Subgroups — D₂₃×#462 #15682831

Order 2944.

480 conjugacy classes of subgroups.

The subgroup lattice has 284 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₁₆×D₂₃	C₂	1	2	yes	maximal
2	C₄⋊Q₈×D₂₃	C₂	1	1	yes	maximal, characteristic
3	C₄×Q₈×D₂₃	C₂	1	1	yes	maximal, characteristic
4	#13092628	C₂	1	1	yes	maximal, characteristic, complemented
5	#13092627	C₂	1	1	yes	maximal, characteristic, complemented
6	#13092626	C₂	1	2	yes	maximal, complemented
7	#13092625	C₂	1	2	yes	maximal, complemented
8	#13092624	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄⋊C₈×D₂₃	C₂	1	1	yes	maximal, characteristic
10	#103×D₂₃	C₂	1	2	yes	maximal
11	C₂₃×#462	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×Q₈×D₂₃	C₂²	1	2	yes	—
13	C₂×Q₈×D₂₃	C₂²	1	1	yes	characteristic
14	C₂×Q₁₆×C₂₃	C₂²	1	2	yes	—
15	C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
16	C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
17	Q₈×Dic₂₃	C₂²	1	1	yes	characteristic
18	#10625115	C₂²	1	2	yes	—
19	C₂×#67275	C₂²	1	2	yes	—
20	C₂×#67275	C₂²	1	2	yes	—
21	Q₁₆×D₂₃	—	2	8	no	—
22	C₂×Dic₉₂	C₂²	1	2	yes	—
23	C₂×C₈×D₂₃	C₂²	1	2	yes	—
24	C₄⋊C₄×D₂₃	—	2	1	no	—
25	C₄⋊C₄×D₂₃	—	2	1	no	—
26	C₄⋊C₄×D₂₃	—	2	1	no	—
27	C₄⋊C₄×D₂₃	C₂²	1	1	yes	characteristic
28	#10625059	—	2	1	no	—
29	#10625059	—	2	1	no	—
30	#10625058	—	2	1	no	—
31	#10625058	C₂²	1	1	yes	characteristic
32	C₄²×D₂₃	—	2	1	no	—
33	C₄²×D₂₃	C₂²	1	1	yes	characteristic
34	#10625040	C₂²	1	1	yes	characteristic
35	C₄×Dic₄₆	—	2	1	no	—
36	C₄×Dic₄₆	C₂²	1	1	yes	characteristic
37	C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
38	C₂₃×#103	C₂²	1	2	yes	—
39	#10625017	C₂²	1	2	yes	—
40	#10624998	C₂²	1	2	yes	—
41	Dic₂₃⋊C₈	C₂²	1	2	yes	—
42	#10624992	C₂²	1	2	yes	—
43	C₄⋊(C₂₃⋊C₈)	C₂²	1	1	yes	characteristic
44	C₂×Q₈×C₂₃	C₂³	1	2	yes	—
45	C₂×Q₈×C₂₃	C₂³	1	1	yes	characteristic
46	Q₈×D₂₃	—	2	2	no	—
47	Q₈×D₂₃	—	2	4	no	—
48	Q₈×D₂₃	—	2	4	no	—
49	Q₈×D₂₃	D₄	1	4	yes	—
50	C₂×C₄×D₂₃	—	2	1	no	—
51	C₂×C₄×D₂₃	—	2	1	no	—
52	C₂×C₄×D₂₃	—	2	2	no	—
53	C₂×C₄×D₂₃	D₄	1	1	yes	characteristic
54	C₂×C₄×D₂₃	D₄	1	1	yes	characteristic
55	C₂×C₄×D₂₃	C₂³	1	1	yes	characteristic
56	C₂×Dic₄₆	—	2	1	no	—
57	C₂×Dic₄₆	—	2	2	no	—
58	C₂×Dic₄₆	C₂³	1	2	yes	—
59	C₂×Dic₄₆	C₂³	1	1	yes	characteristic
60	Q₁₆×C₂₃	—	2	4	no	—
61	C₂×C₈×C₂₃	C₂³	1	2	yes	—
62	C₄⋊C₄×C₂₃	—	2	1	no	—
63	C₄⋊C₄×C₂₃	—	2	1	no	—
64	C₄⋊C₄×C₂₃	—	2	1	no	—
65	C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
66	C₄²×C₂₃	—	2	1	no	—
67	C₄²×C₂₃	C₂³	1	1	yes	characteristic
68	#67275	—	2	4	no	—
69	#67275	—	2	4	no	—
70	C₄⋊Dic₂₃	—	2	1	no	—
71	C₄⋊Dic₂₃	—	2	1	no	—
72	C₄⋊Dic₂₃	—	2	1	no	—
73	C₄⋊Dic₂₃	C₂³	1	1	yes	characteristic
74	Dic₂₃⋊C₄	—	2	1	no	—
75	Dic₂₃⋊C₄	—	2	1	no	—
76	Dic₂₃⋊C₄	—	2	1	no	—
77	Dic₂₃⋊C₄	—	2	2	no	—
78	Dic₂₃⋊C₄	—	2	2	no	—
79	C₄×Dic₂₃	—	2	1	no	—
80	C₄×Dic₂₃	—	2	1	no	—
81	C₄×Dic₂₃	—	2	1	no	—
82	C₄×Dic₂₃	D₄	1	1	yes	characteristic
83	C₄×Dic₂₃	D₄	1	1	yes	characteristic
84	C₄×Dic₂₃	C₂³	1	1	yes	characteristic
85	C₂×C₂₃⋊C₈	C₂³	1	2	yes	—
86	Dic₉₂	—	2	4	no	—
87	C₈×D₂₃	—	2	4	no	—
88	C₂²×D₂₃	C₂×D₄	1	1	yes	characteristic
89	Q₈×C₂₃	—	2	1	no	—
90	Q₈×C₂₃	—	2	2	no	—
91	Q₈×C₂₃	—	2	2	no	—
92	Q₈×C₂₃	C₂×D₄	1	2	yes	—
93	C₂×C₄×C₂₃	—	2	1	no	—
94	C₂×C₄×C₂₃	—	2	1	no	—
95	C₂×C₄×C₂₃	—	2	2	no	—
96	C₂×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
97	C₂×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
98	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
99	C₂×Dic₂₃	—	2	1	no	—
100	C₂×Dic₂₃	—	2	1	no	—
101	C₂×Dic₂₃	—	2	2	no	—
102	C₂×Dic₂₃	C₂×D₄	1	1	yes	characteristic
103	C₂×Dic₂₃	C₂×D₄	1	1	yes	characteristic
104	C₂×Dic₂₃	C₂×D₄	1	1	yes	characteristic
105	C₄×D₂₃	—	2	4	no	—
106	C₄×D₂₃	—	2	2	no	—
107	C₄×D₂₃	—	4	4	no	—
108	C₄×D₂₃	—	4	2	no	—
109	C₄×D₂₃	Q₁₆	1	4	yes	complemented
110	C₄×D₂₃	C₂×D₄	1	2	yes	—
111	C₄×D₂₃	#41	1	2	yes	—
112	Dic₄₆	—	2	1	no	—
113	Dic₄₆	—	2	4	no	—
114	Dic₄₆	—	2	2	no	—
115	Dic₄₆	—	2	2	no	—
116	Dic₄₆	—	4	4	no	—
117	Dic₄₆	C₂×D₄	1	2	yes	—
118	C₈×C₂₃	—	2	2	no	—
119	C₂₃⋊C₈	—	2	2	no	—
120	C₂×#462	—	23	1	no	maximal, Sylow
121	C₂²×C₂₃	C₂²×D₄	1	1	yes	characteristic
122	C₂×D₂₃	#121	1	2	yes	—
123	C₂×D₂₃	C₂×Q₁₆	1	2	yes	—
124	C₂×D₂₃	#137	1	2	yes	—
125	C₄×C₂₃	—	2	2	no	—
126	C₄×C₂₃	—	2	1	no	—
127	C₄×C₂₃	—	4	2	no	—
128	C₄×C₂₃	—	4	1	no	—
129	C₄×C₂₃	C₂×Q₁₆	1	2	yes	complemented
130	C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
131	C₄×C₂₃	C₂×#41	1	1	yes	characteristic
132	Dic₂₃	—	2	2	no	—
133	Dic₂₃	—	2	1	no	—
134	Dic₂₃	—	4	2	no	—
135	Dic₂₃	—	4	1	no	—
136	Dic₂₃	#121	1	2	yes	—
137	Dic₂₃	C₂×Q₁₆	1	2	yes	complemented
138	C₂²×Q₁₆	—	23	2	no	—
139	C₂×C₄⋊Q₈	—	23	1	no	—
140	C₂×C₄×Q₈	—	23	1	no	—
141	#462	—	23	2	no	—
142	#462	—	23	1	no	—
143	#462	—	23	1	no	—
144	#462	—	23	1	no	—
145	#462	—	23	2	no	—
146	#462	D₂₃	1	1	yes	characteristic, direct product factor
147	C₂×C₄⋊C₈	—	23	1	no	—
148	C₂×#103	—	23	2	no	—
149	C₂×C₂₃	C₂×#121	1	1	yes	characteristic
150	C₂×C₂₃	C₂²×Q₁₆	1	1	yes	characteristic
151	C₂×C₂₃	C₂×#137	1	1	yes	characteristic
152	D₂₃	#462	1	4	yes	direct product factor
153	C₂²×Q₈	—	23	1	no	—
154	C₂²×Q₈	—	23	2	no	—
155	C₂×Q₁₆	—	23	2	no	—
156	C₂×Q₁₆	—	23	2	no	—
157	C₂×Q₁₆	—	23	2	no	—
158	C₂×Q₁₆	—	46	8	no	—
159	C₂×Q₁₆	C₂×D₂₃	1	2	yes	—
160	C₂²×C₈	—	23	2	no	—
161	C₄⋊Q₈	—	23	2	no	—
162	C₄⋊Q₈	—	23	1	no	—
163	C₄⋊Q₈	—	46	1	no	—
164	C₄⋊Q₈	—	46	1	no	—
165	C₄⋊Q₈	C₂×D₂₃	1	1	yes	characteristic
166	C₄×Q₈	—	23	1	no	—
167	C₄×Q₈	—	23	1	no	—
168	C₄×Q₈	—	23	1	no	—
169	C₄×Q₈	—	46	1	no	—
170	C₄×Q₈	—	46	1	no	—
171	C₄×Q₈	C₂×D₂₃	1	1	yes	characteristic
172	C₂×C₄⋊C₄	—	23	1	no	—
173	C₂×C₄⋊C₄	—	46	1	no	—
174	C₂×C₄⋊C₄	—	46	1	no	—
175	C₂×C₄⋊C₄	—	46	1	no	—
176	C₂×C₄²	—	23	1	no	—
177	C₂×C₄²	—	46	1	no	—
178	C₄⋊C₈	—	23	2	no	—
179	C₄⋊C₈	—	23	1	no	—
180	C₄⋊C₈	C₂×D₂₃	1	1	yes	characteristic
181	#103	—	23	2	no	—
182	#103	—	23	2	no	—
183	#103	—	23	2	no	—
184	#103	C₂×D₂₃	1	2	yes	—
185	C₂₃	C₂×#462	1	1	yes	characteristic, complemented, Sylow
186	C₂×Q₈	—	23	4	no	—
187	C₂×Q₈	—	23	1	no	—
188	C₂×Q₈	—	23	2	no	—
189	C₂×Q₈	—	46	1	no	—
190	C₂×Q₈	—	46	2	no	—
191	C₂×Q₈	—	46	2	no	—
192	C₂×Q₈	—	46	4	no	—
193	C₂×Q₈	—	46	4	no	—
194	C₂×Q₈	C₂²×D₂₃	1	2	yes	—
195	C₂×Q₈	C₂²×D₂₃	1	1	yes	characteristic
196	C₂²×C₄	—	23	1	no	—
197	C₂²×C₄	—	23	1	no	—
198	C₂²×C₄	—	23	1	no	—
199	C₂²×C₄	—	46	1	no	—
200	C₂²×C₄	—	46	1	no	—
201	C₂²×C₄	—	46	2	no	—
202	Q₁₆	—	2	4	no	—
203	Q₁₆	—	46	4	no	—
204	Q₁₆	—	46	4	no	—
205	Q₁₆	—	46	4	no	—
206	C₂×C₈	—	23	2	no	—
207	C₂×C₈	—	46	4	no	—
208	C₂×C₈	C₂²×D₂₃	1	2	yes	—
209	C₄⋊C₄	—	2	1	no	—
210	C₄⋊C₄	—	2	1	no	—
211	C₄⋊C₄	—	2	1	no	—
212	C₄⋊C₄	—	23	1	no	—
213	C₄⋊C₄	—	46	1	no	—
214	C₄⋊C₄	—	46	1	no	—
215	C₄⋊C₄	—	46	1	no	—
216	C₄⋊C₄	—	46	2	no	—
217	C₄⋊C₄	—	46	2	no	—
218	C₄⋊C₄	—	46	1	no	—
219	C₄⋊C₄	—	46	1	no	—
220	C₄⋊C₄	—	46	1	no	—
221	C₄⋊C₄	C₂²×D₂₃	1	1	yes	characteristic
222	C₄²	—	2	1	no	—
223	C₄²	—	23	1	no	—
224	C₄²	—	23	1	no	—
225	C₄²	—	23	1	no	—
226	C₄²	—	46	1	no	—
227	C₄²	—	46	1	no	—
228	C₄²	—	46	1	no	—
229	C₄²	C₂²×D₂₃	1	1	yes	characteristic
230	C₂³	—	23	1	no	—
231	Q₈	—	2	1	no	—
232	Q₈	—	2	2	no	—
233	Q₈	—	2	2	no	—
234	Q₈	—	23	2	no	—
235	Q₈	—	46	4	no	—
236	Q₈	—	46	1	no	—
237	Q₈	—	46	2	no	—
238	Q₈	—	46	2	no	—
239	Q₈	—	92	4	no	—
240	Q₈	D₄×D₂₃	1	2	yes	—
241	C₂×C₄	—	2	1	no	—
242	C₂×C₄	—	2	1	no	—
243	C₂×C₄	—	2	2	no	—
244	C₂×C₄	—	23	1	no	—
245	C₂×C₄	—	23	1	no	—
246	C₂×C₄	—	23	4	no	—
247	C₂×C₄	—	23	2	no	—
248	C₂×C₄	—	23	2	no	—
249	C₂×C₄	—	23	1	no	—
250	C₂×C₄	—	46	2	no	—
251	C₂×C₄	—	46	4	no	—
252	C₂×C₄	—	46	1	no	—
253	C₂×C₄	—	46	1	no	—
254	C₂×C₄	—	46	2	no	—
255	C₂×C₄	—	92	4	no	—
256	C₂×C₄	—	92	2	no	—
257	C₂×C₄	D₄×D₂₃	1	1	yes	characteristic
258	C₂×C₄	D₄×D₂₃	1	1	yes	characteristic
259	C₂×C₄	C₂³×D₂₃	1	1	yes	characteristic
260	C₈	—	2	2	no	—
261	C₈	—	46	2	no	—
262	C₂²	—	23	2	no	—
263	C₂²	—	23	2	no	—
264	C₂²	—	23	2	no	—
265	C₂²	C₂×D₄×D₂₃	1	1	yes	characteristic
266	C₄	—	2	2	no	—
267	C₄	—	2	1	no	—
268	C₄	—	4	2	no	—
269	C₄	—	4	1	no	—
270	C₄	—	23	2	no	—
271	C₄	—	23	2	no	—
272	C₄	—	46	2	no	—
273	C₄	—	46	1	no	—
274	C₄	—	92	2	no	—
275	C₄	—	92	1	no	—
276	C₄	Q₁₆×D₂₃	1	2	yes	complemented
277	C₄	C₂×D₄×D₂₃	1	1	yes	characteristic
278	C₄	#41×D₂₃	1	1	yes	characteristic
279	C₂	—	23	4	no	—
280	C₂	#121×D₂₃	1	1	yes	characteristic
281	C₂	C₂×Q₁₆×D₂₃	1	1	yes	characteristic
282	C₂	#137×D₂₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₂₃
commutator, cosocle	C₂×C₄×C₂₃	C₂⁴
Frattini	C₂×C₄	C₂³×D₂₃
Fitting	C₂₃×#462	C₂
socle	C₂²×C₂₃	C₂²×D₄
prime radical	C₂²×D₂₃	C₂×D₄
hypercenter	#462	D₂₃
hypocenter	C₂₃	C₂×#462
LCS	G ▷ C₂×C₄×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #462

Complements

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

N	H ≅ G/N	type
4. #13092628	C₂	semidirect
5. #13092627	C₂	semidirect
6. #13092626	C₂	semidirect
7. #13092625	C₂	semidirect
8. #13092624	C₂	semidirect
11. C₂₃×#462	C₂	semidirect
109. C₄×D₂₃	Q₁₆	semidirect
129. C₄×C₂₃	C₂×Q₁₆	semidirect
137. Dic₂₃	C₂×Q₁₆	semidirect
146. #462	D₂₃	direct (N × H)
152. D₂₃	#462	direct (N × H)
185. C₂₃	C₂×#462	semidirect
276. C₄	Q₁₆×D₂₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×Q₁₆×D₂₃	2
C₄⋊Q₈×D₂₃	2
C₄×Q₈×D₂₃	2
#13092628	2
#13092627	2
#13092626	2
#13092625	2
#13092624	2
C₄⋊C₈×D₂₃	2
#103×D₂₃	2
C₂₃×#462	2
C₂×#462	23

Subgroups — D23×#462 #15682831

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₂₃×#462 #15682831