Subgroups — C₂₃×#18523 #19166149

Order 5888.

946 conjugacy classes of subgroups.

The subgroup lattice has 746 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3475	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#3170	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3101	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#3076	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#1650	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#1647	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#1646	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#1643	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#1638	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#1635	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#1634	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#1632	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#1542	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#1476	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₂₃×D₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₃×#556	C₂²	1	1	yes	characteristic
17	C₂₃×#555	C₂²	1	1	yes	characteristic
18	C₂₃×#554	C₂²	1	1	yes	characteristic
19	C₂₃×#553	—	2	1	no	—
20	C₂₃×#552	—	2	1	no	—
21	C₂₃×#552	—	2	1	no	—
22	C₂₃×#551	—	2	2	no	—
23	C₂₃×#547	C₂²	1	1	yes	characteristic
24	C₂₃×#546	—	2	1	no	—
25	C₂₃×#533	C₂²	1	1	yes	characteristic
26	C₂₃×#533	C₂²	1	1	yes	characteristic
27	C₂₃×#529	—	2	2	no	—
28	C₂₃×#529	—	2	1	no	—
29	C₂₃×#525	—	2	1	no	—
30	C₄×#41×C₂₃	—	2	1	no	—
31	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
32	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
33	C₂×C₂₃×#117	—	2	1	no	—
34	C₂₃×#500	C₂²	1	1	yes	characteristic, complemented
35	C₂₃×#494	C₂²	1	1	yes	characteristic, complemented
36	C₂₃×#487	C₂²	1	1	yes	characteristic, complemented
37	C₂₃×#487	C₂²	1	1	yes	characteristic, complemented
38	C₂₃×#483	—	2	1	no	—
39	C₂₃×#479	—	2	1	no	—
40	C₂₃×#478	—	2	1	no	—
41	C₂₃×#477	C₂²	1	1	yes	characteristic, complemented
42	C₂₃×#476	C₂²	1	1	yes	characteristic
43	C₂₃×#476	C₂²	1	1	yes	characteristic
44	C₂₃×#476	C₂²	1	1	yes	characteristic, complemented
45	C₂₃×#475	C₂²	1	1	yes	characteristic, complemented
46	C₂₃×#474	C₂²	1	1	yes	characteristic, complemented
47	C₂₃×#467	—	2	2	no	—
48	C₂₃×#461	C₂²	1	1	yes	characteristic
49	C₂₃×#461	C₂²	1	1	yes	characteristic
50	C₂₃×#450	—	2	1	no	—
51	C₄×Q₁₆×C₂₃	—	2	2	no	—
52	C₄×SD₁₆×C₂₃	—	2	1	no	—
53	C₄×SD₁₆×C₂₃	—	2	1	no	—
54	C₂₃×#431	C₂²	1	1	yes	characteristic
55	C₂₃×#427	—	2	1	no	—
56	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
57	C₂₃×#416	—	2	1	no	—
58	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
59	C₂₃×#333	C₂²	1	1	yes	characteristic, complemented
60	C₂₃×#333	C₂²	1	1	yes	characteristic, complemented
61	C₂₃×#332	C₂²	1	1	yes	characteristic, complemented
62	C₂₃×#332	C₂²	1	1	yes	characteristic, complemented
63	C₂₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic, complemented
64	C₂₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic, complemented
65	C₂₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
66	C₂₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
67	C₂₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
68	C₂₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
69	C₂₃×D₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
70	C₂₃×D₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
71	C₂×#41×C₂₃	—	2	1	no	—
72	C₂×#41×C₂₃	D₄	1	1	yes	characteristic
73	C₂²×D₄×C₂₃	D₄	1	1	yes	characteristic
74	C₂³×C₄×C₂₃	—	2	1	no	—
75	C₂×Q₁₆×C₂₃	—	2	2	no	—
76	C₂×SD₁₆×C₂₃	—	2	1	no	—
77	C₂×SD₁₆×C₂₃	—	2	1	no	—
78	C₂²×C₈×C₂₃	—	2	1	no	—
79	C₂²×C₈×C₂₃	—	2	1	no	—
80	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
81	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
82	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
83	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
84	C₂₃×#126	—	2	2	no	—
85	C₂₃×#126	—	2	2	no	—
86	C₂₃×#126	—	2	2	no	—
87	C₂₃×#125	—	2	2	no	—
88	C₂₃×#125	—	2	1	no	—
89	C₂₃×#125	—	2	1	no	—
90	C₂₃×#125	—	2	1	no	—
91	C₂₃×#124	—	2	2	no	—
92	C₂₃×#124	—	2	1	no	—
93	C₂₃×#123	—	2	2	no	—
94	C₂₃×#123	—	2	2	no	—
95	C₂₃×#123	—	2	2	no	—
96	C₂₃×#123	—	2	2	no	—
97	C₂₃×C₂²⋊Q₈	—	2	2	no	—
98	C₂₃×C₂²⋊Q₈	—	2	1	no	—
99	C₂₃×C₂²⋊Q₈	—	2	1	no	—
100	C₂₃×C₂²⋊Q₈	—	2	1	no	—
101	C₂₃×C₂²⋊Q₈	—	2	1	no	—
102	C₂₃×C₂²⋊Q₈	—	2	1	no	—
103	C₂₃×C₂²⋊Q₈	—	2	1	no	—
104	C₂₃×C₂²⋊Q₈	D₄	1	2	yes	—
105	C₂₃×#121	—	2	2	no	—
106	C₂₃×#121	—	2	1	no	—
107	C₂₃×#121	—	2	1	no	—
108	C₂₃×#121	—	2	1	no	—
109	C₂₃×#120	—	2	2	no	—
110	C₄×Q₈×C₂₃	—	2	1	no	—
111	C₄×Q₈×C₂₃	—	2	1	no	—
112	C₄×Q₈×C₂₃	—	2	1	no	—
113	C₄×Q₈×C₂₃	—	2	1	no	—
114	C₄×Q₈×C₂₃	D₄	1	1	yes	characteristic
115	C₄×Q₈×C₂₃	D₄	1	2	yes	—
116	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
117	C₄×D₄×C₂₃	—	2	2	no	—
118	C₄×D₄×C₂₃	—	2	2	no	—
119	C₄×D₄×C₂₃	—	2	2	no	—
120	C₄×D₄×C₂₃	—	2	1	no	—
121	C₄×D₄×C₂₃	—	2	1	no	—
122	C₄×D₄×C₂₃	—	2	1	no	—
123	C₄×D₄×C₂₃	—	2	1	no	—
124	C₄×D₄×C₂₃	—	2	1	no	—
125	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
126	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
127	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
128	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
129	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
130	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
131	C₂₃×#117	—	2	2	no	—
132	C₂₃×#117	—	2	2	no	—
133	C₂₃×#117	—	2	2	no	—
134	C₂₃×#117	—	2	1	no	—
135	C₂₃×#117	—	2	1	no	—
136	C₂₃×#117	—	2	1	no	—
137	C₂₃×#117	—	2	1	no	—
138	C₂₃×#117	—	2	1	no	—
139	C₂₃×#117	—	2	1	no	—
140	C₂₃×#117	D₄	1	1	yes	characteristic
141	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
142	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
143	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
144	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
145	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
146	C₂×C₄²×C₂₃	—	2	2	no	—
147	C₂×C₄²×C₂₃	—	2	1	no	—
148	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
149	C₂₃×#107	—	2	1	no	—
150	C₂₃×#107	—	2	1	no	—
151	C₂₃×#107	—	2	2	no	—
152	C₂₃×#106	—	2	1	no	—
153	C₂₃×#106	—	2	1	no	—
154	C₂₃×#106	—	2	1	no	—
155	C₂₃×#106	—	2	1	no	—
156	C₂₃×C₄⋊C₈	—	2	1	no	—
157	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
158	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
159	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
160	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
161	C₂₃×#103	—	2	1	no	—
162	C₂₃×#103	—	2	1	no	—
163	C₂₃×#103	—	2	2	no	—
164	C₂₃×#103	—	2	1	no	—
165	C₂₃×#103	—	2	1	no	—
166	C₂₃×#103	—	2	2	no	—
167	C₂₃×#102	—	2	1	no	—
168	C₂₃×#102	—	2	1	no	—
169	C₂₃×#102	—	2	1	no	—
170	C₂₃×#102	—	2	1	no	—
171	C₂₃×C₂²⋊C₈	—	2	1	no	—
172	C₄×C₈×C₂₃	—	2	1	no	—
173	C₄×C₈×C₂₃	—	2	1	no	—
174	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
175	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
176	C₂⁴×C₂₃	—	2	1	no	—
177	#41×C₂₃	—	2	2	no	—
178	#41×C₂₃	—	2	2	no	—
179	#41×C₂₃	—	4	2	no	—
180	#41×C₂₃	—	4	2	no	—
181	C₂×Q₈×C₂₃	—	2	1	no	—
182	C₂×Q₈×C₂₃	—	2	1	no	—
183	C₂×Q₈×C₂₃	—	2	1	no	—
184	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
185	C₂×Q₈×C₂₃	C₂×D₄	1	2	yes	—
186	C₂×D₄×C₂₃	—	2	2	no	—
187	C₂×D₄×C₂₃	—	2	2	no	—
188	C₂×D₄×C₂₃	—	2	1	no	—
189	C₂×D₄×C₂₃	—	2	2	no	—
190	C₂×D₄×C₂₃	—	2	1	no	—
191	C₂×D₄×C₂₃	—	4	1	no	—
192	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
193	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
194	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
195	C₂²×C₄×C₂₃	—	2	2	no	—
196	C₂²×C₄×C₂₃	—	2	1	no	—
197	C₂²×C₄×C₂₃	—	2	2	no	—
198	C₂²×C₄×C₂₃	—	2	1	no	—
199	C₂²×C₄×C₂₃	—	2	1	no	—
200	C₂²×C₄×C₂₃	—	2	1	no	—
201	C₂²×C₄×C₂₃	—	2	1	no	—
202	C₂²×C₄×C₂₃	—	2	1	no	—
203	C₂²×C₄×C₂₃	—	2	1	no	—
204	C₂²×C₄×C₂₃	—	2	1	no	—
205	C₂²×C₄×C₂₃	—	4	2	no	—
206	C₂²×C₄×C₂₃	—	4	2	no	—
207	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
208	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
209	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
210	Q₁₆×C₂₃	—	4	4	no	—
211	SD₁₆×C₂₃	—	4	2	no	—
212	SD₁₆×C₂₃	—	4	2	no	—
213	C₂×C₈×C₂₃	—	2	1	no	—
214	C₂×C₈×C₂₃	—	2	1	no	—
215	C₂×C₈×C₂₃	—	2	1	no	—
216	C₂×C₈×C₂₃	—	2	1	no	—
217	C₂×C₈×C₂₃	—	2	1	no	—
218	C₂×C₈×C₂₃	—	2	1	no	—
219	C₂×C₈×C₂₃	—	4	2	no	—
220	C₂×C₈×C₂₃	—	4	2	no	—
221	C₄⋊C₄×C₂₃	—	2	2	no	—
222	C₄⋊C₄×C₂₃	—	2	2	no	—
223	C₄⋊C₄×C₂₃	—	2	2	no	—
224	C₄⋊C₄×C₂₃	—	2	2	no	—
225	C₄⋊C₄×C₂₃	—	2	1	no	—
226	C₄⋊C₄×C₂₃	—	2	2	no	—
227	C₄⋊C₄×C₂₃	—	2	1	no	—
228	C₄⋊C₄×C₂₃	—	2	2	no	—
229	C₄⋊C₄×C₂₃	—	2	1	no	—
230	C₄⋊C₄×C₂₃	—	2	1	no	—
231	C₄⋊C₄×C₂₃	—	2	1	no	—
232	C₄⋊C₄×C₂₃	—	2	1	no	—
233	C₄⋊C₄×C₂₃	—	2	1	no	—
234	C₄⋊C₄×C₂₃	—	2	1	no	—
235	C₄⋊C₄×C₂₃	—	2	1	no	—
236	C₄⋊C₄×C₂₃	—	2	1	no	—
237	C₄⋊C₄×C₂₃	—	4	1	no	—
238	C₄⋊C₄×C₂₃	—	4	1	no	—
239	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
240	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
241	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
242	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
243	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
244	C₂²⋊C₄×C₂₃	—	2	2	no	—
245	C₂²⋊C₄×C₂₃	—	2	2	no	—
246	C₂²⋊C₄×C₂₃	—	2	2	no	—
247	C₂²⋊C₄×C₂₃	—	2	2	no	—
248	C₂²⋊C₄×C₂₃	—	2	2	no	—
249	C₂²⋊C₄×C₂₃	—	2	2	no	—
250	C₂²⋊C₄×C₂₃	—	2	1	no	—
251	C₂²⋊C₄×C₂₃	—	2	2	no	—
252	C₂²⋊C₄×C₂₃	—	2	1	no	—
253	C₂²⋊C₄×C₂₃	—	2	1	no	—
254	C₂²⋊C₄×C₂₃	—	2	1	no	—
255	C₂²⋊C₄×C₂₃	—	2	1	no	—
256	C₂²⋊C₄×C₂₃	—	2	1	no	—
257	C₂²⋊C₄×C₂₃	—	2	1	no	—
258	C₂²⋊C₄×C₂₃	—	4	1	no	—
259	C₄²×C₂₃	—	2	2	no	—
260	C₄²×C₂₃	—	2	2	no	—
261	C₄²×C₂₃	—	2	1	no	—
262	C₄²×C₂₃	—	2	1	no	—
263	C₄²×C₂₃	—	2	2	no	—
264	C₄²×C₂₃	—	2	1	no	—
265	C₄²×C₂₃	—	4	1	no	—
266	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
267	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
268	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
269	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
270	#18523	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
271	C₂³×C₂₃	—	2	1	no	—
272	C₂³×C₂₃	—	2	1	no	—
273	C₂³×C₂₃	—	2	1	no	—
274	C₂³×C₂₃	—	4	2	no	—
275	C₂³×C₂₃	—	4	2	no	—
276	C₂³×C₂₃	—	8	1	no	—
277	C₂³×C₂₃	#120	1	1	yes	characteristic
278	Q₈×C₂₃	—	2	1	no	—
279	Q₈×C₂₃	—	2	1	no	—
280	Q₈×C₂₃	—	4	2	no	—
281	Q₈×C₂₃	—	4	2	no	—
282	Q₈×C₂₃	—	4	1	no	—
283	Q₈×C₂₃	—	4	1	no	—
284	Q₈×C₂₃	—	4	1	no	—
285	Q₈×C₂₃	—	4	1	no	—
286	D₄×C₂₃	—	2	1	no	—
287	D₄×C₂₃	—	2	1	no	—
288	D₄×C₂₃	—	2	1	no	—
289	D₄×C₂₃	—	2	1	no	—
290	D₄×C₂₃	—	2	1	no	—
291	D₄×C₂₃	—	4	2	no	—
292	D₄×C₂₃	—	4	4	no	—
293	D₄×C₂₃	—	4	2	no	—
294	D₄×C₂₃	—	8	2	no	—
295	D₄×C₂₃	#135	1	2	yes	—
296	C₂×C₄×C₂₃	—	2	1	no	—
297	C₂×C₄×C₂₃	—	2	1	no	—
298	C₂×C₄×C₂₃	—	2	1	no	—
299	C₂×C₄×C₂₃	—	2	1	no	—
300	C₂×C₄×C₂₃	—	2	1	no	—
301	C₂×C₄×C₂₃	—	2	1	no	—
302	C₂×C₄×C₂₃	—	2	2	no	—
303	C₂×C₄×C₂₃	—	2	2	no	—
304	C₂×C₄×C₂₃	—	2	1	no	—
305	C₂×C₄×C₂₃	—	4	1	no	—
306	C₂×C₄×C₂₃	—	4	4	no	—
307	C₂×C₄×C₂₃	—	4	2	no	—
308	C₂×C₄×C₂₃	—	4	1	no	—
309	C₂×C₄×C₂₃	—	4	1	no	—
310	C₂×C₄×C₂₃	—	4	1	no	—
311	C₂×C₄×C₂₃	—	4	1	no	—
312	C₂×C₄×C₂₃	—	4	1	no	—
313	C₂×C₄×C₂₃	—	4	1	no	—
314	C₂×C₄×C₂₃	—	4	2	no	—
315	C₂×C₄×C₂₃	—	4	2	no	—
316	C₂×C₄×C₂₃	—	4	2	no	—
317	C₂×C₄×C₂₃	—	4	1	no	—
318	C₂×C₄×C₂₃	—	4	1	no	—
319	C₂×C₄×C₂₃	—	8	1	no	—
320	C₂×C₄×C₂₃	—	8	2	no	—
321	C₂×C₄×C₂₃	#120	1	1	yes	characteristic
322	C₂×C₄×C₂₃	#120	1	1	yes	characteristic
323	C₂×C₄×C₂₃	#120	1	1	yes	characteristic
324	C₂×C₄×C₂₃	#135	1	2	yes	—
325	C₂×C₄×C₂₃	#137	1	2	yes	—
326	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
327	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
328	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
329	C₈×C₂₃	—	2	2	no	—
330	C₈×C₂₃	—	4	1	no	—
331	C₈×C₂₃	—	4	1	no	—
332	C₈×C₂₃	—	4	1	no	—
333	C₈×C₂₃	—	4	1	no	—
334	C₈×C₂₃	—	4	1	no	—
335	#3475	C₂×C₂₃	1	1	yes	characteristic
336	#3170	C₂×C₂₃	1	1	yes	characteristic, complemented
337	#3101	C₂×C₂₃	1	1	yes	characteristic, complemented
338	#3076	C₂×C₂₃	1	1	yes	characteristic, complemented
339	#1650	C₂×C₂₃	1	1	yes	characteristic, complemented
340	#1647	C₂×C₂₃	1	1	yes	characteristic, complemented
341	#1646	C₂×C₂₃	1	1	yes	characteristic, complemented
342	#1643	C₂×C₂₃	1	1	yes	characteristic, complemented
343	#1638	C₂×C₂₃	1	1	yes	characteristic, complemented
344	#1635	C₂×C₂₃	1	1	yes	characteristic, complemented
345	#1634	C₂×C₂₃	1	1	yes	characteristic, complemented
346	#1632	C₂×C₂₃	1	1	yes	characteristic, complemented
347	#1542	C₂×C₂₃	1	1	yes	characteristic, complemented
348	#1476	C₂×C₂₃	1	1	yes	characteristic, complemented
349	C₂×D₄⋊C₈	C₂×C₂₃	1	1	yes	characteristic, complemented
350	C₂²×C₂₃	—	2	1	no	—
351	C₂²×C₂₃	—	2	1	no	—
352	C₂²×C₂₃	—	2	2	no	—
353	C₂²×C₂₃	—	4	1	no	—
354	C₂²×C₂₃	—	4	1	no	—
355	C₂²×C₂₃	—	4	1	no	—
356	C₂²×C₂₃	—	4	1	no	—
357	C₂²×C₂₃	—	4	1	no	—
358	C₂²×C₂₃	—	4	1	no	—
359	C₂²×C₂₃	—	4	1	no	—
360	C₂²×C₂₃	—	4	1	no	—
361	C₂²×C₂₃	—	8	4	no	—
362	C₂²×C₂₃	#452	1	2	yes	—
363	C₂²×C₂₃	C₂×#120	1	1	yes	characteristic
364	C₄×C₂₃	—	2	1	no	—
365	C₄×C₂₃	—	2	1	no	—
366	C₄×C₂₃	—	2	1	no	—
367	C₄×C₂₃	—	4	1	no	—
368	C₄×C₂₃	—	4	1	no	—
369	C₄×C₂₃	—	4	1	no	—
370	C₄×C₂₃	—	4	1	no	—
371	C₄×C₂₃	—	4	2	no	—
372	C₄×C₂₃	—	4	1	no	—
373	C₄×C₂₃	—	4	2	no	—
374	C₄×C₂₃	—	8	1	no	—
375	C₄×C₂₃	—	8	1	no	—
376	C₄×C₂₃	#452	1	2	yes	—
377	C₄×C₂₃	C₂×#135	1	1	yes	characteristic
378	C₄×C₂₃	C₂×#135	1	1	yes	characteristic
379	C₄×C₂₃	C₂×#137	1	1	yes	characteristic
380	C₄×C₂₃	#575	1	1	yes	characteristic
381	#556	C₂²×C₂₃	1	1	yes	characteristic
382	#555	C₂²×C₂₃	1	1	yes	characteristic
383	#554	C₂²×C₂₃	1	1	yes	characteristic
384	#553	—	2	1	no	—
385	#552	—	2	1	no	—
386	#552	—	2	1	no	—
387	#551	—	2	2	no	—
388	#547	C₂²×C₂₃	1	1	yes	characteristic
389	#546	—	2	1	no	—
390	#533	C₂²×C₂₃	1	1	yes	characteristic
391	#533	C₂²×C₂₃	1	1	yes	characteristic
392	#529	—	2	2	no	—
393	#529	—	2	1	no	—
394	#525	—	2	1	no	—
395	C₄×#41	—	2	1	no	—
396	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
397	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
398	C₂×#117	—	2	1	no	—
399	#500	C₂²×C₂₃	1	1	yes	characteristic, complemented
400	#494	C₂²×C₂₃	1	1	yes	characteristic, complemented
401	#487	C₂²×C₂₃	1	1	yes	characteristic, complemented
402	#487	C₂²×C₂₃	1	1	yes	characteristic, complemented
403	#483	—	2	1	no	—
404	#479	—	2	1	no	—
405	#478	—	2	1	no	—
406	#477	C₂²×C₂₃	1	1	yes	characteristic, complemented
407	#476	C₂²×C₂₃	1	1	yes	characteristic
408	#476	C₂²×C₂₃	1	1	yes	characteristic
409	#476	C₂²×C₂₃	1	1	yes	characteristic, complemented
410	#475	C₂²×C₂₃	1	1	yes	characteristic, complemented
411	#474	C₂²×C₂₃	1	1	yes	characteristic, complemented
412	#467	—	2	2	no	—
413	#461	C₂²×C₂₃	1	1	yes	characteristic
414	#461	C₂²×C₂₃	1	1	yes	characteristic
415	#450	—	2	1	no	—
416	C₄×Q₁₆	—	2	2	no	—
417	C₄×SD₁₆	—	2	1	no	—
418	C₄×SD₁₆	—	2	1	no	—
419	#431	C₂²×C₂₃	1	1	yes	characteristic
420	#427	—	2	1	no	—
421	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
422	#416	—	2	1	no	—
423	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
424	#333	C₂²×C₂₃	1	1	yes	characteristic, complemented
425	#333	C₂²×C₂₃	1	1	yes	characteristic, complemented
426	#332	C₂²×C₂₃	1	1	yes	characteristic, complemented
427	#332	C₂²×C₂₃	1	1	yes	characteristic, complemented
428	Q₈⋊C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
429	Q₈⋊C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
430	D₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
431	D₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
432	D₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
433	D₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
434	D₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
435	D₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
436	C₂×C₂₃	—	2	2	no	—
437	C₂×C₂₃	—	4	2	no	—
438	C₂×C₂₃	—	8	1	no	—
439	C₂×C₂₃	—	8	1	no	—
440	C₂×C₂₃	C₂×#452	1	1	yes	characteristic
441	C₂×C₂₃	#3002	1	1	yes	characteristic
442	C₂×C₂₃	#3018	1	1	yes	characteristic
443	C₂×#41	—	2	1	no	—
444	C₂×#41	D₄×C₂₃	1	1	yes	characteristic
445	C₂²×D₄	D₄×C₂₃	1	1	yes	characteristic
446	C₂³×C₄	—	2	1	no	—
447	C₂×Q₁₆	—	2	2	no	—
448	C₂×SD₁₆	—	2	1	no	—
449	C₂×SD₁₆	—	2	1	no	—
450	C₂²×C₈	—	2	1	no	—
451	C₂²×C₈	—	2	1	no	—
452	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
453	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
454	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
455	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
456	#126	—	2	2	no	—
457	#126	—	2	2	no	—
458	#126	—	2	2	no	—
459	#125	—	2	2	no	—
460	#125	—	2	1	no	—
461	#125	—	2	1	no	—
462	#125	—	2	1	no	—
463	#124	—	2	2	no	—
464	#124	—	2	1	no	—
465	#123	—	2	2	no	—
466	#123	—	2	2	no	—
467	#123	—	2	2	no	—
468	#123	—	2	2	no	—
469	C₂²⋊Q₈	—	2	1	no	—
470	C₂²⋊Q₈	—	2	1	no	—
471	C₂²⋊Q₈	—	2	2	no	—
472	C₂²⋊Q₈	—	2	1	no	—
473	C₂²⋊Q₈	—	2	1	no	—
474	C₂²⋊Q₈	—	2	1	no	—
475	C₂²⋊Q₈	—	2	1	no	—
476	C₂²⋊Q₈	D₄×C₂₃	1	2	yes	—
477	#121	—	2	2	no	—
478	#121	—	2	1	no	—
479	#121	—	2	1	no	—
480	#121	—	2	1	no	—
481	#120	—	2	2	no	—
482	C₄×Q₈	—	2	1	no	—
483	C₄×Q₈	—	2	1	no	—
484	C₄×Q₈	—	2	1	no	—
485	C₄×Q₈	—	2	1	no	—
486	C₄×Q₈	D₄×C₂₃	1	1	yes	characteristic
487	C₄×Q₈	D₄×C₂₃	1	2	yes	—
488	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
489	C₄×D₄	—	2	2	no	—
490	C₄×D₄	—	2	2	no	—
491	C₄×D₄	—	2	2	no	—
492	C₄×D₄	—	2	1	no	—
493	C₄×D₄	—	2	1	no	—
494	C₄×D₄	—	2	1	no	—
495	C₄×D₄	—	2	1	no	—
496	C₄×D₄	—	2	1	no	—
497	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
498	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
499	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
500	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
501	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
502	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
503	#117	—	2	2	no	—
504	#117	—	2	2	no	—
505	#117	—	2	2	no	—
506	#117	—	2	1	no	—
507	#117	—	2	1	no	—
508	#117	—	2	1	no	—
509	#117	—	2	1	no	—
510	#117	—	2	1	no	—
511	#117	—	2	1	no	—
512	#117	D₄×C₂₃	1	1	yes	characteristic
513	C₂×C₄⋊C₄	—	2	1	no	—
514	C₂×C₄⋊C₄	—	2	1	no	—
515	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
516	C₂×C₂²⋊C₄	—	2	2	no	—
517	C₂×C₂²⋊C₄	—	2	1	no	—
518	C₂×C₄²	—	2	2	no	—
519	C₂×C₄²	—	2	1	no	—
520	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
521	#107	—	2	1	no	—
522	#107	—	2	1	no	—
523	#107	—	2	2	no	—
524	#106	—	2	1	no	—
525	#106	—	2	1	no	—
526	#106	—	2	1	no	—
527	#106	—	2	1	no	—
528	C₄⋊C₈	—	2	1	no	—
529	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
530	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
531	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
532	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
533	#103	—	2	1	no	—
534	#103	—	2	1	no	—
535	#103	—	2	2	no	—
536	#103	—	2	1	no	—
537	#103	—	2	1	no	—
538	#103	—	2	2	no	—
539	#102	—	2	1	no	—
540	#102	—	2	1	no	—
541	#102	—	2	1	no	—
542	#102	—	2	1	no	—
543	C₂²⋊C₈	—	2	1	no	—
544	C₄×C₈	—	2	1	no	—
545	C₄×C₈	—	2	1	no	—
546	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
547	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
548	C₂₃	#18523	1	1	yes	characteristic, direct product factor, Sylow
549	C₂⁴	—	2	1	no	—
550	#41	—	2	2	no	—
551	#41	—	2	2	no	—
552	#41	—	4	2	no	—
553	#41	—	4	2	no	—
554	C₂×Q₈	—	2	1	no	—
555	C₂×Q₈	—	2	1	no	—
556	C₂×Q₈	—	2	1	no	—
557	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
558	C₂×Q₈	C₂×D₄×C₂₃	1	2	yes	—
559	C₂×D₄	—	2	2	no	—
560	C₂×D₄	—	2	2	no	—
561	C₂×D₄	—	2	1	no	—
562	C₂×D₄	—	2	2	no	—
563	C₂×D₄	—	2	1	no	—
564	C₂×D₄	—	4	1	no	—
565	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
566	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
567	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
568	C₂²×C₄	—	2	2	no	—
569	C₂²×C₄	—	2	1	no	—
570	C₂²×C₄	—	2	2	no	—
571	C₂²×C₄	—	2	1	no	—
572	C₂²×C₄	—	2	1	no	—
573	C₂²×C₄	—	2	1	no	—
574	C₂²×C₄	—	2	1	no	—
575	C₂²×C₄	—	2	1	no	—
576	C₂²×C₄	—	2	1	no	—
577	C₂²×C₄	—	2	1	no	—
578	C₂²×C₄	—	4	2	no	—
579	C₂²×C₄	—	4	2	no	—
580	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
581	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
582	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
583	Q₁₆	—	4	4	no	—
584	SD₁₆	—	4	2	no	—
585	SD₁₆	—	4	2	no	—
586	C₂×C₈	—	2	1	no	—
587	C₂×C₈	—	2	1	no	—
588	C₂×C₈	—	2	1	no	—
589	C₂×C₈	—	2	1	no	—
590	C₂×C₈	—	2	1	no	—
591	C₂×C₈	—	2	1	no	—
592	C₂×C₈	—	4	2	no	—
593	C₂×C₈	—	4	2	no	—
594	C₄⋊C₄	—	2	2	no	—
595	C₄⋊C₄	—	2	2	no	—
596	C₄⋊C₄	—	2	2	no	—
597	C₄⋊C₄	—	2	2	no	—
598	C₄⋊C₄	—	2	1	no	—
599	C₄⋊C₄	—	2	2	no	—
600	C₄⋊C₄	—	2	1	no	—
601	C₄⋊C₄	—	2	2	no	—
602	C₄⋊C₄	—	2	1	no	—
603	C₄⋊C₄	—	2	1	no	—
604	C₄⋊C₄	—	2	1	no	—
605	C₄⋊C₄	—	2	1	no	—
606	C₄⋊C₄	—	2	1	no	—
607	C₄⋊C₄	—	2	1	no	—
608	C₄⋊C₄	—	2	1	no	—
609	C₄⋊C₄	—	2	1	no	—
610	C₄⋊C₄	—	4	1	no	—
611	C₄⋊C₄	—	4	1	no	—
612	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
613	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
614	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
615	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
616	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
617	C₂²⋊C₄	—	2	2	no	—
618	C₂²⋊C₄	—	2	2	no	—
619	C₂²⋊C₄	—	2	2	no	—
620	C₂²⋊C₄	—	2	2	no	—
621	C₂²⋊C₄	—	2	2	no	—
622	C₂²⋊C₄	—	2	2	no	—
623	C₂²⋊C₄	—	2	1	no	—
624	C₂²⋊C₄	—	2	2	no	—
625	C₂²⋊C₄	—	2	1	no	—
626	C₂²⋊C₄	—	2	1	no	—
627	C₂²⋊C₄	—	2	1	no	—
628	C₂²⋊C₄	—	2	1	no	—
629	C₂²⋊C₄	—	2	1	no	—
630	C₂²⋊C₄	—	2	1	no	—
631	C₂²⋊C₄	—	4	1	no	—
632	C₄²	—	2	2	no	—
633	C₄²	—	2	2	no	—
634	C₄²	—	2	1	no	—
635	C₄²	—	2	2	no	—
636	C₄²	—	2	1	no	—
637	C₄²	—	2	1	no	—
638	C₄²	—	4	1	no	—
639	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
640	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
641	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
642	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
643	C₂³	—	2	1	no	—
644	C₂³	—	2	1	no	—
645	C₂³	—	2	1	no	—
646	C₂³	—	4	2	no	—
647	C₂³	—	4	2	no	—
648	C₂³	—	8	1	no	—
649	C₂³	C₂₃×#120	1	1	yes	characteristic
650	Q₈	—	2	1	no	—
651	Q₈	—	2	1	no	—
652	Q₈	—	4	2	no	—
653	Q₈	—	4	2	no	—
654	Q₈	—	4	1	no	—
655	Q₈	—	4	1	no	—
656	Q₈	—	4	1	no	—
657	Q₈	—	4	1	no	—
658	D₄	—	2	1	no	—
659	D₄	—	2	1	no	—
660	D₄	—	2	1	no	—
661	D₄	—	2	1	no	—
662	D₄	—	2	1	no	—
663	D₄	—	4	2	no	—
664	D₄	—	4	4	no	—
665	D₄	—	4	2	no	—
666	D₄	—	8	2	no	—
667	D₄	C₂₃×#135	1	2	yes	—
668	C₂×C₄	—	2	1	no	—
669	C₂×C₄	—	2	1	no	—
670	C₂×C₄	—	2	1	no	—
671	C₂×C₄	—	2	1	no	—
672	C₂×C₄	—	2	1	no	—
673	C₂×C₄	—	2	1	no	—
674	C₂×C₄	—	2	2	no	—
675	C₂×C₄	—	2	2	no	—
676	C₂×C₄	—	2	1	no	—
677	C₂×C₄	—	4	1	no	—
678	C₂×C₄	—	4	4	no	—
679	C₂×C₄	—	4	2	no	—
680	C₂×C₄	—	4	1	no	—
681	C₂×C₄	—	4	1	no	—
682	C₂×C₄	—	4	1	no	—
683	C₂×C₄	—	4	1	no	—
684	C₂×C₄	—	4	1	no	—
685	C₂×C₄	—	4	1	no	—
686	C₂×C₄	—	4	2	no	—
687	C₂×C₄	—	4	2	no	—
688	C₂×C₄	—	4	2	no	—
689	C₂×C₄	—	4	1	no	—
690	C₂×C₄	—	4	1	no	—
691	C₂×C₄	—	8	1	no	—
692	C₂×C₄	—	8	2	no	—
693	C₂×C₄	C₂₃×#120	1	1	yes	characteristic
694	C₂×C₄	C₂₃×#120	1	1	yes	characteristic
695	C₂×C₄	C₂₃×#120	1	1	yes	characteristic
696	C₂×C₄	C₂₃×#135	1	2	yes	—
697	C₂×C₄	C₂₃×#137	1	2	yes	—
698	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
699	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
700	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
701	C₈	—	2	2	no	—
702	C₈	—	4	1	no	—
703	C₈	—	4	1	no	—
704	C₈	—	4	1	no	—
705	C₈	—	4	1	no	—
706	C₈	—	4	1	no	—
707	C₂²	—	2	1	no	—
708	C₂²	—	2	1	no	—
709	C₂²	—	2	2	no	—
710	C₂²	—	4	1	no	—
711	C₂²	—	4	1	no	—
712	C₂²	—	4	1	no	—
713	C₂²	—	4	1	no	—
714	C₂²	—	4	1	no	—
715	C₂²	—	4	1	no	—
716	C₂²	—	4	1	no	—
717	C₂²	—	4	1	no	—
718	C₂²	—	8	4	no	—
719	C₂²	C₂₃×#452	1	2	yes	—
720	C₂²	C₂×C₂₃×#120	1	1	yes	characteristic
721	C₄	—	2	1	no	—
722	C₄	—	2	1	no	—
723	C₄	—	2	1	no	—
724	C₄	—	4	1	no	—
725	C₄	—	4	1	no	—
726	C₄	—	4	1	no	—
727	C₄	—	4	1	no	—
728	C₄	—	4	2	no	—
729	C₄	—	4	1	no	—
730	C₄	—	4	2	no	—
731	C₄	—	8	1	no	—
732	C₄	—	8	1	no	—
733	C₄	C₂₃×#452	1	2	yes	—
734	C₄	C₂×C₂₃×#135	1	1	yes	characteristic
735	C₄	C₂×C₂₃×#135	1	1	yes	characteristic
736	C₄	C₂×C₂₃×#137	1	1	yes	characteristic
737	C₄	C₂₃×#575	1	1	yes	characteristic
738	C₂	—	2	2	no	—
739	C₂	—	4	2	no	—
740	C₂	—	8	1	no	—
741	C₂	—	8	1	no	—
742	C₂	C₂×C₂₃×#452	1	1	yes	characteristic
743	C₂	C₂₃×#3002	1	1	yes	characteristic
744	C₂	C₂₃×#3018	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₂₃	#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₂₃
socle	C₂²×C₂₃	C₂×#120
prime radical	C₂₃×#3475	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₃ ◁ C₂×C₄²×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂₃×#3170	C₂	semidirect
3. C₂₃×#3101	C₂	semidirect
4. C₂₃×#3076	C₂	semidirect
5. C₂₃×#1650	C₂	semidirect
6. C₂₃×#1647	C₂	semidirect
7. C₂₃×#1646	C₂	semidirect
8. C₂₃×#1643	C₂	semidirect
9. C₂₃×#1638	C₂	semidirect
10. C₂₃×#1635	C₂	semidirect
11. C₂₃×#1634	C₂	semidirect
12. C₂₃×#1632	C₂	semidirect
13. C₂₃×#1542	C₂	semidirect
14. C₂₃×#1476	C₂	semidirect
15. C₂×C₂₃×D₄⋊C₈	C₂	semidirect
34. C₂₃×#500	C₂²	semidirect
35. C₂₃×#494	C₂²	semidirect
36. C₂₃×#487	C₂²	semidirect
37. C₂₃×#487	C₂²	semidirect
41. C₂₃×#477	C₂²	semidirect
44. C₂₃×#476	C₂²	semidirect
45. C₂₃×#475	C₂²	semidirect
46. C₂₃×#474	C₂²	semidirect
59. C₂₃×#333	C₂²	semidirect
60. C₂₃×#333	C₂²	semidirect
61. C₂₃×#332	C₂²	semidirect
62. C₂₃×#332	C₂²	semidirect
63. C₂₃×Q₈⋊C₈	C₂²	semidirect
64. C₂₃×Q₈⋊C₈	C₂²	semidirect
69. C₂₃×D₄⋊C₈	C₂²	semidirect
70. C₂₃×D₄⋊C₈	C₂²	semidirect
270. #18523	C₂₃	direct (N × H)
336. #3170	C₂×C₂₃	semidirect
337. #3101	C₂×C₂₃	semidirect
338. #3076	C₂×C₂₃	semidirect
339. #1650	C₂×C₂₃	semidirect
340. #1647	C₂×C₂₃	semidirect
341. #1646	C₂×C₂₃	semidirect
342. #1643	C₂×C₂₃	semidirect
343. #1638	C₂×C₂₃	semidirect
344. #1635	C₂×C₂₃	semidirect
345. #1634	C₂×C₂₃	semidirect
346. #1632	C₂×C₂₃	semidirect
347. #1542	C₂×C₂₃	semidirect
348. #1476	C₂×C₂₃	semidirect
349. C₂×D₄⋊C₈	C₂×C₂₃	semidirect
399. #500	C₂²×C₂₃	semidirect
400. #494	C₂²×C₂₃	semidirect
401. #487	C₂²×C₂₃	semidirect
402. #487	C₂²×C₂₃	semidirect
406. #477	C₂²×C₂₃	semidirect
409. #476	C₂²×C₂₃	semidirect
410. #475	C₂²×C₂₃	semidirect
411. #474	C₂²×C₂₃	semidirect
424. #333	C₂²×C₂₃	semidirect
425. #333	C₂²×C₂₃	semidirect
426. #332	C₂²×C₂₃	semidirect
427. #332	C₂²×C₂₃	semidirect
428. Q₈⋊C₈	C₂²×C₂₃	semidirect
429. Q₈⋊C₈	C₂²×C₂₃	semidirect
434. D₄⋊C₈	C₂²×C₂₃	semidirect
435. D₄⋊C₈	C₂²×C₂₃	semidirect
548. C₂₃	#18523	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×#3475	2
C₂₃×#3170	2
C₂₃×#3101	2
C₂₃×#3076	2
C₂₃×#1650	2
C₂₃×#1647	2
C₂₃×#1646	2
C₂₃×#1643	2
C₂₃×#1638	2
C₂₃×#1635	2
C₂₃×#1634	2
C₂₃×#1632	2
C₂₃×#1542	2
C₂₃×#1476	2
C₂×C₂₃×D₄⋊C₈	2
#18523	23

Subgroups — C23×#18523 #19166149

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#18523 #19166149