Subgroups — C₇₃×#24708 #32934112

Order 18688.

912 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#476×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#432×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₃×#2857	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×#121×C₇₃	C₂	1	1	yes	maximal, characteristic
5	C₇₃×#2077	C₂	1	2	yes	maximal, complemented
6	C₇₃×#2033	C₂	1	2	yes	maximal
7	C₇₃×#1987	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇₃×#1947	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇₃×#1943	C₂	1	2	yes	maximal, complemented
10	C₇₃×#1936	C₂	1	2	yes	maximal, complemented
11	C₇₃×#1802	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
13	C₂×C₂²⋊Q₈×C₇₃	—	2	1	no	—
14	C₂×#121×C₇₃	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₄×C₇₃	—	2	1	no	—
16	C₂×C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
17	C₂²×C₄²×C₇₃	C₂²	1	1	yes	characteristic
18	#476×C₇₃	—	2	4	no	—
19	#432×C₇₃	—	2	4	no	—
20	C₂×#107×C₇₃	C₂²	1	2	yes	—
21	C₂×#106×C₇₃	C₂²	1	2	yes	—
22	C₂×C₄⋊C₈×C₇₃	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊C₈×C₇₃	C₂²	1	1	yes	characteristic
24	C₂×#102×C₇₃	C₂²	1	2	yes	—
25	C₂×#102×C₇₃	C₂²	1	2	yes	—
26	C₂×C₂²⋊C₈×C₇₃	C₂²	1	2	yes	—
27	C₂×#97×C₇₃	C₂²	1	2	yes	—
28	#391×C₇₃	—	2	1	no	—
29	#390×C₇₃	C₂²	1	1	yes	characteristic
30	#389×C₇₃	—	2	1	no	—
31	#389×C₇₃	C₂²	1	2	yes	—
32	#389×C₇₃	C₂²	1	1	yes	characteristic
33	#388×C₇₃	—	2	1	no	—
34	#386×C₇₃	—	2	1	no	—
35	#384×C₇₃	C₂²	1	1	yes	characteristic
36	#380×C₇₃	—	2	1	no	—
37	#380×C₇₃	C₂²	1	2	yes	—
38	#380×C₇₃	C₂²	1	1	yes	characteristic
39	C₄×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
40	C₄×C₂²⋊C₄×C₇₃	—	2	1	no	—
41	#340×C₇₃	C₂²	1	2	yes	—
42	#340×C₇₃	C₂²	1	2	yes	—
43	#340×C₇₃	C₂²	1	2	yes	—
44	#340×C₇₃	C₂²	1	2	yes	—
45	C₂²×Q₈×C₇₃	—	2	1	no	—
46	C₂²×D₄×C₇₃	—	2	1	no	—
47	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
48	C₂³×C₄×C₇₃	—	2	1	no	—
49	C₂³×C₄×C₇₃	D₄	1	1	yes	characteristic
50	C₂³×C₄×C₇₃	D₄	1	1	yes	characteristic
51	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
52	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
53	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
54	C₄⋊Q₈×C₇₃	—	2	2	no	—
55	C₄⋊Q₈×C₇₃	—	2	2	no	—
56	C₂²⋊Q₈×C₇₃	—	4	4	no	—
57	#121×C₇₃	—	2	2	no	—
58	#121×C₇₃	—	2	2	no	—
59	C₄×D₄×C₇₃	—	2	2	no	—
60	C₄×D₄×C₇₃	—	2	2	no	—
61	C₄×D₄×C₇₃	—	4	4	no	—
62	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
63	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
64	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
65	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
66	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
67	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
68	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
69	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
70	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
71	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
72	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
73	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
74	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
75	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
76	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
77	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
78	C₂×C₄²×C₇₃	—	2	2	no	—
79	C₂×C₄²×C₇₃	—	2	2	no	—
80	C₂×C₄²×C₇₃	—	2	1	no	—
81	C₂×C₄²×C₇₃	D₄	1	1	yes	characteristic
82	C₂×C₄²×C₇₃	D₄	1	1	yes	characteristic
83	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
84	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
85	#107×C₇₃	—	2	4	no	—
86	#106×C₇₃	—	2	4	no	—
87	C₄⋊C₈×C₇₃	—	2	2	no	—
88	C₄⋊C₈×C₇₃	D₄	1	4	yes	complemented
89	#102×C₇₃	—	2	4	no	—
90	#102×C₇₃	—	2	4	no	—
91	C₂²⋊C₈×C₇₃	—	2	4	no	—
92	#97×C₇₃	—	2	4	no	—
93	#95×C₇₃	—	2	1	no	—
94	#95×C₇₃	—	2	1	no	—
95	#95×C₇₃	—	2	1	no	—
96	#95×C₇₃	—	2	2	no	—
97	#95×C₇₃	—	2	2	no	—
98	C₂⁴×C₇₃	—	2	1	no	—
99	C₂⁴×C₇₃	C₂×D₄	1	1	yes	characteristic
100	C₂×Q₈×C₇₃	—	4	2	no	—
101	C₂×Q₈×C₇₃	—	4	2	no	—
102	C₂×Q₈×C₇₃	—	4	2	no	—
103	C₂×D₄×C₇₃	—	2	4	no	—
104	C₂×D₄×C₇₃	—	2	1	no	—
105	C₂×D₄×C₇₃	—	2	1	no	—
106	C₂×D₄×C₇₃	—	2	1	no	—
107	C₂×D₄×C₇₃	—	2	1	no	—
108	C₂×D₄×C₇₃	—	2	1	no	—
109	C₂×D₄×C₇₃	—	4	2	no	—
110	C₂×D₄×C₇₃	—	4	2	no	—
111	C₂×D₄×C₇₃	#41	1	2	yes	—
112	C₂²×C₄×C₇₃	—	2	2	no	—
113	C₂²×C₄×C₇₃	—	2	1	no	—
114	C₂²×C₄×C₇₃	—	2	2	no	—
115	C₂²×C₄×C₇₃	—	2	2	no	—
116	C₂²×C₄×C₇₃	—	2	2	no	—
117	C₂²×C₄×C₇₃	—	2	2	no	—
118	C₂²×C₄×C₇₃	—	2	1	no	—
119	C₂²×C₄×C₇₃	—	2	1	no	—
120	C₂²×C₄×C₇₃	—	2	1	no	—
121	C₂²×C₄×C₇₃	—	2	1	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	—	2	1	no	—
126	C₂²×C₄×C₇₃	—	2	2	no	—
127	C₂²×C₄×C₇₃	—	2	2	no	—
128	C₂²×C₄×C₇₃	—	4	1	no	—
129	C₂²×C₄×C₇₃	—	4	2	no	—
130	C₂²×C₄×C₇₃	—	4	2	no	—
131	C₂²×C₄×C₇₃	—	4	2	no	—
132	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
138	C₂×C₈×C₇₃	—	2	2	no	—
139	C₂×C₈×C₇₃	—	2	2	no	—
140	C₂×C₈×C₇₃	—	2	2	no	—
141	C₂×C₈×C₇₃	—	2	2	no	—
142	C₂×C₈×C₇₃	—	2	2	no	—
143	C₂×C₈×C₇₃	C₂×D₄	1	4	yes	—
144	C₄⋊C₄×C₇₃	—	2	1	no	—
145	C₄⋊C₄×C₇₃	—	2	2	no	—
146	C₄⋊C₄×C₇₃	—	2	1	no	—
147	C₄⋊C₄×C₇₃	—	2	2	no	—
148	C₄⋊C₄×C₇₃	—	2	2	no	—
149	C₄⋊C₄×C₇₃	—	2	1	no	—
150	C₄⋊C₄×C₇₃	—	2	2	no	—
151	C₄⋊C₄×C₇₃	—	2	1	no	—
152	C₄⋊C₄×C₇₃	—	2	1	no	—
153	C₄⋊C₄×C₇₃	—	4	2	no	—
154	C₄⋊C₄×C₇₃	—	4	2	no	—
155	C₄⋊C₄×C₇₃	—	4	4	no	—
156	C₄⋊C₄×C₇₃	—	4	2	no	—
157	C₄⋊C₄×C₇₃	—	4	2	no	—
158	C₄⋊C₄×C₇₃	#41	1	2	yes	—
159	C₂²⋊C₄×C₇₃	—	2	4	no	—
160	C₂²⋊C₄×C₇₃	—	4	2	no	—
161	C₂²⋊C₄×C₇₃	—	4	2	no	—
162	C₂²⋊C₄×C₇₃	—	4	2	no	—
163	C₂²⋊C₄×C₇₃	—	4	4	no	—
164	C₂²⋊C₄×C₇₃	—	4	2	no	—
165	C₄²×C₇₃	—	2	2	no	—
166	C₄²×C₇₃	—	2	2	no	—
167	C₄²×C₇₃	—	2	1	no	—
168	C₄²×C₇₃	—	2	1	no	—
169	C₄²×C₇₃	—	4	2	no	—
170	C₄²×C₇₃	C₂×D₄	1	2	yes	—
171	C₄²×C₇₃	#41	1	2	yes	—
172	C₂³×C₇₃	—	2	1	no	—
173	C₂³×C₇₃	—	2	1	no	—
174	C₂³×C₇₃	—	2	1	no	—
175	C₂³×C₇₃	—	2	1	no	—
176	C₂³×C₇₃	—	2	1	no	—
177	C₂³×C₇₃	—	2	1	no	—
178	C₂³×C₇₃	—	2	2	no	—
179	C₂³×C₇₃	—	4	1	no	—
180	C₂³×C₇₃	—	4	1	no	—
181	C₂³×C₇₃	—	4	1	no	—
182	C₂³×C₇₃	—	4	1	no	—
183	C₂³×C₇₃	—	4	1	no	—
184	C₂³×C₇₃	—	4	1	no	—
185	C₂³×C₇₃	AGL(1,ℤ/8)	1	2	yes	—
186	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
187	Q₈×C₇₃	—	8	4	no	—
188	D₄×C₇₃	—	2	2	no	—
189	D₄×C₇₃	—	2	2	no	—
190	D₄×C₇₃	—	4	8	no	—
191	D₄×C₇₃	—	4	1	no	—
192	D₄×C₇₃	—	4	1	no	—
193	C₂×C₄×C₇₃	—	2	1	no	—
194	C₂×C₄×C₇₃	—	2	1	no	—
195	C₂×C₄×C₇₃	—	2	1	no	—
196	C₂×C₄×C₇₃	—	2	1	no	—
197	C₂×C₄×C₇₃	—	2	1	no	—
198	C₂×C₄×C₇₃	—	2	1	no	—
199	C₂×C₄×C₇₃	—	2	2	no	—
200	C₂×C₄×C₇₃	—	2	1	no	—
201	C₂×C₄×C₇₃	—	2	1	no	—
202	C₂×C₄×C₇₃	—	2	1	no	—
203	C₂×C₄×C₇₃	—	2	1	no	—
204	C₂×C₄×C₇₃	—	2	1	no	—
205	C₂×C₄×C₇₃	—	4	4	no	—
206	C₂×C₄×C₇₃	—	4	1	no	—
207	C₂×C₄×C₇₃	—	4	1	no	—
208	C₂×C₄×C₇₃	—	4	1	no	—
209	C₂×C₄×C₇₃	—	4	1	no	—
210	C₂×C₄×C₇₃	—	4	1	no	—
211	C₂×C₄×C₇₃	—	4	1	no	—
212	C₂×C₄×C₇₃	—	4	4	no	—
213	C₂×C₄×C₇₃	—	4	1	no	—
214	C₂×C₄×C₇₃	—	4	2	no	—
215	C₂×C₄×C₇₃	—	4	2	no	—
216	C₂×C₄×C₇₃	—	4	1	no	—
217	C₂×C₄×C₇₃	—	4	1	no	—
218	C₂×C₄×C₇₃	—	4	2	no	—
219	C₂×C₄×C₇₃	—	4	1	no	—
220	C₂×C₄×C₇₃	—	4	2	no	—
221	C₂×C₄×C₇₃	—	4	2	no	—
222	C₂×C₄×C₇₃	—	4	1	no	—
223	C₂×C₄×C₇₃	—	4	1	no	—
224	C₂×C₄×C₇₃	—	4	2	no	—
225	C₂×C₄×C₇₃	—	8	4	no	—
226	C₂×C₄×C₇₃	#121	1	2	yes	—
227	C₂×C₄×C₇₃	#121	1	2	yes	—
228	C₂×C₄×C₇₃	AGL(1,ℤ/8)	1	2	yes	—
229	C₂×C₄×C₇₃	#137	1	2	yes	—
230	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
231	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
232	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
233	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
234	C₂×C₄×C₇₃	2₋¹⁺⁴	1	1	yes	characteristic
235	C₂×C₄×C₇₃	2₋¹⁺⁴	1	1	yes	characteristic
236	C₈×C₇₃	—	2	4	no	—
237	C₈×C₇₃	—	4	2	no	—
238	C₂²×C₇₃	—	2	2	no	—
239	C₂²×C₇₃	—	2	2	no	—
240	C₂²×C₇₃	—	2	2	no	—
241	C₂²×C₇₃	—	4	1	no	—
242	C₂²×C₇₃	—	4	1	no	—
243	C₂²×C₇₃	—	4	1	no	—
244	C₂²×C₇₃	—	4	1	no	—
245	C₂²×C₇₃	—	4	2	no	—
246	C₂²×C₇₃	—	4	2	no	—
247	C₂²×C₇₃	—	4	2	no	—
248	C₂²×C₇₃	—	8	1	no	—
249	C₂²×C₇₃	—	8	1	no	—
250	C₂²×C₇₃	—	8	1	no	—
251	C₂²×C₇₃	—	8	1	no	—
252	C₂²×C₇₃	C₂×#121	1	1	yes	characteristic
253	C₂²×C₇₃	#525	1	1	yes	characteristic
254	C₂²×C₇₃	#536	1	1	yes	characteristic
255	C₂²×C₇₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
256	C₂²×C₇₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
257	C₂²×C₇₃	C₂×#137	1	1	yes	characteristic
258	C₂²×C₇₃	#575	1	1	yes	characteristic
259	C₄×C₇₃	—	2	2	no	—
260	C₄×C₇₃	—	4	2	no	—
261	C₄×C₇₃	—	4	1	no	—
262	C₄×C₇₃	—	4	1	no	—
263	C₄×C₇₃	—	4	1	no	—
264	C₄×C₇₃	—	8	2	no	—
265	C₄×C₇₃	—	8	1	no	—
266	C₄×C₇₃	—	8	1	no	—
267	C₄×C₇₃	—	8	2	no	—
268	C₄×C₇₃	#468	1	4	yes	—
269	C₄×C₇₃	#547	1	1	yes	characteristic
270	C₄×C₇₃	#548	1	1	yes	characteristic
271	C₄×C₇₃	#552	1	1	yes	characteristic
272	C₄×C₇₃	#556	1	1	yes	characteristic
273	#24708	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
274	C₂×C₇₃	—	4	2	no	—
275	C₂×C₇₃	—	8	2	no	—
276	C₂×C₇₃	#2415	1	1	yes	characteristic
277	C₂×C₇₃	C₂×#468	1	1	yes	characteristic
278	C₂×C₇₃	#3055	1	1	yes	characteristic
279	C₂×C₇₃	#3109	1	1	yes	characteristic
280	C₂×C₇₃	#3116	1	1	yes	characteristic
281	C₂×C₇₃	#3235	1	1	yes	characteristic
282	C₂×C₇₃	#3238	1	1	yes	characteristic
283	C₂×#476	C₂×C₇₃	1	1	yes	characteristic, complemented
284	C₂×#432	C₂×C₇₃	1	1	yes	characteristic, complemented
285	#2857	C₂×C₇₃	1	1	yes	characteristic, complemented
286	C₄×#121	C₂×C₇₃	1	1	yes	characteristic
287	#2077	C₂×C₇₃	1	2	yes	complemented
288	#2033	C₂×C₇₃	1	2	yes	—
289	#1987	C₂×C₇₃	1	1	yes	characteristic, complemented
290	#1947	C₂×C₇₃	1	1	yes	characteristic, complemented
291	#1943	C₂×C₇₃	1	2	yes	complemented
292	#1936	C₂×C₇₃	1	2	yes	complemented
293	#1802	C₂×C₇₃	1	1	yes	characteristic, complemented
294	C₇₃	#24708	1	1	yes	characteristic, direct product factor, Sylow
295	C₂×C₄⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
296	C₂×C₂²⋊Q₈	—	2	1	no	—
297	C₂×#121	C₂²×C₇₃	1	1	yes	characteristic
298	C₂×C₄×D₄	—	2	1	no	—
299	C₂×C₄×D₄	C₂²×C₇₃	1	1	yes	characteristic
300	C₂²×C₄²	C₂²×C₇₃	1	1	yes	characteristic
301	#476	—	2	4	no	—
302	#432	—	2	4	no	—
303	C₂×#107	C₂²×C₇₃	1	2	yes	—
304	C₂×#106	C₂²×C₇₃	1	2	yes	—
305	C₂×C₄⋊C₈	C₂²×C₇₃	1	1	yes	characteristic
306	C₂×C₄⋊C₈	C₂²×C₇₃	1	1	yes	characteristic
307	C₂×#102	C₂²×C₇₃	1	2	yes	—
308	C₂×#102	C₂²×C₇₃	1	2	yes	—
309	C₂×C₂²⋊C₈	C₂²×C₇₃	1	2	yes	—
310	C₂×#97	C₂²×C₇₃	1	2	yes	—
311	#391	—	2	1	no	—
312	#390	C₂²×C₇₃	1	1	yes	characteristic
313	#389	—	2	1	no	—
314	#389	C₂²×C₇₃	1	2	yes	—
315	#389	C₂²×C₇₃	1	1	yes	characteristic
316	#388	—	2	1	no	—
317	#386	—	2	1	no	—
318	#384	C₂²×C₇₃	1	1	yes	characteristic
319	#380	—	2	1	no	—
320	#380	C₂²×C₇₃	1	1	yes	characteristic
321	#380	C₂²×C₇₃	1	2	yes	—
322	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
323	C₄×C₂²⋊C₄	—	2	1	no	—
324	#340	C₂²×C₇₃	1	2	yes	—
325	#340	C₂²×C₇₃	1	2	yes	—
326	#340	C₂²×C₇₃	1	2	yes	—
327	#340	C₂²×C₇₃	1	2	yes	—
328	C₂²×Q₈	—	2	1	no	—
329	C₂²×D₄	—	2	1	no	—
330	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
331	C₂³×C₄	—	2	1	no	—
332	C₂³×C₄	D₄×C₇₃	1	1	yes	characteristic
333	C₂³×C₄	D₄×C₇₃	1	1	yes	characteristic
334	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
335	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
336	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
337	C₄⋊Q₈	—	2	2	no	—
338	C₄⋊Q₈	—	2	2	no	—
339	C₂²⋊Q₈	—	4	4	no	—
340	#121	—	2	2	no	—
341	#121	—	2	2	no	—
342	C₄×D₄	—	2	2	no	—
343	C₄×D₄	—	2	2	no	—
344	C₄×D₄	—	4	4	no	—
345	C₂×C₄⋊C₄	—	2	1	no	—
346	C₂×C₄⋊C₄	—	2	1	no	—
347	C₂×C₄⋊C₄	—	2	2	no	—
348	C₂×C₄⋊C₄	—	2	1	no	—
349	C₂×C₄⋊C₄	—	2	1	no	—
350	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
351	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
352	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
353	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
354	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
355	C₂×C₂²⋊C₄	—	2	1	no	—
356	C₂×C₂²⋊C₄	—	2	1	no	—
357	C₂×C₂²⋊C₄	—	2	2	no	—
358	C₂×C₂²⋊C₄	—	2	1	no	—
359	C₂×C₂²⋊C₄	—	2	1	no	—
360	C₂×C₂²⋊C₄	—	2	1	no	—
361	C₂×C₄²	—	2	2	no	—
362	C₂×C₄²	—	2	2	no	—
363	C₂×C₄²	—	2	1	no	—
364	C₂×C₄²	D₄×C₇₃	1	1	yes	characteristic
365	C₂×C₄²	D₄×C₇₃	1	1	yes	characteristic
366	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
367	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
368	#107	—	2	4	no	—
369	#106	—	2	4	no	—
370	C₄⋊C₈	—	2	2	no	—
371	C₄⋊C₈	D₄×C₇₃	1	4	yes	complemented
372	#102	—	2	4	no	—
373	#102	—	2	4	no	—
374	C₂²⋊C₈	—	2	4	no	—
375	#97	—	2	4	no	—
376	#95	—	2	1	no	—
377	#95	—	2	1	no	—
378	#95	—	2	1	no	—
379	#95	—	2	2	no	—
380	#95	—	2	2	no	—
381	C₂⁴	—	2	1	no	—
382	C₂⁴	C₂×D₄×C₇₃	1	1	yes	characteristic
383	C₂×Q₈	—	4	2	no	—
384	C₂×Q₈	—	4	2	no	—
385	C₂×Q₈	—	4	2	no	—
386	C₂×D₄	—	2	4	no	—
387	C₂×D₄	—	2	1	no	—
388	C₂×D₄	—	2	1	no	—
389	C₂×D₄	—	2	1	no	—
390	C₂×D₄	—	2	1	no	—
391	C₂×D₄	—	2	1	no	—
392	C₂×D₄	—	4	2	no	—
393	C₂×D₄	—	4	2	no	—
394	C₂×D₄	#41×C₇₃	1	2	yes	—
395	C₂²×C₄	—	2	2	no	—
396	C₂²×C₄	—	2	1	no	—
397	C₂²×C₄	—	2	2	no	—
398	C₂²×C₄	—	2	2	no	—
399	C₂²×C₄	—	2	2	no	—
400	C₂²×C₄	—	2	2	no	—
401	C₂²×C₄	—	2	1	no	—
402	C₂²×C₄	—	2	1	no	—
403	C₂²×C₄	—	2	1	no	—
404	C₂²×C₄	—	2	1	no	—
405	C₂²×C₄	—	2	1	no	—
406	C₂²×C₄	—	2	1	no	—
407	C₂²×C₄	—	2	1	no	—
408	C₂²×C₄	—	2	1	no	—
409	C₂²×C₄	—	2	2	no	—
410	C₂²×C₄	—	2	2	no	—
411	C₂²×C₄	—	4	1	no	—
412	C₂²×C₄	—	4	2	no	—
413	C₂²×C₄	—	4	2	no	—
414	C₂²×C₄	—	4	2	no	—
415	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
416	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
417	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
418	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
419	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
420	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
421	C₂×C₈	—	2	2	no	—
422	C₂×C₈	—	2	2	no	—
423	C₂×C₈	—	2	2	no	—
424	C₂×C₈	—	2	2	no	—
425	C₂×C₈	—	2	2	no	—
426	C₂×C₈	C₂×D₄×C₇₃	1	4	yes	—
427	C₄⋊C₄	—	2	1	no	—
428	C₄⋊C₄	—	2	2	no	—
429	C₄⋊C₄	—	2	1	no	—
430	C₄⋊C₄	—	2	2	no	—
431	C₄⋊C₄	—	2	2	no	—
432	C₄⋊C₄	—	2	1	no	—
433	C₄⋊C₄	—	2	2	no	—
434	C₄⋊C₄	—	2	1	no	—
435	C₄⋊C₄	—	2	1	no	—
436	C₄⋊C₄	—	4	2	no	—
437	C₄⋊C₄	—	4	2	no	—
438	C₄⋊C₄	—	4	4	no	—
439	C₄⋊C₄	—	4	2	no	—
440	C₄⋊C₄	—	4	2	no	—
441	C₄⋊C₄	#41×C₇₃	1	2	yes	—
442	C₂²⋊C₄	—	2	4	no	—
443	C₂²⋊C₄	—	4	2	no	—
444	C₂²⋊C₄	—	4	2	no	—
445	C₂²⋊C₄	—	4	2	no	—
446	C₂²⋊C₄	—	4	4	no	—
447	C₂²⋊C₄	—	4	2	no	—
448	C₄²	—	2	2	no	—
449	C₄²	—	2	2	no	—
450	C₄²	—	2	1	no	—
451	C₄²	—	2	1	no	—
452	C₄²	—	4	2	no	—
453	C₄²	C₂×D₄×C₇₃	1	2	yes	—
454	C₄²	#41×C₇₃	1	2	yes	—
455	C₂³	—	2	1	no	—
456	C₂³	—	2	1	no	—
457	C₂³	—	2	1	no	—
458	C₂³	—	2	1	no	—
459	C₂³	—	2	1	no	—
460	C₂³	—	2	1	no	—
461	C₂³	—	2	2	no	—
462	C₂³	—	4	1	no	—
463	C₂³	—	4	1	no	—
464	C₂³	—	4	1	no	—
465	C₂³	—	4	1	no	—
466	C₂³	—	4	1	no	—
467	C₂³	—	4	1	no	—
468	C₂³	AGL(1,ℤ/8)×C₇₃	1	2	yes	—
469	C₂³	C₂²×D₄×C₇₃	1	1	yes	characteristic
470	Q₈	—	8	4	no	—
471	D₄	—	2	2	no	—
472	D₄	—	2	2	no	—
473	D₄	—	4	8	no	—
474	D₄	—	4	1	no	—
475	D₄	—	4	1	no	—
476	C₂×C₄	—	2	1	no	—
477	C₂×C₄	—	2	1	no	—
478	C₂×C₄	—	2	1	no	—
479	C₂×C₄	—	2	1	no	—
480	C₂×C₄	—	2	1	no	—
481	C₂×C₄	—	2	1	no	—
482	C₂×C₄	—	2	2	no	—
483	C₂×C₄	—	2	1	no	—
484	C₂×C₄	—	2	1	no	—
485	C₂×C₄	—	2	1	no	—
486	C₂×C₄	—	2	1	no	—
487	C₂×C₄	—	2	1	no	—
488	C₂×C₄	—	4	4	no	—
489	C₂×C₄	—	4	1	no	—
490	C₂×C₄	—	4	1	no	—
491	C₂×C₄	—	4	4	no	—
492	C₂×C₄	—	4	1	no	—
493	C₂×C₄	—	4	1	no	—
494	C₂×C₄	—	4	1	no	—
495	C₂×C₄	—	4	1	no	—
496	C₂×C₄	—	4	1	no	—
497	C₂×C₄	—	4	2	no	—
498	C₂×C₄	—	4	2	no	—
499	C₂×C₄	—	4	1	no	—
500	C₂×C₄	—	4	1	no	—
501	C₂×C₄	—	4	2	no	—
502	C₂×C₄	—	4	1	no	—
503	C₂×C₄	—	4	2	no	—
504	C₂×C₄	—	4	2	no	—
505	C₂×C₄	—	4	1	no	—
506	C₂×C₄	—	4	1	no	—
507	C₂×C₄	—	4	2	no	—
508	C₂×C₄	—	8	4	no	—
509	C₂×C₄	#121×C₇₃	1	2	yes	—
510	C₂×C₄	#121×C₇₃	1	2	yes	—
511	C₂×C₄	AGL(1,ℤ/8)×C₇₃	1	2	yes	—
512	C₂×C₄	#137×C₇₃	1	2	yes	—
513	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
514	C₂×C₄	C₂×#41×C₇₃	1	1	yes	characteristic
515	C₂×C₄	C₂×#41×C₇₃	1	1	yes	characteristic
516	C₂×C₄	C₂×#41×C₇₃	1	1	yes	characteristic
517	C₂×C₄	2₋¹⁺⁴×C₇₃	1	1	yes	characteristic
518	C₂×C₄	2₋¹⁺⁴×C₇₃	1	1	yes	characteristic
519	C₈	—	2	4	no	—
520	C₈	—	4	2	no	—
521	C₂²	—	2	2	no	—
522	C₂²	—	2	2	no	—
523	C₂²	—	2	2	no	—
524	C₂²	—	4	1	no	—
525	C₂²	—	4	1	no	—
526	C₂²	—	4	1	no	—
527	C₂²	—	4	1	no	—
528	C₂²	—	4	2	no	—
529	C₂²	—	4	2	no	—
530	C₂²	—	4	2	no	—
531	C₂²	—	8	1	no	—
532	C₂²	—	8	1	no	—
533	C₂²	—	8	1	no	—
534	C₂²	—	8	1	no	—
535	C₂²	C₂×#121×C₇₃	1	1	yes	characteristic
536	C₂²	#525×C₇₃	1	1	yes	characteristic
537	C₂²	#536×C₇₃	1	1	yes	characteristic
538	C₂²	C₂×AGL(1,ℤ/8)×C₇₃	1	1	yes	characteristic
539	C₂²	C₂×AGL(1,ℤ/8)×C₇₃	1	1	yes	characteristic
540	C₂²	C₂×#137×C₇₃	1	1	yes	characteristic
541	C₂²	#575×C₇₃	1	1	yes	characteristic
542	C₄	—	2	2	no	—
543	C₄	—	4	1	no	—
544	C₄	—	4	1	no	—
545	C₄	—	4	2	no	—
546	C₄	—	4	1	no	—
547	C₄	—	8	1	no	—
548	C₄	—	8	1	no	—
549	C₄	—	8	2	no	—
550	C₄	—	8	2	no	—
551	C₄	#468×C₇₃	1	4	yes	—
552	C₄	#547×C₇₃	1	1	yes	characteristic
553	C₄	#548×C₇₃	1	1	yes	characteristic
554	C₄	#552×C₇₃	1	1	yes	characteristic
555	C₄	#556×C₇₃	1	1	yes	characteristic
556	C₂	—	4	2	no	—
557	C₂	—	8	2	no	—
558	C₂	C₇₃×#2415	1	1	yes	characteristic
559	C₂	C₂×#468×C₇₃	1	1	yes	characteristic
560	C₂	C₇₃×#3055	1	1	yes	characteristic
561	C₂	C₇₃×#3109	1	1	yes	characteristic
562	C₂	C₇₃×#3116	1	1	yes	characteristic
563	C₂	C₇₃×#3235	1	1	yes	characteristic
564	C₂	C₇₃×#3238	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₃
prime radical	C₂×#121×C₇₃	C₂²
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. C₂×#476×C₇₃	C₂	semidirect
2. C₂×#432×C₇₃	C₂	semidirect
3. C₇₃×#2857	C₂	semidirect
5. C₇₃×#2077	C₂	semidirect
7. C₇₃×#1987	C₂	semidirect
8. C₇₃×#1947	C₂	semidirect
9. C₇₃×#1943	C₂	semidirect
10. C₇₃×#1936	C₂	semidirect
11. C₇₃×#1802	C₂	semidirect
88. C₄⋊C₈×C₇₃	D₄	semidirect
273. #24708	C₇₃	direct (N × H)
283. C₂×#476	C₂×C₇₃	semidirect
284. C₂×#432	C₂×C₇₃	semidirect
285. #2857	C₂×C₇₃	semidirect
287. #2077	C₂×C₇₃	semidirect
289. #1987	C₂×C₇₃	semidirect
290. #1947	C₂×C₇₃	semidirect
291. #1943	C₂×C₇₃	semidirect
292. #1936	C₂×C₇₃	semidirect
293. #1802	C₂×C₇₃	semidirect
294. C₇₃	#24708	direct (N × H)
371. C₄⋊C₈	D₄×C₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#476×C₇₃	2
C₂×#432×C₇₃	2
C₇₃×#2857	2
C₄×#121×C₇₃	2
C₇₃×#2077	2
C₇₃×#2033	2
C₇₃×#1987	2
C₇₃×#1947	2
C₇₃×#1943	2
C₇₃×#1936	2
C₇₃×#1802	2
#24708	73

Subgroups — C73×#24708 #32934112

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#24708 #32934112