Subgroups — C₂₃×#36639 #19184265

Order 5888.

2782 conjugacy classes of subgroups.

The subgroup lattice has 354 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×#2862	C₂	1	2	yes	maximal, complemented
4	C₂₃×#2861	C₂	1	4	yes	maximal, complemented
5	C₂₃×#2858	C₂	1	2	yes	maximal, complemented
6	C₂₃×#2850	C₂	1	8	yes	maximal, complemented
7	C₄×C₂₃×#124	C₂	1	8	yes	maximal, complemented
8	C₂₃×#2297	C₂	1	4	yes	maximal, complemented
9	C₂×C₄³×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#41×C₂₃	C₂²	1	2	yes	—
11	C₂₃×#533	—	2	8	no	—
12	C₂₃×#532	—	2	8	no	—
13	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₂×C₂₃×C₄⋊Q₈	C₂²	1	2	yes	—
15	C₂×C₂₃×#127	C₂²	1	1	yes	characteristic
16	C₂×C₂₃×#125	C₂²	1	2	yes	—
17	C₂×C₂₃×#124	C₂²	1	2	yes	—
18	C₂×C₂₃×#124	C₂²	1	8	yes	—
19	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	4	yes	—
20	C₂×C₂₃×#121	C₂²	1	4	yes	—
21	C₂×C₄×Q₈×C₂₃	C₂²	1	4	yes	—
22	C₂×C₄×D₄×C₂₃	C₂²	1	4	yes	—
23	C₂×C₂₃×#117	C₂²	1	2	yes	—
24	C₂²×C₄²×C₂₃	C₂²	1	2	yes	—
25	C₂²×C₄²×C₂₃	C₂²	1	4	yes	—
26	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
27	C₂₃×#391	C₂²	1	8	yes	—
28	C₂₃×#391	C₂²	1	8	yes	—
29	C₂₃×#390	C₂²	1	8	yes	—
30	C₂₃×#390	C₂²	1	8	yes	—
31	C₂₃×#388	C₂²	1	32	yes	—
32	C₂₃×#386	C₂²	1	16	yes	—
33	C₂₃×#382	C₂²	1	8	yes	—
34	C₄×C₂²⋊C₄×C₂₃	C₂²	1	16	yes	—
35	C₄³×C₂₃	C₂²	1	4	yes	—
36	C₄³×C₂₃	C₂²	1	2	yes	—
37	C₄³×C₂₃	C₂²	1	2	yes	—
38	C₂×#41×C₂₃	—	2	8	no	—
39	C₂×#41×C₂₃	—	2	16	no	—
40	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
41	C₂²×Q₈×C₂₃	C₂³	1	4	yes	—
42	C₂²×D₄×C₂₃	C₂³	1	4	yes	—
43	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
44	C₂²×D₄×C₂₃	C₂³	1	4	yes	—
45	C₂³×C₄×C₂₃	C₂³	1	4	yes	—
46	C₂³×C₄×C₂₃	C₂³	1	4	yes	—
47	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
48	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
49	C₂₃×C₄⋊Q₈	—	2	4	no	—
50	C₂₃×C₄⋊Q₈	—	2	8	no	—
51	C₂₃×#127	—	2	4	no	—
52	C₂₃×#125	—	2	8	no	—
53	C₂₃×#124	—	2	8	no	—
54	C₂₃×#124	—	2	32	no	—
55	C₂₃×C₂²⋊Q₈	—	2	16	no	—
56	C₂₃×#121	—	2	16	no	—
57	C₄×Q₈×C₂₃	—	2	16	no	—
58	C₄×D₄×C₂₃	—	2	16	no	—
59	C₂₃×#117	—	2	8	no	—
60	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
61	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
62	C₂×C₄⋊C₄×C₂₃	C₂³	1	8	yes	—
63	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
64	C₂×C₂²⋊C₄×C₂₃	C₂³	1	32	yes	—
65	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
66	C₂×C₂²⋊C₄×C₂₃	C₂³	1	8	yes	—
67	C₂×C₄²×C₂₃	—	2	8	no	—
68	C₂×C₄²×C₂₃	—	2	16	no	—
69	C₂×C₄²×C₂₃	D₄	1	8	yes	—
70	C₂×C₄²×C₂₃	C₂³	1	8	yes	—
71	C₂×C₄²×C₂₃	C₂³	1	4	yes	—
72	C₂×C₄²×C₂₃	C₂³	1	4	yes	—
73	C₂×C₄²×C₂₃	C₂³	1	4	yes	—
74	C₂×C₄²×C₂₃	C₂³	1	4	yes	—
75	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
76	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
77	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
78	C₂×C₄²×C₂₃	C₂³	1	4	yes	—
79	C₂₃×#95	C₂³	1	32	yes	—
80	C₂⁴×C₂₃	C₂⁴	1	4	yes	—
81	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
82	#41×C₂₃	—	4	32	no	—
83	C₂×Q₈×C₂₃	—	2	8	no	—
84	C₂×Q₈×C₂₃	—	2	4	no	—
85	C₂×Q₈×C₂₃	—	2	16	no	—
86	C₂×Q₈×C₂₃	—	2	8	no	—
87	C₂×D₄×C₂₃	—	2	8	no	—
88	C₂×D₄×C₂₃	—	2	16	no	—
89	C₂×D₄×C₂₃	—	2	8	no	—
90	C₂×D₄×C₂₃	—	2	4	no	—
91	C₂×D₄×C₂₃	—	2	16	no	—
92	C₂×D₄×C₂₃	—	2	8	no	—
93	C₂²×C₄×C₂₃	—	2	8	no	—
94	C₂²×C₄×C₂₃	—	2	16	no	—
95	C₂²×C₄×C₂₃	—	2	8	no	—
96	C₂²×C₄×C₂₃	—	2	8	no	—
97	C₂²×C₄×C₂₃	—	2	16	no	—
98	C₂²×C₄×C₂₃	C₂×D₄	1	8	yes	—
99	C₂²×C₄×C₂₃	C₂×D₄	1	4	yes	—
100	C₂²×C₄×C₂₃	#41	1	8	yes	—
101	C₂²×C₄×C₂₃	C₂⁴	1	8	yes	—
102	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
103	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
104	C₂²×C₄×C₂₃	C₂⁴	1	8	yes	—
105	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
106	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
107	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
108	C₄⋊C₄×C₂₃	—	2	8	no	—
109	C₄⋊C₄×C₂₃	—	2	8	no	—
110	C₄⋊C₄×C₂₃	—	2	16	no	—
111	C₄⋊C₄×C₂₃	—	2	8	no	—
112	C₂²⋊C₄×C₂₃	—	2	8	no	—
113	C₂²⋊C₄×C₂₃	—	2	16	no	—
114	C₂²⋊C₄×C₂₃	—	2	64	no	—
115	C₄²×C₂₃	—	2	8	no	—
116	C₄²×C₂₃	—	2	16	no	—
117	C₄²×C₂₃	—	2	8	no	—
118	C₄²×C₂₃	—	2	8	no	—
119	C₄²×C₂₃	—	2	8	no	—
120	C₄²×C₂₃	C₂×D₄	1	8	yes	—
121	C₄²×C₂₃	C₂×D₄	1	4	yes	—
122	C₄²×C₂₃	C₂×D₄	1	4	yes	—
123	C₄²×C₂₃	#41	1	16	yes	complemented
124	#36639	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	—	2	16	no	—
128	C₂³×C₂₃	—	2	8	no	—
129	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
130	C₂³×C₂₃	C₂×#41	1	4	yes	—
131	C₂³×C₂₃	C₂⁵	1	1	yes	characteristic
132	Q₈×C₂₃	—	4	8	no	—
133	Q₈×C₂₃	—	4	16	no	—
134	D₄×C₂₃	—	4	16	no	—
135	D₄×C₂₃	—	4	8	no	—
136	D₄×C₂₃	—	4	16	no	—
137	C₂×C₄×C₂₃	—	2	32	no	—
138	C₂×C₄×C₂₃	—	2	4	no	—
139	C₂×C₄×C₂₃	—	2	8	no	—
140	C₂×C₄×C₂₃	—	2	8	no	—
141	C₂×C₄×C₂₃	—	2	16	no	—
142	C₂×C₄×C₂₃	—	2	8	no	—
143	C₂×C₄×C₂₃	—	2	4	no	—
144	C₂×C₄×C₂₃	—	2	16	no	—
145	C₂×C₄×C₂₃	—	2	8	no	—
146	C₂×C₄×C₂₃	—	4	16	no	—
147	C₂×C₄×C₂₃	#124	1	16	yes	complemented
148	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
149	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
150	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
151	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
152	C₂×C₄×C₂₃	C₂×#41	1	16	yes	—
153	C₂×C₄×C₂₃	C₂×#41	1	4	yes	—
154	C₂×C₄×C₂₃	C₂×#41	1	4	yes	—
155	C₂×C₄×C₂₃	C₂×#41	1	8	yes	—
156	C₂×#533	C₂×C₂₃	1	1	yes	characteristic, complemented
157	C₂×#532	C₂×C₂₃	1	1	yes	characteristic
158	#2862	C₂×C₂₃	1	2	yes	complemented
159	#2861	C₂×C₂₃	1	4	yes	complemented
160	#2858	C₂×C₂₃	1	2	yes	complemented
161	#2850	C₂×C₂₃	1	8	yes	complemented
162	C₄×#124	C₂×C₂₃	1	8	yes	complemented
163	#2297	C₂×C₂₃	1	4	yes	complemented
164	C₂×C₄³	C₂×C₂₃	1	1	yes	characteristic, complemented
165	C₂²×C₂₃	—	2	4	no	—
166	C₂²×C₂₃	—	2	8	no	—
167	C₂²×C₂₃	—	4	4	no	—
168	C₂²×C₂₃	—	4	8	no	—
169	C₂²×C₂₃	—	4	16	no	—
170	C₂²×C₂₃	C₂×#124	1	4	yes	—
171	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
172	C₂²×C₂₃	C₂²×#41	1	2	yes	—
173	C₂²×C₂₃	C₂²×#41	1	4	yes	—
174	C₄×C₂₃	—	2	4	no	—
175	C₄×C₂₃	—	2	16	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	4	yes	—
180	C₄×C₂₃	#532	1	8	yes	—
181	C₂²×#41	C₂²×C₂₃	1	2	yes	—
182	#533	—	2	8	no	—
183	#532	—	2	8	no	—
184	C₂×C₄⋊Q₈	C₂²×C₂₃	1	2	yes	—
185	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
186	C₂×#127	C₂²×C₂₃	1	1	yes	characteristic
187	C₂×#125	C₂²×C₂₃	1	2	yes	—
188	C₂×#124	C₂²×C₂₃	1	8	yes	—
189	C₂×#124	C₂²×C₂₃	1	2	yes	—
190	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	4	yes	—
191	C₂×#121	C₂²×C₂₃	1	4	yes	—
192	C₂×C₄×Q₈	C₂²×C₂₃	1	4	yes	—
193	C₂×C₄×D₄	C₂²×C₂₃	1	4	yes	—
194	C₂×#117	C₂²×C₂₃	1	2	yes	—
195	C₂²×C₄²	C₂²×C₂₃	1	4	yes	—
196	C₂²×C₄²	C₂²×C₂₃	1	2	yes	—
197	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
198	#391	C₂²×C₂₃	1	8	yes	—
199	#391	C₂²×C₂₃	1	8	yes	—
200	#390	C₂²×C₂₃	1	8	yes	—
201	#390	C₂²×C₂₃	1	8	yes	—
202	#388	C₂²×C₂₃	1	32	yes	—
203	#386	C₂²×C₂₃	1	16	yes	—
204	#382	C₂²×C₂₃	1	8	yes	—
205	C₄×C₂²⋊C₄	C₂²×C₂₃	1	16	yes	—
206	C₄³	C₂²×C₂₃	1	2	yes	—
207	C₄³	C₂²×C₂₃	1	2	yes	—
208	C₄³	C₂²×C₂₃	1	4	yes	—
209	C₂×C₂₃	—	2	4	no	—
210	C₂×C₂₃	—	8	4	no	—
211	C₂×C₂₃	C₂²×#124	1	1	yes	characteristic
212	C₂×C₂₃	C₂×#532	1	2	yes	—
213	C₂×C₂₃	#3444	1	4	yes	—
214	C₂×#41	—	2	8	no	—
215	C₂×#41	—	2	16	no	—
216	C₂²×Q₈	C₂³×C₂₃	1	4	yes	—
217	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
218	C₂²×D₄	C₂³×C₂₃	1	4	yes	—
219	C₂²×D₄	C₂³×C₂₃	1	4	yes	—
220	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
221	C₂³×C₄	C₂³×C₂₃	1	4	yes	—
222	C₂³×C₄	C₂³×C₂₃	1	4	yes	—
223	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
224	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
225	C₄⋊Q₈	—	2	4	no	—
226	C₄⋊Q₈	—	2	8	no	—
227	#127	—	2	4	no	—
228	#125	—	2	8	no	—
229	#124	—	2	8	no	—
230	#124	—	2	32	no	—
231	C₂²⋊Q₈	—	2	16	no	—
232	#121	—	2	16	no	—
233	C₄×Q₈	—	2	16	no	—
234	C₄×D₄	—	2	16	no	—
235	#117	—	2	8	no	—
236	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
237	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
238	C₂×C₄⋊C₄	C₂³×C₂₃	1	8	yes	—
239	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
240	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
241	C₂×C₂²⋊C₄	C₂³×C₂₃	1	8	yes	—
242	C₂×C₂²⋊C₄	C₂³×C₂₃	1	32	yes	—
243	C₂×C₄²	—	2	8	no	—
244	C₂×C₄²	—	2	16	no	—
245	C₂×C₄²	D₄×C₂₃	1	8	yes	—
246	C₂×C₄²	C₂³×C₂₃	1	4	yes	—
247	C₂×C₄²	C₂³×C₂₃	1	4	yes	—
248	C₂×C₄²	C₂³×C₂₃	1	8	yes	—
249	C₂×C₄²	C₂³×C₂₃	1	4	yes	—
250	C₂×C₄²	C₂³×C₂₃	1	4	yes	—
251	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
252	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
253	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
254	C₂×C₄²	C₂³×C₂₃	1	4	yes	—
255	#95	C₂³×C₂₃	1	32	yes	—
256	C₂₃	#36639	1	1	yes	characteristic, direct product factor, Sylow
257	C₂⁴	C₂⁴×C₂₃	1	4	yes	—
258	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
259	#41	—	4	32	no	—
260	C₂×Q₈	—	2	8	no	—
261	C₂×Q₈	—	2	4	no	—
262	C₂×Q₈	—	2	16	no	—
263	C₂×Q₈	—	2	8	no	—
264	C₂×D₄	—	2	8	no	—
265	C₂×D₄	—	2	16	no	—
266	C₂×D₄	—	2	8	no	—
267	C₂×D₄	—	2	4	no	—
268	C₂×D₄	—	2	16	no	—
269	C₂×D₄	—	2	8	no	—
270	C₂²×C₄	—	2	8	no	—
271	C₂²×C₄	—	2	16	no	—
272	C₂²×C₄	—	2	8	no	—
273	C₂²×C₄	—	2	8	no	—
274	C₂²×C₄	—	2	16	no	—
275	C₂²×C₄	C₂×D₄×C₂₃	1	8	yes	—
276	C₂²×C₄	C₂×D₄×C₂₃	1	4	yes	—
277	C₂²×C₄	#41×C₂₃	1	8	yes	—
278	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
279	C₂²×C₄	C₂⁴×C₂₃	1	8	yes	—
280	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
281	C₂²×C₄	C₂⁴×C₂₃	1	8	yes	—
282	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
283	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
284	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
285	C₄⋊C₄	—	2	8	no	—
286	C₄⋊C₄	—	2	8	no	—
287	C₄⋊C₄	—	2	16	no	—
288	C₄⋊C₄	—	2	8	no	—
289	C₂²⋊C₄	—	2	8	no	—
290	C₂²⋊C₄	—	2	16	no	—
291	C₂²⋊C₄	—	2	64	no	—
292	C₄²	—	2	8	no	—
293	C₄²	—	2	16	no	—
294	C₄²	—	2	8	no	—
295	C₄²	—	2	8	no	—
296	C₄²	—	2	8	no	—
297	C₄²	C₂×D₄×C₂₃	1	8	yes	—
298	C₄²	C₂×D₄×C₂₃	1	4	yes	—
299	C₄²	C₂×D₄×C₂₃	1	4	yes	—
300	C₄²	#41×C₂₃	1	16	yes	complemented
301	C₂³	—	2	4	no	—
302	C₂³	—	2	4	no	—
303	C₂³	—	2	16	no	—
304	C₂³	—	2	8	no	—
305	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
306	C₂³	C₂×#41×C₂₃	1	4	yes	—
307	C₂³	C₂⁵×C₂₃	1	1	yes	characteristic
308	Q₈	—	4	8	no	—
309	Q₈	—	4	16	no	—
310	D₄	—	4	16	no	—
311	D₄	—	4	8	no	—
312	D₄	—	4	16	no	—
313	C₂×C₄	—	2	32	no	—
314	C₂×C₄	—	2	4	no	—
315	C₂×C₄	—	2	8	no	—
316	C₂×C₄	—	2	8	no	—
317	C₂×C₄	—	2	16	no	—
318	C₂×C₄	—	2	8	no	—
319	C₂×C₄	—	2	4	no	—
320	C₂×C₄	—	2	16	no	—
321	C₂×C₄	—	2	8	no	—
322	C₂×C₄	—	4	16	no	—
323	C₂×C₄	C₂₃×#124	1	16	yes	complemented
324	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
325	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
326	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
327	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
328	C₂×C₄	C₂×#41×C₂₃	1	16	yes	—
329	C₂×C₄	C₂×#41×C₂₃	1	4	yes	—
330	C₂×C₄	C₂×#41×C₂₃	1	4	yes	—
331	C₂×C₄	C₂×#41×C₂₃	1	8	yes	—
332	C₂²	—	2	4	no	—
333	C₂²	—	2	8	no	—
334	C₂²	—	4	4	no	—
335	C₂²	—	4	8	no	—
336	C₂²	—	4	16	no	—
337	C₂²	C₂×C₂₃×#124	1	4	yes	—
338	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
339	C₂²	C₂²×#41×C₂₃	1	2	yes	—
340	C₂²	C₂²×#41×C₂₃	1	4	yes	—
341	C₄	—	2	4	no	—
342	C₄	—	2	16	no	—
343	C₄	—	4	4	no	—
344	C₄	—	4	8	no	—
345	C₄	C₂×C₂₃×#124	1	4	yes	—
346	C₄	C₂×C₂₃×#124	1	4	yes	—
347	C₄	C₂₃×#532	1	8	yes	—
348	C₂	—	2	4	no	—
349	C₂	—	8	4	no	—
350	C₂	C₂²×C₂₃×#124	1	1	yes	characteristic
351	C₂	C₂×C₂₃×#532	1	2	yes	—
352	C₂	C₂₃×#3444	1	4	yes	—

	subgroup	G/H
center	C₂²×C₄×C₂₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₂₃
socle	C₂³×C₂₃	C₂⁵
prime radical	C₂×C₂₃×#532	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×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×#2862	C₂	semidirect
4. C₂₃×#2861	C₂	semidirect
5. C₂₃×#2858	C₂	semidirect
6. C₂₃×#2850	C₂	semidirect
7. C₄×C₂₃×#124	C₂	semidirect
8. C₂₃×#2297	C₂	semidirect
9. C₂×C₄³×C₂₃	C₂	semidirect
123. C₄²×C₂₃	#41	semidirect
124. #36639	C₂₃	direct (N × H)
147. C₂×C₄×C₂₃	#124	semidirect
156. C₂×#533	C₂×C₂₃	semidirect
158. #2862	C₂×C₂₃	semidirect
159. #2861	C₂×C₂₃	semidirect
160. #2858	C₂×C₂₃	semidirect
161. #2850	C₂×C₂₃	semidirect
162. C₄×#124	C₂×C₂₃	semidirect
163. #2297	C₂×C₂₃	semidirect
164. C₂×C₄³	C₂×C₂₃	semidirect
256. C₂₃	#36639	direct (N × H)
300. C₄²	#41×C₂₃	semidirect
323. C₂×C₄	C₂₃×#124	semidirect

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×#2862	2
C₂₃×#2861	2
C₂₃×#2858	2
C₂₃×#2850	2
C₄×C₂₃×#124	2
C₂₃×#2297	2
C₂×C₄³×C₂₃	2
#36639	23

Subgroups — C23×#36639 #19184265

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#36639 #19184265