Subgroups — C₂₃×#10051 #19157677

Order 5888.

670 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	C₂×C₂₃×#460	C₂	1	1	yes	maximal, characteristic
3	C₂₃×#2546	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#1982	C₂	1	1	yes	maximal, characteristic
5	C₂×C₂₃×#332	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₂₃×Q₈⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#1279	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×SD₁₆×C₂₃	—	2	1	no	—
9	C₂×C₂₃×C₄⋊Q₈	—	2	1	no	—
10	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
11	C₂×C₂₃×#127	C₂²	1	1	yes	characteristic
12	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
13	C₂₃×#486	—	2	2	no	—
14	C₂₃×#486	—	2	2	no	—
15	C₂₃×#460	—	2	2	no	—
16	C₂₃×#460	—	2	2	no	—
17	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
18	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×C₂₃×#102	—	2	1	no	—
20	C₂×C₂₃×#102	—	2	2	no	—
21	C₂×C₂₃×#102	—	2	2	no	—
22	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
23	C₂₃×#398	—	2	2	no	—
24	C₂₃×#391	—	2	1	no	—
25	C₂₃×#389	—	2	2	no	—
26	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
27	C₂₃×#332	—	2	2	no	—
28	C₂₃×Q₈⋊C₈	—	2	2	no	—
29	C₂²×Q₈×C₂₃	—	2	1	no	—
30	C₂²×Q₈×C₂₃	D₄	1	1	yes	characteristic
31	C₂²×D₄×C₂₃	—	2	1	no	—
32	C₂²×D₄×C₂₃	—	2	1	no	—
33	C₂²×D₄×C₂₃	—	2	1	no	—
34	C₂×SD₁₆×C₂₃	—	2	4	no	—
35	C₂×SD₁₆×C₂₃	—	4	2	no	—
36	C₂×SD₁₆×C₂₃	—	4	2	no	—
37	C₂²×C₈×C₂₃	—	2	1	no	—
38	C₂²×C₈×C₂₃	—	2	1	no	—
39	C₂²×C₈×C₂₃	—	2	1	no	—
40	C₂₃×C₄⋊Q₈	—	2	1	no	—
41	C₂₃×C₄⋊Q₈	—	2	1	no	—
42	C₂₃×C₄⋊Q₈	—	2	1	no	—
43	C₂₃×C₄⋊Q₈	—	2	1	no	—
44	C₂₃×C₄⋊Q₈	—	4	2	no	—
45	C₂₃×C₄⋊Q₈	—	4	2	no	—
46	C₂₃×#127	—	2	1	no	—
47	C₂₃×#127	—	2	1	no	—
48	C₂₃×#127	—	2	1	no	—
49	C₂₃×#127	D₄	1	2	yes	—
50	C₄×Q₈×C₂₃	—	2	1	no	—
51	C₄×Q₈×C₂₃	—	2	1	no	—
52	C₄×Q₈×C₂₃	—	2	1	no	—
53	C₄×Q₈×C₂₃	—	2	1	no	—
54	C₂×C₄⋊C₄×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	D₄	1	1	yes	characteristic
58	C₂×C₄⋊C₄×C₂₃	D₄	1	2	yes	—
59	C₂×C₄⋊C₄×C₂₃	D₄	1	2	yes	—
60	C₂×C₄²×C₂₃	—	2	1	no	—
61	C₂×C₄²×C₂₃	—	2	1	no	—
62	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
63	C₂₃×C₄⋊C₈	—	2	1	no	—
64	C₂₃×C₄⋊C₈	—	2	1	no	—
65	C₂₃×C₄⋊C₈	—	2	1	no	—
66	C₂₃×C₄⋊C₈	D₄	1	2	yes	—
67	C₂₃×#102	—	2	4	no	—
68	C₂₃×#102	—	2	8	no	—
69	C₂₃×#102	—	4	4	no	—
70	C₄×C₈×C₂₃	—	2	1	no	—
71	C₄×C₈×C₂₃	D₄	1	2	yes	—
72	C₂₃×#95	—	2	4	no	—
73	C₂₃×#95	—	2	1	no	—
74	C₂⁴×C₂₃	—	4	1	no	—
75	C₂×Q₈×C₂₃	—	2	1	no	—
76	C₂×Q₈×C₂₃	—	2	1	no	—
77	C₂×Q₈×C₂₃	—	2	1	no	—
78	C₂×Q₈×C₂₃	—	2	1	no	—
79	C₂×Q₈×C₂₃	—	2	1	no	—
80	C₂×Q₈×C₂₃	—	4	1	no	—
81	C₂×Q₈×C₂₃	—	4	1	no	—
82	C₂×Q₈×C₂₃	—	4	1	no	—
83	C₂×Q₈×C₂₃	—	4	1	no	—
84	C₂×Q₈×C₂₃	—	4	1	no	—
85	C₂×Q₈×C₂₃	—	4	1	no	—
86	C₂×Q₈×C₂₃	D₈	1	2	yes	—
87	C₂×D₄×C₂₃	—	2	2	no	—
88	C₂×D₄×C₂₃	—	2	2	no	—
89	C₂×D₄×C₂₃	—	2	2	no	—
90	C₂×D₄×C₂₃	—	4	4	no	—
91	C₂×D₄×C₂₃	—	4	1	no	—
92	C₂×D₄×C₂₃	—	4	1	no	—
93	C₂×D₄×C₂₃	—	4	1	no	—
94	C₂×D₄×C₂₃	—	4	1	no	—
95	C₂×D₄×C₂₃	—	4	2	no	—
96	C₂×D₄×C₂₃	—	4	1	no	—
97	C₂×D₄×C₂₃	—	4	1	no	—
98	C₂×D₄×C₂₃	—	4	1	no	—
99	C₂×D₄×C₂₃	—	4	2	no	—
100	C₂²×C₄×C₂₃	—	2	1	no	—
101	C₂²×C₄×C₂₃	—	2	2	no	—
102	C₂²×C₄×C₂₃	—	2	1	no	—
103	C₂²×C₄×C₂₃	—	2	2	no	—
104	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
107	SD₁₆×C₂₃	—	4	8	no	—
108	C₂×C₈×C₂₃	—	2	2	no	—
109	C₂×C₈×C₂₃	—	2	2	no	—
110	C₂×C₈×C₂₃	—	4	2	no	—
111	C₂×C₈×C₂₃	—	4	1	no	—
112	C₂×C₈×C₂₃	—	4	1	no	—
113	C₂×C₈×C₂₃	—	4	1	no	—
114	C₂×C₈×C₂₃	—	4	2	no	—
115	C₄⋊C₄×C₂₃	—	2	2	no	—
116	C₄⋊C₄×C₂₃	—	2	1	no	—
117	C₄⋊C₄×C₂₃	—	2	2	no	—
118	C₄⋊C₄×C₂₃	—	2	1	no	—
119	C₄⋊C₄×C₂₃	—	2	2	no	—
120	C₄⋊C₄×C₂₃	—	4	8	no	—
121	C₄⋊C₄×C₂₃	—	4	1	no	—
122	C₄⋊C₄×C₂₃	—	4	1	no	—
123	C₄⋊C₄×C₂₃	—	4	1	no	—
124	C₄⋊C₄×C₂₃	—	4	1	no	—
125	C₄⋊C₄×C₂₃	SD₁₆	1	4	yes	complemented
126	C₄²×C₂₃	—	4	1	no	—
127	C₄²×C₂₃	—	4	1	no	—
128	C₄²×C₂₃	—	4	1	no	—
129	C₄²×C₂₃	—	4	1	no	—
130	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
131	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
132	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
133	C₄²×C₂₃	#41	1	1	yes	characteristic
134	#10051	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
135	C₂³×C₂₃	—	4	2	no	—
136	C₂³×C₂₃	—	8	1	no	—
137	C₂³×C₂₃	—	8	2	no	—
138	C₂³×C₂₃	—	8	1	no	—
139	C₂³×C₂₃	—	8	2	no	—
140	C₂³×C₂₃	#120	1	1	yes	characteristic
141	Q₈×C₂₃	—	2	2	no	—
142	Q₈×C₂₃	—	2	2	no	—
143	Q₈×C₂₃	—	4	1	no	—
144	Q₈×C₂₃	—	4	1	no	—
145	Q₈×C₂₃	—	8	1	no	—
146	Q₈×C₂₃	—	8	1	no	—
147	Q₈×C₂₃	—	8	1	no	—
148	Q₈×C₂₃	—	8	1	no	—
149	D₄×C₂₃	—	4	4	no	—
150	D₄×C₂₃	—	4	2	no	—
151	D₄×C₂₃	—	4	2	no	—
152	D₄×C₂₃	—	4	4	no	—
153	D₄×C₂₃	—	8	2	no	—
154	D₄×C₂₃	—	8	1	no	—
155	D₄×C₂₃	—	8	1	no	—
156	D₄×C₂₃	—	8	1	no	—
157	D₄×C₂₃	—	8	1	no	—
158	C₂×C₄×C₂₃	—	2	2	no	—
159	C₂×C₄×C₂₃	—	2	2	no	—
160	C₂×C₄×C₂₃	—	2	4	no	—
161	C₂×C₄×C₂₃	—	4	1	no	—
162	C₂×C₄×C₂₃	—	4	2	no	—
163	C₂×C₄×C₂₃	—	4	1	no	—
164	C₂×C₄×C₂₃	—	4	2	no	—
165	C₂×C₄×C₂₃	—	4	1	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	#120	1	1	yes	characteristic
171	C₂×C₄×C₂₃	#120	1	1	yes	characteristic
172	C₂×C₄×C₂₃	#121	1	1	yes	characteristic
173	C₂×C₄×C₂₃	#121	1	1	yes	characteristic
174	C₂×C₄×C₂₃	#121	1	1	yes	characteristic
175	C₂×C₄×C₂₃	#127	1	1	yes	characteristic
176	C₂×C₄×C₂₃	C₂×D₈	1	1	yes	characteristic
177	C₂×C₄×C₂₃	C₂×SD₁₆	1	2	yes	—
178	C₂×C₄×C₂₃	#135	1	1	yes	characteristic
179	C₂×C₄×C₂₃	AGL(1,ℤ/8)	1	1	yes	characteristic
180	C₂×C₄×C₂₃	AGL(1,ℤ/8)	1	1	yes	characteristic
181	C₂×C₄×C₂₃	#137	1	2	yes	—
182	C₈×C₂₃	—	4	2	no	—
183	C₈×C₂₃	—	4	2	no	—
184	C₈×C₂₃	—	8	1	no	—
185	C₂×#486	C₂×C₂₃	1	1	yes	characteristic
186	C₂×#460	C₂×C₂₃	1	1	yes	characteristic
187	#2546	C₂×C₂₃	1	1	yes	characteristic, complemented
188	#1982	C₂×C₂₃	1	1	yes	characteristic
189	C₂×#332	C₂×C₂₃	1	1	yes	characteristic, complemented
190	C₂×Q₈⋊C₈	C₂×C₂₃	1	1	yes	characteristic, complemented
191	#1279	C₂×C₂₃	1	1	yes	characteristic, complemented
192	C₂²×C₂₃	—	8	2	no	—
193	C₂²×C₂₃	—	8	2	no	—
194	C₂²×C₂₃	—	8	2	no	—
195	C₂²×C₂₃	—	16	2	no	—
196	C₂²×C₂₃	—	16	2	no	—
197	C₂²×C₂₃	#392	1	1	yes	characteristic
198	C₂²×C₂₃	#447	1	1	yes	characteristic
199	C₂²×C₂₃	#448	1	2	yes	—
200	C₂²×C₂₃	#449	1	1	yes	characteristic
201	C₂²×C₂₃	#454	1	2	yes	—
202	C₄×C₂₃	—	2	1	no	—
203	C₄×C₂₃	—	2	1	no	—
204	C₄×C₂₃	—	4	4	no	—
205	C₄×C₂₃	—	4	2	no	—
206	C₄×C₂₃	—	8	2	no	—
207	C₄×C₂₃	—	8	1	no	—
208	C₄×C₂₃	#447	1	1	yes	characteristic
209	C₄×C₂₃	#449	1	1	yes	characteristic
210	C₄×C₂₃	#461	1	2	yes	—
211	C₄×C₂₃	#466	1	1	yes	characteristic
212	C₄×C₂₃	#469	1	1	yes	characteristic
213	C₄×C₂₃	#492	1	1	yes	characteristic
214	C₄×C₂₃	#497	1	1	yes	characteristic
215	C₂²×SD₁₆	—	2	1	no	—
216	C₂×C₄⋊Q₈	—	2	1	no	—
217	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
218	C₂×#127	C₂²×C₂₃	1	1	yes	characteristic
219	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
220	#486	—	2	2	no	—
221	#486	—	2	2	no	—
222	#460	—	2	2	no	—
223	#460	—	2	2	no	—
224	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
225	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
226	C₂×#102	—	2	2	no	—
227	C₂×#102	—	2	1	no	—
228	C₂×#102	—	2	2	no	—
229	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
230	#398	—	2	2	no	—
231	#391	—	2	1	no	—
232	#389	—	2	2	no	—
233	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
234	#332	—	2	2	no	—
235	Q₈⋊C₈	—	2	2	no	—
236	C₂×C₂₃	—	16	2	no	—
237	C₂×C₂₃	#1626	1	2	yes	—
238	C₂×C₂₃	#1627	1	2	yes	—
239	C₂×C₂₃	#1999	1	1	yes	characteristic
240	C₂×C₂₃	#2003	1	1	yes	characteristic
241	C₂×C₂₃	#2013	1	1	yes	characteristic
242	C₂²×Q₈	—	2	1	no	—
243	C₂²×Q₈	D₄×C₂₃	1	1	yes	characteristic
244	C₂²×D₄	—	2	1	no	—
245	C₂²×D₄	—	2	1	no	—
246	C₂²×D₄	—	2	1	no	—
247	C₂×SD₁₆	—	2	4	no	—
248	C₂×SD₁₆	—	4	2	no	—
249	C₂×SD₁₆	—	4	2	no	—
250	C₂²×C₈	—	2	1	no	—
251	C₂²×C₈	—	2	1	no	—
252	C₂²×C₈	—	2	1	no	—
253	C₄⋊Q₈	—	2	1	no	—
254	C₄⋊Q₈	—	2	1	no	—
255	C₄⋊Q₈	—	2	1	no	—
256	C₄⋊Q₈	—	2	1	no	—
257	C₄⋊Q₈	—	4	2	no	—
258	C₄⋊Q₈	—	4	2	no	—
259	#127	—	2	1	no	—
260	#127	—	2	1	no	—
261	#127	—	2	1	no	—
262	#127	D₄×C₂₃	1	2	yes	—
263	C₄×Q₈	—	2	1	no	—
264	C₄×Q₈	—	2	1	no	—
265	C₄×Q₈	—	2	1	no	—
266	C₄×Q₈	—	2	1	no	—
267	C₂×C₄⋊C₄	—	2	4	no	—
268	C₂×C₄⋊C₄	—	2	1	no	—
269	C₂×C₄⋊C₄	—	2	1	no	—
270	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
271	C₂×C₄⋊C₄	D₄×C₂₃	1	2	yes	—
272	C₂×C₄⋊C₄	D₄×C₂₃	1	2	yes	—
273	C₂×C₄²	—	2	1	no	—
274	C₂×C₄²	—	2	1	no	—
275	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
276	C₄⋊C₈	—	2	1	no	—
277	C₄⋊C₈	—	2	1	no	—
278	C₄⋊C₈	—	2	1	no	—
279	C₄⋊C₈	D₄×C₂₃	1	2	yes	—
280	#102	—	2	4	no	—
281	#102	—	2	8	no	—
282	#102	—	4	4	no	—
283	C₄×C₈	—	2	1	no	—
284	C₄×C₈	D₄×C₂₃	1	2	yes	—
285	#95	—	2	4	no	—
286	#95	—	2	1	no	—
287	C₂₃	#10051	1	1	yes	characteristic, direct product factor, Sylow
288	C₂⁴	—	4	1	no	—
289	C₂×Q₈	—	2	1	no	—
290	C₂×Q₈	—	2	1	no	—
291	C₂×Q₈	—	2	1	no	—
292	C₂×Q₈	—	2	1	no	—
293	C₂×Q₈	—	2	1	no	—
294	C₂×Q₈	—	4	1	no	—
295	C₂×Q₈	—	4	1	no	—
296	C₂×Q₈	—	4	1	no	—
297	C₂×Q₈	—	4	1	no	—
298	C₂×Q₈	—	4	1	no	—
299	C₂×Q₈	—	4	1	no	—
300	C₂×Q₈	D₈×C₂₃	1	2	yes	—
301	C₂×D₄	—	2	2	no	—
302	C₂×D₄	—	2	2	no	—
303	C₂×D₄	—	2	2	no	—
304	C₂×D₄	—	4	4	no	—
305	C₂×D₄	—	4	1	no	—
306	C₂×D₄	—	4	1	no	—
307	C₂×D₄	—	4	1	no	—
308	C₂×D₄	—	4	1	no	—
309	C₂×D₄	—	4	2	no	—
310	C₂×D₄	—	4	1	no	—
311	C₂×D₄	—	4	1	no	—
312	C₂×D₄	—	4	1	no	—
313	C₂×D₄	—	4	2	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	C₂×D₄×C₂₃	1	1	yes	characteristic
319	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
320	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
321	SD₁₆	—	4	8	no	—
322	C₂×C₈	—	2	2	no	—
323	C₂×C₈	—	2	2	no	—
324	C₂×C₈	—	4	2	no	—
325	C₂×C₈	—	4	1	no	—
326	C₂×C₈	—	4	1	no	—
327	C₂×C₈	—	4	1	no	—
328	C₂×C₈	—	4	2	no	—
329	C₄⋊C₄	—	2	2	no	—
330	C₄⋊C₄	—	2	1	no	—
331	C₄⋊C₄	—	2	2	no	—
332	C₄⋊C₄	—	2	1	no	—
333	C₄⋊C₄	—	2	2	no	—
334	C₄⋊C₄	—	4	8	no	—
335	C₄⋊C₄	—	4	1	no	—
336	C₄⋊C₄	—	4	1	no	—
337	C₄⋊C₄	—	4	1	no	—
338	C₄⋊C₄	—	4	1	no	—
339	C₄⋊C₄	SD₁₆×C₂₃	1	4	yes	complemented
340	C₄²	—	4	1	no	—
341	C₄²	—	4	1	no	—
342	C₄²	—	4	1	no	—
343	C₄²	—	4	1	no	—
344	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
345	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
346	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
347	C₄²	#41×C₂₃	1	1	yes	characteristic
348	C₂³	—	4	2	no	—
349	C₂³	—	8	1	no	—
350	C₂³	—	8	2	no	—
351	C₂³	—	8	1	no	—
352	C₂³	—	8	2	no	—
353	C₂³	C₂₃×#120	1	1	yes	characteristic
354	Q₈	—	2	2	no	—
355	Q₈	—	2	2	no	—
356	Q₈	—	4	1	no	—
357	Q₈	—	4	1	no	—
358	Q₈	—	8	1	no	—
359	Q₈	—	8	1	no	—
360	Q₈	—	8	1	no	—
361	Q₈	—	8	1	no	—
362	D₄	—	4	4	no	—
363	D₄	—	4	2	no	—
364	D₄	—	4	2	no	—
365	D₄	—	4	4	no	—
366	D₄	—	8	2	no	—
367	D₄	—	8	1	no	—
368	D₄	—	8	1	no	—
369	D₄	—	8	1	no	—
370	D₄	—	8	1	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	4	no	—
374	C₂×C₄	—	4	1	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	—	4	1	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	4	1	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	C₂₃×#120	1	1	yes	characteristic
384	C₂×C₄	C₂₃×#120	1	1	yes	characteristic
385	C₂×C₄	C₂₃×#121	1	1	yes	characteristic
386	C₂×C₄	C₂₃×#121	1	1	yes	characteristic
387	C₂×C₄	C₂₃×#121	1	1	yes	characteristic
388	C₂×C₄	C₂₃×#127	1	1	yes	characteristic
389	C₂×C₄	C₂×D₈×C₂₃	1	1	yes	characteristic
390	C₂×C₄	C₂×SD₁₆×C₂₃	1	2	yes	—
391	C₂×C₄	C₂₃×#135	1	1	yes	characteristic
392	C₂×C₄	C₂₃×AGL(1,ℤ/8)	1	1	yes	characteristic
393	C₂×C₄	C₂₃×AGL(1,ℤ/8)	1	1	yes	characteristic
394	C₂×C₄	C₂₃×#137	1	2	yes	—
395	C₈	—	4	2	no	—
396	C₈	—	4	2	no	—
397	C₈	—	8	1	no	—
398	C₂²	—	8	2	no	—
399	C₂²	—	8	2	no	—
400	C₂²	—	8	2	no	—
401	C₂²	—	16	2	no	—
402	C₂²	—	16	2	no	—
403	C₂²	C₂₃×#392	1	1	yes	characteristic
404	C₂²	C₂₃×#447	1	1	yes	characteristic
405	C₂²	C₂₃×#448	1	2	yes	—
406	C₂²	C₂₃×#449	1	1	yes	characteristic
407	C₂²	C₂₃×#454	1	2	yes	—
408	C₄	—	2	1	no	—
409	C₄	—	2	1	no	—
410	C₄	—	4	2	no	—
411	C₄	—	4	4	no	—
412	C₄	—	8	2	no	—
413	C₄	—	8	1	no	—
414	C₄	C₂₃×#447	1	1	yes	characteristic
415	C₄	C₂₃×#449	1	1	yes	characteristic
416	C₄	C₂₃×#461	1	2	yes	—
417	C₄	C₂₃×#466	1	1	yes	characteristic
418	C₄	C₂₃×#469	1	1	yes	characteristic
419	C₄	C₂₃×#492	1	1	yes	characteristic
420	C₄	C₂₃×#497	1	1	yes	characteristic
421	C₂	—	16	2	no	—
422	C₂	C₂₃×#1626	1	2	yes	—
423	C₂	C₂₃×#1627	1	2	yes	—
424	C₂	C₂₃×#1999	1	1	yes	characteristic
425	C₂	C₂₃×#2003	1	1	yes	characteristic
426	C₂	C₂₃×#2013	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₃	#120
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₂₃
prime radical	C₂×C₂₃×#127	C₂²
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₂₃ ◁ C₂×C₄²×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂₃×#2546	C₂	semidirect
5. C₂×C₂₃×#332	C₂	semidirect
6. C₂×C₂₃×Q₈⋊C₈	C₂	semidirect
7. C₂₃×#1279	C₂	semidirect
125. C₄⋊C₄×C₂₃	SD₁₆	semidirect
134. #10051	C₂₃	direct (N × H)
187. #2546	C₂×C₂₃	semidirect
189. C₂×#332	C₂×C₂₃	semidirect
190. C₂×Q₈⋊C₈	C₂×C₂₃	semidirect
191. #1279	C₂×C₂₃	semidirect
287. C₂₃	#10051	direct (N × H)
339. C₄⋊C₄	SD₁₆×C₂₃	semidirect

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
C₂×C₂₃×#460	2
C₂₃×#2546	2
C₂₃×#1982	2
C₂×C₂₃×#332	2
C₂×C₂₃×Q₈⋊C₈	2
C₂₃×#1279	2
#10051	23

Subgroups — C23×#10051 #19157677

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#10051 #19157677