Subgroups — C₂₃×#8569 #19156195

Order 5888.

548 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#2293	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#1831	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₂₃×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₂₃×D₄⋊C₈	C₂	1	2	yes	maximal
5	C₂₃×#1279	C₂	1	2	yes	maximal, complemented
6	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
7	C₂×C₂₃×#117	—	2	1	no	—
8	C₂×C₂₃×C₄⋊C₈	—	2	1	no	—
9	C₂×C₂₃×C₄⋊C₈	C₂²	1	2	yes	—
10	C₂×C₄×C₈×C₂₃	C₂²	1	2	yes	—
11	C₂₃×#390	C₄	1	1	yes	characteristic
12	C₂₃×#390	C₄	1	1	yes	characteristic
13	C₂₃×#389	C₄	1	1	yes	characteristic
14	C₂₃×#389	C₄	1	1	yes	characteristic
15	C₂₃×#388	—	2	1	no	—
16	C₂₃×#388	—	2	1	no	—
17	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
18	C₄×C₂²⋊C₄×C₂₃	—	2	1	no	—
19	C₄³×C₂₃	C₂²	1	1	yes	characteristic
20	C₂₃×#336	—	2	1	no	—
21	C₂₃×#336	—	2	1	no	—
22	C₂₃×#336	—	2	1	no	—
23	C₂₃×D₄⋊C₈	—	2	4	no	—
24	C₂²×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic
25	C₂³×C₄×C₂₃	—	2	1	no	—
26	C₂²×C₈×C₂₃	—	2	2	no	—
27	C₂²×C₈×C₂₃	—	2	2	no	—
28	C₄×D₄×C₂₃	—	2	1	no	—
29	C₄×D₄×C₂₃	—	2	1	no	—
30	C₄×D₄×C₂₃	D₄	1	2	yes	—
31	C₄×D₄×C₂₃	Q₈	1	2	yes	—
32	C₂₃×#117	—	4	4	no	—
33	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
34	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
35	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
36	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
37	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
38	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
39	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
40	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
41	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
42	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
43	C₂×C₄²×C₂₃	—	2	1	no	—
44	C₂×C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
45	C₂×C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
46	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
47	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
48	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
49	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
50	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
51	C₂₃×C₄⋊C₈	—	2	4	no	—
52	C₂₃×C₄⋊C₈	—	2	2	no	—
53	C₂₃×C₄⋊C₈	—	2	2	no	—
54	C₄×C₈×C₂₃	—	2	2	no	—
55	C₄×C₈×C₂₃	—	2	2	no	—
56	C₂₃×#95	—	2	1	no	—
57	C₂₃×#95	—	2	1	no	—
58	C₂₃×#95	—	2	1	no	—
59	C₂⁴×C₂₃	—	2	1	no	—
60	C₂×D₄×C₂₃	—	2	1	no	—
61	C₂×D₄×C₂₃	—	2	2	no	—
62	C₂×D₄×C₂₃	—	2	2	no	—
63	C₂×D₄×C₂₃	C₄⋊C₄	1	2	yes	—
64	C₂²×C₄×C₂₃	—	2	1	no	—
65	C₂²×C₄×C₂₃	—	2	2	no	—
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	—	4	2	no	—
70	C₂²×C₄×C₂₃	—	4	2	no	—
71	C₂²×C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
72	C₂²×C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
73	C₂²×C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
74	C₂²×C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
75	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
76	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
77	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
78	C₂×C₈×C₂₃	—	2	4	no	—
79	C₂×C₈×C₂₃	—	4	2	no	—
80	C₂×C₈×C₂₃	—	4	2	no	—
81	C₂×C₈×C₂₃	—	4	2	no	—
82	C₂×C₈×C₂₃	—	4	2	no	—
83	C₂×C₈×C₂₃	—	4	2	no	—
84	C₄⋊C₄×C₂₃	—	2	1	no	—
85	C₄⋊C₄×C₂₃	—	2	2	no	—
86	C₄⋊C₄×C₂₃	—	2	2	no	—
87	C₄⋊C₄×C₂₃	—	4	2	no	—
88	C₄⋊C₄×C₂₃	—	4	2	no	—
89	C₄⋊C₄×C₂₃	C₄⋊C₄	1	2	yes	—
90	C₂²⋊C₄×C₂₃	—	2	2	no	—
91	C₂²⋊C₄×C₂₃	—	2	2	no	—
92	C₂²⋊C₄×C₂₃	—	4	2	no	—
93	C₂²⋊C₄×C₂₃	—	4	2	no	—
94	C₂²⋊C₄×C₂₃	—	4	2	no	—
95	C₂²⋊C₄×C₂₃	—	4	2	no	—
96	C₄²×C₂₃	—	2	2	no	—
97	C₄²×C₂₃	—	2	2	no	—
98	C₄²×C₂₃	—	2	2	no	—
99	C₄²×C₂₃	—	2	2	no	—
100	C₄²×C₂₃	—	2	2	no	—
101	C₄²×C₂₃	—	4	1	no	—
102	C₄²×C₂₃	—	4	2	no	—
103	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
104	C₄²×C₂₃	C₂×Q₈	1	1	yes	characteristic
105	C₄²×C₂₃	#41	1	1	yes	characteristic
106	C₄²×C₂₃	#41	1	1	yes	characteristic
107	#8569	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
108	C₂³×C₂₃	—	2	2	no	—
109	C₂³×C₂₃	—	4	1	no	—
110	C₂³×C₂₃	—	4	1	no	—
111	C₂³×C₂₃	—	4	1	no	—
112	C₂³×C₂₃	—	4	1	no	—
113	C₂³×C₂₃	—	4	1	no	—
114	C₂³×C₂₃	—	4	1	no	—
115	C₂³×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
116	D₄×C₂₃	—	2	4	no	—
117	D₄×C₂₃	—	4	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	1	no	—
122	C₂×C₄×C₂₃	—	2	2	no	—
123	C₂×C₄×C₂₃	—	2	1	no	—
124	C₂×C₄×C₂₃	—	2	1	no	—
125	C₂×C₄×C₂₃	—	2	1	no	—
126	C₂×C₄×C₂₃	—	2	1	no	—
127	C₂×C₄×C₂₃	—	2	1	no	—
128	C₂×C₄×C₂₃	—	2	1	no	—
129	C₂×C₄×C₂₃	—	2	1	no	—
130	C₂×C₄×C₂₃	—	2	1	no	—
131	C₂×C₄×C₂₃	—	2	1	no	—
132	C₂×C₄×C₂₃	—	4	1	no	—
133	C₂×C₄×C₂₃	—	4	1	no	—
134	C₂×C₄×C₂₃	—	4	4	no	—
135	C₂×C₄×C₂₃	—	4	4	no	—
136	C₂×C₄×C₂₃	—	4	1	no	—
137	C₂×C₄×C₂₃	—	4	1	no	—
138	C₂×C₄×C₂₃	—	4	1	no	—
139	C₂×C₄×C₂₃	—	4	1	no	—
140	C₂×C₄×C₂₃	—	4	1	no	—
141	C₂×C₄×C₂₃	—	4	1	no	—
142	C₂×C₄×C₂₃	#104	1	2	yes	—
143	C₂×C₄×C₂₃	C₂×C₄⋊C₄	1	1	yes	characteristic
144	C₂×C₄×C₂₃	#117	1	1	yes	characteristic
145	C₂×C₄×C₂₃	#121	1	1	yes	characteristic
146	C₂×C₄×C₂₃	#121	1	1	yes	characteristic
147	C₂×C₄×C₂₃	C₂²⋊Q₈	1	1	yes	characteristic
148	C₂×C₄×C₂₃	C₂²⋊Q₈	1	1	yes	characteristic
149	C₂×C₄×C₂₃	#131	1	2	yes	—
150	C₂×C₄×C₂₃	#131	1	2	yes	—
151	C₂×C₄×C₂₃	#135	1	2	yes	—
152	C₂×C₄×C₂₃	AGL(1,ℤ/8)	1	2	yes	—
153	C₈×C₂₃	—	4	4	no	—
154	C₈×C₂₃	—	8	2	no	—
155	#2293	C₂×C₂₃	1	1	yes	characteristic
156	#1831	C₂×C₂₃	1	1	yes	characteristic, complemented
157	C₄×C₄⋊C₈	C₂×C₂₃	1	1	yes	characteristic, complemented
158	C₂×D₄⋊C₈	C₂×C₂₃	1	2	yes	—
159	#1279	C₂×C₂₃	1	2	yes	complemented
160	C₂²×C₂₃	—	4	2	no	—
161	C₂²×C₂₃	—	4	2	no	—
162	C₂²×C₂₃	—	4	2	no	—
163	C₂²×C₂₃	—	8	1	no	—
164	C₂²×C₂₃	—	8	1	no	—
165	C₂²×C₂₃	—	8	1	no	—
166	C₂²×C₂₃	—	8	1	no	—
167	C₂²×C₂₃	#380	1	1	yes	characteristic
168	C₂²×C₂₃	#408	1	1	yes	characteristic
169	C₂²×C₂₃	#408	1	1	yes	characteristic
170	C₂²×C₂₃	#416	1	1	yes	characteristic
171	C₂²×C₂₃	#418	1	1	yes	characteristic
172	C₂²×C₂₃	C₂×#104	1	1	yes	characteristic
173	C₂²×C₂₃	#421	1	1	yes	characteristic
174	C₄×C₂₃	—	2	1	no	—
175	C₄×C₂₃	—	2	1	no	—
176	C₄×C₂₃	—	2	2	no	—
177	C₄×C₂₃	—	4	2	no	—
178	C₄×C₂₃	—	4	1	no	—
179	C₄×C₂₃	—	4	1	no	—
180	C₄×C₂₃	—	4	1	no	—
181	C₄×C₂₃	—	8	1	no	—
182	C₄×C₂₃	—	8	1	no	—
183	C₄×C₂₃	#424	1	2	yes	—
184	C₄×C₂₃	#433	1	2	yes	—
185	C₄×C₂₃	#463	1	2	yes	—
186	C₄×C₂₃	#478	1	2	yes	—
187	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
188	C₂×#117	—	2	1	no	—
189	C₂×C₄⋊C₈	—	2	1	no	—
190	C₂×C₄⋊C₈	C₂²×C₂₃	1	2	yes	—
191	C₂×C₄×C₈	C₂²×C₂₃	1	2	yes	—
192	#390	C₄×C₂₃	1	1	yes	characteristic
193	#390	C₄×C₂₃	1	1	yes	characteristic
194	#389	C₄×C₂₃	1	1	yes	characteristic
195	#389	C₄×C₂₃	1	1	yes	characteristic
196	#388	—	2	1	no	—
197	#388	—	2	1	no	—
198	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
199	C₄×C₂²⋊C₄	—	2	1	no	—
200	C₄³	C₂²×C₂₃	1	1	yes	characteristic
201	#336	—	2	1	no	—
202	#336	—	2	1	no	—
203	#336	—	2	1	no	—
204	D₄⋊C₈	—	2	4	no	—
205	C₂×C₂₃	—	8	2	no	—
206	C₂×C₂₃	#1482	1	1	yes	characteristic
207	C₂×C₂₃	#1484	1	1	yes	characteristic
208	C₂×C₂₃	#1494	1	1	yes	characteristic
209	C₂×C₂₃	#1496	1	1	yes	characteristic
210	C₂×C₂₃	#1798	1	1	yes	characteristic
211	C₂×C₂₃	#1804	1	1	yes	characteristic
212	C₂×C₂₃	#1806	1	1	yes	characteristic
213	C₂²×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
214	C₂³×C₄	—	2	1	no	—
215	C₂²×C₈	—	2	2	no	—
216	C₂²×C₈	—	2	2	no	—
217	C₄×D₄	—	2	1	no	—
218	C₄×D₄	—	2	1	no	—
219	C₄×D₄	D₄×C₂₃	1	2	yes	—
220	C₄×D₄	Q₈×C₂₃	1	2	yes	—
221	#117	—	4	4	no	—
222	C₂×C₄⋊C₄	—	2	1	no	—
223	C₂×C₄⋊C₄	—	2	1	no	—
224	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
225	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
226	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
227	C₂×C₂²⋊C₄	—	2	1	no	—
228	C₂×C₂²⋊C₄	—	2	1	no	—
229	C₂×C₂²⋊C₄	—	2	1	no	—
230	C₂×C₂²⋊C₄	—	2	1	no	—
231	C₂×C₂²⋊C₄	—	2	1	no	—
232	C₂×C₄²	—	2	1	no	—
233	C₂×C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic
234	C₂×C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic
235	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
236	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
237	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
238	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
239	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
240	C₄⋊C₈	—	2	4	no	—
241	C₄⋊C₈	—	2	2	no	—
242	C₄⋊C₈	—	2	2	no	—
243	C₄×C₈	—	2	2	no	—
244	C₄×C₈	—	2	2	no	—
245	#95	—	2	1	no	—
246	#95	—	2	1	no	—
247	#95	—	2	1	no	—
248	C₂₃	#8569	1	1	yes	characteristic, direct product factor, Sylow
249	C₂⁴	—	2	1	no	—
250	C₂×D₄	—	2	1	no	—
251	C₂×D₄	—	2	2	no	—
252	C₂×D₄	—	2	2	no	—
253	C₂×D₄	C₄⋊C₄×C₂₃	1	2	yes	—
254	C₂²×C₄	—	2	1	no	—
255	C₂²×C₄	—	2	2	no	—
256	C₂²×C₄	—	2	2	no	—
257	C₂²×C₄	—	2	1	no	—
258	C₂²×C₄	—	2	1	no	—
259	C₂²×C₄	—	4	2	no	—
260	C₂²×C₄	—	4	2	no	—
261	C₂²×C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
262	C₂²×C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
263	C₂²×C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
264	C₂²×C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
265	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
266	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
267	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
268	C₂×C₈	—	2	4	no	—
269	C₂×C₈	—	4	2	no	—
270	C₂×C₈	—	4	2	no	—
271	C₂×C₈	—	4	2	no	—
272	C₂×C₈	—	4	2	no	—
273	C₂×C₈	—	4	2	no	—
274	C₄⋊C₄	—	2	1	no	—
275	C₄⋊C₄	—	2	2	no	—
276	C₄⋊C₄	—	2	2	no	—
277	C₄⋊C₄	—	4	2	no	—
278	C₄⋊C₄	—	4	2	no	—
279	C₄⋊C₄	C₄⋊C₄×C₂₃	1	2	yes	—
280	C₂²⋊C₄	—	2	2	no	—
281	C₂²⋊C₄	—	2	2	no	—
282	C₂²⋊C₄	—	4	2	no	—
283	C₂²⋊C₄	—	4	2	no	—
284	C₂²⋊C₄	—	4	2	no	—
285	C₂²⋊C₄	—	4	2	no	—
286	C₄²	—	2	2	no	—
287	C₄²	—	2	2	no	—
288	C₄²	—	2	2	no	—
289	C₄²	—	2	2	no	—
290	C₄²	—	2	2	no	—
291	C₄²	—	4	1	no	—
292	C₄²	—	4	2	no	—
293	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
294	C₄²	C₂×Q₈×C₂₃	1	1	yes	characteristic
295	C₄²	#41×C₂₃	1	1	yes	characteristic
296	C₄²	#41×C₂₃	1	1	yes	characteristic
297	C₂³	—	2	2	no	—
298	C₂³	—	4	1	no	—
299	C₂³	—	4	1	no	—
300	C₂³	—	4	1	no	—
301	C₂³	—	4	1	no	—
302	C₂³	—	4	1	no	—
303	C₂³	—	4	1	no	—
304	C₂³	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
305	D₄	—	2	4	no	—
306	D₄	—	4	2	no	—
307	C₂×C₄	—	2	1	no	—
308	C₂×C₄	—	2	1	no	—
309	C₂×C₄	—	2	1	no	—
310	C₂×C₄	—	2	1	no	—
311	C₂×C₄	—	2	2	no	—
312	C₂×C₄	—	2	1	no	—
313	C₂×C₄	—	2	1	no	—
314	C₂×C₄	—	2	1	no	—
315	C₂×C₄	—	2	1	no	—
316	C₂×C₄	—	2	1	no	—
317	C₂×C₄	—	2	1	no	—
318	C₂×C₄	—	2	1	no	—
319	C₂×C₄	—	2	1	no	—
320	C₂×C₄	—	2	1	no	—
321	C₂×C₄	—	4	1	no	—
322	C₂×C₄	—	4	1	no	—
323	C₂×C₄	—	4	4	no	—
324	C₂×C₄	—	4	4	no	—
325	C₂×C₄	—	4	1	no	—
326	C₂×C₄	—	4	1	no	—
327	C₂×C₄	—	4	1	no	—
328	C₂×C₄	—	4	1	no	—
329	C₂×C₄	—	4	1	no	—
330	C₂×C₄	—	4	1	no	—
331	C₂×C₄	C₂₃×#104	1	2	yes	—
332	C₂×C₄	C₂×C₄⋊C₄×C₂₃	1	1	yes	characteristic
333	C₂×C₄	C₂₃×#117	1	1	yes	characteristic
334	C₂×C₄	C₂₃×#121	1	1	yes	characteristic
335	C₂×C₄	C₂₃×#121	1	1	yes	characteristic
336	C₂×C₄	C₂₃×C₂²⋊Q₈	1	1	yes	characteristic
337	C₂×C₄	C₂₃×C₂²⋊Q₈	1	1	yes	characteristic
338	C₂×C₄	C₂₃×#131	1	2	yes	—
339	C₂×C₄	C₂₃×#131	1	2	yes	—
340	C₂×C₄	C₂₃×#135	1	2	yes	—
341	C₂×C₄	C₂₃×AGL(1,ℤ/8)	1	2	yes	—
342	C₈	—	4	4	no	—
343	C₈	—	8	2	no	—
344	C₂²	—	4	2	no	—
345	C₂²	—	4	2	no	—
346	C₂²	—	4	2	no	—
347	C₂²	—	8	1	no	—
348	C₂²	—	8	1	no	—
349	C₂²	—	8	1	no	—
350	C₂²	—	8	1	no	—
351	C₂²	C₂₃×#380	1	1	yes	characteristic
352	C₂²	C₂₃×#408	1	1	yes	characteristic
353	C₂²	C₂₃×#408	1	1	yes	characteristic
354	C₂²	C₂₃×#416	1	1	yes	characteristic
355	C₂²	C₂₃×#418	1	1	yes	characteristic
356	C₂²	C₂×C₂₃×#104	1	1	yes	characteristic
357	C₂²	C₂₃×#421	1	1	yes	characteristic
358	C₄	—	2	2	no	—
359	C₄	—	2	1	no	—
360	C₄	—	2	1	no	—
361	C₄	—	4	1	no	—
362	C₄	—	4	1	no	—
363	C₄	—	4	1	no	—
364	C₄	—	4	2	no	—
365	C₄	—	8	1	no	—
366	C₄	—	8	1	no	—
367	C₄	C₂₃×#424	1	2	yes	—
368	C₄	C₂₃×#433	1	2	yes	—
369	C₄	C₂₃×#463	1	2	yes	—
370	C₄	C₂₃×#478	1	2	yes	—
371	C₂	—	8	2	no	—
372	C₂	C₂₃×#1482	1	1	yes	characteristic
373	C₂	C₂₃×#1484	1	1	yes	characteristic
374	C₂	C₂₃×#1494	1	1	yes	characteristic
375	C₂	C₂₃×#1496	1	1	yes	characteristic
376	C₂	C₂₃×#1798	1	1	yes	characteristic
377	C₂	C₂₃×#1804	1	1	yes	characteristic
378	C₂	C₂₃×#1806	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₂₃	C₂×D₄
commutator	C₂²×C₄	C₂²×C₄×C₂₃
Frattini, cosocle	C₂×C₄²	C₂³×C₂₃
socle	C₂³×C₂₃	C₂×C₂²⋊C₄
prime radical	C₂²×D₄×C₂₃	C₂×C₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₂₃ ◁ C₄³×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂₃×#1831	C₂	semidirect
3. C₄×C₂₃×C₄⋊C₈	C₂	semidirect
5. C₂₃×#1279	C₂	semidirect
107. #8569	C₂₃	direct (N × H)
156. #1831	C₂×C₂₃	semidirect
157. C₄×C₄⋊C₈	C₂×C₂₃	semidirect
159. #1279	C₂×C₂₃	semidirect
248. C₂₃	#8569	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×#2293	2
C₂₃×#1831	2
C₄×C₂₃×C₄⋊C₈	2
C₂×C₂₃×D₄⋊C₈	2
C₂₃×#1279	2
#8569	23

Subgroups — C23×#8569 #19156195

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#8569 #19156195