Subgroups — C₂₃×#33631 #19181257

Order 5888.

556 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3164	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₃×#2948	C₂	1	1	yes	maximal, characteristic
3	C₂₃×#2228	C₂	1	2	yes	maximal, complemented
4	C₂₃×#2228	C₂	1	2	yes	maximal, complemented
5	C₂₃×#2226	C₂	1	2	yes	maximal, complemented
6	C₂₃×#2224	C₂	1	2	yes	maximal, complemented
7	C₂₃×#2159	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#2158	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#2151	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#2140	C₂	1	1	yes	maximal, characteristic
11	C₂×C₂₃×#357	C₂	1	1	yes	maximal, characteristic
12	C₂²×D₈×C₂₃	C₂²	1	1	yes	characteristic
13	C₂₃×#544	—	2	1	no	—
14	C₂₃×#518	—	2	1	no	—
15	C₂×C₂₃×M₃₂	C₂²	1	1	yes	characteristic
16	C₂²×C₁₆×C₂₃	C₂²	1	1	yes	characteristic
17	C₂₃×#501	—	2	2	no	—
18	C₂₃×#500	C₂²	1	2	yes	complemented
19	C₂₃×#499	C₂²	1	2	yes	complemented
20	C₂₃×#442	—	2	2	no	—
21	C₄×D₈×C₂₃	C₂²	1	2	yes	—
22	C₄×D₈×C₂₃	C₂²	1	2	yes	—
23	C₂₃×#428	—	2	1	no	—
24	C₂₃×#427	C₂²	1	1	yes	characteristic
25	C₂₃×#427	C₂²	1	1	yes	characteristic
26	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic
27	C₂₃×#418	—	2	1	no	—
28	C₂₃×#405	C₂²	1	1	yes	characteristic
29	C₂₃×#367	C₂²	1	1	yes	characteristic, complemented
30	C₂₃×#367	C₂²	1	1	yes	characteristic, complemented
31	C₂₃×#367	C₂²	1	2	yes	complemented
32	C₂₃×#366	C₂²	1	1	yes	characteristic, complemented
33	C₂₃×#366	C₂²	1	1	yes	characteristic, complemented
34	C₂₃×#366	C₂²	1	2	yes	complemented
35	C₂₃×C₄⋊C₁₆	C₂²	1	2	yes	complemented
36	C₂₃×C₄⋊C₁₆	C₂²	1	2	yes	complemented
37	C₂₃×#357	C₂²	1	2	yes	—
38	C₂₃×#357	C₂²	1	2	yes	—
39	C₂₃×#357	C₂²	1	2	yes	—
40	C₂₃×#357	C₂²	1	2	yes	—
41	C₂²×D₄×C₂₃	—	2	1	no	—
42	C₂×D₈×C₂₃	—	2	1	no	—
43	C₂×D₈×C₂₃	—	2	2	no	—
44	C₂×D₈×C₂₃	Q₈	1	4	yes	complemented
45	C₂×D₈×C₂₃	C₂³	1	2	yes	—
46	C₂×M₁₆×C₂₃	D₄	1	1	yes	characteristic
47	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
48	C₂₃×C₄⋊Q₈	—	2	2	no	—
49	C₂₃×C₄⋊Q₈	—	4	1	no	—
50	C₂₃×#125	—	2	2	no	—
51	C₂₃×#125	—	4	1	no	—
52	C₂₃×C₂²⋊Q₈	—	4	2	no	—
53	C₄×D₄×C₂₃	—	2	2	no	—
54	C₄×D₄×C₂₃	—	2	2	no	—
55	C₄×D₄×C₂₃	—	4	1	no	—
56	C₄×D₄×C₂₃	—	4	1	no	—
57	C₂₃×#117	—	2	1	no	—
58	C₂₃×#117	—	2	1	no	—
59	C₂₃×#117	D₄	1	1	yes	characteristic
60	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
61	C₂×C₂²⋊C₄×C₂₃	—	4	2	no	—
62	C₂₃×M₃₂	—	2	2	no	—
63	C₂×C₁₆×C₂₃	—	2	2	no	—
64	C₂×C₁₆×C₂₃	C₂³	1	1	yes	characteristic
65	C₂×C₁₆×C₂₃	C₂³	1	2	yes	—
66	C₂×C₁₆×C₂₃	C₂³	1	1	yes	characteristic
67	C₂₃×#107	—	2	1	no	—
68	C₂₃×#107	—	2	2	no	—
69	C₂₃×#107	C₂³	1	2	yes	—
70	C₂₃×#107	C₂³	1	1	yes	characteristic
71	C₂₃×#107	C₂³	1	1	yes	characteristic
72	C₂₃×#107	C₂³	1	1	yes	characteristic
73	C₂₃×#107	C₂³	1	1	yes	characteristic
74	C₂₃×#106	—	2	1	no	—
75	C₂₃×#106	—	2	1	no	—
76	C₂₃×#106	—	2	2	no	—
77	C₂₃×#102	—	2	2	no	—
78	C₂₃×#102	—	2	2	no	—
79	C₂₃×#97	D₄	1	2	yes	—
80	C₄×C₈×C₂₃	C₂³	1	2	yes	—
81	C₂⁴×C₂₃	—	4	1	no	—
82	C₂×Q₈×C₂₃	—	4	2	no	—
83	C₂×D₄×C₂₃	—	2	4	no	—
84	C₂×D₄×C₂₃	—	2	2	no	—
85	C₂×D₄×C₂₃	—	4	1	no	—
86	C₂×D₄×C₂₃	—	4	2	no	—
87	C₂²×C₄×C₂₃	—	4	1	no	—
88	C₂²×C₄×C₂₃	—	4	2	no	—
89	C₂²×C₄×C₂₃	—	4	2	no	—
90	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
91	D₈×C₂₃	—	2	4	no	—
92	D₈×C₂₃	—	2	2	no	—
93	D₈×C₂₃	C₂×Q₈	1	4	yes	—
94	M₁₆×C₂₃	—	2	2	no	—
95	C₂×C₈×C₂₃	C₂×D₄	1	2	yes	—
96	C₂×C₈×C₂₃	C₂×D₄	1	1	yes	characteristic
97	C₂×C₈×C₂₃	C₂×Q₈	1	2	yes	—
98	C₂×C₈×C₂₃	#41	1	2	yes	—
99	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
100	C₄⋊C₄×C₂₃	—	2	1	no	—
101	C₄⋊C₄×C₂₃	—	2	1	no	—
102	C₄⋊C₄×C₂₃	—	2	1	no	—
103	C₄⋊C₄×C₂₃	—	2	2	no	—
104	C₄⋊C₄×C₂₃	—	2	1	no	—
105	C₄⋊C₄×C₂₃	—	4	1	no	—
106	C₄⋊C₄×C₂₃	—	4	2	no	—
107	C₄⋊C₄×C₂₃	—	4	2	no	—
108	C₄⋊C₄×C₂₃	—	4	2	no	—
109	C₄⋊C₄×C₂₃	D₈	1	1	yes	characteristic
110	C₄⋊C₄×C₂₃	D₈	1	1	yes	characteristic
111	C₂²⋊C₄×C₂₃	—	4	1	no	—
112	C₂²⋊C₄×C₂₃	—	4	1	no	—
113	C₂²⋊C₄×C₂₃	—	4	2	no	—
114	C₂²⋊C₄×C₂₃	—	4	2	no	—
115	C₂²⋊C₄×C₂₃	D₈	1	2	yes	—
116	C₄²×C₂₃	—	4	1	no	—
117	C₄²×C₂₃	—	4	1	no	—
118	C₄²×C₂₃	C₂×D₄	1	2	yes	—
119	C₁₆×C₂₃	—	2	1	no	—
120	C₁₆×C₂₃	—	2	1	no	—
121	C₁₆×C₂₃	—	2	2	no	—
122	#33631	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
123	C₂³×C₂₃	—	4	2	no	—
124	C₂³×C₂₃	—	4	4	no	—
125	C₂³×C₂₃	—	16	1	no	—
126	C₂³×C₂₃	—	16	1	no	—
127	C₂³×C₂₃	C₂×D₈	1	1	yes	characteristic
128	Q₈×C₂₃	—	16	2	no	—
129	D₄×C₂₃	—	2	4	no	—
130	D₄×C₂₃	—	4	2	no	—
131	D₄×C₂₃	—	4	4	no	—
132	C₂×C₄×C₂₃	—	4	1	no	—
133	C₂×C₄×C₂₃	—	4	1	no	—
134	C₂×C₄×C₂₃	—	4	1	no	—
135	C₂×C₄×C₂₃	—	4	1	no	—
136	C₂×C₄×C₂₃	—	4	2	no	—
137	C₂×C₄×C₂₃	—	16	2	no	—
138	C₂×C₄×C₂₃	—	16	2	no	—
139	C₂×C₄×C₂₃	—	16	1	no	—
140	C₂×C₄×C₂₃	C₂²⋊Q₈	1	2	yes	—
141	C₂×C₄×C₂₃	C₂×D₈	1	2	yes	—
142	C₂×C₄×C₂₃	C₂×D₈	1	2	yes	—
143	C₂×C₄×C₂₃	C₂×D₈	1	1	yes	characteristic
144	C₂×C₄×C₂₃	#137	1	2	yes	—
145	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
146	C₈×C₂₃	—	2	2	no	—
147	C₈×C₂₃	C₂²⋊Q₈	1	2	yes	—
148	C₈×C₂₃	C₂²×Q₈	1	1	yes	characteristic
149	C₈×C₂₃	C₂×#41	1	1	yes	characteristic
150	#3164	C₂×C₂₃	1	1	yes	characteristic, complemented
151	#2948	C₂×C₂₃	1	1	yes	characteristic
152	#2228	C₂×C₂₃	1	2	yes	complemented
153	#2228	C₂×C₂₃	1	2	yes	complemented
154	#2226	C₂×C₂₃	1	2	yes	complemented
155	#2224	C₂×C₂₃	1	2	yes	complemented
156	#2159	C₂×C₂₃	1	1	yes	characteristic, complemented
157	#2158	C₂×C₂₃	1	1	yes	characteristic, complemented
158	#2151	C₂×C₂₃	1	1	yes	characteristic, complemented
159	#2140	C₂×C₂₃	1	1	yes	characteristic
160	C₂×#357	C₂×C₂₃	1	1	yes	characteristic
161	C₂²×C₂₃	—	2	1	no	—
162	C₂²×C₂₃	—	2	1	no	—
163	C₂²×C₂₃	—	4	4	no	—
164	C₂²×C₂₃	—	8	2	no	—
165	C₂²×C₂₃	—	8	2	no	—
166	C₂²×C₂₃	—	16	4	no	—
167	C₂²×C₂₃	#474	1	2	yes	—
168	C₂²×C₂₃	C₂²×D₈	1	1	yes	characteristic
169	C₄×C₂₃	—	2	2	no	—
170	C₄×C₂₃	—	2	2	no	—
171	C₄×C₂₃	—	8	1	no	—
172	C₄×C₂₃	—	8	2	no	—
173	C₄×C₂₃	—	8	1	no	—
174	C₄×C₂₃	—	8	1	no	—
175	C₄×C₂₃	—	8	1	no	—
176	C₄×C₂₃	#474	1	2	yes	—
177	C₄×C₂₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
178	C₄×C₂₃	C₂×#137	1	1	yes	characteristic
179	C₂²×D₈	C₂²×C₂₃	1	1	yes	characteristic
180	#544	—	2	1	no	—
181	#518	—	2	1	no	—
182	C₂×M₃₂	C₂²×C₂₃	1	1	yes	characteristic
183	C₂²×C₁₆	C₂²×C₂₃	1	1	yes	characteristic
184	#501	—	2	2	no	—
185	#500	C₂²×C₂₃	1	2	yes	complemented
186	#499	C₂²×C₂₃	1	2	yes	complemented
187	#442	—	2	2	no	—
188	C₄×D₈	C₂²×C₂₃	1	2	yes	—
189	C₄×D₈	C₂²×C₂₃	1	2	yes	—
190	#428	—	2	1	no	—
191	#427	C₂²×C₂₃	1	1	yes	characteristic
192	#427	C₂²×C₂₃	1	1	yes	characteristic
193	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic
194	#418	—	2	1	no	—
195	#405	C₂²×C₂₃	1	1	yes	characteristic
196	#367	C₂²×C₂₃	1	1	yes	characteristic, complemented
197	#367	C₂²×C₂₃	1	1	yes	characteristic, complemented
198	#367	C₂²×C₂₃	1	2	yes	complemented
199	#366	C₂²×C₂₃	1	1	yes	characteristic, complemented
200	#366	C₂²×C₂₃	1	1	yes	characteristic, complemented
201	#366	C₂²×C₂₃	1	2	yes	complemented
202	C₄⋊C₁₆	C₂²×C₂₃	1	2	yes	complemented
203	C₄⋊C₁₆	C₂²×C₂₃	1	2	yes	complemented
204	#357	C₂²×C₂₃	1	2	yes	—
205	#357	C₂²×C₂₃	1	2	yes	—
206	#357	C₂²×C₂₃	1	2	yes	—
207	#357	C₂²×C₂₃	1	2	yes	—
208	C₂×C₂₃	—	2	2	no	—
209	C₂×C₂₃	—	8	4	no	—
210	C₂×C₂₃	C₂×#474	1	1	yes	characteristic
211	C₂×C₂₃	#3415	1	1	yes	characteristic
212	C₂×C₂₃	#3416	1	1	yes	characteristic
213	C₂²×D₄	—	2	1	no	—
214	C₂×D₈	—	2	1	no	—
215	C₂×D₈	—	2	2	no	—
216	C₂×D₈	Q₈×C₂₃	1	4	yes	complemented
217	C₂×D₈	C₂³×C₂₃	1	2	yes	—
218	C₂×M₁₆	D₄×C₂₃	1	1	yes	characteristic
219	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
220	C₄⋊Q₈	—	2	2	no	—
221	C₄⋊Q₈	—	4	1	no	—
222	#125	—	2	2	no	—
223	#125	—	4	1	no	—
224	C₂²⋊Q₈	—	4	2	no	—
225	C₄×D₄	—	2	2	no	—
226	C₄×D₄	—	2	2	no	—
227	C₄×D₄	—	4	1	no	—
228	C₄×D₄	—	4	1	no	—
229	#117	—	2	1	no	—
230	#117	—	2	1	no	—
231	#117	D₄×C₂₃	1	1	yes	characteristic
232	C₂×C₄⋊C₄	—	2	1	no	—
233	C₂×C₂²⋊C₄	—	4	2	no	—
234	M₃₂	—	2	2	no	—
235	C₂×C₁₆	—	2	2	no	—
236	C₂×C₁₆	C₂³×C₂₃	1	1	yes	characteristic
237	C₂×C₁₆	C₂³×C₂₃	1	2	yes	—
238	C₂×C₁₆	C₂³×C₂₃	1	1	yes	characteristic
239	#107	—	2	1	no	—
240	#107	—	2	2	no	—
241	#107	C₂³×C₂₃	1	2	yes	—
242	#107	C₂³×C₂₃	1	1	yes	characteristic
243	#107	C₂³×C₂₃	1	1	yes	characteristic
244	#107	C₂³×C₂₃	1	1	yes	characteristic
245	#107	C₂³×C₂₃	1	1	yes	characteristic
246	#106	—	2	1	no	—
247	#106	—	2	1	no	—
248	#106	—	2	2	no	—
249	#102	—	2	2	no	—
250	#102	—	2	2	no	—
251	#97	D₄×C₂₃	1	2	yes	—
252	C₄×C₈	C₂³×C₂₃	1	2	yes	—
253	C₂₃	#33631	1	1	yes	characteristic, direct product factor, Sylow
254	C₂⁴	—	4	1	no	—
255	C₂×Q₈	—	4	2	no	—
256	C₂×D₄	—	2	4	no	—
257	C₂×D₄	—	2	2	no	—
258	C₂×D₄	—	4	1	no	—
259	C₂×D₄	—	4	2	no	—
260	C₂²×C₄	—	4	1	no	—
261	C₂²×C₄	—	4	2	no	—
262	C₂²×C₄	—	4	2	no	—
263	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
264	D₈	—	2	4	no	—
265	D₈	—	2	2	no	—
266	D₈	C₂×Q₈×C₂₃	1	4	yes	—
267	M₁₆	—	2	2	no	—
268	C₂×C₈	C₂×D₄×C₂₃	1	2	yes	—
269	C₂×C₈	C₂×D₄×C₂₃	1	1	yes	characteristic
270	C₂×C₈	C₂×Q₈×C₂₃	1	2	yes	—
271	C₂×C₈	#41×C₂₃	1	2	yes	—
272	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
273	C₄⋊C₄	—	2	1	no	—
274	C₄⋊C₄	—	2	1	no	—
275	C₄⋊C₄	—	2	1	no	—
276	C₄⋊C₄	—	2	2	no	—
277	C₄⋊C₄	—	2	1	no	—
278	C₄⋊C₄	—	4	1	no	—
279	C₄⋊C₄	—	4	2	no	—
280	C₄⋊C₄	—	4	2	no	—
281	C₄⋊C₄	—	4	2	no	—
282	C₄⋊C₄	D₈×C₂₃	1	1	yes	characteristic
283	C₄⋊C₄	D₈×C₂₃	1	1	yes	characteristic
284	C₂²⋊C₄	—	4	1	no	—
285	C₂²⋊C₄	—	4	1	no	—
286	C₂²⋊C₄	—	4	2	no	—
287	C₂²⋊C₄	—	4	2	no	—
288	C₂²⋊C₄	D₈×C₂₃	1	2	yes	—
289	C₄²	—	4	1	no	—
290	C₄²	—	4	1	no	—
291	C₄²	C₂×D₄×C₂₃	1	2	yes	—
292	C₁₆	—	2	1	no	—
293	C₁₆	—	2	1	no	—
294	C₁₆	—	2	2	no	—
295	C₂³	—	4	2	no	—
296	C₂³	—	4	4	no	—
297	C₂³	—	16	1	no	—
298	C₂³	—	16	1	no	—
299	C₂³	C₂×D₈×C₂₃	1	1	yes	characteristic
300	Q₈	—	16	2	no	—
301	D₄	—	2	4	no	—
302	D₄	—	4	2	no	—
303	D₄	—	4	4	no	—
304	C₂×C₄	—	4	1	no	—
305	C₂×C₄	—	4	1	no	—
306	C₂×C₄	—	4	1	no	—
307	C₂×C₄	—	4	1	no	—
308	C₂×C₄	—	4	2	no	—
309	C₂×C₄	—	16	2	no	—
310	C₂×C₄	—	16	2	no	—
311	C₂×C₄	—	16	1	no	—
312	C₂×C₄	C₂₃×C₂²⋊Q₈	1	2	yes	—
313	C₂×C₄	C₂×D₈×C₂₃	1	2	yes	—
314	C₂×C₄	C₂×D₈×C₂₃	1	2	yes	—
315	C₂×C₄	C₂×D₈×C₂₃	1	1	yes	characteristic
316	C₂×C₄	C₂₃×#137	1	2	yes	—
317	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
318	C₈	—	2	2	no	—
319	C₈	C₂₃×C₂²⋊Q₈	1	2	yes	—
320	C₈	C₂²×Q₈×C₂₃	1	1	yes	characteristic
321	C₈	C₂×#41×C₂₃	1	1	yes	characteristic
322	C₂²	—	2	1	no	—
323	C₂²	—	2	1	no	—
324	C₂²	—	4	4	no	—
325	C₂²	—	8	2	no	—
326	C₂²	—	8	2	no	—
327	C₂²	—	16	4	no	—
328	C₂²	C₂₃×#474	1	2	yes	—
329	C₂²	C₂²×D₈×C₂₃	1	1	yes	characteristic
330	C₄	—	2	2	no	—
331	C₄	—	2	2	no	—
332	C₄	—	8	1	no	—
333	C₄	—	8	2	no	—
334	C₄	—	8	1	no	—
335	C₄	—	8	1	no	—
336	C₄	—	8	1	no	—
337	C₄	C₂₃×#474	1	2	yes	—
338	C₄	C₂×C₂₃×C₂²⋊Q₈	1	1	yes	characteristic
339	C₄	C₂×C₂₃×#137	1	1	yes	characteristic
340	C₂	—	2	2	no	—
341	C₂	—	8	4	no	—
342	C₂	C₂×C₂₃×#474	1	1	yes	characteristic
343	C₂	C₂₃×#3415	1	1	yes	characteristic
344	C₂	C₂₃×#3416	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₂₃
prime radical	C₂²×D₈×C₂₃	C₂²
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂₃×#117 ◁ C₂₃×#405 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₃×#3164	C₂	semidirect
3. C₂₃×#2228	C₂	semidirect
4. C₂₃×#2228	C₂	semidirect
5. C₂₃×#2226	C₂	semidirect
6. C₂₃×#2224	C₂	semidirect
7. C₂₃×#2159	C₂	semidirect
8. C₂₃×#2158	C₂	semidirect
9. C₂₃×#2151	C₂	semidirect
18. C₂₃×#500	C₂²	semidirect
19. C₂₃×#499	C₂²	semidirect
29. C₂₃×#367	C₂²	semidirect
30. C₂₃×#367	C₂²	semidirect
31. C₂₃×#367	C₂²	semidirect
32. C₂₃×#366	C₂²	semidirect
33. C₂₃×#366	C₂²	semidirect
34. C₂₃×#366	C₂²	semidirect
35. C₂₃×C₄⋊C₁₆	C₂²	semidirect
36. C₂₃×C₄⋊C₁₆	C₂²	semidirect
44. C₂×D₈×C₂₃	Q₈	semidirect
122. #33631	C₂₃	direct (N × H)
150. #3164	C₂×C₂₃	semidirect
152. #2228	C₂×C₂₃	semidirect
153. #2228	C₂×C₂₃	semidirect
154. #2226	C₂×C₂₃	semidirect
155. #2224	C₂×C₂₃	semidirect
156. #2159	C₂×C₂₃	semidirect
157. #2158	C₂×C₂₃	semidirect
158. #2151	C₂×C₂₃	semidirect
185. #500	C₂²×C₂₃	semidirect
186. #499	C₂²×C₂₃	semidirect
196. #367	C₂²×C₂₃	semidirect
197. #367	C₂²×C₂₃	semidirect
198. #367	C₂²×C₂₃	semidirect
199. #366	C₂²×C₂₃	semidirect
200. #366	C₂²×C₂₃	semidirect
201. #366	C₂²×C₂₃	semidirect
202. C₄⋊C₁₆	C₂²×C₂₃	semidirect
203. C₄⋊C₁₆	C₂²×C₂₃	semidirect
216. C₂×D₈	Q₈×C₂₃	semidirect
253. C₂₃	#33631	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×#3164	2
C₂₃×#2948	2
C₂₃×#2228	2
C₂₃×#2226	2
C₂₃×#2224	2
C₂₃×#2159	2
C₂₃×#2158	2
C₂₃×#2151	2
C₂₃×#2140	2
C₂×C₂₃×#357	2
#33631	23

Subgroups — C23×#33631 #19181257

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#33631 #19181257