Subgroups — C₇₃×#25725 #32935129

Order 18688.

2248 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#127×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#496×C₇₃	C₂	1	2	yes	maximal, complemented
3	C₂×#450×C₇₃	C₂	1	2	yes	maximal, complemented
4	C₂×#447×C₇₃	C₂	1	2	yes	maximal, complemented
5	C₇₃×#2850	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇₃×#2014	C₂	1	2	yes	maximal, complemented
7	C₇₃×#2011	C₂	1	2	yes	maximal, complemented
8	C₇₃×#1961	C₂	1	2	yes	maximal, complemented
9	C₇₃×#1749	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂³×D₄×C₇₃	—	2	2	no	—
11	C₂³×D₄×C₇₃	C₂²	1	2	yes	—
12	C₂²×SD₁₆×C₇₃	C₂²	1	4	yes	complemented
13	C₂²×D₈×C₇₃	C₂²	1	4	yes	complemented
14	C₂×#127×C₇₃	—	2	8	no	—
15	C₂×#127×C₇₃	—	2	2	no	—
16	C₂×#127×C₇₃	C₂²	1	2	yes	—
17	C₂×#127×C₇₃	C₂²	1	2	yes	—
18	C₂×#124×C₇₃	C₂²	1	1	yes	characteristic, complemented
19	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
20	C₂×#121×C₇₃	C₂²	1	1	yes	characteristic
21	C₂²×C₄²×C₇₃	C₂²	1	1	yes	characteristic
22	#496×C₇₃	—	2	8	no	—
23	#450×C₇₃	—	2	8	no	—
24	#447×C₇₃	—	2	8	no	—
25	C₂×#102×C₇₃	C₂²	1	4	yes	complemented
26	C₂×#102×C₇₃	C₂²	1	4	yes	complemented
27	C₂×C₂²⋊C₈×C₇₃	C₂²	1	2	yes	—
28	C₂×#97×C₇₃	C₂²	1	2	yes	complemented
29	#391×C₇₃	C₂²	1	1	yes	characteristic, complemented
30	#390×C₇₃	C₂²	1	1	yes	characteristic, complemented
31	#388×C₇₃	—	2	2	no	—
32	#386×C₇₃	—	2	2	no	—
33	#382×C₇₃	C₂²	1	1	yes	characteristic, complemented
34	#336×C₇₃	C₂²	1	2	yes	complemented
35	C₂⁵×C₇₃	—	2	2	no	—
36	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
37	C₂²×D₄×C₇₃	—	2	16	no	—
38	C₂²×D₄×C₇₃	—	2	8	no	—
39	C₂²×D₄×C₇₃	—	2	1	no	—
40	C₂²×D₄×C₇₃	—	2	2	no	—
41	C₂²×D₄×C₇₃	—	2	4	no	—
42	C₂²×D₄×C₇₃	—	2	4	no	—
43	C₂²×D₄×C₇₃	—	2	4	no	—
44	C₂²×D₄×C₇₃	—	2	4	no	—
45	C₂²×D₄×C₇₃	—	4	4	no	—
46	C₂²×D₄×C₇₃	—	4	8	no	—
47	C₂²×D₄×C₇₃	—	4	8	no	—
48	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
49	C₂²×D₄×C₇₃	C₂³	1	4	yes	—
50	C₂³×C₄×C₇₃	D₄	1	2	yes	—
51	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
52	C₂×SD₁₆×C₇₃	—	2	8	no	—
53	C₂×SD₁₆×C₇₃	—	2	8	no	—
54	C₂×SD₁₆×C₇₃	—	4	4	no	—
55	C₂×D₈×C₇₃	—	2	8	no	—
56	C₂×D₈×C₇₃	—	2	8	no	—
57	C₂×D₈×C₇₃	—	4	4	no	—
58	C₂²×C₈×C₇₃	C₂³	1	4	yes	—
59	#127×C₇₃	—	2	16	no	—
60	#127×C₇₃	—	2	8	no	—
61	#127×C₇₃	—	2	4	no	—
62	#127×C₇₃	D₄	1	8	yes	complemented
63	#124×C₇₃	—	2	4	no	—
64	C₂²⋊Q₈×C₇₃	—	2	4	no	—
65	#121×C₇₃	—	2	4	no	—
66	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
67	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
68	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
69	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
70	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
71	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
72	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
73	C₂×C₄²×C₇₃	—	2	4	no	—
74	C₂×C₄²×C₇₃	D₄	1	2	yes	—
75	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
76	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
77	#102×C₇₃	—	2	8	no	—
78	#102×C₇₃	—	2	8	no	—
79	C₂²⋊C₈×C₇₃	D₄	1	8	yes	complemented
80	#97×C₇₃	—	2	4	no	—
81	#95×C₇₃	—	2	2	no	—
82	#95×C₇₃	—	2	2	no	—
83	C₂⁴×C₇₃	—	2	8	no	—
84	C₂⁴×C₇₃	—	2	4	no	—
85	C₂⁴×C₇₃	—	2	1	no	—
86	C₂⁴×C₇₃	—	4	4	no	—
87	C₂⁴×C₇₃	—	4	8	no	—
88	C₂⁴×C₇₃	—	4	4	no	—
89	C₂⁴×C₇₃	—	4	8	no	—
90	C₂⁴×C₇₃	C₂×D₄	1	1	yes	characteristic
91	C₂×Q₈×C₇₃	—	2	2	no	—
92	C₂×Q₈×C₇₃	—	2	2	no	—
93	C₂×Q₈×C₇₃	—	2	2	no	—
94	C₂×D₄×C₇₃	—	2	8	no	—
95	C₂×D₄×C₇₃	—	2	16	no	—
96	C₂×D₄×C₇₃	—	2	16	no	—
97	C₂×D₄×C₇₃	—	2	4	no	—
98	C₂×D₄×C₇₃	—	2	4	no	—
99	C₂×D₄×C₇₃	—	2	4	no	—
100	C₂×D₄×C₇₃	—	2	2	no	—
101	C₂×D₄×C₇₃	—	2	2	no	—
102	C₂×D₄×C₇₃	—	2	4	no	—
103	C₂×D₄×C₇₃	—	2	4	no	—
104	C₂×D₄×C₇₃	—	2	2	no	—
105	C₂×D₄×C₇₃	—	4	16	no	—
106	C₂×D₄×C₇₃	—	4	16	no	—
107	C₂×D₄×C₇₃	—	4	64	no	—
108	C₂×D₄×C₇₃	—	4	4	no	—
109	C₂×D₄×C₇₃	—	4	8	no	—
110	C₂×D₄×C₇₃	—	4	8	no	—
111	C₂×D₄×C₇₃	—	4	8	no	—
112	C₂×D₄×C₇₃	—	4	2	no	—
113	C₂×D₄×C₇₃	—	4	4	no	—
114	C₂×D₄×C₇₃	—	4	4	no	—
115	C₂×D₄×C₇₃	—	4	8	no	—
116	C₂×D₄×C₇₃	C₂×D₄	1	8	yes	—
117	C₂²×C₄×C₇₃	—	2	4	no	—
118	C₂²×C₄×C₇₃	—	2	4	no	—
119	C₂²×C₄×C₇₃	—	2	4	no	—
120	C₂²×C₄×C₇₃	—	2	2	no	—
121	C₂²×C₄×C₇₃	—	2	2	no	—
122	C₂²×C₄×C₇₃	—	2	1	no	—
123	C₂²×C₄×C₇₃	—	2	1	no	—
124	C₂²×C₄×C₇₃	—	2	1	no	—
125	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
126	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₇₃	C₂×D₄	1	4	yes	—
128	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
129	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
130	SD₁₆×C₇₃	—	4	16	no	—
131	D₈×C₇₃	—	4	16	no	—
132	C₂×C₈×C₇₃	—	2	4	no	—
133	C₂×C₈×C₇₃	—	2	4	no	—
134	C₂×C₈×C₇₃	C₂×D₄	1	8	yes	complemented
135	C₄⋊C₄×C₇₃	—	2	2	no	—
136	C₄⋊C₄×C₇₃	—	2	2	no	—
137	C₄⋊C₄×C₇₃	—	4	2	no	—
138	C₂²⋊C₄×C₇₃	—	4	2	no	—
139	C₂²⋊C₄×C₇₃	—	4	4	no	—
140	C₂²⋊C₄×C₇₃	—	4	2	no	—
141	C₂²⋊C₄×C₇₃	—	4	4	no	—
142	C₄²×C₇₃	—	2	4	no	—
143	C₄²×C₇₃	—	2	2	no	—
144	C₄²×C₇₃	C₂×D₄	1	4	yes	—
145	C₂³×C₇₃	—	2	1	no	—
146	C₂³×C₇₃	—	2	1	no	—
147	C₂³×C₇₃	—	2	2	no	—
148	C₂³×C₇₃	—	2	8	no	—
149	C₂³×C₇₃	—	4	16	no	—
150	C₂³×C₇₃	—	4	32	no	—
151	C₂³×C₇₃	—	4	4	no	—
152	C₂³×C₇₃	—	4	4	no	—
153	C₂³×C₇₃	—	4	8	no	—
154	C₂³×C₇₃	—	4	8	no	—
155	C₂³×C₇₃	—	4	1	no	—
156	C₂³×C₇₃	—	4	1	no	—
157	C₂³×C₇₃	—	4	1	no	—
158	C₂³×C₇₃	—	4	2	no	—
159	C₂³×C₇₃	—	4	2	no	—
160	C₂³×C₇₃	—	8	8	no	—
161	C₂³×C₇₃	—	8	16	no	—
162	C₂³×C₇₃	—	8	8	no	—
163	C₂³×C₇₃	#127	1	2	yes	—
164	C₂³×C₇₃	AGL(1,ℤ/8)	1	4	yes	—
165	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
166	Q₈×C₇₃	—	4	4	no	—
167	D₄×C₇₃	—	2	8	no	—
168	D₄×C₇₃	—	2	8	no	—
169	D₄×C₇₃	—	4	16	no	—
170	D₄×C₇₃	—	4	32	no	—
171	D₄×C₇₃	—	4	32	no	—
172	D₄×C₇₃	—	4	4	no	—
173	D₄×C₇₃	—	4	4	no	—
174	D₄×C₇₃	—	4	4	no	—
175	D₄×C₇₃	—	8	4	no	—
176	C₂×C₄×C₇₃	—	2	16	no	—
177	C₂×C₄×C₇₃	—	2	1	no	—
178	C₂×C₄×C₇₃	—	2	2	no	—
179	C₂×C₄×C₇₃	—	2	1	no	—
180	C₂×C₄×C₇₃	—	2	2	no	—
181	C₂×C₄×C₇₃	—	2	2	no	—
182	C₂×C₄×C₇₃	—	2	2	no	—
183	C₂×C₄×C₇₃	—	2	8	no	—
184	C₂×C₄×C₇₃	—	4	1	no	—
185	C₂×C₄×C₇₃	—	4	1	no	—
186	C₂×C₄×C₇₃	—	4	1	no	—
187	C₂×C₄×C₇₃	—	4	1	no	—
188	C₂×C₄×C₇₃	—	4	1	no	—
189	C₂×C₄×C₇₃	—	4	2	no	—
190	C₂×C₄×C₇₃	—	4	2	no	—
191	C₂×C₄×C₇₃	#120	1	4	yes	—
192	C₂×C₄×C₇₃	#127	1	2	yes	—
193	C₂×C₄×C₇₃	AGL(1,ℤ/8)	1	4	yes	—
194	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
195	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
196	C₂×C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
197	C₈×C₇₃	—	2	8	no	—
198	C₂²×C₇₃	—	2	2	no	—
199	C₂²×C₇₃	—	2	2	no	—
200	C₂²×C₇₃	—	2	4	no	—
201	C₂²×C₇₃	—	2	4	no	—
202	C₂²×C₇₃	—	4	8	no	—
203	C₂²×C₇₃	—	4	16	no	—
204	C₂²×C₇₃	—	8	32	no	—
205	C₂²×C₇₃	—	8	4	no	—
206	C₂²×C₇₃	—	8	4	no	—
207	C₂²×C₇₃	—	8	8	no	—
208	C₂²×C₇₃	—	8	1	no	—
209	C₂²×C₇₃	—	8	1	no	—
210	C₂²×C₇₃	—	8	1	no	—
211	C₂²×C₇₃	—	8	2	no	—
212	C₂²×C₇₃	—	8	2	no	—
213	C₂²×C₇₃	#496	1	4	yes	complemented
214	C₂²×C₇₃	C₂×#120	1	1	yes	characteristic
215	C₂²×C₇₃	C₂×#127	1	1	yes	characteristic
216	C₂²×C₇₃	#535	1	1	yes	characteristic
217	C₂²×C₇₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
218	C₂²×C₇₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
219	C₄×C₇₃	—	2	2	no	—
220	C₄×C₇₃	—	2	4	no	—
221	C₄×C₇₃	—	2	4	no	—
222	C₄×C₇₃	—	8	1	no	—
223	C₄×C₇₃	—	8	1	no	—
224	C₄×C₇₃	—	8	1	no	—
225	C₄×C₇₃	D₄²	1	4	yes	—
226	#25725	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
227	C₂×C₇₃	—	2	4	no	—
228	C₂×C₇₃	—	8	8	no	—
229	C₂×C₇₃	—	16	1	no	—
230	C₂×C₇₃	#2433	1	1	yes	characteristic
231	C₂×C₇₃	#3003	1	2	yes	—
232	C₂×C₇₃	C₂×#496	1	1	yes	characteristic
233	C₂×C₇₃	#3151	1	1	yes	characteristic
234	C₂×C₇₃	#3217	1	2	yes	—
235	C₂²×#127	C₂×C₇₃	1	1	yes	characteristic, complemented
236	C₂×#496	C₂×C₇₃	1	2	yes	complemented
237	C₂×#450	C₂×C₇₃	1	2	yes	complemented
238	C₂×#447	C₂×C₇₃	1	2	yes	complemented
239	#2850	C₂×C₇₃	1	1	yes	characteristic, complemented
240	#2014	C₂×C₇₃	1	2	yes	complemented
241	#2011	C₂×C₇₃	1	2	yes	complemented
242	#1961	C₂×C₇₃	1	2	yes	complemented
243	#1749	C₂×C₇₃	1	1	yes	characteristic, complemented
244	C₇₃	#25725	1	1	yes	characteristic, direct product factor, Sylow
245	C₂³×D₄	—	2	2	no	—
246	C₂³×D₄	C₂²×C₇₃	1	2	yes	—
247	C₂²×SD₁₆	C₂²×C₇₃	1	4	yes	complemented
248	C₂²×D₈	C₂²×C₇₃	1	4	yes	complemented
249	C₂×#127	—	2	8	no	—
250	C₂×#127	—	2	2	no	—
251	C₂×#127	C₂²×C₇₃	1	2	yes	—
252	C₂×#127	C₂²×C₇₃	1	2	yes	—
253	C₂×#124	C₂²×C₇₃	1	1	yes	characteristic, complemented
254	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
255	C₂×#121	C₂²×C₇₃	1	1	yes	characteristic
256	C₂²×C₄²	C₂²×C₇₃	1	1	yes	characteristic
257	#496	—	2	8	no	—
258	#450	—	2	8	no	—
259	#447	—	2	8	no	—
260	C₂×#102	C₂²×C₇₃	1	4	yes	complemented
261	C₂×#102	C₂²×C₇₃	1	4	yes	complemented
262	C₂×C₂²⋊C₈	C₂²×C₇₃	1	2	yes	—
263	C₂×#97	C₂²×C₇₃	1	2	yes	complemented
264	#391	C₂²×C₇₃	1	1	yes	characteristic, complemented
265	#390	C₂²×C₇₃	1	1	yes	characteristic, complemented
266	#388	—	2	2	no	—
267	#386	—	2	2	no	—
268	#382	C₂²×C₇₃	1	1	yes	characteristic, complemented
269	#336	C₂²×C₇₃	1	2	yes	complemented
270	C₂⁵	—	2	2	no	—
271	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
272	C₂²×D₄	—	2	16	no	—
273	C₂²×D₄	—	2	8	no	—
274	C₂²×D₄	—	2	1	no	—
275	C₂²×D₄	—	2	2	no	—
276	C₂²×D₄	—	2	4	no	—
277	C₂²×D₄	—	2	4	no	—
278	C₂²×D₄	—	2	4	no	—
279	C₂²×D₄	—	2	4	no	—
280	C₂²×D₄	—	4	4	no	—
281	C₂²×D₄	—	4	8	no	—
282	C₂²×D₄	—	4	8	no	—
283	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
284	C₂²×D₄	C₂³×C₇₃	1	4	yes	—
285	C₂³×C₄	D₄×C₇₃	1	2	yes	—
286	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
287	C₂×SD₁₆	—	2	8	no	—
288	C₂×SD₁₆	—	2	8	no	—
289	C₂×SD₁₆	—	4	4	no	—
290	C₂×D₈	—	2	8	no	—
291	C₂×D₈	—	2	8	no	—
292	C₂×D₈	—	4	4	no	—
293	C₂²×C₈	C₂³×C₇₃	1	4	yes	—
294	#127	—	2	16	no	—
295	#127	—	2	8	no	—
296	#127	—	2	4	no	—
297	#127	D₄×C₇₃	1	8	yes	complemented
298	#124	—	2	4	no	—
299	C₂²⋊Q₈	—	2	4	no	—
300	#121	—	2	4	no	—
301	C₂×C₄⋊C₄	—	2	1	no	—
302	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
303	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
304	C₂×C₂²⋊C₄	—	2	1	no	—
305	C₂×C₂²⋊C₄	—	2	1	no	—
306	C₂×C₂²⋊C₄	—	2	2	no	—
307	C₂×C₂²⋊C₄	—	2	2	no	—
308	C₂×C₄²	—	2	4	no	—
309	C₂×C₄²	D₄×C₇₃	1	2	yes	—
310	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
311	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
312	#102	—	2	8	no	—
313	#102	—	2	8	no	—
314	C₂²⋊C₈	D₄×C₇₃	1	8	yes	complemented
315	#97	—	2	4	no	—
316	#95	—	2	2	no	—
317	#95	—	2	2	no	—
318	C₂⁴	—	2	8	no	—
319	C₂⁴	—	2	4	no	—
320	C₂⁴	—	2	1	no	—
321	C₂⁴	—	4	4	no	—
322	C₂⁴	—	4	8	no	—
323	C₂⁴	—	4	4	no	—
324	C₂⁴	—	4	8	no	—
325	C₂⁴	C₂×D₄×C₇₃	1	1	yes	characteristic
326	C₂×Q₈	—	2	2	no	—
327	C₂×Q₈	—	2	2	no	—
328	C₂×Q₈	—	2	2	no	—
329	C₂×D₄	—	2	8	no	—
330	C₂×D₄	—	2	16	no	—
331	C₂×D₄	—	2	16	no	—
332	C₂×D₄	—	2	4	no	—
333	C₂×D₄	—	2	4	no	—
334	C₂×D₄	—	2	4	no	—
335	C₂×D₄	—	2	2	no	—
336	C₂×D₄	—	2	2	no	—
337	C₂×D₄	—	2	4	no	—
338	C₂×D₄	—	2	4	no	—
339	C₂×D₄	—	2	2	no	—
340	C₂×D₄	—	4	16	no	—
341	C₂×D₄	—	4	16	no	—
342	C₂×D₄	—	4	64	no	—
343	C₂×D₄	—	4	4	no	—
344	C₂×D₄	—	4	8	no	—
345	C₂×D₄	—	4	8	no	—
346	C₂×D₄	—	4	8	no	—
347	C₂×D₄	—	4	2	no	—
348	C₂×D₄	—	4	4	no	—
349	C₂×D₄	—	4	4	no	—
350	C₂×D₄	—	4	8	no	—
351	C₂×D₄	C₂×D₄×C₇₃	1	8	yes	—
352	C₂²×C₄	—	2	4	no	—
353	C₂²×C₄	—	2	4	no	—
354	C₂²×C₄	—	2	4	no	—
355	C₂²×C₄	—	2	2	no	—
356	C₂²×C₄	—	2	2	no	—
357	C₂²×C₄	—	2	1	no	—
358	C₂²×C₄	—	2	1	no	—
359	C₂²×C₄	—	2	1	no	—
360	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
361	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
362	C₂²×C₄	C₂×D₄×C₇₃	1	4	yes	—
363	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
364	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
365	SD₁₆	—	4	16	no	—
366	D₈	—	4	16	no	—
367	C₂×C₈	—	2	4	no	—
368	C₂×C₈	—	2	4	no	—
369	C₂×C₈	C₂×D₄×C₇₃	1	8	yes	complemented
370	C₄⋊C₄	—	2	2	no	—
371	C₄⋊C₄	—	2	2	no	—
372	C₄⋊C₄	—	4	2	no	—
373	C₂²⋊C₄	—	4	2	no	—
374	C₂²⋊C₄	—	4	4	no	—
375	C₂²⋊C₄	—	4	2	no	—
376	C₂²⋊C₄	—	4	4	no	—
377	C₄²	—	2	4	no	—
378	C₄²	—	2	2	no	—
379	C₄²	C₂×D₄×C₇₃	1	4	yes	—
380	C₂³	—	2	1	no	—
381	C₂³	—	2	1	no	—
382	C₂³	—	2	2	no	—
383	C₂³	—	2	8	no	—
384	C₂³	—	4	32	no	—
385	C₂³	—	4	16	no	—
386	C₂³	—	4	4	no	—
387	C₂³	—	4	4	no	—
388	C₂³	—	4	8	no	—
389	C₂³	—	4	8	no	—
390	C₂³	—	4	1	no	—
391	C₂³	—	4	1	no	—
392	C₂³	—	4	1	no	—
393	C₂³	—	4	2	no	—
394	C₂³	—	4	2	no	—
395	C₂³	—	8	16	no	—
396	C₂³	—	8	8	no	—
397	C₂³	—	8	8	no	—
398	C₂³	#127×C₇₃	1	2	yes	—
399	C₂³	AGL(1,ℤ/8)×C₇₃	1	4	yes	—
400	C₂³	C₂²×D₄×C₇₃	1	1	yes	characteristic
401	Q₈	—	4	4	no	—
402	D₄	—	2	8	no	—
403	D₄	—	2	8	no	—
404	D₄	—	4	32	no	—
405	D₄	—	4	32	no	—
406	D₄	—	4	16	no	—
407	D₄	—	4	4	no	—
408	D₄	—	4	4	no	—
409	D₄	—	4	4	no	—
410	D₄	—	8	4	no	—
411	C₂×C₄	—	2	16	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	1	no	—
414	C₂×C₄	—	2	1	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	2	8	no	—
419	C₂×C₄	—	4	1	no	—
420	C₂×C₄	—	4	1	no	—
421	C₂×C₄	—	4	1	no	—
422	C₂×C₄	—	4	1	no	—
423	C₂×C₄	—	4	1	no	—
424	C₂×C₄	—	4	2	no	—
425	C₂×C₄	—	4	2	no	—
426	C₂×C₄	#120×C₇₃	1	4	yes	—
427	C₂×C₄	#127×C₇₃	1	2	yes	—
428	C₂×C₄	AGL(1,ℤ/8)×C₇₃	1	4	yes	—
429	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
430	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
431	C₂×C₄	H(5,𝔽₂)×C₇₃	1	2	yes	—
432	C₈	—	2	8	no	—
433	C₂²	—	2	4	no	—
434	C₂²	—	2	4	no	—
435	C₂²	—	2	2	no	—
436	C₂²	—	2	2	no	—
437	C₂²	—	4	16	no	—
438	C₂²	—	4	8	no	—
439	C₂²	—	8	32	no	—
440	C₂²	—	8	8	no	—
441	C₂²	—	8	4	no	—
442	C₂²	—	8	4	no	—
443	C₂²	—	8	2	no	—
444	C₂²	—	8	2	no	—
445	C₂²	—	8	1	no	—
446	C₂²	—	8	1	no	—
447	C₂²	—	8	1	no	—
448	C₂²	#496×C₇₃	1	4	yes	complemented
449	C₂²	C₂×#120×C₇₃	1	1	yes	characteristic
450	C₂²	C₂×#127×C₇₃	1	1	yes	characteristic
451	C₂²	#535×C₇₃	1	1	yes	characteristic
452	C₂²	C₂×AGL(1,ℤ/8)×C₇₃	1	2	yes	—
453	C₂²	C₂×AGL(1,ℤ/8)×C₇₃	1	2	yes	—
454	C₄	—	2	4	no	—
455	C₄	—	2	4	no	—
456	C₄	—	2	2	no	—
457	C₄	—	8	1	no	—
458	C₄	—	8	1	no	—
459	C₄	—	8	1	no	—
460	C₄	D₄²×C₇₃	1	4	yes	—
461	C₂	—	2	4	no	—
462	C₂	—	8	8	no	—
463	C₂	—	16	1	no	—
464	C₂	C₇₃×#2433	1	1	yes	characteristic
465	C₂	C₇₃×#3003	1	2	yes	—
466	C₂	C₂×#496×C₇₃	1	1	yes	characteristic
467	C₂	C₇₃×#3151	1	1	yes	characteristic
468	C₂	C₇₃×#3217	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₇₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₃
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×#127×C₇₃	C₂	semidirect
2. C₂×#496×C₇₃	C₂	semidirect
3. C₂×#450×C₇₃	C₂	semidirect
4. C₂×#447×C₇₃	C₂	semidirect
5. C₇₃×#2850	C₂	semidirect
6. C₇₃×#2014	C₂	semidirect
7. C₇₃×#2011	C₂	semidirect
8. C₇₃×#1961	C₂	semidirect
9. C₇₃×#1749	C₂	semidirect
12. C₂²×SD₁₆×C₇₃	C₂²	semidirect
13. C₂²×D₈×C₇₃	C₂²	semidirect
18. C₂×#124×C₇₃	C₂²	semidirect
25. C₂×#102×C₇₃	C₂²	semidirect
26. C₂×#102×C₇₃	C₂²	semidirect
28. C₂×#97×C₇₃	C₂²	semidirect
29. #391×C₇₃	C₂²	semidirect
30. #390×C₇₃	C₂²	semidirect
33. #382×C₇₃	C₂²	semidirect
34. #336×C₇₃	C₂²	semidirect
62. #127×C₇₃	D₄	semidirect
79. C₂²⋊C₈×C₇₃	D₄	semidirect
134. C₂×C₈×C₇₃	C₂×D₄	semidirect
213. C₂²×C₇₃	#496	semidirect
226. #25725	C₇₃	direct (N × H)
235. C₂²×#127	C₂×C₇₃	semidirect
236. C₂×#496	C₂×C₇₃	semidirect
237. C₂×#450	C₂×C₇₃	semidirect
238. C₂×#447	C₂×C₇₃	semidirect
239. #2850	C₂×C₇₃	semidirect
240. #2014	C₂×C₇₃	semidirect
241. #2011	C₂×C₇₃	semidirect
242. #1961	C₂×C₇₃	semidirect
243. #1749	C₂×C₇₃	semidirect
244. C₇₃	#25725	direct (N × H)
247. C₂²×SD₁₆	C₂²×C₇₃	semidirect
248. C₂²×D₈	C₂²×C₇₃	semidirect
253. C₂×#124	C₂²×C₇₃	semidirect
260. C₂×#102	C₂²×C₇₃	semidirect
261. C₂×#102	C₂²×C₇₃	semidirect
263. C₂×#97	C₂²×C₇₃	semidirect
264. #391	C₂²×C₇₃	semidirect
265. #390	C₂²×C₇₃	semidirect
268. #382	C₂²×C₇₃	semidirect
269. #336	C₂²×C₇₃	semidirect
297. #127	D₄×C₇₃	semidirect
314. C₂²⋊C₈	D₄×C₇₃	semidirect
369. C₂×C₈	C₂×D₄×C₇₃	semidirect
448. C₂²	#496×C₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#127×C₇₃	2
C₂×#496×C₇₃	2
C₂×#450×C₇₃	2
C₂×#447×C₇₃	2
C₇₃×#2850	2
C₇₃×#2014	2
C₇₃×#2011	2
C₇₃×#1961	2
C₇₃×#1749	2
#25725	73

Subgroups — C73×#25725 #32935129

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#25725 #32935129