Subgroups — C₂₃×#17549 #19165175

Order 5888.

974 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3523	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#2984	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#2276	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#1509	C₂	1	3	yes	maximal
5	C₂₃×#1506	C₂	1	3	yes	maximal, complemented
6	C₂₃×#1503	C₂	1	3	yes	maximal, complemented
7	C₂₃×#1500	C₂	1	3	yes	maximal
8	C₂₃×#557	C₄	1	1	yes	characteristic, complemented
9	C₂₃×#557	C₄	1	3	yes	complemented
10	C₂₃×#556	C₄	1	3	yes	complemented
11	C₂₃×#552	—	2	3	no	—
12	D₄×Q₈×C₂₃	—	2	1	no	—
13	D₄×Q₈×C₂₃	C₄	1	1	yes	characteristic, complemented
14	C₂₃×#541	—	2	3	no	—
15	C₂₃×#533	C₂²	1	3	yes	—
16	C₂₃×#529	C₂²	1	3	yes	—
17	C₂₃×#519	—	2	1	no	—
18	C₂×C₄×Q₈×C₂₃	—	2	1	no	—
19	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
20	C₂₃×#446	—	2	3	no	—
21	C₈×Q₈×C₂₃	—	2	1	no	—
22	C₂₃×#432	C₂²	1	3	yes	—
23	C₂₃×#431	C₂²	1	3	yes	—
24	C₄×C₄⋊C₄×C₂₃	—	2	3	no	—
25	C₄×C₄⋊C₄×C₂₃	C₂²	1	3	yes	—
26	C₂₃×#376	C₂²	1	3	yes	—
27	C₂₃×#328	C₂²	1	3	yes	—
28	C₂₃×#328	C₂²	1	3	yes	—
29	C₂₃×#328	C₂²	1	6	yes	—
30	C₂₃×#327	C₂²	1	1	yes	characteristic
31	C₂₃×#327	C₂²	1	3	yes	—
32	C₂²×Q₈×C₂₃	—	2	1	no	—
33	C₂²×Q₈×C₂₃	D₄	1	1	yes	characteristic
34	C₂₃×C₄⋊Q₈	—	2	3	no	—
35	C₂₃×C₄⋊Q₈	C₂×C₄	1	3	yes	—
36	C₂₃×C₄⋊Q₈	C₂×C₄	1	3	yes	—
37	C₂₃×#126	—	2	6	no	—
38	C₂₃×#126	—	2	3	no	—
39	C₂₃×#125	—	2	6	no	—
40	C₂₃×#125	—	2	3	no	—
41	C₂₃×#125	—	2	3	no	—
42	C₂₃×#125	C₂×C₄	1	3	yes	—
43	C₂₃×#124	C₂×C₄	1	3	yes	—
44	C₂₃×#123	—	2	3	no	—
45	C₂₃×C₂²⋊Q₈	—	2	3	no	—
46	C₂₃×C₂²⋊Q₈	—	2	3	no	—
47	C₂₃×C₂²⋊Q₈	—	2	3	no	—
48	C₂₃×C₂²⋊Q₈	C₂³	1	3	yes	—
49	C₂₃×#121	C₂³	1	1	yes	characteristic
50	C₄×Q₈×C₂₃	—	2	8	no	—
51	C₄×Q₈×C₂₃	—	2	1	no	—
52	C₄×Q₈×C₂₃	—	2	3	no	—
53	C₄×Q₈×C₂₃	—	2	3	no	—
54	C₄×Q₈×C₂₃	C₂×C₄	1	6	yes	—
55	C₄×Q₈×C₂₃	C₂×C₄	1	3	yes	—
56	C₄×Q₈×C₂₃	C₂×C₄	1	1	yes	characteristic
57	C₄×Q₈×C₂₃	C₂×C₄	1	3	yes	—
58	C₄×Q₈×C₂₃	D₄	1	1	yes	characteristic
59	C₄×Q₈×C₂₃	D₄	1	3	yes	—
60	C₄×D₄×C₂₃	—	2	3	no	—
61	C₄×D₄×C₂₃	C₂×C₄	1	3	yes	—
62	C₂₃×#117	—	2	3	no	—
63	C₂₃×#117	—	2	3	no	—
64	C₂₃×#117	—	2	3	no	—
65	C₂×C₄⋊C₄×C₂₃	—	2	3	no	—
66	C₂×C₄⋊C₄×C₂₃	D₄	1	3	yes	—
67	C₂×C₄²×C₂₃	—	2	3	no	—
68	C₂×C₄²×C₂₃	—	2	3	no	—
69	C₂×C₄²×C₂₃	C₂³	1	3	yes	—
70	C₂₃×C₄⋊C₈	—	2	3	no	—
71	C₂₃×C₄⋊C₈	—	2	3	no	—
72	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
73	C₂₃×C₂²⋊C₈	C₂³	1	3	yes	—
74	C₂₃×#97	—	2	3	no	—
75	C₄×C₈×C₂₃	—	2	3	no	—
76	C₂₃×#95	—	2	3	no	—
77	C₂₃×#95	C₂³	1	1	yes	characteristic
78	C₂₃×#95	C₂³	1	3	yes	—
79	C₂×Q₈×C₂₃	—	2	4	no	—
80	C₂×Q₈×C₂₃	—	2	3	no	—
81	C₂×Q₈×C₂₃	—	4	4	no	—
82	C₂×Q₈×C₂₃	C₂²⋊C₄	1	3	yes	—
83	C₂×Q₈×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
84	C₂×Q₈×C₂₃	C₂²×C₄	1	3	yes	—
85	C₂×D₄×C₂₃	—	2	1	no	—
86	C₂×D₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
87	C₂²×C₄×C₂₃	—	2	3	no	—
88	C₂²×C₄×C₂₃	—	2	1	no	—
89	C₂²×C₄×C₂₃	—	2	3	no	—
90	C₂²×C₄×C₂₃	C₂×D₄	1	3	yes	—
91	C₂²×C₄×C₂₃	C₂×D₄	1	3	yes	—
92	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
93	C₂×C₈×C₂₃	—	2	1	no	—
94	C₂×C₈×C₂₃	—	2	3	no	—
95	C₄⋊C₄×C₂₃	—	2	12	no	—
96	C₄⋊C₄×C₂₃	—	2	3	no	—
97	C₄⋊C₄×C₂₃	—	2	3	no	—
98	C₄⋊C₄×C₂₃	—	2	3	no	—
99	C₄⋊C₄×C₂₃	—	2	3	no	—
100	C₄⋊C₄×C₂₃	—	2	3	no	—
101	C₄⋊C₄×C₂₃	—	2	6	no	—
102	C₄⋊C₄×C₂₃	—	2	3	no	—
103	C₄⋊C₄×C₂₃	—	2	3	no	—
104	C₄⋊C₄×C₂₃	C₂²⋊C₄	1	3	yes	—
105	C₄⋊C₄×C₂₃	C₂²⋊C₄	1	3	yes	—
106	C₄⋊C₄×C₂₃	C₂²⋊C₄	1	6	yes	—
107	C₄⋊C₄×C₂₃	C₂²×C₄	1	3	yes	—
108	C₄⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
109	C₂²⋊C₄×C₂₃	—	2	3	no	—
110	C₂²⋊C₄×C₂₃	—	2	3	no	—
111	C₂²⋊C₄×C₂₃	—	2	3	no	—
112	C₂²⋊C₄×C₂₃	—	2	3	no	—
113	C₂²⋊C₄×C₂₃	—	2	1	no	—
114	C₄²×C₂₃	—	2	12	no	—
115	C₄²×C₂₃	—	2	6	no	—
116	C₄²×C₂₃	—	2	3	no	—
117	C₄²×C₂₃	—	8	3	no	—
118	C₄²×C₂₃	C₂²×C₄	1	3	yes	—
119	C₄²×C₂₃	C₂²×C₄	1	3	yes	—
120	C₄²×C₂₃	C₂×D₄	1	3	yes	—
121	C₄²×C₂₃	C₂×D₄	1	3	yes	—
122	#17549	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
123	C₂³×C₂₃	—	2	1	no	—
124	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
125	Q₈×C₂₃	—	2	6	no	—
126	Q₈×C₂₃	—	4	3	no	—
127	Q₈×C₂₃	—	4	6	no	—
128	Q₈×C₂₃	#104	1	4	yes	—
129	D₄×C₂₃	—	4	1	no	—
130	D₄×C₂₃	—	4	1	no	—
131	D₄×C₂₃	—	4	1	no	—
132	C₂×C₄×C₂₃	—	2	3	no	—
133	C₂×C₄×C₂₃	—	2	3	no	—
134	C₂×C₄×C₂₃	—	2	6	no	—
135	C₂×C₄×C₂₃	—	2	2	no	—
136	C₂×C₄×C₂₃	—	2	6	no	—
137	C₂×C₄×C₂₃	—	2	3	no	—
138	C₂×C₄×C₂₃	—	2	1	no	—
139	C₂×C₄×C₂₃	—	2	3	no	—
140	C₂×C₄×C₂₃	—	4	1	no	—
141	C₂×C₄×C₂₃	—	4	3	no	—
142	C₂×C₄×C₂₃	—	4	1	no	—
143	C₂×C₄×C₂₃	—	4	3	no	—
144	C₂×C₄×C₂₃	—	4	1	no	—
145	C₂×C₄×C₂₃	—	4	6	no	—
146	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	3	yes	—
147	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	3	yes	—
148	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	3	yes	—
149	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	3	yes	—
150	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
151	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
152	C₈×C₂₃	—	4	1	no	—
153	C₈×C₂₃	—	4	3	no	—
154	#3523	C₂×C₂₃	1	1	yes	characteristic
155	#2984	C₂×C₂₃	1	1	yes	characteristic, complemented
156	#2276	C₂×C₂₃	1	1	yes	characteristic, complemented
157	#1509	C₂×C₂₃	1	3	yes	—
158	#1506	C₂×C₂₃	1	3	yes	complemented
159	#1503	C₂×C₂₃	1	3	yes	complemented
160	#1500	C₂×C₂₃	1	3	yes	—
161	C₂²×C₂₃	—	2	1	no	—
162	C₂²×C₂₃	—	2	1	no	—
163	C₂²×C₂₃	—	4	1	no	—
164	C₂²×C₂₃	—	4	1	no	—
165	C₂²×C₂₃	—	4	1	no	—
166	C₂²×C₂₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
167	C₂²×C₂₃	#577	1	1	yes	characteristic
168	C₂²×C₂₃	#578	1	1	yes	characteristic
169	C₄×C₂₃	—	2	1	no	—
170	C₄×C₂₃	—	2	1	no	—
171	C₄×C₂₃	—	2	3	no	—
172	C₄×C₂₃	—	2	3	no	—
173	C₄×C₂₃	—	2	3	no	—
174	C₄×C₂₃	—	4	6	no	—
175	C₄×C₂₃	—	4	2	no	—
176	C₄×C₂₃	—	4	3	no	—
177	C₄×C₂₃	—	4	1	no	—
178	C₄×C₂₃	—	4	3	no	—
179	C₄×C₂₃	C₂×#104	1	6	yes	—
180	#557	C₄×C₂₃	1	1	yes	characteristic, complemented
181	#557	C₄×C₂₃	1	3	yes	complemented
182	#556	C₄×C₂₃	1	3	yes	complemented
183	#552	—	2	3	no	—
184	D₄×Q₈	—	2	1	no	—
185	D₄×Q₈	C₄×C₂₃	1	1	yes	characteristic, complemented
186	#541	—	2	3	no	—
187	#533	C₂²×C₂₃	1	3	yes	—
188	#529	C₂²×C₂₃	1	3	yes	—
189	#519	—	2	1	no	—
190	C₂×C₄×Q₈	—	2	1	no	—
191	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
192	#446	—	2	3	no	—
193	C₈×Q₈	—	2	1	no	—
194	#432	C₂²×C₂₃	1	3	yes	—
195	#431	C₂²×C₂₃	1	3	yes	—
196	C₄×C₄⋊C₄	—	2	3	no	—
197	C₄×C₄⋊C₄	C₂²×C₂₃	1	3	yes	—
198	#376	C₂²×C₂₃	1	3	yes	—
199	#328	C₂²×C₂₃	1	3	yes	—
200	#328	C₂²×C₂₃	1	3	yes	—
201	#328	C₂²×C₂₃	1	6	yes	—
202	#327	C₂²×C₂₃	1	1	yes	characteristic
203	#327	C₂²×C₂₃	1	3	yes	—
204	C₂×C₂₃	—	2	1	no	—
205	C₂×C₂₃	—	2	1	no	—
206	C₂×C₂₃	—	8	1	no	—
207	C₂×C₂₃	#2884	1	1	yes	characteristic
208	C₂×C₂₃	#2898	1	1	yes	characteristic
209	C₂×C₂₃	C₂²×#104	1	1	yes	characteristic
210	C₂²×Q₈	—	2	1	no	—
211	C₂²×Q₈	D₄×C₂₃	1	1	yes	characteristic
212	C₄⋊Q₈	—	2	3	no	—
213	C₄⋊Q₈	C₂×C₄×C₂₃	1	3	yes	—
214	C₄⋊Q₈	C₂×C₄×C₂₃	1	3	yes	—
215	#126	—	2	6	no	—
216	#126	—	2	3	no	—
217	#125	—	2	6	no	—
218	#125	—	2	3	no	—
219	#125	—	2	3	no	—
220	#125	C₂×C₄×C₂₃	1	3	yes	—
221	#124	C₂×C₄×C₂₃	1	3	yes	—
222	#123	—	2	3	no	—
223	C₂²⋊Q₈	—	2	3	no	—
224	C₂²⋊Q₈	—	2	3	no	—
225	C₂²⋊Q₈	—	2	3	no	—
226	C₂²⋊Q₈	C₂³×C₂₃	1	3	yes	—
227	#121	C₂³×C₂₃	1	1	yes	characteristic
228	C₄×Q₈	—	2	8	no	—
229	C₄×Q₈	—	2	1	no	—
230	C₄×Q₈	—	2	3	no	—
231	C₄×Q₈	—	2	3	no	—
232	C₄×Q₈	C₂×C₄×C₂₃	1	3	yes	—
233	C₄×Q₈	C₂×C₄×C₂₃	1	6	yes	—
234	C₄×Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
235	C₄×Q₈	C₂×C₄×C₂₃	1	3	yes	—
236	C₄×Q₈	D₄×C₂₃	1	1	yes	characteristic
237	C₄×Q₈	D₄×C₂₃	1	3	yes	—
238	C₄×D₄	—	2	3	no	—
239	C₄×D₄	C₂×C₄×C₂₃	1	3	yes	—
240	#117	—	2	3	no	—
241	#117	—	2	3	no	—
242	#117	—	2	3	no	—
243	C₂×C₄⋊C₄	—	2	3	no	—
244	C₂×C₄⋊C₄	D₄×C₂₃	1	3	yes	—
245	C₂×C₄²	—	2	3	no	—
246	C₂×C₄²	—	2	3	no	—
247	C₂×C₄²	C₂³×C₂₃	1	3	yes	—
248	C₄⋊C₈	—	2	3	no	—
249	C₄⋊C₈	—	2	3	no	—
250	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
251	C₂²⋊C₈	C₂³×C₂₃	1	3	yes	—
252	#97	—	2	3	no	—
253	C₄×C₈	—	2	3	no	—
254	#95	—	2	3	no	—
255	#95	C₂³×C₂₃	1	1	yes	characteristic
256	#95	C₂³×C₂₃	1	3	yes	—
257	C₂₃	#17549	1	1	yes	characteristic, direct product factor, Sylow
258	C₂×Q₈	—	2	4	no	—
259	C₂×Q₈	—	2	3	no	—
260	C₂×Q₈	—	4	4	no	—
261	C₂×Q₈	C₂²⋊C₄×C₂₃	1	3	yes	—
262	C₂×Q₈	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
263	C₂×Q₈	C₂²×C₄×C₂₃	1	3	yes	—
264	C₂×D₄	—	2	1	no	—
265	C₂×D₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
266	C₂²×C₄	—	2	1	no	—
267	C₂²×C₄	—	2	3	no	—
268	C₂²×C₄	—	2	3	no	—
269	C₂²×C₄	C₂×D₄×C₂₃	1	3	yes	—
270	C₂²×C₄	C₂×D₄×C₂₃	1	3	yes	—
271	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
272	C₂×C₈	—	2	1	no	—
273	C₂×C₈	—	2	3	no	—
274	C₄⋊C₄	—	2	12	no	—
275	C₄⋊C₄	—	2	3	no	—
276	C₄⋊C₄	—	2	3	no	—
277	C₄⋊C₄	—	2	3	no	—
278	C₄⋊C₄	—	2	3	no	—
279	C₄⋊C₄	—	2	3	no	—
280	C₄⋊C₄	—	2	6	no	—
281	C₄⋊C₄	—	2	3	no	—
282	C₄⋊C₄	—	2	3	no	—
283	C₄⋊C₄	C₂²⋊C₄×C₂₃	1	3	yes	—
284	C₄⋊C₄	C₂²⋊C₄×C₂₃	1	3	yes	—
285	C₄⋊C₄	C₂²⋊C₄×C₂₃	1	6	yes	—
286	C₄⋊C₄	C₂²×C₄×C₂₃	1	3	yes	—
287	C₄⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
288	C₂²⋊C₄	—	2	3	no	—
289	C₂²⋊C₄	—	2	3	no	—
290	C₂²⋊C₄	—	2	3	no	—
291	C₂²⋊C₄	—	2	3	no	—
292	C₂²⋊C₄	—	2	1	no	—
293	C₄²	—	2	12	no	—
294	C₄²	—	2	6	no	—
295	C₄²	—	2	3	no	—
296	C₄²	—	8	3	no	—
297	C₄²	C₂²×C₄×C₂₃	1	3	yes	—
298	C₄²	C₂²×C₄×C₂₃	1	3	yes	—
299	C₄²	C₂×D₄×C₂₃	1	3	yes	—
300	C₄²	C₂×D₄×C₂₃	1	3	yes	—
301	C₂³	—	2	1	no	—
302	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
303	Q₈	—	2	6	no	—
304	Q₈	—	4	3	no	—
305	Q₈	—	4	6	no	—
306	Q₈	C₂₃×#104	1	4	yes	—
307	D₄	—	4	1	no	—
308	D₄	—	4	1	no	—
309	D₄	—	4	1	no	—
310	C₂×C₄	—	2	3	no	—
311	C₂×C₄	—	2	3	no	—
312	C₂×C₄	—	2	6	no	—
313	C₂×C₄	—	2	2	no	—
314	C₂×C₄	—	2	6	no	—
315	C₂×C₄	—	2	3	no	—
316	C₂×C₄	—	2	1	no	—
317	C₂×C₄	—	2	3	no	—
318	C₂×C₄	—	4	1	no	—
319	C₂×C₄	—	4	1	no	—
320	C₂×C₄	—	4	3	no	—
321	C₂×C₄	—	4	3	no	—
322	C₂×C₄	—	4	1	no	—
323	C₂×C₄	—	4	6	no	—
324	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	3	yes	—
325	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	3	yes	—
326	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	3	yes	—
327	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	3	yes	—
328	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
329	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
330	C₈	—	4	1	no	—
331	C₈	—	4	3	no	—
332	C₂²	—	2	1	no	—
333	C₂²	—	2	1	no	—
334	C₂²	—	4	1	no	—
335	C₂²	—	4	1	no	—
336	C₂²	—	4	1	no	—
337	C₂²	C₂²×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
338	C₂²	C₂₃×#577	1	1	yes	characteristic
339	C₂²	C₂₃×#578	1	1	yes	characteristic
340	C₄	—	2	1	no	—
341	C₄	—	2	1	no	—
342	C₄	—	2	3	no	—
343	C₄	—	2	3	no	—
344	C₄	—	2	3	no	—
345	C₄	—	4	6	no	—
346	C₄	—	4	2	no	—
347	C₄	—	4	3	no	—
348	C₄	—	4	1	no	—
349	C₄	—	4	3	no	—
350	C₄	C₂×C₂₃×#104	1	6	yes	—
351	C₂	—	2	1	no	—
352	C₂	—	2	1	no	—
353	C₂	—	8	1	no	—
354	C₂	C₂₃×#2884	1	1	yes	characteristic
355	C₂	C₂₃×#2898	1	1	yes	characteristic
356	C₂	C₂²×C₂₃×#104	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂²×C₂²⋊C₄
commutator	C₂×C₄	C₂³×C₄×C₂₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₃
prime radical	C₂₃×#121	C₂³
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂×C₄×Q₈×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂₃×#2984	C₂	semidirect
3. C₂₃×#2276	C₂	semidirect
5. C₂₃×#1506	C₂	semidirect
6. C₂₃×#1503	C₂	semidirect
8. C₂₃×#557	C₄	semidirect
9. C₂₃×#557	C₄	semidirect
10. C₂₃×#556	C₄	semidirect
13. D₄×Q₈×C₂₃	C₄	semidirect
122. #17549	C₂₃	direct (N × H)
155. #2984	C₂×C₂₃	semidirect
156. #2276	C₂×C₂₃	semidirect
158. #1506	C₂×C₂₃	semidirect
159. #1503	C₂×C₂₃	semidirect
180. #557	C₄×C₂₃	semidirect
181. #557	C₄×C₂₃	semidirect
182. #556	C₄×C₂₃	semidirect
185. D₄×Q₈	C₄×C₂₃	semidirect
257. C₂₃	#17549	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂₃×#3523	2
C₂₃×#2984	2
C₂₃×#2276	2
C₂₃×#1509	2
C₂₃×#1506	2
C₂₃×#1503	2
C₂₃×#1500	2
#17549	23

Subgroups — C23×#17549 #19165175

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#17549 #19165175