Subgroups — C₇₃×#25781 #32935185

Order 18688.

1774 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×D₈×C₇₃	C₂	1	1	yes	maximal, characteristic
2	C₂×#495×C₇₃	C₂	1	2	yes	maximal, complemented
3	C₂×#467×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#450×C₇₃	C₂	1	2	yes	maximal, complemented
5	C₇₃×#2435	C₂	1	2	yes	maximal, complemented
6	C₇₃×#2012	C₂	1	4	yes	maximal, complemented
7	C₇₃×#1970	C₂	1	2	yes	maximal, complemented
8	C₈×C₂²⋊C₄×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂³×D₄×C₇₃	C₂²	1	2	yes	—
10	C₂²×Q₁₆×C₇₃	C₂²	1	1	yes	characteristic, complemented
11	C₂²×SD₁₆×C₇₃	C₂²	1	4	yes	complemented
12	C₂²×D₈×C₇₃	—	2	8	no	—
13	C₂²×D₈×C₇₃	—	2	4	no	—
14	C₂²×D₈×C₇₃	C₂²	1	2	yes	—
15	C₂²×D₈×C₇₃	C₂²	1	2	yes	—
16	C₂³×C₈×C₇₃	C₂²	1	1	yes	characteristic
17	C₂×#124×C₇₃	C₂²	1	4	yes	complemented
18	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	2	yes	—
19	#495×C₇₃	—	2	8	no	—
20	#467×C₇₃	—	2	4	no	—
21	#450×C₇₃	—	2	8	no	—
22	C₂×#107×C₇₃	C₂²	1	1	yes	characteristic, complemented
23	C₂×#103×C₇₃	C₂²	1	2	yes	complemented
24	C₂×#102×C₇₃	C₂²	1	4	yes	complemented
25	C₂×C₂²⋊C₈×C₇₃	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₈×C₇₃	C₂²	1	2	yes	complemented
27	#394×C₇₃	—	2	4	no	—
28	#390×C₇₃	C₂²	1	4	yes	complemented
29	#379×C₇₃	—	2	4	no	—
30	C₄×C₂²⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
31	#336×C₇₃	C₂²	1	2	yes	complemented
32	C₂⁵×C₇₃	—	2	2	no	—
33	C₂²×Q₈×C₇₃	C₂³	1	2	yes	—
34	C₂²×D₄×C₇₃	—	2	8	no	—
35	C₂²×D₄×C₇₃	—	2	4	no	—
36	C₂²×D₄×C₇₃	—	2	4	no	—
37	C₂²×D₄×C₇₃	—	2	2	no	—
38	C₂²×D₄×C₇₃	—	4	4	no	—
39	C₂²×D₄×C₇₃	C₂³	1	4	yes	—
40	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
41	C₂×Q₁₆×C₇₃	—	2	2	no	—
42	C₂×Q₁₆×C₇₃	—	2	4	no	—
43	C₂×SD₁₆×C₇₃	—	2	8	no	—
44	C₂×SD₁₆×C₇₃	—	2	8	no	—
45	C₂×SD₁₆×C₇₃	—	4	4	no	—
46	C₂×D₈×C₇₃	—	2	32	no	—
47	C₂×D₈×C₇₃	—	2	8	no	—
48	C₂×D₈×C₇₃	—	2	4	no	—
49	C₂×D₈×C₇₃	—	2	4	no	—
50	C₂×D₈×C₇₃	—	2	4	no	—
51	C₂×D₈×C₇₃	D₄	1	8	yes	—
52	C₂²×C₈×C₇₃	—	2	4	no	—
53	C₂²×C₈×C₇₃	D₄	1	4	yes	—
54	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
55	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
56	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
57	#124×C₇₃	—	2	8	no	—
58	#124×C₇₃	—	4	4	no	—
59	C₂²⋊Q₈×C₇₃	—	2	4	no	—
60	C₂²⋊Q₈×C₇₃	—	2	4	no	—
61	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
62	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
63	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
64	C₂×C₂²⋊C₄×C₇₃	—	2	8	no	—
65	C₂×C₂²⋊C₄×C₇₃	—	2	8	no	—
66	C₂×C₂²⋊C₄×C₇₃	D₄	1	2	yes	—
67	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
68	#107×C₇₃	—	2	2	no	—
69	#103×C₇₃	—	2	4	no	—
70	#102×C₇₃	—	2	8	no	—
71	C₂²⋊C₈×C₇₃	D₄	1	4	yes	—
72	C₄×C₈×C₇₃	—	2	4	no	—
73	#95×C₇₃	D₄	1	2	yes	—
74	C₂⁴×C₇₃	—	2	4	no	—
75	C₂⁴×C₇₃	—	4	8	no	—
76	C₂⁴×C₇₃	—	4	4	no	—
77	C₂⁴×C₇₃	—	4	8	no	—
78	C₂⁴×C₇₃	—	8	4	no	—
79	C₂⁴×C₇₃	C₂×D₄	1	1	yes	characteristic
80	C₂×Q₈×C₇₃	—	2	2	no	—
81	C₂×Q₈×C₇₃	—	2	2	no	—
82	C₂×Q₈×C₇₃	—	2	4	no	—
83	C₂×Q₈×C₇₃	—	2	4	no	—
84	C₂×D₄×C₇₃	—	2	16	no	—
85	C₂×D₄×C₇₃	—	2	4	no	—
86	C₂×D₄×C₇₃	—	2	4	no	—
87	C₂×D₄×C₇₃	—	2	4	no	—
88	C₂×D₄×C₇₃	—	2	4	no	—
89	C₂×D₄×C₇₃	—	2	4	no	—
90	C₂×D₄×C₇₃	—	4	16	no	—
91	C₂×D₄×C₇₃	—	4	8	no	—
92	C₂×D₄×C₇₃	—	4	8	no	—
93	C₂×D₄×C₇₃	—	4	4	no	—
94	C₂×D₄×C₇₃	C₂×D₄	1	8	yes	—
95	C₂²×C₄×C₇₃	—	2	2	no	—
96	C₂²×C₄×C₇₃	—	2	2	no	—
97	C₂²×C₄×C₇₃	—	2	2	no	—
98	C₂²×C₄×C₇₃	—	2	2	no	—
99	C₂²×C₄×C₇₃	C₂×D₄	1	4	yes	—
100	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
102	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
103	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
104	Q₁₆×C₇₃	—	4	4	no	—
105	SD₁₆×C₇₃	—	4	16	no	—
106	D₈×C₇₃	—	2	16	no	—
107	D₈×C₇₃	—	2	16	no	—
108	C₂×C₈×C₇₃	—	2	2	no	—
109	C₂×C₈×C₇₃	—	2	2	no	—
110	C₂×C₈×C₇₃	—	2	2	no	—
111	C₂×C₈×C₇₃	—	2	8	no	—
112	C₂×C₈×C₇₃	C₂×D₄	1	4	yes	—
113	C₂×C₈×C₇₃	C₂×D₄	1	2	yes	—
114	C₂×C₈×C₇₃	C₂×D₄	1	4	yes	—
115	C₂×C₈×C₇₃	C₂×D₄	1	2	yes	—
116	C₄⋊C₄×C₇₃	—	2	2	no	—
117	C₄⋊C₄×C₇₃	—	2	2	no	—
118	C₄⋊C₄×C₇₃	—	4	4	no	—
119	C₂²⋊C₄×C₇₃	—	2	4	no	—
120	C₂²⋊C₄×C₇₃	—	4	16	no	—
121	C₂²⋊C₄×C₇₃	—	4	4	no	—
122	C₂²⋊C₄×C₇₃	—	8	8	no	—
123	C₄²×C₇₃	—	2	2	no	—
124	C₄²×C₇₃	—	2	2	no	—
125	C₂³×C₇₃	—	2	2	no	—
126	C₂³×C₇₃	—	2	2	no	—
127	C₂³×C₇₃	—	2	8	no	—
128	C₂³×C₇₃	—	4	16	no	—
129	C₂³×C₇₃	—	4	4	no	—
130	C₂³×C₇₃	—	4	4	no	—
131	C₂³×C₇₃	—	4	8	no	—
132	C₂³×C₇₃	—	4	8	no	—
133	C₂³×C₇₃	—	8	32	no	—
134	C₂³×C₇₃	—	8	8	no	—
135	C₂³×C₇₃	—	8	8	no	—
136	C₂³×C₇₃	#127	1	2	yes	—
137	C₂³×C₇₃	#135	1	4	yes	—
138	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
139	Q₈×C₇₃	—	4	2	no	—
140	Q₈×C₇₃	—	4	2	no	—
141	Q₈×C₇₃	—	4	4	no	—
142	D₄×C₇₃	—	2	8	no	—
143	D₄×C₇₃	—	2	8	no	—
144	D₄×C₇₃	—	4	16	no	—
145	D₄×C₇₃	—	4	4	no	—
146	D₄×C₇₃	—	4	4	no	—
147	C₂×C₄×C₇₃	—	2	2	no	—
148	C₂×C₄×C₇₃	—	2	2	no	—
149	C₂×C₄×C₇₃	—	2	2	no	—
150	C₂×C₄×C₇₃	—	2	4	no	—
151	C₂×C₄×C₇₃	—	2	4	no	—
152	C₂×C₄×C₇₃	—	2	4	no	—
153	C₂×C₄×C₇₃	—	2	4	no	—
154	C₂×C₄×C₇₃	—	4	2	no	—
155	C₂×C₄×C₇₃	—	4	2	no	—
156	C₂×C₄×C₇₃	—	4	4	no	—
157	C₂×C₄×C₇₃	—	4	4	no	—
158	C₂×C₄×C₇₃	#127	1	2	yes	—
159	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
160	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
161	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
162	C₂×C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
163	C₈×C₇₃	—	2	2	no	—
164	C₈×C₇₃	—	2	4	no	—
165	C₈×C₇₃	#120	1	4	yes	—
166	C₂²×C₇₃	—	2	2	no	—
167	C₂²×C₇₃	—	2	2	no	—
168	C₂²×C₇₃	—	2	8	no	—
169	C₂²×C₇₃	—	4	8	no	—
170	C₂²×C₇₃	—	4	16	no	—
171	C₂²×C₇₃	—	8	32	no	—
172	C₂²×C₇₃	—	8	4	no	—
173	C₂²×C₇₃	—	8	4	no	—
174	C₂²×C₇₃	—	8	8	no	—
175	C₂²×C₇₃	#495	1	4	yes	complemented
176	C₂²×C₇₃	C₂×#127	1	1	yes	characteristic
177	C₂²×C₇₃	D₄²	1	2	yes	—
178	C₂²×C₇₃	C₂×#135	1	2	yes	—
179	C₂²×C₇₃	#576	1	2	yes	—
180	C₄×C₇₃	—	2	2	no	—
181	C₄×C₇₃	—	4	4	no	—
182	C₄×C₇₃	—	8	2	no	—
183	C₄×C₇₃	—	8	2	no	—
184	C₄×C₇₃	C₂×#120	1	1	yes	characteristic
185	C₄×C₇₃	#535	1	1	yes	characteristic
186	C₄×C₇₃	D₄²	1	2	yes	—
187	#25781	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
188	C₂×C₇₃	—	2	4	no	—
189	C₂×C₇₃	—	8	8	no	—
190	C₂×C₇₃	#2433	1	1	yes	characteristic
191	C₂×C₇₃	C₂×#495	1	1	yes	characteristic
192	C₂×C₇₃	#3155	1	1	yes	characteristic
193	C₂×C₇₃	#3280	1	4	yes	—
194	C₂³×D₈	C₂×C₇₃	1	1	yes	characteristic
195	C₂×#495	C₂×C₇₃	1	2	yes	complemented
196	C₂×#467	C₂×C₇₃	1	1	yes	characteristic, complemented
197	C₂×#450	C₂×C₇₃	1	2	yes	complemented
198	#2435	C₂×C₇₃	1	2	yes	complemented
199	#2012	C₂×C₇₃	1	4	yes	complemented
200	#1970	C₂×C₇₃	1	2	yes	complemented
201	C₈×C₂²⋊C₄	C₂×C₇₃	1	1	yes	characteristic, complemented
202	C₇₃	#25781	1	1	yes	characteristic, direct product factor, Sylow
203	C₂³×D₄	C₂²×C₇₃	1	2	yes	—
204	C₂²×Q₁₆	C₂²×C₇₃	1	1	yes	characteristic, complemented
205	C₂²×SD₁₆	C₂²×C₇₃	1	4	yes	complemented
206	C₂²×D₈	—	2	8	no	—
207	C₂²×D₈	—	2	4	no	—
208	C₂²×D₈	C₂²×C₇₃	1	2	yes	—
209	C₂²×D₈	C₂²×C₇₃	1	2	yes	—
210	C₂³×C₈	C₂²×C₇₃	1	1	yes	characteristic
211	C₂×#124	C₂²×C₇₃	1	4	yes	complemented
212	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	2	yes	—
213	#495	—	2	8	no	—
214	#467	—	2	4	no	—
215	#450	—	2	8	no	—
216	C₂×#107	C₂²×C₇₃	1	1	yes	characteristic, complemented
217	C₂×#103	C₂²×C₇₃	1	2	yes	complemented
218	C₂×#102	C₂²×C₇₃	1	4	yes	complemented
219	C₂×C₂²⋊C₈	C₂²×C₇₃	1	1	yes	characteristic
220	C₂×C₄×C₈	C₂²×C₇₃	1	2	yes	complemented
221	#394	—	2	4	no	—
222	#390	C₂²×C₇₃	1	4	yes	complemented
223	#379	—	2	4	no	—
224	C₄×C₂²⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
225	#336	C₂²×C₇₃	1	2	yes	complemented
226	C₂⁵	—	2	2	no	—
227	C₂²×Q₈	C₂³×C₇₃	1	2	yes	—
228	C₂²×D₄	—	2	8	no	—
229	C₂²×D₄	—	2	4	no	—
230	C₂²×D₄	—	2	4	no	—
231	C₂²×D₄	—	2	2	no	—
232	C₂²×D₄	—	4	4	no	—
233	C₂²×D₄	C₂³×C₇₃	1	4	yes	—
234	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
235	C₂×Q₁₆	—	2	2	no	—
236	C₂×Q₁₆	—	2	4	no	—
237	C₂×SD₁₆	—	2	8	no	—
238	C₂×SD₁₆	—	2	8	no	—
239	C₂×SD₁₆	—	4	4	no	—
240	C₂×D₈	—	2	32	no	—
241	C₂×D₈	—	2	8	no	—
242	C₂×D₈	—	2	4	no	—
243	C₂×D₈	—	2	4	no	—
244	C₂×D₈	—	2	4	no	—
245	C₂×D₈	D₄×C₇₃	1	8	yes	—
246	C₂²×C₈	—	2	4	no	—
247	C₂²×C₈	D₄×C₇₃	1	4	yes	—
248	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
249	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
250	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
251	#124	—	2	8	no	—
252	#124	—	4	4	no	—
253	C₂²⋊Q₈	—	2	4	no	—
254	C₂²⋊Q₈	—	2	4	no	—
255	C₂×C₄⋊C₄	—	2	2	no	—
256	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
257	C₂×C₂²⋊C₄	—	2	2	no	—
258	C₂×C₂²⋊C₄	—	2	8	no	—
259	C₂×C₂²⋊C₄	—	2	8	no	—
260	C₂×C₂²⋊C₄	D₄×C₇₃	1	2	yes	—
261	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
262	#107	—	2	2	no	—
263	#103	—	2	4	no	—
264	#102	—	2	8	no	—
265	C₂²⋊C₈	D₄×C₇₃	1	4	yes	—
266	C₄×C₈	—	2	4	no	—
267	#95	D₄×C₇₃	1	2	yes	—
268	C₂⁴	—	2	4	no	—
269	C₂⁴	—	4	8	no	—
270	C₂⁴	—	4	4	no	—
271	C₂⁴	—	4	8	no	—
272	C₂⁴	—	8	4	no	—
273	C₂⁴	C₂×D₄×C₇₃	1	1	yes	characteristic
274	C₂×Q₈	—	2	2	no	—
275	C₂×Q₈	—	2	2	no	—
276	C₂×Q₈	—	2	4	no	—
277	C₂×Q₈	—	2	4	no	—
278	C₂×D₄	—	2	16	no	—
279	C₂×D₄	—	2	4	no	—
280	C₂×D₄	—	2	4	no	—
281	C₂×D₄	—	2	4	no	—
282	C₂×D₄	—	2	4	no	—
283	C₂×D₄	—	2	4	no	—
284	C₂×D₄	—	4	16	no	—
285	C₂×D₄	—	4	8	no	—
286	C₂×D₄	—	4	8	no	—
287	C₂×D₄	—	4	4	no	—
288	C₂×D₄	C₂×D₄×C₇₃	1	8	yes	—
289	C₂²×C₄	—	2	2	no	—
290	C₂²×C₄	—	2	2	no	—
291	C₂²×C₄	—	2	2	no	—
292	C₂²×C₄	—	2	2	no	—
293	C₂²×C₄	C₂×D₄×C₇₃	1	4	yes	—
294	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
295	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
296	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
297	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
298	Q₁₆	—	4	4	no	—
299	SD₁₆	—	4	16	no	—
300	D₈	—	2	16	no	—
301	D₈	—	2	16	no	—
302	C₂×C₈	—	2	2	no	—
303	C₂×C₈	—	2	2	no	—
304	C₂×C₈	—	2	2	no	—
305	C₂×C₈	—	2	8	no	—
306	C₂×C₈	C₂×D₄×C₇₃	1	4	yes	—
307	C₂×C₈	C₂×D₄×C₇₃	1	2	yes	—
308	C₂×C₈	C₂×D₄×C₇₃	1	4	yes	—
309	C₂×C₈	C₂×D₄×C₇₃	1	2	yes	—
310	C₄⋊C₄	—	2	2	no	—
311	C₄⋊C₄	—	2	2	no	—
312	C₄⋊C₄	—	4	4	no	—
313	C₂²⋊C₄	—	2	4	no	—
314	C₂²⋊C₄	—	4	16	no	—
315	C₂²⋊C₄	—	4	4	no	—
316	C₂²⋊C₄	—	8	8	no	—
317	C₄²	—	2	2	no	—
318	C₄²	—	2	2	no	—
319	C₂³	—	2	2	no	—
320	C₂³	—	2	2	no	—
321	C₂³	—	2	8	no	—
322	C₂³	—	4	16	no	—
323	C₂³	—	4	4	no	—
324	C₂³	—	4	4	no	—
325	C₂³	—	4	8	no	—
326	C₂³	—	4	8	no	—
327	C₂³	—	8	32	no	—
328	C₂³	—	8	8	no	—
329	C₂³	—	8	8	no	—
330	C₂³	#127×C₇₃	1	2	yes	—
331	C₂³	#135×C₇₃	1	4	yes	—
332	C₂³	C₂²×D₄×C₇₃	1	1	yes	characteristic
333	Q₈	—	4	2	no	—
334	Q₈	—	4	2	no	—
335	Q₈	—	4	4	no	—
336	D₄	—	2	8	no	—
337	D₄	—	2	8	no	—
338	D₄	—	4	16	no	—
339	D₄	—	4	4	no	—
340	D₄	—	4	4	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	2	4	no	—
345	C₂×C₄	—	2	4	no	—
346	C₂×C₄	—	2	4	no	—
347	C₂×C₄	—	2	4	no	—
348	C₂×C₄	—	4	2	no	—
349	C₂×C₄	—	4	2	no	—
350	C₂×C₄	—	4	4	no	—
351	C₂×C₄	—	4	4	no	—
352	C₂×C₄	#127×C₇₃	1	2	yes	—
353	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
354	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
355	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
356	C₂×C₄	H(5,𝔽₂)×C₇₃	1	2	yes	—
357	C₈	—	2	2	no	—
358	C₈	—	2	4	no	—
359	C₈	#120×C₇₃	1	4	yes	—
360	C₂²	—	2	8	no	—
361	C₂²	—	2	2	no	—
362	C₂²	—	2	2	no	—
363	C₂²	—	4	16	no	—
364	C₂²	—	4	8	no	—
365	C₂²	—	8	32	no	—
366	C₂²	—	8	8	no	—
367	C₂²	—	8	4	no	—
368	C₂²	—	8	4	no	—
369	C₂²	#495×C₇₃	1	4	yes	complemented
370	C₂²	C₂×#127×C₇₃	1	1	yes	characteristic
371	C₂²	D₄²×C₇₃	1	2	yes	—
372	C₂²	C₂×#135×C₇₃	1	2	yes	—
373	C₂²	#576×C₇₃	1	2	yes	—
374	C₄	—	2	2	no	—
375	C₄	—	4	4	no	—
376	C₄	—	8	2	no	—
377	C₄	—	8	2	no	—
378	C₄	C₂×#120×C₇₃	1	1	yes	characteristic
379	C₄	#535×C₇₃	1	1	yes	characteristic
380	C₄	D₄²×C₇₃	1	2	yes	—
381	C₂	—	2	4	no	—
382	C₂	—	8	8	no	—
383	C₂	C₇₃×#2433	1	1	yes	characteristic
384	C₂	C₂×#495×C₇₃	1	1	yes	characteristic
385	C₂	C₇₃×#3155	1	1	yes	characteristic
386	C₂	C₇₃×#3280	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₇₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₃
prime radical	C₂³×D₈×C₇₃	C₂
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×#495×C₇₃	C₂	semidirect
3. C₂×#467×C₇₃	C₂	semidirect
4. C₂×#450×C₇₃	C₂	semidirect
5. C₇₃×#2435	C₂	semidirect
6. C₇₃×#2012	C₂	semidirect
7. C₇₃×#1970	C₂	semidirect
8. C₈×C₂²⋊C₄×C₇₃	C₂	semidirect
10. C₂²×Q₁₆×C₇₃	C₂²	semidirect
11. C₂²×SD₁₆×C₇₃	C₂²	semidirect
17. C₂×#124×C₇₃	C₂²	semidirect
22. C₂×#107×C₇₃	C₂²	semidirect
23. C₂×#103×C₇₃	C₂²	semidirect
24. C₂×#102×C₇₃	C₂²	semidirect
26. C₂×C₄×C₈×C₇₃	C₂²	semidirect
28. #390×C₇₃	C₂²	semidirect
31. #336×C₇₃	C₂²	semidirect
175. C₂²×C₇₃	#495	semidirect
187. #25781	C₇₃	direct (N × H)
195. C₂×#495	C₂×C₇₃	semidirect
196. C₂×#467	C₂×C₇₃	semidirect
197. C₂×#450	C₂×C₇₃	semidirect
198. #2435	C₂×C₇₃	semidirect
199. #2012	C₂×C₇₃	semidirect
200. #1970	C₂×C₇₃	semidirect
201. C₈×C₂²⋊C₄	C₂×C₇₃	semidirect
202. C₇₃	#25781	direct (N × H)
204. C₂²×Q₁₆	C₂²×C₇₃	semidirect
205. C₂²×SD₁₆	C₂²×C₇₃	semidirect
211. C₂×#124	C₂²×C₇₃	semidirect
216. C₂×#107	C₂²×C₇₃	semidirect
217. C₂×#103	C₂²×C₇₃	semidirect
218. C₂×#102	C₂²×C₇₃	semidirect
220. C₂×C₄×C₈	C₂²×C₇₃	semidirect
222. #390	C₂²×C₇₃	semidirect
225. #336	C₂²×C₇₃	semidirect
369. C₂²	#495×C₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₂³×D₈×C₇₃	2
C₂×#495×C₇₃	2
C₂×#467×C₇₃	2
C₂×#450×C₇₃	2
C₇₃×#2435	2
C₇₃×#2012	2
C₇₃×#1970	2
C₈×C₂²⋊C₄×C₇₃	2
#25781	73

Subgroups — C73×#25781 #32935185

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#25781 #32935185