Subgroups — C₇₃×#18309 #32927713

Order 18688.

1168 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₃×#3449	C₂	1	1	yes	maximal, characteristic
2	C₇₃×#3227	C₂	1	2	yes	maximal, complemented
3	C₇₃×#2628	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₃×#1616	C₂	1	4	yes	maximal, complemented
5	C₇₃×#1613	C₂	1	4	yes	maximal, complemented
6	C₇₃×#1517	C₂	1	2	yes	maximal, complemented
7	C₇₃×#1458	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#41×C₇₃	—	2	1	no	—
9	#537×C₇₃	—	2	1	no	—
10	#537×C₇₃	C₂²	1	2	yes	—
11	#536×C₇₃	—	2	2	no	—
12	#535×C₇₃	—	2	2	no	—
13	#534×C₇₃	—	2	1	no	—
14	#534×C₇₃	C₂²	1	2	yes	—
15	#532×C₇₃	—	2	1	no	—
16	#532×C₇₃	C₂²	1	2	yes	—
17	C₂×C₄⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic, complemented
18	#525×C₇₃	—	2	4	no	—
19	C₂×#117×C₇₃	C₂²	1	1	yes	characteristic
20	#498×C₇₃	—	2	2	no	—
21	#486×C₇₃	—	2	2	no	—
22	#481×C₇₃	C₂²	1	8	yes	complemented
23	#476×C₇₃	—	2	4	no	—
24	#431×C₇₃	C₂²	1	2	yes	complemented
25	#400×C₇₃	C₂²	1	2	yes	complemented
26	#399×C₇₃	C₂²	1	2	yes	—
27	#395×C₇₃	—	2	1	no	—
28	#393×C₇₃	—	2	1	no	—
29	#389×C₇₃	—	2	1	no	—
30	#382×C₇₃	C₂²	1	1	yes	characteristic, complemented
31	#380×C₇₃	—	2	1	no	—
32	#327×C₇₃	C₂²	1	8	yes	complemented
33	#324×C₇₃	C₂²	1	2	yes	complemented
34	#323×C₇₃	C₂²	1	2	yes	—
35	C₂×#41×C₇₃	—	2	2	no	—
36	C₂×#41×C₇₃	—	2	2	no	—
37	C₂×#41×C₇₃	—	2	2	no	—
38	C₂×#41×C₇₃	—	2	2	no	—
39	C₂×#41×C₇₃	—	4	4	no	—
40	C₂×#41×C₇₃	—	4	4	no	—
41	C₂²×Q₈×C₇₃	—	2	1	no	—
42	C₂²×Q₈×C₇₃	—	2	1	no	—
43	C₂²×D₄×C₇₃	—	2	1	no	—
44	C₂²×D₄×C₇₃	—	2	2	no	—
45	C₂³×C₄×C₇₃	—	2	2	no	—
46	C₂³×C₄×C₇₃	D₄	1	1	yes	characteristic
47	C₄⋊Q₈×C₇₃	—	2	1	no	—
48	C₄⋊Q₈×C₇₃	—	2	2	no	—
49	C₄⋊Q₈×C₇₃	—	2	2	no	—
50	C₄⋊Q₈×C₇₃	D₄	1	2	yes	—
51	#127×C₇₃	—	2	1	no	—
52	#127×C₇₃	D₄	1	2	yes	—
53	#124×C₇₃	—	2	2	no	—
54	#124×C₇₃	—	2	2	no	—
55	#123×C₇₃	—	2	4	no	—
56	#123×C₇₃	—	2	4	no	—
57	C₂²⋊Q₈×C₇₃	—	2	4	no	—
58	C₂²⋊Q₈×C₇₃	—	2	4	no	—
59	#121×C₇₃	—	2	4	no	—
60	#121×C₇₃	—	2	4	no	—
61	#121×C₇₃	—	2	2	no	—
62	#121×C₇₃	—	2	2	no	—
63	#121×C₇₃	—	2	2	no	—
64	#121×C₇₃	C₂³	1	4	yes	—
65	#120×C₇₃	—	2	4	no	—
66	#120×C₇₃	—	2	4	no	—
67	C₄×D₄×C₇₃	—	2	2	no	—
68	C₄×D₄×C₇₃	—	2	2	no	—
69	C₄×D₄×C₇₃	—	2	2	no	—
70	C₄×D₄×C₇₃	D₄	1	4	yes	—
71	#117×C₇₃	—	2	2	no	—
72	#117×C₇₃	—	2	2	no	—
73	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
74	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
75	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
76	C₂×C₄⋊C₄×C₇₃	D₄	1	1	yes	characteristic
77	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
78	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
79	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
80	C₂×C₂²⋊C₄×C₇₃	D₄	1	1	yes	characteristic
81	C₂×C₂²⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
82	C₂×C₄²×C₇₃	D₄	1	1	yes	characteristic
83	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
84	#106×C₇₃	—	2	8	no	—
85	C₄⋊C₈×C₇₃	—	2	2	no	—
86	#102×C₇₃	—	2	8	no	—
87	C₂²⋊C₈×C₇₃	C₂³	1	4	yes	—
88	C₄×C₈×C₇₃	—	2	2	no	—
89	#95×C₇₃	—	2	2	no	—
90	#95×C₇₃	—	2	1	no	—
91	#95×C₇₃	—	2	2	no	—
92	#95×C₇₃	C₂³	1	2	yes	—
93	C₂⁴×C₇₃	—	2	2	no	—
94	C₂⁴×C₇₃	C₂×D₄	1	1	yes	characteristic
95	#41×C₇₃	—	4	4	no	—
96	#41×C₇₃	—	4	8	no	—
97	#41×C₇₃	—	4	8	no	—
98	#41×C₇₃	—	4	4	no	—
99	#41×C₇₃	—	4	4	no	—
100	#41×C₇₃	—	4	4	no	—
101	C₂×Q₈×C₇₃	—	2	2	no	—
102	C₂×Q₈×C₇₃	—	2	2	no	—
103	C₂×Q₈×C₇₃	—	4	4	no	—
104	C₂×Q₈×C₇₃	—	4	2	no	—
105	C₂×Q₈×C₇₃	—	8	2	no	—
106	C₂×D₄×C₇₃	—	2	4	no	—
107	C₂×D₄×C₇₃	—	2	2	no	—
108	C₂×D₄×C₇₃	—	2	4	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	—	2	2	no	—
113	C₂×D₄×C₇₃	—	4	4	no	—
114	C₂×D₄×C₇₃	—	4	4	no	—
115	C₂×D₄×C₇₃	—	4	4	no	—
116	C₂×D₄×C₇₃	C₂×D₄	1	4	yes	—
117	C₂²×C₄×C₇₃	—	2	1	no	—
118	C₂²×C₄×C₇₃	—	2	1	no	—
119	C₂²×C₄×C₇₃	—	2	2	no	—
120	C₂²×C₄×C₇₃	—	2	4	no	—
121	C₂²×C₄×C₇₃	—	2	2	no	—
122	C₂²×C₄×C₇₃	—	2	4	no	—
123	C₂²×C₄×C₇₃	—	2	2	no	—
124	C₂²×C₄×C₇₃	—	2	2	no	—
125	C₂²×C₄×C₇₃	—	4	8	no	—
126	C₂²×C₄×C₇₃	SD₁₆	1	4	yes	—
127	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
133	C₂×C₈×C₇₃	—	2	4	no	—
134	C₄⋊C₄×C₇₃	—	2	2	no	—
135	C₄⋊C₄×C₇₃	—	2	2	no	—
136	C₄⋊C₄×C₇₃	—	2	2	no	—
137	C₄⋊C₄×C₇₃	—	2	2	no	—
138	C₄⋊C₄×C₇₃	—	2	2	no	—
139	C₄⋊C₄×C₇₃	—	2	4	no	—
140	C₄⋊C₄×C₇₃	—	4	1	no	—
141	C₄⋊C₄×C₇₃	—	4	1	no	—
142	C₄⋊C₄×C₇₃	—	4	2	no	—
143	C₄⋊C₄×C₇₃	—	8	2	no	—
144	C₄⋊C₄×C₇₃	C₂×D₄	1	4	yes	—
145	C₂²⋊C₄×C₇₃	—	2	4	no	—
146	C₂²⋊C₄×C₇₃	—	2	4	no	—
147	C₂²⋊C₄×C₇₃	—	2	2	no	—
148	C₂²⋊C₄×C₇₃	—	2	4	no	—
149	C₂²⋊C₄×C₇₃	—	2	2	no	—
150	C₂²⋊C₄×C₇₃	—	2	4	no	—
151	C₂²⋊C₄×C₇₃	—	8	2	no	—
152	C₄²×C₇₃	—	2	1	no	—
153	C₄²×C₇₃	—	2	1	no	—
154	C₄²×C₇₃	C₂×D₄	1	2	yes	—
155	C₄²×C₇₃	C₂×D₄	1	2	yes	—
156	C₂³×C₇₃	—	2	1	no	—
157	C₂³×C₇₃	—	2	1	no	—
158	C₂³×C₇₃	—	2	4	no	—
159	C₂³×C₇₃	—	4	1	no	—
160	C₂³×C₇₃	—	4	1	no	—
161	C₂³×C₇₃	—	4	4	no	—
162	C₂³×C₇₃	—	8	2	no	—
163	C₂³×C₇₃	—	8	2	no	—
164	C₂³×C₇₃	C₂×SD₁₆	1	2	yes	—
165	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
166	Q₈×C₇₃	—	4	4	no	—
167	Q₈×C₇₃	—	4	4	no	—
168	Q₈×C₇₃	—	8	4	no	—
169	D₄×C₇₃	—	4	4	no	—
170	D₄×C₇₃	—	4	4	no	—
171	D₄×C₇₃	—	4	8	no	—
172	D₄×C₇₃	—	4	4	no	—
173	D₄×C₇₃	—	4	4	no	—
174	D₄×C₇₃	—	4	4	no	—
175	D₄×C₇₃	—	8	2	no	—
176	D₄×C₇₃	—	8	2	no	—
177	D₄×C₇₃	—	8	2	no	—
178	C₂×C₄×C₇₃	—	2	1	no	—
179	C₂×C₄×C₇₃	—	2	1	no	—
180	C₂×C₄×C₇₃	—	2	4	no	—
181	C₂×C₄×C₇₃	—	2	4	no	—
182	C₂×C₄×C₇₃	—	2	1	no	—
183	C₂×C₄×C₇₃	—	2	1	no	—
184	C₂×C₄×C₇₃	—	2	4	no	—
185	C₂×C₄×C₇₃	—	4	1	no	—
186	C₂×C₄×C₇₃	—	4	1	no	—
187	C₂×C₄×C₇₃	—	4	8	no	—
188	C₂×C₄×C₇₃	—	4	4	no	—
189	C₂×C₄×C₇₃	—	4	8	no	—
190	C₂×C₄×C₇₃	—	4	1	no	—
191	C₂×C₄×C₇₃	—	4	1	no	—
192	C₂×C₄×C₇₃	—	4	2	no	—
193	C₂×C₄×C₇₃	—	4	2	no	—
194	C₂×C₄×C₇₃	—	4	2	no	—
195	C₂×C₄×C₇₃	—	4	2	no	—
196	C₂×C₄×C₇₃	—	4	2	no	—
197	C₂×C₄×C₇₃	—	4	2	no	—
198	C₂×C₄×C₇₃	#120	1	2	yes	—
199	C₂×C₄×C₇₃	#120	1	1	yes	characteristic
200	C₂×C₄×C₇₃	#120	1	1	yes	characteristic
201	C₂×C₄×C₇₃	C₂×SD₁₆	1	2	yes	—
202	C₂×C₄×C₇₃	C₂×SD₁₆	1	2	yes	—
203	C₂×C₄×C₇₃	AGL(1,ℤ/8)	1	2	yes	—
204	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
205	C₈×C₇₃	—	4	4	no	—
206	C₂²×C₇₃	—	2	1	no	—
207	C₂²×C₇₃	—	2	1	no	—
208	C₂²×C₇₃	—	2	2	no	—
209	C₂²×C₇₃	—	4	2	no	—
210	C₂²×C₇₃	—	4	1	no	—
211	C₂²×C₇₃	—	4	1	no	—
212	C₂²×C₇₃	—	4	4	no	—
213	C₂²×C₇₃	—	4	4	no	—
214	C₂²×C₇₃	—	4	4	no	—
215	C₂²×C₇₃	—	8	1	no	—
216	C₂²×C₇₃	—	8	8	no	—
217	C₂²×C₇₃	C₂×#120	1	1	yes	characteristic
218	C₂²×C₇₃	C₂²×SD₁₆	1	1	yes	characteristic
219	C₂²×C₇₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
220	C₄×C₇₃	—	2	2	no	—
221	C₄×C₇₃	—	2	2	no	—
222	C₄×C₇₃	—	2	2	no	—
223	C₄×C₇₃	—	4	4	no	—
224	C₄×C₇₃	—	4	1	no	—
225	C₄×C₇₃	—	4	1	no	—
226	C₄×C₇₃	—	8	2	no	—
227	C₄×C₇₃	—	8	2	no	—
228	C₄×C₇₃	#450	1	2	yes	—
229	C₄×C₇₃	#450	1	2	yes	—
230	#18309	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
231	C₂×C₇₃	—	2	1	no	—
232	C₂×C₇₃	—	2	1	no	—
233	C₂×C₇₃	—	4	2	no	—
234	C₂×C₇₃	—	8	4	no	—
235	C₂×C₇₃	C₂×#450	1	1	yes	characteristic
236	C₂×C₇₃	#3021	1	1	yes	characteristic
237	C₂×C₇₃	#3028	1	1	yes	characteristic
238	#3449	C₂×C₇₃	1	1	yes	characteristic
239	#3227	C₂×C₇₃	1	2	yes	complemented
240	#2628	C₂×C₇₃	1	1	yes	characteristic, complemented
241	#1616	C₂×C₇₃	1	4	yes	complemented
242	#1613	C₂×C₇₃	1	4	yes	complemented
243	#1517	C₂×C₇₃	1	2	yes	complemented
244	#1458	C₂×C₇₃	1	1	yes	characteristic, complemented
245	C₇₃	#18309	1	1	yes	characteristic, direct product factor, Sylow
246	C₂²×#41	—	2	1	no	—
247	#537	—	2	1	no	—
248	#537	C₂²×C₇₃	1	2	yes	—
249	#536	—	2	2	no	—
250	#535	—	2	2	no	—
251	#534	—	2	1	no	—
252	#534	C₂²×C₇₃	1	2	yes	—
253	#532	—	2	1	no	—
254	#532	C₂²×C₇₃	1	2	yes	—
255	C₂×C₄⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic, complemented
256	#525	—	2	4	no	—
257	C₂×#117	C₂²×C₇₃	1	1	yes	characteristic
258	#498	—	2	2	no	—
259	#486	—	2	2	no	—
260	#481	C₂²×C₇₃	1	8	yes	complemented
261	#476	—	2	4	no	—
262	#431	C₂²×C₇₃	1	2	yes	complemented
263	#400	C₂²×C₇₃	1	2	yes	complemented
264	#399	C₂²×C₇₃	1	2	yes	—
265	#395	—	2	1	no	—
266	#393	—	2	1	no	—
267	#389	—	2	1	no	—
268	#382	C₂²×C₇₃	1	1	yes	characteristic, complemented
269	#380	—	2	1	no	—
270	#327	C₂²×C₇₃	1	8	yes	complemented
271	#324	C₂²×C₇₃	1	2	yes	complemented
272	#323	C₂²×C₇₃	1	2	yes	—
273	C₂×#41	—	2	2	no	—
274	C₂×#41	—	2	2	no	—
275	C₂×#41	—	2	2	no	—
276	C₂×#41	—	2	2	no	—
277	C₂×#41	—	4	4	no	—
278	C₂×#41	—	4	4	no	—
279	C₂²×Q₈	—	2	1	no	—
280	C₂²×Q₈	—	2	1	no	—
281	C₂²×D₄	—	2	1	no	—
282	C₂²×D₄	—	2	2	no	—
283	C₂³×C₄	—	2	2	no	—
284	C₂³×C₄	D₄×C₇₃	1	1	yes	characteristic
285	C₄⋊Q₈	—	2	1	no	—
286	C₄⋊Q₈	—	2	2	no	—
287	C₄⋊Q₈	—	2	2	no	—
288	C₄⋊Q₈	D₄×C₇₃	1	2	yes	—
289	#127	—	2	1	no	—
290	#127	D₄×C₇₃	1	2	yes	—
291	#124	—	2	2	no	—
292	#124	—	2	2	no	—
293	#123	—	2	4	no	—
294	#123	—	2	4	no	—
295	C₂²⋊Q₈	—	2	4	no	—
296	C₂²⋊Q₈	—	2	4	no	—
297	#121	—	2	4	no	—
298	#121	—	2	4	no	—
299	#121	—	2	2	no	—
300	#121	—	2	2	no	—
301	#121	—	2	2	no	—
302	#121	C₂³×C₇₃	1	4	yes	—
303	#120	—	2	4	no	—
304	#120	—	2	4	no	—
305	C₄×D₄	—	2	2	no	—
306	C₄×D₄	—	2	2	no	—
307	C₄×D₄	—	2	2	no	—
308	C₄×D₄	D₄×C₇₃	1	4	yes	—
309	#117	—	2	2	no	—
310	#117	—	2	2	no	—
311	C₂×C₄⋊C₄	—	2	1	no	—
312	C₂×C₄⋊C₄	—	2	1	no	—
313	C₂×C₄⋊C₄	—	2	2	no	—
314	C₂×C₄⋊C₄	D₄×C₇₃	1	1	yes	characteristic
315	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
316	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
317	C₂×C₂²⋊C₄	—	2	2	no	—
318	C₂×C₂²⋊C₄	D₄×C₇₃	1	1	yes	characteristic
319	C₂×C₂²⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
320	C₂×C₄²	D₄×C₇₃	1	1	yes	characteristic
321	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
322	#106	—	2	8	no	—
323	C₄⋊C₈	—	2	2	no	—
324	#102	—	2	8	no	—
325	C₂²⋊C₈	C₂³×C₇₃	1	4	yes	—
326	C₄×C₈	—	2	2	no	—
327	#95	—	2	2	no	—
328	#95	—	2	1	no	—
329	#95	—	2	2	no	—
330	#95	C₂³×C₇₃	1	2	yes	—
331	C₂⁴	—	2	2	no	—
332	C₂⁴	C₂×D₄×C₇₃	1	1	yes	characteristic
333	#41	—	4	4	no	—
334	#41	—	4	8	no	—
335	#41	—	4	8	no	—
336	#41	—	4	4	no	—
337	#41	—	4	4	no	—
338	#41	—	4	4	no	—
339	C₂×Q₈	—	2	2	no	—
340	C₂×Q₈	—	2	2	no	—
341	C₂×Q₈	—	4	4	no	—
342	C₂×Q₈	—	4	2	no	—
343	C₂×Q₈	—	8	2	no	—
344	C₂×D₄	—	2	4	no	—
345	C₂×D₄	—	2	2	no	—
346	C₂×D₄	—	2	4	no	—
347	C₂×D₄	—	2	2	no	—
348	C₂×D₄	—	2	2	no	—
349	C₂×D₄	—	2	2	no	—
350	C₂×D₄	—	2	2	no	—
351	C₂×D₄	—	4	4	no	—
352	C₂×D₄	—	4	4	no	—
353	C₂×D₄	—	4	4	no	—
354	C₂×D₄	C₂×D₄×C₇₃	1	4	yes	—
355	C₂²×C₄	—	2	1	no	—
356	C₂²×C₄	—	2	1	no	—
357	C₂²×C₄	—	2	2	no	—
358	C₂²×C₄	—	2	4	no	—
359	C₂²×C₄	—	2	2	no	—
360	C₂²×C₄	—	2	4	no	—
361	C₂²×C₄	—	2	2	no	—
362	C₂²×C₄	—	2	2	no	—
363	C₂²×C₄	—	4	8	no	—
364	C₂²×C₄	SD₁₆×C₇₃	1	4	yes	—
365	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
366	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
367	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
368	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
369	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
370	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
371	C₂×C₈	—	2	4	no	—
372	C₄⋊C₄	—	2	2	no	—
373	C₄⋊C₄	—	2	2	no	—
374	C₄⋊C₄	—	2	2	no	—
375	C₄⋊C₄	—	2	2	no	—
376	C₄⋊C₄	—	2	2	no	—
377	C₄⋊C₄	—	2	4	no	—
378	C₄⋊C₄	—	4	1	no	—
379	C₄⋊C₄	—	4	1	no	—
380	C₄⋊C₄	—	4	2	no	—
381	C₄⋊C₄	—	8	2	no	—
382	C₄⋊C₄	C₂×D₄×C₇₃	1	4	yes	—
383	C₂²⋊C₄	—	2	4	no	—
384	C₂²⋊C₄	—	2	4	no	—
385	C₂²⋊C₄	—	2	2	no	—
386	C₂²⋊C₄	—	2	4	no	—
387	C₂²⋊C₄	—	2	2	no	—
388	C₂²⋊C₄	—	2	4	no	—
389	C₂²⋊C₄	—	8	2	no	—
390	C₄²	—	2	1	no	—
391	C₄²	—	2	1	no	—
392	C₄²	C₂×D₄×C₇₃	1	2	yes	—
393	C₄²	C₂×D₄×C₇₃	1	2	yes	—
394	C₂³	—	2	1	no	—
395	C₂³	—	2	1	no	—
396	C₂³	—	2	4	no	—
397	C₂³	—	4	1	no	—
398	C₂³	—	4	1	no	—
399	C₂³	—	4	4	no	—
400	C₂³	—	8	2	no	—
401	C₂³	—	8	2	no	—
402	C₂³	C₂×SD₁₆×C₇₃	1	2	yes	—
403	C₂³	C₂²×D₄×C₇₃	1	1	yes	characteristic
404	Q₈	—	4	4	no	—
405	Q₈	—	4	4	no	—
406	Q₈	—	8	4	no	—
407	D₄	—	4	4	no	—
408	D₄	—	4	4	no	—
409	D₄	—	4	8	no	—
410	D₄	—	4	4	no	—
411	D₄	—	4	4	no	—
412	D₄	—	4	4	no	—
413	D₄	—	8	2	no	—
414	D₄	—	8	2	no	—
415	D₄	—	8	2	no	—
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	2	1	no	—
418	C₂×C₄	—	2	4	no	—
419	C₂×C₄	—	2	4	no	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	—	2	4	no	—
423	C₂×C₄	—	4	1	no	—
424	C₂×C₄	—	4	1	no	—
425	C₂×C₄	—	4	8	no	—
426	C₂×C₄	—	4	4	no	—
427	C₂×C₄	—	4	8	no	—
428	C₂×C₄	—	4	1	no	—
429	C₂×C₄	—	4	1	no	—
430	C₂×C₄	—	4	2	no	—
431	C₂×C₄	—	4	2	no	—
432	C₂×C₄	—	4	2	no	—
433	C₂×C₄	—	4	2	no	—
434	C₂×C₄	—	4	2	no	—
435	C₂×C₄	—	4	2	no	—
436	C₂×C₄	#120×C₇₃	1	2	yes	—
437	C₂×C₄	#120×C₇₃	1	1	yes	characteristic
438	C₂×C₄	#120×C₇₃	1	1	yes	characteristic
439	C₂×C₄	C₂×SD₁₆×C₇₃	1	2	yes	—
440	C₂×C₄	C₂×SD₁₆×C₇₃	1	2	yes	—
441	C₂×C₄	AGL(1,ℤ/8)×C₇₃	1	2	yes	—
442	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
443	C₈	—	4	4	no	—
444	C₂²	—	2	1	no	—
445	C₂²	—	2	1	no	—
446	C₂²	—	2	2	no	—
447	C₂²	—	4	2	no	—
448	C₂²	—	4	1	no	—
449	C₂²	—	4	1	no	—
450	C₂²	—	4	4	no	—
451	C₂²	—	4	4	no	—
452	C₂²	—	4	4	no	—
453	C₂²	—	8	1	no	—
454	C₂²	—	8	8	no	—
455	C₂²	C₂×#120×C₇₃	1	1	yes	characteristic
456	C₂²	C₂²×SD₁₆×C₇₃	1	1	yes	characteristic
457	C₂²	C₂×AGL(1,ℤ/8)×C₇₃	1	1	yes	characteristic
458	C₄	—	2	2	no	—
459	C₄	—	2	2	no	—
460	C₄	—	2	2	no	—
461	C₄	—	4	4	no	—
462	C₄	—	4	1	no	—
463	C₄	—	4	1	no	—
464	C₄	—	8	2	no	—
465	C₄	—	8	2	no	—
466	C₄	#450×C₇₃	1	2	yes	—
467	C₄	#450×C₇₃	1	2	yes	—
468	C₂	—	2	1	no	—
469	C₂	—	2	1	no	—
470	C₂	—	4	2	no	—
471	C₂	—	8	4	no	—
472	C₂	C₂×#450×C₇₃	1	1	yes	characteristic
473	C₂	C₇₃×#3021	1	1	yes	characteristic
474	C₂	C₇₃×#3028	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇₃	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₃
prime radical	C₇₃×#3449	C₂
LCS	G ▷ C₂²×C₄ ▷ 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
2. C₇₃×#3227	C₂	semidirect
3. C₇₃×#2628	C₂	semidirect
4. C₇₃×#1616	C₂	semidirect
5. C₇₃×#1613	C₂	semidirect
6. C₇₃×#1517	C₂	semidirect
7. C₇₃×#1458	C₂	semidirect
17. C₂×C₄⋊Q₈×C₇₃	C₂²	semidirect
22. #481×C₇₃	C₂²	semidirect
24. #431×C₇₃	C₂²	semidirect
25. #400×C₇₃	C₂²	semidirect
30. #382×C₇₃	C₂²	semidirect
32. #327×C₇₃	C₂²	semidirect
33. #324×C₇₃	C₂²	semidirect
230. #18309	C₇₃	direct (N × H)
239. #3227	C₂×C₇₃	semidirect
240. #2628	C₂×C₇₃	semidirect
241. #1616	C₂×C₇₃	semidirect
242. #1613	C₂×C₇₃	semidirect
243. #1517	C₂×C₇₃	semidirect
244. #1458	C₂×C₇₃	semidirect
245. C₇₃	#18309	direct (N × H)
255. C₂×C₄⋊Q₈	C₂²×C₇₃	semidirect
260. #481	C₂²×C₇₃	semidirect
262. #431	C₂²×C₇₃	semidirect
263. #400	C₂²×C₇₃	semidirect
268. #382	C₂²×C₇₃	semidirect
270. #327	C₂²×C₇₃	semidirect
271. #324	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×#3449	2
C₇₃×#3227	2
C₇₃×#2628	2
C₇₃×#1616	2
C₇₃×#1613	2
C₇₃×#1517	2
C₇₃×#1458	2
#18309	73

Subgroups — C73×#18309 #32927713

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#18309 #32927713