Subgroups — C₇₃×#18798 #32928202

Order 18688.

1226 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄×#41×C₇₃	C₂	1	1	yes	maximal, characteristic
2	C₇₃×#3226	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#474×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₃×#3039	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₃×#1649	C₂	1	2	yes	maximal, complemented
6	C₇₃×#1647	C₂	1	2	yes	maximal, complemented
7	C₇₃×#1641	C₂	1	2	yes	maximal, complemented
8	C₇₃×#1639	C₂	1	2	yes	maximal, complemented
9	C₇₃×#1547	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇₃×#1486	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₃×#1477	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#41×C₇₃	—	2	1	no	—
13	C₂×#137×C₇₃	—	2	1	no	—
14	#550×C₇₃	C₂²	1	1	yes	characteristic
15	D₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic
16	#548×C₇₃	—	2	1	no	—
17	#547×C₇₃	—	2	1	no	—
18	#547×C₇₃	C₂²	1	1	yes	characteristic
19	#546×C₇₃	—	2	2	no	—
20	#546×C₇₃	—	2	1	no	—
21	D₄²×C₇₃	—	2	1	no	—
22	D₄²×C₇₃	C₂²	1	1	yes	characteristic
23	#532×C₇₃	—	2	1	no	—
24	#532×C₇₃	C₂²	1	1	yes	characteristic
25	C₂×C₄⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic, complemented
26	#525×C₇₃	—	2	2	no	—
27	#525×C₇₃	—	2	1	no	—
28	C₄×#41×C₇₃	C₂²	1	1	yes	characteristic
29	C₂×C₄×D₄×C₇₃	—	2	1	no	—
30	C₂×C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
31	#500×C₇₃	C₂²	1	2	yes	complemented
32	#486×C₇₃	C₂²	1	2	yes	complemented
33	#480×C₇₃	—	2	2	no	—
34	#474×C₇₃	—	2	2	no	—
35	#474×C₇₃	—	2	1	no	—
36	#474×C₇₃	—	2	1	no	—
37	#474×C₇₃	C₂²	1	2	yes	—
38	#474×C₇₃	C₂²	1	2	yes	complemented
39	#462×C₇₃	—	2	1	no	—
40	#462×C₇₃	C₂²	1	2	yes	complemented
41	#461×C₇₃	—	2	1	no	—
42	#461×C₇₃	C₂²	1	2	yes	complemented
43	#431×C₇₃	C₂²	1	1	yes	characteristic, complemented
44	C₂×#107×C₇₃	—	2	1	no	—
45	#423×C₇₃	C₂²	1	1	yes	characteristic, complemented
46	C₂×C₄⋊C₈×C₇₃	C₂²	1	1	yes	characteristic, complemented
47	#419×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	D₄⋊C₈×C₇₃	C₂²	1	2	yes	—
53	D₄⋊C₈×C₇₃	C₂²	1	2	yes	complemented
54	D₄⋊C₈×C₇₃	C₂²	1	2	yes	complemented
55	C₂×#41×C₇₃	—	2	2	no	—
56	C₂×#41×C₇₃	—	2	2	no	—
57	C₂×#41×C₇₃	—	2	1	no	—
58	C₂×#41×C₇₃	—	2	1	no	—
59	C₂×#41×C₇₃	—	2	1	no	—
60	C₂×#41×C₇₃	—	4	4	no	—
61	C₂×#41×C₇₃	—	4	4	no	—
62	C₂×#41×C₇₃	D₄	1	1	yes	characteristic
63	C₂²×Q₈×C₇₃	—	2	1	no	—
64	C₂²×Q₈×C₇₃	—	2	1	no	—
65	C₂²×D₄×C₇₃	—	2	2	no	—
66	C₂²×D₄×C₇₃	—	2	1	no	—
67	C₂²×D₄×C₇₃	—	2	1	no	—
68	C₂²×D₄×C₇₃	D₄	1	1	yes	characteristic
69	C₂³×C₄×C₇₃	—	2	2	no	—
70	C₂³×C₄×C₇₃	—	2	1	no	—
71	#137×C₇₃	—	4	4	no	—
72	C₂×Q₁₆×C₇₃	—	2	2	no	—
73	C₂×SD₁₆×C₇₃	—	2	2	no	—
74	C₂×M₁₆×C₇₃	—	2	1	no	—
75	C₂²×C₈×C₇₃	—	2	1	no	—
76	C₄⋊Q₈×C₇₃	—	2	1	no	—
77	C₄⋊Q₈×C₇₃	—	2	1	no	—
78	C₄⋊Q₈×C₇₃	—	2	1	no	—
79	C₄⋊Q₈×C₇₃	—	2	1	no	—
80	C₄⋊Q₈×C₇₃	C₂³	1	2	yes	—
81	C₄⋊Q₈×C₇₃	C₂³	1	1	yes	characteristic
82	#127×C₇₃	—	2	1	no	—
83	#127×C₇₃	C₂³	1	1	yes	characteristic
84	#124×C₇₃	—	2	2	no	—
85	#124×C₇₃	—	2	1	no	—
86	#123×C₇₃	—	2	2	no	—
87	#123×C₇₃	—	2	2	no	—
88	#123×C₇₃	—	2	2	no	—
89	C₂²⋊Q₈×C₇₃	—	2	2	no	—
90	C₂²⋊Q₈×C₇₃	—	2	1	no	—
91	C₂²⋊Q₈×C₇₃	—	2	2	no	—
92	C₂²⋊Q₈×C₇₃	—	2	1	no	—
93	#121×C₇₃	—	2	2	no	—
94	#121×C₇₃	—	2	2	no	—
95	#121×C₇₃	—	2	2	no	—
96	#121×C₇₃	—	2	1	no	—
97	#121×C₇₃	—	2	1	no	—
98	#121×C₇₃	—	2	1	no	—
99	#121×C₇₃	—	2	1	no	—
100	#121×C₇₃	—	2	1	no	—
101	#121×C₇₃	D₄	1	2	yes	—
102	#120×C₇₃	—	2	2	no	—
103	#120×C₇₃	—	2	2	no	—
104	#120×C₇₃	—	2	2	no	—
105	C₄×Q₈×C₇₃	D₄	1	1	yes	characteristic
106	C₄×Q₈×C₇₃	C₂³	1	1	yes	characteristic
107	C₄×D₄×C₇₃	—	2	2	no	—
108	C₄×D₄×C₇₃	—	2	2	no	—
109	C₄×D₄×C₇₃	—	2	2	no	—
110	C₄×D₄×C₇₃	—	2	1	no	—
111	C₄×D₄×C₇₃	—	2	1	no	—
112	C₄×D₄×C₇₃	—	2	1	no	—
113	C₄×D₄×C₇₃	—	2	1	no	—
114	C₄×D₄×C₇₃	—	2	1	no	—
115	C₄×D₄×C₇₃	—	2	1	no	—
116	C₄×D₄×C₇₃	—	2	1	no	—
117	C₄×D₄×C₇₃	D₄	1	1	yes	characteristic
118	C₄×D₄×C₇₃	D₄	1	1	yes	characteristic
119	C₄×D₄×C₇₃	D₄	1	1	yes	characteristic
120	C₄×D₄×C₇₃	D₄	1	2	yes	—
121	C₄×D₄×C₇₃	C₂³	1	1	yes	characteristic
122	C₄×D₄×C₇₃	C₂³	1	1	yes	characteristic
123	C₄×D₄×C₇₃	C₂³	1	1	yes	characteristic
124	#117×C₇₃	—	2	1	no	—
125	#117×C₇₃	D₄	1	1	yes	characteristic
126	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
127	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
128	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
129	C₂×C₄⋊C₄×C₇₃	D₄	1	1	yes	characteristic
130	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
131	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
132	C₂×C₄²×C₇₃	—	2	1	no	—
133	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
134	#107×C₇₃	—	2	2	no	—
135	#107×C₇₃	—	2	2	no	—
136	#107×C₇₃	—	2	4	no	—
137	C₄⋊C₈×C₇₃	—	2	1	no	—
138	C₄⋊C₈×C₇₃	—	2	1	no	—
139	C₄⋊C₈×C₇₃	—	2	1	no	—
140	C₄⋊C₈×C₇₃	C₂³	1	2	yes	—
141	C₄⋊C₈×C₇₃	C₂³	1	2	yes	—
142	#103×C₇₃	—	2	2	no	—
143	#103×C₇₃	—	2	2	no	—
144	#102×C₇₃	—	2	2	no	—
145	#102×C₇₃	—	2	2	no	—
146	#102×C₇₃	—	2	4	no	—
147	C₂²⋊C₈×C₇₃	—	2	1	no	—
148	C₄×C₈×C₇₃	C₂³	1	2	yes	—
149	C₂⁴×C₇₃	—	2	2	no	—
150	C₂⁴×C₇₃	—	2	1	no	—
151	#41×C₇₃	—	2	2	no	—
152	#41×C₇₃	—	4	8	no	—
153	#41×C₇₃	—	4	8	no	—
154	#41×C₇₃	—	4	2	no	—
155	#41×C₇₃	—	4	2	no	—
156	#41×C₇₃	—	4	2	no	—
157	#41×C₇₃	—	4	2	no	—
158	#41×C₇₃	—	4	2	no	—
159	#41×C₇₃	—	4	2	no	—
160	#41×C₇₃	D₈	1	4	yes	—
161	C₂×Q₈×C₇₃	—	2	2	no	—
162	C₂×Q₈×C₇₃	—	2	1	no	—
163	C₂×Q₈×C₇₃	—	2	2	no	—
164	C₂×Q₈×C₇₃	—	4	2	no	—
165	C₂×Q₈×C₇₃	—	4	2	no	—
166	C₂×Q₈×C₇₃	—	4	1	no	—
167	C₂×Q₈×C₇₃	—	4	2	no	—
168	C₂×Q₈×C₇₃	—	4	2	no	—
169	C₂×Q₈×C₇₃	C₂×D₄	1	1	yes	characteristic
170	C₂×D₄×C₇₃	—	2	1	no	—
171	C₂×D₄×C₇₃	—	2	2	no	—
172	C₂×D₄×C₇₃	—	2	2	no	—
173	C₂×D₄×C₇₃	—	2	2	no	—
174	C₂×D₄×C₇₃	—	2	2	no	—
175	C₂×D₄×C₇₃	—	2	2	no	—
176	C₂×D₄×C₇₃	—	2	2	no	—
177	C₂×D₄×C₇₃	—	2	2	no	—
178	C₂×D₄×C₇₃	—	2	1	no	—
179	C₂×D₄×C₇₃	—	2	1	no	—
180	C₂×D₄×C₇₃	—	2	1	no	—
181	C₂×D₄×C₇₃	—	4	1	no	—
182	C₂×D₄×C₇₃	—	4	2	no	—
183	C₂×D₄×C₇₃	—	4	8	no	—
184	C₂×D₄×C₇₃	—	4	2	no	—
185	C₂×D₄×C₇₃	—	4	2	no	—
186	C₂×D₄×C₇₃	—	4	2	no	—
187	C₂×D₄×C₇₃	C₂×D₄	1	1	yes	characteristic
188	C₂×D₄×C₇₃	C₂×D₄	1	1	yes	characteristic
189	C₂×D₄×C₇₃	C₂×D₄	1	1	yes	characteristic
190	C₂×D₄×C₇₃	C₂×D₄	1	2	yes	—
191	C₂²×C₄×C₇₃	—	2	1	no	—
192	C₂²×C₄×C₇₃	—	2	2	no	—
193	C₂²×C₄×C₇₃	—	2	2	no	—
194	C₂²×C₄×C₇₃	—	2	2	no	—
195	C₂²×C₄×C₇₃	—	2	1	no	—
196	C₂²×C₄×C₇₃	—	2	1	no	—
197	C₂²×C₄×C₇₃	—	2	2	no	—
198	C₂²×C₄×C₇₃	—	2	1	no	—
199	C₂²×C₄×C₇₃	—	2	1	no	—
200	C₂²×C₄×C₇₃	—	2	1	no	—
201	C₂²×C₄×C₇₃	—	2	1	no	—
202	C₂²×C₄×C₇₃	—	2	1	no	—
203	C₂²×C₄×C₇₃	—	4	8	no	—
204	C₂²×C₄×C₇₃	—	4	2	no	—
205	C₂²×C₄×C₇₃	—	4	2	no	—
206	C₂²×C₄×C₇₃	—	4	1	no	—
207	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
208	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
209	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
210	Q₁₆×C₇₃	—	4	4	no	—
211	SD₁₆×C₇₃	—	4	4	no	—
212	M₁₆×C₇₃	—	4	2	no	—
213	C₂×C₈×C₇₃	—	2	2	no	—
214	C₂×C₈×C₇₃	—	2	2	no	—
215	C₂×C₈×C₇₃	—	2	2	no	—
216	C₂×C₈×C₇₃	—	4	2	no	—
217	C₄⋊C₄×C₇₃	—	2	2	no	—
218	C₄⋊C₄×C₇₃	—	2	2	no	—
219	C₄⋊C₄×C₇₃	—	2	1	no	—
220	C₄⋊C₄×C₇₃	—	2	1	no	—
221	C₄⋊C₄×C₇₃	—	2	1	no	—
222	C₄⋊C₄×C₇₃	—	2	1	no	—
223	C₄⋊C₄×C₇₃	—	2	2	no	—
224	C₄⋊C₄×C₇₃	—	2	2	no	—
225	C₄⋊C₄×C₇₃	—	4	1	no	—
226	C₄⋊C₄×C₇₃	—	4	1	no	—
227	C₄⋊C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
228	C₄⋊C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
229	C₄⋊C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
230	C₄⋊C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
231	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
232	C₂²⋊C₄×C₇₃	—	2	2	no	—
233	C₂²⋊C₄×C₇₃	—	2	2	no	—
234	C₂²⋊C₄×C₇₃	—	2	2	no	—
235	C₂²⋊C₄×C₇₃	—	2	2	no	—
236	C₂²⋊C₄×C₇₃	—	2	1	no	—
237	C₂²⋊C₄×C₇₃	—	2	1	no	—
238	C₂²⋊C₄×C₇₃	—	2	2	no	—
239	C₂²⋊C₄×C₇₃	—	2	1	no	—
240	C₂²⋊C₄×C₇₃	—	2	1	no	—
241	C₂²⋊C₄×C₇₃	—	2	2	no	—
242	C₂²⋊C₄×C₇₃	—	2	1	no	—
243	C₂²⋊C₄×C₇₃	—	2	1	no	—
244	C₂²⋊C₄×C₇₃	—	2	1	no	—
245	C₄²×C₇₃	—	2	1	no	—
246	C₄²×C₇₃	—	2	1	no	—
247	C₄²×C₇₃	—	2	1	no	—
248	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
249	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
250	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
251	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
252	C₂³×C₇₃	—	2	1	no	—
253	C₂³×C₇₃	—	2	1	no	—
254	C₂³×C₇₃	—	2	1	no	—
255	C₂³×C₇₃	—	2	2	no	—
256	C₂³×C₇₃	—	4	2	no	—
257	C₂³×C₇₃	—	4	4	no	—
258	C₂³×C₇₃	—	4	4	no	—
259	C₂³×C₇₃	—	4	2	no	—
260	C₂³×C₇₃	—	8	1	no	—
261	C₂³×C₇₃	—	8	2	no	—
262	C₂³×C₇₃	#120	1	1	yes	characteristic
263	Q₈×C₇₃	—	2	1	no	—
264	Q₈×C₇₃	—	4	4	no	—
265	Q₈×C₇₃	—	4	1	no	—
266	Q₈×C₇₃	—	4	1	no	—
267	Q₈×C₇₃	—	4	2	no	—
268	Q₈×C₇₃	—	4	2	no	—
269	Q₈×C₇₃	—	8	2	no	—
270	Q₈×C₇₃	C₂×D₈	1	2	yes	—
271	D₄×C₇₃	—	2	4	no	—
272	D₄×C₇₃	—	2	1	no	—
273	D₄×C₇₃	—	2	1	no	—
274	D₄×C₇₃	—	2	1	no	—
275	D₄×C₇₃	—	2	1	no	—
276	D₄×C₇₃	—	4	2	no	—
277	D₄×C₇₃	—	4	2	no	—
278	D₄×C₇₃	—	4	4	no	—
279	D₄×C₇₃	—	4	4	no	—
280	D₄×C₇₃	—	4	4	no	—
281	D₄×C₇₃	—	4	4	no	—
282	D₄×C₇₃	—	4	4	no	—
283	D₄×C₇₃	—	4	1	no	—
284	D₄×C₇₃	—	4	1	no	—
285	D₄×C₇₃	—	4	1	no	—
286	D₄×C₇₃	—	4	1	no	—
287	D₄×C₇₃	—	8	2	no	—
288	D₄×C₇₃	C₂×D₈	1	2	yes	—
289	D₄×C₇₃	#137	1	2	yes	complemented
290	C₂×C₄×C₇₃	—	2	1	no	—
291	C₂×C₄×C₇₃	—	2	1	no	—
292	C₂×C₄×C₇₃	—	2	1	no	—
293	C₂×C₄×C₇₃	—	2	4	no	—
294	C₂×C₄×C₇₃	—	2	1	no	—
295	C₂×C₄×C₇₃	—	2	1	no	—
296	C₂×C₄×C₇₃	—	2	1	no	—
297	C₂×C₄×C₇₃	—	2	2	no	—
298	C₂×C₄×C₇₃	—	2	1	no	—
299	C₂×C₄×C₇₃	—	4	1	no	—
300	C₂×C₄×C₇₃	—	4	4	no	—
301	C₂×C₄×C₇₃	—	4	4	no	—
302	C₂×C₄×C₇₃	—	4	4	no	—
303	C₂×C₄×C₇₃	—	4	2	no	—
304	C₂×C₄×C₇₃	—	4	1	no	—
305	C₂×C₄×C₇₃	—	4	1	no	—
306	C₂×C₄×C₇₃	—	4	1	no	—
307	C₂×C₄×C₇₃	—	4	1	no	—
308	C₂×C₄×C₇₃	—	4	1	no	—
309	C₂×C₄×C₇₃	—	4	1	no	—
310	C₂×C₄×C₇₃	—	4	2	no	—
311	C₂×C₄×C₇₃	—	4	4	no	—
312	C₂×C₄×C₇₃	—	4	2	no	—
313	C₂×C₄×C₇₃	—	4	2	no	—
314	C₂×C₄×C₇₃	—	8	1	no	—
315	C₂×C₄×C₇₃	—	8	2	no	—
316	C₂×C₄×C₇₃	#120	1	1	yes	characteristic
317	C₂×C₄×C₇₃	#120	1	1	yes	characteristic
318	C₂×C₄×C₇₃	#120	1	1	yes	characteristic
319	C₂×C₄×C₇₃	C₂×D₈	1	2	yes	—
320	C₂×C₄×C₇₃	AGL(1,ℤ/8)	1	2	yes	—
321	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
322	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
323	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
324	C₈×C₇₃	—	4	2	no	—
325	C₈×C₇₃	—	4	2	no	—
326	C₈×C₇₃	—	4	2	no	—
327	C₂²×C₇₃	—	2	1	no	—
328	C₂²×C₇₃	—	2	1	no	—
329	C₂²×C₇₃	—	2	2	no	—
330	C₂²×C₇₃	—	2	2	no	—
331	C₂²×C₇₃	—	4	1	no	—
332	C₂²×C₇₃	—	4	1	no	—
333	C₂²×C₇₃	—	4	1	no	—
334	C₂²×C₇₃	—	4	1	no	—
335	C₂²×C₇₃	—	4	2	no	—
336	C₂²×C₇₃	—	4	1	no	—
337	C₂²×C₇₃	—	4	1	no	—
338	C₂²×C₇₃	—	4	2	no	—
339	C₂²×C₇₃	—	4	2	no	—
340	C₂²×C₇₃	—	4	1	no	—
341	C₂²×C₇₃	—	8	4	no	—
342	C₂²×C₇₃	—	8	8	no	—
343	C₂²×C₇₃	#447	1	2	yes	—
344	C₂²×C₇₃	C₂×#120	1	1	yes	characteristic
345	C₄×C₇₃	—	2	2	no	—
346	C₄×C₇₃	—	2	1	no	—
347	C₄×C₇₃	—	2	1	no	—
348	C₄×C₇₃	—	2	1	no	—
349	C₄×C₇₃	—	4	1	no	—
350	C₄×C₇₃	—	4	2	no	—
351	C₄×C₇₃	—	4	1	no	—
352	C₄×C₇₃	—	4	1	no	—
353	C₄×C₇₃	—	4	1	no	—
354	C₄×C₇₃	—	8	2	no	—
355	C₄×C₇₃	#447	1	2	yes	—
356	C₄×C₇₃	C₂²×D₈	1	1	yes	characteristic
357	C₄×C₇₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
358	C₄×C₇₃	C₂×#137	1	1	yes	characteristic
359	C₄×C₇₃	#575	1	1	yes	characteristic
360	#18798	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
361	C₂×C₇₃	—	2	2	no	—
362	C₂×C₇₃	—	4	2	no	—
363	C₂×C₇₃	—	4	2	no	—
364	C₂×C₇₃	—	8	1	no	—
365	C₂×C₇₃	—	8	2	no	—
366	C₂×C₇₃	C₂×#447	1	1	yes	characteristic
367	C₂×C₇₃	#3007	1	1	yes	characteristic
368	C₂×C₇₃	#3022	1	1	yes	characteristic
369	D₄×#41	C₂×C₇₃	1	1	yes	characteristic
370	#3226	C₂×C₇₃	1	1	yes	characteristic, complemented
371	C₂×#474	C₂×C₇₃	1	1	yes	characteristic, complemented
372	#3039	C₂×C₇₃	1	1	yes	characteristic, complemented
373	#1649	C₂×C₇₃	1	2	yes	complemented
374	#1647	C₂×C₇₃	1	2	yes	complemented
375	#1641	C₂×C₇₃	1	2	yes	complemented
376	#1639	C₂×C₇₃	1	2	yes	complemented
377	#1547	C₂×C₇₃	1	1	yes	characteristic, complemented
378	#1486	C₂×C₇₃	1	1	yes	characteristic, complemented
379	#1477	C₂×C₇₃	1	1	yes	characteristic, complemented
380	C₇₃	#18798	1	1	yes	characteristic, direct product factor, Sylow
381	C₂²×#41	—	2	1	no	—
382	C₂×#137	—	2	1	no	—
383	#550	C₂²×C₇₃	1	1	yes	characteristic
384	D₄×Q₈	C₂²×C₇₃	1	1	yes	characteristic
385	#548	—	2	1	no	—
386	#547	—	2	1	no	—
387	#547	C₂²×C₇₃	1	1	yes	characteristic
388	#546	—	2	2	no	—
389	#546	—	2	1	no	—
390	D₄²	—	2	1	no	—
391	D₄²	C₂²×C₇₃	1	1	yes	characteristic
392	#532	—	2	1	no	—
393	#532	C₂²×C₇₃	1	1	yes	characteristic
394	C₂×C₄⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic, complemented
395	#525	—	2	2	no	—
396	#525	—	2	1	no	—
397	C₄×#41	C₂²×C₇₃	1	1	yes	characteristic
398	C₂×C₄×D₄	—	2	1	no	—
399	C₂×C₄×D₄	C₂²×C₇₃	1	1	yes	characteristic
400	#500	C₂²×C₇₃	1	2	yes	complemented
401	#486	C₂²×C₇₃	1	2	yes	complemented
402	#480	—	2	2	no	—
403	#474	—	2	2	no	—
404	#474	—	2	1	no	—
405	#474	—	2	1	no	—
406	#474	C₂²×C₇₃	1	2	yes	—
407	#474	C₂²×C₇₃	1	2	yes	complemented
408	#462	—	2	1	no	—
409	#462	C₂²×C₇₃	1	2	yes	complemented
410	#461	—	2	1	no	—
411	#461	C₂²×C₇₃	1	2	yes	complemented
412	#431	C₂²×C₇₃	1	1	yes	characteristic, complemented
413	C₂×#107	—	2	1	no	—
414	#423	C₂²×C₇₃	1	1	yes	characteristic, complemented
415	C₂×C₄⋊C₈	C₂²×C₇₃	1	1	yes	characteristic, complemented
416	#419	—	2	1	no	—
417	C₂×#102	—	2	1	no	—
418	#332	C₂²×C₇₃	1	2	yes	complemented
419	#331	C₂²×C₇₃	1	2	yes	complemented
420	Q₈⋊C₈	C₂²×C₇₃	1	2	yes	complemented
421	D₄⋊C₈	C₂²×C₇₃	1	2	yes	—
422	D₄⋊C₈	C₂²×C₇₃	1	2	yes	complemented
423	D₄⋊C₈	C₂²×C₇₃	1	2	yes	complemented
424	C₂×#41	—	2	2	no	—
425	C₂×#41	—	2	2	no	—
426	C₂×#41	—	2	1	no	—
427	C₂×#41	—	2	1	no	—
428	C₂×#41	—	2	1	no	—
429	C₂×#41	—	4	4	no	—
430	C₂×#41	—	4	4	no	—
431	C₂×#41	D₄×C₇₃	1	1	yes	characteristic
432	C₂²×Q₈	—	2	1	no	—
433	C₂²×Q₈	—	2	1	no	—
434	C₂²×D₄	—	2	2	no	—
435	C₂²×D₄	—	2	1	no	—
436	C₂²×D₄	—	2	1	no	—
437	C₂²×D₄	D₄×C₇₃	1	1	yes	characteristic
438	C₂³×C₄	—	2	2	no	—
439	C₂³×C₄	—	2	1	no	—
440	#137	—	4	4	no	—
441	C₂×Q₁₆	—	2	2	no	—
442	C₂×SD₁₆	—	2	2	no	—
443	C₂×M₁₆	—	2	1	no	—
444	C₂²×C₈	—	2	1	no	—
445	C₄⋊Q₈	—	2	1	no	—
446	C₄⋊Q₈	—	2	1	no	—
447	C₄⋊Q₈	—	2	1	no	—
448	C₄⋊Q₈	—	2	1	no	—
449	C₄⋊Q₈	C₂³×C₇₃	1	2	yes	—
450	C₄⋊Q₈	C₂³×C₇₃	1	1	yes	characteristic
451	#127	—	2	1	no	—
452	#127	C₂³×C₇₃	1	1	yes	characteristic
453	#124	—	2	2	no	—
454	#124	—	2	1	no	—
455	#123	—	2	2	no	—
456	#123	—	2	2	no	—
457	#123	—	2	2	no	—
458	C₂²⋊Q₈	—	2	2	no	—
459	C₂²⋊Q₈	—	2	1	no	—
460	C₂²⋊Q₈	—	2	2	no	—
461	C₂²⋊Q₈	—	2	1	no	—
462	#121	—	2	2	no	—
463	#121	—	2	2	no	—
464	#121	—	2	2	no	—
465	#121	—	2	1	no	—
466	#121	—	2	1	no	—
467	#121	—	2	1	no	—
468	#121	—	2	1	no	—
469	#121	—	2	1	no	—
470	#121	D₄×C₇₃	1	2	yes	—
471	#120	—	2	2	no	—
472	#120	—	2	2	no	—
473	#120	—	2	2	no	—
474	C₄×Q₈	D₄×C₇₃	1	1	yes	characteristic
475	C₄×Q₈	C₂³×C₇₃	1	1	yes	characteristic
476	C₄×D₄	—	2	2	no	—
477	C₄×D₄	—	2	2	no	—
478	C₄×D₄	—	2	2	no	—
479	C₄×D₄	—	2	1	no	—
480	C₄×D₄	—	2	1	no	—
481	C₄×D₄	—	2	1	no	—
482	C₄×D₄	—	2	1	no	—
483	C₄×D₄	—	2	1	no	—
484	C₄×D₄	—	2	1	no	—
485	C₄×D₄	—	2	1	no	—
486	C₄×D₄	D₄×C₇₃	1	1	yes	characteristic
487	C₄×D₄	D₄×C₇₃	1	1	yes	characteristic
488	C₄×D₄	D₄×C₇₃	1	1	yes	characteristic
489	C₄×D₄	D₄×C₇₃	1	2	yes	—
490	C₄×D₄	C₂³×C₇₃	1	1	yes	characteristic
491	C₄×D₄	C₂³×C₇₃	1	1	yes	characteristic
492	C₄×D₄	C₂³×C₇₃	1	1	yes	characteristic
493	#117	—	2	1	no	—
494	#117	D₄×C₇₃	1	1	yes	characteristic
495	C₂×C₄⋊C₄	—	2	1	no	—
496	C₂×C₄⋊C₄	—	2	1	no	—
497	C₂×C₄⋊C₄	—	2	1	no	—
498	C₂×C₄⋊C₄	D₄×C₇₃	1	1	yes	characteristic
499	C₂×C₂²⋊C₄	—	2	2	no	—
500	C₂×C₂²⋊C₄	—	2	1	no	—
501	C₂×C₄²	—	2	1	no	—
502	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
503	#107	—	2	2	no	—
504	#107	—	2	2	no	—
505	#107	—	2	4	no	—
506	C₄⋊C₈	—	2	1	no	—
507	C₄⋊C₈	—	2	1	no	—
508	C₄⋊C₈	—	2	1	no	—
509	C₄⋊C₈	C₂³×C₇₃	1	2	yes	—
510	C₄⋊C₈	C₂³×C₇₃	1	2	yes	—
511	#103	—	2	2	no	—
512	#103	—	2	2	no	—
513	#102	—	2	2	no	—
514	#102	—	2	2	no	—
515	#102	—	2	4	no	—
516	C₂²⋊C₈	—	2	1	no	—
517	C₄×C₈	C₂³×C₇₃	1	2	yes	—
518	C₂⁴	—	2	2	no	—
519	C₂⁴	—	2	1	no	—
520	#41	—	2	2	no	—
521	#41	—	4	8	no	—
522	#41	—	4	8	no	—
523	#41	—	4	2	no	—
524	#41	—	4	2	no	—
525	#41	—	4	2	no	—
526	#41	—	4	2	no	—
527	#41	—	4	2	no	—
528	#41	—	4	2	no	—
529	#41	D₈×C₇₃	1	4	yes	—
530	C₂×Q₈	—	2	2	no	—
531	C₂×Q₈	—	2	1	no	—
532	C₂×Q₈	—	2	2	no	—
533	C₂×Q₈	—	4	2	no	—
534	C₂×Q₈	—	4	2	no	—
535	C₂×Q₈	—	4	1	no	—
536	C₂×Q₈	—	4	2	no	—
537	C₂×Q₈	—	4	2	no	—
538	C₂×Q₈	C₂×D₄×C₇₃	1	1	yes	characteristic
539	C₂×D₄	—	2	1	no	—
540	C₂×D₄	—	2	2	no	—
541	C₂×D₄	—	2	2	no	—
542	C₂×D₄	—	2	2	no	—
543	C₂×D₄	—	2	2	no	—
544	C₂×D₄	—	2	2	no	—
545	C₂×D₄	—	2	2	no	—
546	C₂×D₄	—	2	2	no	—
547	C₂×D₄	—	2	1	no	—
548	C₂×D₄	—	2	1	no	—
549	C₂×D₄	—	2	1	no	—
550	C₂×D₄	—	4	1	no	—
551	C₂×D₄	—	4	2	no	—
552	C₂×D₄	—	4	8	no	—
553	C₂×D₄	—	4	2	no	—
554	C₂×D₄	—	4	2	no	—
555	C₂×D₄	—	4	2	no	—
556	C₂×D₄	C₂×D₄×C₇₃	1	1	yes	characteristic
557	C₂×D₄	C₂×D₄×C₇₃	1	1	yes	characteristic
558	C₂×D₄	C₂×D₄×C₇₃	1	1	yes	characteristic
559	C₂×D₄	C₂×D₄×C₇₃	1	2	yes	—
560	C₂²×C₄	—	2	1	no	—
561	C₂²×C₄	—	2	2	no	—
562	C₂²×C₄	—	2	2	no	—
563	C₂²×C₄	—	2	2	no	—
564	C₂²×C₄	—	2	1	no	—
565	C₂²×C₄	—	2	1	no	—
566	C₂²×C₄	—	2	2	no	—
567	C₂²×C₄	—	2	1	no	—
568	C₂²×C₄	—	2	1	no	—
569	C₂²×C₄	—	2	1	no	—
570	C₂²×C₄	—	2	1	no	—
571	C₂²×C₄	—	2	1	no	—
572	C₂²×C₄	—	4	8	no	—
573	C₂²×C₄	—	4	2	no	—
574	C₂²×C₄	—	4	2	no	—
575	C₂²×C₄	—	4	1	no	—
576	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
577	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
578	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
579	Q₁₆	—	4	4	no	—
580	SD₁₆	—	4	4	no	—
581	M₁₆	—	4	2	no	—
582	C₂×C₈	—	2	2	no	—
583	C₂×C₈	—	2	2	no	—
584	C₂×C₈	—	2	2	no	—
585	C₂×C₈	—	4	2	no	—
586	C₄⋊C₄	—	2	2	no	—
587	C₄⋊C₄	—	2	2	no	—
588	C₄⋊C₄	—	2	1	no	—
589	C₄⋊C₄	—	2	1	no	—
590	C₄⋊C₄	—	2	1	no	—
591	C₄⋊C₄	—	2	1	no	—
592	C₄⋊C₄	—	2	2	no	—
593	C₄⋊C₄	—	2	2	no	—
594	C₄⋊C₄	—	4	1	no	—
595	C₄⋊C₄	—	4	1	no	—
596	C₄⋊C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
597	C₄⋊C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
598	C₄⋊C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
599	C₄⋊C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
600	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
601	C₂²⋊C₄	—	2	2	no	—
602	C₂²⋊C₄	—	2	2	no	—
603	C₂²⋊C₄	—	2	2	no	—
604	C₂²⋊C₄	—	2	2	no	—
605	C₂²⋊C₄	—	2	1	no	—
606	C₂²⋊C₄	—	2	1	no	—
607	C₂²⋊C₄	—	2	2	no	—
608	C₂²⋊C₄	—	2	1	no	—
609	C₂²⋊C₄	—	2	1	no	—
610	C₂²⋊C₄	—	2	2	no	—
611	C₂²⋊C₄	—	2	1	no	—
612	C₂²⋊C₄	—	2	1	no	—
613	C₂²⋊C₄	—	2	1	no	—
614	C₄²	—	2	1	no	—
615	C₄²	—	2	1	no	—
616	C₄²	—	2	1	no	—
617	C₄²	C₂×D₄×C₇₃	1	1	yes	characteristic
618	C₄²	C₂×D₄×C₇₃	1	1	yes	characteristic
619	C₄²	C₂×D₄×C₇₃	1	1	yes	characteristic
620	C₄²	C₂⁴×C₇₃	1	1	yes	characteristic
621	C₂³	—	2	1	no	—
622	C₂³	—	2	1	no	—
623	C₂³	—	2	1	no	—
624	C₂³	—	2	2	no	—
625	C₂³	—	4	2	no	—
626	C₂³	—	4	4	no	—
627	C₂³	—	4	4	no	—
628	C₂³	—	4	2	no	—
629	C₂³	—	8	1	no	—
630	C₂³	—	8	2	no	—
631	C₂³	#120×C₇₃	1	1	yes	characteristic
632	Q₈	—	2	1	no	—
633	Q₈	—	4	4	no	—
634	Q₈	—	4	1	no	—
635	Q₈	—	4	1	no	—
636	Q₈	—	4	2	no	—
637	Q₈	—	4	2	no	—
638	Q₈	—	8	2	no	—
639	Q₈	C₂×D₈×C₇₃	1	2	yes	—
640	D₄	—	2	4	no	—
641	D₄	—	2	1	no	—
642	D₄	—	2	1	no	—
643	D₄	—	2	1	no	—
644	D₄	—	2	1	no	—
645	D₄	—	4	2	no	—
646	D₄	—	4	2	no	—
647	D₄	—	4	4	no	—
648	D₄	—	4	4	no	—
649	D₄	—	4	4	no	—
650	D₄	—	4	4	no	—
651	D₄	—	4	4	no	—
652	D₄	—	4	1	no	—
653	D₄	—	4	1	no	—
654	D₄	—	4	1	no	—
655	D₄	—	4	1	no	—
656	D₄	—	8	2	no	—
657	D₄	C₂×D₈×C₇₃	1	2	yes	—
658	D₄	#137×C₇₃	1	2	yes	complemented
659	C₂×C₄	—	2	1	no	—
660	C₂×C₄	—	2	4	no	—
661	C₂×C₄	—	2	1	no	—
662	C₂×C₄	—	2	1	no	—
663	C₂×C₄	—	2	1	no	—
664	C₂×C₄	—	2	1	no	—
665	C₂×C₄	—	2	1	no	—
666	C₂×C₄	—	2	2	no	—
667	C₂×C₄	—	2	1	no	—
668	C₂×C₄	—	4	1	no	—
669	C₂×C₄	—	4	4	no	—
670	C₂×C₄	—	4	4	no	—
671	C₂×C₄	—	4	4	no	—
672	C₂×C₄	—	4	2	no	—
673	C₂×C₄	—	4	2	no	—
674	C₂×C₄	—	4	4	no	—
675	C₂×C₄	—	4	2	no	—
676	C₂×C₄	—	4	1	no	—
677	C₂×C₄	—	4	1	no	—
678	C₂×C₄	—	4	1	no	—
679	C₂×C₄	—	4	1	no	—
680	C₂×C₄	—	4	1	no	—
681	C₂×C₄	—	4	1	no	—
682	C₂×C₄	—	4	2	no	—
683	C₂×C₄	—	8	1	no	—
684	C₂×C₄	—	8	2	no	—
685	C₂×C₄	#120×C₇₃	1	1	yes	characteristic
686	C₂×C₄	#120×C₇₃	1	1	yes	characteristic
687	C₂×C₄	#120×C₇₃	1	1	yes	characteristic
688	C₂×C₄	C₂×D₈×C₇₃	1	2	yes	—
689	C₂×C₄	AGL(1,ℤ/8)×C₇₃	1	2	yes	—
690	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
691	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
692	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
693	C₈	—	4	2	no	—
694	C₈	—	4	2	no	—
695	C₈	—	4	2	no	—
696	C₂²	—	2	1	no	—
697	C₂²	—	2	1	no	—
698	C₂²	—	2	2	no	—
699	C₂²	—	2	2	no	—
700	C₂²	—	4	1	no	—
701	C₂²	—	4	1	no	—
702	C₂²	—	4	1	no	—
703	C₂²	—	4	1	no	—
704	C₂²	—	4	2	no	—
705	C₂²	—	4	1	no	—
706	C₂²	—	4	1	no	—
707	C₂²	—	4	2	no	—
708	C₂²	—	4	2	no	—
709	C₂²	—	4	1	no	—
710	C₂²	—	8	4	no	—
711	C₂²	—	8	8	no	—
712	C₂²	#447×C₇₃	1	2	yes	—
713	C₂²	C₂×#120×C₇₃	1	1	yes	characteristic
714	C₄	—	2	2	no	—
715	C₄	—	2	1	no	—
716	C₄	—	2	1	no	—
717	C₄	—	2	1	no	—
718	C₄	—	4	1	no	—
719	C₄	—	4	2	no	—
720	C₄	—	4	1	no	—
721	C₄	—	4	1	no	—
722	C₄	—	4	1	no	—
723	C₄	—	8	2	no	—
724	C₄	#447×C₇₃	1	2	yes	—
725	C₄	C₂²×D₈×C₇₃	1	1	yes	characteristic
726	C₄	C₂×AGL(1,ℤ/8)×C₇₃	1	1	yes	characteristic
727	C₄	C₂×#137×C₇₃	1	1	yes	characteristic
728	C₄	#575×C₇₃	1	1	yes	characteristic
729	C₂	—	2	2	no	—
730	C₂	—	4	2	no	—
731	C₂	—	4	2	no	—
732	C₂	—	8	1	no	—
733	C₂	—	8	2	no	—
734	C₂	C₂×#447×C₇₃	1	1	yes	characteristic
735	C₂	C₇₃×#3007	1	1	yes	characteristic
736	C₂	C₇₃×#3022	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇₃	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₇₃
prime radical	D₄×#41×C₇₃	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
2. C₇₃×#3226	C₂	semidirect
3. C₂×#474×C₇₃	C₂	semidirect
4. C₇₃×#3039	C₂	semidirect
5. C₇₃×#1649	C₂	semidirect
6. C₇₃×#1647	C₂	semidirect
7. C₇₃×#1641	C₂	semidirect
8. C₇₃×#1639	C₂	semidirect
9. C₇₃×#1547	C₂	semidirect
10. C₇₃×#1486	C₂	semidirect
11. C₇₃×#1477	C₂	semidirect
25. C₂×C₄⋊Q₈×C₇₃	C₂²	semidirect
31. #500×C₇₃	C₂²	semidirect
32. #486×C₇₃	C₂²	semidirect
38. #474×C₇₃	C₂²	semidirect
40. #462×C₇₃	C₂²	semidirect
42. #461×C₇₃	C₂²	semidirect
43. #431×C₇₃	C₂²	semidirect
45. #423×C₇₃	C₂²	semidirect
46. C₂×C₄⋊C₈×C₇₃	C₂²	semidirect
49. #332×C₇₃	C₂²	semidirect
50. #331×C₇₃	C₂²	semidirect
51. Q₈⋊C₈×C₇₃	C₂²	semidirect
53. D₄⋊C₈×C₇₃	C₂²	semidirect
54. D₄⋊C₈×C₇₃	C₂²	semidirect
289. D₄×C₇₃	#137	semidirect
360. #18798	C₇₃	direct (N × H)
370. #3226	C₂×C₇₃	semidirect
371. C₂×#474	C₂×C₇₃	semidirect
372. #3039	C₂×C₇₃	semidirect
373. #1649	C₂×C₇₃	semidirect
374. #1647	C₂×C₇₃	semidirect
375. #1641	C₂×C₇₃	semidirect
376. #1639	C₂×C₇₃	semidirect
377. #1547	C₂×C₇₃	semidirect
378. #1486	C₂×C₇₃	semidirect
379. #1477	C₂×C₇₃	semidirect
380. C₇₃	#18798	direct (N × H)
394. C₂×C₄⋊Q₈	C₂²×C₇₃	semidirect
400. #500	C₂²×C₇₃	semidirect
401. #486	C₂²×C₇₃	semidirect
407. #474	C₂²×C₇₃	semidirect
409. #462	C₂²×C₇₃	semidirect
411. #461	C₂²×C₇₃	semidirect
412. #431	C₂²×C₇₃	semidirect
414. #423	C₂²×C₇₃	semidirect
415. C₂×C₄⋊C₈	C₂²×C₇₃	semidirect
418. #332	C₂²×C₇₃	semidirect
419. #331	C₂²×C₇₃	semidirect
420. Q₈⋊C₈	C₂²×C₇₃	semidirect
422. D₄⋊C₈	C₂²×C₇₃	semidirect
423. D₄⋊C₈	C₂²×C₇₃	semidirect
658. D₄	#137×C₇₃	semidirect

Maximal subgroups

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

subgroup	index
D₄×#41×C₇₃	2
C₇₃×#3226	2
C₂×#474×C₇₃	2
C₇₃×#3039	2
C₇₃×#1649	2
C₇₃×#1647	2
C₇₃×#1641	2
C₇₃×#1639	2
C₇₃×#1547	2
C₇₃×#1486	2
C₇₃×#1477	2
#18798	73

Subgroups — C73×#18798 #32928202

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#18798 #32928202