Subgroups — C₂₃×#9556 #19157182

Order 5888.

450 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#1954	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#1939	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₂₃×#102	C₂	1	1	yes	maximal, characteristic
4	C₂×C₂₃×D₄⋊C₈	C₂	1	1	yes	maximal, characteristic
5	C₂×C₂₃×#322	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#1279	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#1277	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
9	C₂×C₂₃×C₄⋊C₈	—	2	1	no	—
10	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
11	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
12	C₂×C₂₃×#102	C₄	1	1	yes	characteristic
13	C₂×C₂₃×#102	C₄	1	1	yes	characteristic
14	C₂×C₂₃×C₂²⋊C₈	—	2	1	no	—
15	C₂×C₂₃×C₂²⋊C₈	—	2	1	no	—
16	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
17	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
18	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
19	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
20	C₂₃×#340	C₄	1	1	yes	characteristic
21	C₂₃×#340	C₄	1	1	yes	characteristic
22	C₂₃×#336	—	2	1	no	—
23	C₂₃×D₄⋊C₈	—	2	2	no	—
24	C₂₃×#322	—	2	2	no	—
25	C₂²×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic
26	C₂³×C₄×C₂₃	—	2	1	no	—
27	C₂²×C₈×C₂₃	—	2	1	no	—
28	C₂²×C₈×C₂₃	—	2	1	no	—
29	C₂²×C₈×C₂₃	—	2	1	no	—
30	C₂²×C₈×C₂₃	C₂×C₄	1	1	yes	characteristic
31	C₂²×C₈×C₂₃	C₂×C₄	1	1	yes	characteristic
32	C₂²×C₈×C₂₃	D₄	1	1	yes	characteristic
33	C₂²×C₈×C₂₃	D₄	1	1	yes	characteristic
34	C₄×D₄×C₂₃	—	2	1	no	—
35	C₄×D₄×C₂₃	—	2	1	no	—
36	C₄×D₄×C₂₃	—	2	1	no	—
37	C₄×D₄×C₂₃	—	2	1	no	—
38	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
39	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
40	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
41	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
42	C₂×C₄²×C₂₃	—	2	1	no	—
43	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
44	C₂₃×C₄⋊C₈	—	2	1	no	—
45	C₂₃×C₄⋊C₈	—	2	1	no	—
46	C₂₃×C₄⋊C₈	—	2	1	no	—
47	C₂₃×C₄⋊C₈	—	2	1	no	—
48	C₂₃×C₄⋊C₈	—	4	2	no	—
49	C₂₃×#102	—	2	2	no	—
50	C₂₃×#102	C₈	1	4	yes	complemented
51	C₂₃×C₂²⋊C₈	—	4	2	no	—
52	C₂₃×C₂²⋊C₈	—	4	2	no	—
53	C₄×C₈×C₂₃	—	2	1	no	—
54	C₄×C₈×C₂₃	—	2	1	no	—
55	C₄×C₈×C₂₃	—	2	1	no	—
56	C₄×C₈×C₂₃	—	2	1	no	—
57	C₄×C₈×C₂₃	—	2	1	no	—
58	C₄×C₈×C₂₃	D₄	1	2	yes	—
59	C₂₃×#95	—	2	1	no	—
60	C₂⁴×C₂₃	—	2	1	no	—
61	C₂×D₄×C₂₃	—	2	1	no	—
62	C₂×D₄×C₂₃	—	2	1	no	—
63	C₂×D₄×C₂₃	—	2	1	no	—
64	C₂×D₄×C₂₃	—	2	1	no	—
65	C₂×D₄×C₂₃	—	2	1	no	—
66	C₂×D₄×C₂₃	C₂×C₈	1	2	yes	—
67	C₂²×C₄×C₂₃	—	2	1	no	—
68	C₂²×C₄×C₂₃	—	2	1	no	—
69	C₂²×C₄×C₂₃	—	2	1	no	—
70	C₂²×C₄×C₂₃	—	4	1	no	—
71	C₂²×C₄×C₂₃	—	4	1	no	—
72	C₂²×C₄×C₂₃	—	4	1	no	—
73	C₂²×C₄×C₂₃	—	4	1	no	—
74	C₂²×C₄×C₂₃	—	4	1	no	—
75	C₂²×C₄×C₂₃	—	4	1	no	—
76	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
77	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
78	C₂²×C₄×C₂₃	#41	1	1	yes	characteristic
79	C₂×C₈×C₂₃	—	2	1	no	—
80	C₂×C₈×C₂₃	—	2	1	no	—
81	C₂×C₈×C₂₃	—	2	1	no	—
82	C₂×C₈×C₂₃	—	2	1	no	—
83	C₂×C₈×C₂₃	—	2	1	no	—
84	C₂×C₈×C₂₃	—	2	1	no	—
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	1	no	—
89	C₂×C₈×C₂₃	—	2	1	no	—
90	C₂×C₈×C₂₃	—	4	1	no	—
91	C₂×C₈×C₂₃	—	4	1	no	—
92	C₂×C₈×C₂₃	—	4	1	no	—
93	C₂×C₈×C₂₃	—	4	1	no	—
94	C₂×C₈×C₂₃	—	4	1	no	—
95	C₂×C₈×C₂₃	—	4	1	no	—
96	C₂×C₈×C₂₃	—	4	1	no	—
97	C₂×C₈×C₂₃	—	4	1	no	—
98	C₂×C₈×C₂₃	C₂×C₈	1	2	yes	—
99	C₂×C₈×C₂₃	M₁₆	1	2	yes	—
100	C₄⋊C₄×C₂₃	—	2	1	no	—
101	C₄⋊C₄×C₂₃	—	2	1	no	—
102	C₄⋊C₄×C₂₃	—	2	1	no	—
103	C₄⋊C₄×C₂₃	—	2	1	no	—
104	C₄⋊C₄×C₂₃	—	2	1	no	—
105	C₄⋊C₄×C₂₃	C₂×C₈	1	2	yes	—
106	C₂²⋊C₄×C₂₃	—	4	1	no	—
107	C₂²⋊C₄×C₂₃	—	4	1	no	—
108	C₄²×C₂₃	—	4	1	no	—
109	C₄²×C₂₃	—	4	1	no	—
110	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
111	C₄²×C₂₃	#41	1	1	yes	characteristic
112	C₄²×C₂₃	#41	1	1	yes	characteristic
113	C₄²×C₂₃	#41	1	1	yes	characteristic
114	#9556	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
115	C₂³×C₂₃	—	2	2	no	—
116	C₂³×C₂₃	—	4	1	no	—
117	C₂³×C₂₃	—	4	1	no	—
118	C₂³×C₂₃	—	4	1	no	—
119	C₂³×C₂₃	—	4	1	no	—
120	C₂³×C₂₃	—	4	1	no	—
121	C₂³×C₂₃	—	4	1	no	—
122	C₂³×C₂₃	C₄×D₄	1	1	yes	characteristic
123	D₄×C₂₃	—	2	2	no	—
124	D₄×C₂₃	—	2	2	no	—
125	D₄×C₂₃	—	4	1	no	—
126	D₄×C₂₃	—	4	1	no	—
127	C₂×C₄×C₂₃	—	2	1	no	—
128	C₂×C₄×C₂₃	—	2	1	no	—
129	C₂×C₄×C₂₃	—	2	2	no	—
130	C₂×C₄×C₂₃	—	4	1	no	—
131	C₂×C₄×C₂₃	—	4	1	no	—
132	C₂×C₄×C₂₃	—	4	1	no	—
133	C₂×C₄×C₂₃	—	4	1	no	—
134	C₂×C₄×C₂₃	—	4	1	no	—
135	C₂×C₄×C₂₃	—	4	1	no	—
136	C₂×C₄×C₂₃	—	4	1	no	—
137	C₂×C₄×C₂₃	—	4	1	no	—
138	C₂×C₄×C₂₃	—	8	1	no	—
139	C₂×C₄×C₂₃	—	8	1	no	—
140	C₂×C₄×C₂₃	—	8	1	no	—
141	C₂×C₄×C₂₃	—	8	1	no	—
142	C₂×C₄×C₂₃	#117	1	1	yes	characteristic
143	C₂×C₄×C₂₃	C₄×D₄	1	1	yes	characteristic
144	C₂×C₄×C₂₃	#121	1	1	yes	characteristic
145	C₂×C₄×C₂₃	#123	1	1	yes	characteristic
146	C₂×C₄×C₂₃	#124	1	1	yes	characteristic
147	C₂×C₄×C₂₃	#126	1	1	yes	characteristic
148	C₂×C₄×C₂₃	C₂²×C₈	1	1	yes	characteristic
149	C₂×C₄×C₂₃	C₂×M₁₆	1	1	yes	characteristic
150	C₂×C₄×C₂₃	#131	1	1	yes	characteristic
151	C₂×C₄×C₂₃	#131	1	1	yes	characteristic
152	C₂×C₄×C₂₃	AGL(1,ℤ/8)	1	1	yes	characteristic
153	C₂×C₄×C₂₃	AGL(1,ℤ/8)	1	1	yes	characteristic
154	C₂×C₄×C₂₃	AGL(1,ℤ/8)	1	1	yes	characteristic
155	C₂×C₄×C₂₃	#137	1	1	yes	characteristic
156	C₈×C₂₃	—	2	2	no	—
157	C₈×C₂₃	—	2	2	no	—
158	C₈×C₂₃	—	4	2	no	—
159	C₈×C₂₃	—	4	1	no	—
160	C₈×C₂₃	—	4	1	no	—
161	C₈×C₂₃	—	8	1	no	—
162	C₈×C₂₃	—	8	1	no	—
163	#1954	C₂×C₂₃	1	1	yes	characteristic
164	#1939	C₂×C₂₃	1	1	yes	characteristic, complemented
165	C₄×#102	C₂×C₂₃	1	1	yes	characteristic
166	C₂×D₄⋊C₈	C₂×C₂₃	1	1	yes	characteristic
167	C₂×#322	C₂×C₂₃	1	1	yes	characteristic, complemented
168	#1279	C₂×C₂₃	1	1	yes	characteristic, complemented
169	#1277	C₂×C₂₃	1	1	yes	characteristic, complemented
170	C₂²×C₂₃	—	4	2	no	—
171	C₂²×C₂₃	—	4	2	no	—
172	C₂²×C₂₃	—	4	2	no	—
173	C₂²×C₂₃	—	8	1	no	—
174	C₂²×C₂₃	—	8	1	no	—
175	C₂²×C₂₃	—	8	1	no	—
176	C₂²×C₂₃	—	8	1	no	—
177	C₂²×C₂₃	#388	1	1	yes	characteristic
178	C₂²×C₂₃	C₈×D₄	1	1	yes	characteristic
179	C₂²×C₂₃	#436	1	1	yes	characteristic
180	C₂²×C₂₃	#440	1	1	yes	characteristic
181	C₂²×C₂₃	#442	1	1	yes	characteristic
182	C₂²×C₂₃	#444	1	1	yes	characteristic
183	C₂²×C₂₃	#444	1	1	yes	characteristic
184	C₄×C₂₃	—	2	1	no	—
185	C₄×C₂₃	—	2	1	no	—
186	C₄×C₂₃	—	4	2	no	—
187	C₄×C₂₃	—	8	1	no	—
188	C₄×C₂₃	—	8	1	no	—
189	C₄×C₂₃	#431	1	1	yes	characteristic
190	C₄×C₂₃	#433	1	1	yes	characteristic
191	C₄×C₂₃	C₈×D₄	1	1	yes	characteristic
192	C₄×C₂₃	#435	1	1	yes	characteristic
193	C₄×C₂₃	#468	1	1	yes	characteristic
194	C₄×C₂₃	#469	1	1	yes	characteristic
195	C₄×C₂₃	#489	1	1	yes	characteristic
196	C₄×C₂₃	#490	1	1	yes	characteristic
197	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
198	C₂×C₄⋊C₈	—	2	1	no	—
199	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
200	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
201	C₂×#102	C₄×C₂₃	1	1	yes	characteristic
202	C₂×#102	C₄×C₂₃	1	1	yes	characteristic
203	C₂×C₂²⋊C₈	—	2	1	no	—
204	C₂×C₂²⋊C₈	—	2	1	no	—
205	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
206	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
207	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
208	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
209	#340	C₄×C₂₃	1	1	yes	characteristic
210	#340	C₄×C₂₃	1	1	yes	characteristic
211	#336	—	2	1	no	—
212	D₄⋊C₈	—	2	2	no	—
213	#322	—	2	2	no	—
214	C₂×C₂₃	—	8	2	no	—
215	C₂×C₂₃	SD₁₆⋊C₈	1	1	yes	characteristic
216	C₂×C₂₃	#1580	1	1	yes	characteristic
217	C₂×C₂₃	#1592	1	1	yes	characteristic
218	C₂×C₂₃	#1594	1	1	yes	characteristic
219	C₂×C₂₃	#1923	1	1	yes	characteristic
220	C₂×C₂₃	#1936	1	1	yes	characteristic
221	C₂×C₂₃	#1938	1	1	yes	characteristic
222	C₂²×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
223	C₂³×C₄	—	2	1	no	—
224	C₂²×C₈	—	2	1	no	—
225	C₂²×C₈	—	2	1	no	—
226	C₂²×C₈	—	2	1	no	—
227	C₂²×C₈	C₂×C₄×C₂₃	1	1	yes	characteristic
228	C₂²×C₈	C₂×C₄×C₂₃	1	1	yes	characteristic
229	C₂²×C₈	D₄×C₂₃	1	1	yes	characteristic
230	C₂²×C₈	D₄×C₂₃	1	1	yes	characteristic
231	C₄×D₄	—	2	1	no	—
232	C₄×D₄	—	2	1	no	—
233	C₄×D₄	—	2	1	no	—
234	C₄×D₄	—	2	1	no	—
235	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
236	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
237	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
238	C₂×C₂²⋊C₄	—	2	1	no	—
239	C₂×C₄²	—	2	1	no	—
240	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
241	C₄⋊C₈	—	2	1	no	—
242	C₄⋊C₈	—	2	1	no	—
243	C₄⋊C₈	—	2	1	no	—
244	C₄⋊C₈	—	2	1	no	—
245	C₄⋊C₈	—	4	2	no	—
246	#102	—	2	2	no	—
247	#102	C₈×C₂₃	1	4	yes	complemented
248	C₂²⋊C₈	—	4	2	no	—
249	C₂²⋊C₈	—	4	2	no	—
250	C₄×C₈	—	2	1	no	—
251	C₄×C₈	—	2	1	no	—
252	C₄×C₈	—	2	1	no	—
253	C₄×C₈	—	2	1	no	—
254	C₄×C₈	—	2	1	no	—
255	C₄×C₈	D₄×C₂₃	1	2	yes	—
256	#95	—	2	1	no	—
257	C₂₃	#9556	1	1	yes	characteristic, direct product factor, Sylow
258	C₂⁴	—	2	1	no	—
259	C₂×D₄	—	2	1	no	—
260	C₂×D₄	—	2	1	no	—
261	C₂×D₄	—	2	1	no	—
262	C₂×D₄	—	2	1	no	—
263	C₂×D₄	—	2	1	no	—
264	C₂×D₄	C₂×C₈×C₂₃	1	2	yes	—
265	C₂²×C₄	—	2	1	no	—
266	C₂²×C₄	—	2	1	no	—
267	C₂²×C₄	—	2	1	no	—
268	C₂²×C₄	—	4	1	no	—
269	C₂²×C₄	—	4	1	no	—
270	C₂²×C₄	—	4	1	no	—
271	C₂²×C₄	—	4	1	no	—
272	C₂²×C₄	—	4	1	no	—
273	C₂²×C₄	—	4	1	no	—
274	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
275	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
276	C₂²×C₄	#41×C₂₃	1	1	yes	characteristic
277	C₂×C₈	—	2	1	no	—
278	C₂×C₈	—	2	1	no	—
279	C₂×C₈	—	2	1	no	—
280	C₂×C₈	—	2	1	no	—
281	C₂×C₈	—	2	1	no	—
282	C₂×C₈	—	2	1	no	—
283	C₂×C₈	—	2	2	no	—
284	C₂×C₈	—	2	1	no	—
285	C₂×C₈	—	2	1	no	—
286	C₂×C₈	—	2	1	no	—
287	C₂×C₈	—	2	1	no	—
288	C₂×C₈	—	4	1	no	—
289	C₂×C₈	—	4	1	no	—
290	C₂×C₈	—	4	1	no	—
291	C₂×C₈	—	4	1	no	—
292	C₂×C₈	—	4	1	no	—
293	C₂×C₈	—	4	1	no	—
294	C₂×C₈	—	4	1	no	—
295	C₂×C₈	—	4	1	no	—
296	C₂×C₈	C₂×C₈×C₂₃	1	2	yes	—
297	C₂×C₈	M₁₆×C₂₃	1	2	yes	—
298	C₄⋊C₄	—	2	1	no	—
299	C₄⋊C₄	—	2	1	no	—
300	C₄⋊C₄	—	2	1	no	—
301	C₄⋊C₄	—	2	1	no	—
302	C₄⋊C₄	—	2	1	no	—
303	C₄⋊C₄	C₂×C₈×C₂₃	1	2	yes	—
304	C₂²⋊C₄	—	4	1	no	—
305	C₂²⋊C₄	—	4	1	no	—
306	C₄²	—	4	1	no	—
307	C₄²	—	4	1	no	—
308	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
309	C₄²	#41×C₂₃	1	1	yes	characteristic
310	C₄²	#41×C₂₃	1	1	yes	characteristic
311	C₄²	#41×C₂₃	1	1	yes	characteristic
312	C₂³	—	2	2	no	—
313	C₂³	—	4	1	no	—
314	C₂³	—	4	1	no	—
315	C₂³	—	4	1	no	—
316	C₂³	—	4	1	no	—
317	C₂³	—	4	1	no	—
318	C₂³	—	4	1	no	—
319	C₂³	C₄×D₄×C₂₃	1	1	yes	characteristic
320	D₄	—	2	2	no	—
321	D₄	—	2	2	no	—
322	D₄	—	4	1	no	—
323	D₄	—	4	1	no	—
324	C₂×C₄	—	2	1	no	—
325	C₂×C₄	—	2	1	no	—
326	C₂×C₄	—	2	2	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	—	4	1	no	—
332	C₂×C₄	—	4	1	no	—
333	C₂×C₄	—	4	1	no	—
334	C₂×C₄	—	4	1	no	—
335	C₂×C₄	—	8	1	no	—
336	C₂×C₄	—	8	1	no	—
337	C₂×C₄	—	8	1	no	—
338	C₂×C₄	—	8	1	no	—
339	C₂×C₄	C₂₃×#117	1	1	yes	characteristic
340	C₂×C₄	C₄×D₄×C₂₃	1	1	yes	characteristic
341	C₂×C₄	C₂₃×#121	1	1	yes	characteristic
342	C₂×C₄	C₂₃×#123	1	1	yes	characteristic
343	C₂×C₄	C₂₃×#124	1	1	yes	characteristic
344	C₂×C₄	C₂₃×#126	1	1	yes	characteristic
345	C₂×C₄	C₂²×C₈×C₂₃	1	1	yes	characteristic
346	C₂×C₄	C₂×M₁₆×C₂₃	1	1	yes	characteristic
347	C₂×C₄	C₂₃×#131	1	1	yes	characteristic
348	C₂×C₄	C₂₃×#131	1	1	yes	characteristic
349	C₂×C₄	C₂₃×AGL(1,ℤ/8)	1	1	yes	characteristic
350	C₂×C₄	C₂₃×AGL(1,ℤ/8)	1	1	yes	characteristic
351	C₂×C₄	C₂₃×AGL(1,ℤ/8)	1	1	yes	characteristic
352	C₂×C₄	C₂₃×#137	1	1	yes	characteristic
353	C₈	—	2	2	no	—
354	C₈	—	2	2	no	—
355	C₈	—	4	2	no	—
356	C₈	—	4	1	no	—
357	C₈	—	4	1	no	—
358	C₈	—	8	1	no	—
359	C₈	—	8	1	no	—
360	C₂²	—	4	2	no	—
361	C₂²	—	4	2	no	—
362	C₂²	—	4	2	no	—
363	C₂²	—	8	1	no	—
364	C₂²	—	8	1	no	—
365	C₂²	—	8	1	no	—
366	C₂²	—	8	1	no	—
367	C₂²	C₂₃×#388	1	1	yes	characteristic
368	C₂²	C₈×D₄×C₂₃	1	1	yes	characteristic
369	C₂²	C₂₃×#436	1	1	yes	characteristic
370	C₂²	C₂₃×#440	1	1	yes	characteristic
371	C₂²	C₂₃×#442	1	1	yes	characteristic
372	C₂²	C₂₃×#444	1	1	yes	characteristic
373	C₂²	C₂₃×#444	1	1	yes	characteristic
374	C₄	—	2	1	no	—
375	C₄	—	2	1	no	—
376	C₄	—	4	2	no	—
377	C₄	—	8	1	no	—
378	C₄	—	8	1	no	—
379	C₄	C₂₃×#431	1	1	yes	characteristic
380	C₄	C₂₃×#433	1	1	yes	characteristic
381	C₄	C₈×D₄×C₂₃	1	1	yes	characteristic
382	C₄	C₂₃×#435	1	1	yes	characteristic
383	C₄	C₂₃×#468	1	1	yes	characteristic
384	C₄	C₂₃×#469	1	1	yes	characteristic
385	C₄	C₂₃×#489	1	1	yes	characteristic
386	C₄	C₂₃×#490	1	1	yes	characteristic
387	C₂	—	8	2	no	—
388	C₂	C₂₃×SD₁₆⋊C₈	1	1	yes	characteristic
389	C₂	C₂₃×#1580	1	1	yes	characteristic
390	C₂	C₂₃×#1592	1	1	yes	characteristic
391	C₂	C₂₃×#1594	1	1	yes	characteristic
392	C₂	C₂₃×#1923	1	1	yes	characteristic
393	C₂	C₂₃×#1936	1	1	yes	characteristic
394	C₂	C₂₃×#1938	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₂₃	C₂×D₄
commutator	C₂×C₄	C₂²×C₈×C₂₃
Frattini, cosocle	C₂×C₄²	C₂³×C₂₃
socle	C₂³×C₂₃	C₄×D₄
prime radical	C₂²×D₄×C₂₃	C₂×C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₂₃ ◁ C₂×C₄×C₈×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂₃×#1939	C₂	semidirect
5. C₂×C₂₃×#322	C₂	semidirect
6. C₂₃×#1279	C₂	semidirect
7. C₂₃×#1277	C₂	semidirect
50. C₂₃×#102	C₈	semidirect
114. #9556	C₂₃	direct (N × H)
164. #1939	C₂×C₂₃	semidirect
167. C₂×#322	C₂×C₂₃	semidirect
168. #1279	C₂×C₂₃	semidirect
169. #1277	C₂×C₂₃	semidirect
247. #102	C₈×C₂₃	semidirect
257. C₂₃	#9556	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×#1954	2
C₂₃×#1939	2
C₄×C₂₃×#102	2
C₂×C₂₃×D₄⋊C₈	2
C₂×C₂₃×#322	2
C₂₃×#1279	2
C₂₃×#1277	2
#9556	23

Subgroups — C23×#9556 #19157182

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#9556 #19157182