Subgroups — C₂₃×#60722 #19208348

Order 5888.

2006 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3511	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₃×#3508	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3184	C₂	1	2	yes	maximal, complemented
4	C₂₃×#3182	C₂	1	2	yes	maximal, complemented
5	C₂₃×#3179	C₂	1	8	yes	maximal, complemented
6	C₂₃×#3169	C₂	1	2	yes	maximal, complemented
7	C₂₃×#3167	C₂	1	2	yes	maximal, complemented
8	C₂₃×#3165	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#3151	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#3131	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₂₃×#486	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#3062	C₂	1	4	yes	maximal, complemented
13	C₂₃×#2946	C₂	1	4	yes	maximal, complemented
14	C₄×C₂₃×#131	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	4	yes	—
16	C₂×C₂₃×#131	C₂²	1	2	yes	—
17	C₂₃×#559	—	2	1	no	—
18	C₂₃×#559	—	2	1	no	—
19	C₂₃×#556	—	2	1	no	—
20	C₂₃×#555	—	2	1	no	—
21	C₂₃×#554	—	2	1	no	—
22	C₂₃×#553	—	2	2	no	—
23	C₂₃×#550	—	2	1	no	—
24	C₂₃×#550	—	2	1	no	—
25	C₂₃×#548	—	2	2	no	—
26	C₂₃×#547	—	2	1	no	—
27	C₂₃×#546	—	2	2	no	—
28	C₂₃×#546	—	2	2	no	—
29	C₂₃×#542	C₂²	1	4	yes	complemented
30	C₂₃×#540	C₂²	1	4	yes	—
31	C₂₃×#537	C₂²	1	2	yes	—
32	C₂₃×#535	C₂²	1	2	yes	—
33	C₂₃×#533	C₂²	1	1	yes	characteristic
34	C₂₃×#533	C₂²	1	2	yes	complemented
35	C₂₃×#532	C₂²	1	1	yes	characteristic
36	C₂₃×#532	C₂²	1	2	yes	—
37	C₂₃×#532	C₂²	1	2	yes	—
38	C₂₃×#532	C₂²	1	2	yes	complemented
39	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
40	C₂×C₂₃×#127	C₂²	1	1	yes	characteristic
41	C₂₃×#520	C₂²	1	2	yes	—
42	C₂₃×#518	C₂²	1	2	yes	—
43	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
44	C₂₃×#501	C₂²	1	4	yes	complemented
45	C₂₃×#500	C₂²	1	2	yes	complemented
46	C₂₃×#498	C₂²	1	2	yes	complemented
47	C₂₃×#496	C₂²	1	4	yes	—
48	C₂₃×#493	C₂²	1	2	yes	—
49	C₂₃×#492	C₂²	1	2	yes	—
50	C₂₃×#488	C₂²	1	4	yes	complemented
51	C₂₃×#487	C₂²	1	1	yes	characteristic, complemented
52	C₂₃×#487	C₂²	1	1	yes	characteristic, complemented
53	C₂₃×#486	C₂²	1	2	yes	—
54	C₂₃×#486	C₂²	1	4	yes	—
55	C₂₃×#486	C₂²	1	2	yes	—
56	C₂₃×#486	C₂²	1	1	yes	characteristic, complemented
57	C₂₃×#486	C₂²	1	1	yes	characteristic, complemented
58	C₂₃×#469	C₂²	1	8	yes	complemented
59	C₂₃×#468	C₂²	1	8	yes	complemented
60	C₂₃×#466	C₂²	1	8	yes	complemented
61	C₂₃×#465	C₂²	1	8	yes	complemented
62	C₂₃×#442	C₂²	1	8	yes	complemented
63	C₂₃×#440	C₂²	1	8	yes	complemented
64	C₄×SD₁₆×C₂₃	C₂²	1	8	yes	complemented
65	C₄×D₈×C₂₃	C₂²	1	8	yes	complemented
66	C₂₃×#428	C₂²	1	4	yes	—
67	C₂₃×#416	C₂²	1	4	yes	—
68	C₂×C₂₃×#102	C₂²	1	4	yes	—
69	C₂₃×#405	C₂²	1	2	yes	—
70	C₂₃×#405	C₂²	1	4	yes	complemented
71	C₄×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
72	C₄×M₁₆×C₂₃	C₂²	1	2	yes	complemented
73	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
74	C₂×C₄×C₈×C₂₃	C₂²	1	2	yes	complemented
75	C₂×#41×C₂₃	—	2	2	no	—
76	C₂×#41×C₂₃	—	2	2	no	—
77	C₂×#41×C₂₃	—	2	2	no	—
78	C₂×#41×C₂₃	C₂³	1	2	yes	—
79	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
80	C₂²×Q₈×C₂₃	—	2	1	no	—
81	C₂²×D₄×C₂₃	—	2	1	no	—
82	C₂²×D₄×C₂₃	—	2	1	no	—
83	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
84	C₂₃×AGL(1,ℤ/8)	—	2	16	no	—
85	C₂×SD₁₆×C₂₃	C₂³	1	8	yes	—
86	C₂×D₈×C₂₃	C₂³	1	8	yes	—
87	C₂₃×#131	—	2	8	no	—
88	C₂×M₁₆×C₂₃	C₂³	1	4	yes	—
89	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
90	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
91	C₂²×C₈×C₂₃	C₂³	1	4	yes	—
92	C₂₃×C₄⋊Q₈	—	2	1	no	—
93	C₂₃×C₄⋊Q₈	—	2	1	no	—
94	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
95	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
96	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
97	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
98	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
99	C₂₃×#127	—	2	2	no	—
100	C₂₃×#127	—	2	1	no	—
101	C₂₃×#127	—	2	1	no	—
102	C₂₃×#127	C₂³	1	2	yes	—
103	C₂₃×#127	C₂³	1	2	yes	—
104	C₂₃×#127	C₂³	1	1	yes	characteristic
105	C₂₃×#126	—	2	4	no	—
106	C₂₃×#125	—	2	2	no	—
107	C₂₃×#125	C₂³	1	2	yes	—
108	C₂₃×#124	—	2	2	no	—
109	C₂₃×#124	—	2	4	no	—
110	C₂₃×#124	—	2	2	no	—
111	C₂₃×#124	—	2	2	no	—
112	C₂₃×#124	—	2	2	no	—
113	C₂₃×#124	C₂³	1	2	yes	—
114	C₂₃×#123	—	2	4	no	—
115	C₂₃×#123	—	2	4	no	—
116	C₂₃×#123	—	2	4	no	—
117	C₂₃×C₂²⋊Q₈	—	2	2	no	—
118	C₂₃×C₂²⋊Q₈	—	2	2	no	—
119	C₂₃×C₂²⋊Q₈	—	2	1	no	—
120	C₂₃×C₂²⋊Q₈	—	2	1	no	—
121	C₂₃×C₂²⋊Q₈	—	2	4	no	—
122	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
123	C₂₃×#121	—	2	2	no	—
124	C₂₃×#121	—	2	4	no	—
125	C₂₃×#121	—	2	1	no	—
126	C₂₃×#121	—	2	2	no	—
127	C₂₃×#121	—	2	2	no	—
128	C₂₃×#121	—	2	1	no	—
129	C₂₃×#121	—	2	2	no	—
130	C₂₃×#121	—	2	4	no	—
131	C₂₃×#121	—	2	4	no	—
132	C₂₃×#121	C₂³	1	4	yes	—
133	C₂₃×#121	C₂³	1	4	yes	—
134	C₂₃×#121	C₂³	1	4	yes	—
135	C₂₃×#120	—	2	4	no	—
136	C₄×Q₈×C₂₃	—	2	2	no	—
137	C₄×Q₈×C₂₃	—	2	1	no	—
138	C₄×Q₈×C₂₃	—	2	1	no	—
139	C₄×Q₈×C₂₃	D₄	1	1	yes	characteristic
140	C₄×Q₈×C₂₃	D₄	1	1	yes	characteristic
141	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
142	C₄×D₄×C₂₃	—	2	2	no	—
143	C₄×D₄×C₂₃	—	2	2	no	—
144	C₄×D₄×C₂₃	—	2	4	no	—
145	C₄×D₄×C₂₃	—	2	1	no	—
146	C₄×D₄×C₂₃	—	2	2	no	—
147	C₄×D₄×C₂₃	—	2	1	no	—
148	C₄×D₄×C₂₃	—	2	2	no	—
149	C₄×D₄×C₂₃	—	2	2	no	—
150	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
151	C₄×D₄×C₂₃	D₄	1	2	yes	—
152	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
153	C₄×D₄×C₂₃	D₄	1	2	yes	—
154	C₄×D₄×C₂₃	C₂³	1	4	yes	—
155	C₄×D₄×C₂₃	C₂³	1	4	yes	—
156	C₄×D₄×C₂₃	C₂³	1	4	yes	—
157	C₂₃×#117	—	2	2	no	—
158	C₂₃×#117	—	2	2	no	—
159	C₂₃×#117	C₂³	1	2	yes	—
160	C₂₃×#117	C₂³	1	1	yes	characteristic
161	C₂₃×#117	C₂³	1	2	yes	—
162	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
163	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
164	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
165	C₂×C₂²⋊C₄×C₂₃	—	2	4	no	—
166	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
167	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
168	C₂₃×#107	C₂³	1	8	yes	—
169	C₂₃×#106	C₂³	1	8	yes	—
170	C₂₃×#103	C₂³	1	4	yes	—
171	C₂₃×#103	C₂³	1	4	yes	—
172	C₂₃×#102	C₂³	1	8	yes	—
173	C₂₃×#102	C₂³	1	8	yes	—
174	C₂₃×#102	C₂³	1	4	yes	—
175	C₂₃×#102	C₂³	1	4	yes	—
176	C₂₃×#97	C₂³	1	2	yes	—
177	C₂₃×#97	C₂³	1	4	yes	—
178	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
179	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
180	C₄×C₈×C₂₃	C₂³	1	2	yes	—
181	C₄×C₈×C₂₃	C₂³	1	2	yes	—
182	C₄×C₈×C₂₃	C₂³	1	4	yes	—
183	C₂⁴×C₂₃	—	2	2	no	—
184	#41×C₂₃	—	2	4	no	—
185	#41×C₂₃	—	2	8	no	—
186	#41×C₂₃	—	8	4	no	—
187	#41×C₂₃	—	8	4	no	—
188	#41×C₂₃	—	8	4	no	—
189	C₂×Q₈×C₂₃	—	2	1	no	—
190	C₂×Q₈×C₂₃	—	2	1	no	—
191	C₂×Q₈×C₂₃	—	2	2	no	—
192	C₂×Q₈×C₂₃	—	2	2	no	—
193	C₂×Q₈×C₂₃	—	8	2	no	—
194	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
195	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
196	C₂×D₄×C₂₃	—	2	2	no	—
197	C₂×D₄×C₂₃	—	2	4	no	—
198	C₂×D₄×C₂₃	—	2	4	no	—
199	C₂×D₄×C₂₃	—	2	4	no	—
200	C₂×D₄×C₂₃	—	2	1	no	—
201	C₂×D₄×C₂₃	—	2	2	no	—
202	C₂×D₄×C₂₃	—	2	1	no	—
203	C₂×D₄×C₂₃	—	2	2	no	—
204	C₂×D₄×C₂₃	—	2	2	no	—
205	C₂×D₄×C₂₃	—	2	2	no	—
206	C₂×D₄×C₂₃	—	2	2	no	—
207	C₂×D₄×C₂₃	—	2	8	no	—
208	C₂×D₄×C₂₃	—	8	2	no	—
209	C₂×D₄×C₂₃	—	8	2	no	—
210	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
211	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
212	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
213	C₂×D₄×C₂₃	C₂⁴	1	4	yes	—
214	C₂²×C₄×C₂₃	—	2	2	no	—
215	C₂²×C₄×C₂₃	—	2	2	no	—
216	C₂²×C₄×C₂₃	—	2	4	no	—
217	C₂²×C₄×C₂₃	—	2	4	no	—
218	C₂²×C₄×C₂₃	—	2	4	no	—
219	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
220	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
221	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
222	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
223	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
224	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
225	SD₁₆×C₂₃	—	2	16	no	—
226	D₈×C₂₃	—	2	16	no	—
227	M₁₆×C₂₃	—	2	8	no	—
228	M₁₆×C₂₃	#41	1	8	yes	complemented
229	C₂×C₈×C₂₃	—	2	4	no	—
230	C₂×C₈×C₂₃	—	2	8	no	—
231	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
232	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
233	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
234	C₄⋊C₄×C₂₃	—	2	2	no	—
235	C₄⋊C₄×C₂₃	—	2	2	no	—
236	C₄⋊C₄×C₂₃	—	2	4	no	—
237	C₄⋊C₄×C₂₃	—	2	2	no	—
238	C₄⋊C₄×C₂₃	—	2	1	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	2	no	—
243	C₄⋊C₄×C₂₃	—	2	2	no	—
244	C₄⋊C₄×C₂₃	—	2	4	no	—
245	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
246	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
247	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
248	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
249	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
250	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
251	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
252	C₂²⋊C₄×C₂₃	—	2	2	no	—
253	C₂²⋊C₄×C₂₃	—	2	4	no	—
254	C₂²⋊C₄×C₂₃	—	2	4	no	—
255	C₂²⋊C₄×C₂₃	—	2	4	no	—
256	C₂²⋊C₄×C₂₃	—	2	4	no	—
257	C₂²⋊C₄×C₂₃	—	2	4	no	—
258	C₂²⋊C₄×C₂₃	—	2	4	no	—
259	C₂²⋊C₄×C₂₃	—	2	4	no	—
260	C₂²⋊C₄×C₂₃	—	2	2	no	—
261	C₂²⋊C₄×C₂₃	—	2	2	no	—
262	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
263	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
264	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
265	C₄²×C₂₃	—	2	4	no	—
266	C₄²×C₂₃	—	2	2	no	—
267	C₄²×C₂₃	C₂×D₄	1	2	yes	—
268	C₄²×C₂₃	C₂×D₄	1	2	yes	—
269	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
270	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
271	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
272	C₄²×C₂₃	C₂⁴	1	2	yes	—
273	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
274	#60722	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
275	C₂³×C₂₃	—	2	2	no	—
276	C₂³×C₂₃	—	2	4	no	—
277	C₂³×C₂₃	—	4	4	no	—
278	C₂³×C₂₃	—	8	2	no	—
279	C₂³×C₂₃	—	8	2	no	—
280	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
281	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
282	Q₈×C₂₃	—	2	2	no	—
283	Q₈×C₂₃	—	2	4	no	—
284	Q₈×C₂₃	—	4	4	no	—
285	Q₈×C₂₃	—	4	2	no	—
286	Q₈×C₂₃	—	4	2	no	—
287	Q₈×C₂₃	—	8	2	no	—
288	D₄×C₂₃	—	2	4	no	—
289	D₄×C₂₃	—	2	2	no	—
290	D₄×C₂₃	—	2	4	no	—
291	D₄×C₂₃	—	2	8	no	—
292	D₄×C₂₃	—	4	4	no	—
293	D₄×C₂₃	—	4	4	no	—
294	D₄×C₂₃	—	4	4	no	—
295	D₄×C₂₃	—	4	2	no	—
296	D₄×C₂₃	—	4	2	no	—
297	D₄×C₂₃	—	4	4	no	—
298	D₄×C₂₃	—	8	2	no	—
299	D₄×C₂₃	—	8	2	no	—
300	D₄×C₂₃	—	8	4	no	—
301	D₄×C₂₃	—	8	4	no	—
302	D₄×C₂₃	—	8	4	no	—
303	C₂×C₄×C₂₃	—	2	2	no	—
304	C₂×C₄×C₂₃	—	2	4	no	—
305	C₂×C₄×C₂₃	—	2	2	no	—
306	C₂×C₄×C₂₃	—	2	4	no	—
307	C₂×C₄×C₂₃	—	2	4	no	—
308	C₂×C₄×C₂₃	—	2	2	no	—
309	C₂×C₄×C₂₃	—	2	2	no	—
310	C₂×C₄×C₂₃	—	2	2	no	—
311	C₂×C₄×C₂₃	—	2	4	no	—
312	C₂×C₄×C₂₃	—	4	4	no	—
313	C₂×C₄×C₂₃	—	8	4	no	—
314	C₂×C₄×C₂₃	—	8	4	no	—
315	C₂×C₄×C₂₃	—	8	4	no	—
316	C₂×C₄×C₂₃	—	8	2	no	—
317	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
318	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
319	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
320	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
321	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
322	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
323	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
324	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
325	C₂×C₄×C₂₃	C₂×#41	1	4	yes	—
326	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
327	C₈×C₂₃	—	2	2	no	—
328	C₈×C₂₃	—	2	2	no	—
329	C₈×C₂₃	C₂×#41	1	8	yes	—
330	#3511	C₂×C₂₃	1	1	yes	characteristic, complemented
331	#3508	C₂×C₂₃	1	1	yes	characteristic, complemented
332	#3184	C₂×C₂₃	1	2	yes	complemented
333	#3182	C₂×C₂₃	1	2	yes	complemented
334	#3179	C₂×C₂₃	1	8	yes	complemented
335	#3169	C₂×C₂₃	1	2	yes	complemented
336	#3167	C₂×C₂₃	1	2	yes	complemented
337	#3165	C₂×C₂₃	1	1	yes	characteristic, complemented
338	#3151	C₂×C₂₃	1	1	yes	characteristic, complemented
339	#3131	C₂×C₂₃	1	1	yes	characteristic, complemented
340	C₂×#486	C₂×C₂₃	1	1	yes	characteristic, complemented
341	#3062	C₂×C₂₃	1	4	yes	complemented
342	#2946	C₂×C₂₃	1	4	yes	complemented
343	C₄×#131	C₂×C₂₃	1	1	yes	characteristic, complemented
344	C₂²×C₂₃	—	2	1	no	—
345	C₂²×C₂₃	—	2	1	no	—
346	C₂²×C₂₃	—	2	2	no	—
347	C₂²×C₂₃	—	2	2	no	—
348	C₂²×C₂₃	—	2	2	no	—
349	C₂²×C₂₃	—	4	2	no	—
350	C₂²×C₂₃	—	4	4	no	—
351	C₂²×C₂₃	—	4	2	no	—
352	C₂²×C₂₃	—	4	4	no	—
353	C₂²×C₂₃	—	4	4	no	—
354	C₂²×C₂₃	—	4	2	no	—
355	C₂²×C₂₃	—	16	4	no	—
356	C₂²×C₂₃	#532	1	2	yes	—
357	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
358	C₄×C₂₃	—	2	2	no	—
359	C₄×C₂₃	—	2	2	no	—
360	C₄×C₂₃	—	2	1	no	—
361	C₄×C₂₃	—	2	2	no	—
362	C₄×C₂₃	—	2	1	no	—
363	C₄×C₂₃	—	4	2	no	—
364	C₄×C₂₃	—	4	2	no	—
365	C₄×C₂₃	—	4	4	no	—
366	C₄×C₂₃	—	4	2	no	—
367	C₄×C₂₃	#532	1	2	yes	—
368	C₄×C₂₃	#576	1	2	yes	—
369	C₄×C₂₃	#577	1	2	yes	—
370	C₄×C₂₃	C₂²×#41	1	2	yes	—
371	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	4	yes	—
372	C₂×#131	C₂²×C₂₃	1	2	yes	—
373	#559	—	2	1	no	—
374	#559	—	2	1	no	—
375	#556	—	2	1	no	—
376	#555	—	2	1	no	—
377	#554	—	2	1	no	—
378	#553	—	2	2	no	—
379	#550	—	2	1	no	—
380	#550	—	2	1	no	—
381	#548	—	2	2	no	—
382	#547	—	2	1	no	—
383	#546	—	2	2	no	—
384	#546	—	2	2	no	—
385	#542	C₂²×C₂₃	1	4	yes	complemented
386	#540	C₂²×C₂₃	1	4	yes	—
387	#537	C₂²×C₂₃	1	2	yes	—
388	#535	C₂²×C₂₃	1	2	yes	—
389	#533	C₂²×C₂₃	1	1	yes	characteristic
390	#533	C₂²×C₂₃	1	2	yes	complemented
391	#532	C₂²×C₂₃	1	1	yes	characteristic
392	#532	C₂²×C₂₃	1	2	yes	—
393	#532	C₂²×C₂₃	1	2	yes	—
394	#532	C₂²×C₂₃	1	2	yes	complemented
395	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
396	C₂×#127	C₂²×C₂₃	1	1	yes	characteristic
397	#520	C₂²×C₂₃	1	2	yes	—
398	#518	C₂²×C₂₃	1	2	yes	—
399	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
400	#501	C₂²×C₂₃	1	4	yes	complemented
401	#500	C₂²×C₂₃	1	2	yes	complemented
402	#498	C₂²×C₂₃	1	2	yes	complemented
403	#496	C₂²×C₂₃	1	4	yes	—
404	#493	C₂²×C₂₃	1	2	yes	—
405	#492	C₂²×C₂₃	1	2	yes	—
406	#488	C₂²×C₂₃	1	4	yes	complemented
407	#487	C₂²×C₂₃	1	1	yes	characteristic, complemented
408	#487	C₂²×C₂₃	1	1	yes	characteristic, complemented
409	#486	C₂²×C₂₃	1	2	yes	—
410	#486	C₂²×C₂₃	1	4	yes	—
411	#486	C₂²×C₂₃	1	2	yes	—
412	#486	C₂²×C₂₃	1	1	yes	characteristic, complemented
413	#486	C₂²×C₂₃	1	1	yes	characteristic, complemented
414	#469	C₂²×C₂₃	1	8	yes	complemented
415	#468	C₂²×C₂₃	1	8	yes	complemented
416	#466	C₂²×C₂₃	1	8	yes	complemented
417	#465	C₂²×C₂₃	1	8	yes	complemented
418	#442	C₂²×C₂₃	1	8	yes	complemented
419	#440	C₂²×C₂₃	1	8	yes	complemented
420	C₄×SD₁₆	C₂²×C₂₃	1	8	yes	complemented
421	C₄×D₈	C₂²×C₂₃	1	8	yes	complemented
422	#428	C₂²×C₂₃	1	4	yes	—
423	#416	C₂²×C₂₃	1	4	yes	—
424	C₂×#102	C₂²×C₂₃	1	4	yes	—
425	#405	C₂²×C₂₃	1	2	yes	—
426	#405	C₂²×C₂₃	1	4	yes	complemented
427	C₄×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
428	C₄×M₁₆	C₂²×C₂₃	1	2	yes	complemented
429	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
430	C₂×C₄×C₈	C₂²×C₂₃	1	2	yes	complemented
431	C₂×C₂₃	—	2	2	no	—
432	C₂×C₂₃	—	4	2	no	—
433	C₂×C₂₃	—	8	2	no	—
434	C₂×C₂₃	—	8	4	no	—
435	C₂×C₂₃	C₂×#532	1	1	yes	characteristic
436	C₂×C₂₃	C₂×#576	1	1	yes	characteristic
437	C₂×C₂₃	C₂×#577	1	1	yes	characteristic
438	C₂×#41	—	2	2	no	—
439	C₂×#41	—	2	2	no	—
440	C₂×#41	—	2	2	no	—
441	C₂×#41	C₂³×C₂₃	1	2	yes	—
442	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
443	C₂²×Q₈	—	2	1	no	—
444	C₂²×D₄	—	2	1	no	—
445	C₂²×D₄	—	2	1	no	—
446	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
447	AGL(1,ℤ/8)	—	2	16	no	—
448	C₂×SD₁₆	C₂³×C₂₃	1	8	yes	—
449	C₂×D₈	C₂³×C₂₃	1	8	yes	—
450	#131	—	2	8	no	—
451	C₂×M₁₆	C₂³×C₂₃	1	4	yes	—
452	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
453	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
454	C₂²×C₈	C₂³×C₂₃	1	4	yes	—
455	C₄⋊Q₈	—	2	1	no	—
456	C₄⋊Q₈	—	2	1	no	—
457	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
458	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
459	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
460	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
461	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
462	#127	—	2	2	no	—
463	#127	—	2	1	no	—
464	#127	—	2	1	no	—
465	#127	C₂³×C₂₃	1	2	yes	—
466	#127	C₂³×C₂₃	1	2	yes	—
467	#127	C₂³×C₂₃	1	1	yes	characteristic
468	#126	—	2	4	no	—
469	#125	—	2	2	no	—
470	#125	C₂³×C₂₃	1	2	yes	—
471	#124	—	2	2	no	—
472	#124	—	2	4	no	—
473	#124	—	2	2	no	—
474	#124	—	2	2	no	—
475	#124	—	2	2	no	—
476	#124	C₂³×C₂₃	1	2	yes	—
477	#123	—	2	4	no	—
478	#123	—	2	4	no	—
479	#123	—	2	4	no	—
480	C₂²⋊Q₈	—	2	2	no	—
481	C₂²⋊Q₈	—	2	1	no	—
482	C₂²⋊Q₈	—	2	1	no	—
483	C₂²⋊Q₈	—	2	2	no	—
484	C₂²⋊Q₈	—	2	4	no	—
485	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
486	#121	—	2	2	no	—
487	#121	—	2	4	no	—
488	#121	—	2	2	no	—
489	#121	—	2	2	no	—
490	#121	—	2	1	no	—
491	#121	—	2	1	no	—
492	#121	—	2	2	no	—
493	#121	—	2	4	no	—
494	#121	—	2	4	no	—
495	#121	C₂³×C₂₃	1	4	yes	—
496	#121	C₂³×C₂₃	1	4	yes	—
497	#121	C₂³×C₂₃	1	4	yes	—
498	#120	—	2	4	no	—
499	C₄×Q₈	—	2	1	no	—
500	C₄×Q₈	—	2	1	no	—
501	C₄×Q₈	—	2	2	no	—
502	C₄×Q₈	D₄×C₂₃	1	1	yes	characteristic
503	C₄×Q₈	D₄×C₂₃	1	1	yes	characteristic
504	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
505	C₄×D₄	—	2	2	no	—
506	C₄×D₄	—	2	2	no	—
507	C₄×D₄	—	2	4	no	—
508	C₄×D₄	—	2	2	no	—
509	C₄×D₄	—	2	2	no	—
510	C₄×D₄	—	2	1	no	—
511	C₄×D₄	—	2	1	no	—
512	C₄×D₄	—	2	2	no	—
513	C₄×D₄	D₄×C₂₃	1	2	yes	—
514	C₄×D₄	D₄×C₂₃	1	2	yes	—
515	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
516	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
517	C₄×D₄	C₂³×C₂₃	1	4	yes	—
518	C₄×D₄	C₂³×C₂₃	1	4	yes	—
519	C₄×D₄	C₂³×C₂₃	1	4	yes	—
520	#117	—	2	2	no	—
521	#117	—	2	2	no	—
522	#117	C₂³×C₂₃	1	2	yes	—
523	#117	C₂³×C₂₃	1	1	yes	characteristic
524	#117	C₂³×C₂₃	1	2	yes	—
525	C₂×C₄⋊C₄	—	2	1	no	—
526	C₂×C₄⋊C₄	—	2	2	no	—
527	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
528	C₂×C₂²⋊C₄	—	2	4	no	—
529	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
530	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
531	#107	C₂³×C₂₃	1	8	yes	—
532	#106	C₂³×C₂₃	1	8	yes	—
533	#103	C₂³×C₂₃	1	4	yes	—
534	#103	C₂³×C₂₃	1	4	yes	—
535	#102	C₂³×C₂₃	1	8	yes	—
536	#102	C₂³×C₂₃	1	8	yes	—
537	#102	C₂³×C₂₃	1	4	yes	—
538	#102	C₂³×C₂₃	1	4	yes	—
539	#97	C₂³×C₂₃	1	2	yes	—
540	#97	C₂³×C₂₃	1	4	yes	—
541	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
542	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
543	C₄×C₈	C₂³×C₂₃	1	2	yes	—
544	C₄×C₈	C₂³×C₂₃	1	2	yes	—
545	C₄×C₈	C₂³×C₂₃	1	4	yes	—
546	C₂₃	#60722	1	1	yes	characteristic, direct product factor, Sylow
547	C₂⁴	—	2	2	no	—
548	#41	—	2	4	no	—
549	#41	—	2	8	no	—
550	#41	—	8	4	no	—
551	#41	—	8	4	no	—
552	#41	—	8	4	no	—
553	C₂×Q₈	—	2	1	no	—
554	C₂×Q₈	—	2	1	no	—
555	C₂×Q₈	—	2	2	no	—
556	C₂×Q₈	—	2	2	no	—
557	C₂×Q₈	—	8	2	no	—
558	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
559	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
560	C₂×D₄	—	2	2	no	—
561	C₂×D₄	—	2	4	no	—
562	C₂×D₄	—	2	4	no	—
563	C₂×D₄	—	2	4	no	—
564	C₂×D₄	—	2	1	no	—
565	C₂×D₄	—	2	2	no	—
566	C₂×D₄	—	2	1	no	—
567	C₂×D₄	—	2	2	no	—
568	C₂×D₄	—	2	2	no	—
569	C₂×D₄	—	2	2	no	—
570	C₂×D₄	—	2	2	no	—
571	C₂×D₄	—	2	8	no	—
572	C₂×D₄	—	8	2	no	—
573	C₂×D₄	—	8	2	no	—
574	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
575	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
576	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
577	C₂×D₄	C₂⁴×C₂₃	1	4	yes	—
578	C₂²×C₄	—	2	2	no	—
579	C₂²×C₄	—	2	2	no	—
580	C₂²×C₄	—	2	4	no	—
581	C₂²×C₄	—	2	4	no	—
582	C₂²×C₄	—	2	4	no	—
583	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
584	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
585	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
586	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
587	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
588	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
589	SD₁₆	—	2	16	no	—
590	D₈	—	2	16	no	—
591	M₁₆	—	2	8	no	—
592	M₁₆	#41×C₂₃	1	8	yes	complemented
593	C₂×C₈	—	2	4	no	—
594	C₂×C₈	—	2	8	no	—
595	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
596	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
597	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
598	C₄⋊C₄	—	2	2	no	—
599	C₄⋊C₄	—	2	2	no	—
600	C₄⋊C₄	—	2	4	no	—
601	C₄⋊C₄	—	2	2	no	—
602	C₄⋊C₄	—	2	1	no	—
603	C₄⋊C₄	—	2	1	no	—
604	C₄⋊C₄	—	2	1	no	—
605	C₄⋊C₄	—	2	1	no	—
606	C₄⋊C₄	—	2	2	no	—
607	C₄⋊C₄	—	2	2	no	—
608	C₄⋊C₄	—	2	4	no	—
609	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
610	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
611	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
612	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
613	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
614	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
615	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
616	C₂²⋊C₄	—	2	2	no	—
617	C₂²⋊C₄	—	2	4	no	—
618	C₂²⋊C₄	—	2	4	no	—
619	C₂²⋊C₄	—	2	4	no	—
620	C₂²⋊C₄	—	2	4	no	—
621	C₂²⋊C₄	—	2	4	no	—
622	C₂²⋊C₄	—	2	4	no	—
623	C₂²⋊C₄	—	2	4	no	—
624	C₂²⋊C₄	—	2	2	no	—
625	C₂²⋊C₄	—	2	2	no	—
626	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
627	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
628	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
629	C₄²	—	2	4	no	—
630	C₄²	—	2	2	no	—
631	C₄²	C₂×D₄×C₂₃	1	2	yes	—
632	C₄²	C₂×D₄×C₂₃	1	2	yes	—
633	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
634	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
635	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
636	C₄²	C₂⁴×C₂₃	1	2	yes	—
637	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
638	C₂³	—	2	2	no	—
639	C₂³	—	2	4	no	—
640	C₂³	—	4	4	no	—
641	C₂³	—	8	2	no	—
642	C₂³	—	8	2	no	—
643	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
644	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
645	Q₈	—	2	2	no	—
646	Q₈	—	2	4	no	—
647	Q₈	—	4	4	no	—
648	Q₈	—	4	2	no	—
649	Q₈	—	4	2	no	—
650	Q₈	—	8	2	no	—
651	D₄	—	2	4	no	—
652	D₄	—	2	4	no	—
653	D₄	—	2	8	no	—
654	D₄	—	2	2	no	—
655	D₄	—	4	4	no	—
656	D₄	—	4	4	no	—
657	D₄	—	4	2	no	—
658	D₄	—	4	4	no	—
659	D₄	—	4	2	no	—
660	D₄	—	4	4	no	—
661	D₄	—	8	2	no	—
662	D₄	—	8	2	no	—
663	D₄	—	8	4	no	—
664	D₄	—	8	4	no	—
665	D₄	—	8	4	no	—
666	C₂×C₄	—	2	2	no	—
667	C₂×C₄	—	2	4	no	—
668	C₂×C₄	—	2	2	no	—
669	C₂×C₄	—	2	4	no	—
670	C₂×C₄	—	2	4	no	—
671	C₂×C₄	—	2	2	no	—
672	C₂×C₄	—	2	2	no	—
673	C₂×C₄	—	2	2	no	—
674	C₂×C₄	—	2	4	no	—
675	C₂×C₄	—	4	4	no	—
676	C₂×C₄	—	8	4	no	—
677	C₂×C₄	—	8	4	no	—
678	C₂×C₄	—	8	4	no	—
679	C₂×C₄	—	8	2	no	—
680	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
681	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
682	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
683	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
684	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
685	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
686	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
687	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
688	C₂×C₄	C₂×#41×C₂₃	1	4	yes	—
689	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
690	C₈	—	2	2	no	—
691	C₈	—	2	2	no	—
692	C₈	C₂×#41×C₂₃	1	8	yes	—
693	C₂²	—	2	1	no	—
694	C₂²	—	2	1	no	—
695	C₂²	—	2	2	no	—
696	C₂²	—	2	2	no	—
697	C₂²	—	2	2	no	—
698	C₂²	—	4	2	no	—
699	C₂²	—	4	4	no	—
700	C₂²	—	4	2	no	—
701	C₂²	—	4	4	no	—
702	C₂²	—	4	4	no	—
703	C₂²	—	4	2	no	—
704	C₂²	—	16	4	no	—
705	C₂²	C₂₃×#532	1	2	yes	—
706	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
707	C₄	—	2	2	no	—
708	C₄	—	2	2	no	—
709	C₄	—	2	1	no	—
710	C₄	—	2	2	no	—
711	C₄	—	2	1	no	—
712	C₄	—	4	2	no	—
713	C₄	—	4	2	no	—
714	C₄	—	4	4	no	—
715	C₄	—	4	2	no	—
716	C₄	C₂₃×#532	1	2	yes	—
717	C₄	C₂₃×#576	1	2	yes	—
718	C₄	C₂₃×#577	1	2	yes	—
719	C₄	C₂²×#41×C₂₃	1	2	yes	—
720	C₂	—	2	2	no	—
721	C₂	—	4	2	no	—
722	C₂	—	8	4	no	—
723	C₂	—	8	2	no	—
724	C₂	C₂×C₂₃×#532	1	1	yes	characteristic
725	C₂	C₂×C₂₃×#576	1	1	yes	characteristic
726	C₂	C₂×C₂₃×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₄×#41×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₃×#3511	C₂	semidirect
2. C₂₃×#3508	C₂	semidirect
3. C₂₃×#3184	C₂	semidirect
4. C₂₃×#3182	C₂	semidirect
5. C₂₃×#3179	C₂	semidirect
6. C₂₃×#3169	C₂	semidirect
7. C₂₃×#3167	C₂	semidirect
8. C₂₃×#3165	C₂	semidirect
9. C₂₃×#3151	C₂	semidirect
10. C₂₃×#3131	C₂	semidirect
11. C₂×C₂₃×#486	C₂	semidirect
12. C₂₃×#3062	C₂	semidirect
13. C₂₃×#2946	C₂	semidirect
14. C₄×C₂₃×#131	C₂	semidirect
29. C₂₃×#542	C₂²	semidirect
34. C₂₃×#533	C₂²	semidirect
38. C₂₃×#532	C₂²	semidirect
44. C₂₃×#501	C₂²	semidirect
45. C₂₃×#500	C₂²	semidirect
46. C₂₃×#498	C₂²	semidirect
50. C₂₃×#488	C₂²	semidirect
51. C₂₃×#487	C₂²	semidirect
52. C₂₃×#487	C₂²	semidirect
56. C₂₃×#486	C₂²	semidirect
57. C₂₃×#486	C₂²	semidirect
58. C₂₃×#469	C₂²	semidirect
59. C₂₃×#468	C₂²	semidirect
60. C₂₃×#466	C₂²	semidirect
61. C₂₃×#465	C₂²	semidirect
62. C₂₃×#442	C₂²	semidirect
63. C₂₃×#440	C₂²	semidirect
64. C₄×SD₁₆×C₂₃	C₂²	semidirect
65. C₄×D₈×C₂₃	C₂²	semidirect
70. C₂₃×#405	C₂²	semidirect
72. C₄×M₁₆×C₂₃	C₂²	semidirect
74. C₂×C₄×C₈×C₂₃	C₂²	semidirect
228. M₁₆×C₂₃	#41	semidirect
274. #60722	C₂₃	direct (N × H)
330. #3511	C₂×C₂₃	semidirect
331. #3508	C₂×C₂₃	semidirect
332. #3184	C₂×C₂₃	semidirect
333. #3182	C₂×C₂₃	semidirect
334. #3179	C₂×C₂₃	semidirect
335. #3169	C₂×C₂₃	semidirect
336. #3167	C₂×C₂₃	semidirect
337. #3165	C₂×C₂₃	semidirect
338. #3151	C₂×C₂₃	semidirect
339. #3131	C₂×C₂₃	semidirect
340. C₂×#486	C₂×C₂₃	semidirect
341. #3062	C₂×C₂₃	semidirect
342. #2946	C₂×C₂₃	semidirect
343. C₄×#131	C₂×C₂₃	semidirect
385. #542	C₂²×C₂₃	semidirect
390. #533	C₂²×C₂₃	semidirect
394. #532	C₂²×C₂₃	semidirect
400. #501	C₂²×C₂₃	semidirect
401. #500	C₂²×C₂₃	semidirect
402. #498	C₂²×C₂₃	semidirect
406. #488	C₂²×C₂₃	semidirect
407. #487	C₂²×C₂₃	semidirect
408. #487	C₂²×C₂₃	semidirect
412. #486	C₂²×C₂₃	semidirect
413. #486	C₂²×C₂₃	semidirect
414. #469	C₂²×C₂₃	semidirect
415. #468	C₂²×C₂₃	semidirect
416. #466	C₂²×C₂₃	semidirect
417. #465	C₂²×C₂₃	semidirect
418. #442	C₂²×C₂₃	semidirect
419. #440	C₂²×C₂₃	semidirect
420. C₄×SD₁₆	C₂²×C₂₃	semidirect
421. C₄×D₈	C₂²×C₂₃	semidirect
426. #405	C₂²×C₂₃	semidirect
428. C₄×M₁₆	C₂²×C₂₃	semidirect
430. C₂×C₄×C₈	C₂²×C₂₃	semidirect
546. C₂₃	#60722	direct (N × H)
592. M₁₆	#41×C₂₃	semidirect

Maximal subgroups

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

subgroup	index
C₂₃×#3511	2
C₂₃×#3508	2
C₂₃×#3184	2
C₂₃×#3182	2
C₂₃×#3179	2
C₂₃×#3169	2
C₂₃×#3167	2
C₂₃×#3165	2
C₂₃×#3151	2
C₂₃×#3131	2
C₂×C₂₃×#486	2
C₂₃×#3062	2
C₂₃×#2946	2
C₄×C₂₃×#131	2
#60722	23

Subgroups — C23×#60722 #19208348

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#60722 #19208348