Subgroups — C₂₃×#8026 #19155652

Order 5888.

742 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#431	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#2285	C₂	1	1	yes	maximal, characteristic
3	C₂×C₂₃×#382	C₂	1	1	yes	maximal, characteristic
4	C₂₃×#1294	C₂	1	4	yes	maximal
5	C₂×C₂₃×#117	—	2	1	no	—
6	C₂²×C₄⋊C₄×C₂₃	—	2	1	no	—
7	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
8	C₂₃×#431	—	2	2	no	—
9	C₂₃×#431	C₄	1	4	yes	complemented
10	C₂×C₂₃×C₄⋊C₈	—	2	1	no	—
11	C₂×C₂₃×C₂²⋊C₈	C₂²	1	2	yes	—
12	C₂×C₄×C₈×C₂₃	—	2	1	no	—
13	C₂₃×#384	C₄	1	2	yes	complemented
14	C₂₃×#382	—	2	2	no	—
15	C₂₃×#382	—	2	1	no	—
16	C₂₃×#382	C₄	1	4	yes	complemented
17	C₂₃×#380	—	2	1	no	—
18	C₂₃×#380	C₂²	1	2	yes	—
19	C₄×C₄⋊C₄×C₂₃	—	2	1	no	—
20	C₄×C₄⋊C₄×C₂₃	C₄	1	2	yes	complemented
21	C₂×C₂₃×#95	—	2	1	no	—
22	C₂×C₂₃×#95	C₂²	1	2	yes	—
23	C₂³×C₄×C₂₃	—	2	2	no	—
24	C₂³×C₄×C₂₃	D₄	1	1	yes	characteristic
25	C₂³×C₄×C₂₃	D₄	1	1	yes	characteristic
26	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
27	C₂²×C₈×C₂₃	—	2	2	no	—
28	C₂₃×#117	—	4	2	no	—
29	C₂₃×#117	—	4	2	no	—
30	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
31	C₂×C₄⋊C₄×C₂₃	—	2	4	no	—
32	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
33	C₂×C₄⋊C₄×C₂₃	—	4	2	no	—
34	C₂×C₄⋊C₄×C₂₃	—	4	2	no	—
35	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	4	yes	—
36	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
37	C₂×C₄²×C₂₃	—	2	2	no	—
38	C₂×C₄²×C₂₃	C₂×C₄	1	2	yes	—
39	C₂×C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
40	C₂×C₄²×C₂₃	C₂×C₄	1	2	yes	—
41	C₂×C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
42	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
43	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
44	C₂×C₄²×C₂₃	D₄	1	2	yes	—
45	C₂×C₄²×C₂₃	Q₈	1	2	yes	—
46	C₂₃×C₄⋊C₈	—	2	4	no	—
47	C₂₃×C₂²⋊C₈	—	2	2	no	—
48	C₂₃×C₂²⋊C₈	C₂×C₄	1	4	yes	—
49	C₄×C₈×C₂₃	—	2	4	no	—
50	C₂₃×#95	—	2	4	no	—
51	C₂₃×#95	—	2	2	no	—
52	C₂₃×#95	—	2	2	no	—
53	C₂₃×#95	—	2	2	no	—
54	C₂₃×#95	C₂×C₄	1	4	yes	—
55	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
56	C₂²×C₄×C₂₃	—	2	4	no	—
57	C₂²×C₄×C₂₃	—	2	4	no	—
58	C₂²×C₄×C₂₃	—	4	2	no	—
59	C₂²×C₄×C₂₃	—	4	2	no	—
60	C₂²×C₄×C₂₃	—	4	4	no	—
61	C₂²×C₄×C₂₃	—	4	4	no	—
62	C₂²×C₄×C₂₃	—	4	2	no	—
63	C₂²×C₄×C₂₃	—	4	2	no	—
64	C₂²×C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
65	C₂²×C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
66	C₂²×C₄×C₂₃	C₂²⋊C₄	1	2	yes	—
67	C₂²×C₄×C₂₃	C₂²⋊C₄	1	2	yes	—
68	C₂²×C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
69	C₂²×C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
70	C₂²×C₄×C₂₃	C₄⋊C₄	1	2	yes	—
71	C₂²×C₄×C₂₃	C₄⋊C₄	1	2	yes	—
72	C₂²×C₄×C₂₃	D₈	1	2	yes	—
73	C₂²×C₄×C₂₃	SD₁₆	1	2	yes	—
74	C₂²×C₄×C₂₃	SD₁₆	1	2	yes	—
75	C₂²×C₄×C₂₃	Q₁₆	1	2	yes	—
76	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
77	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
78	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
79	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
80	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
81	C₂²×C₄×C₂₃	C₂×Q₈	1	1	yes	characteristic
82	C₂×C₈×C₂₃	—	2	4	no	—
83	C₂×C₈×C₂₃	—	4	4	no	—
84	C₄⋊C₄×C₂₃	—	4	4	no	—
85	C₄⋊C₄×C₂₃	—	4	4	no	—
86	C₄⋊C₄×C₂₃	—	4	8	no	—
87	C₄⋊C₄×C₂₃	—	4	4	no	—
88	C₂²⋊C₄×C₂₃	—	4	2	no	—
89	C₂²⋊C₄×C₂₃	—	4	2	no	—
90	C₄²×C₂₃	—	4	4	no	—
91	C₄²×C₂₃	C₄²	1	2	yes	—
92	C₄²×C₂₃	C₄²	1	2	yes	—
93	C₄²×C₂₃	C₂²⋊C₄	1	2	yes	—
94	C₄²×C₂₃	C₂²⋊C₄	1	2	yes	—
95	C₄²×C₂₃	C₄⋊C₄	1	2	yes	—
96	C₄²×C₂₃	C₄⋊C₄	1	2	yes	—
97	C₄²×C₂₃	C₄⋊C₄	1	2	yes	—
98	C₄²×C₂₃	C₄⋊C₄	1	2	yes	—
99	#8026	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
100	C₂³×C₂₃	—	2	2	no	—
101	C₂³×C₂₃	—	2	2	no	—
102	C₂³×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
103	C₂³×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
104	C₂³×C₂₃	C₂×C₄⋊C₄	1	1	yes	characteristic
105	C₂³×C₂₃	C₂×D₈	1	1	yes	characteristic
106	C₂³×C₂₃	C₂×SD₁₆	1	1	yes	characteristic
107	C₂³×C₂₃	C₂×SD₁₆	1	1	yes	characteristic
108	C₂³×C₂₃	C₂×Q₁₆	1	1	yes	characteristic
109	C₂×C₄×C₂₃	—	2	2	no	—
110	C₂×C₄×C₂₃	—	2	2	no	—
111	C₂×C₄×C₂₃	—	2	2	no	—
112	C₂×C₄×C₂₃	—	2	2	no	—
113	C₂×C₄×C₂₃	—	4	2	no	—
114	C₂×C₄×C₂₃	—	4	2	no	—
115	C₂×C₄×C₂₃	—	4	1	no	—
116	C₂×C₄×C₂₃	—	4	1	no	—
117	C₂×C₄×C₂₃	—	4	1	no	—
118	C₂×C₄×C₂₃	—	4	1	no	—
119	C₂×C₄×C₂₃	—	4	4	no	—
120	C₂×C₄×C₂₃	—	4	4	no	—
121	C₂×C₄×C₂₃	—	4	4	no	—
122	C₂×C₄×C₂₃	—	4	4	no	—
123	C₂×C₄×C₂₃	—	4	4	no	—
124	C₂×C₄×C₂₃	—	4	4	no	—
125	C₂×C₄×C₂₃	—	8	4	no	—
126	C₂×C₄×C₂₃	—	8	4	no	—
127	C₂×C₄×C₂₃	#95	1	2	yes	—
128	C₂×C₄×C₂₃	#95	1	2	yes	—
129	C₂×C₄×C₂₃	#95	1	2	yes	—
130	C₂×C₄×C₂₃	#95	1	2	yes	—
131	C₂×C₄×C₂₃	#102	1	2	yes	—
132	C₂×C₄×C₂₃	#102	1	4	yes	—
133	C₂×C₄×C₂₃	#102	1	2	yes	—
134	C₂×C₄×C₂₃	#103	1	4	yes	—
135	C₂×C₄×C₂₃	#103	1	2	yes	—
136	C₂×C₄×C₂₃	#103	1	2	yes	—
137	C₂×C₄×C₂₃	#106	1	4	yes	—
138	C₂×C₄×C₂₃	#107	1	4	yes	—
139	C₂×C₄×C₂₃	C₂×C₄²	1	1	yes	characteristic
140	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
141	C₂×C₄×C₂₃	C₂×C₄⋊C₄	1	1	yes	characteristic
142	C₂×C₄×C₂₃	C₂×C₄⋊C₄	1	1	yes	characteristic
143	C₈×C₂₃	—	4	4	no	—
144	C₂×#431	C₂×C₂₃	1	1	yes	characteristic
145	#2285	C₂×C₂₃	1	1	yes	characteristic
146	C₂×#382	C₂×C₂₃	1	1	yes	characteristic
147	#1294	C₂×C₂₃	1	4	yes	—
148	C₂²×C₂₃	—	2	1	no	—
149	C₂²×C₂₃	—	2	1	no	—
150	C₂²×C₂₃	—	2	1	no	—
151	C₂²×C₂₃	—	2	1	no	—
152	C₂²×C₂₃	—	2	2	no	—
153	C₂²×C₂₃	—	2	2	no	—
154	C₂²×C₂₃	—	2	2	no	—
155	C₂²×C₂₃	—	2	2	no	—
156	C₂²×C₂₃	C₂×#95	1	1	yes	characteristic
157	C₂²×C₂₃	#410	1	2	yes	—
158	C₂²×C₂₃	C₂×#102	1	1	yes	characteristic
159	C₂²×C₂₃	C₂×#102	1	1	yes	characteristic
160	C₂²×C₂₃	C₂×#103	1	1	yes	characteristic
161	C₂²×C₂₃	C₂×#103	1	1	yes	characteristic
162	C₂²×C₂₃	#421	1	2	yes	—
163	C₂²×C₂₃	C₂×#106	1	1	yes	characteristic
164	C₂²×C₂₃	C₂×#107	1	1	yes	characteristic
165	C₄×C₂₃	—	2	2	no	—
166	C₄×C₂₃	—	2	2	no	—
167	C₄×C₂₃	—	2	1	no	—
168	C₄×C₂₃	—	2	1	no	—
169	C₄×C₂₃	—	2	1	no	—
170	C₄×C₂₃	—	2	1	no	—
171	C₄×C₂₃	—	8	4	no	—
172	C₄×C₂₃	—	8	4	no	—
173	C₄×C₂₃	#340	1	4	yes	—
174	C₄×C₂₃	#340	1	4	yes	—
175	C₂×#117	—	2	1	no	—
176	C₂²×C₄⋊C₄	—	2	1	no	—
177	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
178	#431	—	2	2	no	—
179	#431	C₄×C₂₃	1	4	yes	complemented
180	C₂×C₄⋊C₈	—	2	1	no	—
181	C₂×C₂²⋊C₈	C₂²×C₂₃	1	2	yes	—
182	C₂×C₄×C₈	—	2	1	no	—
183	#384	C₄×C₂₃	1	2	yes	complemented
184	#382	—	2	2	no	—
185	#382	—	2	1	no	—
186	#382	C₄×C₂₃	1	4	yes	complemented
187	#380	—	2	1	no	—
188	#380	C₂²×C₂₃	1	2	yes	—
189	C₄×C₄⋊C₄	—	2	1	no	—
190	C₄×C₄⋊C₄	C₄×C₂₃	1	2	yes	complemented
191	C₂×#95	—	2	1	no	—
192	C₂×#95	C₂²×C₂₃	1	2	yes	—
193	C₂×C₂₃	—	2	1	no	—
194	C₂×C₂₃	—	2	1	no	—
195	C₂×C₂₃	—	2	1	no	—
196	C₂×C₂₃	—	2	1	no	—
197	C₂×C₂₃	#1517	1	2	yes	—
198	C₂×C₂₃	#1518	1	2	yes	—
199	C₂×C₂₃	#1733	1	1	yes	characteristic
200	C₂×C₂₃	C₂×#340	1	1	yes	characteristic
201	C₂×C₂₃	#1740	1	1	yes	characteristic
202	C₂³×C₄	—	2	2	no	—
203	C₂³×C₄	D₄×C₂₃	1	1	yes	characteristic
204	C₂³×C₄	D₄×C₂₃	1	1	yes	characteristic
205	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
206	C₂²×C₈	—	2	2	no	—
207	#117	—	4	2	no	—
208	#117	—	4	2	no	—
209	C₂×C₄⋊C₄	—	2	4	no	—
210	C₂×C₄⋊C₄	—	2	2	no	—
211	C₂×C₄⋊C₄	—	2	2	no	—
212	C₂×C₄⋊C₄	—	4	2	no	—
213	C₂×C₄⋊C₄	—	4	2	no	—
214	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	4	yes	—
215	C₂×C₂²⋊C₄	—	2	2	no	—
216	C₂×C₄²	—	2	2	no	—
217	C₂×C₄²	C₂×C₄×C₂₃	1	2	yes	—
218	C₂×C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic
219	C₂×C₄²	C₂×C₄×C₂₃	1	2	yes	—
220	C₂×C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic
221	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
222	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
223	C₂×C₄²	D₄×C₂₃	1	2	yes	—
224	C₂×C₄²	Q₈×C₂₃	1	2	yes	—
225	C₄⋊C₈	—	2	4	no	—
226	C₂²⋊C₈	—	2	2	no	—
227	C₂²⋊C₈	C₂×C₄×C₂₃	1	4	yes	—
228	C₄×C₈	—	2	4	no	—
229	#95	—	2	4	no	—
230	#95	—	2	2	no	—
231	#95	—	2	2	no	—
232	#95	—	2	2	no	—
233	#95	C₂×C₄×C₂₃	1	4	yes	—
234	C₂₃	#8026	1	1	yes	characteristic, direct product factor, Sylow
235	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
236	C₂²×C₄	—	2	4	no	—
237	C₂²×C₄	—	2	4	no	—
238	C₂²×C₄	—	4	2	no	—
239	C₂²×C₄	—	4	2	no	—
240	C₂²×C₄	—	4	4	no	—
241	C₂²×C₄	—	4	4	no	—
242	C₂²×C₄	—	4	2	no	—
243	C₂²×C₄	—	4	2	no	—
244	C₂²×C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
245	C₂²×C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
246	C₂²×C₄	C₂²⋊C₄×C₂₃	1	2	yes	—
247	C₂²×C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
248	C₂²×C₄	C₂²⋊C₄×C₂₃	1	2	yes	—
249	C₂²×C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
250	C₂²×C₄	C₄⋊C₄×C₂₃	1	2	yes	—
251	C₂²×C₄	C₄⋊C₄×C₂₃	1	2	yes	—
252	C₂²×C₄	D₈×C₂₃	1	2	yes	—
253	C₂²×C₄	SD₁₆×C₂₃	1	2	yes	—
254	C₂²×C₄	SD₁₆×C₂₃	1	2	yes	—
255	C₂²×C₄	Q₁₆×C₂₃	1	2	yes	—
256	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
257	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
258	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
259	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
260	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
261	C₂²×C₄	C₂×Q₈×C₂₃	1	1	yes	characteristic
262	C₂×C₈	—	2	4	no	—
263	C₂×C₈	—	4	4	no	—
264	C₄⋊C₄	—	4	4	no	—
265	C₄⋊C₄	—	4	4	no	—
266	C₄⋊C₄	—	4	8	no	—
267	C₄⋊C₄	—	4	4	no	—
268	C₂²⋊C₄	—	4	2	no	—
269	C₂²⋊C₄	—	4	2	no	—
270	C₄²	—	4	4	no	—
271	C₄²	C₄²×C₂₃	1	2	yes	—
272	C₄²	C₄²×C₂₃	1	2	yes	—
273	C₄²	C₂²⋊C₄×C₂₃	1	2	yes	—
274	C₄²	C₂²⋊C₄×C₂₃	1	2	yes	—
275	C₄²	C₄⋊C₄×C₂₃	1	2	yes	—
276	C₄²	C₄⋊C₄×C₂₃	1	2	yes	—
277	C₄²	C₄⋊C₄×C₂₃	1	2	yes	—
278	C₄²	C₄⋊C₄×C₂₃	1	2	yes	—
279	C₂³	—	2	2	no	—
280	C₂³	—	2	2	no	—
281	C₂³	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
282	C₂³	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
283	C₂³	C₂×C₄⋊C₄×C₂₃	1	1	yes	characteristic
284	C₂³	C₂×D₈×C₂₃	1	1	yes	characteristic
285	C₂³	C₂×SD₁₆×C₂₃	1	1	yes	characteristic
286	C₂³	C₂×SD₁₆×C₂₃	1	1	yes	characteristic
287	C₂³	C₂×Q₁₆×C₂₃	1	1	yes	characteristic
288	C₂×C₄	—	2	2	no	—
289	C₂×C₄	—	2	2	no	—
290	C₂×C₄	—	2	2	no	—
291	C₂×C₄	—	2	2	no	—
292	C₂×C₄	—	4	2	no	—
293	C₂×C₄	—	4	2	no	—
294	C₂×C₄	—	4	1	no	—
295	C₂×C₄	—	4	1	no	—
296	C₂×C₄	—	4	1	no	—
297	C₂×C₄	—	4	1	no	—
298	C₂×C₄	—	4	4	no	—
299	C₂×C₄	—	4	4	no	—
300	C₂×C₄	—	4	4	no	—
301	C₂×C₄	—	4	4	no	—
302	C₂×C₄	—	4	4	no	—
303	C₂×C₄	—	4	4	no	—
304	C₂×C₄	—	8	4	no	—
305	C₂×C₄	—	8	4	no	—
306	C₂×C₄	C₂₃×#95	1	2	yes	—
307	C₂×C₄	C₂₃×#95	1	2	yes	—
308	C₂×C₄	C₂₃×#95	1	2	yes	—
309	C₂×C₄	C₂₃×#95	1	2	yes	—
310	C₂×C₄	C₂₃×#102	1	2	yes	—
311	C₂×C₄	C₂₃×#102	1	4	yes	—
312	C₂×C₄	C₂₃×#102	1	2	yes	—
313	C₂×C₄	C₂₃×#103	1	4	yes	—
314	C₂×C₄	C₂₃×#103	1	2	yes	—
315	C₂×C₄	C₂₃×#103	1	2	yes	—
316	C₂×C₄	C₂₃×#106	1	4	yes	—
317	C₂×C₄	C₂₃×#107	1	4	yes	—
318	C₂×C₄	C₂×C₄²×C₂₃	1	1	yes	characteristic
319	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
320	C₂×C₄	C₂×C₄⋊C₄×C₂₃	1	1	yes	characteristic
321	C₂×C₄	C₂×C₄⋊C₄×C₂₃	1	1	yes	characteristic
322	C₈	—	4	4	no	—
323	C₂²	—	2	1	no	—
324	C₂²	—	2	1	no	—
325	C₂²	—	2	1	no	—
326	C₂²	—	2	1	no	—
327	C₂²	—	2	2	no	—
328	C₂²	—	2	2	no	—
329	C₂²	—	2	2	no	—
330	C₂²	—	2	2	no	—
331	C₂²	C₂×C₂₃×#95	1	1	yes	characteristic
332	C₂²	C₂₃×#410	1	2	yes	—
333	C₂²	C₂×C₂₃×#102	1	1	yes	characteristic
334	C₂²	C₂×C₂₃×#102	1	1	yes	characteristic
335	C₂²	C₂×C₂₃×#103	1	1	yes	characteristic
336	C₂²	C₂×C₂₃×#103	1	1	yes	characteristic
337	C₂²	C₂₃×#421	1	2	yes	—
338	C₂²	C₂×C₂₃×#106	1	1	yes	characteristic
339	C₂²	C₂×C₂₃×#107	1	1	yes	characteristic
340	C₄	—	2	2	no	—
341	C₄	—	2	2	no	—
342	C₄	—	2	1	no	—
343	C₄	—	2	1	no	—
344	C₄	—	2	1	no	—
345	C₄	—	2	1	no	—
346	C₄	—	8	4	no	—
347	C₄	—	8	4	no	—
348	C₄	C₂₃×#340	1	4	yes	—
349	C₄	C₂₃×#340	1	4	yes	—
350	C₂	—	2	1	no	—
351	C₂	—	2	1	no	—
352	C₂	—	2	1	no	—
353	C₂	—	2	1	no	—
354	C₂	C₂₃×#1517	1	2	yes	—
355	C₂	C₂₃×#1518	1	2	yes	—
356	C₂	C₂₃×#1733	1	1	yes	characteristic
357	C₂	C₂×C₂₃×#340	1	1	yes	characteristic
358	C₂	C₂₃×#1740	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂×C₂²⋊C₄
commutator	C₂×C₄	C₂×C₄²×C₂₃
Frattini, cosocle	C₂³×C₄	C₂³×C₂₃
prime radical	C₂⁴×C₂₃	C₂×D₄
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₂₃ ◁ C₂²×C₄²×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
9. C₂₃×#431	C₄	semidirect
13. C₂₃×#384	C₄	semidirect
16. C₂₃×#382	C₄	semidirect
20. C₄×C₄⋊C₄×C₂₃	C₄	semidirect
99. #8026	C₂₃	direct (N × H)
179. #431	C₄×C₂₃	semidirect
183. #384	C₄×C₂₃	semidirect
186. #382	C₄×C₂₃	semidirect
190. C₄×C₄⋊C₄	C₄×C₂₃	semidirect
234. C₂₃	#8026	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₂₃×#431	2
C₂₃×#2285	2
C₂×C₂₃×#382	2
C₂₃×#1294	2
#8026	23

Subgroups — C23×#8026 #19155652

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#8026 #19155652