Subgroups — C₂₃×#20535 #19168161

Order 5888.

1038 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#432	C₂	1	1	yes	maximal, characteristic
2	C₂×C₂₃×#431	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₄⋊C₄×C₂₃	C₂	1	1	yes	maximal, characteristic
4	C₂₃×#1771	C₂	1	4	yes	maximal, complemented
5	C₂₃×#1770	C₂	1	2	yes	maximal, complemented
6	C₈×C₄⋊C₄×C₂₃	C₂	1	2	yes	maximal, complemented
7	C₂₃×#1749	C₂	1	2	yes	maximal
8	C₄×C₂₃×C₂²⋊C₈	C₂	1	2	yes	maximal
9	C₂²×C₄⋊C₄×C₂₃	C₄	1	2	yes	—
10	C₂²×C₄²×C₂₃	C₂²	1	2	yes	—
11	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
12	C₂₃×#432	C₄	1	8	yes	complemented
13	C₂₃×#431	C₄	1	8	yes	complemented
14	C₂×C₂₃×C₄⋊C₈	C₂²	1	2	yes	—
15	C₂×C₂₃×C₄⋊C₈	C₂²	1	2	yes	—
16	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
17	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
18	C₂×C₂₃×C₂²⋊C₈	C₂²	1	2	yes	—
19	C₂×C₂₃×#97	C₂²	1	4	yes	—
20	C₂×C₂₃×#97	C₂²	1	2	yes	—
21	C₂×C₄×C₈×C₂₃	C₂²	1	4	yes	—
22	C₂×C₄×C₈×C₂₃	C₂²	1	2	yes	—
23	C₄×C₄⋊C₄×C₂₃	C₄	1	2	yes	—
24	C₄×C₄⋊C₄×C₂₃	C₄	1	2	yes	—
25	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
26	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
27	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
28	C₂×C₂₃×#95	C₄	1	2	yes	—
29	C₂₃×#336	C₂²	1	4	yes	—
30	C₂₃×#336	C₂²	1	4	yes	—
31	C₂³×C₄×C₂₃	C₂×C₄	1	4	yes	—
32	C₂³×C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
33	C₂³×C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
34	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
35	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
36	C₂²×C₈×C₂₃	C₂³	1	4	yes	—
37	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
38	C₂×C₄⋊C₄×C₂₃	—	2	8	no	—
39	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
40	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	4	yes	—
41	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
42	C₂×C₄²×C₂₃	—	4	4	no	—
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	4	yes	—
47	C₂×C₄²×C₂₃	C₂×C₄	1	4	yes	—
48	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
49	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
50	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
51	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
52	C₂₃×C₄⋊C₈	C₂×C₄	1	8	yes	complemented
53	C₂₃×C₄⋊C₈	C₂×C₄	1	8	yes	complemented
54	C₂₃×C₂²⋊C₈	C₂×C₄	1	4	yes	—
55	C₂₃×C₂²⋊C₈	C₂×C₄	1	4	yes	—
56	C₂₃×C₂²⋊C₈	C₂×C₄	1	8	yes	—
57	C₂₃×#97	—	4	4	no	—
58	C₂₃×#97	C₂×C₄	1	8	yes	complemented
59	C₄×C₈×C₂₃	—	4	4	no	—
60	C₄×C₈×C₂₃	C₂×C₄	1	8	yes	complemented
61	C₂₃×#95	C₂×C₄	1	2	yes	—
62	C₂₃×#95	C₂×C₄	1	4	yes	—
63	C₂₃×#95	C₂×C₄	1	2	yes	—
64	C₂⁴×C₂₃	C₂²×C₄	1	1	yes	characteristic
65	C₂²×C₄×C₂₃	—	2	4	no	—
66	C₂²×C₄×C₂₃	—	2	4	no	—
67	C₂²×C₄×C₂₃	—	2	2	no	—
68	C₂²×C₄×C₂₃	—	2	2	no	—
69	C₂²×C₄×C₂₃	—	2	8	no	—
70	C₂²×C₄×C₂₃	—	2	8	no	—
71	C₂²×C₄×C₂₃	—	4	4	no	—
72	C₂²×C₄×C₂₃	C₄²	1	4	yes	—
73	C₂²×C₄×C₂₃	C₄²	1	4	yes	—
74	C₂²×C₄×C₂₃	C₂²×C₄	1	4	yes	—
75	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
76	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
77	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
78	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
79	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
80	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
81	C₂²×C₄×C₂₃	C₂²×C₄	1	4	yes	—
82	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
83	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
84	C₂×C₈×C₂₃	—	2	2	no	—
85	C₂×C₈×C₂₃	—	2	4	no	—
86	C₂×C₈×C₂₃	—	2	2	no	—
87	C₂×C₈×C₂₃	—	2	2	no	—
88	C₂×C₈×C₂₃	—	2	4	no	—
89	C₂×C₈×C₂₃	—	2	2	no	—
90	C₂×C₈×C₂₃	C₂²×C₄	1	4	yes	—
91	C₂×C₈×C₂₃	C₂²×C₄	1	4	yes	—
92	C₂×C₈×C₂₃	C₂²×C₄	1	8	yes	—
93	C₄⋊C₄×C₂₃	—	2	8	no	—
94	C₄⋊C₄×C₂₃	—	2	4	no	—
95	C₄⋊C₄×C₂₃	M₁₆	1	8	yes	—
96	C₄²×C₂₃	—	2	4	no	—
97	C₄²×C₂₃	—	2	4	no	—
98	C₄²×C₂₃	—	4	4	no	—
99	C₄²×C₂₃	C₄²	1	4	yes	—
100	C₄²×C₂₃	C₄²	1	4	yes	—
101	C₄²×C₂₃	C₂²×C₄	1	2	yes	—
102	C₄²×C₂₃	C₂²×C₄	1	2	yes	—
103	C₄²×C₂₃	C₂²×C₄	1	2	yes	—
104	C₄²×C₂₃	C₂²×C₄	1	2	yes	—
105	#20535	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
106	C₂³×C₂₃	—	2	1	no	—
107	C₂³×C₂₃	—	2	1	no	—
108	C₂³×C₂₃	—	2	2	no	—
109	C₂³×C₂₃	C₂×C₄²	1	2	yes	—
110	C₂³×C₂₃	#131	1	4	yes	—
111	C₂³×C₂₃	C₂³×C₄	1	1	yes	characteristic
112	C₂×C₄×C₂₃	—	2	4	no	—
113	C₂×C₄×C₂₃	—	2	1	no	—
114	C₂×C₄×C₂₃	—	2	1	no	—
115	C₂×C₄×C₂₃	—	2	2	no	—
116	C₂×C₄×C₂₃	—	2	2	no	—
117	C₂×C₄×C₂₃	—	2	2	no	—
118	C₂×C₄×C₂₃	—	2	4	no	—
119	C₂×C₄×C₂₃	—	2	8	no	—
120	C₂×C₄×C₂₃	—	2	4	no	—
121	C₂×C₄×C₂₃	—	2	4	no	—
122	C₂×C₄×C₂₃	—	2	8	no	—
123	C₂×C₄×C₂₃	—	2	4	no	—
124	C₂×C₄×C₂₃	—	2	4	no	—
125	C₂×C₄×C₂₃	—	2	4	no	—
126	C₂×C₄×C₂₃	—	4	16	no	—
127	C₂×C₄×C₂₃	C₂×C₄²	1	2	yes	—
128	C₂×C₄×C₂₃	C₂×C₄²	1	2	yes	—
129	C₂×C₄×C₂₃	C₂×C₄²	1	2	yes	—
130	C₂×C₄×C₂₃	C₂×C₄²	1	2	yes	—
131	C₂×C₄×C₂₃	C₂×C₄²	1	2	yes	—
132	C₂×C₄×C₂₃	C₂×M₁₆	1	8	yes	—
133	C₂×C₄×C₂₃	C₂×M₁₆	1	4	yes	—
134	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
135	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
136	C₂×C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
137	C₂×C₄×C₂₃	2₋¹⁺⁴	1	2	yes	—
138	C₈×C₂₃	—	2	4	no	—
139	C₈×C₂₃	—	2	8	no	—
140	C₈×C₂₃	—	2	4	no	—
141	C₂×#432	C₂×C₂₃	1	1	yes	characteristic
142	C₂×#431	C₂×C₂₃	1	1	yes	characteristic
143	C₂×C₄×C₄⋊C₄	C₂×C₂₃	1	1	yes	characteristic
144	#1771	C₂×C₂₃	1	4	yes	complemented
145	#1770	C₂×C₂₃	1	2	yes	complemented
146	C₈×C₄⋊C₄	C₂×C₂₃	1	2	yes	complemented
147	#1749	C₂×C₂₃	1	2	yes	—
148	C₄×C₂²⋊C₈	C₂×C₂₃	1	2	yes	—
149	C₂²×C₂₃	—	2	2	no	—
150	C₂²×C₂₃	—	2	4	no	—
151	C₂²×C₂₃	—	2	4	no	—
152	C₂²×C₂₃	—	2	2	no	—
153	C₂²×C₂₃	#405	1	4	yes	—
154	C₂²×C₂₃	C₂²×C₄²	1	1	yes	characteristic
155	C₂²×C₂₃	#518	1	1	yes	characteristic
156	C₂²×C₂₃	#519	1	1	yes	characteristic
157	C₂²×C₂₃	C₂²×M₁₆	1	2	yes	—
158	C₂²×C₂₃	C₂×#131	1	2	yes	—
159	C₄×C₂₃	—	2	2	no	—
160	C₄×C₂₃	—	2	2	no	—
161	C₄×C₂₃	—	2	2	no	—
162	C₄×C₂₃	—	2	8	no	—
163	C₄×C₂₃	—	2	2	no	—
164	C₄×C₂₃	—	4	4	no	—
165	C₄×C₂₃	C₄×M₁₆	1	4	yes	—
166	C₄×C₂₃	#520	1	2	yes	—
167	C₄×C₂₃	#520	1	2	yes	—
168	C₂²×C₄⋊C₄	C₄×C₂₃	1	2	yes	—
169	C₂²×C₄²	C₂²×C₂₃	1	2	yes	—
170	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
171	#432	C₄×C₂₃	1	8	yes	complemented
172	#431	C₄×C₂₃	1	8	yes	complemented
173	C₂×C₄⋊C₈	C₂²×C₂₃	1	2	yes	—
174	C₂×C₄⋊C₈	C₂²×C₂₃	1	2	yes	—
175	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
176	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
177	C₂×C₂²⋊C₈	C₂²×C₂₃	1	2	yes	—
178	C₂×#97	C₂²×C₂₃	1	4	yes	—
179	C₂×#97	C₂²×C₂₃	1	2	yes	—
180	C₂×C₄×C₈	C₂²×C₂₃	1	4	yes	—
181	C₂×C₄×C₈	C₂²×C₂₃	1	2	yes	—
182	C₄×C₄⋊C₄	C₄×C₂₃	1	2	yes	—
183	C₄×C₄⋊C₄	C₄×C₂₃	1	2	yes	—
184	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
185	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
186	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
187	C₂×#95	C₄×C₂₃	1	2	yes	—
188	#336	C₂²×C₂₃	1	4	yes	—
189	#336	C₂²×C₂₃	1	4	yes	—
190	C₂×C₂₃	—	2	4	no	—
191	C₂×C₂₃	#2274	1	1	yes	characteristic
192	C₂×C₂₃	C₂×C₄×M₁₆	1	1	yes	characteristic
193	C₂×C₂₃	C₂×#405	1	1	yes	characteristic
194	C₂×C₂₃	#2974	1	2	yes	—
195	C₂×C₂₃	#2984	1	2	yes	—
196	C₂³×C₄	C₂×C₄×C₂₃	1	4	yes	—
197	C₂³×C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
198	C₂³×C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
199	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
200	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
201	C₂²×C₈	C₂³×C₂₃	1	4	yes	—
202	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
203	C₂×C₄⋊C₄	—	2	8	no	—
204	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
205	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	4	yes	—
206	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
207	C₂×C₄²	—	4	4	no	—
208	C₂×C₄²	C₂×C₄×C₂₃	1	4	yes	—
209	C₂×C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic
210	C₂×C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic
211	C₂×C₄²	C₂×C₄×C₂₃	1	4	yes	—
212	C₂×C₄²	C₂×C₄×C₂₃	1	4	yes	—
213	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
214	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
215	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
216	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
217	C₄⋊C₈	C₂×C₄×C₂₃	1	8	yes	complemented
218	C₄⋊C₈	C₂×C₄×C₂₃	1	8	yes	complemented
219	C₂²⋊C₈	C₂×C₄×C₂₃	1	4	yes	—
220	C₂²⋊C₈	C₂×C₄×C₂₃	1	4	yes	—
221	C₂²⋊C₈	C₂×C₄×C₂₃	1	8	yes	—
222	#97	—	4	4	no	—
223	#97	C₂×C₄×C₂₃	1	8	yes	complemented
224	C₄×C₈	—	4	4	no	—
225	C₄×C₈	C₂×C₄×C₂₃	1	8	yes	complemented
226	#95	C₂×C₄×C₂₃	1	2	yes	—
227	#95	C₂×C₄×C₂₃	1	4	yes	—
228	#95	C₂×C₄×C₂₃	1	2	yes	—
229	C₂₃	#20535	1	1	yes	characteristic, direct product factor, Sylow
230	C₂⁴	C₂²×C₄×C₂₃	1	1	yes	characteristic
231	C₂²×C₄	—	2	4	no	—
232	C₂²×C₄	—	2	4	no	—
233	C₂²×C₄	—	2	2	no	—
234	C₂²×C₄	—	2	2	no	—
235	C₂²×C₄	—	2	8	no	—
236	C₂²×C₄	—	2	8	no	—
237	C₂²×C₄	—	4	4	no	—
238	C₂²×C₄	C₄²×C₂₃	1	4	yes	—
239	C₂²×C₄	C₄²×C₂₃	1	4	yes	—
240	C₂²×C₄	C₂²×C₄×C₂₃	1	4	yes	—
241	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
242	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
243	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
244	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
245	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
246	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
247	C₂²×C₄	C₂²×C₄×C₂₃	1	4	yes	—
248	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
249	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
250	C₂×C₈	—	2	2	no	—
251	C₂×C₈	—	2	4	no	—
252	C₂×C₈	—	2	2	no	—
253	C₂×C₈	—	2	2	no	—
254	C₂×C₈	—	2	4	no	—
255	C₂×C₈	—	2	2	no	—
256	C₂×C₈	C₂²×C₄×C₂₃	1	4	yes	—
257	C₂×C₈	C₂²×C₄×C₂₃	1	4	yes	—
258	C₂×C₈	C₂²×C₄×C₂₃	1	8	yes	—
259	C₄⋊C₄	—	2	8	no	—
260	C₄⋊C₄	—	2	4	no	—
261	C₄⋊C₄	M₁₆×C₂₃	1	8	yes	—
262	C₄²	—	2	4	no	—
263	C₄²	—	2	4	no	—
264	C₄²	—	4	4	no	—
265	C₄²	C₄²×C₂₃	1	4	yes	—
266	C₄²	C₄²×C₂₃	1	4	yes	—
267	C₄²	C₂²×C₄×C₂₃	1	2	yes	—
268	C₄²	C₂²×C₄×C₂₃	1	2	yes	—
269	C₄²	C₂²×C₄×C₂₃	1	2	yes	—
270	C₄²	C₂²×C₄×C₂₃	1	2	yes	—
271	C₂³	—	2	2	no	—
272	C₂³	—	2	1	no	—
273	C₂³	—	2	1	no	—
274	C₂³	C₂×C₄²×C₂₃	1	2	yes	—
275	C₂³	C₂₃×#131	1	4	yes	—
276	C₂³	C₂³×C₄×C₂₃	1	1	yes	characteristic
277	C₂×C₄	—	2	2	no	—
278	C₂×C₄	—	2	4	no	—
279	C₂×C₄	—	2	2	no	—
280	C₂×C₄	—	2	2	no	—
281	C₂×C₄	—	2	8	no	—
282	C₂×C₄	—	2	4	no	—
283	C₂×C₄	—	2	1	no	—
284	C₂×C₄	—	2	1	no	—
285	C₂×C₄	—	2	8	no	—
286	C₂×C₄	—	2	4	no	—
287	C₂×C₄	—	2	4	no	—
288	C₂×C₄	—	2	4	no	—
289	C₂×C₄	—	2	4	no	—
290	C₂×C₄	—	2	4	no	—
291	C₂×C₄	—	4	16	no	—
292	C₂×C₄	C₂×C₄²×C₂₃	1	2	yes	—
293	C₂×C₄	C₂×C₄²×C₂₃	1	2	yes	—
294	C₂×C₄	C₂×C₄²×C₂₃	1	2	yes	—
295	C₂×C₄	C₂×C₄²×C₂₃	1	2	yes	—
296	C₂×C₄	C₂×C₄²×C₂₃	1	2	yes	—
297	C₂×C₄	C₂×M₁₆×C₂₃	1	8	yes	—
298	C₂×C₄	C₂×M₁₆×C₂₃	1	4	yes	—
299	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
300	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
301	C₂×C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
302	C₂×C₄	C₂₃×2₋¹⁺⁴	1	2	yes	—
303	C₈	—	2	4	no	—
304	C₈	—	2	8	no	—
305	C₈	—	2	4	no	—
306	C₂²	—	2	4	no	—
307	C₂²	—	2	4	no	—
308	C₂²	—	2	2	no	—
309	C₂²	—	2	2	no	—
310	C₂²	C₂₃×#405	1	4	yes	—
311	C₂²	C₂²×C₄²×C₂₃	1	1	yes	characteristic
312	C₂²	C₂₃×#518	1	1	yes	characteristic
313	C₂²	C₂₃×#519	1	1	yes	characteristic
314	C₂²	C₂²×M₁₆×C₂₃	1	2	yes	—
315	C₂²	C₂×C₂₃×#131	1	2	yes	—
316	C₄	—	2	8	no	—
317	C₄	—	2	2	no	—
318	C₄	—	2	2	no	—
319	C₄	—	2	2	no	—
320	C₄	—	2	2	no	—
321	C₄	—	4	4	no	—
322	C₄	C₄×M₁₆×C₂₃	1	4	yes	—
323	C₄	C₂₃×#520	1	2	yes	—
324	C₄	C₂₃×#520	1	2	yes	—
325	C₂	—	2	4	no	—
326	C₂	C₂₃×#2274	1	1	yes	characteristic
327	C₂	C₂×C₄×M₁₆×C₂₃	1	1	yes	characteristic
328	C₂	C₂×C₂₃×#405	1	1	yes	characteristic
329	C₂	C₂₃×#2974	1	2	yes	—
330	C₂	C₂₃×#2984	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₂₃	C₂⁴
commutator	C₂²	C₂²×C₄²×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×#1771	C₂	semidirect
5. C₂₃×#1770	C₂	semidirect
6. C₈×C₄⋊C₄×C₂₃	C₂	semidirect
12. C₂₃×#432	C₄	semidirect
13. C₂₃×#431	C₄	semidirect
52. C₂₃×C₄⋊C₈	C₂×C₄	semidirect
53. C₂₃×C₄⋊C₈	C₂×C₄	semidirect
58. C₂₃×#97	C₂×C₄	semidirect
60. C₄×C₈×C₂₃	C₂×C₄	semidirect
105. #20535	C₂₃	direct (N × H)
144. #1771	C₂×C₂₃	semidirect
145. #1770	C₂×C₂₃	semidirect
146. C₈×C₄⋊C₄	C₂×C₂₃	semidirect
171. #432	C₄×C₂₃	semidirect
172. #431	C₄×C₂₃	semidirect
217. C₄⋊C₈	C₂×C₄×C₂₃	semidirect
218. C₄⋊C₈	C₂×C₄×C₂₃	semidirect
223. #97	C₂×C₄×C₂₃	semidirect
225. C₄×C₈	C₂×C₄×C₂₃	semidirect
229. C₂₃	#20535	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₂₃×#432	2
C₂×C₂₃×#431	2
C₂×C₄×C₄⋊C₄×C₂₃	2
C₂₃×#1771	2
C₂₃×#1770	2
C₈×C₄⋊C₄×C₂₃	2
C₂₃×#1749	2
C₄×C₂₃×C₂²⋊C₈	2
#20535	23

Subgroups — C23×#20535 #19168161

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#20535 #19168161