Subgroups — C₂₃×#23679 #19171305

Order 5888.

848 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×Q₁₆×C₂₃	C₂	1	2	yes	maximal
2	C₄×C₂₃×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
3	C₂₃×#2295	C₂	1	1	yes	maximal, characteristic
4	C₂₃×#2083	C₂	1	1	yes	maximal, characteristic
5	C₂₃×#2072	C₂	1	1	yes	maximal, characteristic
6	C₂₃×#2068	C₂	1	2	yes	maximal
7	C₂₃×#2056	C₂	1	2	yes	maximal
8	C₂₃×#2043	C₂	1	1	yes	maximal, characteristic
9	C₂₃×#2016	C₂	1	1	yes	maximal, characteristic
10	C₄×C₂₃×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
11	C₄×C₂₃×#103	C₂	1	2	yes	maximal
12	C₂²×Q₁₆×C₂₃	C₂²	1	2	yes	—
13	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₂×C₄×Q₈×C₂₃	C₂²	1	2	yes	—
15	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
16	C₄×Q₁₆×C₂₃	—	2	8	no	—
17	C₂×C₂₃×#107	C₂²	1	2	yes	—
18	C₂×C₂₃×C₄⋊C₈	C₂²	1	2	yes	—
19	C₂×C₂₃×#103	C₂²	1	2	yes	—
20	C₂×C₂₃×#103	C₂²	1	2	yes	—
21	C₂×C₂₃×#103	C₂²	1	2	yes	—
22	C₂×C₂₃×#103	C₂²	1	2	yes	—
23	C₂×C₄×C₈×C₂₃	C₂²	1	2	yes	—
24	C₂₃×#391	C₂²	1	1	yes	characteristic
25	C₂₃×#391	C₂²	1	1	yes	characteristic
26	C₂₃×#391	C₂²	1	2	yes	—
27	C₂₃×#389	—	2	1	no	—
28	C₂₃×#389	—	2	1	no	—
29	C₂₃×#389	C₂²	1	1	yes	characteristic
30	C₂₃×#389	C₂²	1	1	yes	characteristic
31	C₂₃×#387	—	2	1	no	—
32	C₂₃×#387	—	2	1	no	—
33	C₂₃×#384	C₂²	1	1	yes	characteristic
34	C₄×C₄⋊C₄×C₂₃	—	2	1	no	—
35	C₄×C₄⋊C₄×C₂₃	—	2	1	no	—
36	C₄×C₄⋊C₄×C₂₃	—	2	1	no	—
37	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
38	C₂₃×#376	—	2	1	no	—
39	C₄³×C₂₃	C₂²	1	1	yes	characteristic
40	C₂₃×#340	C₂²	1	2	yes	—
41	C₂₃×#340	C₂²	1	2	yes	—
42	C₂₃×#336	C₂²	1	1	yes	characteristic
43	C₂₃×#336	C₂²	1	1	yes	characteristic
44	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
45	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
46	C₂×Q₁₆×C₂₃	—	2	4	no	—
47	C₂×Q₁₆×C₂₃	—	2	4	no	—
48	C₂×Q₁₆×C₂₃	—	2	4	no	—
49	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
50	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
51	C₂₃×C₄⋊Q₈	—	2	4	no	—
52	C₄×Q₈×C₂₃	—	2	2	no	—
53	C₄×Q₈×C₂₃	—	2	4	no	—
54	C₄×Q₈×C₂₃	—	2	4	no	—
55	C₄×Q₈×C₂₃	D₄	1	4	yes	—
56	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
57	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
58	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
59	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
60	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
61	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
62	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
63	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
64	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
65	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
66	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
67	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
68	C₂×C₄²×C₂₃	—	2	1	no	—
69	C₂×C₄²×C₂₃	—	2	1	no	—
70	C₂×C₄²×C₂₃	—	2	2	no	—
71	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
72	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
73	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
74	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
75	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
76	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
77	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
78	C₂₃×#107	—	2	4	no	—
79	C₂₃×C₄⋊C₈	—	2	4	no	—
80	C₂₃×#103	—	2	4	no	—
81	C₂₃×#103	—	2	4	no	—
82	C₂₃×#103	—	2	4	no	—
83	C₂₃×#103	—	2	4	no	—
84	C₄×C₈×C₂₃	—	2	4	no	—
85	C₂₃×#95	—	2	1	no	—
86	C₂₃×#95	—	2	1	no	—
87	C₂₃×#95	—	2	1	no	—
88	C₂₃×#95	—	2	1	no	—
89	C₂₃×#95	—	2	1	no	—
90	C₂₃×#95	—	2	1	no	—
91	C₂₃×#95	—	2	2	no	—
92	C₂₃×#95	—	2	2	no	—
93	C₂₃×#95	—	2	1	no	—
94	C₂×Q₈×C₂₃	—	2	1	no	—
95	C₂×Q₈×C₂₃	—	2	2	no	—
96	C₂×Q₈×C₂₃	—	2	2	no	—
97	C₂×Q₈×C₂₃	—	2	2	no	—
98	C₂×Q₈×C₂₃	—	2	2	no	—
99	C₂×Q₈×C₂₃	—	2	2	no	—
100	C₂×Q₈×C₂₃	—	2	2	no	—
101	C₂×Q₈×C₂₃	—	2	2	no	—
102	C₂×Q₈×C₂₃	C₂×D₄	1	2	yes	—
103	C₂×Q₈×C₂₃	#41	1	4	yes	—
104	C₂²×C₄×C₂₃	—	2	1	no	—
105	C₂²×C₄×C₂₃	—	2	2	no	—
106	C₂²×C₄×C₂₃	—	2	1	no	—
107	C₂²×C₄×C₂₃	—	2	2	no	—
108	C₂²×C₄×C₂₃	—	2	1	no	—
109	C₂²×C₄×C₂₃	—	2	1	no	—
110	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
117	Q₁₆×C₂₃	—	2	16	no	—
118	C₂×C₈×C₂₃	—	2	2	no	—
119	C₂×C₈×C₂₃	—	2	2	no	—
120	C₂×C₈×C₂₃	—	2	2	no	—
121	C₂×C₈×C₂₃	—	2	2	no	—
122	C₂×C₈×C₂₃	—	2	2	no	—
123	C₂×C₈×C₂₃	#41	1	4	yes	—
124	C₄⋊C₄×C₂₃	—	2	4	no	—
125	C₄⋊C₄×C₂₃	—	2	4	no	—
126	C₄⋊C₄×C₂₃	—	2	4	no	—
127	C₄⋊C₄×C₂₃	—	2	1	no	—
128	C₄⋊C₄×C₂₃	—	2	2	no	—
129	C₄⋊C₄×C₂₃	—	2	2	no	—
130	C₄⋊C₄×C₂₃	—	2	2	no	—
131	C₄⋊C₄×C₂₃	—	2	2	no	—
132	C₄⋊C₄×C₂₃	—	4	2	no	—
133	C₄⋊C₄×C₂₃	—	4	2	no	—
134	C₄⋊C₄×C₂₃	—	4	4	no	—
135	C₄⋊C₄×C₂₃	—	4	2	no	—
136	C₄⋊C₄×C₂₃	—	4	2	no	—
137	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
138	C₄²×C₂₃	—	2	4	no	—
139	C₄²×C₂₃	—	2	2	no	—
140	C₄²×C₂₃	—	2	2	no	—
141	C₄²×C₂₃	—	2	2	no	—
142	C₄²×C₂₃	—	2	2	no	—
143	C₄²×C₂₃	—	4	1	no	—
144	C₄²×C₂₃	—	4	4	no	—
145	C₄²×C₂₃	—	4	2	no	—
146	C₄²×C₂₃	Q₁₆	1	4	yes	complemented
147	C₄²×C₂₃	C₂×D₄	1	2	yes	—
148	C₄²×C₂₃	#41	1	2	yes	—
149	#23679	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
150	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
151	Q₈×C₂₃	—	2	4	no	—
152	Q₈×C₂₃	—	2	4	no	—
153	Q₈×C₂₃	—	2	4	no	—
154	Q₈×C₂₃	—	4	2	no	—
155	Q₈×C₂₃	—	4	2	no	—
156	Q₈×C₂₃	—	4	2	no	—
157	C₂×C₄×C₂₃	—	2	1	no	—
158	C₂×C₄×C₂₃	—	2	1	no	—
159	C₂×C₄×C₂₃	—	2	1	no	—
160	C₂×C₄×C₂₃	—	2	1	no	—
161	C₂×C₄×C₂₃	—	2	1	no	—
162	C₂×C₄×C₂₃	—	2	1	no	—
163	C₂×C₄×C₂₃	—	2	1	no	—
164	C₂×C₄×C₂₃	—	2	1	no	—
165	C₂×C₄×C₂₃	—	2	2	no	—
166	C₂×C₄×C₂₃	—	2	2	no	—
167	C₂×C₄×C₂₃	—	2	4	no	—
168	C₂×C₄×C₂₃	—	2	1	no	—
169	C₂×C₄×C₂₃	—	2	1	no	—
170	C₂×C₄×C₂₃	—	2	1	no	—
171	C₂×C₄×C₂₃	—	4	2	no	—
172	C₂×C₄×C₂₃	—	4	1	no	—
173	C₂×C₄×C₂₃	—	4	2	no	—
174	C₂×C₄×C₂₃	—	4	1	no	—
175	C₂×C₄×C₂₃	—	4	1	no	—
176	C₂×C₄×C₂₃	—	4	1	no	—
177	C₂×C₄×C₂₃	—	4	2	no	—
178	C₂×C₄×C₂₃	—	4	1	no	—
179	C₂×C₄×C₂₃	—	4	1	no	—
180	C₂×C₄×C₂₃	—	4	1	no	—
181	C₂×C₄×C₂₃	—	4	2	no	—
182	C₂×C₄×C₂₃	—	4	1	no	—
183	C₂×C₄×C₂₃	—	4	1	no	—
184	C₂×C₄×C₂₃	—	4	1	no	—
185	C₂×C₄×C₂₃	—	4	2	no	—
186	C₂×C₄×C₂₃	#121	1	2	yes	—
187	C₂×C₄×C₂₃	#121	1	2	yes	—
188	C₂×C₄×C₂₃	C₂×Q₁₆	1	2	yes	—
189	C₂×C₄×C₂₃	C₂×Q₁₆	1	2	yes	—
190	C₂×C₄×C₂₃	C₂×Q₁₆	1	2	yes	—
191	C₂×C₄×C₂₃	#135	1	2	yes	—
192	C₂×C₄×C₂₃	#137	1	2	yes	—
193	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
194	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
195	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
196	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
197	C₈×C₂₃	—	2	4	no	—
198	C₈×C₂₃	—	4	2	no	—
199	C₂×C₄×Q₁₆	C₂×C₂₃	1	2	yes	—
200	C₄×C₄⋊Q₈	C₂×C₂₃	1	1	yes	characteristic
201	#2295	C₂×C₂₃	1	1	yes	characteristic
202	#2083	C₂×C₂₃	1	1	yes	characteristic
203	#2072	C₂×C₂₃	1	1	yes	characteristic
204	#2068	C₂×C₂₃	1	2	yes	—
205	#2056	C₂×C₂₃	1	2	yes	—
206	#2043	C₂×C₂₃	1	1	yes	characteristic
207	#2016	C₂×C₂₃	1	1	yes	characteristic
208	C₄×C₄⋊C₈	C₂×C₂₃	1	1	yes	characteristic
209	C₄×#103	C₂×C₂₃	1	2	yes	—
210	C₂²×C₂₃	C₂×#121	1	1	yes	characteristic
211	C₂²×C₂₃	#525	1	1	yes	characteristic
212	C₂²×C₂₃	#532	1	1	yes	characteristic
213	C₂²×C₂₃	C₂²×Q₁₆	1	1	yes	characteristic
214	C₂²×C₂₃	C₂×#135	1	1	yes	characteristic
215	C₂²×C₂₃	C₂×#137	1	1	yes	characteristic
216	C₂²×C₂₃	#575	1	1	yes	characteristic
217	C₄×C₂₃	—	2	2	no	—
218	C₄×C₂₃	—	2	2	no	—
219	C₄×C₂₃	—	2	2	no	—
220	C₄×C₂₃	—	2	2	no	—
221	C₄×C₂₃	—	4	2	no	—
222	C₄×C₂₃	—	4	4	no	—
223	C₄×C₂₃	—	4	1	no	—
224	C₄×C₂₃	—	4	2	no	—
225	C₄×C₂₃	—	8	1	no	—
226	C₄×C₂₃	—	8	1	no	—
227	C₄×C₂₃	—	8	2	no	—
228	C₄×C₂₃	#462	1	4	yes	—
229	C₄×C₂₃	#525	1	2	yes	—
230	C₄×C₂₃	#529	1	2	yes	—
231	C₂²×Q₁₆	C₂²×C₂₃	1	2	yes	—
232	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
233	C₂×C₄×Q₈	C₂²×C₂₃	1	2	yes	—
234	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
235	C₄×Q₁₆	—	2	8	no	—
236	C₂×#107	C₂²×C₂₃	1	2	yes	—
237	C₂×C₄⋊C₈	C₂²×C₂₃	1	2	yes	—
238	C₂×#103	C₂²×C₂₃	1	2	yes	—
239	C₂×#103	C₂²×C₂₃	1	2	yes	—
240	C₂×#103	C₂²×C₂₃	1	2	yes	—
241	C₂×#103	C₂²×C₂₃	1	2	yes	—
242	C₂×C₄×C₈	C₂²×C₂₃	1	2	yes	—
243	#391	C₂²×C₂₃	1	2	yes	—
244	#391	C₂²×C₂₃	1	1	yes	characteristic
245	#391	C₂²×C₂₃	1	1	yes	characteristic
246	#389	—	2	1	no	—
247	#389	—	2	1	no	—
248	#389	C₂²×C₂₃	1	1	yes	characteristic
249	#389	C₂²×C₂₃	1	1	yes	characteristic
250	#387	—	2	1	no	—
251	#387	—	2	1	no	—
252	#384	C₂²×C₂₃	1	1	yes	characteristic
253	C₄×C₄⋊C₄	—	2	1	no	—
254	C₄×C₄⋊C₄	—	2	1	no	—
255	C₄×C₄⋊C₄	—	2	1	no	—
256	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
257	#376	—	2	1	no	—
258	C₄³	C₂²×C₂₃	1	1	yes	characteristic
259	#340	C₂²×C₂₃	1	2	yes	—
260	#340	C₂²×C₂₃	1	2	yes	—
261	#336	C₂²×C₂₃	1	1	yes	characteristic
262	#336	C₂²×C₂₃	1	1	yes	characteristic
263	C₂×C₂₃	#2392	1	1	yes	characteristic
264	C₂×C₂₃	C₂×#462	1	1	yes	characteristic
265	C₂×C₂₃	#3035	1	1	yes	characteristic
266	C₂×C₂₃	#3104	1	1	yes	characteristic
267	C₂×C₂₃	#3108	1	1	yes	characteristic
268	C₂×C₂₃	#3170	1	1	yes	characteristic
269	C₂×C₂₃	#3172	1	1	yes	characteristic
270	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
271	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
272	C₂×Q₁₆	—	2	4	no	—
273	C₂×Q₁₆	—	2	4	no	—
274	C₂×Q₁₆	—	2	4	no	—
275	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
276	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
277	C₄⋊Q₈	—	2	4	no	—
278	C₄×Q₈	—	2	2	no	—
279	C₄×Q₈	—	2	4	no	—
280	C₄×Q₈	—	2	4	no	—
281	C₄×Q₈	D₄×C₂₃	1	4	yes	—
282	C₂×C₄⋊C₄	—	2	1	no	—
283	C₂×C₄⋊C₄	—	2	1	no	—
284	C₂×C₄⋊C₄	—	2	1	no	—
285	C₂×C₄⋊C₄	—	2	2	no	—
286	C₂×C₄⋊C₄	—	2	1	no	—
287	C₂×C₄⋊C₄	—	2	1	no	—
288	C₂×C₄⋊C₄	—	2	1	no	—
289	C₂×C₄⋊C₄	—	2	1	no	—
290	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
291	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
292	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
293	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
294	C₂×C₄²	—	2	1	no	—
295	C₂×C₄²	—	2	2	no	—
296	C₂×C₄²	—	2	1	no	—
297	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
298	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
299	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
300	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
301	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
302	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
303	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
304	#107	—	2	4	no	—
305	C₄⋊C₈	—	2	4	no	—
306	#103	—	2	4	no	—
307	#103	—	2	4	no	—
308	#103	—	2	4	no	—
309	#103	—	2	4	no	—
310	C₄×C₈	—	2	4	no	—
311	#95	—	2	1	no	—
312	#95	—	2	1	no	—
313	#95	—	2	1	no	—
314	#95	—	2	1	no	—
315	#95	—	2	1	no	—
316	#95	—	2	1	no	—
317	#95	—	2	2	no	—
318	#95	—	2	2	no	—
319	#95	—	2	1	no	—
320	C₂₃	#23679	1	1	yes	characteristic, direct product factor, Sylow
321	C₂×Q₈	—	2	1	no	—
322	C₂×Q₈	—	2	2	no	—
323	C₂×Q₈	—	2	2	no	—
324	C₂×Q₈	—	2	2	no	—
325	C₂×Q₈	—	2	2	no	—
326	C₂×Q₈	—	2	2	no	—
327	C₂×Q₈	—	2	2	no	—
328	C₂×Q₈	—	2	2	no	—
329	C₂×Q₈	C₂×D₄×C₂₃	1	2	yes	—
330	C₂×Q₈	#41×C₂₃	1	4	yes	—
331	C₂²×C₄	—	2	1	no	—
332	C₂²×C₄	—	2	1	no	—
333	C₂²×C₄	—	2	2	no	—
334	C₂²×C₄	—	2	1	no	—
335	C₂²×C₄	—	2	1	no	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
338	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
339	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
340	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
341	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
342	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
343	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
344	Q₁₆	—	2	16	no	—
345	C₂×C₈	—	2	2	no	—
346	C₂×C₈	—	2	2	no	—
347	C₂×C₈	—	2	2	no	—
348	C₂×C₈	—	2	2	no	—
349	C₂×C₈	—	2	2	no	—
350	C₂×C₈	#41×C₂₃	1	4	yes	—
351	C₄⋊C₄	—	2	4	no	—
352	C₄⋊C₄	—	2	4	no	—
353	C₄⋊C₄	—	2	4	no	—
354	C₄⋊C₄	—	2	1	no	—
355	C₄⋊C₄	—	2	2	no	—
356	C₄⋊C₄	—	2	2	no	—
357	C₄⋊C₄	—	2	2	no	—
358	C₄⋊C₄	—	2	2	no	—
359	C₄⋊C₄	—	4	2	no	—
360	C₄⋊C₄	—	4	2	no	—
361	C₄⋊C₄	—	4	4	no	—
362	C₄⋊C₄	—	4	2	no	—
363	C₄⋊C₄	—	4	2	no	—
364	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
365	C₄²	—	2	4	no	—
366	C₄²	—	2	2	no	—
367	C₄²	—	2	2	no	—
368	C₄²	—	2	2	no	—
369	C₄²	—	2	2	no	—
370	C₄²	—	4	1	no	—
371	C₄²	—	4	4	no	—
372	C₄²	—	4	2	no	—
373	C₄²	Q₁₆×C₂₃	1	4	yes	complemented
374	C₄²	C₂×D₄×C₂₃	1	2	yes	—
375	C₄²	#41×C₂₃	1	2	yes	—
376	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
377	Q₈	—	2	4	no	—
378	Q₈	—	2	4	no	—
379	Q₈	—	2	4	no	—
380	Q₈	—	4	2	no	—
381	Q₈	—	4	2	no	—
382	Q₈	—	4	2	no	—
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	2	1	no	—
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	4	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	4	1	no	—
398	C₂×C₄	—	4	1	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	—	4	1	no	—
401	C₂×C₄	—	4	1	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	1	no	—
405	C₂×C₄	—	4	1	no	—
406	C₂×C₄	—	4	1	no	—
407	C₂×C₄	—	4	1	no	—
408	C₂×C₄	—	4	2	no	—
409	C₂×C₄	—	4	2	no	—
410	C₂×C₄	—	4	1	no	—
411	C₂×C₄	—	4	1	no	—
412	C₂×C₄	C₂₃×#121	1	2	yes	—
413	C₂×C₄	C₂₃×#121	1	2	yes	—
414	C₂×C₄	C₂×Q₁₆×C₂₃	1	2	yes	—
415	C₂×C₄	C₂×Q₁₆×C₂₃	1	2	yes	—
416	C₂×C₄	C₂×Q₁₆×C₂₃	1	2	yes	—
417	C₂×C₄	C₂₃×#135	1	2	yes	—
418	C₂×C₄	C₂₃×#137	1	2	yes	—
419	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
420	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
421	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
422	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
423	C₈	—	2	4	no	—
424	C₈	—	4	2	no	—
425	C₂²	C₂×C₂₃×#121	1	1	yes	characteristic
426	C₂²	C₂₃×#525	1	1	yes	characteristic
427	C₂²	C₂₃×#532	1	1	yes	characteristic
428	C₂²	C₂²×Q₁₆×C₂₃	1	1	yes	characteristic
429	C₂²	C₂×C₂₃×#135	1	1	yes	characteristic
430	C₂²	C₂×C₂₃×#137	1	1	yes	characteristic
431	C₂²	C₂₃×#575	1	1	yes	characteristic
432	C₄	—	2	2	no	—
433	C₄	—	2	2	no	—
434	C₄	—	2	2	no	—
435	C₄	—	2	2	no	—
436	C₄	—	4	1	no	—
437	C₄	—	4	2	no	—
438	C₄	—	4	2	no	—
439	C₄	—	4	4	no	—
440	C₄	—	8	1	no	—
441	C₄	—	8	2	no	—
442	C₄	—	8	1	no	—
443	C₄	C₂₃×#462	1	4	yes	—
444	C₄	C₂₃×#525	1	2	yes	—
445	C₄	C₂₃×#529	1	2	yes	—
446	C₂	C₂₃×#2392	1	1	yes	characteristic
447	C₂	C₂×C₂₃×#462	1	1	yes	characteristic
448	C₂	C₂₃×#3035	1	1	yes	characteristic
449	C₂	C₂₃×#3104	1	1	yes	characteristic
450	C₂	C₂₃×#3108	1	1	yes	characteristic
451	C₂	C₂₃×#3170	1	1	yes	characteristic
452	C₂	C₂₃×#3172	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₂₃	C₂×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₃
socle, prime radical	C₂³×C₂₃	C₂²×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₂₃ ◁ C₄³×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
146. C₄²×C₂₃	Q₁₆	semidirect
149. #23679	C₂₃	direct (N × H)
320. C₂₃	#23679	direct (N × H)
373. C₄²	Q₁₆×C₂₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×Q₁₆×C₂₃	2
C₄×C₂₃×C₄⋊Q₈	2
C₂₃×#2295	2
C₂₃×#2083	2
C₂₃×#2072	2
C₂₃×#2068	2
C₂₃×#2056	2
C₂₃×#2043	2
C₂₃×#2016	2
C₄×C₂₃×C₄⋊C₈	2
C₄×C₂₃×#103	2
#23679	23

Subgroups — C23×#23679 #19171305

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#23679 #19171305