Subgroups — C₂₃×#8082 #19155708

Order 5888.

598 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#2920	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#2920	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₂₃×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
4	C₂₃×#1301	C₂	1	4	yes	maximal, complemented
5	C₂³×C₈×C₂₃	—	2	1	no	—
6	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
7	C₂₃×#432	—	2	1	no	—
8	C₂₃×#432	—	2	1	no	—
9	C₂₃×#432	C₄	1	2	yes	—
10	C₂₃×#432	C₄	1	2	yes	—
11	C₂₃×#431	—	2	1	no	—
12	C₂₃×#431	—	2	1	no	—
13	C₂₃×#431	C₄	1	2	yes	—
14	C₂₃×#431	C₂²	1	2	yes	—
15	C₂₃×#423	—	2	1	no	—
16	C₂₃×#423	C₂²	1	2	yes	—
17	C₂×C₂₃×C₄⋊C₈	—	2	1	no	—
18	C₂×C₂₃×C₄⋊C₈	—	2	1	no	—
19	C₂×C₂₃×C₄⋊C₈	—	2	1	no	—
20	C₂×C₂₃×C₄⋊C₈	C₄	1	2	yes	—
21	C₂×C₂₃×C₄⋊C₈	C₄	1	2	yes	—
22	C₂×C₂₃×C₄⋊C₈	C₂²	1	2	yes	—
23	C₂₃×#407	—	2	1	no	—
24	C₂₃×#407	C₄	1	2	yes	—
25	C₄×M₁₆×C₂₃	—	2	1	no	—
26	C₄×M₁₆×C₂₃	—	2	1	no	—
27	C₂³×C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
28	C₂³×C₄×C₂₃	D₄	1	1	yes	characteristic
29	C₂³×C₄×C₂₃	Q₈	1	1	yes	characteristic
30	C₂×M₁₆×C₂₃	—	2	2	no	—
31	C₂×M₁₆×C₂₃	—	2	2	no	—
32	C₂²×C₈×C₂₃	—	2	2	no	—
33	C₂²×C₈×C₂₃	—	2	2	no	—
34	C₂²×C₈×C₂₃	—	2	2	no	—
35	C₂²×C₈×C₂₃	—	4	4	no	—
36	C₂×C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
37	C₂×C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
38	C₂×C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
39	C₂×C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
40	C₂×C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
41	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
42	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
43	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
44	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
45	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
46	C₂×C₄²×C₂₃	Q₈	1	1	yes	characteristic
47	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
48	C₂₃×C₄⋊C₈	—	2	2	no	—
49	C₂₃×C₄⋊C₈	—	2	2	no	—
50	C₂₃×C₄⋊C₈	—	2	2	no	—
51	C₂₃×C₄⋊C₈	—	2	2	no	—
52	C₂₃×C₄⋊C₈	—	2	2	no	—
53	C₂₃×C₄⋊C₈	—	2	2	no	—
54	C₂₃×C₄⋊C₈	C₂×C₄	1	4	yes	—
55	C₂₃×C₄⋊C₈	C₂×C₄	1	4	yes	—
56	C₂₃×C₂²⋊C₈	—	2	2	no	—
57	C₂₃×C₂²⋊C₈	—	2	2	no	—
58	C₂₃×C₂²⋊C₈	—	2	2	no	—
59	C₂₃×C₂²⋊C₈	C₂×C₄	1	4	yes	—
60	C₂₃×#97	—	2	2	no	—
61	C₂₃×#97	—	2	2	no	—
62	C₄×C₈×C₂₃	—	2	2	no	—
63	C₄×C₈×C₂₃	—	2	2	no	—
64	C₂⁴×C₂₃	C₄⋊C₄	1	1	yes	characteristic
65	C₂²×C₄×C₂₃	—	2	4	no	—
66	C₂²×C₄×C₂₃	—	2	2	no	—
67	C₂²×C₄×C₂₃	—	2	2	no	—
68	C₂²×C₄×C₂₃	—	4	2	no	—
69	C₂²×C₄×C₂₃	C₄²	1	1	yes	characteristic
70	C₂²×C₄×C₂₃	C₄²	1	1	yes	characteristic
71	C₂²×C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
72	C₂²×C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
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	1	yes	characteristic
77	C₂²×C₄×C₂₃	C₄⋊C₄	1	1	yes	characteristic
78	C₂²×C₄×C₂₃	C₄⋊C₄	1	1	yes	characteristic
79	C₂²×C₄×C₂₃	C₄⋊C₄	1	1	yes	characteristic
80	C₂²×C₄×C₂₃	C₄⋊C₄	1	1	yes	characteristic
81	C₂²×C₄×C₂₃	C₄⋊C₄	1	1	yes	characteristic
82	C₂²×C₄×C₂₃	C₄⋊C₄	1	1	yes	characteristic
83	C₂²×C₄×C₂₃	C₄⋊C₄	1	1	yes	characteristic
84	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
85	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
86	C₂²×C₄×C₂₃	C₂×Q₈	1	1	yes	characteristic
87	M₁₆×C₂₃	—	4	4	no	—
88	M₁₆×C₂₃	—	4	2	no	—
89	M₁₆×C₂₃	—	4	2	no	—
90	C₂×C₈×C₂₃	—	2	4	no	—
91	C₂×C₈×C₂₃	—	2	4	no	—
92	C₂×C₈×C₂₃	—	2	4	no	—
93	C₂×C₈×C₂₃	—	4	4	no	—
94	C₂×C₈×C₂₃	—	4	4	no	—
95	C₂×C₈×C₂₃	—	4	4	no	—
96	C₄²×C₂₃	C₄²	1	1	yes	characteristic
97	C₄²×C₂₃	C₄²	1	1	yes	characteristic
98	C₄²×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
99	C₄²×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
100	C₄²×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
101	C₄²×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
102	C₄²×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
103	C₄²×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
104	C₄²×C₂₃	C₄⋊C₄	1	1	yes	characteristic
105	C₄²×C₂₃	C₄⋊C₄	1	1	yes	characteristic
106	C₄²×C₂₃	C₄⋊C₄	1	1	yes	characteristic
107	C₄²×C₂₃	C₄⋊C₄	1	1	yes	characteristic
108	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
109	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
110	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
111	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
112	#8082	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
113	C₂³×C₂₃	—	2	2	no	—
114	C₂³×C₂₃	—	2	2	no	—
115	C₂³×C₂₃	—	2	2	no	—
116	C₂³×C₂₃	#95	1	1	yes	characteristic
117	C₂³×C₂₃	#95	1	1	yes	characteristic
118	C₂³×C₂₃	C₂×C₄⋊C₄	1	1	yes	characteristic
119	C₂×C₄×C₂₃	—	2	2	no	—
120	C₂×C₄×C₂₃	—	2	2	no	—
121	C₂×C₄×C₂₃	—	2	2	no	—
122	C₂×C₄×C₂₃	—	2	2	no	—
123	C₂×C₄×C₂₃	—	2	2	no	—
124	C₂×C₄×C₂₃	—	2	2	no	—
125	C₂×C₄×C₂₃	—	2	2	no	—
126	C₂×C₄×C₂₃	—	2	2	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	—	4	1	no	—
134	C₂×C₄×C₂₃	—	4	1	no	—
135	C₂×C₄×C₂₃	—	4	1	no	—
136	C₂×C₄×C₂₃	—	4	1	no	—
137	C₂×C₄×C₂₃	#95	1	1	yes	characteristic
138	C₂×C₄×C₂₃	#95	1	1	yes	characteristic
139	C₂×C₄×C₂₃	#95	1	1	yes	characteristic
140	C₂×C₄×C₂₃	#95	1	1	yes	characteristic
141	C₂×C₄×C₂₃	#95	1	1	yes	characteristic
142	C₂×C₄×C₂₃	#95	1	1	yes	characteristic
143	C₂×C₄×C₂₃	#108	1	4	yes	—
144	C₂×C₄×C₂₃	C₂×C₄²	1	1	yes	characteristic
145	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
146	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
147	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
148	C₂×C₄×C₂₃	C₂×C₄⋊C₄	1	1	yes	characteristic
149	C₂×C₄×C₂₃	C₂×C₄⋊C₄	1	1	yes	characteristic
150	C₂×C₄×C₂₃	AGL(1,ℤ/8)	1	2	yes	—
151	C₂×C₄×C₂₃	#137	1	2	yes	—
152	C₈×C₂₃	—	4	4	no	—
153	C₈×C₂₃	—	4	4	no	—
154	C₈×C₂₃	—	4	4	no	—
155	#2920	C₂×C₂₃	1	1	yes	characteristic
156	#2920	C₂×C₂₃	1	1	yes	characteristic
157	C₂²×C₄⋊C₈	C₂×C₂₃	1	1	yes	characteristic
158	#1301	C₂×C₂₃	1	4	yes	complemented
159	C₂²×C₂₃	—	2	8	no	—
160	C₂²×C₂₃	—	2	1	no	—
161	C₂²×C₂₃	—	2	1	no	—
162	C₂²×C₂₃	—	2	1	no	—
163	C₂²×C₂₃	—	2	1	no	—
164	C₂²×C₂₃	—	2	1	no	—
165	C₂²×C₂₃	—	2	1	no	—
166	C₂²×C₂₃	#341	1	2	yes	—
167	C₂²×C₂₃	#344	1	2	yes	—
168	C₂²×C₂₃	C₂×#95	1	1	yes	characteristic
169	C₂²×C₂₃	#428	1	2	yes	—
170	C₄×C₂₃	—	2	1	no	—
171	C₄×C₂₃	—	2	1	no	—
172	C₄×C₂₃	—	2	1	no	—
173	C₄×C₂₃	—	2	1	no	—
174	C₄×C₂₃	—	2	1	no	—
175	C₄×C₂₃	—	2	1	no	—
176	C₄×C₂₃	—	2	1	no	—
177	C₄×C₂₃	—	2	1	no	—
178	C₄×C₂₃	#341	1	2	yes	—
179	C₄×C₂₃	#417	1	2	yes	—
180	C₄×C₂₃	#418	1	1	yes	characteristic
181	C₄×C₂₃	#419	1	1	yes	characteristic
182	C₄×C₂₃	C₂×#108	1	2	yes	—
183	C₂³×C₈	—	2	1	no	—
184	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
185	#432	—	2	1	no	—
186	#432	—	2	1	no	—
187	#432	C₄×C₂₃	1	2	yes	—
188	#432	C₄×C₂₃	1	2	yes	—
189	#431	—	2	1	no	—
190	#431	—	2	1	no	—
191	#431	C₄×C₂₃	1	2	yes	—
192	#431	C₂²×C₂₃	1	2	yes	—
193	#423	—	2	1	no	—
194	#423	C₂²×C₂₃	1	2	yes	—
195	C₂×C₄⋊C₈	—	2	1	no	—
196	C₂×C₄⋊C₈	—	2	1	no	—
197	C₂×C₄⋊C₈	—	2	1	no	—
198	C₂×C₄⋊C₈	C₄×C₂₃	1	2	yes	—
199	C₂×C₄⋊C₈	C₄×C₂₃	1	2	yes	—
200	C₂×C₄⋊C₈	C₂²×C₂₃	1	2	yes	—
201	#407	—	2	1	no	—
202	#407	C₄×C₂₃	1	2	yes	—
203	C₄×M₁₆	—	2	1	no	—
204	C₄×M₁₆	—	2	1	no	—
205	C₂×C₂₃	—	2	2	no	—
206	C₂×C₂₃	—	2	2	no	—
207	C₂×C₂₃	—	2	2	no	—
208	C₂×C₂₃	#1736	1	1	yes	characteristic
209	C₂×C₂₃	C₂×#341	1	1	yes	characteristic
210	C₂×C₂₃	C₂×#344	1	1	yes	characteristic
211	C₂³×C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
212	C₂³×C₄	D₄×C₂₃	1	1	yes	characteristic
213	C₂³×C₄	Q₈×C₂₃	1	1	yes	characteristic
214	C₂×M₁₆	—	2	2	no	—
215	C₂×M₁₆	—	2	2	no	—
216	C₂²×C₈	—	2	2	no	—
217	C₂²×C₈	—	2	2	no	—
218	C₂²×C₈	—	2	2	no	—
219	C₂²×C₈	—	4	4	no	—
220	C₂×C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic
221	C₂×C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic
222	C₂×C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic
223	C₂×C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic
224	C₂×C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic
225	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
226	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
227	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
228	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
229	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
230	C₂×C₄²	Q₈×C₂₃	1	1	yes	characteristic
231	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
232	C₄⋊C₈	—	2	2	no	—
233	C₄⋊C₈	—	2	2	no	—
234	C₄⋊C₈	—	2	2	no	—
235	C₄⋊C₈	—	2	2	no	—
236	C₄⋊C₈	—	2	2	no	—
237	C₄⋊C₈	—	2	2	no	—
238	C₄⋊C₈	C₂×C₄×C₂₃	1	4	yes	—
239	C₄⋊C₈	C₂×C₄×C₂₃	1	4	yes	—
240	C₂²⋊C₈	—	2	2	no	—
241	C₂²⋊C₈	—	2	2	no	—
242	C₂²⋊C₈	—	2	2	no	—
243	C₂²⋊C₈	C₂×C₄×C₂₃	1	4	yes	—
244	#97	—	2	2	no	—
245	#97	—	2	2	no	—
246	C₄×C₈	—	2	2	no	—
247	C₄×C₈	—	2	2	no	—
248	C₂₃	#8082	1	1	yes	characteristic, direct product factor, Sylow
249	C₂⁴	C₄⋊C₄×C₂₃	1	1	yes	characteristic
250	C₂²×C₄	—	2	4	no	—
251	C₂²×C₄	—	2	2	no	—
252	C₂²×C₄	—	2	2	no	—
253	C₂²×C₄	—	4	2	no	—
254	C₂²×C₄	C₄²×C₂₃	1	1	yes	characteristic
255	C₂²×C₄	C₄²×C₂₃	1	1	yes	characteristic
256	C₂²×C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
257	C₂²×C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
258	C₂²×C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
259	C₂²×C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
260	C₂²×C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
261	C₂²×C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
262	C₂²×C₄	C₄⋊C₄×C₂₃	1	1	yes	characteristic
263	C₂²×C₄	C₄⋊C₄×C₂₃	1	1	yes	characteristic
264	C₂²×C₄	C₄⋊C₄×C₂₃	1	1	yes	characteristic
265	C₂²×C₄	C₄⋊C₄×C₂₃	1	1	yes	characteristic
266	C₂²×C₄	C₄⋊C₄×C₂₃	1	1	yes	characteristic
267	C₂²×C₄	C₄⋊C₄×C₂₃	1	1	yes	characteristic
268	C₂²×C₄	C₄⋊C₄×C₂₃	1	1	yes	characteristic
269	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
270	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
271	C₂²×C₄	C₂×Q₈×C₂₃	1	1	yes	characteristic
272	M₁₆	—	4	4	no	—
273	M₁₆	—	4	2	no	—
274	M₁₆	—	4	2	no	—
275	C₂×C₈	—	2	4	no	—
276	C₂×C₈	—	2	4	no	—
277	C₂×C₈	—	2	4	no	—
278	C₂×C₈	—	4	4	no	—
279	C₂×C₈	—	4	4	no	—
280	C₂×C₈	—	4	4	no	—
281	C₄²	C₄²×C₂₃	1	1	yes	characteristic
282	C₄²	C₄²×C₂₃	1	1	yes	characteristic
283	C₄²	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
284	C₄²	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
285	C₄²	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
286	C₄²	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
287	C₄²	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
288	C₄²	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
289	C₄²	C₄⋊C₄×C₂₃	1	1	yes	characteristic
290	C₄²	C₄⋊C₄×C₂₃	1	1	yes	characteristic
291	C₄²	C₄⋊C₄×C₂₃	1	1	yes	characteristic
292	C₄²	C₄⋊C₄×C₂₃	1	1	yes	characteristic
293	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
294	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
295	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
296	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
297	C₂³	—	2	2	no	—
298	C₂³	—	2	2	no	—
299	C₂³	—	2	2	no	—
300	C₂³	C₂₃×#95	1	1	yes	characteristic
301	C₂³	C₂₃×#95	1	1	yes	characteristic
302	C₂³	C₂×C₄⋊C₄×C₂₃	1	1	yes	characteristic
303	C₂×C₄	—	2	2	no	—
304	C₂×C₄	—	2	2	no	—
305	C₂×C₄	—	2	2	no	—
306	C₂×C₄	—	2	2	no	—
307	C₂×C₄	—	2	2	no	—
308	C₂×C₄	—	2	2	no	—
309	C₂×C₄	—	2	2	no	—
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	2	1	no	—
312	C₂×C₄	—	2	1	no	—
313	C₂×C₄	—	2	1	no	—
314	C₂×C₄	—	2	1	no	—
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	4	1	no	—
318	C₂×C₄	—	4	1	no	—
319	C₂×C₄	—	4	1	no	—
320	C₂×C₄	—	4	1	no	—
321	C₂×C₄	C₂₃×#95	1	1	yes	characteristic
322	C₂×C₄	C₂₃×#95	1	1	yes	characteristic
323	C₂×C₄	C₂₃×#95	1	1	yes	characteristic
324	C₂×C₄	C₂₃×#95	1	1	yes	characteristic
325	C₂×C₄	C₂₃×#95	1	1	yes	characteristic
326	C₂×C₄	C₂₃×#95	1	1	yes	characteristic
327	C₂×C₄	C₂₃×#108	1	4	yes	—
328	C₂×C₄	C₂×C₄²×C₂₃	1	1	yes	characteristic
329	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
330	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
331	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
332	C₂×C₄	C₂×C₄⋊C₄×C₂₃	1	1	yes	characteristic
333	C₂×C₄	C₂×C₄⋊C₄×C₂₃	1	1	yes	characteristic
334	C₂×C₄	C₂₃×AGL(1,ℤ/8)	1	2	yes	—
335	C₂×C₄	C₂₃×#137	1	2	yes	—
336	C₈	—	4	4	no	—
337	C₈	—	4	4	no	—
338	C₈	—	4	4	no	—
339	C₂²	—	2	8	no	—
340	C₂²	—	2	1	no	—
341	C₂²	—	2	1	no	—
342	C₂²	—	2	1	no	—
343	C₂²	—	2	1	no	—
344	C₂²	—	2	1	no	—
345	C₂²	—	2	1	no	—
346	C₂²	C₂₃×#341	1	2	yes	—
347	C₂²	C₂₃×#344	1	2	yes	—
348	C₂²	C₂×C₂₃×#95	1	1	yes	characteristic
349	C₂²	C₂₃×#428	1	2	yes	—
350	C₄	—	2	1	no	—
351	C₄	—	2	1	no	—
352	C₄	—	2	1	no	—
353	C₄	—	2	1	no	—
354	C₄	—	2	1	no	—
355	C₄	—	2	1	no	—
356	C₄	—	2	1	no	—
357	C₄	—	2	1	no	—
358	C₄	C₂₃×#341	1	2	yes	—
359	C₄	C₂₃×#417	1	2	yes	—
360	C₄	C₂₃×#418	1	1	yes	characteristic
361	C₄	C₂₃×#419	1	1	yes	characteristic
362	C₄	C₂×C₂₃×#108	1	2	yes	—
363	C₂	—	2	2	no	—
364	C₂	—	2	2	no	—
365	C₂	—	2	2	no	—
366	C₂	C₂₃×#1736	1	1	yes	characteristic
367	C₂	C₂×C₂₃×#341	1	1	yes	characteristic
368	C₂	C₂×C₂₃×#344	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₂₃	C₂×C₂²⋊C₄
commutator	C₂×C₄	C₂×C₄²×C₂₃
Frattini, cosocle	C₂×C₄²	C₂³×C₂₃
socle	C₂²×C₂₃	C₂×#95
prime radical	C₂⁴×C₂₃	C₄⋊C₄
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₃ ◁ C₂²×C₄²×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₂₃×#1301	C₂	semidirect
112. #8082	C₂₃	direct (N × H)
158. #1301	C₂×C₂₃	semidirect
248. C₂₃	#8082	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×#2920	2
C₂²×C₂₃×C₄⋊C₈	2
C₂₃×#1301	2
#8082	23

Subgroups — C23×#8082 #19155708

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#8082 #19155708