Subgroups — C₇₃×#25683 #32935087

Order 18688.

960 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#541×C₇₃	C₂	1	1	yes	maximal, characteristic
2	C₂×#499×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#491×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₃×#2629	C₂	1	1	yes	maximal, characteristic
5	C₇₃×#2036	C₂	1	2	yes	maximal
6	C₇₃×#2035	C₂	1	2	yes	maximal
7	C₇₃×#1992	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇₃×#1956	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇₃×#1865	C₂	1	2	yes	maximal, complemented
10	C₇₃×#1863	C₂	1	2	yes	maximal, complemented
11	C₇₃×#1750	C₂	1	1	yes	maximal, characteristic
12	#541×C₇₃	—	2	4	no	—
13	#541×C₇₃	—	2	4	no	—
14	C₂×C₄⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
15	C₂×#126×C₇₃	—	2	2	no	—
16	C₂×#125×C₇₃	—	2	2	no	—
17	C₂×#125×C₇₃	C₂²	1	1	yes	characteristic
18	C₂×#125×C₇₃	C₂²	1	1	yes	characteristic
19	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	2	yes	—
20	C₂×C₄×Q₈×C₇₃	C₂²	1	2	yes	—
21	C₂×#117×C₇₃	C₂²	1	1	yes	characteristic
22	#499×C₇₃	—	2	4	no	—
23	#491×C₇₃	—	2	4	no	—
24	C₂×#107×C₇₃	C₂²	1	2	yes	—
25	C₂×#106×C₇₃	C₂²	1	2	yes	—
26	C₂×#103×C₇₃	C₂²	1	2	yes	—
27	C₂×#103×C₇₃	C₂²	1	2	yes	—
28	C₂×#103×C₇₃	C₂²	1	2	yes	—
29	C₂×#103×C₇₃	C₂²	1	2	yes	—
30	C₂×C₂²⋊C₈×C₇₃	C₂²	1	1	yes	characteristic
31	C₂×C₂²⋊C₈×C₇₃	C₂²	1	1	yes	characteristic
32	C₂×#97×C₇₃	C₂²	1	1	yes	characteristic
33	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
34	#398×C₇₃	—	2	2	no	—
35	#396×C₇₃	—	2	2	no	—
36	#389×C₇₃	C₂²	1	2	yes	—
37	#384×C₇₃	C₂²	1	1	yes	characteristic
38	#380×C₇₃	C₂²	1	2	yes	—
39	#340×C₇₃	C₂²	1	2	yes	—
40	#340×C₇₃	C₂²	1	2	yes	—
41	#336×C₇₃	C₂²	1	1	yes	characteristic
42	#336×C₇₃	C₂²	1	1	yes	characteristic
43	C₂²×Q₈×C₇₃	C₂³	1	2	yes	—
44	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
45	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
46	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
47	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
48	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
49	C₄⋊Q₈×C₇₃	—	2	2	no	—
50	C₄⋊Q₈×C₇₃	D₄	1	4	yes	—
51	#126×C₇₃	—	2	16	no	—
52	#125×C₇₃	—	2	16	no	—
53	#125×C₇₃	—	2	2	no	—
54	#125×C₇₃	—	2	2	no	—
55	#125×C₇₃	—	2	2	no	—
56	#125×C₇₃	D₄	1	4	yes	—
57	C₂²⋊Q₈×C₇₃	—	2	4	no	—
58	C₂²⋊Q₈×C₇₃	—	2	4	no	—
59	C₄×Q₈×C₇₃	—	2	4	no	—
60	C₄×Q₈×C₇₃	—	2	4	no	—
61	#117×C₇₃	—	2	2	no	—
62	#117×C₇₃	—	2	2	no	—
63	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
64	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
65	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
66	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
67	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
68	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
69	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
70	C₂×C₄⋊C₄×C₇₃	D₄	1	2	yes	—
71	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
72	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
73	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
74	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
75	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
76	C₂×C₂²⋊C₄×C₇₃	D₄	1	2	yes	—
77	C₂×C₄²×C₇₃	—	2	2	no	—
78	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
79	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
80	#107×C₇₃	—	2	4	no	—
81	#106×C₇₃	—	2	4	no	—
82	#103×C₇₃	—	2	4	no	—
83	#103×C₇₃	—	2	4	no	—
84	#103×C₇₃	—	2	4	no	—
85	#103×C₇₃	—	2	4	no	—
86	C₂²⋊C₈×C₇₃	—	2	2	no	—
87	C₂²⋊C₈×C₇₃	—	2	2	no	—
88	#97×C₇₃	—	2	2	no	—
89	C₄×C₈×C₇₃	—	2	2	no	—
90	#95×C₇₃	—	2	2	no	—
91	#95×C₇₃	—	2	2	no	—
92	C₂⁴×C₇₃	C₂×D₄	1	1	yes	characteristic
93	C₂×Q₈×C₇₃	—	2	2	no	—
94	C₂×Q₈×C₇₃	—	2	2	no	—
95	C₂×Q₈×C₇₃	—	2	2	no	—
96	C₂×Q₈×C₇₃	—	2	2	no	—
97	C₂×Q₈×C₇₃	—	2	2	no	—
98	C₂×Q₈×C₇₃	C₂×D₄	1	4	yes	—
99	C₂²×C₄×C₇₃	—	2	2	no	—
100	C₂²×C₄×C₇₃	—	2	2	no	—
101	C₂²×C₄×C₇₃	—	2	1	no	—
102	C₂²×C₄×C₇₃	—	2	1	no	—
103	C₂²×C₄×C₇₃	—	2	1	no	—
104	C₂²×C₄×C₇₃	—	2	1	no	—
105	C₂²×C₄×C₇₃	—	2	1	no	—
106	C₂²×C₄×C₇₃	—	2	1	no	—
107	C₂²×C₄×C₇₃	—	2	2	no	—
108	C₂²×C₄×C₇₃	—	2	2	no	—
109	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
111	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
112	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
113	C₂×C₈×C₇₃	—	2	1	no	—
114	C₂×C₈×C₇₃	—	2	1	no	—
115	C₂×C₈×C₇₃	—	2	1	no	—
116	C₂×C₈×C₇₃	—	2	1	no	—
117	C₂×C₈×C₇₃	—	2	1	no	—
118	C₂×C₈×C₇₃	—	2	1	no	—
119	C₂×C₈×C₇₃	—	2	1	no	—
120	C₂×C₈×C₇₃	—	2	1	no	—
121	C₂×C₈×C₇₃	—	2	1	no	—
122	C₂×C₈×C₇₃	—	2	1	no	—
123	C₂×C₈×C₇₃	#41	1	2	yes	—
124	C₂×C₈×C₇₃	#41	1	2	yes	—
125	C₄⋊C₄×C₇₃	—	2	8	no	—
126	C₄⋊C₄×C₇₃	—	2	8	no	—
127	C₄⋊C₄×C₇₃	—	2	8	no	—
128	C₄⋊C₄×C₇₃	—	2	8	no	—
129	C₄⋊C₄×C₇₃	—	2	4	no	—
130	C₄⋊C₄×C₇₃	—	2	2	no	—
131	C₄⋊C₄×C₇₃	—	2	2	no	—
132	C₄⋊C₄×C₇₃	—	2	2	no	—
133	C₄⋊C₄×C₇₃	—	2	2	no	—
134	C₄⋊C₄×C₇₃	—	2	2	no	—
135	C₄⋊C₄×C₇₃	—	4	4	no	—
136	C₄⋊C₄×C₇₃	—	8	2	no	—
137	C₄⋊C₄×C₇₃	—	8	2	no	—
138	C₄⋊C₄×C₇₃	C₂×D₄	1	4	yes	—
139	C₂²⋊C₄×C₇₃	—	2	8	no	—
140	C₂²⋊C₄×C₇₃	—	2	4	no	—
141	C₂²⋊C₄×C₇₃	—	8	2	no	—
142	C₄²×C₇₃	—	2	8	no	—
143	C₄²×C₇₃	—	2	1	no	—
144	C₄²×C₇₃	—	2	1	no	—
145	C₄²×C₇₃	C₂×D₄	1	2	yes	—
146	C₄²×C₇₃	C₂×D₄	1	2	yes	—
147	C₂³×C₇₃	—	2	1	no	—
148	C₂³×C₇₃	—	2	1	no	—
149	C₂³×C₇₃	—	2	1	no	—
150	C₂³×C₇₃	—	2	2	no	—
151	C₂³×C₇₃	—	2	2	no	—
152	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
153	Q₈×C₇₃	—	2	4	no	—
154	Q₈×C₇₃	—	2	4	no	—
155	Q₈×C₇₃	—	4	2	no	—
156	Q₈×C₇₃	—	4	2	no	—
157	C₂×C₄×C₇₃	—	2	2	no	—
158	C₂×C₄×C₇₃	—	2	2	no	—
159	C₂×C₄×C₇₃	—	2	2	no	—
160	C₂×C₄×C₇₃	—	2	4	no	—
161	C₂×C₄×C₇₃	—	2	4	no	—
162	C₂×C₄×C₇₃	—	2	1	no	—
163	C₂×C₄×C₇₃	—	2	1	no	—
164	C₂×C₄×C₇₃	—	2	1	no	—
165	C₂×C₄×C₇₃	—	2	2	no	—
166	C₂×C₄×C₇₃	—	2	2	no	—
167	C₂×C₄×C₇₃	—	4	2	no	—
168	C₂×C₄×C₇₃	—	4	2	no	—
169	C₂×C₄×C₇₃	—	4	2	no	—
170	C₂×C₄×C₇₃	—	4	2	no	—
171	C₂×C₄×C₇₃	—	4	1	no	—
172	C₂×C₄×C₇₃	—	4	1	no	—
173	C₂×C₄×C₇₃	—	4	1	no	—
174	C₂×C₄×C₇₃	—	4	1	no	—
175	C₂×C₄×C₇₃	—	4	2	no	—
176	C₂×C₄×C₇₃	—	4	2	no	—
177	C₂×C₄×C₇₃	—	4	2	no	—
178	C₂×C₄×C₇₃	—	4	2	no	—
179	C₂×C₄×C₇₃	—	4	2	no	—
180	C₂×C₄×C₇₃	—	4	2	no	—
181	C₂×C₄×C₇₃	#120	1	4	yes	—
182	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
183	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
184	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
185	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
186	C₂×C₄×C₇₃	2₋¹⁺⁴	1	1	yes	characteristic
187	C₂×C₄×C₇₃	2₋¹⁺⁴	1	1	yes	characteristic
188	C₈×C₇₃	—	2	2	no	—
189	C₈×C₇₃	—	2	2	no	—
190	C₈×C₇₃	—	4	1	no	—
191	C₈×C₇₃	—	4	1	no	—
192	C₂²×C₇₃	—	4	1	no	—
193	C₂²×C₇₃	—	4	1	no	—
194	C₂²×C₇₃	—	4	1	no	—
195	C₂²×C₇₃	—	4	2	no	—
196	C₂²×C₇₃	—	4	2	no	—
197	C₂²×C₇₃	C₂×#120	1	1	yes	characteristic
198	C₂²×C₇₃	#532	1	1	yes	characteristic
199	C₂²×C₇₃	#536	1	1	yes	characteristic
200	C₂²×C₇₃	#577	1	2	yes	—
201	C₂²×C₇₃	#578	1	2	yes	—
202	C₄×C₇₃	—	2	4	no	—
203	C₄×C₇₃	—	4	1	no	—
204	C₄×C₇₃	—	4	4	no	—
205	C₄×C₇₃	—	4	2	no	—
206	C₄×C₇₃	—	4	4	no	—
207	C₄×C₇₃	—	8	2	no	—
208	C₄×C₇₃	—	8	2	no	—
209	C₄×C₇₃	#547	1	1	yes	characteristic
210	C₄×C₇₃	#547	1	1	yes	characteristic
211	C₄×C₇₃	#548	1	1	yes	characteristic
212	C₄×C₇₃	#548	1	1	yes	characteristic
213	#25683	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
214	C₂×C₇₃	—	8	1	no	—
215	C₂×C₇₃	#2432	1	1	yes	characteristic
216	C₂×C₇₃	#3013	1	2	yes	—
217	C₂×C₇₃	#3174	1	1	yes	characteristic
218	C₂×C₇₃	#3177	1	1	yes	characteristic
219	C₂×C₇₃	#3242	1	2	yes	—
220	C₂×#541	C₂×C₇₃	1	1	yes	characteristic
221	C₂×#499	C₂×C₇₃	1	1	yes	characteristic, complemented
222	C₂×#491	C₂×C₇₃	1	1	yes	characteristic, complemented
223	#2629	C₂×C₇₃	1	1	yes	characteristic
224	#2036	C₂×C₇₃	1	2	yes	—
225	#2035	C₂×C₇₃	1	2	yes	—
226	#1992	C₂×C₇₃	1	1	yes	characteristic, complemented
227	#1956	C₂×C₇₃	1	1	yes	characteristic, complemented
228	#1865	C₂×C₇₃	1	2	yes	complemented
229	#1863	C₂×C₇₃	1	2	yes	complemented
230	#1750	C₂×C₇₃	1	1	yes	characteristic
231	C₇₃	#25683	1	1	yes	characteristic, direct product factor, Sylow
232	#541	—	2	4	no	—
233	#541	—	2	4	no	—
234	C₂×C₄⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
235	C₂×#126	—	2	2	no	—
236	C₂×#125	—	2	2	no	—
237	C₂×#125	C₂²×C₇₃	1	1	yes	characteristic
238	C₂×#125	C₂²×C₇₃	1	1	yes	characteristic
239	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	2	yes	—
240	C₂×C₄×Q₈	C₂²×C₇₃	1	2	yes	—
241	C₂×#117	C₂²×C₇₃	1	1	yes	characteristic
242	#499	—	2	4	no	—
243	#491	—	2	4	no	—
244	C₂×#107	C₂²×C₇₃	1	2	yes	—
245	C₂×#106	C₂²×C₇₃	1	2	yes	—
246	C₂×#103	C₂²×C₇₃	1	2	yes	—
247	C₂×#103	C₂²×C₇₃	1	2	yes	—
248	C₂×#103	C₂²×C₇₃	1	2	yes	—
249	C₂×#103	C₂²×C₇₃	1	2	yes	—
250	C₂×C₂²⋊C₈	C₂²×C₇₃	1	1	yes	characteristic
251	C₂×C₂²⋊C₈	C₂²×C₇₃	1	1	yes	characteristic
252	C₂×#97	C₂²×C₇₃	1	1	yes	characteristic
253	C₂×C₄×C₈	C₂²×C₇₃	1	1	yes	characteristic
254	#398	—	2	2	no	—
255	#396	—	2	2	no	—
256	#389	C₂²×C₇₃	1	2	yes	—
257	#384	C₂²×C₇₃	1	1	yes	characteristic
258	#380	C₂²×C₇₃	1	2	yes	—
259	#340	C₂²×C₇₃	1	2	yes	—
260	#340	C₂²×C₇₃	1	2	yes	—
261	#336	C₂²×C₇₃	1	1	yes	characteristic
262	#336	C₂²×C₇₃	1	1	yes	characteristic
263	C₂²×Q₈	C₂³×C₇₃	1	2	yes	—
264	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
265	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
266	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
267	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
268	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
269	C₄⋊Q₈	—	2	2	no	—
270	C₄⋊Q₈	D₄×C₇₃	1	4	yes	—
271	#126	—	2	16	no	—
272	#125	—	2	16	no	—
273	#125	—	2	2	no	—
274	#125	—	2	2	no	—
275	#125	—	2	2	no	—
276	#125	D₄×C₇₃	1	4	yes	—
277	C₂²⋊Q₈	—	2	4	no	—
278	C₂²⋊Q₈	—	2	4	no	—
279	C₄×Q₈	—	2	4	no	—
280	C₄×Q₈	—	2	4	no	—
281	#117	—	2	2	no	—
282	#117	—	2	2	no	—
283	C₂×C₄⋊C₄	—	2	2	no	—
284	C₂×C₄⋊C₄	—	2	2	no	—
285	C₂×C₄⋊C₄	—	2	2	no	—
286	C₂×C₄⋊C₄	—	2	2	no	—
287	C₂×C₄⋊C₄	—	2	2	no	—
288	C₂×C₄⋊C₄	—	2	2	no	—
289	C₂×C₄⋊C₄	—	2	2	no	—
290	C₂×C₄⋊C₄	D₄×C₇₃	1	2	yes	—
291	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
292	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
293	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
294	C₂×C₂²⋊C₄	—	2	2	no	—
295	C₂×C₂²⋊C₄	—	2	2	no	—
296	C₂×C₂²⋊C₄	D₄×C₇₃	1	2	yes	—
297	C₂×C₄²	—	2	2	no	—
298	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
299	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
300	#107	—	2	4	no	—
301	#106	—	2	4	no	—
302	#103	—	2	4	no	—
303	#103	—	2	4	no	—
304	#103	—	2	4	no	—
305	#103	—	2	4	no	—
306	C₂²⋊C₈	—	2	2	no	—
307	C₂²⋊C₈	—	2	2	no	—
308	#97	—	2	2	no	—
309	C₄×C₈	—	2	2	no	—
310	#95	—	2	2	no	—
311	#95	—	2	2	no	—
312	C₂⁴	C₂×D₄×C₇₃	1	1	yes	characteristic
313	C₂×Q₈	—	2	2	no	—
314	C₂×Q₈	—	2	2	no	—
315	C₂×Q₈	—	2	2	no	—
316	C₂×Q₈	—	2	2	no	—
317	C₂×Q₈	—	2	2	no	—
318	C₂×Q₈	C₂×D₄×C₇₃	1	4	yes	—
319	C₂²×C₄	—	2	2	no	—
320	C₂²×C₄	—	2	2	no	—
321	C₂²×C₄	—	2	1	no	—
322	C₂²×C₄	—	2	1	no	—
323	C₂²×C₄	—	2	1	no	—
324	C₂²×C₄	—	2	1	no	—
325	C₂²×C₄	—	2	1	no	—
326	C₂²×C₄	—	2	1	no	—
327	C₂²×C₄	—	2	2	no	—
328	C₂²×C₄	—	2	2	no	—
329	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
330	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
331	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
332	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
333	C₂×C₈	—	2	1	no	—
334	C₂×C₈	—	2	1	no	—
335	C₂×C₈	—	2	1	no	—
336	C₂×C₈	—	2	1	no	—
337	C₂×C₈	—	2	1	no	—
338	C₂×C₈	—	2	1	no	—
339	C₂×C₈	—	2	1	no	—
340	C₂×C₈	—	2	1	no	—
341	C₂×C₈	—	2	1	no	—
342	C₂×C₈	—	2	1	no	—
343	C₂×C₈	#41×C₇₃	1	2	yes	—
344	C₂×C₈	#41×C₇₃	1	2	yes	—
345	C₄⋊C₄	—	2	8	no	—
346	C₄⋊C₄	—	2	8	no	—
347	C₄⋊C₄	—	2	8	no	—
348	C₄⋊C₄	—	2	8	no	—
349	C₄⋊C₄	—	2	4	no	—
350	C₄⋊C₄	—	2	2	no	—
351	C₄⋊C₄	—	2	2	no	—
352	C₄⋊C₄	—	2	2	no	—
353	C₄⋊C₄	—	2	2	no	—
354	C₄⋊C₄	—	2	2	no	—
355	C₄⋊C₄	—	4	4	no	—
356	C₄⋊C₄	—	8	2	no	—
357	C₄⋊C₄	—	8	2	no	—
358	C₄⋊C₄	C₂×D₄×C₇₃	1	4	yes	—
359	C₂²⋊C₄	—	2	8	no	—
360	C₂²⋊C₄	—	2	4	no	—
361	C₂²⋊C₄	—	8	2	no	—
362	C₄²	—	2	8	no	—
363	C₄²	—	2	1	no	—
364	C₄²	—	2	1	no	—
365	C₄²	C₂×D₄×C₇₃	1	2	yes	—
366	C₄²	C₂×D₄×C₇₃	1	2	yes	—
367	C₂³	—	2	1	no	—
368	C₂³	—	2	1	no	—
369	C₂³	—	2	1	no	—
370	C₂³	—	2	2	no	—
371	C₂³	—	2	2	no	—
372	C₂³	C₂²×D₄×C₇₃	1	1	yes	characteristic
373	Q₈	—	2	4	no	—
374	Q₈	—	2	4	no	—
375	Q₈	—	4	2	no	—
376	Q₈	—	4	2	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	4	no	—
381	C₂×C₄	—	2	4	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	4	2	no	—
388	C₂×C₄	—	4	2	no	—
389	C₂×C₄	—	4	2	no	—
390	C₂×C₄	—	4	2	no	—
391	C₂×C₄	—	4	1	no	—
392	C₂×C₄	—	4	1	no	—
393	C₂×C₄	—	4	1	no	—
394	C₂×C₄	—	4	1	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	4	2	no	—
398	C₂×C₄	—	4	2	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	—	4	2	no	—
401	C₂×C₄	#120×C₇₃	1	4	yes	—
402	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
403	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
404	C₂×C₄	C₂×#41×C₇₃	1	1	yes	characteristic
405	C₂×C₄	C₂×#41×C₇₃	1	1	yes	characteristic
406	C₂×C₄	2₋¹⁺⁴×C₇₃	1	1	yes	characteristic
407	C₂×C₄	2₋¹⁺⁴×C₇₃	1	1	yes	characteristic
408	C₈	—	2	2	no	—
409	C₈	—	2	2	no	—
410	C₈	—	4	1	no	—
411	C₈	—	4	1	no	—
412	C₂²	—	4	2	no	—
413	C₂²	—	4	2	no	—
414	C₂²	—	4	1	no	—
415	C₂²	—	4	1	no	—
416	C₂²	—	4	1	no	—
417	C₂²	C₂×#120×C₇₃	1	1	yes	characteristic
418	C₂²	#532×C₇₃	1	1	yes	characteristic
419	C₂²	#536×C₇₃	1	1	yes	characteristic
420	C₂²	#577×C₇₃	1	2	yes	—
421	C₂²	#578×C₇₃	1	2	yes	—
422	C₄	—	2	4	no	—
423	C₄	—	4	2	no	—
424	C₄	—	4	4	no	—
425	C₄	—	4	1	no	—
426	C₄	—	4	4	no	—
427	C₄	—	8	2	no	—
428	C₄	—	8	2	no	—
429	C₄	#547×C₇₃	1	1	yes	characteristic
430	C₄	#547×C₇₃	1	1	yes	characteristic
431	C₄	#548×C₇₃	1	1	yes	characteristic
432	C₄	#548×C₇₃	1	1	yes	characteristic
433	C₂	—	8	1	no	—
434	C₂	C₇₃×#2432	1	1	yes	characteristic
435	C₂	C₇₃×#3013	1	2	yes	—
436	C₂	C₇₃×#3174	1	1	yes	characteristic
437	C₂	C₇₃×#3177	1	1	yes	characteristic
438	C₂	C₇₃×#3242	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₇₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₃
prime radical	C₂⁴×C₇₃	C₂×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇₃ ◁ C₂×#117×C₇₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#499×C₇₃	C₂	semidirect
3. C₂×#491×C₇₃	C₂	semidirect
7. C₇₃×#1992	C₂	semidirect
8. C₇₃×#1956	C₂	semidirect
9. C₇₃×#1865	C₂	semidirect
10. C₇₃×#1863	C₂	semidirect
213. #25683	C₇₃	direct (N × H)
221. C₂×#499	C₂×C₇₃	semidirect
222. C₂×#491	C₂×C₇₃	semidirect
226. #1992	C₂×C₇₃	semidirect
227. #1956	C₂×C₇₃	semidirect
228. #1865	C₂×C₇₃	semidirect
229. #1863	C₂×C₇₃	semidirect
231. C₇₃	#25683	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×#541×C₇₃	2
C₂×#499×C₇₃	2
C₂×#491×C₇₃	2
C₇₃×#2629	2
C₇₃×#2036	2
C₇₃×#2035	2
C₇₃×#1992	2
C₇₃×#1956	2
C₇₃×#1865	2
C₇₃×#1863	2
C₇₃×#1750	2
#25683	73

Subgroups — C73×#25683 #32935087

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#25683 #32935087