Subgroups — C₇₃×#18872 #32928276

Order 18688.

954 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₃×#3503	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇₃×#3246	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₃×#3206	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₃×#3035	C₂	1	1	yes	maximal, characteristic
5	C₇₃×#1645	C₂	1	2	yes	maximal, complemented
6	C₇₃×#1643	C₂	1	2	yes	maximal, complemented
7	C₇₃×#1623	C₂	1	2	yes	maximal, complemented
8	C₇₃×#1622	C₂	1	2	yes	maximal, complemented
9	C₂×#333×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇₃×#1481	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₃×#1477	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#135×C₇₃	—	2	1	no	—
13	Q₈²×C₇₃	C₂²	1	2	yes	—
14	#557×C₇₃	—	2	1	no	—
15	#554×C₇₃	—	2	2	no	—
16	#554×C₇₃	C₂²	1	2	yes	—
17	D₄×Q₈×C₇₃	—	2	2	no	—
18	D₄×Q₈×C₇₃	—	2	1	no	—
19	#544×C₇₃	—	2	2	no	—
20	#544×C₇₃	—	2	1	no	—
21	#533×C₇₃	—	2	1	no	—
22	#533×C₇₃	C₂²	1	1	yes	characteristic
23	#532×C₇₃	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊Q₈×C₇₃	—	2	1	no	—
25	C₂×C₄⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
26	#520×C₇₃	—	2	1	no	—
27	C₄×#41×C₇₃	C₂²	1	1	yes	characteristic
28	#492×C₇₃	C₂²	1	2	yes	—
29	#487×C₇₃	C₂²	1	2	yes	—
30	#476×C₇₃	—	2	1	no	—
31	#475×C₇₃	C₂²	1	2	yes	—
32	#465×C₇₃	—	2	2	no	—
33	#464×C₇₃	—	2	1	no	—
34	#463×C₇₃	—	2	1	no	—
35	#462×C₇₃	C₂²	1	1	yes	characteristic
36	#461×C₇₃	—	2	1	no	—
37	#461×C₇₃	—	2	2	no	—
38	#461×C₇₃	C₂²	1	1	yes	characteristic
39	#460×C₇₃	C₂²	1	2	yes	—
40	#460×C₇₃	C₂²	1	1	yes	characteristic
41	#459×C₇₃	C₂²	1	1	yes	characteristic
42	#448×C₇₃	—	2	2	no	—
43	#431×C₇₃	C₂²	1	1	yes	characteristic
44	C₂×C₄⋊C₈×C₇₃	C₂²	1	1	yes	characteristic
45	C₂×C₄⋊C₈×C₇₃	C₂²	1	1	yes	characteristic
46	#416×C₇₃	—	2	1	no	—
47	#333×C₇₃	C₂²	1	2	yes	—
48	#333×C₇₃	C₂²	1	2	yes	—
49	Q₈⋊C₈×C₇₃	C₂²	1	2	yes	—
50	Q₈⋊C₈×C₇₃	C₂²	1	2	yes	—
51	Q₈⋊C₈×C₇₃	C₂²	1	2	yes	—
52	D₄⋊C₈×C₇₃	C₂²	1	2	yes	—
53	C₂×#41×C₇₃	—	2	1	no	—
54	C₂×#41×C₇₃	D₄	1	1	yes	characteristic
55	C₂²×Q₈×C₇₃	—	2	2	no	—
56	C₂²×Q₈×C₇₃	D₄	1	2	yes	—
57	#135×C₇₃	—	4	4	no	—
58	C₂×Q₁₆×C₇₃	—	2	1	no	—
59	C₂×SD₁₆×C₇₃	—	2	1	no	—
60	C₂×SD₁₆×C₇₃	—	2	1	no	—
61	C₂×SD₁₆×C₇₃	—	2	4	no	—
62	C₂×SD₁₆×C₇₃	—	2	2	no	—
63	C₂×D₈×C₇₃	—	2	1	no	—
64	C₂²×C₈×C₇₃	—	2	1	no	—
65	C₂²×C₈×C₇₃	—	2	1	no	—
66	C₄⋊Q₈×C₇₃	—	2	2	no	—
67	C₄⋊Q₈×C₇₃	—	2	2	no	—
68	C₄⋊Q₈×C₇₃	—	2	4	no	—
69	C₄⋊Q₈×C₇₃	—	2	2	no	—
70	C₄⋊Q₈×C₇₃	—	2	2	no	—
71	C₄⋊Q₈×C₇₃	—	2	1	no	—
72	C₄⋊Q₈×C₇₃	—	2	1	no	—
73	C₄⋊Q₈×C₇₃	D₄	1	2	yes	—
74	C₄⋊Q₈×C₇₃	D₄	1	1	yes	characteristic
75	C₄⋊Q₈×C₇₃	D₄	1	1	yes	characteristic
76	C₄⋊Q₈×C₇₃	C₂³	1	1	yes	characteristic
77	C₄⋊Q₈×C₇₃	C₂³	1	2	yes	—
78	#127×C₇₃	C₂³	1	1	yes	characteristic
79	#125×C₇₃	—	2	2	no	—
80	#125×C₇₃	—	2	4	no	—
81	#125×C₇₃	—	2	2	no	—
82	#125×C₇₃	—	2	1	no	—
83	#124×C₇₃	—	2	1	no	—
84	C₂²⋊Q₈×C₇₃	—	2	2	no	—
85	C₂²⋊Q₈×C₇₃	—	2	4	no	—
86	C₂²⋊Q₈×C₇₃	—	2	4	no	—
87	C₂²⋊Q₈×C₇₃	—	2	2	no	—
88	C₂²⋊Q₈×C₇₃	—	2	4	no	—
89	C₂²⋊Q₈×C₇₃	—	2	1	no	—
90	C₂²⋊Q₈×C₇₃	D₄	1	2	yes	—
91	#121×C₇₃	—	2	1	no	—
92	#121×C₇₃	—	2	1	no	—
93	C₄×Q₈×C₇₃	—	2	2	no	—
94	C₄×Q₈×C₇₃	—	2	2	no	—
95	C₄×Q₈×C₇₃	—	2	2	no	—
96	C₄×Q₈×C₇₃	—	2	1	no	—
97	C₄×Q₈×C₇₃	D₄	1	1	yes	characteristic
98	C₄×Q₈×C₇₃	C₂³	1	1	yes	characteristic
99	C₄×Q₈×C₇₃	C₂³	1	2	yes	—
100	C₄×D₄×C₇₃	—	2	4	no	—
101	C₄×D₄×C₇₃	—	2	2	no	—
102	C₄×D₄×C₇₃	—	2	1	no	—
103	C₄×D₄×C₇₃	—	2	1	no	—
104	C₄×D₄×C₇₃	—	2	1	no	—
105	C₄×D₄×C₇₃	—	2	1	no	—
106	C₄×D₄×C₇₃	D₄	1	1	yes	characteristic
107	C₄×D₄×C₇₃	C₂³	1	1	yes	characteristic
108	#117×C₇₃	—	2	2	no	—
109	#117×C₇₃	—	2	1	no	—
110	#117×C₇₃	—	2	1	no	—
111	#117×C₇₃	D₄	1	1	yes	characteristic
112	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
113	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
114	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
115	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
116	C₂×C₄²×C₇₃	—	2	1	no	—
117	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
118	#106×C₇₃	—	2	2	no	—
119	C₄⋊C₈×C₇₃	—	2	1	no	—
120	C₄⋊C₈×C₇₃	—	2	1	no	—
121	C₄⋊C₈×C₇₃	—	2	1	no	—
122	C₄⋊C₈×C₇₃	C₂³	1	1	yes	characteristic
123	C₄⋊C₈×C₇₃	C₂³	1	1	yes	characteristic
124	C₄⋊C₈×C₇₃	C₂³	1	2	yes	—
125	#103×C₇₃	—	2	4	no	—
126	#103×C₇₃	—	2	2	no	—
127	#103×C₇₃	—	2	1	no	—
128	#103×C₇₃	—	2	1	no	—
129	#102×C₇₃	—	2	1	no	—
130	#102×C₇₃	—	2	1	no	—
131	#102×C₇₃	—	2	2	no	—
132	C₂²⋊C₈×C₇₃	—	2	1	no	—
133	C₄×C₈×C₇₃	C₂³	1	2	yes	—
134	#41×C₇₃	—	2	2	no	—
135	#41×C₇₃	—	4	2	no	—
136	#41×C₇₃	—	4	2	no	—
137	#41×C₇₃	SD₁₆	1	4	yes	complemented
138	C₂×Q₈×C₇₃	—	2	4	no	—
139	C₂×Q₈×C₇₃	—	2	2	no	—
140	C₂×Q₈×C₇₃	—	2	1	no	—
141	C₂×Q₈×C₇₃	—	2	1	no	—
142	C₂×Q₈×C₇₃	—	8	4	no	—
143	C₂×Q₈×C₇₃	—	8	2	no	—
144	C₂×Q₈×C₇₃	C₂×D₄	1	2	yes	—
145	C₂×Q₈×C₇₃	C₂×D₄	1	1	yes	characteristic
146	C₂×Q₈×C₇₃	C₂×D₄	1	4	yes	—
147	C₂×D₄×C₇₃	—	2	1	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	—	4	1	no	—
152	C₂×D₄×C₇₃	C₂×D₄	1	1	yes	characteristic
153	C₂²×C₄×C₇₃	—	2	1	no	—
154	C₂²×C₄×C₇₃	—	2	4	no	—
155	C₂²×C₄×C₇₃	—	2	2	no	—
156	C₂²×C₄×C₇₃	—	2	1	no	—
157	C₂²×C₄×C₇₃	—	2	1	no	—
158	C₂²×C₄×C₇₃	—	4	1	no	—
159	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
160	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
161	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
162	Q₁₆×C₇₃	—	4	2	no	—
163	SD₁₆×C₇₃	—	4	2	no	—
164	SD₁₆×C₇₃	—	4	2	no	—
165	SD₁₆×C₇₃	—	8	2	no	—
166	SD₁₆×C₇₃	—	8	4	no	—
167	D₈×C₇₃	—	4	2	no	—
168	C₂×C₈×C₇₃	—	2	2	no	—
169	C₂×C₈×C₇₃	—	2	2	no	—
170	C₂×C₈×C₇₃	—	2	1	no	—
171	C₂×C₈×C₇₃	—	2	1	no	—
172	C₂×C₈×C₇₃	—	4	2	no	—
173	C₂×C₈×C₇₃	—	8	1	no	—
174	C₄⋊C₄×C₇₃	—	2	4	no	—
175	C₄⋊C₄×C₇₃	—	2	4	no	—
176	C₄⋊C₄×C₇₃	—	2	4	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	2	no	—
181	C₄⋊C₄×C₇₃	—	2	1	no	—
182	C₄⋊C₄×C₇₃	—	2	1	no	—
183	C₄⋊C₄×C₇₃	—	2	1	no	—
184	C₄⋊C₄×C₇₃	—	2	2	no	—
185	C₄⋊C₄×C₇₃	—	2	2	no	—
186	C₄⋊C₄×C₇₃	—	2	2	no	—
187	C₄⋊C₄×C₇₃	—	2	1	no	—
188	C₄⋊C₄×C₇₃	—	2	2	no	—
189	C₄⋊C₄×C₇₃	—	2	1	no	—
190	C₄⋊C₄×C₇₃	—	2	1	no	—
191	C₄⋊C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
192	C₄⋊C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
193	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
194	C₂²⋊C₄×C₇₃	—	2	4	no	—
195	C₂²⋊C₄×C₇₃	—	2	2	no	—
196	C₂²⋊C₄×C₇₃	—	2	1	no	—
197	C₂²⋊C₄×C₇₃	—	2	1	no	—
198	C₂²⋊C₄×C₇₃	—	2	1	no	—
199	C₂²⋊C₄×C₇₃	—	4	1	no	—
200	C₂²⋊C₄×C₇₃	—	4	1	no	—
201	C₄²×C₇₃	—	2	4	no	—
202	C₄²×C₇₃	—	2	1	no	—
203	C₄²×C₇₃	—	2	1	no	—
204	C₄²×C₇₃	—	2	1	no	—
205	C₄²×C₇₃	—	2	2	no	—
206	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
207	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
208	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
209	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
210	C₂³×C₇₃	—	2	1	no	—
211	C₂³×C₇₃	—	4	1	no	—
212	C₂³×C₇₃	#120	1	1	yes	characteristic
213	Q₈×C₇₃	—	2	1	no	—
214	Q₈×C₇₃	—	2	2	no	—
215	Q₈×C₇₃	—	2	2	no	—
216	Q₈×C₇₃	—	4	4	no	—
217	Q₈×C₇₃	—	4	4	no	—
218	Q₈×C₇₃	—	4	2	no	—
219	Q₈×C₇₃	—	4	1	no	—
220	Q₈×C₇₃	—	4	1	no	—
221	Q₈×C₇₃	—	8	4	no	—
222	Q₈×C₇₃	C₂×SD₁₆	1	2	yes	—
223	D₄×C₇₃	—	2	4	no	—
224	D₄×C₇₃	—	2	1	no	—
225	D₄×C₇₃	—	4	2	no	—
226	D₄×C₇₃	—	4	1	no	—
227	D₄×C₇₃	—	4	1	no	—
228	D₄×C₇₃	—	4	1	no	—
229	D₄×C₇₃	—	4	1	no	—
230	D₄×C₇₃	—	8	2	no	—
231	D₄×C₇₃	C₂×SD₁₆	1	2	yes	—
232	C₂×C₄×C₇₃	—	2	1	no	—
233	C₂×C₄×C₇₃	—	2	1	no	—
234	C₂×C₄×C₇₃	—	2	1	no	—
235	C₂×C₄×C₇₃	—	2	4	no	—
236	C₂×C₄×C₇₃	—	2	2	no	—
237	C₂×C₄×C₇₃	—	2	1	no	—
238	C₂×C₄×C₇₃	—	2	1	no	—
239	C₂×C₄×C₇₃	—	2	4	no	—
240	C₂×C₄×C₇₃	—	2	2	no	—
241	C₂×C₄×C₇₃	—	4	1	no	—
242	C₂×C₄×C₇₃	—	4	2	no	—
243	C₂×C₄×C₇₃	—	4	1	no	—
244	C₂×C₄×C₇₃	—	4	1	no	—
245	C₂×C₄×C₇₃	—	4	1	no	—
246	C₂×C₄×C₇₃	—	8	2	no	—
247	C₂×C₄×C₇₃	—	8	4	no	—
248	C₂×C₄×C₇₃	—	8	2	no	—
249	C₂×C₄×C₇₃	#120	1	1	yes	characteristic
250	C₂×C₄×C₇₃	#120	1	1	yes	characteristic
251	C₂×C₄×C₇₃	#120	1	1	yes	characteristic
252	C₂×C₄×C₇₃	C₂×SD₁₆	1	2	yes	—
253	C₂×C₄×C₇₃	#137	1	2	yes	—
254	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
255	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
256	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
257	C₈×C₇₃	—	4	2	no	—
258	C₈×C₇₃	—	4	1	no	—
259	C₈×C₇₃	—	4	1	no	—
260	C₈×C₇₃	—	4	2	no	—
261	C₂²×C₇₃	—	2	1	no	—
262	C₂²×C₇₃	—	2	1	no	—
263	C₂²×C₇₃	—	2	2	no	—
264	C₂²×C₇₃	—	4	1	no	—
265	C₂²×C₇₃	—	4	1	no	—
266	C₂²×C₇₃	—	8	1	no	—
267	C₂²×C₇₃	—	8	1	no	—
268	C₂²×C₇₃	—	8	1	no	—
269	C₂²×C₇₃	#448	1	2	yes	—
270	C₂²×C₇₃	C₂×#120	1	1	yes	characteristic
271	C₄×C₇₃	—	2	2	no	—
272	C₄×C₇₃	—	2	1	no	—
273	C₄×C₇₃	—	2	1	no	—
274	C₄×C₇₃	—	2	1	no	—
275	C₄×C₇₃	—	4	1	no	—
276	C₄×C₇₃	—	4	2	no	—
277	C₄×C₇₃	—	4	1	no	—
278	C₄×C₇₃	—	4	4	no	—
279	C₄×C₇₃	—	4	2	no	—
280	C₄×C₇₃	—	8	1	no	—
281	C₄×C₇₃	#448	1	2	yes	—
282	C₄×C₇₃	C₂²×SD₁₆	1	1	yes	characteristic
283	C₄×C₇₃	C₂×#137	1	1	yes	characteristic
284	C₄×C₇₃	#577	1	1	yes	characteristic
285	C₄×C₇₃	#578	1	1	yes	characteristic
286	#18872	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
287	C₂×C₇₃	—	2	2	no	—
288	C₂×C₇₃	—	4	2	no	—
289	C₂×C₇₃	—	16	1	no	—
290	C₂×C₇₃	C₂×#448	1	1	yes	characteristic
291	C₂×C₇₃	#3013	1	1	yes	characteristic
292	C₂×C₇₃	#3019	1	1	yes	characteristic
293	#3503	C₂×C₇₃	1	1	yes	characteristic, complemented
294	#3246	C₂×C₇₃	1	1	yes	characteristic, complemented
295	#3206	C₂×C₇₃	1	1	yes	characteristic, complemented
296	#3035	C₂×C₇₃	1	1	yes	characteristic
297	#1645	C₂×C₇₃	1	2	yes	complemented
298	#1643	C₂×C₇₃	1	2	yes	complemented
299	#1623	C₂×C₇₃	1	2	yes	complemented
300	#1622	C₂×C₇₃	1	2	yes	complemented
301	C₂×#333	C₂×C₇₃	1	1	yes	characteristic, complemented
302	#1481	C₂×C₇₃	1	1	yes	characteristic, complemented
303	#1477	C₂×C₇₃	1	1	yes	characteristic, complemented
304	C₇₃	#18872	1	1	yes	characteristic, direct product factor, Sylow
305	C₂×#135	—	2	1	no	—
306	Q₈²	C₂²×C₇₃	1	2	yes	—
307	#557	—	2	1	no	—
308	#554	—	2	2	no	—
309	#554	C₂²×C₇₃	1	2	yes	—
310	D₄×Q₈	—	2	2	no	—
311	D₄×Q₈	—	2	1	no	—
312	#544	—	2	2	no	—
313	#544	—	2	1	no	—
314	#533	—	2	1	no	—
315	#533	C₂²×C₇₃	1	1	yes	characteristic
316	#532	C₂²×C₇₃	1	1	yes	characteristic
317	C₂×C₄⋊Q₈	—	2	1	no	—
318	C₂×C₄⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
319	#520	—	2	1	no	—
320	C₄×#41	C₂²×C₇₃	1	1	yes	characteristic
321	#492	C₂²×C₇₃	1	2	yes	—
322	#487	C₂²×C₇₃	1	2	yes	—
323	#476	—	2	1	no	—
324	#475	C₂²×C₇₃	1	2	yes	—
325	#465	—	2	2	no	—
326	#464	—	2	1	no	—
327	#463	—	2	1	no	—
328	#462	C₂²×C₇₃	1	1	yes	characteristic
329	#461	—	2	2	no	—
330	#461	—	2	1	no	—
331	#461	C₂²×C₇₃	1	1	yes	characteristic
332	#460	C₂²×C₇₃	1	2	yes	—
333	#460	C₂²×C₇₃	1	1	yes	characteristic
334	#459	C₂²×C₇₃	1	1	yes	characteristic
335	#448	—	2	2	no	—
336	#431	C₂²×C₇₃	1	1	yes	characteristic
337	C₂×C₄⋊C₈	C₂²×C₇₃	1	1	yes	characteristic
338	C₂×C₄⋊C₈	C₂²×C₇₃	1	1	yes	characteristic
339	#416	—	2	1	no	—
340	#333	C₂²×C₇₃	1	2	yes	—
341	#333	C₂²×C₇₃	1	2	yes	—
342	Q₈⋊C₈	C₂²×C₇₃	1	2	yes	—
343	Q₈⋊C₈	C₂²×C₇₃	1	2	yes	—
344	Q₈⋊C₈	C₂²×C₇₃	1	2	yes	—
345	D₄⋊C₈	C₂²×C₇₃	1	2	yes	—
346	C₂×#41	—	2	1	no	—
347	C₂×#41	D₄×C₇₃	1	1	yes	characteristic
348	C₂²×Q₈	—	2	2	no	—
349	C₂²×Q₈	D₄×C₇₃	1	2	yes	—
350	#135	—	4	4	no	—
351	C₂×Q₁₆	—	2	1	no	—
352	C₂×SD₁₆	—	2	1	no	—
353	C₂×SD₁₆	—	2	1	no	—
354	C₂×SD₁₆	—	2	4	no	—
355	C₂×SD₁₆	—	2	2	no	—
356	C₂×D₈	—	2	1	no	—
357	C₂²×C₈	—	2	1	no	—
358	C₂²×C₈	—	2	1	no	—
359	C₄⋊Q₈	—	2	2	no	—
360	C₄⋊Q₈	—	2	2	no	—
361	C₄⋊Q₈	—	2	4	no	—
362	C₄⋊Q₈	—	2	2	no	—
363	C₄⋊Q₈	—	2	2	no	—
364	C₄⋊Q₈	—	2	1	no	—
365	C₄⋊Q₈	—	2	1	no	—
366	C₄⋊Q₈	D₄×C₇₃	1	2	yes	—
367	C₄⋊Q₈	D₄×C₇₃	1	1	yes	characteristic
368	C₄⋊Q₈	D₄×C₇₃	1	1	yes	characteristic
369	C₄⋊Q₈	C₂³×C₇₃	1	1	yes	characteristic
370	C₄⋊Q₈	C₂³×C₇₃	1	2	yes	—
371	#127	C₂³×C₇₃	1	1	yes	characteristic
372	#125	—	2	2	no	—
373	#125	—	2	4	no	—
374	#125	—	2	2	no	—
375	#125	—	2	1	no	—
376	#124	—	2	1	no	—
377	C₂²⋊Q₈	—	2	2	no	—
378	C₂²⋊Q₈	—	2	4	no	—
379	C₂²⋊Q₈	—	2	4	no	—
380	C₂²⋊Q₈	—	2	2	no	—
381	C₂²⋊Q₈	—	2	4	no	—
382	C₂²⋊Q₈	—	2	1	no	—
383	C₂²⋊Q₈	D₄×C₇₃	1	2	yes	—
384	#121	—	2	1	no	—
385	#121	—	2	1	no	—
386	C₄×Q₈	—	2	2	no	—
387	C₄×Q₈	—	2	2	no	—
388	C₄×Q₈	—	2	2	no	—
389	C₄×Q₈	—	2	1	no	—
390	C₄×Q₈	D₄×C₇₃	1	1	yes	characteristic
391	C₄×Q₈	C₂³×C₇₃	1	1	yes	characteristic
392	C₄×Q₈	C₂³×C₇₃	1	2	yes	—
393	C₄×D₄	—	2	4	no	—
394	C₄×D₄	—	2	2	no	—
395	C₄×D₄	—	2	1	no	—
396	C₄×D₄	—	2	1	no	—
397	C₄×D₄	—	2	1	no	—
398	C₄×D₄	—	2	1	no	—
399	C₄×D₄	D₄×C₇₃	1	1	yes	characteristic
400	C₄×D₄	C₂³×C₇₃	1	1	yes	characteristic
401	#117	—	2	2	no	—
402	#117	—	2	1	no	—
403	#117	—	2	1	no	—
404	#117	D₄×C₇₃	1	1	yes	characteristic
405	C₂×C₄⋊C₄	—	2	2	no	—
406	C₂×C₄⋊C₄	—	2	1	no	—
407	C₂×C₄⋊C₄	—	2	1	no	—
408	C₂×C₄⋊C₄	—	2	2	no	—
409	C₂×C₄²	—	2	1	no	—
410	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
411	#106	—	2	2	no	—
412	C₄⋊C₈	—	2	1	no	—
413	C₄⋊C₈	—	2	1	no	—
414	C₄⋊C₈	—	2	1	no	—
415	C₄⋊C₈	C₂³×C₇₃	1	2	yes	—
416	C₄⋊C₈	C₂³×C₇₃	1	1	yes	characteristic
417	C₄⋊C₈	C₂³×C₇₃	1	1	yes	characteristic
418	#103	—	2	4	no	—
419	#103	—	2	2	no	—
420	#103	—	2	1	no	—
421	#103	—	2	1	no	—
422	#102	—	2	1	no	—
423	#102	—	2	1	no	—
424	#102	—	2	2	no	—
425	C₂²⋊C₈	—	2	1	no	—
426	C₄×C₈	C₂³×C₇₃	1	2	yes	—
427	#41	—	2	2	no	—
428	#41	—	4	2	no	—
429	#41	—	4	2	no	—
430	#41	SD₁₆×C₇₃	1	4	yes	complemented
431	C₂×Q₈	—	2	4	no	—
432	C₂×Q₈	—	2	2	no	—
433	C₂×Q₈	—	2	1	no	—
434	C₂×Q₈	—	2	1	no	—
435	C₂×Q₈	—	8	4	no	—
436	C₂×Q₈	—	8	2	no	—
437	C₂×Q₈	C₂×D₄×C₇₃	1	2	yes	—
438	C₂×Q₈	C₂×D₄×C₇₃	1	1	yes	characteristic
439	C₂×Q₈	C₂×D₄×C₇₃	1	4	yes	—
440	C₂×D₄	—	2	1	no	—
441	C₂×D₄	—	2	1	no	—
442	C₂×D₄	—	2	1	no	—
443	C₂×D₄	—	2	1	no	—
444	C₂×D₄	—	4	1	no	—
445	C₂×D₄	C₂×D₄×C₇₃	1	1	yes	characteristic
446	C₂²×C₄	—	2	1	no	—
447	C₂²×C₄	—	2	4	no	—
448	C₂²×C₄	—	2	2	no	—
449	C₂²×C₄	—	2	1	no	—
450	C₂²×C₄	—	2	1	no	—
451	C₂²×C₄	—	4	1	no	—
452	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
453	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
454	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
455	Q₁₆	—	4	2	no	—
456	SD₁₆	—	4	2	no	—
457	SD₁₆	—	4	2	no	—
458	SD₁₆	—	8	2	no	—
459	SD₁₆	—	8	4	no	—
460	D₈	—	4	2	no	—
461	C₂×C₈	—	2	2	no	—
462	C₂×C₈	—	2	2	no	—
463	C₂×C₈	—	2	1	no	—
464	C₂×C₈	—	2	1	no	—
465	C₂×C₈	—	4	2	no	—
466	C₂×C₈	—	8	1	no	—
467	C₄⋊C₄	—	2	4	no	—
468	C₄⋊C₄	—	2	4	no	—
469	C₄⋊C₄	—	2	4	no	—
470	C₄⋊C₄	—	2	4	no	—
471	C₄⋊C₄	—	2	2	no	—
472	C₄⋊C₄	—	2	1	no	—
473	C₄⋊C₄	—	2	2	no	—
474	C₄⋊C₄	—	2	1	no	—
475	C₄⋊C₄	—	2	1	no	—
476	C₄⋊C₄	—	2	1	no	—
477	C₄⋊C₄	—	2	2	no	—
478	C₄⋊C₄	—	2	2	no	—
479	C₄⋊C₄	—	2	2	no	—
480	C₄⋊C₄	—	2	1	no	—
481	C₄⋊C₄	—	2	2	no	—
482	C₄⋊C₄	—	2	1	no	—
483	C₄⋊C₄	—	2	1	no	—
484	C₄⋊C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
485	C₄⋊C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
486	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
487	C₂²⋊C₄	—	2	4	no	—
488	C₂²⋊C₄	—	2	2	no	—
489	C₂²⋊C₄	—	2	1	no	—
490	C₂²⋊C₄	—	2	1	no	—
491	C₂²⋊C₄	—	2	1	no	—
492	C₂²⋊C₄	—	4	1	no	—
493	C₂²⋊C₄	—	4	1	no	—
494	C₄²	—	2	4	no	—
495	C₄²	—	2	1	no	—
496	C₄²	—	2	1	no	—
497	C₄²	—	2	1	no	—
498	C₄²	—	2	2	no	—
499	C₄²	C₂×D₄×C₇₃	1	1	yes	characteristic
500	C₄²	C₂×D₄×C₇₃	1	1	yes	characteristic
501	C₄²	C₂×D₄×C₇₃	1	1	yes	characteristic
502	C₄²	C₂⁴×C₇₃	1	1	yes	characteristic
503	C₂³	—	2	1	no	—
504	C₂³	—	4	1	no	—
505	C₂³	#120×C₇₃	1	1	yes	characteristic
506	Q₈	—	2	1	no	—
507	Q₈	—	2	2	no	—
508	Q₈	—	2	2	no	—
509	Q₈	—	4	4	no	—
510	Q₈	—	4	4	no	—
511	Q₈	—	4	2	no	—
512	Q₈	—	4	1	no	—
513	Q₈	—	4	1	no	—
514	Q₈	—	8	4	no	—
515	Q₈	C₂×SD₁₆×C₇₃	1	2	yes	—
516	D₄	—	2	4	no	—
517	D₄	—	2	1	no	—
518	D₄	—	4	2	no	—
519	D₄	—	4	1	no	—
520	D₄	—	4	1	no	—
521	D₄	—	4	1	no	—
522	D₄	—	4	1	no	—
523	D₄	—	8	2	no	—
524	D₄	C₂×SD₁₆×C₇₃	1	2	yes	—
525	C₂×C₄	—	2	1	no	—
526	C₂×C₄	—	2	4	no	—
527	C₂×C₄	—	2	1	no	—
528	C₂×C₄	—	2	1	no	—
529	C₂×C₄	—	2	2	no	—
530	C₂×C₄	—	2	1	no	—
531	C₂×C₄	—	2	1	no	—
532	C₂×C₄	—	2	4	no	—
533	C₂×C₄	—	2	2	no	—
534	C₂×C₄	—	4	1	no	—
535	C₂×C₄	—	4	2	no	—
536	C₂×C₄	—	4	1	no	—
537	C₂×C₄	—	4	1	no	—
538	C₂×C₄	—	4	1	no	—
539	C₂×C₄	—	8	2	no	—
540	C₂×C₄	—	8	4	no	—
541	C₂×C₄	—	8	2	no	—
542	C₂×C₄	#120×C₇₃	1	1	yes	characteristic
543	C₂×C₄	#120×C₇₃	1	1	yes	characteristic
544	C₂×C₄	#120×C₇₃	1	1	yes	characteristic
545	C₂×C₄	C₂×SD₁₆×C₇₃	1	2	yes	—
546	C₂×C₄	#137×C₇₃	1	2	yes	—
547	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
548	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
549	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
550	C₈	—	4	2	no	—
551	C₈	—	4	1	no	—
552	C₈	—	4	1	no	—
553	C₈	—	4	2	no	—
554	C₂²	—	2	1	no	—
555	C₂²	—	2	1	no	—
556	C₂²	—	2	2	no	—
557	C₂²	—	4	1	no	—
558	C₂²	—	4	1	no	—
559	C₂²	—	8	1	no	—
560	C₂²	—	8	1	no	—
561	C₂²	—	8	1	no	—
562	C₂²	#448×C₇₃	1	2	yes	—
563	C₂²	C₂×#120×C₇₃	1	1	yes	characteristic
564	C₄	—	2	2	no	—
565	C₄	—	2	1	no	—
566	C₄	—	2	1	no	—
567	C₄	—	2	1	no	—
568	C₄	—	4	1	no	—
569	C₄	—	4	2	no	—
570	C₄	—	4	1	no	—
571	C₄	—	4	4	no	—
572	C₄	—	4	2	no	—
573	C₄	—	8	1	no	—
574	C₄	#448×C₇₃	1	2	yes	—
575	C₄	C₂²×SD₁₆×C₇₃	1	1	yes	characteristic
576	C₄	C₂×#137×C₇₃	1	1	yes	characteristic
577	C₄	#577×C₇₃	1	1	yes	characteristic
578	C₄	#578×C₇₃	1	1	yes	characteristic
579	C₂	—	2	2	no	—
580	C₂	—	4	2	no	—
581	C₂	—	16	1	no	—
582	C₂	C₂×#448×C₇₃	1	1	yes	characteristic
583	C₂	C₇₃×#3013	1	1	yes	characteristic
584	C₂	C₇₃×#3019	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇₃	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₇₃
prime radical	C₇₃×#3035	C₂
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×#3503	C₂	semidirect
2. C₇₃×#3246	C₂	semidirect
3. C₇₃×#3206	C₂	semidirect
5. C₇₃×#1645	C₂	semidirect
6. C₇₃×#1643	C₂	semidirect
7. C₇₃×#1623	C₂	semidirect
8. C₇₃×#1622	C₂	semidirect
9. C₂×#333×C₇₃	C₂	semidirect
10. C₇₃×#1481	C₂	semidirect
11. C₇₃×#1477	C₂	semidirect
137. #41×C₇₃	SD₁₆	semidirect
286. #18872	C₇₃	direct (N × H)
293. #3503	C₂×C₇₃	semidirect
294. #3246	C₂×C₇₃	semidirect
295. #3206	C₂×C₇₃	semidirect
297. #1645	C₂×C₇₃	semidirect
298. #1643	C₂×C₇₃	semidirect
299. #1623	C₂×C₇₃	semidirect
300. #1622	C₂×C₇₃	semidirect
301. C₂×#333	C₂×C₇₃	semidirect
302. #1481	C₂×C₇₃	semidirect
303. #1477	C₂×C₇₃	semidirect
304. C₇₃	#18872	direct (N × H)
430. #41	SD₁₆×C₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₇₃×#3503	2
C₇₃×#3246	2
C₇₃×#3206	2
C₇₃×#3035	2
C₇₃×#1645	2
C₇₃×#1643	2
C₇₃×#1623	2
C₇₃×#1622	2
C₂×#333×C₇₃	2
C₇₃×#1481	2
C₇₃×#1477	2
#18872	73

Subgroups — C73×#18872 #32928276

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#18872 #32928276