Subgroups — C₂×C₂₃×#3142 #19208243

Order 5888.

2182 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#532	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₂₃×#125	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3142	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₂₃×#491	C₂	1	2	yes	maximal, complemented
5	C₂×C₂₃×#490	C₂	1	2	yes	maximal, complemented
6	C₂×C₂₃×#488	C₂	1	4	yes	maximal, complemented
7	C₂×C₂₃×#417	C₂	1	4	yes	maximal, complemented
8	C₂×C₄×M₁₆×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#41×C₂₃	C₂²	1	2	yes	—
10	C₂²×M₁₆×C₂₃	C₂²	1	2	yes	—
11	C₂₃×#532	—	2	4	no	—
12	C₂₃×#532	C₂²	1	8	yes	—
13	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₂×C₂₃×#127	C₂²	1	1	yes	characteristic
15	C₂×C₂₃×#125	—	2	2	no	—
16	C₂×C₂₃×#125	—	2	4	no	—
17	C₂×C₂₃×#125	C₂²	1	2	yes	—
18	C₂×C₂₃×#125	C₂²	1	2	yes	—
19	C₂×C₂₃×#125	C₂²	1	8	yes	complemented
20	C₂×C₂₃×#124	C₂²	1	2	yes	—
21	C₂×C₂₃×#121	—	2	2	no	—
22	C₂×C₄×D₄×C₂₃	—	2	2	no	—
23	C₂²×C₄⋊C₄×C₂₃	—	2	2	no	—
24	C₂²×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
25	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
26	C₂₃×#491	C₂²	1	16	yes	complemented
27	C₂₃×#490	C₂²	1	16	yes	complemented
28	C₂₃×#488	C₂²	1	32	yes	complemented
29	C₂₃×#417	C₂²	1	32	yes	complemented
30	C₂×C₂₃×#103	C₂²	1	8	yes	—
31	C₂×C₂₃×#102	C₂²	1	8	yes	—
32	C₄×M₁₆×C₂₃	C₂²	1	8	yes	complemented
33	C₂×C₂₃×#97	C₂²	1	2	yes	—
34	C₂×C₄×C₈×C₂₃	C₂²	1	2	yes	—
35	C₂×#41×C₂₃	—	2	4	no	—
36	C₂×#41×C₂₃	—	2	16	no	—
37	C₂×#41×C₂₃	C₂³	1	8	yes	—
38	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
39	C₂²×D₄×C₂₃	—	2	2	no	—
40	C₂²×D₄×C₂₃	—	2	2	no	—
41	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
42	C₂³×C₄×C₂₃	—	2	2	no	—
43	C₂³×C₄×C₂₃	—	2	2	no	—
44	C₂³×C₄×C₂₃	D₄	1	2	yes	—
45	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
46	C₂×M₁₆×C₂₃	—	2	8	no	—
47	C₂×M₁₆×C₂₃	C₂³	1	8	yes	—
48	C₂²×C₈×C₂₃	C₂³	1	4	yes	—
49	C₂₃×C₄⋊Q₈	—	2	2	no	—
50	C₂₃×C₄⋊Q₈	C₂³	1	4	yes	—
51	C₂₃×#127	—	2	2	no	—
52	C₂₃×#127	C₂³	1	4	yes	—
53	C₂₃×#125	—	2	4	no	—
54	C₂₃×#125	—	2	4	no	—
55	C₂₃×#125	—	2	16	no	—
56	C₂₃×#125	C₂³	1	8	yes	—
57	C₂₃×#125	C₂³	1	8	yes	—
58	C₂₃×#124	—	2	4	no	—
59	C₂₃×#124	C₂³	1	8	yes	—
60	C₂₃×#121	—	2	16	no	—
61	C₄×D₄×C₂₃	—	2	16	no	—
62	C₂×C₄⋊C₄×C₂₃	—	2	4	no	—
63	C₂×C₄⋊C₄×C₂₃	—	2	4	no	—
64	C₂×C₄⋊C₄×C₂₃	—	2	16	no	—
65	C₂×C₄⋊C₄×C₂₃	—	2	4	no	—
66	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
67	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
68	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
69	C₂×C₄⋊C₄×C₂₃	C₂³	1	8	yes	—
70	C₂×C₂²⋊C₄×C₂₃	—	2	4	no	—
71	C₂×C₄²×C₂₃	D₄	1	2	yes	—
72	C₂×C₄²×C₂₃	D₄	1	4	yes	—
73	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
74	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
75	C₂×C₄²×C₂₃	C₂³	1	4	yes	—
76	C₂₃×#103	C₂³	1	32	yes	—
77	C₂₃×#102	C₂³	1	32	yes	—
78	C₂₃×#97	C₂³	1	8	yes	—
79	C₄×C₈×C₂₃	C₂³	1	8	yes	—
80	C₂⁴×C₂₃	—	2	2	no	—
81	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
82	#41×C₂₃	—	2	32	no	—
83	#41×C₂₃	—	4	16	no	—
84	C₂×Q₈×C₂₃	—	2	2	no	—
85	C₂×Q₈×C₂₃	—	2	8	no	—
86	C₂×Q₈×C₂₃	C₂⁴	1	4	yes	—
87	C₂×D₄×C₂₃	—	2	8	no	—
88	C₂×D₄×C₂₃	—	2	8	no	—
89	C₂×D₄×C₂₃	—	2	2	no	—
90	C₂×D₄×C₂₃	—	2	8	no	—
91	C₂×D₄×C₂₃	—	4	8	no	—
92	C₂×D₄×C₂₃	—	4	8	no	—
93	C₂×D₄×C₂₃	C₂⁴	1	4	yes	—
94	C₂²×C₄×C₂₃	—	2	8	no	—
95	C₂²×C₄×C₂₃	—	2	2	no	—
96	C₂²×C₄×C₂₃	—	2	4	no	—
97	C₂²×C₄×C₂₃	—	2	8	no	—
98	C₂²×C₄×C₂₃	—	4	4	no	—
99	C₂²×C₄×C₂₃	—	4	8	no	—
100	C₂²×C₄×C₂₃	—	4	8	no	—
101	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
102	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
103	C₂²×C₄×C₂₃	C₂×D₄	1	8	yes	—
104	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
105	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₂₃	#41	1	8	yes	—
107	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
108	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
109	M₁₆×C₂₃	—	2	16	no	—
110	C₂×C₈×C₂₃	—	2	8	no	—
111	C₂×C₈×C₂₃	C₂⁴	1	8	yes	—
112	C₄⋊C₄×C₂₃	—	2	16	no	—
113	C₄⋊C₄×C₂₃	—	2	16	no	—
114	C₄⋊C₄×C₂₃	—	2	8	no	—
115	C₄⋊C₄×C₂₃	—	2	4	no	—
116	C₄⋊C₄×C₂₃	—	2	8	no	—
117	C₄⋊C₄×C₂₃	C₂⁴	1	8	yes	—
118	C₂²⋊C₄×C₂₃	—	2	16	no	—
119	C₄²×C₂₃	C₂×D₄	1	8	yes	—
120	C₄²×C₂₃	C₂×D₄	1	2	yes	—
121	C₄²×C₂₃	C₂×D₄	1	2	yes	—
122	C₄²×C₂₃	C₂⁴	1	2	yes	—
123	C₄²×C₂₃	C₂⁴	1	2	yes	—
124	C₂×#3142	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
125	C₂³×C₂₃	—	2	4	no	—
126	C₂³×C₂₃	—	2	4	no	—
127	C₂³×C₂₃	—	4	4	no	—
128	C₂³×C₂₃	—	4	8	no	—
129	C₂³×C₂₃	#124	1	4	yes	—
130	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
131	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
132	Q₈×C₂₃	—	2	8	no	—
133	Q₈×C₂₃	—	4	4	no	—
134	D₄×C₂₃	—	2	8	no	—
135	D₄×C₂₃	—	4	16	no	—
136	D₄×C₂₃	—	4	16	no	—
137	D₄×C₂₃	—	4	4	no	—
138	C₂×C₄×C₂₃	—	2	4	no	—
139	C₂×C₄×C₂₃	—	2	4	no	—
140	C₂×C₄×C₂₃	—	2	4	no	—
141	C₂×C₄×C₂₃	—	2	8	no	—
142	C₂×C₄×C₂₃	—	4	8	no	—
143	C₂×C₄×C₂₃	—	4	16	no	—
144	C₂×C₄×C₂₃	—	4	4	no	—
145	C₂×C₄×C₂₃	—	4	8	no	—
146	C₂×C₄×C₂₃	—	4	16	no	—
147	C₂×C₄×C₂₃	#124	1	4	yes	—
148	C₂×C₄×C₂₃	#124	1	8	yes	—
149	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
150	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
151	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
152	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
153	C₂×C₄×C₂₃	C₂×#41	1	4	yes	—
154	C₂×C₄×C₂₃	C₂×#41	1	8	yes	—
155	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
156	C₈×C₂₃	—	2	8	no	—
157	C₂×#532	C₂×C₂₃	1	1	yes	characteristic
158	C₂²×#125	C₂×C₂₃	1	1	yes	characteristic, complemented
159	#3142	C₂×C₂₃	1	16	yes	direct product factor
160	C₂×#491	C₂×C₂₃	1	2	yes	complemented
161	C₂×#490	C₂×C₂₃	1	2	yes	complemented
162	C₂×#488	C₂×C₂₃	1	4	yes	complemented
163	C₂×#417	C₂×C₂₃	1	4	yes	complemented
164	C₂×C₄×M₁₆	C₂×C₂₃	1	1	yes	characteristic, complemented
165	C₂²×C₂₃	—	2	8	no	—
166	C₂²×C₂₃	—	2	4	no	—
167	C₂²×C₂₃	—	4	4	no	—
168	C₂²×C₂₃	—	4	8	no	—
169	C₂²×C₂₃	—	8	8	no	—
170	C₂²×C₂₃	C₂×#124	1	4	yes	—
171	C₂²×C₂₃	C₂×#124	1	2	yes	—
172	C₂²×C₂₃	#575	1	4	yes	—
173	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
174	C₄×C₂₃	—	2	4	no	—
175	C₄×C₂₃	—	2	4	no	—
176	C₄×C₂₃	—	4	4	no	—
177	C₄×C₂₃	—	4	8	no	—
178	C₄×C₂₃	C₂×#124	1	4	yes	—
179	C₄×C₂₃	C₂×#124	1	2	yes	—
180	C₄×C₂₃	C₂²×#41	1	2	yes	—
181	C₂²×#41	C₂²×C₂₃	1	2	yes	—
182	C₂²×M₁₆	C₂²×C₂₃	1	2	yes	—
183	#532	—	2	4	no	—
184	#532	C₂²×C₂₃	1	8	yes	—
185	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
186	C₂×#127	C₂²×C₂₃	1	1	yes	characteristic
187	C₂×#125	—	2	2	no	—
188	C₂×#125	—	2	4	no	—
189	C₂×#125	C₂²×C₂₃	1	2	yes	—
190	C₂×#125	C₂²×C₂₃	1	2	yes	—
191	C₂×#125	C₂²×C₂₃	1	8	yes	complemented
192	C₂×#124	C₂²×C₂₃	1	2	yes	—
193	C₂×#121	—	2	2	no	—
194	C₂×C₄×D₄	—	2	2	no	—
195	C₂²×C₄⋊C₄	—	2	2	no	—
196	C₂²×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
197	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
198	#491	C₂²×C₂₃	1	16	yes	complemented
199	#490	C₂²×C₂₃	1	16	yes	complemented
200	#488	C₂²×C₂₃	1	32	yes	complemented
201	#417	C₂²×C₂₃	1	32	yes	complemented
202	C₂×#103	C₂²×C₂₃	1	8	yes	—
203	C₂×#102	C₂²×C₂₃	1	8	yes	—
204	C₄×M₁₆	C₂²×C₂₃	1	8	yes	complemented
205	C₂×#97	C₂²×C₂₃	1	2	yes	—
206	C₂×C₄×C₈	C₂²×C₂₃	1	2	yes	—
207	C₂×C₂₃	—	2	4	no	—
208	C₂×C₂₃	—	8	4	no	—
209	C₂×C₂₃	#3142	1	4	yes	direct product factor
210	C₂×C₂₃	C₂²×#124	1	1	yes	characteristic
211	C₂×C₂₃	C₂×#575	1	2	yes	—
212	C₂×#41	—	2	4	no	—
213	C₂×#41	—	2	16	no	—
214	C₂×#41	C₂³×C₂₃	1	8	yes	—
215	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
216	C₂²×D₄	—	2	2	no	—
217	C₂²×D₄	—	2	2	no	—
218	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
219	C₂³×C₄	—	2	2	no	—
220	C₂³×C₄	—	2	2	no	—
221	C₂³×C₄	D₄×C₂₃	1	2	yes	—
222	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
223	C₂×M₁₆	—	2	8	no	—
224	C₂×M₁₆	C₂³×C₂₃	1	8	yes	—
225	C₂²×C₈	C₂³×C₂₃	1	4	yes	—
226	C₄⋊Q₈	—	2	2	no	—
227	C₄⋊Q₈	C₂³×C₂₃	1	4	yes	—
228	#127	—	2	2	no	—
229	#127	C₂³×C₂₃	1	4	yes	—
230	#125	—	2	4	no	—
231	#125	—	2	4	no	—
232	#125	—	2	16	no	—
233	#125	C₂³×C₂₃	1	8	yes	—
234	#125	C₂³×C₂₃	1	8	yes	—
235	#124	—	2	4	no	—
236	#124	C₂³×C₂₃	1	8	yes	—
237	#121	—	2	16	no	—
238	C₄×D₄	—	2	16	no	—
239	C₂×C₄⋊C₄	—	2	4	no	—
240	C₂×C₄⋊C₄	—	2	4	no	—
241	C₂×C₄⋊C₄	—	2	16	no	—
242	C₂×C₄⋊C₄	—	2	2	no	—
243	C₂×C₄⋊C₄	—	2	4	no	—
244	C₂×C₄⋊C₄	—	2	2	no	—
245	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
246	C₂×C₄⋊C₄	C₂³×C₂₃	1	8	yes	—
247	C₂×C₂²⋊C₄	—	2	4	no	—
248	C₂×C₄²	D₄×C₂₃	1	2	yes	—
249	C₂×C₄²	D₄×C₂₃	1	4	yes	—
250	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
251	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
252	C₂×C₄²	C₂³×C₂₃	1	4	yes	—
253	#103	C₂³×C₂₃	1	32	yes	—
254	#102	C₂³×C₂₃	1	32	yes	—
255	#97	C₂³×C₂₃	1	8	yes	—
256	C₄×C₈	C₂³×C₂₃	1	8	yes	—
257	C₂₃	C₂×#3142	1	1	yes	characteristic, direct product factor, Sylow
258	C₂⁴	—	2	2	no	—
259	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
260	#41	—	2	32	no	—
261	#41	—	4	16	no	—
262	C₂×Q₈	—	2	2	no	—
263	C₂×Q₈	—	2	8	no	—
264	C₂×Q₈	C₂⁴×C₂₃	1	4	yes	—
265	C₂×D₄	—	2	8	no	—
266	C₂×D₄	—	2	8	no	—
267	C₂×D₄	—	2	2	no	—
268	C₂×D₄	—	2	8	no	—
269	C₂×D₄	—	4	8	no	—
270	C₂×D₄	—	4	8	no	—
271	C₂×D₄	C₂⁴×C₂₃	1	4	yes	—
272	C₂²×C₄	—	2	2	no	—
273	C₂²×C₄	—	2	8	no	—
274	C₂²×C₄	—	2	4	no	—
275	C₂²×C₄	—	2	8	no	—
276	C₂²×C₄	—	4	4	no	—
277	C₂²×C₄	—	4	8	no	—
278	C₂²×C₄	—	4	8	no	—
279	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
280	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
281	C₂²×C₄	C₂×D₄×C₂₃	1	8	yes	—
282	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
283	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
284	C₂²×C₄	#41×C₂₃	1	8	yes	—
285	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
286	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
287	M₁₆	—	2	16	no	—
288	C₂×C₈	—	2	8	no	—
289	C₂×C₈	C₂⁴×C₂₃	1	8	yes	—
290	C₄⋊C₄	—	2	16	no	—
291	C₄⋊C₄	—	2	16	no	—
292	C₄⋊C₄	—	2	8	no	—
293	C₄⋊C₄	—	2	4	no	—
294	C₄⋊C₄	—	2	8	no	—
295	C₄⋊C₄	C₂⁴×C₂₃	1	8	yes	—
296	C₂²⋊C₄	—	2	16	no	—
297	C₄²	C₂×D₄×C₂₃	1	8	yes	—
298	C₄²	C₂×D₄×C₂₃	1	2	yes	—
299	C₄²	C₂×D₄×C₂₃	1	2	yes	—
300	C₄²	C₂⁴×C₂₃	1	2	yes	—
301	C₄²	C₂⁴×C₂₃	1	2	yes	—
302	C₂³	—	2	4	no	—
303	C₂³	—	2	4	no	—
304	C₂³	—	4	8	no	—
305	C₂³	—	4	4	no	—
306	C₂³	C₂₃×#124	1	4	yes	—
307	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
308	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
309	Q₈	—	2	8	no	—
310	Q₈	—	4	4	no	—
311	D₄	—	2	8	no	—
312	D₄	—	4	16	no	—
313	D₄	—	4	16	no	—
314	D₄	—	4	4	no	—
315	C₂×C₄	—	2	4	no	—
316	C₂×C₄	—	2	4	no	—
317	C₂×C₄	—	2	4	no	—
318	C₂×C₄	—	2	8	no	—
319	C₂×C₄	—	4	8	no	—
320	C₂×C₄	—	4	16	no	—
321	C₂×C₄	—	4	8	no	—
322	C₂×C₄	—	4	4	no	—
323	C₂×C₄	—	4	16	no	—
324	C₂×C₄	C₂₃×#124	1	4	yes	—
325	C₂×C₄	C₂₃×#124	1	8	yes	—
326	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
327	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
328	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
329	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
330	C₂×C₄	C₂×#41×C₂₃	1	4	yes	—
331	C₂×C₄	C₂×#41×C₂₃	1	8	yes	—
332	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
333	C₈	—	2	8	no	—
334	C₂²	—	2	4	no	—
335	C₂²	—	2	8	no	—
336	C₂²	—	4	4	no	—
337	C₂²	—	4	8	no	—
338	C₂²	—	8	8	no	—
339	C₂²	C₂×C₂₃×#124	1	4	yes	—
340	C₂²	C₂×C₂₃×#124	1	2	yes	—
341	C₂²	C₂₃×#575	1	4	yes	—
342	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
343	C₄	—	2	4	no	—
344	C₄	—	2	4	no	—
345	C₄	—	4	4	no	—
346	C₄	—	4	8	no	—
347	C₄	C₂×C₂₃×#124	1	4	yes	—
348	C₄	C₂×C₂₃×#124	1	2	yes	—
349	C₄	C₂²×#41×C₂₃	1	2	yes	—
350	C₂	—	2	4	no	—
351	C₂	—	8	4	no	—
352	C₂	C₂₃×#3142	1	4	yes	direct product factor
353	C₂	C₂²×C₂₃×#124	1	1	yes	characteristic
354	C₂	C₂×C₂₃×#575	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
prime radical	C₂×C₂₃×#532	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ 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
2. C₂²×C₂₃×#125	C₂	semidirect
3. C₂₃×#3142	C₂	direct (N × H)
4. C₂×C₂₃×#491	C₂	semidirect
5. C₂×C₂₃×#490	C₂	semidirect
6. C₂×C₂₃×#488	C₂	semidirect
7. C₂×C₂₃×#417	C₂	semidirect
8. C₂×C₄×M₁₆×C₂₃	C₂	semidirect
19. C₂×C₂₃×#125	C₂²	semidirect
26. C₂₃×#491	C₂²	semidirect
27. C₂₃×#490	C₂²	semidirect
28. C₂₃×#488	C₂²	semidirect
29. C₂₃×#417	C₂²	semidirect
32. C₄×M₁₆×C₂₃	C₂²	semidirect
124. C₂×#3142	C₂₃	direct (N × H)
158. C₂²×#125	C₂×C₂₃	semidirect
159. #3142	C₂×C₂₃	direct (N × H)
160. C₂×#491	C₂×C₂₃	semidirect
161. C₂×#490	C₂×C₂₃	semidirect
162. C₂×#488	C₂×C₂₃	semidirect
163. C₂×#417	C₂×C₂₃	semidirect
164. C₂×C₄×M₁₆	C₂×C₂₃	semidirect
191. C₂×#125	C₂²×C₂₃	semidirect
198. #491	C₂²×C₂₃	semidirect
199. #490	C₂²×C₂₃	semidirect
200. #488	C₂²×C₂₃	semidirect
201. #417	C₂²×C₂₃	semidirect
204. C₄×M₁₆	C₂²×C₂₃	semidirect
209. C₂×C₂₃	#3142	direct (N × H)
257. C₂₃	C₂×#3142	direct (N × H)
352. C₂	C₂₃×#3142	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×#532	2
C₂²×C₂₃×#125	2
C₂₃×#3142	2
C₂×C₂₃×#491	2
C₂×C₂₃×#490	2
C₂×C₂₃×#488	2
C₂×C₂₃×#417	2
C₂×C₄×M₁₆×C₂₃	2
C₂×#3142	23

Subgroups — C2×C23×#3142 #19208243

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₃×#3142 #19208243