Subgroups — C₂₃×#21526 #19169152

Order 5888.

1182 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#466	C₂	1	1	yes	maximal, characteristic
2	C₂×C₂₃×#442	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₂₃×#97	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×C₂₃×#121	C₂	1	2	yes	maximal, complemented
5	C₂₃×#1972	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#1943	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#1936	C₂	1	2	yes	maximal, complemented
8	C₂₃×#1893	C₂	1	2	yes	maximal, complemented
9	C₂₃×#1807	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#1776	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#1762	C₂	1	2	yes	maximal, complemented
12	C₂²×D₈×C₂₃	C₂²	1	1	yes	characteristic
13	C₂³×C₈×C₂₃	C₂²	1	1	yes	characteristic
14	C₂³×C₈×C₂₃	C₂²	1	1	yes	characteristic
15	C₂×C₂₃×#121	C₂²	1	2	yes	—
16	C₂×C₄×D₄×C₂₃	—	2	2	no	—
17	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	—
18	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
19	C₂₃×#466	C₄	1	8	yes	complemented
20	C₂₃×#442	—	2	4	no	—
21	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic
22	C₂×C₂₃×#106	C₂²	1	1	yes	characteristic
23	C₂×C₂₃×#106	C₂²	1	1	yes	characteristic
24	C₂×C₂₃×#102	C₂²	1	2	yes	—
25	C₂×C₂₃×#102	C₂²	1	2	yes	—
26	C₂×C₂₃×#102	C₂²	1	2	yes	—
27	C₂×C₂₃×#97	—	2	4	no	—
28	C₂×C₂₃×#97	C₂²	1	1	yes	characteristic
29	C₂×C₂₃×#97	C₂²	1	1	yes	characteristic
30	C₂×C₂₃×#97	C₂²	1	1	yes	characteristic
31	C₂×C₂₃×#97	C₂²	1	1	yes	characteristic
32	C₂₃×#390	C₂²	1	2	yes	—
33	C₂₃×#389	C₂²	1	2	yes	—
34	C₂₃×#388	—	2	2	no	—
35	C₂₃×#386	—	2	2	no	—
36	C₂₃×#380	C₂²	1	2	yes	—
37	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
38	C₄×C₂²⋊C₄×C₂₃	—	2	2	no	—
39	C₂₃×#340	C₂²	1	2	yes	—
40	C₂₃×#340	C₂²	1	2	yes	—
41	C₂₃×#340	C₂²	1	2	yes	—
42	C₂²×D₄×C₂₃	—	2	2	no	—
43	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
44	C₂³×C₄×C₂₃	—	2	2	no	—
45	C₂³×C₄×C₂₃	D₄	1	2	yes	—
46	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
47	C₂×D₈×C₂₃	—	2	2	no	—
48	C₂×D₈×C₂₃	—	2	2	no	—
49	C₂×D₈×C₂₃	C₂×C₄	1	4	yes	complemented
50	C₂²×C₈×C₂₃	—	2	2	no	—
51	C₂²×C₈×C₂₃	—	2	2	no	—
52	C₂²×C₈×C₂₃	—	2	2	no	—
53	C₂²×C₈×C₂₃	—	2	2	no	—
54	C₂²×C₈×C₂₃	—	2	2	no	—
55	C₂²×C₈×C₂₃	C₂×C₄	1	4	yes	complemented
56	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
57	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
58	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
59	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
60	C₂₃×#121	—	2	4	no	—
61	C₂₃×#121	C₂×C₄	1	8	yes	complemented
62	C₄×D₄×C₂₃	—	2	4	no	—
63	C₄×D₄×C₂₃	—	2	4	no	—
64	C₄×D₄×C₂₃	—	4	8	no	—
65	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
66	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
67	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
68	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
69	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
70	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
71	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
72	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
73	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
74	C₂×C₄²×C₂₃	—	2	2	no	—
75	C₂×C₄²×C₂₃	—	2	2	no	—
76	C₂×C₄²×C₂₃	—	2	2	no	—
77	C₂×C₄²×C₂₃	D₄	1	2	yes	—
78	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
79	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
80	C₂₃×#107	C₂×C₄	1	4	yes	complemented
81	C₂₃×#106	—	2	2	no	—
82	C₂₃×#106	—	2	2	no	—
83	C₂₃×#102	—	2	4	no	—
84	C₂₃×#102	—	2	4	no	—
85	C₂₃×#102	C₂×C₄	1	8	yes	complemented
86	C₂₃×#97	—	2	2	no	—
87	C₂₃×#97	—	2	2	no	—
88	C₂₃×#97	—	2	2	no	—
89	C₂₃×#97	D₄	1	4	yes	complemented
90	C₂₃×#95	—	2	2	no	—
91	C₂₃×#95	—	2	2	no	—
92	C₂₃×#95	—	2	2	no	—
93	C₂⁴×C₂₃	—	2	2	no	—
94	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
95	C₂×D₄×C₂₃	—	2	8	no	—
96	C₂×D₄×C₂₃	—	2	2	no	—
97	C₂×D₄×C₂₃	—	2	2	no	—
98	C₂×D₄×C₂₃	—	2	2	no	—
99	C₂×D₄×C₂₃	—	2	2	no	—
100	C₂×D₄×C₂₃	—	2	2	no	—
101	C₂×D₄×C₂₃	—	4	4	no	—
102	C₂×D₄×C₂₃	—	4	4	no	—
103	C₂×D₄×C₂₃	C₂²×C₄	1	4	yes	—
104	C₂²×C₄×C₂₃	—	2	1	no	—
105	C₂²×C₄×C₂₃	—	2	1	no	—
106	C₂²×C₄×C₂₃	—	2	1	no	—
107	C₂²×C₄×C₂₃	—	2	1	no	—
108	C₂²×C₄×C₂₃	—	2	4	no	—
109	C₂²×C₄×C₂₃	—	2	2	no	—
110	C₂²×C₄×C₂₃	—	2	4	no	—
111	C₂²×C₄×C₂₃	—	2	2	no	—
112	C₂²×C₄×C₂₃	—	2	2	no	—
113	C₂²×C₄×C₂₃	—	4	2	no	—
114	C₂²×C₄×C₂₃	—	4	4	no	—
115	C₂²×C₄×C₂₃	—	4	4	no	—
116	C₂²×C₄×C₂₃	—	4	4	no	—
117	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
118	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
119	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
121	C₂²×C₄×C₂₃	#41	1	2	yes	—
122	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
123	D₈×C₂₃	—	2	8	no	—
124	C₂×C₈×C₂₃	—	2	8	no	—
125	C₂×C₈×C₂₃	—	2	1	no	—
126	C₂×C₈×C₂₃	—	2	1	no	—
127	C₂×C₈×C₂₃	—	2	1	no	—
128	C₂×C₈×C₂₃	—	2	1	no	—
129	C₂×C₈×C₂₃	—	2	1	no	—
130	C₂×C₈×C₂₃	—	2	1	no	—
131	C₂×C₈×C₂₃	—	2	8	no	—
132	C₂×C₈×C₂₃	C₂²×C₄	1	2	yes	—
133	C₂×C₈×C₂₃	C₂²×C₄	1	2	yes	—
134	C₂×C₈×C₂₃	C₂×D₄	1	2	yes	—
135	C₂×C₈×C₂₃	C₂×D₄	1	2	yes	—
136	C₂×C₈×C₂₃	#41	1	2	yes	—
137	C₂×C₈×C₂₃	#41	1	2	yes	—
138	C₄⋊C₄×C₂₃	—	2	2	no	—
139	C₄⋊C₄×C₂₃	—	2	2	no	—
140	C₄⋊C₄×C₂₃	—	2	2	no	—
141	C₄⋊C₄×C₂₃	—	2	2	no	—
142	C₄⋊C₄×C₂₃	—	2	2	no	—
143	C₄⋊C₄×C₂₃	—	4	4	no	—
144	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
145	C₂²⋊C₄×C₂₃	—	2	8	no	—
146	C₂²⋊C₄×C₂₃	—	4	4	no	—
147	C₂²⋊C₄×C₂₃	—	4	4	no	—
148	C₂²⋊C₄×C₂₃	—	4	4	no	—
149	C₂²⋊C₄×C₂₃	—	4	4	no	—
150	C₄²×C₂₃	—	2	4	no	—
151	C₄²×C₂₃	—	2	1	no	—
152	C₄²×C₂₃	—	2	1	no	—
153	C₄²×C₂₃	—	4	4	no	—
154	C₄²×C₂₃	C₂×D₄	1	2	yes	—
155	C₄²×C₂₃	#41	1	2	yes	—
156	#21526	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
157	C₂³×C₂₃	—	2	1	no	—
158	C₂³×C₂₃	—	2	1	no	—
159	C₂³×C₂₃	—	2	2	no	—
160	C₂³×C₂₃	—	2	4	no	—
161	C₂³×C₂₃	—	4	2	no	—
162	C₂³×C₂₃	—	4	2	no	—
163	C₂³×C₂₃	—	4	2	no	—
164	C₂³×C₂₃	—	4	2	no	—
165	C₂³×C₂₃	—	4	2	no	—
166	C₂³×C₂₃	—	4	2	no	—
167	C₂³×C₂₃	C₄×D₄	1	2	yes	—
168	C₂³×C₂₃	AGL(1,ℤ/8)	1	4	yes	—
169	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
170	D₄×C₂₃	—	2	4	no	—
171	D₄×C₂₃	—	2	4	no	—
172	D₄×C₂₃	—	4	16	no	—
173	D₄×C₂₃	—	4	2	no	—
174	D₄×C₂₃	—	4	2	no	—
175	C₂×C₄×C₂₃	—	2	1	no	—
176	C₂×C₄×C₂₃	—	2	1	no	—
177	C₂×C₄×C₂₃	—	2	2	no	—
178	C₂×C₄×C₂₃	—	2	2	no	—
179	C₂×C₄×C₂₃	—	2	2	no	—
180	C₂×C₄×C₂₃	—	2	2	no	—
181	C₂×C₄×C₂₃	—	2	2	no	—
182	C₂×C₄×C₂₃	—	2	2	no	—
183	C₂×C₄×C₂₃	—	2	4	no	—
184	C₂×C₄×C₂₃	—	2	2	no	—
185	C₂×C₄×C₂₃	—	2	2	no	—
186	C₂×C₄×C₂₃	—	2	2	no	—
187	C₂×C₄×C₂₃	—	4	8	no	—
188	C₂×C₄×C₂₃	—	4	2	no	—
189	C₂×C₄×C₂₃	—	4	2	no	—
190	C₂×C₄×C₂₃	—	4	2	no	—
191	C₂×C₄×C₂₃	—	4	2	no	—
192	C₂×C₄×C₂₃	—	4	2	no	—
193	C₂×C₄×C₂₃	—	4	2	no	—
194	C₂×C₄×C₂₃	—	4	2	no	—
195	C₂×C₄×C₂₃	—	4	2	no	—
196	C₂×C₄×C₂₃	—	8	8	no	—
197	C₂×C₄×C₂₃	C₄×D₄	1	2	yes	—
198	C₂×C₄×C₂₃	#121	1	4	yes	—
199	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
200	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
201	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
202	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
203	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
204	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
205	C₈×C₂₃	—	2	2	no	—
206	C₈×C₂₃	—	2	2	no	—
207	C₈×C₂₃	—	2	2	no	—
208	C₈×C₂₃	C₄×D₄	1	4	yes	complemented
209	C₂×#466	C₂×C₂₃	1	1	yes	characteristic
210	C₂×#442	C₂×C₂₃	1	1	yes	characteristic, complemented
211	C₂²×#97	C₂×C₂₃	1	1	yes	characteristic, complemented
212	C₄×#121	C₂×C₂₃	1	2	yes	complemented
213	#1972	C₂×C₂₃	1	1	yes	characteristic, complemented
214	#1943	C₂×C₂₃	1	1	yes	characteristic, complemented
215	#1936	C₂×C₂₃	1	2	yes	complemented
216	#1893	C₂×C₂₃	1	2	yes	complemented
217	#1807	C₂×C₂₃	1	1	yes	characteristic, complemented
218	#1776	C₂×C₂₃	1	1	yes	characteristic, complemented
219	#1762	C₂×C₂₃	1	2	yes	complemented
220	C₂²×C₂₃	—	2	4	no	—
221	C₂²×C₂₃	—	2	2	no	—
222	C₂²×C₂₃	—	2	4	no	—
223	C₂²×C₂₃	—	2	2	no	—
224	C₂²×C₂₃	—	4	4	no	—
225	C₂²×C₂₃	—	4	4	no	—
226	C₂²×C₂₃	—	4	4	no	—
227	C₂²×C₂₃	—	8	2	no	—
228	C₂²×C₂₃	—	8	2	no	—
229	C₂²×C₂₃	—	8	2	no	—
230	C₂²×C₂₃	—	8	2	no	—
231	C₂²×C₂₃	#442	1	4	yes	complemented
232	C₂²×C₂₃	C₂×C₄×D₄	1	1	yes	characteristic
233	C₂²×C₂₃	C₂×#121	1	1	yes	characteristic
234	C₂²×C₂₃	#532	1	1	yes	characteristic
235	C₂²×C₂₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
236	C₂²×C₂₃	#575	1	2	yes	—
237	C₄×C₂₃	—	2	4	no	—
238	C₄×C₂₃	—	2	2	no	—
239	C₄×C₂₃	—	4	4	no	—
240	C₄×C₂₃	—	4	2	no	—
241	C₄×C₂₃	—	8	2	no	—
242	C₄×C₂₃	—	8	2	no	—
243	C₄×C₂₃	C₂×C₄×D₄	1	1	yes	characteristic
244	C₄×C₂₃	C₄×#41	1	1	yes	characteristic
245	C₄×C₂₃	#525	1	1	yes	characteristic
246	C₄×C₂₃	#529	1	1	yes	characteristic
247	C₂²×D₈	C₂²×C₂₃	1	1	yes	characteristic
248	C₂³×C₈	C₂²×C₂₃	1	1	yes	characteristic
249	C₂³×C₈	C₂²×C₂₃	1	1	yes	characteristic
250	C₂×#121	C₂²×C₂₃	1	2	yes	—
251	C₂×C₄×D₄	—	2	2	no	—
252	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	—
253	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
254	#466	C₄×C₂₃	1	8	yes	complemented
255	#442	—	2	4	no	—
256	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic
257	C₂×#106	C₂²×C₂₃	1	1	yes	characteristic
258	C₂×#106	C₂²×C₂₃	1	1	yes	characteristic
259	C₂×#102	C₂²×C₂₃	1	2	yes	—
260	C₂×#102	C₂²×C₂₃	1	2	yes	—
261	C₂×#102	C₂²×C₂₃	1	2	yes	—
262	C₂×#97	—	2	4	no	—
263	C₂×#97	C₂²×C₂₃	1	1	yes	characteristic
264	C₂×#97	C₂²×C₂₃	1	1	yes	characteristic
265	C₂×#97	C₂²×C₂₃	1	1	yes	characteristic
266	C₂×#97	C₂²×C₂₃	1	1	yes	characteristic
267	#390	C₂²×C₂₃	1	2	yes	—
268	#389	C₂²×C₂₃	1	2	yes	—
269	#388	—	2	2	no	—
270	#386	—	2	2	no	—
271	#380	C₂²×C₂₃	1	2	yes	—
272	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
273	C₄×C₂²⋊C₄	—	2	2	no	—
274	#340	C₂²×C₂₃	1	2	yes	—
275	#340	C₂²×C₂₃	1	2	yes	—
276	#340	C₂²×C₂₃	1	2	yes	—
277	C₂×C₂₃	—	2	4	no	—
278	C₂×C₂₃	—	8	4	no	—
279	C₂×C₂₃	C₄×#121	1	1	yes	characteristic
280	C₂×C₂₃	C₂×#442	1	1	yes	characteristic
281	C₂×C₂₃	#2943	1	1	yes	characteristic
282	C₂×C₂₃	#3055	1	2	yes	—
283	C₂×C₂₃	#3180	1	2	yes	—
284	C₂²×D₄	—	2	2	no	—
285	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
286	C₂³×C₄	—	2	2	no	—
287	C₂³×C₄	D₄×C₂₃	1	2	yes	—
288	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
289	C₂×D₈	—	2	2	no	—
290	C₂×D₈	—	2	2	no	—
291	C₂×D₈	C₂×C₄×C₂₃	1	4	yes	complemented
292	C₂²×C₈	—	2	2	no	—
293	C₂²×C₈	—	2	2	no	—
294	C₂²×C₈	—	2	2	no	—
295	C₂²×C₈	—	2	2	no	—
296	C₂²×C₈	—	2	2	no	—
297	C₂²×C₈	C₂×C₄×C₂₃	1	4	yes	complemented
298	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
299	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
300	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
301	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
302	#121	—	2	4	no	—
303	#121	C₂×C₄×C₂₃	1	8	yes	complemented
304	C₄×D₄	—	2	4	no	—
305	C₄×D₄	—	2	4	no	—
306	C₄×D₄	—	4	8	no	—
307	C₂×C₄⋊C₄	—	2	2	no	—
308	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
309	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
310	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
311	C₂×C₂²⋊C₄	—	2	2	no	—
312	C₂×C₂²⋊C₄	—	2	2	no	—
313	C₂×C₂²⋊C₄	—	2	2	no	—
314	C₂×C₂²⋊C₄	—	2	2	no	—
315	C₂×C₂²⋊C₄	—	2	2	no	—
316	C₂×C₄²	—	2	2	no	—
317	C₂×C₄²	—	2	2	no	—
318	C₂×C₄²	—	2	2	no	—
319	C₂×C₄²	D₄×C₂₃	1	2	yes	—
320	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
321	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
322	#107	C₂×C₄×C₂₃	1	4	yes	complemented
323	#106	—	2	2	no	—
324	#106	—	2	2	no	—
325	#102	—	2	4	no	—
326	#102	—	2	4	no	—
327	#102	C₂×C₄×C₂₃	1	8	yes	complemented
328	#97	—	2	2	no	—
329	#97	—	2	2	no	—
330	#97	—	2	2	no	—
331	#97	D₄×C₂₃	1	4	yes	complemented
332	#95	—	2	2	no	—
333	#95	—	2	2	no	—
334	#95	—	2	2	no	—
335	C₂₃	#21526	1	1	yes	characteristic, direct product factor, Sylow
336	C₂⁴	—	2	2	no	—
337	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
338	C₂×D₄	—	2	8	no	—
339	C₂×D₄	—	2	2	no	—
340	C₂×D₄	—	2	2	no	—
341	C₂×D₄	—	2	2	no	—
342	C₂×D₄	—	2	2	no	—
343	C₂×D₄	—	2	2	no	—
344	C₂×D₄	—	4	4	no	—
345	C₂×D₄	—	4	4	no	—
346	C₂×D₄	C₂²×C₄×C₂₃	1	4	yes	—
347	C₂²×C₄	—	2	1	no	—
348	C₂²×C₄	—	2	1	no	—
349	C₂²×C₄	—	2	1	no	—
350	C₂²×C₄	—	2	1	no	—
351	C₂²×C₄	—	2	4	no	—
352	C₂²×C₄	—	2	2	no	—
353	C₂²×C₄	—	2	4	no	—
354	C₂²×C₄	—	2	2	no	—
355	C₂²×C₄	—	2	2	no	—
356	C₂²×C₄	—	4	2	no	—
357	C₂²×C₄	—	4	4	no	—
358	C₂²×C₄	—	4	4	no	—
359	C₂²×C₄	—	4	4	no	—
360	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
361	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
362	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
363	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
364	C₂²×C₄	#41×C₂₃	1	2	yes	—
365	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
366	D₈	—	2	8	no	—
367	C₂×C₈	—	2	8	no	—
368	C₂×C₈	—	2	1	no	—
369	C₂×C₈	—	2	1	no	—
370	C₂×C₈	—	2	1	no	—
371	C₂×C₈	—	2	1	no	—
372	C₂×C₈	—	2	1	no	—
373	C₂×C₈	—	2	1	no	—
374	C₂×C₈	—	2	8	no	—
375	C₂×C₈	C₂²×C₄×C₂₃	1	2	yes	—
376	C₂×C₈	C₂²×C₄×C₂₃	1	2	yes	—
377	C₂×C₈	C₂×D₄×C₂₃	1	2	yes	—
378	C₂×C₈	C₂×D₄×C₂₃	1	2	yes	—
379	C₂×C₈	#41×C₂₃	1	2	yes	—
380	C₂×C₈	#41×C₂₃	1	2	yes	—
381	C₄⋊C₄	—	2	2	no	—
382	C₄⋊C₄	—	2	2	no	—
383	C₄⋊C₄	—	2	2	no	—
384	C₄⋊C₄	—	2	2	no	—
385	C₄⋊C₄	—	2	2	no	—
386	C₄⋊C₄	—	4	4	no	—
387	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
388	C₂²⋊C₄	—	2	8	no	—
389	C₂²⋊C₄	—	4	4	no	—
390	C₂²⋊C₄	—	4	4	no	—
391	C₂²⋊C₄	—	4	4	no	—
392	C₂²⋊C₄	—	4	4	no	—
393	C₄²	—	2	4	no	—
394	C₄²	—	2	1	no	—
395	C₄²	—	2	1	no	—
396	C₄²	—	4	4	no	—
397	C₄²	C₂×D₄×C₂₃	1	2	yes	—
398	C₄²	#41×C₂₃	1	2	yes	—
399	C₂³	—	2	2	no	—
400	C₂³	—	2	1	no	—
401	C₂³	—	2	1	no	—
402	C₂³	—	2	4	no	—
403	C₂³	—	4	2	no	—
404	C₂³	—	4	2	no	—
405	C₂³	—	4	2	no	—
406	C₂³	—	4	2	no	—
407	C₂³	—	4	2	no	—
408	C₂³	—	4	2	no	—
409	C₂³	C₄×D₄×C₂₃	1	2	yes	—
410	C₂³	C₂₃×AGL(1,ℤ/8)	1	4	yes	—
411	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
412	D₄	—	2	4	no	—
413	D₄	—	2	4	no	—
414	D₄	—	4	16	no	—
415	D₄	—	4	2	no	—
416	D₄	—	4	2	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	2	4	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	4	8	no	—
430	C₂×C₄	—	4	2	no	—
431	C₂×C₄	—	4	2	no	—
432	C₂×C₄	—	4	2	no	—
433	C₂×C₄	—	4	2	no	—
434	C₂×C₄	—	4	2	no	—
435	C₂×C₄	—	4	2	no	—
436	C₂×C₄	—	4	2	no	—
437	C₂×C₄	—	4	2	no	—
438	C₂×C₄	—	8	8	no	—
439	C₂×C₄	C₄×D₄×C₂₃	1	2	yes	—
440	C₂×C₄	C₂₃×#121	1	4	yes	—
441	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
442	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
443	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
444	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
445	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
446	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
447	C₈	—	2	2	no	—
448	C₈	—	2	2	no	—
449	C₈	—	2	2	no	—
450	C₈	C₄×D₄×C₂₃	1	4	yes	complemented
451	C₂²	—	2	4	no	—
452	C₂²	—	2	2	no	—
453	C₂²	—	2	4	no	—
454	C₂²	—	2	2	no	—
455	C₂²	—	4	4	no	—
456	C₂²	—	4	4	no	—
457	C₂²	—	4	4	no	—
458	C₂²	—	8	2	no	—
459	C₂²	—	8	2	no	—
460	C₂²	—	8	2	no	—
461	C₂²	—	8	2	no	—
462	C₂²	C₂₃×#442	1	4	yes	complemented
463	C₂²	C₂×C₄×D₄×C₂₃	1	1	yes	characteristic
464	C₂²	C₂×C₂₃×#121	1	1	yes	characteristic
465	C₂²	C₂₃×#532	1	1	yes	characteristic
466	C₂²	C₂×C₂₃×AGL(1,ℤ/8)	1	2	yes	—
467	C₂²	C₂₃×#575	1	2	yes	—
468	C₄	—	2	4	no	—
469	C₄	—	2	2	no	—
470	C₄	—	4	4	no	—
471	C₄	—	4	2	no	—
472	C₄	—	8	2	no	—
473	C₄	—	8	2	no	—
474	C₄	C₂×C₄×D₄×C₂₃	1	1	yes	characteristic
475	C₄	C₄×#41×C₂₃	1	1	yes	characteristic
476	C₄	C₂₃×#525	1	1	yes	characteristic
477	C₄	C₂₃×#529	1	1	yes	characteristic
478	C₂	—	2	4	no	—
479	C₂	—	8	4	no	—
480	C₂	C₄×C₂₃×#121	1	1	yes	characteristic
481	C₂	C₂×C₂₃×#442	1	1	yes	characteristic
482	C₂	C₂₃×#2943	1	1	yes	characteristic
483	C₂	C₂₃×#3055	1	2	yes	—
484	C₂	C₂₃×#3180	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₂₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₃
prime radical	C₂×C₂₃×#466	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ 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
2. C₂×C₂₃×#442	C₂	semidirect
3. C₂²×C₂₃×#97	C₂	semidirect
4. C₄×C₂₃×#121	C₂	semidirect
5. C₂₃×#1972	C₂	semidirect
6. C₂₃×#1943	C₂	semidirect
7. C₂₃×#1936	C₂	semidirect
8. C₂₃×#1893	C₂	semidirect
9. C₂₃×#1807	C₂	semidirect
10. C₂₃×#1776	C₂	semidirect
11. C₂₃×#1762	C₂	semidirect
19. C₂₃×#466	C₄	semidirect
49. C₂×D₈×C₂₃	C₂×C₄	semidirect
55. C₂²×C₈×C₂₃	C₂×C₄	semidirect
61. C₂₃×#121	C₂×C₄	semidirect
80. C₂₃×#107	C₂×C₄	semidirect
85. C₂₃×#102	C₂×C₄	semidirect
89. C₂₃×#97	D₄	semidirect
156. #21526	C₂₃	direct (N × H)
208. C₈×C₂₃	C₄×D₄	semidirect
210. C₂×#442	C₂×C₂₃	semidirect
211. C₂²×#97	C₂×C₂₃	semidirect
212. C₄×#121	C₂×C₂₃	semidirect
213. #1972	C₂×C₂₃	semidirect
214. #1943	C₂×C₂₃	semidirect
215. #1936	C₂×C₂₃	semidirect
216. #1893	C₂×C₂₃	semidirect
217. #1807	C₂×C₂₃	semidirect
218. #1776	C₂×C₂₃	semidirect
219. #1762	C₂×C₂₃	semidirect
231. C₂²×C₂₃	#442	semidirect
254. #466	C₄×C₂₃	semidirect
291. C₂×D₈	C₂×C₄×C₂₃	semidirect
297. C₂²×C₈	C₂×C₄×C₂₃	semidirect
303. #121	C₂×C₄×C₂₃	semidirect
322. #107	C₂×C₄×C₂₃	semidirect
327. #102	C₂×C₄×C₂₃	semidirect
331. #97	D₄×C₂₃	semidirect
335. C₂₃	#21526	direct (N × H)
450. C₈	C₄×D₄×C₂₃	semidirect
462. C₂²	C₂₃×#442	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₂₃×#466	2
C₂×C₂₃×#442	2
C₂²×C₂₃×#97	2
C₄×C₂₃×#121	2
C₂₃×#1972	2
C₂₃×#1943	2
C₂₃×#1936	2
C₂₃×#1893	2
C₂₃×#1807	2
C₂₃×#1776	2
C₂₃×#1762	2
#21526	23

Subgroups — C23×#21526 #19169152

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#21526 #19169152