Subgroups — C₂₃×#60948 #19208574

Order 5888.

1846 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3444	C₂	1	2	yes	maximal, complemented
2	C₂₃×#3249	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3246	C₂	1	2	yes	maximal, complemented
4	C₂₃×#3245	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#3233	C₂	1	4	yes	maximal, complemented
6	C₂₃×#3212	C₂	1	4	yes	maximal, complemented
7	C₂₃×#3191	C₂	1	4	yes	maximal, complemented
8	C₂₃×#3168	C₂	1	4	yes	maximal, complemented
9	C₂₃×#3107	C₂	1	4	yes	maximal, complemented
10	C₂₃×#3106	C₂	1	4	yes	maximal, complemented
11	C₂×C₂₃×#431	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#533	C₂²	1	2	yes	—
13	C₂₃×#533	C₂²	1	2	yes	—
14	C₂₃×#533	C₂²	1	2	yes	—
15	C₂₃×#532	C₂²	1	2	yes	—
16	C₂₃×#532	C₂²	1	2	yes	—
17	C₂₃×#532	C₂²	1	2	yes	—
18	C₂₃×#529	—	2	2	no	—
19	C₂₃×#529	—	2	2	no	—
20	C₂₃×#529	—	2	2	no	—
21	C₂₃×#529	—	2	2	no	—
22	C₂₃×#529	C₂²	1	4	yes	—
23	C₂₃×#529	C₂²	1	4	yes	—
24	C₂₃×#525	—	2	2	no	—
25	C₂₃×#525	—	2	2	no	—
26	C₂₃×#525	C₂²	1	4	yes	—
27	C₄×#41×C₂₃	—	2	2	no	—
28	C₄×#41×C₂₃	—	2	2	no	—
29	C₄×#41×C₂₃	C₂²	1	4	yes	—
30	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
31	C₂₃×#499	C₂²	1	4	yes	complemented
32	C₂₃×#495	C₂²	1	4	yes	complemented
33	C₂₃×#488	C₂²	1	8	yes	complemented
34	C₂₃×#485	C₂²	1	8	yes	—
35	C₂₃×#482	C₂²	1	8	yes	—
36	C₂₃×#477	C₂²	1	4	yes	complemented
37	C₂₃×#476	C₂²	1	4	yes	complemented
38	C₂₃×#475	C₂²	1	4	yes	complemented
39	C₂₃×#474	C₂²	1	4	yes	complemented
40	C₂₃×#467	C₂²	1	4	yes	—
41	C₂₃×#466	C₂²	1	4	yes	—
42	C₂₃×#465	C₂²	1	8	yes	—
43	C₂₃×#462	C₂²	1	4	yes	complemented
44	C₂₃×#461	C₂²	1	4	yes	complemented
45	C₂₃×#460	C₂²	1	4	yes	complemented
46	C₂₃×#459	C₂²	1	4	yes	complemented
47	C₂₃×#452	C₂²	1	8	yes	—
48	C₂₃×#449	C₂²	1	8	yes	—
49	C₄×Q₁₆×C₂₃	C₂²	1	4	yes	complemented
50	C₄×SD₁₆×C₂₃	C₂²	1	8	yes	complemented
51	C₄×D₈×C₂₃	C₂²	1	4	yes	complemented
52	C₂₃×#431	C₂²	1	4	yes	—
53	C₂₃×#431	C₂²	1	4	yes	—
54	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
55	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
56	C₂×C₂₃×C₂²⋊C₈	C₂²	1	2	yes	—
57	C₂×C₄×C₈×C₂₃	C₂²	1	2	yes	—
58	C₂×#41×C₂₃	—	2	2	no	—
59	C₂×#41×C₂₃	—	2	2	no	—
60	C₂×#41×C₂₃	C₂³	1	4	yes	—
61	C₂³×C₄×C₂₃	D₄	1	1	yes	characteristic
62	C₂³×C₄×C₂₃	D₄	1	1	yes	characteristic
63	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
64	C₂×Q₁₆×C₂₃	C₂³	1	4	yes	—
65	C₂×SD₁₆×C₂₃	C₂³	1	8	yes	—
66	C₂×D₈×C₂₃	C₂³	1	4	yes	—
67	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
68	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
69	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
70	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
71	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
72	C₂₃×#127	C₂³	1	2	yes	—
73	C₂₃×#126	—	2	4	no	—
74	C₂₃×#126	—	2	4	no	—
75	C₂₃×#125	—	2	2	no	—
76	C₂₃×#125	—	2	2	no	—
77	C₂₃×#125	C₂³	1	4	yes	—
78	C₂₃×#124	—	2	2	no	—
79	C₂₃×#124	—	2	2	no	—
80	C₂₃×#124	C₂³	1	4	yes	—
81	C₂₃×#123	—	2	4	no	—
82	C₂₃×#123	—	2	4	no	—
83	C₂₃×#123	—	2	4	no	—
84	C₂₃×C₂²⋊Q₈	—	2	2	no	—
85	C₂₃×C₂²⋊Q₈	—	2	2	no	—
86	C₂₃×C₂²⋊Q₈	—	2	2	no	—
87	C₂₃×C₂²⋊Q₈	—	2	2	no	—
88	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
89	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
90	C₂₃×#121	—	2	2	no	—
91	C₂₃×#121	—	2	2	no	—
92	C₂₃×#121	—	2	2	no	—
93	C₂₃×#121	—	2	2	no	—
94	C₂₃×#121	C₂³	1	4	yes	—
95	C₂₃×#121	C₂³	1	4	yes	—
96	C₂₃×#120	—	2	4	no	—
97	C₄×Q₈×C₂₃	—	2	2	no	—
98	C₄×Q₈×C₂₃	—	2	2	no	—
99	C₄×Q₈×C₂₃	—	2	2	no	—
100	C₄×Q₈×C₂₃	—	2	2	no	—
101	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
102	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
103	C₄×D₄×C₂₃	—	2	4	no	—
104	C₄×D₄×C₂₃	—	2	4	no	—
105	C₄×D₄×C₂₃	—	2	4	no	—
106	C₄×D₄×C₂₃	—	2	4	no	—
107	C₄×D₄×C₂₃	—	2	4	no	—
108	C₄×D₄×C₂₃	—	2	4	no	—
109	C₄×D₄×C₂₃	—	2	2	no	—
110	C₄×D₄×C₂₃	—	2	2	no	—
111	C₄×D₄×C₂₃	—	2	2	no	—
112	C₄×D₄×C₂₃	—	2	2	no	—
113	C₄×D₄×C₂₃	C₂³	1	4	yes	—
114	C₄×D₄×C₂₃	C₂³	1	4	yes	—
115	C₂₃×#117	—	2	2	no	—
116	C₂₃×#117	—	2	2	no	—
117	C₂₃×#117	—	2	4	no	—
118	C₂₃×#117	—	2	4	no	—
119	C₂₃×#117	—	2	4	no	—
120	C₂₃×#117	C₂³	1	4	yes	—
121	C₂×C₄²×C₂₃	—	2	4	no	—
122	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
123	C₂×C₄²×C₂₃	D₄	1	2	yes	—
124	C₂×C₄²×C₂₃	D₄	1	2	yes	—
125	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
126	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
127	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
128	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
129	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
130	C₂₃×#107	C₂³	1	4	yes	—
131	C₂₃×#107	C₂³	1	4	yes	—
132	C₂₃×#106	C₂³	1	8	yes	—
133	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
134	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
135	C₂₃×#103	C₂³	1	8	yes	—
136	C₂₃×#103	C₂³	1	8	yes	—
137	C₂₃×#102	C₂³	1	8	yes	—
138	C₂₃×#102	C₂³	1	8	yes	—
139	C₂₃×C₂²⋊C₈	C₂³	1	8	yes	—
140	C₄×C₈×C₂₃	C₂³	1	4	yes	—
141	C₄×C₈×C₂₃	C₂³	1	4	yes	—
142	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
143	#41×C₂₃	—	4	4	no	—
144	#41×C₂₃	—	4	4	no	—
145	#41×C₂₃	—	4	8	no	—
146	#41×C₂₃	—	4	8	no	—
147	C₂×Q₈×C₂₃	—	2	2	no	—
148	C₂×Q₈×C₂₃	—	2	2	no	—
149	C₂×Q₈×C₂₃	C₂⁴	1	4	yes	—
150	C₂×D₄×C₂₃	—	2	4	no	—
151	C₂×D₄×C₂₃	—	2	4	no	—
152	C₂×D₄×C₂₃	—	2	4	no	—
153	C₂×D₄×C₂₃	—	2	2	no	—
154	C₂×D₄×C₂₃	—	2	2	no	—
155	C₂×D₄×C₂₃	C₂⁴	1	4	yes	—
156	C₂²×C₄×C₂₃	—	2	4	no	—
157	C₂²×C₄×C₂₃	—	2	4	no	—
158	C₂²×C₄×C₂₃	—	2	4	no	—
159	C₂²×C₄×C₂₃	—	2	4	no	—
160	C₂²×C₄×C₂₃	—	4	2	no	—
161	C₂²×C₄×C₂₃	—	4	1	no	—
162	C₂²×C₄×C₂₃	—	4	1	no	—
163	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
164	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
165	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
167	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
168	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
169	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
170	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
171	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
172	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
173	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
174	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
175	Q₁₆×C₂₃	—	4	4	no	—
176	SD₁₆×C₂₃	—	4	8	no	—
177	D₈×C₂₃	—	4	4	no	—
178	C₂×C₈×C₂₃	—	4	2	no	—
179	C₂×C₈×C₂₃	—	4	2	no	—
180	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
181	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
182	C₄⋊C₄×C₂₃	—	2	2	no	—
183	C₄⋊C₄×C₂₃	—	2	2	no	—
184	C₄⋊C₄×C₂₃	—	2	2	no	—
185	C₄⋊C₄×C₂₃	—	2	2	no	—
186	C₄⋊C₄×C₂₃	—	2	4	no	—
187	C₄⋊C₄×C₂₃	—	2	4	no	—
188	C₄⋊C₄×C₂₃	—	2	4	no	—
189	C₄⋊C₄×C₂₃	—	2	4	no	—
190	C₄⋊C₄×C₂₃	—	2	4	no	—
191	C₄⋊C₄×C₂₃	—	2	4	no	—
192	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
193	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
194	C₂²⋊C₄×C₂₃	—	2	4	no	—
195	C₂²⋊C₄×C₂₃	—	2	4	no	—
196	C₂²⋊C₄×C₂₃	—	2	4	no	—
197	C₂²⋊C₄×C₂₃	—	2	4	no	—
198	C₂²⋊C₄×C₂₃	—	2	4	no	—
199	C₂²⋊C₄×C₂₃	—	2	4	no	—
200	C₂²⋊C₄×C₂₃	—	2	4	no	—
201	C₂²⋊C₄×C₂₃	—	2	4	no	—
202	C₂²⋊C₄×C₂₃	—	2	4	no	—
203	C₄²×C₂₃	—	2	4	no	—
204	C₄²×C₂₃	—	2	4	no	—
205	C₄²×C₂₃	—	2	4	no	—
206	C₄²×C₂₃	C₂×D₄	1	2	yes	—
207	C₄²×C₂₃	C₂×D₄	1	2	yes	—
208	C₄²×C₂₃	C₂×D₄	1	2	yes	—
209	C₄²×C₂₃	C₂×D₄	1	2	yes	—
210	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
211	C₄²×C₂₃	C₂×D₄	1	2	yes	—
212	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
213	C₄²×C₂₃	C₂⁴	1	2	yes	—
214	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
215	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
216	#60948	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
217	C₂³×C₂₃	—	2	2	no	—
218	C₂³×C₂₃	—	2	4	no	—
219	C₂³×C₂₃	—	4	1	no	—
220	C₂³×C₂₃	—	4	1	no	—
221	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
222	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
223	Q₈×C₂₃	—	2	4	no	—
224	Q₈×C₂₃	—	2	4	no	—
225	Q₈×C₂₃	—	4	4	no	—
226	Q₈×C₂₃	—	4	4	no	—
227	D₄×C₂₃	—	2	4	no	—
228	D₄×C₂₃	—	2	4	no	—
229	D₄×C₂₃	—	4	4	no	—
230	D₄×C₂₃	—	4	8	no	—
231	D₄×C₂₃	—	4	8	no	—
232	D₄×C₂₃	—	4	8	no	—
233	D₄×C₂₃	—	4	4	no	—
234	C₂×C₄×C₂₃	—	2	2	no	—
235	C₂×C₄×C₂₃	—	2	4	no	—
236	C₂×C₄×C₂₃	—	2	4	no	—
237	C₂×C₄×C₂₃	—	2	2	no	—
238	C₂×C₄×C₂₃	—	2	4	no	—
239	C₂×C₄×C₂₃	—	2	1	no	—
240	C₂×C₄×C₂₃	—	2	1	no	—
241	C₂×C₄×C₂₃	—	2	2	no	—
242	C₂×C₄×C₂₃	—	2	2	no	—
243	C₂×C₄×C₂₃	—	2	4	no	—
244	C₂×C₄×C₂₃	—	2	4	no	—
245	C₂×C₄×C₂₃	—	2	4	no	—
246	C₂×C₄×C₂₃	—	4	1	no	—
247	C₂×C₄×C₂₃	—	4	2	no	—
248	C₂×C₄×C₂₃	—	4	2	no	—
249	C₂×C₄×C₂₃	—	4	1	no	—
250	C₂×C₄×C₂₃	—	4	8	no	—
251	C₂×C₄×C₂₃	—	4	8	no	—
252	C₂×C₄×C₂₃	—	4	8	no	—
253	C₂×C₄×C₂₃	#135	1	4	yes	—
254	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
255	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
256	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
257	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
258	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
259	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
260	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
261	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
262	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
263	C₈×C₂₃	—	2	4	no	—
264	C₈×C₂₃	—	2	4	no	—
265	#3444	C₂×C₂₃	1	2	yes	complemented
266	#3249	C₂×C₂₃	1	1	yes	characteristic, complemented
267	#3246	C₂×C₂₃	1	2	yes	complemented
268	#3245	C₂×C₂₃	1	1	yes	characteristic, complemented
269	#3233	C₂×C₂₃	1	4	yes	complemented
270	#3212	C₂×C₂₃	1	4	yes	complemented
271	#3191	C₂×C₂₃	1	4	yes	complemented
272	#3168	C₂×C₂₃	1	4	yes	complemented
273	#3107	C₂×C₂₃	1	4	yes	complemented
274	#3106	C₂×C₂₃	1	4	yes	complemented
275	C₂×#431	C₂×C₂₃	1	1	yes	characteristic, complemented
276	C₂²×C₂₃	—	2	1	no	—
277	C₂²×C₂₃	—	2	1	no	—
278	C₂²×C₂₃	—	2	2	no	—
279	C₂²×C₂₃	—	2	2	no	—
280	C₂²×C₂₃	—	2	2	no	—
281	C₂²×C₂₃	—	4	4	no	—
282	C₂²×C₂₃	—	4	4	no	—
283	C₂²×C₂₃	—	4	4	no	—
284	C₂²×C₂₃	—	4	4	no	—
285	C₂²×C₂₃	C₂×#135	1	2	yes	—
286	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
287	C₄×C₂₃	—	2	2	no	—
288	C₄×C₂₃	—	2	1	no	—
289	C₄×C₂₃	—	2	1	no	—
290	C₄×C₂₃	—	2	1	no	—
291	C₄×C₂₃	—	2	1	no	—
292	C₄×C₂₃	—	2	2	no	—
293	C₄×C₂₃	—	4	4	no	—
294	C₄×C₂₃	—	4	4	no	—
295	C₄×C₂₃	—	4	4	no	—
296	C₄×C₂₃	C₂×#135	1	4	yes	—
297	C₄×C₂₃	#575	1	2	yes	—
298	C₄×C₂₃	#585	1	1	yes	characteristic
299	C₄×C₂₃	#585	1	1	yes	characteristic
300	#533	C₂²×C₂₃	1	2	yes	—
301	#533	C₂²×C₂₃	1	2	yes	—
302	#533	C₂²×C₂₃	1	2	yes	—
303	#532	C₂²×C₂₃	1	2	yes	—
304	#532	C₂²×C₂₃	1	2	yes	—
305	#532	C₂²×C₂₃	1	2	yes	—
306	#529	—	2	2	no	—
307	#529	—	2	2	no	—
308	#529	—	2	2	no	—
309	#529	—	2	2	no	—
310	#529	C₂²×C₂₃	1	4	yes	—
311	#529	C₂²×C₂₃	1	4	yes	—
312	#525	—	2	2	no	—
313	#525	—	2	2	no	—
314	#525	C₂²×C₂₃	1	4	yes	—
315	C₄×#41	—	2	2	no	—
316	C₄×#41	—	2	2	no	—
317	C₄×#41	C₂²×C₂₃	1	4	yes	—
318	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
319	#499	C₂²×C₂₃	1	4	yes	complemented
320	#495	C₂²×C₂₃	1	4	yes	complemented
321	#488	C₂²×C₂₃	1	8	yes	complemented
322	#485	C₂²×C₂₃	1	8	yes	—
323	#482	C₂²×C₂₃	1	8	yes	—
324	#477	C₂²×C₂₃	1	4	yes	complemented
325	#476	C₂²×C₂₃	1	4	yes	complemented
326	#475	C₂²×C₂₃	1	4	yes	complemented
327	#474	C₂²×C₂₃	1	4	yes	complemented
328	#467	C₂²×C₂₃	1	4	yes	—
329	#466	C₂²×C₂₃	1	4	yes	—
330	#465	C₂²×C₂₃	1	8	yes	—
331	#462	C₂²×C₂₃	1	4	yes	complemented
332	#461	C₂²×C₂₃	1	4	yes	complemented
333	#460	C₂²×C₂₃	1	4	yes	complemented
334	#459	C₂²×C₂₃	1	4	yes	complemented
335	#452	C₂²×C₂₃	1	8	yes	—
336	#449	C₂²×C₂₃	1	8	yes	—
337	C₄×Q₁₆	C₂²×C₂₃	1	4	yes	complemented
338	C₄×SD₁₆	C₂²×C₂₃	1	8	yes	complemented
339	C₄×D₈	C₂²×C₂₃	1	4	yes	complemented
340	#431	C₂²×C₂₃	1	4	yes	—
341	#431	C₂²×C₂₃	1	4	yes	—
342	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
343	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
344	C₂×C₂²⋊C₈	C₂²×C₂₃	1	2	yes	—
345	C₂×C₄×C₈	C₂²×C₂₃	1	2	yes	—
346	C₂×C₂₃	—	2	2	no	—
347	C₂×C₂₃	—	4	2	no	—
348	C₂×C₂₃	—	8	4	no	—
349	C₂×C₂₃	#3449	1	1	yes	characteristic
350	C₂×C₂₃	C₂²×#135	1	1	yes	characteristic
351	C₂×C₂₃	C₂×#575	1	1	yes	characteristic
352	C₂×#41	—	2	2	no	—
353	C₂×#41	—	2	2	no	—
354	C₂×#41	C₂³×C₂₃	1	4	yes	—
355	C₂³×C₄	D₄×C₂₃	1	1	yes	characteristic
356	C₂³×C₄	D₄×C₂₃	1	1	yes	characteristic
357	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
358	C₂×Q₁₆	C₂³×C₂₃	1	4	yes	—
359	C₂×SD₁₆	C₂³×C₂₃	1	8	yes	—
360	C₂×D₈	C₂³×C₂₃	1	4	yes	—
361	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
362	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
363	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
364	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
365	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
366	#127	C₂³×C₂₃	1	2	yes	—
367	#126	—	2	4	no	—
368	#126	—	2	4	no	—
369	#125	—	2	2	no	—
370	#125	—	2	2	no	—
371	#125	C₂³×C₂₃	1	4	yes	—
372	#124	—	2	2	no	—
373	#124	—	2	2	no	—
374	#124	C₂³×C₂₃	1	4	yes	—
375	#123	—	2	4	no	—
376	#123	—	2	4	no	—
377	#123	—	2	4	no	—
378	C₂²⋊Q₈	—	2	2	no	—
379	C₂²⋊Q₈	—	2	2	no	—
380	C₂²⋊Q₈	—	2	2	no	—
381	C₂²⋊Q₈	—	2	2	no	—
382	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
383	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
384	#121	—	2	2	no	—
385	#121	—	2	2	no	—
386	#121	—	2	2	no	—
387	#121	—	2	2	no	—
388	#121	C₂³×C₂₃	1	4	yes	—
389	#121	C₂³×C₂₃	1	4	yes	—
390	#120	—	2	4	no	—
391	C₄×Q₈	—	2	2	no	—
392	C₄×Q₈	—	2	2	no	—
393	C₄×Q₈	—	2	2	no	—
394	C₄×Q₈	—	2	2	no	—
395	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
396	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
397	C₄×D₄	—	2	4	no	—
398	C₄×D₄	—	2	4	no	—
399	C₄×D₄	—	2	4	no	—
400	C₄×D₄	—	2	4	no	—
401	C₄×D₄	—	2	4	no	—
402	C₄×D₄	—	2	4	no	—
403	C₄×D₄	—	2	2	no	—
404	C₄×D₄	—	2	2	no	—
405	C₄×D₄	—	2	2	no	—
406	C₄×D₄	—	2	2	no	—
407	C₄×D₄	C₂³×C₂₃	1	4	yes	—
408	C₄×D₄	C₂³×C₂₃	1	4	yes	—
409	#117	—	2	2	no	—
410	#117	—	2	2	no	—
411	#117	—	2	4	no	—
412	#117	—	2	4	no	—
413	#117	—	2	4	no	—
414	#117	C₂³×C₂₃	1	4	yes	—
415	C₂×C₄²	—	2	4	no	—
416	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
417	C₂×C₄²	D₄×C₂₃	1	2	yes	—
418	C₂×C₄²	D₄×C₂₃	1	2	yes	—
419	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
420	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
421	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
422	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
423	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
424	#107	C₂³×C₂₃	1	4	yes	—
425	#107	C₂³×C₂₃	1	4	yes	—
426	#106	C₂³×C₂₃	1	8	yes	—
427	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
428	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
429	#103	C₂³×C₂₃	1	8	yes	—
430	#103	C₂³×C₂₃	1	8	yes	—
431	#102	C₂³×C₂₃	1	8	yes	—
432	#102	C₂³×C₂₃	1	8	yes	—
433	C₂²⋊C₈	C₂³×C₂₃	1	8	yes	—
434	C₄×C₈	C₂³×C₂₃	1	4	yes	—
435	C₄×C₈	C₂³×C₂₃	1	4	yes	—
436	C₂₃	#60948	1	1	yes	characteristic, direct product factor, Sylow
437	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
438	#41	—	4	4	no	—
439	#41	—	4	4	no	—
440	#41	—	4	8	no	—
441	#41	—	4	8	no	—
442	C₂×Q₈	—	2	2	no	—
443	C₂×Q₈	—	2	2	no	—
444	C₂×Q₈	C₂⁴×C₂₃	1	4	yes	—
445	C₂×D₄	—	2	4	no	—
446	C₂×D₄	—	2	4	no	—
447	C₂×D₄	—	2	4	no	—
448	C₂×D₄	—	2	2	no	—
449	C₂×D₄	—	2	2	no	—
450	C₂×D₄	C₂⁴×C₂₃	1	4	yes	—
451	C₂²×C₄	—	2	4	no	—
452	C₂²×C₄	—	2	4	no	—
453	C₂²×C₄	—	2	4	no	—
454	C₂²×C₄	—	2	4	no	—
455	C₂²×C₄	—	4	2	no	—
456	C₂²×C₄	—	4	1	no	—
457	C₂²×C₄	—	4	1	no	—
458	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
459	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
460	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
461	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
462	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
463	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
464	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
465	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
466	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
467	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
468	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
469	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
470	Q₁₆	—	4	4	no	—
471	SD₁₆	—	4	8	no	—
472	D₈	—	4	4	no	—
473	C₂×C₈	—	4	2	no	—
474	C₂×C₈	—	4	2	no	—
475	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
476	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
477	C₄⋊C₄	—	2	2	no	—
478	C₄⋊C₄	—	2	2	no	—
479	C₄⋊C₄	—	2	2	no	—
480	C₄⋊C₄	—	2	2	no	—
481	C₄⋊C₄	—	2	4	no	—
482	C₄⋊C₄	—	2	4	no	—
483	C₄⋊C₄	—	2	4	no	—
484	C₄⋊C₄	—	2	4	no	—
485	C₄⋊C₄	—	2	4	no	—
486	C₄⋊C₄	—	2	4	no	—
487	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
488	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
489	C₂²⋊C₄	—	2	4	no	—
490	C₂²⋊C₄	—	2	4	no	—
491	C₂²⋊C₄	—	2	4	no	—
492	C₂²⋊C₄	—	2	4	no	—
493	C₂²⋊C₄	—	2	4	no	—
494	C₂²⋊C₄	—	2	4	no	—
495	C₂²⋊C₄	—	2	4	no	—
496	C₂²⋊C₄	—	2	4	no	—
497	C₂²⋊C₄	—	2	4	no	—
498	C₄²	—	2	4	no	—
499	C₄²	—	2	4	no	—
500	C₄²	—	2	4	no	—
501	C₄²	C₂×D₄×C₂₃	1	2	yes	—
502	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
503	C₄²	C₂×D₄×C₂₃	1	2	yes	—
504	C₄²	C₂×D₄×C₂₃	1	2	yes	—
505	C₄²	C₂×D₄×C₂₃	1	2	yes	—
506	C₄²	C₂×D₄×C₂₃	1	2	yes	—
507	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
508	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
509	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
510	C₄²	C₂⁴×C₂₃	1	2	yes	—
511	C₂³	—	2	2	no	—
512	C₂³	—	2	4	no	—
513	C₂³	—	4	1	no	—
514	C₂³	—	4	1	no	—
515	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
516	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
517	Q₈	—	2	4	no	—
518	Q₈	—	2	4	no	—
519	Q₈	—	4	4	no	—
520	Q₈	—	4	4	no	—
521	D₄	—	2	4	no	—
522	D₄	—	2	4	no	—
523	D₄	—	4	4	no	—
524	D₄	—	4	8	no	—
525	D₄	—	4	8	no	—
526	D₄	—	4	8	no	—
527	D₄	—	4	4	no	—
528	C₂×C₄	—	2	2	no	—
529	C₂×C₄	—	2	4	no	—
530	C₂×C₄	—	2	4	no	—
531	C₂×C₄	—	2	4	no	—
532	C₂×C₄	—	2	2	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	2	1	no	—
535	C₂×C₄	—	2	2	no	—
536	C₂×C₄	—	2	2	no	—
537	C₂×C₄	—	2	4	no	—
538	C₂×C₄	—	2	4	no	—
539	C₂×C₄	—	2	4	no	—
540	C₂×C₄	—	4	1	no	—
541	C₂×C₄	—	4	2	no	—
542	C₂×C₄	—	4	1	no	—
543	C₂×C₄	—	4	2	no	—
544	C₂×C₄	—	4	8	no	—
545	C₂×C₄	—	4	8	no	—
546	C₂×C₄	—	4	8	no	—
547	C₂×C₄	C₂₃×#135	1	4	yes	—
548	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
549	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
550	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
551	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
552	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
553	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
554	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
555	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
556	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
557	C₈	—	2	4	no	—
558	C₈	—	2	4	no	—
559	C₂²	—	2	1	no	—
560	C₂²	—	2	1	no	—
561	C₂²	—	2	2	no	—
562	C₂²	—	2	2	no	—
563	C₂²	—	2	2	no	—
564	C₂²	—	4	4	no	—
565	C₂²	—	4	4	no	—
566	C₂²	—	4	4	no	—
567	C₂²	—	4	4	no	—
568	C₂²	C₂×C₂₃×#135	1	2	yes	—
569	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
570	C₄	—	2	2	no	—
571	C₄	—	2	1	no	—
572	C₄	—	2	1	no	—
573	C₄	—	2	1	no	—
574	C₄	—	2	2	no	—
575	C₄	—	2	1	no	—
576	C₄	—	4	4	no	—
577	C₄	—	4	4	no	—
578	C₄	—	4	4	no	—
579	C₄	C₂×C₂₃×#135	1	4	yes	—
580	C₄	C₂₃×#575	1	2	yes	—
581	C₄	C₂₃×#585	1	1	yes	characteristic
582	C₄	C₂₃×#585	1	1	yes	characteristic
583	C₂	—	2	2	no	—
584	C₂	—	4	2	no	—
585	C₂	—	8	4	no	—
586	C₂	C₂₃×#3449	1	1	yes	characteristic
587	C₂	C₂²×C₂₃×#135	1	1	yes	characteristic
588	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
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
1. C₂₃×#3444	C₂	semidirect
2. C₂₃×#3249	C₂	semidirect
3. C₂₃×#3246	C₂	semidirect
4. C₂₃×#3245	C₂	semidirect
5. C₂₃×#3233	C₂	semidirect
6. C₂₃×#3212	C₂	semidirect
7. C₂₃×#3191	C₂	semidirect
8. C₂₃×#3168	C₂	semidirect
9. C₂₃×#3107	C₂	semidirect
10. C₂₃×#3106	C₂	semidirect
11. C₂×C₂₃×#431	C₂	semidirect
31. C₂₃×#499	C₂²	semidirect
32. C₂₃×#495	C₂²	semidirect
33. C₂₃×#488	C₂²	semidirect
36. C₂₃×#477	C₂²	semidirect
37. C₂₃×#476	C₂²	semidirect
38. C₂₃×#475	C₂²	semidirect
39. C₂₃×#474	C₂²	semidirect
43. C₂₃×#462	C₂²	semidirect
44. C₂₃×#461	C₂²	semidirect
45. C₂₃×#460	C₂²	semidirect
46. C₂₃×#459	C₂²	semidirect
49. C₄×Q₁₆×C₂₃	C₂²	semidirect
50. C₄×SD₁₆×C₂₃	C₂²	semidirect
51. C₄×D₈×C₂₃	C₂²	semidirect
216. #60948	C₂₃	direct (N × H)
265. #3444	C₂×C₂₃	semidirect
266. #3249	C₂×C₂₃	semidirect
267. #3246	C₂×C₂₃	semidirect
268. #3245	C₂×C₂₃	semidirect
269. #3233	C₂×C₂₃	semidirect
270. #3212	C₂×C₂₃	semidirect
271. #3191	C₂×C₂₃	semidirect
272. #3168	C₂×C₂₃	semidirect
273. #3107	C₂×C₂₃	semidirect
274. #3106	C₂×C₂₃	semidirect
275. C₂×#431	C₂×C₂₃	semidirect
319. #499	C₂²×C₂₃	semidirect
320. #495	C₂²×C₂₃	semidirect
321. #488	C₂²×C₂₃	semidirect
324. #477	C₂²×C₂₃	semidirect
325. #476	C₂²×C₂₃	semidirect
326. #475	C₂²×C₂₃	semidirect
327. #474	C₂²×C₂₃	semidirect
331. #462	C₂²×C₂₃	semidirect
332. #461	C₂²×C₂₃	semidirect
333. #460	C₂²×C₂₃	semidirect
334. #459	C₂²×C₂₃	semidirect
337. C₄×Q₁₆	C₂²×C₂₃	semidirect
338. C₄×SD₁₆	C₂²×C₂₃	semidirect
339. C₄×D₈	C₂²×C₂₃	semidirect
436. C₂₃	#60948	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂₃×#3444	2
C₂₃×#3249	2
C₂₃×#3246	2
C₂₃×#3245	2
C₂₃×#3233	2
C₂₃×#3212	2
C₂₃×#3191	2
C₂₃×#3168	2
C₂₃×#3107	2
C₂₃×#3106	2
C₂×C₂₃×#431	2
#60948	23

Subgroups — C23×#60948 #19208574

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#60948 #19208574