Subgroups — C₇₃×#24578 #32933982

Order 18688.

896 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#481×C₇₃	C₂	1	1	yes	maximal, characteristic
2	C₂²×#106×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₃×#2501	C₂	1	1	yes	maximal, characteristic
4	C₇₃×#2345	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₃×#2084	C₂	1	2	yes	maximal, complemented
6	C₇₃×#2065	C₂	1	2	yes	maximal, complemented
7	C₇₃×#1948	C₂	1	2	yes	maximal, complemented
8	C₇₃×#1926	C₂	1	2	yes	maximal, complemented
9	C₇₃×#1893	C₂	1	1	yes	maximal, characteristic
10	C₇₃×#1850	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₃×#1823	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂³×C₈×C₇₃	C₂²	1	1	yes	characteristic
13	C₂×#123×C₇₃	—	2	1	no	—
14	C₂×#123×C₇₃	—	2	1	no	—
15	C₂×#121×C₇₃	C₂²	1	1	yes	characteristic
16	C₂²×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
17	C₂²×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
18	#481×C₇₃	—	2	4	no	—
19	C₂×#106×C₇₃	—	2	4	no	—
20	C₂×#106×C₇₃	C₂²	1	1	yes	characteristic
21	C₂×#106×C₇₃	C₂²	1	2	yes	—
22	C₂×#106×C₇₃	C₂²	1	2	yes	—
23	C₂×#106×C₇₃	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊C₈×C₇₃	C₂²	1	2	yes	—
25	C₂×#102×C₇₃	C₂²	1	1	yes	characteristic
26	C₂×#102×C₇₃	C₂²	1	2	yes	—
27	C₂×#102×C₇₃	C₂²	1	1	yes	characteristic
28	C₂×C₂²⋊C₈×C₇₃	C₂²	1	1	yes	characteristic
29	#399×C₇₃	—	2	2	no	—
30	#390×C₇₃	C₂²	1	2	yes	—
31	#389×C₇₃	C₂²	1	2	yes	—
32	#387×C₇₃	—	2	2	no	—
33	#384×C₇₃	C₂²	1	2	yes	—
34	#380×C₇₃	—	2	1	no	—
35	#380×C₇₃	C₂²	1	1	yes	characteristic
36	C₄×C₄⋊C₄×C₇₃	C₂²	1	2	yes	—
37	C₄×C₂²⋊C₄×C₇₃	—	2	1	no	—
38	C₄×C₂²⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
39	#340×C₇₃	C₂²	1	2	yes	—
40	#340×C₇₃	C₂²	1	2	yes	—
41	#340×C₇₃	C₂²	1	2	yes	—
42	#336×C₇₃	C₂²	1	2	yes	—
43	C₂²×D₄×C₇₃	—	2	1	no	—
44	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
45	C₂³×C₄×C₇₃	—	2	1	no	—
46	C₂³×C₄×C₇₃	—	2	1	no	—
47	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
48	C₂²×C₈×C₇₃	—	2	2	no	—
49	C₂²×C₈×C₇₃	—	2	4	no	—
50	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
51	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
52	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
53	#123×C₇₃	—	4	4	no	—
54	#123×C₇₃	—	4	4	no	—
55	#121×C₇₃	—	2	2	no	—
56	#121×C₇₃	—	2	2	no	—
57	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
58	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
59	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
60	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
61	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
62	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
63	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
64	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
65	C₂×C₄⋊C₄×C₇₃	D₄	1	4	yes	—
66	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
67	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
68	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
69	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
70	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
71	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
72	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
73	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
74	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
75	C₂×C₂²⋊C₄×C₇₃	D₄	1	1	yes	characteristic
76	C₂×C₂²⋊C₄×C₇₃	D₄	1	1	yes	characteristic
77	C₂×C₄²×C₇₃	—	2	2	no	—
78	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
79	#106×C₇₃	—	2	4	no	—
80	#106×C₇₃	—	2	4	no	—
81	#106×C₇₃	—	2	2	no	—
82	#106×C₇₃	—	2	2	no	—
83	C₄⋊C₈×C₇₃	—	2	4	no	—
84	#102×C₇₃	—	2	4	no	—
85	#102×C₇₃	—	2	2	no	—
86	#102×C₇₃	—	2	2	no	—
87	C₂²⋊C₈×C₇₃	—	2	2	no	—
88	#95×C₇₃	—	2	2	no	—
89	#95×C₇₃	—	2	2	no	—
90	#95×C₇₃	—	2	1	no	—
91	#95×C₇₃	D₄	1	2	yes	—
92	C₂⁴×C₇₃	—	2	1	no	—
93	C₂⁴×C₇₃	C₂×D₄	1	1	yes	characteristic
94	C₂×D₄×C₇₃	—	2	1	no	—
95	C₂×D₄×C₇₃	—	2	2	no	—
96	C₂×D₄×C₇₃	—	2	1	no	—
97	C₂×D₄×C₇₃	—	2	2	no	—
98	C₂×D₄×C₇₃	—	4	2	no	—
99	C₂×D₄×C₇₃	—	4	2	no	—
100	C₂×D₄×C₇₃	—	4	2	no	—
101	C₂²×C₄×C₇₃	—	2	2	no	—
102	C₂²×C₄×C₇₃	—	2	2	no	—
103	C₂²×C₄×C₇₃	—	2	1	no	—
104	C₂²×C₄×C₇₃	—	2	1	no	—
105	C₂²×C₄×C₇₃	—	2	4	no	—
106	C₂²×C₄×C₇₃	—	2	2	no	—
107	C₂²×C₄×C₇₃	—	2	2	no	—
108	C₂²×C₄×C₇₃	—	2	1	no	—
109	C₂²×C₄×C₇₃	—	4	2	no	—
110	C₂²×C₄×C₇₃	—	4	2	no	—
111	C₂²×C₄×C₇₃	—	4	2	no	—
112	C₂²×C₄×C₇₃	—	8	2	no	—
113	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
114	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
116	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
117	C₂²×C₄×C₇₃	#41	1	2	yes	—
118	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
119	C₂×C₈×C₇₃	—	2	8	no	—
120	C₂×C₈×C₇₃	—	2	2	no	—
121	C₂×C₈×C₇₃	—	2	2	no	—
122	C₂×C₈×C₇₃	—	2	1	no	—
123	C₂×C₈×C₇₃	—	2	1	no	—
124	C₂×C₈×C₇₃	—	2	2	no	—
125	C₂×C₈×C₇₃	—	2	2	no	—
126	C₂×C₈×C₇₃	#41	1	4	yes	—
127	C₄⋊C₄×C₇₃	—	2	4	no	—
128	C₄⋊C₄×C₇₃	—	2	1	no	—
129	C₄⋊C₄×C₇₃	—	2	1	no	—
130	C₄⋊C₄×C₇₃	—	2	2	no	—
131	C₄⋊C₄×C₇₃	—	2	1	no	—
132	C₄⋊C₄×C₇₃	—	2	2	no	—
133	C₄⋊C₄×C₇₃	—	2	2	no	—
134	C₄⋊C₄×C₇₃	—	2	1	no	—
135	C₄⋊C₄×C₇₃	—	2	2	no	—
136	C₄⋊C₄×C₇₃	—	4	4	no	—
137	C₄⋊C₄×C₇₃	—	4	2	no	—
138	C₄⋊C₄×C₇₃	—	4	4	no	—
139	C₄⋊C₄×C₇₃	—	8	2	no	—
140	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
141	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
142	C₂²⋊C₄×C₇₃	—	2	2	no	—
143	C₂²⋊C₄×C₇₃	—	4	4	no	—
144	C₂²⋊C₄×C₇₃	—	4	2	no	—
145	C₂²⋊C₄×C₇₃	—	4	2	no	—
146	C₂²⋊C₄×C₇₃	—	4	4	no	—
147	C₂²⋊C₄×C₇₃	SD₁₆	1	4	yes	—
148	C₄²×C₇₃	—	2	2	no	—
149	C₄²×C₇₃	—	2	2	no	—
150	C₄²×C₇₃	—	8	2	no	—
151	C₂³×C₇₃	—	2	2	no	—
152	C₂³×C₇₃	—	2	2	no	—
153	C₂³×C₇₃	—	4	1	no	—
154	C₂³×C₇₃	—	4	2	no	—
155	C₂³×C₇₃	—	4	1	no	—
156	C₂³×C₇₃	—	4	1	no	—
157	C₂³×C₇₃	—	4	2	no	—
158	C₂³×C₇₃	#121	1	2	yes	—
159	C₂³×C₇₃	C₂×SD₁₆	1	2	yes	—
160	C₂³×C₇₃	AGL(1,ℤ/8)	1	2	yes	—
161	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
162	D₄×C₇₃	—	4	1	no	—
163	D₄×C₇₃	—	4	1	no	—
164	D₄×C₇₃	—	4	2	no	—
165	D₄×C₇₃	—	8	4	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	4	no	—
172	C₂×C₄×C₇₃	—	2	2	no	—
173	C₂×C₄×C₇₃	—	2	2	no	—
174	C₂×C₄×C₇₃	—	2	2	no	—
175	C₂×C₄×C₇₃	—	2	2	no	—
176	C₂×C₄×C₇₃	—	2	2	no	—
177	C₂×C₄×C₇₃	—	4	2	no	—
178	C₂×C₄×C₇₃	—	4	2	no	—
179	C₂×C₄×C₇₃	—	4	1	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	1	no	—
184	C₂×C₄×C₇₃	—	4	2	no	—
185	C₂×C₄×C₇₃	—	4	2	no	—
186	C₂×C₄×C₇₃	—	4	1	no	—
187	C₂×C₄×C₇₃	—	4	2	no	—
188	C₂×C₄×C₇₃	—	8	4	no	—
189	C₂×C₄×C₇₃	—	8	4	no	—
190	C₂×C₄×C₇₃	#121	1	2	yes	—
191	C₂×C₄×C₇₃	C₂×SD₁₆	1	4	yes	—
192	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
193	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
194	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
195	C₂×C₄×C₇₃	2₋¹⁺⁴	1	2	yes	—
196	C₈×C₇₃	—	2	4	no	—
197	C₈×C₇₃	—	4	1	no	—
198	C₈×C₇₃	—	4	1	no	—
199	C₂²×C₇₃	—	2	4	no	—
200	C₂²×C₇₃	—	2	4	no	—
201	C₂²×C₇₃	—	2	2	no	—
202	C₂²×C₇₃	—	2	2	no	—
203	C₂²×C₇₃	—	8	2	no	—
204	C₂²×C₇₃	—	8	2	no	—
205	C₂²×C₇₃	—	8	1	no	—
206	C₂²×C₇₃	—	8	1	no	—
207	C₂²×C₇₃	—	8	1	no	—
208	C₂²×C₇₃	#460	1	4	yes	—
209	C₂²×C₇₃	C₂×#121	1	1	yes	characteristic
210	C₂²×C₇₃	#547	1	2	yes	—
211	C₂²×C₇₃	C₂²×SD₁₆	1	1	yes	characteristic
212	C₂²×C₇₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
213	C₂²×C₇₃	#577	1	2	yes	—
214	C₄×C₇₃	—	2	4	no	—
215	C₄×C₇₃	—	2	2	no	—
216	C₄×C₇₃	—	4	2	no	—
217	C₄×C₇₃	—	4	2	no	—
218	C₄×C₇₃	—	4	2	no	—
219	C₄×C₇₃	—	8	2	no	—
220	C₄×C₇₃	—	8	2	no	—
221	C₄×C₇₃	—	8	1	no	—
222	C₄×C₇₃	#525	1	1	yes	characteristic
223	C₄×C₇₃	#536	1	1	yes	characteristic
224	C₄×C₇₃	#552	1	2	yes	—
225	#24578	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
226	C₂×C₇₃	—	2	4	no	—
227	C₂×C₇₃	—	16	1	no	—
228	C₂×C₇₃	#2413	1	1	yes	characteristic
229	C₂×C₇₃	C₂×#460	1	1	yes	characteristic
230	C₂×C₇₃	#3042	1	1	yes	characteristic
231	C₂×C₇₃	#3335	1	2	yes	—
232	C₂×C₇₃	#3345	1	2	yes	—
233	C₂×#481	C₂×C₇₃	1	1	yes	characteristic
234	C₂²×#106	C₂×C₇₃	1	1	yes	characteristic, complemented
235	#2501	C₂×C₇₃	1	1	yes	characteristic
236	#2345	C₂×C₇₃	1	1	yes	characteristic, complemented
237	#2084	C₂×C₇₃	1	2	yes	complemented
238	#2065	C₂×C₇₃	1	2	yes	complemented
239	#1948	C₂×C₇₃	1	2	yes	complemented
240	#1926	C₂×C₇₃	1	2	yes	complemented
241	#1893	C₂×C₇₃	1	1	yes	characteristic
242	#1850	C₂×C₇₃	1	1	yes	characteristic, complemented
243	#1823	C₂×C₇₃	1	1	yes	characteristic, complemented
244	C₇₃	#24578	1	1	yes	characteristic, direct product factor, Sylow
245	C₂³×C₈	C₂²×C₇₃	1	1	yes	characteristic
246	C₂×#123	—	2	1	no	—
247	C₂×#123	—	2	1	no	—
248	C₂×#121	C₂²×C₇₃	1	1	yes	characteristic
249	C₂²×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
250	C₂²×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
251	#481	—	2	4	no	—
252	C₂×#106	—	2	4	no	—
253	C₂×#106	C₂²×C₇₃	1	2	yes	—
254	C₂×#106	C₂²×C₇₃	1	1	yes	characteristic
255	C₂×#106	C₂²×C₇₃	1	1	yes	characteristic
256	C₂×#106	C₂²×C₇₃	1	2	yes	—
257	C₂×C₄⋊C₈	C₂²×C₇₃	1	2	yes	—
258	C₂×#102	C₂²×C₇₃	1	1	yes	characteristic
259	C₂×#102	C₂²×C₇₃	1	2	yes	—
260	C₂×#102	C₂²×C₇₃	1	1	yes	characteristic
261	C₂×C₂²⋊C₈	C₂²×C₇₃	1	1	yes	characteristic
262	#399	—	2	2	no	—
263	#390	C₂²×C₇₃	1	2	yes	—
264	#389	C₂²×C₇₃	1	2	yes	—
265	#387	—	2	2	no	—
266	#384	C₂²×C₇₃	1	2	yes	—
267	#380	—	2	1	no	—
268	#380	C₂²×C₇₃	1	1	yes	characteristic
269	C₄×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
270	C₄×C₂²⋊C₄	—	2	1	no	—
271	C₄×C₂²⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
272	#340	C₂²×C₇₃	1	2	yes	—
273	#340	C₂²×C₇₃	1	2	yes	—
274	#340	C₂²×C₇₃	1	2	yes	—
275	#336	C₂²×C₇₃	1	2	yes	—
276	C₂²×D₄	—	2	1	no	—
277	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
278	C₂³×C₄	—	2	1	no	—
279	C₂³×C₄	—	2	1	no	—
280	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
281	C₂²×C₈	—	2	2	no	—
282	C₂²×C₈	—	2	4	no	—
283	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
284	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
285	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
286	#123	—	4	4	no	—
287	#123	—	4	4	no	—
288	#121	—	2	2	no	—
289	#121	—	2	2	no	—
290	C₂×C₄⋊C₄	—	2	1	no	—
291	C₂×C₄⋊C₄	—	2	2	no	—
292	C₂×C₄⋊C₄	—	2	2	no	—
293	C₂×C₄⋊C₄	—	2	2	no	—
294	C₂×C₄⋊C₄	—	2	1	no	—
295	C₂×C₄⋊C₄	—	2	2	no	—
296	C₂×C₄⋊C₄	—	2	2	no	—
297	C₂×C₄⋊C₄	—	2	2	no	—
298	C₂×C₄⋊C₄	D₄×C₇₃	1	4	yes	—
299	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
300	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
301	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
302	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
303	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
304	C₂×C₂²⋊C₄	—	2	1	no	—
305	C₂×C₂²⋊C₄	—	2	1	no	—
306	C₂×C₂²⋊C₄	—	2	2	no	—
307	C₂×C₂²⋊C₄	—	2	2	no	—
308	C₂×C₂²⋊C₄	D₄×C₇₃	1	1	yes	characteristic
309	C₂×C₂²⋊C₄	D₄×C₇₃	1	1	yes	characteristic
310	C₂×C₄²	—	2	2	no	—
311	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
312	#106	—	2	4	no	—
313	#106	—	2	4	no	—
314	#106	—	2	2	no	—
315	#106	—	2	2	no	—
316	C₄⋊C₈	—	2	4	no	—
317	#102	—	2	4	no	—
318	#102	—	2	2	no	—
319	#102	—	2	2	no	—
320	C₂²⋊C₈	—	2	2	no	—
321	#95	—	2	2	no	—
322	#95	—	2	2	no	—
323	#95	—	2	1	no	—
324	#95	D₄×C₇₃	1	2	yes	—
325	C₂⁴	—	2	1	no	—
326	C₂⁴	C₂×D₄×C₇₃	1	1	yes	characteristic
327	C₂×D₄	—	2	1	no	—
328	C₂×D₄	—	2	2	no	—
329	C₂×D₄	—	2	1	no	—
330	C₂×D₄	—	2	2	no	—
331	C₂×D₄	—	4	2	no	—
332	C₂×D₄	—	4	2	no	—
333	C₂×D₄	—	4	2	no	—
334	C₂²×C₄	—	2	2	no	—
335	C₂²×C₄	—	2	2	no	—
336	C₂²×C₄	—	2	1	no	—
337	C₂²×C₄	—	2	1	no	—
338	C₂²×C₄	—	2	4	no	—
339	C₂²×C₄	—	2	2	no	—
340	C₂²×C₄	—	2	2	no	—
341	C₂²×C₄	—	2	1	no	—
342	C₂²×C₄	—	4	2	no	—
343	C₂²×C₄	—	4	2	no	—
344	C₂²×C₄	—	4	2	no	—
345	C₂²×C₄	—	8	2	no	—
346	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
347	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
348	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
349	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
350	C₂²×C₄	#41×C₇₃	1	2	yes	—
351	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
352	C₂×C₈	—	2	8	no	—
353	C₂×C₈	—	2	2	no	—
354	C₂×C₈	—	2	2	no	—
355	C₂×C₈	—	2	1	no	—
356	C₂×C₈	—	2	1	no	—
357	C₂×C₈	—	2	2	no	—
358	C₂×C₈	—	2	2	no	—
359	C₂×C₈	#41×C₇₃	1	4	yes	—
360	C₄⋊C₄	—	2	4	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	2	no	—
366	C₄⋊C₄	—	2	2	no	—
367	C₄⋊C₄	—	2	1	no	—
368	C₄⋊C₄	—	2	2	no	—
369	C₄⋊C₄	—	4	4	no	—
370	C₄⋊C₄	—	4	2	no	—
371	C₄⋊C₄	—	4	4	no	—
372	C₄⋊C₄	—	8	2	no	—
373	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
374	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
375	C₂²⋊C₄	—	2	2	no	—
376	C₂²⋊C₄	—	4	4	no	—
377	C₂²⋊C₄	—	4	2	no	—
378	C₂²⋊C₄	—	4	2	no	—
379	C₂²⋊C₄	—	4	4	no	—
380	C₂²⋊C₄	SD₁₆×C₇₃	1	4	yes	—
381	C₄²	—	2	2	no	—
382	C₄²	—	2	2	no	—
383	C₄²	—	8	2	no	—
384	C₂³	—	2	2	no	—
385	C₂³	—	2	2	no	—
386	C₂³	—	4	1	no	—
387	C₂³	—	4	2	no	—
388	C₂³	—	4	1	no	—
389	C₂³	—	4	1	no	—
390	C₂³	—	4	2	no	—
391	C₂³	#121×C₇₃	1	2	yes	—
392	C₂³	C₂×SD₁₆×C₇₃	1	2	yes	—
393	C₂³	AGL(1,ℤ/8)×C₇₃	1	2	yes	—
394	C₂³	C₂²×D₄×C₇₃	1	1	yes	characteristic
395	D₄	—	4	1	no	—
396	D₄	—	4	1	no	—
397	D₄	—	4	2	no	—
398	D₄	—	8	4	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	4	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	4	2	no	—
412	C₂×C₄	—	4	1	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	—	4	1	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	4	2	no	—
419	C₂×C₄	—	4	1	no	—
420	C₂×C₄	—	4	2	no	—
421	C₂×C₄	—	8	4	no	—
422	C₂×C₄	—	8	4	no	—
423	C₂×C₄	#121×C₇₃	1	2	yes	—
424	C₂×C₄	C₂×SD₁₆×C₇₃	1	4	yes	—
425	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
426	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
427	C₂×C₄	C₂×#41×C₇₃	1	1	yes	characteristic
428	C₂×C₄	2₋¹⁺⁴×C₇₃	1	2	yes	—
429	C₈	—	2	4	no	—
430	C₈	—	4	1	no	—
431	C₈	—	4	1	no	—
432	C₂²	—	2	2	no	—
433	C₂²	—	2	4	no	—
434	C₂²	—	2	4	no	—
435	C₂²	—	2	2	no	—
436	C₂²	—	8	1	no	—
437	C₂²	—	8	1	no	—
438	C₂²	—	8	2	no	—
439	C₂²	—	8	2	no	—
440	C₂²	—	8	1	no	—
441	C₂²	#460×C₇₃	1	4	yes	—
442	C₂²	C₂×#121×C₇₃	1	1	yes	characteristic
443	C₂²	#547×C₇₃	1	2	yes	—
444	C₂²	C₂²×SD₁₆×C₇₃	1	1	yes	characteristic
445	C₂²	C₂×AGL(1,ℤ/8)×C₇₃	1	1	yes	characteristic
446	C₂²	#577×C₇₃	1	2	yes	—
447	C₄	—	2	4	no	—
448	C₄	—	2	2	no	—
449	C₄	—	4	2	no	—
450	C₄	—	4	2	no	—
451	C₄	—	4	2	no	—
452	C₄	—	8	2	no	—
453	C₄	—	8	1	no	—
454	C₄	—	8	2	no	—
455	C₄	#525×C₇₃	1	1	yes	characteristic
456	C₄	#536×C₇₃	1	1	yes	characteristic
457	C₄	#552×C₇₃	1	2	yes	—
458	C₂	—	2	4	no	—
459	C₂	—	16	1	no	—
460	C₂	C₇₃×#2413	1	1	yes	characteristic
461	C₂	C₂×#460×C₇₃	1	1	yes	characteristic
462	C₂	C₇₃×#3042	1	1	yes	characteristic
463	C₂	C₇₃×#3335	1	2	yes	—
464	C₂	C₇₃×#3345	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₇₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₃
prime radical	C₂×#121×C₇₃	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇₃ ◁ C₄×C₂²⋊C₄×C₇₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×#106×C₇₃	C₂	semidirect
4. C₇₃×#2345	C₂	semidirect
5. C₇₃×#2084	C₂	semidirect
6. C₇₃×#2065	C₂	semidirect
7. C₇₃×#1948	C₂	semidirect
8. C₇₃×#1926	C₂	semidirect
10. C₇₃×#1850	C₂	semidirect
11. C₇₃×#1823	C₂	semidirect
225. #24578	C₇₃	direct (N × H)
234. C₂²×#106	C₂×C₇₃	semidirect
236. #2345	C₂×C₇₃	semidirect
237. #2084	C₂×C₇₃	semidirect
238. #2065	C₂×C₇₃	semidirect
239. #1948	C₂×C₇₃	semidirect
240. #1926	C₂×C₇₃	semidirect
242. #1850	C₂×C₇₃	semidirect
243. #1823	C₂×C₇₃	semidirect
244. C₇₃	#24578	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×#481×C₇₃	2
C₂²×#106×C₇₃	2
C₇₃×#2501	2
C₇₃×#2345	2
C₇₃×#2084	2
C₇₃×#2065	2
C₇₃×#1948	2
C₇₃×#1926	2
C₇₃×#1893	2
C₇₃×#1850	2
C₇₃×#1823	2
#24578	73

Subgroups — C73×#24578 #32933982

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#24578 #32933982