Subgroups — C₇₃×#59667 #32969071

Order 18688.

2004 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#557×C₇₃	C₂	1	2	yes	maximal
2	C₇₃×#2713	C₂	1	4	yes	maximal
3	C₇₃×#2581	C₂	1	2	yes	maximal
4	C₇₃×#2552	C₂	1	1	yes	maximal, characteristic
5	C₇₃×#2551	C₂	1	2	yes	maximal
6	C₇₃×#2551	C₂	1	1	yes	maximal, characteristic
7	C₇₃×#2506	C₂	1	2	yes	maximal
8	C₇₃×#2506	C₂	1	2	yes	maximal
9	C₇₃×#2462	C₂	1	4	yes	maximal
10	C₇₃×#2453	C₂	1	2	yes	maximal
11	C₇₃×#2451	C₂	1	2	yes	maximal
12	C₇₃×#2365	C₂	1	2	yes	maximal
13	C₇₃×#2365	C₂	1	1	yes	maximal, characteristic
14	C₇₃×#2365	C₂	1	1	yes	maximal, characteristic
15	C₄×C₄⋊Q₈×C₇₃	C₂	1	1	yes	maximal, characteristic
16	C₄×C₄⋊Q₈×C₇₃	C₂	1	1	yes	maximal, characteristic
17	C₄×#125×C₇₃	C₂	1	1	yes	maximal, characteristic
18	#557×C₇₃	—	2	16	no	—
19	C₂×C₄⋊Q₈×C₇₃	C₂²	1	2	yes	—
20	C₂×C₄⋊Q₈×C₇₃	C₂²	1	4	yes	—
21	C₂×C₄⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊Q₈×C₇₃	C₂²	1	2	yes	—
23	C₂×C₄⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
24	C₂×#125×C₇₃	C₂²	1	2	yes	—
25	C₂×#125×C₇₃	C₂²	1	4	yes	—
26	C₂×#125×C₇₃	C₂²	1	4	yes	—
27	C₂×#125×C₇₃	C₂²	1	1	yes	characteristic
28	C₂×C₄×Q₈×C₇₃	C₂²	1	2	yes	—
29	C₂×C₄×Q₈×C₇₃	C₂²	1	2	yes	—
30	C₂×C₄×Q₈×C₇₃	C₂²	1	4	yes	—
31	C₂×C₄×Q₈×C₇₃	C₂²	1	2	yes	—
32	C₂×C₄×Q₈×C₇₃	C₂²	1	2	yes	—
33	#400×C₇₃	C₂²	1	4	yes	—
34	#400×C₇₃	C₂²	1	4	yes	—
35	#398×C₇₃	C₂²	1	4	yes	—
36	#398×C₇₃	C₂²	1	4	yes	—
37	#398×C₇₃	C₂²	1	4	yes	—
38	#395×C₇₃	C₂²	1	4	yes	—
39	#395×C₇₃	C₂²	1	4	yes	—
40	#395×C₇₃	C₂²	1	4	yes	—
41	#391×C₇₃	C₂²	1	2	yes	—
42	#391×C₇₃	C₂²	1	4	yes	—
43	#391×C₇₃	C₂²	1	2	yes	—
44	#391×C₇₃	C₂²	1	2	yes	—
45	#391×C₇₃	C₂²	1	2	yes	—
46	#389×C₇₃	C₂²	1	1	yes	characteristic
47	#389×C₇₃	C₂²	1	2	yes	—
48	#389×C₇₃	C₂²	1	1	yes	characteristic
49	#389×C₇₃	C₂²	1	4	yes	—
50	#389×C₇₃	C₂²	1	2	yes	—
51	#389×C₇₃	C₂²	1	2	yes	—
52	#389×C₇₃	C₂²	1	2	yes	—
53	#389×C₇₃	C₂²	1	2	yes	—
54	#389×C₇₃	C₂²	1	1	yes	characteristic
55	#389×C₇₃	C₂²	1	2	yes	—
56	#389×C₇₃	C₂²	1	2	yes	—
57	#389×C₇₃	C₂²	1	2	yes	—
58	#389×C₇₃	C₂²	1	2	yes	—
59	#389×C₇₃	C₂²	1	1	yes	characteristic
60	#387×C₇₃	C₂²	1	4	yes	—
61	#387×C₇₃	C₂²	1	4	yes	—
62	#387×C₇₃	C₂²	1	2	yes	—
63	#387×C₇₃	C₂²	1	4	yes	—
64	#387×C₇₃	C₂²	1	4	yes	—
65	#387×C₇₃	C₂²	1	2	yes	—
66	#387×C₇₃	C₂²	1	4	yes	—
67	#387×C₇₃	C₂²	1	4	yes	—
68	#384×C₇₃	C₂²	1	1	yes	characteristic
69	#384×C₇₃	C₂²	1	2	yes	—
70	#384×C₇₃	C₂²	1	1	yes	characteristic
71	#382×C₇₃	C₂²	1	1	yes	characteristic
72	C₄×C₄⋊C₄×C₇₃	C₂²	1	2	yes	—
73	C₄×C₄⋊C₄×C₇₃	C₂²	1	2	yes	—
74	C₄×C₄⋊C₄×C₇₃	C₂²	1	2	yes	—
75	C₄×C₄⋊C₄×C₇₃	C₂²	1	2	yes	—
76	C₄×C₄⋊C₄×C₇₃	C₂²	1	2	yes	—
77	C₄×C₄⋊C₄×C₇₃	C₂²	1	2	yes	—
78	C₄×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
79	C₄×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
80	C₄×C₄⋊C₄×C₇₃	C₂²	1	2	yes	—
81	C₄×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
82	C₄×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
83	C₄³×C₇₃	C₂²	1	1	yes	characteristic
84	C₂²×Q₈×C₇₃	C₂³	1	4	yes	—
85	C₂²×Q₈×C₇₃	C₂³	1	2	yes	—
86	C₂²×Q₈×C₇₃	C₂³	1	2	yes	—
87	C₄⋊Q₈×C₇₃	—	2	16	no	—
88	C₄⋊Q₈×C₇₃	—	2	8	no	—
89	C₄⋊Q₈×C₇₃	—	2	4	no	—
90	C₄⋊Q₈×C₇₃	—	2	8	no	—
91	C₄⋊Q₈×C₇₃	Q₈	1	8	yes	complemented
92	#125×C₇₃	—	2	16	no	—
93	#125×C₇₃	—	2	8	no	—
94	#125×C₇₃	—	2	16	no	—
95	#125×C₇₃	D₄	1	8	yes	—
96	C₄×Q₈×C₇₃	—	2	8	no	—
97	C₄×Q₈×C₇₃	—	2	16	no	—
98	C₄×Q₈×C₇₃	—	2	8	no	—
99	C₄×Q₈×C₇₃	—	2	8	no	—
100	C₄×Q₈×C₇₃	—	2	8	no	—
101	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
102	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
103	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
104	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
105	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
106	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
107	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
108	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
109	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
110	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
111	C₂×C₄⋊C₄×C₇₃	C₂³	1	4	yes	—
112	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
113	C₂×C₄⋊C₄×C₇₃	C₂³	1	4	yes	—
114	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
115	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
116	C₂×C₄⋊C₄×C₇₃	C₂³	1	4	yes	—
117	C₂×C₄⋊C₄×C₇₃	C₂³	1	4	yes	—
118	C₂×C₄⋊C₄×C₇₃	C₂³	1	4	yes	—
119	C₂×C₄⋊C₄×C₇₃	C₂³	1	4	yes	—
120	C₂×C₄⋊C₄×C₇₃	C₂³	1	4	yes	—
121	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
122	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
123	C₂×C₄⋊C₄×C₇₃	C₂³	1	4	yes	—
124	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
125	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
126	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
127	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
128	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
129	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
130	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
131	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
132	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
133	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
134	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
135	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
136	C₂×C₄²×C₇₃	C₂³	1	4	yes	—
137	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
138	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
139	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
140	C₂×C₄²×C₇₃	C₂³	1	4	yes	—
141	C₂×C₄²×C₇₃	C₂³	1	4	yes	—
142	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
143	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
144	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
145	#95×C₇₃	C₂³	1	2	yes	—
146	#95×C₇₃	C₂³	1	2	yes	—
147	#95×C₇₃	C₂³	1	2	yes	—
148	#95×C₇₃	C₂³	1	2	yes	—
149	#95×C₇₃	C₂³	1	2	yes	—
150	#95×C₇₃	C₂³	1	2	yes	—
151	#95×C₇₃	C₂³	1	4	yes	—
152	#95×C₇₃	C₂³	1	2	yes	—
153	#95×C₇₃	C₂³	1	2	yes	—
154	#95×C₇₃	C₂³	1	2	yes	—
155	#95×C₇₃	C₂³	1	4	yes	—
156	#95×C₇₃	C₂³	1	4	yes	—
157	#95×C₇₃	C₂³	1	4	yes	—
158	#95×C₇₃	C₂³	1	2	yes	—
159	#95×C₇₃	C₂³	1	4	yes	—
160	#95×C₇₃	C₂³	1	4	yes	—
161	#95×C₇₃	C₂³	1	4	yes	—
162	#95×C₇₃	C₂³	1	4	yes	—
163	C₂×Q₈×C₇₃	—	2	4	no	—
164	C₂×Q₈×C₇₃	—	2	8	no	—
165	C₂×Q₈×C₇₃	—	2	4	no	—
166	C₂×Q₈×C₇₃	—	2	4	no	—
167	C₂×Q₈×C₇₃	—	2	8	no	—
168	C₂×Q₈×C₇₃	—	2	4	no	—
169	C₂×Q₈×C₇₃	—	4	2	no	—
170	C₂×Q₈×C₇₃	—	4	4	no	—
171	C₂×Q₈×C₇₃	C₂×Q₈	1	8	yes	—
172	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
173	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
174	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
175	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
176	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
177	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
178	C₂²×C₄×C₇₃	C₂⁴	1	4	yes	—
179	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
180	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
181	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
182	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
183	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
184	C₂²×C₄×C₇₃	C₂⁴	1	4	yes	—
185	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
186	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
187	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
188	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
189	C₄⋊C₄×C₇₃	—	2	4	no	—
190	C₄⋊C₄×C₇₃	—	2	8	no	—
191	C₄⋊C₄×C₇₃	—	2	4	no	—
192	C₄⋊C₄×C₇₃	—	2	8	no	—
193	C₄⋊C₄×C₇₃	—	2	4	no	—
194	C₄⋊C₄×C₇₃	—	2	8	no	—
195	C₄⋊C₄×C₇₃	—	2	8	no	—
196	C₄⋊C₄×C₇₃	—	2	4	no	—
197	C₄⋊C₄×C₇₃	—	2	8	no	—
198	C₄⋊C₄×C₇₃	—	2	8	no	—
199	C₄⋊C₄×C₇₃	—	2	4	no	—
200	C₄⋊C₄×C₇₃	—	2	8	no	—
201	C₄⋊C₄×C₇₃	—	2	4	no	—
202	C₄⋊C₄×C₇₃	—	2	2	no	—
203	C₄⋊C₄×C₇₃	—	2	4	no	—
204	C₄⋊C₄×C₇₃	—	2	4	no	—
205	C₄⋊C₄×C₇₃	—	2	2	no	—
206	C₄⋊C₄×C₇₃	—	2	2	no	—
207	C₄⋊C₄×C₇₃	—	2	2	no	—
208	C₄⋊C₄×C₇₃	—	2	2	no	—
209	C₄⋊C₄×C₇₃	—	4	2	no	—
210	C₄⋊C₄×C₇₃	—	4	2	no	—
211	C₄⋊C₄×C₇₃	—	4	4	no	—
212	C₄⋊C₄×C₇₃	C₂×D₄	1	8	yes	—
213	C₄⋊C₄×C₇₃	C₂×D₄	1	4	yes	—
214	C₄⋊C₄×C₇₃	C₂×D₄	1	4	yes	—
215	C₄⋊C₄×C₇₃	C₂×D₄	1	8	yes	—
216	C₄⋊C₄×C₇₃	C₂×Q₈	1	8	yes	—
217	C₄⋊C₄×C₇₃	C₂×Q₈	1	8	yes	—
218	C₄⋊C₄×C₇₃	#41	1	4	yes	—
219	C₄²×C₇₃	—	2	8	no	—
220	C₄²×C₇₃	—	2	8	no	—
221	C₄²×C₇₃	—	2	4	no	—
222	C₄²×C₇₃	—	2	8	no	—
223	C₄²×C₇₃	—	2	4	no	—
224	C₄²×C₇₃	—	2	2	no	—
225	C₄²×C₇₃	—	2	4	no	—
226	C₄²×C₇₃	—	2	2	no	—
227	C₄²×C₇₃	—	2	2	no	—
228	C₄²×C₇₃	—	2	4	no	—
229	C₄²×C₇₃	—	2	2	no	—
230	C₄²×C₇₃	—	4	1	no	—
231	C₄²×C₇₃	C₂×D₄	1	4	yes	—
232	C₄²×C₇₃	C₂×Q₈	1	4	yes	—
233	C₂³×C₇₃	C₂⁵	1	1	yes	characteristic
234	Q₈×C₇₃	—	2	16	no	—
235	Q₈×C₇₃	—	4	8	no	—
236	Q₈×C₇₃	—	4	16	no	—
237	C₂×C₄×C₇₃	—	2	4	no	—
238	C₂×C₄×C₇₃	—	2	2	no	—
239	C₂×C₄×C₇₃	—	2	1	no	—
240	C₂×C₄×C₇₃	—	2	1	no	—
241	C₂×C₄×C₇₃	—	2	2	no	—
242	C₂×C₄×C₇₃	—	2	1	no	—
243	C₂×C₄×C₇₃	—	2	2	no	—
244	C₂×C₄×C₇₃	—	2	1	no	—
245	C₂×C₄×C₇₃	—	2	1	no	—
246	C₂×C₄×C₇₃	—	2	1	no	—
247	C₂×C₄×C₇₃	—	2	2	no	—
248	C₂×C₄×C₇₃	—	2	4	no	—
249	C₂×C₄×C₇₃	—	2	1	no	—
250	C₂×C₄×C₇₃	—	2	1	no	—
251	C₂×C₄×C₇₃	—	2	2	no	—
252	C₂×C₄×C₇₃	—	2	2	no	—
253	C₂×C₄×C₇₃	—	2	2	no	—
254	C₂×C₄×C₇₃	—	2	2	no	—
255	C₂×C₄×C₇₃	—	2	4	no	—
256	C₂×C₄×C₇₃	—	2	2	no	—
257	C₂×C₄×C₇₃	—	2	2	no	—
258	C₂×C₄×C₇₃	—	2	2	no	—
259	C₂×C₄×C₇₃	—	2	4	no	—
260	C₂×C₄×C₇₃	—	2	1	no	—
261	C₂×C₄×C₇₃	—	2	1	no	—
262	C₂×C₄×C₇₃	—	2	2	no	—
263	C₂×C₄×C₇₃	—	2	2	no	—
264	C₂×C₄×C₇₃	—	2	2	no	—
265	C₂×C₄×C₇₃	—	2	2	no	—
266	C₂×C₄×C₇₃	—	2	2	no	—
267	C₂×C₄×C₇₃	—	2	2	no	—
268	C₂×C₄×C₇₃	—	2	2	no	—
269	C₂×C₄×C₇₃	—	2	2	no	—
270	C₂×C₄×C₇₃	—	2	1	no	—
271	C₂×C₄×C₇₃	—	2	2	no	—
272	C₂×C₄×C₇₃	—	2	4	no	—
273	C₂×C₄×C₇₃	—	2	2	no	—
274	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
275	C₂×C₄×C₇₃	C₂²×D₄	1	4	yes	—
276	C₂×C₄×C₇₃	C₂²×D₄	1	4	yes	—
277	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
278	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
279	C₂×C₄×C₇₃	C₂²×Q₈	1	2	yes	—
280	C₂×C₄×C₇₃	C₂²×Q₈	1	8	yes	—
281	C₂×C₄×C₇₃	C₂²×Q₈	1	2	yes	—
282	C₂×C₄×C₇₃	C₂²×Q₈	1	2	yes	—
283	C₂×C₄×C₇₃	C₂×#41	1	4	yes	—
284	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
285	C₂×C₄×C₇₃	2₋¹⁺⁴	1	2	yes	—
286	C₂×C₄×C₇₃	2₋¹⁺⁴	1	2	yes	—
287	C₂×C₄×C₇₃	2₋¹⁺⁴	1	2	yes	—
288	C₂²×C₇₃	C₂³×D₄	1	1	yes	characteristic
289	C₂²×C₇₃	C₂³×Q₈	1	1	yes	characteristic
290	C₂²×C₇₃	C₂²×#41	1	1	yes	characteristic
291	C₂²×C₇₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
292	C₂²×C₇₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
293	C₂²×C₇₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
294	C₂²×C₇₃	#585	1	1	yes	characteristic
295	C₄×C₇₃	—	2	8	no	—
296	C₄×C₇₃	—	2	2	no	—
297	C₄×C₇₃	—	2	4	no	—
298	C₄×C₇₃	—	2	4	no	—
299	C₄×C₇₃	—	2	2	no	—
300	C₄×C₇₃	—	2	4	no	—
301	C₄×C₇₃	—	2	2	no	—
302	C₄×C₇₃	—	2	2	no	—
303	C₄×C₇₃	—	4	4	no	—
304	C₄×C₇₃	—	4	2	no	—
305	C₄×C₇₃	—	4	2	no	—
306	C₄×C₇₃	—	4	2	no	—
307	C₄×C₇₃	—	4	2	no	—
308	C₄×C₇₃	—	4	1	no	—
309	C₄×C₇₃	—	4	2	no	—
310	C₄×C₇₃	D₄×Q₈	1	4	yes	—
311	C₄×C₇₃	#557	1	4	yes	complemented
312	#59667	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
313	C₂×C₇₃	C₂×D₄×Q₈	1	1	yes	characteristic
314	C₂×C₇₃	D₄×#41	1	1	yes	characteristic
315	C₂×C₇₃	C₂×#557	1	1	yes	characteristic
316	C₂×C₇₃	#3499	1	1	yes	characteristic
317	C₂×C₇₃	#3502	1	1	yes	characteristic
318	C₂×C₇₃	#3523	1	1	yes	characteristic
319	C₂×C₇₃	#3555	1	1	yes	characteristic
320	C₂×#557	C₂×C₇₃	1	2	yes	—
321	#2713	C₂×C₇₃	1	4	yes	—
322	#2581	C₂×C₇₃	1	2	yes	—
323	#2552	C₂×C₇₃	1	1	yes	characteristic
324	#2551	C₂×C₇₃	1	2	yes	—
325	#2551	C₂×C₇₃	1	1	yes	characteristic
326	#2506	C₂×C₇₃	1	2	yes	—
327	#2506	C₂×C₇₃	1	2	yes	—
328	#2462	C₂×C₇₃	1	4	yes	—
329	#2453	C₂×C₇₃	1	2	yes	—
330	#2451	C₂×C₇₃	1	2	yes	—
331	#2365	C₂×C₇₃	1	1	yes	characteristic
332	#2365	C₂×C₇₃	1	1	yes	characteristic
333	#2365	C₂×C₇₃	1	2	yes	—
334	C₄×C₄⋊Q₈	C₂×C₇₃	1	1	yes	characteristic
335	C₄×C₄⋊Q₈	C₂×C₇₃	1	1	yes	characteristic
336	C₄×#125	C₂×C₇₃	1	1	yes	characteristic
337	C₇₃	#59667	1	1	yes	characteristic, direct product factor, Sylow
338	#557	—	2	16	no	—
339	C₂×C₄⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
340	C₂×C₄⋊Q₈	C₂²×C₇₃	1	2	yes	—
341	C₂×C₄⋊Q₈	C₂²×C₇₃	1	2	yes	—
342	C₂×C₄⋊Q₈	C₂²×C₇₃	1	4	yes	—
343	C₂×C₄⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
344	C₂×#125	C₂²×C₇₃	1	2	yes	—
345	C₂×#125	C₂²×C₇₃	1	4	yes	—
346	C₂×#125	C₂²×C₇₃	1	4	yes	—
347	C₂×#125	C₂²×C₇₃	1	1	yes	characteristic
348	C₂×C₄×Q₈	C₂²×C₇₃	1	2	yes	—
349	C₂×C₄×Q₈	C₂²×C₇₃	1	2	yes	—
350	C₂×C₄×Q₈	C₂²×C₇₃	1	2	yes	—
351	C₂×C₄×Q₈	C₂²×C₇₃	1	2	yes	—
352	C₂×C₄×Q₈	C₂²×C₇₃	1	4	yes	—
353	#400	C₂²×C₇₃	1	4	yes	—
354	#400	C₂²×C₇₃	1	4	yes	—
355	#398	C₂²×C₇₃	1	4	yes	—
356	#398	C₂²×C₇₃	1	4	yes	—
357	#398	C₂²×C₇₃	1	4	yes	—
358	#395	C₂²×C₇₃	1	4	yes	—
359	#395	C₂²×C₇₃	1	4	yes	—
360	#395	C₂²×C₇₃	1	4	yes	—
361	#391	C₂²×C₇₃	1	2	yes	—
362	#391	C₂²×C₇₃	1	2	yes	—
363	#391	C₂²×C₇₃	1	2	yes	—
364	#391	C₂²×C₇₃	1	2	yes	—
365	#391	C₂²×C₇₃	1	4	yes	—
366	#389	C₂²×C₇₃	1	1	yes	characteristic
367	#389	C₂²×C₇₃	1	1	yes	characteristic
368	#389	C₂²×C₇₃	1	1	yes	characteristic
369	#389	C₂²×C₇₃	1	2	yes	—
370	#389	C₂²×C₇₃	1	2	yes	—
371	#389	C₂²×C₇₃	1	1	yes	characteristic
372	#389	C₂²×C₇₃	1	2	yes	—
373	#389	C₂²×C₇₃	1	2	yes	—
374	#389	C₂²×C₇₃	1	2	yes	—
375	#389	C₂²×C₇₃	1	2	yes	—
376	#389	C₂²×C₇₃	1	2	yes	—
377	#389	C₂²×C₇₃	1	2	yes	—
378	#389	C₂²×C₇₃	1	4	yes	—
379	#389	C₂²×C₇₃	1	2	yes	—
380	#387	C₂²×C₇₃	1	2	yes	—
381	#387	C₂²×C₇₃	1	2	yes	—
382	#387	C₂²×C₇₃	1	4	yes	—
383	#387	C₂²×C₇₃	1	4	yes	—
384	#387	C₂²×C₇₃	1	4	yes	—
385	#387	C₂²×C₇₃	1	4	yes	—
386	#387	C₂²×C₇₃	1	4	yes	—
387	#387	C₂²×C₇₃	1	4	yes	—
388	#384	C₂²×C₇₃	1	1	yes	characteristic
389	#384	C₂²×C₇₃	1	1	yes	characteristic
390	#384	C₂²×C₇₃	1	2	yes	—
391	#382	C₂²×C₇₃	1	1	yes	characteristic
392	C₄×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
393	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
394	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
395	C₄×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
396	C₄×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
397	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
398	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
399	C₄×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
400	C₄×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
401	C₄×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
402	C₄×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
403	C₄³	C₂²×C₇₃	1	1	yes	characteristic
404	C₂²×Q₈	C₂³×C₇₃	1	2	yes	—
405	C₂²×Q₈	C₂³×C₇₃	1	4	yes	—
406	C₂²×Q₈	C₂³×C₇₃	1	2	yes	—
407	C₄⋊Q₈	—	2	16	no	—
408	C₄⋊Q₈	—	2	8	no	—
409	C₄⋊Q₈	—	2	4	no	—
410	C₄⋊Q₈	—	2	8	no	—
411	C₄⋊Q₈	Q₈×C₇₃	1	8	yes	complemented
412	#125	—	2	16	no	—
413	#125	—	2	8	no	—
414	#125	—	2	16	no	—
415	#125	D₄×C₇₃	1	8	yes	—
416	C₄×Q₈	—	2	8	no	—
417	C₄×Q₈	—	2	16	no	—
418	C₄×Q₈	—	2	8	no	—
419	C₄×Q₈	—	2	8	no	—
420	C₄×Q₈	—	2	8	no	—
421	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
422	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
423	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
424	C₂×C₄⋊C₄	C₂³×C₇₃	1	4	yes	—
425	C₂×C₄⋊C₄	C₂³×C₇₃	1	4	yes	—
426	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
427	C₂×C₄⋊C₄	C₂³×C₇₃	1	4	yes	—
428	C₂×C₄⋊C₄	C₂³×C₇₃	1	4	yes	—
429	C₂×C₄⋊C₄	C₂³×C₇₃	1	4	yes	—
430	C₂×C₄⋊C₄	C₂³×C₇₃	1	4	yes	—
431	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
432	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
433	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
434	C₂×C₄⋊C₄	C₂³×C₇₃	1	4	yes	—
435	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
436	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
437	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
438	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
439	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
440	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
441	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
442	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
443	C₂×C₄⋊C₄	C₂³×C₇₃	1	4	yes	—
444	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
445	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
446	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
447	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
448	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
449	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
450	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
451	C₂×C₄²	C₂³×C₇₃	1	4	yes	—
452	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
453	C₂×C₄²	C₂³×C₇₃	1	4	yes	—
454	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
455	C₂×C₄²	C₂³×C₇₃	1	4	yes	—
456	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
457	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
458	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
459	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
460	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
461	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
462	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
463	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
464	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
465	#95	C₂³×C₇₃	1	2	yes	—
466	#95	C₂³×C₇₃	1	2	yes	—
467	#95	C₂³×C₇₃	1	2	yes	—
468	#95	C₂³×C₇₃	1	2	yes	—
469	#95	C₂³×C₇₃	1	2	yes	—
470	#95	C₂³×C₇₃	1	2	yes	—
471	#95	C₂³×C₇₃	1	4	yes	—
472	#95	C₂³×C₇₃	1	2	yes	—
473	#95	C₂³×C₇₃	1	2	yes	—
474	#95	C₂³×C₇₃	1	2	yes	—
475	#95	C₂³×C₇₃	1	4	yes	—
476	#95	C₂³×C₇₃	1	4	yes	—
477	#95	C₂³×C₇₃	1	4	yes	—
478	#95	C₂³×C₇₃	1	2	yes	—
479	#95	C₂³×C₇₃	1	4	yes	—
480	#95	C₂³×C₇₃	1	4	yes	—
481	#95	C₂³×C₇₃	1	4	yes	—
482	#95	C₂³×C₇₃	1	4	yes	—
483	C₂×Q₈	—	2	4	no	—
484	C₂×Q₈	—	2	8	no	—
485	C₂×Q₈	—	2	4	no	—
486	C₂×Q₈	—	2	4	no	—
487	C₂×Q₈	—	2	8	no	—
488	C₂×Q₈	—	2	4	no	—
489	C₂×Q₈	—	4	2	no	—
490	C₂×Q₈	—	4	4	no	—
491	C₂×Q₈	C₂×Q₈×C₇₃	1	8	yes	—
492	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
493	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
494	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
495	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
496	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
497	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
498	C₂²×C₄	C₂⁴×C₇₃	1	4	yes	—
499	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
500	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
501	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
502	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
503	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
504	C₂²×C₄	C₂⁴×C₇₃	1	4	yes	—
505	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
506	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
507	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
508	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
509	C₄⋊C₄	—	2	4	no	—
510	C₄⋊C₄	—	2	8	no	—
511	C₄⋊C₄	—	2	4	no	—
512	C₄⋊C₄	—	2	8	no	—
513	C₄⋊C₄	—	2	4	no	—
514	C₄⋊C₄	—	2	8	no	—
515	C₄⋊C₄	—	2	8	no	—
516	C₄⋊C₄	—	2	4	no	—
517	C₄⋊C₄	—	2	8	no	—
518	C₄⋊C₄	—	2	8	no	—
519	C₄⋊C₄	—	2	4	no	—
520	C₄⋊C₄	—	2	8	no	—
521	C₄⋊C₄	—	2	2	no	—
522	C₄⋊C₄	—	2	4	no	—
523	C₄⋊C₄	—	2	4	no	—
524	C₄⋊C₄	—	2	4	no	—
525	C₄⋊C₄	—	2	2	no	—
526	C₄⋊C₄	—	2	2	no	—
527	C₄⋊C₄	—	2	2	no	—
528	C₄⋊C₄	—	2	2	no	—
529	C₄⋊C₄	—	4	2	no	—
530	C₄⋊C₄	—	4	2	no	—
531	C₄⋊C₄	—	4	4	no	—
532	C₄⋊C₄	C₂×D₄×C₇₃	1	8	yes	—
533	C₄⋊C₄	C₂×D₄×C₇₃	1	4	yes	—
534	C₄⋊C₄	C₂×D₄×C₇₃	1	4	yes	—
535	C₄⋊C₄	C₂×D₄×C₇₃	1	8	yes	—
536	C₄⋊C₄	C₂×Q₈×C₇₃	1	8	yes	—
537	C₄⋊C₄	C₂×Q₈×C₇₃	1	8	yes	—
538	C₄⋊C₄	#41×C₇₃	1	4	yes	—
539	C₄²	—	2	8	no	—
540	C₄²	—	2	8	no	—
541	C₄²	—	2	4	no	—
542	C₄²	—	2	8	no	—
543	C₄²	—	2	4	no	—
544	C₄²	—	2	2	no	—
545	C₄²	—	2	4	no	—
546	C₄²	—	2	2	no	—
547	C₄²	—	2	2	no	—
548	C₄²	—	2	2	no	—
549	C₄²	—	2	4	no	—
550	C₄²	—	4	1	no	—
551	C₄²	C₂×D₄×C₇₃	1	4	yes	—
552	C₄²	C₂×Q₈×C₇₃	1	4	yes	—
553	C₂³	C₂⁵×C₇₃	1	1	yes	characteristic
554	Q₈	—	2	16	no	—
555	Q₈	—	4	8	no	—
556	Q₈	—	4	16	no	—
557	C₂×C₄	—	2	4	no	—
558	C₂×C₄	—	2	2	no	—
559	C₂×C₄	—	2	1	no	—
560	C₂×C₄	—	2	1	no	—
561	C₂×C₄	—	2	2	no	—
562	C₂×C₄	—	2	1	no	—
563	C₂×C₄	—	2	2	no	—
564	C₂×C₄	—	2	1	no	—
565	C₂×C₄	—	2	1	no	—
566	C₂×C₄	—	2	1	no	—
567	C₂×C₄	—	2	2	no	—
568	C₂×C₄	—	2	4	no	—
569	C₂×C₄	—	2	1	no	—
570	C₂×C₄	—	2	1	no	—
571	C₂×C₄	—	2	2	no	—
572	C₂×C₄	—	2	2	no	—
573	C₂×C₄	—	2	2	no	—
574	C₂×C₄	—	2	2	no	—
575	C₂×C₄	—	2	4	no	—
576	C₂×C₄	—	2	2	no	—
577	C₂×C₄	—	2	2	no	—
578	C₂×C₄	—	2	2	no	—
579	C₂×C₄	—	2	4	no	—
580	C₂×C₄	—	2	1	no	—
581	C₂×C₄	—	2	1	no	—
582	C₂×C₄	—	2	2	no	—
583	C₂×C₄	—	2	2	no	—
584	C₂×C₄	—	2	2	no	—
585	C₂×C₄	—	2	2	no	—
586	C₂×C₄	—	2	2	no	—
587	C₂×C₄	—	2	2	no	—
588	C₂×C₄	—	2	2	no	—
589	C₂×C₄	—	2	2	no	—
590	C₂×C₄	—	2	1	no	—
591	C₂×C₄	—	2	2	no	—
592	C₂×C₄	—	2	4	no	—
593	C₂×C₄	—	2	2	no	—
594	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
595	C₂×C₄	C₂²×D₄×C₇₃	1	4	yes	—
596	C₂×C₄	C₂²×D₄×C₇₃	1	4	yes	—
597	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
598	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
599	C₂×C₄	C₂²×Q₈×C₇₃	1	2	yes	—
600	C₂×C₄	C₂²×Q₈×C₇₃	1	8	yes	—
601	C₂×C₄	C₂²×Q₈×C₇₃	1	2	yes	—
602	C₂×C₄	C₂²×Q₈×C₇₃	1	2	yes	—
603	C₂×C₄	C₂×#41×C₇₃	1	4	yes	—
604	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
605	C₂×C₄	2₋¹⁺⁴×C₇₃	1	2	yes	—
606	C₂×C₄	2₋¹⁺⁴×C₇₃	1	2	yes	—
607	C₂×C₄	2₋¹⁺⁴×C₇₃	1	2	yes	—
608	C₂²	C₂³×D₄×C₇₃	1	1	yes	characteristic
609	C₂²	C₂³×Q₈×C₇₃	1	1	yes	characteristic
610	C₂²	C₂²×#41×C₇₃	1	1	yes	characteristic
611	C₂²	C₂×2₋¹⁺⁴×C₇₃	1	1	yes	characteristic
612	C₂²	C₂×2₋¹⁺⁴×C₇₃	1	1	yes	characteristic
613	C₂²	C₂×2₋¹⁺⁴×C₇₃	1	1	yes	characteristic
614	C₂²	#585×C₇₃	1	1	yes	characteristic
615	C₄	—	2	8	no	—
616	C₄	—	2	2	no	—
617	C₄	—	2	4	no	—
618	C₄	—	2	4	no	—
619	C₄	—	2	2	no	—
620	C₄	—	2	4	no	—
621	C₄	—	2	2	no	—
622	C₄	—	2	2	no	—
623	C₄	—	4	4	no	—
624	C₄	—	4	2	no	—
625	C₄	—	4	2	no	—
626	C₄	—	4	2	no	—
627	C₄	—	4	2	no	—
628	C₄	—	4	1	no	—
629	C₄	—	4	2	no	—
630	C₄	D₄×Q₈×C₇₃	1	4	yes	—
631	C₄	#557×C₇₃	1	4	yes	complemented
632	C₂	C₂×D₄×Q₈×C₇₃	1	1	yes	characteristic
633	C₂	D₄×#41×C₇₃	1	1	yes	characteristic
634	C₂	C₂×#557×C₇₃	1	1	yes	characteristic
635	C₂	C₇₃×#3499	1	1	yes	characteristic
636	C₂	C₇₃×#3502	1	1	yes	characteristic
637	C₂	C₇₃×#3523	1	1	yes	characteristic
638	C₂	C₇₃×#3555	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₇₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₇₃
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₇₃ ◁ G

Complements

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

N	H ≅ G/N	type
91. C₄⋊Q₈×C₇₃	Q₈	semidirect
311. C₄×C₇₃	#557	semidirect
312. #59667	C₇₃	direct (N × H)
337. C₇₃	#59667	direct (N × H)
411. C₄⋊Q₈	Q₈×C₇₃	semidirect
631. C₄	#557×C₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#557×C₇₃	2
C₇₃×#2713	2
C₇₃×#2581	2
C₇₃×#2552	2
C₇₃×#2551	2
C₇₃×#2506	2
C₇₃×#2462	2
C₇₃×#2453	2
C₇₃×#2451	2
C₇₃×#2365	2
C₄×C₄⋊Q₈×C₇₃	2
C₄×#125×C₇₃	2
#59667	73

Subgroups — C73×#59667 #32969071

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#59667 #32969071