Subgroups — C₂₃×#60868 #19208494

Order 5888.

1754 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3458	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₃×#540	C₂	1	1	yes	maximal, characteristic
3	C₂₃×#3241	C₂	1	16	yes	maximal, complemented
4	C₂₃×#3166	C₂	1	2	yes	maximal, complemented
5	C₂₃×#3138	C₂	1	2	yes	maximal, complemented
6	C₂₃×#3094	C₂	1	4	yes	maximal, complemented
7	C₂₃×#3077	C₂	1	4	yes	maximal, complemented
8	C₂₃×#2921	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#544	—	2	2	no	—
10	C₂₃×#544	C₂²	1	8	yes	complemented
11	C₂₃×#543	—	2	2	no	—
12	C₂₃×#540	—	2	4	no	—
13	C₂₃×#540	C₂²	1	8	yes	—
14	C₂₃×#533	—	2	4	no	—
15	C₂₃×#533	C₂²	1	2	yes	—
16	C₂₃×#533	C₂²	1	2	yes	—
17	C₂×C₂₃×#127	C₂²	1	1	yes	characteristic
18	C₂×C₂₃×#125	C₂²	1	1	yes	characteristic
19	C₂×C₂₃×#123	—	2	2	no	—
20	C₂×C₂₃×#121	—	2	2	no	—
21	C₂×C₂₃×#121	C₂²	1	2	yes	—
22	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	—
23	C₂×C₂₃×#117	C₂²	1	2	yes	—
24	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
25	C₂₃×#501	C₂²	1	8	yes	complemented
26	C₂₃×#499	C₂²	1	8	yes	complemented
27	C₂₃×#490	C₂²	1	8	yes	complemented
28	C₂₃×#486	C₂²	1	8	yes	complemented
29	C₂₃×#482	C₂²	1	16	yes	complemented
30	C₂₃×#481	C₂²	1	8	yes	complemented
31	C₂₃×#480	C₂²	1	8	yes	complemented
32	C₂₃×#478	C₂²	1	16	yes	complemented
33	C₂₃×#476	C₂²	1	8	yes	complemented
34	C₂₃×#474	C₂²	1	8	yes	complemented
35	C₂₃×#433	C₂²	1	8	yes	complemented
36	C₂₃×#428	C₂²	1	8	yes	—
37	C₂₃×#423	C₂²	1	2	yes	—
38	C₂₃×#418	C₂²	1	8	yes	—
39	C₂₃×#407	C₂²	1	2	yes	—
40	C₄×M₁₆×C₂₃	C₂²	1	2	yes	—
41	C₂²×D₄×C₂₃	—	2	2	no	—
42	C₂²×D₄×C₂₃	—	2	2	no	—
43	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
44	C₂³×C₄×C₂₃	—	2	2	no	—
45	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
46	C₂×M₁₆×C₂₃	C₂³	1	4	yes	—
47	C₂₃×C₄⋊Q₈	—	2	8	no	—
48	C₂₃×C₄⋊Q₈	C₂³	1	4	yes	—
49	C₂₃×C₄⋊Q₈	C₂³	1	4	yes	—
50	C₂₃×#127	—	2	2	no	—
51	C₂₃×#127	C₂³	1	4	yes	—
52	C₂₃×#125	—	2	8	no	—
53	C₂₃×#125	—	2	2	no	—
54	C₂₃×#125	C₂³	1	4	yes	—
55	C₂₃×#125	C₂³	1	4	yes	—
56	C₂₃×#125	C₂³	1	4	yes	—
57	C₂₃×#123	—	2	16	no	—
58	C₂₃×C₂²⋊Q₈	—	2	4	no	—
59	C₂₃×C₂²⋊Q₈	—	2	4	no	—
60	C₂₃×C₂²⋊Q₈	—	2	8	no	—
61	C₂₃×C₂²⋊Q₈	—	2	8	no	—
62	C₂₃×#121	—	2	4	no	—
63	C₂₃×#121	—	2	16	no	—
64	C₂₃×#121	C₂³	1	8	yes	—
65	C₄×Q₈×C₂₃	—	2	4	no	—
66	C₄×Q₈×C₂₃	—	2	4	no	—
67	C₄×D₄×C₂₃	—	2	4	no	—
68	C₄×D₄×C₂₃	C₂³	1	8	yes	—
69	C₂₃×#117	—	2	2	no	—
70	C₂₃×#117	—	2	2	no	—
71	C₂₃×#117	D₄	1	4	yes	—
72	C₂₃×#117	C₂³	1	4	yes	—
73	C₂₃×#117	C₂³	1	4	yes	—
74	C₂₃×#117	C₂³	1	4	yes	—
75	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
76	C₂×C₄⋊C₄×C₂₃	D₄	1	2	yes	—
77	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
78	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
79	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
80	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
81	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
82	C₂×C₂²⋊C₄×C₂₃	D₄	1	2	yes	—
83	C₂×C₄²×C₂₃	—	2	2	no	—
84	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
85	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
86	C₂₃×#107	C₂³	1	16	yes	—
87	C₂₃×#106	C₂³	1	16	yes	—
88	C₂₃×C₄⋊C₈	C₂³	1	8	yes	—
89	C₂₃×#102	C₂³	1	16	yes	—
90	C₂₃×#102	C₂³	1	16	yes	—
91	C₂₃×C₂²⋊C₈	C₂³	1	8	yes	—
92	C₂₃×#97	C₂³	1	4	yes	—
93	C₄×C₈×C₂₃	C₂³	1	4	yes	—
94	C₂⁴×C₂₃	—	2	2	no	—
95	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
96	C₂×Q₈×C₂₃	—	2	4	no	—
97	C₂×Q₈×C₂₃	—	2	4	no	—
98	C₂×D₄×C₂₃	—	2	8	no	—
99	C₂×D₄×C₂₃	—	2	2	no	—
100	C₂×D₄×C₂₃	—	2	8	no	—
101	C₂×D₄×C₂₃	—	2	8	no	—
102	C₂×D₄×C₂₃	—	8	4	no	—
103	C₂×D₄×C₂₃	—	8	4	no	—
104	C₂×D₄×C₂₃	C₂⁴	1	4	yes	—
105	C₂²×C₄×C₂₃	—	2	4	no	—
106	C₂²×C₄×C₂₃	—	2	2	no	—
107	C₂²×C₄×C₂₃	—	2	4	no	—
108	C₂²×C₄×C₂₃	—	2	8	no	—
109	C₂²×C₄×C₂₃	—	8	4	no	—
110	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
111	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
113	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
114	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
115	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
116	M₁₆×C₂₃	—	2	8	no	—
117	C₂×C₈×C₂₃	C₂⁴	1	8	yes	—
118	C₄⋊C₄×C₂₃	—	2	8	no	—
119	C₄⋊C₄×C₂₃	—	2	4	no	—
120	C₄⋊C₄×C₂₃	—	2	2	no	—
121	C₄⋊C₄×C₂₃	—	2	4	no	—
122	C₄⋊C₄×C₂₃	—	2	4	no	—
123	C₄⋊C₄×C₂₃	—	2	8	no	—
124	C₄⋊C₄×C₂₃	—	2	8	no	—
125	C₄⋊C₄×C₂₃	C₂×D₄	1	8	yes	—
126	C₄⋊C₄×C₂₃	C₂⁴	1	8	yes	—
127	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
128	C₂²⋊C₄×C₂₃	—	2	4	no	—
129	C₂²⋊C₄×C₂₃	—	2	4	no	—
130	C₂²⋊C₄×C₂₃	—	2	8	no	—
131	C₂²⋊C₄×C₂₃	—	2	8	no	—
132	C₂²⋊C₄×C₂₃	C₂×D₄	1	8	yes	—
133	C₄²×C₂₃	—	2	4	no	—
134	C₄²×C₂₃	—	2	4	no	—
135	C₄²×C₂₃	C₂×D₄	1	2	yes	—
136	C₄²×C₂₃	C₂×D₄	1	2	yes	—
137	C₄²×C₂₃	C₂⁴	1	2	yes	—
138	C₄²×C₂₃	C₂⁴	1	2	yes	—
139	#60868	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
140	C₂³×C₂₃	—	2	2	no	—
141	C₂³×C₂₃	—	2	4	no	—
142	C₂³×C₂₃	—	4	2	no	—
143	C₂³×C₂₃	—	4	4	no	—
144	C₂³×C₂₃	—	4	4	no	—
145	C₂³×C₂₃	—	4	4	no	—
146	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
147	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
148	Q₈×C₂₃	—	8	4	no	—
149	Q₈×C₂₃	—	8	4	no	—
150	D₄×C₂₃	—	2	8	no	—
151	D₄×C₂₃	—	4	4	no	—
152	D₄×C₂₃	—	8	8	no	—
153	D₄×C₂₃	—	8	8	no	—
154	C₂×C₄×C₂₃	—	2	2	no	—
155	C₂×C₄×C₂₃	—	2	4	no	—
156	C₂×C₄×C₂₃	—	2	4	no	—
157	C₂×C₄×C₂₃	—	2	8	no	—
158	C₂×C₄×C₂₃	—	2	4	no	—
159	C₂×C₄×C₂₃	—	4	2	no	—
160	C₂×C₄×C₂₃	—	4	2	no	—
161	C₂×C₄×C₂₃	—	4	4	no	—
162	C₂×C₄×C₂₃	—	8	8	no	—
163	C₂×C₄×C₂₃	—	8	4	no	—
164	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
165	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
166	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
167	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
168	C₂×C₄×C₂₃	2₋¹⁺⁴	1	4	yes	—
169	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
170	C₈×C₂₃	—	2	8	no	—
171	#3458	C₂×C₂₃	1	1	yes	characteristic, complemented
172	C₂×#540	C₂×C₂₃	1	1	yes	characteristic
173	#3241	C₂×C₂₃	1	16	yes	complemented
174	#3166	C₂×C₂₃	1	2	yes	complemented
175	#3138	C₂×C₂₃	1	2	yes	complemented
176	#3094	C₂×C₂₃	1	4	yes	complemented
177	#3077	C₂×C₂₃	1	4	yes	complemented
178	#2921	C₂×C₂₃	1	1	yes	characteristic, complemented
179	C₂²×C₂₃	—	2	2	no	—
180	C₂²×C₂₃	—	2	4	no	—
181	C₂²×C₂₃	—	2	2	no	—
182	C₂²×C₂₃	—	4	4	no	—
183	C₂²×C₂₃	—	4	4	no	—
184	C₂²×C₂₃	—	4	4	no	—
185	C₂²×C₂₃	—	8	2	no	—
186	C₂²×C₂₃	—	8	8	no	—
187	C₂²×C₂₃	#536	1	2	yes	—
188	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
189	C₄×C₂₃	—	2	4	no	—
190	C₄×C₂₃	—	2	4	no	—
191	C₄×C₂₃	—	2	2	no	—
192	C₄×C₂₃	—	4	4	no	—
193	C₄×C₂₃	—	4	8	no	—
194	C₄×C₂₃	#536	1	2	yes	—
195	C₄×C₂₃	C₂×2₋¹⁺⁴	1	2	yes	—
196	#544	—	2	2	no	—
197	#544	C₂²×C₂₃	1	8	yes	complemented
198	#543	—	2	2	no	—
199	#540	—	2	4	no	—
200	#540	C₂²×C₂₃	1	8	yes	—
201	#533	—	2	4	no	—
202	#533	C₂²×C₂₃	1	2	yes	—
203	#533	C₂²×C₂₃	1	2	yes	—
204	C₂×#127	C₂²×C₂₃	1	1	yes	characteristic
205	C₂×#125	C₂²×C₂₃	1	1	yes	characteristic
206	C₂×#123	—	2	2	no	—
207	C₂×#121	—	2	2	no	—
208	C₂×#121	C₂²×C₂₃	1	2	yes	—
209	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	—
210	C₂×#117	C₂²×C₂₃	1	2	yes	—
211	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
212	#501	C₂²×C₂₃	1	8	yes	complemented
213	#499	C₂²×C₂₃	1	8	yes	complemented
214	#490	C₂²×C₂₃	1	8	yes	complemented
215	#486	C₂²×C₂₃	1	8	yes	complemented
216	#482	C₂²×C₂₃	1	16	yes	complemented
217	#481	C₂²×C₂₃	1	8	yes	complemented
218	#480	C₂²×C₂₃	1	8	yes	complemented
219	#478	C₂²×C₂₃	1	16	yes	complemented
220	#476	C₂²×C₂₃	1	8	yes	complemented
221	#474	C₂²×C₂₃	1	8	yes	complemented
222	#433	C₂²×C₂₃	1	8	yes	complemented
223	#428	C₂²×C₂₃	1	8	yes	—
224	#423	C₂²×C₂₃	1	2	yes	—
225	#418	C₂²×C₂₃	1	8	yes	—
226	#407	C₂²×C₂₃	1	2	yes	—
227	C₄×M₁₆	C₂²×C₂₃	1	2	yes	—
228	C₂×C₂₃	—	2	2	no	—
229	C₂×C₂₃	—	4	2	no	—
230	C₂×C₂₃	—	8	4	no	—
231	C₂×C₂₃	C₂×#536	1	1	yes	characteristic
232	C₂×C₂₃	#3585	1	2	yes	—
233	C₂²×D₄	—	2	2	no	—
234	C₂²×D₄	—	2	2	no	—
235	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
236	C₂³×C₄	—	2	2	no	—
237	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
238	C₂×M₁₆	C₂³×C₂₃	1	4	yes	—
239	C₄⋊Q₈	—	2	8	no	—
240	C₄⋊Q₈	C₂³×C₂₃	1	4	yes	—
241	C₄⋊Q₈	C₂³×C₂₃	1	4	yes	—
242	#127	—	2	2	no	—
243	#127	C₂³×C₂₃	1	4	yes	—
244	#125	—	2	8	no	—
245	#125	—	2	2	no	—
246	#125	C₂³×C₂₃	1	4	yes	—
247	#125	C₂³×C₂₃	1	4	yes	—
248	#125	C₂³×C₂₃	1	4	yes	—
249	#123	—	2	16	no	—
250	C₂²⋊Q₈	—	2	4	no	—
251	C₂²⋊Q₈	—	2	4	no	—
252	C₂²⋊Q₈	—	2	8	no	—
253	C₂²⋊Q₈	—	2	8	no	—
254	#121	—	2	4	no	—
255	#121	—	2	16	no	—
256	#121	C₂³×C₂₃	1	8	yes	—
257	C₄×Q₈	—	2	4	no	—
258	C₄×Q₈	—	2	4	no	—
259	C₄×D₄	—	2	4	no	—
260	C₄×D₄	C₂³×C₂₃	1	8	yes	—
261	#117	—	2	2	no	—
262	#117	—	2	2	no	—
263	#117	D₄×C₂₃	1	4	yes	—
264	#117	C₂³×C₂₃	1	4	yes	—
265	#117	C₂³×C₂₃	1	4	yes	—
266	#117	C₂³×C₂₃	1	4	yes	—
267	C₂×C₄⋊C₄	—	2	2	no	—
268	C₂×C₄⋊C₄	D₄×C₂₃	1	2	yes	—
269	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
270	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
271	C₂×C₂²⋊C₄	—	2	2	no	—
272	C₂×C₂²⋊C₄	—	2	2	no	—
273	C₂×C₂²⋊C₄	—	2	2	no	—
274	C₂×C₂²⋊C₄	D₄×C₂₃	1	2	yes	—
275	C₂×C₄²	—	2	2	no	—
276	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
277	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
278	#107	C₂³×C₂₃	1	16	yes	—
279	#106	C₂³×C₂₃	1	16	yes	—
280	C₄⋊C₈	C₂³×C₂₃	1	8	yes	—
281	#102	C₂³×C₂₃	1	16	yes	—
282	#102	C₂³×C₂₃	1	16	yes	—
283	C₂²⋊C₈	C₂³×C₂₃	1	8	yes	—
284	#97	C₂³×C₂₃	1	4	yes	—
285	C₄×C₈	C₂³×C₂₃	1	4	yes	—
286	C₂₃	#60868	1	1	yes	characteristic, direct product factor, Sylow
287	C₂⁴	—	2	2	no	—
288	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
289	C₂×Q₈	—	2	4	no	—
290	C₂×Q₈	—	2	4	no	—
291	C₂×D₄	—	2	8	no	—
292	C₂×D₄	—	2	2	no	—
293	C₂×D₄	—	2	8	no	—
294	C₂×D₄	—	2	8	no	—
295	C₂×D₄	—	8	4	no	—
296	C₂×D₄	—	8	4	no	—
297	C₂×D₄	C₂⁴×C₂₃	1	4	yes	—
298	C₂²×C₄	—	2	4	no	—
299	C₂²×C₄	—	2	2	no	—
300	C₂²×C₄	—	2	4	no	—
301	C₂²×C₄	—	2	8	no	—
302	C₂²×C₄	—	8	4	no	—
303	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
304	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
305	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
306	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
307	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
308	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
309	M₁₆	—	2	8	no	—
310	C₂×C₈	C₂⁴×C₂₃	1	8	yes	—
311	C₄⋊C₄	—	2	8	no	—
312	C₄⋊C₄	—	2	4	no	—
313	C₄⋊C₄	—	2	2	no	—
314	C₄⋊C₄	—	2	4	no	—
315	C₄⋊C₄	—	2	4	no	—
316	C₄⋊C₄	—	2	8	no	—
317	C₄⋊C₄	—	2	8	no	—
318	C₄⋊C₄	C₂×D₄×C₂₃	1	8	yes	—
319	C₄⋊C₄	C₂⁴×C₂₃	1	8	yes	—
320	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
321	C₂²⋊C₄	—	2	4	no	—
322	C₂²⋊C₄	—	2	4	no	—
323	C₂²⋊C₄	—	2	8	no	—
324	C₂²⋊C₄	—	2	8	no	—
325	C₂²⋊C₄	C₂×D₄×C₂₃	1	8	yes	—
326	C₄²	—	2	4	no	—
327	C₄²	—	2	4	no	—
328	C₄²	C₂×D₄×C₂₃	1	2	yes	—
329	C₄²	C₂×D₄×C₂₃	1	2	yes	—
330	C₄²	C₂⁴×C₂₃	1	2	yes	—
331	C₄²	C₂⁴×C₂₃	1	2	yes	—
332	C₂³	—	2	2	no	—
333	C₂³	—	2	4	no	—
334	C₂³	—	4	2	no	—
335	C₂³	—	4	4	no	—
336	C₂³	—	4	4	no	—
337	C₂³	—	4	4	no	—
338	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
339	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
340	Q₈	—	8	4	no	—
341	Q₈	—	8	4	no	—
342	D₄	—	2	8	no	—
343	D₄	—	4	4	no	—
344	D₄	—	8	8	no	—
345	D₄	—	8	8	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	4	no	—
348	C₂×C₄	—	2	4	no	—
349	C₂×C₄	—	2	8	no	—
350	C₂×C₄	—	2	4	no	—
351	C₂×C₄	—	4	2	no	—
352	C₂×C₄	—	4	2	no	—
353	C₂×C₄	—	4	4	no	—
354	C₂×C₄	—	8	8	no	—
355	C₂×C₄	—	8	4	no	—
356	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
357	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
358	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
359	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
360	C₂×C₄	C₂₃×2₋¹⁺⁴	1	4	yes	—
361	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
362	C₈	—	2	8	no	—
363	C₂²	—	2	2	no	—
364	C₂²	—	2	2	no	—
365	C₂²	—	2	4	no	—
366	C₂²	—	4	4	no	—
367	C₂²	—	4	4	no	—
368	C₂²	—	4	4	no	—
369	C₂²	—	8	2	no	—
370	C₂²	—	8	8	no	—
371	C₂²	C₂₃×#536	1	2	yes	—
372	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
373	C₄	—	2	2	no	—
374	C₄	—	2	4	no	—
375	C₄	—	2	4	no	—
376	C₄	—	4	4	no	—
377	C₄	—	4	8	no	—
378	C₄	C₂₃×#536	1	2	yes	—
379	C₄	C₂×C₂₃×2₋¹⁺⁴	1	2	yes	—
380	C₂	—	2	2	no	—
381	C₂	—	4	2	no	—
382	C₂	—	8	4	no	—
383	C₂	C₂×C₂₃×#536	1	1	yes	characteristic
384	C₂	C₂₃×#3585	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
prime radical	C₂×C₂₃×#540	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂×C₂₃×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₃×#3458	C₂	semidirect
3. C₂₃×#3241	C₂	semidirect
4. C₂₃×#3166	C₂	semidirect
5. C₂₃×#3138	C₂	semidirect
6. C₂₃×#3094	C₂	semidirect
7. C₂₃×#3077	C₂	semidirect
8. C₂₃×#2921	C₂	semidirect
10. C₂₃×#544	C₂²	semidirect
25. C₂₃×#501	C₂²	semidirect
26. C₂₃×#499	C₂²	semidirect
27. C₂₃×#490	C₂²	semidirect
28. C₂₃×#486	C₂²	semidirect
29. C₂₃×#482	C₂²	semidirect
30. C₂₃×#481	C₂²	semidirect
31. C₂₃×#480	C₂²	semidirect
32. C₂₃×#478	C₂²	semidirect
33. C₂₃×#476	C₂²	semidirect
34. C₂₃×#474	C₂²	semidirect
35. C₂₃×#433	C₂²	semidirect
139. #60868	C₂₃	direct (N × H)
171. #3458	C₂×C₂₃	semidirect
173. #3241	C₂×C₂₃	semidirect
174. #3166	C₂×C₂₃	semidirect
175. #3138	C₂×C₂₃	semidirect
176. #3094	C₂×C₂₃	semidirect
177. #3077	C₂×C₂₃	semidirect
178. #2921	C₂×C₂₃	semidirect
197. #544	C₂²×C₂₃	semidirect
212. #501	C₂²×C₂₃	semidirect
213. #499	C₂²×C₂₃	semidirect
214. #490	C₂²×C₂₃	semidirect
215. #486	C₂²×C₂₃	semidirect
216. #482	C₂²×C₂₃	semidirect
217. #481	C₂²×C₂₃	semidirect
218. #480	C₂²×C₂₃	semidirect
219. #478	C₂²×C₂₃	semidirect
220. #476	C₂²×C₂₃	semidirect
221. #474	C₂²×C₂₃	semidirect
222. #433	C₂²×C₂₃	semidirect
286. C₂₃	#60868	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂₃×#3458	2
C₂×C₂₃×#540	2
C₂₃×#3241	2
C₂₃×#3166	2
C₂₃×#3138	2
C₂₃×#3094	2
C₂₃×#3077	2
C₂₃×#2921	2
#60868	23

Subgroups — C23×#60868 #19208494

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#60868 #19208494