Subgroups — C₂×C₂₃×#3138 #19208239

Order 5888.

2806 conjugacy classes of subgroups.

The subgroup lattice has 338 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	C₂²×C₂₃×#127	C₂	1	1	yes	maximal, characteristic
3	C₂₃×#3138	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₂₃×#490	C₂	1	4	yes	maximal, complemented
5	C₂×C₂₃×#486	C₂	1	4	yes	maximal, complemented
6	C₂×C₂₃×#418	C₂	1	4	yes	maximal, complemented
7	C₂×C₄×M₁₆×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂³×D₄×C₂₃	—	2	2	no	—
9	C₂³×D₄×C₂₃	C₂²	1	2	yes	—
10	C₂²×M₁₆×C₂₃	C₂²	1	2	yes	—
11	C₂₃×#533	—	2	4	no	—
12	C₂₃×#533	C₂²	1	8	yes	complemented
13	C₂×C₂₃×C₄⋊Q₈	C₂²	1	2	yes	complemented
14	C₂×C₂₃×#127	—	2	2	no	—
15	C₂×C₂₃×#127	—	2	4	no	—
16	C₂×C₂₃×#127	C₂²	1	2	yes	—
17	C₂×C₂₃×#127	C₂²	1	2	yes	—
18	C₂×C₂₃×#127	C₂²	1	8	yes	—
19	C₂×C₂₃×#125	C₂²	1	2	yes	complemented
20	C₂×C₂₃×C₂²⋊Q₈	—	2	2	no	—
21	C₂×C₄×Q₈×C₂₃	—	2	2	no	—
22	C₂×C₂₃×#117	C₂²	1	2	yes	—
23	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
24	C₂₃×#490	C₂²	1	32	yes	complemented
25	C₂₃×#486	C₂²	1	32	yes	complemented
26	C₂₃×#418	C₂²	1	32	yes	complemented
27	C₂×C₂₃×#102	C₂²	1	16	yes	complemented
28	C₄×M₁₆×C₂₃	C₂²	1	8	yes	complemented
29	C₂×C₂₃×#97	C₂²	1	2	yes	complemented
30	C₂×C₄×C₈×C₂₃	C₂²	1	2	yes	complemented
31	C₂⁵×C₂₃	—	2	2	no	—
32	C₂²×Q₈×C₂₃	—	2	2	no	—
33	C₂²×D₄×C₂₃	—	2	16	no	—
34	C₂²×D₄×C₂₃	—	2	4	no	—
35	C₂²×D₄×C₂₃	—	2	4	no	—
36	C₂²×D₄×C₂₃	—	2	4	no	—
37	C₂²×D₄×C₂₃	—	2	2	no	—
38	C₂²×D₄×C₂₃	—	2	16	no	—
39	C₂²×D₄×C₂₃	—	4	16	no	—
40	C₂²×D₄×C₂₃	C₂³	1	4	yes	—
41	C₂²×D₄×C₂₃	C₂³	1	8	yes	—
42	C₂³×C₄×C₂₃	D₄	1	2	yes	—
43	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
44	C₂×M₁₆×C₂₃	—	2	8	no	—
45	C₂×M₁₆×C₂₃	C₂³	1	8	yes	—
46	C₂²×C₈×C₂₃	C₂³	1	4	yes	—
47	C₂₃×C₄⋊Q₈	—	2	4	no	—
48	C₂₃×C₄⋊Q₈	C₂³	1	8	yes	complemented
49	C₂₃×#127	—	2	16	no	—
50	C₂₃×#127	—	2	4	no	—
51	C₂₃×#127	—	2	4	no	—
52	C₂₃×#127	C₂³	1	8	yes	—
53	C₂₃×#127	C₂³	1	8	yes	—
54	C₂₃×#125	—	2	4	no	—
55	C₂₃×#125	C₂³	1	8	yes	complemented
56	C₂₃×C₂²⋊Q₈	—	2	16	no	—
57	C₄×Q₈×C₂₃	—	2	16	no	—
58	C₂₃×#117	—	2	4	no	—
59	C₂₃×#117	C₂³	1	8	yes	—
60	C₂×C₄⋊C₄×C₂₃	—	2	4	no	—
61	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
62	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
63	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
64	C₂×C₄²×C₂₃	—	2	2	no	—
65	C₂×C₄²×C₂₃	D₄	1	2	yes	—
66	C₂×C₄²×C₂₃	D₄	1	4	yes	—
67	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
68	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
69	C₂×C₄²×C₂₃	C₂³	1	4	yes	—
70	C₂₃×#102	C₂³	1	64	yes	complemented
71	C₂₃×#97	C₂³	1	8	yes	complemented
72	C₄×C₈×C₂₃	C₂³	1	8	yes	complemented
73	C₂⁴×C₂₃	—	2	8	no	—
74	C₂⁴×C₂₃	—	2	4	no	—
75	C₂⁴×C₂₃	—	4	16	no	—
76	C₂⁴×C₂₃	—	4	8	no	—
77	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
78	C₂×Q₈×C₂₃	—	2	8	no	—
79	C₂×Q₈×C₂₃	—	4	8	no	—
80	C₂×D₄×C₂₃	—	2	8	no	—
81	C₂×D₄×C₂₃	—	2	4	no	—
82	C₂×D₄×C₂₃	—	2	16	no	—
83	C₂×D₄×C₂₃	—	2	16	no	—
84	C₂×D₄×C₂₃	—	2	16	no	—
85	C₂×D₄×C₂₃	—	2	32	no	—
86	C₂×D₄×C₂₃	—	4	16	no	—
87	C₂×D₄×C₂₃	—	4	64	no	—
88	C₂×D₄×C₂₃	—	4	16	no	—
89	C₂×D₄×C₂₃	—	4	8	no	—
90	C₂×D₄×C₂₃	—	4	16	no	—
91	C₂×D₄×C₂₃	C₂⁴	1	8	yes	—
92	C₂²×C₄×C₂₃	—	2	8	no	—
93	C₂²×C₄×C₂₃	—	2	4	no	—
94	C₂²×C₄×C₂₃	C₂×D₄	1	8	yes	—
95	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
96	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
97	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
99	C₂²×C₄×C₂₃	#41	1	8	yes	—
100	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
101	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
102	M₁₆×C₂₃	—	2	16	no	—
103	C₂×C₈×C₂₃	—	2	8	no	—
104	C₂×C₈×C₂₃	C₂⁴	1	8	yes	—
105	C₄⋊C₄×C₂₃	—	2	16	no	—
106	C₄⋊C₄×C₂₃	—	2	8	no	—
107	C₄⋊C₄×C₂₃	—	2	4	no	—
108	C₄⋊C₄×C₂₃	C₂⁴	1	8	yes	—
109	C₂²⋊C₄×C₂₃	—	2	8	no	—
110	C₄²×C₂₃	—	2	8	no	—
111	C₄²×C₂₃	C₂×D₄	1	8	yes	—
112	C₄²×C₂₃	C₂×D₄	1	2	yes	—
113	C₄²×C₂₃	C₂×D₄	1	2	yes	—
114	C₄²×C₂₃	C₂⁴	1	2	yes	—
115	C₄²×C₂₃	C₂⁴	1	2	yes	—
116	C₂×#3138	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
117	C₂³×C₂₃	—	2	4	no	—
118	C₂³×C₂₃	—	2	8	no	—
119	C₂³×C₂₃	—	4	32	no	—
120	C₂³×C₂₃	—	4	16	no	—
121	C₂³×C₂₃	—	4	8	no	—
122	C₂³×C₂₃	—	4	16	no	—
123	C₂³×C₂₃	—	8	32	no	—
124	C₂³×C₂₃	#124	1	4	yes	—
125	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
126	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
127	Q₈×C₂₃	—	4	16	no	—
128	D₄×C₂₃	—	2	16	no	—
129	D₄×C₂₃	—	4	32	no	—
130	D₄×C₂₃	—	4	16	no	—
131	D₄×C₂₃	—	4	8	no	—
132	D₄×C₂₃	—	4	32	no	—
133	C₂×C₄×C₂₃	—	2	4	no	—
134	C₂×C₄×C₂₃	—	2	16	no	—
135	C₂×C₄×C₂₃	—	2	8	no	—
136	C₂×C₄×C₂₃	—	4	8	no	—
137	C₂×C₄×C₂₃	#124	1	8	yes	—
138	C₂×C₄×C₂₃	#124	1	4	yes	—
139	C₂×C₄×C₂₃	AGL(1,ℤ/8)	1	8	yes	—
140	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
141	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
142	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
143	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
144	C₂×C₄×C₂₃	C₂×#41	1	4	yes	—
145	C₂×C₄×C₂₃	C₂×#41	1	8	yes	—
146	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
147	C₈×C₂₃	—	2	8	no	—
148	C₂×#533	C₂×C₂₃	1	1	yes	characteristic, complemented
149	C₂²×#127	C₂×C₂₃	1	1	yes	characteristic
150	#3138	C₂×C₂₃	1	16	yes	direct product factor
151	C₂×#490	C₂×C₂₃	1	4	yes	complemented
152	C₂×#486	C₂×C₂₃	1	4	yes	complemented
153	C₂×#418	C₂×C₂₃	1	4	yes	complemented
154	C₂×C₄×M₁₆	C₂×C₂₃	1	1	yes	characteristic, complemented
155	C₂²×C₂₃	—	2	8	no	—
156	C₂²×C₂₃	—	2	4	no	—
157	C₂²×C₂₃	—	4	8	no	—
158	C₂²×C₂₃	—	4	16	no	—
159	C₂²×C₂₃	—	8	32	no	—
160	C₂²×C₂₃	—	8	16	no	—
161	C₂²×C₂₃	C₂×#124	1	4	yes	—
162	C₂²×C₂₃	C₂×#124	1	2	yes	—
163	C₂²×C₂₃	C₂×AGL(1,ℤ/8)	1	4	yes	—
164	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
165	C₄×C₂₃	—	2	4	no	—
166	C₄×C₂₃	—	4	8	no	—
167	C₄×C₂₃	C₂×#124	1	4	yes	—
168	C₄×C₂₃	C₂×#124	1	2	yes	—
169	C₄×C₂₃	C₂×AGL(1,ℤ/8)	1	8	yes	—
170	C₄×C₂₃	C₂²×#41	1	2	yes	—
171	C₂³×D₄	—	2	2	no	—
172	C₂³×D₄	C₂²×C₂₃	1	2	yes	—
173	C₂²×M₁₆	C₂²×C₂₃	1	2	yes	—
174	#533	—	2	4	no	—
175	#533	C₂²×C₂₃	1	8	yes	complemented
176	C₂×C₄⋊Q₈	C₂²×C₂₃	1	2	yes	complemented
177	C₂×#127	—	2	2	no	—
178	C₂×#127	—	2	4	no	—
179	C₂×#127	C₂²×C₂₃	1	2	yes	—
180	C₂×#127	C₂²×C₂₃	1	2	yes	—
181	C₂×#127	C₂²×C₂₃	1	8	yes	—
182	C₂×#125	C₂²×C₂₃	1	2	yes	complemented
183	C₂×C₂²⋊Q₈	—	2	2	no	—
184	C₂×C₄×Q₈	—	2	2	no	—
185	C₂×#117	C₂²×C₂₃	1	2	yes	—
186	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
187	#490	C₂²×C₂₃	1	32	yes	complemented
188	#486	C₂²×C₂₃	1	32	yes	complemented
189	#418	C₂²×C₂₃	1	32	yes	complemented
190	C₂×#102	C₂²×C₂₃	1	16	yes	complemented
191	C₄×M₁₆	C₂²×C₂₃	1	8	yes	complemented
192	C₂×#97	C₂²×C₂₃	1	2	yes	complemented
193	C₂×C₄×C₈	C₂²×C₂₃	1	2	yes	complemented
194	C₂×C₂₃	—	2	4	no	—
195	C₂×C₂₃	—	8	8	no	—
196	C₂×C₂₃	#3138	1	4	yes	direct product factor
197	C₂×C₂₃	C₂²×#124	1	1	yes	characteristic
198	C₂×C₂₃	C₂²×AGL(1,ℤ/8)	1	2	yes	—
199	C₂⁵	—	2	2	no	—
200	C₂²×Q₈	—	2	2	no	—
201	C₂²×D₄	—	2	2	no	—
202	C₂²×D₄	—	2	4	no	—
203	C₂²×D₄	—	2	4	no	—
204	C₂²×D₄	—	2	16	no	—
205	C₂²×D₄	—	2	4	no	—
206	C₂²×D₄	—	2	16	no	—
207	C₂²×D₄	—	4	16	no	—
208	C₂²×D₄	C₂³×C₂₃	1	4	yes	—
209	C₂²×D₄	C₂³×C₂₃	1	8	yes	—
210	C₂³×C₄	D₄×C₂₃	1	2	yes	—
211	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
212	C₂×M₁₆	—	2	8	no	—
213	C₂×M₁₆	C₂³×C₂₃	1	8	yes	—
214	C₂²×C₈	C₂³×C₂₃	1	4	yes	—
215	C₄⋊Q₈	—	2	4	no	—
216	C₄⋊Q₈	C₂³×C₂₃	1	8	yes	complemented
217	#127	—	2	16	no	—
218	#127	—	2	4	no	—
219	#127	—	2	4	no	—
220	#127	C₂³×C₂₃	1	8	yes	—
221	#127	C₂³×C₂₃	1	8	yes	—
222	#125	—	2	4	no	—
223	#125	C₂³×C₂₃	1	8	yes	complemented
224	C₂²⋊Q₈	—	2	16	no	—
225	C₄×Q₈	—	2	16	no	—
226	#117	—	2	4	no	—
227	#117	C₂³×C₂₃	1	8	yes	—
228	C₂×C₄⋊C₄	—	2	4	no	—
229	C₂×C₄⋊C₄	—	2	2	no	—
230	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
231	C₂×C₂²⋊C₄	—	2	2	no	—
232	C₂×C₄²	—	2	2	no	—
233	C₂×C₄²	D₄×C₂₃	1	2	yes	—
234	C₂×C₄²	D₄×C₂₃	1	4	yes	—
235	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
236	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
237	C₂×C₄²	C₂³×C₂₃	1	4	yes	—
238	#102	C₂³×C₂₃	1	64	yes	complemented
239	#97	C₂³×C₂₃	1	8	yes	complemented
240	C₄×C₈	C₂³×C₂₃	1	8	yes	complemented
241	C₂₃	C₂×#3138	1	1	yes	characteristic, direct product factor, Sylow
242	C₂⁴	—	2	8	no	—
243	C₂⁴	—	2	4	no	—
244	C₂⁴	—	4	16	no	—
245	C₂⁴	—	4	8	no	—
246	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
247	C₂×Q₈	—	2	8	no	—
248	C₂×Q₈	—	4	8	no	—
249	C₂×D₄	—	2	8	no	—
250	C₂×D₄	—	2	4	no	—
251	C₂×D₄	—	2	16	no	—
252	C₂×D₄	—	2	16	no	—
253	C₂×D₄	—	2	16	no	—
254	C₂×D₄	—	2	32	no	—
255	C₂×D₄	—	4	16	no	—
256	C₂×D₄	—	4	64	no	—
257	C₂×D₄	—	4	16	no	—
258	C₂×D₄	—	4	8	no	—
259	C₂×D₄	—	4	16	no	—
260	C₂×D₄	C₂⁴×C₂₃	1	8	yes	—
261	C₂²×C₄	—	2	8	no	—
262	C₂²×C₄	—	2	4	no	—
263	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
264	C₂²×C₄	C₂×D₄×C₂₃	1	8	yes	—
265	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
266	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
267	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
268	C₂²×C₄	#41×C₂₃	1	8	yes	—
269	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
270	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
271	M₁₆	—	2	16	no	—
272	C₂×C₈	—	2	8	no	—
273	C₂×C₈	C₂⁴×C₂₃	1	8	yes	—
274	C₄⋊C₄	—	2	16	no	—
275	C₄⋊C₄	—	2	8	no	—
276	C₄⋊C₄	—	2	4	no	—
277	C₄⋊C₄	C₂⁴×C₂₃	1	8	yes	—
278	C₂²⋊C₄	—	2	8	no	—
279	C₄²	—	2	8	no	—
280	C₄²	C₂×D₄×C₂₃	1	8	yes	—
281	C₄²	C₂×D₄×C₂₃	1	2	yes	—
282	C₄²	C₂×D₄×C₂₃	1	2	yes	—
283	C₄²	C₂⁴×C₂₃	1	2	yes	—
284	C₄²	C₂⁴×C₂₃	1	2	yes	—
285	C₂³	—	2	4	no	—
286	C₂³	—	2	8	no	—
287	C₂³	—	4	32	no	—
288	C₂³	—	4	16	no	—
289	C₂³	—	4	16	no	—
290	C₂³	—	4	8	no	—
291	C₂³	—	8	32	no	—
292	C₂³	C₂₃×#124	1	4	yes	—
293	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
294	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
295	Q₈	—	4	16	no	—
296	D₄	—	2	16	no	—
297	D₄	—	4	32	no	—
298	D₄	—	4	32	no	—
299	D₄	—	4	16	no	—
300	D₄	—	4	8	no	—
301	C₂×C₄	—	2	4	no	—
302	C₂×C₄	—	2	16	no	—
303	C₂×C₄	—	2	8	no	—
304	C₂×C₄	—	4	8	no	—
305	C₂×C₄	C₂₃×#124	1	8	yes	—
306	C₂×C₄	C₂₃×#124	1	4	yes	—
307	C₂×C₄	C₂₃×AGL(1,ℤ/8)	1	8	yes	—
308	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
309	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
310	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
311	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
312	C₂×C₄	C₂×#41×C₂₃	1	4	yes	—
313	C₂×C₄	C₂×#41×C₂₃	1	8	yes	—
314	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
315	C₈	—	2	8	no	—
316	C₂²	—	2	4	no	—
317	C₂²	—	2	8	no	—
318	C₂²	—	4	8	no	—
319	C₂²	—	4	16	no	—
320	C₂²	—	8	32	no	—
321	C₂²	—	8	16	no	—
322	C₂²	C₂×C₂₃×#124	1	4	yes	—
323	C₂²	C₂×C₂₃×#124	1	2	yes	—
324	C₂²	C₂×C₂₃×AGL(1,ℤ/8)	1	4	yes	—
325	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
326	C₄	—	2	4	no	—
327	C₄	—	4	8	no	—
328	C₄	C₂×C₂₃×#124	1	4	yes	—
329	C₄	C₂×C₂₃×#124	1	2	yes	—
330	C₄	C₂×C₂₃×AGL(1,ℤ/8)	1	8	yes	—
331	C₄	C₂²×#41×C₂₃	1	2	yes	—
332	C₂	—	2	4	no	—
333	C₂	—	8	8	no	—
334	C₂	C₂₃×#3138	1	4	yes	direct product factor
335	C₂	C₂²×C₂₃×#124	1	1	yes	characteristic
336	C₂	C₂²×C₂₃×AGL(1,ℤ/8)	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
prime radical	C₂²×C₂₃×#127	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
1. C₂×C₂₃×#533	C₂	semidirect
3. C₂₃×#3138	C₂	direct (N × H)
4. C₂×C₂₃×#490	C₂	semidirect
5. C₂×C₂₃×#486	C₂	semidirect
6. C₂×C₂₃×#418	C₂	semidirect
7. C₂×C₄×M₁₆×C₂₃	C₂	semidirect
12. C₂₃×#533	C₂²	semidirect
13. C₂×C₂₃×C₄⋊Q₈	C₂²	semidirect
19. C₂×C₂₃×#125	C₂²	semidirect
24. C₂₃×#490	C₂²	semidirect
25. C₂₃×#486	C₂²	semidirect
26. C₂₃×#418	C₂²	semidirect
27. C₂×C₂₃×#102	C₂²	semidirect
28. C₄×M₁₆×C₂₃	C₂²	semidirect
29. C₂×C₂₃×#97	C₂²	semidirect
30. C₂×C₄×C₈×C₂₃	C₂²	semidirect
48. C₂₃×C₄⋊Q₈	C₂³	semidirect
55. C₂₃×#125	C₂³	semidirect
70. C₂₃×#102	C₂³	semidirect
71. C₂₃×#97	C₂³	semidirect
72. C₄×C₈×C₂₃	C₂³	semidirect
116. C₂×#3138	C₂₃	direct (N × H)
148. C₂×#533	C₂×C₂₃	semidirect
150. #3138	C₂×C₂₃	direct (N × H)
151. C₂×#490	C₂×C₂₃	semidirect
152. C₂×#486	C₂×C₂₃	semidirect
153. C₂×#418	C₂×C₂₃	semidirect
154. C₂×C₄×M₁₆	C₂×C₂₃	semidirect
175. #533	C₂²×C₂₃	semidirect
176. C₂×C₄⋊Q₈	C₂²×C₂₃	semidirect
182. C₂×#125	C₂²×C₂₃	semidirect
187. #490	C₂²×C₂₃	semidirect
188. #486	C₂²×C₂₃	semidirect
189. #418	C₂²×C₂₃	semidirect
190. C₂×#102	C₂²×C₂₃	semidirect
191. C₄×M₁₆	C₂²×C₂₃	semidirect
192. C₂×#97	C₂²×C₂₃	semidirect
193. C₂×C₄×C₈	C₂²×C₂₃	semidirect
196. C₂×C₂₃	#3138	direct (N × H)
216. C₄⋊Q₈	C₂³×C₂₃	semidirect
223. #125	C₂³×C₂₃	semidirect
238. #102	C₂³×C₂₃	semidirect
239. #97	C₂³×C₂₃	semidirect
240. C₄×C₈	C₂³×C₂₃	semidirect
241. C₂₃	C₂×#3138	direct (N × H)
334. C₂	C₂₃×#3138	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
C₂²×C₂₃×#127	2
C₂₃×#3138	2
C₂×C₂₃×#490	2
C₂×C₂₃×#486	2
C₂×C₂₃×#418	2
C₂×C₄×M₁₆×C₂₃	2
C₂×#3138	23

Subgroups — C2×C23×#3138 #19208239

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₃×#3138 #19208239