Subgroups — C₂₃×#19390 #19167016

Order 5888.

674 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×#3229	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₃×#3077	C₂	1	1	yes	maximal, characteristic
3	C₂×C₂₃×#461	C₂	1	1	yes	maximal, characteristic
4	C₂₃×#2972	C₂	1	1	yes	maximal, characteristic
5	C₂₃×#1679	C₂	1	4	yes	maximal, complemented
6	C₂₃×#1671	C₂	1	4	yes	maximal, complemented
7	C₂₃×#1570	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#1546	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#1542	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×SD₁₆×C₂₃	—	2	1	no	—
11	C₂₃×#533	C₂²	1	1	yes	characteristic
12	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
13	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
14	C₂₃×#498	C₂²	1	2	yes	complemented
15	C₂₃×#487	C₂²	1	2	yes	complemented
16	C₂₃×#483	—	2	2	no	—
17	C₂₃×#478	—	2	2	no	—
18	C₂₃×#476	C₂²	1	2	yes	—
19	C₂₃×#475	—	2	2	no	—
20	C₂₃×#474	C₂²	1	2	yes	—
21	C₂₃×#461	—	2	2	no	—
22	C₂₃×#461	C₂²	1	4	yes	—
23	C₈×D₄×C₂₃	—	2	2	no	—
24	C₈×D₄×C₂₃	C₂²	1	4	yes	—
25	C₂₃×#431	C₂²	1	1	yes	characteristic
26	C₂₃×#431	C₂²	1	1	yes	characteristic
27	C₂₃×#428	—	2	1	no	—
28	C₂₃×#423	C₂²	1	1	yes	characteristic
29	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
30	C₂₃×#418	—	2	1	no	—
31	C₂×C₂₃×#103	—	2	1	no	—
32	C₂×C₂₃×C₂²⋊C₈	—	2	2	no	—
33	C₂₃×#334	C₂²	1	4	yes	complemented
34	C₂₃×#333	C₂²	1	2	yes	complemented
35	C₂₃×#332	C₂²	1	4	yes	complemented
36	C₂₃×#332	C₂²	1	2	yes	complemented
37	C₂²×Q₈×C₂₃	—	2	1	no	—
38	C₂²×D₄×C₂₃	D₄	1	1	yes	characteristic
39	C₂³×C₄×C₂₃	—	2	1	no	—
40	C₂×SD₁₆×C₂₃	—	2	4	no	—
41	C₂×SD₁₆×C₂₃	—	4	4	no	—
42	C₂×M₁₆×C₂₃	—	2	1	no	—
43	C₂²×C₈×C₂₃	—	2	1	no	—
44	C₂²×C₈×C₂₃	—	2	4	no	—
45	C₂₃×C₄⋊Q₈	—	2	1	no	—
46	C₂₃×C₄⋊Q₈	—	2	1	no	—
47	C₂₃×C₄⋊Q₈	—	2	1	no	—
48	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
49	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
50	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
51	C₂₃×#125	—	2	1	no	—
52	C₂₃×C₂²⋊Q₈	—	2	1	no	—
53	C₂₃×C₂²⋊Q₈	—	2	1	no	—
54	C₄×Q₈×C₂₃	—	2	1	no	—
55	C₄×Q₈×C₂₃	—	2	1	no	—
56	C₄×D₄×C₂₃	—	2	1	no	—
57	C₄×D₄×C₂₃	—	2	1	no	—
58	C₄×D₄×C₂₃	D₄	1	2	yes	—
59	C₄×D₄×C₂₃	C₂³	1	2	yes	—
60	C₂₃×#117	—	2	1	no	—
61	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
62	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
63	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
64	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
65	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
66	C₂₃×#107	—	2	2	no	—
67	C₂₃×#106	—	2	4	no	—
68	C₂₃×#106	—	2	2	no	—
69	C₂₃×C₄⋊C₈	—	2	1	no	—
70	C₂₃×C₄⋊C₈	—	2	1	no	—
71	C₂₃×C₄⋊C₈	D₄	1	2	yes	—
72	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
73	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
74	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
75	C₂₃×#103	—	2	4	no	—
76	C₂₃×#103	—	2	4	no	—
77	C₂₃×#102	—	2	2	no	—
78	C₂₃×#102	—	2	2	no	—
79	C₂₃×C₂²⋊C₈	—	2	1	no	—
80	C₂₃×C₂²⋊C₈	—	2	4	no	—
81	C₂₃×C₂²⋊C₈	D₄	1	2	yes	—
82	C₄×C₈×C₂₃	—	2	1	no	—
83	C₄×C₈×C₂₃	C₂³	1	2	yes	—
84	C₂⁴×C₂₃	—	2	1	no	—
85	C₂×Q₈×C₂₃	—	2	1	no	—
86	C₂×Q₈×C₂₃	—	2	2	no	—
87	C₂×Q₈×C₂₃	—	2	1	no	—
88	C₂×Q₈×C₂₃	—	4	1	no	—
89	C₂×Q₈×C₂₃	—	4	2	no	—
90	C₂×Q₈×C₂₃	—	4	2	no	—
91	C₂×D₄×C₂₃	—	2	1	no	—
92	C₂×D₄×C₂₃	—	2	2	no	—
93	C₂×D₄×C₂₃	SD₁₆	1	4	yes	—
94	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
95	C₂²×C₄×C₂₃	—	2	1	no	—
96	C₂²×C₄×C₂₃	—	2	2	no	—
97	C₂²×C₄×C₂₃	—	2	2	no	—
98	C₂²×C₄×C₂₃	—	4	1	no	—
99	C₂²×C₄×C₂₃	—	8	2	no	—
100	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₂₃	#41	1	1	yes	characteristic
103	SD₁₆×C₂₃	—	4	8	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	2	no	—
108	C₂×C₈×C₂₃	—	4	2	no	—
109	C₂×C₈×C₂₃	—	8	4	no	—
110	C₂×C₈×C₂₃	C₂×D₄	1	4	yes	—
111	C₄⋊C₄×C₂₃	—	2	1	no	—
112	C₄⋊C₄×C₂₃	—	2	1	no	—
113	C₄⋊C₄×C₂₃	—	2	1	no	—
114	C₄⋊C₄×C₂₃	—	2	2	no	—
115	C₄⋊C₄×C₂₃	—	2	1	no	—
116	C₄⋊C₄×C₂₃	—	2	2	no	—
117	C₄⋊C₄×C₂₃	—	2	1	no	—
118	C₄⋊C₄×C₂₃	—	4	1	no	—
119	C₄⋊C₄×C₂₃	—	4	1	no	—
120	C₄⋊C₄×C₂₃	—	4	1	no	—
121	C₄⋊C₄×C₂₃	—	4	1	no	—
122	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
123	C₂²⋊C₄×C₂₃	—	2	2	no	—
124	C₂²⋊C₄×C₂₃	—	2	2	no	—
125	C₂²⋊C₄×C₂₃	—	4	1	no	—
126	C₄²×C₂₃	—	4	1	no	—
127	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
128	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
129	C₄²×C₂₃	#41	1	1	yes	characteristic
130	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
131	#19390	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
132	C₂³×C₂₃	—	2	2	no	—
133	C₂³×C₂₃	—	2	4	no	—
134	C₂³×C₂₃	—	8	1	no	—
135	C₂³×C₂₃	—	8	1	no	—
136	C₂³×C₂₃	#121	1	1	yes	characteristic
137	Q₈×C₂₃	—	4	2	no	—
138	Q₈×C₂₃	—	4	2	no	—
139	Q₈×C₂₃	—	4	2	no	—
140	Q₈×C₂₃	—	8	1	no	—
141	Q₈×C₂₃	—	8	2	no	—
142	D₄×C₂₃	—	2	2	no	—
143	D₄×C₂₃	—	2	4	no	—
144	D₄×C₂₃	C₂×SD₁₆	1	4	yes	—
145	C₂×C₄×C₂₃	—	2	2	no	—
146	C₂×C₄×C₂₃	—	2	2	no	—
147	C₂×C₄×C₂₃	—	4	1	no	—
148	C₂×C₄×C₂₃	—	4	4	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	—	8	2	no	—
153	C₂×C₄×C₂₃	—	8	1	no	—
154	C₂×C₄×C₂₃	—	8	2	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	C₂×SD₁₆	1	2	yes	—
159	C₂×C₄×C₂₃	#135	1	2	yes	—
160	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
161	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
162	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
163	C₈×C₂₃	—	2	4	no	—
164	C₈×C₂₃	—	4	2	no	—
165	C₈×C₂₃	—	4	2	no	—
166	C₈×C₂₃	—	4	2	no	—
167	#3229	C₂×C₂₃	1	1	yes	characteristic, complemented
168	#3077	C₂×C₂₃	1	1	yes	characteristic
169	C₂×#461	C₂×C₂₃	1	1	yes	characteristic
170	#2972	C₂×C₂₃	1	1	yes	characteristic
171	#1679	C₂×C₂₃	1	4	yes	complemented
172	#1671	C₂×C₂₃	1	4	yes	complemented
173	#1570	C₂×C₂₃	1	1	yes	characteristic, complemented
174	#1546	C₂×C₂₃	1	1	yes	characteristic, complemented
175	#1542	C₂×C₂₃	1	1	yes	characteristic, complemented
176	C₂²×C₂₃	—	2	1	no	—
177	C₂²×C₂₃	—	2	1	no	—
178	C₂²×C₂₃	—	2	4	no	—
179	C₂²×C₂₃	—	4	2	no	—
180	C₂²×C₂₃	—	4	2	no	—
181	C₂²×C₂₃	—	8	4	no	—
182	C₂²×C₂₃	#465	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	—	4	2	no	—
188	C₄×C₂₃	—	8	1	no	—
189	C₄×C₂₃	—	8	2	no	—
190	C₄×C₂₃	—	8	1	no	—
191	C₄×C₂₃	#465	1	2	yes	—
192	C₄×C₂₃	C₂²×SD₁₆	1	1	yes	characteristic
193	C₄×C₂₃	C₂×#135	1	1	yes	characteristic
194	C₄×C₂₃	#577	1	2	yes	—
195	C₂²×SD₁₆	—	2	1	no	—
196	#533	C₂²×C₂₃	1	1	yes	characteristic
197	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
198	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
199	#498	C₂²×C₂₃	1	2	yes	complemented
200	#487	C₂²×C₂₃	1	2	yes	complemented
201	#483	—	2	2	no	—
202	#478	—	2	2	no	—
203	#476	C₂²×C₂₃	1	2	yes	—
204	#475	—	2	2	no	—
205	#474	C₂²×C₂₃	1	2	yes	—
206	#461	—	2	2	no	—
207	#461	C₂²×C₂₃	1	4	yes	—
208	C₈×D₄	—	2	2	no	—
209	C₈×D₄	C₂²×C₂₃	1	4	yes	—
210	#431	C₂²×C₂₃	1	1	yes	characteristic
211	#431	C₂²×C₂₃	1	1	yes	characteristic
212	#428	—	2	1	no	—
213	#423	C₂²×C₂₃	1	1	yes	characteristic
214	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
215	#418	—	2	1	no	—
216	C₂×#103	—	2	1	no	—
217	C₂×C₂²⋊C₈	—	2	2	no	—
218	#334	C₂²×C₂₃	1	4	yes	complemented
219	#333	C₂²×C₂₃	1	2	yes	complemented
220	#332	C₂²×C₂₃	1	2	yes	complemented
221	#332	C₂²×C₂₃	1	4	yes	complemented
222	C₂×C₂₃	—	2	2	no	—
223	C₂×C₂₃	—	4	4	no	—
224	C₂×C₂₃	#3042	1	1	yes	characteristic
225	C₂×C₂₃	C₂×#465	1	1	yes	characteristic
226	C₂×C₂₃	#3069	1	1	yes	characteristic
227	C₂²×Q₈	—	2	1	no	—
228	C₂²×D₄	D₄×C₂₃	1	1	yes	characteristic
229	C₂³×C₄	—	2	1	no	—
230	C₂×SD₁₆	—	2	4	no	—
231	C₂×SD₁₆	—	4	4	no	—
232	C₂×M₁₆	—	2	1	no	—
233	C₂²×C₈	—	2	1	no	—
234	C₂²×C₈	—	2	4	no	—
235	C₄⋊Q₈	—	2	1	no	—
236	C₄⋊Q₈	—	2	1	no	—
237	C₄⋊Q₈	—	2	1	no	—
238	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
239	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
240	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
241	#125	—	2	1	no	—
242	C₂²⋊Q₈	—	2	1	no	—
243	C₂²⋊Q₈	—	2	1	no	—
244	C₄×Q₈	—	2	1	no	—
245	C₄×Q₈	—	2	1	no	—
246	C₄×D₄	—	2	1	no	—
247	C₄×D₄	—	2	1	no	—
248	C₄×D₄	D₄×C₂₃	1	2	yes	—
249	C₄×D₄	C₂³×C₂₃	1	2	yes	—
250	#117	—	2	1	no	—
251	C₂×C₄⋊C₄	—	2	1	no	—
252	C₂×C₄⋊C₄	—	2	1	no	—
253	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
254	C₂×C₂²⋊C₄	—	2	1	no	—
255	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
256	#107	—	2	2	no	—
257	#106	—	2	4	no	—
258	#106	—	2	2	no	—
259	C₄⋊C₈	—	2	1	no	—
260	C₄⋊C₈	—	2	1	no	—
261	C₄⋊C₈	D₄×C₂₃	1	2	yes	—
262	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
263	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
264	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
265	#103	—	2	4	no	—
266	#103	—	2	4	no	—
267	#102	—	2	2	no	—
268	#102	—	2	2	no	—
269	C₂²⋊C₈	—	2	1	no	—
270	C₂²⋊C₈	—	2	4	no	—
271	C₂²⋊C₈	D₄×C₂₃	1	2	yes	—
272	C₄×C₈	—	2	1	no	—
273	C₄×C₈	C₂³×C₂₃	1	2	yes	—
274	C₂₃	#19390	1	1	yes	characteristic, direct product factor, Sylow
275	C₂⁴	—	2	1	no	—
276	C₂×Q₈	—	2	1	no	—
277	C₂×Q₈	—	2	2	no	—
278	C₂×Q₈	—	2	1	no	—
279	C₂×Q₈	—	4	1	no	—
280	C₂×Q₈	—	4	2	no	—
281	C₂×Q₈	—	4	2	no	—
282	C₂×D₄	—	2	1	no	—
283	C₂×D₄	—	2	2	no	—
284	C₂×D₄	SD₁₆×C₂₃	1	4	yes	—
285	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
286	C₂²×C₄	—	2	1	no	—
287	C₂²×C₄	—	2	2	no	—
288	C₂²×C₄	—	2	2	no	—
289	C₂²×C₄	—	4	1	no	—
290	C₂²×C₄	—	8	2	no	—
291	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
292	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
293	C₂²×C₄	#41×C₂₃	1	1	yes	characteristic
294	SD₁₆	—	4	8	no	—
295	M₁₆	—	4	2	no	—
296	C₂×C₈	—	2	2	no	—
297	C₂×C₈	—	2	2	no	—
298	C₂×C₈	—	2	2	no	—
299	C₂×C₈	—	4	2	no	—
300	C₂×C₈	—	8	4	no	—
301	C₂×C₈	C₂×D₄×C₂₃	1	4	yes	—
302	C₄⋊C₄	—	2	1	no	—
303	C₄⋊C₄	—	2	1	no	—
304	C₄⋊C₄	—	2	1	no	—
305	C₄⋊C₄	—	2	2	no	—
306	C₄⋊C₄	—	2	1	no	—
307	C₄⋊C₄	—	2	2	no	—
308	C₄⋊C₄	—	2	1	no	—
309	C₄⋊C₄	—	4	1	no	—
310	C₄⋊C₄	—	4	1	no	—
311	C₄⋊C₄	—	4	1	no	—
312	C₄⋊C₄	—	4	1	no	—
313	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
314	C₂²⋊C₄	—	2	2	no	—
315	C₂²⋊C₄	—	2	2	no	—
316	C₂²⋊C₄	—	4	1	no	—
317	C₄²	—	4	1	no	—
318	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
319	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
320	C₄²	#41×C₂₃	1	1	yes	characteristic
321	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
322	C₂³	—	2	2	no	—
323	C₂³	—	2	4	no	—
324	C₂³	—	8	1	no	—
325	C₂³	—	8	1	no	—
326	C₂³	C₂₃×#121	1	1	yes	characteristic
327	Q₈	—	4	2	no	—
328	Q₈	—	4	2	no	—
329	Q₈	—	4	2	no	—
330	Q₈	—	8	1	no	—
331	Q₈	—	8	2	no	—
332	D₄	—	2	2	no	—
333	D₄	—	2	4	no	—
334	D₄	C₂×SD₁₆×C₂₃	1	4	yes	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	4	1	no	—
338	C₂×C₄	—	4	4	no	—
339	C₂×C₄	—	4	1	no	—
340	C₂×C₄	—	4	1	no	—
341	C₂×C₄	—	4	2	no	—
342	C₂×C₄	—	8	2	no	—
343	C₂×C₄	—	8	1	no	—
344	C₂×C₄	—	8	2	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	C₂×SD₁₆×C₂₃	1	2	yes	—
349	C₂×C₄	C₂₃×#135	1	2	yes	—
350	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
351	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
352	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
353	C₈	—	2	4	no	—
354	C₈	—	4	2	no	—
355	C₈	—	4	2	no	—
356	C₈	—	4	2	no	—
357	C₂²	—	2	1	no	—
358	C₂²	—	2	1	no	—
359	C₂²	—	2	4	no	—
360	C₂²	—	4	2	no	—
361	C₂²	—	4	2	no	—
362	C₂²	—	8	4	no	—
363	C₂²	C₂₃×#465	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	—	4	2	no	—
369	C₄	—	8	1	no	—
370	C₄	—	8	2	no	—
371	C₄	—	8	1	no	—
372	C₄	C₂₃×#465	1	2	yes	—
373	C₄	C₂²×SD₁₆×C₂₃	1	1	yes	characteristic
374	C₄	C₂×C₂₃×#135	1	1	yes	characteristic
375	C₄	C₂₃×#577	1	2	yes	—
376	C₂	—	2	2	no	—
377	C₂	—	4	4	no	—
378	C₂	C₂₃×#3042	1	1	yes	characteristic
379	C₂	C₂×C₂₃×#465	1	1	yes	characteristic
380	C₂	C₂₃×#3069	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₂₃
prime radical	C₂²×D₄×C₂₃	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
1. C₂₃×#3229	C₂	semidirect
5. C₂₃×#1679	C₂	semidirect
6. C₂₃×#1671	C₂	semidirect
7. C₂₃×#1570	C₂	semidirect
8. C₂₃×#1546	C₂	semidirect
9. C₂₃×#1542	C₂	semidirect
14. C₂₃×#498	C₂²	semidirect
15. C₂₃×#487	C₂²	semidirect
33. C₂₃×#334	C₂²	semidirect
34. C₂₃×#333	C₂²	semidirect
35. C₂₃×#332	C₂²	semidirect
36. C₂₃×#332	C₂²	semidirect
131. #19390	C₂₃	direct (N × H)
167. #3229	C₂×C₂₃	semidirect
171. #1679	C₂×C₂₃	semidirect
172. #1671	C₂×C₂₃	semidirect
173. #1570	C₂×C₂₃	semidirect
174. #1546	C₂×C₂₃	semidirect
175. #1542	C₂×C₂₃	semidirect
199. #498	C₂²×C₂₃	semidirect
200. #487	C₂²×C₂₃	semidirect
218. #334	C₂²×C₂₃	semidirect
219. #333	C₂²×C₂₃	semidirect
220. #332	C₂²×C₂₃	semidirect
221. #332	C₂²×C₂₃	semidirect
274. C₂₃	#19390	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×#3229	2
C₂₃×#3077	2
C₂×C₂₃×#461	2
C₂₃×#2972	2
C₂₃×#1679	2
C₂₃×#1671	2
C₂₃×#1570	2
C₂₃×#1546	2
C₂₃×#1542	2
#19390	23

Subgroups — C23×#19390 #19167016

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#19390 #19167016