Subgroups — C₂₃×#24660 #19172286

Order 5888.

876 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#462	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₃×#432	C₂	1	1	yes	maximal, characteristic
3	C₂₃×#2857	C₂	1	1	yes	maximal, characteristic
4	C₄×C₂₃×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic
5	C₂₃×#2035	C₂	1	2	yes	maximal
6	C₂₃×#2001	C₂	1	2	yes	maximal
7	C₂₃×#1981	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#1971	C₂	1	2	yes	maximal, complemented
9	C₂₃×#1948	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#1935	C₂	1	2	yes	maximal, complemented
11	C₂₃×#1803	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×Q₁₆×C₂₃	C₂²	1	2	yes	—
13	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
15	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	2	yes	—
16	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
17	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
18	C₂₃×#462	—	2	4	no	—
19	C₂₃×#432	—	2	4	no	—
20	C₂×C₂₃×#106	C₂²	1	2	yes	—
21	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×C₂₃×#103	C₂²	1	2	yes	—
24	C₂×C₂₃×#103	C₂²	1	2	yes	—
25	C₂×C₂₃×#103	C₂²	1	2	yes	—
26	C₂×C₂₃×#103	C₂²	1	2	yes	—
27	C₂×C₂₃×C₂²⋊C₈	C₂²	1	2	yes	—
28	C₂×C₂₃×#97	C₂²	1	2	yes	—
29	C₂₃×#391	C₂²	1	2	yes	—
30	C₂₃×#391	C₂²	1	1	yes	characteristic
31	C₂₃×#389	—	2	1	no	—
32	C₂₃×#389	—	2	1	no	—
33	C₂₃×#389	C₂²	1	1	yes	characteristic
34	C₂₃×#387	—	2	1	no	—
35	C₂₃×#385	—	2	1	no	—
36	C₂₃×#384	C₂²	1	1	yes	characteristic
37	C₂₃×#380	—	2	1	no	—
38	C₂₃×#380	—	2	1	no	—
39	C₂₃×#380	C₂²	1	1	yes	characteristic
40	C₄×C₄⋊C₄×C₂₃	—	2	1	no	—
41	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
42	C₄×C₂²⋊C₄×C₂₃	—	2	1	no	—
43	C₂₃×#340	C₂²	1	2	yes	—
44	C₂₃×#340	C₂²	1	2	yes	—
45	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
46	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
47	C₂³×C₄×C₂₃	D₄	1	1	yes	characteristic
48	C₂³×C₄×C₂₃	D₄	1	1	yes	characteristic
49	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
50	C₂×Q₁₆×C₂₃	—	2	4	no	—
51	C₂×Q₁₆×C₂₃	—	2	4	no	—
52	C₂×Q₁₆×C₂₃	—	4	2	no	—
53	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
54	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
55	C₂₃×C₄⋊Q₈	—	2	2	no	—
56	C₂₃×C₄⋊Q₈	—	2	2	no	—
57	C₂₃×C₂²⋊Q₈	—	2	2	no	—
58	C₂₃×C₂²⋊Q₈	—	2	2	no	—
59	C₂₃×C₂²⋊Q₈	—	4	2	no	—
60	C₂₃×C₂²⋊Q₈	—	4	2	no	—
61	C₄×Q₈×C₂₃	—	2	2	no	—
62	C₄×Q₈×C₂₃	—	2	2	no	—
63	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
64	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
65	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
66	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
67	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
68	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
69	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
70	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
71	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
72	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
73	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
74	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
75	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
76	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
77	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
78	C₂×C₄²×C₂₃	—	2	2	no	—
79	C₂×C₄²×C₂₃	—	2	2	no	—
80	C₂×C₄²×C₂₃	—	2	1	no	—
81	C₂×C₄²×C₂₃	—	2	1	no	—
82	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
83	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
84	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
85	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
86	C₂₃×#106	—	4	2	no	—
87	C₂₃×C₄⋊C₈	—	2	2	no	—
88	C₂₃×C₄⋊C₈	D₄	1	4	yes	—
89	C₂₃×#103	—	2	4	no	—
90	C₂₃×#103	—	2	4	no	—
91	C₂₃×#103	—	4	2	no	—
92	C₂₃×#103	—	4	2	no	—
93	C₂₃×C₂²⋊C₈	—	2	4	no	—
94	C₂₃×#97	—	2	4	no	—
95	C₂₃×#95	—	2	1	no	—
96	C₂₃×#95	—	2	1	no	—
97	C₂₃×#95	—	2	1	no	—
98	C₂₃×#95	—	2	1	no	—
99	C₂₃×#95	—	2	1	no	—
100	C₂₃×#95	—	2	2	no	—
101	C₂₃×#95	—	2	2	no	—
102	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
103	C₂×Q₈×C₂₃	—	2	1	no	—
104	C₂×Q₈×C₂₃	—	2	1	no	—
105	C₂×Q₈×C₂₃	—	2	2	no	—
106	C₂×Q₈×C₂₃	—	2	1	no	—
107	C₂×Q₈×C₂₃	—	2	2	no	—
108	C₂×Q₈×C₂₃	—	2	2	no	—
109	C₂×Q₈×C₂₃	—	2	2	no	—
110	C₂×Q₈×C₂₃	—	2	1	no	—
111	C₂×Q₈×C₂₃	—	2	1	no	—
112	C₂×Q₈×C₂₃	—	2	2	no	—
113	C₂×Q₈×C₂₃	—	2	2	no	—
114	C₂×Q₈×C₂₃	#41	1	2	yes	—
115	C₂²×C₄×C₂₃	—	2	2	no	—
116	C₂²×C₄×C₂₃	—	2	1	no	—
117	C₂²×C₄×C₂₃	—	2	1	no	—
118	C₂²×C₄×C₂₃	—	2	2	no	—
119	C₂²×C₄×C₂₃	—	2	2	no	—
120	C₂²×C₄×C₂₃	—	2	2	no	—
121	C₂²×C₄×C₂₃	—	2	2	no	—
122	C₂²×C₄×C₂₃	—	2	1	no	—
123	C₂²×C₄×C₂₃	—	2	1	no	—
124	C₂²×C₄×C₂₃	—	2	1	no	—
125	C₂²×C₄×C₂₃	—	2	1	no	—
126	C₂²×C₄×C₂₃	—	2	1	no	—
127	C₂²×C₄×C₂₃	—	2	1	no	—
128	C₂²×C₄×C₂₃	—	2	1	no	—
129	C₂²×C₄×C₂₃	—	2	1	no	—
130	C₂²×C₄×C₂₃	—	2	2	no	—
131	C₂²×C₄×C₂₃	—	2	2	no	—
132	C₂²×C₄×C₂₃	—	4	1	no	—
133	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
139	Q₁₆×C₂₃	—	4	8	no	—
140	C₂×C₈×C₂₃	—	2	2	no	—
141	C₂×C₈×C₂₃	—	2	2	no	—
142	C₂×C₈×C₂₃	—	2	2	no	—
143	C₂×C₈×C₂₃	—	2	2	no	—
144	C₂×C₈×C₂₃	—	2	2	no	—
145	C₂×C₈×C₂₃	C₂×D₄	1	4	yes	—
146	C₄⋊C₄×C₂₃	—	2	4	no	—
147	C₄⋊C₄×C₂₃	—	2	1	no	—
148	C₄⋊C₄×C₂₃	—	2	1	no	—
149	C₄⋊C₄×C₂₃	—	2	1	no	—
150	C₄⋊C₄×C₂₃	—	2	1	no	—
151	C₄⋊C₄×C₂₃	—	2	2	no	—
152	C₄⋊C₄×C₂₃	—	2	1	no	—
153	C₄⋊C₄×C₂₃	—	2	2	no	—
154	C₄⋊C₄×C₂₃	—	4	2	no	—
155	C₄⋊C₄×C₂₃	—	4	2	no	—
156	C₄⋊C₄×C₂₃	—	4	4	no	—
157	C₄⋊C₄×C₂₃	—	4	2	no	—
158	C₄⋊C₄×C₂₃	—	4	2	no	—
159	C₄⋊C₄×C₂₃	—	4	2	no	—
160	C₄⋊C₄×C₂₃	—	4	2	no	—
161	C₄⋊C₄×C₂₃	#41	1	2	yes	—
162	C₂²⋊C₄×C₂₃	—	2	4	no	—
163	C₂²⋊C₄×C₂₃	—	4	4	no	—
164	C₂²⋊C₄×C₂₃	—	4	2	no	—
165	C₄²×C₂₃	—	2	2	no	—
166	C₄²×C₂₃	—	2	2	no	—
167	C₄²×C₂₃	—	2	1	no	—
168	C₄²×C₂₃	—	2	1	no	—
169	C₄²×C₂₃	—	4	2	no	—
170	C₄²×C₂₃	—	4	2	no	—
171	C₄²×C₂₃	C₂×D₄	1	2	yes	—
172	C₄²×C₂₃	#41	1	2	yes	—
173	#24660	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
174	C₂³×C₂₃	—	2	1	no	—
175	C₂³×C₂₃	—	2	1	no	—
176	C₂³×C₂₃	—	2	1	no	—
177	C₂³×C₂₃	—	2	1	no	—
178	C₂³×C₂₃	—	2	1	no	—
179	C₂³×C₂₃	—	2	1	no	—
180	C₂³×C₂₃	#137	1	2	yes	—
181	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
182	Q₈×C₂₃	—	2	2	no	—
183	Q₈×C₂₃	—	2	2	no	—
184	Q₈×C₂₃	—	4	1	no	—
185	Q₈×C₂₃	—	4	1	no	—
186	Q₈×C₂₃	—	4	2	no	—
187	Q₈×C₂₃	—	4	2	no	—
188	Q₈×C₂₃	—	4	2	no	—
189	Q₈×C₂₃	—	4	2	no	—
190	C₂×C₄×C₂₃	—	2	1	no	—
191	C₂×C₄×C₂₃	—	2	1	no	—
192	C₂×C₄×C₂₃	—	2	1	no	—
193	C₂×C₄×C₂₃	—	2	1	no	—
194	C₂×C₄×C₂₃	—	2	1	no	—
195	C₂×C₄×C₂₃	—	2	2	no	—
196	C₂×C₄×C₂₃	—	2	2	no	—
197	C₂×C₄×C₂₃	—	2	1	no	—
198	C₂×C₄×C₂₃	—	2	1	no	—
199	C₂×C₄×C₂₃	—	2	1	no	—
200	C₂×C₄×C₂₃	—	2	1	no	—
201	C₂×C₄×C₂₃	—	2	1	no	—
202	C₂×C₄×C₂₃	—	2	1	no	—
203	C₂×C₄×C₂₃	—	4	4	no	—
204	C₂×C₄×C₂₃	—	4	1	no	—
205	C₂×C₄×C₂₃	—	4	1	no	—
206	C₂×C₄×C₂₃	—	4	1	no	—
207	C₂×C₄×C₂₃	—	4	1	no	—
208	C₂×C₄×C₂₃	—	4	1	no	—
209	C₂×C₄×C₂₃	—	4	1	no	—
210	C₂×C₄×C₂₃	—	4	1	no	—
211	C₂×C₄×C₂₃	—	4	1	no	—
212	C₂×C₄×C₂₃	—	4	4	no	—
213	C₂×C₄×C₂₃	—	4	1	no	—
214	C₂×C₄×C₂₃	—	4	2	no	—
215	C₂×C₄×C₂₃	—	4	2	no	—
216	C₂×C₄×C₂₃	—	4	2	no	—
217	C₂×C₄×C₂₃	—	4	2	no	—
218	C₂×C₄×C₂₃	—	4	1	no	—
219	C₂×C₄×C₂₃	—	4	1	no	—
220	C₂×C₄×C₂₃	—	4	1	no	—
221	C₂×C₄×C₂₃	—	4	1	no	—
222	C₂×C₄×C₂₃	—	4	2	no	—
223	C₂×C₄×C₂₃	—	4	2	no	—
224	C₂×C₄×C₂₃	—	4	1	no	—
225	C₂×C₄×C₂₃	#121	1	2	yes	—
226	C₂×C₄×C₂₃	#121	1	2	yes	—
227	C₂×C₄×C₂₃	#137	1	2	yes	—
228	C₂×C₄×C₂₃	#137	1	2	yes	—
229	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
230	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
231	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
232	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
233	C₂×C₄×C₂₃	H(5,𝔽₂)	1	1	yes	characteristic
234	C₂×C₄×C₂₃	H(5,𝔽₂)	1	1	yes	characteristic
235	C₈×C₂₃	—	2	4	no	—
236	C₈×C₂₃	—	4	2	no	—
237	C₂×#462	C₂×C₂₃	1	1	yes	characteristic, complemented
238	C₂×#432	C₂×C₂₃	1	1	yes	characteristic
239	#2857	C₂×C₂₃	1	1	yes	characteristic
240	C₄×C₂²⋊Q₈	C₂×C₂₃	1	1	yes	characteristic
241	#2035	C₂×C₂₃	1	2	yes	—
242	#2001	C₂×C₂₃	1	2	yes	—
243	#1981	C₂×C₂₃	1	1	yes	characteristic, complemented
244	#1971	C₂×C₂₃	1	2	yes	complemented
245	#1948	C₂×C₂₃	1	1	yes	characteristic, complemented
246	#1935	C₂×C₂₃	1	2	yes	complemented
247	#1803	C₂×C₂₃	1	1	yes	characteristic, complemented
248	C₂²×C₂₃	—	2	2	no	—
249	C₂²×C₂₃	—	2	2	no	—
250	C₂²×C₂₃	—	2	2	no	—
251	C₂²×C₂₃	—	4	1	no	—
252	C₂²×C₂₃	—	4	1	no	—
253	C₂²×C₂₃	—	4	1	no	—
254	C₂²×C₂₃	—	4	1	no	—
255	C₂²×C₂₃	C₂×#121	1	1	yes	characteristic
256	C₂²×C₂₃	#525	1	1	yes	characteristic
257	C₂²×C₂₃	#535	1	1	yes	characteristic
258	C₂²×C₂₃	C₂×#137	1	1	yes	characteristic
259	C₂²×C₂₃	C₂×#137	1	1	yes	characteristic
260	C₂²×C₂₃	C₂×#137	1	1	yes	characteristic
261	C₂²×C₂₃	#575	1	1	yes	characteristic
262	C₄×C₂₃	—	2	2	no	—
263	C₄×C₂₃	—	4	2	no	—
264	C₄×C₂₃	—	4	1	no	—
265	C₄×C₂₃	—	4	2	no	—
266	C₄×C₂₃	—	4	1	no	—
267	C₄×C₂₃	—	4	1	no	—
268	C₄×C₂₃	—	8	2	no	—
269	C₄×C₂₃	—	8	2	no	—
270	C₄×C₂₃	—	8	1	no	—
271	C₄×C₂₃	—	8	1	no	—
272	C₄×C₂₃	#470	1	4	yes	—
273	C₄×C₂₃	#546	1	1	yes	characteristic
274	C₄×C₂₃	#550	1	1	yes	characteristic
275	C₄×C₂₃	#553	1	1	yes	characteristic
276	C₄×C₂₃	#555	1	1	yes	characteristic
277	C₂²×Q₁₆	C₂²×C₂₃	1	2	yes	—
278	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
279	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
280	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	2	yes	—
281	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
282	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
283	#462	—	2	4	no	—
284	#432	—	2	4	no	—
285	C₂×#106	C₂²×C₂₃	1	2	yes	—
286	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
287	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
288	C₂×#103	C₂²×C₂₃	1	2	yes	—
289	C₂×#103	C₂²×C₂₃	1	2	yes	—
290	C₂×#103	C₂²×C₂₃	1	2	yes	—
291	C₂×#103	C₂²×C₂₃	1	2	yes	—
292	C₂×C₂²⋊C₈	C₂²×C₂₃	1	2	yes	—
293	C₂×#97	C₂²×C₂₃	1	2	yes	—
294	#391	C₂²×C₂₃	1	2	yes	—
295	#391	C₂²×C₂₃	1	1	yes	characteristic
296	#389	—	2	1	no	—
297	#389	—	2	1	no	—
298	#389	C₂²×C₂₃	1	1	yes	characteristic
299	#387	—	2	1	no	—
300	#385	—	2	1	no	—
301	#384	C₂²×C₂₃	1	1	yes	characteristic
302	#380	—	2	1	no	—
303	#380	—	2	1	no	—
304	#380	C₂²×C₂₃	1	1	yes	characteristic
305	C₄×C₄⋊C₄	—	2	1	no	—
306	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
307	C₄×C₂²⋊C₄	—	2	1	no	—
308	#340	C₂²×C₂₃	1	2	yes	—
309	#340	C₂²×C₂₃	1	2	yes	—
310	C₂×C₂₃	—	4	2	no	—
311	C₂×C₂₃	#2414	1	1	yes	characteristic
312	C₂×C₂₃	C₂×#470	1	1	yes	characteristic
313	C₂×C₂₃	#3056	1	1	yes	characteristic
314	C₂×C₂₃	#3113	1	1	yes	characteristic
315	C₂×C₂₃	#3116	1	1	yes	characteristic
316	C₂×C₂₃	#3216	1	1	yes	characteristic
317	C₂×C₂₃	#3218	1	1	yes	characteristic
318	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
319	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
320	C₂³×C₄	D₄×C₂₃	1	1	yes	characteristic
321	C₂³×C₄	D₄×C₂₃	1	1	yes	characteristic
322	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
323	C₂×Q₁₆	—	2	4	no	—
324	C₂×Q₁₆	—	2	4	no	—
325	C₂×Q₁₆	—	4	2	no	—
326	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
327	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
328	C₄⋊Q₈	—	2	2	no	—
329	C₄⋊Q₈	—	2	2	no	—
330	C₂²⋊Q₈	—	2	2	no	—
331	C₂²⋊Q₈	—	2	2	no	—
332	C₂²⋊Q₈	—	4	2	no	—
333	C₂²⋊Q₈	—	4	2	no	—
334	C₄×Q₈	—	2	2	no	—
335	C₄×Q₈	—	2	2	no	—
336	C₂×C₄⋊C₄	—	2	1	no	—
337	C₂×C₄⋊C₄	—	2	1	no	—
338	C₂×C₄⋊C₄	—	2	2	no	—
339	C₂×C₄⋊C₄	—	2	1	no	—
340	C₂×C₄⋊C₄	—	2	1	no	—
341	C₂×C₄⋊C₄	—	2	1	no	—
342	C₂×C₄⋊C₄	—	2	1	no	—
343	C₂×C₄⋊C₄	—	2	1	no	—
344	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
345	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
346	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
347	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
348	C₂×C₂²⋊C₄	—	2	1	no	—
349	C₂×C₂²⋊C₄	—	2	2	no	—
350	C₂×C₂²⋊C₄	—	2	1	no	—
351	C₂×C₄²	—	2	2	no	—
352	C₂×C₄²	—	2	2	no	—
353	C₂×C₄²	—	2	1	no	—
354	C₂×C₄²	—	2	1	no	—
355	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
356	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
357	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
358	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
359	#106	—	4	2	no	—
360	C₄⋊C₈	—	2	2	no	—
361	C₄⋊C₈	D₄×C₂₃	1	4	yes	—
362	#103	—	2	4	no	—
363	#103	—	2	4	no	—
364	#103	—	4	2	no	—
365	#103	—	4	2	no	—
366	C₂²⋊C₈	—	2	4	no	—
367	#97	—	2	4	no	—
368	#95	—	2	1	no	—
369	#95	—	2	1	no	—
370	#95	—	2	1	no	—
371	#95	—	2	1	no	—
372	#95	—	2	1	no	—
373	#95	—	2	2	no	—
374	#95	—	2	2	no	—
375	C₂₃	#24660	1	1	yes	characteristic, direct product factor, Sylow
376	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
377	C₂×Q₈	—	2	1	no	—
378	C₂×Q₈	—	2	1	no	—
379	C₂×Q₈	—	2	2	no	—
380	C₂×Q₈	—	2	1	no	—
381	C₂×Q₈	—	2	2	no	—
382	C₂×Q₈	—	2	2	no	—
383	C₂×Q₈	—	2	2	no	—
384	C₂×Q₈	—	2	1	no	—
385	C₂×Q₈	—	2	1	no	—
386	C₂×Q₈	—	2	2	no	—
387	C₂×Q₈	—	2	2	no	—
388	C₂×Q₈	#41×C₂₃	1	2	yes	—
389	C₂²×C₄	—	2	2	no	—
390	C₂²×C₄	—	2	1	no	—
391	C₂²×C₄	—	2	1	no	—
392	C₂²×C₄	—	2	2	no	—
393	C₂²×C₄	—	2	2	no	—
394	C₂²×C₄	—	2	2	no	—
395	C₂²×C₄	—	2	2	no	—
396	C₂²×C₄	—	2	1	no	—
397	C₂²×C₄	—	2	1	no	—
398	C₂²×C₄	—	2	1	no	—
399	C₂²×C₄	—	2	1	no	—
400	C₂²×C₄	—	2	1	no	—
401	C₂²×C₄	—	2	1	no	—
402	C₂²×C₄	—	2	1	no	—
403	C₂²×C₄	—	2	1	no	—
404	C₂²×C₄	—	2	2	no	—
405	C₂²×C₄	—	2	2	no	—
406	C₂²×C₄	—	4	1	no	—
407	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
408	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
409	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
410	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
411	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
412	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
413	Q₁₆	—	4	8	no	—
414	C₂×C₈	—	2	2	no	—
415	C₂×C₈	—	2	2	no	—
416	C₂×C₈	—	2	2	no	—
417	C₂×C₈	—	2	2	no	—
418	C₂×C₈	—	2	2	no	—
419	C₂×C₈	C₂×D₄×C₂₃	1	4	yes	—
420	C₄⋊C₄	—	2	4	no	—
421	C₄⋊C₄	—	2	1	no	—
422	C₄⋊C₄	—	2	1	no	—
423	C₄⋊C₄	—	2	1	no	—
424	C₄⋊C₄	—	2	1	no	—
425	C₄⋊C₄	—	2	2	no	—
426	C₄⋊C₄	—	2	1	no	—
427	C₄⋊C₄	—	2	2	no	—
428	C₄⋊C₄	—	4	4	no	—
429	C₄⋊C₄	—	4	2	no	—
430	C₄⋊C₄	—	4	2	no	—
431	C₄⋊C₄	—	4	2	no	—
432	C₄⋊C₄	—	4	2	no	—
433	C₄⋊C₄	—	4	2	no	—
434	C₄⋊C₄	—	4	2	no	—
435	C₄⋊C₄	#41×C₂₃	1	2	yes	—
436	C₂²⋊C₄	—	2	4	no	—
437	C₂²⋊C₄	—	4	4	no	—
438	C₂²⋊C₄	—	4	2	no	—
439	C₄²	—	2	2	no	—
440	C₄²	—	2	2	no	—
441	C₄²	—	2	1	no	—
442	C₄²	—	2	1	no	—
443	C₄²	—	4	2	no	—
444	C₄²	—	4	2	no	—
445	C₄²	C₂×D₄×C₂₃	1	2	yes	—
446	C₄²	#41×C₂₃	1	2	yes	—
447	C₂³	—	2	1	no	—
448	C₂³	—	2	1	no	—
449	C₂³	—	2	1	no	—
450	C₂³	—	2	1	no	—
451	C₂³	—	2	1	no	—
452	C₂³	—	2	1	no	—
453	C₂³	C₂₃×#137	1	2	yes	—
454	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
455	Q₈	—	2	2	no	—
456	Q₈	—	2	2	no	—
457	Q₈	—	4	1	no	—
458	Q₈	—	4	1	no	—
459	Q₈	—	4	2	no	—
460	Q₈	—	4	2	no	—
461	Q₈	—	4	2	no	—
462	Q₈	—	4	2	no	—
463	C₂×C₄	—	2	1	no	—
464	C₂×C₄	—	2	1	no	—
465	C₂×C₄	—	2	1	no	—
466	C₂×C₄	—	2	1	no	—
467	C₂×C₄	—	2	1	no	—
468	C₂×C₄	—	2	1	no	—
469	C₂×C₄	—	2	1	no	—
470	C₂×C₄	—	2	1	no	—
471	C₂×C₄	—	2	1	no	—
472	C₂×C₄	—	2	2	no	—
473	C₂×C₄	—	2	2	no	—
474	C₂×C₄	—	2	1	no	—
475	C₂×C₄	—	2	1	no	—
476	C₂×C₄	—	4	4	no	—
477	C₂×C₄	—	4	1	no	—
478	C₂×C₄	—	4	1	no	—
479	C₂×C₄	—	4	1	no	—
480	C₂×C₄	—	4	1	no	—
481	C₂×C₄	—	4	1	no	—
482	C₂×C₄	—	4	1	no	—
483	C₂×C₄	—	4	1	no	—
484	C₂×C₄	—	4	4	no	—
485	C₂×C₄	—	4	1	no	—
486	C₂×C₄	—	4	1	no	—
487	C₂×C₄	—	4	1	no	—
488	C₂×C₄	—	4	1	no	—
489	C₂×C₄	—	4	2	no	—
490	C₂×C₄	—	4	2	no	—
491	C₂×C₄	—	4	1	no	—
492	C₂×C₄	—	4	1	no	—
493	C₂×C₄	—	4	2	no	—
494	C₂×C₄	—	4	2	no	—
495	C₂×C₄	—	4	2	no	—
496	C₂×C₄	—	4	2	no	—
497	C₂×C₄	—	4	1	no	—
498	C₂×C₄	C₂₃×#121	1	2	yes	—
499	C₂×C₄	C₂₃×#121	1	2	yes	—
500	C₂×C₄	C₂₃×#137	1	2	yes	—
501	C₂×C₄	C₂₃×#137	1	2	yes	—
502	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
503	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
504	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
505	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
506	C₂×C₄	C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
507	C₂×C₄	C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
508	C₈	—	2	4	no	—
509	C₈	—	4	2	no	—
510	C₂²	—	2	2	no	—
511	C₂²	—	2	2	no	—
512	C₂²	—	2	2	no	—
513	C₂²	—	4	1	no	—
514	C₂²	—	4	1	no	—
515	C₂²	—	4	1	no	—
516	C₂²	—	4	1	no	—
517	C₂²	C₂×C₂₃×#121	1	1	yes	characteristic
518	C₂²	C₂₃×#525	1	1	yes	characteristic
519	C₂²	C₂₃×#535	1	1	yes	characteristic
520	C₂²	C₂×C₂₃×#137	1	1	yes	characteristic
521	C₂²	C₂×C₂₃×#137	1	1	yes	characteristic
522	C₂²	C₂×C₂₃×#137	1	1	yes	characteristic
523	C₂²	C₂₃×#575	1	1	yes	characteristic
524	C₄	—	2	2	no	—
525	C₄	—	4	1	no	—
526	C₄	—	4	2	no	—
527	C₄	—	4	1	no	—
528	C₄	—	4	1	no	—
529	C₄	—	4	2	no	—
530	C₄	—	8	2	no	—
531	C₄	—	8	2	no	—
532	C₄	—	8	1	no	—
533	C₄	—	8	1	no	—
534	C₄	C₂₃×#470	1	4	yes	—
535	C₄	C₂₃×#546	1	1	yes	characteristic
536	C₄	C₂₃×#550	1	1	yes	characteristic
537	C₄	C₂₃×#553	1	1	yes	characteristic
538	C₄	C₂₃×#555	1	1	yes	characteristic
539	C₂	—	4	2	no	—
540	C₂	C₂₃×#2414	1	1	yes	characteristic
541	C₂	C₂×C₂₃×#470	1	1	yes	characteristic
542	C₂	C₂₃×#3056	1	1	yes	characteristic
543	C₂	C₂₃×#3113	1	1	yes	characteristic
544	C₂	C₂₃×#3116	1	1	yes	characteristic
545	C₂	C₂₃×#3216	1	1	yes	characteristic
546	C₂	C₂₃×#3218	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₃
prime radical	C₂⁴×C₂₃	C₂×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₃ ◁ C₂²×C₄²×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₂₃×#462	C₂	semidirect
7. C₂₃×#1981	C₂	semidirect
8. C₂₃×#1971	C₂	semidirect
9. C₂₃×#1948	C₂	semidirect
10. C₂₃×#1935	C₂	semidirect
11. C₂₃×#1803	C₂	semidirect
173. #24660	C₂₃	direct (N × H)
237. C₂×#462	C₂×C₂₃	semidirect
243. #1981	C₂×C₂₃	semidirect
244. #1971	C₂×C₂₃	semidirect
245. #1948	C₂×C₂₃	semidirect
246. #1935	C₂×C₂₃	semidirect
247. #1803	C₂×C₂₃	semidirect
375. C₂₃	#24660	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×#462	2
C₂×C₂₃×#432	2
C₂₃×#2857	2
C₄×C₂₃×C₂²⋊Q₈	2
C₂₃×#2035	2
C₂₃×#2001	2
C₂₃×#1981	2
C₂₃×#1971	2
C₂₃×#1948	2
C₂₃×#1935	2
C₂₃×#1803	2
#24660	23

Subgroups — C23×#24660 #19172286

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#24660 #19172286