Subgroups — C₂₃×#9667 #19157293

Order 5888.

478 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×SD₁₆×C₂₃	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#1564	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#1479	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#1478	C₂	1	1	yes	maximal, characteristic
5	C₂₃×#1461	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#1460	C₂	1	1	yes	maximal, characteristic
7	C₂₃×#1450	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×SD₁₆×C₂₃	C₄	1	1	yes	characteristic
9	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
10	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
11	C₄×SD₁₆×C₂₃	—	2	1	no	—
12	C₄×SD₁₆×C₂₃	—	2	1	no	—
13	C₄×SD₁₆×C₂₃	—	2	1	no	—
14	C₄×SD₁₆×C₂₃	—	2	1	no	—
15	C₂₃×#431	C₂²	1	1	yes	characteristic
16	C₂₃×#431	C₂²	1	1	yes	characteristic
17	C₂₃×#431	C₂²	1	1	yes	characteristic
18	C₂₃×#431	C₂²	1	1	yes	characteristic
19	C₂×C₂₃×#106	C₄	1	1	yes	characteristic
20	C₂×C₂₃×#103	C₄	1	1	yes	characteristic
21	C₂×C₂₃×#102	C₄	1	1	yes	characteristic
22	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
23	C₂₃×#335	—	2	1	no	—
24	C₂₃×#334	—	2	1	no	—
25	C₂₃×Q₈⋊C₈	—	2	2	no	—
26	C₂₃×D₄⋊C₈	—	2	2	no	—
27	C₂₃×#324	—	2	2	no	—
28	C₂₃×#323	—	2	2	no	—
29	C₂₃×#322	—	2	1	no	—
30	C₈²×C₂₃	—	2	1	no	—
31	C₂²×Q₈×C₂₃	C₂×C₄	1	1	yes	characteristic
32	C₂²×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic
33	C₂³×C₄×C₂₃	—	2	1	no	—
34	C₂×SD₁₆×C₂₃	—	2	1	no	—
35	C₂×SD₁₆×C₂₃	—	2	1	no	—
36	C₂×SD₁₆×C₂₃	—	2	2	no	—
37	C₂×SD₁₆×C₂₃	C₈	1	4	yes	complemented
38	C₂²×C₈×C₂₃	C₂×C₄	1	1	yes	characteristic
39	C₂²×C₈×C₂₃	C₂×C₄	1	1	yes	characteristic
40	C₄×Q₈×C₂₃	—	2	1	no	—
41	C₄×Q₈×C₂₃	—	2	1	no	—
42	C₄×Q₈×C₂₃	—	2	1	no	—
43	C₄×Q₈×C₂₃	—	2	1	no	—
44	C₄×D₄×C₂₃	—	2	1	no	—
45	C₄×D₄×C₂₃	—	2	1	no	—
46	C₄×D₄×C₂₃	—	2	1	no	—
47	C₄×D₄×C₂₃	—	2	1	no	—
48	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
49	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
50	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
51	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
52	C₂×C₄²×C₂₃	—	2	1	no	—
53	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
54	C₂₃×#106	—	2	1	no	—
55	C₂₃×#106	—	2	1	no	—
56	C₂₃×C₄⋊C₈	—	2	1	no	—
57	C₂₃×C₄⋊C₈	—	2	1	no	—
58	C₂₃×C₄⋊C₈	—	2	1	no	—
59	C₂₃×C₄⋊C₈	D₄	1	2	yes	—
60	C₂₃×#103	—	2	1	no	—
61	C₂₃×#103	—	2	1	no	—
62	C₂₃×#102	—	2	1	no	—
63	C₂₃×#102	—	2	1	no	—
64	C₂₃×C₂²⋊C₈	—	2	1	no	—
65	C₂₃×C₂²⋊C₈	—	2	1	no	—
66	C₂₃×C₂²⋊C₈	—	2	1	no	—
67	C₂₃×C₂²⋊C₈	D₄	1	2	yes	—
68	C₄×C₈×C₂₃	—	2	1	no	—
69	C₄×C₈×C₂₃	—	2	1	no	—
70	C₄×C₈×C₂₃	—	2	1	no	—
71	C₄×C₈×C₂₃	—	2	1	no	—
72	C₄×C₈×C₂₃	D₄	1	1	yes	characteristic
73	C₄×C₈×C₂₃	D₄	1	1	yes	characteristic
74	C₄×C₈×C₂₃	D₄	1	1	yes	characteristic
75	C₄×C₈×C₂₃	D₄	1	1	yes	characteristic
76	C₂⁴×C₂₃	—	2	1	no	—
77	C₂×Q₈×C₂₃	—	2	1	no	—
78	C₂×Q₈×C₂₃	—	2	1	no	—
79	C₂×Q₈×C₂₃	—	2	1	no	—
80	C₂×Q₈×C₂₃	—	2	1	no	—
81	C₂×Q₈×C₂₃	—	2	1	no	—
82	C₂×Q₈×C₂₃	C₂×C₈	1	2	yes	—
83	C₂×D₄×C₂₃	—	2	1	no	—
84	C₂×D₄×C₂₃	—	2	1	no	—
85	C₂×D₄×C₂₃	—	2	1	no	—
86	C₂×D₄×C₂₃	—	2	1	no	—
87	C₂×D₄×C₂₃	—	2	1	no	—
88	C₂×D₄×C₂₃	C₂×C₈	1	2	yes	—
89	C₂²×C₄×C₂₃	—	2	1	no	—
90	C₂²×C₄×C₂₃	—	2	1	no	—
91	C₂²×C₄×C₂₃	—	2	1	no	—
92	C₂²×C₄×C₂₃	—	4	1	no	—
93	C₂²×C₄×C₂₃	—	4	1	no	—
94	C₂²×C₄×C₂₃	—	8	2	no	—
95	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
96	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₄×C₂₃	#41	1	1	yes	characteristic
98	SD₁₆×C₂₃	—	2	4	no	—
99	SD₁₆×C₂₃	—	2	4	no	—
100	C₂×C₈×C₂₃	—	2	1	no	—
101	C₂×C₈×C₂₃	—	2	1	no	—
102	C₂×C₈×C₂₃	—	2	2	no	—
103	C₂×C₈×C₂₃	—	2	2	no	—
104	C₂×C₈×C₂₃	—	4	1	no	—
105	C₂×C₈×C₂₃	—	4	1	no	—
106	C₂×C₈×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
107	C₂×C₈×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
108	C₂×C₈×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
109	C₂×C₈×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
110	C₂×C₈×C₂₃	C₂×C₈	1	2	yes	—
111	C₂×C₈×C₂₃	M₁₆	1	2	yes	—
112	C₄⋊C₄×C₂₃	—	2	1	no	—
113	C₄⋊C₄×C₂₃	—	2	1	no	—
114	C₄⋊C₄×C₂₃	—	2	1	no	—
115	C₄⋊C₄×C₂₃	—	2	1	no	—
116	C₄⋊C₄×C₂₃	—	4	1	no	—
117	C₄⋊C₄×C₂₃	—	4	1	no	—
118	C₂²⋊C₄×C₂₃	—	4	1	no	—
119	C₂²⋊C₄×C₂₃	—	4	1	no	—
120	C₄²×C₂₃	—	4	1	no	—
121	C₄²×C₂₃	—	4	1	no	—
122	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
123	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
124	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
125	C₄²×C₂₃	#41	1	1	yes	characteristic
126	#9667	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
127	C₂³×C₂₃	—	2	2	no	—
128	C₂³×C₂₃	—	4	1	no	—
129	C₂³×C₂₃	—	4	1	no	—
130	C₂³×C₂₃	—	8	1	no	—
131	C₂³×C₂₃	—	8	1	no	—
132	C₂³×C₂₃	C₄×D₄	1	1	yes	characteristic
133	Q₈×C₂₃	—	2	2	no	—
134	Q₈×C₂₃	—	2	2	no	—
135	Q₈×C₂₃	—	4	1	no	—
136	Q₈×C₂₃	—	4	1	no	—
137	D₄×C₂₃	—	2	2	no	—
138	D₄×C₂₃	—	2	2	no	—
139	D₄×C₂₃	—	4	1	no	—
140	D₄×C₂₃	—	4	1	no	—
141	C₂×C₄×C₂₃	—	2	2	no	—
142	C₂×C₄×C₂₃	—	2	2	no	—
143	C₂×C₄×C₂₃	—	4	1	no	—
144	C₂×C₄×C₂₃	—	4	1	no	—
145	C₂×C₄×C₂₃	—	4	1	no	—
146	C₂×C₄×C₂₃	—	4	1	no	—
147	C₂×C₄×C₂₃	—	4	1	no	—
148	C₂×C₄×C₂₃	—	8	2	no	—
149	C₂×C₄×C₂₃	—	8	2	no	—
150	C₂×C₄×C₂₃	—	8	1	no	—
151	C₂×C₄×C₂₃	—	8	1	no	—
152	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
153	C₂×C₄×C₂₃	C₄×D₄	1	1	yes	characteristic
154	C₂×C₄×C₂₃	#121	1	1	yes	characteristic
155	C₂×C₄×C₂₃	#121	1	1	yes	characteristic
156	C₂×C₄×C₂₃	#124	1	1	yes	characteristic
157	C₂×C₄×C₂₃	#127	1	1	yes	characteristic
158	C₂×C₄×C₂₃	C₂²×C₈	1	1	yes	characteristic
159	C₂×C₄×C₂₃	C₂×M₁₆	1	1	yes	characteristic
160	C₂×C₄×C₂₃	#131	1	1	yes	characteristic
161	C₂×C₄×C₂₃	#131	1	1	yes	characteristic
162	C₈×C₂₃	—	2	1	no	—
163	C₈×C₂₃	—	2	1	no	—
164	C₈×C₂₃	—	4	2	no	—
165	C₈×C₂₃	—	4	2	no	—
166	C₈×C₂₃	—	8	1	no	—
167	C₈×C₂₃	—	8	1	no	—
168	C₈×C₂₃	C₂²⋊C₈	1	2	yes	—
169	C₈×C₂₃	C₂²⋊C₈	1	2	yes	—
170	C₂×C₄×SD₁₆	C₂×C₂₃	1	1	yes	characteristic
171	#1564	C₂×C₂₃	1	1	yes	characteristic, complemented
172	#1479	C₂×C₂₃	1	1	yes	characteristic, complemented
173	#1478	C₂×C₂₃	1	1	yes	characteristic
174	#1461	C₂×C₂₃	1	1	yes	characteristic, complemented
175	#1460	C₂×C₂₃	1	1	yes	characteristic
176	#1450	C₂×C₂₃	1	1	yes	characteristic, complemented
177	C₂²×C₂₃	—	2	1	no	—
178	C₂²×C₂₃	—	2	1	no	—
179	C₂²×C₂₃	—	4	2	no	—
180	C₂²×C₂₃	—	8	2	no	—
181	C₂²×C₂₃	—	8	2	no	—
182	C₂²×C₂₃	—	8	1	no	—
183	C₂²×C₂₃	—	8	1	no	—
184	C₂²×C₂₃	#390	1	1	yes	characteristic
185	C₂²×C₂₃	C₈×D₄	1	1	yes	characteristic
186	C₂²×C₂₃	#436	1	1	yes	characteristic
187	C₄×C₂₃	—	2	1	no	—
188	C₄×C₂₃	—	2	1	no	—
189	C₄×C₂₃	—	2	1	no	—
190	C₄×C₂₃	—	4	2	no	—
191	C₄×C₂₃	—	8	1	no	—
192	C₄×C₂₃	—	8	1	no	—
193	C₄×C₂₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
194	C₄×C₂₃	#408	1	1	yes	characteristic
195	C₄×C₂₃	C₈×D₄	1	1	yes	characteristic
196	C₄×C₂₃	#436	1	1	yes	characteristic
197	C₄×C₂₃	#471	1	2	yes	—
198	C₂²×SD₁₆	C₄×C₂₃	1	1	yes	characteristic
199	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
200	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
201	C₄×SD₁₆	—	2	1	no	—
202	C₄×SD₁₆	—	2	1	no	—
203	C₄×SD₁₆	—	2	1	no	—
204	C₄×SD₁₆	—	2	1	no	—
205	#431	C₂²×C₂₃	1	1	yes	characteristic
206	#431	C₂²×C₂₃	1	1	yes	characteristic
207	#431	C₂²×C₂₃	1	1	yes	characteristic
208	#431	C₂²×C₂₃	1	1	yes	characteristic
209	C₂×#106	C₄×C₂₃	1	1	yes	characteristic
210	C₂×#103	C₄×C₂₃	1	1	yes	characteristic
211	C₂×#102	C₄×C₂₃	1	1	yes	characteristic
212	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
213	#335	—	2	1	no	—
214	#334	—	2	1	no	—
215	Q₈⋊C₈	—	2	2	no	—
216	D₄⋊C₈	—	2	2	no	—
217	#324	—	2	2	no	—
218	#323	—	2	2	no	—
219	#322	—	2	1	no	—
220	C₈²	—	2	1	no	—
221	C₂×C₂₃	—	2	1	no	—
222	C₂×C₂₃	—	2	1	no	—
223	C₂×C₂₃	—	8	2	no	—
224	C₂×C₂₃	#1954	1	1	yes	characteristic
225	C₂×C₂₃	#1976	1	1	yes	characteristic
226	C₂×C₂₃	#1977	1	1	yes	characteristic
227	C₂²×Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
228	C₂²×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
229	C₂³×C₄	—	2	1	no	—
230	C₂×SD₁₆	—	2	1	no	—
231	C₂×SD₁₆	—	2	1	no	—
232	C₂×SD₁₆	—	2	2	no	—
233	C₂×SD₁₆	C₈×C₂₃	1	4	yes	complemented
234	C₂²×C₈	C₂×C₄×C₂₃	1	1	yes	characteristic
235	C₂²×C₈	C₂×C₄×C₂₃	1	1	yes	characteristic
236	C₄×Q₈	—	2	1	no	—
237	C₄×Q₈	—	2	1	no	—
238	C₄×Q₈	—	2	1	no	—
239	C₄×Q₈	—	2	1	no	—
240	C₄×D₄	—	2	1	no	—
241	C₄×D₄	—	2	1	no	—
242	C₄×D₄	—	2	1	no	—
243	C₄×D₄	—	2	1	no	—
244	C₂×C₄⋊C₄	—	2	1	no	—
245	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
246	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
247	C₂×C₂²⋊C₄	—	2	1	no	—
248	C₂×C₄²	—	2	1	no	—
249	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
250	#106	—	2	1	no	—
251	#106	—	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	#103	—	2	1	no	—
257	#103	—	2	1	no	—
258	#102	—	2	1	no	—
259	#102	—	2	1	no	—
260	C₂²⋊C₈	—	2	1	no	—
261	C₂²⋊C₈	—	2	1	no	—
262	C₂²⋊C₈	—	2	1	no	—
263	C₂²⋊C₈	D₄×C₂₃	1	2	yes	—
264	C₄×C₈	—	2	1	no	—
265	C₄×C₈	—	2	1	no	—
266	C₄×C₈	—	2	1	no	—
267	C₄×C₈	—	2	1	no	—
268	C₄×C₈	D₄×C₂₃	1	1	yes	characteristic
269	C₄×C₈	D₄×C₂₃	1	1	yes	characteristic
270	C₄×C₈	D₄×C₂₃	1	1	yes	characteristic
271	C₄×C₈	D₄×C₂₃	1	1	yes	characteristic
272	C₂₃	#9667	1	1	yes	characteristic, direct product factor, Sylow
273	C₂⁴	—	2	1	no	—
274	C₂×Q₈	—	2	1	no	—
275	C₂×Q₈	—	2	1	no	—
276	C₂×Q₈	—	2	1	no	—
277	C₂×Q₈	—	2	1	no	—
278	C₂×Q₈	—	2	1	no	—
279	C₂×Q₈	C₂×C₈×C₂₃	1	2	yes	—
280	C₂×D₄	—	2	1	no	—
281	C₂×D₄	—	2	1	no	—
282	C₂×D₄	—	2	1	no	—
283	C₂×D₄	—	2	1	no	—
284	C₂×D₄	—	2	1	no	—
285	C₂×D₄	C₂×C₈×C₂₃	1	2	yes	—
286	C₂²×C₄	—	2	1	no	—
287	C₂²×C₄	—	2	1	no	—
288	C₂²×C₄	—	2	1	no	—
289	C₂²×C₄	—	4	1	no	—
290	C₂²×C₄	—	4	1	no	—
291	C₂²×C₄	—	8	2	no	—
292	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
293	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
294	C₂²×C₄	#41×C₂₃	1	1	yes	characteristic
295	SD₁₆	—	2	4	no	—
296	SD₁₆	—	2	4	no	—
297	C₂×C₈	—	2	1	no	—
298	C₂×C₈	—	2	1	no	—
299	C₂×C₈	—	2	2	no	—
300	C₂×C₈	—	2	2	no	—
301	C₂×C₈	—	4	1	no	—
302	C₂×C₈	—	4	1	no	—
303	C₂×C₈	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
304	C₂×C₈	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
305	C₂×C₈	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
306	C₂×C₈	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
307	C₂×C₈	C₂×C₈×C₂₃	1	2	yes	—
308	C₂×C₈	M₁₆×C₂₃	1	2	yes	—
309	C₄⋊C₄	—	2	1	no	—
310	C₄⋊C₄	—	2	1	no	—
311	C₄⋊C₄	—	2	1	no	—
312	C₄⋊C₄	—	2	1	no	—
313	C₄⋊C₄	—	4	1	no	—
314	C₄⋊C₄	—	4	1	no	—
315	C₂²⋊C₄	—	4	1	no	—
316	C₂²⋊C₄	—	4	1	no	—
317	C₄²	—	4	1	no	—
318	C₄²	—	4	1	no	—
319	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
320	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
321	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
322	C₄²	#41×C₂₃	1	1	yes	characteristic
323	C₂³	—	2	2	no	—
324	C₂³	—	4	1	no	—
325	C₂³	—	4	1	no	—
326	C₂³	—	8	1	no	—
327	C₂³	—	8	1	no	—
328	C₂³	C₄×D₄×C₂₃	1	1	yes	characteristic
329	Q₈	—	2	2	no	—
330	Q₈	—	2	2	no	—
331	Q₈	—	4	1	no	—
332	Q₈	—	4	1	no	—
333	D₄	—	2	2	no	—
334	D₄	—	2	2	no	—
335	D₄	—	4	1	no	—
336	D₄	—	4	1	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	4	1	no	—
340	C₂×C₄	—	4	1	no	—
341	C₂×C₄	—	4	1	no	—
342	C₂×C₄	—	4	1	no	—
343	C₂×C₄	—	4	1	no	—
344	C₂×C₄	—	8	2	no	—
345	C₂×C₄	—	8	2	no	—
346	C₂×C₄	—	8	1	no	—
347	C₂×C₄	—	8	1	no	—
348	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
349	C₂×C₄	C₄×D₄×C₂₃	1	1	yes	characteristic
350	C₂×C₄	C₂₃×#121	1	1	yes	characteristic
351	C₂×C₄	C₂₃×#121	1	1	yes	characteristic
352	C₂×C₄	C₂₃×#124	1	1	yes	characteristic
353	C₂×C₄	C₂₃×#127	1	1	yes	characteristic
354	C₂×C₄	C₂²×C₈×C₂₃	1	1	yes	characteristic
355	C₂×C₄	C₂×M₁₆×C₂₃	1	1	yes	characteristic
356	C₂×C₄	C₂₃×#131	1	1	yes	characteristic
357	C₂×C₄	C₂₃×#131	1	1	yes	characteristic
358	C₈	—	2	1	no	—
359	C₈	—	2	1	no	—
360	C₈	—	4	2	no	—
361	C₈	—	4	2	no	—
362	C₈	—	8	1	no	—
363	C₈	—	8	1	no	—
364	C₈	C₂₃×C₂²⋊C₈	1	2	yes	—
365	C₈	C₂₃×C₂²⋊C₈	1	2	yes	—
366	C₂²	—	2	1	no	—
367	C₂²	—	2	1	no	—
368	C₂²	—	4	2	no	—
369	C₂²	—	8	2	no	—
370	C₂²	—	8	2	no	—
371	C₂²	—	8	1	no	—
372	C₂²	—	8	1	no	—
373	C₂²	C₂₃×#390	1	1	yes	characteristic
374	C₂²	C₈×D₄×C₂₃	1	1	yes	characteristic
375	C₂²	C₂₃×#436	1	1	yes	characteristic
376	C₄	—	2	1	no	—
377	C₄	—	2	1	no	—
378	C₄	—	2	1	no	—
379	C₄	—	4	2	no	—
380	C₄	—	8	1	no	—
381	C₄	—	8	1	no	—
382	C₄	C₂×C₂₃×C₂²⋊C₈	1	1	yes	characteristic
383	C₄	C₂₃×#408	1	1	yes	characteristic
384	C₄	C₈×D₄×C₂₃	1	1	yes	characteristic
385	C₄	C₂₃×#436	1	1	yes	characteristic
386	C₄	C₂₃×#471	1	2	yes	—
387	C₂	—	2	1	no	—
388	C₂	—	2	1	no	—
389	C₂	—	8	2	no	—
390	C₂	C₂₃×#1954	1	1	yes	characteristic
391	C₂	C₂₃×#1976	1	1	yes	characteristic
392	C₂	C₂₃×#1977	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₂₃	#121
commutator	C₂×C₄	C₂²×C₈×C₂₃
Frattini, cosocle	C₂×C₄²	C₂³×C₂₃
socle	C₂²×C₂₃	#390
prime radical	C₂²×D₄×C₂₃	C₂×C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₃ ◁ C₂×C₄²×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂₃×#1564	C₂	semidirect
3. C₂₃×#1479	C₂	semidirect
5. C₂₃×#1461	C₂	semidirect
7. C₂₃×#1450	C₂	semidirect
37. C₂×SD₁₆×C₂₃	C₈	semidirect
126. #9667	C₂₃	direct (N × H)
171. #1564	C₂×C₂₃	semidirect
172. #1479	C₂×C₂₃	semidirect
174. #1461	C₂×C₂₃	semidirect
176. #1450	C₂×C₂₃	semidirect
233. C₂×SD₁₆	C₈×C₂₃	semidirect
272. C₂₃	#9667	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×C₄×SD₁₆×C₂₃	2
C₂₃×#1564	2
C₂₃×#1479	2
C₂₃×#1478	2
C₂₃×#1461	2
C₂₃×#1460	2
C₂₃×#1450	2
#9667	23

Subgroups — C23×#9667 #19157293

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#9667 #19157293