Subgroups — C₂₃×#21645 #19169271

Order 5888.

778 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#487	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#2331	C₂	1	1	yes	maximal, characteristic
3	C₂₃×#2327	C₂	1	1	yes	maximal, characteristic
4	C₂₃×#1993	C₂	1	1	yes	maximal, characteristic
5	C₂₃×#1960	C₂	1	1	yes	maximal, characteristic
6	C₂₃×#1935	C₂	1	2	yes	maximal
7	C₂₃×#1933	C₂	1	2	yes	maximal
8	C₂₃×#1835	C₂	1	1	yes	maximal, characteristic
9	C₂₃×#1763	C₂	1	2	yes	maximal
10	C₄×C₂₃×#103	C₂	1	2	yes	maximal
11	C₂₃×#1726	C₂	1	1	yes	maximal, characteristic
12	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
13	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₂×C₄×Q₈×C₂₃	C₂²	1	2	yes	—
15	C₂₃×#487	C₄	1	8	yes	complemented
16	C₂×C₂₃×#103	C₂²	1	2	yes	—
17	C₂×C₂₃×#103	C₂²	1	2	yes	—
18	C₂×C₂₃×#103	C₂²	1	2	yes	—
19	C₂×C₂₃×#103	C₂²	1	2	yes	—
20	C₂×C₂₃×#97	C₂²	1	1	yes	characteristic
21	C₂×C₂₃×#97	C₂²	1	1	yes	characteristic
22	C₂×C₂₃×#97	C₂²	1	1	yes	characteristic
23	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
24	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
26	C₂₃×#391	—	2	2	no	—
27	C₂₃×#391	C₂²	1	2	yes	—
28	C₂₃×#389	C₂²	1	2	yes	—
29	C₂₃×#387	—	2	2	no	—
30	C₂₃×#387	—	2	2	no	—
31	C₂₃×#387	—	2	2	no	—
32	C₂₃×#382	C₂²	1	1	yes	characteristic
33	C₂₃×#382	C₂²	1	1	yes	characteristic
34	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
35	C₂₃×#376	C₂²	1	1	yes	characteristic
36	C₂₃×#340	C₂²	1	2	yes	—
37	C₂₃×#340	C₂²	1	2	yes	—
38	C₂₃×#340	C₂²	1	2	yes	—
39	C₂₃×#340	C₂²	1	2	yes	—
40	C₂²×Q₈×C₂₃	—	2	1	no	—
41	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
42	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
43	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
44	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
45	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
46	C₂₃×C₄⋊Q₈	—	2	2	no	—
47	C₂₃×C₄⋊Q₈	—	2	2	no	—
48	C₂₃×C₄⋊Q₈	C₂×C₄	1	4	yes	—
49	C₂₃×C₄⋊Q₈	C₂×C₄	1	4	yes	—
50	C₄×Q₈×C₂₃	—	2	4	no	—
51	C₄×Q₈×C₂₃	—	2	4	no	—
52	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
53	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
54	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
55	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
56	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
57	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
58	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
59	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
60	C₂×C₄²×C₂₃	—	2	2	no	—
61	C₂×C₄²×C₂₃	—	2	2	no	—
62	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
63	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
64	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
65	C₂₃×#103	—	2	4	no	—
66	C₂₃×#103	—	2	4	no	—
67	C₂₃×#103	C₂×C₄	1	8	yes	—
68	C₂₃×#103	C₂×C₄	1	8	yes	—
69	C₂₃×#97	—	2	2	no	—
70	C₂₃×#97	—	2	2	no	—
71	C₂₃×#97	—	2	2	no	—
72	C₄×C₈×C₂₃	—	2	2	no	—
73	C₄×C₈×C₂₃	—	2	2	no	—
74	C₄×C₈×C₂₃	C₂×C₄	1	4	yes	—
75	C₂₃×#95	—	2	2	no	—
76	C₂₃×#95	—	2	1	no	—
77	C₂₃×#95	—	2	1	no	—
78	C₂₃×#95	—	2	1	no	—
79	C₂₃×#95	—	2	1	no	—
80	C₂₃×#95	—	2	4	no	—
81	C₂₃×#95	—	2	2	no	—
82	C₂₃×#95	D₄	1	2	yes	—
83	C₂₃×#95	D₄	1	2	yes	—
84	C₂×Q₈×C₂₃	—	2	4	no	—
85	C₂×Q₈×C₂₃	—	2	2	no	—
86	C₂×Q₈×C₂₃	—	2	2	no	—
87	C₂×Q₈×C₂₃	—	2	2	no	—
88	C₂×Q₈×C₂₃	—	2	2	no	—
89	C₂×Q₈×C₂₃	—	2	2	no	—
90	C₂×Q₈×C₂₃	—	8	2	no	—
91	C₂×Q₈×C₂₃	C₂²×C₄	1	4	yes	—
92	C₂²×C₄×C₂₃	—	2	2	no	—
93	C₂²×C₄×C₂₃	—	2	2	no	—
94	C₂²×C₄×C₂₃	—	2	2	no	—
95	C₂²×C₄×C₂₃	—	2	2	no	—
96	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
97	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
100	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
101	C₂×C₈×C₂₃	—	2	1	no	—
102	C₂×C₈×C₂₃	—	2	1	no	—
103	C₂×C₈×C₂₃	—	2	1	no	—
104	C₂×C₈×C₂₃	—	2	1	no	—
105	C₂×C₈×C₂₃	—	2	1	no	—
106	C₂×C₈×C₂₃	—	2	1	no	—
107	C₂×C₈×C₂₃	—	2	1	no	—
108	C₂×C₈×C₂₃	—	2	1	no	—
109	C₂×C₈×C₂₃	C₂²×C₄	1	2	yes	—
110	C₂×C₈×C₂₃	C₂²×C₄	1	2	yes	—
111	C₂×C₈×C₂₃	#41	1	2	yes	—
112	C₂×C₈×C₂₃	#41	1	2	yes	—
113	C₄⋊C₄×C₂₃	—	2	4	no	—
114	C₄⋊C₄×C₂₃	—	2	4	no	—
115	C₄⋊C₄×C₂₃	—	2	4	no	—
116	C₄⋊C₄×C₂₃	—	2	2	no	—
117	C₄⋊C₄×C₂₃	—	2	2	no	—
118	C₄⋊C₄×C₂₃	—	2	2	no	—
119	C₄⋊C₄×C₂₃	—	2	2	no	—
120	C₄⋊C₄×C₂₃	—	2	2	no	—
121	C₄⋊C₄×C₂₃	—	4	4	no	—
122	C₄⋊C₄×C₂₃	—	8	2	no	—
123	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
124	C₄²×C₂₃	—	2	1	no	—
125	C₄²×C₂₃	—	2	1	no	—
126	C₄²×C₂₃	—	4	4	no	—
127	C₄²×C₂₃	—	8	2	no	—
128	C₄²×C₂₃	C₂²×C₄	1	2	yes	—
129	C₄²×C₂₃	#41	1	2	yes	—
130	C₄²×C₂₃	#41	1	2	yes	—
131	C₄²×C₂₃	#41	1	2	yes	—
132	#21645	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
133	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
134	Q₈×C₂₃	—	2	4	no	—
135	Q₈×C₂₃	—	2	4	no	—
136	Q₈×C₂₃	—	4	2	no	—
137	Q₈×C₂₃	—	4	2	no	—
138	Q₈×C₂₃	—	8	4	no	—
139	C₂×C₄×C₂₃	—	2	2	no	—
140	C₂×C₄×C₂₃	—	2	2	no	—
141	C₂×C₄×C₂₃	—	2	2	no	—
142	C₂×C₄×C₂₃	—	2	2	no	—
143	C₂×C₄×C₂₃	—	2	4	no	—
144	C₂×C₄×C₂₃	—	2	4	no	—
145	C₂×C₄×C₂₃	—	2	2	no	—
146	C₂×C₄×C₂₃	—	2	2	no	—
147	C₂×C₄×C₂₃	—	2	2	no	—
148	C₂×C₄×C₂₃	—	4	2	no	—
149	C₂×C₄×C₂₃	—	4	2	no	—
150	C₂×C₄×C₂₃	—	4	2	no	—
151	C₂×C₄×C₂₃	—	4	2	no	—
152	C₂×C₄×C₂₃	—	4	2	no	—
153	C₂×C₄×C₂₃	—	4	2	no	—
154	C₂×C₄×C₂₃	—	4	2	no	—
155	C₂×C₄×C₂₃	—	4	2	no	—
156	C₂×C₄×C₂₃	—	4	2	no	—
157	C₂×C₄×C₂₃	—	4	2	no	—
158	C₂×C₄×C₂₃	C₄×D₄	1	2	yes	—
159	C₂×C₄×C₂₃	C₄×D₄	1	2	yes	—
160	C₂×C₄×C₂₃	#124	1	4	yes	—
161	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
162	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
163	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
164	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
165	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
166	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
167	C₈×C₂₃	—	2	2	no	—
168	C₈×C₂₃	—	2	2	no	—
169	C₈×C₂₃	—	2	2	no	—
170	C₈×C₂₃	—	2	2	no	—
171	C₂×#487	C₂×C₂₃	1	1	yes	characteristic
172	#2331	C₂×C₂₃	1	1	yes	characteristic
173	#2327	C₂×C₂₃	1	1	yes	characteristic
174	#1993	C₂×C₂₃	1	1	yes	characteristic
175	#1960	C₂×C₂₃	1	1	yes	characteristic
176	#1935	C₂×C₂₃	1	2	yes	—
177	#1933	C₂×C₂₃	1	2	yes	—
178	#1835	C₂×C₂₃	1	1	yes	characteristic
179	#1763	C₂×C₂₃	1	2	yes	—
180	C₄×#103	C₂×C₂₃	1	2	yes	—
181	#1726	C₂×C₂₃	1	1	yes	characteristic
182	C₂²×C₂₃	C₂×C₄×D₄	1	1	yes	characteristic
183	C₂²×C₂₃	C₂×#124	1	1	yes	characteristic
184	C₂²×C₂₃	#532	1	1	yes	characteristic
185	C₂²×C₂₃	#577	1	2	yes	—
186	C₂²×C₂₃	#578	1	2	yes	—
187	C₄×C₂₃	—	2	4	no	—
188	C₄×C₂₃	—	2	2	no	—
189	C₄×C₂₃	—	2	2	no	—
190	C₄×C₂₃	—	4	2	no	—
191	C₄×C₂₃	—	4	4	no	—
192	C₄×C₂₃	—	4	4	no	—
193	C₄×C₂₃	—	8	2	no	—
194	C₄×C₂₃	—	8	2	no	—
195	C₄×C₂₃	C₄×#41	1	1	yes	characteristic
196	C₄×C₂₃	C₄×#41	1	1	yes	characteristic
197	C₄×C₂₃	#529	1	1	yes	characteristic
198	C₄×C₂₃	#529	1	1	yes	characteristic
199	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
200	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
201	C₂×C₄×Q₈	C₂²×C₂₃	1	2	yes	—
202	#487	C₄×C₂₃	1	8	yes	complemented
203	C₂×#103	C₂²×C₂₃	1	2	yes	—
204	C₂×#103	C₂²×C₂₃	1	2	yes	—
205	C₂×#103	C₂²×C₂₃	1	2	yes	—
206	C₂×#103	C₂²×C₂₃	1	2	yes	—
207	C₂×#97	C₂²×C₂₃	1	1	yes	characteristic
208	C₂×#97	C₂²×C₂₃	1	1	yes	characteristic
209	C₂×#97	C₂²×C₂₃	1	1	yes	characteristic
210	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
211	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
212	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
213	#391	—	2	2	no	—
214	#391	C₂²×C₂₃	1	2	yes	—
215	#389	C₂²×C₂₃	1	2	yes	—
216	#387	—	2	2	no	—
217	#387	—	2	2	no	—
218	#387	—	2	2	no	—
219	#382	C₂²×C₂₃	1	1	yes	characteristic
220	#382	C₂²×C₂₃	1	1	yes	characteristic
221	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
222	#376	C₂²×C₂₃	1	1	yes	characteristic
223	#340	C₂²×C₂₃	1	2	yes	—
224	#340	C₂²×C₂₃	1	2	yes	—
225	#340	C₂²×C₂₃	1	2	yes	—
226	#340	C₂²×C₂₃	1	2	yes	—
227	C₂×C₂₃	C₄×#124	1	1	yes	characteristic
228	C₂×C₂₃	#2949	1	1	yes	characteristic
229	C₂×C₂₃	#2950	1	1	yes	characteristic
230	C₂×C₂₃	#3137	1	2	yes	—
231	C₂×C₂₃	#3178	1	2	yes	—
232	C₂²×Q₈	—	2	1	no	—
233	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
234	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
235	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
236	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
237	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
238	C₄⋊Q₈	—	2	2	no	—
239	C₄⋊Q₈	—	2	2	no	—
240	C₄⋊Q₈	C₂×C₄×C₂₃	1	4	yes	—
241	C₄⋊Q₈	C₂×C₄×C₂₃	1	4	yes	—
242	C₄×Q₈	—	2	4	no	—
243	C₄×Q₈	—	2	4	no	—
244	C₂×C₄⋊C₄	—	2	1	no	—
245	C₂×C₄⋊C₄	—	2	1	no	—
246	C₂×C₄⋊C₄	—	2	1	no	—
247	C₂×C₄⋊C₄	—	2	2	no	—
248	C₂×C₄⋊C₄	—	2	2	no	—
249	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
250	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
251	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
252	C₂×C₄²	—	2	2	no	—
253	C₂×C₄²	—	2	2	no	—
254	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
255	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
256	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
257	#103	—	2	4	no	—
258	#103	—	2	4	no	—
259	#103	C₂×C₄×C₂₃	1	8	yes	—
260	#103	C₂×C₄×C₂₃	1	8	yes	—
261	#97	—	2	2	no	—
262	#97	—	2	2	no	—
263	#97	—	2	2	no	—
264	C₄×C₈	—	2	2	no	—
265	C₄×C₈	—	2	2	no	—
266	C₄×C₈	C₂×C₄×C₂₃	1	4	yes	—
267	#95	—	2	2	no	—
268	#95	—	2	1	no	—
269	#95	—	2	1	no	—
270	#95	—	2	1	no	—
271	#95	—	2	1	no	—
272	#95	—	2	4	no	—
273	#95	—	2	2	no	—
274	#95	D₄×C₂₃	1	2	yes	—
275	#95	D₄×C₂₃	1	2	yes	—
276	C₂₃	#21645	1	1	yes	characteristic, direct product factor, Sylow
277	C₂×Q₈	—	2	4	no	—
278	C₂×Q₈	—	2	2	no	—
279	C₂×Q₈	—	2	2	no	—
280	C₂×Q₈	—	2	2	no	—
281	C₂×Q₈	—	2	2	no	—
282	C₂×Q₈	—	2	2	no	—
283	C₂×Q₈	—	8	2	no	—
284	C₂×Q₈	C₂²×C₄×C₂₃	1	4	yes	—
285	C₂²×C₄	—	2	2	no	—
286	C₂²×C₄	—	2	2	no	—
287	C₂²×C₄	—	2	2	no	—
288	C₂²×C₄	—	2	2	no	—
289	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
290	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
291	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
292	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
293	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
294	C₂×C₈	—	2	1	no	—
295	C₂×C₈	—	2	1	no	—
296	C₂×C₈	—	2	1	no	—
297	C₂×C₈	—	2	1	no	—
298	C₂×C₈	—	2	1	no	—
299	C₂×C₈	—	2	1	no	—
300	C₂×C₈	—	2	1	no	—
301	C₂×C₈	—	2	1	no	—
302	C₂×C₈	C₂²×C₄×C₂₃	1	2	yes	—
303	C₂×C₈	C₂²×C₄×C₂₃	1	2	yes	—
304	C₂×C₈	#41×C₂₃	1	2	yes	—
305	C₂×C₈	#41×C₂₃	1	2	yes	—
306	C₄⋊C₄	—	2	4	no	—
307	C₄⋊C₄	—	2	4	no	—
308	C₄⋊C₄	—	2	4	no	—
309	C₄⋊C₄	—	2	2	no	—
310	C₄⋊C₄	—	2	2	no	—
311	C₄⋊C₄	—	2	2	no	—
312	C₄⋊C₄	—	2	2	no	—
313	C₄⋊C₄	—	2	2	no	—
314	C₄⋊C₄	—	4	4	no	—
315	C₄⋊C₄	—	8	2	no	—
316	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
317	C₄²	—	2	1	no	—
318	C₄²	—	2	1	no	—
319	C₄²	—	4	4	no	—
320	C₄²	—	8	2	no	—
321	C₄²	C₂²×C₄×C₂₃	1	2	yes	—
322	C₄²	#41×C₂₃	1	2	yes	—
323	C₄²	#41×C₂₃	1	2	yes	—
324	C₄²	#41×C₂₃	1	2	yes	—
325	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
326	Q₈	—	2	4	no	—
327	Q₈	—	2	4	no	—
328	Q₈	—	4	2	no	—
329	Q₈	—	4	2	no	—
330	Q₈	—	8	4	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	4	no	—
338	C₂×C₄	—	2	4	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	4	2	no	—
341	C₂×C₄	—	4	2	no	—
342	C₂×C₄	—	4	2	no	—
343	C₂×C₄	—	4	2	no	—
344	C₂×C₄	—	4	2	no	—
345	C₂×C₄	—	4	2	no	—
346	C₂×C₄	—	4	2	no	—
347	C₂×C₄	—	4	2	no	—
348	C₂×C₄	—	4	2	no	—
349	C₂×C₄	—	4	2	no	—
350	C₂×C₄	C₄×D₄×C₂₃	1	2	yes	—
351	C₂×C₄	C₄×D₄×C₂₃	1	2	yes	—
352	C₂×C₄	C₂₃×#124	1	4	yes	—
353	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
354	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
355	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
356	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
357	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
358	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
359	C₈	—	2	2	no	—
360	C₈	—	2	2	no	—
361	C₈	—	2	2	no	—
362	C₈	—	2	2	no	—
363	C₂²	C₂×C₄×D₄×C₂₃	1	1	yes	characteristic
364	C₂²	C₂×C₂₃×#124	1	1	yes	characteristic
365	C₂²	C₂₃×#532	1	1	yes	characteristic
366	C₂²	C₂₃×#577	1	2	yes	—
367	C₂²	C₂₃×#578	1	2	yes	—
368	C₄	—	2	2	no	—
369	C₄	—	2	2	no	—
370	C₄	—	2	4	no	—
371	C₄	—	4	2	no	—
372	C₄	—	4	4	no	—
373	C₄	—	4	4	no	—
374	C₄	—	8	2	no	—
375	C₄	—	8	2	no	—
376	C₄	C₄×#41×C₂₃	1	1	yes	characteristic
377	C₄	C₄×#41×C₂₃	1	1	yes	characteristic
378	C₄	C₂₃×#529	1	1	yes	characteristic
379	C₄	C₂₃×#529	1	1	yes	characteristic
380	C₂	C₄×C₂₃×#124	1	1	yes	characteristic
381	C₂	C₂₃×#2949	1	1	yes	characteristic
382	C₂	C₂₃×#2950	1	1	yes	characteristic
383	C₂	C₂₃×#3137	1	2	yes	—
384	C₂	C₂₃×#3178	1	2	yes	—

	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 ◁ C₂₃×#376 ◁ G

Complements

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

N	H ≅ G/N	type
15. C₂₃×#487	C₄	semidirect
132. #21645	C₂₃	direct (N × H)
202. #487	C₄×C₂₃	semidirect
276. C₂₃	#21645	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×#487	2
C₂₃×#2331	2
C₂₃×#2327	2
C₂₃×#1993	2
C₂₃×#1960	2
C₂₃×#1935	2
C₂₃×#1933	2
C₂₃×#1835	2
C₂₃×#1763	2
C₄×C₂₃×#103	2
C₂₃×#1726	2
#21645	23

Subgroups — C23×#21645 #19169271

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#21645 #19169271