Subgroups — C₂₃×#22692 #19170318

Order 5888.

862 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#443	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#2951	C₂	1	2	yes	maximal
3	C₂₃×#2913	C₂	1	2	yes	maximal, complemented
4	C₂₃×#1952	C₂	1	2	yes	maximal, complemented
5	C₂₃×#1859	C₂	1	4	yes	maximal, complemented
6	C₂₃×#1845	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#1816	C₂	1	2	yes	maximal, complemented
8	C₂₃×#1772	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₂₃×#135	C₂²	1	1	yes	characteristic
10	C₂×C₂₃×#131	C₂²	1	2	yes	—
11	C₂₃×#520	C₂²	1	4	yes	—
12	C₂₃×#443	C₄	1	8	yes	complemented
13	C₂₃×#440	—	2	4	no	—
14	C₄×Q₁₆×C₂₃	—	2	2	no	—
15	C₄×D₈×C₂₃	—	2	2	no	—
16	C₂×C₂₃×#108	C₂²	1	1	yes	characteristic
17	C₂×C₂₃×#108	C₂²	1	1	yes	characteristic
18	C₂₃×#428	—	2	4	no	—
19	C₂₃×#428	C₂²	1	4	yes	—
20	C₂₃×#427	—	2	2	no	—
21	C₂₃×#427	C₂²	1	1	yes	characteristic
22	C₂×C₂₃×#107	—	2	2	no	—
23	C₂×C₂₃×#107	C₂²	1	2	yes	—
24	C₂×C₂₃×#107	C₂²	1	2	yes	—
25	C₂×C₂₃×#104	C₂²	1	2	yes	—
26	C₂₃×#417	C₂²	1	4	yes	—
27	C₂₃×#405	C₂²	1	2	yes	—
28	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
29	C₂₃×#384	C₂²	1	2	yes	—
30	C₂₃×#343	C₂²	1	4	yes	—
31	C₂₃×#339	C₂²	1	2	yes	—
32	C₂×#41×C₂₃	C₂³	1	2	yes	—
33	C₂₃×#135	C₂×C₄	1	4	yes	—
34	C₂₃×#135	Q₈	1	4	yes	—
35	C₂×Q₁₆×C₂₃	D₄	1	1	yes	characteristic
36	C₂×SD₁₆×C₂₃	D₄	1	2	yes	—
37	C₂×D₈×C₂₃	D₄	1	1	yes	characteristic
38	C₂₃×#131	—	2	4	no	—
39	C₂₃×#131	C₂×C₄	1	8	yes	complemented
40	C₂×M₁₆×C₂₃	—	2	2	no	—
41	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
42	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
43	C₂²×C₈×C₂₃	—	2	2	no	—
44	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
45	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
46	C₄×Q₈×C₂₃	—	2	4	no	—
47	C₄×D₄×C₂₃	—	2	4	no	—
48	C₄×D₄×C₂₃	—	4	4	no	—
49	C₂₃×#117	—	2	4	no	—
50	C₂₃×#117	C₂³	1	2	yes	—
51	C₂×C₄⋊C₄×C₂₃	—	2	4	no	—
52	C₂×C₄⋊C₄×C₂₃	—	4	2	no	—
53	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
54	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
55	C₂₃×#108	—	2	2	no	—
56	C₂₃×#108	C₂×C₄	1	4	yes	complemented
57	C₂₃×#107	—	2	2	no	—
58	C₂₃×#107	—	2	2	no	—
59	C₂₃×#107	—	2	2	no	—
60	C₂₃×#107	—	2	2	no	—
61	C₂₃×#107	—	2	4	no	—
62	C₂₃×#107	D₄	1	1	yes	characteristic
63	C₂₃×#107	D₄	1	1	yes	characteristic
64	C₂₃×#106	—	2	4	no	—
65	C₂₃×#106	D₄	1	2	yes	—
66	C₂₃×#104	C₂×C₄	1	8	yes	complemented
67	C₂₃×#103	—	2	4	no	—
68	C₂₃×#102	—	2	4	no	—
69	C₂₃×#97	—	2	2	no	—
70	C₄×C₈×C₂₃	—	2	2	no	—
71	C₄×C₈×C₂₃	C₂×C₄	1	4	yes	complemented
72	#41×C₂₃	—	2	2	no	—
73	#41×C₂₃	—	2	2	no	—
74	#41×C₂₃	C₂²×C₄	1	4	yes	—
75	#41×C₂₃	C₂×Q₈	1	4	yes	—
76	C₂×Q₈×C₂₃	C₂×D₄	1	2	yes	—
77	C₂×D₄×C₂₃	—	2	2	no	—
78	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
79	C₂²×C₄×C₂₃	—	2	1	no	—
80	C₂²×C₄×C₂₃	—	2	2	no	—
81	C₂²×C₄×C₂₃	—	2	4	no	—
82	C₂²×C₄×C₂₃	—	4	4	no	—
83	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
84	Q₁₆×C₂₃	C₄⋊C₄	1	4	yes	complemented
85	SD₁₆×C₂₃	C₄⋊C₄	1	8	yes	complemented
86	D₈×C₂₃	C₄⋊C₄	1	4	yes	complemented
87	M₁₆×C₂₃	—	2	2	no	—
88	M₁₆×C₂₃	—	2	8	no	—
89	M₁₆×C₂₃	—	2	2	no	—
90	M₁₆×C₂₃	—	2	2	no	—
91	M₁₆×C₂₃	C₂²×C₄	1	4	yes	—
92	C₂×C₈×C₂₃	—	2	2	no	—
93	C₂×C₈×C₂₃	—	2	8	no	—
94	C₂×C₈×C₂₃	—	2	2	no	—
95	C₂×C₈×C₂₃	C₂²×C₄	1	2	yes	—
96	C₂×C₈×C₂₃	C₂²×C₄	1	2	yes	—
97	C₂×C₈×C₂₃	C₂×D₄	1	1	yes	characteristic
98	C₂×C₈×C₂₃	C₂×D₄	1	1	yes	characteristic
99	C₂×C₈×C₂₃	C₂×D₄	1	1	yes	characteristic
100	C₂×C₈×C₂₃	C₂×D₄	1	1	yes	characteristic
101	C₂×C₈×C₂₃	C₂×Q₈	1	2	yes	—
102	C₂×C₈×C₂₃	#41	1	2	yes	—
103	C₄⋊C₄×C₂₃	—	2	4	no	—
104	C₄⋊C₄×C₂₃	—	2	4	no	—
105	C₄⋊C₄×C₂₃	—	4	4	no	—
106	C₄⋊C₄×C₂₃	—	8	4	no	—
107	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
108	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
109	C₂²⋊C₄×C₂₃	—	2	2	no	—
110	C₂²⋊C₄×C₂₃	—	4	4	no	—
111	C₄²×C₂₃	—	2	2	no	—
112	C₄²×C₂₃	—	2	1	no	—
113	C₄²×C₂₃	—	4	4	no	—
114	C₄²×C₂₃	C₂²×C₄	1	2	yes	—
115	#22692	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
116	C₂³×C₂₃	—	2	2	no	—
117	C₂³×C₂₃	H(5,𝔽₂)	1	1	yes	characteristic
118	Q₈×C₂₃	—	2	2	no	—
119	Q₈×C₂₃	C₂×C₄⋊C₄	1	4	yes	—
120	D₄×C₂₃	—	2	4	no	—
121	D₄×C₂₃	—	2	4	no	—
122	D₄×C₂₃	—	2	2	no	—
123	D₄×C₂₃	C₂×C₄⋊C₄	1	4	yes	—
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	4	no	—
129	C₂×C₄×C₂₃	—	2	4	no	—
130	C₂×C₄×C₂₃	—	2	2	no	—
131	C₂×C₄×C₂₃	—	2	2	no	—
132	C₂×C₄×C₂₃	—	4	4	no	—
133	C₂×C₄×C₂₃	—	8	4	no	—
134	C₂×C₄×C₂₃	—	16	4	no	—
135	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
136	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
137	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
138	C₂×C₄×C₂₃	C₂²×Q₈	1	1	yes	characteristic
139	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
140	C₂×C₄×C₂₃	2₋¹⁺⁴	1	1	yes	characteristic
141	C₈×C₂₃	—	2	4	no	—
142	C₈×C₂₃	—	4	2	no	—
143	C₈×C₂₃	C₂×C₄⋊C₄	1	2	yes	—
144	C₈×C₂₃	C₂×C₄⋊C₄	1	2	yes	—
145	C₈×C₂₃	C₄×D₄	1	2	yes	—
146	C₈×C₂₃	C₄×D₄	1	2	yes	—
147	C₂×#443	C₂×C₂₃	1	1	yes	characteristic
148	#2951	C₂×C₂₃	1	2	yes	—
149	#2913	C₂×C₂₃	1	2	yes	complemented
150	#1952	C₂×C₂₃	1	2	yes	complemented
151	#1859	C₂×C₂₃	1	4	yes	complemented
152	#1845	C₂×C₂₃	1	1	yes	characteristic, complemented
153	#1816	C₂×C₂₃	1	2	yes	complemented
154	#1772	C₂×C₂₃	1	1	yes	characteristic, complemented
155	C₂²×C₂₃	—	2	1	no	—
156	C₂²×C₂₃	—	2	1	no	—
157	C₂²×C₂₃	—	2	4	no	—
158	C₂²×C₂₃	—	4	2	no	—
159	C₂²×C₂₃	—	4	2	no	—
160	C₂²×C₂₃	#520	1	1	yes	characteristic
161	C₂²×C₂₃	D₄²	1	1	yes	characteristic
162	C₂²×C₂₃	#554	1	1	yes	characteristic
163	C₄×C₂₃	—	2	4	no	—
164	C₄×C₂₃	—	2	4	no	—
165	C₄×C₂₃	—	4	2	no	—
166	C₄×C₂₃	—	4	2	no	—
167	C₄×C₂₃	—	8	4	no	—
168	C₄×C₂₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
169	C₄×C₂₃	C₂×C₄×D₄	1	1	yes	characteristic
170	C₄×C₂₃	#547	1	1	yes	characteristic
171	C₄×C₂₃	D₄×Q₈	1	1	yes	characteristic
172	C₂×#135	C₂²×C₂₃	1	1	yes	characteristic
173	C₂×#131	C₂²×C₂₃	1	2	yes	—
174	#520	C₂²×C₂₃	1	4	yes	—
175	#443	C₄×C₂₃	1	8	yes	complemented
176	#440	—	2	4	no	—
177	C₄×Q₁₆	—	2	2	no	—
178	C₄×D₈	—	2	2	no	—
179	C₂×#108	C₂²×C₂₃	1	1	yes	characteristic
180	C₂×#108	C₂²×C₂₃	1	1	yes	characteristic
181	#428	—	2	4	no	—
182	#428	C₂²×C₂₃	1	4	yes	—
183	#427	—	2	2	no	—
184	#427	C₂²×C₂₃	1	1	yes	characteristic
185	C₂×#107	—	2	2	no	—
186	C₂×#107	C₂²×C₂₃	1	2	yes	—
187	C₂×#107	C₂²×C₂₃	1	2	yes	—
188	C₂×#104	C₂²×C₂₃	1	2	yes	—
189	#417	C₂²×C₂₃	1	4	yes	—
190	#405	C₂²×C₂₃	1	2	yes	—
191	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
192	#384	C₂²×C₂₃	1	2	yes	—
193	#343	C₂²×C₂₃	1	4	yes	—
194	#339	C₂²×C₂₃	1	2	yes	—
195	C₂×C₂₃	—	2	1	no	—
196	C₂×C₂₃	—	2	1	no	—
197	C₂×C₂₃	—	4	4	no	—
198	C₂×C₂₃	D₄×C₄⋊C₄	1	1	yes	characteristic
199	C₂×C₂₃	#3292	1	1	yes	characteristic
200	C₂×C₂₃	#3293	1	1	yes	characteristic
201	C₂×#41	C₂³×C₂₃	1	2	yes	—
202	#135	C₂×C₄×C₂₃	1	4	yes	—
203	#135	Q₈×C₂₃	1	4	yes	—
204	C₂×Q₁₆	D₄×C₂₃	1	1	yes	characteristic
205	C₂×SD₁₆	D₄×C₂₃	1	2	yes	—
206	C₂×D₈	D₄×C₂₃	1	1	yes	characteristic
207	#131	—	2	4	no	—
208	#131	C₂×C₄×C₂₃	1	8	yes	complemented
209	C₂×M₁₆	—	2	2	no	—
210	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
211	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
212	C₂²×C₈	—	2	2	no	—
213	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
214	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
215	C₄×Q₈	—	2	4	no	—
216	C₄×D₄	—	2	4	no	—
217	C₄×D₄	—	4	4	no	—
218	#117	—	2	4	no	—
219	#117	C₂³×C₂₃	1	2	yes	—
220	C₂×C₄⋊C₄	—	2	4	no	—
221	C₂×C₄⋊C₄	—	4	2	no	—
222	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
223	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
224	#108	—	2	2	no	—
225	#108	C₂×C₄×C₂₃	1	4	yes	complemented
226	#107	—	2	2	no	—
227	#107	—	2	2	no	—
228	#107	—	2	2	no	—
229	#107	—	2	2	no	—
230	#107	—	2	4	no	—
231	#107	D₄×C₂₃	1	1	yes	characteristic
232	#107	D₄×C₂₃	1	1	yes	characteristic
233	#106	—	2	4	no	—
234	#106	D₄×C₂₃	1	2	yes	—
235	#104	C₂×C₄×C₂₃	1	8	yes	complemented
236	#103	—	2	4	no	—
237	#102	—	2	4	no	—
238	#97	—	2	2	no	—
239	C₄×C₈	—	2	2	no	—
240	C₄×C₈	C₂×C₄×C₂₃	1	4	yes	complemented
241	C₂₃	#22692	1	1	yes	characteristic, direct product factor, Sylow
242	#41	—	2	2	no	—
243	#41	—	2	2	no	—
244	#41	C₂²×C₄×C₂₃	1	4	yes	—
245	#41	C₂×Q₈×C₂₃	1	4	yes	—
246	C₂×Q₈	C₂×D₄×C₂₃	1	2	yes	—
247	C₂×D₄	—	2	2	no	—
248	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
249	C₂²×C₄	—	2	1	no	—
250	C₂²×C₄	—	2	2	no	—
251	C₂²×C₄	—	2	4	no	—
252	C₂²×C₄	—	4	4	no	—
253	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
254	Q₁₆	C₄⋊C₄×C₂₃	1	4	yes	complemented
255	SD₁₆	C₄⋊C₄×C₂₃	1	8	yes	complemented
256	D₈	C₄⋊C₄×C₂₃	1	4	yes	complemented
257	M₁₆	—	2	2	no	—
258	M₁₆	—	2	8	no	—
259	M₁₆	—	2	2	no	—
260	M₁₆	—	2	2	no	—
261	M₁₆	C₂²×C₄×C₂₃	1	4	yes	—
262	C₂×C₈	—	2	2	no	—
263	C₂×C₈	—	2	8	no	—
264	C₂×C₈	—	2	2	no	—
265	C₂×C₈	C₂²×C₄×C₂₃	1	2	yes	—
266	C₂×C₈	C₂²×C₄×C₂₃	1	2	yes	—
267	C₂×C₈	C₂×D₄×C₂₃	1	1	yes	characteristic
268	C₂×C₈	C₂×D₄×C₂₃	1	1	yes	characteristic
269	C₂×C₈	C₂×D₄×C₂₃	1	1	yes	characteristic
270	C₂×C₈	C₂×D₄×C₂₃	1	1	yes	characteristic
271	C₂×C₈	C₂×Q₈×C₂₃	1	2	yes	—
272	C₂×C₈	#41×C₂₃	1	2	yes	—
273	C₄⋊C₄	—	2	4	no	—
274	C₄⋊C₄	—	2	4	no	—
275	C₄⋊C₄	—	4	4	no	—
276	C₄⋊C₄	—	8	4	no	—
277	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
278	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
279	C₂²⋊C₄	—	2	2	no	—
280	C₂²⋊C₄	—	4	4	no	—
281	C₄²	—	2	2	no	—
282	C₄²	—	2	1	no	—
283	C₄²	—	4	4	no	—
284	C₄²	C₂²×C₄×C₂₃	1	2	yes	—
285	C₂³	—	2	2	no	—
286	C₂³	C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
287	Q₈	—	2	2	no	—
288	Q₈	C₂×C₄⋊C₄×C₂₃	1	4	yes	—
289	D₄	—	2	4	no	—
290	D₄	—	2	4	no	—
291	D₄	—	2	2	no	—
292	D₄	C₂×C₄⋊C₄×C₂₃	1	4	yes	—
293	C₂×C₄	—	2	2	no	—
294	C₂×C₄	—	2	2	no	—
295	C₂×C₄	—	2	2	no	—
296	C₂×C₄	—	2	2	no	—
297	C₂×C₄	—	2	4	no	—
298	C₂×C₄	—	2	4	no	—
299	C₂×C₄	—	2	2	no	—
300	C₂×C₄	—	2	2	no	—
301	C₂×C₄	—	4	4	no	—
302	C₂×C₄	—	8	4	no	—
303	C₂×C₄	—	16	4	no	—
304	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
305	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
306	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
307	C₂×C₄	C₂²×Q₈×C₂₃	1	1	yes	characteristic
308	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
309	C₂×C₄	C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
310	C₈	—	2	4	no	—
311	C₈	—	4	2	no	—
312	C₈	C₂×C₄⋊C₄×C₂₃	1	2	yes	—
313	C₈	C₂×C₄⋊C₄×C₂₃	1	2	yes	—
314	C₈	C₄×D₄×C₂₃	1	2	yes	—
315	C₈	C₄×D₄×C₂₃	1	2	yes	—
316	C₂²	—	2	1	no	—
317	C₂²	—	2	1	no	—
318	C₂²	—	2	4	no	—
319	C₂²	—	4	2	no	—
320	C₂²	—	4	2	no	—
321	C₂²	C₂₃×#520	1	1	yes	characteristic
322	C₂²	D₄²×C₂₃	1	1	yes	characteristic
323	C₂²	C₂₃×#554	1	1	yes	characteristic
324	C₄	—	2	4	no	—
325	C₄	—	2	4	no	—
326	C₄	—	4	2	no	—
327	C₄	—	4	2	no	—
328	C₄	—	8	4	no	—
329	C₄	C₂²×C₄⋊C₄×C₂₃	1	1	yes	characteristic
330	C₄	C₂×C₄×D₄×C₂₃	1	1	yes	characteristic
331	C₄	C₂₃×#547	1	1	yes	characteristic
332	C₄	D₄×Q₈×C₂₃	1	1	yes	characteristic
333	C₂	—	2	1	no	—
334	C₂	—	2	1	no	—
335	C₂	—	4	4	no	—
336	C₂	D₄×C₄⋊C₄×C₂₃	1	1	yes	characteristic
337	C₂	C₂₃×#3292	1	1	yes	characteristic
338	C₂	C₂₃×#3293	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₃	D₄²
commutator	C₂×C₄	C₂³×C₄×C₂₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₃
prime radical	C₂×C₂₃×#135	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂²×C₄×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂₃×#2913	C₂	semidirect
4. C₂₃×#1952	C₂	semidirect
5. C₂₃×#1859	C₂	semidirect
6. C₂₃×#1845	C₂	semidirect
7. C₂₃×#1816	C₂	semidirect
8. C₂₃×#1772	C₂	semidirect
12. C₂₃×#443	C₄	semidirect
39. C₂₃×#131	C₂×C₄	semidirect
56. C₂₃×#108	C₂×C₄	semidirect
66. C₂₃×#104	C₂×C₄	semidirect
71. C₄×C₈×C₂₃	C₂×C₄	semidirect
84. Q₁₆×C₂₃	C₄⋊C₄	semidirect
85. SD₁₆×C₂₃	C₄⋊C₄	semidirect
86. D₈×C₂₃	C₄⋊C₄	semidirect
115. #22692	C₂₃	direct (N × H)
149. #2913	C₂×C₂₃	semidirect
150. #1952	C₂×C₂₃	semidirect
151. #1859	C₂×C₂₃	semidirect
152. #1845	C₂×C₂₃	semidirect
153. #1816	C₂×C₂₃	semidirect
154. #1772	C₂×C₂₃	semidirect
175. #443	C₄×C₂₃	semidirect
208. #131	C₂×C₄×C₂₃	semidirect
225. #108	C₂×C₄×C₂₃	semidirect
235. #104	C₂×C₄×C₂₃	semidirect
240. C₄×C₈	C₂×C₄×C₂₃	semidirect
241. C₂₃	#22692	direct (N × H)
254. Q₁₆	C₄⋊C₄×C₂₃	semidirect
255. SD₁₆	C₄⋊C₄×C₂₃	semidirect
256. D₈	C₄⋊C₄×C₂₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₂₃×#443	2
C₂₃×#2951	2
C₂₃×#2913	2
C₂₃×#1952	2
C₂₃×#1859	2
C₂₃×#1845	2
C₂₃×#1816	2
C₂₃×#1772	2
#22692	23

Subgroups — C23×#22692 #19170318

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#22692 #19170318