Subgroups — C₇₃×#23815 #32933219

Order 18688.

946 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₄⋊Q₈×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×#127×C₇₃	C₂	1	1	yes	maximal, characteristic
3	C₇₃×#2099	C₂	1	2	yes	maximal, complemented
4	C₇₃×#2071	C₂	1	2	yes	maximal, complemented
5	C₇₃×#2041	C₂	1	2	yes	maximal
6	C₇₃×#2023	C₂	1	2	yes	maximal, complemented
7	C₄×#102×C₇₃	C₂	1	4	yes	maximal, complemented
8	C₇₃×#1744	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₄⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
10	C₂×#127×C₇₃	C₂²	1	1	yes	characteristic
11	C₂×C₄×Q₈×C₇₃	—	2	1	no	—
12	C₂×C₄×D₄×C₇₃	—	2	1	no	—
13	C₂×C₄×D₄×C₇₃	—	2	1	no	—
14	C₂×C₄×D₄×C₇₃	C₂²	1	2	yes	—
15	C₂×#102×C₇₃	C₂²	1	4	yes	—
16	C₂×#102×C₇₃	C₂²	1	4	yes	—
17	C₂×C₄×C₈×C₇₃	C₂²	1	2	yes	—
18	#391×C₇₃	—	2	1	no	—
19	#390×C₇₃	—	2	1	no	—
20	#390×C₇₃	—	2	1	no	—
21	#390×C₇₃	C₂²	1	2	yes	—
22	#389×C₇₃	—	2	1	no	—
23	#389×C₇₃	C₂²	1	2	yes	—
24	#384×C₇₃	C₂²	1	1	yes	characteristic
25	#384×C₇₃	C₂²	1	1	yes	characteristic
26	C₄×C₄⋊C₄×C₇₃	—	2	1	no	—
27	C₄×C₄⋊C₄×C₇₃	C₂²	1	2	yes	—
28	C₄³×C₇₃	C₂²	1	1	yes	characteristic
29	#340×C₇₃	C₂²	1	4	yes	—
30	#340×C₇₃	C₂²	1	4	yes	—
31	#336×C₇₃	C₂²	1	2	yes	—
32	#336×C₇₃	C₂²	1	2	yes	—
33	C₂²×Q₈×C₇₃	—	2	1	no	—
34	C₂²×D₄×C₇₃	—	2	1	no	—
35	C₂²×D₄×C₇₃	—	2	1	no	—
36	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
37	C₂³×C₄×C₇₃	—	2	2	no	—
38	C₂²×C₈×C₇₃	C₂³	1	4	yes	—
39	C₄⋊Q₈×C₇₃	—	2	4	no	—
40	#127×C₇₃	—	2	4	no	—
41	C₄×Q₈×C₇₃	—	4	4	no	—
42	C₄×D₄×C₇₃	—	2	8	no	—
43	C₄×D₄×C₇₃	—	4	4	no	—
44	C₄×D₄×C₇₃	—	4	4	no	—
45	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
46	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
47	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
48	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
49	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
50	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
51	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
52	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
53	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
54	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
55	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
56	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
57	C₂×C₄²×C₇₃	—	2	2	no	—
58	C₂×C₄²×C₇₃	D₄	1	1	yes	characteristic
59	C₂×C₄²×C₇₃	D₄	1	1	yes	characteristic
60	C₂×C₄²×C₇₃	D₄	1	1	yes	characteristic
61	C₂×C₄²×C₇₃	D₄	1	1	yes	characteristic
62	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
63	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
64	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
65	#102×C₇₃	—	2	8	no	—
66	#102×C₇₃	—	2	8	no	—
67	C₄×C₈×C₇₃	—	2	4	no	—
68	#95×C₇₃	—	2	2	no	—
69	#95×C₇₃	—	2	2	no	—
70	C₂⁴×C₇₃	—	2	2	no	—
71	C₂×Q₈×C₇₃	—	2	4	no	—
72	C₂×Q₈×C₇₃	—	4	2	no	—
73	C₂×Q₈×C₇₃	—	4	2	no	—
74	C₂×D₄×C₇₃	—	2	4	no	—
75	C₂×D₄×C₇₃	—	2	4	no	—
76	C₂×D₄×C₇₃	—	2	4	no	—
77	C₂×D₄×C₇₃	—	2	4	no	—
78	C₂×D₄×C₇₃	—	2	2	no	—
79	C₂×D₄×C₇₃	—	4	2	no	—
80	C₂×D₄×C₇₃	—	4	2	no	—
81	C₂×D₄×C₇₃	—	4	2	no	—
82	C₂×D₄×C₇₃	—	4	2	no	—
83	C₂×D₄×C₇₃	#41	1	4	yes	—
84	C₂²×C₄×C₇₃	—	2	2	no	—
85	C₂²×C₄×C₇₃	—	2	2	no	—
86	C₂²×C₄×C₇₃	—	2	2	no	—
87	C₂²×C₄×C₇₃	—	4	4	no	—
88	C₂²×C₄×C₇₃	—	4	4	no	—
89	C₂²×C₄×C₇₃	—	4	4	no	—
90	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
91	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
94	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
97	C₂×C₈×C₇₃	—	2	4	no	—
98	C₂×C₈×C₇₃	—	2	4	no	—
99	C₂×C₈×C₇₃	—	2	4	no	—
100	C₄⋊C₄×C₇₃	—	2	4	no	—
101	C₄⋊C₄×C₇₃	—	2	2	no	—
102	C₄⋊C₄×C₇₃	—	2	4	no	—
103	C₄⋊C₄×C₇₃	—	2	4	no	—
104	C₄⋊C₄×C₇₃	—	4	2	no	—
105	C₄⋊C₄×C₇₃	—	4	2	no	—
106	C₄⋊C₄×C₇₃	—	4	4	no	—
107	C₄⋊C₄×C₇₃	—	4	2	no	—
108	C₄⋊C₄×C₇₃	—	4	2	no	—
109	C₄⋊C₄×C₇₃	#41	1	4	yes	—
110	C₂²⋊C₄×C₇₃	—	4	4	no	—
111	C₂²⋊C₄×C₇₃	—	4	4	no	—
112	C₂²⋊C₄×C₇₃	—	4	4	no	—
113	C₄²×C₇₃	—	2	2	no	—
114	C₄²×C₇₃	—	2	2	no	—
115	C₄²×C₇₃	—	4	1	no	—
116	C₄²×C₇₃	—	4	1	no	—
117	C₄²×C₇₃	—	4	4	no	—
118	C₄²×C₇₃	D₈	1	4	yes	—
119	C₄²×C₇₃	SD₁₆	1	4	yes	—
120	C₄²×C₇₃	#41	1	4	yes	—
121	C₂³×C₇₃	—	2	4	no	—
122	C₂³×C₇₃	—	4	2	no	—
123	C₂³×C₇₃	—	4	2	no	—
124	C₂³×C₇₃	—	4	2	no	—
125	C₂³×C₇₃	—	4	2	no	—
126	C₂³×C₇₃	—	4	2	no	—
127	C₂³×C₇₃	—	4	2	no	—
128	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
129	Q₈×C₇₃	—	4	8	no	—
130	D₄×C₇₃	—	2	8	no	—
131	D₄×C₇₃	—	4	8	no	—
132	D₄×C₇₃	—	4	8	no	—
133	D₄×C₇₃	—	4	4	no	—
134	C₂×C₄×C₇₃	—	2	1	no	—
135	C₂×C₄×C₇₃	—	2	1	no	—
136	C₂×C₄×C₇₃	—	2	1	no	—
137	C₂×C₄×C₇₃	—	2	1	no	—
138	C₂×C₄×C₇₃	—	2	1	no	—
139	C₂×C₄×C₇₃	—	2	1	no	—
140	C₂×C₄×C₇₃	—	2	1	no	—
141	C₂×C₄×C₇₃	—	2	1	no	—
142	C₂×C₄×C₇₃	—	2	1	no	—
143	C₂×C₄×C₇₃	—	2	1	no	—
144	C₂×C₄×C₇₃	—	2	4	no	—
145	C₂×C₄×C₇₃	—	4	2	no	—
146	C₂×C₄×C₇₃	—	4	2	no	—
147	C₂×C₄×C₇₃	—	4	2	no	—
148	C₂×C₄×C₇₃	—	4	2	no	—
149	C₂×C₄×C₇₃	—	4	2	no	—
150	C₂×C₄×C₇₃	—	4	2	no	—
151	C₂×C₄×C₇₃	—	4	2	no	—
152	C₂×C₄×C₇₃	—	4	2	no	—
153	C₂×C₄×C₇₃	—	8	8	no	—
154	C₂×C₄×C₇₃	#124	1	2	yes	—
155	C₂×C₄×C₇₃	#124	1	2	yes	—
156	C₂×C₄×C₇₃	C₂×D₈	1	2	yes	—
157	C₂×C₄×C₇₃	C₂×D₈	1	2	yes	—
158	C₂×C₄×C₇₃	C₂×D₈	1	2	yes	—
159	C₂×C₄×C₇₃	C₂×SD₁₆	1	2	yes	—
160	C₂×C₄×C₇₃	C₂×SD₁₆	1	2	yes	—
161	C₂×C₄×C₇₃	C₂×SD₁₆	1	2	yes	—
162	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
163	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
164	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
165	C₈×C₇₃	—	4	4	no	—
166	C₂²×C₇₃	—	4	4	no	—
167	C₂²×C₇₃	—	4	4	no	—
168	C₂²×C₇₃	—	4	4	no	—
169	C₂²×C₇₃	—	8	2	no	—
170	C₂²×C₇₃	—	8	2	no	—
171	C₂²×C₇₃	—	8	2	no	—
172	C₂²×C₇₃	—	8	2	no	—
173	C₂²×C₇₃	#525	1	1	yes	characteristic
174	C₂²×C₇₃	#525	1	1	yes	characteristic
175	C₂²×C₇₃	C₂×#124	1	1	yes	characteristic
176	C₂²×C₇₃	C₂²×D₈	1	1	yes	characteristic
177	C₂²×C₇₃	C₂²×SD₁₆	1	1	yes	characteristic
178	C₂²×C₇₃	#575	1	1	yes	characteristic
179	C₂²×C₇₃	#575	1	1	yes	characteristic
180	C₄×C₇₃	—	2	2	no	—
181	C₄×C₇₃	—	2	2	no	—
182	C₄×C₇₃	—	2	2	no	—
183	C₄×C₇₃	—	2	2	no	—
184	C₄×C₇₃	—	2	2	no	—
185	C₄×C₇₃	—	4	4	no	—
186	C₄×C₇₃	—	8	2	no	—
187	C₄×C₇₃	—	8	2	no	—
188	C₄×C₇₃	#486	1	4	yes	—
189	C₄×C₇₃	#529	1	4	yes	—
190	#23815	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
191	C₂×C₇₃	—	8	4	no	—
192	C₂×C₇₃	#2398	1	1	yes	characteristic
193	C₂×C₇₃	#3100	1	1	yes	characteristic
194	C₂×C₇₃	#3100	1	1	yes	characteristic
195	C₂×C₇₃	#3101	1	1	yes	characteristic
196	C₂×C₇₃	#3103	1	1	yes	characteristic
197	C₂×C₇₃	C₂×#486	1	1	yes	characteristic
198	C₂×C₇₃	#3135	1	1	yes	characteristic
199	C₄×C₄⋊Q₈	C₂×C₇₃	1	1	yes	characteristic, complemented
200	C₄×#127	C₂×C₇₃	1	1	yes	characteristic
201	#2099	C₂×C₇₃	1	2	yes	complemented
202	#2071	C₂×C₇₃	1	2	yes	complemented
203	#2041	C₂×C₇₃	1	2	yes	—
204	#2023	C₂×C₇₃	1	2	yes	complemented
205	C₄×#102	C₂×C₇₃	1	4	yes	complemented
206	#1744	C₂×C₇₃	1	1	yes	characteristic, complemented
207	C₇₃	#23815	1	1	yes	characteristic, direct product factor, Sylow
208	C₂×C₄⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
209	C₂×#127	C₂²×C₇₃	1	1	yes	characteristic
210	C₂×C₄×Q₈	—	2	1	no	—
211	C₂×C₄×D₄	—	2	1	no	—
212	C₂×C₄×D₄	—	2	1	no	—
213	C₂×C₄×D₄	C₂²×C₇₃	1	2	yes	—
214	C₂×#102	C₂²×C₇₃	1	4	yes	—
215	C₂×#102	C₂²×C₇₃	1	4	yes	—
216	C₂×C₄×C₈	C₂²×C₇₃	1	2	yes	—
217	#391	—	2	1	no	—
218	#390	—	2	1	no	—
219	#390	—	2	1	no	—
220	#390	C₂²×C₇₃	1	2	yes	—
221	#389	—	2	1	no	—
222	#389	C₂²×C₇₃	1	2	yes	—
223	#384	C₂²×C₇₃	1	1	yes	characteristic
224	#384	C₂²×C₇₃	1	1	yes	characteristic
225	C₄×C₄⋊C₄	—	2	1	no	—
226	C₄×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
227	C₄³	C₂²×C₇₃	1	1	yes	characteristic
228	#340	C₂²×C₇₃	1	4	yes	—
229	#340	C₂²×C₇₃	1	4	yes	—
230	#336	C₂²×C₇₃	1	2	yes	—
231	#336	C₂²×C₇₃	1	2	yes	—
232	C₂²×Q₈	—	2	1	no	—
233	C₂²×D₄	—	2	1	no	—
234	C₂²×D₄	—	2	1	no	—
235	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
236	C₂³×C₄	—	2	2	no	—
237	C₂²×C₈	C₂³×C₇₃	1	4	yes	—
238	C₄⋊Q₈	—	2	4	no	—
239	#127	—	2	4	no	—
240	C₄×Q₈	—	4	4	no	—
241	C₄×D₄	—	2	8	no	—
242	C₄×D₄	—	4	4	no	—
243	C₄×D₄	—	4	4	no	—
244	C₂×C₄⋊C₄	—	2	1	no	—
245	C₂×C₄⋊C₄	—	2	1	no	—
246	C₂×C₄⋊C₄	—	2	1	no	—
247	C₂×C₄⋊C₄	—	2	1	no	—
248	C₂×C₄⋊C₄	—	2	2	no	—
249	C₂×C₄⋊C₄	—	2	1	no	—
250	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
251	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
252	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
253	C₂×C₂²⋊C₄	—	2	2	no	—
254	C₂×C₂²⋊C₄	—	2	2	no	—
255	C₂×C₂²⋊C₄	—	2	2	no	—
256	C₂×C₄²	—	2	2	no	—
257	C₂×C₄²	D₄×C₇₃	1	1	yes	characteristic
258	C₂×C₄²	D₄×C₇₃	1	1	yes	characteristic
259	C₂×C₄²	D₄×C₇₃	1	1	yes	characteristic
260	C₂×C₄²	D₄×C₇₃	1	1	yes	characteristic
261	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
262	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
263	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
264	#102	—	2	8	no	—
265	#102	—	2	8	no	—
266	C₄×C₈	—	2	4	no	—
267	#95	—	2	2	no	—
268	#95	—	2	2	no	—
269	C₂⁴	—	2	2	no	—
270	C₂×Q₈	—	2	4	no	—
271	C₂×Q₈	—	4	2	no	—
272	C₂×Q₈	—	4	2	no	—
273	C₂×D₄	—	2	4	no	—
274	C₂×D₄	—	2	4	no	—
275	C₂×D₄	—	2	4	no	—
276	C₂×D₄	—	2	4	no	—
277	C₂×D₄	—	2	2	no	—
278	C₂×D₄	—	4	2	no	—
279	C₂×D₄	—	4	2	no	—
280	C₂×D₄	—	4	2	no	—
281	C₂×D₄	—	4	2	no	—
282	C₂×D₄	#41×C₇₃	1	4	yes	—
283	C₂²×C₄	—	2	2	no	—
284	C₂²×C₄	—	2	2	no	—
285	C₂²×C₄	—	2	2	no	—
286	C₂²×C₄	—	4	4	no	—
287	C₂²×C₄	—	4	4	no	—
288	C₂²×C₄	—	4	4	no	—
289	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
290	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
291	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
292	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
293	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
294	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
295	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
296	C₂×C₈	—	2	4	no	—
297	C₂×C₈	—	2	4	no	—
298	C₂×C₈	—	2	4	no	—
299	C₄⋊C₄	—	2	4	no	—
300	C₄⋊C₄	—	2	2	no	—
301	C₄⋊C₄	—	2	4	no	—
302	C₄⋊C₄	—	2	4	no	—
303	C₄⋊C₄	—	4	2	no	—
304	C₄⋊C₄	—	4	2	no	—
305	C₄⋊C₄	—	4	4	no	—
306	C₄⋊C₄	—	4	2	no	—
307	C₄⋊C₄	—	4	2	no	—
308	C₄⋊C₄	#41×C₇₃	1	4	yes	—
309	C₂²⋊C₄	—	4	4	no	—
310	C₂²⋊C₄	—	4	4	no	—
311	C₂²⋊C₄	—	4	4	no	—
312	C₄²	—	2	2	no	—
313	C₄²	—	2	2	no	—
314	C₄²	—	4	1	no	—
315	C₄²	—	4	1	no	—
316	C₄²	—	4	4	no	—
317	C₄²	D₈×C₇₃	1	4	yes	—
318	C₄²	SD₁₆×C₇₃	1	4	yes	—
319	C₄²	#41×C₇₃	1	4	yes	—
320	C₂³	—	2	4	no	—
321	C₂³	—	4	2	no	—
322	C₂³	—	4	2	no	—
323	C₂³	—	4	2	no	—
324	C₂³	—	4	2	no	—
325	C₂³	—	4	2	no	—
326	C₂³	—	4	2	no	—
327	C₂³	C₂²×D₄×C₇₃	1	1	yes	characteristic
328	Q₈	—	4	8	no	—
329	D₄	—	2	8	no	—
330	D₄	—	4	8	no	—
331	D₄	—	4	8	no	—
332	D₄	—	4	4	no	—
333	C₂×C₄	—	2	1	no	—
334	C₂×C₄	—	2	1	no	—
335	C₂×C₄	—	2	1	no	—
336	C₂×C₄	—	2	1	no	—
337	C₂×C₄	—	2	1	no	—
338	C₂×C₄	—	2	1	no	—
339	C₂×C₄	—	2	1	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	2	4	no	—
344	C₂×C₄	—	4	2	no	—
345	C₂×C₄	—	4	2	no	—
346	C₂×C₄	—	4	2	no	—
347	C₂×C₄	—	4	2	no	—
348	C₂×C₄	—	4	2	no	—
349	C₂×C₄	—	4	2	no	—
350	C₂×C₄	—	4	2	no	—
351	C₂×C₄	—	4	2	no	—
352	C₂×C₄	—	8	8	no	—
353	C₂×C₄	#124×C₇₃	1	2	yes	—
354	C₂×C₄	#124×C₇₃	1	2	yes	—
355	C₂×C₄	C₂×D₈×C₇₃	1	2	yes	—
356	C₂×C₄	C₂×D₈×C₇₃	1	2	yes	—
357	C₂×C₄	C₂×D₈×C₇₃	1	2	yes	—
358	C₂×C₄	C₂×SD₁₆×C₇₃	1	2	yes	—
359	C₂×C₄	C₂×SD₁₆×C₇₃	1	2	yes	—
360	C₂×C₄	C₂×SD₁₆×C₇₃	1	2	yes	—
361	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
362	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
363	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
364	C₈	—	4	4	no	—
365	C₂²	—	4	4	no	—
366	C₂²	—	4	4	no	—
367	C₂²	—	4	4	no	—
368	C₂²	—	8	2	no	—
369	C₂²	—	8	2	no	—
370	C₂²	—	8	2	no	—
371	C₂²	—	8	2	no	—
372	C₂²	#525×C₇₃	1	1	yes	characteristic
373	C₂²	#525×C₇₃	1	1	yes	characteristic
374	C₂²	C₂×#124×C₇₃	1	1	yes	characteristic
375	C₂²	C₂²×D₈×C₇₃	1	1	yes	characteristic
376	C₂²	C₂²×SD₁₆×C₇₃	1	1	yes	characteristic
377	C₂²	#575×C₇₃	1	1	yes	characteristic
378	C₂²	#575×C₇₃	1	1	yes	characteristic
379	C₄	—	2	2	no	—
380	C₄	—	2	2	no	—
381	C₄	—	2	2	no	—
382	C₄	—	2	2	no	—
383	C₄	—	2	2	no	—
384	C₄	—	4	4	no	—
385	C₄	—	8	2	no	—
386	C₄	—	8	2	no	—
387	C₄	#486×C₇₃	1	4	yes	—
388	C₄	#529×C₇₃	1	4	yes	—
389	C₂	—	8	4	no	—
390	C₂	C₇₃×#2398	1	1	yes	characteristic
391	C₂	C₇₃×#3100	1	1	yes	characteristic
392	C₂	C₇₃×#3100	1	1	yes	characteristic
393	C₂	C₇₃×#3101	1	1	yes	characteristic
394	C₂	C₇₃×#3103	1	1	yes	characteristic
395	C₂	C₂×#486×C₇₃	1	1	yes	characteristic
396	C₂	C₇₃×#3135	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₇₃	C₂×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₃
socle	C₂³×C₇₃	C₂²×D₄
prime radical	C₂×#127×C₇₃	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₇₃ ◁ C₄³×C₇₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄×C₄⋊Q₈×C₇₃	C₂	semidirect
3. C₇₃×#2099	C₂	semidirect
4. C₇₃×#2071	C₂	semidirect
6. C₇₃×#2023	C₂	semidirect
7. C₄×#102×C₇₃	C₂	semidirect
8. C₇₃×#1744	C₂	semidirect
190. #23815	C₇₃	direct (N × H)
199. C₄×C₄⋊Q₈	C₂×C₇₃	semidirect
201. #2099	C₂×C₇₃	semidirect
202. #2071	C₂×C₇₃	semidirect
204. #2023	C₂×C₇₃	semidirect
205. C₄×#102	C₂×C₇₃	semidirect
206. #1744	C₂×C₇₃	semidirect
207. C₇₃	#23815	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄×C₄⋊Q₈×C₇₃	2
C₄×#127×C₇₃	2
C₇₃×#2099	2
C₇₃×#2071	2
C₇₃×#2041	2
C₇₃×#2023	2
C₄×#102×C₇₃	2
C₇₃×#1744	2
#23815	73

Subgroups — C73×#23815 #32933219

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#23815 #32933219