Subgroups — C₂₃×#8444 #19156070

Order 5888.

1116 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#550	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#1957	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#1803	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#1802	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₂₃×#331	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₂₃×Q₈⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₂₃×D₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#41×C₂₃	—	2	1	no	—
9	C₂₃×#550	—	2	2	no	—
10	C₂₃×#550	—	2	2	no	—
11	C₂₃×#550	—	2	2	no	—
12	C₂₃×#550	C₄	1	4	yes	complemented
13	C₂×C₂₃×#127	—	2	1	no	—
14	C₂×C₂₃×#127	C₂²	1	1	yes	characteristic
15	C₂×C₂₃×#121	—	2	2	no	—
16	C₂×C₂₃×#121	—	2	1	no	—
17	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
18	C₂×C₄×D₄×C₂₃	—	2	1	no	—
19	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
20	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₂₃×#103	—	2	1	no	—
23	C₂×C₂₃×#102	—	2	2	no	—
24	C₂×C₂₃×#102	—	2	1	no	—
25	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
26	C₂₃×#384	C₂²	1	1	yes	characteristic
27	C₂₃×#340	—	2	1	no	—
28	C₂₃×#340	—	2	1	no	—
29	C₂₃×#331	—	2	2	no	—
30	C₂₃×Q₈⋊C₈	—	2	2	no	—
31	C₂₃×D₄⋊C₈	—	2	2	no	—
32	C₂×#41×C₂₃	—	2	4	no	—
33	C₂×#41×C₂₃	—	2	4	no	—
34	C₂×#41×C₂₃	—	4	2	no	—
35	C₂×#41×C₂₃	—	4	2	no	—
36	C₂×#41×C₂₃	—	4	2	no	—
37	C₂×#41×C₂₃	—	4	2	no	—
38	C₂²×Q₈×C₂₃	D₄	1	1	yes	characteristic
39	C₂²×D₄×C₂₃	—	2	2	no	—
40	C₂²×D₄×C₂₃	—	2	2	no	—
41	C₂²×D₄×C₂₃	—	2	1	no	—
42	C₂²×D₄×C₂₃	—	2	1	no	—
43	C₂²×D₄×C₂₃	D₄	1	1	yes	characteristic
44	C₂²×D₄×C₂₃	D₄	1	2	yes	—
45	C₂³×C₄×C₂₃	—	2	2	no	—
46	C₂³×C₄×C₂₃	—	2	1	no	—
47	C₂²×C₈×C₂₃	—	2	1	no	—
48	C₂²×C₈×C₂₃	—	2	1	no	—
49	C₂²×C₈×C₂₃	—	2	1	no	—
50	C₂₃×#127	—	2	4	no	—
51	C₂₃×#127	—	2	4	no	—
52	C₂₃×#127	—	2	1	no	—
53	C₂₃×#127	—	2	1	no	—
54	C₂₃×#127	C₂×C₄	1	2	yes	—
55	C₂₃×#127	D₄	1	2	yes	—
56	C₂₃×#121	—	2	4	no	—
57	C₂₃×#121	—	2	8	no	—
58	C₂₃×#121	—	2	8	no	—
59	C₂₃×#121	—	2	4	no	—
60	C₄×Q₈×C₂₃	—	2	1	no	—
61	C₄×Q₈×C₂₃	—	2	1	no	—
62	C₄×Q₈×C₂₃	C₂×C₄	1	2	yes	—
63	C₄×Q₈×C₂₃	D₄	1	2	yes	—
64	C₄×D₄×C₂₃	—	2	4	no	—
65	C₄×D₄×C₂₃	—	2	4	no	—
66	C₄×D₄×C₂₃	—	2	1	no	—
67	C₄×D₄×C₂₃	—	2	1	no	—
68	C₄×D₄×C₂₃	C₂×C₄	1	2	yes	—
69	C₄×D₄×C₂₃	D₄	1	2	yes	—
70	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
71	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
72	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
73	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
74	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
75	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
76	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
77	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
78	C₂×C₄²×C₂₃	—	2	1	no	—
79	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
80	C₂₃×C₄⋊C₈	—	2	1	no	—
81	C₂₃×C₄⋊C₈	—	2	1	no	—
82	C₂₃×C₄⋊C₈	—	2	1	no	—
83	C₂₃×C₄⋊C₈	—	2	1	no	—
84	C₂₃×#103	—	4	2	no	—
85	C₂₃×#102	—	4	4	no	—
86	C₂₃×#102	—	4	2	no	—
87	C₄×C₈×C₂₃	—	2	1	no	—
88	C₄×C₈×C₂₃	—	2	1	no	—
89	C₂⁴×C₂₃	—	2	1	no	—
90	C₂⁴×C₂₃	—	2	2	no	—
91	#41×C₂₃	—	4	8	no	—
92	#41×C₂₃	—	4	8	no	—
93	#41×C₂₃	—	4	8	no	—
94	#41×C₂₃	—	4	8	no	—
95	C₂×Q₈×C₂₃	—	2	1	no	—
96	C₂×Q₈×C₂₃	—	2	1	no	—
97	C₂×Q₈×C₂₃	—	2	1	no	—
98	C₂×Q₈×C₂₃	C₂²⋊C₄	1	2	yes	—
99	C₂×Q₈×C₂₃	D₈	1	2	yes	—
100	C₂×Q₈×C₂₃	SD₁₆	1	2	yes	—
101	C₂×D₄×C₂₃	—	2	8	no	—
102	C₂×D₄×C₂₃	—	2	8	no	—
103	C₂×D₄×C₂₃	—	2	2	no	—
104	C₂×D₄×C₂₃	—	2	2	no	—
105	C₂×D₄×C₂₃	—	2	1	no	—
106	C₂×D₄×C₂₃	—	2	2	no	—
107	C₂×D₄×C₂₃	—	2	2	no	—
108	C₂×D₄×C₂₃	—	2	2	no	—
109	C₂×D₄×C₂₃	—	2	1	no	—
110	C₂×D₄×C₂₃	—	2	1	no	—
111	C₂×D₄×C₂₃	—	2	1	no	—
112	C₂×D₄×C₂₃	—	2	1	no	—
113	C₂×D₄×C₂₃	—	4	4	no	—
114	C₂×D₄×C₂₃	—	4	4	no	—
115	C₂×D₄×C₂₃	—	4	2	no	—
116	C₂×D₄×C₂₃	—	4	2	no	—
117	C₂×D₄×C₂₃	—	4	1	no	—
118	C₂×D₄×C₂₃	—	4	1	no	—
119	C₂×D₄×C₂₃	—	4	1	no	—
120	C₂×D₄×C₂₃	—	4	1	no	—
121	C₂×D₄×C₂₃	—	4	1	no	—
122	C₂×D₄×C₂₃	—	4	1	no	—
123	C₂×D₄×C₂₃	—	4	1	no	—
124	C₂×D₄×C₂₃	—	4	1	no	—
125	C₂×D₄×C₂₃	—	8	2	no	—
126	C₂×D₄×C₂₃	—	8	2	no	—
127	C₂×D₄×C₂₃	C₂²⋊C₄	1	2	yes	—
128	C₂×D₄×C₂₃	C₂²⋊C₄	1	4	yes	—
129	C₂²×C₄×C₂₃	—	2	1	no	—
130	C₂²×C₄×C₂₃	—	2	8	no	—
131	C₂²×C₄×C₂₃	—	2	1	no	—
132	C₂²×C₄×C₂₃	—	2	1	no	—
133	C₂²×C₄×C₂₃	—	2	2	no	—
134	C₂²×C₄×C₂₃	—	2	2	no	—
135	C₂²×C₄×C₂₃	—	4	4	no	—
136	C₂²×C₄×C₂₃	—	4	4	no	—
137	C₂²×C₄×C₂₃	—	4	1	no	—
138	C₂²×C₄×C₂₃	—	4	1	no	—
139	C₂²×C₄×C₂₃	—	4	1	no	—
140	C₂²×C₄×C₂₃	—	4	1	no	—
141	C₂²×C₄×C₂₃	—	4	1	no	—
142	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
143	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
145	C₂×C₈×C₂₃	—	2	2	no	—
146	C₂×C₈×C₂₃	—	4	1	no	—
147	C₂×C₈×C₂₃	—	4	1	no	—
148	C₂×C₈×C₂₃	—	4	1	no	—
149	C₂×C₈×C₂₃	—	4	1	no	—
150	C₂×C₈×C₂₃	—	4	1	no	—
151	C₂×C₈×C₂₃	—	4	1	no	—
152	C₂×C₈×C₂₃	—	4	1	no	—
153	C₂×C₈×C₂₃	—	4	1	no	—
154	C₄⋊C₄×C₂₃	—	2	2	no	—
155	C₄⋊C₄×C₂₃	—	2	2	no	—
156	C₄⋊C₄×C₂₃	—	2	1	no	—
157	C₄⋊C₄×C₂₃	—	2	1	no	—
158	C₄⋊C₄×C₂₃	—	4	2	no	—
159	C₄⋊C₄×C₂₃	—	4	1	no	—
160	C₄⋊C₄×C₂₃	—	4	1	no	—
161	C₄⋊C₄×C₂₃	—	4	1	no	—
162	C₄⋊C₄×C₂₃	—	4	1	no	—
163	C₄⋊C₄×C₂₃	C₂²⋊C₄	1	2	yes	—
164	C₄⋊C₄×C₂₃	C₂²⋊C₄	1	2	yes	—
165	C₂²⋊C₄×C₂₃	—	2	8	no	—
166	C₂²⋊C₄×C₂₃	—	2	2	no	—
167	C₂²⋊C₄×C₂₃	—	2	2	no	—
168	C₄²×C₂₃	—	2	2	no	—
169	C₄²×C₂₃	—	2	2	no	—
170	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
171	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
172	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
173	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
174	#8444	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
175	C₂³×C₂₃	—	2	4	no	—
176	C₂³×C₂₃	—	2	2	no	—
177	C₂³×C₂₃	—	4	2	no	—
178	C₂³×C₂₃	—	4	1	no	—
179	C₂³×C₂₃	—	4	1	no	—
180	C₂³×C₂₃	—	4	2	no	—
181	C₂³×C₂₃	—	4	2	no	—
182	C₂³×C₂₃	—	4	1	no	—
183	C₂³×C₂₃	—	4	1	no	—
184	C₂³×C₂₃	—	4	2	no	—
185	C₂³×C₂₃	—	4	2	no	—
186	C₂³×C₂₃	—	4	1	no	—
187	C₂³×C₂₃	—	4	2	no	—
188	C₂³×C₂₃	—	4	1	no	—
189	C₂³×C₂₃	#120	1	1	yes	characteristic
190	Q₈×C₂₃	—	2	2	no	—
191	Q₈×C₂₃	—	2	2	no	—
192	Q₈×C₂₃	—	2	2	no	—
193	Q₈×C₂₃	#102	1	4	yes	complemented
194	D₄×C₂₃	—	2	2	no	—
195	D₄×C₂₃	—	2	2	no	—
196	D₄×C₂₃	—	4	4	no	—
197	D₄×C₂₃	—	4	16	no	—
198	D₄×C₂₃	—	4	2	no	—
199	D₄×C₂₃	—	4	2	no	—
200	D₄×C₂₃	—	4	2	no	—
201	D₄×C₂₃	—	4	2	no	—
202	D₄×C₂₃	—	4	2	no	—
203	D₄×C₂₃	—	4	1	no	—
204	D₄×C₂₃	—	4	2	no	—
205	D₄×C₂₃	—	4	2	no	—
206	D₄×C₂₃	—	4	1	no	—
207	D₄×C₂₃	—	4	2	no	—
208	D₄×C₂₃	—	8	2	no	—
209	D₄×C₂₃	—	8	8	no	—
210	C₂×C₄×C₂₃	—	2	2	no	—
211	C₂×C₄×C₂₃	—	2	2	no	—
212	C₂×C₄×C₂₃	—	2	2	no	—
213	C₂×C₄×C₂₃	—	2	1	no	—
214	C₂×C₄×C₂₃	—	2	1	no	—
215	C₂×C₄×C₂₃	—	2	2	no	—
216	C₂×C₄×C₂₃	—	2	2	no	—
217	C₂×C₄×C₂₃	—	4	16	no	—
218	C₂×C₄×C₂₃	—	4	1	no	—
219	C₂×C₄×C₂₃	—	4	1	no	—
220	C₂×C₄×C₂₃	—	4	1	no	—
221	C₂×C₄×C₂₃	—	4	1	no	—
222	C₂×C₄×C₂₃	—	4	2	no	—
223	C₂×C₄×C₂₃	—	4	2	no	—
224	C₂×C₄×C₂₃	—	4	2	no	—
225	C₂×C₄×C₂₃	—	4	2	no	—
226	C₂×C₄×C₂₃	—	8	1	no	—
227	C₂×C₄×C₂₃	—	8	1	no	—
228	C₂×C₄×C₂₃	—	8	1	no	—
229	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
230	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
231	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
232	C₂×C₄×C₂₃	#120	1	1	yes	characteristic
233	C₂×C₄×C₂₃	#120	1	1	yes	characteristic
234	C₂×C₄×C₂₃	#120	1	1	yes	characteristic
235	C₂×C₄×C₂₃	C₂×D₈	1	1	yes	characteristic
236	C₂×C₄×C₂₃	C₂×SD₁₆	1	1	yes	characteristic
237	C₂×C₄×C₂₃	#135	1	1	yes	characteristic
238	C₂×C₄×C₂₃	#135	1	1	yes	characteristic
239	C₂×C₄×C₂₃	AGL(1,ℤ/8)	1	1	yes	characteristic
240	C₂×C₄×C₂₃	AGL(1,ℤ/8)	1	1	yes	characteristic
241	C₂×C₄×C₂₃	AGL(1,ℤ/8)	1	1	yes	characteristic
242	C₂×C₄×C₂₃	#137	1	1	yes	characteristic
243	C₈×C₂₃	—	4	2	no	—
244	C₈×C₂₃	—	8	1	no	—
245	C₈×C₂₃	—	8	1	no	—
246	C₂×#550	C₂×C₂₃	1	1	yes	characteristic
247	#1957	C₂×C₂₃	1	1	yes	characteristic, complemented
248	#1803	C₂×C₂₃	1	1	yes	characteristic, complemented
249	#1802	C₂×C₂₃	1	1	yes	characteristic, complemented
250	C₂×#331	C₂×C₂₃	1	1	yes	characteristic, complemented
251	C₂×Q₈⋊C₈	C₂×C₂₃	1	1	yes	characteristic, complemented
252	C₂×D₄⋊C₈	C₂×C₂₃	1	1	yes	characteristic, complemented
253	C₂²×C₂₃	—	4	4	no	—
254	C₂²×C₂₃	—	4	2	no	—
255	C₂²×C₂₃	—	4	4	no	—
256	C₂²×C₂₃	—	4	2	no	—
257	C₂²×C₂₃	—	4	2	no	—
258	C₂²×C₂₃	—	4	4	no	—
259	C₂²×C₂₃	—	8	1	no	—
260	C₂²×C₂₃	—	8	2	no	—
261	C₂²×C₂₃	—	8	1	no	—
262	C₂²×C₂₃	—	8	2	no	—
263	C₂²×C₂₃	—	8	1	no	—
264	C₂²×C₂₃	—	8	2	no	—
265	C₂²×C₂₃	—	8	1	no	—
266	C₂²×C₂₃	—	8	2	no	—
267	C₂²×C₂₃	#379	1	1	yes	characteristic
268	C₂²×C₂₃	#447	1	1	yes	characteristic
269	C₂²×C₂₃	#449	1	1	yes	characteristic
270	C₂²×C₂₃	#450	1	1	yes	characteristic
271	C₂²×C₂₃	#452	1	1	yes	characteristic
272	C₂²×C₂₃	#453	1	1	yes	characteristic
273	C₂²×C₂₃	#455	1	1	yes	characteristic
274	C₄×C₂₃	—	2	1	no	—
275	C₄×C₂₃	—	2	1	no	—
276	C₄×C₂₃	—	2	4	no	—
277	C₄×C₂₃	—	4	2	no	—
278	C₄×C₂₃	—	4	2	no	—
279	C₄×C₂₃	—	16	1	no	—
280	C₄×C₂₃	C₂×#102	1	1	yes	characteristic
281	C₄×C₂₃	#416	1	1	yes	characteristic
282	C₄×C₂₃	#417	1	1	yes	characteristic
283	C₄×C₂₃	#418	1	1	yes	characteristic
284	C₄×C₂₃	#447	1	1	yes	characteristic
285	C₄×C₂₃	#449	1	1	yes	characteristic
286	C₄×C₂₃	#450	1	1	yes	characteristic
287	C₄×C₂₃	#452	1	1	yes	characteristic
288	C₂²×#41	—	2	1	no	—
289	#550	—	2	2	no	—
290	#550	—	2	2	no	—
291	#550	—	2	2	no	—
292	#550	C₄×C₂₃	1	4	yes	complemented
293	C₂×#127	—	2	1	no	—
294	C₂×#127	C₂²×C₂₃	1	1	yes	characteristic
295	C₂×#121	—	2	2	no	—
296	C₂×#121	—	2	1	no	—
297	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
298	C₂×C₄×D₄	—	2	1	no	—
299	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
300	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
301	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
302	C₂×#103	—	2	1	no	—
303	C₂×#102	—	2	1	no	—
304	C₂×#102	—	2	2	no	—
305	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
306	#384	C₂²×C₂₃	1	1	yes	characteristic
307	#340	—	2	1	no	—
308	#340	—	2	1	no	—
309	#331	—	2	2	no	—
310	Q₈⋊C₈	—	2	2	no	—
311	D₄⋊C₈	—	2	2	no	—
312	C₂×C₂₃	—	8	4	no	—
313	C₂×C₂₃	—	8	2	no	—
314	C₂×C₂₃	#1621	1	1	yes	characteristic
315	C₂×C₂₃	#1631	1	1	yes	characteristic
316	C₂×C₂₃	#1641	1	1	yes	characteristic
317	C₂×C₂₃	#1642	1	1	yes	characteristic
318	C₂×C₂₃	#1786	1	1	yes	characteristic
319	C₂×C₂₃	#1788	1	1	yes	characteristic
320	C₂×C₂₃	#1792	1	1	yes	characteristic
321	C₂×#41	—	2	4	no	—
322	C₂×#41	—	2	4	no	—
323	C₂×#41	—	4	2	no	—
324	C₂×#41	—	4	2	no	—
325	C₂×#41	—	4	2	no	—
326	C₂×#41	—	4	2	no	—
327	C₂²×Q₈	D₄×C₂₃	1	1	yes	characteristic
328	C₂²×D₄	—	2	2	no	—
329	C₂²×D₄	—	2	2	no	—
330	C₂²×D₄	—	2	1	no	—
331	C₂²×D₄	—	2	1	no	—
332	C₂²×D₄	D₄×C₂₃	1	1	yes	characteristic
333	C₂²×D₄	D₄×C₂₃	1	2	yes	—
334	C₂³×C₄	—	2	2	no	—
335	C₂³×C₄	—	2	1	no	—
336	C₂²×C₈	—	2	1	no	—
337	C₂²×C₈	—	2	1	no	—
338	C₂²×C₈	—	2	1	no	—
339	#127	—	2	4	no	—
340	#127	—	2	4	no	—
341	#127	—	2	1	no	—
342	#127	—	2	1	no	—
343	#127	C₂×C₄×C₂₃	1	2	yes	—
344	#127	D₄×C₂₃	1	2	yes	—
345	#121	—	2	4	no	—
346	#121	—	2	8	no	—
347	#121	—	2	8	no	—
348	#121	—	2	4	no	—
349	C₄×Q₈	—	2	1	no	—
350	C₄×Q₈	—	2	1	no	—
351	C₄×Q₈	C₂×C₄×C₂₃	1	2	yes	—
352	C₄×Q₈	D₄×C₂₃	1	2	yes	—
353	C₄×D₄	—	2	4	no	—
354	C₄×D₄	—	2	4	no	—
355	C₄×D₄	—	2	1	no	—
356	C₄×D₄	—	2	1	no	—
357	C₄×D₄	C₂×C₄×C₂₃	1	2	yes	—
358	C₄×D₄	D₄×C₂₃	1	2	yes	—
359	C₂×C₄⋊C₄	—	2	1	no	—
360	C₂×C₄⋊C₄	—	2	1	no	—
361	C₂×C₄⋊C₄	—	2	1	no	—
362	C₂×C₄⋊C₄	—	2	1	no	—
363	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
364	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
365	C₂×C₂²⋊C₄	—	2	2	no	—
366	C₂×C₂²⋊C₄	—	2	1	no	—
367	C₂×C₄²	—	2	1	no	—
368	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
369	C₄⋊C₈	—	2	1	no	—
370	C₄⋊C₈	—	2	1	no	—
371	C₄⋊C₈	—	2	1	no	—
372	C₄⋊C₈	—	2	1	no	—
373	#103	—	4	2	no	—
374	#102	—	4	4	no	—
375	#102	—	4	2	no	—
376	C₄×C₈	—	2	1	no	—
377	C₄×C₈	—	2	1	no	—
378	C₂₃	#8444	1	1	yes	characteristic, direct product factor, Sylow
379	C₂⁴	—	2	1	no	—
380	C₂⁴	—	2	2	no	—
381	#41	—	4	8	no	—
382	#41	—	4	8	no	—
383	#41	—	4	8	no	—
384	#41	—	4	8	no	—
385	C₂×Q₈	—	2	1	no	—
386	C₂×Q₈	—	2	1	no	—
387	C₂×Q₈	—	2	1	no	—
388	C₂×Q₈	C₂²⋊C₄×C₂₃	1	2	yes	—
389	C₂×Q₈	D₈×C₂₃	1	2	yes	—
390	C₂×Q₈	SD₁₆×C₂₃	1	2	yes	—
391	C₂×D₄	—	2	8	no	—
392	C₂×D₄	—	2	8	no	—
393	C₂×D₄	—	2	2	no	—
394	C₂×D₄	—	2	2	no	—
395	C₂×D₄	—	2	1	no	—
396	C₂×D₄	—	2	2	no	—
397	C₂×D₄	—	2	2	no	—
398	C₂×D₄	—	2	2	no	—
399	C₂×D₄	—	2	1	no	—
400	C₂×D₄	—	2	1	no	—
401	C₂×D₄	—	2	1	no	—
402	C₂×D₄	—	2	1	no	—
403	C₂×D₄	—	4	4	no	—
404	C₂×D₄	—	4	4	no	—
405	C₂×D₄	—	4	2	no	—
406	C₂×D₄	—	4	2	no	—
407	C₂×D₄	—	4	1	no	—
408	C₂×D₄	—	4	1	no	—
409	C₂×D₄	—	4	1	no	—
410	C₂×D₄	—	4	1	no	—
411	C₂×D₄	—	4	1	no	—
412	C₂×D₄	—	4	1	no	—
413	C₂×D₄	—	4	1	no	—
414	C₂×D₄	—	4	1	no	—
415	C₂×D₄	—	8	2	no	—
416	C₂×D₄	—	8	2	no	—
417	C₂×D₄	C₂²⋊C₄×C₂₃	1	2	yes	—
418	C₂×D₄	C₂²⋊C₄×C₂₃	1	4	yes	—
419	C₂²×C₄	—	2	1	no	—
420	C₂²×C₄	—	2	8	no	—
421	C₂²×C₄	—	2	1	no	—
422	C₂²×C₄	—	2	1	no	—
423	C₂²×C₄	—	2	2	no	—
424	C₂²×C₄	—	2	2	no	—
425	C₂²×C₄	—	4	4	no	—
426	C₂²×C₄	—	4	4	no	—
427	C₂²×C₄	—	4	1	no	—
428	C₂²×C₄	—	4	1	no	—
429	C₂²×C₄	—	4	1	no	—
430	C₂²×C₄	—	4	1	no	—
431	C₂²×C₄	—	4	1	no	—
432	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
433	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
434	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
435	C₂×C₈	—	2	2	no	—
436	C₂×C₈	—	4	1	no	—
437	C₂×C₈	—	4	1	no	—
438	C₂×C₈	—	4	1	no	—
439	C₂×C₈	—	4	1	no	—
440	C₂×C₈	—	4	1	no	—
441	C₂×C₈	—	4	1	no	—
442	C₂×C₈	—	4	1	no	—
443	C₂×C₈	—	4	1	no	—
444	C₄⋊C₄	—	2	2	no	—
445	C₄⋊C₄	—	2	2	no	—
446	C₄⋊C₄	—	2	1	no	—
447	C₄⋊C₄	—	2	1	no	—
448	C₄⋊C₄	—	4	2	no	—
449	C₄⋊C₄	—	4	1	no	—
450	C₄⋊C₄	—	4	1	no	—
451	C₄⋊C₄	—	4	1	no	—
452	C₄⋊C₄	—	4	1	no	—
453	C₄⋊C₄	C₂²⋊C₄×C₂₃	1	2	yes	—
454	C₄⋊C₄	C₂²⋊C₄×C₂₃	1	2	yes	—
455	C₂²⋊C₄	—	2	8	no	—
456	C₂²⋊C₄	—	2	2	no	—
457	C₂²⋊C₄	—	2	2	no	—
458	C₄²	—	2	2	no	—
459	C₄²	—	2	2	no	—
460	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
461	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
462	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
463	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
464	C₂³	—	2	2	no	—
465	C₂³	—	2	4	no	—
466	C₂³	—	4	2	no	—
467	C₂³	—	4	1	no	—
468	C₂³	—	4	1	no	—
469	C₂³	—	4	2	no	—
470	C₂³	—	4	2	no	—
471	C₂³	—	4	1	no	—
472	C₂³	—	4	1	no	—
473	C₂³	—	4	2	no	—
474	C₂³	—	4	2	no	—
475	C₂³	—	4	1	no	—
476	C₂³	—	4	2	no	—
477	C₂³	—	4	1	no	—
478	C₂³	C₂₃×#120	1	1	yes	characteristic
479	Q₈	—	2	2	no	—
480	Q₈	—	2	2	no	—
481	Q₈	—	2	2	no	—
482	Q₈	C₂₃×#102	1	4	yes	complemented
483	D₄	—	2	2	no	—
484	D₄	—	2	2	no	—
485	D₄	—	4	4	no	—
486	D₄	—	4	16	no	—
487	D₄	—	4	2	no	—
488	D₄	—	4	2	no	—
489	D₄	—	4	2	no	—
490	D₄	—	4	2	no	—
491	D₄	—	4	2	no	—
492	D₄	—	4	1	no	—
493	D₄	—	4	2	no	—
494	D₄	—	4	2	no	—
495	D₄	—	4	1	no	—
496	D₄	—	4	2	no	—
497	D₄	—	8	2	no	—
498	D₄	—	8	8	no	—
499	C₂×C₄	—	2	2	no	—
500	C₂×C₄	—	2	2	no	—
501	C₂×C₄	—	2	2	no	—
502	C₂×C₄	—	2	1	no	—
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	2	2	no	—
505	C₂×C₄	—	2	2	no	—
506	C₂×C₄	—	4	16	no	—
507	C₂×C₄	—	4	1	no	—
508	C₂×C₄	—	4	1	no	—
509	C₂×C₄	—	4	1	no	—
510	C₂×C₄	—	4	1	no	—
511	C₂×C₄	—	4	2	no	—
512	C₂×C₄	—	4	2	no	—
513	C₂×C₄	—	4	2	no	—
514	C₂×C₄	—	4	2	no	—
515	C₂×C₄	—	8	1	no	—
516	C₂×C₄	—	8	1	no	—
517	C₂×C₄	—	8	1	no	—
518	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
519	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
520	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
521	C₂×C₄	C₂₃×#120	1	1	yes	characteristic
522	C₂×C₄	C₂₃×#120	1	1	yes	characteristic
523	C₂×C₄	C₂₃×#120	1	1	yes	characteristic
524	C₂×C₄	C₂×D₈×C₂₃	1	1	yes	characteristic
525	C₂×C₄	C₂×SD₁₆×C₂₃	1	1	yes	characteristic
526	C₂×C₄	C₂₃×#135	1	1	yes	characteristic
527	C₂×C₄	C₂₃×#135	1	1	yes	characteristic
528	C₂×C₄	C₂₃×AGL(1,ℤ/8)	1	1	yes	characteristic
529	C₂×C₄	C₂₃×AGL(1,ℤ/8)	1	1	yes	characteristic
530	C₂×C₄	C₂₃×AGL(1,ℤ/8)	1	1	yes	characteristic
531	C₂×C₄	C₂₃×#137	1	1	yes	characteristic
532	C₈	—	4	2	no	—
533	C₈	—	8	1	no	—
534	C₈	—	8	1	no	—
535	C₂²	—	4	4	no	—
536	C₂²	—	4	2	no	—
537	C₂²	—	4	2	no	—
538	C₂²	—	4	4	no	—
539	C₂²	—	4	4	no	—
540	C₂²	—	4	2	no	—
541	C₂²	—	8	1	no	—
542	C₂²	—	8	2	no	—
543	C₂²	—	8	1	no	—
544	C₂²	—	8	2	no	—
545	C₂²	—	8	1	no	—
546	C₂²	—	8	2	no	—
547	C₂²	—	8	1	no	—
548	C₂²	—	8	2	no	—
549	C₂²	C₂₃×#379	1	1	yes	characteristic
550	C₂²	C₂₃×#447	1	1	yes	characteristic
551	C₂²	C₂₃×#449	1	1	yes	characteristic
552	C₂²	C₂₃×#450	1	1	yes	characteristic
553	C₂²	C₂₃×#452	1	1	yes	characteristic
554	C₂²	C₂₃×#453	1	1	yes	characteristic
555	C₂²	C₂₃×#455	1	1	yes	characteristic
556	C₄	—	2	4	no	—
557	C₄	—	2	1	no	—
558	C₄	—	2	1	no	—
559	C₄	—	4	2	no	—
560	C₄	—	4	2	no	—
561	C₄	—	16	1	no	—
562	C₄	C₂×C₂₃×#102	1	1	yes	characteristic
563	C₄	C₂₃×#416	1	1	yes	characteristic
564	C₄	C₂₃×#417	1	1	yes	characteristic
565	C₄	C₂₃×#418	1	1	yes	characteristic
566	C₄	C₂₃×#447	1	1	yes	characteristic
567	C₄	C₂₃×#449	1	1	yes	characteristic
568	C₄	C₂₃×#450	1	1	yes	characteristic
569	C₄	C₂₃×#452	1	1	yes	characteristic
570	C₂	—	8	2	no	—
571	C₂	—	8	4	no	—
572	C₂	C₂₃×#1621	1	1	yes	characteristic
573	C₂	C₂₃×#1631	1	1	yes	characteristic
574	C₂	C₂₃×#1641	1	1	yes	characteristic
575	C₂	C₂₃×#1642	1	1	yes	characteristic
576	C₂	C₂₃×#1786	1	1	yes	characteristic
577	C₂	C₂₃×#1788	1	1	yes	characteristic
578	C₂	C₂₃×#1792	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₃	#120
commutator	C₄²	C₂²×C₄×C₂₃
Frattini, cosocle	C₂×C₄²	C₂³×C₂₃
prime radical	C₂×C₂₃×#550	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₂₃ ◁ C₂×C₄²×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂₃×#1957	C₂	semidirect
3. C₂₃×#1803	C₂	semidirect
4. C₂₃×#1802	C₂	semidirect
5. C₂×C₂₃×#331	C₂	semidirect
6. C₂×C₂₃×Q₈⋊C₈	C₂	semidirect
7. C₂×C₂₃×D₄⋊C₈	C₂	semidirect
12. C₂₃×#550	C₄	semidirect
174. #8444	C₂₃	direct (N × H)
193. Q₈×C₂₃	#102	semidirect
247. #1957	C₂×C₂₃	semidirect
248. #1803	C₂×C₂₃	semidirect
249. #1802	C₂×C₂₃	semidirect
250. C₂×#331	C₂×C₂₃	semidirect
251. C₂×Q₈⋊C₈	C₂×C₂₃	semidirect
252. C₂×D₄⋊C₈	C₂×C₂₃	semidirect
292. #550	C₄×C₂₃	semidirect
378. C₂₃	#8444	direct (N × H)
482. Q₈	C₂₃×#102	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₂₃×#550	2
C₂₃×#1957	2
C₂₃×#1803	2
C₂₃×#1802	2
C₂×C₂₃×#331	2
C₂×C₂₃×Q₈⋊C₈	2
C₂×C₂₃×D₄⋊C₈	2
#8444	23

Subgroups — C23×#8444 #19156070

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#8444 #19156070