Subgroups — C₂₃×#22682 #19170308

Order 5888.

1062 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×D₈×C₂₃	C₂	1	2	yes	maximal
2	C₂×C₄×D₈×C₂₃	C₂	1	1	yes	maximal, characteristic
3	C₂₃×#2349	C₂	1	2	yes	maximal, complemented
4	C₂₃×#1942	C₂	1	2	yes	maximal, complemented
5	C₂₃×#1864	C₂	1	4	yes	maximal, complemented
6	C₂₃×#1846	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#1804	C₂	1	2	yes	maximal, complemented
8	C₈×C₄⋊C₄×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×D₈×C₂₃	C₂²	1	1	yes	characteristic
10	C₂×C₄×D₄×C₂₃	C₂²	1	4	yes	—
11	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	—
12	C₄×D₈×C₂₃	—	2	8	no	—
13	C₄×D₈×C₂₃	C₄	1	8	yes	complemented
14	C₂×C₂₃×#107	C₂²	1	2	yes	—
15	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic
16	C₂×C₂₃×#106	C₂²	1	2	yes	—
17	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
18	C₂×C₂₃×#102	C₂²	1	4	yes	—
19	C₂×C₂₃×#102	C₂²	1	2	yes	—
20	C₂×C₄×C₈×C₂₃	C₂²	1	2	yes	—
21	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
22	C₂₃×#389	C₂²	1	4	yes	—
23	C₂₃×#385	—	2	4	no	—
24	C₂₃×#382	C₂²	1	2	yes	—
25	C₂₃×#380	—	2	2	no	—
26	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
27	C₂×C₂₃×#95	—	2	2	no	—
28	C₂₃×#340	C₂²	1	4	yes	—
29	C₂₃×#336	C₂²	1	2	yes	—
30	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
31	C₂³×C₄×C₂₃	—	2	2	no	—
32	C₂³×C₄×C₂₃	—	2	4	no	—
33	C₂×D₈×C₂₃	C₂×C₄	1	4	yes	—
34	C₂×D₈×C₂₃	D₄	1	4	yes	—
35	C₂×D₈×C₂₃	Q₈	1	4	yes	—
36	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
37	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
38	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
39	C₄×D₄×C₂₃	—	2	8	no	—
40	C₄×D₄×C₂₃	—	2	4	no	—
41	C₄×D₄×C₂₃	—	4	4	no	—
42	C₄×D₄×C₂₃	C₂×C₄	1	8	yes	complemented
43	C₂×C₄⋊C₄×C₂₃	—	2	4	no	—
44	C₂×C₄⋊C₄×C₂₃	D₄	1	2	yes	—
45	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
46	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
47	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
48	C₂×C₂²⋊C₄×C₂₃	—	2	4	no	—
49	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
50	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
51	C₂₃×#107	—	2	4	no	—
52	C₂₃×#107	C₂×C₄	1	4	yes	complemented
53	C₂₃×#106	—	4	2	no	—
54	C₂₃×C₄⋊C₈	—	2	2	no	—
55	C₂₃×#102	—	2	8	no	—
56	C₂₃×#102	C₂×C₄	1	8	yes	complemented
57	C₄×C₈×C₂₃	—	2	4	no	—
58	C₄×C₈×C₂₃	C₂×C₄	1	4	yes	complemented
59	C₂₃×#95	—	2	2	no	—
60	C₂₃×#95	—	2	4	no	—
61	C₂₃×#95	—	2	2	no	—
62	C₂₃×#95	D₄	1	1	yes	characteristic
63	C₂₃×#95	D₄	1	1	yes	characteristic
64	C₂⁴×C₂₃	—	2	2	no	—
65	C₂×D₄×C₂₃	—	2	2	no	—
66	C₂×D₄×C₂₃	—	2	2	no	—
67	C₂×D₄×C₂₃	—	2	2	no	—
68	C₂×D₄×C₂₃	C₂²×C₄	1	4	yes	—
69	C₂×D₄×C₂₃	C₂×D₄	1	4	yes	—
70	C₂×D₄×C₂₃	C₂×Q₈	1	4	yes	—
71	C₂²×C₄×C₂₃	—	2	2	no	—
72	C₂²×C₄×C₂₃	—	2	8	no	—
73	C₂²×C₄×C₂₃	—	2	4	no	—
74	C₂²×C₄×C₂₃	—	4	8	no	—
75	C₂²×C₄×C₂₃	—	4	8	no	—
76	C₂²×C₄×C₂₃	—	8	4	no	—
77	C₂²×C₄×C₂₃	—	8	4	no	—
78	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
79	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
80	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
81	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
82	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
83	D₈×C₂₃	C₄⋊C₄	1	16	yes	complemented
84	C₂×C₈×C₂₃	—	2	1	no	—
85	C₂×C₈×C₂₃	—	2	1	no	—
86	C₂×C₈×C₂₃	—	2	2	no	—
87	C₂×C₈×C₂₃	—	2	2	no	—
88	C₂×C₈×C₂₃	—	2	2	no	—
89	C₂×C₈×C₂₃	C₂²×C₄	1	2	yes	—
90	C₂×C₈×C₂₃	C₂²×C₄	1	2	yes	—
91	C₂×C₈×C₂₃	C₂×D₄	1	2	yes	—
92	C₂×C₈×C₂₃	C₂×Q₈	1	2	yes	—
93	C₄⋊C₄×C₂₃	—	2	4	no	—
94	C₄⋊C₄×C₂₃	—	2	2	no	—
95	C₄⋊C₄×C₂₃	—	2	4	no	—
96	C₄⋊C₄×C₂₃	—	2	4	no	—
97	C₄⋊C₄×C₂₃	—	8	4	no	—
98	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
99	C₂²⋊C₄×C₂₃	—	2	8	no	—
100	C₂²⋊C₄×C₂₃	—	4	8	no	—
101	C₄²×C₂₃	—	2	2	no	—
102	C₄²×C₂₃	—	2	2	no	—
103	C₄²×C₂₃	C₂²×C₄	1	2	yes	—
104	C₄²×C₂₃	#41	1	2	yes	—
105	#22682	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
106	C₂³×C₂₃	—	2	4	no	—
107	C₂³×C₂₃	—	2	4	no	—
108	C₂³×C₂₃	—	2	4	no	—
109	C₂³×C₂₃	—	4	4	no	—
110	C₂³×C₂₃	—	4	4	no	—
111	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
112	D₄×C₂₃	—	2	4	no	—
113	D₄×C₂₃	—	2	4	no	—
114	D₄×C₂₃	—	2	4	no	—
115	D₄×C₂₃	C₂×C₄⋊C₄	1	8	yes	—
116	C₂×C₄×C₂₃	—	2	2	no	—
117	C₂×C₄×C₂₃	—	2	2	no	—
118	C₂×C₄×C₂₃	—	2	2	no	—
119	C₂×C₄×C₂₃	—	2	2	no	—
120	C₂×C₄×C₂₃	—	2	4	no	—
121	C₂×C₄×C₂₃	—	2	2	no	—
122	C₂×C₄×C₂₃	—	2	2	no	—
123	C₂×C₄×C₂₃	—	2	2	no	—
124	C₂×C₄×C₂₃	—	4	4	no	—
125	C₂×C₄×C₂₃	—	4	4	no	—
126	C₂×C₄×C₂₃	—	4	4	no	—
127	C₂×C₄×C₂₃	—	4	4	no	—
128	C₂×C₄×C₂₃	—	8	8	no	—
129	C₂×C₄×C₂₃	—	8	16	no	—
130	C₂×C₄×C₂₃	C₄×D₄	1	2	yes	—
131	C₂×C₄×C₂₃	C₄×D₄	1	2	yes	—
132	C₂×C₄×C₂₃	#135	1	4	yes	—
133	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
134	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
135	C₂×C₄×C₂₃	C₂²×Q₈	1	1	yes	characteristic
136	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
137	C₂×C₄×C₂₃	H(5,𝔽₂)	1	1	yes	characteristic
138	C₂×C₄×C₂₃	2₋¹⁺⁴	1	1	yes	characteristic
139	C₈×C₂₃	—	2	2	no	—
140	C₈×C₂₃	—	4	2	no	—
141	C₈×C₂₃	C₂×C₄⋊C₄	1	4	yes	—
142	C₂×C₄×D₈	C₂×C₂₃	1	2	yes	—
143	C₂×C₄×D₈	C₂×C₂₃	1	1	yes	characteristic
144	#2349	C₂×C₂₃	1	2	yes	complemented
145	#1942	C₂×C₂₃	1	2	yes	complemented
146	#1864	C₂×C₂₃	1	4	yes	complemented
147	#1846	C₂×C₂₃	1	1	yes	characteristic, complemented
148	#1804	C₂×C₂₃	1	2	yes	complemented
149	C₈×C₄⋊C₄	C₂×C₂₃	1	1	yes	characteristic, complemented
150	C₂²×C₂₃	—	2	8	no	—
151	C₂²×C₂₃	—	4	8	no	—
152	C₂²×C₂₃	—	4	4	no	—
153	C₂²×C₂₃	—	4	4	no	—
154	C₂²×C₂₃	—	4	8	no	—
155	C₂²×C₂₃	C₂×C₄×D₄	1	1	yes	characteristic
156	C₂²×C₂₃	D₄²	1	1	yes	characteristic
157	C₂²×C₂₃	D₄×Q₈	1	1	yes	characteristic
158	C₂²×C₂₃	C₂×#135	1	2	yes	—
159	C₂²×C₂₃	#576	1	2	yes	—
160	C₄×C₂₃	—	2	2	no	—
161	C₄×C₂₃	—	2	2	no	—
162	C₄×C₂₃	—	2	4	no	—
163	C₄×C₂₃	—	4	4	no	—
164	C₄×C₂₃	—	4	2	no	—
165	C₄×C₂₃	—	8	4	no	—
166	C₄×C₂₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
167	C₄×C₂₃	#520	1	1	yes	characteristic
168	C₄×C₂₃	#547	1	1	yes	characteristic
169	C₄×C₂₃	#554	1	1	yes	characteristic
170	C₂²×D₈	C₂²×C₂₃	1	1	yes	characteristic
171	C₂×C₄×D₄	C₂²×C₂₃	1	4	yes	—
172	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	—
173	C₄×D₈	—	2	8	no	—
174	C₄×D₈	C₄×C₂₃	1	8	yes	complemented
175	C₂×#107	C₂²×C₂₃	1	2	yes	—
176	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic
177	C₂×#106	C₂²×C₂₃	1	2	yes	—
178	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
179	C₂×#102	C₂²×C₂₃	1	4	yes	—
180	C₂×#102	C₂²×C₂₃	1	2	yes	—
181	C₂×C₄×C₈	C₂²×C₂₃	1	2	yes	—
182	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
183	#389	C₂²×C₂₃	1	4	yes	—
184	#385	—	2	4	no	—
185	#382	C₂²×C₂₃	1	2	yes	—
186	#380	—	2	2	no	—
187	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
188	C₂×#95	—	2	2	no	—
189	#340	C₂²×C₂₃	1	4	yes	—
190	#336	C₂²×C₂₃	1	2	yes	—
191	C₂×C₂₃	—	4	8	no	—
192	C₂×C₂₃	D₄×C₄⋊C₄	1	1	yes	characteristic
193	C₂×C₂₃	C₄×#135	1	1	yes	characteristic
194	C₂×C₂₃	#2948	1	1	yes	characteristic
195	C₂×C₂₃	#3280	1	2	yes	—
196	C₂×C₂₃	#3380	1	2	yes	—
197	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
198	C₂³×C₄	—	2	2	no	—
199	C₂³×C₄	—	2	4	no	—
200	C₂×D₈	C₂×C₄×C₂₃	1	4	yes	—
201	C₂×D₈	D₄×C₂₃	1	4	yes	—
202	C₂×D₈	Q₈×C₂₃	1	4	yes	—
203	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
204	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
205	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
206	C₄×D₄	—	2	8	no	—
207	C₄×D₄	—	2	4	no	—
208	C₄×D₄	—	4	4	no	—
209	C₄×D₄	C₂×C₄×C₂₃	1	8	yes	complemented
210	C₂×C₄⋊C₄	—	2	4	no	—
211	C₂×C₄⋊C₄	D₄×C₂₃	1	2	yes	—
212	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
213	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
214	C₂×C₂²⋊C₄	—	2	2	no	—
215	C₂×C₂²⋊C₄	—	2	4	no	—
216	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
217	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
218	#107	—	2	4	no	—
219	#107	C₂×C₄×C₂₃	1	4	yes	complemented
220	#106	—	4	2	no	—
221	C₄⋊C₈	—	2	2	no	—
222	#102	—	2	8	no	—
223	#102	C₂×C₄×C₂₃	1	8	yes	complemented
224	C₄×C₈	—	2	4	no	—
225	C₄×C₈	C₂×C₄×C₂₃	1	4	yes	complemented
226	#95	—	2	2	no	—
227	#95	—	2	4	no	—
228	#95	—	2	2	no	—
229	#95	D₄×C₂₃	1	1	yes	characteristic
230	#95	D₄×C₂₃	1	1	yes	characteristic
231	C₂₃	#22682	1	1	yes	characteristic, direct product factor, Sylow
232	C₂⁴	—	2	2	no	—
233	C₂×D₄	—	2	2	no	—
234	C₂×D₄	—	2	2	no	—
235	C₂×D₄	—	2	2	no	—
236	C₂×D₄	C₂²×C₄×C₂₃	1	4	yes	—
237	C₂×D₄	C₂×D₄×C₂₃	1	4	yes	—
238	C₂×D₄	C₂×Q₈×C₂₃	1	4	yes	—
239	C₂²×C₄	—	2	2	no	—
240	C₂²×C₄	—	2	8	no	—
241	C₂²×C₄	—	2	4	no	—
242	C₂²×C₄	—	4	8	no	—
243	C₂²×C₄	—	4	8	no	—
244	C₂²×C₄	—	8	4	no	—
245	C₂²×C₄	—	8	4	no	—
246	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
247	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
248	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
249	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
250	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
251	D₈	C₄⋊C₄×C₂₃	1	16	yes	complemented
252	C₂×C₈	—	2	1	no	—
253	C₂×C₈	—	2	1	no	—
254	C₂×C₈	—	2	2	no	—
255	C₂×C₈	—	2	2	no	—
256	C₂×C₈	—	2	2	no	—
257	C₂×C₈	C₂²×C₄×C₂₃	1	2	yes	—
258	C₂×C₈	C₂²×C₄×C₂₃	1	2	yes	—
259	C₂×C₈	C₂×D₄×C₂₃	1	2	yes	—
260	C₂×C₈	C₂×Q₈×C₂₃	1	2	yes	—
261	C₄⋊C₄	—	2	4	no	—
262	C₄⋊C₄	—	2	2	no	—
263	C₄⋊C₄	—	2	4	no	—
264	C₄⋊C₄	—	2	4	no	—
265	C₄⋊C₄	—	8	4	no	—
266	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
267	C₂²⋊C₄	—	2	8	no	—
268	C₂²⋊C₄	—	4	8	no	—
269	C₄²	—	2	2	no	—
270	C₄²	—	2	2	no	—
271	C₄²	C₂²×C₄×C₂₃	1	2	yes	—
272	C₄²	#41×C₂₃	1	2	yes	—
273	C₂³	—	2	4	no	—
274	C₂³	—	2	4	no	—
275	C₂³	—	2	4	no	—
276	C₂³	—	4	4	no	—
277	C₂³	—	4	4	no	—
278	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
279	D₄	—	2	4	no	—
280	D₄	—	2	4	no	—
281	D₄	—	2	4	no	—
282	D₄	C₂×C₄⋊C₄×C₂₃	1	8	yes	—
283	C₂×C₄	—	2	2	no	—
284	C₂×C₄	—	2	2	no	—
285	C₂×C₄	—	2	2	no	—
286	C₂×C₄	—	2	2	no	—
287	C₂×C₄	—	2	2	no	—
288	C₂×C₄	—	2	2	no	—
289	C₂×C₄	—	2	4	no	—
290	C₂×C₄	—	2	2	no	—
291	C₂×C₄	—	4	4	no	—
292	C₂×C₄	—	4	4	no	—
293	C₂×C₄	—	4	4	no	—
294	C₂×C₄	—	4	4	no	—
295	C₂×C₄	—	8	8	no	—
296	C₂×C₄	—	8	16	no	—
297	C₂×C₄	C₄×D₄×C₂₃	1	2	yes	—
298	C₂×C₄	C₄×D₄×C₂₃	1	2	yes	—
299	C₂×C₄	C₂₃×#135	1	4	yes	—
300	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
301	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
302	C₂×C₄	C₂²×Q₈×C₂₃	1	1	yes	characteristic
303	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
304	C₂×C₄	C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
305	C₂×C₄	C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
306	C₈	—	2	2	no	—
307	C₈	—	4	2	no	—
308	C₈	C₂×C₄⋊C₄×C₂₃	1	4	yes	—
309	C₂²	—	2	8	no	—
310	C₂²	—	4	4	no	—
311	C₂²	—	4	4	no	—
312	C₂²	—	4	8	no	—
313	C₂²	—	4	8	no	—
314	C₂²	C₂×C₄×D₄×C₂₃	1	1	yes	characteristic
315	C₂²	D₄²×C₂₃	1	1	yes	characteristic
316	C₂²	D₄×Q₈×C₂₃	1	1	yes	characteristic
317	C₂²	C₂×C₂₃×#135	1	2	yes	—
318	C₂²	C₂₃×#576	1	2	yes	—
319	C₄	—	2	2	no	—
320	C₄	—	2	2	no	—
321	C₄	—	2	4	no	—
322	C₄	—	4	4	no	—
323	C₄	—	4	2	no	—
324	C₄	—	8	4	no	—
325	C₄	C₂²×C₄⋊C₄×C₂₃	1	1	yes	characteristic
326	C₄	C₂₃×#520	1	1	yes	characteristic
327	C₄	C₂₃×#547	1	1	yes	characteristic
328	C₄	C₂₃×#554	1	1	yes	characteristic
329	C₂	—	4	8	no	—
330	C₂	D₄×C₄⋊C₄×C₂₃	1	1	yes	characteristic
331	C₂	C₄×C₂₃×#135	1	1	yes	characteristic
332	C₂	C₂₃×#2948	1	1	yes	characteristic
333	C₂	C₂₃×#3280	1	2	yes	—
334	C₂	C₂₃×#3380	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₂₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₃
prime radical	C₂²×D₈×C₂₃	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₃ ◁ C₄×C₄⋊C₄×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂₃×#2349	C₂	semidirect
4. C₂₃×#1942	C₂	semidirect
5. C₂₃×#1864	C₂	semidirect
6. C₂₃×#1846	C₂	semidirect
7. C₂₃×#1804	C₂	semidirect
8. C₈×C₄⋊C₄×C₂₃	C₂	semidirect
13. C₄×D₈×C₂₃	C₄	semidirect
42. C₄×D₄×C₂₃	C₂×C₄	semidirect
52. C₂₃×#107	C₂×C₄	semidirect
56. C₂₃×#102	C₂×C₄	semidirect
58. C₄×C₈×C₂₃	C₂×C₄	semidirect
83. D₈×C₂₃	C₄⋊C₄	semidirect
105. #22682	C₂₃	direct (N × H)
144. #2349	C₂×C₂₃	semidirect
145. #1942	C₂×C₂₃	semidirect
146. #1864	C₂×C₂₃	semidirect
147. #1846	C₂×C₂₃	semidirect
148. #1804	C₂×C₂₃	semidirect
149. C₈×C₄⋊C₄	C₂×C₂₃	semidirect
174. C₄×D₈	C₄×C₂₃	semidirect
209. C₄×D₄	C₂×C₄×C₂₃	semidirect
219. #107	C₂×C₄×C₂₃	semidirect
223. #102	C₂×C₄×C₂₃	semidirect
225. C₄×C₈	C₂×C₄×C₂₃	semidirect
231. C₂₃	#22682	direct (N × H)
251. D₈	C₄⋊C₄×C₂₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×D₈×C₂₃	2
C₂₃×#2349	2
C₂₃×#1942	2
C₂₃×#1864	2
C₂₃×#1846	2
C₂₃×#1804	2
C₈×C₄⋊C₄×C₂₃	2
#22682	23

Subgroups — C23×#22682 #19170308

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#22682 #19170308