Subgroups — C₇₃×#25721 #32935125

Order 18688.

2374 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#127×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#493×C₇₃	C₂	1	2	yes	maximal, complemented
3	C₂×#447×C₇₃	C₂	1	4	yes	maximal, complemented
4	C₇₃×#2856	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₃×#2011	C₂	1	4	yes	maximal, complemented
6	C₇₃×#1957	C₂	1	2	yes	maximal, complemented
7	C₄×C₂²⋊C₈×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂³×D₄×C₇₃	—	2	2	no	—
9	C₂³×D₄×C₇₃	C₂²	1	2	yes	—
10	C₂²×D₈×C₇₃	C₂²	1	8	yes	complemented
11	C₂×#127×C₇₃	—	2	8	no	—
12	C₂×#127×C₇₃	—	2	2	no	—
13	C₂×#127×C₇₃	C₂²	1	2	yes	—
14	C₂×#127×C₇₃	C₂²	1	2	yes	—
15	C₂×#127×C₇₃	C₂²	1	1	yes	characteristic, complemented
16	C₂×#121×C₇₃	—	2	2	no	—
17	C₂×#121×C₇₃	C₂²	1	2	yes	—
18	C₂²×C₄²×C₇₃	C₂²	1	1	yes	characteristic
19	#493×C₇₃	—	2	8	no	—
20	#447×C₇₃	—	2	16	no	—
21	C₂×#102×C₇₃	C₂²	1	8	yes	complemented
22	C₂×C₂²⋊C₈×C₇₃	C₂²	1	2	yes	—
23	C₂×C₄×C₈×C₇₃	C₂²	1	2	yes	complemented
24	#390×C₇₃	—	2	2	no	—
25	#390×C₇₃	C₂²	1	2	yes	complemented
26	#384×C₇₃	C₂²	1	1	yes	characteristic, complemented
27	#336×C₇₃	C₂²	1	2	yes	complemented
28	C₂⁵×C₇₃	—	2	2	no	—
29	C₂²×D₄×C₇₃	—	2	16	no	—
30	C₂²×D₄×C₇₃	—	2	8	no	—
31	C₂²×D₄×C₇₃	—	2	2	no	—
32	C₂²×D₄×C₇₃	—	2	2	no	—
33	C₂²×D₄×C₇₃	—	2	4	no	—
34	C₂²×D₄×C₇₃	—	2	4	no	—
35	C₂²×D₄×C₇₃	—	2	8	no	—
36	C₂²×D₄×C₇₃	—	2	2	no	—
37	C₂²×D₄×C₇₃	—	4	4	no	—
38	C₂²×D₄×C₇₃	—	4	8	no	—
39	C₂²×D₄×C₇₃	—	4	8	no	—
40	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
41	C₂²×D₄×C₇₃	C₂³	1	4	yes	—
42	C₂³×C₄×C₇₃	D₄	1	2	yes	—
43	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
44	C₂×D₈×C₇₃	—	2	16	no	—
45	C₂×D₈×C₇₃	—	2	16	no	—
46	C₂×D₈×C₇₃	—	4	8	no	—
47	C₂²×C₈×C₇₃	C₂³	1	4	yes	—
48	#127×C₇₃	—	2	16	no	—
49	#127×C₇₃	—	2	8	no	—
50	#127×C₇₃	—	2	4	no	—
51	#127×C₇₃	—	2	4	no	—
52	#127×C₇₃	D₄	1	8	yes	complemented
53	#121×C₇₃	—	2	8	no	—
54	#121×C₇₃	—	4	8	no	—
55	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
56	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
57	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
58	C₂×C₂²⋊C₄×C₇₃	—	2	4	no	—
59	C₂×C₄²×C₇₃	—	2	4	no	—
60	C₂×C₄²×C₇₃	D₄	1	2	yes	—
61	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
62	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
63	#102×C₇₃	—	2	16	no	—
64	C₂²⋊C₈×C₇₃	D₄	1	8	yes	complemented
65	C₄×C₈×C₇₃	—	2	4	no	—
66	C₂⁴×C₇₃	—	2	8	no	—
67	C₂⁴×C₇₃	—	2	4	no	—
68	C₂⁴×C₇₃	—	2	2	no	—
69	C₂⁴×C₇₃	—	4	4	no	—
70	C₂⁴×C₇₃	—	4	8	no	—
71	C₂⁴×C₇₃	—	4	4	no	—
72	C₂⁴×C₇₃	—	4	8	no	—
73	C₂⁴×C₇₃	C₂×D₄	1	1	yes	characteristic
74	C₂×D₄×C₇₃	—	2	8	no	—
75	C₂×D₄×C₇₃	—	2	16	no	—
76	C₂×D₄×C₇₃	—	2	16	no	—
77	C₂×D₄×C₇₃	—	2	8	no	—
78	C₂×D₄×C₇₃	—	2	4	no	—
79	C₂×D₄×C₇₃	—	2	4	no	—
80	C₂×D₄×C₇₃	—	2	4	no	—
81	C₂×D₄×C₇₃	—	2	8	no	—
82	C₂×D₄×C₇₃	—	2	4	no	—
83	C₂×D₄×C₇₃	—	4	32	no	—
84	C₂×D₄×C₇₃	—	4	4	no	—
85	C₂×D₄×C₇₃	—	4	8	no	—
86	C₂×D₄×C₇₃	—	4	64	no	—
87	C₂×D₄×C₇₃	—	4	4	no	—
88	C₂×D₄×C₇₃	—	4	8	no	—
89	C₂×D₄×C₇₃	—	4	4	no	—
90	C₂×D₄×C₇₃	—	4	4	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	—	4	8	no	—
95	C₂×D₄×C₇₃	—	4	4	no	—
96	C₂×D₄×C₇₃	C₂×D₄	1	8	yes	—
97	C₂²×C₄×C₇₃	—	2	4	no	—
98	C₂²×C₄×C₇₃	—	2	4	no	—
99	C₂²×C₄×C₇₃	—	2	2	no	—
100	C₂²×C₄×C₇₃	—	2	2	no	—
101	C₂²×C₄×C₇₃	—	2	2	no	—
102	C₂²×C₄×C₇₃	D₈	1	8	yes	complemented
103	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₇₃	C₂×D₄	1	4	yes	—
105	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
106	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
107	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
108	D₈×C₇₃	—	4	32	no	—
109	C₂×C₈×C₇₃	—	2	4	no	—
110	C₂×C₈×C₇₃	—	2	4	no	—
111	C₂×C₈×C₇₃	C₂×D₄	1	8	yes	complemented
112	C₄⋊C₄×C₇₃	—	2	4	no	—
113	C₄⋊C₄×C₇₃	—	4	4	no	—
114	C₂²⋊C₄×C₇₃	—	4	4	no	—
115	C₂²⋊C₄×C₇₃	—	4	8	no	—
116	C₄²×C₇₃	—	2	4	no	—
117	C₄²×C₇₃	—	2	2	no	—
118	C₄²×C₇₃	C₂×D₄	1	4	yes	—
119	C₂³×C₇₃	—	2	1	no	—
120	C₂³×C₇₃	—	2	1	no	—
121	C₂³×C₇₃	—	2	2	no	—
122	C₂³×C₇₃	—	2	8	no	—
123	C₂³×C₇₃	—	4	16	no	—
124	C₂³×C₇₃	—	4	32	no	—
125	C₂³×C₇₃	—	4	4	no	—
126	C₂³×C₇₃	—	4	4	no	—
127	C₂³×C₇₃	—	4	8	no	—
128	C₂³×C₇₃	—	4	8	no	—
129	C₂³×C₇₃	—	4	2	no	—
130	C₂³×C₇₃	—	4	2	no	—
131	C₂³×C₇₃	—	4	2	no	—
132	C₂³×C₇₃	—	4	4	no	—
133	C₂³×C₇₃	—	4	4	no	—
134	C₂³×C₇₃	—	8	8	no	—
135	C₂³×C₇₃	—	8	16	no	—
136	C₂³×C₇₃	—	8	8	no	—
137	C₂³×C₇₃	#127	1	2	yes	—
138	C₂³×C₇₃	C₂×D₈	1	4	yes	—
139	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
140	D₄×C₇₃	—	2	16	no	—
141	D₄×C₇₃	—	4	16	no	—
142	D₄×C₇₃	—	4	32	no	—
143	D₄×C₇₃	—	4	8	no	—
144	D₄×C₇₃	—	4	8	no	—
145	D₄×C₇₃	—	4	32	no	—
146	D₄×C₇₃	—	8	8	no	—
147	D₄×C₇₃	—	8	8	no	—
148	C₂×C₄×C₇₃	—	2	1	no	—
149	C₂×C₄×C₇₃	—	2	2	no	—
150	C₂×C₄×C₇₃	—	2	1	no	—
151	C₂×C₄×C₇₃	—	2	2	no	—
152	C₂×C₄×C₇₃	—	2	8	no	—
153	C₂×C₄×C₇₃	—	2	16	no	—
154	C₂×C₄×C₇₃	—	4	2	no	—
155	C₂×C₄×C₇₃	—	4	4	no	—
156	C₂×C₄×C₇₃	#120	1	4	yes	—
157	C₂×C₄×C₇₃	#127	1	2	yes	—
158	C₂×C₄×C₇₃	C₂×D₈	1	4	yes	—
159	C₂×C₄×C₇₃	C₂×D₈	1	4	yes	—
160	C₂×C₄×C₇₃	AGL(1,ℤ/8)	1	4	yes	—
161	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
162	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
163	C₂×C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
164	C₈×C₇₃	—	2	8	no	—
165	C₂²×C₇₃	—	2	2	no	—
166	C₂²×C₇₃	—	2	2	no	—
167	C₂²×C₇₃	—	2	4	no	—
168	C₂²×C₇₃	—	2	4	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	—	8	2	no	—
176	C₂²×C₇₃	—	8	2	no	—
177	C₂²×C₇₃	—	8	2	no	—
178	C₂²×C₇₃	—	8	4	no	—
179	C₂²×C₇₃	—	8	4	no	—
180	C₂²×C₇₃	#493	1	4	yes	complemented
181	C₂²×C₇₃	C₂×#120	1	1	yes	characteristic
182	C₂²×C₇₃	C₂×#127	1	1	yes	characteristic
183	C₂²×C₇₃	#535	1	1	yes	characteristic
184	C₂²×C₇₃	C₂²×D₈	1	2	yes	—
185	C₂²×C₇₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
186	C₄×C₇₃	—	2	2	no	—
187	C₄×C₇₃	—	2	4	no	—
188	C₄×C₇₃	—	8	2	no	—
189	C₄×C₇₃	#447	1	8	yes	complemented
190	C₄×C₇₃	D₄²	1	4	yes	—
191	#25721	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
192	C₂×C₇₃	—	2	4	no	—
193	C₂×C₇₃	—	8	8	no	—
194	C₂×C₇₃	—	16	2	no	—
195	C₂×C₇₃	#2433	1	1	yes	characteristic
196	C₂×C₇₃	C₂×#447	1	2	yes	—
197	C₂×C₇₃	C₂×#493	1	1	yes	characteristic
198	C₂×C₇₃	#3151	1	1	yes	characteristic
199	C₂×C₇₃	#3205	1	2	yes	—
200	C₂²×#127	C₂×C₇₃	1	1	yes	characteristic, complemented
201	C₂×#493	C₂×C₇₃	1	2	yes	complemented
202	C₂×#447	C₂×C₇₃	1	4	yes	complemented
203	#2856	C₂×C₇₃	1	1	yes	characteristic, complemented
204	#2011	C₂×C₇₃	1	4	yes	complemented
205	#1957	C₂×C₇₃	1	2	yes	complemented
206	C₄×C₂²⋊C₈	C₂×C₇₃	1	1	yes	characteristic, complemented
207	C₇₃	#25721	1	1	yes	characteristic, direct product factor, Sylow
208	C₂³×D₄	—	2	2	no	—
209	C₂³×D₄	C₂²×C₇₃	1	2	yes	—
210	C₂²×D₈	C₂²×C₇₃	1	8	yes	complemented
211	C₂×#127	—	2	8	no	—
212	C₂×#127	—	2	2	no	—
213	C₂×#127	C₂²×C₇₃	1	2	yes	—
214	C₂×#127	C₂²×C₇₃	1	2	yes	—
215	C₂×#127	C₂²×C₇₃	1	1	yes	characteristic, complemented
216	C₂×#121	—	2	2	no	—
217	C₂×#121	C₂²×C₇₃	1	2	yes	—
218	C₂²×C₄²	C₂²×C₇₃	1	1	yes	characteristic
219	#493	—	2	8	no	—
220	#447	—	2	16	no	—
221	C₂×#102	C₂²×C₇₃	1	8	yes	complemented
222	C₂×C₂²⋊C₈	C₂²×C₇₃	1	2	yes	—
223	C₂×C₄×C₈	C₂²×C₇₃	1	2	yes	complemented
224	#390	—	2	2	no	—
225	#390	C₂²×C₇₃	1	2	yes	complemented
226	#384	C₂²×C₇₃	1	1	yes	characteristic, complemented
227	#336	C₂²×C₇₃	1	2	yes	complemented
228	C₂⁵	—	2	2	no	—
229	C₂²×D₄	—	2	16	no	—
230	C₂²×D₄	—	2	8	no	—
231	C₂²×D₄	—	2	2	no	—
232	C₂²×D₄	—	2	2	no	—
233	C₂²×D₄	—	2	4	no	—
234	C₂²×D₄	—	2	4	no	—
235	C₂²×D₄	—	2	8	no	—
236	C₂²×D₄	—	2	2	no	—
237	C₂²×D₄	—	4	4	no	—
238	C₂²×D₄	—	4	8	no	—
239	C₂²×D₄	—	4	8	no	—
240	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
241	C₂²×D₄	C₂³×C₇₃	1	4	yes	—
242	C₂³×C₄	D₄×C₇₃	1	2	yes	—
243	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
244	C₂×D₈	—	2	16	no	—
245	C₂×D₈	—	2	16	no	—
246	C₂×D₈	—	4	8	no	—
247	C₂²×C₈	C₂³×C₇₃	1	4	yes	—
248	#127	—	2	16	no	—
249	#127	—	2	8	no	—
250	#127	—	2	4	no	—
251	#127	—	2	4	no	—
252	#127	D₄×C₇₃	1	8	yes	complemented
253	#121	—	2	8	no	—
254	#121	—	4	8	no	—
255	C₂×C₄⋊C₄	—	2	2	no	—
256	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
257	C₂×C₂²⋊C₄	—	2	4	no	—
258	C₂×C₂²⋊C₄	—	2	2	no	—
259	C₂×C₄²	—	2	4	no	—
260	C₂×C₄²	D₄×C₇₃	1	2	yes	—
261	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
262	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
263	#102	—	2	16	no	—
264	C₂²⋊C₈	D₄×C₇₃	1	8	yes	complemented
265	C₄×C₈	—	2	4	no	—
266	C₂⁴	—	2	8	no	—
267	C₂⁴	—	2	4	no	—
268	C₂⁴	—	2	2	no	—
269	C₂⁴	—	4	4	no	—
270	C₂⁴	—	4	8	no	—
271	C₂⁴	—	4	4	no	—
272	C₂⁴	—	4	8	no	—
273	C₂⁴	C₂×D₄×C₇₃	1	1	yes	characteristic
274	C₂×D₄	—	2	8	no	—
275	C₂×D₄	—	2	16	no	—
276	C₂×D₄	—	2	16	no	—
277	C₂×D₄	—	2	8	no	—
278	C₂×D₄	—	2	4	no	—
279	C₂×D₄	—	2	4	no	—
280	C₂×D₄	—	2	4	no	—
281	C₂×D₄	—	2	8	no	—
282	C₂×D₄	—	2	4	no	—
283	C₂×D₄	—	4	32	no	—
284	C₂×D₄	—	4	4	no	—
285	C₂×D₄	—	4	8	no	—
286	C₂×D₄	—	4	64	no	—
287	C₂×D₄	—	4	4	no	—
288	C₂×D₄	—	4	8	no	—
289	C₂×D₄	—	4	4	no	—
290	C₂×D₄	—	4	4	no	—
291	C₂×D₄	—	4	8	no	—
292	C₂×D₄	—	4	8	no	—
293	C₂×D₄	—	4	4	no	—
294	C₂×D₄	—	4	8	no	—
295	C₂×D₄	—	4	4	no	—
296	C₂×D₄	C₂×D₄×C₇₃	1	8	yes	—
297	C₂²×C₄	—	2	4	no	—
298	C₂²×C₄	—	2	4	no	—
299	C₂²×C₄	—	2	2	no	—
300	C₂²×C₄	—	2	2	no	—
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	D₈×C₇₃	1	8	yes	complemented
303	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
304	C₂²×C₄	C₂×D₄×C₇₃	1	4	yes	—
305	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
306	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
307	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
308	D₈	—	4	32	no	—
309	C₂×C₈	—	2	4	no	—
310	C₂×C₈	—	2	4	no	—
311	C₂×C₈	C₂×D₄×C₇₃	1	8	yes	complemented
312	C₄⋊C₄	—	2	4	no	—
313	C₄⋊C₄	—	4	4	no	—
314	C₂²⋊C₄	—	4	4	no	—
315	C₂²⋊C₄	—	4	8	no	—
316	C₄²	—	2	4	no	—
317	C₄²	—	2	2	no	—
318	C₄²	C₂×D₄×C₇₃	1	4	yes	—
319	C₂³	—	2	1	no	—
320	C₂³	—	2	1	no	—
321	C₂³	—	2	2	no	—
322	C₂³	—	2	8	no	—
323	C₂³	—	4	32	no	—
324	C₂³	—	4	16	no	—
325	C₂³	—	4	4	no	—
326	C₂³	—	4	4	no	—
327	C₂³	—	4	8	no	—
328	C₂³	—	4	8	no	—
329	C₂³	—	4	2	no	—
330	C₂³	—	4	2	no	—
331	C₂³	—	4	2	no	—
332	C₂³	—	4	4	no	—
333	C₂³	—	4	4	no	—
334	C₂³	—	8	8	no	—
335	C₂³	—	8	16	no	—
336	C₂³	—	8	8	no	—
337	C₂³	#127×C₇₃	1	2	yes	—
338	C₂³	C₂×D₈×C₇₃	1	4	yes	—
339	C₂³	C₂²×D₄×C₇₃	1	1	yes	characteristic
340	D₄	—	2	16	no	—
341	D₄	—	4	32	no	—
342	D₄	—	4	16	no	—
343	D₄	—	4	32	no	—
344	D₄	—	4	8	no	—
345	D₄	—	4	8	no	—
346	D₄	—	8	8	no	—
347	D₄	—	8	8	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	2	1	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	16	no	—
353	C₂×C₄	—	2	8	no	—
354	C₂×C₄	—	4	2	no	—
355	C₂×C₄	—	4	4	no	—
356	C₂×C₄	#120×C₇₃	1	4	yes	—
357	C₂×C₄	#127×C₇₃	1	2	yes	—
358	C₂×C₄	C₂×D₈×C₇₃	1	4	yes	—
359	C₂×C₄	C₂×D₈×C₇₃	1	4	yes	—
360	C₂×C₄	AGL(1,ℤ/8)×C₇₃	1	4	yes	—
361	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
362	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
363	C₂×C₄	H(5,𝔽₂)×C₇₃	1	2	yes	—
364	C₈	—	2	8	no	—
365	C₂²	—	2	4	no	—
366	C₂²	—	2	2	no	—
367	C₂²	—	2	2	no	—
368	C₂²	—	2	4	no	—
369	C₂²	—	4	16	no	—
370	C₂²	—	4	8	no	—
371	C₂²	—	8	32	no	—
372	C₂²	—	8	4	no	—
373	C₂²	—	8	4	no	—
374	C₂²	—	8	8	no	—
375	C₂²	—	8	4	no	—
376	C₂²	—	8	2	no	—
377	C₂²	—	8	2	no	—
378	C₂²	—	8	2	no	—
379	C₂²	—	8	4	no	—
380	C₂²	#493×C₇₃	1	4	yes	complemented
381	C₂²	C₂×#120×C₇₃	1	1	yes	characteristic
382	C₂²	C₂×#127×C₇₃	1	1	yes	characteristic
383	C₂²	#535×C₇₃	1	1	yes	characteristic
384	C₂²	C₂²×D₈×C₇₃	1	2	yes	—
385	C₂²	C₂×AGL(1,ℤ/8)×C₇₃	1	2	yes	—
386	C₄	—	2	4	no	—
387	C₄	—	2	2	no	—
388	C₄	—	8	2	no	—
389	C₄	#447×C₇₃	1	8	yes	complemented
390	C₄	D₄²×C₇₃	1	4	yes	—
391	C₂	—	2	4	no	—
392	C₂	—	8	8	no	—
393	C₂	—	16	2	no	—
394	C₂	C₇₃×#2433	1	1	yes	characteristic
395	C₂	C₂×#447×C₇₃	1	2	yes	—
396	C₂	C₂×#493×C₇₃	1	1	yes	characteristic
397	C₂	C₇₃×#3151	1	1	yes	characteristic
398	C₂	C₇₃×#3205	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₇₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₃
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. C₂²×#127×C₇₃	C₂	semidirect
2. C₂×#493×C₇₃	C₂	semidirect
3. C₂×#447×C₇₃	C₂	semidirect
4. C₇₃×#2856	C₂	semidirect
5. C₇₃×#2011	C₂	semidirect
6. C₇₃×#1957	C₂	semidirect
7. C₄×C₂²⋊C₈×C₇₃	C₂	semidirect
10. C₂²×D₈×C₇₃	C₂²	semidirect
15. C₂×#127×C₇₃	C₂²	semidirect
21. C₂×#102×C₇₃	C₂²	semidirect
23. C₂×C₄×C₈×C₇₃	C₂²	semidirect
25. #390×C₇₃	C₂²	semidirect
26. #384×C₇₃	C₂²	semidirect
27. #336×C₇₃	C₂²	semidirect
52. #127×C₇₃	D₄	semidirect
64. C₂²⋊C₈×C₇₃	D₄	semidirect
102. C₂²×C₄×C₇₃	D₈	semidirect
111. C₂×C₈×C₇₃	C₂×D₄	semidirect
180. C₂²×C₇₃	#493	semidirect
189. C₄×C₇₃	#447	semidirect
191. #25721	C₇₃	direct (N × H)
200. C₂²×#127	C₂×C₇₃	semidirect
201. C₂×#493	C₂×C₇₃	semidirect
202. C₂×#447	C₂×C₇₃	semidirect
203. #2856	C₂×C₇₃	semidirect
204. #2011	C₂×C₇₃	semidirect
205. #1957	C₂×C₇₃	semidirect
206. C₄×C₂²⋊C₈	C₂×C₇₃	semidirect
207. C₇₃	#25721	direct (N × H)
210. C₂²×D₈	C₂²×C₇₃	semidirect
215. C₂×#127	C₂²×C₇₃	semidirect
221. C₂×#102	C₂²×C₇₃	semidirect
223. C₂×C₄×C₈	C₂²×C₇₃	semidirect
225. #390	C₂²×C₇₃	semidirect
226. #384	C₂²×C₇₃	semidirect
227. #336	C₂²×C₇₃	semidirect
252. #127	D₄×C₇₃	semidirect
264. C₂²⋊C₈	D₄×C₇₃	semidirect
302. C₂²×C₄	D₈×C₇₃	semidirect
311. C₂×C₈	C₂×D₄×C₇₃	semidirect
380. C₂²	#493×C₇₃	semidirect
389. C₄	#447×C₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#127×C₇₃	2
C₂×#493×C₇₃	2
C₂×#447×C₇₃	2
C₇₃×#2856	2
C₇₃×#2011	2
C₇₃×#1957	2
C₄×C₂²⋊C₈×C₇₃	2
#25721	73

Subgroups — C73×#25721 #32935125

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#25721 #32935125