Subgroups — C₂₃×#33506 #19181132

Order 5888.

494 conjugacy classes of subgroups.

The subgroup lattice has 326 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#2966	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#2183	C₂	1	2	yes	maximal, complemented
3	C₂₃×#2168	C₂	1	2	yes	maximal, complemented
4	C₂₃×#2168	C₂	1	2	yes	maximal, complemented
5	D₄×C₁₆×C₂₃	C₂	1	2	yes	maximal, complemented
6	C₂₃×#2164	C₂	1	2	yes	maximal, complemented
7	C₂₃×#2163	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#2151	C₂	1	2	yes	maximal, complemented
9	C₂×C₂₃×C₄⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#529	C₄	1	1	yes	characteristic
11	C₂×C₂₃×M₃₂	C₂²	1	2	yes	—
12	C₂²×C₁₆×C₂₃	C₂²	1	1	yes	characteristic
13	C₂²×C₁₆×C₂₃	C₂²	1	1	yes	characteristic
14	C₂²×C₁₆×C₂₃	C₂²	1	2	yes	—
15	C₂₃×#446	C₄	1	1	yes	characteristic
16	C₈×Q₈×C₂₃	C₂²	1	1	yes	characteristic
17	C₂₃×#436	C₄	1	1	yes	characteristic
18	C₂₃×#435	C₄	1	2	yes	—
19	C₈×D₄×C₂₃	C₂²	1	2	yes	—
20	C₈×D₄×C₂₃	C₂²	1	1	yes	characteristic
21	C₂₃×#433	C₄	1	2	yes	—
22	C₂₃×#432	C₄	1	1	yes	characteristic
23	C₂₃×#405	C₂²	1	2	yes	—
24	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
25	C₂₃×C₄⋊C₁₆	C₂²	1	2	yes	—
26	C₂₃×C₄⋊C₁₆	C₂²	1	2	yes	—
27	C₂₃×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
28	C₂₃×C₄⋊C₁₆	C₂²	1	2	yes	—
29	C₂₃×C₄⋊C₁₆	C₂²	1	2	yes	—
30	C₂₃×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
31	C₂₃×C₂²⋊C₁₆	C₂²	1	2	yes	—
32	C₂₃×C₂²⋊C₁₆	C₂²	1	2	yes	—
33	C₂₃×C₂²⋊C₁₆	C₂²	1	2	yes	—
34	C₂₃×#346	C₂²	1	2	yes	—
35	C₂₃×#346	C₂²	1	2	yes	—
36	C₄×C₁₆×C₂₃	C₂²	1	2	yes	—
37	C₂×M₁₆×C₂₃	C₂×C₄	1	2	yes	—
38	C₂²×C₈×C₂₃	C₂×C₄	1	1	yes	characteristic
39	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
40	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
41	C₂₃×#126	C₈	1	2	yes	—
42	C₂₃×#125	C₈	1	1	yes	characteristic
43	C₂₃×#124	C₈	1	1	yes	characteristic
44	C₂₃×#123	C₈	1	2	yes	—
45	C₂₃×C₂²⋊Q₈	C₈	1	1	yes	characteristic
46	C₂₃×#121	C₈	1	1	yes	characteristic
47	C₄×Q₈×C₂₃	C₂×C₄	1	1	yes	characteristic
48	C₄×D₄×C₂₃	C₂×C₄	1	2	yes	—
49	C₄×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic
50	C₂₃×#117	C₂×C₄	1	2	yes	—
51	C₂×C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
52	C₂₃×M₃₂	—	4	2	no	—
53	C₂×C₁₆×C₂₃	—	4	1	no	—
54	C₂×C₁₆×C₂₃	—	4	2	no	—
55	C₂×C₁₆×C₂₃	—	4	1	no	—
56	C₂×C₁₆×C₂₃	C₂³	1	2	yes	—
57	C₂×C₁₆×C₂₃	C₂³	1	2	yes	—
58	C₂×C₁₆×C₂₃	C₂³	1	2	yes	—
59	C₂×C₁₆×C₂₃	C₂³	1	2	yes	—
60	C₂₃×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
61	C₂₃×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
62	C₂₃×C₄⋊C₈	C₂×C₄	1	2	yes	—
63	C₂₃×C₄⋊C₈	C₂×C₄	1	2	yes	—
64	C₂₃×C₂²⋊C₈	C₂×C₄	1	2	yes	—
65	C₂₃×C₂²⋊C₈	C₂×C₄	1	2	yes	—
66	C₂₃×C₂²⋊C₈	C₂×C₄	1	2	yes	—
67	C₂₃×#97	C₂×C₄	1	2	yes	—
68	C₂₃×#97	C₂×C₄	1	2	yes	—
69	C₄×C₈×C₂₃	C₂×C₄	1	1	yes	characteristic
70	C₄×C₈×C₂₃	C₂×C₄	1	1	yes	characteristic
71	C₄×C₈×C₂₃	C₂³	1	2	yes	—
72	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
73	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
74	C₂×Q₈×C₂₃	C₂×C₈	1	1	yes	characteristic
75	C₂×D₄×C₂₃	C₂×C₈	1	2	yes	—
76	C₂×D₄×C₂₃	C₂×C₈	1	1	yes	characteristic
77	C₂²×C₄×C₂₃	C₂×C₈	1	1	yes	characteristic
78	C₂²×C₄×C₂₃	C₂×C₈	1	1	yes	characteristic
79	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
80	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
81	M₁₆×C₂₃	—	4	2	no	—
82	C₂×C₈×C₂₃	—	2	1	no	—
83	C₂×C₈×C₂₃	—	2	2	no	—
84	C₂×C₈×C₂₃	—	2	1	no	—
85	C₂×C₈×C₂₃	—	2	2	no	—
86	C₂×C₈×C₂₃	—	4	1	no	—
87	C₂×C₈×C₂₃	C₂²×C₄	1	1	yes	characteristic
88	C₂×C₈×C₂₃	C₂²×C₄	1	1	yes	characteristic
89	C₂×C₈×C₂₃	C₂²×C₄	1	2	yes	—
90	C₂×C₈×C₂₃	C₂²×C₄	1	2	yes	—
91	C₂×C₈×C₂₃	C₂²×C₄	1	1	yes	characteristic
92	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
93	C₄⋊C₄×C₂₃	C₂×C₈	1	2	yes	—
94	C₄⋊C₄×C₂₃	C₂×C₈	1	2	yes	—
95	C₄⋊C₄×C₂₃	C₂×C₈	1	1	yes	characteristic
96	C₄⋊C₄×C₂₃	C₂×C₈	1	2	yes	—
97	C₄⋊C₄×C₂₃	C₂×C₈	1	1	yes	characteristic
98	C₄⋊C₄×C₂₃	C₂×C₈	1	2	yes	—
99	C₂²⋊C₄×C₂₃	C₂×C₈	1	2	yes	—
100	C₂²⋊C₄×C₂₃	C₂×C₈	1	2	yes	—
101	C₂²⋊C₄×C₂₃	C₂×C₈	1	2	yes	—
102	C₂²⋊C₄×C₂₃	C₂×C₈	1	2	yes	—
103	C₂²⋊C₄×C₂₃	C₂×C₈	1	2	yes	—
104	C₄²×C₂₃	C₂×C₈	1	1	yes	characteristic
105	C₄²×C₂₃	C₂×C₈	1	1	yes	characteristic
106	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
107	C₄²×C₂₃	C₂²×C₄	1	2	yes	—
108	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
109	C₁₆×C₂₃	—	2	2	no	—
110	C₁₆×C₂₃	—	2	2	no	—
111	C₁₆×C₂₃	—	2	2	no	—
112	C₁₆×C₂₃	—	2	2	no	—
113	#33506	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
114	C₂³×C₂₃	C₂²×C₈	1	2	yes	—
115	C₂³×C₂₃	C₂²×C₈	1	1	yes	characteristic
116	Q₈×C₂₃	—	4	1	no	—
117	D₄×C₂₃	—	2	4	no	—
118	D₄×C₂₃	—	4	1	no	—
119	C₂×C₄×C₂₃	—	2	2	no	—
120	C₂×C₄×C₂₃	—	2	1	no	—
121	C₂×C₄×C₂₃	—	2	2	no	—
122	C₂×C₄×C₂₃	—	2	1	no	—
123	C₂×C₄×C₂₃	—	2	2	no	—
124	C₂×C₄×C₂₃	—	4	1	no	—
125	C₂×C₄×C₂₃	C₂²×C₈	1	1	yes	characteristic
126	C₂×C₄×C₂₃	C₂²×C₈	1	1	yes	characteristic
127	C₂×C₄×C₂₃	C₂²×C₈	1	1	yes	characteristic
128	C₂×C₄×C₂₃	C₂²×C₈	1	1	yes	characteristic
129	C₂×C₄×C₂₃	C₂²×C₈	1	1	yes	characteristic
130	C₂×C₄×C₂₃	C₂²×C₈	1	2	yes	—
131	C₂×C₄×C₂₃	C₂²×C₈	1	2	yes	—
132	C₂×C₄×C₂₃	C₂²×C₈	1	2	yes	—
133	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
134	C₈×C₂₃	—	2	1	no	—
135	C₈×C₂₃	—	2	2	no	—
136	C₈×C₂₃	—	2	1	no	—
137	C₈×C₂₃	—	2	1	no	—
138	C₈×C₂₃	—	2	2	no	—
139	C₈×C₂₃	H(5,𝔽₂)	1	1	yes	characteristic
140	C₈×C₂₃	2₋¹⁺⁴	1	1	yes	characteristic
141	#2966	C₂×C₂₃	1	1	yes	characteristic
142	#2183	C₂×C₂₃	1	2	yes	complemented
143	#2168	C₂×C₂₃	1	2	yes	complemented
144	#2168	C₂×C₂₃	1	2	yes	complemented
145	D₄×C₁₆	C₂×C₂₃	1	2	yes	complemented
146	#2164	C₂×C₂₃	1	2	yes	complemented
147	#2163	C₂×C₂₃	1	1	yes	characteristic, complemented
148	#2151	C₂×C₂₃	1	2	yes	complemented
149	C₂×C₄⋊C₁₆	C₂×C₂₃	1	1	yes	characteristic, complemented
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	#504	1	2	yes	—
156	C₂²×C₂₃	C₂³×C₈	1	1	yes	characteristic
157	C₄×C₂₃	—	2	1	no	—
158	C₄×C₂₃	—	2	1	no	—
159	C₄×C₂₃	—	2	2	no	—
160	C₄×C₂₃	—	2	1	no	—
161	C₄×C₂₃	—	2	1	no	—
162	C₄×C₂₃	—	2	2	no	—
163	C₄×C₂₃	—	2	1	no	—
164	C₄×C₂₃	—	2	2	no	—
165	C₄×C₂₃	#520	1	1	yes	characteristic
166	C₄×C₂₃	#568	1	1	yes	characteristic
167	#529	C₄×C₂₃	1	1	yes	characteristic
168	C₂×M₃₂	C₂²×C₂₃	1	2	yes	—
169	C₂²×C₁₆	C₂²×C₂₃	1	1	yes	characteristic
170	C₂²×C₁₆	C₂²×C₂₃	1	1	yes	characteristic
171	C₂²×C₁₆	C₂²×C₂₃	1	2	yes	—
172	#446	C₄×C₂₃	1	1	yes	characteristic
173	C₈×Q₈	C₂²×C₂₃	1	1	yes	characteristic
174	#436	C₄×C₂₃	1	1	yes	characteristic
175	#435	C₄×C₂₃	1	2	yes	—
176	C₈×D₄	C₂²×C₂₃	1	2	yes	—
177	C₈×D₄	C₂²×C₂₃	1	1	yes	characteristic
178	#433	C₄×C₂₃	1	2	yes	—
179	#432	C₄×C₂₃	1	1	yes	characteristic
180	#405	C₂²×C₂₃	1	2	yes	—
181	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
182	C₄⋊C₁₆	C₂²×C₂₃	1	2	yes	—
183	C₄⋊C₁₆	C₂²×C₂₃	1	2	yes	—
184	C₄⋊C₁₆	C₂²×C₂₃	1	1	yes	characteristic
185	C₄⋊C₁₆	C₂²×C₂₃	1	2	yes	—
186	C₄⋊C₁₆	C₂²×C₂₃	1	2	yes	—
187	C₄⋊C₁₆	C₂²×C₂₃	1	1	yes	characteristic
188	C₂²⋊C₁₆	C₂²×C₂₃	1	2	yes	—
189	C₂²⋊C₁₆	C₂²×C₂₃	1	2	yes	—
190	C₂²⋊C₁₆	C₂²×C₂₃	1	2	yes	—
191	#346	C₂²×C₂₃	1	2	yes	—
192	#346	C₂²×C₂₃	1	2	yes	—
193	C₄×C₁₆	C₂²×C₂₃	1	2	yes	—
194	C₂×C₂₃	—	2	2	no	—
195	C₂×C₂₃	—	4	2	no	—
196	C₂×C₂₃	#2988	1	1	yes	characteristic
197	C₂×C₂₃	C₂×#504	1	1	yes	characteristic
198	C₂×C₂₃	#3407	1	1	yes	characteristic
199	C₂×M₁₆	C₂×C₄×C₂₃	1	2	yes	—
200	C₂²×C₈	C₂×C₄×C₂₃	1	1	yes	characteristic
201	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
202	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
203	#126	C₈×C₂₃	1	2	yes	—
204	#125	C₈×C₂₃	1	1	yes	characteristic
205	#124	C₈×C₂₃	1	1	yes	characteristic
206	#123	C₈×C₂₃	1	2	yes	—
207	C₂²⋊Q₈	C₈×C₂₃	1	1	yes	characteristic
208	#121	C₈×C₂₃	1	1	yes	characteristic
209	C₄×Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
210	C₄×D₄	C₂×C₄×C₂₃	1	2	yes	—
211	C₄×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
212	#117	C₂×C₄×C₂₃	1	2	yes	—
213	C₂×C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic
214	M₃₂	—	4	2	no	—
215	C₂×C₁₆	—	4	1	no	—
216	C₂×C₁₆	—	4	2	no	—
217	C₂×C₁₆	—	4	1	no	—
218	C₂×C₁₆	C₂³×C₂₃	1	2	yes	—
219	C₂×C₁₆	C₂³×C₂₃	1	2	yes	—
220	C₂×C₁₆	C₂³×C₂₃	1	2	yes	—
221	C₂×C₁₆	C₂³×C₂₃	1	2	yes	—
222	C₄⋊C₈	C₂×C₄×C₂₃	1	1	yes	characteristic
223	C₄⋊C₈	C₂×C₄×C₂₃	1	1	yes	characteristic
224	C₄⋊C₈	C₂×C₄×C₂₃	1	2	yes	—
225	C₄⋊C₈	C₂×C₄×C₂₃	1	2	yes	—
226	C₂²⋊C₈	C₂×C₄×C₂₃	1	2	yes	—
227	C₂²⋊C₈	C₂×C₄×C₂₃	1	2	yes	—
228	C₂²⋊C₈	C₂×C₄×C₂₃	1	2	yes	—
229	#97	C₂×C₄×C₂₃	1	2	yes	—
230	#97	C₂×C₄×C₂₃	1	2	yes	—
231	C₄×C₈	C₂×C₄×C₂₃	1	1	yes	characteristic
232	C₄×C₈	C₂×C₄×C₂₃	1	1	yes	characteristic
233	C₄×C₈	C₂³×C₂₃	1	2	yes	—
234	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
235	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
236	C₂₃	#33506	1	1	yes	characteristic, direct product factor, Sylow
237	C₂×Q₈	C₂×C₈×C₂₃	1	1	yes	characteristic
238	C₂×D₄	C₂×C₈×C₂₃	1	2	yes	—
239	C₂×D₄	C₂×C₈×C₂₃	1	1	yes	characteristic
240	C₂²×C₄	C₂×C₈×C₂₃	1	1	yes	characteristic
241	C₂²×C₄	C₂×C₈×C₂₃	1	1	yes	characteristic
242	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
243	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
244	M₁₆	—	4	2	no	—
245	C₂×C₈	—	2	1	no	—
246	C₂×C₈	—	2	2	no	—
247	C₂×C₈	—	2	1	no	—
248	C₂×C₈	—	2	2	no	—
249	C₂×C₈	—	4	1	no	—
250	C₂×C₈	C₂²×C₄×C₂₃	1	1	yes	characteristic
251	C₂×C₈	C₂²×C₄×C₂₃	1	1	yes	characteristic
252	C₂×C₈	C₂²×C₄×C₂₃	1	1	yes	characteristic
253	C₂×C₈	C₂²×C₄×C₂₃	1	2	yes	—
254	C₂×C₈	C₂²×C₄×C₂₃	1	2	yes	—
255	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
256	C₄⋊C₄	C₂×C₈×C₂₃	1	2	yes	—
257	C₄⋊C₄	C₂×C₈×C₂₃	1	2	yes	—
258	C₄⋊C₄	C₂×C₈×C₂₃	1	1	yes	characteristic
259	C₄⋊C₄	C₂×C₈×C₂₃	1	2	yes	—
260	C₄⋊C₄	C₂×C₈×C₂₃	1	1	yes	characteristic
261	C₄⋊C₄	C₂×C₈×C₂₃	1	2	yes	—
262	C₂²⋊C₄	C₂×C₈×C₂₃	1	2	yes	—
263	C₂²⋊C₄	C₂×C₈×C₂₃	1	2	yes	—
264	C₂²⋊C₄	C₂×C₈×C₂₃	1	2	yes	—
265	C₂²⋊C₄	C₂×C₈×C₂₃	1	2	yes	—
266	C₂²⋊C₄	C₂×C₈×C₂₃	1	2	yes	—
267	C₄²	C₂×C₈×C₂₃	1	1	yes	characteristic
268	C₄²	C₂×C₈×C₂₃	1	1	yes	characteristic
269	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
270	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
271	C₄²	C₂²×C₄×C₂₃	1	2	yes	—
272	C₁₆	—	2	2	no	—
273	C₁₆	—	2	2	no	—
274	C₁₆	—	2	2	no	—
275	C₁₆	—	2	2	no	—
276	C₂³	C₂²×C₈×C₂₃	1	2	yes	—
277	C₂³	C₂²×C₈×C₂₃	1	1	yes	characteristic
278	Q₈	—	4	1	no	—
279	D₄	—	2	4	no	—
280	D₄	—	4	1	no	—
281	C₂×C₄	—	2	2	no	—
282	C₂×C₄	—	2	1	no	—
283	C₂×C₄	—	2	2	no	—
284	C₂×C₄	—	2	1	no	—
285	C₂×C₄	—	2	2	no	—
286	C₂×C₄	—	4	1	no	—
287	C₂×C₄	C₂²×C₈×C₂₃	1	1	yes	characteristic
288	C₂×C₄	C₂²×C₈×C₂₃	1	1	yes	characteristic
289	C₂×C₄	C₂²×C₈×C₂₃	1	1	yes	characteristic
290	C₂×C₄	C₂²×C₈×C₂₃	1	1	yes	characteristic
291	C₂×C₄	C₂²×C₈×C₂₃	1	1	yes	characteristic
292	C₂×C₄	C₂²×C₈×C₂₃	1	2	yes	—
293	C₂×C₄	C₂²×C₈×C₂₃	1	2	yes	—
294	C₂×C₄	C₂²×C₈×C₂₃	1	2	yes	—
295	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
296	C₈	—	2	1	no	—
297	C₈	—	2	1	no	—
298	C₈	—	2	2	no	—
299	C₈	—	2	1	no	—
300	C₈	—	2	2	no	—
301	C₈	C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
302	C₈	C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
303	C₂²	—	2	1	no	—
304	C₂²	—	2	1	no	—
305	C₂²	—	2	2	no	—
306	C₂²	—	2	2	no	—
307	C₂²	—	2	2	no	—
308	C₂²	C₂₃×#504	1	2	yes	—
309	C₂²	C₂³×C₈×C₂₃	1	1	yes	characteristic
310	C₄	—	2	1	no	—
311	C₄	—	2	2	no	—
312	C₄	—	2	1	no	—
313	C₄	—	2	1	no	—
314	C₄	—	2	2	no	—
315	C₄	—	2	1	no	—
316	C₄	—	2	1	no	—
317	C₄	—	2	2	no	—
318	C₄	C₂₃×#520	1	1	yes	characteristic
319	C₄	C₂₃×#568	1	1	yes	characteristic
320	C₂	—	2	2	no	—
321	C₂	—	4	2	no	—
322	C₂	C₂₃×#2988	1	1	yes	characteristic
323	C₂	C₂×C₂₃×#504	1	1	yes	characteristic
324	C₂	C₂₃×#3407	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈×C₂₃	C₂⁴
commutator	C₂²	C₂³×C₈×C₂₃
Frattini, cosocle	C₂×C₈	C₂⁴×C₂₃
socle	C₂²×C₂₃	C₂³×C₈
prime radical	C₂₃×#121	C₈
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂₃×#2183	C₂	semidirect
3. C₂₃×#2168	C₂	semidirect
4. C₂₃×#2168	C₂	semidirect
5. D₄×C₁₆×C₂₃	C₂	semidirect
6. C₂₃×#2164	C₂	semidirect
7. C₂₃×#2163	C₂	semidirect
8. C₂₃×#2151	C₂	semidirect
9. C₂×C₂₃×C₄⋊C₁₆	C₂	semidirect
113. #33506	C₂₃	direct (N × H)
142. #2183	C₂×C₂₃	semidirect
143. #2168	C₂×C₂₃	semidirect
144. #2168	C₂×C₂₃	semidirect
145. D₄×C₁₆	C₂×C₂₃	semidirect
146. #2164	C₂×C₂₃	semidirect
147. #2163	C₂×C₂₃	semidirect
148. #2151	C₂×C₂₃	semidirect
149. C₂×C₄⋊C₁₆	C₂×C₂₃	semidirect
236. C₂₃	#33506	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂₃×#2966	2
C₂₃×#2183	2
C₂₃×#2168	2
D₄×C₁₆×C₂₃	2
C₂₃×#2164	2
C₂₃×#2163	2
C₂₃×#2151	2
C₂×C₂₃×C₄⋊C₁₆	2
#33506	23

Subgroups — C23×#33506 #19181132

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#33506 #19181132