Subgroups — C₂₃×#20541 #19168167

Order 5888.

886 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#433	C₂	1	2	yes	maximal
2	C₂₃×#2296	C₂	1	1	yes	maximal, characteristic
3	C₂₃×#1771	C₂	1	2	yes	maximal, complemented
4	C₂₃×#1771	C₂	1	2	yes	maximal, complemented
5	C₂₃×#1770	C₂	1	2	yes	maximal, complemented
6	C₈×C₄⋊C₄×C₂₃	C₂	1	2	yes	maximal, complemented
7	C₂₃×#1750	C₂	1	2	yes	maximal
8	C₂₃×#1749	C₂	1	1	yes	maximal, characteristic
9	C₄×C₂₃×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic
10	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
11	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
12	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
13	C₂₃×#433	C₄	1	16	yes	complemented
14	C₂×C₂₃×C₄⋊C₈	C₂²	1	2	yes	—
15	C₂×C₂₃×C₄⋊C₈	C₂²	1	2	yes	—
16	C₂×C₂₃×C₂²⋊C₈	C₂²	1	2	yes	—
17	C₂×C₂₃×C₂²⋊C₈	C₂²	1	2	yes	—
18	C₂×C₂₃×#97	C₂²	1	1	yes	characteristic
19	C₂×C₂₃×#97	C₂²	1	1	yes	characteristic
20	C₂×C₂₃×#97	C₂²	1	2	yes	—
21	C₂×C₂₃×#97	C₂²	1	2	yes	—
22	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
23	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
24	C₂×C₄×C₈×C₂₃	C₂²	1	2	yes	—
25	C₂×C₄×C₈×C₂₃	C₂²	1	2	yes	—
26	C₂₃×#389	C₄	1	2	yes	—
27	C₂₃×#389	C₄	1	2	yes	—
28	C₂₃×#385	C₄	1	4	yes	—
29	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
30	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
31	C₂₃×#336	C₂²	1	2	yes	—
32	C₂₃×#336	C₂²	1	2	yes	—
33	C₂₃×#336	C₂²	1	2	yes	—
34	C₂₃×#336	C₂²	1	2	yes	—
35	C₂³×C₄×C₂₃	C₂×C₄	1	2	yes	—
36	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
37	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
38	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
39	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
40	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
41	C₂₃×#117	—	4	1	no	—
42	C₂₃×#117	—	4	1	no	—
43	C₂₃×#117	C₂×C₄	1	8	yes	—
44	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	4	yes	—
45	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	4	yes	—
46	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
47	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
48	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
49	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
50	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
51	C₂×C₄²×C₂₃	—	4	1	no	—
52	C₂×C₄²×C₂₃	—	4	1	no	—
53	C₂×C₄²×C₂₃	C₂×C₄	1	2	yes	—
54	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
55	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
56	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
57	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
58	C₂₃×C₄⋊C₈	C₂×C₄	1	8	yes	complemented
59	C₂₃×C₄⋊C₈	C₂×C₄	1	8	yes	complemented
60	C₂₃×C₂²⋊C₈	C₂×C₄	1	8	yes	—
61	C₂₃×C₂²⋊C₈	C₂×C₄	1	8	yes	—
62	C₂₃×#97	—	4	1	no	—
63	C₂₃×#97	—	4	1	no	—
64	C₂₃×#97	—	4	2	no	—
65	C₂₃×#97	C₂×C₄	1	8	yes	complemented
66	C₄×C₈×C₂₃	—	4	1	no	—
67	C₄×C₈×C₂₃	—	4	1	no	—
68	C₄×C₈×C₂₃	—	4	2	no	—
69	C₄×C₈×C₂₃	C₂×C₄	1	8	yes	complemented
70	C₂₃×#95	C₂×C₄	1	4	yes	—
71	C₂₃×#95	C₂×C₄	1	4	yes	—
72	C₂⁴×C₂₃	C₂²×C₄	1	1	yes	characteristic
73	C₂²×C₄×C₂₃	—	2	1	no	—
74	C₂²×C₄×C₂₃	—	2	1	no	—
75	C₂²×C₄×C₂₃	—	2	2	no	—
76	C₂²×C₄×C₂₃	—	2	4	no	—
77	C₂²×C₄×C₂₃	—	4	2	no	—
78	C₂²×C₄×C₂₃	—	4	2	no	—
79	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
80	C₂²×C₄×C₂₃	C₂²×C₄	1	4	yes	—
81	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
82	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
83	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
84	C₂²×C₄×C₂₃	C₂²×C₄	1	4	yes	—
85	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
86	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
87	C₂×C₈×C₂₃	—	2	2	no	—
88	C₂×C₈×C₂₃	—	2	2	no	—
89	C₂×C₈×C₂₃	—	2	2	no	—
90	C₂×C₈×C₂₃	—	2	2	no	—
91	C₂×C₈×C₂₃	—	2	2	no	—
92	C₂×C₈×C₂₃	—	2	2	no	—
93	C₂×C₈×C₂₃	—	2	2	no	—
94	C₂×C₈×C₂₃	—	2	2	no	—
95	C₂×C₈×C₂₃	C₂²×C₄	1	4	yes	—
96	C₂×C₈×C₂₃	C₂²×C₄	1	4	yes	—
97	C₂×C₈×C₂₃	C₂²×C₄	1	4	yes	—
98	C₂×C₈×C₂₃	C₂²×C₄	1	4	yes	—
99	C₄⋊C₄×C₂₃	—	2	8	no	—
100	C₄⋊C₄×C₂₃	—	4	4	no	—
101	C₄⋊C₄×C₂₃	—	4	2	no	—
102	C₄⋊C₄×C₂₃	C₄²	1	4	yes	—
103	C₄⋊C₄×C₂₃	C₄²	1	4	yes	—
104	C₂²⋊C₄×C₂₃	—	4	2	no	—
105	C₂²⋊C₄×C₂₃	C₄²	1	8	yes	—
106	C₄²×C₂₃	—	2	1	no	—
107	C₄²×C₂₃	—	2	1	no	—
108	C₄²×C₂₃	—	2	1	no	—
109	C₄²×C₂₃	—	2	1	no	—
110	C₄²×C₂₃	—	2	2	no	—
111	C₄²×C₂₃	—	2	2	no	—
112	C₄²×C₂₃	—	4	2	no	—
113	C₄²×C₂₃	C₂²×C₄	1	4	yes	—
114	C₄²×C₂₃	C₂²×C₄	1	4	yes	—
115	#20541	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
116	C₂³×C₂₃	—	2	1	no	—
117	C₂³×C₂₃	—	2	1	no	—
118	C₂³×C₂₃	—	2	2	no	—
119	C₂³×C₂₃	—	2	2	no	—
120	C₂³×C₂₃	C₂×C₄²	1	2	yes	—
121	C₂³×C₂₃	C₂³×C₄	1	1	yes	characteristic
122	C₂×C₄×C₂₃	—	2	2	no	—
123	C₂×C₄×C₂₃	—	2	1	no	—
124	C₂×C₄×C₂₃	—	2	1	no	—
125	C₂×C₄×C₂₃	—	2	4	no	—
126	C₂×C₄×C₂₃	—	2	4	no	—
127	C₂×C₄×C₂₃	—	2	2	no	—
128	C₂×C₄×C₂₃	—	2	4	no	—
129	C₂×C₄×C₂₃	—	2	4	no	—
130	C₂×C₄×C₂₃	—	2	2	no	—
131	C₂×C₄×C₂₃	—	2	4	no	—
132	C₂×C₄×C₂₃	—	2	4	no	—
133	C₂×C₄×C₂₃	—	2	2	no	—
134	C₂×C₄×C₂₃	—	2	2	no	—
135	C₂×C₄×C₂₃	—	2	4	no	—
136	C₂×C₄×C₂₃	—	4	8	no	—
137	C₂×C₄×C₂₃	C₂×C₄²	1	4	yes	—
138	C₂×C₄×C₂₃	C₂×C₄²	1	4	yes	—
139	C₂×C₄×C₂₃	C₂×C₄²	1	2	yes	—
140	C₂×C₄×C₂₃	#131	1	4	yes	—
141	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
142	C₂×C₄×C₂₃	H(5,𝔽₂)	1	1	yes	characteristic
143	C₂×C₄×C₂₃	H(5,𝔽₂)	1	1	yes	characteristic
144	C₂×C₄×C₂₃	2₋¹⁺⁴	1	2	yes	—
145	C₈×C₂₃	—	2	4	no	—
146	C₈×C₂₃	—	2	4	no	—
147	C₈×C₂₃	—	2	4	no	—
148	C₈×C₂₃	—	2	4	no	—
149	C₂×#433	C₂×C₂₃	1	2	yes	—
150	#2296	C₂×C₂₃	1	1	yes	characteristic
151	#1771	C₂×C₂₃	1	2	yes	complemented
152	#1771	C₂×C₂₃	1	2	yes	complemented
153	#1770	C₂×C₂₃	1	2	yes	complemented
154	C₈×C₄⋊C₄	C₂×C₂₃	1	2	yes	complemented
155	#1750	C₂×C₂₃	1	2	yes	—
156	#1749	C₂×C₂₃	1	1	yes	characteristic
157	C₄×C₂²⋊C₈	C₂×C₂₃	1	1	yes	characteristic
158	C₂²×C₂₃	—	2	2	no	—
159	C₂²×C₂₃	—	2	2	no	—
160	C₂²×C₂₃	—	2	2	no	—
161	C₂²×C₂₃	—	4	2	no	—
162	C₂²×C₂₃	—	4	2	no	—
163	C₂²×C₂₃	C₂²×C₄²	1	1	yes	characteristic
164	C₂²×C₂₃	#518	1	1	yes	characteristic
165	C₂²×C₂₃	#519	1	1	yes	characteristic
166	C₂²×C₂₃	C₂×#131	1	2	yes	—
167	C₂²×C₂₃	#568	1	2	yes	—
168	C₄×C₂₃	—	2	4	no	—
169	C₄×C₂₃	—	2	4	no	—
170	C₄×C₂₃	—	2	4	no	—
171	C₄×C₂₃	—	2	2	no	—
172	C₄×C₂₃	—	4	4	no	—
173	C₄×C₂₃	—	4	2	no	—
174	C₄×C₂₃	#520	1	2	yes	—
175	C₄×C₂₃	#520	1	2	yes	—
176	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
177	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
178	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
179	#433	C₄×C₂₃	1	16	yes	complemented
180	C₂×C₄⋊C₈	C₂²×C₂₃	1	2	yes	—
181	C₂×C₄⋊C₈	C₂²×C₂₃	1	2	yes	—
182	C₂×C₂²⋊C₈	C₂²×C₂₃	1	2	yes	—
183	C₂×C₂²⋊C₈	C₂²×C₂₃	1	2	yes	—
184	C₂×#97	C₂²×C₂₃	1	1	yes	characteristic
185	C₂×#97	C₂²×C₂₃	1	1	yes	characteristic
186	C₂×#97	C₂²×C₂₃	1	2	yes	—
187	C₂×#97	C₂²×C₂₃	1	2	yes	—
188	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
189	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
190	C₂×C₄×C₈	C₂²×C₂₃	1	2	yes	—
191	C₂×C₄×C₈	C₂²×C₂₃	1	2	yes	—
192	#389	C₄×C₂₃	1	2	yes	—
193	#389	C₄×C₂₃	1	2	yes	—
194	#385	C₄×C₂₃	1	4	yes	—
195	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
196	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
197	#336	C₂²×C₂₃	1	2	yes	—
198	#336	C₂²×C₂₃	1	2	yes	—
199	#336	C₂²×C₂₃	1	2	yes	—
200	#336	C₂²×C₂₃	1	2	yes	—
201	C₂×C₂₃	—	4	2	no	—
202	C₂×C₂₃	#2274	1	1	yes	characteristic
203	C₂×C₂₃	C₄×#131	1	1	yes	characteristic
204	C₂×C₂₃	#2875	1	1	yes	characteristic
205	C₂×C₂₃	#2976	1	2	yes	—
206	C₂×C₂₃	#2985	1	2	yes	—
207	C₂³×C₄	C₂×C₄×C₂₃	1	2	yes	—
208	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
209	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
210	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
211	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
212	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
213	#117	—	4	1	no	—
214	#117	—	4	1	no	—
215	#117	C₂×C₄×C₂₃	1	8	yes	—
216	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	4	yes	—
217	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
218	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	4	yes	—
219	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
220	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
221	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
222	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
223	C₂×C₄²	—	4	1	no	—
224	C₂×C₄²	—	4	1	no	—
225	C₂×C₄²	C₂×C₄×C₂₃	1	2	yes	—
226	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
227	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
228	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
229	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
230	C₄⋊C₈	C₂×C₄×C₂₃	1	8	yes	complemented
231	C₄⋊C₈	C₂×C₄×C₂₃	1	8	yes	complemented
232	C₂²⋊C₈	C₂×C₄×C₂₃	1	8	yes	—
233	C₂²⋊C₈	C₂×C₄×C₂₃	1	8	yes	—
234	#97	—	4	1	no	—
235	#97	—	4	1	no	—
236	#97	—	4	2	no	—
237	#97	C₂×C₄×C₂₃	1	8	yes	complemented
238	C₄×C₈	—	4	1	no	—
239	C₄×C₈	—	4	1	no	—
240	C₄×C₈	—	4	2	no	—
241	C₄×C₈	C₂×C₄×C₂₃	1	8	yes	complemented
242	#95	C₂×C₄×C₂₃	1	4	yes	—
243	#95	C₂×C₄×C₂₃	1	4	yes	—
244	C₂₃	#20541	1	1	yes	characteristic, direct product factor, Sylow
245	C₂⁴	C₂²×C₄×C₂₃	1	1	yes	characteristic
246	C₂²×C₄	—	2	1	no	—
247	C₂²×C₄	—	2	1	no	—
248	C₂²×C₄	—	2	2	no	—
249	C₂²×C₄	—	2	4	no	—
250	C₂²×C₄	—	4	2	no	—
251	C₂²×C₄	—	4	2	no	—
252	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
253	C₂²×C₄	C₂²×C₄×C₂₃	1	4	yes	—
254	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
255	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
256	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
257	C₂²×C₄	C₂²×C₄×C₂₃	1	4	yes	—
258	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
259	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
260	C₂×C₈	—	2	2	no	—
261	C₂×C₈	—	2	2	no	—
262	C₂×C₈	—	2	2	no	—
263	C₂×C₈	—	2	2	no	—
264	C₂×C₈	—	2	2	no	—
265	C₂×C₈	—	2	2	no	—
266	C₂×C₈	—	2	2	no	—
267	C₂×C₈	—	2	2	no	—
268	C₂×C₈	C₂²×C₄×C₂₃	1	4	yes	—
269	C₂×C₈	C₂²×C₄×C₂₃	1	4	yes	—
270	C₂×C₈	C₂²×C₄×C₂₃	1	4	yes	—
271	C₂×C₈	C₂²×C₄×C₂₃	1	4	yes	—
272	C₄⋊C₄	—	2	8	no	—
273	C₄⋊C₄	—	4	2	no	—
274	C₄⋊C₄	—	4	4	no	—
275	C₄⋊C₄	C₄²×C₂₃	1	4	yes	—
276	C₄⋊C₄	C₄²×C₂₃	1	4	yes	—
277	C₂²⋊C₄	—	4	2	no	—
278	C₂²⋊C₄	C₄²×C₂₃	1	8	yes	—
279	C₄²	—	2	1	no	—
280	C₄²	—	2	1	no	—
281	C₄²	—	2	2	no	—
282	C₄²	—	2	1	no	—
283	C₄²	—	2	1	no	—
284	C₄²	—	2	2	no	—
285	C₄²	—	4	2	no	—
286	C₄²	C₂²×C₄×C₂₃	1	4	yes	—
287	C₄²	C₂²×C₄×C₂₃	1	4	yes	—
288	C₂³	—	2	2	no	—
289	C₂³	—	2	2	no	—
290	C₂³	—	2	1	no	—
291	C₂³	—	2	1	no	—
292	C₂³	C₂×C₄²×C₂₃	1	2	yes	—
293	C₂³	C₂³×C₄×C₂₃	1	1	yes	characteristic
294	C₂×C₄	—	2	4	no	—
295	C₂×C₄	—	2	4	no	—
296	C₂×C₄	—	2	2	no	—
297	C₂×C₄	—	2	2	no	—
298	C₂×C₄	—	2	1	no	—
299	C₂×C₄	—	2	1	no	—
300	C₂×C₄	—	2	4	no	—
301	C₂×C₄	—	2	4	no	—
302	C₂×C₄	—	2	4	no	—
303	C₂×C₄	—	2	2	no	—
304	C₂×C₄	—	2	2	no	—
305	C₂×C₄	—	2	4	no	—
306	C₂×C₄	—	2	2	no	—
307	C₂×C₄	—	2	4	no	—
308	C₂×C₄	—	4	8	no	—
309	C₂×C₄	C₂×C₄²×C₂₃	1	4	yes	—
310	C₂×C₄	C₂×C₄²×C₂₃	1	4	yes	—
311	C₂×C₄	C₂×C₄²×C₂₃	1	2	yes	—
312	C₂×C₄	C₂₃×#131	1	4	yes	—
313	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
314	C₂×C₄	C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
315	C₂×C₄	C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
316	C₂×C₄	C₂₃×2₋¹⁺⁴	1	2	yes	—
317	C₈	—	2	4	no	—
318	C₈	—	2	4	no	—
319	C₈	—	2	4	no	—
320	C₈	—	2	4	no	—
321	C₂²	—	2	2	no	—
322	C₂²	—	2	2	no	—
323	C₂²	—	2	2	no	—
324	C₂²	—	4	2	no	—
325	C₂²	—	4	2	no	—
326	C₂²	C₂²×C₄²×C₂₃	1	1	yes	characteristic
327	C₂²	C₂₃×#518	1	1	yes	characteristic
328	C₂²	C₂₃×#519	1	1	yes	characteristic
329	C₂²	C₂×C₂₃×#131	1	2	yes	—
330	C₂²	C₂₃×#568	1	2	yes	—
331	C₄	—	2	4	no	—
332	C₄	—	2	2	no	—
333	C₄	—	2	4	no	—
334	C₄	—	2	4	no	—
335	C₄	—	4	2	no	—
336	C₄	—	4	4	no	—
337	C₄	C₂₃×#520	1	2	yes	—
338	C₄	C₂₃×#520	1	2	yes	—
339	C₂	—	4	2	no	—
340	C₂	C₂₃×#2274	1	1	yes	characteristic
341	C₂	C₄×C₂₃×#131	1	1	yes	characteristic
342	C₂	C₂₃×#2875	1	1	yes	characteristic
343	C₂	C₂₃×#2976	1	2	yes	—
344	C₂	C₂₃×#2985	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
3. C₂₃×#1771	C₂	semidirect
4. C₂₃×#1771	C₂	semidirect
5. C₂₃×#1770	C₂	semidirect
6. C₈×C₄⋊C₄×C₂₃	C₂	semidirect
13. C₂₃×#433	C₄	semidirect
58. C₂₃×C₄⋊C₈	C₂×C₄	semidirect
59. C₂₃×C₄⋊C₈	C₂×C₄	semidirect
65. C₂₃×#97	C₂×C₄	semidirect
69. C₄×C₈×C₂₃	C₂×C₄	semidirect
115. #20541	C₂₃	direct (N × H)
151. #1771	C₂×C₂₃	semidirect
152. #1771	C₂×C₂₃	semidirect
153. #1770	C₂×C₂₃	semidirect
154. C₈×C₄⋊C₄	C₂×C₂₃	semidirect
179. #433	C₄×C₂₃	semidirect
230. C₄⋊C₈	C₂×C₄×C₂₃	semidirect
231. C₄⋊C₈	C₂×C₄×C₂₃	semidirect
237. #97	C₂×C₄×C₂₃	semidirect
241. C₄×C₈	C₂×C₄×C₂₃	semidirect
244. C₂₃	#20541	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×#433	2
C₂₃×#2296	2
C₂₃×#1771	2
C₂₃×#1770	2
C₈×C₄⋊C₄×C₂₃	2
C₂₃×#1750	2
C₂₃×#1749	2
C₄×C₂₃×C₂²⋊C₈	2
#20541	23

Subgroups — C23×#20541 #19168167

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#20541 #19168167