Subgroups — C₂₃×#21682 #19169308

Order 5888.

1230 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#436	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₃×#435	C₂	1	4	yes	maximal, complemented
3	C₂×C₈×D₄×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×C₂₃×#127	C₂	1	1	yes	maximal, characteristic
5	C₂₃×#1955	C₂	1	4	yes	maximal, complemented
6	C₂₃×#1954	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#1954	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#1842	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×C₂₃×#97	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×M₁₆×C₂₃	C₂²	1	2	yes	—
11	C₂³×C₈×C₂₃	C₂²	1	2	yes	—
12	C₂×C₂₃×#127	C₄	1	1	yes	characteristic
13	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
14	C₂×C₄×D₄×C₂₃	C₂²	1	4	yes	—
15	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
16	C₂₃×#436	—	2	4	no	—
17	C₂₃×#435	—	2	16	no	—
18	C₈×D₄×C₂₃	—	2	4	no	—
19	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×C₂₃×C₄⋊C₈	C₂²	1	4	yes	—
21	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₂₃×C₂²⋊C₈	C₂²	1	2	yes	—
23	C₂×C₂₃×C₂²⋊C₈	C₂²	1	4	yes	—
24	C₂×C₂₃×C₂²⋊C₈	C₂²	1	4	yes	—
25	C₂×C₂₃×C₂²⋊C₈	C₂²	1	2	yes	—
26	C₂×C₂₃×#97	C₂²	1	2	yes	—
27	C₂×C₂₃×#97	C₂²	1	2	yes	—
28	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
30	C₂₃×#390	C₄	1	1	yes	characteristic
31	C₂₃×#390	C₄	1	1	yes	characteristic
32	C₂₃×#390	C₄	1	4	yes	—
33	C₂₃×#384	C₄	1	1	yes	characteristic
34	C₄³×C₂₃	C₂²	1	1	yes	characteristic
35	C₂²×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic
36	C₂²×D₄×C₂₃	C₂×C₄	1	4	yes	—
37	C₂²×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic
38	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
39	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
40	C₂×M₁₆×C₂₃	—	2	8	no	—
41	C₂×M₁₆×C₂₃	—	2	4	no	—
42	C₂²×C₈×C₂₃	—	2	4	no	—
43	C₂²×C₈×C₂₃	—	2	8	no	—
44	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
45	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
46	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
47	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
48	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
49	C₂₃×#127	—	2	4	no	—
50	C₄×D₄×C₂₃	—	2	2	no	—
51	C₄×D₄×C₂₃	—	2	8	no	—
52	C₄×D₄×C₂₃	—	2	2	no	—
53	C₄×D₄×C₂₃	—	2	2	no	—
54	C₄×D₄×C₂₃	—	2	2	no	—
55	C₄×D₄×C₂₃	—	2	8	no	—
56	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	4	yes	—
57	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
59	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	4	yes	—
60	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
61	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
62	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	4	yes	—
63	C₂×C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
64	C₂×C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
65	C₂×C₄²×C₂₃	C₂×C₄	1	2	yes	—
66	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
67	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
68	C₂₃×C₄⋊C₈	—	2	2	no	—
69	C₂₃×C₄⋊C₈	—	2	8	no	—
70	C₂₃×C₄⋊C₈	—	2	2	no	—
71	C₂₃×C₂²⋊C₈	—	2	4	no	—
72	C₂₃×C₂²⋊C₈	—	2	8	no	—
73	C₂₃×C₂²⋊C₈	—	2	8	no	—
74	C₂₃×C₂²⋊C₈	—	2	4	no	—
75	C₂₃×#97	—	2	4	no	—
76	C₂₃×#97	D₄	1	8	yes	complemented
77	C₄×C₈×C₂₃	—	2	2	no	—
78	C₄×C₈×C₂₃	D₄	1	4	yes	complemented
79	C₂⁴×C₂₃	C₂²×C₄	1	2	yes	—
80	C₂⁴×C₂₃	C₂²×C₄	1	2	yes	—
81	C₂×D₄×C₂₃	—	2	8	no	—
82	C₂×D₄×C₂₃	—	2	2	no	—
83	C₂×D₄×C₂₃	—	2	8	no	—
84	C₂×D₄×C₂₃	—	2	2	no	—
85	C₂×D₄×C₂₃	—	2	2	no	—
86	C₂×D₄×C₂₃	—	2	2	no	—
87	C₂×D₄×C₂₃	—	2	2	no	—
88	C₂×D₄×C₂₃	—	4	4	no	—
89	C₂×D₄×C₂₃	M₁₆	1	4	yes	complemented
90	C₂²×C₄×C₂₃	—	2	2	no	—
91	C₂²×C₄×C₂₃	—	2	4	no	—
92	C₂²×C₄×C₂₃	—	2	4	no	—
93	C₂²×C₄×C₂₃	—	2	2	no	—
94	C₂²×C₄×C₂₃	—	2	2	no	—
95	C₂²×C₄×C₂₃	—	2	4	no	—
96	C₂²×C₄×C₂₃	—	2	2	no	—
97	C₂²×C₄×C₂₃	—	2	4	no	—
98	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
99	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
100	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
101	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
102	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
103	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
104	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
105	M₁₆×C₂₃	—	4	8	no	—
106	C₂×C₈×C₂₃	—	2	2	no	—
107	C₂×C₈×C₂₃	—	2	2	no	—
108	C₂×C₈×C₂₃	—	2	2	no	—
109	C₂×C₈×C₂₃	—	2	2	no	—
110	C₂×C₈×C₂₃	—	2	4	no	—
111	C₂×C₈×C₂₃	—	2	4	no	—
112	C₂×C₈×C₂₃	—	2	2	no	—
113	C₂×C₈×C₂₃	—	4	8	no	—
114	C₂×C₈×C₂₃	C₂×D₄	1	2	yes	—
115	C₂×C₈×C₂₃	C₂×D₄	1	4	yes	—
116	C₂×C₈×C₂₃	C₂×D₄	1	2	yes	—
117	C₂×C₈×C₂₃	C₂×D₄	1	4	yes	—
118	C₄⋊C₄×C₂₃	—	2	8	no	—
119	C₄⋊C₄×C₂₃	—	2	2	no	—
120	C₄⋊C₄×C₂₃	—	2	2	no	—
121	C₂²⋊C₄×C₂₃	—	2	4	no	—
122	C₂²⋊C₄×C₂₃	—	2	8	no	—
123	C₂²⋊C₄×C₂₃	—	2	8	no	—
124	C₂²⋊C₄×C₂₃	—	2	4	no	—
125	C₄²×C₂₃	—	2	2	no	—
126	C₄²×C₂₃	—	2	2	no	—
127	C₄²×C₂₃	—	4	2	no	—
128	C₄²×C₂₃	C₂×D₄	1	2	yes	—
129	C₄²×C₂₃	C₂×D₄	1	4	yes	—
130	C₄²×C₂₃	#41	1	2	yes	—
131	C₄²×C₂₃	#41	1	4	yes	—
132	#21682	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
133	C₂³×C₂₃	—	2	2	no	—
134	C₂³×C₂₃	—	2	4	no	—
135	C₂³×C₂₃	—	2	2	no	—
136	C₂³×C₂₃	—	2	4	no	—
137	C₂³×C₂₃	—	2	2	no	—
138	C₂³×C₂₃	—	2	4	no	—
139	C₂³×C₂₃	—	2	2	no	—
140	C₂³×C₂₃	—	2	2	no	—
141	C₂³×C₂₃	—	2	4	no	—
142	C₂³×C₂₃	C₂×M₁₆	1	4	yes	—
143	C₂³×C₂₃	C₂³×C₄	1	1	yes	characteristic
144	D₄×C₂₃	—	2	8	no	—
145	D₄×C₂₃	—	4	16	no	—
146	D₄×C₂₃	—	4	4	no	—
147	C₂×C₄×C₂₃	—	2	2	no	—
148	C₂×C₄×C₂₃	—	2	2	no	—
149	C₂×C₄×C₂₃	—	2	2	no	—
150	C₂×C₄×C₂₃	—	2	2	no	—
151	C₂×C₄×C₂₃	—	2	2	no	—
152	C₂×C₄×C₂₃	—	2	2	no	—
153	C₂×C₄×C₂₃	—	2	2	no	—
154	C₂×C₄×C₂₃	—	2	4	no	—
155	C₂×C₄×C₂₃	—	2	4	no	—
156	C₂×C₄×C₂₃	—	4	2	no	—
157	C₂×C₄×C₂₃	—	4	2	no	—
158	C₂×C₄×C₂₃	—	4	2	no	—
159	C₂×C₄×C₂₃	—	4	4	no	—
160	C₂×C₄×C₂₃	—	4	4	no	—
161	C₂×C₄×C₂₃	—	4	2	no	—
162	C₂×C₄×C₂₃	C₄×D₄	1	2	yes	—
163	C₂×C₄×C₂₃	C₄×D₄	1	4	yes	—
164	C₂×C₄×C₂₃	C₄×D₄	1	4	yes	—
165	C₂×C₄×C₂₃	C₄×D₄	1	2	yes	—
166	C₂×C₄×C₂₃	C₂×M₁₆	1	2	yes	—
167	C₂×C₄×C₂₃	#131	1	2	yes	—
168	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
169	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
170	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
171	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
172	C₈×C₂₃	—	2	4	no	—
173	C₈×C₂₃	—	2	2	no	—
174	C₈×C₂₃	—	4	2	no	—
175	C₈×C₂₃	—	4	2	no	—
176	C₈×C₂₃	#127	1	4	yes	complemented
177	C₂×#436	C₂×C₂₃	1	1	yes	characteristic, complemented
178	C₂×#435	C₂×C₂₃	1	4	yes	complemented
179	C₂×C₈×D₄	C₂×C₂₃	1	1	yes	characteristic, complemented
180	C₄×#127	C₂×C₂₃	1	1	yes	characteristic
181	#1955	C₂×C₂₃	1	4	yes	complemented
182	#1954	C₂×C₂₃	1	1	yes	characteristic, complemented
183	#1954	C₂×C₂₃	1	1	yes	characteristic, complemented
184	#1842	C₂×C₂₃	1	1	yes	characteristic, complemented
185	C₄×#97	C₂×C₂₃	1	1	yes	characteristic, complemented
186	C₂²×C₂₃	—	2	4	no	—
187	C₂²×C₂₃	—	2	8	no	—
188	C₂²×C₂₃	—	4	2	no	—
189	C₂²×C₂₃	—	4	2	no	—
190	C₂²×C₂₃	—	4	4	no	—
191	C₂²×C₂₃	—	4	2	no	—
192	C₂²×C₂₃	—	4	2	no	—
193	C₂²×C₂₃	—	4	2	no	—
194	C₂²×C₂₃	—	4	4	no	—
195	C₂²×C₂₃	—	4	4	no	—
196	C₂²×C₂₃	C₂×C₄×D₄	1	1	yes	characteristic
197	C₂²×C₂₃	C₂×C₄×D₄	1	2	yes	—
198	C₂²×C₂₃	C₂²×M₁₆	1	1	yes	characteristic
199	C₂²×C₂₃	C₂×#131	1	1	yes	characteristic
200	C₂²×C₂₃	#568	1	2	yes	—
201	C₄×C₂₃	—	2	2	no	—
202	C₄×C₂₃	—	2	4	no	—
203	C₄×C₂₃	—	2	4	no	—
204	C₄×C₂₃	—	4	2	no	—
205	C₄×C₂₃	—	4	2	no	—
206	C₄×C₂₃	#435	1	4	yes	complemented
207	C₄×C₂₃	C₂×#127	1	1	yes	characteristic
208	C₄×C₂₃	#532	1	2	yes	—
209	C₄×C₂₃	#532	1	1	yes	characteristic
210	C₂²×M₁₆	C₂²×C₂₃	1	2	yes	—
211	C₂³×C₈	C₂²×C₂₃	1	2	yes	—
212	C₂×#127	C₄×C₂₃	1	1	yes	characteristic
213	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
214	C₂×C₄×D₄	C₂²×C₂₃	1	4	yes	—
215	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
216	#436	—	2	4	no	—
217	#435	—	2	16	no	—
218	C₈×D₄	—	2	4	no	—
219	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
220	C₂×C₄⋊C₈	C₂²×C₂₃	1	4	yes	—
221	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
222	C₂×C₂²⋊C₈	C₂²×C₂₃	1	2	yes	—
223	C₂×C₂²⋊C₈	C₂²×C₂₃	1	4	yes	—
224	C₂×C₂²⋊C₈	C₂²×C₂₃	1	4	yes	—
225	C₂×C₂²⋊C₈	C₂²×C₂₃	1	2	yes	—
226	C₂×#97	C₂²×C₂₃	1	2	yes	—
227	C₂×#97	C₂²×C₂₃	1	2	yes	—
228	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
229	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
230	#390	C₄×C₂₃	1	1	yes	characteristic
231	#390	C₄×C₂₃	1	1	yes	characteristic
232	#390	C₄×C₂₃	1	4	yes	—
233	#384	C₄×C₂₃	1	1	yes	characteristic
234	C₄³	C₂²×C₂₃	1	1	yes	characteristic
235	C₂×C₂₃	—	4	4	no	—
236	C₂×C₂₃	—	8	2	no	—
237	C₂×C₂₃	C₄×#127	1	1	yes	characteristic
238	C₂×C₂₃	C₂×#435	1	1	yes	characteristic
239	C₂×C₂₃	#2932	1	1	yes	characteristic
240	C₂×C₂₃	D₄×M₁₆	1	2	yes	—
241	C₂×C₂₃	#2935	1	2	yes	—
242	C₂²×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
243	C₂²×D₄	C₂×C₄×C₂₃	1	4	yes	—
244	C₂²×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
245	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
246	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
247	C₂×M₁₆	—	2	8	no	—
248	C₂×M₁₆	—	2	4	no	—
249	C₂²×C₈	—	2	4	no	—
250	C₂²×C₈	—	2	8	no	—
251	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
252	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
253	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
254	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
255	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
256	#127	—	2	4	no	—
257	C₄×D₄	—	2	2	no	—
258	C₄×D₄	—	2	8	no	—
259	C₄×D₄	—	2	2	no	—
260	C₄×D₄	—	2	2	no	—
261	C₄×D₄	—	2	2	no	—
262	C₄×D₄	—	2	8	no	—
263	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	4	yes	—
264	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
265	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
266	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	4	yes	—
267	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
268	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
269	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	4	yes	—
270	C₂×C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic
271	C₂×C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic
272	C₂×C₄²	C₂×C₄×C₂₃	1	2	yes	—
273	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
274	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
275	C₄⋊C₈	—	2	2	no	—
276	C₄⋊C₈	—	2	8	no	—
277	C₄⋊C₈	—	2	2	no	—
278	C₂²⋊C₈	—	2	4	no	—
279	C₂²⋊C₈	—	2	8	no	—
280	C₂²⋊C₈	—	2	8	no	—
281	C₂²⋊C₈	—	2	4	no	—
282	#97	—	2	4	no	—
283	#97	D₄×C₂₃	1	8	yes	complemented
284	C₄×C₈	—	2	2	no	—
285	C₄×C₈	D₄×C₂₃	1	4	yes	complemented
286	C₂₃	#21682	1	1	yes	characteristic, direct product factor, Sylow
287	C₂⁴	C₂²×C₄×C₂₃	1	2	yes	—
288	C₂⁴	C₂²×C₄×C₂₃	1	2	yes	—
289	C₂×D₄	—	2	8	no	—
290	C₂×D₄	—	2	2	no	—
291	C₂×D₄	—	2	8	no	—
292	C₂×D₄	—	2	2	no	—
293	C₂×D₄	—	2	2	no	—
294	C₂×D₄	—	2	2	no	—
295	C₂×D₄	—	2	2	no	—
296	C₂×D₄	—	4	4	no	—
297	C₂×D₄	M₁₆×C₂₃	1	4	yes	complemented
298	C₂²×C₄	—	2	2	no	—
299	C₂²×C₄	—	2	4	no	—
300	C₂²×C₄	—	2	4	no	—
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	—	2	2	no	—
303	C₂²×C₄	—	2	4	no	—
304	C₂²×C₄	—	2	2	no	—
305	C₂²×C₄	—	2	4	no	—
306	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
307	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
308	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
309	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
310	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
311	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
312	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
313	M₁₆	—	4	8	no	—
314	C₂×C₈	—	2	2	no	—
315	C₂×C₈	—	2	2	no	—
316	C₂×C₈	—	2	2	no	—
317	C₂×C₈	—	2	2	no	—
318	C₂×C₈	—	2	4	no	—
319	C₂×C₈	—	2	4	no	—
320	C₂×C₈	—	2	2	no	—
321	C₂×C₈	—	4	8	no	—
322	C₂×C₈	C₂×D₄×C₂₃	1	2	yes	—
323	C₂×C₈	C₂×D₄×C₂₃	1	4	yes	—
324	C₂×C₈	C₂×D₄×C₂₃	1	2	yes	—
325	C₂×C₈	C₂×D₄×C₂₃	1	4	yes	—
326	C₄⋊C₄	—	2	8	no	—
327	C₄⋊C₄	—	2	2	no	—
328	C₄⋊C₄	—	2	2	no	—
329	C₂²⋊C₄	—	2	4	no	—
330	C₂²⋊C₄	—	2	8	no	—
331	C₂²⋊C₄	—	2	8	no	—
332	C₂²⋊C₄	—	2	4	no	—
333	C₄²	—	2	2	no	—
334	C₄²	—	2	2	no	—
335	C₄²	—	4	2	no	—
336	C₄²	C₂×D₄×C₂₃	1	2	yes	—
337	C₄²	C₂×D₄×C₂₃	1	4	yes	—
338	C₄²	#41×C₂₃	1	2	yes	—
339	C₄²	#41×C₂₃	1	4	yes	—
340	C₂³	—	2	2	no	—
341	C₂³	—	2	4	no	—
342	C₂³	—	2	2	no	—
343	C₂³	—	2	4	no	—
344	C₂³	—	2	2	no	—
345	C₂³	—	2	2	no	—
346	C₂³	—	2	4	no	—
347	C₂³	—	2	2	no	—
348	C₂³	—	2	4	no	—
349	C₂³	C₂×M₁₆×C₂₃	1	4	yes	—
350	C₂³	C₂³×C₄×C₂₃	1	1	yes	characteristic
351	D₄	—	2	8	no	—
352	D₄	—	4	16	no	—
353	D₄	—	4	4	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	4	no	—
362	C₂×C₄	—	2	4	no	—
363	C₂×C₄	—	4	2	no	—
364	C₂×C₄	—	4	2	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	4	4	no	—
367	C₂×C₄	—	4	4	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	C₄×D₄×C₂₃	1	2	yes	—
370	C₂×C₄	C₄×D₄×C₂₃	1	4	yes	—
371	C₂×C₄	C₄×D₄×C₂₃	1	4	yes	—
372	C₂×C₄	C₄×D₄×C₂₃	1	2	yes	—
373	C₂×C₄	C₂×M₁₆×C₂₃	1	2	yes	—
374	C₂×C₄	C₂₃×#131	1	2	yes	—
375	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
376	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
377	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
378	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
379	C₈	—	2	4	no	—
380	C₈	—	2	2	no	—
381	C₈	—	4	2	no	—
382	C₈	—	4	2	no	—
383	C₈	C₂₃×#127	1	4	yes	complemented
384	C₂²	—	2	4	no	—
385	C₂²	—	2	8	no	—
386	C₂²	—	4	2	no	—
387	C₂²	—	4	4	no	—
388	C₂²	—	4	2	no	—
389	C₂²	—	4	2	no	—
390	C₂²	—	4	2	no	—
391	C₂²	—	4	4	no	—
392	C₂²	—	4	4	no	—
393	C₂²	—	4	2	no	—
394	C₂²	C₂×C₄×D₄×C₂₃	1	1	yes	characteristic
395	C₂²	C₂×C₄×D₄×C₂₃	1	2	yes	—
396	C₂²	C₂²×M₁₆×C₂₃	1	1	yes	characteristic
397	C₂²	C₂×C₂₃×#131	1	1	yes	characteristic
398	C₂²	C₂₃×#568	1	2	yes	—
399	C₄	—	2	2	no	—
400	C₄	—	2	4	no	—
401	C₄	—	2	4	no	—
402	C₄	—	4	2	no	—
403	C₄	—	4	2	no	—
404	C₄	C₂₃×#435	1	4	yes	complemented
405	C₄	C₂×C₂₃×#127	1	1	yes	characteristic
406	C₄	C₂₃×#532	1	2	yes	—
407	C₄	C₂₃×#532	1	1	yes	characteristic
408	C₂	—	4	4	no	—
409	C₂	—	8	2	no	—
410	C₂	C₄×C₂₃×#127	1	1	yes	characteristic
411	C₂	C₂×C₂₃×#435	1	1	yes	characteristic
412	C₂	C₂₃×#2932	1	1	yes	characteristic
413	C₂	D₄×M₁₆×C₂₃	1	2	yes	—
414	C₂	C₂₃×#2935	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₂₃	C₂⁴
commutator	C₂³	C₂³×C₄×C₂₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₃
socle	C₂³×C₂₃	C₂³×C₄
prime radical	C₂×C₂₃×#127	C₄
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₂₃×#436	C₂	semidirect
2. C₂×C₂₃×#435	C₂	semidirect
3. C₂×C₈×D₄×C₂₃	C₂	semidirect
5. C₂₃×#1955	C₂	semidirect
6. C₂₃×#1954	C₂	semidirect
7. C₂₃×#1954	C₂	semidirect
8. C₂₃×#1842	C₂	semidirect
9. C₄×C₂₃×#97	C₂	semidirect
76. C₂₃×#97	D₄	semidirect
78. C₄×C₈×C₂₃	D₄	semidirect
89. C₂×D₄×C₂₃	M₁₆	semidirect
132. #21682	C₂₃	direct (N × H)
176. C₈×C₂₃	#127	semidirect
177. C₂×#436	C₂×C₂₃	semidirect
178. C₂×#435	C₂×C₂₃	semidirect
179. C₂×C₈×D₄	C₂×C₂₃	semidirect
181. #1955	C₂×C₂₃	semidirect
182. #1954	C₂×C₂₃	semidirect
183. #1954	C₂×C₂₃	semidirect
184. #1842	C₂×C₂₃	semidirect
185. C₄×#97	C₂×C₂₃	semidirect
206. C₄×C₂₃	#435	semidirect
283. #97	D₄×C₂₃	semidirect
285. C₄×C₈	D₄×C₂₃	semidirect
286. C₂₃	#21682	direct (N × H)
297. C₂×D₄	M₁₆×C₂₃	semidirect
383. C₈	C₂₃×#127	semidirect
404. C₄	C₂₃×#435	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₂₃×#436	2
C₂×C₂₃×#435	2
C₂×C₈×D₄×C₂₃	2
C₄×C₂₃×#127	2
C₂₃×#1955	2
C₂₃×#1954	2
C₂₃×#1842	2
C₄×C₂₃×#97	2
#21682	23

Subgroups — C23×#21682 #19169308

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#21682 #19169308