Subgroups — C₂₃×#8834 #19156460

Order 5888.

476 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#432	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#1797	C₂	1	1	yes	maximal, characteristic
3	C₄×C₂₃×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic
4	C₂×C₂₃×#335	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₂₃×#334	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#1277	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#1277	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
9	C₂₃×#432	—	2	2	no	—
10	C₂₃×#432	—	2	2	no	—
11	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
12	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
13	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
14	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
15	C₂×C₂₃×C₂²⋊C₈	—	2	1	no	—
16	C₂×C₂₃×C₂²⋊C₈	—	2	1	no	—
17	C₂×C₂₃×C₂²⋊C₈	C₄	1	1	yes	characteristic
18	C₂×C₂₃×C₂²⋊C₈	C₄	1	1	yes	characteristic
19	C₂×C₂₃×#97	—	2	1	no	—
20	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
21	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
22	C₂₃×#336	—	2	1	no	—
23	C₂₃×#336	C₄	1	1	yes	characteristic
24	C₂₃×#336	C₄	1	1	yes	characteristic
25	C₂₃×#335	—	2	2	no	—
26	C₂₃×#334	—	2	2	no	—
27	C₂³×C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
28	C₂³×C₄×C₂₃	D₄	1	1	yes	characteristic
29	C₂³×C₄×C₂₃	Q₈	1	1	yes	characteristic
30	C₂²×C₈×C₂₃	—	2	1	no	—
31	C₂²×C₈×C₂₃	—	2	1	no	—
32	C₂²×C₈×C₂₃	—	2	1	no	—
33	C₂²×C₈×C₂₃	—	2	1	no	—
34	C₂²×C₈×C₂₃	C₂×C₄	1	1	yes	characteristic
35	C₂²×C₈×C₂₃	C₂×C₄	1	1	yes	characteristic
36	C₂²×C₈×C₂₃	C₂×C₄	1	1	yes	characteristic
37	C₂²×C₈×C₂₃	C₂×C₄	1	1	yes	characteristic
38	C₂×C₄²×C₂₃	—	2	1	no	—
39	C₂×C₄²×C₂₃	—	2	1	no	—
40	C₂×C₄²×C₂₃	—	2	1	no	—
41	C₂×C₄²×C₂₃	—	2	1	no	—
42	C₂×C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
43	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
44	C₂×C₄²×C₂₃	Q₈	1	1	yes	characteristic
45	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
46	C₂₃×C₄⋊C₈	—	2	1	no	—
47	C₂₃×C₄⋊C₈	—	2	1	no	—
48	C₂₃×C₄⋊C₈	—	2	1	no	—
49	C₂₃×C₄⋊C₈	—	2	1	no	—
50	C₂₃×C₄⋊C₈	—	2	1	no	—
51	C₂₃×C₄⋊C₈	—	2	1	no	—
52	C₂₃×C₄⋊C₈	D₄	1	2	yes	—
53	C₂₃×C₄⋊C₈	D₄	1	2	yes	—
54	C₂₃×C₂²⋊C₈	—	2	4	no	—
55	C₂₃×C₂²⋊C₈	—	2	2	no	—
56	C₂₃×C₂²⋊C₈	—	2	2	no	—
57	C₂₃×C₂²⋊C₈	—	4	2	no	—
58	C₂₃×#97	—	2	4	no	—
59	C₄×C₈×C₂₃	—	2	1	no	—
60	C₄×C₈×C₂₃	—	2	1	no	—
61	C₄×C₈×C₂₃	—	2	1	no	—
62	C₄×C₈×C₂₃	—	2	1	no	—
63	C₂⁴×C₂₃	C₄⋊C₄	1	1	yes	characteristic
64	C₂²×C₄×C₂₃	—	2	2	no	—
65	C₂²×C₄×C₂₃	—	2	1	no	—
66	C₂²×C₄×C₂₃	—	2	1	no	—
67	C₂²×C₄×C₂₃	—	2	1	no	—
68	C₂²×C₄×C₂₃	—	2	1	no	—
69	C₂²×C₄×C₂₃	—	2	1	no	—
70	C₂²×C₄×C₂₃	—	2	1	no	—
71	C₂²×C₄×C₂₃	—	2	1	no	—
72	C₂²×C₄×C₂₃	—	2	1	no	—
73	C₂²×C₄×C₂₃	—	2	1	no	—
74	C₂²×C₄×C₂₃	—	2	1	no	—
75	C₂²×C₄×C₂₃	—	2	1	no	—
76	C₂²×C₄×C₂₃	—	2	1	no	—
77	C₂²×C₄×C₂₃	—	2	1	no	—
78	C₂²×C₄×C₂₃	—	2	1	no	—
79	C₂²×C₄×C₂₃	—	4	1	no	—
80	C₂²×C₄×C₂₃	C₄⋊C₄	1	1	yes	characteristic
81	C₂²×C₄×C₂₃	C₄⋊C₄	1	1	yes	characteristic
82	C₂²×C₄×C₂₃	C₄⋊C₄	1	1	yes	characteristic
83	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
84	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
85	C₂²×C₄×C₂₃	C₂×Q₈	1	1	yes	characteristic
86	C₂×C₈×C₂₃	—	2	1	no	—
87	C₂×C₈×C₂₃	—	2	1	no	—
88	C₂×C₈×C₂₃	—	2	1	no	—
89	C₂×C₈×C₂₃	—	2	1	no	—
90	C₂×C₈×C₂₃	—	2	1	no	—
91	C₂×C₈×C₂₃	—	2	1	no	—
92	C₂×C₈×C₂₃	—	2	2	no	—
93	C₂×C₈×C₂₃	—	2	2	no	—
94	C₂×C₈×C₂₃	—	2	1	no	—
95	C₂×C₈×C₂₃	—	2	1	no	—
96	C₂×C₈×C₂₃	—	2	1	no	—
97	C₂×C₈×C₂₃	—	2	1	no	—
98	C₂×C₈×C₂₃	—	4	1	no	—
99	C₂×C₈×C₂₃	—	4	1	no	—
100	C₂×C₈×C₂₃	—	4	1	no	—
101	C₂×C₈×C₂₃	—	4	1	no	—
102	C₂×C₈×C₂₃	—	4	1	no	—
103	C₂×C₈×C₂₃	—	4	1	no	—
104	C₂×C₈×C₂₃	—	4	1	no	—
105	C₂×C₈×C₂₃	—	4	1	no	—
106	C₂×C₈×C₂₃	—	4	1	no	—
107	C₂×C₈×C₂₃	—	4	1	no	—
108	C₂×C₈×C₂₃	M₁₆	1	2	yes	—
109	C₂×C₈×C₂₃	M₁₆	1	2	yes	—
110	C₄²×C₂₃	—	2	1	no	—
111	C₄²×C₂₃	—	2	1	no	—
112	C₄²×C₂₃	—	2	1	no	—
113	C₄²×C₂₃	—	2	1	no	—
114	C₄²×C₂₃	—	2	1	no	—
115	C₄²×C₂₃	—	2	1	no	—
116	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
117	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
118	C₄²×C₂₃	#41	1	1	yes	characteristic
119	C₄²×C₂₃	#41	1	1	yes	characteristic
120	#8834	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
121	C₂³×C₂₃	—	2	1	no	—
122	C₂³×C₂₃	—	2	1	no	—
123	C₂³×C₂₃	—	2	1	no	—
124	C₂³×C₂₃	—	2	1	no	—
125	C₂³×C₂₃	—	2	1	no	—
126	C₂³×C₂₃	—	2	1	no	—
127	C₂³×C₂₃	#108	1	2	yes	—
128	C₂³×C₂₃	C₂×C₄⋊C₄	1	1	yes	characteristic
129	C₂×C₄×C₂₃	—	2	1	no	—
130	C₂×C₄×C₂₃	—	2	1	no	—
131	C₂×C₄×C₂₃	—	2	1	no	—
132	C₂×C₄×C₂₃	—	2	1	no	—
133	C₂×C₄×C₂₃	—	2	1	no	—
134	C₂×C₄×C₂₃	—	2	1	no	—
135	C₂×C₄×C₂₃	—	2	1	no	—
136	C₂×C₄×C₂₃	—	2	1	no	—
137	C₂×C₄×C₂₃	—	2	1	no	—
138	C₂×C₄×C₂₃	—	2	1	no	—
139	C₂×C₄×C₂₃	—	2	1	no	—
140	C₂×C₄×C₂₃	—	4	2	no	—
141	C₂×C₄×C₂₃	—	4	2	no	—
142	C₂×C₄×C₂₃	—	4	1	no	—
143	C₂×C₄×C₂₃	—	4	1	no	—
144	C₂×C₄×C₂₃	—	4	1	no	—
145	C₂×C₄×C₂₃	—	4	1	no	—
146	C₂×C₄×C₂₃	—	4	1	no	—
147	C₂×C₄×C₂₃	—	4	1	no	—
148	C₂×C₄×C₂₃	—	4	1	no	—
149	C₂×C₄×C₂₃	—	4	1	no	—
150	C₂×C₄×C₂₃	C₄×D₄	1	1	yes	characteristic
151	C₂×C₄×C₂₃	C₄×D₄	1	1	yes	characteristic
152	C₂×C₄×C₂₃	#120	1	1	yes	characteristic
153	C₂×C₄×C₂₃	C₂²⋊Q₈	1	1	yes	characteristic
154	C₂×C₄×C₂₃	C₂²⋊Q₈	1	1	yes	characteristic
155	C₂×C₄×C₂₃	#123	1	1	yes	characteristic
156	C₂×C₄×C₂₃	C₂×M₁₆	1	1	yes	characteristic
157	C₂×C₄×C₂₃	C₂×M₁₆	1	1	yes	characteristic
158	C₂×C₄×C₂₃	#131	1	1	yes	characteristic
159	C₂×C₄×C₂₃	#131	1	1	yes	characteristic
160	C₂×C₄×C₂₃	#135	1	1	yes	characteristic
161	C₂×C₄×C₂₃	#135	1	1	yes	characteristic
162	C₂×C₄×C₂₃	AGL(1,ℤ/8)	1	1	yes	characteristic
163	C₂×C₄×C₂₃	#137	1	1	yes	characteristic
164	C₈×C₂₃	—	2	2	no	—
165	C₈×C₂₃	—	2	2	no	—
166	C₈×C₂₃	—	4	1	no	—
167	C₈×C₂₃	—	4	1	no	—
168	C₈×C₂₃	—	4	2	no	—
169	C₈×C₂₃	—	4	2	no	—
170	C₈×C₂₃	—	8	1	no	—
171	C₈×C₂₃	—	8	1	no	—
172	C₂×#432	C₂×C₂₃	1	1	yes	characteristic
173	#1797	C₂×C₂₃	1	1	yes	characteristic
174	C₄×C₂²⋊C₈	C₂×C₂₃	1	1	yes	characteristic
175	C₂×#335	C₂×C₂₃	1	1	yes	characteristic, complemented
176	C₂×#334	C₂×C₂₃	1	1	yes	characteristic, complemented
177	#1277	C₂×C₂₃	1	1	yes	characteristic, complemented
178	#1277	C₂×C₂₃	1	1	yes	characteristic, complemented
179	C₂²×C₂₃	—	2	2	no	—
180	C₂²×C₂₃	—	2	2	no	—
181	C₂²×C₂₃	—	2	2	no	—
182	C₂²×C₂₃	—	4	1	no	—
183	C₂²×C₂₃	—	4	1	no	—
184	C₂²×C₂₃	—	4	1	no	—
185	C₂²×C₂₃	—	4	1	no	—
186	C₂²×C₂₃	#385	1	1	yes	characteristic
187	C₂²×C₂₃	#423	1	1	yes	characteristic
188	C₂²×C₂₃	#424	1	1	yes	characteristic
189	C₂²×C₂₃	#427	1	1	yes	characteristic
190	C₂²×C₂₃	#428	1	1	yes	characteristic
191	C₂²×C₂₃	C₂×#108	1	1	yes	characteristic
192	C₂²×C₂₃	#430	1	1	yes	characteristic
193	C₄×C₂₃	—	2	1	no	—
194	C₄×C₂₃	—	2	1	no	—
195	C₄×C₂₃	—	4	1	no	—
196	C₄×C₂₃	—	4	1	no	—
197	C₄×C₂₃	—	4	1	no	—
198	C₄×C₂₃	#435	1	1	yes	characteristic
199	C₄×C₂₃	#435	1	1	yes	characteristic
200	C₄×C₂₃	#436	1	1	yes	characteristic
201	C₄×C₂₃	#436	1	1	yes	characteristic
202	C₄×C₂₃	#449	1	1	yes	characteristic
203	C₄×C₂₃	#452	1	1	yes	characteristic
204	C₄×C₂₃	#482	1	1	yes	characteristic
205	C₄×C₂₃	#485	1	1	yes	characteristic
206	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
207	#432	—	2	2	no	—
208	#432	—	2	2	no	—
209	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
210	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
211	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
212	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
213	C₂×C₂²⋊C₈	—	2	1	no	—
214	C₂×C₂²⋊C₈	—	2	1	no	—
215	C₂×C₂²⋊C₈	C₄×C₂₃	1	1	yes	characteristic
216	C₂×C₂²⋊C₈	C₄×C₂₃	1	1	yes	characteristic
217	C₂×#97	—	2	1	no	—
218	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
219	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
220	#336	—	2	1	no	—
221	#336	C₄×C₂₃	1	1	yes	characteristic
222	#336	C₄×C₂₃	1	1	yes	characteristic
223	#335	—	2	2	no	—
224	#334	—	2	2	no	—
225	C₂×C₂₃	—	4	2	no	—
226	C₂×C₂₃	#1568	1	1	yes	characteristic
227	C₂×C₂₃	#1569	1	1	yes	characteristic
228	C₂×C₂₃	#1572	1	1	yes	characteristic
229	C₂×C₂₃	#1573	1	1	yes	characteristic
230	C₂×C₂₃	#1851	1	1	yes	characteristic
231	C₂×C₂₃	#1854	1	1	yes	characteristic
232	C₂×C₂₃	#1855	1	1	yes	characteristic
233	C₂³×C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
234	C₂³×C₄	D₄×C₂₃	1	1	yes	characteristic
235	C₂³×C₄	Q₈×C₂₃	1	1	yes	characteristic
236	C₂²×C₈	—	2	1	no	—
237	C₂²×C₈	—	2	1	no	—
238	C₂²×C₈	—	2	1	no	—
239	C₂²×C₈	—	2	1	no	—
240	C₂²×C₈	C₂×C₄×C₂₃	1	1	yes	characteristic
241	C₂²×C₈	C₂×C₄×C₂₃	1	1	yes	characteristic
242	C₂²×C₈	C₂×C₄×C₂₃	1	1	yes	characteristic
243	C₂²×C₈	C₂×C₄×C₂₃	1	1	yes	characteristic
244	C₂×C₄²	—	2	1	no	—
245	C₂×C₄²	—	2	1	no	—
246	C₂×C₄²	—	2	1	no	—
247	C₂×C₄²	—	2	1	no	—
248	C₂×C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic
249	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
250	C₂×C₄²	Q₈×C₂₃	1	1	yes	characteristic
251	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
252	C₄⋊C₈	—	2	1	no	—
253	C₄⋊C₈	—	2	1	no	—
254	C₄⋊C₈	—	2	1	no	—
255	C₄⋊C₈	—	2	1	no	—
256	C₄⋊C₈	—	2	1	no	—
257	C₄⋊C₈	—	2	1	no	—
258	C₄⋊C₈	D₄×C₂₃	1	2	yes	—
259	C₄⋊C₈	D₄×C₂₃	1	2	yes	—
260	C₂²⋊C₈	—	2	4	no	—
261	C₂²⋊C₈	—	2	2	no	—
262	C₂²⋊C₈	—	2	2	no	—
263	C₂²⋊C₈	—	4	2	no	—
264	#97	—	2	4	no	—
265	C₄×C₈	—	2	1	no	—
266	C₄×C₈	—	2	1	no	—
267	C₄×C₈	—	2	1	no	—
268	C₄×C₈	—	2	1	no	—
269	C₂₃	#8834	1	1	yes	characteristic, direct product factor, Sylow
270	C₂⁴	C₄⋊C₄×C₂₃	1	1	yes	characteristic
271	C₂²×C₄	—	2	2	no	—
272	C₂²×C₄	—	2	1	no	—
273	C₂²×C₄	—	2	1	no	—
274	C₂²×C₄	—	2	1	no	—
275	C₂²×C₄	—	2	1	no	—
276	C₂²×C₄	—	2	1	no	—
277	C₂²×C₄	—	2	1	no	—
278	C₂²×C₄	—	2	1	no	—
279	C₂²×C₄	—	2	1	no	—
280	C₂²×C₄	—	2	1	no	—
281	C₂²×C₄	—	2	1	no	—
282	C₂²×C₄	—	2	1	no	—
283	C₂²×C₄	—	2	1	no	—
284	C₂²×C₄	—	2	1	no	—
285	C₂²×C₄	—	2	1	no	—
286	C₂²×C₄	—	4	1	no	—
287	C₂²×C₄	C₄⋊C₄×C₂₃	1	1	yes	characteristic
288	C₂²×C₄	C₄⋊C₄×C₂₃	1	1	yes	characteristic
289	C₂²×C₄	C₄⋊C₄×C₂₃	1	1	yes	characteristic
290	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
291	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
292	C₂²×C₄	C₂×Q₈×C₂₃	1	1	yes	characteristic
293	C₂×C₈	—	2	1	no	—
294	C₂×C₈	—	2	1	no	—
295	C₂×C₈	—	2	1	no	—
296	C₂×C₈	—	2	1	no	—
297	C₂×C₈	—	2	1	no	—
298	C₂×C₈	—	2	1	no	—
299	C₂×C₈	—	2	2	no	—
300	C₂×C₈	—	2	2	no	—
301	C₂×C₈	—	2	1	no	—
302	C₂×C₈	—	2	1	no	—
303	C₂×C₈	—	2	1	no	—
304	C₂×C₈	—	2	1	no	—
305	C₂×C₈	—	4	1	no	—
306	C₂×C₈	—	4	1	no	—
307	C₂×C₈	—	4	1	no	—
308	C₂×C₈	—	4	1	no	—
309	C₂×C₈	—	4	1	no	—
310	C₂×C₈	—	4	1	no	—
311	C₂×C₈	—	4	1	no	—
312	C₂×C₈	—	4	1	no	—
313	C₂×C₈	—	4	1	no	—
314	C₂×C₈	—	4	1	no	—
315	C₂×C₈	M₁₆×C₂₃	1	2	yes	—
316	C₂×C₈	M₁₆×C₂₃	1	2	yes	—
317	C₄²	—	2	1	no	—
318	C₄²	—	2	1	no	—
319	C₄²	—	2	1	no	—
320	C₄²	—	2	1	no	—
321	C₄²	—	2	1	no	—
322	C₄²	—	2	1	no	—
323	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
324	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
325	C₄²	#41×C₂₃	1	1	yes	characteristic
326	C₄²	#41×C₂₃	1	1	yes	characteristic
327	C₂³	—	2	1	no	—
328	C₂³	—	2	1	no	—
329	C₂³	—	2	1	no	—
330	C₂³	—	2	1	no	—
331	C₂³	—	2	1	no	—
332	C₂³	—	2	1	no	—
333	C₂³	C₂₃×#108	1	2	yes	—
334	C₂³	C₂×C₄⋊C₄×C₂₃	1	1	yes	characteristic
335	C₂×C₄	—	2	1	no	—
336	C₂×C₄	—	2	1	no	—
337	C₂×C₄	—	2	1	no	—
338	C₂×C₄	—	2	1	no	—
339	C₂×C₄	—	2	1	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	2	1	no	—
344	C₂×C₄	—	2	1	no	—
345	C₂×C₄	—	2	1	no	—
346	C₂×C₄	—	4	2	no	—
347	C₂×C₄	—	4	2	no	—
348	C₂×C₄	—	4	1	no	—
349	C₂×C₄	—	4	1	no	—
350	C₂×C₄	—	4	1	no	—
351	C₂×C₄	—	4	1	no	—
352	C₂×C₄	—	4	1	no	—
353	C₂×C₄	—	4	1	no	—
354	C₂×C₄	—	4	1	no	—
355	C₂×C₄	—	4	1	no	—
356	C₂×C₄	C₄×D₄×C₂₃	1	1	yes	characteristic
357	C₂×C₄	C₄×D₄×C₂₃	1	1	yes	characteristic
358	C₂×C₄	C₂₃×#120	1	1	yes	characteristic
359	C₂×C₄	C₂₃×C₂²⋊Q₈	1	1	yes	characteristic
360	C₂×C₄	C₂₃×C₂²⋊Q₈	1	1	yes	characteristic
361	C₂×C₄	C₂₃×#123	1	1	yes	characteristic
362	C₂×C₄	C₂×M₁₆×C₂₃	1	1	yes	characteristic
363	C₂×C₄	C₂×M₁₆×C₂₃	1	1	yes	characteristic
364	C₂×C₄	C₂₃×#131	1	1	yes	characteristic
365	C₂×C₄	C₂₃×#131	1	1	yes	characteristic
366	C₂×C₄	C₂₃×#135	1	1	yes	characteristic
367	C₂×C₄	C₂₃×#135	1	1	yes	characteristic
368	C₂×C₄	C₂₃×AGL(1,ℤ/8)	1	1	yes	characteristic
369	C₂×C₄	C₂₃×#137	1	1	yes	characteristic
370	C₈	—	2	2	no	—
371	C₈	—	2	2	no	—
372	C₈	—	4	1	no	—
373	C₈	—	4	1	no	—
374	C₈	—	4	2	no	—
375	C₈	—	4	2	no	—
376	C₈	—	8	1	no	—
377	C₈	—	8	1	no	—
378	C₂²	—	2	2	no	—
379	C₂²	—	2	2	no	—
380	C₂²	—	2	2	no	—
381	C₂²	—	4	1	no	—
382	C₂²	—	4	1	no	—
383	C₂²	—	4	1	no	—
384	C₂²	—	4	1	no	—
385	C₂²	C₂₃×#385	1	1	yes	characteristic
386	C₂²	C₂₃×#423	1	1	yes	characteristic
387	C₂²	C₂₃×#424	1	1	yes	characteristic
388	C₂²	C₂₃×#427	1	1	yes	characteristic
389	C₂²	C₂₃×#428	1	1	yes	characteristic
390	C₂²	C₂×C₂₃×#108	1	1	yes	characteristic
391	C₂²	C₂₃×#430	1	1	yes	characteristic
392	C₄	—	2	1	no	—
393	C₄	—	2	1	no	—
394	C₄	—	4	1	no	—
395	C₄	—	4	1	no	—
396	C₄	—	4	1	no	—
397	C₄	C₂₃×#435	1	1	yes	characteristic
398	C₄	C₂₃×#435	1	1	yes	characteristic
399	C₄	C₂₃×#436	1	1	yes	characteristic
400	C₄	C₂₃×#436	1	1	yes	characteristic
401	C₄	C₂₃×#449	1	1	yes	characteristic
402	C₄	C₂₃×#452	1	1	yes	characteristic
403	C₄	C₂₃×#482	1	1	yes	characteristic
404	C₄	C₂₃×#485	1	1	yes	characteristic
405	C₂	—	4	2	no	—
406	C₂	C₂₃×#1568	1	1	yes	characteristic
407	C₂	C₂₃×#1569	1	1	yes	characteristic
408	C₂	C₂₃×#1572	1	1	yes	characteristic
409	C₂	C₂₃×#1573	1	1	yes	characteristic
410	C₂	C₂₃×#1851	1	1	yes	characteristic
411	C₂	C₂₃×#1854	1	1	yes	characteristic
412	C₂	C₂₃×#1855	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
4. C₂×C₂₃×#335	C₂	semidirect
5. C₂×C₂₃×#334	C₂	semidirect
6. C₂₃×#1277	C₂	semidirect
7. C₂₃×#1277	C₂	semidirect
120. #8834	C₂₃	direct (N × H)
175. C₂×#335	C₂×C₂₃	semidirect
176. C₂×#334	C₂×C₂₃	semidirect
177. #1277	C₂×C₂₃	semidirect
178. #1277	C₂×C₂₃	semidirect
269. C₂₃	#8834	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×#432	2
C₂₃×#1797	2
C₄×C₂₃×C₂²⋊C₈	2
C₂×C₂₃×#335	2
C₂×C₂₃×#334	2
C₂₃×#1277	2
#8834	23

Subgroups — C23×#8834 #19156460

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#8834 #19156460