Subgroups — C₂₃×#60943 #19208569

Order 5888.

1802 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#533	C₂	1	2	yes	maximal
2	C₂₃×#3249	C₂	1	4	yes	maximal, complemented
3	C₂₃×#3230	C₂	1	4	yes	maximal, complemented
4	C₂₃×#3209	C₂	1	4	yes	maximal, complemented
5	C₂₃×#3189	C₂	1	4	yes	maximal
6	C₂₃×#3170	C₂	1	4	yes	maximal, complemented
7	C₂₃×#3104	C₂	1	8	yes	maximal, complemented
8	C₂×C₂₃×#431	C₂	1	1	yes	maximal, characteristic
9	C₂₃×#533	—	2	2	no	—
10	C₂₃×#533	—	2	2	no	—
11	C₂₃×#533	—	2	2	no	—
12	C₂₃×#533	—	2	2	no	—
13	C₂₃×#533	C₂²	1	4	yes	—
14	C₂₃×#533	C₂²	1	4	yes	—
15	C₂₃×#533	C₂²	1	4	yes	—
16	C₂₃×#533	C₂²	1	4	yes	—
17	C₂×C₂₃×C₄⋊Q₈	C₂²	1	2	yes	—
18	C₂×C₂₃×C₄⋊Q₈	C₂²	1	2	yes	—
19	C₂×C₂₃×#125	—	2	2	no	—
20	C₂×C₂₃×C₂²⋊Q₈	—	2	2	no	—
21	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	4	yes	—
22	C₂×C₄×Q₈×C₂₃	—	2	2	no	—
23	C₂×C₄×Q₈×C₂₃	C₂²	1	4	yes	—
24	C₂×C₂₃×#117	—	2	2	no	—
25	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
26	C₂₃×#500	C₂²	1	4	yes	complemented
27	C₂₃×#494	C₂²	1	4	yes	complemented
28	C₂₃×#487	C₂²	1	8	yes	complemented
29	C₂₃×#484	C₂²	1	16	yes	—
30	C₂₃×#477	C₂²	1	16	yes	complemented
31	C₂₃×#467	C₂²	1	16	yes	—
32	C₂₃×#462	C₂²	1	16	yes	complemented
33	C₂₃×#451	C₂²	1	16	yes	—
34	C₄×Q₁₆×C₂₃	C₂²	1	16	yes	complemented
35	C₂₃×#431	C₂²	1	4	yes	—
36	C₂₃×#431	C₂²	1	4	yes	—
37	C₂×C₂₃×C₄⋊C₈	C₂²	1	2	yes	—
38	C₂×C₂₃×C₂²⋊C₈	C₂²	1	2	yes	—
39	C₂×C₄×C₈×C₂₃	C₂²	1	2	yes	—
40	C₂²×Q₈×C₂₃	—	2	2	no	—
41	C₂²×Q₈×C₂₃	C₂³	1	4	yes	—
42	C₂³×C₄×C₂₃	D₄	1	1	yes	characteristic
43	C₂³×C₄×C₂₃	D₄	1	1	yes	characteristic
44	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
45	C₂×Q₁₆×C₂₃	C₂³	1	16	yes	—
46	C₂²×C₈×C₂₃	C₂³	1	4	yes	—
47	C₂₃×C₄⋊Q₈	—	2	2	no	—
48	C₂₃×C₄⋊Q₈	—	2	2	no	—
49	C₂₃×C₄⋊Q₈	—	2	2	no	—
50	C₂₃×C₄⋊Q₈	—	2	2	no	—
51	C₂₃×C₄⋊Q₈	C₂³	1	4	yes	—
52	C₂₃×C₄⋊Q₈	C₂³	1	4	yes	—
53	C₂₃×C₄⋊Q₈	C₂³	1	4	yes	—
54	C₂₃×C₄⋊Q₈	C₂³	1	4	yes	—
55	C₂₃×#125	—	2	4	no	—
56	C₂₃×#125	—	2	4	no	—
57	C₂₃×#125	—	2	4	no	—
58	C₂₃×#125	—	2	4	no	—
59	C₂₃×C₂²⋊Q₈	—	2	4	no	—
60	C₂₃×C₂²⋊Q₈	—	2	4	no	—
61	C₂₃×C₂²⋊Q₈	—	2	4	no	—
62	C₂₃×C₂²⋊Q₈	—	2	4	no	—
63	C₂₃×C₂²⋊Q₈	—	2	4	no	—
64	C₂₃×C₂²⋊Q₈	—	2	4	no	—
65	C₂₃×C₂²⋊Q₈	C₂³	1	8	yes	—
66	C₂₃×C₂²⋊Q₈	C₂³	1	8	yes	—
67	C₄×Q₈×C₂₃	—	2	4	no	—
68	C₄×Q₈×C₂₃	—	2	4	no	—
69	C₄×Q₈×C₂₃	—	2	4	no	—
70	C₄×Q₈×C₂₃	—	2	4	no	—
71	C₄×Q₈×C₂₃	—	2	4	no	—
72	C₄×Q₈×C₂₃	—	2	4	no	—
73	C₄×Q₈×C₂₃	C₂³	1	8	yes	—
74	C₄×Q₈×C₂₃	C₂³	1	8	yes	—
75	C₂₃×#117	—	2	4	no	—
76	C₂₃×#117	—	2	4	no	—
77	C₂₃×#117	—	2	4	no	—
78	C₂₃×#117	—	2	4	no	—
79	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
80	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
81	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
82	C₂×C₄⋊C₄×C₂₃	—	2	4	no	—
83	C₂×C₄⋊C₄×C₂₃	—	2	4	no	—
84	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
85	C₂×C₂²⋊C₄×C₂₃	—	2	4	no	—
86	C₂×C₄²×C₂₃	—	2	4	no	—
87	C₂×C₄²×C₂₃	D₄	1	2	yes	—
88	C₂×C₄²×C₂₃	D₄	1	2	yes	—
89	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
90	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
91	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
92	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
93	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
94	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
95	C₂₃×#107	C₂³	1	16	yes	—
96	C₂₃×C₄⋊C₈	C₂³	1	8	yes	—
97	C₂₃×#103	C₂³	1	32	yes	—
98	C₂₃×C₂²⋊C₈	C₂³	1	8	yes	—
99	C₄×C₈×C₂₃	C₂³	1	4	yes	—
100	C₄×C₈×C₂₃	C₂³	1	4	yes	—
101	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
102	C₂×Q₈×C₂₃	—	2	4	no	—
103	C₂×Q₈×C₂₃	—	2	4	no	—
104	C₂×Q₈×C₂₃	—	2	4	no	—
105	C₂×Q₈×C₂₃	—	4	8	no	—
106	C₂×Q₈×C₂₃	—	4	8	no	—
107	C₂×Q₈×C₂₃	C₂⁴	1	8	yes	—
108	C₂²×C₄×C₂₃	—	2	4	no	—
109	C₂²×C₄×C₂₃	—	2	4	no	—
110	C₂²×C₄×C₂₃	—	4	2	no	—
111	C₂²×C₄×C₂₃	—	4	2	no	—
112	C₂²×C₄×C₂₃	Q₁₆	1	8	yes	complemented
113	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
114	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
116	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
118	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
120	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
122	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
124	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
125	Q₁₆×C₂₃	—	4	16	no	—
126	C₂×C₈×C₂₃	—	4	4	no	—
127	C₂×C₈×C₂₃	C₂⁴	1	8	yes	—
128	C₄⋊C₄×C₂₃	—	2	4	no	—
129	C₄⋊C₄×C₂₃	—	2	4	no	—
130	C₄⋊C₄×C₂₃	—	2	4	no	—
131	C₄⋊C₄×C₂₃	—	2	4	no	—
132	C₄⋊C₄×C₂₃	—	2	4	no	—
133	C₄⋊C₄×C₂₃	—	2	4	no	—
134	C₄⋊C₄×C₂₃	—	2	8	no	—
135	C₄⋊C₄×C₂₃	—	2	8	no	—
136	C₄⋊C₄×C₂₃	—	2	8	no	—
137	C₄⋊C₄×C₂₃	—	2	8	no	—
138	C₄⋊C₄×C₂₃	—	2	4	no	—
139	C₄⋊C₄×C₂₃	C₂⁴	1	8	yes	—
140	C₂²⋊C₄×C₂₃	—	2	8	no	—
141	C₂²⋊C₄×C₂₃	—	2	8	no	—
142	C₄²×C₂₃	—	2	8	no	—
143	C₄²×C₂₃	—	2	8	no	—
144	C₄²×C₂₃	C₂×D₄	1	2	yes	—
145	C₄²×C₂₃	C₂×D₄	1	2	yes	—
146	C₄²×C₂₃	C₂×D₄	1	2	yes	—
147	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
148	C₄²×C₂₃	C₂×D₄	1	2	yes	—
149	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
150	C₄²×C₂₃	C₂×D₄	1	2	yes	—
151	C₄²×C₂₃	C₂⁴	1	2	yes	—
152	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
153	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
154	#60943	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
155	C₂³×C₂₃	—	4	1	no	—
156	C₂³×C₂₃	—	4	1	no	—
157	C₂³×C₂₃	C₂×Q₁₆	1	4	yes	—
158	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
159	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
160	Q₈×C₂₃	—	2	16	no	—
161	Q₈×C₂₃	—	4	8	no	—
162	Q₈×C₂₃	—	4	8	no	—
163	Q₈×C₂₃	—	4	8	no	—
164	C₂×C₄×C₂₃	—	2	2	no	—
165	C₂×C₄×C₂₃	—	2	4	no	—
166	C₂×C₄×C₂₃	—	2	2	no	—
167	C₂×C₄×C₂₃	—	2	4	no	—
168	C₂×C₄×C₂₃	—	2	8	no	—
169	C₂×C₄×C₂₃	—	2	8	no	—
170	C₂×C₄×C₂₃	—	4	2	no	—
171	C₂×C₄×C₂₃	—	4	1	no	—
172	C₂×C₄×C₂₃	—	4	2	no	—
173	C₂×C₄×C₂₃	—	4	1	no	—
174	C₂×C₄×C₂₃	—	4	8	no	—
175	C₂×C₄×C₂₃	—	4	8	no	—
176	C₂×C₄×C₂₃	C₂×Q₁₆	1	8	yes	—
177	C₂×C₄×C₂₃	C₂×Q₁₆	1	4	yes	—
178	C₂×C₄×C₂₃	C₂×Q₁₆	1	8	yes	—
179	C₂×C₄×C₂₃	C₂×Q₁₆	1	4	yes	—
180	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
181	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
182	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
183	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
184	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
185	C₂×C₄×C₂₃	C₂²×D₄	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	C₂⁵	1	1	yes	characteristic
189	C₈×C₂₃	—	2	8	no	—
190	C₂×#533	C₂×C₂₃	1	2	yes	—
191	#3249	C₂×C₂₃	1	4	yes	complemented
192	#3230	C₂×C₂₃	1	4	yes	complemented
193	#3209	C₂×C₂₃	1	4	yes	complemented
194	#3189	C₂×C₂₃	1	4	yes	—
195	#3170	C₂×C₂₃	1	4	yes	complemented
196	#3104	C₂×C₂₃	1	8	yes	complemented
197	C₂×#431	C₂×C₂₃	1	1	yes	characteristic
198	C₂²×C₂₃	—	2	2	no	—
199	C₂²×C₂₃	—	2	1	no	—
200	C₂²×C₂₃	—	2	2	no	—
201	C₂²×C₂₃	—	2	1	no	—
202	C₂²×C₂₃	—	4	4	no	—
203	C₂²×C₂₃	C₂²×Q₁₆	1	2	yes	—
204	C₂²×C₂₃	C₂²×Q₁₆	1	4	yes	—
205	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
206	C₄×C₂₃	—	2	1	no	—
207	C₄×C₂₃	—	2	2	no	—
208	C₄×C₂₃	—	2	1	no	—
209	C₄×C₂₃	—	2	2	no	—
210	C₄×C₂₃	—	4	8	no	—
211	C₄×C₂₃	—	4	8	no	—
212	C₄×C₂₃	C₂²×Q₁₆	1	4	yes	—
213	C₄×C₂₃	C₂²×Q₁₆	1	2	yes	—
214	C₄×C₂₃	C₂²×Q₁₆	1	2	yes	—
215	C₄×C₂₃	#575	1	2	yes	—
216	C₄×C₂₃	#585	1	2	yes	—
217	#533	—	2	2	no	—
218	#533	—	2	2	no	—
219	#533	—	2	2	no	—
220	#533	—	2	2	no	—
221	#533	C₂²×C₂₃	1	4	yes	—
222	#533	C₂²×C₂₃	1	4	yes	—
223	#533	C₂²×C₂₃	1	4	yes	—
224	#533	C₂²×C₂₃	1	4	yes	—
225	C₂×C₄⋊Q₈	C₂²×C₂₃	1	2	yes	—
226	C₂×C₄⋊Q₈	C₂²×C₂₃	1	2	yes	—
227	C₂×#125	—	2	2	no	—
228	C₂×C₂²⋊Q₈	—	2	2	no	—
229	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	4	yes	—
230	C₂×C₄×Q₈	—	2	2	no	—
231	C₂×C₄×Q₈	C₂²×C₂₃	1	4	yes	—
232	C₂×#117	—	2	2	no	—
233	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
234	#500	C₂²×C₂₃	1	4	yes	complemented
235	#494	C₂²×C₂₃	1	4	yes	complemented
236	#487	C₂²×C₂₃	1	8	yes	complemented
237	#484	C₂²×C₂₃	1	16	yes	—
238	#477	C₂²×C₂₃	1	16	yes	complemented
239	#467	C₂²×C₂₃	1	16	yes	—
240	#462	C₂²×C₂₃	1	16	yes	complemented
241	#451	C₂²×C₂₃	1	16	yes	—
242	C₄×Q₁₆	C₂²×C₂₃	1	16	yes	complemented
243	#431	C₂²×C₂₃	1	4	yes	—
244	#431	C₂²×C₂₃	1	4	yes	—
245	C₂×C₄⋊C₈	C₂²×C₂₃	1	2	yes	—
246	C₂×C₂²⋊C₈	C₂²×C₂₃	1	2	yes	—
247	C₂×C₄×C₈	C₂²×C₂₃	1	2	yes	—
248	C₂×C₂₃	—	2	4	no	—
249	C₂×C₂₃	—	2	2	no	—
250	C₂×C₂₃	#3449	1	1	yes	characteristic
251	C₂×C₂₃	C₂³×Q₁₆	1	1	yes	characteristic
252	C₂×C₂₃	C₂×#575	1	1	yes	characteristic
253	C₂²×Q₈	—	2	2	no	—
254	C₂²×Q₈	C₂³×C₂₃	1	4	yes	—
255	C₂³×C₄	D₄×C₂₃	1	1	yes	characteristic
256	C₂³×C₄	D₄×C₂₃	1	1	yes	characteristic
257	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
258	C₂×Q₁₆	C₂³×C₂₃	1	16	yes	—
259	C₂²×C₈	C₂³×C₂₃	1	4	yes	—
260	C₄⋊Q₈	—	2	2	no	—
261	C₄⋊Q₈	—	2	2	no	—
262	C₄⋊Q₈	—	2	2	no	—
263	C₄⋊Q₈	—	2	2	no	—
264	C₄⋊Q₈	C₂³×C₂₃	1	4	yes	—
265	C₄⋊Q₈	C₂³×C₂₃	1	4	yes	—
266	C₄⋊Q₈	C₂³×C₂₃	1	4	yes	—
267	C₄⋊Q₈	C₂³×C₂₃	1	4	yes	—
268	#125	—	2	4	no	—
269	#125	—	2	4	no	—
270	#125	—	2	4	no	—
271	#125	—	2	4	no	—
272	C₂²⋊Q₈	—	2	4	no	—
273	C₂²⋊Q₈	—	2	4	no	—
274	C₂²⋊Q₈	—	2	4	no	—
275	C₂²⋊Q₈	—	2	4	no	—
276	C₂²⋊Q₈	—	2	4	no	—
277	C₂²⋊Q₈	—	2	4	no	—
278	C₂²⋊Q₈	C₂³×C₂₃	1	8	yes	—
279	C₂²⋊Q₈	C₂³×C₂₃	1	8	yes	—
280	C₄×Q₈	—	2	4	no	—
281	C₄×Q₈	—	2	4	no	—
282	C₄×Q₈	—	2	4	no	—
283	C₄×Q₈	—	2	4	no	—
284	C₄×Q₈	—	2	4	no	—
285	C₄×Q₈	—	2	4	no	—
286	C₄×Q₈	C₂³×C₂₃	1	8	yes	—
287	C₄×Q₈	C₂³×C₂₃	1	8	yes	—
288	#117	—	2	4	no	—
289	#117	—	2	4	no	—
290	#117	—	2	4	no	—
291	#117	—	2	4	no	—
292	C₂×C₄⋊C₄	—	2	2	no	—
293	C₂×C₄⋊C₄	—	2	2	no	—
294	C₂×C₄⋊C₄	—	2	2	no	—
295	C₂×C₄⋊C₄	—	2	4	no	—
296	C₂×C₄⋊C₄	—	2	4	no	—
297	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
298	C₂×C₂²⋊C₄	—	2	4	no	—
299	C₂×C₄²	—	2	4	no	—
300	C₂×C₄²	D₄×C₂₃	1	2	yes	—
301	C₂×C₄²	D₄×C₂₃	1	2	yes	—
302	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
303	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
304	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
305	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
306	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
307	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
308	#107	C₂³×C₂₃	1	16	yes	—
309	C₄⋊C₈	C₂³×C₂₃	1	8	yes	—
310	#103	C₂³×C₂₃	1	32	yes	—
311	C₂²⋊C₈	C₂³×C₂₃	1	8	yes	—
312	C₄×C₈	C₂³×C₂₃	1	4	yes	—
313	C₄×C₈	C₂³×C₂₃	1	4	yes	—
314	C₂₃	#60943	1	1	yes	characteristic, direct product factor, Sylow
315	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
316	C₂×Q₈	—	2	4	no	—
317	C₂×Q₈	—	2	4	no	—
318	C₂×Q₈	—	2	4	no	—
319	C₂×Q₈	—	4	8	no	—
320	C₂×Q₈	—	4	8	no	—
321	C₂×Q₈	C₂⁴×C₂₃	1	8	yes	—
322	C₂²×C₄	—	2	4	no	—
323	C₂²×C₄	—	2	4	no	—
324	C₂²×C₄	—	4	2	no	—
325	C₂²×C₄	—	4	2	no	—
326	C₂²×C₄	Q₁₆×C₂₃	1	8	yes	complemented
327	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
328	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
329	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
330	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
331	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
332	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
333	C₂²×C₄	C₂×D₄×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	1	yes	characteristic
337	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
338	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
339	Q₁₆	—	4	16	no	—
340	C₂×C₈	—	4	4	no	—
341	C₂×C₈	C₂⁴×C₂₃	1	8	yes	—
342	C₄⋊C₄	—	2	4	no	—
343	C₄⋊C₄	—	2	4	no	—
344	C₄⋊C₄	—	2	4	no	—
345	C₄⋊C₄	—	2	4	no	—
346	C₄⋊C₄	—	2	4	no	—
347	C₄⋊C₄	—	2	4	no	—
348	C₄⋊C₄	—	2	8	no	—
349	C₄⋊C₄	—	2	8	no	—
350	C₄⋊C₄	—	2	8	no	—
351	C₄⋊C₄	—	2	8	no	—
352	C₄⋊C₄	—	2	4	no	—
353	C₄⋊C₄	C₂⁴×C₂₃	1	8	yes	—
354	C₂²⋊C₄	—	2	8	no	—
355	C₂²⋊C₄	—	2	8	no	—
356	C₄²	—	2	8	no	—
357	C₄²	—	2	8	no	—
358	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
359	C₄²	C₂×D₄×C₂₃	1	2	yes	—
360	C₄²	C₂×D₄×C₂₃	1	2	yes	—
361	C₄²	C₂×D₄×C₂₃	1	2	yes	—
362	C₄²	C₂×D₄×C₂₃	1	2	yes	—
363	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
364	C₄²	C₂×D₄×C₂₃	1	2	yes	—
365	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
366	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
367	C₄²	C₂⁴×C₂₃	1	2	yes	—
368	C₂³	—	4	1	no	—
369	C₂³	—	4	1	no	—
370	C₂³	C₂×Q₁₆×C₂₃	1	4	yes	—
371	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
372	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
373	Q₈	—	2	16	no	—
374	Q₈	—	4	8	no	—
375	Q₈	—	4	8	no	—
376	Q₈	—	4	8	no	—
377	C₂×C₄	—	2	4	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	4	no	—
381	C₂×C₄	—	2	8	no	—
382	C₂×C₄	—	2	8	no	—
383	C₂×C₄	—	4	1	no	—
384	C₂×C₄	—	4	2	no	—
385	C₂×C₄	—	4	1	no	—
386	C₂×C₄	—	4	2	no	—
387	C₂×C₄	—	4	8	no	—
388	C₂×C₄	—	4	8	no	—
389	C₂×C₄	C₂×Q₁₆×C₂₃	1	8	yes	—
390	C₂×C₄	C₂×Q₁₆×C₂₃	1	8	yes	—
391	C₂×C₄	C₂×Q₁₆×C₂₃	1	4	yes	—
392	C₂×C₄	C₂×Q₁₆×C₂₃	1	4	yes	—
393	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
394	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
395	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
396	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
397	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
398	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
399	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
400	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
401	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
402	C₈	—	2	8	no	—
403	C₂²	—	2	2	no	—
404	C₂²	—	2	1	no	—
405	C₂²	—	2	2	no	—
406	C₂²	—	2	1	no	—
407	C₂²	—	4	4	no	—
408	C₂²	C₂²×Q₁₆×C₂₃	1	2	yes	—
409	C₂²	C₂²×Q₁₆×C₂₃	1	4	yes	—
410	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
411	C₄	—	2	2	no	—
412	C₄	—	2	1	no	—
413	C₄	—	2	2	no	—
414	C₄	—	2	1	no	—
415	C₄	—	4	8	no	—
416	C₄	—	4	8	no	—
417	C₄	C₂²×Q₁₆×C₂₃	1	2	yes	—
418	C₄	C₂²×Q₁₆×C₂₃	1	4	yes	—
419	C₄	C₂²×Q₁₆×C₂₃	1	2	yes	—
420	C₄	C₂₃×#575	1	2	yes	—
421	C₄	C₂₃×#585	1	2	yes	—
422	C₂	—	2	4	no	—
423	C₂	—	2	2	no	—
424	C₂	C₂₃×#3449	1	1	yes	characteristic
425	C₂	C₂³×Q₁₆×C₂₃	1	1	yes	characteristic
426	C₂	C₂×C₂₃×#575	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₂₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
socle	C₂²×C₂₃	C₂³×D₄
prime radical	C₂⁴×C₂₃	C₂×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₃ ◁ C₂²×C₄²×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂₃×#3249	C₂	semidirect
3. C₂₃×#3230	C₂	semidirect
4. C₂₃×#3209	C₂	semidirect
6. C₂₃×#3170	C₂	semidirect
7. C₂₃×#3104	C₂	semidirect
26. C₂₃×#500	C₂²	semidirect
27. C₂₃×#494	C₂²	semidirect
28. C₂₃×#487	C₂²	semidirect
30. C₂₃×#477	C₂²	semidirect
32. C₂₃×#462	C₂²	semidirect
34. C₄×Q₁₆×C₂₃	C₂²	semidirect
112. C₂²×C₄×C₂₃	Q₁₆	semidirect
154. #60943	C₂₃	direct (N × H)
191. #3249	C₂×C₂₃	semidirect
192. #3230	C₂×C₂₃	semidirect
193. #3209	C₂×C₂₃	semidirect
195. #3170	C₂×C₂₃	semidirect
196. #3104	C₂×C₂₃	semidirect
234. #500	C₂²×C₂₃	semidirect
235. #494	C₂²×C₂₃	semidirect
236. #487	C₂²×C₂₃	semidirect
238. #477	C₂²×C₂₃	semidirect
240. #462	C₂²×C₂₃	semidirect
242. C₄×Q₁₆	C₂²×C₂₃	semidirect
314. C₂₃	#60943	direct (N × H)
326. C₂²×C₄	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×C₂₃×#533	2
C₂₃×#3249	2
C₂₃×#3230	2
C₂₃×#3209	2
C₂₃×#3189	2
C₂₃×#3170	2
C₂₃×#3104	2
C₂×C₂₃×#431	2
#60943	23

Subgroups — C23×#60943 #19208569

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#60943 #19208569