Subgroups — C₂₃×#21972 #19169598

Order 5888.

946 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#431	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₂₃×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
3	C₄×C₂₃×#117	C₂	1	1	yes	maximal, characteristic
4	C₂₃×#1939	C₂	1	4	yes	maximal, complemented
5	C₂₃×#1850	C₂	1	4	yes	maximal
6	C₂₃×#1842	C₂	1	2	yes	maximal, complemented
7	C₂₃×#1831	C₂	1	2	yes	maximal, complemented
8	C₂³×C₈×C₂₃	C₂²	1	2	yes	—
9	C₂×C₂₃×#117	C₄	1	1	yes	characteristic
10	C₂×C₂₃×#117	C₄	1	1	yes	characteristic
11	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
12	C₂₃×#431	—	2	4	no	—
13	C₂×C₂₃×C₄⋊C₈	—	2	4	no	—
14	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
15	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
16	C₂×C₂₃×C₄⋊C₈	C₂²	1	2	yes	—
17	C₂×C₂₃×C₄⋊C₈	C₂²	1	2	yes	—
18	C₂×C₂₃×C₄⋊C₈	C₂²	1	8	yes	—
19	C₂×C₂₃×C₂²⋊C₈	C₂²	1	2	yes	—
20	C₂×C₄×C₈×C₂₃	C₂²	1	2	yes	—
21	C₄×C₄⋊C₄×C₂₃	C₄	1	2	yes	—
22	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
23	C₄×C₂²⋊C₄×C₂₃	C₄	1	2	yes	—
24	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
25	C₂₃×#376	C₄	1	2	yes	—
26	C₄³×C₂₃	C₂²	1	2	yes	—
27	C₂₃×#336	C₂²	1	8	yes	—
28	C₂³×C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
29	C₂³×C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
30	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
31	C₂²×C₈×C₂₃	—	2	4	no	—
32	C₂²×C₈×C₂₃	—	4	4	no	—
33	C₂²×C₈×C₂₃	C₂³	1	4	yes	—
34	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
35	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
36	C₂₃×#117	—	2	4	no	—
37	C₂₃×#117	C₈	1	8	yes	complemented
38	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
39	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
40	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
41	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
42	C₂×C₄²×C₂₃	C₂×C₄	1	2	yes	—
43	C₂×C₄²×C₂₃	C₂×C₄	1	4	yes	—
44	C₂×C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
45	C₂×C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
46	C₂×C₄²×C₂₃	C₂×C₄	1	2	yes	—
47	C₂×C₄²×C₂₃	D₄	1	4	yes	—
48	C₂×C₄²×C₂₃	Q₈	1	4	yes	—
49	C₂×C₄²×C₂₃	C₂³	1	4	yes	—
50	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
51	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
52	C₂₃×C₄⋊C₈	—	2	4	no	—
53	C₂₃×C₄⋊C₈	—	2	4	no	—
54	C₂₃×C₄⋊C₈	—	2	2	no	—
55	C₂₃×C₄⋊C₈	—	2	2	no	—
56	C₂₃×C₄⋊C₈	—	4	8	no	—
57	C₂₃×C₂²⋊C₈	—	2	4	no	—
58	C₄×C₈×C₂₃	—	2	4	no	—
59	C₂₃×#95	C₂×C₄	1	4	yes	—
60	C₂₃×#95	C₂×C₄	1	4	yes	—
61	C₂⁴×C₂₃	C₂²×C₄	1	1	yes	characteristic
62	C₂²×C₄×C₂₃	—	2	2	no	—
63	C₂²×C₄×C₂₃	—	2	2	no	—
64	C₂²×C₄×C₂₃	—	4	2	no	—
65	C₂²×C₄×C₂₃	C₄⋊C₄	1	4	yes	—
66	C₂²×C₄×C₂₃	C₄⋊C₄	1	4	yes	—
67	C₂²×C₄×C₂₃	C₂×C₈	1	4	yes	—
68	C₂²×C₄×C₂₃	M₁₆	1	4	yes	—
69	C₂²×C₄×C₂₃	C₂²×C₄	1	4	yes	—
70	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
71	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
72	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
73	C₂²×C₄×C₂₃	C₂²×C₄	1	4	yes	—
74	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
75	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
76	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
77	C₂²×C₄×C₂₃	C₂×Q₈	1	2	yes	—
78	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
79	C₂×C₈×C₂₃	—	2	4	no	—
80	C₂×C₈×C₂₃	—	2	2	no	—
81	C₂×C₈×C₂₃	—	2	2	no	—
82	C₂×C₈×C₂₃	—	2	4	no	—
83	C₂×C₈×C₂₃	—	2	8	no	—
84	C₂×C₈×C₂₃	—	2	4	no	—
85	C₂×C₈×C₂₃	—	4	8	no	—
86	C₄⋊C₄×C₂₃	—	2	4	no	—
87	C₄⋊C₄×C₂₃	C₂×C₈	1	8	yes	complemented
88	C₂²⋊C₄×C₂₃	—	2	4	no	—
89	C₂²⋊C₄×C₂₃	C₂×C₈	1	8	yes	—
90	C₄²×C₂₃	—	2	4	no	—
91	C₄²×C₂₃	—	2	4	no	—
92	C₄²×C₂₃	—	2	4	no	—
93	C₄²×C₂₃	—	4	4	no	—
94	C₄²×C₂₃	C₄⋊C₄	1	4	yes	—
95	C₄²×C₂₃	C₄⋊C₄	1	4	yes	—
96	C₄²×C₂₃	C₂×C₈	1	8	yes	complemented
97	C₄²×C₂₃	C₂×D₄	1	2	yes	—
98	C₄²×C₂₃	C₂×D₄	1	2	yes	—
99	C₄²×C₂₃	C₂×Q₈	1	2	yes	—
100	C₄²×C₂₃	C₂×Q₈	1	2	yes	—
101	#21972	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
102	C₂³×C₂₃	—	2	2	no	—
103	C₂³×C₂₃	—	2	2	no	—
104	C₂³×C₂₃	C₂×C₄⋊C₄	1	2	yes	—
105	C₂³×C₂₃	C₂²×C₈	1	2	yes	—
106	C₂³×C₂₃	C₂×M₁₆	1	2	yes	—
107	C₂³×C₂₃	C₂³×C₄	1	1	yes	characteristic
108	C₂×C₄×C₂₃	—	2	4	no	—
109	C₂×C₄×C₂₃	—	2	2	no	—
110	C₂×C₄×C₂₃	—	2	2	no	—
111	C₂×C₄×C₂₃	—	2	4	no	—
112	C₂×C₄×C₂₃	—	2	2	no	—
113	C₂×C₄×C₂₃	—	2	2	no	—
114	C₂×C₄×C₂₃	—	2	2	no	—
115	C₂×C₄×C₂₃	—	2	4	no	—
116	C₂×C₄×C₂₃	—	2	4	no	—
117	C₂×C₄×C₂₃	—	2	4	no	—
118	C₂×C₄×C₂₃	—	2	4	no	—
119	C₂×C₄×C₂₃	—	4	4	no	—
120	C₂×C₄×C₂₃	C₄⋊C₈	1	16	yes	complemented
121	C₂×C₄×C₂₃	C₂×C₄⋊C₄	1	2	yes	—
122	C₂×C₄×C₂₃	C₂×C₄⋊C₄	1	2	yes	—
123	C₂×C₄×C₂₃	C₂×C₄⋊C₄	1	2	yes	—
124	C₂×C₄×C₂₃	C₂×C₄⋊C₄	1	2	yes	—
125	C₂×C₄×C₂₃	C₂×C₄⋊C₄	1	2	yes	—
126	C₂×C₄×C₂₃	C₂²×C₈	1	8	yes	—
127	C₂×C₄×C₂₃	C₂²×C₈	1	2	yes	—
128	C₂×C₄×C₂₃	C₂²×C₈	1	2	yes	—
129	C₂×C₄×C₂₃	C₂×M₁₆	1	2	yes	—
130	C₂×C₄×C₂₃	C₂×M₁₆	1	2	yes	—
131	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
132	C₂×C₄×C₂₃	C₂²×Q₈	1	1	yes	characteristic
133	C₂×C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
134	C₂×C₄×C₂₃	2₋¹⁺⁴	1	2	yes	—
135	C₈×C₂₃	—	4	2	no	—
136	C₈×C₂₃	—	4	4	no	—
137	C₈×C₂₃	—	4	2	no	—
138	C₂×#431	C₂×C₂₃	1	1	yes	characteristic
139	C₂²×C₄⋊C₈	C₂×C₂₃	1	1	yes	characteristic
140	C₄×#117	C₂×C₂₃	1	1	yes	characteristic
141	#1939	C₂×C₂₃	1	4	yes	complemented
142	#1850	C₂×C₂₃	1	4	yes	—
143	#1842	C₂×C₂₃	1	2	yes	complemented
144	#1831	C₂×C₂₃	1	2	yes	complemented
145	C₂²×C₂₃	—	2	2	no	—
146	C₂²×C₂₃	—	2	2	no	—
147	C₂²×C₂₃	—	2	4	no	—
148	C₂²×C₂₃	—	2	4	no	—
149	C₂²×C₂₃	C₂×C₄⋊C₈	1	4	yes	—
150	C₂²×C₂₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
151	C₂²×C₂₃	#520	1	2	yes	—
152	C₂²×C₂₃	C₂³×C₈	1	1	yes	characteristic
153	C₂²×C₂₃	C₂²×M₁₆	1	1	yes	characteristic
154	C₂²×C₂₃	#568	1	2	yes	—
155	C₄×C₂₃	—	2	2	no	—
156	C₄×C₂₃	—	2	2	no	—
157	C₄×C₂₃	—	2	2	no	—
158	C₄×C₂₃	—	2	8	no	—
159	C₄×C₂₃	—	4	4	no	—
160	C₄×C₂₃	C₂×C₄⋊C₈	1	4	yes	—
161	C₄×C₂₃	C₂×C₄⋊C₈	1	4	yes	—
162	C₄×C₂₃	#535	1	1	yes	characteristic
163	C₄×C₂₃	#536	1	1	yes	characteristic
164	C₄×C₂₃	#544	1	2	yes	—
165	C₂³×C₈	C₂²×C₂₃	1	2	yes	—
166	C₂×#117	C₄×C₂₃	1	1	yes	characteristic
167	C₂×#117	C₄×C₂₃	1	1	yes	characteristic
168	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
169	#431	—	2	4	no	—
170	C₂×C₄⋊C₈	—	2	4	no	—
171	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
172	C₂×C₄⋊C₈	C₂²×C₂₃	1	2	yes	—
173	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
174	C₂×C₄⋊C₈	C₂²×C₂₃	1	2	yes	—
175	C₂×C₄⋊C₈	C₂²×C₂₃	1	8	yes	—
176	C₂×C₂²⋊C₈	C₂²×C₂₃	1	2	yes	—
177	C₂×C₄×C₈	C₂²×C₂₃	1	2	yes	—
178	C₄×C₄⋊C₄	C₄×C₂₃	1	2	yes	—
179	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
180	C₄×C₂²⋊C₄	C₄×C₂₃	1	2	yes	—
181	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
182	#376	C₄×C₂₃	1	2	yes	—
183	C₄³	C₂²×C₂₃	1	2	yes	—
184	#336	C₂²×C₂₃	1	8	yes	—
185	C₂×C₂₃	—	2	4	no	—
186	C₂×C₂₃	#2317	1	1	yes	characteristic
187	C₂×C₂₃	C₂²×C₄⋊C₈	1	1	yes	characteristic
188	C₂×C₂₃	#2905	1	1	yes	characteristic
189	C₂×C₂₃	#2988	1	2	yes	—
190	C₂×C₂₃	#2989	1	2	yes	—
191	C₂³×C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
192	C₂³×C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
193	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
194	C₂²×C₈	—	2	4	no	—
195	C₂²×C₈	—	4	4	no	—
196	C₂²×C₈	C₂³×C₂₃	1	4	yes	—
197	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
198	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
199	#117	—	2	4	no	—
200	#117	C₈×C₂₃	1	8	yes	complemented
201	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
202	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
203	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
204	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
205	C₂×C₄²	C₂×C₄×C₂₃	1	2	yes	—
206	C₂×C₄²	C₂×C₄×C₂₃	1	4	yes	—
207	C₂×C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic
208	C₂×C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic
209	C₂×C₄²	C₂×C₄×C₂₃	1	2	yes	—
210	C₂×C₄²	D₄×C₂₃	1	4	yes	—
211	C₂×C₄²	Q₈×C₂₃	1	4	yes	—
212	C₂×C₄²	C₂³×C₂₃	1	4	yes	—
213	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
214	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
215	C₄⋊C₈	—	2	4	no	—
216	C₄⋊C₈	—	2	4	no	—
217	C₄⋊C₈	—	2	2	no	—
218	C₄⋊C₈	—	2	2	no	—
219	C₄⋊C₈	—	4	8	no	—
220	C₂²⋊C₈	—	2	4	no	—
221	C₄×C₈	—	2	4	no	—
222	#95	C₂×C₄×C₂₃	1	4	yes	—
223	#95	C₂×C₄×C₂₃	1	4	yes	—
224	C₂₃	#21972	1	1	yes	characteristic, direct product factor, Sylow
225	C₂⁴	C₂²×C₄×C₂₃	1	1	yes	characteristic
226	C₂²×C₄	—	2	2	no	—
227	C₂²×C₄	—	2	2	no	—
228	C₂²×C₄	—	4	2	no	—
229	C₂²×C₄	C₄⋊C₄×C₂₃	1	4	yes	—
230	C₂²×C₄	C₄⋊C₄×C₂₃	1	4	yes	—
231	C₂²×C₄	C₂×C₈×C₂₃	1	4	yes	—
232	C₂²×C₄	M₁₆×C₂₃	1	4	yes	—
233	C₂²×C₄	C₂²×C₄×C₂₃	1	4	yes	—
234	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
235	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
236	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
237	C₂²×C₄	C₂²×C₄×C₂₃	1	4	yes	—
238	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
239	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
240	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
241	C₂²×C₄	C₂×Q₈×C₂₃	1	2	yes	—
242	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
243	C₂×C₈	—	2	2	no	—
244	C₂×C₈	—	2	2	no	—
245	C₂×C₈	—	2	4	no	—
246	C₂×C₈	—	2	4	no	—
247	C₂×C₈	—	2	8	no	—
248	C₂×C₈	—	2	4	no	—
249	C₂×C₈	—	4	8	no	—
250	C₄⋊C₄	—	2	4	no	—
251	C₄⋊C₄	C₂×C₈×C₂₃	1	8	yes	complemented
252	C₂²⋊C₄	—	2	4	no	—
253	C₂²⋊C₄	C₂×C₈×C₂₃	1	8	yes	—
254	C₄²	—	2	4	no	—
255	C₄²	—	2	4	no	—
256	C₄²	—	2	4	no	—
257	C₄²	—	4	4	no	—
258	C₄²	C₄⋊C₄×C₂₃	1	4	yes	—
259	C₄²	C₄⋊C₄×C₂₃	1	4	yes	—
260	C₄²	C₂×C₈×C₂₃	1	8	yes	complemented
261	C₄²	C₂×D₄×C₂₃	1	2	yes	—
262	C₄²	C₂×D₄×C₂₃	1	2	yes	—
263	C₄²	C₂×Q₈×C₂₃	1	2	yes	—
264	C₄²	C₂×Q₈×C₂₃	1	2	yes	—
265	C₂³	—	2	2	no	—
266	C₂³	—	2	2	no	—
267	C₂³	C₂×C₄⋊C₄×C₂₃	1	2	yes	—
268	C₂³	C₂²×C₈×C₂₃	1	2	yes	—
269	C₂³	C₂×M₁₆×C₂₃	1	2	yes	—
270	C₂³	C₂³×C₄×C₂₃	1	1	yes	characteristic
271	C₂×C₄	—	2	2	no	—
272	C₂×C₄	—	2	4	no	—
273	C₂×C₄	—	2	2	no	—
274	C₂×C₄	—	2	4	no	—
275	C₂×C₄	—	2	2	no	—
276	C₂×C₄	—	2	2	no	—
277	C₂×C₄	—	2	2	no	—
278	C₂×C₄	—	2	4	no	—
279	C₂×C₄	—	2	4	no	—
280	C₂×C₄	—	2	4	no	—
281	C₂×C₄	—	2	4	no	—
282	C₂×C₄	—	4	4	no	—
283	C₂×C₄	C₂₃×C₄⋊C₈	1	16	yes	complemented
284	C₂×C₄	C₂×C₄⋊C₄×C₂₃	1	2	yes	—
285	C₂×C₄	C₂×C₄⋊C₄×C₂₃	1	2	yes	—
286	C₂×C₄	C₂×C₄⋊C₄×C₂₃	1	2	yes	—
287	C₂×C₄	C₂×C₄⋊C₄×C₂₃	1	2	yes	—
288	C₂×C₄	C₂×C₄⋊C₄×C₂₃	1	2	yes	—
289	C₂×C₄	C₂²×C₈×C₂₃	1	8	yes	—
290	C₂×C₄	C₂²×C₈×C₂₃	1	2	yes	—
291	C₂×C₄	C₂²×C₈×C₂₃	1	2	yes	—
292	C₂×C₄	C₂×M₁₆×C₂₃	1	2	yes	—
293	C₂×C₄	C₂×M₁₆×C₂₃	1	2	yes	—
294	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
295	C₂×C₄	C₂²×Q₈×C₂₃	1	1	yes	characteristic
296	C₂×C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
297	C₂×C₄	C₂₃×2₋¹⁺⁴	1	2	yes	—
298	C₈	—	4	4	no	—
299	C₈	—	4	2	no	—
300	C₈	—	4	2	no	—
301	C₂²	—	2	4	no	—
302	C₂²	—	2	4	no	—
303	C₂²	—	2	2	no	—
304	C₂²	—	2	2	no	—
305	C₂²	C₂×C₂₃×C₄⋊C₈	1	4	yes	—
306	C₂²	C₂²×C₄⋊C₄×C₂₃	1	1	yes	characteristic
307	C₂²	C₂₃×#520	1	2	yes	—
308	C₂²	C₂³×C₈×C₂₃	1	1	yes	characteristic
309	C₂²	C₂²×M₁₆×C₂₃	1	1	yes	characteristic
310	C₂²	C₂₃×#568	1	2	yes	—
311	C₄	—	2	8	no	—
312	C₄	—	2	2	no	—
313	C₄	—	2	2	no	—
314	C₄	—	2	2	no	—
315	C₄	—	4	4	no	—
316	C₄	C₂×C₂₃×C₄⋊C₈	1	4	yes	—
317	C₄	C₂×C₂₃×C₄⋊C₈	1	4	yes	—
318	C₄	C₂₃×#535	1	1	yes	characteristic
319	C₄	C₂₃×#536	1	1	yes	characteristic
320	C₄	C₂₃×#544	1	2	yes	—
321	C₂	—	2	4	no	—
322	C₂	C₂₃×#2317	1	1	yes	characteristic
323	C₂	C₂²×C₂₃×C₄⋊C₈	1	1	yes	characteristic
324	C₂	C₂₃×#2905	1	1	yes	characteristic
325	C₂	C₂₃×#2988	1	2	yes	—
326	C₂	C₂₃×#2989	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₂₃	C₂⁴
commutator	C₂²	C₂³×C₈×C₂₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₃
socle	C₂³×C₂₃	C₂³×C₄
prime radical	C₂⁴×C₂₃	C₂²×C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₂₃×#1939	C₂	semidirect
6. C₂₃×#1842	C₂	semidirect
7. C₂₃×#1831	C₂	semidirect
37. C₂₃×#117	C₈	semidirect
87. C₄⋊C₄×C₂₃	C₂×C₈	semidirect
96. C₄²×C₂₃	C₂×C₈	semidirect
101. #21972	C₂₃	direct (N × H)
120. C₂×C₄×C₂₃	C₄⋊C₈	semidirect
141. #1939	C₂×C₂₃	semidirect
143. #1842	C₂×C₂₃	semidirect
144. #1831	C₂×C₂₃	semidirect
200. #117	C₈×C₂₃	semidirect
224. C₂₃	#21972	direct (N × H)
251. C₄⋊C₄	C₂×C₈×C₂₃	semidirect
260. C₄²	C₂×C₈×C₂₃	semidirect
283. C₂×C₄	C₂₃×C₄⋊C₈	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₂₃×#431	2
C₂²×C₂₃×C₄⋊C₈	2
C₄×C₂₃×#117	2
C₂₃×#1939	2
C₂₃×#1850	2
C₂₃×#1842	2
C₂₃×#1831	2
#21972	23

Subgroups — C23×#21972 #19169598

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#21972 #19169598