Subgroups — C₂₃×#20546 #19168172

Order 5888.

1006 conjugacy classes of subgroups.

The subgroup lattice has 322 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	C₂²×C₂₃×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
3	C₄×C₂₃×#117	C₂	1	1	yes	maximal, characteristic
4	C₂₃×#1771	C₂	1	4	yes	maximal, complemented
5	C₂₃×#1767	C₂	1	2	yes	maximal, complemented
6	C₄×C₂₃×C₄⋊C₈	C₂	1	2	yes	maximal, complemented
7	C₂₃×#1752	C₂	1	2	yes	maximal
8	C₈×C₂²⋊C₄×C₂₃	C₂	1	2	yes	maximal
9	C₂³×C₈×C₂₃	C₂²	1	2	yes	—
10	C₂×C₂₃×#117	C₄	1	2	yes	—
11	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
12	C₂₃×#432	C₄	1	8	yes	complemented
13	C₂×C₂₃×C₄⋊C₈	C₄	1	8	yes	complemented
14	C₂×C₂₃×C₄⋊C₈	C₂²	1	2	yes	—
15	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
16	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
17	C₂×C₂₃×C₄⋊C₈	C₂²	1	2	yes	—
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	C₄×C₄⋊C₄×C₂₃	C₄	1	2	yes	—
23	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
24	C₄×C₂²⋊C₄×C₂₃	C₄	1	2	yes	—
25	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
26	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
27	C₂₃×#376	C₄	1	2	yes	—
28	C₄³×C₂₃	C₂²	1	2	yes	—
29	C₂₃×#336	C₂²	1	4	yes	—
30	C₂₃×#336	C₂²	1	4	yes	—
31	C₂³×C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
32	C₂³×C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
33	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
34	C₂²×C₈×C₂₃	—	4	4	no	—
35	C₂²×C₈×C₂₃	C₂×C₄	1	8	yes	—
36	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
37	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
38	C₂²×C₈×C₂₃	C₂³	1	4	yes	—
39	C₂₃×#117	—	2	8	no	—
40	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	4	yes	—
41	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
42	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
43	C₂×C₄²×C₂₃	C₂×C₄	1	4	yes	—
44	C₂×C₄²×C₂₃	C₂×C₄	1	4	yes	—
45	C₂×C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
46	C₂×C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
47	C₂×C₄²×C₂₃	C₂×C₄	1	4	yes	—
48	C₂×C₄²×C₂₃	C₂×C₄	1	4	yes	—
49	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
50	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
51	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
52	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
53	C₂₃×C₄⋊C₈	C₂×C₄	1	4	yes	—
54	C₂₃×C₄⋊C₈	C₂×C₄	1	4	yes	—
55	C₂₃×C₄⋊C₈	C₂×C₄	1	8	yes	—
56	C₂₃×C₄⋊C₈	C₂×C₄	1	8	yes	—
57	C₂₃×C₂²⋊C₈	C₂×C₄	1	8	yes	—
58	C₂₃×#97	—	4	4	no	—
59	C₂₃×#97	C₂×C₄	1	8	yes	—
60	C₄×C₈×C₂₃	—	4	4	no	—
61	C₂₃×#95	C₂×C₄	1	4	yes	—
62	C₂₃×#95	C₂×C₄	1	2	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	C₄²	1	4	yes	—
70	C₂²×C₄×C₂₃	C₄²	1	4	yes	—
71	C₂²×C₄×C₂₃	C₂²×C₄	1	4	yes	—
72	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
73	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
74	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
75	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
76	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
77	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
78	C₂²×C₄×C₂₃	C₂²×C₄	1	4	yes	—
79	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
80	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
81	C₂×C₈×C₂₃	—	2	4	no	—
82	C₂×C₈×C₂₃	—	2	4	no	—
83	C₂×C₈×C₂₃	—	2	4	no	—
84	C₂×C₈×C₂₃	—	2	4	no	—
85	C₂×C₈×C₂₃	—	4	8	no	—
86	C₂×C₈×C₂₃	C₂²×C₄	1	4	yes	—
87	C₂×C₈×C₂₃	C₂²×C₄	1	4	yes	—
88	C₂×C₈×C₂₃	C₂²×C₄	1	8	yes	—
89	C₄⋊C₄×C₂₃	—	2	8	no	—
90	C₂²⋊C₄×C₂₃	—	2	4	no	—
91	C₂²⋊C₄×C₂₃	M₁₆	1	8	yes	—
92	C₄²×C₂₃	—	2	8	no	—
93	C₄²×C₂₃	—	2	8	no	—
94	C₄²×C₂₃	—	2	2	no	—
95	C₄²×C₂₃	—	2	2	no	—
96	C₄²×C₂₃	—	2	2	no	—
97	C₄²×C₂₃	—	2	2	no	—
98	C₄²×C₂₃	C₄²	1	4	yes	—
99	C₄²×C₂₃	C₄²	1	4	yes	—
100	C₄²×C₂₃	C₂²×C₄	1	2	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	#20546	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
105	C₂³×C₂₃	—	2	2	no	—
106	C₂³×C₂₃	—	2	2	no	—
107	C₂³×C₂₃	C₂×C₄²	1	2	yes	—
108	C₂³×C₂₃	C₂×M₁₆	1	4	yes	—
109	C₂³×C₂₃	C₂³×C₄	1	1	yes	characteristic
110	C₂×C₄×C₂₃	—	2	4	no	—
111	C₂×C₄×C₂₃	—	2	2	no	—
112	C₂×C₄×C₂₃	—	2	2	no	—
113	C₂×C₄×C₂₃	—	2	2	no	—
114	C₂×C₄×C₂₃	—	2	4	no	—
115	C₂×C₄×C₂₃	—	2	2	no	—
116	C₂×C₄×C₂₃	—	2	8	no	—
117	C₂×C₄×C₂₃	—	2	2	no	—
118	C₂×C₄×C₂₃	—	2	2	no	—
119	C₂×C₄×C₂₃	—	2	4	no	—
120	C₂×C₄×C₂₃	—	2	8	no	—
121	C₂×C₄×C₂₃	—	2	4	no	—
122	C₂×C₄×C₂₃	—	2	4	no	—
123	C₂×C₄×C₂₃	—	2	4	no	—
124	C₂×C₄×C₂₃	C₂×C₄²	1	2	yes	—
125	C₂×C₄×C₂₃	C₂×C₄²	1	2	yes	—
126	C₂×C₄×C₂₃	C₂×C₄²	1	2	yes	—
127	C₂×C₄×C₂₃	C₂×C₄²	1	2	yes	—
128	C₂×C₄×C₂₃	C₂×C₄²	1	2	yes	—
129	C₂×C₄×C₂₃	C₂×M₁₆	1	8	yes	—
130	C₂×C₄×C₂₃	#131	1	4	yes	—
131	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
132	C₂×C₄×C₂₃	C₂³×C₄	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	—	2	4	no	—
136	C₈×C₂₃	—	2	4	no	—
137	C₈×C₂₃	—	2	8	no	—
138	C₂×#432	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	#1771	C₂×C₂₃	1	4	yes	complemented
142	#1767	C₂×C₂₃	1	2	yes	complemented
143	C₄×C₄⋊C₈	C₂×C₂₃	1	2	yes	complemented
144	#1752	C₂×C₂₃	1	2	yes	—
145	C₈×C₂²⋊C₄	C₂×C₂₃	1	2	yes	—
146	C₂²×C₂₃	—	2	2	no	—
147	C₂²×C₂₃	—	2	8	no	—
148	C₂²×C₂₃	—	2	2	no	—
149	C₂²×C₂₃	C₄×M₁₆	1	4	yes	—
150	C₂²×C₂₃	C₂²×C₄²	1	1	yes	characteristic
151	C₂²×C₂₃	#520	1	2	yes	—
152	C₂²×C₂₃	C₂²×M₁₆	1	2	yes	—
153	C₂²×C₂₃	C₂×#131	1	2	yes	—
154	C₄×C₂₃	—	2	2	no	—
155	C₄×C₂₃	—	2	2	no	—
156	C₄×C₂₃	—	2	2	no	—
157	C₄×C₂₃	—	2	8	no	—
158	C₄×C₂₃	—	2	2	no	—
159	C₄×C₂₃	—	4	4	no	—
160	C₄×C₂₃	#405	1	4	yes	—
161	C₄×C₂₃	#518	1	1	yes	characteristic
162	C₄×C₂₃	#519	1	1	yes	characteristic
163	C₄×C₂₃	#520	1	2	yes	—
164	C₂³×C₈	C₂²×C₂₃	1	2	yes	—
165	C₂×#117	C₄×C₂₃	1	2	yes	—
166	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
167	#432	C₄×C₂₃	1	8	yes	complemented
168	C₂×C₄⋊C₈	C₄×C₂₃	1	8	yes	complemented
169	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
170	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
171	C₂×C₄⋊C₈	C₂²×C₂₃	1	2	yes	—
172	C₂×C₄⋊C₈	C₂²×C₂₃	1	2	yes	—
173	C₂×C₂²⋊C₈	C₂²×C₂₃	1	2	yes	—
174	C₂×#97	C₂²×C₂₃	1	4	yes	—
175	C₂×#97	C₂²×C₂₃	1	2	yes	—
176	C₂×C₄×C₈	C₂²×C₂₃	1	4	yes	—
177	C₄×C₄⋊C₄	C₄×C₂₃	1	2	yes	—
178	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
179	C₄×C₂²⋊C₄	C₄×C₂₃	1	2	yes	—
180	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
181	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
182	#376	C₄×C₂₃	1	2	yes	—
183	C₄³	C₂²×C₂₃	1	2	yes	—
184	#336	C₂²×C₂₃	1	4	yes	—
185	#336	C₂²×C₂₃	1	4	yes	—
186	C₂×C₂₃	—	2	4	no	—
187	C₂×C₂₃	#2274	1	1	yes	characteristic
188	C₂×C₂₃	C₂×C₄×M₁₆	1	1	yes	characteristic
189	C₂×C₂₃	C₂×#405	1	1	yes	characteristic
190	C₂×C₂₃	#2990	1	4	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	—	4	4	no	—
195	C₂²×C₈	C₂×C₄×C₂₃	1	8	yes	—
196	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
197	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
198	C₂²×C₈	C₂³×C₂₃	1	4	yes	—
199	#117	—	2	8	no	—
200	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	4	yes	—
201	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
202	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
203	C₂×C₄²	C₂×C₄×C₂₃	1	4	yes	—
204	C₂×C₄²	C₂×C₄×C₂₃	1	4	yes	—
205	C₂×C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic
206	C₂×C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic
207	C₂×C₄²	C₂×C₄×C₂₃	1	4	yes	—
208	C₂×C₄²	C₂×C₄×C₂₃	1	4	yes	—
209	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
210	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
211	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
212	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
213	C₄⋊C₈	C₂×C₄×C₂₃	1	4	yes	—
214	C₄⋊C₈	C₂×C₄×C₂₃	1	4	yes	—
215	C₄⋊C₈	C₂×C₄×C₂₃	1	8	yes	—
216	C₄⋊C₈	C₂×C₄×C₂₃	1	8	yes	—
217	C₂²⋊C₈	C₂×C₄×C₂₃	1	8	yes	—
218	#97	—	4	4	no	—
219	#97	C₂×C₄×C₂₃	1	8	yes	—
220	C₄×C₈	—	4	4	no	—
221	#95	C₂×C₄×C₂₃	1	4	yes	—
222	#95	C₂×C₄×C₂₃	1	2	yes	—
223	#95	C₂×C₄×C₂₃	1	2	yes	—
224	C₂₃	#20546	1	1	yes	characteristic, direct product factor, Sylow
225	C₂⁴	C₂²×C₄×C₂₃	1	1	yes	characteristic
226	C₂²×C₄	—	2	4	no	—
227	C₂²×C₄	—	2	4	no	—
228	C₂²×C₄	—	2	2	no	—
229	C₂²×C₄	—	2	2	no	—
230	C₂²×C₄	C₄²×C₂₃	1	4	yes	—
231	C₂²×C₄	C₄²×C₂₃	1	4	yes	—
232	C₂²×C₄	C₂²×C₄×C₂₃	1	4	yes	—
233	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
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	2	yes	—
238	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
239	C₂²×C₄	C₂²×C₄×C₂₃	1	4	yes	—
240	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
241	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
242	C₂×C₈	—	2	4	no	—
243	C₂×C₈	—	2	4	no	—
244	C₂×C₈	—	2	4	no	—
245	C₂×C₈	—	2	4	no	—
246	C₂×C₈	—	4	8	no	—
247	C₂×C₈	C₂²×C₄×C₂₃	1	8	yes	—
248	C₂×C₈	C₂²×C₄×C₂₃	1	4	yes	—
249	C₂×C₈	C₂²×C₄×C₂₃	1	4	yes	—
250	C₄⋊C₄	—	2	8	no	—
251	C₂²⋊C₄	—	2	4	no	—
252	C₂²⋊C₄	M₁₆×C₂₃	1	8	yes	—
253	C₄²	—	2	8	no	—
254	C₄²	—	2	8	no	—
255	C₄²	—	2	2	no	—
256	C₄²	—	2	2	no	—
257	C₄²	—	2	2	no	—
258	C₄²	—	2	2	no	—
259	C₄²	C₄²×C₂₃	1	4	yes	—
260	C₄²	C₄²×C₂₃	1	4	yes	—
261	C₄²	C₂²×C₄×C₂₃	1	2	yes	—
262	C₄²	C₂²×C₄×C₂₃	1	2	yes	—
263	C₄²	C₂²×C₄×C₂₃	1	2	yes	—
264	C₄²	C₂²×C₄×C₂₃	1	2	yes	—
265	C₂³	—	2	2	no	—
266	C₂³	—	2	2	no	—
267	C₂³	C₂×C₄²×C₂₃	1	2	yes	—
268	C₂³	C₂×M₁₆×C₂₃	1	4	yes	—
269	C₂³	C₂³×C₄×C₂₃	1	1	yes	characteristic
270	C₂×C₄	—	2	2	no	—
271	C₂×C₄	—	2	2	no	—
272	C₂×C₄	—	2	4	no	—
273	C₂×C₄	—	2	2	no	—
274	C₂×C₄	—	2	8	no	—
275	C₂×C₄	—	2	4	no	—
276	C₂×C₄	—	2	2	no	—
277	C₂×C₄	—	2	8	no	—
278	C₂×C₄	—	2	2	no	—
279	C₂×C₄	—	2	2	no	—
280	C₂×C₄	—	2	4	no	—
281	C₂×C₄	—	2	4	no	—
282	C₂×C₄	—	2	4	no	—
283	C₂×C₄	—	2	4	no	—
284	C₂×C₄	C₂×C₄²×C₂₃	1	2	yes	—
285	C₂×C₄	C₂×C₄²×C₂₃	1	2	yes	—
286	C₂×C₄	C₂×C₄²×C₂₃	1	2	yes	—
287	C₂×C₄	C₂×C₄²×C₂₃	1	2	yes	—
288	C₂×C₄	C₂×C₄²×C₂₃	1	2	yes	—
289	C₂×C₄	C₂×M₁₆×C₂₃	1	8	yes	—
290	C₂×C₄	C₂₃×#131	1	4	yes	—
291	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
292	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
293	C₂×C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
294	C₂×C₄	C₂₃×2₋¹⁺⁴	1	2	yes	—
295	C₈	—	2	4	no	—
296	C₈	—	2	4	no	—
297	C₈	—	2	8	no	—
298	C₂²	—	2	8	no	—
299	C₂²	—	2	2	no	—
300	C₂²	—	2	2	no	—
301	C₂²	C₄×M₁₆×C₂₃	1	4	yes	—
302	C₂²	C₂²×C₄²×C₂₃	1	1	yes	characteristic
303	C₂²	C₂₃×#520	1	2	yes	—
304	C₂²	C₂²×M₁₆×C₂₃	1	2	yes	—
305	C₂²	C₂×C₂₃×#131	1	2	yes	—
306	C₄	—	2	8	no	—
307	C₄	—	2	2	no	—
308	C₄	—	2	2	no	—
309	C₄	—	2	2	no	—
310	C₄	—	2	2	no	—
311	C₄	—	4	4	no	—
312	C₄	C₂₃×#405	1	4	yes	—
313	C₄	C₂₃×#518	1	1	yes	characteristic
314	C₄	C₂₃×#519	1	1	yes	characteristic
315	C₄	C₂₃×#520	1	2	yes	—
316	C₂	—	2	4	no	—
317	C₂	C₂₃×#2274	1	1	yes	characteristic
318	C₂	C₂×C₄×M₁₆×C₂₃	1	1	yes	characteristic
319	C₂	C₂×C₂₃×#405	1	1	yes	characteristic
320	C₂	C₂₃×#2990	1	4	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×#1767	C₂	semidirect
6. C₄×C₂₃×C₄⋊C₈	C₂	semidirect
12. C₂₃×#432	C₄	semidirect
13. C₂×C₂₃×C₄⋊C₈	C₄	semidirect
104. #20546	C₂₃	direct (N × H)
141. #1771	C₂×C₂₃	semidirect
142. #1767	C₂×C₂₃	semidirect
143. C₄×C₄⋊C₈	C₂×C₂₃	semidirect
167. #432	C₄×C₂₃	semidirect
168. C₂×C₄⋊C₈	C₄×C₂₃	semidirect
224. C₂₃	#20546	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
C₂²×C₂₃×C₄⋊C₈	2
C₄×C₂₃×#117	2
C₂₃×#1771	2
C₂₃×#1767	2
C₄×C₂₃×C₄⋊C₈	2
C₂₃×#1752	2
C₈×C₂²⋊C₄×C₂₃	2
#20546	23

Subgroups — C23×#20546 #19168172

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#20546 #19168172