₄	—	4	2	no	—
552	C₂×C₄	—	2	2	no	—
553	C₂×C₄	—	2	2	no	—
554	C₂×C₄	—	2	2	no	—
555	C₂×C₄	—	2	2	no	—
556	C₂×C₄	—	2	2	no	—
557	C₂×C₄	—	2	2	no	—
558	C₂×C₄	—	2	2	no	—
559	C₂×C₄	—	2	2	no	—
560	C₂×C₄	—	2	2	no	—
561	C₂×C₄	—	2	2	no	—
562	C₂×C₄	—	2	2	no	—
563	C₂×C₄	—	2	2	no	—
564	C₂×C₄	—	2	2	no	—
565	C₂×C₄	—	2	4	no	—
566	C₂×C₄	—	4	1	no	—
567	C₂×C₄	—	4	1	no	—
568	C₂×C₄	—	4	1	no	—
569	C₂×C₄	—	4	1	no	—
570	C₂×C₄	—	4	1	no	—
571	C₂×C₄	—	4	1	no	—
572	C₂×C₄	—	4	1	no	—
573	C₂×C₄	—	4	4	no	—
574	C₂×C₄	—	4	4	no	—
575	C₂×C₄	—	4	2	no	—
576	C₂×C₄	—	4	2	no	—
577	C₂×C₄	C₂×C₂²⋊C₄×C₇₃	1	1	yes	characteristic
578	C₂×C₄	C₂×C₂²⋊C₄×C₇₃	1	1	yes	characteristic
579	C₂×C₄	C₂×C₂²⋊C₄×C₇₃	1	1	yes	characteristic
580	C₂×C₄	C₂×C₂²⋊C₄×C₇₃	1	1	yes	characteristic
581	C₂×C₄	C₂×C₂²⋊C₄×C₇₃	1	1	yes	characteristic
582	C₂×C₄	C₂×C₂²⋊C₄×C₇₃	1	1	yes	characteristic
583	C₂×C₄	C₂×C₂²⋊C₄×C₇₃	1	1	yes	characteristic
584	C₂×C₄	C₂×C₂²⋊C₄×C₇₃	1	1	yes	characteristic
585	C₂×C₄	C₂×C₂²⋊C₄×C₇₃	1	1	yes	characteristic
586	C₂×C₄	C₂×C₂²⋊C₄×C₇₃	1	1	yes	characteristic
587	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
588	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
589	C₂×C₄	C₂×#41×C₇₃	1	4	yes	—
590	C₈	—	2	8	no	—
591	C₈	—	4	4	no	—
592	C₂²	—	2	1	no	—
593	C₂²	—	2	1	no	—
594	C₂²	—	2	1	no	—
595	C₂²	—	2	1	no	—
596	C₂²	—	2	1	no	—
597	C₂²	—	2	1	no	—
598	C₂²	—	2	1	no	—
599	C₂²	—	4	4	no	—
600	C₂²	—	4	2	no	—
601	C₂²	—	4	2	no	—
602	C₂²	—	4	2	no	—
603	C₂²	—	8	4	no	—
604	C₂²	#413×C₇₃	1	2	yes	—
605	C₂²	C₂²×C₂²⋊C₄×C₇₃	1	1	yes	characteristic
606	C₂²	C₄×#41×C₇₃	1	2	yes	—
607	C₄	—	2	1	no	—
608	C₄	—	2	1	no	—
609	C₄	—	2	1	no	—
610	C₄	—	2	1	no	—
611	C₄	—	2	1	no	—
612	C₄	—	2	1	no	—
613	C₄	—	2	1	no	—
614	C₄	—	2	1	no	—
615	C₄	—	2	1	no	—
616	C₄	—	4	2	no	—
617	C₄	—	4	2	no	—
618	C₄	—	4	2	no	—
619	C₄	#413×C₇₃	1	2	yes	—
620	C₄	#525×C₇₃	1	2	yes	—
621	C₄	#532×C₇₃	1	2	yes	—
622	C₂	—	2	2	no	—
623	C₂	—	2	2	no	—
624	C₂	—	4	1	no	—
625	C₂	—	8	2	no	—
626	C₂	C₇₃×#2297	1	1	yes	characteristic
627	C₂	C₂×#413×C₇₃	1	1	yes	characteristic
628	C₂	C₂×#413×C₇₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₇₃	C₂×C₂²⋊C₄
commutator	C₂³	C₂³×C₄×C₇₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₃
socle	C₂²×C₇₃	C₂²×C₂²⋊C₄
prime radical	C₂×#121×C₇₃	C₂²
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₇₃ ◁ C₂²×C₄²×C₇₃ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₇₃×#2920	C₂	semidirect
3. C₂×C₄×M₁₆×C₇₃	C₂	semidirect
4. C₇₃×#1998	C₂	semidirect
5. C₇₃×#1967	C₂	semidirect
6. C₇₃×#1901	C₂	semidirect
8. C₄×#101×C₇₃	C₂	semidirect
9. C₄×#100×C₇₃	C₂	semidirect
307. #21426	C₇₃	direct (N × H)
316. #2920	C₂×C₇₃	semidirect
317. C₂×C₄×M₁₆	C₂×C₇₃	semidirect
318. #1998	C₂×C₇₃	semidirect
319. #1967	C₂×C₇₃	semidirect
320. #1901	C₂×C₇₃	semidirect
322. C₄×#101	C₂×C₇₃	semidirect
323. C₄×#100	C₂×C₇₃	semidirect
324. C₇₃	#21426	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#529×C₇₃	2
C₇₃×#2920	2
C₂×C₄×M₁₆×C₇₃	2
C₇₃×#1998	2
C₇₃×#1967	2
C₇₃×#1901	2
C₇₃×#1900	2
C₄×#101×C₇₃	2
C₄×#100×C₇₃	2
#21426	73

Subgroups — C73×#21426 #32930830

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#21426 #32930830