Subgroups — C₂₃×#21581 #19169207

Order 5888.

964 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#484	C₂	1	1	yes	maximal, characteristic
2	C₄×C₂₃×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₄⋊C₄×C₂₃	C₂	1	1	yes	maximal, characteristic
4	C₂₃×#1927	C₂	1	2	yes	maximal, complemented
5	C₂₃×#1918	C₂	1	2	yes	maximal, complemented
6	C₂₃×#1872	C₂	1	1	yes	maximal, characteristic
7	C₂₃×#1853	C₂	1	1	yes	maximal, characteristic
8	C₂₃×#1824	C₂	1	1	yes	maximal, characteristic
9	C₂₃×#1776	C₂	1	2	yes	maximal, complemented
10	C₂₃×#1763	C₂	1	2	yes	maximal, complemented
11	C₂₃×#1749	C₂	1	1	yes	maximal, characteristic
12	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
13	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
14	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
15	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
16	C₂²×C₄²×C₂₃	—	2	1	no	—
17	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
18	C₂₃×#484	C₄	1	8	yes	complemented
19	C₂×C₂₃×#107	C₂²	1	2	yes	—
20	C₂×C₂₃×#106	C₂²	1	2	yes	—
21	C₂×C₂₃×#103	C₂²	1	2	yes	—
22	C₂×C₂₃×#103	C₂²	1	2	yes	—
23	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₂₃×#97	C₂²	1	2	yes	—
26	C₂₃×#391	C₂²	1	1	yes	characteristic
27	C₂₃×#389	C₂²	1	1	yes	characteristic
28	C₂₃×#387	—	2	1	no	—
29	C₂₃×#385	—	2	1	no	—
30	C₂₃×#380	C₂²	1	1	yes	characteristic
31	C₄×C₄⋊C₄×C₂₃	—	2	1	no	—
32	C₄×C₄⋊C₄×C₂₃	—	2	1	no	—
33	C₄×C₄⋊C₄×C₂₃	—	2	1	no	—
34	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
35	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
36	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
37	C₄×C₂²⋊C₄×C₂₃	—	2	1	no	—
38	C₂×C₂₃×#95	—	2	1	no	—
39	C₂₃×#340	C₂²	1	2	yes	—
40	C₂₃×#340	C₂²	1	2	yes	—
41	C₂₃×#340	C₂²	1	2	yes	—
42	C₂₃×#340	C₂²	1	2	yes	—
43	C₂₃×#336	C₂²	1	2	yes	—
44	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
45	C₂³×C₄×C₂₃	—	2	1	no	—
46	C₂³×C₄×C₂₃	—	2	1	no	—
47	C₂³×C₄×C₂₃	D₄	1	1	yes	characteristic
48	C₂³×C₄×C₂₃	D₄	1	1	yes	characteristic
49	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
50	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
51	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
52	C₂₃×C₂²⋊Q₈	—	2	2	no	—
53	C₂₃×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
54	C₄×Q₈×C₂₃	—	2	4	no	—
55	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
56	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
57	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
58	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
59	C₂×C₄⋊C₄×C₂₃	—	2	4	no	—
60	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
61	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
62	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	4	yes	—
63	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
64	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
65	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
66	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
67	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
68	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
69	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
70	C₂×C₄²×C₂₃	—	2	4	no	—
71	C₂×C₄²×C₂₃	—	2	1	no	—
72	C₂×C₄²×C₂₃	—	2	1	no	—
73	C₂×C₄²×C₂₃	—	2	2	no	—
74	C₂×C₄²×C₂₃	—	2	2	no	—
75	C₂×C₄²×C₂₃	—	4	4	no	—
76	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
77	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
78	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
79	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
80	C₂₃×#107	C₂×C₄	1	8	yes	complemented
81	C₂₃×#106	—	2	4	no	—
82	C₂₃×#103	—	2	4	no	—
83	C₂₃×#103	C₂×C₄	1	8	yes	complemented
84	C₂₃×C₂²⋊C₈	—	2	2	no	—
85	C₂₃×C₂²⋊C₈	C₂×C₄	1	4	yes	—
86	C₂₃×#97	—	2	4	no	—
87	C₂₃×#95	—	2	2	no	—
88	C₂₃×#95	—	2	2	no	—
89	C₂₃×#95	—	2	1	no	—
90	C₂₃×#95	—	2	1	no	—
91	C₂₃×#95	—	2	1	no	—
92	C₂₃×#95	—	2	1	no	—
93	C₂₃×#95	—	2	1	no	—
94	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
95	C₂×Q₈×C₂₃	—	2	1	no	—
96	C₂×Q₈×C₂₃	—	2	2	no	—
97	C₂×Q₈×C₂₃	—	2	2	no	—
98	C₂×Q₈×C₂₃	C₂²×C₄	1	2	yes	—
99	C₂²×C₄×C₂₃	—	2	2	no	—
100	C₂²×C₄×C₂₃	—	2	2	no	—
101	C₂²×C₄×C₂₃	—	2	2	no	—
102	C₂²×C₄×C₂₃	—	2	2	no	—
103	C₂²×C₄×C₂₃	—	2	2	no	—
104	C₂²×C₄×C₂₃	—	2	4	no	—
105	C₂²×C₄×C₂₃	—	2	4	no	—
106	C₂²×C₄×C₂₃	—	2	2	no	—
107	C₂²×C₄×C₂₃	—	2	2	no	—
108	C₂²×C₄×C₂₃	—	2	2	no	—
109	C₂²×C₄×C₂₃	—	2	1	no	—
110	C₂²×C₄×C₂₃	—	2	1	no	—
111	C₂²×C₄×C₂₃	—	2	2	no	—
112	C₂²×C₄×C₂₃	—	2	1	no	—
113	C₂²×C₄×C₂₃	—	2	1	no	—
114	C₂²×C₄×C₂₃	—	4	1	no	—
115	C₂²×C₄×C₂₃	—	4	2	no	—
116	C₂²×C₄×C₂₃	—	4	2	no	—
117	C₂²×C₄×C₂₃	—	4	2	no	—
118	C₂²×C₄×C₂₃	—	4	2	no	—
119	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
120	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₂₃	#41	1	2	yes	—
126	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
127	C₂×C₈×C₂₃	—	2	2	no	—
128	C₂×C₈×C₂₃	—	2	2	no	—
129	C₂×C₈×C₂₃	—	2	2	no	—
130	C₂×C₈×C₂₃	—	2	2	no	—
131	C₂×C₈×C₂₃	—	2	2	no	—
132	C₂×C₈×C₂₃	C₂²×C₄	1	4	yes	—
133	C₄⋊C₄×C₂₃	—	2	4	no	—
134	C₄⋊C₄×C₂₃	—	2	4	no	—
135	C₄⋊C₄×C₂₃	—	2	4	no	—
136	C₄⋊C₄×C₂₃	—	2	2	no	—
137	C₄⋊C₄×C₂₃	—	2	2	no	—
138	C₄⋊C₄×C₂₃	—	2	1	no	—
139	C₄⋊C₄×C₂₃	—	2	2	no	—
140	C₄⋊C₄×C₂₃	—	2	2	no	—
141	C₄⋊C₄×C₂₃	—	4	2	no	—
142	C₄⋊C₄×C₂₃	—	4	2	no	—
143	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
144	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
145	C₄⋊C₄×C₂₃	#41	1	4	yes	—
146	C₂²⋊C₄×C₂₃	—	2	4	no	—
147	C₂²⋊C₄×C₂₃	—	4	2	no	—
148	C₄²×C₂₃	—	2	2	no	—
149	C₄²×C₂₃	—	2	2	no	—
150	C₄²×C₂₃	—	2	2	no	—
151	C₄²×C₂₃	—	4	2	no	—
152	C₄²×C₂₃	—	4	4	no	—
153	C₄²×C₂₃	—	4	2	no	—
154	C₄²×C₂₃	—	4	4	no	—
155	C₄²×C₂₃	#41	1	4	yes	—
156	#21581	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	1	no	—
160	C₂³×C₂₃	—	2	1	no	—
161	C₂³×C₂₃	C₄×D₄	1	2	yes	—
162	C₂³×C₂₃	#137	1	2	yes	—
163	C₂³×C₂₃	#137	1	2	yes	—
164	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
165	Q₈×C₂₃	—	2	4	no	—
166	Q₈×C₂₃	—	4	2	no	—
167	C₂×C₄×C₂₃	—	2	8	no	—
168	C₂×C₄×C₂₃	—	2	1	no	—
169	C₂×C₄×C₂₃	—	2	1	no	—
170	C₂×C₄×C₂₃	—	2	1	no	—
171	C₂×C₄×C₂₃	—	2	1	no	—
172	C₂×C₄×C₂₃	—	2	1	no	—
173	C₂×C₄×C₂₃	—	2	1	no	—
174	C₂×C₄×C₂₃	—	2	1	no	—
175	C₂×C₄×C₂₃	—	2	1	no	—
176	C₂×C₄×C₂₃	—	2	4	no	—
177	C₂×C₄×C₂₃	—	2	4	no	—
178	C₂×C₄×C₂₃	—	2	2	no	—
179	C₂×C₄×C₂₃	—	2	2	no	—
180	C₂×C₄×C₂₃	—	2	4	no	—
181	C₂×C₄×C₂₃	—	2	1	no	—
182	C₂×C₄×C₂₃	—	2	4	no	—
183	C₂×C₄×C₂₃	—	2	1	no	—
184	C₂×C₄×C₂₃	—	2	1	no	—
185	C₂×C₄×C₂₃	—	4	4	no	—
186	C₂×C₄×C₂₃	—	4	8	no	—
187	C₂×C₄×C₂₃	—	4	8	no	—
188	C₂×C₄×C₂₃	—	4	1	no	—
189	C₂×C₄×C₂₃	—	4	1	no	—
190	C₂×C₄×C₂₃	—	4	2	no	—
191	C₂×C₄×C₂₃	—	4	2	no	—
192	C₂×C₄×C₂₃	—	4	1	no	—
193	C₂×C₄×C₂₃	—	4	2	no	—
194	C₂×C₄×C₂₃	—	4	1	no	—
195	C₂×C₄×C₂₃	—	4	2	no	—
196	C₂×C₄×C₂₃	—	4	1	no	—
197	C₂×C₄×C₂₃	—	4	1	no	—
198	C₂×C₄×C₂₃	—	4	1	no	—
199	C₂×C₄×C₂₃	—	4	1	no	—
200	C₂×C₄×C₂₃	—	4	1	no	—
201	C₂×C₄×C₂₃	—	4	1	no	—
202	C₂×C₄×C₂₃	C₄×D₄	1	2	yes	—
203	C₂×C₄×C₂₃	#123	1	2	yes	—
204	C₂×C₄×C₂₃	#123	1	2	yes	—
205	C₂×C₄×C₂₃	AGL(1,ℤ/8)	1	2	yes	—
206	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
207	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
208	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
209	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
210	C₈×C₂₃	—	2	4	no	—
211	C₈×C₂₃	—	4	2	no	—
212	C₂×#484	C₂×C₂₃	1	1	yes	characteristic
213	C₄×C₂²⋊Q₈	C₂×C₂₃	1	1	yes	characteristic
214	C₂×C₄×C₄⋊C₄	C₂×C₂₃	1	1	yes	characteristic
215	#1927	C₂×C₂₃	1	2	yes	complemented
216	#1918	C₂×C₂₃	1	2	yes	complemented
217	#1872	C₂×C₂₃	1	1	yes	characteristic
218	#1853	C₂×C₂₃	1	1	yes	characteristic
219	#1824	C₂×C₂₃	1	1	yes	characteristic
220	#1776	C₂×C₂₃	1	2	yes	complemented
221	#1763	C₂×C₂₃	1	2	yes	complemented
222	#1749	C₂×C₂₃	1	1	yes	characteristic
223	C₂²×C₂₃	—	2	2	no	—
224	C₂²×C₂₃	—	2	2	no	—
225	C₂²×C₂₃	—	2	2	no	—
226	C₂²×C₂₃	—	2	2	no	—
227	C₂²×C₂₃	—	2	2	no	—
228	C₂²×C₂₃	—	2	2	no	—
229	C₂²×C₂₃	#441	1	4	yes	—
230	C₂²×C₂₃	C₂×C₄×D₄	1	1	yes	characteristic
231	C₂²×C₂₃	C₂×#123	1	1	yes	characteristic
232	C₂²×C₂₃	#525	1	1	yes	characteristic
233	C₂²×C₂₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
234	C₂²×C₂₃	C₂×#137	1	1	yes	characteristic
235	C₂²×C₂₃	C₂×#137	1	1	yes	characteristic
236	C₂²×C₂₃	#575	1	1	yes	characteristic
237	C₄×C₂₃	—	2	2	no	—
238	C₄×C₂₃	—	2	2	no	—
239	C₄×C₂₃	—	2	2	no	—
240	C₄×C₂₃	—	2	2	no	—
241	C₄×C₂₃	—	4	1	no	—
242	C₄×C₂₃	—	4	4	no	—
243	C₄×C₂₃	—	4	2	no	—
244	C₄×C₂₃	—	4	4	no	—
245	C₄×C₂₃	—	4	2	no	—
246	C₄×C₂₃	—	8	1	no	—
247	C₄×C₂₃	—	8	1	no	—
248	C₄×C₂₃	C₄×#41	1	2	yes	—
249	C₄×C₂₃	#529	1	2	yes	—
250	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
251	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
252	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
253	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
254	C₂²×C₄²	—	2	1	no	—
255	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
256	#484	C₄×C₂₃	1	8	yes	complemented
257	C₂×#107	C₂²×C₂₃	1	2	yes	—
258	C₂×#106	C₂²×C₂₃	1	2	yes	—
259	C₂×#103	C₂²×C₂₃	1	2	yes	—
260	C₂×#103	C₂²×C₂₃	1	2	yes	—
261	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
262	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
263	C₂×#97	C₂²×C₂₃	1	2	yes	—
264	#391	C₂²×C₂₃	1	1	yes	characteristic
265	#389	C₂²×C₂₃	1	1	yes	characteristic
266	#387	—	2	1	no	—
267	#385	—	2	1	no	—
268	#380	C₂²×C₂₃	1	1	yes	characteristic
269	C₄×C₄⋊C₄	—	2	1	no	—
270	C₄×C₄⋊C₄	—	2	1	no	—
271	C₄×C₄⋊C₄	—	2	1	no	—
272	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
273	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
274	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
275	C₄×C₂²⋊C₄	—	2	1	no	—
276	C₂×#95	—	2	1	no	—
277	#340	C₂²×C₂₃	1	2	yes	—
278	#340	C₂²×C₂₃	1	2	yes	—
279	#340	C₂²×C₂₃	1	2	yes	—
280	#340	C₂²×C₂₃	1	2	yes	—
281	#336	C₂²×C₂₃	1	2	yes	—
282	C₂×C₂₃	—	2	4	no	—
283	C₂×C₂₃	C₄×#123	1	1	yes	characteristic
284	C₂×C₂₃	C₂×#441	1	1	yes	characteristic
285	C₂×C₂₃	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
286	C₂×C₂₃	#3092	1	1	yes	characteristic
287	C₂×C₂₃	#3095	1	1	yes	characteristic
288	C₂×C₂₃	#3110	1	1	yes	characteristic
289	C₂×C₂₃	#3117	1	1	yes	characteristic
290	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
291	C₂³×C₄	—	2	1	no	—
292	C₂³×C₄	—	2	1	no	—
293	C₂³×C₄	D₄×C₂₃	1	1	yes	characteristic
294	C₂³×C₄	D₄×C₂₃	1	1	yes	characteristic
295	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
296	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
297	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
298	C₂²⋊Q₈	—	2	2	no	—
299	C₂²⋊Q₈	C₂×C₄×C₂₃	1	4	yes	—
300	C₄×Q₈	—	2	4	no	—
301	C₂×C₄⋊C₄	—	2	1	no	—
302	C₂×C₄⋊C₄	—	2	1	no	—
303	C₂×C₄⋊C₄	—	2	1	no	—
304	C₂×C₄⋊C₄	—	2	2	no	—
305	C₂×C₄⋊C₄	—	2	4	no	—
306	C₂×C₄⋊C₄	—	2	1	no	—
307	C₂×C₄⋊C₄	—	2	1	no	—
308	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	4	yes	—
309	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
310	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
311	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
312	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
313	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
314	C₂×C₂²⋊C₄	—	2	1	no	—
315	C₂×C₂²⋊C₄	—	2	1	no	—
316	C₂×C₄²	—	2	4	no	—
317	C₂×C₄²	—	2	1	no	—
318	C₂×C₄²	—	2	1	no	—
319	C₂×C₄²	—	2	2	no	—
320	C₂×C₄²	—	2	2	no	—
321	C₂×C₄²	—	4	4	no	—
322	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
323	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
324	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
325	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
326	#107	C₂×C₄×C₂₃	1	8	yes	complemented
327	#106	—	2	4	no	—
328	#103	—	2	4	no	—
329	#103	C₂×C₄×C₂₃	1	8	yes	complemented
330	C₂²⋊C₈	—	2	2	no	—
331	C₂²⋊C₈	C₂×C₄×C₂₃	1	4	yes	—
332	#97	—	2	4	no	—
333	#95	—	2	2	no	—
334	#95	—	2	2	no	—
335	#95	—	2	1	no	—
336	#95	—	2	1	no	—
337	#95	—	2	1	no	—
338	#95	—	2	1	no	—
339	#95	—	2	1	no	—
340	C₂₃	#21581	1	1	yes	characteristic, direct product factor, Sylow
341	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
342	C₂×Q₈	—	2	1	no	—
343	C₂×Q₈	—	2	2	no	—
344	C₂×Q₈	—	2	2	no	—
345	C₂×Q₈	C₂²×C₄×C₂₃	1	2	yes	—
346	C₂²×C₄	—	2	2	no	—
347	C₂²×C₄	—	2	2	no	—
348	C₂²×C₄	—	2	2	no	—
349	C₂²×C₄	—	2	2	no	—
350	C₂²×C₄	—	2	2	no	—
351	C₂²×C₄	—	2	4	no	—
352	C₂²×C₄	—	2	4	no	—
353	C₂²×C₄	—	2	2	no	—
354	C₂²×C₄	—	2	2	no	—
355	C₂²×C₄	—	2	2	no	—
356	C₂²×C₄	—	2	1	no	—
357	C₂²×C₄	—	2	1	no	—
358	C₂²×C₄	—	2	2	no	—
359	C₂²×C₄	—	2	1	no	—
360	C₂²×C₄	—	2	1	no	—
361	C₂²×C₄	—	4	1	no	—
362	C₂²×C₄	—	4	2	no	—
363	C₂²×C₄	—	4	2	no	—
364	C₂²×C₄	—	4	2	no	—
365	C₂²×C₄	—	4	2	no	—
366	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
367	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
368	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
369	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
370	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
371	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
372	C₂²×C₄	#41×C₂₃	1	2	yes	—
373	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
374	C₂×C₈	—	2	2	no	—
375	C₂×C₈	—	2	2	no	—
376	C₂×C₈	—	2	2	no	—
377	C₂×C₈	—	2	2	no	—
378	C₂×C₈	—	2	2	no	—
379	C₂×C₈	C₂²×C₄×C₂₃	1	4	yes	—
380	C₄⋊C₄	—	2	4	no	—
381	C₄⋊C₄	—	2	4	no	—
382	C₄⋊C₄	—	2	4	no	—
383	C₄⋊C₄	—	2	2	no	—
384	C₄⋊C₄	—	2	2	no	—
385	C₄⋊C₄	—	2	1	no	—
386	C₄⋊C₄	—	2	2	no	—
387	C₄⋊C₄	—	2	2	no	—
388	C₄⋊C₄	—	4	2	no	—
389	C₄⋊C₄	—	4	2	no	—
390	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
391	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
392	C₄⋊C₄	#41×C₂₃	1	4	yes	—
393	C₂²⋊C₄	—	2	4	no	—
394	C₂²⋊C₄	—	4	2	no	—
395	C₄²	—	2	2	no	—
396	C₄²	—	2	2	no	—
397	C₄²	—	2	2	no	—
398	C₄²	—	4	4	no	—
399	C₄²	—	4	2	no	—
400	C₄²	—	4	2	no	—
401	C₄²	—	4	4	no	—
402	C₄²	#41×C₂₃	1	4	yes	—
403	C₂³	—	2	1	no	—
404	C₂³	—	2	1	no	—
405	C₂³	—	2	1	no	—
406	C₂³	—	2	1	no	—
407	C₂³	C₄×D₄×C₂₃	1	2	yes	—
408	C₂³	C₂₃×#137	1	2	yes	—
409	C₂³	C₂₃×#137	1	2	yes	—
410	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
411	Q₈	—	2	4	no	—
412	Q₈	—	4	2	no	—
413	C₂×C₄	—	2	8	no	—
414	C₂×C₄	—	2	1	no	—
415	C₂×C₄	—	2	1	no	—
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	2	1	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	—	2	4	no	—
423	C₂×C₄	—	2	4	no	—
424	C₂×C₄	—	2	1	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	2	4	no	—
429	C₂×C₄	—	2	1	no	—
430	C₂×C₄	—	2	4	no	—
431	C₂×C₄	—	4	4	no	—
432	C₂×C₄	—	4	8	no	—
433	C₂×C₄	—	4	8	no	—
434	C₂×C₄	—	4	2	no	—
435	C₂×C₄	—	4	2	no	—
436	C₂×C₄	—	4	1	no	—
437	C₂×C₄	—	4	2	no	—
438	C₂×C₄	—	4	1	no	—
439	C₂×C₄	—	4	2	no	—
440	C₂×C₄	—	4	1	no	—
441	C₂×C₄	—	4	1	no	—
442	C₂×C₄	—	4	1	no	—
443	C₂×C₄	—	4	1	no	—
444	C₂×C₄	—	4	1	no	—
445	C₂×C₄	—	4	1	no	—
446	C₂×C₄	—	4	1	no	—
447	C₂×C₄	—	4	1	no	—
448	C₂×C₄	C₄×D₄×C₂₃	1	2	yes	—
449	C₂×C₄	C₂₃×#123	1	2	yes	—
450	C₂×C₄	C₂₃×#123	1	2	yes	—
451	C₂×C₄	C₂₃×AGL(1,ℤ/8)	1	2	yes	—
452	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
453	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
454	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
455	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
456	C₈	—	2	4	no	—
457	C₈	—	4	2	no	—
458	C₂²	—	2	2	no	—
459	C₂²	—	2	2	no	—
460	C₂²	—	2	2	no	—
461	C₂²	—	2	2	no	—
462	C₂²	—	2	2	no	—
463	C₂²	—	2	2	no	—
464	C₂²	C₂₃×#441	1	4	yes	—
465	C₂²	C₂×C₄×D₄×C₂₃	1	1	yes	characteristic
466	C₂²	C₂×C₂₃×#123	1	1	yes	characteristic
467	C₂²	C₂₃×#525	1	1	yes	characteristic
468	C₂²	C₂×C₂₃×AGL(1,ℤ/8)	1	1	yes	characteristic
469	C₂²	C₂×C₂₃×#137	1	1	yes	characteristic
470	C₂²	C₂×C₂₃×#137	1	1	yes	characteristic
471	C₂²	C₂₃×#575	1	1	yes	characteristic
472	C₄	—	2	2	no	—
473	C₄	—	2	2	no	—
474	C₄	—	2	2	no	—
475	C₄	—	2	2	no	—
476	C₄	—	4	4	no	—
477	C₄	—	4	2	no	—
478	C₄	—	4	2	no	—
479	C₄	—	4	1	no	—
480	C₄	—	4	4	no	—
481	C₄	—	8	1	no	—
482	C₄	—	8	1	no	—
483	C₄	C₄×#41×C₂₃	1	2	yes	—
484	C₄	C₂₃×#529	1	2	yes	—
485	C₂	—	2	4	no	—
486	C₂	C₄×C₂₃×#123	1	1	yes	characteristic
487	C₂	C₂×C₂₃×#441	1	1	yes	characteristic
488	C₂	C₄×C₂₃×AGL(1,ℤ/8)	1	1	yes	characteristic
489	C₂	C₂₃×#3092	1	1	yes	characteristic
490	C₂	C₂₃×#3095	1	1	yes	characteristic
491	C₂	C₂₃×#3110	1	1	yes	characteristic
492	C₂	C₂₃×#3117	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₂₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₃
prime radical	C₂⁴×C₂₃	C₂×D₄
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
4. C₂₃×#1927	C₂	semidirect
5. C₂₃×#1918	C₂	semidirect
9. C₂₃×#1776	C₂	semidirect
10. C₂₃×#1763	C₂	semidirect
18. C₂₃×#484	C₄	semidirect
80. C₂₃×#107	C₂×C₄	semidirect
83. C₂₃×#103	C₂×C₄	semidirect
156. #21581	C₂₃	direct (N × H)
215. #1927	C₂×C₂₃	semidirect
216. #1918	C₂×C₂₃	semidirect
220. #1776	C₂×C₂₃	semidirect
221. #1763	C₂×C₂₃	semidirect
256. #484	C₄×C₂₃	semidirect
326. #107	C₂×C₄×C₂₃	semidirect
329. #103	C₂×C₄×C₂₃	semidirect
340. C₂₃	#21581	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×#484	2
C₄×C₂₃×C₂²⋊Q₈	2
C₂×C₄×C₄⋊C₄×C₂₃	2
C₂₃×#1927	2
C₂₃×#1918	2
C₂₃×#1872	2
C₂₃×#1853	2
C₂₃×#1824	2
C₂₃×#1776	2
C₂₃×#1763	2
C₂₃×#1749	2
#21581	23

Subgroups — C23×#21581 #19169207

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#21581 #19169207