Subgroups — C₂₃×#33585 #19181211

Order 5888.

748 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#509	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₂₃×D₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3155	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#2948	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#2210	C₂	1	4	yes	maximal, complemented
6	C₂₃×#2206	C₂	1	4	yes	maximal, complemented
7	C₂₃×#2151	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#2140	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#2138	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₂₃×AGL(1,ℤ/8)	—	2	1	no	—
11	C₂×C₂₃×#135	C₂²	1	1	yes	characteristic
12	C₂²×D₈×C₂₃	C₂²	1	1	yes	characteristic
13	C₂²×D₈×C₂₃	C₂²	1	1	yes	characteristic
14	C₂₃×#535	—	2	1	no	—
15	C₂₃×#518	—	2	1	no	—
16	C₂₃×#509	—	2	4	no	—
17	C₂×C₂₃×SD₃₂	C₂²	1	2	yes	complemented
18	C₂×C₂₃×D₁₆	—	2	4	no	—
19	C₂×C₂₃×D₁₆	C₂²	1	4	yes	—
20	C₂×C₂₃×D₁₆	C₂²	1	2	yes	complemented
21	C₂×C₂₃×M₃₂	C₂²	1	1	yes	characteristic
22	C₂²×C₁₆×C₂₃	C₂²	1	1	yes	characteristic
23	C₂₃×#496	—	2	2	no	—
24	C₂₃×#495	C₂²	1	2	yes	complemented
25	C₂₃×#493	C₂²	1	2	yes	complemented
26	C₂₃×#442	—	2	2	no	—
27	C₄×D₈×C₂₃	C₂²	1	4	yes	complemented
28	C₂₃×#427	C₂²	1	1	yes	characteristic
29	C₂₃×#418	—	2	1	no	—
30	C₂₃×#405	C₂²	1	1	yes	characteristic
31	C₂₃×C₄⋊C₁₆	C₂²	1	4	yes	complemented
32	C₂₃×#358	C₂²	1	2	yes	complemented
33	C₂₃×#357	C₂²	1	2	yes	complemented
34	C₂₃×#357	C₂²	1	4	yes	complemented
35	C₂×#41×C₂₃	—	2	1	no	—
36	C₂²×D₄×C₂₃	—	2	1	no	—
37	C₂²×D₄×C₂₃	—	2	1	no	—
38	C₂₃×AGL(1,ℤ/8)	—	4	4	no	—
39	C₂₃×#135	—	2	2	no	—
40	C₂₃×#135	—	2	2	no	—
41	C₂×Q₁₆×C₂₃	C₂³	1	1	yes	characteristic
42	C₂×SD₁₆×C₂₃	—	2	1	no	—
43	C₂×SD₁₆×C₂₃	—	2	2	no	—
44	C₂×D₈×C₂₃	—	2	1	no	—
45	C₂×D₈×C₂₃	—	2	2	no	—
46	C₂×D₈×C₂₃	—	2	1	no	—
47	C₂×D₈×C₂₃	—	2	2	no	—
48	C₂×D₈×C₂₃	—	2	2	no	—
49	C₂×D₈×C₂₃	—	2	2	no	—
50	C₂×D₈×C₂₃	D₄	1	4	yes	complemented
51	C₂×D₈×C₂₃	C₂³	1	2	yes	—
52	C₂×D₈×C₂₃	C₂³	1	1	yes	characteristic
53	C₂×D₈×C₂₃	C₂³	1	2	yes	—
54	C₂×M₁₆×C₂₃	D₄	1	1	yes	characteristic
55	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
56	C₂₃×#127	—	2	2	no	—
57	C₂₃×#124	—	2	2	no	—
58	C₂₃×#121	—	4	2	no	—
59	C₂₃×#120	—	4	2	no	—
60	C₄×D₄×C₂₃	—	2	4	no	—
61	C₄×D₄×C₂₃	—	4	2	no	—
62	C₂₃×#117	—	2	1	no	—
63	C₂₃×#117	D₄	1	1	yes	characteristic
64	C₂×C₂²⋊C₄×C₂₃	—	4	2	no	—
65	C₂₃×SD₃₂	—	2	4	no	—
66	C₂₃×D₁₆	—	2	8	no	—
67	C₂₃×D₁₆	—	2	4	no	—
68	C₂₃×M₃₂	—	2	2	no	—
69	C₂×C₁₆×C₂₃	—	2	2	no	—
70	C₂×C₁₆×C₂₃	C₂³	1	2	yes	—
71	C₂×C₁₆×C₂₃	C₂³	1	2	yes	—
72	C₂₃×#107	C₂³	1	2	yes	—
73	C₂₃×#106	—	2	1	no	—
74	C₂₃×#102	—	2	4	no	—
75	C₂₃×#97	D₄	1	2	yes	—
76	C₄×C₈×C₂₃	C₂³	1	2	yes	—
77	C₂⁴×C₂₃	—	4	1	no	—
78	C₂⁴×C₂₃	—	4	1	no	—
79	#41×C₂₃	—	4	2	no	—
80	#41×C₂₃	—	4	2	no	—
81	C₂×Q₈×C₂₃	—	2	1	no	—
82	C₂×D₄×C₂₃	—	2	4	no	—
83	C₂×D₄×C₂₃	—	2	2	no	—
84	C₂×D₄×C₂₃	—	2	2	no	—
85	C₂×D₄×C₂₃	—	2	1	no	—
86	C₂×D₄×C₂₃	—	4	1	no	—
87	C₂×D₄×C₂₃	—	4	2	no	—
88	C₂×D₄×C₂₃	—	4	1	no	—
89	C₂×D₄×C₂₃	—	4	1	no	—
90	C₂×D₄×C₂₃	—	4	4	no	—
91	C₂×D₄×C₂₃	—	4	2	no	—
92	C₂×D₄×C₂₃	—	4	2	no	—
93	C₂²×C₄×C₂₃	—	4	1	no	—
94	C₂²×C₄×C₂₃	—	4	4	no	—
95	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
96	Q₁₆×C₂₃	—	2	1	no	—
97	Q₁₆×C₂₃	—	2	1	no	—
98	SD₁₆×C₂₃	—	4	4	no	—
99	SD₁₆×C₂₃	—	4	2	no	—
100	D₈×C₂₃	—	2	4	no	—
101	D₈×C₂₃	—	2	2	no	—
102	D₈×C₂₃	—	2	1	no	—
103	D₈×C₂₃	—	2	2	no	—
104	D₈×C₂₃	—	2	2	no	—
105	D₈×C₂₃	—	2	1	no	—
106	D₈×C₂₃	—	4	4	no	—
107	D₈×C₂₃	—	4	2	no	—
108	D₈×C₂₃	C₂×D₄	1	4	yes	—
109	M₁₆×C₂₃	—	2	2	no	—
110	C₂×C₈×C₂₃	C₂×D₄	1	2	yes	—
111	C₂×C₈×C₂₃	C₂×D₄	1	1	yes	characteristic
112	C₂×C₈×C₂₃	C₂×D₄	1	2	yes	—
113	C₂×C₈×C₂₃	#41	1	2	yes	—
114	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
115	C₄⋊C₄×C₂₃	—	2	2	no	—
116	C₄⋊C₄×C₂₃	D₈	1	2	yes	—
117	C₂²⋊C₄×C₂₃	—	4	1	no	—
118	C₂²⋊C₄×C₂₃	—	4	4	no	—
119	C₂²⋊C₄×C₂₃	—	4	4	no	—
120	C₂²⋊C₄×C₂₃	D₈	1	2	yes	—
121	C₄²×C₂₃	—	4	1	no	—
122	C₄²×C₂₃	C₂×D₄	1	2	yes	—
123	C₁₆×C₂₃	—	2	2	no	—
124	C₁₆×C₂₃	—	2	2	no	—
125	#33585	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
126	C₂³×C₂₃	—	4	2	no	—
127	C₂³×C₂₃	—	4	4	no	—
128	C₂³×C₂₃	—	4	2	no	—
129	C₂³×C₂₃	—	4	1	no	—
130	C₂³×C₂₃	—	8	2	no	—
131	C₂³×C₂₃	—	16	2	no	—
132	C₂³×C₂₃	—	16	2	no	—
133	C₂³×C₂₃	C₂×D₈	1	1	yes	characteristic
134	Q₈×C₂₃	—	4	1	no	—
135	Q₈×C₂₃	—	4	1	no	—
136	D₄×C₂₃	—	2	4	no	—
137	D₄×C₂₃	—	4	2	no	—
138	D₄×C₂₃	—	4	1	no	—
139	D₄×C₂₃	—	4	2	no	—
140	D₄×C₂₃	—	4	1	no	—
141	D₄×C₂₃	—	4	2	no	—
142	D₄×C₂₃	—	4	4	no	—
143	D₄×C₂₃	—	8	2	no	—
144	D₄×C₂₃	—	8	2	no	—
145	D₄×C₂₃	—	16	4	no	—
146	C₂×C₄×C₂₃	—	4	2	no	—
147	C₂×C₄×C₂₃	—	4	1	no	—
148	C₂×C₄×C₂₃	—	8	2	no	—
149	C₂×C₄×C₂₃	—	16	4	no	—
150	C₂×C₄×C₂₃	#121	1	2	yes	—
151	C₂×C₄×C₂₃	C₂×D₈	1	4	yes	—
152	C₂×C₄×C₂₃	C₂×D₈	1	1	yes	characteristic
153	C₂×C₄×C₂₃	AGL(1,ℤ/8)	1	2	yes	—
154	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
155	C₈×C₂₃	—	2	2	no	—
156	C₈×C₂₃	#121	1	2	yes	—
157	C₈×C₂₃	C₂²×D₄	1	1	yes	characteristic
158	C₈×C₂₃	C₂×#41	1	1	yes	characteristic
159	C₂×#509	C₂×C₂₃	1	1	yes	characteristic, complemented
160	C₂²×D₁₆	C₂×C₂₃	1	1	yes	characteristic, complemented
161	#3155	C₂×C₂₃	1	1	yes	characteristic, complemented
162	#2948	C₂×C₂₃	1	1	yes	characteristic, complemented
163	#2210	C₂×C₂₃	1	4	yes	complemented
164	#2206	C₂×C₂₃	1	4	yes	complemented
165	#2151	C₂×C₂₃	1	1	yes	characteristic, complemented
166	#2140	C₂×C₂₃	1	1	yes	characteristic, complemented
167	#2138	C₂×C₂₃	1	1	yes	characteristic, complemented
168	C₂²×C₂₃	—	2	2	no	—
169	C₂²×C₂₃	—	4	4	no	—
170	C₂²×C₂₃	—	8	4	no	—
171	C₂²×C₂₃	—	8	2	no	—
172	C₂²×C₂₃	—	8	4	no	—
173	C₂²×C₂₃	—	8	1	no	—
174	C₂²×C₂₃	—	8	2	no	—
175	C₂²×C₂₃	—	16	4	no	—
176	C₂²×C₂₃	—	16	4	no	—
177	C₂²×C₂₃	#459	1	2	yes	—
178	C₂²×C₂₃	C₂²×D₈	1	1	yes	characteristic
179	C₄×C₂₃	—	2	4	no	—
180	C₄×C₂₃	—	8	2	no	—
181	C₄×C₂₃	—	8	1	no	—
182	C₄×C₂₃	#459	1	2	yes	—
183	C₄×C₂₃	C₂×#121	1	1	yes	characteristic
184	C₄×C₂₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
185	C₂×AGL(1,ℤ/8)	—	2	1	no	—
186	C₂×#135	C₂²×C₂₃	1	1	yes	characteristic
187	C₂²×D₈	C₂²×C₂₃	1	1	yes	characteristic
188	C₂²×D₈	C₂²×C₂₃	1	1	yes	characteristic
189	#535	—	2	1	no	—
190	#518	—	2	1	no	—
191	#509	—	2	4	no	—
192	C₂×SD₃₂	C₂²×C₂₃	1	2	yes	complemented
193	C₂×D₁₆	—	2	4	no	—
194	C₂×D₁₆	C₂²×C₂₃	1	4	yes	—
195	C₂×D₁₆	C₂²×C₂₃	1	2	yes	complemented
196	C₂×M₃₂	C₂²×C₂₃	1	1	yes	characteristic
197	C₂²×C₁₆	C₂²×C₂₃	1	1	yes	characteristic
198	#496	—	2	2	no	—
199	#495	C₂²×C₂₃	1	2	yes	complemented
200	#493	C₂²×C₂₃	1	2	yes	complemented
201	#442	—	2	2	no	—
202	C₄×D₈	C₂²×C₂₃	1	4	yes	complemented
203	#427	C₂²×C₂₃	1	1	yes	characteristic
204	#418	—	2	1	no	—
205	#405	C₂²×C₂₃	1	1	yes	characteristic
206	C₄⋊C₁₆	C₂²×C₂₃	1	4	yes	complemented
207	#358	C₂²×C₂₃	1	2	yes	complemented
208	#357	C₂²×C₂₃	1	2	yes	complemented
209	#357	C₂²×C₂₃	1	4	yes	complemented
210	C₂×C₂₃	—	2	2	no	—
211	C₂×C₂₃	—	8	4	no	—
212	C₂×C₂₃	—	16	1	no	—
213	C₂×C₂₃	—	16	2	no	—
214	C₂×C₂₃	C₂×#459	1	1	yes	characteristic
215	C₂×C₂₃	#3415	1	2	yes	—
216	C₂×#41	—	2	1	no	—
217	C₂²×D₄	—	2	1	no	—
218	C₂²×D₄	—	2	1	no	—
219	AGL(1,ℤ/8)	—	4	4	no	—
220	#135	—	2	2	no	—
221	#135	—	2	2	no	—
222	C₂×Q₁₆	C₂³×C₂₃	1	1	yes	characteristic
223	C₂×SD₁₆	—	2	1	no	—
224	C₂×SD₁₆	—	2	2	no	—
225	C₂×D₈	—	2	1	no	—
226	C₂×D₈	—	2	2	no	—
227	C₂×D₈	—	2	1	no	—
228	C₂×D₈	—	2	2	no	—
229	C₂×D₈	—	2	2	no	—
230	C₂×D₈	—	2	2	no	—
231	C₂×D₈	D₄×C₂₃	1	4	yes	complemented
232	C₂×D₈	C₂³×C₂₃	1	2	yes	—
233	C₂×D₈	C₂³×C₂₃	1	1	yes	characteristic
234	C₂×D₈	C₂³×C₂₃	1	2	yes	—
235	C₂×M₁₆	D₄×C₂₃	1	1	yes	characteristic
236	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
237	#127	—	2	2	no	—
238	#124	—	2	2	no	—
239	#121	—	4	2	no	—
240	#120	—	4	2	no	—
241	C₄×D₄	—	2	4	no	—
242	C₄×D₄	—	4	2	no	—
243	#117	—	2	1	no	—
244	#117	D₄×C₂₃	1	1	yes	characteristic
245	C₂×C₂²⋊C₄	—	4	2	no	—
246	SD₃₂	—	2	4	no	—
247	D₁₆	—	2	8	no	—
248	D₁₆	—	2	4	no	—
249	M₃₂	—	2	2	no	—
250	C₂×C₁₆	—	2	2	no	—
251	C₂×C₁₆	C₂³×C₂₃	1	2	yes	—
252	C₂×C₁₆	C₂³×C₂₃	1	2	yes	—
253	#107	C₂³×C₂₃	1	2	yes	—
254	#106	—	2	1	no	—
255	#102	—	2	4	no	—
256	#97	D₄×C₂₃	1	2	yes	—
257	C₄×C₈	C₂³×C₂₃	1	2	yes	—
258	C₂₃	#33585	1	1	yes	characteristic, direct product factor, Sylow
259	C₂⁴	—	4	1	no	—
260	C₂⁴	—	4	1	no	—
261	#41	—	4	2	no	—
262	#41	—	4	2	no	—
263	C₂×Q₈	—	2	1	no	—
264	C₂×D₄	—	2	4	no	—
265	C₂×D₄	—	2	2	no	—
266	C₂×D₄	—	2	2	no	—
267	C₂×D₄	—	2	1	no	—
268	C₂×D₄	—	4	1	no	—
269	C₂×D₄	—	4	2	no	—
270	C₂×D₄	—	4	1	no	—
271	C₂×D₄	—	4	1	no	—
272	C₂×D₄	—	4	4	no	—
273	C₂×D₄	—	4	2	no	—
274	C₂×D₄	—	4	2	no	—
275	C₂²×C₄	—	4	1	no	—
276	C₂²×C₄	—	4	4	no	—
277	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
278	Q₁₆	—	2	1	no	—
279	Q₁₆	—	2	1	no	—
280	SD₁₆	—	4	4	no	—
281	SD₁₆	—	4	2	no	—
282	D₈	—	2	4	no	—
283	D₈	—	2	2	no	—
284	D₈	—	2	1	no	—
285	D₈	—	2	2	no	—
286	D₈	—	2	2	no	—
287	D₈	—	2	1	no	—
288	D₈	—	4	4	no	—
289	D₈	—	4	2	no	—
290	D₈	C₂×D₄×C₂₃	1	4	yes	—
291	M₁₆	—	2	2	no	—
292	C₂×C₈	C₂×D₄×C₂₃	1	2	yes	—
293	C₂×C₈	C₂×D₄×C₂₃	1	1	yes	characteristic
294	C₂×C₈	C₂×D₄×C₂₃	1	2	yes	—
295	C₂×C₈	#41×C₂₃	1	2	yes	—
296	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
297	C₄⋊C₄	—	2	2	no	—
298	C₄⋊C₄	D₈×C₂₃	1	2	yes	—
299	C₂²⋊C₄	—	4	1	no	—
300	C₂²⋊C₄	—	4	4	no	—
301	C₂²⋊C₄	—	4	4	no	—
302	C₂²⋊C₄	D₈×C₂₃	1	2	yes	—
303	C₄²	—	4	1	no	—
304	C₄²	C₂×D₄×C₂₃	1	2	yes	—
305	C₁₆	—	2	2	no	—
306	C₁₆	—	2	2	no	—
307	C₂³	—	4	2	no	—
308	C₂³	—	4	4	no	—
309	C₂³	—	4	2	no	—
310	C₂³	—	4	1	no	—
311	C₂³	—	8	2	no	—
312	C₂³	—	16	2	no	—
313	C₂³	—	16	2	no	—
314	C₂³	C₂×D₈×C₂₃	1	1	yes	characteristic
315	Q₈	—	4	1	no	—
316	Q₈	—	4	1	no	—
317	D₄	—	2	4	no	—
318	D₄	—	4	2	no	—
319	D₄	—	4	1	no	—
320	D₄	—	4	2	no	—
321	D₄	—	4	4	no	—
322	D₄	—	4	2	no	—
323	D₄	—	4	1	no	—
324	D₄	—	8	2	no	—
325	D₄	—	8	2	no	—
326	D₄	—	16	4	no	—
327	C₂×C₄	—	4	2	no	—
328	C₂×C₄	—	4	1	no	—
329	C₂×C₄	—	8	2	no	—
330	C₂×C₄	—	16	4	no	—
331	C₂×C₄	C₂₃×#121	1	2	yes	—
332	C₂×C₄	C₂×D₈×C₂₃	1	4	yes	—
333	C₂×C₄	C₂×D₈×C₂₃	1	1	yes	characteristic
334	C₂×C₄	C₂₃×AGL(1,ℤ/8)	1	2	yes	—
335	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
336	C₈	—	2	2	no	—
337	C₈	C₂₃×#121	1	2	yes	—
338	C₈	C₂²×D₄×C₂₃	1	1	yes	characteristic
339	C₈	C₂×#41×C₂₃	1	1	yes	characteristic
340	C₂²	—	2	2	no	—
341	C₂²	—	4	4	no	—
342	C₂²	—	8	4	no	—
343	C₂²	—	8	1	no	—
344	C₂²	—	8	2	no	—
345	C₂²	—	8	2	no	—
346	C₂²	—	8	4	no	—
347	C₂²	—	16	4	no	—
348	C₂²	—	16	4	no	—
349	C₂²	C₂₃×#459	1	2	yes	—
350	C₂²	C₂²×D₈×C₂₃	1	1	yes	characteristic
351	C₄	—	2	4	no	—
352	C₄	—	8	1	no	—
353	C₄	—	8	2	no	—
354	C₄	C₂₃×#459	1	2	yes	—
355	C₄	C₂×C₂₃×#121	1	1	yes	characteristic
356	C₄	C₂×C₂₃×AGL(1,ℤ/8)	1	1	yes	characteristic
357	C₂	—	2	2	no	—
358	C₂	—	8	4	no	—
359	C₂	—	16	2	no	—
360	C₂	—	16	1	no	—
361	C₂	C₂×C₂₃×#459	1	1	yes	characteristic
362	C₂	C₂₃×#3415	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₂₃
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂₃×#117 ◁ C₂₃×#405 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₂₃×#509	C₂	semidirect
2. C₂²×C₂₃×D₁₆	C₂	semidirect
3. C₂₃×#3155	C₂	semidirect
4. C₂₃×#2948	C₂	semidirect
5. C₂₃×#2210	C₂	semidirect
6. C₂₃×#2206	C₂	semidirect
7. C₂₃×#2151	C₂	semidirect
8. C₂₃×#2140	C₂	semidirect
9. C₂₃×#2138	C₂	semidirect
17. C₂×C₂₃×SD₃₂	C₂²	semidirect
20. C₂×C₂₃×D₁₆	C₂²	semidirect
24. C₂₃×#495	C₂²	semidirect
25. C₂₃×#493	C₂²	semidirect
27. C₄×D₈×C₂₃	C₂²	semidirect
31. C₂₃×C₄⋊C₁₆	C₂²	semidirect
32. C₂₃×#358	C₂²	semidirect
33. C₂₃×#357	C₂²	semidirect
34. C₂₃×#357	C₂²	semidirect
50. C₂×D₈×C₂₃	D₄	semidirect
125. #33585	C₂₃	direct (N × H)
159. C₂×#509	C₂×C₂₃	semidirect
160. C₂²×D₁₆	C₂×C₂₃	semidirect
161. #3155	C₂×C₂₃	semidirect
162. #2948	C₂×C₂₃	semidirect
163. #2210	C₂×C₂₃	semidirect
164. #2206	C₂×C₂₃	semidirect
165. #2151	C₂×C₂₃	semidirect
166. #2140	C₂×C₂₃	semidirect
167. #2138	C₂×C₂₃	semidirect
192. C₂×SD₃₂	C₂²×C₂₃	semidirect
195. C₂×D₁₆	C₂²×C₂₃	semidirect
199. #495	C₂²×C₂₃	semidirect
200. #493	C₂²×C₂₃	semidirect
202. C₄×D₈	C₂²×C₂₃	semidirect
206. C₄⋊C₁₆	C₂²×C₂₃	semidirect
207. #358	C₂²×C₂₃	semidirect
208. #357	C₂²×C₂₃	semidirect
209. #357	C₂²×C₂₃	semidirect
231. C₂×D₈	D₄×C₂₃	semidirect
258. C₂₃	#33585	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₂₃×#509	2
C₂²×C₂₃×D₁₆	2
C₂₃×#3155	2
C₂₃×#2948	2
C₂₃×#2210	2
C₂₃×#2206	2
C₂₃×#2151	2
C₂₃×#2140	2
C₂₃×#2138	2
#33585	23

Subgroups — C23×#33585 #19181211

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#33585 #19181211