Subgroups — C₂₃×#23371 #19170997

Order 5888.

604 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₂₃×#125	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#1940	C₂	1	2	yes	maximal
3	C₂₃×#1939	C₂	1	2	yes	maximal
4	C₂₃×#1917	C₂	1	2	yes	maximal
5	C₂₃×#1917	C₂	1	2	yes	maximal
6	C₂₃×#1916	C₂	1	2	yes	maximal
7	C₂₃×#1916	C₂	1	2	yes	maximal
8	C₂₃×#1831	C₂	1	1	yes	maximal, characteristic
9	C₂₃×#1831	C₂	1	1	yes	maximal, characteristic
10	C₂×C₂₃×#125	C₄	1	1	yes	characteristic
11	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
12	C₂×C₂₃×C₄⋊C₈	C₂²	1	2	yes	—
13	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
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×#97	C₂²	1	2	yes	—
18	C₂×C₄×C₈×C₂₃	C₂²	1	2	yes	—
19	C₂₃×#389	C₄	1	1	yes	characteristic
20	C₂₃×#389	C₄	1	1	yes	characteristic
21	C₂₃×#387	C₄	1	2	yes	—
22	C₂₃×#387	C₄	1	2	yes	—
23	C₂₃×#382	C₄	1	1	yes	characteristic
24	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
25	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
26	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
27	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
28	C₄³×C₂₃	C₂²	1	1	yes	characteristic
29	C₂₃×#336	C₂²	1	2	yes	—
30	C₂₃×#336	C₂²	1	2	yes	—
31	C₂₃×#336	C₂²	1	2	yes	—
32	C₂₃×#336	C₂²	1	2	yes	—
33	C₂₃×#336	C₂²	1	2	yes	—
34	C₂₃×#336	C₂²	1	2	yes	—
35	C₂₃×#336	C₂²	1	2	yes	—
36	C₂₃×#336	C₂²	1	2	yes	—
37	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
38	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
39	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
40	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
41	C₂₃×#125	—	2	4	no	—
42	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
43	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
44	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
45	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
46	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
47	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
48	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
49	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
50	C₂×C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
51	C₂×C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
52	C₂×C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
54	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
55	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
56	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
57	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
58	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
59	C₂₃×C₄⋊C₈	—	4	1	no	—
60	C₂₃×C₄⋊C₈	—	4	1	no	—
61	C₂₃×C₄⋊C₈	—	4	1	no	—
62	C₂₃×C₄⋊C₈	—	4	1	no	—
63	C₂₃×C₄⋊C₈	—	4	2	no	—
64	C₂₃×C₄⋊C₈	—	4	2	no	—
65	C₂₃×#97	—	4	2	no	—
66	C₄×C₈×C₂₃	—	4	2	no	—
67	C₂₃×#95	C₂×C₄	1	2	yes	—
68	C₂₃×#95	C₂×C₄	1	2	yes	—
69	C₂₃×#95	C₂×C₄	1	2	yes	—
70	C₂₃×#95	C₂×C₄	1	2	yes	—
71	C₂₃×#95	C₂×C₄	1	2	yes	—
72	C₂₃×#95	C₂×C₄	1	2	yes	—
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	2	yes	—
79	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
80	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
81	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
82	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
83	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
84	C₂×C₈×C₂₃	—	2	2	no	—
85	C₂×C₈×C₂₃	—	2	2	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	—	2	2	no	—
90	C₂×C₈×C₂₃	—	2	2	no	—
91	C₂×C₈×C₂₃	—	2	2	no	—
92	C₂×C₈×C₂₃	—	2	2	no	—
93	C₂×C₈×C₂₃	—	2	2	no	—
94	C₂×C₈×C₂₃	—	2	2	no	—
95	C₂×C₈×C₂₃	—	2	2	no	—
96	C₄⋊C₄×C₂₃	—	2	4	no	—
97	C₄⋊C₄×C₂₃	—	2	4	no	—
98	C₄⋊C₄×C₂₃	—	2	2	no	—
99	C₄⋊C₄×C₂₃	—	2	4	no	—
100	C₄⋊C₄×C₂₃	—	2	4	no	—
101	C₄⋊C₄×C₂₃	—	4	1	no	—
102	C₄⋊C₄×C₂₃	—	4	1	no	—
103	C₄⋊C₄×C₂₃	M₁₆	1	4	yes	—
104	C₄²×C₂₃	—	2	2	no	—
105	C₄²×C₂₃	—	2	2	no	—
106	C₄²×C₂₃	—	2	2	no	—
107	C₄²×C₂₃	—	2	1	no	—
108	C₄²×C₂₃	—	2	1	no	—
109	C₄²×C₂₃	—	2	2	no	—
110	C₄²×C₂₃	—	2	2	no	—
111	C₄²×C₂₃	—	2	1	no	—
112	C₄²×C₂₃	—	2	1	no	—
113	C₄²×C₂₃	—	2	1	no	—
114	C₄²×C₂₃	—	2	1	no	—
115	C₄²×C₂₃	—	2	2	no	—
116	C₄²×C₂₃	—	2	2	no	—
117	C₄²×C₂₃	—	4	1	no	—
118	#23371	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
119	C₂³×C₂₃	C₂³×C₄	1	1	yes	characteristic
120	C₂×C₄×C₂₃	—	2	1	no	—
121	C₂×C₄×C₂₃	—	2	2	no	—
122	C₂×C₄×C₂₃	—	2	1	no	—
123	C₂×C₄×C₂₃	—	2	1	no	—
124	C₂×C₄×C₂₃	—	2	2	no	—
125	C₂×C₄×C₂₃	—	2	1	no	—
126	C₂×C₄×C₂₃	—	2	1	no	—
127	C₂×C₄×C₂₃	—	2	1	no	—
128	C₂×C₄×C₂₃	—	2	1	no	—
129	C₂×C₄×C₂₃	—	2	1	no	—
130	C₂×C₄×C₂₃	—	2	1	no	—
131	C₂×C₄×C₂₃	—	2	2	no	—
132	C₂×C₄×C₂₃	—	2	2	no	—
133	C₂×C₄×C₂₃	—	2	2	no	—
134	C₂×C₄×C₂₃	—	2	1	no	—
135	C₂×C₄×C₂₃	—	2	1	no	—
136	C₂×C₄×C₂₃	—	2	2	no	—
137	C₂×C₄×C₂₃	—	2	1	no	—
138	C₂×C₄×C₂₃	—	2	1	no	—
139	C₂×C₄×C₂₃	—	2	1	no	—
140	C₂×C₄×C₂₃	—	2	1	no	—
141	C₂×C₄×C₂₃	—	2	2	no	—
142	C₂×C₄×C₂₃	—	2	2	no	—
143	C₂×C₄×C₂₃	—	2	2	no	—
144	C₂×C₄×C₂₃	—	2	2	no	—
145	C₂×C₄×C₂₃	—	2	2	no	—
146	C₂×C₄×C₂₃	C₂×M₁₆	1	2	yes	—
147	C₂×C₄×C₂₃	C₂×M₁₆	1	4	yes	—
148	C₂×C₄×C₂₃	#131	1	2	yes	—
149	C₂×C₄×C₂₃	#131	1	2	yes	—
150	C₂×C₄×C₂₃	H(5,𝔽₂)	1	1	yes	characteristic
151	C₂×C₄×C₂₃	H(5,𝔽₂)	1	1	yes	characteristic
152	C₂×C₄×C₂₃	2₋¹⁺⁴	1	1	yes	characteristic
153	C₂×C₄×C₂₃	2₋¹⁺⁴	1	1	yes	characteristic
154	C₂×C₄×C₂₃	2₋¹⁺⁴	1	1	yes	characteristic
155	C₂×C₄×C₂₃	2₋¹⁺⁴	1	1	yes	characteristic
156	C₈×C₂₃	—	4	2	no	—
157	C₈×C₂₃	—	4	2	no	—
158	C₈×C₂₃	—	4	2	no	—
159	C₈×C₂₃	—	4	2	no	—
160	C₄×#125	C₂×C₂₃	1	1	yes	characteristic
161	#1940	C₂×C₂₃	1	2	yes	—
162	#1939	C₂×C₂₃	1	2	yes	—
163	#1917	C₂×C₂₃	1	2	yes	—
164	#1917	C₂×C₂₃	1	2	yes	—
165	#1916	C₂×C₂₃	1	2	yes	—
166	#1916	C₂×C₂₃	1	2	yes	—
167	#1831	C₂×C₂₃	1	1	yes	characteristic
168	#1831	C₂×C₂₃	1	1	yes	characteristic
169	C₂²×C₂₃	#519	1	1	yes	characteristic
170	C₂²×C₂₃	#520	1	1	yes	characteristic
171	C₂²×C₂₃	#520	1	1	yes	characteristic
172	C₂²×C₂₃	C₂²×M₁₆	1	1	yes	characteristic
173	C₂²×C₂₃	C₂×#131	1	1	yes	characteristic
174	C₂²×C₂₃	C₂×#131	1	1	yes	characteristic
175	C₂²×C₂₃	#568	1	1	yes	characteristic
176	C₄×C₂₃	—	2	2	no	—
177	C₄×C₂₃	—	2	4	no	—
178	C₄×C₂₃	—	2	2	no	—
179	C₄×C₂₃	—	2	2	no	—
180	C₄×C₂₃	—	4	1	no	—
181	C₄×C₂₃	—	4	1	no	—
182	C₄×C₂₃	—	4	1	no	—
183	C₄×C₂₃	—	4	2	no	—
184	C₄×C₂₃	—	4	2	no	—
185	C₄×C₂₃	—	4	2	no	—
186	C₄×C₂₃	#562	1	1	yes	characteristic
187	C₄×C₂₃	#563	1	1	yes	characteristic
188	C₄×C₂₃	#563	1	1	yes	characteristic
189	C₄×C₂₃	#564	1	1	yes	characteristic
190	C₂×#125	C₄×C₂₃	1	1	yes	characteristic
191	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
192	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
193	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
194	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
195	C₂×C₄⋊C₈	C₂²×C₂₃	1	2	yes	—
196	C₂×C₄⋊C₈	C₂²×C₂₃	1	2	yes	—
197	C₂×#97	C₂²×C₂₃	1	2	yes	—
198	C₂×C₄×C₈	C₂²×C₂₃	1	2	yes	—
199	#389	C₄×C₂₃	1	1	yes	characteristic
200	#389	C₄×C₂₃	1	1	yes	characteristic
201	#387	C₄×C₂₃	1	2	yes	—
202	#387	C₄×C₂₃	1	2	yes	—
203	#382	C₄×C₂₃	1	1	yes	characteristic
204	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
205	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
206	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
207	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
208	C₄³	C₂²×C₂₃	1	1	yes	characteristic
209	#336	C₂²×C₂₃	1	2	yes	—
210	#336	C₂²×C₂₃	1	2	yes	—
211	#336	C₂²×C₂₃	1	2	yes	—
212	#336	C₂²×C₂₃	1	2	yes	—
213	#336	C₂²×C₂₃	1	2	yes	—
214	#336	C₂²×C₂₃	1	2	yes	—
215	#336	C₂²×C₂₃	1	2	yes	—
216	#336	C₂²×C₂₃	1	2	yes	—
217	C₂×C₂₃	#2382	1	1	yes	characteristic
218	C₂×C₂₃	#2983	1	1	yes	characteristic
219	C₂×C₂₃	#2986	1	1	yes	characteristic
220	C₂×C₂₃	#2990	1	1	yes	characteristic
221	C₂×C₂₃	#2991	1	1	yes	characteristic
222	C₂×C₂₃	#2992	1	1	yes	characteristic
223	C₂×C₂₃	#2992	1	1	yes	characteristic
224	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
225	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
226	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
227	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
228	#125	—	2	4	no	—
229	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
230	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
231	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
232	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
233	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
234	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
235	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
236	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
237	C₂×C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic
238	C₂×C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic
239	C₂×C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic
240	C₂×C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic
241	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
242	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
243	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
244	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
245	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
246	C₄⋊C₈	—	4	2	no	—
247	C₄⋊C₈	—	4	2	no	—
248	C₄⋊C₈	—	4	1	no	—
249	C₄⋊C₈	—	4	1	no	—
250	C₄⋊C₈	—	4	1	no	—
251	C₄⋊C₈	—	4	1	no	—
252	#97	—	4	2	no	—
253	C₄×C₈	—	4	2	no	—
254	#95	C₂×C₄×C₂₃	1	2	yes	—
255	#95	C₂×C₄×C₂₃	1	2	yes	—
256	#95	C₂×C₄×C₂₃	1	2	yes	—
257	#95	C₂×C₄×C₂₃	1	2	yes	—
258	#95	C₂×C₄×C₂₃	1	2	yes	—
259	#95	C₂×C₄×C₂₃	1	2	yes	—
260	C₂₃	#23371	1	1	yes	characteristic, direct product factor, Sylow
261	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
262	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
263	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
264	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
265	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
266	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
267	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
268	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
269	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
270	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
271	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
272	C₂×C₈	—	2	2	no	—
273	C₂×C₈	—	2	2	no	—
274	C₂×C₈	—	2	2	no	—
275	C₂×C₈	—	2	2	no	—
276	C₂×C₈	—	2	2	no	—
277	C₂×C₈	—	2	2	no	—
278	C₂×C₈	—	2	2	no	—
279	C₂×C₈	—	2	2	no	—
280	C₂×C₈	—	2	2	no	—
281	C₂×C₈	—	2	2	no	—
282	C₂×C₈	—	2	2	no	—
283	C₂×C₈	—	2	2	no	—
284	C₄⋊C₄	—	2	4	no	—
285	C₄⋊C₄	—	2	4	no	—
286	C₄⋊C₄	—	2	2	no	—
287	C₄⋊C₄	—	2	4	no	—
288	C₄⋊C₄	—	2	4	no	—
289	C₄⋊C₄	—	4	1	no	—
290	C₄⋊C₄	—	4	1	no	—
291	C₄⋊C₄	M₁₆×C₂₃	1	4	yes	—
292	C₄²	—	2	2	no	—
293	C₄²	—	2	2	no	—
294	C₄²	—	2	2	no	—
295	C₄²	—	2	2	no	—
296	C₄²	—	2	2	no	—
297	C₄²	—	2	1	no	—
298	C₄²	—	2	1	no	—
299	C₄²	—	2	1	no	—
300	C₄²	—	2	1	no	—
301	C₄²	—	2	1	no	—
302	C₄²	—	2	1	no	—
303	C₄²	—	2	2	no	—
304	C₄²	—	2	2	no	—
305	C₄²	—	4	1	no	—
306	C₂³	C₂³×C₄×C₂₃	1	1	yes	characteristic
307	C₂×C₄	—	2	2	no	—
308	C₂×C₄	—	2	1	no	—
309	C₂×C₄	—	2	1	no	—
310	C₂×C₄	—	2	1	no	—
311	C₂×C₄	—	2	1	no	—
312	C₂×C₄	—	2	2	no	—
313	C₂×C₄	—	2	1	no	—
314	C₂×C₄	—	2	1	no	—
315	C₂×C₄	—	2	1	no	—
316	C₂×C₄	—	2	1	no	—
317	C₂×C₄	—	2	2	no	—
318	C₂×C₄	—	2	1	no	—
319	C₂×C₄	—	2	1	no	—
320	C₂×C₄	—	2	1	no	—
321	C₂×C₄	—	2	1	no	—
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	—	2	2	no	—
325	C₂×C₄	—	2	2	no	—
326	C₂×C₄	—	2	2	no	—
327	C₂×C₄	—	2	1	no	—
328	C₂×C₄	—	2	1	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	1	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	C₂×M₁₆×C₂₃	1	2	yes	—
334	C₂×C₄	C₂×M₁₆×C₂₃	1	4	yes	—
335	C₂×C₄	C₂₃×#131	1	2	yes	—
336	C₂×C₄	C₂₃×#131	1	2	yes	—
337	C₂×C₄	C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
338	C₂×C₄	C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
339	C₂×C₄	C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
340	C₂×C₄	C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
341	C₂×C₄	C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
342	C₂×C₄	C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
343	C₈	—	4	2	no	—
344	C₈	—	4	2	no	—
345	C₈	—	4	2	no	—
346	C₈	—	4	2	no	—
347	C₂²	C₂₃×#519	1	1	yes	characteristic
348	C₂²	C₂₃×#520	1	1	yes	characteristic
349	C₂²	C₂₃×#520	1	1	yes	characteristic
350	C₂²	C₂²×M₁₆×C₂₃	1	1	yes	characteristic
351	C₂²	C₂×C₂₃×#131	1	1	yes	characteristic
352	C₂²	C₂×C₂₃×#131	1	1	yes	characteristic
353	C₂²	C₂₃×#568	1	1	yes	characteristic
354	C₄	—	2	2	no	—
355	C₄	—	2	4	no	—
356	C₄	—	2	2	no	—
357	C₄	—	2	2	no	—
358	C₄	—	4	1	no	—
359	C₄	—	4	1	no	—
360	C₄	—	4	1	no	—
361	C₄	—	4	2	no	—
362	C₄	—	4	2	no	—
363	C₄	—	4	2	no	—
364	C₄	C₂₃×#562	1	1	yes	characteristic
365	C₄	C₂₃×#563	1	1	yes	characteristic
366	C₄	C₂₃×#563	1	1	yes	characteristic
367	C₄	C₂₃×#564	1	1	yes	characteristic
368	C₂	C₂₃×#2382	1	1	yes	characteristic
369	C₂	C₂₃×#2983	1	1	yes	characteristic
370	C₂	C₂₃×#2986	1	1	yes	characteristic
371	C₂	C₂₃×#2990	1	1	yes	characteristic
372	C₂	C₂₃×#2991	1	1	yes	characteristic
373	C₂	C₂₃×#2992	1	1	yes	characteristic
374	C₂	C₂₃×#2992	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
118. #23371	C₂₃	direct (N × H)
260. C₂₃	#23371	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄×C₂₃×#125	2
C₂₃×#1940	2
C₂₃×#1939	2
C₂₃×#1917	2
C₂₃×#1916	2
C₂₃×#1831	2
#23371	23

Subgroups — C23×#23371 #19170997

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#23371 #19170997