Subgroups — C₂₃×#20786 #19168412

Order 5888.

758 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₂₃×#117	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#1840	C₂	1	2	yes	maximal, complemented
3	C₂₃×#1831	C₂	1	2	yes	maximal, complemented
4	C₂₃×#1818	C₂	1	2	yes	maximal
5	C₂₃×#1797	C₂	1	2	yes	maximal
6	C₂₃×#1767	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄×C₂₃×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#1750	C₂	1	2	yes	maximal
9	C₂₃×#1746	C₂	1	2	yes	maximal, complemented
10	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
11	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
12	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
13	C₂×C₂₃×C₄⋊C₈	C₂²	1	2	yes	—
14	C₂×C₂₃×C₄⋊C₈	C₂²	1	2	yes	—
15	C₂×C₂₃×C₂²⋊C₈	C₂²	1	4	yes	—
16	C₂×C₂₃×#97	C₂²	1	2	yes	—
17	C₂×C₄×C₈×C₂₃	C₂²	1	2	yes	—
18	C₄×C₄⋊C₄×C₂₃	C₄	1	2	yes	—
19	C₄×C₄⋊C₄×C₂₃	C₄	1	2	yes	—
20	C₄×C₂²⋊C₄×C₂₃	C₄	1	2	yes	—
21	C₄×C₂²⋊C₄×C₂₃	C₄	1	2	yes	—
22	C₂₃×#376	C₂²	1	1	yes	characteristic
23	C₂₃×#376	C₂²	1	1	yes	characteristic
24	C₄³×C₂₃	C₂²	1	1	yes	characteristic
25	C₄³×C₂₃	C₂²	1	1	yes	characteristic
26	C₂₃×#336	C₂²	1	4	yes	—
27	C₂₃×#336	C₂²	1	4	yes	—
28	C₂₃×#336	C₂²	1	4	yes	—
29	C₂₃×#336	C₂²	1	2	yes	—
30	C₂₃×#336	C₂²	1	2	yes	—
31	C₂³×C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
32	C₂³×C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
33	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
34	C₂²×C₈×C₂₃	C₂³	1	4	yes	—
35	C₂²×C₈×C₂₃	C₂³	1	4	yes	—
36	C₂₃×#117	—	2	4	no	—
37	C₂₃×#117	—	2	2	no	—
38	C₂₃×#117	—	2	2	no	—
39	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
40	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
41	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
42	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
43	C₂×C₄²×C₂₃	—	2	4	no	—
44	C₂×C₄²×C₂₃	C₂×C₄	1	2	yes	—
45	C₂×C₄²×C₂₃	C₂×C₄	1	2	yes	—
46	C₂×C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
47	C₂×C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
48	C₂×C₄²×C₂₃	C₂×C₄	1	2	yes	—
49	C₂×C₄²×C₂₃	C₂×C₄	1	2	yes	—
50	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
51	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
52	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
53	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
54	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
55	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
56	C₂₃×C₄⋊C₈	—	2	4	no	—
57	C₂₃×C₄⋊C₈	—	2	4	no	—
58	C₂₃×C₂²⋊C₈	—	2	8	no	—
59	C₂₃×#97	—	2	4	no	—
60	C₄×C₈×C₂₃	—	2	4	no	—
61	C₂₃×#95	C₂×C₄	1	2	yes	—
62	C₂₃×#95	C₂×C₄	1	2	yes	—
63	C₂₃×#95	C₂×C₄	1	2	yes	—
64	C₂₃×#95	C₂×C₄	1	2	yes	—
65	C₂⁴×C₂₃	C₂²×C₄	1	1	yes	characteristic
66	C₂²×C₄×C₂₃	—	2	2	no	—
67	C₂²×C₄×C₂₃	—	2	1	no	—
68	C₂²×C₄×C₂₃	—	2	1	no	—
69	C₂²×C₄×C₂₃	—	2	2	no	—
70	C₂²×C₄×C₂₃	—	2	2	no	—
71	C₂²×C₄×C₂₃	—	2	4	no	—
72	C₂²×C₄×C₂₃	—	4	2	no	—
73	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
74	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
75	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
76	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
77	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
78	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
79	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
80	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
81	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
82	C₂²×C₄×C₂₃	#41	1	4	yes	—
83	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
84	C₂×C₈×C₂₃	—	2	4	no	—
85	C₂×C₈×C₂₃	—	2	4	no	—
86	C₂×C₈×C₂₃	—	2	4	no	—
87	C₂×C₈×C₂₃	—	2	4	no	—
88	C₂×C₈×C₂₃	—	2	4	no	—
89	C₂×C₈×C₂₃	—	2	4	no	—
90	C₄⋊C₄×C₂₃	—	2	4	no	—
91	C₄⋊C₄×C₂₃	—	2	4	no	—
92	C₂²⋊C₄×C₂₃	—	2	4	no	—
93	C₂²⋊C₄×C₂₃	—	2	4	no	—
94	C₄²×C₂₃	—	2	2	no	—
95	C₄²×C₂₃	—	2	2	no	—
96	C₄²×C₂₃	—	2	4	no	—
97	C₄²×C₂₃	—	2	4	no	—
98	C₄²×C₂₃	—	2	2	no	—
99	C₄²×C₂₃	—	2	2	no	—
100	C₄²×C₂₃	—	2	2	no	—
101	C₄²×C₂₃	—	2	1	no	—
102	C₄²×C₂₃	—	2	1	no	—
103	C₄²×C₂₃	—	4	2	no	—
104	C₄²×C₂₃	—	4	2	no	—
105	C₄²×C₂₃	#41	1	4	yes	—
106	C₄²×C₂₃	#41	1	2	yes	—
107	C₄²×C₂₃	#41	1	2	yes	—
108	#20786	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
109	C₂³×C₂₃	—	2	1	no	—
110	C₂³×C₂₃	—	2	1	no	—
111	C₂³×C₂₃	—	2	2	no	—
112	C₂³×C₂₃	—	2	2	no	—
113	C₂³×C₂₃	#117	1	2	yes	—
114	C₂³×C₂₃	C₂³×C₄	1	1	yes	characteristic
115	C₂×C₄×C₂₃	—	2	1	no	—
116	C₂×C₄×C₂₃	—	2	1	no	—
117	C₂×C₄×C₂₃	—	2	2	no	—
118	C₂×C₄×C₂₃	—	2	2	no	—
119	C₂×C₄×C₂₃	—	2	2	no	—
120	C₂×C₄×C₂₃	—	2	4	no	—
121	C₂×C₄×C₂₃	—	2	4	no	—
122	C₂×C₄×C₂₃	—	2	1	no	—
123	C₂×C₄×C₂₃	—	2	1	no	—
124	C₂×C₄×C₂₃	—	2	2	no	—
125	C₂×C₄×C₂₃	—	2	2	no	—
126	C₂×C₄×C₂₃	—	2	2	no	—
127	C₂×C₄×C₂₃	—	2	2	no	—
128	C₂×C₄×C₂₃	—	2	2	no	—
129	C₂×C₄×C₂₃	—	2	2	no	—
130	C₂×C₄×C₂₃	—	2	2	no	—
131	C₂×C₄×C₂₃	—	2	2	no	—
132	C₂×C₄×C₂₃	—	2	2	no	—
133	C₂×C₄×C₂₃	—	2	2	no	—
134	C₂×C₄×C₂₃	—	2	2	no	—
135	C₂×C₄×C₂₃	—	4	4	no	—
136	C₂×C₄×C₂₃	—	4	4	no	—
137	C₂×C₄×C₂₃	#117	1	2	yes	—
138	C₂×C₄×C₂₃	#117	1	4	yes	—
139	C₂×C₄×C₂₃	#117	1	2	yes	—
140	C₂×C₄×C₂₃	#117	1	2	yes	—
141	C₂×C₄×C₂₃	#131	1	4	yes	—
142	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
143	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
144	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
145	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
146	C₈×C₂₃	—	4	4	no	—
147	C₈×C₂₃	—	4	4	no	—
148	C₄×#117	C₂×C₂₃	1	1	yes	characteristic
149	#1840	C₂×C₂₃	1	2	yes	complemented
150	#1831	C₂×C₂₃	1	2	yes	complemented
151	#1818	C₂×C₂₃	1	2	yes	—
152	#1797	C₂×C₂₃	1	2	yes	—
153	#1767	C₂×C₂₃	1	1	yes	characteristic, complemented
154	C₄×C₄⋊C₈	C₂×C₂₃	1	1	yes	characteristic, complemented
155	#1750	C₂×C₂₃	1	2	yes	—
156	#1746	C₂×C₂₃	1	2	yes	complemented
157	C₂²×C₂₃	—	2	4	no	—
158	C₂²×C₂₃	—	2	2	no	—
159	C₂²×C₂₃	—	4	1	no	—
160	C₂²×C₂₃	—	4	1	no	—
161	C₂²×C₂₃	—	4	2	no	—
162	C₂²×C₂₃	C₂×#117	1	1	yes	characteristic
163	C₂²×C₂₃	C₂×#117	1	1	yes	characteristic
164	C₂²×C₂₃	C₂×#117	1	1	yes	characteristic
165	C₂²×C₂₃	C₂×#131	1	2	yes	—
166	C₂²×C₂₃	#568	1	2	yes	—
167	C₄×C₂₃	—	2	2	no	—
168	C₄×C₂₃	—	2	4	no	—
169	C₄×C₂₃	—	2	2	no	—
170	C₄×C₂₃	—	4	1	no	—
171	C₄×C₂₃	—	4	1	no	—
172	C₄×C₂₃	—	4	2	no	—
173	C₄×C₂₃	—	4	2	no	—
174	C₄×C₂₃	—	4	2	no	—
175	C₄×C₂₃	#433	1	4	yes	—
176	C₄×C₂₃	#529	1	2	yes	—
177	C₄×C₂₃	#529	1	2	yes	—
178	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
179	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
180	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
181	C₂×C₄⋊C₈	C₂²×C₂₃	1	2	yes	—
182	C₂×C₄⋊C₈	C₂²×C₂₃	1	2	yes	—
183	C₂×C₂²⋊C₈	C₂²×C₂₃	1	4	yes	—
184	C₂×#97	C₂²×C₂₃	1	2	yes	—
185	C₂×C₄×C₈	C₂²×C₂₃	1	2	yes	—
186	C₄×C₄⋊C₄	C₄×C₂₃	1	2	yes	—
187	C₄×C₄⋊C₄	C₄×C₂₃	1	2	yes	—
188	C₄×C₂²⋊C₄	C₄×C₂₃	1	2	yes	—
189	C₄×C₂²⋊C₄	C₄×C₂₃	1	2	yes	—
190	#376	C₂²×C₂₃	1	1	yes	characteristic
191	#376	C₂²×C₂₃	1	1	yes	characteristic
192	C₄³	C₂²×C₂₃	1	1	yes	characteristic
193	C₄³	C₂²×C₂₃	1	1	yes	characteristic
194	#336	C₂²×C₂₃	1	4	yes	—
195	#336	C₂²×C₂₃	1	4	yes	—
196	#336	C₂²×C₂₃	1	2	yes	—
197	#336	C₂²×C₂₃	1	2	yes	—
198	#336	C₂²×C₂₃	1	4	yes	—
199	C₂×C₂₃	—	4	2	no	—
200	C₂×C₂₃	#2283	1	1	yes	characteristic
201	C₂×C₂₃	C₂×#433	1	1	yes	characteristic
202	C₂×C₂₃	#2921	1	1	yes	characteristic
203	C₂×C₂₃	#2925	1	2	yes	—
204	C₂×C₂₃	#2925	1	2	yes	—
205	C₂³×C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
206	C₂³×C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
207	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
208	C₂²×C₈	C₂³×C₂₃	1	4	yes	—
209	C₂²×C₈	C₂³×C₂₃	1	4	yes	—
210	#117	—	2	4	no	—
211	#117	—	2	2	no	—
212	#117	—	2	2	no	—
213	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
214	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
215	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
216	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
217	C₂×C₄²	—	2	4	no	—
218	C₂×C₄²	C₂×C₄×C₂₃	1	2	yes	—
219	C₂×C₄²	C₂×C₄×C₂₃	1	2	yes	—
220	C₂×C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic
221	C₂×C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic
222	C₂×C₄²	C₂×C₄×C₂₃	1	2	yes	—
223	C₂×C₄²	C₂×C₄×C₂₃	1	2	yes	—
224	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
225	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
226	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
227	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
228	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
229	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
230	C₄⋊C₈	—	2	4	no	—
231	C₄⋊C₈	—	2	4	no	—
232	C₂²⋊C₈	—	2	8	no	—
233	#97	—	2	4	no	—
234	C₄×C₈	—	2	4	no	—
235	#95	C₂×C₄×C₂₃	1	2	yes	—
236	#95	C₂×C₄×C₂₃	1	2	yes	—
237	#95	C₂×C₄×C₂₃	1	2	yes	—
238	#95	C₂×C₄×C₂₃	1	2	yes	—
239	C₂₃	#20786	1	1	yes	characteristic, direct product factor, Sylow
240	C₂⁴	C₂²×C₄×C₂₃	1	1	yes	characteristic
241	C₂²×C₄	—	2	2	no	—
242	C₂²×C₄	—	2	1	no	—
243	C₂²×C₄	—	2	1	no	—
244	C₂²×C₄	—	2	2	no	—
245	C₂²×C₄	—	2	2	no	—
246	C₂²×C₄	—	2	4	no	—
247	C₂²×C₄	—	4	2	no	—
248	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
249	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
250	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
251	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
252	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
253	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
254	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
255	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
256	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
257	C₂²×C₄	#41×C₂₃	1	4	yes	—
258	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
259	C₂×C₈	—	2	4	no	—
260	C₂×C₈	—	2	4	no	—
261	C₂×C₈	—	2	4	no	—
262	C₂×C₈	—	2	4	no	—
263	C₂×C₈	—	2	4	no	—
264	C₂×C₈	—	2	4	no	—
265	C₄⋊C₄	—	2	4	no	—
266	C₄⋊C₄	—	2	4	no	—
267	C₂²⋊C₄	—	2	4	no	—
268	C₂²⋊C₄	—	2	4	no	—
269	C₄²	—	2	2	no	—
270	C₄²	—	2	2	no	—
271	C₄²	—	2	4	no	—
272	C₄²	—	2	4	no	—
273	C₄²	—	2	2	no	—
274	C₄²	—	2	2	no	—
275	C₄²	—	2	2	no	—
276	C₄²	—	2	1	no	—
277	C₄²	—	2	1	no	—
278	C₄²	—	4	2	no	—
279	C₄²	—	4	2	no	—
280	C₄²	#41×C₂₃	1	2	yes	—
281	C₄²	#41×C₂₃	1	2	yes	—
282	C₄²	#41×C₂₃	1	4	yes	—
283	C₂³	—	2	2	no	—
284	C₂³	—	2	2	no	—
285	C₂³	—	2	1	no	—
286	C₂³	—	2	1	no	—
287	C₂³	C₂₃×#117	1	2	yes	—
288	C₂³	C₂³×C₄×C₂₃	1	1	yes	characteristic
289	C₂×C₄	—	2	2	no	—
290	C₂×C₄	—	2	2	no	—
291	C₂×C₄	—	2	2	no	—
292	C₂×C₄	—	2	1	no	—
293	C₂×C₄	—	2	1	no	—
294	C₂×C₄	—	2	4	no	—
295	C₂×C₄	—	2	4	no	—
296	C₂×C₄	—	2	2	no	—
297	C₂×C₄	—	2	2	no	—
298	C₂×C₄	—	2	2	no	—
299	C₂×C₄	—	2	2	no	—
300	C₂×C₄	—	2	2	no	—
301	C₂×C₄	—	2	2	no	—
302	C₂×C₄	—	2	2	no	—
303	C₂×C₄	—	2	2	no	—
304	C₂×C₄	—	2	1	no	—
305	C₂×C₄	—	2	1	no	—
306	C₂×C₄	—	2	2	no	—
307	C₂×C₄	—	2	2	no	—
308	C₂×C₄	—	2	2	no	—
309	C₂×C₄	—	4	4	no	—
310	C₂×C₄	—	4	4	no	—
311	C₂×C₄	C₂₃×#117	1	2	yes	—
312	C₂×C₄	C₂₃×#117	1	4	yes	—
313	C₂×C₄	C₂₃×#117	1	2	yes	—
314	C₂×C₄	C₂₃×#117	1	2	yes	—
315	C₂×C₄	C₂₃×#131	1	4	yes	—
316	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
317	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
318	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
319	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
320	C₈	—	4	4	no	—
321	C₈	—	4	4	no	—
322	C₂²	—	2	4	no	—
323	C₂²	—	2	2	no	—
324	C₂²	—	4	1	no	—
325	C₂²	—	4	1	no	—
326	C₂²	—	4	2	no	—
327	C₂²	C₂×C₂₃×#117	1	1	yes	characteristic
328	C₂²	C₂×C₂₃×#117	1	1	yes	characteristic
329	C₂²	C₂×C₂₃×#117	1	1	yes	characteristic
330	C₂²	C₂×C₂₃×#131	1	2	yes	—
331	C₂²	C₂₃×#568	1	2	yes	—
332	C₄	—	2	2	no	—
333	C₄	—	2	4	no	—
334	C₄	—	2	2	no	—
335	C₄	—	4	1	no	—
336	C₄	—	4	1	no	—
337	C₄	—	4	2	no	—
338	C₄	—	4	2	no	—
339	C₄	—	4	2	no	—
340	C₄	C₂₃×#433	1	4	yes	—
341	C₄	C₂₃×#529	1	2	yes	—
342	C₄	C₂₃×#529	1	2	yes	—
343	C₂	—	4	2	no	—
344	C₂	C₂₃×#2283	1	1	yes	characteristic
345	C₂	C₂×C₂₃×#433	1	1	yes	characteristic
346	C₂	C₂₃×#2921	1	1	yes	characteristic
347	C₂	C₂₃×#2925	1	2	yes	—
348	C₂	C₂₃×#2925	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
2. C₂₃×#1840	C₂	semidirect
3. C₂₃×#1831	C₂	semidirect
6. C₂₃×#1767	C₂	semidirect
7. C₄×C₂₃×C₄⋊C₈	C₂	semidirect
9. C₂₃×#1746	C₂	semidirect
108. #20786	C₂₃	direct (N × H)
149. #1840	C₂×C₂₃	semidirect
150. #1831	C₂×C₂₃	semidirect
153. #1767	C₂×C₂₃	semidirect
154. C₄×C₄⋊C₈	C₂×C₂₃	semidirect
156. #1746	C₂×C₂₃	semidirect
239. C₂₃	#20786	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄×C₂₃×#117	2
C₂₃×#1840	2
C₂₃×#1831	2
C₂₃×#1818	2
C₂₃×#1797	2
C₂₃×#1767	2
C₄×C₂₃×C₄⋊C₈	2
C₂₃×#1750	2
C₂₃×#1746	2
#20786	23

Subgroups — C23×#20786 #19168412

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#20786 #19168412