Subgroups — C₇₃×#10747 #32920151

Order 18688.

1214 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₃×#3428	C₂	1	1	yes	maximal, characteristic
2	C₂×#413×C₇₃	C₂	1	1	yes	maximal, characteristic
3	C₂×#408×C₇₃	C₂	1	1	yes	maximal, characteristic
4	C₇₃×#1742	C₂	1	2	yes	maximal, complemented
5	C₇₃×#1729	C₂	1	2	yes	maximal, complemented
6	C₂²×#41×C₇₃	C₂²	1	1	yes	characteristic
7	C₂²×M₁₆×C₇₃	C₂²	1	2	yes	—
8	C₂²×M₁₆×C₇₃	C₂²	1	1	yes	characteristic
9	C₂³×C₈×C₇₃	C₂²	1	1	yes	characteristic
10	#520×C₇₃	—	2	4	no	—
11	#519×C₇₃	—	2	1	no	—
12	#518×C₇₃	—	2	1	no	—
13	#518×C₇₃	C₄	1	4	yes	—
14	C₄×#41×C₇₃	—	2	4	no	—
15	C₂×#117×C₇₃	—	2	2	no	—
16	C₂×#117×C₇₃	C₂²	1	2	yes	—
17	#413×C₇₃	—	2	2	no	—
18	#413×C₇₃	C₄	1	4	yes	complemented
19	C₂×#101×C₇₃	—	2	1	no	—
20	C₂×#100×C₇₃	—	2	1	no	—
21	#408×C₇₃	—	2	2	no	—
22	#408×C₇₃	C₄	1	4	yes	complemented
23	C₂×C₂²⋊C₈×C₇₃	—	2	2	no	—
24	#343×C₇₃	—	2	4	no	—
25	#336×C₇₃	—	2	4	no	—
26	C₂×#41×C₇₃	—	2	2	no	—
27	C₂×#41×C₇₃	—	2	2	no	—
28	C₂×#41×C₇₃	—	2	2	no	—
29	C₂×#41×C₇₃	—	2	2	no	—
30	C₂×#41×C₇₃	C₂×C₄	1	2	yes	—
31	C₂×#41×C₇₃	C₂×C₄	1	2	yes	—
32	C₂×#41×C₇₃	D₄	1	2	yes	—
33	C₂×#41×C₇₃	Q₈	1	2	yes	—
34	C₂²×Q₈×C₇₃	D₄	1	1	yes	characteristic
35	C₂²×D₄×C₇₃	C₂×C₄	1	2	yes	—
36	C₂²×D₄×C₇₃	D₄	1	1	yes	characteristic
37	C₂³×C₄×C₇₃	D₄	1	2	yes	—
38	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
39	C₂×M₁₆×C₇₃	—	2	1	no	—
40	C₂×M₁₆×C₇₃	—	2	2	no	—
41	C₂×M₁₆×C₇₃	—	2	2	no	—
42	C₂×M₁₆×C₇₃	—	2	2	no	—
43	C₂×M₁₆×C₇₃	—	2	2	no	—
44	C₂×M₁₆×C₇₃	—	2	2	no	—
45	C₂×M₁₆×C₇₃	—	2	2	no	—
46	C₂×M₁₆×C₇₃	—	2	2	no	—
47	C₂×M₁₆×C₇₃	C₂×C₄	1	2	yes	complemented
48	C₂×M₁₆×C₇₃	C₂×C₄	1	4	yes	complemented
49	C₂²×C₈×C₇₃	—	2	1	no	—
50	C₂²×C₈×C₇₃	—	2	1	no	—
51	C₂²×C₈×C₇₃	—	2	1	no	—
52	C₂²×C₈×C₇₃	—	2	2	no	—
53	C₂²×C₈×C₇₃	—	2	2	no	—
54	C₂²×C₈×C₇₃	—	2	2	no	—
55	C₂²×C₈×C₇₃	C₂×C₄	1	2	yes	complemented
56	C₄×Q₈×C₇₃	—	2	8	no	—
57	C₄×D₄×C₇₃	—	2	8	no	—
58	C₄×D₄×C₇₃	—	2	16	no	—
59	#117×C₇₃	—	2	4	no	—
60	#117×C₇₃	—	2	4	no	—
61	#117×C₇₃	—	2	4	no	—
62	#117×C₇₃	—	2	2	no	—
63	#117×C₇₃	—	2	2	no	—
64	#117×C₇₃	—	2	2	no	—
65	#117×C₇₃	—	2	2	no	—
66	C₂×C₄⋊C₄×C₇₃	—	2	4	no	—
67	C₂×C₄⋊C₄×C₇₃	D₄	1	4	yes	—
68	C₂×C₂²⋊C₄×C₇₃	—	2	4	no	—
69	C₂×C₂²⋊C₄×C₇₃	C₂×C₄	1	4	yes	—
70	C₂×C₄²×C₇₃	—	2	4	no	—
71	C₂×C₄²×C₇₃	D₄	1	4	yes	—
72	#101×C₇₃	—	2	4	no	—
73	#100×C₇₃	—	2	4	no	—
74	C₂²⋊C₈×C₇₃	—	2	8	no	—
75	C₂⁴×C₇₃	C₂²⋊C₄	1	2	yes	—
76	C₂⁴×C₇₃	C₂²×C₄	1	1	yes	characteristic
77	#41×C₇₃	—	2	4	no	—
78	#41×C₇₃	—	2	4	no	—
79	#41×C₇₃	—	2	4	no	—
80	#41×C₇₃	—	2	4	no	—
81	#41×C₇₃	—	2	4	no	—
82	#41×C₇₃	—	2	4	no	—
83	#41×C₇₃	—	2	4	no	—
84	#41×C₇₃	—	2	4	no	—
85	C₂×Q₈×C₇₃	—	2	2	no	—
86	C₂×Q₈×C₇₃	—	2	2	no	—
87	C₂×Q₈×C₇₃	C₂²⋊C₄	1	2	yes	—
88	C₂×Q₈×C₇₃	C₄⋊C₄	1	2	yes	—
89	C₂×D₄×C₇₃	—	2	4	no	—
90	C₂×D₄×C₇₃	—	2	4	no	—
91	C₂×D₄×C₇₃	—	2	2	no	—
92	C₂×D₄×C₇₃	—	2	2	no	—
93	C₂×D₄×C₇₃	C₄²	1	4	yes	—
94	C₂×D₄×C₇₃	C₂²⋊C₄	1	2	yes	—
95	C₂×D₄×C₇₃	C₄⋊C₄	1	4	yes	—
96	C₂×D₄×C₇₃	C₄⋊C₄	1	2	yes	—
97	C₂²×C₄×C₇₃	—	2	2	no	—
98	C₂²×C₄×C₇₃	—	2	2	no	—
99	C₂²×C₄×C₇₃	—	2	2	no	—
100	C₂²×C₄×C₇₃	—	2	2	no	—
101	C₂²×C₄×C₇₃	—	2	8	no	—
102	C₂²×C₄×C₇₃	C₂²⋊C₄	1	2	yes	—
103	C₂²×C₄×C₇₃	C₂²⋊C₄	1	4	yes	—
104	C₂²×C₄×C₇₃	C₂²⋊C₄	1	8	yes	—
105	C₂²×C₄×C₇₃	C₄⋊C₄	1	4	yes	—
106	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
107	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
108	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
112	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
113	C₂²×C₄×C₇₃	C₂×Q₈	1	1	yes	characteristic
114	C₂²×C₄×C₇₃	#41	1	2	yes	—
115	C₂²×C₄×C₇₃	#41	1	2	yes	—
116	M₁₆×C₇₃	—	2	4	no	—
117	M₁₆×C₇₃	—	2	4	no	—
118	M₁₆×C₇₃	—	2	4	no	—
119	M₁₆×C₇₃	—	4	2	no	—
120	M₁₆×C₇₃	—	4	2	no	—
121	M₁₆×C₇₃	—	4	2	no	—
122	C₂×C₈×C₇₃	—	2	2	no	—
123	C₂×C₈×C₇₃	—	2	2	no	—
124	C₂×C₈×C₇₃	—	2	4	no	—
125	C₂×C₈×C₇₃	—	2	4	no	—
126	C₂×C₈×C₇₃	—	4	2	no	—
127	C₂×C₈×C₇₃	—	4	1	no	—
128	C₂×C₈×C₇₃	—	4	1	no	—
129	C₂×C₈×C₇₃	—	4	2	no	—
130	C₂×C₈×C₇₃	—	4	2	no	—
131	C₂×C₈×C₇₃	—	4	1	no	—
132	C₂×C₈×C₇₃	—	4	1	no	—
133	C₄⋊C₄×C₇₃	—	2	8	no	—
134	C₄⋊C₄×C₇₃	—	2	4	no	—
135	C₄⋊C₄×C₇₃	—	2	4	no	—
136	C₂²⋊C₄×C₇₃	—	2	8	no	—
137	C₂²⋊C₄×C₇₃	—	2	4	no	—
138	C₂²⋊C₄×C₇₃	—	2	4	no	—
139	C₄²×C₇₃	—	2	8	no	—
140	C₄²×C₇₃	—	2	4	no	—
141	C₄²×C₇₃	—	2	4	no	—
142	C₂³×C₇₃	—	2	2	no	—
143	C₂³×C₇₃	—	2	2	no	—
144	C₂³×C₇₃	—	4	2	no	—
145	C₂³×C₇₃	—	4	4	no	—
146	C₂³×C₇₃	#95	1	4	yes	—
147	C₂³×C₇₃	C₂×C₄²	1	1	yes	characteristic
148	C₂³×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
149	C₂³×C₇₃	C₂×C₂²⋊C₄	1	2	yes	—
150	C₂³×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
151	C₂³×C₇₃	#117	1	2	yes	—
152	Q₈×C₇₃	—	2	4	no	—
153	Q₈×C₇₃	—	2	4	no	—
154	D₄×C₇₃	—	2	8	no	—
155	D₄×C₇₃	—	2	8	no	—
156	D₄×C₇₃	—	2	4	no	—
157	D₄×C₇₃	—	2	4	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	4	no	—
163	C₂×C₄×C₇₃	—	2	4	no	—
164	C₂×C₄×C₇₃	—	2	8	no	—
165	C₂×C₄×C₇₃	—	4	8	no	—
166	C₂×C₄×C₇₃	—	8	8	no	—
167	C₂×C₄×C₇₃	#95	1	4	yes	—
168	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
169	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
170	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
171	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
172	C₂×C₄×C₇₃	C₄×D₄	1	2	yes	—
173	C₂×C₄×C₇₃	C₄×D₄	1	2	yes	—
174	C₂×C₄×C₇₃	C₄×D₄	1	2	yes	—
175	C₂×C₄×C₇₃	C₄×D₄	1	2	yes	—
176	C₂×C₄×C₇₃	#120	1	2	yes	—
177	C₂×C₄×C₇₃	#120	1	1	yes	characteristic
178	C₂×C₄×C₇₃	#120	1	1	yes	characteristic
179	C₂×C₄×C₇₃	#121	1	2	yes	—
180	C₂×C₄×C₇₃	#121	1	2	yes	—
181	C₂×C₄×C₇₃	C₂²⋊Q₈	1	2	yes	—
182	C₂×C₄×C₇₃	C₂²⋊Q₈	1	2	yes	—
183	C₂×C₄×C₇₃	#123	1	1	yes	characteristic
184	C₂×C₄×C₇₃	#123	1	1	yes	characteristic
185	C₂×C₄×C₇₃	#123	1	2	yes	—
186	C₈×C₇₃	—	4	2	no	—
187	C₈×C₇₃	—	4	2	no	—
188	C₈×C₇₃	—	4	4	no	—
189	C₂²×C₇₃	—	2	4	no	—
190	C₂²×C₇₃	—	2	2	no	—
191	C₂²×C₇₃	—	2	4	no	—
192	C₂²×C₇₃	—	4	1	no	—
193	C₂²×C₇₃	—	4	1	no	—
194	C₂²×C₇₃	—	4	2	no	—
195	C₂²×C₇₃	—	4	4	no	—
196	C₂²×C₇₃	—	4	4	no	—
197	C₂²×C₇₃	—	8	2	no	—
198	C₂²×C₇₃	C₂×#95	1	1	yes	characteristic
199	C₂²×C₇₃	C₄×C₂²⋊C₄	1	2	yes	—
200	C₂²×C₇₃	#379	1	1	yes	characteristic
201	C₂²×C₇₃	#380	1	2	yes	—
202	C₂²×C₇₃	#381	1	1	yes	characteristic
203	C₄×C₇₃	—	2	4	no	—
204	C₄×C₇₃	—	4	8	no	—
205	C₄×C₇₃	#385	1	1	yes	characteristic
206	C₄×C₇₃	#385	1	1	yes	characteristic
207	C₄×C₇₃	#385	1	2	yes	—
208	C₄×C₇₃	#386	1	1	yes	characteristic
209	C₄×C₇₃	#386	1	1	yes	characteristic
210	C₄×C₇₃	#386	1	2	yes	—
211	#10747	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
212	C₂×C₇₃	—	2	1	no	—
213	C₂×C₇₃	—	2	1	no	—
214	C₂×C₇₃	—	2	2	no	—
215	C₂×C₇₃	—	2	2	no	—
216	C₂×C₇₃	—	4	4	no	—
217	C₂×C₇₃	C₂²⋊#95	1	1	yes	characteristic
218	C₂×C₇₃	#1791	1	2	yes	—
219	#3428	C₂×C₇₃	1	1	yes	characteristic
220	C₂×#413	C₂×C₇₃	1	1	yes	characteristic
221	C₂×#408	C₂×C₇₃	1	1	yes	characteristic
222	#1742	C₂×C₇₃	1	2	yes	complemented
223	#1729	C₂×C₇₃	1	2	yes	complemented
224	C₇₃	#10747	1	1	yes	characteristic, direct product factor, Sylow
225	C₂²×#41	C₂²×C₇₃	1	1	yes	characteristic
226	C₂²×M₁₆	C₂²×C₇₃	1	1	yes	characteristic
227	C₂²×M₁₆	C₂²×C₇₃	1	2	yes	—
228	C₂³×C₈	C₂²×C₇₃	1	1	yes	characteristic
229	#520	—	2	4	no	—
230	#519	—	2	1	no	—
231	#518	—	2	1	no	—
232	#518	C₄×C₇₃	1	4	yes	—
233	C₄×#41	—	2	4	no	—
234	C₂×#117	—	2	2	no	—
235	C₂×#117	C₂²×C₇₃	1	2	yes	—
236	#413	—	2	2	no	—
237	#413	C₄×C₇₃	1	4	yes	complemented
238	C₂×#101	—	2	1	no	—
239	C₂×#100	—	2	1	no	—
240	#408	—	2	2	no	—
241	#408	C₄×C₇₃	1	4	yes	complemented
242	C₂×C₂²⋊C₈	—	2	2	no	—
243	#343	—	2	4	no	—
244	#336	—	2	4	no	—
245	C₂×#41	—	2	2	no	—
246	C₂×#41	—	2	2	no	—
247	C₂×#41	—	2	2	no	—
248	C₂×#41	—	2	2	no	—
249	C₂×#41	C₂×C₄×C₇₃	1	2	yes	—
250	C₂×#41	C₂×C₄×C₇₃	1	2	yes	—
251	C₂×#41	D₄×C₇₃	1	2	yes	—
252	C₂×#41	Q₈×C₇₃	1	2	yes	—
253	C₂²×Q₈	D₄×C₇₃	1	1	yes	characteristic
254	C₂²×D₄	C₂×C₄×C₇₃	1	2	yes	—
255	C₂²×D₄	D₄×C₇₃	1	1	yes	characteristic
256	C₂³×C₄	D₄×C₇₃	1	2	yes	—
257	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
258	C₂×M₁₆	—	2	1	no	—
259	C₂×M₁₆	—	2	2	no	—
260	C₂×M₁₆	—	2	2	no	—
261	C₂×M₁₆	—	2	2	no	—
262	C₂×M₁₆	—	2	2	no	—
263	C₂×M₁₆	—	2	2	no	—
264	C₂×M₁₆	—	2	2	no	—
265	C₂×M₁₆	—	2	2	no	—
266	C₂×M₁₆	C₂×C₄×C₇₃	1	2	yes	complemented
267	C₂×M₁₆	C₂×C₄×C₇₃	1	4	yes	complemented
268	C₂²×C₈	—	2	2	no	—
269	C₂²×C₈	—	2	1	no	—
270	C₂²×C₈	—	2	1	no	—
271	C₂²×C₈	—	2	2	no	—
272	C₂²×C₈	—	2	1	no	—
273	C₂²×C₈	—	2	2	no	—
274	C₂²×C₈	C₂×C₄×C₇₃	1	2	yes	complemented
275	C₄×Q₈	—	2	8	no	—
276	C₄×D₄	—	2	8	no	—
277	C₄×D₄	—	2	16	no	—
278	#117	—	2	4	no	—
279	#117	—	2	4	no	—
280	#117	—	2	4	no	—
281	#117	—	2	2	no	—
282	#117	—	2	2	no	—
283	#117	—	2	2	no	—
284	#117	—	2	2	no	—
285	C₂×C₄⋊C₄	—	2	4	no	—
286	C₂×C₄⋊C₄	D₄×C₇₃	1	4	yes	—
287	C₂×C₂²⋊C₄	—	2	4	no	—
288	C₂×C₂²⋊C₄	C₂×C₄×C₇₃	1	4	yes	—
289	C₂×C₄²	—	2	4	no	—
290	C₂×C₄²	D₄×C₇₃	1	4	yes	—
291	#101	—	2	4	no	—
292	#100	—	2	4	no	—
293	C₂²⋊C₈	—	2	8	no	—
294	C₂⁴	C₂²⋊C₄×C₇₃	1	2	yes	—
295	C₂⁴	C₂²×C₄×C₇₃	1	1	yes	characteristic
296	#41	—	2	4	no	—
297	#41	—	2	4	no	—
298	#41	—	2	4	no	—
299	#41	—	2	4	no	—
300	#41	—	2	4	no	—
301	#41	—	2	4	no	—
302	#41	—	2	4	no	—
303	#41	—	2	4	no	—
304	C₂×Q₈	—	2	2	no	—
305	C₂×Q₈	—	2	2	no	—
306	C₂×Q₈	C₂²⋊C₄×C₇₃	1	2	yes	—
307	C₂×Q₈	C₄⋊C₄×C₇₃	1	2	yes	—
308	C₂×D₄	—	2	4	no	—
309	C₂×D₄	—	2	4	no	—
310	C₂×D₄	—	2	2	no	—
311	C₂×D₄	—	2	2	no	—
312	C₂×D₄	C₄²×C₇₃	1	4	yes	—
313	C₂×D₄	C₂²⋊C₄×C₇₃	1	2	yes	—
314	C₂×D₄	C₄⋊C₄×C₇₃	1	4	yes	—
315	C₂×D₄	C₄⋊C₄×C₇₃	1	2	yes	—
316	C₂²×C₄	—	2	2	no	—
317	C₂²×C₄	—	2	2	no	—
318	C₂²×C₄	—	2	2	no	—
319	C₂²×C₄	—	2	2	no	—
320	C₂²×C₄	—	2	8	no	—
321	C₂²×C₄	C₂²⋊C₄×C₇₃	1	2	yes	—
322	C₂²×C₄	C₂²⋊C₄×C₇₃	1	4	yes	—
323	C₂²×C₄	C₂²⋊C₄×C₇₃	1	8	yes	—
324	C₂²×C₄	C₄⋊C₄×C₇₃	1	4	yes	—
325	C₂²×C₄	C₂²×C₄×C₇₃	1	1	yes	characteristic
326	C₂²×C₄	C₂²×C₄×C₇₃	1	1	yes	characteristic
327	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
328	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
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	C₂×Q₈×C₇₃	1	1	yes	characteristic
333	C₂²×C₄	#41×C₇₃	1	2	yes	—
334	C₂²×C₄	#41×C₇₃	1	2	yes	—
335	M₁₆	—	2	4	no	—
336	M₁₆	—	2	4	no	—
337	M₁₆	—	2	4	no	—
338	M₁₆	—	4	2	no	—
339	M₁₆	—	4	2	no	—
340	M₁₆	—	4	2	no	—
341	C₂×C₈	—	2	2	no	—
342	C₂×C₈	—	2	2	no	—
343	C₂×C₈	—	2	4	no	—
344	C₂×C₈	—	2	4	no	—
345	C₂×C₈	—	4	1	no	—
346	C₂×C₈	—	4	2	no	—
347	C₂×C₈	—	4	1	no	—
348	C₂×C₈	—	4	2	no	—
349	C₂×C₈	—	4	2	no	—
350	C₂×C₈	—	4	1	no	—
351	C₂×C₈	—	4	1	no	—
352	C₄⋊C₄	—	2	8	no	—
353	C₄⋊C₄	—	2	4	no	—
354	C₄⋊C₄	—	2	4	no	—
355	C₂²⋊C₄	—	2	8	no	—
356	C₂²⋊C₄	—	2	4	no	—
357	C₂²⋊C₄	—	2	4	no	—
358	C₄²	—	2	8	no	—
359	C₄²	—	2	4	no	—
360	C₄²	—	2	4	no	—
361	C₂³	—	2	2	no	—
362	C₂³	—	2	2	no	—
363	C₂³	—	4	2	no	—
364	C₂³	—	4	4	no	—
365	C₂³	#95×C₇₃	1	4	yes	—
366	C₂³	C₂×C₄²×C₇₃	1	1	yes	characteristic
367	C₂³	C₂×C₂²⋊C₄×C₇₃	1	2	yes	—
368	C₂³	C₂×C₂²⋊C₄×C₇₃	1	1	yes	characteristic
369	C₂³	C₂×C₄⋊C₄×C₇₃	1	1	yes	characteristic
370	C₂³	#117×C₇₃	1	2	yes	—
371	Q₈	—	2	4	no	—
372	Q₈	—	2	4	no	—
373	D₄	—	2	8	no	—
374	D₄	—	2	8	no	—
375	D₄	—	2	4	no	—
376	D₄	—	2	4	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	4	no	—
380	C₂×C₄	—	2	4	no	—
381	C₂×C₄	—	2	4	no	—
382	C₂×C₄	—	2	4	no	—
383	C₂×C₄	—	2	8	no	—
384	C₂×C₄	—	4	8	no	—
385	C₂×C₄	—	8	8	no	—
386	C₂×C₄	#95×C₇₃	1	4	yes	—
387	C₂×C₄	C₂×C₂²⋊C₄×C₇₃	1	1	yes	characteristic
388	C₂×C₄	C₂×C₂²⋊C₄×C₇₃	1	1	yes	characteristic
389	C₂×C₄	C₂×C₄⋊C₄×C₇₃	1	1	yes	characteristic
390	C₂×C₄	C₂×C₄⋊C₄×C₇₃	1	1	yes	characteristic
391	C₂×C₄	C₄×D₄×C₇₃	1	2	yes	—
392	C₂×C₄	C₄×D₄×C₇₃	1	2	yes	—
393	C₂×C₄	C₄×D₄×C₇₃	1	2	yes	—
394	C₂×C₄	C₄×D₄×C₇₃	1	2	yes	—
395	C₂×C₄	#120×C₇₃	1	1	yes	characteristic
396	C₂×C₄	#120×C₇₃	1	2	yes	—
397	C₂×C₄	#120×C₇₃	1	1	yes	characteristic
398	C₂×C₄	#121×C₇₃	1	2	yes	—
399	C₂×C₄	#121×C₇₃	1	2	yes	—
400	C₂×C₄	C₂²⋊Q₈×C₇₃	1	2	yes	—
401	C₂×C₄	C₂²⋊Q₈×C₇₃	1	2	yes	—
402	C₂×C₄	#123×C₇₃	1	1	yes	characteristic
403	C₂×C₄	#123×C₇₃	1	1	yes	characteristic
404	C₂×C₄	#123×C₇₃	1	2	yes	—
405	C₈	—	4	2	no	—
406	C₈	—	4	2	no	—
407	C₈	—	4	4	no	—
408	C₂²	—	2	4	no	—
409	C₂²	—	2	2	no	—
410	C₂²	—	2	4	no	—
411	C₂²	—	4	1	no	—
412	C₂²	—	4	1	no	—
413	C₂²	—	4	2	no	—
414	C₂²	—	4	4	no	—
415	C₂²	—	4	4	no	—
416	C₂²	—	8	2	no	—
417	C₂²	C₂×#95×C₇₃	1	1	yes	characteristic
418	C₂²	C₄×C₂²⋊C₄×C₇₃	1	2	yes	—
419	C₂²	#379×C₇₃	1	1	yes	characteristic
420	C₂²	#380×C₇₃	1	2	yes	—
421	C₂²	#381×C₇₃	1	1	yes	characteristic
422	C₄	—	2	4	no	—
423	C₄	—	4	8	no	—
424	C₄	#385×C₇₃	1	1	yes	characteristic
425	C₄	#385×C₇₃	1	1	yes	characteristic
426	C₄	#385×C₇₃	1	2	yes	—
427	C₄	#386×C₇₃	1	1	yes	characteristic
428	C₄	#386×C₇₃	1	1	yes	characteristic
429	C₄	#386×C₇₃	1	2	yes	—
430	C₂	—	2	1	no	—
431	C₂	—	2	1	no	—
432	C₂	—	2	2	no	—
433	C₂	—	2	2	no	—
434	C₂	—	4	4	no	—
435	C₂	C₇₃×C₂²⋊#95	1	1	yes	characteristic
436	C₂	C₇₃×#1791	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₇₃	#120
commutator	C₂³	C₂×C₄²×C₇₃
Frattini, cosocle	C₂³×C₄	C₂³×C₇₃
socle	C₂²×C₇₃	#379
prime radical	C₂²×#41×C₇₃	C₂²
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₇₃ ◁ C₂³×C₄×C₇₃ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₇₃×#1742	C₂	semidirect
5. C₇₃×#1729	C₂	semidirect
18. #413×C₇₃	C₄	semidirect
22. #408×C₇₃	C₄	semidirect
47. C₂×M₁₆×C₇₃	C₂×C₄	semidirect
48. C₂×M₁₆×C₇₃	C₂×C₄	semidirect
55. C₂²×C₈×C₇₃	C₂×C₄	semidirect
211. #10747	C₇₃	direct (N × H)
222. #1742	C₂×C₇₃	semidirect
223. #1729	C₂×C₇₃	semidirect
224. C₇₃	#10747	direct (N × H)
237. #413	C₄×C₇₃	semidirect
241. #408	C₄×C₇₃	semidirect
266. C₂×M₁₆	C₂×C₄×C₇₃	semidirect
267. C₂×M₁₆	C₂×C₄×C₇₃	semidirect
274. C₂²×C₈	C₂×C₄×C₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₇₃×#3428	2
C₂×#413×C₇₃	2
C₂×#408×C₇₃	2
C₇₃×#1742	2
C₇₃×#1729	2
#10747	73

Subgroups — C73×#10747 #32920151

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#10747 #32920151