Subgroups — C₂₃×#10863 #19158489

Order 5888.

942 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₂₃×#107	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₂₃×#106	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₂₃×#97	C₂	1	1	yes	maximal, characteristic
4	C₂×C₂₃×#340	C₂	1	2	yes	maximal
5	C₂₃×C₄⋊#95	C₂	1	2	yes	maximal
6	C₂³×C₈×C₂₃	C₂²	1	1	yes	characteristic
7	C₂³×C₈×C₂₃	C₂²	1	1	yes	characteristic
8	C₂²×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
9	C₂²×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
10	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
11	C₂×C₂₃×#107	—	2	2	no	—
12	C₂×C₂₃×#107	—	2	2	no	—
13	C₂×C₂₃×#107	C₄	1	4	yes	complemented
14	C₂×C₂₃×#106	—	2	2	no	—
15	C₂×C₂₃×#106	—	2	2	no	—
16	C₂×C₂₃×#106	C₄	1	4	yes	complemented
17	C₂×C₂₃×#97	—	2	2	no	—
18	C₂×C₂₃×#97	—	2	2	no	—
19	C₂×C₂₃×#97	C₄	1	4	yes	complemented
20	C₂×C₂₃×#95	—	2	4	no	—
21	C₂₃×#340	—	2	4	no	—
22	C₂³×C₄×C₂₃	—	2	2	no	—
23	C₂³×C₄×C₂₃	—	2	2	no	—
24	C₂³×C₄×C₂₃	D₄	1	2	yes	—
25	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
26	C₂²×C₈×C₂₃	—	2	1	no	—
27	C₂²×C₈×C₂₃	—	2	1	no	—
28	C₂²×C₈×C₂₃	—	2	1	no	—
29	C₂²×C₈×C₂₃	—	2	1	no	—
30	C₂²×C₈×C₂₃	C₂×C₄	1	2	yes	—
31	C₂²×C₈×C₂₃	C₂×C₄	1	2	yes	—
32	C₂²×C₈×C₂₃	C₂×C₄	1	2	yes	—
33	C₂²×C₈×C₂₃	C₂×C₄	1	2	yes	—
34	C₂²×C₈×C₂₃	D₄	1	2	yes	—
35	C₂²×C₈×C₂₃	D₄	1	2	yes	—
36	C₂²×C₈×C₂₃	D₄	1	2	yes	—
37	C₂²×C₈×C₂₃	D₄	1	2	yes	—
38	C₂²×C₈×C₂₃	Q₈	1	2	yes	—
39	C₂²×C₈×C₂₃	Q₈	1	2	yes	—
40	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
41	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
42	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
43	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
44	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
45	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
46	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
47	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
48	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
49	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
50	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	4	yes	—
51	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	4	yes	—
52	C₂×C₄²×C₂₃	—	2	1	no	—
53	C₂×C₄²×C₂₃	—	2	1	no	—
54	C₂×C₄²×C₂₃	—	2	1	no	—
55	C₂×C₄²×C₂₃	—	2	1	no	—
56	C₂×C₄²×C₂₃	C₂×C₄	1	2	yes	—
57	C₂×C₄²×C₂₃	Q₈	1	2	yes	—
58	C₂₃×#107	—	2	8	no	—
59	C₂₃×#106	—	2	8	no	—
60	C₂₃×#97	—	2	8	no	—
61	C₂₃×#95	—	4	8	no	—
62	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
63	C₂²×C₄×C₂₃	—	2	2	no	—
64	C₂²×C₄×C₂₃	—	2	2	no	—
65	C₂²×C₄×C₂₃	—	2	4	no	—
66	C₂²×C₄×C₂₃	—	2	4	no	—
67	C₂²×C₄×C₂₃	—	2	4	no	—
68	C₂²×C₄×C₂₃	—	2	4	no	—
69	C₂²×C₄×C₂₃	—	4	2	no	—
70	C₂²×C₄×C₂₃	—	4	2	no	—
71	C₂²×C₄×C₂₃	—	4	2	no	—
72	C₂²×C₄×C₂₃	—	4	2	no	—
73	C₂²×C₄×C₂₃	—	4	4	no	—
74	C₂²×C₄×C₂₃	—	4	4	no	—
75	C₂²×C₄×C₂₃	—	4	4	no	—
76	C₂²×C₄×C₂₃	—	4	4	no	—
77	C₂²×C₄×C₂₃	C₄⋊C₄	1	4	yes	—
78	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
79	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
80	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
81	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
82	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
83	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
84	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
85	C₂²×C₄×C₂₃	C₂×Q₈	1	1	yes	characteristic
86	C₂²×C₄×C₂₃	C₂×Q₈	1	1	yes	characteristic
87	C₂²×C₄×C₂₃	C₂×Q₈	1	1	yes	characteristic
88	C₂²×C₄×C₂₃	#41	1	1	yes	characteristic
89	C₂²×C₄×C₂₃	#41	1	1	yes	characteristic
90	C₂²×C₄×C₂₃	#41	1	1	yes	characteristic
91	C₂²×C₄×C₂₃	#41	1	1	yes	characteristic
92	C₂×C₈×C₂₃	—	2	2	no	—
93	C₂×C₈×C₂₃	—	2	2	no	—
94	C₂×C₈×C₂₃	—	2	2	no	—
95	C₂×C₈×C₂₃	—	2	2	no	—
96	C₂×C₈×C₂₃	—	2	2	no	—
97	C₂×C₈×C₂₃	—	2	2	no	—
98	C₂×C₈×C₂₃	C₄²	1	4	yes	—
99	C₂×C₈×C₂₃	C₂²⋊C₄	1	4	yes	—
100	C₂×C₈×C₂₃	C₂²⋊C₄	1	4	yes	—
101	C₂×C₈×C₂₃	C₂²⋊C₄	1	4	yes	—
102	C₂×C₈×C₂₃	C₄⋊C₄	1	4	yes	—
103	C₂×C₈×C₂₃	C₄⋊C₄	1	4	yes	—
104	C₂×C₈×C₂₃	C₄⋊C₄	1	4	yes	—
105	C₂×C₈×C₂₃	C₄⋊C₄	1	4	yes	—
106	C₄⋊C₄×C₂₃	—	2	4	no	—
107	C₄⋊C₄×C₂₃	—	2	4	no	—
108	C₄⋊C₄×C₂₃	—	2	4	no	—
109	C₄⋊C₄×C₂₃	—	2	4	no	—
110	C₄⋊C₄×C₂₃	—	4	2	no	—
111	C₄⋊C₄×C₂₃	—	4	2	no	—
112	C₄⋊C₄×C₂₃	—	4	2	no	—
113	C₄⋊C₄×C₂₃	—	4	2	no	—
114	C₄²×C₂₃	—	2	2	no	—
115	C₄²×C₂₃	—	2	2	no	—
116	C₄²×C₂₃	—	2	2	no	—
117	C₄²×C₂₃	—	2	2	no	—
118	#10863	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
119	C₂³×C₂₃	C₂×C₄⋊C₄	1	1	yes	characteristic
120	C₂³×C₂₃	C₄×D₄	1	1	yes	characteristic
121	C₂³×C₂₃	C₄×D₄	1	1	yes	characteristic
122	C₂³×C₂₃	#121	1	1	yes	characteristic
123	C₂³×C₂₃	#121	1	1	yes	characteristic
124	C₂³×C₂₃	#127	1	1	yes	characteristic
125	C₂³×C₂₃	C₄⋊Q₈	1	1	yes	characteristic
126	C₂³×C₂₃	AGL(1,ℤ/8)	1	4	yes	—
127	C₂³×C₂₃	#137	1	4	yes	—
128	C₂×C₄×C₂₃	—	2	4	no	—
129	C₂×C₄×C₂₃	—	2	8	no	—
130	C₂×C₄×C₂₃	—	4	4	no	—
131	C₂×C₄×C₂₃	—	4	2	no	—
132	C₂×C₄×C₂₃	—	4	2	no	—
133	C₂×C₄×C₂₃	—	4	4	no	—
134	C₂×C₄×C₂₃	—	4	4	no	—
135	C₂×C₄×C₂₃	—	4	8	no	—
136	C₂×C₄×C₂₃	—	4	8	no	—
137	C₂×C₄×C₂₃	—	8	4	no	—
138	C₂×C₄×C₂₃	—	8	4	no	—
139	C₂×C₄×C₂₃	—	8	2	no	—
140	C₂×C₄×C₂₃	—	8	2	no	—
141	C₂×C₄×C₂₃	—	8	2	no	—
142	C₂×C₄×C₂₃	—	8	2	no	—
143	C₂×C₄×C₂₃	C₂×C₄²	1	1	yes	characteristic
144	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
145	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
146	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
147	C₂×C₄×C₂₃	C₂×C₄⋊C₄	1	1	yes	characteristic
148	C₂×C₄×C₂₃	C₂×C₄⋊C₄	1	1	yes	characteristic
149	C₂×C₄×C₂₃	C₂×C₄⋊C₄	1	1	yes	characteristic
150	C₂×C₄×C₂₃	C₂×C₄⋊C₄	1	1	yes	characteristic
151	C₂×C₄×C₂₃	#117	1	1	yes	characteristic
152	C₂×C₄×C₂₃	#117	1	1	yes	characteristic
153	C₂×C₄×C₂₃	C₄×D₄	1	1	yes	characteristic
154	C₂×C₄×C₂₃	C₄×D₄	1	1	yes	characteristic
155	C₂×C₄×C₂₃	C₄×Q₈	1	1	yes	characteristic
156	C₂×C₄×C₂₃	C₄×Q₈	1	1	yes	characteristic
157	C₂×C₄×C₂₃	C₄×Q₈	1	1	yes	characteristic
158	C₂×C₄×C₂₃	C₄×Q₈	1	1	yes	characteristic
159	C₂×C₄×C₂₃	#121	1	1	yes	characteristic
160	C₂×C₄×C₂₃	#121	1	1	yes	characteristic
161	C₂×C₄×C₂₃	C₂²⋊Q₈	1	1	yes	characteristic
162	C₂×C₄×C₂₃	C₂²⋊Q₈	1	1	yes	characteristic
163	C₂×C₄×C₂₃	C₂²⋊Q₈	1	1	yes	characteristic
164	C₂×C₄×C₂₃	C₂²⋊Q₈	1	1	yes	characteristic
165	C₂×C₄×C₂₃	#124	1	1	yes	characteristic
166	C₂×C₄×C₂₃	#124	1	1	yes	characteristic
167	C₂×C₄×C₂₃	#125	1	1	yes	characteristic
168	C₂×C₄×C₂₃	#125	1	1	yes	characteristic
169	C₂×C₄×C₂₃	C₄⋊Q₈	1	1	yes	characteristic
170	C₂×C₄×C₂₃	C₄⋊Q₈	1	1	yes	characteristic
171	C₈×C₂₃	—	2	4	no	—
172	C₈×C₂₃	#95	1	8	yes	complemented
173	C₂²×#107	C₂×C₂₃	1	1	yes	characteristic
174	C₂²×#106	C₂×C₂₃	1	1	yes	characteristic
175	C₂²×#97	C₂×C₂₃	1	1	yes	characteristic
176	C₂×#340	C₂×C₂₃	1	2	yes	—
177	C₄⋊#95	C₂×C₂₃	1	2	yes	—
178	C₂²×C₂₃	C₄×C₄⋊C₄	1	1	yes	characteristic
179	C₂²×C₂₃	#380	1	1	yes	characteristic
180	C₂²×C₂₃	#384	1	1	yes	characteristic
181	C₂²×C₂₃	#389	1	1	yes	characteristic
182	C₂²×C₂₃	#389	1	1	yes	characteristic
183	C₂²×C₂₃	#390	1	1	yes	characteristic
184	C₂²×C₂₃	#390	1	1	yes	characteristic
185	C₂²×C₂₃	#428	1	4	yes	—
186	C₂²×C₂₃	#440	1	4	yes	—
187	C₂²×C₂₃	#441	1	2	yes	—
188	C₂²×C₂₃	#442	1	2	yes	—
189	C₂²×C₂₃	#468	1	4	yes	—
190	C₂²×C₂₃	#469	1	2	yes	—
191	C₂²×C₂₃	#470	1	2	yes	—
192	C₂²×C₂₃	#496	1	2	yes	—
193	C₂²×C₂₃	#497	1	2	yes	—
194	C₂²×C₂₃	#501	1	4	yes	—
195	C₄×C₂₃	—	4	4	no	—
196	C₄×C₂₃	—	8	4	no	—
197	C₄×C₂₃	—	8	4	no	—
198	C₄×C₂₃	C₂×#95	1	1	yes	characteristic
199	C₄×C₂₃	C₄×C₄⋊C₄	1	1	yes	characteristic
200	C₄×C₂₃	#380	1	1	yes	characteristic
201	C₄×C₂₃	#382	1	1	yes	characteristic
202	C₄×C₂₃	#389	1	1	yes	characteristic
203	C₄×C₂₃	#389	1	1	yes	characteristic
204	C₄×C₂₃	#391	1	1	yes	characteristic
205	C₄×C₂₃	#391	1	1	yes	characteristic
206	C₂³×C₈	C₂²×C₂₃	1	1	yes	characteristic
207	C₂³×C₈	C₂²×C₂₃	1	1	yes	characteristic
208	C₂²×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
209	C₂²×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
210	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
211	C₂×#107	—	2	2	no	—
212	C₂×#107	—	2	2	no	—
213	C₂×#107	C₄×C₂₃	1	4	yes	complemented
214	C₂×#106	—	2	2	no	—
215	C₂×#106	—	2	2	no	—
216	C₂×#106	C₄×C₂₃	1	4	yes	complemented
217	C₂×#97	—	2	2	no	—
218	C₂×#97	—	2	2	no	—
219	C₂×#97	C₄×C₂₃	1	4	yes	complemented
220	C₂×#95	—	2	4	no	—
221	#340	—	2	4	no	—
222	C₂×C₂₃	C₄⋊#95	1	1	yes	characteristic
223	C₂×C₂₃	#1776	1	2	yes	—
224	C₂×C₂₃	#1809	1	2	yes	—
225	C₂×C₂₃	#1847	1	2	yes	—
226	C₂×C₂₃	#1943	1	2	yes	—
227	C₂×C₂₃	#1944	1	2	yes	—
228	C₂×C₂₃	#1971	1	1	yes	characteristic
229	C₂×C₂₃	#1972	1	1	yes	characteristic
230	C₂×C₂₃	#1973	1	2	yes	—
231	C₂³×C₄	—	2	2	no	—
232	C₂³×C₄	—	2	2	no	—
233	C₂³×C₄	D₄×C₂₃	1	2	yes	—
234	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
235	C₂²×C₈	—	2	1	no	—
236	C₂²×C₈	—	2	1	no	—
237	C₂²×C₈	—	2	1	no	—
238	C₂²×C₈	—	2	1	no	—
239	C₂²×C₈	C₂×C₄×C₂₃	1	2	yes	—
240	C₂²×C₈	C₂×C₄×C₂₃	1	2	yes	—
241	C₂²×C₈	C₂×C₄×C₂₃	1	2	yes	—
242	C₂²×C₈	C₂×C₄×C₂₃	1	2	yes	—
243	C₂²×C₈	D₄×C₂₃	1	2	yes	—
244	C₂²×C₈	D₄×C₂₃	1	2	yes	—
245	C₂²×C₈	D₄×C₂₃	1	2	yes	—
246	C₂²×C₈	D₄×C₂₃	1	2	yes	—
247	C₂²×C₈	Q₈×C₂₃	1	2	yes	—
248	C₂²×C₈	Q₈×C₂₃	1	2	yes	—
249	C₂×C₄⋊C₄	—	2	2	no	—
250	C₂×C₄⋊C₄	—	2	2	no	—
251	C₂×C₄⋊C₄	—	2	2	no	—
252	C₂×C₄⋊C₄	—	2	2	no	—
253	C₂×C₄⋊C₄	—	2	2	no	—
254	C₂×C₄⋊C₄	—	2	2	no	—
255	C₂×C₄⋊C₄	—	2	2	no	—
256	C₂×C₄⋊C₄	—	2	2	no	—
257	C₂×C₄⋊C₄	—	2	2	no	—
258	C₂×C₄⋊C₄	—	2	2	no	—
259	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	4	yes	—
260	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	4	yes	—
261	C₂×C₄²	—	2	1	no	—
262	C₂×C₄²	—	2	1	no	—
263	C₂×C₄²	—	2	1	no	—
264	C₂×C₄²	—	2	1	no	—
265	C₂×C₄²	C₂×C₄×C₂₃	1	2	yes	—
266	C₂×C₄²	Q₈×C₂₃	1	2	yes	—
267	#107	—	2	8	no	—
268	#106	—	2	8	no	—
269	#97	—	2	8	no	—
270	#95	—	4	8	no	—
271	C₂₃	#10863	1	1	yes	characteristic, direct product factor, Sylow
272	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
273	C₂²×C₄	—	2	2	no	—
274	C₂²×C₄	—	2	2	no	—
275	C₂²×C₄	—	2	4	no	—
276	C₂²×C₄	—	2	4	no	—
277	C₂²×C₄	—	2	4	no	—
278	C₂²×C₄	—	2	4	no	—
279	C₂²×C₄	—	4	2	no	—
280	C₂²×C₄	—	4	2	no	—
281	C₂²×C₄	—	4	2	no	—
282	C₂²×C₄	—	4	2	no	—
283	C₂²×C₄	—	4	4	no	—
284	C₂²×C₄	—	4	4	no	—
285	C₂²×C₄	—	4	4	no	—
286	C₂²×C₄	—	4	4	no	—
287	C₂²×C₄	C₄⋊C₄×C₂₃	1	4	yes	—
288	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
289	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
290	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
291	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
292	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
293	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
294	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
295	C₂²×C₄	C₂×Q₈×C₂₃	1	1	yes	characteristic
296	C₂²×C₄	C₂×Q₈×C₂₃	1	1	yes	characteristic
297	C₂²×C₄	C₂×Q₈×C₂₃	1	1	yes	characteristic
298	C₂²×C₄	#41×C₂₃	1	1	yes	characteristic
299	C₂²×C₄	#41×C₂₃	1	1	yes	characteristic
300	C₂²×C₄	#41×C₂₃	1	1	yes	characteristic
301	C₂²×C₄	#41×C₂₃	1	1	yes	characteristic
302	C₂×C₈	—	2	2	no	—
303	C₂×C₈	—	2	2	no	—
304	C₂×C₈	—	2	2	no	—
305	C₂×C₈	—	2	2	no	—
306	C₂×C₈	—	2	2	no	—
307	C₂×C₈	—	2	2	no	—
308	C₂×C₈	C₄²×C₂₃	1	4	yes	—
309	C₂×C₈	C₂²⋊C₄×C₂₃	1	4	yes	—
310	C₂×C₈	C₂²⋊C₄×C₂₃	1	4	yes	—
311	C₂×C₈	C₂²⋊C₄×C₂₃	1	4	yes	—
312	C₂×C₈	C₄⋊C₄×C₂₃	1	4	yes	—
313	C₂×C₈	C₄⋊C₄×C₂₃	1	4	yes	—
314	C₂×C₈	C₄⋊C₄×C₂₃	1	4	yes	—
315	C₂×C₈	C₄⋊C₄×C₂₃	1	4	yes	—
316	C₄⋊C₄	—	2	4	no	—
317	C₄⋊C₄	—	2	4	no	—
318	C₄⋊C₄	—	2	4	no	—
319	C₄⋊C₄	—	2	4	no	—
320	C₄⋊C₄	—	4	2	no	—
321	C₄⋊C₄	—	4	2	no	—
322	C₄⋊C₄	—	4	2	no	—
323	C₄⋊C₄	—	4	2	no	—
324	C₄²	—	2	2	no	—
325	C₄²	—	2	2	no	—
326	C₄²	—	2	2	no	—
327	C₄²	—	2	2	no	—
328	C₂³	C₂×C₄⋊C₄×C₂₃	1	1	yes	characteristic
329	C₂³	C₄×D₄×C₂₃	1	1	yes	characteristic
330	C₂³	C₄×D₄×C₂₃	1	1	yes	characteristic
331	C₂³	C₂₃×#121	1	1	yes	characteristic
332	C₂³	C₂₃×#121	1	1	yes	characteristic
333	C₂³	C₂₃×#127	1	1	yes	characteristic
334	C₂³	C₂₃×C₄⋊Q₈	1	1	yes	characteristic
335	C₂³	C₂₃×AGL(1,ℤ/8)	1	4	yes	—
336	C₂³	C₂₃×#137	1	4	yes	—
337	C₂×C₄	—	2	4	no	—
338	C₂×C₄	—	2	8	no	—
339	C₂×C₄	—	4	4	no	—
340	C₂×C₄	—	4	2	no	—
341	C₂×C₄	—	4	2	no	—
342	C₂×C₄	—	4	4	no	—
343	C₂×C₄	—	4	4	no	—
344	C₂×C₄	—	4	8	no	—
345	C₂×C₄	—	4	8	no	—
346	C₂×C₄	—	8	4	no	—
347	C₂×C₄	—	8	4	no	—
348	C₂×C₄	—	8	2	no	—
349	C₂×C₄	—	8	2	no	—
350	C₂×C₄	—	8	2	no	—
351	C₂×C₄	—	8	2	no	—
352	C₂×C₄	C₂×C₄²×C₂₃	1	1	yes	characteristic
353	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
354	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
355	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
356	C₂×C₄	C₂×C₄⋊C₄×C₂₃	1	1	yes	characteristic
357	C₂×C₄	C₂×C₄⋊C₄×C₂₃	1	1	yes	characteristic
358	C₂×C₄	C₂×C₄⋊C₄×C₂₃	1	1	yes	characteristic
359	C₂×C₄	C₂×C₄⋊C₄×C₂₃	1	1	yes	characteristic
360	C₂×C₄	C₂₃×#117	1	1	yes	characteristic
361	C₂×C₄	C₂₃×#117	1	1	yes	characteristic
362	C₂×C₄	C₄×D₄×C₂₃	1	1	yes	characteristic
363	C₂×C₄	C₄×D₄×C₂₃	1	1	yes	characteristic
364	C₂×C₄	C₄×Q₈×C₂₃	1	1	yes	characteristic
365	C₂×C₄	C₄×Q₈×C₂₃	1	1	yes	characteristic
366	C₂×C₄	C₄×Q₈×C₂₃	1	1	yes	characteristic
367	C₂×C₄	C₄×Q₈×C₂₃	1	1	yes	characteristic
368	C₂×C₄	C₂₃×#121	1	1	yes	characteristic
369	C₂×C₄	C₂₃×#121	1	1	yes	characteristic
370	C₂×C₄	C₂₃×C₂²⋊Q₈	1	1	yes	characteristic
371	C₂×C₄	C₂₃×C₂²⋊Q₈	1	1	yes	characteristic
372	C₂×C₄	C₂₃×C₂²⋊Q₈	1	1	yes	characteristic
373	C₂×C₄	C₂₃×C₂²⋊Q₈	1	1	yes	characteristic
374	C₂×C₄	C₂₃×#124	1	1	yes	characteristic
375	C₂×C₄	C₂₃×#124	1	1	yes	characteristic
376	C₂×C₄	C₂₃×#125	1	1	yes	characteristic
377	C₂×C₄	C₂₃×#125	1	1	yes	characteristic
378	C₂×C₄	C₂₃×C₄⋊Q₈	1	1	yes	characteristic
379	C₂×C₄	C₂₃×C₄⋊Q₈	1	1	yes	characteristic
380	C₈	—	2	4	no	—
381	C₈	C₂₃×#95	1	8	yes	complemented
382	C₂²	C₄×C₄⋊C₄×C₂₃	1	1	yes	characteristic
383	C₂²	C₂₃×#380	1	1	yes	characteristic
384	C₂²	C₂₃×#384	1	1	yes	characteristic
385	C₂²	C₂₃×#389	1	1	yes	characteristic
386	C₂²	C₂₃×#389	1	1	yes	characteristic
387	C₂²	C₂₃×#390	1	1	yes	characteristic
388	C₂²	C₂₃×#390	1	1	yes	characteristic
389	C₂²	C₂₃×#428	1	4	yes	—
390	C₂²	C₂₃×#440	1	4	yes	—
391	C₂²	C₂₃×#441	1	2	yes	—
392	C₂²	C₂₃×#442	1	2	yes	—
393	C₂²	C₂₃×#468	1	4	yes	—
394	C₂²	C₂₃×#469	1	2	yes	—
395	C₂²	C₂₃×#470	1	2	yes	—
396	C₂²	C₂₃×#496	1	2	yes	—
397	C₂²	C₂₃×#497	1	2	yes	—
398	C₂²	C₂₃×#501	1	4	yes	—
399	C₄	—	4	4	no	—
400	C₄	—	8	4	no	—
401	C₄	—	8	4	no	—
402	C₄	C₂×C₂₃×#95	1	1	yes	characteristic
403	C₄	C₄×C₄⋊C₄×C₂₃	1	1	yes	characteristic
404	C₄	C₂₃×#380	1	1	yes	characteristic
405	C₄	C₂₃×#382	1	1	yes	characteristic
406	C₄	C₂₃×#389	1	1	yes	characteristic
407	C₄	C₂₃×#389	1	1	yes	characteristic
408	C₄	C₂₃×#391	1	1	yes	characteristic
409	C₄	C₂₃×#391	1	1	yes	characteristic
410	C₂	C₂₃×C₄⋊#95	1	1	yes	characteristic
411	C₂	C₂₃×#1776	1	2	yes	—
412	C₂	C₂₃×#1809	1	2	yes	—
413	C₂	C₂₃×#1847	1	2	yes	—
414	C₂	C₂₃×#1943	1	2	yes	—
415	C₂	C₂₃×#1944	1	2	yes	—
416	C₂	C₂₃×#1971	1	1	yes	characteristic
417	C₂	C₂₃×#1972	1	1	yes	characteristic
418	C₂	C₂₃×#1973	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
13. C₂×C₂₃×#107	C₄	semidirect
16. C₂×C₂₃×#106	C₄	semidirect
19. C₂×C₂₃×#97	C₄	semidirect
118. #10863	C₂₃	direct (N × H)
172. C₈×C₂₃	#95	semidirect
213. C₂×#107	C₄×C₂₃	semidirect
216. C₂×#106	C₄×C₂₃	semidirect
219. C₂×#97	C₄×C₂₃	semidirect
271. C₂₃	#10863	direct (N × H)
381. C₈	C₂₃×#95	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₂₃×#107	2
C₂²×C₂₃×#106	2
C₂²×C₂₃×#97	2
C₂×C₂₃×#340	2
C₂₃×C₄⋊#95	2
#10863	23

Subgroups — C23×#10863 #19158489

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#10863 #19158489