Subgroups — C₇₃×#24398 #32933802

Order 18688.

1476 conjugacy classes of subgroups.

The subgroup lattice has 730 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×AGL(1,ℤ/8)×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#472×C₇₃	C₂	1	2	yes	maximal, complemented
3	C₇₃×#3006	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#447×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₃×#2880	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇₃×#2051	C₂	1	2	yes	maximal, complemented
7	C₇₃×#2018	C₂	1	2	yes	maximal, complemented
8	C₇₃×#1907	C₂	1	2	yes	maximal, complemented
9	C₇₃×#1900	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇₃×#1855	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₃×#1783	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#41×C₇₃	C₂²	1	1	yes	characteristic
13	C₂³×D₄×C₇₃	C₂²	1	1	yes	characteristic
14	C₂×AGL(1,ℤ/8)×C₇₃	—	2	1	no	—
15	C₂×AGL(1,ℤ/8)×C₇₃	—	2	1	no	—
16	C₂×AGL(1,ℤ/8)×C₇₃	—	2	8	no	—
17	C₂×AGL(1,ℤ/8)×C₇₃	C₂²	1	2	yes	—
18	C₂×AGL(1,ℤ/8)×C₇₃	C₂²	1	2	yes	—
19	C₂×AGL(1,ℤ/8)×C₇₃	C₂²	1	1	yes	characteristic, complemented
20	C₂×AGL(1,ℤ/8)×C₇₃	C₂²	1	1	yes	characteristic, complemented
21	C₂²×SD₁₆×C₇₃	—	2	1	no	—
22	C₂²×D₈×C₇₃	—	2	1	no	—
23	C₂²×D₈×C₇₃	C₂²	1	2	yes	complemented
24	C₂×#131×C₇₃	C₂²	1	2	yes	complemented
25	C₂²×M₁₆×C₇₃	C₂²	1	1	yes	characteristic
26	C₂×#121×C₇₃	C₂²	1	1	yes	characteristic
27	#472×C₇₃	—	2	8	no	—
28	#449×C₇₃	—	2	1	no	—
29	#449×C₇₃	—	2	1	no	—
30	#448×C₇₃	—	2	1	no	—
31	#447×C₇₃	—	2	1	no	—
32	#447×C₇₃	—	2	1	no	—
33	#447×C₇₃	—	2	1	no	—
34	#447×C₇₃	—	2	2	no	—
35	C₂×#108×C₇₃	C₂²	1	2	yes	complemented
36	#417×C₇₃	C₂²	1	1	yes	characteristic, complemented
37	#417×C₇₃	C₂²	1	1	yes	characteristic, complemented
38	C₂×#102×C₇₃	C₂²	1	2	yes	complemented
39	C₂×#100×C₇₃	C₂²	1	2	yes	complemented
40	C₂×#100×C₇₃	C₂²	1	2	yes	complemented
41	C₂×#100×C₇₃	C₂²	1	2	yes	complemented
42	#408×C₇₃	—	2	2	no	—
43	#408×C₇₃	C₂²	1	2	yes	complemented
44	#407×C₇₃	—	2	1	no	—
45	#407×C₇₃	C₂²	1	1	yes	characteristic
46	#407×C₇₃	C₂²	1	1	yes	characteristic
47	C₂×C₂²⋊C₈×C₇₃	—	2	1	no	—
48	C₂×C₂²⋊C₈×C₇₃	C₂²	1	1	yes	characteristic
49	#343×C₇₃	C₂²	1	2	yes	complemented
50	#341×C₇₃	C₂²	1	2	yes	complemented
51	C₂⁵×C₇₃	—	2	1	no	—
52	C₂×#41×C₇₃	—	2	1	no	—
53	C₂×#41×C₇₃	—	2	1	no	—
54	C₂×#41×C₇₃	—	2	4	no	—
55	C₂×#41×C₇₃	—	4	2	no	—
56	C₂×#41×C₇₃	D₄	1	1	yes	characteristic
57	C₂×#41×C₇₃	D₄	1	1	yes	characteristic
58	C₂×#41×C₇₃	C₂³	1	1	yes	characteristic
59	C₂×#41×C₇₃	C₂³	1	1	yes	characteristic
60	C₂²×Q₈×C₇₃	D₄	1	1	yes	characteristic
61	C₂²×D₄×C₇₃	—	2	4	no	—
62	C₂²×D₄×C₇₃	—	2	1	no	—
63	C₂²×D₄×C₇₃	—	2	1	no	—
64	C₂²×D₄×C₇₃	—	2	1	no	—
65	C₂²×D₄×C₇₃	—	2	1	no	—
66	C₂²×D₄×C₇₃	—	2	1	no	—
67	C₂²×D₄×C₇₃	—	2	1	no	—
68	C₂²×D₄×C₇₃	—	2	1	no	—
69	C₂²×D₄×C₇₃	—	4	2	no	—
70	C₂²×D₄×C₇₃	D₄	1	1	yes	characteristic
71	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
72	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
73	C₂³×C₄×C₇₃	—	2	1	no	—
74	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
75	AGL(1,ℤ/8)×C₇₃	—	2	8	no	—
76	AGL(1,ℤ/8)×C₇₃	—	2	8	no	—
77	AGL(1,ℤ/8)×C₇₃	—	2	4	no	—
78	AGL(1,ℤ/8)×C₇₃	—	2	4	no	—
79	AGL(1,ℤ/8)×C₇₃	—	2	4	no	—
80	AGL(1,ℤ/8)×C₇₃	—	2	4	no	—
81	AGL(1,ℤ/8)×C₇₃	—	4	2	no	—
82	AGL(1,ℤ/8)×C₇₃	D₄	1	8	yes	complemented
83	C₂×SD₁₆×C₇₃	—	2	8	no	—
84	C₂×SD₁₆×C₇₃	—	2	2	no	—
85	C₂×SD₁₆×C₇₃	—	2	2	no	—
86	C₂×SD₁₆×C₇₃	—	2	1	no	—
87	C₂×SD₁₆×C₇₃	—	2	1	no	—
88	C₂×D₈×C₇₃	—	2	8	no	—
89	C₂×D₈×C₇₃	—	2	2	no	—
90	C₂×D₈×C₇₃	—	2	2	no	—
91	C₂×D₈×C₇₃	—	2	1	no	—
92	C₂×D₈×C₇₃	—	2	1	no	—
93	C₂×D₈×C₇₃	—	2	4	no	—
94	C₂×D₈×C₇₃	—	2	2	no	—
95	C₂×D₈×C₇₃	—	2	2	no	—
96	C₂×D₈×C₇₃	—	4	2	no	—
97	#131×C₇₃	—	2	4	no	—
98	#131×C₇₃	—	4	2	no	—
99	C₂×M₁₆×C₇₃	—	2	1	no	—
100	C₂×M₁₆×C₇₃	—	2	4	no	—
101	C₂×M₁₆×C₇₃	—	2	2	no	—
102	C₂×M₁₆×C₇₃	C₂³	1	2	yes	—
103	C₂×M₁₆×C₇₃	C₂³	1	1	yes	characteristic
104	C₂×M₁₆×C₇₃	C₂³	1	1	yes	characteristic
105	C₂×M₁₆×C₇₃	C₂³	1	2	yes	—
106	C₂²×C₈×C₇₃	—	2	1	no	—
107	C₂²×C₈×C₇₃	—	2	2	no	—
108	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
109	#121×C₇₃	—	2	1	no	—
110	#121×C₇₃	—	2	1	no	—
111	#121×C₇₃	—	2	1	no	—
112	#121×C₇₃	—	2	1	no	—
113	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
114	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
115	#108×C₇₃	—	2	4	no	—
116	#103×C₇₃	—	2	1	no	—
117	#103×C₇₃	—	2	1	no	—
118	#102×C₇₃	—	2	1	no	—
119	#102×C₇₃	—	2	1	no	—
120	#102×C₇₃	—	2	2	no	—
121	#102×C₇₃	—	2	2	no	—
122	#100×C₇₃	—	2	4	no	—
123	#100×C₇₃	—	2	4	no	—
124	#100×C₇₃	—	4	2	no	—
125	C₂²⋊C₈×C₇₃	—	2	1	no	—
126	C₂²⋊C₈×C₇₃	—	2	1	no	—
127	C₂²⋊C₈×C₇₃	—	2	1	no	—
128	C₂²⋊C₈×C₇₃	—	2	1	no	—
129	C₂²⋊C₈×C₇₃	—	2	2	no	—
130	C₂²⋊C₈×C₇₃	—	2	2	no	—
131	C₂²⋊C₈×C₇₃	D₄	1	1	yes	characteristic
132	C₂²⋊C₈×C₇₃	D₄	1	1	yes	characteristic
133	C₂²⋊C₈×C₇₃	D₄	1	2	yes	—
134	C₂⁴×C₇₃	—	2	1	no	—
135	C₂⁴×C₇₃	—	2	2	no	—
136	C₂⁴×C₇₃	—	2	1	no	—
137	C₂⁴×C₇₃	—	4	4	no	—
138	C₂⁴×C₇₃	—	4	1	no	—
139	C₂⁴×C₇₃	—	4	1	no	—
140	C₂⁴×C₇₃	—	8	2	no	—
141	C₂⁴×C₇₃	—	8	2	no	—
142	C₂⁴×C₇₃	#41	1	1	yes	characteristic
143	#41×C₇₃	—	2	2	no	—
144	#41×C₇₃	—	2	2	no	—
145	#41×C₇₃	—	2	2	no	—
146	#41×C₇₃	—	2	2	no	—
147	#41×C₇₃	—	2	2	no	—
148	#41×C₇₃	—	4	4	no	—
149	#41×C₇₃	—	4	1	no	—
150	#41×C₇₃	—	4	1	no	—
151	#41×C₇₃	—	4	4	no	—
152	#41×C₇₃	C₂×D₄	1	4	yes	—
153	C₂×Q₈×C₇₃	—	2	1	no	—
154	C₂×Q₈×C₇₃	—	2	2	no	—
155	C₂×Q₈×C₇₃	—	4	1	no	—
156	C₂×Q₈×C₇₃	C₂×D₄	1	1	yes	characteristic
157	C₂×Q₈×C₇₃	C₂×D₄	1	1	yes	characteristic
158	C₂×D₄×C₇₃	—	2	1	no	—
159	C₂×D₄×C₇₃	—	2	4	no	—
160	C₂×D₄×C₇₃	—	2	4	no	—
161	C₂×D₄×C₇₃	—	2	2	no	—
162	C₂×D₄×C₇₃	—	2	1	no	—
163	C₂×D₄×C₇₃	—	2	1	no	—
164	C₂×D₄×C₇₃	—	2	1	no	—
165	C₂×D₄×C₇₃	—	2	1	no	—
166	C₂×D₄×C₇₃	—	2	2	no	—
167	C₂×D₄×C₇₃	—	2	2	no	—
168	C₂×D₄×C₇₃	—	2	2	no	—
169	C₂×D₄×C₇₃	—	2	2	no	—
170	C₂×D₄×C₇₃	—	2	1	no	—
171	C₂×D₄×C₇₃	—	2	1	no	—
172	C₂×D₄×C₇₃	—	2	2	no	—
173	C₂×D₄×C₇₃	—	2	2	no	—
174	C₂×D₄×C₇₃	—	2	2	no	—
175	C₂×D₄×C₇₃	—	4	1	no	—
176	C₂×D₄×C₇₃	—	4	4	no	—
177	C₂×D₄×C₇₃	—	4	4	no	—
178	C₂×D₄×C₇₃	—	4	4	no	—
179	C₂×D₄×C₇₃	—	4	2	no	—
180	C₂×D₄×C₇₃	—	4	2	no	—
181	C₂×D₄×C₇₃	—	4	4	no	—
182	C₂×D₄×C₇₃	—	4	1	no	—
183	C₂×D₄×C₇₃	—	4	1	no	—
184	C₂×D₄×C₇₃	—	4	1	no	—
185	C₂×D₄×C₇₃	—	4	1	no	—
186	C₂×D₄×C₇₃	—	8	2	no	—
187	C₂×D₄×C₇₃	C₂×D₄	1	4	yes	—
188	C₂×D₄×C₇₃	C₂×D₄	1	1	yes	characteristic
189	C₂×D₄×C₇₃	C₂×D₄	1	1	yes	characteristic
190	C₂²×C₄×C₇₃	—	2	1	no	—
191	C₂²×C₄×C₇₃	—	2	2	no	—
192	C₂²×C₄×C₇₃	—	2	2	no	—
193	C₂²×C₄×C₇₃	—	2	1	no	—
194	C₂²×C₄×C₇₃	—	2	1	no	—
195	C₂²×C₄×C₇₃	—	2	1	no	—
196	C₂²×C₄×C₇₃	—	2	1	no	—
197	C₂²×C₄×C₇₃	—	2	1	no	—
198	C₂²×C₄×C₇₃	—	4	4	no	—
199	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
200	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
201	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
202	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
203	C₂²×C₄×C₇₃	#41	1	1	yes	characteristic
204	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
205	SD₁₆×C₇₃	—	2	8	no	—
206	SD₁₆×C₇₃	—	2	8	no	—
207	SD₁₆×C₇₃	—	4	2	no	—
208	SD₁₆×C₇₃	—	4	2	no	—
209	D₈×C₇₃	—	2	8	no	—
210	D₈×C₇₃	—	2	8	no	—
211	D₈×C₇₃	—	4	4	no	—
212	D₈×C₇₃	—	4	4	no	—
213	D₈×C₇₃	—	4	2	no	—
214	D₈×C₇₃	—	4	2	no	—
215	M₁₆×C₇₃	—	2	4	no	—
216	M₁₆×C₇₃	—	2	2	no	—
217	M₁₆×C₇₃	—	2	2	no	—
218	M₁₆×C₇₃	—	2	2	no	—
219	M₁₆×C₇₃	—	2	2	no	—
220	M₁₆×C₇₃	—	2	2	no	—
221	M₁₆×C₇₃	—	4	4	no	—
222	M₁₆×C₇₃	C₂×D₄	1	4	yes	—
223	C₂×C₈×C₇₃	—	2	4	no	—
224	C₂×C₈×C₇₃	—	2	2	no	—
225	C₂×C₈×C₇₃	—	2	2	no	—
226	C₂×C₈×C₇₃	—	2	2	no	—
227	C₂×C₈×C₇₃	—	2	2	no	—
228	C₂×C₈×C₇₃	—	2	1	no	—
229	C₂×C₈×C₇₃	—	2	1	no	—
230	C₂×C₈×C₇₃	—	4	4	no	—
231	C₂×C₈×C₇₃	C₂×D₄	1	2	yes	—
232	C₂×C₈×C₇₃	C₂×D₄	1	2	yes	—
233	C₄⋊C₄×C₇₃	—	2	1	no	—
234	C₄⋊C₄×C₇₃	—	2	1	no	—
235	C₂²⋊C₄×C₇₃	—	4	1	no	—
236	C₂²⋊C₄×C₇₃	—	4	1	no	—
237	C₂³×C₇₃	—	2	1	no	—
238	C₂³×C₇₃	—	2	2	no	—
239	C₂³×C₇₃	—	2	2	no	—
240	C₂³×C₇₃	—	2	1	no	—
241	C₂³×C₇₃	—	2	4	no	—
242	C₂³×C₇₃	—	4	1	no	—
243	C₂³×C₇₃	—	4	2	no	—
244	C₂³×C₇₃	—	4	4	no	—
245	C₂³×C₇₃	—	4	4	no	—
246	C₂³×C₇₃	—	4	2	no	—
247	C₂³×C₇₃	—	4	2	no	—
248	C₂³×C₇₃	—	4	2	no	—
249	C₂³×C₇₃	—	4	1	no	—
250	C₂³×C₇₃	—	4	2	no	—
251	C₂³×C₇₃	—	8	1	no	—
252	C₂³×C₇₃	—	8	2	no	—
253	C₂³×C₇₃	—	8	2	no	—
254	C₂³×C₇₃	—	8	2	no	—
255	C₂³×C₇₃	—	8	2	no	—
256	C₂³×C₇₃	—	8	2	no	—
257	C₂³×C₇₃	—	8	1	no	—
258	C₂³×C₇₃	—	8	1	no	—
259	C₂³×C₇₃	—	8	16	no	—
260	C₂³×C₇₃	—	8	2	no	—
261	C₂³×C₇₃	#121	1	1	yes	characteristic
262	C₂³×C₇₃	#121	1	1	yes	characteristic
263	C₂³×C₇₃	C₂×#41	1	1	yes	characteristic
264	Q₈×C₇₃	—	2	1	no	—
265	Q₈×C₇₃	—	2	1	no	—
266	Q₈×C₇₃	—	2	1	no	—
267	Q₈×C₇₃	—	4	2	no	—
268	Q₈×C₇₃	#120	1	2	yes	—
269	D₄×C₇₃	—	2	4	no	—
270	D₄×C₇₃	—	2	1	no	—
271	D₄×C₇₃	—	2	4	no	—
272	D₄×C₇₃	—	2	1	no	—
273	D₄×C₇₃	—	2	1	no	—
274	D₄×C₇₃	—	2	4	no	—
275	D₄×C₇₃	—	4	2	no	—
276	D₄×C₇₃	—	4	2	no	—
277	D₄×C₇₃	—	4	4	no	—
278	D₄×C₇₃	—	4	4	no	—
279	D₄×C₇₃	—	4	2	no	—
280	D₄×C₇₃	—	4	2	no	—
281	D₄×C₇₃	—	4	1	no	—
282	D₄×C₇₃	—	4	2	no	—
283	D₄×C₇₃	—	4	1	no	—
284	D₄×C₇₃	—	4	2	no	—
285	D₄×C₇₃	—	4	2	no	—
286	D₄×C₇₃	—	8	2	no	—
287	D₄×C₇₃	—	8	2	no	—
288	D₄×C₇₃	#120	1	2	yes	—
289	C₂×C₄×C₇₃	—	2	1	no	—
290	C₂×C₄×C₇₃	—	2	2	no	—
291	C₂×C₄×C₇₃	—	2	1	no	—
292	C₂×C₄×C₇₃	—	2	1	no	—
293	C₂×C₄×C₇₃	—	2	1	no	—
294	C₂×C₄×C₇₃	—	2	1	no	—
295	C₂×C₄×C₇₃	—	2	4	no	—
296	C₂×C₄×C₇₃	—	2	2	no	—
297	C₂×C₄×C₇₃	—	2	2	no	—
298	C₂×C₄×C₇₃	—	2	1	no	—
299	C₂×C₄×C₇₃	—	4	2	no	—
300	C₂×C₄×C₇₃	—	4	2	no	—
301	C₂×C₄×C₇₃	—	4	2	no	—
302	C₂×C₄×C₇₃	—	4	2	no	—
303	C₂×C₄×C₇₃	—	4	1	no	—
304	C₂×C₄×C₇₃	—	8	1	no	—
305	C₂×C₄×C₇₃	#121	1	1	yes	characteristic
306	C₂×C₄×C₇₃	#121	1	1	yes	characteristic
307	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
308	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
309	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
310	C₂×C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
311	C₈×C₇₃	—	2	4	no	—
312	C₈×C₇₃	—	2	2	no	—
313	C₈×C₇₃	—	2	2	no	—
314	C₈×C₇₃	—	4	1	no	—
315	C₈×C₇₃	—	4	1	no	—
316	C₈×C₇₃	—	4	2	no	—
317	C₂²×C₇₃	—	2	1	no	—
318	C₂²×C₇₃	—	2	1	no	—
319	C₂²×C₇₃	—	2	1	no	—
320	C₂²×C₇₃	—	2	1	no	—
321	C₂²×C₇₃	—	2	1	no	—
322	C₂²×C₇₃	—	2	2	no	—
323	C₂²×C₇₃	—	2	1	no	—
324	C₂²×C₇₃	—	2	1	no	—
325	C₂²×C₇₃	—	4	4	no	—
326	C₂²×C₇₃	—	4	1	no	—
327	C₂²×C₇₃	—	4	1	no	—
328	C₂²×C₇₃	—	4	1	no	—
329	C₂²×C₇₃	—	4	4	no	—
330	C₂²×C₇₃	—	4	1	no	—
331	C₂²×C₇₃	—	4	1	no	—
332	C₂²×C₇₃	—	8	4	no	—
333	C₂²×C₇₃	—	8	4	no	—
334	C₂²×C₇₃	—	8	8	no	—
335	C₂²×C₇₃	—	8	4	no	—
336	C₂²×C₇₃	—	8	8	no	—
337	C₂²×C₇₃	—	8	2	no	—
338	C₂²×C₇₃	—	8	2	no	—
339	C₂²×C₇₃	—	8	1	no	—
340	C₂²×C₇₃	—	8	1	no	—
341	C₂²×C₇₃	—	8	1	no	—
342	C₂²×C₇₃	—	16	2	no	—
343	C₂²×C₇₃	#472	1	2	yes	complemented
344	C₂²×C₇₃	C₂×#121	1	1	yes	characteristic
345	C₂²×C₇₃	#546	1	2	yes	—
346	C₄×C₇₃	—	2	1	no	—
347	C₄×C₇₃	—	2	1	no	—
348	C₄×C₇₃	—	2	2	no	—
349	C₄×C₇₃	—	4	1	no	—
350	C₄×C₇₃	—	8	1	no	—
351	C₄×C₇₃	C₂×#120	1	1	yes	characteristic
352	C₄×C₇₃	#534	1	1	yes	characteristic
353	C₄×C₇₃	D₄²	1	2	yes	—
354	#24398	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
355	C₂×C₇₃	—	2	2	no	—
356	C₂×C₇₃	—	2	2	no	—
357	C₂×C₇₃	—	4	1	no	—
358	C₂×C₇₃	—	4	2	no	—
359	C₂×C₇₃	—	8	1	no	—
360	C₂×C₇₃	—	8	4	no	—
361	C₂×C₇₃	—	16	1	no	—
362	C₂×C₇₃	#2410	1	1	yes	characteristic
363	C₂×C₇₃	C₂×#472	1	1	yes	characteristic
364	C₂×C₇₃	#3068	1	1	yes	characteristic
365	C₂²×AGL(1,ℤ/8)	C₂×C₇₃	1	1	yes	characteristic, complemented
366	C₂×#472	C₂×C₇₃	1	2	yes	complemented
367	#3006	C₂×C₇₃	1	1	yes	characteristic, complemented
368	C₂×#447	C₂×C₇₃	1	1	yes	characteristic, complemented
369	#2880	C₂×C₇₃	1	1	yes	characteristic, complemented
370	#2051	C₂×C₇₃	1	2	yes	complemented
371	#2018	C₂×C₇₃	1	2	yes	complemented
372	#1907	C₂×C₇₃	1	2	yes	complemented
373	#1900	C₂×C₇₃	1	1	yes	characteristic, complemented
374	#1855	C₂×C₇₃	1	1	yes	characteristic, complemented
375	#1783	C₂×C₇₃	1	1	yes	characteristic, complemented
376	C₇₃	#24398	1	1	yes	characteristic, direct product factor, Sylow
377	C₂²×#41	C₂²×C₇₃	1	1	yes	characteristic
378	C₂³×D₄	C₂²×C₇₃	1	1	yes	characteristic
379	C₂×AGL(1,ℤ/8)	—	2	1	no	—
380	C₂×AGL(1,ℤ/8)	—	2	1	no	—
381	C₂×AGL(1,ℤ/8)	—	2	8	no	—
382	C₂×AGL(1,ℤ/8)	C₂²×C₇₃	1	2	yes	—
383	C₂×AGL(1,ℤ/8)	C₂²×C₇₃	1	2	yes	—
384	C₂×AGL(1,ℤ/8)	C₂²×C₇₃	1	1	yes	characteristic, complemented
385	C₂×AGL(1,ℤ/8)	C₂²×C₇₃	1	1	yes	characteristic, complemented
386	C₂²×SD₁₆	—	2	1	no	—
387	C₂²×D₈	—	2	1	no	—
388	C₂²×D₈	C₂²×C₇₃	1	2	yes	complemented
389	C₂×#131	C₂²×C₇₃	1	2	yes	complemented
390	C₂²×M₁₆	C₂²×C₇₃	1	1	yes	characteristic
391	C₂×#121	C₂²×C₇₃	1	1	yes	characteristic
392	#472	—	2	8	no	—
393	#449	—	2	1	no	—
394	#449	—	2	1	no	—
395	#448	—	2	1	no	—
396	#447	—	2	1	no	—
397	#447	—	2	1	no	—
398	#447	—	2	1	no	—
399	#447	—	2	2	no	—
400	C₂×#108	C₂²×C₇₃	1	2	yes	complemented
401	#417	C₂²×C₇₃	1	1	yes	characteristic, complemented
402	#417	C₂²×C₇₃	1	1	yes	characteristic, complemented
403	C₂×#102	C₂²×C₇₃	1	2	yes	complemented
404	C₂×#100	C₂²×C₇₃	1	2	yes	complemented
405	C₂×#100	C₂²×C₇₃	1	2	yes	complemented
406	C₂×#100	C₂²×C₇₃	1	2	yes	complemented
407	#408	—	2	2	no	—
408	#408	C₂²×C₇₃	1	2	yes	complemented
409	#407	—	2	1	no	—
410	#407	C₂²×C₇₃	1	1	yes	characteristic
411	#407	C₂²×C₇₃	1	1	yes	characteristic
412	C₂×C₂²⋊C₈	—	2	1	no	—
413	C₂×C₂²⋊C₈	C₂²×C₇₃	1	1	yes	characteristic
414	#343	C₂²×C₇₃	1	2	yes	complemented
415	#341	C₂²×C₇₃	1	2	yes	complemented
416	C₂⁵	—	2	1	no	—
417	C₂×#41	—	2	1	no	—
418	C₂×#41	—	2	1	no	—
419	C₂×#41	—	2	4	no	—
420	C₂×#41	—	4	2	no	—
421	C₂×#41	D₄×C₇₃	1	1	yes	characteristic
422	C₂×#41	D₄×C₇₃	1	1	yes	characteristic
423	C₂×#41	C₂³×C₇₃	1	1	yes	characteristic
424	C₂×#41	C₂³×C₇₃	1	1	yes	characteristic
425	C₂²×Q₈	D₄×C₇₃	1	1	yes	characteristic
426	C₂²×D₄	—	2	4	no	—
427	C₂²×D₄	—	2	1	no	—
428	C₂²×D₄	—	2	1	no	—
429	C₂²×D₄	—	2	1	no	—
430	C₂²×D₄	—	2	1	no	—
431	C₂²×D₄	—	2	1	no	—
432	C₂²×D₄	—	2	1	no	—
433	C₂²×D₄	—	2	1	no	—
434	C₂²×D₄	—	4	2	no	—
435	C₂²×D₄	D₄×C₇₃	1	1	yes	characteristic
436	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
437	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
438	C₂³×C₄	—	2	1	no	—
439	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
440	AGL(1,ℤ/8)	—	2	8	no	—
441	AGL(1,ℤ/8)	—	2	8	no	—
442	AGL(1,ℤ/8)	—	2	4	no	—
443	AGL(1,ℤ/8)	—	2	4	no	—
444	AGL(1,ℤ/8)	—	2	4	no	—
445	AGL(1,ℤ/8)	—	2	4	no	—
446	AGL(1,ℤ/8)	—	4	2	no	—
447	AGL(1,ℤ/8)	D₄×C₇₃	1	8	yes	complemented
448	C₂×SD₁₆	—	2	8	no	—
449	C₂×SD₁₆	—	2	2	no	—
450	C₂×SD₁₆	—	2	2	no	—
451	C₂×SD₁₆	—	2	1	no	—
452	C₂×SD₁₆	—	2	1	no	—
453	C₂×D₈	—	2	8	no	—
454	C₂×D₈	—	2	2	no	—
455	C₂×D₈	—	2	2	no	—
456	C₂×D₈	—	2	4	no	—
457	C₂×D₈	—	2	1	no	—
458	C₂×D₈	—	2	1	no	—
459	C₂×D₈	—	2	2	no	—
460	C₂×D₈	—	2	2	no	—
461	C₂×D₈	—	4	2	no	—
462	#131	—	2	4	no	—
463	#131	—	4	2	no	—
464	C₂×M₁₆	—	2	1	no	—
465	C₂×M₁₆	—	2	4	no	—
466	C₂×M₁₆	—	2	2	no	—
467	C₂×M₁₆	C₂³×C₇₃	1	2	yes	—
468	C₂×M₁₆	C₂³×C₇₃	1	1	yes	characteristic
469	C₂×M₁₆	C₂³×C₇₃	1	1	yes	characteristic
470	C₂×M₁₆	C₂³×C₇₃	1	2	yes	—
471	C₂²×C₈	—	2	1	no	—
472	C₂²×C₈	—	2	2	no	—
473	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
474	#121	—	2	1	no	—
475	#121	—	2	1	no	—
476	#121	—	2	1	no	—
477	#121	—	2	1	no	—
478	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
479	C₂×C₂²⋊C₄	—	2	1	no	—
480	#108	—	2	4	no	—
481	#103	—	2	1	no	—
482	#103	—	2	1	no	—
483	#102	—	2	1	no	—
484	#102	—	2	1	no	—
485	#102	—	2	2	no	—
486	#102	—	2	2	no	—
487	#100	—	2	4	no	—
488	#100	—	2	4	no	—
489	#100	—	4	2	no	—
490	C₂²⋊C₈	—	2	1	no	—
491	C₂²⋊C₈	—	2	1	no	—
492	C₂²⋊C₈	—	2	1	no	—
493	C₂²⋊C₈	—	2	1	no	—
494	C₂²⋊C₈	—	2	2	no	—
495	C₂²⋊C₈	—	2	2	no	—
496	C₂²⋊C₈	D₄×C₇₃	1	1	yes	characteristic
497	C₂²⋊C₈	D₄×C₇₃	1	1	yes	characteristic
498	C₂²⋊C₈	D₄×C₇₃	1	2	yes	—
499	C₂⁴	—	2	1	no	—
500	C₂⁴	—	2	2	no	—
501	C₂⁴	—	2	1	no	—
502	C₂⁴	—	4	4	no	—
503	C₂⁴	—	4	1	no	—
504	C₂⁴	—	4	1	no	—
505	C₂⁴	—	8	2	no	—
506	C₂⁴	—	8	2	no	—
507	C₂⁴	#41×C₇₃	1	1	yes	characteristic
508	#41	—	2	2	no	—
509	#41	—	2	2	no	—
510	#41	—	2	2	no	—
511	#41	—	2	2	no	—
512	#41	—	2	2	no	—
513	#41	—	4	4	no	—
514	#41	—	4	1	no	—
515	#41	—	4	1	no	—
516	#41	—	4	4	no	—
517	#41	C₂×D₄×C₇₃	1	4	yes	—
518	C₂×Q₈	—	2	1	no	—
519	C₂×Q₈	—	2	2	no	—
520	C₂×Q₈	—	4	1	no	—
521	C₂×Q₈	C₂×D₄×C₇₃	1	1	yes	characteristic
522	C₂×Q₈	C₂×D₄×C₇₃	1	1	yes	characteristic
523	C₂×D₄	—	2	1	no	—
524	C₂×D₄	—	2	4	no	—
525	C₂×D₄	—	2	4	no	—
526	C₂×D₄	—	2	2	no	—
527	C₂×D₄	—	2	1	no	—
528	C₂×D₄	—	2	1	no	—
529	C₂×D₄	—	2	1	no	—
530	C₂×D₄	—	2	1	no	—
531	C₂×D₄	—	2	2	no	—
532	C₂×D₄	—	2	2	no	—
533	C₂×D₄	—	2	2	no	—
534	C₂×D₄	—	2	2	no	—
535	C₂×D₄	—	2	1	no	—
536	C₂×D₄	—	2	1	no	—
537	C₂×D₄	—	2	2	no	—
538	C₂×D₄	—	2	2	no	—
539	C₂×D₄	—	2	2	no	—
540	C₂×D₄	—	4	1	no	—
541	C₂×D₄	—	4	4	no	—
542	C₂×D₄	—	4	4	no	—
543	C₂×D₄	—	4	4	no	—
544	C₂×D₄	—	4	2	no	—
545	C₂×D₄	—	4	2	no	—
546	C₂×D₄	—	4	4	no	—
547	C₂×D₄	—	4	1	no	—
548	C₂×D₄	—	4	1	no	—
549	C₂×D₄	—	4	1	no	—
550	C₂×D₄	—	4	1	no	—
551	C₂×D₄	—	8	2	no	—
552	C₂×D₄	C₂×D₄×C₇₃	1	4	yes	—
553	C₂×D₄	C₂×D₄×C₇₃	1	1	yes	characteristic
554	C₂×D₄	C₂×D₄×C₇₃	1	1	yes	characteristic
555	C₂²×C₄	—	2	1	no	—
556	C₂²×C₄	—	2	2	no	—
557	C₂²×C₄	—	2	2	no	—
558	C₂²×C₄	—	2	1	no	—
559	C₂²×C₄	—	2	1	no	—
560	C₂²×C₄	—	2	1	no	—
561	C₂²×C₄	—	2	1	no	—
562	C₂²×C₄	—	2	1	no	—
563	C₂²×C₄	—	4	4	no	—
564	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
565	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
566	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
567	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
568	C₂²×C₄	#41×C₇₃	1	1	yes	characteristic
569	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
570	SD₁₆	—	2	8	no	—
571	SD₁₆	—	2	8	no	—
572	SD₁₆	—	4	2	no	—
573	SD₁₆	—	4	2	no	—
574	D₈	—	2	8	no	—
575	D₈	—	2	8	no	—
576	D₈	—	4	4	no	—
577	D₈	—	4	4	no	—
578	D₈	—	4	2	no	—
579	D₈	—	4	2	no	—
580	M₁₆	—	2	4	no	—
581	M₁₆	—	2	2	no	—
582	M₁₆	—	2	2	no	—
583	M₁₆	—	2	2	no	—
584	M₁₆	—	2	2	no	—
585	M₁₆	—	2	2	no	—
586	M₁₆	—	4	4	no	—
587	M₁₆	C₂×D₄×C₇₃	1	4	yes	—
588	C₂×C₈	—	2	4	no	—
589	C₂×C₈	—	2	2	no	—
590	C₂×C₈	—	2	2	no	—
591	C₂×C₈	—	2	2	no	—
592	C₂×C₈	—	2	2	no	—
593	C₂×C₈	—	2	1	no	—
594	C₂×C₈	—	2	1	no	—
595	C₂×C₈	—	4	4	no	—
596	C₂×C₈	C₂×D₄×C₇₃	1	2	yes	—
597	C₂×C₈	C₂×D₄×C₇₃	1	2	yes	—
598	C₄⋊C₄	—	2	1	no	—
599	C₄⋊C₄	—	2	1	no	—
600	C₂²⋊C₄	—	4	1	no	—
601	C₂²⋊C₄	—	4	1	no	—
602	C₂³	—	2	2	no	—
603	C₂³	—	2	1	no	—
604	C₂³	—	2	2	no	—
605	C₂³	—	2	1	no	—
606	C₂³	—	2	4	no	—
607	C₂³	—	4	1	no	—
608	C₂³	—	4	2	no	—
609	C₂³	—	4	4	no	—
610	C₂³	—	4	4	no	—
611	C₂³	—	4	2	no	—
612	C₂³	—	4	2	no	—
613	C₂³	—	4	2	no	—
614	C₂³	—	4	1	no	—
615	C₂³	—	4	2	no	—
616	C₂³	—	8	1	no	—
617	C₂³	—	8	2	no	—
618	C₂³	—	8	2	no	—
619	C₂³	—	8	2	no	—
620	C₂³	—	8	2	no	—
621	C₂³	—	8	2	no	—
622	C₂³	—	8	1	no	—
623	C₂³	—	8	1	no	—
624	C₂³	—	8	16	no	—
625	C₂³	—	8	2	no	—
626	C₂³	#121×C₇₃	1	1	yes	characteristic
627	C₂³	#121×C₇₃	1	1	yes	characteristic
628	C₂³	C₂×#41×C₇₃	1	1	yes	characteristic
629	Q₈	—	2	1	no	—
630	Q₈	—	2	1	no	—
631	Q₈	—	2	1	no	—
632	Q₈	—	4	2	no	—
633	Q₈	#120×C₇₃	1	2	yes	—
634	D₄	—	2	4	no	—
635	D₄	—	2	1	no	—
636	D₄	—	2	4	no	—
637	D₄	—	2	1	no	—
638	D₄	—	2	1	no	—
639	D₄	—	2	4	no	—
640	D₄	—	4	2	no	—
641	D₄	—	4	2	no	—
642	D₄	—	4	4	no	—
643	D₄	—	4	4	no	—
644	D₄	—	4	2	no	—
645	D₄	—	4	2	no	—
646	D₄	—	4	1	no	—
647	D₄	—	4	2	no	—
648	D₄	—	4	1	no	—
649	D₄	—	4	2	no	—
650	D₄	—	4	2	no	—
651	D₄	—	8	2	no	—
652	D₄	—	8	2	no	—
653	D₄	#120×C₇₃	1	2	yes	—
654	C₂×C₄	—	2	1	no	—
655	C₂×C₄	—	2	2	no	—
656	C₂×C₄	—	2	1	no	—
657	C₂×C₄	—	2	1	no	—
658	C₂×C₄	—	2	1	no	—
659	C₂×C₄	—	2	1	no	—
660	C₂×C₄	—	2	4	no	—
661	C₂×C₄	—	2	2	no	—
662	C₂×C₄	—	2	2	no	—
663	C₂×C₄	—	2	1	no	—
664	C₂×C₄	—	4	2	no	—
665	C₂×C₄	—	4	2	no	—
666	C₂×C₄	—	4	2	no	—
667	C₂×C₄	—	4	2	no	—
668	C₂×C₄	—	4	1	no	—
669	C₂×C₄	—	8	1	no	—
670	C₂×C₄	#121×C₇₃	1	1	yes	characteristic
671	C₂×C₄	#121×C₇₃	1	1	yes	characteristic
672	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
673	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
674	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
675	C₂×C₄	H(5,𝔽₂)×C₇₃	1	2	yes	—
676	C₈	—	2	4	no	—
677	C₈	—	2	2	no	—
678	C₈	—	2	2	no	—
679	C₈	—	4	1	no	—
680	C₈	—	4	1	no	—
681	C₈	—	4	2	no	—
682	C₂²	—	2	1	no	—
683	C₂²	—	2	1	no	—
684	C₂²	—	2	1	no	—
685	C₂²	—	2	1	no	—
686	C₂²	—	2	1	no	—
687	C₂²	—	2	1	no	—
688	C₂²	—	2	1	no	—
689	C₂²	—	2	2	no	—
690	C₂²	—	4	4	no	—
691	C₂²	—	4	1	no	—
692	C₂²	—	4	1	no	—
693	C₂²	—	4	1	no	—
694	C₂²	—	4	1	no	—
695	C₂²	—	4	1	no	—
696	C₂²	—	4	4	no	—
697	C₂²	—	8	4	no	—
698	C₂²	—	8	4	no	—
699	C₂²	—	8	8	no	—
700	C₂²	—	8	4	no	—
701	C₂²	—	8	8	no	—
702	C₂²	—	8	2	no	—
703	C₂²	—	8	2	no	—
704	C₂²	—	8	1	no	—
705	C₂²	—	8	1	no	—
706	C₂²	—	8	1	no	—
707	C₂²	—	16	2	no	—
708	C₂²	#472×C₇₃	1	2	yes	complemented
709	C₂²	C₂×#121×C₇₃	1	1	yes	characteristic
710	C₂²	#546×C₇₃	1	2	yes	—
711	C₄	—	2	1	no	—
712	C₄	—	2	1	no	—
713	C₄	—	2	2	no	—
714	C₄	—	4	1	no	—
715	C₄	—	8	1	no	—
716	C₄	C₂×#120×C₇₃	1	1	yes	characteristic
717	C₄	#534×C₇₃	1	1	yes	characteristic
718	C₄	D₄²×C₇₃	1	2	yes	—
719	C₂	—	2	2	no	—
720	C₂	—	2	2	no	—
721	C₂	—	4	1	no	—
722	C₂	—	4	2	no	—
723	C₂	—	8	1	no	—
724	C₂	—	8	4	no	—
725	C₂	—	16	1	no	—
726	C₂	C₇₃×#2410	1	1	yes	characteristic
727	C₂	C₂×#472×C₇₃	1	1	yes	characteristic
728	C₂	C₇₃×#3068	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂²×AGL(1,ℤ/8)×C₇₃	C₂	semidirect
2. C₂×#472×C₇₃	C₂	semidirect
3. C₇₃×#3006	C₂	semidirect
4. C₂×#447×C₇₃	C₂	semidirect
5. C₇₃×#2880	C₂	semidirect
6. C₇₃×#2051	C₂	semidirect
7. C₇₃×#2018	C₂	semidirect
8. C₇₃×#1907	C₂	semidirect
9. C₇₃×#1900	C₂	semidirect
10. C₇₃×#1855	C₂	semidirect
11. C₇₃×#1783	C₂	semidirect
19. C₂×AGL(1,ℤ/8)×C₇₃	C₂²	semidirect
20. C₂×AGL(1,ℤ/8)×C₇₃	C₂²	semidirect
23. C₂²×D₈×C₇₃	C₂²	semidirect
24. C₂×#131×C₇₃	C₂²	semidirect
35. C₂×#108×C₇₃	C₂²	semidirect
36. #417×C₇₃	C₂²	semidirect
37. #417×C₇₃	C₂²	semidirect
38. C₂×#102×C₇₃	C₂²	semidirect
39. C₂×#100×C₇₃	C₂²	semidirect
40. C₂×#100×C₇₃	C₂²	semidirect
41. C₂×#100×C₇₃	C₂²	semidirect
43. #408×C₇₃	C₂²	semidirect
49. #343×C₇₃	C₂²	semidirect
50. #341×C₇₃	C₂²	semidirect
82. AGL(1,ℤ/8)×C₇₃	D₄	semidirect
343. C₂²×C₇₃	#472	semidirect
354. #24398	C₇₃	direct (N × H)
365. C₂²×AGL(1,ℤ/8)	C₂×C₇₃	semidirect
366. C₂×#472	C₂×C₇₃	semidirect
367. #3006	C₂×C₇₃	semidirect
368. C₂×#447	C₂×C₇₃	semidirect
369. #2880	C₂×C₇₃	semidirect
370. #2051	C₂×C₇₃	semidirect
371. #2018	C₂×C₇₃	semidirect
372. #1907	C₂×C₇₃	semidirect
373. #1900	C₂×C₇₃	semidirect
374. #1855	C₂×C₇₃	semidirect
375. #1783	C₂×C₇₃	semidirect
376. C₇₃	#24398	direct (N × H)
384. C₂×AGL(1,ℤ/8)	C₂²×C₇₃	semidirect
385. C₂×AGL(1,ℤ/8)	C₂²×C₇₃	semidirect
388. C₂²×D₈	C₂²×C₇₃	semidirect
389. C₂×#131	C₂²×C₇₃	semidirect
400. C₂×#108	C₂²×C₇₃	semidirect
401. #417	C₂²×C₇₃	semidirect
402. #417	C₂²×C₇₃	semidirect
403. C₂×#102	C₂²×C₇₃	semidirect
404. C₂×#100	C₂²×C₇₃	semidirect
405. C₂×#100	C₂²×C₇₃	semidirect
406. C₂×#100	C₂²×C₇₃	semidirect
408. #408	C₂²×C₇₃	semidirect
414. #343	C₂²×C₇₃	semidirect
415. #341	C₂²×C₇₃	semidirect
447. AGL(1,ℤ/8)	D₄×C₇₃	semidirect
708. C₂²	#472×C₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₂²×AGL(1,ℤ/8)×C₇₃	2
C₂×#472×C₇₃	2
C₇₃×#3006	2
C₂×#447×C₇₃	2
C₇₃×#2880	2
C₇₃×#2051	2
C₇₃×#2018	2
C₇₃×#1907	2
C₇₃×#1900	2
C₇₃×#1855	2
C₇₃×#1783	2
#24398	73

Subgroups — C73×#24398 #32933802

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#24398 #32933802