Subgroups — C₂₃×#12978 #19160604

Order 5888.

494 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	C₂²×C₂₃×M₃₂	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₃×#2929	C₂	1	1	yes	maximal, characteristic
3	C₂×C₂₃×#350	C₂	1	2	yes	maximal, complemented
4	C₂×C₂₃×C₂²⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#1379	C₂	1	2	yes	maximal, complemented
6	C₂×C₂₃×#131	C₂²	1	1	yes	characteristic
7	C₂³×C₈×C₂₃	C₂²	1	1	yes	characteristic
8	C₂₃×#525	C₄	1	1	yes	characteristic
9	C₂×C₂₃×M₃₂	—	2	1	no	—
10	C₂×C₂₃×M₃₂	—	2	4	no	—
11	C₂×C₂₃×M₃₂	C₂²	1	2	yes	—
12	C₂²×C₁₆×C₂₃	—	2	1	no	—
13	C₂²×C₁₆×C₂₃	C₂²	1	2	yes	—
14	C₂₃×#435	—	2	1	no	—
15	C₂₃×#435	—	2	1	no	—
16	C₈×D₄×C₂₃	—	2	1	no	—
17	C₈×D₄×C₂₃	—	2	1	no	—
18	C₂₃×#424	C₄	1	1	yes	characteristic
19	C₂₃×#408	C₄	1	1	yes	characteristic
20	C₂₃×#407	C₄	1	1	yes	characteristic
21	C₂₃×#405	C₂²	1	1	yes	characteristic
22	C₂₃×#350	—	2	4	no	—
23	C₂₃×C₂²⋊C₁₆	—	2	1	no	—
24	C₂₃×C₂²⋊C₁₆	—	2	1	no	—
25	C₂×#41×C₂₃	C₂×C₄	1	1	yes	characteristic
26	C₂³×C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
27	C₂₃×#131	—	2	2	no	—
28	C₂₃×#131	—	2	2	no	—
29	C₂×M₁₆×C₂₃	—	2	1	no	—
30	C₂×M₁₆×C₂₃	C₂×C₄	1	1	yes	characteristic
31	C₂×M₁₆×C₂₃	C₂×C₄	1	1	yes	characteristic
32	C₂²×C₈×C₂₃	—	2	2	no	—
33	C₂²×C₈×C₂₃	—	2	2	no	—
34	C₂²×C₈×C₂₃	—	2	1	no	—
35	C₂²×C₈×C₂₃	C₂×C₄	1	1	yes	characteristic
36	C₂²×C₈×C₂₃	D₄	1	1	yes	characteristic
37	C₂²×C₈×C₂₃	D₄	1	1	yes	characteristic
38	C₂²×C₈×C₂₃	D₄	1	1	yes	characteristic
39	C₂²×C₈×C₂₃	D₄	1	1	yes	characteristic
40	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
41	C₂₃×#123	—	2	1	no	—
42	C₂₃×C₂²⋊Q₈	C₈	1	1	yes	characteristic
43	C₂₃×C₂²⋊Q₈	C₈	1	1	yes	characteristic
44	C₂₃×#121	C₈	1	1	yes	characteristic
45	C₂₃×#121	C₈	1	1	yes	characteristic
46	C₂₃×#120	—	2	1	no	—
47	C₄×D₄×C₂₃	—	2	1	no	—
48	C₄×D₄×C₂₃	—	2	1	no	—
49	C₂₃×#117	C₂×C₄	1	1	yes	characteristic
50	C₂₃×M₃₂	—	2	4	no	—
51	C₂₃×M₃₂	—	2	2	no	—
52	C₂₃×M₃₂	D₄	1	4	yes	complemented
53	C₂×C₁₆×C₂₃	—	2	4	no	—
54	C₂×C₁₆×C₂₃	—	2	2	no	—
55	C₂×C₁₆×C₂₃	—	2	2	no	—
56	C₂×C₁₆×C₂₃	—	2	2	no	—
57	C₂×C₁₆×C₂₃	—	2	2	no	—
58	C₂₃×C₄⋊C₈	—	2	1	no	—
59	C₂₃×C₄⋊C₈	—	2	1	no	—
60	C₂₃×C₂²⋊C₈	—	2	1	no	—
61	C₂₃×C₂²⋊C₈	—	2	1	no	—
62	C₂₃×C₂²⋊C₈	—	2	1	no	—
63	C₂₃×C₂²⋊C₈	—	2	1	no	—
64	C₂₃×#97	—	2	1	no	—
65	C₄×C₈×C₂₃	—	2	1	no	—
66	C₂⁴×C₂₃	M₁₆	1	1	yes	characteristic
67	#41×C₂₃	—	2	2	no	—
68	#41×C₂₃	—	2	2	no	—
69	C₂×Q₈×C₂₃	C₂×C₈	1	1	yes	characteristic
70	C₂×D₄×C₂₃	—	2	1	no	—
71	C₂×D₄×C₂₃	—	2	1	no	—
72	C₂×D₄×C₂₃	—	2	1	no	—
73	C₂×D₄×C₂₃	C₂×C₈	1	1	yes	characteristic
74	C₂²×C₄×C₂₃	—	2	2	no	—
75	C₂²×C₄×C₂₃	—	2	2	no	—
76	C₂²×C₄×C₂₃	—	2	1	no	—
77	C₂²×C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
78	C₂²×C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
79	C₂²×C₄×C₂₃	C₂×C₈	1	1	yes	characteristic
80	C₂²×C₄×C₂₃	C₂×C₈	1	1	yes	characteristic
81	C₂²×C₄×C₂₃	M₁₆	1	1	yes	characteristic
82	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
83	M₁₆×C₂₃	—	2	2	no	—
84	M₁₆×C₂₃	—	2	2	no	—
85	M₁₆×C₂₃	—	4	2	no	—
86	C₂×C₈×C₂₃	—	2	2	no	—
87	C₂×C₈×C₂₃	—	2	1	no	—
88	C₂×C₈×C₂₃	—	2	1	no	—
89	C₂×C₈×C₂₃	—	2	2	no	—
90	C₂×C₈×C₂₃	—	2	2	no	—
91	C₂×C₈×C₂₃	—	2	1	no	—
92	C₂×C₈×C₂₃	—	2	1	no	—
93	C₂×C₈×C₂₃	—	2	1	no	—
94	C₂×C₈×C₂₃	—	2	1	no	—
95	C₂×C₈×C₂₃	—	4	1	no	—
96	C₂×C₈×C₂₃	—	4	1	no	—
97	C₂×C₈×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
98	C₂×C₈×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
99	C₂×C₈×C₂₃	C₂×D₄	1	2	yes	—
100	C₂×C₈×C₂₃	C₂×D₄	1	1	yes	characteristic
101	C₂×C₈×C₂₃	C₂×D₄	1	1	yes	characteristic
102	C₂×C₈×C₂₃	#41	1	2	yes	—
103	C₄⋊C₄×C₂₃	—	2	1	no	—
104	C₄⋊C₄×C₂₃	—	2	1	no	—
105	C₄⋊C₄×C₂₃	C₂×C₈	1	1	yes	characteristic
106	C₄⋊C₄×C₂₃	C₂×C₈	1	1	yes	characteristic
107	C₂²⋊C₄×C₂₃	—	2	1	no	—
108	C₂²⋊C₄×C₂₃	—	2	1	no	—
109	C₂²⋊C₄×C₂₃	—	2	1	no	—
110	C₂²⋊C₄×C₂₃	—	2	1	no	—
111	C₂²⋊C₄×C₂₃	—	2	1	no	—
112	C₄²×C₂₃	—	2	1	no	—
113	C₁₆×C₂₃	—	2	4	no	—
114	C₁₆×C₂₃	—	4	2	no	—
115	#12978	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
116	C₂³×C₂₃	—	2	2	no	—
117	C₂³×C₂₃	—	2	2	no	—
118	C₂³×C₂₃	—	2	1	no	—
119	C₂³×C₂₃	—	4	1	no	—
120	C₂³×C₂₃	C₂²⋊C₈	1	1	yes	characteristic
121	C₂³×C₂₃	C₂²⋊C₈	1	1	yes	characteristic
122	C₂³×C₂₃	C₂×M₁₆	1	1	yes	characteristic
123	Q₈×C₂₃	—	2	2	no	—
124	D₄×C₂₃	—	2	2	no	—
125	D₄×C₂₃	—	4	2	no	—
126	D₄×C₂₃	—	4	2	no	—
127	D₄×C₂₃	—	4	2	no	—
128	C₂×C₄×C₂₃	—	2	2	no	—
129	C₂×C₄×C₂₃	—	2	1	no	—
130	C₂×C₄×C₂₃	—	2	1	no	—
131	C₂×C₄×C₂₃	—	2	1	no	—
132	C₂×C₄×C₂₃	—	2	1	no	—
133	C₂×C₄×C₂₃	—	2	2	no	—
134	C₂×C₄×C₂₃	—	2	2	no	—
135	C₂×C₄×C₂₃	—	2	1	no	—
136	C₂×C₄×C₂₃	—	2	1	no	—
137	C₂×C₄×C₂₃	—	2	1	no	—
138	C₂×C₄×C₂₃	—	4	1	no	—
139	C₂×C₄×C₂₃	—	4	1	no	—
140	C₂×C₄×C₂₃	C₂²⋊C₈	1	1	yes	characteristic
141	C₂×C₄×C₂₃	C₂²⋊C₈	1	1	yes	characteristic
142	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
143	C₂×C₄×C₂₃	C₄×D₄	1	2	yes	—
144	C₂×C₄×C₂₃	C₂²×C₈	1	1	yes	characteristic
145	C₂×C₄×C₂₃	#131	1	2	yes	—
146	C₈×C₂₃	—	2	1	no	—
147	C₈×C₂₃	—	2	1	no	—
148	C₈×C₂₃	—	4	1	no	—
149	C₈×C₂₃	—	4	1	no	—
150	C₈×C₂₃	#120	1	1	yes	characteristic
151	C₈×C₂₃	#121	1	2	yes	—
152	C₈×C₂₃	#123	1	1	yes	characteristic
153	C₂²×M₃₂	C₂×C₂₃	1	1	yes	characteristic, complemented
154	#2929	C₂×C₂₃	1	1	yes	characteristic
155	C₂×#350	C₂×C₂₃	1	2	yes	complemented
156	C₂×C₂²⋊C₁₆	C₂×C₂₃	1	1	yes	characteristic, complemented
157	#1379	C₂×C₂₃	1	2	yes	complemented
158	C₂²×C₂₃	—	2	1	no	—
159	C₂²×C₂₃	—	2	1	no	—
160	C₂²×C₂₃	—	2	1	no	—
161	C₂²×C₂₃	—	2	1	no	—
162	C₂²×C₂₃	—	2	1	no	—
163	C₂²×C₂₃	—	2	1	no	—
164	C₂²×C₂₃	—	2	1	no	—
165	C₂²×C₂₃	—	4	4	no	—
166	C₂²×C₂₃	—	4	1	no	—
167	C₂²×C₂₃	—	4	1	no	—
168	C₂²×C₂₃	—	4	1	no	—
169	C₂²×C₂₃	#350	1	2	yes	complemented
170	C₂²×C₂₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
171	C₂²×C₂₃	#435	1	2	yes	—
172	C₄×C₂₃	—	2	1	no	—
173	C₄×C₂₃	—	2	1	no	—
174	C₄×C₂₃	—	4	1	no	—
175	C₄×C₂₃	—	4	1	no	—
176	C₄×C₂₃	—	4	1	no	—
177	C₄×C₂₃	#386	1	1	yes	characteristic
178	C₄×C₂₃	#408	1	1	yes	characteristic
179	C₄×C₂₃	C₈×D₄	1	2	yes	—
180	C₂×#131	C₂²×C₂₃	1	1	yes	characteristic
181	C₂³×C₈	C₂²×C₂₃	1	1	yes	characteristic
182	#525	C₄×C₂₃	1	1	yes	characteristic
183	C₂×M₃₂	—	2	1	no	—
184	C₂×M₃₂	—	2	4	no	—
185	C₂×M₃₂	C₂²×C₂₃	1	2	yes	—
186	C₂²×C₁₆	—	2	1	no	—
187	C₂²×C₁₆	C₂²×C₂₃	1	2	yes	—
188	#435	—	2	1	no	—
189	#435	—	2	1	no	—
190	C₈×D₄	—	2	1	no	—
191	C₈×D₄	—	2	1	no	—
192	#424	C₄×C₂₃	1	1	yes	characteristic
193	#408	C₄×C₂₃	1	1	yes	characteristic
194	#407	C₄×C₂₃	1	1	yes	characteristic
195	#405	C₂²×C₂₃	1	1	yes	characteristic
196	#350	—	2	4	no	—
197	C₂²⋊C₁₆	—	2	1	no	—
198	C₂²⋊C₁₆	—	2	1	no	—
199	C₂×C₂₃	—	2	2	no	—
200	C₂×C₂₃	—	2	2	no	—
201	C₂×C₂₃	—	4	1	no	—
202	C₂×C₂₃	—	8	1	no	—
203	C₂×C₂₃	#1869	1	1	yes	characteristic
204	C₂×C₂₃	C₂×#350	1	1	yes	characteristic
205	C₂×C₂₃	#2117	1	1	yes	characteristic
206	C₂×#41	C₂×C₄×C₂₃	1	1	yes	characteristic
207	C₂³×C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
208	#131	—	2	2	no	—
209	#131	—	2	2	no	—
210	C₂×M₁₆	—	2	1	no	—
211	C₂×M₁₆	C₂×C₄×C₂₃	1	1	yes	characteristic
212	C₂×M₁₆	C₂×C₄×C₂₃	1	1	yes	characteristic
213	C₂²×C₈	—	2	2	no	—
214	C₂²×C₈	—	2	2	no	—
215	C₂²×C₈	—	2	1	no	—
216	C₂²×C₈	C₂×C₄×C₂₃	1	1	yes	characteristic
217	C₂²×C₈	D₄×C₂₃	1	1	yes	characteristic
218	C₂²×C₈	D₄×C₂₃	1	1	yes	characteristic
219	C₂²×C₈	D₄×C₂₃	1	1	yes	characteristic
220	C₂²×C₈	D₄×C₂₃	1	1	yes	characteristic
221	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
222	#123	—	2	1	no	—
223	C₂²⋊Q₈	C₈×C₂₃	1	1	yes	characteristic
224	C₂²⋊Q₈	C₈×C₂₃	1	1	yes	characteristic
225	#121	C₈×C₂₃	1	1	yes	characteristic
226	#121	C₈×C₂₃	1	1	yes	characteristic
227	#120	—	2	1	no	—
228	C₄×D₄	—	2	1	no	—
229	C₄×D₄	—	2	1	no	—
230	#117	C₂×C₄×C₂₃	1	1	yes	characteristic
231	M₃₂	—	2	4	no	—
232	M₃₂	—	2	2	no	—
233	M₃₂	D₄×C₂₃	1	4	yes	complemented
234	C₂×C₁₆	—	2	4	no	—
235	C₂×C₁₆	—	2	2	no	—
236	C₂×C₁₆	—	2	2	no	—
237	C₂×C₁₆	—	2	2	no	—
238	C₂×C₁₆	—	2	2	no	—
239	C₄⋊C₈	—	2	1	no	—
240	C₄⋊C₈	—	2	1	no	—
241	C₂²⋊C₈	—	2	1	no	—
242	C₂²⋊C₈	—	2	1	no	—
243	C₂²⋊C₈	—	2	1	no	—
244	C₂²⋊C₈	—	2	1	no	—
245	#97	—	2	1	no	—
246	C₄×C₈	—	2	1	no	—
247	C₂₃	#12978	1	1	yes	characteristic, direct product factor, Sylow
248	C₂⁴	M₁₆×C₂₃	1	1	yes	characteristic
249	#41	—	2	2	no	—
250	#41	—	2	2	no	—
251	C₂×Q₈	C₂×C₈×C₂₃	1	1	yes	characteristic
252	C₂×D₄	—	2	1	no	—
253	C₂×D₄	—	2	1	no	—
254	C₂×D₄	—	2	1	no	—
255	C₂×D₄	C₂×C₈×C₂₃	1	1	yes	characteristic
256	C₂²×C₄	—	2	2	no	—
257	C₂²×C₄	—	2	2	no	—
258	C₂²×C₄	—	2	1	no	—
259	C₂²×C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
260	C₂²×C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
261	C₂²×C₄	C₂×C₈×C₂₃	1	1	yes	characteristic
262	C₂²×C₄	C₂×C₈×C₂₃	1	1	yes	characteristic
263	C₂²×C₄	M₁₆×C₂₃	1	1	yes	characteristic
264	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
265	M₁₆	—	2	2	no	—
266	M₁₆	—	2	2	no	—
267	M₁₆	—	4	2	no	—
268	C₂×C₈	—	2	2	no	—
269	C₂×C₈	—	2	1	no	—
270	C₂×C₈	—	2	1	no	—
271	C₂×C₈	—	2	2	no	—
272	C₂×C₈	—	2	2	no	—
273	C₂×C₈	—	2	1	no	—
274	C₂×C₈	—	2	1	no	—
275	C₂×C₈	—	2	1	no	—
276	C₂×C₈	—	2	1	no	—
277	C₂×C₈	—	4	1	no	—
278	C₂×C₈	—	4	1	no	—
279	C₂×C₈	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
280	C₂×C₈	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
281	C₂×C₈	C₂×D₄×C₂₃	1	2	yes	—
282	C₂×C₈	C₂×D₄×C₂₃	1	1	yes	characteristic
283	C₂×C₈	C₂×D₄×C₂₃	1	1	yes	characteristic
284	C₂×C₈	#41×C₂₃	1	2	yes	—
285	C₄⋊C₄	—	2	1	no	—
286	C₄⋊C₄	—	2	1	no	—
287	C₄⋊C₄	C₂×C₈×C₂₃	1	1	yes	characteristic
288	C₄⋊C₄	C₂×C₈×C₂₃	1	1	yes	characteristic
289	C₂²⋊C₄	—	2	1	no	—
290	C₂²⋊C₄	—	2	1	no	—
291	C₂²⋊C₄	—	2	1	no	—
292	C₂²⋊C₄	—	2	1	no	—
293	C₂²⋊C₄	—	2	1	no	—
294	C₄²	—	2	1	no	—
295	C₁₆	—	2	4	no	—
296	C₁₆	—	4	2	no	—
297	C₂³	—	2	2	no	—
298	C₂³	—	2	2	no	—
299	C₂³	—	2	1	no	—
300	C₂³	—	4	1	no	—
301	C₂³	C₂₃×C₂²⋊C₈	1	1	yes	characteristic
302	C₂³	C₂₃×C₂²⋊C₈	1	1	yes	characteristic
303	C₂³	C₂×M₁₆×C₂₃	1	1	yes	characteristic
304	Q₈	—	2	2	no	—
305	D₄	—	2	2	no	—
306	D₄	—	4	2	no	—
307	D₄	—	4	2	no	—
308	D₄	—	4	2	no	—
309	C₂×C₄	—	2	2	no	—
310	C₂×C₄	—	2	1	no	—
311	C₂×C₄	—	2	1	no	—
312	C₂×C₄	—	2	1	no	—
313	C₂×C₄	—	2	1	no	—
314	C₂×C₄	—	2	2	no	—
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	2	1	no	—
317	C₂×C₄	—	2	1	no	—
318	C₂×C₄	—	2	1	no	—
319	C₂×C₄	—	4	1	no	—
320	C₂×C₄	—	4	1	no	—
321	C₂×C₄	C₂₃×C₂²⋊C₈	1	1	yes	characteristic
322	C₂×C₄	C₂₃×C₂²⋊C₈	1	1	yes	characteristic
323	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
324	C₂×C₄	C₄×D₄×C₂₃	1	2	yes	—
325	C₂×C₄	C₂²×C₈×C₂₃	1	1	yes	characteristic
326	C₂×C₄	C₂₃×#131	1	2	yes	—
327	C₈	—	2	1	no	—
328	C₈	—	2	1	no	—
329	C₈	—	4	1	no	—
330	C₈	—	4	1	no	—
331	C₈	C₂₃×#120	1	1	yes	characteristic
332	C₈	C₂₃×#121	1	2	yes	—
333	C₈	C₂₃×#123	1	1	yes	characteristic
334	C₂²	—	2	1	no	—
335	C₂²	—	2	1	no	—
336	C₂²	—	2	1	no	—
337	C₂²	—	2	1	no	—
338	C₂²	—	2	1	no	—
339	C₂²	—	2	1	no	—
340	C₂²	—	2	1	no	—
341	C₂²	—	4	4	no	—
342	C₂²	—	4	1	no	—
343	C₂²	—	4	1	no	—
344	C₂²	—	4	1	no	—
345	C₂²	C₂₃×#350	1	2	yes	complemented
346	C₂²	C₂×C₂₃×C₂²⋊C₈	1	1	yes	characteristic
347	C₂²	C₂₃×#435	1	2	yes	—
348	C₄	—	2	1	no	—
349	C₄	—	2	1	no	—
350	C₄	—	4	1	no	—
351	C₄	—	4	1	no	—
352	C₄	—	4	1	no	—
353	C₄	C₂₃×#386	1	1	yes	characteristic
354	C₄	C₂₃×#408	1	1	yes	characteristic
355	C₄	C₈×D₄×C₂₃	1	2	yes	—
356	C₂	—	2	2	no	—
357	C₂	—	2	2	no	—
358	C₂	—	4	1	no	—
359	C₂	—	8	1	no	—
360	C₂	C₂₃×#1869	1	1	yes	characteristic
361	C₂	C₂×C₂₃×#350	1	1	yes	characteristic
362	C₂	C₂₃×#2117	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈×C₂₃	C₂×D₄
commutator	C₂×C₄	C₂²×C₈×C₂₃
Frattini, cosocle	C₂²×C₈	C₂³×C₂₃
socle	C₂²×C₂₃	C₂×C₂²⋊C₈
prime radical	C₂₃×#525	C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₂₃ ◁ C₂³×C₈×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₂₃×M₃₂	C₂	semidirect
3. C₂×C₂₃×#350	C₂	semidirect
4. C₂×C₂₃×C₂²⋊C₁₆	C₂	semidirect
5. C₂₃×#1379	C₂	semidirect
52. C₂₃×M₃₂	D₄	semidirect
115. #12978	C₂₃	direct (N × H)
153. C₂²×M₃₂	C₂×C₂₃	semidirect
155. C₂×#350	C₂×C₂₃	semidirect
156. C₂×C₂²⋊C₁₆	C₂×C₂₃	semidirect
157. #1379	C₂×C₂₃	semidirect
169. C₂²×C₂₃	#350	semidirect
233. M₃₂	D₄×C₂₃	semidirect
247. C₂₃	#12978	direct (N × H)
345. C₂²	C₂₃×#350	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₂₃×M₃₂	2
C₂₃×#2929	2
C₂×C₂₃×#350	2
C₂×C₂₃×C₂²⋊C₁₆	2
C₂₃×#1379	2
#12978	23

Subgroups — C23×#12978 #19160604

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#12978 #19160604