Subgroups — C₇₃×#24357 #32933761

Order 18688.

1526 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×SD₁₆×C₇₃	C₂	1	1	yes	maximal, characteristic
2	C₂×#464×C₇₃	C₂	1	2	yes	maximal, complemented
3	C₂×#451×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₃×#2435	C₂	1	1	yes	maximal, characteristic
5	Q₈×C₂²⋊C₄×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇₃×#2055	C₂	1	2	yes	maximal, complemented
7	C₇₃×#2015	C₂	1	2	yes	maximal, complemented
8	C₇₃×#1892	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇₃×#1880	C₂	1	2	yes	maximal, complemented
10	C₇₃×#1850	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₃×#1786	C₂	1	1	yes	maximal, characteristic
12	C₂³×Q₈×C₇₃	C₂²	1	1	yes	characteristic
13	C₂³×D₄×C₇₃	C₂²	1	1	yes	characteristic
14	C₂²×Q₁₆×C₇₃	C₂²	1	1	yes	characteristic, complemented
15	C₂²×Q₁₆×C₇₃	C₂²	1	1	yes	characteristic, complemented
16	C₂²×SD₁₆×C₇₃	—	2	4	no	—
17	C₂²×SD₁₆×C₇₃	—	2	8	no	—
18	C₂²×SD₁₆×C₇₃	C₂²	1	2	yes	—
19	C₂²×SD₁₆×C₇₃	C₂²	1	2	yes	—
20	C₂³×C₈×C₇₃	C₂²	1	1	yes	characteristic
21	C₂×#124×C₇₃	C₂²	1	2	yes	—
22	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
23	C₂×C₄×Q₈×C₇₃	C₂²	1	2	yes	complemented
24	#464×C₇₃	—	2	8	no	—
25	#451×C₇₃	—	2	4	no	—
26	C₂×C₄⋊C₈×C₇₃	C₂²	1	2	yes	complemented
27	C₂×#103×C₇₃	C₂²	1	1	yes	characteristic, complemented
28	C₂×#103×C₇₃	C₂²	1	1	yes	characteristic, complemented
29	C₂×#103×C₇₃	C₂²	1	2	yes	complemented
30	C₂×#102×C₇₃	C₂²	1	2	yes	—
31	C₂×#102×C₇₃	C₂²	1	2	yes	—
32	C₂×C₂²⋊C₈×C₇₃	C₂²	1	1	yes	characteristic
33	#394×C₇₃	—	2	2	no	—
34	#391×C₇₃	—	2	2	no	—
35	#391×C₇₃	C₂²	1	2	yes	complemented
36	#390×C₇₃	C₂²	1	2	yes	—
37	#380×C₇₃	—	2	1	no	—
38	#380×C₇₃	C₂²	1	1	yes	characteristic
39	#379×C₇₃	—	2	1	no	—
40	#379×C₇₃	—	2	1	no	—
41	C₄×C₂²⋊C₄×C₇₃	—	2	1	no	—
42	C₄×C₂²⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
43	#340×C₇₃	C₂²	1	2	yes	complemented
44	#336×C₇₃	C₂²	1	2	yes	complemented
45	C₂⁵×C₇₃	—	2	1	no	—
46	C₂²×Q₈×C₇₃	—	2	1	no	—
47	C₂²×Q₈×C₇₃	—	2	2	no	—
48	C₂²×Q₈×C₇₃	—	2	4	no	—
49	C₂²×Q₈×C₇₃	—	4	2	no	—
50	C₂²×Q₈×C₇₃	D₄	1	4	yes	—
51	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
52	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
53	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
54	C₂²×D₄×C₇₃	—	2	4	no	—
55	C₂²×D₄×C₇₃	—	2	2	no	—
56	C₂²×D₄×C₇₃	—	2	1	no	—
57	C₂²×D₄×C₇₃	—	2	2	no	—
58	C₂²×D₄×C₇₃	—	4	2	no	—
59	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
60	C₂³×C₄×C₇₃	—	2	1	no	—
61	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
62	C₂×Q₁₆×C₇₃	—	2	2	no	—
63	C₂×Q₁₆×C₇₃	—	2	2	no	—
64	C₂×Q₁₆×C₇₃	—	2	4	no	—
65	C₂×Q₁₆×C₇₃	—	4	2	no	—
66	C₂×SD₁₆×C₇₃	—	2	32	no	—
67	C₂×SD₁₆×C₇₃	—	2	4	no	—
68	C₂×SD₁₆×C₇₃	—	2	4	no	—
69	C₂×SD₁₆×C₇₃	—	2	4	no	—
70	C₂×SD₁₆×C₇₃	—	2	4	no	—
71	C₂×SD₁₆×C₇₃	—	2	4	no	—
72	C₂×SD₁₆×C₇₃	D₄	1	8	yes	—
73	C₂²×C₈×C₇₃	—	2	2	no	—
74	C₂²×C₈×C₇₃	—	2	4	no	—
75	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
76	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
77	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
78	#124×C₇₃	—	2	4	no	—
79	#124×C₇₃	—	4	2	no	—
80	C₂²⋊Q₈×C₇₃	—	2	2	no	—
81	C₂²⋊Q₈×C₇₃	—	2	2	no	—
82	C₄×Q₈×C₇₃	—	2	4	no	—
83	C₄×Q₈×C₇₃	—	4	2	no	—
84	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
85	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
86	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
87	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
88	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
89	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
90	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
91	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
92	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
93	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
94	C₂×C₂²⋊C₄×C₇₃	D₄	1	1	yes	characteristic
95	C₂×C₂²⋊C₄×C₇₃	D₄	1	1	yes	characteristic
96	C₂×C₄²×C₇₃	—	2	2	no	—
97	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
98	C₄⋊C₈×C₇₃	—	2	4	no	—
99	#103×C₇₃	—	2	2	no	—
100	#103×C₇₃	—	2	2	no	—
101	#103×C₇₃	—	2	4	no	—
102	#102×C₇₃	—	2	4	no	—
103	#102×C₇₃	—	4	2	no	—
104	C₂²⋊C₈×C₇₃	—	2	2	no	—
105	#95×C₇₃	—	2	2	no	—
106	#95×C₇₃	—	2	2	no	—
107	#95×C₇₃	—	2	1	no	—
108	#95×C₇₃	D₄	1	2	yes	—
109	C₂⁴×C₇₃	—	2	2	no	—
110	C₂⁴×C₇₃	—	4	4	no	—
111	C₂⁴×C₇₃	—	4	2	no	—
112	C₂⁴×C₇₃	—	4	2	no	—
113	C₂⁴×C₇₃	—	4	2	no	—
114	C₂⁴×C₇₃	—	8	2	no	—
115	C₂⁴×C₇₃	C₂×D₄	1	1	yes	characteristic
116	C₂×Q₈×C₇₃	—	2	4	no	—
117	C₂×Q₈×C₇₃	—	2	1	no	—
118	C₂×Q₈×C₇₃	—	2	1	no	—
119	C₂×Q₈×C₇₃	—	2	2	no	—
120	C₂×Q₈×C₇₃	—	2	8	no	—
121	C₂×Q₈×C₇₃	—	2	2	no	—
122	C₂×Q₈×C₇₃	—	2	2	no	—
123	C₂×Q₈×C₇₃	—	2	1	no	—
124	C₂×Q₈×C₇₃	—	2	1	no	—
125	C₂×Q₈×C₇₃	—	2	2	no	—
126	C₂×Q₈×C₇₃	—	2	2	no	—
127	C₂×Q₈×C₇₃	—	4	4	no	—
128	C₂×Q₈×C₇₃	—	4	4	no	—
129	C₂×Q₈×C₇₃	—	4	8	no	—
130	C₂×Q₈×C₇₃	C₂×D₄	1	2	yes	—
131	C₂×Q₈×C₇₃	C₂×D₄	1	2	yes	—
132	C₂×Q₈×C₇₃	C₂×D₄	1	4	yes	—
133	C₂×D₄×C₇₃	—	2	8	no	—
134	C₂×D₄×C₇₃	—	2	2	no	—
135	C₂×D₄×C₇₃	—	2	2	no	—
136	C₂×D₄×C₇₃	—	2	2	no	—
137	C₂×D₄×C₇₃	—	2	2	no	—
138	C₂×D₄×C₇₃	—	2	2	no	—
139	C₂×D₄×C₇₃	—	4	8	no	—
140	C₂×D₄×C₇₃	—	4	4	no	—
141	C₂×D₄×C₇₃	—	4	4	no	—
142	C₂×D₄×C₇₃	—	4	2	no	—
143	C₂×D₄×C₇₃	C₂×D₄	1	4	yes	—
144	C₂²×C₄×C₇₃	—	2	1	no	—
145	C₂²×C₄×C₇₃	—	2	2	no	—
146	C₂²×C₄×C₇₃	—	2	2	no	—
147	C₂²×C₄×C₇₃	—	2	4	no	—
148	C₂²×C₄×C₇₃	—	2	1	no	—
149	C₂²×C₄×C₇₃	—	2	2	no	—
150	C₂²×C₄×C₇₃	—	2	1	no	—
151	C₂²×C₄×C₇₃	—	2	1	no	—
152	C₂²×C₄×C₇₃	—	4	4	no	—
153	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
154	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
155	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
156	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
157	C₂²×C₄×C₇₃	#41	1	2	yes	—
158	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
159	Q₁₆×C₇₃	—	4	4	no	—
160	Q₁₆×C₇₃	—	4	4	no	—
161	SD₁₆×C₇₃	—	2	16	no	—
162	SD₁₆×C₇₃	—	2	16	no	—
163	C₂×C₈×C₇₃	—	2	8	no	—
164	C₂×C₈×C₇₃	—	2	2	no	—
165	C₂×C₈×C₇₃	—	2	2	no	—
166	C₂×C₈×C₇₃	—	2	1	no	—
167	C₂×C₈×C₇₃	—	2	1	no	—
168	C₂×C₈×C₇₃	—	2	2	no	—
169	C₂×C₈×C₇₃	—	2	2	no	—
170	C₂×C₈×C₇₃	C₂×D₄	1	4	yes	—
171	C₄⋊C₄×C₇₃	—	2	2	no	—
172	C₄⋊C₄×C₇₃	—	2	1	no	—
173	C₄⋊C₄×C₇₃	—	2	1	no	—
174	C₄⋊C₄×C₇₃	—	2	2	no	—
175	C₄⋊C₄×C₇₃	—	4	4	no	—
176	C₄⋊C₄×C₇₃	—	4	2	no	—
177	C₂²⋊C₄×C₇₃	—	2	2	no	—
178	C₂²⋊C₄×C₇₃	—	2	2	no	—
179	C₂²⋊C₄×C₇₃	—	4	4	no	—
180	C₂²⋊C₄×C₇₃	—	4	4	no	—
181	C₂²⋊C₄×C₇₃	—	4	2	no	—
182	C₂²⋊C₄×C₇₃	—	4	2	no	—
183	C₂²⋊C₄×C₇₃	—	8	2	no	—
184	C₂²⋊C₄×C₇₃	—	8	2	no	—
185	C₄²×C₇₃	—	2	2	no	—
186	C₄²×C₇₃	—	2	2	no	—
187	C₄²×C₇₃	—	4	4	no	—
188	C₂³×C₇₃	—	2	2	no	—
189	C₂³×C₇₃	—	2	2	no	—
190	C₂³×C₇₃	—	2	4	no	—
191	C₂³×C₇₃	—	4	8	no	—
192	C₂³×C₇₃	—	4	2	no	—
193	C₂³×C₇₃	—	4	2	no	—
194	C₂³×C₇₃	—	4	2	no	—
195	C₂³×C₇₃	—	4	2	no	—
196	C₂³×C₇₃	—	4	2	no	—
197	C₂³×C₇₃	—	4	2	no	—
198	C₂³×C₇₃	—	8	8	no	—
199	C₂³×C₇₃	—	8	8	no	—
200	C₂³×C₇₃	—	8	4	no	—
201	C₂³×C₇₃	—	8	4	no	—
202	C₂³×C₇₃	#121	1	2	yes	—
203	C₂³×C₇₃	#135	1	2	yes	—
204	C₂³×C₇₃	#137	1	2	yes	—
205	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
206	Q₈×C₇₃	—	2	2	no	—
207	Q₈×C₇₃	—	2	4	no	—
208	Q₈×C₇₃	—	2	2	no	—
209	Q₈×C₇₃	—	2	2	no	—
210	Q₈×C₇₃	—	4	8	no	—
211	Q₈×C₇₃	—	4	2	no	—
212	Q₈×C₇₃	—	4	1	no	—
213	Q₈×C₇₃	—	4	1	no	—
214	Q₈×C₇₃	—	4	2	no	—
215	Q₈×C₇₃	#120	1	4	yes	—
216	D₄×C₇₃	—	2	4	no	—
217	D₄×C₇₃	—	2	4	no	—
218	D₄×C₇₃	—	4	8	no	—
219	D₄×C₇₃	—	4	2	no	—
220	D₄×C₇₃	—	4	2	no	—
221	C₂×C₄×C₇₃	—	2	2	no	—
222	C₂×C₄×C₇₃	—	2	4	no	—
223	C₂×C₄×C₇₃	—	2	2	no	—
224	C₂×C₄×C₇₃	—	2	2	no	—
225	C₂×C₄×C₇₃	—	2	2	no	—
226	C₂×C₄×C₇₃	—	2	4	no	—
227	C₂×C₄×C₇₃	—	2	2	no	—
228	C₂×C₄×C₇₃	—	2	2	no	—
229	C₂×C₄×C₇₃	—	2	2	no	—
230	C₂×C₄×C₇₃	—	2	2	no	—
231	C₂×C₄×C₇₃	—	2	2	no	—
232	C₂×C₄×C₇₃	—	2	2	no	—
233	C₂×C₄×C₇₃	—	2	2	no	—
234	C₂×C₄×C₇₃	—	4	8	no	—
235	C₂×C₄×C₇₃	—	4	2	no	—
236	C₂×C₄×C₇₃	—	4	1	no	—
237	C₂×C₄×C₇₃	—	4	1	no	—
238	C₂×C₄×C₇₃	—	4	2	no	—
239	C₂×C₄×C₇₃	—	4	2	no	—
240	C₂×C₄×C₇₃	—	4	2	no	—
241	C₂×C₄×C₇₃	—	4	2	no	—
242	C₂×C₄×C₇₃	—	4	2	no	—
243	C₂×C₄×C₇₃	#121	1	2	yes	—
244	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
245	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
246	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
247	C₂×C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
248	C₈×C₇₃	—	2	4	no	—
249	C₈×C₇₃	—	4	1	no	—
250	C₈×C₇₃	—	4	1	no	—
251	C₂²×C₇₃	—	2	2	no	—
252	C₂²×C₇₃	—	2	4	no	—
253	C₂²×C₇₃	—	2	4	no	—
254	C₂²×C₇₃	—	2	2	no	—
255	C₂²×C₇₃	—	4	4	no	—
256	C₂²×C₇₃	—	4	4	no	—
257	C₂²×C₇₃	—	4	4	no	—
258	C₂²×C₇₃	—	8	16	no	—
259	C₂²×C₇₃	—	8	2	no	—
260	C₂²×C₇₃	—	8	2	no	—
261	C₂²×C₇₃	—	8	2	no	—
262	C₂²×C₇₃	—	8	2	no	—
263	C₂²×C₇₃	#464	1	4	yes	complemented
264	C₂²×C₇₃	C₂×#121	1	1	yes	characteristic
265	C₂²×C₇₃	D₄²	1	2	yes	—
266	C₂²×C₇₃	C₂×#135	1	1	yes	characteristic
267	C₂²×C₇₃	C₂×#137	1	1	yes	characteristic
268	C₂²×C₇₃	#577	1	2	yes	—
269	C₄×C₇₃	—	2	2	no	—
270	C₄×C₇₃	—	2	4	no	—
271	C₄×C₇₃	—	4	2	no	—
272	C₄×C₇₃	—	4	2	no	—
273	C₄×C₇₃	—	4	2	no	—
274	C₄×C₇₃	—	8	1	no	—
275	C₄×C₇₃	—	8	2	no	—
276	C₄×C₇₃	—	8	1	no	—
277	C₄×C₇₃	C₂×#120	1	1	yes	characteristic
278	C₄×C₇₃	#534	1	1	yes	characteristic
279	C₄×C₇₃	#546	1	2	yes	—
280	#24357	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
281	C₂×C₇₃	—	2	4	no	—
282	C₂×C₇₃	—	8	4	no	—
283	C₂×C₇₃	#2410	1	1	yes	characteristic
284	C₂×C₇₃	C₂×#464	1	1	yes	characteristic
285	C₂×C₇₃	#3043	1	1	yes	characteristic
286	C₂×C₇₃	#3266	1	2	yes	—
287	C₂×C₇₃	#3282	1	2	yes	—
288	C₂³×SD₁₆	C₂×C₇₃	1	1	yes	characteristic
289	C₂×#464	C₂×C₇₃	1	2	yes	complemented
290	C₂×#451	C₂×C₇₃	1	1	yes	characteristic, complemented
291	#2435	C₂×C₇₃	1	1	yes	characteristic
292	Q₈×C₂²⋊C₄	C₂×C₇₃	1	1	yes	characteristic, complemented
293	#2055	C₂×C₇₃	1	2	yes	complemented
294	#2015	C₂×C₇₃	1	2	yes	complemented
295	#1892	C₂×C₇₃	1	1	yes	characteristic, complemented
296	#1880	C₂×C₇₃	1	2	yes	complemented
297	#1850	C₂×C₇₃	1	1	yes	characteristic, complemented
298	#1786	C₂×C₇₃	1	1	yes	characteristic
299	C₇₃	#24357	1	1	yes	characteristic, direct product factor, Sylow
300	C₂³×Q₈	C₂²×C₇₃	1	1	yes	characteristic
301	C₂³×D₄	C₂²×C₇₃	1	1	yes	characteristic
302	C₂²×Q₁₆	C₂²×C₇₃	1	1	yes	characteristic, complemented
303	C₂²×Q₁₆	C₂²×C₇₃	1	1	yes	characteristic, complemented
304	C₂²×SD₁₆	—	2	4	no	—
305	C₂²×SD₁₆	—	2	8	no	—
306	C₂²×SD₁₆	C₂²×C₇₃	1	2	yes	—
307	C₂²×SD₁₆	C₂²×C₇₃	1	2	yes	—
308	C₂³×C₈	C₂²×C₇₃	1	1	yes	characteristic
309	C₂×#124	C₂²×C₇₃	1	2	yes	—
310	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
311	C₂×C₄×Q₈	C₂²×C₇₃	1	2	yes	complemented
312	#464	—	2	8	no	—
313	#451	—	2	4	no	—
314	C₂×C₄⋊C₈	C₂²×C₇₃	1	2	yes	complemented
315	C₂×#103	C₂²×C₇₃	1	1	yes	characteristic, complemented
316	C₂×#103	C₂²×C₇₃	1	1	yes	characteristic, complemented
317	C₂×#103	C₂²×C₇₃	1	2	yes	complemented
318	C₂×#102	C₂²×C₇₃	1	2	yes	—
319	C₂×#102	C₂²×C₇₃	1	2	yes	—
320	C₂×C₂²⋊C₈	C₂²×C₇₃	1	1	yes	characteristic
321	#394	—	2	2	no	—
322	#391	—	2	2	no	—
323	#391	C₂²×C₇₃	1	2	yes	complemented
324	#390	C₂²×C₇₃	1	2	yes	—
325	#380	—	2	1	no	—
326	#380	C₂²×C₇₃	1	1	yes	characteristic
327	#379	—	2	1	no	—
328	#379	—	2	1	no	—
329	C₄×C₂²⋊C₄	—	2	1	no	—
330	C₄×C₂²⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
331	#340	C₂²×C₇₃	1	2	yes	complemented
332	#336	C₂²×C₇₃	1	2	yes	complemented
333	C₂⁵	—	2	1	no	—
334	C₂²×Q₈	—	2	1	no	—
335	C₂²×Q₈	—	2	2	no	—
336	C₂²×Q₈	—	2	4	no	—
337	C₂²×Q₈	—	4	2	no	—
338	C₂²×Q₈	D₄×C₇₃	1	4	yes	—
339	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
340	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
341	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
342	C₂²×D₄	—	2	4	no	—
343	C₂²×D₄	—	2	2	no	—
344	C₂²×D₄	—	2	1	no	—
345	C₂²×D₄	—	2	2	no	—
346	C₂²×D₄	—	4	2	no	—
347	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
348	C₂³×C₄	—	2	1	no	—
349	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
350	C₂×Q₁₆	—	2	2	no	—
351	C₂×Q₁₆	—	2	2	no	—
352	C₂×Q₁₆	—	2	4	no	—
353	C₂×Q₁₆	—	4	2	no	—
354	C₂×SD₁₆	—	2	32	no	—
355	C₂×SD₁₆	—	2	4	no	—
356	C₂×SD₁₆	—	2	4	no	—
357	C₂×SD₁₆	—	2	4	no	—
358	C₂×SD₁₆	—	2	4	no	—
359	C₂×SD₁₆	—	2	4	no	—
360	C₂×SD₁₆	D₄×C₇₃	1	8	yes	—
361	C₂²×C₈	—	2	2	no	—
362	C₂²×C₈	—	2	4	no	—
363	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
364	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
365	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
366	#124	—	2	4	no	—
367	#124	—	4	2	no	—
368	C₂²⋊Q₈	—	2	2	no	—
369	C₂²⋊Q₈	—	2	2	no	—
370	C₄×Q₈	—	2	4	no	—
371	C₄×Q₈	—	4	2	no	—
372	C₂×C₄⋊C₄	—	2	2	no	—
373	C₂×C₄⋊C₄	—	2	1	no	—
374	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
375	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
376	C₂×C₂²⋊C₄	—	2	1	no	—
377	C₂×C₂²⋊C₄	—	2	1	no	—
378	C₂×C₂²⋊C₄	—	2	2	no	—
379	C₂×C₂²⋊C₄	—	2	2	no	—
380	C₂×C₂²⋊C₄	—	2	2	no	—
381	C₂×C₂²⋊C₄	—	2	2	no	—
382	C₂×C₂²⋊C₄	D₄×C₇₃	1	1	yes	characteristic
383	C₂×C₂²⋊C₄	D₄×C₇₃	1	1	yes	characteristic
384	C₂×C₄²	—	2	2	no	—
385	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
386	C₄⋊C₈	—	2	4	no	—
387	#103	—	2	2	no	—
388	#103	—	2	2	no	—
389	#103	—	2	4	no	—
390	#102	—	2	4	no	—
391	#102	—	4	2	no	—
392	C₂²⋊C₈	—	2	2	no	—
393	#95	—	2	2	no	—
394	#95	—	2	2	no	—
395	#95	—	2	1	no	—
396	#95	D₄×C₇₃	1	2	yes	—
397	C₂⁴	—	2	2	no	—
398	C₂⁴	—	4	4	no	—
399	C₂⁴	—	4	2	no	—
400	C₂⁴	—	4	2	no	—
401	C₂⁴	—	4	2	no	—
402	C₂⁴	—	8	2	no	—
403	C₂⁴	C₂×D₄×C₇₃	1	1	yes	characteristic
404	C₂×Q₈	—	2	4	no	—
405	C₂×Q₈	—	2	1	no	—
406	C₂×Q₈	—	2	1	no	—
407	C₂×Q₈	—	2	2	no	—
408	C₂×Q₈	—	2	8	no	—
409	C₂×Q₈	—	2	2	no	—
410	C₂×Q₈	—	2	2	no	—
411	C₂×Q₈	—	2	1	no	—
412	C₂×Q₈	—	2	1	no	—
413	C₂×Q₈	—	2	2	no	—
414	C₂×Q₈	—	2	2	no	—
415	C₂×Q₈	—	4	4	no	—
416	C₂×Q₈	—	4	4	no	—
417	C₂×Q₈	—	4	8	no	—
418	C₂×Q₈	C₂×D₄×C₇₃	1	2	yes	—
419	C₂×Q₈	C₂×D₄×C₇₃	1	2	yes	—
420	C₂×Q₈	C₂×D₄×C₇₃	1	4	yes	—
421	C₂×D₄	—	2	8	no	—
422	C₂×D₄	—	2	2	no	—
423	C₂×D₄	—	2	2	no	—
424	C₂×D₄	—	2	2	no	—
425	C₂×D₄	—	2	2	no	—
426	C₂×D₄	—	2	2	no	—
427	C₂×D₄	—	4	8	no	—
428	C₂×D₄	—	4	4	no	—
429	C₂×D₄	—	4	4	no	—
430	C₂×D₄	—	4	2	no	—
431	C₂×D₄	C₂×D₄×C₇₃	1	4	yes	—
432	C₂²×C₄	—	2	1	no	—
433	C₂²×C₄	—	2	2	no	—
434	C₂²×C₄	—	2	2	no	—
435	C₂²×C₄	—	2	4	no	—
436	C₂²×C₄	—	2	1	no	—
437	C₂²×C₄	—	2	2	no	—
438	C₂²×C₄	—	2	1	no	—
439	C₂²×C₄	—	2	1	no	—
440	C₂²×C₄	—	4	4	no	—
441	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
442	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
443	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
444	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
445	C₂²×C₄	#41×C₇₃	1	2	yes	—
446	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
447	Q₁₆	—	4	4	no	—
448	Q₁₆	—	4	4	no	—
449	SD₁₆	—	2	16	no	—
450	SD₁₆	—	2	16	no	—
451	C₂×C₈	—	2	8	no	—
452	C₂×C₈	—	2	2	no	—
453	C₂×C₈	—	2	2	no	—
454	C₂×C₈	—	2	1	no	—
455	C₂×C₈	—	2	1	no	—
456	C₂×C₈	—	2	2	no	—
457	C₂×C₈	—	2	2	no	—
458	C₂×C₈	C₂×D₄×C₇₃	1	4	yes	—
459	C₄⋊C₄	—	2	2	no	—
460	C₄⋊C₄	—	2	1	no	—
461	C₄⋊C₄	—	2	1	no	—
462	C₄⋊C₄	—	2	2	no	—
463	C₄⋊C₄	—	4	4	no	—
464	C₄⋊C₄	—	4	2	no	—
465	C₂²⋊C₄	—	2	2	no	—
466	C₂²⋊C₄	—	2	2	no	—
467	C₂²⋊C₄	—	4	4	no	—
468	C₂²⋊C₄	—	4	4	no	—
469	C₂²⋊C₄	—	4	2	no	—
470	C₂²⋊C₄	—	4	2	no	—
471	C₂²⋊C₄	—	8	2	no	—
472	C₂²⋊C₄	—	8	2	no	—
473	C₄²	—	2	2	no	—
474	C₄²	—	2	2	no	—
475	C₄²	—	4	4	no	—
476	C₂³	—	2	2	no	—
477	C₂³	—	2	2	no	—
478	C₂³	—	2	4	no	—
479	C₂³	—	4	8	no	—
480	C₂³	—	4	2	no	—
481	C₂³	—	4	2	no	—
482	C₂³	—	4	2	no	—
483	C₂³	—	4	2	no	—
484	C₂³	—	4	2	no	—
485	C₂³	—	4	2	no	—
486	C₂³	—	8	8	no	—
487	C₂³	—	8	8	no	—
488	C₂³	—	8	4	no	—
489	C₂³	—	8	4	no	—
490	C₂³	#121×C₇₃	1	2	yes	—
491	C₂³	#135×C₇₃	1	2	yes	—
492	C₂³	#137×C₇₃	1	2	yes	—
493	C₂³	C₂²×D₄×C₇₃	1	1	yes	characteristic
494	Q₈	—	2	2	no	—
495	Q₈	—	2	4	no	—
496	Q₈	—	2	2	no	—
497	Q₈	—	2	2	no	—
498	Q₈	—	4	8	no	—
499	Q₈	—	4	2	no	—
500	Q₈	—	4	1	no	—
501	Q₈	—	4	1	no	—
502	Q₈	—	4	2	no	—
503	Q₈	#120×C₇₃	1	4	yes	—
504	D₄	—	2	4	no	—
505	D₄	—	2	4	no	—
506	D₄	—	4	8	no	—
507	D₄	—	4	2	no	—
508	D₄	—	4	2	no	—
509	C₂×C₄	—	2	2	no	—
510	C₂×C₄	—	2	4	no	—
511	C₂×C₄	—	2	2	no	—
512	C₂×C₄	—	2	2	no	—
513	C₂×C₄	—	2	2	no	—
514	C₂×C₄	—	2	4	no	—
515	C₂×C₄	—	2	2	no	—
516	C₂×C₄	—	2	2	no	—
517	C₂×C₄	—	2	2	no	—
518	C₂×C₄	—	2	2	no	—
519	C₂×C₄	—	2	2	no	—
520	C₂×C₄	—	2	2	no	—
521	C₂×C₄	—	2	2	no	—
522	C₂×C₄	—	4	8	no	—
523	C₂×C₄	—	4	2	no	—
524	C₂×C₄	—	4	1	no	—
525	C₂×C₄	—	4	1	no	—
526	C₂×C₄	—	4	2	no	—
527	C₂×C₄	—	4	2	no	—
528	C₂×C₄	—	4	2	no	—
529	C₂×C₄	—	4	2	no	—
530	C₂×C₄	—	4	2	no	—
531	C₂×C₄	#121×C₇₃	1	2	yes	—
532	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
533	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
534	C₂×C₄	C₂×#41×C₇₃	1	1	yes	characteristic
535	C₂×C₄	H(5,𝔽₂)×C₇₃	1	2	yes	—
536	C₈	—	2	4	no	—
537	C₈	—	4	1	no	—
538	C₈	—	4	1	no	—
539	C₂²	—	2	4	no	—
540	C₂²	—	2	4	no	—
541	C₂²	—	2	2	no	—
542	C₂²	—	2	2	no	—
543	C₂²	—	4	4	no	—
544	C₂²	—	4	4	no	—
545	C₂²	—	4	4	no	—
546	C₂²	—	8	16	no	—
547	C₂²	—	8	2	no	—
548	C₂²	—	8	2	no	—
549	C₂²	—	8	2	no	—
550	C₂²	—	8	2	no	—
551	C₂²	#464×C₇₃	1	4	yes	complemented
552	C₂²	C₂×#121×C₇₃	1	1	yes	characteristic
553	C₂²	D₄²×C₇₃	1	2	yes	—
554	C₂²	C₂×#135×C₇₃	1	1	yes	characteristic
555	C₂²	C₂×#137×C₇₃	1	1	yes	characteristic
556	C₂²	#577×C₇₃	1	2	yes	—
557	C₄	—	2	2	no	—
558	C₄	—	2	4	no	—
559	C₄	—	4	2	no	—
560	C₄	—	4	2	no	—
561	C₄	—	4	2	no	—
562	C₄	—	8	2	no	—
563	C₄	—	8	1	no	—
564	C₄	—	8	1	no	—
565	C₄	C₂×#120×C₇₃	1	1	yes	characteristic
566	C₄	#534×C₇₃	1	1	yes	characteristic
567	C₄	#546×C₇₃	1	2	yes	—
568	C₂	—	2	4	no	—
569	C₂	—	8	4	no	—
570	C₂	C₇₃×#2410	1	1	yes	characteristic
571	C₂	C₂×#464×C₇₃	1	1	yes	characteristic
572	C₂	C₇₃×#3043	1	1	yes	characteristic
573	C₂	C₇₃×#3266	1	2	yes	—
574	C₂	C₇₃×#3282	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
2. C₂×#464×C₇₃	C₂	semidirect
3. C₂×#451×C₇₃	C₂	semidirect
5. Q₈×C₂²⋊C₄×C₇₃	C₂	semidirect
6. C₇₃×#2055	C₂	semidirect
7. C₇₃×#2015	C₂	semidirect
8. C₇₃×#1892	C₂	semidirect
9. C₇₃×#1880	C₂	semidirect
10. C₇₃×#1850	C₂	semidirect
14. C₂²×Q₁₆×C₇₃	C₂²	semidirect
15. C₂²×Q₁₆×C₇₃	C₂²	semidirect
23. C₂×C₄×Q₈×C₇₃	C₂²	semidirect
26. C₂×C₄⋊C₈×C₇₃	C₂²	semidirect
27. C₂×#103×C₇₃	C₂²	semidirect
28. C₂×#103×C₇₃	C₂²	semidirect
29. C₂×#103×C₇₃	C₂²	semidirect
35. #391×C₇₃	C₂²	semidirect
43. #340×C₇₃	C₂²	semidirect
44. #336×C₇₃	C₂²	semidirect
263. C₂²×C₇₃	#464	semidirect
280. #24357	C₇₃	direct (N × H)
289. C₂×#464	C₂×C₇₃	semidirect
290. C₂×#451	C₂×C₇₃	semidirect
292. Q₈×C₂²⋊C₄	C₂×C₇₃	semidirect
293. #2055	C₂×C₇₃	semidirect
294. #2015	C₂×C₇₃	semidirect
295. #1892	C₂×C₇₃	semidirect
296. #1880	C₂×C₇₃	semidirect
297. #1850	C₂×C₇₃	semidirect
299. C₇₃	#24357	direct (N × H)
302. C₂²×Q₁₆	C₂²×C₇₃	semidirect
303. C₂²×Q₁₆	C₂²×C₇₃	semidirect
311. C₂×C₄×Q₈	C₂²×C₇₃	semidirect
314. C₂×C₄⋊C₈	C₂²×C₇₃	semidirect
315. C₂×#103	C₂²×C₇₃	semidirect
316. C₂×#103	C₂²×C₇₃	semidirect
317. C₂×#103	C₂²×C₇₃	semidirect
323. #391	C₂²×C₇₃	semidirect
331. #340	C₂²×C₇₃	semidirect
332. #336	C₂²×C₇₃	semidirect
551. C₂²	#464×C₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₂³×SD₁₆×C₇₃	2
C₂×#464×C₇₃	2
C₂×#451×C₇₃	2
C₇₃×#2435	2
Q₈×C₂²⋊C₄×C₇₃	2
C₇₃×#2055	2
C₇₃×#2015	2
C₇₃×#1892	2
C₇₃×#1880	2
C₇₃×#1850	2
C₇₃×#1786	2
#24357	73

Subgroups — C73×#24357 #32933761

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#24357 #32933761