Subgroups — C₂×C₇₃×#1489 #32926850

Order 18688.

1378 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#41×C₇₃	C₂	1	1	yes	maximal, characteristic
2	C₂×#423×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×M₁₆×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₃×#1489	C₂	1	8	yes	maximal, direct product factor
5	C₂×Q₈⋊C₈×C₇₃	C₂	1	2	yes	maximal, complemented
6	C₂×D₄⋊C₈×C₇₃	C₂	1	2	yes	maximal, complemented
7	C₂²×#41×C₇₃	C₄	1	1	yes	characteristic
8	C₂²×M₁₆×C₇₃	—	2	1	no	—
9	C₂²×M₁₆×C₇₃	—	2	1	no	—
10	C₄×#41×C₇₃	—	2	2	no	—
11	C₄×#41×C₇₃	—	2	2	no	—
12	C₄×#41×C₇₃	C₄	1	4	yes	—
13	C₄×#41×C₇₃	C₂²	1	4	yes	—
14	C₂×C₄×Q₈×C₇₃	C₄	1	1	yes	characteristic
15	C₂×C₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic
16	C₂×C₄×D₄×C₇₃	—	2	1	no	—
17	C₂×C₄×D₄×C₇₃	—	2	1	no	—
18	C₂×C₄×D₄×C₇₃	C₄	1	1	yes	characteristic
19	C₂×C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
20	C₂×#117×C₇₃	—	2	1	no	—
21	C₂×#117×C₇₃	C₄	1	1	yes	characteristic
22	C₂²×C₄²×C₇₃	—	2	1	no	—
23	C₂²×C₄²×C₇₃	C₂²	1	1	yes	characteristic
24	#423×C₇₃	—	2	2	no	—
25	#423×C₇₃	C₂²	1	4	yes	complemented
26	C₂×C₄⋊C₈×C₇₃	—	2	1	no	—
27	C₂×C₄⋊C₈×C₇₃	C₂²	1	2	yes	—
28	C₄×M₁₆×C₇₃	—	2	2	no	—
29	C₄×M₁₆×C₇₃	C₂²	1	4	yes	complemented
30	C₂×#97×C₇₃	—	2	1	no	—
31	C₂×C₄×C₈×C₇₃	C₂²	1	2	yes	—
32	Q₈⋊C₈×C₇₃	C₂²	1	8	yes	complemented
33	D₄⋊C₈×C₇₃	C₂²	1	8	yes	complemented
34	C₂×#41×C₇₃	—	2	4	no	—
35	C₂×#41×C₇₃	—	2	4	no	—
36	C₂×#41×C₇₃	—	2	2	no	—
37	C₂×#41×C₇₃	C₂×C₄	1	4	yes	—
38	C₂²×Q₈×C₇₃	C₂×C₄	1	1	yes	characteristic
39	C₂²×D₄×C₇₃	—	2	1	no	—
40	C₂²×D₄×C₇₃	C₂×C₄	1	1	yes	characteristic
41	C₂³×C₄×C₇₃	—	2	1	no	—
42	C₂³×C₄×C₇₃	—	2	1	no	—
43	C₂³×C₄×C₇₃	—	2	1	no	—
44	C₂³×C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
45	C₂³×C₄×C₇₃	D₄	1	1	yes	characteristic
46	C₂³×C₄×C₇₃	D₄	1	1	yes	characteristic
47	C₂×M₁₆×C₇₃	—	2	8	no	—
48	C₂×M₁₆×C₇₃	—	2	4	no	—
49	C₂×M₁₆×C₇₃	—	2	4	no	—
50	C₂×M₁₆×C₇₃	—	4	4	no	—
51	C₂²×C₈×C₇₃	—	2	2	no	—
52	C₂²×C₈×C₇₃	—	2	2	no	—
53	C₄×Q₈×C₇₃	—	2	2	no	—
54	C₄×Q₈×C₇₃	—	2	1	no	—
55	C₄×Q₈×C₇₃	—	2	1	no	—
56	C₄×Q₈×C₇₃	C₂×C₄	1	4	yes	—
57	C₄×Q₈×C₇₃	C₂×C₄	1	2	yes	—
58	C₄×Q₈×C₇₃	C₂³	1	2	yes	—
59	C₄×D₄×C₇₃	—	2	4	no	—
60	C₄×D₄×C₇₃	—	2	4	no	—
61	C₄×D₄×C₇₃	—	2	4	no	—
62	C₄×D₄×C₇₃	—	2	4	no	—
63	C₄×D₄×C₇₃	—	2	2	no	—
64	C₄×D₄×C₇₃	—	2	1	no	—
65	C₄×D₄×C₇₃	—	2	1	no	—
66	C₄×D₄×C₇₃	C₂×C₄	1	4	yes	—
67	C₄×D₄×C₇₃	C₂×C₄	1	2	yes	—
68	C₄×D₄×C₇₃	C₂³	1	2	yes	—
69	#117×C₇₃	—	2	2	no	—
70	#117×C₇₃	—	2	4	no	—
71	#117×C₇₃	—	2	4	no	—
72	#117×C₇₃	C₂×C₄	1	4	yes	—
73	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
74	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
75	C₂×C₄⋊C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
76	C₂×C₄⋊C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
77	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
78	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
79	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
80	C₂×C₄²×C₇₃	—	2	1	no	—
81	C₂×C₄²×C₇₃	—	2	1	no	—
82	C₂×C₄²×C₇₃	—	2	1	no	—
83	C₂×C₄²×C₇₃	—	2	4	no	—
84	C₂×C₄²×C₇₃	—	2	4	no	—
85	C₂×C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
86	C₂×C₄²×C₇₃	C₂×C₄	1	2	yes	—
87	C₂×C₄²×C₇₃	D₄	1	1	yes	characteristic
88	C₂×C₄²×C₇₃	D₄	1	2	yes	—
89	C₂×C₄²×C₇₃	D₄	1	2	yes	—
90	C₂×C₄²×C₇₃	D₄	1	1	yes	characteristic
91	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
92	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
93	C₄⋊C₈×C₇₃	—	2	4	no	—
94	C₄⋊C₈×C₇₃	—	2	2	no	—
95	C₄⋊C₈×C₇₃	C₂³	1	4	yes	—
96	#97×C₇₃	—	2	4	no	—
97	C₄×C₈×C₇₃	—	2	2	no	—
98	C₄×C₈×C₇₃	C₂³	1	4	yes	—
99	C₂⁴×C₇₃	—	2	1	no	—
100	C₂⁴×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
101	#41×C₇₃	—	2	16	no	—
102	#41×C₇₃	—	2	8	no	—
103	#41×C₇₃	—	2	8	no	—
104	C₂×Q₈×C₇₃	—	2	1	no	—
105	C₂×Q₈×C₇₃	—	2	2	no	—
106	C₂×Q₈×C₇₃	M₁₆	1	4	yes	complemented
107	C₂×Q₈×C₇₃	C₂²×C₄	1	2	yes	—
108	C₂×D₄×C₇₃	—	2	8	no	—
109	C₂×D₄×C₇₃	—	2	4	no	—
110	C₂×D₄×C₇₃	—	2	1	no	—
111	C₂×D₄×C₇₃	—	2	2	no	—
112	C₂×D₄×C₇₃	M₁₆	1	4	yes	complemented
113	C₂×D₄×C₇₃	C₂²×C₄	1	2	yes	—
114	C₂²×C₄×C₇₃	—	2	8	no	—
115	C₂²×C₄×C₇₃	—	2	1	no	—
116	C₂²×C₄×C₇₃	—	2	4	no	—
117	C₂²×C₄×C₇₃	—	2	4	no	—
118	C₂²×C₄×C₇₃	—	2	2	no	—
119	C₂²×C₄×C₇₃	—	2	2	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	2	no	—
125	C₂²×C₄×C₇₃	—	2	4	no	—
126	C₂²×C₄×C₇₃	—	2	2	no	—
127	C₂²×C₄×C₇₃	—	4	4	no	—
128	C₂²×C₄×C₇₃	—	4	2	no	—
129	C₂²×C₄×C₇₃	—	4	2	no	—
130	C₂²×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
131	C₂²×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
132	C₂²×C₄×C₇₃	C₂²⋊C₄	1	2	yes	—
133	C₂²×C₄×C₇₃	C₂²⋊C₄	1	2	yes	—
134	C₂²×C₄×C₇₃	C₂²⋊C₄	1	2	yes	—
135	C₂²×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
136	C₂²×C₄×C₇₃	C₂²×C₄	1	2	yes	—
137	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
138	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
140	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
141	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
142	M₁₆×C₇₃	—	2	16	no	—
143	M₁₆×C₇₃	—	4	8	no	—
144	C₂×C₈×C₇₃	—	2	8	no	—
145	C₂×C₈×C₇₃	—	2	4	no	—
146	C₂×C₈×C₇₃	—	2	4	no	—
147	C₂×C₈×C₇₃	—	4	4	no	—
148	C₄⋊C₄×C₇₃	—	2	4	no	—
149	C₄⋊C₄×C₇₃	—	2	2	no	—
150	C₄⋊C₄×C₇₃	—	2	1	no	—
151	C₄⋊C₄×C₇₃	—	2	1	no	—
152	C₄⋊C₄×C₇₃	—	2	2	no	—
153	C₄⋊C₄×C₇₃	C₂²×C₄	1	2	yes	—
154	C₄⋊C₄×C₇₃	C₂²×C₄	1	2	yes	—
155	C₂²⋊C₄×C₇₃	—	2	4	no	—
156	C₂²⋊C₄×C₇₃	—	2	4	no	—
157	C₂²⋊C₄×C₇₃	—	2	2	no	—
158	C₂²⋊C₄×C₇₃	—	2	2	no	—
159	C₄²×C₇₃	—	2	4	no	—
160	C₄²×C₇₃	—	2	2	no	—
161	C₄²×C₇₃	—	2	4	no	—
162	C₄²×C₇₃	—	2	2	no	—
163	C₄²×C₇₃	C₂²⋊C₄	1	2	yes	—
164	C₄²×C₇₃	C₂²⋊C₄	1	2	yes	—
165	C₄²×C₇₃	C₂²⋊C₄	1	2	yes	—
166	C₄²×C₇₃	C₂²×C₄	1	1	yes	characteristic
167	C₄²×C₇₃	C₂²×C₄	1	2	yes	—
168	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
169	C₄²×C₇₃	C₂×D₄	1	2	yes	—
170	C₄²×C₇₃	C₂×D₄	1	2	yes	—
171	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
172	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
173	C₂³×C₇₃	—	2	2	no	—
174	C₂³×C₇₃	—	2	2	no	—
175	C₂³×C₇₃	—	2	4	no	—
176	C₂³×C₇₃	—	2	2	no	—
177	C₂³×C₇₃	—	2	2	no	—
178	C₂³×C₇₃	—	4	2	no	—
179	C₂³×C₇₃	—	4	2	no	—
180	C₂³×C₇₃	C₂×C₂²⋊C₄	1	2	yes	—
181	C₂³×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
182	Q₈×C₇₃	—	2	2	no	—
183	Q₈×C₇₃	—	2	4	no	—
184	Q₈×C₇₃	C₂×M₁₆	1	4	yes	complemented
185	D₄×C₇₃	—	2	16	no	—
186	D₄×C₇₃	—	2	2	no	—
187	D₄×C₇₃	—	2	4	no	—
188	D₄×C₇₃	C₂×M₁₆	1	4	yes	complemented
189	C₂×C₄×C₇₃	—	2	16	no	—
190	C₂×C₄×C₇₃	—	2	2	no	—
191	C₂×C₄×C₇₃	—	2	2	no	—
192	C₂×C₄×C₇₃	—	2	4	no	—
193	C₂×C₄×C₇₃	—	2	2	no	—
194	C₂×C₄×C₇₃	—	2	2	no	—
195	C₂×C₄×C₇₃	—	2	2	no	—
196	C₂×C₄×C₇₃	—	2	2	no	—
197	C₂×C₄×C₇₃	—	2	2	no	—
198	C₂×C₄×C₇₃	—	2	2	no	—
199	C₂×C₄×C₇₃	—	2	4	no	—
200	C₂×C₄×C₇₃	—	2	4	no	—
201	C₂×C₄×C₇₃	—	2	4	no	—
202	C₂×C₄×C₇₃	—	2	4	no	—
203	C₂×C₄×C₇₃	—	2	2	no	—
204	C₂×C₄×C₇₃	—	2	2	no	—
205	C₂×C₄×C₇₃	—	4	2	no	—
206	C₂×C₄×C₇₃	—	4	2	no	—
207	C₂×C₄×C₇₃	—	4	2	no	—
208	C₂×C₄×C₇₃	—	4	2	no	—
209	C₂×C₄×C₇₃	—	4	4	no	—
210	C₂×C₄×C₇₃	—	4	8	no	—
211	C₂×C₄×C₇₃	#104	1	4	yes	—
212	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	2	yes	—
213	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	2	yes	—
214	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
215	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
216	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
217	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	2	yes	—
218	C₂×C₄×C₇₃	C₂×M₁₆	1	2	yes	—
219	C₂×C₄×C₇₃	C₂×M₁₆	1	2	yes	—
220	C₂×C₄×C₇₃	AGL(1,ℤ/8)	1	2	yes	—
221	C₂×C₄×C₇₃	#137	1	2	yes	—
222	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
223	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
224	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
225	C₈×C₇₃	—	2	8	no	—
226	C₈×C₇₃	—	4	4	no	—
227	C₂²×C₇₃	—	2	2	no	—
228	C₂²×C₇₃	—	2	4	no	—
229	C₂²×C₇₃	—	2	2	no	—
230	C₂²×C₇₃	—	2	2	no	—
231	C₂²×C₇₃	—	4	2	no	—
232	C₂²×C₇₃	—	4	2	no	—
233	C₂²×C₇₃	—	4	4	no	—
234	C₂²×C₇₃	—	4	8	no	—
235	C₂²×C₇₃	#407	1	2	yes	—
236	C₂²×C₇₃	#417	1	2	yes	—
237	C₂²×C₇₃	C₂×#104	1	2	yes	—
238	C₂²×C₇₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
239	C₄×C₇₃	—	2	2	no	—
240	C₄×C₇₃	—	2	4	no	—
241	C₄×C₇₃	—	2	2	no	—
242	C₄×C₇₃	—	2	1	no	—
243	C₄×C₇₃	—	2	1	no	—
244	C₄×C₇₃	—	4	2	no	—
245	C₄×C₇₃	—	4	2	no	—
246	C₄×C₇₃	#407	1	2	yes	—
247	C₄×C₇₃	#417	1	2	yes	—
248	C₄×C₇₃	C₂×#104	1	4	yes	—
249	C₄×C₇₃	C₂²×M₁₆	1	1	yes	characteristic
250	C₄×C₇₃	C₂²×M₁₆	1	1	yes	characteristic
251	C₄×C₇₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
252	C₄×C₇₃	C₂×#137	1	1	yes	characteristic
253	C₂×#1489	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
254	C₂×C₇₃	—	4	2	no	—
255	C₂×C₇₃	—	4	4	no	—
256	C₂×C₇₃	#1489	1	4	yes	direct product factor
257	C₂×C₇₃	C₂×#407	1	1	yes	characteristic
258	C₂×C₇₃	C₂×#417	1	1	yes	characteristic
259	C₂×C₇₃	C₂²×#104	1	1	yes	characteristic
260	C₂×C₄×#41	C₂×C₇₃	1	1	yes	characteristic
261	C₂×#423	C₂×C₇₃	1	1	yes	characteristic, complemented
262	C₂×C₄×M₁₆	C₂×C₇₃	1	1	yes	characteristic, complemented
263	#1489	C₂×C₇₃	1	8	yes	direct product factor
264	C₂×Q₈⋊C₈	C₂×C₇₃	1	2	yes	complemented
265	C₂×D₄⋊C₈	C₂×C₇₃	1	2	yes	complemented
266	C₇₃	C₂×#1489	1	1	yes	characteristic, direct product factor, Sylow
267	C₂²×#41	C₄×C₇₃	1	1	yes	characteristic
268	C₂²×M₁₆	—	2	1	no	—
269	C₂²×M₁₆	—	2	1	no	—
270	C₄×#41	—	2	2	no	—
271	C₄×#41	—	2	2	no	—
272	C₄×#41	C₄×C₇₃	1	4	yes	—
273	C₄×#41	C₂²×C₇₃	1	4	yes	—
274	C₂×C₄×Q₈	C₄×C₇₃	1	1	yes	characteristic
275	C₂×C₄×Q₈	C₂²×C₇₃	1	1	yes	characteristic
276	C₂×C₄×D₄	—	2	1	no	—
277	C₂×C₄×D₄	—	2	1	no	—
278	C₂×C₄×D₄	C₄×C₇₃	1	1	yes	characteristic
279	C₂×C₄×D₄	C₂²×C₇₃	1	1	yes	characteristic
280	C₂×#117	—	2	1	no	—
281	C₂×#117	C₄×C₇₃	1	1	yes	characteristic
282	C₂²×C₄²	—	2	1	no	—
283	C₂²×C₄²	C₂²×C₇₃	1	1	yes	characteristic
284	#423	—	2	2	no	—
285	#423	C₂²×C₇₃	1	4	yes	complemented
286	C₂×C₄⋊C₈	—	2	1	no	—
287	C₂×C₄⋊C₈	C₂²×C₇₃	1	2	yes	—
288	C₄×M₁₆	—	2	2	no	—
289	C₄×M₁₆	C₂²×C₇₃	1	4	yes	complemented
290	C₂×#97	—	2	1	no	—
291	C₂×C₄×C₈	C₂²×C₇₃	1	2	yes	—
292	Q₈⋊C₈	C₂²×C₇₃	1	8	yes	complemented
293	D₄⋊C₈	C₂²×C₇₃	1	8	yes	complemented
294	C₂×#41	—	2	4	no	—
295	C₂×#41	—	2	4	no	—
296	C₂×#41	—	2	2	no	—
297	C₂×#41	C₂×C₄×C₇₃	1	4	yes	—
298	C₂²×Q₈	C₂×C₄×C₇₃	1	1	yes	characteristic
299	C₂²×D₄	—	2	1	no	—
300	C₂²×D₄	C₂×C₄×C₇₃	1	1	yes	characteristic
301	C₂³×C₄	—	2	1	no	—
302	C₂³×C₄	—	2	1	no	—
303	C₂³×C₄	—	2	1	no	—
304	C₂³×C₄	C₂×C₄×C₇₃	1	1	yes	characteristic
305	C₂³×C₄	D₄×C₇₃	1	1	yes	characteristic
306	C₂³×C₄	D₄×C₇₃	1	1	yes	characteristic
307	C₂×M₁₆	—	2	8	no	—
308	C₂×M₁₆	—	2	4	no	—
309	C₂×M₁₆	—	2	4	no	—
310	C₂×M₁₆	—	4	4	no	—
311	C₂²×C₈	—	2	2	no	—
312	C₂²×C₈	—	2	2	no	—
313	C₄×Q₈	—	2	2	no	—
314	C₄×Q₈	—	2	1	no	—
315	C₄×Q₈	—	2	1	no	—
316	C₄×Q₈	C₂×C₄×C₇₃	1	4	yes	—
317	C₄×Q₈	C₂×C₄×C₇₃	1	2	yes	—
318	C₄×Q₈	C₂³×C₇₃	1	2	yes	—
319	C₄×D₄	—	2	4	no	—
320	C₄×D₄	—	2	4	no	—
321	C₄×D₄	—	2	4	no	—
322	C₄×D₄	—	2	4	no	—
323	C₄×D₄	—	2	2	no	—
324	C₄×D₄	—	2	1	no	—
325	C₄×D₄	—	2	1	no	—
326	C₄×D₄	C₂×C₄×C₇₃	1	4	yes	—
327	C₄×D₄	C₂×C₄×C₇₃	1	2	yes	—
328	C₄×D₄	C₂³×C₇₃	1	2	yes	—
329	#117	—	2	2	no	—
330	#117	—	2	4	no	—
331	#117	—	2	4	no	—
332	#117	C₂×C₄×C₇₃	1	4	yes	—
333	C₂×C₄⋊C₄	—	2	1	no	—
334	C₂×C₄⋊C₄	—	2	1	no	—
335	C₂×C₄⋊C₄	C₂×C₄×C₇₃	1	1	yes	characteristic
336	C₂×C₄⋊C₄	C₂×C₄×C₇₃	1	1	yes	characteristic
337	C₂×C₂²⋊C₄	—	2	1	no	—
338	C₂×C₂²⋊C₄	—	2	1	no	—
339	C₂×C₂²⋊C₄	—	2	1	no	—
340	C₂×C₄²	—	2	1	no	—
341	C₂×C₄²	—	2	1	no	—
342	C₂×C₄²	—	2	1	no	—
343	C₂×C₄²	—	2	4	no	—
344	C₂×C₄²	—	2	4	no	—
345	C₂×C₄²	C₂×C₄×C₇₃	1	1	yes	characteristic
346	C₂×C₄²	C₂×C₄×C₇₃	1	2	yes	—
347	C₂×C₄²	D₄×C₇₃	1	1	yes	characteristic
348	C₂×C₄²	D₄×C₇₃	1	2	yes	—
349	C₂×C₄²	D₄×C₇₃	1	2	yes	—
350	C₂×C₄²	D₄×C₇₃	1	1	yes	characteristic
351	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
352	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
353	C₄⋊C₈	—	2	4	no	—
354	C₄⋊C₈	—	2	2	no	—
355	C₄⋊C₈	C₂³×C₇₃	1	4	yes	—
356	#97	—	2	4	no	—
357	C₄×C₈	—	2	2	no	—
358	C₄×C₈	C₂³×C₇₃	1	4	yes	—
359	C₂⁴	—	2	1	no	—
360	C₂⁴	C₂²⋊C₄×C₇₃	1	1	yes	characteristic
361	#41	—	2	16	no	—
362	#41	—	2	8	no	—
363	#41	—	2	8	no	—
364	C₂×Q₈	—	2	1	no	—
365	C₂×Q₈	—	2	2	no	—
366	C₂×Q₈	M₁₆×C₇₃	1	4	yes	complemented
367	C₂×Q₈	C₂²×C₄×C₇₃	1	2	yes	—
368	C₂×D₄	—	2	8	no	—
369	C₂×D₄	—	2	4	no	—
370	C₂×D₄	—	2	1	no	—
371	C₂×D₄	—	2	2	no	—
372	C₂×D₄	M₁₆×C₇₃	1	4	yes	complemented
373	C₂×D₄	C₂²×C₄×C₇₃	1	2	yes	—
374	C₂²×C₄	—	2	8	no	—
375	C₂²×C₄	—	2	1	no	—
376	C₂²×C₄	—	2	4	no	—
377	C₂²×C₄	—	2	4	no	—
378	C₂²×C₄	—	2	2	no	—
379	C₂²×C₄	—	2	2	no	—
380	C₂²×C₄	—	2	2	no	—
381	C₂²×C₄	—	2	2	no	—
382	C₂²×C₄	—	2	1	no	—
383	C₂²×C₄	—	2	1	no	—
384	C₂²×C₄	—	2	2	no	—
385	C₂²×C₄	—	2	4	no	—
386	C₂²×C₄	—	2	2	no	—
387	C₂²×C₄	—	4	4	no	—
388	C₂²×C₄	—	4	2	no	—
389	C₂²×C₄	—	4	2	no	—
390	C₂²×C₄	C₂²⋊C₄×C₇₃	1	1	yes	characteristic
391	C₂²×C₄	C₂²⋊C₄×C₇₃	1	1	yes	characteristic
392	C₂²×C₄	C₂²⋊C₄×C₇₃	1	2	yes	—
393	C₂²×C₄	C₂²⋊C₄×C₇₃	1	2	yes	—
394	C₂²×C₄	C₂²⋊C₄×C₇₃	1	2	yes	—
395	C₂²×C₄	C₂²⋊C₄×C₇₃	1	1	yes	characteristic
396	C₂²×C₄	C₂²×C₄×C₇₃	1	2	yes	—
397	C₂²×C₄	C₂²×C₄×C₇₃	1	1	yes	characteristic
398	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
399	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
400	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
401	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
402	M₁₆	—	2	16	no	—
403	M₁₆	—	4	8	no	—
404	C₂×C₈	—	2	8	no	—
405	C₂×C₈	—	2	4	no	—
406	C₂×C₈	—	2	4	no	—
407	C₂×C₈	—	4	4	no	—
408	C₄⋊C₄	—	2	4	no	—
409	C₄⋊C₄	—	2	2	no	—
410	C₄⋊C₄	—	2	1	no	—
411	C₄⋊C₄	—	2	1	no	—
412	C₄⋊C₄	—	2	2	no	—
413	C₄⋊C₄	C₂²×C₄×C₇₃	1	2	yes	—
414	C₄⋊C₄	C₂²×C₄×C₇₃	1	2	yes	—
415	C₂²⋊C₄	—	2	4	no	—
416	C₂²⋊C₄	—	2	4	no	—
417	C₂²⋊C₄	—	2	2	no	—
418	C₂²⋊C₄	—	2	2	no	—
419	C₄²	—	2	4	no	—
420	C₄²	—	2	2	no	—
421	C₄²	—	2	4	no	—
422	C₄²	—	2	2	no	—
423	C₄²	C₂²⋊C₄×C₇₃	1	2	yes	—
424	C₄²	C₂²⋊C₄×C₇₃	1	2	yes	—
425	C₄²	C₂²⋊C₄×C₇₃	1	2	yes	—
426	C₄²	C₂²×C₄×C₇₃	1	1	yes	characteristic
427	C₄²	C₂²×C₄×C₇₃	1	2	yes	—
428	C₄²	C₂×D₄×C₇₃	1	1	yes	characteristic
429	C₄²	C₂×D₄×C₇₃	1	2	yes	—
430	C₄²	C₂×D₄×C₇₃	1	2	yes	—
431	C₄²	C₂×D₄×C₇₃	1	1	yes	characteristic
432	C₄²	C₂⁴×C₇₃	1	1	yes	characteristic
433	C₂³	—	2	2	no	—
434	C₂³	—	2	4	no	—
435	C₂³	—	2	2	no	—
436	C₂³	—	2	2	no	—
437	C₂³	—	2	2	no	—
438	C₂³	—	4	2	no	—
439	C₂³	—	4	2	no	—
440	C₂³	C₂×C₂²⋊C₄×C₇₃	1	2	yes	—
441	C₂³	C₂×C₂²⋊C₄×C₇₃	1	1	yes	characteristic
442	Q₈	—	2	4	no	—
443	Q₈	—	2	2	no	—
444	Q₈	C₂×M₁₆×C₇₃	1	4	yes	complemented
445	D₄	—	2	16	no	—
446	D₄	—	2	4	no	—
447	D₄	—	2	2	no	—
448	D₄	C₂×M₁₆×C₇₃	1	4	yes	complemented
449	C₂×C₄	—	2	16	no	—
450	C₂×C₄	—	2	2	no	—
451	C₂×C₄	—	2	4	no	—
452	C₂×C₄	—	2	2	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	2	2	no	—
455	C₂×C₄	—	2	4	no	—
456	C₂×C₄	—	2	4	no	—
457	C₂×C₄	—	2	4	no	—
458	C₂×C₄	—	2	4	no	—
459	C₂×C₄	—	2	2	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	2	2	no	—
462	C₂×C₄	—	2	2	no	—
463	C₂×C₄	—	2	2	no	—
464	C₂×C₄	—	2	2	no	—
465	C₂×C₄	—	4	2	no	—
466	C₂×C₄	—	4	2	no	—
467	C₂×C₄	—	4	4	no	—
468	C₂×C₄	—	4	8	no	—
469	C₂×C₄	—	4	2	no	—
470	C₂×C₄	—	4	2	no	—
471	C₂×C₄	#104×C₇₃	1	4	yes	—
472	C₂×C₄	C₂×C₂²⋊C₄×C₇₃	1	2	yes	—
473	C₂×C₄	C₂×C₂²⋊C₄×C₇₃	1	2	yes	—
474	C₂×C₄	C₂×C₂²⋊C₄×C₇₃	1	1	yes	characteristic
475	C₂×C₄	C₂×C₂²⋊C₄×C₇₃	1	1	yes	characteristic
476	C₂×C₄	C₂×C₂²⋊C₄×C₇₃	1	1	yes	characteristic
477	C₂×C₄	C₂×C₂²⋊C₄×C₇₃	1	2	yes	—
478	C₂×C₄	C₂×M₁₆×C₇₃	1	2	yes	—
479	C₂×C₄	C₂×M₁₆×C₇₃	1	2	yes	—
480	C₂×C₄	AGL(1,ℤ/8)×C₇₃	1	2	yes	—
481	C₂×C₄	#137×C₇₃	1	2	yes	—
482	C₂×C₄	C₂³×C₄×C₇₃	1	1	yes	characteristic
483	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
484	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
485	C₈	—	2	8	no	—
486	C₈	—	4	4	no	—
487	C₂²	—	2	2	no	—
488	C₂²	—	2	4	no	—
489	C₂²	—	2	2	no	—
490	C₂²	—	2	2	no	—
491	C₂²	—	4	4	no	—
492	C₂²	—	4	8	no	—
493	C₂²	—	4	2	no	—
494	C₂²	—	4	2	no	—
495	C₂²	#407×C₇₃	1	2	yes	—
496	C₂²	#417×C₇₃	1	2	yes	—
497	C₂²	C₂×#104×C₇₃	1	2	yes	—
498	C₂²	C₂²×C₂²⋊C₄×C₇₃	1	1	yes	characteristic
499	C₄	—	2	2	no	—
500	C₄	—	2	4	no	—
501	C₄	—	2	2	no	—
502	C₄	—	2	1	no	—
503	C₄	—	2	1	no	—
504	C₄	—	4	2	no	—
505	C₄	—	4	2	no	—
506	C₄	#407×C₇₃	1	2	yes	—
507	C₄	#417×C₇₃	1	2	yes	—
508	C₄	C₂×#104×C₇₃	1	4	yes	—
509	C₄	C₂²×M₁₆×C₇₃	1	1	yes	characteristic
510	C₄	C₂²×M₁₆×C₇₃	1	1	yes	characteristic
511	C₄	C₂×AGL(1,ℤ/8)×C₇₃	1	1	yes	characteristic
512	C₄	C₂×#137×C₇₃	1	1	yes	characteristic
513	C₂	—	4	2	no	—
514	C₂	—	4	4	no	—
515	C₂	C₇₃×#1489	1	4	yes	direct product factor
516	C₂	C₂×#407×C₇₃	1	1	yes	characteristic
517	C₂	C₂×#417×C₇₃	1	1	yes	characteristic
518	C₂	C₂²×#104×C₇₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₇₃	C₂×D₄
commutator	C₂×C₄	C₂³×C₄×C₇₃
Frattini, cosocle	C₄²	C₂⁴×C₇₃
socle	C₂³×C₇₃	C₂×C₂²⋊C₄
prime radical	C₂²×#41×C₇₃	C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₇₃ ◁ C₂²×C₄²×C₇₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#423×C₇₃	C₂	semidirect
3. C₂×C₄×M₁₆×C₇₃	C₂	semidirect
4. C₇₃×#1489	C₂	direct (N × H)
5. C₂×Q₈⋊C₈×C₇₃	C₂	semidirect
6. C₂×D₄⋊C₈×C₇₃	C₂	semidirect
25. #423×C₇₃	C₂²	semidirect
29. C₄×M₁₆×C₇₃	C₂²	semidirect
32. Q₈⋊C₈×C₇₃	C₂²	semidirect
33. D₄⋊C₈×C₇₃	C₂²	semidirect
106. C₂×Q₈×C₇₃	M₁₆	semidirect
112. C₂×D₄×C₇₃	M₁₆	semidirect
184. Q₈×C₇₃	C₂×M₁₆	semidirect
188. D₄×C₇₃	C₂×M₁₆	semidirect
253. C₂×#1489	C₇₃	direct (N × H)
256. C₂×C₇₃	#1489	direct (N × H)
261. C₂×#423	C₂×C₇₃	semidirect
262. C₂×C₄×M₁₆	C₂×C₇₃	semidirect
263. #1489	C₂×C₇₃	direct (N × H)
264. C₂×Q₈⋊C₈	C₂×C₇₃	semidirect
265. C₂×D₄⋊C₈	C₂×C₇₃	semidirect
266. C₇₃	C₂×#1489	direct (N × H)
285. #423	C₂²×C₇₃	semidirect
289. C₄×M₁₆	C₂²×C₇₃	semidirect
292. Q₈⋊C₈	C₂²×C₇₃	semidirect
293. D₄⋊C₈	C₂²×C₇₃	semidirect
366. C₂×Q₈	M₁₆×C₇₃	semidirect
372. C₂×D₄	M₁₆×C₇₃	semidirect
444. Q₈	C₂×M₁₆×C₇₃	semidirect
448. D₄	C₂×M₁₆×C₇₃	semidirect
515. C₂	C₇₃×#1489	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄×#41×C₇₃	2
C₂×#423×C₇₃	2
C₂×C₄×M₁₆×C₇₃	2
C₇₃×#1489	2
C₂×Q₈⋊C₈×C₇₃	2
C₂×D₄⋊C₈×C₇₃	2
C₂×#1489	73

Subgroups — C2×C73×#1489 #32926850

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇₃×#1489 #32926850