Subgroups — C₂₃×#21535 #19169161

Order 5888.

1010 conjugacy classes of subgroups.

The subgroup lattice has 694 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#468	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×SD₁₆×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₂₃×#405	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#2324	C₂	1	1	yes	maximal, characteristic
5	C₂₃×#2323	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#1973	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#1943	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#1934	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#1933	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#1893	C₂	1	1	yes	maximal, characteristic
11	C₂₃×#1892	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#1809	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄×C₂₃×#107	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#1763	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#1762	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic
17	C₂²×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
18	C₂³×C₈×C₂₃	C₂²	1	1	yes	characteristic
19	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
20	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
21	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
23	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
24	C₂₃×#468	C₄	1	8	yes	complemented
25	C₄×SD₁₆×C₂₃	—	2	4	no	—
26	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic
27	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic
28	C₂×C₂₃×#106	C₂²	1	1	yes	characteristic
29	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
30	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
31	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
32	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
33	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
34	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
35	C₂₃×#405	—	2	4	no	—
36	C₂×C₂₃×#97	C₂²	1	1	yes	characteristic
37	C₂×C₂₃×#97	C₂²	1	1	yes	characteristic
38	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
39	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
40	C₂₃×#391	C₂²	1	1	yes	characteristic
41	C₂₃×#390	—	2	1	no	—
42	C₂₃×#390	C₂²	1	1	yes	characteristic
43	C₂₃×#389	—	2	1	no	—
44	C₂₃×#389	C₂²	1	1	yes	characteristic
45	C₂₃×#389	C₂²	1	1	yes	characteristic
46	C₂₃×#388	—	2	1	no	—
47	C₂₃×#388	—	2	1	no	—
48	C₂₃×#388	—	2	1	no	—
49	C₂₃×#387	—	2	1	no	—
50	C₂₃×#386	—	2	1	no	—
51	C₂₃×#385	—	2	1	no	—
52	C₂₃×#380	C₂²	1	1	yes	characteristic
53	C₂₃×#380	C₂²	1	1	yes	characteristic
54	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
55	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
56	C₂₃×#340	C₂²	1	1	yes	characteristic
57	C₂₃×#340	C₂²	1	1	yes	characteristic
58	C₂₃×#340	C₂²	1	1	yes	characteristic
59	C₂₃×#340	C₂²	1	1	yes	characteristic
60	C₂₃×#340	C₂²	1	1	yes	characteristic
61	C₂₃×#340	C₂²	1	1	yes	characteristic
62	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
63	C₂²×D₄×C₂₃	—	2	1	no	—
64	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
65	C₂³×C₄×C₂₃	—	2	1	no	—
66	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
67	C₂×SD₁₆×C₂₃	—	2	2	no	—
68	C₂×SD₁₆×C₂₃	—	2	2	no	—
69	C₂×SD₁₆×C₂₃	C₂×C₄	1	4	yes	—
70	C₂×M₁₆×C₂₃	—	2	2	no	—
71	C₂×M₁₆×C₂₃	—	2	2	no	—
72	C₂×M₁₆×C₂₃	C₂×C₄	1	4	yes	complemented
73	C₂²×C₈×C₂₃	—	2	2	no	—
74	C₂²×C₈×C₂₃	—	2	2	no	—
75	C₂²×C₈×C₂₃	—	2	2	no	—
76	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
77	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
78	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
79	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
80	C₂₃×C₂²⋊Q₈	—	2	2	no	—
81	C₂₃×C₂²⋊Q₈	C₂×C₄	1	4	yes	complemented
82	C₂₃×#121	—	2	2	no	—
83	C₂₃×#121	C₂×C₄	1	4	yes	—
84	C₄×Q₈×C₂₃	—	2	2	no	—
85	C₄×Q₈×C₂₃	—	2	2	no	—
86	C₄×D₄×C₂₃	—	2	2	no	—
87	C₄×D₄×C₂₃	—	2	2	no	—
88	C₂₃×#117	—	2	2	no	—
89	C₂₃×#117	—	2	2	no	—
90	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
91	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
92	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
93	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
94	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
95	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
96	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
97	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
98	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
99	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
100	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
101	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
102	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
103	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
104	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
105	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
106	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
107	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
108	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
109	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
110	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
111	C₂×C₄²×C₂₃	—	2	1	no	—
112	C₂×C₄²×C₂₃	—	2	1	no	—
113	C₂×C₄²×C₂₃	—	2	1	no	—
114	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
115	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
116	C₂₃×#107	—	2	2	no	—
117	C₂₃×#107	C₂×C₄	1	4	yes	complemented
118	C₂₃×#106	—	2	2	no	—
119	C₂₃×#103	—	2	2	no	—
120	C₂₃×#103	—	2	2	no	—
121	C₂₃×#103	C₂×C₄	1	4	yes	complemented
122	C₂₃×#102	—	2	2	no	—
123	C₂₃×#102	—	2	2	no	—
124	C₂₃×#102	C₂×C₄	1	4	yes	—
125	C₂₃×#97	—	2	2	no	—
126	C₂₃×#97	—	2	2	no	—
127	C₄×C₈×C₂₃	—	2	2	no	—
128	C₄×C₈×C₂₃	D₄	1	4	yes	complemented
129	C₂₃×#95	—	2	1	no	—
130	C₂₃×#95	—	2	1	no	—
131	C₂₃×#95	—	2	1	no	—
132	C₂₃×#95	—	2	1	no	—
133	C₂₃×#95	—	2	1	no	—
134	C₂₃×#95	—	2	1	no	—
135	C₂₃×#95	—	2	1	no	—
136	C₂₃×#95	—	2	1	no	—
137	C₂⁴×C₂₃	—	2	1	no	—
138	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
139	C₂×Q₈×C₂₃	—	2	1	no	—
140	C₂×Q₈×C₂₃	—	2	1	no	—
141	C₂×Q₈×C₂₃	—	2	1	no	—
142	C₂×Q₈×C₂₃	—	2	1	no	—
143	C₂×Q₈×C₂₃	—	2	1	no	—
144	C₂×Q₈×C₂₃	C₂²×C₄	1	2	yes	—
145	C₂×D₄×C₂₃	—	2	4	no	—
146	C₂×D₄×C₂₃	—	2	1	no	—
147	C₂×D₄×C₂₃	—	2	1	no	—
148	C₂×D₄×C₂₃	—	2	1	no	—
149	C₂×D₄×C₂₃	—	2	1	no	—
150	C₂×D₄×C₂₃	—	2	1	no	—
151	C₂×D₄×C₂₃	—	8	1	no	—
152	C₂×D₄×C₂₃	—	8	1	no	—
153	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
154	C₂²×C₄×C₂₃	—	2	1	no	—
155	C₂²×C₄×C₂₃	—	2	1	no	—
156	C₂²×C₄×C₂₃	—	2	1	no	—
157	C₂²×C₄×C₂₃	—	2	1	no	—
158	C₂²×C₄×C₂₃	—	2	1	no	—
159	C₂²×C₄×C₂₃	—	2	1	no	—
160	C₂²×C₄×C₂₃	—	2	1	no	—
161	C₂²×C₄×C₂₃	—	2	1	no	—
162	C₂²×C₄×C₂₃	—	2	1	no	—
163	C₂²×C₄×C₂₃	—	2	1	no	—
164	C₂²×C₄×C₂₃	—	2	1	no	—
165	C₂²×C₄×C₂₃	—	4	2	no	—
166	C₂²×C₄×C₂₃	—	8	1	no	—
167	C₂²×C₄×C₂₃	—	8	1	no	—
168	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
169	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
170	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
171	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
172	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
173	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
174	C₂²×C₄×C₂₃	#41	1	2	yes	—
175	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
176	SD₁₆×C₂₃	—	2	8	no	—
177	M₁₆×C₂₃	—	2	8	no	—
178	C₂×C₈×C₂₃	—	2	8	no	—
179	C₂×C₈×C₂₃	—	2	1	no	—
180	C₂×C₈×C₂₃	—	2	1	no	—
181	C₂×C₈×C₂₃	—	2	1	no	—
182	C₂×C₈×C₂₃	—	2	1	no	—
183	C₂×C₈×C₂₃	—	2	1	no	—
184	C₂×C₈×C₂₃	—	2	1	no	—
185	C₂×C₈×C₂₃	C₂²×C₄	1	2	yes	—
186	C₂×C₈×C₂₃	C₂²×C₄	1	2	yes	—
187	C₂×C₈×C₂₃	C₂×D₄	1	2	yes	—
188	C₂×C₈×C₂₃	C₂×D₄	1	2	yes	—
189	C₂×C₈×C₂₃	#41	1	2	yes	—
190	C₂×C₈×C₂₃	#41	1	2	yes	—
191	C₄⋊C₄×C₂₃	—	2	4	no	—
192	C₄⋊C₄×C₂₃	—	2	2	no	—
193	C₄⋊C₄×C₂₃	—	2	2	no	—
194	C₄⋊C₄×C₂₃	—	2	1	no	—
195	C₄⋊C₄×C₂₃	—	2	1	no	—
196	C₄⋊C₄×C₂₃	—	2	1	no	—
197	C₄⋊C₄×C₂₃	—	2	1	no	—
198	C₄⋊C₄×C₂₃	—	2	1	no	—
199	C₄⋊C₄×C₂₃	—	2	1	no	—
200	C₄⋊C₄×C₂₃	—	2	1	no	—
201	C₄⋊C₄×C₂₃	—	2	1	no	—
202	C₄⋊C₄×C₂₃	—	2	1	no	—
203	C₄⋊C₄×C₂₃	—	2	1	no	—
204	C₄⋊C₄×C₂₃	—	4	2	no	—
205	C₄⋊C₄×C₂₃	—	8	1	no	—
206	C₄⋊C₄×C₂₃	—	8	1	no	—
207	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
208	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
209	C₂²⋊C₄×C₂₃	—	2	4	no	—
210	C₂²⋊C₄×C₂₃	—	2	4	no	—
211	C₂²⋊C₄×C₂₃	—	2	2	no	—
212	C₂²⋊C₄×C₂₃	—	2	2	no	—
213	C₂²⋊C₄×C₂₃	—	4	2	no	—
214	C₂²⋊C₄×C₂₃	—	8	1	no	—
215	C₂²⋊C₄×C₂₃	—	8	1	no	—
216	C₂²⋊C₄×C₂₃	—	8	1	no	—
217	C₂²⋊C₄×C₂₃	—	8	1	no	—
218	C₄²×C₂₃	—	2	1	no	—
219	C₄²×C₂₃	—	2	1	no	—
220	C₄²×C₂₃	—	4	2	no	—
221	C₄²×C₂₃	—	8	1	no	—
222	C₄²×C₂₃	—	8	1	no	—
223	C₄²×C₂₃	C₂×D₄	1	2	yes	—
224	C₄²×C₂₃	#41	1	2	yes	—
225	#21535	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
226	C₂³×C₂₃	—	2	1	no	—
227	C₂³×C₂₃	—	2	1	no	—
228	C₂³×C₂₃	—	2	1	no	—
229	C₂³×C₂₃	—	2	1	no	—
230	C₂³×C₂₃	—	2	1	no	—
231	C₂³×C₂₃	—	2	1	no	—
232	C₂³×C₂₃	—	2	2	no	—
233	C₂³×C₂₃	—	4	1	no	—
234	C₂³×C₂₃	—	4	1	no	—
235	C₂³×C₂₃	—	4	1	no	—
236	C₂³×C₂₃	—	4	1	no	—
237	C₂³×C₂₃	—	4	1	no	—
238	C₂³×C₂₃	—	4	1	no	—
239	C₂³×C₂₃	C₄×D₄	1	2	yes	—
240	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
241	Q₈×C₂₃	—	2	2	no	—
242	Q₈×C₂₃	—	2	2	no	—
243	Q₈×C₂₃	—	4	1	no	—
244	Q₈×C₂₃	—	4	1	no	—
245	D₄×C₂₃	—	2	2	no	—
246	D₄×C₂₃	—	2	2	no	—
247	D₄×C₂₃	—	4	1	no	—
248	D₄×C₂₃	—	4	1	no	—
249	D₄×C₂₃	—	8	4	no	—
250	C₂×C₄×C₂₃	—	2	1	no	—
251	C₂×C₄×C₂₃	—	2	1	no	—
252	C₂×C₄×C₂₃	—	2	1	no	—
253	C₂×C₄×C₂₃	—	2	1	no	—
254	C₂×C₄×C₂₃	—	2	1	no	—
255	C₂×C₄×C₂₃	—	2	1	no	—
256	C₂×C₄×C₂₃	—	2	2	no	—
257	C₂×C₄×C₂₃	—	2	2	no	—
258	C₂×C₄×C₂₃	—	2	2	no	—
259	C₂×C₄×C₂₃	—	2	2	no	—
260	C₂×C₄×C₂₃	—	2	2	no	—
261	C₂×C₄×C₂₃	—	2	2	no	—
262	C₂×C₄×C₂₃	—	2	2	no	—
263	C₂×C₄×C₂₃	—	2	1	no	—
264	C₂×C₄×C₂₃	—	2	1	no	—
265	C₂×C₄×C₂₃	—	2	1	no	—
266	C₂×C₄×C₂₃	—	2	1	no	—
267	C₂×C₄×C₂₃	—	2	1	no	—
268	C₂×C₄×C₂₃	—	2	1	no	—
269	C₂×C₄×C₂₃	—	4	1	no	—
270	C₂×C₄×C₂₃	—	4	1	no	—
271	C₂×C₄×C₂₃	—	4	1	no	—
272	C₂×C₄×C₂₃	—	4	1	no	—
273	C₂×C₄×C₂₃	—	4	1	no	—
274	C₂×C₄×C₂₃	—	4	1	no	—
275	C₂×C₄×C₂₃	—	4	1	no	—
276	C₂×C₄×C₂₃	—	4	1	no	—
277	C₂×C₄×C₂₃	—	4	1	no	—
278	C₂×C₄×C₂₃	—	4	1	no	—
279	C₂×C₄×C₂₃	—	4	1	no	—
280	C₂×C₄×C₂₃	—	4	1	no	—
281	C₂×C₄×C₂₃	—	4	1	no	—
282	C₂×C₄×C₂₃	—	4	1	no	—
283	C₂×C₄×C₂₃	—	4	1	no	—
284	C₂×C₄×C₂₃	—	4	1	no	—
285	C₂×C₄×C₂₃	—	4	1	no	—
286	C₂×C₄×C₂₃	—	4	1	no	—
287	C₂×C₄×C₂₃	—	8	4	no	—
288	C₂×C₄×C₂₃	C₄×D₄	1	2	yes	—
289	C₂×C₄×C₂₃	#121	1	2	yes	—
290	C₂×C₄×C₂₃	#121	1	2	yes	—
291	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
292	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
293	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
294	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
295	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
296	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
297	C₈×C₂₃	—	2	2	no	—
298	C₈×C₂₃	—	2	2	no	—
299	C₈×C₂₃	—	2	2	no	—
300	C₈×C₂₃	C₄×D₄	1	4	yes	—
301	C₂×#468	C₂×C₂₃	1	1	yes	characteristic
302	C₂×C₄×SD₁₆	C₂×C₂₃	1	1	yes	characteristic, complemented
303	C₂×#405	C₂×C₂₃	1	1	yes	characteristic, complemented
304	#2324	C₂×C₂₃	1	1	yes	characteristic
305	#2323	C₂×C₂₃	1	1	yes	characteristic, complemented
306	#1973	C₂×C₂₃	1	1	yes	characteristic, complemented
307	#1943	C₂×C₂₃	1	1	yes	characteristic, complemented
308	#1934	C₂×C₂₃	1	1	yes	characteristic, complemented
309	#1933	C₂×C₂₃	1	1	yes	characteristic, complemented
310	#1893	C₂×C₂₃	1	1	yes	characteristic
311	#1892	C₂×C₂₃	1	1	yes	characteristic, complemented
312	#1809	C₂×C₂₃	1	1	yes	characteristic, complemented
313	C₄×#107	C₂×C₂₃	1	1	yes	characteristic, complemented
314	#1763	C₂×C₂₃	1	1	yes	characteristic, complemented
315	#1762	C₂×C₂₃	1	1	yes	characteristic, complemented
316	C₂²×C₂₃	—	2	2	no	—
317	C₂²×C₂₃	—	2	2	no	—
318	C₂²×C₂₃	—	2	2	no	—
319	C₂²×C₂₃	—	4	1	no	—
320	C₂²×C₂₃	—	4	1	no	—
321	C₂²×C₂₃	—	4	1	no	—
322	C₂²×C₂₃	—	4	1	no	—
323	C₂²×C₂₃	—	4	2	no	—
324	C₂²×C₂₃	—	4	2	no	—
325	C₂²×C₂₃	—	4	2	no	—
326	C₂²×C₂₃	—	8	1	no	—
327	C₂²×C₂₃	—	8	1	no	—
328	C₂²×C₂₃	—	8	1	no	—
329	C₂²×C₂₃	—	8	1	no	—
330	C₂²×C₂₃	C₂×C₄×D₄	1	1	yes	characteristic
331	C₂²×C₂₃	C₂×#121	1	1	yes	characteristic
332	C₂²×C₂₃	#532	1	1	yes	characteristic
333	C₂²×C₂₃	#576	1	1	yes	characteristic
334	C₂²×C₂₃	#577	1	1	yes	characteristic
335	C₂²×C₂₃	#577	1	1	yes	characteristic
336	C₂²×C₂₃	#578	1	1	yes	characteristic
337	C₄×C₂₃	—	2	2	no	—
338	C₄×C₂₃	—	2	2	no	—
339	C₄×C₂₃	—	2	2	no	—
340	C₄×C₂₃	—	4	2	no	—
341	C₄×C₂₃	—	4	2	no	—
342	C₄×C₂₃	—	4	1	no	—
343	C₄×C₂₃	—	4	1	no	—
344	C₄×C₂₃	—	4	2	no	—
345	C₄×C₂₃	—	8	1	no	—
346	C₄×C₂₃	—	8	1	no	—
347	C₄×C₂₃	—	8	1	no	—
348	C₄×C₂₃	—	8	1	no	—
349	C₄×C₂₃	C₂×C₄×D₄	1	1	yes	characteristic
350	C₄×C₂₃	C₄×#41	1	1	yes	characteristic
351	C₄×C₂₃	#525	1	1	yes	characteristic
352	C₄×C₂₃	#529	1	1	yes	characteristic
353	C₂²×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic
354	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
355	C₂³×C₈	C₂²×C₂₃	1	1	yes	characteristic
356	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
357	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
358	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
359	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
360	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
361	#468	C₄×C₂₃	1	8	yes	complemented
362	C₄×SD₁₆	—	2	4	no	—
363	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic
364	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic
365	C₂×#106	C₂²×C₂₃	1	1	yes	characteristic
366	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
367	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
368	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
369	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
370	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
371	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
372	#405	—	2	4	no	—
373	C₂×#97	C₂²×C₂₃	1	1	yes	characteristic
374	C₂×#97	C₂²×C₂₃	1	1	yes	characteristic
375	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
376	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
377	#391	C₂²×C₂₃	1	1	yes	characteristic
378	#390	—	2	1	no	—
379	#390	C₂²×C₂₃	1	1	yes	characteristic
380	#389	—	2	1	no	—
381	#389	C₂²×C₂₃	1	1	yes	characteristic
382	#389	C₂²×C₂₃	1	1	yes	characteristic
383	#388	—	2	1	no	—
384	#388	—	2	1	no	—
385	#388	—	2	1	no	—
386	#387	—	2	1	no	—
387	#386	—	2	1	no	—
388	#385	—	2	1	no	—
389	#380	C₂²×C₂₃	1	1	yes	characteristic
390	#380	C₂²×C₂₃	1	1	yes	characteristic
391	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
392	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
393	#340	C₂²×C₂₃	1	1	yes	characteristic
394	#340	C₂²×C₂₃	1	1	yes	characteristic
395	#340	C₂²×C₂₃	1	1	yes	characteristic
396	#340	C₂²×C₂₃	1	1	yes	characteristic
397	#340	C₂²×C₂₃	1	1	yes	characteristic
398	#340	C₂²×C₂₃	1	1	yes	characteristic
399	C₂×C₂₃	—	4	2	no	—
400	C₂×C₂₃	—	8	2	no	—
401	C₂×C₂₃	C₄×#121	1	1	yes	characteristic
402	C₂×C₂₃	#2946	1	1	yes	characteristic
403	C₂×C₂₃	#2947	1	1	yes	characteristic
404	C₂×C₂₃	#3057	1	1	yes	characteristic
405	C₂×C₂₃	#3061	1	1	yes	characteristic
406	C₂×C₂₃	#3178	1	1	yes	characteristic
407	C₂×C₂₃	#3179	1	1	yes	characteristic
408	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
409	C₂²×D₄	—	2	1	no	—
410	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
411	C₂³×C₄	—	2	1	no	—
412	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
413	C₂×SD₁₆	—	2	2	no	—
414	C₂×SD₁₆	—	2	2	no	—
415	C₂×SD₁₆	C₂×C₄×C₂₃	1	4	yes	—
416	C₂×M₁₆	—	2	2	no	—
417	C₂×M₁₆	—	2	2	no	—
418	C₂×M₁₆	C₂×C₄×C₂₃	1	4	yes	complemented
419	C₂²×C₈	—	2	2	no	—
420	C₂²×C₈	—	2	2	no	—
421	C₂²×C₈	—	2	2	no	—
422	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
423	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
424	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
425	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
426	C₂²⋊Q₈	—	2	2	no	—
427	C₂²⋊Q₈	C₂×C₄×C₂₃	1	4	yes	complemented
428	#121	—	2	2	no	—
429	#121	C₂×C₄×C₂₃	1	4	yes	—
430	C₄×Q₈	—	2	2	no	—
431	C₄×Q₈	—	2	2	no	—
432	C₄×D₄	—	2	2	no	—
433	C₄×D₄	—	2	2	no	—
434	#117	—	2	2	no	—
435	#117	—	2	2	no	—
436	C₂×C₄⋊C₄	—	2	1	no	—
437	C₂×C₄⋊C₄	—	2	1	no	—
438	C₂×C₄⋊C₄	—	2	1	no	—
439	C₂×C₄⋊C₄	—	2	1	no	—
440	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
441	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
442	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
443	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
444	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
445	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
446	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
447	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
448	C₂×C₂²⋊C₄	—	2	1	no	—
449	C₂×C₂²⋊C₄	—	2	1	no	—
450	C₂×C₂²⋊C₄	—	2	1	no	—
451	C₂×C₂²⋊C₄	—	2	1	no	—
452	C₂×C₂²⋊C₄	—	2	1	no	—
453	C₂×C₂²⋊C₄	—	2	1	no	—
454	C₂×C₂²⋊C₄	—	2	1	no	—
455	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
456	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
457	C₂×C₄²	—	2	1	no	—
458	C₂×C₄²	—	2	1	no	—
459	C₂×C₄²	—	2	1	no	—
460	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
461	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
462	#107	—	2	2	no	—
463	#107	C₂×C₄×C₂₃	1	4	yes	complemented
464	#106	—	2	2	no	—
465	#103	—	2	2	no	—
466	#103	—	2	2	no	—
467	#103	C₂×C₄×C₂₃	1	4	yes	complemented
468	#102	—	2	2	no	—
469	#102	—	2	2	no	—
470	#102	C₂×C₄×C₂₃	1	4	yes	—
471	#97	—	2	2	no	—
472	#97	—	2	2	no	—
473	C₄×C₈	—	2	2	no	—
474	C₄×C₈	D₄×C₂₃	1	4	yes	complemented
475	#95	—	2	1	no	—
476	#95	—	2	1	no	—
477	#95	—	2	1	no	—
478	#95	—	2	1	no	—
479	#95	—	2	1	no	—
480	#95	—	2	1	no	—
481	#95	—	2	1	no	—
482	#95	—	2	1	no	—
483	C₂₃	#21535	1	1	yes	characteristic, direct product factor, Sylow
484	C₂⁴	—	2	1	no	—
485	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
486	C₂×Q₈	—	2	1	no	—
487	C₂×Q₈	—	2	1	no	—
488	C₂×Q₈	—	2	1	no	—
489	C₂×Q₈	—	2	1	no	—
490	C₂×Q₈	—	2	1	no	—
491	C₂×Q₈	C₂²×C₄×C₂₃	1	2	yes	—
492	C₂×D₄	—	2	4	no	—
493	C₂×D₄	—	2	1	no	—
494	C₂×D₄	—	2	1	no	—
495	C₂×D₄	—	2	1	no	—
496	C₂×D₄	—	2	1	no	—
497	C₂×D₄	—	2	1	no	—
498	C₂×D₄	—	8	1	no	—
499	C₂×D₄	—	8	1	no	—
500	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
501	C₂²×C₄	—	2	1	no	—
502	C₂²×C₄	—	2	1	no	—
503	C₂²×C₄	—	2	1	no	—
504	C₂²×C₄	—	2	1	no	—
505	C₂²×C₄	—	2	1	no	—
506	C₂²×C₄	—	2	1	no	—
507	C₂²×C₄	—	2	1	no	—
508	C₂²×C₄	—	2	1	no	—
509	C₂²×C₄	—	2	1	no	—
510	C₂²×C₄	—	2	1	no	—
511	C₂²×C₄	—	2	1	no	—
512	C₂²×C₄	—	4	2	no	—
513	C₂²×C₄	—	8	1	no	—
514	C₂²×C₄	—	8	1	no	—
515	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
516	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
517	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
518	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
519	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
520	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
521	C₂²×C₄	#41×C₂₃	1	2	yes	—
522	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
523	SD₁₆	—	2	8	no	—
524	M₁₆	—	2	8	no	—
525	C₂×C₈	—	2	8	no	—
526	C₂×C₈	—	2	1	no	—
527	C₂×C₈	—	2	1	no	—
528	C₂×C₈	—	2	1	no	—
529	C₂×C₈	—	2	1	no	—
530	C₂×C₈	—	2	1	no	—
531	C₂×C₈	—	2	1	no	—
532	C₂×C₈	C₂²×C₄×C₂₃	1	2	yes	—
533	C₂×C₈	C₂²×C₄×C₂₃	1	2	yes	—
534	C₂×C₈	C₂×D₄×C₂₃	1	2	yes	—
535	C₂×C₈	C₂×D₄×C₂₃	1	2	yes	—
536	C₂×C₈	#41×C₂₃	1	2	yes	—
537	C₂×C₈	#41×C₂₃	1	2	yes	—
538	C₄⋊C₄	—	2	4	no	—
539	C₄⋊C₄	—	2	2	no	—
540	C₄⋊C₄	—	2	2	no	—
541	C₄⋊C₄	—	2	1	no	—
542	C₄⋊C₄	—	2	1	no	—
543	C₄⋊C₄	—	2	1	no	—
544	C₄⋊C₄	—	2	1	no	—
545	C₄⋊C₄	—	2	1	no	—
546	C₄⋊C₄	—	2	1	no	—
547	C₄⋊C₄	—	2	1	no	—
548	C₄⋊C₄	—	2	1	no	—
549	C₄⋊C₄	—	2	1	no	—
550	C₄⋊C₄	—	2	1	no	—
551	C₄⋊C₄	—	4	2	no	—
552	C₄⋊C₄	—	8	1	no	—
553	C₄⋊C₄	—	8	1	no	—
554	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
555	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
556	C₂²⋊C₄	—	2	4	no	—
557	C₂²⋊C₄	—	2	4	no	—
558	C₂²⋊C₄	—	2	2	no	—
559	C₂²⋊C₄	—	2	2	no	—
560	C₂²⋊C₄	—	4	2	no	—
561	C₂²⋊C₄	—	8	1	no	—
562	C₂²⋊C₄	—	8	1	no	—
563	C₂²⋊C₄	—	8	1	no	—
564	C₂²⋊C₄	—	8	1	no	—
565	C₄²	—	2	1	no	—
566	C₄²	—	2	1	no	—
567	C₄²	—	4	2	no	—
568	C₄²	—	8	1	no	—
569	C₄²	—	8	1	no	—
570	C₄²	C₂×D₄×C₂₃	1	2	yes	—
571	C₄²	#41×C₂₃	1	2	yes	—
572	C₂³	—	2	1	no	—
573	C₂³	—	2	1	no	—
574	C₂³	—	2	1	no	—
575	C₂³	—	2	1	no	—
576	C₂³	—	2	1	no	—
577	C₂³	—	2	1	no	—
578	C₂³	—	2	2	no	—
579	C₂³	—	4	1	no	—
580	C₂³	—	4	1	no	—
581	C₂³	—	4	1	no	—
582	C₂³	—	4	1	no	—
583	C₂³	—	4	1	no	—
584	C₂³	—	4	1	no	—
585	C₂³	C₄×D₄×C₂₃	1	2	yes	—
586	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
587	Q₈	—	2	2	no	—
588	Q₈	—	2	2	no	—
589	Q₈	—	4	1	no	—
590	Q₈	—	4	1	no	—
591	D₄	—	2	2	no	—
592	D₄	—	2	2	no	—
593	D₄	—	4	1	no	—
594	D₄	—	4	1	no	—
595	D₄	—	8	4	no	—
596	C₂×C₄	—	2	1	no	—
597	C₂×C₄	—	2	1	no	—
598	C₂×C₄	—	2	1	no	—
599	C₂×C₄	—	2	1	no	—
600	C₂×C₄	—	2	1	no	—
601	C₂×C₄	—	2	1	no	—
602	C₂×C₄	—	2	2	no	—
603	C₂×C₄	—	2	2	no	—
604	C₂×C₄	—	2	2	no	—
605	C₂×C₄	—	2	2	no	—
606	C₂×C₄	—	2	1	no	—
607	C₂×C₄	—	2	1	no	—
608	C₂×C₄	—	2	1	no	—
609	C₂×C₄	—	2	1	no	—
610	C₂×C₄	—	2	2	no	—
611	C₂×C₄	—	2	2	no	—
612	C₂×C₄	—	2	2	no	—
613	C₂×C₄	—	2	1	no	—
614	C₂×C₄	—	2	1	no	—
615	C₂×C₄	—	4	1	no	—
616	C₂×C₄	—	4	1	no	—
617	C₂×C₄	—	4	1	no	—
618	C₂×C₄	—	4	1	no	—
619	C₂×C₄	—	4	1	no	—
620	C₂×C₄	—	4	1	no	—
621	C₂×C₄	—	4	1	no	—
622	C₂×C₄	—	4	1	no	—
623	C₂×C₄	—	4	1	no	—
624	C₂×C₄	—	4	1	no	—
625	C₂×C₄	—	4	1	no	—
626	C₂×C₄	—	4	1	no	—
627	C₂×C₄	—	4	1	no	—
628	C₂×C₄	—	4	1	no	—
629	C₂×C₄	—	4	1	no	—
630	C₂×C₄	—	4	1	no	—
631	C₂×C₄	—	4	1	no	—
632	C₂×C₄	—	4	1	no	—
633	C₂×C₄	—	8	4	no	—
634	C₂×C₄	C₄×D₄×C₂₃	1	2	yes	—
635	C₂×C₄	C₂₃×#121	1	2	yes	—
636	C₂×C₄	C₂₃×#121	1	2	yes	—
637	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
638	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
639	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
640	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
641	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
642	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
643	C₈	—	2	2	no	—
644	C₈	—	2	2	no	—
645	C₈	—	2	2	no	—
646	C₈	C₄×D₄×C₂₃	1	4	yes	—
647	C₂²	—	2	2	no	—
648	C₂²	—	2	2	no	—
649	C₂²	—	2	2	no	—
650	C₂²	—	4	1	no	—
651	C₂²	—	4	1	no	—
652	C₂²	—	4	1	no	—
653	C₂²	—	4	1	no	—
654	C₂²	—	4	2	no	—
655	C₂²	—	4	2	no	—
656	C₂²	—	4	2	no	—
657	C₂²	—	8	1	no	—
658	C₂²	—	8	1	no	—
659	C₂²	—	8	1	no	—
660	C₂²	—	8	1	no	—
661	C₂²	C₂×C₄×D₄×C₂₃	1	1	yes	characteristic
662	C₂²	C₂×C₂₃×#121	1	1	yes	characteristic
663	C₂²	C₂₃×#532	1	1	yes	characteristic
664	C₂²	C₂₃×#576	1	1	yes	characteristic
665	C₂²	C₂₃×#577	1	1	yes	characteristic
666	C₂²	C₂₃×#577	1	1	yes	characteristic
667	C₂²	C₂₃×#578	1	1	yes	characteristic
668	C₄	—	2	2	no	—
669	C₄	—	2	2	no	—
670	C₄	—	2	2	no	—
671	C₄	—	4	2	no	—
672	C₄	—	4	2	no	—
673	C₄	—	4	1	no	—
674	C₄	—	4	1	no	—
675	C₄	—	4	2	no	—
676	C₄	—	8	1	no	—
677	C₄	—	8	1	no	—
678	C₄	—	8	1	no	—
679	C₄	—	8	1	no	—
680	C₄	C₂×C₄×D₄×C₂₃	1	1	yes	characteristic
681	C₄	C₄×#41×C₂₃	1	1	yes	characteristic
682	C₄	C₂₃×#525	1	1	yes	characteristic
683	C₄	C₂₃×#529	1	1	yes	characteristic
684	C₂	—	4	2	no	—
685	C₂	—	8	2	no	—
686	C₂	C₄×C₂₃×#121	1	1	yes	characteristic
687	C₂	C₂₃×#2946	1	1	yes	characteristic
688	C₂	C₂₃×#2947	1	1	yes	characteristic
689	C₂	C₂₃×#3057	1	1	yes	characteristic
690	C₂	C₂₃×#3061	1	1	yes	characteristic
691	C₂	C₂₃×#3178	1	1	yes	characteristic
692	C₂	C₂₃×#3179	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₂₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₃
prime radical	C₂×C₂₃×#121	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₃ ◁ C₂×C₂₃×#117 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×SD₁₆×C₂₃	C₂	semidirect
3. C₂×C₂₃×#405	C₂	semidirect
5. C₂₃×#2323	C₂	semidirect
6. C₂₃×#1973	C₂	semidirect
7. C₂₃×#1943	C₂	semidirect
8. C₂₃×#1934	C₂	semidirect
9. C₂₃×#1933	C₂	semidirect
11. C₂₃×#1892	C₂	semidirect
12. C₂₃×#1809	C₂	semidirect
13. C₄×C₂₃×#107	C₂	semidirect
14. C₂₃×#1763	C₂	semidirect
15. C₂₃×#1762	C₂	semidirect
24. C₂₃×#468	C₄	semidirect
72. C₂×M₁₆×C₂₃	C₂×C₄	semidirect
81. C₂₃×C₂²⋊Q₈	C₂×C₄	semidirect
117. C₂₃×#107	C₂×C₄	semidirect
121. C₂₃×#103	C₂×C₄	semidirect
128. C₄×C₈×C₂₃	D₄	semidirect
225. #21535	C₂₃	direct (N × H)
302. C₂×C₄×SD₁₆	C₂×C₂₃	semidirect
303. C₂×#405	C₂×C₂₃	semidirect
305. #2323	C₂×C₂₃	semidirect
306. #1973	C₂×C₂₃	semidirect
307. #1943	C₂×C₂₃	semidirect
308. #1934	C₂×C₂₃	semidirect
309. #1933	C₂×C₂₃	semidirect
311. #1892	C₂×C₂₃	semidirect
312. #1809	C₂×C₂₃	semidirect
313. C₄×#107	C₂×C₂₃	semidirect
314. #1763	C₂×C₂₃	semidirect
315. #1762	C₂×C₂₃	semidirect
361. #468	C₄×C₂₃	semidirect
418. C₂×M₁₆	C₂×C₄×C₂₃	semidirect
427. C₂²⋊Q₈	C₂×C₄×C₂₃	semidirect
463. #107	C₂×C₄×C₂₃	semidirect
467. #103	C₂×C₄×C₂₃	semidirect
474. C₄×C₈	D₄×C₂₃	semidirect
483. C₂₃	#21535	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×#468	2
C₂×C₄×SD₁₆×C₂₃	2
C₂×C₂₃×#405	2
C₂₃×#2324	2
C₂₃×#2323	2
C₂₃×#1973	2
C₂₃×#1943	2
C₂₃×#1934	2
C₂₃×#1933	2
C₂₃×#1893	2
C₂₃×#1892	2
C₂₃×#1809	2
C₄×C₂₃×#107	2
C₂₃×#1763	2
C₂₃×#1762	2
#21535	23

Subgroups — C23×#21535 #19169161

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#21535 #19169161