Subgroups — C₂₃×#18962 #19166588

Order 5888.

964 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3546	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₃×#3253	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3247	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#3207	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#1638	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#1635	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#1631	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#1629	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#1628	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#1625	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#1621	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#1619	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#1547	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#1495	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#1480	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₃×#560	—	2	2	no	—
17	C₂₃×#556	C₂²	1	1	yes	characteristic
18	C₂₃×#553	—	2	1	no	—
19	C₂₃×#550	—	2	1	no	—
20	C₂₃×#550	C₂²	1	1	yes	characteristic
21	C₂₃×#547	C₂²	1	1	yes	characteristic
22	C₂₃×#546	—	2	1	no	—
23	C₂₃×#546	—	2	1	no	—
24	D₄²×C₂₃	C₂²	1	1	yes	characteristic
25	C₂₃×#542	—	2	1	no	—
26	C₂₃×#538	—	2	2	no	—
27	C₂₃×#537	—	2	1	no	—
28	C₂₃×#535	—	2	1	no	—
29	C₂₃×#535	—	2	1	no	—
30	C₂₃×#532	C₂²	1	1	yes	characteristic
31	C₂₃×#532	C₂²	1	1	yes	characteristic
32	C₂₃×#532	C₂²	1	1	yes	characteristic, complemented
33	C₂₃×#529	C₂²	1	1	yes	characteristic
34	C₂₃×#493	C₂²	1	1	yes	characteristic
35	C₂₃×#492	C₂²	1	1	yes	characteristic
36	C₂₃×#487	C₂²	1	1	yes	characteristic, complemented
37	C₂₃×#486	C₂²	1	1	yes	characteristic, complemented
38	C₂₃×#478	—	2	1	no	—
39	C₂₃×#477	C₂²	1	1	yes	characteristic, complemented
40	C₂₃×#476	—	2	1	no	—
41	C₂₃×#476	C₂²	1	1	yes	characteristic
42	C₂₃×#476	C₂²	1	1	yes	characteristic
43	C₂₃×#476	C₂²	1	1	yes	characteristic, complemented
44	C₂₃×#469	—	2	1	no	—
45	C₂₃×#469	—	2	1	no	—
46	C₂₃×#466	—	2	1	no	—
47	C₂₃×#465	—	2	1	no	—
48	C₂₃×#463	—	2	1	no	—
49	C₂₃×#463	—	2	2	no	—
50	C₂₃×#460	C₂²	1	1	yes	characteristic, complemented
51	C₂₃×#459	—	2	1	no	—
52	C₂₃×#459	C₂²	1	1	yes	characteristic
53	C₂₃×#459	C₂²	1	1	yes	characteristic
54	C₂₃×#459	C₂²	1	1	yes	characteristic, complemented
55	C₂₃×#449	—	2	2	no	—
56	C₂₃×#431	C₂²	1	1	yes	characteristic, complemented
57	C₂₃×#423	C₂²	1	1	yes	characteristic, complemented
58	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
59	C₂₃×#332	C₂²	1	1	yes	characteristic, complemented
60	C₂₃×#332	C₂²	1	1	yes	characteristic, complemented
61	C₂₃×#331	C₂²	1	1	yes	characteristic
62	C₂₃×#331	C₂²	1	1	yes	characteristic
63	C₂₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic, complemented
64	C₂₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic, complemented
65	C₂₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
66	C₂₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
67	C₂₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
68	C₂₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
69	C₂₃×D₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
70	C₂₃×D₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
71	C₂×#41×C₂₃	—	2	1	no	—
72	C₂×#41×C₂₃	—	2	1	no	—
73	C₂×#41×C₂₃	—	2	1	no	—
74	C₂×#41×C₂₃	—	2	1	no	—
75	C₂×#41×C₂₃	—	2	1	no	—
76	C₂²×D₄×C₂₃	—	2	1	no	—
77	C₂²×D₄×C₂₃	—	2	1	no	—
78	C₂×SD₁₆×C₂₃	—	2	1	no	—
79	C₂×SD₁₆×C₂₃	—	2	2	no	—
80	C₂×D₈×C₂₃	—	2	2	no	—
81	C₂×D₈×C₂₃	—	2	1	no	—
82	C₂×D₈×C₂₃	—	2	1	no	—
83	C₂×D₈×C₂₃	—	2	1	no	—
84	C₂×M₁₆×C₂₃	—	2	1	no	—
85	C₂²×C₈×C₂₃	—	2	1	no	—
86	C₂₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
87	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
88	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
89	C₂₃×#127	—	2	2	no	—
90	C₂₃×#127	—	2	1	no	—
91	C₂₃×#127	D₄	1	1	yes	characteristic
92	C₂₃×#127	C₂³	1	1	yes	characteristic
93	C₂₃×#127	C₂³	1	1	yes	characteristic
94	C₂₃×#126	—	2	2	no	—
95	C₂₃×#126	—	2	2	no	—
96	C₂₃×#126	—	2	1	no	—
97	C₂₃×#125	D₄	1	1	yes	characteristic
98	C₂₃×#124	—	2	2	no	—
99	C₂₃×#124	—	2	1	no	—
100	C₂₃×#124	—	2	1	no	—
101	C₂₃×#124	—	2	1	no	—
102	C₂₃×#124	—	2	1	no	—
103	C₂₃×#124	D₄	1	1	yes	characteristic
104	C₂₃×#123	—	2	2	no	—
105	C₂₃×#123	—	2	2	no	—
106	C₂₃×#123	—	2	1	no	—
107	C₂₃×#123	—	2	2	no	—
108	C₂₃×C₂²⋊Q₈	—	2	2	no	—
109	C₂₃×C₂²⋊Q₈	—	2	1	no	—
110	C₂₃×C₂²⋊Q₈	—	2	1	no	—
111	C₂₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
112	C₂₃×#121	—	2	2	no	—
113	C₂₃×#121	—	2	2	no	—
114	C₂₃×#121	—	2	2	no	—
115	C₂₃×#121	—	2	2	no	—
116	C₂₃×#121	—	2	2	no	—
117	C₂₃×#121	—	2	1	no	—
118	C₂₃×#121	—	2	2	no	—
119	C₂₃×#121	—	2	1	no	—
120	C₂₃×#121	—	2	1	no	—
121	C₂₃×#121	—	2	1	no	—
122	C₂₃×#121	—	2	1	no	—
123	C₂₃×#121	—	2	1	no	—
124	C₂₃×#121	—	2	1	no	—
125	C₂₃×#121	—	2	1	no	—
126	C₂₃×#121	D₄	1	1	yes	characteristic
127	C₂₃×#121	D₄	1	2	yes	—
128	C₂₃×#121	D₄	1	1	yes	characteristic
129	C₂₃×#121	D₄	1	1	yes	characteristic
130	C₂₃×#120	—	2	2	no	—
131	C₂₃×#120	—	2	2	no	—
132	C₂₃×#120	—	2	2	no	—
133	C₂₃×#120	—	2	2	no	—
134	C₄×Q₈×C₂₃	—	2	1	no	—
135	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
136	C₄×D₄×C₂₃	—	2	2	no	—
137	C₄×D₄×C₂₃	—	2	1	no	—
138	C₄×D₄×C₂₃	—	2	1	no	—
139	C₄×D₄×C₂₃	—	2	1	no	—
140	C₄×D₄×C₂₃	—	2	1	no	—
141	C₄×D₄×C₂₃	—	2	1	no	—
142	C₄×D₄×C₂₃	—	2	1	no	—
143	C₄×D₄×C₂₃	D₄	1	2	yes	—
144	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
145	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
146	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
147	C₂₃×#117	—	2	1	no	—
148	C₂₃×#117	—	2	1	no	—
149	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
150	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
151	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
152	C₂₃×#107	—	2	1	no	—
153	C₂₃×#106	—	2	1	no	—
154	C₂₃×#106	—	2	1	no	—
155	C₂₃×#106	—	2	1	no	—
156	C₂₃×C₄⋊C₈	—	2	1	no	—
157	C₂₃×C₄⋊C₈	—	2	1	no	—
158	C₂₃×C₄⋊C₈	—	2	1	no	—
159	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
160	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
161	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
162	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
163	C₂₃×#103	—	2	1	no	—
164	C₂₃×#103	—	2	2	no	—
165	C₂₃×#102	—	2	1	no	—
166	C₂₃×#102	—	2	1	no	—
167	C₂₃×#102	—	2	1	no	—
168	C₂₃×#102	—	2	2	no	—
169	C₂₃×#102	—	2	1	no	—
170	C₂₃×#102	—	2	1	no	—
171	C₂₃×#102	—	2	1	no	—
172	C₂₃×#102	—	2	1	no	—
173	C₂₃×C₂²⋊C₈	—	2	1	no	—
174	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
175	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
176	C₂⁴×C₂₃	—	2	2	no	—
177	#41×C₂₃	—	8	1	no	—
178	#41×C₂₃	—	8	1	no	—
179	#41×C₂₃	—	8	1	no	—
180	#41×C₂₃	—	8	1	no	—
181	#41×C₂₃	—	8	1	no	—
182	#41×C₂₃	—	8	1	no	—
183	#41×C₂₃	—	8	1	no	—
184	#41×C₂₃	—	8	1	no	—
185	#41×C₂₃	—	8	2	no	—
186	C₂×Q₈×C₂₃	—	2	1	no	—
187	C₂×Q₈×C₂₃	—	2	1	no	—
188	C₂×Q₈×C₂₃	—	2	1	no	—
189	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
190	C₂×D₄×C₂₃	—	2	2	no	—
191	C₂×D₄×C₂₃	—	2	2	no	—
192	C₂×D₄×C₂₃	—	2	2	no	—
193	C₂×D₄×C₂₃	—	2	2	no	—
194	C₂×D₄×C₂₃	—	2	2	no	—
195	C₂×D₄×C₂₃	—	2	1	no	—
196	C₂×D₄×C₂₃	—	2	1	no	—
197	C₂×D₄×C₂₃	—	2	2	no	—
198	C₂×D₄×C₂₃	—	2	1	no	—
199	C₂×D₄×C₂₃	—	2	1	no	—
200	C₂×D₄×C₂₃	—	2	1	no	—
201	C₂×D₄×C₂₃	—	2	1	no	—
202	C₂×D₄×C₂₃	—	2	1	no	—
203	C₂×D₄×C₂₃	—	2	1	no	—
204	C₂×D₄×C₂₃	—	2	1	no	—
205	C₂×D₄×C₂₃	—	2	1	no	—
206	C₂×D₄×C₂₃	—	4	1	no	—
207	C₂×D₄×C₂₃	—	8	1	no	—
208	C₂×D₄×C₂₃	—	8	1	no	—
209	C₂×D₄×C₂₃	—	8	1	no	—
210	C₂×D₄×C₂₃	—	8	1	no	—
211	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
212	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
213	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
214	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
215	C₂²×C₄×C₂₃	—	2	2	no	—
216	C₂²×C₄×C₂₃	—	2	2	no	—
217	C₂²×C₄×C₂₃	—	2	1	no	—
218	C₂²×C₄×C₂₃	—	2	1	no	—
219	C₂²×C₄×C₂₃	—	2	1	no	—
220	C₂²×C₄×C₂₃	—	2	2	no	—
221	C₂²×C₄×C₂₃	—	4	1	no	—
222	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
223	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
224	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
225	SD₁₆×C₂₃	—	8	1	no	—
226	SD₁₆×C₂₃	—	8	2	no	—
227	D₈×C₂₃	—	8	1	no	—
228	D₈×C₂₃	—	8	1	no	—
229	D₈×C₂₃	—	8	1	no	—
230	D₈×C₂₃	—	8	2	no	—
231	M₁₆×C₂₃	—	8	1	no	—
232	C₂×C₈×C₂₃	—	2	1	no	—
233	C₂×C₈×C₂₃	—	2	1	no	—
234	C₂×C₈×C₂₃	—	2	1	no	—
235	C₂×C₈×C₂₃	—	2	1	no	—
236	C₂×C₈×C₂₃	—	2	1	no	—
237	C₂×C₈×C₂₃	—	2	1	no	—
238	C₂×C₈×C₂₃	—	8	1	no	—
239	C₄⋊C₄×C₂₃	—	2	2	no	—
240	C₄⋊C₄×C₂₃	—	2	2	no	—
241	C₄⋊C₄×C₂₃	—	2	1	no	—
242	C₄⋊C₄×C₂₃	—	2	1	no	—
243	C₄⋊C₄×C₂₃	—	2	1	no	—
244	C₄⋊C₄×C₂₃	—	2	1	no	—
245	C₄⋊C₄×C₂₃	—	2	1	no	—
246	C₄⋊C₄×C₂₃	—	2	1	no	—
247	C₄⋊C₄×C₂₃	—	2	1	no	—
248	C₄⋊C₄×C₂₃	—	2	1	no	—
249	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
250	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
251	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
252	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
253	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
254	C₂²⋊C₄×C₂₃	—	2	2	no	—
255	C₂²⋊C₄×C₂₃	—	2	2	no	—
256	C₂²⋊C₄×C₂₃	—	2	2	no	—
257	C₂²⋊C₄×C₂₃	—	2	2	no	—
258	C₂²⋊C₄×C₂₃	—	2	2	no	—
259	C₂²⋊C₄×C₂₃	—	2	1	no	—
260	C₂²⋊C₄×C₂₃	—	2	1	no	—
261	C₂²⋊C₄×C₂₃	—	2	1	no	—
262	C₂²⋊C₄×C₂₃	—	2	1	no	—
263	C₂²⋊C₄×C₂₃	—	2	1	no	—
264	C₂²⋊C₄×C₂₃	—	2	1	no	—
265	C₂²⋊C₄×C₂₃	—	2	2	no	—
266	C₂²⋊C₄×C₂₃	—	2	2	no	—
267	C₂²⋊C₄×C₂₃	—	2	1	no	—
268	C₂²⋊C₄×C₂₃	—	2	1	no	—
269	C₂²⋊C₄×C₂₃	—	2	1	no	—
270	C₂²⋊C₄×C₂₃	—	4	1	no	—
271	C₂²⋊C₄×C₂₃	—	4	1	no	—
272	C₄²×C₂₃	—	2	2	no	—
273	C₄²×C₂₃	—	2	1	no	—
274	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
275	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
276	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
277	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
278	#18962	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
279	C₂³×C₂₃	—	2	1	no	—
280	C₂³×C₂₃	—	2	1	no	—
281	C₂³×C₂₃	—	2	2	no	—
282	C₂³×C₂₃	—	2	1	no	—
283	C₂³×C₂₃	—	4	1	no	—
284	C₂³×C₂₃	—	8	2	no	—
285	C₂³×C₂₃	—	8	2	no	—
286	C₂³×C₂₃	—	8	2	no	—
287	C₂³×C₂₃	#120	1	1	yes	characteristic
288	Q₈×C₂₃	—	2	1	no	—
289	Q₈×C₂₃	—	2	1	no	—
290	Q₈×C₂₃	—	4	2	no	—
291	Q₈×C₂₃	—	4	1	no	—
292	Q₈×C₂₃	—	4	1	no	—
293	Q₈×C₂₃	—	8	1	no	—
294	D₄×C₂₃	—	2	1	no	—
295	D₄×C₂₃	—	2	1	no	—
296	D₄×C₂₃	—	2	1	no	—
297	D₄×C₂₃	—	2	1	no	—
298	D₄×C₂₃	—	2	1	no	—
299	D₄×C₂₃	—	2	1	no	—
300	D₄×C₂₃	—	4	2	no	—
301	D₄×C₂₃	—	4	2	no	—
302	D₄×C₂₃	—	4	1	no	—
303	D₄×C₂₃	—	4	1	no	—
304	D₄×C₂₃	—	4	1	no	—
305	D₄×C₂₃	—	4	1	no	—
306	D₄×C₂₃	—	4	1	no	—
307	D₄×C₂₃	—	4	1	no	—
308	D₄×C₂₃	—	4	1	no	—
309	D₄×C₂₃	—	4	1	no	—
310	D₄×C₂₃	—	8	1	no	—
311	D₄×C₂₃	—	8	1	no	—
312	D₄×C₂₃	—	8	1	no	—
313	D₄×C₂₃	—	8	1	no	—
314	D₄×C₂₃	—	8	1	no	—
315	D₄×C₂₃	—	8	2	no	—
316	D₄×C₂₃	—	8	2	no	—
317	D₄×C₂₃	—	8	2	no	—
318	D₄×C₂₃	—	8	2	no	—
319	D₄×C₂₃	—	8	2	no	—
320	D₄×C₂₃	—	8	2	no	—
321	D₄×C₂₃	—	8	2	no	—
322	C₂×C₄×C₂₃	—	2	1	no	—
323	C₂×C₄×C₂₃	—	2	1	no	—
324	C₂×C₄×C₂₃	—	2	1	no	—
325	C₂×C₄×C₂₃	—	2	1	no	—
326	C₂×C₄×C₂₃	—	2	1	no	—
327	C₂×C₄×C₂₃	—	2	1	no	—
328	C₂×C₄×C₂₃	—	2	1	no	—
329	C₂×C₄×C₂₃	—	2	2	no	—
330	C₂×C₄×C₂₃	—	2	1	no	—
331	C₂×C₄×C₂₃	—	2	1	no	—
332	C₂×C₄×C₂₃	—	4	1	no	—
333	C₂×C₄×C₂₃	—	4	1	no	—
334	C₂×C₄×C₂₃	—	4	1	no	—
335	C₂×C₄×C₂₃	—	4	1	no	—
336	C₂×C₄×C₂₃	—	4	1	no	—
337	C₂×C₄×C₂₃	—	4	1	no	—
338	C₂×C₄×C₂₃	—	4	1	no	—
339	C₂×C₄×C₂₃	—	4	1	no	—
340	C₂×C₄×C₂₃	—	8	2	no	—
341	C₂×C₄×C₂₃	—	8	2	no	—
342	C₂×C₄×C₂₃	—	8	2	no	—
343	C₂×C₄×C₂₃	—	8	2	no	—
344	C₂×C₄×C₂₃	#120	1	1	yes	characteristic
345	C₂×C₄×C₂₃	#120	1	1	yes	characteristic
346	C₂×C₄×C₂₃	#120	1	1	yes	characteristic
347	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
348	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
349	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
350	C₈×C₂₃	—	4	1	no	—
351	C₈×C₂₃	—	4	1	no	—
352	C₈×C₂₃	—	4	1	no	—
353	C₈×C₂₃	—	4	1	no	—
354	C₈×C₂₃	—	4	1	no	—
355	C₈×C₂₃	—	4	1	no	—
356	#3546	C₂×C₂₃	1	1	yes	characteristic, complemented
357	#3253	C₂×C₂₃	1	1	yes	characteristic, complemented
358	#3247	C₂×C₂₃	1	1	yes	characteristic, complemented
359	#3207	C₂×C₂₃	1	1	yes	characteristic, complemented
360	#1638	C₂×C₂₃	1	1	yes	characteristic, complemented
361	#1635	C₂×C₂₃	1	1	yes	characteristic, complemented
362	#1631	C₂×C₂₃	1	1	yes	characteristic, complemented
363	#1629	C₂×C₂₃	1	1	yes	characteristic, complemented
364	#1628	C₂×C₂₃	1	1	yes	characteristic, complemented
365	#1625	C₂×C₂₃	1	1	yes	characteristic, complemented
366	#1621	C₂×C₂₃	1	1	yes	characteristic, complemented
367	#1619	C₂×C₂₃	1	1	yes	characteristic, complemented
368	#1547	C₂×C₂₃	1	1	yes	characteristic, complemented
369	#1495	C₂×C₂₃	1	1	yes	characteristic, complemented
370	#1480	C₂×C₂₃	1	1	yes	characteristic, complemented
371	C₂²×C₂₃	—	2	1	no	—
372	C₂²×C₂₃	—	2	1	no	—
373	C₂²×C₂₃	—	2	1	no	—
374	C₂²×C₂₃	—	4	1	no	—
375	C₂²×C₂₃	—	4	1	no	—
376	C₂²×C₂₃	—	4	1	no	—
377	C₂²×C₂₃	—	4	1	no	—
378	C₂²×C₂₃	—	4	2	no	—
379	C₂²×C₂₃	—	4	2	no	—
380	C₂²×C₂₃	—	4	1	no	—
381	C₂²×C₂₃	—	4	1	no	—
382	C₂²×C₂₃	—	4	2	no	—
383	C₂²×C₂₃	—	4	1	no	—
384	C₂²×C₂₃	—	4	1	no	—
385	C₂²×C₂₃	—	4	1	no	—
386	C₂²×C₂₃	—	8	1	no	—
387	C₂²×C₂₃	—	8	1	no	—
388	C₂²×C₂₃	—	8	1	no	—
389	C₂²×C₂₃	—	16	4	no	—
390	C₂²×C₂₃	C₂×#120	1	1	yes	characteristic
391	C₄×C₂₃	—	2	1	no	—
392	C₄×C₂₃	—	2	1	no	—
393	C₄×C₂₃	—	2	1	no	—
394	C₄×C₂₃	—	2	1	no	—
395	C₄×C₂₃	—	4	1	no	—
396	C₄×C₂₃	—	4	1	no	—
397	C₄×C₂₃	—	4	1	no	—
398	C₄×C₂₃	—	4	1	no	—
399	C₄×C₂₃	—	4	2	no	—
400	C₄×C₂₃	—	4	1	no	—
401	C₄×C₂₃	—	8	1	no	—
402	C₄×C₂₃	#576	1	1	yes	characteristic
403	C₄×C₂₃	#576	1	1	yes	characteristic
404	C₄×C₂₃	#577	1	1	yes	characteristic
405	C₄×C₂₃	#577	1	1	yes	characteristic
406	#560	—	2	2	no	—
407	#556	C₂²×C₂₃	1	1	yes	characteristic
408	#553	—	2	1	no	—
409	#550	—	2	1	no	—
410	#550	C₂²×C₂₃	1	1	yes	characteristic
411	#547	C₂²×C₂₃	1	1	yes	characteristic
412	#546	—	2	1	no	—
413	#546	—	2	1	no	—
414	D₄²	C₂²×C₂₃	1	1	yes	characteristic
415	#542	—	2	1	no	—
416	#538	—	2	2	no	—
417	#537	—	2	1	no	—
418	#535	—	2	1	no	—
419	#535	—	2	1	no	—
420	#532	C₂²×C₂₃	1	1	yes	characteristic
421	#532	C₂²×C₂₃	1	1	yes	characteristic
422	#532	C₂²×C₂₃	1	1	yes	characteristic, complemented
423	#529	C₂²×C₂₃	1	1	yes	characteristic
424	#493	C₂²×C₂₃	1	1	yes	characteristic
425	#492	C₂²×C₂₃	1	1	yes	characteristic
426	#487	C₂²×C₂₃	1	1	yes	characteristic, complemented
427	#486	C₂²×C₂₃	1	1	yes	characteristic, complemented
428	#478	—	2	1	no	—
429	#477	C₂²×C₂₃	1	1	yes	characteristic, complemented
430	#476	—	2	1	no	—
431	#476	C₂²×C₂₃	1	1	yes	characteristic
432	#476	C₂²×C₂₃	1	1	yes	characteristic
433	#476	C₂²×C₂₃	1	1	yes	characteristic, complemented
434	#469	—	2	1	no	—
435	#469	—	2	1	no	—
436	#466	—	2	1	no	—
437	#465	—	2	1	no	—
438	#463	—	2	1	no	—
439	#463	—	2	2	no	—
440	#460	C₂²×C₂₃	1	1	yes	characteristic, complemented
441	#459	—	2	1	no	—
442	#459	C₂²×C₂₃	1	1	yes	characteristic
443	#459	C₂²×C₂₃	1	1	yes	characteristic
444	#459	C₂²×C₂₃	1	1	yes	characteristic, complemented
445	#449	—	2	2	no	—
446	#431	C₂²×C₂₃	1	1	yes	characteristic, complemented
447	#423	C₂²×C₂₃	1	1	yes	characteristic, complemented
448	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
449	#332	C₂²×C₂₃	1	1	yes	characteristic, complemented
450	#332	C₂²×C₂₃	1	1	yes	characteristic, complemented
451	#331	C₂²×C₂₃	1	1	yes	characteristic
452	#331	C₂²×C₂₃	1	1	yes	characteristic
453	Q₈⋊C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
454	Q₈⋊C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
455	D₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
456	D₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
457	D₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
458	D₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
459	D₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
460	D₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
461	C₂×C₂₃	—	4	1	no	—
462	C₂×C₂₃	—	8	1	no	—
463	C₂×C₂₃	—	8	2	no	—
464	C₂×C₂₃	—	8	1	no	—
465	C₂×C₂₃	—	8	1	no	—
466	C₂×C₂₃	—	16	1	no	—
467	C₂×C₂₃	#3012	1	1	yes	characteristic
468	C₂×C₂₃	#3012	1	1	yes	characteristic
469	C₂×C₂₃	#3021	1	1	yes	characteristic
470	C₂×#41	—	2	1	no	—
471	C₂×#41	—	2	1	no	—
472	C₂×#41	—	2	1	no	—
473	C₂×#41	—	2	1	no	—
474	C₂×#41	—	2	1	no	—
475	C₂²×D₄	—	2	1	no	—
476	C₂²×D₄	—	2	1	no	—
477	C₂×SD₁₆	—	2	1	no	—
478	C₂×SD₁₆	—	2	2	no	—
479	C₂×D₈	—	2	2	no	—
480	C₂×D₈	—	2	1	no	—
481	C₂×D₈	—	2	1	no	—
482	C₂×D₈	—	2	1	no	—
483	C₂×M₁₆	—	2	1	no	—
484	C₂²×C₈	—	2	1	no	—
485	C₄⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
486	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
487	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
488	#127	—	2	2	no	—
489	#127	—	2	1	no	—
490	#127	D₄×C₂₃	1	1	yes	characteristic
491	#127	C₂³×C₂₃	1	1	yes	characteristic
492	#127	C₂³×C₂₃	1	1	yes	characteristic
493	#126	—	2	2	no	—
494	#126	—	2	2	no	—
495	#126	—	2	1	no	—
496	#125	D₄×C₂₃	1	1	yes	characteristic
497	#124	—	2	2	no	—
498	#124	—	2	1	no	—
499	#124	—	2	1	no	—
500	#124	—	2	1	no	—
501	#124	—	2	1	no	—
502	#124	D₄×C₂₃	1	1	yes	characteristic
503	#123	—	2	2	no	—
504	#123	—	2	2	no	—
505	#123	—	2	1	no	—
506	#123	—	2	2	no	—
507	C₂²⋊Q₈	—	2	2	no	—
508	C₂²⋊Q₈	—	2	1	no	—
509	C₂²⋊Q₈	—	2	1	no	—
510	C₂²⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
511	#121	—	2	2	no	—
512	#121	—	2	2	no	—
513	#121	—	2	2	no	—
514	#121	—	2	2	no	—
515	#121	—	2	2	no	—
516	#121	—	2	1	no	—
517	#121	—	2	2	no	—
518	#121	—	2	1	no	—
519	#121	—	2	1	no	—
520	#121	—	2	1	no	—
521	#121	—	2	1	no	—
522	#121	—	2	1	no	—
523	#121	—	2	1	no	—
524	#121	—	2	1	no	—
525	#121	D₄×C₂₃	1	1	yes	characteristic
526	#121	D₄×C₂₃	1	1	yes	characteristic
527	#121	D₄×C₂₃	1	1	yes	characteristic
528	#121	D₄×C₂₃	1	2	yes	—
529	#120	—	2	2	no	—
530	#120	—	2	2	no	—
531	#120	—	2	2	no	—
532	#120	—	2	2	no	—
533	C₄×Q₈	—	2	1	no	—
534	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
535	C₄×D₄	—	2	2	no	—
536	C₄×D₄	—	2	1	no	—
537	C₄×D₄	—	2	1	no	—
538	C₄×D₄	—	2	1	no	—
539	C₄×D₄	—	2	1	no	—
540	C₄×D₄	—	2	1	no	—
541	C₄×D₄	—	2	1	no	—
542	C₄×D₄	D₄×C₂₃	1	2	yes	—
543	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
544	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
545	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
546	#117	—	2	1	no	—
547	#117	—	2	1	no	—
548	C₂×C₄⋊C₄	—	2	1	no	—
549	C₂×C₂²⋊C₄	—	2	2	no	—
550	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
551	#107	—	2	1	no	—
552	#106	—	2	1	no	—
553	#106	—	2	1	no	—
554	#106	—	2	1	no	—
555	C₄⋊C₈	—	2	1	no	—
556	C₄⋊C₈	—	2	1	no	—
557	C₄⋊C₈	—	2	1	no	—
558	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
559	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
560	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
561	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
562	#103	—	2	1	no	—
563	#103	—	2	2	no	—
564	#102	—	2	1	no	—
565	#102	—	2	1	no	—
566	#102	—	2	1	no	—
567	#102	—	2	2	no	—
568	#102	—	2	1	no	—
569	#102	—	2	1	no	—
570	#102	—	2	1	no	—
571	#102	—	2	1	no	—
572	C₂²⋊C₈	—	2	1	no	—
573	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
574	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
575	C₂₃	#18962	1	1	yes	characteristic, direct product factor, Sylow
576	C₂⁴	—	2	2	no	—
577	#41	—	8	1	no	—
578	#41	—	8	1	no	—
579	#41	—	8	1	no	—
580	#41	—	8	1	no	—
581	#41	—	8	1	no	—
582	#41	—	8	1	no	—
583	#41	—	8	1	no	—
584	#41	—	8	1	no	—
585	#41	—	8	2	no	—
586	C₂×Q₈	—	2	1	no	—
587	C₂×Q₈	—	2	1	no	—
588	C₂×Q₈	—	2	1	no	—
589	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
590	C₂×D₄	—	2	2	no	—
591	C₂×D₄	—	2	2	no	—
592	C₂×D₄	—	2	2	no	—
593	C₂×D₄	—	2	2	no	—
594	C₂×D₄	—	2	2	no	—
595	C₂×D₄	—	2	1	no	—
596	C₂×D₄	—	2	1	no	—
597	C₂×D₄	—	2	2	no	—
598	C₂×D₄	—	2	1	no	—
599	C₂×D₄	—	2	1	no	—
600	C₂×D₄	—	2	1	no	—
601	C₂×D₄	—	2	1	no	—
602	C₂×D₄	—	2	1	no	—
603	C₂×D₄	—	2	1	no	—
604	C₂×D₄	—	2	1	no	—
605	C₂×D₄	—	2	1	no	—
606	C₂×D₄	—	4	1	no	—
607	C₂×D₄	—	8	1	no	—
608	C₂×D₄	—	8	1	no	—
609	C₂×D₄	—	8	1	no	—
610	C₂×D₄	—	8	1	no	—
611	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
612	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
613	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
614	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
615	C₂²×C₄	—	2	2	no	—
616	C₂²×C₄	—	2	2	no	—
617	C₂²×C₄	—	2	1	no	—
618	C₂²×C₄	—	2	1	no	—
619	C₂²×C₄	—	2	1	no	—
620	C₂²×C₄	—	2	2	no	—
621	C₂²×C₄	—	4	1	no	—
622	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
623	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
624	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
625	SD₁₆	—	8	1	no	—
626	SD₁₆	—	8	2	no	—
627	D₈	—	8	1	no	—
628	D₈	—	8	1	no	—
629	D₈	—	8	1	no	—
630	D₈	—	8	2	no	—
631	M₁₆	—	8	1	no	—
632	C₂×C₈	—	2	1	no	—
633	C₂×C₈	—	2	1	no	—
634	C₂×C₈	—	2	1	no	—
635	C₂×C₈	—	2	1	no	—
636	C₂×C₈	—	2	1	no	—
637	C₂×C₈	—	2	1	no	—
638	C₂×C₈	—	8	1	no	—
639	C₄⋊C₄	—	2	2	no	—
640	C₄⋊C₄	—	2	2	no	—
641	C₄⋊C₄	—	2	1	no	—
642	C₄⋊C₄	—	2	1	no	—
643	C₄⋊C₄	—	2	1	no	—
644	C₄⋊C₄	—	2	1	no	—
645	C₄⋊C₄	—	2	1	no	—
646	C₄⋊C₄	—	2	1	no	—
647	C₄⋊C₄	—	2	1	no	—
648	C₄⋊C₄	—	2	1	no	—
649	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
650	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
651	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
652	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
653	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
654	C₂²⋊C₄	—	2	2	no	—
655	C₂²⋊C₄	—	2	2	no	—
656	C₂²⋊C₄	—	2	2	no	—
657	C₂²⋊C₄	—	2	2	no	—
658	C₂²⋊C₄	—	2	2	no	—
659	C₂²⋊C₄	—	2	1	no	—
660	C₂²⋊C₄	—	2	1	no	—
661	C₂²⋊C₄	—	2	1	no	—
662	C₂²⋊C₄	—	2	1	no	—
663	C₂²⋊C₄	—	2	1	no	—
664	C₂²⋊C₄	—	2	1	no	—
665	C₂²⋊C₄	—	2	2	no	—
666	C₂²⋊C₄	—	2	2	no	—
667	C₂²⋊C₄	—	2	1	no	—
668	C₂²⋊C₄	—	2	1	no	—
669	C₂²⋊C₄	—	2	1	no	—
670	C₂²⋊C₄	—	4	1	no	—
671	C₂²⋊C₄	—	4	1	no	—
672	C₄²	—	2	2	no	—
673	C₄²	—	2	1	no	—
674	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
675	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
676	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
677	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
678	C₂³	—	2	1	no	—
679	C₂³	—	2	1	no	—
680	C₂³	—	2	2	no	—
681	C₂³	—	2	1	no	—
682	C₂³	—	4	1	no	—
683	C₂³	—	8	2	no	—
684	C₂³	—	8	2	no	—
685	C₂³	—	8	2	no	—
686	C₂³	C₂₃×#120	1	1	yes	characteristic
687	Q₈	—	2	1	no	—
688	Q₈	—	2	1	no	—
689	Q₈	—	4	2	no	—
690	Q₈	—	4	1	no	—
691	Q₈	—	4	1	no	—
692	Q₈	—	8	1	no	—
693	D₄	—	2	1	no	—
694	D₄	—	2	1	no	—
695	D₄	—	2	1	no	—
696	D₄	—	2	1	no	—
697	D₄	—	2	1	no	—
698	D₄	—	2	1	no	—
699	D₄	—	4	2	no	—
700	D₄	—	4	2	no	—
701	D₄	—	4	1	no	—
702	D₄	—	4	1	no	—
703	D₄	—	4	1	no	—
704	D₄	—	4	1	no	—
705	D₄	—	4	1	no	—
706	D₄	—	4	1	no	—
707	D₄	—	4	1	no	—
708	D₄	—	4	1	no	—
709	D₄	—	8	1	no	—
710	D₄	—	8	1	no	—
711	D₄	—	8	1	no	—
712	D₄	—	8	1	no	—
713	D₄	—	8	2	no	—
714	D₄	—	8	1	no	—
715	D₄	—	8	2	no	—
716	D₄	—	8	2	no	—
717	D₄	—	8	2	no	—
718	D₄	—	8	2	no	—
719	D₄	—	8	2	no	—
720	D₄	—	8	2	no	—
721	C₂×C₄	—	2	1	no	—
722	C₂×C₄	—	2	1	no	—
723	C₂×C₄	—	2	1	no	—
724	C₂×C₄	—	2	1	no	—
725	C₂×C₄	—	2	1	no	—
726	C₂×C₄	—	2	1	no	—
727	C₂×C₄	—	2	1	no	—
728	C₂×C₄	—	2	2	no	—
729	C₂×C₄	—	2	1	no	—
730	C₂×C₄	—	2	1	no	—
731	C₂×C₄	—	4	1	no	—
732	C₂×C₄	—	4	1	no	—
733	C₂×C₄	—	4	1	no	—
734	C₂×C₄	—	4	1	no	—
735	C₂×C₄	—	4	1	no	—
736	C₂×C₄	—	4	1	no	—
737	C₂×C₄	—	4	1	no	—
738	C₂×C₄	—	4	1	no	—
739	C₂×C₄	—	8	2	no	—
740	C₂×C₄	—	8	2	no	—
741	C₂×C₄	—	8	2	no	—
742	C₂×C₄	—	8	2	no	—
743	C₂×C₄	C₂₃×#120	1	1	yes	characteristic
744	C₂×C₄	C₂₃×#120	1	1	yes	characteristic
745	C₂×C₄	C₂₃×#120	1	1	yes	characteristic
746	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
747	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
748	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
749	C₈	—	4	1	no	—
750	C₈	—	4	1	no	—
751	C₈	—	4	1	no	—
752	C₈	—	4	1	no	—
753	C₈	—	4	1	no	—
754	C₈	—	4	1	no	—
755	C₂²	—	2	1	no	—
756	C₂²	—	2	1	no	—
757	C₂²	—	2	1	no	—
758	C₂²	—	4	1	no	—
759	C₂²	—	4	1	no	—
760	C₂²	—	4	1	no	—
761	C₂²	—	4	1	no	—
762	C₂²	—	4	2	no	—
763	C₂²	—	4	2	no	—
764	C₂²	—	4	1	no	—
765	C₂²	—	4	1	no	—
766	C₂²	—	4	2	no	—
767	C₂²	—	4	1	no	—
768	C₂²	—	4	1	no	—
769	C₂²	—	4	1	no	—
770	C₂²	—	8	1	no	—
771	C₂²	—	8	1	no	—
772	C₂²	—	8	1	no	—
773	C₂²	—	16	4	no	—
774	C₂²	C₂×C₂₃×#120	1	1	yes	characteristic
775	C₄	—	2	1	no	—
776	C₄	—	2	1	no	—
777	C₄	—	2	1	no	—
778	C₄	—	2	1	no	—
779	C₄	—	4	1	no	—
780	C₄	—	4	1	no	—
781	C₄	—	4	1	no	—
782	C₄	—	4	1	no	—
783	C₄	—	4	2	no	—
784	C₄	—	4	1	no	—
785	C₄	—	8	1	no	—
786	C₄	C₂₃×#576	1	1	yes	characteristic
787	C₄	C₂₃×#576	1	1	yes	characteristic
788	C₄	C₂₃×#577	1	1	yes	characteristic
789	C₄	C₂₃×#577	1	1	yes	characteristic
790	C₂	—	4	1	no	—
791	C₂	—	8	1	no	—
792	C₂	—	8	1	no	—
793	C₂	—	8	2	no	—
794	C₂	—	8	1	no	—
795	C₂	—	16	1	no	—
796	C₂	C₂₃×#3012	1	1	yes	characteristic
797	C₂	C₂₃×#3012	1	1	yes	characteristic
798	C₂	C₂₃×#3021	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₂₃
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂×C₄²×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₃×#3546	C₂	semidirect
2. C₂₃×#3253	C₂	semidirect
3. C₂₃×#3247	C₂	semidirect
4. C₂₃×#3207	C₂	semidirect
5. C₂₃×#1638	C₂	semidirect
6. C₂₃×#1635	C₂	semidirect
7. C₂₃×#1631	C₂	semidirect
8. C₂₃×#1629	C₂	semidirect
9. C₂₃×#1628	C₂	semidirect
10. C₂₃×#1625	C₂	semidirect
11. C₂₃×#1621	C₂	semidirect
12. C₂₃×#1619	C₂	semidirect
13. C₂₃×#1547	C₂	semidirect
14. C₂₃×#1495	C₂	semidirect
15. C₂₃×#1480	C₂	semidirect
32. C₂₃×#532	C₂²	semidirect
36. C₂₃×#487	C₂²	semidirect
37. C₂₃×#486	C₂²	semidirect
39. C₂₃×#477	C₂²	semidirect
43. C₂₃×#476	C₂²	semidirect
50. C₂₃×#460	C₂²	semidirect
54. C₂₃×#459	C₂²	semidirect
56. C₂₃×#431	C₂²	semidirect
57. C₂₃×#423	C₂²	semidirect
58. C₂×C₂₃×C₄⋊C₈	C₂²	semidirect
59. C₂₃×#332	C₂²	semidirect
60. C₂₃×#332	C₂²	semidirect
63. C₂₃×Q₈⋊C₈	C₂²	semidirect
64. C₂₃×Q₈⋊C₈	C₂²	semidirect
69. C₂₃×D₄⋊C₈	C₂²	semidirect
70. C₂₃×D₄⋊C₈	C₂²	semidirect
278. #18962	C₂₃	direct (N × H)
356. #3546	C₂×C₂₃	semidirect
357. #3253	C₂×C₂₃	semidirect
358. #3247	C₂×C₂₃	semidirect
359. #3207	C₂×C₂₃	semidirect
360. #1638	C₂×C₂₃	semidirect
361. #1635	C₂×C₂₃	semidirect
362. #1631	C₂×C₂₃	semidirect
363. #1629	C₂×C₂₃	semidirect
364. #1628	C₂×C₂₃	semidirect
365. #1625	C₂×C₂₃	semidirect
366. #1621	C₂×C₂₃	semidirect
367. #1619	C₂×C₂₃	semidirect
368. #1547	C₂×C₂₃	semidirect
369. #1495	C₂×C₂₃	semidirect
370. #1480	C₂×C₂₃	semidirect
422. #532	C₂²×C₂₃	semidirect
426. #487	C₂²×C₂₃	semidirect
427. #486	C₂²×C₂₃	semidirect
429. #477	C₂²×C₂₃	semidirect
433. #476	C₂²×C₂₃	semidirect
440. #460	C₂²×C₂₃	semidirect
444. #459	C₂²×C₂₃	semidirect
446. #431	C₂²×C₂₃	semidirect
447. #423	C₂²×C₂₃	semidirect
448. C₂×C₄⋊C₈	C₂²×C₂₃	semidirect
449. #332	C₂²×C₂₃	semidirect
450. #332	C₂²×C₂₃	semidirect
453. Q₈⋊C₈	C₂²×C₂₃	semidirect
454. Q₈⋊C₈	C₂²×C₂₃	semidirect
459. D₄⋊C₈	C₂²×C₂₃	semidirect
460. D₄⋊C₈	C₂²×C₂₃	semidirect
575. C₂₃	#18962	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂₃×#3546	2
C₂₃×#3253	2
C₂₃×#3247	2
C₂₃×#3207	2
C₂₃×#1638	2
C₂₃×#1635	2
C₂₃×#1631	2
C₂₃×#1629	2
C₂₃×#1628	2
C₂₃×#1625	2
C₂₃×#1621	2
C₂₃×#1619	2
C₂₃×#1547	2
C₂₃×#1495	2
C₂₃×#1480	2
#18962	23

Subgroups — C23×#18962 #19166588

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#18962 #19166588