Subgroups — C₇₃×#23806 #32933210

Order 18688.

1174 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#442×C₇₃	C₂	1	2	yes	maximal, complemented
2	C₂×#440×C₇₃	C₂	1	2	yes	maximal, complemented
3	C₄×#127×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×#124×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₃×#2096	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇₃×#2093	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇₃×#2092	C₂	1	2	yes	maximal, complemented
8	C₇₃×#2014	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇₃×#2012	C₂	1	2	yes	maximal, complemented
10	C₇₃×#2011	C₂	1	1	yes	maximal, characteristic
11	C₇₃×#1745	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×SD₁₆×C₇₃	C₂²	1	2	yes	—
13	C₂²×D₈×C₇₃	C₂²	1	2	yes	—
14	C₂×#127×C₇₃	C₂²	1	1	yes	characteristic
15	C₂×#124×C₇₃	C₂²	1	1	yes	characteristic
16	C₂×C₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic
17	C₂×C₄×D₄×C₇₃	—	2	2	no	—
18	C₂×C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
19	C₂×C₄×D₄×C₇₃	C₂²	1	2	yes	—
20	#442×C₇₃	—	2	8	no	—
21	#440×C₇₃	—	2	8	no	—
22	C₂×#107×C₇₃	C₂²	1	2	yes	—
23	C₂×#106×C₇₃	C₂²	1	2	yes	—
24	C₂×#103×C₇₃	C₂²	1	2	yes	—
25	C₂×#102×C₇₃	C₂²	1	2	yes	—
26	C₂×#102×C₇₃	C₂²	1	2	yes	—
27	C₂×#102×C₇₃	C₂²	1	2	yes	—
28	C₂×#97×C₇₃	C₂²	1	2	yes	—
29	#391×C₇₃	C₂²	1	1	yes	characteristic
30	#390×C₇₃	—	2	2	no	—
31	#390×C₇₃	C₂²	1	1	yes	characteristic
32	#390×C₇₃	C₂²	1	2	yes	—
33	#388×C₇₃	—	2	2	no	—
34	#384×C₇₃	C₂²	1	1	yes	characteristic
35	#382×C₇₃	C₂²	1	1	yes	characteristic
36	C₄×C₂²⋊C₄×C₇₃	—	2	2	no	—
37	C₄³×C₇₃	C₂²	1	1	yes	characteristic
38	#336×C₇₃	C₂²	1	1	yes	characteristic
39	#336×C₇₃	C₂²	1	2	yes	—
40	#336×C₇₃	C₂²	1	1	yes	characteristic
41	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
42	C₂²×D₄×C₇₃	—	2	2	no	—
43	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
44	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
45	C₂³×C₄×C₇₃	—	2	1	no	—
46	C₂³×C₄×C₇₃	—	2	2	no	—
47	C₂×SD₁₆×C₇₃	—	2	4	no	—
48	C₂×SD₁₆×C₇₃	—	2	4	no	—
49	C₂×SD₁₆×C₇₃	—	2	4	no	—
50	C₂×D₈×C₇₃	—	2	4	no	—
51	C₂×D₈×C₇₃	—	2	4	no	—
52	C₂×D₈×C₇₃	—	2	4	no	—
53	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
54	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
55	#127×C₇₃	—	2	4	no	—
56	#124×C₇₃	—	2	2	no	—
57	#124×C₇₃	—	2	2	no	—
58	C₄×Q₈×C₇₃	—	2	4	no	—
59	C₄×D₄×C₇₃	—	2	4	no	—
60	C₄×D₄×C₇₃	—	2	4	no	—
61	C₄×D₄×C₇₃	—	2	4	no	—
62	C₄×D₄×C₇₃	—	4	8	no	—
63	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
64	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
65	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
66	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
67	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
68	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
69	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
70	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
71	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
72	C₂×C₂²⋊C₄×C₇₃	—	2	4	no	—
73	C₂×C₄²×C₇₃	—	2	1	no	—
74	C₂×C₄²×C₇₃	D₄	1	2	yes	—
75	C₂×C₄²×C₇₃	D₄	1	2	yes	—
76	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
77	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
78	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
79	#107×C₇₃	—	2	4	no	—
80	#106×C₇₃	—	2	4	no	—
81	#103×C₇₃	—	2	4	no	—
82	#102×C₇₃	—	2	4	no	—
83	#102×C₇₃	—	2	4	no	—
84	#102×C₇₃	—	2	4	no	—
85	#97×C₇₃	D₄	1	8	yes	complemented
86	#95×C₇₃	—	2	2	no	—
87	#95×C₇₃	—	2	2	no	—
88	C₂⁴×C₇₃	—	2	1	no	—
89	C₂⁴×C₇₃	—	2	2	no	—
90	C₂×Q₈×C₇₃	—	2	1	no	—
91	C₂×Q₈×C₇₃	—	2	2	no	—
92	C₂×Q₈×C₇₃	—	2	2	no	—
93	C₂×Q₈×C₇₃	#41	1	2	yes	—
94	C₂×D₄×C₇₃	—	2	8	no	—
95	C₂×D₄×C₇₃	—	2	2	no	—
96	C₂×D₄×C₇₃	—	2	2	no	—
97	C₂×D₄×C₇₃	—	2	2	no	—
98	C₂×D₄×C₇₃	—	2	2	no	—
99	C₂×D₄×C₇₃	—	2	2	no	—
100	C₂×D₄×C₇₃	—	2	2	no	—
101	C₂×D₄×C₇₃	—	2	1	no	—
102	C₂×D₄×C₇₃	—	2	2	no	—
103	C₂×D₄×C₇₃	—	4	4	no	—
104	C₂×D₄×C₇₃	—	4	4	no	—
105	C₂×D₄×C₇₃	#41	1	2	yes	—
106	C₂×D₄×C₇₃	#41	1	4	yes	—
107	C₂²×C₄×C₇₃	—	2	1	no	—
108	C₂²×C₄×C₇₃	—	2	1	no	—
109	C₂²×C₄×C₇₃	—	2	1	no	—
110	C₂²×C₄×C₇₃	—	2	2	no	—
111	C₂²×C₄×C₇₃	—	4	8	no	—
112	C₂²×C₄×C₇₃	—	4	4	no	—
113	C₂²×C₄×C₇₃	—	4	2	no	—
114	C₂²×C₄×C₇₃	—	4	4	no	—
115	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
116	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
119	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
120	SD₁₆×C₇₃	—	2	16	no	—
121	D₈×C₇₃	—	2	16	no	—
122	C₂×C₈×C₇₃	—	2	2	no	—
123	C₂×C₈×C₇₃	—	2	2	no	—
124	C₂×C₈×C₇₃	—	2	2	no	—
125	C₂×C₈×C₇₃	—	2	2	no	—
126	C₂×C₈×C₇₃	C₂×D₄	1	4	yes	—
127	C₂×C₈×C₇₃	C₂×D₄	1	4	yes	—
128	C₄⋊C₄×C₇₃	—	2	2	no	—
129	C₄⋊C₄×C₇₃	—	2	2	no	—
130	C₄⋊C₄×C₇₃	—	2	2	no	—
131	C₄⋊C₄×C₇₃	—	2	2	no	—
132	C₄⋊C₄×C₇₃	—	4	2	no	—
133	C₄⋊C₄×C₇₃	—	4	4	no	—
134	C₂²⋊C₄×C₇₃	—	2	8	no	—
135	C₂²⋊C₄×C₇₃	—	4	8	no	—
136	C₂²⋊C₄×C₇₃	—	4	4	no	—
137	C₂²⋊C₄×C₇₃	—	4	2	no	—
138	C₂²⋊C₄×C₇₃	—	4	4	no	—
139	C₄²×C₇₃	—	2	4	no	—
140	C₄²×C₇₃	—	2	1	no	—
141	C₄²×C₇₃	—	2	1	no	—
142	C₄²×C₇₃	—	2	2	no	—
143	C₄²×C₇₃	—	4	2	no	—
144	C₄²×C₇₃	—	4	2	no	—
145	C₄²×C₇₃	C₂×D₄	1	4	yes	—
146	C₂³×C₇₃	—	2	2	no	—
147	C₂³×C₇₃	—	2	4	no	—
148	C₂³×C₇₃	—	4	1	no	—
149	C₂³×C₇₃	—	4	2	no	—
150	C₂³×C₇₃	—	4	2	no	—
151	C₂³×C₇₃	—	4	1	no	—
152	C₂³×C₇₃	—	4	4	no	—
153	C₂³×C₇₃	—	4	2	no	—
154	C₂³×C₇₃	—	4	2	no	—
155	C₂³×C₇₃	—	4	4	no	—
156	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
157	Q₈×C₇₃	—	2	4	no	—
158	Q₈×C₇₃	—	4	2	no	—
159	D₄×C₇₃	—	2	4	no	—
160	D₄×C₇₃	—	2	4	no	—
161	D₄×C₇₃	—	2	4	no	—
162	D₄×C₇₃	—	4	16	no	—
163	D₄×C₇₃	—	4	2	no	—
164	D₄×C₇₃	—	4	2	no	—
165	D₄×C₇₃	—	4	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	—	2	2	no	—
170	C₂×C₄×C₇₃	—	2	2	no	—
171	C₂×C₄×C₇₃	—	2	2	no	—
172	C₂×C₄×C₇₃	—	2	2	no	—
173	C₂×C₄×C₇₃	—	2	2	no	—
174	C₂×C₄×C₇₃	—	4	1	no	—
175	C₂×C₄×C₇₃	—	4	1	no	—
176	C₂×C₄×C₇₃	—	4	1	no	—
177	C₂×C₄×C₇₃	—	4	2	no	—
178	C₂×C₄×C₇₃	—	4	1	no	—
179	C₂×C₄×C₇₃	—	4	4	no	—
180	C₂×C₄×C₇₃	—	4	2	no	—
181	C₂×C₄×C₇₃	—	4	2	no	—
182	C₂×C₄×C₇₃	—	8	8	no	—
183	C₂×C₄×C₇₃	—	8	4	no	—
184	C₂×C₄×C₇₃	#127	1	2	yes	—
185	C₂×C₄×C₇₃	#127	1	2	yes	—
186	C₂×C₄×C₇₃	AGL(1,ℤ/8)	1	4	yes	—
187	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
188	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
189	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
190	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
191	C₈×C₇₃	—	2	4	no	—
192	C₈×C₇₃	—	2	4	no	—
193	C₂²×C₇₃	—	4	8	no	—
194	C₂²×C₇₃	—	4	4	no	—
195	C₂²×C₇₃	—	4	2	no	—
196	C₂²×C₇₃	—	4	4	no	—
197	C₂²×C₇₃	—	8	2	no	—
198	C₂²×C₇₃	—	8	4	no	—
199	C₂²×C₇₃	—	8	2	no	—
200	C₂²×C₇₃	—	8	1	no	—
201	C₂²×C₇₃	—	8	1	no	—
202	C₂²×C₇₃	—	8	2	no	—
203	C₂²×C₇₃	#525	1	1	yes	characteristic
204	C₂²×C₇₃	#525	1	1	yes	characteristic
205	C₂²×C₇₃	C₂×#127	1	1	yes	characteristic
206	C₂²×C₇₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
207	C₂²×C₇₃	#575	1	2	yes	—
208	C₄×C₇₃	—	2	4	no	—
209	C₄×C₇₃	—	2	2	no	—
210	C₄×C₇₃	—	2	2	no	—
211	C₄×C₇₃	—	4	2	no	—
212	C₄×C₇₃	—	4	2	no	—
213	C₄×C₇₃	—	8	1	no	—
214	C₄×C₇₃	—	8	2	no	—
215	C₄×C₇₃	—	8	1	no	—
216	C₄×C₇₃	#525	1	2	yes	—
217	C₄×C₇₃	#525	1	2	yes	—
218	#23806	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
219	C₂×C₇₃	—	8	4	no	—
220	C₂×C₇₃	—	8	2	no	—
221	C₂×C₇₃	#2397	1	1	yes	characteristic
222	C₂×C₇₃	#3114	1	2	yes	—
223	C₂×C₇₃	#3115	1	2	yes	—
224	C₂×C₇₃	#3151	1	1	yes	characteristic
225	C₂×C₇₃	#3153	1	1	yes	characteristic
226	C₂×#442	C₂×C₇₃	1	2	yes	complemented
227	C₂×#440	C₂×C₇₃	1	2	yes	complemented
228	C₄×#127	C₂×C₇₃	1	1	yes	characteristic, complemented
229	C₄×#124	C₂×C₇₃	1	1	yes	characteristic, complemented
230	#2096	C₂×C₇₃	1	1	yes	characteristic, complemented
231	#2093	C₂×C₇₃	1	1	yes	characteristic, complemented
232	#2092	C₂×C₇₃	1	2	yes	complemented
233	#2014	C₂×C₇₃	1	1	yes	characteristic, complemented
234	#2012	C₂×C₇₃	1	2	yes	complemented
235	#2011	C₂×C₇₃	1	1	yes	characteristic
236	#1745	C₂×C₇₃	1	1	yes	characteristic, complemented
237	C₇₃	#23806	1	1	yes	characteristic, direct product factor, Sylow
238	C₂²×SD₁₆	C₂²×C₇₃	1	2	yes	—
239	C₂²×D₈	C₂²×C₇₃	1	2	yes	—
240	C₂×#127	C₂²×C₇₃	1	1	yes	characteristic
241	C₂×#124	C₂²×C₇₃	1	1	yes	characteristic
242	C₂×C₄×Q₈	C₂²×C₇₃	1	1	yes	characteristic
243	C₂×C₄×D₄	—	2	2	no	—
244	C₂×C₄×D₄	C₂²×C₇₃	1	2	yes	—
245	C₂×C₄×D₄	C₂²×C₇₃	1	1	yes	characteristic
246	#442	—	2	8	no	—
247	#440	—	2	8	no	—
248	C₂×#107	C₂²×C₇₃	1	2	yes	—
249	C₂×#106	C₂²×C₇₃	1	2	yes	—
250	C₂×#103	C₂²×C₇₃	1	2	yes	—
251	C₂×#102	C₂²×C₇₃	1	2	yes	—
252	C₂×#102	C₂²×C₇₃	1	2	yes	—
253	C₂×#102	C₂²×C₇₃	1	2	yes	—
254	C₂×#97	C₂²×C₇₃	1	2	yes	—
255	#391	C₂²×C₇₃	1	1	yes	characteristic
256	#390	—	2	2	no	—
257	#390	C₂²×C₇₃	1	2	yes	—
258	#390	C₂²×C₇₃	1	1	yes	characteristic
259	#388	—	2	2	no	—
260	#384	C₂²×C₇₃	1	1	yes	characteristic
261	#382	C₂²×C₇₃	1	1	yes	characteristic
262	C₄×C₂²⋊C₄	—	2	2	no	—
263	C₄³	C₂²×C₇₃	1	1	yes	characteristic
264	#336	C₂²×C₇₃	1	2	yes	—
265	#336	C₂²×C₇₃	1	1	yes	characteristic
266	#336	C₂²×C₇₃	1	1	yes	characteristic
267	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
268	C₂²×D₄	—	2	2	no	—
269	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
270	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
271	C₂³×C₄	—	2	2	no	—
272	C₂³×C₄	—	2	1	no	—
273	C₂×SD₁₆	—	2	4	no	—
274	C₂×SD₁₆	—	2	4	no	—
275	C₂×SD₁₆	—	2	4	no	—
276	C₂×D₈	—	2	4	no	—
277	C₂×D₈	—	2	4	no	—
278	C₂×D₈	—	2	4	no	—
279	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
280	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
281	#127	—	2	4	no	—
282	#124	—	2	2	no	—
283	#124	—	2	2	no	—
284	C₄×Q₈	—	2	4	no	—
285	C₄×D₄	—	2	4	no	—
286	C₄×D₄	—	2	4	no	—
287	C₄×D₄	—	2	4	no	—
288	C₄×D₄	—	4	8	no	—
289	C₂×C₄⋊C₄	—	2	2	no	—
290	C₂×C₄⋊C₄	—	2	1	no	—
291	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
292	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
293	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
294	C₂×C₂²⋊C₄	—	2	2	no	—
295	C₂×C₂²⋊C₄	—	2	4	no	—
296	C₂×C₂²⋊C₄	—	2	1	no	—
297	C₂×C₂²⋊C₄	—	2	2	no	—
298	C₂×C₂²⋊C₄	—	2	2	no	—
299	C₂×C₄²	—	2	1	no	—
300	C₂×C₄²	D₄×C₇₃	1	2	yes	—
301	C₂×C₄²	D₄×C₇₃	1	2	yes	—
302	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
303	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
304	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
305	#107	—	2	4	no	—
306	#106	—	2	4	no	—
307	#103	—	2	4	no	—
308	#102	—	2	4	no	—
309	#102	—	2	4	no	—
310	#102	—	2	4	no	—
311	#97	D₄×C₇₃	1	8	yes	complemented
312	#95	—	2	2	no	—
313	#95	—	2	2	no	—
314	C₂⁴	—	2	1	no	—
315	C₂⁴	—	2	2	no	—
316	C₂×Q₈	—	2	1	no	—
317	C₂×Q₈	—	2	2	no	—
318	C₂×Q₈	—	2	2	no	—
319	C₂×Q₈	#41×C₇₃	1	2	yes	—
320	C₂×D₄	—	2	8	no	—
321	C₂×D₄	—	2	2	no	—
322	C₂×D₄	—	2	2	no	—
323	C₂×D₄	—	2	2	no	—
324	C₂×D₄	—	2	2	no	—
325	C₂×D₄	—	2	2	no	—
326	C₂×D₄	—	2	2	no	—
327	C₂×D₄	—	2	1	no	—
328	C₂×D₄	—	2	2	no	—
329	C₂×D₄	—	4	4	no	—
330	C₂×D₄	—	4	4	no	—
331	C₂×D₄	#41×C₇₃	1	2	yes	—
332	C₂×D₄	#41×C₇₃	1	4	yes	—
333	C₂²×C₄	—	2	1	no	—
334	C₂²×C₄	—	2	1	no	—
335	C₂²×C₄	—	2	1	no	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	4	8	no	—
338	C₂²×C₄	—	4	4	no	—
339	C₂²×C₄	—	4	2	no	—
340	C₂²×C₄	—	4	4	no	—
341	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
342	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
343	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
344	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
345	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
346	SD₁₆	—	2	16	no	—
347	D₈	—	2	16	no	—
348	C₂×C₈	—	2	2	no	—
349	C₂×C₈	—	2	2	no	—
350	C₂×C₈	—	2	2	no	—
351	C₂×C₈	—	2	2	no	—
352	C₂×C₈	C₂×D₄×C₇₃	1	4	yes	—
353	C₂×C₈	C₂×D₄×C₇₃	1	4	yes	—
354	C₄⋊C₄	—	2	2	no	—
355	C₄⋊C₄	—	2	2	no	—
356	C₄⋊C₄	—	2	2	no	—
357	C₄⋊C₄	—	2	2	no	—
358	C₄⋊C₄	—	4	2	no	—
359	C₄⋊C₄	—	4	4	no	—
360	C₂²⋊C₄	—	2	8	no	—
361	C₂²⋊C₄	—	4	8	no	—
362	C₂²⋊C₄	—	4	4	no	—
363	C₂²⋊C₄	—	4	2	no	—
364	C₂²⋊C₄	—	4	4	no	—
365	C₄²	—	2	4	no	—
366	C₄²	—	2	1	no	—
367	C₄²	—	2	1	no	—
368	C₄²	—	2	2	no	—
369	C₄²	—	4	2	no	—
370	C₄²	—	4	2	no	—
371	C₄²	C₂×D₄×C₇₃	1	4	yes	—
372	C₂³	—	2	2	no	—
373	C₂³	—	2	4	no	—
374	C₂³	—	4	1	no	—
375	C₂³	—	4	2	no	—
376	C₂³	—	4	2	no	—
377	C₂³	—	4	1	no	—
378	C₂³	—	4	4	no	—
379	C₂³	—	4	2	no	—
380	C₂³	—	4	2	no	—
381	C₂³	—	4	4	no	—
382	C₂³	C₂²×D₄×C₇₃	1	1	yes	characteristic
383	Q₈	—	2	4	no	—
384	Q₈	—	4	2	no	—
385	D₄	—	2	4	no	—
386	D₄	—	2	4	no	—
387	D₄	—	2	4	no	—
388	D₄	—	4	16	no	—
389	D₄	—	4	2	no	—
390	D₄	—	4	2	no	—
391	D₄	—	4	2	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	4	1	no	—
401	C₂×C₄	—	4	1	no	—
402	C₂×C₄	—	4	1	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	1	no	—
405	C₂×C₄	—	4	4	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	8	8	no	—
409	C₂×C₄	—	8	4	no	—
410	C₂×C₄	#127×C₇₃	1	2	yes	—
411	C₂×C₄	#127×C₇₃	1	2	yes	—
412	C₂×C₄	AGL(1,ℤ/8)×C₇₃	1	4	yes	—
413	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
414	C₂×C₄	C₂×#41×C₇₃	1	1	yes	characteristic
415	C₂×C₄	C₂×#41×C₇₃	1	1	yes	characteristic
416	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
417	C₈	—	2	4	no	—
418	C₈	—	2	4	no	—
419	C₂²	—	4	8	no	—
420	C₂²	—	4	4	no	—
421	C₂²	—	4	2	no	—
422	C₂²	—	4	4	no	—
423	C₂²	—	8	2	no	—
424	C₂²	—	8	4	no	—
425	C₂²	—	8	2	no	—
426	C₂²	—	8	1	no	—
427	C₂²	—	8	1	no	—
428	C₂²	—	8	2	no	—
429	C₂²	#525×C₇₃	1	1	yes	characteristic
430	C₂²	#525×C₇₃	1	1	yes	characteristic
431	C₂²	C₂×#127×C₇₃	1	1	yes	characteristic
432	C₂²	C₂×AGL(1,ℤ/8)×C₇₃	1	2	yes	—
433	C₂²	#575×C₇₃	1	2	yes	—
434	C₄	—	2	4	no	—
435	C₄	—	2	2	no	—
436	C₄	—	2	2	no	—
437	C₄	—	4	2	no	—
438	C₄	—	4	2	no	—
439	C₄	—	8	2	no	—
440	C₄	—	8	1	no	—
441	C₄	—	8	1	no	—
442	C₄	#525×C₇₃	1	2	yes	—
443	C₄	#525×C₇₃	1	2	yes	—
444	C₂	—	8	4	no	—
445	C₂	—	8	2	no	—
446	C₂	C₇₃×#2397	1	1	yes	characteristic
447	C₂	C₇₃×#3114	1	2	yes	—
448	C₂	C₇₃×#3115	1	2	yes	—
449	C₂	C₇₃×#3151	1	1	yes	characteristic
450	C₂	C₇₃×#3153	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₃
prime radical	C₇₃×#2011	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇₃ ◁ C₄³×C₇₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#442×C₇₃	C₂	semidirect
2. C₂×#440×C₇₃	C₂	semidirect
3. C₄×#127×C₇₃	C₂	semidirect
4. C₄×#124×C₇₃	C₂	semidirect
5. C₇₃×#2096	C₂	semidirect
6. C₇₃×#2093	C₂	semidirect
7. C₇₃×#2092	C₂	semidirect
8. C₇₃×#2014	C₂	semidirect
9. C₇₃×#2012	C₂	semidirect
11. C₇₃×#1745	C₂	semidirect
85. #97×C₇₃	D₄	semidirect
218. #23806	C₇₃	direct (N × H)
226. C₂×#442	C₂×C₇₃	semidirect
227. C₂×#440	C₂×C₇₃	semidirect
228. C₄×#127	C₂×C₇₃	semidirect
229. C₄×#124	C₂×C₇₃	semidirect
230. #2096	C₂×C₇₃	semidirect
231. #2093	C₂×C₇₃	semidirect
232. #2092	C₂×C₇₃	semidirect
233. #2014	C₂×C₇₃	semidirect
234. #2012	C₂×C₇₃	semidirect
236. #1745	C₂×C₇₃	semidirect
237. C₇₃	#23806	direct (N × H)
311. #97	D₄×C₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#442×C₇₃	2
C₂×#440×C₇₃	2
C₄×#127×C₇₃	2
C₄×#124×C₇₃	2
C₇₃×#2096	2
C₇₃×#2093	2
C₇₃×#2092	2
C₇₃×#2014	2
C₇₃×#2012	2
C₇₃×#2011	2
C₇₃×#1745	2
#23806	73

Subgroups — C73×#23806 #32933210

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#23806 #32933210