Subgroups — C₇₃×#18836 #32928240

Order 18688.

972 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₃×#3515	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇₃×#3217	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₃×#3208	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₃×#3038	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₃×#1626	C₂	1	2	yes	maximal, complemented
6	C₇₃×#1625	C₂	1	2	yes	maximal, complemented
7	C₇₃×#1622	C₂	1	2	yes	maximal, complemented
8	C₇₃×#1622	C₂	1	2	yes	maximal, complemented
9	C₇₃×#1559	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇₃×#1495	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₃×#1488	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×AGL(1,ℤ/8)×C₇₃	—	2	1	no	—
13	#557×C₇₃	C₂²	1	1	yes	characteristic, complemented
14	#554×C₇₃	C₂²	1	1	yes	characteristic, complemented
15	#554×C₇₃	C₂²	1	1	yes	characteristic, complemented
16	#553×C₇₃	—	2	1	no	—
17	#552×C₇₃	—	2	1	no	—
18	#552×C₇₃	—	2	2	no	—
19	#552×C₇₃	—	2	1	no	—
20	#547×C₇₃	—	2	1	no	—
21	#547×C₇₃	C₂²	1	1	yes	characteristic, complemented
22	#541×C₇₃	—	2	1	no	—
23	#539×C₇₃	—	2	2	no	—
24	#533×C₇₃	C₂²	1	1	yes	characteristic
25	C₂×#127×C₇₃	C₂²	1	1	yes	characteristic
26	#529×C₇₃	—	2	1	no	—
27	#529×C₇₃	C₂²	1	1	yes	characteristic
28	C₂×#125×C₇₃	—	2	1	no	—
29	#520×C₇₃	—	2	1	no	—
30	C₄×#41×C₇₃	C₂²	1	1	yes	characteristic
31	#496×C₇₃	—	2	1	no	—
32	#492×C₇₃	C₂²	1	2	yes	—
33	#490×C₇₃	—	2	1	no	—
34	#486×C₇₃	C₂²	1	2	yes	—
35	#460×C₇₃	—	2	2	no	—
36	#460×C₇₃	—	2	1	no	—
37	#460×C₇₃	C₂²	1	2	yes	—
38	#460×C₇₃	C₂²	1	2	yes	—
39	#459×C₇₃	—	2	1	no	—
40	#459×C₇₃	C₂²	1	2	yes	—
41	#459×C₇₃	C₂²	1	2	yes	—
42	#450×C₇₃	—	2	2	no	—
43	#450×C₇₃	—	2	1	no	—
44	#447×C₇₃	—	2	1	no	—
45	#432×C₇₃	C₂²	1	1	yes	characteristic
46	#431×C₇₃	C₂²	1	1	yes	characteristic
47	#423×C₇₃	C₂²	1	1	yes	characteristic
48	#418×C₇₃	—	2	1	no	—
49	#333×C₇₃	C₂²	1	2	yes	complemented
50	#332×C₇₃	C₂²	1	2	yes	complemented
51	Q₈⋊C₈×C₇₃	C₂²	1	2	yes	complemented
52	Q₈⋊C₈×C₇₃	C₂²	1	2	yes	complemented
53	D₄⋊C₈×C₇₃	C₂²	1	2	yes	complemented
54	D₄⋊C₈×C₇₃	C₂²	1	2	yes	complemented
55	C₂×#41×C₇₃	—	2	1	no	—
56	C₂×#41×C₇₃	D₄	1	1	yes	characteristic
57	C₂²×D₄×C₇₃	—	2	1	no	—
58	C₂²×D₄×C₇₃	—	2	1	no	—
59	C₂²×D₄×C₇₃	—	2	1	no	—
60	AGL(1,ℤ/8)×C₇₃	—	4	4	no	—
61	C₂×SD₁₆×C₇₃	—	2	2	no	—
62	C₂×SD₁₆×C₇₃	—	2	4	no	—
63	C₂×SD₁₆×C₇₃	—	2	2	no	—
64	C₂×D₈×C₇₃	—	2	2	no	—
65	C₂×D₈×C₇₃	—	2	2	no	—
66	C₂×M₁₆×C₇₃	—	2	1	no	—
67	C₄⋊Q₈×C₇₃	—	2	1	no	—
68	C₄⋊Q₈×C₇₃	C₂³	1	1	yes	characteristic
69	C₄⋊Q₈×C₇₃	C₂³	1	1	yes	characteristic
70	#127×C₇₃	—	2	1	no	—
71	#127×C₇₃	—	2	1	no	—
72	#127×C₇₃	—	2	1	no	—
73	#127×C₇₃	C₂³	1	2	yes	—
74	#126×C₇₃	—	2	2	no	—
75	#126×C₇₃	—	2	2	no	—
76	#126×C₇₃	—	2	2	no	—
77	#126×C₇₃	—	2	1	no	—
78	#125×C₇₃	—	2	2	no	—
79	#125×C₇₃	—	2	2	no	—
80	#125×C₇₃	—	2	2	no	—
81	#125×C₇₃	—	2	1	no	—
82	#125×C₇₃	—	2	1	no	—
83	#125×C₇₃	—	2	2	no	—
84	#125×C₇₃	—	2	1	no	—
85	#125×C₇₃	—	2	1	no	—
86	#125×C₇₃	D₄	1	1	yes	characteristic
87	#124×C₇₃	D₄	1	1	yes	characteristic
88	#123×C₇₃	—	2	2	no	—
89	#123×C₇₃	—	2	2	no	—
90	#123×C₇₃	—	2	2	no	—
91	#123×C₇₃	—	2	1	no	—
92	#123×C₇₃	—	2	2	no	—
93	C₂²⋊Q₈×C₇₃	—	2	1	no	—
94	C₂²⋊Q₈×C₇₃	—	2	2	no	—
95	C₂²⋊Q₈×C₇₃	—	2	2	no	—
96	C₂²⋊Q₈×C₇₃	—	2	1	no	—
97	C₂²⋊Q₈×C₇₃	—	2	1	no	—
98	C₂²⋊Q₈×C₇₃	—	2	1	no	—
99	C₂²⋊Q₈×C₇₃	D₄	1	1	yes	characteristic
100	C₂²⋊Q₈×C₇₃	D₄	1	2	yes	—
101	#121×C₇₃	—	2	2	no	—
102	#121×C₇₃	—	2	1	no	—
103	#121×C₇₃	D₄	1	1	yes	characteristic
104	C₄×Q₈×C₇₃	—	2	1	no	—
105	C₄×Q₈×C₇₃	—	2	1	no	—
106	C₄×Q₈×C₇₃	—	2	1	no	—
107	C₄×Q₈×C₇₃	D₄	1	1	yes	characteristic
108	C₄×Q₈×C₇₃	D₄	1	2	yes	—
109	C₄×Q₈×C₇₃	C₂³	1	1	yes	characteristic
110	C₄×Q₈×C₇₃	C₂³	1	1	yes	characteristic
111	C₄×D₄×C₇₃	—	2	2	no	—
112	C₄×D₄×C₇₃	—	2	2	no	—
113	C₄×D₄×C₇₃	—	2	1	no	—
114	C₄×D₄×C₇₃	—	2	1	no	—
115	C₄×D₄×C₇₃	—	2	1	no	—
116	C₄×D₄×C₇₃	—	2	1	no	—
117	C₄×D₄×C₇₃	—	2	1	no	—
118	C₄×D₄×C₇₃	D₄	1	1	yes	characteristic
119	C₄×D₄×C₇₃	C₂³	1	1	yes	characteristic
120	C₄×D₄×C₇₃	C₂³	1	1	yes	characteristic
121	#117×C₇₃	—	2	2	no	—
122	#117×C₇₃	—	2	2	no	—
123	#117×C₇₃	—	2	1	no	—
124	#117×C₇₃	—	2	1	no	—
125	#117×C₇₃	—	2	1	no	—
126	#117×C₇₃	D₄	1	1	yes	characteristic
127	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
128	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
129	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
130	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
131	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
132	C₂×C₄²×C₇₃	—	2	1	no	—
133	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
134	C₄⋊C₈×C₇₃	—	2	1	no	—
135	C₄⋊C₈×C₇₃	—	2	1	no	—
136	C₄⋊C₈×C₇₃	C₂³	1	2	yes	—
137	C₄⋊C₈×C₇₃	C₂³	1	2	yes	—
138	#102×C₇₃	—	2	2	no	—
139	#102×C₇₃	—	2	2	no	—
140	#102×C₇₃	—	2	2	no	—
141	#102×C₇₃	—	2	2	no	—
142	#102×C₇₃	—	2	4	no	—
143	C₂²⋊C₈×C₇₃	—	2	1	no	—
144	C₂²⋊C₈×C₇₃	—	2	1	no	—
145	#97×C₇₃	—	2	1	no	—
146	C₄×C₈×C₇₃	C₂³	1	2	yes	—
147	C₂⁴×C₇₃	—	4	1	no	—
148	#41×C₇₃	—	2	2	no	—
149	#41×C₇₃	—	4	1	no	—
150	#41×C₇₃	—	4	2	no	—
151	#41×C₇₃	—	4	2	no	—
152	C₂×Q₈×C₇₃	—	2	1	no	—
153	C₂×Q₈×C₇₃	C₂×D₄	1	1	yes	characteristic
154	C₂×Q₈×C₇₃	C₂×D₄	1	1	yes	characteristic
155	C₂×Q₈×C₇₃	C₂×D₄	1	2	yes	—
156	C₂×D₄×C₇₃	—	2	2	no	—
157	C₂×D₄×C₇₃	—	2	1	no	—
158	C₂×D₄×C₇₃	—	2	1	no	—
159	C₂×D₄×C₇₃	—	2	2	no	—
160	C₂×D₄×C₇₃	—	2	2	no	—
161	C₂×D₄×C₇₃	—	2	2	no	—
162	C₂×D₄×C₇₃	—	4	2	no	—
163	C₂×D₄×C₇₃	—	4	2	no	—
164	C₂×D₄×C₇₃	—	4	1	no	—
165	C₂×D₄×C₇₃	—	4	1	no	—
166	C₂×D₄×C₇₃	—	4	1	no	—
167	C₂×D₄×C₇₃	—	8	2	no	—
168	C₂×D₄×C₇₃	—	8	2	no	—
169	C₂×D₄×C₇₃	C₂×D₄	1	1	yes	characteristic
170	C₂×D₄×C₇₃	C₂×D₄	1	1	yes	characteristic
171	C₂²×C₄×C₇₃	—	2	2	no	—
172	C₂²×C₄×C₇₃	—	2	2	no	—
173	C₂²×C₄×C₇₃	—	2	2	no	—
174	C₂²×C₄×C₇₃	—	2	1	no	—
175	C₂²×C₄×C₇₃	—	2	1	no	—
176	C₂²×C₄×C₇₃	—	2	1	no	—
177	C₂²×C₄×C₇₃	—	2	1	no	—
178	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
179	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
180	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
181	SD₁₆×C₇₃	—	4	4	no	—
182	SD₁₆×C₇₃	—	8	2	no	—
183	SD₁₆×C₇₃	—	8	4	no	—
184	D₈×C₇₃	—	4	4	no	—
185	D₈×C₇₃	—	8	2	no	—
186	M₁₆×C₇₃	—	4	2	no	—
187	C₂×C₈×C₇₃	—	2	2	no	—
188	C₂×C₈×C₇₃	—	2	2	no	—
189	C₂×C₈×C₇₃	—	2	2	no	—
190	C₄⋊C₄×C₇₃	—	2	2	no	—
191	C₄⋊C₄×C₇₃	—	2	2	no	—
192	C₄⋊C₄×C₇₃	—	2	2	no	—
193	C₄⋊C₄×C₇₃	—	2	2	no	—
194	C₄⋊C₄×C₇₃	—	2	2	no	—
195	C₄⋊C₄×C₇₃	—	2	2	no	—
196	C₄⋊C₄×C₇₃	—	2	2	no	—
197	C₄⋊C₄×C₇₃	—	2	2	no	—
198	C₄⋊C₄×C₇₃	—	2	1	no	—
199	C₄⋊C₄×C₇₃	—	2	1	no	—
200	C₄⋊C₄×C₇₃	—	2	2	no	—
201	C₄⋊C₄×C₇₃	—	2	2	no	—
202	C₄⋊C₄×C₇₃	—	2	1	no	—
203	C₄⋊C₄×C₇₃	—	2	1	no	—
204	C₄⋊C₄×C₇₃	—	2	1	no	—
205	C₄⋊C₄×C₇₃	—	2	1	no	—
206	C₄⋊C₄×C₇₃	—	2	1	no	—
207	C₄⋊C₄×C₇₃	—	2	1	no	—
208	C₄⋊C₄×C₇₃	—	2	1	no	—
209	C₄⋊C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
210	C₄⋊C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
211	C₄⋊C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
212	C₄⋊C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
213	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
214	C₂²⋊C₄×C₇₃	—	2	2	no	—
215	C₂²⋊C₄×C₇₃	—	2	2	no	—
216	C₂²⋊C₄×C₇₃	—	2	2	no	—
217	C₂²⋊C₄×C₇₃	—	2	2	no	—
218	C₂²⋊C₄×C₇₃	—	2	1	no	—
219	C₂²⋊C₄×C₇₃	—	2	1	no	—
220	C₂²⋊C₄×C₇₃	—	2	1	no	—
221	C₂²⋊C₄×C₇₃	—	2	1	no	—
222	C₂²⋊C₄×C₇₃	—	2	1	no	—
223	C₂²⋊C₄×C₇₃	—	2	1	no	—
224	C₂²⋊C₄×C₇₃	—	2	1	no	—
225	C₂²⋊C₄×C₇₃	—	2	1	no	—
226	C₄²×C₇₃	—	2	2	no	—
227	C₄²×C₇₃	—	2	1	no	—
228	C₄²×C₇₃	—	2	1	no	—
229	C₄²×C₇₃	—	2	2	no	—
230	C₄²×C₇₃	—	2	1	no	—
231	C₄²×C₇₃	—	2	1	no	—
232	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
233	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
234	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
235	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
236	C₂³×C₇₃	—	2	1	no	—
237	C₂³×C₇₃	—	2	1	no	—
238	C₂³×C₇₃	—	4	2	no	—
239	C₂³×C₇₃	—	8	2	no	—
240	C₂³×C₇₃	—	8	2	no	—
241	C₂³×C₇₃	—	8	2	no	—
242	C₂³×C₇₃	#120	1	1	yes	characteristic
243	Q₈×C₇₃	—	2	1	no	—
244	Q₈×C₇₃	—	2	1	no	—
245	Q₈×C₇₃	—	2	2	no	—
246	Q₈×C₇₃	—	4	2	no	—
247	Q₈×C₇₃	—	4	1	no	—
248	Q₈×C₇₃	—	4	1	no	—
249	D₄×C₇₃	—	2	1	no	—
250	D₄×C₇₃	—	2	2	no	—
251	D₄×C₇₃	—	4	4	no	—
252	D₄×C₇₃	—	4	2	no	—
253	D₄×C₇₃	—	4	4	no	—
254	D₄×C₇₃	—	4	2	no	—
255	D₄×C₇₃	—	4	2	no	—
256	D₄×C₇₃	—	4	2	no	—
257	D₄×C₇₃	—	4	2	no	—
258	D₄×C₇₃	—	8	2	no	—
259	D₄×C₇₃	—	8	2	no	—
260	D₄×C₇₃	—	8	2	no	—
261	D₄×C₇₃	—	8	1	no	—
262	D₄×C₇₃	AGL(1,ℤ/8)	1	2	yes	—
263	C₂×C₄×C₇₃	—	2	1	no	—
264	C₂×C₄×C₇₃	—	2	1	no	—
265	C₂×C₄×C₇₃	—	2	2	no	—
266	C₂×C₄×C₇₃	—	2	1	no	—
267	C₂×C₄×C₇₃	—	2	1	no	—
268	C₂×C₄×C₇₃	—	2	1	no	—
269	C₂×C₄×C₇₃	—	2	1	no	—
270	C₂×C₄×C₇₃	—	2	2	no	—
271	C₂×C₄×C₇₃	—	2	2	no	—
272	C₂×C₄×C₇₃	—	2	1	no	—
273	C₂×C₄×C₇₃	—	2	1	no	—
274	C₂×C₄×C₇₃	—	4	1	no	—
275	C₂×C₄×C₇₃	—	4	2	no	—
276	C₂×C₄×C₇₃	—	4	4	no	—
277	C₂×C₄×C₇₃	—	4	1	no	—
278	C₂×C₄×C₇₃	—	4	1	no	—
279	C₂×C₄×C₇₃	—	4	2	no	—
280	C₂×C₄×C₇₃	—	8	1	no	—
281	C₂×C₄×C₇₃	—	8	2	no	—
282	C₂×C₄×C₇₃	—	8	2	no	—
283	C₂×C₄×C₇₃	#120	1	1	yes	characteristic
284	C₂×C₄×C₇₃	#120	1	1	yes	characteristic
285	C₂×C₄×C₇₃	#120	1	1	yes	characteristic
286	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
287	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
288	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
289	C₈×C₇₃	—	4	2	no	—
290	C₈×C₇₃	—	4	2	no	—
291	C₈×C₇₃	—	4	2	no	—
292	C₂²×C₇₃	—	2	1	no	—
293	C₂²×C₇₃	—	2	2	no	—
294	C₂²×C₇₃	—	2	1	no	—
295	C₂²×C₇₃	—	2	1	no	—
296	C₂²×C₇₃	—	4	1	no	—
297	C₂²×C₇₃	—	4	1	no	—
298	C₂²×C₇₃	—	4	1	no	—
299	C₂²×C₇₃	—	4	1	no	—
300	C₂²×C₇₃	—	4	1	no	—
301	C₂²×C₇₃	—	8	2	no	—
302	C₂²×C₇₃	—	8	2	no	—
303	C₂²×C₇₃	—	8	2	no	—
304	C₂²×C₇₃	—	16	4	no	—
305	C₂²×C₇₃	C₂×#120	1	1	yes	characteristic
306	C₄×C₇₃	—	2	1	no	—
307	C₄×C₇₃	—	2	1	no	—
308	C₄×C₇₃	—	2	1	no	—
309	C₄×C₇₃	—	2	1	no	—
310	C₄×C₇₃	—	4	1	no	—
311	C₄×C₇₃	—	4	1	no	—
312	C₄×C₇₃	—	4	2	no	—
313	C₄×C₇₃	—	4	1	no	—
314	C₄×C₇₃	—	4	1	no	—
315	C₄×C₇₃	—	4	1	no	—
316	C₄×C₇₃	—	4	1	no	—
317	C₄×C₇₃	—	4	2	no	—
318	C₄×C₇₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
319	C₄×C₇₃	#575	1	1	yes	characteristic
320	C₄×C₇₃	#577	1	2	yes	—
321	#18836	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
322	C₂×C₇₃	—	4	1	no	—
323	C₂×C₇₃	—	4	2	no	—
324	C₂×C₇₃	—	8	1	no	—
325	C₂×C₇₃	—	16	2	no	—
326	C₂×C₇₃	#3006	1	1	yes	characteristic
327	C₂×C₇₃	#3010	1	1	yes	characteristic
328	C₂×C₇₃	#3021	1	1	yes	characteristic
329	#3515	C₂×C₇₃	1	1	yes	characteristic, complemented
330	#3217	C₂×C₇₃	1	1	yes	characteristic, complemented
331	#3208	C₂×C₇₃	1	1	yes	characteristic, complemented
332	#3038	C₂×C₇₃	1	1	yes	characteristic, complemented
333	#1626	C₂×C₇₃	1	2	yes	complemented
334	#1625	C₂×C₇₃	1	2	yes	complemented
335	#1622	C₂×C₇₃	1	2	yes	complemented
336	#1622	C₂×C₇₃	1	2	yes	complemented
337	#1559	C₂×C₇₃	1	1	yes	characteristic, complemented
338	#1495	C₂×C₇₃	1	1	yes	characteristic, complemented
339	#1488	C₂×C₇₃	1	1	yes	characteristic, complemented
340	C₇₃	#18836	1	1	yes	characteristic, direct product factor, Sylow
341	C₂×AGL(1,ℤ/8)	—	2	1	no	—
342	#557	C₂²×C₇₃	1	1	yes	characteristic, complemented
343	#554	C₂²×C₇₃	1	1	yes	characteristic, complemented
344	#554	C₂²×C₇₃	1	1	yes	characteristic, complemented
345	#553	—	2	1	no	—
346	#552	—	2	1	no	—
347	#552	—	2	2	no	—
348	#552	—	2	1	no	—
349	#547	—	2	1	no	—
350	#547	C₂²×C₇₃	1	1	yes	characteristic, complemented
351	#541	—	2	1	no	—
352	#539	—	2	2	no	—
353	#533	C₂²×C₇₃	1	1	yes	characteristic
354	C₂×#127	C₂²×C₇₃	1	1	yes	characteristic
355	#529	—	2	1	no	—
356	#529	C₂²×C₇₃	1	1	yes	characteristic
357	C₂×#125	—	2	1	no	—
358	#520	—	2	1	no	—
359	C₄×#41	C₂²×C₇₃	1	1	yes	characteristic
360	#496	—	2	1	no	—
361	#492	C₂²×C₇₃	1	2	yes	—
362	#490	—	2	1	no	—
363	#486	C₂²×C₇₃	1	2	yes	—
364	#460	—	2	2	no	—
365	#460	—	2	1	no	—
366	#460	C₂²×C₇₃	1	2	yes	—
367	#460	C₂²×C₇₃	1	2	yes	—
368	#459	—	2	1	no	—
369	#459	C₂²×C₇₃	1	2	yes	—
370	#459	C₂²×C₇₃	1	2	yes	—
371	#450	—	2	2	no	—
372	#450	—	2	1	no	—
373	#447	—	2	1	no	—
374	#432	C₂²×C₇₃	1	1	yes	characteristic
375	#431	C₂²×C₇₃	1	1	yes	characteristic
376	#423	C₂²×C₇₃	1	1	yes	characteristic
377	#418	—	2	1	no	—
378	#333	C₂²×C₇₃	1	2	yes	complemented
379	#332	C₂²×C₇₃	1	2	yes	complemented
380	Q₈⋊C₈	C₂²×C₇₃	1	2	yes	complemented
381	Q₈⋊C₈	C₂²×C₇₃	1	2	yes	complemented
382	D₄⋊C₈	C₂²×C₇₃	1	2	yes	complemented
383	D₄⋊C₈	C₂²×C₇₃	1	2	yes	complemented
384	C₂×#41	—	2	1	no	—
385	C₂×#41	D₄×C₇₃	1	1	yes	characteristic
386	C₂²×D₄	—	2	1	no	—
387	C₂²×D₄	—	2	1	no	—
388	C₂²×D₄	—	2	1	no	—
389	AGL(1,ℤ/8)	—	4	4	no	—
390	C₂×SD₁₆	—	2	2	no	—
391	C₂×SD₁₆	—	2	4	no	—
392	C₂×SD₁₆	—	2	2	no	—
393	C₂×D₈	—	2	2	no	—
394	C₂×D₈	—	2	2	no	—
395	C₂×M₁₆	—	2	1	no	—
396	C₄⋊Q₈	—	2	1	no	—
397	C₄⋊Q₈	C₂³×C₇₃	1	1	yes	characteristic
398	C₄⋊Q₈	C₂³×C₇₃	1	1	yes	characteristic
399	#127	—	2	1	no	—
400	#127	—	2	1	no	—
401	#127	—	2	1	no	—
402	#127	C₂³×C₇₃	1	2	yes	—
403	#126	—	2	2	no	—
404	#126	—	2	2	no	—
405	#126	—	2	2	no	—
406	#126	—	2	1	no	—
407	#125	—	2	2	no	—
408	#125	—	2	2	no	—
409	#125	—	2	2	no	—
410	#125	—	2	1	no	—
411	#125	—	2	1	no	—
412	#125	—	2	2	no	—
413	#125	—	2	1	no	—
414	#125	—	2	1	no	—
415	#125	D₄×C₇₃	1	1	yes	characteristic
416	#124	D₄×C₇₃	1	1	yes	characteristic
417	#123	—	2	2	no	—
418	#123	—	2	2	no	—
419	#123	—	2	2	no	—
420	#123	—	2	1	no	—
421	#123	—	2	2	no	—
422	C₂²⋊Q₈	—	2	1	no	—
423	C₂²⋊Q₈	—	2	2	no	—
424	C₂²⋊Q₈	—	2	2	no	—
425	C₂²⋊Q₈	—	2	1	no	—
426	C₂²⋊Q₈	—	2	1	no	—
427	C₂²⋊Q₈	—	2	1	no	—
428	C₂²⋊Q₈	D₄×C₇₃	1	1	yes	characteristic
429	C₂²⋊Q₈	D₄×C₇₃	1	2	yes	—
430	#121	—	2	2	no	—
431	#121	—	2	1	no	—
432	#121	D₄×C₇₃	1	1	yes	characteristic
433	C₄×Q₈	—	2	1	no	—
434	C₄×Q₈	—	2	1	no	—
435	C₄×Q₈	—	2	1	no	—
436	C₄×Q₈	D₄×C₇₃	1	1	yes	characteristic
437	C₄×Q₈	D₄×C₇₃	1	2	yes	—
438	C₄×Q₈	C₂³×C₇₃	1	1	yes	characteristic
439	C₄×Q₈	C₂³×C₇₃	1	1	yes	characteristic
440	C₄×D₄	—	2	2	no	—
441	C₄×D₄	—	2	2	no	—
442	C₄×D₄	—	2	1	no	—
443	C₄×D₄	—	2	1	no	—
444	C₄×D₄	—	2	1	no	—
445	C₄×D₄	—	2	1	no	—
446	C₄×D₄	—	2	1	no	—
447	C₄×D₄	D₄×C₇₃	1	1	yes	characteristic
448	C₄×D₄	C₂³×C₇₃	1	1	yes	characteristic
449	C₄×D₄	C₂³×C₇₃	1	1	yes	characteristic
450	#117	—	2	2	no	—
451	#117	—	2	2	no	—
452	#117	—	2	1	no	—
453	#117	—	2	1	no	—
454	#117	—	2	1	no	—
455	#117	D₄×C₇₃	1	1	yes	characteristic
456	C₂×C₄⋊C₄	—	2	2	no	—
457	C₂×C₄⋊C₄	—	2	2	no	—
458	C₂×C₄⋊C₄	—	2	1	no	—
459	C₂×C₄⋊C₄	—	2	1	no	—
460	C₂×C₄⋊C₄	—	2	1	no	—
461	C₂×C₄²	—	2	1	no	—
462	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
463	C₄⋊C₈	—	2	1	no	—
464	C₄⋊C₈	—	2	1	no	—
465	C₄⋊C₈	C₂³×C₇₃	1	2	yes	—
466	C₄⋊C₈	C₂³×C₇₃	1	2	yes	—
467	#102	—	2	2	no	—
468	#102	—	2	2	no	—
469	#102	—	2	2	no	—
470	#102	—	2	2	no	—
471	#102	—	2	4	no	—
472	C₂²⋊C₈	—	2	1	no	—
473	C₂²⋊C₈	—	2	1	no	—
474	#97	—	2	1	no	—
475	C₄×C₈	C₂³×C₇₃	1	2	yes	—
476	C₂⁴	—	4	1	no	—
477	#41	—	2	2	no	—
478	#41	—	4	1	no	—
479	#41	—	4	2	no	—
480	#41	—	4	2	no	—
481	C₂×Q₈	—	2	1	no	—
482	C₂×Q₈	C₂×D₄×C₇₃	1	1	yes	characteristic
483	C₂×Q₈	C₂×D₄×C₇₃	1	1	yes	characteristic
484	C₂×Q₈	C₂×D₄×C₇₃	1	2	yes	—
485	C₂×D₄	—	2	2	no	—
486	C₂×D₄	—	2	1	no	—
487	C₂×D₄	—	2	1	no	—
488	C₂×D₄	—	2	2	no	—
489	C₂×D₄	—	2	2	no	—
490	C₂×D₄	—	2	2	no	—
491	C₂×D₄	—	4	2	no	—
492	C₂×D₄	—	4	2	no	—
493	C₂×D₄	—	4	1	no	—
494	C₂×D₄	—	4	1	no	—
495	C₂×D₄	—	4	1	no	—
496	C₂×D₄	—	8	2	no	—
497	C₂×D₄	—	8	2	no	—
498	C₂×D₄	C₂×D₄×C₇₃	1	1	yes	characteristic
499	C₂×D₄	C₂×D₄×C₇₃	1	1	yes	characteristic
500	C₂²×C₄	—	2	2	no	—
501	C₂²×C₄	—	2	2	no	—
502	C₂²×C₄	—	2	2	no	—
503	C₂²×C₄	—	2	1	no	—
504	C₂²×C₄	—	2	1	no	—
505	C₂²×C₄	—	2	1	no	—
506	C₂²×C₄	—	2	1	no	—
507	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
508	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
509	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
510	SD₁₆	—	4	4	no	—
511	SD₁₆	—	8	2	no	—
512	SD₁₆	—	8	4	no	—
513	D₈	—	4	4	no	—
514	D₈	—	8	2	no	—
515	M₁₆	—	4	2	no	—
516	C₂×C₈	—	2	2	no	—
517	C₂×C₈	—	2	2	no	—
518	C₂×C₈	—	2	2	no	—
519	C₄⋊C₄	—	2	2	no	—
520	C₄⋊C₄	—	2	2	no	—
521	C₄⋊C₄	—	2	2	no	—
522	C₄⋊C₄	—	2	2	no	—
523	C₄⋊C₄	—	2	2	no	—
524	C₄⋊C₄	—	2	2	no	—
525	C₄⋊C₄	—	2	2	no	—
526	C₄⋊C₄	—	2	2	no	—
527	C₄⋊C₄	—	2	1	no	—
528	C₄⋊C₄	—	2	1	no	—
529	C₄⋊C₄	—	2	2	no	—
530	C₄⋊C₄	—	2	2	no	—
531	C₄⋊C₄	—	2	1	no	—
532	C₄⋊C₄	—	2	1	no	—
533	C₄⋊C₄	—	2	1	no	—
534	C₄⋊C₄	—	2	1	no	—
535	C₄⋊C₄	—	2	1	no	—
536	C₄⋊C₄	—	2	1	no	—
537	C₄⋊C₄	—	2	1	no	—
538	C₄⋊C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
539	C₄⋊C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
540	C₄⋊C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
541	C₄⋊C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
542	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
543	C₂²⋊C₄	—	2	2	no	—
544	C₂²⋊C₄	—	2	2	no	—
545	C₂²⋊C₄	—	2	2	no	—
546	C₂²⋊C₄	—	2	2	no	—
547	C₂²⋊C₄	—	2	1	no	—
548	C₂²⋊C₄	—	2	1	no	—
549	C₂²⋊C₄	—	2	1	no	—
550	C₂²⋊C₄	—	2	1	no	—
551	C₂²⋊C₄	—	2	1	no	—
552	C₂²⋊C₄	—	2	1	no	—
553	C₂²⋊C₄	—	2	1	no	—
554	C₂²⋊C₄	—	2	1	no	—
555	C₄²	—	2	2	no	—
556	C₄²	—	2	1	no	—
557	C₄²	—	2	1	no	—
558	C₄²	—	2	2	no	—
559	C₄²	—	2	1	no	—
560	C₄²	—	2	1	no	—
561	C₄²	C₂×D₄×C₇₃	1	1	yes	characteristic
562	C₄²	C₂×D₄×C₇₃	1	1	yes	characteristic
563	C₄²	C₂×D₄×C₇₃	1	1	yes	characteristic
564	C₄²	C₂⁴×C₇₃	1	1	yes	characteristic
565	C₂³	—	2	1	no	—
566	C₂³	—	2	1	no	—
567	C₂³	—	4	2	no	—
568	C₂³	—	8	2	no	—
569	C₂³	—	8	2	no	—
570	C₂³	—	8	2	no	—
571	C₂³	#120×C₇₃	1	1	yes	characteristic
572	Q₈	—	2	1	no	—
573	Q₈	—	2	1	no	—
574	Q₈	—	2	2	no	—
575	Q₈	—	4	2	no	—
576	Q₈	—	4	1	no	—
577	Q₈	—	4	1	no	—
578	D₄	—	2	1	no	—
579	D₄	—	2	2	no	—
580	D₄	—	4	4	no	—
581	D₄	—	4	2	no	—
582	D₄	—	4	4	no	—
583	D₄	—	4	2	no	—
584	D₄	—	4	2	no	—
585	D₄	—	4	2	no	—
586	D₄	—	4	2	no	—
587	D₄	—	8	2	no	—
588	D₄	—	8	2	no	—
589	D₄	—	8	2	no	—
590	D₄	—	8	1	no	—
591	D₄	AGL(1,ℤ/8)×C₇₃	1	2	yes	—
592	C₂×C₄	—	2	1	no	—
593	C₂×C₄	—	2	1	no	—
594	C₂×C₄	—	2	2	no	—
595	C₂×C₄	—	2	1	no	—
596	C₂×C₄	—	2	1	no	—
597	C₂×C₄	—	2	1	no	—
598	C₂×C₄	—	2	1	no	—
599	C₂×C₄	—	2	2	no	—
600	C₂×C₄	—	2	2	no	—
601	C₂×C₄	—	2	1	no	—
602	C₂×C₄	—	2	1	no	—
603	C₂×C₄	—	4	1	no	—
604	C₂×C₄	—	4	2	no	—
605	C₂×C₄	—	4	4	no	—
606	C₂×C₄	—	4	1	no	—
607	C₂×C₄	—	4	1	no	—
608	C₂×C₄	—	4	2	no	—
609	C₂×C₄	—	8	1	no	—
610	C₂×C₄	—	8	2	no	—
611	C₂×C₄	—	8	2	no	—
612	C₂×C₄	#120×C₇₃	1	1	yes	characteristic
613	C₂×C₄	#120×C₇₃	1	1	yes	characteristic
614	C₂×C₄	#120×C₇₃	1	1	yes	characteristic
615	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
616	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
617	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
618	C₈	—	4	2	no	—
619	C₈	—	4	2	no	—
620	C₈	—	4	2	no	—
621	C₂²	—	2	1	no	—
622	C₂²	—	2	2	no	—
623	C₂²	—	2	1	no	—
624	C₂²	—	2	1	no	—
625	C₂²	—	4	1	no	—
626	C₂²	—	4	1	no	—
627	C₂²	—	4	1	no	—
628	C₂²	—	4	1	no	—
629	C₂²	—	4	1	no	—
630	C₂²	—	8	2	no	—
631	C₂²	—	8	2	no	—
632	C₂²	—	8	2	no	—
633	C₂²	—	16	4	no	—
634	C₂²	C₂×#120×C₇₃	1	1	yes	characteristic
635	C₄	—	2	1	no	—
636	C₄	—	2	1	no	—
637	C₄	—	2	1	no	—
638	C₄	—	2	1	no	—
639	C₄	—	4	1	no	—
640	C₄	—	4	1	no	—
641	C₄	—	4	2	no	—
642	C₄	—	4	1	no	—
643	C₄	—	4	1	no	—
644	C₄	—	4	1	no	—
645	C₄	—	4	1	no	—
646	C₄	—	4	2	no	—
647	C₄	C₂×AGL(1,ℤ/8)×C₇₃	1	1	yes	characteristic
648	C₄	#575×C₇₃	1	1	yes	characteristic
649	C₄	#577×C₇₃	1	2	yes	—
650	C₂	—	4	1	no	—
651	C₂	—	4	2	no	—
652	C₂	—	8	1	no	—
653	C₂	—	16	2	no	—
654	C₂	C₇₃×#3006	1	1	yes	characteristic
655	C₂	C₇₃×#3010	1	1	yes	characteristic
656	C₂	C₇₃×#3021	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇₃	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₇₃
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₇₃ ◁ C₂×C₄²×C₇₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇₃×#3515	C₂	semidirect
2. C₇₃×#3217	C₂	semidirect
3. C₇₃×#3208	C₂	semidirect
4. C₇₃×#3038	C₂	semidirect
5. C₇₃×#1626	C₂	semidirect
6. C₇₃×#1625	C₂	semidirect
7. C₇₃×#1622	C₂	semidirect
8. C₇₃×#1622	C₂	semidirect
9. C₇₃×#1559	C₂	semidirect
10. C₇₃×#1495	C₂	semidirect
11. C₇₃×#1488	C₂	semidirect
13. #557×C₇₃	C₂²	semidirect
14. #554×C₇₃	C₂²	semidirect
15. #554×C₇₃	C₂²	semidirect
21. #547×C₇₃	C₂²	semidirect
49. #333×C₇₃	C₂²	semidirect
50. #332×C₇₃	C₂²	semidirect
51. Q₈⋊C₈×C₇₃	C₂²	semidirect
52. Q₈⋊C₈×C₇₃	C₂²	semidirect
53. D₄⋊C₈×C₇₃	C₂²	semidirect
54. D₄⋊C₈×C₇₃	C₂²	semidirect
321. #18836	C₇₃	direct (N × H)
329. #3515	C₂×C₇₃	semidirect
330. #3217	C₂×C₇₃	semidirect
331. #3208	C₂×C₇₃	semidirect
332. #3038	C₂×C₇₃	semidirect
333. #1626	C₂×C₇₃	semidirect
334. #1625	C₂×C₇₃	semidirect
335. #1622	C₂×C₇₃	semidirect
336. #1622	C₂×C₇₃	semidirect
337. #1559	C₂×C₇₃	semidirect
338. #1495	C₂×C₇₃	semidirect
339. #1488	C₂×C₇₃	semidirect
340. C₇₃	#18836	direct (N × H)
342. #557	C₂²×C₇₃	semidirect
343. #554	C₂²×C₇₃	semidirect
344. #554	C₂²×C₇₃	semidirect
350. #547	C₂²×C₇₃	semidirect
378. #333	C₂²×C₇₃	semidirect
379. #332	C₂²×C₇₃	semidirect
380. Q₈⋊C₈	C₂²×C₇₃	semidirect
381. Q₈⋊C₈	C₂²×C₇₃	semidirect
382. D₄⋊C₈	C₂²×C₇₃	semidirect
383. D₄⋊C₈	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×#3515	2
C₇₃×#3217	2
C₇₃×#3208	2
C₇₃×#3038	2
C₇₃×#1626	2
C₇₃×#1625	2
C₇₃×#1622	2
C₇₃×#1559	2
C₇₃×#1495	2
C₇₃×#1488	2
#18836	73

Subgroups — C73×#18836 #32928240

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#18836 #32928240