Subgroups — C₇₃×#24399 #32933803

Order 18688.

1450 conjugacy classes of subgroups.

The subgroup lattice has 712 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
2	C₂×#471×C₇₃	C₂	1	2	yes	maximal, complemented
3	C₇₃×#3007	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#450×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×#2019	C₂	1	2	yes	maximal, complemented
8	C₇₃×#1907	C₂	1	2	yes	maximal, complemented
9	C₇₃×#1901	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×#137×C₇₃	C₂²	1	1	yes	characteristic, complemented
15	C₂×#137×C₇₃	C₂²	1	1	yes	characteristic, complemented
16	C₂×AGL(1,ℤ/8)×C₇₃	—	2	1	no	—
17	C₂×AGL(1,ℤ/8)×C₇₃	—	2	1	no	—
18	C₂×AGL(1,ℤ/8)×C₇₃	—	2	8	no	—
19	C₂×AGL(1,ℤ/8)×C₇₃	C₂²	1	2	yes	—
20	C₂×AGL(1,ℤ/8)×C₇₃	C₂²	1	2	yes	—
21	C₂²×SD₁₆×C₇₃	—	2	1	no	—
22	C₂²×SD₁₆×C₇₃	C₂²	1	2	yes	complemented
23	C₂²×D₈×C₇₃	—	2	1	no	—
24	C₂×#131×C₇₃	C₂²	1	2	yes	complemented
25	C₂²×M₁₆×C₇₃	C₂²	1	1	yes	characteristic
26	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
27	#471×C₇₃	—	2	8	no	—
28	#452×C₇₃	—	2	1	no	—
29	#452×C₇₃	—	2	1	no	—
30	#451×C₇₃	—	2	1	no	—
31	#450×C₇₃	—	2	1	no	—
32	#450×C₇₃	—	2	1	no	—
33	#450×C₇₃	—	2	1	no	—
34	#450×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×#101×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×Q₈×C₇₃	C₂³	1	1	yes	characteristic
62	C₂²×D₄×C₇₃	—	2	4	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	2	yes	—
72	C₂³×C₄×C₇₃	—	2	1	no	—
73	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
74	#137×C₇₃	—	2	4	no	—
75	#137×C₇₃	—	4	2	no	—
76	AGL(1,ℤ/8)×C₇₃	—	2	8	no	—
77	AGL(1,ℤ/8)×C₇₃	—	2	8	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	D₄	1	8	yes	—
82	C₂×Q₁₆×C₇₃	—	2	1	no	—
83	C₂×Q₁₆×C₇₃	—	2	1	no	—
84	C₂×SD₁₆×C₇₃	—	2	8	no	—
85	C₂×SD₁₆×C₇₃	—	2	2	no	—
86	C₂×SD₁₆×C₇₃	—	2	2	no	—
87	C₂×SD₁₆×C₇₃	—	2	1	no	—
88	C₂×SD₁₆×C₇₃	—	2	1	no	—
89	C₂×SD₁₆×C₇₃	—	2	4	no	—
90	C₂×SD₁₆×C₇₃	—	2	2	no	—
91	C₂×SD₁₆×C₇₃	—	2	2	no	—
92	C₂×SD₁₆×C₇₃	—	4	2	no	—
93	C₂×D₈×C₇₃	—	2	8	no	—
94	C₂×D₈×C₇₃	—	2	2	no	—
95	C₂×D₈×C₇₃	—	2	2	no	—
96	#131×C₇₃	—	2	4	no	—
97	#131×C₇₃	—	4	2	no	—
98	C₂×M₁₆×C₇₃	—	2	1	no	—
99	C₂×M₁₆×C₇₃	—	2	4	no	—
100	C₂×M₁₆×C₇₃	—	2	2	no	—
101	C₂×M₁₆×C₇₃	C₂³	1	2	yes	—
102	C₂×M₁₆×C₇₃	C₂³	1	1	yes	characteristic
103	C₂×M₁₆×C₇₃	C₂³	1	1	yes	characteristic
104	C₂×M₁₆×C₇₃	C₂³	1	2	yes	—
105	C₂²×C₈×C₇₃	—	2	1	no	—
106	C₂²×C₈×C₇₃	—	2	2	no	—
107	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
108	C₂²⋊Q₈×C₇₃	—	2	1	no	—
109	C₂²⋊Q₈×C₇₃	—	2	1	no	—
110	C₂²⋊Q₈×C₇₃	—	2	1	no	—
111	C₂²⋊Q₈×C₇₃	—	2	1	no	—
112	C₂×C₄⋊C₄×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	#101×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	—	4	4	no	—
137	C₂⁴×C₇₃	—	4	1	no	—
138	C₂⁴×C₇₃	—	4	1	no	—
139	C₂⁴×C₇₃	—	8	2	no	—
140	C₂⁴×C₇₃	—	8	2	no	—
141	C₂⁴×C₇₃	#41	1	1	yes	characteristic
142	#41×C₇₃	—	2	2	no	—
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	—	4	4	no	—
148	#41×C₇₃	—	4	1	no	—
149	#41×C₇₃	—	4	1	no	—
150	#41×C₇₃	—	4	4	no	—
151	#41×C₇₃	C₂×D₄	1	4	yes	—
152	C₂×Q₈×C₇₃	—	2	1	no	—
153	C₂×Q₈×C₇₃	—	2	2	no	—
154	C₂×Q₈×C₇₃	—	2	2	no	—
155	C₂×Q₈×C₇₃	—	2	1	no	—
156	C₂×Q₈×C₇₃	—	2	1	no	—
157	C₂×Q₈×C₇₃	—	2	2	no	—
158	C₂×Q₈×C₇₃	—	4	1	no	—
159	C₂×Q₈×C₇₃	C₂×D₄	1	1	yes	characteristic
160	C₂×Q₈×C₇₃	C₂×D₄	1	1	yes	characteristic
161	C₂×D₄×C₇₃	—	2	1	no	—
162	C₂×D₄×C₇₃	—	2	4	no	—
163	C₂×D₄×C₇₃	—	2	4	no	—
164	C₂×D₄×C₇₃	—	2	2	no	—
165	C₂×D₄×C₇₃	—	2	1	no	—
166	C₂×D₄×C₇₃	—	2	1	no	—
167	C₂×D₄×C₇₃	—	2	1	no	—
168	C₂×D₄×C₇₃	—	2	1	no	—
169	C₂×D₄×C₇₃	—	2	2	no	—
170	C₂×D₄×C₇₃	—	2	2	no	—
171	C₂×D₄×C₇₃	—	2	2	no	—
172	C₂×D₄×C₇₃	—	2	2	no	—
173	C₂×D₄×C₇₃	—	2	2	no	—
174	C₂×D₄×C₇₃	—	4	1	no	—
175	C₂×D₄×C₇₃	—	4	4	no	—
176	C₂×D₄×C₇₃	—	4	4	no	—
177	C₂×D₄×C₇₃	—	4	4	no	—
178	C₂×D₄×C₇₃	—	4	2	no	—
179	C₂×D₄×C₇₃	—	4	2	no	—
180	C₂×D₄×C₇₃	—	4	4	no	—
181	C₂×D₄×C₇₃	—	4	1	no	—
182	C₂×D₄×C₇₃	—	4	1	no	—
183	C₂×D₄×C₇₃	C₂×D₄	1	4	yes	—
184	C₂×D₄×C₇₃	C₂×D₄	1	1	yes	characteristic
185	C₂×D₄×C₇₃	C₂×D₄	1	1	yes	characteristic
186	C₂²×C₄×C₇₃	—	2	1	no	—
187	C₂²×C₄×C₇₃	—	2	2	no	—
188	C₂²×C₄×C₇₃	—	2	2	no	—
189	C₂²×C₄×C₇₃	—	2	1	no	—
190	C₂²×C₄×C₇₃	—	2	1	no	—
191	C₂²×C₄×C₇₃	—	2	1	no	—
192	C₂²×C₄×C₇₃	—	2	1	no	—
193	C₂²×C₄×C₇₃	—	2	1	no	—
194	C₂²×C₄×C₇₃	—	2	1	no	—
195	C₂²×C₄×C₇₃	—	4	4	no	—
196	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
197	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
198	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
199	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
200	C₂²×C₄×C₇₃	#41	1	1	yes	characteristic
201	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
202	Q₁₆×C₇₃	—	4	2	no	—
203	Q₁₆×C₇₃	—	4	2	no	—
204	SD₁₆×C₇₃	—	2	8	no	—
205	SD₁₆×C₇₃	—	2	8	no	—
206	SD₁₆×C₇₃	—	4	4	no	—
207	SD₁₆×C₇₃	—	4	4	no	—
208	SD₁₆×C₇₃	—	4	2	no	—
209	SD₁₆×C₇₃	—	4	2	no	—
210	D₈×C₇₃	—	2	8	no	—
211	D₈×C₇₃	—	2	8	no	—
212	M₁₆×C₇₃	—	2	4	no	—
213	M₁₆×C₇₃	—	2	2	no	—
214	M₁₆×C₇₃	—	2	2	no	—
215	M₁₆×C₇₃	—	2	2	no	—
216	M₁₆×C₇₃	—	2	2	no	—
217	M₁₆×C₇₃	—	2	2	no	—
218	M₁₆×C₇₃	—	4	4	no	—
219	M₁₆×C₇₃	C₂×D₄	1	4	yes	—
220	C₂×C₈×C₇₃	—	2	4	no	—
221	C₂×C₈×C₇₃	—	2	2	no	—
222	C₂×C₈×C₇₃	—	2	2	no	—
223	C₂×C₈×C₇₃	—	2	2	no	—
224	C₂×C₈×C₇₃	—	2	2	no	—
225	C₂×C₈×C₇₃	—	2	1	no	—
226	C₂×C₈×C₇₃	—	2	1	no	—
227	C₂×C₈×C₇₃	—	4	4	no	—
228	C₂×C₈×C₇₃	C₂×D₄	1	2	yes	—
229	C₂×C₈×C₇₃	C₂×D₄	1	2	yes	—
230	C₄⋊C₄×C₇₃	—	2	1	no	—
231	C₄⋊C₄×C₇₃	—	2	1	no	—
232	C₄⋊C₄×C₇₃	—	4	1	no	—
233	C₄⋊C₄×C₇₃	—	4	1	no	—
234	C₂²⋊C₄×C₇₃	—	4	1	no	—
235	C₂²⋊C₄×C₇₃	—	4	1	no	—
236	C₂³×C₇₃	—	2	1	no	—
237	C₂³×C₇₃	—	2	2	no	—
238	C₂³×C₇₃	—	2	2	no	—
239	C₂³×C₇₃	—	2	1	no	—
240	C₂³×C₇₃	—	2	4	no	—
241	C₂³×C₇₃	—	4	1	no	—
242	C₂³×C₇₃	—	4	2	no	—
243	C₂³×C₇₃	—	4	4	no	—
244	C₂³×C₇₃	—	4	4	no	—
245	C₂³×C₇₃	—	4	2	no	—
246	C₂³×C₇₃	—	4	2	no	—
247	C₂³×C₇₃	—	4	2	no	—
248	C₂³×C₇₃	—	8	1	no	—
249	C₂³×C₇₃	—	8	2	no	—
250	C₂³×C₇₃	—	8	2	no	—
251	C₂³×C₇₃	—	8	2	no	—
252	C₂³×C₇₃	—	8	2	no	—
253	C₂³×C₇₃	—	8	2	no	—
254	C₂³×C₇₃	—	8	16	no	—
255	C₂³×C₇₃	—	8	2	no	—
256	C₂³×C₇₃	#121	1	1	yes	characteristic
257	C₂³×C₇₃	#121	1	1	yes	characteristic
258	C₂³×C₇₃	C₂×#41	1	1	yes	characteristic
259	Q₈×C₇₃	—	2	1	no	—
260	Q₈×C₇₃	—	2	1	no	—
261	Q₈×C₇₃	—	2	1	no	—
262	Q₈×C₇₃	—	4	2	no	—
263	Q₈×C₇₃	—	4	1	no	—
264	Q₈×C₇₃	—	4	1	no	—
265	Q₈×C₇₃	—	4	2	no	—
266	Q₈×C₇₃	#120	1	2	yes	—
267	D₄×C₇₃	—	2	4	no	—
268	D₄×C₇₃	—	2	1	no	—
269	D₄×C₇₃	—	2	4	no	—
270	D₄×C₇₃	—	2	1	no	—
271	D₄×C₇₃	—	2	1	no	—
272	D₄×C₇₃	—	2	4	no	—
273	D₄×C₇₃	—	4	2	no	—
274	D₄×C₇₃	—	4	2	no	—
275	D₄×C₇₃	—	4	4	no	—
276	D₄×C₇₃	—	4	4	no	—
277	D₄×C₇₃	—	4	2	no	—
278	D₄×C₇₃	—	4	2	no	—
279	D₄×C₇₃	—	4	2	no	—
280	D₄×C₇₃	—	4	2	no	—
281	D₄×C₇₃	#120	1	2	yes	—
282	C₂×C₄×C₇₃	—	2	1	no	—
283	C₂×C₄×C₇₃	—	2	2	no	—
284	C₂×C₄×C₇₃	—	2	1	no	—
285	C₂×C₄×C₇₃	—	2	1	no	—
286	C₂×C₄×C₇₃	—	2	1	no	—
287	C₂×C₄×C₇₃	—	2	1	no	—
288	C₂×C₄×C₇₃	—	2	4	no	—
289	C₂×C₄×C₇₃	—	2	2	no	—
290	C₂×C₄×C₇₃	—	2	2	no	—
291	C₂×C₄×C₇₃	—	2	1	no	—
292	C₂×C₄×C₇₃	—	4	2	no	—
293	C₂×C₄×C₇₃	—	4	2	no	—
294	C₂×C₄×C₇₃	—	4	2	no	—
295	C₂×C₄×C₇₃	—	4	2	no	—
296	C₂×C₄×C₇₃	—	4	1	no	—
297	C₂×C₄×C₇₃	—	4	1	no	—
298	C₂×C₄×C₇₃	—	4	2	no	—
299	C₂×C₄×C₇₃	—	8	1	no	—
300	C₂×C₄×C₇₃	#121	1	1	yes	characteristic
301	C₂×C₄×C₇₃	#121	1	1	yes	characteristic
302	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
303	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
304	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
305	C₂×C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
306	C₈×C₇₃	—	2	4	no	—
307	C₈×C₇₃	—	2	2	no	—
308	C₈×C₇₃	—	2	2	no	—
309	C₈×C₇₃	—	4	1	no	—
310	C₈×C₇₃	—	4	1	no	—
311	C₈×C₇₃	—	4	2	no	—
312	C₂²×C₇₃	—	2	1	no	—
313	C₂²×C₇₃	—	2	1	no	—
314	C₂²×C₇₃	—	2	1	no	—
315	C₂²×C₇₃	—	2	1	no	—
316	C₂²×C₇₃	—	2	1	no	—
317	C₂²×C₇₃	—	2	2	no	—
318	C₂²×C₇₃	—	2	1	no	—
319	C₂²×C₇₃	—	2	1	no	—
320	C₂²×C₇₃	—	4	4	no	—
321	C₂²×C₇₃	—	4	1	no	—
322	C₂²×C₇₃	—	4	1	no	—
323	C₂²×C₇₃	—	4	1	no	—
324	C₂²×C₇₃	—	4	4	no	—
325	C₂²×C₇₃	—	4	1	no	—
326	C₂²×C₇₃	—	4	1	no	—
327	C₂²×C₇₃	—	8	4	no	—
328	C₂²×C₇₃	—	8	4	no	—
329	C₂²×C₇₃	—	8	8	no	—
330	C₂²×C₇₃	—	8	4	no	—
331	C₂²×C₇₃	—	8	8	no	—
332	C₂²×C₇₃	—	8	2	no	—
333	C₂²×C₇₃	—	8	2	no	—
334	C₂²×C₇₃	#471	1	2	yes	complemented
335	C₂²×C₇₃	C₂×#121	1	1	yes	characteristic
336	C₂²×C₇₃	#546	1	2	yes	—
337	C₄×C₇₃	—	2	1	no	—
338	C₄×C₇₃	—	2	1	no	—
339	C₄×C₇₃	—	2	2	no	—
340	C₄×C₇₃	—	4	1	no	—
341	C₄×C₇₃	—	8	1	no	—
342	C₄×C₇₃	—	8	1	no	—
343	C₄×C₇₃	C₂×#120	1	1	yes	characteristic
344	C₄×C₇₃	#534	1	1	yes	characteristic
345	C₄×C₇₃	D₄²	1	2	yes	—
346	#24399	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
347	C₂×C₇₃	—	2	2	no	—
348	C₂×C₇₃	—	2	2	no	—
349	C₂×C₇₃	—	4	1	no	—
350	C₂×C₇₃	—	4	2	no	—
351	C₂×C₇₃	—	8	1	no	—
352	C₂×C₇₃	—	8	4	no	—
353	C₂×C₇₃	#2410	1	1	yes	characteristic
354	C₂×C₇₃	C₂×#471	1	1	yes	characteristic
355	C₂×C₇₃	#3068	1	1	yes	characteristic
356	C₂²×AGL(1,ℤ/8)	C₂×C₇₃	1	1	yes	characteristic
357	C₂×#471	C₂×C₇₃	1	2	yes	complemented
358	#3007	C₂×C₇₃	1	1	yes	characteristic, complemented
359	C₂×#450	C₂×C₇₃	1	1	yes	characteristic, complemented
360	#2880	C₂×C₇₃	1	1	yes	characteristic, complemented
361	#2051	C₂×C₇₃	1	2	yes	complemented
362	#2019	C₂×C₇₃	1	2	yes	complemented
363	#1907	C₂×C₇₃	1	2	yes	complemented
364	#1901	C₂×C₇₃	1	1	yes	characteristic, complemented
365	#1855	C₂×C₇₃	1	1	yes	characteristic, complemented
366	#1783	C₂×C₇₃	1	1	yes	characteristic, complemented
367	C₇₃	#24399	1	1	yes	characteristic, direct product factor, Sylow
368	C₂²×#41	C₂²×C₇₃	1	1	yes	characteristic
369	C₂³×D₄	C₂²×C₇₃	1	1	yes	characteristic
370	C₂×#137	C₂²×C₇₃	1	1	yes	characteristic, complemented
371	C₂×#137	C₂²×C₇₃	1	1	yes	characteristic, complemented
372	C₂×AGL(1,ℤ/8)	—	2	1	no	—
373	C₂×AGL(1,ℤ/8)	—	2	1	no	—
374	C₂×AGL(1,ℤ/8)	—	2	8	no	—
375	C₂×AGL(1,ℤ/8)	C₂²×C₇₃	1	2	yes	—
376	C₂×AGL(1,ℤ/8)	C₂²×C₇₃	1	2	yes	—
377	C₂²×SD₁₆	—	2	1	no	—
378	C₂²×SD₁₆	C₂²×C₇₃	1	2	yes	complemented
379	C₂²×D₈	—	2	1	no	—
380	C₂×#131	C₂²×C₇₃	1	2	yes	complemented
381	C₂²×M₁₆	C₂²×C₇₃	1	1	yes	characteristic
382	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
383	#471	—	2	8	no	—
384	#452	—	2	1	no	—
385	#452	—	2	1	no	—
386	#451	—	2	1	no	—
387	#450	—	2	1	no	—
388	#450	—	2	1	no	—
389	#450	—	2	1	no	—
390	#450	—	2	2	no	—
391	C₂×#108	C₂²×C₇₃	1	2	yes	complemented
392	#417	C₂²×C₇₃	1	1	yes	characteristic, complemented
393	#417	C₂²×C₇₃	1	1	yes	characteristic, complemented
394	C₂×#102	C₂²×C₇₃	1	2	yes	complemented
395	C₂×#101	C₂²×C₇₃	1	2	yes	complemented
396	C₂×#100	C₂²×C₇₃	1	2	yes	complemented
397	C₂×#100	C₂²×C₇₃	1	2	yes	complemented
398	#408	—	2	2	no	—
399	#408	C₂²×C₇₃	1	2	yes	complemented
400	#407	—	2	1	no	—
401	#407	C₂²×C₇₃	1	1	yes	characteristic
402	#407	C₂²×C₇₃	1	1	yes	characteristic
403	C₂×C₂²⋊C₈	—	2	1	no	—
404	C₂×C₂²⋊C₈	C₂²×C₇₃	1	1	yes	characteristic
405	#343	C₂²×C₇₃	1	2	yes	complemented
406	#341	C₂²×C₇₃	1	2	yes	complemented
407	C₂⁵	—	2	1	no	—
408	C₂×#41	—	2	1	no	—
409	C₂×#41	—	2	1	no	—
410	C₂×#41	—	2	4	no	—
411	C₂×#41	—	4	2	no	—
412	C₂×#41	D₄×C₇₃	1	1	yes	characteristic
413	C₂×#41	D₄×C₇₃	1	1	yes	characteristic
414	C₂×#41	C₂³×C₇₃	1	1	yes	characteristic
415	C₂×#41	C₂³×C₇₃	1	1	yes	characteristic
416	C₂²×Q₈	D₄×C₇₃	1	1	yes	characteristic
417	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
418	C₂²×D₄	—	2	4	no	—
419	C₂²×D₄	—	2	1	no	—
420	C₂²×D₄	—	2	1	no	—
421	C₂²×D₄	—	2	1	no	—
422	C₂²×D₄	—	2	1	no	—
423	C₂²×D₄	—	2	1	no	—
424	C₂²×D₄	—	2	1	no	—
425	C₂²×D₄	—	4	2	no	—
426	C₂²×D₄	D₄×C₇₃	1	1	yes	characteristic
427	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
428	C₂³×C₄	—	2	1	no	—
429	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
430	#137	—	2	4	no	—
431	#137	—	4	2	no	—
432	AGL(1,ℤ/8)	—	2	8	no	—
433	AGL(1,ℤ/8)	—	2	8	no	—
434	AGL(1,ℤ/8)	—	2	4	no	—
435	AGL(1,ℤ/8)	—	2	4	no	—
436	AGL(1,ℤ/8)	—	2	4	no	—
437	AGL(1,ℤ/8)	D₄×C₇₃	1	8	yes	—
438	C₂×Q₁₆	—	2	1	no	—
439	C₂×Q₁₆	—	2	1	no	—
440	C₂×SD₁₆	—	2	8	no	—
441	C₂×SD₁₆	—	2	2	no	—
442	C₂×SD₁₆	—	2	2	no	—
443	C₂×SD₁₆	—	2	4	no	—
444	C₂×SD₁₆	—	2	1	no	—
445	C₂×SD₁₆	—	2	1	no	—
446	C₂×SD₁₆	—	2	2	no	—
447	C₂×SD₁₆	—	2	2	no	—
448	C₂×SD₁₆	—	4	2	no	—
449	C₂×D₈	—	2	8	no	—
450	C₂×D₈	—	2	2	no	—
451	C₂×D₈	—	2	2	no	—
452	#131	—	2	4	no	—
453	#131	—	4	2	no	—
454	C₂×M₁₆	—	2	1	no	—
455	C₂×M₁₆	—	2	4	no	—
456	C₂×M₁₆	—	2	2	no	—
457	C₂×M₁₆	C₂³×C₇₃	1	2	yes	—
458	C₂×M₁₆	C₂³×C₇₃	1	1	yes	characteristic
459	C₂×M₁₆	C₂³×C₇₃	1	1	yes	characteristic
460	C₂×M₁₆	C₂³×C₇₃	1	2	yes	—
461	C₂²×C₈	—	2	1	no	—
462	C₂²×C₈	—	2	2	no	—
463	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
464	C₂²⋊Q₈	—	2	1	no	—
465	C₂²⋊Q₈	—	2	1	no	—
466	C₂²⋊Q₈	—	2	1	no	—
467	C₂²⋊Q₈	—	2	1	no	—
468	C₂×C₄⋊C₄	—	2	1	no	—
469	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
470	C₂×C₂²⋊C₄	—	2	1	no	—
471	#108	—	2	4	no	—
472	#103	—	2	1	no	—
473	#103	—	2	1	no	—
474	#102	—	2	1	no	—
475	#102	—	2	1	no	—
476	#102	—	2	2	no	—
477	#102	—	2	2	no	—
478	#101	—	2	4	no	—
479	#100	—	2	4	no	—
480	#100	—	4	2	no	—
481	C₂²⋊C₈	—	2	1	no	—
482	C₂²⋊C₈	—	2	1	no	—
483	C₂²⋊C₈	—	2	1	no	—
484	C₂²⋊C₈	—	2	1	no	—
485	C₂²⋊C₈	—	2	2	no	—
486	C₂²⋊C₈	—	2	2	no	—
487	C₂²⋊C₈	D₄×C₇₃	1	1	yes	characteristic
488	C₂²⋊C₈	D₄×C₇₃	1	1	yes	characteristic
489	C₂²⋊C₈	D₄×C₇₃	1	2	yes	—
490	C₂⁴	—	2	1	no	—
491	C₂⁴	—	2	2	no	—
492	C₂⁴	—	4	4	no	—
493	C₂⁴	—	4	1	no	—
494	C₂⁴	—	4	1	no	—
495	C₂⁴	—	8	2	no	—
496	C₂⁴	—	8	2	no	—
497	C₂⁴	#41×C₇₃	1	1	yes	characteristic
498	#41	—	2	2	no	—
499	#41	—	2	2	no	—
500	#41	—	2	2	no	—
501	#41	—	2	2	no	—
502	#41	—	2	2	no	—
503	#41	—	4	4	no	—
504	#41	—	4	1	no	—
505	#41	—	4	1	no	—
506	#41	—	4	4	no	—
507	#41	C₂×D₄×C₇₃	1	4	yes	—
508	C₂×Q₈	—	2	1	no	—
509	C₂×Q₈	—	2	2	no	—
510	C₂×Q₈	—	2	2	no	—
511	C₂×Q₈	—	2	1	no	—
512	C₂×Q₈	—	2	1	no	—
513	C₂×Q₈	—	2	2	no	—
514	C₂×Q₈	—	4	1	no	—
515	C₂×Q₈	C₂×D₄×C₇₃	1	1	yes	characteristic
516	C₂×Q₈	C₂×D₄×C₇₃	1	1	yes	characteristic
517	C₂×D₄	—	2	1	no	—
518	C₂×D₄	—	2	4	no	—
519	C₂×D₄	—	2	4	no	—
520	C₂×D₄	—	2	2	no	—
521	C₂×D₄	—	2	1	no	—
522	C₂×D₄	—	2	1	no	—
523	C₂×D₄	—	2	1	no	—
524	C₂×D₄	—	2	1	no	—
525	C₂×D₄	—	2	2	no	—
526	C₂×D₄	—	2	2	no	—
527	C₂×D₄	—	2	2	no	—
528	C₂×D₄	—	2	2	no	—
529	C₂×D₄	—	2	2	no	—
530	C₂×D₄	—	4	1	no	—
531	C₂×D₄	—	4	4	no	—
532	C₂×D₄	—	4	4	no	—
533	C₂×D₄	—	4	4	no	—
534	C₂×D₄	—	4	2	no	—
535	C₂×D₄	—	4	2	no	—
536	C₂×D₄	—	4	4	no	—
537	C₂×D₄	—	4	1	no	—
538	C₂×D₄	—	4	1	no	—
539	C₂×D₄	C₂×D₄×C₇₃	1	4	yes	—
540	C₂×D₄	C₂×D₄×C₇₃	1	1	yes	characteristic
541	C₂×D₄	C₂×D₄×C₇₃	1	1	yes	characteristic
542	C₂²×C₄	—	2	1	no	—
543	C₂²×C₄	—	2	2	no	—
544	C₂²×C₄	—	2	2	no	—
545	C₂²×C₄	—	2	1	no	—
546	C₂²×C₄	—	2	1	no	—
547	C₂²×C₄	—	2	1	no	—
548	C₂²×C₄	—	2	1	no	—
549	C₂²×C₄	—	2	1	no	—
550	C₂²×C₄	—	2	1	no	—
551	C₂²×C₄	—	4	4	no	—
552	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
553	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
554	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
555	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
556	C₂²×C₄	#41×C₇₃	1	1	yes	characteristic
557	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
558	Q₁₆	—	4	2	no	—
559	Q₁₆	—	4	2	no	—
560	SD₁₆	—	2	8	no	—
561	SD₁₆	—	2	8	no	—
562	SD₁₆	—	4	4	no	—
563	SD₁₆	—	4	4	no	—
564	SD₁₆	—	4	2	no	—
565	SD₁₆	—	4	2	no	—
566	D₈	—	2	8	no	—
567	D₈	—	2	8	no	—
568	M₁₆	—	2	4	no	—
569	M₁₆	—	2	2	no	—
570	M₁₆	—	2	2	no	—
571	M₁₆	—	2	2	no	—
572	M₁₆	—	2	2	no	—
573	M₁₆	—	2	2	no	—
574	M₁₆	—	4	4	no	—
575	M₁₆	C₂×D₄×C₇₃	1	4	yes	—
576	C₂×C₈	—	2	4	no	—
577	C₂×C₈	—	2	2	no	—
578	C₂×C₈	—	2	2	no	—
579	C₂×C₈	—	2	2	no	—
580	C₂×C₈	—	2	2	no	—
581	C₂×C₈	—	2	1	no	—
582	C₂×C₈	—	2	1	no	—
583	C₂×C₈	—	4	4	no	—
584	C₂×C₈	C₂×D₄×C₇₃	1	2	yes	—
585	C₂×C₈	C₂×D₄×C₇₃	1	2	yes	—
586	C₄⋊C₄	—	2	1	no	—
587	C₄⋊C₄	—	2	1	no	—
588	C₄⋊C₄	—	4	1	no	—
589	C₄⋊C₄	—	4	1	no	—
590	C₂²⋊C₄	—	4	1	no	—
591	C₂²⋊C₄	—	4	1	no	—
592	C₂³	—	2	2	no	—
593	C₂³	—	2	1	no	—
594	C₂³	—	2	2	no	—
595	C₂³	—	2	1	no	—
596	C₂³	—	2	4	no	—
597	C₂³	—	4	1	no	—
598	C₂³	—	4	2	no	—
599	C₂³	—	4	4	no	—
600	C₂³	—	4	4	no	—
601	C₂³	—	4	2	no	—
602	C₂³	—	4	2	no	—
603	C₂³	—	4	2	no	—
604	C₂³	—	8	1	no	—
605	C₂³	—	8	2	no	—
606	C₂³	—	8	2	no	—
607	C₂³	—	8	2	no	—
608	C₂³	—	8	2	no	—
609	C₂³	—	8	2	no	—
610	C₂³	—	8	16	no	—
611	C₂³	—	8	2	no	—
612	C₂³	#121×C₇₃	1	1	yes	characteristic
613	C₂³	#121×C₇₃	1	1	yes	characteristic
614	C₂³	C₂×#41×C₇₃	1	1	yes	characteristic
615	Q₈	—	2	1	no	—
616	Q₈	—	2	1	no	—
617	Q₈	—	2	1	no	—
618	Q₈	—	4	2	no	—
619	Q₈	—	4	1	no	—
620	Q₈	—	4	1	no	—
621	Q₈	—	4	2	no	—
622	Q₈	#120×C₇₃	1	2	yes	—
623	D₄	—	2	4	no	—
624	D₄	—	2	1	no	—
625	D₄	—	2	4	no	—
626	D₄	—	2	1	no	—
627	D₄	—	2	1	no	—
628	D₄	—	2	4	no	—
629	D₄	—	4	2	no	—
630	D₄	—	4	2	no	—
631	D₄	—	4	4	no	—
632	D₄	—	4	4	no	—
633	D₄	—	4	2	no	—
634	D₄	—	4	2	no	—
635	D₄	—	4	2	no	—
636	D₄	—	4	2	no	—
637	D₄	#120×C₇₃	1	2	yes	—
638	C₂×C₄	—	2	1	no	—
639	C₂×C₄	—	2	2	no	—
640	C₂×C₄	—	2	1	no	—
641	C₂×C₄	—	2	1	no	—
642	C₂×C₄	—	2	1	no	—
643	C₂×C₄	—	2	1	no	—
644	C₂×C₄	—	2	4	no	—
645	C₂×C₄	—	2	2	no	—
646	C₂×C₄	—	2	2	no	—
647	C₂×C₄	—	2	1	no	—
648	C₂×C₄	—	4	2	no	—
649	C₂×C₄	—	4	2	no	—
650	C₂×C₄	—	4	2	no	—
651	C₂×C₄	—	4	2	no	—
652	C₂×C₄	—	4	1	no	—
653	C₂×C₄	—	4	1	no	—
654	C₂×C₄	—	4	2	no	—
655	C₂×C₄	—	8	1	no	—
656	C₂×C₄	#121×C₇₃	1	1	yes	characteristic
657	C₂×C₄	#121×C₇₃	1	1	yes	characteristic
658	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
659	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
660	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
661	C₂×C₄	H(5,𝔽₂)×C₇₃	1	2	yes	—
662	C₈	—	2	4	no	—
663	C₈	—	2	2	no	—
664	C₈	—	2	2	no	—
665	C₈	—	4	1	no	—
666	C₈	—	4	1	no	—
667	C₈	—	4	2	no	—
668	C₂²	—	2	1	no	—
669	C₂²	—	2	1	no	—
670	C₂²	—	2	1	no	—
671	C₂²	—	2	1	no	—
672	C₂²	—	2	1	no	—
673	C₂²	—	2	1	no	—
674	C₂²	—	2	1	no	—
675	C₂²	—	2	2	no	—
676	C₂²	—	4	4	no	—
677	C₂²	—	4	1	no	—
678	C₂²	—	4	1	no	—
679	C₂²	—	4	1	no	—
680	C₂²	—	4	1	no	—
681	C₂²	—	4	1	no	—
682	C₂²	—	4	4	no	—
683	C₂²	—	8	4	no	—
684	C₂²	—	8	4	no	—
685	C₂²	—	8	8	no	—
686	C₂²	—	8	4	no	—
687	C₂²	—	8	8	no	—
688	C₂²	—	8	2	no	—
689	C₂²	—	8	2	no	—
690	C₂²	#471×C₇₃	1	2	yes	complemented
691	C₂²	C₂×#121×C₇₃	1	1	yes	characteristic
692	C₂²	#546×C₇₃	1	2	yes	—
693	C₄	—	2	1	no	—
694	C₄	—	2	1	no	—
695	C₄	—	2	2	no	—
696	C₄	—	4	1	no	—
697	C₄	—	8	1	no	—
698	C₄	—	8	1	no	—
699	C₄	C₂×#120×C₇₃	1	1	yes	characteristic
700	C₄	#534×C₇₃	1	1	yes	characteristic
701	C₄	D₄²×C₇₃	1	2	yes	—
702	C₂	—	2	2	no	—
703	C₂	—	2	2	no	—
704	C₂	—	4	1	no	—
705	C₂	—	4	2	no	—
706	C₂	—	8	1	no	—
707	C₂	—	8	4	no	—
708	C₂	C₇₃×#2410	1	1	yes	characteristic
709	C₂	C₂×#471×C₇₃	1	1	yes	characteristic
710	C₂	C₇₃×#3068	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇₃	C₂×#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₃
prime radical	C₂²×AGL(1,ℤ/8)×C₇₃	C₂
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
2. C₂×#471×C₇₃	C₂	semidirect
3. C₇₃×#3007	C₂	semidirect
4. C₂×#450×C₇₃	C₂	semidirect
5. C₇₃×#2880	C₂	semidirect
6. C₇₃×#2051	C₂	semidirect
7. C₇₃×#2019	C₂	semidirect
8. C₇₃×#1907	C₂	semidirect
9. C₇₃×#1901	C₂	semidirect
10. C₇₃×#1855	C₂	semidirect
11. C₇₃×#1783	C₂	semidirect
14. C₂×#137×C₇₃	C₂²	semidirect
15. C₂×#137×C₇₃	C₂²	semidirect
22. C₂²×SD₁₆×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×#101×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
334. C₂²×C₇₃	#471	semidirect
346. #24399	C₇₃	direct (N × H)
357. C₂×#471	C₂×C₇₃	semidirect
358. #3007	C₂×C₇₃	semidirect
359. C₂×#450	C₂×C₇₃	semidirect
360. #2880	C₂×C₇₃	semidirect
361. #2051	C₂×C₇₃	semidirect
362. #2019	C₂×C₇₃	semidirect
363. #1907	C₂×C₇₃	semidirect
364. #1901	C₂×C₇₃	semidirect
365. #1855	C₂×C₇₃	semidirect
366. #1783	C₂×C₇₃	semidirect
367. C₇₃	#24399	direct (N × H)
370. C₂×#137	C₂²×C₇₃	semidirect
371. C₂×#137	C₂²×C₇₃	semidirect
378. C₂²×SD₁₆	C₂²×C₇₃	semidirect
380. C₂×#131	C₂²×C₇₃	semidirect
391. C₂×#108	C₂²×C₇₃	semidirect
392. #417	C₂²×C₇₃	semidirect
393. #417	C₂²×C₇₃	semidirect
394. C₂×#102	C₂²×C₇₃	semidirect
395. C₂×#101	C₂²×C₇₃	semidirect
396. C₂×#100	C₂²×C₇₃	semidirect
397. C₂×#100	C₂²×C₇₃	semidirect
399. #408	C₂²×C₇₃	semidirect
405. #343	C₂²×C₇₃	semidirect
406. #341	C₂²×C₇₃	semidirect
690. C₂²	#471×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×#471×C₇₃	2
C₇₃×#3007	2
C₂×#450×C₇₃	2
C₇₃×#2880	2
C₇₃×#2051	2
C₇₃×#2019	2
C₇₃×#1907	2
C₇₃×#1901	2
C₇₃×#1855	2
C₇₃×#1783	2
#24399	73

Subgroups — C73×#24399 #32933803

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#24399 #32933803