Subgroups — C₂₃×#17952 #19165578

Order 5888.

606 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3101	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#2985	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#2975	C₂	1	1	yes	maximal, characteristic
4	C₂₃×#1592	C₂	1	2	yes	maximal, complemented
5	C₂₃×#1590	C₂	1	2	yes	maximal, complemented
6	C₂₃×#1588	C₂	1	2	yes	maximal, complemented
7	C₂₃×#1583	C₂	1	2	yes	maximal, complemented
8	C₂₃×#1572	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#1490	C₂	1	1	yes	maximal, characteristic
10	C₂₃×#1485	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#1453	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#533	C₂²	1	1	yes	characteristic
13	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
14	C₂₃×#483	C₄	1	2	yes	—
15	C₂₃×#476	C₄	1	2	yes	—
16	C₂₃×#461	C₄	1	2	yes	—
17	C₂₃×#450	C₄	1	2	yes	—
18	C₂₃×#446	—	2	2	no	—
19	C₂₃×#446	C₂²	1	2	yes	complemented
20	C₈×Q₈×C₂₃	C₂²	1	2	yes	complemented
21	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	—
22	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	—
23	C₂₃×#436	—	2	2	no	—
24	C₂₃×#436	C₂²	1	2	yes	—
25	C₂₃×#436	C₂²	1	2	yes	—
26	C₂₃×#433	—	2	2	no	—
27	C₂₃×#432	C₂²	1	1	yes	characteristic
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×#407	—	2	2	no	—
32	C₄×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
33	C₂₃×#335	C₂²	1	2	yes	complemented
34	C₂₃×#334	C₂²	1	2	yes	complemented
35	C₂₃×Q₈⋊C₈	C₂²	1	2	yes	complemented
36	C₂₃×Q₈⋊C₈	C₂²	1	2	yes	complemented
37	C₂₃×D₄⋊C₈	C₂²	1	2	yes	—
38	C₂₃×D₄⋊C₈	C₂²	1	2	yes	—
39	C₂₃×#322	C₂²	1	1	yes	characteristic, complemented
40	C₂₃×#322	C₂²	1	1	yes	characteristic, complemented
41	C₂₃×#322	C₂²	1	1	yes	characteristic, complemented
42	C₈²×C₂₃	C₂²	1	1	yes	characteristic, complemented
43	C₂²×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic
44	C₂³×C₄×C₂₃	—	2	1	no	—
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	C₂×M₁₆×C₂₃	—	2	2	no	—
50	C₂₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
51	C₂₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
52	C₂₃×#125	—	2	1	no	—
53	C₂₃×C₂²⋊Q₈	—	2	1	no	—
54	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
55	C₄×Q₈×C₂₃	—	2	1	no	—
56	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
57	C₄×D₄×C₂₃	—	2	1	no	—
58	C₄×D₄×C₂₃	—	2	1	no	—
59	C₄×D₄×C₂₃	C₂×C₄	1	2	yes	—
60	C₄×D₄×C₂₃	C₂³	1	2	yes	—
61	C₂₃×#117	—	2	1	no	—
62	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
63	C₂×C₂²⋊C₄×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	2	no	—
84	C₂₃×#97	—	2	1	no	—
85	C₂₃×#97	—	2	1	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	C₂⁴×C₂₃	—	2	1	no	—
95	C₂×Q₈×C₂₃	—	2	1	no	—
96	C₂×Q₈×C₂₃	C₂²×C₄	1	2	yes	—
97	C₂×D₄×C₂₃	—	2	1	no	—
98	C₂×D₄×C₂₃	—	4	2	no	—
99	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
100	C₂²×C₄×C₂₃	—	2	1	no	—
101	C₂²×C₄×C₂₃	—	2	2	no	—
102	C₂²×C₄×C₂₃	—	2	2	no	—
103	C₂²×C₄×C₂₃	—	8	2	no	—
104	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
105	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₂₃	#41	1	1	yes	characteristic
107	SD₁₆×C₂₃	—	4	2	no	—
108	SD₁₆×C₂₃	—	4	2	no	—
109	M₁₆×C₂₃	—	4	2	no	—
110	M₁₆×C₂₃	—	8	2	no	—
111	M₁₆×C₂₃	—	8	2	no	—
112	C₂×C₈×C₂₃	—	2	1	no	—
113	C₂×C₈×C₂₃	—	2	2	no	—
114	C₂×C₈×C₂₃	—	2	2	no	—
115	C₂×C₈×C₂₃	—	2	1	no	—
116	C₂×C₈×C₂₃	C₂²×C₄	1	2	yes	—
117	C₂×C₈×C₂₃	C₂²×C₄	1	2	yes	—
118	C₂×C₈×C₂₃	C₂×D₄	1	2	yes	—
119	C₂×C₈×C₂₃	C₂×D₄	1	2	yes	—
120	C₄⋊C₄×C₂₃	—	2	1	no	—
121	C₄⋊C₄×C₂₃	—	2	1	no	—
122	C₄⋊C₄×C₂₃	—	2	1	no	—
123	C₄⋊C₄×C₂₃	—	2	1	no	—
124	C₄⋊C₄×C₂₃	—	2	2	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	C₂²⋊C₄×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	#17952	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
137	C₂³×C₂₃	—	2	2	no	—
138	C₂³×C₂₃	—	4	2	no	—
139	C₂³×C₂₃	—	8	1	no	—
140	C₂³×C₂₃	—	8	1	no	—
141	C₂³×C₂₃	C₄×D₄	1	1	yes	characteristic
142	Q₈×C₂₃	—	2	2	no	—
143	Q₈×C₂₃	—	2	2	no	—
144	Q₈×C₂₃	—	8	1	no	—
145	D₄×C₂₃	—	2	2	no	—
146	D₄×C₂₃	—	2	2	no	—
147	D₄×C₂₃	—	4	2	no	—
148	C₂×C₄×C₂₃	—	2	2	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	—	4	1	no	—
154	C₂×C₄×C₂₃	—	4	2	no	—
155	C₂×C₄×C₂₃	—	4	2	no	—
156	C₂×C₄×C₂₃	—	8	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	#3101	C₂×C₂₃	1	1	yes	characteristic
173	#2985	C₂×C₂₃	1	1	yes	characteristic, complemented
174	#2975	C₂×C₂₃	1	1	yes	characteristic
175	#1592	C₂×C₂₃	1	2	yes	complemented
176	#1590	C₂×C₂₃	1	2	yes	complemented
177	#1588	C₂×C₂₃	1	2	yes	complemented
178	#1583	C₂×C₂₃	1	2	yes	complemented
179	#1572	C₂×C₂₃	1	1	yes	characteristic, complemented
180	#1490	C₂×C₂₃	1	1	yes	characteristic
181	#1485	C₂×C₂₃	1	1	yes	characteristic, complemented
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	—	8	4	no	—
190	C₂²×C₂₃	C₂×C₄×D₄	1	1	yes	characteristic
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	—	4	2	no	—
198	C₄×C₂₃	#568	1	2	yes	—
199	C₄×C₂₃	#577	1	2	yes	—
200	#533	C₂²×C₂₃	1	1	yes	characteristic
201	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
202	#483	C₄×C₂₃	1	2	yes	—
203	#476	C₄×C₂₃	1	2	yes	—
204	#461	C₄×C₂₃	1	2	yes	—
205	#450	C₄×C₂₃	1	2	yes	—
206	#446	—	2	2	no	—
207	#446	C₂²×C₂₃	1	2	yes	complemented
208	C₈×Q₈	C₂²×C₂₃	1	2	yes	complemented
209	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	—
210	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	—
211	#436	—	2	2	no	—
212	#436	C₂²×C₂₃	1	2	yes	—
213	#436	C₂²×C₂₃	1	2	yes	—
214	#433	—	2	2	no	—
215	#432	C₂²×C₂₃	1	1	yes	characteristic
216	#431	C₂²×C₂₃	1	1	yes	characteristic
217	#431	C₂²×C₂₃	1	1	yes	characteristic
218	#431	C₂²×C₂₃	1	1	yes	characteristic
219	#407	—	2	2	no	—
220	C₄×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
221	#335	C₂²×C₂₃	1	2	yes	complemented
222	#334	C₂²×C₂₃	1	2	yes	complemented
223	Q₈⋊C₈	C₂²×C₂₃	1	2	yes	complemented
224	Q₈⋊C₈	C₂²×C₂₃	1	2	yes	complemented
225	D₄⋊C₈	C₂²×C₂₃	1	2	yes	—
226	D₄⋊C₈	C₂²×C₂₃	1	2	yes	—
227	#322	C₂²×C₂₃	1	1	yes	characteristic, complemented
228	#322	C₂²×C₂₃	1	1	yes	characteristic, complemented
229	#322	C₂²×C₂₃	1	1	yes	characteristic, complemented
230	C₈²	C₂²×C₂₃	1	1	yes	characteristic, complemented
231	C₂×C₂₃	—	4	1	no	—
232	C₂×C₂₃	—	8	2	no	—
233	C₂×C₂₃	#2930	1	1	yes	characteristic
234	C₂×C₂₃	#2949	1	1	yes	characteristic
235	C₂×C₂₃	#2956	1	1	yes	characteristic
236	C₂²×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
237	C₂³×C₄	—	2	1	no	—
238	C₂×SD₁₆	C₂×C₄×C₂₃	1	2	yes	—
239	C₂×SD₁₆	C₂×C₄×C₂₃	1	2	yes	—
240	C₂×M₁₆	—	2	1	no	—
241	C₂×M₁₆	—	2	2	no	—
242	C₂×M₁₆	—	2	2	no	—
243	C₄⋊Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
244	C₄⋊Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
245	#125	—	2	1	no	—
246	C₂²⋊Q₈	—	2	1	no	—
247	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
248	C₄×Q₈	—	2	1	no	—
249	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
250	C₄×D₄	—	2	1	no	—
251	C₄×D₄	—	2	1	no	—
252	C₄×D₄	C₂×C₄×C₂₃	1	2	yes	—
253	C₄×D₄	C₂³×C₂₃	1	2	yes	—
254	#117	—	2	1	no	—
255	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
256	C₂×C₂²⋊C₄	—	2	1	no	—
257	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
258	#106	C₂×C₄×C₂₃	1	2	yes	—
259	#106	C₂×C₄×C₂₃	1	2	yes	—
260	C₄⋊C₈	—	2	2	no	—
261	C₄⋊C₈	—	2	2	no	—
262	C₄⋊C₈	C₂×C₄×C₂₃	1	2	yes	—
263	C₄⋊C₈	D₄×C₂₃	1	2	yes	—
264	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
265	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
266	#103	C₂×C₄×C₂₃	1	2	yes	—
267	#103	C₂×C₄×C₂₃	1	2	yes	—
268	#102	C₂×C₄×C₂₃	1	2	yes	—
269	#102	C₂×C₄×C₂₃	1	2	yes	—
270	C₂²⋊C₈	—	2	1	no	—
271	C₂²⋊C₈	—	2	1	no	—
272	C₂²⋊C₈	—	2	2	no	—
273	C₂²⋊C₈	—	2	2	no	—
274	C₂²⋊C₈	C₂×C₄×C₂₃	1	2	yes	—
275	C₂²⋊C₈	D₄×C₂₃	1	2	yes	—
276	#97	—	2	2	no	—
277	#97	—	2	1	no	—
278	#97	—	2	1	no	—
279	C₄×C₈	—	2	2	no	—
280	C₄×C₈	—	2	1	no	—
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	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
287	C₂₃	#17952	1	1	yes	characteristic, direct product factor, Sylow
288	C₂⁴	—	2	1	no	—
289	C₂×Q₈	—	2	1	no	—
290	C₂×Q₈	C₂²×C₄×C₂₃	1	2	yes	—
291	C₂×D₄	—	2	1	no	—
292	C₂×D₄	—	4	2	no	—
293	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
294	C₂²×C₄	—	2	1	no	—
295	C₂²×C₄	—	2	2	no	—
296	C₂²×C₄	—	2	2	no	—
297	C₂²×C₄	—	8	2	no	—
298	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
299	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
300	C₂²×C₄	#41×C₂₃	1	1	yes	characteristic
301	SD₁₆	—	4	2	no	—
302	SD₁₆	—	4	2	no	—
303	M₁₆	—	4	2	no	—
304	M₁₆	—	8	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	C₂²×C₄×C₂₃	1	2	yes	—
311	C₂×C₈	C₂²×C₄×C₂₃	1	2	yes	—
312	C₂×C₈	C₂×D₄×C₂₃	1	2	yes	—
313	C₂×C₈	C₂×D₄×C₂₃	1	2	yes	—
314	C₄⋊C₄	—	2	1	no	—
315	C₄⋊C₄	—	2	1	no	—
316	C₄⋊C₄	—	2	1	no	—
317	C₄⋊C₄	—	2	1	no	—
318	C₄⋊C₄	—	2	2	no	—
319	C₄⋊C₄	—	2	2	no	—
320	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
321	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
322	C₂²⋊C₄	—	2	2	no	—
323	C₂²⋊C₄	—	2	2	no	—
324	C₂²⋊C₄	—	2	2	no	—
325	C₄²	—	2	2	no	—
326	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
327	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
328	C₄²	#41×C₂₃	1	1	yes	characteristic
329	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
330	C₂³	—	2	2	no	—
331	C₂³	—	4	2	no	—
332	C₂³	—	8	1	no	—
333	C₂³	—	8	1	no	—
334	C₂³	C₄×D₄×C₂₃	1	1	yes	characteristic
335	Q₈	—	2	2	no	—
336	Q₈	—	2	2	no	—
337	Q₈	—	8	1	no	—
338	D₄	—	2	2	no	—
339	D₄	—	2	2	no	—
340	D₄	—	4	2	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	2	no	—
350	C₂×C₄	—	8	1	no	—
351	C₂×C₄	C₄×D₄×C₂₃	1	1	yes	characteristic
352	C₂×C₄	C₄×D₄×C₂₃	1	1	yes	characteristic
353	C₂×C₄	C₄×D₄×C₂₃	1	1	yes	characteristic
354	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
355	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
356	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
357	C₈	—	2	2	no	—
358	C₈	—	2	2	no	—
359	C₈	—	2	2	no	—
360	C₈	—	2	2	no	—
361	C₈	—	2	2	no	—
362	C₈	—	4	1	no	—
363	C₈	—	4	2	no	—
364	C₈	—	4	2	no	—
365	C₂²	—	2	1	no	—
366	C₂²	—	2	1	no	—
367	C₂²	—	2	1	no	—
368	C₂²	—	4	2	no	—
369	C₂²	—	4	2	no	—
370	C₂²	—	4	2	no	—
371	C₂²	—	8	4	no	—
372	C₂²	C₂×C₄×D₄×C₂₃	1	1	yes	characteristic
373	C₄	—	2	1	no	—
374	C₄	—	2	1	no	—
375	C₄	—	2	1	no	—
376	C₄	—	2	1	no	—
377	C₄	—	4	2	no	—
378	C₄	—	4	2	no	—
379	C₄	—	4	2	no	—
380	C₄	C₂₃×#568	1	2	yes	—
381	C₄	C₂₃×#577	1	2	yes	—
382	C₂	—	4	1	no	—
383	C₂	—	8	2	no	—
384	C₂	C₂₃×#2930	1	1	yes	characteristic
385	C₂	C₂₃×#2949	1	1	yes	characteristic
386	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	C₂²×D₄×C₂₃	C₂×C₄
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×#2985	C₂	semidirect
4. C₂₃×#1592	C₂	semidirect
5. C₂₃×#1590	C₂	semidirect
6. C₂₃×#1588	C₂	semidirect
7. C₂₃×#1583	C₂	semidirect
8. C₂₃×#1572	C₂	semidirect
10. C₂₃×#1485	C₂	semidirect
11. C₂₃×#1453	C₂	semidirect
19. C₂₃×#446	C₂²	semidirect
20. C₈×Q₈×C₂₃	C₂²	semidirect
33. C₂₃×#335	C₂²	semidirect
34. C₂₃×#334	C₂²	semidirect
35. C₂₃×Q₈⋊C₈	C₂²	semidirect
36. C₂₃×Q₈⋊C₈	C₂²	semidirect
39. C₂₃×#322	C₂²	semidirect
40. C₂₃×#322	C₂²	semidirect
41. C₂₃×#322	C₂²	semidirect
42. C₈²×C₂₃	C₂²	semidirect
136. #17952	C₂₃	direct (N × H)
173. #2985	C₂×C₂₃	semidirect
175. #1592	C₂×C₂₃	semidirect
176. #1590	C₂×C₂₃	semidirect
177. #1588	C₂×C₂₃	semidirect
178. #1583	C₂×C₂₃	semidirect
179. #1572	C₂×C₂₃	semidirect
181. #1485	C₂×C₂₃	semidirect
182. #1453	C₂×C₂₃	semidirect
207. #446	C₂²×C₂₃	semidirect
208. C₈×Q₈	C₂²×C₂₃	semidirect
221. #335	C₂²×C₂₃	semidirect
222. #334	C₂²×C₂₃	semidirect
223. Q₈⋊C₈	C₂²×C₂₃	semidirect
224. Q₈⋊C₈	C₂²×C₂₃	semidirect
227. #322	C₂²×C₂₃	semidirect
228. #322	C₂²×C₂₃	semidirect
229. #322	C₂²×C₂₃	semidirect
230. C₈²	C₂²×C₂₃	semidirect
287. C₂₃	#17952	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×#3101	2
C₂₃×#2985	2
C₂₃×#2975	2
C₂₃×#1592	2
C₂₃×#1590	2
C₂₃×#1588	2
C₂₃×#1583	2
C₂₃×#1572	2
C₂₃×#1490	2
C₂₃×#1485	2
C₂₃×#1453	2
#17952	23

Subgroups — C23×#17952 #19165578

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#17952 #19165578