Subgroups — C₇₃×#18790 #32928194

Order 18688.

1054 conjugacy classes of subgroups.

The subgroup lattice has 694 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₃×#3480	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇₃×#3205	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₃×#3038	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#460×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₃×#1628	C₂	1	2	yes	maximal, complemented
6	C₇₃×#1626	C₂	1	2	yes	maximal, complemented
7	C₇₃×#1621	C₂	1	2	yes	maximal, complemented
8	C₇₃×#1620	C₂	1	2	yes	maximal, complemented
9	C₇₃×#1547	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇₃×#1487	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₃×#1477	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×AGL(1,ℤ/8)×C₇₃	—	2	1	no	—
13	C₂²×SD₁₆×C₇₃	—	2	1	no	—
14	#559×C₇₃	—	2	1	no	—
15	#559×C₇₃	C₂²	1	1	yes	characteristic, complemented
16	#557×C₇₃	C₂²	1	1	yes	characteristic, complemented
17	#556×C₇₃	—	2	1	no	—
18	#556×C₇₃	C₂²	1	1	yes	characteristic, complemented
19	#553×C₇₃	—	2	2	no	—
20	#553×C₇₃	—	2	1	no	—
21	#550×C₇₃	C₂²	1	1	yes	characteristic, complemented
22	#548×C₇₃	—	2	1	no	—
23	#532×C₇₃	—	2	1	no	—
24	#532×C₇₃	C₂²	1	1	yes	characteristic
25	C₂×#127×C₇₃	C₂²	1	1	yes	characteristic
26	#529×C₇₃	—	2	1	no	—
27	#529×C₇₃	—	2	2	no	—
28	C₄×#41×C₇₃	—	2	1	no	—
29	C₄×#41×C₇₃	—	2	1	no	—
30	C₄×#41×C₇₃	C₂²	1	1	yes	characteristic
31	C₂×C₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic
32	#493×C₇₃	C₂²	1	2	yes	—
33	#486×C₇₃	C₂²	1	2	yes	—
34	#460×C₇₃	—	2	1	no	—
35	#460×C₇₃	—	2	1	no	—
36	#460×C₇₃	—	2	1	no	—
37	#460×C₇₃	C₂²	1	2	yes	—
38	#460×C₇₃	C₂²	1	2	yes	—
39	#460×C₇₃	C₂²	1	2	yes	—
40	#459×C₇₃	—	2	1	no	—
41	#459×C₇₃	—	2	2	no	—
42	#459×C₇₃	C₂²	1	2	yes	—
43	#447×C₇₃	—	2	2	no	—
44	#431×C₇₃	C₂²	1	1	yes	characteristic
45	#423×C₇₃	C₂²	1	1	yes	characteristic
46	C₂×C₄⋊C₈×C₇₃	C₂²	1	1	yes	characteristic
47	#418×C₇₃	—	2	1	no	—
48	C₂×#102×C₇₃	—	2	1	no	—
49	#332×C₇₃	C₂²	1	2	yes	complemented
50	#331×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	Q₈⋊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	—	2	1	no	—
57	C₂×#41×C₇₃	D₄	1	1	yes	characteristic
58	C₂²×Q₈×C₇₃	D₄	1	1	yes	characteristic
59	C₂²×D₄×C₇₃	—	2	1	no	—
60	C₂²×D₄×C₇₃	—	2	1	no	—
61	C₂²×D₄×C₇₃	—	2	1	no	—
62	AGL(1,ℤ/8)×C₇₃	—	4	4	no	—
63	C₂×SD₁₆×C₇₃	—	2	2	no	—
64	C₂×SD₁₆×C₇₃	—	2	2	no	—
65	C₂×SD₁₆×C₇₃	—	2	2	no	—
66	C₂×SD₁₆×C₇₃	—	4	4	no	—
67	C₂×D₈×C₇₃	—	2	2	no	—
68	C₂×D₈×C₇₃	—	2	4	no	—
69	C₂×M₁₆×C₇₃	—	2	1	no	—
70	C₂²×C₈×C₇₃	—	2	1	no	—
71	C₄⋊Q₈×C₇₃	—	2	1	no	—
72	C₄⋊Q₈×C₇₃	C₂³	1	1	yes	characteristic
73	#127×C₇₃	—	2	1	no	—
74	#127×C₇₃	—	2	1	no	—
75	#127×C₇₃	—	2	1	no	—
76	#127×C₇₃	—	2	1	no	—
77	#127×C₇₃	C₂³	1	2	yes	—
78	#127×C₇₃	C₂³	1	1	yes	characteristic
79	#126×C₇₃	—	2	2	no	—
80	#126×C₇₃	—	2	2	no	—
81	#126×C₇₃	—	2	2	no	—
82	#125×C₇₃	—	2	2	no	—
83	#125×C₇₃	—	2	1	no	—
84	#124×C₇₃	—	2	2	no	—
85	#124×C₇₃	—	2	1	no	—
86	#124×C₇₃	—	2	1	no	—
87	#124×C₇₃	—	2	1	no	—
88	#124×C₇₃	—	2	1	no	—
89	#123×C₇₃	—	2	2	no	—
90	#123×C₇₃	—	2	2	no	—
91	#123×C₇₃	—	2	2	no	—
92	C₂²⋊Q₈×C₇₃	—	2	2	no	—
93	C₂²⋊Q₈×C₇₃	—	2	1	no	—
94	#121×C₇₃	—	2	2	no	—
95	#121×C₇₃	—	2	2	no	—
96	#121×C₇₃	—	2	2	no	—
97	#121×C₇₃	—	2	1	no	—
98	#121×C₇₃	—	2	1	no	—
99	#121×C₇₃	D₄	1	2	yes	—
100	C₄×Q₈×C₇₃	—	2	1	no	—
101	C₄×Q₈×C₇₃	—	2	1	no	—
102	C₄×Q₈×C₇₃	—	2	1	no	—
103	C₄×Q₈×C₇₃	—	2	1	no	—
104	C₄×Q₈×C₇₃	—	2	1	no	—
105	C₄×Q₈×C₇₃	D₄	1	1	yes	characteristic
106	C₄×Q₈×C₇₃	D₄	1	1	yes	characteristic
107	C₄×Q₈×C₇₃	D₄	1	1	yes	characteristic
108	C₄×Q₈×C₇₃	C₂³	1	1	yes	characteristic
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	2	no	—
114	C₄×D₄×C₇₃	—	2	2	no	—
115	C₄×D₄×C₇₃	—	2	2	no	—
116	C₄×D₄×C₇₃	—	2	1	no	—
117	C₄×D₄×C₇₃	—	2	1	no	—
118	C₄×D₄×C₇₃	—	2	1	no	—
119	C₄×D₄×C₇₃	—	2	1	no	—
120	C₄×D₄×C₇₃	—	2	1	no	—
121	C₄×D₄×C₇₃	—	2	1	no	—
122	C₄×D₄×C₇₃	D₄	1	1	yes	characteristic
123	C₄×D₄×C₇₃	D₄	1	2	yes	—
124	C₄×D₄×C₇₃	C₂³	1	1	yes	characteristic
125	#117×C₇₃	—	2	2	no	—
126	#117×C₇₃	—	2	2	no	—
127	#117×C₇₃	—	2	1	no	—
128	#117×C₇₃	—	2	1	no	—
129	#117×C₇₃	D₄	1	1	yes	characteristic
130	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
131	C₂×C₄⋊C₄×C₇₃	D₄	1	1	yes	characteristic
132	C₂×C₄²×C₇₃	—	2	2	no	—
133	C₂×C₄²×C₇₃	—	2	1	no	—
134	C₂×C₄²×C₇₃	—	2	1	no	—
135	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
136	C₄⋊C₈×C₇₃	—	2	1	no	—
137	C₄⋊C₈×C₇₃	—	2	1	no	—
138	C₄⋊C₈×C₇₃	—	2	1	no	—
139	C₄⋊C₈×C₇₃	C₂³	1	2	yes	—
140	C₄⋊C₈×C₇₃	C₂³	1	2	yes	—
141	#102×C₇₃	—	2	2	no	—
142	#102×C₇₃	—	2	2	no	—
143	#102×C₇₃	—	2	2	no	—
144	#102×C₇₃	—	2	2	no	—
145	#102×C₇₃	—	2	4	no	—
146	C₂²⋊C₈×C₇₃	—	2	1	no	—
147	C₄×C₈×C₇₃	C₂³	1	2	yes	—
148	C₂⁴×C₇₃	—	4	1	no	—
149	#41×C₇₃	—	2	2	no	—
150	#41×C₇₃	—	2	2	no	—
151	#41×C₇₃	—	4	2	no	—
152	#41×C₇₃	—	4	2	no	—
153	#41×C₇₃	—	4	2	no	—
154	#41×C₇₃	—	4	2	no	—
155	C₂×Q₈×C₇₃	—	2	1	no	—
156	C₂×Q₈×C₇₃	—	2	1	no	—
157	C₂×Q₈×C₇₃	—	2	2	no	—
158	C₂×Q₈×C₇₃	—	4	1	no	—
159	C₂×Q₈×C₇₃	C₂×D₄	1	1	yes	characteristic
160	C₂×Q₈×C₇₃	C₂×D₄	1	1	yes	characteristic
161	C₂×Q₈×C₇₃	C₂×D₄	1	1	yes	characteristic
162	C₂×D₄×C₇₃	—	2	2	no	—
163	C₂×D₄×C₇₃	—	2	1	no	—
164	C₂×D₄×C₇₃	—	2	2	no	—
165	C₂×D₄×C₇₃	—	2	2	no	—
166	C₂×D₄×C₇₃	—	2	1	no	—
167	C₂×D₄×C₇₃	—	2	1	no	—
168	C₂×D₄×C₇₃	—	2	2	no	—
169	C₂×D₄×C₇₃	—	2	2	no	—
170	C₂×D₄×C₇₃	—	2	2	no	—
171	C₂×D₄×C₇₃	—	4	2	no	—
172	C₂×D₄×C₇₃	—	4	2	no	—
173	C₂×D₄×C₇₃	—	4	1	no	—
174	C₂×D₄×C₇₃	—	4	1	no	—
175	C₂×D₄×C₇₃	—	4	1	no	—
176	C₂×D₄×C₇₃	—	4	2	no	—
177	C₂×D₄×C₇₃	—	4	2	no	—
178	C₂×D₄×C₇₃	—	8	2	no	—
179	C₂×D₄×C₇₃	C₂×D₄	1	1	yes	characteristic
180	C₂×D₄×C₇₃	C₂×D₄	1	2	yes	—
181	C₂²×C₄×C₇₃	—	2	2	no	—
182	C₂²×C₄×C₇₃	—	2	1	no	—
183	C₂²×C₄×C₇₃	—	2	2	no	—
184	C₂²×C₄×C₇₃	—	2	1	no	—
185	C₂²×C₄×C₇₃	—	2	1	no	—
186	C₂²×C₄×C₇₃	—	2	2	no	—
187	C₂²×C₄×C₇₃	—	2	1	no	—
188	C₂²×C₄×C₇₃	—	2	1	no	—
189	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
190	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
191	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
192	SD₁₆×C₇₃	—	4	4	no	—
193	SD₁₆×C₇₃	—	4	4	no	—
194	SD₁₆×C₇₃	—	4	4	no	—
195	D₈×C₇₃	—	4	4	no	—
196	D₈×C₇₃	—	8	4	no	—
197	M₁₆×C₇₃	—	4	2	no	—
198	C₂×C₈×C₇₃	—	2	2	no	—
199	C₂×C₈×C₇₃	—	2	2	no	—
200	C₂×C₈×C₇₃	—	2	2	no	—
201	C₂×C₈×C₇₃	—	4	2	no	—
202	C₄⋊C₄×C₇₃	—	2	2	no	—
203	C₄⋊C₄×C₇₃	—	2	2	no	—
204	C₄⋊C₄×C₇₃	—	2	2	no	—
205	C₄⋊C₄×C₇₃	—	2	2	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	—	2	1	no	—
210	C₄⋊C₄×C₇₃	—	2	1	no	—
211	C₄⋊C₄×C₇₃	—	2	1	no	—
212	C₄⋊C₄×C₇₃	—	2	1	no	—
213	C₄⋊C₄×C₇₃	—	2	1	no	—
214	C₄⋊C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
215	C₄⋊C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
216	C₄⋊C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
217	C₄⋊C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
218	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
219	C₂²⋊C₄×C₇₃	—	2	2	no	—
220	C₂²⋊C₄×C₇₃	—	2	2	no	—
221	C₂²⋊C₄×C₇₃	—	2	2	no	—
222	C₂²⋊C₄×C₇₃	—	2	2	no	—
223	C₂²⋊C₄×C₇₃	—	2	2	no	—
224	C₂²⋊C₄×C₇₃	—	2	2	no	—
225	C₂²⋊C₄×C₇₃	—	2	1	no	—
226	C₂²⋊C₄×C₇₃	—	2	2	no	—
227	C₂²⋊C₄×C₇₃	—	2	1	no	—
228	C₂²⋊C₄×C₇₃	—	2	2	no	—
229	C₂²⋊C₄×C₇₃	—	2	1	no	—
230	C₄²×C₇₃	—	2	2	no	—
231	C₄²×C₇₃	—	2	2	no	—
232	C₄²×C₇₃	—	2	1	no	—
233	C₄²×C₇₃	—	2	1	no	—
234	C₄²×C₇₃	—	2	1	no	—
235	C₄²×C₇₃	—	2	1	no	—
236	C₄²×C₇₃	—	2	1	no	—
237	C₄²×C₇₃	—	2	1	no	—
238	C₄²×C₇₃	—	2	1	no	—
239	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
240	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
241	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
242	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
243	C₂³×C₇₃	—	2	1	no	—
244	C₂³×C₇₃	—	2	2	no	—
245	C₂³×C₇₃	—	4	2	no	—
246	C₂³×C₇₃	—	8	2	no	—
247	C₂³×C₇₃	—	8	2	no	—
248	C₂³×C₇₃	—	8	2	no	—
249	C₂³×C₇₃	#120	1	1	yes	characteristic
250	Q₈×C₇₃	—	2	1	no	—
251	Q₈×C₇₃	—	2	1	no	—
252	Q₈×C₇₃	—	2	1	no	—
253	Q₈×C₇₃	—	2	1	no	—
254	Q₈×C₇₃	—	2	1	no	—
255	Q₈×C₇₃	—	4	2	no	—
256	Q₈×C₇₃	—	4	1	no	—
257	Q₈×C₇₃	—	4	1	no	—
258	Q₈×C₇₃	AGL(1,ℤ/8)	1	2	yes	complemented
259	D₄×C₇₃	—	2	1	no	—
260	D₄×C₇₃	—	2	1	no	—
261	D₄×C₇₃	—	4	2	no	—
262	D₄×C₇₃	—	4	4	no	—
263	D₄×C₇₃	—	4	4	no	—
264	D₄×C₇₃	—	4	2	no	—
265	D₄×C₇₃	—	4	4	no	—
266	D₄×C₇₃	—	4	1	no	—
267	D₄×C₇₃	—	4	2	no	—
268	D₄×C₇₃	—	4	1	no	—
269	D₄×C₇₃	—	4	1	no	—
270	D₄×C₇₃	—	4	2	no	—
271	D₄×C₇₃	—	4	2	no	—
272	D₄×C₇₃	—	4	1	no	—
273	D₄×C₇₃	—	4	2	no	—
274	D₄×C₇₃	—	8	2	no	—
275	D₄×C₇₃	—	8	2	no	—
276	D₄×C₇₃	—	8	2	no	—
277	D₄×C₇₃	—	8	2	no	—
278	C₂×C₄×C₇₃	—	2	1	no	—
279	C₂×C₄×C₇₃	—	2	1	no	—
280	C₂×C₄×C₇₃	—	2	1	no	—
281	C₂×C₄×C₇₃	—	2	1	no	—
282	C₂×C₄×C₇₃	—	2	1	no	—
283	C₂×C₄×C₇₃	—	2	1	no	—
284	C₂×C₄×C₇₃	—	2	1	no	—
285	C₂×C₄×C₇₃	—	2	1	no	—
286	C₂×C₄×C₇₃	—	2	2	no	—
287	C₂×C₄×C₇₃	—	2	1	no	—
288	C₂×C₄×C₇₃	—	4	1	no	—
289	C₂×C₄×C₇₃	—	4	2	no	—
290	C₂×C₄×C₇₃	—	4	4	no	—
291	C₂×C₄×C₇₃	—	4	1	no	—
292	C₂×C₄×C₇₃	—	4	1	no	—
293	C₂×C₄×C₇₃	—	4	2	no	—
294	C₂×C₄×C₇₃	—	4	4	no	—
295	C₂×C₄×C₇₃	—	8	1	no	—
296	C₂×C₄×C₇₃	—	8	1	no	—
297	C₂×C₄×C₇₃	—	8	2	no	—
298	C₂×C₄×C₇₃	#120	1	1	yes	characteristic
299	C₂×C₄×C₇₃	#120	1	1	yes	characteristic
300	C₂×C₄×C₇₃	#120	1	1	yes	characteristic
301	C₂×C₄×C₇₃	#135	1	2	yes	—
302	C₂×C₄×C₇₃	AGL(1,ℤ/8)	1	2	yes	—
303	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
304	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
305	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
306	C₈×C₇₃	—	4	2	no	—
307	C₈×C₇₃	—	4	2	no	—
308	C₈×C₇₃	—	4	2	no	—
309	C₂²×C₇₃	—	2	1	no	—
310	C₂²×C₇₃	—	2	1	no	—
311	C₂²×C₇₃	—	4	1	no	—
312	C₂²×C₇₃	—	4	2	no	—
313	C₂²×C₇₃	—	4	2	no	—
314	C₂²×C₇₃	—	4	1	no	—
315	C₂²×C₇₃	—	4	2	no	—
316	C₂²×C₇₃	—	4	1	no	—
317	C₂²×C₇₃	—	8	2	no	—
318	C₂²×C₇₃	—	8	2	no	—
319	C₂²×C₇₃	—	8	2	no	—
320	C₂²×C₇₃	—	16	4	no	—
321	C₂²×C₇₃	#449	1	2	yes	—
322	C₂²×C₇₃	C₂×#120	1	1	yes	characteristic
323	C₄×C₇₃	—	2	1	no	—
324	C₄×C₇₃	—	2	2	no	—
325	C₄×C₇₃	—	2	1	no	—
326	C₄×C₇₃	—	2	1	no	—
327	C₄×C₇₃	—	4	1	no	—
328	C₄×C₇₃	—	4	2	no	—
329	C₄×C₇₃	—	4	1	no	—
330	C₄×C₇₃	—	4	1	no	—
331	C₄×C₇₃	—	4	1	no	—
332	C₄×C₇₃	—	4	1	no	—
333	C₄×C₇₃	—	4	1	no	—
334	C₄×C₇₃	#449	1	2	yes	—
335	C₄×C₇₃	C₂×#135	1	1	yes	characteristic
336	C₄×C₇₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
337	C₄×C₇₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
338	C₄×C₇₃	#575	1	1	yes	characteristic
339	#18790	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
340	C₂×C₇₃	—	2	2	no	—
341	C₂×C₇₃	—	8	1	no	—
342	C₂×C₇₃	—	8	2	no	—
343	C₂×C₇₃	—	16	2	no	—
344	C₂×C₇₃	C₂×#449	1	1	yes	characteristic
345	C₂×C₇₃	#3006	1	1	yes	characteristic
346	C₂×C₇₃	#3021	1	1	yes	characteristic
347	#3480	C₂×C₇₃	1	1	yes	characteristic, complemented
348	#3205	C₂×C₇₃	1	1	yes	characteristic, complemented
349	#3038	C₂×C₇₃	1	1	yes	characteristic, complemented
350	C₂×#460	C₂×C₇₃	1	1	yes	characteristic, complemented
351	#1628	C₂×C₇₃	1	2	yes	complemented
352	#1626	C₂×C₇₃	1	2	yes	complemented
353	#1621	C₂×C₇₃	1	2	yes	complemented
354	#1620	C₂×C₇₃	1	2	yes	complemented
355	#1547	C₂×C₇₃	1	1	yes	characteristic, complemented
356	#1487	C₂×C₇₃	1	1	yes	characteristic, complemented
357	#1477	C₂×C₇₃	1	1	yes	characteristic, complemented
358	C₇₃	#18790	1	1	yes	characteristic, direct product factor, Sylow
359	C₂×AGL(1,ℤ/8)	—	2	1	no	—
360	C₂²×SD₁₆	—	2	1	no	—
361	#559	—	2	1	no	—
362	#559	C₂²×C₇₃	1	1	yes	characteristic, complemented
363	#557	C₂²×C₇₃	1	1	yes	characteristic, complemented
364	#556	—	2	1	no	—
365	#556	C₂²×C₇₃	1	1	yes	characteristic, complemented
366	#553	—	2	2	no	—
367	#553	—	2	1	no	—
368	#550	C₂²×C₇₃	1	1	yes	characteristic, complemented
369	#548	—	2	1	no	—
370	#532	—	2	1	no	—
371	#532	C₂²×C₇₃	1	1	yes	characteristic
372	C₂×#127	C₂²×C₇₃	1	1	yes	characteristic
373	#529	—	2	1	no	—
374	#529	—	2	2	no	—
375	C₄×#41	—	2	1	no	—
376	C₄×#41	—	2	1	no	—
377	C₄×#41	C₂²×C₇₃	1	1	yes	characteristic
378	C₂×C₄×Q₈	C₂²×C₇₃	1	1	yes	characteristic
379	#493	C₂²×C₇₃	1	2	yes	—
380	#486	C₂²×C₇₃	1	2	yes	—
381	#460	—	2	1	no	—
382	#460	—	2	1	no	—
383	#460	—	2	1	no	—
384	#460	C₂²×C₇₃	1	2	yes	—
385	#460	C₂²×C₇₃	1	2	yes	—
386	#460	C₂²×C₇₃	1	2	yes	—
387	#459	—	2	2	no	—
388	#459	—	2	1	no	—
389	#459	C₂²×C₇₃	1	2	yes	—
390	#447	—	2	2	no	—
391	#431	C₂²×C₇₃	1	1	yes	characteristic
392	#423	C₂²×C₇₃	1	1	yes	characteristic
393	C₂×C₄⋊C₈	C₂²×C₇₃	1	1	yes	characteristic
394	#418	—	2	1	no	—
395	C₂×#102	—	2	1	no	—
396	#332	C₂²×C₇₃	1	2	yes	complemented
397	#331	C₂²×C₇₃	1	2	yes	complemented
398	Q₈⋊C₈	C₂²×C₇₃	1	2	yes	complemented
399	Q₈⋊C₈	C₂²×C₇₃	1	2	yes	complemented
400	Q₈⋊C₈	C₂²×C₇₃	1	2	yes	complemented
401	D₄⋊C₈	C₂²×C₇₃	1	2	yes	complemented
402	C₂×#41	—	2	1	no	—
403	C₂×#41	—	2	1	no	—
404	C₂×#41	D₄×C₇₃	1	1	yes	characteristic
405	C₂²×Q₈	D₄×C₇₃	1	1	yes	characteristic
406	C₂²×D₄	—	2	1	no	—
407	C₂²×D₄	—	2	1	no	—
408	C₂²×D₄	—	2	1	no	—
409	AGL(1,ℤ/8)	—	4	4	no	—
410	C₂×SD₁₆	—	2	2	no	—
411	C₂×SD₁₆	—	2	2	no	—
412	C₂×SD₁₆	—	2	2	no	—
413	C₂×SD₁₆	—	4	4	no	—
414	C₂×D₈	—	2	2	no	—
415	C₂×D₈	—	2	4	no	—
416	C₂×M₁₆	—	2	1	no	—
417	C₂²×C₈	—	2	1	no	—
418	C₄⋊Q₈	—	2	1	no	—
419	C₄⋊Q₈	C₂³×C₇₃	1	1	yes	characteristic
420	#127	—	2	1	no	—
421	#127	—	2	1	no	—
422	#127	—	2	1	no	—
423	#127	—	2	1	no	—
424	#127	C₂³×C₇₃	1	2	yes	—
425	#127	C₂³×C₇₃	1	1	yes	characteristic
426	#126	—	2	2	no	—
427	#126	—	2	2	no	—
428	#126	—	2	2	no	—
429	#125	—	2	2	no	—
430	#125	—	2	1	no	—
431	#124	—	2	2	no	—
432	#124	—	2	1	no	—
433	#124	—	2	1	no	—
434	#124	—	2	1	no	—
435	#124	—	2	1	no	—
436	#123	—	2	2	no	—
437	#123	—	2	2	no	—
438	#123	—	2	2	no	—
439	C₂²⋊Q₈	—	2	2	no	—
440	C₂²⋊Q₈	—	2	1	no	—
441	#121	—	2	2	no	—
442	#121	—	2	2	no	—
443	#121	—	2	2	no	—
444	#121	—	2	1	no	—
445	#121	—	2	1	no	—
446	#121	D₄×C₇₃	1	2	yes	—
447	C₄×Q₈	—	2	1	no	—
448	C₄×Q₈	—	2	1	no	—
449	C₄×Q₈	—	2	1	no	—
450	C₄×Q₈	—	2	1	no	—
451	C₄×Q₈	—	2	1	no	—
452	C₄×Q₈	D₄×C₇₃	1	1	yes	characteristic
453	C₄×Q₈	D₄×C₇₃	1	1	yes	characteristic
454	C₄×Q₈	D₄×C₇₃	1	1	yes	characteristic
455	C₄×Q₈	C₂³×C₇₃	1	1	yes	characteristic
456	C₄×Q₈	C₂³×C₇₃	1	1	yes	characteristic
457	C₄×Q₈	C₂³×C₇₃	1	1	yes	characteristic
458	C₄×D₄	—	2	2	no	—
459	C₄×D₄	—	2	2	no	—
460	C₄×D₄	—	2	2	no	—
461	C₄×D₄	—	2	2	no	—
462	C₄×D₄	—	2	2	no	—
463	C₄×D₄	—	2	1	no	—
464	C₄×D₄	—	2	1	no	—
465	C₄×D₄	—	2	1	no	—
466	C₄×D₄	—	2	1	no	—
467	C₄×D₄	—	2	1	no	—
468	C₄×D₄	—	2	1	no	—
469	C₄×D₄	D₄×C₇₃	1	1	yes	characteristic
470	C₄×D₄	D₄×C₇₃	1	2	yes	—
471	C₄×D₄	C₂³×C₇₃	1	1	yes	characteristic
472	#117	—	2	2	no	—
473	#117	—	2	2	no	—
474	#117	—	2	1	no	—
475	#117	—	2	1	no	—
476	#117	D₄×C₇₃	1	1	yes	characteristic
477	C₂×C₄⋊C₄	—	2	1	no	—
478	C₂×C₄⋊C₄	D₄×C₇₃	1	1	yes	characteristic
479	C₂×C₄²	—	2	2	no	—
480	C₂×C₄²	—	2	1	no	—
481	C₂×C₄²	—	2	1	no	—
482	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
483	C₄⋊C₈	—	2	1	no	—
484	C₄⋊C₈	—	2	1	no	—
485	C₄⋊C₈	—	2	1	no	—
486	C₄⋊C₈	C₂³×C₇₃	1	2	yes	—
487	C₄⋊C₈	C₂³×C₇₃	1	2	yes	—
488	#102	—	2	2	no	—
489	#102	—	2	2	no	—
490	#102	—	2	2	no	—
491	#102	—	2	2	no	—
492	#102	—	2	4	no	—
493	C₂²⋊C₈	—	2	1	no	—
494	C₄×C₈	C₂³×C₇₃	1	2	yes	—
495	C₂⁴	—	4	1	no	—
496	#41	—	2	2	no	—
497	#41	—	2	2	no	—
498	#41	—	4	2	no	—
499	#41	—	4	2	no	—
500	#41	—	4	2	no	—
501	#41	—	4	2	no	—
502	C₂×Q₈	—	2	1	no	—
503	C₂×Q₈	—	2	1	no	—
504	C₂×Q₈	—	2	2	no	—
505	C₂×Q₈	—	4	1	no	—
506	C₂×Q₈	C₂×D₄×C₇₃	1	1	yes	characteristic
507	C₂×Q₈	C₂×D₄×C₇₃	1	1	yes	characteristic
508	C₂×Q₈	C₂×D₄×C₇₃	1	1	yes	characteristic
509	C₂×D₄	—	2	2	no	—
510	C₂×D₄	—	2	1	no	—
511	C₂×D₄	—	2	2	no	—
512	C₂×D₄	—	2	2	no	—
513	C₂×D₄	—	2	1	no	—
514	C₂×D₄	—	2	1	no	—
515	C₂×D₄	—	2	2	no	—
516	C₂×D₄	—	2	2	no	—
517	C₂×D₄	—	2	2	no	—
518	C₂×D₄	—	4	2	no	—
519	C₂×D₄	—	4	2	no	—
520	C₂×D₄	—	4	1	no	—
521	C₂×D₄	—	4	1	no	—
522	C₂×D₄	—	4	1	no	—
523	C₂×D₄	—	4	2	no	—
524	C₂×D₄	—	4	2	no	—
525	C₂×D₄	—	8	2	no	—
526	C₂×D₄	C₂×D₄×C₇₃	1	1	yes	characteristic
527	C₂×D₄	C₂×D₄×C₇₃	1	2	yes	—
528	C₂²×C₄	—	2	2	no	—
529	C₂²×C₄	—	2	1	no	—
530	C₂²×C₄	—	2	2	no	—
531	C₂²×C₄	—	2	1	no	—
532	C₂²×C₄	—	2	1	no	—
533	C₂²×C₄	—	2	2	no	—
534	C₂²×C₄	—	2	1	no	—
535	C₂²×C₄	—	2	1	no	—
536	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
537	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
538	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
539	SD₁₆	—	4	4	no	—
540	SD₁₆	—	4	4	no	—
541	SD₁₆	—	4	4	no	—
542	D₈	—	4	4	no	—
543	D₈	—	8	4	no	—
544	M₁₆	—	4	2	no	—
545	C₂×C₈	—	2	2	no	—
546	C₂×C₈	—	2	2	no	—
547	C₂×C₈	—	2	2	no	—
548	C₂×C₈	—	4	2	no	—
549	C₄⋊C₄	—	2	2	no	—
550	C₄⋊C₄	—	2	2	no	—
551	C₄⋊C₄	—	2	2	no	—
552	C₄⋊C₄	—	2	2	no	—
553	C₄⋊C₄	—	2	1	no	—
554	C₄⋊C₄	—	2	1	no	—
555	C₄⋊C₄	—	2	1	no	—
556	C₄⋊C₄	—	2	1	no	—
557	C₄⋊C₄	—	2	1	no	—
558	C₄⋊C₄	—	2	1	no	—
559	C₄⋊C₄	—	2	1	no	—
560	C₄⋊C₄	—	2	1	no	—
561	C₄⋊C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
562	C₄⋊C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
563	C₄⋊C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
564	C₄⋊C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
565	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
566	C₂²⋊C₄	—	2	2	no	—
567	C₂²⋊C₄	—	2	2	no	—
568	C₂²⋊C₄	—	2	2	no	—
569	C₂²⋊C₄	—	2	2	no	—
570	C₂²⋊C₄	—	2	2	no	—
571	C₂²⋊C₄	—	2	2	no	—
572	C₂²⋊C₄	—	2	1	no	—
573	C₂²⋊C₄	—	2	2	no	—
574	C₂²⋊C₄	—	2	1	no	—
575	C₂²⋊C₄	—	2	2	no	—
576	C₂²⋊C₄	—	2	1	no	—
577	C₄²	—	2	2	no	—
578	C₄²	—	2	2	no	—
579	C₄²	—	2	1	no	—
580	C₄²	—	2	1	no	—
581	C₄²	—	2	1	no	—
582	C₄²	—	2	1	no	—
583	C₄²	—	2	1	no	—
584	C₄²	—	2	1	no	—
585	C₄²	—	2	1	no	—
586	C₄²	C₂×D₄×C₇₃	1	1	yes	characteristic
587	C₄²	C₂×D₄×C₇₃	1	1	yes	characteristic
588	C₄²	C₂×D₄×C₇₃	1	1	yes	characteristic
589	C₄²	C₂⁴×C₇₃	1	1	yes	characteristic
590	C₂³	—	2	1	no	—
591	C₂³	—	2	2	no	—
592	C₂³	—	4	2	no	—
593	C₂³	—	8	2	no	—
594	C₂³	—	8	2	no	—
595	C₂³	—	8	2	no	—
596	C₂³	#120×C₇₃	1	1	yes	characteristic
597	Q₈	—	2	1	no	—
598	Q₈	—	2	1	no	—
599	Q₈	—	2	1	no	—
600	Q₈	—	2	1	no	—
601	Q₈	—	2	1	no	—
602	Q₈	—	4	2	no	—
603	Q₈	—	4	1	no	—
604	Q₈	—	4	1	no	—
605	Q₈	AGL(1,ℤ/8)×C₇₃	1	2	yes	complemented
606	D₄	—	2	1	no	—
607	D₄	—	2	1	no	—
608	D₄	—	4	2	no	—
609	D₄	—	4	4	no	—
610	D₄	—	4	4	no	—
611	D₄	—	4	2	no	—
612	D₄	—	4	4	no	—
613	D₄	—	4	1	no	—
614	D₄	—	4	2	no	—
615	D₄	—	4	1	no	—
616	D₄	—	4	1	no	—
617	D₄	—	4	2	no	—
618	D₄	—	4	2	no	—
619	D₄	—	4	1	no	—
620	D₄	—	4	2	no	—
621	D₄	—	8	2	no	—
622	D₄	—	8	2	no	—
623	D₄	—	8	2	no	—
624	D₄	—	8	2	no	—
625	C₂×C₄	—	2	1	no	—
626	C₂×C₄	—	2	1	no	—
627	C₂×C₄	—	2	1	no	—
628	C₂×C₄	—	2	1	no	—
629	C₂×C₄	—	2	1	no	—
630	C₂×C₄	—	2	1	no	—
631	C₂×C₄	—	2	1	no	—
632	C₂×C₄	—	2	1	no	—
633	C₂×C₄	—	2	2	no	—
634	C₂×C₄	—	2	1	no	—
635	C₂×C₄	—	4	1	no	—
636	C₂×C₄	—	4	2	no	—
637	C₂×C₄	—	4	4	no	—
638	C₂×C₄	—	4	2	no	—
639	C₂×C₄	—	4	4	no	—
640	C₂×C₄	—	4	1	no	—
641	C₂×C₄	—	4	1	no	—
642	C₂×C₄	—	8	1	no	—
643	C₂×C₄	—	8	1	no	—
644	C₂×C₄	—	8	2	no	—
645	C₂×C₄	#120×C₇₃	1	1	yes	characteristic
646	C₂×C₄	#120×C₇₃	1	1	yes	characteristic
647	C₂×C₄	#120×C₇₃	1	1	yes	characteristic
648	C₂×C₄	#135×C₇₃	1	2	yes	—
649	C₂×C₄	AGL(1,ℤ/8)×C₇₃	1	2	yes	—
650	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
651	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
652	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
653	C₈	—	4	2	no	—
654	C₈	—	4	2	no	—
655	C₈	—	4	2	no	—
656	C₂²	—	2	1	no	—
657	C₂²	—	2	1	no	—
658	C₂²	—	4	1	no	—
659	C₂²	—	4	2	no	—
660	C₂²	—	4	2	no	—
661	C₂²	—	4	1	no	—
662	C₂²	—	4	2	no	—
663	C₂²	—	4	1	no	—
664	C₂²	—	8	2	no	—
665	C₂²	—	8	2	no	—
666	C₂²	—	8	2	no	—
667	C₂²	—	16	4	no	—
668	C₂²	#449×C₇₃	1	2	yes	—
669	C₂²	C₂×#120×C₇₃	1	1	yes	characteristic
670	C₄	—	2	1	no	—
671	C₄	—	2	2	no	—
672	C₄	—	2	1	no	—
673	C₄	—	2	1	no	—
674	C₄	—	4	1	no	—
675	C₄	—	4	2	no	—
676	C₄	—	4	1	no	—
677	C₄	—	4	1	no	—
678	C₄	—	4	1	no	—
679	C₄	—	4	1	no	—
680	C₄	—	4	1	no	—
681	C₄	#449×C₇₃	1	2	yes	—
682	C₄	C₂×#135×C₇₃	1	1	yes	characteristic
683	C₄	C₂×AGL(1,ℤ/8)×C₇₃	1	1	yes	characteristic
684	C₄	C₂×AGL(1,ℤ/8)×C₇₃	1	1	yes	characteristic
685	C₄	#575×C₇₃	1	1	yes	characteristic
686	C₂	—	2	2	no	—
687	C₂	—	8	1	no	—
688	C₂	—	8	2	no	—
689	C₂	—	16	2	no	—
690	C₂	C₂×#449×C₇₃	1	1	yes	characteristic
691	C₂	C₇₃×#3006	1	1	yes	characteristic
692	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×#3480	C₂	semidirect
2. C₇₃×#3205	C₂	semidirect
3. C₇₃×#3038	C₂	semidirect
4. C₂×#460×C₇₃	C₂	semidirect
5. C₇₃×#1628	C₂	semidirect
6. C₇₃×#1626	C₂	semidirect
7. C₇₃×#1621	C₂	semidirect
8. C₇₃×#1620	C₂	semidirect
9. C₇₃×#1547	C₂	semidirect
10. C₇₃×#1487	C₂	semidirect
11. C₇₃×#1477	C₂	semidirect
15. #559×C₇₃	C₂²	semidirect
16. #557×C₇₃	C₂²	semidirect
18. #556×C₇₃	C₂²	semidirect
21. #550×C₇₃	C₂²	semidirect
49. #332×C₇₃	C₂²	semidirect
50. #331×C₇₃	C₂²	semidirect
51. Q₈⋊C₈×C₇₃	C₂²	semidirect
52. Q₈⋊C₈×C₇₃	C₂²	semidirect
53. Q₈⋊C₈×C₇₃	C₂²	semidirect
54. D₄⋊C₈×C₇₃	C₂²	semidirect
258. Q₈×C₇₃	AGL(1,ℤ/8)	semidirect
339. #18790	C₇₃	direct (N × H)
347. #3480	C₂×C₇₃	semidirect
348. #3205	C₂×C₇₃	semidirect
349. #3038	C₂×C₇₃	semidirect
350. C₂×#460	C₂×C₇₃	semidirect
351. #1628	C₂×C₇₃	semidirect
352. #1626	C₂×C₇₃	semidirect
353. #1621	C₂×C₇₃	semidirect
354. #1620	C₂×C₇₃	semidirect
355. #1547	C₂×C₇₃	semidirect
356. #1487	C₂×C₇₃	semidirect
357. #1477	C₂×C₇₃	semidirect
358. C₇₃	#18790	direct (N × H)
362. #559	C₂²×C₇₃	semidirect
363. #557	C₂²×C₇₃	semidirect
365. #556	C₂²×C₇₃	semidirect
368. #550	C₂²×C₇₃	semidirect
396. #332	C₂²×C₇₃	semidirect
397. #331	C₂²×C₇₃	semidirect
398. Q₈⋊C₈	C₂²×C₇₃	semidirect
399. Q₈⋊C₈	C₂²×C₇₃	semidirect
400. Q₈⋊C₈	C₂²×C₇₃	semidirect
401. D₄⋊C₈	C₂²×C₇₃	semidirect
605. Q₈	AGL(1,ℤ/8)×C₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₇₃×#3480	2
C₇₃×#3205	2
C₇₃×#3038	2
C₂×#460×C₇₃	2
C₇₃×#1628	2
C₇₃×#1626	2
C₇₃×#1621	2
C₇₃×#1620	2
C₇₃×#1547	2
C₇₃×#1487	2
C₇₃×#1477	2
#18790	73

Subgroups — C73×#18790 #32928194

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#18790 #32928194