Subgroups — C₇₃×#29109 #32938513

Order 18688.

1122 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₃×#2857	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#390×C₇₃	C₂	1	1	yes	maximal, characteristic
3	C₇₃×#2071	C₂	1	2	yes	maximal, complemented
4	C₇₃×#2023	C₂	1	2	yes	maximal, complemented
5	C₇₃×#1936	C₂	1	4	yes	maximal, complemented
6	C₇₃×#1824	C₂	1	2	yes	maximal, complemented
7	C₇₃×#1786	C₂	1	2	yes	maximal
8	C₇₃×#1749	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂³×D₄×C₇₃	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic, complemented
11	C₂×C₂²⋊Q₈×C₇₃	—	2	1	no	—
12	C₂²×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
13	C₂²×C₂²⋊C₄×C₇₃	—	2	1	no	—
14	C₂²×C₂²⋊C₄×C₇₃	—	2	1	no	—
15	C₂²×C₄²×C₇₃	C₂²	1	1	yes	characteristic
16	C₂×#102×C₇₃	C₂²	1	4	yes	—
17	C₂×#102×C₇₃	C₂²	1	4	yes	—
18	C₂×C₂²⋊C₈×C₇₃	C₂²	1	2	yes	—
19	C₂×#97×C₇₃	C₂²	1	2	yes	complemented
20	#391×C₇₃	—	2	1	no	—
21	#390×C₇₃	—	2	1	no	—
22	#390×C₇₃	—	2	1	no	—
23	#390×C₇₃	C₂²	1	2	yes	—
24	#390×C₇₃	C₂²	1	2	yes	—
25	#389×C₇₃	—	2	1	no	—
26	#389×C₇₃	C₂²	1	2	yes	complemented
27	#384×C₇₃	C₂²	1	1	yes	characteristic, complemented
28	#380×C₇₃	—	2	1	no	—
29	#380×C₇₃	C₂²	1	2	yes	—
30	#340×C₇₃	C₂²	1	4	yes	complemented
31	#340×C₇₃	C₂²	1	4	yes	complemented
32	#336×C₇₃	C₂²	1	2	yes	complemented
33	C₂⁵×C₇₃	—	2	1	no	—
34	C₂²×Q₈×C₇₃	—	2	1	no	—
35	C₂²×D₄×C₇₃	—	2	4	no	—
36	C₂²×D₄×C₇₃	—	2	1	no	—
37	C₂²×D₄×C₇₃	—	2	4	no	—
38	C₂²×D₄×C₇₃	—	4	2	no	—
39	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
40	C₂³×C₄×C₇₃	—	2	1	no	—
41	C₂³×C₄×C₇₃	D₄	1	1	yes	characteristic
42	C₂³×C₄×C₇₃	D₄	1	1	yes	characteristic
43	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
44	C₂²×C₈×C₇₃	C₂³	1	4	yes	—
45	C₄⋊Q₈×C₇₃	—	4	2	no	—
46	C₂²⋊Q₈×C₇₃	—	4	4	no	—
47	C₂×C₄⋊C₄×C₇₃	—	2	4	no	—
48	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
49	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
50	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
51	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
52	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
53	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
54	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
55	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
56	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
57	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
58	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
59	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
60	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
61	C₂×C₂²⋊C₄×C₇₃	—	4	4	no	—
62	C₂×C₂²⋊C₄×C₇₃	—	4	4	no	—
63	C₂×C₄²×C₇₃	—	4	2	no	—
64	C₂×C₄²×C₇₃	D₄	1	1	yes	characteristic
65	C₂×C₄²×C₇₃	D₄	1	1	yes	characteristic
66	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
67	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
68	#102×C₇₃	—	2	8	no	—
69	#102×C₇₃	—	4	4	no	—
70	C₂²⋊C₈×C₇₃	—	2	4	no	—
71	#97×C₇₃	—	4	2	no	—
72	#95×C₇₃	—	2	2	no	—
73	#95×C₇₃	—	2	2	no	—
74	C₂⁴×C₇₃	—	2	4	no	—
75	C₂⁴×C₇₃	—	2	2	no	—
76	C₂⁴×C₇₃	—	4	2	no	—
77	C₂⁴×C₇₃	—	4	2	no	—
78	C₂⁴×C₇₃	—	4	2	no	—
79	C₂⁴×C₇₃	—	4	2	no	—
80	C₂⁴×C₇₃	—	4	2	no	—
81	C₂⁴×C₇₃	—	4	2	no	—
82	C₂⁴×C₇₃	C₂×D₄	1	1	yes	characteristic
83	C₂×Q₈×C₇₃	—	4	2	no	—
84	C₂×Q₈×C₇₃	—	4	2	no	—
85	C₂×Q₈×C₇₃	—	4	2	no	—
86	C₂×D₄×C₇₃	—	2	4	no	—
87	C₂×D₄×C₇₃	—	2	4	no	—
88	C₂×D₄×C₇₃	—	2	2	no	—
89	C₂×D₄×C₇₃	—	2	4	no	—
90	C₂×D₄×C₇₃	—	4	16	no	—
91	C₂×D₄×C₇₃	—	4	2	no	—
92	C₂×D₄×C₇₃	—	4	2	no	—
93	C₂×D₄×C₇₃	#41	1	4	yes	—
94	C₂²×C₄×C₇₃	—	2	2	no	—
95	C₂²×C₄×C₇₃	—	2	2	no	—
96	C₂²×C₄×C₇₃	—	2	2	no	—
97	C₂²×C₄×C₇₃	—	2	2	no	—
98	C₂²×C₄×C₇₃	—	2	2	no	—
99	C₂²×C₄×C₇₃	—	2	2	no	—
100	C₂²×C₄×C₇₃	—	2	2	no	—
101	C₂²×C₄×C₇₃	—	2	2	no	—
102	C₂²×C₄×C₇₃	—	2	2	no	—
103	C₂²×C₄×C₇₃	—	4	1	no	—
104	C₂²×C₄×C₇₃	—	4	1	no	—
105	C₂²×C₄×C₇₃	—	4	2	no	—
106	C₂²×C₄×C₇₃	—	4	2	no	—
107	C₂²×C₄×C₇₃	—	4	2	no	—
108	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₇₃	#41	1	4	yes	—
114	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
115	C₂×C₈×C₇₃	—	2	4	no	—
116	C₂×C₈×C₇₃	—	2	4	no	—
117	C₂×C₈×C₇₃	—	2	4	no	—
118	C₄⋊C₄×C₇₃	—	2	4	no	—
119	C₄⋊C₄×C₇₃	—	2	4	no	—
120	C₄⋊C₄×C₇₃	—	2	4	no	—
121	C₄⋊C₄×C₇₃	—	4	2	no	—
122	C₄⋊C₄×C₇₃	—	4	4	no	—
123	C₄⋊C₄×C₇₃	—	4	2	no	—
124	C₄⋊C₄×C₇₃	—	4	2	no	—
125	C₄⋊C₄×C₇₃	—	4	2	no	—
126	C₂²⋊C₄×C₇₃	—	4	4	no	—
127	C₂²⋊C₄×C₇₃	—	4	4	no	—
128	C₂²⋊C₄×C₇₃	—	4	4	no	—
129	C₂²⋊C₄×C₇₃	—	4	4	no	—
130	C₂²⋊C₄×C₇₃	—	4	4	no	—
131	C₄²×C₇₃	—	2	2	no	—
132	C₄²×C₇₃	—	2	2	no	—
133	C₄²×C₇₃	—	4	1	no	—
134	C₄²×C₇₃	—	4	1	no	—
135	C₂³×C₇₃	—	2	1	no	—
136	C₂³×C₇₃	—	2	1	no	—
137	C₂³×C₇₃	—	2	1	no	—
138	C₂³×C₇₃	—	2	1	no	—
139	C₂³×C₇₃	—	2	4	no	—
140	C₂³×C₇₃	—	4	8	no	—
141	C₂³×C₇₃	—	4	8	no	—
142	C₂³×C₇₃	—	4	8	no	—
143	C₂³×C₇₃	—	4	2	no	—
144	C₂³×C₇₃	—	4	2	no	—
145	C₂³×C₇₃	—	4	2	no	—
146	C₂³×C₇₃	—	4	2	no	—
147	C₂³×C₇₃	—	4	2	no	—
148	C₂³×C₇₃	—	4	2	no	—
149	C₂³×C₇₃	—	8	4	no	—
150	C₂³×C₇₃	—	8	4	no	—
151	C₂³×C₇₃	—	8	4	no	—
152	C₂³×C₇₃	—	8	4	no	—
153	C₂³×C₇₃	#124	1	2	yes	—
154	C₂³×C₇₃	AGL(1,ℤ/8)	1	2	yes	—
155	C₂³×C₇₃	#137	1	2	yes	—
156	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
157	Q₈×C₇₃	—	8	4	no	—
158	D₄×C₇₃	—	2	8	no	—
159	D₄×C₇₃	—	4	8	no	—
160	D₄×C₇₃	—	4	4	no	—
161	C₂×C₄×C₇₃	—	2	1	no	—
162	C₂×C₄×C₇₃	—	2	1	no	—
163	C₂×C₄×C₇₃	—	2	1	no	—
164	C₂×C₄×C₇₃	—	2	1	no	—
165	C₂×C₄×C₇₃	—	2	1	no	—
166	C₂×C₄×C₇₃	—	2	1	no	—
167	C₂×C₄×C₇₃	—	2	8	no	—
168	C₂×C₄×C₇₃	—	2	1	no	—
169	C₂×C₄×C₇₃	—	2	1	no	—
170	C₂×C₄×C₇₃	—	2	1	no	—
171	C₂×C₄×C₇₃	—	2	1	no	—
172	C₂×C₄×C₇₃	—	2	1	no	—
173	C₂×C₄×C₇₃	—	2	1	no	—
174	C₂×C₄×C₇₃	—	4	4	no	—
175	C₂×C₄×C₇₃	—	4	4	no	—
176	C₂×C₄×C₇₃	—	4	2	no	—
177	C₂×C₄×C₇₃	—	4	2	no	—
178	C₂×C₄×C₇₃	—	4	2	no	—
179	C₂×C₄×C₇₃	—	4	2	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	2	no	—
184	C₂×C₄×C₇₃	—	4	2	no	—
185	C₂×C₄×C₇₃	—	8	4	no	—
186	C₂×C₄×C₇₃	#124	1	2	yes	—
187	C₂×C₄×C₇₃	AGL(1,ℤ/8)	1	2	yes	—
188	C₂×C₄×C₇₃	AGL(1,ℤ/8)	1	2	yes	—
189	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
190	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
191	C₂×C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
192	C₈×C₇₃	—	4	4	no	—
193	C₂²×C₇₃	—	2	2	no	—
194	C₂²×C₇₃	—	2	2	no	—
195	C₂²×C₇₃	—	2	2	no	—
196	C₂²×C₇₃	—	2	2	no	—
197	C₂²×C₇₃	—	2	2	no	—
198	C₂²×C₇₃	—	2	2	no	—
199	C₂²×C₇₃	—	4	4	no	—
200	C₂²×C₇₃	—	4	4	no	—
201	C₂²×C₇₃	—	4	4	no	—
202	C₂²×C₇₃	—	8	16	no	—
203	C₂²×C₇₃	—	8	2	no	—
204	C₂²×C₇₃	—	8	2	no	—
205	C₂²×C₇₃	—	8	2	no	—
206	C₂²×C₇₃	—	8	2	no	—
207	C₂²×C₇₃	#489	1	4	yes	—
208	C₂²×C₇₃	#525	1	1	yes	characteristic
209	C₂²×C₇₃	C₂×#124	1	1	yes	characteristic
210	C₂²×C₇₃	#534	1	1	yes	characteristic
211	C₂²×C₇₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
212	C₂²×C₇₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
213	C₂²×C₇₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
214	C₂²×C₇₃	C₂×#137	1	1	yes	characteristic
215	C₄×C₇₃	—	2	2	no	—
216	C₄×C₇₃	—	2	2	no	—
217	C₄×C₇₃	—	2	2	no	—
218	C₄×C₇₃	—	4	1	no	—
219	C₄×C₇₃	—	4	1	no	—
220	C₄×C₇₃	—	8	2	no	—
221	C₄×C₇₃	—	8	2	no	—
222	C₄×C₇₃	—	8	2	no	—
223	C₄×C₇₃	#551	1	4	yes	—
224	#29109	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
225	C₂×C₇₃	—	2	4	no	—
226	C₂×C₇₃	—	8	4	no	—
227	C₂×C₇₃	#2561	1	1	yes	characteristic
228	C₂×C₇₃	#3109	1	1	yes	characteristic
229	C₂×C₇₃	#3110	1	1	yes	characteristic
230	C₂×C₇₃	C₂×#489	1	1	yes	characteristic
231	C₂×C₇₃	#3138	1	1	yes	characteristic
232	C₂×C₇₃	#3192	1	1	yes	characteristic
233	C₂×C₇₃	#3193	1	1	yes	characteristic
234	#2857	C₂×C₇₃	1	1	yes	characteristic, complemented
235	C₂×#390	C₂×C₇₃	1	1	yes	characteristic
236	#2071	C₂×C₇₃	1	2	yes	complemented
237	#2023	C₂×C₇₃	1	2	yes	complemented
238	#1936	C₂×C₇₃	1	4	yes	complemented
239	#1824	C₂×C₇₃	1	2	yes	complemented
240	#1786	C₂×C₇₃	1	2	yes	—
241	#1749	C₂×C₇₃	1	1	yes	characteristic, complemented
242	C₇₃	#29109	1	1	yes	characteristic, direct product factor, Sylow
243	C₂³×D₄	C₂²×C₇₃	1	1	yes	characteristic
244	C₂×C₄⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic, complemented
245	C₂×C₂²⋊Q₈	—	2	1	no	—
246	C₂²×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
247	C₂²×C₂²⋊C₄	—	2	1	no	—
248	C₂²×C₂²⋊C₄	—	2	1	no	—
249	C₂²×C₄²	C₂²×C₇₃	1	1	yes	characteristic
250	C₂×#102	C₂²×C₇₃	1	4	yes	—
251	C₂×#102	C₂²×C₇₃	1	4	yes	—
252	C₂×C₂²⋊C₈	C₂²×C₇₃	1	2	yes	—
253	C₂×#97	C₂²×C₇₃	1	2	yes	complemented
254	#391	—	2	1	no	—
255	#390	—	2	1	no	—
256	#390	—	2	1	no	—
257	#390	C₂²×C₇₃	1	2	yes	—
258	#390	C₂²×C₇₃	1	2	yes	—
259	#389	—	2	1	no	—
260	#389	C₂²×C₇₃	1	2	yes	complemented
261	#384	C₂²×C₇₃	1	1	yes	characteristic, complemented
262	#380	—	2	1	no	—
263	#380	C₂²×C₇₃	1	2	yes	—
264	#340	C₂²×C₇₃	1	4	yes	complemented
265	#340	C₂²×C₇₃	1	4	yes	complemented
266	#336	C₂²×C₇₃	1	2	yes	complemented
267	C₂⁵	—	2	1	no	—
268	C₂²×Q₈	—	2	1	no	—
269	C₂²×D₄	—	2	4	no	—
270	C₂²×D₄	—	2	1	no	—
271	C₂²×D₄	—	2	4	no	—
272	C₂²×D₄	—	4	2	no	—
273	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
274	C₂³×C₄	—	2	1	no	—
275	C₂³×C₄	D₄×C₇₃	1	1	yes	characteristic
276	C₂³×C₄	D₄×C₇₃	1	1	yes	characteristic
277	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
278	C₂²×C₈	C₂³×C₇₃	1	4	yes	—
279	C₄⋊Q₈	—	4	2	no	—
280	C₂²⋊Q₈	—	4	4	no	—
281	C₂×C₄⋊C₄	—	2	4	no	—
282	C₂×C₄⋊C₄	—	2	1	no	—
283	C₂×C₄⋊C₄	—	2	1	no	—
284	C₂×C₄⋊C₄	—	2	2	no	—
285	C₂×C₄⋊C₄	—	2	1	no	—
286	C₂×C₄⋊C₄	—	2	1	no	—
287	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
288	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
289	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
290	C₂×C₂²⋊C₄	—	2	2	no	—
291	C₂×C₂²⋊C₄	—	2	2	no	—
292	C₂×C₂²⋊C₄	—	2	2	no	—
293	C₂×C₂²⋊C₄	—	2	2	no	—
294	C₂×C₂²⋊C₄	—	2	2	no	—
295	C₂×C₂²⋊C₄	—	4	4	no	—
296	C₂×C₂²⋊C₄	—	4	4	no	—
297	C₂×C₄²	—	4	2	no	—
298	C₂×C₄²	D₄×C₇₃	1	1	yes	characteristic
299	C₂×C₄²	D₄×C₇₃	1	1	yes	characteristic
300	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
301	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
302	#102	—	2	8	no	—
303	#102	—	4	4	no	—
304	C₂²⋊C₈	—	2	4	no	—
305	#97	—	4	2	no	—
306	#95	—	2	2	no	—
307	#95	—	2	2	no	—
308	C₂⁴	—	2	4	no	—
309	C₂⁴	—	2	2	no	—
310	C₂⁴	—	4	2	no	—
311	C₂⁴	—	4	2	no	—
312	C₂⁴	—	4	2	no	—
313	C₂⁴	—	4	2	no	—
314	C₂⁴	—	4	2	no	—
315	C₂⁴	—	4	2	no	—
316	C₂⁴	C₂×D₄×C₇₃	1	1	yes	characteristic
317	C₂×Q₈	—	4	2	no	—
318	C₂×Q₈	—	4	2	no	—
319	C₂×Q₈	—	4	2	no	—
320	C₂×D₄	—	2	4	no	—
321	C₂×D₄	—	2	4	no	—
322	C₂×D₄	—	2	2	no	—
323	C₂×D₄	—	2	4	no	—
324	C₂×D₄	—	4	16	no	—
325	C₂×D₄	—	4	2	no	—
326	C₂×D₄	—	4	2	no	—
327	C₂×D₄	#41×C₇₃	1	4	yes	—
328	C₂²×C₄	—	2	2	no	—
329	C₂²×C₄	—	2	2	no	—
330	C₂²×C₄	—	2	2	no	—
331	C₂²×C₄	—	2	2	no	—
332	C₂²×C₄	—	2	2	no	—
333	C₂²×C₄	—	2	2	no	—
334	C₂²×C₄	—	2	2	no	—
335	C₂²×C₄	—	2	2	no	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	4	1	no	—
338	C₂²×C₄	—	4	1	no	—
339	C₂²×C₄	—	4	2	no	—
340	C₂²×C₄	—	4	2	no	—
341	C₂²×C₄	—	4	2	no	—
342	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
343	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
344	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
345	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
346	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
347	C₂²×C₄	#41×C₇₃	1	4	yes	—
348	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
349	C₂×C₈	—	2	4	no	—
350	C₂×C₈	—	2	4	no	—
351	C₂×C₈	—	2	4	no	—
352	C₄⋊C₄	—	2	4	no	—
353	C₄⋊C₄	—	2	4	no	—
354	C₄⋊C₄	—	2	4	no	—
355	C₄⋊C₄	—	4	2	no	—
356	C₄⋊C₄	—	4	4	no	—
357	C₄⋊C₄	—	4	2	no	—
358	C₄⋊C₄	—	4	2	no	—
359	C₄⋊C₄	—	4	2	no	—
360	C₂²⋊C₄	—	4	4	no	—
361	C₂²⋊C₄	—	4	4	no	—
362	C₂²⋊C₄	—	4	4	no	—
363	C₂²⋊C₄	—	4	4	no	—
364	C₂²⋊C₄	—	4	4	no	—
365	C₄²	—	2	2	no	—
366	C₄²	—	2	2	no	—
367	C₄²	—	4	1	no	—
368	C₄²	—	4	1	no	—
369	C₂³	—	2	1	no	—
370	C₂³	—	2	1	no	—
371	C₂³	—	2	1	no	—
372	C₂³	—	2	1	no	—
373	C₂³	—	2	4	no	—
374	C₂³	—	4	8	no	—
375	C₂³	—	4	8	no	—
376	C₂³	—	4	8	no	—
377	C₂³	—	4	2	no	—
378	C₂³	—	4	2	no	—
379	C₂³	—	4	2	no	—
380	C₂³	—	4	2	no	—
381	C₂³	—	4	2	no	—
382	C₂³	—	4	2	no	—
383	C₂³	—	8	4	no	—
384	C₂³	—	8	4	no	—
385	C₂³	—	8	4	no	—
386	C₂³	—	8	4	no	—
387	C₂³	#124×C₇₃	1	2	yes	—
388	C₂³	AGL(1,ℤ/8)×C₇₃	1	2	yes	—
389	C₂³	#137×C₇₃	1	2	yes	—
390	C₂³	C₂²×D₄×C₇₃	1	1	yes	characteristic
391	Q₈	—	8	4	no	—
392	D₄	—	2	8	no	—
393	D₄	—	4	8	no	—
394	D₄	—	4	4	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	8	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	2	1	no	—
404	C₂×C₄	—	2	1	no	—
405	C₂×C₄	—	2	1	no	—
406	C₂×C₄	—	2	1	no	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	4	4	no	—
409	C₂×C₄	—	4	4	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	4	2	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	4	2	no	—
419	C₂×C₄	—	8	4	no	—
420	C₂×C₄	#124×C₇₃	1	2	yes	—
421	C₂×C₄	AGL(1,ℤ/8)×C₇₃	1	2	yes	—
422	C₂×C₄	AGL(1,ℤ/8)×C₇₃	1	2	yes	—
423	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
424	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
425	C₂×C₄	H(5,𝔽₂)×C₇₃	1	2	yes	—
426	C₈	—	4	4	no	—
427	C₂²	—	2	2	no	—
428	C₂²	—	2	2	no	—
429	C₂²	—	2	2	no	—
430	C₂²	—	2	2	no	—
431	C₂²	—	2	2	no	—
432	C₂²	—	2	2	no	—
433	C₂²	—	4	4	no	—
434	C₂²	—	4	4	no	—
435	C₂²	—	4	4	no	—
436	C₂²	—	8	16	no	—
437	C₂²	—	8	2	no	—
438	C₂²	—	8	2	no	—
439	C₂²	—	8	2	no	—
440	C₂²	—	8	2	no	—
441	C₂²	#489×C₇₃	1	4	yes	—
442	C₂²	#525×C₇₃	1	1	yes	characteristic
443	C₂²	C₂×#124×C₇₃	1	1	yes	characteristic
444	C₂²	#534×C₇₃	1	1	yes	characteristic
445	C₂²	C₂×AGL(1,ℤ/8)×C₇₃	1	1	yes	characteristic
446	C₂²	C₂×AGL(1,ℤ/8)×C₇₃	1	1	yes	characteristic
447	C₂²	C₂×AGL(1,ℤ/8)×C₇₃	1	1	yes	characteristic
448	C₂²	C₂×#137×C₇₃	1	1	yes	characteristic
449	C₄	—	2	2	no	—
450	C₄	—	2	2	no	—
451	C₄	—	2	2	no	—
452	C₄	—	4	1	no	—
453	C₄	—	4	1	no	—
454	C₄	—	8	2	no	—
455	C₄	—	8	2	no	—
456	C₄	—	8	2	no	—
457	C₄	#551×C₇₃	1	4	yes	—
458	C₂	—	2	4	no	—
459	C₂	—	8	4	no	—
460	C₂	C₇₃×#2561	1	1	yes	characteristic
461	C₂	C₇₃×#3109	1	1	yes	characteristic
462	C₂	C₇₃×#3110	1	1	yes	characteristic
463	C₂	C₂×#489×C₇₃	1	1	yes	characteristic
464	C₂	C₇₃×#3138	1	1	yes	characteristic
465	C₂	C₇₃×#3192	1	1	yes	characteristic
466	C₂	C₇₃×#3193	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₃
prime radical	C₂³×D₄×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. C₇₃×#2857	C₂	semidirect
3. C₇₃×#2071	C₂	semidirect
4. C₇₃×#2023	C₂	semidirect
5. C₇₃×#1936	C₂	semidirect
6. C₇₃×#1824	C₂	semidirect
8. C₇₃×#1749	C₂	semidirect
10. C₂×C₄⋊Q₈×C₇₃	C₂²	semidirect
19. C₂×#97×C₇₃	C₂²	semidirect
26. #389×C₇₃	C₂²	semidirect
27. #384×C₇₃	C₂²	semidirect
30. #340×C₇₃	C₂²	semidirect
31. #340×C₇₃	C₂²	semidirect
32. #336×C₇₃	C₂²	semidirect
224. #29109	C₇₃	direct (N × H)
234. #2857	C₂×C₇₃	semidirect
236. #2071	C₂×C₇₃	semidirect
237. #2023	C₂×C₇₃	semidirect
238. #1936	C₂×C₇₃	semidirect
239. #1824	C₂×C₇₃	semidirect
241. #1749	C₂×C₇₃	semidirect
242. C₇₃	#29109	direct (N × H)
244. C₂×C₄⋊Q₈	C₂²×C₇₃	semidirect
253. C₂×#97	C₂²×C₇₃	semidirect
260. #389	C₂²×C₇₃	semidirect
261. #384	C₂²×C₇₃	semidirect
264. #340	C₂²×C₇₃	semidirect
265. #340	C₂²×C₇₃	semidirect
266. #336	C₂²×C₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₇₃×#2857	2
C₂×#390×C₇₃	2
C₇₃×#2071	2
C₇₃×#2023	2
C₇₃×#1936	2
C₇₃×#1824	2
C₇₃×#1786	2
C₇₃×#1749	2
#29109	73

Subgroups — C73×#29109 #32938513

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#29109 #32938513