Subgroups — C₂₃×#18059 #19165685

Order 5888.

656 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#2991	C₂	1	2	yes	maximal, complemented
2	C₄×C₂₃×#135	C₂	1	1	yes	maximal, characteristic
3	C₂₃×#1589	C₂	1	2	yes	maximal, complemented
4	C₂₃×#1588	C₂	1	4	yes	maximal, complemented
5	C₈×Q₁₆×C₂₃	C₂	1	2	yes	maximal, complemented
6	C₂₃×#1567	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#1489	C₂	1	2	yes	maximal, complemented
8	C₈×M₁₆×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₂₃×#135	C₄	1	1	yes	characteristic
10	C₄×#41×C₂₃	C₂²	1	2	yes	—
11	C₈×Q₈×C₂₃	C₂²	1	4	yes	—
12	C₄×Q₁₆×C₂₃	C₄	1	1	yes	characteristic
13	C₄×Q₁₆×C₂₃	C₂²	1	1	yes	characteristic
14	C₄×SD₁₆×C₂₃	C₄	1	2	yes	—
15	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	—
16	C₄×D₈×C₂₃	C₄	1	1	yes	characteristic
17	C₄×D₈×C₂₃	C₂²	1	1	yes	characteristic
18	C₂₃×#436	—	2	4	no	—
19	C₂₃×#436	C₂²	1	4	yes	—
20	C₂₃×#431	—	2	2	no	—
21	C₂₃×#431	C₂²	1	1	yes	characteristic
22	C₂₃×#427	C₄	1	1	yes	characteristic
23	C₂₃×#423	—	2	2	no	—
24	C₂₃×#423	C₂²	1	2	yes	—
25	C₂₃×#416	C₄	1	2	yes	—
26	C₄×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
28	C₂₃×#335	C₂²	1	2	yes	—
29	C₂₃×#335	C₂²	1	2	yes	—
30	C₂₃×Q₈⋊C₈	C₂²	1	4	yes	—
31	C₂₃×D₄⋊C₈	C₂²	1	4	yes	—
32	C₂₃×#322	C₂²	1	2	yes	—
33	C₈²×C₂₃	C₂²	1	2	yes	—
34	C₂×#41×C₂₃	C₂×C₄	1	2	yes	—
35	C₂₃×#135	—	2	4	no	—
36	C₂×Q₁₆×C₂₃	C₂×C₄	1	1	yes	characteristic
37	C₂×SD₁₆×C₂₃	C₂×C₄	1	2	yes	—
38	C₂×D₈×C₂₃	C₂×C₄	1	1	yes	characteristic
39	C₂×M₁₆×C₂₃	—	2	1	no	—
40	C₂×M₁₆×C₂₃	—	2	2	no	—
41	C₂×M₁₆×C₂₃	—	2	4	no	—
42	C₂²×C₈×C₂₃	C₂×C₄	1	1	yes	characteristic
43	C₂²×C₈×C₂₃	C₂×C₄	1	1	yes	characteristic
44	C₄×Q₈×C₂₃	C₂×C₄	1	2	yes	—
45	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
46	C₄×D₄×C₂₃	—	2	2	no	—
47	C₄×D₄×C₂₃	—	2	2	no	—
48	C₄×D₄×C₂₃	C₂×C₄	1	2	yes	—
49	C₄×D₄×C₂₃	C₂³	1	2	yes	—
50	C₂₃×#117	—	2	2	no	—
51	C₂₃×#117	C₂×C₄	1	2	yes	—
52	C₂×C₄²×C₂₃	—	2	2	no	—
53	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
54	C₂₃×#107	C₂×C₄	1	1	yes	characteristic
55	C₂₃×#107	C₂×C₄	1	1	yes	characteristic
56	C₂₃×#106	C₂×C₄	1	2	yes	—
57	C₂₃×C₄⋊C₈	—	2	4	no	—
58	C₂₃×C₄⋊C₈	—	2	2	no	—
59	C₂₃×C₄⋊C₈	D₄	1	1	yes	characteristic
60	C₂₃×C₄⋊C₈	D₄	1	1	yes	characteristic
61	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
62	C₂₃×#103	C₂×C₄	1	2	yes	—
63	C₂₃×#103	C₂×C₄	1	2	yes	—
64	C₂₃×#102	C₂×C₄	1	2	yes	—
65	C₂₃×#102	C₂×C₄	1	2	yes	—
66	C₂₃×C₂²⋊C₈	—	2	4	no	—
67	C₂₃×C₂²⋊C₈	D₄	1	2	yes	—
68	C₂₃×#97	—	2	1	no	—
69	C₄×C₈×C₂₃	—	2	4	no	—
70	C₄×C₈×C₂₃	C₂×C₄	1	1	yes	characteristic
71	C₄×C₈×C₂₃	C₂×C₄	1	1	yes	characteristic
72	C₄×C₈×C₂₃	C₂³	1	2	yes	—
73	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
74	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
75	C₄×C₈×C₂₃	C₂³	1	2	yes	—
76	#41×C₂₃	—	2	4	no	—
77	#41×C₂₃	—	4	2	no	—
78	C₂×Q₈×C₂₃	C₂²×C₄	1	2	yes	—
79	C₂×D₄×C₂₃	—	2	2	no	—
80	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
81	C₂²×C₄×C₂₃	—	2	2	no	—
82	C₂²×C₄×C₂₃	—	2	2	no	—
83	C₂²×C₄×C₂₃	—	2	2	no	—
84	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
85	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
86	C₂²×C₄×C₂₃	#41	1	1	yes	characteristic
87	Q₁₆×C₂₃	M₁₆	1	4	yes	complemented
88	SD₁₆×C₂₃	—	2	4	no	—
89	D₈×C₂₃	—	2	2	no	—
90	M₁₆×C₂₃	—	2	4	no	—
91	M₁₆×C₂₃	—	8	4	no	—
92	M₁₆×C₂₃	—	8	2	no	—
93	C₂×C₈×C₂₃	—	2	2	no	—
94	C₂×C₈×C₂₃	—	2	2	no	—
95	C₂×C₈×C₂₃	—	2	4	no	—
96	C₂×C₈×C₂₃	—	4	1	no	—
97	C₂×C₈×C₂₃	C₂²×C₄	1	1	yes	characteristic
98	C₂×C₈×C₂₃	C₂²×C₄	1	1	yes	characteristic
99	C₂×C₈×C₂₃	C₂²×C₄	1	1	yes	characteristic
100	C₂×C₈×C₂₃	C₂²×C₄	1	1	yes	characteristic
101	C₂×C₈×C₂₃	C₂×D₄	1	2	yes	—
102	C₂×C₈×C₂₃	C₂×D₄	1	2	yes	—
103	C₄⋊C₄×C₂₃	—	2	2	no	—
104	C₄⋊C₄×C₂₃	—	2	2	no	—
105	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
106	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
107	C₂²⋊C₄×C₂₃	—	2	2	no	—
108	C₂²⋊C₄×C₂₃	—	2	2	no	—
109	C₂²⋊C₄×C₂₃	—	2	2	no	—
110	C₄²×C₂₃	—	2	2	no	—
111	C₄²×C₂₃	—	2	2	no	—
112	C₄²×C₂₃	—	2	2	no	—
113	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
114	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
115	C₄²×C₂₃	#41	1	1	yes	characteristic
116	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
117	#18059	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
118	C₂³×C₂₃	—	2	2	no	—
119	C₂³×C₂₃	C₄×D₄	1	1	yes	characteristic
120	Q₈×C₂₃	—	2	2	no	—
121	Q₈×C₂₃	C₂×M₁₆	1	4	yes	—
122	D₄×C₂₃	—	2	2	no	—
123	D₄×C₂₃	—	2	2	no	—
124	D₄×C₂₃	—	4	4	no	—
125	C₂×C₄×C₂₃	—	2	2	no	—
126	C₂×C₄×C₂₃	—	2	1	no	—
127	C₂×C₄×C₂₃	—	2	1	no	—
128	C₂×C₄×C₂₃	—	2	1	no	—
129	C₂×C₄×C₂₃	—	2	1	no	—
130	C₂×C₄×C₂₃	—	2	2	no	—
131	C₂×C₄×C₂₃	—	2	2	no	—
132	C₂×C₄×C₂₃	—	2	2	no	—
133	C₂×C₄×C₂₃	—	4	4	no	—
134	C₂×C₄×C₂₃	—	4	2	no	—
135	C₂×C₄×C₂₃	—	4	2	no	—
136	C₂×C₄×C₂₃	—	4	4	no	—
137	C₂×C₄×C₂₃	C₄×D₄	1	1	yes	characteristic
138	C₂×C₄×C₂₃	C₄×D₄	1	1	yes	characteristic
139	C₂×C₄×C₂₃	C₄×D₄	1	1	yes	characteristic
140	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
141	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
142	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
143	C₈×C₂₃	—	2	4	no	—
144	C₈×C₂₃	—	2	1	no	—
145	C₈×C₂₃	—	2	1	no	—
146	C₈×C₂₃	—	2	1	no	—
147	C₈×C₂₃	—	2	2	no	—
148	C₈×C₂₃	—	2	2	no	—
149	C₈×C₂₃	—	4	4	no	—
150	C₈×C₂₃	C₂×M₁₆	1	2	yes	—
151	#2991	C₂×C₂₃	1	2	yes	complemented
152	C₄×#135	C₂×C₂₃	1	1	yes	characteristic
153	#1589	C₂×C₂₃	1	2	yes	complemented
154	#1588	C₂×C₂₃	1	4	yes	complemented
155	C₈×Q₁₆	C₂×C₂₃	1	2	yes	complemented
156	#1567	C₂×C₂₃	1	1	yes	characteristic, complemented
157	#1489	C₂×C₂₃	1	2	yes	complemented
158	C₈×M₁₆	C₂×C₂₃	1	1	yes	characteristic, complemented
159	C₂²×C₂₃	—	2	1	no	—
160	C₂²×C₂₃	—	2	1	no	—
161	C₂²×C₂₃	—	2	1	no	—
162	C₂²×C₂₃	—	4	2	no	—
163	C₂²×C₂₃	—	4	2	no	—
164	C₂²×C₂₃	—	4	2	no	—
165	C₂²×C₂₃	C₂×C₄×D₄	1	1	yes	characteristic
166	C₄×C₂₃	—	2	1	no	—
167	C₄×C₂₃	—	2	4	no	—
168	C₄×C₂₃	—	2	1	no	—
169	C₄×C₂₃	—	2	1	no	—
170	C₄×C₂₃	—	4	2	no	—
171	C₄×C₂₃	—	4	2	no	—
172	C₄×C₂₃	#443	1	2	yes	—
173	C₄×C₂₃	C₂²×M₁₆	1	1	yes	characteristic
174	C₄×C₂₃	#568	1	1	yes	characteristic
175	C₄×C₂₃	#576	1	1	yes	characteristic
176	C₄×C₂₃	#578	1	1	yes	characteristic
177	C₂×#135	C₄×C₂₃	1	1	yes	characteristic
178	C₄×#41	C₂²×C₂₃	1	2	yes	—
179	C₈×Q₈	C₂²×C₂₃	1	4	yes	—
180	C₄×Q₁₆	C₄×C₂₃	1	1	yes	characteristic
181	C₄×Q₁₆	C₂²×C₂₃	1	1	yes	characteristic
182	C₄×SD₁₆	C₄×C₂₃	1	2	yes	—
183	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	—
184	C₄×D₈	C₄×C₂₃	1	1	yes	characteristic
185	C₄×D₈	C₂²×C₂₃	1	1	yes	characteristic
186	#436	—	2	4	no	—
187	#436	C₂²×C₂₃	1	4	yes	—
188	#431	—	2	2	no	—
189	#431	C₂²×C₂₃	1	1	yes	characteristic
190	#427	C₄×C₂₃	1	1	yes	characteristic
191	#423	—	2	2	no	—
192	#423	C₂²×C₂₃	1	2	yes	—
193	#416	C₄×C₂₃	1	2	yes	—
194	C₄×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
195	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
196	#335	C₂²×C₂₃	1	2	yes	—
197	#335	C₂²×C₂₃	1	2	yes	—
198	Q₈⋊C₈	C₂²×C₂₃	1	4	yes	—
199	D₄⋊C₈	C₂²×C₂₃	1	4	yes	—
200	#322	C₂²×C₂₃	1	2	yes	—
201	C₈²	C₂²×C₂₃	1	2	yes	—
202	C₂×C₂₃	—	4	1	no	—
203	C₂×C₂₃	—	8	2	no	—
204	C₂×C₂₃	D₄×M₁₆	1	1	yes	characteristic
205	C₂×C₂₃	#2951	1	1	yes	characteristic
206	C₂×C₂₃	C₂×#443	1	1	yes	characteristic
207	C₂×#41	C₂×C₄×C₂₃	1	2	yes	—
208	#135	—	2	4	no	—
209	C₂×Q₁₆	C₂×C₄×C₂₃	1	1	yes	characteristic
210	C₂×SD₁₆	C₂×C₄×C₂₃	1	2	yes	—
211	C₂×D₈	C₂×C₄×C₂₃	1	1	yes	characteristic
212	C₂×M₁₆	—	2	1	no	—
213	C₂×M₁₆	—	2	2	no	—
214	C₂×M₁₆	—	2	4	no	—
215	C₂²×C₈	C₂×C₄×C₂₃	1	1	yes	characteristic
216	C₂²×C₈	C₂×C₄×C₂₃	1	1	yes	characteristic
217	C₄×Q₈	C₂×C₄×C₂₃	1	2	yes	—
218	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
219	C₄×D₄	—	2	2	no	—
220	C₄×D₄	—	2	2	no	—
221	C₄×D₄	C₂×C₄×C₂₃	1	2	yes	—
222	C₄×D₄	C₂³×C₂₃	1	2	yes	—
223	#117	—	2	2	no	—
224	#117	C₂×C₄×C₂₃	1	2	yes	—
225	C₂×C₄²	—	2	2	no	—
226	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
227	#107	C₂×C₄×C₂₃	1	1	yes	characteristic
228	#107	C₂×C₄×C₂₃	1	1	yes	characteristic
229	#106	C₂×C₄×C₂₃	1	2	yes	—
230	C₄⋊C₈	—	2	4	no	—
231	C₄⋊C₈	—	2	2	no	—
232	C₄⋊C₈	D₄×C₂₃	1	1	yes	characteristic
233	C₄⋊C₈	D₄×C₂₃	1	1	yes	characteristic
234	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
235	#103	C₂×C₄×C₂₃	1	2	yes	—
236	#103	C₂×C₄×C₂₃	1	2	yes	—
237	#102	C₂×C₄×C₂₃	1	2	yes	—
238	#102	C₂×C₄×C₂₃	1	2	yes	—
239	C₂²⋊C₈	—	2	4	no	—
240	C₂²⋊C₈	D₄×C₂₃	1	2	yes	—
241	#97	—	2	1	no	—
242	C₄×C₈	—	2	4	no	—
243	C₄×C₈	C₂×C₄×C₂₃	1	1	yes	characteristic
244	C₄×C₈	C₂×C₄×C₂₃	1	1	yes	characteristic
245	C₄×C₈	C₂³×C₂₃	1	2	yes	—
246	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
247	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
248	C₄×C₈	C₂³×C₂₃	1	2	yes	—
249	C₂₃	#18059	1	1	yes	characteristic, direct product factor, Sylow
250	#41	—	2	4	no	—
251	#41	—	4	2	no	—
252	C₂×Q₈	C₂²×C₄×C₂₃	1	2	yes	—
253	C₂×D₄	—	2	2	no	—
254	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
255	C₂²×C₄	—	2	2	no	—
256	C₂²×C₄	—	2	2	no	—
257	C₂²×C₄	—	2	2	no	—
258	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
259	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
260	C₂²×C₄	#41×C₂₃	1	1	yes	characteristic
261	Q₁₆	M₁₆×C₂₃	1	4	yes	complemented
262	SD₁₆	—	2	4	no	—
263	D₈	—	2	2	no	—
264	M₁₆	—	2	4	no	—
265	M₁₆	—	8	4	no	—
266	M₁₆	—	8	2	no	—
267	C₂×C₈	—	2	2	no	—
268	C₂×C₈	—	2	2	no	—
269	C₂×C₈	—	2	4	no	—
270	C₂×C₈	—	4	1	no	—
271	C₂×C₈	C₂²×C₄×C₂₃	1	1	yes	characteristic
272	C₂×C₈	C₂²×C₄×C₂₃	1	1	yes	characteristic
273	C₂×C₈	C₂²×C₄×C₂₃	1	1	yes	characteristic
274	C₂×C₈	C₂²×C₄×C₂₃	1	1	yes	characteristic
275	C₂×C₈	C₂×D₄×C₂₃	1	2	yes	—
276	C₂×C₈	C₂×D₄×C₂₃	1	2	yes	—
277	C₄⋊C₄	—	2	2	no	—
278	C₄⋊C₄	—	2	2	no	—
279	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
280	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
281	C₂²⋊C₄	—	2	2	no	—
282	C₂²⋊C₄	—	2	2	no	—
283	C₂²⋊C₄	—	2	2	no	—
284	C₄²	—	2	2	no	—
285	C₄²	—	2	2	no	—
286	C₄²	—	2	2	no	—
287	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
288	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
289	C₄²	#41×C₂₃	1	1	yes	characteristic
290	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
291	C₂³	—	2	2	no	—
292	C₂³	C₄×D₄×C₂₃	1	1	yes	characteristic
293	Q₈	—	2	2	no	—
294	Q₈	C₂×M₁₆×C₂₃	1	4	yes	—
295	D₄	—	2	2	no	—
296	D₄	—	2	2	no	—
297	D₄	—	4	4	no	—
298	C₂×C₄	—	2	2	no	—
299	C₂×C₄	—	2	1	no	—
300	C₂×C₄	—	2	1	no	—
301	C₂×C₄	—	2	1	no	—
302	C₂×C₄	—	2	1	no	—
303	C₂×C₄	—	2	2	no	—
304	C₂×C₄	—	2	2	no	—
305	C₂×C₄	—	2	2	no	—
306	C₂×C₄	—	4	4	no	—
307	C₂×C₄	—	4	2	no	—
308	C₂×C₄	—	4	2	no	—
309	C₂×C₄	—	4	4	no	—
310	C₂×C₄	C₄×D₄×C₂₃	1	1	yes	characteristic
311	C₂×C₄	C₄×D₄×C₂₃	1	1	yes	characteristic
312	C₂×C₄	C₄×D₄×C₂₃	1	1	yes	characteristic
313	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
314	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
315	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
316	C₈	—	2	4	no	—
317	C₈	—	2	1	no	—
318	C₈	—	2	1	no	—
319	C₈	—	2	1	no	—
320	C₈	—	2	2	no	—
321	C₈	—	2	2	no	—
322	C₈	—	4	4	no	—
323	C₈	C₂×M₁₆×C₂₃	1	2	yes	—
324	C₂²	—	2	1	no	—
325	C₂²	—	2	1	no	—
326	C₂²	—	2	1	no	—
327	C₂²	—	4	2	no	—
328	C₂²	—	4	2	no	—
329	C₂²	—	4	2	no	—
330	C₂²	C₂×C₄×D₄×C₂₃	1	1	yes	characteristic
331	C₄	—	2	1	no	—
332	C₄	—	2	4	no	—
333	C₄	—	2	1	no	—
334	C₄	—	2	1	no	—
335	C₄	—	4	2	no	—
336	C₄	—	4	2	no	—
337	C₄	C₂₃×#443	1	2	yes	—
338	C₄	C₂²×M₁₆×C₂₃	1	1	yes	characteristic
339	C₄	C₂₃×#568	1	1	yes	characteristic
340	C₄	C₂₃×#576	1	1	yes	characteristic
341	C₄	C₂₃×#578	1	1	yes	characteristic
342	C₂	—	4	1	no	—
343	C₂	—	8	2	no	—
344	C₂	D₄×M₁₆×C₂₃	1	1	yes	characteristic
345	C₂	C₂₃×#2951	1	1	yes	characteristic
346	C₂	C₂×C₂₃×#443	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₂₃	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₂₃
Frattini, cosocle	C₄²	C₂⁴×C₂₃
socle	C₂²×C₂₃	C₂×C₄×D₄
prime radical	C₂×C₂₃×#135	C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₃ ◁ C₂₃×#431 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₃×#2991	C₂	semidirect
3. C₂₃×#1589	C₂	semidirect
4. C₂₃×#1588	C₂	semidirect
5. C₈×Q₁₆×C₂₃	C₂	semidirect
6. C₂₃×#1567	C₂	semidirect
7. C₂₃×#1489	C₂	semidirect
8. C₈×M₁₆×C₂₃	C₂	semidirect
87. Q₁₆×C₂₃	M₁₆	semidirect
117. #18059	C₂₃	direct (N × H)
151. #2991	C₂×C₂₃	semidirect
153. #1589	C₂×C₂₃	semidirect
154. #1588	C₂×C₂₃	semidirect
155. C₈×Q₁₆	C₂×C₂₃	semidirect
156. #1567	C₂×C₂₃	semidirect
157. #1489	C₂×C₂₃	semidirect
158. C₈×M₁₆	C₂×C₂₃	semidirect
249. C₂₃	#18059	direct (N × H)
261. Q₁₆	M₁₆×C₂₃	semidirect

Maximal subgroups

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

subgroup	index
C₂₃×#2991	2
C₄×C₂₃×#135	2
C₂₃×#1589	2
C₂₃×#1588	2
C₈×Q₁₆×C₂₃	2
C₂₃×#1567	2
C₂₃×#1489	2
C₈×M₁₆×C₂₃	2
#18059	23

Subgroups — C23×#18059 #19165685

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#18059 #19165685