Subgroups — C₂₃×#60065 #19207691

Order 5888.

4874 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#585	C₂	1	1	yes	maximal, characteristic
2	C₂×C₂₃×#568	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₂₃×#131	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#2880	C₂	1	16	yes	maximal, complemented
5	C₂₃×#2879	C₂	1	6	yes	maximal, complemented
6	C₂×C₂₃×#408	C₂	1	6	yes	maximal, complemented
7	C₂₃×#585	—	2	8	no	—
8	C₂₃×#585	—	2	8	no	—
9	C₂×C₂₃×2₋¹⁺⁴	C₄	1	4	yes	—
10	C₂×C₂₃×2₋¹⁺⁴	C₄	1	2	yes	—
11	C₂×C₂₃×H(5,𝔽₂)	C₄	1	4	yes	—
12	C₂×C₂₃×H(5,𝔽₂)	C₄	1	6	yes	—
13	C₂²×#41×C₂₃	C₂²	1	6	yes	—
14	C₂²×#41×C₂₃	C₂²	1	8	yes	—
15	C₂²×#41×C₂₃	C₂²	1	1	yes	characteristic
16	C₂₃×#568	—	2	8	no	—
17	C₂×C₂₃×#131	—	2	8	no	—
18	C₂×C₂₃×#131	C₂²	1	8	yes	complemented
19	C₂×C₂₃×#131	C₂²	1	8	yes	complemented
20	C₂²×M₁₆×C₂₃	C₂²	1	3	yes	complemented
21	C₂²×M₁₆×C₂₃	C₂²	1	6	yes	complemented
22	C₂³×C₈×C₂₃	C₂²	1	3	yes	complemented
23	C₂₃×#408	C₂²	1	4	yes	complemented
24	C₂₃×#408	C₂²	1	12	yes	complemented
25	C₂₃×#408	C₂²	1	24	yes	complemented
26	C₂₃×#408	C₂²	1	24	yes	complemented
27	C₂₃×#407	C₂²	1	24	yes	complemented
28	C₂×C₂₃×C₂²⋊C₈	C₂²	1	24	yes	complemented
29	C₂₃×2₋¹⁺⁴	—	2	32	no	—
30	C₂₃×2₋¹⁺⁴	—	2	16	no	—
31	C₂₃×H(5,𝔽₂)	—	2	32	no	—
32	C₂₃×H(5,𝔽₂)	—	2	48	no	—
33	C₂×#41×C₂₃	—	2	32	no	—
34	C₂×#41×C₂₃	—	2	32	no	—
35	C₂×#41×C₂₃	—	2	24	no	—
36	C₂×#41×C₂₃	—	2	24	no	—
37	C₂×#41×C₂₃	C₂×C₄	1	8	yes	—
38	C₂×#41×C₂₃	C₂×C₄	1	24	yes	—
39	C₂×#41×C₂₃	C₂×C₄	1	12	yes	—
40	C₂×#41×C₂₃	C₂×C₄	1	12	yes	—
41	C₂×#41×C₂₃	C₂×C₄	1	4	yes	—
42	C₂×#41×C₂₃	D₄	1	8	yes	—
43	C₂×#41×C₂₃	D₄	1	8	yes	—
44	C₂×#41×C₂₃	C₂³	1	4	yes	—
45	C₂×#41×C₂₃	C₂³	1	12	yes	—
46	C₂×#41×C₂₃	C₂³	1	4	yes	—
47	C₂²×Q₈×C₂₃	C₂×C₄	1	8	yes	—
48	C₂²×Q₈×C₂₃	C₂×C₄	1	6	yes	—
49	C₂²×Q₈×C₂₃	C₂×C₄	1	1	yes	characteristic
50	C₂²×D₄×C₂₃	C₂×C₄	1	12	yes	—
51	C₂²×D₄×C₂₃	C₂×C₄	1	24	yes	—
52	C₂²×D₄×C₂₃	C₂×C₄	1	6	yes	—
53	C₂²×D₄×C₂₃	C₂×C₄	1	3	yes	—
54	C₂³×C₄×C₂₃	C₂³	1	12	yes	—
55	C₂³×C₄×C₂₃	C₂³	1	3	yes	—
56	C₂₃×#131	—	2	32	no	—
57	C₂₃×#131	—	2	32	no	—
58	C₂×M₁₆×C₂₃	—	2	12	no	—
59	C₂×M₁₆×C₂₃	—	2	24	no	—
60	C₂×M₁₆×C₂₃	C₂³	1	4	yes	—
61	C₂×M₁₆×C₂₃	C₂³	1	12	yes	—
62	C₂×M₁₆×C₂₃	C₂³	1	12	yes	—
63	C₂²×C₈×C₂₃	—	2	12	no	—
64	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
65	C₂²×C₈×C₂₃	C₂³	1	3	yes	—
66	C₂²×C₈×C₂₃	C₂³	1	12	yes	—
67	C₂²×C₈×C₂₃	C₂³	1	12	yes	—
68	C₂₃×C₂²⋊C₈	C₂³	1	16	yes	—
69	C₂₃×C₂²⋊C₈	C₂³	1	48	yes	—
70	C₂⁴×C₂₃	C₂²×C₄	1	12	yes	—
71	C₂⁴×C₂₃	C₂²×C₄	1	3	yes	—
72	#41×C₂₃	—	2	32	no	—
73	#41×C₂₃	—	2	96	no	—
74	#41×C₂₃	—	2	48	no	—
75	#41×C₂₃	—	2	48	no	—
76	#41×C₂₃	—	2	8	no	—
77	#41×C₂₃	—	2	24	no	—
78	#41×C₂₃	—	2	24	no	—
79	#41×C₂₃	—	2	8	no	—
80	#41×C₂₃	C₂²⋊C₄	1	32	yes	—
81	#41×C₂₃	C₂×D₄	1	16	yes	—
82	#41×C₂₃	C₂×D₄	1	16	yes	—
83	C₂×Q₈×C₂₃	—	2	32	no	—
84	C₂×Q₈×C₂₃	—	2	24	no	—
85	C₂×Q₈×C₂₃	C₂²⋊C₄	1	8	yes	—
86	C₂×Q₈×C₂₃	C₂²×C₄	1	12	yes	—
87	C₂×Q₈×C₂₃	C₂²×C₄	1	4	yes	—
88	C₂×Q₈×C₂₃	C₂²×C₄	1	4	yes	—
89	C₂×D₄×C₂₃	—	2	48	no	—
90	C₂×D₄×C₂₃	—	2	96	no	—
91	C₂×D₄×C₂₃	—	2	24	no	—
92	C₂×D₄×C₂₃	C₂²⋊C₄	1	24	yes	—
93	C₂×D₄×C₂₃	C₂²×C₄	1	24	yes	—
94	C₂×D₄×C₂₃	C₂²×C₄	1	8	yes	—
95	C₂×D₄×C₂₃	C₂²×C₄	1	12	yes	—
96	C₂×D₄×C₂₃	C₂²×C₄	1	4	yes	—
97	C₂×D₄×C₂₃	C₂²×C₄	1	12	yes	—
98	C₂²×C₄×C₂₃	—	2	24	no	—
99	C₂²×C₄×C₂₃	—	2	24	no	—
100	C₂²×C₄×C₂₃	C₂²×C₄	1	12	yes	—
101	C₂²×C₄×C₂₃	C₂²×C₄	1	24	yes	—
102	C₂²×C₄×C₂₃	C₂²×C₄	1	6	yes	—
103	C₂²×C₄×C₂₃	C₂²×C₄	1	3	yes	—
104	C₂²×C₄×C₂₃	C₂×D₄	1	12	yes	—
105	C₂²×C₄×C₂₃	C₂×D₄	1	12	yes	—
106	C₂²×C₄×C₂₃	C₂⁴	1	8	yes	—
107	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
108	C₂²×C₄×C₂₃	C₂⁴	1	6	yes	—
109	M₁₆×C₂₃	—	2	8	no	—
110	M₁₆×C₂₃	—	2	24	no	—
111	M₁₆×C₂₃	—	2	24	no	—
112	C₂×C₈×C₂₃	—	2	2	no	—
113	C₂×C₈×C₂₃	—	2	6	no	—
114	C₂×C₈×C₂₃	—	2	24	no	—
115	C₂×C₈×C₂₃	—	2	24	no	—
116	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
117	C₂×C₈×C₂₃	C₂⁴	1	6	yes	—
118	C₂×C₈×C₂₃	C₂⁴	1	8	yes	—
119	#60065	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
120	C₂³×C₂₃	—	2	24	no	—
121	C₂³×C₂₃	—	4	6	no	—
122	C₂³×C₂₃	—	4	24	no	—
123	C₂³×C₂₃	C₂×C₂²⋊C₄	1	12	yes	—
124	C₂³×C₂₃	C₂³×C₄	1	8	yes	—
125	C₂³×C₂₃	C₂³×C₄	1	6	yes	—
126	C₂³×C₂₃	C₂³×C₄	1	1	yes	characteristic
127	Q₈×C₂₃	—	2	24	no	—
128	Q₈×C₂₃	—	2	8	no	—
129	Q₈×C₂₃	C₂×C₂²⋊C₄	1	16	yes	—
130	D₄×C₂₃	—	2	48	no	—
131	D₄×C₂₃	—	2	16	no	—
132	D₄×C₂₃	—	2	24	no	—
133	D₄×C₂₃	—	2	8	no	—
134	D₄×C₂₃	C₂×C₂²⋊C₄	1	48	yes	—
135	C₂×C₄×C₂₃	—	2	24	no	—
136	C₂×C₄×C₂₃	—	2	48	no	—
137	C₂×C₄×C₂₃	—	2	8	no	—
138	C₂×C₄×C₂₃	—	2	8	no	—
139	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	24	yes	—
140	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	12	yes	—
141	C₂×C₄×C₂₃	C₂³×C₄	1	8	yes	—
142	C₂×C₄×C₂₃	C₂³×C₄	1	6	yes	—
143	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
144	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
145	C₂×C₄×C₂₃	C₂²×D₄	1	12	yes	—
146	C₂×C₄×C₂₃	C₂²×D₄	1	12	yes	—
147	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
148	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
149	C₈×C₂₃	—	2	2	no	—
150	C₈×C₂₃	—	2	6	no	—
151	C₈×C₂₃	—	2	8	no	—
152	C₂×#585	C₂×C₂₃	1	1	yes	characteristic
153	C₂×#568	C₂×C₂₃	1	1	yes	characteristic, complemented
154	C₂²×#131	C₂×C₂₃	1	1	yes	characteristic, complemented
155	#2880	C₂×C₂₃	1	16	yes	complemented
156	#2879	C₂×C₂₃	1	6	yes	complemented
157	C₂×#408	C₂×C₂₃	1	6	yes	complemented
158	C₂²×C₂₃	—	2	2	no	—
159	C₂²×C₂₃	—	2	12	no	—
160	C₂²×C₂₃	—	2	8	no	—
161	C₂²×C₂₃	—	2	16	no	—
162	C₂²×C₂₃	—	4	12	no	—
163	C₂²×C₂₃	—	8	24	no	—
164	C₂²×C₂₃	C₂²×C₂²⋊C₄	1	12	yes	—
165	C₂²×C₂₃	C₂²×C₂²⋊C₄	1	2	yes	—
166	C₂²×C₂₃	C₂⁴×C₄	1	1	yes	characteristic
167	C₄×C₂₃	—	2	8	no	—
168	C₄×C₂₃	C₂²×C₂²⋊C₄	1	12	yes	—
169	C₄×C₂₃	C₂²×C₂²⋊C₄	1	2	yes	—
170	C₄×C₂₃	C₂³×D₄	1	1	yes	characteristic
171	C₄×C₂₃	C₂³×D₄	1	1	yes	characteristic
172	#585	—	2	8	no	—
173	#585	—	2	8	no	—
174	C₂×2₋¹⁺⁴	C₄×C₂₃	1	4	yes	—
175	C₂×2₋¹⁺⁴	C₄×C₂₃	1	2	yes	—
176	C₂×H(5,𝔽₂)	C₄×C₂₃	1	4	yes	—
177	C₂×H(5,𝔽₂)	C₄×C₂₃	1	6	yes	—
178	C₂²×#41	C₂²×C₂₃	1	6	yes	—
179	C₂²×#41	C₂²×C₂₃	1	8	yes	—
180	C₂²×#41	C₂²×C₂₃	1	1	yes	characteristic
181	#568	—	2	8	no	—
182	C₂×#131	—	2	8	no	—
183	C₂×#131	C₂²×C₂₃	1	8	yes	complemented
184	C₂×#131	C₂²×C₂₃	1	8	yes	complemented
185	C₂²×M₁₆	C₂²×C₂₃	1	6	yes	complemented
186	C₂²×M₁₆	C₂²×C₂₃	1	3	yes	complemented
187	C₂³×C₈	C₂²×C₂₃	1	3	yes	complemented
188	#408	C₂²×C₂₃	1	4	yes	complemented
189	#408	C₂²×C₂₃	1	12	yes	complemented
190	#408	C₂²×C₂₃	1	24	yes	complemented
191	#408	C₂²×C₂₃	1	24	yes	complemented
192	#407	C₂²×C₂₃	1	24	yes	complemented
193	C₂×C₂²⋊C₈	C₂²×C₂₃	1	24	yes	complemented
194	C₂×C₂₃	—	2	2	no	—
195	C₂×C₂₃	—	2	12	no	—
196	C₂×C₂₃	—	4	8	no	—
197	C₂×C₂₃	C₂³×C₂²⋊C₄	1	1	yes	characteristic
198	C₂×C₂₃	#3573	1	2	yes	—
199	2₋¹⁺⁴	—	2	32	no	—
200	2₋¹⁺⁴	—	2	16	no	—
201	H(5,𝔽₂)	—	2	32	no	—
202	H(5,𝔽₂)	—	2	48	no	—
203	C₂×#41	—	2	32	no	—
204	C₂×#41	—	2	32	no	—
205	C₂×#41	—	2	24	no	—
206	C₂×#41	—	2	24	no	—
207	C₂×#41	C₂×C₄×C₂₃	1	8	yes	—
208	C₂×#41	C₂×C₄×C₂₃	1	24	yes	—
209	C₂×#41	C₂×C₄×C₂₃	1	12	yes	—
210	C₂×#41	C₂×C₄×C₂₃	1	12	yes	—
211	C₂×#41	C₂×C₄×C₂₃	1	4	yes	—
212	C₂×#41	D₄×C₂₃	1	8	yes	—
213	C₂×#41	D₄×C₂₃	1	8	yes	—
214	C₂×#41	C₂³×C₂₃	1	4	yes	—
215	C₂×#41	C₂³×C₂₃	1	12	yes	—
216	C₂×#41	C₂³×C₂₃	1	4	yes	—
217	C₂²×Q₈	C₂×C₄×C₂₃	1	8	yes	—
218	C₂²×Q₈	C₂×C₄×C₂₃	1	6	yes	—
219	C₂²×Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
220	C₂²×D₄	C₂×C₄×C₂₃	1	12	yes	—
221	C₂²×D₄	C₂×C₄×C₂₃	1	24	yes	—
222	C₂²×D₄	C₂×C₄×C₂₃	1	6	yes	—
223	C₂²×D₄	C₂×C₄×C₂₃	1	3	yes	—
224	C₂³×C₄	C₂³×C₂₃	1	12	yes	—
225	C₂³×C₄	C₂³×C₂₃	1	3	yes	—
226	#131	—	2	32	no	—
227	#131	—	2	32	no	—
228	C₂×M₁₆	—	2	12	no	—
229	C₂×M₁₆	—	2	24	no	—
230	C₂×M₁₆	C₂³×C₂₃	1	4	yes	—
231	C₂×M₁₆	C₂³×C₂₃	1	12	yes	—
232	C₂×M₁₆	C₂³×C₂₃	1	12	yes	—
233	C₂²×C₈	—	2	12	no	—
234	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
235	C₂²×C₈	C₂³×C₂₃	1	3	yes	—
236	C₂²×C₈	C₂³×C₂₃	1	12	yes	—
237	C₂²×C₈	C₂³×C₂₃	1	12	yes	—
238	C₂²⋊C₈	C₂³×C₂₃	1	16	yes	—
239	C₂²⋊C₈	C₂³×C₂₃	1	48	yes	—
240	C₂₃	#60065	1	1	yes	characteristic, direct product factor, Sylow
241	C₂⁴	C₂²×C₄×C₂₃	1	12	yes	—
242	C₂⁴	C₂²×C₄×C₂₃	1	3	yes	—
243	#41	—	2	32	no	—
244	#41	—	2	96	no	—
245	#41	—	2	48	no	—
246	#41	—	2	48	no	—
247	#41	—	2	8	no	—
248	#41	—	2	24	no	—
249	#41	—	2	24	no	—
250	#41	—	2	8	no	—
251	#41	C₂²⋊C₄×C₂₃	1	32	yes	—
252	#41	C₂×D₄×C₂₃	1	16	yes	—
253	#41	C₂×D₄×C₂₃	1	16	yes	—
254	C₂×Q₈	—	2	32	no	—
255	C₂×Q₈	—	2	24	no	—
256	C₂×Q₈	C₂²⋊C₄×C₂₃	1	8	yes	—
257	C₂×Q₈	C₂²×C₄×C₂₃	1	12	yes	—
258	C₂×Q₈	C₂²×C₄×C₂₃	1	4	yes	—
259	C₂×Q₈	C₂²×C₄×C₂₃	1	4	yes	—
260	C₂×D₄	—	2	48	no	—
261	C₂×D₄	—	2	96	no	—
262	C₂×D₄	—	2	24	no	—
263	C₂×D₄	C₂²⋊C₄×C₂₃	1	24	yes	—
264	C₂×D₄	C₂²×C₄×C₂₃	1	24	yes	—
265	C₂×D₄	C₂²×C₄×C₂₃	1	8	yes	—
266	C₂×D₄	C₂²×C₄×C₂₃	1	12	yes	—
267	C₂×D₄	C₂²×C₄×C₂₃	1	4	yes	—
268	C₂×D₄	C₂²×C₄×C₂₃	1	12	yes	—
269	C₂²×C₄	—	2	24	no	—
270	C₂²×C₄	—	2	24	no	—
271	C₂²×C₄	C₂²×C₄×C₂₃	1	12	yes	—
272	C₂²×C₄	C₂²×C₄×C₂₃	1	24	yes	—
273	C₂²×C₄	C₂²×C₄×C₂₃	1	6	yes	—
274	C₂²×C₄	C₂²×C₄×C₂₃	1	3	yes	—
275	C₂²×C₄	C₂×D₄×C₂₃	1	12	yes	—
276	C₂²×C₄	C₂×D₄×C₂₃	1	12	yes	—
277	C₂²×C₄	C₂⁴×C₂₃	1	8	yes	—
278	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
279	C₂²×C₄	C₂⁴×C₂₃	1	6	yes	—
280	M₁₆	—	2	8	no	—
281	M₁₆	—	2	24	no	—
282	M₁₆	—	2	24	no	—
283	C₂×C₈	—	2	2	no	—
284	C₂×C₈	—	2	6	no	—
285	C₂×C₈	—	2	24	no	—
286	C₂×C₈	—	2	24	no	—
287	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
288	C₂×C₈	C₂⁴×C₂₃	1	8	yes	—
289	C₂×C₈	C₂⁴×C₂₃	1	6	yes	—
290	C₂³	—	2	24	no	—
291	C₂³	—	4	6	no	—
292	C₂³	—	4	24	no	—
293	C₂³	C₂×C₂²⋊C₄×C₂₃	1	12	yes	—
294	C₂³	C₂³×C₄×C₂₃	1	8	yes	—
295	C₂³	C₂³×C₄×C₂₃	1	6	yes	—
296	C₂³	C₂³×C₄×C₂₃	1	1	yes	characteristic
297	Q₈	—	2	24	no	—
298	Q₈	—	2	8	no	—
299	Q₈	C₂×C₂²⋊C₄×C₂₃	1	16	yes	—
300	D₄	—	2	48	no	—
301	D₄	—	2	16	no	—
302	D₄	—	2	24	no	—
303	D₄	—	2	8	no	—
304	D₄	C₂×C₂²⋊C₄×C₂₃	1	48	yes	—
305	C₂×C₄	—	2	24	no	—
306	C₂×C₄	—	2	8	no	—
307	C₂×C₄	—	2	8	no	—
308	C₂×C₄	—	2	48	no	—
309	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	24	yes	—
310	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	12	yes	—
311	C₂×C₄	C₂³×C₄×C₂₃	1	8	yes	—
312	C₂×C₄	C₂³×C₄×C₂₃	1	6	yes	—
313	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
314	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
315	C₂×C₄	C₂²×D₄×C₂₃	1	12	yes	—
316	C₂×C₄	C₂²×D₄×C₂₃	1	12	yes	—
317	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
318	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
319	C₈	—	2	2	no	—
320	C₈	—	2	6	no	—
321	C₈	—	2	8	no	—
322	C₂²	—	2	2	no	—
323	C₂²	—	2	12	no	—
324	C₂²	—	2	16	no	—
325	C₂²	—	2	8	no	—
326	C₂²	—	4	12	no	—
327	C₂²	—	8	24	no	—
328	C₂²	C₂²×C₂²⋊C₄×C₂₃	1	12	yes	—
329	C₂²	C₂²×C₂²⋊C₄×C₂₃	1	2	yes	—
330	C₂²	C₂⁴×C₄×C₂₃	1	1	yes	characteristic
331	C₄	—	2	8	no	—
332	C₄	C₂²×C₂²⋊C₄×C₂₃	1	12	yes	—
333	C₄	C₂²×C₂²⋊C₄×C₂₃	1	2	yes	—
334	C₄	C₂³×D₄×C₂₃	1	1	yes	characteristic
335	C₄	C₂³×D₄×C₂₃	1	1	yes	characteristic
336	C₂	—	2	2	no	—
337	C₂	—	2	12	no	—
338	C₂	—	4	8	no	—
339	C₂	C₂³×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
340	C₂	C₂₃×#3573	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₂₃	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₂₃
Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
socle	C₂²×C₂₃	C₂⁴×C₄
prime radical	C₂×C₂₃×#585	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₂₃×#568	C₂	semidirect
3. C₂²×C₂₃×#131	C₂	semidirect
4. C₂₃×#2880	C₂	semidirect
5. C₂₃×#2879	C₂	semidirect
6. C₂×C₂₃×#408	C₂	semidirect
18. C₂×C₂₃×#131	C₂²	semidirect
19. C₂×C₂₃×#131	C₂²	semidirect
20. C₂²×M₁₆×C₂₃	C₂²	semidirect
21. C₂²×M₁₆×C₂₃	C₂²	semidirect
22. C₂³×C₈×C₂₃	C₂²	semidirect
23. C₂₃×#408	C₂²	semidirect
24. C₂₃×#408	C₂²	semidirect
25. C₂₃×#408	C₂²	semidirect
26. C₂₃×#408	C₂²	semidirect
27. C₂₃×#407	C₂²	semidirect
28. C₂×C₂₃×C₂²⋊C₈	C₂²	semidirect
119. #60065	C₂₃	direct (N × H)
153. C₂×#568	C₂×C₂₃	semidirect
154. C₂²×#131	C₂×C₂₃	semidirect
155. #2880	C₂×C₂₃	semidirect
156. #2879	C₂×C₂₃	semidirect
157. C₂×#408	C₂×C₂₃	semidirect
183. C₂×#131	C₂²×C₂₃	semidirect
184. C₂×#131	C₂²×C₂₃	semidirect
185. C₂²×M₁₆	C₂²×C₂₃	semidirect
186. C₂²×M₁₆	C₂²×C₂₃	semidirect
187. C₂³×C₈	C₂²×C₂₃	semidirect
188. #408	C₂²×C₂₃	semidirect
189. #408	C₂²×C₂₃	semidirect
190. #408	C₂²×C₂₃	semidirect
191. #408	C₂²×C₂₃	semidirect
192. #407	C₂²×C₂₃	semidirect
193. C₂×C₂²⋊C₈	C₂²×C₂₃	semidirect
240. C₂₃	#60065	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×#585	2
C₂×C₂₃×#568	2
C₂²×C₂₃×#131	2
C₂₃×#2880	2
C₂₃×#2879	2
C₂×C₂₃×#408	2
#60065	23

Subgroups — C23×#60065 #19207691

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#60065 #19207691