Subgroups — C₇₃×#24972 #32934376

Order 18688.

770 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₃×#2538	C₂	1	1	yes	maximal, characteristic
2	C₇₃×#2354	C₂	1	1	yes	maximal, characteristic
3	C₇₃×#2077	C₂	1	2	yes	maximal, complemented
4	C₇₃×#2035	C₂	1	2	yes	maximal, complemented
5	C₇₃×#1954	C₂	1	1	yes	maximal, characteristic
6	C₇₃×#1948	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇₃×#1873	C₂	1	2	yes	maximal, complemented
8	C₇₃×#1834	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇₃×#1825	C₂	1	2	yes	maximal, complemented
10	C₇₃×#1803	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×#103×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	2	yes	—
13	C₂×C₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic
14	C₂×C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
15	C₂×#117×C₇₃	C₂²	1	2	yes	—
16	C₂×#106×C₇₃	C₂²	1	2	yes	—
17	C₂×C₄⋊C₈×C₇₃	C₂²	1	1	yes	characteristic
18	C₂×#103×C₇₃	C₂²	1	1	yes	characteristic
19	C₂×#103×C₇₃	C₂²	1	1	yes	characteristic
20	C₂×#103×C₇₃	C₂²	1	2	yes	—
21	C₂×C₂²⋊C₈×C₇₃	C₂²	1	2	yes	—
22	C₂×C₂²⋊C₈×C₇₃	C₂²	1	2	yes	—
23	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
24	#396×C₇₃	—	2	2	no	—
25	#390×C₇₃	—	2	1	no	—
26	#390×C₇₃	—	2	1	no	—
27	#389×C₇₃	—	2	1	no	—
28	#388×C₇₃	—	2	2	no	—
29	#384×C₇₃	C₂²	1	1	yes	characteristic
30	#384×C₇₃	C₂²	1	1	yes	characteristic
31	#380×C₇₃	C₂²	1	2	yes	—
32	#380×C₇₃	C₂²	1	2	yes	—
33	C₄×C₄⋊C₄×C₇₃	—	2	1	no	—
34	C₄×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
35	#340×C₇₃	C₂²	1	2	yes	—
36	#340×C₇₃	C₂²	1	1	yes	characteristic
37	#340×C₇₃	C₂²	1	1	yes	characteristic
38	#340×C₇₃	C₂²	1	2	yes	—
39	#340×C₇₃	C₂²	1	2	yes	—
40	#340×C₇₃	C₂²	1	2	yes	—
41	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
42	C₂²×D₄×C₇₃	D₄	1	1	yes	characteristic
43	C₂³×C₄×C₇₃	C₂³	1	2	yes	—
44	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
45	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
46	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
47	C₂²⋊Q₈×C₇₃	—	2	4	no	—
48	C₂²⋊Q₈×C₇₃	—	4	2	no	—
49	C₄×Q₈×C₇₃	—	2	2	no	—
50	C₄×Q₈×C₇₃	—	2	2	no	—
51	C₄×D₄×C₇₃	—	2	2	no	—
52	C₄×D₄×C₇₃	—	2	2	no	—
53	#117×C₇₃	—	2	4	no	—
54	#117×C₇₃	—	4	2	no	—
55	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
56	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
57	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
58	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
59	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
60	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
61	C₂×C₄⋊C₄×C₇₃	D₄	1	1	yes	characteristic
62	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
63	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
64	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
65	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
66	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
67	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
68	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
69	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
70	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
71	C₂×C₂²⋊C₄×C₇₃	D₄	1	2	yes	—
72	C₂×C₄²×C₇₃	—	2	1	no	—
73	C₂×C₄²×C₇₃	—	2	2	no	—
74	C₂×C₄²×C₇₃	—	2	1	no	—
75	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
76	#106×C₇₃	—	4	2	no	—
77	C₄⋊C₈×C₇₃	—	2	2	no	—
78	#103×C₇₃	—	2	2	no	—
79	#103×C₇₃	—	2	2	no	—
80	#103×C₇₃	—	4	2	no	—
81	C₂²⋊C₈×C₇₃	—	4	2	no	—
82	C₂²⋊C₈×C₇₃	—	4	2	no	—
83	C₄×C₈×C₇₃	—	2	2	no	—
84	#95×C₇₃	—	2	2	no	—
85	#95×C₇₃	—	2	1	no	—
86	#95×C₇₃	—	2	2	no	—
87	C₂⁴×C₇₃	C₂×D₄	1	2	yes	—
88	C₂×Q₈×C₇₃	—	2	1	no	—
89	C₂×Q₈×C₇₃	—	2	1	no	—
90	C₂×Q₈×C₇₃	—	2	1	no	—
91	C₂×Q₈×C₇₃	—	2	1	no	—
92	C₂×Q₈×C₇₃	—	2	1	no	—
93	C₂×Q₈×C₇₃	#41	1	2	yes	—
94	C₂×D₄×C₇₃	—	2	2	no	—
95	C₂×D₄×C₇₃	—	2	2	no	—
96	C₂×D₄×C₇₃	—	2	2	no	—
97	C₂²×C₄×C₇₃	—	2	1	no	—
98	C₂²×C₄×C₇₃	—	2	1	no	—
99	C₂²×C₄×C₇₃	—	2	2	no	—
100	C₂²×C₄×C₇₃	—	2	2	no	—
101	C₂²×C₄×C₇₃	—	2	2	no	—
102	C₂²×C₄×C₇₃	—	2	2	no	—
103	C₂²×C₄×C₇₃	—	2	2	no	—
104	C₂²×C₄×C₇₃	—	2	2	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	2	yes	—
110	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
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	2	no	—
118	C₂×C₈×C₇₃	—	2	1	no	—
119	C₂×C₈×C₇₃	—	2	1	no	—
120	C₂×C₈×C₇₃	—	2	2	no	—
121	C₂×C₈×C₇₃	—	2	2	no	—
122	C₄⋊C₄×C₇₃	—	2	2	no	—
123	C₄⋊C₄×C₇₃	—	2	1	no	—
124	C₄⋊C₄×C₇₃	—	2	1	no	—
125	C₄⋊C₄×C₇₃	—	2	2	no	—
126	C₄⋊C₄×C₇₃	—	2	1	no	—
127	C₄⋊C₄×C₇₃	—	2	1	no	—
128	C₄⋊C₄×C₇₃	—	2	2	no	—
129	C₄⋊C₄×C₇₃	—	2	2	no	—
130	C₄⋊C₄×C₇₃	—	2	1	no	—
131	C₄⋊C₄×C₇₃	—	2	2	no	—
132	C₄⋊C₄×C₇₃	—	4	4	no	—
133	C₄⋊C₄×C₇₃	—	4	2	no	—
134	C₄⋊C₄×C₇₃	—	4	2	no	—
135	C₄⋊C₄×C₇₃	—	4	2	no	—
136	C₄⋊C₄×C₇₃	—	8	1	no	—
137	C₄⋊C₄×C₇₃	—	8	1	no	—
138	C₄⋊C₄×C₇₃	#41	1	2	yes	—
139	C₂²⋊C₄×C₇₃	—	2	4	no	—
140	C₂²⋊C₄×C₇₃	—	4	4	no	—
141	C₂²⋊C₄×C₇₃	—	4	4	no	—
142	C₂²⋊C₄×C₇₃	—	8	2	no	—
143	C₂²⋊C₄×C₇₃	—	8	2	no	—
144	C₄²×C₇₃	—	4	4	no	—
145	C₄²×C₇₃	—	4	2	no	—
146	C₄²×C₇₃	—	4	2	no	—
147	C₄²×C₇₃	#41	1	2	yes	—
148	C₄²×C₇₃	#41	1	2	yes	—
149	C₂³×C₇₃	—	2	2	no	—
150	C₂³×C₇₃	—	2	2	no	—
151	C₂³×C₇₃	—	2	2	no	—
152	C₂³×C₇₃	—	2	2	no	—
153	C₂³×C₇₃	—	2	2	no	—
154	C₂³×C₇₃	—	2	2	no	—
155	C₂³×C₇₃	—	2	2	no	—
156	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
157	Q₈×C₇₃	—	2	2	no	—
158	Q₈×C₇₃	—	2	2	no	—
159	Q₈×C₇₃	—	4	1	no	—
160	Q₈×C₇₃	—	4	1	no	—
161	D₄×C₇₃	—	4	4	no	—
162	C₂×C₄×C₇₃	—	2	1	no	—
163	C₂×C₄×C₇₃	—	2	1	no	—
164	C₂×C₄×C₇₃	—	2	2	no	—
165	C₂×C₄×C₇₃	—	2	2	no	—
166	C₂×C₄×C₇₃	—	2	2	no	—
167	C₂×C₄×C₇₃	—	2	2	no	—
168	C₂×C₄×C₇₃	—	2	2	no	—
169	C₂×C₄×C₇₃	—	4	1	no	—
170	C₂×C₄×C₇₃	—	4	1	no	—
171	C₂×C₄×C₇₃	—	4	1	no	—
172	C₂×C₄×C₇₃	—	4	1	no	—
173	C₂×C₄×C₇₃	—	4	2	no	—
174	C₂×C₄×C₇₃	—	4	2	no	—
175	C₂×C₄×C₇₃	—	4	2	no	—
176	C₂×C₄×C₇₃	—	4	2	no	—
177	C₂×C₄×C₇₃	—	4	1	no	—
178	C₂×C₄×C₇₃	—	4	2	no	—
179	C₂×C₄×C₇₃	—	4	2	no	—
180	C₂×C₄×C₇₃	—	4	1	no	—
181	C₂×C₄×C₇₃	—	4	2	no	—
182	C₂×C₄×C₇₃	—	4	2	no	—
183	C₂×C₄×C₇₃	—	4	1	no	—
184	C₂×C₄×C₇₃	—	4	1	no	—
185	C₂×C₄×C₇₃	—	4	1	no	—
186	C₂×C₄×C₇₃	—	4	2	no	—
187	C₂×C₄×C₇₃	—	4	2	no	—
188	C₂×C₄×C₇₃	—	4	1	no	—
189	C₂×C₄×C₇₃	#123	1	2	yes	—
190	C₂×C₄×C₇₃	#123	1	2	yes	—
191	C₂×C₄×C₇₃	#135	1	2	yes	—
192	C₂×C₄×C₇₃	#137	1	2	yes	—
193	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
194	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
195	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
196	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
197	C₂×C₄×C₇₃	H(5,𝔽₂)	1	1	yes	characteristic
198	C₂×C₄×C₇₃	H(5,𝔽₂)	1	1	yes	characteristic
199	C₈×C₇₃	—	4	2	no	—
200	C₈×C₇₃	—	4	1	no	—
201	C₈×C₇₃	—	4	1	no	—
202	C₂²×C₇₃	—	4	2	no	—
203	C₂²×C₇₃	—	4	2	no	—
204	C₂²×C₇₃	—	4	2	no	—
205	C₂²×C₇₃	—	4	2	no	—
206	C₂²×C₇₃	—	4	2	no	—
207	C₂²×C₇₃	—	4	2	no	—
208	C₂²×C₇₃	—	4	2	no	—
209	C₂²×C₇₃	C₂×#123	1	1	yes	characteristic
210	C₂²×C₇₃	#546	1	1	yes	characteristic
211	C₂²×C₇₃	#546	1	1	yes	characteristic
212	C₂²×C₇₃	C₂×#135	1	1	yes	characteristic
213	C₂²×C₇₃	C₂×#137	1	1	yes	characteristic
214	C₂²×C₇₃	#577	1	1	yes	characteristic
215	C₂²×C₇₃	#577	1	1	yes	characteristic
216	C₄×C₇₃	—	2	2	no	—
217	C₄×C₇₃	—	4	2	no	—
218	C₄×C₇₃	—	4	2	no	—
219	C₄×C₇₃	—	4	2	no	—
220	C₄×C₇₃	—	8	1	no	—
221	C₄×C₇₃	—	8	1	no	—
222	C₄×C₇₃	—	8	2	no	—
223	C₄×C₇₃	—	8	2	no	—
224	C₄×C₇₃	#485	1	4	yes	—
225	C₄×C₇₃	#529	1	1	yes	characteristic
226	C₄×C₇₃	#540	1	1	yes	characteristic
227	C₄×C₇₃	#553	1	1	yes	characteristic
228	C₄×C₇₃	#555	1	1	yes	characteristic
229	#24972	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
230	C₂×C₇₃	—	8	2	no	—
231	C₂×C₇₃	#2420	1	1	yes	characteristic
232	C₂×C₇₃	C₂×#485	1	1	yes	characteristic
233	C₂×C₇₃	#3099	1	1	yes	characteristic
234	C₂×C₇₃	#3304	1	1	yes	characteristic
235	C₂×C₇₃	#3304	1	1	yes	characteristic
236	C₂×C₇₃	#3329	1	1	yes	characteristic
237	C₂×C₇₃	#3331	1	1	yes	characteristic
238	#2538	C₂×C₇₃	1	1	yes	characteristic
239	#2354	C₂×C₇₃	1	1	yes	characteristic
240	#2077	C₂×C₇₃	1	2	yes	complemented
241	#2035	C₂×C₇₃	1	2	yes	complemented
242	#1954	C₂×C₇₃	1	1	yes	characteristic
243	#1948	C₂×C₇₃	1	1	yes	characteristic, complemented
244	#1873	C₂×C₇₃	1	2	yes	complemented
245	#1834	C₂×C₇₃	1	1	yes	characteristic, complemented
246	#1825	C₂×C₇₃	1	2	yes	complemented
247	#1803	C₂×C₇₃	1	1	yes	characteristic, complemented
248	C₄×#103	C₂×C₇₃	1	1	yes	characteristic, complemented
249	C₇₃	#24972	1	1	yes	characteristic, direct product factor, Sylow
250	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	2	yes	—
251	C₂×C₄×Q₈	C₂²×C₇₃	1	1	yes	characteristic
252	C₂×C₄×D₄	C₂²×C₇₃	1	1	yes	characteristic
253	C₂×#117	C₂²×C₇₃	1	2	yes	—
254	C₂×#106	C₂²×C₇₃	1	2	yes	—
255	C₂×C₄⋊C₈	C₂²×C₇₃	1	1	yes	characteristic
256	C₂×#103	C₂²×C₇₃	1	1	yes	characteristic
257	C₂×#103	C₂²×C₇₃	1	1	yes	characteristic
258	C₂×#103	C₂²×C₇₃	1	2	yes	—
259	C₂×C₂²⋊C₈	C₂²×C₇₃	1	2	yes	—
260	C₂×C₂²⋊C₈	C₂²×C₇₃	1	2	yes	—
261	C₂×C₄×C₈	C₂²×C₇₃	1	1	yes	characteristic
262	#396	—	2	2	no	—
263	#390	—	2	1	no	—
264	#390	—	2	1	no	—
265	#389	—	2	1	no	—
266	#388	—	2	2	no	—
267	#384	C₂²×C₇₃	1	1	yes	characteristic
268	#384	C₂²×C₇₃	1	1	yes	characteristic
269	#380	C₂²×C₇₃	1	2	yes	—
270	#380	C₂²×C₇₃	1	2	yes	—
271	C₄×C₄⋊C₄	—	2	1	no	—
272	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
273	#340	C₂²×C₇₃	1	2	yes	—
274	#340	C₂²×C₇₃	1	1	yes	characteristic
275	#340	C₂²×C₇₃	1	2	yes	—
276	#340	C₂²×C₇₃	1	1	yes	characteristic
277	#340	C₂²×C₇₃	1	2	yes	—
278	#340	C₂²×C₇₃	1	2	yes	—
279	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
280	C₂²×D₄	D₄×C₇₃	1	1	yes	characteristic
281	C₂³×C₄	C₂³×C₇₃	1	2	yes	—
282	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
283	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
284	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
285	C₂²⋊Q₈	—	2	4	no	—
286	C₂²⋊Q₈	—	4	2	no	—
287	C₄×Q₈	—	2	2	no	—
288	C₄×Q₈	—	2	2	no	—
289	C₄×D₄	—	2	2	no	—
290	C₄×D₄	—	2	2	no	—
291	#117	—	2	4	no	—
292	#117	—	4	2	no	—
293	C₂×C₄⋊C₄	—	2	1	no	—
294	C₂×C₄⋊C₄	—	2	2	no	—
295	C₂×C₄⋊C₄	—	2	1	no	—
296	C₂×C₄⋊C₄	—	2	1	no	—
297	C₂×C₄⋊C₄	—	2	1	no	—
298	C₂×C₄⋊C₄	—	2	1	no	—
299	C₂×C₄⋊C₄	D₄×C₇₃	1	1	yes	characteristic
300	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
301	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
302	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
303	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
304	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
305	C₂×C₂²⋊C₄	—	2	2	no	—
306	C₂×C₂²⋊C₄	—	2	2	no	—
307	C₂×C₂²⋊C₄	—	2	2	no	—
308	C₂×C₂²⋊C₄	—	2	2	no	—
309	C₂×C₂²⋊C₄	D₄×C₇₃	1	2	yes	—
310	C₂×C₄²	—	2	2	no	—
311	C₂×C₄²	—	2	1	no	—
312	C₂×C₄²	—	2	1	no	—
313	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
314	#106	—	4	2	no	—
315	C₄⋊C₈	—	2	2	no	—
316	#103	—	2	2	no	—
317	#103	—	2	2	no	—
318	#103	—	4	2	no	—
319	C₂²⋊C₈	—	4	2	no	—
320	C₂²⋊C₈	—	4	2	no	—
321	C₄×C₈	—	2	2	no	—
322	#95	—	2	2	no	—
323	#95	—	2	1	no	—
324	#95	—	2	2	no	—
325	C₂⁴	C₂×D₄×C₇₃	1	2	yes	—
326	C₂×Q₈	—	2	1	no	—
327	C₂×Q₈	—	2	1	no	—
328	C₂×Q₈	—	2	1	no	—
329	C₂×Q₈	—	2	1	no	—
330	C₂×Q₈	—	2	1	no	—
331	C₂×Q₈	#41×C₇₃	1	2	yes	—
332	C₂×D₄	—	2	2	no	—
333	C₂×D₄	—	2	2	no	—
334	C₂×D₄	—	2	2	no	—
335	C₂²×C₄	—	2	1	no	—
336	C₂²×C₄	—	2	1	no	—
337	C₂²×C₄	—	2	2	no	—
338	C₂²×C₄	—	2	2	no	—
339	C₂²×C₄	—	2	2	no	—
340	C₂²×C₄	—	2	2	no	—
341	C₂²×C₄	—	2	2	no	—
342	C₂²×C₄	—	2	2	no	—
343	C₂²×C₄	—	2	1	no	—
344	C₂²×C₄	—	2	1	no	—
345	C₂²×C₄	—	2	2	no	—
346	C₂²×C₄	—	2	2	no	—
347	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
348	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
349	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
350	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
351	C₂×C₈	—	2	1	no	—
352	C₂×C₈	—	2	1	no	—
353	C₂×C₈	—	2	1	no	—
354	C₂×C₈	—	2	1	no	—
355	C₂×C₈	—	2	2	no	—
356	C₂×C₈	—	2	1	no	—
357	C₂×C₈	—	2	1	no	—
358	C₂×C₈	—	2	2	no	—
359	C₂×C₈	—	2	2	no	—
360	C₄⋊C₄	—	2	2	no	—
361	C₄⋊C₄	—	2	1	no	—
362	C₄⋊C₄	—	2	1	no	—
363	C₄⋊C₄	—	2	2	no	—
364	C₄⋊C₄	—	2	1	no	—
365	C₄⋊C₄	—	2	1	no	—
366	C₄⋊C₄	—	2	2	no	—
367	C₄⋊C₄	—	2	2	no	—
368	C₄⋊C₄	—	2	1	no	—
369	C₄⋊C₄	—	2	2	no	—
370	C₄⋊C₄	—	4	4	no	—
371	C₄⋊C₄	—	4	2	no	—
372	C₄⋊C₄	—	4	2	no	—
373	C₄⋊C₄	—	4	2	no	—
374	C₄⋊C₄	—	8	1	no	—
375	C₄⋊C₄	—	8	1	no	—
376	C₄⋊C₄	#41×C₇₃	1	2	yes	—
377	C₂²⋊C₄	—	2	4	no	—
378	C₂²⋊C₄	—	4	4	no	—
379	C₂²⋊C₄	—	4	4	no	—
380	C₂²⋊C₄	—	8	2	no	—
381	C₂²⋊C₄	—	8	2	no	—
382	C₄²	—	4	4	no	—
383	C₄²	—	4	2	no	—
384	C₄²	—	4	2	no	—
385	C₄²	#41×C₇₃	1	2	yes	—
386	C₄²	#41×C₇₃	1	2	yes	—
387	C₂³	—	2	2	no	—
388	C₂³	—	2	2	no	—
389	C₂³	—	2	2	no	—
390	C₂³	—	2	2	no	—
391	C₂³	—	2	2	no	—
392	C₂³	—	2	2	no	—
393	C₂³	—	2	2	no	—
394	C₂³	C₂²×D₄×C₇₃	1	1	yes	characteristic
395	Q₈	—	2	2	no	—
396	Q₈	—	2	2	no	—
397	Q₈	—	4	1	no	—
398	Q₈	—	4	1	no	—
399	D₄	—	4	4	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	4	1	no	—
408	C₂×C₄	—	4	1	no	—
409	C₂×C₄	—	4	1	no	—
410	C₂×C₄	—	4	1	no	—
411	C₂×C₄	—	4	2	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	4	1	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	4	1	no	—
419	C₂×C₄	—	4	2	no	—
420	C₂×C₄	—	4	2	no	—
421	C₂×C₄	—	4	1	no	—
422	C₂×C₄	—	4	1	no	—
423	C₂×C₄	—	4	1	no	—
424	C₂×C₄	—	4	2	no	—
425	C₂×C₄	—	4	2	no	—
426	C₂×C₄	—	4	1	no	—
427	C₂×C₄	#123×C₇₃	1	2	yes	—
428	C₂×C₄	#123×C₇₃	1	2	yes	—
429	C₂×C₄	#135×C₇₃	1	2	yes	—
430	C₂×C₄	#137×C₇₃	1	2	yes	—
431	C₂×C₄	C₂×#41×C₇₃	1	1	yes	characteristic
432	C₂×C₄	C₂×#41×C₇₃	1	1	yes	characteristic
433	C₂×C₄	C₂×#41×C₇₃	1	1	yes	characteristic
434	C₂×C₄	C₂×#41×C₇₃	1	1	yes	characteristic
435	C₂×C₄	H(5,𝔽₂)×C₇₃	1	1	yes	characteristic
436	C₂×C₄	H(5,𝔽₂)×C₇₃	1	1	yes	characteristic
437	C₈	—	4	2	no	—
438	C₈	—	4	1	no	—
439	C₈	—	4	1	no	—
440	C₂²	—	4	2	no	—
441	C₂²	—	4	2	no	—
442	C₂²	—	4	2	no	—
443	C₂²	—	4	2	no	—
444	C₂²	—	4	2	no	—
445	C₂²	—	4	2	no	—
446	C₂²	—	4	2	no	—
447	C₂²	C₂×#123×C₇₃	1	1	yes	characteristic
448	C₂²	#546×C₇₃	1	1	yes	characteristic
449	C₂²	#546×C₇₃	1	1	yes	characteristic
450	C₂²	C₂×#135×C₇₃	1	1	yes	characteristic
451	C₂²	C₂×#137×C₇₃	1	1	yes	characteristic
452	C₂²	#577×C₇₃	1	1	yes	characteristic
453	C₂²	#577×C₇₃	1	1	yes	characteristic
454	C₄	—	2	2	no	—
455	C₄	—	4	2	no	—
456	C₄	—	4	2	no	—
457	C₄	—	4	2	no	—
458	C₄	—	8	2	no	—
459	C₄	—	8	2	no	—
460	C₄	—	8	1	no	—
461	C₄	—	8	1	no	—
462	C₄	#485×C₇₃	1	4	yes	—
463	C₄	#529×C₇₃	1	1	yes	characteristic
464	C₄	#540×C₇₃	1	1	yes	characteristic
465	C₄	#553×C₇₃	1	1	yes	characteristic
466	C₄	#555×C₇₃	1	1	yes	characteristic
467	C₂	—	8	2	no	—
468	C₂	C₇₃×#2420	1	1	yes	characteristic
469	C₂	C₂×#485×C₇₃	1	1	yes	characteristic
470	C₂	C₇₃×#3099	1	1	yes	characteristic
471	C₂	C₇₃×#3304	1	1	yes	characteristic
472	C₂	C₇₃×#3304	1	1	yes	characteristic
473	C₂	C₇₃×#3329	1	1	yes	characteristic
474	C₂	C₇₃×#3331	1	1	yes	characteristic

	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
3. C₇₃×#2077	C₂	semidirect
4. C₇₃×#2035	C₂	semidirect
6. C₇₃×#1948	C₂	semidirect
7. C₇₃×#1873	C₂	semidirect
8. C₇₃×#1834	C₂	semidirect
9. C₇₃×#1825	C₂	semidirect
10. C₇₃×#1803	C₂	semidirect
11. C₄×#103×C₇₃	C₂	semidirect
229. #24972	C₇₃	direct (N × H)
240. #2077	C₂×C₇₃	semidirect
241. #2035	C₂×C₇₃	semidirect
243. #1948	C₂×C₇₃	semidirect
244. #1873	C₂×C₇₃	semidirect
245. #1834	C₂×C₇₃	semidirect
246. #1825	C₂×C₇₃	semidirect
247. #1803	C₂×C₇₃	semidirect
248. C₄×#103	C₂×C₇₃	semidirect
249. C₇₃	#24972	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇₃×#2538	2
C₇₃×#2354	2
C₇₃×#2077	2
C₇₃×#2035	2
C₇₃×#1954	2
C₇₃×#1948	2
C₇₃×#1873	2
C₇₃×#1834	2
C₇₃×#1825	2
C₇₃×#1803	2
C₄×#103×C₇₃	2
#24972	73

Subgroups — C73×#24972 #32934376

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#24972 #32934376