Subgroups — C₇₃×#25712 #32935116

Order 18688.

1060 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#554×C₇₃	C₂	1	1	yes	maximal, characteristic
2	C₂×#501×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#479×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₃×#2562	C₂	1	1	yes	maximal, characteristic
5	C₇₃×#2036	C₂	1	2	yes	maximal, complemented
6	C₇₃×#2035	C₂	1	2	yes	maximal, complemented
7	C₇₃×#1988	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇₃×#1955	C₂	1	1	yes	maximal, characteristic
9	C₇₃×#1853	C₂	1	2	yes	maximal, complemented
10	C₇₃×#1852	C₂	1	2	yes	maximal, complemented
11	C₇₃×#1763	C₂	1	1	yes	maximal, characteristic, complemented
12	#554×C₇₃	—	2	4	no	—
13	#554×C₇₃	—	2	4	no	—
14	C₂×C₄⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
15	C₂×#125×C₇₃	—	2	1	no	—
16	C₂×#125×C₇₃	C₂²	1	1	yes	characteristic
17	C₂×C₂²⋊Q₈×C₇₃	—	2	2	no	—
18	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	2	yes	—
19	C₂×C₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic
20	C₂×C₄×D₄×C₇₃	—	2	1	no	—
21	C₂×C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
22	C₂²×C₄⋊C₄×C₇₃	C₂²	1	2	yes	—
23	#501×C₇₃	—	2	4	no	—
24	#479×C₇₃	—	2	4	no	—
25	C₂×#107×C₇₃	C₂²	1	2	yes	—
26	C₂×#107×C₇₃	C₂²	1	1	yes	characteristic
27	C₂×#106×C₇₃	C₂²	1	2	yes	—
28	C₂×#106×C₇₃	C₂²	1	1	yes	characteristic
29	C₂×C₄⋊C₈×C₇₃	C₂²	1	1	yes	characteristic
30	C₂×#103×C₇₃	C₂²	1	2	yes	—
31	C₂×#103×C₇₃	C₂²	1	1	yes	characteristic
32	C₂×#103×C₇₃	C₂²	1	1	yes	characteristic
33	C₂×C₂²⋊C₈×C₇₃	C₂²	1	2	yes	—
34	C₂×C₂²⋊C₈×C₇₃	C₂²	1	2	yes	—
35	C₂×#97×C₇₃	C₂²	1	1	yes	characteristic
36	#400×C₇₃	—	2	1	no	—
37	#394×C₇₃	—	2	1	no	—
38	#388×C₇₃	—	2	2	no	—
39	#380×C₇₃	C₂²	1	2	yes	—
40	#380×C₇₃	C₂²	1	2	yes	—
41	C₄×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
42	#340×C₇₃	C₂²	1	2	yes	—
43	#340×C₇₃	C₂²	1	2	yes	—
44	#340×C₇₃	C₂²	1	2	yes	—
45	C₂²×Q₈×C₇₃	—	2	1	no	—
46	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
47	C₂²×D₄×C₇₃	D₄	1	1	yes	characteristic
48	C₂³×C₄×C₇₃	—	2	2	no	—
49	C₂³×C₄×C₇₃	C₂³	1	2	yes	—
50	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
51	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
52	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
53	C₄⋊Q₈×C₇₃	—	2	2	no	—
54	C₄⋊Q₈×C₇₃	D₄	1	4	yes	—
55	#125×C₇₃	—	2	8	no	—
56	#125×C₇₃	—	2	2	no	—
57	#125×C₇₃	—	2	2	no	—
58	C₂²⋊Q₈×C₇₃	—	2	16	no	—
59	C₂²⋊Q₈×C₇₃	—	2	4	no	—
60	C₂²⋊Q₈×C₇₃	—	2	4	no	—
61	C₄×Q₈×C₇₃	—	2	2	no	—
62	C₄×Q₈×C₇₃	D₄	1	4	yes	—
63	C₄×D₄×C₇₃	—	2	8	no	—
64	C₄×D₄×C₇₃	—	2	2	no	—
65	C₄×D₄×C₇₃	—	2	2	no	—
66	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
67	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
68	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
69	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
70	C₂×C₄⋊C₄×C₇₃	—	2	4	no	—
71	C₂×C₄⋊C₄×C₇₃	—	2	4	no	—
72	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
73	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
74	C₂×C₄⋊C₄×C₇₃	D₄	1	1	yes	characteristic
75	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
76	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
77	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
78	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
79	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
80	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
81	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
82	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
83	C₂×C₂²⋊C₄×C₇₃	D₄	1	2	yes	—
84	C₂×C₄²×C₇₃	—	2	1	no	—
85	C₂×C₄²×C₇₃	—	2	1	no	—
86	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
87	#107×C₇₃	—	2	2	no	—
88	#107×C₇₃	—	2	4	no	—
89	#106×C₇₃	—	2	2	no	—
90	#106×C₇₃	—	2	4	no	—
91	C₄⋊C₈×C₇₃	—	2	2	no	—
92	#103×C₇₃	—	2	2	no	—
93	#103×C₇₃	—	2	2	no	—
94	#103×C₇₃	—	2	4	no	—
95	C₂²⋊C₈×C₇₃	—	2	4	no	—
96	C₂²⋊C₈×C₇₃	—	2	4	no	—
97	#97×C₇₃	—	2	2	no	—
98	#95×C₇₃	—	2	1	no	—
99	#95×C₇₃	—	2	2	no	—
100	#95×C₇₃	—	2	2	no	—
101	C₂⁴×C₇₃	C₂×D₄	1	2	yes	—
102	C₂×Q₈×C₇₃	—	2	4	no	—
103	C₂×Q₈×C₇₃	—	2	1	no	—
104	C₂×Q₈×C₇₃	—	2	2	no	—
105	C₂×Q₈×C₇₃	—	2	2	no	—
106	C₂×Q₈×C₇₃	—	8	1	no	—
107	C₂×Q₈×C₇₃	—	8	1	no	—
108	C₂×Q₈×C₇₃	C₂×D₄	1	2	yes	—
109	C₂×D₄×C₇₃	—	2	4	no	—
110	C₂×D₄×C₇₃	—	2	2	no	—
111	C₂²×C₄×C₇₃	—	2	1	no	—
112	C₂²×C₄×C₇₃	—	2	1	no	—
113	C₂²×C₄×C₇₃	—	2	2	no	—
114	C₂²×C₄×C₇₃	—	2	8	no	—
115	C₂²×C₄×C₇₃	—	2	2	no	—
116	C₂²×C₄×C₇₃	—	2	2	no	—
117	C₂²×C₄×C₇₃	—	2	2	no	—
118	C₂²×C₄×C₇₃	—	2	2	no	—
119	C₂²×C₄×C₇₃	—	2	2	no	—
120	C₂²×C₄×C₇₃	—	2	2	no	—
121	C₂²×C₄×C₇₃	—	2	2	no	—
122	C₂²×C₄×C₇₃	—	2	1	no	—
123	C₂²×C₄×C₇₃	—	2	1	no	—
124	C₂²×C₄×C₇₃	—	8	2	no	—
125	C₂²×C₄×C₇₃	—	8	2	no	—
126	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
127	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
130	C₂×C₈×C₇₃	—	2	2	no	—
131	C₂×C₈×C₇₃	—	2	2	no	—
132	C₂×C₈×C₇₃	—	2	1	no	—
133	C₂×C₈×C₇₃	—	2	1	no	—
134	C₂×C₈×C₇₃	—	2	2	no	—
135	C₂×C₈×C₇₃	—	2	2	no	—
136	C₂×C₈×C₇₃	#41	1	4	yes	—
137	C₄⋊C₄×C₇₃	—	2	8	no	—
138	C₄⋊C₄×C₇₃	—	2	8	no	—
139	C₄⋊C₄×C₇₃	—	2	4	no	—
140	C₄⋊C₄×C₇₃	—	2	4	no	—
141	C₄⋊C₄×C₇₃	—	2	2	no	—
142	C₄⋊C₄×C₇₃	—	2	1	no	—
143	C₄⋊C₄×C₇₃	—	2	2	no	—
144	C₄⋊C₄×C₇₃	—	2	1	no	—
145	C₄⋊C₄×C₇₃	—	2	1	no	—
146	C₄⋊C₄×C₇₃	—	2	1	no	—
147	C₄⋊C₄×C₇₃	—	2	1	no	—
148	C₄⋊C₄×C₇₃	—	2	2	no	—
149	C₄⋊C₄×C₇₃	—	2	2	no	—
150	C₄⋊C₄×C₇₃	—	4	2	no	—
151	C₄⋊C₄×C₇₃	—	4	2	no	—
152	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
153	C₄⋊C₄×C₇₃	C₂×D₄	1	4	yes	—
154	C₂²⋊C₄×C₇₃	—	2	8	no	—
155	C₂²⋊C₄×C₇₃	—	2	4	no	—
156	C₂²⋊C₄×C₇₃	—	4	4	no	—
157	C₂²⋊C₄×C₇₃	—	8	2	no	—
158	C₄²×C₇₃	—	2	4	no	—
159	C₄²×C₇₃	—	8	1	no	—
160	C₄²×C₇₃	C₂×D₄	1	2	yes	—
161	C₄²×C₇₃	C₂×D₄	1	2	yes	—
162	C₂³×C₇₃	—	2	2	no	—
163	C₂³×C₇₃	—	2	2	no	—
164	C₂³×C₇₃	—	2	2	no	—
165	C₂³×C₇₃	—	2	2	no	—
166	C₂³×C₇₃	—	2	2	no	—
167	C₂³×C₇₃	—	2	2	no	—
168	C₂³×C₇₃	#137	1	4	yes	—
169	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
170	Q₈×C₇₃	—	2	2	no	—
171	Q₈×C₇₃	—	2	2	no	—
172	Q₈×C₇₃	—	4	2	no	—
173	Q₈×C₇₃	—	8	4	no	—
174	D₄×C₇₃	—	2	8	no	—
175	C₂×C₄×C₇₃	—	2	2	no	—
176	C₂×C₄×C₇₃	—	2	1	no	—
177	C₂×C₄×C₇₃	—	2	1	no	—
178	C₂×C₄×C₇₃	—	2	2	no	—
179	C₂×C₄×C₇₃	—	2	2	no	—
180	C₂×C₄×C₇₃	—	2	2	no	—
181	C₂×C₄×C₇₃	—	2	4	no	—
182	C₂×C₄×C₇₃	—	2	2	no	—
183	C₂×C₄×C₇₃	—	2	2	no	—
184	C₂×C₄×C₇₃	—	4	2	no	—
185	C₂×C₄×C₇₃	—	4	1	no	—
186	C₂×C₄×C₇₃	—	4	2	no	—
187	C₂×C₄×C₇₃	—	4	1	no	—
188	C₂×C₄×C₇₃	—	4	2	no	—
189	C₂×C₄×C₇₃	—	4	2	no	—
190	C₂×C₄×C₇₃	—	4	2	no	—
191	C₂×C₄×C₇₃	—	4	2	no	—
192	C₂×C₄×C₇₃	—	4	2	no	—
193	C₂×C₄×C₇₃	—	4	1	no	—
194	C₂×C₄×C₇₃	—	4	1	no	—
195	C₂×C₄×C₇₃	—	4	2	no	—
196	C₂×C₄×C₇₃	—	4	2	no	—
197	C₂×C₄×C₇₃	—	4	2	no	—
198	C₂×C₄×C₇₃	—	4	2	no	—
199	C₂×C₄×C₇₃	—	4	1	no	—
200	C₂×C₄×C₇₃	—	4	1	no	—
201	C₂×C₄×C₇₃	—	8	8	no	—
202	C₂×C₄×C₇₃	#120	1	2	yes	—
203	C₂×C₄×C₇₃	#120	1	2	yes	—
204	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
205	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
206	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
207	C₂×C₄×C₇₃	2₋¹⁺⁴	1	2	yes	—
208	C₈×C₇₃	—	2	4	no	—
209	C₈×C₇₃	—	4	1	no	—
210	C₈×C₇₃	—	4	1	no	—
211	C₂²×C₇₃	—	2	4	no	—
212	C₂²×C₇₃	—	2	4	no	—
213	C₂²×C₇₃	—	2	4	no	—
214	C₂²×C₇₃	—	4	2	no	—
215	C₂²×C₇₃	—	4	2	no	—
216	C₂²×C₇₃	—	4	2	no	—
217	C₂²×C₇₃	—	4	2	no	—
218	C₂²×C₇₃	C₂×#120	1	1	yes	characteristic
219	C₂²×C₇₃	#547	1	2	yes	—
220	C₂²×C₇₃	C₂×#137	1	2	yes	—
221	C₂²×C₇₃	#576	1	1	yes	characteristic
222	C₂²×C₇₃	#577	1	1	yes	characteristic
223	C₄×C₇₃	—	2	2	no	—
224	C₄×C₇₃	—	2	2	no	—
225	C₄×C₇₃	—	4	2	no	—
226	C₄×C₇₃	—	4	2	no	—
227	C₄×C₇₃	—	4	2	no	—
228	C₄×C₇₃	—	4	4	no	—
229	C₄×C₇₃	—	8	2	no	—
230	C₄×C₇₃	—	8	1	no	—
231	C₄×C₇₃	—	8	1	no	—
232	C₄×C₇₃	#532	1	1	yes	characteristic
233	C₄×C₇₃	#536	1	1	yes	characteristic
234	C₄×C₇₃	#548	1	2	yes	—
235	#25712	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
236	C₂×C₇₃	—	4	4	no	—
237	C₂×C₇₃	#2432	1	1	yes	characteristic
238	C₂×C₇₃	#3004	1	1	yes	characteristic
239	C₂×C₇₃	#3012	1	1	yes	characteristic
240	C₂×C₇₃	#3344	1	2	yes	—
241	C₂×C₇₃	#3346	1	2	yes	—
242	C₂×#554	C₂×C₇₃	1	1	yes	characteristic
243	C₂×#501	C₂×C₇₃	1	1	yes	characteristic, complemented
244	C₂×#479	C₂×C₇₃	1	1	yes	characteristic, complemented
245	#2562	C₂×C₇₃	1	1	yes	characteristic
246	#2036	C₂×C₇₃	1	2	yes	complemented
247	#2035	C₂×C₇₃	1	2	yes	complemented
248	#1988	C₂×C₇₃	1	1	yes	characteristic, complemented
249	#1955	C₂×C₇₃	1	1	yes	characteristic
250	#1853	C₂×C₇₃	1	2	yes	complemented
251	#1852	C₂×C₇₃	1	2	yes	complemented
252	#1763	C₂×C₇₃	1	1	yes	characteristic, complemented
253	C₇₃	#25712	1	1	yes	characteristic, direct product factor, Sylow
254	#554	—	2	4	no	—
255	#554	—	2	4	no	—
256	C₂×C₄⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
257	C₂×#125	—	2	1	no	—
258	C₂×#125	C₂²×C₇₃	1	1	yes	characteristic
259	C₂×C₂²⋊Q₈	—	2	2	no	—
260	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	2	yes	—
261	C₂×C₄×Q₈	C₂²×C₇₃	1	1	yes	characteristic
262	C₂×C₄×D₄	—	2	1	no	—
263	C₂×C₄×D₄	C₂²×C₇₃	1	1	yes	characteristic
264	C₂²×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
265	#501	—	2	4	no	—
266	#479	—	2	4	no	—
267	C₂×#107	C₂²×C₇₃	1	1	yes	characteristic
268	C₂×#107	C₂²×C₇₃	1	2	yes	—
269	C₂×#106	C₂²×C₇₃	1	1	yes	characteristic
270	C₂×#106	C₂²×C₇₃	1	2	yes	—
271	C₂×C₄⋊C₈	C₂²×C₇₃	1	1	yes	characteristic
272	C₂×#103	C₂²×C₇₃	1	1	yes	characteristic
273	C₂×#103	C₂²×C₇₃	1	1	yes	characteristic
274	C₂×#103	C₂²×C₇₃	1	2	yes	—
275	C₂×C₂²⋊C₈	C₂²×C₇₃	1	2	yes	—
276	C₂×C₂²⋊C₈	C₂²×C₇₃	1	2	yes	—
277	C₂×#97	C₂²×C₇₃	1	1	yes	characteristic
278	#400	—	2	1	no	—
279	#394	—	2	1	no	—
280	#388	—	2	2	no	—
281	#380	C₂²×C₇₃	1	2	yes	—
282	#380	C₂²×C₇₃	1	2	yes	—
283	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
284	#340	C₂²×C₇₃	1	2	yes	—
285	#340	C₂²×C₇₃	1	2	yes	—
286	#340	C₂²×C₇₃	1	2	yes	—
287	C₂²×Q₈	—	2	1	no	—
288	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
289	C₂²×D₄	D₄×C₇₃	1	1	yes	characteristic
290	C₂³×C₄	—	2	2	no	—
291	C₂³×C₄	C₂³×C₇₃	1	2	yes	—
292	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
293	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
294	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
295	C₄⋊Q₈	—	2	2	no	—
296	C₄⋊Q₈	D₄×C₇₃	1	4	yes	—
297	#125	—	2	8	no	—
298	#125	—	2	2	no	—
299	#125	—	2	2	no	—
300	C₂²⋊Q₈	—	2	16	no	—
301	C₂²⋊Q₈	—	2	4	no	—
302	C₂²⋊Q₈	—	2	4	no	—
303	C₄×Q₈	—	2	2	no	—
304	C₄×Q₈	D₄×C₇₃	1	4	yes	—
305	C₄×D₄	—	2	8	no	—
306	C₄×D₄	—	2	2	no	—
307	C₄×D₄	—	2	2	no	—
308	C₂×C₄⋊C₄	—	2	2	no	—
309	C₂×C₄⋊C₄	—	2	1	no	—
310	C₂×C₄⋊C₄	—	2	1	no	—
311	C₂×C₄⋊C₄	—	2	2	no	—
312	C₂×C₄⋊C₄	—	2	4	no	—
313	C₂×C₄⋊C₄	—	2	4	no	—
314	C₂×C₄⋊C₄	—	2	1	no	—
315	C₂×C₄⋊C₄	—	2	1	no	—
316	C₂×C₄⋊C₄	D₄×C₇₃	1	1	yes	characteristic
317	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
318	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
319	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
320	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
321	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
322	C₂×C₂²⋊C₄	—	2	2	no	—
323	C₂×C₂²⋊C₄	—	2	2	no	—
324	C₂×C₂²⋊C₄	—	2	2	no	—
325	C₂×C₂²⋊C₄	D₄×C₇₃	1	2	yes	—
326	C₂×C₄²	—	2	1	no	—
327	C₂×C₄²	—	2	1	no	—
328	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
329	#107	—	2	2	no	—
330	#107	—	2	4	no	—
331	#106	—	2	2	no	—
332	#106	—	2	4	no	—
333	C₄⋊C₈	—	2	2	no	—
334	#103	—	2	2	no	—
335	#103	—	2	2	no	—
336	#103	—	2	4	no	—
337	C₂²⋊C₈	—	2	4	no	—
338	C₂²⋊C₈	—	2	4	no	—
339	#97	—	2	2	no	—
340	#95	—	2	1	no	—
341	#95	—	2	2	no	—
342	#95	—	2	2	no	—
343	C₂⁴	C₂×D₄×C₇₃	1	2	yes	—
344	C₂×Q₈	—	2	4	no	—
345	C₂×Q₈	—	2	1	no	—
346	C₂×Q₈	—	2	2	no	—
347	C₂×Q₈	—	2	2	no	—
348	C₂×Q₈	—	8	1	no	—
349	C₂×Q₈	—	8	1	no	—
350	C₂×Q₈	C₂×D₄×C₇₃	1	2	yes	—
351	C₂×D₄	—	2	4	no	—
352	C₂×D₄	—	2	2	no	—
353	C₂²×C₄	—	2	1	no	—
354	C₂²×C₄	—	2	1	no	—
355	C₂²×C₄	—	2	2	no	—
356	C₂²×C₄	—	2	8	no	—
357	C₂²×C₄	—	2	2	no	—
358	C₂²×C₄	—	2	2	no	—
359	C₂²×C₄	—	2	2	no	—
360	C₂²×C₄	—	2	2	no	—
361	C₂²×C₄	—	2	2	no	—
362	C₂²×C₄	—	2	2	no	—
363	C₂²×C₄	—	2	2	no	—
364	C₂²×C₄	—	2	1	no	—
365	C₂²×C₄	—	2	1	no	—
366	C₂²×C₄	—	8	2	no	—
367	C₂²×C₄	—	8	2	no	—
368	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
369	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
370	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
371	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
372	C₂×C₈	—	2	2	no	—
373	C₂×C₈	—	2	2	no	—
374	C₂×C₈	—	2	1	no	—
375	C₂×C₈	—	2	1	no	—
376	C₂×C₈	—	2	2	no	—
377	C₂×C₈	—	2	2	no	—
378	C₂×C₈	#41×C₇₃	1	4	yes	—
379	C₄⋊C₄	—	2	8	no	—
380	C₄⋊C₄	—	2	8	no	—
381	C₄⋊C₄	—	2	4	no	—
382	C₄⋊C₄	—	2	4	no	—
383	C₄⋊C₄	—	2	2	no	—
384	C₄⋊C₄	—	2	1	no	—
385	C₄⋊C₄	—	2	2	no	—
386	C₄⋊C₄	—	2	1	no	—
387	C₄⋊C₄	—	2	1	no	—
388	C₄⋊C₄	—	2	1	no	—
389	C₄⋊C₄	—	2	1	no	—
390	C₄⋊C₄	—	2	2	no	—
391	C₄⋊C₄	—	2	2	no	—
392	C₄⋊C₄	—	4	2	no	—
393	C₄⋊C₄	—	4	2	no	—
394	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
395	C₄⋊C₄	C₂×D₄×C₇₃	1	4	yes	—
396	C₂²⋊C₄	—	2	8	no	—
397	C₂²⋊C₄	—	2	4	no	—
398	C₂²⋊C₄	—	4	4	no	—
399	C₂²⋊C₄	—	8	2	no	—
400	C₄²	—	2	4	no	—
401	C₄²	—	8	1	no	—
402	C₄²	C₂×D₄×C₇₃	1	2	yes	—
403	C₄²	C₂×D₄×C₇₃	1	2	yes	—
404	C₂³	—	2	2	no	—
405	C₂³	—	2	2	no	—
406	C₂³	—	2	2	no	—
407	C₂³	—	2	2	no	—
408	C₂³	—	2	2	no	—
409	C₂³	—	2	2	no	—
410	C₂³	#137×C₇₃	1	4	yes	—
411	C₂³	C₂²×D₄×C₇₃	1	1	yes	characteristic
412	Q₈	—	2	2	no	—
413	Q₈	—	2	2	no	—
414	Q₈	—	4	2	no	—
415	Q₈	—	8	4	no	—
416	D₄	—	2	8	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	2	4	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	4	2	no	—
427	C₂×C₄	—	4	1	no	—
428	C₂×C₄	—	4	2	no	—
429	C₂×C₄	—	4	1	no	—
430	C₂×C₄	—	4	2	no	—
431	C₂×C₄	—	4	2	no	—
432	C₂×C₄	—	4	2	no	—
433	C₂×C₄	—	4	2	no	—
434	C₂×C₄	—	4	2	no	—
435	C₂×C₄	—	4	1	no	—
436	C₂×C₄	—	4	1	no	—
437	C₂×C₄	—	4	2	no	—
438	C₂×C₄	—	4	2	no	—
439	C₂×C₄	—	4	2	no	—
440	C₂×C₄	—	4	2	no	—
441	C₂×C₄	—	4	1	no	—
442	C₂×C₄	—	4	1	no	—
443	C₂×C₄	—	8	8	no	—
444	C₂×C₄	#120×C₇₃	1	2	yes	—
445	C₂×C₄	#120×C₇₃	1	2	yes	—
446	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
447	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
448	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
449	C₂×C₄	2₋¹⁺⁴×C₇₃	1	2	yes	—
450	C₈	—	2	4	no	—
451	C₈	—	4	1	no	—
452	C₈	—	4	1	no	—
453	C₂²	—	2	4	no	—
454	C₂²	—	2	4	no	—
455	C₂²	—	2	4	no	—
456	C₂²	—	4	2	no	—
457	C₂²	—	4	2	no	—
458	C₂²	—	4	2	no	—
459	C₂²	—	4	2	no	—
460	C₂²	C₂×#120×C₇₃	1	1	yes	characteristic
461	C₂²	#547×C₇₃	1	2	yes	—
462	C₂²	C₂×#137×C₇₃	1	2	yes	—
463	C₂²	#576×C₇₃	1	1	yes	characteristic
464	C₂²	#577×C₇₃	1	1	yes	characteristic
465	C₄	—	2	2	no	—
466	C₄	—	2	2	no	—
467	C₄	—	4	2	no	—
468	C₄	—	4	4	no	—
469	C₄	—	4	2	no	—
470	C₄	—	4	2	no	—
471	C₄	—	8	1	no	—
472	C₄	—	8	1	no	—
473	C₄	—	8	2	no	—
474	C₄	#532×C₇₃	1	1	yes	characteristic
475	C₄	#536×C₇₃	1	1	yes	characteristic
476	C₄	#548×C₇₃	1	2	yes	—
477	C₂	—	4	4	no	—
478	C₂	C₇₃×#2432	1	1	yes	characteristic
479	C₂	C₇₃×#3004	1	1	yes	characteristic
480	C₂	C₇₃×#3012	1	1	yes	characteristic
481	C₂	C₇₃×#3344	1	2	yes	—
482	C₂	C₇₃×#3346	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₇₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₃
prime radical	C₂²×D₄×C₇₃	D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇₃ ◁ C₂×C₄×D₄×C₇₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#501×C₇₃	C₂	semidirect
3. C₂×#479×C₇₃	C₂	semidirect
5. C₇₃×#2036	C₂	semidirect
6. C₇₃×#2035	C₂	semidirect
7. C₇₃×#1988	C₂	semidirect
9. C₇₃×#1853	C₂	semidirect
10. C₇₃×#1852	C₂	semidirect
11. C₇₃×#1763	C₂	semidirect
235. #25712	C₇₃	direct (N × H)
243. C₂×#501	C₂×C₇₃	semidirect
244. C₂×#479	C₂×C₇₃	semidirect
246. #2036	C₂×C₇₃	semidirect
247. #2035	C₂×C₇₃	semidirect
248. #1988	C₂×C₇₃	semidirect
250. #1853	C₂×C₇₃	semidirect
251. #1852	C₂×C₇₃	semidirect
252. #1763	C₂×C₇₃	semidirect
253. C₇₃	#25712	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×#554×C₇₃	2
C₂×#501×C₇₃	2
C₂×#479×C₇₃	2
C₇₃×#2562	2
C₇₃×#2036	2
C₇₃×#2035	2
C₇₃×#1988	2
C₇₃×#1955	2
C₇₃×#1853	2
C₇₃×#1852	2
C₇₃×#1763	2
#25712	73

Subgroups — C73×#25712 #32935116

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#25712 #32935116