Subgroups — C₂₃×#10052 #19157678

Order 5888.

738 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#486	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₃×#459	C₂	1	1	yes	maximal, characteristic
3	C₂₃×#2542	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#1982	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₂₃×#332	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₂₃×D₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#1279	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×D₈×C₂₃	—	2	1	no	—
9	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
10	C₂×C₂₃×#127	C₂²	1	1	yes	characteristic
11	C₂×C₂₃×C₂²⋊Q₈	—	2	2	no	—
12	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
13	C₂₃×#486	—	2	2	no	—
14	C₂₃×#486	—	2	2	no	—
15	C₂₃×#459	—	2	2	no	—
16	C₂₃×#459	—	2	2	no	—
17	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
18	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×C₂₃×#102	—	2	1	no	—
20	C₂×C₂₃×#102	—	2	2	no	—
21	C₂×C₂₃×#102	—	2	2	no	—
22	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
23	C₂₃×#399	—	2	2	no	—
24	C₂₃×#390	—	2	1	no	—
25	C₂₃×#384	—	2	1	no	—
26	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
27	C₂₃×#332	—	2	2	no	—
28	C₂₃×D₄⋊C₈	—	2	2	no	—
29	C₂²×Q₈×C₂₃	—	2	1	no	—
30	C₂²×D₄×C₂₃	—	2	1	no	—
31	C₂²×D₄×C₂₃	—	2	1	no	—
32	C₂²×D₄×C₂₃	—	2	1	no	—
33	C₂²×D₄×C₂₃	D₄	1	1	yes	characteristic
34	C₂³×C₄×C₂₃	—	2	1	no	—
35	C₂×D₈×C₂₃	—	2	4	no	—
36	C₂×D₈×C₂₃	—	4	2	no	—
37	C₂×D₈×C₂₃	—	4	2	no	—
38	C₂²×C₈×C₂₃	—	2	1	no	—
39	C₂²×C₈×C₂₃	—	2	1	no	—
40	C₂²×C₈×C₂₃	—	2	1	no	—
41	C₂₃×C₄⋊Q₈	—	2	1	no	—
42	C₂₃×C₄⋊Q₈	—	2	1	no	—
43	C₂₃×C₄⋊Q₈	—	2	1	no	—
44	C₂₃×C₄⋊Q₈	—	2	1	no	—
45	C₂₃×#127	—	2	1	no	—
46	C₂₃×#127	—	2	1	no	—
47	C₂₃×#127	—	2	1	no	—
48	C₂₃×#127	D₄	1	2	yes	—
49	C₂₃×C₂²⋊Q₈	—	4	4	no	—
50	C₂₃×C₂²⋊Q₈	—	4	4	no	—
51	C₄×D₄×C₂₃	—	2	1	no	—
52	C₄×D₄×C₂₃	—	2	1	no	—
53	C₄×D₄×C₂₃	—	2	1	no	—
54	C₄×D₄×C₂₃	—	2	1	no	—
55	C₂×C₄⋊C₄×C₂₃	—	2	4	no	—
56	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
57	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
58	C₂×C₄⋊C₄×C₂₃	D₄	1	2	yes	—
59	C₂×C₄⋊C₄×C₂₃	D₄	1	2	yes	—
60	C₂×C₂²⋊C₄×C₂₃	—	2	4	no	—
61	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
62	C₂×C₄²×C₂₃	—	2	1	no	—
63	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
64	C₂₃×C₄⋊C₈	—	2	1	no	—
65	C₂₃×C₄⋊C₈	—	2	1	no	—
66	C₂₃×C₄⋊C₈	—	2	1	no	—
67	C₂₃×C₄⋊C₈	D₄	1	2	yes	—
68	C₂₃×#102	—	2	4	no	—
69	C₂₃×#102	—	2	8	no	—
70	C₂₃×#102	—	4	4	no	—
71	C₄×C₈×C₂₃	—	2	1	no	—
72	C₄×C₈×C₂₃	D₄	1	2	yes	—
73	C₂₃×#95	—	2	1	no	—
74	C₂⁴×C₂₃	—	2	1	no	—
75	C₂⁴×C₂₃	—	4	1	no	—
76	C₂×Q₈×C₂₃	—	4	1	no	—
77	C₂×Q₈×C₂₃	—	4	1	no	—
78	C₂×Q₈×C₂₃	—	4	2	no	—
79	C₂×Q₈×C₂₃	—	4	2	no	—
80	C₂×D₄×C₂₃	—	2	1	no	—
81	C₂×D₄×C₂₃	—	2	2	no	—
82	C₂×D₄×C₂₃	—	2	2	no	—
83	C₂×D₄×C₂₃	—	2	1	no	—
84	C₂×D₄×C₂₃	—	2	2	no	—
85	C₂×D₄×C₂₃	—	2	1	no	—
86	C₂×D₄×C₂₃	—	2	1	no	—
87	C₂×D₄×C₂₃	—	2	1	no	—
88	C₂×D₄×C₂₃	—	4	4	no	—
89	C₂×D₄×C₂₃	—	4	1	no	—
90	C₂×D₄×C₂₃	—	4	1	no	—
91	C₂×D₄×C₂₃	—	4	1	no	—
92	C₂×D₄×C₂₃	—	4	2	no	—
93	C₂×D₄×C₂₃	—	4	1	no	—
94	C₂×D₄×C₂₃	—	4	1	no	—
95	C₂×D₄×C₂₃	—	4	1	no	—
96	C₂×D₄×C₂₃	—	4	2	no	—
97	C₂×D₄×C₂₃	—	4	1	no	—
98	C₂×D₄×C₂₃	SD₁₆	1	2	yes	—
99	C₂²×C₄×C₂₃	—	2	2	no	—
100	C₂²×C₄×C₂₃	—	2	2	no	—
101	C₂²×C₄×C₂₃	—	2	1	no	—
102	C₂²×C₄×C₂₃	—	4	1	no	—
103	C₂²×C₄×C₂₃	—	4	1	no	—
104	C₂²×C₄×C₂₃	—	4	2	no	—
105	C₂²×C₄×C₂₃	—	4	2	no	—
106	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
109	D₈×C₂₃	—	4	8	no	—
110	C₂×C₈×C₂₃	—	2	2	no	—
111	C₂×C₈×C₂₃	—	2	2	no	—
112	C₂×C₈×C₂₃	—	4	2	no	—
113	C₂×C₈×C₂₃	—	4	1	no	—
114	C₂×C₈×C₂₃	—	4	1	no	—
115	C₂×C₈×C₂₃	—	4	1	no	—
116	C₂×C₈×C₂₃	—	4	2	no	—
117	C₄⋊C₄×C₂₃	—	2	2	no	—
118	C₄⋊C₄×C₂₃	—	2	1	no	—
119	C₄⋊C₄×C₂₃	—	2	2	no	—
120	C₄⋊C₄×C₂₃	—	2	1	no	—
121	C₄⋊C₄×C₂₃	—	2	2	no	—
122	C₄⋊C₄×C₂₃	—	4	8	no	—
123	C₄⋊C₄×C₂₃	—	4	1	no	—
124	C₄⋊C₄×C₂₃	—	4	1	no	—
125	C₄⋊C₄×C₂₃	D₈	1	4	yes	complemented
126	C₂²⋊C₄×C₂₃	—	4	8	no	—
127	C₂²⋊C₄×C₂₃	—	4	1	no	—
128	C₂²⋊C₄×C₂₃	—	4	1	no	—
129	C₄²×C₂₃	—	4	1	no	—
130	C₄²×C₂₃	—	4	1	no	—
131	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
132	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
133	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
134	C₄²×C₂₃	#41	1	1	yes	characteristic
135	#10052	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
136	C₂³×C₂₃	—	2	2	no	—
137	C₂³×C₂₃	—	4	1	no	—
138	C₂³×C₂₃	—	4	2	no	—
139	C₂³×C₂₃	—	4	1	no	—
140	C₂³×C₂₃	—	4	2	no	—
141	C₂³×C₂₃	—	4	2	no	—
142	C₂³×C₂₃	—	8	2	no	—
143	C₂³×C₂₃	—	8	1	no	—
144	C₂³×C₂₃	—	8	1	no	—
145	C₂³×C₂₃	—	8	2	no	—
146	C₂³×C₂₃	#120	1	1	yes	characteristic
147	Q₈×C₂₃	—	8	2	no	—
148	Q₈×C₂₃	—	8	1	no	—
149	Q₈×C₂₃	—	8	1	no	—
150	D₄×C₂₃	—	2	2	no	—
151	D₄×C₂₃	—	2	2	no	—
152	D₄×C₂₃	—	4	4	no	—
153	D₄×C₂₃	—	4	2	no	—
154	D₄×C₂₃	—	4	1	no	—
155	D₄×C₂₃	—	4	2	no	—
156	D₄×C₂₃	—	4	4	no	—
157	D₄×C₂₃	—	4	1	no	—
158	D₄×C₂₃	—	8	2	no	—
159	D₄×C₂₃	—	8	1	no	—
160	D₄×C₂₃	—	8	1	no	—
161	D₄×C₂₃	—	8	1	no	—
162	D₄×C₂₃	—	8	1	no	—
163	C₂×C₄×C₂₃	—	2	2	no	—
164	C₂×C₄×C₂₃	—	2	4	no	—
165	C₂×C₄×C₂₃	—	4	2	no	—
166	C₂×C₄×C₂₃	—	4	2	no	—
167	C₂×C₄×C₂₃	—	4	1	no	—
168	C₂×C₄×C₂₃	—	4	2	no	—
169	C₂×C₄×C₂₃	—	4	4	no	—
170	C₂×C₄×C₂₃	—	4	2	no	—
171	C₂×C₄×C₂₃	—	8	2	no	—
172	C₂×C₄×C₂₃	—	8	1	no	—
173	C₂×C₄×C₂₃	—	8	1	no	—
174	C₂×C₄×C₂₃	#120	1	1	yes	characteristic
175	C₂×C₄×C₂₃	#120	1	1	yes	characteristic
176	C₂×C₄×C₂₃	#121	1	1	yes	characteristic
177	C₂×C₄×C₂₃	#121	1	1	yes	characteristic
178	C₂×C₄×C₂₃	#121	1	1	yes	characteristic
179	C₂×C₄×C₂₃	#127	1	1	yes	characteristic
180	C₂×C₄×C₂₃	C₂×D₈	1	2	yes	—
181	C₂×C₄×C₂₃	C₂×SD₁₆	1	1	yes	characteristic
182	C₂×C₄×C₂₃	#135	1	1	yes	characteristic
183	C₂×C₄×C₂₃	AGL(1,ℤ/8)	1	1	yes	characteristic
184	C₂×C₄×C₂₃	AGL(1,ℤ/8)	1	2	yes	—
185	C₂×C₄×C₂₃	#137	1	1	yes	characteristic
186	C₈×C₂₃	—	4	2	no	—
187	C₈×C₂₃	—	4	2	no	—
188	C₈×C₂₃	—	8	1	no	—
189	C₂×#486	C₂×C₂₃	1	1	yes	characteristic, complemented
190	C₂×#459	C₂×C₂₃	1	1	yes	characteristic
191	#2542	C₂×C₂₃	1	1	yes	characteristic, complemented
192	#1982	C₂×C₂₃	1	1	yes	characteristic, complemented
193	C₂×#332	C₂×C₂₃	1	1	yes	characteristic, complemented
194	C₂×D₄⋊C₈	C₂×C₂₃	1	1	yes	characteristic, complemented
195	#1279	C₂×C₂₃	1	1	yes	characteristic, complemented
196	C₂²×C₂₃	—	4	4	no	—
197	C₂²×C₂₃	—	4	2	no	—
198	C₂²×C₂₃	—	8	2	no	—
199	C₂²×C₂₃	—	8	1	no	—
200	C₂²×C₂₃	—	8	1	no	—
201	C₂²×C₂₃	—	8	2	no	—
202	C₂²×C₂₃	—	8	2	no	—
203	C₂²×C₂₃	—	8	2	no	—
204	C₂²×C₂₃	—	16	2	no	—
205	C₂²×C₂₃	—	16	2	no	—
206	C₂²×C₂₃	#392	1	1	yes	characteristic
207	C₂²×C₂₃	#447	1	2	yes	—
208	C₂²×C₂₃	#448	1	1	yes	characteristic
209	C₂²×C₂₃	#449	1	1	yes	characteristic
210	C₂²×C₂₃	#454	1	2	yes	—
211	C₄×C₂₃	—	2	1	no	—
212	C₄×C₂₃	—	2	1	no	—
213	C₄×C₂₃	—	4	4	no	—
214	C₄×C₂₃	—	8	1	no	—
215	C₄×C₂₃	—	8	2	no	—
216	C₄×C₂₃	#450	1	1	yes	characteristic
217	C₄×C₂₃	#452	1	1	yes	characteristic
218	C₄×C₂₃	#459	1	2	yes	—
219	C₄×C₂₃	#465	1	1	yes	characteristic
220	C₄×C₂₃	#468	1	1	yes	characteristic
221	C₄×C₂₃	#493	1	1	yes	characteristic
222	C₄×C₂₃	#496	1	1	yes	characteristic
223	C₂²×D₈	—	2	1	no	—
224	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
225	C₂×#127	C₂²×C₂₃	1	1	yes	characteristic
226	C₂×C₂²⋊Q₈	—	2	2	no	—
227	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
228	#486	—	2	2	no	—
229	#486	—	2	2	no	—
230	#459	—	2	2	no	—
231	#459	—	2	2	no	—
232	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
233	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
234	C₂×#102	—	2	2	no	—
235	C₂×#102	—	2	1	no	—
236	C₂×#102	—	2	2	no	—
237	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
238	#399	—	2	2	no	—
239	#390	—	2	1	no	—
240	#384	—	2	1	no	—
241	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
242	#332	—	2	2	no	—
243	D₄⋊C₈	—	2	2	no	—
244	C₂×C₂₃	—	8	2	no	—
245	C₂×C₂₃	—	16	2	no	—
246	C₂×C₂₃	#1625	1	2	yes	—
247	C₂×C₂₃	#1627	1	2	yes	—
248	C₂×C₂₃	#2000	1	1	yes	characteristic
249	C₂×C₂₃	#2003	1	1	yes	characteristic
250	C₂×C₂₃	#2011	1	1	yes	characteristic
251	C₂²×Q₈	—	2	1	no	—
252	C₂²×D₄	—	2	1	no	—
253	C₂²×D₄	—	2	1	no	—
254	C₂²×D₄	—	2	1	no	—
255	C₂²×D₄	D₄×C₂₃	1	1	yes	characteristic
256	C₂³×C₄	—	2	1	no	—
257	C₂×D₈	—	2	4	no	—
258	C₂×D₈	—	4	2	no	—
259	C₂×D₈	—	4	2	no	—
260	C₂²×C₈	—	2	1	no	—
261	C₂²×C₈	—	2	1	no	—
262	C₂²×C₈	—	2	1	no	—
263	C₄⋊Q₈	—	2	1	no	—
264	C₄⋊Q₈	—	2	1	no	—
265	C₄⋊Q₈	—	2	1	no	—
266	C₄⋊Q₈	—	2	1	no	—
267	#127	—	2	1	no	—
268	#127	—	2	1	no	—
269	#127	—	2	1	no	—
270	#127	D₄×C₂₃	1	2	yes	—
271	C₂²⋊Q₈	—	4	4	no	—
272	C₂²⋊Q₈	—	4	4	no	—
273	C₄×D₄	—	2	1	no	—
274	C₄×D₄	—	2	1	no	—
275	C₄×D₄	—	2	1	no	—
276	C₄×D₄	—	2	1	no	—
277	C₂×C₄⋊C₄	—	2	4	no	—
278	C₂×C₄⋊C₄	—	2	1	no	—
279	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
280	C₂×C₄⋊C₄	D₄×C₂₃	1	2	yes	—
281	C₂×C₄⋊C₄	D₄×C₂₃	1	2	yes	—
282	C₂×C₂²⋊C₄	—	2	4	no	—
283	C₂×C₂²⋊C₄	—	2	1	no	—
284	C₂×C₄²	—	2	1	no	—
285	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
286	C₄⋊C₈	—	2	1	no	—
287	C₄⋊C₈	—	2	1	no	—
288	C₄⋊C₈	—	2	1	no	—
289	C₄⋊C₈	D₄×C₂₃	1	2	yes	—
290	#102	—	2	4	no	—
291	#102	—	2	8	no	—
292	#102	—	4	4	no	—
293	C₄×C₈	—	2	1	no	—
294	C₄×C₈	D₄×C₂₃	1	2	yes	—
295	#95	—	2	1	no	—
296	C₂₃	#10052	1	1	yes	characteristic, direct product factor, Sylow
297	C₂⁴	—	2	1	no	—
298	C₂⁴	—	4	1	no	—
299	C₂×Q₈	—	4	1	no	—
300	C₂×Q₈	—	4	1	no	—
301	C₂×Q₈	—	4	2	no	—
302	C₂×Q₈	—	4	2	no	—
303	C₂×D₄	—	2	1	no	—
304	C₂×D₄	—	2	2	no	—
305	C₂×D₄	—	2	2	no	—
306	C₂×D₄	—	2	1	no	—
307	C₂×D₄	—	2	2	no	—
308	C₂×D₄	—	2	1	no	—
309	C₂×D₄	—	2	1	no	—
310	C₂×D₄	—	2	1	no	—
311	C₂×D₄	—	4	4	no	—
312	C₂×D₄	—	4	1	no	—
313	C₂×D₄	—	4	1	no	—
314	C₂×D₄	—	4	1	no	—
315	C₂×D₄	—	4	2	no	—
316	C₂×D₄	—	4	1	no	—
317	C₂×D₄	—	4	1	no	—
318	C₂×D₄	—	4	1	no	—
319	C₂×D₄	—	4	2	no	—
320	C₂×D₄	—	4	1	no	—
321	C₂×D₄	SD₁₆×C₂₃	1	2	yes	—
322	C₂²×C₄	—	2	2	no	—
323	C₂²×C₄	—	2	2	no	—
324	C₂²×C₄	—	2	1	no	—
325	C₂²×C₄	—	4	1	no	—
326	C₂²×C₄	—	4	1	no	—
327	C₂²×C₄	—	4	2	no	—
328	C₂²×C₄	—	4	2	no	—
329	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
330	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
331	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
332	D₈	—	4	8	no	—
333	C₂×C₈	—	2	2	no	—
334	C₂×C₈	—	2	2	no	—
335	C₂×C₈	—	4	2	no	—
336	C₂×C₈	—	4	1	no	—
337	C₂×C₈	—	4	1	no	—
338	C₂×C₈	—	4	1	no	—
339	C₂×C₈	—	4	2	no	—
340	C₄⋊C₄	—	2	2	no	—
341	C₄⋊C₄	—	2	1	no	—
342	C₄⋊C₄	—	2	2	no	—
343	C₄⋊C₄	—	2	1	no	—
344	C₄⋊C₄	—	2	2	no	—
345	C₄⋊C₄	—	4	8	no	—
346	C₄⋊C₄	—	4	1	no	—
347	C₄⋊C₄	—	4	1	no	—
348	C₄⋊C₄	D₈×C₂₃	1	4	yes	complemented
349	C₂²⋊C₄	—	4	8	no	—
350	C₂²⋊C₄	—	4	1	no	—
351	C₂²⋊C₄	—	4	1	no	—
352	C₄²	—	4	1	no	—
353	C₄²	—	4	1	no	—
354	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
355	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
356	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
357	C₄²	#41×C₂₃	1	1	yes	characteristic
358	C₂³	—	2	2	no	—
359	C₂³	—	4	1	no	—
360	C₂³	—	4	2	no	—
361	C₂³	—	4	1	no	—
362	C₂³	—	4	2	no	—
363	C₂³	—	4	2	no	—
364	C₂³	—	8	2	no	—
365	C₂³	—	8	1	no	—
366	C₂³	—	8	1	no	—
367	C₂³	—	8	2	no	—
368	C₂³	C₂₃×#120	1	1	yes	characteristic
369	Q₈	—	8	2	no	—
370	Q₈	—	8	1	no	—
371	Q₈	—	8	1	no	—
372	D₄	—	2	2	no	—
373	D₄	—	2	2	no	—
374	D₄	—	4	4	no	—
375	D₄	—	4	2	no	—
376	D₄	—	4	1	no	—
377	D₄	—	4	2	no	—
378	D₄	—	4	4	no	—
379	D₄	—	4	1	no	—
380	D₄	—	8	2	no	—
381	D₄	—	8	1	no	—
382	D₄	—	8	1	no	—
383	D₄	—	8	1	no	—
384	D₄	—	8	1	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	4	no	—
387	C₂×C₄	—	4	2	no	—
388	C₂×C₄	—	4	2	no	—
389	C₂×C₄	—	4	1	no	—
390	C₂×C₄	—	4	2	no	—
391	C₂×C₄	—	4	4	no	—
392	C₂×C₄	—	4	2	no	—
393	C₂×C₄	—	8	2	no	—
394	C₂×C₄	—	8	1	no	—
395	C₂×C₄	—	8	1	no	—
396	C₂×C₄	C₂₃×#120	1	1	yes	characteristic
397	C₂×C₄	C₂₃×#120	1	1	yes	characteristic
398	C₂×C₄	C₂₃×#121	1	1	yes	characteristic
399	C₂×C₄	C₂₃×#121	1	1	yes	characteristic
400	C₂×C₄	C₂₃×#121	1	1	yes	characteristic
401	C₂×C₄	C₂₃×#127	1	1	yes	characteristic
402	C₂×C₄	C₂×D₈×C₂₃	1	2	yes	—
403	C₂×C₄	C₂×SD₁₆×C₂₃	1	1	yes	characteristic
404	C₂×C₄	C₂₃×#135	1	1	yes	characteristic
405	C₂×C₄	C₂₃×AGL(1,ℤ/8)	1	1	yes	characteristic
406	C₂×C₄	C₂₃×AGL(1,ℤ/8)	1	2	yes	—
407	C₂×C₄	C₂₃×#137	1	1	yes	characteristic
408	C₈	—	4	2	no	—
409	C₈	—	4	2	no	—
410	C₈	—	8	1	no	—
411	C₂²	—	4	2	no	—
412	C₂²	—	4	4	no	—
413	C₂²	—	8	1	no	—
414	C₂²	—	8	1	no	—
415	C₂²	—	8	2	no	—
416	C₂²	—	8	2	no	—
417	C₂²	—	8	2	no	—
418	C₂²	—	8	2	no	—
419	C₂²	—	16	2	no	—
420	C₂²	—	16	2	no	—
421	C₂²	C₂₃×#392	1	1	yes	characteristic
422	C₂²	C₂₃×#447	1	2	yes	—
423	C₂²	C₂₃×#448	1	1	yes	characteristic
424	C₂²	C₂₃×#449	1	1	yes	characteristic
425	C₂²	C₂₃×#454	1	2	yes	—
426	C₄	—	2	1	no	—
427	C₄	—	2	1	no	—
428	C₄	—	4	4	no	—
429	C₄	—	8	1	no	—
430	C₄	—	8	2	no	—
431	C₄	C₂₃×#450	1	1	yes	characteristic
432	C₄	C₂₃×#452	1	1	yes	characteristic
433	C₄	C₂₃×#459	1	2	yes	—
434	C₄	C₂₃×#465	1	1	yes	characteristic
435	C₄	C₂₃×#468	1	1	yes	characteristic
436	C₄	C₂₃×#493	1	1	yes	characteristic
437	C₄	C₂₃×#496	1	1	yes	characteristic
438	C₂	—	8	2	no	—
439	C₂	—	16	2	no	—
440	C₂	C₂₃×#1625	1	2	yes	—
441	C₂	C₂₃×#1627	1	2	yes	—
442	C₂	C₂₃×#2000	1	1	yes	characteristic
443	C₂	C₂₃×#2003	1	1	yes	characteristic
444	C₂	C₂₃×#2011	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₃	#120
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₂₃
prime radical	C₂×C₂₃×#459	C₂
LCS	G ▷ C₂×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
1. C₂×C₂₃×#486	C₂	semidirect
3. C₂₃×#2542	C₂	semidirect
4. C₂₃×#1982	C₂	semidirect
5. C₂×C₂₃×#332	C₂	semidirect
6. C₂×C₂₃×D₄⋊C₈	C₂	semidirect
7. C₂₃×#1279	C₂	semidirect
125. C₄⋊C₄×C₂₃	D₈	semidirect
135. #10052	C₂₃	direct (N × H)
189. C₂×#486	C₂×C₂₃	semidirect
191. #2542	C₂×C₂₃	semidirect
192. #1982	C₂×C₂₃	semidirect
193. C₂×#332	C₂×C₂₃	semidirect
194. C₂×D₄⋊C₈	C₂×C₂₃	semidirect
195. #1279	C₂×C₂₃	semidirect
296. C₂₃	#10052	direct (N × H)
348. C₄⋊C₄	D₈×C₂₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₂₃×#486	2
C₂×C₂₃×#459	2
C₂₃×#2542	2
C₂₃×#1982	2
C₂×C₂₃×#332	2
C₂×C₂₃×D₄⋊C₈	2
C₂₃×#1279	2
#10052	23

Subgroups — C23×#10052 #19157678

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#10052 #19157678