Subgroups — C₂₃×#17550 #19165176

Order 5888.

1030 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3522	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#2984	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#2276	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#1509	C₂	1	3	yes	maximal, complemented
5	C₂₃×#1505	C₂	1	3	yes	maximal, complemented
6	C₂₃×#1502	C₂	1	3	yes	maximal, complemented
7	C₂₃×#1500	C₂	1	3	yes	maximal, complemented
8	C₂₃×#559	C₄	1	3	yes	complemented
9	Q₈²×C₂₃	C₄	1	1	yes	characteristic, complemented
10	C₂₃×#554	C₄	1	3	yes	complemented
11	C₂₃×#550	C₄	1	1	yes	characteristic, complemented
12	C₂₃×#548	—	2	1	no	—
13	C₂₃×#547	—	2	3	no	—
14	C₂₃×#542	—	2	3	no	—
15	C₂₃×#532	C₂²	1	3	yes	—
16	C₂₃×#529	C₂²	1	3	yes	—
17	C₂₃×#520	—	2	1	no	—
18	C₂×C₄×Q₈×C₂₃	—	2	1	no	—
19	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
20	C₂₃×#446	—	2	3	no	—
21	C₈×Q₈×C₂₃	—	2	1	no	—
22	C₂₃×#432	C₂²	1	3	yes	—
23	C₂₃×#431	C₂²	1	3	yes	—
24	C₄×C₄⋊C₄×C₂₃	—	2	3	no	—
25	C₄×C₄⋊C₄×C₂₃	C₂²	1	3	yes	—
26	C₂₃×#376	C₂²	1	3	yes	—
27	C₂₃×#328	C₂²	1	1	yes	characteristic
28	C₂₃×#328	C₂²	1	3	yes	—
29	C₂₃×#327	C₂²	1	3	yes	—
30	C₂₃×#327	C₂²	1	3	yes	—
31	C₂₃×#327	C₂²	1	6	yes	—
32	C₂×#41×C₂₃	—	2	1	no	—
33	C₂×#41×C₂₃	—	2	3	no	—
34	C₂²×Q₈×C₂₃	D₄	1	1	yes	characteristic
35	C₂₃×C₄⋊Q₈	—	2	3	no	—
36	C₂₃×C₄⋊Q₈	C₂×C₄	1	3	yes	—
37	C₂₃×#127	C₂×C₄	1	3	yes	—
38	C₂₃×#126	—	2	3	no	—
39	C₂₃×#125	C₂×C₄	1	3	yes	—
40	C₂₃×#124	—	2	3	no	—
41	C₂₃×#124	—	2	3	no	—
42	C₂₃×#124	C₂×C₄	1	3	yes	—
43	C₂₃×#123	—	2	3	no	—
44	C₂₃×#123	—	2	6	no	—
45	C₂₃×C₂²⋊Q₈	—	2	3	no	—
46	C₂₃×C₂²⋊Q₈	—	2	6	no	—
47	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
48	C₂₃×#121	—	2	3	no	—
49	C₂₃×#121	—	2	3	no	—
50	C₂₃×#121	C₂³	1	3	yes	—
51	C₄×Q₈×C₂₃	—	2	8	no	—
52	C₄×Q₈×C₂₃	—	2	1	no	—
53	C₄×Q₈×C₂₃	C₂×C₄	1	3	yes	—
54	C₄×Q₈×C₂₃	C₂×C₄	1	1	yes	characteristic
55	C₄×Q₈×C₂₃	C₂×C₄	1	3	yes	—
56	C₄×Q₈×C₂₃	D₄	1	1	yes	characteristic
57	C₄×Q₈×C₂₃	D₄	1	3	yes	—
58	C₄×D₄×C₂₃	—	2	3	no	—
59	C₄×D₄×C₂₃	—	2	3	no	—
60	C₄×D₄×C₂₃	—	2	3	no	—
61	C₄×D₄×C₂₃	C₂×C₄	1	3	yes	—
62	C₄×D₄×C₂₃	C₂×C₄	1	6	yes	—
63	C₂₃×#117	—	2	3	no	—
64	C₂×C₄⋊C₄×C₂₃	—	2	3	no	—
65	C₂×C₄⋊C₄×C₂₃	—	2	3	no	—
66	C₂×C₄⋊C₄×C₂₃	D₄	1	3	yes	—
67	C₂×C₄²×C₂₃	—	2	3	no	—
68	C₂×C₄²×C₂₃	—	2	3	no	—
69	C₂×C₄²×C₂₃	C₂³	1	3	yes	—
70	C₂₃×C₄⋊C₈	—	2	3	no	—
71	C₂₃×C₄⋊C₈	—	2	3	no	—
72	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
73	C₂₃×C₂²⋊C₈	C₂³	1	3	yes	—
74	C₂₃×#97	—	2	3	no	—
75	C₄×C₈×C₂₃	—	2	3	no	—
76	C₂₃×#95	—	2	3	no	—
77	C₂₃×#95	C₂³	1	1	yes	characteristic
78	C₂₃×#95	C₂³	1	3	yes	—
79	#41×C₂₃	—	4	4	no	—
80	#41×C₂₃	—	8	3	no	—
81	#41×C₂₃	—	8	3	no	—
82	C₂×Q₈×C₂₃	—	2	4	no	—
83	C₂×Q₈×C₂₃	—	2	3	no	—
84	C₂×Q₈×C₂₃	C₂²⋊C₄	1	3	yes	—
85	C₂×Q₈×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
86	C₂×Q₈×C₂₃	C₂²×C₄	1	1	yes	characteristic
87	C₂×D₄×C₂₃	—	2	3	no	—
88	C₂×D₄×C₂₃	—	2	3	no	—
89	C₂×D₄×C₂₃	—	2	3	no	—
90	C₂×D₄×C₂₃	C₂²×C₄	1	3	yes	—
91	C₂²×C₄×C₂₃	—	2	3	no	—
92	C₂²×C₄×C₂₃	—	2	1	no	—
93	C₂²×C₄×C₂₃	—	2	3	no	—
94	C₂²×C₄×C₂₃	—	2	6	no	—
95	C₂²×C₄×C₂₃	C₂×D₄	1	3	yes	—
96	C₂²×C₄×C₂₃	C₂×D₄	1	3	yes	—
97	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
98	C₂×C₈×C₂₃	—	2	1	no	—
99	C₂×C₈×C₂₃	—	2	3	no	—
100	C₄⋊C₄×C₂₃	—	2	12	no	—
101	C₄⋊C₄×C₂₃	—	2	3	no	—
102	C₄⋊C₄×C₂₃	—	2	3	no	—
103	C₄⋊C₄×C₂₃	—	2	3	no	—
104	C₄⋊C₄×C₂₃	—	2	3	no	—
105	C₄⋊C₄×C₂₃	—	2	1	no	—
106	C₄⋊C₄×C₂₃	C₂²⋊C₄	1	3	yes	—
107	C₄⋊C₄×C₂₃	C₂²⋊C₄	1	3	yes	—
108	C₄⋊C₄×C₂₃	C₂²⋊C₄	1	6	yes	—
109	C₄⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
110	C₄⋊C₄×C₂₃	C₂²×C₄	1	3	yes	—
111	C₂²⋊C₄×C₂₃	—	2	1	no	—
112	C₂²⋊C₄×C₂₃	—	2	3	no	—
113	C₂²⋊C₄×C₂₃	—	2	3	no	—
114	C₂²⋊C₄×C₂₃	—	2	3	no	—
115	C₂²⋊C₄×C₂₃	—	2	6	no	—
116	C₂²⋊C₄×C₂₃	—	2	3	no	—
117	C₄²×C₂₃	—	2	12	no	—
118	C₄²×C₂₃	—	2	3	no	—
119	C₄²×C₂₃	—	8	3	no	—
120	C₄²×C₂₃	C₂²×C₄	1	3	yes	—
121	C₄²×C₂₃	C₂²×C₄	1	3	yes	—
122	C₄²×C₂₃	C₂×D₄	1	3	yes	—
123	C₄²×C₂₃	C₂×D₄	1	3	yes	—
124	#17550	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
125	C₂³×C₂₃	—	2	3	no	—
126	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
127	Q₈×C₂₃	—	2	6	no	—
128	Q₈×C₂₃	—	4	1	no	—
129	Q₈×C₂₃	—	8	3	no	—
130	Q₈×C₂₃	#104	1	4	yes	—
131	D₄×C₂₃	—	4	3	no	—
132	D₄×C₂₃	—	4	3	no	—
133	D₄×C₂₃	—	4	3	no	—
134	D₄×C₂₃	—	4	6	no	—
135	D₄×C₂₃	—	8	3	no	—
136	C₂×C₄×C₂₃	—	2	3	no	—
137	C₂×C₄×C₂₃	—	2	3	no	—
138	C₂×C₄×C₂₃	—	2	6	no	—
139	C₂×C₄×C₂₃	—	2	2	no	—
140	C₂×C₄×C₂₃	—	2	6	no	—
141	C₂×C₄×C₂₃	—	2	1	no	—
142	C₂×C₄×C₂₃	—	2	3	no	—
143	C₂×C₄×C₂₃	—	2	1	no	—
144	C₂×C₄×C₂₃	—	4	1	no	—
145	C₂×C₄×C₂₃	—	4	3	no	—
146	C₂×C₄×C₂₃	—	4	1	no	—
147	C₂×C₄×C₂₃	—	4	3	no	—
148	C₂×C₄×C₂₃	—	4	1	no	—
149	C₂×C₄×C₂₃	—	4	6	no	—
150	C₂×C₄×C₂₃	—	8	6	no	—
151	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	3	yes	—
152	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	3	yes	—
153	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	3	yes	—
154	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	3	yes	—
155	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
156	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
157	C₈×C₂₃	—	4	1	no	—
158	C₈×C₂₃	—	4	3	no	—
159	#3522	C₂×C₂₃	1	1	yes	characteristic
160	#2984	C₂×C₂₃	1	1	yes	characteristic, complemented
161	#2276	C₂×C₂₃	1	1	yes	characteristic, complemented
162	#1509	C₂×C₂₃	1	3	yes	complemented
163	#1505	C₂×C₂₃	1	3	yes	complemented
164	#1502	C₂×C₂₃	1	3	yes	complemented
165	#1500	C₂×C₂₃	1	3	yes	complemented
166	C₂²×C₂₃	—	2	1	no	—
167	C₂²×C₂₃	—	2	1	no	—
168	C₂²×C₂₃	—	4	3	no	—
169	C₂²×C₂₃	—	4	3	no	—
170	C₂²×C₂₃	—	4	3	no	—
171	C₂²×C₂₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
172	C₂²×C₂₃	#576	1	1	yes	characteristic
173	C₂²×C₂₃	#577	1	1	yes	characteristic
174	C₄×C₂₃	—	2	1	no	—
175	C₄×C₂₃	—	2	1	no	—
176	C₄×C₂₃	—	2	3	no	—
177	C₄×C₂₃	—	2	3	no	—
178	C₄×C₂₃	—	2	3	no	—
179	C₄×C₂₃	—	4	6	no	—
180	C₄×C₂₃	—	4	2	no	—
181	C₄×C₂₃	—	4	1	no	—
182	C₄×C₂₃	—	4	3	no	—
183	C₄×C₂₃	—	4	1	no	—
184	C₄×C₂₃	C₂×#104	1	6	yes	—
185	#559	C₄×C₂₃	1	3	yes	complemented
186	Q₈²	C₄×C₂₃	1	1	yes	characteristic, complemented
187	#554	C₄×C₂₃	1	3	yes	complemented
188	#550	C₄×C₂₃	1	1	yes	characteristic, complemented
189	#548	—	2	1	no	—
190	#547	—	2	3	no	—
191	#542	—	2	3	no	—
192	#532	C₂²×C₂₃	1	3	yes	—
193	#529	C₂²×C₂₃	1	3	yes	—
194	#520	—	2	1	no	—
195	C₂×C₄×Q₈	—	2	1	no	—
196	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
197	#446	—	2	3	no	—
198	C₈×Q₈	—	2	1	no	—
199	#432	C₂²×C₂₃	1	3	yes	—
200	#431	C₂²×C₂₃	1	3	yes	—
201	C₄×C₄⋊C₄	—	2	3	no	—
202	C₄×C₄⋊C₄	C₂²×C₂₃	1	3	yes	—
203	#376	C₂²×C₂₃	1	3	yes	—
204	#328	C₂²×C₂₃	1	1	yes	characteristic
205	#328	C₂²×C₂₃	1	3	yes	—
206	#327	C₂²×C₂₃	1	3	yes	—
207	#327	C₂²×C₂₃	1	3	yes	—
208	#327	C₂²×C₂₃	1	6	yes	—
209	C₂×C₂₃	—	2	1	no	—
210	C₂×C₂₃	—	2	1	no	—
211	C₂×C₂₃	—	8	3	no	—
212	C₂×C₂₃	#2884	1	1	yes	characteristic
213	C₂×C₂₃	#2897	1	1	yes	characteristic
214	C₂×C₂₃	C₂²×#104	1	1	yes	characteristic
215	C₂×#41	—	2	1	no	—
216	C₂×#41	—	2	3	no	—
217	C₂²×Q₈	D₄×C₂₃	1	1	yes	characteristic
218	C₄⋊Q₈	—	2	3	no	—
219	C₄⋊Q₈	C₂×C₄×C₂₃	1	3	yes	—
220	#127	C₂×C₄×C₂₃	1	3	yes	—
221	#126	—	2	3	no	—
222	#125	C₂×C₄×C₂₃	1	3	yes	—
223	#124	—	2	3	no	—
224	#124	—	2	3	no	—
225	#124	C₂×C₄×C₂₃	1	3	yes	—
226	#123	—	2	3	no	—
227	#123	—	2	6	no	—
228	C₂²⋊Q₈	—	2	3	no	—
229	C₂²⋊Q₈	—	2	6	no	—
230	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
231	#121	—	2	3	no	—
232	#121	—	2	3	no	—
233	#121	C₂³×C₂₃	1	3	yes	—
234	C₄×Q₈	—	2	8	no	—
235	C₄×Q₈	—	2	1	no	—
236	C₄×Q₈	C₂×C₄×C₂₃	1	3	yes	—
237	C₄×Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
238	C₄×Q₈	C₂×C₄×C₂₃	1	3	yes	—
239	C₄×Q₈	D₄×C₂₃	1	1	yes	characteristic
240	C₄×Q₈	D₄×C₂₃	1	3	yes	—
241	C₄×D₄	—	2	3	no	—
242	C₄×D₄	—	2	3	no	—
243	C₄×D₄	—	2	3	no	—
244	C₄×D₄	C₂×C₄×C₂₃	1	3	yes	—
245	C₄×D₄	C₂×C₄×C₂₃	1	6	yes	—
246	#117	—	2	3	no	—
247	C₂×C₄⋊C₄	—	2	3	no	—
248	C₂×C₄⋊C₄	—	2	3	no	—
249	C₂×C₄⋊C₄	D₄×C₂₃	1	3	yes	—
250	C₂×C₄²	—	2	3	no	—
251	C₂×C₄²	—	2	3	no	—
252	C₂×C₄²	C₂³×C₂₃	1	3	yes	—
253	C₄⋊C₈	—	2	3	no	—
254	C₄⋊C₈	—	2	3	no	—
255	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
256	C₂²⋊C₈	C₂³×C₂₃	1	3	yes	—
257	#97	—	2	3	no	—
258	C₄×C₈	—	2	3	no	—
259	#95	—	2	3	no	—
260	#95	C₂³×C₂₃	1	1	yes	characteristic
261	#95	C₂³×C₂₃	1	3	yes	—
262	C₂₃	#17550	1	1	yes	characteristic, direct product factor, Sylow
263	#41	—	4	4	no	—
264	#41	—	8	3	no	—
265	#41	—	8	3	no	—
266	C₂×Q₈	—	2	4	no	—
267	C₂×Q₈	—	2	3	no	—
268	C₂×Q₈	C₂²⋊C₄×C₂₃	1	3	yes	—
269	C₂×Q₈	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
270	C₂×Q₈	C₂²×C₄×C₂₃	1	1	yes	characteristic
271	C₂×D₄	—	2	3	no	—
272	C₂×D₄	—	2	3	no	—
273	C₂×D₄	—	2	3	no	—
274	C₂×D₄	C₂²×C₄×C₂₃	1	3	yes	—
275	C₂²×C₄	—	2	1	no	—
276	C₂²×C₄	—	2	3	no	—
277	C₂²×C₄	—	2	3	no	—
278	C₂²×C₄	—	2	6	no	—
279	C₂²×C₄	C₂×D₄×C₂₃	1	3	yes	—
280	C₂²×C₄	C₂×D₄×C₂₃	1	3	yes	—
281	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
282	C₂×C₈	—	2	1	no	—
283	C₂×C₈	—	2	3	no	—
284	C₄⋊C₄	—	2	12	no	—
285	C₄⋊C₄	—	2	3	no	—
286	C₄⋊C₄	—	2	3	no	—
287	C₄⋊C₄	—	2	3	no	—
288	C₄⋊C₄	—	2	3	no	—
289	C₄⋊C₄	—	2	1	no	—
290	C₄⋊C₄	C₂²⋊C₄×C₂₃	1	3	yes	—
291	C₄⋊C₄	C₂²⋊C₄×C₂₃	1	3	yes	—
292	C₄⋊C₄	C₂²⋊C₄×C₂₃	1	6	yes	—
293	C₄⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
294	C₄⋊C₄	C₂²×C₄×C₂₃	1	3	yes	—
295	C₂²⋊C₄	—	2	1	no	—
296	C₂²⋊C₄	—	2	3	no	—
297	C₂²⋊C₄	—	2	3	no	—
298	C₂²⋊C₄	—	2	3	no	—
299	C₂²⋊C₄	—	2	6	no	—
300	C₂²⋊C₄	—	2	3	no	—
301	C₄²	—	2	12	no	—
302	C₄²	—	2	3	no	—
303	C₄²	—	8	3	no	—
304	C₄²	C₂²×C₄×C₂₃	1	3	yes	—
305	C₄²	C₂²×C₄×C₂₃	1	3	yes	—
306	C₄²	C₂×D₄×C₂₃	1	3	yes	—
307	C₄²	C₂×D₄×C₂₃	1	3	yes	—
308	C₂³	—	2	3	no	—
309	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
310	Q₈	—	2	6	no	—
311	Q₈	—	4	1	no	—
312	Q₈	—	8	3	no	—
313	Q₈	C₂₃×#104	1	4	yes	—
314	D₄	—	4	3	no	—
315	D₄	—	4	3	no	—
316	D₄	—	4	3	no	—
317	D₄	—	4	6	no	—
318	D₄	—	8	3	no	—
319	C₂×C₄	—	2	3	no	—
320	C₂×C₄	—	2	3	no	—
321	C₂×C₄	—	2	6	no	—
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	—	2	6	no	—
324	C₂×C₄	—	2	1	no	—
325	C₂×C₄	—	2	3	no	—
326	C₂×C₄	—	2	1	no	—
327	C₂×C₄	—	4	1	no	—
328	C₂×C₄	—	4	1	no	—
329	C₂×C₄	—	4	3	no	—
330	C₂×C₄	—	4	3	no	—
331	C₂×C₄	—	4	1	no	—
332	C₂×C₄	—	4	6	no	—
333	C₂×C₄	—	8	6	no	—
334	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	3	yes	—
335	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	3	yes	—
336	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	3	yes	—
337	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	3	yes	—
338	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
339	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
340	C₈	—	4	1	no	—
341	C₈	—	4	3	no	—
342	C₂²	—	2	1	no	—
343	C₂²	—	2	1	no	—
344	C₂²	—	4	3	no	—
345	C₂²	—	4	3	no	—
346	C₂²	—	4	3	no	—
347	C₂²	C₂²×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
348	C₂²	C₂₃×#576	1	1	yes	characteristic
349	C₂²	C₂₃×#577	1	1	yes	characteristic
350	C₄	—	2	1	no	—
351	C₄	—	2	1	no	—
352	C₄	—	2	3	no	—
353	C₄	—	2	3	no	—
354	C₄	—	2	3	no	—
355	C₄	—	4	6	no	—
356	C₄	—	4	2	no	—
357	C₄	—	4	1	no	—
358	C₄	—	4	3	no	—
359	C₄	—	4	1	no	—
360	C₄	C₂×C₂₃×#104	1	6	yes	—
361	C₂	—	2	1	no	—
362	C₂	—	2	1	no	—
363	C₂	—	8	3	no	—
364	C₂	C₂₃×#2884	1	1	yes	characteristic
365	C₂	C₂₃×#2897	1	1	yes	characteristic
366	C₂	C₂²×C₂₃×#104	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂²×C₂²⋊C₄
commutator	C₂×C₄	C₂³×C₄×C₂₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₃
prime radical	C₂₃×#3522	C₂
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂×C₄×Q₈×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂₃×#2984	C₂	semidirect
3. C₂₃×#2276	C₂	semidirect
4. C₂₃×#1509	C₂	semidirect
5. C₂₃×#1505	C₂	semidirect
6. C₂₃×#1502	C₂	semidirect
7. C₂₃×#1500	C₂	semidirect
8. C₂₃×#559	C₄	semidirect
9. Q₈²×C₂₃	C₄	semidirect
10. C₂₃×#554	C₄	semidirect
11. C₂₃×#550	C₄	semidirect
124. #17550	C₂₃	direct (N × H)
160. #2984	C₂×C₂₃	semidirect
161. #2276	C₂×C₂₃	semidirect
162. #1509	C₂×C₂₃	semidirect
163. #1505	C₂×C₂₃	semidirect
164. #1502	C₂×C₂₃	semidirect
165. #1500	C₂×C₂₃	semidirect
185. #559	C₄×C₂₃	semidirect
186. Q₈²	C₄×C₂₃	semidirect
187. #554	C₄×C₂₃	semidirect
188. #550	C₄×C₂₃	semidirect
262. C₂₃	#17550	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×#3522	2
C₂₃×#2984	2
C₂₃×#2276	2
C₂₃×#1509	2
C₂₃×#1505	2
C₂₃×#1502	2
C₂₃×#1500	2
#17550	23

Subgroups — C23×#17550 #19165176

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#17550 #19165176