Subgroups — C₂₃×#8939 #19156565

Order 5888.

768 conjugacy classes of subgroups.

The subgroup lattice has 470 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, complemented
2	C₄×C₂₃×#121	C₂	1	1	yes	maximal, characteristic
3	C₄×C₂₃×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₂₃×D₄⋊C₈	C₂	1	2	yes	maximal, complemented
5	C₂₃×#1279	C₂	1	2	yes	maximal, complemented
6	C₂³×C₈×C₂₃	—	2	1	no	—
7	C₂×C₂₃×#121	C₄	1	1	yes	characteristic
8	C₂×C₄×D₄×C₂₃	—	2	1	no	—
9	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
10	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
11	C₂×C₂₃×C₄⋊C₈	—	2	1	no	—
12	C₂×C₂₃×C₄⋊C₈	—	2	4	no	—
13	C₂×C₂₃×C₄⋊C₈	C₂²	1	2	yes	—
14	C₂×C₂₃×C₂²⋊C₈	—	2	1	no	—
15	C₂×C₄×C₈×C₂₃	C₂²	1	2	yes	—
16	C₂₃×#390	C₄	1	1	yes	characteristic
17	C₂₃×#389	C₄	1	1	yes	characteristic
18	C₂₃×#388	—	2	1	no	—
19	C₂₃×#386	—	2	1	no	—
20	C₂₃×#380	C₄	1	1	yes	characteristic
21	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
22	C₄×C₂²⋊C₄×C₂₃	—	2	1	no	—
23	C₂₃×#336	—	2	1	no	—
24	C₂₃×D₄⋊C₈	—	2	4	no	—
25	C₂²×D₄×C₂₃	—	2	1	no	—
26	C₂²×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic
27	C₂³×C₄×C₂₃	—	2	1	no	—
28	C₂³×C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
29	C₂³×C₄×C₂₃	D₄	1	1	yes	characteristic
30	C₂³×C₄×C₂₃	D₄	1	1	yes	characteristic
31	C₂²×C₈×C₂₃	—	2	4	no	—
32	C₂²×C₈×C₂₃	—	2	2	no	—
33	C₂²×C₈×C₂₃	—	2	2	no	—
34	C₂²×C₈×C₂₃	—	4	2	no	—
35	C₂²×C₈×C₂₃	—	4	2	no	—
36	C₂₃×#121	—	2	2	no	—
37	C₂₃×#121	C₈	1	4	yes	complemented
38	C₄×D₄×C₂₃	—	2	2	no	—
39	C₄×D₄×C₂₃	—	2	2	no	—
40	C₄×D₄×C₂₃	—	4	2	no	—
41	C₄×D₄×C₂₃	—	4	2	no	—
42	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
43	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
44	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
45	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
46	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
47	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
48	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
49	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
50	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
51	C₂×C₄²×C₂₃	—	2	2	no	—
52	C₂×C₄²×C₂₃	—	2	2	no	—
53	C₂×C₄²×C₂₃	—	2	1	no	—
54	C₂×C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
56	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
57	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
58	C₂₃×C₄⋊C₈	—	2	4	no	—
59	C₂₃×C₄⋊C₈	—	2	2	no	—
60	C₂₃×C₄⋊C₈	D₄	1	4	yes	complemented
61	C₂₃×C₂²⋊C₈	—	2	4	no	—
62	C₄×C₈×C₂₃	—	2	2	no	—
63	C₄×C₈×C₂₃	—	2	2	no	—
64	C₂₃×#95	—	2	1	no	—
65	C₂₃×#95	—	2	1	no	—
66	C₂₃×#95	—	2	1	no	—
67	C₂⁴×C₂₃	—	2	1	no	—
68	C₂⁴×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
69	C₂×D₄×C₂₃	—	2	4	no	—
70	C₂×D₄×C₂₃	—	2	2	no	—
71	C₂×D₄×C₂₃	—	2	1	no	—
72	C₂×D₄×C₂₃	—	2	2	no	—
73	C₂×D₄×C₂₃	—	4	2	no	—
74	C₂×D₄×C₂₃	—	4	2	no	—
75	C₂×D₄×C₂₃	C₂×C₈	1	2	yes	complemented
76	C₂²×C₄×C₂₃	—	2	2	no	—
77	C₂²×C₄×C₂₃	—	2	1	no	—
78	C₂²×C₄×C₂₃	—	2	1	no	—
79	C₂²×C₄×C₂₃	—	2	2	no	—
80	C₂²×C₄×C₂₃	—	2	1	no	—
81	C₂²×C₄×C₂₃	—	2	1	no	—
82	C₂²×C₄×C₂₃	—	2	2	no	—
83	C₂²×C₄×C₂₃	—	2	1	no	—
84	C₂²×C₄×C₂₃	—	2	2	no	—
85	C₂²×C₄×C₂₃	—	2	1	no	—
86	C₂²×C₄×C₂₃	—	2	1	no	—
87	C₂²×C₄×C₂₃	—	4	1	no	—
88	C₂²×C₄×C₂₃	—	4	1	no	—
89	C₂²×C₄×C₂₃	—	4	1	no	—
90	C₂²×C₄×C₂₃	—	4	1	no	—
91	C₂²×C₄×C₂₃	—	4	1	no	—
92	C₂²×C₄×C₂₃	—	4	1	no	—
93	C₂²×C₄×C₂₃	—	4	1	no	—
94	C₂²×C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
95	C₂²×C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
96	C₂²×C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
97	C₂²×C₄×C₂₃	C₂×C₈	1	2	yes	—
98	C₂²×C₄×C₂₃	M₁₆	1	2	yes	—
99	C₂²×C₄×C₂₃	D₈	1	2	yes	—
100	C₂²×C₄×C₂₃	SD₁₆	1	2	yes	—
101	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
102	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
104	C₂×C₈×C₂₃	—	2	4	no	—
105	C₂×C₈×C₂₃	—	2	4	no	—
106	C₂×C₈×C₂₃	—	4	2	no	—
107	C₂×C₈×C₂₃	—	4	8	no	—
108	C₂×C₈×C₂₃	—	4	2	no	—
109	C₂×C₈×C₂₃	—	4	2	no	—
110	C₂×C₈×C₂₃	—	4	2	no	—
111	C₄⋊C₄×C₂₃	—	2	1	no	—
112	C₄⋊C₄×C₂₃	—	2	2	no	—
113	C₄⋊C₄×C₂₃	—	2	2	no	—
114	C₄⋊C₄×C₂₃	—	4	2	no	—
115	C₄⋊C₄×C₂₃	C₂×C₈	1	2	yes	complemented
116	C₂²⋊C₄×C₂₃	—	2	4	no	—
117	C₂²⋊C₄×C₂₃	—	4	2	no	—
118	C₂²⋊C₄×C₂₃	—	4	2	no	—
119	C₂²⋊C₄×C₂₃	—	4	2	no	—
120	C₂²⋊C₄×C₂₃	—	4	2	no	—
121	C₄²×C₂₃	—	2	2	no	—
122	C₄²×C₂₃	—	2	1	no	—
123	C₄²×C₂₃	—	2	2	no	—
124	C₄²×C₂₃	—	2	1	no	—
125	C₄²×C₂₃	—	4	1	no	—
126	C₄²×C₂₃	—	4	1	no	—
127	C₄²×C₂₃	C₂×D₄	1	2	yes	—
128	C₄²×C₂₃	#41	1	2	yes	—
129	#8939	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
130	C₂³×C₂₃	—	2	1	no	—
131	C₂³×C₂₃	—	2	1	no	—
132	C₂³×C₂₃	—	2	1	no	—
133	C₂³×C₂₃	—	2	1	no	—
134	C₂³×C₂₃	—	2	2	no	—
135	C₂³×C₂₃	—	4	1	no	—
136	C₂³×C₂₃	—	4	1	no	—
137	C₂³×C₂₃	—	4	1	no	—
138	C₂³×C₂₃	—	4	1	no	—
139	C₂³×C₂₃	—	4	1	no	—
140	C₂³×C₂₃	—	4	1	no	—
141	C₂³×C₂₃	C₂²⋊C₈	1	2	yes	—
142	C₂³×C₂₃	#102	1	2	yes	—
143	C₂³×C₂₃	#104	1	2	yes	—
144	C₂³×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
145	D₄×C₂₃	—	2	4	no	—
146	D₄×C₂₃	—	4	8	no	—
147	D₄×C₂₃	—	4	2	no	—
148	C₂×C₄×C₂₃	—	2	1	no	—
149	C₂×C₄×C₂₃	—	2	1	no	—
150	C₂×C₄×C₂₃	—	2	1	no	—
151	C₂×C₄×C₂₃	—	2	1	no	—
152	C₂×C₄×C₂₃	—	2	1	no	—
153	C₂×C₄×C₂₃	—	2	1	no	—
154	C₂×C₄×C₂₃	—	2	4	no	—
155	C₂×C₄×C₂₃	—	2	4	no	—
156	C₂×C₄×C₂₃	—	2	2	no	—
157	C₂×C₄×C₂₃	—	2	2	no	—
158	C₂×C₄×C₂₃	—	2	2	no	—
159	C₂×C₄×C₂₃	—	2	2	no	—
160	C₂×C₄×C₂₃	—	2	1	no	—
161	C₂×C₄×C₂₃	—	2	2	no	—
162	C₂×C₄×C₂₃	—	2	1	no	—
163	C₂×C₄×C₂₃	—	2	1	no	—
164	C₂×C₄×C₂₃	—	4	4	no	—
165	C₂×C₄×C₂₃	—	4	1	no	—
166	C₂×C₄×C₂₃	—	4	1	no	—
167	C₂×C₄×C₂₃	—	4	1	no	—
168	C₂×C₄×C₂₃	—	4	1	no	—
169	C₂×C₄×C₂₃	—	4	1	no	—
170	C₂×C₄×C₂₃	—	4	1	no	—
171	C₂×C₄×C₂₃	—	4	1	no	—
172	C₂×C₄×C₂₃	—	4	1	no	—
173	C₂×C₄×C₂₃	—	8	1	no	—
174	C₂×C₄×C₂₃	—	8	1	no	—
175	C₂×C₄×C₂₃	—	8	1	no	—
176	C₂×C₄×C₂₃	—	8	1	no	—
177	C₂×C₄×C₂₃	C₂²⋊C₈	1	2	yes	—
178	C₂×C₄×C₂₃	#102	1	2	yes	—
179	C₂×C₄×C₂₃	C₄×D₄	1	2	yes	—
180	C₂×C₄×C₂₃	#120	1	1	yes	characteristic
181	C₂×C₄×C₂₃	#121	1	2	yes	—
182	C₂×C₄×C₂₃	#123	1	1	yes	characteristic
183	C₂×C₄×C₂₃	C₂²×C₈	1	1	yes	characteristic
184	C₂×C₄×C₂₃	C₂×M₁₆	1	1	yes	characteristic
185	C₂×C₄×C₂₃	#131	1	2	yes	—
186	C₂×C₄×C₂₃	C₂×D₈	1	1	yes	characteristic
187	C₂×C₄×C₂₃	C₂×SD₁₆	1	1	yes	characteristic
188	C₂×C₄×C₂₃	AGL(1,ℤ/8)	1	1	yes	characteristic
189	C₂×C₄×C₂₃	#137	1	1	yes	characteristic
190	C₈×C₂₃	—	4	4	no	—
191	C₈×C₂₃	—	4	4	no	—
192	C₂²×C₄⋊C₈	C₂×C₂₃	1	1	yes	characteristic, complemented
193	C₄×#121	C₂×C₂₃	1	1	yes	characteristic
194	C₄×C₂²⋊C₈	C₂×C₂₃	1	1	yes	characteristic, complemented
195	C₂×D₄⋊C₈	C₂×C₂₃	1	2	yes	complemented
196	#1279	C₂×C₂₃	1	2	yes	complemented
197	C₂²×C₂₃	—	2	2	no	—
198	C₂²×C₂₃	—	2	2	no	—
199	C₂²×C₂₃	—	2	2	no	—
200	C₂²×C₂₃	—	2	2	no	—
201	C₂²×C₂₃	—	2	2	no	—
202	C₂²×C₂₃	—	2	2	no	—
203	C₂²×C₂₃	—	4	2	no	—
204	C₂²×C₂₃	—	4	2	no	—
205	C₂²×C₂₃	—	4	2	no	—
206	C₂²×C₂₃	—	8	1	no	—
207	C₂²×C₂₃	—	8	1	no	—
208	C₂²×C₂₃	—	8	1	no	—
209	C₂²×C₂₃	—	8	1	no	—
210	C₂²×C₂₃	D₄⋊C₈	1	4	yes	complemented
211	C₂²×C₂₃	#386	1	1	yes	characteristic
212	C₂²×C₂₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
213	C₂²×C₂₃	#408	1	1	yes	characteristic
214	C₂²×C₂₃	C₂×#102	1	1	yes	characteristic
215	C₂²×C₂₃	#417	1	1	yes	characteristic
216	C₂²×C₂₃	C₂×#104	1	1	yes	characteristic
217	C₂²×C₂₃	#421	1	1	yes	characteristic
218	C₄×C₂₃	—	2	2	no	—
219	C₄×C₂₃	—	2	2	no	—
220	C₄×C₂₃	—	2	2	no	—
221	C₄×C₂₃	—	4	1	no	—
222	C₄×C₂₃	—	4	2	no	—
223	C₄×C₂₃	—	8	1	no	—
224	C₄×C₂₃	—	8	1	no	—
225	C₄×C₂₃	C₈×D₄	1	2	yes	—
226	C₄×C₂₃	#435	1	2	yes	—
227	C₄×C₂₃	#447	1	1	yes	characteristic
228	C₄×C₂₃	#448	1	1	yes	characteristic
229	C₄×C₂₃	#480	1	1	yes	characteristic
230	C₄×C₂₃	#481	1	1	yes	characteristic
231	C₂³×C₈	—	2	1	no	—
232	C₂×#121	C₄×C₂₃	1	1	yes	characteristic
233	C₂×C₄×D₄	—	2	1	no	—
234	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
235	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
236	C₂×C₄⋊C₈	—	2	1	no	—
237	C₂×C₄⋊C₈	—	2	4	no	—
238	C₂×C₄⋊C₈	C₂²×C₂₃	1	2	yes	—
239	C₂×C₂²⋊C₈	—	2	1	no	—
240	C₂×C₄×C₈	C₂²×C₂₃	1	2	yes	—
241	#390	C₄×C₂₃	1	1	yes	characteristic
242	#389	C₄×C₂₃	1	1	yes	characteristic
243	#388	—	2	1	no	—
244	#386	—	2	1	no	—
245	#380	C₄×C₂₃	1	1	yes	characteristic
246	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
247	C₄×C₂²⋊C₄	—	2	1	no	—
248	#336	—	2	1	no	—
249	D₄⋊C₈	—	2	4	no	—
250	C₂×C₂₃	—	2	4	no	—
251	C₂×C₂₃	—	8	2	no	—
252	C₂×C₂₃	C₂×D₄⋊C₈	1	1	yes	characteristic
253	C₂×C₂₃	#1477	1	1	yes	characteristic
254	C₂×C₂₃	#1480	1	1	yes	characteristic
255	C₂×C₂₃	#1483	1	1	yes	characteristic
256	C₂×C₂₃	#1869	1	1	yes	characteristic
257	C₂×C₂₃	#1871	1	1	yes	characteristic
258	C₂×C₂₃	#1874	1	1	yes	characteristic
259	C₂²×D₄	—	2	1	no	—
260	C₂²×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
261	C₂³×C₄	—	2	1	no	—
262	C₂³×C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
263	C₂³×C₄	D₄×C₂₃	1	1	yes	characteristic
264	C₂³×C₄	D₄×C₂₃	1	1	yes	characteristic
265	C₂²×C₈	—	2	4	no	—
266	C₂²×C₈	—	2	2	no	—
267	C₂²×C₈	—	2	2	no	—
268	C₂²×C₈	—	4	2	no	—
269	C₂²×C₈	—	4	2	no	—
270	#121	—	2	2	no	—
271	#121	C₈×C₂₃	1	4	yes	complemented
272	C₄×D₄	—	2	2	no	—
273	C₄×D₄	—	2	2	no	—
274	C₄×D₄	—	4	2	no	—
275	C₄×D₄	—	4	2	no	—
276	C₂×C₄⋊C₄	—	2	1	no	—
277	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
278	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
279	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
280	C₂×C₂²⋊C₄	—	2	1	no	—
281	C₂×C₂²⋊C₄	—	2	1	no	—
282	C₂×C₂²⋊C₄	—	2	1	no	—
283	C₂×C₂²⋊C₄	—	2	1	no	—
284	C₂×C₂²⋊C₄	—	2	1	no	—
285	C₂×C₄²	—	2	2	no	—
286	C₂×C₄²	—	2	2	no	—
287	C₂×C₄²	—	2	1	no	—
288	C₂×C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic
289	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
290	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
291	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
292	C₄⋊C₈	—	2	4	no	—
293	C₄⋊C₈	—	2	2	no	—
294	C₄⋊C₈	D₄×C₂₃	1	4	yes	complemented
295	C₂²⋊C₈	—	2	4	no	—
296	C₄×C₈	—	2	2	no	—
297	C₄×C₈	—	2	2	no	—
298	#95	—	2	1	no	—
299	#95	—	2	1	no	—
300	#95	—	2	1	no	—
301	C₂₃	#8939	1	1	yes	characteristic, direct product factor, Sylow
302	C₂⁴	—	2	1	no	—
303	C₂⁴	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
304	C₂×D₄	—	2	4	no	—
305	C₂×D₄	—	2	2	no	—
306	C₂×D₄	—	2	1	no	—
307	C₂×D₄	—	2	2	no	—
308	C₂×D₄	—	4	2	no	—
309	C₂×D₄	—	4	2	no	—
310	C₂×D₄	C₂×C₈×C₂₃	1	2	yes	complemented
311	C₂²×C₄	—	2	2	no	—
312	C₂²×C₄	—	2	1	no	—
313	C₂²×C₄	—	2	1	no	—
314	C₂²×C₄	—	2	2	no	—
315	C₂²×C₄	—	2	1	no	—
316	C₂²×C₄	—	2	1	no	—
317	C₂²×C₄	—	2	2	no	—
318	C₂²×C₄	—	2	1	no	—
319	C₂²×C₄	—	2	2	no	—
320	C₂²×C₄	—	2	1	no	—
321	C₂²×C₄	—	2	1	no	—
322	C₂²×C₄	—	4	1	no	—
323	C₂²×C₄	—	4	1	no	—
324	C₂²×C₄	—	4	1	no	—
325	C₂²×C₄	—	4	1	no	—
326	C₂²×C₄	—	4	1	no	—
327	C₂²×C₄	—	4	1	no	—
328	C₂²×C₄	—	4	1	no	—
329	C₂²×C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
330	C₂²×C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
331	C₂²×C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
332	C₂²×C₄	C₂×C₈×C₂₃	1	2	yes	—
333	C₂²×C₄	M₁₆×C₂₃	1	2	yes	—
334	C₂²×C₄	D₈×C₂₃	1	2	yes	—
335	C₂²×C₄	SD₁₆×C₂₃	1	2	yes	—
336	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
337	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
338	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
339	C₂×C₈	—	2	4	no	—
340	C₂×C₈	—	2	4	no	—
341	C₂×C₈	—	4	8	no	—
342	C₂×C₈	—	4	2	no	—
343	C₂×C₈	—	4	2	no	—
344	C₂×C₈	—	4	2	no	—
345	C₂×C₈	—	4	2	no	—
346	C₄⋊C₄	—	2	1	no	—
347	C₄⋊C₄	—	2	2	no	—
348	C₄⋊C₄	—	2	2	no	—
349	C₄⋊C₄	—	4	2	no	—
350	C₄⋊C₄	C₂×C₈×C₂₃	1	2	yes	complemented
351	C₂²⋊C₄	—	2	4	no	—
352	C₂²⋊C₄	—	4	2	no	—
353	C₂²⋊C₄	—	4	2	no	—
354	C₂²⋊C₄	—	4	2	no	—
355	C₂²⋊C₄	—	4	2	no	—
356	C₄²	—	2	2	no	—
357	C₄²	—	2	1	no	—
358	C₄²	—	2	2	no	—
359	C₄²	—	2	1	no	—
360	C₄²	—	4	1	no	—
361	C₄²	—	4	1	no	—
362	C₄²	C₂×D₄×C₂₃	1	2	yes	—
363	C₄²	#41×C₂₃	1	2	yes	—
364	C₂³	—	2	1	no	—
365	C₂³	—	2	1	no	—
366	C₂³	—	2	1	no	—
367	C₂³	—	2	1	no	—
368	C₂³	—	2	2	no	—
369	C₂³	—	4	1	no	—
370	C₂³	—	4	1	no	—
371	C₂³	—	4	1	no	—
372	C₂³	—	4	1	no	—
373	C₂³	—	4	1	no	—
374	C₂³	—	4	1	no	—
375	C₂³	C₂₃×C₂²⋊C₈	1	2	yes	—
376	C₂³	C₂₃×#102	1	2	yes	—
377	C₂³	C₂₃×#104	1	2	yes	—
378	C₂³	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
379	D₄	—	2	4	no	—
380	D₄	—	4	8	no	—
381	D₄	—	4	2	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	2	1	no	—
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	4	no	—
389	C₂×C₄	—	2	4	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	4	4	no	—
399	C₂×C₄	—	4	1	no	—
400	C₂×C₄	—	4	1	no	—
401	C₂×C₄	—	4	1	no	—
402	C₂×C₄	—	4	1	no	—
403	C₂×C₄	—	4	1	no	—
404	C₂×C₄	—	4	1	no	—
405	C₂×C₄	—	4	1	no	—
406	C₂×C₄	—	4	1	no	—
407	C₂×C₄	—	8	1	no	—
408	C₂×C₄	—	8	1	no	—
409	C₂×C₄	—	8	1	no	—
410	C₂×C₄	—	8	1	no	—
411	C₂×C₄	C₂₃×C₂²⋊C₈	1	2	yes	—
412	C₂×C₄	C₂₃×#102	1	2	yes	—
413	C₂×C₄	C₄×D₄×C₂₃	1	2	yes	—
414	C₂×C₄	C₂₃×#120	1	1	yes	characteristic
415	C₂×C₄	C₂₃×#121	1	2	yes	—
416	C₂×C₄	C₂₃×#123	1	1	yes	characteristic
417	C₂×C₄	C₂²×C₈×C₂₃	1	1	yes	characteristic
418	C₂×C₄	C₂×M₁₆×C₂₃	1	1	yes	characteristic
419	C₂×C₄	C₂₃×#131	1	2	yes	—
420	C₂×C₄	C₂×D₈×C₂₃	1	1	yes	characteristic
421	C₂×C₄	C₂×SD₁₆×C₂₃	1	1	yes	characteristic
422	C₂×C₄	C₂₃×AGL(1,ℤ/8)	1	1	yes	characteristic
423	C₂×C₄	C₂₃×#137	1	1	yes	characteristic
424	C₈	—	4	4	no	—
425	C₈	—	4	4	no	—
426	C₂²	—	2	2	no	—
427	C₂²	—	2	2	no	—
428	C₂²	—	2	2	no	—
429	C₂²	—	2	2	no	—
430	C₂²	—	2	2	no	—
431	C₂²	—	2	2	no	—
432	C₂²	—	4	2	no	—
433	C₂²	—	4	2	no	—
434	C₂²	—	4	2	no	—
435	C₂²	—	8	1	no	—
436	C₂²	—	8	1	no	—
437	C₂²	—	8	1	no	—
438	C₂²	—	8	1	no	—
439	C₂²	C₂₃×D₄⋊C₈	1	4	yes	complemented
440	C₂²	C₂₃×#386	1	1	yes	characteristic
441	C₂²	C₂×C₂₃×C₂²⋊C₈	1	1	yes	characteristic
442	C₂²	C₂₃×#408	1	1	yes	characteristic
443	C₂²	C₂×C₂₃×#102	1	1	yes	characteristic
444	C₂²	C₂₃×#417	1	1	yes	characteristic
445	C₂²	C₂×C₂₃×#104	1	1	yes	characteristic
446	C₂²	C₂₃×#421	1	1	yes	characteristic
447	C₄	—	2	2	no	—
448	C₄	—	2	2	no	—
449	C₄	—	2	2	no	—
450	C₄	—	4	2	no	—
451	C₄	—	4	1	no	—
452	C₄	—	8	1	no	—
453	C₄	—	8	1	no	—
454	C₄	C₈×D₄×C₂₃	1	2	yes	—
455	C₄	C₂₃×#435	1	2	yes	—
456	C₄	C₂₃×#447	1	1	yes	characteristic
457	C₄	C₂₃×#448	1	1	yes	characteristic
458	C₄	C₂₃×#480	1	1	yes	characteristic
459	C₄	C₂₃×#481	1	1	yes	characteristic
460	C₂	—	2	4	no	—
461	C₂	—	8	2	no	—
462	C₂	C₂×C₂₃×D₄⋊C₈	1	1	yes	characteristic
463	C₂	C₂₃×#1477	1	1	yes	characteristic
464	C₂	C₂₃×#1480	1	1	yes	characteristic
465	C₂	C₂₃×#1483	1	1	yes	characteristic
466	C₂	C₂₃×#1869	1	1	yes	characteristic
467	C₂	C₂₃×#1871	1	1	yes	characteristic
468	C₂	C₂₃×#1874	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₂₃	C₂×D₄
commutator	C₂×C₄	C₂²×C₈×C₂₃
Frattini, cosocle	C₂×C₄²	C₂³×C₂₃
socle	C₂³×C₂₃	C₂×C₂²⋊C₄
prime radical	C₂×C₂₃×#121	C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₂₃ ◁ C₂²×C₄²×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₂₃×C₄⋊C₈	C₂	semidirect
3. C₄×C₂₃×C₂²⋊C₈	C₂	semidirect
4. C₂×C₂₃×D₄⋊C₈	C₂	semidirect
5. C₂₃×#1279	C₂	semidirect
37. C₂₃×#121	C₈	semidirect
60. C₂₃×C₄⋊C₈	D₄	semidirect
75. C₂×D₄×C₂₃	C₂×C₈	semidirect
115. C₄⋊C₄×C₂₃	C₂×C₈	semidirect
129. #8939	C₂₃	direct (N × H)
192. C₂²×C₄⋊C₈	C₂×C₂₃	semidirect
194. C₄×C₂²⋊C₈	C₂×C₂₃	semidirect
195. C₂×D₄⋊C₈	C₂×C₂₃	semidirect
196. #1279	C₂×C₂₃	semidirect
210. C₂²×C₂₃	D₄⋊C₈	semidirect
271. #121	C₈×C₂₃	semidirect
294. C₄⋊C₈	D₄×C₂₃	semidirect
301. C₂₃	#8939	direct (N × H)
310. C₂×D₄	C₂×C₈×C₂₃	semidirect
350. C₄⋊C₄	C₂×C₈×C₂₃	semidirect
439. C₂²	C₂₃×D₄⋊C₈	semidirect

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
C₄×C₂₃×#121	2
C₄×C₂₃×C₂²⋊C₈	2
C₂×C₂₃×D₄⋊C₈	2
C₂₃×#1279	2
#8939	23

Subgroups — C23×#8939 #19156565

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#8939 #19156565