Subgroups — C₂₃×#19749 #19167375

Order 5888.

822 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3185	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₃×#3182	C₂	1	2	yes	maximal, complemented
3	C₂₃×#3151	C₂	1	1	yes	maximal, characteristic
4	C₂₃×#3138	C₂	1	2	yes	maximal, complemented
5	C₂₃×#1722	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#1719	C₂	1	2	yes	maximal, complemented
7	C₂₃×#1717	C₂	1	2	yes	maximal, complemented
8	C₂₃×#1715	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#1709	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#1708	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#1455	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₂₃×AGL(1,ℤ/8)	—	2	2	no	—
13	C₂₃×#533	C₂²	1	2	yes	—
14	C₂₃×#532	C₂²	1	1	yes	characteristic
15	C₂×C₂₃×#127	C₂²	1	1	yes	characteristic
16	C₂₃×#500	C₂²	1	2	yes	complemented
17	C₂₃×#498	C₂²	1	1	yes	characteristic, complemented
18	C₂₃×#496	—	2	2	no	—
19	C₂₃×#494	C₂²	1	1	yes	characteristic, complemented
20	C₂₃×#493	C₂²	1	1	yes	characteristic
21	C₂₃×#493	C₂²	1	1	yes	characteristic
22	C₂₃×#492	C₂²	1	1	yes	characteristic
23	C₂₃×#492	C₂²	1	1	yes	characteristic
24	C₂₃×#492	C₂²	1	2	yes	complemented
25	C₂₃×#490	—	2	4	no	—
26	C₂₃×#487	C₂²	1	2	yes	complemented
27	C₂₃×#487	C₂²	1	2	yes	complemented
28	C₂₃×#486	C₂²	1	2	yes	—
29	C₂₃×#486	C₂²	1	2	yes	—
30	C₂₃×#486	C₂²	1	2	yes	—
31	C₂₃×#486	C₂²	1	2	yes	—
32	C₂₃×#486	C₂²	1	2	yes	complemented
33	C₂₃×#470	—	2	2	no	—
34	C₂₃×#468	—	2	4	no	—
35	C₂₃×#441	—	2	2	no	—
36	C₂₃×#440	—	2	4	no	—
37	C₂₃×#418	—	2	4	no	—
38	C₄×M₁₆×C₂₃	C₂²	1	2	yes	—
39	C₄×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
40	C₂₃×#322	C₂²	1	1	yes	characteristic, complemented
41	C₂₃×#322	C₂²	1	2	yes	complemented
42	C₈²×C₂₃	C₂²	1	1	yes	characteristic, complemented
43	C₂×#41×C₂₃	—	2	1	no	—
44	C₂²×D₄×C₂₃	—	2	1	no	—
45	C₂²×D₄×C₂₃	—	2	2	no	—
46	C₂₃×AGL(1,ℤ/8)	—	4	8	no	—
47	C₂×Q₁₆×C₂₃	—	2	2	no	—
48	C₂×SD₁₆×C₂₃	—	2	2	no	—
49	C₂×SD₁₆×C₂₃	—	2	2	no	—
50	C₂×SD₁₆×C₂₃	—	2	4	no	—
51	C₂×D₈×C₂₃	—	2	2	no	—
52	C₂×D₈×C₂₃	—	2	2	no	—
53	C₂×M₁₆×C₂₃	D₄	1	2	yes	—
54	C₂×M₁₆×C₂₃	D₄	1	4	yes	—
55	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
56	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
57	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
58	C₂₃×#127	—	2	2	no	—
59	C₂₃×#127	—	2	1	no	—
60	C₂₃×#127	C₂³	1	1	yes	characteristic
61	C₂₃×#127	C₂³	1	1	yes	characteristic
62	C₂₃×#127	C₂³	1	1	yes	characteristic
63	C₂₃×#125	—	2	2	no	—
64	C₂₃×#124	—	2	1	no	—
65	C₂₃×C₂²⋊Q₈	—	2	2	no	—
66	C₂₃×C₂²⋊Q₈	—	2	2	no	—
67	C₂₃×#121	—	2	2	no	—
68	C₄×Q₈×C₂₃	—	2	2	no	—
69	C₄×Q₈×C₂₃	—	2	2	no	—
70	C₄×D₄×C₂₃	—	2	2	no	—
71	C₂₃×#117	—	2	2	no	—
72	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
73	C₂₃×#107	—	2	4	no	—
74	C₂₃×#106	—	2	2	no	—
75	C₂₃×#103	—	2	4	no	—
76	C₂₃×#103	—	2	4	no	—
77	C₂₃×#102	—	2	4	no	—
78	C₂₃×#102	—	2	4	no	—
79	C₂₃×#102	—	2	4	no	—
80	C₂₃×#102	—	2	4	no	—
81	C₂₃×#102	—	2	4	no	—
82	C₂₃×#97	D₄	1	4	yes	—
83	C₂₃×#97	D₄	1	2	yes	—
84	C₄×C₈×C₂₃	C₂³	1	2	yes	—
85	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
86	C₄×C₈×C₂₃	C₂³	1	2	yes	—
87	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
88	C₂⁴×C₂₃	—	4	1	no	—
89	#41×C₂₃	—	4	4	no	—
90	C₂×Q₈×C₂₃	—	2	2	no	—
91	C₂×Q₈×C₂₃	—	2	2	no	—
92	C₂×Q₈×C₂₃	—	2	1	no	—
93	C₂×D₄×C₂₃	—	2	2	no	—
94	C₂×D₄×C₂₃	—	2	2	no	—
95	C₂×D₄×C₂₃	—	2	2	no	—
96	C₂×D₄×C₂₃	—	2	1	no	—
97	C₂×D₄×C₂₃	—	2	1	no	—
98	C₂×D₄×C₂₃	—	2	1	no	—
99	C₂×D₄×C₂₃	—	4	4	no	—
100	C₂×D₄×C₂₃	—	4	8	no	—
101	C₂×D₄×C₂₃	—	4	1	no	—
102	C₂×D₄×C₂₃	—	4	2	no	—
103	C₂×D₄×C₂₃	—	4	1	no	—
104	C₂²×C₄×C₂₃	—	4	1	no	—
105	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
106	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
107	Q₁₆×C₂₃	—	4	4	no	—
108	SD₁₆×C₂₃	—	4	8	no	—
109	SD₁₆×C₂₃	—	4	4	no	—
110	SD₁₆×C₂₃	—	4	4	no	—
111	D₈×C₂₃	—	4	4	no	—
112	D₈×C₂₃	—	4	4	no	—
113	M₁₆×C₂₃	—	2	4	no	—
114	M₁₆×C₂₃	—	4	4	no	—
115	C₂×C₈×C₂₃	C₂×D₄	1	4	yes	—
116	C₂×C₈×C₂₃	C₂×D₄	1	4	yes	—
117	C₂×C₈×C₂₃	C₂×D₄	1	2	yes	—
118	C₂×C₈×C₂₃	C₂×D₄	1	2	yes	—
119	C₄⋊C₄×C₂₃	—	2	2	no	—
120	C₄⋊C₄×C₂₃	—	2	2	no	—
121	C₄⋊C₄×C₂₃	—	2	2	no	—
122	C₄⋊C₄×C₂₃	—	2	2	no	—
123	C₄⋊C₄×C₂₃	—	2	2	no	—
124	C₄⋊C₄×C₂₃	—	4	2	no	—
125	C₄⋊C₄×C₂₃	—	4	2	no	—
126	C₂²⋊C₄×C₂₃	—	4	2	no	—
127	C₂²⋊C₄×C₂₃	—	4	2	no	—
128	C₄²×C₂₃	—	4	2	no	—
129	C₄²×C₂₃	C₂×D₄	1	2	yes	—
130	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
131	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
132	#19749	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
133	C₂³×C₂₃	—	4	1	no	—
134	C₂³×C₂₃	—	4	1	no	—
135	C₂³×C₂₃	—	4	1	no	—
136	C₂³×C₂₃	—	8	2	no	—
137	C₂³×C₂₃	—	8	4	no	—
138	C₂³×C₂₃	#127	1	1	yes	characteristic
139	Q₈×C₂₃	—	4	2	no	—
140	Q₈×C₂₃	—	4	4	no	—
141	Q₈×C₂₃	—	4	4	no	—
142	D₄×C₂₃	—	4	2	no	—
143	D₄×C₂₃	—	4	2	no	—
144	D₄×C₂₃	—	4	2	no	—
145	D₄×C₂₃	—	4	4	no	—
146	D₄×C₂₃	—	4	4	no	—
147	D₄×C₂₃	—	4	4	no	—
148	D₄×C₂₃	—	8	2	no	—
149	D₄×C₂₃	—	8	4	no	—
150	D₄×C₂₃	—	8	2	no	—
151	C₂×C₄×C₂₃	—	2	2	no	—
152	C₂×C₄×C₂₃	—	2	4	no	—
153	C₂×C₄×C₂₃	—	4	2	no	—
154	C₂×C₄×C₂₃	—	4	2	no	—
155	C₂×C₄×C₂₃	—	4	1	no	—
156	C₂×C₄×C₂₃	—	8	2	no	—
157	C₂×C₄×C₂₃	#127	1	2	yes	—
158	C₂×C₄×C₂₃	#127	1	1	yes	characteristic
159	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
160	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
161	C₈×C₂₃	—	2	2	no	—
162	C₈×C₂₃	—	2	4	no	—
163	C₈×C₂₃	—	2	4	no	—
164	C₈×C₂₃	AGL(1,ℤ/8)	1	4	yes	—
165	#3185	C₂×C₂₃	1	1	yes	characteristic, complemented
166	#3182	C₂×C₂₃	1	2	yes	complemented
167	#3151	C₂×C₂₃	1	1	yes	characteristic
168	#3138	C₂×C₂₃	1	2	yes	complemented
169	#1722	C₂×C₂₃	1	1	yes	characteristic, complemented
170	#1719	C₂×C₂₃	1	2	yes	complemented
171	#1717	C₂×C₂₃	1	2	yes	complemented
172	#1715	C₂×C₂₃	1	1	yes	characteristic, complemented
173	#1709	C₂×C₂₃	1	1	yes	characteristic, complemented
174	#1708	C₂×C₂₃	1	1	yes	characteristic, complemented
175	#1455	C₂×C₂₃	1	1	yes	characteristic, complemented
176	C₂²×C₂₃	—	2	1	no	—
177	C₂²×C₂₃	—	2	2	no	—
178	C₂²×C₂₃	—	8	1	no	—
179	C₂²×C₂₃	—	8	1	no	—
180	C₂²×C₂₃	—	8	1	no	—
181	C₂²×C₂₃	—	8	2	no	—
182	C₂²×C₂₃	—	8	2	no	—
183	C₂²×C₂₃	—	8	2	no	—
184	C₂²×C₂₃	—	16	4	no	—
185	C₂²×C₂₃	C₂×#127	1	1	yes	characteristic
186	C₄×C₂₃	—	2	1	no	—
187	C₄×C₂₃	—	2	2	no	—
188	C₄×C₂₃	—	8	1	no	—
189	C₄×C₂₃	—	8	2	no	—
190	C₄×C₂₃	—	8	2	no	—
191	C₄×C₂₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
192	C₄×C₂₃	#575	1	4	yes	—
193	C₂×AGL(1,ℤ/8)	—	2	2	no	—
194	#533	C₂²×C₂₃	1	2	yes	—
195	#532	C₂²×C₂₃	1	1	yes	characteristic
196	C₂×#127	C₂²×C₂₃	1	1	yes	characteristic
197	#500	C₂²×C₂₃	1	2	yes	complemented
198	#498	C₂²×C₂₃	1	1	yes	characteristic, complemented
199	#496	—	2	2	no	—
200	#494	C₂²×C₂₃	1	1	yes	characteristic, complemented
201	#493	C₂²×C₂₃	1	1	yes	characteristic
202	#493	C₂²×C₂₃	1	1	yes	characteristic
203	#492	C₂²×C₂₃	1	1	yes	characteristic
204	#492	C₂²×C₂₃	1	1	yes	characteristic
205	#492	C₂²×C₂₃	1	2	yes	complemented
206	#490	—	2	4	no	—
207	#487	C₂²×C₂₃	1	2	yes	complemented
208	#487	C₂²×C₂₃	1	2	yes	complemented
209	#486	C₂²×C₂₃	1	2	yes	—
210	#486	C₂²×C₂₃	1	2	yes	—
211	#486	C₂²×C₂₃	1	2	yes	—
212	#486	C₂²×C₂₃	1	2	yes	—
213	#486	C₂²×C₂₃	1	2	yes	complemented
214	#470	—	2	2	no	—
215	#468	—	2	4	no	—
216	#441	—	2	2	no	—
217	#440	—	2	4	no	—
218	#418	—	2	4	no	—
219	C₄×M₁₆	C₂²×C₂₃	1	2	yes	—
220	C₄×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
221	#322	C₂²×C₂₃	1	1	yes	characteristic, complemented
222	#322	C₂²×C₂₃	1	2	yes	complemented
223	C₈²	C₂²×C₂₃	1	1	yes	characteristic, complemented
224	C₂×C₂₃	—	4	1	no	—
225	C₂×C₂₃	—	16	1	no	—
226	C₂×C₂₃	—	16	1	no	—
227	C₂×C₂₃	—	16	1	no	—
228	C₂×C₂₃	#3151	1	1	yes	characteristic
229	C₂×C₂₃	#3153	1	2	yes	—
230	C₂×#41	—	2	1	no	—
231	C₂²×D₄	—	2	1	no	—
232	C₂²×D₄	—	2	2	no	—
233	AGL(1,ℤ/8)	—	4	8	no	—
234	C₂×Q₁₆	—	2	2	no	—
235	C₂×SD₁₆	—	2	2	no	—
236	C₂×SD₁₆	—	2	2	no	—
237	C₂×SD₁₆	—	2	4	no	—
238	C₂×D₈	—	2	2	no	—
239	C₂×D₈	—	2	2	no	—
240	C₂×M₁₆	D₄×C₂₃	1	2	yes	—
241	C₂×M₁₆	D₄×C₂₃	1	4	yes	—
242	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
243	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
244	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
245	#127	—	2	2	no	—
246	#127	—	2	1	no	—
247	#127	C₂³×C₂₃	1	1	yes	characteristic
248	#127	C₂³×C₂₃	1	1	yes	characteristic
249	#127	C₂³×C₂₃	1	1	yes	characteristic
250	#125	—	2	2	no	—
251	#124	—	2	1	no	—
252	C₂²⋊Q₈	—	2	2	no	—
253	C₂²⋊Q₈	—	2	2	no	—
254	#121	—	2	2	no	—
255	C₄×Q₈	—	2	2	no	—
256	C₄×Q₈	—	2	2	no	—
257	C₄×D₄	—	2	2	no	—
258	#117	—	2	2	no	—
259	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
260	#107	—	2	4	no	—
261	#106	—	2	2	no	—
262	#103	—	2	4	no	—
263	#103	—	2	4	no	—
264	#102	—	2	4	no	—
265	#102	—	2	4	no	—
266	#102	—	2	4	no	—
267	#102	—	2	4	no	—
268	#102	—	2	4	no	—
269	#97	D₄×C₂₃	1	4	yes	—
270	#97	D₄×C₂₃	1	2	yes	—
271	C₄×C₈	C₂³×C₂₃	1	2	yes	—
272	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
273	C₄×C₈	C₂³×C₂₃	1	2	yes	—
274	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
275	C₂₃	#19749	1	1	yes	characteristic, direct product factor, Sylow
276	C₂⁴	—	4	1	no	—
277	#41	—	4	4	no	—
278	C₂×Q₈	—	2	2	no	—
279	C₂×Q₈	—	2	2	no	—
280	C₂×Q₈	—	2	1	no	—
281	C₂×D₄	—	2	2	no	—
282	C₂×D₄	—	2	2	no	—
283	C₂×D₄	—	2	2	no	—
284	C₂×D₄	—	2	1	no	—
285	C₂×D₄	—	2	1	no	—
286	C₂×D₄	—	2	1	no	—
287	C₂×D₄	—	4	4	no	—
288	C₂×D₄	—	4	8	no	—
289	C₂×D₄	—	4	1	no	—
290	C₂×D₄	—	4	2	no	—
291	C₂×D₄	—	4	1	no	—
292	C₂²×C₄	—	4	1	no	—
293	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
294	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
295	Q₁₆	—	4	4	no	—
296	SD₁₆	—	4	4	no	—
297	SD₁₆	—	4	8	no	—
298	SD₁₆	—	4	4	no	—
299	D₈	—	4	4	no	—
300	D₈	—	4	4	no	—
301	M₁₆	—	2	4	no	—
302	M₁₆	—	4	4	no	—
303	C₂×C₈	C₂×D₄×C₂₃	1	4	yes	—
304	C₂×C₈	C₂×D₄×C₂₃	1	4	yes	—
305	C₂×C₈	C₂×D₄×C₂₃	1	2	yes	—
306	C₂×C₈	C₂×D₄×C₂₃	1	2	yes	—
307	C₄⋊C₄	—	2	2	no	—
308	C₄⋊C₄	—	2	2	no	—
309	C₄⋊C₄	—	2	2	no	—
310	C₄⋊C₄	—	2	2	no	—
311	C₄⋊C₄	—	2	2	no	—
312	C₄⋊C₄	—	4	2	no	—
313	C₄⋊C₄	—	4	2	no	—
314	C₂²⋊C₄	—	4	2	no	—
315	C₂²⋊C₄	—	4	2	no	—
316	C₄²	—	4	2	no	—
317	C₄²	C₂×D₄×C₂₃	1	2	yes	—
318	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
319	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
320	C₂³	—	4	1	no	—
321	C₂³	—	4	1	no	—
322	C₂³	—	4	1	no	—
323	C₂³	—	8	2	no	—
324	C₂³	—	8	4	no	—
325	C₂³	C₂₃×#127	1	1	yes	characteristic
326	Q₈	—	4	2	no	—
327	Q₈	—	4	4	no	—
328	Q₈	—	4	4	no	—
329	D₄	—	4	2	no	—
330	D₄	—	4	2	no	—
331	D₄	—	4	2	no	—
332	D₄	—	4	4	no	—
333	D₄	—	4	4	no	—
334	D₄	—	4	4	no	—
335	D₄	—	8	2	no	—
336	D₄	—	8	4	no	—
337	D₄	—	8	2	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	2	4	no	—
340	C₂×C₄	—	4	2	no	—
341	C₂×C₄	—	4	2	no	—
342	C₂×C₄	—	4	1	no	—
343	C₂×C₄	—	8	2	no	—
344	C₂×C₄	C₂₃×#127	1	2	yes	—
345	C₂×C₄	C₂₃×#127	1	1	yes	characteristic
346	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
347	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
348	C₈	—	2	2	no	—
349	C₈	—	2	4	no	—
350	C₈	—	2	4	no	—
351	C₈	C₂₃×AGL(1,ℤ/8)	1	4	yes	—
352	C₂²	—	2	1	no	—
353	C₂²	—	2	2	no	—
354	C₂²	—	8	1	no	—
355	C₂²	—	8	1	no	—
356	C₂²	—	8	1	no	—
357	C₂²	—	8	2	no	—
358	C₂²	—	8	2	no	—
359	C₂²	—	8	2	no	—
360	C₂²	—	16	4	no	—
361	C₂²	C₂×C₂₃×#127	1	1	yes	characteristic
362	C₄	—	2	1	no	—
363	C₄	—	2	2	no	—
364	C₄	—	8	1	no	—
365	C₄	—	8	2	no	—
366	C₄	—	8	2	no	—
367	C₄	C₂×C₂₃×AGL(1,ℤ/8)	1	2	yes	—
368	C₄	C₂₃×#575	1	4	yes	—
369	C₂	—	4	1	no	—
370	C₂	—	16	1	no	—
371	C₂	—	16	1	no	—
372	C₂	—	16	1	no	—
373	C₂	C₂₃×#3151	1	1	yes	characteristic
374	C₂	C₂₃×#3153	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂×#127
commutator, Frattini, cosocle	C₄²	C₂⁴×C₂₃
prime radical	C₂₃×#3151	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂×C₄²×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₃×#3185	C₂	semidirect
2. C₂₃×#3182	C₂	semidirect
4. C₂₃×#3138	C₂	semidirect
5. C₂₃×#1722	C₂	semidirect
6. C₂₃×#1719	C₂	semidirect
7. C₂₃×#1717	C₂	semidirect
8. C₂₃×#1715	C₂	semidirect
9. C₂₃×#1709	C₂	semidirect
10. C₂₃×#1708	C₂	semidirect
11. C₂₃×#1455	C₂	semidirect
16. C₂₃×#500	C₂²	semidirect
17. C₂₃×#498	C₂²	semidirect
19. C₂₃×#494	C₂²	semidirect
24. C₂₃×#492	C₂²	semidirect
26. C₂₃×#487	C₂²	semidirect
27. C₂₃×#487	C₂²	semidirect
32. C₂₃×#486	C₂²	semidirect
40. C₂₃×#322	C₂²	semidirect
41. C₂₃×#322	C₂²	semidirect
42. C₈²×C₂₃	C₂²	semidirect
132. #19749	C₂₃	direct (N × H)
165. #3185	C₂×C₂₃	semidirect
166. #3182	C₂×C₂₃	semidirect
168. #3138	C₂×C₂₃	semidirect
169. #1722	C₂×C₂₃	semidirect
170. #1719	C₂×C₂₃	semidirect
171. #1717	C₂×C₂₃	semidirect
172. #1715	C₂×C₂₃	semidirect
173. #1709	C₂×C₂₃	semidirect
174. #1708	C₂×C₂₃	semidirect
175. #1455	C₂×C₂₃	semidirect
197. #500	C₂²×C₂₃	semidirect
198. #498	C₂²×C₂₃	semidirect
200. #494	C₂²×C₂₃	semidirect
205. #492	C₂²×C₂₃	semidirect
207. #487	C₂²×C₂₃	semidirect
208. #487	C₂²×C₂₃	semidirect
213. #486	C₂²×C₂₃	semidirect
221. #322	C₂²×C₂₃	semidirect
222. #322	C₂²×C₂₃	semidirect
223. C₈²	C₂²×C₂₃	semidirect
275. C₂₃	#19749	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×#3185	2
C₂₃×#3182	2
C₂₃×#3151	2
C₂₃×#3138	2
C₂₃×#1722	2
C₂₃×#1719	2
C₂₃×#1717	2
C₂₃×#1715	2
C₂₃×#1709	2
C₂₃×#1708	2
C₂₃×#1455	2
#19749	23

Subgroups — C23×#19749 #19167375

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#19749 #19167375