Subgroups — C₂₃×#8043 #19155669

Order 5888.

790 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#431	C₂	1	1	yes	maximal, characteristic
2	C₂×C₂₃×#423	C₂	1	1	yes	maximal, characteristic
3	C₂×C₂₃×#384	C₂	1	1	yes	maximal, characteristic
4	C₂₃×#1296	C₂	1	4	yes	maximal, complemented
5	C₂²×M₁₆×C₂₃	—	2	1	no	—
6	C₂²×C₄⋊C₄×C₂₃	—	2	1	no	—
7	C₂²×C₄⋊C₄×C₂₃	—	2	1	no	—
8	C₂²×C₄⋊C₄×C₂₃	C₄	1	2	yes	—
9	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
10	C₂₃×#431	—	2	2	no	—
11	C₂₃×#431	C₄	1	4	yes	complemented
12	C₂₃×#423	—	2	2	no	—
13	C₂₃×#423	C₄	1	4	yes	complemented
14	C₂×C₂₃×C₄⋊C₈	—	2	1	no	—
15	C₂×C₂₃×C₄⋊C₈	C₂²	1	2	yes	—
16	C₂×C₂₃×C₄⋊C₈	C₂²	1	2	yes	—
17	C₂×C₂₃×C₂²⋊C₈	—	2	1	no	—
18	C₂×C₄×C₈×C₂₃	—	2	1	no	—
19	C₂₃×#384	—	2	1	no	—
20	C₂₃×#384	—	2	1	no	—
21	C₂₃×#384	C₄	1	2	yes	—
22	C₂₃×#384	C₂²	1	2	yes	—
23	C₂³×C₄×C₂₃	—	2	2	no	—
24	C₂³×C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
25	C₂³×C₄×C₂₃	D₄	1	1	yes	characteristic
26	C₂³×C₄×C₂₃	D₄	1	1	yes	characteristic
27	C₂×M₁₆×C₂₃	—	2	4	no	—
28	C₂×M₁₆×C₂₃	—	4	2	no	—
29	C₂×M₁₆×C₂₃	—	4	2	no	—
30	C₂²×C₈×C₂₃	—	2	2	no	—
31	C₂²×C₈×C₂₃	—	2	2	no	—
32	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
33	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
34	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
35	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
36	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
37	C₂×C₄⋊C₄×C₂₃	—	4	4	no	—
38	C₂×C₄⋊C₄×C₂₃	—	4	2	no	—
39	C₂×C₄⋊C₄×C₂₃	—	4	2	no	—
40	C₂×C₄⋊C₄×C₂₃	—	4	4	no	—
41	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	4	yes	—
42	C₂×C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
43	C₂×C₄²×C₂₃	C₂×C₄	1	2	yes	—
44	C₂×C₄²×C₂₃	C₂×C₄	1	2	yes	—
45	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
46	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
47	C₂×C₄²×C₂₃	D₄	1	2	yes	—
48	C₂×C₄²×C₂₃	Q₈	1	2	yes	—
49	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
50	C₂₃×C₄⋊C₈	—	2	4	no	—
51	C₂₃×C₄⋊C₈	—	2	2	no	—
52	C₂₃×C₄⋊C₈	—	2	2	no	—
53	C₂₃×C₄⋊C₈	C₂×C₄	1	4	yes	complemented
54	C₂₃×C₄⋊C₈	C₂×C₄	1	4	yes	complemented
55	C₂₃×C₂²⋊C₈	—	2	4	no	—
56	C₄×C₈×C₂₃	—	2	4	no	—
57	C₂⁴×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
58	C₂²×C₄×C₂₃	—	2	2	no	—
59	C₂²×C₄×C₂₃	—	2	2	no	—
60	C₂²×C₄×C₂₃	—	2	2	no	—
61	C₂²×C₄×C₂₃	—	2	2	no	—
62	C₂²×C₄×C₂₃	—	2	4	no	—
63	C₂²×C₄×C₂₃	—	4	4	no	—
64	C₂²×C₄×C₂₃	—	4	4	no	—
65	C₂²×C₄×C₂₃	—	4	4	no	—
66	C₂²×C₄×C₂₃	C₄²	1	2	yes	—
67	C₂²×C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
68	C₂²×C₄×C₂₃	C₂²⋊C₄	1	2	yes	—
69	C₂²×C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
70	C₂²×C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
71	C₂²×C₄×C₂₃	C₂²⋊C₄	1	2	yes	—
72	C₂²×C₄×C₂₃	C₄⋊C₄	1	2	yes	—
73	C₂²×C₄×C₂₃	C₄⋊C₄	1	2	yes	—
74	C₂²×C₄×C₂₃	C₄⋊C₄	1	2	yes	—
75	C₂²×C₄×C₂₃	D₈	1	2	yes	—
76	C₂²×C₄×C₂₃	SD₁₆	1	2	yes	—
77	C₂²×C₄×C₂₃	SD₁₆	1	2	yes	—
78	C₂²×C₄×C₂₃	Q₁₆	1	2	yes	—
79	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
80	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
81	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
82	M₁₆×C₂₃	—	4	8	no	—
83	C₂×C₈×C₂₃	—	2	4	no	—
84	C₂×C₈×C₂₃	—	2	4	no	—
85	C₂×C₈×C₂₃	—	4	2	no	—
86	C₂×C₈×C₂₃	—	4	2	no	—
87	C₂×C₈×C₂₃	—	4	2	no	—
88	C₂×C₈×C₂₃	—	4	2	no	—
89	C₄⋊C₄×C₂₃	—	4	4	no	—
90	C₄⋊C₄×C₂₃	—	4	4	no	—
91	C₄⋊C₄×C₂₃	—	4	4	no	—
92	C₄⋊C₄×C₂₃	—	4	4	no	—
93	C₄⋊C₄×C₂₃	—	4	2	no	—
94	C₄⋊C₄×C₂₃	—	4	2	no	—
95	C₄⋊C₄×C₂₃	—	4	4	no	—
96	C₄²×C₂₃	C₄²	1	2	yes	—
97	C₄²×C₂₃	C₂²⋊C₄	1	2	yes	—
98	C₄²×C₂₃	C₂²⋊C₄	1	2	yes	—
99	C₄²×C₂₃	C₄⋊C₄	1	2	yes	—
100	C₄²×C₂₃	C₄⋊C₄	1	2	yes	—
101	C₄²×C₂₃	C₄⋊C₄	1	2	yes	—
102	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
103	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
104	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
105	C₄²×C₂₃	C₂×Q₈	1	1	yes	characteristic
106	#8043	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
107	C₂³×C₂₃	—	2	1	no	—
108	C₂³×C₂₃	—	2	1	no	—
109	C₂³×C₂₃	—	2	1	no	—
110	C₂³×C₂₃	—	2	1	no	—
111	C₂³×C₂₃	#95	1	2	yes	—
112	C₂³×C₂₃	#102	1	2	yes	—
113	C₂³×C₂₃	#103	1	2	yes	—
114	C₂³×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
115	C₂×C₄×C₂₃	—	2	1	no	—
116	C₂×C₄×C₂₃	—	2	1	no	—
117	C₂×C₄×C₂₃	—	2	1	no	—
118	C₂×C₄×C₂₃	—	2	1	no	—
119	C₂×C₄×C₂₃	—	2	4	no	—
120	C₂×C₄×C₂₃	—	2	4	no	—
121	C₂×C₄×C₂₃	—	2	4	no	—
122	C₂×C₄×C₂₃	—	2	4	no	—
123	C₂×C₄×C₂₃	—	4	4	no	—
124	C₂×C₄×C₂₃	—	4	4	no	—
125	C₂×C₄×C₂₃	—	4	4	no	—
126	C₂×C₄×C₂₃	—	8	8	no	—
127	C₂×C₄×C₂₃	#95	1	2	yes	—
128	C₂×C₄×C₂₃	#95	1	2	yes	—
129	C₂×C₄×C₂₃	#95	1	2	yes	—
130	C₂×C₄×C₂₃	#100	1	2	yes	—
131	C₂×C₄×C₂₃	#101	1	2	yes	—
132	C₂×C₄×C₂₃	#102	1	2	yes	—
133	C₂×C₄×C₂₃	#102	1	4	yes	—
134	C₂×C₄×C₂₃	#103	1	2	yes	—
135	C₂×C₄×C₂₃	#103	1	4	yes	—
136	C₂×C₄×C₂₃	#106	1	4	yes	—
137	C₂×C₄×C₂₃	#107	1	4	yes	—
138	C₂×C₄×C₂₃	C₂×C₄²	1	1	yes	characteristic
139	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
140	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
141	C₂×C₄×C₂₃	C₂×C₄⋊C₄	1	1	yes	characteristic
142	C₂×C₄×C₂₃	C₂×C₄⋊C₄	1	1	yes	characteristic
143	C₂×C₄×C₂₃	C₂×C₄⋊C₄	1	1	yes	characteristic
144	C₂×C₄×C₂₃	C₂×D₈	1	1	yes	characteristic
145	C₂×C₄×C₂₃	C₂×SD₁₆	1	1	yes	characteristic
146	C₂×C₄×C₂₃	C₂×SD₁₆	1	1	yes	characteristic
147	C₂×C₄×C₂₃	C₂×Q₁₆	1	1	yes	characteristic
148	C₂×C₄×C₂₃	AGL(1,ℤ/8)	1	2	yes	—
149	C₂×C₄×C₂₃	#137	1	2	yes	—
150	C₈×C₂₃	—	4	4	no	—
151	C₈×C₂₃	—	4	4	no	—
152	C₂×#431	C₂×C₂₃	1	1	yes	characteristic
153	C₂×#423	C₂×C₂₃	1	1	yes	characteristic
154	C₂×#384	C₂×C₂₃	1	1	yes	characteristic
155	#1296	C₂×C₂₃	1	4	yes	complemented
156	C₂²×C₂₃	—	2	2	no	—
157	C₂²×C₂₃	—	2	2	no	—
158	C₂²×C₂₃	—	2	2	no	—
159	C₂²×C₂₃	—	2	2	no	—
160	C₂²×C₂₃	—	2	2	no	—
161	C₂²×C₂₃	—	2	2	no	—
162	C₂²×C₂₃	#340	1	4	yes	—
163	C₂²×C₂₃	C₂×#95	1	1	yes	characteristic
164	C₂²×C₂₃	C₂×#100	1	1	yes	characteristic
165	C₂²×C₂₃	C₂×#101	1	1	yes	characteristic
166	C₂²×C₂₃	C₂×#102	1	1	yes	characteristic
167	C₂²×C₂₃	C₂×#103	1	1	yes	characteristic
168	C₂²×C₂₃	#418	1	1	yes	characteristic
169	C₂²×C₂₃	#419	1	1	yes	characteristic
170	C₄×C₂₃	—	2	2	no	—
171	C₄×C₂₃	—	2	1	no	—
172	C₄×C₂₃	—	2	1	no	—
173	C₄×C₂₃	—	8	4	no	—
174	C₄×C₂₃	#340	1	4	yes	—
175	C₄×C₂₃	#343	1	4	yes	—
176	C₄×C₂₃	C₂×#102	1	1	yes	characteristic
177	C₄×C₂₃	C₂×#103	1	1	yes	characteristic
178	C₄×C₂₃	#417	1	2	yes	—
179	C₄×C₂₃	C₂×#106	1	1	yes	characteristic
180	C₄×C₂₃	C₂×#107	1	1	yes	characteristic
181	C₄×C₂₃	#428	1	2	yes	—
182	C₂²×M₁₆	—	2	1	no	—
183	C₂²×C₄⋊C₄	—	2	1	no	—
184	C₂²×C₄⋊C₄	—	2	1	no	—
185	C₂²×C₄⋊C₄	C₄×C₂₃	1	2	yes	—
186	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
187	#431	—	2	2	no	—
188	#431	C₄×C₂₃	1	4	yes	complemented
189	#423	—	2	2	no	—
190	#423	C₄×C₂₃	1	4	yes	complemented
191	C₂×C₄⋊C₈	—	2	1	no	—
192	C₂×C₄⋊C₈	C₂²×C₂₃	1	2	yes	—
193	C₂×C₄⋊C₈	C₂²×C₂₃	1	2	yes	—
194	C₂×C₂²⋊C₈	—	2	1	no	—
195	C₂×C₄×C₈	—	2	1	no	—
196	#384	—	2	1	no	—
197	#384	—	2	1	no	—
198	#384	C₄×C₂₃	1	2	yes	—
199	#384	C₂²×C₂₃	1	2	yes	—
200	C₂×C₂₃	—	2	4	no	—
201	C₂×C₂₃	#1545	1	1	yes	characteristic
202	C₂×C₂₃	#1546	1	1	yes	characteristic
203	C₂×C₂₃	#1548	1	1	yes	characteristic
204	C₂×C₂₃	#1549	1	1	yes	characteristic
205	C₂×C₂₃	C₂×#340	1	1	yes	characteristic
206	C₂×C₂₃	#1736	1	1	yes	characteristic
207	C₂×C₂₃	C₂×#343	1	1	yes	characteristic
208	C₂³×C₄	—	2	2	no	—
209	C₂³×C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
210	C₂³×C₄	D₄×C₂₃	1	1	yes	characteristic
211	C₂³×C₄	D₄×C₂₃	1	1	yes	characteristic
212	C₂×M₁₆	—	2	4	no	—
213	C₂×M₁₆	—	4	2	no	—
214	C₂×M₁₆	—	4	2	no	—
215	C₂²×C₈	—	2	2	no	—
216	C₂²×C₈	—	2	2	no	—
217	C₂×C₄⋊C₄	—	2	2	no	—
218	C₂×C₄⋊C₄	—	2	2	no	—
219	C₂×C₄⋊C₄	—	2	2	no	—
220	C₂×C₄⋊C₄	—	2	2	no	—
221	C₂×C₄⋊C₄	—	2	2	no	—
222	C₂×C₄⋊C₄	—	4	4	no	—
223	C₂×C₄⋊C₄	—	4	2	no	—
224	C₂×C₄⋊C₄	—	4	2	no	—
225	C₂×C₄⋊C₄	—	4	4	no	—
226	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	4	yes	—
227	C₂×C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic
228	C₂×C₄²	C₂×C₄×C₂₃	1	2	yes	—
229	C₂×C₄²	C₂×C₄×C₂₃	1	2	yes	—
230	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
231	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
232	C₂×C₄²	D₄×C₂₃	1	2	yes	—
233	C₂×C₄²	Q₈×C₂₃	1	2	yes	—
234	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
235	C₄⋊C₈	—	2	4	no	—
236	C₄⋊C₈	—	2	2	no	—
237	C₄⋊C₈	—	2	2	no	—
238	C₄⋊C₈	C₂×C₄×C₂₃	1	4	yes	complemented
239	C₄⋊C₈	C₂×C₄×C₂₃	1	4	yes	complemented
240	C₂²⋊C₈	—	2	4	no	—
241	C₄×C₈	—	2	4	no	—
242	C₂₃	#8043	1	1	yes	characteristic, direct product factor, Sylow
243	C₂⁴	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
244	C₂²×C₄	—	2	2	no	—
245	C₂²×C₄	—	2	2	no	—
246	C₂²×C₄	—	2	2	no	—
247	C₂²×C₄	—	2	2	no	—
248	C₂²×C₄	—	2	4	no	—
249	C₂²×C₄	—	4	4	no	—
250	C₂²×C₄	—	4	4	no	—
251	C₂²×C₄	—	4	4	no	—
252	C₂²×C₄	C₄²×C₂₃	1	2	yes	—
253	C₂²×C₄	C₂²⋊C₄×C₂₃	1	2	yes	—
254	C₂²×C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
255	C₂²×C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
256	C₂²×C₄	C₂²⋊C₄×C₂₃	1	2	yes	—
257	C₂²×C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
258	C₂²×C₄	C₄⋊C₄×C₂₃	1	2	yes	—
259	C₂²×C₄	C₄⋊C₄×C₂₃	1	2	yes	—
260	C₂²×C₄	C₄⋊C₄×C₂₃	1	2	yes	—
261	C₂²×C₄	D₈×C₂₃	1	2	yes	—
262	C₂²×C₄	SD₁₆×C₂₃	1	2	yes	—
263	C₂²×C₄	SD₁₆×C₂₃	1	2	yes	—
264	C₂²×C₄	Q₁₆×C₂₃	1	2	yes	—
265	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
266	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
267	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
268	M₁₆	—	4	8	no	—
269	C₂×C₈	—	2	4	no	—
270	C₂×C₈	—	2	4	no	—
271	C₂×C₈	—	4	2	no	—
272	C₂×C₈	—	4	2	no	—
273	C₂×C₈	—	4	2	no	—
274	C₂×C₈	—	4	2	no	—
275	C₄⋊C₄	—	4	4	no	—
276	C₄⋊C₄	—	4	4	no	—
277	C₄⋊C₄	—	4	4	no	—
278	C₄⋊C₄	—	4	4	no	—
279	C₄⋊C₄	—	4	2	no	—
280	C₄⋊C₄	—	4	2	no	—
281	C₄⋊C₄	—	4	4	no	—
282	C₄²	C₄²×C₂₃	1	2	yes	—
283	C₄²	C₂²⋊C₄×C₂₃	1	2	yes	—
284	C₄²	C₂²⋊C₄×C₂₃	1	2	yes	—
285	C₄²	C₄⋊C₄×C₂₃	1	2	yes	—
286	C₄²	C₄⋊C₄×C₂₃	1	2	yes	—
287	C₄²	C₄⋊C₄×C₂₃	1	2	yes	—
288	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
289	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
290	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
291	C₄²	C₂×Q₈×C₂₃	1	1	yes	characteristic
292	C₂³	—	2	1	no	—
293	C₂³	—	2	1	no	—
294	C₂³	—	2	1	no	—
295	C₂³	—	2	1	no	—
296	C₂³	C₂₃×#95	1	2	yes	—
297	C₂³	C₂₃×#102	1	2	yes	—
298	C₂³	C₂₃×#103	1	2	yes	—
299	C₂³	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
300	C₂×C₄	—	2	1	no	—
301	C₂×C₄	—	2	1	no	—
302	C₂×C₄	—	2	1	no	—
303	C₂×C₄	—	2	1	no	—
304	C₂×C₄	—	2	4	no	—
305	C₂×C₄	—	2	4	no	—
306	C₂×C₄	—	2	4	no	—
307	C₂×C₄	—	2	4	no	—
308	C₂×C₄	—	4	4	no	—
309	C₂×C₄	—	4	4	no	—
310	C₂×C₄	—	4	4	no	—
311	C₂×C₄	—	8	8	no	—
312	C₂×C₄	C₂₃×#95	1	2	yes	—
313	C₂×C₄	C₂₃×#95	1	2	yes	—
314	C₂×C₄	C₂₃×#95	1	2	yes	—
315	C₂×C₄	C₂₃×#100	1	2	yes	—
316	C₂×C₄	C₂₃×#101	1	2	yes	—
317	C₂×C₄	C₂₃×#102	1	2	yes	—
318	C₂×C₄	C₂₃×#102	1	4	yes	—
319	C₂×C₄	C₂₃×#103	1	2	yes	—
320	C₂×C₄	C₂₃×#103	1	4	yes	—
321	C₂×C₄	C₂₃×#106	1	4	yes	—
322	C₂×C₄	C₂₃×#107	1	4	yes	—
323	C₂×C₄	C₂×C₄²×C₂₃	1	1	yes	characteristic
324	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
325	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
326	C₂×C₄	C₂×C₄⋊C₄×C₂₃	1	1	yes	characteristic
327	C₂×C₄	C₂×C₄⋊C₄×C₂₃	1	1	yes	characteristic
328	C₂×C₄	C₂×C₄⋊C₄×C₂₃	1	1	yes	characteristic
329	C₂×C₄	C₂×D₈×C₂₃	1	1	yes	characteristic
330	C₂×C₄	C₂×SD₁₆×C₂₃	1	1	yes	characteristic
331	C₂×C₄	C₂×SD₁₆×C₂₃	1	1	yes	characteristic
332	C₂×C₄	C₂×Q₁₆×C₂₃	1	1	yes	characteristic
333	C₂×C₄	C₂₃×AGL(1,ℤ/8)	1	2	yes	—
334	C₂×C₄	C₂₃×#137	1	2	yes	—
335	C₈	—	4	4	no	—
336	C₈	—	4	4	no	—
337	C₂²	—	2	2	no	—
338	C₂²	—	2	2	no	—
339	C₂²	—	2	2	no	—
340	C₂²	—	2	2	no	—
341	C₂²	—	2	2	no	—
342	C₂²	—	2	2	no	—
343	C₂²	C₂₃×#340	1	4	yes	—
344	C₂²	C₂×C₂₃×#95	1	1	yes	characteristic
345	C₂²	C₂×C₂₃×#100	1	1	yes	characteristic
346	C₂²	C₂×C₂₃×#101	1	1	yes	characteristic
347	C₂²	C₂×C₂₃×#102	1	1	yes	characteristic
348	C₂²	C₂×C₂₃×#103	1	1	yes	characteristic
349	C₂²	C₂₃×#418	1	1	yes	characteristic
350	C₂²	C₂₃×#419	1	1	yes	characteristic
351	C₄	—	2	2	no	—
352	C₄	—	2	1	no	—
353	C₄	—	2	1	no	—
354	C₄	—	8	4	no	—
355	C₄	C₂₃×#340	1	4	yes	—
356	C₄	C₂₃×#343	1	4	yes	—
357	C₄	C₂×C₂₃×#102	1	1	yes	characteristic
358	C₄	C₂×C₂₃×#103	1	1	yes	characteristic
359	C₄	C₂₃×#417	1	2	yes	—
360	C₄	C₂×C₂₃×#106	1	1	yes	characteristic
361	C₄	C₂×C₂₃×#107	1	1	yes	characteristic
362	C₄	C₂₃×#428	1	2	yes	—
363	C₂	—	2	4	no	—
364	C₂	C₂₃×#1545	1	1	yes	characteristic
365	C₂	C₂₃×#1546	1	1	yes	characteristic
366	C₂	C₂₃×#1548	1	1	yes	characteristic
367	C₂	C₂₃×#1549	1	1	yes	characteristic
368	C₂	C₂×C₂₃×#340	1	1	yes	characteristic
369	C₂	C₂₃×#1736	1	1	yes	characteristic
370	C₂	C₂×C₂₃×#343	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
4. C₂₃×#1296	C₂	semidirect
11. C₂₃×#431	C₄	semidirect
13. C₂₃×#423	C₄	semidirect
53. C₂₃×C₄⋊C₈	C₂×C₄	semidirect
54. C₂₃×C₄⋊C₈	C₂×C₄	semidirect
106. #8043	C₂₃	direct (N × H)
155. #1296	C₂×C₂₃	semidirect
188. #431	C₄×C₂₃	semidirect
190. #423	C₄×C₂₃	semidirect
238. C₄⋊C₈	C₂×C₄×C₂₃	semidirect
239. C₄⋊C₈	C₂×C₄×C₂₃	semidirect
242. C₂₃	#8043	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₂₃×#431	2
C₂×C₂₃×#423	2
C₂×C₂₃×#384	2
C₂₃×#1296	2
#8043	23

Subgroups — C23×#8043 #19155669

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#8043 #19155669