Subgroups — C₇₃×#25812 #32935216

Order 18688.

1078 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#533×C₇₃	C₂	1	1	yes	maximal, characteristic
2	C₂×#500×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#498×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₃×#2857	C₂	1	1	yes	maximal, characteristic
5	C₇₃×#2059	C₂	1	4	yes	maximal, complemented
6	C₇₃×#1990	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇₃×#1990	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇₃×#1854	C₂	1	4	yes	maximal
9	C₄×C₂²⋊C₈×C₇₃	C₂	1	1	yes	maximal, characteristic
10	#533×C₇₃	—	2	4	no	—
11	#533×C₇₃	—	2	4	no	—
12	C₂×C₄⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
15	C₂×#125×C₇₃	C₂²	1	2	yes	—
16	C₂×C₂²⋊Q₈×C₇₃	—	2	1	no	—
17	C₂×C₂²⋊Q₈×C₇₃	—	2	1	no	—
18	C₂×C₂²⋊Q₈×C₇₃	—	2	1	no	—
19	C₂×C₄×Q₈×C₇₃	—	2	1	no	—
20	C₂×C₄×Q₈×C₇₃	—	2	1	no	—
21	C₂×#117×C₇₃	C₂²	1	2	yes	—
22	C₂²×C₄²×C₇₃	C₂²	1	1	yes	characteristic
23	#500×C₇₃	—	2	4	no	—
24	#498×C₇₃	—	2	4	no	—
25	C₂×#107×C₇₃	C₂²	1	4	yes	—
26	C₂×#106×C₇₃	C₂²	1	4	yes	—
27	C₂×C₂²⋊C₈×C₇₃	C₂²	1	2	yes	—
28	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
30	#391×C₇₃	—	2	1	no	—
31	#389×C₇₃	—	2	1	no	—
32	#389×C₇₃	C₂²	1	2	yes	—
33	#384×C₇₃	C₂²	1	1	yes	characteristic
34	#380×C₇₃	—	2	1	no	—
35	#380×C₇₃	C₂²	1	2	yes	—
36	#340×C₇₃	C₂²	1	4	yes	—
37	#340×C₇₃	C₂²	1	4	yes	—
38	#336×C₇₃	C₂²	1	2	yes	—
39	C₂²×Q₈×C₇₃	—	2	1	no	—
40	C₂²×Q₈×C₇₃	—	2	1	no	—
41	C₂²×Q₈×C₇₃	—	2	1	no	—
42	C₂³×C₄×C₇₃	D₄	1	1	yes	characteristic
43	C₂³×C₄×C₇₃	D₄	1	1	yes	characteristic
44	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
45	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
46	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
47	C₄⋊Q₈×C₇₃	—	2	2	no	—
48	C₄⋊Q₈×C₇₃	—	2	2	no	—
49	C₄⋊Q₈×C₇₃	—	2	2	no	—
50	C₄⋊Q₈×C₇₃	—	2	2	no	—
51	C₄⋊Q₈×C₇₃	D₄	1	4	yes	—
52	C₄⋊Q₈×C₇₃	D₄	1	4	yes	—
53	#125×C₇₃	—	2	4	no	—
54	#125×C₇₃	—	2	4	no	—
55	C₂²⋊Q₈×C₇₃	—	2	8	no	—
56	C₂²⋊Q₈×C₇₃	—	2	8	no	—
57	C₂²⋊Q₈×C₇₃	—	4	4	no	—
58	C₄×Q₈×C₇₃	—	2	8	no	—
59	C₄×Q₈×C₇₃	—	2	8	no	—
60	#117×C₇₃	—	2	4	no	—
61	#117×C₇₃	—	2	4	no	—
62	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
63	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
64	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
65	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
66	C₂×C₄⋊C₄×C₇₃	—	2	1	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	C₂³	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×C₄²×C₇₃	—	2	2	no	—
77	C₂×C₄²×C₇₃	—	2	2	no	—
78	C₂×C₄²×C₇₃	—	2	2	no	—
79	C₂×C₄²×C₇₃	D₄	1	1	yes	characteristic
80	C₂×C₄²×C₇₃	D₄	1	1	yes	characteristic
81	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
82	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
83	#107×C₇₃	—	2	8	no	—
84	#106×C₇₃	—	2	8	no	—
85	C₂²⋊C₈×C₇₃	Q₈	1	8	yes	complemented
86	C₄×C₈×C₇₃	—	2	2	no	—
87	C₄×C₈×C₇₃	—	2	2	no	—
88	#95×C₇₃	—	2	2	no	—
89	#95×C₇₃	—	2	2	no	—
90	C₂⁴×C₇₃	C₂×D₄	1	1	yes	characteristic
91	C₂×Q₈×C₇₃	—	2	4	no	—
92	C₂×Q₈×C₇₃	—	2	4	no	—
93	C₂×Q₈×C₇₃	—	4	2	no	—
94	C₂×Q₈×C₇₃	—	4	2	no	—
95	C₂×Q₈×C₇₃	—	4	2	no	—
96	C₂×Q₈×C₇₃	—	4	2	no	—
97	C₂×Q₈×C₇₃	—	4	2	no	—
98	C₂×Q₈×C₇₃	—	4	2	no	—
99	C₂×Q₈×C₇₃	—	4	2	no	—
100	C₂²×C₄×C₇₃	—	2	1	no	—
101	C₂²×C₄×C₇₃	—	2	1	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	2	no	—
106	C₂²×C₄×C₇₃	—	2	2	no	—
107	C₂²×C₄×C₇₃	—	2	2	no	—
108	C₂²×C₄×C₇₃	—	2	2	no	—
109	C₂²×C₄×C₇₃	—	2	2	no	—
110	C₂²×C₄×C₇₃	—	2	2	no	—
111	C₂²×C₄×C₇₃	—	2	2	no	—
112	C₂²×C₄×C₇₃	—	2	2	no	—
113	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
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×Q₈	1	4	yes	—
119	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
120	C₂×C₈×C₇₃	—	2	2	no	—
121	C₂×C₈×C₇₃	—	2	2	no	—
122	C₂×C₈×C₇₃	—	2	2	no	—
123	C₂×C₈×C₇₃	—	2	2	no	—
124	C₂×C₈×C₇₃	C₂×Q₈	1	4	yes	—
125	C₂×C₈×C₇₃	C₂×Q₈	1	4	yes	—
126	C₄⋊C₄×C₇₃	—	2	8	no	—
127	C₄⋊C₄×C₇₃	—	2	8	no	—
128	C₄⋊C₄×C₇₃	—	2	4	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	4	no	—
135	C₄⋊C₄×C₇₃	—	4	4	no	—
136	C₄⋊C₄×C₇₃	—	4	2	no	—
137	C₄⋊C₄×C₇₃	—	4	2	no	—
138	C₄⋊C₄×C₇₃	—	4	2	no	—
139	C₄⋊C₄×C₇₃	C₂×D₄	1	4	yes	—
140	C₄⋊C₄×C₇₃	C₂×D₄	1	4	yes	—
141	C₂²⋊C₄×C₇₃	—	2	8	no	—
142	C₂²⋊C₄×C₇₃	—	4	4	no	—
143	C₄²×C₇₃	—	2	8	no	—
144	C₄²×C₇₃	—	2	2	no	—
145	C₄²×C₇₃	—	2	2	no	—
146	C₄²×C₇₃	—	2	1	no	—
147	C₄²×C₇₃	—	2	1	no	—
148	C₄²×C₇₃	C₂×D₄	1	2	yes	—
149	C₄²×C₇₃	C₂×D₄	1	2	yes	—
150	C₂³×C₇₃	—	2	1	no	—
151	C₂³×C₇₃	—	2	1	no	—
152	C₂³×C₇₃	—	2	1	no	—
153	C₂³×C₇₃	—	2	1	no	—
154	C₂³×C₇₃	—	2	1	no	—
155	C₂³×C₇₃	—	2	1	no	—
156	C₂³×C₇₃	C₄⋊Q₈	1	2	yes	—
157	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
158	Q₈×C₇₃	—	4	8	no	—
159	Q₈×C₇₃	—	4	8	no	—
160	Q₈×C₇₃	—	8	4	no	—
161	C₂×C₄×C₇₃	—	2	1	no	—
162	C₂×C₄×C₇₃	—	2	1	no	—
163	C₂×C₄×C₇₃	—	2	4	no	—
164	C₂×C₄×C₇₃	—	2	4	no	—
165	C₂×C₄×C₇₃	—	2	1	no	—
166	C₂×C₄×C₇₃	—	2	1	no	—
167	C₂×C₄×C₇₃	—	2	4	no	—
168	C₂×C₄×C₇₃	—	2	4	no	—
169	C₂×C₄×C₇₃	—	2	1	no	—
170	C₂×C₄×C₇₃	—	2	1	no	—
171	C₂×C₄×C₇₃	—	2	1	no	—
172	C₂×C₄×C₇₃	—	2	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	4	no	—
178	C₂×C₄×C₇₃	—	4	4	no	—
179	C₂×C₄×C₇₃	—	4	2	no	—
180	C₂×C₄×C₇₃	—	4	2	no	—
181	C₂×C₄×C₇₃	—	4	2	no	—
182	C₂×C₄×C₇₃	—	4	2	no	—
183	C₂×C₄×C₇₃	—	4	2	no	—
184	C₂×C₄×C₇₃	—	4	2	no	—
185	C₂×C₄×C₇₃	#120	1	2	yes	—
186	C₂×C₄×C₇₃	#120	1	2	yes	—
187	C₂×C₄×C₇₃	C₄⋊Q₈	1	2	yes	—
188	C₂×C₄×C₇₃	#135	1	2	yes	—
189	C₂×C₄×C₇₃	#135	1	2	yes	—
190	C₂×C₄×C₇₃	AGL(1,ℤ/8)	1	2	yes	—
191	C₂×C₄×C₇₃	#137	1	2	yes	—
192	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
193	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
194	C₂×C₄×C₇₃	C₂²×Q₈	1	2	yes	—
195	C₂×C₄×C₇₃	2₋¹⁺⁴	1	2	yes	—
196	C₈×C₇₃	—	2	4	no	—
197	C₈×C₇₃	—	2	4	no	—
198	C₂²×C₇₃	—	2	2	no	—
199	C₂²×C₇₃	—	2	2	no	—
200	C₂²×C₇₃	—	2	2	no	—
201	C₂²×C₇₃	—	4	1	no	—
202	C₂²×C₇₃	—	4	1	no	—
203	C₂²×C₇₃	—	4	1	no	—
204	C₂²×C₇₃	—	4	1	no	—
205	C₂²×C₇₃	C₂×#120	1	1	yes	characteristic
206	C₂²×C₇₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
207	C₂²×C₇₃	#536	1	1	yes	characteristic
208	C₂²×C₇₃	C₂×#135	1	1	yes	characteristic
209	C₂²×C₇₃	C₂×#135	1	1	yes	characteristic
210	C₂²×C₇₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
211	C₂²×C₇₃	C₂×#137	1	1	yes	characteristic
212	C₄×C₇₃	—	2	2	no	—
213	C₄×C₇₃	—	4	1	no	—
214	C₄×C₇₃	—	4	4	no	—
215	C₄×C₇₃	—	4	1	no	—
216	C₄×C₇₃	—	4	4	no	—
217	C₄×C₇₃	—	8	2	no	—
218	C₄×C₇₃	—	8	2	no	—
219	C₄×C₇₃	#449	1	4	yes	—
220	C₄×C₇₃	#452	1	4	yes	—
221	C₄×C₇₃	D₄×Q₈	1	2	yes	—
222	C₄×C₇₃	D₄×Q₈	1	2	yes	—
223	#25812	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
224	C₂×C₇₃	—	4	2	no	—
225	C₂×C₇₃	#2434	1	1	yes	characteristic
226	C₂×C₇₃	C₂×#449	1	1	yes	characteristic
227	C₂×C₇₃	C₂×#452	1	1	yes	characteristic
228	C₂×C₇₃	#3160	1	1	yes	characteristic
229	C₂×C₇₃	#3165	1	1	yes	characteristic
230	C₂×C₇₃	#3228	1	1	yes	characteristic
231	C₂×C₇₃	#3231	1	1	yes	characteristic
232	C₂×#533	C₂×C₇₃	1	1	yes	characteristic
233	C₂×#500	C₂×C₇₃	1	1	yes	characteristic, complemented
234	C₂×#498	C₂×C₇₃	1	1	yes	characteristic, complemented
235	#2857	C₂×C₇₃	1	1	yes	characteristic
236	#2059	C₂×C₇₃	1	4	yes	complemented
237	#1990	C₂×C₇₃	1	1	yes	characteristic, complemented
238	#1990	C₂×C₇₃	1	1	yes	characteristic, complemented
239	#1854	C₂×C₇₃	1	4	yes	—
240	C₄×C₂²⋊C₈	C₂×C₇₃	1	1	yes	characteristic
241	C₇₃	#25812	1	1	yes	characteristic, direct product factor, Sylow
242	#533	—	2	4	no	—
243	#533	—	2	4	no	—
244	C₂×C₄⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
245	C₂×C₄⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
246	C₂×C₄⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
247	C₂×#125	C₂²×C₇₃	1	2	yes	—
248	C₂×C₂²⋊Q₈	—	2	1	no	—
249	C₂×C₂²⋊Q₈	—	2	1	no	—
250	C₂×C₂²⋊Q₈	—	2	1	no	—
251	C₂×C₄×Q₈	—	2	1	no	—
252	C₂×C₄×Q₈	—	2	1	no	—
253	C₂×#117	C₂²×C₇₃	1	2	yes	—
254	C₂²×C₄²	C₂²×C₇₃	1	1	yes	characteristic
255	#500	—	2	4	no	—
256	#498	—	2	4	no	—
257	C₂×#107	C₂²×C₇₃	1	4	yes	—
258	C₂×#106	C₂²×C₇₃	1	4	yes	—
259	C₂×C₂²⋊C₈	C₂²×C₇₃	1	2	yes	—
260	C₂×C₄×C₈	C₂²×C₇₃	1	1	yes	characteristic
261	C₂×C₄×C₈	C₂²×C₇₃	1	1	yes	characteristic
262	#391	—	2	1	no	—
263	#389	—	2	1	no	—
264	#389	C₂²×C₇₃	1	2	yes	—
265	#384	C₂²×C₇₃	1	1	yes	characteristic
266	#380	—	2	1	no	—
267	#380	C₂²×C₇₃	1	2	yes	—
268	#340	C₂²×C₇₃	1	4	yes	—
269	#340	C₂²×C₇₃	1	4	yes	—
270	#336	C₂²×C₇₃	1	2	yes	—
271	C₂²×Q₈	—	2	1	no	—
272	C₂²×Q₈	—	2	1	no	—
273	C₂²×Q₈	—	2	1	no	—
274	C₂³×C₄	D₄×C₇₃	1	1	yes	characteristic
275	C₂³×C₄	D₄×C₇₃	1	1	yes	characteristic
276	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
277	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
278	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
279	C₄⋊Q₈	—	2	2	no	—
280	C₄⋊Q₈	—	2	2	no	—
281	C₄⋊Q₈	—	2	2	no	—
282	C₄⋊Q₈	—	2	2	no	—
283	C₄⋊Q₈	D₄×C₇₃	1	4	yes	—
284	C₄⋊Q₈	D₄×C₇₃	1	4	yes	—
285	#125	—	2	4	no	—
286	#125	—	2	4	no	—
287	C₂²⋊Q₈	—	2	8	no	—
288	C₂²⋊Q₈	—	2	8	no	—
289	C₂²⋊Q₈	—	4	4	no	—
290	C₄×Q₈	—	2	8	no	—
291	C₄×Q₈	—	2	8	no	—
292	#117	—	2	4	no	—
293	#117	—	2	4	no	—
294	C₂×C₄⋊C₄	—	2	2	no	—
295	C₂×C₄⋊C₄	—	2	2	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	—	2	2	no	—
300	C₂×C₄⋊C₄	—	2	1	no	—
301	C₂×C₄⋊C₄	—	2	1	no	—
302	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
303	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
304	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
305	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
306	C₂×C₂²⋊C₄	—	2	2	no	—
307	C₂×C₂²⋊C₄	—	2	2	no	—
308	C₂×C₄²	—	2	2	no	—
309	C₂×C₄²	—	2	2	no	—
310	C₂×C₄²	—	2	2	no	—
311	C₂×C₄²	D₄×C₇₃	1	1	yes	characteristic
312	C₂×C₄²	D₄×C₇₃	1	1	yes	characteristic
313	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
314	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
315	#107	—	2	8	no	—
316	#106	—	2	8	no	—
317	C₂²⋊C₈	Q₈×C₇₃	1	8	yes	complemented
318	C₄×C₈	—	2	2	no	—
319	C₄×C₈	—	2	2	no	—
320	#95	—	2	2	no	—
321	#95	—	2	2	no	—
322	C₂⁴	C₂×D₄×C₇₃	1	1	yes	characteristic
323	C₂×Q₈	—	2	4	no	—
324	C₂×Q₈	—	2	4	no	—
325	C₂×Q₈	—	4	2	no	—
326	C₂×Q₈	—	4	2	no	—
327	C₂×Q₈	—	4	2	no	—
328	C₂×Q₈	—	4	2	no	—
329	C₂×Q₈	—	4	2	no	—
330	C₂×Q₈	—	4	2	no	—
331	C₂×Q₈	—	4	2	no	—
332	C₂²×C₄	—	2	1	no	—
333	C₂²×C₄	—	2	1	no	—
334	C₂²×C₄	—	2	2	no	—
335	C₂²×C₄	—	2	2	no	—
336	C₂²×C₄	—	2	2	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	2	no	—
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
346	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
347	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
348	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
349	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
350	C₂²×C₄	C₂×Q₈×C₇₃	1	4	yes	—
351	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
352	C₂×C₈	—	2	2	no	—
353	C₂×C₈	—	2	2	no	—
354	C₂×C₈	—	2	2	no	—
355	C₂×C₈	—	2	2	no	—
356	C₂×C₈	C₂×Q₈×C₇₃	1	4	yes	—
357	C₂×C₈	C₂×Q₈×C₇₃	1	4	yes	—
358	C₄⋊C₄	—	2	8	no	—
359	C₄⋊C₄	—	2	8	no	—
360	C₄⋊C₄	—	2	4	no	—
361	C₄⋊C₄	—	2	4	no	—
362	C₄⋊C₄	—	2	2	no	—
363	C₄⋊C₄	—	2	2	no	—
364	C₄⋊C₄	—	2	2	no	—
365	C₄⋊C₄	—	2	2	no	—
366	C₄⋊C₄	—	2	4	no	—
367	C₄⋊C₄	—	4	4	no	—
368	C₄⋊C₄	—	4	2	no	—
369	C₄⋊C₄	—	4	2	no	—
370	C₄⋊C₄	—	4	2	no	—
371	C₄⋊C₄	C₂×D₄×C₇₃	1	4	yes	—
372	C₄⋊C₄	C₂×D₄×C₇₃	1	4	yes	—
373	C₂²⋊C₄	—	2	8	no	—
374	C₂²⋊C₄	—	4	4	no	—
375	C₄²	—	2	8	no	—
376	C₄²	—	2	2	no	—
377	C₄²	—	2	2	no	—
378	C₄²	—	2	1	no	—
379	C₄²	—	2	1	no	—
380	C₄²	C₂×D₄×C₇₃	1	2	yes	—
381	C₄²	C₂×D₄×C₇₃	1	2	yes	—
382	C₂³	—	2	1	no	—
383	C₂³	—	2	1	no	—
384	C₂³	—	2	1	no	—
385	C₂³	—	2	1	no	—
386	C₂³	—	2	1	no	—
387	C₂³	—	2	1	no	—
388	C₂³	C₄⋊Q₈×C₇₃	1	2	yes	—
389	C₂³	C₂²×D₄×C₇₃	1	1	yes	characteristic
390	Q₈	—	4	8	no	—
391	Q₈	—	4	8	no	—
392	Q₈	—	8	4	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	2	4	no	—
396	C₂×C₄	—	2	4	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	4	no	—
400	C₂×C₄	—	2	4	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	2	1	no	—
404	C₂×C₄	—	2	1	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	4	2	no	—
409	C₂×C₄	—	4	4	no	—
410	C₂×C₄	—	4	4	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	2	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	#120×C₇₃	1	2	yes	—
418	C₂×C₄	#120×C₇₃	1	2	yes	—
419	C₂×C₄	C₄⋊Q₈×C₇₃	1	2	yes	—
420	C₂×C₄	#135×C₇₃	1	2	yes	—
421	C₂×C₄	#135×C₇₃	1	2	yes	—
422	C₂×C₄	AGL(1,ℤ/8)×C₇₃	1	2	yes	—
423	C₂×C₄	#137×C₇₃	1	2	yes	—
424	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
425	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
426	C₂×C₄	C₂²×Q₈×C₇₃	1	2	yes	—
427	C₂×C₄	2₋¹⁺⁴×C₇₃	1	2	yes	—
428	C₈	—	2	4	no	—
429	C₈	—	2	4	no	—
430	C₂²	—	2	2	no	—
431	C₂²	—	2	2	no	—
432	C₂²	—	2	2	no	—
433	C₂²	—	4	1	no	—
434	C₂²	—	4	1	no	—
435	C₂²	—	4	1	no	—
436	C₂²	—	4	1	no	—
437	C₂²	C₂×#120×C₇₃	1	1	yes	characteristic
438	C₂²	C₂×C₄⋊Q₈×C₇₃	1	1	yes	characteristic
439	C₂²	#536×C₇₃	1	1	yes	characteristic
440	C₂²	C₂×#135×C₇₃	1	1	yes	characteristic
441	C₂²	C₂×#135×C₇₃	1	1	yes	characteristic
442	C₂²	C₂×AGL(1,ℤ/8)×C₇₃	1	1	yes	characteristic
443	C₂²	C₂×#137×C₇₃	1	1	yes	characteristic
444	C₄	—	2	2	no	—
445	C₄	—	4	1	no	—
446	C₄	—	4	4	no	—
447	C₄	—	4	1	no	—
448	C₄	—	4	4	no	—
449	C₄	—	8	2	no	—
450	C₄	—	8	2	no	—
451	C₄	#449×C₇₃	1	4	yes	—
452	C₄	#452×C₇₃	1	4	yes	—
453	C₄	D₄×Q₈×C₇₃	1	2	yes	—
454	C₄	D₄×Q₈×C₇₃	1	2	yes	—
455	C₂	—	4	2	no	—
456	C₂	C₇₃×#2434	1	1	yes	characteristic
457	C₂	C₂×#449×C₇₃	1	1	yes	characteristic
458	C₂	C₂×#452×C₇₃	1	1	yes	characteristic
459	C₂	C₇₃×#3160	1	1	yes	characteristic
460	C₂	C₇₃×#3165	1	1	yes	characteristic
461	C₂	C₇₃×#3228	1	1	yes	characteristic
462	C₂	C₇₃×#3231	1	1	yes	characteristic

	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 ◁ C₂²×C₄²×C₇₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#500×C₇₃	C₂	semidirect
3. C₂×#498×C₇₃	C₂	semidirect
5. C₇₃×#2059	C₂	semidirect
6. C₇₃×#1990	C₂	semidirect
7. C₇₃×#1990	C₂	semidirect
85. C₂²⋊C₈×C₇₃	Q₈	semidirect
223. #25812	C₇₃	direct (N × H)
233. C₂×#500	C₂×C₇₃	semidirect
234. C₂×#498	C₂×C₇₃	semidirect
236. #2059	C₂×C₇₃	semidirect
237. #1990	C₂×C₇₃	semidirect
238. #1990	C₂×C₇₃	semidirect
241. C₇₃	#25812	direct (N × H)
317. C₂²⋊C₈	Q₈×C₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#533×C₇₃	2
C₂×#500×C₇₃	2
C₂×#498×C₇₃	2
C₇₃×#2857	2
C₇₃×#2059	2
C₇₃×#1990	2
C₇₃×#1854	2
C₄×C₂²⋊C₈×C₇₃	2
#25812	73

Subgroups — C73×#25812 #32935216

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#25812 #32935216