Subgroups — C₂₃×#22731 #19170357

Order 5888.

730 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	C₂×C₂₃×#446	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#2355	C₂	1	2	yes	maximal
3	C₂₃×#1949	C₂	1	2	yes	maximal
4	C₂₃×#1949	C₂	1	2	yes	maximal
5	C₂₃×#1947	C₂	1	2	yes	maximal
6	C₂₃×#1847	C₂	1	2	yes	maximal
7	C₂₃×#1846	C₂	1	1	yes	maximal, characteristic
8	C₂₃×#1776	C₂	1	2	yes	maximal
9	C₄×C₂₃×#107	C₂	1	1	yes	maximal, characteristic
10	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
11	C₂₃×#446	C₄	1	8	yes	complemented
12	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic
13	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic
14	C₂×C₂₃×#107	C₂²	1	2	yes	—
15	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic
16	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic
17	C₂×C₂₃×#106	C₂²	1	2	yes	—
18	C₂×C₂₃×#106	C₂²	1	2	yes	—
19	C₂×C₂₃×C₄⋊C₈	C₂²	1	2	yes	—
20	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×C₂₃×#97	C₂²	1	2	yes	—
22	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
23	C₂₃×#391	—	2	2	no	—
24	C₂₃×#387	—	2	2	no	—
25	C₂₃×#387	—	2	2	no	—
26	C₂₃×#384	C₂²	1	2	yes	—
27	C₂₃×#382	C₂²	1	2	yes	—
28	C₂₃×#382	C₂²	1	2	yes	—
29	C₄×C₄⋊C₄×C₂₃	—	2	2	no	—
30	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
31	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
32	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
33	C₂₃×#340	C₂²	1	2	yes	—
34	C₂₃×#340	C₂²	1	2	yes	—
35	C₂₃×#340	C₂²	1	2	yes	—
36	C₂²×Q₈×C₂₃	D₄	1	1	yes	characteristic
37	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
38	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
39	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
40	C₄×Q₈×C₂₃	C₂×C₄	1	4	yes	—
41	C₄×Q₈×C₂₃	Q₈	1	4	yes	—
42	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
43	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
44	C₂×C₄⋊C₄×C₂₃	D₄	1	2	yes	—
45	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
46	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
47	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
48	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
49	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
50	C₂×C₄²×C₂₃	—	2	2	no	—
51	C₂×C₄²×C₂₃	—	2	2	no	—
52	C₂×C₄²×C₂₃	—	2	2	no	—
53	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
54	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
55	C₂₃×#107	—	2	2	no	—
56	C₂₃×#107	—	4	1	no	—
57	C₂₃×#107	—	4	2	no	—
58	C₂₃×#107	—	4	1	no	—
59	C₂₃×#107	Q₈	1	4	yes	complemented
60	C₂₃×#106	—	2	4	no	—
61	C₂₃×#106	—	4	2	no	—
62	C₂₃×C₄⋊C₈	C₂×C₄	1	4	yes	—
63	C₂₃×C₄⋊C₈	C₂×C₄	1	8	yes	—
64	C₂₃×#97	C₂×C₄	1	8	yes	—
65	C₄×C₈×C₂₃	C₂×C₄	1	4	yes	—
66	C₂₃×#95	—	2	2	no	—
67	C₂₃×#95	—	2	2	no	—
68	C₂₃×#95	—	2	2	no	—
69	C₂₃×#95	—	2	2	no	—
70	C₂₃×#95	—	2	2	no	—
71	C₂₃×#95	—	2	2	no	—
72	C₂₃×#95	—	2	2	no	—
73	C₂×Q₈×C₂₃	—	4	1	no	—
74	C₂×Q₈×C₂₃	—	4	1	no	—
75	C₂×Q₈×C₂₃	C₄⋊C₄	1	4	yes	—
76	C₂²×C₄×C₂₃	—	2	2	no	—
77	C₂²×C₄×C₂₃	—	2	2	no	—
78	C₂²×C₄×C₂₃	—	2	2	no	—
79	C₂²×C₄×C₂₃	—	2	2	no	—
80	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
81	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
82	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
83	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
84	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
85	C₂×C₈×C₂₃	—	2	2	no	—
86	C₂×C₈×C₂₃	—	2	1	no	—
87	C₂×C₈×C₂₃	—	2	1	no	—
88	C₂×C₈×C₂₃	—	2	2	no	—
89	C₂×C₈×C₂₃	C₂²×C₄	1	2	yes	—
90	C₂×C₈×C₂₃	C₂²×C₄	1	4	yes	—
91	C₂×C₈×C₂₃	C₂²×C₄	1	2	yes	—
92	C₂×C₈×C₂₃	C₂×Q₈	1	2	yes	—
93	C₂×C₈×C₂₃	#41	1	2	yes	—
94	C₄⋊C₄×C₂₃	—	2	2	no	—
95	C₄⋊C₄×C₂₃	—	2	2	no	—
96	C₄⋊C₄×C₂₃	—	2	2	no	—
97	C₄⋊C₄×C₂₃	—	2	2	no	—
98	C₄⋊C₄×C₂₃	—	2	2	no	—
99	C₄⋊C₄×C₂₃	—	2	2	no	—
100	C₄⋊C₄×C₂₃	—	2	2	no	—
101	C₄⋊C₄×C₂₃	—	4	4	no	—
102	C₄⋊C₄×C₂₃	—	8	2	no	—
103	C₄⋊C₄×C₂₃	C₄⋊C₄	1	8	yes	—
104	C₄⋊C₄×C₂₃	C₄⋊C₄	1	4	yes	—
105	C₄⋊C₄×C₂₃	C₂×Q₈	1	4	yes	—
106	C₄²×C₂₃	—	4	4	no	—
107	C₄²×C₂₃	—	8	2	no	—
108	C₄²×C₂₃	—	8	2	no	—
109	C₄²×C₂₃	C₂²×C₄	1	2	yes	—
110	C₄²×C₂₃	C₂²×C₄	1	4	yes	—
111	C₄²×C₂₃	C₂×Q₈	1	2	yes	—
112	C₄²×C₂₃	C₂×Q₈	1	4	yes	—
113	#22731	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
114	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
115	Q₈×C₂₃	—	4	4	no	—
116	C₂×C₄×C₂₃	—	2	2	no	—
117	C₂×C₄×C₂₃	—	2	2	no	—
118	C₂×C₄×C₂₃	—	2	1	no	—
119	C₂×C₄×C₂₃	—	2	1	no	—
120	C₂×C₄×C₂₃	—	2	1	no	—
121	C₂×C₄×C₂₃	—	2	2	no	—
122	C₂×C₄×C₂₃	—	2	1	no	—
123	C₂×C₄×C₂₃	—	2	2	no	—
124	C₂×C₄×C₂₃	—	2	4	no	—
125	C₂×C₄×C₂₃	—	4	2	no	—
126	C₂×C₄×C₂₃	—	4	2	no	—
127	C₂×C₄×C₂₃	—	4	2	no	—
128	C₂×C₄×C₂₃	—	4	2	no	—
129	C₂×C₄×C₂₃	—	4	2	no	—
130	C₂×C₄×C₂₃	—	4	2	no	—
131	C₂×C₄×C₂₃	—	4	2	no	—
132	C₂×C₄×C₂₃	—	4	2	no	—
133	C₂×C₄×C₂₃	—	4	2	no	—
134	C₂×C₄×C₂₃	—	4	2	no	—
135	C₂×C₄×C₂₃	—	4	2	no	—
136	C₂×C₄×C₂₃	C₂×C₄⋊C₄	1	2	yes	—
137	C₂×C₄×C₂₃	C₂×C₄⋊C₄	1	4	yes	—
138	C₂×C₄×C₂₃	C₂×C₄⋊C₄	1	2	yes	—
139	C₂×C₄×C₂₃	C₂×C₄⋊C₄	1	4	yes	—
140	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
141	C₂×C₄×C₂₃	C₂²×Q₈	1	1	yes	characteristic
142	C₂×C₄×C₂₃	C₂²×Q₈	1	1	yes	characteristic
143	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
144	C₂×C₄×C₂₃	H(5,𝔽₂)	1	1	yes	characteristic
145	C₂×C₄×C₂₃	2₋¹⁺⁴	1	1	yes	characteristic
146	C₈×C₂₃	—	2	4	no	—
147	C₈×C₂₃	—	2	2	no	—
148	C₈×C₂₃	C₄×Q₈	1	4	yes	—
149	C₂×#446	C₂×C₂₃	1	1	yes	characteristic
150	#2355	C₂×C₂₃	1	2	yes	—
151	#1949	C₂×C₂₃	1	2	yes	—
152	#1949	C₂×C₂₃	1	2	yes	—
153	#1947	C₂×C₂₃	1	2	yes	—
154	#1847	C₂×C₂₃	1	2	yes	—
155	#1846	C₂×C₂₃	1	1	yes	characteristic
156	#1776	C₂×C₂₃	1	2	yes	—
157	C₄×#107	C₂×C₂₃	1	1	yes	characteristic
158	C₂²×C₂₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
159	C₂²×C₂₃	D₄×Q₈	1	1	yes	characteristic
160	C₂²×C₂₃	#550	1	1	yes	characteristic
161	C₂²×C₂₃	#575	1	1	yes	characteristic
162	C₂²×C₂₃	#575	1	1	yes	characteristic
163	C₂²×C₂₃	#576	1	1	yes	characteristic
164	C₂²×C₂₃	#578	1	1	yes	characteristic
165	C₄×C₂₃	—	2	4	no	—
166	C₄×C₂₃	—	2	2	no	—
167	C₄×C₂₃	—	2	2	no	—
168	C₄×C₂₃	—	2	4	no	—
169	C₄×C₂₃	—	4	4	no	—
170	C₄×C₂₃	—	8	2	no	—
171	C₄×C₂₃	—	8	2	no	—
172	C₄×C₂₃	—	8	2	no	—
173	C₄×C₂₃	C₂×C₄×Q₈	1	1	yes	characteristic
174	C₄×C₂₃	#520	1	1	yes	characteristic
175	C₄×C₂₃	#557	1	1	yes	characteristic
176	C₄×C₂₃	Q₈²	1	1	yes	characteristic
177	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
178	#446	C₄×C₂₃	1	8	yes	complemented
179	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic
180	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic
181	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic
182	C₂×#107	C₂²×C₂₃	1	2	yes	—
183	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic
184	C₂×#106	C₂²×C₂₃	1	2	yes	—
185	C₂×#106	C₂²×C₂₃	1	2	yes	—
186	C₂×C₄⋊C₈	C₂²×C₂₃	1	2	yes	—
187	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
188	C₂×#97	C₂²×C₂₃	1	2	yes	—
189	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
190	#391	—	2	2	no	—
191	#387	—	2	2	no	—
192	#387	—	2	2	no	—
193	#384	C₂²×C₂₃	1	2	yes	—
194	#382	C₂²×C₂₃	1	2	yes	—
195	#382	C₂²×C₂₃	1	2	yes	—
196	C₄×C₄⋊C₄	—	2	2	no	—
197	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
198	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
199	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
200	#340	C₂²×C₂₃	1	2	yes	—
201	#340	C₂²×C₂₃	1	2	yes	—
202	#340	C₂²×C₂₃	1	2	yes	—
203	C₂×C₂₃	Q₈×C₄⋊C₄	1	1	yes	characteristic
204	C₂×C₂₃	#2911	1	1	yes	characteristic
205	C₂×C₂₃	#2913	1	1	yes	characteristic
206	C₂×C₂₃	#3389	1	1	yes	characteristic
207	C₂×C₂₃	#3390	1	1	yes	characteristic
208	C₂×C₂₃	#3402	1	1	yes	characteristic
209	C₂×C₂₃	#3403	1	1	yes	characteristic
210	C₂²×Q₈	D₄×C₂₃	1	1	yes	characteristic
211	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
212	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
213	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
214	C₄×Q₈	C₂×C₄×C₂₃	1	4	yes	—
215	C₄×Q₈	Q₈×C₂₃	1	4	yes	—
216	C₂×C₄⋊C₄	—	2	2	no	—
217	C₂×C₄⋊C₄	—	2	2	no	—
218	C₂×C₄⋊C₄	D₄×C₂₃	1	2	yes	—
219	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
220	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
221	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
222	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
223	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
224	C₂×C₄²	—	2	2	no	—
225	C₂×C₄²	—	2	2	no	—
226	C₂×C₄²	—	2	2	no	—
227	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
228	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
229	#107	—	2	2	no	—
230	#107	—	4	1	no	—
231	#107	—	4	2	no	—
232	#107	—	4	1	no	—
233	#107	Q₈×C₂₃	1	4	yes	complemented
234	#106	—	2	4	no	—
235	#106	—	4	2	no	—
236	C₄⋊C₈	C₂×C₄×C₂₃	1	4	yes	—
237	C₄⋊C₈	C₂×C₄×C₂₃	1	8	yes	—
238	#97	C₂×C₄×C₂₃	1	8	yes	—
239	C₄×C₈	C₂×C₄×C₂₃	1	4	yes	—
240	#95	—	2	2	no	—
241	#95	—	2	2	no	—
242	#95	—	2	2	no	—
243	#95	—	2	2	no	—
244	#95	—	2	2	no	—
245	#95	—	2	2	no	—
246	#95	—	2	2	no	—
247	C₂₃	#22731	1	1	yes	characteristic, direct product factor, Sylow
248	C₂×Q₈	—	4	1	no	—
249	C₂×Q₈	—	4	1	no	—
250	C₂×Q₈	C₄⋊C₄×C₂₃	1	4	yes	—
251	C₂²×C₄	—	2	2	no	—
252	C₂²×C₄	—	2	2	no	—
253	C₂²×C₄	—	2	2	no	—
254	C₂²×C₄	—	2	2	no	—
255	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
256	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
257	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
258	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
259	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
260	C₂×C₈	—	2	2	no	—
261	C₂×C₈	—	2	1	no	—
262	C₂×C₈	—	2	1	no	—
263	C₂×C₈	—	2	2	no	—
264	C₂×C₈	C₂²×C₄×C₂₃	1	2	yes	—
265	C₂×C₈	C₂²×C₄×C₂₃	1	4	yes	—
266	C₂×C₈	C₂²×C₄×C₂₃	1	2	yes	—
267	C₂×C₈	C₂×Q₈×C₂₃	1	2	yes	—
268	C₂×C₈	#41×C₂₃	1	2	yes	—
269	C₄⋊C₄	—	2	2	no	—
270	C₄⋊C₄	—	2	2	no	—
271	C₄⋊C₄	—	2	2	no	—
272	C₄⋊C₄	—	2	2	no	—
273	C₄⋊C₄	—	2	2	no	—
274	C₄⋊C₄	—	2	2	no	—
275	C₄⋊C₄	—	2	2	no	—
276	C₄⋊C₄	—	4	4	no	—
277	C₄⋊C₄	—	8	2	no	—
278	C₄⋊C₄	C₄⋊C₄×C₂₃	1	8	yes	—
279	C₄⋊C₄	C₄⋊C₄×C₂₃	1	4	yes	—
280	C₄⋊C₄	C₂×Q₈×C₂₃	1	4	yes	—
281	C₄²	—	4	4	no	—
282	C₄²	—	8	2	no	—
283	C₄²	—	8	2	no	—
284	C₄²	C₂²×C₄×C₂₃	1	2	yes	—
285	C₄²	C₂²×C₄×C₂₃	1	4	yes	—
286	C₄²	C₂×Q₈×C₂₃	1	2	yes	—
287	C₄²	C₂×Q₈×C₂₃	1	4	yes	—
288	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
289	Q₈	—	4	4	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	1	no	—
295	C₂×C₄	—	2	2	no	—
296	C₂×C₄	—	2	1	no	—
297	C₂×C₄	—	2	2	no	—
298	C₂×C₄	—	2	4	no	—
299	C₂×C₄	—	4	2	no	—
300	C₂×C₄	—	4	2	no	—
301	C₂×C₄	—	4	2	no	—
302	C₂×C₄	—	4	2	no	—
303	C₂×C₄	—	4	2	no	—
304	C₂×C₄	—	4	2	no	—
305	C₂×C₄	—	4	2	no	—
306	C₂×C₄	—	4	2	no	—
307	C₂×C₄	—	4	2	no	—
308	C₂×C₄	—	4	2	no	—
309	C₂×C₄	—	4	2	no	—
310	C₂×C₄	C₂×C₄⋊C₄×C₂₃	1	2	yes	—
311	C₂×C₄	C₂×C₄⋊C₄×C₂₃	1	4	yes	—
312	C₂×C₄	C₂×C₄⋊C₄×C₂₃	1	2	yes	—
313	C₂×C₄	C₂×C₄⋊C₄×C₂₃	1	4	yes	—
314	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
315	C₂×C₄	C₂²×Q₈×C₂₃	1	1	yes	characteristic
316	C₂×C₄	C₂²×Q₈×C₂₃	1	1	yes	characteristic
317	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
318	C₂×C₄	C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
319	C₂×C₄	C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
320	C₈	—	2	4	no	—
321	C₈	—	2	2	no	—
322	C₈	C₄×Q₈×C₂₃	1	4	yes	—
323	C₂²	C₂²×C₄⋊C₄×C₂₃	1	1	yes	characteristic
324	C₂²	D₄×Q₈×C₂₃	1	1	yes	characteristic
325	C₂²	C₂₃×#550	1	1	yes	characteristic
326	C₂²	C₂₃×#575	1	1	yes	characteristic
327	C₂²	C₂₃×#575	1	1	yes	characteristic
328	C₂²	C₂₃×#576	1	1	yes	characteristic
329	C₂²	C₂₃×#578	1	1	yes	characteristic
330	C₄	—	2	4	no	—
331	C₄	—	2	2	no	—
332	C₄	—	2	2	no	—
333	C₄	—	2	4	no	—
334	C₄	—	4	4	no	—
335	C₄	—	8	2	no	—
336	C₄	—	8	2	no	—
337	C₄	—	8	2	no	—
338	C₄	C₂×C₄×Q₈×C₂₃	1	1	yes	characteristic
339	C₄	C₂₃×#520	1	1	yes	characteristic
340	C₄	C₂₃×#557	1	1	yes	characteristic
341	C₄	Q₈²×C₂₃	1	1	yes	characteristic
342	C₂	Q₈×C₄⋊C₄×C₂₃	1	1	yes	characteristic
343	C₂	C₂₃×#2911	1	1	yes	characteristic
344	C₂	C₂₃×#2913	1	1	yes	characteristic
345	C₂	C₂₃×#3389	1	1	yes	characteristic
346	C₂	C₂₃×#3390	1	1	yes	characteristic
347	C₂	C₂₃×#3402	1	1	yes	characteristic
348	C₂	C₂₃×#3403	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₂₃	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₂₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₃ ◁ C₂×C₄×Q₈×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
11. C₂₃×#446	C₄	semidirect
59. C₂₃×#107	Q₈	semidirect
113. #22731	C₂₃	direct (N × H)
178. #446	C₄×C₂₃	semidirect
233. #107	Q₈×C₂₃	semidirect
247. C₂₃	#22731	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₂₃×#446	2
C₂₃×#2355	2
C₂₃×#1949	2
C₂₃×#1947	2
C₂₃×#1847	2
C₂₃×#1846	2
C₂₃×#1776	2
C₄×C₂₃×#107	2
#22731	23

Subgroups — C23×#22731 #19170357

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#22731 #19170357