Subgroups — C₂₃×#17923 #19165549

Order 5888.

626 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3103	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#2982	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#2981	C₂	1	1	yes	maximal, characteristic
4	C₂₃×#1588	C₂	1	2	yes	maximal, complemented
5	C₂₃×#1583	C₂	1	2	yes	maximal, complemented
6	C₂₃×SD₁₆⋊C₈	C₂	1	2	yes	maximal, complemented
7	C₈×SD₁₆×C₂₃	C₂	1	2	yes	maximal, complemented
8	C₂₃×#1572	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#1491	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#1484	C₂	1	1	yes	maximal, characteristic
11	C₂₃×#1453	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#532	C₂²	1	1	yes	characteristic
13	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
14	C₂₃×#481	C₄	1	2	yes	—
15	C₂₃×#475	C₄	1	2	yes	—
16	C₂₃×#460	C₄	1	2	yes	—
17	C₂₃×#448	C₄	1	2	yes	—
18	C₈×Q₈×C₂₃	—	2	2	no	—
19	C₈×Q₈×C₂₃	C₂²	1	2	yes	—
20	C₈×Q₈×C₂₃	C₂²	1	2	yes	—
21	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	—
22	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	—
23	C₂₃×#436	C₂²	1	2	yes	—
24	C₂₃×#435	—	2	2	no	—
25	C₈×D₄×C₂₃	C₂²	1	2	yes	—
26	C₂₃×#432	C₂²	1	1	yes	characteristic
27	C₂₃×#431	—	2	2	no	—
28	C₂₃×#431	C₂²	1	1	yes	characteristic
29	C₂₃×#431	C₂²	1	1	yes	characteristic
30	C₂₃×#431	C₂²	1	1	yes	characteristic
31	C₂₃×#408	—	2	2	no	—
32	C₄×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
33	C₂₃×#335	C₂²	1	2	yes	—
34	C₂₃×#334	C₂²	1	2	yes	—
35	C₂₃×Q₈⋊C₈	C₂²	1	2	yes	—
36	C₂₃×Q₈⋊C₈	C₂²	1	2	yes	—
37	C₂₃×D₄⋊C₈	C₂²	1	2	yes	—
38	C₂₃×D₄⋊C₈	C₂²	1	2	yes	—
39	C₂₃×#322	C₂²	1	1	yes	characteristic
40	C₂₃×#322	C₂²	1	1	yes	characteristic
41	C₂₃×#322	C₂²	1	1	yes	characteristic
42	C₈²×C₂₃	C₂²	1	1	yes	characteristic
43	C₂×#41×C₂₃	—	2	1	no	—
44	C₂²×Q₈×C₂₃	C₂×C₄	1	1	yes	characteristic
45	C₂×SD₁₆×C₂₃	C₂×C₄	1	2	yes	—
46	C₂×SD₁₆×C₂₃	C₂×C₄	1	2	yes	—
47	C₂×M₁₆×C₂₃	—	2	1	no	—
48	C₂×M₁₆×C₂₃	—	2	2	no	—
49	C₂²×C₈×C₂₃	—	2	2	no	—
50	C₂₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
51	C₂₃×#127	C₂×C₄	1	1	yes	characteristic
52	C₂₃×#124	—	2	1	no	—
53	C₂₃×#121	—	2	1	no	—
54	C₂₃×#121	C₂×C₄	1	2	yes	—
55	C₄×Q₈×C₂₃	—	2	1	no	—
56	C₄×Q₈×C₂₃	—	2	1	no	—
57	C₄×Q₈×C₂₃	C₂×C₄	1	2	yes	—
58	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
59	C₄×D₄×C₂₃	—	2	1	no	—
60	C₄×D₄×C₂₃	C₂³	1	2	yes	—
61	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
62	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
63	C₂×C₄²×C₂₃	—	2	1	no	—
64	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
65	C₂₃×#106	C₂×C₄	1	2	yes	—
66	C₂₃×#106	C₂×C₄	1	2	yes	—
67	C₂₃×C₄⋊C₈	—	2	2	no	—
68	C₂₃×C₄⋊C₈	—	2	2	no	—
69	C₂₃×C₄⋊C₈	C₂×C₄	1	2	yes	—
70	C₂₃×C₄⋊C₈	D₄	1	2	yes	—
71	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
72	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
73	C₂₃×#103	C₂×C₄	1	2	yes	—
74	C₂₃×#103	C₂×C₄	1	2	yes	—
75	C₂₃×#102	C₂×C₄	1	2	yes	—
76	C₂₃×#102	C₂×C₄	1	2	yes	—
77	C₂₃×C₂²⋊C₈	—	2	1	no	—
78	C₂₃×C₂²⋊C₈	—	2	1	no	—
79	C₂₃×C₂²⋊C₈	—	2	2	no	—
80	C₂₃×C₂²⋊C₈	—	2	2	no	—
81	C₂₃×C₂²⋊C₈	C₂×C₄	1	2	yes	—
82	C₂₃×C₂²⋊C₈	D₄	1	2	yes	—
83	C₂₃×#97	—	2	1	no	—
84	C₂₃×#97	—	2	1	no	—
85	C₄×C₈×C₂₃	—	2	2	no	—
86	C₄×C₈×C₂₃	—	2	2	no	—
87	C₄×C₈×C₂₃	—	2	1	no	—
88	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
89	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
90	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
91	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
92	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
93	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
94	#41×C₂₃	—	8	2	no	—
95	C₂×Q₈×C₂₃	—	2	4	no	—
96	C₂×Q₈×C₂₃	—	2	1	no	—
97	C₂×Q₈×C₂₃	—	2	1	no	—
98	C₂×Q₈×C₂₃	C₂²×C₄	1	2	yes	—
99	C₂×D₄×C₂₃	—	2	2	no	—
100	C₂×D₄×C₂₃	—	2	1	no	—
101	C₂×D₄×C₂₃	—	2	1	no	—
102	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
103	C₂²×C₄×C₂₃	—	2	1	no	—
104	C₂²×C₄×C₂₃	—	2	1	no	—
105	C₂²×C₄×C₂₃	—	2	2	no	—
106	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
107	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₂₃	#41	1	1	yes	characteristic
109	SD₁₆×C₂₃	—	2	4	no	—
110	SD₁₆×C₂₃	—	2	4	no	—
111	M₁₆×C₂₃	—	4	2	no	—
112	M₁₆×C₂₃	—	8	2	no	—
113	C₂×C₈×C₂₃	—	2	1	no	—
114	C₂×C₈×C₂₃	—	2	2	no	—
115	C₂×C₈×C₂₃	—	2	2	no	—
116	C₂×C₈×C₂₃	—	2	1	no	—
117	C₂×C₈×C₂₃	—	8	2	no	—
118	C₂×C₈×C₂₃	C₂²×C₄	1	2	yes	—
119	C₂×C₈×C₂₃	C₂²×C₄	1	2	yes	—
120	C₂×C₈×C₂₃	C₂×D₄	1	2	yes	—
121	C₂×C₈×C₂₃	C₂×D₄	1	2	yes	—
122	C₄⋊C₄×C₂₃	—	2	2	no	—
123	C₄⋊C₄×C₂₃	—	2	1	no	—
124	C₄⋊C₄×C₂₃	—	2	1	no	—
125	C₄⋊C₄×C₂₃	—	2	2	no	—
126	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
127	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
128	C₂²⋊C₄×C₂₃	—	2	2	no	—
129	C₂²⋊C₄×C₂₃	—	2	2	no	—
130	C₄²×C₂₃	—	2	2	no	—
131	C₄²×C₂₃	—	2	2	no	—
132	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
133	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
134	C₄²×C₂₃	#41	1	1	yes	characteristic
135	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
136	#17923	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
137	C₂³×C₂₃	—	2	2	no	—
138	C₂³×C₂₃	C₄×D₄	1	1	yes	characteristic
139	Q₈×C₂₃	—	2	4	no	—
140	Q₈×C₂₃	—	2	2	no	—
141	Q₈×C₂₃	—	8	1	no	—
142	Q₈×C₂₃	#131	1	4	yes	—
143	D₄×C₂₃	—	2	2	no	—
144	D₄×C₂₃	—	2	2	no	—
145	D₄×C₂₃	—	8	1	no	—
146	D₄×C₂₃	—	8	1	no	—
147	D₄×C₂₃	—	8	2	no	—
148	C₂×C₄×C₂₃	—	2	4	no	—
149	C₂×C₄×C₂₃	—	2	2	no	—
150	C₂×C₄×C₂₃	—	2	2	no	—
151	C₂×C₄×C₂₃	—	2	2	no	—
152	C₂×C₄×C₂₃	—	2	2	no	—
153	C₂×C₄×C₂₃	—	2	2	no	—
154	C₂×C₄×C₂₃	—	4	1	no	—
155	C₂×C₄×C₂₃	—	4	2	no	—
156	C₂×C₄×C₂₃	—	4	2	no	—
157	C₂×C₄×C₂₃	—	8	1	no	—
158	C₂×C₄×C₂₃	C₄×D₄	1	1	yes	characteristic
159	C₂×C₄×C₂₃	C₄×D₄	1	1	yes	characteristic
160	C₂×C₄×C₂₃	C₄×D₄	1	1	yes	characteristic
161	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
162	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
163	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
164	C₈×C₂₃	—	2	2	no	—
165	C₈×C₂₃	—	2	2	no	—
166	C₈×C₂₃	—	2	2	no	—
167	C₈×C₂₃	—	2	2	no	—
168	C₈×C₂₃	—	2	2	no	—
169	C₈×C₂₃	—	4	1	no	—
170	C₈×C₂₃	—	4	2	no	—
171	C₈×C₂₃	—	4	2	no	—
172	#3103	C₂×C₂₃	1	1	yes	characteristic
173	#2982	C₂×C₂₃	1	1	yes	characteristic, complemented
174	#2981	C₂×C₂₃	1	1	yes	characteristic
175	#1588	C₂×C₂₃	1	2	yes	complemented
176	#1583	C₂×C₂₃	1	2	yes	complemented
177	SD₁₆⋊C₈	C₂×C₂₃	1	2	yes	complemented
178	C₈×SD₁₆	C₂×C₂₃	1	2	yes	complemented
179	#1572	C₂×C₂₃	1	1	yes	characteristic, complemented
180	#1491	C₂×C₂₃	1	1	yes	characteristic, complemented
181	#1484	C₂×C₂₃	1	1	yes	characteristic
182	#1453	C₂×C₂₃	1	1	yes	characteristic, complemented
183	C₂²×C₂₃	—	2	1	no	—
184	C₂²×C₂₃	—	2	1	no	—
185	C₂²×C₂₃	—	2	1	no	—
186	C₂²×C₂₃	—	4	2	no	—
187	C₂²×C₂₃	—	4	2	no	—
188	C₂²×C₂₃	—	4	2	no	—
189	C₂²×C₂₃	C₂×C₄×D₄	1	1	yes	characteristic
190	C₄×C₂₃	—	2	4	no	—
191	C₄×C₂₃	—	2	1	no	—
192	C₄×C₂₃	—	2	1	no	—
193	C₄×C₂₃	—	2	1	no	—
194	C₄×C₂₃	—	2	1	no	—
195	C₄×C₂₃	—	4	2	no	—
196	C₄×C₂₃	—	4	2	no	—
197	C₄×C₂₃	C₂×#131	1	2	yes	—
198	C₄×C₂₃	#577	1	2	yes	—
199	#532	C₂²×C₂₃	1	1	yes	characteristic
200	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
201	#481	C₄×C₂₃	1	2	yes	—
202	#475	C₄×C₂₃	1	2	yes	—
203	#460	C₄×C₂₃	1	2	yes	—
204	#448	C₄×C₂₃	1	2	yes	—
205	C₈×Q₈	—	2	2	no	—
206	C₈×Q₈	C₂²×C₂₃	1	2	yes	—
207	C₈×Q₈	C₂²×C₂₃	1	2	yes	—
208	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	—
209	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	—
210	#436	C₂²×C₂₃	1	2	yes	—
211	#435	—	2	2	no	—
212	C₈×D₄	C₂²×C₂₃	1	2	yes	—
213	#432	C₂²×C₂₃	1	1	yes	characteristic
214	#431	—	2	2	no	—
215	#431	C₂²×C₂₃	1	1	yes	characteristic
216	#431	C₂²×C₂₃	1	1	yes	characteristic
217	#431	C₂²×C₂₃	1	1	yes	characteristic
218	#408	—	2	2	no	—
219	C₄×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
220	#335	C₂²×C₂₃	1	2	yes	—
221	#334	C₂²×C₂₃	1	2	yes	—
222	Q₈⋊C₈	C₂²×C₂₃	1	2	yes	—
223	Q₈⋊C₈	C₂²×C₂₃	1	2	yes	—
224	D₄⋊C₈	C₂²×C₂₃	1	2	yes	—
225	D₄⋊C₈	C₂²×C₂₃	1	2	yes	—
226	#322	C₂²×C₂₃	1	1	yes	characteristic
227	#322	C₂²×C₂₃	1	1	yes	characteristic
228	#322	C₂²×C₂₃	1	1	yes	characteristic
229	C₈²	C₂²×C₂₃	1	1	yes	characteristic
230	C₂×C₂₃	—	4	1	no	—
231	C₂×C₂₃	—	8	2	no	—
232	C₂×C₂₃	#2929	1	1	yes	characteristic
233	C₂×C₂₃	#2949	1	1	yes	characteristic
234	C₂×C₂₃	#2956	1	1	yes	characteristic
235	C₂×#41	—	2	1	no	—
236	C₂²×Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
237	C₂×SD₁₆	C₂×C₄×C₂₃	1	2	yes	—
238	C₂×SD₁₆	C₂×C₄×C₂₃	1	2	yes	—
239	C₂×M₁₆	—	2	1	no	—
240	C₂×M₁₆	—	2	2	no	—
241	C₂²×C₈	—	2	2	no	—
242	C₄⋊Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
243	#127	C₂×C₄×C₂₃	1	1	yes	characteristic
244	#124	—	2	1	no	—
245	#121	—	2	1	no	—
246	#121	C₂×C₄×C₂₃	1	2	yes	—
247	C₄×Q₈	—	2	1	no	—
248	C₄×Q₈	—	2	1	no	—
249	C₄×Q₈	C₂×C₄×C₂₃	1	2	yes	—
250	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
251	C₄×D₄	—	2	1	no	—
252	C₄×D₄	C₂³×C₂₃	1	2	yes	—
253	C₂×C₄⋊C₄	—	2	1	no	—
254	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
255	C₂×C₄²	—	2	1	no	—
256	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
257	#106	C₂×C₄×C₂₃	1	2	yes	—
258	#106	C₂×C₄×C₂₃	1	2	yes	—
259	C₄⋊C₈	—	2	2	no	—
260	C₄⋊C₈	—	2	2	no	—
261	C₄⋊C₈	C₂×C₄×C₂₃	1	2	yes	—
262	C₄⋊C₈	D₄×C₂₃	1	2	yes	—
263	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
264	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
265	#103	C₂×C₄×C₂₃	1	2	yes	—
266	#103	C₂×C₄×C₂₃	1	2	yes	—
267	#102	C₂×C₄×C₂₃	1	2	yes	—
268	#102	C₂×C₄×C₂₃	1	2	yes	—
269	C₂²⋊C₈	—	2	1	no	—
270	C₂²⋊C₈	—	2	1	no	—
271	C₂²⋊C₈	—	2	2	no	—
272	C₂²⋊C₈	—	2	2	no	—
273	C₂²⋊C₈	C₂×C₄×C₂₃	1	2	yes	—
274	C₂²⋊C₈	D₄×C₂₃	1	2	yes	—
275	#97	—	2	1	no	—
276	#97	—	2	1	no	—
277	C₄×C₈	—	2	2	no	—
278	C₄×C₈	—	2	2	no	—
279	C₄×C₈	—	2	1	no	—
280	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
281	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
282	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
283	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
284	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
285	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
286	C₂₃	#17923	1	1	yes	characteristic, direct product factor, Sylow
287	#41	—	8	2	no	—
288	C₂×Q₈	—	2	4	no	—
289	C₂×Q₈	—	2	1	no	—
290	C₂×Q₈	—	2	1	no	—
291	C₂×Q₈	C₂²×C₄×C₂₃	1	2	yes	—
292	C₂×D₄	—	2	2	no	—
293	C₂×D₄	—	2	1	no	—
294	C₂×D₄	—	2	1	no	—
295	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
296	C₂²×C₄	—	2	1	no	—
297	C₂²×C₄	—	2	1	no	—
298	C₂²×C₄	—	2	2	no	—
299	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
300	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
301	C₂²×C₄	#41×C₂₃	1	1	yes	characteristic
302	SD₁₆	—	2	4	no	—
303	SD₁₆	—	2	4	no	—
304	M₁₆	—	4	2	no	—
305	M₁₆	—	8	2	no	—
306	C₂×C₈	—	2	1	no	—
307	C₂×C₈	—	2	2	no	—
308	C₂×C₈	—	2	2	no	—
309	C₂×C₈	—	2	1	no	—
310	C₂×C₈	—	8	2	no	—
311	C₂×C₈	C₂²×C₄×C₂₃	1	2	yes	—
312	C₂×C₈	C₂²×C₄×C₂₃	1	2	yes	—
313	C₂×C₈	C₂×D₄×C₂₃	1	2	yes	—
314	C₂×C₈	C₂×D₄×C₂₃	1	2	yes	—
315	C₄⋊C₄	—	2	2	no	—
316	C₄⋊C₄	—	2	1	no	—
317	C₄⋊C₄	—	2	1	no	—
318	C₄⋊C₄	—	2	2	no	—
319	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
320	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
321	C₂²⋊C₄	—	2	2	no	—
322	C₂²⋊C₄	—	2	2	no	—
323	C₄²	—	2	2	no	—
324	C₄²	—	2	2	no	—
325	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
326	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
327	C₄²	#41×C₂₃	1	1	yes	characteristic
328	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
329	C₂³	—	2	2	no	—
330	C₂³	C₄×D₄×C₂₃	1	1	yes	characteristic
331	Q₈	—	2	4	no	—
332	Q₈	—	2	2	no	—
333	Q₈	—	8	1	no	—
334	Q₈	C₂₃×#131	1	4	yes	—
335	D₄	—	2	2	no	—
336	D₄	—	2	2	no	—
337	D₄	—	8	1	no	—
338	D₄	—	8	1	no	—
339	D₄	—	8	2	no	—
340	C₂×C₄	—	2	4	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	4	1	no	—
347	C₂×C₄	—	4	2	no	—
348	C₂×C₄	—	4	2	no	—
349	C₂×C₄	—	8	1	no	—
350	C₂×C₄	C₄×D₄×C₂₃	1	1	yes	characteristic
351	C₂×C₄	C₄×D₄×C₂₃	1	1	yes	characteristic
352	C₂×C₄	C₄×D₄×C₂₃	1	1	yes	characteristic
353	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
354	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
355	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
356	C₈	—	2	2	no	—
357	C₈	—	2	2	no	—
358	C₈	—	2	2	no	—
359	C₈	—	2	2	no	—
360	C₈	—	2	2	no	—
361	C₈	—	4	1	no	—
362	C₈	—	4	2	no	—
363	C₈	—	4	2	no	—
364	C₂²	—	2	1	no	—
365	C₂²	—	2	1	no	—
366	C₂²	—	2	1	no	—
367	C₂²	—	4	2	no	—
368	C₂²	—	4	2	no	—
369	C₂²	—	4	2	no	—
370	C₂²	C₂×C₄×D₄×C₂₃	1	1	yes	characteristic
371	C₄	—	2	4	no	—
372	C₄	—	2	1	no	—
373	C₄	—	2	1	no	—
374	C₄	—	2	1	no	—
375	C₄	—	2	1	no	—
376	C₄	—	4	2	no	—
377	C₄	—	4	2	no	—
378	C₄	C₂×C₂₃×#131	1	2	yes	—
379	C₄	C₂₃×#577	1	2	yes	—
380	C₂	—	4	1	no	—
381	C₂	—	8	2	no	—
382	C₂	C₂₃×#2929	1	1	yes	characteristic
383	C₂	C₂₃×#2949	1	1	yes	characteristic
384	C₂	C₂₃×#2956	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₂₃	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₂₃
Frattini, cosocle	C₄²	C₂⁴×C₂₃
socle	C₂²×C₂₃	C₂×C₄×D₄
prime radical	C₂₃×#532	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₃ ◁ C₂₃×#431 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂₃×#2982	C₂	semidirect
4. C₂₃×#1588	C₂	semidirect
5. C₂₃×#1583	C₂	semidirect
6. C₂₃×SD₁₆⋊C₈	C₂	semidirect
7. C₈×SD₁₆×C₂₃	C₂	semidirect
8. C₂₃×#1572	C₂	semidirect
9. C₂₃×#1491	C₂	semidirect
11. C₂₃×#1453	C₂	semidirect
136. #17923	C₂₃	direct (N × H)
173. #2982	C₂×C₂₃	semidirect
175. #1588	C₂×C₂₃	semidirect
176. #1583	C₂×C₂₃	semidirect
177. SD₁₆⋊C₈	C₂×C₂₃	semidirect
178. C₈×SD₁₆	C₂×C₂₃	semidirect
179. #1572	C₂×C₂₃	semidirect
180. #1491	C₂×C₂₃	semidirect
182. #1453	C₂×C₂₃	semidirect
286. C₂₃	#17923	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×#3103	2
C₂₃×#2982	2
C₂₃×#2981	2
C₂₃×#1588	2
C₂₃×#1583	2
C₂₃×SD₁₆⋊C₈	2
C₈×SD₁₆×C₂₃	2
C₂₃×#1572	2
C₂₃×#1491	2
C₂₃×#1484	2
C₂₃×#1453	2
#17923	23

Subgroups — C23×#17923 #19165549

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#17923 #19165549