Subgroups — C₇₃×#18610 #32928014

Order 18688.

1140 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₃×#3497	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇₃×#3214	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₃×#3184	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₃×#3103	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₃×#1651	C₂	1	2	yes	maximal, complemented
6	C₇₃×#1642	C₂	1	2	yes	maximal, complemented
7	C₇₃×#1627	C₂	1	2	yes	maximal, complemented
8	C₇₃×#1621	C₂	1	2	yes	maximal, complemented
9	C₇₃×#1553	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇₃×#1491	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₃×#1484	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×2₋¹⁺⁴×C₇₃	—	2	1	no	—
13	#550×C₇₃	—	2	1	no	—
14	#550×C₇₃	C₂²	1	2	yes	—
15	D₄×Q₈×C₇₃	—	2	1	no	—
16	D₄×Q₈×C₇₃	C₂²	1	2	yes	—
17	#548×C₇₃	—	2	2	no	—
18	#548×C₇₃	—	2	2	no	—
19	#537×C₇₃	—	2	2	no	—
20	#537×C₇₃	—	2	1	no	—
21	#532×C₇₃	—	2	2	no	—
22	#532×C₇₃	C₂²	1	1	yes	characteristic
23	#532×C₇₃	C₂²	1	1	yes	characteristic
24	#532×C₇₃	C₂²	1	1	yes	characteristic
25	C₂×C₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic
26	#498×C₇₃	C₂²	1	1	yes	characteristic
27	#496×C₇₃	—	2	1	no	—
28	#493×C₇₃	C₂²	1	1	yes	characteristic
29	#489×C₇₃	—	2	1	no	—
30	#486×C₇₃	C₂²	1	1	yes	characteristic
31	#486×C₇₃	C₂²	1	1	yes	characteristic
32	#481×C₇₃	—	2	1	no	—
33	#475×C₇₃	C₂²	1	2	yes	—
34	#469×C₇₃	—	2	2	no	—
35	#461×C₇₃	C₂²	1	2	yes	—
36	#460×C₇₃	C₂²	1	2	yes	—
37	#459×C₇₃	C₂²	1	2	yes	—
38	#449×C₇₃	—	2	2	no	—
39	#448×C₇₃	—	2	1	no	—
40	#442×C₇₃	—	2	2	no	—
41	C₄×SD₁₆×C₇₃	—	2	2	no	—
42	#432×C₇₃	C₂²	1	1	yes	characteristic
43	#431×C₇₃	C₂²	1	1	yes	characteristic
44	C₄×M₁₆×C₇₃	C₂²	1	1	yes	characteristic
45	#332×C₇₃	C₂²	1	2	yes	—
46	#331×C₇₃	C₂²	1	2	yes	—
47	Q₈⋊C₈×C₇₃	C₂²	1	2	yes	—
48	Q₈⋊C₈×C₇₃	C₂²	1	2	yes	—
49	D₄⋊C₈×C₇₃	C₂²	1	2	yes	—
50	D₄⋊C₈×C₇₃	C₂²	1	2	yes	—
51	2₋¹⁺⁴×C₇₃	—	4	8	no	—
52	C₂×#41×C₇₃	—	2	4	no	—
53	C₂×#41×C₇₃	—	2	2	no	—
54	C₂×#41×C₇₃	—	2	2	no	—
55	C₂×#41×C₇₃	—	2	1	no	—
56	C₂×#41×C₇₃	—	2	1	no	—
57	C₂×#41×C₇₃	—	2	1	no	—
58	C₂²×Q₈×C₇₃	—	2	2	no	—
59	C₂²×Q₈×C₇₃	—	2	2	no	—
60	C₂²×Q₈×C₇₃	D₄	1	1	yes	characteristic
61	C₂×SD₁₆×C₇₃	—	2	2	no	—
62	C₂×SD₁₆×C₇₃	—	2	2	no	—
63	C₂×D₈×C₇₃	—	2	2	no	—
64	C₂×D₈×C₇₃	—	2	2	no	—
65	C₂×M₁₆×C₇₃	—	2	1	no	—
66	C₄⋊Q₈×C₇₃	—	2	2	no	—
67	C₄⋊Q₈×C₇₃	D₄	1	1	yes	characteristic
68	C₄⋊Q₈×C₇₃	C₂³	1	1	yes	characteristic
69	C₄⋊Q₈×C₇₃	C₂³	1	1	yes	characteristic
70	#127×C₇₃	—	2	2	no	—
71	#127×C₇₃	D₄	1	1	yes	characteristic
72	#127×C₇₃	C₂³	1	1	yes	characteristic
73	#127×C₇₃	C₂³	1	1	yes	characteristic
74	#124×C₇₃	—	2	4	no	—
75	#124×C₇₃	—	2	1	no	—
76	#124×C₇₃	—	2	1	no	—
77	#124×C₇₃	—	2	1	no	—
78	C₂²⋊Q₈×C₇₃	—	2	2	no	—
79	C₂²⋊Q₈×C₇₃	—	2	4	no	—
80	C₂²⋊Q₈×C₇₃	—	2	2	no	—
81	C₂²⋊Q₈×C₇₃	—	2	4	no	—
82	#121×C₇₃	—	2	4	no	—
83	#121×C₇₃	—	2	2	no	—
84	#121×C₇₃	—	2	4	no	—
85	#121×C₇₃	—	2	4	no	—
86	#121×C₇₃	—	2	1	no	—
87	#121×C₇₃	—	2	1	no	—
88	#121×C₇₃	—	2	2	no	—
89	#121×C₇₃	—	2	1	no	—
90	#121×C₇₃	—	2	1	no	—
91	#121×C₇₃	D₄	1	2	yes	—
92	#121×C₇₃	D₄	1	2	yes	—
93	C₄×Q₈×C₇₃	—	2	1	no	—
94	C₄×Q₈×C₇₃	—	2	1	no	—
95	C₄×Q₈×C₇₃	D₄	1	2	yes	—
96	C₄×Q₈×C₇₃	C₂³	1	2	yes	—
97	C₄×D₄×C₇₃	—	2	4	no	—
98	C₄×D₄×C₇₃	—	2	2	no	—
99	C₄×D₄×C₇₃	—	2	2	no	—
100	C₄×D₄×C₇₃	—	2	1	no	—
101	C₄×D₄×C₇₃	—	2	1	no	—
102	C₄×D₄×C₇₃	—	2	1	no	—
103	C₄×D₄×C₇₃	—	2	1	no	—
104	C₄×D₄×C₇₃	D₄	1	2	yes	—
105	C₄×D₄×C₇₃	C₂³	1	2	yes	—
106	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
107	C₂×C₄⋊C₄×C₇₃	D₄	1	1	yes	characteristic
108	C₂×C₄²×C₇₃	—	2	1	no	—
109	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
110	#106×C₇₃	—	2	2	no	—
111	#106×C₇₃	—	2	2	no	—
112	C₄⋊C₈×C₇₃	C₂³	1	2	yes	—
113	C₄⋊C₈×C₇₃	C₂³	1	2	yes	—
114	#103×C₇₃	—	2	2	no	—
115	#103×C₇₃	—	2	2	no	—
116	#102×C₇₃	—	2	2	no	—
117	#102×C₇₃	—	2	2	no	—
118	#102×C₇₃	—	2	2	no	—
119	#102×C₇₃	—	2	2	no	—
120	C₂²⋊C₈×C₇₃	—	2	1	no	—
121	C₂²⋊C₈×C₇₃	—	2	1	no	—
122	#97×C₇₃	—	2	1	no	—
123	#97×C₇₃	—	2	1	no	—
124	C₄×C₈×C₇₃	—	2	1	no	—
125	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
126	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
127	#41×C₇₃	—	4	16	no	—
128	#41×C₇₃	—	4	4	no	—
129	#41×C₇₃	—	4	4	no	—
130	#41×C₇₃	—	4	8	no	—
131	#41×C₇₃	—	4	4	no	—
132	#41×C₇₃	—	4	4	no	—
133	#41×C₇₃	—	8	2	no	—
134	C₂×Q₈×C₇₃	—	2	4	no	—
135	C₂×Q₈×C₇₃	—	2	4	no	—
136	C₂×Q₈×C₇₃	—	2	1	no	—
137	C₂×Q₈×C₇₃	—	2	1	no	—
138	C₂×Q₈×C₇₃	—	2	1	no	—
139	C₂×Q₈×C₇₃	—	2	1	no	—
140	C₂×Q₈×C₇₃	—	4	8	no	—
141	C₂×Q₈×C₇₃	—	4	4	no	—
142	C₂×Q₈×C₇₃	—	4	4	no	—
143	C₂×Q₈×C₇₃	C₂×D₄	1	2	yes	—
144	C₂×D₄×C₇₃	—	2	4	no	—
145	C₂×D₄×C₇₃	—	2	2	no	—
146	C₂×D₄×C₇₃	—	2	2	no	—
147	C₂×D₄×C₇₃	—	2	4	no	—
148	C₂×D₄×C₇₃	—	2	1	no	—
149	C₂×D₄×C₇₃	—	2	1	no	—
150	C₂×D₄×C₇₃	—	2	1	no	—
151	C₂×D₄×C₇₃	—	2	1	no	—
152	C₂×D₄×C₇₃	—	2	1	no	—
153	C₂×D₄×C₇₃	—	2	1	no	—
154	C₂×D₄×C₇₃	—	2	1	no	—
155	C₂×D₄×C₇₃	—	4	1	no	—
156	C₂×D₄×C₇₃	C₂×D₄	1	2	yes	—
157	C₂×D₄×C₇₃	C₂×D₄	1	2	yes	—
158	C₂²×C₄×C₇₃	—	2	1	no	—
159	C₂²×C₄×C₇₃	—	2	4	no	—
160	C₂²×C₄×C₇₃	—	2	4	no	—
161	C₂²×C₄×C₇₃	—	2	1	no	—
162	C₂²×C₄×C₇₃	—	2	2	no	—
163	C₂²×C₄×C₇₃	—	2	2	no	—
164	C₂²×C₄×C₇₃	—	4	1	no	—
165	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
168	SD₁₆×C₇₃	—	4	4	no	—
169	SD₁₆×C₇₃	—	8	2	no	—
170	D₈×C₇₃	—	4	4	no	—
171	D₈×C₇₃	—	8	2	no	—
172	M₁₆×C₇₃	—	4	2	no	—
173	C₂×C₈×C₇₃	—	2	1	no	—
174	C₂×C₈×C₇₃	—	2	2	no	—
175	C₂×C₈×C₇₃	—	2	1	no	—
176	C₂×C₈×C₇₃	—	2	2	no	—
177	C₄⋊C₄×C₇₃	—	2	4	no	—
178	C₄⋊C₄×C₇₃	—	2	2	no	—
179	C₄⋊C₄×C₇₃	—	2	1	no	—
180	C₄⋊C₄×C₇₃	—	2	1	no	—
181	C₄⋊C₄×C₇₃	—	2	2	no	—
182	C₄⋊C₄×C₇₃	—	2	1	no	—
183	C₄⋊C₄×C₇₃	—	2	1	no	—
184	C₄⋊C₄×C₇₃	—	2	1	no	—
185	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
186	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
187	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
188	C₂²⋊C₄×C₇₃	—	2	4	no	—
189	C₂²⋊C₄×C₇₃	—	2	4	no	—
190	C₂²⋊C₄×C₇₃	—	2	2	no	—
191	C₂²⋊C₄×C₇₃	—	2	2	no	—
192	C₂²⋊C₄×C₇₃	—	2	2	no	—
193	C₂²⋊C₄×C₇₃	—	2	2	no	—
194	C₂²⋊C₄×C₇₃	—	4	1	no	—
195	C₂²⋊C₄×C₇₃	—	4	1	no	—
196	C₄²×C₇₃	—	2	2	no	—
197	C₄²×C₇₃	—	2	2	no	—
198	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
199	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
200	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
201	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
202	C₂³×C₇₃	—	2	2	no	—
203	C₂³×C₇₃	—	2	2	no	—
204	C₂³×C₇₃	—	4	1	no	—
205	C₂³×C₇₃	#120	1	1	yes	characteristic
206	Q₈×C₇₃	—	2	4	no	—
207	Q₈×C₇₃	—	2	2	no	—
208	Q₈×C₇₃	—	4	8	no	—
209	Q₈×C₇₃	—	4	2	no	—
210	Q₈×C₇₃	—	4	2	no	—
211	Q₈×C₇₃	—	4	2	no	—
212	Q₈×C₇₃	AGL(1,ℤ/8)	1	4	yes	—
213	D₄×C₇₃	—	2	2	no	—
214	D₄×C₇₃	—	2	2	no	—
215	D₄×C₇₃	—	4	2	no	—
216	D₄×C₇₃	—	4	8	no	—
217	D₄×C₇₃	—	4	2	no	—
218	D₄×C₇₃	—	4	2	no	—
219	D₄×C₇₃	—	4	4	no	—
220	D₄×C₇₃	—	4	4	no	—
221	D₄×C₇₃	—	4	2	no	—
222	D₄×C₇₃	—	4	2	no	—
223	D₄×C₇₃	—	4	2	no	—
224	D₄×C₇₃	—	4	2	no	—
225	D₄×C₇₃	—	8	1	no	—
226	D₄×C₇₃	—	8	4	no	—
227	D₄×C₇₃	—	8	2	no	—
228	C₂×C₄×C₇₃	—	2	4	no	—
229	C₂×C₄×C₇₃	—	2	2	no	—
230	C₂×C₄×C₇₃	—	2	2	no	—
231	C₂×C₄×C₇₃	—	2	2	no	—
232	C₂×C₄×C₇₃	—	2	2	no	—
233	C₂×C₄×C₇₃	—	2	2	no	—
234	C₂×C₄×C₇₃	—	2	2	no	—
235	C₂×C₄×C₇₃	—	4	1	no	—
236	C₂×C₄×C₇₃	—	4	8	no	—
237	C₂×C₄×C₇₃	—	4	8	no	—
238	C₂×C₄×C₇₃	—	4	4	no	—
239	C₂×C₄×C₇₃	—	4	2	no	—
240	C₂×C₄×C₇₃	—	4	2	no	—
241	C₂×C₄×C₇₃	—	4	1	no	—
242	C₂×C₄×C₇₃	—	8	2	no	—
243	C₂×C₄×C₇₃	—	8	1	no	—
244	C₂×C₄×C₇₃	#120	1	1	yes	characteristic
245	C₂×C₄×C₇₃	#120	1	1	yes	characteristic
246	C₂×C₄×C₇₃	#120	1	1	yes	characteristic
247	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
248	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
249	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
250	C₈×C₇₃	—	2	2	no	—
251	C₈×C₇₃	—	4	1	no	—
252	C₈×C₇₃	—	4	2	no	—
253	C₈×C₇₃	—	4	2	no	—
254	C₂²×C₇₃	—	2	1	no	—
255	C₂²×C₇₃	—	2	1	no	—
256	C₂²×C₇₃	—	2	1	no	—
257	C₂²×C₇₃	—	4	2	no	—
258	C₂²×C₇₃	—	4	2	no	—
259	C₂²×C₇₃	—	4	2	no	—
260	C₂²×C₇₃	—	4	2	no	—
261	C₂²×C₇₃	—	4	2	no	—
262	C₂²×C₇₃	—	4	2	no	—
263	C₂²×C₇₃	—	8	1	no	—
264	C₂²×C₇₃	—	8	1	no	—
265	C₂²×C₇₃	—	8	1	no	—
266	C₂²×C₇₃	C₂×#120	1	1	yes	characteristic
267	C₄×C₇₃	—	2	4	no	—
268	C₄×C₇₃	—	2	1	no	—
269	C₄×C₇₃	—	2	1	no	—
270	C₄×C₇₃	—	2	1	no	—
271	C₄×C₇₃	—	2	1	no	—
272	C₄×C₇₃	—	4	2	no	—
273	C₄×C₇₃	—	4	2	no	—
274	C₄×C₇₃	—	4	2	no	—
275	C₄×C₇₃	—	8	1	no	—
276	C₄×C₇₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
277	C₄×C₇₃	#577	1	2	yes	—
278	#18610	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
279	C₂×C₇₃	—	4	1	no	—
280	C₂×C₇₃	—	8	2	no	—
281	C₂×C₇₃	—	8	2	no	—
282	C₂×C₇₃	—	16	1	no	—
283	C₂×C₇₃	#3003	1	1	yes	characteristic
284	C₂×C₇₃	#3010	1	1	yes	characteristic
285	C₂×C₇₃	#3018	1	1	yes	characteristic
286	#3497	C₂×C₇₃	1	1	yes	characteristic, complemented
287	#3214	C₂×C₇₃	1	1	yes	characteristic, complemented
288	#3184	C₂×C₇₃	1	1	yes	characteristic, complemented
289	#3103	C₂×C₇₃	1	1	yes	characteristic, complemented
290	#1651	C₂×C₇₃	1	2	yes	complemented
291	#1642	C₂×C₇₃	1	2	yes	complemented
292	#1627	C₂×C₇₃	1	2	yes	complemented
293	#1621	C₂×C₇₃	1	2	yes	complemented
294	#1553	C₂×C₇₃	1	1	yes	characteristic, complemented
295	#1491	C₂×C₇₃	1	1	yes	characteristic, complemented
296	#1484	C₂×C₇₃	1	1	yes	characteristic, complemented
297	C₇₃	#18610	1	1	yes	characteristic, direct product factor, Sylow
298	C₂×2₋¹⁺⁴	—	2	1	no	—
299	#550	—	2	1	no	—
300	#550	C₂²×C₇₃	1	2	yes	—
301	D₄×Q₈	—	2	1	no	—
302	D₄×Q₈	C₂²×C₇₃	1	2	yes	—
303	#548	—	2	2	no	—
304	#548	—	2	2	no	—
305	#537	—	2	2	no	—
306	#537	—	2	1	no	—
307	#532	—	2	2	no	—
308	#532	C₂²×C₇₃	1	1	yes	characteristic
309	#532	C₂²×C₇₃	1	1	yes	characteristic
310	#532	C₂²×C₇₃	1	1	yes	characteristic
311	C₂×C₄×Q₈	C₂²×C₇₃	1	1	yes	characteristic
312	#498	C₂²×C₇₃	1	1	yes	characteristic
313	#496	—	2	1	no	—
314	#493	C₂²×C₇₃	1	1	yes	characteristic
315	#489	—	2	1	no	—
316	#486	C₂²×C₇₃	1	1	yes	characteristic
317	#486	C₂²×C₇₃	1	1	yes	characteristic
318	#481	—	2	1	no	—
319	#475	C₂²×C₇₃	1	2	yes	—
320	#469	—	2	2	no	—
321	#461	C₂²×C₇₃	1	2	yes	—
322	#460	C₂²×C₇₃	1	2	yes	—
323	#459	C₂²×C₇₃	1	2	yes	—
324	#449	—	2	2	no	—
325	#448	—	2	1	no	—
326	#442	—	2	2	no	—
327	C₄×SD₁₆	—	2	2	no	—
328	#432	C₂²×C₇₃	1	1	yes	characteristic
329	#431	C₂²×C₇₃	1	1	yes	characteristic
330	C₄×M₁₆	C₂²×C₇₃	1	1	yes	characteristic
331	#332	C₂²×C₇₃	1	2	yes	—
332	#331	C₂²×C₇₃	1	2	yes	—
333	Q₈⋊C₈	C₂²×C₇₃	1	2	yes	—
334	Q₈⋊C₈	C₂²×C₇₃	1	2	yes	—
335	D₄⋊C₈	C₂²×C₇₃	1	2	yes	—
336	D₄⋊C₈	C₂²×C₇₃	1	2	yes	—
337	2₋¹⁺⁴	—	4	8	no	—
338	C₂×#41	—	2	4	no	—
339	C₂×#41	—	2	2	no	—
340	C₂×#41	—	2	2	no	—
341	C₂×#41	—	2	1	no	—
342	C₂×#41	—	2	1	no	—
343	C₂×#41	—	2	1	no	—
344	C₂²×Q₈	—	2	2	no	—
345	C₂²×Q₈	—	2	2	no	—
346	C₂²×Q₈	D₄×C₇₃	1	1	yes	characteristic
347	C₂×SD₁₆	—	2	2	no	—
348	C₂×SD₁₆	—	2	2	no	—
349	C₂×D₈	—	2	2	no	—
350	C₂×D₈	—	2	2	no	—
351	C₂×M₁₆	—	2	1	no	—
352	C₄⋊Q₈	—	2	2	no	—
353	C₄⋊Q₈	D₄×C₇₃	1	1	yes	characteristic
354	C₄⋊Q₈	C₂³×C₇₃	1	1	yes	characteristic
355	C₄⋊Q₈	C₂³×C₇₃	1	1	yes	characteristic
356	#127	—	2	2	no	—
357	#127	D₄×C₇₃	1	1	yes	characteristic
358	#127	C₂³×C₇₃	1	1	yes	characteristic
359	#127	C₂³×C₇₃	1	1	yes	characteristic
360	#124	—	2	4	no	—
361	#124	—	2	1	no	—
362	#124	—	2	1	no	—
363	#124	—	2	1	no	—
364	C₂²⋊Q₈	—	2	2	no	—
365	C₂²⋊Q₈	—	2	4	no	—
366	C₂²⋊Q₈	—	2	2	no	—
367	C₂²⋊Q₈	—	2	4	no	—
368	#121	—	2	4	no	—
369	#121	—	2	2	no	—
370	#121	—	2	4	no	—
371	#121	—	2	4	no	—
372	#121	—	2	1	no	—
373	#121	—	2	1	no	—
374	#121	—	2	2	no	—
375	#121	—	2	1	no	—
376	#121	—	2	1	no	—
377	#121	D₄×C₇₃	1	2	yes	—
378	#121	D₄×C₇₃	1	2	yes	—
379	C₄×Q₈	—	2	1	no	—
380	C₄×Q₈	—	2	1	no	—
381	C₄×Q₈	D₄×C₇₃	1	2	yes	—
382	C₄×Q₈	C₂³×C₇₃	1	2	yes	—
383	C₄×D₄	—	2	4	no	—
384	C₄×D₄	—	2	2	no	—
385	C₄×D₄	—	2	2	no	—
386	C₄×D₄	—	2	1	no	—
387	C₄×D₄	—	2	1	no	—
388	C₄×D₄	—	2	1	no	—
389	C₄×D₄	—	2	1	no	—
390	C₄×D₄	D₄×C₇₃	1	2	yes	—
391	C₄×D₄	C₂³×C₇₃	1	2	yes	—
392	C₂×C₄⋊C₄	—	2	1	no	—
393	C₂×C₄⋊C₄	D₄×C₇₃	1	1	yes	characteristic
394	C₂×C₄²	—	2	1	no	—
395	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
396	#106	—	2	2	no	—
397	#106	—	2	2	no	—
398	C₄⋊C₈	C₂³×C₇₃	1	2	yes	—
399	C₄⋊C₈	C₂³×C₇₃	1	2	yes	—
400	#103	—	2	2	no	—
401	#103	—	2	2	no	—
402	#102	—	2	2	no	—
403	#102	—	2	2	no	—
404	#102	—	2	2	no	—
405	#102	—	2	2	no	—
406	C₂²⋊C₈	—	2	1	no	—
407	C₂²⋊C₈	—	2	1	no	—
408	#97	—	2	1	no	—
409	#97	—	2	1	no	—
410	C₄×C₈	—	2	1	no	—
411	C₄×C₈	C₂³×C₇₃	1	1	yes	characteristic
412	C₄×C₈	C₂³×C₇₃	1	1	yes	characteristic
413	#41	—	4	16	no	—
414	#41	—	4	4	no	—
415	#41	—	4	4	no	—
416	#41	—	4	8	no	—
417	#41	—	4	4	no	—
418	#41	—	4	4	no	—
419	#41	—	8	2	no	—
420	C₂×Q₈	—	2	4	no	—
421	C₂×Q₈	—	2	4	no	—
422	C₂×Q₈	—	2	1	no	—
423	C₂×Q₈	—	2	1	no	—
424	C₂×Q₈	—	2	1	no	—
425	C₂×Q₈	—	2	1	no	—
426	C₂×Q₈	—	4	8	no	—
427	C₂×Q₈	—	4	4	no	—
428	C₂×Q₈	—	4	4	no	—
429	C₂×Q₈	C₂×D₄×C₇₃	1	2	yes	—
430	C₂×D₄	—	2	4	no	—
431	C₂×D₄	—	2	2	no	—
432	C₂×D₄	—	2	2	no	—
433	C₂×D₄	—	2	4	no	—
434	C₂×D₄	—	2	1	no	—
435	C₂×D₄	—	2	1	no	—
436	C₂×D₄	—	2	1	no	—
437	C₂×D₄	—	2	1	no	—
438	C₂×D₄	—	2	1	no	—
439	C₂×D₄	—	2	1	no	—
440	C₂×D₄	—	2	1	no	—
441	C₂×D₄	—	4	1	no	—
442	C₂×D₄	C₂×D₄×C₇₃	1	2	yes	—
443	C₂×D₄	C₂×D₄×C₇₃	1	2	yes	—
444	C₂²×C₄	—	2	1	no	—
445	C₂²×C₄	—	2	4	no	—
446	C₂²×C₄	—	2	4	no	—
447	C₂²×C₄	—	2	1	no	—
448	C₂²×C₄	—	2	2	no	—
449	C₂²×C₄	—	2	2	no	—
450	C₂²×C₄	—	4	1	no	—
451	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
452	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
453	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
454	SD₁₆	—	4	4	no	—
455	SD₁₆	—	8	2	no	—
456	D₈	—	4	4	no	—
457	D₈	—	8	2	no	—
458	M₁₆	—	4	2	no	—
459	C₂×C₈	—	2	1	no	—
460	C₂×C₈	—	2	2	no	—
461	C₂×C₈	—	2	1	no	—
462	C₂×C₈	—	2	2	no	—
463	C₄⋊C₄	—	2	4	no	—
464	C₄⋊C₄	—	2	2	no	—
465	C₄⋊C₄	—	2	1	no	—
466	C₄⋊C₄	—	2	1	no	—
467	C₄⋊C₄	—	2	2	no	—
468	C₄⋊C₄	—	2	1	no	—
469	C₄⋊C₄	—	2	1	no	—
470	C₄⋊C₄	—	2	1	no	—
471	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
472	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
473	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
474	C₂²⋊C₄	—	2	4	no	—
475	C₂²⋊C₄	—	2	4	no	—
476	C₂²⋊C₄	—	2	2	no	—
477	C₂²⋊C₄	—	2	2	no	—
478	C₂²⋊C₄	—	2	2	no	—
479	C₂²⋊C₄	—	2	2	no	—
480	C₂²⋊C₄	—	4	1	no	—
481	C₂²⋊C₄	—	4	1	no	—
482	C₄²	—	2	2	no	—
483	C₄²	—	2	2	no	—
484	C₄²	C₂×D₄×C₇₃	1	1	yes	characteristic
485	C₄²	C₂×D₄×C₇₃	1	1	yes	characteristic
486	C₄²	C₂×D₄×C₇₃	1	1	yes	characteristic
487	C₄²	C₂⁴×C₇₃	1	1	yes	characteristic
488	C₂³	—	2	2	no	—
489	C₂³	—	2	2	no	—
490	C₂³	—	4	1	no	—
491	C₂³	#120×C₇₃	1	1	yes	characteristic
492	Q₈	—	2	4	no	—
493	Q₈	—	2	2	no	—
494	Q₈	—	4	8	no	—
495	Q₈	—	4	2	no	—
496	Q₈	—	4	2	no	—
497	Q₈	—	4	2	no	—
498	Q₈	AGL(1,ℤ/8)×C₇₃	1	4	yes	—
499	D₄	—	2	2	no	—
500	D₄	—	2	2	no	—
501	D₄	—	4	2	no	—
502	D₄	—	4	8	no	—
503	D₄	—	4	2	no	—
504	D₄	—	4	2	no	—
505	D₄	—	4	4	no	—
506	D₄	—	4	4	no	—
507	D₄	—	4	2	no	—
508	D₄	—	4	2	no	—
509	D₄	—	4	2	no	—
510	D₄	—	4	2	no	—
511	D₄	—	8	1	no	—
512	D₄	—	8	4	no	—
513	D₄	—	8	2	no	—
514	C₂×C₄	—	2	4	no	—
515	C₂×C₄	—	2	2	no	—
516	C₂×C₄	—	2	2	no	—
517	C₂×C₄	—	2	2	no	—
518	C₂×C₄	—	2	2	no	—
519	C₂×C₄	—	2	2	no	—
520	C₂×C₄	—	2	2	no	—
521	C₂×C₄	—	4	1	no	—
522	C₂×C₄	—	4	8	no	—
523	C₂×C₄	—	4	8	no	—
524	C₂×C₄	—	4	4	no	—
525	C₂×C₄	—	4	2	no	—
526	C₂×C₄	—	4	2	no	—
527	C₂×C₄	—	4	1	no	—
528	C₂×C₄	—	8	2	no	—
529	C₂×C₄	—	8	1	no	—
530	C₂×C₄	#120×C₇₃	1	1	yes	characteristic
531	C₂×C₄	#120×C₇₃	1	1	yes	characteristic
532	C₂×C₄	#120×C₇₃	1	1	yes	characteristic
533	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
534	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
535	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
536	C₈	—	2	2	no	—
537	C₈	—	4	1	no	—
538	C₈	—	4	2	no	—
539	C₈	—	4	2	no	—
540	C₂²	—	2	1	no	—
541	C₂²	—	2	1	no	—
542	C₂²	—	2	1	no	—
543	C₂²	—	4	2	no	—
544	C₂²	—	4	2	no	—
545	C₂²	—	4	2	no	—
546	C₂²	—	4	2	no	—
547	C₂²	—	4	2	no	—
548	C₂²	—	4	2	no	—
549	C₂²	—	8	1	no	—
550	C₂²	—	8	1	no	—
551	C₂²	—	8	1	no	—
552	C₂²	C₂×#120×C₇₃	1	1	yes	characteristic
553	C₄	—	2	4	no	—
554	C₄	—	2	1	no	—
555	C₄	—	2	1	no	—
556	C₄	—	2	1	no	—
557	C₄	—	2	1	no	—
558	C₄	—	4	2	no	—
559	C₄	—	4	2	no	—
560	C₄	—	4	2	no	—
561	C₄	—	8	1	no	—
562	C₄	C₂×AGL(1,ℤ/8)×C₇₃	1	2	yes	—
563	C₄	#577×C₇₃	1	2	yes	—
564	C₂	—	4	1	no	—
565	C₂	—	8	2	no	—
566	C₂	—	8	2	no	—
567	C₂	—	16	1	no	—
568	C₂	C₇₃×#3003	1	1	yes	characteristic
569	C₂	C₇₃×#3010	1	1	yes	characteristic
570	C₂	C₇₃×#3018	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×#3497	C₂	semidirect
2. C₇₃×#3214	C₂	semidirect
3. C₇₃×#3184	C₂	semidirect
4. C₇₃×#3103	C₂	semidirect
5. C₇₃×#1651	C₂	semidirect
6. C₇₃×#1642	C₂	semidirect
7. C₇₃×#1627	C₂	semidirect
8. C₇₃×#1621	C₂	semidirect
9. C₇₃×#1553	C₂	semidirect
10. C₇₃×#1491	C₂	semidirect
11. C₇₃×#1484	C₂	semidirect
278. #18610	C₇₃	direct (N × H)
286. #3497	C₂×C₇₃	semidirect
287. #3214	C₂×C₇₃	semidirect
288. #3184	C₂×C₇₃	semidirect
289. #3103	C₂×C₇₃	semidirect
290. #1651	C₂×C₇₃	semidirect
291. #1642	C₂×C₇₃	semidirect
292. #1627	C₂×C₇₃	semidirect
293. #1621	C₂×C₇₃	semidirect
294. #1553	C₂×C₇₃	semidirect
295. #1491	C₂×C₇₃	semidirect
296. #1484	C₂×C₇₃	semidirect
297. C₇₃	#18610	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇₃×#3497	2
C₇₃×#3214	2
C₇₃×#3184	2
C₇₃×#3103	2
C₇₃×#1651	2
C₇₃×#1642	2
C₇₃×#1627	2
C₇₃×#1621	2
C₇₃×#1553	2
C₇₃×#1491	2
C₇₃×#1484	2
#18610	73

Subgroups — C73×#18610 #32928014

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#18610 #32928014