Subgroups — C₂₃×#18638 #19166264

Order 5888.

956 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3520	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₃×#3247	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3131	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#3109	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#1638	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#1637	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#1635	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#1635	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#1628	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#1627	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#1625	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#1625	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#1552	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#1494	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₂₃×D₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₃×#556	C₂²	1	1	yes	characteristic
17	C₂₃×#554	—	2	1	no	—
18	C₂₃×#552	—	2	1	no	—
19	C₂₃×#551	—	2	2	no	—
20	D₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
21	C₂₃×#548	—	2	1	no	—
22	C₂₃×#547	C₂²	1	1	yes	characteristic
23	C₂₃×#547	C₂²	1	1	yes	characteristic
24	C₂₃×#546	—	2	1	no	—
25	C₂₃×#542	—	2	1	no	—
26	C₂₃×#539	—	2	2	no	—
27	C₂₃×#533	C₂²	1	1	yes	characteristic
28	C₂₃×#532	C₂²	1	1	yes	characteristic
29	C₂₃×#529	C₂²	1	1	yes	characteristic
30	C₂₃×#525	—	2	1	no	—
31	C₂×C₂₃×C₂²⋊Q₈	—	2	1	no	—
32	C₂₃×#520	—	2	1	no	—
33	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
34	C₂₃×#488	—	2	2	no	—
35	C₂₃×#487	C₂²	1	1	yes	characteristic, complemented
36	C₂₃×#487	C₂²	1	1	yes	characteristic, complemented
37	C₂₃×#486	C₂²	1	1	yes	characteristic, complemented
38	C₂₃×#486	C₂²	1	1	yes	characteristic, complemented
39	C₂₃×#481	—	2	1	no	—
40	C₂₃×#478	—	2	1	no	—
41	C₂₃×#477	C₂²	1	1	yes	characteristic, complemented
42	C₂₃×#476	C₂²	1	1	yes	characteristic
43	C₂₃×#476	C₂²	1	1	yes	characteristic
44	C₂₃×#476	C₂²	1	1	yes	characteristic, complemented
45	C₂₃×#466	—	2	1	no	—
46	C₂₃×#465	—	2	1	no	—
47	C₂₃×#463	—	2	1	no	—
48	C₂₃×#460	C₂²	1	1	yes	characteristic, complemented
49	C₂₃×#459	C₂²	1	1	yes	characteristic
50	C₂₃×#459	C₂²	1	1	yes	characteristic
51	C₂₃×#459	C₂²	1	1	yes	characteristic, complemented
52	C₂₃×#447	—	2	1	no	—
53	C₂₃×#442	—	2	1	no	—
54	C₂₃×#442	—	2	1	no	—
55	C₂₃×#432	C₂²	1	1	yes	characteristic
56	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
57	C₂₃×#416	—	2	2	no	—
58	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
59	C₂₃×#332	C₂²	1	1	yes	characteristic, complemented
60	C₂₃×#332	C₂²	1	1	yes	characteristic, complemented
61	C₂₃×#332	C₂²	1	1	yes	characteristic, complemented
62	C₂₃×#332	C₂²	1	1	yes	characteristic, complemented
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	C₂²×Q₈×C₂₃	—	2	1	no	—
75	C₂²×D₄×C₂₃	D₄	1	1	yes	characteristic
76	C₂³×C₄×C₂₃	—	2	1	no	—
77	C₂×SD₁₆×C₂₃	—	2	1	no	—
78	C₂×D₈×C₂₃	—	2	1	no	—
79	C₂×D₈×C₂₃	—	2	1	no	—
80	C₂×D₈×C₂₃	—	2	1	no	—
81	C₂²×C₈×C₂₃	—	2	1	no	—
82	C₂²×C₈×C₂₃	—	2	1	no	—
83	C₂₃×C₄⋊Q₈	—	2	1	no	—
84	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
85	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
86	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
87	C₂₃×#127	C₂³	1	1	yes	characteristic
88	C₂₃×#126	—	2	2	no	—
89	C₂₃×#126	—	2	2	no	—
90	C₂₃×#126	—	2	1	no	—
91	C₂₃×#125	—	2	2	no	—
92	C₂₃×#125	D₄	1	1	yes	characteristic
93	C₂₃×#125	D₄	1	2	yes	—
94	C₂₃×#124	—	2	2	no	—
95	C₂₃×#124	—	2	1	no	—
96	C₂₃×#124	—	2	1	no	—
97	C₂₃×#124	D₄	1	1	yes	characteristic
98	C₂₃×#123	—	2	2	no	—
99	C₂₃×#123	—	2	2	no	—
100	C₂₃×#123	—	2	1	no	—
101	C₂₃×#123	—	2	2	no	—
102	C₂₃×#123	—	2	2	no	—
103	C₂₃×C₂²⋊Q₈	—	2	2	no	—
104	C₂₃×C₂²⋊Q₈	—	2	2	no	—
105	C₂₃×C₂²⋊Q₈	—	2	2	no	—
106	C₂₃×C₂²⋊Q₈	—	2	1	no	—
107	C₂₃×C₂²⋊Q₈	—	2	1	no	—
108	C₂₃×C₂²⋊Q₈	—	2	1	no	—
109	C₂₃×C₂²⋊Q₈	—	2	1	no	—
110	C₂₃×C₂²⋊Q₈	—	2	1	no	—
111	C₂₃×C₂²⋊Q₈	—	2	2	no	—
112	C₂₃×C₂²⋊Q₈	—	2	1	no	—
113	C₂₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
114	C₂₃×#121	—	2	2	no	—
115	C₂₃×#121	—	2	1	no	—
116	C₂₃×#121	—	2	1	no	—
117	C₂₃×#121	—	2	1	no	—
118	C₂₃×#121	—	2	1	no	—
119	C₂₃×#121	D₄	1	1	yes	characteristic
120	C₂₃×#120	—	2	2	no	—
121	C₄×Q₈×C₂₃	—	2	1	no	—
122	C₄×Q₈×C₂₃	—	2	1	no	—
123	C₄×Q₈×C₂₃	—	2	1	no	—
124	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
125	C₄×D₄×C₂₃	—	2	2	no	—
126	C₄×D₄×C₂₃	—	2	2	no	—
127	C₄×D₄×C₂₃	—	2	2	no	—
128	C₄×D₄×C₂₃	—	2	1	no	—
129	C₄×D₄×C₂₃	—	2	1	no	—
130	C₄×D₄×C₂₃	—	2	1	no	—
131	C₄×D₄×C₂₃	—	2	1	no	—
132	C₄×D₄×C₂₃	—	2	1	no	—
133	C₄×D₄×C₂₃	—	2	1	no	—
134	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
135	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
136	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
137	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
138	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
139	C₂₃×#117	—	2	2	no	—
140	C₂₃×#117	—	2	1	no	—
141	C₂₃×#117	—	2	1	no	—
142	C₂₃×#117	D₄	1	2	yes	—
143	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
144	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
145	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
146	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
147	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
148	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
149	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
150	C₂₃×#107	—	2	1	no	—
151	C₂₃×#106	—	2	1	no	—
152	C₂₃×#106	—	2	1	no	—
153	C₂₃×#106	—	2	1	no	—
154	C₂₃×C₄⋊C₈	—	2	1	no	—
155	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
156	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
157	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
158	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
159	C₂₃×#103	—	2	1	no	—
160	C₂₃×#103	—	2	2	no	—
161	C₂₃×#103	—	2	2	no	—
162	C₂₃×#102	—	2	1	no	—
163	C₂₃×#102	—	2	1	no	—
164	C₂₃×#102	—	2	1	no	—
165	C₂₃×#102	—	2	2	no	—
166	C₂₃×#102	—	2	2	no	—
167	C₂₃×#102	—	2	1	no	—
168	C₂₃×#102	—	2	1	no	—
169	C₂₃×#102	—	2	1	no	—
170	C₂₃×#102	—	2	1	no	—
171	C₂₃×C₂²⋊C₈	—	2	1	no	—
172	C₂₃×#97	—	2	1	no	—
173	C₄×C₈×C₂₃	—	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	1	no	—
177	#41×C₂₃	—	4	4	no	—
178	#41×C₂₃	—	4	2	no	—
179	#41×C₂₃	—	4	2	no	—
180	#41×C₂₃	—	8	1	no	—
181	#41×C₂₃	—	8	1	no	—
182	C₂×Q₈×C₂₃	—	2	2	no	—
183	C₂×Q₈×C₂₃	—	2	1	no	—
184	C₂×Q₈×C₂₃	—	2	1	no	—
185	C₂×Q₈×C₂₃	—	2	1	no	—
186	C₂×Q₈×C₂₃	—	8	1	no	—
187	C₂×Q₈×C₂₃	—	8	1	no	—
188	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
189	C₂×D₄×C₂₃	—	2	2	no	—
190	C₂×D₄×C₂₃	—	2	2	no	—
191	C₂×D₄×C₂₃	—	2	1	no	—
192	C₂×D₄×C₂₃	—	2	2	no	—
193	C₂×D₄×C₂₃	—	2	1	no	—
194	C₂×D₄×C₂₃	—	2	1	no	—
195	C₂×D₄×C₂₃	—	2	1	no	—
196	C₂×D₄×C₂₃	—	2	1	no	—
197	C₂×D₄×C₂₃	—	4	1	no	—
198	C₂×D₄×C₂₃	—	4	1	no	—
199	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
200	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
201	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
202	C₂²×C₄×C₂₃	—	2	2	no	—
203	C₂²×C₄×C₂₃	—	2	2	no	—
204	C₂²×C₄×C₂₃	—	2	2	no	—
205	C₂²×C₄×C₂₃	—	2	1	no	—
206	C₂²×C₄×C₂₃	—	2	1	no	—
207	C₂²×C₄×C₂₃	—	2	1	no	—
208	C₂²×C₄×C₂₃	—	2	1	no	—
209	C₂²×C₄×C₂₃	—	2	1	no	—
210	C₂²×C₄×C₂₃	—	2	1	no	—
211	C₂²×C₄×C₂₃	—	4	1	no	—
212	C₂²×C₄×C₂₃	—	8	1	no	—
213	C₂²×C₄×C₂₃	—	8	1	no	—
214	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
215	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
216	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
217	SD₁₆×C₂₃	—	8	1	no	—
218	D₈×C₂₃	—	4	2	no	—
219	D₈×C₂₃	—	4	2	no	—
220	D₈×C₂₃	—	8	1	no	—
221	C₂×C₈×C₂₃	—	2	1	no	—
222	C₂×C₈×C₂₃	—	2	1	no	—
223	C₂×C₈×C₂₃	—	2	1	no	—
224	C₂×C₈×C₂₃	—	2	1	no	—
225	C₂×C₈×C₂₃	—	2	1	no	—
226	C₂×C₈×C₂₃	—	2	1	no	—
227	C₂×C₈×C₂₃	—	4	2	no	—
228	C₂×C₈×C₂₃	—	8	1	no	—
229	C₄⋊C₄×C₂₃	—	2	2	no	—
230	C₄⋊C₄×C₂₃	—	2	2	no	—
231	C₄⋊C₄×C₂₃	—	2	2	no	—
232	C₄⋊C₄×C₂₃	—	2	2	no	—
233	C₄⋊C₄×C₂₃	—	2	1	no	—
234	C₄⋊C₄×C₂₃	—	2	2	no	—
235	C₄⋊C₄×C₂₃	—	2	1	no	—
236	C₄⋊C₄×C₂₃	—	2	1	no	—
237	C₄⋊C₄×C₂₃	—	2	1	no	—
238	C₄⋊C₄×C₂₃	—	2	2	no	—
239	C₄⋊C₄×C₂₃	—	2	1	no	—
240	C₄⋊C₄×C₂₃	—	2	1	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	C₂×D₄	1	2	yes	—
245	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
246	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
247	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
248	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
249	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
250	C₂²⋊C₄×C₂₃	—	2	2	no	—
251	C₂²⋊C₄×C₂₃	—	2	2	no	—
252	C₂²⋊C₄×C₂₃	—	2	2	no	—
253	C₂²⋊C₄×C₂₃	—	2	2	no	—
254	C₂²⋊C₄×C₂₃	—	2	2	no	—
255	C₂²⋊C₄×C₂₃	—	2	1	no	—
256	C₂²⋊C₄×C₂₃	—	2	2	no	—
257	C₂²⋊C₄×C₂₃	—	2	1	no	—
258	C₂²⋊C₄×C₂₃	—	2	1	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	—	4	1	no	—
266	C₂²⋊C₄×C₂₃	—	4	1	no	—
267	C₄²×C₂₃	—	2	2	no	—
268	C₄²×C₂₃	—	2	2	no	—
269	C₄²×C₂₃	—	2	1	no	—
270	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
271	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
272	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
273	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
274	#18638	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
275	C₂³×C₂₃	—	2	1	no	—
276	C₂³×C₂₃	—	2	1	no	—
277	C₂³×C₂₃	—	2	1	no	—
278	C₂³×C₂₃	—	4	2	no	—
279	C₂³×C₂₃	—	4	2	no	—
280	C₂³×C₂₃	—	4	1	no	—
281	C₂³×C₂₃	—	8	1	no	—
282	C₂³×C₂₃	#120	1	1	yes	characteristic
283	Q₈×C₂₃	—	2	1	no	—
284	Q₈×C₂₃	—	2	1	no	—
285	Q₈×C₂₃	—	4	2	no	—
286	Q₈×C₂₃	—	4	1	no	—
287	Q₈×C₂₃	—	4	1	no	—
288	Q₈×C₂₃	—	4	1	no	—
289	Q₈×C₂₃	—	4	1	no	—
290	Q₈×C₂₃	—	8	2	no	—
291	D₄×C₂₃	—	2	1	no	—
292	D₄×C₂₃	—	2	1	no	—
293	D₄×C₂₃	—	2	1	no	—
294	D₄×C₂₃	—	2	1	no	—
295	D₄×C₂₃	—	2	1	no	—
296	D₄×C₂₃	—	4	2	no	—
297	D₄×C₂₃	—	4	2	no	—
298	D₄×C₂₃	—	4	4	no	—
299	D₄×C₂₃	—	4	2	no	—
300	D₄×C₂₃	—	4	1	no	—
301	D₄×C₂₃	—	4	1	no	—
302	D₄×C₂₃	—	4	1	no	—
303	D₄×C₂₃	—	4	1	no	—
304	D₄×C₂₃	—	8	2	no	—
305	D₄×C₂₃	—	8	2	no	—
306	D₄×C₂₃	#135	1	2	yes	—
307	C₂×C₄×C₂₃	—	2	2	no	—
308	C₂×C₄×C₂₃	—	2	1	no	—
309	C₂×C₄×C₂₃	—	2	1	no	—
310	C₂×C₄×C₂₃	—	2	1	no	—
311	C₂×C₄×C₂₃	—	2	1	no	—
312	C₂×C₄×C₂₃	—	2	1	no	—
313	C₂×C₄×C₂₃	—	2	2	no	—
314	C₂×C₄×C₂₃	—	2	1	no	—
315	C₂×C₄×C₂₃	—	2	1	no	—
316	C₂×C₄×C₂₃	—	2	2	no	—
317	C₂×C₄×C₂₃	—	2	1	no	—
318	C₂×C₄×C₂₃	—	2	1	no	—
319	C₂×C₄×C₂₃	—	4	4	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	—	4	1	no	—
325	C₂×C₄×C₂₃	—	4	1	no	—
326	C₂×C₄×C₂₃	—	4	1	no	—
327	C₂×C₄×C₂₃	—	8	1	no	—
328	C₂×C₄×C₂₃	—	8	1	no	—
329	C₂×C₄×C₂₃	—	8	2	no	—
330	C₂×C₄×C₂₃	—	8	1	no	—
331	C₂×C₄×C₂₃	—	8	2	no	—
332	C₂×C₄×C₂₃	—	8	2	no	—
333	C₂×C₄×C₂₃	#120	1	1	yes	characteristic
334	C₂×C₄×C₂₃	#120	1	1	yes	characteristic
335	C₂×C₄×C₂₃	#120	1	1	yes	characteristic
336	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
337	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
338	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
339	C₈×C₂₃	—	4	1	no	—
340	C₈×C₂₃	—	4	1	no	—
341	C₈×C₂₃	—	4	1	no	—
342	C₈×C₂₃	—	4	1	no	—
343	C₈×C₂₃	—	4	1	no	—
344	C₈×C₂₃	—	4	1	no	—
345	#3520	C₂×C₂₃	1	1	yes	characteristic, complemented
346	#3247	C₂×C₂₃	1	1	yes	characteristic, complemented
347	#3131	C₂×C₂₃	1	1	yes	characteristic, complemented
348	#3109	C₂×C₂₃	1	1	yes	characteristic, complemented
349	#1638	C₂×C₂₃	1	1	yes	characteristic, complemented
350	#1637	C₂×C₂₃	1	1	yes	characteristic, complemented
351	#1635	C₂×C₂₃	1	1	yes	characteristic, complemented
352	#1635	C₂×C₂₃	1	1	yes	characteristic, complemented
353	#1628	C₂×C₂₃	1	1	yes	characteristic, complemented
354	#1627	C₂×C₂₃	1	1	yes	characteristic, complemented
355	#1625	C₂×C₂₃	1	1	yes	characteristic, complemented
356	#1625	C₂×C₂₃	1	1	yes	characteristic, complemented
357	#1552	C₂×C₂₃	1	1	yes	characteristic, complemented
358	#1494	C₂×C₂₃	1	1	yes	characteristic, complemented
359	C₂×D₄⋊C₈	C₂×C₂₃	1	1	yes	characteristic, complemented
360	C₂²×C₂₃	—	2	1	no	—
361	C₂²×C₂₃	—	2	1	no	—
362	C₂²×C₂₃	—	2	2	no	—
363	C₂²×C₂₃	—	4	1	no	—
364	C₂²×C₂₃	—	4	1	no	—
365	C₂²×C₂₃	—	4	1	no	—
366	C₂²×C₂₃	—	4	1	no	—
367	C₂²×C₂₃	—	4	1	no	—
368	C₂²×C₂₃	—	4	1	no	—
369	C₂²×C₂₃	—	4	1	no	—
370	C₂²×C₂₃	—	4	1	no	—
371	C₂²×C₂₃	—	8	4	no	—
372	C₂²×C₂₃	—	8	1	no	—
373	C₂²×C₂₃	—	8	1	no	—
374	C₂²×C₂₃	—	8	1	no	—
375	C₂²×C₂₃	#454	1	2	yes	—
376	C₂²×C₂₃	C₂×#120	1	1	yes	characteristic
377	C₄×C₂₃	—	2	1	no	—
378	C₄×C₂₃	—	2	1	no	—
379	C₄×C₂₃	—	2	1	no	—
380	C₄×C₂₃	—	2	1	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	—	4	2	no	—
386	C₄×C₂₃	—	4	1	no	—
387	C₄×C₂₃	—	4	1	no	—
388	C₄×C₂₃	—	8	1	no	—
389	C₄×C₂₃	C₂×#135	1	1	yes	characteristic
390	C₄×C₂₃	#575	1	1	yes	characteristic
391	C₄×C₂₃	#576	1	1	yes	characteristic
392	C₄×C₂₃	#577	1	1	yes	characteristic
393	#556	C₂²×C₂₃	1	1	yes	characteristic
394	#554	—	2	1	no	—
395	#552	—	2	1	no	—
396	#551	—	2	2	no	—
397	D₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
398	#548	—	2	1	no	—
399	#547	C₂²×C₂₃	1	1	yes	characteristic
400	#547	C₂²×C₂₃	1	1	yes	characteristic
401	#546	—	2	1	no	—
402	#542	—	2	1	no	—
403	#539	—	2	2	no	—
404	#533	C₂²×C₂₃	1	1	yes	characteristic
405	#532	C₂²×C₂₃	1	1	yes	characteristic
406	#529	C₂²×C₂₃	1	1	yes	characteristic
407	#525	—	2	1	no	—
408	C₂×C₂²⋊Q₈	—	2	1	no	—
409	#520	—	2	1	no	—
410	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
411	#488	—	2	2	no	—
412	#487	C₂²×C₂₃	1	1	yes	characteristic, complemented
413	#487	C₂²×C₂₃	1	1	yes	characteristic, complemented
414	#486	C₂²×C₂₃	1	1	yes	characteristic, complemented
415	#486	C₂²×C₂₃	1	1	yes	characteristic, complemented
416	#481	—	2	1	no	—
417	#478	—	2	1	no	—
418	#477	C₂²×C₂₃	1	1	yes	characteristic, complemented
419	#476	C₂²×C₂₃	1	1	yes	characteristic
420	#476	C₂²×C₂₃	1	1	yes	characteristic
421	#476	C₂²×C₂₃	1	1	yes	characteristic, complemented
422	#466	—	2	1	no	—
423	#465	—	2	1	no	—
424	#463	—	2	1	no	—
425	#460	C₂²×C₂₃	1	1	yes	characteristic, complemented
426	#459	C₂²×C₂₃	1	1	yes	characteristic
427	#459	C₂²×C₂₃	1	1	yes	characteristic
428	#459	C₂²×C₂₃	1	1	yes	characteristic, complemented
429	#447	—	2	1	no	—
430	#442	—	2	1	no	—
431	#442	—	2	1	no	—
432	#432	C₂²×C₂₃	1	1	yes	characteristic
433	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
434	#416	—	2	2	no	—
435	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
436	#332	C₂²×C₂₃	1	1	yes	characteristic, complemented
437	#332	C₂²×C₂₃	1	1	yes	characteristic, complemented
438	#332	C₂²×C₂₃	1	1	yes	characteristic, complemented
439	#332	C₂²×C₂₃	1	1	yes	characteristic, complemented
440	Q₈⋊C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
441	Q₈⋊C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
442	D₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
443	D₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
444	D₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
445	D₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
446	D₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
447	D₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
448	C₂×C₂₃	—	2	2	no	—
449	C₂×C₂₃	—	4	2	no	—
450	C₂×C₂₃	—	8	1	no	—
451	C₂×C₂₃	—	8	1	no	—
452	C₂×C₂₃	—	16	1	no	—
453	C₂×C₂₃	#3002	1	1	yes	characteristic
454	C₂×C₂₃	#3012	1	1	yes	characteristic
455	C₂×C₂₃	C₂×#454	1	1	yes	characteristic
456	C₂×#41	—	2	1	no	—
457	C₂×#41	—	2	1	no	—
458	C₂×#41	—	2	1	no	—
459	C₂²×Q₈	—	2	1	no	—
460	C₂²×D₄	D₄×C₂₃	1	1	yes	characteristic
461	C₂³×C₄	—	2	1	no	—
462	C₂×SD₁₆	—	2	1	no	—
463	C₂×D₈	—	2	1	no	—
464	C₂×D₈	—	2	1	no	—
465	C₂×D₈	—	2	1	no	—
466	C₂²×C₈	—	2	1	no	—
467	C₂²×C₈	—	2	1	no	—
468	C₄⋊Q₈	—	2	1	no	—
469	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
470	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
471	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
472	#127	C₂³×C₂₃	1	1	yes	characteristic
473	#126	—	2	2	no	—
474	#126	—	2	2	no	—
475	#126	—	2	1	no	—
476	#125	—	2	2	no	—
477	#125	D₄×C₂₃	1	1	yes	characteristic
478	#125	D₄×C₂₃	1	2	yes	—
479	#124	—	2	2	no	—
480	#124	—	2	1	no	—
481	#124	—	2	1	no	—
482	#124	D₄×C₂₃	1	1	yes	characteristic
483	#123	—	2	2	no	—
484	#123	—	2	2	no	—
485	#123	—	2	1	no	—
486	#123	—	2	2	no	—
487	#123	—	2	2	no	—
488	C₂²⋊Q₈	—	2	2	no	—
489	C₂²⋊Q₈	—	2	2	no	—
490	C₂²⋊Q₈	—	2	2	no	—
491	C₂²⋊Q₈	—	2	1	no	—
492	C₂²⋊Q₈	—	2	1	no	—
493	C₂²⋊Q₈	—	2	1	no	—
494	C₂²⋊Q₈	—	2	1	no	—
495	C₂²⋊Q₈	—	2	1	no	—
496	C₂²⋊Q₈	—	2	2	no	—
497	C₂²⋊Q₈	—	2	1	no	—
498	C₂²⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
499	#121	—	2	2	no	—
500	#121	—	2	1	no	—
501	#121	—	2	1	no	—
502	#121	—	2	1	no	—
503	#121	—	2	1	no	—
504	#121	D₄×C₂₃	1	1	yes	characteristic
505	#120	—	2	2	no	—
506	C₄×Q₈	—	2	1	no	—
507	C₄×Q₈	—	2	1	no	—
508	C₄×Q₈	—	2	1	no	—
509	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
510	C₄×D₄	—	2	2	no	—
511	C₄×D₄	—	2	2	no	—
512	C₄×D₄	—	2	2	no	—
513	C₄×D₄	—	2	1	no	—
514	C₄×D₄	—	2	1	no	—
515	C₄×D₄	—	2	1	no	—
516	C₄×D₄	—	2	1	no	—
517	C₄×D₄	—	2	1	no	—
518	C₄×D₄	—	2	1	no	—
519	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
520	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
521	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
522	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
523	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
524	#117	—	2	2	no	—
525	#117	—	2	1	no	—
526	#117	—	2	1	no	—
527	#117	D₄×C₂₃	1	2	yes	—
528	C₂×C₄⋊C₄	—	2	2	no	—
529	C₂×C₄⋊C₄	—	2	1	no	—
530	C₂×C₄⋊C₄	—	2	1	no	—
531	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
532	C₂×C₂²⋊C₄	—	2	2	no	—
533	C₂×C₂²⋊C₄	—	2	1	no	—
534	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
535	#107	—	2	1	no	—
536	#106	—	2	1	no	—
537	#106	—	2	1	no	—
538	#106	—	2	1	no	—
539	C₄⋊C₈	—	2	1	no	—
540	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
541	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
542	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
543	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
544	#103	—	2	1	no	—
545	#103	—	2	2	no	—
546	#103	—	2	2	no	—
547	#102	—	2	1	no	—
548	#102	—	2	1	no	—
549	#102	—	2	1	no	—
550	#102	—	2	2	no	—
551	#102	—	2	2	no	—
552	#102	—	2	1	no	—
553	#102	—	2	1	no	—
554	#102	—	2	1	no	—
555	#102	—	2	1	no	—
556	C₂²⋊C₈	—	2	1	no	—
557	#97	—	2	1	no	—
558	C₄×C₈	—	2	1	no	—
559	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
560	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
561	C₂₃	#18638	1	1	yes	characteristic, direct product factor, Sylow
562	C₂⁴	—	2	1	no	—
563	#41	—	4	4	no	—
564	#41	—	4	2	no	—
565	#41	—	4	2	no	—
566	#41	—	8	1	no	—
567	#41	—	8	1	no	—
568	C₂×Q₈	—	2	2	no	—
569	C₂×Q₈	—	2	1	no	—
570	C₂×Q₈	—	2	1	no	—
571	C₂×Q₈	—	2	1	no	—
572	C₂×Q₈	—	8	1	no	—
573	C₂×Q₈	—	8	1	no	—
574	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
575	C₂×D₄	—	2	2	no	—
576	C₂×D₄	—	2	2	no	—
577	C₂×D₄	—	2	1	no	—
578	C₂×D₄	—	2	2	no	—
579	C₂×D₄	—	2	1	no	—
580	C₂×D₄	—	2	1	no	—
581	C₂×D₄	—	2	1	no	—
582	C₂×D₄	—	2	1	no	—
583	C₂×D₄	—	4	1	no	—
584	C₂×D₄	—	4	1	no	—
585	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
586	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
587	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
588	C₂²×C₄	—	2	2	no	—
589	C₂²×C₄	—	2	2	no	—
590	C₂²×C₄	—	2	2	no	—
591	C₂²×C₄	—	2	1	no	—
592	C₂²×C₄	—	2	1	no	—
593	C₂²×C₄	—	2	1	no	—
594	C₂²×C₄	—	2	1	no	—
595	C₂²×C₄	—	2	1	no	—
596	C₂²×C₄	—	2	1	no	—
597	C₂²×C₄	—	4	1	no	—
598	C₂²×C₄	—	8	1	no	—
599	C₂²×C₄	—	8	1	no	—
600	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
601	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
602	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
603	SD₁₆	—	8	1	no	—
604	D₈	—	4	2	no	—
605	D₈	—	4	2	no	—
606	D₈	—	8	1	no	—
607	C₂×C₈	—	2	1	no	—
608	C₂×C₈	—	2	1	no	—
609	C₂×C₈	—	2	1	no	—
610	C₂×C₈	—	2	1	no	—
611	C₂×C₈	—	2	1	no	—
612	C₂×C₈	—	2	1	no	—
613	C₂×C₈	—	4	2	no	—
614	C₂×C₈	—	8	1	no	—
615	C₄⋊C₄	—	2	2	no	—
616	C₄⋊C₄	—	2	2	no	—
617	C₄⋊C₄	—	2	2	no	—
618	C₄⋊C₄	—	2	2	no	—
619	C₄⋊C₄	—	2	1	no	—
620	C₄⋊C₄	—	2	2	no	—
621	C₄⋊C₄	—	2	1	no	—
622	C₄⋊C₄	—	2	1	no	—
623	C₄⋊C₄	—	2	1	no	—
624	C₄⋊C₄	—	2	2	no	—
625	C₄⋊C₄	—	2	1	no	—
626	C₄⋊C₄	—	2	1	no	—
627	C₄⋊C₄	—	2	1	no	—
628	C₄⋊C₄	—	2	1	no	—
629	C₄⋊C₄	—	2	1	no	—
630	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
631	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
632	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
633	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
634	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
635	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
636	C₂²⋊C₄	—	2	2	no	—
637	C₂²⋊C₄	—	2	2	no	—
638	C₂²⋊C₄	—	2	2	no	—
639	C₂²⋊C₄	—	2	2	no	—
640	C₂²⋊C₄	—	2	2	no	—
641	C₂²⋊C₄	—	2	1	no	—
642	C₂²⋊C₄	—	2	2	no	—
643	C₂²⋊C₄	—	2	1	no	—
644	C₂²⋊C₄	—	2	1	no	—
645	C₂²⋊C₄	—	2	1	no	—
646	C₂²⋊C₄	—	2	1	no	—
647	C₂²⋊C₄	—	2	1	no	—
648	C₂²⋊C₄	—	2	1	no	—
649	C₂²⋊C₄	—	2	1	no	—
650	C₂²⋊C₄	—	2	1	no	—
651	C₂²⋊C₄	—	4	1	no	—
652	C₂²⋊C₄	—	4	1	no	—
653	C₄²	—	2	2	no	—
654	C₄²	—	2	2	no	—
655	C₄²	—	2	1	no	—
656	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
657	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
658	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
659	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
660	C₂³	—	2	1	no	—
661	C₂³	—	2	1	no	—
662	C₂³	—	2	1	no	—
663	C₂³	—	4	2	no	—
664	C₂³	—	4	2	no	—
665	C₂³	—	4	1	no	—
666	C₂³	—	8	1	no	—
667	C₂³	C₂₃×#120	1	1	yes	characteristic
668	Q₈	—	2	1	no	—
669	Q₈	—	2	1	no	—
670	Q₈	—	4	2	no	—
671	Q₈	—	4	1	no	—
672	Q₈	—	4	1	no	—
673	Q₈	—	4	1	no	—
674	Q₈	—	4	1	no	—
675	Q₈	—	8	2	no	—
676	D₄	—	2	1	no	—
677	D₄	—	2	1	no	—
678	D₄	—	2	1	no	—
679	D₄	—	2	1	no	—
680	D₄	—	2	1	no	—
681	D₄	—	4	2	no	—
682	D₄	—	4	2	no	—
683	D₄	—	4	4	no	—
684	D₄	—	4	2	no	—
685	D₄	—	4	1	no	—
686	D₄	—	4	1	no	—
687	D₄	—	4	1	no	—
688	D₄	—	4	1	no	—
689	D₄	—	8	2	no	—
690	D₄	—	8	2	no	—
691	D₄	C₂₃×#135	1	2	yes	—
692	C₂×C₄	—	2	2	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	2	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	—	2	1	no	—
704	C₂×C₄	—	4	4	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	—	8	1	no	—
713	C₂×C₄	—	8	1	no	—
714	C₂×C₄	—	8	2	no	—
715	C₂×C₄	—	8	1	no	—
716	C₂×C₄	—	8	2	no	—
717	C₂×C₄	—	8	2	no	—
718	C₂×C₄	C₂₃×#120	1	1	yes	characteristic
719	C₂×C₄	C₂₃×#120	1	1	yes	characteristic
720	C₂×C₄	C₂₃×#120	1	1	yes	characteristic
721	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
722	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
723	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
724	C₈	—	4	1	no	—
725	C₈	—	4	1	no	—
726	C₈	—	4	1	no	—
727	C₈	—	4	1	no	—
728	C₈	—	4	1	no	—
729	C₈	—	4	1	no	—
730	C₂²	—	2	1	no	—
731	C₂²	—	2	1	no	—
732	C₂²	—	2	2	no	—
733	C₂²	—	4	1	no	—
734	C₂²	—	4	1	no	—
735	C₂²	—	4	1	no	—
736	C₂²	—	4	1	no	—
737	C₂²	—	4	1	no	—
738	C₂²	—	4	1	no	—
739	C₂²	—	4	1	no	—
740	C₂²	—	4	1	no	—
741	C₂²	—	8	4	no	—
742	C₂²	—	8	1	no	—
743	C₂²	—	8	1	no	—
744	C₂²	—	8	1	no	—
745	C₂²	C₂₃×#454	1	2	yes	—
746	C₂²	C₂×C₂₃×#120	1	1	yes	characteristic
747	C₄	—	2	1	no	—
748	C₄	—	2	1	no	—
749	C₄	—	2	1	no	—
750	C₄	—	2	1	no	—
751	C₄	—	4	1	no	—
752	C₄	—	4	2	no	—
753	C₄	—	4	1	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	C₂×C₂₃×#135	1	1	yes	characteristic
760	C₄	C₂₃×#575	1	1	yes	characteristic
761	C₄	C₂₃×#576	1	1	yes	characteristic
762	C₄	C₂₃×#577	1	1	yes	characteristic
763	C₂	—	2	2	no	—
764	C₂	—	4	2	no	—
765	C₂	—	8	1	no	—
766	C₂	—	8	1	no	—
767	C₂	—	16	1	no	—
768	C₂	C₂₃×#3002	1	1	yes	characteristic
769	C₂	C₂₃×#3012	1	1	yes	characteristic
770	C₂	C₂×C₂₃×#454	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×#3520	C₂	semidirect
2. C₂₃×#3247	C₂	semidirect
3. C₂₃×#3131	C₂	semidirect
4. C₂₃×#3109	C₂	semidirect
5. C₂₃×#1638	C₂	semidirect
6. C₂₃×#1637	C₂	semidirect
7. C₂₃×#1635	C₂	semidirect
8. C₂₃×#1635	C₂	semidirect
9. C₂₃×#1628	C₂	semidirect
10. C₂₃×#1627	C₂	semidirect
11. C₂₃×#1625	C₂	semidirect
12. C₂₃×#1625	C₂	semidirect
13. C₂₃×#1552	C₂	semidirect
14. C₂₃×#1494	C₂	semidirect
15. C₂×C₂₃×D₄⋊C₈	C₂	semidirect
35. C₂₃×#487	C₂²	semidirect
36. C₂₃×#487	C₂²	semidirect
37. C₂₃×#486	C₂²	semidirect
38. C₂₃×#486	C₂²	semidirect
41. C₂₃×#477	C₂²	semidirect
44. C₂₃×#476	C₂²	semidirect
48. C₂₃×#460	C₂²	semidirect
51. C₂₃×#459	C₂²	semidirect
59. C₂₃×#332	C₂²	semidirect
60. C₂₃×#332	C₂²	semidirect
61. C₂₃×#332	C₂²	semidirect
62. 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
274. #18638	C₂₃	direct (N × H)
345. #3520	C₂×C₂₃	semidirect
346. #3247	C₂×C₂₃	semidirect
347. #3131	C₂×C₂₃	semidirect
348. #3109	C₂×C₂₃	semidirect
349. #1638	C₂×C₂₃	semidirect
350. #1637	C₂×C₂₃	semidirect
351. #1635	C₂×C₂₃	semidirect
352. #1635	C₂×C₂₃	semidirect
353. #1628	C₂×C₂₃	semidirect
354. #1627	C₂×C₂₃	semidirect
355. #1625	C₂×C₂₃	semidirect
356. #1625	C₂×C₂₃	semidirect
357. #1552	C₂×C₂₃	semidirect
358. #1494	C₂×C₂₃	semidirect
359. C₂×D₄⋊C₈	C₂×C₂₃	semidirect
412. #487	C₂²×C₂₃	semidirect
413. #487	C₂²×C₂₃	semidirect
414. #486	C₂²×C₂₃	semidirect
415. #486	C₂²×C₂₃	semidirect
418. #477	C₂²×C₂₃	semidirect
421. #476	C₂²×C₂₃	semidirect
425. #460	C₂²×C₂₃	semidirect
428. #459	C₂²×C₂₃	semidirect
436. #332	C₂²×C₂₃	semidirect
437. #332	C₂²×C₂₃	semidirect
438. #332	C₂²×C₂₃	semidirect
439. #332	C₂²×C₂₃	semidirect
440. Q₈⋊C₈	C₂²×C₂₃	semidirect
441. Q₈⋊C₈	C₂²×C₂₃	semidirect
446. D₄⋊C₈	C₂²×C₂₃	semidirect
447. D₄⋊C₈	C₂²×C₂₃	semidirect
561. C₂₃	#18638	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×#3520	2
C₂₃×#3247	2
C₂₃×#3131	2
C₂₃×#3109	2
C₂₃×#1638	2
C₂₃×#1637	2
C₂₃×#1635	2
C₂₃×#1628	2
C₂₃×#1627	2
C₂₃×#1625	2
C₂₃×#1552	2
C₂₃×#1494	2
C₂×C₂₃×D₄⋊C₈	2
#18638	23

Subgroups — C23×#18638 #19166264

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#18638 #19166264