Subgroups — C₂²×C₂₃×#459 #19208029

Order 5888.

3910 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×D₈×C₂₃	C₂	1	2	yes	maximal, complemented
2	C₂²×C₂₃×#127	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₄×D₄×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₂₃×#459	C₂	1	24	yes	maximal, direct product factor
5	C₂²×C₂₃×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₂₃×#102	C₂	1	2	yes	maximal, complemented
7	C₂³×D₄×C₂₃	—	2	1	no	—
8	C₂³×D₄×C₂₃	—	2	1	no	—
9	C₂³×D₄×C₂₃	C₂²	1	2	yes	—
10	C₂³×D₄×C₂₃	C₂²	1	1	yes	characteristic
11	C₂⁴×C₄×C₂₃	—	2	1	no	—
12	C₂²×D₈×C₂₃	—	2	16	no	—
13	C₂²×D₈×C₂₃	C₂²	1	24	yes	complemented
14	C₂³×C₈×C₂₃	C₂²	1	2	yes	—
15	C₂×C₂₃×#127	—	2	6	no	—
16	C₂×C₂₃×#127	C₂²	1	12	yes	complemented
17	C₂×C₄×D₄×C₂₃	—	2	6	no	—
18	C₂×C₄×D₄×C₂₃	C₂²	1	12	yes	complemented
19	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
20	C₂²×C₂²⋊C₄×C₂₃	—	2	1	no	—
21	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
22	C₂₃×#459	C₂²	1	64	yes	direct product factor
23	C₂×C₂₃×C₄⋊C₈	C₂²	1	12	yes	complemented
24	C₂×C₂₃×#102	C₂²	1	24	yes	complemented
25	C₂⁵×C₂₃	—	2	1	no	—
26	C₂⁵×C₂₃	—	2	2	no	—
27	C₂²×D₄×C₂₃	—	2	3	no	—
28	C₂²×D₄×C₂₃	—	2	8	no	—
29	C₂²×D₄×C₂₃	—	2	12	no	—
30	C₂²×D₄×C₂₃	—	2	12	no	—
31	C₂²×D₄×C₂₃	—	2	6	no	—
32	C₂²×D₄×C₂₃	—	2	4	no	—
33	C₂²×D₄×C₂₃	—	2	8	no	—
34	C₂²×D₄×C₂₃	—	4	8	no	—
35	C₂²×D₄×C₂₃	—	4	8	no	—
36	C₂²×D₄×C₂₃	D₄	1	8	yes	complemented
37	C₂²×D₄×C₂₃	C₂³	1	12	yes	—
38	C₂²×D₄×C₂₃	C₂³	1	6	yes	—
39	C₂³×C₄×C₂₃	—	2	1	no	—
40	C₂³×C₄×C₂₃	—	2	12	no	—
41	C₂³×C₄×C₂₃	—	4	8	no	—
42	C₂³×C₄×C₂₃	D₄	1	1	yes	characteristic
43	C₂³×C₄×C₂₃	D₄	1	1	yes	characteristic
44	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
45	C₂×D₈×C₂₃	—	2	96	no	—
46	C₂×D₈×C₂₃	C₂³	1	32	yes	complemented
47	C₂²×C₈×C₂₃	—	2	8	no	—
48	C₂²×C₈×C₂₃	C₂³	1	12	yes	—
49	C₂₃×#127	—	2	24	no	—
50	C₂₃×#127	C₂³	1	16	yes	complemented
51	C₄×D₄×C₂₃	—	2	24	no	—
52	C₄×D₄×C₂₃	C₂³	1	16	yes	complemented
53	C₂×C₄⋊C₄×C₂₃	—	2	3	no	—
54	C₂×C₄⋊C₄×C₂₃	C₂³	1	6	yes	—
55	C₂×C₂²⋊C₄×C₂₃	—	2	12	no	—
56	C₂×C₄²×C₂₃	D₄	1	6	yes	—
57	C₂×C₄²×C₂₃	C₂³	1	6	yes	—
58	C₂₃×C₄⋊C₈	C₂³	1	16	yes	complemented
59	C₂₃×#102	C₂³	1	32	yes	complemented
60	C₂⁴×C₂₃	—	2	8	no	—
61	C₂⁴×C₂₃	—	2	6	no	—
62	C₂⁴×C₂₃	—	2	12	no	—
63	C₂⁴×C₂₃	—	4	4	no	—
64	C₂⁴×C₂₃	—	4	4	no	—
65	C₂⁴×C₂₃	—	4	8	no	—
66	C₂⁴×C₂₃	—	4	8	no	—
67	C₂⁴×C₂₃	—	4	8	no	—
68	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
69	C₂×D₄×C₂₃	—	2	24	no	—
70	C₂×D₄×C₂₃	—	2	6	no	—
71	C₂×D₄×C₂₃	—	2	24	no	—
72	C₂×D₄×C₂₃	—	2	12	no	—
73	C₂×D₄×C₂₃	—	2	16	no	—
74	C₂×D₄×C₂₃	—	2	16	no	—
75	C₂×D₄×C₂₃	—	2	12	no	—
76	C₂×D₄×C₂₃	—	2	24	no	—
77	C₂×D₄×C₂₃	—	4	48	no	—
78	C₂×D₄×C₂₃	—	4	24	no	—
79	C₂×D₄×C₂₃	—	4	48	no	—
80	C₂×D₄×C₂₃	C₂×D₄	1	24	yes	complemented
81	C₂×D₄×C₂₃	C₂⁴	1	8	yes	—
82	C₂×D₄×C₂₃	C₂⁴	1	4	yes	—
83	C₂²×C₄×C₂₃	—	2	4	no	—
84	C₂²×C₄×C₂₃	—	2	6	no	—
85	C₂²×C₄×C₂₃	—	2	16	no	—
86	C₂²×C₄×C₂₃	—	4	4	no	—
87	C₂²×C₄×C₂₃	—	4	48	no	—
88	C₂²×C₄×C₂₃	D₈	1	8	yes	complemented
89	C₂²×C₄×C₂₃	C₂×D₄	1	6	yes	—
90	C₂²×C₄×C₂₃	C₂×D₄	1	3	yes	—
91	C₂²×C₄×C₂₃	C₂×D₄	1	4	yes	—
92	C₂²×C₄×C₂₃	C₂×D₄	1	6	yes	—
93	C₂²×C₄×C₂₃	#41	1	4	yes	—
94	C₂²×C₄×C₂₃	C₂⁴	1	3	yes	—
95	D₈×C₂₃	—	2	64	no	—
96	C₂×C₈×C₂₃	—	2	24	no	—
97	C₂×C₈×C₂₃	C₂⁴	1	8	yes	—
98	C₄⋊C₄×C₂₃	—	2	6	no	—
99	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
100	C₂²⋊C₄×C₂₃	—	2	16	no	—
101	C₄²×C₂₃	C₂×D₄	1	12	yes	—
102	C₄²×C₂₃	C₂⁴	1	4	yes	—
103	C₂²×#459	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
104	C₂³×C₂₃	—	2	24	no	—
105	C₂³×C₂₃	—	2	4	no	—
106	C₂³×C₂₃	—	2	8	no	—
107	C₂³×C₂₃	—	4	12	no	—
108	C₂³×C₂₃	—	4	12	no	—
109	C₂³×C₂₃	—	4	32	no	—
110	C₂³×C₂₃	—	4	24	no	—
111	C₂³×C₂₃	—	4	24	no	—
112	C₂³×C₂₃	—	4	24	no	—
113	C₂³×C₂₃	—	8	32	no	—
114	C₂³×C₂₃	#121	1	4	yes	—
115	C₂³×C₂₃	C₂×D₈	1	4	yes	—
116	C₂³×C₂₃	AGL(1,ℤ/8)	1	4	yes	—
117	C₂³×C₂₃	C₂²×D₄	1	3	yes	—
118	D₄×C₂₃	—	2	24	no	—
119	D₄×C₂₃	—	2	8	no	—
120	D₄×C₂₃	—	2	4	no	—
121	D₄×C₂₃	—	2	8	no	—
122	D₄×C₂₃	—	4	32	no	—
123	D₄×C₂₃	—	4	24	no	—
124	D₄×C₂₃	—	4	32	no	—
125	D₄×C₂₃	C₂²×D₄	1	8	yes	complemented
126	C₂×C₄×C₂₃	—	2	12	no	—
127	C₂×C₄×C₂₃	—	2	4	no	—
128	C₂×C₄×C₂₃	—	4	12	no	—
129	C₂×C₄×C₂₃	—	4	32	no	—
130	C₂×C₄×C₂₃	#121	1	12	yes	—
131	C₂×C₄×C₂₃	C₂×D₈	1	24	yes	complemented
132	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
133	C₂×C₄×C₂₃	C₂²×D₄	1	3	yes	—
134	C₂×C₄×C₂₃	C₂²×D₄	1	6	yes	—
135	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
136	C₂×C₄×C₂₃	C₂×#41	1	6	yes	—
137	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
138	C₈×C₂₃	—	2	8	no	—
139	C₂³×D₈	C₂×C₂₃	1	2	yes	complemented
140	C₂²×#127	C₂×C₂₃	1	1	yes	characteristic, complemented
141	C₂²×C₄×D₄	C₂×C₂₃	1	1	yes	characteristic, complemented
142	C₂×#459	C₂×C₂₃	1	24	yes	direct product factor
143	C₂²×C₄⋊C₈	C₂×C₂₃	1	1	yes	characteristic, complemented
144	C₂²×#102	C₂×C₂₃	1	2	yes	complemented
145	C₂²×C₂₃	—	2	8	no	—
146	C₂²×C₂₃	—	4	48	no	—
147	C₂²×C₂₃	—	4	4	no	—
148	C₂²×C₂₃	—	4	4	no	—
149	C₂²×C₂₃	—	4	8	no	—
150	C₂²×C₂₃	—	4	8	no	—
151	C₂²×C₂₃	—	4	8	no	—
152	C₂²×C₂₃	—	8	48	no	—
153	C₂²×C₂₃	#459	1	16	yes	direct product factor
154	C₂²×C₂₃	C₂×#121	1	6	yes	—
155	C₂²×C₂₃	C₂²×D₈	1	6	yes	—
156	C₂²×C₂₃	C₂×AGL(1,ℤ/8)	1	6	yes	—
157	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
158	C₄×C₂₃	—	2	4	no	—
159	C₄×C₂₃	—	4	4	no	—
160	C₄×C₂₃	C₂×#121	1	6	yes	—
161	C₄×C₂₃	C₂²×D₈	1	8	yes	complemented
162	C₄×C₂₃	C₂³×D₄	1	1	yes	characteristic
163	C₄×C₂₃	C₂²×#41	1	1	yes	characteristic
164	C₂³×D₄	—	2	1	no	—
165	C₂³×D₄	—	2	1	no	—
166	C₂³×D₄	C₂²×C₂₃	1	2	yes	—
167	C₂³×D₄	C₂²×C₂₃	1	1	yes	characteristic
168	C₂⁴×C₄	—	2	1	no	—
169	C₂²×D₈	—	2	16	no	—
170	C₂²×D₈	C₂²×C₂₃	1	24	yes	complemented
171	C₂³×C₈	C₂²×C₂₃	1	2	yes	—
172	C₂×#127	—	2	6	no	—
173	C₂×#127	C₂²×C₂₃	1	12	yes	complemented
174	C₂×C₄×D₄	—	2	6	no	—
175	C₂×C₄×D₄	C₂²×C₂₃	1	12	yes	complemented
176	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
177	C₂²×C₂²⋊C₄	—	2	1	no	—
178	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
179	#459	C₂²×C₂₃	1	64	yes	direct product factor
180	C₂×C₄⋊C₈	C₂²×C₂₃	1	12	yes	complemented
181	C₂×#102	C₂²×C₂₃	1	24	yes	complemented
182	C₂×C₂₃	—	4	8	no	—
183	C₂×C₂₃	—	8	8	no	—
184	C₂×C₂₃	C₂×#459	1	12	yes	direct product factor
185	C₂×C₂₃	C₂²×#121	1	1	yes	characteristic
186	C₂×C₂₃	C₂³×D₈	1	1	yes	characteristic
187	C₂×C₂₃	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
188	C₂⁵	—	2	1	no	—
189	C₂⁵	—	2	2	no	—
190	C₂²×D₄	—	2	3	no	—
191	C₂²×D₄	—	2	8	no	—
192	C₂²×D₄	—	2	6	no	—
193	C₂²×D₄	—	2	12	no	—
194	C₂²×D₄	—	2	12	no	—
195	C₂²×D₄	—	2	4	no	—
196	C₂²×D₄	—	2	8	no	—
197	C₂²×D₄	—	4	8	no	—
198	C₂²×D₄	—	4	8	no	—
199	C₂²×D₄	D₄×C₂₃	1	8	yes	complemented
200	C₂²×D₄	C₂³×C₂₃	1	12	yes	—
201	C₂²×D₄	C₂³×C₂₃	1	6	yes	—
202	C₂³×C₄	—	2	1	no	—
203	C₂³×C₄	—	2	12	no	—
204	C₂³×C₄	—	4	8	no	—
205	C₂³×C₄	D₄×C₂₃	1	1	yes	characteristic
206	C₂³×C₄	D₄×C₂₃	1	1	yes	characteristic
207	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
208	C₂×D₈	—	2	96	no	—
209	C₂×D₈	C₂³×C₂₃	1	32	yes	complemented
210	C₂²×C₈	—	2	8	no	—
211	C₂²×C₈	C₂³×C₂₃	1	12	yes	—
212	#127	—	2	24	no	—
213	#127	C₂³×C₂₃	1	16	yes	complemented
214	C₄×D₄	—	2	24	no	—
215	C₄×D₄	C₂³×C₂₃	1	16	yes	complemented
216	C₂×C₄⋊C₄	—	2	3	no	—
217	C₂×C₄⋊C₄	C₂³×C₂₃	1	6	yes	—
218	C₂×C₂²⋊C₄	—	2	12	no	—
219	C₂×C₄²	D₄×C₂₃	1	6	yes	—
220	C₂×C₄²	C₂³×C₂₃	1	6	yes	—
221	C₄⋊C₈	C₂³×C₂₃	1	16	yes	complemented
222	#102	C₂³×C₂₃	1	32	yes	complemented
223	C₂₃	C₂²×#459	1	1	yes	characteristic, direct product factor, Sylow
224	C₂⁴	—	2	8	no	—
225	C₂⁴	—	2	6	no	—
226	C₂⁴	—	2	12	no	—
227	C₂⁴	—	4	4	no	—
228	C₂⁴	—	4	4	no	—
229	C₂⁴	—	4	8	no	—
230	C₂⁴	—	4	8	no	—
231	C₂⁴	—	4	8	no	—
232	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
233	C₂×D₄	—	2	24	no	—
234	C₂×D₄	—	2	6	no	—
235	C₂×D₄	—	2	24	no	—
236	C₂×D₄	—	2	12	no	—
237	C₂×D₄	—	2	16	no	—
238	C₂×D₄	—	2	16	no	—
239	C₂×D₄	—	2	12	no	—
240	C₂×D₄	—	2	24	no	—
241	C₂×D₄	—	4	48	no	—
242	C₂×D₄	—	4	24	no	—
243	C₂×D₄	—	4	48	no	—
244	C₂×D₄	C₂×D₄×C₂₃	1	24	yes	complemented
245	C₂×D₄	C₂⁴×C₂₃	1	8	yes	—
246	C₂×D₄	C₂⁴×C₂₃	1	4	yes	—
247	C₂²×C₄	—	2	4	no	—
248	C₂²×C₄	—	2	6	no	—
249	C₂²×C₄	—	2	16	no	—
250	C₂²×C₄	—	4	4	no	—
251	C₂²×C₄	—	4	48	no	—
252	C₂²×C₄	D₈×C₂₃	1	8	yes	complemented
253	C₂²×C₄	C₂×D₄×C₂₃	1	6	yes	—
254	C₂²×C₄	C₂×D₄×C₂₃	1	3	yes	—
255	C₂²×C₄	C₂×D₄×C₂₃	1	4	yes	—
256	C₂²×C₄	C₂×D₄×C₂₃	1	6	yes	—
257	C₂²×C₄	#41×C₂₃	1	4	yes	—
258	C₂²×C₄	C₂⁴×C₂₃	1	3	yes	—
259	D₈	—	2	64	no	—
260	C₂×C₈	—	2	24	no	—
261	C₂×C₈	C₂⁴×C₂₃	1	8	yes	—
262	C₄⋊C₄	—	2	6	no	—
263	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
264	C₂²⋊C₄	—	2	16	no	—
265	C₄²	C₂×D₄×C₂₃	1	12	yes	—
266	C₄²	C₂⁴×C₂₃	1	4	yes	—
267	C₂³	—	2	4	no	—
268	C₂³	—	2	24	no	—
269	C₂³	—	2	8	no	—
270	C₂³	—	4	12	no	—
271	C₂³	—	4	12	no	—
272	C₂³	—	4	32	no	—
273	C₂³	—	4	24	no	—
274	C₂³	—	4	24	no	—
275	C₂³	—	4	24	no	—
276	C₂³	—	8	32	no	—
277	C₂³	C₂₃×#121	1	4	yes	—
278	C₂³	C₂×D₈×C₂₃	1	4	yes	—
279	C₂³	C₂₃×AGL(1,ℤ/8)	1	4	yes	—
280	C₂³	C₂²×D₄×C₂₃	1	3	yes	—
281	D₄	—	2	8	no	—
282	D₄	—	2	4	no	—
283	D₄	—	2	8	no	—
284	D₄	—	2	24	no	—
285	D₄	—	4	32	no	—
286	D₄	—	4	32	no	—
287	D₄	—	4	24	no	—
288	D₄	C₂²×D₄×C₂₃	1	8	yes	complemented
289	C₂×C₄	—	2	12	no	—
290	C₂×C₄	—	2	4	no	—
291	C₂×C₄	—	4	12	no	—
292	C₂×C₄	—	4	32	no	—
293	C₂×C₄	C₂₃×#121	1	12	yes	—
294	C₂×C₄	C₂×D₈×C₂₃	1	24	yes	complemented
295	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
296	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
297	C₂×C₄	C₂²×D₄×C₂₃	1	6	yes	—
298	C₂×C₄	C₂²×D₄×C₂₃	1	3	yes	—
299	C₂×C₄	C₂×#41×C₂₃	1	6	yes	—
300	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
301	C₈	—	2	8	no	—
302	C₂²	—	2	8	no	—
303	C₂²	—	4	48	no	—
304	C₂²	—	4	4	no	—
305	C₂²	—	4	4	no	—
306	C₂²	—	4	8	no	—
307	C₂²	—	4	8	no	—
308	C₂²	—	4	8	no	—
309	C₂²	—	8	48	no	—
310	C₂²	C₂₃×#459	1	16	yes	direct product factor
311	C₂²	C₂×C₂₃×#121	1	6	yes	—
312	C₂²	C₂²×D₈×C₂₃	1	6	yes	—
313	C₂²	C₂×C₂₃×AGL(1,ℤ/8)	1	6	yes	—
314	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
315	C₄	—	2	4	no	—
316	C₄	—	4	4	no	—
317	C₄	C₂×C₂₃×#121	1	6	yes	—
318	C₄	C₂²×D₈×C₂₃	1	8	yes	complemented
319	C₄	C₂³×D₄×C₂₃	1	1	yes	characteristic
320	C₄	C₂²×#41×C₂₃	1	1	yes	characteristic
321	C₂	—	4	8	no	—
322	C₂	—	8	8	no	—
323	C₂	C₂×C₂₃×#459	1	12	yes	direct product factor
324	C₂	C₂²×C₂₃×#121	1	1	yes	characteristic
325	C₂	C₂³×D₈×C₂₃	1	1	yes	characteristic
326	C₂	C₂²×C₂₃×AGL(1,ℤ/8)	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₂₃	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₂₃ ◁ C₂²×C₄²×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂³×D₈×C₂₃	C₂	semidirect
2. C₂²×C₂₃×#127	C₂	semidirect
3. C₂²×C₄×D₄×C₂₃	C₂	semidirect
4. C₂×C₂₃×#459	C₂	direct (N × H)
5. C₂²×C₂₃×C₄⋊C₈	C₂	semidirect
6. C₂²×C₂₃×#102	C₂	semidirect
13. C₂²×D₈×C₂₃	C₂²	semidirect
16. C₂×C₂₃×#127	C₂²	semidirect
18. C₂×C₄×D₄×C₂₃	C₂²	semidirect
22. C₂₃×#459	C₂²	direct (N × H)
23. C₂×C₂₃×C₄⋊C₈	C₂²	semidirect
24. C₂×C₂₃×#102	C₂²	semidirect
36. C₂²×D₄×C₂₃	D₄	semidirect
46. C₂×D₈×C₂₃	C₂³	semidirect
50. C₂₃×#127	C₂³	semidirect
52. C₄×D₄×C₂₃	C₂³	semidirect
58. C₂₃×C₄⋊C₈	C₂³	semidirect
59. C₂₃×#102	C₂³	semidirect
80. C₂×D₄×C₂₃	C₂×D₄	semidirect
88. C₂²×C₄×C₂₃	D₈	semidirect
103. C₂²×#459	C₂₃	direct (N × H)
125. D₄×C₂₃	C₂²×D₄	semidirect
131. C₂×C₄×C₂₃	C₂×D₈	semidirect
139. C₂³×D₈	C₂×C₂₃	semidirect
140. C₂²×#127	C₂×C₂₃	semidirect
141. C₂²×C₄×D₄	C₂×C₂₃	semidirect
142. C₂×#459	C₂×C₂₃	direct (N × H)
143. C₂²×C₄⋊C₈	C₂×C₂₃	semidirect
144. C₂²×#102	C₂×C₂₃	semidirect
153. C₂²×C₂₃	#459	direct (N × H)
161. C₄×C₂₃	C₂²×D₈	semidirect
170. C₂²×D₈	C₂²×C₂₃	semidirect
173. C₂×#127	C₂²×C₂₃	semidirect
175. C₂×C₄×D₄	C₂²×C₂₃	semidirect
179. #459	C₂²×C₂₃	direct (N × H)
180. C₂×C₄⋊C₈	C₂²×C₂₃	semidirect
181. C₂×#102	C₂²×C₂₃	semidirect
184. C₂×C₂₃	C₂×#459	direct (N × H)
199. C₂²×D₄	D₄×C₂₃	semidirect
209. C₂×D₈	C₂³×C₂₃	semidirect
213. #127	C₂³×C₂₃	semidirect
215. C₄×D₄	C₂³×C₂₃	semidirect
221. C₄⋊C₈	C₂³×C₂₃	semidirect
222. #102	C₂³×C₂₃	semidirect
223. C₂₃	C₂²×#459	direct (N × H)
244. C₂×D₄	C₂×D₄×C₂₃	semidirect
252. C₂²×C₄	D₈×C₂₃	semidirect
288. D₄	C₂²×D₄×C₂₃	semidirect
294. C₂×C₄	C₂×D₈×C₂₃	semidirect
310. C₂²	C₂₃×#459	direct (N × H)
318. C₄	C₂²×D₈×C₂₃	semidirect
323. C₂	C₂×C₂₃×#459	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂³×D₈×C₂₃	2
C₂²×C₂₃×#127	2
C₂²×C₄×D₄×C₂₃	2
C₂×C₂₃×#459	2
C₂²×C₂₃×C₄⋊C₈	2
C₂²×C₂₃×#102	2
C₂²×#459	23

Subgroups — C22×C23×#459 #19208029

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₂₃×#459 #19208029