Subgroups — C₇₃×#22263 #32931667

Order 18688.

1002 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#436×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₈×D₄×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₃×#2397	C₂	1	1	yes	maximal, characteristic
4	C₇₃×#1955	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₃×#1955	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇₃×#1870	C₂	1	4	yes	maximal, complemented
7	C₇₃×#1869	C₂	1	4	yes	maximal, complemented
8	C₇₃×#1832	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇₃×#1746	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×M₁₆×C₇₃	C₂²	1	2	yes	—
11	C₂³×C₈×C₇₃	C₂²	1	2	yes	—
12	C₂×C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
13	C₂×C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
14	C₂×C₄×D₄×C₇₃	C₂²	1	4	yes	—
15	#436×C₇₃	—	2	4	no	—
16	C₈×D₄×C₇₃	—	2	4	no	—
17	C₂×C₄⋊C₈×C₇₃	C₂²	1	1	yes	characteristic
18	C₂×C₄⋊C₈×C₇₃	C₂²	1	1	yes	characteristic
19	C₂×C₂²⋊C₈×C₇₃	C₂²	1	2	yes	—
20	C₂×C₂²⋊C₈×C₇₃	C₂²	1	2	yes	—
21	C₂×C₂²⋊C₈×C₇₃	C₂²	1	4	yes	—
22	C₂×C₂²⋊C₈×C₇₃	C₂²	1	4	yes	—
23	C₂×#97×C₇₃	C₂²	1	1	yes	characteristic
24	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
25	#399×C₇₃	C₄	1	2	yes	—
26	#399×C₇₃	C₄	1	2	yes	—
27	#392×C₇₃	C₄	1	2	yes	—
28	#392×C₇₃	C₄	1	2	yes	—
29	#376×C₇₃	C₂²	1	1	yes	characteristic
30	#336×C₇₃	C₂²	1	2	yes	—
31	#336×C₇₃	C₂²	1	2	yes	—
32	#336×C₇₃	C₂²	1	4	yes	—
33	C₂²×D₄×C₇₃	C₂×C₄	1	1	yes	characteristic
34	C₂²×D₄×C₇₃	C₂×C₄	1	4	yes	—
35	C₂²×D₄×C₇₃	C₂×C₄	1	1	yes	characteristic
36	C₂³×C₄×C₇₃	C₂³	1	2	yes	—
37	C₂³×C₄×C₇₃	C₂³	1	2	yes	—
38	C₂×M₁₆×C₇₃	—	2	4	no	—
39	C₂×M₁₆×C₇₃	—	4	4	no	—
40	C₂²×C₈×C₇₃	—	2	4	no	—
41	C₂²×C₈×C₇₃	—	4	4	no	—
42	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
43	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
44	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
45	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
46	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
47	C₄×D₄×C₇₃	—	2	2	no	—
48	C₄×D₄×C₇₃	—	2	2	no	—
49	C₄×D₄×C₇₃	—	2	2	no	—
50	C₄×D₄×C₇₃	—	2	2	no	—
51	C₄×D₄×C₇₃	—	4	4	no	—
52	C₄×D₄×C₇₃	—	4	4	no	—
53	C₂×C₄⋊C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
54	C₂×C₄⋊C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄⋊C₄×C₇₃	C₂×C₄	1	4	yes	—
56	C₂×C₂²⋊C₄×C₇₃	C₂×C₄	1	2	yes	—
57	C₂×C₂²⋊C₄×C₇₃	C₂×C₄	1	2	yes	—
58	C₂×C₂²⋊C₄×C₇₃	C₂×C₄	1	4	yes	—
59	C₂×C₂²⋊C₄×C₇₃	C₂×C₄	1	4	yes	—
60	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
61	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
62	C₄⋊C₈×C₇₃	—	2	2	no	—
63	C₄⋊C₈×C₇₃	—	2	2	no	—
64	C₂²⋊C₈×C₇₃	—	2	4	no	—
65	C₂²⋊C₈×C₇₃	—	2	4	no	—
66	C₂²⋊C₈×C₇₃	—	4	4	no	—
67	C₂²⋊C₈×C₇₃	—	4	4	no	—
68	#97×C₇₃	—	2	2	no	—
69	C₄×C₈×C₇₃	D₄	1	4	yes	complemented
70	#95×C₇₃	C₂×C₄	1	2	yes	—
71	#95×C₇₃	C₂×C₄	1	2	yes	—
72	C₂⁴×C₇₃	C₂²×C₄	1	2	yes	—
73	C₂⁴×C₇₃	C₂²×C₄	1	2	yes	—
74	C₂×D₄×C₇₃	—	2	4	no	—
75	C₂×D₄×C₇₃	—	2	8	no	—
76	C₂×D₄×C₇₃	—	2	2	no	—
77	C₂×D₄×C₇₃	—	2	2	no	—
78	C₂×D₄×C₇₃	—	4	4	no	—
79	C₂×D₄×C₇₃	—	4	2	no	—
80	C₂×D₄×C₇₃	—	4	4	no	—
81	C₂²×C₄×C₇₃	—	2	2	no	—
82	C₂²×C₄×C₇₃	—	2	2	no	—
83	C₂²×C₄×C₇₃	—	2	2	no	—
84	C₂²×C₄×C₇₃	—	2	2	no	—
85	C₂²×C₄×C₇₃	—	2	4	no	—
86	C₂²×C₄×C₇₃	—	2	4	no	—
87	C₂²×C₄×C₇₃	—	2	4	no	—
88	C₂²×C₄×C₇₃	—	2	4	no	—
89	C₂²×C₄×C₇₃	C₂²×C₄	1	4	yes	—
90	C₂²×C₄×C₇₃	C₂²×C₄	1	2	yes	—
91	C₂²×C₄×C₇₃	C₂²×C₄	1	2	yes	—
92	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
93	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
94	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
95	M₁₆×C₇₃	—	4	8	no	—
96	C₂×C₈×C₇₃	—	2	2	no	—
97	C₂×C₈×C₇₃	—	2	2	no	—
98	C₂×C₈×C₇₃	—	2	2	no	—
99	C₂×C₈×C₇₃	—	2	2	no	—
100	C₂×C₈×C₇₃	—	2	2	no	—
101	C₂×C₈×C₇₃	—	2	2	no	—
102	C₂×C₈×C₇₃	—	2	2	no	—
103	C₂×C₈×C₇₃	—	2	4	no	—
104	C₂×C₈×C₇₃	—	2	4	no	—
105	C₂×C₈×C₇₃	—	4	8	no	—
106	C₂×C₈×C₇₃	C₂×D₄	1	2	yes	—
107	C₂×C₈×C₇₃	C₂×D₄	1	2	yes	—
108	C₄⋊C₄×C₇₃	—	2	2	no	—
109	C₄⋊C₄×C₇₃	—	2	2	no	—
110	C₄⋊C₄×C₇₃	—	4	4	no	—
111	C₂²⋊C₄×C₇₃	—	2	4	no	—
112	C₂²⋊C₄×C₇₃	—	2	4	no	—
113	C₂²⋊C₄×C₇₃	—	4	4	no	—
114	C₂²⋊C₄×C₇₃	—	4	4	no	—
115	C₄²×C₇₃	—	2	2	no	—
116	C₄²×C₇₃	—	2	2	no	—
117	C₄²×C₇₃	C₂×D₄	1	2	yes	—
118	C₄²×C₇₃	#41	1	2	yes	—
119	C₂³×C₇₃	—	2	2	no	—
120	C₂³×C₇₃	—	2	4	no	—
121	C₂³×C₇₃	—	2	2	no	—
122	C₂³×C₇₃	—	2	4	no	—
123	C₂³×C₇₃	—	2	2	no	—
124	C₂³×C₇₃	—	2	4	no	—
125	C₂³×C₇₃	—	2	4	no	—
126	C₂³×C₇₃	—	2	2	no	—
127	C₂³×C₇₃	—	2	2	no	—
128	C₂³×C₇₃	#131	1	4	yes	—
129	C₂³×C₇₃	C₂³×C₄	1	1	yes	characteristic
130	D₄×C₇₃	—	2	8	no	—
131	D₄×C₇₃	—	4	4	no	—
132	D₄×C₇₃	—	4	16	no	—
133	C₂×C₄×C₇₃	—	2	2	no	—
134	C₂×C₄×C₇₃	—	2	2	no	—
135	C₂×C₄×C₇₃	—	2	2	no	—
136	C₂×C₄×C₇₃	—	2	2	no	—
137	C₂×C₄×C₇₃	—	2	4	no	—
138	C₂×C₄×C₇₃	—	2	4	no	—
139	C₂×C₄×C₇₃	—	2	4	no	—
140	C₂×C₄×C₇₃	—	2	4	no	—
141	C₂×C₄×C₇₃	—	2	4	no	—
142	C₂×C₄×C₇₃	—	4	2	no	—
143	C₂×C₄×C₇₃	—	4	2	no	—
144	C₂×C₄×C₇₃	—	4	2	no	—
145	C₂×C₄×C₇₃	—	4	2	no	—
146	C₂×C₄×C₇₃	—	4	4	no	—
147	C₂×C₄×C₇₃	—	4	4	no	—
148	C₂×C₄×C₇₃	C₄×D₄	1	2	yes	—
149	C₂×C₄×C₇₃	C₄×D₄	1	2	yes	—
150	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
151	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
152	C₂×C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
153	C₂×C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
154	C₈×C₇₃	—	2	2	no	—
155	C₈×C₇₃	—	2	2	no	—
156	C₈×C₇₃	—	4	2	no	—
157	C₈×C₇₃	—	4	2	no	—
158	C₈×C₇₃	—	4	2	no	—
159	C₂²×C₇₃	—	2	4	no	—
160	C₂²×C₇₃	—	2	8	no	—
161	C₂²×C₇₃	—	4	2	no	—
162	C₂²×C₇₃	—	4	2	no	—
163	C₂²×C₇₃	—	4	4	no	—
164	C₂²×C₇₃	—	4	2	no	—
165	C₂²×C₇₃	—	4	2	no	—
166	C₂²×C₇₃	—	4	2	no	—
167	C₂²×C₇₃	—	4	4	no	—
168	C₂²×C₇₃	—	4	4	no	—
169	C₂²×C₇₃	C₂×C₄×D₄	1	1	yes	characteristic
170	C₂²×C₇₃	#518	1	2	yes	—
171	C₂²×C₇₃	C₂×#131	1	2	yes	—
172	C₂²×C₇₃	#568	1	2	yes	—
173	C₄×C₇₃	—	2	2	no	—
174	C₄×C₇₃	—	2	2	no	—
175	C₄×C₇₃	—	4	2	no	—
176	C₄×C₇₃	—	4	2	no	—
177	C₄×C₇₃	—	4	4	no	—
178	C₄×C₇₃	#535	1	1	yes	characteristic
179	C₄×C₇₃	#535	1	1	yes	characteristic
180	C₄×C₇₃	#540	1	2	yes	—
181	#22263	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
182	C₂×C₇₃	—	4	4	no	—
183	C₂×C₇₃	—	8	2	no	—
184	C₂×C₇₃	#2328	1	1	yes	characteristic
185	C₂×C₇₃	#2929	1	1	yes	characteristic
186	C₂×C₇₃	#2930	1	1	yes	characteristic
187	C₂×C₇₃	#2976	1	4	yes	—
188	C₂×#436	C₂×C₇₃	1	1	yes	characteristic, complemented
189	C₂×C₈×D₄	C₂×C₇₃	1	1	yes	characteristic, complemented
190	#2397	C₂×C₇₃	1	1	yes	characteristic
191	#1955	C₂×C₇₃	1	1	yes	characteristic, complemented
192	#1955	C₂×C₇₃	1	1	yes	characteristic, complemented
193	#1870	C₂×C₇₃	1	4	yes	complemented
194	#1869	C₂×C₇₃	1	4	yes	complemented
195	#1832	C₂×C₇₃	1	1	yes	characteristic, complemented
196	#1746	C₂×C₇₃	1	1	yes	characteristic, complemented
197	C₇₃	#22263	1	1	yes	characteristic, direct product factor, Sylow
198	C₂²×M₁₆	C₂²×C₇₃	1	2	yes	—
199	C₂³×C₈	C₂²×C₇₃	1	2	yes	—
200	C₂×C₄×D₄	C₂²×C₇₃	1	1	yes	characteristic
201	C₂×C₄×D₄	C₂²×C₇₃	1	1	yes	characteristic
202	C₂×C₄×D₄	C₂²×C₇₃	1	4	yes	—
203	#436	—	2	4	no	—
204	C₈×D₄	—	2	4	no	—
205	C₂×C₄⋊C₈	C₂²×C₇₃	1	1	yes	characteristic
206	C₂×C₄⋊C₈	C₂²×C₇₃	1	1	yes	characteristic
207	C₂×C₂²⋊C₈	C₂²×C₇₃	1	2	yes	—
208	C₂×C₂²⋊C₈	C₂²×C₇₃	1	2	yes	—
209	C₂×C₂²⋊C₈	C₂²×C₇₃	1	4	yes	—
210	C₂×C₂²⋊C₈	C₂²×C₇₃	1	4	yes	—
211	C₂×#97	C₂²×C₇₃	1	1	yes	characteristic
212	C₂×C₄×C₈	C₂²×C₇₃	1	1	yes	characteristic
213	#399	C₄×C₇₃	1	2	yes	—
214	#399	C₄×C₇₃	1	2	yes	—
215	#392	C₄×C₇₃	1	2	yes	—
216	#392	C₄×C₇₃	1	2	yes	—
217	#376	C₂²×C₇₃	1	1	yes	characteristic
218	#336	C₂²×C₇₃	1	4	yes	—
219	#336	C₂²×C₇₃	1	2	yes	—
220	#336	C₂²×C₇₃	1	2	yes	—
221	C₂²×D₄	C₂×C₄×C₇₃	1	1	yes	characteristic
222	C₂²×D₄	C₂×C₄×C₇₃	1	4	yes	—
223	C₂²×D₄	C₂×C₄×C₇₃	1	1	yes	characteristic
224	C₂³×C₄	C₂³×C₇₃	1	2	yes	—
225	C₂³×C₄	C₂³×C₇₃	1	2	yes	—
226	C₂×M₁₆	—	2	4	no	—
227	C₂×M₁₆	—	4	4	no	—
228	C₂²×C₈	—	2	4	no	—
229	C₂²×C₈	—	4	4	no	—
230	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
231	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
232	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
233	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
234	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
235	C₄×D₄	—	2	2	no	—
236	C₄×D₄	—	2	2	no	—
237	C₄×D₄	—	2	2	no	—
238	C₄×D₄	—	2	2	no	—
239	C₄×D₄	—	4	4	no	—
240	C₄×D₄	—	4	4	no	—
241	C₂×C₄⋊C₄	C₂×C₄×C₇₃	1	1	yes	characteristic
242	C₂×C₄⋊C₄	C₂×C₄×C₇₃	1	1	yes	characteristic
243	C₂×C₄⋊C₄	C₂×C₄×C₇₃	1	4	yes	—
244	C₂×C₂²⋊C₄	C₂×C₄×C₇₃	1	2	yes	—
245	C₂×C₂²⋊C₄	C₂×C₄×C₇₃	1	2	yes	—
246	C₂×C₂²⋊C₄	C₂×C₄×C₇₃	1	4	yes	—
247	C₂×C₂²⋊C₄	C₂×C₄×C₇₃	1	4	yes	—
248	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
249	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
250	C₄⋊C₈	—	2	2	no	—
251	C₄⋊C₈	—	2	2	no	—
252	C₂²⋊C₈	—	2	4	no	—
253	C₂²⋊C₈	—	2	4	no	—
254	C₂²⋊C₈	—	4	4	no	—
255	C₂²⋊C₈	—	4	4	no	—
256	#97	—	2	2	no	—
257	C₄×C₈	D₄×C₇₃	1	4	yes	complemented
258	#95	C₂×C₄×C₇₃	1	2	yes	—
259	#95	C₂×C₄×C₇₃	1	2	yes	—
260	C₂⁴	C₂²×C₄×C₇₃	1	2	yes	—
261	C₂⁴	C₂²×C₄×C₇₃	1	2	yes	—
262	C₂×D₄	—	2	4	no	—
263	C₂×D₄	—	2	8	no	—
264	C₂×D₄	—	2	2	no	—
265	C₂×D₄	—	2	2	no	—
266	C₂×D₄	—	4	4	no	—
267	C₂×D₄	—	4	2	no	—
268	C₂×D₄	—	4	4	no	—
269	C₂²×C₄	—	2	2	no	—
270	C₂²×C₄	—	2	2	no	—
271	C₂²×C₄	—	2	2	no	—
272	C₂²×C₄	—	2	2	no	—
273	C₂²×C₄	—	2	4	no	—
274	C₂²×C₄	—	2	4	no	—
275	C₂²×C₄	—	2	4	no	—
276	C₂²×C₄	—	2	4	no	—
277	C₂²×C₄	C₂²×C₄×C₇₃	1	4	yes	—
278	C₂²×C₄	C₂²×C₄×C₇₃	1	2	yes	—
279	C₂²×C₄	C₂²×C₄×C₇₃	1	2	yes	—
280	C₂²×C₄	C₂²×C₄×C₇₃	1	1	yes	characteristic
281	C₂²×C₄	C₂²×C₄×C₇₃	1	1	yes	characteristic
282	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
283	M₁₆	—	4	8	no	—
284	C₂×C₈	—	2	2	no	—
285	C₂×C₈	—	2	2	no	—
286	C₂×C₈	—	2	2	no	—
287	C₂×C₈	—	2	2	no	—
288	C₂×C₈	—	2	2	no	—
289	C₂×C₈	—	2	2	no	—
290	C₂×C₈	—	2	2	no	—
291	C₂×C₈	—	2	4	no	—
292	C₂×C₈	—	2	4	no	—
293	C₂×C₈	—	4	8	no	—
294	C₂×C₈	C₂×D₄×C₇₃	1	2	yes	—
295	C₂×C₈	C₂×D₄×C₇₃	1	2	yes	—
296	C₄⋊C₄	—	2	2	no	—
297	C₄⋊C₄	—	2	2	no	—
298	C₄⋊C₄	—	4	4	no	—
299	C₂²⋊C₄	—	2	4	no	—
300	C₂²⋊C₄	—	2	4	no	—
301	C₂²⋊C₄	—	4	4	no	—
302	C₂²⋊C₄	—	4	4	no	—
303	C₄²	—	2	2	no	—
304	C₄²	—	2	2	no	—
305	C₄²	C₂×D₄×C₇₃	1	2	yes	—
306	C₄²	#41×C₇₃	1	2	yes	—
307	C₂³	—	2	2	no	—
308	C₂³	—	2	4	no	—
309	C₂³	—	2	2	no	—
310	C₂³	—	2	4	no	—
311	C₂³	—	2	2	no	—
312	C₂³	—	2	4	no	—
313	C₂³	—	2	4	no	—
314	C₂³	—	2	2	no	—
315	C₂³	—	2	2	no	—
316	C₂³	#131×C₇₃	1	4	yes	—
317	C₂³	C₂³×C₄×C₇₃	1	1	yes	characteristic
318	D₄	—	2	8	no	—
319	D₄	—	4	4	no	—
320	D₄	—	4	16	no	—
321	C₂×C₄	—	2	2	no	—
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	—	2	2	no	—
325	C₂×C₄	—	2	4	no	—
326	C₂×C₄	—	2	4	no	—
327	C₂×C₄	—	2	4	no	—
328	C₂×C₄	—	2	4	no	—
329	C₂×C₄	—	2	4	no	—
330	C₂×C₄	—	4	2	no	—
331	C₂×C₄	—	4	2	no	—
332	C₂×C₄	—	4	2	no	—
333	C₂×C₄	—	4	2	no	—
334	C₂×C₄	—	4	4	no	—
335	C₂×C₄	—	4	4	no	—
336	C₂×C₄	C₄×D₄×C₇₃	1	2	yes	—
337	C₂×C₄	C₄×D₄×C₇₃	1	2	yes	—
338	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
339	C₂×C₄	C₂×#41×C₇₃	1	1	yes	characteristic
340	C₂×C₄	H(5,𝔽₂)×C₇₃	1	2	yes	—
341	C₂×C₄	H(5,𝔽₂)×C₇₃	1	2	yes	—
342	C₈	—	2	2	no	—
343	C₈	—	2	2	no	—
344	C₈	—	4	2	no	—
345	C₈	—	4	2	no	—
346	C₈	—	4	2	no	—
347	C₂²	—	2	8	no	—
348	C₂²	—	2	4	no	—
349	C₂²	—	4	4	no	—
350	C₂²	—	4	2	no	—
351	C₂²	—	4	2	no	—
352	C₂²	—	4	4	no	—
353	C₂²	—	4	4	no	—
354	C₂²	—	4	2	no	—
355	C₂²	—	4	2	no	—
356	C₂²	—	4	2	no	—
357	C₂²	C₂×C₄×D₄×C₇₃	1	1	yes	characteristic
358	C₂²	#518×C₇₃	1	2	yes	—
359	C₂²	C₂×#131×C₇₃	1	2	yes	—
360	C₂²	#568×C₇₃	1	2	yes	—
361	C₄	—	2	2	no	—
362	C₄	—	2	2	no	—
363	C₄	—	4	4	no	—
364	C₄	—	4	2	no	—
365	C₄	—	4	2	no	—
366	C₄	#535×C₇₃	1	1	yes	characteristic
367	C₄	#535×C₇₃	1	1	yes	characteristic
368	C₄	#540×C₇₃	1	2	yes	—
369	C₂	—	4	4	no	—
370	C₂	—	8	2	no	—
371	C₂	C₇₃×#2328	1	1	yes	characteristic
372	C₂	C₇₃×#2929	1	1	yes	characteristic
373	C₂	C₇₃×#2930	1	1	yes	characteristic
374	C₂	C₇₃×#2976	1	4	yes	—

	subgroup	G/H
center	C₂²×C₄×C₇₃	C₂⁴
commutator	C₂³	C₂³×C₄×C₇₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₃
socle	C₂³×C₇₃	C₂³×C₄
prime radical	C₇₃×#2397	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₇₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#436×C₇₃	C₂	semidirect
2. C₂×C₈×D₄×C₇₃	C₂	semidirect
4. C₇₃×#1955	C₂	semidirect
5. C₇₃×#1955	C₂	semidirect
6. C₇₃×#1870	C₂	semidirect
7. C₇₃×#1869	C₂	semidirect
8. C₇₃×#1832	C₂	semidirect
9. C₇₃×#1746	C₂	semidirect
69. C₄×C₈×C₇₃	D₄	semidirect
181. #22263	C₇₃	direct (N × H)
188. C₂×#436	C₂×C₇₃	semidirect
189. C₂×C₈×D₄	C₂×C₇₃	semidirect
191. #1955	C₂×C₇₃	semidirect
192. #1955	C₂×C₇₃	semidirect
193. #1870	C₂×C₇₃	semidirect
194. #1869	C₂×C₇₃	semidirect
195. #1832	C₂×C₇₃	semidirect
196. #1746	C₂×C₇₃	semidirect
197. C₇₃	#22263	direct (N × H)
257. C₄×C₈	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×#436×C₇₃	2
C₂×C₈×D₄×C₇₃	2
C₇₃×#2397	2
C₇₃×#1955	2
C₇₃×#1870	2
C₇₃×#1869	2
C₇₃×#1832	2
C₇₃×#1746	2
#22263	73

Subgroups — C73×#22263 #32931667

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#22263 #32931667