Subgroups — C₂₃×#23826 #19171452

Order 5888.

746 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₂₃×#125	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×C₂₃×#124	C₂	1	1	yes	maximal, characteristic
3	C₂₃×#2101	C₂	1	2	yes	maximal, complemented
4	C₂₃×#2074	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#2073	C₂	1	1	yes	maximal, characteristic
6	C₂₃×#2042	C₂	1	2	yes	maximal
7	C₂₃×#2026	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#2025	C₂	1	1	yes	maximal, characteristic
9	C₂₃×#1763	C₂	1	2	yes	maximal, complemented
10	C₂₃×#1762	C₂	1	2	yes	maximal
11	C₂₃×#1745	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₂₃×#125	C₂²	1	1	yes	characteristic
13	C₂×C₂₃×#124	C₂²	1	1	yes	characteristic
14	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
16	C₂×C₂₃×#103	C₂²	1	2	yes	—
17	C₂×C₂₃×#103	C₂²	1	2	yes	—
18	C₂×C₂₃×#102	C₂²	1	2	yes	—
19	C₂×C₂₃×#102	C₂²	1	2	yes	—
20	C₂×C₂₃×#97	C₂²	1	2	yes	—
21	C₂₃×#391	C₂²	1	1	yes	characteristic
22	C₂₃×#390	C₂²	1	1	yes	characteristic
23	C₂₃×#389	C₂²	1	2	yes	—
24	C₂₃×#388	—	2	2	no	—
25	C₂₃×#387	—	2	2	no	—
26	C₂₃×#382	C₂²	1	1	yes	characteristic
27	C₂₃×#382	C₂²	1	1	yes	characteristic
28	C₄×C₄⋊C₄×C₂₃	—	2	2	no	—
29	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
30	C₄×C₂²⋊C₄×C₂₃	—	2	2	no	—
31	C₄³×C₂₃	C₂²	1	1	yes	characteristic
32	C₂₃×#340	C₂²	1	2	yes	—
33	C₂₃×#340	C₂²	1	2	yes	—
34	C₂₃×#340	C₂²	1	2	yes	—
35	C₂₃×#340	C₂²	1	2	yes	—
36	C₂₃×#336	C₂²	1	1	yes	characteristic
37	C₂₃×#336	C₂²	1	1	yes	characteristic
38	C₂₃×#336	C₂²	1	2	yes	—
39	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
40	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
41	C₂³×C₄×C₂₃	—	2	1	no	—
42	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
43	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
44	C₂₃×#125	—	2	4	no	—
45	C₂₃×#124	—	2	2	no	—
46	C₂₃×#124	—	2	2	no	—
47	C₄×Q₈×C₂₃	—	2	4	no	—
48	C₄×D₄×C₂₃	—	2	4	no	—
49	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
50	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
51	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
52	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
53	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
54	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
55	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
56	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
57	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
58	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
59	C₂×C₄²×C₂₃	—	2	1	no	—
60	C₂×C₄²×C₂₃	—	2	2	no	—
61	C₂×C₄²×C₂₃	D₄	1	2	yes	—
62	C₂×C₄²×C₂₃	D₄	1	2	yes	—
63	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
64	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
65	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
66	C₂₃×#103	—	2	4	no	—
67	C₂₃×#103	—	2	4	no	—
68	C₂₃×#102	—	2	4	no	—
69	C₂₃×#102	—	2	4	no	—
70	C₂₃×#97	—	2	4	no	—
71	C₂₃×#95	—	2	2	no	—
72	C₂₃×#95	—	2	2	no	—
73	C₂₃×#95	—	2	2	no	—
74	C₂₃×#95	—	2	2	no	—
75	C₂₃×#95	—	2	2	no	—
76	C₂⁴×C₂₃	—	2	1	no	—
77	C₂×Q₈×C₂₃	—	2	1	no	—
78	C₂×Q₈×C₂₃	—	2	2	no	—
79	C₂×Q₈×C₂₃	—	2	2	no	—
80	C₂×Q₈×C₂₃	#41	1	2	yes	—
81	C₂×D₄×C₂₃	—	2	2	no	—
82	C₂×D₄×C₂₃	—	2	2	no	—
83	C₂×D₄×C₂₃	—	2	1	no	—
84	C₂×D₄×C₂₃	#41	1	2	yes	—
85	C₂²×C₄×C₂₃	—	2	1	no	—
86	C₂²×C₄×C₂₃	—	2	2	no	—
87	C₂²×C₄×C₂₃	—	2	1	no	—
88	C₂²×C₄×C₂₃	—	2	2	no	—
89	C₂²×C₄×C₂₃	—	2	1	no	—
90	C₂²×C₄×C₂₃	—	4	4	no	—
91	C₂²×C₄×C₂₃	—	4	2	no	—
92	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
93	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
94	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
97	C₂×C₈×C₂₃	—	2	2	no	—
98	C₂×C₈×C₂₃	—	2	2	no	—
99	C₂×C₈×C₂₃	—	2	2	no	—
100	C₂×C₈×C₂₃	—	2	2	no	—
101	C₂×C₈×C₂₃	—	2	2	no	—
102	C₂×C₈×C₂₃	—	2	2	no	—
103	C₄⋊C₄×C₂₃	—	2	8	no	—
104	C₄⋊C₄×C₂₃	—	2	2	no	—
105	C₄⋊C₄×C₂₃	—	2	2	no	—
106	C₄⋊C₄×C₂₃	—	2	2	no	—
107	C₄⋊C₄×C₂₃	—	2	2	no	—
108	C₄⋊C₄×C₂₃	—	2	2	no	—
109	C₄⋊C₄×C₂₃	—	4	4	no	—
110	C₄⋊C₄×C₂₃	—	4	2	no	—
111	C₄⋊C₄×C₂₃	#41	1	4	yes	—
112	C₂²⋊C₄×C₂₃	—	2	8	no	—
113	C₂²⋊C₄×C₂₃	—	4	4	no	—
114	C₂²⋊C₄×C₂₃	—	4	2	no	—
115	C₄²×C₂₃	—	2	1	no	—
116	C₄²×C₂₃	—	2	1	no	—
117	C₄²×C₂₃	—	2	2	no	—
118	C₄²×C₂₃	—	4	2	no	—
119	C₄²×C₂₃	—	4	2	no	—
120	C₄²×C₂₃	—	4	4	no	—
121	C₄²×C₂₃	—	4	2	no	—
122	C₄²×C₂₃	#41	1	4	yes	—
123	#23826	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
124	C₂³×C₂₃	—	2	2	no	—
125	C₂³×C₂₃	—	4	1	no	—
126	C₂³×C₂₃	—	4	1	no	—
127	C₂³×C₂₃	—	4	2	no	—
128	C₂³×C₂₃	—	4	2	no	—
129	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
130	Q₈×C₂₃	—	2	4	no	—
131	Q₈×C₂₃	—	4	2	no	—
132	D₄×C₂₃	—	2	4	no	—
133	D₄×C₂₃	—	4	2	no	—
134	C₂×C₄×C₂₃	—	2	2	no	—
135	C₂×C₄×C₂₃	—	2	2	no	—
136	C₂×C₄×C₂₃	—	2	2	no	—
137	C₂×C₄×C₂₃	—	2	2	no	—
138	C₂×C₄×C₂₃	—	2	2	no	—
139	C₂×C₄×C₂₃	—	2	4	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	2	no	—
144	C₂×C₄×C₂₃	—	4	1	no	—
145	C₂×C₄×C₂₃	—	4	1	no	—
146	C₂×C₄×C₂₃	—	4	2	no	—
147	C₂×C₄×C₂₃	—	4	2	no	—
148	C₂×C₄×C₂₃	—	4	2	no	—
149	C₂×C₄×C₂₃	—	4	1	no	—
150	C₂×C₄×C₂₃	—	4	1	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	—	8	4	no	—
156	C₂×C₄×C₂₃	#124	1	2	yes	—
157	C₂×C₄×C₂₃	#124	1	2	yes	—
158	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
159	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
160	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
161	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
162	C₈×C₂₃	—	4	2	no	—
163	C₈×C₂₃	—	4	2	no	—
164	C₄×#125	C₂×C₂₃	1	1	yes	characteristic, complemented
165	C₄×#124	C₂×C₂₃	1	1	yes	characteristic
166	#2101	C₂×C₂₃	1	2	yes	complemented
167	#2074	C₂×C₂₃	1	1	yes	characteristic, complemented
168	#2073	C₂×C₂₃	1	1	yes	characteristic
169	#2042	C₂×C₂₃	1	2	yes	—
170	#2026	C₂×C₂₃	1	1	yes	characteristic, complemented
171	#2025	C₂×C₂₃	1	1	yes	characteristic
172	#1763	C₂×C₂₃	1	2	yes	complemented
173	#1762	C₂×C₂₃	1	2	yes	—
174	#1745	C₂×C₂₃	1	1	yes	characteristic, complemented
175	C₂²×C₂₃	—	4	4	no	—
176	C₂²×C₂₃	—	4	2	no	—
177	C₂²×C₂₃	—	8	2	no	—
178	C₂²×C₂₃	—	8	1	no	—
179	C₂²×C₂₃	—	8	1	no	—
180	C₂²×C₂₃	#525	1	1	yes	characteristic
181	C₂²×C₂₃	#525	1	1	yes	characteristic
182	C₂²×C₂₃	C₂×#124	1	1	yes	characteristic
183	C₂²×C₂₃	#575	1	2	yes	—
184	C₂²×C₂₃	#575	1	2	yes	—
185	C₄×C₂₃	—	2	2	no	—
186	C₄×C₂₃	—	2	2	no	—
187	C₄×C₂₃	—	4	2	no	—
188	C₄×C₂₃	—	4	2	no	—
189	C₄×C₂₃	—	4	4	no	—
190	C₄×C₂₃	—	4	2	no	—
191	C₄×C₂₃	—	8	2	no	—
192	C₄×C₂₃	—	8	1	no	—
193	C₄×C₂₃	—	8	1	no	—
194	C₄×C₂₃	#529	1	2	yes	—
195	C₄×C₂₃	#529	1	2	yes	—
196	C₂×#125	C₂²×C₂₃	1	1	yes	characteristic
197	C₂×#124	C₂²×C₂₃	1	1	yes	characteristic
198	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
199	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
200	C₂×#103	C₂²×C₂₃	1	2	yes	—
201	C₂×#103	C₂²×C₂₃	1	2	yes	—
202	C₂×#102	C₂²×C₂₃	1	2	yes	—
203	C₂×#102	C₂²×C₂₃	1	2	yes	—
204	C₂×#97	C₂²×C₂₃	1	2	yes	—
205	#391	C₂²×C₂₃	1	1	yes	characteristic
206	#390	C₂²×C₂₃	1	1	yes	characteristic
207	#389	C₂²×C₂₃	1	2	yes	—
208	#388	—	2	2	no	—
209	#387	—	2	2	no	—
210	#382	C₂²×C₂₃	1	1	yes	characteristic
211	#382	C₂²×C₂₃	1	1	yes	characteristic
212	C₄×C₄⋊C₄	—	2	2	no	—
213	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
214	C₄×C₂²⋊C₄	—	2	2	no	—
215	C₄³	C₂²×C₂₃	1	1	yes	characteristic
216	#340	C₂²×C₂₃	1	2	yes	—
217	#340	C₂²×C₂₃	1	2	yes	—
218	#340	C₂²×C₂₃	1	2	yes	—
219	#340	C₂²×C₂₃	1	2	yes	—
220	#336	C₂²×C₂₃	1	1	yes	characteristic
221	#336	C₂²×C₂₃	1	1	yes	characteristic
222	#336	C₂²×C₂₃	1	2	yes	—
223	C₂×C₂₃	—	8	2	no	—
224	C₂×C₂₃	#2398	1	1	yes	characteristic
225	C₂×C₂₃	#3111	1	2	yes	—
226	C₂×C₂₃	#3111	1	2	yes	—
227	C₂×C₂₃	#3140	1	1	yes	characteristic
228	C₂×C₂₃	#3142	1	1	yes	characteristic
229	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
230	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
231	C₂³×C₄	—	2	1	no	—
232	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
233	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
234	#125	—	2	4	no	—
235	#124	—	2	2	no	—
236	#124	—	2	2	no	—
237	C₄×Q₈	—	2	4	no	—
238	C₄×D₄	—	2	4	no	—
239	C₂×C₄⋊C₄	—	2	2	no	—
240	C₂×C₄⋊C₄	—	2	1	no	—
241	C₂×C₄⋊C₄	—	2	2	no	—
242	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
243	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
244	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
245	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
246	C₂×C₂²⋊C₄	—	2	2	no	—
247	C₂×C₂²⋊C₄	—	2	1	no	—
248	C₂×C₂²⋊C₄	—	2	2	no	—
249	C₂×C₄²	—	2	1	no	—
250	C₂×C₄²	—	2	2	no	—
251	C₂×C₄²	D₄×C₂₃	1	2	yes	—
252	C₂×C₄²	D₄×C₂₃	1	2	yes	—
253	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
254	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
255	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
256	#103	—	2	4	no	—
257	#103	—	2	4	no	—
258	#102	—	2	4	no	—
259	#102	—	2	4	no	—
260	#97	—	2	4	no	—
261	#95	—	2	2	no	—
262	#95	—	2	2	no	—
263	#95	—	2	2	no	—
264	#95	—	2	2	no	—
265	#95	—	2	2	no	—
266	C₂₃	#23826	1	1	yes	characteristic, direct product factor, Sylow
267	C₂⁴	—	2	1	no	—
268	C₂×Q₈	—	2	1	no	—
269	C₂×Q₈	—	2	2	no	—
270	C₂×Q₈	—	2	2	no	—
271	C₂×Q₈	#41×C₂₃	1	2	yes	—
272	C₂×D₄	—	2	2	no	—
273	C₂×D₄	—	2	2	no	—
274	C₂×D₄	—	2	1	no	—
275	C₂×D₄	#41×C₂₃	1	2	yes	—
276	C₂²×C₄	—	2	1	no	—
277	C₂²×C₄	—	2	2	no	—
278	C₂²×C₄	—	2	2	no	—
279	C₂²×C₄	—	2	1	no	—
280	C₂²×C₄	—	2	1	no	—
281	C₂²×C₄	—	4	4	no	—
282	C₂²×C₄	—	4	2	no	—
283	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
284	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
285	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
286	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
287	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
288	C₂×C₈	—	2	2	no	—
289	C₂×C₈	—	2	2	no	—
290	C₂×C₈	—	2	2	no	—
291	C₂×C₈	—	2	2	no	—
292	C₂×C₈	—	2	2	no	—
293	C₂×C₈	—	2	2	no	—
294	C₄⋊C₄	—	2	8	no	—
295	C₄⋊C₄	—	2	2	no	—
296	C₄⋊C₄	—	2	2	no	—
297	C₄⋊C₄	—	2	2	no	—
298	C₄⋊C₄	—	2	2	no	—
299	C₄⋊C₄	—	2	2	no	—
300	C₄⋊C₄	—	4	4	no	—
301	C₄⋊C₄	—	4	2	no	—
302	C₄⋊C₄	#41×C₂₃	1	4	yes	—
303	C₂²⋊C₄	—	2	8	no	—
304	C₂²⋊C₄	—	4	4	no	—
305	C₂²⋊C₄	—	4	2	no	—
306	C₄²	—	2	1	no	—
307	C₄²	—	2	1	no	—
308	C₄²	—	2	2	no	—
309	C₄²	—	4	2	no	—
310	C₄²	—	4	2	no	—
311	C₄²	—	4	4	no	—
312	C₄²	—	4	2	no	—
313	C₄²	#41×C₂₃	1	4	yes	—
314	C₂³	—	2	2	no	—
315	C₂³	—	4	2	no	—
316	C₂³	—	4	2	no	—
317	C₂³	—	4	1	no	—
318	C₂³	—	4	1	no	—
319	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
320	Q₈	—	2	4	no	—
321	Q₈	—	4	2	no	—
322	D₄	—	2	4	no	—
323	D₄	—	4	2	no	—
324	C₂×C₄	—	2	2	no	—
325	C₂×C₄	—	2	2	no	—
326	C₂×C₄	—	2	2	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	2	4	no	—
334	C₂×C₄	—	4	2	no	—
335	C₂×C₄	—	4	2	no	—
336	C₂×C₄	—	4	1	no	—
337	C₂×C₄	—	4	1	no	—
338	C₂×C₄	—	4	2	no	—
339	C₂×C₄	—	4	2	no	—
340	C₂×C₄	—	4	2	no	—
341	C₂×C₄	—	4	2	no	—
342	C₂×C₄	—	4	2	no	—
343	C₂×C₄	—	4	1	no	—
344	C₂×C₄	—	4	1	no	—
345	C₂×C₄	—	8	4	no	—
346	C₂×C₄	C₂₃×#124	1	2	yes	—
347	C₂×C₄	C₂₃×#124	1	2	yes	—
348	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
349	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
350	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
351	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
352	C₈	—	4	2	no	—
353	C₈	—	4	2	no	—
354	C₂²	—	4	2	no	—
355	C₂²	—	4	4	no	—
356	C₂²	—	8	2	no	—
357	C₂²	—	8	1	no	—
358	C₂²	—	8	1	no	—
359	C₂²	C₂₃×#525	1	1	yes	characteristic
360	C₂²	C₂₃×#525	1	1	yes	characteristic
361	C₂²	C₂×C₂₃×#124	1	1	yes	characteristic
362	C₂²	C₂₃×#575	1	2	yes	—
363	C₂²	C₂₃×#575	1	2	yes	—
364	C₄	—	2	2	no	—
365	C₄	—	2	2	no	—
366	C₄	—	4	2	no	—
367	C₄	—	4	2	no	—
368	C₄	—	4	2	no	—
369	C₄	—	4	4	no	—
370	C₄	—	8	2	no	—
371	C₄	—	8	1	no	—
372	C₄	—	8	1	no	—
373	C₄	C₂₃×#529	1	2	yes	—
374	C₄	C₂₃×#529	1	2	yes	—
375	C₂	—	8	2	no	—
376	C₂	C₂₃×#2398	1	1	yes	characteristic
377	C₂	C₂₃×#3111	1	2	yes	—
378	C₂	C₂₃×#3111	1	2	yes	—
379	C₂	C₂₃×#3140	1	1	yes	characteristic
380	C₂	C₂₃×#3142	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₃
prime radical	C₂²×D₄×C₂₃	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₃ ◁ C₄³×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄×C₂₃×#125	C₂	semidirect
3. C₂₃×#2101	C₂	semidirect
4. C₂₃×#2074	C₂	semidirect
7. C₂₃×#2026	C₂	semidirect
9. C₂₃×#1763	C₂	semidirect
11. C₂₃×#1745	C₂	semidirect
123. #23826	C₂₃	direct (N × H)
164. C₄×#125	C₂×C₂₃	semidirect
166. #2101	C₂×C₂₃	semidirect
167. #2074	C₂×C₂₃	semidirect
170. #2026	C₂×C₂₃	semidirect
172. #1763	C₂×C₂₃	semidirect
174. #1745	C₂×C₂₃	semidirect
266. C₂₃	#23826	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₄×C₂₃×#125	2
C₄×C₂₃×#124	2
C₂₃×#2101	2
C₂₃×#2074	2
C₂₃×#2073	2
C₂₃×#2042	2
C₂₃×#2026	2
C₂₃×#2025	2
C₂₃×#1763	2
C₂₃×#1762	2
C₂₃×#1745	2
#23826	23

Subgroups — C23×#23826 #19171452

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#23826 #19171452