Subgroups — C₂₃×#17892 #19165518

Order 5888.

648 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#2965	C₂	1	1	yes	maximal, characteristic
2	C₂×C₂₃×#446	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₂₃×#137	C₂	1	1	yes	maximal, characteristic
4	C₂₃×#1593	C₂	1	2	yes	maximal, complemented
5	C₂₃×#1592	C₂	1	2	yes	maximal, complemented
6	C₂₃×#1591	C₂	1	2	yes	maximal, complemented
7	C₂₃×#1590	C₂	1	2	yes	maximal, complemented
8	C₂₃×#1565	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#1479	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#1477	C₂	1	1	yes	maximal, characteristic
11	C₈×M₁₆×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₂₃×#137	C₄	1	1	yes	characteristic
13	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
14	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
15	C₂₃×#446	—	2	1	no	—
16	C₂₃×#446	—	2	1	no	—
17	C₂₃×#446	C₂²	1	2	yes	—
18	C₂₃×#446	C₂²	1	2	yes	—
19	C₂₃×#446	C₂²	1	1	yes	characteristic
20	C₂₃×#446	C₂²	1	1	yes	characteristic
21	C₂₃×#441	C₄	1	2	yes	—
22	C₂₃×#440	C₄	1	2	yes	—
23	C₄×Q₁₆×C₂₃	C₂²	1	2	yes	—
24	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	—
25	C₂₃×#436	C₂²	1	1	yes	characteristic
26	C₂₃×#436	C₂²	1	1	yes	characteristic
27	C₂₃×#435	—	2	1	no	—
28	C₂₃×#435	—	2	1	no	—
29	C₂₃×#431	—	2	1	no	—
30	C₂₃×#431	C₂²	1	1	yes	characteristic
31	C₂₃×#431	C₂²	1	1	yes	characteristic
32	C₂₃×#428	C₄	1	1	yes	characteristic
33	C₂×C₂₃×C₄⋊C₈	—	2	1	no	—
34	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
35	C₂₃×#419	C₄	1	1	yes	characteristic
36	C₂₃×#417	C₄	1	1	yes	characteristic
37	C₄×M₁₆×C₂₃	—	2	1	no	—
38	C₄×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
39	C₂×C₂₃×#97	—	2	1	no	—
40	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
41	C₂₃×#335	C₂²	1	2	yes	—
42	C₂₃×#334	C₂²	1	2	yes	—
43	C₂₃×Q₈⋊C₈	C₂²	1	2	yes	—
44	C₂₃×Q₈⋊C₈	C₂²	1	2	yes	—
45	C₂₃×Q₈⋊C₈	C₂²	1	2	yes	—
46	C₂₃×D₄⋊C₈	C₂²	1	2	yes	—
47	C₂₃×#322	C₂²	1	2	yes	—
48	C₈²×C₂₃	C₂²	1	2	yes	—
49	C₂×#41×C₂₃	C₂×C₄	1	1	yes	characteristic
50	C₂²×Q₈×C₂₃	C₂×C₄	1	1	yes	characteristic
51	C₂₃×#137	—	2	4	no	—
52	C₂×Q₁₆×C₂₃	C₂×C₄	1	2	yes	—
53	C₂×SD₁₆×C₂₃	C₂×C₄	1	2	yes	—
54	C₂×M₁₆×C₂₃	—	2	1	no	—
55	C₂×M₁₆×C₂₃	—	2	1	no	—
56	C₂×M₁₆×C₂₃	C₂×C₄	1	1	yes	characteristic
57	C₂×M₁₆×C₂₃	C₂×C₄	1	1	yes	characteristic
58	C₂²×C₈×C₂₃	—	2	1	no	—
59	C₂²×C₈×C₂₃	D₄	1	1	yes	characteristic
60	C₂²×C₈×C₂₃	D₄	1	1	yes	characteristic
61	C₄×Q₈×C₂₃	—	2	1	no	—
62	C₄×Q₈×C₂₃	—	2	1	no	—
63	C₄×Q₈×C₂₃	C₂×C₄	1	2	yes	—
64	C₄×Q₈×C₂₃	C₂×C₄	1	1	yes	characteristic
65	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
66	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
67	C₄×D₄×C₂₃	—	2	1	no	—
68	C₄×D₄×C₂₃	—	2	1	no	—
69	C₄×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic
70	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
71	C₂₃×#117	—	2	1	no	—
72	C₂₃×#117	C₂×C₄	1	1	yes	characteristic
73	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
74	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
75	C₂×C₄²×C₂₃	—	2	1	no	—
76	C₂×C₄²×C₂₃	—	2	1	no	—
77	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
78	C₂₃×#107	C₂×C₄	1	2	yes	—
79	C₂₃×#106	C₂×C₄	1	2	yes	—
80	C₂₃×C₄⋊C₈	—	2	2	no	—
81	C₂₃×C₄⋊C₈	—	2	2	no	—
82	C₂₃×C₄⋊C₈	—	2	1	no	—
83	C₂₃×C₄⋊C₈	—	2	1	no	—
84	C₂₃×C₄⋊C₈	—	2	1	no	—
85	C₂₃×C₄⋊C₈	—	2	1	no	—
86	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
87	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
88	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
89	C₂₃×#103	C₂×C₄	1	2	yes	—
90	C₂₃×#103	C₂×C₄	1	2	yes	—
91	C₂₃×#103	C₂×C₄	1	2	yes	—
92	C₂₃×#102	C₂×C₄	1	2	yes	—
93	C₂₃×C₂²⋊C₈	—	2	1	no	—
94	C₂₃×C₂²⋊C₈	—	2	1	no	—
95	C₂₃×C₂²⋊C₈	—	2	1	no	—
96	C₂₃×C₂²⋊C₈	—	2	1	no	—
97	C₂₃×#97	—	2	2	no	—
98	C₂₃×#97	—	2	2	no	—
99	C₂₃×#97	—	2	1	no	—
100	C₂₃×#97	—	2	1	no	—
101	C₂₃×#97	C₂×C₄	1	2	yes	—
102	C₄×C₈×C₂₃	—	2	1	no	—
103	C₄×C₈×C₂₃	D₄	1	1	yes	characteristic
104	C₄×C₈×C₂₃	D₄	1	1	yes	characteristic
105	C₄×C₈×C₂₃	C₂³	1	2	yes	—
106	C₄×C₈×C₂₃	C₂³	1	2	yes	—
107	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
108	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
109	#41×C₂₃	—	2	2	no	—
110	#41×C₂₃	—	2	2	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	C₂²×C₄	1	2	yes	—
115	C₂×Q₈×C₂₃	C₂²×C₄	1	1	yes	characteristic
116	C₂×D₄×C₂₃	—	2	1	no	—
117	C₂×D₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
118	C₂²×C₄×C₂₃	—	2	1	no	—
119	C₂²×C₄×C₂₃	—	2	1	no	—
120	C₂²×C₄×C₂₃	—	2	1	no	—
121	C₂²×C₄×C₂₃	—	2	1	no	—
122	C₂²×C₄×C₂₃	—	2	1	no	—
123	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
124	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₂₃	#41	1	1	yes	characteristic
126	Q₁₆×C₂₃	—	2	4	no	—
127	SD₁₆×C₂₃	—	2	4	no	—
128	M₁₆×C₂₃	—	2	2	no	—
129	M₁₆×C₂₃	—	4	2	no	—
130	M₁₆×C₂₃	—	4	2	no	—
131	M₁₆×C₂₃	M₁₆	1	4	yes	complemented
132	C₂×C₈×C₂₃	—	2	2	no	—
133	C₂×C₈×C₂₃	—	2	2	no	—
134	C₂×C₈×C₂₃	—	2	1	no	—
135	C₂×C₈×C₂₃	—	2	1	no	—
136	C₂×C₈×C₂₃	—	2	2	no	—
137	C₂×C₈×C₂₃	—	4	1	no	—
138	C₂×C₈×C₂₃	—	4	2	no	—
139	C₂×C₈×C₂₃	C₂²×C₄	1	2	yes	—
140	C₂×C₈×C₂₃	C₂²×C₄	1	2	yes	—
141	C₂×C₈×C₂₃	C₂×D₄	1	1	yes	characteristic
142	C₂×C₈×C₂₃	C₂×D₄	1	1	yes	characteristic
143	C₂×C₈×C₂₃	C₂×D₄	1	1	yes	characteristic
144	C₂×C₈×C₂₃	C₂×D₄	1	1	yes	characteristic
145	C₄⋊C₄×C₂₃	—	2	2	no	—
146	C₄⋊C₄×C₂₃	—	2	1	no	—
147	C₄⋊C₄×C₂₃	—	2	1	no	—
148	C₄⋊C₄×C₂₃	—	2	2	no	—
149	C₄⋊C₄×C₂₃	—	2	1	no	—
150	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
151	C₄⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
152	C₄⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
153	C₂²⋊C₄×C₂₃	—	2	1	no	—
154	C₂²⋊C₄×C₂₃	—	2	1	no	—
155	C₂²⋊C₄×C₂₃	—	2	1	no	—
156	C₄²×C₂₃	—	2	1	no	—
157	C₄²×C₂₃	—	2	1	no	—
158	C₄²×C₂₃	—	2	2	no	—
159	C₄²×C₂₃	—	2	1	no	—
160	C₄²×C₂₃	—	2	2	no	—
161	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
162	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
163	C₄²×C₂₃	#41	1	1	yes	characteristic
164	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
165	#17892	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
166	C₂³×C₂₃	—	2	1	no	—
167	C₂³×C₂₃	C₄×D₄	1	1	yes	characteristic
168	Q₈×C₂₃	—	2	2	no	—
169	Q₈×C₂₃	—	2	1	no	—
170	Q₈×C₂₃	—	2	2	no	—
171	Q₈×C₂₃	—	2	1	no	—
172	Q₈×C₂₃	—	4	2	no	—
173	D₄×C₂₃	—	2	1	no	—
174	D₄×C₂₃	—	2	1	no	—
175	D₄×C₂₃	—	4	2	no	—
176	C₂×C₄×C₂₃	—	2	1	no	—
177	C₂×C₄×C₂₃	—	2	1	no	—
178	C₂×C₄×C₂₃	—	2	1	no	—
179	C₂×C₄×C₂₃	—	2	1	no	—
180	C₂×C₄×C₂₃	—	2	2	no	—
181	C₂×C₄×C₂₃	—	2	1	no	—
182	C₂×C₄×C₂₃	—	2	2	no	—
183	C₂×C₄×C₂₃	—	4	1	no	—
184	C₂×C₄×C₂₃	—	4	2	no	—
185	C₂×C₄×C₂₃	—	4	2	no	—
186	C₂×C₄×C₂₃	—	4	2	no	—
187	C₂×C₄×C₂₃	—	4	1	no	—
188	C₂×C₄×C₂₃	—	4	1	no	—
189	C₂×C₄×C₂₃	—	4	2	no	—
190	C₂×C₄×C₂₃	C₄×D₄	1	1	yes	characteristic
191	C₂×C₄×C₂₃	C₄×D₄	1	1	yes	characteristic
192	C₂×C₄×C₂₃	C₄×D₄	1	1	yes	characteristic
193	C₂×C₄×C₂₃	C₂×M₁₆	1	2	yes	—
194	C₂×C₄×C₂₃	#131	1	2	yes	—
195	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
196	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
197	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
198	C₈×C₂₃	—	2	2	no	—
199	C₈×C₂₃	—	2	1	no	—
200	C₈×C₂₃	—	2	1	no	—
201	C₈×C₂₃	—	2	1	no	—
202	C₈×C₂₃	—	4	2	no	—
203	C₈×C₂₃	—	4	1	no	—
204	C₈×C₂₃	—	4	2	no	—
205	C₈×C₂₃	—	4	1	no	—
206	C₈×C₂₃	C₂×M₁₆	1	4	yes	—
207	C₈×C₂₃	#137	1	2	yes	complemented
208	#2965	C₂×C₂₃	1	1	yes	characteristic
209	C₂×#446	C₂×C₂₃	1	1	yes	characteristic, complemented
210	C₄×#137	C₂×C₂₃	1	1	yes	characteristic
211	#1593	C₂×C₂₃	1	2	yes	complemented
212	#1592	C₂×C₂₃	1	2	yes	complemented
213	#1591	C₂×C₂₃	1	2	yes	complemented
214	#1590	C₂×C₂₃	1	2	yes	complemented
215	#1565	C₂×C₂₃	1	1	yes	characteristic, complemented
216	#1479	C₂×C₂₃	1	1	yes	characteristic, complemented
217	#1477	C₂×C₂₃	1	1	yes	characteristic
218	C₈×M₁₆	C₂×C₂₃	1	1	yes	characteristic, complemented
219	C₂²×C₂₃	—	2	1	no	—
220	C₂²×C₂₃	—	2	1	no	—
221	C₂²×C₂₃	—	4	1	no	—
222	C₂²×C₂₃	—	4	1	no	—
223	C₂²×C₂₃	—	4	1	no	—
224	C₂²×C₂₃	#436	1	2	yes	—
225	C₂²×C₂₃	C₂×C₄×D₄	1	1	yes	characteristic
226	C₄×C₂₃	—	2	1	no	—
227	C₄×C₂₃	—	2	1	no	—
228	C₄×C₂₃	—	2	1	no	—
229	C₄×C₂₃	—	4	1	no	—
230	C₄×C₂₃	—	4	2	no	—
231	C₄×C₂₃	—	4	1	no	—
232	C₄×C₂₃	—	4	1	no	—
233	C₄×C₂₃	—	4	2	no	—
234	C₄×C₂₃	#436	1	2	yes	—
235	C₄×C₂₃	C₂²×M₁₆	1	1	yes	characteristic
236	C₄×C₂₃	C₂×#131	1	1	yes	characteristic
237	C₄×C₂₃	C₂×#137	1	1	yes	characteristic
238	C₄×C₂₃	#575	1	1	yes	characteristic
239	C₂×#137	C₄×C₂₃	1	1	yes	characteristic
240	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
241	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
242	#446	—	2	1	no	—
243	#446	—	2	1	no	—
244	#446	C₂²×C₂₃	1	2	yes	—
245	#446	C₂²×C₂₃	1	1	yes	characteristic
246	#446	C₂²×C₂₃	1	2	yes	—
247	#446	C₂²×C₂₃	1	1	yes	characteristic
248	#441	C₄×C₂₃	1	2	yes	—
249	#440	C₄×C₂₃	1	2	yes	—
250	C₄×Q₁₆	C₂²×C₂₃	1	2	yes	—
251	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	—
252	#436	C₂²×C₂₃	1	1	yes	characteristic
253	#436	C₂²×C₂₃	1	1	yes	characteristic
254	#435	—	2	1	no	—
255	#435	—	2	1	no	—
256	#431	—	2	1	no	—
257	#431	C₂²×C₂₃	1	1	yes	characteristic
258	#431	C₂²×C₂₃	1	1	yes	characteristic
259	#428	C₄×C₂₃	1	1	yes	characteristic
260	C₂×C₄⋊C₈	—	2	1	no	—
261	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
262	#419	C₄×C₂₃	1	1	yes	characteristic
263	#417	C₄×C₂₃	1	1	yes	characteristic
264	C₄×M₁₆	—	2	1	no	—
265	C₄×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
266	C₂×#97	—	2	1	no	—
267	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
268	#335	C₂²×C₂₃	1	2	yes	—
269	#334	C₂²×C₂₃	1	2	yes	—
270	Q₈⋊C₈	C₂²×C₂₃	1	2	yes	—
271	Q₈⋊C₈	C₂²×C₂₃	1	2	yes	—
272	Q₈⋊C₈	C₂²×C₂₃	1	2	yes	—
273	D₄⋊C₈	C₂²×C₂₃	1	2	yes	—
274	#322	C₂²×C₂₃	1	2	yes	—
275	C₈²	C₂²×C₂₃	1	2	yes	—
276	C₂×C₂₃	—	2	2	no	—
277	C₂×C₂₃	—	8	1	no	—
278	C₂×C₂₃	C₂×#436	1	1	yes	characteristic
279	C₂×C₂₃	C₄×#137	1	1	yes	characteristic
280	C₂×C₂₃	#2955	1	1	yes	characteristic
281	C₂×#41	C₂×C₄×C₂₃	1	1	yes	characteristic
282	C₂²×Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
283	#137	—	2	4	no	—
284	C₂×Q₁₆	C₂×C₄×C₂₃	1	2	yes	—
285	C₂×SD₁₆	C₂×C₄×C₂₃	1	2	yes	—
286	C₂×M₁₆	—	2	1	no	—
287	C₂×M₁₆	—	2	1	no	—
288	C₂×M₁₆	C₂×C₄×C₂₃	1	1	yes	characteristic
289	C₂×M₁₆	C₂×C₄×C₂₃	1	1	yes	characteristic
290	C₂²×C₈	—	2	1	no	—
291	C₂²×C₈	D₄×C₂₃	1	1	yes	characteristic
292	C₂²×C₈	D₄×C₂₃	1	1	yes	characteristic
293	C₄×Q₈	—	2	1	no	—
294	C₄×Q₈	—	2	1	no	—
295	C₄×Q₈	C₂×C₄×C₂₃	1	2	yes	—
296	C₄×Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
297	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
298	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
299	C₄×D₄	—	2	1	no	—
300	C₄×D₄	—	2	1	no	—
301	C₄×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
302	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
303	#117	—	2	1	no	—
304	#117	C₂×C₄×C₂₃	1	1	yes	characteristic
305	C₂×C₄⋊C₄	—	2	1	no	—
306	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
307	C₂×C₄²	—	2	1	no	—
308	C₂×C₄²	—	2	1	no	—
309	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
310	#107	C₂×C₄×C₂₃	1	2	yes	—
311	#106	C₂×C₄×C₂₃	1	2	yes	—
312	C₄⋊C₈	—	2	2	no	—
313	C₄⋊C₈	—	2	2	no	—
314	C₄⋊C₈	—	2	1	no	—
315	C₄⋊C₈	—	2	1	no	—
316	C₄⋊C₈	—	2	1	no	—
317	C₄⋊C₈	—	2	1	no	—
318	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
319	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
320	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
321	#103	C₂×C₄×C₂₃	1	2	yes	—
322	#103	C₂×C₄×C₂₃	1	2	yes	—
323	#103	C₂×C₄×C₂₃	1	2	yes	—
324	#102	C₂×C₄×C₂₃	1	2	yes	—
325	C₂²⋊C₈	—	2	1	no	—
326	C₂²⋊C₈	—	2	1	no	—
327	C₂²⋊C₈	—	2	1	no	—
328	C₂²⋊C₈	—	2	1	no	—
329	#97	—	2	2	no	—
330	#97	—	2	2	no	—
331	#97	—	2	1	no	—
332	#97	—	2	1	no	—
333	#97	C₂×C₄×C₂₃	1	2	yes	—
334	C₄×C₈	—	2	1	no	—
335	C₄×C₈	D₄×C₂₃	1	1	yes	characteristic
336	C₄×C₈	D₄×C₂₃	1	1	yes	characteristic
337	C₄×C₈	C₂³×C₂₃	1	2	yes	—
338	C₄×C₈	C₂³×C₂₃	1	2	yes	—
339	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
340	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
341	C₂₃	#17892	1	1	yes	characteristic, direct product factor, Sylow
342	#41	—	2	2	no	—
343	#41	—	2	2	no	—
344	C₂×Q₈	—	2	1	no	—
345	C₂×Q₈	—	2	2	no	—
346	C₂×Q₈	—	2	2	no	—
347	C₂×Q₈	C₂²×C₄×C₂₃	1	2	yes	—
348	C₂×Q₈	C₂²×C₄×C₂₃	1	1	yes	characteristic
349	C₂×D₄	—	2	1	no	—
350	C₂×D₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
351	C₂²×C₄	—	2	1	no	—
352	C₂²×C₄	—	2	1	no	—
353	C₂²×C₄	—	2	1	no	—
354	C₂²×C₄	—	2	1	no	—
355	C₂²×C₄	—	2	1	no	—
356	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
357	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
358	C₂²×C₄	#41×C₂₃	1	1	yes	characteristic
359	Q₁₆	—	2	4	no	—
360	SD₁₆	—	2	4	no	—
361	M₁₆	—	2	2	no	—
362	M₁₆	—	4	2	no	—
363	M₁₆	—	4	2	no	—
364	M₁₆	M₁₆×C₂₃	1	4	yes	complemented
365	C₂×C₈	—	2	2	no	—
366	C₂×C₈	—	2	1	no	—
367	C₂×C₈	—	2	1	no	—
368	C₂×C₈	—	2	2	no	—
369	C₂×C₈	—	2	2	no	—
370	C₂×C₈	—	4	1	no	—
371	C₂×C₈	—	4	2	no	—
372	C₂×C₈	C₂²×C₄×C₂₃	1	2	yes	—
373	C₂×C₈	C₂²×C₄×C₂₃	1	2	yes	—
374	C₂×C₈	C₂×D₄×C₂₃	1	1	yes	characteristic
375	C₂×C₈	C₂×D₄×C₂₃	1	1	yes	characteristic
376	C₂×C₈	C₂×D₄×C₂₃	1	1	yes	characteristic
377	C₂×C₈	C₂×D₄×C₂₃	1	1	yes	characteristic
378	C₄⋊C₄	—	2	2	no	—
379	C₄⋊C₄	—	2	1	no	—
380	C₄⋊C₄	—	2	1	no	—
381	C₄⋊C₄	—	2	2	no	—
382	C₄⋊C₄	—	2	1	no	—
383	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
384	C₄⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
385	C₄⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
386	C₂²⋊C₄	—	2	1	no	—
387	C₂²⋊C₄	—	2	1	no	—
388	C₂²⋊C₄	—	2	1	no	—
389	C₄²	—	2	1	no	—
390	C₄²	—	2	1	no	—
391	C₄²	—	2	2	no	—
392	C₄²	—	2	1	no	—
393	C₄²	—	2	2	no	—
394	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
395	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
396	C₄²	#41×C₂₃	1	1	yes	characteristic
397	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
398	C₂³	—	2	1	no	—
399	C₂³	C₄×D₄×C₂₃	1	1	yes	characteristic
400	Q₈	—	2	2	no	—
401	Q₈	—	2	1	no	—
402	Q₈	—	2	2	no	—
403	Q₈	—	2	1	no	—
404	Q₈	—	4	2	no	—
405	D₄	—	2	1	no	—
406	D₄	—	2	1	no	—
407	D₄	—	4	2	no	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	2	1	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	1	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	4	1	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	4	2	no	—
419	C₂×C₄	—	4	1	no	—
420	C₂×C₄	—	4	1	no	—
421	C₂×C₄	—	4	2	no	—
422	C₂×C₄	C₄×D₄×C₂₃	1	1	yes	characteristic
423	C₂×C₄	C₄×D₄×C₂₃	1	1	yes	characteristic
424	C₂×C₄	C₄×D₄×C₂₃	1	1	yes	characteristic
425	C₂×C₄	C₂×M₁₆×C₂₃	1	2	yes	—
426	C₂×C₄	C₂₃×#131	1	2	yes	—
427	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
428	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
429	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
430	C₈	—	2	2	no	—
431	C₈	—	2	1	no	—
432	C₈	—	2	1	no	—
433	C₈	—	2	1	no	—
434	C₈	—	4	2	no	—
435	C₈	—	4	1	no	—
436	C₈	—	4	2	no	—
437	C₈	—	4	1	no	—
438	C₈	C₂×M₁₆×C₂₃	1	4	yes	—
439	C₈	C₂₃×#137	1	2	yes	complemented
440	C₂²	—	2	1	no	—
441	C₂²	—	2	1	no	—
442	C₂²	—	4	1	no	—
443	C₂²	—	4	1	no	—
444	C₂²	—	4	1	no	—
445	C₂²	C₂₃×#436	1	2	yes	—
446	C₂²	C₂×C₄×D₄×C₂₃	1	1	yes	characteristic
447	C₄	—	2	1	no	—
448	C₄	—	2	1	no	—
449	C₄	—	2	1	no	—
450	C₄	—	4	1	no	—
451	C₄	—	4	2	no	—
452	C₄	—	4	1	no	—
453	C₄	—	4	1	no	—
454	C₄	—	4	2	no	—
455	C₄	C₂₃×#436	1	2	yes	—
456	C₄	C₂²×M₁₆×C₂₃	1	1	yes	characteristic
457	C₄	C₂×C₂₃×#131	1	1	yes	characteristic
458	C₄	C₂×C₂₃×#137	1	1	yes	characteristic
459	C₄	C₂₃×#575	1	1	yes	characteristic
460	C₂	—	2	2	no	—
461	C₂	—	8	1	no	—
462	C₂	C₂×C₂₃×#436	1	1	yes	characteristic
463	C₂	C₄×C₂₃×#137	1	1	yes	characteristic
464	C₂	C₂₃×#2955	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₂₃	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₂₃
Frattini, cosocle	C₄²	C₂⁴×C₂₃
socle	C₂²×C₂₃	C₂×C₄×D₄
prime radical	C₂×#41×C₂₃	C₂×C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₃ ◁ C₂×C₄×C₈×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₂₃×#446	C₂	semidirect
4. C₂₃×#1593	C₂	semidirect
5. C₂₃×#1592	C₂	semidirect
6. C₂₃×#1591	C₂	semidirect
7. C₂₃×#1590	C₂	semidirect
8. C₂₃×#1565	C₂	semidirect
9. C₂₃×#1479	C₂	semidirect
11. C₈×M₁₆×C₂₃	C₂	semidirect
131. M₁₆×C₂₃	M₁₆	semidirect
165. #17892	C₂₃	direct (N × H)
207. C₈×C₂₃	#137	semidirect
209. C₂×#446	C₂×C₂₃	semidirect
211. #1593	C₂×C₂₃	semidirect
212. #1592	C₂×C₂₃	semidirect
213. #1591	C₂×C₂₃	semidirect
214. #1590	C₂×C₂₃	semidirect
215. #1565	C₂×C₂₃	semidirect
216. #1479	C₂×C₂₃	semidirect
218. C₈×M₁₆	C₂×C₂₃	semidirect
341. C₂₃	#17892	direct (N × H)
364. M₁₆	M₁₆×C₂₃	semidirect
439. C₈	C₂₃×#137	semidirect

Maximal subgroups

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

subgroup	index
C₂₃×#2965	2
C₂×C₂₃×#446	2
C₄×C₂₃×#137	2
C₂₃×#1593	2
C₂₃×#1592	2
C₂₃×#1591	2
C₂₃×#1590	2
C₂₃×#1565	2
C₂₃×#1479	2
C₂₃×#1477	2
C₈×M₁₆×C₂₃	2
#17892	23

Subgroups — C23×#17892 #19165518

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#17892 #19165518