Subgroups — C₂₃×#3557 #15671176

Order 2944.

930 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#563	C₂	1	4	yes	maximal, complemented
2	C₂₃×#559	C₂	1	2	yes	maximal, complemented
3	C₂₃×#557	C₂	1	2	yes	maximal, complemented
4	C₂₃×#556	C₂	1	2	yes	maximal, complemented
5	C₂₃×#554	C₂	1	2	yes	maximal, complemented
6	C₂₃×#552	C₂	1	4	yes	maximal, complemented
7	C₂₃×#542	C₂	1	4	yes	maximal, complemented
8	C₂₃×#542	C₂	1	2	yes	maximal, complemented
9	C₂₃×#541	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#540	C₂	1	1	yes	maximal, characteristic
11	C₂₃×#539	C₂	1	4	yes	maximal, complemented
12	C₂₃×#533	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#529	C₂	1	2	yes	maximal, complemented
14	C₂₃×C₄⋊Q₈	C₂²	1	2	yes	—
15	C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
16	C₂₃×C₄⋊Q₈	C₂²	1	4	yes	—
17	C₂₃×C₄⋊Q₈	C₂²	1	2	yes	—
18	C₂₃×#127	C₂²	1	1	yes	characteristic
19	C₂₃×#126	C₂²	1	4	yes	—
20	C₂₃×#126	C₂²	1	4	yes	—
21	C₂₃×#126	C₂²	1	4	yes	—
22	C₂₃×#126	C₂²	1	4	yes	—
23	C₂₃×#126	C₂²	1	4	yes	—
24	C₂₃×#125	C₂²	1	2	yes	—
25	C₂₃×#125	C₂²	1	4	yes	—
26	C₂₃×#125	C₂²	1	4	yes	—
27	C₂₃×#125	C₂²	1	1	yes	characteristic
28	C₂₃×#125	C₂²	1	2	yes	—
29	C₂₃×#125	C₂²	1	1	yes	characteristic
30	C₂₃×#125	C₂²	1	4	yes	—
31	C₂₃×#124	C₂²	1	2	yes	—
32	C₂₃×#124	C₂²	1	2	yes	—
33	C₂₃×#124	C₂²	1	4	yes	—
34	C₂₃×#124	C₂²	1	4	yes	—
35	C₂₃×#123	C₂²	1	4	yes	—
36	C₂₃×#123	C₂²	1	4	yes	—
37	C₂₃×#123	C₂²	1	4	yes	—
38	C₂₃×#123	C₂²	1	4	yes	—
39	C₂₃×#123	C₂²	1	4	yes	—
40	C₂₃×C₂²⋊Q₈	C₂²	1	4	yes	—
41	C₂₃×C₂²⋊Q₈	C₂²	1	4	yes	—
42	C₂₃×C₂²⋊Q₈	C₂²	1	4	yes	—
43	C₂₃×C₂²⋊Q₈	C₂²	1	4	yes	—
44	C₂₃×C₂²⋊Q₈	C₂²	1	4	yes	—
45	C₂₃×C₂²⋊Q₈	C₂²	1	2	yes	—
46	C₂₃×C₂²⋊Q₈	C₂²	1	2	yes	—
47	C₂₃×C₂²⋊Q₈	C₂²	1	2	yes	—
48	C₂₃×#121	C₂²	1	2	yes	—
49	C₂₃×#121	C₂²	1	4	yes	—
50	C₄×Q₈×C₂₃	C₂²	1	4	yes	—
51	C₄×Q₈×C₂₃	C₂²	1	2	yes	—
52	C₄×Q₈×C₂₃	C₂²	1	2	yes	—
53	C₄×Q₈×C₂₃	C₂²	1	2	yes	—
54	C₄×Q₈×C₂₃	C₂²	1	2	yes	—
55	C₄×Q₈×C₂₃	C₂²	1	2	yes	—
56	C₄×D₄×C₂₃	C₂²	1	4	yes	—
57	C₄×D₄×C₂₃	C₂²	1	2	yes	—
58	C₄×D₄×C₂₃	C₂²	1	2	yes	—
59	C₄×D₄×C₂₃	C₂²	1	2	yes	—
60	C₄×D₄×C₂₃	C₂²	1	4	yes	—
61	C₂₃×#117	C₂²	1	4	yes	—
62	C₂₃×#117	C₂²	1	4	yes	—
63	C₂₃×#117	C₂²	1	1	yes	characteristic
64	C₂₃×#117	C₂²	1	1	yes	characteristic
65	C₂×C₄⋊C₄×C₂₃	C₂²	1	4	yes	—
66	C₂×C₄²×C₂₃	C₂²	1	1	yes	characteristic
67	C₂×Q₈×C₂₃	C₂³	1	2	yes	—
68	C₂×Q₈×C₂₃	C₂³	1	2	yes	—
69	C₂×Q₈×C₂₃	C₂³	1	4	yes	—
70	C₂×Q₈×C₂₃	C₂³	1	2	yes	—
71	C₂×D₄×C₂₃	C₂³	1	2	yes	—
72	C₂×D₄×C₂₃	C₂³	1	4	yes	—
73	C₂×D₄×C₂₃	C₂³	1	4	yes	—
74	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
75	C₂²×C₄×C₂₃	C₂³	1	2	yes	—
76	C₂²×C₄×C₂₃	C₂³	1	4	yes	—
77	C₂²×C₄×C₂₃	C₂³	1	4	yes	—
78	C₂²×C₄×C₂₃	C₂³	1	4	yes	—
79	C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
80	C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
81	C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
82	C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
83	C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
84	C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
85	C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
86	C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
87	C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
88	C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
89	C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
90	C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
91	C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
92	C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
93	C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
94	C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
95	C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
96	C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
97	C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
98	C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
99	C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
100	C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
101	C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
102	C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
103	C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
104	C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
105	C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
106	C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
107	C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
108	C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
109	C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
110	C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
111	C₄²×C₂₃	C₂³	1	1	yes	characteristic
112	C₄²×C₂₃	C₂³	1	2	yes	—
113	C₄²×C₂₃	C₂³	1	1	yes	characteristic
114	C₄²×C₂₃	C₂³	1	4	yes	—
115	C₄²×C₂₃	C₂³	1	1	yes	characteristic
116	C₄²×C₂₃	C₂³	1	2	yes	—
117	C₄²×C₂₃	C₂³	1	1	yes	characteristic
118	C₄²×C₂₃	C₂³	1	4	yes	—
119	C₄²×C₂₃	C₂³	1	4	yes	—
120	C₂³×C₂₃	C₂⁴	1	1	yes	characteristic
121	C₂³×C₂₃	C₂⁴	1	4	yes	—
122	Q₈×C₂₃	—	2	4	no	—
123	Q₈×C₂₃	—	4	2	no	—
124	Q₈×C₂₃	—	4	4	no	—
125	Q₈×C₂₃	—	4	2	no	—
126	D₄×C₂₃	—	2	4	no	—
127	D₄×C₂₃	—	4	4	no	—
128	D₄×C₂₃	—	4	4	no	—
129	C₂×C₄×C₂₃	—	2	2	no	—
130	C₂×C₄×C₂₃	—	4	4	no	—
131	C₂×C₄×C₂₃	—	4	2	no	—
132	C₂×C₄×C₂₃	—	4	4	no	—
133	C₂×C₄×C₂₃	—	4	4	no	—
134	C₂×C₄×C₂₃	C₂⁴	1	2	yes	—
135	C₂×C₄×C₂₃	C₂⁴	1	4	yes	—
136	C₂×C₄×C₂₃	C₂⁴	1	2	yes	—
137	C₂×C₄×C₂₃	C₂⁴	1	2	yes	—
138	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
139	C₂×C₄×C₂₃	C₂⁴	1	2	yes	—
140	C₂×C₄×C₂₃	C₂⁴	1	4	yes	—
141	C₂×C₄×C₂₃	C₂⁴	1	2	yes	—
142	C₂×C₄×C₂₃	C₂⁴	1	2	yes	—
143	C₂×C₄×C₂₃	C₂⁴	1	4	yes	—
144	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
145	#3557	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
146	C₂²×C₂₃	—	2	1	no	—
147	C₂²×C₂₃	—	2	4	no	—
148	C₂²×C₂₃	—	2	4	no	—
149	C₂²×C₂₃	—	2	2	no	—
150	C₂²×C₂₃	—	2	4	no	—
151	C₂²×C₂₃	C₂⁵	1	1	yes	characteristic
152	C₄×C₂₃	—	2	1	no	—
153	C₄×C₂₃	—	2	4	no	—
154	C₄×C₂₃	—	2	2	no	—
155	C₄×C₂₃	—	2	4	no	—
156	C₄×C₂₃	—	2	2	no	—
157	C₄×C₂₃	—	2	2	no	—
158	C₄×C₂₃	—	2	4	no	—
159	C₄×C₂₃	—	2	2	no	—
160	C₄×C₂₃	—	2	2	no	—
161	C₄×C₂₃	—	2	2	no	—
162	C₄×C₂₃	2₋¹⁺⁴	1	2	yes	—
163	#563	C₂×C₂₃	1	4	yes	complemented
164	#559	C₂×C₂₃	1	2	yes	complemented
165	#557	C₂×C₂₃	1	2	yes	complemented
166	#556	C₂×C₂₃	1	2	yes	complemented
167	#554	C₂×C₂₃	1	2	yes	complemented
168	#552	C₂×C₂₃	1	4	yes	complemented
169	#542	C₂×C₂₃	1	2	yes	complemented
170	#542	C₂×C₂₃	1	4	yes	complemented
171	#541	C₂×C₂₃	1	1	yes	characteristic, complemented
172	#540	C₂×C₂₃	1	1	yes	characteristic
173	#539	C₂×C₂₃	1	4	yes	complemented
174	#533	C₂×C₂₃	1	1	yes	characteristic, complemented
175	#529	C₂×C₂₃	1	2	yes	complemented
176	C₂×C₂₃	—	4	1	no	—
177	C₂×C₂₃	—	4	4	no	—
178	C₂×C₂₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
179	C₂×C₂₃	#585	1	2	yes	—
180	C₄⋊Q₈	C₂²×C₂₃	1	2	yes	—
181	C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
182	C₄⋊Q₈	C₂²×C₂₃	1	2	yes	—
183	C₄⋊Q₈	C₂²×C₂₃	1	4	yes	—
184	#127	C₂²×C₂₃	1	1	yes	characteristic
185	#126	C₂²×C₂₃	1	4	yes	—
186	#126	C₂²×C₂₃	1	4	yes	—
187	#126	C₂²×C₂₃	1	4	yes	—
188	#126	C₂²×C₂₃	1	4	yes	—
189	#126	C₂²×C₂₃	1	4	yes	—
190	#125	C₂²×C₂₃	1	2	yes	—
191	#125	C₂²×C₂₃	1	2	yes	—
192	#125	C₂²×C₂₃	1	4	yes	—
193	#125	C₂²×C₂₃	1	4	yes	—
194	#125	C₂²×C₂₃	1	1	yes	characteristic
195	#125	C₂²×C₂₃	1	4	yes	—
196	#125	C₂²×C₂₃	1	1	yes	characteristic
197	#124	C₂²×C₂₃	1	2	yes	—
198	#124	C₂²×C₂₃	1	4	yes	—
199	#124	C₂²×C₂₃	1	2	yes	—
200	#124	C₂²×C₂₃	1	4	yes	—
201	#123	C₂²×C₂₃	1	4	yes	—
202	#123	C₂²×C₂₃	1	4	yes	—
203	#123	C₂²×C₂₃	1	4	yes	—
204	#123	C₂²×C₂₃	1	4	yes	—
205	#123	C₂²×C₂₃	1	4	yes	—
206	C₂²⋊Q₈	C₂²×C₂₃	1	2	yes	—
207	C₂²⋊Q₈	C₂²×C₂₃	1	2	yes	—
208	C₂²⋊Q₈	C₂²×C₂₃	1	2	yes	—
209	C₂²⋊Q₈	C₂²×C₂₃	1	4	yes	—
210	C₂²⋊Q₈	C₂²×C₂₃	1	4	yes	—
211	C₂²⋊Q₈	C₂²×C₂₃	1	4	yes	—
212	C₂²⋊Q₈	C₂²×C₂₃	1	4	yes	—
213	C₂²⋊Q₈	C₂²×C₂₃	1	4	yes	—
214	#121	C₂²×C₂₃	1	2	yes	—
215	#121	C₂²×C₂₃	1	4	yes	—
216	C₄×Q₈	C₂²×C₂₃	1	2	yes	—
217	C₄×Q₈	C₂²×C₂₃	1	2	yes	—
218	C₄×Q₈	C₂²×C₂₃	1	2	yes	—
219	C₄×Q₈	C₂²×C₂₃	1	2	yes	—
220	C₄×Q₈	C₂²×C₂₃	1	4	yes	—
221	C₄×Q₈	C₂²×C₂₃	1	2	yes	—
222	C₄×D₄	C₂²×C₂₃	1	4	yes	—
223	C₄×D₄	C₂²×C₂₃	1	2	yes	—
224	C₄×D₄	C₂²×C₂₃	1	4	yes	—
225	C₄×D₄	C₂²×C₂₃	1	2	yes	—
226	C₄×D₄	C₂²×C₂₃	1	2	yes	—
227	#117	C₂²×C₂₃	1	4	yes	—
228	#117	C₂²×C₂₃	1	1	yes	characteristic
229	#117	C₂²×C₂₃	1	1	yes	characteristic
230	#117	C₂²×C₂₃	1	4	yes	—
231	C₂×C₄⋊C₄	C₂²×C₂₃	1	4	yes	—
232	C₂×C₄²	C₂²×C₂₃	1	1	yes	characteristic
233	C₂₃	#3557	1	1	yes	characteristic, direct product factor, Sylow
234	C₂×Q₈	C₂³×C₂₃	1	2	yes	—
235	C₂×Q₈	C₂³×C₂₃	1	2	yes	—
236	C₂×Q₈	C₂³×C₂₃	1	4	yes	—
237	C₂×Q₈	C₂³×C₂₃	1	2	yes	—
238	C₂×D₄	C₂³×C₂₃	1	2	yes	—
239	C₂×D₄	C₂³×C₂₃	1	4	yes	—
240	C₂×D₄	C₂³×C₂₃	1	4	yes	—
241	C₂²×C₄	C₂³×C₂₃	1	1	yes	characteristic
242	C₂²×C₄	C₂³×C₂₃	1	2	yes	—
243	C₂²×C₄	C₂³×C₂₃	1	4	yes	—
244	C₂²×C₄	C₂³×C₂₃	1	4	yes	—
245	C₂²×C₄	C₂³×C₂₃	1	4	yes	—
246	C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
247	C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
248	C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
249	C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
250	C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
251	C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
252	C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
253	C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
254	C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
255	C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
256	C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
257	C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
258	C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
259	C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
260	C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
261	C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
262	C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
263	C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
264	C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
265	C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
266	C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
267	C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
268	C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
269	C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
270	C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
271	C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
272	C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
273	C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
274	C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
275	C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
276	C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
277	C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
278	C₄²	C₂³×C₂₃	1	1	yes	characteristic
279	C₄²	C₂³×C₂₃	1	2	yes	—
280	C₄²	C₂³×C₂₃	1	1	yes	characteristic
281	C₄²	C₂³×C₂₃	1	4	yes	—
282	C₄²	C₂³×C₂₃	1	1	yes	characteristic
283	C₄²	C₂³×C₂₃	1	2	yes	—
284	C₄²	C₂³×C₂₃	1	1	yes	characteristic
285	C₄²	C₂³×C₂₃	1	4	yes	—
286	C₄²	C₂³×C₂₃	1	4	yes	—
287	C₂³	C₂⁴×C₂₃	1	1	yes	characteristic
288	C₂³	C₂⁴×C₂₃	1	4	yes	—
289	Q₈	—	2	4	no	—
290	Q₈	—	4	2	no	—
291	Q₈	—	4	4	no	—
292	Q₈	—	4	2	no	—
293	D₄	—	2	4	no	—
294	D₄	—	4	4	no	—
295	D₄	—	4	4	no	—
296	C₂×C₄	—	2	2	no	—
297	C₂×C₄	—	4	4	no	—
298	C₂×C₄	—	4	2	no	—
299	C₂×C₄	—	4	4	no	—
300	C₂×C₄	—	4	4	no	—
301	C₂×C₄	C₂⁴×C₂₃	1	2	yes	—
302	C₂×C₄	C₂⁴×C₂₃	1	4	yes	—
303	C₂×C₄	C₂⁴×C₂₃	1	2	yes	—
304	C₂×C₄	C₂⁴×C₂₃	1	2	yes	—
305	C₂×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
306	C₂×C₄	C₂⁴×C₂₃	1	2	yes	—
307	C₂×C₄	C₂⁴×C₂₃	1	4	yes	—
308	C₂×C₄	C₂⁴×C₂₃	1	2	yes	—
309	C₂×C₄	C₂⁴×C₂₃	1	2	yes	—
310	C₂×C₄	C₂⁴×C₂₃	1	4	yes	—
311	C₂×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
312	C₂²	—	2	1	no	—
313	C₂²	—	2	4	no	—
314	C₂²	—	2	4	no	—
315	C₂²	—	2	2	no	—
316	C₂²	—	2	4	no	—
317	C₂²	C₂⁵×C₂₃	1	1	yes	characteristic
318	C₄	—	2	1	no	—
319	C₄	—	2	4	no	—
320	C₄	—	2	2	no	—
321	C₄	—	2	4	no	—
322	C₄	—	2	2	no	—
323	C₄	—	2	2	no	—
324	C₄	—	2	4	no	—
325	C₄	—	2	2	no	—
326	C₄	—	2	2	no	—
327	C₄	—	2	2	no	—
328	C₄	C₂₃×2₋¹⁺⁴	1	2	yes	—
329	C₂	—	4	1	no	—
330	C₂	—	4	4	no	—
331	C₂	C₂×C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
332	C₂	C₂₃×#585	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁵×C₂₃
prime radical	C₂₃×#540	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₃×#563	C₂	semidirect
2. C₂₃×#559	C₂	semidirect
3. C₂₃×#557	C₂	semidirect
4. C₂₃×#556	C₂	semidirect
5. C₂₃×#554	C₂	semidirect
6. C₂₃×#552	C₂	semidirect
7. C₂₃×#542	C₂	semidirect
8. C₂₃×#542	C₂	semidirect
9. C₂₃×#541	C₂	semidirect
11. C₂₃×#539	C₂	semidirect
12. C₂₃×#533	C₂	semidirect
13. C₂₃×#529	C₂	semidirect
145. #3557	C₂₃	direct (N × H)
163. #563	C₂×C₂₃	semidirect
164. #559	C₂×C₂₃	semidirect
165. #557	C₂×C₂₃	semidirect
166. #556	C₂×C₂₃	semidirect
167. #554	C₂×C₂₃	semidirect
168. #552	C₂×C₂₃	semidirect
169. #542	C₂×C₂₃	semidirect
170. #542	C₂×C₂₃	semidirect
171. #541	C₂×C₂₃	semidirect
173. #539	C₂×C₂₃	semidirect
174. #533	C₂×C₂₃	semidirect
175. #529	C₂×C₂₃	semidirect
233. C₂₃	#3557	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×#563	2
C₂₃×#559	2
C₂₃×#557	2
C₂₃×#556	2
C₂₃×#554	2
C₂₃×#552	2
C₂₃×#542	2
C₂₃×#541	2
C₂₃×#540	2
C₂₃×#539	2
C₂₃×#533	2
C₂₃×#529	2
#3557	23

Subgroups — C23×#3557 #15671176

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#3557 #15671176