Subgroups — C₂₃×#18618 #19166244

Order 5888.

1084 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3519	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₃×#3247	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3147	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#3109	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#1634	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#1632	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×#1624	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#1622	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×#1551	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	C₂×C₂₃×#135	—	2	2	no	—
17	C₂₃×#555	C₂²	1	1	yes	characteristic
18	C₂₃×#554	C₂²	1	1	yes	characteristic
19	C₂₃×#553	—	2	1	no	—
20	C₂₃×#553	—	2	1	no	—
21	C₂₃×#550	C₂²	1	1	yes	characteristic
22	C₂₃×#546	—	2	2	no	—
23	C₂₃×#546	—	2	1	no	—
24	D₄²×C₂₃	—	2	1	no	—
25	D₄²×C₂₃	C₂²	1	1	yes	characteristic
26	C₂₃×#540	—	2	1	no	—
27	C₂₃×#538	—	2	2	no	—
28	C₂₃×#532	C₂²	1	1	yes	characteristic
29	C₂₃×#532	C₂²	1	1	yes	characteristic, complemented
30	C₂₃×#529	C₂²	1	1	yes	characteristic
31	C₂₃×#525	—	2	1	no	—
32	C₂×C₂₃×#121	—	2	1	no	—
33	C₂₃×#518	—	2	1	no	—
34	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
35	C₂₃×#495	—	2	2	no	—
36	C₂₃×#494	C₂²	1	1	yes	characteristic, complemented
37	C₂₃×#493	C₂²	1	1	yes	characteristic, complemented
38	C₂₃×#492	C₂²	1	1	yes	characteristic, complemented
39	C₂₃×#492	C₂²	1	1	yes	characteristic, complemented
40	C₂₃×#481	—	2	1	no	—
41	C₂₃×#478	—	2	1	no	—
42	C₂₃×#477	C₂²	1	1	yes	characteristic, complemented
43	C₂₃×#476	C₂²	1	1	yes	characteristic
44	C₂₃×#476	C₂²	1	1	yes	characteristic, complemented
45	C₂₃×#476	C₂²	1	1	yes	characteristic, complemented
46	C₂₃×#466	—	2	1	no	—
47	C₂₃×#465	—	2	1	no	—
48	C₂₃×#463	—	2	1	no	—
49	C₂₃×#460	C₂²	1	1	yes	characteristic, complemented
50	C₂₃×#459	C₂²	1	1	yes	characteristic
51	C₂₃×#459	C₂²	1	1	yes	characteristic, complemented
52	C₂₃×#459	C₂²	1	1	yes	characteristic, complemented
53	C₂₃×#447	—	2	1	no	—
54	C₂₃×#442	—	2	1	no	—
55	C₂₃×#442	—	2	1	no	—
56	C₂₃×#432	C₂²	1	1	yes	characteristic, complemented
57	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
58	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
59	C₂₃×#333	C₂²	1	1	yes	characteristic, complemented
60	C₂₃×#333	C₂²	1	1	yes	characteristic, complemented
61	C₂₃×#331	C₂²	1	1	yes	characteristic, complemented
62	C₂₃×#331	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, complemented
68	C₂₃×D₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
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	2	yes	—
74	C₂²×D₄×C₂₃	—	2	2	no	—
75	C₂²×D₄×C₂₃	—	2	1	no	—
76	C₂²×D₄×C₂₃	—	2	1	no	—
77	C₂²×D₄×C₂₃	D₄	1	1	yes	characteristic
78	C₂³×C₄×C₂₃	—	2	1	no	—
79	C₂₃×#135	—	4	8	no	—
80	C₂×Q₁₆×C₂₃	—	2	2	no	—
81	C₂×SD₁₆×C₂₃	—	2	2	no	—
82	C₂×SD₁₆×C₂₃	—	2	2	no	—
83	C₂×SD₁₆×C₂₃	—	2	1	no	—
84	C₂×D₈×C₂₃	—	2	2	no	—
85	C₂×D₈×C₂₃	—	2	1	no	—
86	C₂×D₈×C₂₃	—	2	1	no	—
87	C₂×D₈×C₂₃	—	2	1	no	—
88	C₂²×C₈×C₂₃	—	2	1	no	—
89	C₂²×C₈×C₂₃	—	2	1	no	—
90	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
91	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
92	C₂₃×#127	—	2	1	no	—
93	C₂₃×#127	C₂³	1	1	yes	characteristic
94	C₂₃×#127	C₂³	1	1	yes	characteristic
95	C₂₃×#126	—	2	2	no	—
96	C₂₃×#126	—	2	1	no	—
97	C₂₃×#125	—	2	1	no	—
98	C₂₃×#125	D₄	1	1	yes	characteristic
99	C₂₃×#124	—	2	2	no	—
100	C₂₃×#124	—	2	1	no	—
101	C₂₃×#124	D₄	1	1	yes	characteristic
102	C₂₃×#124	D₄	1	2	yes	—
103	C₂₃×#123	—	2	2	no	—
104	C₂₃×#123	—	2	2	no	—
105	C₂₃×#123	—	2	2	no	—
106	C₂₃×#123	—	2	1	no	—
107	C₂₃×C₂²⋊Q₈	—	2	1	no	—
108	C₂₃×C₂²⋊Q₈	—	2	2	no	—
109	C₂₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
110	C₂₃×#121	—	2	2	no	—
111	C₂₃×#121	—	2	2	no	—
112	C₂₃×#121	—	2	2	no	—
113	C₂₃×#121	—	2	2	no	—
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	—	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	D₄	1	1	yes	characteristic
125	C₂₃×#120	—	2	2	no	—
126	C₂₃×#120	—	2	2	no	—
127	C₂₃×#120	—	2	2	no	—
128	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
129	C₄×D₄×C₂₃	—	2	2	no	—
130	C₄×D₄×C₂₃	—	2	2	no	—
131	C₄×D₄×C₂₃	—	2	2	no	—
132	C₄×D₄×C₂₃	—	2	1	no	—
133	C₄×D₄×C₂₃	—	2	1	no	—
134	C₄×D₄×C₂₃	—	2	1	no	—
135	C₄×D₄×C₂₃	—	2	1	no	—
136	C₄×D₄×C₂₃	—	2	1	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	D₄	1	1	yes	characteristic
142	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
143	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
144	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
145	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
146	C₂₃×#117	—	2	1	no	—
147	C₂₃×#117	—	2	1	no	—
148	C₂₃×#117	—	2	1	no	—
149	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
150	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
151	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
152	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
153	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
154	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
155	C₂₃×#107	—	2	1	no	—
156	C₂₃×#106	—	2	1	no	—
157	C₂₃×#106	—	2	1	no	—
158	C₂₃×#106	—	2	1	no	—
159	C₂₃×C₄⋊C₈	—	2	1	no	—
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×C₄⋊C₈	C₂³	1	1	yes	characteristic
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	1	no	—
172	C₂₃×C₂²⋊C₈	—	2	1	no	—
173	C₂₃×#97	—	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	2	no	—
178	C₂⁴×C₂₃	—	2	1	no	—
179	#41×C₂₃	—	4	4	no	—
180	#41×C₂₃	—	4	4	no	—
181	#41×C₂₃	—	8	1	no	—
182	#41×C₂₃	—	8	1	no	—
183	C₂×Q₈×C₂₃	—	2	1	no	—
184	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
185	C₂×Q₈×C₂₃	C₂×D₄	1	2	yes	—
186	C₂×D₄×C₂₃	—	2	2	no	—
187	C₂×D₄×C₂₃	—	2	2	no	—
188	C₂×D₄×C₂₃	—	2	2	no	—
189	C₂×D₄×C₂₃	—	2	1	no	—
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	1	no	—
195	C₂×D₄×C₂₃	—	2	1	no	—
196	C₂×D₄×C₂₃	—	2	1	no	—
197	C₂×D₄×C₂₃	—	2	1	no	—
198	C₂×D₄×C₂₃	—	2	1	no	—
199	C₂×D₄×C₂₃	—	2	1	no	—
200	C₂×D₄×C₂₃	—	4	1	no	—
201	C₂×D₄×C₂₃	—	4	2	no	—
202	C₂×D₄×C₂₃	—	4	2	no	—
203	C₂×D₄×C₂₃	—	4	1	no	—
204	C₂×D₄×C₂₃	—	8	1	no	—
205	C₂×D₄×C₂₃	—	8	1	no	—
206	C₂×D₄×C₂₃	—	8	4	no	—
207	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
208	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
209	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
210	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
211	C₂²×C₄×C₂₃	—	2	2	no	—
212	C₂²×C₄×C₂₃	—	2	2	no	—
213	C₂²×C₄×C₂₃	—	2	1	no	—
214	C₂²×C₄×C₂₃	—	2	1	no	—
215	C₂²×C₄×C₂₃	—	2	1	no	—
216	C₂²×C₄×C₂₃	—	2	1	no	—
217	C₂²×C₄×C₂₃	—	2	1	no	—
218	C₂²×C₄×C₂₃	—	2	2	no	—
219	C₂²×C₄×C₂₃	—	2	1	no	—
220	C₂²×C₄×C₂₃	—	4	1	no	—
221	C₂²×C₄×C₂₃	—	8	1	no	—
222	C₂²×C₄×C₂₃	—	8	1	no	—
223	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
224	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
225	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
226	Q₁₆×C₂₃	—	4	4	no	—
227	SD₁₆×C₂₃	—	4	4	no	—
228	SD₁₆×C₂₃	—	4	4	no	—
229	SD₁₆×C₂₃	—	8	1	no	—
230	D₈×C₂₃	—	4	4	no	—
231	D₈×C₂₃	—	4	2	no	—
232	D₈×C₂₃	—	4	2	no	—
233	D₈×C₂₃	—	8	1	no	—
234	C₂×C₈×C₂₃	—	2	4	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	—	2	1	no	—
239	C₂×C₈×C₂₃	—	2	1	no	—
240	C₂×C₈×C₂₃	—	2	1	no	—
241	C₂×C₈×C₂₃	—	8	1	no	—
242	C₄⋊C₄×C₂₃	—	2	2	no	—
243	C₄⋊C₄×C₂₃	—	2	2	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	—	2	1	no	—
250	C₄⋊C₄×C₂₃	—	2	1	no	—
251	C₄⋊C₄×C₂₃	—	2	1	no	—
252	C₄⋊C₄×C₂₃	—	2	1	no	—
253	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
254	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
255	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
256	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
257	C₂²⋊C₄×C₂₃	—	2	2	no	—
258	C₂²⋊C₄×C₂₃	—	2	2	no	—
259	C₂²⋊C₄×C₂₃	—	2	2	no	—
260	C₂²⋊C₄×C₂₃	—	2	2	no	—
261	C₂²⋊C₄×C₂₃	—	2	2	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	1	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	2	no	—
270	C₂²⋊C₄×C₂₃	—	2	1	no	—
271	C₂²⋊C₄×C₂₃	—	2	1	no	—
272	C₂²⋊C₄×C₂₃	—	2	1	no	—
273	C₂²⋊C₄×C₂₃	—	4	1	no	—
274	C₂²⋊C₄×C₂₃	—	4	1	no	—
275	C₄²×C₂₃	—	2	2	no	—
276	C₄²×C₂₃	—	2	1	no	—
277	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
278	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
279	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
280	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
281	#18618	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
282	C₂³×C₂₃	—	2	1	no	—
283	C₂³×C₂₃	—	2	1	no	—
284	C₂³×C₂₃	—	2	1	no	—
285	C₂³×C₂₃	—	2	2	no	—
286	C₂³×C₂₃	—	4	2	no	—
287	C₂³×C₂₃	—	4	4	no	—
288	C₂³×C₂₃	—	4	2	no	—
289	C₂³×C₂₃	—	4	1	no	—
290	C₂³×C₂₃	—	8	1	no	—
291	C₂³×C₂₃	—	8	2	no	—
292	C₂³×C₂₃	—	8	2	no	—
293	C₂³×C₂₃	#120	1	1	yes	characteristic
294	Q₈×C₂₃	—	2	1	no	—
295	Q₈×C₂₃	—	2	1	no	—
296	Q₈×C₂₃	—	4	2	no	—
297	Q₈×C₂₃	—	4	2	no	—
298	D₄×C₂₃	—	2	1	no	—
299	D₄×C₂₃	—	2	1	no	—
300	D₄×C₂₃	—	2	1	no	—
301	D₄×C₂₃	—	2	1	no	—
302	D₄×C₂₃	—	2	1	no	—
303	D₄×C₂₃	—	4	2	no	—
304	D₄×C₂₃	—	4	2	no	—
305	D₄×C₂₃	—	4	2	no	—
306	D₄×C₂₃	—	4	4	no	—
307	D₄×C₂₃	—	4	2	no	—
308	D₄×C₂₃	—	4	4	no	—
309	D₄×C₂₃	—	4	1	no	—
310	D₄×C₂₃	—	4	1	no	—
311	D₄×C₂₃	—	4	1	no	—
312	D₄×C₂₃	—	4	1	no	—
313	D₄×C₂₃	—	4	1	no	—
314	D₄×C₂₃	—	4	1	no	—
315	D₄×C₂₃	—	4	1	no	—
316	D₄×C₂₃	—	4	1	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	D₄×C₂₃	#135	1	2	yes	complemented
323	C₂×C₄×C₂₃	—	2	2	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	1	no	—
330	C₂×C₄×C₂₃	—	2	1	no	—
331	C₂×C₄×C₂₃	—	2	2	no	—
332	C₂×C₄×C₂₃	—	2	1	no	—
333	C₂×C₄×C₂₃	—	2	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	—	4	1	no	—
341	C₂×C₄×C₂₃	—	8	1	no	—
342	C₂×C₄×C₂₃	—	8	1	no	—
343	C₂×C₄×C₂₃	—	8	2	no	—
344	C₂×C₄×C₂₃	—	8	2	no	—
345	C₂×C₄×C₂₃	—	8	1	no	—
346	C₂×C₄×C₂₃	—	8	2	no	—
347	C₂×C₄×C₂₃	—	8	2	no	—
348	C₂×C₄×C₂₃	#120	1	1	yes	characteristic
349	C₂×C₄×C₂₃	#120	1	1	yes	characteristic
350	C₂×C₄×C₂₃	#120	1	1	yes	characteristic
351	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
352	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
353	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
354	C₈×C₂₃	—	2	2	no	—
355	C₈×C₂₃	—	2	2	no	—
356	C₈×C₂₃	—	4	1	no	—
357	C₈×C₂₃	—	4	1	no	—
358	C₈×C₂₃	—	4	1	no	—
359	C₈×C₂₃	—	4	1	no	—
360	#3519	C₂×C₂₃	1	1	yes	characteristic, complemented
361	#3247	C₂×C₂₃	1	1	yes	characteristic, complemented
362	#3147	C₂×C₂₃	1	1	yes	characteristic, complemented
363	#3109	C₂×C₂₃	1	1	yes	characteristic, complemented
364	#1634	C₂×C₂₃	1	1	yes	characteristic, complemented
365	#1632	C₂×C₂₃	1	1	yes	characteristic, complemented
366	#1631	C₂×C₂₃	1	1	yes	characteristic, complemented
367	#1629	C₂×C₂₃	1	1	yes	characteristic, complemented
368	#1624	C₂×C₂₃	1	1	yes	characteristic, complemented
369	#1622	C₂×C₂₃	1	1	yes	characteristic, complemented
370	#1621	C₂×C₂₃	1	1	yes	characteristic, complemented
371	#1619	C₂×C₂₃	1	1	yes	characteristic, complemented
372	#1551	C₂×C₂₃	1	1	yes	characteristic, complemented
373	#1494	C₂×C₂₃	1	1	yes	characteristic, complemented
374	C₂×D₄⋊C₈	C₂×C₂₃	1	1	yes	characteristic, complemented
375	C₂²×C₂₃	—	2	1	no	—
376	C₂²×C₂₃	—	2	1	no	—
377	C₂²×C₂₃	—	2	2	no	—
378	C₂²×C₂₃	—	4	1	no	—
379	C₂²×C₂₃	—	4	1	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	2	no	—
385	C₂²×C₂₃	—	4	1	no	—
386	C₂²×C₂₃	—	4	2	no	—
387	C₂²×C₂₃	—	4	1	no	—
388	C₂²×C₂₃	—	4	1	no	—
389	C₂²×C₂₃	—	8	4	no	—
390	C₂²×C₂₃	—	8	1	no	—
391	C₂²×C₂₃	—	8	1	no	—
392	C₂²×C₂₃	—	8	1	no	—
393	C₂²×C₂₃	—	16	4	no	—
394	C₂²×C₂₃	#453	1	2	yes	—
395	C₂²×C₂₃	C₂×#120	1	1	yes	characteristic
396	C₄×C₂₃	—	2	1	no	—
397	C₄×C₂₃	—	2	1	no	—
398	C₄×C₂₃	—	2	1	no	—
399	C₄×C₂₃	—	2	1	no	—
400	C₄×C₂₃	—	4	1	no	—
401	C₄×C₂₃	—	4	1	no	—
402	C₄×C₂₃	—	4	1	no	—
403	C₄×C₂₃	—	4	1	no	—
404	C₄×C₂₃	—	4	1	no	—
405	C₄×C₂₃	—	4	2	no	—
406	C₄×C₂₃	—	8	1	no	—
407	C₄×C₂₃	C₂×#135	1	1	yes	characteristic
408	C₄×C₂₃	#575	1	1	yes	characteristic
409	C₄×C₂₃	#576	1	1	yes	characteristic
410	C₄×C₂₃	#577	1	1	yes	characteristic
411	C₂×#135	—	2	2	no	—
412	#555	C₂²×C₂₃	1	1	yes	characteristic
413	#554	C₂²×C₂₃	1	1	yes	characteristic
414	#553	—	2	1	no	—
415	#553	—	2	1	no	—
416	#550	C₂²×C₂₃	1	1	yes	characteristic
417	#546	—	2	2	no	—
418	#546	—	2	1	no	—
419	D₄²	—	2	1	no	—
420	D₄²	C₂²×C₂₃	1	1	yes	characteristic
421	#540	—	2	1	no	—
422	#538	—	2	2	no	—
423	#532	C₂²×C₂₃	1	1	yes	characteristic
424	#532	C₂²×C₂₃	1	1	yes	characteristic, complemented
425	#529	C₂²×C₂₃	1	1	yes	characteristic
426	#525	—	2	1	no	—
427	C₂×#121	—	2	1	no	—
428	#518	—	2	1	no	—
429	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
430	#495	—	2	2	no	—
431	#494	C₂²×C₂₃	1	1	yes	characteristic, complemented
432	#493	C₂²×C₂₃	1	1	yes	characteristic, complemented
433	#492	C₂²×C₂₃	1	1	yes	characteristic, complemented
434	#492	C₂²×C₂₃	1	1	yes	characteristic, complemented
435	#481	—	2	1	no	—
436	#478	—	2	1	no	—
437	#477	C₂²×C₂₃	1	1	yes	characteristic, complemented
438	#476	C₂²×C₂₃	1	1	yes	characteristic
439	#476	C₂²×C₂₃	1	1	yes	characteristic, complemented
440	#476	C₂²×C₂₃	1	1	yes	characteristic, complemented
441	#466	—	2	1	no	—
442	#465	—	2	1	no	—
443	#463	—	2	1	no	—
444	#460	C₂²×C₂₃	1	1	yes	characteristic, complemented
445	#459	C₂²×C₂₃	1	1	yes	characteristic
446	#459	C₂²×C₂₃	1	1	yes	characteristic, complemented
447	#459	C₂²×C₂₃	1	1	yes	characteristic, complemented
448	#447	—	2	1	no	—
449	#442	—	2	1	no	—
450	#442	—	2	1	no	—
451	#432	C₂²×C₂₃	1	1	yes	characteristic, complemented
452	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
453	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
454	#333	C₂²×C₂₃	1	1	yes	characteristic, complemented
455	#333	C₂²×C₂₃	1	1	yes	characteristic, complemented
456	#331	C₂²×C₂₃	1	1	yes	characteristic, complemented
457	#331	C₂²×C₂₃	1	1	yes	characteristic, complemented
458	Q₈⋊C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
459	Q₈⋊C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
460	D₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
461	D₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
462	D₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
463	D₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
464	D₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
465	D₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
466	C₂×C₂₃	—	2	2	no	—
467	C₂×C₂₃	—	4	2	no	—
468	C₂×C₂₃	—	8	1	no	—
469	C₂×C₂₃	—	8	2	no	—
470	C₂×C₂₃	—	8	1	no	—
471	C₂×C₂₃	—	16	1	no	—
472	C₂×C₂₃	#3002	1	1	yes	characteristic
473	C₂×C₂₃	#3012	1	1	yes	characteristic
474	C₂×C₂₃	C₂×#453	1	1	yes	characteristic
475	C₂×#41	—	2	1	no	—
476	C₂×#41	—	2	1	no	—
477	C₂×#41	D₄×C₂₃	1	2	yes	—
478	C₂²×D₄	—	2	2	no	—
479	C₂²×D₄	—	2	1	no	—
480	C₂²×D₄	—	2	1	no	—
481	C₂²×D₄	D₄×C₂₃	1	1	yes	characteristic
482	C₂³×C₄	—	2	1	no	—
483	#135	—	4	8	no	—
484	C₂×Q₁₆	—	2	2	no	—
485	C₂×SD₁₆	—	2	2	no	—
486	C₂×SD₁₆	—	2	2	no	—
487	C₂×SD₁₆	—	2	1	no	—
488	C₂×D₈	—	2	2	no	—
489	C₂×D₈	—	2	1	no	—
490	C₂×D₈	—	2	1	no	—
491	C₂×D₈	—	2	1	no	—
492	C₂²×C₈	—	2	1	no	—
493	C₂²×C₈	—	2	1	no	—
494	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
495	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
496	#127	—	2	1	no	—
497	#127	C₂³×C₂₃	1	1	yes	characteristic
498	#127	C₂³×C₂₃	1	1	yes	characteristic
499	#126	—	2	2	no	—
500	#126	—	2	1	no	—
501	#125	—	2	1	no	—
502	#125	D₄×C₂₃	1	1	yes	characteristic
503	#124	—	2	2	no	—
504	#124	—	2	1	no	—
505	#124	D₄×C₂₃	1	1	yes	characteristic
506	#124	D₄×C₂₃	1	2	yes	—
507	#123	—	2	2	no	—
508	#123	—	2	2	no	—
509	#123	—	2	2	no	—
510	#123	—	2	1	no	—
511	C₂²⋊Q₈	—	2	1	no	—
512	C₂²⋊Q₈	—	2	2	no	—
513	C₂²⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
514	#121	—	2	2	no	—
515	#121	—	2	2	no	—
516	#121	—	2	2	no	—
517	#121	—	2	2	no	—
518	#121	—	2	1	no	—
519	#121	—	2	2	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	—	2	1	no	—
526	#121	—	2	1	no	—
527	#121	—	2	1	no	—
528	#121	D₄×C₂₃	1	1	yes	characteristic
529	#120	—	2	2	no	—
530	#120	—	2	2	no	—
531	#120	—	2	2	no	—
532	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
533	C₄×D₄	—	2	2	no	—
534	C₄×D₄	—	2	2	no	—
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	—	2	1	no	—
543	C₄×D₄	—	2	1	no	—
544	C₄×D₄	—	2	1	no	—
545	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
546	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
547	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
548	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
549	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
550	#117	—	2	1	no	—
551	#117	—	2	1	no	—
552	#117	—	2	1	no	—
553	C₂×C₄⋊C₄	—	2	1	no	—
554	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
555	C₂×C₂²⋊C₄	—	2	2	no	—
556	C₂×C₂²⋊C₄	—	2	2	no	—
557	C₂×C₂²⋊C₄	—	2	1	no	—
558	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
559	#107	—	2	1	no	—
560	#106	—	2	1	no	—
561	#106	—	2	1	no	—
562	#106	—	2	1	no	—
563	C₄⋊C₈	—	2	1	no	—
564	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
565	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
566	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
567	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
568	#103	—	2	1	no	—
569	#102	—	2	1	no	—
570	#102	—	2	1	no	—
571	#102	—	2	1	no	—
572	#102	—	2	1	no	—
573	#102	—	2	1	no	—
574	#102	—	2	1	no	—
575	#102	—	2	1	no	—
576	C₂²⋊C₈	—	2	1	no	—
577	#97	—	2	1	no	—
578	C₄×C₈	—	2	1	no	—
579	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
580	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
581	C₂₃	#18618	1	1	yes	characteristic, direct product factor, Sylow
582	C₂⁴	—	2	2	no	—
583	C₂⁴	—	2	1	no	—
584	#41	—	4	4	no	—
585	#41	—	4	4	no	—
586	#41	—	8	1	no	—
587	#41	—	8	1	no	—
588	C₂×Q₈	—	2	1	no	—
589	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
590	C₂×Q₈	C₂×D₄×C₂₃	1	2	yes	—
591	C₂×D₄	—	2	2	no	—
592	C₂×D₄	—	2	2	no	—
593	C₂×D₄	—	2	2	no	—
594	C₂×D₄	—	2	1	no	—
595	C₂×D₄	—	2	2	no	—
596	C₂×D₄	—	2	2	no	—
597	C₂×D₄	—	2	2	no	—
598	C₂×D₄	—	2	2	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	—	4	1	no	—
606	C₂×D₄	—	4	2	no	—
607	C₂×D₄	—	4	2	no	—
608	C₂×D₄	—	4	1	no	—
609	C₂×D₄	—	8	1	no	—
610	C₂×D₄	—	8	1	no	—
611	C₂×D₄	—	8	4	no	—
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	1	yes	characteristic
615	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
616	C₂²×C₄	—	2	2	no	—
617	C₂²×C₄	—	2	2	no	—
618	C₂²×C₄	—	2	1	no	—
619	C₂²×C₄	—	2	1	no	—
620	C₂²×C₄	—	2	1	no	—
621	C₂²×C₄	—	2	1	no	—
622	C₂²×C₄	—	2	1	no	—
623	C₂²×C₄	—	2	2	no	—
624	C₂²×C₄	—	2	1	no	—
625	C₂²×C₄	—	4	1	no	—
626	C₂²×C₄	—	8	1	no	—
627	C₂²×C₄	—	8	1	no	—
628	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
629	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
630	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
631	Q₁₆	—	4	4	no	—
632	SD₁₆	—	4	4	no	—
633	SD₁₆	—	4	4	no	—
634	SD₁₆	—	8	1	no	—
635	D₈	—	4	4	no	—
636	D₈	—	4	2	no	—
637	D₈	—	4	2	no	—
638	D₈	—	8	1	no	—
639	C₂×C₈	—	2	4	no	—
640	C₂×C₈	—	2	1	no	—
641	C₂×C₈	—	2	1	no	—
642	C₂×C₈	—	2	1	no	—
643	C₂×C₈	—	2	1	no	—
644	C₂×C₈	—	2	1	no	—
645	C₂×C₈	—	2	1	no	—
646	C₂×C₈	—	8	1	no	—
647	C₄⋊C₄	—	2	2	no	—
648	C₄⋊C₄	—	2	2	no	—
649	C₄⋊C₄	—	2	1	no	—
650	C₄⋊C₄	—	2	1	no	—
651	C₄⋊C₄	—	2	1	no	—
652	C₄⋊C₄	—	2	1	no	—
653	C₄⋊C₄	—	2	1	no	—
654	C₄⋊C₄	—	2	1	no	—
655	C₄⋊C₄	—	2	1	no	—
656	C₄⋊C₄	—	2	1	no	—
657	C₄⋊C₄	—	2	1	no	—
658	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
659	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
660	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
661	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
662	C₂²⋊C₄	—	2	2	no	—
663	C₂²⋊C₄	—	2	2	no	—
664	C₂²⋊C₄	—	2	2	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	—	2	1	no	—
671	C₂²⋊C₄	—	2	2	no	—
672	C₂²⋊C₄	—	2	1	no	—
673	C₂²⋊C₄	—	2	1	no	—
674	C₂²⋊C₄	—	2	2	no	—
675	C₂²⋊C₄	—	2	1	no	—
676	C₂²⋊C₄	—	2	1	no	—
677	C₂²⋊C₄	—	2	1	no	—
678	C₂²⋊C₄	—	4	1	no	—
679	C₂²⋊C₄	—	4	1	no	—
680	C₄²	—	2	2	no	—
681	C₄²	—	2	1	no	—
682	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
683	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
684	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
685	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
686	C₂³	—	2	1	no	—
687	C₂³	—	2	1	no	—
688	C₂³	—	2	1	no	—
689	C₂³	—	2	2	no	—
690	C₂³	—	4	2	no	—
691	C₂³	—	4	4	no	—
692	C₂³	—	4	2	no	—
693	C₂³	—	4	1	no	—
694	C₂³	—	8	1	no	—
695	C₂³	—	8	2	no	—
696	C₂³	—	8	2	no	—
697	C₂³	C₂₃×#120	1	1	yes	characteristic
698	Q₈	—	2	1	no	—
699	Q₈	—	2	1	no	—
700	Q₈	—	4	2	no	—
701	Q₈	—	4	2	no	—
702	D₄	—	2	1	no	—
703	D₄	—	2	1	no	—
704	D₄	—	2	1	no	—
705	D₄	—	2	1	no	—
706	D₄	—	2	1	no	—
707	D₄	—	4	2	no	—
708	D₄	—	4	2	no	—
709	D₄	—	4	2	no	—
710	D₄	—	4	4	no	—
711	D₄	—	4	2	no	—
712	D₄	—	4	4	no	—
713	D₄	—	4	1	no	—
714	D₄	—	4	1	no	—
715	D₄	—	4	1	no	—
716	D₄	—	4	1	no	—
717	D₄	—	4	1	no	—
718	D₄	—	4	1	no	—
719	D₄	—	4	1	no	—
720	D₄	—	4	1	no	—
721	D₄	—	8	2	no	—
722	D₄	—	8	2	no	—
723	D₄	—	8	2	no	—
724	D₄	—	8	2	no	—
725	D₄	—	8	2	no	—
726	D₄	C₂₃×#135	1	2	yes	complemented
727	C₂×C₄	—	2	2	no	—
728	C₂×C₄	—	2	1	no	—
729	C₂×C₄	—	2	1	no	—
730	C₂×C₄	—	2	1	no	—
731	C₂×C₄	—	2	1	no	—
732	C₂×C₄	—	2	1	no	—
733	C₂×C₄	—	2	1	no	—
734	C₂×C₄	—	2	1	no	—
735	C₂×C₄	—	2	2	no	—
736	C₂×C₄	—	2	1	no	—
737	C₂×C₄	—	2	1	no	—
738	C₂×C₄	—	4	1	no	—
739	C₂×C₄	—	4	1	no	—
740	C₂×C₄	—	4	1	no	—
741	C₂×C₄	—	4	1	no	—
742	C₂×C₄	—	4	1	no	—
743	C₂×C₄	—	4	1	no	—
744	C₂×C₄	—	4	1	no	—
745	C₂×C₄	—	8	1	no	—
746	C₂×C₄	—	8	1	no	—
747	C₂×C₄	—	8	2	no	—
748	C₂×C₄	—	8	2	no	—
749	C₂×C₄	—	8	1	no	—
750	C₂×C₄	—	8	2	no	—
751	C₂×C₄	—	8	2	no	—
752	C₂×C₄	C₂₃×#120	1	1	yes	characteristic
753	C₂×C₄	C₂₃×#120	1	1	yes	characteristic
754	C₂×C₄	C₂₃×#120	1	1	yes	characteristic
755	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
756	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
757	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
758	C₈	—	2	2	no	—
759	C₈	—	2	2	no	—
760	C₈	—	4	1	no	—
761	C₈	—	4	1	no	—
762	C₈	—	4	1	no	—
763	C₈	—	4	1	no	—
764	C₂²	—	2	1	no	—
765	C₂²	—	2	1	no	—
766	C₂²	—	2	2	no	—
767	C₂²	—	4	1	no	—
768	C₂²	—	4	1	no	—
769	C₂²	—	4	1	no	—
770	C₂²	—	4	1	no	—
771	C₂²	—	4	2	no	—
772	C₂²	—	4	1	no	—
773	C₂²	—	4	2	no	—
774	C₂²	—	4	1	no	—
775	C₂²	—	4	2	no	—
776	C₂²	—	4	1	no	—
777	C₂²	—	4	1	no	—
778	C₂²	—	8	4	no	—
779	C₂²	—	8	1	no	—
780	C₂²	—	8	1	no	—
781	C₂²	—	8	1	no	—
782	C₂²	—	16	4	no	—
783	C₂²	C₂₃×#453	1	2	yes	—
784	C₂²	C₂×C₂₃×#120	1	1	yes	characteristic
785	C₄	—	2	1	no	—
786	C₄	—	2	1	no	—
787	C₄	—	2	1	no	—
788	C₄	—	2	1	no	—
789	C₄	—	4	1	no	—
790	C₄	—	4	1	no	—
791	C₄	—	4	1	no	—
792	C₄	—	4	1	no	—
793	C₄	—	4	1	no	—
794	C₄	—	4	2	no	—
795	C₄	—	8	1	no	—
796	C₄	C₂×C₂₃×#135	1	1	yes	characteristic
797	C₄	C₂₃×#575	1	1	yes	characteristic
798	C₄	C₂₃×#576	1	1	yes	characteristic
799	C₄	C₂₃×#577	1	1	yes	characteristic
800	C₂	—	2	2	no	—
801	C₂	—	4	2	no	—
802	C₂	—	8	1	no	—
803	C₂	—	8	1	no	—
804	C₂	—	8	2	no	—
805	C₂	—	16	1	no	—
806	C₂	C₂₃×#3002	1	1	yes	characteristic
807	C₂	C₂₃×#3012	1	1	yes	characteristic
808	C₂	C₂×C₂₃×#453	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×#3519	C₂	semidirect
2. C₂₃×#3247	C₂	semidirect
3. C₂₃×#3147	C₂	semidirect
4. C₂₃×#3109	C₂	semidirect
5. C₂₃×#1634	C₂	semidirect
6. C₂₃×#1632	C₂	semidirect
7. C₂₃×#1631	C₂	semidirect
8. C₂₃×#1629	C₂	semidirect
9. C₂₃×#1624	C₂	semidirect
10. C₂₃×#1622	C₂	semidirect
11. C₂₃×#1621	C₂	semidirect
12. C₂₃×#1619	C₂	semidirect
13. C₂₃×#1551	C₂	semidirect
14. C₂₃×#1494	C₂	semidirect
15. C₂×C₂₃×D₄⋊C₈	C₂	semidirect
29. C₂₃×#532	C₂²	semidirect
36. C₂₃×#494	C₂²	semidirect
37. C₂₃×#493	C₂²	semidirect
38. C₂₃×#492	C₂²	semidirect
39. C₂₃×#492	C₂²	semidirect
42. C₂₃×#477	C₂²	semidirect
44. C₂₃×#476	C₂²	semidirect
45. C₂₃×#476	C₂²	semidirect
49. C₂₃×#460	C₂²	semidirect
51. C₂₃×#459	C₂²	semidirect
52. C₂₃×#459	C₂²	semidirect
56. C₂₃×#432	C₂²	semidirect
57. C₂×C₂₃×C₄⋊C₈	C₂²	semidirect
58. C₂×C₄×C₈×C₂₃	C₂²	semidirect
59. C₂₃×#333	C₂²	semidirect
60. C₂₃×#333	C₂²	semidirect
61. C₂₃×#331	C₂²	semidirect
62. C₂₃×#331	C₂²	semidirect
63. C₂₃×Q₈⋊C₈	C₂²	semidirect
64. C₂₃×Q₈⋊C₈	C₂²	semidirect
67. C₂₃×D₄⋊C₈	C₂²	semidirect
68. C₂₃×D₄⋊C₈	C₂²	semidirect
69. C₂₃×D₄⋊C₈	C₂²	semidirect
70. C₂₃×D₄⋊C₈	C₂²	semidirect
281. #18618	C₂₃	direct (N × H)
322. D₄×C₂₃	#135	semidirect
360. #3519	C₂×C₂₃	semidirect
361. #3247	C₂×C₂₃	semidirect
362. #3147	C₂×C₂₃	semidirect
363. #3109	C₂×C₂₃	semidirect
364. #1634	C₂×C₂₃	semidirect
365. #1632	C₂×C₂₃	semidirect
366. #1631	C₂×C₂₃	semidirect
367. #1629	C₂×C₂₃	semidirect
368. #1624	C₂×C₂₃	semidirect
369. #1622	C₂×C₂₃	semidirect
370. #1621	C₂×C₂₃	semidirect
371. #1619	C₂×C₂₃	semidirect
372. #1551	C₂×C₂₃	semidirect
373. #1494	C₂×C₂₃	semidirect
374. C₂×D₄⋊C₈	C₂×C₂₃	semidirect
424. #532	C₂²×C₂₃	semidirect
431. #494	C₂²×C₂₃	semidirect
432. #493	C₂²×C₂₃	semidirect
433. #492	C₂²×C₂₃	semidirect
434. #492	C₂²×C₂₃	semidirect
437. #477	C₂²×C₂₃	semidirect
439. #476	C₂²×C₂₃	semidirect
440. #476	C₂²×C₂₃	semidirect
444. #460	C₂²×C₂₃	semidirect
446. #459	C₂²×C₂₃	semidirect
447. #459	C₂²×C₂₃	semidirect
451. #432	C₂²×C₂₃	semidirect
452. C₂×C₄⋊C₈	C₂²×C₂₃	semidirect
453. C₂×C₄×C₈	C₂²×C₂₃	semidirect
454. #333	C₂²×C₂₃	semidirect
455. #333	C₂²×C₂₃	semidirect
456. #331	C₂²×C₂₃	semidirect
457. #331	C₂²×C₂₃	semidirect
458. Q₈⋊C₈	C₂²×C₂₃	semidirect
459. Q₈⋊C₈	C₂²×C₂₃	semidirect
462. D₄⋊C₈	C₂²×C₂₃	semidirect
463. D₄⋊C₈	C₂²×C₂₃	semidirect
464. D₄⋊C₈	C₂²×C₂₃	semidirect
465. D₄⋊C₈	C₂²×C₂₃	semidirect
581. C₂₃	#18618	direct (N × H)
726. 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×#3519	2
C₂₃×#3247	2
C₂₃×#3147	2
C₂₃×#3109	2
C₂₃×#1634	2
C₂₃×#1632	2
C₂₃×#1631	2
C₂₃×#1629	2
C₂₃×#1624	2
C₂₃×#1622	2
C₂₃×#1621	2
C₂₃×#1619	2
C₂₃×#1551	2
C₂₃×#1494	2
C₂×C₂₃×D₄⋊C₈	2
#18618	23

Subgroups — C23×#18618 #19166244

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#18618 #19166244