Subgroups — C₂₃×#60715 #19208341

Order 5888.

1830 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3509	C₂	1	2	yes	maximal
2	C₂₃×#3185	C₂	1	4	yes	maximal, complemented
3	C₂₃×#3177	C₂	1	8	yes	maximal, complemented
4	C₂₃×#3170	C₂	1	4	yes	maximal, complemented
5	C₂₃×#3160	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₂₃×#494	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#3139	C₂	1	2	yes	maximal, complemented
8	C₂₃×#3059	C₂	1	4	yes	maximal
9	C₂₃×#2950	C₂	1	4	yes	maximal, complemented
10	C₄×C₂₃×#131	C₂	1	1	yes	maximal, characteristic
11	C₂²×Q₁₆×C₂₃	C₂²	1	4	yes	—
12	C₂×C₂₃×#131	C₂²	1	2	yes	—
13	C₂₃×#557	—	2	4	no	—
14	C₂₃×#556	—	2	4	no	—
15	C₂₃×#552	—	2	8	no	—
16	C₂₃×#541	C₂²	1	8	yes	—
17	C₂₃×#536	C₂²	1	4	yes	—
18	C₂₃×#533	C₂²	1	8	yes	—
19	C₂₃×#533	C₂²	1	2	yes	—
20	C₂×C₂₃×C₄⋊Q₈	C₂²	1	2	yes	—
21	C₂₃×#519	C₂²	1	4	yes	—
22	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
23	C₂₃×#500	C₂²	1	2	yes	—
24	C₂₃×#499	C₂²	1	4	yes	—
25	C₂₃×#498	C₂²	1	2	yes	—
26	C₂₃×#494	C₂²	1	2	yes	—
27	C₂₃×#494	C₂²	1	4	yes	—
28	C₂₃×#494	C₂²	1	2	yes	—
29	C₂₃×#491	C₂²	1	8	yes	—
30	C₂₃×#487	C₂²	1	8	yes	—
31	C₂₃×#470	C₂²	1	16	yes	—
32	C₂₃×#467	C₂²	1	16	yes	—
33	C₂₃×#441	C₂²	1	16	yes	—
34	C₄×Q₁₆×C₂₃	C₂²	1	16	yes	—
35	C₂₃×#427	C₂²	1	4	yes	—
36	C₂₃×#419	C₂²	1	8	yes	—
37	C₂₃×#405	C₂²	1	4	yes	—
38	C₂₃×#405	C₂²	1	2	yes	—
39	C₄×M₁₆×C₂₃	C₂²	1	2	yes	—
40	C₄×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
41	C₂×C₄×C₈×C₂₃	C₂²	1	2	yes	—
42	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
43	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
44	C₂²×Q₈×C₂₃	C₂³	1	4	yes	—
45	C₂×Q₁₆×C₂₃	—	2	16	no	—
46	C₂×Q₁₆×C₂₃	C₂³	1	8	yes	—
47	C₂×Q₁₆×C₂₃	C₂³	1	8	yes	—
48	C₂₃×#131	—	2	8	no	—
49	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
50	C₂×M₁₆×C₂₃	C₂³	1	4	yes	—
51	C₂²×C₈×C₂₃	C₂³	1	4	yes	—
52	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
53	C₂₃×C₄⋊Q₈	—	2	4	no	—
54	C₂₃×C₄⋊Q₈	—	2	4	no	—
55	C₂₃×C₄⋊Q₈	C₂³	1	4	yes	—
56	C₂₃×C₄⋊Q₈	C₂³	1	4	yes	—
57	C₂₃×C₄⋊Q₈	C₂³	1	4	yes	—
58	C₂₃×#126	—	2	16	no	—
59	C₂₃×#125	—	2	16	no	—
60	C₂₃×#125	—	2	8	no	—
61	C₂₃×#125	C₂³	1	4	yes	—
62	C₂₃×#124	—	2	4	no	—
63	C₂₃×#123	—	2	8	no	—
64	C₂₃×C₂²⋊Q₈	—	2	4	no	—
65	C₂₃×C₂²⋊Q₈	—	2	8	no	—
66	C₂₃×C₂²⋊Q₈	C₂³	1	16	yes	—
67	C₄×Q₈×C₂₃	—	2	8	no	—
68	C₄×Q₈×C₂₃	—	2	8	no	—
69	C₄×Q₈×C₂₃	—	2	4	no	—
70	C₄×Q₈×C₂₃	D₄	1	2	yes	—
71	C₄×Q₈×C₂₃	C₂³	1	16	yes	—
72	C₄×D₄×C₂₃	D₄	1	4	yes	—
73	C₄×D₄×C₂₃	D₄	1	2	yes	—
74	C₂₃×#117	—	2	8	no	—
75	C₂₃×#117	—	2	8	no	—
76	C₂₃×#117	C₂³	1	4	yes	—
77	C₂₃×#117	C₂³	1	1	yes	characteristic
78	C₂₃×#117	C₂³	1	2	yes	—
79	C₂×C₄⋊C₄×C₂₃	—	2	4	no	—
80	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
81	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
82	C₂₃×#107	C₂³	1	8	yes	—
83	C₂₃×#106	C₂³	1	8	yes	—
84	C₂₃×#103	C₂³	1	32	yes	—
85	C₂₃×#97	C₂³	1	4	yes	—
86	C₂₃×#97	C₂³	1	2	yes	—
87	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
88	C₄×C₈×C₂₃	C₂³	1	2	yes	—
89	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
90	C₄×C₈×C₂₃	C₂³	1	4	yes	—
91	C₄×C₈×C₂₃	C₂³	1	2	yes	—
92	#41×C₂₃	—	2	4	no	—
93	C₂×Q₈×C₂₃	—	2	4	no	—
94	C₂×Q₈×C₂₃	—	2	4	no	—
95	C₂×Q₈×C₂₃	—	2	16	no	—
96	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
97	C₂×Q₈×C₂₃	C₂⁴	1	8	yes	—
98	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
99	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₂₃	—	2	4	no	—
101	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
102	C₂²×C₄×C₂₃	C₂×D₄	1	4	yes	—
103	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
104	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
105	Q₁₆×C₂₃	—	2	16	no	—
106	Q₁₆×C₂₃	—	2	16	no	—
107	M₁₆×C₂₃	—	2	4	no	—
108	M₁₆×C₂₃	—	2	8	no	—
109	C₂×C₈×C₂₃	—	2	8	no	—
110	C₂×C₈×C₂₃	#41	1	8	yes	—
111	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
112	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
113	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
114	C₄⋊C₄×C₂₃	—	2	8	no	—
115	C₄⋊C₄×C₂₃	—	2	8	no	—
116	C₄⋊C₄×C₂₃	—	2	4	no	—
117	C₄⋊C₄×C₂₃	—	2	16	no	—
118	C₄⋊C₄×C₂₃	—	2	8	no	—
119	C₄⋊C₄×C₂₃	—	2	16	no	—
120	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
121	C₄⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
122	C₄⋊C₄×C₂₃	C₂⁴	1	8	yes	—
123	C₂²⋊C₄×C₂₃	—	2	4	no	—
124	C₂²⋊C₄×C₂₃	—	2	16	no	—
125	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
126	C₂²⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
127	C₄²×C₂₃	—	2	16	no	—
128	C₄²×C₂₃	—	2	4	no	—
129	C₄²×C₂₃	C₂×D₄	1	4	yes	—
130	C₄²×C₂₃	C₂×D₄	1	2	yes	—
131	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
132	C₄²×C₂₃	C₂⁴	1	2	yes	—
133	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
134	#60715	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
135	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
136	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
137	Q₈×C₂₃	—	2	2	no	—
138	Q₈×C₂₃	—	2	16	no	—
139	Q₈×C₂₃	—	4	8	no	—
140	Q₈×C₂₃	—	4	8	no	—
141	D₄×C₂₃	—	2	4	no	—
142	D₄×C₂₃	—	2	2	no	—
143	C₂×C₄×C₂₃	—	2	4	no	—
144	C₂×C₄×C₂₃	—	2	8	no	—
145	C₂×C₄×C₂₃	—	2	4	no	—
146	C₂×C₄×C₂₃	—	2	8	no	—
147	C₂×C₄×C₂₃	—	2	8	no	—
148	C₂×C₄×C₂₃	—	4	8	no	—
149	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
150	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
151	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
152	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
153	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
154	C₂×C₄×C₂₃	C₂×#41	1	4	yes	—
155	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
156	C₈×C₂₃	—	2	4	no	—
157	C₈×C₂₃	C₂×#41	1	4	yes	—
158	C₈×C₂₃	C₂×#41	1	4	yes	—
159	#3509	C₂×C₂₃	1	2	yes	—
160	#3185	C₂×C₂₃	1	4	yes	complemented
161	#3177	C₂×C₂₃	1	8	yes	complemented
162	#3170	C₂×C₂₃	1	4	yes	complemented
163	#3160	C₂×C₂₃	1	1	yes	characteristic, complemented
164	C₂×#494	C₂×C₂₃	1	1	yes	characteristic, complemented
165	#3139	C₂×C₂₃	1	2	yes	complemented
166	#3059	C₂×C₂₃	1	4	yes	—
167	#2950	C₂×C₂₃	1	4	yes	complemented
168	C₄×#131	C₂×C₂₃	1	1	yes	characteristic
169	C₂²×C₂₃	—	2	2	no	—
170	C₂²×C₂₃	—	2	2	no	—
171	C₂²×C₂₃	—	2	4	no	—
172	C₂²×C₂₃	#532	1	2	yes	—
173	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
174	C₄×C₂₃	—	2	2	no	—
175	C₄×C₂₃	—	2	4	no	—
176	C₄×C₂₃	—	2	2	no	—
177	C₄×C₂₃	—	4	8	no	—
178	C₄×C₂₃	—	4	8	no	—
179	C₄×C₂₃	#532	1	2	yes	—
180	C₄×C₂₃	#578	1	4	yes	—
181	C₄×C₂₃	C₂²×#41	1	2	yes	—
182	C₂²×Q₁₆	C₂²×C₂₃	1	4	yes	—
183	C₂×#131	C₂²×C₂₃	1	2	yes	—
184	#557	—	2	4	no	—
185	#556	—	2	4	no	—
186	#552	—	2	8	no	—
187	#541	C₂²×C₂₃	1	8	yes	—
188	#536	C₂²×C₂₃	1	4	yes	—
189	#533	C₂²×C₂₃	1	8	yes	—
190	#533	C₂²×C₂₃	1	2	yes	—
191	C₂×C₄⋊Q₈	C₂²×C₂₃	1	2	yes	—
192	#519	C₂²×C₂₃	1	4	yes	—
193	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
194	#500	C₂²×C₂₃	1	2	yes	—
195	#499	C₂²×C₂₃	1	4	yes	—
196	#498	C₂²×C₂₃	1	2	yes	—
197	#494	C₂²×C₂₃	1	2	yes	—
198	#494	C₂²×C₂₃	1	4	yes	—
199	#494	C₂²×C₂₃	1	2	yes	—
200	#491	C₂²×C₂₃	1	8	yes	—
201	#487	C₂²×C₂₃	1	8	yes	—
202	#470	C₂²×C₂₃	1	16	yes	—
203	#467	C₂²×C₂₃	1	16	yes	—
204	#441	C₂²×C₂₃	1	16	yes	—
205	C₄×Q₁₆	C₂²×C₂₃	1	16	yes	—
206	#427	C₂²×C₂₃	1	4	yes	—
207	#419	C₂²×C₂₃	1	8	yes	—
208	#405	C₂²×C₂₃	1	4	yes	—
209	#405	C₂²×C₂₃	1	2	yes	—
210	C₄×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
211	C₄×M₁₆	C₂²×C₂₃	1	2	yes	—
212	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
213	C₂×C₄×C₈	C₂²×C₂₃	1	2	yes	—
214	C₂×C₂₃	—	2	2	no	—
215	C₂×C₂₃	—	4	2	no	—
216	C₂×C₂₃	C₂×#532	1	1	yes	characteristic
217	C₂×C₂₃	C₂×#578	1	2	yes	—
218	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
219	C₂²×Q₈	C₂³×C₂₃	1	4	yes	—
220	C₂×Q₁₆	—	2	16	no	—
221	C₂×Q₁₆	C₂³×C₂₃	1	8	yes	—
222	C₂×Q₁₆	C₂³×C₂₃	1	8	yes	—
223	#131	—	2	8	no	—
224	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
225	C₂×M₁₆	C₂³×C₂₃	1	4	yes	—
226	C₂²×C₈	C₂³×C₂₃	1	4	yes	—
227	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
228	C₄⋊Q₈	—	2	4	no	—
229	C₄⋊Q₈	—	2	4	no	—
230	C₄⋊Q₈	C₂³×C₂₃	1	4	yes	—
231	C₄⋊Q₈	C₂³×C₂₃	1	4	yes	—
232	C₄⋊Q₈	C₂³×C₂₃	1	4	yes	—
233	#126	—	2	16	no	—
234	#125	—	2	16	no	—
235	#125	—	2	8	no	—
236	#125	C₂³×C₂₃	1	4	yes	—
237	#124	—	2	4	no	—
238	#123	—	2	8	no	—
239	C₂²⋊Q₈	—	2	4	no	—
240	C₂²⋊Q₈	—	2	8	no	—
241	C₂²⋊Q₈	C₂³×C₂₃	1	16	yes	—
242	C₄×Q₈	—	2	8	no	—
243	C₄×Q₈	—	2	8	no	—
244	C₄×Q₈	—	2	4	no	—
245	C₄×Q₈	D₄×C₂₃	1	2	yes	—
246	C₄×Q₈	C₂³×C₂₃	1	16	yes	—
247	C₄×D₄	D₄×C₂₃	1	4	yes	—
248	C₄×D₄	D₄×C₂₃	1	2	yes	—
249	#117	—	2	8	no	—
250	#117	—	2	8	no	—
251	#117	C₂³×C₂₃	1	4	yes	—
252	#117	C₂³×C₂₃	1	1	yes	characteristic
253	#117	C₂³×C₂₃	1	2	yes	—
254	C₂×C₄⋊C₄	—	2	4	no	—
255	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
256	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
257	#107	C₂³×C₂₃	1	8	yes	—
258	#106	C₂³×C₂₃	1	8	yes	—
259	#103	C₂³×C₂₃	1	32	yes	—
260	#97	C₂³×C₂₃	1	4	yes	—
261	#97	C₂³×C₂₃	1	2	yes	—
262	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
263	C₄×C₈	C₂³×C₂₃	1	2	yes	—
264	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
265	C₄×C₈	C₂³×C₂₃	1	4	yes	—
266	C₄×C₈	C₂³×C₂₃	1	2	yes	—
267	C₂₃	#60715	1	1	yes	characteristic, direct product factor, Sylow
268	#41	—	2	4	no	—
269	C₂×Q₈	—	2	4	no	—
270	C₂×Q₈	—	2	4	no	—
271	C₂×Q₈	—	2	16	no	—
272	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
273	C₂×Q₈	C₂⁴×C₂₃	1	8	yes	—
274	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
275	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
276	C₂²×C₄	—	2	4	no	—
277	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
278	C₂²×C₄	C₂×D₄×C₂₃	1	4	yes	—
279	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
280	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
281	Q₁₆	—	2	16	no	—
282	Q₁₆	—	2	16	no	—
283	M₁₆	—	2	4	no	—
284	M₁₆	—	2	8	no	—
285	C₂×C₈	—	2	8	no	—
286	C₂×C₈	#41×C₂₃	1	8	yes	—
287	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
288	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
289	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
290	C₄⋊C₄	—	2	8	no	—
291	C₄⋊C₄	—	2	8	no	—
292	C₄⋊C₄	—	2	4	no	—
293	C₄⋊C₄	—	2	16	no	—
294	C₄⋊C₄	—	2	8	no	—
295	C₄⋊C₄	—	2	16	no	—
296	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
297	C₄⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
298	C₄⋊C₄	C₂⁴×C₂₃	1	8	yes	—
299	C₂²⋊C₄	—	2	4	no	—
300	C₂²⋊C₄	—	2	16	no	—
301	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
302	C₂²⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
303	C₄²	—	2	16	no	—
304	C₄²	—	2	4	no	—
305	C₄²	C₂×D₄×C₂₃	1	4	yes	—
306	C₄²	C₂×D₄×C₂₃	1	2	yes	—
307	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
308	C₄²	C₂⁴×C₂₃	1	2	yes	—
309	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
310	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
311	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
312	Q₈	—	2	2	no	—
313	Q₈	—	2	16	no	—
314	Q₈	—	4	8	no	—
315	Q₈	—	4	8	no	—
316	D₄	—	2	4	no	—
317	D₄	—	2	2	no	—
318	C₂×C₄	—	2	4	no	—
319	C₂×C₄	—	2	8	no	—
320	C₂×C₄	—	2	4	no	—
321	C₂×C₄	—	2	8	no	—
322	C₂×C₄	—	2	8	no	—
323	C₂×C₄	—	4	8	no	—
324	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
325	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
326	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
327	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
328	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
329	C₂×C₄	C₂×#41×C₂₃	1	4	yes	—
330	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
331	C₈	—	2	4	no	—
332	C₈	C₂×#41×C₂₃	1	4	yes	—
333	C₈	C₂×#41×C₂₃	1	4	yes	—
334	C₂²	—	2	2	no	—
335	C₂²	—	2	2	no	—
336	C₂²	—	2	4	no	—
337	C₂²	C₂₃×#532	1	2	yes	—
338	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
339	C₄	—	2	2	no	—
340	C₄	—	2	4	no	—
341	C₄	—	2	2	no	—
342	C₄	—	4	8	no	—
343	C₄	—	4	8	no	—
344	C₄	C₂₃×#532	1	2	yes	—
345	C₄	C₂₃×#578	1	4	yes	—
346	C₄	C₂²×#41×C₂₃	1	2	yes	—
347	C₂	—	2	2	no	—
348	C₂	—	4	2	no	—
349	C₂	C₂×C₂₃×#532	1	1	yes	characteristic
350	C₂	C₂×C₂₃×#578	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
prime radical	C₂×#41×C₂₃	C₂³
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₄×#41×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂₃×#3185	C₂	semidirect
3. C₂₃×#3177	C₂	semidirect
4. C₂₃×#3170	C₂	semidirect
5. C₂₃×#3160	C₂	semidirect
6. C₂×C₂₃×#494	C₂	semidirect
7. C₂₃×#3139	C₂	semidirect
9. C₂₃×#2950	C₂	semidirect
134. #60715	C₂₃	direct (N × H)
160. #3185	C₂×C₂₃	semidirect
161. #3177	C₂×C₂₃	semidirect
162. #3170	C₂×C₂₃	semidirect
163. #3160	C₂×C₂₃	semidirect
164. C₂×#494	C₂×C₂₃	semidirect
165. #3139	C₂×C₂₃	semidirect
167. #2950	C₂×C₂₃	semidirect
267. C₂₃	#60715	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×#3509	2
C₂₃×#3185	2
C₂₃×#3177	2
C₂₃×#3170	2
C₂₃×#3160	2
C₂×C₂₃×#494	2
C₂₃×#3139	2
C₂₃×#3059	2
C₂₃×#2950	2
C₄×C₂₃×#131	2
#60715	23

Subgroups — C23×#60715 #19208341

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#60715 #19208341