Subgroups — C₇₃×#22567 #32931971

Order 18688.

962 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#103×C₇₃	C₂	1	1	yes	maximal, characteristic
2	C₇₃×#2345	C₂	1	1	yes	maximal, characteristic
3	Q₈×C₂²⋊C₄×C₇₃	C₂	1	1	yes	maximal, characteristic
4	C₇₃×#1935	C₂	1	2	yes	maximal, complemented
5	C₇₃×#1927	C₂	1	2	yes	maximal, complemented
6	C₇₃×#1865	C₂	1	2	yes	maximal, complemented
7	C₇₃×#1824	C₂	1	1	yes	maximal, characteristic
8	C₇₃×#1807	C₂	1	1	yes	maximal, characteristic
9	C₇₃×#1787	C₂	1	1	yes	maximal, characteristic
10	C₇₃×#1763	C₂	1	2	yes	maximal, complemented
11	C₇₃×#1752	C₂	1	1	yes	maximal, characteristic
12	C₂³×Q₈×C₇₃	C₂²	1	1	yes	characteristic
13	C₂³×C₈×C₇₃	C₂²	1	1	yes	characteristic
14	C₂×C₄×Q₈×C₇₃	C₂²	1	2	yes	—
15	C₂²×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
16	C₂×#106×C₇₃	C₂²	1	2	yes	—
17	C₂×#103×C₇₃	C₄	1	8	yes	complemented
18	C₂×#103×C₇₃	C₂²	1	2	yes	—
19	C₂×#103×C₇₃	C₂²	1	2	yes	—
20	C₂×#103×C₇₃	C₂²	1	1	yes	characteristic
21	C₂×#103×C₇₃	C₂²	1	1	yes	characteristic
22	C₂×#103×C₇₃	C₂²	1	1	yes	characteristic
23	C₂×#103×C₇₃	C₂²	1	1	yes	characteristic
24	C₂×C₂²⋊C₈×C₇₃	C₂²	1	1	yes	characteristic
25	C₂×#97×C₇₃	C₂²	1	2	yes	—
26	#391×C₇₃	—	2	2	no	—
27	#391×C₇₃	C₂²	1	2	yes	—
28	#389×C₇₃	C₂²	1	2	yes	—
29	#387×C₇₃	—	2	2	no	—
30	#380×C₇₃	—	2	1	no	—
31	#380×C₇₃	—	2	1	no	—
32	#380×C₇₃	C₂²	1	1	yes	characteristic
33	#380×C₇₃	C₂²	1	1	yes	characteristic
34	C₄×C₄⋊C₄×C₇₃	C₂²	1	2	yes	—
35	C₄×C₂²⋊C₄×C₇₃	—	2	1	no	—
36	C₄×C₂²⋊C₄×C₇₃	—	2	1	no	—
37	C₄×C₂²⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
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	C₂²×Q₈×C₇₃	—	2	1	no	—
43	C₂²×Q₈×C₇₃	—	2	2	no	—
44	C₂²×Q₈×C₇₃	—	2	4	no	—
45	C₂²×Q₈×C₇₃	—	4	2	no	—
46	C₂²×Q₈×C₇₃	C₂×C₄	1	4	yes	—
47	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
48	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
49	C₂³×C₄×C₇₃	—	2	1	no	—
50	C₂³×C₄×C₇₃	—	2	1	no	—
51	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
52	C₂²×C₈×C₇₃	—	4	2	no	—
53	C₂²×C₈×C₇₃	C₂×C₄	1	4	yes	—
54	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
55	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
56	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
57	C₄×Q₈×C₇₃	—	2	4	no	—
58	C₄×Q₈×C₇₃	—	4	2	no	—
59	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
60	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
61	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
62	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
63	C₂×C₄⋊C₄×C₇₃	C₂×C₄	1	4	yes	—
64	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
65	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
66	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
67	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
68	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
69	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
70	C₂×C₂²⋊C₄×C₇₃	D₄	1	1	yes	characteristic
71	C₂×C₂²⋊C₄×C₇₃	D₄	1	1	yes	characteristic
72	C₂×C₄²×C₇₃	—	2	2	no	—
73	C₂×C₄²×C₇₃	—	2	2	no	—
74	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
75	#106×C₇₃	—	4	2	no	—
76	#103×C₇₃	—	2	4	no	—
77	#103×C₇₃	—	4	2	no	—
78	#103×C₇₃	C₂×C₄	1	4	yes	—
79	#103×C₇₃	C₂×C₄	1	4	yes	—
80	#103×C₇₃	C₂×C₄	1	4	yes	—
81	#103×C₇₃	C₂×C₄	1	4	yes	—
82	C₂²⋊C₈×C₇₃	—	2	2	no	—
83	#97×C₇₃	—	4	2	no	—
84	#95×C₇₃	—	2	2	no	—
85	#95×C₇₃	—	2	2	no	—
86	#95×C₇₃	—	2	2	no	—
87	#95×C₇₃	—	2	2	no	—
88	#95×C₇₃	—	2	1	no	—
89	#95×C₇₃	—	2	1	no	—
90	#95×C₇₃	D₄	1	2	yes	—
91	C₂⁴×C₇₃	C₂×D₄	1	1	yes	characteristic
92	C₂×Q₈×C₇₃	—	2	4	no	—
93	C₂×Q₈×C₇₃	—	2	1	no	—
94	C₂×Q₈×C₇₃	—	2	1	no	—
95	C₂×Q₈×C₇₃	—	2	2	no	—
96	C₂×Q₈×C₇₃	—	2	8	no	—
97	C₂×Q₈×C₇₃	—	2	2	no	—
98	C₂×Q₈×C₇₃	—	2	2	no	—
99	C₂×Q₈×C₇₃	—	4	4	no	—
100	C₂×Q₈×C₇₃	—	4	4	no	—
101	C₂×Q₈×C₇₃	—	4	8	no	—
102	C₂×Q₈×C₇₃	C₂²×C₄	1	2	yes	—
103	C₂×Q₈×C₇₃	C₂²×C₄	1	2	yes	—
104	C₂×Q₈×C₇₃	#41	1	4	yes	—
105	C₂²×C₄×C₇₃	—	2	1	no	—
106	C₂²×C₄×C₇₃	—	2	2	no	—
107	C₂²×C₄×C₇₃	—	2	2	no	—
108	C₂²×C₄×C₇₃	—	2	4	no	—
109	C₂²×C₄×C₇₃	—	2	1	no	—
110	C₂²×C₄×C₇₃	—	2	1	no	—
111	C₂²×C₄×C₇₃	—	2	1	no	—
112	C₂²×C₄×C₇₃	—	2	4	no	—
113	C₂²×C₄×C₇₃	—	2	2	no	—
114	C₂²×C₄×C₇₃	—	2	2	no	—
115	C₂²×C₄×C₇₃	—	4	4	no	—
116	C₂²×C₄×C₇₃	—	8	2	no	—
117	C₂²×C₄×C₇₃	C₂²×C₄	1	2	yes	—
118	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
119	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
120	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₇₃	#41	1	2	yes	—
122	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
123	C₂×C₈×C₇₃	—	2	2	no	—
124	C₂×C₈×C₇₃	—	2	2	no	—
125	C₂×C₈×C₇₃	—	2	2	no	—
126	C₂×C₈×C₇₃	—	2	2	no	—
127	C₂×C₈×C₇₃	—	2	2	no	—
128	C₂×C₈×C₇₃	—	4	4	no	—
129	C₂×C₈×C₇₃	C₂²×C₄	1	2	yes	—
130	C₂×C₈×C₇₃	C₂²×C₄	1	2	yes	—
131	C₄⋊C₄×C₇₃	—	2	4	no	—
132	C₄⋊C₄×C₇₃	—	2	1	no	—
133	C₄⋊C₄×C₇₃	—	2	1	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	—	4	4	no	—
139	C₄⋊C₄×C₇₃	—	8	2	no	—
140	C₄⋊C₄×C₇₃	C₂²×C₄	1	2	yes	—
141	C₄⋊C₄×C₇₃	C₂²×C₄	1	2	yes	—
142	C₂²⋊C₄×C₇₃	—	2	2	no	—
143	C₂²⋊C₄×C₇₃	—	2	2	no	—
144	C₂²⋊C₄×C₇₃	—	4	2	no	—
145	C₂²⋊C₄×C₇₃	—	4	2	no	—
146	C₄²×C₇₃	—	2	2	no	—
147	C₄²×C₇₃	—	2	2	no	—
148	C₄²×C₇₃	—	4	4	no	—
149	C₄²×C₇₃	—	8	2	no	—
150	C₂³×C₇₃	—	2	2	no	—
151	C₂³×C₇₃	—	2	2	no	—
152	C₂³×C₇₃	C₄×D₄	1	2	yes	—
153	C₂³×C₇₃	#137	1	2	yes	—
154	C₂³×C₇₃	#137	1	2	yes	—
155	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
156	Q₈×C₇₃	—	2	2	no	—
157	Q₈×C₇₃	—	2	4	no	—
158	Q₈×C₇₃	—	2	2	no	—
159	Q₈×C₇₃	—	2	2	no	—
160	Q₈×C₇₃	—	4	8	no	—
161	Q₈×C₇₃	—	4	2	no	—
162	Q₈×C₇₃	#117	1	4	yes	—
163	C₂×C₄×C₇₃	—	2	2	no	—
164	C₂×C₄×C₇₃	—	2	4	no	—
165	C₂×C₄×C₇₃	—	2	2	no	—
166	C₂×C₄×C₇₃	—	2	2	no	—
167	C₂×C₄×C₇₃	—	2	2	no	—
168	C₂×C₄×C₇₃	—	2	4	no	—
169	C₂×C₄×C₇₃	—	2	2	no	—
170	C₂×C₄×C₇₃	—	2	2	no	—
171	C₂×C₄×C₇₃	—	2	2	no	—
172	C₂×C₄×C₇₃	—	2	2	no	—
173	C₂×C₄×C₇₃	—	2	2	no	—
174	C₂×C₄×C₇₃	—	2	2	no	—
175	C₂×C₄×C₇₃	—	2	2	no	—
176	C₂×C₄×C₇₃	—	2	2	no	—
177	C₂×C₄×C₇₃	—	2	2	no	—
178	C₂×C₄×C₇₃	—	4	8	no	—
179	C₂×C₄×C₇₃	—	4	2	no	—
180	C₂×C₄×C₇₃	—	4	2	no	—
181	C₂×C₄×C₇₃	—	4	2	no	—
182	C₂×C₄×C₇₃	—	4	2	no	—
183	C₂×C₄×C₇₃	—	4	2	no	—
184	C₂×C₄×C₇₃	—	4	2	no	—
185	C₂×C₄×C₇₃	—	4	2	no	—
186	C₂×C₄×C₇₃	—	4	2	no	—
187	C₂×C₄×C₇₃	—	4	2	no	—
188	C₂×C₄×C₇₃	—	8	4	no	—
189	C₂×C₄×C₇₃	C₄×D₄	1	2	yes	—
190	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
191	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
192	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
193	C₂×C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
194	C₈×C₇₃	—	2	2	no	—
195	C₈×C₇₃	—	2	2	no	—
196	C₈×C₇₃	—	4	2	no	—
197	C₂²×C₇₃	—	2	2	no	—
198	C₂²×C₇₃	—	2	2	no	—
199	C₂²×C₇₃	—	2	4	no	—
200	C₂²×C₇₃	—	2	4	no	—
201	C₂²×C₇₃	#441	1	4	yes	—
202	C₂²×C₇₃	C₂×C₄×D₄	1	1	yes	characteristic
203	C₂²×C₇₃	#546	1	2	yes	—
204	C₂²×C₇₃	C₂×#137	1	1	yes	characteristic
205	C₂²×C₇₃	C₂×#137	1	1	yes	characteristic
206	C₂²×C₇₃	#577	1	2	yes	—
207	C₄×C₇₃	—	2	2	no	—
208	C₄×C₇₃	—	2	4	no	—
209	C₄×C₇₃	—	4	2	no	—
210	C₄×C₇₃	—	4	2	no	—
211	C₄×C₇₃	—	4	2	no	—
212	C₄×C₇₃	—	4	2	no	—
213	C₄×C₇₃	—	4	2	no	—
214	C₄×C₇₃	—	8	2	no	—
215	C₄×C₇₃	—	8	2	no	—
216	C₄×C₇₃	C₂×#117	1	1	yes	characteristic
217	C₄×C₇₃	#518	1	1	yes	characteristic
218	C₄×C₇₃	#551	1	2	yes	—
219	#22567	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
220	C₂×C₇₃	—	2	4	no	—
221	C₂×C₇₃	#2342	1	1	yes	characteristic
222	C₂×C₇₃	C₂×#441	1	1	yes	characteristic
223	C₂×C₇₃	#2949	1	1	yes	characteristic
224	C₂×C₇₃	#3316	1	2	yes	—
225	C₂×C₇₃	#3320	1	2	yes	—
226	C₂²×#103	C₂×C₇₃	1	1	yes	characteristic
227	#2345	C₂×C₇₃	1	1	yes	characteristic
228	Q₈×C₂²⋊C₄	C₂×C₇₃	1	1	yes	characteristic
229	#1935	C₂×C₇₃	1	2	yes	complemented
230	#1927	C₂×C₇₃	1	2	yes	complemented
231	#1865	C₂×C₇₃	1	2	yes	complemented
232	#1824	C₂×C₇₃	1	1	yes	characteristic
233	#1807	C₂×C₇₃	1	1	yes	characteristic
234	#1787	C₂×C₇₃	1	1	yes	characteristic
235	#1763	C₂×C₇₃	1	2	yes	complemented
236	#1752	C₂×C₇₃	1	1	yes	characteristic
237	C₇₃	#22567	1	1	yes	characteristic, direct product factor, Sylow
238	C₂³×Q₈	C₂²×C₇₃	1	1	yes	characteristic
239	C₂³×C₈	C₂²×C₇₃	1	1	yes	characteristic
240	C₂×C₄×Q₈	C₂²×C₇₃	1	2	yes	—
241	C₂²×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
242	C₂×#106	C₂²×C₇₃	1	2	yes	—
243	C₂×#103	C₄×C₇₃	1	8	yes	complemented
244	C₂×#103	C₂²×C₇₃	1	2	yes	—
245	C₂×#103	C₂²×C₇₃	1	2	yes	—
246	C₂×#103	C₂²×C₇₃	1	1	yes	characteristic
247	C₂×#103	C₂²×C₇₃	1	1	yes	characteristic
248	C₂×#103	C₂²×C₇₃	1	1	yes	characteristic
249	C₂×#103	C₂²×C₇₃	1	1	yes	characteristic
250	C₂×C₂²⋊C₈	C₂²×C₇₃	1	1	yes	characteristic
251	C₂×#97	C₂²×C₇₃	1	2	yes	—
252	#391	—	2	2	no	—
253	#391	C₂²×C₇₃	1	2	yes	—
254	#389	C₂²×C₇₃	1	2	yes	—
255	#387	—	2	2	no	—
256	#380	—	2	1	no	—
257	#380	—	2	1	no	—
258	#380	C₂²×C₇₃	1	1	yes	characteristic
259	#380	C₂²×C₇₃	1	1	yes	characteristic
260	C₄×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
261	C₄×C₂²⋊C₄	—	2	1	no	—
262	C₄×C₂²⋊C₄	—	2	1	no	—
263	C₄×C₂²⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
264	#340	C₂²×C₇₃	1	2	yes	—
265	#340	C₂²×C₇₃	1	2	yes	—
266	#340	C₂²×C₇₃	1	2	yes	—
267	#336	C₂²×C₇₃	1	2	yes	—
268	C₂²×Q₈	—	2	1	no	—
269	C₂²×Q₈	—	2	2	no	—
270	C₂²×Q₈	—	2	4	no	—
271	C₂²×Q₈	—	4	2	no	—
272	C₂²×Q₈	C₂×C₄×C₇₃	1	4	yes	—
273	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
274	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
275	C₂³×C₄	—	2	1	no	—
276	C₂³×C₄	—	2	1	no	—
277	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
278	C₂²×C₈	—	4	2	no	—
279	C₂²×C₈	C₂×C₄×C₇₃	1	4	yes	—
280	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
281	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
282	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
283	C₄×Q₈	—	2	4	no	—
284	C₄×Q₈	—	4	2	no	—
285	C₂×C₄⋊C₄	—	2	1	no	—
286	C₂×C₄⋊C₄	—	2	2	no	—
287	C₂×C₄⋊C₄	—	2	2	no	—
288	C₂×C₄⋊C₄	—	2	2	no	—
289	C₂×C₄⋊C₄	C₂×C₄×C₇₃	1	4	yes	—
290	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
291	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
292	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
293	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
294	C₂×C₂²⋊C₄	—	2	1	no	—
295	C₂×C₂²⋊C₄	—	2	1	no	—
296	C₂×C₂²⋊C₄	D₄×C₇₃	1	1	yes	characteristic
297	C₂×C₂²⋊C₄	D₄×C₇₃	1	1	yes	characteristic
298	C₂×C₄²	—	2	2	no	—
299	C₂×C₄²	—	2	2	no	—
300	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
301	#106	—	4	2	no	—
302	#103	—	2	4	no	—
303	#103	—	4	2	no	—
304	#103	C₂×C₄×C₇₃	1	4	yes	—
305	#103	C₂×C₄×C₇₃	1	4	yes	—
306	#103	C₂×C₄×C₇₃	1	4	yes	—
307	#103	C₂×C₄×C₇₃	1	4	yes	—
308	C₂²⋊C₈	—	2	2	no	—
309	#97	—	4	2	no	—
310	#95	—	2	2	no	—
311	#95	—	2	2	no	—
312	#95	—	2	2	no	—
313	#95	—	2	2	no	—
314	#95	—	2	1	no	—
315	#95	—	2	1	no	—
316	#95	D₄×C₇₃	1	2	yes	—
317	C₂⁴	C₂×D₄×C₇₃	1	1	yes	characteristic
318	C₂×Q₈	—	2	4	no	—
319	C₂×Q₈	—	2	1	no	—
320	C₂×Q₈	—	2	1	no	—
321	C₂×Q₈	—	2	2	no	—
322	C₂×Q₈	—	2	8	no	—
323	C₂×Q₈	—	2	2	no	—
324	C₂×Q₈	—	2	2	no	—
325	C₂×Q₈	—	4	4	no	—
326	C₂×Q₈	—	4	4	no	—
327	C₂×Q₈	—	4	8	no	—
328	C₂×Q₈	C₂²×C₄×C₇₃	1	2	yes	—
329	C₂×Q₈	C₂²×C₄×C₇₃	1	2	yes	—
330	C₂×Q₈	#41×C₇₃	1	4	yes	—
331	C₂²×C₄	—	2	1	no	—
332	C₂²×C₄	—	2	2	no	—
333	C₂²×C₄	—	2	2	no	—
334	C₂²×C₄	—	2	4	no	—
335	C₂²×C₄	—	2	1	no	—
336	C₂²×C₄	—	2	1	no	—
337	C₂²×C₄	—	2	1	no	—
338	C₂²×C₄	—	2	4	no	—
339	C₂²×C₄	—	2	2	no	—
340	C₂²×C₄	—	2	2	no	—
341	C₂²×C₄	—	4	4	no	—
342	C₂²×C₄	—	8	2	no	—
343	C₂²×C₄	C₂²×C₄×C₇₃	1	2	yes	—
344	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
345	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
346	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
347	C₂²×C₄	#41×C₇₃	1	2	yes	—
348	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
349	C₂×C₈	—	2	2	no	—
350	C₂×C₈	—	2	2	no	—
351	C₂×C₈	—	2	2	no	—
352	C₂×C₈	—	2	2	no	—
353	C₂×C₈	—	2	2	no	—
354	C₂×C₈	—	4	4	no	—
355	C₂×C₈	C₂²×C₄×C₇₃	1	2	yes	—
356	C₂×C₈	C₂²×C₄×C₇₃	1	2	yes	—
357	C₄⋊C₄	—	2	4	no	—
358	C₄⋊C₄	—	2	1	no	—
359	C₄⋊C₄	—	2	1	no	—
360	C₄⋊C₄	—	2	2	no	—
361	C₄⋊C₄	—	2	2	no	—
362	C₄⋊C₄	—	2	2	no	—
363	C₄⋊C₄	—	2	2	no	—
364	C₄⋊C₄	—	4	4	no	—
365	C₄⋊C₄	—	8	2	no	—
366	C₄⋊C₄	C₂²×C₄×C₇₃	1	2	yes	—
367	C₄⋊C₄	C₂²×C₄×C₇₃	1	2	yes	—
368	C₂²⋊C₄	—	2	2	no	—
369	C₂²⋊C₄	—	2	2	no	—
370	C₂²⋊C₄	—	4	2	no	—
371	C₂²⋊C₄	—	4	2	no	—
372	C₄²	—	2	2	no	—
373	C₄²	—	2	2	no	—
374	C₄²	—	4	4	no	—
375	C₄²	—	8	2	no	—
376	C₂³	—	2	2	no	—
377	C₂³	—	2	2	no	—
378	C₂³	C₄×D₄×C₇₃	1	2	yes	—
379	C₂³	#137×C₇₃	1	2	yes	—
380	C₂³	#137×C₇₃	1	2	yes	—
381	C₂³	C₂²×D₄×C₇₃	1	1	yes	characteristic
382	Q₈	—	2	2	no	—
383	Q₈	—	2	4	no	—
384	Q₈	—	2	2	no	—
385	Q₈	—	2	2	no	—
386	Q₈	—	4	8	no	—
387	Q₈	—	4	2	no	—
388	Q₈	#117×C₇₃	1	4	yes	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	4	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	4	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	4	8	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	4	2	no	—
409	C₂×C₄	—	4	2	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	4	2	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	—	8	4	no	—
415	C₂×C₄	C₄×D₄×C₇₃	1	2	yes	—
416	C₂×C₄	C₂³×C₄×C₇₃	1	1	yes	characteristic
417	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
418	C₂×C₄	C₂×#41×C₇₃	1	1	yes	characteristic
419	C₂×C₄	H(5,𝔽₂)×C₇₃	1	2	yes	—
420	C₈	—	2	2	no	—
421	C₈	—	2	2	no	—
422	C₈	—	4	2	no	—
423	C₂²	—	2	4	no	—
424	C₂²	—	2	4	no	—
425	C₂²	—	2	2	no	—
426	C₂²	—	2	2	no	—
427	C₂²	#441×C₇₃	1	4	yes	—
428	C₂²	C₂×C₄×D₄×C₇₃	1	1	yes	characteristic
429	C₂²	#546×C₇₃	1	2	yes	—
430	C₂²	C₂×#137×C₇₃	1	1	yes	characteristic
431	C₂²	C₂×#137×C₇₃	1	1	yes	characteristic
432	C₂²	#577×C₇₃	1	2	yes	—
433	C₄	—	2	2	no	—
434	C₄	—	2	4	no	—
435	C₄	—	4	2	no	—
436	C₄	—	4	2	no	—
437	C₄	—	4	2	no	—
438	C₄	—	4	2	no	—
439	C₄	—	4	2	no	—
440	C₄	—	8	2	no	—
441	C₄	—	8	2	no	—
442	C₄	C₂×#117×C₇₃	1	1	yes	characteristic
443	C₄	#518×C₇₃	1	1	yes	characteristic
444	C₄	#551×C₇₃	1	2	yes	—
445	C₂	—	2	4	no	—
446	C₂	C₇₃×#2342	1	1	yes	characteristic
447	C₂	C₂×#441×C₇₃	1	1	yes	characteristic
448	C₂	C₇₃×#2949	1	1	yes	characteristic
449	C₂	C₇₃×#3316	1	2	yes	—
450	C₂	C₇₃×#3320	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
4. C₇₃×#1935	C₂	semidirect
5. C₇₃×#1927	C₂	semidirect
6. C₇₃×#1865	C₂	semidirect
10. C₇₃×#1763	C₂	semidirect
17. C₂×#103×C₇₃	C₄	semidirect
219. #22567	C₇₃	direct (N × H)
229. #1935	C₂×C₇₃	semidirect
230. #1927	C₂×C₇₃	semidirect
231. #1865	C₂×C₇₃	semidirect
235. #1763	C₂×C₇₃	semidirect
237. C₇₃	#22567	direct (N × H)
243. C₂×#103	C₄×C₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#103×C₇₃	2
C₇₃×#2345	2
Q₈×C₂²⋊C₄×C₇₃	2
C₇₃×#1935	2
C₇₃×#1927	2
C₇₃×#1865	2
C₇₃×#1824	2
C₇₃×#1807	2
C₇₃×#1787	2
C₇₃×#1763	2
C₇₃×#1752	2
#22567	73

Subgroups — C73×#22567 #32931971

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#22567 #32931971