Subgroups — C₂₃×#8976 #19156602

Order 5888.

592 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#476	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#2354	C₂	1	1	yes	maximal, characteristic
3	C₂₃×#1987	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#1956	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₂₃×D₄⋊C₈	C₂	1	1	yes	maximal, characteristic
6	C₂₃×#1296	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#1279	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
9	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
10	C₂×C₂₃×#117	—	2	1	no	—
11	C₂₃×#476	—	2	2	no	—
12	C₂₃×#476	C₄	1	4	yes	complemented
13	C₂×C₂₃×#106	—	2	1	no	—
14	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
15	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
16	C₂×C₂₃×#103	—	2	2	no	—
17	C₂×C₂₃×#102	—	2	1	no	—
18	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
19	C₂₃×#390	—	2	1	no	—
20	C₂₃×#388	—	2	2	no	—
21	C₂₃×#384	C₂²	1	1	yes	characteristic
22	C₂₃×#380	—	2	1	no	—
23	C₄×C₄⋊C₄×C₂₃	—	2	1	no	—
24	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
25	C₂₃×#340	—	2	1	no	—
26	C₂₃×#340	—	2	1	no	—
27	C₂₃×D₄⋊C₈	—	2	2	no	—
28	C₂²×Q₈×C₂₃	—	2	1	no	—
29	C₂²×D₄×C₂₃	D₄	1	1	yes	characteristic
30	C₂³×C₄×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	C₂₃×C₄⋊Q₈	—	2	1	no	—
35	C₂₃×C₄⋊Q₈	—	2	1	no	—
36	C₂₃×C₄⋊Q₈	—	2	1	no	—
37	C₂₃×C₄⋊Q₈	C₂×C₄	1	2	yes	—
38	C₄×D₄×C₂₃	—	2	1	no	—
39	C₄×D₄×C₂₃	—	2	1	no	—
40	C₄×D₄×C₂₃	C₂×C₄	1	2	yes	—
41	C₄×D₄×C₂₃	D₄	1	2	yes	—
42	C₂₃×#117	—	4	2	no	—
43	C₂₃×#117	—	4	2	no	—
44	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
45	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
46	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
47	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
48	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
49	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
50	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
51	C₂×C₄⋊C₄×C₂₃	D₄	1	2	yes	—
52	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
53	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
54	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
55	C₂×C₄²×C₂₃	—	2	2	no	—
56	C₂×C₄²×C₂₃	—	2	1	no	—
57	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
58	C₂₃×#106	—	2	4	no	—
59	C₂₃×C₄⋊C₈	—	2	1	no	—
60	C₂₃×C₄⋊C₈	—	2	1	no	—
61	C₂₃×C₄⋊C₈	—	2	1	no	—
62	C₂₃×C₄⋊C₈	C₂×C₄	1	2	yes	—
63	C₂₃×#103	—	4	4	no	—
64	C₂₃×#102	—	2	4	no	—
65	C₄×C₈×C₂₃	—	2	1	no	—
66	C₄×C₈×C₂₃	—	2	1	no	—
67	C₂₃×#95	—	2	2	no	—
68	C₂₃×#95	—	2	1	no	—
69	C₂⁴×C₂₃	—	2	1	no	—
70	C₂×Q₈×C₂₃	—	2	2	no	—
71	C₂×Q₈×C₂₃	—	4	2	no	—
72	C₂×Q₈×C₂₃	—	4	2	no	—
73	C₂×Q₈×C₂₃	—	4	1	no	—
74	C₂×D₄×C₂₃	—	2	1	no	—
75	C₂×D₄×C₂₃	—	2	1	no	—
76	C₂×D₄×C₂₃	—	2	1	no	—
77	C₂×D₄×C₂₃	—	2	1	no	—
78	C₂×D₄×C₂₃	—	2	1	no	—
79	C₂×D₄×C₂₃	C₂²⋊C₄	1	2	yes	—
80	C₂²×C₄×C₂₃	—	2	1	no	—
81	C₂²×C₄×C₂₃	—	2	1	no	—
82	C₂²×C₄×C₂₃	—	2	2	no	—
83	C₂²×C₄×C₂₃	—	2	2	no	—
84	C₂²×C₄×C₂₃	—	2	2	no	—
85	C₂²×C₄×C₂₃	—	2	1	no	—
86	C₂²×C₄×C₂₃	—	4	1	no	—
87	C₂²×C₄×C₂₃	—	4	1	no	—
88	C₂²×C₄×C₂₃	—	4	1	no	—
89	C₂²×C₄×C₂₃	—	4	1	no	—
90	C₂²×C₄×C₂₃	—	4	1	no	—
91	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
94	C₂×C₈×C₂₃	—	2	2	no	—
95	C₂×C₈×C₂₃	—	2	2	no	—
96	C₂×C₈×C₂₃	—	4	1	no	—
97	C₂×C₈×C₂₃	—	4	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	C₄⋊C₄×C₂₃	—	2	1	no	—
104	C₄⋊C₄×C₂₃	—	2	1	no	—
105	C₄⋊C₄×C₂₃	—	2	2	no	—
106	C₄⋊C₄×C₂₃	—	2	2	no	—
107	C₄⋊C₄×C₂₃	—	2	1	no	—
108	C₄⋊C₄×C₂₃	—	2	1	no	—
109	C₄⋊C₄×C₂₃	—	4	2	no	—
110	C₄⋊C₄×C₂₃	—	4	1	no	—
111	C₄⋊C₄×C₂₃	—	4	1	no	—
112	C₄⋊C₄×C₂₃	—	4	1	no	—
113	C₄⋊C₄×C₂₃	—	4	1	no	—
114	C₄⋊C₄×C₂₃	—	4	1	no	—
115	C₄⋊C₄×C₂₃	—	4	1	no	—
116	C₄⋊C₄×C₂₃	C₂²⋊C₄	1	2	yes	—
117	C₄⋊C₄×C₂₃	SD₁₆	1	2	yes	—
118	C₂²⋊C₄×C₂₃	—	2	2	no	—
119	C₂²⋊C₄×C₂₃	—	2	2	no	—
120	C₂²⋊C₄×C₂₃	—	4	4	no	—
121	C₂²⋊C₄×C₂₃	—	8	2	no	—
122	C₄²×C₂₃	—	4	4	no	—
123	C₄²×C₂₃	—	4	1	no	—
124	C₄²×C₂₃	—	4	1	no	—
125	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
126	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
127	C₄²×C₂₃	#41	1	1	yes	characteristic
128	C₄²×C₂₃	#41	1	1	yes	characteristic
129	#8976	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
130	C₂³×C₂₃	—	2	2	no	—
131	C₂³×C₂₃	—	4	1	no	—
132	C₂³×C₂₃	—	4	1	no	—
133	C₂³×C₂₃	—	4	1	no	—
134	C₂³×C₂₃	—	4	1	no	—
135	C₂³×C₂₃	—	4	1	no	—
136	C₂³×C₂₃	—	4	1	no	—
137	C₂³×C₂₃	#120	1	1	yes	characteristic
138	Q₈×C₂₃	—	4	4	no	—
139	Q₈×C₂₃	—	8	2	no	—
140	D₄×C₂₃	—	2	2	no	—
141	D₄×C₂₃	—	2	2	no	—
142	D₄×C₂₃	—	4	1	no	—
143	D₄×C₂₃	—	4	1	no	—
144	C₂×C₄×C₂₃	—	2	1	no	—
145	C₂×C₄×C₂₃	—	2	1	no	—
146	C₂×C₄×C₂₃	—	2	2	no	—
147	C₂×C₄×C₂₃	—	2	2	no	—
148	C₂×C₄×C₂₃	—	4	1	no	—
149	C₂×C₄×C₂₃	—	4	1	no	—
150	C₂×C₄×C₂₃	—	4	1	no	—
151	C₂×C₄×C₂₃	—	4	1	no	—
152	C₂×C₄×C₂₃	—	4	2	no	—
153	C₂×C₄×C₂₃	—	4	2	no	—
154	C₂×C₄×C₂₃	—	4	2	no	—
155	C₂×C₄×C₂₃	—	4	2	no	—
156	C₂×C₄×C₂₃	—	4	2	no	—
157	C₂×C₄×C₂₃	—	4	2	no	—
158	C₂×C₄×C₂₃	—	4	1	no	—
159	C₂×C₄×C₂₃	—	4	1	no	—
160	C₂×C₄×C₂₃	—	4	2	no	—
161	C₂×C₄×C₂₃	—	4	1	no	—
162	C₂×C₄×C₂₃	—	4	2	no	—
163	C₂×C₄×C₂₃	—	8	1	no	—
164	C₂×C₄×C₂₃	—	8	1	no	—
165	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
166	C₂×C₄×C₂₃	C₄×D₄	1	1	yes	characteristic
167	C₂×C₄×C₂₃	C₄×D₄	1	1	yes	characteristic
168	C₂×C₄×C₂₃	#121	1	1	yes	characteristic
169	C₂×C₄×C₂₃	#121	1	1	yes	characteristic
170	C₂×C₄×C₂₃	#123	1	1	yes	characteristic
171	C₂×C₄×C₂₃	C₂×SD₁₆	1	1	yes	characteristic
172	C₂×C₄×C₂₃	#135	1	1	yes	characteristic
173	C₂×C₄×C₂₃	#135	1	1	yes	characteristic
174	C₂×C₄×C₂₃	#135	1	1	yes	characteristic
175	C₂×C₄×C₂₃	AGL(1,ℤ/8)	1	1	yes	characteristic
176	C₂×C₄×C₂₃	#137	1	1	yes	characteristic
177	C₂×C₄×C₂₃	#137	1	1	yes	characteristic
178	C₂×C₄×C₂₃	#137	1	1	yes	characteristic
179	C₈×C₂₃	—	4	2	no	—
180	C₈×C₂₃	—	4	2	no	—
181	C₈×C₂₃	—	8	1	no	—
182	C₂×#476	C₂×C₂₃	1	1	yes	characteristic
183	#2354	C₂×C₂₃	1	1	yes	characteristic
184	#1987	C₂×C₂₃	1	1	yes	characteristic, complemented
185	#1956	C₂×C₂₃	1	1	yes	characteristic, complemented
186	C₂×D₄⋊C₈	C₂×C₂₃	1	1	yes	characteristic
187	#1296	C₂×C₂₃	1	1	yes	characteristic, complemented
188	#1279	C₂×C₂₃	1	1	yes	characteristic, complemented
189	C₂²×C₂₃	—	4	2	no	—
190	C₂²×C₂₃	—	4	2	no	—
191	C₂²×C₂₃	—	4	2	no	—
192	C₂²×C₂₃	—	8	1	no	—
193	C₂²×C₂₃	—	8	1	no	—
194	C₂²×C₂₃	—	8	1	no	—
195	C₂²×C₂₃	—	8	1	no	—
196	C₂²×C₂₃	#386	1	1	yes	characteristic
197	C₂²×C₂₃	#450	1	1	yes	characteristic
198	C₂²×C₂₃	#452	1	1	yes	characteristic
199	C₂²×C₂₃	#452	1	1	yes	characteristic
200	C₂²×C₂₃	#452	1	1	yes	characteristic
201	C₂²×C₂₃	#453	1	1	yes	characteristic
202	C₂²×C₂₃	#454	1	1	yes	characteristic
203	C₄×C₂₃	—	2	1	no	—
204	C₄×C₂₃	—	2	1	no	—
205	C₄×C₂₃	—	4	2	no	—
206	C₄×C₂₃	—	4	2	no	—
207	C₄×C₂₃	—	8	2	no	—
208	C₄×C₂₃	—	8	2	no	—
209	C₄×C₂₃	—	8	1	no	—
210	C₄×C₂₃	#416	1	1	yes	characteristic
211	C₄×C₂₃	#419	1	1	yes	characteristic
212	C₄×C₂₃	C₄×SD₁₆	1	1	yes	characteristic
213	C₄×C₂₃	#440	1	1	yes	characteristic
214	C₄×C₂₃	#461	1	1	yes	characteristic
215	C₄×C₂₃	#463	1	1	yes	characteristic
216	C₄×C₂₃	#485	1	1	yes	characteristic
217	C₄×C₂₃	#485	1	1	yes	characteristic
218	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
219	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
220	C₂×#117	—	2	1	no	—
221	#476	—	2	2	no	—
222	#476	C₄×C₂₃	1	4	yes	complemented
223	C₂×#106	—	2	1	no	—
224	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
225	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
226	C₂×#103	—	2	2	no	—
227	C₂×#102	—	2	1	no	—
228	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
229	#390	—	2	1	no	—
230	#388	—	2	2	no	—
231	#384	C₂²×C₂₃	1	1	yes	characteristic
232	#380	—	2	1	no	—
233	C₄×C₄⋊C₄	—	2	1	no	—
234	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
235	#340	—	2	1	no	—
236	#340	—	2	1	no	—
237	D₄⋊C₈	—	2	2	no	—
238	C₂×C₂₃	—	8	2	no	—
239	C₂×C₂₃	#1631	1	1	yes	characteristic
240	C₂×C₂₃	#1634	1	1	yes	characteristic
241	C₂×C₂₃	#1635	1	1	yes	characteristic
242	C₂×C₂₃	#1638	1	1	yes	characteristic
243	C₂×C₂₃	#1873	1	1	yes	characteristic
244	C₂×C₂₃	#1877	1	1	yes	characteristic
245	C₂×C₂₃	#1883	1	1	yes	characteristic
246	C₂²×Q₈	—	2	1	no	—
247	C₂²×D₄	D₄×C₂₃	1	1	yes	characteristic
248	C₂³×C₄	—	2	1	no	—
249	C₂²×C₈	—	2	1	no	—
250	C₂²×C₈	—	2	1	no	—
251	C₂²×C₈	—	2	1	no	—
252	C₄⋊Q₈	—	2	1	no	—
253	C₄⋊Q₈	—	2	1	no	—
254	C₄⋊Q₈	—	2	1	no	—
255	C₄⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
256	C₄×D₄	—	2	1	no	—
257	C₄×D₄	—	2	1	no	—
258	C₄×D₄	C₂×C₄×C₂₃	1	2	yes	—
259	C₄×D₄	D₄×C₂₃	1	2	yes	—
260	#117	—	4	2	no	—
261	#117	—	4	2	no	—
262	C₂×C₄⋊C₄	—	2	1	no	—
263	C₂×C₄⋊C₄	—	2	1	no	—
264	C₂×C₄⋊C₄	—	2	1	no	—
265	C₂×C₄⋊C₄	—	2	1	no	—
266	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
267	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
268	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
269	C₂×C₄⋊C₄	D₄×C₂₃	1	2	yes	—
270	C₂×C₂²⋊C₄	—	2	1	no	—
271	C₂×C₂²⋊C₄	—	2	2	no	—
272	C₂×C₂²⋊C₄	—	2	2	no	—
273	C₂×C₄²	—	2	2	no	—
274	C₂×C₄²	—	2	1	no	—
275	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
276	#106	—	2	4	no	—
277	C₄⋊C₈	—	2	1	no	—
278	C₄⋊C₈	—	2	1	no	—
279	C₄⋊C₈	—	2	1	no	—
280	C₄⋊C₈	C₂×C₄×C₂₃	1	2	yes	—
281	#103	—	4	4	no	—
282	#102	—	2	4	no	—
283	C₄×C₈	—	2	1	no	—
284	C₄×C₈	—	2	1	no	—
285	#95	—	2	2	no	—
286	#95	—	2	1	no	—
287	C₂₃	#8976	1	1	yes	characteristic, direct product factor, Sylow
288	C₂⁴	—	2	1	no	—
289	C₂×Q₈	—	2	2	no	—
290	C₂×Q₈	—	4	2	no	—
291	C₂×Q₈	—	4	2	no	—
292	C₂×Q₈	—	4	1	no	—
293	C₂×D₄	—	2	1	no	—
294	C₂×D₄	—	2	1	no	—
295	C₂×D₄	—	2	1	no	—
296	C₂×D₄	—	2	1	no	—
297	C₂×D₄	—	2	1	no	—
298	C₂×D₄	C₂²⋊C₄×C₂₃	1	2	yes	—
299	C₂²×C₄	—	2	1	no	—
300	C₂²×C₄	—	2	1	no	—
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	—	2	2	no	—
303	C₂²×C₄	—	2	1	no	—
304	C₂²×C₄	—	2	2	no	—
305	C₂²×C₄	—	4	1	no	—
306	C₂²×C₄	—	4	1	no	—
307	C₂²×C₄	—	4	1	no	—
308	C₂²×C₄	—	4	1	no	—
309	C₂²×C₄	—	4	1	no	—
310	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
311	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
312	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
313	C₂×C₈	—	2	2	no	—
314	C₂×C₈	—	2	2	no	—
315	C₂×C₈	—	4	1	no	—
316	C₂×C₈	—	4	1	no	—
317	C₂×C₈	—	4	1	no	—
318	C₂×C₈	—	4	1	no	—
319	C₂×C₈	—	4	1	no	—
320	C₂×C₈	—	4	1	no	—
321	C₂×C₈	—	4	1	no	—
322	C₄⋊C₄	—	2	1	no	—
323	C₄⋊C₄	—	2	1	no	—
324	C₄⋊C₄	—	2	2	no	—
325	C₄⋊C₄	—	2	2	no	—
326	C₄⋊C₄	—	2	1	no	—
327	C₄⋊C₄	—	2	1	no	—
328	C₄⋊C₄	—	4	2	no	—
329	C₄⋊C₄	—	4	1	no	—
330	C₄⋊C₄	—	4	1	no	—
331	C₄⋊C₄	—	4	1	no	—
332	C₄⋊C₄	—	4	1	no	—
333	C₄⋊C₄	—	4	1	no	—
334	C₄⋊C₄	—	4	1	no	—
335	C₄⋊C₄	C₂²⋊C₄×C₂₃	1	2	yes	—
336	C₄⋊C₄	SD₁₆×C₂₃	1	2	yes	—
337	C₂²⋊C₄	—	2	2	no	—
338	C₂²⋊C₄	—	2	2	no	—
339	C₂²⋊C₄	—	4	4	no	—
340	C₂²⋊C₄	—	8	2	no	—
341	C₄²	—	4	4	no	—
342	C₄²	—	4	1	no	—
343	C₄²	—	4	1	no	—
344	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
345	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
346	C₄²	#41×C₂₃	1	1	yes	characteristic
347	C₄²	#41×C₂₃	1	1	yes	characteristic
348	C₂³	—	2	2	no	—
349	C₂³	—	4	1	no	—
350	C₂³	—	4	1	no	—
351	C₂³	—	4	1	no	—
352	C₂³	—	4	1	no	—
353	C₂³	—	4	1	no	—
354	C₂³	—	4	1	no	—
355	C₂³	C₂₃×#120	1	1	yes	characteristic
356	Q₈	—	4	4	no	—
357	Q₈	—	8	2	no	—
358	D₄	—	2	2	no	—
359	D₄	—	2	2	no	—
360	D₄	—	4	1	no	—
361	D₄	—	4	1	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	2	1	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	4	1	no	—
367	C₂×C₄	—	4	1	no	—
368	C₂×C₄	—	4	1	no	—
369	C₂×C₄	—	4	1	no	—
370	C₂×C₄	—	4	2	no	—
371	C₂×C₄	—	4	2	no	—
372	C₂×C₄	—	4	2	no	—
373	C₂×C₄	—	4	2	no	—
374	C₂×C₄	—	4	2	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	—	4	1	no	—
377	C₂×C₄	—	4	1	no	—
378	C₂×C₄	—	4	2	no	—
379	C₂×C₄	—	4	1	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	8	1	no	—
382	C₂×C₄	—	8	1	no	—
383	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
384	C₂×C₄	C₄×D₄×C₂₃	1	1	yes	characteristic
385	C₂×C₄	C₄×D₄×C₂₃	1	1	yes	characteristic
386	C₂×C₄	C₂₃×#121	1	1	yes	characteristic
387	C₂×C₄	C₂₃×#121	1	1	yes	characteristic
388	C₂×C₄	C₂₃×#123	1	1	yes	characteristic
389	C₂×C₄	C₂×SD₁₆×C₂₃	1	1	yes	characteristic
390	C₂×C₄	C₂₃×#135	1	1	yes	characteristic
391	C₂×C₄	C₂₃×#135	1	1	yes	characteristic
392	C₂×C₄	C₂₃×#135	1	1	yes	characteristic
393	C₂×C₄	C₂₃×AGL(1,ℤ/8)	1	1	yes	characteristic
394	C₂×C₄	C₂₃×#137	1	1	yes	characteristic
395	C₂×C₄	C₂₃×#137	1	1	yes	characteristic
396	C₂×C₄	C₂₃×#137	1	1	yes	characteristic
397	C₈	—	4	2	no	—
398	C₈	—	4	2	no	—
399	C₈	—	8	1	no	—
400	C₂²	—	4	2	no	—
401	C₂²	—	4	2	no	—
402	C₂²	—	4	2	no	—
403	C₂²	—	8	1	no	—
404	C₂²	—	8	1	no	—
405	C₂²	—	8	1	no	—
406	C₂²	—	8	1	no	—
407	C₂²	C₂₃×#386	1	1	yes	characteristic
408	C₂²	C₂₃×#450	1	1	yes	characteristic
409	C₂²	C₂₃×#452	1	1	yes	characteristic
410	C₂²	C₂₃×#452	1	1	yes	characteristic
411	C₂²	C₂₃×#452	1	1	yes	characteristic
412	C₂²	C₂₃×#453	1	1	yes	characteristic
413	C₂²	C₂₃×#454	1	1	yes	characteristic
414	C₄	—	2	1	no	—
415	C₄	—	2	1	no	—
416	C₄	—	4	2	no	—
417	C₄	—	4	2	no	—
418	C₄	—	8	2	no	—
419	C₄	—	8	1	no	—
420	C₄	—	8	2	no	—
421	C₄	C₂₃×#416	1	1	yes	characteristic
422	C₄	C₂₃×#419	1	1	yes	characteristic
423	C₄	C₄×SD₁₆×C₂₃	1	1	yes	characteristic
424	C₄	C₂₃×#440	1	1	yes	characteristic
425	C₄	C₂₃×#461	1	1	yes	characteristic
426	C₄	C₂₃×#463	1	1	yes	characteristic
427	C₄	C₂₃×#485	1	1	yes	characteristic
428	C₄	C₂₃×#485	1	1	yes	characteristic
429	C₂	—	8	2	no	—
430	C₂	C₂₃×#1631	1	1	yes	characteristic
431	C₂	C₂₃×#1634	1	1	yes	characteristic
432	C₂	C₂₃×#1635	1	1	yes	characteristic
433	C₂	C₂₃×#1638	1	1	yes	characteristic
434	C₂	C₂₃×#1873	1	1	yes	characteristic
435	C₂	C₂₃×#1877	1	1	yes	characteristic
436	C₂	C₂₃×#1883	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	C₂²×D₄×C₂₃	D₄
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
3. C₂₃×#1987	C₂	semidirect
4. C₂₃×#1956	C₂	semidirect
6. C₂₃×#1296	C₂	semidirect
7. C₂₃×#1279	C₂	semidirect
12. C₂₃×#476	C₄	semidirect
129. #8976	C₂₃	direct (N × H)
184. #1987	C₂×C₂₃	semidirect
185. #1956	C₂×C₂₃	semidirect
187. #1296	C₂×C₂₃	semidirect
188. #1279	C₂×C₂₃	semidirect
222. #476	C₄×C₂₃	semidirect
287. C₂₃	#8976	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×#476	2
C₂₃×#2354	2
C₂₃×#1987	2
C₂₃×#1956	2
C₂×C₂₃×D₄⋊C₈	2
C₂₃×#1296	2
C₂₃×#1279	2
#8976	23

Subgroups — C23×#8976 #19156602

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#8976 #19156602