Subgroups — C₇₃×#23634 #32933038

Order 18688.

1010 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#417×C₇₃	C₂	1	1	yes	maximal, characteristic
2	C₂×#416×C₇₃	C₂	1	1	yes	maximal, characteristic
3	C₇₃×#2317	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₃×#2311	C₂	1	1	yes	maximal, characteristic
5	C₇₃×#2074	C₂	1	2	yes	maximal, complemented
6	C₇₃×#2073	C₂	1	2	yes	maximal, complemented
7	C₇₃×#2072	C₂	1	2	yes	maximal, complemented
8	C₇₃×#2071	C₂	1	2	yes	maximal, complemented
9	C₇₃×#1736	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#340×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₃×#1729	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#41×C₇₃	C₂²	1	1	yes	characteristic
13	C₂²×M₁₆×C₇₃	C₂²	1	1	yes	characteristic
14	C₂³×C₈×C₇₃	C₂²	1	1	yes	characteristic
15	C₂×#117×C₇₃	C₂²	1	1	yes	characteristic
16	C₂×#117×C₇₃	C₂²	1	1	yes	characteristic
17	C₂²×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
18	C₂²×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
19	#417×C₇₃	—	2	4	no	—
20	#416×C₇₃	—	2	4	no	—
21	C₂×#103×C₇₃	C₂²	1	1	yes	characteristic
22	C₂×#103×C₇₃	C₂²	1	2	yes	—
23	C₂×#103×C₇₃	C₂²	1	1	yes	characteristic
24	C₂×#102×C₇₃	C₂²	1	1	yes	characteristic
25	C₂×#102×C₇₃	C₂²	1	2	yes	—
26	C₂×#102×C₇₃	C₂²	1	1	yes	characteristic
27	#391×C₇₃	C₂²	1	2	yes	—
28	#390×C₇₃	C₂²	1	2	yes	—
29	#389×C₇₃	—	2	1	no	—
30	#389×C₇₃	—	2	1	no	—
31	#386×C₇₃	—	2	2	no	—
32	#385×C₇₃	—	2	2	no	—
33	#384×C₇₃	C₂²	1	2	yes	—
34	#382×C₇₃	C₂²	1	2	yes	—
35	#380×C₇₃	—	2	1	no	—
36	#380×C₇₃	—	2	1	no	—
37	#340×C₇₃	C₂²	1	2	yes	—
38	#340×C₇₃	C₂²	1	2	yes	—
39	#340×C₇₃	C₂²	1	2	yes	—
40	#340×C₇₃	C₂²	1	2	yes	—
41	#336×C₇₃	C₂²	1	2	yes	—
42	#336×C₇₃	C₂²	1	2	yes	—
43	C₂×#41×C₇₃	—	2	2	no	—
44	C₂×#41×C₇₃	—	2	2	no	—
45	C₂×#41×C₇₃	—	2	2	no	—
46	C₂×#41×C₇₃	—	2	2	no	—
47	C₂×#41×C₇₃	—	2	2	no	—
48	C₂×#41×C₇₃	D₄	1	4	yes	—
49	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
50	C₂²×D₄×C₇₃	—	2	1	no	—
51	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
52	C₂³×C₄×C₇₃	—	2	1	no	—
53	C₂³×C₄×C₇₃	—	2	1	no	—
54	C₂³×C₄×C₇₃	—	2	1	no	—
55	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
56	C₂×M₁₆×C₇₃	—	2	2	no	—
57	C₂×M₁₆×C₇₃	—	2	2	no	—
58	C₂×M₁₆×C₇₃	—	2	2	no	—
59	C₂²×C₈×C₇₃	—	2	2	no	—
60	C₂²×C₈×C₇₃	—	2	2	no	—
61	C₂²×C₈×C₇₃	—	2	2	no	—
62	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
63	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
64	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
65	#117×C₇₃	—	2	2	no	—
66	#117×C₇₃	—	2	2	no	—
67	#117×C₇₃	—	2	2	no	—
68	#117×C₇₃	—	2	2	no	—
69	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
70	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
71	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
72	C₂×C₄⋊C₄×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	—	2	2	no	—
77	C₂×C₄⋊C₄×C₇₃	D₄	1	1	yes	characteristic
78	C₂×C₄⋊C₄×C₇₃	D₄	1	1	yes	characteristic
79	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
80	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
81	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
82	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
83	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
84	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
85	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
86	C₂×C₂²⋊C₄×C₇₃	D₄	1	2	yes	—
87	C₂×C₄²×C₇₃	—	2	1	no	—
88	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
89	#103×C₇₃	—	2	2	no	—
90	#103×C₇₃	—	2	2	no	—
91	#103×C₇₃	—	2	4	no	—
92	#102×C₇₃	—	2	2	no	—
93	#102×C₇₃	—	2	2	no	—
94	#102×C₇₃	—	2	4	no	—
95	#95×C₇₃	—	2	2	no	—
96	#95×C₇₃	—	2	2	no	—
97	#95×C₇₃	—	2	2	no	—
98	#95×C₇₃	—	2	2	no	—
99	C₂⁴×C₇₃	—	2	1	no	—
100	C₂⁴×C₇₃	C₂×D₄	1	1	yes	characteristic
101	#41×C₇₃	—	2	8	no	—
102	#41×C₇₃	—	2	8	no	—
103	#41×C₇₃	—	4	4	no	—
104	#41×C₇₃	—	4	4	no	—
105	C₂×Q₈×C₇₃	—	2	1	no	—
106	C₂×Q₈×C₇₃	—	2	1	no	—
107	C₂×Q₈×C₇₃	—	2	1	no	—
108	C₂×Q₈×C₇₃	—	2	1	no	—
109	C₂×Q₈×C₇₃	—	2	1	no	—
110	C₂×Q₈×C₇₃	C₂×D₄	1	2	yes	—
111	C₂×D₄×C₇₃	—	2	4	no	—
112	C₂×D₄×C₇₃	—	2	1	no	—
113	C₂×D₄×C₇₃	—	2	1	no	—
114	C₂×D₄×C₇₃	—	2	1	no	—
115	C₂×D₄×C₇₃	—	2	1	no	—
116	C₂×D₄×C₇₃	—	2	1	no	—
117	C₂×D₄×C₇₃	—	4	2	no	—
118	C₂×D₄×C₇₃	—	4	2	no	—
119	C₂×D₄×C₇₃	C₂×D₄	1	2	yes	—
120	C₂²×C₄×C₇₃	—	2	1	no	—
121	C₂²×C₄×C₇₃	—	2	4	no	—
122	C₂²×C₄×C₇₃	—	2	1	no	—
123	C₂²×C₄×C₇₃	—	2	2	no	—
124	C₂²×C₄×C₇₃	—	2	2	no	—
125	C₂²×C₄×C₇₃	—	2	1	no	—
126	C₂²×C₄×C₇₃	—	4	2	no	—
127	C₂²×C₄×C₇₃	—	4	2	no	—
128	C₂²×C₄×C₇₃	—	4	2	no	—
129	C₂²×C₄×C₇₃	—	4	2	no	—
130	C₂²×C₄×C₇₃	—	8	1	no	—
131	C₂²×C₄×C₇₃	—	8	1	no	—
132	C₂²×C₄×C₇₃	—	8	1	no	—
133	C₂²×C₄×C₇₃	—	8	1	no	—
134	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
135	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
136	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
138	C₂²×C₄×C₇₃	#41	1	2	yes	—
139	C₂²×C₄×C₇₃	#41	1	2	yes	—
140	C₂²×C₄×C₇₃	#41	1	2	yes	—
141	C₂²×C₄×C₇₃	#41	1	2	yes	—
142	C₂²×C₄×C₇₃	#41	1	2	yes	—
143	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
144	M₁₆×C₇₃	—	4	4	no	—
145	C₂×C₈×C₇₃	—	2	1	no	—
146	C₂×C₈×C₇₃	—	2	1	no	—
147	C₂×C₈×C₇₃	—	2	2	no	—
148	C₂×C₈×C₇₃	—	2	1	no	—
149	C₂×C₈×C₇₃	—	2	1	no	—
150	C₂×C₈×C₇₃	—	2	1	no	—
151	C₂×C₈×C₇₃	—	2	1	no	—
152	C₂×C₈×C₇₃	—	2	2	no	—
153	C₂×C₈×C₇₃	—	2	2	no	—
154	C₂×C₈×C₇₃	—	4	4	no	—
155	C₄⋊C₄×C₇₃	—	2	2	no	—
156	C₄⋊C₄×C₇₃	—	2	2	no	—
157	C₄⋊C₄×C₇₃	—	2	2	no	—
158	C₄⋊C₄×C₇₃	—	2	1	no	—
159	C₄⋊C₄×C₇₃	—	2	1	no	—
160	C₄⋊C₄×C₇₃	—	2	2	no	—
161	C₄⋊C₄×C₇₃	—	2	2	no	—
162	C₄⋊C₄×C₇₃	—	2	2	no	—
163	C₄⋊C₄×C₇₃	—	2	1	no	—
164	C₄⋊C₄×C₇₃	—	2	1	no	—
165	C₄⋊C₄×C₇₃	—	4	2	no	—
166	C₄⋊C₄×C₇₃	—	4	2	no	—
167	C₄⋊C₄×C₇₃	—	8	2	no	—
168	C₄⋊C₄×C₇₃	—	8	2	no	—
169	C₂²⋊C₄×C₇₃	—	2	4	no	—
170	C₂²⋊C₄×C₇₃	—	4	2	no	—
171	C₂²⋊C₄×C₇₃	—	8	2	no	—
172	C₂²⋊C₄×C₇₃	—	8	2	no	—
173	C₄²×C₇₃	—	2	2	no	—
174	C₄²×C₇₃	—	2	2	no	—
175	C₄²×C₇₃	—	4	2	no	—
176	C₂³×C₇₃	—	2	1	no	—
177	C₂³×C₇₃	—	2	1	no	—
178	C₂³×C₇₃	—	2	1	no	—
179	C₂³×C₇₃	—	2	1	no	—
180	C₂³×C₇₃	—	2	2	no	—
181	C₂³×C₇₃	—	4	1	no	—
182	C₂³×C₇₃	—	4	1	no	—
183	C₂³×C₇₃	—	4	1	no	—
184	C₂³×C₇₃	—	4	1	no	—
185	C₂³×C₇₃	—	4	1	no	—
186	C₂³×C₇₃	—	4	1	no	—
187	C₂³×C₇₃	#121	1	2	yes	—
188	C₂³×C₇₃	#123	1	2	yes	—
189	C₂³×C₇₃	#124	1	2	yes	—
190	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
191	Q₈×C₇₃	—	2	2	no	—
192	Q₈×C₇₃	—	2	2	no	—
193	Q₈×C₇₃	—	4	1	no	—
194	Q₈×C₇₃	—	4	1	no	—
195	D₄×C₇₃	—	2	2	no	—
196	D₄×C₇₃	—	2	2	no	—
197	D₄×C₇₃	—	4	8	no	—
198	D₄×C₇₃	—	4	1	no	—
199	D₄×C₇₃	—	4	1	no	—
200	C₂×C₄×C₇₃	—	2	2	no	—
201	C₂×C₄×C₇₃	—	2	2	no	—
202	C₂×C₄×C₇₃	—	2	2	no	—
203	C₂×C₄×C₇₃	—	2	2	no	—
204	C₂×C₄×C₇₃	—	2	2	no	—
205	C₂×C₄×C₇₃	—	2	2	no	—
206	C₂×C₄×C₇₃	—	2	2	no	—
207	C₂×C₄×C₇₃	—	4	1	no	—
208	C₂×C₄×C₇₃	—	4	1	no	—
209	C₂×C₄×C₇₃	—	4	8	no	—
210	C₂×C₄×C₇₃	—	4	1	no	—
211	C₂×C₄×C₇₃	—	4	1	no	—
212	C₂×C₄×C₇₃	—	4	2	no	—
213	C₂×C₄×C₇₃	—	4	2	no	—
214	C₂×C₄×C₇₃	—	4	2	no	—
215	C₂×C₄×C₇₃	—	4	1	no	—
216	C₂×C₄×C₇₃	—	4	2	no	—
217	C₂×C₄×C₇₃	—	4	2	no	—
218	C₂×C₄×C₇₃	—	4	1	no	—
219	C₂×C₄×C₇₃	—	4	2	no	—
220	C₂×C₄×C₇₃	—	4	1	no	—
221	C₂×C₄×C₇₃	—	4	1	no	—
222	C₂×C₄×C₇₃	—	8	4	no	—
223	C₂×C₄×C₇₃	—	8	4	no	—
224	C₂×C₄×C₇₃	#121	1	2	yes	—
225	C₂×C₄×C₇₃	#123	1	4	yes	—
226	C₂×C₄×C₇₃	#123	1	4	yes	—
227	C₂×C₄×C₇₃	#123	1	2	yes	—
228	C₂×C₄×C₇₃	#124	1	2	yes	—
229	C₂×C₄×C₇₃	#126	1	4	yes	—
230	C₂×C₄×C₇₃	#126	1	4	yes	—
231	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
232	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
233	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
234	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
235	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
236	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
237	C₈×C₇₃	—	4	1	no	—
238	C₈×C₇₃	—	4	1	no	—
239	C₈×C₇₃	—	4	2	no	—
240	C₂²×C₇₃	—	2	2	no	—
241	C₂²×C₇₃	—	2	2	no	—
242	C₂²×C₇₃	—	2	2	no	—
243	C₂²×C₇₃	—	2	2	no	—
244	C₂²×C₇₃	—	2	2	no	—
245	C₂²×C₇₃	—	2	2	no	—
246	C₂²×C₇₃	—	4	2	no	—
247	C₂²×C₇₃	—	4	2	no	—
248	C₂²×C₇₃	—	4	2	no	—
249	C₂²×C₇₃	—	8	1	no	—
250	C₂²×C₇₃	—	8	1	no	—
251	C₂²×C₇₃	—	8	1	no	—
252	C₂²×C₇₃	—	8	1	no	—
253	C₂²×C₇₃	#397	1	4	yes	—
254	C₂²×C₇₃	C₂×#121	1	1	yes	characteristic
255	C₂²×C₇₃	C₂×#123	1	1	yes	characteristic
256	C₂²×C₇₃	C₂×#124	1	1	yes	characteristic
257	C₂²×C₇₃	#576	1	1	yes	characteristic
258	C₂²×C₇₃	#577	1	1	yes	characteristic
259	C₂²×C₇₃	#577	1	1	yes	characteristic
260	C₂²×C₇₃	#578	1	1	yes	characteristic
261	C₄×C₇₃	—	4	2	no	—
262	C₄×C₇₃	—	4	2	no	—
263	C₄×C₇₃	—	4	2	no	—
264	C₄×C₇₃	—	8	2	no	—
265	C₄×C₇₃	—	8	1	no	—
266	C₄×C₇₃	—	8	2	no	—
267	C₄×C₇₃	—	8	1	no	—
268	C₄×C₇₃	#397	1	4	yes	—
269	C₄×C₇₃	C₂×#123	1	1	yes	characteristic
270	C₄×C₇₃	C₂×#123	1	1	yes	characteristic
271	C₄×C₇₃	C₂×#126	1	1	yes	characteristic
272	C₄×C₇₃	C₂×#126	1	1	yes	characteristic
273	#23634	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
274	C₂×C₇₃	—	2	4	no	—
275	C₂×C₇₃	—	8	2	no	—
276	C₂×C₇₃	C₂×#397	1	1	yes	characteristic
277	C₂×C₇₃	#3045	1	1	yes	characteristic
278	C₂×C₇₃	#3046	1	1	yes	characteristic
279	C₂×C₇₃	#3098	1	1	yes	characteristic
280	C₂×C₇₃	#3099	1	1	yes	characteristic
281	C₂×C₇₃	#3136	1	1	yes	characteristic
282	C₂×C₇₃	#3137	1	1	yes	characteristic
283	C₂×#417	C₂×C₇₃	1	1	yes	characteristic
284	C₂×#416	C₂×C₇₃	1	1	yes	characteristic
285	#2317	C₂×C₇₃	1	1	yes	characteristic, complemented
286	#2311	C₂×C₇₃	1	1	yes	characteristic
287	#2074	C₂×C₇₃	1	2	yes	complemented
288	#2073	C₂×C₇₃	1	2	yes	complemented
289	#2072	C₂×C₇₃	1	2	yes	complemented
290	#2071	C₂×C₇₃	1	2	yes	complemented
291	#1736	C₂×C₇₃	1	1	yes	characteristic, complemented
292	C₂×#340	C₂×C₇₃	1	1	yes	characteristic, complemented
293	#1729	C₂×C₇₃	1	1	yes	characteristic, complemented
294	C₇₃	#23634	1	1	yes	characteristic, direct product factor, Sylow
295	C₂²×#41	C₂²×C₇₃	1	1	yes	characteristic
296	C₂²×M₁₆	C₂²×C₇₃	1	1	yes	characteristic
297	C₂³×C₈	C₂²×C₇₃	1	1	yes	characteristic
298	C₂×#117	C₂²×C₇₃	1	1	yes	characteristic
299	C₂×#117	C₂²×C₇₃	1	1	yes	characteristic
300	C₂²×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
301	C₂²×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
302	#417	—	2	4	no	—
303	#416	—	2	4	no	—
304	C₂×#103	C₂²×C₇₃	1	1	yes	characteristic
305	C₂×#103	C₂²×C₇₃	1	2	yes	—
306	C₂×#103	C₂²×C₇₃	1	1	yes	characteristic
307	C₂×#102	C₂²×C₇₃	1	1	yes	characteristic
308	C₂×#102	C₂²×C₇₃	1	2	yes	—
309	C₂×#102	C₂²×C₇₃	1	1	yes	characteristic
310	#391	C₂²×C₇₃	1	2	yes	—
311	#390	C₂²×C₇₃	1	2	yes	—
312	#389	—	2	1	no	—
313	#389	—	2	1	no	—
314	#386	—	2	2	no	—
315	#385	—	2	2	no	—
316	#384	C₂²×C₇₃	1	2	yes	—
317	#382	C₂²×C₇₃	1	2	yes	—
318	#380	—	2	1	no	—
319	#380	—	2	1	no	—
320	#340	C₂²×C₇₃	1	2	yes	—
321	#340	C₂²×C₇₃	1	2	yes	—
322	#340	C₂²×C₇₃	1	2	yes	—
323	#340	C₂²×C₇₃	1	2	yes	—
324	#336	C₂²×C₇₃	1	2	yes	—
325	#336	C₂²×C₇₃	1	2	yes	—
326	C₂×#41	—	2	2	no	—
327	C₂×#41	—	2	2	no	—
328	C₂×#41	—	2	2	no	—
329	C₂×#41	—	2	2	no	—
330	C₂×#41	—	2	2	no	—
331	C₂×#41	D₄×C₇₃	1	4	yes	—
332	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
333	C₂²×D₄	—	2	1	no	—
334	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
335	C₂³×C₄	—	2	1	no	—
336	C₂³×C₄	—	2	1	no	—
337	C₂³×C₄	—	2	1	no	—
338	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
339	C₂×M₁₆	—	2	2	no	—
340	C₂×M₁₆	—	2	2	no	—
341	C₂×M₁₆	—	2	2	no	—
342	C₂²×C₈	—	2	2	no	—
343	C₂²×C₈	—	2	2	no	—
344	C₂²×C₈	—	2	2	no	—
345	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
346	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
347	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
348	#117	—	2	2	no	—
349	#117	—	2	2	no	—
350	#117	—	2	2	no	—
351	#117	—	2	2	no	—
352	C₂×C₄⋊C₄	—	2	2	no	—
353	C₂×C₄⋊C₄	—	2	2	no	—
354	C₂×C₄⋊C₄	—	2	2	no	—
355	C₂×C₄⋊C₄	—	2	2	no	—
356	C₂×C₄⋊C₄	—	2	1	no	—
357	C₂×C₄⋊C₄	—	2	1	no	—
358	C₂×C₄⋊C₄	—	2	2	no	—
359	C₂×C₄⋊C₄	—	2	2	no	—
360	C₂×C₄⋊C₄	D₄×C₇₃	1	1	yes	characteristic
361	C₂×C₄⋊C₄	D₄×C₇₃	1	1	yes	characteristic
362	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
363	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
364	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
365	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
366	C₂×C₂²⋊C₄	—	2	1	no	—
367	C₂×C₂²⋊C₄	—	2	2	no	—
368	C₂×C₂²⋊C₄	—	2	2	no	—
369	C₂×C₂²⋊C₄	D₄×C₇₃	1	2	yes	—
370	C₂×C₄²	—	2	1	no	—
371	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
372	#103	—	2	2	no	—
373	#103	—	2	2	no	—
374	#103	—	2	4	no	—
375	#102	—	2	2	no	—
376	#102	—	2	2	no	—
377	#102	—	2	4	no	—
378	#95	—	2	2	no	—
379	#95	—	2	2	no	—
380	#95	—	2	2	no	—
381	#95	—	2	2	no	—
382	C₂⁴	—	2	1	no	—
383	C₂⁴	C₂×D₄×C₇₃	1	1	yes	characteristic
384	#41	—	2	8	no	—
385	#41	—	2	8	no	—
386	#41	—	4	4	no	—
387	#41	—	4	4	no	—
388	C₂×Q₈	—	2	1	no	—
389	C₂×Q₈	—	2	1	no	—
390	C₂×Q₈	—	2	1	no	—
391	C₂×Q₈	—	2	1	no	—
392	C₂×Q₈	—	2	1	no	—
393	C₂×Q₈	C₂×D₄×C₇₃	1	2	yes	—
394	C₂×D₄	—	2	4	no	—
395	C₂×D₄	—	2	1	no	—
396	C₂×D₄	—	2	1	no	—
397	C₂×D₄	—	2	1	no	—
398	C₂×D₄	—	2	1	no	—
399	C₂×D₄	—	2	1	no	—
400	C₂×D₄	—	4	2	no	—
401	C₂×D₄	—	4	2	no	—
402	C₂×D₄	C₂×D₄×C₇₃	1	2	yes	—
403	C₂²×C₄	—	2	1	no	—
404	C₂²×C₄	—	2	4	no	—
405	C₂²×C₄	—	2	1	no	—
406	C₂²×C₄	—	2	2	no	—
407	C₂²×C₄	—	2	2	no	—
408	C₂²×C₄	—	2	1	no	—
409	C₂²×C₄	—	4	2	no	—
410	C₂²×C₄	—	4	2	no	—
411	C₂²×C₄	—	4	2	no	—
412	C₂²×C₄	—	4	2	no	—
413	C₂²×C₄	—	8	1	no	—
414	C₂²×C₄	—	8	1	no	—
415	C₂²×C₄	—	8	1	no	—
416	C₂²×C₄	—	8	1	no	—
417	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
418	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
419	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
420	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
421	C₂²×C₄	#41×C₇₃	1	2	yes	—
422	C₂²×C₄	#41×C₇₃	1	2	yes	—
423	C₂²×C₄	#41×C₇₃	1	2	yes	—
424	C₂²×C₄	#41×C₇₃	1	2	yes	—
425	C₂²×C₄	#41×C₇₃	1	2	yes	—
426	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
427	M₁₆	—	4	4	no	—
428	C₂×C₈	—	2	1	no	—
429	C₂×C₈	—	2	1	no	—
430	C₂×C₈	—	2	2	no	—
431	C₂×C₈	—	2	1	no	—
432	C₂×C₈	—	2	1	no	—
433	C₂×C₈	—	2	1	no	—
434	C₂×C₈	—	2	1	no	—
435	C₂×C₈	—	2	2	no	—
436	C₂×C₈	—	2	2	no	—
437	C₂×C₈	—	4	4	no	—
438	C₄⋊C₄	—	2	2	no	—
439	C₄⋊C₄	—	2	2	no	—
440	C₄⋊C₄	—	2	2	no	—
441	C₄⋊C₄	—	2	1	no	—
442	C₄⋊C₄	—	2	1	no	—
443	C₄⋊C₄	—	2	2	no	—
444	C₄⋊C₄	—	2	2	no	—
445	C₄⋊C₄	—	2	2	no	—
446	C₄⋊C₄	—	2	1	no	—
447	C₄⋊C₄	—	2	1	no	—
448	C₄⋊C₄	—	4	2	no	—
449	C₄⋊C₄	—	4	2	no	—
450	C₄⋊C₄	—	8	2	no	—
451	C₄⋊C₄	—	8	2	no	—
452	C₂²⋊C₄	—	2	4	no	—
453	C₂²⋊C₄	—	4	2	no	—
454	C₂²⋊C₄	—	8	2	no	—
455	C₂²⋊C₄	—	8	2	no	—
456	C₄²	—	2	2	no	—
457	C₄²	—	2	2	no	—
458	C₄²	—	4	2	no	—
459	C₂³	—	2	1	no	—
460	C₂³	—	2	1	no	—
461	C₂³	—	2	1	no	—
462	C₂³	—	2	1	no	—
463	C₂³	—	2	2	no	—
464	C₂³	—	4	1	no	—
465	C₂³	—	4	1	no	—
466	C₂³	—	4	1	no	—
467	C₂³	—	4	1	no	—
468	C₂³	—	4	1	no	—
469	C₂³	—	4	1	no	—
470	C₂³	#121×C₇₃	1	2	yes	—
471	C₂³	#123×C₇₃	1	2	yes	—
472	C₂³	#124×C₇₃	1	2	yes	—
473	C₂³	C₂²×D₄×C₇₃	1	1	yes	characteristic
474	Q₈	—	2	2	no	—
475	Q₈	—	2	2	no	—
476	Q₈	—	4	1	no	—
477	Q₈	—	4	1	no	—
478	D₄	—	2	2	no	—
479	D₄	—	2	2	no	—
480	D₄	—	4	8	no	—
481	D₄	—	4	1	no	—
482	D₄	—	4	1	no	—
483	C₂×C₄	—	2	2	no	—
484	C₂×C₄	—	2	2	no	—
485	C₂×C₄	—	2	2	no	—
486	C₂×C₄	—	2	2	no	—
487	C₂×C₄	—	2	2	no	—
488	C₂×C₄	—	2	2	no	—
489	C₂×C₄	—	2	2	no	—
490	C₂×C₄	—	4	1	no	—
491	C₂×C₄	—	4	1	no	—
492	C₂×C₄	—	4	8	no	—
493	C₂×C₄	—	4	1	no	—
494	C₂×C₄	—	4	1	no	—
495	C₂×C₄	—	4	2	no	—
496	C₂×C₄	—	4	2	no	—
497	C₂×C₄	—	4	2	no	—
498	C₂×C₄	—	4	1	no	—
499	C₂×C₄	—	4	2	no	—
500	C₂×C₄	—	4	2	no	—
501	C₂×C₄	—	4	1	no	—
502	C₂×C₄	—	4	2	no	—
503	C₂×C₄	—	4	1	no	—
504	C₂×C₄	—	4	1	no	—
505	C₂×C₄	—	8	4	no	—
506	C₂×C₄	—	8	4	no	—
507	C₂×C₄	#121×C₇₃	1	2	yes	—
508	C₂×C₄	#123×C₇₃	1	2	yes	—
509	C₂×C₄	#123×C₇₃	1	4	yes	—
510	C₂×C₄	#123×C₇₃	1	4	yes	—
511	C₂×C₄	#124×C₇₃	1	2	yes	—
512	C₂×C₄	#126×C₇₃	1	4	yes	—
513	C₂×C₄	#126×C₇₃	1	4	yes	—
514	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
515	C₂×C₄	C₂×#41×C₇₃	1	1	yes	characteristic
516	C₂×C₄	C₂×#41×C₇₃	1	1	yes	characteristic
517	C₂×C₄	C₂×#41×C₇₃	1	1	yes	characteristic
518	C₂×C₄	C₂×#41×C₇₃	1	1	yes	characteristic
519	C₂×C₄	C₂×#41×C₇₃	1	1	yes	characteristic
520	C₈	—	4	1	no	—
521	C₈	—	4	1	no	—
522	C₈	—	4	2	no	—
523	C₂²	—	2	2	no	—
524	C₂²	—	2	2	no	—
525	C₂²	—	2	2	no	—
526	C₂²	—	2	2	no	—
527	C₂²	—	2	2	no	—
528	C₂²	—	2	2	no	—
529	C₂²	—	4	2	no	—
530	C₂²	—	4	2	no	—
531	C₂²	—	4	2	no	—
532	C₂²	—	8	1	no	—
533	C₂²	—	8	1	no	—
534	C₂²	—	8	1	no	—
535	C₂²	—	8	1	no	—
536	C₂²	#397×C₇₃	1	4	yes	—
537	C₂²	C₂×#121×C₇₃	1	1	yes	characteristic
538	C₂²	C₂×#123×C₇₃	1	1	yes	characteristic
539	C₂²	C₂×#124×C₇₃	1	1	yes	characteristic
540	C₂²	#576×C₇₃	1	1	yes	characteristic
541	C₂²	#577×C₇₃	1	1	yes	characteristic
542	C₂²	#577×C₇₃	1	1	yes	characteristic
543	C₂²	#578×C₇₃	1	1	yes	characteristic
544	C₄	—	4	2	no	—
545	C₄	—	4	2	no	—
546	C₄	—	4	2	no	—
547	C₄	—	8	2	no	—
548	C₄	—	8	1	no	—
549	C₄	—	8	1	no	—
550	C₄	—	8	2	no	—
551	C₄	#397×C₇₃	1	4	yes	—
552	C₄	C₂×#123×C₇₃	1	1	yes	characteristic
553	C₄	C₂×#123×C₇₃	1	1	yes	characteristic
554	C₄	C₂×#126×C₇₃	1	1	yes	characteristic
555	C₄	C₂×#126×C₇₃	1	1	yes	characteristic
556	C₂	—	2	4	no	—
557	C₂	—	8	2	no	—
558	C₂	C₂×#397×C₇₃	1	1	yes	characteristic
559	C₂	C₇₃×#3045	1	1	yes	characteristic
560	C₂	C₇₃×#3046	1	1	yes	characteristic
561	C₂	C₇₃×#3098	1	1	yes	characteristic
562	C₂	C₇₃×#3099	1	1	yes	characteristic
563	C₂	C₇₃×#3136	1	1	yes	characteristic
564	C₂	C₇₃×#3137	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₃
prime radical	C₂²×#41×C₇₃	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇₃ ◁ C₂×#117×C₇₃ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
3. C₇₃×#2317	C₂	semidirect
5. C₇₃×#2074	C₂	semidirect
6. C₇₃×#2073	C₂	semidirect
7. C₇₃×#2072	C₂	semidirect
8. C₇₃×#2071	C₂	semidirect
9. C₇₃×#1736	C₂	semidirect
10. C₂×#340×C₇₃	C₂	semidirect
11. C₇₃×#1729	C₂	semidirect
273. #23634	C₇₃	direct (N × H)
285. #2317	C₂×C₇₃	semidirect
287. #2074	C₂×C₇₃	semidirect
288. #2073	C₂×C₇₃	semidirect
289. #2072	C₂×C₇₃	semidirect
290. #2071	C₂×C₇₃	semidirect
291. #1736	C₂×C₇₃	semidirect
292. C₂×#340	C₂×C₇₃	semidirect
293. #1729	C₂×C₇₃	semidirect
294. C₇₃	#23634	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#417×C₇₃	2
C₂×#416×C₇₃	2
C₇₃×#2317	2
C₇₃×#2311	2
C₇₃×#2074	2
C₇₃×#2073	2
C₇₃×#2072	2
C₇₃×#2071	2
C₇₃×#1736	2
C₂×#340×C₇₃	2
C₇₃×#1729	2
#23634	73

Subgroups — C73×#23634 #32933038

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#23634 #32933038