Subgroups — C₂₃×#18522 #19166148

Order 5888.

1000 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	C₂₃×#3475	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₃×#3167	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3100	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#3035	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#1654	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#1652	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#1646	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#1644	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×#1624	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#1622	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#1542	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#1476	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₂₃×D₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₂₃×#135	—	2	1	no	—
17	C₂₃×#556	C₂²	1	1	yes	characteristic
18	C₂₃×#555	C₂²	1	1	yes	characteristic
19	C₂₃×#554	C₂²	1	1	yes	characteristic
20	C₂₃×#553	—	2	1	no	—
21	C₂₃×#552	—	2	1	no	—
22	C₂₃×#552	—	2	1	no	—
23	C₂₃×#551	—	2	2	no	—
24	C₂₃×#547	C₂²	1	1	yes	characteristic
25	C₂₃×#546	—	2	1	no	—
26	C₂₃×#533	C₂²	1	1	yes	characteristic
27	C₂₃×#532	C₂²	1	1	yes	characteristic
28	C₂₃×#529	—	2	2	no	—
29	C₂₃×#529	—	2	1	no	—
30	C₂₃×#525	—	2	1	no	—
31	C₄×#41×C₂₃	—	2	1	no	—
32	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
33	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
34	C₂×C₂₃×#117	—	2	1	no	—
35	C₂₃×#498	C₂²	1	1	yes	characteristic, complemented
36	C₂₃×#492	C₂²	1	1	yes	characteristic, complemented
37	C₂₃×#487	C₂²	1	1	yes	characteristic, complemented
38	C₂₃×#486	C₂²	1	1	yes	characteristic, complemented
39	C₂₃×#480	—	2	1	no	—
40	C₂₃×#474	C₂²	1	1	yes	characteristic
41	C₂₃×#474	C₂²	1	1	yes	characteristic
42	C₂₃×#465	—	2	2	no	—
43	C₂₃×#464	—	2	1	no	—
44	C₂₃×#463	—	2	1	no	—
45	C₂₃×#462	C₂²	1	1	yes	characteristic, complemented
46	C₂₃×#461	C₂²	1	1	yes	characteristic, complemented
47	C₂₃×#460	C₂²	1	1	yes	characteristic, complemented
48	C₂₃×#459	C₂²	1	1	yes	characteristic
49	C₂₃×#459	C₂²	1	1	yes	characteristic
50	C₂₃×#459	C₂²	1	1	yes	characteristic, complemented
51	C₂₃×#447	—	2	1	no	—
52	C₄×SD₁₆×C₂₃	—	2	2	no	—
53	C₄×D₈×C₂₃	—	2	1	no	—
54	C₄×D₈×C₂₃	—	2	1	no	—
55	C₂₃×#431	C₂²	1	1	yes	characteristic
56	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
57	C₂₃×#416	—	2	1	no	—
58	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
59	C₂₃×#333	C₂²	1	1	yes	characteristic, complemented
60	C₂₃×#333	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	D₄	1	1	yes	characteristic
74	C₂²×D₄×C₂₃	D₄	1	1	yes	characteristic
75	C₂³×C₄×C₂₃	—	2	1	no	—
76	C₂₃×#135	—	4	4	no	—
77	C₂×Q₁₆×C₂₃	—	2	1	no	—
78	C₂×SD₁₆×C₂₃	—	2	1	no	—
79	C₂×SD₁₆×C₂₃	—	2	2	no	—
80	C₂×SD₁₆×C₂₃	—	2	1	no	—
81	C₂×D₈×C₂₃	—	2	1	no	—
82	C₂×D₈×C₂₃	—	2	1	no	—
83	C₂×D₈×C₂₃	—	2	1	no	—
84	C₂²×C₈×C₂₃	—	2	1	no	—
85	C₂²×C₈×C₂₃	—	2	1	no	—
86	C₂₃×C₄⋊Q₈	C₂³	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	C₂³	1	1	yes	characteristic
90	C₂₃×#126	—	2	2	no	—
91	C₂₃×#126	—	2	2	no	—
92	C₂₃×#126	—	2	2	no	—
93	C₂₃×#125	—	2	2	no	—
94	C₂₃×#125	—	2	1	no	—
95	C₂₃×#125	—	2	1	no	—
96	C₂₃×#124	—	2	2	no	—
97	C₂₃×#124	—	2	1	no	—
98	C₂₃×#124	—	2	1	no	—
99	C₂₃×#123	—	2	2	no	—
100	C₂₃×#123	—	2	2	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	1	no	—
105	C₂₃×C₂²⋊Q₈	—	2	1	no	—
106	C₂₃×C₂²⋊Q₈	—	2	1	no	—
107	C₂₃×C₂²⋊Q₈	—	2	1	no	—
108	C₂₃×C₂²⋊Q₈	D₄	1	2	yes	—
109	C₂₃×#121	—	2	2	no	—
110	C₂₃×#121	—	2	1	no	—
111	C₂₃×#121	—	2	1	no	—
112	C₂₃×#121	—	2	1	no	—
113	C₂₃×#121	—	2	1	no	—
114	C₂₃×#121	—	2	1	no	—
115	C₂₃×#120	—	2	2	no	—
116	C₄×Q₈×C₂₃	—	2	1	no	—
117	C₄×Q₈×C₂₃	—	2	1	no	—
118	C₄×Q₈×C₂₃	D₄	1	1	yes	characteristic
119	C₄×Q₈×C₂₃	D₄	1	2	yes	—
120	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
121	C₄×D₄×C₂₃	—	2	2	no	—
122	C₄×D₄×C₂₃	—	2	2	no	—
123	C₄×D₄×C₂₃	—	2	2	no	—
124	C₄×D₄×C₂₃	—	2	1	no	—
125	C₄×D₄×C₂₃	—	2	1	no	—
126	C₄×D₄×C₂₃	—	2	1	no	—
127	C₄×D₄×C₂₃	—	2	1	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	D₄	1	1	yes	characteristic
132	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
133	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
134	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
135	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
136	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
137	C₂₃×#117	—	2	2	no	—
138	C₂₃×#117	—	2	2	no	—
139	C₂₃×#117	—	2	2	no	—
140	C₂₃×#117	—	2	1	no	—
141	C₂₃×#117	—	2	1	no	—
142	C₂₃×#117	—	2	1	no	—
143	C₂₃×#117	—	2	1	no	—
144	C₂₃×#117	—	2	1	no	—
145	C₂₃×#117	D₄	1	1	yes	characteristic
146	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
147	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
148	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
149	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
150	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
151	C₂×C₄²×C₂₃	—	2	2	no	—
152	C₂×C₄²×C₂₃	—	2	1	no	—
153	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
154	C₂₃×#107	—	2	1	no	—
155	C₂₃×#107	—	2	1	no	—
156	C₂₃×#106	—	2	2	no	—
157	C₂₃×C₄⋊C₈	—	2	1	no	—
158	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
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×#103	—	2	2	no	—
163	C₂₃×#103	—	2	1	no	—
164	C₂₃×#103	—	2	1	no	—
165	C₂₃×#102	—	2	1	no	—
166	C₂₃×#102	—	2	1	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×#102	—	2	2	no	—
172	C₂₃×C₂²⋊C₈	—	2	1	no	—
173	C₄×C₈×C₂₃	—	2	1	no	—
174	C₄×C₈×C₂₃	—	2	1	no	—
175	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
176	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
177	C₂⁴×C₂₃	—	2	1	no	—
178	#41×C₂₃	—	2	2	no	—
179	#41×C₂₃	—	2	2	no	—
180	#41×C₂₃	—	4	2	no	—
181	#41×C₂₃	—	4	2	no	—
182	#41×C₂₃	—	4	2	no	—
183	#41×C₂₃	—	4	2	no	—
184	C₂×Q₈×C₂₃	—	2	1	no	—
185	C₂×Q₈×C₂₃	—	2	1	no	—
186	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
187	C₂×Q₈×C₂₃	C₂×D₄	1	2	yes	—
188	C₂×D₄×C₂₃	—	2	2	no	—
189	C₂×D₄×C₂₃	—	2	2	no	—
190	C₂×D₄×C₂₃	—	2	1	no	—
191	C₂×D₄×C₂₃	—	2	2	no	—
192	C₂×D₄×C₂₃	—	2	1	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	—	4	1	no	—
197	C₂×D₄×C₂₃	—	4	1	no	—
198	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
199	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
200	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
201	C₂²×C₄×C₂₃	—	2	2	no	—
202	C₂²×C₄×C₂₃	—	2	1	no	—
203	C₂²×C₄×C₂₃	—	2	2	no	—
204	C₂²×C₄×C₂₃	—	2	1	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	2	no	—
212	C₂²×C₄×C₂₃	—	4	2	no	—
213	C₂²×C₄×C₂₃	—	4	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	Q₁₆×C₂₃	—	4	2	no	—
218	SD₁₆×C₂₃	—	4	4	no	—
219	SD₁₆×C₂₃	—	4	2	no	—
220	SD₁₆×C₂₃	—	4	2	no	—
221	D₈×C₂₃	—	4	2	no	—
222	D₈×C₂₃	—	4	2	no	—
223	D₈×C₂₃	—	4	2	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	—	2	1	no	—
228	C₂×C₈×C₂₃	—	2	1	no	—
229	C₂×C₈×C₂₃	—	2	1	no	—
230	C₂×C₈×C₂₃	—	4	2	no	—
231	C₂×C₈×C₂₃	—	4	2	no	—
232	C₄⋊C₄×C₂₃	—	2	2	no	—
233	C₄⋊C₄×C₂₃	—	2	2	no	—
234	C₄⋊C₄×C₂₃	—	2	2	no	—
235	C₄⋊C₄×C₂₃	—	2	2	no	—
236	C₄⋊C₄×C₂₃	—	2	1	no	—
237	C₄⋊C₄×C₂₃	—	2	2	no	—
238	C₄⋊C₄×C₂₃	—	2	1	no	—
239	C₄⋊C₄×C₂₃	—	2	2	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	—	2	1	no	—
245	C₄⋊C₄×C₂₃	—	2	1	no	—
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	2	yes	—
249	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
250	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
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	2	no	—
256	C₂²⋊C₄×C₂₃	—	2	2	no	—
257	C₂²⋊C₄×C₂₃	—	2	1	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	—	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	—	2	1	no	—
271	C₄²×C₂₃	—	2	2	no	—
272	C₄²×C₂₃	—	2	1	no	—
273	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
274	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
275	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
276	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
277	#18522	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
278	C₂³×C₂₃	—	2	1	no	—
279	C₂³×C₂₃	—	2	1	no	—
280	C₂³×C₂₃	—	2	1	no	—
281	C₂³×C₂₃	—	4	2	no	—
282	C₂³×C₂₃	—	4	2	no	—
283	C₂³×C₂₃	—	4	1	no	—
284	C₂³×C₂₃	—	8	1	no	—
285	C₂³×C₂₃	#120	1	1	yes	characteristic
286	Q₈×C₂₃	—	2	1	no	—
287	Q₈×C₂₃	—	2	1	no	—
288	Q₈×C₂₃	—	4	2	no	—
289	Q₈×C₂₃	—	4	1	no	—
290	Q₈×C₂₃	—	4	1	no	—
291	Q₈×C₂₃	—	4	1	no	—
292	Q₈×C₂₃	—	4	1	no	—
293	D₄×C₂₃	—	2	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	—	4	2	no	—
299	D₄×C₂₃	—	4	2	no	—
300	D₄×C₂₃	—	4	4	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	—	8	2	no	—
307	D₄×C₂₃	—	8	2	no	—
308	D₄×C₂₃	#135	1	2	yes	complemented
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	1	no	—
314	C₂×C₄×C₂₃	—	2	1	no	—
315	C₂×C₄×C₂₃	—	2	2	no	—
316	C₂×C₄×C₂₃	—	2	2	no	—
317	C₂×C₄×C₂₃	—	2	1	no	—
318	C₂×C₄×C₂₃	—	4	1	no	—
319	C₂×C₄×C₂₃	—	4	4	no	—
320	C₂×C₄×C₂₃	—	4	2	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	—	4	2	no	—
328	C₂×C₄×C₂₃	—	4	2	no	—
329	C₂×C₄×C₂₃	—	4	2	no	—
330	C₂×C₄×C₂₃	—	4	1	no	—
331	C₂×C₄×C₂₃	—	8	1	no	—
332	C₂×C₄×C₂₃	—	8	2	no	—
333	C₂×C₄×C₂₃	—	8	2	no	—
334	C₂×C₄×C₂₃	#120	1	1	yes	characteristic
335	C₂×C₄×C₂₃	#120	1	1	yes	characteristic
336	C₂×C₄×C₂₃	#120	1	1	yes	characteristic
337	C₂×C₄×C₂₃	#135	1	2	yes	—
338	C₂×C₄×C₂₃	AGL(1,ℤ/8)	1	2	yes	—
339	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
340	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
341	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
342	C₈×C₂₃	—	2	2	no	—
343	C₈×C₂₃	—	4	1	no	—
344	C₈×C₂₃	—	4	1	no	—
345	C₈×C₂₃	—	4	1	no	—
346	C₈×C₂₃	—	4	1	no	—
347	C₈×C₂₃	—	4	1	no	—
348	#3475	C₂×C₂₃	1	1	yes	characteristic, complemented
349	#3167	C₂×C₂₃	1	1	yes	characteristic, complemented
350	#3100	C₂×C₂₃	1	1	yes	characteristic, complemented
351	#3035	C₂×C₂₃	1	1	yes	characteristic, complemented
352	#1654	C₂×C₂₃	1	1	yes	characteristic, complemented
353	#1652	C₂×C₂₃	1	1	yes	characteristic, complemented
354	#1646	C₂×C₂₃	1	1	yes	characteristic, complemented
355	#1644	C₂×C₂₃	1	1	yes	characteristic, complemented
356	#1628	C₂×C₂₃	1	1	yes	characteristic, complemented
357	#1625	C₂×C₂₃	1	1	yes	characteristic, complemented
358	#1624	C₂×C₂₃	1	1	yes	characteristic, complemented
359	#1622	C₂×C₂₃	1	1	yes	characteristic, complemented
360	#1542	C₂×C₂₃	1	1	yes	characteristic, complemented
361	#1476	C₂×C₂₃	1	1	yes	characteristic, complemented
362	C₂×D₄⋊C₈	C₂×C₂₃	1	1	yes	characteristic, complemented
363	C₂²×C₂₃	—	2	1	no	—
364	C₂²×C₂₃	—	2	1	no	—
365	C₂²×C₂₃	—	2	2	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	—	4	1	no	—
372	C₂²×C₂₃	—	4	1	no	—
373	C₂²×C₂₃	—	4	1	no	—
374	C₂²×C₂₃	—	8	4	no	—
375	C₂²×C₂₃	—	8	1	no	—
376	C₂²×C₂₃	—	8	1	no	—
377	C₂²×C₂₃	—	8	1	no	—
378	C₂²×C₂₃	#449	1	2	yes	—
379	C₂²×C₂₃	C₂×#120	1	1	yes	characteristic
380	C₄×C₂₃	—	2	1	no	—
381	C₄×C₂₃	—	2	1	no	—
382	C₄×C₂₃	—	2	1	no	—
383	C₄×C₂₃	—	4	1	no	—
384	C₄×C₂₃	—	4	1	no	—
385	C₄×C₂₃	—	4	1	no	—
386	C₄×C₂₃	—	4	1	no	—
387	C₄×C₂₃	—	4	2	no	—
388	C₄×C₂₃	—	4	1	no	—
389	C₄×C₂₃	—	4	2	no	—
390	C₄×C₂₃	—	8	1	no	—
391	C₄×C₂₃	#449	1	2	yes	—
392	C₄×C₂₃	C₂×#135	1	1	yes	characteristic
393	C₄×C₂₃	C₂×#135	1	1	yes	characteristic
394	C₄×C₂₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
395	C₄×C₂₃	#575	1	1	yes	characteristic
396	C₂×#135	—	2	1	no	—
397	#556	C₂²×C₂₃	1	1	yes	characteristic
398	#555	C₂²×C₂₃	1	1	yes	characteristic
399	#554	C₂²×C₂₃	1	1	yes	characteristic
400	#553	—	2	1	no	—
401	#552	—	2	1	no	—
402	#552	—	2	1	no	—
403	#551	—	2	2	no	—
404	#547	C₂²×C₂₃	1	1	yes	characteristic
405	#546	—	2	1	no	—
406	#533	C₂²×C₂₃	1	1	yes	characteristic
407	#532	C₂²×C₂₃	1	1	yes	characteristic
408	#529	—	2	2	no	—
409	#529	—	2	1	no	—
410	#525	—	2	1	no	—
411	C₄×#41	—	2	1	no	—
412	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
413	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
414	C₂×#117	—	2	1	no	—
415	#498	C₂²×C₂₃	1	1	yes	characteristic, complemented
416	#492	C₂²×C₂₃	1	1	yes	characteristic, complemented
417	#487	C₂²×C₂₃	1	1	yes	characteristic, complemented
418	#486	C₂²×C₂₃	1	1	yes	characteristic, complemented
419	#480	—	2	1	no	—
420	#474	C₂²×C₂₃	1	1	yes	characteristic
421	#474	C₂²×C₂₃	1	1	yes	characteristic
422	#465	—	2	2	no	—
423	#464	—	2	1	no	—
424	#463	—	2	1	no	—
425	#462	C₂²×C₂₃	1	1	yes	characteristic, complemented
426	#461	C₂²×C₂₃	1	1	yes	characteristic, complemented
427	#460	C₂²×C₂₃	1	1	yes	characteristic, complemented
428	#459	C₂²×C₂₃	1	1	yes	characteristic
429	#459	C₂²×C₂₃	1	1	yes	characteristic
430	#459	C₂²×C₂₃	1	1	yes	characteristic, complemented
431	#447	—	2	1	no	—
432	C₄×SD₁₆	—	2	2	no	—
433	C₄×D₈	—	2	1	no	—
434	C₄×D₈	—	2	1	no	—
435	#431	C₂²×C₂₃	1	1	yes	characteristic
436	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
437	#416	—	2	1	no	—
438	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
439	#333	C₂²×C₂₃	1	1	yes	characteristic, complemented
440	#333	C₂²×C₂₃	1	1	yes	characteristic, complemented
441	#332	C₂²×C₂₃	1	1	yes	characteristic, complemented
442	#332	C₂²×C₂₃	1	1	yes	characteristic, complemented
443	Q₈⋊C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
444	Q₈⋊C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
445	D₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
446	D₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
447	D₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
448	D₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
449	D₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
450	D₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
451	C₂×C₂₃	—	2	2	no	—
452	C₂×C₂₃	—	4	2	no	—
453	C₂×C₂₃	—	8	1	no	—
454	C₂×C₂₃	—	8	1	no	—
455	C₂×C₂₃	—	16	1	no	—
456	C₂×C₂₃	C₂×#449	1	1	yes	characteristic
457	C₂×C₂₃	#3002	1	1	yes	characteristic
458	C₂×C₂₃	#3018	1	1	yes	characteristic
459	C₂×#41	—	2	1	no	—
460	C₂×#41	—	2	1	no	—
461	C₂×#41	D₄×C₂₃	1	1	yes	characteristic
462	C₂²×D₄	D₄×C₂₃	1	1	yes	characteristic
463	C₂³×C₄	—	2	1	no	—
464	#135	—	4	4	no	—
465	C₂×Q₁₆	—	2	1	no	—
466	C₂×SD₁₆	—	2	1	no	—
467	C₂×SD₁₆	—	2	2	no	—
468	C₂×SD₁₆	—	2	1	no	—
469	C₂×D₈	—	2	1	no	—
470	C₂×D₈	—	2	1	no	—
471	C₂×D₈	—	2	1	no	—
472	C₂²×C₈	—	2	1	no	—
473	C₂²×C₈	—	2	1	no	—
474	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
475	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
476	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
477	#127	C₂³×C₂₃	1	1	yes	characteristic
478	#126	—	2	2	no	—
479	#126	—	2	2	no	—
480	#126	—	2	2	no	—
481	#125	—	2	2	no	—
482	#125	—	2	1	no	—
483	#125	—	2	1	no	—
484	#124	—	2	2	no	—
485	#124	—	2	1	no	—
486	#124	—	2	1	no	—
487	#123	—	2	2	no	—
488	#123	—	2	2	no	—
489	#123	—	2	2	no	—
490	#123	—	2	2	no	—
491	C₂²⋊Q₈	—	2	1	no	—
492	C₂²⋊Q₈	—	2	1	no	—
493	C₂²⋊Q₈	—	2	2	no	—
494	C₂²⋊Q₈	—	2	1	no	—
495	C₂²⋊Q₈	—	2	1	no	—
496	C₂²⋊Q₈	D₄×C₂₃	1	2	yes	—
497	#121	—	2	2	no	—
498	#121	—	2	1	no	—
499	#121	—	2	1	no	—
500	#121	—	2	1	no	—
501	#121	—	2	1	no	—
502	#121	—	2	1	no	—
503	#120	—	2	2	no	—
504	C₄×Q₈	—	2	1	no	—
505	C₄×Q₈	—	2	1	no	—
506	C₄×Q₈	D₄×C₂₃	1	1	yes	characteristic
507	C₄×Q₈	D₄×C₂₃	1	2	yes	—
508	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
509	C₄×D₄	—	2	2	no	—
510	C₄×D₄	—	2	2	no	—
511	C₄×D₄	—	2	2	no	—
512	C₄×D₄	—	2	1	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	D₄×C₂₃	1	1	yes	characteristic
522	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
523	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
524	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
525	#117	—	2	2	no	—
526	#117	—	2	2	no	—
527	#117	—	2	2	no	—
528	#117	—	2	1	no	—
529	#117	—	2	1	no	—
530	#117	—	2	1	no	—
531	#117	—	2	1	no	—
532	#117	—	2	1	no	—
533	#117	D₄×C₂₃	1	1	yes	characteristic
534	C₂×C₄⋊C₄	—	2	1	no	—
535	C₂×C₄⋊C₄	—	2	1	no	—
536	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
537	C₂×C₂²⋊C₄	—	2	2	no	—
538	C₂×C₂²⋊C₄	—	2	1	no	—
539	C₂×C₄²	—	2	2	no	—
540	C₂×C₄²	—	2	1	no	—
541	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
542	#107	—	2	1	no	—
543	#107	—	2	1	no	—
544	#106	—	2	2	no	—
545	C₄⋊C₈	—	2	1	no	—
546	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
547	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
548	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
549	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
550	#103	—	2	2	no	—
551	#103	—	2	1	no	—
552	#103	—	2	1	no	—
553	#102	—	2	1	no	—
554	#102	—	2	1	no	—
555	#102	—	2	1	no	—
556	#102	—	2	1	no	—
557	#102	—	2	1	no	—
558	#102	—	2	1	no	—
559	#102	—	2	2	no	—
560	C₂²⋊C₈	—	2	1	no	—
561	C₄×C₈	—	2	1	no	—
562	C₄×C₈	—	2	1	no	—
563	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
564	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
565	C₂₃	#18522	1	1	yes	characteristic, direct product factor, Sylow
566	C₂⁴	—	2	1	no	—
567	#41	—	2	2	no	—
568	#41	—	2	2	no	—
569	#41	—	4	2	no	—
570	#41	—	4	2	no	—
571	#41	—	4	2	no	—
572	#41	—	4	2	no	—
573	C₂×Q₈	—	2	1	no	—
574	C₂×Q₈	—	2	1	no	—
575	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
576	C₂×Q₈	C₂×D₄×C₂₃	1	2	yes	—
577	C₂×D₄	—	2	2	no	—
578	C₂×D₄	—	2	2	no	—
579	C₂×D₄	—	2	1	no	—
580	C₂×D₄	—	2	2	no	—
581	C₂×D₄	—	2	1	no	—
582	C₂×D₄	—	2	1	no	—
583	C₂×D₄	—	2	1	no	—
584	C₂×D₄	—	2	1	no	—
585	C₂×D₄	—	4	1	no	—
586	C₂×D₄	—	4	1	no	—
587	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
588	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
589	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
590	C₂²×C₄	—	2	2	no	—
591	C₂²×C₄	—	2	1	no	—
592	C₂²×C₄	—	2	2	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	—	2	1	no	—
598	C₂²×C₄	—	2	1	no	—
599	C₂²×C₄	—	2	1	no	—
600	C₂²×C₄	—	4	2	no	—
601	C₂²×C₄	—	4	2	no	—
602	C₂²×C₄	—	4	1	no	—
603	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
604	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
605	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
606	Q₁₆	—	4	2	no	—
607	SD₁₆	—	4	4	no	—
608	SD₁₆	—	4	2	no	—
609	SD₁₆	—	4	2	no	—
610	D₈	—	4	2	no	—
611	D₈	—	4	2	no	—
612	D₈	—	4	2	no	—
613	C₂×C₈	—	2	1	no	—
614	C₂×C₈	—	2	1	no	—
615	C₂×C₈	—	2	1	no	—
616	C₂×C₈	—	2	1	no	—
617	C₂×C₈	—	2	1	no	—
618	C₂×C₈	—	2	1	no	—
619	C₂×C₈	—	4	2	no	—
620	C₂×C₈	—	4	2	no	—
621	C₄⋊C₄	—	2	2	no	—
622	C₄⋊C₄	—	2	2	no	—
623	C₄⋊C₄	—	2	2	no	—
624	C₄⋊C₄	—	2	2	no	—
625	C₄⋊C₄	—	2	1	no	—
626	C₄⋊C₄	—	2	2	no	—
627	C₄⋊C₄	—	2	1	no	—
628	C₄⋊C₄	—	2	2	no	—
629	C₄⋊C₄	—	2	1	no	—
630	C₄⋊C₄	—	2	1	no	—
631	C₄⋊C₄	—	2	1	no	—
632	C₄⋊C₄	—	2	1	no	—
633	C₄⋊C₄	—	2	1	no	—
634	C₄⋊C₄	—	2	1	no	—
635	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
636	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
637	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
638	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
639	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
640	C₂²⋊C₄	—	2	2	no	—
641	C₂²⋊C₄	—	2	2	no	—
642	C₂²⋊C₄	—	2	2	no	—
643	C₂²⋊C₄	—	2	2	no	—
644	C₂²⋊C₄	—	2	2	no	—
645	C₂²⋊C₄	—	2	2	no	—
646	C₂²⋊C₄	—	2	1	no	—
647	C₂²⋊C₄	—	2	2	no	—
648	C₂²⋊C₄	—	2	1	no	—
649	C₂²⋊C₄	—	2	1	no	—
650	C₂²⋊C₄	—	2	1	no	—
651	C₂²⋊C₄	—	2	1	no	—
652	C₂²⋊C₄	—	2	1	no	—
653	C₂²⋊C₄	—	2	1	no	—
654	C₂²⋊C₄	—	4	1	no	—
655	C₂²⋊C₄	—	4	1	no	—
656	C₄²	—	2	2	no	—
657	C₄²	—	2	2	no	—
658	C₄²	—	2	1	no	—
659	C₄²	—	2	2	no	—
660	C₄²	—	2	1	no	—
661	C₄²	—	2	1	no	—
662	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
663	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
664	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
665	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
666	C₂³	—	2	1	no	—
667	C₂³	—	2	1	no	—
668	C₂³	—	2	1	no	—
669	C₂³	—	4	2	no	—
670	C₂³	—	4	2	no	—
671	C₂³	—	4	1	no	—
672	C₂³	—	8	1	no	—
673	C₂³	C₂₃×#120	1	1	yes	characteristic
674	Q₈	—	2	1	no	—
675	Q₈	—	2	1	no	—
676	Q₈	—	4	2	no	—
677	Q₈	—	4	1	no	—
678	Q₈	—	4	1	no	—
679	Q₈	—	4	1	no	—
680	Q₈	—	4	1	no	—
681	D₄	—	2	1	no	—
682	D₄	—	2	1	no	—
683	D₄	—	2	1	no	—
684	D₄	—	2	1	no	—
685	D₄	—	2	1	no	—
686	D₄	—	4	2	no	—
687	D₄	—	4	2	no	—
688	D₄	—	4	4	no	—
689	D₄	—	4	2	no	—
690	D₄	—	4	1	no	—
691	D₄	—	4	1	no	—
692	D₄	—	4	1	no	—
693	D₄	—	4	1	no	—
694	D₄	—	8	2	no	—
695	D₄	—	8	2	no	—
696	D₄	C₂₃×#135	1	2	yes	complemented
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	1	no	—
702	C₂×C₄	—	2	1	no	—
703	C₂×C₄	—	2	2	no	—
704	C₂×C₄	—	2	2	no	—
705	C₂×C₄	—	2	1	no	—
706	C₂×C₄	—	4	1	no	—
707	C₂×C₄	—	4	4	no	—
708	C₂×C₄	—	4	2	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	2	no	—
716	C₂×C₄	—	4	2	no	—
717	C₂×C₄	—	4	2	no	—
718	C₂×C₄	—	4	1	no	—
719	C₂×C₄	—	8	1	no	—
720	C₂×C₄	—	8	2	no	—
721	C₂×C₄	—	8	2	no	—
722	C₂×C₄	C₂₃×#120	1	1	yes	characteristic
723	C₂×C₄	C₂₃×#120	1	1	yes	characteristic
724	C₂×C₄	C₂₃×#120	1	1	yes	characteristic
725	C₂×C₄	C₂₃×#135	1	2	yes	—
726	C₂×C₄	C₂₃×AGL(1,ℤ/8)	1	2	yes	—
727	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
728	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
729	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
730	C₈	—	2	2	no	—
731	C₈	—	4	1	no	—
732	C₈	—	4	1	no	—
733	C₈	—	4	1	no	—
734	C₈	—	4	1	no	—
735	C₈	—	4	1	no	—
736	C₂²	—	2	1	no	—
737	C₂²	—	2	1	no	—
738	C₂²	—	2	2	no	—
739	C₂²	—	4	1	no	—
740	C₂²	—	4	1	no	—
741	C₂²	—	4	1	no	—
742	C₂²	—	4	1	no	—
743	C₂²	—	4	1	no	—
744	C₂²	—	4	1	no	—
745	C₂²	—	4	1	no	—
746	C₂²	—	4	1	no	—
747	C₂²	—	8	4	no	—
748	C₂²	—	8	1	no	—
749	C₂²	—	8	1	no	—
750	C₂²	—	8	1	no	—
751	C₂²	C₂₃×#449	1	2	yes	—
752	C₂²	C₂×C₂₃×#120	1	1	yes	characteristic
753	C₄	—	2	1	no	—
754	C₄	—	2	1	no	—
755	C₄	—	2	1	no	—
756	C₄	—	4	1	no	—
757	C₄	—	4	1	no	—
758	C₄	—	4	1	no	—
759	C₄	—	4	1	no	—
760	C₄	—	4	2	no	—
761	C₄	—	4	1	no	—
762	C₄	—	4	2	no	—
763	C₄	—	8	1	no	—
764	C₄	C₂₃×#449	1	2	yes	—
765	C₄	C₂×C₂₃×#135	1	1	yes	characteristic
766	C₄	C₂×C₂₃×#135	1	1	yes	characteristic
767	C₄	C₂×C₂₃×AGL(1,ℤ/8)	1	1	yes	characteristic
768	C₄	C₂₃×#575	1	1	yes	characteristic
769	C₂	—	2	2	no	—
770	C₂	—	4	2	no	—
771	C₂	—	8	1	no	—
772	C₂	—	8	1	no	—
773	C₂	—	16	1	no	—
774	C₂	C₂×C₂₃×#449	1	1	yes	characteristic
775	C₂	C₂₃×#3002	1	1	yes	characteristic
776	C₂	C₂₃×#3018	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₂₃	#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₂₃
socle	C₂²×C₂₃	C₂×#120
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₃ ◁ C₂×C₄²×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₃×#3475	C₂	semidirect
2. C₂₃×#3167	C₂	semidirect
3. C₂₃×#3100	C₂	semidirect
4. C₂₃×#3035	C₂	semidirect
5. C₂₃×#1654	C₂	semidirect
6. C₂₃×#1652	C₂	semidirect
7. C₂₃×#1646	C₂	semidirect
8. C₂₃×#1644	C₂	semidirect
9. C₂₃×#1628	C₂	semidirect
10. C₂₃×#1625	C₂	semidirect
11. C₂₃×#1624	C₂	semidirect
12. C₂₃×#1622	C₂	semidirect
13. C₂₃×#1542	C₂	semidirect
14. C₂₃×#1476	C₂	semidirect
15. C₂×C₂₃×D₄⋊C₈	C₂	semidirect
35. C₂₃×#498	C₂²	semidirect
36. C₂₃×#492	C₂²	semidirect
37. C₂₃×#487	C₂²	semidirect
38. C₂₃×#486	C₂²	semidirect
45. C₂₃×#462	C₂²	semidirect
46. C₂₃×#461	C₂²	semidirect
47. C₂₃×#460	C₂²	semidirect
50. C₂₃×#459	C₂²	semidirect
59. C₂₃×#333	C₂²	semidirect
60. C₂₃×#333	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
277. #18522	C₂₃	direct (N × H)
308. D₄×C₂₃	#135	semidirect
348. #3475	C₂×C₂₃	semidirect
349. #3167	C₂×C₂₃	semidirect
350. #3100	C₂×C₂₃	semidirect
351. #3035	C₂×C₂₃	semidirect
352. #1654	C₂×C₂₃	semidirect
353. #1652	C₂×C₂₃	semidirect
354. #1646	C₂×C₂₃	semidirect
355. #1644	C₂×C₂₃	semidirect
356. #1628	C₂×C₂₃	semidirect
357. #1625	C₂×C₂₃	semidirect
358. #1624	C₂×C₂₃	semidirect
359. #1622	C₂×C₂₃	semidirect
360. #1542	C₂×C₂₃	semidirect
361. #1476	C₂×C₂₃	semidirect
362. C₂×D₄⋊C₈	C₂×C₂₃	semidirect
415. #498	C₂²×C₂₃	semidirect
416. #492	C₂²×C₂₃	semidirect
417. #487	C₂²×C₂₃	semidirect
418. #486	C₂²×C₂₃	semidirect
425. #462	C₂²×C₂₃	semidirect
426. #461	C₂²×C₂₃	semidirect
427. #460	C₂²×C₂₃	semidirect
430. #459	C₂²×C₂₃	semidirect
439. #333	C₂²×C₂₃	semidirect
440. #333	C₂²×C₂₃	semidirect
441. #332	C₂²×C₂₃	semidirect
442. #332	C₂²×C₂₃	semidirect
443. Q₈⋊C₈	C₂²×C₂₃	semidirect
444. Q₈⋊C₈	C₂²×C₂₃	semidirect
449. D₄⋊C₈	C₂²×C₂₃	semidirect
450. D₄⋊C₈	C₂²×C₂₃	semidirect
565. C₂₃	#18522	direct (N × H)
696. D₄	C₂₃×#135	semidirect

Maximal subgroups

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

subgroup	index
C₂₃×#3475	2
C₂₃×#3167	2
C₂₃×#3100	2
C₂₃×#3035	2
C₂₃×#1654	2
C₂₃×#1652	2
C₂₃×#1646	2
C₂₃×#1644	2
C₂₃×#1628	2
C₂₃×#1625	2
C₂₃×#1624	2
C₂₃×#1622	2
C₂₃×#1542	2
C₂₃×#1476	2
C₂×C₂₃×D₄⋊C₈	2
#18522	23

Subgroups — C23×#18522 #19166148

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#18522 #19166148