Subgroups — C₂₃×#11255 #19158881

Order 5888.

846 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₂₃×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
2	C₂×C₂₃×#336	C₂	1	2	yes	maximal
3	C₂×C₂₃×#336	C₂	1	1	yes	maximal, characteristic
4	C₂×C₂₃×#336	C₂	1	2	yes	maximal
5	C₄×C₂₃×#95	C₂	1	1	yes	maximal, characteristic
6	C₂³×C₈×C₂₃	C₂²	1	1	yes	characteristic
7	C₂³×C₈×C₂₃	C₂²	1	2	yes	—
8	C₂³×C₈×C₂₃	C₂²	1	1	yes	characteristic
9	C₂²×C₄²×C₂₃	C₂²	1	2	yes	—
10	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
11	C₂×C₂₃×C₄⋊C₈	—	2	4	no	—
12	C₂×C₂₃×C₄⋊C₈	—	2	2	no	—
13	C₂×C₂₃×#95	C₄	1	2	yes	—
14	C₂×C₂₃×#95	C₄	1	1	yes	characteristic
15	C₂×C₂₃×#95	C₄	1	1	yes	characteristic
16	C₂₃×#336	—	2	4	no	—
17	C₂₃×#336	—	2	4	no	—
18	C₂₃×#336	—	2	2	no	—
19	C₂³×C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
20	C₂³×C₄×C₂₃	C₂×C₄	1	2	yes	—
21	C₂³×C₄×C₂₃	C₂×C₄	1	2	yes	—
22	C₂³×C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
23	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
24	C₂²×C₈×C₂₃	—	2	2	no	—
25	C₂²×C₈×C₂₃	—	2	1	no	—
26	C₂²×C₈×C₂₃	—	2	2	no	—
27	C₂²×C₈×C₂₃	—	2	1	no	—
28	C₂²×C₈×C₂₃	—	2	2	no	—
29	C₂²×C₈×C₂₃	—	2	2	no	—
30	C₂²×C₈×C₂₃	—	2	2	no	—
31	C₂²×C₈×C₂₃	—	2	1	no	—
32	C₂²×C₈×C₂₃	—	2	2	no	—
33	C₂²×C₈×C₂₃	—	2	1	no	—
34	C₂²×C₈×C₂₃	—	2	2	no	—
35	C₂²×C₈×C₂₃	—	2	2	no	—
36	C₂²×C₈×C₂₃	—	2	2	no	—
37	C₂²×C₈×C₂₃	—	2	2	no	—
38	C₂²×C₈×C₂₃	D₄	1	2	yes	—
39	C₂²×C₈×C₂₃	D₄	1	4	yes	—
40	C₂²×C₈×C₂₃	Q₈	1	2	yes	—
41	C₂×C₄²×C₂₃	—	2	2	no	—
42	C₂×C₄²×C₂₃	—	2	2	no	—
43	C₂×C₄²×C₂₃	—	2	2	no	—
44	C₂×C₄²×C₂₃	—	2	2	no	—
45	C₂×C₄²×C₂₃	—	2	2	no	—
46	C₂×C₄²×C₂₃	—	2	2	no	—
47	C₂×C₄²×C₂₃	—	2	2	no	—
48	C₂×C₄²×C₂₃	—	2	2	no	—
49	C₂×C₄²×C₂₃	D₄	1	2	yes	—
50	C₂×C₄²×C₂₃	Q₈	1	2	yes	—
51	C₂₃×C₄⋊C₈	—	2	8	no	—
52	C₂₃×#95	—	2	4	no	—
53	C₂₃×#95	—	2	2	no	—
54	C₂₃×#95	C₈	1	4	yes	complemented
55	C₂⁴×C₂₃	C₂²×C₄	1	1	yes	characteristic
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	2	no	—
60	C₂²×C₄×C₂₃	—	2	2	no	—
61	C₂²×C₄×C₂₃	—	2	2	no	—
62	C₂²×C₄×C₂₃	—	2	2	no	—
63	C₂²×C₄×C₂₃	—	2	2	no	—
64	C₂²×C₄×C₂₃	—	2	2	no	—
65	C₂²×C₄×C₂₃	—	2	2	no	—
66	C₂²×C₄×C₂₃	—	2	2	no	—
67	C₂²×C₄×C₂₃	—	2	2	no	—
68	C₂²×C₄×C₂₃	—	2	1	no	—
69	C₂²×C₄×C₂₃	—	2	1	no	—
70	C₂²×C₄×C₂₃	—	2	2	no	—
71	C₂²×C₄×C₂₃	—	2	2	no	—
72	C₂²×C₄×C₂₃	—	2	2	no	—
73	C₂²×C₄×C₂₃	—	2	2	no	—
74	C₂²×C₄×C₂₃	C₄⋊C₄	1	2	yes	—
75	C₂²×C₄×C₂₃	C₄⋊C₄	1	2	yes	—
76	C₂²×C₄×C₂₃	C₂×C₈	1	4	yes	—
77	C₂²×C₄×C₂₃	C₂×C₈	1	2	yes	—
78	C₂²×C₄×C₂₃	M₁₆	1	4	yes	—
79	C₂²×C₄×C₂₃	M₁₆	1	2	yes	—
80	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
81	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
82	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
83	C₂²×C₄×C₂₃	C₂×Q₈	1	1	yes	characteristic
84	C₂²×C₄×C₂₃	C₂×Q₈	1	1	yes	characteristic
85	C₂²×C₄×C₂₃	#41	1	1	yes	characteristic
86	C₂²×C₄×C₂₃	#41	1	2	yes	—
87	C₂²×C₄×C₂₃	#41	1	2	yes	—
88	C₂²×C₄×C₂₃	#41	1	2	yes	—
89	C₂²×C₄×C₂₃	#41	1	1	yes	characteristic
90	C₂×C₈×C₂₃	—	2	4	no	—
91	C₂×C₈×C₂₃	—	2	4	no	—
92	C₂×C₈×C₂₃	—	2	2	no	—
93	C₂×C₈×C₂₃	—	2	4	no	—
94	C₂×C₈×C₂₃	—	2	2	no	—
95	C₂×C₈×C₂₃	—	2	4	no	—
96	C₂×C₈×C₂₃	—	2	4	no	—
97	C₂×C₈×C₂₃	—	4	1	no	—
98	C₂×C₈×C₂₃	—	4	2	no	—
99	C₂×C₈×C₂₃	—	4	2	no	—
100	C₂×C₈×C₂₃	—	4	2	no	—
101	C₂×C₈×C₂₃	—	4	1	no	—
102	C₂×C₈×C₂₃	—	4	1	no	—
103	C₂×C₈×C₂₃	—	4	2	no	—
104	C₂×C₈×C₂₃	—	4	2	no	—
105	C₂×C₈×C₂₃	—	4	1	no	—
106	C₂×C₈×C₂₃	—	4	2	no	—
107	C₄²×C₂₃	—	2	2	no	—
108	C₄²×C₂₃	—	2	4	no	—
109	C₄²×C₂₃	—	2	2	no	—
110	C₄²×C₂₃	—	4	2	no	—
111	C₄²×C₂₃	—	4	2	no	—
112	C₄²×C₂₃	—	4	2	no	—
113	C₄²×C₂₃	—	4	2	no	—
114	#11255	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
115	C₂³×C₂₃	C₂×C₄⋊C₄	1	1	yes	characteristic
116	C₂³×C₂₃	#117	1	2	yes	—
117	C₂³×C₂₃	C₄×D₄	1	2	yes	—
118	C₂³×C₂₃	C₄×D₄	1	1	yes	characteristic
119	C₂³×C₂₃	C₄×Q₈	1	1	yes	characteristic
120	C₂³×C₂₃	C₂²×C₈	1	1	yes	characteristic
121	C₂³×C₂₃	C₂×M₁₆	1	1	yes	characteristic
122	C₂³×C₂₃	C₂×M₁₆	1	2	yes	—
123	C₂³×C₂₃	#131	1	2	yes	—
124	C₂³×C₂₃	#131	1	1	yes	characteristic
125	C₂³×C₂₃	#131	1	1	yes	characteristic
126	C₂×C₄×C₂₃	—	2	2	no	—
127	C₂×C₄×C₂₃	—	2	2	no	—
128	C₂×C₄×C₂₃	—	2	4	no	—
129	C₂×C₄×C₂₃	—	2	4	no	—
130	C₂×C₄×C₂₃	—	2	2	no	—
131	C₂×C₄×C₂₃	—	2	2	no	—
132	C₂×C₄×C₂₃	—	2	2	no	—
133	C₂×C₄×C₂₃	—	2	4	no	—
134	C₂×C₄×C₂₃	—	2	4	no	—
135	C₂×C₄×C₂₃	—	2	4	no	—
136	C₂×C₄×C₂₃	—	2	4	no	—
137	C₂×C₄×C₂₃	—	2	4	no	—
138	C₂×C₄×C₂₃	—	2	4	no	—
139	C₂×C₄×C₂₃	—	4	2	no	—
140	C₂×C₄×C₂₃	—	4	2	no	—
141	C₂×C₄×C₂₃	—	4	2	no	—
142	C₂×C₄×C₂₃	—	4	2	no	—
143	C₂×C₄×C₂₃	—	4	2	no	—
144	C₂×C₄×C₂₃	—	4	2	no	—
145	C₂×C₄×C₂₃	—	4	2	no	—
146	C₂×C₄×C₂₃	—	4	2	no	—
147	C₂×C₄×C₂₃	—	4	2	no	—
148	C₂×C₄×C₂₃	—	4	2	no	—
149	C₂×C₄×C₂₃	C₄⋊C₈	1	4	yes	—
150	C₂×C₄×C₂₃	#120	1	1	yes	characteristic
151	C₂×C₄×C₂₃	#121	1	1	yes	characteristic
152	C₂×C₄×C₂₃	#121	1	2	yes	—
153	C₂×C₄×C₂₃	C₂²⋊Q₈	1	2	yes	—
154	C₂×C₄×C₂₃	C₂²⋊Q₈	1	1	yes	characteristic
155	C₂×C₄×C₂₃	C₂²⋊Q₈	1	2	yes	—
156	C₂×C₄×C₂₃	#123	1	2	yes	—
157	C₂×C₄×C₂₃	#123	1	2	yes	—
158	C₂×C₄×C₂₃	#123	1	1	yes	characteristic
159	C₂×C₄×C₂₃	#124	1	1	yes	characteristic
160	C₂×C₄×C₂₃	#124	1	2	yes	—
161	C₂×C₄×C₂₃	#124	1	1	yes	characteristic
162	C₂×C₄×C₂₃	#125	1	2	yes	—
163	C₂×C₄×C₂₃	#125	1	2	yes	—
164	C₂×C₄×C₂₃	#125	1	1	yes	characteristic
165	C₂×C₄×C₂₃	#126	1	2	yes	—
166	C₂×C₄×C₂₃	#126	1	2	yes	—
167	C₂×C₄×C₂₃	C₄⋊Q₈	1	1	yes	characteristic
168	C₈×C₂₃	—	4	2	no	—
169	C₈×C₂₃	—	4	4	no	—
170	C₈×C₂₃	—	4	2	no	—
171	C₂²×C₄⋊C₈	C₂×C₂₃	1	1	yes	characteristic
172	C₂×#336	C₂×C₂₃	1	2	yes	—
173	C₂×#336	C₂×C₂₃	1	2	yes	—
174	C₂×#336	C₂×C₂₃	1	1	yes	characteristic
175	C₄×#95	C₂×C₂₃	1	1	yes	characteristic
176	C₂²×C₂₃	#382	1	1	yes	characteristic
177	C₂²×C₂₃	#385	1	1	yes	characteristic
178	C₂²×C₂₃	#387	1	2	yes	—
179	C₂²×C₂₃	#388	1	2	yes	—
180	C₂²×C₂₃	#389	1	1	yes	characteristic
181	C₂²×C₂₃	C₂×C₄⋊C₈	1	1	yes	characteristic
182	C₂²×C₂₃	#423	1	1	yes	characteristic
183	C₂²×C₂₃	#424	1	1	yes	characteristic
184	C₂²×C₂₃	#424	1	1	yes	characteristic
185	C₂²×C₂₃	#431	1	2	yes	—
186	C₂²×C₂₃	#432	1	2	yes	—
187	C₂²×C₂₃	#433	1	2	yes	—
188	C₂²×C₂₃	#433	1	2	yes	—
189	C₂²×C₂₃	C₈×D₄	1	2	yes	—
190	C₂²×C₂₃	C₈×D₄	1	1	yes	characteristic
191	C₂²×C₂₃	#435	1	2	yes	—
192	C₂²×C₂₃	#435	1	2	yes	—
193	C₂²×C₂₃	#435	1	2	yes	—
194	C₂²×C₂₃	#436	1	2	yes	—
195	C₂²×C₂₃	#436	1	1	yes	characteristic
196	C₂²×C₂₃	C₈×Q₈	1	1	yes	characteristic
197	C₂²×C₂₃	#446	1	2	yes	—
198	C₂²×C₂₃	#446	1	1	yes	characteristic
199	C₄×C₂₃	—	2	4	no	—
200	C₄×C₂₃	—	4	2	no	—
201	C₄×C₂₃	—	4	4	no	—
202	C₄×C₂₃	—	4	4	no	—
203	C₄×C₂₃	#393	1	1	yes	characteristic
204	C₄×C₂₃	#394	1	1	yes	characteristic
205	C₄×C₂₃	#397	1	1	yes	characteristic
206	C₄×C₂₃	#398	1	2	yes	—
207	C₄×C₂₃	#400	1	1	yes	characteristic
208	C₄×C₂₃	#400	1	2	yes	—
209	C₂³×C₈	C₂²×C₂₃	1	2	yes	—
210	C₂³×C₈	C₂²×C₂₃	1	1	yes	characteristic
211	C₂³×C₈	C₂²×C₂₃	1	1	yes	characteristic
212	C₂²×C₄²	C₂²×C₂₃	1	2	yes	—
213	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
214	C₂×C₄⋊C₈	—	2	4	no	—
215	C₂×C₄⋊C₈	—	2	2	no	—
216	C₂×#95	C₄×C₂₃	1	2	yes	—
217	C₂×#95	C₄×C₂₃	1	1	yes	characteristic
218	C₂×#95	C₄×C₂₃	1	1	yes	characteristic
219	#336	—	2	4	no	—
220	#336	—	2	4	no	—
221	#336	—	2	2	no	—
222	C₂×C₂₃	#1442	1	1	yes	characteristic
223	C₂×C₂₃	#1831	1	1	yes	characteristic
224	C₂×C₂₃	#1832	1	1	yes	characteristic
225	C₂×C₂₃	#1850	1	1	yes	characteristic
226	C₂×C₂₃	#1851	1	1	yes	characteristic
227	C₂×C₂₃	#1916	1	2	yes	—
228	C₂×C₂₃	#1917	1	2	yes	—
229	C₂×C₂₃	#1923	1	2	yes	—
230	C₂×C₂₃	#1924	1	2	yes	—
231	C₂×C₂₃	#1939	1	1	yes	characteristic
232	C₂×C₂₃	#1940	1	1	yes	characteristic
233	C₂³×C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
234	C₂³×C₄	C₂×C₄×C₂₃	1	2	yes	—
235	C₂³×C₄	C₂×C₄×C₂₃	1	2	yes	—
236	C₂³×C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
237	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
238	C₂²×C₈	—	2	2	no	—
239	C₂²×C₈	—	2	1	no	—
240	C₂²×C₈	—	2	2	no	—
241	C₂²×C₈	—	2	1	no	—
242	C₂²×C₈	—	2	2	no	—
243	C₂²×C₈	—	2	2	no	—
244	C₂²×C₈	—	2	2	no	—
245	C₂²×C₈	—	2	1	no	—
246	C₂²×C₈	—	2	2	no	—
247	C₂²×C₈	—	2	1	no	—
248	C₂²×C₈	—	2	2	no	—
249	C₂²×C₈	—	2	2	no	—
250	C₂²×C₈	—	2	2	no	—
251	C₂²×C₈	—	2	2	no	—
252	C₂²×C₈	D₄×C₂₃	1	2	yes	—
253	C₂²×C₈	D₄×C₂₃	1	4	yes	—
254	C₂²×C₈	Q₈×C₂₃	1	2	yes	—
255	C₂×C₄²	—	2	2	no	—
256	C₂×C₄²	—	2	2	no	—
257	C₂×C₄²	—	2	2	no	—
258	C₂×C₄²	—	2	2	no	—
259	C₂×C₄²	—	2	2	no	—
260	C₂×C₄²	—	2	2	no	—
261	C₂×C₄²	—	2	2	no	—
262	C₂×C₄²	—	2	2	no	—
263	C₂×C₄²	D₄×C₂₃	1	2	yes	—
264	C₂×C₄²	Q₈×C₂₃	1	2	yes	—
265	C₄⋊C₈	—	2	8	no	—
266	#95	—	2	4	no	—
267	#95	—	2	2	no	—
268	#95	C₈×C₂₃	1	4	yes	complemented
269	C₂₃	#11255	1	1	yes	characteristic, direct product factor, Sylow
270	C₂⁴	C₂²×C₄×C₂₃	1	1	yes	characteristic
271	C₂²×C₄	—	2	2	no	—
272	C₂²×C₄	—	2	2	no	—
273	C₂²×C₄	—	2	2	no	—
274	C₂²×C₄	—	2	2	no	—
275	C₂²×C₄	—	2	2	no	—
276	C₂²×C₄	—	2	2	no	—
277	C₂²×C₄	—	2	2	no	—
278	C₂²×C₄	—	2	2	no	—
279	C₂²×C₄	—	2	2	no	—
280	C₂²×C₄	—	2	2	no	—
281	C₂²×C₄	—	2	2	no	—
282	C₂²×C₄	—	2	2	no	—
283	C₂²×C₄	—	2	1	no	—
284	C₂²×C₄	—	2	1	no	—
285	C₂²×C₄	—	2	2	no	—
286	C₂²×C₄	—	2	2	no	—
287	C₂²×C₄	—	2	2	no	—
288	C₂²×C₄	—	2	2	no	—
289	C₂²×C₄	C₄⋊C₄×C₂₃	1	2	yes	—
290	C₂²×C₄	C₄⋊C₄×C₂₃	1	2	yes	—
291	C₂²×C₄	C₂×C₈×C₂₃	1	4	yes	—
292	C₂²×C₄	C₂×C₈×C₂₃	1	2	yes	—
293	C₂²×C₄	M₁₆×C₂₃	1	4	yes	—
294	C₂²×C₄	M₁₆×C₂₃	1	2	yes	—
295	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
296	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
297	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
298	C₂²×C₄	C₂×Q₈×C₂₃	1	1	yes	characteristic
299	C₂²×C₄	C₂×Q₈×C₂₃	1	1	yes	characteristic
300	C₂²×C₄	#41×C₂₃	1	1	yes	characteristic
301	C₂²×C₄	#41×C₂₃	1	2	yes	—
302	C₂²×C₄	#41×C₂₃	1	2	yes	—
303	C₂²×C₄	#41×C₂₃	1	2	yes	—
304	C₂²×C₄	#41×C₂₃	1	1	yes	characteristic
305	C₂×C₈	—	2	4	no	—
306	C₂×C₈	—	2	4	no	—
307	C₂×C₈	—	2	2	no	—
308	C₂×C₈	—	2	4	no	—
309	C₂×C₈	—	2	2	no	—
310	C₂×C₈	—	2	4	no	—
311	C₂×C₈	—	2	4	no	—
312	C₂×C₈	—	4	1	no	—
313	C₂×C₈	—	4	2	no	—
314	C₂×C₈	—	4	2	no	—
315	C₂×C₈	—	4	2	no	—
316	C₂×C₈	—	4	1	no	—
317	C₂×C₈	—	4	1	no	—
318	C₂×C₈	—	4	2	no	—
319	C₂×C₈	—	4	2	no	—
320	C₂×C₈	—	4	1	no	—
321	C₂×C₈	—	4	2	no	—
322	C₄²	—	2	2	no	—
323	C₄²	—	2	4	no	—
324	C₄²	—	2	2	no	—
325	C₄²	—	4	2	no	—
326	C₄²	—	4	2	no	—
327	C₄²	—	4	2	no	—
328	C₄²	—	4	2	no	—
329	C₂³	C₂×C₄⋊C₄×C₂₃	1	1	yes	characteristic
330	C₂³	C₂₃×#117	1	2	yes	—
331	C₂³	C₄×D₄×C₂₃	1	2	yes	—
332	C₂³	C₄×D₄×C₂₃	1	1	yes	characteristic
333	C₂³	C₄×Q₈×C₂₃	1	1	yes	characteristic
334	C₂³	C₂²×C₈×C₂₃	1	1	yes	characteristic
335	C₂³	C₂×M₁₆×C₂₃	1	1	yes	characteristic
336	C₂³	C₂×M₁₆×C₂₃	1	2	yes	—
337	C₂³	C₂₃×#131	1	2	yes	—
338	C₂³	C₂₃×#131	1	1	yes	characteristic
339	C₂³	C₂₃×#131	1	1	yes	characteristic
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	2	4	no	—
343	C₂×C₄	—	2	4	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	4	no	—
348	C₂×C₄	—	2	4	no	—
349	C₂×C₄	—	2	4	no	—
350	C₂×C₄	—	2	4	no	—
351	C₂×C₄	—	2	4	no	—
352	C₂×C₄	—	2	4	no	—
353	C₂×C₄	—	4	2	no	—
354	C₂×C₄	—	4	2	no	—
355	C₂×C₄	—	4	2	no	—
356	C₂×C₄	—	4	2	no	—
357	C₂×C₄	—	4	2	no	—
358	C₂×C₄	—	4	2	no	—
359	C₂×C₄	—	4	2	no	—
360	C₂×C₄	—	4	2	no	—
361	C₂×C₄	—	4	2	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	C₂₃×C₄⋊C₈	1	4	yes	—
364	C₂×C₄	C₂₃×#120	1	1	yes	characteristic
365	C₂×C₄	C₂₃×#121	1	1	yes	characteristic
366	C₂×C₄	C₂₃×#121	1	2	yes	—
367	C₂×C₄	C₂₃×C₂²⋊Q₈	1	2	yes	—
368	C₂×C₄	C₂₃×C₂²⋊Q₈	1	1	yes	characteristic
369	C₂×C₄	C₂₃×C₂²⋊Q₈	1	2	yes	—
370	C₂×C₄	C₂₃×#123	1	2	yes	—
371	C₂×C₄	C₂₃×#123	1	2	yes	—
372	C₂×C₄	C₂₃×#123	1	1	yes	characteristic
373	C₂×C₄	C₂₃×#124	1	1	yes	characteristic
374	C₂×C₄	C₂₃×#124	1	2	yes	—
375	C₂×C₄	C₂₃×#124	1	1	yes	characteristic
376	C₂×C₄	C₂₃×#125	1	2	yes	—
377	C₂×C₄	C₂₃×#125	1	2	yes	—
378	C₂×C₄	C₂₃×#125	1	1	yes	characteristic
379	C₂×C₄	C₂₃×#126	1	2	yes	—
380	C₂×C₄	C₂₃×#126	1	2	yes	—
381	C₂×C₄	C₂₃×C₄⋊Q₈	1	1	yes	characteristic
382	C₈	—	4	2	no	—
383	C₈	—	4	4	no	—
384	C₈	—	4	2	no	—
385	C₂²	C₂₃×#382	1	1	yes	characteristic
386	C₂²	C₂₃×#385	1	1	yes	characteristic
387	C₂²	C₂₃×#387	1	2	yes	—
388	C₂²	C₂₃×#388	1	2	yes	—
389	C₂²	C₂₃×#389	1	1	yes	characteristic
390	C₂²	C₂×C₂₃×C₄⋊C₈	1	1	yes	characteristic
391	C₂²	C₂₃×#423	1	1	yes	characteristic
392	C₂²	C₂₃×#424	1	1	yes	characteristic
393	C₂²	C₂₃×#424	1	1	yes	characteristic
394	C₂²	C₂₃×#431	1	2	yes	—
395	C₂²	C₂₃×#432	1	2	yes	—
396	C₂²	C₂₃×#433	1	2	yes	—
397	C₂²	C₂₃×#433	1	2	yes	—
398	C₂²	C₈×D₄×C₂₃	1	2	yes	—
399	C₂²	C₈×D₄×C₂₃	1	1	yes	characteristic
400	C₂²	C₂₃×#435	1	2	yes	—
401	C₂²	C₂₃×#435	1	2	yes	—
402	C₂²	C₂₃×#435	1	2	yes	—
403	C₂²	C₂₃×#436	1	2	yes	—
404	C₂²	C₂₃×#436	1	1	yes	characteristic
405	C₂²	C₈×Q₈×C₂₃	1	1	yes	characteristic
406	C₂²	C₂₃×#446	1	2	yes	—
407	C₂²	C₂₃×#446	1	1	yes	characteristic
408	C₄	—	2	4	no	—
409	C₄	—	4	4	no	—
410	C₄	—	4	4	no	—
411	C₄	—	4	2	no	—
412	C₄	C₂₃×#393	1	1	yes	characteristic
413	C₄	C₂₃×#394	1	1	yes	characteristic
414	C₄	C₂₃×#397	1	1	yes	characteristic
415	C₄	C₂₃×#398	1	2	yes	—
416	C₄	C₂₃×#400	1	1	yes	characteristic
417	C₄	C₂₃×#400	1	2	yes	—
418	C₂	C₂₃×#1442	1	1	yes	characteristic
419	C₂	C₂₃×#1831	1	1	yes	characteristic
420	C₂	C₂₃×#1832	1	1	yes	characteristic
421	C₂	C₂₃×#1850	1	1	yes	characteristic
422	C₂	C₂₃×#1851	1	1	yes	characteristic
423	C₂	C₂₃×#1916	1	2	yes	—
424	C₂	C₂₃×#1917	1	2	yes	—
425	C₂	C₂₃×#1923	1	2	yes	—
426	C₂	C₂₃×#1924	1	2	yes	—
427	C₂	C₂₃×#1939	1	1	yes	characteristic
428	C₂	C₂₃×#1940	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₄×C₂₃	C₂³
commutator	C₂³	C₂²×C₈×C₂₃
Frattini, cosocle	C₂³×C₄	C₂³×C₂₃
socle, prime radical	C₂⁴×C₂₃	C₂²×C₄
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₄×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
54. C₂₃×#95	C₈	semidirect
114. #11255	C₂₃	direct (N × H)
268. #95	C₈×C₂₃	semidirect
269. C₂₃	#11255	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₂₃×C₄⋊C₈	2
C₂×C₂₃×#336	2
C₄×C₂₃×#95	2
#11255	23

Subgroups — C23×#11255 #19158881

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#11255 #19158881