Subgroups — C₇₃×#25726 #32935130

Order 18688.

1560 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄⋊Q₈×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#497×C₇₃	C₂	1	2	yes	maximal, complemented
3	C₂×#451×C₇₃	C₂	1	2	yes	maximal, complemented
4	C₂×#448×C₇₃	C₂	1	2	yes	maximal
5	C₇₃×#2850	C₂	1	1	yes	maximal, characteristic
6	C₇₃×#2016	C₂	1	2	yes	maximal, complemented
7	C₇₃×#2013	C₂	1	2	yes	maximal, complemented
8	C₇₃×#1960	C₂	1	2	yes	maximal, complemented
9	C₇₃×#1749	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂³×Q₈×C₇₃	C₂²	1	2	yes	—
11	C₂²×Q₁₆×C₇₃	C₂²	1	4	yes	—
12	C₂²×SD₁₆×C₇₃	C₂²	1	4	yes	—
13	C₂×C₄⋊Q₈×C₇₃	—	2	8	no	—
14	C₂×C₄⋊Q₈×C₇₃	—	2	2	no	—
15	C₂×C₄⋊Q₈×C₇₃	C₂²	1	2	yes	—
16	C₂×C₄⋊Q₈×C₇₃	C₂²	1	2	yes	—
17	C₂×#124×C₇₃	C₂²	1	1	yes	characteristic
18	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
19	C₂×#121×C₇₃	C₂²	1	1	yes	characteristic
20	C₂²×C₄⋊C₄×C₇₃	—	2	2	no	—
21	C₂²×C₄²×C₇₃	C₂²	1	1	yes	characteristic
22	#497×C₇₃	—	2	8	no	—
23	#451×C₇₃	—	2	8	no	—
24	#448×C₇₃	—	2	8	no	—
25	C₂×#103×C₇₃	C₂²	1	4	yes	—
26	C₂×#103×C₇₃	C₂²	1	4	yes	—
27	C₂×C₂²⋊C₈×C₇₃	C₂²	1	2	yes	—
28	C₂×#97×C₇₃	C₂²	1	2	yes	—
29	#391×C₇₃	C₂²	1	1	yes	characteristic
30	#390×C₇₃	C₂²	1	1	yes	characteristic
31	#388×C₇₃	—	2	2	no	—
32	#386×C₇₃	—	2	2	no	—
33	#382×C₇₃	C₂²	1	1	yes	characteristic
34	#336×C₇₃	C₂²	1	2	yes	—
35	C₂²×Q₈×C₇₃	—	2	8	no	—
36	C₂²×Q₈×C₇₃	—	2	2	no	—
37	C₂²×Q₈×C₇₃	—	2	4	no	—
38	C₂²×Q₈×C₇₃	—	2	4	no	—
39	C₂²×Q₈×C₇₃	—	4	4	no	—
40	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
41	C₂²×Q₈×C₇₃	C₂³	1	4	yes	—
42	C₂²×D₄×C₇₃	—	2	1	no	—
43	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
44	C₂³×C₄×C₇₃	—	2	2	no	—
45	C₂³×C₄×C₇₃	D₄	1	2	yes	—
46	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
47	C₂×Q₁₆×C₇₃	—	2	8	no	—
48	C₂×Q₁₆×C₇₃	—	2	8	no	—
49	C₂×Q₁₆×C₇₃	—	4	4	no	—
50	C₂×SD₁₆×C₇₃	—	2	8	no	—
51	C₂×SD₁₆×C₇₃	—	2	8	no	—
52	C₂×SD₁₆×C₇₃	—	4	4	no	—
53	C₂²×C₈×C₇₃	C₂³	1	4	yes	—
54	C₄⋊Q₈×C₇₃	—	2	16	no	—
55	C₄⋊Q₈×C₇₃	—	2	8	no	—
56	C₄⋊Q₈×C₇₃	—	2	4	no	—
57	C₄⋊Q₈×C₇₃	D₄	1	8	yes	complemented
58	#124×C₇₃	—	2	4	no	—
59	C₂²⋊Q₈×C₇₃	—	2	4	no	—
60	#121×C₇₃	—	2	4	no	—
61	C₂×C₄⋊C₄×C₇₃	—	2	16	no	—
62	C₂×C₄⋊C₄×C₇₃	—	2	4	no	—
63	C₂×C₄⋊C₄×C₇₃	—	2	4	no	—
64	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
65	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
66	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
67	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
68	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
69	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
70	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
71	C₂×C₄²×C₇₃	—	2	4	no	—
72	C₂×C₄²×C₇₃	D₄	1	2	yes	—
73	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
74	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
75	#103×C₇₃	—	2	8	no	—
76	#103×C₇₃	—	2	8	no	—
77	C₂²⋊C₈×C₇₃	D₄	1	8	yes	—
78	#97×C₇₃	—	2	4	no	—
79	#95×C₇₃	—	2	2	no	—
80	#95×C₇₃	—	2	2	no	—
81	C₂⁴×C₇₃	—	2	1	no	—
82	C₂⁴×C₇₃	C₂×D₄	1	1	yes	characteristic
83	C₂×Q₈×C₇₃	—	2	8	no	—
84	C₂×Q₈×C₇₃	—	2	4	no	—
85	C₂×Q₈×C₇₃	—	2	4	no	—
86	C₂×Q₈×C₇₃	—	2	4	no	—
87	C₂×Q₈×C₇₃	—	2	2	no	—
88	C₂×Q₈×C₇₃	—	2	2	no	—
89	C₂×Q₈×C₇₃	—	2	4	no	—
90	C₂×Q₈×C₇₃	—	2	4	no	—
91	C₂×Q₈×C₇₃	—	2	2	no	—
92	C₂×Q₈×C₇₃	—	4	16	no	—
93	C₂×Q₈×C₇₃	—	4	16	no	—
94	C₂×Q₈×C₇₃	—	4	4	no	—
95	C₂×Q₈×C₇₃	—	4	4	no	—
96	C₂×Q₈×C₇₃	C₂×D₄	1	8	yes	—
97	C₂×D₄×C₇₃	—	2	2	no	—
98	C₂×D₄×C₇₃	—	2	2	no	—
99	C₂×D₄×C₇₃	—	2	2	no	—
100	C₂×D₄×C₇₃	—	4	2	no	—
101	C₂×D₄×C₇₃	—	4	4	no	—
102	C₂²×C₄×C₇₃	—	2	4	no	—
103	C₂²×C₄×C₇₃	—	2	4	no	—
104	C₂²×C₄×C₇₃	—	2	4	no	—
105	C₂²×C₄×C₇₃	—	2	2	no	—
106	C₂²×C₄×C₇₃	—	2	2	no	—
107	C₂²×C₄×C₇₃	—	2	8	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	—	4	4	no	—
113	C₂²×C₄×C₇₃	—	4	4	no	—
114	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
115	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₇₃	C₂×D₄	1	4	yes	—
117	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
118	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
119	Q₁₆×C₇₃	—	4	16	no	—
120	SD₁₆×C₇₃	—	4	16	no	—
121	C₂×C₈×C₇₃	—	2	4	no	—
122	C₂×C₈×C₇₃	—	2	4	no	—
123	C₂×C₈×C₇₃	C₂×D₄	1	8	yes	—
124	C₄⋊C₄×C₇₃	—	2	16	no	—
125	C₄⋊C₄×C₇₃	—	2	16	no	—
126	C₄⋊C₄×C₇₃	—	2	2	no	—
127	C₄⋊C₄×C₇₃	—	2	2	no	—
128	C₄⋊C₄×C₇₃	—	4	2	no	—
129	C₂²⋊C₄×C₇₃	—	4	2	no	—
130	C₂²⋊C₄×C₇₃	—	4	4	no	—
131	C₂²⋊C₄×C₇₃	—	4	2	no	—
132	C₂²⋊C₄×C₇₃	—	4	4	no	—
133	C₄²×C₇₃	—	2	4	no	—
134	C₄²×C₇₃	—	2	2	no	—
135	C₄²×C₇₃	C₂×D₄	1	4	yes	—
136	C₂³×C₇₃	—	2	1	no	—
137	C₂³×C₇₃	—	2	1	no	—
138	C₂³×C₇₃	—	2	2	no	—
139	C₂³×C₇₃	—	4	1	no	—
140	C₂³×C₇₃	—	4	1	no	—
141	C₂³×C₇₃	—	4	1	no	—
142	C₂³×C₇₃	—	4	2	no	—
143	C₂³×C₇₃	—	4	2	no	—
144	C₂³×C₇₃	#127	1	2	yes	—
145	C₂³×C₇₃	#137	1	4	yes	—
146	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
147	Q₈×C₇₃	—	2	8	no	—
148	Q₈×C₇₃	—	2	8	no	—
149	Q₈×C₇₃	—	4	16	no	—
150	Q₈×C₇₃	—	4	4	no	—
151	Q₈×C₇₃	—	4	4	no	—
152	Q₈×C₇₃	—	4	4	no	—
153	D₄×C₇₃	—	4	4	no	—
154	D₄×C₇₃	—	8	4	no	—
155	C₂×C₄×C₇₃	—	2	16	no	—
156	C₂×C₄×C₇₃	—	2	2	no	—
157	C₂×C₄×C₇₃	—	2	1	no	—
158	C₂×C₄×C₇₃	—	2	1	no	—
159	C₂×C₄×C₇₃	—	2	2	no	—
160	C₂×C₄×C₇₃	—	2	2	no	—
161	C₂×C₄×C₇₃	—	2	2	no	—
162	C₂×C₄×C₇₃	—	2	8	no	—
163	C₂×C₄×C₇₃	—	2	8	no	—
164	C₂×C₄×C₇₃	—	4	16	no	—
165	C₂×C₄×C₇₃	—	4	4	no	—
166	C₂×C₄×C₇₃	—	4	4	no	—
167	C₂×C₄×C₇₃	—	4	1	no	—
168	C₂×C₄×C₇₃	—	4	1	no	—
169	C₂×C₄×C₇₃	—	4	1	no	—
170	C₂×C₄×C₇₃	—	4	1	no	—
171	C₂×C₄×C₇₃	—	4	1	no	—
172	C₂×C₄×C₇₃	—	4	2	no	—
173	C₂×C₄×C₇₃	—	4	2	no	—
174	C₂×C₄×C₇₃	#120	1	4	yes	—
175	C₂×C₄×C₇₃	#127	1	2	yes	—
176	C₂×C₄×C₇₃	#137	1	4	yes	—
177	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
178	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
179	C₂×C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
180	C₈×C₇₃	—	2	8	no	—
181	C₂²×C₇₃	—	2	2	no	—
182	C₂²×C₇₃	—	2	2	no	—
183	C₂²×C₇₃	—	2	4	no	—
184	C₂²×C₇₃	—	2	4	no	—
185	C₂²×C₇₃	—	8	1	no	—
186	C₂²×C₇₃	—	8	1	no	—
187	C₂²×C₇₃	—	8	1	no	—
188	C₂²×C₇₃	—	8	2	no	—
189	C₂²×C₇₃	—	8	2	no	—
190	C₂²×C₇₃	#497	1	4	yes	complemented
191	C₂²×C₇₃	C₂×#120	1	1	yes	characteristic
192	C₂²×C₇₃	C₂×#127	1	1	yes	characteristic
193	C₂²×C₇₃	#535	1	1	yes	characteristic
194	C₂²×C₇₃	C₂×#137	1	2	yes	—
195	C₂²×C₇₃	C₂×#137	1	2	yes	—
196	C₄×C₇₃	—	2	2	no	—
197	C₄×C₇₃	—	2	4	no	—
198	C₄×C₇₃	—	2	4	no	—
199	C₄×C₇₃	—	4	8	no	—
200	C₄×C₇₃	—	8	1	no	—
201	C₄×C₇₃	—	8	1	no	—
202	C₄×C₇₃	—	8	1	no	—
203	C₄×C₇₃	D₄²	1	4	yes	—
204	#25726	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
205	C₂×C₇₃	—	2	4	no	—
206	C₂×C₇₃	—	16	1	no	—
207	C₂×C₇₃	#2433	1	1	yes	characteristic
208	C₂×C₇₃	#3004	1	2	yes	—
209	C₂×C₇₃	C₂×#497	1	1	yes	characteristic
210	C₂×C₇₃	#3152	1	1	yes	characteristic
211	C₂×C₇₃	#3218	1	2	yes	—
212	C₂²×C₄⋊Q₈	C₂×C₇₃	1	1	yes	characteristic, complemented
213	C₂×#497	C₂×C₇₃	1	2	yes	complemented
214	C₂×#451	C₂×C₇₃	1	2	yes	complemented
215	C₂×#448	C₂×C₇₃	1	2	yes	—
216	#2850	C₂×C₇₃	1	1	yes	characteristic
217	#2016	C₂×C₇₃	1	2	yes	complemented
218	#2013	C₂×C₇₃	1	2	yes	complemented
219	#1960	C₂×C₇₃	1	2	yes	complemented
220	#1749	C₂×C₇₃	1	1	yes	characteristic, complemented
221	C₇₃	#25726	1	1	yes	characteristic, direct product factor, Sylow
222	C₂³×Q₈	C₂²×C₇₃	1	2	yes	—
223	C₂²×Q₁₆	C₂²×C₇₃	1	4	yes	—
224	C₂²×SD₁₆	C₂²×C₇₃	1	4	yes	—
225	C₂×C₄⋊Q₈	—	2	8	no	—
226	C₂×C₄⋊Q₈	—	2	2	no	—
227	C₂×C₄⋊Q₈	C₂²×C₇₃	1	2	yes	—
228	C₂×C₄⋊Q₈	C₂²×C₇₃	1	2	yes	—
229	C₂×#124	C₂²×C₇₃	1	1	yes	characteristic
230	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
231	C₂×#121	C₂²×C₇₃	1	1	yes	characteristic
232	C₂²×C₄⋊C₄	—	2	2	no	—
233	C₂²×C₄²	C₂²×C₇₃	1	1	yes	characteristic
234	#497	—	2	8	no	—
235	#451	—	2	8	no	—
236	#448	—	2	8	no	—
237	C₂×#103	C₂²×C₇₃	1	4	yes	—
238	C₂×#103	C₂²×C₇₃	1	4	yes	—
239	C₂×C₂²⋊C₈	C₂²×C₇₃	1	2	yes	—
240	C₂×#97	C₂²×C₇₃	1	2	yes	—
241	#391	C₂²×C₇₃	1	1	yes	characteristic
242	#390	C₂²×C₇₃	1	1	yes	characteristic
243	#388	—	2	2	no	—
244	#386	—	2	2	no	—
245	#382	C₂²×C₇₃	1	1	yes	characteristic
246	#336	C₂²×C₇₃	1	2	yes	—
247	C₂²×Q₈	—	2	8	no	—
248	C₂²×Q₈	—	2	2	no	—
249	C₂²×Q₈	—	2	4	no	—
250	C₂²×Q₈	—	2	4	no	—
251	C₂²×Q₈	—	4	4	no	—
252	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
253	C₂²×Q₈	C₂³×C₇₃	1	4	yes	—
254	C₂²×D₄	—	2	1	no	—
255	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
256	C₂³×C₄	—	2	2	no	—
257	C₂³×C₄	D₄×C₇₃	1	2	yes	—
258	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
259	C₂×Q₁₆	—	2	8	no	—
260	C₂×Q₁₆	—	2	8	no	—
261	C₂×Q₁₆	—	4	4	no	—
262	C₂×SD₁₆	—	2	8	no	—
263	C₂×SD₁₆	—	2	8	no	—
264	C₂×SD₁₆	—	4	4	no	—
265	C₂²×C₈	C₂³×C₇₃	1	4	yes	—
266	C₄⋊Q₈	—	2	16	no	—
267	C₄⋊Q₈	—	2	8	no	—
268	C₄⋊Q₈	—	2	4	no	—
269	C₄⋊Q₈	D₄×C₇₃	1	8	yes	complemented
270	#124	—	2	4	no	—
271	C₂²⋊Q₈	—	2	4	no	—
272	#121	—	2	4	no	—
273	C₂×C₄⋊C₄	—	2	16	no	—
274	C₂×C₄⋊C₄	—	2	4	no	—
275	C₂×C₄⋊C₄	—	2	4	no	—
276	C₂×C₄⋊C₄	—	2	1	no	—
277	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
278	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
279	C₂×C₂²⋊C₄	—	2	1	no	—
280	C₂×C₂²⋊C₄	—	2	1	no	—
281	C₂×C₂²⋊C₄	—	2	2	no	—
282	C₂×C₂²⋊C₄	—	2	2	no	—
283	C₂×C₄²	—	2	4	no	—
284	C₂×C₄²	D₄×C₇₃	1	2	yes	—
285	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
286	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
287	#103	—	2	8	no	—
288	#103	—	2	8	no	—
289	C₂²⋊C₈	D₄×C₇₃	1	8	yes	—
290	#97	—	2	4	no	—
291	#95	—	2	2	no	—
292	#95	—	2	2	no	—
293	C₂⁴	—	2	1	no	—
294	C₂⁴	C₂×D₄×C₇₃	1	1	yes	characteristic
295	C₂×Q₈	—	2	8	no	—
296	C₂×Q₈	—	2	4	no	—
297	C₂×Q₈	—	2	4	no	—
298	C₂×Q₈	—	2	4	no	—
299	C₂×Q₈	—	2	2	no	—
300	C₂×Q₈	—	2	2	no	—
301	C₂×Q₈	—	2	4	no	—
302	C₂×Q₈	—	2	4	no	—
303	C₂×Q₈	—	2	2	no	—
304	C₂×Q₈	—	4	16	no	—
305	C₂×Q₈	—	4	16	no	—
306	C₂×Q₈	—	4	4	no	—
307	C₂×Q₈	—	4	4	no	—
308	C₂×Q₈	C₂×D₄×C₇₃	1	8	yes	—
309	C₂×D₄	—	2	2	no	—
310	C₂×D₄	—	2	2	no	—
311	C₂×D₄	—	2	2	no	—
312	C₂×D₄	—	4	2	no	—
313	C₂×D₄	—	4	4	no	—
314	C₂²×C₄	—	2	4	no	—
315	C₂²×C₄	—	2	4	no	—
316	C₂²×C₄	—	2	4	no	—
317	C₂²×C₄	—	2	2	no	—
318	C₂²×C₄	—	2	2	no	—
319	C₂²×C₄	—	2	8	no	—
320	C₂²×C₄	—	2	4	no	—
321	C₂²×C₄	—	2	1	no	—
322	C₂²×C₄	—	2	1	no	—
323	C₂²×C₄	—	2	1	no	—
324	C₂²×C₄	—	4	4	no	—
325	C₂²×C₄	—	4	4	no	—
326	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
327	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
328	C₂²×C₄	C₂×D₄×C₇₃	1	4	yes	—
329	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
330	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
331	Q₁₆	—	4	16	no	—
332	SD₁₆	—	4	16	no	—
333	C₂×C₈	—	2	4	no	—
334	C₂×C₈	—	2	4	no	—
335	C₂×C₈	C₂×D₄×C₇₃	1	8	yes	—
336	C₄⋊C₄	—	2	16	no	—
337	C₄⋊C₄	—	2	16	no	—
338	C₄⋊C₄	—	2	2	no	—
339	C₄⋊C₄	—	2	2	no	—
340	C₄⋊C₄	—	4	2	no	—
341	C₂²⋊C₄	—	4	2	no	—
342	C₂²⋊C₄	—	4	4	no	—
343	C₂²⋊C₄	—	4	2	no	—
344	C₂²⋊C₄	—	4	4	no	—
345	C₄²	—	2	4	no	—
346	C₄²	—	2	2	no	—
347	C₄²	C₂×D₄×C₇₃	1	4	yes	—
348	C₂³	—	2	1	no	—
349	C₂³	—	2	1	no	—
350	C₂³	—	2	2	no	—
351	C₂³	—	4	1	no	—
352	C₂³	—	4	1	no	—
353	C₂³	—	4	1	no	—
354	C₂³	—	4	2	no	—
355	C₂³	—	4	2	no	—
356	C₂³	#127×C₇₃	1	2	yes	—
357	C₂³	#137×C₇₃	1	4	yes	—
358	C₂³	C₂²×D₄×C₇₃	1	1	yes	characteristic
359	Q₈	—	2	8	no	—
360	Q₈	—	2	8	no	—
361	Q₈	—	4	16	no	—
362	Q₈	—	4	4	no	—
363	Q₈	—	4	4	no	—
364	Q₈	—	4	4	no	—
365	D₄	—	4	4	no	—
366	D₄	—	8	4	no	—
367	C₂×C₄	—	2	16	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	2	1	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	8	no	—
375	C₂×C₄	—	2	8	no	—
376	C₂×C₄	—	4	16	no	—
377	C₂×C₄	—	4	4	no	—
378	C₂×C₄	—	4	4	no	—
379	C₂×C₄	—	4	1	no	—
380	C₂×C₄	—	4	1	no	—
381	C₂×C₄	—	4	1	no	—
382	C₂×C₄	—	4	1	no	—
383	C₂×C₄	—	4	1	no	—
384	C₂×C₄	—	4	2	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	#120×C₇₃	1	4	yes	—
387	C₂×C₄	#127×C₇₃	1	2	yes	—
388	C₂×C₄	#137×C₇₃	1	4	yes	—
389	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
390	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
391	C₂×C₄	H(5,𝔽₂)×C₇₃	1	2	yes	—
392	C₈	—	2	8	no	—
393	C₂²	—	2	4	no	—
394	C₂²	—	2	4	no	—
395	C₂²	—	2	2	no	—
396	C₂²	—	2	2	no	—
397	C₂²	—	8	2	no	—
398	C₂²	—	8	2	no	—
399	C₂²	—	8	1	no	—
400	C₂²	—	8	1	no	—
401	C₂²	—	8	1	no	—
402	C₂²	#497×C₇₃	1	4	yes	complemented
403	C₂²	C₂×#120×C₇₃	1	1	yes	characteristic
404	C₂²	C₂×#127×C₇₃	1	1	yes	characteristic
405	C₂²	#535×C₇₃	1	1	yes	characteristic
406	C₂²	C₂×#137×C₇₃	1	2	yes	—
407	C₂²	C₂×#137×C₇₃	1	2	yes	—
408	C₄	—	2	4	no	—
409	C₄	—	2	4	no	—
410	C₄	—	2	2	no	—
411	C₄	—	4	8	no	—
412	C₄	—	8	1	no	—
413	C₄	—	8	1	no	—
414	C₄	—	8	1	no	—
415	C₄	D₄²×C₇₃	1	4	yes	—
416	C₂	—	2	4	no	—
417	C₂	—	16	1	no	—
418	C₂	C₇₃×#2433	1	1	yes	characteristic
419	C₂	C₇₃×#3004	1	2	yes	—
420	C₂	C₂×#497×C₇₃	1	1	yes	characteristic
421	C₂	C₇₃×#3152	1	1	yes	characteristic
422	C₂	C₇₃×#3218	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₇₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₃
prime radical	C₂×#121×C₇₃	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇₃ ◁ C₂²×C₄²×C₇₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₄⋊Q₈×C₇₃	C₂	semidirect
2. C₂×#497×C₇₃	C₂	semidirect
3. C₂×#451×C₇₃	C₂	semidirect
6. C₇₃×#2016	C₂	semidirect
7. C₇₃×#2013	C₂	semidirect
8. C₇₃×#1960	C₂	semidirect
9. C₇₃×#1749	C₂	semidirect
57. C₄⋊Q₈×C₇₃	D₄	semidirect
190. C₂²×C₇₃	#497	semidirect
204. #25726	C₇₃	direct (N × H)
212. C₂²×C₄⋊Q₈	C₂×C₇₃	semidirect
213. C₂×#497	C₂×C₇₃	semidirect
214. C₂×#451	C₂×C₇₃	semidirect
217. #2016	C₂×C₇₃	semidirect
218. #2013	C₂×C₇₃	semidirect
219. #1960	C₂×C₇₃	semidirect
220. #1749	C₂×C₇₃	semidirect
221. C₇₃	#25726	direct (N × H)
269. C₄⋊Q₈	D₄×C₇₃	semidirect
402. C₂²	#497×C₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₄⋊Q₈×C₇₃	2
C₂×#497×C₇₃	2
C₂×#451×C₇₃	2
C₂×#448×C₇₃	2
C₇₃×#2850	2
C₇₃×#2016	2
C₇₃×#2013	2
C₇₃×#1960	2
C₇₃×#1749	2
#25726	73

Subgroups — C73×#25726 #32935130

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#25726 #32935130