Subgroups — C₇₃×#23617 #32933021

Order 18688.

1178 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#428×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#423×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#417×C₇₃	C₂	1	1	yes	maximal, characteristic
4	C₂×#417×C₇₃	C₂	1	1	yes	maximal, characteristic
5	C₇₃×#2297	C₂	1	1	yes	maximal, characteristic
6	C₂×#389×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇₃×#2068	C₂	1	2	yes	maximal, complemented
8	C₇₃×#2067	C₂	1	2	yes	maximal, complemented
9	C₇₃×#2066	C₂	1	2	yes	maximal, complemented
10	C₇₃×#2065	C₂	1	2	yes	maximal, complemented
11	C₇₃×#1736	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#41×C₇₃	C₂²	1	1	yes	characteristic
13	C₂²×M₁₆×C₇₃	C₂²	1	1	yes	characteristic
14	C₂²×M₁₆×C₇₃	C₂²	1	1	yes	characteristic
15	C₂×#117×C₇₃	C₂²	1	1	yes	characteristic
16	C₂²×C₄⋊C₄×C₇₃	—	2	1	no	—
17	C₂²×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
18	C₂²×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
19	C₂²×C₄²×C₇₃	C₂²	1	1	yes	characteristic
20	#428×C₇₃	—	2	4	no	—
21	C₂×#107×C₇₃	C₂²	1	2	yes	—
22	C₂×#106×C₇₃	C₂²	1	2	yes	—
23	#423×C₇₃	—	2	4	no	—
24	C₂×C₄⋊C₈×C₇₃	C₂²	1	2	yes	—
25	C₂×C₄⋊C₈×C₇₃	C₂²	1	2	yes	—
26	#417×C₇₃	—	2	4	no	—
27	#417×C₇₃	—	2	4	no	—
28	C₂×#103×C₇₃	C₂²	1	2	yes	—
29	C₂×#103×C₇₃	C₂²	1	2	yes	—
30	C₂×#102×C₇₃	C₂²	1	2	yes	—
31	C₂×#102×C₇₃	C₂²	1	2	yes	—
32	#391×C₇₃	C₂²	1	1	yes	characteristic
33	#391×C₇₃	C₂²	1	1	yes	characteristic
34	#390×C₇₃	C₂²	1	1	yes	characteristic
35	#390×C₇₃	C₂²	1	1	yes	characteristic
36	#389×C₇₃	—	2	1	no	—
37	#389×C₇₃	—	2	1	no	—
38	#389×C₇₃	C₂²	1	2	yes	—
39	#389×C₇₃	C₂²	1	2	yes	—
40	#386×C₇₃	—	2	1	no	—
41	#386×C₇₃	—	2	1	no	—
42	C₄×C₂²⋊C₄×C₇₃	—	2	1	no	—
43	C₄×C₂²⋊C₄×C₇₃	—	2	1	no	—
44	C₂×#95×C₇₃	—	2	1	no	—
45	#340×C₇₃	C₂²	1	2	yes	—
46	#340×C₇₃	C₂²	1	2	yes	—
47	C₂×#41×C₇₃	—	2	2	no	—
48	C₂×#41×C₇₃	—	2	2	no	—
49	C₂×#41×C₇₃	—	2	2	no	—
50	C₂×#41×C₇₃	—	2	2	no	—
51	C₂×#41×C₇₃	—	2	2	no	—
52	C₂×#41×C₇₃	Q₈	1	4	yes	—
53	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
54	C₂²×D₄×C₇₃	—	2	1	no	—
55	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
56	C₂³×C₄×C₇₃	—	2	1	no	—
57	C₂³×C₄×C₇₃	—	2	1	no	—
58	C₂³×C₄×C₇₃	—	2	1	no	—
59	C₂³×C₄×C₇₃	D₄	1	1	yes	characteristic
60	C₂³×C₄×C₇₃	D₄	1	1	yes	characteristic
61	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
62	C₂×M₁₆×C₇₃	—	2	2	no	—
63	C₂×M₁₆×C₇₃	—	2	2	no	—
64	C₂×M₁₆×C₇₃	—	2	2	no	—
65	C₂×M₁₆×C₇₃	—	2	2	no	—
66	C₂×M₁₆×C₇₃	—	2	2	no	—
67	C₂×M₁₆×C₇₃	D₄	1	4	yes	—
68	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
69	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
70	#117×C₇₃	—	2	2	no	—
71	#117×C₇₃	—	2	2	no	—
72	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
73	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
74	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
75	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
76	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
77	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
78	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
79	C₂×C₄⋊C₄×C₇₃	—	4	4	no	—
80	C₂×C₄⋊C₄×C₇₃	D₄	1	4	yes	—
81	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
82	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
83	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
84	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
85	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
86	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
87	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
88	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
89	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
90	C₂×C₄²×C₇₃	—	2	2	no	—
91	C₂×C₄²×C₇₃	—	2	2	no	—
92	C₂×C₄²×C₇₃	—	2	1	no	—
93	C₂×C₄²×C₇₃	D₄	1	1	yes	characteristic
94	C₂×C₄²×C₇₃	D₄	1	1	yes	characteristic
95	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
96	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
97	#107×C₇₃	—	2	4	no	—
98	#106×C₇₃	—	2	4	no	—
99	C₄⋊C₈×C₇₃	—	2	4	no	—
100	C₄⋊C₈×C₇₃	—	2	4	no	—
101	#103×C₇₃	—	2	4	no	—
102	#103×C₇₃	—	2	4	no	—
103	#102×C₇₃	—	2	4	no	—
104	#102×C₇₃	—	2	4	no	—
105	#95×C₇₃	—	2	1	no	—
106	#95×C₇₃	—	2	1	no	—
107	#95×C₇₃	—	2	1	no	—
108	#95×C₇₃	—	2	1	no	—
109	#95×C₇₃	—	2	2	no	—
110	#95×C₇₃	—	2	2	no	—
111	C₂⁴×C₇₃	—	2	1	no	—
112	C₂⁴×C₇₃	C₂×D₄	1	1	yes	characteristic
113	#41×C₇₃	—	2	8	no	—
114	#41×C₇₃	—	2	8	no	—
115	#41×C₇₃	—	4	4	no	—
116	#41×C₇₃	—	4	4	no	—
117	C₂×Q₈×C₇₃	—	2	1	no	—
118	C₂×Q₈×C₇₃	—	2	1	no	—
119	C₂×Q₈×C₇₃	—	2	1	no	—
120	C₂×Q₈×C₇₃	—	2	1	no	—
121	C₂×Q₈×C₇₃	—	2	1	no	—
122	C₂×Q₈×C₇₃	C₂×Q₈	1	2	yes	—
123	C₂×D₄×C₇₃	—	2	4	no	—
124	C₂×D₄×C₇₃	—	2	1	no	—
125	C₂×D₄×C₇₃	—	2	1	no	—
126	C₂×D₄×C₇₃	—	2	1	no	—
127	C₂×D₄×C₇₃	—	2	1	no	—
128	C₂×D₄×C₇₃	—	2	1	no	—
129	C₂×D₄×C₇₃	—	4	2	no	—
130	C₂×D₄×C₇₃	—	4	2	no	—
131	C₂×D₄×C₇₃	C₂×Q₈	1	2	yes	—
132	C₂²×C₄×C₇₃	—	2	2	no	—
133	C₂²×C₄×C₇₃	—	2	2	no	—
134	C₂²×C₄×C₇₃	—	2	4	no	—
135	C₂²×C₄×C₇₃	—	2	1	no	—
136	C₂²×C₄×C₇₃	—	2	2	no	—
137	C₂²×C₄×C₇₃	—	2	4	no	—
138	C₂²×C₄×C₇₃	—	2	2	no	—
139	C₂²×C₄×C₇₃	—	2	2	no	—
140	C₂²×C₄×C₇₃	—	2	1	no	—
141	C₂²×C₄×C₇₃	—	2	1	no	—
142	C₂²×C₄×C₇₃	—	2	2	no	—
143	C₂²×C₄×C₇₃	—	4	1	no	—
144	C₂²×C₄×C₇₃	—	4	1	no	—
145	C₂²×C₄×C₇₃	—	4	2	no	—
146	C₂²×C₄×C₇₃	—	4	2	no	—
147	C₂²×C₄×C₇₃	—	4	2	no	—
148	C₂²×C₄×C₇₃	—	4	2	no	—
149	C₂²×C₄×C₇₃	—	4	2	no	—
150	C₂²×C₄×C₇₃	—	4	2	no	—
151	C₂²×C₄×C₇₃	—	4	2	no	—
152	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
153	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
154	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
155	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
156	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
157	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
158	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
159	C₂²×C₄×C₇₃	C₂×Q₈	1	2	yes	—
160	C₂²×C₄×C₇₃	#41	1	2	yes	—
161	C₂²×C₄×C₇₃	#41	1	2	yes	—
162	C₂²×C₄×C₇₃	#41	1	2	yes	—
163	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
164	M₁₆×C₇₃	—	2	8	no	—
165	M₁₆×C₇₃	—	4	4	no	—
166	C₂×C₈×C₇₃	—	2	2	no	—
167	C₂×C₈×C₇₃	—	2	2	no	—
168	C₂×C₈×C₇₃	—	2	2	no	—
169	C₂×C₈×C₇₃	—	2	2	no	—
170	C₂×C₈×C₇₃	—	2	2	no	—
171	C₂×C₈×C₇₃	C₂×D₄	1	4	yes	—
172	C₄⋊C₄×C₇₃	—	2	4	no	—
173	C₄⋊C₄×C₇₃	—	2	2	no	—
174	C₄⋊C₄×C₇₃	—	2	2	no	—
175	C₄⋊C₄×C₇₃	—	2	1	no	—
176	C₄⋊C₄×C₇₃	—	2	1	no	—
177	C₄⋊C₄×C₇₃	—	2	2	no	—
178	C₄⋊C₄×C₇₃	—	2	1	no	—
179	C₄⋊C₄×C₇₃	—	2	1	no	—
180	C₄⋊C₄×C₇₃	—	4	4	no	—
181	C₄⋊C₄×C₇₃	—	4	2	no	—
182	C₄⋊C₄×C₇₃	—	4	4	no	—
183	C₄⋊C₄×C₇₃	C₂×D₄	1	4	yes	—
184	C₂²⋊C₄×C₇₃	—	4	2	no	—
185	C₂²⋊C₄×C₇₃	—	4	2	no	—
186	C₂²⋊C₄×C₇₃	—	4	2	no	—
187	C₂²⋊C₄×C₇₃	—	4	2	no	—
188	C₂²⋊C₄×C₇₃	—	4	2	no	—
189	C₄²×C₇₃	—	2	2	no	—
190	C₄²×C₇₃	—	2	2	no	—
191	C₄²×C₇₃	—	2	1	no	—
192	C₄²×C₇₃	—	2	1	no	—
193	C₄²×C₇₃	—	2	1	no	—
194	C₄²×C₇₃	—	2	1	no	—
195	C₄²×C₇₃	—	4	2	no	—
196	C₂³×C₇₃	—	2	1	no	—
197	C₂³×C₇₃	—	2	1	no	—
198	C₂³×C₇₃	—	2	1	no	—
199	C₂³×C₇₃	—	2	1	no	—
200	C₂³×C₇₃	—	2	2	no	—
201	C₂³×C₇₃	—	4	1	no	—
202	C₂³×C₇₃	—	4	1	no	—
203	C₂³×C₇₃	—	4	1	no	—
204	C₂³×C₇₃	—	4	1	no	—
205	C₂³×C₇₃	—	4	1	no	—
206	C₂³×C₇₃	—	4	1	no	—
207	C₂³×C₇₃	#121	1	2	yes	—
208	C₂³×C₇₃	#121	1	2	yes	—
209	C₂³×C₇₃	C₂²⋊Q₈	1	2	yes	—
210	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
211	Q₈×C₇₃	—	2	2	no	—
212	Q₈×C₇₃	—	2	2	no	—
213	Q₈×C₇₃	—	4	1	no	—
214	Q₈×C₇₃	—	4	1	no	—
215	D₄×C₇₃	—	2	2	no	—
216	D₄×C₇₃	—	2	2	no	—
217	D₄×C₇₃	—	4	8	no	—
218	D₄×C₇₃	—	4	1	no	—
219	D₄×C₇₃	—	4	1	no	—
220	C₂×C₄×C₇₃	—	2	1	no	—
221	C₂×C₄×C₇₃	—	2	1	no	—
222	C₂×C₄×C₇₃	—	2	1	no	—
223	C₂×C₄×C₇₃	—	2	1	no	—
224	C₂×C₄×C₇₃	—	2	1	no	—
225	C₂×C₄×C₇₃	—	2	1	no	—
226	C₂×C₄×C₇₃	—	2	4	no	—
227	C₂×C₄×C₇₃	—	2	2	no	—
228	C₂×C₄×C₇₃	—	2	1	no	—
229	C₂×C₄×C₇₃	—	2	1	no	—
230	C₂×C₄×C₇₃	—	2	1	no	—
231	C₂×C₄×C₇₃	—	2	1	no	—
232	C₂×C₄×C₇₃	—	4	4	no	—
233	C₂×C₄×C₇₃	—	4	4	no	—
234	C₂×C₄×C₇₃	—	4	8	no	—
235	C₂×C₄×C₇₃	—	4	1	no	—
236	C₂×C₄×C₇₃	—	4	1	no	—
237	C₂×C₄×C₇₃	—	4	2	no	—
238	C₂×C₄×C₇₃	—	4	2	no	—
239	C₂×C₄×C₇₃	—	4	8	no	—
240	C₂×C₄×C₇₃	—	4	1	no	—
241	C₂×C₄×C₇₃	—	4	1	no	—
242	C₂×C₄×C₇₃	—	4	2	no	—
243	C₂×C₄×C₇₃	—	4	1	no	—
244	C₂×C₄×C₇₃	—	4	2	no	—
245	C₂×C₄×C₇₃	—	4	1	no	—
246	C₂×C₄×C₇₃	—	4	1	no	—
247	C₂×C₄×C₇₃	—	4	1	no	—
248	C₂×C₄×C₇₃	—	4	2	no	—
249	C₂×C₄×C₇₃	—	8	4	no	—
250	C₂×C₄×C₇₃	#121	1	4	yes	—
251	C₂×C₄×C₇₃	#121	1	2	yes	—
252	C₂×C₄×C₇₃	#121	1	2	yes	—
253	C₂×C₄×C₇₃	C₂²⋊Q₈	1	4	yes	—
254	C₂×C₄×C₇₃	C₂²⋊Q₈	1	4	yes	—
255	C₂×C₄×C₇₃	C₂²⋊Q₈	1	2	yes	—
256	C₂×C₄×C₇₃	#126	1	4	yes	—
257	C₂×C₄×C₇₃	AGL(1,ℤ/8)	1	2	yes	—
258	C₂×C₄×C₇₃	#137	1	2	yes	—
259	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
260	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
261	C₂×C₄×C₇₃	C₂²×Q₈	1	1	yes	characteristic
262	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
263	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
264	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
265	C₈×C₇₃	—	2	4	no	—
266	C₈×C₇₃	—	4	2	no	—
267	C₂²×C₇₃	—	2	2	no	—
268	C₂²×C₇₃	—	2	2	no	—
269	C₂²×C₇₃	—	2	2	no	—
270	C₂²×C₇₃	—	2	2	no	—
271	C₂²×C₇₃	—	2	2	no	—
272	C₂²×C₇₃	—	2	2	no	—
273	C₂²×C₇₃	—	4	2	no	—
274	C₂²×C₇₃	—	4	2	no	—
275	C₂²×C₇₃	—	4	2	no	—
276	C₂²×C₇₃	—	8	1	no	—
277	C₂²×C₇₃	—	8	1	no	—
278	C₂²×C₇₃	—	8	1	no	—
279	C₂²×C₇₃	—	8	1	no	—
280	C₂²×C₇₃	#396	1	4	yes	—
281	C₂²×C₇₃	C₂×#121	1	1	yes	characteristic
282	C₂²×C₇₃	C₂×#121	1	1	yes	characteristic
283	C₂²×C₇₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
284	C₂²×C₇₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
285	C₂²×C₇₃	C₂×#137	1	1	yes	characteristic
286	C₂²×C₇₃	#575	1	1	yes	characteristic
287	C₂²×C₇₃	#575	1	1	yes	characteristic
288	C₄×C₇₃	—	2	2	no	—
289	C₄×C₇₃	—	2	2	no	—
290	C₄×C₇₃	—	4	2	no	—
291	C₄×C₇₃	—	4	4	no	—
292	C₄×C₇₃	—	4	1	no	—
293	C₄×C₇₃	—	4	1	no	—
294	C₄×C₇₃	—	8	1	no	—
295	C₄×C₇₃	—	8	1	no	—
296	C₄×C₇₃	—	8	2	no	—
297	C₄×C₇₃	#396	1	4	yes	—
298	C₄×C₇₃	C₂×#121	1	1	yes	characteristic
299	C₄×C₇₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
300	C₄×C₇₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
301	C₄×C₇₃	C₂×#126	1	1	yes	characteristic
302	#23617	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
303	C₂×C₇₃	—	2	4	no	—
304	C₂×C₇₃	—	8	2	no	—
305	C₂×C₇₃	C₂×#396	1	1	yes	characteristic
306	C₂×C₇₃	#3036	1	1	yes	characteristic
307	C₂×C₇₃	#3037	1	1	yes	characteristic
308	C₂×C₇₃	#3055	1	1	yes	characteristic
309	C₂×C₇₃	#3056	1	1	yes	characteristic
310	C₂×C₇₃	#3079	1	1	yes	characteristic
311	C₂×C₇₃	#3080	1	1	yes	characteristic
312	C₂×#428	C₂×C₇₃	1	1	yes	characteristic, complemented
313	C₂×#423	C₂×C₇₃	1	1	yes	characteristic, complemented
314	C₂×#417	C₂×C₇₃	1	1	yes	characteristic
315	C₂×#417	C₂×C₇₃	1	1	yes	characteristic
316	#2297	C₂×C₇₃	1	1	yes	characteristic
317	C₂×#389	C₂×C₇₃	1	1	yes	characteristic, complemented
318	#2068	C₂×C₇₃	1	2	yes	complemented
319	#2067	C₂×C₇₃	1	2	yes	complemented
320	#2066	C₂×C₇₃	1	2	yes	complemented
321	#2065	C₂×C₇₃	1	2	yes	complemented
322	#1736	C₂×C₇₃	1	1	yes	characteristic, complemented
323	C₇₃	#23617	1	1	yes	characteristic, direct product factor, Sylow
324	C₂²×#41	C₂²×C₇₃	1	1	yes	characteristic
325	C₂²×M₁₆	C₂²×C₇₃	1	1	yes	characteristic
326	C₂²×M₁₆	C₂²×C₇₃	1	1	yes	characteristic
327	C₂×#117	C₂²×C₇₃	1	1	yes	characteristic
328	C₂²×C₄⋊C₄	—	2	1	no	—
329	C₂²×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
330	C₂²×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
331	C₂²×C₄²	C₂²×C₇₃	1	1	yes	characteristic
332	#428	—	2	4	no	—
333	C₂×#107	C₂²×C₇₃	1	2	yes	—
334	C₂×#106	C₂²×C₇₃	1	2	yes	—
335	#423	—	2	4	no	—
336	C₂×C₄⋊C₈	C₂²×C₇₃	1	2	yes	—
337	C₂×C₄⋊C₈	C₂²×C₇₃	1	2	yes	—
338	#417	—	2	4	no	—
339	#417	—	2	4	no	—
340	C₂×#103	C₂²×C₇₃	1	2	yes	—
341	C₂×#103	C₂²×C₇₃	1	2	yes	—
342	C₂×#102	C₂²×C₇₃	1	2	yes	—
343	C₂×#102	C₂²×C₇₃	1	2	yes	—
344	#391	C₂²×C₇₃	1	1	yes	characteristic
345	#391	C₂²×C₇₃	1	1	yes	characteristic
346	#390	C₂²×C₇₃	1	1	yes	characteristic
347	#390	C₂²×C₇₃	1	1	yes	characteristic
348	#389	—	2	1	no	—
349	#389	—	2	1	no	—
350	#389	C₂²×C₇₃	1	2	yes	—
351	#389	C₂²×C₇₃	1	2	yes	—
352	#386	—	2	1	no	—
353	#386	—	2	1	no	—
354	C₄×C₂²⋊C₄	—	2	1	no	—
355	C₄×C₂²⋊C₄	—	2	1	no	—
356	C₂×#95	—	2	1	no	—
357	#340	C₂²×C₇₃	1	2	yes	—
358	#340	C₂²×C₇₃	1	2	yes	—
359	C₂×#41	—	2	2	no	—
360	C₂×#41	—	2	2	no	—
361	C₂×#41	—	2	2	no	—
362	C₂×#41	—	2	2	no	—
363	C₂×#41	—	2	2	no	—
364	C₂×#41	Q₈×C₇₃	1	4	yes	—
365	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
366	C₂²×D₄	—	2	1	no	—
367	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
368	C₂³×C₄	—	2	1	no	—
369	C₂³×C₄	—	2	1	no	—
370	C₂³×C₄	—	2	1	no	—
371	C₂³×C₄	D₄×C₇₃	1	1	yes	characteristic
372	C₂³×C₄	D₄×C₇₃	1	1	yes	characteristic
373	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
374	C₂×M₁₆	—	2	2	no	—
375	C₂×M₁₆	—	2	2	no	—
376	C₂×M₁₆	—	2	2	no	—
377	C₂×M₁₆	—	2	2	no	—
378	C₂×M₁₆	—	2	2	no	—
379	C₂×M₁₆	D₄×C₇₃	1	4	yes	—
380	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
381	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
382	#117	—	2	2	no	—
383	#117	—	2	2	no	—
384	C₂×C₄⋊C₄	—	2	1	no	—
385	C₂×C₄⋊C₄	—	2	2	no	—
386	C₂×C₄⋊C₄	—	2	2	no	—
387	C₂×C₄⋊C₄	—	2	2	no	—
388	C₂×C₄⋊C₄	—	2	2	no	—
389	C₂×C₄⋊C₄	—	2	2	no	—
390	C₂×C₄⋊C₄	—	2	1	no	—
391	C₂×C₄⋊C₄	—	4	4	no	—
392	C₂×C₄⋊C₄	D₄×C₇₃	1	4	yes	—
393	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
394	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
395	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
396	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
397	C₂×C₂²⋊C₄	—	2	1	no	—
398	C₂×C₂²⋊C₄	—	2	1	no	—
399	C₂×C₂²⋊C₄	—	2	1	no	—
400	C₂×C₂²⋊C₄	—	2	1	no	—
401	C₂×C₂²⋊C₄	—	2	1	no	—
402	C₂×C₄²	—	2	2	no	—
403	C₂×C₄²	—	2	2	no	—
404	C₂×C₄²	—	2	1	no	—
405	C₂×C₄²	D₄×C₇₃	1	1	yes	characteristic
406	C₂×C₄²	D₄×C₇₃	1	1	yes	characteristic
407	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
408	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
409	#107	—	2	4	no	—
410	#106	—	2	4	no	—
411	C₄⋊C₈	—	2	4	no	—
412	C₄⋊C₈	—	2	4	no	—
413	#103	—	2	4	no	—
414	#103	—	2	4	no	—
415	#102	—	2	4	no	—
416	#102	—	2	4	no	—
417	#95	—	2	2	no	—
418	#95	—	2	2	no	—
419	#95	—	2	1	no	—
420	#95	—	2	1	no	—
421	#95	—	2	1	no	—
422	#95	—	2	1	no	—
423	C₂⁴	—	2	1	no	—
424	C₂⁴	C₂×D₄×C₇₃	1	1	yes	characteristic
425	#41	—	2	8	no	—
426	#41	—	2	8	no	—
427	#41	—	4	4	no	—
428	#41	—	4	4	no	—
429	C₂×Q₈	—	2	1	no	—
430	C₂×Q₈	—	2	1	no	—
431	C₂×Q₈	—	2	1	no	—
432	C₂×Q₈	—	2	1	no	—
433	C₂×Q₈	—	2	1	no	—
434	C₂×Q₈	C₂×Q₈×C₇₃	1	2	yes	—
435	C₂×D₄	—	2	4	no	—
436	C₂×D₄	—	2	1	no	—
437	C₂×D₄	—	2	1	no	—
438	C₂×D₄	—	2	1	no	—
439	C₂×D₄	—	2	1	no	—
440	C₂×D₄	—	2	1	no	—
441	C₂×D₄	—	4	2	no	—
442	C₂×D₄	—	4	2	no	—
443	C₂×D₄	C₂×Q₈×C₇₃	1	2	yes	—
444	C₂²×C₄	—	2	2	no	—
445	C₂²×C₄	—	2	2	no	—
446	C₂²×C₄	—	2	4	no	—
447	C₂²×C₄	—	2	1	no	—
448	C₂²×C₄	—	2	2	no	—
449	C₂²×C₄	—	2	4	no	—
450	C₂²×C₄	—	2	2	no	—
451	C₂²×C₄	—	2	2	no	—
452	C₂²×C₄	—	2	1	no	—
453	C₂²×C₄	—	2	1	no	—
454	C₂²×C₄	—	2	2	no	—
455	C₂²×C₄	—	4	1	no	—
456	C₂²×C₄	—	4	1	no	—
457	C₂²×C₄	—	4	2	no	—
458	C₂²×C₄	—	4	2	no	—
459	C₂²×C₄	—	4	2	no	—
460	C₂²×C₄	—	4	2	no	—
461	C₂²×C₄	—	4	2	no	—
462	C₂²×C₄	—	4	2	no	—
463	C₂²×C₄	—	4	2	no	—
464	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
465	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
466	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
467	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
468	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
469	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
470	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
471	C₂²×C₄	C₂×Q₈×C₇₃	1	2	yes	—
472	C₂²×C₄	#41×C₇₃	1	2	yes	—
473	C₂²×C₄	#41×C₇₃	1	2	yes	—
474	C₂²×C₄	#41×C₇₃	1	2	yes	—
475	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
476	M₁₆	—	2	8	no	—
477	M₁₆	—	4	4	no	—
478	C₂×C₈	—	2	2	no	—
479	C₂×C₈	—	2	2	no	—
480	C₂×C₈	—	2	2	no	—
481	C₂×C₈	—	2	2	no	—
482	C₂×C₈	—	2	2	no	—
483	C₂×C₈	C₂×D₄×C₇₃	1	4	yes	—
484	C₄⋊C₄	—	2	4	no	—
485	C₄⋊C₄	—	2	2	no	—
486	C₄⋊C₄	—	2	2	no	—
487	C₄⋊C₄	—	2	1	no	—
488	C₄⋊C₄	—	2	1	no	—
489	C₄⋊C₄	—	2	2	no	—
490	C₄⋊C₄	—	2	1	no	—
491	C₄⋊C₄	—	2	1	no	—
492	C₄⋊C₄	—	4	4	no	—
493	C₄⋊C₄	—	4	2	no	—
494	C₄⋊C₄	—	4	4	no	—
495	C₄⋊C₄	C₂×D₄×C₇₃	1	4	yes	—
496	C₂²⋊C₄	—	4	2	no	—
497	C₂²⋊C₄	—	4	2	no	—
498	C₂²⋊C₄	—	4	2	no	—
499	C₂²⋊C₄	—	4	2	no	—
500	C₂²⋊C₄	—	4	2	no	—
501	C₄²	—	2	2	no	—
502	C₄²	—	2	2	no	—
503	C₄²	—	2	1	no	—
504	C₄²	—	2	1	no	—
505	C₄²	—	2	1	no	—
506	C₄²	—	2	1	no	—
507	C₄²	—	4	2	no	—
508	C₂³	—	2	1	no	—
509	C₂³	—	2	1	no	—
510	C₂³	—	2	1	no	—
511	C₂³	—	2	1	no	—
512	C₂³	—	2	2	no	—
513	C₂³	—	4	1	no	—
514	C₂³	—	4	1	no	—
515	C₂³	—	4	1	no	—
516	C₂³	—	4	1	no	—
517	C₂³	—	4	1	no	—
518	C₂³	—	4	1	no	—
519	C₂³	#121×C₇₃	1	2	yes	—
520	C₂³	#121×C₇₃	1	2	yes	—
521	C₂³	C₂²⋊Q₈×C₇₃	1	2	yes	—
522	C₂³	C₂²×D₄×C₇₃	1	1	yes	characteristic
523	Q₈	—	2	2	no	—
524	Q₈	—	2	2	no	—
525	Q₈	—	4	1	no	—
526	Q₈	—	4	1	no	—
527	D₄	—	2	2	no	—
528	D₄	—	2	2	no	—
529	D₄	—	4	8	no	—
530	D₄	—	4	1	no	—
531	D₄	—	4	1	no	—
532	C₂×C₄	—	2	1	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	2	1	no	—
535	C₂×C₄	—	2	1	no	—
536	C₂×C₄	—	2	1	no	—
537	C₂×C₄	—	2	1	no	—
538	C₂×C₄	—	2	4	no	—
539	C₂×C₄	—	2	2	no	—
540	C₂×C₄	—	2	1	no	—
541	C₂×C₄	—	2	1	no	—
542	C₂×C₄	—	2	1	no	—
543	C₂×C₄	—	2	1	no	—
544	C₂×C₄	—	4	4	no	—
545	C₂×C₄	—	4	4	no	—
546	C₂×C₄	—	4	8	no	—
547	C₂×C₄	—	4	1	no	—
548	C₂×C₄	—	4	1	no	—
549	C₂×C₄	—	4	2	no	—
550	C₂×C₄	—	4	2	no	—
551	C₂×C₄	—	4	8	no	—
552	C₂×C₄	—	4	1	no	—
553	C₂×C₄	—	4	1	no	—
554	C₂×C₄	—	4	2	no	—
555	C₂×C₄	—	4	1	no	—
556	C₂×C₄	—	4	2	no	—
557	C₂×C₄	—	4	1	no	—
558	C₂×C₄	—	4	1	no	—
559	C₂×C₄	—	4	1	no	—
560	C₂×C₄	—	4	2	no	—
561	C₂×C₄	—	8	4	no	—
562	C₂×C₄	#121×C₇₃	1	2	yes	—
563	C₂×C₄	#121×C₇₃	1	2	yes	—
564	C₂×C₄	#121×C₇₃	1	4	yes	—
565	C₂×C₄	C₂²⋊Q₈×C₇₃	1	2	yes	—
566	C₂×C₄	C₂²⋊Q₈×C₇₃	1	4	yes	—
567	C₂×C₄	C₂²⋊Q₈×C₇₃	1	4	yes	—
568	C₂×C₄	#126×C₇₃	1	4	yes	—
569	C₂×C₄	AGL(1,ℤ/8)×C₇₃	1	2	yes	—
570	C₂×C₄	#137×C₇₃	1	2	yes	—
571	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
572	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
573	C₂×C₄	C₂²×Q₈×C₇₃	1	1	yes	characteristic
574	C₂×C₄	C₂×#41×C₇₃	1	1	yes	characteristic
575	C₂×C₄	C₂×#41×C₇₃	1	1	yes	characteristic
576	C₂×C₄	C₂×#41×C₇₃	1	1	yes	characteristic
577	C₈	—	2	4	no	—
578	C₈	—	4	2	no	—
579	C₂²	—	2	2	no	—
580	C₂²	—	2	2	no	—
581	C₂²	—	2	2	no	—
582	C₂²	—	2	2	no	—
583	C₂²	—	2	2	no	—
584	C₂²	—	2	2	no	—
585	C₂²	—	4	2	no	—
586	C₂²	—	4	2	no	—
587	C₂²	—	4	2	no	—
588	C₂²	—	8	1	no	—
589	C₂²	—	8	1	no	—
590	C₂²	—	8	1	no	—
591	C₂²	—	8	1	no	—
592	C₂²	#396×C₇₃	1	4	yes	—
593	C₂²	C₂×#121×C₇₃	1	1	yes	characteristic
594	C₂²	C₂×#121×C₇₃	1	1	yes	characteristic
595	C₂²	C₂×C₂²⋊Q₈×C₇₃	1	1	yes	characteristic
596	C₂²	C₂×AGL(1,ℤ/8)×C₇₃	1	1	yes	characteristic
597	C₂²	C₂×#137×C₇₃	1	1	yes	characteristic
598	C₂²	#575×C₇₃	1	1	yes	characteristic
599	C₂²	#575×C₇₃	1	1	yes	characteristic
600	C₄	—	2	2	no	—
601	C₄	—	2	2	no	—
602	C₄	—	4	4	no	—
603	C₄	—	4	1	no	—
604	C₄	—	4	1	no	—
605	C₄	—	4	2	no	—
606	C₄	—	8	1	no	—
607	C₄	—	8	1	no	—
608	C₄	—	8	2	no	—
609	C₄	#396×C₇₃	1	4	yes	—
610	C₄	C₂×#121×C₇₃	1	1	yes	characteristic
611	C₄	C₂×C₂²⋊Q₈×C₇₃	1	1	yes	characteristic
612	C₄	C₂×C₂²⋊Q₈×C₇₃	1	1	yes	characteristic
613	C₄	C₂×#126×C₇₃	1	1	yes	characteristic
614	C₂	—	2	4	no	—
615	C₂	—	8	2	no	—
616	C₂	C₂×#396×C₇₃	1	1	yes	characteristic
617	C₂	C₇₃×#3036	1	1	yes	characteristic
618	C₂	C₇₃×#3037	1	1	yes	characteristic
619	C₂	C₇₃×#3055	1	1	yes	characteristic
620	C₂	C₇₃×#3056	1	1	yes	characteristic
621	C₂	C₇₃×#3079	1	1	yes	characteristic
622	C₂	C₇₃×#3080	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₃
prime radical	C₂²×#41×C₇₃	C₂²
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
1. C₂×#428×C₇₃	C₂	semidirect
2. C₂×#423×C₇₃	C₂	semidirect
6. C₂×#389×C₇₃	C₂	semidirect
7. C₇₃×#2068	C₂	semidirect
8. C₇₃×#2067	C₂	semidirect
9. C₇₃×#2066	C₂	semidirect
10. C₇₃×#2065	C₂	semidirect
11. C₇₃×#1736	C₂	semidirect
302. #23617	C₇₃	direct (N × H)
312. C₂×#428	C₂×C₇₃	semidirect
313. C₂×#423	C₂×C₇₃	semidirect
317. C₂×#389	C₂×C₇₃	semidirect
318. #2068	C₂×C₇₃	semidirect
319. #2067	C₂×C₇₃	semidirect
320. #2066	C₂×C₇₃	semidirect
321. #2065	C₂×C₇₃	semidirect
322. #1736	C₂×C₇₃	semidirect
323. C₇₃	#23617	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×#428×C₇₃	2
C₂×#423×C₇₃	2
C₂×#417×C₇₃	2
C₇₃×#2297	2
C₂×#389×C₇₃	2
C₇₃×#2068	2
C₇₃×#2067	2
C₇₃×#2066	2
C₇₃×#2065	2
C₇₃×#1736	2
#23617	73

Subgroups — C73×#23617 #32933021

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#23617 #32933021