Subgroups — C₂₃×#21362 #19168988

Order 5888.

914 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#431	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#2285	C₂	1	1	yes	maximal, characteristic
3	C₄×C₂₃×#117	C₂	1	1	yes	maximal, characteristic
4	C₂₃×#1948	C₂	1	2	yes	maximal, complemented
5	C₂₃×#1947	C₂	1	2	yes	maximal, complemented
6	C₂₃×#1854	C₂	1	4	yes	maximal
7	C₄×C₂₃×#107	C₂	1	2	yes	maximal, complemented
8	C₄×C₂₃×#106	C₂	1	2	yes	maximal, complemented
9	C₂×C₂₃×#117	—	2	1	no	—
10	C₂×C₂₃×#117	C₂²	1	2	yes	—
11	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
12	C₂₃×#431	C₄	1	8	yes	complemented
13	C₂×C₂₃×#107	C₂²	1	4	yes	—
14	C₂×C₂₃×#106	C₂²	1	4	yes	—
15	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
16	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
17	C₂×C₂₃×C₂²⋊C₈	C₂²	1	2	yes	—
18	C₂×C₄×C₈×C₂₃	C₂²	1	2	yes	—
19	C₂₃×#384	C₂²	1	2	yes	—
20	C₂₃×#382	—	2	1	no	—
21	C₂₃×#380	—	2	1	no	—
22	C₂₃×#380	C₂²	1	2	yes	—
23	C₄×C₄⋊C₄×C₂₃	—	2	1	no	—
24	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
25	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
26	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
27	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
28	C₄×C₂²⋊C₄×C₂₃	—	2	1	no	—
29	C₄×C₂²⋊C₄×C₂₃	—	2	1	no	—
30	C₂₃×#376	—	2	1	no	—
31	C₄³×C₂₃	—	2	1	no	—
32	C₂₃×#340	C₂²	1	4	yes	—
33	C₂₃×#340	C₂²	1	4	yes	—
34	C₂³×C₄×C₂₃	D₄	1	1	yes	characteristic
35	C₂³×C₄×C₂₃	D₄	1	1	yes	characteristic
36	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
37	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
38	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
39	C₂₃×#117	—	2	4	no	—
40	C₂₃×#117	—	2	4	no	—
41	C₂₃×#117	—	4	4	no	—
42	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
43	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
44	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
45	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
46	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
47	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
48	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
49	C₂×C₄²×C₂₃	—	2	2	no	—
50	C₂×C₄²×C₂₃	—	2	2	no	—
51	C₂×C₄²×C₂₃	—	2	1	no	—
52	C₂×C₄²×C₂₃	—	2	1	no	—
53	C₂×C₄²×C₂₃	—	2	2	no	—
54	C₂×C₄²×C₂₃	C₂×C₄	1	4	yes	—
55	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
56	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
57	C₂×C₄²×C₂₃	Q₈	1	4	yes	—
58	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
59	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
60	C₂₃×#107	—	2	8	no	—
61	C₂₃×#106	—	2	8	no	—
62	C₂₃×C₄⋊C₈	C₂×C₄	1	4	yes	—
63	C₂₃×C₄⋊C₈	C₂×C₄	1	4	yes	—
64	C₂₃×C₂²⋊C₈	C₂×C₄	1	8	yes	—
65	C₄×C₈×C₂₃	C₂×C₄	1	8	yes	—
66	C₂₃×#95	—	2	2	no	—
67	C₂₃×#95	—	2	1	no	—
68	C₂₃×#95	—	2	1	no	—
69	C₂₃×#95	—	2	2	no	—
70	C₂₃×#95	—	2	2	no	—
71	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
72	C₂²×C₄×C₂₃	—	2	4	no	—
73	C₂²×C₄×C₂₃	—	2	2	no	—
74	C₂²×C₄×C₂₃	—	2	2	no	—
75	C₂²×C₄×C₂₃	—	2	2	no	—
76	C₂²×C₄×C₂₃	—	2	2	no	—
77	C₂²×C₄×C₂₃	—	2	2	no	—
78	C₂²×C₄×C₂₃	—	2	2	no	—
79	C₂²×C₄×C₂₃	—	2	4	no	—
80	C₂²×C₄×C₂₃	C₄⋊C₄	1	4	yes	—
81	C₂²×C₄×C₂₃	C₄⋊C₄	1	4	yes	—
82	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
83	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
84	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
85	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
86	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
87	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
88	C₂²×C₄×C₂₃	C₂×Q₈	1	2	yes	—
89	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
90	C₂×C₈×C₂₃	—	2	4	no	—
91	C₂×C₈×C₂₃	—	2	4	no	—
92	C₂×C₈×C₂₃	C₂²×C₄	1	4	yes	—
93	C₂×C₈×C₂₃	C₂²×C₄	1	4	yes	—
94	C₄⋊C₄×C₂₃	—	2	2	no	—
95	C₄⋊C₄×C₂₃	—	2	2	no	—
96	C₄⋊C₄×C₂₃	—	2	4	no	—
97	C₄⋊C₄×C₂₃	—	2	4	no	—
98	C₄⋊C₄×C₂₃	—	4	4	no	—
99	C₄⋊C₄×C₂₃	—	4	4	no	—
100	C₄⋊C₄×C₂₃	#41	1	4	yes	—
101	C₄⋊C₄×C₂₃	#41	1	4	yes	—
102	C₂²⋊C₄×C₂₃	—	2	8	no	—
103	C₂²⋊C₄×C₂₃	—	4	4	no	—
104	C₄²×C₂₃	—	2	8	no	—
105	C₄²×C₂₃	—	4	4	no	—
106	C₄²×C₂₃	—	4	2	no	—
107	C₄²×C₂₃	—	4	4	no	—
108	C₄²×C₂₃	—	4	2	no	—
109	C₄²×C₂₃	C₄⋊C₄	1	4	yes	—
110	C₄²×C₂₃	C₄⋊C₄	1	4	yes	—
111	C₄²×C₂₃	C₂²×C₄	1	2	yes	—
112	C₄²×C₂₃	C₂²×C₄	1	2	yes	—
113	C₄²×C₂₃	C₂×Q₈	1	2	yes	—
114	C₄²×C₂₃	C₂×Q₈	1	2	yes	—
115	#21362	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
116	C₂³×C₂₃	—	2	2	no	—
117	C₂³×C₂₃	—	2	2	no	—
118	C₂³×C₂₃	—	2	1	no	—
119	C₂³×C₂₃	—	2	1	no	—
120	C₂³×C₂₃	C₂×C₄⋊C₄	1	2	yes	—
121	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
122	C₂×C₄×C₂₃	—	2	2	no	—
123	C₂×C₄×C₂₃	—	2	2	no	—
124	C₂×C₄×C₂₃	—	2	1	no	—
125	C₂×C₄×C₂₃	—	2	1	no	—
126	C₂×C₄×C₂₃	—	2	2	no	—
127	C₂×C₄×C₂₃	—	2	2	no	—
128	C₂×C₄×C₂₃	—	2	4	no	—
129	C₂×C₄×C₂₃	—	2	8	no	—
130	C₂×C₄×C₂₃	—	2	8	no	—
131	C₂×C₄×C₂₃	—	2	4	no	—
132	C₂×C₄×C₂₃	—	2	4	no	—
133	C₂×C₄×C₂₃	—	4	2	no	—
134	C₂×C₄×C₂₃	—	4	2	no	—
135	C₂×C₄×C₂₃	—	4	2	no	—
136	C₂×C₄×C₂₃	—	4	2	no	—
137	C₂×C₄×C₂₃	—	4	4	no	—
138	C₂×C₄×C₂₃	—	4	4	no	—
139	C₂×C₄×C₂₃	—	4	4	no	—
140	C₂×C₄×C₂₃	C₂×C₄⋊C₄	1	2	yes	—
141	C₂×C₄×C₂₃	C₂×C₄⋊C₄	1	2	yes	—
142	C₂×C₄×C₂₃	C₂×C₄⋊C₄	1	2	yes	—
143	C₂×C₄×C₂₃	C₂×C₄⋊C₄	1	2	yes	—
144	C₂×C₄×C₂₃	C₂×C₄⋊C₄	1	2	yes	—
145	C₂×C₄×C₂₃	#135	1	4	yes	—
146	C₂×C₄×C₂₃	AGL(1,ℤ/8)	1	2	yes	—
147	C₂×C₄×C₂₃	#137	1	2	yes	—
148	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
149	C₂×C₄×C₂₃	C₂²×Q₈	1	1	yes	characteristic
150	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
151	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
152	C₈×C₂₃	—	2	4	no	—
153	C₈×C₂₃	—	2	4	no	—
154	C₂×#431	C₂×C₂₃	1	1	yes	characteristic
155	#2285	C₂×C₂₃	1	1	yes	characteristic
156	C₄×#117	C₂×C₂₃	1	1	yes	characteristic
157	#1948	C₂×C₂₃	1	2	yes	complemented
158	#1947	C₂×C₂₃	1	2	yes	complemented
159	#1854	C₂×C₂₃	1	4	yes	—
160	C₄×#107	C₂×C₂₃	1	2	yes	complemented
161	C₄×#106	C₂×C₂₃	1	2	yes	complemented
162	C₂²×C₂₃	—	2	2	no	—
163	C₂²×C₂₃	—	2	2	no	—
164	C₂²×C₂₃	—	2	2	no	—
165	C₂²×C₂₃	—	4	2	no	—
166	C₂²×C₂₃	—	4	2	no	—
167	C₂²×C₂₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
168	C₂²×C₂₃	#525	1	2	yes	—
169	C₂²×C₂₃	C₂×#135	1	2	yes	—
170	C₂²×C₂₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
171	C₂²×C₂₃	C₂×#137	1	1	yes	characteristic
172	C₄×C₂₃	—	2	2	no	—
173	C₄×C₂₃	—	2	2	no	—
174	C₄×C₂₃	—	2	2	no	—
175	C₄×C₂₃	—	4	4	no	—
176	C₄×C₂₃	—	4	4	no	—
177	C₄×C₂₃	—	8	4	no	—
178	C₄×C₂₃	#427	1	4	yes	—
179	C₄×C₂₃	#428	1	4	yes	—
180	C₄×C₂₃	C₄×#41	1	1	yes	characteristic
181	C₄×C₂₃	C₄×#41	1	1	yes	characteristic
182	C₄×C₂₃	#533	1	2	yes	—
183	C₂×#117	—	2	1	no	—
184	C₂×#117	C₂²×C₂₃	1	2	yes	—
185	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
186	#431	C₄×C₂₃	1	8	yes	complemented
187	C₂×#107	C₂²×C₂₃	1	4	yes	—
188	C₂×#106	C₂²×C₂₃	1	4	yes	—
189	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
190	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
191	C₂×C₂²⋊C₈	C₂²×C₂₃	1	2	yes	—
192	C₂×C₄×C₈	C₂²×C₂₃	1	2	yes	—
193	#384	C₂²×C₂₃	1	2	yes	—
194	#382	—	2	1	no	—
195	#380	—	2	1	no	—
196	#380	C₂²×C₂₃	1	2	yes	—
197	C₄×C₄⋊C₄	—	2	1	no	—
198	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
199	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
200	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
201	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
202	C₄×C₂²⋊C₄	—	2	1	no	—
203	C₄×C₂²⋊C₄	—	2	1	no	—
204	#376	—	2	1	no	—
205	C₄³	—	2	1	no	—
206	#340	C₂²×C₂₃	1	4	yes	—
207	#340	C₂²×C₂₃	1	4	yes	—
208	C₂×C₂₃	—	4	2	no	—
209	C₂×C₂₃	#2296	1	1	yes	characteristic
210	C₂×C₂₃	C₂×#427	1	1	yes	characteristic
211	C₂×C₂₃	C₂×#428	1	1	yes	characteristic
212	C₂×C₂₃	#3106	1	2	yes	—
213	C₂×C₂₃	#3107	1	2	yes	—
214	C₂³×C₄	D₄×C₂₃	1	1	yes	characteristic
215	C₂³×C₄	D₄×C₂₃	1	1	yes	characteristic
216	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
217	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
218	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
219	#117	—	2	4	no	—
220	#117	—	2	4	no	—
221	#117	—	4	4	no	—
222	C₂×C₄⋊C₄	—	2	2	no	—
223	C₂×C₄⋊C₄	—	2	2	no	—
224	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
225	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
226	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
227	C₂×C₂²⋊C₄	—	2	2	no	—
228	C₂×C₂²⋊C₄	—	2	2	no	—
229	C₂×C₄²	—	2	2	no	—
230	C₂×C₄²	—	2	2	no	—
231	C₂×C₄²	—	2	2	no	—
232	C₂×C₄²	—	2	1	no	—
233	C₂×C₄²	—	2	1	no	—
234	C₂×C₄²	C₂×C₄×C₂₃	1	4	yes	—
235	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
236	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
237	C₂×C₄²	Q₈×C₂₃	1	4	yes	—
238	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
239	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
240	#107	—	2	8	no	—
241	#106	—	2	8	no	—
242	C₄⋊C₈	C₂×C₄×C₂₃	1	4	yes	—
243	C₄⋊C₈	C₂×C₄×C₂₃	1	4	yes	—
244	C₂²⋊C₈	C₂×C₄×C₂₃	1	8	yes	—
245	C₄×C₈	C₂×C₄×C₂₃	1	8	yes	—
246	#95	—	2	1	no	—
247	#95	—	2	1	no	—
248	#95	—	2	2	no	—
249	#95	—	2	2	no	—
250	#95	—	2	2	no	—
251	C₂₃	#21362	1	1	yes	characteristic, direct product factor, Sylow
252	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
253	C₂²×C₄	—	2	4	no	—
254	C₂²×C₄	—	2	2	no	—
255	C₂²×C₄	—	2	2	no	—
256	C₂²×C₄	—	2	2	no	—
257	C₂²×C₄	—	2	2	no	—
258	C₂²×C₄	—	2	2	no	—
259	C₂²×C₄	—	2	2	no	—
260	C₂²×C₄	—	2	4	no	—
261	C₂²×C₄	C₄⋊C₄×C₂₃	1	4	yes	—
262	C₂²×C₄	C₄⋊C₄×C₂₃	1	4	yes	—
263	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
264	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
265	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
266	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
267	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
268	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
269	C₂²×C₄	C₂×Q₈×C₂₃	1	2	yes	—
270	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
271	C₂×C₈	—	2	4	no	—
272	C₂×C₈	—	2	4	no	—
273	C₂×C₈	C₂²×C₄×C₂₃	1	4	yes	—
274	C₂×C₈	C₂²×C₄×C₂₃	1	4	yes	—
275	C₄⋊C₄	—	2	2	no	—
276	C₄⋊C₄	—	2	2	no	—
277	C₄⋊C₄	—	2	4	no	—
278	C₄⋊C₄	—	2	4	no	—
279	C₄⋊C₄	—	4	4	no	—
280	C₄⋊C₄	—	4	4	no	—
281	C₄⋊C₄	#41×C₂₃	1	4	yes	—
282	C₄⋊C₄	#41×C₂₃	1	4	yes	—
283	C₂²⋊C₄	—	2	8	no	—
284	C₂²⋊C₄	—	4	4	no	—
285	C₄²	—	2	8	no	—
286	C₄²	—	4	4	no	—
287	C₄²	—	4	4	no	—
288	C₄²	—	4	2	no	—
289	C₄²	—	4	2	no	—
290	C₄²	C₄⋊C₄×C₂₃	1	4	yes	—
291	C₄²	C₄⋊C₄×C₂₃	1	4	yes	—
292	C₄²	C₂²×C₄×C₂₃	1	2	yes	—
293	C₄²	C₂²×C₄×C₂₃	1	2	yes	—
294	C₄²	C₂×Q₈×C₂₃	1	2	yes	—
295	C₄²	C₂×Q₈×C₂₃	1	2	yes	—
296	C₂³	—	2	2	no	—
297	C₂³	—	2	1	no	—
298	C₂³	—	2	1	no	—
299	C₂³	—	2	2	no	—
300	C₂³	C₂×C₄⋊C₄×C₂₃	1	2	yes	—
301	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
302	C₂×C₄	—	2	2	no	—
303	C₂×C₄	—	2	1	no	—
304	C₂×C₄	—	2	1	no	—
305	C₂×C₄	—	2	2	no	—
306	C₂×C₄	—	2	8	no	—
307	C₂×C₄	—	2	8	no	—
308	C₂×C₄	—	2	2	no	—
309	C₂×C₄	—	2	2	no	—
310	C₂×C₄	—	2	4	no	—
311	C₂×C₄	—	2	4	no	—
312	C₂×C₄	—	2	4	no	—
313	C₂×C₄	—	4	2	no	—
314	C₂×C₄	—	4	2	no	—
315	C₂×C₄	—	4	2	no	—
316	C₂×C₄	—	4	2	no	—
317	C₂×C₄	—	4	4	no	—
318	C₂×C₄	—	4	4	no	—
319	C₂×C₄	—	4	4	no	—
320	C₂×C₄	C₂×C₄⋊C₄×C₂₃	1	2	yes	—
321	C₂×C₄	C₂×C₄⋊C₄×C₂₃	1	2	yes	—
322	C₂×C₄	C₂×C₄⋊C₄×C₂₃	1	2	yes	—
323	C₂×C₄	C₂×C₄⋊C₄×C₂₃	1	2	yes	—
324	C₂×C₄	C₂×C₄⋊C₄×C₂₃	1	2	yes	—
325	C₂×C₄	C₂₃×#135	1	4	yes	—
326	C₂×C₄	C₂₃×AGL(1,ℤ/8)	1	2	yes	—
327	C₂×C₄	C₂₃×#137	1	2	yes	—
328	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
329	C₂×C₄	C₂²×Q₈×C₂₃	1	1	yes	characteristic
330	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
331	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
332	C₈	—	2	4	no	—
333	C₈	—	2	4	no	—
334	C₂²	—	2	2	no	—
335	C₂²	—	2	2	no	—
336	C₂²	—	2	2	no	—
337	C₂²	—	4	2	no	—
338	C₂²	—	4	2	no	—
339	C₂²	C₂²×C₄⋊C₄×C₂₃	1	1	yes	characteristic
340	C₂²	C₂₃×#525	1	2	yes	—
341	C₂²	C₂×C₂₃×#135	1	2	yes	—
342	C₂²	C₂×C₂₃×AGL(1,ℤ/8)	1	1	yes	characteristic
343	C₂²	C₂×C₂₃×#137	1	1	yes	characteristic
344	C₄	—	2	2	no	—
345	C₄	—	2	2	no	—
346	C₄	—	2	2	no	—
347	C₄	—	4	4	no	—
348	C₄	—	4	4	no	—
349	C₄	—	8	4	no	—
350	C₄	C₂₃×#427	1	4	yes	—
351	C₄	C₂₃×#428	1	4	yes	—
352	C₄	C₄×#41×C₂₃	1	1	yes	characteristic
353	C₄	C₄×#41×C₂₃	1	1	yes	characteristic
354	C₄	C₂₃×#533	1	2	yes	—
355	C₂	—	4	2	no	—
356	C₂	C₂₃×#2296	1	1	yes	characteristic
357	C₂	C₂×C₂₃×#427	1	1	yes	characteristic
358	C₂	C₂×C₂₃×#428	1	1	yes	characteristic
359	C₂	C₂₃×#3106	1	2	yes	—
360	C₂	C₂₃×#3107	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₂₃	C₂×D₄
commutator	C₂×C₄	C₂³×C₄×C₂₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₃
socle	C₂³×C₂₃	C₂²×D₄
prime radical	C₂⁴×C₂₃	C₂×D₄
LCS	G ▷ C₂×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. C₂₃×#1948	C₂	semidirect
5. C₂₃×#1947	C₂	semidirect
7. C₄×C₂₃×#107	C₂	semidirect
8. C₄×C₂₃×#106	C₂	semidirect
12. C₂₃×#431	C₄	semidirect
115. #21362	C₂₃	direct (N × H)
157. #1948	C₂×C₂₃	semidirect
158. #1947	C₂×C₂₃	semidirect
160. C₄×#107	C₂×C₂₃	semidirect
161. C₄×#106	C₂×C₂₃	semidirect
186. #431	C₄×C₂₃	semidirect
251. C₂₃	#21362	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×#431	2
C₂₃×#2285	2
C₄×C₂₃×#117	2
C₂₃×#1948	2
C₂₃×#1947	2
C₂₃×#1854	2
C₄×C₂₃×#107	2
C₄×C₂₃×#106	2
#21362	23

Subgroups — C23×#21362 #19168988

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#21362 #19168988