Subgroups — C₂₃×#21527 #19169153

Order 5888.

1014 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#467	C₂	1	1	yes	maximal, characteristic
2	C₂×C₂₃×#441	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₂₃×#97	C₂	1	1	yes	maximal, characteristic
4	C₄×C₂₃×C₂²⋊Q₈	C₂	1	2	yes	maximal
5	C₂₃×#1971	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#1943	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#1935	C₂	1	2	yes	maximal, complemented
8	C₂₃×#1892	C₂	1	2	yes	maximal
9	C₂₃×#1807	C₂	1	1	yes	maximal, characteristic
10	C₂₃×#1776	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#1763	C₂	1	2	yes	maximal, complemented
12	C₂²×Q₁₆×C₂₃	C₂²	1	1	yes	characteristic
13	C₂³×C₈×C₂₃	C₂²	1	1	yes	characteristic
14	C₂³×C₈×C₂₃	C₂²	1	1	yes	characteristic
15	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	2	yes	—
16	C₂×C₄×Q₈×C₂₃	C₂²	1	2	yes	—
17	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
18	C₂₃×#467	C₄	1	8	yes	complemented
19	C₂₃×#441	—	2	4	no	—
20	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic
21	C₂×C₂₃×#106	C₂²	1	1	yes	characteristic
22	C₂×C₂₃×#106	C₂²	1	1	yes	characteristic
23	C₂×C₂₃×#103	C₂²	1	2	yes	—
24	C₂×C₂₃×#103	C₂²	1	2	yes	—
25	C₂×C₂₃×#103	C₂²	1	2	yes	—
26	C₂×C₂₃×#97	—	2	4	no	—
27	C₂×C₂₃×#97	C₂²	1	1	yes	characteristic
28	C₂×C₂₃×#97	C₂²	1	1	yes	characteristic
29	C₂×C₂₃×#97	C₂²	1	1	yes	characteristic
30	C₂×C₂₃×#97	C₂²	1	1	yes	characteristic
31	C₂₃×#391	C₂²	1	2	yes	—
32	C₂₃×#389	C₂²	1	2	yes	—
33	C₂₃×#387	—	2	2	no	—
34	C₂₃×#385	—	2	2	no	—
35	C₂₃×#380	C₂²	1	2	yes	—
36	C₄×C₄⋊C₄×C₂₃	—	2	2	no	—
37	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
38	C₄×C₂²⋊C₄×C₂₃	—	2	2	no	—
39	C₂₃×#340	C₂²	1	2	yes	—
40	C₂₃×#340	C₂²	1	2	yes	—
41	C₂₃×#340	C₂²	1	2	yes	—
42	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
43	C₂³×C₄×C₂₃	D₄	1	2	yes	—
44	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
45	C₂×Q₁₆×C₂₃	—	2	2	no	—
46	C₂×Q₁₆×C₂₃	—	2	2	no	—
47	C₂×Q₁₆×C₂₃	C₂×C₄	1	4	yes	complemented
48	C₂²×C₈×C₂₃	—	2	2	no	—
49	C₂²×C₈×C₂₃	—	2	2	no	—
50	C₂²×C₈×C₂₃	—	2	2	no	—
51	C₂²×C₈×C₂₃	—	2	2	no	—
52	C₂²×C₈×C₂₃	—	2	2	no	—
53	C₂²×C₈×C₂₃	C₂×C₄	1	4	yes	—
54	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
55	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
56	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
57	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
58	C₂₃×C₂²⋊Q₈	—	2	4	no	—
59	C₂₃×C₂²⋊Q₈	C₂×C₄	1	8	yes	—
60	C₄×Q₈×C₂₃	—	2	4	no	—
61	C₄×Q₈×C₂₃	—	2	4	no	—
62	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
63	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
64	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
65	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
66	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
67	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
68	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
69	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
70	C₂×C₄²×C₂₃	—	2	2	no	—
71	C₂×C₄²×C₂₃	—	2	2	no	—
72	C₂×C₄²×C₂₃	—	2	2	no	—
73	C₂×C₄²×C₂₃	—	2	2	no	—
74	C₂×C₄²×C₂₃	D₄	1	2	yes	—
75	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
76	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
77	C₂₃×#107	C₂×C₄	1	4	yes	complemented
78	C₂₃×#106	—	2	2	no	—
79	C₂₃×#106	—	2	2	no	—
80	C₂₃×#103	—	2	4	no	—
81	C₂₃×#103	—	2	4	no	—
82	C₂₃×#103	C₂×C₄	1	8	yes	complemented
83	C₂₃×#97	—	2	2	no	—
84	C₂₃×#97	—	2	2	no	—
85	C₂₃×#97	—	2	2	no	—
86	C₂₃×#97	D₄	1	4	yes	—
87	C₂₃×#95	—	2	2	no	—
88	C₂₃×#95	—	2	2	no	—
89	C₂₃×#95	—	2	2	no	—
90	C₂₃×#95	—	2	2	no	—
91	C₂₃×#95	—	2	2	no	—
92	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
93	C₂×Q₈×C₂₃	—	2	2	no	—
94	C₂×Q₈×C₂₃	—	2	2	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	C₂²×C₄	1	4	yes	—
99	C₂²×C₄×C₂₃	—	2	1	no	—
100	C₂²×C₄×C₂₃	—	2	1	no	—
101	C₂²×C₄×C₂₃	—	2	1	no	—
102	C₂²×C₄×C₂₃	—	2	1	no	—
103	C₂²×C₄×C₂₃	—	2	4	no	—
104	C₂²×C₄×C₂₃	—	2	2	no	—
105	C₂²×C₄×C₂₃	—	2	2	no	—
106	C₂²×C₄×C₂₃	—	2	4	no	—
107	C₂²×C₄×C₂₃	—	2	2	no	—
108	C₂²×C₄×C₂₃	—	2	2	no	—
109	C₂²×C₄×C₂₃	—	4	2	no	—
110	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
111	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
112	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
114	C₂²×C₄×C₂₃	#41	1	2	yes	—
115	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
116	Q₁₆×C₂₃	—	2	8	no	—
117	C₂×C₈×C₂₃	—	2	8	no	—
118	C₂×C₈×C₂₃	—	2	1	no	—
119	C₂×C₈×C₂₃	—	2	1	no	—
120	C₂×C₈×C₂₃	—	2	1	no	—
121	C₂×C₈×C₂₃	—	2	1	no	—
122	C₂×C₈×C₂₃	—	2	1	no	—
123	C₂×C₈×C₂₃	—	2	1	no	—
124	C₂×C₈×C₂₃	—	2	8	no	—
125	C₂×C₈×C₂₃	C₂²×C₄	1	2	yes	—
126	C₂×C₈×C₂₃	C₂²×C₄	1	2	yes	—
127	C₂×C₈×C₂₃	C₂×D₄	1	2	yes	—
128	C₂×C₈×C₂₃	C₂×D₄	1	2	yes	—
129	C₂×C₈×C₂₃	#41	1	2	yes	—
130	C₂×C₈×C₂₃	#41	1	2	yes	—
131	C₄⋊C₄×C₂₃	—	2	8	no	—
132	C₄⋊C₄×C₂₃	—	2	2	no	—
133	C₄⋊C₄×C₂₃	—	2	2	no	—
134	C₄⋊C₄×C₂₃	—	2	2	no	—
135	C₄⋊C₄×C₂₃	—	2	2	no	—
136	C₄⋊C₄×C₂₃	—	2	2	no	—
137	C₄⋊C₄×C₂₃	—	4	4	no	—
138	C₄⋊C₄×C₂₃	—	4	4	no	—
139	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
140	C₂²⋊C₄×C₂₃	—	2	8	no	—
141	C₂²⋊C₄×C₂₃	—	4	4	no	—
142	C₄²×C₂₃	—	2	4	no	—
143	C₄²×C₂₃	—	2	1	no	—
144	C₄²×C₂₃	—	2	1	no	—
145	C₄²×C₂₃	—	4	4	no	—
146	C₄²×C₂₃	—	4	4	no	—
147	C₄²×C₂₃	C₂×D₄	1	2	yes	—
148	C₄²×C₂₃	#41	1	2	yes	—
149	#21527	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
150	C₂³×C₂₃	—	2	1	no	—
151	C₂³×C₂₃	—	2	1	no	—
152	C₂³×C₂₃	—	2	2	no	—
153	C₂³×C₂₃	C₄×D₄	1	2	yes	—
154	C₂³×C₂₃	#137	1	4	yes	—
155	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
156	Q₈×C₂₃	—	2	4	no	—
157	Q₈×C₂₃	—	2	4	no	—
158	Q₈×C₂₃	—	4	2	no	—
159	Q₈×C₂₃	—	4	2	no	—
160	C₂×C₄×C₂₃	—	2	1	no	—
161	C₂×C₄×C₂₃	—	2	1	no	—
162	C₂×C₄×C₂₃	—	2	2	no	—
163	C₂×C₄×C₂₃	—	2	2	no	—
164	C₂×C₄×C₂₃	—	2	2	no	—
165	C₂×C₄×C₂₃	—	2	2	no	—
166	C₂×C₄×C₂₃	—	2	2	no	—
167	C₂×C₄×C₂₃	—	2	2	no	—
168	C₂×C₄×C₂₃	—	2	4	no	—
169	C₂×C₄×C₂₃	—	2	4	no	—
170	C₂×C₄×C₂₃	—	2	2	no	—
171	C₂×C₄×C₂₃	—	2	2	no	—
172	C₂×C₄×C₂₃	—	2	2	no	—
173	C₂×C₄×C₂₃	—	4	8	no	—
174	C₂×C₄×C₂₃	—	4	2	no	—
175	C₂×C₄×C₂₃	—	4	2	no	—
176	C₂×C₄×C₂₃	—	4	2	no	—
177	C₂×C₄×C₂₃	—	4	2	no	—
178	C₂×C₄×C₂₃	—	4	2	no	—
179	C₂×C₄×C₂₃	—	4	2	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	#121	1	4	yes	—
186	C₂×C₄×C₂₃	C₂³×C₄	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	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
192	C₈×C₂₃	—	2	2	no	—
193	C₈×C₂₃	—	2	2	no	—
194	C₈×C₂₃	—	2	2	no	—
195	C₈×C₂₃	C₄×D₄	1	4	yes	—
196	C₂×#467	C₂×C₂₃	1	1	yes	characteristic
197	C₂×#441	C₂×C₂₃	1	1	yes	characteristic, complemented
198	C₂²×#97	C₂×C₂₃	1	1	yes	characteristic
199	C₄×C₂²⋊Q₈	C₂×C₂₃	1	2	yes	—
200	#1971	C₂×C₂₃	1	1	yes	characteristic, complemented
201	#1943	C₂×C₂₃	1	1	yes	characteristic, complemented
202	#1935	C₂×C₂₃	1	2	yes	complemented
203	#1892	C₂×C₂₃	1	2	yes	—
204	#1807	C₂×C₂₃	1	1	yes	characteristic
205	#1776	C₂×C₂₃	1	1	yes	characteristic, complemented
206	#1763	C₂×C₂₃	1	2	yes	complemented
207	C₂²×C₂₃	—	2	4	no	—
208	C₂²×C₂₃	—	2	2	no	—
209	C₂²×C₂₃	—	2	4	no	—
210	C₂²×C₂₃	—	2	2	no	—
211	C₂²×C₂₃	#441	1	4	yes	complemented
212	C₂²×C₂₃	C₂×C₄×D₄	1	1	yes	characteristic
213	C₂²×C₂₃	C₂×#121	1	1	yes	characteristic
214	C₂²×C₂₃	#532	1	1	yes	characteristic
215	C₂²×C₂₃	C₂×#137	1	2	yes	—
216	C₂²×C₂₃	#575	1	2	yes	—
217	C₄×C₂₃	—	2	4	no	—
218	C₄×C₂₃	—	2	2	no	—
219	C₄×C₂₃	—	4	4	no	—
220	C₄×C₂₃	—	4	2	no	—
221	C₄×C₂₃	—	4	4	no	—
222	C₄×C₂₃	—	8	2	no	—
223	C₄×C₂₃	—	8	2	no	—
224	C₄×C₂₃	C₂×C₄×D₄	1	1	yes	characteristic
225	C₄×C₂₃	C₄×#41	1	1	yes	characteristic
226	C₄×C₂₃	#525	1	1	yes	characteristic
227	C₄×C₂₃	#529	1	1	yes	characteristic
228	C₂²×Q₁₆	C₂²×C₂₃	1	1	yes	characteristic
229	C₂³×C₈	C₂²×C₂₃	1	1	yes	characteristic
230	C₂³×C₈	C₂²×C₂₃	1	1	yes	characteristic
231	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	2	yes	—
232	C₂×C₄×Q₈	C₂²×C₂₃	1	2	yes	—
233	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
234	#467	C₄×C₂₃	1	8	yes	complemented
235	#441	—	2	4	no	—
236	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic
237	C₂×#106	C₂²×C₂₃	1	1	yes	characteristic
238	C₂×#106	C₂²×C₂₃	1	1	yes	characteristic
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×#97	—	2	4	no	—
243	C₂×#97	C₂²×C₂₃	1	1	yes	characteristic
244	C₂×#97	C₂²×C₂₃	1	1	yes	characteristic
245	C₂×#97	C₂²×C₂₃	1	1	yes	characteristic
246	C₂×#97	C₂²×C₂₃	1	1	yes	characteristic
247	#391	C₂²×C₂₃	1	2	yes	—
248	#389	C₂²×C₂₃	1	2	yes	—
249	#387	—	2	2	no	—
250	#385	—	2	2	no	—
251	#380	C₂²×C₂₃	1	2	yes	—
252	C₄×C₄⋊C₄	—	2	2	no	—
253	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
254	C₄×C₂²⋊C₄	—	2	2	no	—
255	#340	C₂²×C₂₃	1	2	yes	—
256	#340	C₂²×C₂₃	1	2	yes	—
257	#340	C₂²×C₂₃	1	2	yes	—
258	C₂×C₂₃	—	2	4	no	—
259	C₂×C₂₃	C₄×#121	1	1	yes	characteristic
260	C₂×C₂₃	C₂×#441	1	1	yes	characteristic
261	C₂×C₂₃	#2943	1	1	yes	characteristic
262	C₂×C₂₃	#3056	1	2	yes	—
263	C₂×C₂₃	#3181	1	2	yes	—
264	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
265	C₂³×C₄	D₄×C₂₃	1	2	yes	—
266	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
267	C₂×Q₁₆	—	2	2	no	—
268	C₂×Q₁₆	—	2	2	no	—
269	C₂×Q₁₆	C₂×C₄×C₂₃	1	4	yes	complemented
270	C₂²×C₈	—	2	2	no	—
271	C₂²×C₈	—	2	2	no	—
272	C₂²×C₈	—	2	2	no	—
273	C₂²×C₈	—	2	2	no	—
274	C₂²×C₈	—	2	2	no	—
275	C₂²×C₈	C₂×C₄×C₂₃	1	4	yes	—
276	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
277	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
278	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
279	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
280	C₂²⋊Q₈	—	2	4	no	—
281	C₂²⋊Q₈	C₂×C₄×C₂₃	1	8	yes	—
282	C₄×Q₈	—	2	4	no	—
283	C₄×Q₈	—	2	4	no	—
284	C₂×C₄⋊C₄	—	2	2	no	—
285	C₂×C₄⋊C₄	—	2	2	no	—
286	C₂×C₄⋊C₄	—	2	2	no	—
287	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
288	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
289	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
290	C₂×C₂²⋊C₄	—	2	2	no	—
291	C₂×C₂²⋊C₄	—	2	2	no	—
292	C₂×C₄²	—	2	2	no	—
293	C₂×C₄²	—	2	2	no	—
294	C₂×C₄²	—	2	2	no	—
295	C₂×C₄²	—	2	2	no	—
296	C₂×C₄²	D₄×C₂₃	1	2	yes	—
297	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
298	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
299	#107	C₂×C₄×C₂₃	1	4	yes	complemented
300	#106	—	2	2	no	—
301	#106	—	2	2	no	—
302	#103	—	2	4	no	—
303	#103	—	2	4	no	—
304	#103	C₂×C₄×C₂₃	1	8	yes	complemented
305	#97	—	2	2	no	—
306	#97	—	2	2	no	—
307	#97	—	2	2	no	—
308	#97	D₄×C₂₃	1	4	yes	—
309	#95	—	2	2	no	—
310	#95	—	2	2	no	—
311	#95	—	2	2	no	—
312	#95	—	2	2	no	—
313	#95	—	2	2	no	—
314	C₂₃	#21527	1	1	yes	characteristic, direct product factor, Sylow
315	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
316	C₂×Q₈	—	2	2	no	—
317	C₂×Q₈	—	2	2	no	—
318	C₂×Q₈	—	2	2	no	—
319	C₂×Q₈	—	2	2	no	—
320	C₂×Q₈	—	2	2	no	—
321	C₂×Q₈	C₂²×C₄×C₂₃	1	4	yes	—
322	C₂²×C₄	—	2	1	no	—
323	C₂²×C₄	—	2	1	no	—
324	C₂²×C₄	—	2	1	no	—
325	C₂²×C₄	—	2	1	no	—
326	C₂²×C₄	—	2	4	no	—
327	C₂²×C₄	—	2	2	no	—
328	C₂²×C₄	—	2	2	no	—
329	C₂²×C₄	—	2	4	no	—
330	C₂²×C₄	—	2	2	no	—
331	C₂²×C₄	—	2	2	no	—
332	C₂²×C₄	—	4	2	no	—
333	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
334	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
335	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
336	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
337	C₂²×C₄	#41×C₂₃	1	2	yes	—
338	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
339	Q₁₆	—	2	8	no	—
340	C₂×C₈	—	2	8	no	—
341	C₂×C₈	—	2	1	no	—
342	C₂×C₈	—	2	1	no	—
343	C₂×C₈	—	2	1	no	—
344	C₂×C₈	—	2	1	no	—
345	C₂×C₈	—	2	1	no	—
346	C₂×C₈	—	2	1	no	—
347	C₂×C₈	—	2	8	no	—
348	C₂×C₈	C₂²×C₄×C₂₃	1	2	yes	—
349	C₂×C₈	C₂²×C₄×C₂₃	1	2	yes	—
350	C₂×C₈	C₂×D₄×C₂₃	1	2	yes	—
351	C₂×C₈	C₂×D₄×C₂₃	1	2	yes	—
352	C₂×C₈	#41×C₂₃	1	2	yes	—
353	C₂×C₈	#41×C₂₃	1	2	yes	—
354	C₄⋊C₄	—	2	8	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	—	2	2	no	—
360	C₄⋊C₄	—	4	4	no	—
361	C₄⋊C₄	—	4	4	no	—
362	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
363	C₂²⋊C₄	—	2	8	no	—
364	C₂²⋊C₄	—	4	4	no	—
365	C₄²	—	2	4	no	—
366	C₄²	—	2	1	no	—
367	C₄²	—	2	1	no	—
368	C₄²	—	4	4	no	—
369	C₄²	—	4	4	no	—
370	C₄²	C₂×D₄×C₂₃	1	2	yes	—
371	C₄²	#41×C₂₃	1	2	yes	—
372	C₂³	—	2	2	no	—
373	C₂³	—	2	1	no	—
374	C₂³	—	2	1	no	—
375	C₂³	C₄×D₄×C₂₃	1	2	yes	—
376	C₂³	C₂₃×#137	1	4	yes	—
377	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
378	Q₈	—	2	4	no	—
379	Q₈	—	2	4	no	—
380	Q₈	—	4	2	no	—
381	Q₈	—	4	2	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	2	1	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	4	no	—
393	C₂×C₄	—	2	4	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	4	8	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	4	2	no	—
398	C₂×C₄	—	4	2	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	—	4	2	no	—
401	C₂×C₄	—	4	2	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	C₄×D₄×C₂₃	1	2	yes	—
407	C₂×C₄	C₂₃×#121	1	4	yes	—
408	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
409	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
410	C₂×C₄	C₂×#41×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	—	2	2	no	—
417	C₈	C₄×D₄×C₂₃	1	4	yes	—
418	C₂²	—	2	4	no	—
419	C₂²	—	2	2	no	—
420	C₂²	—	2	4	no	—
421	C₂²	—	2	2	no	—
422	C₂²	C₂₃×#441	1	4	yes	complemented
423	C₂²	C₂×C₄×D₄×C₂₃	1	1	yes	characteristic
424	C₂²	C₂×C₂₃×#121	1	1	yes	characteristic
425	C₂²	C₂₃×#532	1	1	yes	characteristic
426	C₂²	C₂×C₂₃×#137	1	2	yes	—
427	C₂²	C₂₃×#575	1	2	yes	—
428	C₄	—	2	4	no	—
429	C₄	—	2	2	no	—
430	C₄	—	4	4	no	—
431	C₄	—	4	2	no	—
432	C₄	—	4	4	no	—
433	C₄	—	8	2	no	—
434	C₄	—	8	2	no	—
435	C₄	C₂×C₄×D₄×C₂₃	1	1	yes	characteristic
436	C₄	C₄×#41×C₂₃	1	1	yes	characteristic
437	C₄	C₂₃×#525	1	1	yes	characteristic
438	C₄	C₂₃×#529	1	1	yes	characteristic
439	C₂	—	2	4	no	—
440	C₂	C₄×C₂₃×#121	1	1	yes	characteristic
441	C₂	C₂×C₂₃×#441	1	1	yes	characteristic
442	C₂	C₂₃×#2943	1	1	yes	characteristic
443	C₂	C₂₃×#3056	1	2	yes	—
444	C₂	C₂₃×#3181	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
2. C₂×C₂₃×#441	C₂	semidirect
5. C₂₃×#1971	C₂	semidirect
6. C₂₃×#1943	C₂	semidirect
7. C₂₃×#1935	C₂	semidirect
10. C₂₃×#1776	C₂	semidirect
11. C₂₃×#1763	C₂	semidirect
18. C₂₃×#467	C₄	semidirect
47. C₂×Q₁₆×C₂₃	C₂×C₄	semidirect
77. C₂₃×#107	C₂×C₄	semidirect
82. C₂₃×#103	C₂×C₄	semidirect
149. #21527	C₂₃	direct (N × H)
197. C₂×#441	C₂×C₂₃	semidirect
200. #1971	C₂×C₂₃	semidirect
201. #1943	C₂×C₂₃	semidirect
202. #1935	C₂×C₂₃	semidirect
205. #1776	C₂×C₂₃	semidirect
206. #1763	C₂×C₂₃	semidirect
211. C₂²×C₂₃	#441	semidirect
234. #467	C₄×C₂₃	semidirect
269. C₂×Q₁₆	C₂×C₄×C₂₃	semidirect
299. #107	C₂×C₄×C₂₃	semidirect
304. #103	C₂×C₄×C₂₃	semidirect
314. C₂₃	#21527	direct (N × H)
422. C₂²	C₂₃×#441	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₂₃×#467	2
C₂×C₂₃×#441	2
C₂²×C₂₃×#97	2
C₄×C₂₃×C₂²⋊Q₈	2
C₂₃×#1971	2
C₂₃×#1943	2
C₂₃×#1935	2
C₂₃×#1892	2
C₂₃×#1807	2
C₂₃×#1776	2
C₂₃×#1763	2
#21527	23

Subgroups — C23×#21527 #19169153

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#21527 #19169153