Subgroups — C₂₃×#21707 #19169333

Order 5888.

998 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3147	C₂	1	1	yes	maximal, characteristic
2	C₂×C₂₃×#444	C₂	1	2	yes	maximal, complemented
3	C₂×C₂₃×#443	C₂	1	2	yes	maximal, complemented
4	C₂₃×#2932	C₂	1	2	yes	maximal, complemented
5	C₂₃×#1975	C₂	1	2	yes	maximal, complemented
6	C₂₃×#1974	C₂	1	2	yes	maximal, complemented
7	C₂₃×#1963	C₂	1	2	yes	maximal, complemented
8	C₂₃×#1848	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#1726	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₂₃×#135	C₂²	1	2	yes	—
11	C₂×C₂₃×#135	C₂²	1	2	yes	—
12	C₂×C₂₃×#131	C₂²	1	4	yes	—
13	C₂₃×#532	C₂²	1	2	yes	—
14	C₂₃×#495	C₄	1	2	yes	complemented
15	C₂₃×#495	C₄	1	2	yes	complemented
16	C₂₃×#494	C₄	1	1	yes	characteristic, complemented
17	C₂₃×#493	C₄	1	1	yes	characteristic, complemented
18	C₂₃×#492	C₄	1	2	yes	complemented
19	C₂₃×#444	—	2	8	no	—
20	C₂₃×#443	—	2	8	no	—
21	C₂₃×#435	—	2	8	no	—
22	C₂×C₂₃×#108	C₂²	1	2	yes	—
23	C₂×C₂₃×#108	C₂²	1	2	yes	—
24	C₂₃×#423	C₂²	1	2	yes	—
25	C₂×C₂₃×#104	C₂²	1	4	yes	—
26	C₂×C₂₃×#104	C₂²	1	4	yes	—
27	C₂₃×#408	C₂²	1	4	yes	—
28	C₂×C₂₃×#97	C₂²	1	1	yes	characteristic
29	C₂×C₂₃×#97	C₂²	1	1	yes	characteristic
30	C₂×C₂₃×#97	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
32	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
33	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
34	C₂₃×#376	C₂²	1	1	yes	characteristic
35	C₂×#41×C₂₃	C₂³	1	4	yes	—
36	C₂₃×#135	—	2	4	no	—
37	C₂₃×#135	—	2	4	no	—
38	C₂₃×#135	—	2	4	no	—
39	C₂₃×#135	—	2	4	no	—
40	C₂×Q₁₆×C₂₃	C₂×C₄	1	2	yes	—
41	C₂×Q₁₆×C₂₃	C₂×C₄	1	2	yes	—
42	C₂×SD₁₆×C₂₃	C₂×C₄	1	4	yes	—
43	C₂×SD₁₆×C₂₃	C₂×C₄	1	4	yes	—
44	C₂×D₈×C₂₃	C₂×C₄	1	2	yes	—
45	C₂×D₈×C₂₃	C₂×C₄	1	2	yes	—
46	C₂₃×#131	—	2	8	no	—
47	C₂₃×#131	—	2	8	no	—
48	C₂×M₁₆×C₂₃	—	2	4	no	—
49	C₂×M₁₆×C₂₃	C₂³	1	4	yes	—
50	C₂²×C₈×C₂₃	—	2	4	no	—
51	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
52	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
53	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
54	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
55	C₂₃×C₄⋊Q₈	C₂×C₄	1	2	yes	—
56	C₂₃×#127	C₂×C₄	1	2	yes	—
57	C₂₃×#124	C₂×C₄	1	4	yes	—
58	C₂₃×#121	—	2	4	no	—
59	C₄×D₄×C₂₃	—	2	4	no	—
60	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
61	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
62	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
63	C₂₃×#108	—	2	4	no	—
64	C₂₃×#108	—	2	4	no	—
65	C₂₃×C₄⋊C₈	—	2	4	no	—
66	C₂₃×#104	—	2	8	no	—
67	C₂₃×#104	—	2	8	no	—
68	C₂₃×C₂²⋊C₈	—	2	8	no	—
69	C₂₃×#97	—	2	2	no	—
70	C₂₃×#97	D₄	1	4	yes	—
71	C₂₃×#97	D₄	1	4	yes	complemented
72	C₄×C₈×C₂₃	—	2	2	no	—
73	C₄×C₈×C₂₃	C₂×C₄	1	1	yes	characteristic
74	C₄×C₈×C₂₃	C₂×C₄	1	1	yes	characteristic
75	C₄×C₈×C₂₃	C₂×C₄	1	1	yes	characteristic
76	C₄×C₈×C₂₃	C₂×C₄	1	1	yes	characteristic
77	C₄×C₈×C₂₃	D₄	1	4	yes	complemented
78	C₂₃×#95	—	2	2	no	—
79	#41×C₂₃	—	2	4	no	—
80	#41×C₂₃	—	2	4	no	—
81	#41×C₂₃	—	2	4	no	—
82	#41×C₂₃	—	2	4	no	—
83	C₂×Q₈×C₂₃	C₂²×C₄	1	4	yes	—
84	C₂×D₄×C₂₃	—	2	4	no	—
85	C₂×D₄×C₂₃	—	2	4	no	—
86	C₂×D₄×C₂₃	C₂²×C₄	1	4	yes	—
87	C₂²×C₄×C₂₃	—	2	1	no	—
88	C₂²×C₄×C₂₃	—	2	1	no	—
89	C₂²×C₄×C₂₃	—	2	4	no	—
90	C₂²×C₄×C₂₃	#41	1	2	yes	—
91	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
92	Q₁₆×C₂₃	—	2	4	no	—
93	Q₁₆×C₂₃	—	2	4	no	—
94	SD₁₆×C₂₃	—	2	8	no	—
95	SD₁₆×C₂₃	—	2	8	no	—
96	D₈×C₂₃	—	2	4	no	—
97	D₈×C₂₃	—	2	4	no	—
98	M₁₆×C₂₃	—	2	4	no	—
99	M₁₆×C₂₃	—	2	4	no	—
100	M₁₆×C₂₃	—	4	8	no	—
101	C₂×C₈×C₂₃	—	2	1	no	—
102	C₂×C₈×C₂₃	—	2	1	no	—
103	C₂×C₈×C₂₃	—	2	4	no	—
104	C₂×C₈×C₂₃	—	4	8	no	—
105	C₂×C₈×C₂₃	C₂²×C₄	1	1	yes	characteristic
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	C₂×D₄	1	2	yes	—
110	C₂×C₈×C₂₃	C₂×D₄	1	2	yes	—
111	C₂×C₈×C₂₃	C₂×D₄	1	2	yes	—
112	C₂×C₈×C₂₃	C₂×D₄	1	2	yes	—
113	C₂×C₈×C₂₃	C₂×D₄	1	2	yes	—
114	C₂×C₈×C₂₃	C₂×D₄	1	2	yes	—
115	C₂×C₈×C₂₃	#41	1	2	yes	—
116	C₂×C₈×C₂₃	#41	1	2	yes	—
117	C₄⋊C₄×C₂₃	—	2	4	no	—
118	C₂²⋊C₄×C₂₃	—	2	8	no	—
119	C₄²×C₂₃	—	2	1	no	—
120	C₄²×C₂₃	—	2	1	no	—
121	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
122	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
123	C₄²×C₂₃	C₂×D₄	1	2	yes	—
124	C₄²×C₂₃	C₂×D₄	1	2	yes	—
125	C₄²×C₂₃	C₂×D₄	1	2	yes	—
126	#21707	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
127	C₂³×C₂₃	—	2	4	no	—
128	C₂³×C₂₃	C₂×#41	1	1	yes	characteristic
129	Q₈×C₂₃	—	2	4	no	—
130	Q₈×C₂₃	—	2	4	no	—
131	D₄×C₂₃	—	2	4	no	—
132	D₄×C₂₃	—	2	4	no	—
133	D₄×C₂₃	—	4	4	no	—
134	D₄×C₂₃	—	4	4	no	—
135	D₄×C₂₃	—	8	4	no	—
136	C₂×C₄×C₂₃	—	2	4	no	—
137	C₂×C₄×C₂₃	—	2	2	no	—
138	C₂×C₄×C₂₃	—	2	2	no	—
139	C₂×C₄×C₂₃	—	4	2	no	—
140	C₂×C₄×C₂₃	—	4	2	no	—
141	C₂×C₄×C₂₃	—	4	2	no	—
142	C₂×C₄×C₂₃	—	4	4	no	—
143	C₂×C₄×C₂₃	—	4	4	no	—
144	C₂×C₄×C₂₃	C₄×D₄	1	2	yes	—
145	C₂×C₄×C₂₃	C₄×D₄	1	2	yes	—
146	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
147	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
148	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
149	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
150	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
151	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
152	C₈×C₂₃	—	2	2	no	—
153	C₈×C₂₃	—	4	4	no	—
154	C₈×C₂₃	C₄×D₄	1	2	yes	—
155	C₈×C₂₃	C₄×D₄	1	2	yes	—
156	C₈×C₂₃	C₄×D₄	1	2	yes	—
157	C₈×C₂₃	C₄×D₄	1	2	yes	—
158	C₈×C₂₃	#127	1	4	yes	—
159	#3147	C₂×C₂₃	1	1	yes	characteristic
160	C₂×#444	C₂×C₂₃	1	2	yes	complemented
161	C₂×#443	C₂×C₂₃	1	2	yes	complemented
162	#2932	C₂×C₂₃	1	2	yes	complemented
163	#1975	C₂×C₂₃	1	2	yes	complemented
164	#1974	C₂×C₂₃	1	2	yes	complemented
165	#1963	C₂×C₂₃	1	2	yes	complemented
166	#1848	C₂×C₂₃	1	1	yes	characteristic, complemented
167	#1726	C₂×C₂₃	1	1	yes	characteristic, complemented
168	C₂²×C₂₃	—	2	2	no	—
169	C₂²×C₂₃	—	4	4	no	—
170	C₂²×C₂₃	—	4	8	no	—
171	C₂²×C₂₃	C₂×C₄×D₄	1	1	yes	characteristic
172	C₂²×C₂₃	#532	1	1	yes	characteristic
173	C₂²×C₂₃	#532	1	1	yes	characteristic
174	C₄×C₂₃	—	2	2	no	—
175	C₄×C₂₃	—	2	2	no	—
176	C₄×C₂₃	—	4	2	no	—
177	C₄×C₂₃	—	4	2	no	—
178	C₄×C₂₃	—	4	4	no	—
179	C₄×C₂₃	C₂×C₄×D₄	1	1	yes	characteristic
180	C₄×C₂₃	C₂×C₄×D₄	1	1	yes	characteristic
181	C₄×C₂₃	C₂×#127	1	1	yes	characteristic
182	C₄×C₂₃	#532	1	1	yes	characteristic
183	C₂×#135	C₂²×C₂₃	1	2	yes	—
184	C₂×#135	C₂²×C₂₃	1	2	yes	—
185	C₂×#131	C₂²×C₂₃	1	4	yes	—
186	#532	C₂²×C₂₃	1	2	yes	—
187	#495	C₄×C₂₃	1	2	yes	complemented
188	#495	C₄×C₂₃	1	2	yes	complemented
189	#494	C₄×C₂₃	1	1	yes	characteristic, complemented
190	#493	C₄×C₂₃	1	1	yes	characteristic, complemented
191	#492	C₄×C₂₃	1	2	yes	complemented
192	#444	—	2	8	no	—
193	#443	—	2	8	no	—
194	#435	—	2	8	no	—
195	C₂×#108	C₂²×C₂₃	1	2	yes	—
196	C₂×#108	C₂²×C₂₃	1	2	yes	—
197	#423	C₂²×C₂₃	1	2	yes	—
198	C₂×#104	C₂²×C₂₃	1	4	yes	—
199	C₂×#104	C₂²×C₂₃	1	4	yes	—
200	#408	C₂²×C₂₃	1	4	yes	—
201	C₂×#97	C₂²×C₂₃	1	1	yes	characteristic
202	C₂×#97	C₂²×C₂₃	1	1	yes	characteristic
203	C₂×#97	C₂²×C₂₃	1	1	yes	characteristic
204	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
205	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
206	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
207	#376	C₂²×C₂₃	1	1	yes	characteristic
208	C₂×C₂₃	—	2	1	no	—
209	C₂×C₂₃	—	2	1	no	—
210	C₂×C₂₃	—	8	4	no	—
211	C₂×C₂₃	C₄×#127	1	1	yes	characteristic
212	C₂×C₂₃	#2957	1	2	yes	—
213	C₂×#41	C₂³×C₂₃	1	4	yes	—
214	#135	—	2	4	no	—
215	#135	—	2	4	no	—
216	#135	—	2	4	no	—
217	#135	—	2	4	no	—
218	C₂×Q₁₆	C₂×C₄×C₂₃	1	2	yes	—
219	C₂×Q₁₆	C₂×C₄×C₂₃	1	2	yes	—
220	C₂×SD₁₆	C₂×C₄×C₂₃	1	4	yes	—
221	C₂×SD₁₆	C₂×C₄×C₂₃	1	4	yes	—
222	C₂×D₈	C₂×C₄×C₂₃	1	2	yes	—
223	C₂×D₈	C₂×C₄×C₂₃	1	2	yes	—
224	#131	—	2	8	no	—
225	#131	—	2	8	no	—
226	C₂×M₁₆	—	2	4	no	—
227	C₂×M₁₆	C₂³×C₂₃	1	4	yes	—
228	C₂²×C₈	—	2	4	no	—
229	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
230	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
231	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
232	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
233	C₄⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
234	#127	C₂×C₄×C₂₃	1	2	yes	—
235	#124	C₂×C₄×C₂₃	1	4	yes	—
236	#121	—	2	4	no	—
237	C₄×D₄	—	2	4	no	—
238	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
239	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
240	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
241	#108	—	2	4	no	—
242	#108	—	2	4	no	—
243	C₄⋊C₈	—	2	4	no	—
244	#104	—	2	8	no	—
245	#104	—	2	8	no	—
246	C₂²⋊C₈	—	2	8	no	—
247	#97	—	2	2	no	—
248	#97	D₄×C₂₃	1	4	yes	—
249	#97	D₄×C₂₃	1	4	yes	complemented
250	C₄×C₈	—	2	2	no	—
251	C₄×C₈	C₂×C₄×C₂₃	1	1	yes	characteristic
252	C₄×C₈	C₂×C₄×C₂₃	1	1	yes	characteristic
253	C₄×C₈	C₂×C₄×C₂₃	1	1	yes	characteristic
254	C₄×C₈	C₂×C₄×C₂₃	1	1	yes	characteristic
255	C₄×C₈	D₄×C₂₃	1	4	yes	complemented
256	#95	—	2	2	no	—
257	C₂₃	#21707	1	1	yes	characteristic, direct product factor, Sylow
258	#41	—	2	4	no	—
259	#41	—	2	4	no	—
260	#41	—	2	4	no	—
261	#41	—	2	4	no	—
262	C₂×Q₈	C₂²×C₄×C₂₃	1	4	yes	—
263	C₂×D₄	—	2	4	no	—
264	C₂×D₄	—	2	4	no	—
265	C₂×D₄	C₂²×C₄×C₂₃	1	4	yes	—
266	C₂²×C₄	—	2	1	no	—
267	C₂²×C₄	—	2	1	no	—
268	C₂²×C₄	—	2	4	no	—
269	C₂²×C₄	#41×C₂₃	1	2	yes	—
270	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
271	Q₁₆	—	2	4	no	—
272	Q₁₆	—	2	4	no	—
273	SD₁₆	—	2	8	no	—
274	SD₁₆	—	2	8	no	—
275	D₈	—	2	4	no	—
276	D₈	—	2	4	no	—
277	M₁₆	—	2	4	no	—
278	M₁₆	—	2	4	no	—
279	M₁₆	—	4	8	no	—
280	C₂×C₈	—	2	1	no	—
281	C₂×C₈	—	2	1	no	—
282	C₂×C₈	—	2	4	no	—
283	C₂×C₈	—	4	8	no	—
284	C₂×C₈	C₂²×C₄×C₂₃	1	1	yes	characteristic
285	C₂×C₈	C₂²×C₄×C₂₃	1	1	yes	characteristic
286	C₂×C₈	C₂²×C₄×C₂₃	1	1	yes	characteristic
287	C₂×C₈	C₂²×C₄×C₂₃	1	1	yes	characteristic
288	C₂×C₈	C₂×D₄×C₂₃	1	2	yes	—
289	C₂×C₈	C₂×D₄×C₂₃	1	2	yes	—
290	C₂×C₈	C₂×D₄×C₂₃	1	2	yes	—
291	C₂×C₈	C₂×D₄×C₂₃	1	2	yes	—
292	C₂×C₈	C₂×D₄×C₂₃	1	2	yes	—
293	C₂×C₈	C₂×D₄×C₂₃	1	2	yes	—
294	C₂×C₈	#41×C₂₃	1	2	yes	—
295	C₂×C₈	#41×C₂₃	1	2	yes	—
296	C₄⋊C₄	—	2	4	no	—
297	C₂²⋊C₄	—	2	8	no	—
298	C₄²	—	2	1	no	—
299	C₄²	—	2	1	no	—
300	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
301	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
302	C₄²	C₂×D₄×C₂₃	1	2	yes	—
303	C₄²	C₂×D₄×C₂₃	1	2	yes	—
304	C₄²	C₂×D₄×C₂₃	1	2	yes	—
305	C₂³	—	2	4	no	—
306	C₂³	C₂×#41×C₂₃	1	1	yes	characteristic
307	Q₈	—	2	4	no	—
308	Q₈	—	2	4	no	—
309	D₄	—	2	4	no	—
310	D₄	—	2	4	no	—
311	D₄	—	4	4	no	—
312	D₄	—	4	4	no	—
313	D₄	—	8	4	no	—
314	C₂×C₄	—	2	4	no	—
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	4	2	no	—
318	C₂×C₄	—	4	2	no	—
319	C₂×C₄	—	4	2	no	—
320	C₂×C₄	—	4	4	no	—
321	C₂×C₄	—	4	4	no	—
322	C₂×C₄	C₄×D₄×C₂₃	1	2	yes	—
323	C₂×C₄	C₄×D₄×C₂₃	1	2	yes	—
324	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
325	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
326	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
327	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
328	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
329	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
330	C₈	—	2	2	no	—
331	C₈	—	4	4	no	—
332	C₈	C₄×D₄×C₂₃	1	2	yes	—
333	C₈	C₄×D₄×C₂₃	1	2	yes	—
334	C₈	C₄×D₄×C₂₃	1	2	yes	—
335	C₈	C₄×D₄×C₂₃	1	2	yes	—
336	C₈	C₂₃×#127	1	4	yes	—
337	C₂²	—	2	2	no	—
338	C₂²	—	4	8	no	—
339	C₂²	—	4	4	no	—
340	C₂²	C₂×C₄×D₄×C₂₃	1	1	yes	characteristic
341	C₂²	C₂₃×#532	1	1	yes	characteristic
342	C₂²	C₂₃×#532	1	1	yes	characteristic
343	C₄	—	2	2	no	—
344	C₄	—	2	2	no	—
345	C₄	—	4	2	no	—
346	C₄	—	4	2	no	—
347	C₄	—	4	4	no	—
348	C₄	C₂×C₄×D₄×C₂₃	1	1	yes	characteristic
349	C₄	C₂×C₄×D₄×C₂₃	1	1	yes	characteristic
350	C₄	C₂×C₂₃×#127	1	1	yes	characteristic
351	C₄	C₂₃×#532	1	1	yes	characteristic
352	C₂	—	2	1	no	—
353	C₂	—	2	1	no	—
354	C₂	—	8	4	no	—
355	C₂	C₄×C₂₃×#127	1	1	yes	characteristic
356	C₂	C₂₃×#2957	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₂₃	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₂₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₃
socle	C₂²×C₂₃	C₂×C₄×D₄
prime radical	C₂₃×#3147	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₃ ◁ C₂×C₂₃×#97 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₂₃×#444	C₂	semidirect
3. C₂×C₂₃×#443	C₂	semidirect
4. C₂₃×#2932	C₂	semidirect
5. C₂₃×#1975	C₂	semidirect
6. C₂₃×#1974	C₂	semidirect
7. C₂₃×#1963	C₂	semidirect
8. C₂₃×#1848	C₂	semidirect
9. C₂₃×#1726	C₂	semidirect
14. C₂₃×#495	C₄	semidirect
15. C₂₃×#495	C₄	semidirect
16. C₂₃×#494	C₄	semidirect
17. C₂₃×#493	C₄	semidirect
18. C₂₃×#492	C₄	semidirect
71. C₂₃×#97	D₄	semidirect
77. C₄×C₈×C₂₃	D₄	semidirect
126. #21707	C₂₃	direct (N × H)
160. C₂×#444	C₂×C₂₃	semidirect
161. C₂×#443	C₂×C₂₃	semidirect
162. #2932	C₂×C₂₃	semidirect
163. #1975	C₂×C₂₃	semidirect
164. #1974	C₂×C₂₃	semidirect
165. #1963	C₂×C₂₃	semidirect
166. #1848	C₂×C₂₃	semidirect
167. #1726	C₂×C₂₃	semidirect
187. #495	C₄×C₂₃	semidirect
188. #495	C₄×C₂₃	semidirect
189. #494	C₄×C₂₃	semidirect
190. #493	C₄×C₂₃	semidirect
191. #492	C₄×C₂₃	semidirect
249. #97	D₄×C₂₃	semidirect
255. C₄×C₈	D₄×C₂₃	semidirect
257. C₂₃	#21707	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×#3147	2
C₂×C₂₃×#444	2
C₂×C₂₃×#443	2
C₂₃×#2932	2
C₂₃×#1975	2
C₂₃×#1974	2
C₂₃×#1963	2
C₂₃×#1848	2
C₂₃×#1726	2
#21707	23

Subgroups — C23×#21707 #19169333

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#21707 #19169333