Subgroups — C₂₃×#20860 #19168486

Order 5888.

1296 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#568	C₂	1	1	yes	maximal, characteristic
2	C₂×C₂₃×#430	C₂	1	2	yes	maximal, complemented
3	C₂×C₂₃×#413	C₂	1	1	yes	maximal, characteristic
4	C₂₃×#2879	C₂	1	1	yes	maximal, characteristic
5	C₂₃×#1858	C₂	1	8	yes	maximal, complemented
6	C₂₃×#1738	C₂	1	2	yes	maximal, complemented
7	C₂²×#41×C₂₃	C₂²	1	1	yes	characteristic
8	C₂₃×#568	—	2	2	no	—
9	C₂₃×#568	—	2	4	no	—
10	C₂₃×#568	C₂²	1	4	yes	—
11	C₂×C₂₃×#131	—	2	4	no	—
12	C₂²×M₁₆×C₂₃	—	2	2	no	—
13	C₂²×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
14	C₂²×M₁₆×C₂₃	C₂²	1	2	yes	—
15	C₂²×M₁₆×C₂₃	C₂²	1	2	yes	—
16	C₂²×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
17	C₂₃×#430	—	2	4	no	—
18	C₂₃×#430	C₂²	1	8	yes	complemented
19	C₂×C₂₃×#108	—	2	4	no	—
20	C₂₃×#413	C₄	1	4	yes	—
21	C₂₃×#413	C₂²	1	4	yes	—
22	C₂×C₂₃×#101	C₄	1	2	yes	—
23	C₂×C₂₃×#100	C₄	1	2	yes	—
24	C₂₃×#408	—	2	2	no	—
25	C₂₃×#408	C₂²	1	4	yes	—
26	C₂₃×#407	—	2	2	no	—
27	C₂₃×#341	C₂²	1	8	yes	complemented
28	C₂×#41×C₂₃	—	2	2	no	—
29	C₂×#41×C₂₃	—	2	2	no	—
30	C₂×#41×C₂₃	—	2	2	no	—
31	C₂×#41×C₂₃	—	2	2	no	—
32	C₂×#41×C₂₃	C₂×C₄	1	2	yes	—
33	C₂×#41×C₂₃	D₄	1	2	yes	—
34	C₂×#41×C₂₃	Q₈	1	2	yes	—
35	C₂×#41×C₂₃	C₂³	1	2	yes	—
36	C₂²×Q₈×C₂₃	C₂×C₄	1	1	yes	characteristic
37	C₂²×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic
38	C₂²×D₄×C₂₃	Q₈	1	2	yes	—
39	C₂³×C₄×C₂₃	D₄	1	2	yes	—
40	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
41	C₂₃×#131	—	2	16	no	—
42	C₂₃×#131	—	2	16	no	—
43	C₂×M₁₆×C₂₃	—	2	4	no	—
44	C₂×M₁₆×C₂₃	—	2	8	no	—
45	C₂×M₁₆×C₂₃	—	2	2	no	—
46	C₂×M₁₆×C₂₃	—	2	8	no	—
47	C₂×M₁₆×C₂₃	—	2	2	no	—
48	C₂×M₁₆×C₂₃	—	2	2	no	—
49	C₂×M₁₆×C₂₃	—	2	2	no	—
50	C₂×M₁₆×C₂₃	—	2	2	no	—
51	C₂×M₁₆×C₂₃	—	2	2	no	—
52	C₂×M₁₆×C₂₃	—	2	1	no	—
53	C₂×M₁₆×C₂₃	—	2	1	no	—
54	C₂×M₁₆×C₂₃	—	2	1	no	—
55	C₂×M₁₆×C₂₃	—	2	2	no	—
56	C₂×M₁₆×C₂₃	—	2	2	no	—
57	C₂×M₁₆×C₂₃	—	2	2	no	—
58	C₂×M₁₆×C₂₃	—	2	2	no	—
59	C₂×M₁₆×C₂₃	C₂×C₄	1	4	yes	—
60	C₂×M₁₆×C₂₃	C₂×C₄	1	4	yes	—
61	C₂×M₁₆×C₂₃	D₄	1	4	yes	—
62	C₂×M₁₆×C₂₃	D₄	1	4	yes	—
63	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
64	C₂×M₁₆×C₂₃	C₂³	1	4	yes	—
65	C₂×M₁₆×C₂₃	C₂³	1	4	yes	—
66	C₂²×C₈×C₂₃	—	2	4	no	—
67	C₂²×C₈×C₂₃	—	2	2	no	—
68	C₂²×C₈×C₂₃	—	2	2	no	—
69	C₂²×C₈×C₂₃	—	2	1	no	—
70	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
71	C₂₃×#108	—	2	16	no	—
72	C₂₃×#101	C₂×C₄	1	8	yes	—
73	C₂₃×#100	C₂×C₄	1	8	yes	—
74	C₂₃×C₂²⋊C₈	—	2	8	no	—
75	C₂⁴×C₂₃	C₄⋊C₄	1	2	yes	—
76	C₂⁴×C₂₃	C₂×Q₈	1	1	yes	characteristic
77	#41×C₂₃	—	2	4	no	—
78	#41×C₂₃	—	2	4	no	—
79	#41×C₂₃	—	2	4	no	—
80	#41×C₂₃	—	2	4	no	—
81	#41×C₂₃	—	2	4	no	—
82	#41×C₂₃	—	2	4	no	—
83	#41×C₂₃	—	2	4	no	—
84	#41×C₂₃	—	2	4	no	—
85	C₂×Q₈×C₂₃	—	2	2	no	—
86	C₂×Q₈×C₂₃	—	2	2	no	—
87	C₂×Q₈×C₂₃	C₄⋊C₄	1	2	yes	—
88	C₂×Q₈×C₂₃	C₂²×C₄	1	2	yes	—
89	C₂×D₄×C₂₃	—	2	4	no	—
90	C₂×D₄×C₂₃	—	2	4	no	—
91	C₂×D₄×C₂₃	—	2	2	no	—
92	C₂×D₄×C₂₃	—	2	2	no	—
93	C₂×D₄×C₂₃	C₄⋊C₄	1	2	yes	—
94	C₂×D₄×C₂₃	C₄⋊C₄	1	4	yes	—
95	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
96	C₂×D₄×C₂₃	C₂×Q₈	1	4	yes	—
97	C₂²×C₄×C₂₃	—	2	2	no	—
98	C₂²×C₄×C₂₃	—	2	2	no	—
99	C₂²×C₄×C₂₃	—	2	2	no	—
100	C₂²×C₄×C₂₃	—	2	2	no	—
101	C₂²×C₄×C₂₃	C₄⋊C₄	1	2	yes	—
102	C₂²×C₄×C₂₃	C₄⋊C₄	1	4	yes	—
103	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
104	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
105	C₂²×C₄×C₂₃	C₂×D₄	1	4	yes	—
106	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
109	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
110	C₂²×C₄×C₂₃	C₂×Q₈	1	1	yes	characteristic
111	C₂²×C₄×C₂₃	#41	1	2	yes	—
112	C₂²×C₄×C₂₃	#41	1	2	yes	—
113	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
114	M₁₆×C₂₃	—	2	16	no	—
115	M₁₆×C₂₃	—	2	4	no	—
116	M₁₆×C₂₃	—	2	4	no	—
117	M₁₆×C₂₃	—	2	4	no	—
118	M₁₆×C₂₃	—	2	4	no	—
119	M₁₆×C₂₃	—	2	4	no	—
120	M₁₆×C₂₃	—	2	4	no	—
121	M₁₆×C₂₃	—	2	4	no	—
122	M₁₆×C₂₃	—	4	1	no	—
123	M₁₆×C₂₃	—	4	1	no	—
124	M₁₆×C₂₃	—	4	1	no	—
125	M₁₆×C₂₃	—	4	1	no	—
126	M₁₆×C₂₃	—	4	2	no	—
127	M₁₆×C₂₃	C₂²×C₄	1	8	yes	—
128	M₁₆×C₂₃	C₂×D₄	1	8	yes	—
129	C₂×C₈×C₂₃	—	2	16	no	—
130	C₂×C₈×C₂₃	—	2	4	no	—
131	C₂×C₈×C₂₃	—	2	4	no	—
132	C₂×C₈×C₂₃	—	2	4	no	—
133	C₂×C₈×C₂₃	—	2	4	no	—
134	C₂×C₈×C₂₃	—	2	4	no	—
135	C₂×C₈×C₂₃	—	2	4	no	—
136	C₂×C₈×C₂₃	—	2	2	no	—
137	C₂×C₈×C₂₃	—	2	2	no	—
138	C₂×C₈×C₂₃	—	2	4	no	—
139	C₂×C₈×C₂₃	—	4	2	no	—
140	#20860	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
141	C₂³×C₂₃	—	2	2	no	—
142	C₂³×C₂₃	—	2	2	no	—
143	C₂³×C₂₃	—	8	1	no	—
144	C₂³×C₂₃	—	8	2	no	—
145	C₂³×C₂₃	C₂×C₄⋊C₄	1	4	yes	—
146	C₂³×C₂₃	C₂×C₄⋊C₄	1	1	yes	characteristic
147	C₂³×C₂₃	C₂×C₄⋊C₄	1	1	yes	characteristic
148	C₂³×C₂₃	C₂²⋊Q₈	1	2	yes	—
149	C₂³×C₂₃	C₂²⋊Q₈	1	2	yes	—
150	C₂³×C₂₃	C₂²×Q₈	1	1	yes	characteristic
151	Q₈×C₂₃	—	2	4	no	—
152	Q₈×C₂₃	—	2	4	no	—
153	D₄×C₂₃	—	2	8	no	—
154	D₄×C₂₃	—	2	8	no	—
155	D₄×C₂₃	—	2	4	no	—
156	D₄×C₂₃	—	2	4	no	—
157	C₂×C₄×C₂₃	—	2	2	no	—
158	C₂×C₄×C₂₃	—	2	2	no	—
159	C₂×C₄×C₂₃	—	2	4	no	—
160	C₂×C₄×C₂₃	—	2	4	no	—
161	C₂×C₄×C₂₃	—	2	4	no	—
162	C₂×C₄×C₂₃	—	2	4	no	—
163	C₂×C₄×C₂₃	C₂×C₄⋊C₄	1	4	yes	—
164	C₂×C₄×C₂₃	C₂×C₄⋊C₄	1	1	yes	characteristic
165	C₂×C₄×C₂₃	C₂×C₄⋊C₄	1	1	yes	characteristic
166	C₂×C₄×C₂₃	C₄×D₄	1	2	yes	—
167	C₂×C₄×C₂₃	C₄×D₄	1	2	yes	—
168	C₂×C₄×C₂₃	C₄×D₄	1	2	yes	—
169	C₂×C₄×C₂₃	C₄×D₄	1	2	yes	—
170	C₂×C₄×C₂₃	#120	1	1	yes	characteristic
171	C₂×C₄×C₂₃	#120	1	2	yes	—
172	C₂×C₄×C₂₃	#120	1	1	yes	characteristic
173	C₂×C₄×C₂₃	C₂²⋊Q₈	1	2	yes	—
174	C₂×C₄×C₂₃	C₂²⋊Q₈	1	2	yes	—
175	C₂×C₄×C₂₃	#123	1	1	yes	characteristic
176	C₂×C₄×C₂₃	#123	1	1	yes	characteristic
177	C₂×C₄×C₂₃	#123	1	2	yes	—
178	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
179	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
180	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
181	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
182	C₈×C₂₃	—	2	8	no	—
183	C₈×C₂₃	—	2	8	no	—
184	C₈×C₂₃	—	4	2	no	—
185	C₈×C₂₃	—	4	2	no	—
186	C₂×#568	C₂×C₂₃	1	1	yes	characteristic
187	C₂×#430	C₂×C₂₃	1	2	yes	complemented
188	C₂×#413	C₂×C₂₃	1	1	yes	characteristic
189	#2879	C₂×C₂₃	1	1	yes	characteristic
190	#1858	C₂×C₂₃	1	8	yes	complemented
191	#1738	C₂×C₂₃	1	2	yes	complemented
192	C₂²×C₂₃	—	2	4	no	—
193	C₂²×C₂₃	—	4	1	no	—
194	C₂²×C₂₃	—	4	1	no	—
195	C₂²×C₂₃	—	4	2	no	—
196	C₂²×C₂₃	—	4	2	no	—
197	C₂²×C₂₃	—	4	1	no	—
198	C₂²×C₂₃	—	4	4	no	—
199	C₂²×C₂₃	—	4	4	no	—
200	C₂²×C₂₃	—	8	2	no	—
201	C₂²×C₂₃	#385	1	1	yes	characteristic
202	C₂²×C₂₃	#385	1	1	yes	characteristic
203	C₂²×C₂₃	#385	1	2	yes	—
204	C₂²×C₂₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
205	C₂²×C₂₃	C₂×C₂²⋊Q₈	1	2	yes	—
206	C₄×C₂₃	—	2	4	no	—
207	C₄×C₂₃	#385	1	1	yes	characteristic
208	C₄×C₂₃	#385	1	1	yes	characteristic
209	C₄×C₂₃	#385	1	2	yes	—
210	C₄×C₂₃	C₂×C₄×D₄	1	2	yes	—
211	C₄×C₂₃	C₂×#120	1	1	yes	characteristic
212	C₄×C₂₃	C₂×#123	1	1	yes	characteristic
213	C₂²×#41	C₂²×C₂₃	1	1	yes	characteristic
214	#568	—	2	2	no	—
215	#568	—	2	4	no	—
216	#568	C₂²×C₂₃	1	4	yes	—
217	C₂×#131	—	2	4	no	—
218	C₂²×M₁₆	—	2	2	no	—
219	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
220	C₂²×M₁₆	C₂²×C₂₃	1	2	yes	—
221	C₂²×M₁₆	C₂²×C₂₃	1	2	yes	—
222	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
223	#430	—	2	4	no	—
224	#430	C₂²×C₂₃	1	8	yes	complemented
225	C₂×#108	—	2	4	no	—
226	#413	C₄×C₂₃	1	4	yes	—
227	#413	C₂²×C₂₃	1	4	yes	—
228	C₂×#101	C₄×C₂₃	1	2	yes	—
229	C₂×#100	C₄×C₂₃	1	2	yes	—
230	#408	—	2	2	no	—
231	#408	C₂²×C₂₃	1	4	yes	—
232	#407	—	2	2	no	—
233	#341	C₂²×C₂₃	1	8	yes	complemented
234	C₂×C₂₃	—	2	1	no	—
235	C₂×C₂₃	—	2	1	no	—
236	C₂×C₂₃	—	2	1	no	—
237	C₂×C₂₃	—	2	2	no	—
238	C₂×C₂₃	—	2	2	no	—
239	C₂×C₂₃	—	4	4	no	—
240	C₂×C₂₃	C₂×#385	1	1	yes	characteristic
241	C₂×#41	—	2	2	no	—
242	C₂×#41	—	2	2	no	—
243	C₂×#41	—	2	2	no	—
244	C₂×#41	—	2	2	no	—
245	C₂×#41	C₂×C₄×C₂₃	1	2	yes	—
246	C₂×#41	D₄×C₂₃	1	2	yes	—
247	C₂×#41	Q₈×C₂₃	1	2	yes	—
248	C₂×#41	C₂³×C₂₃	1	2	yes	—
249	C₂²×Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
250	C₂²×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
251	C₂²×D₄	Q₈×C₂₃	1	2	yes	—
252	C₂³×C₄	D₄×C₂₃	1	2	yes	—
253	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
254	#131	—	2	16	no	—
255	#131	—	2	16	no	—
256	C₂×M₁₆	—	2	4	no	—
257	C₂×M₁₆	—	2	8	no	—
258	C₂×M₁₆	—	2	2	no	—
259	C₂×M₁₆	—	2	8	no	—
260	C₂×M₁₆	—	2	2	no	—
261	C₂×M₁₆	—	2	2	no	—
262	C₂×M₁₆	—	2	2	no	—
263	C₂×M₁₆	—	2	2	no	—
264	C₂×M₁₆	—	2	2	no	—
265	C₂×M₁₆	—	2	1	no	—
266	C₂×M₁₆	—	2	1	no	—
267	C₂×M₁₆	—	2	1	no	—
268	C₂×M₁₆	—	2	2	no	—
269	C₂×M₁₆	—	2	2	no	—
270	C₂×M₁₆	—	2	2	no	—
271	C₂×M₁₆	—	2	2	no	—
272	C₂×M₁₆	C₂×C₄×C₂₃	1	4	yes	—
273	C₂×M₁₆	C₂×C₄×C₂₃	1	4	yes	—
274	C₂×M₁₆	D₄×C₂₃	1	4	yes	—
275	C₂×M₁₆	D₄×C₂₃	1	4	yes	—
276	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
277	C₂×M₁₆	C₂³×C₂₃	1	4	yes	—
278	C₂×M₁₆	C₂³×C₂₃	1	4	yes	—
279	C₂²×C₈	—	2	4	no	—
280	C₂²×C₈	—	2	2	no	—
281	C₂²×C₈	—	2	2	no	—
282	C₂²×C₈	—	2	1	no	—
283	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
284	#108	—	2	16	no	—
285	#101	C₂×C₄×C₂₃	1	8	yes	—
286	#100	C₂×C₄×C₂₃	1	8	yes	—
287	C₂²⋊C₈	—	2	8	no	—
288	C₂₃	#20860	1	1	yes	characteristic, direct product factor, Sylow
289	C₂⁴	C₄⋊C₄×C₂₃	1	2	yes	—
290	C₂⁴	C₂×Q₈×C₂₃	1	1	yes	characteristic
291	#41	—	2	4	no	—
292	#41	—	2	4	no	—
293	#41	—	2	4	no	—
294	#41	—	2	4	no	—
295	#41	—	2	4	no	—
296	#41	—	2	4	no	—
297	#41	—	2	4	no	—
298	#41	—	2	4	no	—
299	C₂×Q₈	—	2	2	no	—
300	C₂×Q₈	—	2	2	no	—
301	C₂×Q₈	C₄⋊C₄×C₂₃	1	2	yes	—
302	C₂×Q₈	C₂²×C₄×C₂₃	1	2	yes	—
303	C₂×D₄	—	2	4	no	—
304	C₂×D₄	—	2	4	no	—
305	C₂×D₄	—	2	2	no	—
306	C₂×D₄	—	2	2	no	—
307	C₂×D₄	C₄⋊C₄×C₂₃	1	2	yes	—
308	C₂×D₄	C₄⋊C₄×C₂₃	1	4	yes	—
309	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
310	C₂×D₄	C₂×Q₈×C₂₃	1	4	yes	—
311	C₂²×C₄	—	2	2	no	—
312	C₂²×C₄	—	2	2	no	—
313	C₂²×C₄	—	2	2	no	—
314	C₂²×C₄	—	2	2	no	—
315	C₂²×C₄	C₄⋊C₄×C₂₃	1	2	yes	—
316	C₂²×C₄	C₄⋊C₄×C₂₃	1	4	yes	—
317	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
318	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
319	C₂²×C₄	C₂×D₄×C₂₃	1	4	yes	—
320	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
321	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
322	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
323	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
324	C₂²×C₄	C₂×Q₈×C₂₃	1	1	yes	characteristic
325	C₂²×C₄	#41×C₂₃	1	2	yes	—
326	C₂²×C₄	#41×C₂₃	1	2	yes	—
327	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
328	M₁₆	—	2	16	no	—
329	M₁₆	—	2	4	no	—
330	M₁₆	—	2	4	no	—
331	M₁₆	—	2	4	no	—
332	M₁₆	—	2	4	no	—
333	M₁₆	—	2	4	no	—
334	M₁₆	—	2	4	no	—
335	M₁₆	—	2	4	no	—
336	M₁₆	—	4	1	no	—
337	M₁₆	—	4	1	no	—
338	M₁₆	—	4	1	no	—
339	M₁₆	—	4	1	no	—
340	M₁₆	—	4	2	no	—
341	M₁₆	C₂²×C₄×C₂₃	1	8	yes	—
342	M₁₆	C₂×D₄×C₂₃	1	8	yes	—
343	C₂×C₈	—	2	16	no	—
344	C₂×C₈	—	2	4	no	—
345	C₂×C₈	—	2	4	no	—
346	C₂×C₈	—	2	4	no	—
347	C₂×C₈	—	2	4	no	—
348	C₂×C₈	—	2	4	no	—
349	C₂×C₈	—	2	4	no	—
350	C₂×C₈	—	2	2	no	—
351	C₂×C₈	—	2	2	no	—
352	C₂×C₈	—	2	4	no	—
353	C₂×C₈	—	4	2	no	—
354	C₂³	—	2	2	no	—
355	C₂³	—	2	2	no	—
356	C₂³	—	8	1	no	—
357	C₂³	—	8	2	no	—
358	C₂³	C₂×C₄⋊C₄×C₂₃	1	4	yes	—
359	C₂³	C₂×C₄⋊C₄×C₂₃	1	1	yes	characteristic
360	C₂³	C₂×C₄⋊C₄×C₂₃	1	1	yes	characteristic
361	C₂³	C₂₃×C₂²⋊Q₈	1	2	yes	—
362	C₂³	C₂₃×C₂²⋊Q₈	1	2	yes	—
363	C₂³	C₂²×Q₈×C₂₃	1	1	yes	characteristic
364	Q₈	—	2	4	no	—
365	Q₈	—	2	4	no	—
366	D₄	—	2	8	no	—
367	D₄	—	2	8	no	—
368	D₄	—	2	4	no	—
369	D₄	—	2	4	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	4	no	—
373	C₂×C₄	—	2	4	no	—
374	C₂×C₄	—	2	4	no	—
375	C₂×C₄	—	2	4	no	—
376	C₂×C₄	C₂×C₄⋊C₄×C₂₃	1	4	yes	—
377	C₂×C₄	C₂×C₄⋊C₄×C₂₃	1	1	yes	characteristic
378	C₂×C₄	C₂×C₄⋊C₄×C₂₃	1	1	yes	characteristic
379	C₂×C₄	C₄×D₄×C₂₃	1	2	yes	—
380	C₂×C₄	C₄×D₄×C₂₃	1	2	yes	—
381	C₂×C₄	C₄×D₄×C₂₃	1	2	yes	—
382	C₂×C₄	C₄×D₄×C₂₃	1	2	yes	—
383	C₂×C₄	C₂₃×#120	1	1	yes	characteristic
384	C₂×C₄	C₂₃×#120	1	2	yes	—
385	C₂×C₄	C₂₃×#120	1	1	yes	characteristic
386	C₂×C₄	C₂₃×C₂²⋊Q₈	1	2	yes	—
387	C₂×C₄	C₂₃×C₂²⋊Q₈	1	2	yes	—
388	C₂×C₄	C₂₃×#123	1	1	yes	characteristic
389	C₂×C₄	C₂₃×#123	1	1	yes	characteristic
390	C₂×C₄	C₂₃×#123	1	2	yes	—
391	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
392	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
393	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
394	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
395	C₈	—	2	8	no	—
396	C₈	—	2	8	no	—
397	C₈	—	4	2	no	—
398	C₈	—	4	2	no	—
399	C₂²	—	2	4	no	—
400	C₂²	—	4	1	no	—
401	C₂²	—	4	1	no	—
402	C₂²	—	4	2	no	—
403	C₂²	—	4	2	no	—
404	C₂²	—	4	1	no	—
405	C₂²	—	4	4	no	—
406	C₂²	—	4	4	no	—
407	C₂²	—	8	2	no	—
408	C₂²	C₂₃×#385	1	1	yes	characteristic
409	C₂²	C₂₃×#385	1	1	yes	characteristic
410	C₂²	C₂₃×#385	1	2	yes	—
411	C₂²	C₂²×C₄⋊C₄×C₂₃	1	1	yes	characteristic
412	C₂²	C₂×C₂₃×C₂²⋊Q₈	1	2	yes	—
413	C₄	—	2	4	no	—
414	C₄	C₂₃×#385	1	1	yes	characteristic
415	C₄	C₂₃×#385	1	1	yes	characteristic
416	C₄	C₂₃×#385	1	2	yes	—
417	C₄	C₂×C₄×D₄×C₂₃	1	2	yes	—
418	C₄	C₂×C₂₃×#120	1	1	yes	characteristic
419	C₄	C₂×C₂₃×#123	1	1	yes	characteristic
420	C₂	—	2	1	no	—
421	C₂	—	2	1	no	—
422	C₂	—	2	1	no	—
423	C₂	—	2	2	no	—
424	C₂	—	2	2	no	—
425	C₂	—	4	4	no	—
426	C₂	C₂×C₂₃×#385	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₂₃	C₂×#120
commutator	C₂×C₄	C₂³×C₄×C₂₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₃
socle	C₂×C₂₃	C₂×#385
prime radical	C₂²×#41×C₂₃	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₂₃ ◁ C₂³×C₄×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₂₃×#430	C₂	semidirect
5. C₂₃×#1858	C₂	semidirect
6. C₂₃×#1738	C₂	semidirect
18. C₂₃×#430	C₂²	semidirect
27. C₂₃×#341	C₂²	semidirect
140. #20860	C₂₃	direct (N × H)
187. C₂×#430	C₂×C₂₃	semidirect
190. #1858	C₂×C₂₃	semidirect
191. #1738	C₂×C₂₃	semidirect
224. #430	C₂²×C₂₃	semidirect
233. #341	C₂²×C₂₃	semidirect
288. C₂₃	#20860	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×#568	2
C₂×C₂₃×#430	2
C₂×C₂₃×#413	2
C₂₃×#2879	2
C₂₃×#1858	2
C₂₃×#1738	2
#20860	23

Subgroups — C23×#20860 #19168486

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#20860 #19168486