Subgroups — C₂₃×#21644 #19169270

Order 5888.

890 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#486	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#2331	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#2328	C₂	1	1	yes	maximal, characteristic
4	C₂₃×#1993	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#1961	C₂	1	1	yes	maximal, characteristic
6	C₂₃×#1936	C₂	1	2	yes	maximal, complemented
7	C₂₃×#1934	C₂	1	2	yes	maximal, complemented
8	C₂₃×#1835	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#1762	C₂	1	2	yes	maximal, complemented
10	C₄×C₂₃×#102	C₂	1	2	yes	maximal, complemented
11	C₂₃×#1726	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
13	C₂×C₂₃×#127	C₂²	1	1	yes	characteristic
14	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	—
15	C₂₃×#486	C₄	1	8	yes	complemented
16	C₂×C₂₃×#102	C₂²	1	2	yes	—
17	C₂×C₂₃×#102	C₂²	1	2	yes	—
18	C₂×C₂₃×#102	C₂²	1	2	yes	—
19	C₂×C₂₃×#102	C₂²	1	2	yes	—
20	C₂×C₂₃×#97	C₂²	1	1	yes	characteristic
21	C₂×C₂₃×#97	C₂²	1	1	yes	characteristic
22	C₂×C₂₃×#97	C₂²	1	1	yes	characteristic
23	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
24	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
26	C₂₃×#391	—	2	2	no	—
27	C₂₃×#390	C₂²	1	2	yes	—
28	C₂₃×#389	C₂²	1	2	yes	—
29	C₂₃×#387	—	2	2	no	—
30	C₂₃×#386	—	2	2	no	—
31	C₂₃×#386	—	2	2	no	—
32	C₂₃×#382	C₂²	1	1	yes	characteristic
33	C₂₃×#382	C₂²	1	1	yes	characteristic
34	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
35	C₂₃×#376	C₂²	1	1	yes	characteristic
36	C₂₃×#340	C₂²	1	2	yes	—
37	C₂₃×#340	C₂²	1	2	yes	—
38	C₂₃×#340	C₂²	1	2	yes	—
39	C₂₃×#340	C₂²	1	2	yes	—
40	C₂²×Q₈×C₂₃	—	2	1	no	—
41	C₂²×D₄×C₂₃	—	2	1	no	—
42	C₂²×D₄×C₂₃	—	2	1	no	—
43	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
44	C₂³×C₄×C₂₃	—	2	2	no	—
45	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
46	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
47	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
48	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
49	C₂₃×C₄⋊Q₈	—	2	2	no	—
50	C₂₃×C₄⋊Q₈	C₂×C₄	1	4	yes	complemented
51	C₂₃×#127	—	2	2	no	—
52	C₂₃×#127	C₂×C₄	1	4	yes	—
53	C₄×D₄×C₂₃	—	2	4	no	—
54	C₄×D₄×C₂₃	—	2	4	no	—
55	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
56	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
57	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
58	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
59	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
60	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
61	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
62	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
63	C₂×C₄²×C₂₃	—	2	2	no	—
64	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
65	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
66	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
67	C₂₃×#102	—	2	4	no	—
68	C₂₃×#102	—	2	4	no	—
69	C₂₃×#102	C₂×C₄	1	8	yes	complemented
70	C₂₃×#102	C₂×C₄	1	8	yes	complemented
71	C₂₃×#97	—	2	2	no	—
72	C₂₃×#97	—	2	2	no	—
73	C₂₃×#97	—	2	2	no	—
74	C₄×C₈×C₂₃	—	2	2	no	—
75	C₄×C₈×C₂₃	—	2	2	no	—
76	C₄×C₈×C₂₃	C₂×C₄	1	4	yes	complemented
77	C₂₃×#95	—	2	2	no	—
78	C₂₃×#95	—	2	1	no	—
79	C₂₃×#95	—	2	1	no	—
80	C₂₃×#95	—	2	1	no	—
81	C₂₃×#95	—	2	1	no	—
82	C₂₃×#95	—	2	2	no	—
83	C₂₃×#95	D₄	1	2	yes	—
84	C₂₃×#95	D₄	1	2	yes	—
85	C₂⁴×C₂₃	—	2	2	no	—
86	C₂×Q₈×C₂₃	—	2	4	no	—
87	C₂×Q₈×C₂₃	—	8	2	no	—
88	C₂×D₄×C₂₃	—	2	4	no	—
89	C₂×D₄×C₂₃	—	2	4	no	—
90	C₂×D₄×C₂₃	—	2	2	no	—
91	C₂×D₄×C₂₃	—	2	2	no	—
92	C₂×D₄×C₂₃	—	2	2	no	—
93	C₂×D₄×C₂₃	—	2	2	no	—
94	C₂×D₄×C₂₃	—	2	2	no	—
95	C₂×D₄×C₂₃	—	8	2	no	—
96	C₂×D₄×C₂₃	—	8	2	no	—
97	C₂×D₄×C₂₃	C₂²×C₄	1	4	yes	—
98	C₂²×C₄×C₂₃	—	2	2	no	—
99	C₂²×C₄×C₂₃	—	2	2	no	—
100	C₂²×C₄×C₂₃	—	2	2	no	—
101	C₂²×C₄×C₂₃	—	4	4	no	—
102	C₂²×C₄×C₂₃	—	8	2	no	—
103	C₂²×C₄×C₂₃	—	8	2	no	—
104	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
105	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
108	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
109	C₂×C₈×C₂₃	—	2	1	no	—
110	C₂×C₈×C₂₃	—	2	1	no	—
111	C₂×C₈×C₂₃	—	2	1	no	—
112	C₂×C₈×C₂₃	—	2	1	no	—
113	C₂×C₈×C₂₃	—	2	1	no	—
114	C₂×C₈×C₂₃	—	2	1	no	—
115	C₂×C₈×C₂₃	—	2	1	no	—
116	C₂×C₈×C₂₃	—	2	1	no	—
117	C₂×C₈×C₂₃	C₂²×C₄	1	2	yes	—
118	C₂×C₈×C₂₃	C₂²×C₄	1	2	yes	—
119	C₂×C₈×C₂₃	#41	1	2	yes	—
120	C₂×C₈×C₂₃	#41	1	2	yes	—
121	C₄⋊C₄×C₂₃	—	2	4	no	—
122	C₄⋊C₄×C₂₃	—	2	2	no	—
123	C₄⋊C₄×C₂₃	—	2	2	no	—
124	C₄⋊C₄×C₂₃	—	2	2	no	—
125	C₄⋊C₄×C₂₃	—	2	2	no	—
126	C₄⋊C₄×C₂₃	—	2	2	no	—
127	C₄⋊C₄×C₂₃	—	8	2	no	—
128	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
129	C₂²⋊C₄×C₂₃	—	4	4	no	—
130	C₂²⋊C₄×C₂₃	—	8	2	no	—
131	C₂²⋊C₄×C₂₃	—	8	2	no	—
132	C₄²×C₂₃	—	2	1	no	—
133	C₄²×C₂₃	—	2	1	no	—
134	C₄²×C₂₃	—	8	2	no	—
135	C₄²×C₂₃	C₂²×C₄	1	2	yes	—
136	C₄²×C₂₃	#41	1	2	yes	—
137	C₄²×C₂₃	#41	1	2	yes	—
138	C₄²×C₂₃	#41	1	2	yes	—
139	#21644	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
140	C₂³×C₂₃	—	2	4	no	—
141	C₂³×C₂₃	—	4	2	no	—
142	C₂³×C₂₃	—	4	2	no	—
143	C₂³×C₂₃	—	4	2	no	—
144	C₂³×C₂₃	—	4	2	no	—
145	C₂³×C₂₃	—	4	2	no	—
146	C₂³×C₂₃	—	4	2	no	—
147	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
148	Q₈×C₂₃	—	8	4	no	—
149	D₄×C₂₃	—	2	4	no	—
150	D₄×C₂₃	—	2	4	no	—
151	D₄×C₂₃	—	4	2	no	—
152	D₄×C₂₃	—	4	2	no	—
153	D₄×C₂₃	—	8	4	no	—
154	D₄×C₂₃	—	8	4	no	—
155	C₂×C₄×C₂₃	—	2	2	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	4	no	—
160	C₂×C₄×C₂₃	—	2	2	no	—
161	C₂×C₄×C₂₃	—	2	2	no	—
162	C₂×C₄×C₂₃	—	2	2	no	—
163	C₂×C₄×C₂₃	—	4	2	no	—
164	C₂×C₄×C₂₃	—	4	2	no	—
165	C₂×C₄×C₂₃	—	4	2	no	—
166	C₂×C₄×C₂₃	—	4	2	no	—
167	C₂×C₄×C₂₃	—	4	2	no	—
168	C₂×C₄×C₂₃	—	4	2	no	—
169	C₂×C₄×C₂₃	—	4	2	no	—
170	C₂×C₄×C₂₃	—	4	2	no	—
171	C₂×C₄×C₂₃	—	8	8	no	—
172	C₂×C₄×C₂₃	C₄×D₄	1	2	yes	—
173	C₂×C₄×C₂₃	C₄×D₄	1	2	yes	—
174	C₂×C₄×C₂₃	#124	1	4	yes	—
175	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
176	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
177	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
178	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
179	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
180	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
181	C₈×C₂₃	—	2	2	no	—
182	C₈×C₂₃	—	2	2	no	—
183	C₈×C₂₃	—	2	2	no	—
184	C₈×C₂₃	—	2	2	no	—
185	C₂×#486	C₂×C₂₃	1	1	yes	characteristic
186	#2331	C₂×C₂₃	1	1	yes	characteristic, complemented
187	#2328	C₂×C₂₃	1	1	yes	characteristic
188	#1993	C₂×C₂₃	1	1	yes	characteristic, complemented
189	#1961	C₂×C₂₃	1	1	yes	characteristic
190	#1936	C₂×C₂₃	1	2	yes	complemented
191	#1934	C₂×C₂₃	1	2	yes	complemented
192	#1835	C₂×C₂₃	1	1	yes	characteristic, complemented
193	#1762	C₂×C₂₃	1	2	yes	complemented
194	C₄×#102	C₂×C₂₃	1	2	yes	complemented
195	#1726	C₂×C₂₃	1	1	yes	characteristic, complemented
196	C₂²×C₂₃	—	4	4	no	—
197	C₂²×C₂₃	—	4	4	no	—
198	C₂²×C₂₃	—	4	4	no	—
199	C₂²×C₂₃	—	8	2	no	—
200	C₂²×C₂₃	—	8	2	no	—
201	C₂²×C₂₃	—	8	2	no	—
202	C₂²×C₂₃	—	8	2	no	—
203	C₂²×C₂₃	C₂×C₄×D₄	1	1	yes	characteristic
204	C₂²×C₂₃	C₂×#124	1	1	yes	characteristic
205	C₂²×C₂₃	#532	1	1	yes	characteristic
206	C₂²×C₂₃	#576	1	2	yes	—
207	C₂²×C₂₃	#577	1	2	yes	—
208	C₄×C₂₃	—	2	4	no	—
209	C₄×C₂₃	—	2	2	no	—
210	C₄×C₂₃	—	2	2	no	—
211	C₄×C₂₃	—	4	2	no	—
212	C₄×C₂₃	—	4	4	no	—
213	C₄×C₂₃	—	8	2	no	—
214	C₄×C₂₃	—	8	2	no	—
215	C₄×C₂₃	C₄×#41	1	1	yes	characteristic
216	C₄×C₂₃	C₄×#41	1	1	yes	characteristic
217	C₄×C₂₃	#529	1	1	yes	characteristic
218	C₄×C₂₃	#529	1	1	yes	characteristic
219	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
220	C₂×#127	C₂²×C₂₃	1	1	yes	characteristic
221	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	—
222	#486	C₄×C₂₃	1	8	yes	complemented
223	C₂×#102	C₂²×C₂₃	1	2	yes	—
224	C₂×#102	C₂²×C₂₃	1	2	yes	—
225	C₂×#102	C₂²×C₂₃	1	2	yes	—
226	C₂×#102	C₂²×C₂₃	1	2	yes	—
227	C₂×#97	C₂²×C₂₃	1	1	yes	characteristic
228	C₂×#97	C₂²×C₂₃	1	1	yes	characteristic
229	C₂×#97	C₂²×C₂₃	1	1	yes	characteristic
230	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
231	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
232	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
233	#391	—	2	2	no	—
234	#390	C₂²×C₂₃	1	2	yes	—
235	#389	C₂²×C₂₃	1	2	yes	—
236	#387	—	2	2	no	—
237	#386	—	2	2	no	—
238	#386	—	2	2	no	—
239	#382	C₂²×C₂₃	1	1	yes	characteristic
240	#382	C₂²×C₂₃	1	1	yes	characteristic
241	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
242	#376	C₂²×C₂₃	1	1	yes	characteristic
243	#340	C₂²×C₂₃	1	2	yes	—
244	#340	C₂²×C₂₃	1	2	yes	—
245	#340	C₂²×C₂₃	1	2	yes	—
246	#340	C₂²×C₂₃	1	2	yes	—
247	C₂×C₂₃	—	8	4	no	—
248	C₂×C₂₃	C₄×#124	1	1	yes	characteristic
249	C₂×C₂₃	#2948	1	1	yes	characteristic
250	C₂×C₂₃	#2949	1	1	yes	characteristic
251	C₂×C₂₃	#3136	1	2	yes	—
252	C₂×C₂₃	#3179	1	2	yes	—
253	C₂²×Q₈	—	2	1	no	—
254	C₂²×D₄	—	2	1	no	—
255	C₂²×D₄	—	2	1	no	—
256	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
257	C₂³×C₄	—	2	2	no	—
258	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
259	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
260	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
261	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
262	C₄⋊Q₈	—	2	2	no	—
263	C₄⋊Q₈	C₂×C₄×C₂₃	1	4	yes	complemented
264	#127	—	2	2	no	—
265	#127	C₂×C₄×C₂₃	1	4	yes	—
266	C₄×D₄	—	2	4	no	—
267	C₄×D₄	—	2	4	no	—
268	C₂×C₄⋊C₄	—	2	1	no	—
269	C₂×C₄⋊C₄	—	2	2	no	—
270	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
271	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
272	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
273	C₂×C₂²⋊C₄	—	2	2	no	—
274	C₂×C₂²⋊C₄	—	2	2	no	—
275	C₂×C₂²⋊C₄	—	2	2	no	—
276	C₂×C₄²	—	2	2	no	—
277	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
278	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
279	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
280	#102	—	2	4	no	—
281	#102	—	2	4	no	—
282	#102	C₂×C₄×C₂₃	1	8	yes	complemented
283	#102	C₂×C₄×C₂₃	1	8	yes	complemented
284	#97	—	2	2	no	—
285	#97	—	2	2	no	—
286	#97	—	2	2	no	—
287	C₄×C₈	—	2	2	no	—
288	C₄×C₈	—	2	2	no	—
289	C₄×C₈	C₂×C₄×C₂₃	1	4	yes	complemented
290	#95	—	2	2	no	—
291	#95	—	2	1	no	—
292	#95	—	2	1	no	—
293	#95	—	2	1	no	—
294	#95	—	2	1	no	—
295	#95	—	2	2	no	—
296	#95	D₄×C₂₃	1	2	yes	—
297	#95	D₄×C₂₃	1	2	yes	—
298	C₂₃	#21644	1	1	yes	characteristic, direct product factor, Sylow
299	C₂⁴	—	2	2	no	—
300	C₂×Q₈	—	2	4	no	—
301	C₂×Q₈	—	8	2	no	—
302	C₂×D₄	—	2	4	no	—
303	C₂×D₄	—	2	4	no	—
304	C₂×D₄	—	2	2	no	—
305	C₂×D₄	—	2	2	no	—
306	C₂×D₄	—	2	2	no	—
307	C₂×D₄	—	2	2	no	—
308	C₂×D₄	—	2	2	no	—
309	C₂×D₄	—	8	2	no	—
310	C₂×D₄	—	8	2	no	—
311	C₂×D₄	C₂²×C₄×C₂₃	1	4	yes	—
312	C₂²×C₄	—	2	2	no	—
313	C₂²×C₄	—	2	2	no	—
314	C₂²×C₄	—	2	2	no	—
315	C₂²×C₄	—	4	4	no	—
316	C₂²×C₄	—	8	2	no	—
317	C₂²×C₄	—	8	2	no	—
318	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
319	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
320	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
321	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
322	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
323	C₂×C₈	—	2	1	no	—
324	C₂×C₈	—	2	1	no	—
325	C₂×C₈	—	2	1	no	—
326	C₂×C₈	—	2	1	no	—
327	C₂×C₈	—	2	1	no	—
328	C₂×C₈	—	2	1	no	—
329	C₂×C₈	—	2	1	no	—
330	C₂×C₈	—	2	1	no	—
331	C₂×C₈	C₂²×C₄×C₂₃	1	2	yes	—
332	C₂×C₈	C₂²×C₄×C₂₃	1	2	yes	—
333	C₂×C₈	#41×C₂₃	1	2	yes	—
334	C₂×C₈	#41×C₂₃	1	2	yes	—
335	C₄⋊C₄	—	2	4	no	—
336	C₄⋊C₄	—	2	2	no	—
337	C₄⋊C₄	—	2	2	no	—
338	C₄⋊C₄	—	2	2	no	—
339	C₄⋊C₄	—	2	2	no	—
340	C₄⋊C₄	—	2	2	no	—
341	C₄⋊C₄	—	8	2	no	—
342	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
343	C₂²⋊C₄	—	4	4	no	—
344	C₂²⋊C₄	—	8	2	no	—
345	C₂²⋊C₄	—	8	2	no	—
346	C₄²	—	2	1	no	—
347	C₄²	—	2	1	no	—
348	C₄²	—	8	2	no	—
349	C₄²	C₂²×C₄×C₂₃	1	2	yes	—
350	C₄²	#41×C₂₃	1	2	yes	—
351	C₄²	#41×C₂₃	1	2	yes	—
352	C₄²	#41×C₂₃	1	2	yes	—
353	C₂³	—	2	4	no	—
354	C₂³	—	4	2	no	—
355	C₂³	—	4	2	no	—
356	C₂³	—	4	2	no	—
357	C₂³	—	4	2	no	—
358	C₂³	—	4	2	no	—
359	C₂³	—	4	2	no	—
360	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
361	Q₈	—	8	4	no	—
362	D₄	—	2	4	no	—
363	D₄	—	2	4	no	—
364	D₄	—	4	2	no	—
365	D₄	—	4	2	no	—
366	D₄	—	8	4	no	—
367	D₄	—	8	4	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	4	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	4	2	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	—	8	8	no	—
385	C₂×C₄	C₄×D₄×C₂₃	1	2	yes	—
386	C₂×C₄	C₄×D₄×C₂₃	1	2	yes	—
387	C₂×C₄	C₂₃×#124	1	4	yes	—
388	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
389	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
390	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
391	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
392	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
393	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
394	C₈	—	2	2	no	—
395	C₈	—	2	2	no	—
396	C₈	—	2	2	no	—
397	C₈	—	2	2	no	—
398	C₂²	—	4	4	no	—
399	C₂²	—	4	4	no	—
400	C₂²	—	4	4	no	—
401	C₂²	—	8	2	no	—
402	C₂²	—	8	2	no	—
403	C₂²	—	8	2	no	—
404	C₂²	—	8	2	no	—
405	C₂²	C₂×C₄×D₄×C₂₃	1	1	yes	characteristic
406	C₂²	C₂×C₂₃×#124	1	1	yes	characteristic
407	C₂²	C₂₃×#532	1	1	yes	characteristic
408	C₂²	C₂₃×#576	1	2	yes	—
409	C₂²	C₂₃×#577	1	2	yes	—
410	C₄	—	2	2	no	—
411	C₄	—	2	2	no	—
412	C₄	—	2	4	no	—
413	C₄	—	4	2	no	—
414	C₄	—	4	4	no	—
415	C₄	—	8	2	no	—
416	C₄	—	8	2	no	—
417	C₄	C₄×#41×C₂₃	1	1	yes	characteristic
418	C₄	C₄×#41×C₂₃	1	1	yes	characteristic
419	C₄	C₂₃×#529	1	1	yes	characteristic
420	C₄	C₂₃×#529	1	1	yes	characteristic
421	C₂	—	8	4	no	—
422	C₂	C₄×C₂₃×#124	1	1	yes	characteristic
423	C₂	C₂₃×#2948	1	1	yes	characteristic
424	C₂	C₂₃×#2949	1	1	yes	characteristic
425	C₂	C₂₃×#3136	1	2	yes	—
426	C₂	C₂₃×#3179	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×#127	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₃ ◁ C₂₃×#376 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂₃×#2331	C₂	semidirect
4. C₂₃×#1993	C₂	semidirect
6. C₂₃×#1936	C₂	semidirect
7. C₂₃×#1934	C₂	semidirect
8. C₂₃×#1835	C₂	semidirect
9. C₂₃×#1762	C₂	semidirect
10. C₄×C₂₃×#102	C₂	semidirect
11. C₂₃×#1726	C₂	semidirect
15. C₂₃×#486	C₄	semidirect
50. C₂₃×C₄⋊Q₈	C₂×C₄	semidirect
69. C₂₃×#102	C₂×C₄	semidirect
70. C₂₃×#102	C₂×C₄	semidirect
76. C₄×C₈×C₂₃	C₂×C₄	semidirect
139. #21644	C₂₃	direct (N × H)
186. #2331	C₂×C₂₃	semidirect
188. #1993	C₂×C₂₃	semidirect
190. #1936	C₂×C₂₃	semidirect
191. #1934	C₂×C₂₃	semidirect
192. #1835	C₂×C₂₃	semidirect
193. #1762	C₂×C₂₃	semidirect
194. C₄×#102	C₂×C₂₃	semidirect
195. #1726	C₂×C₂₃	semidirect
222. #486	C₄×C₂₃	semidirect
263. C₄⋊Q₈	C₂×C₄×C₂₃	semidirect
282. #102	C₂×C₄×C₂₃	semidirect
283. #102	C₂×C₄×C₂₃	semidirect
289. C₄×C₈	C₂×C₄×C₂₃	semidirect
298. C₂₃	#21644	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×#486	2
C₂₃×#2331	2
C₂₃×#2328	2
C₂₃×#1993	2
C₂₃×#1961	2
C₂₃×#1936	2
C₂₃×#1934	2
C₂₃×#1835	2
C₂₃×#1762	2
C₄×C₂₃×#102	2
C₂₃×#1726	2
#21644	23

Subgroups — C23×#21644 #19169270

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#21644 #19169270