Subgroups — C₂₃×#13319 #19160945

Order 5888.

572 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₂₃×D₁₆	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₃×#472	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3058	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₂₃×#361	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#2140	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₂₃×#350	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#1382	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₂₃×AGL(1,ℤ/8)	—	2	1	no	—
9	C₂²×D₈×C₂₃	C₂²	1	1	yes	characteristic
10	C₂²×D₈×C₂₃	C₂²	1	1	yes	characteristic
11	C₂×C₂₃×#131	C₂²	1	1	yes	characteristic
12	C₂₃×#535	—	2	1	no	—
13	C₂×C₂₃×D₁₆	—	2	2	no	—
14	C₂×C₂₃×D₁₆	—	2	2	no	—
15	C₂×C₂₃×D₁₆	—	2	2	no	—
16	C₂×C₂₃×M₃₂	C₂²	1	1	yes	characteristic
17	C₂²×C₁₆×C₂₃	C₂²	1	1	yes	characteristic
18	C₂₃×#472	—	2	2	no	—
19	C₂₃×#472	—	2	2	no	—
20	C₂₃×#469	—	2	2	no	—
21	C₂₃×#466	—	2	2	no	—
22	C₂×C₂₃×#108	C₂²	1	1	yes	characteristic
23	C₂₃×#427	C₂²	1	1	yes	characteristic
24	C₂₃×#418	—	2	1	no	—
25	C₂×C₂₃×#100	—	2	1	no	—
26	C₂₃×#361	—	2	2	no	—
27	C₂₃×#357	—	2	2	no	—
28	C₂₃×#350	—	2	2	no	—
29	C₂×#41×C₂₃	D₄	1	1	yes	characteristic
30	C₂²×D₄×C₂₃	—	2	1	no	—
31	C₂²×D₄×C₂₃	—	2	1	no	—
32	C₂₃×AGL(1,ℤ/8)	—	2	4	no	—
33	C₂₃×AGL(1,ℤ/8)	—	4	2	no	—
34	C₂×SD₁₆×C₂₃	—	4	1	no	—
35	C₂×D₈×C₂₃	—	2	1	no	—
36	C₂×D₈×C₂₃	—	2	1	no	—
37	C₂×D₈×C₂₃	—	2	1	no	—
38	C₂×D₈×C₂₃	—	2	1	no	—
39	C₂×D₈×C₂₃	—	2	1	no	—
40	C₂×D₈×C₂₃	—	2	1	no	—
41	C₂×D₈×C₂₃	—	2	1	no	—
42	C₂×D₈×C₂₃	—	2	1	no	—
43	C₂×D₈×C₂₃	—	2	1	no	—
44	C₂×D₈×C₂₃	—	2	1	no	—
45	C₂×D₈×C₂₃	—	4	1	no	—
46	C₂×D₈×C₂₃	D₄	1	2	yes	—
47	C₂×D₈×C₂₃	D₄	1	2	yes	complemented
48	C₂₃×#131	—	2	1	no	—
49	C₂₃×#131	—	2	1	no	—
50	C₂₃×#131	—	2	1	no	—
51	C₂₃×#131	—	2	1	no	—
52	C₂×M₁₆×C₂₃	—	2	1	no	—
53	C₂×M₁₆×C₂₃	—	2	1	no	—
54	C₂×M₁₆×C₂₃	D₄	1	1	yes	characteristic
55	C₂²×C₈×C₂₃	—	2	1	no	—
56	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
57	C₂₃×#127	—	4	1	no	—
58	C₂₃×#124	—	4	1	no	—
59	C₂₃×#121	—	2	4	no	—
60	C₂₃×#120	—	4	2	no	—
61	C₂₃×#117	—	2	1	no	—
62	C₂₃×D₁₆	—	2	8	no	—
63	C₂₃×M₃₂	—	2	1	no	—
64	C₂₃×M₃₂	—	2	1	no	—
65	C₂×C₁₆×C₂₃	—	2	1	no	—
66	C₂×C₁₆×C₂₃	—	2	1	no	—
67	C₂×C₁₆×C₂₃	—	2	1	no	—
68	C₂×C₁₆×C₂₃	D₄	1	2	yes	complemented
69	C₂₃×#108	—	2	1	no	—
70	C₂₃×#108	D₄	1	2	yes	complemented
71	C₂₃×#107	D₄	1	2	yes	—
72	C₂₃×#106	—	2	1	no	—
73	C₂₃×#102	—	2	4	no	—
74	C₂₃×#100	—	2	4	no	—
75	C₂⁴×C₂₃	—	4	1	no	—
76	C₂⁴×C₂₃	—	4	1	no	—
77	#41×C₂₃	—	2	1	no	—
78	#41×C₂₃	—	2	1	no	—
79	#41×C₂₃	—	2	1	no	—
80	#41×C₂₃	—	2	1	no	—
81	C₂×Q₈×C₂₃	D₈	1	1	yes	characteristic
82	C₂×D₄×C₂₃	—	2	1	no	—
83	C₂×D₄×C₂₃	—	2	2	no	—
84	C₂×D₄×C₂₃	—	2	2	no	—
85	C₂×D₄×C₂₃	—	4	4	no	—
86	C₂×D₄×C₂₃	—	4	1	no	—
87	C₂×D₄×C₂₃	—	4	1	no	—
88	C₂×D₄×C₂₃	—	4	1	no	—
89	C₂×D₄×C₂₃	—	4	1	no	—
90	C₂×D₄×C₂₃	—	4	1	no	—
91	C₂×D₄×C₂₃	—	4	1	no	—
92	C₂×D₄×C₂₃	—	4	1	no	—
93	C₂×D₄×C₂₃	—	4	1	no	—
94	C₂×D₄×C₂₃	—	4	1	no	—
95	C₂×D₄×C₂₃	—	4	1	no	—
96	C₂×D₄×C₂₃	D₈	1	1	yes	characteristic
97	C₂²×C₄×C₂₃	—	2	1	no	—
98	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
99	SD₁₆×C₂₃	—	4	4	no	—
100	D₈×C₂₃	—	2	2	no	—
101	D₈×C₂₃	—	2	2	no	—
102	D₈×C₂₃	—	2	2	no	—
103	D₈×C₂₃	—	2	2	no	—
104	D₈×C₂₃	—	4	4	no	—
105	D₈×C₂₃	—	4	1	no	—
106	D₈×C₂₃	—	4	1	no	—
107	D₈×C₂₃	—	4	1	no	—
108	D₈×C₂₃	—	4	1	no	—
109	M₁₆×C₂₃	—	2	1	no	—
110	M₁₆×C₂₃	—	2	2	no	—
111	M₁₆×C₂₃	—	2	1	no	—
112	M₁₆×C₂₃	—	4	1	no	—
113	M₁₆×C₂₃	—	4	1	no	—
114	M₁₆×C₂₃	—	4	1	no	—
115	C₂×C₈×C₂₃	—	2	1	no	—
116	C₂×C₈×C₂₃	—	4	1	no	—
117	C₂×C₈×C₂₃	—	4	1	no	—
118	C₂×C₈×C₂₃	—	4	1	no	—
119	C₂×C₈×C₂₃	C₂×D₄	1	1	yes	characteristic
120	C₂×C₈×C₂₃	C₂×D₄	1	1	yes	characteristic
121	C₂×C₈×C₂₃	C₂×D₄	1	1	yes	characteristic
122	C₂×C₈×C₂₃	C₂×D₄	1	1	yes	characteristic
123	C₂×C₈×C₂₃	C₂×D₄	1	1	yes	characteristic
124	C₂×C₈×C₂₃	#41	1	1	yes	characteristic
125	C₄⋊C₄×C₂₃	—	2	2	no	—
126	C₂²⋊C₄×C₂₃	—	4	4	no	—
127	C₂²⋊C₄×C₂₃	—	4	1	no	—
128	C₄²×C₂₃	—	4	1	no	—
129	C₁₆×C₂₃	—	2	2	no	—
130	C₁₆×C₂₃	—	4	1	no	—
131	#13319	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
132	C₂³×C₂₃	—	2	1	no	—
133	C₂³×C₂₃	—	4	2	no	—
134	C₂³×C₂₃	—	4	2	no	—
135	C₂³×C₂₃	—	8	1	no	—
136	C₂³×C₂₃	—	8	1	no	—
137	C₂³×C₂₃	—	8	1	no	—
138	C₂³×C₂₃	—	8	1	no	—
139	C₂³×C₂₃	—	16	2	no	—
140	C₂³×C₂₃	—	16	2	no	—
141	C₂³×C₂₃	AGL(1,ℤ/8)	1	1	yes	characteristic
142	Q₈×C₂₃	—	2	1	no	—
143	Q₈×C₂₃	—	2	1	no	—
144	D₄×C₂₃	—	2	1	no	—
145	D₄×C₂₃	—	2	1	no	—
146	D₄×C₂₃	—	4	1	no	—
147	D₄×C₂₃	—	4	1	no	—
148	D₄×C₂₃	—	4	2	no	—
149	D₄×C₂₃	—	4	2	no	—
150	D₄×C₂₃	—	4	2	no	—
151	D₄×C₂₃	—	4	2	no	—
152	D₄×C₂₃	—	8	1	no	—
153	D₄×C₂₃	—	8	1	no	—
154	D₄×C₂₃	—	8	1	no	—
155	D₄×C₂₃	—	8	1	no	—
156	D₄×C₂₃	—	16	4	no	—
157	C₂×C₄×C₂₃	—	2	1	no	—
158	C₂×C₄×C₂₃	—	4	1	no	—
159	C₂×C₄×C₂₃	—	4	1	no	—
160	C₂×C₄×C₂₃	—	4	2	no	—
161	C₂×C₄×C₂₃	#120	1	1	yes	characteristic
162	C₂×C₄×C₂₃	#120	1	1	yes	characteristic
163	C₂×C₄×C₂₃	#121	1	1	yes	characteristic
164	C₂×C₄×C₂₃	C₂×D₈	1	1	yes	characteristic
165	C₂×C₄×C₂₃	#135	1	1	yes	characteristic
166	C₂×C₄×C₂₃	AGL(1,ℤ/8)	1	1	yes	characteristic
167	C₈×C₂₃	—	4	1	no	—
168	C₈×C₂₃	—	4	2	no	—
169	C₈×C₂₃	#120	1	1	yes	characteristic
170	C₈×C₂₃	#121	1	1	yes	characteristic
171	C₈×C₂₃	#121	1	1	yes	characteristic
172	C₈×C₂₃	#127	1	1	yes	characteristic
173	C₂²×D₁₆	C₂×C₂₃	1	1	yes	characteristic, complemented
174	C₂×#472	C₂×C₂₃	1	1	yes	characteristic, complemented
175	#3058	C₂×C₂₃	1	1	yes	characteristic, complemented
176	C₂×#361	C₂×C₂₃	1	1	yes	characteristic, complemented
177	#2140	C₂×C₂₃	1	1	yes	characteristic, complemented
178	C₂×#350	C₂×C₂₃	1	1	yes	characteristic, complemented
179	#1382	C₂×C₂₃	1	1	yes	characteristic, complemented
180	C₂²×C₂₃	—	2	2	no	—
181	C₂²×C₂₃	—	4	2	no	—
182	C₂²×C₂₃	—	4	1	no	—
183	C₂²×C₂₃	—	8	4	no	—
184	C₂²×C₂₃	—	8	2	no	—
185	C₂²×C₂₃	—	8	2	no	—
186	C₂²×C₂₃	—	16	2	no	—
187	C₂²×C₂₃	—	16	2	no	—
188	C₂²×C₂₃	—	16	2	no	—
189	C₂²×C₂₃	—	16	2	no	—
190	C₂²×C₂₃	—	16	2	no	—
191	C₂²×C₂₃	#447	1	1	yes	characteristic
192	C₂²×C₂₃	#449	1	1	yes	characteristic
193	C₂²×C₂₃	#469	1	1	yes	characteristic
194	C₄×C₂₃	—	4	1	no	—
195	C₄×C₂₃	—	8	2	no	—
196	C₄×C₂₃	#392	1	1	yes	characteristic
197	C₄×C₂₃	#447	1	1	yes	characteristic
198	C₄×C₂₃	#449	1	1	yes	characteristic
199	C₄×C₂₃	#466	1	1	yes	characteristic
200	C₂×AGL(1,ℤ/8)	—	2	1	no	—
201	C₂²×D₈	C₂²×C₂₃	1	1	yes	characteristic
202	C₂²×D₈	C₂²×C₂₃	1	1	yes	characteristic
203	C₂×#131	C₂²×C₂₃	1	1	yes	characteristic
204	#535	—	2	1	no	—
205	C₂×D₁₆	—	2	2	no	—
206	C₂×D₁₆	—	2	2	no	—
207	C₂×D₁₆	—	2	2	no	—
208	C₂×M₃₂	C₂²×C₂₃	1	1	yes	characteristic
209	C₂²×C₁₆	C₂²×C₂₃	1	1	yes	characteristic
210	#472	—	2	2	no	—
211	#472	—	2	2	no	—
212	#469	—	2	2	no	—
213	#466	—	2	2	no	—
214	C₂×#108	C₂²×C₂₃	1	1	yes	characteristic
215	#427	C₂²×C₂₃	1	1	yes	characteristic
216	#418	—	2	1	no	—
217	C₂×#100	—	2	1	no	—
218	#361	—	2	2	no	—
219	#357	—	2	2	no	—
220	#350	—	2	2	no	—
221	C₂×C₂₃	—	2	1	no	—
222	C₂×C₂₃	—	2	1	no	—
223	C₂×C₂₃	—	8	1	no	—
224	C₂×C₂₃	—	16	2	no	—
225	C₂×C₂₃	—	16	2	no	—
226	C₂×C₂₃	#1999	1	1	yes	characteristic
227	C₂×C₂₃	#2192	1	2	yes	—
228	C₂×#41	D₄×C₂₃	1	1	yes	characteristic
229	C₂²×D₄	—	2	1	no	—
230	C₂²×D₄	—	2	1	no	—
231	AGL(1,ℤ/8)	—	2	4	no	—
232	AGL(1,ℤ/8)	—	4	2	no	—
233	C₂×SD₁₆	—	4	1	no	—
234	C₂×D₈	—	2	1	no	—
235	C₂×D₈	—	2	1	no	—
236	C₂×D₈	—	2	1	no	—
237	C₂×D₈	—	2	1	no	—
238	C₂×D₈	—	2	1	no	—
239	C₂×D₈	—	2	1	no	—
240	C₂×D₈	—	2	1	no	—
241	C₂×D₈	—	2	1	no	—
242	C₂×D₈	—	2	1	no	—
243	C₂×D₈	—	2	1	no	—
244	C₂×D₈	—	4	1	no	—
245	C₂×D₈	D₄×C₂₃	1	2	yes	—
246	C₂×D₈	D₄×C₂₃	1	2	yes	complemented
247	#131	—	2	1	no	—
248	#131	—	2	1	no	—
249	#131	—	2	1	no	—
250	#131	—	2	1	no	—
251	C₂×M₁₆	—	2	1	no	—
252	C₂×M₁₆	—	2	1	no	—
253	C₂×M₁₆	D₄×C₂₃	1	1	yes	characteristic
254	C₂²×C₈	—	2	1	no	—
255	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
256	#127	—	4	1	no	—
257	#124	—	4	1	no	—
258	#121	—	2	4	no	—
259	#120	—	4	2	no	—
260	#117	—	2	1	no	—
261	D₁₆	—	2	8	no	—
262	M₃₂	—	2	1	no	—
263	M₃₂	—	2	1	no	—
264	C₂×C₁₆	—	2	1	no	—
265	C₂×C₁₆	—	2	1	no	—
266	C₂×C₁₆	—	2	1	no	—
267	C₂×C₁₆	D₄×C₂₃	1	2	yes	complemented
268	#108	—	2	1	no	—
269	#108	D₄×C₂₃	1	2	yes	complemented
270	#107	D₄×C₂₃	1	2	yes	—
271	#106	—	2	1	no	—
272	#102	—	2	4	no	—
273	#100	—	2	4	no	—
274	C₂₃	#13319	1	1	yes	characteristic, direct product factor, Sylow
275	C₂⁴	—	4	1	no	—
276	C₂⁴	—	4	1	no	—
277	#41	—	2	1	no	—
278	#41	—	2	1	no	—
279	#41	—	2	1	no	—
280	#41	—	2	1	no	—
281	C₂×Q₈	D₈×C₂₃	1	1	yes	characteristic
282	C₂×D₄	—	2	1	no	—
283	C₂×D₄	—	2	2	no	—
284	C₂×D₄	—	2	2	no	—
285	C₂×D₄	—	4	4	no	—
286	C₂×D₄	—	4	1	no	—
287	C₂×D₄	—	4	1	no	—
288	C₂×D₄	—	4	1	no	—
289	C₂×D₄	—	4	1	no	—
290	C₂×D₄	—	4	1	no	—
291	C₂×D₄	—	4	1	no	—
292	C₂×D₄	—	4	1	no	—
293	C₂×D₄	—	4	1	no	—
294	C₂×D₄	—	4	1	no	—
295	C₂×D₄	—	4	1	no	—
296	C₂×D₄	D₈×C₂₃	1	1	yes	characteristic
297	C₂²×C₄	—	2	1	no	—
298	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
299	SD₁₆	—	4	4	no	—
300	D₈	—	2	2	no	—
301	D₈	—	2	2	no	—
302	D₈	—	2	2	no	—
303	D₈	—	2	2	no	—
304	D₈	—	4	4	no	—
305	D₈	—	4	1	no	—
306	D₈	—	4	1	no	—
307	D₈	—	4	1	no	—
308	D₈	—	4	1	no	—
309	M₁₆	—	2	1	no	—
310	M₁₆	—	2	2	no	—
311	M₁₆	—	2	1	no	—
312	M₁₆	—	4	1	no	—
313	M₁₆	—	4	1	no	—
314	M₁₆	—	4	1	no	—
315	C₂×C₈	—	2	1	no	—
316	C₂×C₈	—	4	1	no	—
317	C₂×C₈	—	4	1	no	—
318	C₂×C₈	—	4	1	no	—
319	C₂×C₈	C₂×D₄×C₂₃	1	1	yes	characteristic
320	C₂×C₈	C₂×D₄×C₂₃	1	1	yes	characteristic
321	C₂×C₈	C₂×D₄×C₂₃	1	1	yes	characteristic
322	C₂×C₈	C₂×D₄×C₂₃	1	1	yes	characteristic
323	C₂×C₈	C₂×D₄×C₂₃	1	1	yes	characteristic
324	C₂×C₈	#41×C₂₃	1	1	yes	characteristic
325	C₄⋊C₄	—	2	2	no	—
326	C₂²⋊C₄	—	4	4	no	—
327	C₂²⋊C₄	—	4	1	no	—
328	C₄²	—	4	1	no	—
329	C₁₆	—	2	2	no	—
330	C₁₆	—	4	1	no	—
331	C₂³	—	2	1	no	—
332	C₂³	—	4	2	no	—
333	C₂³	—	4	2	no	—
334	C₂³	—	8	1	no	—
335	C₂³	—	8	1	no	—
336	C₂³	—	8	1	no	—
337	C₂³	—	8	1	no	—
338	C₂³	—	16	2	no	—
339	C₂³	—	16	2	no	—
340	C₂³	C₂₃×AGL(1,ℤ/8)	1	1	yes	characteristic
341	Q₈	—	2	1	no	—
342	Q₈	—	2	1	no	—
343	D₄	—	2	1	no	—
344	D₄	—	2	1	no	—
345	D₄	—	4	1	no	—
346	D₄	—	4	1	no	—
347	D₄	—	4	2	no	—
348	D₄	—	4	2	no	—
349	D₄	—	4	2	no	—
350	D₄	—	4	2	no	—
351	D₄	—	8	1	no	—
352	D₄	—	8	1	no	—
353	D₄	—	8	1	no	—
354	D₄	—	8	1	no	—
355	D₄	—	16	4	no	—
356	C₂×C₄	—	2	1	no	—
357	C₂×C₄	—	4	1	no	—
358	C₂×C₄	—	4	1	no	—
359	C₂×C₄	—	4	2	no	—
360	C₂×C₄	C₂₃×#120	1	1	yes	characteristic
361	C₂×C₄	C₂₃×#120	1	1	yes	characteristic
362	C₂×C₄	C₂₃×#121	1	1	yes	characteristic
363	C₂×C₄	C₂×D₈×C₂₃	1	1	yes	characteristic
364	C₂×C₄	C₂₃×#135	1	1	yes	characteristic
365	C₂×C₄	C₂₃×AGL(1,ℤ/8)	1	1	yes	characteristic
366	C₈	—	4	1	no	—
367	C₈	—	4	2	no	—
368	C₈	C₂₃×#120	1	1	yes	characteristic
369	C₈	C₂₃×#121	1	1	yes	characteristic
370	C₈	C₂₃×#121	1	1	yes	characteristic
371	C₈	C₂₃×#127	1	1	yes	characteristic
372	C₂²	—	2	2	no	—
373	C₂²	—	4	2	no	—
374	C₂²	—	4	1	no	—
375	C₂²	—	8	4	no	—
376	C₂²	—	8	2	no	—
377	C₂²	—	8	2	no	—
378	C₂²	—	16	2	no	—
379	C₂²	—	16	2	no	—
380	C₂²	—	16	2	no	—
381	C₂²	—	16	2	no	—
382	C₂²	—	16	2	no	—
383	C₂²	C₂₃×#447	1	1	yes	characteristic
384	C₂²	C₂₃×#449	1	1	yes	characteristic
385	C₂²	C₂₃×#469	1	1	yes	characteristic
386	C₄	—	4	1	no	—
387	C₄	—	8	2	no	—
388	C₄	C₂₃×#392	1	1	yes	characteristic
389	C₄	C₂₃×#447	1	1	yes	characteristic
390	C₄	C₂₃×#449	1	1	yes	characteristic
391	C₄	C₂₃×#466	1	1	yes	characteristic
392	C₂	—	2	1	no	—
393	C₂	—	2	1	no	—
394	C₂	—	8	1	no	—
395	C₂	—	16	2	no	—
396	C₂	—	16	2	no	—
397	C₂	C₂₃×#1999	1	1	yes	characteristic
398	C₂	C₂₃×#2192	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₂₃	#447
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₂₃
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂²×C₄×C₂₃ ◁ C₂×C₂₃×#131 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₂₃×D₁₆	C₂	semidirect
2. C₂×C₂₃×#472	C₂	semidirect
3. C₂₃×#3058	C₂	semidirect
4. C₂×C₂₃×#361	C₂	semidirect
5. C₂₃×#2140	C₂	semidirect
6. C₂×C₂₃×#350	C₂	semidirect
7. C₂₃×#1382	C₂	semidirect
47. C₂×D₈×C₂₃	D₄	semidirect
68. C₂×C₁₆×C₂₃	D₄	semidirect
70. C₂₃×#108	D₄	semidirect
131. #13319	C₂₃	direct (N × H)
173. C₂²×D₁₆	C₂×C₂₃	semidirect
174. C₂×#472	C₂×C₂₃	semidirect
175. #3058	C₂×C₂₃	semidirect
176. C₂×#361	C₂×C₂₃	semidirect
177. #2140	C₂×C₂₃	semidirect
178. C₂×#350	C₂×C₂₃	semidirect
179. #1382	C₂×C₂₃	semidirect
246. C₂×D₈	D₄×C₂₃	semidirect
267. C₂×C₁₆	D₄×C₂₃	semidirect
269. #108	D₄×C₂₃	semidirect
274. C₂₃	#13319	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×D₁₆	2
C₂×C₂₃×#472	2
C₂₃×#3058	2
C₂×C₂₃×#361	2
C₂₃×#2140	2
C₂×C₂₃×#350	2
C₂₃×#1382	2
#13319	23

Subgroups — C23×#13319 #19160945

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#13319 #19160945