Subgroups — C₂₃×#24901 #19172527

Order 5888.

1156 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#450	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×SD₁₆×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#2423	C₂	1	1	yes	maximal, characteristic, complemented
4	D₄×C₂²⋊C₄×C₂₃	C₂	1	1	yes	maximal, characteristic
5	C₂₃×#2094	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#2077	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#2055	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#2035	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#1934	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#1923	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#1880	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#1877	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#1864	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#1802	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#1786	C₂	1	1	yes	maximal, characteristic
16	C₂³×D₄×C₂₃	C₂²	1	1	yes	characteristic
17	C₂²×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic
18	C₂²×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic
19	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
20	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
21	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
23	C₂²×C₂²⋊C₄×C₂₃	—	2	1	no	—
24	C₂₃×#450	—	2	4	no	—
25	C₄×SD₁₆×C₂₃	—	2	4	no	—
26	C₂×C₂₃×#106	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₂₃×#106	C₂²	1	1	yes	characteristic, complemented
28	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic, complemented
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×C₂²⋊C₈	C₂²	1	1	yes	characteristic
38	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
39	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
40	C₂₃×#399	—	2	1	no	—
41	C₂₃×#398	—	2	1	no	—
42	C₂₃×#391	C₂²	1	1	yes	characteristic, complemented
43	C₂₃×#390	C₂²	1	1	yes	characteristic
44	C₂₃×#390	C₂²	1	1	yes	characteristic
45	C₂₃×#389	C₂²	1	1	yes	characteristic, complemented
46	C₂₃×#388	—	2	1	no	—
47	C₂₃×#387	—	2	1	no	—
48	C₂₃×#386	—	2	1	no	—
49	C₂₃×#386	—	2	1	no	—
50	C₂₃×#384	C₂²	1	1	yes	characteristic, complemented
51	C₂₃×#380	C₂²	1	1	yes	characteristic
52	C₂₃×#380	C₂²	1	1	yes	characteristic
53	C₂₃×#379	—	2	1	no	—
54	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
55	C₂₃×#340	C₂²	1	1	yes	characteristic, complemented
56	C₂₃×#340	C₂²	1	1	yes	characteristic, complemented
57	C₂₃×#340	C₂²	1	1	yes	characteristic, complemented
58	C₂₃×#340	C₂²	1	1	yes	characteristic, complemented
59	C₂₃×#336	C₂²	1	1	yes	characteristic, complemented
60	C₂₃×#336	C₂²	1	1	yes	characteristic, complemented
61	C₂⁵×C₂₃	—	2	1	no	—
62	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
63	C₂²×D₄×C₂₃	—	2	2	no	—
64	C₂²×D₄×C₂₃	—	2	2	no	—
65	C₂²×D₄×C₂₃	—	2	2	no	—
66	C₂²×D₄×C₂₃	—	2	2	no	—
67	C₂²×D₄×C₂₃	—	2	1	no	—
68	C₂²×D₄×C₂₃	—	4	1	no	—
69	C₂²×D₄×C₂₃	—	4	1	no	—
70	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
71	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
72	C₂³×C₄×C₂₃	—	2	1	no	—
73	C₂³×C₄×C₂₃	—	2	1	no	—
74	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
75	C₂×SD₁₆×C₂₃	—	2	2	no	—
76	C₂×SD₁₆×C₂₃	—	2	2	no	—
77	C₂×SD₁₆×C₂₃	—	2	2	no	—
78	C₂×SD₁₆×C₂₃	—	2	2	no	—
79	C₂×SD₁₆×C₂₃	—	4	1	no	—
80	C₂×SD₁₆×C₂₃	D₄	1	4	yes	—
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×C₂²⋊Q₈	—	2	2	no	—
86	C₂₃×C₂²⋊Q₈	—	4	1	no	—
87	C₄×Q₈×C₂₃	—	2	2	no	—
88	C₄×Q₈×C₂₃	—	4	1	no	—
89	C₄×D₄×C₂₃	—	2	2	no	—
90	C₄×D₄×C₂₃	—	2	2	no	—
91	C₄×D₄×C₂₃	—	4	1	no	—
92	C₄×D₄×C₂₃	—	4	1	no	—
93	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
94	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
95	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
96	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
97	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
98	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
99	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
100	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
101	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
102	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
103	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
104	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
105	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
106	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
107	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
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	—	4	4	no	—
113	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
114	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
115	C₂×C₄²×C₂₃	—	2	1	no	—
116	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
117	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
118	C₂₃×#106	—	2	2	no	—
119	C₂₃×#106	—	4	1	no	—
120	C₂₃×C₄⋊C₈	—	4	1	no	—
121	C₂₃×#103	—	2	2	no	—
122	C₂₃×#103	—	4	1	no	—
123	C₂₃×#102	—	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×C₂²⋊C₈	—	2	2	no	—
130	C₂₃×C₂²⋊C₈	—	4	1	no	—
131	C₄×C₈×C₂₃	—	2	2	no	—
132	C₂₃×#95	—	2	1	no	—
133	C₂₃×#95	—	2	1	no	—
134	C₂₃×#95	—	2	1	no	—
135	C₂₃×#95	—	2	1	no	—
136	C₂₃×#95	—	2	1	no	—
137	C₂₃×#95	D₄	1	1	yes	characteristic
138	C₂₃×#95	D₄	1	1	yes	characteristic
139	C₂⁴×C₂₃	—	2	1	no	—
140	C₂⁴×C₂₃	—	2	4	no	—
141	C₂⁴×C₂₃	—	2	1	no	—
142	C₂⁴×C₂₃	—	4	2	no	—
143	C₂⁴×C₂₃	—	4	2	no	—
144	C₂⁴×C₂₃	—	4	2	no	—
145	C₂⁴×C₂₃	—	4	2	no	—
146	C₂⁴×C₂₃	—	8	1	no	—
147	C₂⁴×C₂₃	—	8	1	no	—
148	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
149	C₂×Q₈×C₂₃	—	2	1	no	—
150	C₂×Q₈×C₂₃	—	2	1	no	—
151	C₂×Q₈×C₂₃	—	2	1	no	—
152	C₂×Q₈×C₂₃	—	2	1	no	—
153	C₂×Q₈×C₂₃	—	2	1	no	—
154	C₂×Q₈×C₂₃	C₂×D₄	1	2	yes	—
155	C₂×D₄×C₂₃	—	2	4	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	—	2	1	no	—
161	C₂×D₄×C₂₃	—	2	1	no	—
162	C₂×D₄×C₂₃	—	2	1	no	—
163	C₂×D₄×C₂₃	—	2	1	no	—
164	C₂×D₄×C₂₃	—	4	2	no	—
165	C₂×D₄×C₂₃	—	4	2	no	—
166	C₂×D₄×C₂₃	—	4	4	no	—
167	C₂×D₄×C₂₃	—	4	4	no	—
168	C₂×D₄×C₂₃	—	4	4	no	—
169	C₂×D₄×C₂₃	—	4	4	no	—
170	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
171	C₂×D₄×C₂₃	#41	1	2	yes	—
172	C₂×D₄×C₂₃	#41	1	2	yes	—
173	C₂×D₄×C₂₃	#41	1	2	yes	—
174	C₂²×C₄×C₂₃	—	2	1	no	—
175	C₂²×C₄×C₂₃	—	2	1	no	—
176	C₂²×C₄×C₂₃	—	2	1	no	—
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	—	4	2	no	—
187	C₂²×C₄×C₂₃	—	4	2	no	—
188	C₂²×C₄×C₂₃	—	4	2	no	—
189	C₂²×C₄×C₂₃	—	4	2	no	—
190	C₂²×C₄×C₂₃	—	8	1	no	—
191	C₂²×C₄×C₂₃	—	8	1	no	—
192	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
193	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
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	C₂⁴	1	1	yes	characteristic
198	SD₁₆×C₂₃	—	2	8	no	—
199	SD₁₆×C₂₃	—	4	4	no	—
200	C₂×C₈×C₂₃	—	2	1	no	—
201	C₂×C₈×C₂₃	—	2	1	no	—
202	C₂×C₈×C₂₃	—	2	1	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	C₂×D₄	1	2	yes	—
212	C₄⋊C₄×C₂₃	—	2	1	no	—
213	C₄⋊C₄×C₂₃	—	2	1	no	—
214	C₄⋊C₄×C₂₃	—	2	1	no	—
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	—	4	2	no	—
223	C₄⋊C₄×C₂₃	—	4	2	no	—
224	C₄⋊C₄×C₂₃	—	4	2	no	—
225	C₄⋊C₄×C₂₃	—	8	1	no	—
226	C₄⋊C₄×C₂₃	—	8	1	no	—
227	C₂²⋊C₄×C₂₃	—	4	1	no	—
228	C₂²⋊C₄×C₂₃	—	4	2	no	—
229	C₂²⋊C₄×C₂₃	—	4	2	no	—
230	C₂²⋊C₄×C₂₃	—	4	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	—	8	1	no	—
235	C₂²⋊C₄×C₂₃	—	8	1	no	—
236	C₂²⋊C₄×C₂₃	—	8	1	no	—
237	C₂²⋊C₄×C₂₃	SD₁₆	1	4	yes	complemented
238	C₄²×C₂₃	—	2	1	no	—
239	C₄²×C₂₃	—	2	1	no	—
240	C₄²×C₂₃	—	2	1	no	—
241	C₄²×C₂₃	—	2	1	no	—
242	C₄²×C₂₃	—	4	2	no	—
243	#24901	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
244	C₂³×C₂₃	—	2	1	no	—
245	C₂³×C₂₃	—	2	2	no	—
246	C₂³×C₂₃	—	2	1	no	—
247	C₂³×C₂₃	—	2	2	no	—
248	C₂³×C₂₃	—	2	2	no	—
249	C₂³×C₂₃	—	2	1	no	—
250	C₂³×C₂₃	—	2	1	no	—
251	C₂³×C₂₃	—	2	1	no	—
252	C₂³×C₂₃	—	2	1	no	—
253	C₂³×C₂₃	—	2	2	no	—
254	C₂³×C₂₃	—	4	8	no	—
255	C₂³×C₂₃	—	4	8	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	—	8	4	no	—
267	C₂³×C₂₃	—	8	4	no	—
268	C₂³×C₂₃	—	8	4	no	—
269	C₂³×C₂₃	—	8	4	no	—
270	C₂³×C₂₃	—	8	4	no	—
271	C₂³×C₂₃	C₂×SD₁₆	1	2	yes	—
272	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
273	Q₈×C₂₃	—	2	2	no	—
274	Q₈×C₂₃	—	2	2	no	—
275	Q₈×C₂₃	—	4	1	no	—
276	Q₈×C₂₃	—	4	1	no	—
277	D₄×C₂₃	—	2	2	no	—
278	D₄×C₂₃	—	2	2	no	—
279	D₄×C₂₃	—	2	2	no	—
280	D₄×C₂₃	—	2	2	no	—
281	D₄×C₂₃	—	2	2	no	—
282	D₄×C₂₃	—	4	8	no	—
283	D₄×C₂₃	—	4	1	no	—
284	D₄×C₂₃	—	4	1	no	—
285	D₄×C₂₃	#123	1	4	yes	—
286	C₂×C₄×C₂₃	—	2	1	no	—
287	C₂×C₄×C₂₃	—	2	1	no	—
288	C₂×C₄×C₂₃	—	2	1	no	—
289	C₂×C₄×C₂₃	—	2	1	no	—
290	C₂×C₄×C₂₃	—	2	1	no	—
291	C₂×C₄×C₂₃	—	2	1	no	—
292	C₂×C₄×C₂₃	—	2	2	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	—	4	1	no	—
301	C₂×C₄×C₂₃	—	4	1	no	—
302	C₂×C₄×C₂₃	—	4	1	no	—
303	C₂×C₄×C₂₃	—	4	1	no	—
304	C₂×C₄×C₂₃	—	4	1	no	—
305	C₂×C₄×C₂₃	—	4	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	—	8	4	no	—
322	C₂×C₄×C₂₃	—	8	4	no	—
323	C₂×C₄×C₂₃	C₂×SD₁₆	1	2	yes	—
324	C₂×C₄×C₂₃	C₂×SD₁₆	1	2	yes	—
325	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
326	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
327	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
328	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
329	C₂×C₄×C₂₃	H(5,𝔽₂)	1	1	yes	characteristic
330	C₂×C₄×C₂₃	H(5,𝔽₂)	1	1	yes	characteristic
331	C₈×C₂₃	—	2	2	no	—
332	C₈×C₂₃	—	4	1	no	—
333	C₈×C₂₃	—	4	1	no	—
334	C₈×C₂₃	—	4	1	no	—
335	C₂×#450	C₂×C₂₃	1	1	yes	characteristic
336	C₂×C₄×SD₁₆	C₂×C₂₃	1	1	yes	characteristic, complemented
337	#2423	C₂×C₂₃	1	1	yes	characteristic, complemented
338	D₄×C₂²⋊C₄	C₂×C₂₃	1	1	yes	characteristic
339	#2094	C₂×C₂₃	1	1	yes	characteristic, complemented
340	#2077	C₂×C₂₃	1	1	yes	characteristic, complemented
341	#2055	C₂×C₂₃	1	1	yes	characteristic, complemented
342	#2035	C₂×C₂₃	1	1	yes	characteristic, complemented
343	#1934	C₂×C₂₃	1	1	yes	characteristic, complemented
344	#1923	C₂×C₂₃	1	1	yes	characteristic, complemented
345	#1880	C₂×C₂₃	1	1	yes	characteristic, complemented
346	#1877	C₂×C₂₃	1	1	yes	characteristic, complemented
347	#1864	C₂×C₂₃	1	1	yes	characteristic, complemented
348	#1802	C₂×C₂₃	1	1	yes	characteristic, complemented
349	#1786	C₂×C₂₃	1	1	yes	characteristic
350	C₂²×C₂₃	—	2	2	no	—
351	C₂²×C₂₃	—	2	4	no	—
352	C₂²×C₂₃	—	2	2	no	—
353	C₂²×C₂₃	—	2	2	no	—
354	C₂²×C₂₃	—	4	2	no	—
355	C₂²×C₂₃	—	4	1	no	—
356	C₂²×C₂₃	—	4	2	no	—
357	C₂²×C₂₃	—	4	1	no	—
358	C₂²×C₂₃	—	4	1	no	—
359	C₂²×C₂₃	—	4	2	no	—
360	C₂²×C₂₃	—	4	2	no	—
361	C₂²×C₂₃	—	4	2	no	—
362	C₂²×C₂₃	—	4	1	no	—
363	C₂²×C₂₃	—	4	2	no	—
364	C₂²×C₂₃	—	4	2	no	—
365	C₂²×C₂₃	—	4	2	no	—
366	C₂²×C₂₃	—	4	2	no	—
367	C₂²×C₂₃	—	8	16	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	#525	1	1	yes	characteristic
373	C₂²×C₂₃	D₄²	1	1	yes	characteristic
374	C₂²×C₂₃	#546	1	1	yes	characteristic
375	C₂²×C₂₃	C₂²×SD₁₆	1	1	yes	characteristic
376	C₂²×C₂₃	#575	1	1	yes	characteristic
377	C₂²×C₂₃	#576	1	1	yes	characteristic
378	C₂²×C₂₃	#577	1	1	yes	characteristic
379	C₄×C₂₃	—	2	2	no	—
380	C₄×C₂₃	—	2	2	no	—
381	C₄×C₂₃	—	4	1	no	—
382	C₄×C₂₃	—	4	2	no	—
383	C₄×C₂₃	—	4	1	no	—
384	C₄×C₂₃	—	4	1	no	—
385	C₄×C₂₃	—	8	1	no	—
386	C₄×C₂₃	—	8	1	no	—
387	C₄×C₂₃	—	8	1	no	—
388	C₄×C₂₃	—	8	1	no	—
389	C₄×C₂₃	—	8	1	no	—
390	C₄×C₂₃	C₂×#123	1	1	yes	characteristic
391	C₄×C₂₃	#538	1	1	yes	characteristic
392	C₄×C₂₃	#546	1	1	yes	characteristic
393	C₄×C₂₃	#551	1	1	yes	characteristic
394	C₂³×D₄	C₂²×C₂₃	1	1	yes	characteristic
395	C₂²×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic
396	C₂²×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic
397	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
398	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
399	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
400	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
401	C₂²×C₂²⋊C₄	—	2	1	no	—
402	#450	—	2	4	no	—
403	C₄×SD₁₆	—	2	4	no	—
404	C₂×#106	C₂²×C₂₃	1	1	yes	characteristic, complemented
405	C₂×#106	C₂²×C₂₃	1	1	yes	characteristic, complemented
406	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
407	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic, complemented
408	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic, complemented
409	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
410	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
411	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
412	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
413	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
414	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
415	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
416	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
417	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
418	#399	—	2	1	no	—
419	#398	—	2	1	no	—
420	#391	C₂²×C₂₃	1	1	yes	characteristic, complemented
421	#390	C₂²×C₂₃	1	1	yes	characteristic
422	#390	C₂²×C₂₃	1	1	yes	characteristic
423	#389	C₂²×C₂₃	1	1	yes	characteristic, complemented
424	#388	—	2	1	no	—
425	#387	—	2	1	no	—
426	#386	—	2	1	no	—
427	#386	—	2	1	no	—
428	#384	C₂²×C₂₃	1	1	yes	characteristic, complemented
429	#380	C₂²×C₂₃	1	1	yes	characteristic
430	#380	C₂²×C₂₃	1	1	yes	characteristic
431	#379	—	2	1	no	—
432	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
433	#340	C₂²×C₂₃	1	1	yes	characteristic, complemented
434	#340	C₂²×C₂₃	1	1	yes	characteristic, complemented
435	#340	C₂²×C₂₃	1	1	yes	characteristic, complemented
436	#340	C₂²×C₂₃	1	1	yes	characteristic, complemented
437	#336	C₂²×C₂₃	1	1	yes	characteristic, complemented
438	#336	C₂²×C₂₃	1	1	yes	characteristic, complemented
439	C₂×C₂₃	—	4	2	no	—
440	C₂×C₂₃	—	4	4	no	—
441	C₂×C₂₃	—	8	2	no	—
442	C₂×C₂₃	#2418	1	1	yes	characteristic
443	C₂×C₂₃	#3101	1	1	yes	characteristic
444	C₂×C₂₃	#3118	1	1	yes	characteristic
445	C₂×C₂₃	#3268	1	1	yes	characteristic
446	C₂×C₂₃	D₄×SD₁₆	1	1	yes	characteristic
447	C₂×C₂₃	#3295	1	1	yes	characteristic
448	C₂×C₂₃	#3323	1	1	yes	characteristic
449	C₂⁵	—	2	1	no	—
450	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
451	C₂²×D₄	—	2	2	no	—
452	C₂²×D₄	—	2	2	no	—
453	C₂²×D₄	—	2	2	no	—
454	C₂²×D₄	—	2	2	no	—
455	C₂²×D₄	—	2	1	no	—
456	C₂²×D₄	—	4	1	no	—
457	C₂²×D₄	—	4	1	no	—
458	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
459	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
460	C₂³×C₄	—	2	1	no	—
461	C₂³×C₄	—	2	1	no	—
462	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
463	C₂×SD₁₆	—	2	2	no	—
464	C₂×SD₁₆	—	2	2	no	—
465	C₂×SD₁₆	—	2	2	no	—
466	C₂×SD₁₆	—	2	2	no	—
467	C₂×SD₁₆	—	4	1	no	—
468	C₂×SD₁₆	D₄×C₂₃	1	4	yes	—
469	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
470	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
471	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
472	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
473	C₂²⋊Q₈	—	2	2	no	—
474	C₂²⋊Q₈	—	4	1	no	—
475	C₄×Q₈	—	2	2	no	—
476	C₄×Q₈	—	4	1	no	—
477	C₄×D₄	—	2	2	no	—
478	C₄×D₄	—	2	2	no	—
479	C₄×D₄	—	4	1	no	—
480	C₄×D₄	—	4	1	no	—
481	C₂×C₄⋊C₄	—	2	1	no	—
482	C₂×C₄⋊C₄	—	2	1	no	—
483	C₂×C₄⋊C₄	—	2	1	no	—
484	C₂×C₄⋊C₄	—	2	1	no	—
485	C₂×C₄⋊C₄	—	2	1	no	—
486	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
487	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
488	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
489	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
490	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
491	C₂×C₂²⋊C₄	—	2	1	no	—
492	C₂×C₂²⋊C₄	—	2	1	no	—
493	C₂×C₂²⋊C₄	—	2	1	no	—
494	C₂×C₂²⋊C₄	—	2	1	no	—
495	C₂×C₂²⋊C₄	—	2	1	no	—
496	C₂×C₂²⋊C₄	—	2	1	no	—
497	C₂×C₂²⋊C₄	—	2	1	no	—
498	C₂×C₂²⋊C₄	—	2	1	no	—
499	C₂×C₂²⋊C₄	—	2	1	no	—
500	C₂×C₂²⋊C₄	—	4	4	no	—
501	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
502	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
503	C₂×C₄²	—	2	1	no	—
504	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
505	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
506	#106	—	2	2	no	—
507	#106	—	4	1	no	—
508	C₄⋊C₈	—	4	1	no	—
509	#103	—	2	2	no	—
510	#103	—	4	1	no	—
511	#102	—	2	2	no	—
512	#102	—	2	2	no	—
513	#102	—	2	2	no	—
514	#102	—	2	2	no	—
515	#102	—	2	2	no	—
516	#102	—	4	1	no	—
517	C₂²⋊C₈	—	2	2	no	—
518	C₂²⋊C₈	—	4	1	no	—
519	C₄×C₈	—	2	2	no	—
520	#95	—	2	1	no	—
521	#95	—	2	1	no	—
522	#95	—	2	1	no	—
523	#95	—	2	1	no	—
524	#95	—	2	1	no	—
525	#95	D₄×C₂₃	1	1	yes	characteristic
526	#95	D₄×C₂₃	1	1	yes	characteristic
527	C₂₃	#24901	1	1	yes	characteristic, direct product factor, Sylow
528	C₂⁴	—	2	1	no	—
529	C₂⁴	—	2	4	no	—
530	C₂⁴	—	2	1	no	—
531	C₂⁴	—	4	2	no	—
532	C₂⁴	—	4	2	no	—
533	C₂⁴	—	4	2	no	—
534	C₂⁴	—	4	2	no	—
535	C₂⁴	—	8	1	no	—
536	C₂⁴	—	8	1	no	—
537	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
538	C₂×Q₈	—	2	1	no	—
539	C₂×Q₈	—	2	1	no	—
540	C₂×Q₈	—	2	1	no	—
541	C₂×Q₈	—	2	1	no	—
542	C₂×Q₈	—	2	1	no	—
543	C₂×Q₈	C₂×D₄×C₂₃	1	2	yes	—
544	C₂×D₄	—	2	4	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	—	4	2	no	—
554	C₂×D₄	—	4	2	no	—
555	C₂×D₄	—	4	4	no	—
556	C₂×D₄	—	4	4	no	—
557	C₂×D₄	—	4	4	no	—
558	C₂×D₄	—	4	4	no	—
559	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
560	C₂×D₄	#41×C₂₃	1	2	yes	—
561	C₂×D₄	#41×C₂₃	1	2	yes	—
562	C₂×D₄	#41×C₂₃	1	2	yes	—
563	C₂²×C₄	—	2	1	no	—
564	C₂²×C₄	—	2	1	no	—
565	C₂²×C₄	—	2	1	no	—
566	C₂²×C₄	—	2	1	no	—
567	C₂²×C₄	—	2	1	no	—
568	C₂²×C₄	—	2	1	no	—
569	C₂²×C₄	—	2	1	no	—
570	C₂²×C₄	—	2	1	no	—
571	C₂²×C₄	—	2	1	no	—
572	C₂²×C₄	—	2	1	no	—
573	C₂²×C₄	—	2	1	no	—
574	C₂²×C₄	—	2	1	no	—
575	C₂²×C₄	—	4	2	no	—
576	C₂²×C₄	—	4	2	no	—
577	C₂²×C₄	—	4	2	no	—
578	C₂²×C₄	—	4	2	no	—
579	C₂²×C₄	—	8	1	no	—
580	C₂²×C₄	—	8	1	no	—
581	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
582	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
583	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
584	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
585	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
586	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
587	SD₁₆	—	2	8	no	—
588	SD₁₆	—	4	4	no	—
589	C₂×C₈	—	2	1	no	—
590	C₂×C₈	—	2	1	no	—
591	C₂×C₈	—	2	1	no	—
592	C₂×C₈	—	2	1	no	—
593	C₂×C₈	—	2	1	no	—
594	C₂×C₈	—	2	1	no	—
595	C₂×C₈	—	2	1	no	—
596	C₂×C₈	—	2	1	no	—
597	C₂×C₈	—	2	1	no	—
598	C₂×C₈	—	2	1	no	—
599	C₂×C₈	—	2	1	no	—
600	C₂×C₈	C₂×D₄×C₂₃	1	2	yes	—
601	C₄⋊C₄	—	2	1	no	—
602	C₄⋊C₄	—	2	1	no	—
603	C₄⋊C₄	—	2	1	no	—
604	C₄⋊C₄	—	2	1	no	—
605	C₄⋊C₄	—	2	1	no	—
606	C₄⋊C₄	—	2	1	no	—
607	C₄⋊C₄	—	2	1	no	—
608	C₄⋊C₄	—	2	1	no	—
609	C₄⋊C₄	—	2	1	no	—
610	C₄⋊C₄	—	2	1	no	—
611	C₄⋊C₄	—	4	2	no	—
612	C₄⋊C₄	—	4	2	no	—
613	C₄⋊C₄	—	4	2	no	—
614	C₄⋊C₄	—	8	1	no	—
615	C₄⋊C₄	—	8	1	no	—
616	C₂²⋊C₄	—	4	1	no	—
617	C₂²⋊C₄	—	4	2	no	—
618	C₂²⋊C₄	—	4	2	no	—
619	C₂²⋊C₄	—	4	2	no	—
620	C₂²⋊C₄	—	4	2	no	—
621	C₂²⋊C₄	—	4	2	no	—
622	C₂²⋊C₄	—	4	2	no	—
623	C₂²⋊C₄	—	8	1	no	—
624	C₂²⋊C₄	—	8	1	no	—
625	C₂²⋊C₄	—	8	1	no	—
626	C₂²⋊C₄	SD₁₆×C₂₃	1	4	yes	complemented
627	C₄²	—	2	1	no	—
628	C₄²	—	2	1	no	—
629	C₄²	—	2	1	no	—
630	C₄²	—	2	1	no	—
631	C₄²	—	4	2	no	—
632	C₂³	—	2	1	no	—
633	C₂³	—	2	1	no	—
634	C₂³	—	2	1	no	—
635	C₂³	—	2	1	no	—
636	C₂³	—	2	2	no	—
637	C₂³	—	2	1	no	—
638	C₂³	—	2	2	no	—
639	C₂³	—	2	2	no	—
640	C₂³	—	2	1	no	—
641	C₂³	—	2	2	no	—
642	C₂³	—	4	8	no	—
643	C₂³	—	4	8	no	—
644	C₂³	—	4	1	no	—
645	C₂³	—	4	1	no	—
646	C₂³	—	4	1	no	—
647	C₂³	—	4	1	no	—
648	C₂³	—	4	1	no	—
649	C₂³	—	4	1	no	—
650	C₂³	—	4	1	no	—
651	C₂³	—	4	1	no	—
652	C₂³	—	4	1	no	—
653	C₂³	—	4	1	no	—
654	C₂³	—	8	4	no	—
655	C₂³	—	8	4	no	—
656	C₂³	—	8	4	no	—
657	C₂³	—	8	4	no	—
658	C₂³	—	8	4	no	—
659	C₂³	C₂×SD₁₆×C₂₃	1	2	yes	—
660	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
661	Q₈	—	2	2	no	—
662	Q₈	—	2	2	no	—
663	Q₈	—	4	1	no	—
664	Q₈	—	4	1	no	—
665	D₄	—	2	2	no	—
666	D₄	—	2	2	no	—
667	D₄	—	2	2	no	—
668	D₄	—	2	2	no	—
669	D₄	—	2	2	no	—
670	D₄	—	4	8	no	—
671	D₄	—	4	1	no	—
672	D₄	—	4	1	no	—
673	D₄	C₂₃×#123	1	4	yes	—
674	C₂×C₄	—	2	1	no	—
675	C₂×C₄	—	2	1	no	—
676	C₂×C₄	—	2	1	no	—
677	C₂×C₄	—	2	1	no	—
678	C₂×C₄	—	2	1	no	—
679	C₂×C₄	—	2	1	no	—
680	C₂×C₄	—	2	1	no	—
681	C₂×C₄	—	2	1	no	—
682	C₂×C₄	—	2	1	no	—
683	C₂×C₄	—	2	1	no	—
684	C₂×C₄	—	2	2	no	—
685	C₂×C₄	—	2	1	no	—
686	C₂×C₄	—	2	1	no	—
687	C₂×C₄	—	2	1	no	—
688	C₂×C₄	—	4	1	no	—
689	C₂×C₄	—	4	1	no	—
690	C₂×C₄	—	4	1	no	—
691	C₂×C₄	—	4	1	no	—
692	C₂×C₄	—	4	1	no	—
693	C₂×C₄	—	4	1	no	—
694	C₂×C₄	—	4	1	no	—
695	C₂×C₄	—	4	1	no	—
696	C₂×C₄	—	4	1	no	—
697	C₂×C₄	—	4	1	no	—
698	C₂×C₄	—	4	1	no	—
699	C₂×C₄	—	4	1	no	—
700	C₂×C₄	—	4	1	no	—
701	C₂×C₄	—	4	1	no	—
702	C₂×C₄	—	4	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	—	8	4	no	—
710	C₂×C₄	—	8	4	no	—
711	C₂×C₄	C₂×SD₁₆×C₂₃	1	2	yes	—
712	C₂×C₄	C₂×SD₁₆×C₂₃	1	2	yes	—
713	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
714	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
715	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
716	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
717	C₂×C₄	C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
718	C₂×C₄	C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
719	C₈	—	2	2	no	—
720	C₈	—	4	1	no	—
721	C₈	—	4	1	no	—
722	C₈	—	4	1	no	—
723	C₂²	—	2	4	no	—
724	C₂²	—	2	2	no	—
725	C₂²	—	2	2	no	—
726	C₂²	—	2	2	no	—
727	C₂²	—	4	1	no	—
728	C₂²	—	4	1	no	—
729	C₂²	—	4	2	no	—
730	C₂²	—	4	2	no	—
731	C₂²	—	4	2	no	—
732	C₂²	—	4	1	no	—
733	C₂²	—	4	2	no	—
734	C₂²	—	4	2	no	—
735	C₂²	—	4	1	no	—
736	C₂²	—	4	2	no	—
737	C₂²	—	4	2	no	—
738	C₂²	—	4	2	no	—
739	C₂²	—	4	2	no	—
740	C₂²	—	8	16	no	—
741	C₂²	—	8	1	no	—
742	C₂²	—	8	1	no	—
743	C₂²	—	8	1	no	—
744	C₂²	—	8	1	no	—
745	C₂²	C₂₃×#525	1	1	yes	characteristic
746	C₂²	D₄²×C₂₃	1	1	yes	characteristic
747	C₂²	C₂₃×#546	1	1	yes	characteristic
748	C₂²	C₂²×SD₁₆×C₂₃	1	1	yes	characteristic
749	C₂²	C₂₃×#575	1	1	yes	characteristic
750	C₂²	C₂₃×#576	1	1	yes	characteristic
751	C₂²	C₂₃×#577	1	1	yes	characteristic
752	C₄	—	2	2	no	—
753	C₄	—	2	2	no	—
754	C₄	—	4	1	no	—
755	C₄	—	4	2	no	—
756	C₄	—	4	1	no	—
757	C₄	—	4	1	no	—
758	C₄	—	8	1	no	—
759	C₄	—	8	1	no	—
760	C₄	—	8	1	no	—
761	C₄	—	8	1	no	—
762	C₄	—	8	1	no	—
763	C₄	C₂×C₂₃×#123	1	1	yes	characteristic
764	C₄	C₂₃×#538	1	1	yes	characteristic
765	C₄	C₂₃×#546	1	1	yes	characteristic
766	C₄	C₂₃×#551	1	1	yes	characteristic
767	C₂	—	4	2	no	—
768	C₂	—	4	4	no	—
769	C₂	—	8	2	no	—
770	C₂	C₂₃×#2418	1	1	yes	characteristic
771	C₂	C₂₃×#3101	1	1	yes	characteristic
772	C₂	C₂₃×#3118	1	1	yes	characteristic
773	C₂	C₂₃×#3268	1	1	yes	characteristic
774	C₂	D₄×SD₁₆×C₂₃	1	1	yes	characteristic
775	C₂	C₂₃×#3295	1	1	yes	characteristic
776	C₂	C₂₃×#3323	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₃
prime radical	C₂³×D₄×C₂₃	C₂²
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
2. C₂×C₄×SD₁₆×C₂₃	C₂	semidirect
3. C₂₃×#2423	C₂	semidirect
5. C₂₃×#2094	C₂	semidirect
6. C₂₃×#2077	C₂	semidirect
7. C₂₃×#2055	C₂	semidirect
8. C₂₃×#2035	C₂	semidirect
9. C₂₃×#1934	C₂	semidirect
10. C₂₃×#1923	C₂	semidirect
11. C₂₃×#1880	C₂	semidirect
12. C₂₃×#1877	C₂	semidirect
13. C₂₃×#1864	C₂	semidirect
14. C₂₃×#1802	C₂	semidirect
20. C₂×C₄×Q₈×C₂₃	C₂²	semidirect
26. C₂×C₂₃×#106	C₂²	semidirect
27. C₂×C₂₃×#106	C₂²	semidirect
28. C₂×C₂₃×C₄⋊C₈	C₂²	semidirect
29. C₂×C₂₃×#103	C₂²	semidirect
30. C₂×C₂₃×#103	C₂²	semidirect
39. C₂×C₄×C₈×C₂₃	C₂²	semidirect
42. C₂₃×#391	C₂²	semidirect
45. C₂₃×#389	C₂²	semidirect
50. C₂₃×#384	C₂²	semidirect
55. C₂₃×#340	C₂²	semidirect
56. C₂₃×#340	C₂²	semidirect
57. C₂₃×#340	C₂²	semidirect
58. C₂₃×#340	C₂²	semidirect
59. C₂₃×#336	C₂²	semidirect
60. C₂₃×#336	C₂²	semidirect
237. C₂²⋊C₄×C₂₃	SD₁₆	semidirect
243. #24901	C₂₃	direct (N × H)
336. C₂×C₄×SD₁₆	C₂×C₂₃	semidirect
337. #2423	C₂×C₂₃	semidirect
339. #2094	C₂×C₂₃	semidirect
340. #2077	C₂×C₂₃	semidirect
341. #2055	C₂×C₂₃	semidirect
342. #2035	C₂×C₂₃	semidirect
343. #1934	C₂×C₂₃	semidirect
344. #1923	C₂×C₂₃	semidirect
345. #1880	C₂×C₂₃	semidirect
346. #1877	C₂×C₂₃	semidirect
347. #1864	C₂×C₂₃	semidirect
348. #1802	C₂×C₂₃	semidirect
398. C₂×C₄×Q₈	C₂²×C₂₃	semidirect
404. C₂×#106	C₂²×C₂₃	semidirect
405. C₂×#106	C₂²×C₂₃	semidirect
406. C₂×C₄⋊C₈	C₂²×C₂₃	semidirect
407. C₂×#103	C₂²×C₂₃	semidirect
408. C₂×#103	C₂²×C₂₃	semidirect
417. C₂×C₄×C₈	C₂²×C₂₃	semidirect
420. #391	C₂²×C₂₃	semidirect
423. #389	C₂²×C₂₃	semidirect
428. #384	C₂²×C₂₃	semidirect
433. #340	C₂²×C₂₃	semidirect
434. #340	C₂²×C₂₃	semidirect
435. #340	C₂²×C₂₃	semidirect
436. #340	C₂²×C₂₃	semidirect
437. #336	C₂²×C₂₃	semidirect
438. #336	C₂²×C₂₃	semidirect
527. C₂₃	#24901	direct (N × H)
626. C₂²⋊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×#450	2
C₂×C₄×SD₁₆×C₂₃	2
C₂₃×#2423	2
D₄×C₂²⋊C₄×C₂₃	2
C₂₃×#2094	2
C₂₃×#2077	2
C₂₃×#2055	2
C₂₃×#2035	2
C₂₃×#1934	2
C₂₃×#1923	2
C₂₃×#1880	2
C₂₃×#1877	2
C₂₃×#1864	2
C₂₃×#1802	2
C₂₃×#1786	2
#24901	23

Subgroups — C23×#24901 #19172527

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#24901 #19172527