Subgroups — C₇₃×#26463 #32935867

Order 18688.

898 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#478×C₇₃	C₂	1	2	yes	maximal, complemented
2	C₇₃×#2552	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₃×#2366	C₂	1	1	yes	maximal, characteristic
4	C₇₃×#2065	C₂	1	2	yes	maximal, complemented
5	C₇₃×#2025	C₂	1	2	yes	maximal, complemented
6	C₇₃×#1982	C₂	1	1	yes	maximal, characteristic
7	C₇₃×#1957	C₂	1	1	yes	maximal, characteristic
8	C₇₃×#1947	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇₃×#1939	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇₃×#1862	C₂	1	2	yes	maximal, complemented
11	C₄×#106×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#127×C₇₃	C₂²	1	1	yes	characteristic
13	C₂×#125×C₇₃	C₂²	1	2	yes	—
14	C₂×C₄×D₄×C₇₃	—	2	1	no	—
15	C₂×C₄×D₄×C₇₃	C₂²	1	2	yes	—
16	#478×C₇₃	—	2	8	no	—
17	C₂×#107×C₇₃	C₂²	1	2	yes	—
18	C₂×#106×C₇₃	C₂²	1	1	yes	characteristic
19	C₂×#106×C₇₃	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊C₈×C₇₃	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊C₈×C₇₃	C₂²	1	2	yes	—
22	C₂×#102×C₇₃	C₂²	1	2	yes	—
23	C₂×#102×C₇₃	C₂²	1	2	yes	—
24	C₂×#102×C₇₃	C₂²	1	2	yes	—
25	C₂×#102×C₇₃	C₂²	1	2	yes	—
26	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
27	#398×C₇₃	—	2	2	no	—
28	#390×C₇₃	—	2	1	no	—
29	#390×C₇₃	C₂²	1	2	yes	—
30	#389×C₇₃	—	2	1	no	—
31	#389×C₇₃	C₂²	1	2	yes	—
32	#386×C₇₃	—	2	2	no	—
33	#384×C₇₃	—	2	1	no	—
34	#384×C₇₃	C₂²	1	1	yes	characteristic
35	C₄×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
36	C₄×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
37	C₄×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
38	#340×C₇₃	C₂²	1	2	yes	—
39	#340×C₇₃	C₂²	1	1	yes	characteristic
40	#340×C₇₃	C₂²	1	1	yes	characteristic
41	#336×C₇₃	C₂²	1	2	yes	—
42	C₂²×D₄×C₇₃	—	2	1	no	—
43	C₂²×D₄×C₇₃	—	2	1	no	—
44	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
45	C₂³×C₄×C₇₃	—	2	2	no	—
46	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
47	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
48	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
49	#127×C₇₃	—	2	2	no	—
50	#127×C₇₃	Q₈	1	4	yes	—
51	#125×C₇₃	—	2	4	no	—
52	#125×C₇₃	—	4	2	no	—
53	C₄×D₄×C₇₃	—	2	4	no	—
54	C₄×D₄×C₇₃	—	4	2	no	—
55	C₄×D₄×C₇₃	—	4	4	no	—
56	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
57	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
58	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
59	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
60	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
61	C₂×C₄⋊C₄×C₇₃	D₄	1	1	yes	characteristic
62	C₂×C₄⋊C₄×C₇₃	D₄	1	1	yes	characteristic
63	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
64	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
65	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
66	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
67	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
68	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
69	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
70	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
71	C₂×C₄²×C₇₃	—	2	1	no	—
72	C₂×C₄²×C₇₃	—	2	1	no	—
73	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
74	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
75	#107×C₇₃	—	2	4	no	—
76	#106×C₇₃	—	2	2	no	—
77	#106×C₇₃	D₄	1	4	yes	complemented
78	C₄⋊C₈×C₇₃	—	2	4	no	—
79	C₄⋊C₈×C₇₃	—	2	2	no	—
80	#102×C₇₃	—	2	4	no	—
81	#102×C₇₃	—	2	4	no	—
82	#102×C₇₃	—	2	4	no	—
83	#102×C₇₃	—	4	2	no	—
84	C₄×C₈×C₇₃	—	2	2	no	—
85	#95×C₇₃	—	2	1	no	—
86	#95×C₇₃	—	2	1	no	—
87	#95×C₇₃	—	2	2	no	—
88	#95×C₇₃	D₄	1	2	yes	—
89	C₂⁴×C₇₃	—	2	2	no	—
90	C₂×D₄×C₇₃	—	2	4	no	—
91	C₂×D₄×C₇₃	—	2	4	no	—
92	C₂×D₄×C₇₃	—	2	2	no	—
93	C₂×D₄×C₇₃	—	2	2	no	—
94	C₂×D₄×C₇₃	—	2	2	no	—
95	C₂×D₄×C₇₃	—	2	2	no	—
96	C₂×D₄×C₇₃	—	2	2	no	—
97	C₂×D₄×C₇₃	—	4	2	no	—
98	C₂×D₄×C₇₃	—	4	2	no	—
99	C₂×D₄×C₇₃	—	8	1	no	—
100	C₂×D₄×C₇₃	—	8	1	no	—
101	C₂×D₄×C₇₃	C₂×Q₈	1	4	yes	—
102	C₂²×C₄×C₇₃	—	2	1	no	—
103	C₂²×C₄×C₇₃	—	2	1	no	—
104	C₂²×C₄×C₇₃	—	2	1	no	—
105	C₂²×C₄×C₇₃	—	2	1	no	—
106	C₂²×C₄×C₇₃	—	2	2	no	—
107	C₂²×C₄×C₇₃	—	4	4	no	—
108	C₂²×C₄×C₇₃	—	4	4	no	—
109	C₂²×C₄×C₇₃	—	8	2	no	—
110	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
111	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
112	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
115	C₂×C₈×C₇₃	—	2	1	no	—
116	C₂×C₈×C₇₃	—	2	1	no	—
117	C₂×C₈×C₇₃	—	2	2	no	—
118	C₂×C₈×C₇₃	—	2	1	no	—
119	C₂×C₈×C₇₃	—	2	2	no	—
120	C₂×C₈×C₇₃	—	2	2	no	—
121	C₂×C₈×C₇₃	—	2	1	no	—
122	C₂×C₈×C₇₃	—	2	1	no	—
123	C₂×C₈×C₇₃	C₂×D₄	1	2	yes	—
124	C₄⋊C₄×C₇₃	—	2	2	no	—
125	C₄⋊C₄×C₇₃	—	2	2	no	—
126	C₄⋊C₄×C₇₃	—	2	1	no	—
127	C₄⋊C₄×C₇₃	—	2	1	no	—
128	C₄⋊C₄×C₇₃	—	2	1	no	—
129	C₄⋊C₄×C₇₃	—	2	2	no	—
130	C₄⋊C₄×C₇₃	—	2	1	no	—
131	C₄⋊C₄×C₇₃	—	2	2	no	—
132	C₄⋊C₄×C₇₃	—	2	1	no	—
133	C₄⋊C₄×C₇₃	—	4	4	no	—
134	C₄⋊C₄×C₇₃	—	4	4	no	—
135	C₄⋊C₄×C₇₃	—	4	2	no	—
136	C₄⋊C₄×C₇₃	—	8	1	no	—
137	C₄⋊C₄×C₇₃	—	8	2	no	—
138	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
139	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
140	C₄⋊C₄×C₇₃	#41	1	2	yes	—
141	C₂²⋊C₄×C₇₃	—	4	4	no	—
142	C₂²⋊C₄×C₇₃	—	4	4	no	—
143	C₂²⋊C₄×C₇₃	—	8	2	no	—
144	C₄²×C₇₃	—	2	2	no	—
145	C₄²×C₇₃	—	2	2	no	—
146	C₄²×C₇₃	—	4	2	no	—
147	C₄²×C₇₃	—	4	2	no	—
148	C₄²×C₇₃	C₂×Q₈	1	2	yes	—
149	C₄²×C₇₃	#41	1	2	yes	—
150	C₂³×C₇₃	—	2	4	no	—
151	C₂³×C₇₃	—	4	2	no	—
152	C₂³×C₇₃	—	4	2	no	—
153	C₂³×C₇₃	—	4	2	no	—
154	C₂³×C₇₃	—	4	2	no	—
155	C₂³×C₇₃	—	4	2	no	—
156	C₂³×C₇₃	—	4	2	no	—
157	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
158	D₄×C₇₃	—	2	4	no	—
159	D₄×C₇₃	—	2	4	no	—
160	D₄×C₇₃	—	4	2	no	—
161	D₄×C₇₃	—	4	2	no	—
162	D₄×C₇₃	—	4	8	no	—
163	D₄×C₇₃	—	8	4	no	—
164	C₂×C₄×C₇₃	—	2	1	no	—
165	C₂×C₄×C₇₃	—	2	1	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	2	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	—	4	1	no	—
176	C₂×C₄×C₇₃	—	4	1	no	—
177	C₂×C₄×C₇₃	—	4	1	no	—
178	C₂×C₄×C₇₃	—	4	1	no	—
179	C₂×C₄×C₇₃	—	4	1	no	—
180	C₂×C₄×C₇₃	—	4	1	no	—
181	C₂×C₄×C₇₃	—	4	2	no	—
182	C₂×C₄×C₇₃	—	4	1	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	—	8	8	no	—
188	C₂×C₄×C₇₃	C₂²⋊Q₈	1	2	yes	—
189	C₂×C₄×C₇₃	C₂²⋊Q₈	1	2	yes	—
190	C₂×C₄×C₇₃	#135	1	2	yes	—
191	C₂×C₄×C₇₃	AGL(1,ℤ/8)	1	2	yes	—
192	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
193	C₂×C₄×C₇₃	C₂²×Q₈	1	1	yes	characteristic
194	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
195	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
196	C₂×C₄×C₇₃	H(5,𝔽₂)	1	1	yes	characteristic
197	C₂×C₄×C₇₃	2₋¹⁺⁴	1	1	yes	characteristic
198	C₈×C₇₃	—	2	2	no	—
199	C₈×C₇₃	—	4	2	no	—
200	C₈×C₇₃	—	4	1	no	—
201	C₂²×C₇₃	—	4	4	no	—
202	C₂²×C₇₃	—	4	4	no	—
203	C₂²×C₇₃	—	4	4	no	—
204	C₂²×C₇₃	—	8	2	no	—
205	C₂²×C₇₃	—	8	2	no	—
206	C₂²×C₇₃	—	8	2	no	—
207	C₂²×C₇₃	—	8	2	no	—
208	C₂²×C₇₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
209	C₂²×C₇₃	D₄²	1	1	yes	characteristic
210	C₂²×C₇₃	#548	1	1	yes	characteristic
211	C₂²×C₇₃	C₂×#135	1	1	yes	characteristic
212	C₂²×C₇₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
213	C₂²×C₇₃	#576	1	1	yes	characteristic
214	C₂²×C₇₃	#577	1	1	yes	characteristic
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	—	4	2	no	—
220	C₄×C₇₃	—	4	2	no	—
221	C₄×C₇₃	—	8	1	no	—
222	C₄×C₇₃	—	8	2	no	—
223	C₄×C₇₃	#478	1	4	yes	complemented
224	C₄×C₇₃	#532	1	1	yes	characteristic
225	C₄×C₇₃	#542	1	1	yes	characteristic
226	C₄×C₇₃	D₄×Q₈	1	1	yes	characteristic
227	C₄×C₇₃	#554	1	1	yes	characteristic
228	#26463	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
229	C₂×C₇₃	—	8	4	no	—
230	C₂×C₇₃	#2452	1	1	yes	characteristic
231	C₂×C₇₃	C₂×#478	1	1	yes	characteristic
232	C₂×C₇₃	#3081	1	1	yes	characteristic
233	C₂×C₇₃	#3274	1	1	yes	characteristic
234	C₂×C₇₃	#3284	1	1	yes	characteristic
235	C₂×C₇₃	#3361	1	1	yes	characteristic
236	C₂×C₇₃	#3368	1	1	yes	characteristic
237	C₂×#478	C₂×C₇₃	1	2	yes	complemented
238	#2552	C₂×C₇₃	1	1	yes	characteristic, complemented
239	#2366	C₂×C₇₃	1	1	yes	characteristic
240	#2065	C₂×C₇₃	1	2	yes	complemented
241	#2025	C₂×C₇₃	1	2	yes	complemented
242	#1982	C₂×C₇₃	1	1	yes	characteristic
243	#1957	C₂×C₇₃	1	1	yes	characteristic
244	#1947	C₂×C₇₃	1	1	yes	characteristic, complemented
245	#1939	C₂×C₇₃	1	1	yes	characteristic, complemented
246	#1862	C₂×C₇₃	1	2	yes	complemented
247	C₄×#106	C₂×C₇₃	1	1	yes	characteristic, complemented
248	C₇₃	#26463	1	1	yes	characteristic, direct product factor, Sylow
249	C₂×#127	C₂²×C₇₃	1	1	yes	characteristic
250	C₂×#125	C₂²×C₇₃	1	2	yes	—
251	C₂×C₄×D₄	—	2	1	no	—
252	C₂×C₄×D₄	C₂²×C₇₃	1	2	yes	—
253	#478	—	2	8	no	—
254	C₂×#107	C₂²×C₇₃	1	2	yes	—
255	C₂×#106	C₂²×C₇₃	1	1	yes	characteristic
256	C₂×#106	C₂²×C₇₃	1	1	yes	characteristic
257	C₂×C₄⋊C₈	C₂²×C₇₃	1	2	yes	—
258	C₂×C₄⋊C₈	C₂²×C₇₃	1	1	yes	characteristic
259	C₂×#102	C₂²×C₇₃	1	2	yes	—
260	C₂×#102	C₂²×C₇₃	1	2	yes	—
261	C₂×#102	C₂²×C₇₃	1	2	yes	—
262	C₂×#102	C₂²×C₇₃	1	2	yes	—
263	C₂×C₄×C₈	C₂²×C₇₃	1	1	yes	characteristic
264	#398	—	2	2	no	—
265	#390	—	2	1	no	—
266	#390	C₂²×C₇₃	1	2	yes	—
267	#389	—	2	1	no	—
268	#389	C₂²×C₇₃	1	2	yes	—
269	#386	—	2	2	no	—
270	#384	—	2	1	no	—
271	#384	C₂²×C₇₃	1	1	yes	characteristic
272	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
273	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
274	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
275	#340	C₂²×C₇₃	1	2	yes	—
276	#340	C₂²×C₇₃	1	1	yes	characteristic
277	#340	C₂²×C₇₃	1	1	yes	characteristic
278	#336	C₂²×C₇₃	1	2	yes	—
279	C₂²×D₄	—	2	1	no	—
280	C₂²×D₄	—	2	1	no	—
281	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
282	C₂³×C₄	—	2	2	no	—
283	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
284	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
285	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
286	#127	—	2	2	no	—
287	#127	Q₈×C₇₃	1	4	yes	—
288	#125	—	2	4	no	—
289	#125	—	4	2	no	—
290	C₄×D₄	—	2	4	no	—
291	C₄×D₄	—	4	2	no	—
292	C₄×D₄	—	4	4	no	—
293	C₂×C₄⋊C₄	—	2	2	no	—
294	C₂×C₄⋊C₄	—	2	2	no	—
295	C₂×C₄⋊C₄	—	2	1	no	—
296	C₂×C₄⋊C₄	—	2	2	no	—
297	C₂×C₄⋊C₄	—	2	1	no	—
298	C₂×C₄⋊C₄	D₄×C₇₃	1	1	yes	characteristic
299	C₂×C₄⋊C₄	D₄×C₇₃	1	1	yes	characteristic
300	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
301	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
302	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
303	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
304	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
305	C₂×C₂²⋊C₄	—	2	2	no	—
306	C₂×C₂²⋊C₄	—	2	2	no	—
307	C₂×C₂²⋊C₄	—	2	2	no	—
308	C₂×C₄²	—	2	1	no	—
309	C₂×C₄²	—	2	1	no	—
310	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
311	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
312	#107	—	2	4	no	—
313	#106	—	2	2	no	—
314	#106	D₄×C₇₃	1	4	yes	complemented
315	C₄⋊C₈	—	2	4	no	—
316	C₄⋊C₈	—	2	2	no	—
317	#102	—	2	4	no	—
318	#102	—	2	4	no	—
319	#102	—	2	4	no	—
320	#102	—	4	2	no	—
321	C₄×C₈	—	2	2	no	—
322	#95	—	2	1	no	—
323	#95	—	2	1	no	—
324	#95	—	2	2	no	—
325	#95	D₄×C₇₃	1	2	yes	—
326	C₂⁴	—	2	2	no	—
327	C₂×D₄	—	2	4	no	—
328	C₂×D₄	—	2	4	no	—
329	C₂×D₄	—	2	2	no	—
330	C₂×D₄	—	2	2	no	—
331	C₂×D₄	—	2	2	no	—
332	C₂×D₄	—	2	2	no	—
333	C₂×D₄	—	2	2	no	—
334	C₂×D₄	—	4	2	no	—
335	C₂×D₄	—	4	2	no	—
336	C₂×D₄	—	8	1	no	—
337	C₂×D₄	—	8	1	no	—
338	C₂×D₄	C₂×Q₈×C₇₃	1	4	yes	—
339	C₂²×C₄	—	2	1	no	—
340	C₂²×C₄	—	2	1	no	—
341	C₂²×C₄	—	2	1	no	—
342	C₂²×C₄	—	2	1	no	—
343	C₂²×C₄	—	2	2	no	—
344	C₂²×C₄	—	4	4	no	—
345	C₂²×C₄	—	4	4	no	—
346	C₂²×C₄	—	8	2	no	—
347	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
348	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
349	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
350	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
351	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
352	C₂×C₈	—	2	1	no	—
353	C₂×C₈	—	2	1	no	—
354	C₂×C₈	—	2	2	no	—
355	C₂×C₈	—	2	1	no	—
356	C₂×C₈	—	2	2	no	—
357	C₂×C₈	—	2	2	no	—
358	C₂×C₈	—	2	1	no	—
359	C₂×C₈	—	2	1	no	—
360	C₂×C₈	C₂×D₄×C₇₃	1	2	yes	—
361	C₄⋊C₄	—	2	2	no	—
362	C₄⋊C₄	—	2	2	no	—
363	C₄⋊C₄	—	2	1	no	—
364	C₄⋊C₄	—	2	1	no	—
365	C₄⋊C₄	—	2	1	no	—
366	C₄⋊C₄	—	2	2	no	—
367	C₄⋊C₄	—	2	1	no	—
368	C₄⋊C₄	—	2	2	no	—
369	C₄⋊C₄	—	2	1	no	—
370	C₄⋊C₄	—	4	4	no	—
371	C₄⋊C₄	—	4	4	no	—
372	C₄⋊C₄	—	4	2	no	—
373	C₄⋊C₄	—	8	1	no	—
374	C₄⋊C₄	—	8	2	no	—
375	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
376	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
377	C₄⋊C₄	#41×C₇₃	1	2	yes	—
378	C₂²⋊C₄	—	4	4	no	—
379	C₂²⋊C₄	—	4	4	no	—
380	C₂²⋊C₄	—	8	2	no	—
381	C₄²	—	2	2	no	—
382	C₄²	—	2	2	no	—
383	C₄²	—	4	2	no	—
384	C₄²	—	4	2	no	—
385	C₄²	C₂×Q₈×C₇₃	1	2	yes	—
386	C₄²	#41×C₇₃	1	2	yes	—
387	C₂³	—	2	4	no	—
388	C₂³	—	4	2	no	—
389	C₂³	—	4	2	no	—
390	C₂³	—	4	2	no	—
391	C₂³	—	4	2	no	—
392	C₂³	—	4	2	no	—
393	C₂³	—	4	2	no	—
394	C₂³	C₂²×D₄×C₇₃	1	1	yes	characteristic
395	D₄	—	2	4	no	—
396	D₄	—	2	4	no	—
397	D₄	—	4	8	no	—
398	D₄	—	4	2	no	—
399	D₄	—	4	2	no	—
400	D₄	—	8	4	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	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	—	2	2	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	4	1	no	—
413	C₂×C₄	—	4	1	no	—
414	C₂×C₄	—	4	1	no	—
415	C₂×C₄	—	4	1	no	—
416	C₂×C₄	—	4	1	no	—
417	C₂×C₄	—	4	1	no	—
418	C₂×C₄	—	4	2	no	—
419	C₂×C₄	—	4	1	no	—
420	C₂×C₄	—	4	1	no	—
421	C₂×C₄	—	4	2	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	—	4	1	no	—
424	C₂×C₄	—	8	8	no	—
425	C₂×C₄	C₂²⋊Q₈×C₇₃	1	2	yes	—
426	C₂×C₄	C₂²⋊Q₈×C₇₃	1	2	yes	—
427	C₂×C₄	#135×C₇₃	1	2	yes	—
428	C₂×C₄	AGL(1,ℤ/8)×C₇₃	1	2	yes	—
429	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
430	C₂×C₄	C₂²×Q₈×C₇₃	1	1	yes	characteristic
431	C₂×C₄	C₂×#41×C₇₃	1	1	yes	characteristic
432	C₂×C₄	C₂×#41×C₇₃	1	1	yes	characteristic
433	C₂×C₄	H(5,𝔽₂)×C₇₃	1	1	yes	characteristic
434	C₂×C₄	2₋¹⁺⁴×C₇₃	1	1	yes	characteristic
435	C₈	—	2	2	no	—
436	C₈	—	4	2	no	—
437	C₈	—	4	1	no	—
438	C₂²	—	4	4	no	—
439	C₂²	—	4	4	no	—
440	C₂²	—	4	4	no	—
441	C₂²	—	8	2	no	—
442	C₂²	—	8	2	no	—
443	C₂²	—	8	2	no	—
444	C₂²	—	8	2	no	—
445	C₂²	C₂×C₂²⋊Q₈×C₇₃	1	1	yes	characteristic
446	C₂²	D₄²×C₇₃	1	1	yes	characteristic
447	C₂²	#548×C₇₃	1	1	yes	characteristic
448	C₂²	C₂×#135×C₇₃	1	1	yes	characteristic
449	C₂²	C₂×AGL(1,ℤ/8)×C₇₃	1	1	yes	characteristic
450	C₂²	#576×C₇₃	1	1	yes	characteristic
451	C₂²	#577×C₇₃	1	1	yes	characteristic
452	C₄	—	2	2	no	—
453	C₄	—	4	2	no	—
454	C₄	—	4	2	no	—
455	C₄	—	4	2	no	—
456	C₄	—	4	2	no	—
457	C₄	—	4	2	no	—
458	C₄	—	8	2	no	—
459	C₄	—	8	1	no	—
460	C₄	#478×C₇₃	1	4	yes	complemented
461	C₄	#532×C₇₃	1	1	yes	characteristic
462	C₄	#542×C₇₃	1	1	yes	characteristic
463	C₄	D₄×Q₈×C₇₃	1	1	yes	characteristic
464	C₄	#554×C₇₃	1	1	yes	characteristic
465	C₂	—	8	4	no	—
466	C₂	C₇₃×#2452	1	1	yes	characteristic
467	C₂	C₂×#478×C₇₃	1	1	yes	characteristic
468	C₂	C₇₃×#3081	1	1	yes	characteristic
469	C₂	C₇₃×#3274	1	1	yes	characteristic
470	C₂	C₇₃×#3284	1	1	yes	characteristic
471	C₂	C₇₃×#3361	1	1	yes	characteristic
472	C₂	C₇₃×#3368	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₃
prime radical	C₂×#127×C₇₃	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇₃ ◁ C₄×C₄⋊C₄×C₇₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#478×C₇₃	C₂	semidirect
2. C₇₃×#2552	C₂	semidirect
4. C₇₃×#2065	C₂	semidirect
5. C₇₃×#2025	C₂	semidirect
8. C₇₃×#1947	C₂	semidirect
9. C₇₃×#1939	C₂	semidirect
10. C₇₃×#1862	C₂	semidirect
11. C₄×#106×C₇₃	C₂	semidirect
77. #106×C₇₃	D₄	semidirect
223. C₄×C₇₃	#478	semidirect
228. #26463	C₇₃	direct (N × H)
237. C₂×#478	C₂×C₇₃	semidirect
238. #2552	C₂×C₇₃	semidirect
240. #2065	C₂×C₇₃	semidirect
241. #2025	C₂×C₇₃	semidirect
244. #1947	C₂×C₇₃	semidirect
245. #1939	C₂×C₇₃	semidirect
246. #1862	C₂×C₇₃	semidirect
247. C₄×#106	C₂×C₇₃	semidirect
248. C₇₃	#26463	direct (N × H)
314. #106	D₄×C₇₃	semidirect
460. C₄	#478×C₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#478×C₇₃	2
C₇₃×#2552	2
C₇₃×#2366	2
C₇₃×#2065	2
C₇₃×#2025	2
C₇₃×#1982	2
C₇₃×#1957	2
C₇₃×#1947	2
C₇₃×#1939	2
C₇₃×#1862	2
C₄×#106×C₇₃	2
#26463	73

Subgroups — C73×#26463 #32935867

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#26463 #32935867