Subgroups — C₂×C₂₃×#3131 #19208231

Order 5888.

2222 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#533	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₃×#532	C₂	1	1	yes	maximal, characteristic
3	C₂₃×#3131	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₂₃×#488	C₂	1	4	yes	maximal, complemented
5	C₂×C₂₃×#487	C₂	1	2	yes	maximal, complemented
6	C₂×C₂₃×#486	C₂	1	2	yes	maximal, complemented
7	C₂×C₂₃×#416	C₂	1	4	yes	maximal, complemented
8	C₂²×C₄×C₈×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#41×C₂₃	C₂²	1	2	yes	—
10	C₂³×C₈×C₂₃	C₂²	1	2	yes	—
11	C₂₃×#533	—	2	4	no	—
12	C₂₃×#533	C₂²	1	8	yes	complemented
13	C₂₃×#532	—	2	4	no	—
14	C₂₃×#532	C₂²	1	8	yes	—
15	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
16	C₂×C₂₃×C₄⋊Q₈	C₂²	1	2	yes	—
17	C₂×C₂₃×#127	C₂²	1	1	yes	characteristic
18	C₂×C₂₃×#125	C₂²	1	2	yes	—
19	C₂×C₂₃×#124	C₂²	1	2	yes	—
20	C₂×C₂₃×C₂²⋊Q₈	—	2	2	no	—
21	C₂×C₂₃×#121	—	2	2	no	—
22	C₂×C₄×Q₈×C₂₃	—	2	2	no	—
23	C₂×C₄×D₄×C₂₃	—	2	2	no	—
24	C₂×C₂₃×#117	C₂²	1	2	yes	—
25	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
26	C₂₃×#488	C₂²	1	32	yes	complemented
27	C₂₃×#487	C₂²	1	16	yes	complemented
28	C₂₃×#486	C₂²	1	16	yes	complemented
29	C₂₃×#416	C₂²	1	32	yes	complemented
30	C₂×C₂₃×#103	C₂²	1	8	yes	—
31	C₂×C₂₃×#102	C₂²	1	8	yes	—
32	C₂×C₄×C₈×C₂₃	C₂²	1	2	yes	—
33	C₂×C₄×C₈×C₂₃	C₂²	1	2	yes	—
34	C₂×C₄×C₈×C₂₃	C₂²	1	8	yes	complemented
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	—	2	2	no	—
39	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
40	C₂²×D₄×C₂₃	—	2	2	no	—
41	C₂²×D₄×C₂₃	—	2	2	no	—
42	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
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	C₂²×C₈×C₂₃	—	2	8	no	—
47	C₂²×C₈×C₂₃	C₂³	1	4	yes	—
48	C₂²×C₈×C₂₃	C₂³	1	8	yes	—
49	C₂₃×C₄⋊Q₈	—	2	2	no	—
50	C₂₃×C₄⋊Q₈	—	2	4	no	—
51	C₂₃×C₄⋊Q₈	C₂³	1	4	yes	—
52	C₂₃×C₄⋊Q₈	C₂³	1	8	yes	—
53	C₂₃×#127	—	2	2	no	—
54	C₂₃×#127	C₂³	1	4	yes	—
55	C₂₃×#125	—	2	4	no	—
56	C₂₃×#125	C₂³	1	8	yes	—
57	C₂₃×#124	—	2	4	no	—
58	C₂₃×#124	C₂³	1	8	yes	—
59	C₂₃×C₂²⋊Q₈	—	2	16	no	—
60	C₂₃×#121	—	2	16	no	—
61	C₄×Q₈×C₂₃	—	2	16	no	—
62	C₄×D₄×C₂₃	—	2	16	no	—
63	C₂₃×#117	—	2	4	no	—
64	C₂₃×#117	C₂³	1	8	yes	—
65	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
66	C₂×C₄⋊C₄×C₂₃	—	2	4	no	—
67	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
68	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
69	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
70	C₂×C₂²⋊C₄×C₂₃	—	2	4	no	—
71	C₂×C₄²×C₂₃	—	2	2	no	—
72	C₂×C₄²×C₂₃	D₄	1	4	yes	—
73	C₂×C₄²×C₂₃	D₄	1	2	yes	—
74	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
75	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
76	C₂×C₄²×C₂₃	C₂³	1	4	yes	—
77	C₂₃×#103	C₂³	1	32	yes	—
78	C₂₃×#102	C₂³	1	32	yes	—
79	C₄×C₈×C₂₃	C₂³	1	8	yes	—
80	C₄×C₈×C₂₃	C₂³	1	8	yes	—
81	C₂⁴×C₂₃	—	2	2	no	—
82	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
83	#41×C₂₃	—	2	32	no	—
84	#41×C₂₃	—	4	16	no	—
85	C₂×Q₈×C₂₃	—	2	8	no	—
86	C₂×Q₈×C₂₃	—	2	2	no	—
87	C₂×Q₈×C₂₃	—	2	8	no	—
88	C₂×Q₈×C₂₃	—	4	8	no	—
89	C₂×Q₈×C₂₃	C₂⁴	1	4	yes	—
90	C₂×D₄×C₂₃	—	2	8	no	—
91	C₂×D₄×C₂₃	—	2	8	no	—
92	C₂×D₄×C₂₃	—	2	2	no	—
93	C₂×D₄×C₂₃	—	2	8	no	—
94	C₂×D₄×C₂₃	—	4	8	no	—
95	C₂×D₄×C₂₃	—	4	8	no	—
96	C₂×D₄×C₂₃	C₂⁴	1	4	yes	—
97	C₂²×C₄×C₂₃	—	2	8	no	—
98	C₂²×C₄×C₂₃	—	2	4	no	—
99	C₂²×C₄×C₂₃	—	2	2	no	—
100	C₂²×C₄×C₂₃	—	2	8	no	—
101	C₂²×C₄×C₂₃	—	4	8	no	—
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	2	yes	—
106	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₂₃	#41	1	8	yes	—
108	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
109	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
110	C₂×C₈×C₂₃	—	2	8	no	—
111	C₂×C₈×C₂₃	—	2	16	no	—
112	C₂×C₈×C₂₃	C₂⁴	1	8	yes	—
113	C₄⋊C₄×C₂₃	—	2	8	no	—
114	C₄⋊C₄×C₂₃	—	2	16	no	—
115	C₄⋊C₄×C₂₃	—	2	8	no	—
116	C₄⋊C₄×C₂₃	—	2	4	no	—
117	C₄⋊C₄×C₂₃	C₂⁴	1	8	yes	—
118	C₂²⋊C₄×C₂₃	—	2	8	no	—
119	C₂²⋊C₄×C₂₃	—	2	16	no	—
120	C₄²×C₂₃	—	2	8	no	—
121	C₄²×C₂₃	C₂×D₄	1	8	yes	—
122	C₄²×C₂₃	C₂×D₄	1	2	yes	—
123	C₄²×C₂₃	C₂×D₄	1	2	yes	—
124	C₄²×C₂₃	C₂⁴	1	2	yes	—
125	C₄²×C₂₃	C₂⁴	1	2	yes	—
126	C₂×#3131	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
127	C₂³×C₂₃	—	2	4	no	—
128	C₂³×C₂₃	—	2	4	no	—
129	C₂³×C₂₃	—	4	4	no	—
130	C₂³×C₂₃	—	4	8	no	—
131	C₂³×C₂₃	#124	1	4	yes	—
132	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
133	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
134	Q₈×C₂₃	—	2	8	no	—
135	Q₈×C₂₃	—	4	4	no	—
136	Q₈×C₂₃	—	4	16	no	—
137	D₄×C₂₃	—	2	8	no	—
138	D₄×C₂₃	—	4	16	no	—
139	D₄×C₂₃	—	4	4	no	—
140	D₄×C₂₃	—	4	16	no	—
141	C₂×C₄×C₂₃	—	2	4	no	—
142	C₂×C₄×C₂₃	—	2	16	no	—
143	C₂×C₄×C₂₃	—	2	8	no	—
144	C₂×C₄×C₂₃	—	2	4	no	—
145	C₂×C₄×C₂₃	—	4	4	no	—
146	C₂×C₄×C₂₃	—	4	8	no	—
147	C₂×C₄×C₂₃	—	4	16	no	—
148	C₂×C₄×C₂₃	#124	1	4	yes	—
149	C₂×C₄×C₂₃	#124	1	8	yes	—
150	C₂×C₄×C₂₃	#135	1	8	yes	—
151	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
152	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
153	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
154	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
155	C₂×C₄×C₂₃	C₂×#41	1	4	yes	—
156	C₂×C₄×C₂₃	C₂×#41	1	8	yes	—
157	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
158	C₈×C₂₃	—	2	8	no	—
159	C₂×#533	C₂×C₂₃	1	1	yes	characteristic, complemented
160	C₂×#532	C₂×C₂₃	1	1	yes	characteristic
161	#3131	C₂×C₂₃	1	16	yes	direct product factor
162	C₂×#488	C₂×C₂₃	1	4	yes	complemented
163	C₂×#487	C₂×C₂₃	1	2	yes	complemented
164	C₂×#486	C₂×C₂₃	1	2	yes	complemented
165	C₂×#416	C₂×C₂₃	1	4	yes	complemented
166	C₂²×C₄×C₈	C₂×C₂₃	1	1	yes	characteristic, complemented
167	C₂²×C₂₃	—	2	8	no	—
168	C₂²×C₂₃	—	2	4	no	—
169	C₂²×C₂₃	—	4	4	no	—
170	C₂²×C₂₃	—	4	8	no	—
171	C₂²×C₂₃	—	8	8	no	—
172	C₂²×C₂₃	C₂×#124	1	4	yes	—
173	C₂²×C₂₃	C₂×#124	1	2	yes	—
174	C₂²×C₂₃	C₂×#135	1	4	yes	—
175	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
176	C₄×C₂₃	—	2	4	no	—
177	C₄×C₂₃	—	4	4	no	—
178	C₄×C₂₃	—	4	8	no	—
179	C₄×C₂₃	C₂×#124	1	4	yes	—
180	C₄×C₂₃	C₂×#124	1	2	yes	—
181	C₄×C₂₃	C₂×#135	1	8	yes	—
182	C₄×C₂₃	C₂²×#41	1	2	yes	—
183	C₂²×#41	C₂²×C₂₃	1	2	yes	—
184	C₂³×C₈	C₂²×C₂₃	1	2	yes	—
185	#533	—	2	4	no	—
186	#533	C₂²×C₂₃	1	8	yes	complemented
187	#532	—	2	4	no	—
188	#532	C₂²×C₂₃	1	8	yes	—
189	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
190	C₂×C₄⋊Q₈	C₂²×C₂₃	1	2	yes	—
191	C₂×#127	C₂²×C₂₃	1	1	yes	characteristic
192	C₂×#125	C₂²×C₂₃	1	2	yes	—
193	C₂×#124	C₂²×C₂₃	1	2	yes	—
194	C₂×C₂²⋊Q₈	—	2	2	no	—
195	C₂×#121	—	2	2	no	—
196	C₂×C₄×Q₈	—	2	2	no	—
197	C₂×C₄×D₄	—	2	2	no	—
198	C₂×#117	C₂²×C₂₃	1	2	yes	—
199	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
200	#488	C₂²×C₂₃	1	32	yes	complemented
201	#487	C₂²×C₂₃	1	16	yes	complemented
202	#486	C₂²×C₂₃	1	16	yes	complemented
203	#416	C₂²×C₂₃	1	32	yes	complemented
204	C₂×#103	C₂²×C₂₃	1	8	yes	—
205	C₂×#102	C₂²×C₂₃	1	8	yes	—
206	C₂×C₄×C₈	C₂²×C₂₃	1	2	yes	—
207	C₂×C₄×C₈	C₂²×C₂₃	1	2	yes	—
208	C₂×C₄×C₈	C₂²×C₂₃	1	8	yes	complemented
209	C₂×C₂₃	—	2	4	no	—
210	C₂×C₂₃	—	8	4	no	—
211	C₂×C₂₃	#3131	1	4	yes	direct product factor
212	C₂×C₂₃	C₂²×#124	1	1	yes	characteristic
213	C₂×C₂₃	C₂²×#135	1	2	yes	—
214	C₂×#41	—	2	4	no	—
215	C₂×#41	—	2	16	no	—
216	C₂×#41	C₂³×C₂₃	1	8	yes	—
217	C₂²×Q₈	—	2	2	no	—
218	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
219	C₂²×D₄	—	2	2	no	—
220	C₂²×D₄	—	2	2	no	—
221	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
222	C₂³×C₄	—	2	2	no	—
223	C₂³×C₄	D₄×C₂₃	1	2	yes	—
224	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
225	C₂²×C₈	—	2	8	no	—
226	C₂²×C₈	C₂³×C₂₃	1	4	yes	—
227	C₂²×C₈	C₂³×C₂₃	1	8	yes	—
228	C₄⋊Q₈	—	2	2	no	—
229	C₄⋊Q₈	—	2	4	no	—
230	C₄⋊Q₈	C₂³×C₂₃	1	4	yes	—
231	C₄⋊Q₈	C₂³×C₂₃	1	8	yes	—
232	#127	—	2	2	no	—
233	#127	C₂³×C₂₃	1	4	yes	—
234	#125	—	2	4	no	—
235	#125	C₂³×C₂₃	1	8	yes	—
236	#124	—	2	4	no	—
237	#124	C₂³×C₂₃	1	8	yes	—
238	C₂²⋊Q₈	—	2	16	no	—
239	#121	—	2	16	no	—
240	C₄×Q₈	—	2	16	no	—
241	C₄×D₄	—	2	16	no	—
242	#117	—	2	4	no	—
243	#117	C₂³×C₂₃	1	8	yes	—
244	C₂×C₄⋊C₄	—	2	2	no	—
245	C₂×C₄⋊C₄	—	2	4	no	—
246	C₂×C₄⋊C₄	—	2	2	no	—
247	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
248	C₂×C₂²⋊C₄	—	2	2	no	—
249	C₂×C₂²⋊C₄	—	2	4	no	—
250	C₂×C₄²	—	2	2	no	—
251	C₂×C₄²	D₄×C₂₃	1	2	yes	—
252	C₂×C₄²	D₄×C₂₃	1	4	yes	—
253	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
254	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
255	C₂×C₄²	C₂³×C₂₃	1	4	yes	—
256	#103	C₂³×C₂₃	1	32	yes	—
257	#102	C₂³×C₂₃	1	32	yes	—
258	C₄×C₈	C₂³×C₂₃	1	8	yes	—
259	C₄×C₈	C₂³×C₂₃	1	8	yes	—
260	C₂₃	C₂×#3131	1	1	yes	characteristic, direct product factor, Sylow
261	C₂⁴	—	2	2	no	—
262	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
263	#41	—	2	32	no	—
264	#41	—	4	16	no	—
265	C₂×Q₈	—	2	8	no	—
266	C₂×Q₈	—	2	2	no	—
267	C₂×Q₈	—	2	8	no	—
268	C₂×Q₈	—	4	8	no	—
269	C₂×Q₈	C₂⁴×C₂₃	1	4	yes	—
270	C₂×D₄	—	2	8	no	—
271	C₂×D₄	—	2	8	no	—
272	C₂×D₄	—	2	2	no	—
273	C₂×D₄	—	2	8	no	—
274	C₂×D₄	—	4	8	no	—
275	C₂×D₄	—	4	8	no	—
276	C₂×D₄	C₂⁴×C₂₃	1	4	yes	—
277	C₂²×C₄	—	2	8	no	—
278	C₂²×C₄	—	2	4	no	—
279	C₂²×C₄	—	2	2	no	—
280	C₂²×C₄	—	2	8	no	—
281	C₂²×C₄	—	4	8	no	—
282	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
283	C₂²×C₄	C₂×D₄×C₂₃	1	8	yes	—
284	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
285	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
286	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
287	C₂²×C₄	#41×C₂₃	1	8	yes	—
288	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
289	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
290	C₂×C₈	—	2	8	no	—
291	C₂×C₈	—	2	16	no	—
292	C₂×C₈	C₂⁴×C₂₃	1	8	yes	—
293	C₄⋊C₄	—	2	8	no	—
294	C₄⋊C₄	—	2	16	no	—
295	C₄⋊C₄	—	2	8	no	—
296	C₄⋊C₄	—	2	4	no	—
297	C₄⋊C₄	C₂⁴×C₂₃	1	8	yes	—
298	C₂²⋊C₄	—	2	8	no	—
299	C₂²⋊C₄	—	2	16	no	—
300	C₄²	—	2	8	no	—
301	C₄²	C₂×D₄×C₂₃	1	8	yes	—
302	C₄²	C₂×D₄×C₂₃	1	2	yes	—
303	C₄²	C₂×D₄×C₂₃	1	2	yes	—
304	C₄²	C₂⁴×C₂₃	1	2	yes	—
305	C₄²	C₂⁴×C₂₃	1	2	yes	—
306	C₂³	—	2	4	no	—
307	C₂³	—	2	4	no	—
308	C₂³	—	4	8	no	—
309	C₂³	—	4	4	no	—
310	C₂³	C₂₃×#124	1	4	yes	—
311	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
312	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
313	Q₈	—	2	8	no	—
314	Q₈	—	4	16	no	—
315	Q₈	—	4	4	no	—
316	D₄	—	2	8	no	—
317	D₄	—	4	16	no	—
318	D₄	—	4	16	no	—
319	D₄	—	4	4	no	—
320	C₂×C₄	—	2	4	no	—
321	C₂×C₄	—	2	16	no	—
322	C₂×C₄	—	2	8	no	—
323	C₂×C₄	—	2	4	no	—
324	C₂×C₄	—	4	8	no	—
325	C₂×C₄	—	4	4	no	—
326	C₂×C₄	—	4	16	no	—
327	C₂×C₄	C₂₃×#124	1	4	yes	—
328	C₂×C₄	C₂₃×#124	1	8	yes	—
329	C₂×C₄	C₂₃×#135	1	8	yes	—
330	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
331	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
332	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
333	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
334	C₂×C₄	C₂×#41×C₂₃	1	4	yes	—
335	C₂×C₄	C₂×#41×C₂₃	1	8	yes	—
336	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
337	C₈	—	2	8	no	—
338	C₂²	—	2	4	no	—
339	C₂²	—	2	8	no	—
340	C₂²	—	4	4	no	—
341	C₂²	—	4	8	no	—
342	C₂²	—	8	8	no	—
343	C₂²	C₂×C₂₃×#124	1	4	yes	—
344	C₂²	C₂×C₂₃×#124	1	2	yes	—
345	C₂²	C₂×C₂₃×#135	1	4	yes	—
346	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
347	C₄	—	2	4	no	—
348	C₄	—	4	4	no	—
349	C₄	—	4	8	no	—
350	C₄	C₂×C₂₃×#124	1	4	yes	—
351	C₄	C₂×C₂₃×#124	1	2	yes	—
352	C₄	C₂×C₂₃×#135	1	8	yes	—
353	C₄	C₂²×#41×C₂₃	1	2	yes	—
354	C₂	—	2	4	no	—
355	C₂	—	8	4	no	—
356	C₂	C₂₃×#3131	1	4	yes	direct product factor
357	C₂	C₂²×C₂₃×#124	1	1	yes	characteristic
358	C₂	C₂²×C₂₃×#135	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₂₃	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
socle	C₂³×C₂₃	C₂²×D₄
prime radical	C₂×C₂₃×#532	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₂₃ ◁ C₂²×C₄²×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₂₃×#533	C₂	semidirect
3. C₂₃×#3131	C₂	direct (N × H)
4. C₂×C₂₃×#488	C₂	semidirect
5. C₂×C₂₃×#487	C₂	semidirect
6. C₂×C₂₃×#486	C₂	semidirect
7. C₂×C₂₃×#416	C₂	semidirect
8. C₂²×C₄×C₈×C₂₃	C₂	semidirect
12. C₂₃×#533	C₂²	semidirect
26. C₂₃×#488	C₂²	semidirect
27. C₂₃×#487	C₂²	semidirect
28. C₂₃×#486	C₂²	semidirect
29. C₂₃×#416	C₂²	semidirect
34. C₂×C₄×C₈×C₂₃	C₂²	semidirect
126. C₂×#3131	C₂₃	direct (N × H)
159. C₂×#533	C₂×C₂₃	semidirect
161. #3131	C₂×C₂₃	direct (N × H)
162. C₂×#488	C₂×C₂₃	semidirect
163. C₂×#487	C₂×C₂₃	semidirect
164. C₂×#486	C₂×C₂₃	semidirect
165. C₂×#416	C₂×C₂₃	semidirect
166. C₂²×C₄×C₈	C₂×C₂₃	semidirect
186. #533	C₂²×C₂₃	semidirect
200. #488	C₂²×C₂₃	semidirect
201. #487	C₂²×C₂₃	semidirect
202. #486	C₂²×C₂₃	semidirect
203. #416	C₂²×C₂₃	semidirect
208. C₂×C₄×C₈	C₂²×C₂₃	semidirect
211. C₂×C₂₃	#3131	direct (N × H)
260. C₂₃	C₂×#3131	direct (N × H)
356. C₂	C₂₃×#3131	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×#533	2
C₂×C₂₃×#532	2
C₂₃×#3131	2
C₂×C₂₃×#488	2
C₂×C₂₃×#487	2
C₂×C₂₃×#486	2
C₂×C₂₃×#416	2
C₂²×C₄×C₈×C₂₃	2
C₂×#3131	23

Subgroups — C2×C23×#3131 #19208231

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₃×#3131 #19208231