Subgroups — C₂₃×#11323 #19158949

Order 5888.

974 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₂₃×#106	C₂	1	2	yes	maximal
2	C₂×C₂₃×#384	C₂	1	1	yes	maximal, characteristic
3	C₂×C₂₃×#340	C₂	1	2	yes	maximal
4	C₂×C₂₃×#336	C₂	1	1	yes	maximal, characteristic
5	C₂₃×C₄⋊#95	C₂	1	1	yes	maximal, characteristic
6	C₂³×C₈×C₂₃	C₂²	1	2	yes	—
7	C₂²×C₄⋊C₄×C₂₃	—	2	2	no	—
8	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
9	C₂²×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
10	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
11	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
12	C₂×C₂₃×#106	—	2	4	no	—
13	C₂×C₂₃×#106	—	2	4	no	—
14	C₂×C₂₃×#106	—	2	4	no	—
15	C₂₃×#384	—	2	4	no	—
16	C₂×C₂₃×#95	—	2	2	no	—
17	C₂₃×#340	—	2	4	no	—
18	C₂₃×#336	C₄	1	4	yes	complemented
19	C₂³×C₄×C₂₃	—	2	1	no	—
20	C₂³×C₄×C₂₃	—	2	1	no	—
21	C₂³×C₄×C₂₃	—	2	2	no	—
22	C₂³×C₄×C₂₃	D₄	1	2	yes	—
23	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
24	C₂²×C₈×C₂₃	—	2	2	no	—
25	C₂²×C₈×C₂₃	—	2	2	no	—
26	C₂²×C₈×C₂₃	—	2	2	no	—
27	C₂²×C₈×C₂₃	—	2	2	no	—
28	C₂²×C₈×C₂₃	C₂×C₄	1	4	yes	—
29	C₂²×C₈×C₂₃	D₄	1	4	yes	—
30	C₂²×C₈×C₂₃	Q₈	1	4	yes	—
31	C₂×C₄⋊C₄×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	—	2	2	no	—
38	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
39	C₂×C₄⋊C₄×C₂₃	—	2	8	no	—
40	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
41	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
42	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
43	C₂×C₄⋊C₄×C₂₃	—	4	4	no	—
44	C₂×C₄⋊C₄×C₂₃	—	4	4	no	—
45	C₂×C₄⋊C₄×C₂₃	D₄	1	4	yes	—
46	C₂×C₄⋊C₄×C₂₃	D₄	1	2	yes	—
47	C₂×C₄⋊C₄×C₂₃	Q₈	1	2	yes	—
48	C₂×C₄²×C₂₃	—	2	2	no	—
49	C₂×C₄²×C₂₃	—	2	2	no	—
50	C₂×C₄²×C₂₃	C₂×C₄	1	2	yes	—
51	C₂×C₄²×C₂₃	Q₈	1	2	yes	—
52	C₂₃×#106	—	2	16	no	—
53	C₂₃×#95	—	4	4	no	—
54	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
55	C₂²×C₄×C₂₃	—	2	2	no	—
56	C₂²×C₄×C₂₃	—	2	2	no	—
57	C₂²×C₄×C₂₃	—	2	2	no	—
58	C₂²×C₄×C₂₃	—	2	2	no	—
59	C₂²×C₄×C₂₃	—	2	4	no	—
60	C₂²×C₄×C₂₃	—	2	2	no	—
61	C₂²×C₄×C₂₃	—	2	2	no	—
62	C₂²×C₄×C₂₃	—	4	1	no	—
63	C₂²×C₄×C₂₃	—	4	2	no	—
64	C₂²×C₄×C₂₃	—	4	1	no	—
65	C₂²×C₄×C₂₃	—	4	2	no	—
66	C₂²×C₄×C₂₃	—	4	1	no	—
67	C₂²×C₄×C₂₃	—	4	1	no	—
68	C₂²×C₄×C₂₃	—	4	4	no	—
69	C₂²×C₄×C₂₃	—	4	2	no	—
70	C₂²×C₄×C₂₃	—	4	2	no	—
71	C₂²×C₄×C₂₃	—	4	4	no	—
72	C₂²×C₄×C₂₃	—	4	2	no	—
73	C₂²×C₄×C₂₃	—	4	2	no	—
74	C₂²×C₄×C₂₃	C₄⋊C₄	1	4	yes	—
75	C₂²×C₄×C₂₃	SD₁₆	1	4	yes	—
76	C₂²×C₄×C₂₃	SD₁₆	1	4	yes	—
77	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
78	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
79	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
80	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
81	C₂²×C₄×C₂₃	C₂×Q₈	1	2	yes	—
82	C₂²×C₄×C₂₃	C₂×Q₈	1	1	yes	characteristic
83	C₂²×C₄×C₂₃	C₂×Q₈	1	1	yes	characteristic
84	C₂²×C₄×C₂₃	#41	1	2	yes	—
85	C₂²×C₄×C₂₃	#41	1	1	yes	characteristic
86	C₂²×C₄×C₂₃	#41	1	1	yes	characteristic
87	C₂×C₈×C₂₃	—	2	4	no	—
88	C₂×C₈×C₂₃	—	2	4	no	—
89	C₂×C₈×C₂₃	—	2	4	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	C₄⋊C₄	1	8	yes	complemented
94	C₄⋊C₄×C₂₃	—	2	4	no	—
95	C₄⋊C₄×C₂₃	—	2	4	no	—
96	C₄⋊C₄×C₂₃	—	2	4	no	—
97	C₄⋊C₄×C₂₃	—	2	4	no	—
98	C₄⋊C₄×C₂₃	—	4	16	no	—
99	C₄⋊C₄×C₂₃	—	4	2	no	—
100	C₄⋊C₄×C₂₃	—	4	2	no	—
101	C₄⋊C₄×C₂₃	—	4	2	no	—
102	C₄⋊C₄×C₂₃	—	4	2	no	—
103	C₄²×C₂₃	—	2	4	no	—
104	C₄²×C₂₃	—	2	4	no	—
105	#11323	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
106	C₂³×C₂₃	C₂×C₄⋊C₄	1	1	yes	characteristic
107	C₂³×C₂₃	#120	1	1	yes	characteristic
108	C₂³×C₂₃	#121	1	1	yes	characteristic
109	C₂³×C₂₃	C₂²⋊Q₈	1	1	yes	characteristic
110	C₂³×C₂₃	#123	1	1	yes	characteristic
111	C₂³×C₂₃	#127	1	1	yes	characteristic
112	C₂³×C₂₃	C₄⋊Q₈	1	1	yes	characteristic
113	C₂³×C₂₃	C₂×SD₁₆	1	2	yes	—
114	C₂³×C₂₃	C₂×SD₁₆	1	2	yes	—
115	C₂³×C₂₃	AGL(1,ℤ/8)	1	2	yes	—
116	C₂³×C₂₃	#137	1	2	yes	—
117	C₂×C₄×C₂₃	—	2	4	no	—
118	C₂×C₄×C₂₃	—	2	4	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	2	no	—
124	C₂×C₄×C₂₃	—	4	4	no	—
125	C₂×C₄×C₂₃	—	4	2	no	—
126	C₂×C₄×C₂₃	—	4	8	no	—
127	C₂×C₄×C₂₃	—	4	4	no	—
128	C₂×C₄×C₂₃	—	4	4	no	—
129	C₂×C₄×C₂₃	—	8	2	no	—
130	C₂×C₄×C₂₃	—	8	4	no	—
131	C₂×C₄×C₂₃	—	8	2	no	—
132	C₂×C₄×C₂₃	—	8	1	no	—
133	C₂×C₄×C₂₃	—	8	1	no	—
134	C₂×C₄×C₂₃	—	8	2	no	—
135	C₂×C₄×C₂₃	—	8	1	no	—
136	C₂×C₄×C₂₃	—	8	2	no	—
137	C₂×C₄×C₂₃	—	8	1	no	—
138	C₂×C₄×C₂₃	#106	1	8	yes	complemented
139	C₂×C₄×C₂₃	C₂×C₄⋊C₄	1	2	yes	—
140	C₂×C₄×C₂₃	C₄×D₄	1	1	yes	characteristic
141	C₂×C₄×C₂₃	C₄×D₄	1	2	yes	—
142	C₂×C₄×C₂₃	C₄×Q₈	1	1	yes	characteristic
143	C₂×C₄×C₂₃	#120	1	2	yes	—
144	C₂×C₄×C₂₃	#121	1	2	yes	—
145	C₂×C₄×C₂₃	C₂²⋊Q₈	1	2	yes	—
146	C₂×C₄×C₂₃	C₂²⋊Q₈	1	2	yes	—
147	C₂×C₄×C₂₃	C₂²⋊Q₈	1	2	yes	—
148	C₂×C₄×C₂₃	C₂²⋊Q₈	1	2	yes	—
149	C₂×C₄×C₂₃	#123	1	2	yes	—
150	C₂×C₄×C₂₃	#125	1	2	yes	—
151	C₂×C₄×C₂₃	#125	1	1	yes	characteristic
152	C₂×C₄×C₂₃	C₄⋊Q₈	1	2	yes	—
153	C₂×C₄×C₂₃	C₄⋊Q₈	1	1	yes	characteristic
154	C₂×C₄×C₂₃	C₄⋊Q₈	1	2	yes	—
155	C₈×C₂₃	—	2	8	no	—
156	C₂²×#106	C₂×C₂₃	1	2	yes	—
157	C₂×#384	C₂×C₂₃	1	1	yes	characteristic
158	C₂×#340	C₂×C₂₃	1	2	yes	—
159	C₂×#336	C₂×C₂₃	1	1	yes	characteristic
160	C₄⋊#95	C₂×C₂₃	1	1	yes	characteristic
161	C₂²×C₂₃	#384	1	1	yes	characteristic
162	C₂²×C₂₃	#385	1	1	yes	characteristic
163	C₂²×C₂₃	#389	1	1	yes	characteristic
164	C₂²×C₂₃	#392	1	1	yes	characteristic
165	C₂²×C₂₃	#395	1	1	yes	characteristic
166	C₂²×C₂₃	#398	1	1	yes	characteristic
167	C₂²×C₂₃	#399	1	1	yes	characteristic
168	C₂²×C₂₃	C₂×#106	1	2	yes	—
169	C₂²×C₂₃	#428	1	2	yes	—
170	C₂²×C₂₃	#448	1	2	yes	—
171	C₂²×C₂₃	#450	1	2	yes	—
172	C₂²×C₂₃	#460	1	2	yes	—
173	C₂²×C₂₃	#461	1	2	yes	—
174	C₂²×C₂₃	#475	1	2	yes	—
175	C₂²×C₂₃	#476	1	2	yes	—
176	C₂²×C₂₃	#481	1	2	yes	—
177	C₂²×C₂₃	#483	1	2	yes	—
178	C₂²×C₂₃	#492	1	1	yes	characteristic
179	C₂²×C₂₃	#492	1	1	yes	characteristic
180	C₂²×C₂₃	#496	1	1	yes	characteristic
181	C₂²×C₂₃	#497	1	1	yes	characteristic
182	C₂²×C₂₃	#498	1	2	yes	—
183	C₂²×C₂₃	#501	1	2	yes	—
184	C₄×C₂₃	—	2	8	no	—
185	C₄×C₂₃	—	8	2	no	—
186	C₄×C₂₃	—	8	2	no	—
187	C₄×C₂₃	—	8	4	no	—
188	C₄×C₂₃	#385	1	2	yes	—
189	C₄×C₂₃	#389	1	2	yes	—
190	C₄×C₂₃	#395	1	2	yes	—
191	C₄×C₂₃	#398	1	2	yes	—
192	C₂³×C₈	C₂²×C₂₃	1	2	yes	—
193	C₂²×C₄⋊C₄	—	2	2	no	—
194	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
195	C₂²×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
196	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
197	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
198	C₂×#106	—	2	4	no	—
199	C₂×#106	—	2	4	no	—
200	C₂×#106	—	2	4	no	—
201	#384	—	2	4	no	—
202	C₂×#95	—	2	2	no	—
203	#340	—	2	4	no	—
204	#336	C₄×C₂₃	1	4	yes	complemented
205	C₂×C₂₃	#1444	1	1	yes	characteristic
206	C₂×C₂₃	#1844	1	1	yes	characteristic
207	C₂×C₂₃	#1847	1	1	yes	characteristic
208	C₂×C₂₃	#1853	1	2	yes	—
209	C₂×C₂₃	#1948	1	2	yes	—
210	C₂×C₂₃	#2013	1	1	yes	characteristic
211	C₂×C₂₃	#2014	1	1	yes	characteristic
212	C₂×C₂₃	#2058	1	2	yes	—
213	C₂×C₂₃	#2084	1	2	yes	—
214	C₂×C₂₃	#2094	1	1	yes	characteristic
215	C₂×C₂₃	#2096	1	1	yes	characteristic
216	C₂³×C₄	—	2	2	no	—
217	C₂³×C₄	—	2	1	no	—
218	C₂³×C₄	—	2	1	no	—
219	C₂³×C₄	D₄×C₂₃	1	2	yes	—
220	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
221	C₂²×C₈	—	2	2	no	—
222	C₂²×C₈	—	2	2	no	—
223	C₂²×C₈	—	2	2	no	—
224	C₂²×C₈	—	2	2	no	—
225	C₂²×C₈	C₂×C₄×C₂₃	1	4	yes	—
226	C₂²×C₈	D₄×C₂₃	1	4	yes	—
227	C₂²×C₈	Q₈×C₂₃	1	4	yes	—
228	C₂×C₄⋊C₄	—	2	2	no	—
229	C₂×C₄⋊C₄	—	2	2	no	—
230	C₂×C₄⋊C₄	—	2	2	no	—
231	C₂×C₄⋊C₄	—	2	2	no	—
232	C₂×C₄⋊C₄	—	2	2	no	—
233	C₂×C₄⋊C₄	—	2	2	no	—
234	C₂×C₄⋊C₄	—	2	2	no	—
235	C₂×C₄⋊C₄	—	2	2	no	—
236	C₂×C₄⋊C₄	—	2	8	no	—
237	C₂×C₄⋊C₄	—	2	2	no	—
238	C₂×C₄⋊C₄	—	2	1	no	—
239	C₂×C₄⋊C₄	—	2	1	no	—
240	C₂×C₄⋊C₄	—	4	4	no	—
241	C₂×C₄⋊C₄	—	4	4	no	—
242	C₂×C₄⋊C₄	D₄×C₂₃	1	4	yes	—
243	C₂×C₄⋊C₄	D₄×C₂₃	1	2	yes	—
244	C₂×C₄⋊C₄	Q₈×C₂₃	1	2	yes	—
245	C₂×C₄²	—	2	2	no	—
246	C₂×C₄²	—	2	2	no	—
247	C₂×C₄²	C₂×C₄×C₂₃	1	2	yes	—
248	C₂×C₄²	Q₈×C₂₃	1	2	yes	—
249	#106	—	2	16	no	—
250	#95	—	4	4	no	—
251	C₂₃	#11323	1	1	yes	characteristic, direct product factor, Sylow
252	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
253	C₂²×C₄	—	2	2	no	—
254	C₂²×C₄	—	2	2	no	—
255	C₂²×C₄	—	2	2	no	—
256	C₂²×C₄	—	2	2	no	—
257	C₂²×C₄	—	2	4	no	—
258	C₂²×C₄	—	2	2	no	—
259	C₂²×C₄	—	2	2	no	—
260	C₂²×C₄	—	4	1	no	—
261	C₂²×C₄	—	4	2	no	—
262	C₂²×C₄	—	4	1	no	—
263	C₂²×C₄	—	4	2	no	—
264	C₂²×C₄	—	4	1	no	—
265	C₂²×C₄	—	4	1	no	—
266	C₂²×C₄	—	4	2	no	—
267	C₂²×C₄	—	4	2	no	—
268	C₂²×C₄	—	4	4	no	—
269	C₂²×C₄	—	4	4	no	—
270	C₂²×C₄	—	4	2	no	—
271	C₂²×C₄	—	4	2	no	—
272	C₂²×C₄	C₄⋊C₄×C₂₃	1	4	yes	—
273	C₂²×C₄	SD₁₆×C₂₃	1	4	yes	—
274	C₂²×C₄	SD₁₆×C₂₃	1	4	yes	—
275	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
276	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
277	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
278	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
279	C₂²×C₄	C₂×Q₈×C₂₃	1	2	yes	—
280	C₂²×C₄	C₂×Q₈×C₂₃	1	1	yes	characteristic
281	C₂²×C₄	C₂×Q₈×C₂₃	1	1	yes	characteristic
282	C₂²×C₄	#41×C₂₃	1	2	yes	—
283	C₂²×C₄	#41×C₂₃	1	1	yes	characteristic
284	C₂²×C₄	#41×C₂₃	1	1	yes	characteristic
285	C₂×C₈	—	2	4	no	—
286	C₂×C₈	—	2	4	no	—
287	C₂×C₈	—	2	4	no	—
288	C₂×C₈	—	2	4	no	—
289	C₂×C₈	—	2	4	no	—
290	C₂×C₈	—	2	4	no	—
291	C₂×C₈	C₄⋊C₄×C₂₃	1	8	yes	complemented
292	C₄⋊C₄	—	2	4	no	—
293	C₄⋊C₄	—	2	4	no	—
294	C₄⋊C₄	—	2	4	no	—
295	C₄⋊C₄	—	2	4	no	—
296	C₄⋊C₄	—	4	16	no	—
297	C₄⋊C₄	—	4	2	no	—
298	C₄⋊C₄	—	4	2	no	—
299	C₄⋊C₄	—	4	2	no	—
300	C₄⋊C₄	—	4	2	no	—
301	C₄²	—	2	4	no	—
302	C₄²	—	2	4	no	—
303	C₂³	C₂×C₄⋊C₄×C₂₃	1	1	yes	characteristic
304	C₂³	C₂₃×#120	1	1	yes	characteristic
305	C₂³	C₂₃×#121	1	1	yes	characteristic
306	C₂³	C₂₃×C₂²⋊Q₈	1	1	yes	characteristic
307	C₂³	C₂₃×#123	1	1	yes	characteristic
308	C₂³	C₂₃×#127	1	1	yes	characteristic
309	C₂³	C₂₃×C₄⋊Q₈	1	1	yes	characteristic
310	C₂³	C₂×SD₁₆×C₂₃	1	2	yes	—
311	C₂³	C₂×SD₁₆×C₂₃	1	2	yes	—
312	C₂³	C₂₃×AGL(1,ℤ/8)	1	2	yes	—
313	C₂³	C₂₃×#137	1	2	yes	—
314	C₂×C₄	—	2	4	no	—
315	C₂×C₄	—	2	4	no	—
316	C₂×C₄	—	2	4	no	—
317	C₂×C₄	—	2	4	no	—
318	C₂×C₄	—	2	4	no	—
319	C₂×C₄	—	2	4	no	—
320	C₂×C₄	—	4	2	no	—
321	C₂×C₄	—	4	4	no	—
322	C₂×C₄	—	4	2	no	—
323	C₂×C₄	—	4	8	no	—
324	C₂×C₄	—	4	4	no	—
325	C₂×C₄	—	4	4	no	—
326	C₂×C₄	—	8	2	no	—
327	C₂×C₄	—	8	4	no	—
328	C₂×C₄	—	8	2	no	—
329	C₂×C₄	—	8	1	no	—
330	C₂×C₄	—	8	2	no	—
331	C₂×C₄	—	8	1	no	—
332	C₂×C₄	—	8	2	no	—
333	C₂×C₄	—	8	1	no	—
334	C₂×C₄	—	8	1	no	—
335	C₂×C₄	C₂₃×#106	1	8	yes	complemented
336	C₂×C₄	C₂×C₄⋊C₄×C₂₃	1	2	yes	—
337	C₂×C₄	C₄×D₄×C₂₃	1	1	yes	characteristic
338	C₂×C₄	C₄×D₄×C₂₃	1	2	yes	—
339	C₂×C₄	C₄×Q₈×C₂₃	1	1	yes	characteristic
340	C₂×C₄	C₂₃×#120	1	2	yes	—
341	C₂×C₄	C₂₃×#121	1	2	yes	—
342	C₂×C₄	C₂₃×C₂²⋊Q₈	1	2	yes	—
343	C₂×C₄	C₂₃×C₂²⋊Q₈	1	2	yes	—
344	C₂×C₄	C₂₃×C₂²⋊Q₈	1	2	yes	—
345	C₂×C₄	C₂₃×C₂²⋊Q₈	1	2	yes	—
346	C₂×C₄	C₂₃×#123	1	2	yes	—
347	C₂×C₄	C₂₃×#125	1	2	yes	—
348	C₂×C₄	C₂₃×#125	1	1	yes	characteristic
349	C₂×C₄	C₂₃×C₄⋊Q₈	1	2	yes	—
350	C₂×C₄	C₂₃×C₄⋊Q₈	1	1	yes	characteristic
351	C₂×C₄	C₂₃×C₄⋊Q₈	1	2	yes	—
352	C₈	—	2	8	no	—
353	C₂²	C₂₃×#384	1	1	yes	characteristic
354	C₂²	C₂₃×#385	1	1	yes	characteristic
355	C₂²	C₂₃×#389	1	1	yes	characteristic
356	C₂²	C₂₃×#392	1	1	yes	characteristic
357	C₂²	C₂₃×#395	1	1	yes	characteristic
358	C₂²	C₂₃×#398	1	1	yes	characteristic
359	C₂²	C₂₃×#399	1	1	yes	characteristic
360	C₂²	C₂×C₂₃×#106	1	2	yes	—
361	C₂²	C₂₃×#428	1	2	yes	—
362	C₂²	C₂₃×#448	1	2	yes	—
363	C₂²	C₂₃×#450	1	2	yes	—
364	C₂²	C₂₃×#460	1	2	yes	—
365	C₂²	C₂₃×#461	1	2	yes	—
366	C₂²	C₂₃×#475	1	2	yes	—
367	C₂²	C₂₃×#476	1	2	yes	—
368	C₂²	C₂₃×#481	1	2	yes	—
369	C₂²	C₂₃×#483	1	2	yes	—
370	C₂²	C₂₃×#492	1	1	yes	characteristic
371	C₂²	C₂₃×#492	1	1	yes	characteristic
372	C₂²	C₂₃×#496	1	1	yes	characteristic
373	C₂²	C₂₃×#497	1	1	yes	characteristic
374	C₂²	C₂₃×#498	1	2	yes	—
375	C₂²	C₂₃×#501	1	2	yes	—
376	C₄	—	2	8	no	—
377	C₄	—	8	2	no	—
378	C₄	—	8	4	no	—
379	C₄	—	8	2	no	—
380	C₄	C₂₃×#385	1	2	yes	—
381	C₄	C₂₃×#389	1	2	yes	—
382	C₄	C₂₃×#395	1	2	yes	—
383	C₄	C₂₃×#398	1	2	yes	—
384	C₂	C₂₃×#1444	1	1	yes	characteristic
385	C₂	C₂₃×#1844	1	1	yes	characteristic
386	C₂	C₂₃×#1847	1	1	yes	characteristic
387	C₂	C₂₃×#1853	1	2	yes	—
388	C₂	C₂₃×#1948	1	2	yes	—
389	C₂	C₂₃×#2013	1	1	yes	characteristic
390	C₂	C₂₃×#2014	1	1	yes	characteristic
391	C₂	C₂₃×#2058	1	2	yes	—
392	C₂	C₂₃×#2084	1	2	yes	—
393	C₂	C₂₃×#2094	1	1	yes	characteristic
394	C₂	C₂₃×#2096	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₂₃	C₂×D₄
commutator	C₂²×C₄	C₂²×C₄×C₂₃
Frattini, cosocle	C₂³×C₄	C₂³×C₂₃
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₂₃ ◁ C₂²×C₄²×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
18. C₂₃×#336	C₄	semidirect
93. C₂×C₈×C₂₃	C₄⋊C₄	semidirect
105. #11323	C₂₃	direct (N × H)
138. C₂×C₄×C₂₃	#106	semidirect
204. #336	C₄×C₂₃	semidirect
251. C₂₃	#11323	direct (N × H)
291. C₂×C₈	C₄⋊C₄×C₂₃	semidirect
335. C₂×C₄	C₂₃×#106	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₂₃×#106	2
C₂×C₂₃×#384	2
C₂×C₂₃×#340	2
C₂×C₂₃×#336	2
C₂₃×C₄⋊#95	2
#11323	23

Subgroups — C23×#11323 #19158949

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#11323 #19158949