Subgroups — C₂₃×#25944 #19173570

Order 5888.

1100 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#557	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₃×#490	C₂	1	1	yes	maximal, characteristic
3	C₂×C₂₃×#460	C₂	1	1	yes	maximal, characteristic
4	C₂₃×#2548	C₂	1	1	yes	maximal, characteristic
5	C₂₃×#2025	C₂	1	2	yes	maximal, complemented
6	C₂₃×#2023	C₂	1	2	yes	maximal, complemented
7	C₂₃×#1989	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#1985	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#1880	C₂	1	2	yes	maximal, complemented
10	C₂₃×#1880	C₂	1	2	yes	maximal, complemented
11	C₂₃×#1763	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×SD₁₆×C₂₃	C₂²	1	2	yes	—
13	C₂₃×#557	—	2	4	no	—
14	C₂₃×#557	—	2	4	no	—
15	C₂×C₂₃×C₄⋊Q₈	—	2	1	no	—
16	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
17	C₂×C₂₃×#127	C₂²	1	1	yes	characteristic
18	C₂×C₂₃×#125	—	2	1	no	—
19	C₂×C₂₃×#125	—	2	1	no	—
20	C₂×C₂₃×#125	C₂²	1	1	yes	characteristic
21	C₂×C₂₃×#125	C₂²	1	1	yes	characteristic
22	C₂×C₂₃×#124	—	2	1	no	—
23	C₂×C₄×Q₈×C₂₃	—	2	1	no	—
24	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
25	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
26	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
27	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
28	C₂₃×#490	—	2	4	no	—
29	C₂₃×#460	—	2	4	no	—
30	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
31	C₂×C₂₃×#103	C₂²	1	2	yes	—
32	C₂×C₂₃×#102	C₂²	1	2	yes	—
33	C₂×C₂₃×#102	C₂²	1	2	yes	—
34	C₂×C₂₃×#102	C₂²	1	2	yes	—
35	C₂×C₂₃×#97	C₂²	1	1	yes	characteristic
36	C₂₃×#394	—	2	1	no	—
37	C₂₃×#394	—	2	1	no	—
38	C₂₃×#390	—	2	1	no	—
39	C₂₃×#390	C₂²	1	2	yes	—
40	C₂₃×#390	C₂²	1	2	yes	—
41	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
42	C₂₃×#340	C₂²	1	2	yes	—
43	C₂₃×#340	C₂²	1	2	yes	—
44	C₂₃×#340	C₂²	1	2	yes	—
45	C₂₃×#336	C₂²	1	2	yes	—
46	C₂₃×#336	C₂²	1	2	yes	—
47	C₂²×Q₈×C₂₃	—	2	1	no	—
48	C₂²×Q₈×C₂₃	D₄	1	1	yes	characteristic
49	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
50	C₂²×D₄×C₂₃	—	2	1	no	—
51	C₂²×D₄×C₂₃	—	2	1	no	—
52	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
53	C₂×SD₁₆×C₂₃	—	2	4	no	—
54	C₂×SD₁₆×C₂₃	—	2	4	no	—
55	C₂×SD₁₆×C₂₃	—	2	4	no	—
56	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
57	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
58	C₂₃×C₄⋊Q₈	—	2	8	no	—
59	C₂₃×C₄⋊Q₈	—	2	2	no	—
60	C₂₃×C₄⋊Q₈	—	2	2	no	—
61	C₂₃×#127	—	2	2	no	—
62	C₂₃×#127	—	2	2	no	—
63	C₂₃×#125	—	2	8	no	—
64	C₂₃×#125	—	2	8	no	—
65	C₂₃×#125	—	2	2	no	—
66	C₂₃×#125	—	2	2	no	—
67	C₂₃×#125	—	2	2	no	—
68	C₂₃×#125	D₄	1	4	yes	—
69	C₂₃×#124	—	4	4	no	—
70	C₄×Q₈×C₂₃	—	2	8	no	—
71	C₄×Q₈×C₂₃	—	2	2	no	—
72	C₄×Q₈×C₂₃	—	2	2	no	—
73	C₄×Q₈×C₂₃	—	2	2	no	—
74	C₄×Q₈×C₂₃	—	2	2	no	—
75	C₄×Q₈×C₂₃	—	2	2	no	—
76	C₄×Q₈×C₂₃	—	2	2	no	—
77	C₄×Q₈×C₂₃	—	2	2	no	—
78	C₄×Q₈×C₂₃	D₄	1	4	yes	—
79	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
80	C₂×C₄⋊C₄×C₂₃	—	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	—	2	1	no	—
87	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
88	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
89	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
90	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
91	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
92	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
93	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
94	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
95	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
96	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
97	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
98	C₂×C₄²×C₂₃	—	2	1	no	—
99	C₂×C₄²×C₂₃	—	2	1	no	—
100	C₂×C₄²×C₂₃	—	2	1	no	—
101	C₂×C₄²×C₂₃	—	2	1	no	—
102	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
103	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
104	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
105	C₂₃×C₄⋊C₈	—	2	2	no	—
106	C₂₃×#103	—	2	4	no	—
107	C₂₃×#102	—	2	4	no	—
108	C₂₃×#102	—	2	4	no	—
109	C₂₃×#102	—	2	4	no	—
110	C₂₃×#97	—	2	2	no	—
111	C₂₃×#95	—	2	1	no	—
112	C₂⁴×C₂₃	—	2	2	no	—
113	C₂×Q₈×C₂₃	—	2	4	no	—
114	C₂×Q₈×C₂₃	—	2	2	no	—
115	C₂×Q₈×C₂₃	—	2	2	no	—
116	C₂×Q₈×C₂₃	—	2	1	no	—
117	C₂×Q₈×C₂₃	—	2	2	no	—
118	C₂×Q₈×C₂₃	—	4	1	no	—
119	C₂×Q₈×C₂₃	—	4	2	no	—
120	C₂×Q₈×C₂₃	—	4	2	no	—
121	C₂×Q₈×C₂₃	C₂×D₄	1	2	yes	—
122	C₂×Q₈×C₂₃	#41	1	4	yes	—
123	C₂×D₄×C₂₃	—	2	2	no	—
124	C₂×D₄×C₂₃	—	2	2	no	—
125	C₂×D₄×C₂₃	—	2	2	no	—
126	C₂×D₄×C₂₃	—	2	2	no	—
127	C₂×D₄×C₂₃	—	2	2	no	—
128	C₂×D₄×C₂₃	—	2	2	no	—
129	C₂×D₄×C₂₃	—	4	2	no	—
130	C₂×D₄×C₂₃	—	4	2	no	—
131	C₂×D₄×C₂₃	—	4	2	no	—
132	C₂×D₄×C₂₃	—	4	2	no	—
133	C₂×D₄×C₂₃	—	8	2	no	—
134	C₂²×C₄×C₂₃	—	2	1	no	—
135	C₂²×C₄×C₂₃	—	2	1	no	—
136	C₂²×C₄×C₂₃	—	2	1	no	—
137	C₂²×C₄×C₂₃	—	2	1	no	—
138	C₂²×C₄×C₂₃	—	2	2	no	—
139	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
141	C₂²×C₄×C₂₃	C₂×D₄	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	C₂⁴	1	1	yes	characteristic
146	SD₁₆×C₂₃	—	4	8	no	—
147	C₂×C₈×C₂₃	—	2	2	no	—
148	C₂×C₈×C₂₃	—	2	2	no	—
149	C₂×C₈×C₂₃	—	2	2	no	—
150	C₂×C₈×C₂₃	—	2	2	no	—
151	C₂×C₈×C₂₃	—	2	2	no	—
152	C₂×C₈×C₂₃	—	2	2	no	—
153	C₄⋊C₄×C₂₃	—	2	4	no	—
154	C₄⋊C₄×C₂₃	—	2	4	no	—
155	C₄⋊C₄×C₂₃	—	2	4	no	—
156	C₄⋊C₄×C₂₃	—	2	4	no	—
157	C₄⋊C₄×C₂₃	—	2	4	no	—
158	C₄⋊C₄×C₂₃	—	2	4	no	—
159	C₄⋊C₄×C₂₃	—	2	4	no	—
160	C₄⋊C₄×C₂₃	—	2	4	no	—
161	C₄⋊C₄×C₂₃	—	2	2	no	—
162	C₄⋊C₄×C₂₃	—	2	2	no	—
163	C₄⋊C₄×C₂₃	—	2	2	no	—
164	C₄⋊C₄×C₂₃	—	2	1	no	—
165	C₄⋊C₄×C₂₃	—	2	1	no	—
166	C₄⋊C₄×C₂₃	—	2	1	no	—
167	C₄⋊C₄×C₂₃	—	2	2	no	—
168	C₄⋊C₄×C₂₃	—	2	2	no	—
169	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
170	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
171	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
172	C₂²⋊C₄×C₂₃	—	4	4	no	—
173	C₂²⋊C₄×C₂₃	—	4	4	no	—
174	C₂²⋊C₄×C₂₃	—	8	2	no	—
175	C₂²⋊C₄×C₂₃	—	8	2	no	—
176	C₄²×C₂₃	—	2	4	no	—
177	C₄²×C₂₃	—	2	4	no	—
178	C₄²×C₂₃	—	2	4	no	—
179	C₄²×C₂₃	—	2	1	no	—
180	C₄²×C₂₃	—	2	1	no	—
181	C₄²×C₂₃	—	2	1	no	—
182	C₄²×C₂₃	—	2	1	no	—
183	C₄²×C₂₃	—	4	2	no	—
184	C₄²×C₂₃	C₂×D₄	1	2	yes	—
185	C₄²×C₂₃	C₂×D₄	1	2	yes	—
186	#25944	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
187	C₂³×C₂₃	—	4	2	no	—
188	C₂³×C₂₃	—	4	2	no	—
189	C₂³×C₂₃	—	4	2	no	—
190	C₂³×C₂₃	—	4	2	no	—
191	C₂³×C₂₃	—	4	2	no	—
192	C₂³×C₂₃	—	4	2	no	—
193	C₂³×C₂₃	—	4	2	no	—
194	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
195	Q₈×C₂₃	—	2	2	no	—
196	Q₈×C₂₃	—	2	4	no	—
197	Q₈×C₂₃	—	4	4	no	—
198	Q₈×C₂₃	—	4	8	no	—
199	Q₈×C₂₃	#124	1	4	yes	complemented
200	D₄×C₂₃	—	4	2	no	—
201	D₄×C₂₃	—	4	2	no	—
202	D₄×C₂₃	—	4	2	no	—
203	D₄×C₂₃	—	4	2	no	—
204	D₄×C₂₃	—	8	4	no	—
205	D₄×C₂₃	—	8	4	no	—
206	C₂×C₄×C₂₃	—	2	2	no	—
207	C₂×C₄×C₂₃	—	2	1	no	—
208	C₂×C₄×C₂₃	—	2	4	no	—
209	C₂×C₄×C₂₃	—	2	1	no	—
210	C₂×C₄×C₂₃	—	2	1	no	—
211	C₂×C₄×C₂₃	—	2	1	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	1	no	—
217	C₂×C₄×C₂₃	—	2	2	no	—
218	C₂×C₄×C₂₃	—	2	2	no	—
219	C₂×C₄×C₂₃	—	2	1	no	—
220	C₂×C₄×C₂₃	—	2	1	no	—
221	C₂×C₄×C₂₃	—	2	2	no	—
222	C₂×C₄×C₂₃	—	2	2	no	—
223	C₂×C₄×C₂₃	—	4	1	no	—
224	C₂×C₄×C₂₃	—	4	1	no	—
225	C₂×C₄×C₂₃	—	4	1	no	—
226	C₂×C₄×C₂₃	—	4	1	no	—
227	C₂×C₄×C₂₃	—	4	2	no	—
228	C₂×C₄×C₂₃	—	4	2	no	—
229	C₂×C₄×C₂₃	—	4	2	no	—
230	C₂×C₄×C₂₃	—	4	2	no	—
231	C₂×C₄×C₂₃	#120	1	2	yes	—
232	C₂×C₄×C₂₃	#120	1	2	yes	—
233	C₂×C₄×C₂₃	AGL(1,ℤ/8)	1	2	yes	—
234	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
235	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
236	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
237	C₂×C₄×C₂₃	2₋¹⁺⁴	1	2	yes	—
238	C₈×C₂₃	—	4	2	no	—
239	C₈×C₂₃	—	4	2	no	—
240	C₂×#557	C₂×C₂₃	1	1	yes	characteristic, complemented
241	C₂×#490	C₂×C₂₃	1	1	yes	characteristic
242	C₂×#460	C₂×C₂₃	1	1	yes	characteristic
243	#2548	C₂×C₂₃	1	1	yes	characteristic
244	#2025	C₂×C₂₃	1	2	yes	complemented
245	#2023	C₂×C₂₃	1	2	yes	complemented
246	#1989	C₂×C₂₃	1	1	yes	characteristic, complemented
247	#1985	C₂×C₂₃	1	1	yes	characteristic, complemented
248	#1880	C₂×C₂₃	1	2	yes	complemented
249	#1880	C₂×C₂₃	1	2	yes	complemented
250	#1763	C₂×C₂₃	1	1	yes	characteristic, complemented
251	C₂²×C₂₃	—	8	2	no	—
252	C₂²×C₂₃	—	8	2	no	—
253	C₂²×C₂₃	—	8	2	no	—
254	C₂²×C₂₃	—	8	2	no	—
255	C₂²×C₂₃	—	8	2	no	—
256	C₂²×C₂₃	—	8	2	no	—
257	C₂²×C₂₃	—	8	2	no	—
258	C₂²×C₂₃	C₂×#120	1	1	yes	characteristic
259	C₂²×C₂₃	#548	1	2	yes	—
260	C₂²×C₂₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
261	C₂²×C₂₃	#575	1	1	yes	characteristic
262	C₂²×C₂₃	#577	1	2	yes	—
263	C₄×C₂₃	—	2	4	no	—
264	C₄×C₂₃	—	2	2	no	—
265	C₄×C₂₃	—	2	2	no	—
266	C₄×C₂₃	—	2	2	no	—
267	C₄×C₂₃	—	4	1	no	—
268	C₄×C₂₃	—	4	2	no	—
269	C₄×C₂₃	—	4	2	no	—
270	C₄×C₂₃	—	4	1	no	—
271	C₄×C₂₃	—	4	1	no	—
272	C₄×C₂₃	—	4	2	no	—
273	C₄×C₂₃	—	8	2	no	—
274	C₄×C₂₃	C₂×#124	1	1	yes	characteristic
275	C₄×C₂₃	#536	1	1	yes	characteristic
276	C₄×C₂₃	#548	1	2	yes	—
277	C₂²×SD₁₆	C₂²×C₂₃	1	2	yes	—
278	#557	—	2	4	no	—
279	#557	—	2	4	no	—
280	C₂×C₄⋊Q₈	—	2	1	no	—
281	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
282	C₂×#127	C₂²×C₂₃	1	1	yes	characteristic
283	C₂×#125	—	2	1	no	—
284	C₂×#125	—	2	1	no	—
285	C₂×#125	C₂²×C₂₃	1	1	yes	characteristic
286	C₂×#125	C₂²×C₂₃	1	1	yes	characteristic
287	C₂×#124	—	2	1	no	—
288	C₂×C₄×Q₈	—	2	1	no	—
289	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
290	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
291	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
292	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
293	#490	—	2	4	no	—
294	#460	—	2	4	no	—
295	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
296	C₂×#103	C₂²×C₂₃	1	2	yes	—
297	C₂×#102	C₂²×C₂₃	1	2	yes	—
298	C₂×#102	C₂²×C₂₃	1	2	yes	—
299	C₂×#102	C₂²×C₂₃	1	2	yes	—
300	C₂×#97	C₂²×C₂₃	1	1	yes	characteristic
301	#394	—	2	1	no	—
302	#394	—	2	1	no	—
303	#390	—	2	1	no	—
304	#390	C₂²×C₂₃	1	2	yes	—
305	#390	C₂²×C₂₃	1	2	yes	—
306	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
307	#340	C₂²×C₂₃	1	2	yes	—
308	#340	C₂²×C₂₃	1	2	yes	—
309	#340	C₂²×C₂₃	1	2	yes	—
310	#336	C₂²×C₂₃	1	2	yes	—
311	#336	C₂²×C₂₃	1	2	yes	—
312	C₂×C₂₃	—	16	2	no	—
313	C₂×C₂₃	#2436	1	1	yes	characteristic
314	C₂×C₂₃	#3006	1	1	yes	characteristic
315	C₂×C₂₃	#3010	1	1	yes	characteristic
316	C₂×C₂₃	#3368	1	2	yes	—
317	C₂×C₂₃	#3371	1	2	yes	—
318	C₂²×Q₈	—	2	1	no	—
319	C₂²×Q₈	D₄×C₂₃	1	1	yes	characteristic
320	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
321	C₂²×D₄	—	2	1	no	—
322	C₂²×D₄	—	2	1	no	—
323	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
324	C₂×SD₁₆	—	2	4	no	—
325	C₂×SD₁₆	—	2	4	no	—
326	C₂×SD₁₆	—	2	4	no	—
327	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
328	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
329	C₄⋊Q₈	—	2	8	no	—
330	C₄⋊Q₈	—	2	2	no	—
331	C₄⋊Q₈	—	2	2	no	—
332	#127	—	2	2	no	—
333	#127	—	2	2	no	—
334	#125	—	2	8	no	—
335	#125	—	2	8	no	—
336	#125	—	2	2	no	—
337	#125	—	2	2	no	—
338	#125	—	2	2	no	—
339	#125	D₄×C₂₃	1	4	yes	—
340	#124	—	4	4	no	—
341	C₄×Q₈	—	2	8	no	—
342	C₄×Q₈	—	2	2	no	—
343	C₄×Q₈	—	2	2	no	—
344	C₄×Q₈	—	2	2	no	—
345	C₄×Q₈	—	2	2	no	—
346	C₄×Q₈	—	2	2	no	—
347	C₄×Q₈	—	2	2	no	—
348	C₄×Q₈	—	2	2	no	—
349	C₄×Q₈	D₄×C₂₃	1	4	yes	—
350	C₂×C₄⋊C₄	—	2	1	no	—
351	C₂×C₄⋊C₄	—	2	1	no	—
352	C₂×C₄⋊C₄	—	2	1	no	—
353	C₂×C₄⋊C₄	—	2	1	no	—
354	C₂×C₄⋊C₄	—	2	1	no	—
355	C₂×C₄⋊C₄	—	2	1	no	—
356	C₂×C₄⋊C₄	—	2	1	no	—
357	C₂×C₄⋊C₄	—	2	1	no	—
358	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
359	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
360	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
361	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
362	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
363	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
364	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
365	C₂×C₂²⋊C₄	—	2	2	no	—
366	C₂×C₂²⋊C₄	—	2	2	no	—
367	C₂×C₂²⋊C₄	—	2	2	no	—
368	C₂×C₂²⋊C₄	—	2	2	no	—
369	C₂×C₄²	—	2	1	no	—
370	C₂×C₄²	—	2	1	no	—
371	C₂×C₄²	—	2	1	no	—
372	C₂×C₄²	—	2	1	no	—
373	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
374	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
375	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
376	C₄⋊C₈	—	2	2	no	—
377	#103	—	2	4	no	—
378	#102	—	2	4	no	—
379	#102	—	2	4	no	—
380	#102	—	2	4	no	—
381	#97	—	2	2	no	—
382	#95	—	2	1	no	—
383	C₂₃	#25944	1	1	yes	characteristic, direct product factor, Sylow
384	C₂⁴	—	2	2	no	—
385	C₂×Q₈	—	2	4	no	—
386	C₂×Q₈	—	2	2	no	—
387	C₂×Q₈	—	2	2	no	—
388	C₂×Q₈	—	2	1	no	—
389	C₂×Q₈	—	2	2	no	—
390	C₂×Q₈	—	4	1	no	—
391	C₂×Q₈	—	4	2	no	—
392	C₂×Q₈	—	4	2	no	—
393	C₂×Q₈	C₂×D₄×C₂₃	1	2	yes	—
394	C₂×Q₈	#41×C₂₃	1	4	yes	—
395	C₂×D₄	—	2	2	no	—
396	C₂×D₄	—	2	2	no	—
397	C₂×D₄	—	2	2	no	—
398	C₂×D₄	—	2	2	no	—
399	C₂×D₄	—	2	2	no	—
400	C₂×D₄	—	2	2	no	—
401	C₂×D₄	—	4	2	no	—
402	C₂×D₄	—	4	2	no	—
403	C₂×D₄	—	4	2	no	—
404	C₂×D₄	—	4	2	no	—
405	C₂×D₄	—	8	2	no	—
406	C₂²×C₄	—	2	1	no	—
407	C₂²×C₄	—	2	1	no	—
408	C₂²×C₄	—	2	1	no	—
409	C₂²×C₄	—	2	1	no	—
410	C₂²×C₄	—	2	2	no	—
411	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
412	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
413	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
414	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
415	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
416	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
417	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
418	SD₁₆	—	4	8	no	—
419	C₂×C₈	—	2	2	no	—
420	C₂×C₈	—	2	2	no	—
421	C₂×C₈	—	2	2	no	—
422	C₂×C₈	—	2	2	no	—
423	C₂×C₈	—	2	2	no	—
424	C₂×C₈	—	2	2	no	—
425	C₄⋊C₄	—	2	4	no	—
426	C₄⋊C₄	—	2	4	no	—
427	C₄⋊C₄	—	2	4	no	—
428	C₄⋊C₄	—	2	4	no	—
429	C₄⋊C₄	—	2	4	no	—
430	C₄⋊C₄	—	2	4	no	—
431	C₄⋊C₄	—	2	4	no	—
432	C₄⋊C₄	—	2	4	no	—
433	C₄⋊C₄	—	2	2	no	—
434	C₄⋊C₄	—	2	2	no	—
435	C₄⋊C₄	—	2	2	no	—
436	C₄⋊C₄	—	2	1	no	—
437	C₄⋊C₄	—	2	1	no	—
438	C₄⋊C₄	—	2	1	no	—
439	C₄⋊C₄	—	2	2	no	—
440	C₄⋊C₄	—	2	2	no	—
441	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
442	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
443	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
444	C₂²⋊C₄	—	4	4	no	—
445	C₂²⋊C₄	—	4	4	no	—
446	C₂²⋊C₄	—	8	2	no	—
447	C₂²⋊C₄	—	8	2	no	—
448	C₄²	—	2	4	no	—
449	C₄²	—	2	4	no	—
450	C₄²	—	2	4	no	—
451	C₄²	—	2	1	no	—
452	C₄²	—	2	1	no	—
453	C₄²	—	2	1	no	—
454	C₄²	—	2	1	no	—
455	C₄²	—	4	2	no	—
456	C₄²	C₂×D₄×C₂₃	1	2	yes	—
457	C₄²	C₂×D₄×C₂₃	1	2	yes	—
458	C₂³	—	4	2	no	—
459	C₂³	—	4	2	no	—
460	C₂³	—	4	2	no	—
461	C₂³	—	4	2	no	—
462	C₂³	—	4	2	no	—
463	C₂³	—	4	2	no	—
464	C₂³	—	4	2	no	—
465	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
466	Q₈	—	2	4	no	—
467	Q₈	—	2	2	no	—
468	Q₈	—	4	4	no	—
469	Q₈	—	4	8	no	—
470	Q₈	C₂₃×#124	1	4	yes	complemented
471	D₄	—	4	2	no	—
472	D₄	—	4	2	no	—
473	D₄	—	4	2	no	—
474	D₄	—	4	2	no	—
475	D₄	—	8	4	no	—
476	D₄	—	8	4	no	—
477	C₂×C₄	—	2	4	no	—
478	C₂×C₄	—	2	1	no	—
479	C₂×C₄	—	2	1	no	—
480	C₂×C₄	—	2	1	no	—
481	C₂×C₄	—	2	2	no	—
482	C₂×C₄	—	2	2	no	—
483	C₂×C₄	—	2	1	no	—
484	C₂×C₄	—	2	1	no	—
485	C₂×C₄	—	2	1	no	—
486	C₂×C₄	—	2	2	no	—
487	C₂×C₄	—	2	2	no	—
488	C₂×C₄	—	2	1	no	—
489	C₂×C₄	—	2	1	no	—
490	C₂×C₄	—	2	2	no	—
491	C₂×C₄	—	2	1	no	—
492	C₂×C₄	—	2	2	no	—
493	C₂×C₄	—	2	2	no	—
494	C₂×C₄	—	4	1	no	—
495	C₂×C₄	—	4	1	no	—
496	C₂×C₄	—	4	1	no	—
497	C₂×C₄	—	4	1	no	—
498	C₂×C₄	—	4	2	no	—
499	C₂×C₄	—	4	2	no	—
500	C₂×C₄	—	4	2	no	—
501	C₂×C₄	—	4	2	no	—
502	C₂×C₄	C₂₃×#120	1	2	yes	—
503	C₂×C₄	C₂₃×#120	1	2	yes	—
504	C₂×C₄	C₂₃×AGL(1,ℤ/8)	1	2	yes	—
505	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
506	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
507	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
508	C₂×C₄	C₂₃×2₋¹⁺⁴	1	2	yes	—
509	C₈	—	4	2	no	—
510	C₈	—	4	2	no	—
511	C₂²	—	8	2	no	—
512	C₂²	—	8	2	no	—
513	C₂²	—	8	2	no	—
514	C₂²	—	8	2	no	—
515	C₂²	—	8	2	no	—
516	C₂²	—	8	2	no	—
517	C₂²	—	8	2	no	—
518	C₂²	C₂×C₂₃×#120	1	1	yes	characteristic
519	C₂²	C₂₃×#548	1	2	yes	—
520	C₂²	C₂×C₂₃×AGL(1,ℤ/8)	1	1	yes	characteristic
521	C₂²	C₂₃×#575	1	1	yes	characteristic
522	C₂²	C₂₃×#577	1	2	yes	—
523	C₄	—	2	4	no	—
524	C₄	—	2	2	no	—
525	C₄	—	2	2	no	—
526	C₄	—	2	2	no	—
527	C₄	—	4	1	no	—
528	C₄	—	4	2	no	—
529	C₄	—	4	2	no	—
530	C₄	—	4	1	no	—
531	C₄	—	4	1	no	—
532	C₄	—	4	2	no	—
533	C₄	—	8	2	no	—
534	C₄	C₂×C₂₃×#124	1	1	yes	characteristic
535	C₄	C₂₃×#536	1	1	yes	characteristic
536	C₄	C₂₃×#548	1	2	yes	—
537	C₂	—	16	2	no	—
538	C₂	C₂₃×#2436	1	1	yes	characteristic
539	C₂	C₂₃×#3006	1	1	yes	characteristic
540	C₂	C₂₃×#3010	1	1	yes	characteristic
541	C₂	C₂₃×#3368	1	2	yes	—
542	C₂	C₂₃×#3371	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₃
prime radical	C₂×C₂₃×#127	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₃ ◁ C₂×C₄×Q₈×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₂₃×#557	C₂	semidirect
5. C₂₃×#2025	C₂	semidirect
6. C₂₃×#2023	C₂	semidirect
7. C₂₃×#1989	C₂	semidirect
8. C₂₃×#1985	C₂	semidirect
9. C₂₃×#1880	C₂	semidirect
10. C₂₃×#1880	C₂	semidirect
11. C₂₃×#1763	C₂	semidirect
186. #25944	C₂₃	direct (N × H)
199. Q₈×C₂₃	#124	semidirect
240. C₂×#557	C₂×C₂₃	semidirect
244. #2025	C₂×C₂₃	semidirect
245. #2023	C₂×C₂₃	semidirect
246. #1989	C₂×C₂₃	semidirect
247. #1985	C₂×C₂₃	semidirect
248. #1880	C₂×C₂₃	semidirect
249. #1880	C₂×C₂₃	semidirect
250. #1763	C₂×C₂₃	semidirect
383. C₂₃	#25944	direct (N × H)
470. Q₈	C₂₃×#124	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₂₃×#557	2
C₂×C₂₃×#490	2
C₂×C₂₃×#460	2
C₂₃×#2548	2
C₂₃×#2025	2
C₂₃×#2023	2
C₂₃×#1989	2
C₂₃×#1985	2
C₂₃×#1880	2
C₂₃×#1763	2
#25944	23

Subgroups — C23×#25944 #19173570

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#25944 #19173570