Subgroups — C₂₃×#21546 #19169172

Order 5888.

958 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3050	C₂	1	1	yes	maximal, characteristic
2	C₂×C₂₃×#444	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#2929	C₂	1	2	yes	maximal, complemented
4	C₂²×C₂₃×#97	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#1975	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#1946	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#1938	C₂	1	2	yes	maximal, complemented
8	C₂₃×#1896	C₂	1	2	yes	maximal, complemented
9	C₂₃×#1810	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#1773	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#1765	C₂	1	2	yes	maximal, complemented
12	C₂×C₂₃×#135	C₂²	1	1	yes	characteristic
13	C₂×C₂₃×#131	C₂²	1	2	yes	—
14	C₂³×C₈×C₂₃	C₂²	1	1	yes	characteristic
15	C₂³×C₈×C₂₃	C₂²	1	1	yes	characteristic
16	C₂₃×#525	C₂²	1	2	yes	—
17	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
18	C₂₃×#467	C₄	1	2	yes	complemented
19	C₂₃×#466	C₄	1	2	yes	complemented
20	C₂₃×#465	C₄	1	4	yes	complemented
21	C₂₃×#444	—	2	4	no	—
22	C₂₃×#435	—	2	4	no	—
23	C₈×D₄×C₂₃	—	2	4	no	—
24	C₂×C₂₃×#108	C₂²	1	1	yes	characteristic
25	C₂×C₂₃×#108	C₂²	1	1	yes	characteristic
26	C₂₃×#427	C₂²	1	1	yes	characteristic
27	C₂₃×#424	C₂²	1	2	yes	—
28	C₂×C₂₃×#104	C₂²	1	2	yes	—
29	C₂×C₂₃×#104	C₂²	1	2	yes	—
30	C₂₃×#416	C₂²	1	2	yes	—
31	C₂₃×#408	C₂²	1	2	yes	—
32	C₂₃×#407	C₂²	1	2	yes	—
33	C₂₃×#405	C₂²	1	2	yes	—
34	C₂×C₂₃×#97	—	2	4	no	—
35	C₂×C₂₃×#97	C₂²	1	1	yes	characteristic
36	C₂×C₂₃×#97	C₂²	1	1	yes	characteristic
37	C₂×C₂₃×#97	C₂²	1	1	yes	characteristic
38	C₂×C₂₃×#97	C₂²	1	1	yes	characteristic
39	C₂₃×#341	C₂²	1	2	yes	—
40	C₂₃×#339	C₂²	1	2	yes	—
41	C₂₃×#339	C₂²	1	2	yes	—
42	C₂×#41×C₂₃	C₂³	1	2	yes	—
43	C₂³×C₄×C₂₃	—	2	1	no	—
44	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
45	C₂₃×#135	—	2	2	no	—
46	C₂₃×#135	—	2	2	no	—
47	C₂×Q₁₆×C₂₃	C₂×C₄	1	1	yes	characteristic, complemented
48	C₂×SD₁₆×C₂₃	C₂×C₄	1	2	yes	complemented
49	C₂×D₈×C₂₃	C₂×C₄	1	1	yes	characteristic, complemented
50	C₂₃×#131	—	2	4	no	—
51	C₂₃×#131	—	2	4	no	—
52	C₂×M₁₆×C₂₃	—	2	2	no	—
53	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
54	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
55	C₂²×C₈×C₂₃	—	2	2	no	—
56	C₂²×C₈×C₂₃	—	2	2	no	—
57	C₂²×C₈×C₂₃	—	2	2	no	—
58	C₂²×C₈×C₂₃	—	2	2	no	—
59	C₂²×C₈×C₂₃	—	2	2	no	—
60	C₂²×C₈×C₂₃	C₂×C₄	1	2	yes	—
61	C₂²×C₈×C₂₃	C₂×C₄	1	2	yes	—
62	C₂²×C₈×C₂₃	D₄	1	4	yes	—
63	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
64	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
65	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
66	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
67	C₂₃×#123	—	2	2	no	—
68	C₂₃×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
69	C₂₃×#121	C₂×C₄	1	4	yes	—
70	C₂₃×#120	—	2	2	no	—
71	C₄×D₄×C₂₃	—	2	4	no	—
72	C₂₃×#117	C₂³	1	2	yes	—
73	C₂×C₄²×C₂₃	—	2	1	no	—
74	C₂×C₄²×C₂₃	—	2	2	no	—
75	C₂×C₄²×C₂₃	—	2	2	no	—
76	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
77	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
78	C₂₃×#108	—	2	2	no	—
79	C₂₃×#108	—	2	2	no	—
80	C₂₃×#107	C₂×C₄	1	2	yes	complemented
81	C₂₃×#106	C₂×C₄	1	2	yes	complemented
82	C₂₃×C₄⋊C₈	—	2	4	no	—
83	C₂₃×#104	—	2	4	no	—
84	C₂₃×#104	—	2	4	no	—
85	C₂₃×#103	C₂×C₄	1	4	yes	complemented
86	C₂₃×#102	C₂×C₄	1	4	yes	complemented
87	C₂₃×C₂²⋊C₈	—	2	4	no	—
88	C₂₃×C₂²⋊C₈	—	2	4	no	—
89	C₂₃×#97	—	2	2	no	—
90	C₂₃×#97	—	2	2	no	—
91	C₂₃×#97	—	2	2	no	—
92	C₂₃×#97	—	2	2	no	—
93	C₂₃×#97	D₄	1	4	yes	complemented
94	C₄×C₈×C₂₃	—	2	2	no	—
95	C₂⁴×C₂₃	#41	1	1	yes	characteristic
96	#41×C₂₃	—	2	2	no	—
97	#41×C₂₃	—	2	2	no	—
98	#41×C₂₃	—	2	2	no	—
99	#41×C₂₃	—	2	2	no	—
100	C₂×Q₈×C₂₃	C₂²×C₄	1	2	yes	—
101	C₂×D₄×C₂₃	—	2	4	no	—
102	C₂×D₄×C₂₃	—	2	2	no	—
103	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
104	C₂²×C₄×C₂₃	—	2	1	no	—
105	C₂²×C₄×C₂₃	—	2	1	no	—
106	C₂²×C₄×C₂₃	—	2	1	no	—
107	C₂²×C₄×C₂₃	—	2	1	no	—
108	C₂²×C₄×C₂₃	—	2	4	no	—
109	C₂²×C₄×C₂₃	—	2	1	no	—
110	C₂²×C₄×C₂₃	—	2	1	no	—
111	C₂²×C₄×C₂₃	—	2	2	no	—
112	C₂²×C₄×C₂₃	—	4	4	no	—
113	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
114	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
115	C₂²×C₄×C₂₃	#41	1	1	yes	characteristic
116	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
117	Q₁₆×C₂₃	—	2	2	no	—
118	SD₁₆×C₂₃	—	2	4	no	—
119	D₈×C₂₃	—	2	2	no	—
120	M₁₆×C₂₃	—	2	2	no	—
121	M₁₆×C₂₃	—	2	2	no	—
122	M₁₆×C₂₃	—	2	2	no	—
123	M₁₆×C₂₃	—	2	2	no	—
124	M₁₆×C₂₃	—	4	4	no	—
125	C₂×C₈×C₂₃	—	2	1	no	—
126	C₂×C₈×C₂₃	—	2	1	no	—
127	C₂×C₈×C₂₃	—	2	1	no	—
128	C₂×C₈×C₂₃	—	2	1	no	—
129	C₂×C₈×C₂₃	—	2	4	no	—
130	C₂×C₈×C₂₃	—	2	4	no	—
131	C₂×C₈×C₂₃	—	2	8	no	—
132	C₂×C₈×C₂₃	—	2	2	no	—
133	C₂×C₈×C₂₃	—	2	2	no	—
134	C₂×C₈×C₂₃	—	4	4	no	—
135	C₂×C₈×C₂₃	C₂²×C₄	1	2	yes	—
136	C₂×C₈×C₂₃	C₂²×C₄	1	1	yes	characteristic
137	C₂×C₈×C₂₃	C₂²×C₄	1	1	yes	characteristic
138	C₂×C₈×C₂₃	C₂×D₄	1	2	yes	—
139	C₂×C₈×C₂₃	C₂×D₄	1	2	yes	—
140	C₂×C₈×C₂₃	C₂×D₄	1	2	yes	—
141	C₂×C₈×C₂₃	C₂×D₄	1	2	yes	—
142	C₂×C₈×C₂₃	#41	1	2	yes	—
143	C₂×C₈×C₂₃	#41	1	2	yes	—
144	C₄⋊C₄×C₂₃	—	2	4	no	—
145	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
146	C₂²⋊C₄×C₂₃	—	2	4	no	—
147	C₂²⋊C₄×C₂₃	—	2	2	no	—
148	C₂²⋊C₄×C₂₃	—	2	4	no	—
149	C₄²×C₂₃	—	2	4	no	—
150	C₄²×C₂₃	—	2	1	no	—
151	C₄²×C₂₃	—	2	2	no	—
152	C₄²×C₂₃	—	2	1	no	—
153	C₄²×C₂₃	C₂×D₄	1	2	yes	—
154	C₄²×C₂₃	#41	1	2	yes	—
155	#21546	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
156	C₂³×C₂₃	—	2	1	no	—
157	C₂³×C₂₃	—	2	1	no	—
158	C₂³×C₂₃	—	2	4	no	—
159	C₂³×C₂₃	—	2	2	no	—
160	C₂³×C₂₃	C₄×D₄	1	2	yes	—
161	C₂³×C₂₃	C₂×#41	1	1	yes	characteristic
162	Q₈×C₂₃	—	2	2	no	—
163	Q₈×C₂₃	—	2	2	no	—
164	D₄×C₂₃	—	2	2	no	—
165	D₄×C₂₃	—	2	2	no	—
166	D₄×C₂₃	—	4	2	no	—
167	D₄×C₂₃	—	4	2	no	—
168	D₄×C₂₃	—	4	8	no	—
169	C₂×C₄×C₂₃	—	2	1	no	—
170	C₂×C₄×C₂₃	—	2	1	no	—
171	C₂×C₄×C₂₃	—	2	2	no	—
172	C₂×C₄×C₂₃	—	2	2	no	—
173	C₂×C₄×C₂₃	—	2	2	no	—
174	C₂×C₄×C₂₃	—	2	2	no	—
175	C₂×C₄×C₂₃	—	2	4	no	—
176	C₂×C₄×C₂₃	—	2	2	no	—
177	C₂×C₄×C₂₃	—	2	2	no	—
178	C₂×C₄×C₂₃	—	2	2	no	—
179	C₂×C₄×C₂₃	—	4	8	no	—
180	C₂×C₄×C₂₃	—	4	2	no	—
181	C₂×C₄×C₂₃	—	4	2	no	—
182	C₂×C₄×C₂₃	—	4	2	no	—
183	C₂×C₄×C₂₃	—	4	2	no	—
184	C₂×C₄×C₂₃	C₄×D₄	1	2	yes	—
185	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
186	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
187	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
188	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
189	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
190	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
191	C₈×C₂₃	—	2	2	no	—
192	C₈×C₂₃	—	2	2	no	—
193	C₈×C₂₃	—	4	2	no	—
194	C₈×C₂₃	—	4	2	no	—
195	C₈×C₂₃	C₄×D₄	1	2	yes	—
196	C₈×C₂₃	C₄×D₄	1	2	yes	—
197	C₈×C₂₃	#121	1	4	yes	—
198	#3050	C₂×C₂₃	1	1	yes	characteristic
199	C₂×#444	C₂×C₂₃	1	1	yes	characteristic, complemented
200	#2929	C₂×C₂₃	1	2	yes	complemented
201	C₂²×#97	C₂×C₂₃	1	1	yes	characteristic, complemented
202	#1975	C₂×C₂₃	1	1	yes	characteristic, complemented
203	#1946	C₂×C₂₃	1	1	yes	characteristic, complemented
204	#1938	C₂×C₂₃	1	2	yes	complemented
205	#1896	C₂×C₂₃	1	2	yes	complemented
206	#1810	C₂×C₂₃	1	1	yes	characteristic, complemented
207	#1773	C₂×C₂₃	1	1	yes	characteristic, complemented
208	#1765	C₂×C₂₃	1	2	yes	complemented
209	C₂²×C₂₃	—	2	4	no	—
210	C₂²×C₂₃	—	2	4	no	—
211	C₂²×C₂₃	—	2	2	no	—
212	C₂²×C₂₃	—	2	2	no	—
213	C₂²×C₂₃	—	2	2	no	—
214	C₂²×C₂₃	—	4	4	no	—
215	C₂²×C₂₃	—	4	2	no	—
216	C₂²×C₂₃	#444	1	4	yes	complemented
217	C₂²×C₂₃	C₂×C₄×D₄	1	1	yes	characteristic
218	C₂²×C₂₃	#525	1	1	yes	characteristic
219	C₂²×C₂₃	#529	1	1	yes	characteristic
220	C₄×C₂₃	—	2	2	no	—
221	C₄×C₂₃	—	4	2	no	—
222	C₄×C₂₃	—	4	2	no	—
223	C₄×C₂₃	—	4	4	no	—
224	C₄×C₂₃	—	4	2	no	—
225	C₄×C₂₃	C₂×C₄×D₄	1	1	yes	characteristic
226	C₄×C₂₃	C₄×#41	1	1	yes	characteristic
227	C₄×C₂₃	C₂×#121	1	1	yes	characteristic
228	C₄×C₂₃	#532	1	1	yes	characteristic
229	C₂×#135	C₂²×C₂₃	1	1	yes	characteristic
230	C₂×#131	C₂²×C₂₃	1	2	yes	—
231	C₂³×C₈	C₂²×C₂₃	1	1	yes	characteristic
232	C₂³×C₈	C₂²×C₂₃	1	1	yes	characteristic
233	#525	C₂²×C₂₃	1	2	yes	—
234	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
235	#467	C₄×C₂₃	1	2	yes	complemented
236	#466	C₄×C₂₃	1	2	yes	complemented
237	#465	C₄×C₂₃	1	4	yes	complemented
238	#444	—	2	4	no	—
239	#435	—	2	4	no	—
240	C₈×D₄	—	2	4	no	—
241	C₂×#108	C₂²×C₂₃	1	1	yes	characteristic
242	C₂×#108	C₂²×C₂₃	1	1	yes	characteristic
243	#427	C₂²×C₂₃	1	1	yes	characteristic
244	#424	C₂²×C₂₃	1	2	yes	—
245	C₂×#104	C₂²×C₂₃	1	2	yes	—
246	C₂×#104	C₂²×C₂₃	1	2	yes	—
247	#416	C₂²×C₂₃	1	2	yes	—
248	#408	C₂²×C₂₃	1	2	yes	—
249	#407	C₂²×C₂₃	1	2	yes	—
250	#405	C₂²×C₂₃	1	2	yes	—
251	C₂×#97	—	2	4	no	—
252	C₂×#97	C₂²×C₂₃	1	1	yes	characteristic
253	C₂×#97	C₂²×C₂₃	1	1	yes	characteristic
254	C₂×#97	C₂²×C₂₃	1	1	yes	characteristic
255	C₂×#97	C₂²×C₂₃	1	1	yes	characteristic
256	#341	C₂²×C₂₃	1	2	yes	—
257	#339	C₂²×C₂₃	1	2	yes	—
258	#339	C₂²×C₂₃	1	2	yes	—
259	C₂×C₂₃	—	2	1	no	—
260	C₂×C₂₃	—	2	1	no	—
261	C₂×C₂₃	—	2	4	no	—
262	C₂×C₂₃	—	8	2	no	—
263	C₂×C₂₃	C₄×#121	1	1	yes	characteristic
264	C₂×C₂₃	C₂×#444	1	2	yes	—
265	C₂×#41	C₂³×C₂₃	1	2	yes	—
266	C₂³×C₄	—	2	1	no	—
267	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
268	#135	—	2	2	no	—
269	#135	—	2	2	no	—
270	C₂×Q₁₆	C₂×C₄×C₂₃	1	1	yes	characteristic, complemented
271	C₂×SD₁₆	C₂×C₄×C₂₃	1	2	yes	complemented
272	C₂×D₈	C₂×C₄×C₂₃	1	1	yes	characteristic, complemented
273	#131	—	2	4	no	—
274	#131	—	2	4	no	—
275	C₂×M₁₆	—	2	2	no	—
276	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
277	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
278	C₂²×C₈	—	2	2	no	—
279	C₂²×C₈	—	2	2	no	—
280	C₂²×C₈	—	2	2	no	—
281	C₂²×C₈	—	2	2	no	—
282	C₂²×C₈	—	2	2	no	—
283	C₂²×C₈	C₂×C₄×C₂₃	1	2	yes	—
284	C₂²×C₈	C₂×C₄×C₂₃	1	2	yes	—
285	C₂²×C₈	D₄×C₂₃	1	4	yes	—
286	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
287	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
288	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
289	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
290	#123	—	2	2	no	—
291	C₂²⋊Q₈	C₂×C₄×C₂₃	1	4	yes	—
292	#121	C₂×C₄×C₂₃	1	4	yes	—
293	#120	—	2	2	no	—
294	C₄×D₄	—	2	4	no	—
295	#117	C₂³×C₂₃	1	2	yes	—
296	C₂×C₄²	—	2	1	no	—
297	C₂×C₄²	—	2	2	no	—
298	C₂×C₄²	—	2	2	no	—
299	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
300	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
301	#108	—	2	2	no	—
302	#108	—	2	2	no	—
303	#107	C₂×C₄×C₂₃	1	2	yes	complemented
304	#106	C₂×C₄×C₂₃	1	2	yes	complemented
305	C₄⋊C₈	—	2	4	no	—
306	#104	—	2	4	no	—
307	#104	—	2	4	no	—
308	#103	C₂×C₄×C₂₃	1	4	yes	complemented
309	#102	C₂×C₄×C₂₃	1	4	yes	complemented
310	C₂²⋊C₈	—	2	4	no	—
311	C₂²⋊C₈	—	2	4	no	—
312	#97	—	2	2	no	—
313	#97	—	2	2	no	—
314	#97	—	2	2	no	—
315	#97	—	2	2	no	—
316	#97	D₄×C₂₃	1	4	yes	complemented
317	C₄×C₈	—	2	2	no	—
318	C₂₃	#21546	1	1	yes	characteristic, direct product factor, Sylow
319	C₂⁴	#41×C₂₃	1	1	yes	characteristic
320	#41	—	2	2	no	—
321	#41	—	2	2	no	—
322	#41	—	2	2	no	—
323	#41	—	2	2	no	—
324	C₂×Q₈	C₂²×C₄×C₂₃	1	2	yes	—
325	C₂×D₄	—	2	4	no	—
326	C₂×D₄	—	2	2	no	—
327	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
328	C₂²×C₄	—	2	1	no	—
329	C₂²×C₄	—	2	1	no	—
330	C₂²×C₄	—	2	1	no	—
331	C₂²×C₄	—	2	1	no	—
332	C₂²×C₄	—	2	4	no	—
333	C₂²×C₄	—	2	1	no	—
334	C₂²×C₄	—	2	1	no	—
335	C₂²×C₄	—	2	2	no	—
336	C₂²×C₄	—	4	4	no	—
337	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
338	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
339	C₂²×C₄	#41×C₂₃	1	1	yes	characteristic
340	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
341	Q₁₆	—	2	2	no	—
342	SD₁₆	—	2	4	no	—
343	D₈	—	2	2	no	—
344	M₁₆	—	2	2	no	—
345	M₁₆	—	2	2	no	—
346	M₁₆	—	2	2	no	—
347	M₁₆	—	2	2	no	—
348	M₁₆	—	4	4	no	—
349	C₂×C₈	—	2	1	no	—
350	C₂×C₈	—	2	1	no	—
351	C₂×C₈	—	2	1	no	—
352	C₂×C₈	—	2	1	no	—
353	C₂×C₈	—	2	4	no	—
354	C₂×C₈	—	2	4	no	—
355	C₂×C₈	—	2	8	no	—
356	C₂×C₈	—	2	2	no	—
357	C₂×C₈	—	2	2	no	—
358	C₂×C₈	—	4	4	no	—
359	C₂×C₈	C₂²×C₄×C₂₃	1	2	yes	—
360	C₂×C₈	C₂²×C₄×C₂₃	1	1	yes	characteristic
361	C₂×C₈	C₂²×C₄×C₂₃	1	1	yes	characteristic
362	C₂×C₈	C₂×D₄×C₂₃	1	2	yes	—
363	C₂×C₈	C₂×D₄×C₂₃	1	2	yes	—
364	C₂×C₈	C₂×D₄×C₂₃	1	2	yes	—
365	C₂×C₈	C₂×D₄×C₂₃	1	2	yes	—
366	C₂×C₈	#41×C₂₃	1	2	yes	—
367	C₂×C₈	#41×C₂₃	1	2	yes	—
368	C₄⋊C₄	—	2	4	no	—
369	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
370	C₂²⋊C₄	—	2	4	no	—
371	C₂²⋊C₄	—	2	2	no	—
372	C₂²⋊C₄	—	2	4	no	—
373	C₄²	—	2	4	no	—
374	C₄²	—	2	2	no	—
375	C₄²	—	2	1	no	—
376	C₄²	—	2	1	no	—
377	C₄²	C₂×D₄×C₂₃	1	2	yes	—
378	C₄²	#41×C₂₃	1	2	yes	—
379	C₂³	—	2	4	no	—
380	C₂³	—	2	1	no	—
381	C₂³	—	2	1	no	—
382	C₂³	—	2	2	no	—
383	C₂³	C₄×D₄×C₂₃	1	2	yes	—
384	C₂³	C₂×#41×C₂₃	1	1	yes	characteristic
385	Q₈	—	2	2	no	—
386	Q₈	—	2	2	no	—
387	D₄	—	2	2	no	—
388	D₄	—	2	2	no	—
389	D₄	—	4	8	no	—
390	D₄	—	4	2	no	—
391	D₄	—	4	2	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	4	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	4	8	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	C₄×D₄×C₂₃	1	2	yes	—
408	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
409	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
410	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
411	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
412	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
413	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
414	C₈	—	2	2	no	—
415	C₈	—	2	2	no	—
416	C₈	—	4	2	no	—
417	C₈	—	4	2	no	—
418	C₈	C₄×D₄×C₂₃	1	2	yes	—
419	C₈	C₄×D₄×C₂₃	1	2	yes	—
420	C₈	C₂₃×#121	1	4	yes	—
421	C₂²	—	2	4	no	—
422	C₂²	—	2	4	no	—
423	C₂²	—	2	2	no	—
424	C₂²	—	2	2	no	—
425	C₂²	—	2	2	no	—
426	C₂²	—	4	4	no	—
427	C₂²	—	4	2	no	—
428	C₂²	C₂₃×#444	1	4	yes	complemented
429	C₂²	C₂×C₄×D₄×C₂₃	1	1	yes	characteristic
430	C₂²	C₂₃×#525	1	1	yes	characteristic
431	C₂²	C₂₃×#529	1	1	yes	characteristic
432	C₄	—	2	2	no	—
433	C₄	—	4	2	no	—
434	C₄	—	4	2	no	—
435	C₄	—	4	4	no	—
436	C₄	—	4	2	no	—
437	C₄	C₂×C₄×D₄×C₂₃	1	1	yes	characteristic
438	C₄	C₄×#41×C₂₃	1	1	yes	characteristic
439	C₄	C₂×C₂₃×#121	1	1	yes	characteristic
440	C₄	C₂₃×#532	1	1	yes	characteristic
441	C₂	—	2	1	no	—
442	C₂	—	2	4	no	—
443	C₂	—	2	1	no	—
444	C₂	—	8	2	no	—
445	C₂	C₄×C₂₃×#121	1	1	yes	characteristic
446	C₂	C₂×C₂₃×#444	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₂₃	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₂₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₃
socle	C₂²×C₂₃	C₂×C₄×D₄
prime radical	C₂₃×#3050	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₃ ◁ C₂³×C₈×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₂₃×#444	C₂	semidirect
3. C₂₃×#2929	C₂	semidirect
4. C₂²×C₂₃×#97	C₂	semidirect
5. C₂₃×#1975	C₂	semidirect
6. C₂₃×#1946	C₂	semidirect
7. C₂₃×#1938	C₂	semidirect
8. C₂₃×#1896	C₂	semidirect
9. C₂₃×#1810	C₂	semidirect
10. C₂₃×#1773	C₂	semidirect
11. C₂₃×#1765	C₂	semidirect
18. C₂₃×#467	C₄	semidirect
19. C₂₃×#466	C₄	semidirect
20. C₂₃×#465	C₄	semidirect
47. C₂×Q₁₆×C₂₃	C₂×C₄	semidirect
48. C₂×SD₁₆×C₂₃	C₂×C₄	semidirect
49. C₂×D₈×C₂₃	C₂×C₄	semidirect
80. C₂₃×#107	C₂×C₄	semidirect
81. C₂₃×#106	C₂×C₄	semidirect
85. C₂₃×#103	C₂×C₄	semidirect
86. C₂₃×#102	C₂×C₄	semidirect
93. C₂₃×#97	D₄	semidirect
155. #21546	C₂₃	direct (N × H)
199. C₂×#444	C₂×C₂₃	semidirect
200. #2929	C₂×C₂₃	semidirect
201. C₂²×#97	C₂×C₂₃	semidirect
202. #1975	C₂×C₂₃	semidirect
203. #1946	C₂×C₂₃	semidirect
204. #1938	C₂×C₂₃	semidirect
205. #1896	C₂×C₂₃	semidirect
206. #1810	C₂×C₂₃	semidirect
207. #1773	C₂×C₂₃	semidirect
208. #1765	C₂×C₂₃	semidirect
216. C₂²×C₂₃	#444	semidirect
235. #467	C₄×C₂₃	semidirect
236. #466	C₄×C₂₃	semidirect
237. #465	C₄×C₂₃	semidirect
270. C₂×Q₁₆	C₂×C₄×C₂₃	semidirect
271. C₂×SD₁₆	C₂×C₄×C₂₃	semidirect
272. C₂×D₈	C₂×C₄×C₂₃	semidirect
303. #107	C₂×C₄×C₂₃	semidirect
304. #106	C₂×C₄×C₂₃	semidirect
308. #103	C₂×C₄×C₂₃	semidirect
309. #102	C₂×C₄×C₂₃	semidirect
316. #97	D₄×C₂₃	semidirect
318. C₂₃	#21546	direct (N × H)
428. C₂²	C₂₃×#444	semidirect

Maximal subgroups

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

subgroup	index
C₂₃×#3050	2
C₂×C₂₃×#444	2
C₂₃×#2929	2
C₂²×C₂₃×#97	2
C₂₃×#1975	2
C₂₃×#1946	2
C₂₃×#1938	2
C₂₃×#1896	2
C₂₃×#1810	2
C₂₃×#1773	2
C₂₃×#1765	2
#21546	23

Subgroups — C23×#21546 #19169172

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#21546 #19169172