Subgroups — C₇₃×#25789 #32935193

Order 18688.

1500 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×Q₁₆×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#497×C₇₃	C₂	1	2	yes	maximal, complemented
3	C₂×#465×C₇₃	C₂	1	1	yes	maximal, characteristic
4	C₂×#451×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#448×C₇₃	C₂	1	1	yes	maximal, characteristic
6	C₇₃×#2436	C₂	1	1	yes	maximal, characteristic
7	C₇₃×#2434	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇₃×#2016	C₂	1	2	yes	maximal, complemented
9	C₇₃×#2015	C₂	1	2	yes	maximal, complemented
10	C₇₃×#1971	C₂	1	2	yes	maximal, complemented
11	C₇₃×#1752	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂³×Q₈×C₇₃	C₂²	1	1	yes	characteristic
13	C₂³×Q₈×C₇₃	C₂²	1	1	yes	characteristic
14	C₂²×Q₁₆×C₇₃	—	2	8	no	—
15	C₂²×Q₁₆×C₇₃	—	2	4	no	—
16	C₂²×Q₁₆×C₇₃	C₂²	1	2	yes	—
17	C₂²×Q₁₆×C₇₃	C₂²	1	2	yes	—
18	C₂²×Q₁₆×C₇₃	C₂²	1	2	yes	—
19	C₂²×SD₁₆×C₇₃	C₂²	1	1	yes	characteristic
20	C₂²×SD₁₆×C₇₃	C₂²	1	2	yes	—
21	C₂³×C₈×C₇₃	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊Q₈×C₇₃	C₂²	1	2	yes	—
23	C₂×#124×C₇₃	C₂²	1	2	yes	—
24	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
25	C₂×#121×C₇₃	C₂²	1	1	yes	characteristic
26	#497×C₇₃	—	2	8	no	—
27	#465×C₇₃	—	2	4	no	—
28	#451×C₇₃	—	2	4	no	—
29	#448×C₇₃	—	2	4	no	—
30	C₂×#106×C₇₃	C₂²	1	1	yes	characteristic
31	C₂×#103×C₇₃	C₂²	1	2	yes	—
32	C₂×#103×C₇₃	C₂²	1	2	yes	—
33	C₂×#103×C₇₃	C₂²	1	1	yes	characteristic
34	C₂×#102×C₇₃	C₂²	1	1	yes	characteristic
35	C₂×C₂²⋊C₈×C₇₃	C₂²	1	1	yes	characteristic
36	C₂×#97×C₇₃	C₂²	1	2	yes	—
37	#395×C₇₃	—	2	2	no	—
38	#393×C₇₃	—	2	2	no	—
39	#391×C₇₃	C₂²	1	2	yes	—
40	#391×C₇₃	C₂²	1	2	yes	—
41	#386×C₇₃	—	2	2	no	—
42	#385×C₇₃	—	2	2	no	—
43	C₄×C₂²⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
44	#336×C₇₃	C₂²	1	2	yes	—
45	C₂²×Q₈×C₇₃	—	2	1	no	—
46	C₂²×Q₈×C₇₃	—	2	1	no	—
47	C₂²×Q₈×C₇₃	—	2	4	no	—
48	C₂²×Q₈×C₇₃	—	2	4	no	—
49	C₂²×Q₈×C₇₃	—	2	2	no	—
50	C₂²×Q₈×C₇₃	—	2	2	no	—
51	C₂²×Q₈×C₇₃	—	2	2	no	—
52	C₂²×Q₈×C₇₃	—	2	2	no	—
53	C₂²×Q₈×C₇₃	—	4	2	no	—
54	C₂²×Q₈×C₇₃	—	4	2	no	—
55	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
56	C₂²×Q₈×C₇₃	C₂³	1	2	yes	—
57	C₂²×Q₈×C₇₃	C₂³	1	2	yes	—
58	C₂²×D₄×C₇₃	—	2	1	no	—
59	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
60	C₂³×C₄×C₇₃	—	2	1	no	—
61	C₂³×C₄×C₇₃	—	2	1	no	—
62	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
63	C₂×Q₁₆×C₇₃	—	2	32	no	—
64	C₂×Q₁₆×C₇₃	—	2	4	no	—
65	C₂×Q₁₆×C₇₃	—	2	4	no	—
66	C₂×Q₁₆×C₇₃	—	2	4	no	—
67	C₂×Q₁₆×C₇₃	—	2	4	no	—
68	C₂×Q₁₆×C₇₃	—	2	4	no	—
69	C₂×Q₁₆×C₇₃	—	2	4	no	—
70	C₂×Q₁₆×C₇₃	—	2	4	no	—
71	C₂×Q₁₆×C₇₃	—	4	2	no	—
72	C₂×Q₁₆×C₇₃	D₄	1	8	yes	complemented
73	C₂×SD₁₆×C₇₃	—	2	4	no	—
74	C₂×SD₁₆×C₇₃	—	2	4	no	—
75	C₂×SD₁₆×C₇₃	—	2	2	no	—
76	C₂×SD₁₆×C₇₃	—	2	4	no	—
77	C₂×SD₁₆×C₇₃	—	4	2	no	—
78	C₂²×C₈×C₇₃	—	2	4	no	—
79	C₂²×C₈×C₇₃	D₄	1	4	yes	—
80	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
81	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
82	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
83	C₄⋊Q₈×C₇₃	—	2	4	no	—
84	C₄⋊Q₈×C₇₃	—	4	2	no	—
85	#124×C₇₃	—	2	4	no	—
86	#124×C₇₃	—	4	2	no	—
87	C₂²⋊Q₈×C₇₃	—	2	2	no	—
88	C₂²⋊Q₈×C₇₃	—	2	2	no	—
89	#121×C₇₃	—	2	2	no	—
90	#121×C₇₃	—	2	2	no	—
91	C₂×C₄⋊C₄×C₇₃	—	2	4	no	—
92	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
93	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
94	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
95	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
96	C₂×C₂²⋊C₄×C₇₃	—	2	4	no	—
97	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
98	C₂×C₂²⋊C₄×C₇₃	D₄	1	2	yes	—
99	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
100	#106×C₇₃	—	2	2	no	—
101	#103×C₇₃	—	2	4	no	—
102	#103×C₇₃	—	2	4	no	—
103	#103×C₇₃	—	2	2	no	—
104	#102×C₇₃	—	2	2	no	—
105	C₂²⋊C₈×C₇₃	D₄	1	4	yes	—
106	#97×C₇₃	—	2	4	no	—
107	#95×C₇₃	—	2	4	no	—
108	#95×C₇₃	—	2	4	no	—
109	#95×C₇₃	D₄	1	2	yes	—
110	C₂⁴×C₇₃	—	2	1	no	—
111	C₂⁴×C₇₃	C₂×D₄	1	1	yes	characteristic
112	C₂×Q₈×C₇₃	—	2	2	no	—
113	C₂×Q₈×C₇₃	—	2	2	no	—
114	C₂×Q₈×C₇₃	—	2	8	no	—
115	C₂×Q₈×C₇₃	—	2	8	no	—
116	C₂×Q₈×C₇₃	—	2	2	no	—
117	C₂×Q₈×C₇₃	—	2	2	no	—
118	C₂×Q₈×C₇₃	—	2	2	no	—
119	C₂×Q₈×C₇₃	—	2	2	no	—
120	C₂×Q₈×C₇₃	—	2	2	no	—
121	C₂×Q₈×C₇₃	—	2	2	no	—
122	C₂×Q₈×C₇₃	—	2	1	no	—
123	C₂×Q₈×C₇₃	—	2	1	no	—
124	C₂×Q₈×C₇₃	—	2	2	no	—
125	C₂×Q₈×C₇₃	—	2	2	no	—
126	C₂×Q₈×C₇₃	—	2	2	no	—
127	C₂×Q₈×C₇₃	—	2	2	no	—
128	C₂×Q₈×C₇₃	—	4	4	no	—
129	C₂×Q₈×C₇₃	—	4	4	no	—
130	C₂×Q₈×C₇₃	—	4	8	no	—
131	C₂×Q₈×C₇₃	—	4	8	no	—
132	C₂×Q₈×C₇₃	—	4	4	no	—
133	C₂×Q₈×C₇₃	—	4	4	no	—
134	C₂×Q₈×C₇₃	—	4	2	no	—
135	C₂×Q₈×C₇₃	—	4	2	no	—
136	C₂×Q₈×C₇₃	C₂×D₄	1	4	yes	—
137	C₂×Q₈×C₇₃	C₂×D₄	1	4	yes	—
138	C₂×D₄×C₇₃	—	2	1	no	—
139	C₂×D₄×C₇₃	—	2	1	no	—
140	C₂×D₄×C₇₃	—	2	2	no	—
141	C₂×D₄×C₇₃	—	2	2	no	—
142	C₂×D₄×C₇₃	—	4	2	no	—
143	C₂×D₄×C₇₃	—	4	4	no	—
144	C₂²×C₄×C₇₃	—	2	2	no	—
145	C₂²×C₄×C₇₃	—	2	2	no	—
146	C₂²×C₄×C₇₃	—	2	2	no	—
147	C₂²×C₄×C₇₃	—	2	2	no	—
148	C₂²×C₄×C₇₃	—	2	1	no	—
149	C₂²×C₄×C₇₃	—	2	1	no	—
150	C₂²×C₄×C₇₃	—	2	1	no	—
151	C₂²×C₄×C₇₃	—	4	4	no	—
152	C₂²×C₄×C₇₃	—	4	4	no	—
153	C₂²×C₄×C₇₃	—	4	2	no	—
154	C₂²×C₄×C₇₃	—	4	2	no	—
155	C₂²×C₄×C₇₃	C₂×D₄	1	4	yes	—
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	C₂⁴	1	1	yes	characteristic
160	Q₁₆×C₇₃	—	2	16	no	—
161	Q₁₆×C₇₃	—	2	16	no	—
162	Q₁₆×C₇₃	—	4	8	no	—
163	SD₁₆×C₇₃	—	4	8	no	—
164	SD₁₆×C₇₃	—	4	4	no	—
165	C₂×C₈×C₇₃	—	2	2	no	—
166	C₂×C₈×C₇₃	—	2	2	no	—
167	C₂×C₈×C₇₃	—	2	2	no	—
168	C₂×C₈×C₇₃	—	2	8	no	—
169	C₂×C₈×C₇₃	C₂×D₄	1	4	yes	—
170	C₂×C₈×C₇₃	C₂×D₄	1	2	yes	—
171	C₂×C₈×C₇₃	C₂×D₄	1	4	yes	—
172	C₂×C₈×C₇₃	C₂×D₄	1	2	yes	—
173	C₄⋊C₄×C₇₃	—	2	1	no	—
174	C₄⋊C₄×C₇₃	—	2	1	no	—
175	C₄⋊C₄×C₇₃	—	2	1	no	—
176	C₄⋊C₄×C₇₃	—	2	1	no	—
177	C₄⋊C₄×C₇₃	—	4	8	no	—
178	C₄⋊C₄×C₇₃	—	4	2	no	—
179	C₂²⋊C₄×C₇₃	—	2	4	no	—
180	C₂²⋊C₄×C₇₃	—	4	8	no	—
181	C₂²⋊C₄×C₇₃	—	4	2	no	—
182	C₂²⋊C₄×C₇₃	—	4	2	no	—
183	C₄²×C₇₃	—	2	2	no	—
184	C₄²×C₇₃	—	2	2	no	—
185	C₂³×C₇₃	—	2	2	no	—
186	C₂³×C₇₃	—	2	2	no	—
187	C₂³×C₇₃	—	4	1	no	—
188	C₂³×C₇₃	—	4	2	no	—
189	C₂³×C₇₃	—	4	2	no	—
190	C₂³×C₇₃	—	4	2	no	—
191	C₂³×C₇₃	#127	1	2	yes	—
192	C₂³×C₇₃	#137	1	4	yes	—
193	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
194	Q₈×C₇₃	—	2	4	no	—
195	Q₈×C₇₃	—	2	4	no	—
196	Q₈×C₇₃	—	2	4	no	—
197	Q₈×C₇₃	—	2	4	no	—
198	Q₈×C₇₃	—	4	8	no	—
199	Q₈×C₇₃	—	4	8	no	—
200	Q₈×C₇₃	—	4	2	no	—
201	Q₈×C₇₃	—	4	2	no	—
202	Q₈×C₇₃	—	4	2	no	—
203	Q₈×C₇₃	—	4	2	no	—
204	Q₈×C₇₃	—	4	1	no	—
205	Q₈×C₇₃	—	4	1	no	—
206	Q₈×C₇₃	—	4	2	no	—
207	D₄×C₇₃	—	4	1	no	—
208	D₄×C₇₃	—	4	1	no	—
209	D₄×C₇₃	—	4	2	no	—
210	D₄×C₇₃	—	8	4	no	—
211	C₂×C₄×C₇₃	—	2	2	no	—
212	C₂×C₄×C₇₃	—	2	2	no	—
213	C₂×C₄×C₇₃	—	2	2	no	—
214	C₂×C₄×C₇₃	—	2	4	no	—
215	C₂×C₄×C₇₃	—	2	4	no	—
216	C₂×C₄×C₇₃	—	2	4	no	—
217	C₂×C₄×C₇₃	—	2	4	no	—
218	C₂×C₄×C₇₃	—	2	4	no	—
219	C₂×C₄×C₇₃	—	2	4	no	—
220	C₂×C₄×C₇₃	—	4	8	no	—
221	C₂×C₄×C₇₃	—	4	8	no	—
222	C₂×C₄×C₇₃	—	4	2	no	—
223	C₂×C₄×C₇₃	—	4	2	no	—
224	C₂×C₄×C₇₃	—	4	2	no	—
225	C₂×C₄×C₇₃	—	4	2	no	—
226	C₂×C₄×C₇₃	—	4	1	no	—
227	C₂×C₄×C₇₃	—	4	1	no	—
228	C₂×C₄×C₇₃	—	4	1	no	—
229	C₂×C₄×C₇₃	—	4	2	no	—
230	C₂×C₄×C₇₃	—	4	2	no	—
231	C₂×C₄×C₇₃	—	4	2	no	—
232	C₂×C₄×C₇₃	#127	1	2	yes	—
233	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
234	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
235	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
236	C₂×C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
237	C₈×C₇₃	—	2	2	no	—
238	C₈×C₇₃	—	2	4	no	—
239	C₈×C₇₃	#120	1	4	yes	—
240	C₂²×C₇₃	—	2	2	no	—
241	C₂²×C₇₃	—	2	2	no	—
242	C₂²×C₇₃	—	2	8	no	—
243	C₂²×C₇₃	—	8	1	no	—
244	C₂²×C₇₃	—	8	1	no	—
245	C₂²×C₇₃	—	8	1	no	—
246	C₂²×C₇₃	—	8	4	no	—
247	C₂²×C₇₃	#497	1	4	yes	complemented
248	C₂²×C₇₃	C₂×#127	1	1	yes	characteristic
249	C₂²×C₇₃	D₄²	1	2	yes	—
250	C₂²×C₇₃	C₂×#137	1	2	yes	—
251	C₂²×C₇₃	#578	1	2	yes	—
252	C₄×C₇₃	—	2	2	no	—
253	C₄×C₇₃	—	4	4	no	—
254	C₄×C₇₃	—	4	4	no	—
255	C₄×C₇₃	—	4	4	no	—
256	C₄×C₇₃	—	8	1	no	—
257	C₄×C₇₃	—	8	1	no	—
258	C₄×C₇₃	—	8	1	no	—
259	C₄×C₇₃	C₂×#120	1	1	yes	characteristic
260	C₄×C₇₃	#535	1	1	yes	characteristic
261	C₄×C₇₃	D₄²	1	2	yes	—
262	#25789	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
263	C₂×C₇₃	—	2	4	no	—
264	C₂×C₇₃	—	16	1	no	—
265	C₂×C₇₃	#2433	1	1	yes	characteristic
266	C₂×C₇₃	C₂×#497	1	1	yes	characteristic
267	C₂×C₇₃	#3156	1	1	yes	characteristic
268	C₂×C₇₃	#3270	1	4	yes	—
269	C₂³×Q₁₆	C₂×C₇₃	1	1	yes	characteristic, complemented
270	C₂×#497	C₂×C₇₃	1	2	yes	complemented
271	C₂×#465	C₂×C₇₃	1	1	yes	characteristic
272	C₂×#451	C₂×C₇₃	1	1	yes	characteristic, complemented
273	C₂×#448	C₂×C₇₃	1	1	yes	characteristic
274	#2436	C₂×C₇₃	1	1	yes	characteristic
275	#2434	C₂×C₇₃	1	1	yes	characteristic, complemented
276	#2016	C₂×C₇₃	1	2	yes	complemented
277	#2015	C₂×C₇₃	1	2	yes	complemented
278	#1971	C₂×C₇₃	1	2	yes	complemented
279	#1752	C₂×C₇₃	1	1	yes	characteristic, complemented
280	C₇₃	#25789	1	1	yes	characteristic, direct product factor, Sylow
281	C₂³×Q₈	C₂²×C₇₃	1	1	yes	characteristic
282	C₂³×Q₈	C₂²×C₇₃	1	1	yes	characteristic
283	C₂²×Q₁₆	—	2	8	no	—
284	C₂²×Q₁₆	—	2	4	no	—
285	C₂²×Q₁₆	C₂²×C₇₃	1	2	yes	—
286	C₂²×Q₁₆	C₂²×C₇₃	1	2	yes	—
287	C₂²×Q₁₆	C₂²×C₇₃	1	2	yes	—
288	C₂²×SD₁₆	C₂²×C₇₃	1	1	yes	characteristic
289	C₂²×SD₁₆	C₂²×C₇₃	1	2	yes	—
290	C₂³×C₈	C₂²×C₇₃	1	1	yes	characteristic
291	C₂×C₄⋊Q₈	C₂²×C₇₃	1	2	yes	—
292	C₂×#124	C₂²×C₇₃	1	2	yes	—
293	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
294	C₂×#121	C₂²×C₇₃	1	1	yes	characteristic
295	#497	—	2	8	no	—
296	#465	—	2	4	no	—
297	#451	—	2	4	no	—
298	#448	—	2	4	no	—
299	C₂×#106	C₂²×C₇₃	1	1	yes	characteristic
300	C₂×#103	C₂²×C₇₃	1	2	yes	—
301	C₂×#103	C₂²×C₇₃	1	2	yes	—
302	C₂×#103	C₂²×C₇₃	1	1	yes	characteristic
303	C₂×#102	C₂²×C₇₃	1	1	yes	characteristic
304	C₂×C₂²⋊C₈	C₂²×C₇₃	1	1	yes	characteristic
305	C₂×#97	C₂²×C₇₃	1	2	yes	—
306	#395	—	2	2	no	—
307	#393	—	2	2	no	—
308	#391	C₂²×C₇₃	1	2	yes	—
309	#391	C₂²×C₇₃	1	2	yes	—
310	#386	—	2	2	no	—
311	#385	—	2	2	no	—
312	C₄×C₂²⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
313	#336	C₂²×C₇₃	1	2	yes	—
314	C₂²×Q₈	—	2	1	no	—
315	C₂²×Q₈	—	2	1	no	—
316	C₂²×Q₈	—	2	4	no	—
317	C₂²×Q₈	—	2	4	no	—
318	C₂²×Q₈	—	2	2	no	—
319	C₂²×Q₈	—	2	2	no	—
320	C₂²×Q₈	—	2	2	no	—
321	C₂²×Q₈	—	2	2	no	—
322	C₂²×Q₈	—	4	2	no	—
323	C₂²×Q₈	—	4	2	no	—
324	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
325	C₂²×Q₈	C₂³×C₇₃	1	2	yes	—
326	C₂²×Q₈	C₂³×C₇₃	1	2	yes	—
327	C₂²×D₄	—	2	1	no	—
328	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
329	C₂³×C₄	—	2	1	no	—
330	C₂³×C₄	—	2	1	no	—
331	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
332	C₂×Q₁₆	—	2	32	no	—
333	C₂×Q₁₆	—	2	4	no	—
334	C₂×Q₁₆	—	2	4	no	—
335	C₂×Q₁₆	—	2	4	no	—
336	C₂×Q₁₆	—	2	4	no	—
337	C₂×Q₁₆	—	2	4	no	—
338	C₂×Q₁₆	—	2	4	no	—
339	C₂×Q₁₆	—	2	4	no	—
340	C₂×Q₁₆	—	4	2	no	—
341	C₂×Q₁₆	D₄×C₇₃	1	8	yes	complemented
342	C₂×SD₁₆	—	2	4	no	—
343	C₂×SD₁₆	—	2	4	no	—
344	C₂×SD₁₆	—	2	2	no	—
345	C₂×SD₁₆	—	2	4	no	—
346	C₂×SD₁₆	—	4	2	no	—
347	C₂²×C₈	—	2	4	no	—
348	C₂²×C₈	D₄×C₇₃	1	4	yes	—
349	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
350	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
351	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
352	C₄⋊Q₈	—	2	4	no	—
353	C₄⋊Q₈	—	4	2	no	—
354	#124	—	2	4	no	—
355	#124	—	4	2	no	—
356	C₂²⋊Q₈	—	2	2	no	—
357	C₂²⋊Q₈	—	2	2	no	—
358	#121	—	2	2	no	—
359	#121	—	2	2	no	—
360	C₂×C₄⋊C₄	—	2	1	no	—
361	C₂×C₄⋊C₄	—	2	4	no	—
362	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
363	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
364	C₂×C₂²⋊C₄	—	2	1	no	—
365	C₂×C₂²⋊C₄	—	2	1	no	—
366	C₂×C₂²⋊C₄	—	2	4	no	—
367	C₂×C₂²⋊C₄	D₄×C₇₃	1	2	yes	—
368	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
369	#106	—	2	2	no	—
370	#103	—	2	4	no	—
371	#103	—	2	4	no	—
372	#103	—	2	2	no	—
373	#102	—	2	2	no	—
374	C₂²⋊C₈	D₄×C₇₃	1	4	yes	—
375	#97	—	2	4	no	—
376	#95	—	2	4	no	—
377	#95	—	2	4	no	—
378	#95	D₄×C₇₃	1	2	yes	—
379	C₂⁴	—	2	1	no	—
380	C₂⁴	C₂×D₄×C₇₃	1	1	yes	characteristic
381	C₂×Q₈	—	2	2	no	—
382	C₂×Q₈	—	2	2	no	—
383	C₂×Q₈	—	2	8	no	—
384	C₂×Q₈	—	2	8	no	—
385	C₂×Q₈	—	2	2	no	—
386	C₂×Q₈	—	2	2	no	—
387	C₂×Q₈	—	2	2	no	—
388	C₂×Q₈	—	2	2	no	—
389	C₂×Q₈	—	2	2	no	—
390	C₂×Q₈	—	2	2	no	—
391	C₂×Q₈	—	2	1	no	—
392	C₂×Q₈	—	2	1	no	—
393	C₂×Q₈	—	2	2	no	—
394	C₂×Q₈	—	2	2	no	—
395	C₂×Q₈	—	2	2	no	—
396	C₂×Q₈	—	2	2	no	—
397	C₂×Q₈	—	4	4	no	—
398	C₂×Q₈	—	4	4	no	—
399	C₂×Q₈	—	4	8	no	—
400	C₂×Q₈	—	4	8	no	—
401	C₂×Q₈	—	4	4	no	—
402	C₂×Q₈	—	4	4	no	—
403	C₂×Q₈	—	4	2	no	—
404	C₂×Q₈	—	4	2	no	—
405	C₂×Q₈	C₂×D₄×C₇₃	1	4	yes	—
406	C₂×Q₈	C₂×D₄×C₇₃	1	4	yes	—
407	C₂×D₄	—	2	1	no	—
408	C₂×D₄	—	2	1	no	—
409	C₂×D₄	—	2	2	no	—
410	C₂×D₄	—	2	2	no	—
411	C₂×D₄	—	4	2	no	—
412	C₂×D₄	—	4	4	no	—
413	C₂²×C₄	—	2	2	no	—
414	C₂²×C₄	—	2	2	no	—
415	C₂²×C₄	—	2	2	no	—
416	C₂²×C₄	—	2	2	no	—
417	C₂²×C₄	—	2	1	no	—
418	C₂²×C₄	—	2	1	no	—
419	C₂²×C₄	—	2	1	no	—
420	C₂²×C₄	—	4	4	no	—
421	C₂²×C₄	—	4	4	no	—
422	C₂²×C₄	—	4	2	no	—
423	C₂²×C₄	—	4	2	no	—
424	C₂²×C₄	C₂×D₄×C₇₃	1	4	yes	—
425	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
426	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
427	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
428	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
429	Q₁₆	—	2	16	no	—
430	Q₁₆	—	2	16	no	—
431	Q₁₆	—	4	8	no	—
432	SD₁₆	—	4	8	no	—
433	SD₁₆	—	4	4	no	—
434	C₂×C₈	—	2	2	no	—
435	C₂×C₈	—	2	2	no	—
436	C₂×C₈	—	2	2	no	—
437	C₂×C₈	—	2	8	no	—
438	C₂×C₈	C₂×D₄×C₇₃	1	4	yes	—
439	C₂×C₈	C₂×D₄×C₇₃	1	2	yes	—
440	C₂×C₈	C₂×D₄×C₇₃	1	4	yes	—
441	C₂×C₈	C₂×D₄×C₇₃	1	2	yes	—
442	C₄⋊C₄	—	2	1	no	—
443	C₄⋊C₄	—	2	1	no	—
444	C₄⋊C₄	—	2	1	no	—
445	C₄⋊C₄	—	2	1	no	—
446	C₄⋊C₄	—	4	8	no	—
447	C₄⋊C₄	—	4	2	no	—
448	C₂²⋊C₄	—	2	4	no	—
449	C₂²⋊C₄	—	4	8	no	—
450	C₂²⋊C₄	—	4	2	no	—
451	C₂²⋊C₄	—	4	2	no	—
452	C₄²	—	2	2	no	—
453	C₄²	—	2	2	no	—
454	C₂³	—	2	2	no	—
455	C₂³	—	2	2	no	—
456	C₂³	—	4	1	no	—
457	C₂³	—	4	2	no	—
458	C₂³	—	4	2	no	—
459	C₂³	—	4	2	no	—
460	C₂³	#127×C₇₃	1	2	yes	—
461	C₂³	#137×C₇₃	1	4	yes	—
462	C₂³	C₂²×D₄×C₇₃	1	1	yes	characteristic
463	Q₈	—	2	4	no	—
464	Q₈	—	2	4	no	—
465	Q₈	—	2	4	no	—
466	Q₈	—	2	4	no	—
467	Q₈	—	4	8	no	—
468	Q₈	—	4	8	no	—
469	Q₈	—	4	2	no	—
470	Q₈	—	4	2	no	—
471	Q₈	—	4	2	no	—
472	Q₈	—	4	2	no	—
473	Q₈	—	4	1	no	—
474	Q₈	—	4	1	no	—
475	Q₈	—	4	2	no	—
476	D₄	—	4	1	no	—
477	D₄	—	4	1	no	—
478	D₄	—	4	2	no	—
479	D₄	—	8	4	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	2	2	no	—
482	C₂×C₄	—	2	2	no	—
483	C₂×C₄	—	2	4	no	—
484	C₂×C₄	—	2	4	no	—
485	C₂×C₄	—	2	4	no	—
486	C₂×C₄	—	2	4	no	—
487	C₂×C₄	—	2	4	no	—
488	C₂×C₄	—	2	4	no	—
489	C₂×C₄	—	4	8	no	—
490	C₂×C₄	—	4	8	no	—
491	C₂×C₄	—	4	2	no	—
492	C₂×C₄	—	4	2	no	—
493	C₂×C₄	—	4	2	no	—
494	C₂×C₄	—	4	2	no	—
495	C₂×C₄	—	4	1	no	—
496	C₂×C₄	—	4	1	no	—
497	C₂×C₄	—	4	1	no	—
498	C₂×C₄	—	4	2	no	—
499	C₂×C₄	—	4	2	no	—
500	C₂×C₄	—	4	2	no	—
501	C₂×C₄	#127×C₇₃	1	2	yes	—
502	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
503	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
504	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
505	C₂×C₄	H(5,𝔽₂)×C₇₃	1	2	yes	—
506	C₈	—	2	2	no	—
507	C₈	—	2	4	no	—
508	C₈	#120×C₇₃	1	4	yes	—
509	C₂²	—	2	8	no	—
510	C₂²	—	2	2	no	—
511	C₂²	—	2	2	no	—
512	C₂²	—	8	4	no	—
513	C₂²	—	8	1	no	—
514	C₂²	—	8	1	no	—
515	C₂²	—	8	1	no	—
516	C₂²	#497×C₇₃	1	4	yes	complemented
517	C₂²	C₂×#127×C₇₃	1	1	yes	characteristic
518	C₂²	D₄²×C₇₃	1	2	yes	—
519	C₂²	C₂×#137×C₇₃	1	2	yes	—
520	C₂²	#578×C₇₃	1	2	yes	—
521	C₄	—	2	2	no	—
522	C₄	—	4	4	no	—
523	C₄	—	4	4	no	—
524	C₄	—	4	4	no	—
525	C₄	—	8	1	no	—
526	C₄	—	8	1	no	—
527	C₄	—	8	1	no	—
528	C₄	C₂×#120×C₇₃	1	1	yes	characteristic
529	C₄	#535×C₇₃	1	1	yes	characteristic
530	C₄	D₄²×C₇₃	1	2	yes	—
531	C₂	—	2	4	no	—
532	C₂	—	16	1	no	—
533	C₂	C₇₃×#2433	1	1	yes	characteristic
534	C₂	C₂×#497×C₇₃	1	1	yes	characteristic
535	C₂	C₇₃×#3156	1	1	yes	characteristic
536	C₂	C₇₃×#3270	1	4	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
1. C₂³×Q₁₆×C₇₃	C₂	semidirect
2. C₂×#497×C₇₃	C₂	semidirect
4. C₂×#451×C₇₃	C₂	semidirect
7. C₇₃×#2434	C₂	semidirect
8. C₇₃×#2016	C₂	semidirect
9. C₇₃×#2015	C₂	semidirect
10. C₇₃×#1971	C₂	semidirect
11. C₇₃×#1752	C₂	semidirect
72. C₂×Q₁₆×C₇₃	D₄	semidirect
247. C₂²×C₇₃	#497	semidirect
262. #25789	C₇₃	direct (N × H)
269. C₂³×Q₁₆	C₂×C₇₃	semidirect
270. C₂×#497	C₂×C₇₃	semidirect
272. C₂×#451	C₂×C₇₃	semidirect
275. #2434	C₂×C₇₃	semidirect
276. #2016	C₂×C₇₃	semidirect
277. #2015	C₂×C₇₃	semidirect
278. #1971	C₂×C₇₃	semidirect
279. #1752	C₂×C₇₃	semidirect
280. C₇₃	#25789	direct (N × H)
341. C₂×Q₁₆	D₄×C₇₃	semidirect
516. C₂²	#497×C₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₂³×Q₁₆×C₇₃	2
C₂×#497×C₇₃	2
C₂×#465×C₇₃	2
C₂×#451×C₇₃	2
C₂×#448×C₇₃	2
C₇₃×#2436	2
C₇₃×#2434	2
C₇₃×#2016	2
C₇₃×#2015	2
C₇₃×#1971	2
C₇₃×#1752	2
#25789	73

Subgroups — C73×#25789 #32935193

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#25789 #32935193