Subgroups — C₂₃×#19354 #19166980

Order 5888.

648 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	C₂₃×#3239	C₂	1	2	yes	maximal
2	C₂×C₂₃×#494	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#2966	C₂	1	1	yes	maximal, characteristic
4	C₂₃×#1690	C₂	1	2	yes	maximal, complemented
5	C₂₃×#1689	C₂	1	2	yes	maximal, complemented
6	C₂₃×#1670	C₂	1	2	yes	maximal, complemented
7	C₂₃×#1669	C₂	1	2	yes	maximal, complemented
8	C₂₃×#1568	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#1556	C₂	1	2	yes	maximal, complemented
10	C₂²×Q₁₆×C₂₃	—	2	1	no	—
11	C₂²×Q₁₆×C₂₃	—	2	1	no	—
12	C₂×C₂₃×C₄⋊Q₈	C₂²	1	2	yes	—
13	C₂₃×#529	C₂²	1	1	yes	characteristic
14	C₂₃×#501	—	2	2	no	—
15	C₂₃×#494	—	2	1	no	—
16	C₂₃×#494	—	2	1	no	—
17	C₂₃×#494	C₂²	1	2	yes	—
18	C₂₃×#494	C₂²	1	2	yes	—
19	C₂₃×#489	—	2	2	no	—
20	C₂₃×#484	—	2	2	no	—
21	C₂₃×#481	—	2	2	no	—
22	C₂₃×#475	C₂²	1	4	yes	—
23	C₂₃×#474	C₂²	1	4	yes	—
24	C₂₃×#446	C₂²	1	1	yes	characteristic
25	C₈×Q₈×C₂₃	C₂²	1	1	yes	characteristic
26	C₂₃×#436	C₂²	1	1	yes	characteristic
27	C₂₃×#435	—	2	1	no	—
28	C₈×D₄×C₂₃	—	2	1	no	—
29	C₈×D₄×C₂₃	C₂²	1	1	yes	characteristic
30	C₂₃×#433	—	2	1	no	—
31	C₂₃×#432	C₂²	1	1	yes	characteristic
32	C₂₃×#432	C₂²	1	2	yes	—
33	C₂₃×#405	—	2	1	no	—
34	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
35	C₂₃×#335	C₂²	1	2	yes	—
36	C₂₃×#334	C₂²	1	2	yes	—
37	C₂₃×#332	C₂²	1	4	yes	—
38	C₂₃×#332	C₂²	1	4	yes	—
39	C₂²×Q₈×C₂₃	—	2	2	no	—
40	C₂×Q₁₆×C₂₃	—	2	2	no	—
41	C₂×Q₁₆×C₂₃	—	2	2	no	—
42	C₂×Q₁₆×C₂₃	—	2	2	no	—
43	C₂×Q₁₆×C₂₃	—	2	2	no	—
44	C₂×Q₁₆×C₂₃	—	4	4	no	—
45	C₂×Q₁₆×C₂₃	—	4	4	no	—
46	C₂×M₁₆×C₂₃	—	2	1	no	—
47	C₂²×C₈×C₂₃	—	2	1	no	—
48	C₂²×C₈×C₂₃	D₄	1	1	yes	characteristic
49	C₂²×C₈×C₂₃	D₄	1	1	yes	characteristic
50	C₂₃×C₄⋊Q₈	—	2	2	no	—
51	C₂₃×C₄⋊Q₈	—	2	2	no	—
52	C₂₃×C₄⋊Q₈	—	2	2	no	—
53	C₂₃×C₄⋊Q₈	C₂³	1	4	yes	—
54	C₂₃×#126	—	2	1	no	—
55	C₂₃×#125	D₄	1	1	yes	characteristic
56	C₂₃×#124	D₄	1	1	yes	characteristic
57	C₂₃×#123	—	2	1	no	—
58	C₂₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
59	C₂₃×#121	D₄	1	1	yes	characteristic
60	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
61	C₄×D₄×C₂₃	—	2	1	no	—
62	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
63	C₂₃×#117	—	2	1	no	—
64	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
65	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
66	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
67	C₂₃×#107	—	2	4	no	—
68	C₂₃×#106	—	2	4	no	—
69	C₂₃×C₄⋊C₈	—	2	1	no	—
70	C₂₃×C₄⋊C₈	—	2	1	no	—
71	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
72	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
73	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
74	C₂₃×#103	—	2	4	no	—
75	C₂₃×#102	—	2	4	no	—
76	C₂₃×C₂²⋊C₈	—	2	1	no	—
77	C₂₃×C₂²⋊C₈	—	2	2	no	—
78	C₂₃×C₂²⋊C₈	—	2	1	no	—
79	C₂₃×C₂²⋊C₈	—	2	1	no	—
80	C₂₃×#97	—	2	1	no	—
81	C₂₃×#97	—	2	1	no	—
82	C₂₃×#97	—	2	2	no	—
83	C₄×C₈×C₂₃	—	2	1	no	—
84	C₄×C₈×C₂₃	D₄	1	1	yes	characteristic
85	C₄×C₈×C₂₃	D₄	1	1	yes	characteristic
86	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
87	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
88	C₂×Q₈×C₂₃	—	2	4	no	—
89	C₂×Q₈×C₂₃	—	4	4	no	—
90	C₂×Q₈×C₂₃	—	4	4	no	—
91	C₂×Q₈×C₂₃	—	4	2	no	—
92	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
93	C₂×D₄×C₂₃	—	2	1	no	—
94	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₄×C₂₃	—	2	1	no	—
96	C₂²×C₄×C₂₃	—	4	2	no	—
97	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₂₃	#41	1	1	yes	characteristic
100	Q₁₆×C₂₃	—	4	4	no	—
101	Q₁₆×C₂₃	—	4	4	no	—
102	Q₁₆×C₂₃	—	4	4	no	—
103	Q₁₆×C₂₃	—	4	4	no	—
104	M₁₆×C₂₃	—	4	2	no	—
105	C₂×C₈×C₂₃	—	2	2	no	—
106	C₂×C₈×C₂₃	—	2	2	no	—
107	C₂×C₈×C₂₃	—	2	4	no	—
108	C₂×C₈×C₂₃	—	2	1	no	—
109	C₂×C₈×C₂₃	—	2	1	no	—
110	C₂×C₈×C₂₃	—	4	2	no	—
111	C₂×C₈×C₂₃	C₂×D₄	1	1	yes	characteristic
112	C₂×C₈×C₂₃	C₂×D₄	1	1	yes	characteristic
113	C₂×C₈×C₂₃	C₂×D₄	1	1	yes	characteristic
114	C₂×C₈×C₂₃	C₂×D₄	1	1	yes	characteristic
115	C₄⋊C₄×C₂₃	—	2	1	no	—
116	C₄⋊C₄×C₂₃	—	2	1	no	—
117	C₄⋊C₄×C₂₃	—	2	1	no	—
118	C₄⋊C₄×C₂₃	—	2	1	no	—
119	C₄⋊C₄×C₂₃	—	2	4	no	—
120	C₄⋊C₄×C₂₃	—	2	4	no	—
121	C₄⋊C₄×C₂₃	—	4	2	no	—
122	C₄⋊C₄×C₂₃	—	4	2	no	—
123	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
124	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
125	C₂²⋊C₄×C₂₃	—	2	1	no	—
126	C₂²⋊C₄×C₂₃	—	2	1	no	—
127	C₂²⋊C₄×C₂₃	—	2	1	no	—
128	C₂²⋊C₄×C₂₃	—	2	1	no	—
129	C₂²⋊C₄×C₂₃	—	2	1	no	—
130	C₄²×C₂₃	—	2	1	no	—
131	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
132	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
133	C₄²×C₂₃	#41	1	1	yes	characteristic
134	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
135	#19354	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
136	C₂³×C₂₃	—	2	1	no	—
137	C₂³×C₂₃	#121	1	1	yes	characteristic
138	Q₈×C₂₃	—	2	2	no	—
139	Q₈×C₂₃	—	4	4	no	—
140	Q₈×C₂₃	—	4	4	no	—
141	Q₈×C₂₃	—	8	4	no	—
142	D₄×C₂₃	—	2	2	no	—
143	D₄×C₂₃	—	4	2	no	—
144	C₂×C₄×C₂₃	—	2	2	no	—
145	C₂×C₄×C₂₃	—	2	1	no	—
146	C₂×C₄×C₂₃	—	2	1	no	—
147	C₂×C₄×C₂₃	—	2	2	no	—
148	C₂×C₄×C₂₃	—	2	1	no	—
149	C₂×C₄×C₂₃	—	2	1	no	—
150	C₂×C₄×C₂₃	—	2	1	no	—
151	C₂×C₄×C₂₃	—	4	1	no	—
152	C₂×C₄×C₂₃	—	4	1	no	—
153	C₂×C₄×C₂₃	—	4	4	no	—
154	C₂×C₄×C₂₃	—	8	4	no	—
155	C₂×C₄×C₂₃	#121	1	1	yes	characteristic
156	C₂×C₄×C₂₃	#121	1	1	yes	characteristic
157	C₂×C₄×C₂₃	#121	1	1	yes	characteristic
158	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
159	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
160	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
161	C₈×C₂₃	—	2	1	no	—
162	C₈×C₂₃	—	2	1	no	—
163	C₈×C₂₃	—	4	1	no	—
164	C₈×C₂₃	—	4	1	no	—
165	C₈×C₂₃	—	4	4	no	—
166	C₈×C₂₃	AGL(1,ℤ/8)	1	2	yes	—
167	C₈×C₂₃	AGL(1,ℤ/8)	1	2	yes	—
168	#3239	C₂×C₂₃	1	2	yes	—
169	C₂×#494	C₂×C₂₃	1	1	yes	characteristic, complemented
170	#2966	C₂×C₂₃	1	1	yes	characteristic
171	#1690	C₂×C₂₃	1	2	yes	complemented
172	#1689	C₂×C₂₃	1	2	yes	complemented
173	#1670	C₂×C₂₃	1	2	yes	complemented
174	#1669	C₂×C₂₃	1	2	yes	complemented
175	#1568	C₂×C₂₃	1	1	yes	characteristic, complemented
176	#1556	C₂×C₂₃	1	2	yes	complemented
177	C₂²×C₂₃	—	2	1	no	—
178	C₂²×C₂₃	—	2	1	no	—
179	C₂²×C₂₃	—	4	1	no	—
180	C₂²×C₂₃	—	4	1	no	—
181	C₂²×C₂₃	—	4	1	no	—
182	C₂²×C₂₃	#473	1	2	yes	—
183	C₂²×C₂₃	C₂×#121	1	1	yes	characteristic
184	C₄×C₂₃	—	2	1	no	—
185	C₄×C₂₃	—	2	1	no	—
186	C₄×C₂₃	—	2	1	no	—
187	C₄×C₂₃	—	2	1	no	—
188	C₄×C₂₃	—	4	1	no	—
189	C₄×C₂₃	—	4	1	no	—
190	C₄×C₂₃	—	4	1	no	—
191	C₄×C₂₃	—	8	4	no	—
192	C₄×C₂₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
193	C₄×C₂₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
194	C₄×C₂₃	#578	1	2	yes	—
195	C₂²×Q₁₆	—	2	1	no	—
196	C₂²×Q₁₆	—	2	1	no	—
197	C₂×C₄⋊Q₈	C₂²×C₂₃	1	2	yes	—
198	#529	C₂²×C₂₃	1	1	yes	characteristic
199	#501	—	2	2	no	—
200	#494	—	2	1	no	—
201	#494	—	2	1	no	—
202	#494	C₂²×C₂₃	1	2	yes	—
203	#494	C₂²×C₂₃	1	2	yes	—
204	#489	—	2	2	no	—
205	#484	—	2	2	no	—
206	#481	—	2	2	no	—
207	#475	C₂²×C₂₃	1	4	yes	—
208	#474	C₂²×C₂₃	1	4	yes	—
209	#446	C₂²×C₂₃	1	1	yes	characteristic
210	C₈×Q₈	C₂²×C₂₃	1	1	yes	characteristic
211	#436	C₂²×C₂₃	1	1	yes	characteristic
212	#435	—	2	1	no	—
213	C₈×D₄	—	2	1	no	—
214	C₈×D₄	C₂²×C₂₃	1	1	yes	characteristic
215	#433	—	2	1	no	—
216	#432	C₂²×C₂₃	1	1	yes	characteristic
217	#432	C₂²×C₂₃	1	2	yes	—
218	#405	—	2	1	no	—
219	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
220	#335	C₂²×C₂₃	1	2	yes	—
221	#334	C₂²×C₂₃	1	2	yes	—
222	#332	C₂²×C₂₃	1	4	yes	—
223	#332	C₂²×C₂₃	1	4	yes	—
224	C₂×C₂₃	—	2	2	no	—
225	C₂×C₂₃	—	8	1	no	—
226	C₂×C₂₃	#3038	1	1	yes	characteristic
227	C₂×C₂₃	#3059	1	1	yes	characteristic
228	C₂×C₂₃	C₂×#473	1	1	yes	characteristic
229	C₂²×Q₈	—	2	2	no	—
230	C₂×Q₁₆	—	2	2	no	—
231	C₂×Q₁₆	—	2	2	no	—
232	C₂×Q₁₆	—	2	2	no	—
233	C₂×Q₁₆	—	2	2	no	—
234	C₂×Q₁₆	—	4	4	no	—
235	C₂×Q₁₆	—	4	4	no	—
236	C₂×M₁₆	—	2	1	no	—
237	C₂²×C₈	—	2	1	no	—
238	C₂²×C₈	D₄×C₂₃	1	1	yes	characteristic
239	C₂²×C₈	D₄×C₂₃	1	1	yes	characteristic
240	C₄⋊Q₈	—	2	2	no	—
241	C₄⋊Q₈	—	2	2	no	—
242	C₄⋊Q₈	—	2	2	no	—
243	C₄⋊Q₈	C₂³×C₂₃	1	4	yes	—
244	#126	—	2	1	no	—
245	#125	D₄×C₂₃	1	1	yes	characteristic
246	#124	D₄×C₂₃	1	1	yes	characteristic
247	#123	—	2	1	no	—
248	C₂²⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
249	#121	D₄×C₂₃	1	1	yes	characteristic
250	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
251	C₄×D₄	—	2	1	no	—
252	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
253	#117	—	2	1	no	—
254	C₂×C₄⋊C₄	—	2	2	no	—
255	C₂×C₄⋊C₄	—	2	2	no	—
256	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
257	#107	—	2	4	no	—
258	#106	—	2	4	no	—
259	C₄⋊C₈	—	2	1	no	—
260	C₄⋊C₈	—	2	1	no	—
261	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
262	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
263	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
264	#103	—	2	4	no	—
265	#102	—	2	4	no	—
266	C₂²⋊C₈	—	2	1	no	—
267	C₂²⋊C₈	—	2	2	no	—
268	C₂²⋊C₈	—	2	1	no	—
269	C₂²⋊C₈	—	2	1	no	—
270	#97	—	2	1	no	—
271	#97	—	2	1	no	—
272	#97	—	2	2	no	—
273	C₄×C₈	—	2	1	no	—
274	C₄×C₈	D₄×C₂₃	1	1	yes	characteristic
275	C₄×C₈	D₄×C₂₃	1	1	yes	characteristic
276	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
277	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
278	C₂₃	#19354	1	1	yes	characteristic, direct product factor, Sylow
279	C₂×Q₈	—	2	4	no	—
280	C₂×Q₈	—	4	4	no	—
281	C₂×Q₈	—	4	4	no	—
282	C₂×Q₈	—	4	2	no	—
283	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
284	C₂×D₄	—	2	1	no	—
285	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
286	C₂²×C₄	—	2	1	no	—
287	C₂²×C₄	—	4	2	no	—
288	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
289	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
290	C₂²×C₄	#41×C₂₃	1	1	yes	characteristic
291	Q₁₆	—	4	4	no	—
292	Q₁₆	—	4	4	no	—
293	Q₁₆	—	4	4	no	—
294	Q₁₆	—	4	4	no	—
295	M₁₆	—	4	2	no	—
296	C₂×C₈	—	2	2	no	—
297	C₂×C₈	—	2	2	no	—
298	C₂×C₈	—	2	1	no	—
299	C₂×C₈	—	2	1	no	—
300	C₂×C₈	—	2	4	no	—
301	C₂×C₈	—	4	2	no	—
302	C₂×C₈	C₂×D₄×C₂₃	1	1	yes	characteristic
303	C₂×C₈	C₂×D₄×C₂₃	1	1	yes	characteristic
304	C₂×C₈	C₂×D₄×C₂₃	1	1	yes	characteristic
305	C₂×C₈	C₂×D₄×C₂₃	1	1	yes	characteristic
306	C₄⋊C₄	—	2	1	no	—
307	C₄⋊C₄	—	2	1	no	—
308	C₄⋊C₄	—	2	1	no	—
309	C₄⋊C₄	—	2	1	no	—
310	C₄⋊C₄	—	2	4	no	—
311	C₄⋊C₄	—	2	4	no	—
312	C₄⋊C₄	—	4	2	no	—
313	C₄⋊C₄	—	4	2	no	—
314	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
315	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
316	C₂²⋊C₄	—	2	1	no	—
317	C₂²⋊C₄	—	2	1	no	—
318	C₂²⋊C₄	—	2	1	no	—
319	C₂²⋊C₄	—	2	1	no	—
320	C₂²⋊C₄	—	2	1	no	—
321	C₄²	—	2	1	no	—
322	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
323	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
324	C₄²	#41×C₂₃	1	1	yes	characteristic
325	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
326	C₂³	—	2	1	no	—
327	C₂³	C₂₃×#121	1	1	yes	characteristic
328	Q₈	—	2	2	no	—
329	Q₈	—	4	4	no	—
330	Q₈	—	4	4	no	—
331	Q₈	—	8	4	no	—
332	D₄	—	2	2	no	—
333	D₄	—	4	2	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	1	no	—
336	C₂×C₄	—	2	1	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	1	no	—
339	C₂×C₄	—	2	1	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	4	1	no	—
342	C₂×C₄	—	4	1	no	—
343	C₂×C₄	—	4	4	no	—
344	C₂×C₄	—	8	4	no	—
345	C₂×C₄	C₂₃×#121	1	1	yes	characteristic
346	C₂×C₄	C₂₃×#121	1	1	yes	characteristic
347	C₂×C₄	C₂₃×#121	1	1	yes	characteristic
348	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
349	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
350	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
351	C₈	—	2	1	no	—
352	C₈	—	2	1	no	—
353	C₈	—	4	1	no	—
354	C₈	—	4	1	no	—
355	C₈	—	4	4	no	—
356	C₈	C₂₃×AGL(1,ℤ/8)	1	2	yes	—
357	C₈	C₂₃×AGL(1,ℤ/8)	1	2	yes	—
358	C₂²	—	2	1	no	—
359	C₂²	—	2	1	no	—
360	C₂²	—	4	1	no	—
361	C₂²	—	4	1	no	—
362	C₂²	—	4	1	no	—
363	C₂²	C₂₃×#473	1	2	yes	—
364	C₂²	C₂×C₂₃×#121	1	1	yes	characteristic
365	C₄	—	2	1	no	—
366	C₄	—	2	1	no	—
367	C₄	—	2	1	no	—
368	C₄	—	2	1	no	—
369	C₄	—	4	1	no	—
370	C₄	—	4	1	no	—
371	C₄	—	4	1	no	—
372	C₄	—	8	4	no	—
373	C₄	C₂×C₂₃×AGL(1,ℤ/8)	1	1	yes	characteristic
374	C₄	C₂×C₂₃×AGL(1,ℤ/8)	1	1	yes	characteristic
375	C₄	C₂₃×#578	1	2	yes	—
376	C₂	—	2	2	no	—
377	C₂	—	8	1	no	—
378	C₂	C₂₃×#3038	1	1	yes	characteristic
379	C₂	C₂₃×#3059	1	1	yes	characteristic
380	C₂	C₂×C₂₃×#473	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₂₃
prime radical	C₂₃×#121	D₄
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂×C₄²×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₂₃×#494	C₂	semidirect
4. C₂₃×#1690	C₂	semidirect
5. C₂₃×#1689	C₂	semidirect
6. C₂₃×#1670	C₂	semidirect
7. C₂₃×#1669	C₂	semidirect
8. C₂₃×#1568	C₂	semidirect
9. C₂₃×#1556	C₂	semidirect
135. #19354	C₂₃	direct (N × H)
169. C₂×#494	C₂×C₂₃	semidirect
171. #1690	C₂×C₂₃	semidirect
172. #1689	C₂×C₂₃	semidirect
173. #1670	C₂×C₂₃	semidirect
174. #1669	C₂×C₂₃	semidirect
175. #1568	C₂×C₂₃	semidirect
176. #1556	C₂×C₂₃	semidirect
278. C₂₃	#19354	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×#3239	2
C₂×C₂₃×#494	2
C₂₃×#2966	2
C₂₃×#1690	2
C₂₃×#1689	2
C₂₃×#1670	2
C₂₃×#1669	2
C₂₃×#1568	2
C₂₃×#1556	2
#19354	23

Subgroups — C23×#19354 #19166980

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#19354 #19166980