Subgroups — C₂₃×#34381 #19182007

Order 5888.

2134 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₂₃×#126	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#2383	C₂	1	4	yes	maximal, complemented
3	C₂₃×#2373	C₂	1	4	yes	maximal, complemented
4	C₂₃×#2345	C₂	1	2	yes	maximal, complemented
5	C₂₃×#2344	C₂	1	2	yes	maximal, complemented
6	C₂₃×#2342	C₂	1	2	yes	maximal
7	C₂₃×#2342	C₂	1	2	yes	maximal
8	C₂₃×#2334	C₂	1	4	yes	maximal, complemented
9	C₂₃×#2334	C₂	1	4	yes	maximal, complemented
10	C₂₃×#2316	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#2315	C₂	1	1	yes	maximal, characteristic
12	C₂₃×#2313	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#2312	C₂	1	1	yes	maximal, characteristic
14	C₂₃×#2285	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#2283	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₂₃×#126	C₄	1	16	yes	complemented
17	C₂×C₂₃×#126	C₂²	1	2	yes	—
18	C₂×C₂₃×#126	C₂²	1	2	yes	—
19	C₂×C₂₃×#126	C₂²	1	2	yes	—
20	C₂×C₂₃×#126	C₂²	1	2	yes	—
21	C₂×C₂₃×#117	C₂²	1	2	yes	—
22	C₂×C₂₃×#117	C₂²	1	2	yes	—
23	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
24	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
25	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
26	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
27	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
28	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
29	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
30	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
31	C₂₃×#389	C₂²	1	4	yes	complemented
32	C₂₃×#389	C₂²	1	4	yes	complemented
33	C₂₃×#389	C₂²	1	4	yes	complemented
34	C₂₃×#389	C₂²	1	4	yes	complemented
35	C₂₃×#388	C₂²	1	4	yes	—
36	C₂₃×#388	C₂²	1	4	yes	—
37	C₂₃×#388	C₂²	1	4	yes	—
38	C₂₃×#388	C₂²	1	4	yes	—
39	C₂₃×#388	C₂²	1	4	yes	—
40	C₂₃×#388	C₂²	1	4	yes	—
41	C₂₃×#387	C₂²	1	4	yes	complemented
42	C₂₃×#387	C₂²	1	4	yes	complemented
43	C₂₃×#387	C₂²	1	4	yes	complemented
44	C₂₃×#387	C₂²	1	4	yes	complemented
45	C₂₃×#387	C₂²	1	4	yes	complemented
46	C₂₃×#387	C₂²	1	4	yes	complemented
47	C₂₃×#385	C₂²	1	4	yes	—
48	C₂₃×#385	C₂²	1	4	yes	—
49	C₂₃×#385	C₂²	1	4	yes	—
50	C₂₃×#385	C₂²	1	4	yes	—
51	C₂₃×#384	C₂²	1	2	yes	complemented
52	C₂₃×#383	C₂²	1	2	yes	complemented
53	C₂₃×#382	C₂²	1	2	yes	complemented
54	C₂₃×#382	C₂²	1	2	yes	complemented
55	C₂₃×#381	C₂²	1	2	yes	—
56	C₂₃×#381	C₂²	1	2	yes	—
57	C₂₃×#380	C₂²	1	1	yes	characteristic
58	C₂₃×#380	C₂²	1	1	yes	characteristic
59	C₂₃×#380	C₂²	1	1	yes	characteristic
60	C₂₃×#380	C₂²	1	1	yes	characteristic
61	C₂₃×#380	C₂²	1	2	yes	—
62	C₂₃×#380	C₂²	1	2	yes	—
63	C₂₃×#380	C₂²	1	2	yes	—
64	C₂₃×#379	C₂²	1	2	yes	—
65	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	complemented
66	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	complemented
67	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	complemented
68	C₄×C₄⋊C₄×C₂₃	C₂²	1	4	yes	complemented
69	C₄×C₄⋊C₄×C₂₃	C₂²	1	4	yes	complemented
70	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
71	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
72	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
73	C₄×C₂²⋊C₄×C₂₃	C₂²	1	4	yes	—
74	C₄×C₂²⋊C₄×C₂₃	C₂²	1	4	yes	—
75	C₂₃×#376	C₂²	1	2	yes	complemented
76	C₂⁵×C₂₃	C₂³	1	1	yes	characteristic
77	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
78	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
79	C₂³×C₄×C₂₃	C₂³	1	4	yes	—
80	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
81	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
82	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
83	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
84	C₂₃×#126	C₂×C₄	1	16	yes	complemented
85	C₂₃×#126	C₂×C₄	1	16	yes	complemented
86	C₂₃×#126	C₂×C₄	1	16	yes	complemented
87	C₂₃×#126	C₂×C₄	1	16	yes	complemented
88	C₂₃×#117	—	4	4	no	—
89	C₂₃×#117	—	4	4	no	—
90	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	8	yes	complemented
91	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	8	yes	complemented
92	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	8	yes	complemented
93	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
94	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
95	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
96	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
97	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
98	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
99	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
100	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
101	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
102	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
103	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
104	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
105	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
106	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
107	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
108	C₂×C₂²⋊C₄×C₂₃	—	4	4	no	—
109	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	8	yes	—
110	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	8	yes	—
111	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	8	yes	—
112	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
113	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
114	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
115	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
116	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
117	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
118	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
119	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
120	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
121	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
122	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
123	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
124	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
125	C₂×C₄²×C₂₃	C₂×C₄	1	8	yes	complemented
126	C₂×C₄²×C₂₃	C₂³	1	4	yes	—
127	C₂×C₄²×C₂₃	C₂³	1	4	yes	—
128	C₂×C₄²×C₂₃	C₂³	1	4	yes	—
129	C₂×C₄²×C₂₃	C₂³	1	4	yes	—
130	C₂×C₄²×C₂₃	C₂³	1	4	yes	—
131	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
132	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
133	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
134	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
135	C₂₃×#95	C₂³	1	4	yes	—
136	C₂₃×#95	C₂³	1	2	yes	—
137	C₂₃×#95	C₂³	1	2	yes	—
138	C₂₃×#95	C₂³	1	4	yes	—
139	C₂₃×#95	C₂³	1	4	yes	—
140	C₂₃×#95	C₂³	1	4	yes	—
141	C₂₃×#95	C₂³	1	4	yes	—
142	C₂₃×#95	C₂³	1	4	yes	—
143	C₂₃×#95	C₂³	1	4	yes	—
144	C₂₃×#95	C₂³	1	2	yes	—
145	C₂₃×#95	C₂³	1	2	yes	—
146	C₂₃×#95	C₂³	1	4	yes	—
147	C₂₃×#95	C₂³	1	4	yes	—
148	C₂₃×#95	C₂³	1	4	yes	—
149	C₂⁴×C₂₃	—	2	2	no	—
150	C₂⁴×C₂₃	—	2	2	no	—
151	C₂⁴×C₂₃	—	4	2	no	—
152	C₂⁴×C₂₃	—	4	2	no	—
153	C₂⁴×C₂₃	C₂²×C₄	1	4	yes	—
154	C₂⁴×C₂₃	C₂⁴	1	2	yes	—
155	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
156	C₂²×C₄×C₂₃	—	2	2	no	—
157	C₂²×C₄×C₂₃	—	2	2	no	—
158	C₂²×C₄×C₂₃	—	2	2	no	—
159	C₂²×C₄×C₂₃	—	2	2	no	—
160	C₂²×C₄×C₂₃	—	4	2	no	—
161	C₂²×C₄×C₂₃	—	4	2	no	—
162	C₂²×C₄×C₂₃	—	4	2	no	—
163	C₂²×C₄×C₂₃	—	4	2	no	—
164	C₂²×C₄×C₂₃	—	4	4	no	—
165	C₂²×C₄×C₂₃	—	4	4	no	—
166	C₂²×C₄×C₂₃	—	4	4	no	—
167	C₂²×C₄×C₂₃	C₂²×C₄	1	4	yes	—
168	C₂²×C₄×C₂₃	C₂²×C₄	1	4	yes	—
169	C₂²×C₄×C₂₃	C₂²×C₄	1	4	yes	—
170	C₂²×C₄×C₂₃	C₂²×C₄	1	4	yes	—
171	C₂²×C₄×C₂₃	C₂²×C₄	1	4	yes	—
172	C₂²×C₄×C₂₃	C₂²×C₄	1	4	yes	—
173	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
174	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
175	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
176	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
177	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
178	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
179	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
180	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
181	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
182	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
183	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
184	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
185	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
186	C₄⋊C₄×C₂₃	—	4	4	no	—
187	C₄⋊C₄×C₂₃	—	4	4	no	—
188	C₄⋊C₄×C₂₃	—	4	2	no	—
189	C₄⋊C₄×C₂₃	—	4	4	no	—
190	C₄⋊C₄×C₂₃	—	4	2	no	—
191	C₄⋊C₄×C₂₃	—	4	2	no	—
192	C₄⋊C₄×C₂₃	—	4	2	no	—
193	C₄⋊C₄×C₂₃	—	4	4	no	—
194	C₄⋊C₄×C₂₃	—	4	4	no	—
195	C₄⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
196	C₄⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
197	C₄⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
198	C₄⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
199	C₄⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
200	C₄⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
201	C₂²⋊C₄×C₂₃	—	2	4	no	—
202	C₂²⋊C₄×C₂₃	—	2	4	no	—
203	C₂²⋊C₄×C₂₃	—	2	4	no	—
204	C₂²⋊C₄×C₂₃	—	2	4	no	—
205	C₂²⋊C₄×C₂₃	—	4	4	no	—
206	C₂²⋊C₄×C₂₃	—	4	4	no	—
207	C₂²⋊C₄×C₂₃	—	4	4	no	—
208	C₂²⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
209	C₂²⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
210	C₂²⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
211	C₂²⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
212	C₂²⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
213	C₂²⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
214	C₄²×C₂₃	—	4	4	no	—
215	C₄²×C₂₃	—	4	4	no	—
216	C₄²×C₂₃	—	4	4	no	—
217	C₄²×C₂₃	—	4	4	no	—
218	C₄²×C₂₃	—	4	4	no	—
219	C₄²×C₂₃	C₂²×C₄	1	4	yes	—
220	C₄²×C₂₃	C₂²×C₄	1	4	yes	—
221	C₄²×C₂₃	C₂²×C₄	1	4	yes	—
222	C₄²×C₂₃	C₂²×C₄	1	4	yes	—
223	#34381	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
224	C₂³×C₂₃	—	2	2	no	—
225	C₂³×C₂₃	—	2	2	no	—
226	C₂³×C₂₃	—	2	2	no	—
227	C₂³×C₂₃	—	2	2	no	—
228	C₂³×C₂₃	—	2	4	no	—
229	C₂³×C₂₃	—	2	4	no	—
230	C₂³×C₂₃	—	2	8	no	—
231	C₂³×C₂₃	—	4	4	no	—
232	C₂³×C₂₃	—	4	4	no	—
233	C₂³×C₂₃	—	8	4	no	—
234	C₂³×C₂₃	—	8	4	no	—
235	C₂³×C₂₃	C₂³×C₄	1	4	yes	—
236	C₂³×C₂₃	C₂³×C₄	1	2	yes	—
237	C₂³×C₂₃	H(5,𝔽₂)	1	2	yes	—
238	C₂³×C₂₃	2₋¹⁺⁴	1	2	yes	—
239	C₂³×C₂₃	C₂⁵	1	1	yes	characteristic
240	C₂×C₄×C₂₃	—	2	8	no	—
241	C₂×C₄×C₂₃	—	2	8	no	—
242	C₂×C₄×C₂₃	—	2	1	no	—
243	C₂×C₄×C₂₃	—	2	2	no	—
244	C₂×C₄×C₂₃	—	2	1	no	—
245	C₂×C₄×C₂₃	—	2	1	no	—
246	C₂×C₄×C₂₃	—	2	2	no	—
247	C₂×C₄×C₂₃	—	2	1	no	—
248	C₂×C₄×C₂₃	—	2	2	no	—
249	C₂×C₄×C₂₃	—	2	4	no	—
250	C₂×C₄×C₂₃	—	2	4	no	—
251	C₂×C₄×C₂₃	—	2	2	no	—
252	C₂×C₄×C₂₃	—	2	2	no	—
253	C₂×C₄×C₂₃	—	2	2	no	—
254	C₂×C₄×C₂₃	—	2	4	no	—
255	C₂×C₄×C₂₃	—	2	4	no	—
256	C₂×C₄×C₂₃	—	2	4	no	—
257	C₂×C₄×C₂₃	—	2	4	no	—
258	C₂×C₄×C₂₃	—	2	4	no	—
259	C₂×C₄×C₂₃	—	2	4	no	—
260	C₂×C₄×C₂₃	—	2	4	no	—
261	C₂×C₄×C₂₃	—	2	4	no	—
262	C₂×C₄×C₂₃	—	2	4	no	—
263	C₂×C₄×C₂₃	—	2	4	no	—
264	C₂×C₄×C₂₃	—	2	4	no	—
265	C₂×C₄×C₂₃	—	2	4	no	—
266	C₂×C₄×C₂₃	—	4	4	no	—
267	C₂×C₄×C₂₃	—	4	4	no	—
268	C₂×C₄×C₂₃	—	4	4	no	—
269	C₂×C₄×C₂₃	—	4	4	no	—
270	C₂×C₄×C₂₃	—	8	8	no	—
271	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
272	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
273	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
274	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
275	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
276	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
277	C₂×C₄×C₂₃	C₂³×C₄	1	4	yes	—
278	C₂×C₄×C₂₃	C₂³×C₄	1	4	yes	—
279	C₂×C₄×C₂₃	C₂³×C₄	1	4	yes	—
280	C₂²×#126	C₂×C₂₃	1	1	yes	characteristic
281	#2383	C₂×C₂₃	1	4	yes	complemented
282	#2373	C₂×C₂₃	1	4	yes	complemented
283	#2345	C₂×C₂₃	1	2	yes	complemented
284	#2344	C₂×C₂₃	1	2	yes	complemented
285	#2342	C₂×C₂₃	1	2	yes	—
286	#2342	C₂×C₂₃	1	2	yes	—
287	#2334	C₂×C₂₃	1	4	yes	complemented
288	#2334	C₂×C₂₃	1	4	yes	complemented
289	#2316	C₂×C₂₃	1	1	yes	characteristic, complemented
290	#2315	C₂×C₂₃	1	1	yes	characteristic
291	#2313	C₂×C₂₃	1	1	yes	characteristic, complemented
292	#2312	C₂×C₂₃	1	1	yes	characteristic
293	#2285	C₂×C₂₃	1	1	yes	characteristic, complemented
294	#2283	C₂×C₂₃	1	1	yes	characteristic, complemented
295	C₂²×C₂₃	—	2	2	no	—
296	C₂²×C₂₃	—	2	2	no	—
297	C₂²×C₂₃	—	2	4	no	—
298	C₂²×C₂₃	—	2	4	no	—
299	C₂²×C₂₃	—	2	4	no	—
300	C₂²×C₂₃	—	2	4	no	—
301	C₂²×C₂₃	—	2	4	no	—
302	C₂²×C₂₃	—	4	4	no	—
303	C₂²×C₂₃	—	4	4	no	—
304	C₂²×C₂₃	—	8	8	no	—
305	C₂²×C₂₃	#520	1	4	yes	—
306	C₂²×C₂₃	C₂⁴×C₄	1	1	yes	characteristic
307	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
308	C₂²×C₂₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
309	C₂²×C₂₃	#585	1	2	yes	—
310	C₂²×C₂₃	#585	1	2	yes	—
311	C₄×C₂₃	—	2	2	no	—
312	C₄×C₂₃	—	2	4	no	—
313	C₄×C₂₃	—	2	2	no	—
314	C₄×C₂₃	—	2	2	no	—
315	C₄×C₂₃	—	2	4	no	—
316	C₄×C₂₃	—	2	4	no	—
317	C₄×C₂₃	—	2	2	no	—
318	C₄×C₂₃	—	2	2	no	—
319	C₄×C₂₃	—	2	2	no	—
320	C₄×C₂₃	—	4	4	no	—
321	C₄×C₂₃	—	4	4	no	—
322	C₄×C₂₃	—	4	4	no	—
323	C₄×C₂₃	—	4	4	no	—
324	C₂×#126	C₄×C₂₃	1	16	yes	complemented
325	C₂×#126	C₂²×C₂₃	1	2	yes	—
326	C₂×#126	C₂²×C₂₃	1	2	yes	—
327	C₂×#126	C₂²×C₂₃	1	2	yes	—
328	C₂×#126	C₂²×C₂₃	1	2	yes	—
329	C₂×#117	C₂²×C₂₃	1	2	yes	—
330	C₂×#117	C₂²×C₂₃	1	2	yes	—
331	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
332	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
333	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
334	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
335	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
336	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
337	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
338	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
339	#389	C₂²×C₂₃	1	4	yes	complemented
340	#389	C₂²×C₂₃	1	4	yes	complemented
341	#389	C₂²×C₂₃	1	4	yes	complemented
342	#389	C₂²×C₂₃	1	4	yes	complemented
343	#388	C₂²×C₂₃	1	4	yes	—
344	#388	C₂²×C₂₃	1	4	yes	—
345	#388	C₂²×C₂₃	1	4	yes	—
346	#388	C₂²×C₂₃	1	4	yes	—
347	#388	C₂²×C₂₃	1	4	yes	—
348	#388	C₂²×C₂₃	1	4	yes	—
349	#387	C₂²×C₂₃	1	4	yes	complemented
350	#387	C₂²×C₂₃	1	4	yes	complemented
351	#387	C₂²×C₂₃	1	4	yes	complemented
352	#387	C₂²×C₂₃	1	4	yes	complemented
353	#387	C₂²×C₂₃	1	4	yes	complemented
354	#387	C₂²×C₂₃	1	4	yes	complemented
355	#385	C₂²×C₂₃	1	4	yes	—
356	#385	C₂²×C₂₃	1	4	yes	—
357	#385	C₂²×C₂₃	1	4	yes	—
358	#385	C₂²×C₂₃	1	4	yes	—
359	#384	C₂²×C₂₃	1	2	yes	complemented
360	#383	C₂²×C₂₃	1	2	yes	complemented
361	#382	C₂²×C₂₃	1	2	yes	complemented
362	#382	C₂²×C₂₃	1	2	yes	complemented
363	#381	C₂²×C₂₃	1	2	yes	—
364	#381	C₂²×C₂₃	1	2	yes	—
365	#380	C₂²×C₂₃	1	1	yes	characteristic
366	#380	C₂²×C₂₃	1	1	yes	characteristic
367	#380	C₂²×C₂₃	1	1	yes	characteristic
368	#380	C₂²×C₂₃	1	1	yes	characteristic
369	#380	C₂²×C₂₃	1	2	yes	—
370	#380	C₂²×C₂₃	1	2	yes	—
371	#380	C₂²×C₂₃	1	2	yes	—
372	#379	C₂²×C₂₃	1	2	yes	—
373	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	complemented
374	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	complemented
375	C₄×C₄⋊C₄	C₂²×C₂₃	1	4	yes	complemented
376	C₄×C₄⋊C₄	C₂²×C₂₃	1	4	yes	complemented
377	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	complemented
378	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
379	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
380	C₄×C₂²⋊C₄	C₂²×C₂₃	1	4	yes	—
381	C₄×C₂²⋊C₄	C₂²×C₂₃	1	4	yes	—
382	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
383	#376	C₂²×C₂₃	1	2	yes	complemented
384	C₂×C₂₃	—	2	4	no	—
385	C₂×C₂₃	—	4	4	no	—
386	C₂×C₂₃	C₂×#520	1	1	yes	characteristic
387	C₂×C₂₃	#3428	1	1	yes	characteristic
388	C₂×C₂₃	#3428	1	1	yes	characteristic
389	C₂×C₂₃	#3560	1	2	yes	—
390	C₂×C₂₃	#3564	1	2	yes	—
391	C₂⁵	C₂³×C₂₃	1	1	yes	characteristic
392	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
393	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
394	C₂³×C₄	C₂³×C₂₃	1	4	yes	—
395	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
396	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
397	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
398	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
399	#126	C₂×C₄×C₂₃	1	16	yes	complemented
400	#126	C₂×C₄×C₂₃	1	16	yes	complemented
401	#126	C₂×C₄×C₂₃	1	16	yes	complemented
402	#126	C₂×C₄×C₂₃	1	16	yes	complemented
403	#117	—	4	4	no	—
404	#117	—	4	4	no	—
405	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	8	yes	complemented
406	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	8	yes	complemented
407	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	8	yes	complemented
408	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
409	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
410	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
411	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
412	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
413	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
414	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
415	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
416	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
417	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
418	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
419	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
420	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
421	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
422	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
423	C₂×C₂²⋊C₄	—	4	4	no	—
424	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	8	yes	—
425	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	8	yes	—
426	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	8	yes	—
427	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
428	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
429	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
430	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
431	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
432	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
433	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
434	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
435	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
436	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
437	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
438	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
439	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
440	C₂×C₄²	C₂×C₄×C₂₃	1	8	yes	complemented
441	C₂×C₄²	C₂³×C₂₃	1	4	yes	—
442	C₂×C₄²	C₂³×C₂₃	1	4	yes	—
443	C₂×C₄²	C₂³×C₂₃	1	4	yes	—
444	C₂×C₄²	C₂³×C₂₃	1	4	yes	—
445	C₂×C₄²	C₂³×C₂₃	1	4	yes	—
446	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
447	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
448	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
449	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
450	#95	C₂³×C₂₃	1	4	yes	—
451	#95	C₂³×C₂₃	1	2	yes	—
452	#95	C₂³×C₂₃	1	2	yes	—
453	#95	C₂³×C₂₃	1	4	yes	—
454	#95	C₂³×C₂₃	1	4	yes	—
455	#95	C₂³×C₂₃	1	4	yes	—
456	#95	C₂³×C₂₃	1	4	yes	—
457	#95	C₂³×C₂₃	1	4	yes	—
458	#95	C₂³×C₂₃	1	4	yes	—
459	#95	C₂³×C₂₃	1	2	yes	—
460	#95	C₂³×C₂₃	1	2	yes	—
461	#95	C₂³×C₂₃	1	4	yes	—
462	#95	C₂³×C₂₃	1	4	yes	—
463	#95	C₂³×C₂₃	1	4	yes	—
464	C₂₃	#34381	1	1	yes	characteristic, direct product factor, Sylow
465	C₂⁴	—	2	2	no	—
466	C₂⁴	—	2	2	no	—
467	C₂⁴	—	4	2	no	—
468	C₂⁴	—	4	2	no	—
469	C₂⁴	C₂²×C₄×C₂₃	1	4	yes	—
470	C₂⁴	C₂⁴×C₂₃	1	2	yes	—
471	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
472	C₂²×C₄	—	2	2	no	—
473	C₂²×C₄	—	2	2	no	—
474	C₂²×C₄	—	2	2	no	—
475	C₂²×C₄	—	2	2	no	—
476	C₂²×C₄	—	4	2	no	—
477	C₂²×C₄	—	4	2	no	—
478	C₂²×C₄	—	4	2	no	—
479	C₂²×C₄	—	4	2	no	—
480	C₂²×C₄	—	4	4	no	—
481	C₂²×C₄	—	4	4	no	—
482	C₂²×C₄	—	4	4	no	—
483	C₂²×C₄	C₂²×C₄×C₂₃	1	4	yes	—
484	C₂²×C₄	C₂²×C₄×C₂₃	1	4	yes	—
485	C₂²×C₄	C₂²×C₄×C₂₃	1	4	yes	—
486	C₂²×C₄	C₂²×C₄×C₂₃	1	4	yes	—
487	C₂²×C₄	C₂²×C₄×C₂₃	1	4	yes	—
488	C₂²×C₄	C₂²×C₄×C₂₃	1	4	yes	—
489	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
490	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
491	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
492	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
493	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
494	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
495	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
496	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
497	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
498	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
499	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
500	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
501	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
502	C₄⋊C₄	—	4	4	no	—
503	C₄⋊C₄	—	4	4	no	—
504	C₄⋊C₄	—	4	4	no	—
505	C₄⋊C₄	—	4	4	no	—
506	C₄⋊C₄	—	4	2	no	—
507	C₄⋊C₄	—	4	4	no	—
508	C₄⋊C₄	—	4	2	no	—
509	C₄⋊C₄	—	4	2	no	—
510	C₄⋊C₄	—	4	2	no	—
511	C₄⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
512	C₄⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
513	C₄⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
514	C₄⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
515	C₄⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
516	C₄⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
517	C₂²⋊C₄	—	2	4	no	—
518	C₂²⋊C₄	—	2	4	no	—
519	C₂²⋊C₄	—	2	4	no	—
520	C₂²⋊C₄	—	2	4	no	—
521	C₂²⋊C₄	—	4	4	no	—
522	C₂²⋊C₄	—	4	4	no	—
523	C₂²⋊C₄	—	4	4	no	—
524	C₂²⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
525	C₂²⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
526	C₂²⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
527	C₂²⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
528	C₂²⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
529	C₂²⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
530	C₄²	—	4	4	no	—
531	C₄²	—	4	4	no	—
532	C₄²	—	4	4	no	—
533	C₄²	—	4	4	no	—
534	C₄²	—	4	4	no	—
535	C₄²	C₂²×C₄×C₂₃	1	4	yes	—
536	C₄²	C₂²×C₄×C₂₃	1	4	yes	—
537	C₄²	C₂²×C₄×C₂₃	1	4	yes	—
538	C₄²	C₂²×C₄×C₂₃	1	4	yes	—
539	C₂³	—	2	2	no	—
540	C₂³	—	2	2	no	—
541	C₂³	—	2	2	no	—
542	C₂³	—	2	2	no	—
543	C₂³	—	2	4	no	—
544	C₂³	—	2	4	no	—
545	C₂³	—	2	8	no	—
546	C₂³	—	4	4	no	—
547	C₂³	—	4	4	no	—
548	C₂³	—	8	4	no	—
549	C₂³	—	8	4	no	—
550	C₂³	C₂³×C₄×C₂₃	1	4	yes	—
551	C₂³	C₂³×C₄×C₂₃	1	2	yes	—
552	C₂³	C₂₃×H(5,𝔽₂)	1	2	yes	—
553	C₂³	C₂₃×2₋¹⁺⁴	1	2	yes	—
554	C₂³	C₂⁵×C₂₃	1	1	yes	characteristic
555	C₂×C₄	—	2	1	no	—
556	C₂×C₄	—	2	2	no	—
557	C₂×C₄	—	2	1	no	—
558	C₂×C₄	—	2	1	no	—
559	C₂×C₄	—	2	2	no	—
560	C₂×C₄	—	2	1	no	—
561	C₂×C₄	—	2	2	no	—
562	C₂×C₄	—	2	4	no	—
563	C₂×C₄	—	2	4	no	—
564	C₂×C₄	—	2	2	no	—
565	C₂×C₄	—	2	2	no	—
566	C₂×C₄	—	2	2	no	—
567	C₂×C₄	—	2	8	no	—
568	C₂×C₄	—	2	8	no	—
569	C₂×C₄	—	2	4	no	—
570	C₂×C₄	—	2	4	no	—
571	C₂×C₄	—	2	4	no	—
572	C₂×C₄	—	2	4	no	—
573	C₂×C₄	—	2	4	no	—
574	C₂×C₄	—	2	4	no	—
575	C₂×C₄	—	2	4	no	—
576	C₂×C₄	—	2	4	no	—
577	C₂×C₄	—	2	4	no	—
578	C₂×C₄	—	2	4	no	—
579	C₂×C₄	—	2	4	no	—
580	C₂×C₄	—	2	4	no	—
581	C₂×C₄	—	4	4	no	—
582	C₂×C₄	—	4	4	no	—
583	C₂×C₄	—	4	4	no	—
584	C₂×C₄	—	4	4	no	—
585	C₂×C₄	—	8	8	no	—
586	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
587	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
588	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
589	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
590	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
591	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
592	C₂×C₄	C₂³×C₄×C₂₃	1	4	yes	—
593	C₂×C₄	C₂³×C₄×C₂₃	1	4	yes	—
594	C₂×C₄	C₂³×C₄×C₂₃	1	4	yes	—
595	C₂²	—	2	2	no	—
596	C₂²	—	2	2	no	—
597	C₂²	—	2	4	no	—
598	C₂²	—	2	4	no	—
599	C₂²	—	2	4	no	—
600	C₂²	—	2	4	no	—
601	C₂²	—	2	4	no	—
602	C₂²	—	4	4	no	—
603	C₂²	—	4	4	no	—
604	C₂²	—	8	8	no	—
605	C₂²	C₂₃×#520	1	4	yes	—
606	C₂²	C₂⁴×C₄×C₂₃	1	1	yes	characteristic
607	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
608	C₂²	C₂×C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
609	C₂²	C₂₃×#585	1	2	yes	—
610	C₂²	C₂₃×#585	1	2	yes	—
611	C₄	—	2	2	no	—
612	C₄	—	2	4	no	—
613	C₄	—	2	2	no	—
614	C₄	—	2	2	no	—
615	C₄	—	2	4	no	—
616	C₄	—	2	4	no	—
617	C₄	—	2	2	no	—
618	C₄	—	2	2	no	—
619	C₄	—	2	2	no	—
620	C₄	—	4	4	no	—
621	C₄	—	4	4	no	—
622	C₄	—	4	4	no	—
623	C₄	—	4	4	no	—
624	C₂	—	2	4	no	—
625	C₂	—	4	4	no	—
626	C₂	C₂×C₂₃×#520	1	1	yes	characteristic
627	C₂	C₂₃×#3428	1	1	yes	characteristic
628	C₂	C₂₃×#3428	1	1	yes	characteristic
629	C₂	C₂₃×#3560	1	2	yes	—
630	C₂	C₂₃×#3564	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
2. C₂₃×#2383	C₂	semidirect
3. C₂₃×#2373	C₂	semidirect
4. C₂₃×#2345	C₂	semidirect
5. C₂₃×#2344	C₂	semidirect
8. C₂₃×#2334	C₂	semidirect
9. C₂₃×#2334	C₂	semidirect
10. C₂₃×#2316	C₂	semidirect
12. C₂₃×#2313	C₂	semidirect
14. C₂₃×#2285	C₂	semidirect
15. C₂₃×#2283	C₂	semidirect
16. C₂×C₂₃×#126	C₄	semidirect
31. C₂₃×#389	C₂²	semidirect
32. C₂₃×#389	C₂²	semidirect
33. C₂₃×#389	C₂²	semidirect
34. C₂₃×#389	C₂²	semidirect
41. C₂₃×#387	C₂²	semidirect
42. C₂₃×#387	C₂²	semidirect
43. C₂₃×#387	C₂²	semidirect
44. C₂₃×#387	C₂²	semidirect
45. C₂₃×#387	C₂²	semidirect
46. C₂₃×#387	C₂²	semidirect
51. C₂₃×#384	C₂²	semidirect
52. C₂₃×#383	C₂²	semidirect
53. C₂₃×#382	C₂²	semidirect
54. C₂₃×#382	C₂²	semidirect
65. C₄×C₄⋊C₄×C₂₃	C₂²	semidirect
66. C₄×C₄⋊C₄×C₂₃	C₂²	semidirect
67. C₄×C₄⋊C₄×C₂₃	C₂²	semidirect
68. C₄×C₄⋊C₄×C₂₃	C₂²	semidirect
69. C₄×C₄⋊C₄×C₂₃	C₂²	semidirect
75. C₂₃×#376	C₂²	semidirect
84. C₂₃×#126	C₂×C₄	semidirect
85. C₂₃×#126	C₂×C₄	semidirect
86. C₂₃×#126	C₂×C₄	semidirect
87. C₂₃×#126	C₂×C₄	semidirect
90. C₂×C₄⋊C₄×C₂₃	C₂×C₄	semidirect
91. C₂×C₄⋊C₄×C₂₃	C₂×C₄	semidirect
92. C₂×C₄⋊C₄×C₂₃	C₂×C₄	semidirect
125. C₂×C₄²×C₂₃	C₂×C₄	semidirect
223. #34381	C₂₃	direct (N × H)
281. #2383	C₂×C₂₃	semidirect
282. #2373	C₂×C₂₃	semidirect
283. #2345	C₂×C₂₃	semidirect
284. #2344	C₂×C₂₃	semidirect
287. #2334	C₂×C₂₃	semidirect
288. #2334	C₂×C₂₃	semidirect
289. #2316	C₂×C₂₃	semidirect
291. #2313	C₂×C₂₃	semidirect
293. #2285	C₂×C₂₃	semidirect
294. #2283	C₂×C₂₃	semidirect
324. C₂×#126	C₄×C₂₃	semidirect
339. #389	C₂²×C₂₃	semidirect
340. #389	C₂²×C₂₃	semidirect
341. #389	C₂²×C₂₃	semidirect
342. #389	C₂²×C₂₃	semidirect
349. #387	C₂²×C₂₃	semidirect
350. #387	C₂²×C₂₃	semidirect
351. #387	C₂²×C₂₃	semidirect
352. #387	C₂²×C₂₃	semidirect
353. #387	C₂²×C₂₃	semidirect
354. #387	C₂²×C₂₃	semidirect
359. #384	C₂²×C₂₃	semidirect
360. #383	C₂²×C₂₃	semidirect
361. #382	C₂²×C₂₃	semidirect
362. #382	C₂²×C₂₃	semidirect
373. C₄×C₄⋊C₄	C₂²×C₂₃	semidirect
374. C₄×C₄⋊C₄	C₂²×C₂₃	semidirect
375. C₄×C₄⋊C₄	C₂²×C₂₃	semidirect
376. C₄×C₄⋊C₄	C₂²×C₂₃	semidirect
377. C₄×C₄⋊C₄	C₂²×C₂₃	semidirect
383. #376	C₂²×C₂₃	semidirect
399. #126	C₂×C₄×C₂₃	semidirect
400. #126	C₂×C₄×C₂₃	semidirect
401. #126	C₂×C₄×C₂₃	semidirect
402. #126	C₂×C₄×C₂₃	semidirect
405. C₂×C₄⋊C₄	C₂×C₄×C₂₃	semidirect
406. C₂×C₄⋊C₄	C₂×C₄×C₂₃	semidirect
407. C₂×C₄⋊C₄	C₂×C₄×C₂₃	semidirect
440. C₂×C₄²	C₂×C₄×C₂₃	semidirect
464. C₂₃	#34381	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₂₃×#126	2
C₂₃×#2383	2
C₂₃×#2373	2
C₂₃×#2345	2
C₂₃×#2344	2
C₂₃×#2342	2
C₂₃×#2334	2
C₂₃×#2316	2
C₂₃×#2315	2
C₂₃×#2313	2
C₂₃×#2312	2
C₂₃×#2285	2
C₂₃×#2283	2
#34381	23

Subgroups — C23×#34381 #19182007

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#34381 #19182007