Subgroups — C₇₃×#19356 #32928760

Order 18688.

678 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₃×#3251	C₂	1	2	yes	maximal, complemented
2	C₇₃×#3147	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₃×#2966	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₃×#1686	C₂	1	2	yes	maximal, complemented
5	C₇₃×#1685	C₂	1	2	yes	maximal, complemented
6	C₇₃×#1670	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇₃×#1669	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇₃×#1668	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇₃×#1667	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇₃×#1567	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₃×#1557	C₂	1	2	yes	maximal, complemented
12	C₂×#135×C₇₃	—	2	1	no	—
13	C₂×#135×C₇₃	—	2	1	no	—
14	#532×C₇₃	C₂²	1	2	yes	—
15	#529×C₇₃	C₂²	1	1	yes	characteristic
16	#495×C₇₃	—	2	1	no	—
17	#495×C₇₃	—	2	1	no	—
18	#494×C₇₃	C₂²	1	1	yes	characteristic
19	#493×C₇₃	C₂²	1	1	yes	characteristic
20	#492×C₇₃	C₂²	1	2	yes	—
21	#478×C₇₃	—	2	2	no	—
22	#475×C₇₃	C₂²	1	2	yes	—
23	#474×C₇₃	C₂²	1	2	yes	—
24	#469×C₇₃	—	2	2	no	—
25	#468×C₇₃	—	2	2	no	—
26	#463×C₇₃	—	2	2	no	—
27	#460×C₇₃	C₂²	1	2	yes	—
28	#459×C₇₃	C₂²	1	2	yes	—
29	#446×C₇₃	C₂²	1	1	yes	characteristic
30	C₈×Q₈×C₇₃	C₂²	1	1	yes	characteristic
31	#436×C₇₃	C₂²	1	1	yes	characteristic
32	#435×C₇₃	—	2	1	no	—
33	C₈×D₄×C₇₃	—	2	1	no	—
34	C₈×D₄×C₇₃	C₂²	1	1	yes	characteristic
35	#433×C₇₃	—	2	1	no	—
36	#432×C₇₃	C₂²	1	1	yes	characteristic
37	#423×C₇₃	C₂²	1	2	yes	—
38	#405×C₇₃	—	2	1	no	—
39	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
40	#335×C₇₃	C₂²	1	2	yes	—
41	#335×C₇₃	C₂²	1	1	yes	characteristic
42	#335×C₇₃	C₂²	1	1	yes	characteristic
43	#332×C₇₃	C₂²	1	2	yes	—
44	#332×C₇₃	C₂²	1	2	yes	—
45	#331×C₇₃	C₂²	1	2	yes	—
46	#331×C₇₃	C₂²	1	2	yes	—
47	C₂×#41×C₇₃	—	2	2	no	—
48	#135×C₇₃	—	4	4	no	—
49	#135×C₇₃	—	4	4	no	—
50	C₂×Q₁₆×C₇₃	—	2	1	no	—
51	C₂×Q₁₆×C₇₃	—	2	1	no	—
52	C₂×SD₁₆×C₇₃	—	2	2	no	—
53	C₂×SD₁₆×C₇₃	—	2	2	no	—
54	C₂×SD₁₆×C₇₃	—	2	2	no	—
55	C₂×D₈×C₇₃	—	2	2	no	—
56	C₂×D₈×C₇₃	—	2	1	no	—
57	C₂×D₈×C₇₃	—	2	1	no	—
58	C₂×M₁₆×C₇₃	—	2	2	no	—
59	C₂×M₁₆×C₇₃	—	2	1	no	—
60	C₂²×C₈×C₇₃	—	2	1	no	—
61	C₂²×C₈×C₇₃	D₄	1	1	yes	characteristic
62	C₂²×C₈×C₇₃	D₄	1	1	yes	characteristic
63	C₄⋊Q₈×C₇₃	C₂³	1	2	yes	—
64	#127×C₇₃	C₂³	1	2	yes	—
65	#126×C₇₃	—	2	1	no	—
66	#125×C₇₃	D₄	1	1	yes	characteristic
67	#124×C₇₃	—	2	2	no	—
68	#124×C₇₃	D₄	1	1	yes	characteristic
69	#123×C₇₃	—	2	1	no	—
70	C₂²⋊Q₈×C₇₃	D₄	1	1	yes	characteristic
71	#121×C₇₃	—	2	2	no	—
72	#121×C₇₃	—	2	2	no	—
73	#121×C₇₃	D₄	1	1	yes	characteristic
74	C₄×Q₈×C₇₃	C₂³	1	1	yes	characteristic
75	C₄×D₄×C₇₃	—	2	1	no	—
76	C₄×D₄×C₇₃	—	2	2	no	—
77	C₄×D₄×C₇₃	—	2	2	no	—
78	C₄×D₄×C₇₃	C₂³	1	1	yes	characteristic
79	#117×C₇₃	—	2	1	no	—
80	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
81	#107×C₇₃	—	2	2	no	—
82	#106×C₇₃	—	2	2	no	—
83	C₄⋊C₈×C₇₃	—	2	1	no	—
84	C₄⋊C₈×C₇₃	—	2	1	no	—
85	C₄⋊C₈×C₇₃	—	2	2	no	—
86	C₄⋊C₈×C₇₃	C₂³	1	2	yes	—
87	C₄⋊C₈×C₇₃	C₂³	1	2	yes	—
88	C₄⋊C₈×C₇₃	C₂³	1	1	yes	characteristic
89	C₄⋊C₈×C₇₃	C₂³	1	1	yes	characteristic
90	#103×C₇₃	—	2	2	no	—
91	#102×C₇₃	—	2	2	no	—
92	#102×C₇₃	—	2	2	no	—
93	#102×C₇₃	—	2	2	no	—
94	C₂²⋊C₈×C₇₃	—	2	1	no	—
95	C₂²⋊C₈×C₇₃	—	2	1	no	—
96	C₂²⋊C₈×C₇₃	—	2	1	no	—
97	#97×C₇₃	—	2	1	no	—
98	#97×C₇₃	—	2	1	no	—
99	C₄×C₈×C₇₃	—	2	1	no	—
100	C₄×C₈×C₇₃	D₄	1	1	yes	characteristic
101	C₄×C₈×C₇₃	D₄	1	1	yes	characteristic
102	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
103	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
104	#41×C₇₃	—	4	4	no	—
105	#41×C₇₃	—	4	4	no	—
106	C₂×Q₈×C₇₃	—	2	2	no	—
107	C₂×Q₈×C₇₃	C₂×D₄	1	1	yes	characteristic
108	C₂×D₄×C₇₃	—	2	1	no	—
109	C₂×D₄×C₇₃	—	2	2	no	—
110	C₂×D₄×C₇₃	—	2	2	no	—
111	C₂×D₄×C₇₃	—	2	2	no	—
112	C₂×D₄×C₇₃	—	4	2	no	—
113	C₂×D₄×C₇₃	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₇₃	—	2	1	no	—
115	C₂²×C₄×C₇₃	—	4	2	no	—
116	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₇₃	#41	1	1	yes	characteristic
119	Q₁₆×C₇₃	—	4	2	no	—
120	Q₁₆×C₇₃	—	4	2	no	—
121	SD₁₆×C₇₃	—	4	4	no	—
122	SD₁₆×C₇₃	—	4	4	no	—
123	SD₁₆×C₇₃	—	8	2	no	—
124	D₈×C₇₃	—	4	2	no	—
125	D₈×C₇₃	—	4	2	no	—
126	D₈×C₇₃	—	8	2	no	—
127	M₁₆×C₇₃	—	4	2	no	—
128	M₁₆×C₇₃	—	8	2	no	—
129	C₂×C₈×C₇₃	—	2	2	no	—
130	C₂×C₈×C₇₃	—	2	2	no	—
131	C₂×C₈×C₇₃	—	2	1	no	—
132	C₂×C₈×C₇₃	—	2	1	no	—
133	C₂×C₈×C₇₃	—	2	2	no	—
134	C₂×C₈×C₇₃	—	2	2	no	—
135	C₂×C₈×C₇₃	—	4	2	no	—
136	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
137	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
138	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
139	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
140	C₄⋊C₄×C₇₃	—	2	1	no	—
141	C₄⋊C₄×C₇₃	—	2	1	no	—
142	C₄⋊C₄×C₇₃	—	2	1	no	—
143	C₄⋊C₄×C₇₃	—	2	1	no	—
144	C₄⋊C₄×C₇₃	—	2	2	no	—
145	C₄⋊C₄×C₇₃	—	2	2	no	—
146	C₄⋊C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
147	C₄⋊C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
148	C₂²⋊C₄×C₇₃	—	2	1	no	—
149	C₂²⋊C₄×C₇₃	—	2	1	no	—
150	C₂²⋊C₄×C₇₃	—	2	1	no	—
151	C₂²⋊C₄×C₇₃	—	2	1	no	—
152	C₂²⋊C₄×C₇₃	—	2	1	no	—
153	C₂²⋊C₄×C₇₃	—	4	2	no	—
154	C₂²⋊C₄×C₇₃	—	4	2	no	—
155	C₄²×C₇₃	—	2	1	no	—
156	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
157	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
158	C₄²×C₇₃	#41	1	1	yes	characteristic
159	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
160	C₂³×C₇₃	—	2	1	no	—
161	C₂³×C₇₃	—	4	2	no	—
162	C₂³×C₇₃	#121	1	1	yes	characteristic
163	Q₈×C₇₃	—	2	1	no	—
164	Q₈×C₇₃	—	2	1	no	—
165	Q₈×C₇₃	—	4	2	no	—
166	Q₈×C₇₃	—	4	2	no	—
167	D₄×C₇₃	—	2	1	no	—
168	D₄×C₇₃	—	2	1	no	—
169	D₄×C₇₃	—	4	2	no	—
170	D₄×C₇₃	—	4	2	no	—
171	D₄×C₇₃	—	4	2	no	—
172	D₄×C₇₃	—	4	2	no	—
173	D₄×C₇₃	—	4	2	no	—
174	D₄×C₇₃	—	8	2	no	—
175	D₄×C₇₃	—	8	4	no	—
176	C₂×C₄×C₇₃	—	2	1	no	—
177	C₂×C₄×C₇₃	—	2	1	no	—
178	C₂×C₄×C₇₃	—	2	1	no	—
179	C₂×C₄×C₇₃	—	2	1	no	—
180	C₂×C₄×C₇₃	—	2	1	no	—
181	C₂×C₄×C₇₃	—	2	1	no	—
182	C₂×C₄×C₇₃	—	2	1	no	—
183	C₂×C₄×C₇₃	—	4	1	no	—
184	C₂×C₄×C₇₃	—	4	1	no	—
185	C₂×C₄×C₇₃	—	4	1	no	—
186	C₂×C₄×C₇₃	—	4	2	no	—
187	C₂×C₄×C₇₃	—	8	4	no	—
188	C₂×C₄×C₇₃	#121	1	1	yes	characteristic
189	C₂×C₄×C₇₃	#121	1	1	yes	characteristic
190	C₂×C₄×C₇₃	#121	1	1	yes	characteristic
191	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
192	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
193	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
194	C₈×C₇₃	—	2	1	no	—
195	C₈×C₇₃	—	2	1	no	—
196	C₈×C₇₃	—	4	1	no	—
197	C₈×C₇₃	—	4	1	no	—
198	C₈×C₇₃	—	4	2	no	—
199	C₈×C₇₃	—	4	2	no	—
200	C₈×C₇₃	AGL(1,ℤ/8)	1	2	yes	—
201	C₈×C₇₃	AGL(1,ℤ/8)	1	2	yes	—
202	C₂²×C₇₃	—	2	1	no	—
203	C₂²×C₇₃	—	2	1	no	—
204	C₂²×C₇₃	—	2	1	no	—
205	C₂²×C₇₃	—	4	1	no	—
206	C₂²×C₇₃	—	4	1	no	—
207	C₂²×C₇₃	—	4	1	no	—
208	C₂²×C₇₃	—	8	2	no	—
209	C₂²×C₇₃	—	8	2	no	—
210	C₂²×C₇₃	—	8	2	no	—
211	C₂²×C₇₃	C₂×#121	1	1	yes	characteristic
212	C₄×C₇₃	—	2	1	no	—
213	C₄×C₇₃	—	2	1	no	—
214	C₄×C₇₃	—	2	1	no	—
215	C₄×C₇₃	—	2	1	no	—
216	C₄×C₇₃	—	4	1	no	—
217	C₄×C₇₃	—	4	1	no	—
218	C₄×C₇₃	—	4	1	no	—
219	C₄×C₇₃	—	8	2	no	—
220	C₄×C₇₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
221	C₄×C₇₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
222	C₄×C₇₃	#576	1	1	yes	characteristic
223	C₄×C₇₃	#578	1	1	yes	characteristic
224	#19356	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
225	C₂×C₇₃	—	4	1	no	—
226	C₂×C₇₃	—	8	1	no	—
227	C₂×C₇₃	—	16	2	no	—
228	C₂×C₇₃	#3038	1	1	yes	characteristic
229	C₂×C₇₃	#3061	1	1	yes	characteristic
230	C₂×C₇₃	#3067	1	1	yes	characteristic
231	#3251	C₂×C₇₃	1	2	yes	complemented
232	#3147	C₂×C₇₃	1	1	yes	characteristic, complemented
233	#2966	C₂×C₇₃	1	1	yes	characteristic, complemented
234	#1686	C₂×C₇₃	1	2	yes	complemented
235	#1685	C₂×C₇₃	1	2	yes	complemented
236	#1670	C₂×C₇₃	1	1	yes	characteristic, complemented
237	#1669	C₂×C₇₃	1	1	yes	characteristic, complemented
238	#1668	C₂×C₇₃	1	1	yes	characteristic, complemented
239	#1667	C₂×C₇₃	1	1	yes	characteristic, complemented
240	#1567	C₂×C₇₃	1	1	yes	characteristic, complemented
241	#1557	C₂×C₇₃	1	2	yes	complemented
242	C₇₃	#19356	1	1	yes	characteristic, direct product factor, Sylow
243	C₂×#135	—	2	1	no	—
244	C₂×#135	—	2	1	no	—
245	#532	C₂²×C₇₃	1	2	yes	—
246	#529	C₂²×C₇₃	1	1	yes	characteristic
247	#495	—	2	1	no	—
248	#495	—	2	1	no	—
249	#494	C₂²×C₇₃	1	1	yes	characteristic
250	#493	C₂²×C₇₃	1	1	yes	characteristic
251	#492	C₂²×C₇₃	1	2	yes	—
252	#478	—	2	2	no	—
253	#475	C₂²×C₇₃	1	2	yes	—
254	#474	C₂²×C₇₃	1	2	yes	—
255	#469	—	2	2	no	—
256	#468	—	2	2	no	—
257	#463	—	2	2	no	—
258	#460	C₂²×C₇₃	1	2	yes	—
259	#459	C₂²×C₇₃	1	2	yes	—
260	#446	C₂²×C₇₃	1	1	yes	characteristic
261	C₈×Q₈	C₂²×C₇₃	1	1	yes	characteristic
262	#436	C₂²×C₇₃	1	1	yes	characteristic
263	#435	—	2	1	no	—
264	C₈×D₄	—	2	1	no	—
265	C₈×D₄	C₂²×C₇₃	1	1	yes	characteristic
266	#433	—	2	1	no	—
267	#432	C₂²×C₇₃	1	1	yes	characteristic
268	#423	C₂²×C₇₃	1	2	yes	—
269	#405	—	2	1	no	—
270	C₂×C₄×C₈	C₂²×C₇₃	1	1	yes	characteristic
271	#335	C₂²×C₇₃	1	1	yes	characteristic
272	#335	C₂²×C₇₃	1	1	yes	characteristic
273	#335	C₂²×C₇₃	1	2	yes	—
274	#332	C₂²×C₇₃	1	2	yes	—
275	#332	C₂²×C₇₃	1	2	yes	—
276	#331	C₂²×C₇₃	1	2	yes	—
277	#331	C₂²×C₇₃	1	2	yes	—
278	C₂×#41	—	2	2	no	—
279	#135	—	4	4	no	—
280	#135	—	4	4	no	—
281	C₂×Q₁₆	—	2	1	no	—
282	C₂×Q₁₆	—	2	1	no	—
283	C₂×SD₁₆	—	2	2	no	—
284	C₂×SD₁₆	—	2	2	no	—
285	C₂×SD₁₆	—	2	2	no	—
286	C₂×D₈	—	2	2	no	—
287	C₂×D₈	—	2	1	no	—
288	C₂×D₈	—	2	1	no	—
289	C₂×M₁₆	—	2	2	no	—
290	C₂×M₁₆	—	2	1	no	—
291	C₂²×C₈	—	2	1	no	—
292	C₂²×C₈	D₄×C₇₃	1	1	yes	characteristic
293	C₂²×C₈	D₄×C₇₃	1	1	yes	characteristic
294	C₄⋊Q₈	C₂³×C₇₃	1	2	yes	—
295	#127	C₂³×C₇₃	1	2	yes	—
296	#126	—	2	1	no	—
297	#125	D₄×C₇₃	1	1	yes	characteristic
298	#124	—	2	2	no	—
299	#124	D₄×C₇₃	1	1	yes	characteristic
300	#123	—	2	1	no	—
301	C₂²⋊Q₈	D₄×C₇₃	1	1	yes	characteristic
302	#121	—	2	2	no	—
303	#121	—	2	2	no	—
304	#121	D₄×C₇₃	1	1	yes	characteristic
305	C₄×Q₈	C₂³×C₇₃	1	1	yes	characteristic
306	C₄×D₄	—	2	1	no	—
307	C₄×D₄	—	2	2	no	—
308	C₄×D₄	—	2	2	no	—
309	C₄×D₄	C₂³×C₇₃	1	1	yes	characteristic
310	#117	—	2	1	no	—
311	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
312	#107	—	2	2	no	—
313	#106	—	2	2	no	—
314	C₄⋊C₈	—	2	1	no	—
315	C₄⋊C₈	—	2	1	no	—
316	C₄⋊C₈	—	2	2	no	—
317	C₄⋊C₈	C₂³×C₇₃	1	1	yes	characteristic
318	C₄⋊C₈	C₂³×C₇₃	1	1	yes	characteristic
319	C₄⋊C₈	C₂³×C₇₃	1	2	yes	—
320	C₄⋊C₈	C₂³×C₇₃	1	2	yes	—
321	#103	—	2	2	no	—
322	#102	—	2	2	no	—
323	#102	—	2	2	no	—
324	#102	—	2	2	no	—
325	C₂²⋊C₈	—	2	1	no	—
326	C₂²⋊C₈	—	2	1	no	—
327	C₂²⋊C₈	—	2	1	no	—
328	#97	—	2	1	no	—
329	#97	—	2	1	no	—
330	C₄×C₈	—	2	1	no	—
331	C₄×C₈	D₄×C₇₃	1	1	yes	characteristic
332	C₄×C₈	D₄×C₇₃	1	1	yes	characteristic
333	C₄×C₈	C₂³×C₇₃	1	1	yes	characteristic
334	C₄×C₈	C₂³×C₇₃	1	1	yes	characteristic
335	#41	—	4	4	no	—
336	#41	—	4	4	no	—
337	C₂×Q₈	—	2	2	no	—
338	C₂×Q₈	C₂×D₄×C₇₃	1	1	yes	characteristic
339	C₂×D₄	—	2	1	no	—
340	C₂×D₄	—	2	2	no	—
341	C₂×D₄	—	2	2	no	—
342	C₂×D₄	—	2	2	no	—
343	C₂×D₄	—	4	2	no	—
344	C₂×D₄	C₂×D₄×C₇₃	1	1	yes	characteristic
345	C₂²×C₄	—	2	1	no	—
346	C₂²×C₄	—	4	2	no	—
347	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
348	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
349	C₂²×C₄	#41×C₇₃	1	1	yes	characteristic
350	Q₁₆	—	4	2	no	—
351	Q₁₆	—	4	2	no	—
352	SD₁₆	—	4	4	no	—
353	SD₁₆	—	4	4	no	—
354	SD₁₆	—	8	2	no	—
355	D₈	—	4	2	no	—
356	D₈	—	4	2	no	—
357	D₈	—	8	2	no	—
358	M₁₆	—	4	2	no	—
359	M₁₆	—	8	2	no	—
360	C₂×C₈	—	2	2	no	—
361	C₂×C₈	—	2	2	no	—
362	C₂×C₈	—	2	1	no	—
363	C₂×C₈	—	2	1	no	—
364	C₂×C₈	—	2	2	no	—
365	C₂×C₈	—	2	2	no	—
366	C₂×C₈	—	4	2	no	—
367	C₂×C₈	C₂×D₄×C₇₃	1	1	yes	characteristic
368	C₂×C₈	C₂×D₄×C₇₃	1	1	yes	characteristic
369	C₂×C₈	C₂×D₄×C₇₃	1	1	yes	characteristic
370	C₂×C₈	C₂×D₄×C₇₃	1	1	yes	characteristic
371	C₄⋊C₄	—	2	1	no	—
372	C₄⋊C₄	—	2	1	no	—
373	C₄⋊C₄	—	2	1	no	—
374	C₄⋊C₄	—	2	1	no	—
375	C₄⋊C₄	—	2	2	no	—
376	C₄⋊C₄	—	2	2	no	—
377	C₄⋊C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
378	C₄⋊C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
379	C₂²⋊C₄	—	2	1	no	—
380	C₂²⋊C₄	—	2	1	no	—
381	C₂²⋊C₄	—	2	1	no	—
382	C₂²⋊C₄	—	2	1	no	—
383	C₂²⋊C₄	—	2	1	no	—
384	C₂²⋊C₄	—	4	2	no	—
385	C₂²⋊C₄	—	4	2	no	—
386	C₄²	—	2	1	no	—
387	C₄²	C₂×D₄×C₇₃	1	1	yes	characteristic
388	C₄²	C₂×D₄×C₇₃	1	1	yes	characteristic
389	C₄²	#41×C₇₃	1	1	yes	characteristic
390	C₄²	C₂⁴×C₇₃	1	1	yes	characteristic
391	C₂³	—	2	1	no	—
392	C₂³	—	4	2	no	—
393	C₂³	#121×C₇₃	1	1	yes	characteristic
394	Q₈	—	2	1	no	—
395	Q₈	—	2	1	no	—
396	Q₈	—	4	2	no	—
397	Q₈	—	4	2	no	—
398	D₄	—	2	1	no	—
399	D₄	—	2	1	no	—
400	D₄	—	4	2	no	—
401	D₄	—	4	2	no	—
402	D₄	—	4	2	no	—
403	D₄	—	4	2	no	—
404	D₄	—	4	2	no	—
405	D₄	—	8	2	no	—
406	D₄	—	8	4	no	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	2	1	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	2	1	no	—
414	C₂×C₄	—	4	1	no	—
415	C₂×C₄	—	4	1	no	—
416	C₂×C₄	—	4	1	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	8	4	no	—
419	C₂×C₄	#121×C₇₃	1	1	yes	characteristic
420	C₂×C₄	#121×C₇₃	1	1	yes	characteristic
421	C₂×C₄	#121×C₇₃	1	1	yes	characteristic
422	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
423	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
424	C₂×C₄	C₂×#41×C₇₃	1	1	yes	characteristic
425	C₈	—	2	1	no	—
426	C₈	—	2	1	no	—
427	C₈	—	4	1	no	—
428	C₈	—	4	1	no	—
429	C₈	—	4	2	no	—
430	C₈	—	4	2	no	—
431	C₈	AGL(1,ℤ/8)×C₇₃	1	2	yes	—
432	C₈	AGL(1,ℤ/8)×C₇₃	1	2	yes	—
433	C₂²	—	2	1	no	—
434	C₂²	—	2	1	no	—
435	C₂²	—	2	1	no	—
436	C₂²	—	4	1	no	—
437	C₂²	—	4	1	no	—
438	C₂²	—	4	1	no	—
439	C₂²	—	8	2	no	—
440	C₂²	—	8	2	no	—
441	C₂²	—	8	2	no	—
442	C₂²	C₂×#121×C₇₃	1	1	yes	characteristic
443	C₄	—	2	1	no	—
444	C₄	—	2	1	no	—
445	C₄	—	2	1	no	—
446	C₄	—	2	1	no	—
447	C₄	—	4	1	no	—
448	C₄	—	4	1	no	—
449	C₄	—	4	1	no	—
450	C₄	—	8	2	no	—
451	C₄	C₂×AGL(1,ℤ/8)×C₇₃	1	1	yes	characteristic
452	C₄	C₂×AGL(1,ℤ/8)×C₇₃	1	1	yes	characteristic
453	C₄	#576×C₇₃	1	1	yes	characteristic
454	C₄	#578×C₇₃	1	1	yes	characteristic
455	C₂	—	4	1	no	—
456	C₂	—	8	1	no	—
457	C₂	—	16	2	no	—
458	C₂	C₇₃×#3038	1	1	yes	characteristic
459	C₂	C₇₃×#3061	1	1	yes	characteristic
460	C₂	C₇₃×#3067	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇₃	C₂×#121
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×#3251	C₂	semidirect
2. C₇₃×#3147	C₂	semidirect
3. C₇₃×#2966	C₂	semidirect
4. C₇₃×#1686	C₂	semidirect
5. C₇₃×#1685	C₂	semidirect
6. C₇₃×#1670	C₂	semidirect
7. C₇₃×#1669	C₂	semidirect
8. C₇₃×#1668	C₂	semidirect
9. C₇₃×#1667	C₂	semidirect
10. C₇₃×#1567	C₂	semidirect
11. C₇₃×#1557	C₂	semidirect
224. #19356	C₇₃	direct (N × H)
231. #3251	C₂×C₇₃	semidirect
232. #3147	C₂×C₇₃	semidirect
233. #2966	C₂×C₇₃	semidirect
234. #1686	C₂×C₇₃	semidirect
235. #1685	C₂×C₇₃	semidirect
236. #1670	C₂×C₇₃	semidirect
237. #1669	C₂×C₇₃	semidirect
238. #1668	C₂×C₇₃	semidirect
239. #1667	C₂×C₇₃	semidirect
240. #1567	C₂×C₇₃	semidirect
241. #1557	C₂×C₇₃	semidirect
242. C₇₃	#19356	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×#3251	2
C₇₃×#3147	2
C₇₃×#2966	2
C₇₃×#1686	2
C₇₃×#1685	2
C₇₃×#1670	2
C₇₃×#1669	2
C₇₃×#1668	2
C₇₃×#1667	2
C₇₃×#1567	2
C₇₃×#1557	2
#19356	73

Subgroups — C73×#19356 #32928760

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#19356 #32928760