Subgroups — C₂₃×#11144 #19158770

Order 5888.

1002 conjugacy classes of subgroups.

The subgroup lattice has 634 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#428	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₃×#418	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₂₃×#102	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₂₃×#100	C₂	1	1	yes	maximal, characteristic
5	C₂×C₂₃×#343	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₂₃×#341	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#1729	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂³×D₄×C₂₃	C₂²	1	1	yes	characteristic
9	C₂²×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
10	C₂²×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
11	C₂²×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
12	C₂³×C₈×C₂₃	C₂²	1	1	yes	characteristic
13	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
14	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
15	C₂₃×#428	—	2	2	no	—
16	C₂₃×#428	—	2	2	no	—
17	C₂×C₂₃×#107	—	2	1	no	—
18	C₂×C₂₃×#106	—	2	1	no	—
19	C₂₃×#418	—	2	2	no	—
20	C₂₃×#418	—	2	2	no	—
21	C₂×C₂₃×#102	—	2	2	no	—
22	C₂×C₂₃×#102	—	2	2	no	—
23	C₂×C₂₃×#102	—	2	2	no	—
24	C₂×C₂₃×#102	—	2	1	no	—
25	C₂×C₂₃×#102	—	2	1	no	—
26	C₂×C₂₃×#100	—	2	2	no	—
27	C₂×C₂₃×#100	—	2	2	no	—
28	C₂×C₂₃×#100	C₄	1	4	yes	complemented
29	C₂₃×#343	—	2	2	no	—
30	C₂₃×#341	—	2	2	no	—
31	C₂₃×#336	—	2	2	no	—
32	C₂⁵×C₂₃	—	2	1	no	—
33	C₂²×D₄×C₂₃	—	2	1	no	—
34	C₂²×D₄×C₂₃	—	2	1	no	—
35	C₂²×D₄×C₂₃	—	2	1	no	—
36	C₂²×D₄×C₂₃	—	2	1	no	—
37	C₂²×D₄×C₂₃	—	2	1	no	—
38	C₂²×D₄×C₂₃	—	2	1	no	—
39	C₂²×D₄×C₂₃	—	2	1	no	—
40	C₂²×D₄×C₂₃	—	2	1	no	—
41	C₂²×D₄×C₂₃	—	2	1	no	—
42	C₂²×D₄×C₂₃	—	2	1	no	—
43	C₂²×D₄×C₂₃	—	2	1	no	—
44	C₂²×D₄×C₂₃	C₂×C₄	1	2	yes	—
45	C₂²×D₄×C₂₃	D₄	1	2	yes	—
46	C₂²×D₄×C₂₃	Q₈	1	2	yes	—
47	C₂³×C₄×C₂₃	—	2	1	no	—
48	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
49	C₂×M₁₆×C₂₃	—	2	1	no	—
50	C₂×M₁₆×C₂₃	—	2	1	no	—
51	C₂×M₁₆×C₂₃	—	2	1	no	—
52	C₂×M₁₆×C₂₃	—	2	1	no	—
53	C₂×M₁₆×C₂₃	—	2	1	no	—
54	C₂×M₁₆×C₂₃	—	2	1	no	—
55	C₂×M₁₆×C₂₃	—	2	1	no	—
56	C₂×M₁₆×C₂₃	—	2	1	no	—
57	C₂×M₁₆×C₂₃	—	2	1	no	—
58	C₂×M₁₆×C₂₃	—	2	1	no	—
59	C₂×M₁₆×C₂₃	—	2	1	no	—
60	C₂×M₁₆×C₂₃	—	2	1	no	—
61	C₂×M₁₆×C₂₃	—	2	1	no	—
62	C₂×M₁₆×C₂₃	C₂×C₄	1	2	yes	—
63	C₂×M₁₆×C₂₃	C₂×C₄	1	2	yes	—
64	C₂×M₁₆×C₂₃	D₄	1	2	yes	—
65	C₂×M₁₆×C₂₃	D₄	1	2	yes	—
66	C₂×M₁₆×C₂₃	D₄	1	2	yes	—
67	C₂²×C₈×C₂₃	—	2	1	no	—
68	C₂²×C₈×C₂₃	—	2	1	no	—
69	C₂²×C₈×C₂₃	—	2	1	no	—
70	C₂²×C₈×C₂₃	—	2	1	no	—
71	C₂²×C₈×C₂₃	—	2	1	no	—
72	C₂²×C₈×C₂₃	—	2	1	no	—
73	C₂²×C₈×C₂₃	—	2	1	no	—
74	C₂²×C₈×C₂₃	—	2	1	no	—
75	C₂²×C₈×C₂₃	—	2	1	no	—
76	C₂²×C₈×C₂₃	D₄	1	2	yes	—
77	C₂₃×#117	—	2	1	no	—
78	C₂₃×#117	—	2	1	no	—
79	C₂₃×#117	—	2	1	no	—
80	C₂₃×#117	—	2	1	no	—
81	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
82	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
83	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
84	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
85	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
86	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
87	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
88	C₂×C₄⋊C₄×C₂₃	D₄	1	2	yes	—
89	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
90	C₂×C₄²×C₂₃	—	2	1	no	—
91	C₂₃×#107	—	2	4	no	—
92	C₂₃×#106	—	2	4	no	—
93	C₂₃×#102	—	2	8	no	—
94	C₂₃×#102	—	2	4	no	—
95	C₂₃×#102	—	2	4	no	—
96	C₂₃×#100	—	2	8	no	—
97	C₂⁴×C₂₃	—	2	2	no	—
98	C₂⁴×C₂₃	—	2	2	no	—
99	C₂⁴×C₂₃	—	2	2	no	—
100	C₂⁴×C₂₃	—	4	1	no	—
101	C₂⁴×C₂₃	—	4	1	no	—
102	C₂⁴×C₂₃	—	4	1	no	—
103	C₂⁴×C₂₃	—	4	1	no	—
104	C₂⁴×C₂₃	—	8	2	no	—
105	C₂⁴×C₂₃	—	8	2	no	—
106	C₂⁴×C₂₃	#41	1	1	yes	characteristic
107	C₂×D₄×C₂₃	—	2	2	no	—
108	C₂×D₄×C₂₃	—	2	2	no	—
109	C₂×D₄×C₂₃	—	2	2	no	—
110	C₂×D₄×C₂₃	—	2	2	no	—
111	C₂×D₄×C₂₃	—	2	2	no	—
112	C₂×D₄×C₂₃	—	2	2	no	—
113	C₂×D₄×C₂₃	—	2	2	no	—
114	C₂×D₄×C₂₃	—	2	2	no	—
115	C₂×D₄×C₂₃	—	2	2	no	—
116	C₂×D₄×C₂₃	—	2	2	no	—
117	C₂×D₄×C₂₃	—	2	2	no	—
118	C₂×D₄×C₂₃	—	2	2	no	—
119	C₂×D₄×C₂₃	—	2	2	no	—
120	C₂×D₄×C₂₃	—	2	2	no	—
121	C₂×D₄×C₂₃	—	2	2	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	—	4	1	no	—
126	C₂×D₄×C₂₃	—	4	1	no	—
127	C₂×D₄×C₂₃	—	4	1	no	—
128	C₂×D₄×C₂₃	—	4	1	no	—
129	C₂×D₄×C₂₃	—	4	1	no	—
130	C₂×D₄×C₂₃	—	4	1	no	—
131	C₂×D₄×C₂₃	—	4	1	no	—
132	C₂×D₄×C₂₃	—	4	1	no	—
133	C₂×D₄×C₂₃	—	4	1	no	—
134	C₂×D₄×C₂₃	C₄⋊C₄	1	4	yes	—
135	C₂²×C₄×C₂₃	—	2	1	no	—
136	C₂²×C₄×C₂₃	—	2	1	no	—
137	C₂²×C₄×C₂₃	—	2	2	no	—
138	C₂²×C₄×C₂₃	—	4	1	no	—
139	C₂²×C₄×C₂₃	—	4	1	no	—
140	C₂²×C₄×C₂₃	—	8	2	no	—
141	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
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	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
148	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
149	C₂²×C₄×C₂₃	C₂×Q₈	1	1	yes	characteristic
150	C₂²×C₄×C₂₃	#41	1	1	yes	characteristic
151	C₂²×C₄×C₂₃	#41	1	1	yes	characteristic
152	C₂²×C₄×C₂₃	#41	1	1	yes	characteristic
153	C₂²×C₄×C₂₃	#41	1	1	yes	characteristic
154	C₂²×C₄×C₂₃	#41	1	1	yes	characteristic
155	M₁₆×C₂₃	—	2	2	no	—
156	M₁₆×C₂₃	—	2	2	no	—
157	M₁₆×C₂₃	—	2	2	no	—
158	M₁₆×C₂₃	—	2	2	no	—
159	M₁₆×C₂₃	—	2	2	no	—
160	M₁₆×C₂₃	—	2	2	no	—
161	M₁₆×C₂₃	—	2	2	no	—
162	M₁₆×C₂₃	—	4	1	no	—
163	M₁₆×C₂₃	—	4	1	no	—
164	M₁₆×C₂₃	—	4	1	no	—
165	M₁₆×C₂₃	—	4	1	no	—
166	M₁₆×C₂₃	C₂²⋊C₄	1	4	yes	—
167	C₂×C₈×C₂₃	—	2	2	no	—
168	C₂×C₈×C₂₃	—	2	2	no	—
169	C₂×C₈×C₂₃	—	2	2	no	—
170	C₂×C₈×C₂₃	—	2	2	no	—
171	C₂×C₈×C₂₃	—	2	2	no	—
172	C₂×C₈×C₂₃	—	2	2	no	—
173	C₂×C₈×C₂₃	—	2	2	no	—
174	C₂×C₈×C₂₃	—	2	2	no	—
175	C₂×C₈×C₂₃	—	4	1	no	—
176	C₂×C₈×C₂₃	—	4	1	no	—
177	C₂×C₈×C₂₃	—	4	1	no	—
178	C₂×C₈×C₂₃	—	4	1	no	—
179	C₂×C₈×C₂₃	—	4	1	no	—
180	C₂×C₈×C₂₃	—	4	1	no	—
181	C₂×C₈×C₂₃	—	4	1	no	—
182	C₂×C₈×C₂₃	—	4	1	no	—
183	C₄⋊C₄×C₂₃	—	2	2	no	—
184	C₄⋊C₄×C₂₃	—	2	1	no	—
185	C₄⋊C₄×C₂₃	—	2	1	no	—
186	C₄⋊C₄×C₂₃	—	2	1	no	—
187	C₄⋊C₄×C₂₃	—	2	2	no	—
188	C₄⋊C₄×C₂₃	—	2	1	no	—
189	C₄⋊C₄×C₂₃	—	4	1	no	—
190	C₄⋊C₄×C₂₃	—	4	1	no	—
191	C₂²⋊C₄×C₂₃	—	4	1	no	—
192	C₂²⋊C₄×C₂₃	—	4	1	no	—
193	C₄²×C₂₃	—	4	1	no	—
194	C₄²×C₂₃	—	4	1	no	—
195	#11144	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
196	C₂³×C₂₃	—	2	2	no	—
197	C₂³×C₂₃	—	2	2	no	—
198	C₂³×C₂₃	—	2	4	no	—
199	C₂³×C₂₃	—	4	2	no	—
200	C₂³×C₂₃	—	4	2	no	—
201	C₂³×C₂₃	—	4	2	no	—
202	C₂³×C₂₃	—	4	2	no	—
203	C₂³×C₂₃	—	4	2	no	—
204	C₂³×C₂₃	—	4	2	no	—
205	C₂³×C₂₃	—	8	4	no	—
206	C₂³×C₂₃	—	8	4	no	—
207	C₂³×C₂₃	—	8	2	no	—
208	C₂³×C₂₃	—	8	2	no	—
209	C₂³×C₂₃	—	8	4	no	—
210	C₂³×C₂₃	—	8	4	no	—
211	C₂³×C₂₃	—	8	2	no	—
212	C₂³×C₂₃	—	8	2	no	—
213	C₂³×C₂₃	—	8	2	no	—
214	C₂³×C₂₃	—	8	2	no	—
215	C₂³×C₂₃	#117	1	1	yes	characteristic
216	C₂³×C₂₃	#121	1	1	yes	characteristic
217	C₂³×C₂₃	#121	1	1	yes	characteristic
218	C₂³×C₂₃	#121	1	1	yes	characteristic
219	C₂³×C₂₃	C₂²⋊Q₈	1	1	yes	characteristic
220	C₂³×C₂₃	#126	1	1	yes	characteristic
221	C₂³×C₂₃	#126	1	1	yes	characteristic
222	D₄×C₂₃	—	2	4	no	—
223	D₄×C₂₃	—	2	4	no	—
224	D₄×C₂₃	—	4	2	no	—
225	D₄×C₂₃	—	4	2	no	—
226	D₄×C₂₃	—	4	2	no	—
227	D₄×C₂₃	—	4	2	no	—
228	D₄×C₂₃	—	4	2	no	—
229	D₄×C₂₃	—	4	2	no	—
230	C₂×C₄×C₂₃	—	4	1	no	—
231	C₂×C₄×C₂₃	—	4	1	no	—
232	C₂×C₄×C₂₃	—	4	2	no	—
233	C₂×C₄×C₂₃	—	4	2	no	—
234	C₂×C₄×C₂₃	—	4	2	no	—
235	C₂×C₄×C₂₃	—	8	2	no	—
236	C₂×C₄×C₂₃	—	8	2	no	—
237	C₂×C₄×C₂₃	—	8	2	no	—
238	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
239	C₂×C₄×C₂₃	C₂×C₄⋊C₄	1	1	yes	characteristic
240	C₂×C₄×C₂₃	C₄×D₄	1	1	yes	characteristic
241	C₂×C₄×C₂₃	C₄×D₄	1	1	yes	characteristic
242	C₂×C₄×C₂₃	C₄×D₄	1	1	yes	characteristic
243	C₂×C₄×C₂₃	C₄×D₄	1	1	yes	characteristic
244	C₂×C₄×C₂₃	#120	1	1	yes	characteristic
245	C₂×C₄×C₂₃	#120	1	1	yes	characteristic
246	C₂×C₄×C₂₃	#120	1	1	yes	characteristic
247	C₂×C₄×C₂₃	#121	1	1	yes	characteristic
248	C₂×C₄×C₂₃	#121	1	1	yes	characteristic
249	C₂×C₄×C₂₃	#121	1	1	yes	characteristic
250	C₂×C₄×C₂₃	#121	1	1	yes	characteristic
251	C₂×C₄×C₂₃	#121	1	1	yes	characteristic
252	C₂×C₄×C₂₃	C₂²⋊Q₈	1	1	yes	characteristic
253	C₂×C₄×C₂₃	C₂²⋊Q₈	1	1	yes	characteristic
254	C₂×C₄×C₂₃	C₂²⋊Q₈	1	1	yes	characteristic
255	C₂×C₄×C₂₃	C₂²⋊Q₈	1	1	yes	characteristic
256	C₂×C₄×C₂₃	C₂²⋊Q₈	1	1	yes	characteristic
257	C₂×C₄×C₂₃	#123	1	1	yes	characteristic
258	C₂×C₄×C₂₃	#123	1	1	yes	characteristic
259	C₂×C₄×C₂₃	#123	1	1	yes	characteristic
260	C₂×C₄×C₂₃	#123	1	1	yes	characteristic
261	C₂×C₄×C₂₃	#123	1	1	yes	characteristic
262	C₂×C₄×C₂₃	#124	1	1	yes	characteristic
263	C₂×C₄×C₂₃	#124	1	1	yes	characteristic
264	C₂×C₄×C₂₃	#124	1	1	yes	characteristic
265	C₂×C₄×C₂₃	#127	1	1	yes	characteristic
266	C₈×C₂₃	—	2	4	no	—
267	C₈×C₂₃	—	4	2	no	—
268	C₈×C₂₃	—	4	2	no	—
269	C₈×C₂₃	—	4	2	no	—
270	C₂×#428	C₂×C₂₃	1	1	yes	characteristic, complemented
271	C₂×#418	C₂×C₂₃	1	1	yes	characteristic
272	C₂²×#102	C₂×C₂₃	1	1	yes	characteristic
273	C₂²×#100	C₂×C₂₃	1	1	yes	characteristic
274	C₂×#343	C₂×C₂₃	1	1	yes	characteristic, complemented
275	C₂×#341	C₂×C₂₃	1	1	yes	characteristic, complemented
276	#1729	C₂×C₂₃	1	1	yes	characteristic, complemented
277	C₂²×C₂₃	—	2	2	no	—
278	C₂²×C₂₃	—	2	2	no	—
279	C₂²×C₂₃	—	2	2	no	—
280	C₂²×C₂₃	—	2	2	no	—
281	C₂²×C₂₃	—	2	1	no	—
282	C₂²×C₂₃	—	2	1	no	—
283	C₂²×C₂₃	—	2	1	no	—
284	C₂²×C₂₃	—	2	1	no	—
285	C₂²×C₂₃	—	4	4	no	—
286	C₂²×C₂₃	—	8	4	no	—
287	C₂²×C₂₃	—	8	4	no	—
288	C₂²×C₂₃	—	8	4	no	—
289	C₂²×C₂₃	—	8	4	no	—
290	C₂²×C₂₃	—	8	4	no	—
291	C₂²×C₂₃	—	8	4	no	—
292	C₂²×C₂₃	—	8	2	no	—
293	C₂²×C₂₃	—	8	2	no	—
294	C₂²×C₂₃	#380	1	1	yes	characteristic
295	C₂²×C₂₃	#388	1	1	yes	characteristic
296	C₂²×C₂₃	#388	1	1	yes	characteristic
297	C₂²×C₂₃	#392	1	1	yes	characteristic
298	C₂²×C₂₃	#396	1	1	yes	characteristic
299	C₂²×C₂₃	#396	1	1	yes	characteristic
300	C₂²×C₂₃	#397	1	1	yes	characteristic
301	C₂²×C₂₃	#471	1	2	yes	—
302	C₂²×C₂₃	#472	1	2	yes	—
303	C₄×C₂₃	—	8	1	no	—
304	C₄×C₂₃	—	8	2	no	—
305	C₄×C₂₃	—	8	1	no	—
306	C₄×C₂₃	#385	1	1	yes	characteristic
307	C₄×C₂₃	#385	1	1	yes	characteristic
308	C₄×C₂₃	#386	1	1	yes	characteristic
309	C₄×C₂₃	#390	1	1	yes	characteristic
310	C₄×C₂₃	#393	1	1	yes	characteristic
311	C₄×C₂₃	#394	1	1	yes	characteristic
312	C₄×C₂₃	#394	1	1	yes	characteristic
313	C₄×C₂₃	#399	1	1	yes	characteristic
314	C₂³×D₄	C₂²×C₂₃	1	1	yes	characteristic
315	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
316	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
317	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
318	C₂³×C₈	C₂²×C₂₃	1	1	yes	characteristic
319	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
320	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
321	#428	—	2	2	no	—
322	#428	—	2	2	no	—
323	C₂×#107	—	2	1	no	—
324	C₂×#106	—	2	1	no	—
325	#418	—	2	2	no	—
326	#418	—	2	2	no	—
327	C₂×#102	—	2	2	no	—
328	C₂×#102	—	2	2	no	—
329	C₂×#102	—	2	2	no	—
330	C₂×#102	—	2	1	no	—
331	C₂×#102	—	2	1	no	—
332	C₂×#100	—	2	2	no	—
333	C₂×#100	—	2	2	no	—
334	C₂×#100	C₄×C₂₃	1	4	yes	complemented
335	#343	—	2	2	no	—
336	#341	—	2	2	no	—
337	#336	—	2	2	no	—
338	C₂×C₂₃	—	2	1	no	—
339	C₂×C₂₃	—	2	1	no	—
340	C₂×C₂₃	—	2	1	no	—
341	C₂×C₂₃	—	2	1	no	—
342	C₂×C₂₃	—	8	4	no	—
343	C₂×C₂₃	#1439	1	1	yes	characteristic
344	C₂×C₂₃	#1931	1	2	yes	—
345	C₂×C₂₃	#2018	1	1	yes	characteristic
346	C₂×C₂₃	#2019	1	1	yes	characteristic
347	C₂×C₂₃	#2063	1	2	yes	—
348	C₂⁵	—	2	1	no	—
349	C₂²×D₄	—	2	1	no	—
350	C₂²×D₄	—	2	1	no	—
351	C₂²×D₄	—	2	1	no	—
352	C₂²×D₄	—	2	1	no	—
353	C₂²×D₄	—	2	1	no	—
354	C₂²×D₄	—	2	1	no	—
355	C₂²×D₄	—	2	1	no	—
356	C₂²×D₄	—	2	1	no	—
357	C₂²×D₄	—	2	1	no	—
358	C₂²×D₄	—	2	1	no	—
359	C₂²×D₄	—	2	1	no	—
360	C₂²×D₄	C₂×C₄×C₂₃	1	2	yes	—
361	C₂²×D₄	D₄×C₂₃	1	2	yes	—
362	C₂²×D₄	Q₈×C₂₃	1	2	yes	—
363	C₂³×C₄	—	2	1	no	—
364	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
365	C₂×M₁₆	—	2	1	no	—
366	C₂×M₁₆	—	2	1	no	—
367	C₂×M₁₆	—	2	1	no	—
368	C₂×M₁₆	—	2	1	no	—
369	C₂×M₁₆	—	2	1	no	—
370	C₂×M₁₆	—	2	1	no	—
371	C₂×M₁₆	—	2	1	no	—
372	C₂×M₁₆	—	2	1	no	—
373	C₂×M₁₆	—	2	1	no	—
374	C₂×M₁₆	—	2	1	no	—
375	C₂×M₁₆	—	2	1	no	—
376	C₂×M₁₆	—	2	1	no	—
377	C₂×M₁₆	—	2	1	no	—
378	C₂×M₁₆	C₂×C₄×C₂₃	1	2	yes	—
379	C₂×M₁₆	C₂×C₄×C₂₃	1	2	yes	—
380	C₂×M₁₆	D₄×C₂₃	1	2	yes	—
381	C₂×M₁₆	D₄×C₂₃	1	2	yes	—
382	C₂×M₁₆	D₄×C₂₃	1	2	yes	—
383	C₂²×C₈	—	2	1	no	—
384	C₂²×C₈	—	2	1	no	—
385	C₂²×C₈	—	2	1	no	—
386	C₂²×C₈	—	2	1	no	—
387	C₂²×C₈	—	2	1	no	—
388	C₂²×C₈	—	2	1	no	—
389	C₂²×C₈	—	2	1	no	—
390	C₂²×C₈	—	2	1	no	—
391	C₂²×C₈	—	2	1	no	—
392	C₂²×C₈	D₄×C₂₃	1	2	yes	—
393	#117	—	2	1	no	—
394	#117	—	2	1	no	—
395	#117	—	2	1	no	—
396	#117	—	2	1	no	—
397	C₂×C₄⋊C₄	—	2	1	no	—
398	C₂×C₄⋊C₄	—	2	1	no	—
399	C₂×C₄⋊C₄	—	2	1	no	—
400	C₂×C₄⋊C₄	—	2	1	no	—
401	C₂×C₄⋊C₄	—	2	1	no	—
402	C₂×C₄⋊C₄	D₄×C₂₃	1	2	yes	—
403	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
404	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
405	C₂×C₂²⋊C₄	—	2	1	no	—
406	C₂×C₄²	—	2	1	no	—
407	#107	—	2	4	no	—
408	#106	—	2	4	no	—
409	#102	—	2	8	no	—
410	#102	—	2	4	no	—
411	#102	—	2	4	no	—
412	#100	—	2	8	no	—
413	C₂₃	#11144	1	1	yes	characteristic, direct product factor, Sylow
414	C₂⁴	—	2	2	no	—
415	C₂⁴	—	2	2	no	—
416	C₂⁴	—	2	2	no	—
417	C₂⁴	—	4	1	no	—
418	C₂⁴	—	4	1	no	—
419	C₂⁴	—	4	1	no	—
420	C₂⁴	—	4	1	no	—
421	C₂⁴	—	8	2	no	—
422	C₂⁴	—	8	2	no	—
423	C₂⁴	#41×C₂₃	1	1	yes	characteristic
424	C₂×D₄	—	2	2	no	—
425	C₂×D₄	—	2	2	no	—
426	C₂×D₄	—	2	2	no	—
427	C₂×D₄	—	2	2	no	—
428	C₂×D₄	—	2	2	no	—
429	C₂×D₄	—	2	2	no	—
430	C₂×D₄	—	2	2	no	—
431	C₂×D₄	—	2	2	no	—
432	C₂×D₄	—	2	2	no	—
433	C₂×D₄	—	2	2	no	—
434	C₂×D₄	—	2	2	no	—
435	C₂×D₄	—	2	2	no	—
436	C₂×D₄	—	2	2	no	—
437	C₂×D₄	—	2	2	no	—
438	C₂×D₄	—	2	2	no	—
439	C₂×D₄	—	4	1	no	—
440	C₂×D₄	—	4	1	no	—
441	C₂×D₄	—	4	1	no	—
442	C₂×D₄	—	4	1	no	—
443	C₂×D₄	—	4	1	no	—
444	C₂×D₄	—	4	1	no	—
445	C₂×D₄	—	4	1	no	—
446	C₂×D₄	—	4	1	no	—
447	C₂×D₄	—	4	1	no	—
448	C₂×D₄	—	4	1	no	—
449	C₂×D₄	—	4	1	no	—
450	C₂×D₄	—	4	1	no	—
451	C₂×D₄	C₄⋊C₄×C₂₃	1	4	yes	—
452	C₂²×C₄	—	2	1	no	—
453	C₂²×C₄	—	2	1	no	—
454	C₂²×C₄	—	2	2	no	—
455	C₂²×C₄	—	4	1	no	—
456	C₂²×C₄	—	4	1	no	—
457	C₂²×C₄	—	8	2	no	—
458	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
459	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
460	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
461	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
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	1	yes	characteristic
465	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
466	C₂²×C₄	C₂×Q₈×C₂₃	1	1	yes	characteristic
467	C₂²×C₄	#41×C₂₃	1	1	yes	characteristic
468	C₂²×C₄	#41×C₂₃	1	1	yes	characteristic
469	C₂²×C₄	#41×C₂₃	1	1	yes	characteristic
470	C₂²×C₄	#41×C₂₃	1	1	yes	characteristic
471	C₂²×C₄	#41×C₂₃	1	1	yes	characteristic
472	M₁₆	—	2	2	no	—
473	M₁₆	—	2	2	no	—
474	M₁₆	—	2	2	no	—
475	M₁₆	—	2	2	no	—
476	M₁₆	—	2	2	no	—
477	M₁₆	—	2	2	no	—
478	M₁₆	—	2	2	no	—
479	M₁₆	—	4	1	no	—
480	M₁₆	—	4	1	no	—
481	M₁₆	—	4	1	no	—
482	M₁₆	—	4	1	no	—
483	M₁₆	C₂²⋊C₄×C₂₃	1	4	yes	—
484	C₂×C₈	—	2	2	no	—
485	C₂×C₈	—	2	2	no	—
486	C₂×C₈	—	2	2	no	—
487	C₂×C₈	—	2	2	no	—
488	C₂×C₈	—	2	2	no	—
489	C₂×C₈	—	2	2	no	—
490	C₂×C₈	—	2	2	no	—
491	C₂×C₈	—	2	2	no	—
492	C₂×C₈	—	4	1	no	—
493	C₂×C₈	—	4	1	no	—
494	C₂×C₈	—	4	1	no	—
495	C₂×C₈	—	4	1	no	—
496	C₂×C₈	—	4	1	no	—
497	C₂×C₈	—	4	1	no	—
498	C₂×C₈	—	4	1	no	—
499	C₂×C₈	—	4	1	no	—
500	C₄⋊C₄	—	2	2	no	—
501	C₄⋊C₄	—	2	1	no	—
502	C₄⋊C₄	—	2	1	no	—
503	C₄⋊C₄	—	2	1	no	—
504	C₄⋊C₄	—	2	2	no	—
505	C₄⋊C₄	—	2	1	no	—
506	C₄⋊C₄	—	4	1	no	—
507	C₄⋊C₄	—	4	1	no	—
508	C₂²⋊C₄	—	4	1	no	—
509	C₂²⋊C₄	—	4	1	no	—
510	C₄²	—	4	1	no	—
511	C₄²	—	4	1	no	—
512	C₂³	—	2	2	no	—
513	C₂³	—	2	2	no	—
514	C₂³	—	2	4	no	—
515	C₂³	—	4	2	no	—
516	C₂³	—	4	2	no	—
517	C₂³	—	4	2	no	—
518	C₂³	—	4	2	no	—
519	C₂³	—	4	2	no	—
520	C₂³	—	4	2	no	—
521	C₂³	—	8	4	no	—
522	C₂³	—	8	2	no	—
523	C₂³	—	8	2	no	—
524	C₂³	—	8	4	no	—
525	C₂³	—	8	4	no	—
526	C₂³	—	8	2	no	—
527	C₂³	—	8	2	no	—
528	C₂³	—	8	4	no	—
529	C₂³	—	8	2	no	—
530	C₂³	—	8	2	no	—
531	C₂³	C₂₃×#117	1	1	yes	characteristic
532	C₂³	C₂₃×#121	1	1	yes	characteristic
533	C₂³	C₂₃×#121	1	1	yes	characteristic
534	C₂³	C₂₃×#121	1	1	yes	characteristic
535	C₂³	C₂₃×C₂²⋊Q₈	1	1	yes	characteristic
536	C₂³	C₂₃×#126	1	1	yes	characteristic
537	C₂³	C₂₃×#126	1	1	yes	characteristic
538	D₄	—	2	4	no	—
539	D₄	—	2	4	no	—
540	D₄	—	4	2	no	—
541	D₄	—	4	2	no	—
542	D₄	—	4	2	no	—
543	D₄	—	4	2	no	—
544	D₄	—	4	2	no	—
545	D₄	—	4	2	no	—
546	C₂×C₄	—	4	1	no	—
547	C₂×C₄	—	4	1	no	—
548	C₂×C₄	—	4	2	no	—
549	C₂×C₄	—	4	2	no	—
550	C₂×C₄	—	4	2	no	—
551	C₂×C₄	—	8	2	no	—
552	C₂×C₄	—	8	2	no	—
553	C₂×C₄	—	8	2	no	—
554	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
555	C₂×C₄	C₂×C₄⋊C₄×C₂₃	1	1	yes	characteristic
556	C₂×C₄	C₄×D₄×C₂₃	1	1	yes	characteristic
557	C₂×C₄	C₄×D₄×C₂₃	1	1	yes	characteristic
558	C₂×C₄	C₄×D₄×C₂₃	1	1	yes	characteristic
559	C₂×C₄	C₄×D₄×C₂₃	1	1	yes	characteristic
560	C₂×C₄	C₂₃×#120	1	1	yes	characteristic
561	C₂×C₄	C₂₃×#120	1	1	yes	characteristic
562	C₂×C₄	C₂₃×#120	1	1	yes	characteristic
563	C₂×C₄	C₂₃×#121	1	1	yes	characteristic
564	C₂×C₄	C₂₃×#121	1	1	yes	characteristic
565	C₂×C₄	C₂₃×#121	1	1	yes	characteristic
566	C₂×C₄	C₂₃×#121	1	1	yes	characteristic
567	C₂×C₄	C₂₃×#121	1	1	yes	characteristic
568	C₂×C₄	C₂₃×C₂²⋊Q₈	1	1	yes	characteristic
569	C₂×C₄	C₂₃×C₂²⋊Q₈	1	1	yes	characteristic
570	C₂×C₄	C₂₃×C₂²⋊Q₈	1	1	yes	characteristic
571	C₂×C₄	C₂₃×C₂²⋊Q₈	1	1	yes	characteristic
572	C₂×C₄	C₂₃×C₂²⋊Q₈	1	1	yes	characteristic
573	C₂×C₄	C₂₃×#123	1	1	yes	characteristic
574	C₂×C₄	C₂₃×#123	1	1	yes	characteristic
575	C₂×C₄	C₂₃×#123	1	1	yes	characteristic
576	C₂×C₄	C₂₃×#123	1	1	yes	characteristic
577	C₂×C₄	C₂₃×#123	1	1	yes	characteristic
578	C₂×C₄	C₂₃×#124	1	1	yes	characteristic
579	C₂×C₄	C₂₃×#124	1	1	yes	characteristic
580	C₂×C₄	C₂₃×#124	1	1	yes	characteristic
581	C₂×C₄	C₂₃×#127	1	1	yes	characteristic
582	C₈	—	2	4	no	—
583	C₈	—	4	2	no	—
584	C₈	—	4	2	no	—
585	C₈	—	4	2	no	—
586	C₂²	—	2	2	no	—
587	C₂²	—	2	2	no	—
588	C₂²	—	2	1	no	—
589	C₂²	—	2	1	no	—
590	C₂²	—	2	1	no	—
591	C₂²	—	2	1	no	—
592	C₂²	—	2	2	no	—
593	C₂²	—	2	2	no	—
594	C₂²	—	4	4	no	—
595	C₂²	—	8	4	no	—
596	C₂²	—	8	4	no	—
597	C₂²	—	8	4	no	—
598	C₂²	—	8	4	no	—
599	C₂²	—	8	4	no	—
600	C₂²	—	8	2	no	—
601	C₂²	—	8	2	no	—
602	C₂²	—	8	4	no	—
603	C₂²	C₂₃×#380	1	1	yes	characteristic
604	C₂²	C₂₃×#388	1	1	yes	characteristic
605	C₂²	C₂₃×#388	1	1	yes	characteristic
606	C₂²	C₂₃×#392	1	1	yes	characteristic
607	C₂²	C₂₃×#396	1	1	yes	characteristic
608	C₂²	C₂₃×#396	1	1	yes	characteristic
609	C₂²	C₂₃×#397	1	1	yes	characteristic
610	C₂²	C₂₃×#471	1	2	yes	—
611	C₂²	C₂₃×#472	1	2	yes	—
612	C₄	—	8	1	no	—
613	C₄	—	8	2	no	—
614	C₄	—	8	1	no	—
615	C₄	C₂₃×#385	1	1	yes	characteristic
616	C₄	C₂₃×#385	1	1	yes	characteristic
617	C₄	C₂₃×#386	1	1	yes	characteristic
618	C₄	C₂₃×#390	1	1	yes	characteristic
619	C₄	C₂₃×#393	1	1	yes	characteristic
620	C₄	C₂₃×#394	1	1	yes	characteristic
621	C₄	C₂₃×#394	1	1	yes	characteristic
622	C₄	C₂₃×#399	1	1	yes	characteristic
623	C₂	—	2	1	no	—
624	C₂	—	2	1	no	—
625	C₂	—	2	1	no	—
626	C₂	—	2	1	no	—
627	C₂	—	8	4	no	—
628	C₂	C₂₃×#1439	1	1	yes	characteristic
629	C₂	C₂₃×#1931	1	2	yes	—
630	C₂	C₂₃×#2018	1	1	yes	characteristic
631	C₂	C₂₃×#2019	1	1	yes	characteristic
632	C₂	C₂₃×#2063	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₂₃	#121
commutator	C₂²×C₄	C₂²×C₄×C₂₃
Frattini, cosocle	C₂³×C₄	C₂³×C₂₃
prime radical	C₂³×D₄×C₂₃	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₃ ◁ C₂³×C₄×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₂₃×#428	C₂	semidirect
5. C₂×C₂₃×#343	C₂	semidirect
6. C₂×C₂₃×#341	C₂	semidirect
7. C₂₃×#1729	C₂	semidirect
28. C₂×C₂₃×#100	C₄	semidirect
195. #11144	C₂₃	direct (N × H)
270. C₂×#428	C₂×C₂₃	semidirect
274. C₂×#343	C₂×C₂₃	semidirect
275. C₂×#341	C₂×C₂₃	semidirect
276. #1729	C₂×C₂₃	semidirect
334. C₂×#100	C₄×C₂₃	semidirect
413. C₂₃	#11144	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₂₃×#428	2
C₂×C₂₃×#418	2
C₂²×C₂₃×#102	2
C₂²×C₂₃×#100	2
C₂×C₂₃×#343	2
C₂×C₂₃×#341	2
C₂₃×#1729	2
#11144	23

Subgroups — C23×#11144 #19158770

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#11144 #19158770