Subgroups — C₇₃×#33786 #32943190

Order 18688.

618 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₃×#3176	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇₃×#3155	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₃×#2250	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₃×#2246	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₃×#2244	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇₃×#2242	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇₃×#2210	C₂	1	2	yes	maximal, complemented
8	C₇₃×#2206	C₂	1	2	yes	maximal, complemented
9	C₇₃×#2186	C₂	1	2	yes	maximal, complemented
10	C₇₃×#2184	C₂	1	2	yes	maximal, complemented
11	C₇₃×#2164	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×AGL(1,ℤ/8)×C₇₃	—	2	1	no	—
13	C₂×#135×C₇₃	C₂²	1	1	yes	characteristic
14	C₂²×D₈×C₇₃	C₂²	1	1	yes	characteristic
15	#540×C₇₃	—	2	1	no	—
16	#535×C₇₃	—	2	1	no	—
17	C₂×SD₃₂×C₇₃	C₂²	1	2	yes	complemented
18	C₂×D₁₆×C₇₃	C₂²	1	2	yes	—
19	C₂×D₁₆×C₇₃	C₂²	1	2	yes	—
20	C₂×D₁₆×C₇₃	C₂²	1	2	yes	complemented
21	#499×C₇₃	C₂²	1	1	yes	characteristic, complemented
22	#496×C₇₃	—	2	1	no	—
23	#496×C₇₃	—	2	1	no	—
24	#495×C₇₃	C₂²	1	1	yes	characteristic
25	#495×C₇₃	C₂²	1	1	yes	characteristic
26	#493×C₇₃	C₂²	1	1	yes	characteristic
27	#493×C₇₃	C₂²	1	1	yes	characteristic
28	#493×C₇₃	C₂²	1	1	yes	characteristic, complemented
29	#490×C₇₃	—	2	1	no	—
30	#469×C₇₃	—	2	1	no	—
31	#466×C₇₃	C₂²	1	2	yes	—
32	#442×C₇₃	—	2	1	no	—
33	C₄×D₈×C₇₃	C₂²	1	2	yes	complemented
34	#405×C₇₃	C₂²	1	1	yes	characteristic
35	C₄⋊C₁₆×C₇₃	C₂²	1	2	yes	complemented
36	#358×C₇₃	C₂²	1	2	yes	complemented
37	#357×C₇₃	C₂²	1	2	yes	—
38	#357×C₇₃	C₂²	1	2	yes	—
39	#357×C₇₃	C₂²	1	2	yes	complemented
40	C₂²⋊C₁₆×C₇₃	C₂²	1	2	yes	—
41	#346×C₇₃	C₂²	1	1	yes	characteristic, complemented
42	C₄×C₁₆×C₇₃	C₂²	1	1	yes	characteristic, complemented
43	C₂×#41×C₇₃	—	2	1	no	—
44	C₂²×D₄×C₇₃	—	2	1	no	—
45	AGL(1,ℤ/8)×C₇₃	—	4	4	no	—
46	#135×C₇₃	—	4	2	no	—
47	C₂×Q₁₆×C₇₃	C₂³	1	1	yes	characteristic
48	C₂×SD₁₆×C₇₃	—	2	1	no	—
49	C₂×SD₁₆×C₇₃	—	2	1	no	—
50	C₂×SD₁₆×C₇₃	—	2	1	no	—
51	C₂×D₈×C₇₃	—	2	1	no	—
52	C₂×D₈×C₇₃	—	2	1	no	—
53	C₂×D₈×C₇₃	—	2	1	no	—
54	C₂×D₈×C₇₃	—	2	1	no	—
55	C₂×D₈×C₇₃	—	4	2	no	—
56	C₂×D₈×C₇₃	C₂³	1	2	yes	—
57	C₂×D₈×C₇₃	C₂³	1	1	yes	characteristic
58	C₂×D₈×C₇₃	C₂³	1	1	yes	characteristic
59	C₂×D₈×C₇₃	C₂³	1	1	yes	characteristic
60	C₂×M₁₆×C₇₃	D₄	1	1	yes	characteristic
61	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
62	#127×C₇₃	—	2	1	no	—
63	#127×C₇₃	—	2	1	no	—
64	#127×C₇₃	—	2	1	no	—
65	#125×C₇₃	—	2	1	no	—
66	#124×C₇₃	—	2	1	no	—
67	#124×C₇₃	—	2	1	no	—
68	#123×C₇₃	—	4	2	no	—
69	#121×C₇₃	—	2	2	no	—
70	#121×C₇₃	—	4	2	no	—
71	#121×C₇₃	—	4	2	no	—
72	#120×C₇₃	—	4	2	no	—
73	C₄×D₄×C₇₃	—	2	2	no	—
74	#117×C₇₃	D₄	1	1	yes	characteristic
75	SD₃₂×C₇₃	—	4	2	no	—
76	D₁₆×C₇₃	—	4	2	no	—
77	D₁₆×C₇₃	—	4	2	no	—
78	D₁₆×C₇₃	—	4	2	no	—
79	C₂×C₁₆×C₇₃	C₂³	1	2	yes	—
80	C₂×C₁₆×C₇₃	C₂³	1	2	yes	—
81	#107×C₇₃	C₂³	1	2	yes	—
82	#106×C₇₃	—	2	1	no	—
83	#102×C₇₃	—	2	2	no	—
84	#102×C₇₃	—	2	2	no	—
85	#97×C₇₃	D₄	1	1	yes	characteristic
86	#97×C₇₃	D₄	1	1	yes	characteristic
87	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
88	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
89	C₂⁴×C₇₃	—	4	1	no	—
90	#41×C₇₃	—	4	2	no	—
91	#41×C₇₃	—	4	2	no	—
92	C₂×Q₈×C₇₃	—	2	1	no	—
93	C₂×D₄×C₇₃	—	2	2	no	—
94	C₂×D₄×C₇₃	—	2	1	no	—
95	C₂×D₄×C₇₃	—	2	1	no	—
96	C₂×D₄×C₇₃	—	2	1	no	—
97	C₂×D₄×C₇₃	—	4	2	no	—
98	C₂×D₄×C₇₃	—	4	2	no	—
99	C₂×D₄×C₇₃	—	4	1	no	—
100	C₂×D₄×C₇₃	—	4	2	no	—
101	C₂×D₄×C₇₃	—	4	1	no	—
102	C₂×D₄×C₇₃	—	4	2	no	—
103	C₂×D₄×C₇₃	—	4	2	no	—
104	C₂×D₄×C₇₃	—	4	2	no	—
105	C₂²×C₄×C₇₃	—	4	1	no	—
106	C₂²×C₄×C₇₃	—	4	2	no	—
107	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
108	Q₁₆×C₇₃	—	2	2	no	—
109	SD₁₆×C₇₃	—	4	2	no	—
110	SD₁₆×C₇₃	—	4	2	no	—
111	SD₁₆×C₇₃	—	4	2	no	—
112	D₈×C₇₃	—	2	2	no	—
113	D₈×C₇₃	—	2	2	no	—
114	D₈×C₇₃	—	2	2	no	—
115	D₈×C₇₃	—	2	2	no	—
116	D₈×C₇₃	—	2	2	no	—
117	D₈×C₇₃	—	4	2	no	—
118	D₈×C₇₃	—	4	2	no	—
119	D₈×C₇₃	—	4	2	no	—
120	D₈×C₇₃	—	4	2	no	—
121	M₁₆×C₇₃	—	2	2	no	—
122	C₂×C₈×C₇₃	—	2	2	no	—
123	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
124	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
125	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
126	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
127	C₄⋊C₄×C₇₃	—	2	2	no	—
128	C₄⋊C₄×C₇₃	—	4	2	no	—
129	C₄⋊C₄×C₇₃	D₈	1	2	yes	—
130	C₂²⋊C₄×C₇₃	—	4	2	no	—
131	C₂²⋊C₄×C₇₃	—	4	2	no	—
132	C₂²⋊C₄×C₇₃	—	4	2	no	—
133	C₂²⋊C₄×C₇₃	—	4	2	no	—
134	C₂²⋊C₄×C₇₃	D₈	1	2	yes	—
135	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
136	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
137	C₁₆×C₇₃	—	2	2	no	—
138	C₁₆×C₇₃	—	2	2	no	—
139	C₂³×C₇₃	—	4	2	no	—
140	C₂³×C₇₃	—	4	1	no	—
141	C₂³×C₇₃	—	4	1	no	—
142	C₂³×C₇₃	—	4	1	no	—
143	C₂³×C₇₃	—	8	2	no	—
144	C₂³×C₇₃	—	16	2	no	—
145	C₂³×C₇₃	C₂×D₈	1	1	yes	characteristic
146	Q₈×C₇₃	—	4	1	no	—
147	Q₈×C₇₃	—	4	1	no	—
148	D₄×C₇₃	—	4	1	no	—
149	D₄×C₇₃	—	4	1	no	—
150	D₄×C₇₃	—	4	1	no	—
151	D₄×C₇₃	—	4	2	no	—
152	D₄×C₇₃	—	4	1	no	—
153	D₄×C₇₃	—	4	1	no	—
154	D₄×C₇₃	—	4	1	no	—
155	D₄×C₇₃	—	4	2	no	—
156	D₄×C₇₃	—	8	2	no	—
157	D₄×C₇₃	—	8	2	no	—
158	D₄×C₇₃	—	16	2	no	—
159	D₄×C₇₃	—	16	2	no	—
160	D₄×C₇₃	—	16	2	no	—
161	D₄×C₇₃	—	16	2	no	—
162	C₂×C₄×C₇₃	—	2	1	no	—
163	C₂×C₄×C₇₃	—	2	1	no	—
164	C₂×C₄×C₇₃	—	4	1	no	—
165	C₂×C₄×C₇₃	—	4	2	no	—
166	C₂×C₄×C₇₃	—	8	2	no	—
167	C₂×C₄×C₇₃	—	16	2	no	—
168	C₂×C₄×C₇₃	C₂×D₈	1	2	yes	—
169	C₂×C₄×C₇₃	C₂×D₈	1	2	yes	—
170	C₂×C₄×C₇₃	C₂×D₈	1	1	yes	characteristic
171	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
172	C₈×C₇₃	—	2	1	no	—
173	C₈×C₇₃	—	2	1	no	—
174	C₈×C₇₃	AGL(1,ℤ/8)	1	2	yes	—
175	C₈×C₇₃	H(5,𝔽₂)	1	2	yes	—
176	C₂²×C₇₃	—	2	2	no	—
177	C₂²×C₇₃	—	2	1	no	—
178	C₂²×C₇₃	—	8	2	no	—
179	C₂²×C₇₃	—	8	2	no	—
180	C₂²×C₇₃	—	8	2	no	—
181	C₂²×C₇₃	—	8	2	no	—
182	C₂²×C₇₃	—	8	2	no	—
183	C₂²×C₇₃	—	8	1	no	—
184	C₂²×C₇₃	—	8	1	no	—
185	C₂²×C₇₃	—	8	1	no	—
186	C₂²×C₇₃	—	8	2	no	—
187	C₂²×C₇₃	—	16	4	no	—
188	C₂²×C₇₃	C₂²×D₈	1	1	yes	characteristic
189	C₄×C₇₃	—	2	2	no	—
190	C₄×C₇₃	—	2	2	no	—
191	C₄×C₇₃	—	2	1	no	—
192	C₄×C₇₃	—	8	2	no	—
193	C₄×C₇₃	—	8	1	no	—
194	C₄×C₇₃	#535	1	1	yes	characteristic
195	C₄×C₇₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
196	#33786	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
197	C₂×C₇₃	—	4	1	no	—
198	C₂×C₇₃	—	16	2	no	—
199	C₂×C₇₃	—	16	1	no	—
200	C₂×C₇₃	—	16	1	no	—
201	C₂×C₇₃	—	16	1	no	—
202	C₂×C₇₃	#3205	1	1	yes	characteristic
203	C₂×C₇₃	#3415	1	2	yes	—
204	#3176	C₂×C₇₃	1	1	yes	characteristic, complemented
205	#3155	C₂×C₇₃	1	1	yes	characteristic, complemented
206	#2250	C₂×C₇₃	1	1	yes	characteristic, complemented
207	#2246	C₂×C₇₃	1	1	yes	characteristic, complemented
208	#2244	C₂×C₇₃	1	1	yes	characteristic, complemented
209	#2242	C₂×C₇₃	1	1	yes	characteristic, complemented
210	#2210	C₂×C₇₃	1	2	yes	complemented
211	#2206	C₂×C₇₃	1	2	yes	complemented
212	#2186	C₂×C₇₃	1	2	yes	complemented
213	#2184	C₂×C₇₃	1	2	yes	complemented
214	#2164	C₂×C₇₃	1	1	yes	characteristic, complemented
215	C₇₃	#33786	1	1	yes	characteristic, direct product factor, Sylow
216	C₂×AGL(1,ℤ/8)	—	2	1	no	—
217	C₂×#135	C₂²×C₇₃	1	1	yes	characteristic
218	C₂²×D₈	C₂²×C₇₃	1	1	yes	characteristic
219	#540	—	2	1	no	—
220	#535	—	2	1	no	—
221	C₂×SD₃₂	C₂²×C₇₃	1	2	yes	complemented
222	C₂×D₁₆	C₂²×C₇₃	1	2	yes	—
223	C₂×D₁₆	C₂²×C₇₃	1	2	yes	—
224	C₂×D₁₆	C₂²×C₇₃	1	2	yes	complemented
225	#499	C₂²×C₇₃	1	1	yes	characteristic, complemented
226	#496	—	2	1	no	—
227	#496	—	2	1	no	—
228	#495	C₂²×C₇₃	1	1	yes	characteristic
229	#495	C₂²×C₇₃	1	1	yes	characteristic
230	#493	C₂²×C₇₃	1	1	yes	characteristic
231	#493	C₂²×C₇₃	1	1	yes	characteristic
232	#493	C₂²×C₇₃	1	1	yes	characteristic, complemented
233	#490	—	2	1	no	—
234	#469	—	2	1	no	—
235	#466	C₂²×C₇₃	1	2	yes	—
236	#442	—	2	1	no	—
237	C₄×D₈	C₂²×C₇₃	1	2	yes	complemented
238	#405	C₂²×C₇₃	1	1	yes	characteristic
239	C₄⋊C₁₆	C₂²×C₇₃	1	2	yes	complemented
240	#358	C₂²×C₇₃	1	2	yes	complemented
241	#357	C₂²×C₇₃	1	2	yes	—
242	#357	C₂²×C₇₃	1	2	yes	—
243	#357	C₂²×C₇₃	1	2	yes	complemented
244	C₂²⋊C₁₆	C₂²×C₇₃	1	2	yes	—
245	#346	C₂²×C₇₃	1	1	yes	characteristic, complemented
246	C₄×C₁₆	C₂²×C₇₃	1	1	yes	characteristic, complemented
247	C₂×#41	—	2	1	no	—
248	C₂²×D₄	—	2	1	no	—
249	AGL(1,ℤ/8)	—	4	4	no	—
250	#135	—	4	2	no	—
251	C₂×Q₁₆	C₂³×C₇₃	1	1	yes	characteristic
252	C₂×SD₁₆	—	2	1	no	—
253	C₂×SD₁₆	—	2	1	no	—
254	C₂×SD₁₆	—	2	1	no	—
255	C₂×D₈	—	2	1	no	—
256	C₂×D₈	—	2	1	no	—
257	C₂×D₈	—	2	1	no	—
258	C₂×D₈	—	2	1	no	—
259	C₂×D₈	—	4	2	no	—
260	C₂×D₈	C₂³×C₇₃	1	1	yes	characteristic
261	C₂×D₈	C₂³×C₇₃	1	1	yes	characteristic
262	C₂×D₈	C₂³×C₇₃	1	1	yes	characteristic
263	C₂×D₈	C₂³×C₇₃	1	2	yes	—
264	C₂×M₁₆	D₄×C₇₃	1	1	yes	characteristic
265	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
266	#127	—	2	1	no	—
267	#127	—	2	1	no	—
268	#127	—	2	1	no	—
269	#125	—	2	1	no	—
270	#124	—	2	1	no	—
271	#124	—	2	1	no	—
272	#123	—	4	2	no	—
273	#121	—	2	2	no	—
274	#121	—	4	2	no	—
275	#121	—	4	2	no	—
276	#120	—	4	2	no	—
277	C₄×D₄	—	2	2	no	—
278	#117	D₄×C₇₃	1	1	yes	characteristic
279	SD₃₂	—	4	2	no	—
280	D₁₆	—	4	2	no	—
281	D₁₆	—	4	2	no	—
282	D₁₆	—	4	2	no	—
283	C₂×C₁₆	C₂³×C₇₃	1	2	yes	—
284	C₂×C₁₆	C₂³×C₇₃	1	2	yes	—
285	#107	C₂³×C₇₃	1	2	yes	—
286	#106	—	2	1	no	—
287	#102	—	2	2	no	—
288	#102	—	2	2	no	—
289	#97	D₄×C₇₃	1	1	yes	characteristic
290	#97	D₄×C₇₃	1	1	yes	characteristic
291	C₄×C₈	C₂³×C₇₃	1	1	yes	characteristic
292	C₄×C₈	C₂³×C₇₃	1	1	yes	characteristic
293	C₂⁴	—	4	1	no	—
294	#41	—	4	2	no	—
295	#41	—	4	2	no	—
296	C₂×Q₈	—	2	1	no	—
297	C₂×D₄	—	2	2	no	—
298	C₂×D₄	—	2	1	no	—
299	C₂×D₄	—	2	1	no	—
300	C₂×D₄	—	2	1	no	—
301	C₂×D₄	—	4	2	no	—
302	C₂×D₄	—	4	2	no	—
303	C₂×D₄	—	4	1	no	—
304	C₂×D₄	—	4	2	no	—
305	C₂×D₄	—	4	1	no	—
306	C₂×D₄	—	4	2	no	—
307	C₂×D₄	—	4	2	no	—
308	C₂×D₄	—	4	2	no	—
309	C₂²×C₄	—	4	1	no	—
310	C₂²×C₄	—	4	2	no	—
311	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
312	Q₁₆	—	2	2	no	—
313	SD₁₆	—	4	2	no	—
314	SD₁₆	—	4	2	no	—
315	SD₁₆	—	4	2	no	—
316	D₈	—	2	2	no	—
317	D₈	—	2	2	no	—
318	D₈	—	2	2	no	—
319	D₈	—	2	2	no	—
320	D₈	—	2	2	no	—
321	D₈	—	4	2	no	—
322	D₈	—	4	2	no	—
323	D₈	—	4	2	no	—
324	D₈	—	4	2	no	—
325	M₁₆	—	2	2	no	—
326	C₂×C₈	—	2	2	no	—
327	C₂×C₈	C₂×D₄×C₇₃	1	1	yes	characteristic
328	C₂×C₈	C₂×D₄×C₇₃	1	1	yes	characteristic
329	C₂×C₈	C₂×D₄×C₇₃	1	1	yes	characteristic
330	C₂×C₈	C₂⁴×C₇₃	1	1	yes	characteristic
331	C₄⋊C₄	—	2	2	no	—
332	C₄⋊C₄	—	4	2	no	—
333	C₄⋊C₄	D₈×C₇₃	1	2	yes	—
334	C₂²⋊C₄	—	4	2	no	—
335	C₂²⋊C₄	—	4	2	no	—
336	C₂²⋊C₄	—	4	2	no	—
337	C₂²⋊C₄	—	4	2	no	—
338	C₂²⋊C₄	D₈×C₇₃	1	2	yes	—
339	C₄²	C₂×D₄×C₇₃	1	1	yes	characteristic
340	C₄²	C₂×D₄×C₇₃	1	1	yes	characteristic
341	C₁₆	—	2	2	no	—
342	C₁₆	—	2	2	no	—
343	C₂³	—	4	2	no	—
344	C₂³	—	4	1	no	—
345	C₂³	—	4	1	no	—
346	C₂³	—	4	1	no	—
347	C₂³	—	8	2	no	—
348	C₂³	—	16	2	no	—
349	C₂³	C₂×D₈×C₇₃	1	1	yes	characteristic
350	Q₈	—	4	1	no	—
351	Q₈	—	4	1	no	—
352	D₄	—	4	1	no	—
353	D₄	—	4	1	no	—
354	D₄	—	4	1	no	—
355	D₄	—	4	2	no	—
356	D₄	—	4	1	no	—
357	D₄	—	4	1	no	—
358	D₄	—	4	1	no	—
359	D₄	—	4	2	no	—
360	D₄	—	8	2	no	—
361	D₄	—	8	2	no	—
362	D₄	—	16	2	no	—
363	D₄	—	16	2	no	—
364	D₄	—	16	2	no	—
365	D₄	—	16	2	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	4	1	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	8	2	no	—
371	C₂×C₄	—	16	2	no	—
372	C₂×C₄	C₂×D₈×C₇₃	1	2	yes	—
373	C₂×C₄	C₂×D₈×C₇₃	1	2	yes	—
374	C₂×C₄	C₂×D₈×C₇₃	1	1	yes	characteristic
375	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
376	C₈	—	2	1	no	—
377	C₈	—	2	1	no	—
378	C₈	AGL(1,ℤ/8)×C₇₃	1	2	yes	—
379	C₈	H(5,𝔽₂)×C₇₃	1	2	yes	—
380	C₂²	—	2	2	no	—
381	C₂²	—	2	1	no	—
382	C₂²	—	8	2	no	—
383	C₂²	—	8	2	no	—
384	C₂²	—	8	2	no	—
385	C₂²	—	8	2	no	—
386	C₂²	—	8	2	no	—
387	C₂²	—	8	1	no	—
388	C₂²	—	8	1	no	—
389	C₂²	—	8	1	no	—
390	C₂²	—	8	2	no	—
391	C₂²	—	16	4	no	—
392	C₂²	C₂²×D₈×C₇₃	1	1	yes	characteristic
393	C₄	—	2	2	no	—
394	C₄	—	2	2	no	—
395	C₄	—	2	1	no	—
396	C₄	—	8	2	no	—
397	C₄	—	8	1	no	—
398	C₄	#535×C₇₃	1	1	yes	characteristic
399	C₄	C₂×AGL(1,ℤ/8)×C₇₃	1	1	yes	characteristic
400	C₂	—	4	1	no	—
401	C₂	—	16	1	no	—
402	C₂	—	16	1	no	—
403	C₂	—	16	2	no	—
404	C₂	—	16	1	no	—
405	C₂	C₇₃×#3205	1	1	yes	characteristic
406	C₂	C₇₃×#3415	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₇₃	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₇₃
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇₃ ◁ #117×C₇₃ ◁ #405×C₇₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇₃×#3176	C₂	semidirect
2. C₇₃×#3155	C₂	semidirect
3. C₇₃×#2250	C₂	semidirect
4. C₇₃×#2246	C₂	semidirect
5. C₇₃×#2244	C₂	semidirect
6. C₇₃×#2242	C₂	semidirect
7. C₇₃×#2210	C₂	semidirect
8. C₇₃×#2206	C₂	semidirect
9. C₇₃×#2186	C₂	semidirect
10. C₇₃×#2184	C₂	semidirect
11. C₇₃×#2164	C₂	semidirect
17. C₂×SD₃₂×C₇₃	C₂²	semidirect
20. C₂×D₁₆×C₇₃	C₂²	semidirect
21. #499×C₇₃	C₂²	semidirect
28. #493×C₇₃	C₂²	semidirect
33. C₄×D₈×C₇₃	C₂²	semidirect
35. C₄⋊C₁₆×C₇₃	C₂²	semidirect
36. #358×C₇₃	C₂²	semidirect
39. #357×C₇₃	C₂²	semidirect
41. #346×C₇₃	C₂²	semidirect
42. C₄×C₁₆×C₇₃	C₂²	semidirect
196. #33786	C₇₃	direct (N × H)
204. #3176	C₂×C₇₃	semidirect
205. #3155	C₂×C₇₃	semidirect
206. #2250	C₂×C₇₃	semidirect
207. #2246	C₂×C₇₃	semidirect
208. #2244	C₂×C₇₃	semidirect
209. #2242	C₂×C₇₃	semidirect
210. #2210	C₂×C₇₃	semidirect
211. #2206	C₂×C₇₃	semidirect
212. #2186	C₂×C₇₃	semidirect
213. #2184	C₂×C₇₃	semidirect
214. #2164	C₂×C₇₃	semidirect
215. C₇₃	#33786	direct (N × H)
221. C₂×SD₃₂	C₂²×C₇₃	semidirect
224. C₂×D₁₆	C₂²×C₇₃	semidirect
225. #499	C₂²×C₇₃	semidirect
232. #493	C₂²×C₇₃	semidirect
237. C₄×D₈	C₂²×C₇₃	semidirect
239. C₄⋊C₁₆	C₂²×C₇₃	semidirect
240. #358	C₂²×C₇₃	semidirect
243. #357	C₂²×C₇₃	semidirect
245. #346	C₂²×C₇₃	semidirect
246. C₄×C₁₆	C₂²×C₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₇₃×#3176	2
C₇₃×#3155	2
C₇₃×#2250	2
C₇₃×#2246	2
C₇₃×#2244	2
C₇₃×#2242	2
C₇₃×#2210	2
C₇₃×#2206	2
C₇₃×#2186	2
C₇₃×#2184	2
C₇₃×#2164	2
#33786	73

Subgroups — C73×#33786 #32943190

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#33786 #32943190