Subgroups — C₂₃×#33629 #19181255

Order 5888.

574 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#500	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×C₂₃×#135	C₂	1	1	yes	maximal, characteristic
3	C₂₃×#2227	C₂	1	2	yes	maximal, complemented
4	C₂₃×#2226	C₂	1	2	yes	maximal, complemented
5	C₂₃×#2225	C₂	1	2	yes	maximal, complemented
6	C₂₃×#2224	C₂	1	2	yes	maximal, complemented
7	C₂₃×#2159	C₂	1	2	yes	maximal, complemented
8	C₂₃×#2150	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#2139	C₂	1	2	yes	maximal
10	C₂×C₂₃×#135	C₂²	1	1	yes	characteristic
11	C₂×C₂₃×C₄⋊Q₈	—	2	1	no	—
12	C₄×#41×C₂₃	—	2	1	no	—
13	C₂×C₂₃×M₃₂	C₂²	1	2	yes	—
14	C₂₃×#500	—	2	1	no	—
15	C₂₃×#500	—	2	1	no	—
16	C₂₃×#500	C₂²	1	2	yes	—
17	C₂₃×#500	C₂²	1	2	yes	—
18	C₄×Q₁₆×C₂₃	C₂²	1	1	yes	characteristic
19	C₄×Q₁₆×C₂₃	C₂²	1	1	yes	characteristic
20	C₄×SD₁₆×C₂₃	—	2	1	no	—
21	C₄×SD₁₆×C₂₃	—	2	1	no	—
22	C₄×D₈×C₂₃	C₂²	1	1	yes	characteristic
23	C₄×D₈×C₂₃	C₂²	1	1	yes	characteristic
24	C₂₃×#427	C₂²	1	1	yes	characteristic
25	C₂×C₂₃×#107	—	2	1	no	—
26	C₂×C₂₃×#107	C₂²	1	2	yes	—
27	C₂₃×#416	—	2	1	no	—
28	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
29	C₂₃×#367	C₂²	1	4	yes	—
30	C₂₃×#366	C₂²	1	4	yes	—
31	C₂₃×C₄⋊C₁₆	C₂²	1	2	yes	—
32	C₂₃×C₄⋊C₁₆	C₂²	1	2	yes	—
33	C₂₃×#358	C₂²	1	4	yes	—
34	C₂₃×#357	C₂²	1	4	yes	—
35	C₂×#41×C₂₃	—	2	1	no	—
36	C₂²×Q₈×C₂₃	—	4	1	no	—
37	C₂₃×#135	—	2	2	no	—
38	C₂₃×#135	Q₈	1	4	yes	complemented
39	C₂×Q₁₆×C₂₃	C₂³	1	1	yes	characteristic
40	C₂×SD₁₆×C₂₃	—	2	1	no	—
41	C₂×D₈×C₂₃	C₂³	1	1	yes	characteristic
42	C₂²×C₈×C₂₃	D₄	1	1	yes	characteristic
43	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
44	C₂₃×C₄⋊Q₈	—	2	2	no	—
45	C₂₃×C₄⋊Q₈	—	2	2	no	—
46	C₂₃×C₄⋊Q₈	—	4	1	no	—
47	C₂₃×C₄⋊Q₈	—	4	1	no	—
48	C₄×Q₈×C₂₃	—	2	1	no	—
49	C₄×Q₈×C₂₃	—	2	1	no	—
50	C₄×D₄×C₂₃	—	2	1	no	—
51	C₄×D₄×C₂₃	—	2	1	no	—
52	C₄×D₄×C₂₃	—	4	1	no	—
53	C₄×D₄×C₂₃	—	4	1	no	—
54	C₂₃×#117	—	2	1	no	—
55	C₂₃×#117	—	4	1	no	—
56	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
57	C₂×C₄⋊C₄×C₂₃	—	4	1	no	—
58	C₂×C₄²×C₂₃	—	4	1	no	—
59	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
60	C₂₃×M₃₂	—	2	4	no	—
61	C₂×C₁₆×C₂₃	C₂³	1	4	yes	—
62	C₂₃×#107	—	2	2	no	—
63	C₂₃×#107	—	2	2	no	—
64	C₂₃×#107	—	2	2	no	—
65	C₂₃×#107	C₂³	1	4	yes	—
66	C₂₃×#107	C₂³	1	1	yes	characteristic
67	C₂₃×#107	C₂³	1	1	yes	characteristic
68	C₂₃×#106	—	2	1	no	—
69	C₂₃×#103	—	2	1	no	—
70	C₂₃×#103	—	2	1	no	—
71	C₂₃×#102	—	2	1	no	—
72	C₂₃×#102	—	2	1	no	—
73	C₄×C₈×C₂₃	D₄	1	1	yes	characteristic
74	C₄×C₈×C₂₃	D₄	1	1	yes	characteristic
75	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
76	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
77	#41×C₂₃	—	2	4	no	—
78	#41×C₂₃	—	4	2	no	—
79	C₂×Q₈×C₂₃	—	2	1	no	—
80	C₂×Q₈×C₂₃	—	4	2	no	—
81	C₂×Q₈×C₂₃	—	4	2	no	—
82	C₂×Q₈×C₂₃	—	8	4	no	—
83	C₂×D₄×C₂₃	—	2	1	no	—
84	C₂×D₄×C₂₃	—	4	1	no	—
85	C₂²×C₄×C₂₃	—	4	1	no	—
86	C₂²×C₄×C₂₃	—	4	2	no	—
87	C₂²×C₄×C₂₃	—	4	1	no	—
88	C₂²×C₄×C₂₃	—	4	1	no	—
89	C₂²×C₄×C₂₃	D₈	1	1	yes	characteristic
90	C₂²×C₄×C₂₃	D₈	1	1	yes	characteristic
91	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
92	Q₁₆×C₂₃	—	2	1	no	—
93	Q₁₆×C₂₃	C₂×Q₈	1	2	yes	complemented
94	SD₁₆×C₂₃	—	2	4	no	—
95	D₈×C₂₃	—	2	1	no	—
96	D₈×C₂₃	C₂×Q₈	1	2	yes	complemented
97	C₂×C₈×C₂₃	—	2	2	no	—
98	C₂×C₈×C₂₃	C₂×D₄	1	1	yes	characteristic
99	C₂×C₈×C₂₃	C₂×D₄	1	1	yes	characteristic
100	C₂×C₈×C₂₃	C₂×D₄	1	1	yes	characteristic
101	C₂×C₈×C₂₃	C₂×Q₈	1	2	yes	—
102	C₂×C₈×C₂₃	#41	1	2	yes	—
103	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
104	C₄⋊C₄×C₂₃	—	2	1	no	—
105	C₄⋊C₄×C₂₃	—	2	1	no	—
106	C₄⋊C₄×C₂₃	—	2	4	no	—
107	C₄⋊C₄×C₂₃	—	4	2	no	—
108	C₄⋊C₄×C₂₃	—	4	2	no	—
109	C₄⋊C₄×C₂₃	—	4	2	no	—
110	C₄⋊C₄×C₂₃	—	4	1	no	—
111	C₄⋊C₄×C₂₃	—	4	1	no	—
112	C₂²⋊C₄×C₂₃	—	4	1	no	—
113	C₂²⋊C₄×C₂₃	—	4	1	no	—
114	C₂²⋊C₄×C₂₃	—	4	1	no	—
115	C₄²×C₂₃	—	4	1	no	—
116	C₄²×C₂₃	—	4	1	no	—
117	C₄²×C₂₃	—	4	1	no	—
118	C₄²×C₂₃	D₈	1	1	yes	characteristic
119	C₄²×C₂₃	D₈	1	1	yes	characteristic
120	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
121	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
122	C₁₆×C₂₃	—	2	4	no	—
123	#33629	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
124	C₂³×C₂₃	—	4	1	no	—
125	C₂³×C₂₃	C₂×D₈	1	1	yes	characteristic
126	Q₈×C₂₃	—	2	2	no	—
127	Q₈×C₂₃	—	4	1	no	—
128	Q₈×C₂₃	—	8	4	no	—
129	Q₈×C₂₃	—	8	4	no	—
130	D₄×C₂₃	—	2	2	no	—
131	D₄×C₂₃	—	4	4	no	—
132	D₄×C₂₃	—	4	1	no	—
133	C₂×C₄×C₂₃	—	2	2	no	—
134	C₂×C₄×C₂₃	—	2	2	no	—
135	C₂×C₄×C₂₃	—	4	1	no	—
136	C₂×C₄×C₂₃	—	4	4	no	—
137	C₂×C₄×C₂₃	—	4	1	no	—
138	C₂×C₄×C₂₃	—	4	1	no	—
139	C₂×C₄×C₂₃	—	4	4	no	—
140	C₂×C₄×C₂₃	—	8	4	no	—
141	C₂×C₄×C₂₃	—	8	2	no	—
142	C₂×C₄×C₂₃	—	8	2	no	—
143	C₂×C₄×C₂₃	C₂²⋊Q₈	1	2	yes	—
144	C₂×C₄×C₂₃	C₂×D₈	1	1	yes	characteristic
145	C₂×C₄×C₂₃	C₂×D₈	1	1	yes	characteristic
146	C₂×C₄×C₂₃	C₂×D₈	1	1	yes	characteristic
147	C₂×C₄×C₂₃	C₂×D₈	1	1	yes	characteristic
148	C₂×C₄×C₂₃	C₂×D₈	1	1	yes	characteristic
149	C₂×C₄×C₂₃	#137	1	2	yes	—
150	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
151	C₈×C₂₃	—	2	1	no	—
152	C₈×C₂₃	—	2	1	no	—
153	C₈×C₂₃	C₂²⋊Q₈	1	2	yes	—
154	C₈×C₂₃	C₂²×Q₈	1	1	yes	characteristic
155	C₈×C₂₃	C₂×#41	1	1	yes	characteristic
156	C₂×#500	C₂×C₂₃	1	1	yes	characteristic, complemented
157	C₄×#135	C₂×C₂₃	1	1	yes	characteristic
158	#2227	C₂×C₂₃	1	2	yes	complemented
159	#2226	C₂×C₂₃	1	2	yes	complemented
160	#2225	C₂×C₂₃	1	2	yes	complemented
161	#2224	C₂×C₂₃	1	2	yes	complemented
162	#2159	C₂×C₂₃	1	2	yes	complemented
163	#2150	C₂×C₂₃	1	1	yes	characteristic, complemented
164	#2139	C₂×C₂₃	1	2	yes	—
165	C₂²×C₂₃	—	2	1	no	—
166	C₂²×C₂₃	—	2	1	no	—
167	C₂²×C₂₃	—	4	2	no	—
168	C₂²×C₂₃	—	8	1	no	—
169	C₂²×C₂₃	—	8	1	no	—
170	C₂²×C₂₃	#474	1	2	yes	—
171	C₂²×C₂₃	C₂²×D₈	1	1	yes	characteristic
172	C₄×C₂₃	—	2	1	no	—
173	C₄×C₂₃	—	2	1	no	—
174	C₄×C₂₃	—	4	2	no	—
175	C₄×C₂₃	—	8	1	no	—
176	C₄×C₂₃	—	8	4	no	—
177	C₄×C₂₃	—	8	1	no	—
178	C₄×C₂₃	#474	1	2	yes	—
179	C₄×C₂₃	#509	1	2	yes	—
180	C₄×C₂₃	#510	1	2	yes	—
181	C₄×C₂₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
182	C₄×C₂₃	C₂×#137	1	1	yes	characteristic
183	C₂×#135	C₂²×C₂₃	1	1	yes	characteristic
184	C₂×C₄⋊Q₈	—	2	1	no	—
185	C₄×#41	—	2	1	no	—
186	C₂×M₃₂	C₂²×C₂₃	1	2	yes	—
187	#500	—	2	1	no	—
188	#500	—	2	1	no	—
189	#500	C₂²×C₂₃	1	2	yes	—
190	#500	C₂²×C₂₃	1	2	yes	—
191	C₄×Q₁₆	C₂²×C₂₃	1	1	yes	characteristic
192	C₄×Q₁₆	C₂²×C₂₃	1	1	yes	characteristic
193	C₄×SD₁₆	—	2	1	no	—
194	C₄×SD₁₆	—	2	1	no	—
195	C₄×D₈	C₂²×C₂₃	1	1	yes	characteristic
196	C₄×D₈	C₂²×C₂₃	1	1	yes	characteristic
197	#427	C₂²×C₂₃	1	1	yes	characteristic
198	C₂×#107	—	2	1	no	—
199	C₂×#107	C₂²×C₂₃	1	2	yes	—
200	#416	—	2	1	no	—
201	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
202	#367	C₂²×C₂₃	1	4	yes	—
203	#366	C₂²×C₂₃	1	4	yes	—
204	C₄⋊C₁₆	C₂²×C₂₃	1	2	yes	—
205	C₄⋊C₁₆	C₂²×C₂₃	1	2	yes	—
206	#358	C₂²×C₂₃	1	4	yes	—
207	#357	C₂²×C₂₃	1	4	yes	—
208	C₂×C₂₃	—	2	2	no	—
209	C₂×C₂₃	—	8	2	no	—
210	C₂×C₂₃	C₂×#474	1	1	yes	characteristic
211	C₂×C₂₃	C₂×#509	1	1	yes	characteristic
212	C₂×C₂₃	C₂×#510	1	1	yes	characteristic
213	C₂×#41	—	2	1	no	—
214	C₂²×Q₈	—	4	1	no	—
215	#135	—	2	2	no	—
216	#135	Q₈×C₂₃	1	4	yes	complemented
217	C₂×Q₁₆	C₂³×C₂₃	1	1	yes	characteristic
218	C₂×SD₁₆	—	2	1	no	—
219	C₂×D₈	C₂³×C₂₃	1	1	yes	characteristic
220	C₂²×C₈	D₄×C₂₃	1	1	yes	characteristic
221	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
222	C₄⋊Q₈	—	2	2	no	—
223	C₄⋊Q₈	—	2	2	no	—
224	C₄⋊Q₈	—	4	1	no	—
225	C₄⋊Q₈	—	4	1	no	—
226	C₄×Q₈	—	2	1	no	—
227	C₄×Q₈	—	2	1	no	—
228	C₄×D₄	—	2	1	no	—
229	C₄×D₄	—	2	1	no	—
230	C₄×D₄	—	4	1	no	—
231	C₄×D₄	—	4	1	no	—
232	#117	—	2	1	no	—
233	#117	—	4	1	no	—
234	C₂×C₄⋊C₄	—	2	2	no	—
235	C₂×C₄⋊C₄	—	4	1	no	—
236	C₂×C₄²	—	4	1	no	—
237	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
238	M₃₂	—	2	4	no	—
239	C₂×C₁₆	C₂³×C₂₃	1	4	yes	—
240	#107	—	2	2	no	—
241	#107	—	2	2	no	—
242	#107	—	2	2	no	—
243	#107	C₂³×C₂₃	1	4	yes	—
244	#107	C₂³×C₂₃	1	1	yes	characteristic
245	#107	C₂³×C₂₃	1	1	yes	characteristic
246	#106	—	2	1	no	—
247	#103	—	2	1	no	—
248	#103	—	2	1	no	—
249	#102	—	2	1	no	—
250	#102	—	2	1	no	—
251	C₄×C₈	D₄×C₂₃	1	1	yes	characteristic
252	C₄×C₈	D₄×C₂₃	1	1	yes	characteristic
253	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
254	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
255	C₂₃	#33629	1	1	yes	characteristic, direct product factor, Sylow
256	#41	—	2	4	no	—
257	#41	—	4	2	no	—
258	C₂×Q₈	—	2	1	no	—
259	C₂×Q₈	—	4	2	no	—
260	C₂×Q₈	—	4	2	no	—
261	C₂×Q₈	—	8	4	no	—
262	C₂×D₄	—	2	1	no	—
263	C₂×D₄	—	4	1	no	—
264	C₂²×C₄	—	4	1	no	—
265	C₂²×C₄	—	4	2	no	—
266	C₂²×C₄	—	4	1	no	—
267	C₂²×C₄	—	4	1	no	—
268	C₂²×C₄	D₈×C₂₃	1	1	yes	characteristic
269	C₂²×C₄	D₈×C₂₃	1	1	yes	characteristic
270	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
271	Q₁₆	—	2	1	no	—
272	Q₁₆	C₂×Q₈×C₂₃	1	2	yes	complemented
273	SD₁₆	—	2	4	no	—
274	D₈	—	2	1	no	—
275	D₈	C₂×Q₈×C₂₃	1	2	yes	complemented
276	C₂×C₈	—	2	2	no	—
277	C₂×C₈	C₂×D₄×C₂₃	1	1	yes	characteristic
278	C₂×C₈	C₂×D₄×C₂₃	1	1	yes	characteristic
279	C₂×C₈	C₂×D₄×C₂₃	1	1	yes	characteristic
280	C₂×C₈	C₂×Q₈×C₂₃	1	2	yes	—
281	C₂×C₈	#41×C₂₃	1	2	yes	—
282	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
283	C₄⋊C₄	—	2	1	no	—
284	C₄⋊C₄	—	2	1	no	—
285	C₄⋊C₄	—	2	4	no	—
286	C₄⋊C₄	—	4	2	no	—
287	C₄⋊C₄	—	4	2	no	—
288	C₄⋊C₄	—	4	2	no	—
289	C₄⋊C₄	—	4	1	no	—
290	C₄⋊C₄	—	4	1	no	—
291	C₂²⋊C₄	—	4	1	no	—
292	C₂²⋊C₄	—	4	1	no	—
293	C₂²⋊C₄	—	4	1	no	—
294	C₄²	—	4	1	no	—
295	C₄²	—	4	1	no	—
296	C₄²	—	4	1	no	—
297	C₄²	D₈×C₂₃	1	1	yes	characteristic
298	C₄²	D₈×C₂₃	1	1	yes	characteristic
299	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
300	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
301	C₁₆	—	2	4	no	—
302	C₂³	—	4	1	no	—
303	C₂³	C₂×D₈×C₂₃	1	1	yes	characteristic
304	Q₈	—	2	2	no	—
305	Q₈	—	4	1	no	—
306	Q₈	—	8	4	no	—
307	Q₈	—	8	4	no	—
308	D₄	—	2	2	no	—
309	D₄	—	4	4	no	—
310	D₄	—	4	1	no	—
311	C₂×C₄	—	2	2	no	—
312	C₂×C₄	—	2	2	no	—
313	C₂×C₄	—	4	1	no	—
314	C₂×C₄	—	4	4	no	—
315	C₂×C₄	—	4	1	no	—
316	C₂×C₄	—	4	1	no	—
317	C₂×C₄	—	4	4	no	—
318	C₂×C₄	—	8	4	no	—
319	C₂×C₄	—	8	2	no	—
320	C₂×C₄	—	8	2	no	—
321	C₂×C₄	C₂₃×C₂²⋊Q₈	1	2	yes	—
322	C₂×C₄	C₂×D₈×C₂₃	1	1	yes	characteristic
323	C₂×C₄	C₂×D₈×C₂₃	1	1	yes	characteristic
324	C₂×C₄	C₂×D₈×C₂₃	1	1	yes	characteristic
325	C₂×C₄	C₂×D₈×C₂₃	1	1	yes	characteristic
326	C₂×C₄	C₂×D₈×C₂₃	1	1	yes	characteristic
327	C₂×C₄	C₂₃×#137	1	2	yes	—
328	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
329	C₈	—	2	1	no	—
330	C₈	—	2	1	no	—
331	C₈	C₂₃×C₂²⋊Q₈	1	2	yes	—
332	C₈	C₂²×Q₈×C₂₃	1	1	yes	characteristic
333	C₈	C₂×#41×C₂₃	1	1	yes	characteristic
334	C₂²	—	2	1	no	—
335	C₂²	—	2	1	no	—
336	C₂²	—	4	2	no	—
337	C₂²	—	8	1	no	—
338	C₂²	—	8	1	no	—
339	C₂²	C₂₃×#474	1	2	yes	—
340	C₂²	C₂²×D₈×C₂₃	1	1	yes	characteristic
341	C₄	—	2	1	no	—
342	C₄	—	2	1	no	—
343	C₄	—	4	2	no	—
344	C₄	—	8	4	no	—
345	C₄	—	8	1	no	—
346	C₄	—	8	1	no	—
347	C₄	C₂₃×#474	1	2	yes	—
348	C₄	C₂₃×#509	1	2	yes	—
349	C₄	C₂₃×#510	1	2	yes	—
350	C₄	C₂×C₂₃×C₂²⋊Q₈	1	1	yes	characteristic
351	C₄	C₂×C₂₃×#137	1	1	yes	characteristic
352	C₂	—	2	2	no	—
353	C₂	—	8	2	no	—
354	C₂	C₂×C₂₃×#474	1	1	yes	characteristic
355	C₂	C₂×C₂₃×#509	1	1	yes	characteristic
356	C₂	C₂×C₂₃×#510	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₂₃
prime radical	C₂×C₂₃×#135	C₂²
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂×C₄²×C₂₃ ◁ C₂×C₄×C₈×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₂₃×#500	C₂	semidirect
3. C₂₃×#2227	C₂	semidirect
4. C₂₃×#2226	C₂	semidirect
5. C₂₃×#2225	C₂	semidirect
6. C₂₃×#2224	C₂	semidirect
7. C₂₃×#2159	C₂	semidirect
8. C₂₃×#2150	C₂	semidirect
38. C₂₃×#135	Q₈	semidirect
93. Q₁₆×C₂₃	C₂×Q₈	semidirect
96. D₈×C₂₃	C₂×Q₈	semidirect
123. #33629	C₂₃	direct (N × H)
156. C₂×#500	C₂×C₂₃	semidirect
158. #2227	C₂×C₂₃	semidirect
159. #2226	C₂×C₂₃	semidirect
160. #2225	C₂×C₂₃	semidirect
161. #2224	C₂×C₂₃	semidirect
162. #2159	C₂×C₂₃	semidirect
163. #2150	C₂×C₂₃	semidirect
216. #135	Q₈×C₂₃	semidirect
255. C₂₃	#33629	direct (N × H)
272. Q₁₆	C₂×Q₈×C₂₃	semidirect
275. D₈	C₂×Q₈×C₂₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₂₃×#500	2
C₄×C₂₃×#135	2
C₂₃×#2227	2
C₂₃×#2226	2
C₂₃×#2225	2
C₂₃×#2224	2
C₂₃×#2159	2
C₂₃×#2150	2
C₂₃×#2139	2
#33629	23

Subgroups — C23×#33629 #19181255

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#33629 #19181255