Subgroups — C₂₃×#8432 #19156058

Order 5888.

740 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3501	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#1804	C₂	1	1	yes	maximal, characteristic
3	C₂₃×#1542	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#1518	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#1518	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#1481	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#1478	C₂	1	1	yes	maximal, characteristic
8	C₂₃×#554	—	2	1	no	—
9	C₂₃×#554	—	2	2	no	—
10	C₂₃×#554	—	2	2	no	—
11	C₂₃×#554	C₄	1	2	yes	complemented
12	D₄×Q₈×C₂₃	—	2	1	no	—
13	D₄×Q₈×C₂₃	C₄	1	2	yes	complemented
14	C₂₃×#544	—	2	1	no	—
15	C₂₃×#543	—	2	2	no	—
16	C₂₃×#533	C₂²	1	1	yes	characteristic
17	C₂₃×#533	C₂²	1	1	yes	characteristic
18	C₂×C₂₃×C₂²⋊Q₈	—	2	2	no	—
19	C₂₃×#518	—	2	1	no	—
20	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
21	C₂₃×#431	C₂²	1	1	yes	characteristic
22	C₂₃×#431	C₂²	1	1	yes	characteristic
23	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₂₃×#102	—	2	1	no	—
25	C₂₃×#382	C₂²	1	1	yes	characteristic
26	C₂₃×#340	—	2	1	no	—
27	C₂₃×#333	—	2	1	no	—
28	C₂₃×#332	—	2	1	no	—
29	C₂₃×#328	—	2	2	no	—
30	C₂₃×#328	—	2	2	no	—
31	C₂₃×Q₈⋊C₈	—	2	2	no	—
32	C₂₃×D₄⋊C₈	—	2	2	no	—
33	C₂²×Q₈×C₂₃	—	2	2	no	—
34	C₂²×D₄×C₂₃	D₄	1	1	yes	characteristic
35	C₂³×C₄×C₂₃	—	2	1	no	—
36	C₂²×C₈×C₂₃	—	2	1	no	—
37	C₂₃×C₄⋊Q₈	—	2	2	no	—
38	C₂₃×C₄⋊Q₈	—	2	2	no	—
39	C₂₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
40	C₂₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
41	C₂₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
42	C₂₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
43	C₂₃×#125	—	2	2	no	—
44	C₂₃×#125	—	2	2	no	—
45	C₂₃×#125	—	2	1	no	—
46	C₂₃×#125	—	2	1	no	—
47	C₂₃×C₂²⋊Q₈	—	2	4	no	—
48	C₂₃×C₂²⋊Q₈	—	2	4	no	—
49	C₂₃×C₂²⋊Q₈	—	2	4	no	—
50	C₂₃×C₂²⋊Q₈	—	2	4	no	—
51	C₂₃×C₂²⋊Q₈	—	2	2	no	—
52	C₂₃×C₂²⋊Q₈	—	2	4	no	—
53	C₂₃×C₂²⋊Q₈	—	2	1	no	—
54	C₂₃×C₂²⋊Q₈	—	2	1	no	—
55	C₂₃×C₂²⋊Q₈	—	2	2	no	—
56	C₂₃×C₂²⋊Q₈	—	2	4	no	—
57	C₂₃×C₂²⋊Q₈	D₄	1	2	yes	—
58	C₂₃×C₂²⋊Q₈	D₄	1	2	yes	—
59	C₄×Q₈×C₂₃	—	2	1	no	—
60	C₄×Q₈×C₂₃	—	2	1	no	—
61	C₄×Q₈×C₂₃	C₂×C₄	1	2	yes	—
62	C₄×Q₈×C₂₃	D₄	1	2	yes	—
63	C₄×D₄×C₂₃	—	2	2	no	—
64	C₄×D₄×C₂₃	—	2	2	no	—
65	C₄×D₄×C₂₃	—	2	2	no	—
66	C₄×D₄×C₂₃	—	2	2	no	—
67	C₄×D₄×C₂₃	—	2	1	no	—
68	C₄×D₄×C₂₃	—	2	1	no	—
69	C₄×D₄×C₂₃	C₂×C₄	1	2	yes	—
70	C₄×D₄×C₂₃	D₄	1	2	yes	—
71	C₂₃×#117	—	2	1	no	—
72	C₂₃×#117	—	2	1	no	—
73	C₂×C₄⋊C₄×C₂₃	—	2	4	no	—
74	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
75	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
76	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
77	C₂×C₂²⋊C₄×C₂₃	—	2	4	no	—
78	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
79	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
80	C₂₃×C₄⋊C₈	—	2	1	no	—
81	C₂₃×C₄⋊C₈	—	2	1	no	—
82	C₂₃×C₄⋊C₈	—	2	1	no	—
83	C₂₃×C₄⋊C₈	—	2	1	no	—
84	C₂₃×#102	—	4	2	no	—
85	C₂₃×C₂²⋊C₈	—	2	1	no	—
86	C₂₃×C₂²⋊C₈	—	2	1	no	—
87	C₄×C₈×C₂₃	—	2	1	no	—
88	C₄×C₈×C₂₃	—	2	1	no	—
89	C₂₃×#95	—	2	1	no	—
90	C₂₃×#95	—	2	1	no	—
91	C₂⁴×C₂₃	—	2	1	no	—
92	C₂×Q₈×C₂₃	—	2	4	no	—
93	C₂×Q₈×C₂₃	—	2	1	no	—
94	C₂×Q₈×C₂₃	—	2	1	no	—
95	C₂×Q₈×C₂₃	—	8	4	no	—
96	C₂×Q₈×C₂₃	C₂²⋊C₄	1	2	yes	—
97	C₂×Q₈×C₂₃	C₂²⋊C₄	1	2	yes	—
98	C₂×D₄×C₂₃	—	2	1	no	—
99	C₂×D₄×C₂₃	—	2	1	no	—
100	C₂×D₄×C₂₃	—	2	1	no	—
101	C₂×D₄×C₂₃	C₂²⋊C₄	1	2	yes	—
102	C₂×D₄×C₂₃	SD₁₆	1	2	yes	—
103	C₂×D₄×C₂₃	Q₁₆	1	2	yes	—
104	C₂²×C₄×C₂₃	—	2	4	no	—
105	C₂²×C₄×C₂₃	—	2	4	no	—
106	C₂²×C₄×C₂₃	—	2	1	no	—
107	C₂²×C₄×C₂₃	—	2	2	no	—
108	C₂²×C₄×C₂₃	—	2	2	no	—
109	C₂²×C₄×C₂₃	—	4	1	no	—
110	C₂²×C₄×C₂₃	—	8	2	no	—
111	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
114	C₂×C₈×C₂₃	—	4	1	no	—
115	C₂×C₈×C₂₃	—	4	1	no	—
116	C₂×C₈×C₂₃	—	4	1	no	—
117	C₂×C₈×C₂₃	—	4	1	no	—
118	C₂×C₈×C₂₃	—	4	1	no	—
119	C₄⋊C₄×C₂₃	—	2	4	no	—
120	C₄⋊C₄×C₂₃	—	2	4	no	—
121	C₄⋊C₄×C₂₃	—	2	4	no	—
122	C₄⋊C₄×C₂₃	—	2	1	no	—
123	C₄⋊C₄×C₂₃	—	2	1	no	—
124	C₄⋊C₄×C₂₃	—	2	1	no	—
125	C₄⋊C₄×C₂₃	—	2	2	no	—
126	C₄⋊C₄×C₂₃	—	2	2	no	—
127	C₄⋊C₄×C₂₃	—	2	2	no	—
128	C₄⋊C₄×C₂₃	—	2	1	no	—
129	C₄⋊C₄×C₂₃	—	2	1	no	—
130	C₄⋊C₄×C₂₃	—	2	1	no	—
131	C₄⋊C₄×C₂₃	—	2	1	no	—
132	C₄⋊C₄×C₂₃	—	2	2	no	—
133	C₄⋊C₄×C₂₃	—	4	1	no	—
134	C₄⋊C₄×C₂₃	—	4	1	no	—
135	C₄⋊C₄×C₂₃	C₂²⋊C₄	1	2	yes	—
136	C₄⋊C₄×C₂₃	C₂²⋊C₄	1	2	yes	—
137	C₄⋊C₄×C₂₃	C₂²⋊C₄	1	2	yes	—
138	C₂²⋊C₄×C₂₃	—	2	4	no	—
139	C₂²⋊C₄×C₂₃	—	2	4	no	—
140	C₂²⋊C₄×C₂₃	—	2	2	no	—
141	C₂²⋊C₄×C₂₃	—	2	2	no	—
142	C₂²⋊C₄×C₂₃	—	2	2	no	—
143	C₂²⋊C₄×C₂₃	—	2	2	no	—
144	C₄²×C₂₃	—	2	2	no	—
145	C₄²×C₂₃	—	2	2	no	—
146	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
147	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
148	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
149	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
150	#8432	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
151	C₂³×C₂₃	—	2	2	no	—
152	C₂³×C₂₃	—	2	2	no	—
153	C₂³×C₂₃	—	2	2	no	—
154	C₂³×C₂₃	—	8	1	no	—
155	C₂³×C₂₃	—	8	1	no	—
156	C₂³×C₂₃	#120	1	1	yes	characteristic
157	Q₈×C₂₃	—	4	2	no	—
158	Q₈×C₂₃	—	4	2	no	—
159	Q₈×C₂₃	—	4	2	no	—
160	Q₈×C₂₃	—	8	1	no	—
161	Q₈×C₂₃	—	8	4	no	—
162	D₄×C₂₃	—	2	2	no	—
163	D₄×C₂₃	—	2	2	no	—
164	D₄×C₂₃	—	2	2	no	—
165	D₄×C₂₃	#103	1	4	yes	—
166	C₂×C₄×C₂₃	—	2	2	no	—
167	C₂×C₄×C₂₃	—	2	2	no	—
168	C₂×C₄×C₂₃	—	2	2	no	—
169	C₂×C₄×C₂₃	—	2	2	no	—
170	C₂×C₄×C₂₃	—	2	2	no	—
171	C₂×C₄×C₂₃	—	4	1	no	—
172	C₂×C₄×C₂₃	—	4	1	no	—
173	C₂×C₄×C₂₃	—	4	4	no	—
174	C₂×C₄×C₂₃	—	8	2	no	—
175	C₂×C₄×C₂₃	—	8	1	no	—
176	C₂×C₄×C₂₃	—	8	4	no	—
177	C₂×C₄×C₂₃	—	8	4	no	—
178	C₂×C₄×C₂₃	—	8	1	no	—
179	C₂×C₄×C₂₃	—	8	1	no	—
180	C₂×C₄×C₂₃	—	8	1	no	—
181	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
182	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
183	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
184	C₂×C₄×C₂₃	#120	1	1	yes	characteristic
185	C₂×C₄×C₂₃	#120	1	1	yes	characteristic
186	C₂×C₄×C₂₃	#120	1	1	yes	characteristic
187	C₂×C₄×C₂₃	C₂×SD₁₆	1	1	yes	characteristic
188	C₂×C₄×C₂₃	C₂×Q₁₆	1	1	yes	characteristic
189	C₂×C₄×C₂₃	#137	1	1	yes	characteristic
190	C₂×C₄×C₂₃	#137	1	1	yes	characteristic
191	C₈×C₂₃	—	8	1	no	—
192	C₈×C₂₃	—	8	1	no	—
193	C₈×C₂₃	—	8	1	no	—
194	#3501	C₂×C₂₃	1	1	yes	characteristic
195	#1804	C₂×C₂₃	1	1	yes	characteristic
196	#1542	C₂×C₂₃	1	1	yes	characteristic, complemented
197	#1518	C₂×C₂₃	1	1	yes	characteristic, complemented
198	#1518	C₂×C₂₃	1	1	yes	characteristic, complemented
199	#1481	C₂×C₂₃	1	1	yes	characteristic, complemented
200	#1478	C₂×C₂₃	1	1	yes	characteristic
201	C₂²×C₂₃	—	2	1	no	—
202	C₂²×C₂₃	—	2	1	no	—
203	C₂²×C₂₃	—	2	4	no	—
204	C₂²×C₂₃	—	4	2	no	—
205	C₂²×C₂₃	—	4	2	no	—
206	C₂²×C₂₃	—	8	2	no	—
207	C₂²×C₂₃	—	8	2	no	—
208	C₂²×C₂₃	#379	1	1	yes	characteristic
209	C₂²×C₂₃	#448	1	1	yes	characteristic
210	C₂²×C₂₃	#451	1	1	yes	characteristic
211	C₄×C₂₃	—	2	1	no	—
212	C₄×C₂₃	—	2	1	no	—
213	C₄×C₂₃	—	2	1	no	—
214	C₄×C₂₃	—	2	1	no	—
215	C₄×C₂₃	—	4	2	no	—
216	C₄×C₂₃	—	4	2	no	—
217	C₄×C₂₃	—	4	2	no	—
218	C₄×C₂₃	—	4	2	no	—
219	C₄×C₂₃	—	4	2	no	—
220	C₄×C₂₃	—	16	1	no	—
221	C₄×C₂₃	C₂×#103	1	1	yes	characteristic
222	C₄×C₂₃	#419	1	1	yes	characteristic
223	C₄×C₂₃	#448	1	1	yes	characteristic
224	C₄×C₂₃	#451	1	1	yes	characteristic
225	#554	—	2	1	no	—
226	#554	—	2	2	no	—
227	#554	—	2	2	no	—
228	#554	C₄×C₂₃	1	2	yes	complemented
229	D₄×Q₈	—	2	1	no	—
230	D₄×Q₈	C₄×C₂₃	1	2	yes	complemented
231	#544	—	2	1	no	—
232	#543	—	2	2	no	—
233	#533	C₂²×C₂₃	1	1	yes	characteristic
234	#533	C₂²×C₂₃	1	1	yes	characteristic
235	C₂×C₂²⋊Q₈	—	2	2	no	—
236	#518	—	2	1	no	—
237	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
238	#431	C₂²×C₂₃	1	1	yes	characteristic
239	#431	C₂²×C₂₃	1	1	yes	characteristic
240	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
241	C₂×#102	—	2	1	no	—
242	#382	C₂²×C₂₃	1	1	yes	characteristic
243	#340	—	2	1	no	—
244	#333	—	2	1	no	—
245	#332	—	2	1	no	—
246	#328	—	2	2	no	—
247	#328	—	2	2	no	—
248	Q₈⋊C₈	—	2	2	no	—
249	D₄⋊C₈	—	2	2	no	—
250	C₂×C₂₃	—	2	1	no	—
251	C₂×C₂₃	—	2	1	no	—
252	C₂×C₂₃	—	4	4	no	—
253	C₂×C₂₃	#1787	1	1	yes	characteristic
254	C₂×C₂₃	#1794	1	1	yes	characteristic
255	C₂×C₂₃	#1795	1	1	yes	characteristic
256	C₂²×Q₈	—	2	2	no	—
257	C₂²×D₄	D₄×C₂₃	1	1	yes	characteristic
258	C₂³×C₄	—	2	1	no	—
259	C₂²×C₈	—	2	1	no	—
260	C₄⋊Q₈	—	2	2	no	—
261	C₄⋊Q₈	—	2	2	no	—
262	C₄⋊Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
263	C₄⋊Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
264	C₄⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
265	C₄⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
266	#125	—	2	2	no	—
267	#125	—	2	2	no	—
268	#125	—	2	1	no	—
269	#125	—	2	1	no	—
270	C₂²⋊Q₈	—	2	4	no	—
271	C₂²⋊Q₈	—	2	4	no	—
272	C₂²⋊Q₈	—	2	4	no	—
273	C₂²⋊Q₈	—	2	4	no	—
274	C₂²⋊Q₈	—	2	2	no	—
275	C₂²⋊Q₈	—	2	4	no	—
276	C₂²⋊Q₈	—	2	1	no	—
277	C₂²⋊Q₈	—	2	1	no	—
278	C₂²⋊Q₈	—	2	2	no	—
279	C₂²⋊Q₈	—	2	4	no	—
280	C₂²⋊Q₈	D₄×C₂₃	1	2	yes	—
281	C₂²⋊Q₈	D₄×C₂₃	1	2	yes	—
282	C₄×Q₈	—	2	1	no	—
283	C₄×Q₈	—	2	1	no	—
284	C₄×Q₈	C₂×C₄×C₂₃	1	2	yes	—
285	C₄×Q₈	D₄×C₂₃	1	2	yes	—
286	C₄×D₄	—	2	2	no	—
287	C₄×D₄	—	2	2	no	—
288	C₄×D₄	—	2	2	no	—
289	C₄×D₄	—	2	2	no	—
290	C₄×D₄	—	2	1	no	—
291	C₄×D₄	—	2	1	no	—
292	C₄×D₄	C₂×C₄×C₂₃	1	2	yes	—
293	C₄×D₄	D₄×C₂₃	1	2	yes	—
294	#117	—	2	1	no	—
295	#117	—	2	1	no	—
296	C₂×C₄⋊C₄	—	2	4	no	—
297	C₂×C₄⋊C₄	—	2	2	no	—
298	C₂×C₄⋊C₄	—	2	1	no	—
299	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
300	C₂×C₂²⋊C₄	—	2	4	no	—
301	C₂×C₂²⋊C₄	—	2	1	no	—
302	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
303	C₄⋊C₈	—	2	1	no	—
304	C₄⋊C₈	—	2	1	no	—
305	C₄⋊C₈	—	2	1	no	—
306	C₄⋊C₈	—	2	1	no	—
307	#102	—	4	2	no	—
308	C₂²⋊C₈	—	2	1	no	—
309	C₂²⋊C₈	—	2	1	no	—
310	C₄×C₈	—	2	1	no	—
311	C₄×C₈	—	2	1	no	—
312	#95	—	2	1	no	—
313	#95	—	2	1	no	—
314	C₂₃	#8432	1	1	yes	characteristic, direct product factor, Sylow
315	C₂⁴	—	2	1	no	—
316	C₂×Q₈	—	2	4	no	—
317	C₂×Q₈	—	2	1	no	—
318	C₂×Q₈	—	2	1	no	—
319	C₂×Q₈	—	8	4	no	—
320	C₂×Q₈	C₂²⋊C₄×C₂₃	1	2	yes	—
321	C₂×Q₈	C₂²⋊C₄×C₂₃	1	2	yes	—
322	C₂×D₄	—	2	1	no	—
323	C₂×D₄	—	2	1	no	—
324	C₂×D₄	—	2	1	no	—
325	C₂×D₄	C₂²⋊C₄×C₂₃	1	2	yes	—
326	C₂×D₄	SD₁₆×C₂₃	1	2	yes	—
327	C₂×D₄	Q₁₆×C₂₃	1	2	yes	—
328	C₂²×C₄	—	2	4	no	—
329	C₂²×C₄	—	2	4	no	—
330	C₂²×C₄	—	2	1	no	—
331	C₂²×C₄	—	2	2	no	—
332	C₂²×C₄	—	2	2	no	—
333	C₂²×C₄	—	4	1	no	—
334	C₂²×C₄	—	8	2	no	—
335	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
336	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
337	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
338	C₂×C₈	—	4	1	no	—
339	C₂×C₈	—	4	1	no	—
340	C₂×C₈	—	4	1	no	—
341	C₂×C₈	—	4	1	no	—
342	C₂×C₈	—	4	1	no	—
343	C₄⋊C₄	—	2	4	no	—
344	C₄⋊C₄	—	2	4	no	—
345	C₄⋊C₄	—	2	4	no	—
346	C₄⋊C₄	—	2	1	no	—
347	C₄⋊C₄	—	2	1	no	—
348	C₄⋊C₄	—	2	1	no	—
349	C₄⋊C₄	—	2	2	no	—
350	C₄⋊C₄	—	2	2	no	—
351	C₄⋊C₄	—	2	2	no	—
352	C₄⋊C₄	—	2	1	no	—
353	C₄⋊C₄	—	2	1	no	—
354	C₄⋊C₄	—	2	1	no	—
355	C₄⋊C₄	—	2	1	no	—
356	C₄⋊C₄	—	2	2	no	—
357	C₄⋊C₄	—	4	1	no	—
358	C₄⋊C₄	—	4	1	no	—
359	C₄⋊C₄	C₂²⋊C₄×C₂₃	1	2	yes	—
360	C₄⋊C₄	C₂²⋊C₄×C₂₃	1	2	yes	—
361	C₄⋊C₄	C₂²⋊C₄×C₂₃	1	2	yes	—
362	C₂²⋊C₄	—	2	4	no	—
363	C₂²⋊C₄	—	2	4	no	—
364	C₂²⋊C₄	—	2	2	no	—
365	C₂²⋊C₄	—	2	2	no	—
366	C₂²⋊C₄	—	2	2	no	—
367	C₂²⋊C₄	—	2	2	no	—
368	C₄²	—	2	2	no	—
369	C₄²	—	2	2	no	—
370	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
371	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
372	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
373	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
374	C₂³	—	2	2	no	—
375	C₂³	—	2	2	no	—
376	C₂³	—	2	2	no	—
377	C₂³	—	8	1	no	—
378	C₂³	—	8	1	no	—
379	C₂³	C₂₃×#120	1	1	yes	characteristic
380	Q₈	—	4	2	no	—
381	Q₈	—	4	2	no	—
382	Q₈	—	4	2	no	—
383	Q₈	—	8	1	no	—
384	Q₈	—	8	4	no	—
385	D₄	—	2	2	no	—
386	D₄	—	2	2	no	—
387	D₄	—	2	2	no	—
388	D₄	C₂₃×#103	1	4	yes	—
389	C₂×C₄	—	2	2	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	—	4	1	no	—
395	C₂×C₄	—	4	1	no	—
396	C₂×C₄	—	4	4	no	—
397	C₂×C₄	—	8	2	no	—
398	C₂×C₄	—	8	1	no	—
399	C₂×C₄	—	8	4	no	—
400	C₂×C₄	—	8	4	no	—
401	C₂×C₄	—	8	1	no	—
402	C₂×C₄	—	8	1	no	—
403	C₂×C₄	—	8	1	no	—
404	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
405	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
406	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
407	C₂×C₄	C₂₃×#120	1	1	yes	characteristic
408	C₂×C₄	C₂₃×#120	1	1	yes	characteristic
409	C₂×C₄	C₂₃×#120	1	1	yes	characteristic
410	C₂×C₄	C₂×SD₁₆×C₂₃	1	1	yes	characteristic
411	C₂×C₄	C₂×Q₁₆×C₂₃	1	1	yes	characteristic
412	C₂×C₄	C₂₃×#137	1	1	yes	characteristic
413	C₂×C₄	C₂₃×#137	1	1	yes	characteristic
414	C₈	—	8	1	no	—
415	C₈	—	8	1	no	—
416	C₈	—	8	1	no	—
417	C₂²	—	2	1	no	—
418	C₂²	—	2	1	no	—
419	C₂²	—	2	4	no	—
420	C₂²	—	4	2	no	—
421	C₂²	—	4	2	no	—
422	C₂²	—	8	2	no	—
423	C₂²	—	8	2	no	—
424	C₂²	C₂₃×#379	1	1	yes	characteristic
425	C₂²	C₂₃×#448	1	1	yes	characteristic
426	C₂²	C₂₃×#451	1	1	yes	characteristic
427	C₄	—	2	1	no	—
428	C₄	—	2	1	no	—
429	C₄	—	2	1	no	—
430	C₄	—	2	1	no	—
431	C₄	—	4	2	no	—
432	C₄	—	4	2	no	—
433	C₄	—	4	2	no	—
434	C₄	—	4	2	no	—
435	C₄	—	4	2	no	—
436	C₄	—	16	1	no	—
437	C₄	C₂×C₂₃×#103	1	1	yes	characteristic
438	C₄	C₂₃×#419	1	1	yes	characteristic
439	C₄	C₂₃×#448	1	1	yes	characteristic
440	C₄	C₂₃×#451	1	1	yes	characteristic
441	C₂	—	2	1	no	—
442	C₂	—	2	1	no	—
443	C₂	—	4	4	no	—
444	C₂	C₂₃×#1787	1	1	yes	characteristic
445	C₂	C₂₃×#1794	1	1	yes	characteristic
446	C₂	C₂₃×#1795	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₃	#379
commutator	C₄²	C₂²×C₄×C₂₃
Frattini, cosocle	C₂×C₄²	C₂³×C₂₃
prime radical	C₂²×D₄×C₂₃	D₄
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂×C₄²×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂₃×#1542	C₂	semidirect
4. C₂₃×#1518	C₂	semidirect
5. C₂₃×#1518	C₂	semidirect
6. C₂₃×#1481	C₂	semidirect
11. C₂₃×#554	C₄	semidirect
13. D₄×Q₈×C₂₃	C₄	semidirect
150. #8432	C₂₃	direct (N × H)
196. #1542	C₂×C₂₃	semidirect
197. #1518	C₂×C₂₃	semidirect
198. #1518	C₂×C₂₃	semidirect
199. #1481	C₂×C₂₃	semidirect
228. #554	C₄×C₂₃	semidirect
230. D₄×Q₈	C₄×C₂₃	semidirect
314. C₂₃	#8432	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂₃×#3501	2
C₂₃×#1804	2
C₂₃×#1542	2
C₂₃×#1518	2
C₂₃×#1481	2
C₂₃×#1478	2
#8432	23

Subgroups — C23×#8432 #19156058

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#8432 #19156058