Subgroups — C₇₃×#25756 #32935160

Order 18688.

1650 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄×Q₈×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#492×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#460×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#448×C₇₃	C₂	1	4	yes	maximal, complemented
5	C₇₃×#2541	C₂	1	1	yes	maximal, characteristic
6	C₇₃×#2000	C₂	1	4	yes	maximal, complemented
7	C₇₃×#1981	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇₃×#1954	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×#103×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂³×Q₈×C₇₃	C₂²	1	2	yes	—
11	C₂²×SD₁₆×C₇₃	C₂²	1	2	yes	—
12	C₂²×SD₁₆×C₇₃	C₂²	1	4	yes	—
13	D₄×Q₈×C₇₃	—	2	4	no	—
14	D₄×Q₈×C₇₃	—	2	4	no	—
15	C₂×C₄⋊Q₈×C₇₃	—	2	1	no	—
16	C₂×C₄⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
17	C₂×#127×C₇₃	—	2	1	no	—
18	C₂×#127×C₇₃	C₂²	1	1	yes	characteristic
19	C₂×C₂²⋊Q₈×C₇₃	—	2	2	no	—
20	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	2	yes	—
21	C₂×#121×C₇₃	C₂²	1	4	yes	—
22	C₂×C₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic
23	C₂×C₄×D₄×C₇₃	—	2	1	no	—
24	C₂×C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
25	#492×C₇₃	—	2	4	no	—
26	#460×C₇₃	—	2	4	no	—
27	#448×C₇₃	—	2	16	no	—
28	C₂×C₄⋊C₈×C₇₃	C₂²	1	1	yes	characteristic
29	C₂×#103×C₇₃	C₂²	1	4	yes	—
30	C₂×#103×C₇₃	C₂²	1	2	yes	—
31	C₂×#102×C₇₃	C₂²	1	2	yes	—
32	C₂×C₂²⋊C₈×C₇₃	C₂²	1	4	yes	—
33	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
34	#392×C₇₃	—	2	2	no	—
35	#390×C₇₃	—	2	1	no	—
36	C₄×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
37	#340×C₇₃	C₂²	1	2	yes	—
38	C₂²×Q₈×C₇₃	—	2	4	no	—
39	C₂²×Q₈×C₇₃	—	2	4	no	—
40	C₂²×Q₈×C₇₃	—	2	2	no	—
41	C₂²×Q₈×C₇₃	—	2	8	no	—
42	C₂²×Q₈×C₇₃	—	4	4	no	—
43	C₂²×Q₈×C₇₃	C₂³	1	2	yes	—
44	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
45	C₂²×D₄×C₇₃	—	2	4	no	—
46	C₂²×D₄×C₇₃	—	2	1	no	—
47	C₂²×D₄×C₇₃	—	2	1	no	—
48	C₂²×D₄×C₇₃	D₄	1	1	yes	characteristic
49	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
50	C₂³×C₄×C₇₃	—	2	2	no	—
51	C₂³×C₄×C₇₃	C₂³	1	2	yes	—
52	C₂×SD₁₆×C₇₃	—	2	8	no	—
53	C₂×SD₁₆×C₇₃	—	2	4	no	—
54	C₂×SD₁₆×C₇₃	—	2	8	no	—
55	C₂×SD₁₆×C₇₃	—	2	8	no	—
56	C₂×SD₁₆×C₇₃	—	4	4	no	—
57	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
58	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
59	C₄⋊Q₈×C₇₃	—	2	8	no	—
60	C₄⋊Q₈×C₇₃	—	2	2	no	—
61	C₄⋊Q₈×C₇₃	D₄	1	4	yes	complemented
62	#127×C₇₃	—	2	2	no	—
63	#127×C₇₃	—	2	2	no	—
64	#127×C₇₃	—	4	4	no	—
65	C₂²⋊Q₈×C₇₃	—	2	16	no	—
66	C₂²⋊Q₈×C₇₃	—	2	4	no	—
67	C₂²⋊Q₈×C₇₃	—	2	4	no	—
68	#121×C₇₃	—	2	8	no	—
69	#121×C₇₃	—	4	4	no	—
70	C₄×Q₈×C₇₃	—	2	2	no	—
71	C₄×Q₈×C₇₃	D₄	1	4	yes	complemented
72	C₄×D₄×C₇₃	—	2	8	no	—
73	C₄×D₄×C₇₃	—	2	2	no	—
74	C₄×D₄×C₇₃	—	2	2	no	—
75	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
76	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
77	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
78	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
79	C₂×C₄⋊C₄×C₇₃	D₄	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×C₂²⋊C₄×C₇₃	—	2	2	no	—
83	C₂×C₂²⋊C₄×C₇₃	—	2	4	no	—
84	C₂×C₂²⋊C₄×C₇₃	D₄	1	2	yes	—
85	C₂×C₄²×C₇₃	—	2	1	no	—
86	C₂×C₄²×C₇₃	—	2	1	no	—
87	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
88	C₄⋊C₈×C₇₃	—	2	2	no	—
89	#103×C₇₃	—	2	8	no	—
90	#103×C₇₃	D₄	1	8	yes	complemented
91	#102×C₇₃	—	2	4	no	—
92	C₂²⋊C₈×C₇₃	—	2	8	no	—
93	C₄×C₈×C₇₃	—	2	2	no	—
94	#95×C₇₃	—	2	1	no	—
95	C₂⁴×C₇₃	—	2	2	no	—
96	C₂⁴×C₇₃	C₂×D₄	1	2	yes	—
97	C₂×Q₈×C₇₃	—	2	8	no	—
98	C₂×Q₈×C₇₃	—	2	1	no	—
99	C₂×Q₈×C₇₃	—	2	2	no	—
100	C₂×Q₈×C₇₃	—	2	2	no	—
101	C₂×Q₈×C₇₃	—	2	4	no	—
102	C₂×Q₈×C₇₃	—	2	4	no	—
103	C₂×Q₈×C₇₃	—	4	8	no	—
104	C₂×Q₈×C₇₃	—	4	16	no	—
105	C₂×Q₈×C₇₃	—	4	8	no	—
106	C₂×Q₈×C₇₃	—	4	8	no	—
107	C₂×Q₈×C₇₃	C₂×D₄	1	4	yes	—
108	C₂×Q₈×C₇₃	C₂×D₄	1	4	yes	—
109	C₂×Q₈×C₇₃	C₂×D₄	1	2	yes	—
110	C₂×D₄×C₇₃	—	2	2	no	—
111	C₂×D₄×C₇₃	—	2	2	no	—
112	C₂×D₄×C₇₃	—	2	2	no	—
113	C₂×D₄×C₇₃	—	2	4	no	—
114	C₂×D₄×C₇₃	—	2	2	no	—
115	C₂×D₄×C₇₃	—	2	4	no	—
116	C₂×D₄×C₇₃	—	4	8	no	—
117	C₂×D₄×C₇₃	—	4	8	no	—
118	C₂×D₄×C₇₃	—	4	2	no	—
119	C₂×D₄×C₇₃	—	4	2	no	—
120	C₂×D₄×C₇₃	—	4	2	no	—
121	C₂×D₄×C₇₃	—	4	2	no	—
122	C₂×D₄×C₇₃	—	8	2	no	—
123	C₂×D₄×C₇₃	—	8	4	no	—
124	C₂×D₄×C₇₃	SD₁₆	1	4	yes	complemented
125	C₂²×C₄×C₇₃	—	2	1	no	—
126	C₂²×C₄×C₇₃	—	2	8	no	—
127	C₂²×C₄×C₇₃	—	2	2	no	—
128	C₂²×C₄×C₇₃	—	2	1	no	—
129	C₂²×C₄×C₇₃	—	2	2	no	—
130	C₂²×C₄×C₇₃	—	2	4	no	—
131	C₂²×C₄×C₇₃	—	2	2	no	—
132	C₂²×C₄×C₇₃	—	2	2	no	—
133	C₂²×C₄×C₇₃	—	2	4	no	—
134	C₂²×C₄×C₇₃	—	4	8	no	—
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	1	yes	characteristic
138	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
139	SD₁₆×C₇₃	—	4	16	no	—
140	SD₁₆×C₇₃	—	4	8	no	—
141	C₂×C₈×C₇₃	—	2	2	no	—
142	C₂×C₈×C₇₃	—	2	2	no	—
143	C₂×C₈×C₇₃	—	2	4	no	—
144	C₂×C₈×C₇₃	—	2	2	no	—
145	C₂×C₈×C₇₃	C₂×D₄	1	4	yes	—
146	C₄⋊C₄×C₇₃	—	2	8	no	—
147	C₄⋊C₄×C₇₃	—	2	4	no	—
148	C₄⋊C₄×C₇₃	—	2	4	no	—
149	C₄⋊C₄×C₇₃	—	2	4	no	—
150	C₄⋊C₄×C₇₃	—	2	2	no	—
151	C₄⋊C₄×C₇₃	—	2	1	no	—
152	C₄⋊C₄×C₇₃	—	2	2	no	—
153	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
154	C₄⋊C₄×C₇₃	C₂×D₄	1	4	yes	—
155	C₂²⋊C₄×C₇₃	—	2	8	no	—
156	C₂²⋊C₄×C₇₃	—	2	4	no	—
157	C₂²⋊C₄×C₇₃	—	4	8	no	—
158	C₄²×C₇₃	—	2	4	no	—
159	C₄²×C₇₃	—	4	2	no	—
160	C₄²×C₇₃	C₂×D₄	1	2	yes	—
161	C₄²×C₇₃	C₂×D₄	1	2	yes	—
162	C₂³×C₇₃	—	2	2	no	—
163	C₂³×C₇₃	—	2	4	no	—
164	C₂³×C₇₃	—	2	2	no	—
165	C₂³×C₇₃	—	2	4	no	—
166	C₂³×C₇₃	—	4	2	no	—
167	C₂³×C₇₃	—	4	4	no	—
168	C₂³×C₇₃	—	4	2	no	—
169	C₂³×C₇₃	—	4	2	no	—
170	C₂³×C₇₃	—	4	4	no	—
171	C₂³×C₇₃	C₂×SD₁₆	1	4	yes	—
172	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
173	Q₈×C₇₃	—	2	2	no	—
174	Q₈×C₇₃	—	2	4	no	—
175	Q₈×C₇₃	—	2	8	no	—
176	Q₈×C₇₃	—	4	16	no	—
177	Q₈×C₇₃	—	4	2	no	—
178	Q₈×C₇₃	—	4	2	no	—
179	Q₈×C₇₃	#127	1	4	yes	complemented
180	D₄×C₇₃	—	2	8	no	—
181	D₄×C₇₃	—	4	2	no	—
182	D₄×C₇₃	—	4	2	no	—
183	D₄×C₇₃	—	4	4	no	—
184	D₄×C₇₃	—	8	4	no	—
185	D₄×C₇₃	—	8	16	no	—
186	D₄×C₇₃	—	8	4	no	—
187	C₂×C₄×C₇₃	—	2	2	no	—
188	C₂×C₄×C₇₃	—	2	4	no	—
189	C₂×C₄×C₇₃	—	2	2	no	—
190	C₂×C₄×C₇₃	—	2	2	no	—
191	C₂×C₄×C₇₃	—	2	4	no	—
192	C₂×C₄×C₇₃	—	2	2	no	—
193	C₂×C₄×C₇₃	—	2	4	no	—
194	C₂×C₄×C₇₃	—	2	4	no	—
195	C₂×C₄×C₇₃	—	4	16	no	—
196	C₂×C₄×C₇₃	—	4	4	no	—
197	C₂×C₄×C₇₃	—	4	2	no	—
198	C₂×C₄×C₇₃	—	4	2	no	—
199	C₂×C₄×C₇₃	—	4	2	no	—
200	C₂×C₄×C₇₃	—	4	2	no	—
201	C₂×C₄×C₇₃	—	4	2	no	—
202	C₂×C₄×C₇₃	—	4	4	no	—
203	C₂×C₄×C₇₃	#120	1	2	yes	—
204	C₂×C₄×C₇₃	#120	1	2	yes	—
205	C₂×C₄×C₇₃	C₂×SD₁₆	1	2	yes	—
206	C₂×C₄×C₇₃	#137	1	2	yes	—
207	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
208	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
209	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
210	C₂×C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
211	C₈×C₇₃	—	2	4	no	—
212	C₈×C₇₃	—	4	2	no	—
213	C₂²×C₇₃	—	2	4	no	—
214	C₂²×C₇₃	—	2	8	no	—
215	C₂²×C₇₃	—	4	2	no	—
216	C₂²×C₇₃	—	4	2	no	—
217	C₂²×C₇₃	—	4	4	no	—
218	C₂²×C₇₃	—	8	2	no	—
219	C₂²×C₇₃	—	8	2	no	—
220	C₂²×C₇₃	—	8	2	no	—
221	C₂²×C₇₃	—	8	4	no	—
222	C₂²×C₇₃	—	8	4	no	—
223	C₂²×C₇₃	C₂×#120	1	1	yes	characteristic
224	C₂²×C₇₃	D₄²	1	2	yes	—
225	C₂²×C₇₃	C₂²×SD₁₆	1	1	yes	characteristic
226	C₂²×C₇₃	C₂×#137	1	1	yes	characteristic
227	C₂²×C₇₃	#577	1	2	yes	—
228	C₄×C₇₃	—	2	4	no	—
229	C₄×C₇₃	—	2	2	no	—
230	C₄×C₇₃	—	4	2	no	—
231	C₄×C₇₃	—	4	4	no	—
232	C₄×C₇₃	—	4	2	no	—
233	C₄×C₇₃	—	4	4	no	—
234	C₄×C₇₃	#448	1	4	yes	complemented
235	C₄×C₇₃	C₂×#127	1	1	yes	characteristic
236	C₄×C₇₃	#535	1	1	yes	characteristic
237	C₄×C₇₃	D₄²	1	2	yes	—
238	#25756	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
239	C₂×C₇₃	—	4	4	no	—
240	C₂×C₇₃	—	16	2	no	—
241	C₂×C₇₃	#2433	1	1	yes	characteristic
242	C₂×C₇₃	C₂×#448	1	1	yes	characteristic
243	C₂×C₇₃	#3010	1	1	yes	characteristic
244	C₂×C₇₃	#3278	1	2	yes	—
245	C₂×C₇₃	D₄×SD₁₆	1	2	yes	—
246	C₂×D₄×Q₈	C₂×C₇₃	1	1	yes	characteristic, complemented
247	C₂×#492	C₂×C₇₃	1	1	yes	characteristic, complemented
248	C₂×#460	C₂×C₇₃	1	1	yes	characteristic, complemented
249	C₂×#448	C₂×C₇₃	1	4	yes	complemented
250	#2541	C₂×C₇₃	1	1	yes	characteristic
251	#2000	C₂×C₇₃	1	4	yes	complemented
252	#1981	C₂×C₇₃	1	1	yes	characteristic, complemented
253	#1954	C₂×C₇₃	1	1	yes	characteristic, complemented
254	C₄×#103	C₂×C₇₃	1	1	yes	characteristic, complemented
255	C₇₃	#25756	1	1	yes	characteristic, direct product factor, Sylow
256	C₂³×Q₈	C₂²×C₇₃	1	2	yes	—
257	C₂²×SD₁₆	C₂²×C₇₃	1	2	yes	—
258	C₂²×SD₁₆	C₂²×C₇₃	1	4	yes	—
259	D₄×Q₈	—	2	4	no	—
260	D₄×Q₈	—	2	4	no	—
261	C₂×C₄⋊Q₈	—	2	1	no	—
262	C₂×C₄⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
263	C₂×#127	—	2	1	no	—
264	C₂×#127	C₂²×C₇₃	1	1	yes	characteristic
265	C₂×C₂²⋊Q₈	—	2	2	no	—
266	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	2	yes	—
267	C₂×#121	C₂²×C₇₃	1	4	yes	—
268	C₂×C₄×Q₈	C₂²×C₇₃	1	1	yes	characteristic
269	C₂×C₄×D₄	—	2	1	no	—
270	C₂×C₄×D₄	C₂²×C₇₃	1	1	yes	characteristic
271	#492	—	2	4	no	—
272	#460	—	2	4	no	—
273	#448	—	2	16	no	—
274	C₂×C₄⋊C₈	C₂²×C₇₃	1	1	yes	characteristic
275	C₂×#103	C₂²×C₇₃	1	4	yes	—
276	C₂×#103	C₂²×C₇₃	1	2	yes	—
277	C₂×#102	C₂²×C₇₃	1	2	yes	—
278	C₂×C₂²⋊C₈	C₂²×C₇₃	1	4	yes	—
279	C₂×C₄×C₈	C₂²×C₇₃	1	1	yes	characteristic
280	#392	—	2	2	no	—
281	#390	—	2	1	no	—
282	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
283	#340	C₂²×C₇₃	1	2	yes	—
284	C₂²×Q₈	—	2	4	no	—
285	C₂²×Q₈	—	2	4	no	—
286	C₂²×Q₈	—	2	2	no	—
287	C₂²×Q₈	—	2	8	no	—
288	C₂²×Q₈	—	4	4	no	—
289	C₂²×Q₈	C₂³×C₇₃	1	2	yes	—
290	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
291	C₂²×D₄	—	2	4	no	—
292	C₂²×D₄	—	2	1	no	—
293	C₂²×D₄	—	2	1	no	—
294	C₂²×D₄	D₄×C₇₃	1	1	yes	characteristic
295	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
296	C₂³×C₄	—	2	2	no	—
297	C₂³×C₄	C₂³×C₇₃	1	2	yes	—
298	C₂×SD₁₆	—	2	8	no	—
299	C₂×SD₁₆	—	2	4	no	—
300	C₂×SD₁₆	—	2	8	no	—
301	C₂×SD₁₆	—	2	8	no	—
302	C₂×SD₁₆	—	4	4	no	—
303	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
304	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
305	C₄⋊Q₈	—	2	8	no	—
306	C₄⋊Q₈	—	2	2	no	—
307	C₄⋊Q₈	D₄×C₇₃	1	4	yes	complemented
308	#127	—	2	2	no	—
309	#127	—	2	2	no	—
310	#127	—	4	4	no	—
311	C₂²⋊Q₈	—	2	16	no	—
312	C₂²⋊Q₈	—	2	4	no	—
313	C₂²⋊Q₈	—	2	4	no	—
314	#121	—	2	8	no	—
315	#121	—	4	4	no	—
316	C₄×Q₈	—	2	2	no	—
317	C₄×Q₈	D₄×C₇₃	1	4	yes	complemented
318	C₄×D₄	—	2	8	no	—
319	C₄×D₄	—	2	2	no	—
320	C₄×D₄	—	2	2	no	—
321	C₂×C₄⋊C₄	—	2	1	no	—
322	C₂×C₄⋊C₄	—	2	1	no	—
323	C₂×C₄⋊C₄	—	2	1	no	—
324	C₂×C₄⋊C₄	—	2	2	no	—
325	C₂×C₄⋊C₄	D₄×C₇₃	1	1	yes	characteristic
326	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
327	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
328	C₂×C₂²⋊C₄	—	2	2	no	—
329	C₂×C₂²⋊C₄	—	2	4	no	—
330	C₂×C₂²⋊C₄	D₄×C₇₃	1	2	yes	—
331	C₂×C₄²	—	2	1	no	—
332	C₂×C₄²	—	2	1	no	—
333	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
334	C₄⋊C₈	—	2	2	no	—
335	#103	—	2	8	no	—
336	#103	D₄×C₇₃	1	8	yes	complemented
337	#102	—	2	4	no	—
338	C₂²⋊C₈	—	2	8	no	—
339	C₄×C₈	—	2	2	no	—
340	#95	—	2	1	no	—
341	C₂⁴	—	2	2	no	—
342	C₂⁴	C₂×D₄×C₇₃	1	2	yes	—
343	C₂×Q₈	—	2	8	no	—
344	C₂×Q₈	—	2	1	no	—
345	C₂×Q₈	—	2	2	no	—
346	C₂×Q₈	—	2	2	no	—
347	C₂×Q₈	—	2	4	no	—
348	C₂×Q₈	—	2	4	no	—
349	C₂×Q₈	—	4	8	no	—
350	C₂×Q₈	—	4	16	no	—
351	C₂×Q₈	—	4	8	no	—
352	C₂×Q₈	—	4	8	no	—
353	C₂×Q₈	C₂×D₄×C₇₃	1	4	yes	—
354	C₂×Q₈	C₂×D₄×C₇₃	1	4	yes	—
355	C₂×Q₈	C₂×D₄×C₇₃	1	2	yes	—
356	C₂×D₄	—	2	2	no	—
357	C₂×D₄	—	2	2	no	—
358	C₂×D₄	—	2	2	no	—
359	C₂×D₄	—	2	4	no	—
360	C₂×D₄	—	2	2	no	—
361	C₂×D₄	—	2	4	no	—
362	C₂×D₄	—	4	8	no	—
363	C₂×D₄	—	4	8	no	—
364	C₂×D₄	—	4	2	no	—
365	C₂×D₄	—	4	2	no	—
366	C₂×D₄	—	4	2	no	—
367	C₂×D₄	—	4	2	no	—
368	C₂×D₄	—	8	2	no	—
369	C₂×D₄	—	8	4	no	—
370	C₂×D₄	SD₁₆×C₇₃	1	4	yes	complemented
371	C₂²×C₄	—	2	1	no	—
372	C₂²×C₄	—	2	8	no	—
373	C₂²×C₄	—	2	2	no	—
374	C₂²×C₄	—	2	1	no	—
375	C₂²×C₄	—	2	2	no	—
376	C₂²×C₄	—	2	4	no	—
377	C₂²×C₄	—	2	2	no	—
378	C₂²×C₄	—	2	2	no	—
379	C₂²×C₄	—	2	4	no	—
380	C₂²×C₄	—	4	8	no	—
381	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
382	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
383	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
384	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
385	SD₁₆	—	4	16	no	—
386	SD₁₆	—	4	8	no	—
387	C₂×C₈	—	2	2	no	—
388	C₂×C₈	—	2	2	no	—
389	C₂×C₈	—	2	4	no	—
390	C₂×C₈	—	2	2	no	—
391	C₂×C₈	C₂×D₄×C₇₃	1	4	yes	—
392	C₄⋊C₄	—	2	8	no	—
393	C₄⋊C₄	—	2	4	no	—
394	C₄⋊C₄	—	2	4	no	—
395	C₄⋊C₄	—	2	4	no	—
396	C₄⋊C₄	—	2	2	no	—
397	C₄⋊C₄	—	2	1	no	—
398	C₄⋊C₄	—	2	2	no	—
399	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
400	C₄⋊C₄	C₂×D₄×C₇₃	1	4	yes	—
401	C₂²⋊C₄	—	2	8	no	—
402	C₂²⋊C₄	—	2	4	no	—
403	C₂²⋊C₄	—	4	8	no	—
404	C₄²	—	2	4	no	—
405	C₄²	—	4	2	no	—
406	C₄²	C₂×D₄×C₇₃	1	2	yes	—
407	C₄²	C₂×D₄×C₇₃	1	2	yes	—
408	C₂³	—	2	2	no	—
409	C₂³	—	2	4	no	—
410	C₂³	—	2	2	no	—
411	C₂³	—	2	4	no	—
412	C₂³	—	4	2	no	—
413	C₂³	—	4	4	no	—
414	C₂³	—	4	2	no	—
415	C₂³	—	4	2	no	—
416	C₂³	—	4	4	no	—
417	C₂³	C₂×SD₁₆×C₇₃	1	4	yes	—
418	C₂³	C₂²×D₄×C₇₃	1	1	yes	characteristic
419	Q₈	—	2	2	no	—
420	Q₈	—	2	4	no	—
421	Q₈	—	2	8	no	—
422	Q₈	—	4	16	no	—
423	Q₈	—	4	2	no	—
424	Q₈	—	4	2	no	—
425	Q₈	#127×C₇₃	1	4	yes	complemented
426	D₄	—	2	8	no	—
427	D₄	—	4	2	no	—
428	D₄	—	4	2	no	—
429	D₄	—	4	4	no	—
430	D₄	—	8	4	no	—
431	D₄	—	8	16	no	—
432	D₄	—	8	4	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	4	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	2	4	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	2	4	no	—
440	C₂×C₄	—	2	4	no	—
441	C₂×C₄	—	4	16	no	—
442	C₂×C₄	—	4	4	no	—
443	C₂×C₄	—	4	2	no	—
444	C₂×C₄	—	4	2	no	—
445	C₂×C₄	—	4	2	no	—
446	C₂×C₄	—	4	2	no	—
447	C₂×C₄	—	4	2	no	—
448	C₂×C₄	—	4	4	no	—
449	C₂×C₄	#120×C₇₃	1	2	yes	—
450	C₂×C₄	#120×C₇₃	1	2	yes	—
451	C₂×C₄	C₂×SD₁₆×C₇₃	1	2	yes	—
452	C₂×C₄	#137×C₇₃	1	2	yes	—
453	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
454	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
455	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
456	C₂×C₄	H(5,𝔽₂)×C₇₃	1	2	yes	—
457	C₈	—	2	4	no	—
458	C₈	—	4	2	no	—
459	C₂²	—	2	4	no	—
460	C₂²	—	2	8	no	—
461	C₂²	—	4	2	no	—
462	C₂²	—	4	4	no	—
463	C₂²	—	4	2	no	—
464	C₂²	—	8	2	no	—
465	C₂²	—	8	2	no	—
466	C₂²	—	8	4	no	—
467	C₂²	—	8	4	no	—
468	C₂²	—	8	2	no	—
469	C₂²	C₂×#120×C₇₃	1	1	yes	characteristic
470	C₂²	D₄²×C₇₃	1	2	yes	—
471	C₂²	C₂²×SD₁₆×C₇₃	1	1	yes	characteristic
472	C₂²	C₂×#137×C₇₃	1	1	yes	characteristic
473	C₂²	#577×C₇₃	1	2	yes	—
474	C₄	—	2	2	no	—
475	C₄	—	2	4	no	—
476	C₄	—	4	2	no	—
477	C₄	—	4	4	no	—
478	C₄	—	4	2	no	—
479	C₄	—	4	4	no	—
480	C₄	#448×C₇₃	1	4	yes	complemented
481	C₄	C₂×#127×C₇₃	1	1	yes	characteristic
482	C₄	#535×C₇₃	1	1	yes	characteristic
483	C₄	D₄²×C₇₃	1	2	yes	—
484	C₂	—	4	4	no	—
485	C₂	—	16	2	no	—
486	C₂	C₇₃×#2433	1	1	yes	characteristic
487	C₂	C₂×#448×C₇₃	1	1	yes	characteristic
488	C₂	C₇₃×#3010	1	1	yes	characteristic
489	C₂	C₇₃×#3278	1	2	yes	—
490	C₂	D₄×SD₁₆×C₇₃	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₇₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₃
prime radical	C₇₃×#2541	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇₃ ◁ C₂×C₄×D₄×C₇₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×D₄×Q₈×C₇₃	C₂	semidirect
2. C₂×#492×C₇₃	C₂	semidirect
3. C₂×#460×C₇₃	C₂	semidirect
4. C₂×#448×C₇₃	C₂	semidirect
6. C₇₃×#2000	C₂	semidirect
7. C₇₃×#1981	C₂	semidirect
8. C₇₃×#1954	C₂	semidirect
9. C₄×#103×C₇₃	C₂	semidirect
61. C₄⋊Q₈×C₇₃	D₄	semidirect
71. C₄×Q₈×C₇₃	D₄	semidirect
90. #103×C₇₃	D₄	semidirect
124. C₂×D₄×C₇₃	SD₁₆	semidirect
179. Q₈×C₇₃	#127	semidirect
234. C₄×C₇₃	#448	semidirect
238. #25756	C₇₃	direct (N × H)
246. C₂×D₄×Q₈	C₂×C₇₃	semidirect
247. C₂×#492	C₂×C₇₃	semidirect
248. C₂×#460	C₂×C₇₃	semidirect
249. C₂×#448	C₂×C₇₃	semidirect
251. #2000	C₂×C₇₃	semidirect
252. #1981	C₂×C₇₃	semidirect
253. #1954	C₂×C₇₃	semidirect
254. C₄×#103	C₂×C₇₃	semidirect
255. C₇₃	#25756	direct (N × H)
307. C₄⋊Q₈	D₄×C₇₃	semidirect
317. C₄×Q₈	D₄×C₇₃	semidirect
336. #103	D₄×C₇₃	semidirect
370. C₂×D₄	SD₁₆×C₇₃	semidirect
425. Q₈	#127×C₇₃	semidirect
480. C₄	#448×C₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₄×Q₈×C₇₃	2
C₂×#492×C₇₃	2
C₂×#460×C₇₃	2
C₂×#448×C₇₃	2
C₇₃×#2541	2
C₇₃×#2000	2
C₇₃×#1981	2
C₇₃×#1954	2
C₄×#103×C₇₃	2
#25756	73

Subgroups — C73×#25756 #32935160

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#25756 #32935160