Subgroups — C₂₃×#26984 #19174610

Order 5888.

1050 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#469	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₃×#442	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#2428	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#2422	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#2084	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#2034	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#2011	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#1999	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#1957	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#1936	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#1934	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#1895	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#1879	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#1864	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#1753	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×D₈×C₂₃	C₂²	1	1	yes	characteristic
17	C₂²×D₈×C₂₃	C₂²	1	1	yes	characteristic
18	C₂²×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
19	C₂×C₂₃×#127	C₂²	1	1	yes	characteristic
20	C₂×C₂₃×#123	—	2	1	no	—
21	C₂×C₂₃×#121	—	2	1	no	—
22	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
23	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
24	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
25	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
26	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
27	C₂₃×#469	—	2	4	no	—
28	C₂₃×#442	—	2	4	no	—
29	C₂×C₂₃×#106	C₂²	1	1	yes	characteristic
30	C₂×C₂₃×#106	C₂²	1	1	yes	characteristic
31	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
32	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
33	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
34	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
35	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
36	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
37	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
38	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
39	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
40	C₂×C₂₃×#97	C₂²	1	1	yes	characteristic
41	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
42	C₂₃×#397	—	2	1	no	—
43	C₂₃×#394	—	2	1	no	—
44	C₂₃×#394	—	2	1	no	—
45	C₂₃×#392	—	2	1	no	—
46	C₂₃×#390	C₂²	1	1	yes	characteristic
47	C₂₃×#390	C₂²	1	1	yes	characteristic
48	C₂₃×#389	C₂²	1	1	yes	characteristic
49	C₂₃×#389	C₂²	1	1	yes	characteristic
50	C₂₃×#386	—	2	1	no	—
51	C₂₃×#385	—	2	1	no	—
52	C₂₃×#384	C₂²	1	1	yes	characteristic
53	C₂₃×#380	C₂²	1	1	yes	characteristic
54	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
55	C₂₃×#340	C₂²	1	1	yes	characteristic
56	C₂₃×#340	C₂²	1	1	yes	characteristic
57	C₂₃×#340	C₂²	1	1	yes	characteristic
58	C₂₃×#340	C₂²	1	1	yes	characteristic
59	C₂₃×#336	C₂²	1	1	yes	characteristic
60	C₂₃×#336	C₂²	1	1	yes	characteristic
61	C₂²×D₄×C₂₃	—	2	1	no	—
62	C₂²×D₄×C₂₃	—	2	1	no	—
63	C₂²×D₄×C₂₃	—	2	1	no	—
64	C₂²×D₄×C₂₃	—	2	1	no	—
65	C₂²×D₄×C₂₃	—	2	1	no	—
66	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
67	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
68	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
69	C₂³×C₄×C₂₃	—	2	1	no	—
70	C₂³×C₄×C₂₃	—	2	1	no	—
71	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
72	C₂×D₈×C₂₃	—	2	2	no	—
73	C₂×D₈×C₂₃	—	2	2	no	—
74	C₂×D₈×C₂₃	—	2	2	no	—
75	C₂×D₈×C₂₃	—	2	2	no	—
76	C₂×D₈×C₂₃	—	2	2	no	—
77	C₂×D₈×C₂₃	—	4	1	no	—
78	C₂×M₁₆×C₂₃	—	2	2	no	—
79	C₂×M₁₆×C₂₃	—	2	2	no	—
80	C₂×M₁₆×C₂₃	—	4	1	no	—
81	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
82	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
83	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
84	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
85	C₂₃×#127	—	2	2	no	—
86	C₂₃×#127	—	4	1	no	—
87	C₂₃×#123	—	4	4	no	—
88	C₂₃×#121	—	2	2	no	—
89	C₂₃×#121	—	2	2	no	—
90	C₂₃×#121	—	2	2	no	—
91	C₂₃×#121	—	4	4	no	—
92	C₂₃×#121	—	4	1	no	—
93	C₂₃×#121	—	4	1	no	—
94	C₂₃×#121	—	4	1	no	—
95	C₄×D₄×C₂₃	—	2	2	no	—
96	C₄×D₄×C₂₃	—	2	2	no	—
97	C₄×D₄×C₂₃	—	4	1	no	—
98	C₄×D₄×C₂₃	—	4	1	no	—
99	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
100	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
101	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
102	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
103	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
104	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
105	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
106	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
107	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
108	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
109	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
110	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
111	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
112	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
113	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
114	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
115	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
116	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
117	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
118	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
119	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
120	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
121	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
122	C₂₃×#106	—	2	2	no	—
123	C₂₃×#106	—	2	2	no	—
124	C₂₃×#102	—	2	2	no	—
125	C₂₃×#102	—	2	2	no	—
126	C₂₃×#102	—	2	2	no	—
127	C₂₃×#102	—	2	2	no	—
128	C₂₃×#102	—	4	1	no	—
129	C₂₃×#102	—	4	1	no	—
130	C₂₃×#102	—	4	1	no	—
131	C₂₃×#102	D₄	1	4	yes	complemented
132	C₂₃×C₂²⋊C₈	—	2	2	no	—
133	C₂₃×#97	—	2	2	no	—
134	C₄×C₈×C₂₃	—	4	1	no	—
135	C₂₃×#95	—	2	1	no	—
136	C₂₃×#95	—	2	1	no	—
137	C₂₃×#95	—	2	1	no	—
138	C₂₃×#95	D₄	1	1	yes	characteristic
139	C₂₃×#95	D₄	1	1	yes	characteristic
140	C₂⁴×C₂₃	—	2	1	no	—
141	C₂⁴×C₂₃	—	2	1	no	—
142	C₂⁴×C₂₃	—	2	1	no	—
143	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
144	C₂×D₄×C₂₃	—	2	1	no	—
145	C₂×D₄×C₂₃	—	2	1	no	—
146	C₂×D₄×C₂₃	—	2	1	no	—
147	C₂×D₄×C₂₃	—	2	1	no	—
148	C₂×D₄×C₂₃	—	2	1	no	—
149	C₂×D₄×C₂₃	—	2	1	no	—
150	C₂×D₄×C₂₃	—	2	1	no	—
151	C₂×D₄×C₂₃	—	2	1	no	—
152	C₂×D₄×C₂₃	—	2	1	no	—
153	C₂×D₄×C₂₃	—	2	1	no	—
154	C₂×D₄×C₂₃	—	2	1	no	—
155	C₂×D₄×C₂₃	—	2	1	no	—
156	C₂×D₄×C₂₃	—	2	1	no	—
157	C₂×D₄×C₂₃	—	2	1	no	—
158	C₂×D₄×C₂₃	—	2	1	no	—
159	C₂×D₄×C₂₃	—	2	1	no	—
160	C₂×D₄×C₂₃	—	4	2	no	—
161	C₂×D₄×C₂₃	—	4	2	no	—
162	C₂×D₄×C₂₃	—	4	2	no	—
163	C₂×D₄×C₂₃	—	4	2	no	—
164	C₂×D₄×C₂₃	—	4	2	no	—
165	C₂×D₄×C₂₃	—	4	2	no	—
166	C₂×D₄×C₂₃	—	4	2	no	—
167	C₂×D₄×C₂₃	—	4	2	no	—
168	C₂×D₄×C₂₃	—	4	2	no	—
169	C₂×D₄×C₂₃	—	4	2	no	—
170	C₂×D₄×C₂₃	—	8	1	no	—
171	C₂×D₄×C₂₃	—	8	1	no	—
172	C₂×D₄×C₂₃	—	8	1	no	—
173	C₂×D₄×C₂₃	—	8	1	no	—
174	C₂×D₄×C₂₃	—	8	1	no	—
175	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
176	C₂×D₄×C₂₃	#41	1	2	yes	—
177	C₂²×C₄×C₂₃	—	2	1	no	—
178	C₂²×C₄×C₂₃	—	2	1	no	—
179	C₂²×C₄×C₂₃	—	2	1	no	—
180	C₂²×C₄×C₂₃	—	2	1	no	—
181	C₂²×C₄×C₂₃	—	2	1	no	—
182	C₂²×C₄×C₂₃	—	2	1	no	—
183	C₂²×C₄×C₂₃	—	2	1	no	—
184	C₂²×C₄×C₂₃	—	2	1	no	—
185	C₂²×C₄×C₂₃	—	2	1	no	—
186	C₂²×C₄×C₂₃	—	2	1	no	—
187	C₂²×C₄×C₂₃	—	2	1	no	—
188	C₂²×C₄×C₂₃	—	4	2	no	—
189	C₂²×C₄×C₂₃	—	4	2	no	—
190	C₂²×C₄×C₂₃	—	4	2	no	—
191	C₂²×C₄×C₂₃	—	4	2	no	—
192	C₂²×C₄×C₂₃	—	8	1	no	—
193	C₂²×C₄×C₂₃	—	8	1	no	—
194	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
195	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
196	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
197	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
198	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
199	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
200	D₈×C₂₃	—	2	8	no	—
201	D₈×C₂₃	—	4	4	no	—
202	M₁₆×C₂₃	—	4	4	no	—
203	C₂×C₈×C₂₃	—	2	1	no	—
204	C₂×C₈×C₂₃	—	2	1	no	—
205	C₂×C₈×C₂₃	—	2	1	no	—
206	C₂×C₈×C₂₃	—	2	1	no	—
207	C₂×C₈×C₂₃	—	2	1	no	—
208	C₂×C₈×C₂₃	—	2	1	no	—
209	C₂×C₈×C₂₃	—	2	1	no	—
210	C₂×C₈×C₂₃	—	2	1	no	—
211	C₂×C₈×C₂₃	—	2	1	no	—
212	C₂×C₈×C₂₃	C₂×D₄	1	2	yes	—
213	C₂×C₈×C₂₃	#41	1	2	yes	—
214	C₂×C₈×C₂₃	#41	1	2	yes	—
215	C₄⋊C₄×C₂₃	—	2	1	no	—
216	C₄⋊C₄×C₂₃	—	2	1	no	—
217	C₄⋊C₄×C₂₃	—	2	1	no	—
218	C₄⋊C₄×C₂₃	—	2	1	no	—
219	C₄⋊C₄×C₂₃	—	2	1	no	—
220	C₄⋊C₄×C₂₃	—	2	1	no	—
221	C₄⋊C₄×C₂₃	—	2	1	no	—
222	C₄⋊C₄×C₂₃	—	2	1	no	—
223	C₄⋊C₄×C₂₃	—	2	1	no	—
224	C₄⋊C₄×C₂₃	—	4	2	no	—
225	C₄⋊C₄×C₂₃	—	4	2	no	—
226	C₄⋊C₄×C₂₃	—	4	2	no	—
227	C₄⋊C₄×C₂₃	—	8	1	no	—
228	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
229	C₂²⋊C₄×C₂₃	—	2	2	no	—
230	C₂²⋊C₄×C₂₃	—	2	2	no	—
231	C₂²⋊C₄×C₂₃	—	4	2	no	—
232	C₂²⋊C₄×C₂₃	—	4	2	no	—
233	C₂²⋊C₄×C₂₃	—	4	2	no	—
234	C₂²⋊C₄×C₂₃	—	4	2	no	—
235	C₂²⋊C₄×C₂₃	—	4	2	no	—
236	C₂²⋊C₄×C₂₃	—	4	2	no	—
237	C₂²⋊C₄×C₂₃	—	4	2	no	—
238	C₂²⋊C₄×C₂₃	—	4	2	no	—
239	C₂²⋊C₄×C₂₃	—	4	2	no	—
240	C₂²⋊C₄×C₂₃	—	8	1	no	—
241	C₄²×C₂₃	—	2	1	no	—
242	C₄²×C₂₃	—	2	1	no	—
243	C₄²×C₂₃	—	2	1	no	—
244	C₄²×C₂₃	—	2	1	no	—
245	#26984	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
246	C₂³×C₂₃	—	2	1	no	—
247	C₂³×C₂₃	—	2	2	no	—
248	C₂³×C₂₃	—	2	1	no	—
249	C₂³×C₂₃	—	2	2	no	—
250	C₂³×C₂₃	—	2	1	no	—
251	C₂³×C₂₃	—	2	1	no	—
252	C₂³×C₂₃	—	2	1	no	—
253	C₂³×C₂₃	—	2	1	no	—
254	C₂³×C₂₃	—	2	1	no	—
255	C₂³×C₂₃	—	4	1	no	—
256	C₂³×C₂₃	—	4	1	no	—
257	C₂³×C₂₃	—	4	1	no	—
258	C₂³×C₂₃	—	4	1	no	—
259	C₂³×C₂₃	—	4	1	no	—
260	C₂³×C₂₃	—	4	1	no	—
261	C₂³×C₂₃	—	4	1	no	—
262	C₂³×C₂₃	—	4	1	no	—
263	C₂³×C₂₃	—	4	1	no	—
264	C₂³×C₂₃	—	4	1	no	—
265	C₂³×C₂₃	—	4	1	no	—
266	C₂³×C₂₃	—	4	1	no	—
267	C₂³×C₂₃	—	4	1	no	—
268	C₂³×C₂₃	—	4	1	no	—
269	C₂³×C₂₃	—	4	1	no	—
270	C₂³×C₂₃	—	4	1	no	—
271	C₂³×C₂₃	—	4	1	no	—
272	C₂³×C₂₃	—	4	1	no	—
273	C₂³×C₂₃	—	4	1	no	—
274	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
275	D₄×C₂₃	—	2	2	no	—
276	D₄×C₂₃	—	2	2	no	—
277	D₄×C₂₃	—	2	2	no	—
278	D₄×C₂₃	—	2	2	no	—
279	D₄×C₂₃	—	4	1	no	—
280	D₄×C₂₃	—	4	1	no	—
281	D₄×C₂₃	—	4	1	no	—
282	D₄×C₂₃	—	4	1	no	—
283	D₄×C₂₃	—	4	1	no	—
284	D₄×C₂₃	—	4	1	no	—
285	D₄×C₂₃	—	4	1	no	—
286	D₄×C₂₃	—	4	1	no	—
287	D₄×C₂₃	—	8	4	no	—
288	D₄×C₂₃	—	8	4	no	—
289	D₄×C₂₃	—	8	4	no	—
290	D₄×C₂₃	—	8	4	no	—
291	D₄×C₂₃	—	8	4	no	—
292	C₂×C₄×C₂₃	—	2	1	no	—
293	C₂×C₄×C₂₃	—	2	1	no	—
294	C₂×C₄×C₂₃	—	2	1	no	—
295	C₂×C₄×C₂₃	—	2	1	no	—
296	C₂×C₄×C₂₃	—	2	1	no	—
297	C₂×C₄×C₂₃	—	2	1	no	—
298	C₂×C₄×C₂₃	—	2	1	no	—
299	C₂×C₄×C₂₃	—	2	1	no	—
300	C₂×C₄×C₂₃	—	2	2	no	—
301	C₂×C₄×C₂₃	—	2	1	no	—
302	C₂×C₄×C₂₃	—	2	1	no	—
303	C₂×C₄×C₂₃	—	2	1	no	—
304	C₂×C₄×C₂₃	—	2	1	no	—
305	C₂×C₄×C₂₃	—	2	1	no	—
306	C₂×C₄×C₂₃	—	4	1	no	—
307	C₂×C₄×C₂₃	—	4	1	no	—
308	C₂×C₄×C₂₃	—	4	1	no	—
309	C₂×C₄×C₂₃	—	4	1	no	—
310	C₂×C₄×C₂₃	—	4	1	no	—
311	C₂×C₄×C₂₃	—	4	1	no	—
312	C₂×C₄×C₂₃	—	4	1	no	—
313	C₂×C₄×C₂₃	—	4	1	no	—
314	C₂×C₄×C₂₃	—	4	1	no	—
315	C₂×C₄×C₂₃	—	4	1	no	—
316	C₂×C₄×C₂₃	—	4	1	no	—
317	C₂×C₄×C₂₃	—	4	1	no	—
318	C₂×C₄×C₂₃	—	4	1	no	—
319	C₂×C₄×C₂₃	—	4	1	no	—
320	C₂×C₄×C₂₃	—	4	1	no	—
321	C₂×C₄×C₂₃	—	4	1	no	—
322	C₂×C₄×C₂₃	—	4	1	no	—
323	C₂×C₄×C₂₃	—	4	1	no	—
324	C₂×C₄×C₂₃	—	8	4	no	—
325	C₂×C₄×C₂₃	—	8	4	no	—
326	C₂×C₄×C₂₃	AGL(1,ℤ/8)	1	2	yes	—
327	C₂×C₄×C₂₃	AGL(1,ℤ/8)	1	2	yes	—
328	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
329	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
330	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
331	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
332	C₂×C₄×C₂₃	H(5,𝔽₂)	1	1	yes	characteristic
333	C₂×C₄×C₂₃	H(5,𝔽₂)	1	1	yes	characteristic
334	C₈×C₂₃	—	2	2	no	—
335	C₈×C₂₃	—	2	2	no	—
336	C₈×C₂₃	—	2	2	no	—
337	C₈×C₂₃	—	4	1	no	—
338	C₂×#469	C₂×C₂₃	1	1	yes	characteristic, complemented
339	C₂×#442	C₂×C₂₃	1	1	yes	characteristic, complemented
340	#2428	C₂×C₂₃	1	1	yes	characteristic, complemented
341	#2422	C₂×C₂₃	1	1	yes	characteristic, complemented
342	#2084	C₂×C₂₃	1	1	yes	characteristic, complemented
343	#2034	C₂×C₂₃	1	1	yes	characteristic, complemented
344	#2011	C₂×C₂₃	1	1	yes	characteristic, complemented
345	#1999	C₂×C₂₃	1	1	yes	characteristic, complemented
346	#1957	C₂×C₂₃	1	1	yes	characteristic, complemented
347	#1936	C₂×C₂₃	1	1	yes	characteristic, complemented
348	#1934	C₂×C₂₃	1	1	yes	characteristic, complemented
349	#1895	C₂×C₂₃	1	1	yes	characteristic, complemented
350	#1879	C₂×C₂₃	1	1	yes	characteristic, complemented
351	#1864	C₂×C₂₃	1	1	yes	characteristic, complemented
352	#1753	C₂×C₂₃	1	1	yes	characteristic, complemented
353	C₂²×C₂₃	—	4	1	no	—
354	C₂²×C₂₃	—	4	1	no	—
355	C₂²×C₂₃	—	4	1	no	—
356	C₂²×C₂₃	—	4	2	no	—
357	C₂²×C₂₃	—	4	2	no	—
358	C₂²×C₂₃	—	4	1	no	—
359	C₂²×C₂₃	—	4	2	no	—
360	C₂²×C₂₃	—	4	2	no	—
361	C₂²×C₂₃	—	4	1	no	—
362	C₂²×C₂₃	—	4	2	no	—
363	C₂²×C₂₃	—	4	1	no	—
364	C₂²×C₂₃	—	4	1	no	—
365	C₂²×C₂₃	—	4	2	no	—
366	C₂²×C₂₃	—	8	1	no	—
367	C₂²×C₂₃	—	8	1	no	—
368	C₂²×C₂₃	—	8	1	no	—
369	C₂²×C₂₃	—	8	1	no	—
370	C₂²×C₂₃	—	8	1	no	—
371	C₂²×C₂₃	—	8	1	no	—
372	C₂²×C₂₃	—	8	1	no	—
373	C₂²×C₂₃	—	8	1	no	—
374	C₂²×C₂₃	—	8	1	no	—
375	C₂²×C₂₃	—	8	1	no	—
376	C₂²×C₂₃	—	8	1	no	—
377	C₂²×C₂₃	—	8	1	no	—
378	C₂²×C₂₃	—	8	1	no	—
379	C₂²×C₂₃	—	8	1	no	—
380	C₂²×C₂₃	—	8	1	no	—
381	C₂²×C₂₃	#532	1	1	yes	characteristic
382	C₂²×C₂₃	D₄²	1	1	yes	characteristic
383	C₂²×C₂₃	#546	1	1	yes	characteristic
384	C₂²×C₂₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
385	C₂²×C₂₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
386	C₂²×C₂₃	#576	1	1	yes	characteristic
387	C₂²×C₂₃	#577	1	1	yes	characteristic
388	C₄×C₂₃	—	2	2	no	—
389	C₄×C₂₃	—	2	2	no	—
390	C₄×C₂₃	—	4	1	no	—
391	C₄×C₂₃	—	4	1	no	—
392	C₄×C₂₃	—	4	2	no	—
393	C₄×C₂₃	—	4	1	no	—
394	C₄×C₂₃	—	8	1	no	—
395	C₄×C₂₃	—	8	1	no	—
396	C₄×C₂₃	—	8	1	no	—
397	C₄×C₂₃	—	8	1	no	—
398	C₄×C₂₃	#525	1	1	yes	characteristic
399	C₄×C₂₃	#540	1	1	yes	characteristic
400	C₄×C₂₃	#546	1	1	yes	characteristic
401	C₄×C₂₃	#553	1	1	yes	characteristic
402	C₂²×D₈	C₂²×C₂₃	1	1	yes	characteristic
403	C₂²×D₈	C₂²×C₂₃	1	1	yes	characteristic
404	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
405	C₂×#127	C₂²×C₂₃	1	1	yes	characteristic
406	C₂×#123	—	2	1	no	—
407	C₂×#121	—	2	1	no	—
408	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
409	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
410	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
411	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
412	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
413	#469	—	2	4	no	—
414	#442	—	2	4	no	—
415	C₂×#106	C₂²×C₂₃	1	1	yes	characteristic
416	C₂×#106	C₂²×C₂₃	1	1	yes	characteristic
417	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
418	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
419	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
420	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
421	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
422	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
423	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
424	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
425	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
426	C₂×#97	C₂²×C₂₃	1	1	yes	characteristic
427	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
428	#397	—	2	1	no	—
429	#394	—	2	1	no	—
430	#394	—	2	1	no	—
431	#392	—	2	1	no	—
432	#390	C₂²×C₂₃	1	1	yes	characteristic
433	#390	C₂²×C₂₃	1	1	yes	characteristic
434	#389	C₂²×C₂₃	1	1	yes	characteristic
435	#389	C₂²×C₂₃	1	1	yes	characteristic
436	#386	—	2	1	no	—
437	#385	—	2	1	no	—
438	#384	C₂²×C₂₃	1	1	yes	characteristic
439	#380	C₂²×C₂₃	1	1	yes	characteristic
440	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
441	#340	C₂²×C₂₃	1	1	yes	characteristic
442	#340	C₂²×C₂₃	1	1	yes	characteristic
443	#340	C₂²×C₂₃	1	1	yes	characteristic
444	#340	C₂²×C₂₃	1	1	yes	characteristic
445	#336	C₂²×C₂₃	1	1	yes	characteristic
446	#336	C₂²×C₂₃	1	1	yes	characteristic
447	C₂×C₂₃	—	8	1	no	—
448	C₂×C₂₃	—	8	2	no	—
449	C₂×C₂₃	—	8	2	no	—
450	C₂×C₂₃	—	16	1	no	—
451	C₂×C₂₃	#2464	1	1	yes	characteristic
452	C₂×C₂₃	#3179	1	1	yes	characteristic
453	C₂×C₂₃	#3184	1	1	yes	characteristic
454	C₂×C₂₃	#3272	1	1	yes	characteristic
455	C₂×C₂₃	#3274	1	1	yes	characteristic
456	C₂×C₂₃	#3306	1	1	yes	characteristic
457	C₂×C₂₃	#3318	1	1	yes	characteristic
458	C₂²×D₄	—	2	1	no	—
459	C₂²×D₄	—	2	1	no	—
460	C₂²×D₄	—	2	1	no	—
461	C₂²×D₄	—	2	1	no	—
462	C₂²×D₄	—	2	1	no	—
463	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
464	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
465	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
466	C₂³×C₄	—	2	1	no	—
467	C₂³×C₄	—	2	1	no	—
468	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
469	C₂×D₈	—	2	2	no	—
470	C₂×D₈	—	2	2	no	—
471	C₂×D₈	—	2	2	no	—
472	C₂×D₈	—	2	2	no	—
473	C₂×D₈	—	2	2	no	—
474	C₂×D₈	—	4	1	no	—
475	C₂×M₁₆	—	2	2	no	—
476	C₂×M₁₆	—	2	2	no	—
477	C₂×M₁₆	—	4	1	no	—
478	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
479	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
480	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
481	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
482	#127	—	2	2	no	—
483	#127	—	4	1	no	—
484	#123	—	4	4	no	—
485	#121	—	2	2	no	—
486	#121	—	2	2	no	—
487	#121	—	2	2	no	—
488	#121	—	4	4	no	—
489	#121	—	4	1	no	—
490	#121	—	4	1	no	—
491	#121	—	4	1	no	—
492	C₄×D₄	—	2	2	no	—
493	C₄×D₄	—	2	2	no	—
494	C₄×D₄	—	4	1	no	—
495	C₄×D₄	—	4	1	no	—
496	C₂×C₄⋊C₄	—	2	1	no	—
497	C₂×C₄⋊C₄	—	2	1	no	—
498	C₂×C₄⋊C₄	—	2	1	no	—
499	C₂×C₄⋊C₄	—	2	1	no	—
500	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
501	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
502	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
503	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
504	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
505	C₂×C₂²⋊C₄	—	2	1	no	—
506	C₂×C₂²⋊C₄	—	2	1	no	—
507	C₂×C₂²⋊C₄	—	2	1	no	—
508	C₂×C₂²⋊C₄	—	2	1	no	—
509	C₂×C₂²⋊C₄	—	2	1	no	—
510	C₂×C₂²⋊C₄	—	2	1	no	—
511	C₂×C₂²⋊C₄	—	2	1	no	—
512	C₂×C₂²⋊C₄	—	2	1	no	—
513	C₂×C₂²⋊C₄	—	2	1	no	—
514	C₂×C₂²⋊C₄	—	2	1	no	—
515	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
516	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
517	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
518	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
519	#106	—	2	2	no	—
520	#106	—	2	2	no	—
521	#102	—	2	2	no	—
522	#102	—	2	2	no	—
523	#102	—	2	2	no	—
524	#102	—	2	2	no	—
525	#102	—	4	1	no	—
526	#102	—	4	1	no	—
527	#102	—	4	1	no	—
528	#102	D₄×C₂₃	1	4	yes	complemented
529	C₂²⋊C₈	—	2	2	no	—
530	#97	—	2	2	no	—
531	C₄×C₈	—	4	1	no	—
532	#95	—	2	1	no	—
533	#95	—	2	1	no	—
534	#95	—	2	1	no	—
535	#95	D₄×C₂₃	1	1	yes	characteristic
536	#95	D₄×C₂₃	1	1	yes	characteristic
537	C₂₃	#26984	1	1	yes	characteristic, direct product factor, Sylow
538	C₂⁴	—	2	1	no	—
539	C₂⁴	—	2	1	no	—
540	C₂⁴	—	2	1	no	—
541	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
542	C₂×D₄	—	2	1	no	—
543	C₂×D₄	—	2	1	no	—
544	C₂×D₄	—	2	1	no	—
545	C₂×D₄	—	2	1	no	—
546	C₂×D₄	—	2	1	no	—
547	C₂×D₄	—	2	1	no	—
548	C₂×D₄	—	2	1	no	—
549	C₂×D₄	—	2	1	no	—
550	C₂×D₄	—	2	1	no	—
551	C₂×D₄	—	2	1	no	—
552	C₂×D₄	—	2	1	no	—
553	C₂×D₄	—	2	1	no	—
554	C₂×D₄	—	2	1	no	—
555	C₂×D₄	—	2	1	no	—
556	C₂×D₄	—	2	1	no	—
557	C₂×D₄	—	2	1	no	—
558	C₂×D₄	—	4	2	no	—
559	C₂×D₄	—	4	2	no	—
560	C₂×D₄	—	4	2	no	—
561	C₂×D₄	—	4	2	no	—
562	C₂×D₄	—	4	2	no	—
563	C₂×D₄	—	4	2	no	—
564	C₂×D₄	—	4	2	no	—
565	C₂×D₄	—	4	2	no	—
566	C₂×D₄	—	4	2	no	—
567	C₂×D₄	—	4	2	no	—
568	C₂×D₄	—	8	1	no	—
569	C₂×D₄	—	8	1	no	—
570	C₂×D₄	—	8	1	no	—
571	C₂×D₄	—	8	1	no	—
572	C₂×D₄	—	8	1	no	—
573	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
574	C₂×D₄	#41×C₂₃	1	2	yes	—
575	C₂²×C₄	—	2	1	no	—
576	C₂²×C₄	—	2	1	no	—
577	C₂²×C₄	—	2	1	no	—
578	C₂²×C₄	—	2	1	no	—
579	C₂²×C₄	—	2	1	no	—
580	C₂²×C₄	—	2	1	no	—
581	C₂²×C₄	—	2	1	no	—
582	C₂²×C₄	—	2	1	no	—
583	C₂²×C₄	—	2	1	no	—
584	C₂²×C₄	—	2	1	no	—
585	C₂²×C₄	—	2	1	no	—
586	C₂²×C₄	—	4	2	no	—
587	C₂²×C₄	—	4	2	no	—
588	C₂²×C₄	—	4	2	no	—
589	C₂²×C₄	—	4	2	no	—
590	C₂²×C₄	—	8	1	no	—
591	C₂²×C₄	—	8	1	no	—
592	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
593	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
594	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
595	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
596	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
597	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
598	D₈	—	2	8	no	—
599	D₈	—	4	4	no	—
600	M₁₆	—	4	4	no	—
601	C₂×C₈	—	2	1	no	—
602	C₂×C₈	—	2	1	no	—
603	C₂×C₈	—	2	1	no	—
604	C₂×C₈	—	2	1	no	—
605	C₂×C₈	—	2	1	no	—
606	C₂×C₈	—	2	1	no	—
607	C₂×C₈	—	2	1	no	—
608	C₂×C₈	—	2	1	no	—
609	C₂×C₈	—	2	1	no	—
610	C₂×C₈	C₂×D₄×C₂₃	1	2	yes	—
611	C₂×C₈	#41×C₂₃	1	2	yes	—
612	C₂×C₈	#41×C₂₃	1	2	yes	—
613	C₄⋊C₄	—	2	1	no	—
614	C₄⋊C₄	—	2	1	no	—
615	C₄⋊C₄	—	2	1	no	—
616	C₄⋊C₄	—	2	1	no	—
617	C₄⋊C₄	—	2	1	no	—
618	C₄⋊C₄	—	2	1	no	—
619	C₄⋊C₄	—	2	1	no	—
620	C₄⋊C₄	—	2	1	no	—
621	C₄⋊C₄	—	2	1	no	—
622	C₄⋊C₄	—	4	2	no	—
623	C₄⋊C₄	—	4	2	no	—
624	C₄⋊C₄	—	4	2	no	—
625	C₄⋊C₄	—	8	1	no	—
626	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
627	C₂²⋊C₄	—	2	2	no	—
628	C₂²⋊C₄	—	2	2	no	—
629	C₂²⋊C₄	—	4	2	no	—
630	C₂²⋊C₄	—	4	2	no	—
631	C₂²⋊C₄	—	4	2	no	—
632	C₂²⋊C₄	—	4	2	no	—
633	C₂²⋊C₄	—	4	2	no	—
634	C₂²⋊C₄	—	4	2	no	—
635	C₂²⋊C₄	—	4	2	no	—
636	C₂²⋊C₄	—	4	2	no	—
637	C₂²⋊C₄	—	4	2	no	—
638	C₂²⋊C₄	—	8	1	no	—
639	C₄²	—	2	1	no	—
640	C₄²	—	2	1	no	—
641	C₄²	—	2	1	no	—
642	C₄²	—	2	1	no	—
643	C₂³	—	2	1	no	—
644	C₂³	—	2	1	no	—
645	C₂³	—	2	1	no	—
646	C₂³	—	2	1	no	—
647	C₂³	—	2	1	no	—
648	C₂³	—	2	2	no	—
649	C₂³	—	2	1	no	—
650	C₂³	—	2	2	no	—
651	C₂³	—	2	1	no	—
652	C₂³	—	4	1	no	—
653	C₂³	—	4	1	no	—
654	C₂³	—	4	1	no	—
655	C₂³	—	4	1	no	—
656	C₂³	—	4	1	no	—
657	C₂³	—	4	1	no	—
658	C₂³	—	4	1	no	—
659	C₂³	—	4	1	no	—
660	C₂³	—	4	1	no	—
661	C₂³	—	4	1	no	—
662	C₂³	—	4	1	no	—
663	C₂³	—	4	1	no	—
664	C₂³	—	4	1	no	—
665	C₂³	—	4	1	no	—
666	C₂³	—	4	1	no	—
667	C₂³	—	4	1	no	—
668	C₂³	—	4	1	no	—
669	C₂³	—	4	1	no	—
670	C₂³	—	4	1	no	—
671	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
672	D₄	—	2	2	no	—
673	D₄	—	2	2	no	—
674	D₄	—	2	2	no	—
675	D₄	—	2	2	no	—
676	D₄	—	4	1	no	—
677	D₄	—	4	1	no	—
678	D₄	—	4	1	no	—
679	D₄	—	4	1	no	—
680	D₄	—	4	1	no	—
681	D₄	—	4	1	no	—
682	D₄	—	4	1	no	—
683	D₄	—	4	1	no	—
684	D₄	—	8	4	no	—
685	D₄	—	8	4	no	—
686	D₄	—	8	4	no	—
687	D₄	—	8	4	no	—
688	D₄	—	8	4	no	—
689	C₂×C₄	—	2	1	no	—
690	C₂×C₄	—	2	1	no	—
691	C₂×C₄	—	2	1	no	—
692	C₂×C₄	—	2	1	no	—
693	C₂×C₄	—	2	1	no	—
694	C₂×C₄	—	2	1	no	—
695	C₂×C₄	—	2	1	no	—
696	C₂×C₄	—	2	1	no	—
697	C₂×C₄	—	2	1	no	—
698	C₂×C₄	—	2	1	no	—
699	C₂×C₄	—	2	1	no	—
700	C₂×C₄	—	2	1	no	—
701	C₂×C₄	—	2	2	no	—
702	C₂×C₄	—	2	1	no	—
703	C₂×C₄	—	4	1	no	—
704	C₂×C₄	—	4	1	no	—
705	C₂×C₄	—	4	1	no	—
706	C₂×C₄	—	4	1	no	—
707	C₂×C₄	—	4	1	no	—
708	C₂×C₄	—	4	1	no	—
709	C₂×C₄	—	4	1	no	—
710	C₂×C₄	—	4	1	no	—
711	C₂×C₄	—	4	1	no	—
712	C₂×C₄	—	4	1	no	—
713	C₂×C₄	—	4	1	no	—
714	C₂×C₄	—	4	1	no	—
715	C₂×C₄	—	4	1	no	—
716	C₂×C₄	—	4	1	no	—
717	C₂×C₄	—	4	1	no	—
718	C₂×C₄	—	4	1	no	—
719	C₂×C₄	—	4	1	no	—
720	C₂×C₄	—	4	1	no	—
721	C₂×C₄	—	8	4	no	—
722	C₂×C₄	—	8	4	no	—
723	C₂×C₄	C₂₃×AGL(1,ℤ/8)	1	2	yes	—
724	C₂×C₄	C₂₃×AGL(1,ℤ/8)	1	2	yes	—
725	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
726	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
727	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
728	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
729	C₂×C₄	C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
730	C₂×C₄	C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
731	C₈	—	2	2	no	—
732	C₈	—	2	2	no	—
733	C₈	—	2	2	no	—
734	C₈	—	4	1	no	—
735	C₂²	—	4	1	no	—
736	C₂²	—	4	1	no	—
737	C₂²	—	4	1	no	—
738	C₂²	—	4	2	no	—
739	C₂²	—	4	2	no	—
740	C₂²	—	4	1	no	—
741	C₂²	—	4	2	no	—
742	C₂²	—	4	2	no	—
743	C₂²	—	4	1	no	—
744	C₂²	—	4	2	no	—
745	C₂²	—	4	1	no	—
746	C₂²	—	4	1	no	—
747	C₂²	—	4	2	no	—
748	C₂²	—	8	1	no	—
749	C₂²	—	8	1	no	—
750	C₂²	—	8	1	no	—
751	C₂²	—	8	1	no	—
752	C₂²	—	8	1	no	—
753	C₂²	—	8	1	no	—
754	C₂²	—	8	1	no	—
755	C₂²	—	8	1	no	—
756	C₂²	—	8	1	no	—
757	C₂²	—	8	1	no	—
758	C₂²	—	8	1	no	—
759	C₂²	—	8	1	no	—
760	C₂²	—	8	1	no	—
761	C₂²	—	8	1	no	—
762	C₂²	—	8	1	no	—
763	C₂²	C₂₃×#532	1	1	yes	characteristic
764	C₂²	D₄²×C₂₃	1	1	yes	characteristic
765	C₂²	C₂₃×#546	1	1	yes	characteristic
766	C₂²	C₂×C₂₃×AGL(1,ℤ/8)	1	1	yes	characteristic
767	C₂²	C₂×C₂₃×AGL(1,ℤ/8)	1	1	yes	characteristic
768	C₂²	C₂₃×#576	1	1	yes	characteristic
769	C₂²	C₂₃×#577	1	1	yes	characteristic
770	C₄	—	2	2	no	—
771	C₄	—	2	2	no	—
772	C₄	—	4	1	no	—
773	C₄	—	4	1	no	—
774	C₄	—	4	2	no	—
775	C₄	—	4	1	no	—
776	C₄	—	8	1	no	—
777	C₄	—	8	1	no	—
778	C₄	—	8	1	no	—
779	C₄	—	8	1	no	—
780	C₄	C₂₃×#525	1	1	yes	characteristic
781	C₄	C₂₃×#540	1	1	yes	characteristic
782	C₄	C₂₃×#546	1	1	yes	characteristic
783	C₄	C₂₃×#553	1	1	yes	characteristic
784	C₂	—	8	1	no	—
785	C₂	—	8	2	no	—
786	C₂	—	8	2	no	—
787	C₂	—	16	1	no	—
788	C₂	C₂₃×#2464	1	1	yes	characteristic
789	C₂	C₂₃×#3179	1	1	yes	characteristic
790	C₂	C₂₃×#3184	1	1	yes	characteristic
791	C₂	C₂₃×#3272	1	1	yes	characteristic
792	C₂	C₂₃×#3274	1	1	yes	characteristic
793	C₂	C₂₃×#3306	1	1	yes	characteristic
794	C₂	C₂₃×#3318	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₂₃×#469	C₂	semidirect
2. C₂×C₂₃×#442	C₂	semidirect
3. C₂₃×#2428	C₂	semidirect
4. C₂₃×#2422	C₂	semidirect
5. C₂₃×#2084	C₂	semidirect
6. C₂₃×#2034	C₂	semidirect
7. C₂₃×#2011	C₂	semidirect
8. C₂₃×#1999	C₂	semidirect
9. C₂₃×#1957	C₂	semidirect
10. C₂₃×#1936	C₂	semidirect
11. C₂₃×#1934	C₂	semidirect
12. C₂₃×#1895	C₂	semidirect
13. C₂₃×#1879	C₂	semidirect
14. C₂₃×#1864	C₂	semidirect
15. C₂₃×#1753	C₂	semidirect
131. C₂₃×#102	D₄	semidirect
245. #26984	C₂₃	direct (N × H)
338. C₂×#469	C₂×C₂₃	semidirect
339. C₂×#442	C₂×C₂₃	semidirect
340. #2428	C₂×C₂₃	semidirect
341. #2422	C₂×C₂₃	semidirect
342. #2084	C₂×C₂₃	semidirect
343. #2034	C₂×C₂₃	semidirect
344. #2011	C₂×C₂₃	semidirect
345. #1999	C₂×C₂₃	semidirect
346. #1957	C₂×C₂₃	semidirect
347. #1936	C₂×C₂₃	semidirect
348. #1934	C₂×C₂₃	semidirect
349. #1895	C₂×C₂₃	semidirect
350. #1879	C₂×C₂₃	semidirect
351. #1864	C₂×C₂₃	semidirect
352. #1753	C₂×C₂₃	semidirect
528. #102	D₄×C₂₃	semidirect
537. C₂₃	#26984	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×#469	2
C₂×C₂₃×#442	2
C₂₃×#2428	2
C₂₃×#2422	2
C₂₃×#2084	2
C₂₃×#2034	2
C₂₃×#2011	2
C₂₃×#1999	2
C₂₃×#1957	2
C₂₃×#1936	2
C₂₃×#1934	2
C₂₃×#1895	2
C₂₃×#1879	2
C₂₃×#1864	2
C₂₃×#1753	2
#26984	23

Subgroups — C23×#26984 #19174610

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#26984 #19174610