Subgroups — C₂₃×#60688 #19208314

Order 5888.

2010 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3444	C₂	1	2	yes	maximal, complemented
2	C₂₃×#3181	C₂	1	8	yes	maximal, complemented
3	C₂₃×#3180	C₂	1	8	yes	maximal, complemented
4	C₂₃×#3162	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#3150	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#3135	C₂	1	2	yes	maximal, complemented
7	C₂₃×#3050	C₂	1	4	yes	maximal, complemented
8	C₂₃×#2943	C₂	1	4	yes	maximal, complemented
9	C₂²×C₂₃×#97	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₂₃×#135	C₂²	1	4	yes	—
11	C₂³×C₈×C₂₃	C₂²	1	2	yes	—
12	C₂₃×#533	C₂²	1	4	yes	—
13	C₂₃×#533	C₂²	1	2	yes	—
14	C₂₃×#532	C₂²	1	2	yes	—
15	C₂₃×#532	C₂²	1	4	yes	—
16	C₂₃×#529	—	2	4	no	—
17	C₂₃×#529	—	2	4	no	—
18	C₂₃×#529	C₂²	1	8	yes	—
19	C₂₃×#525	—	2	4	no	—
20	C₂₃×#525	C₂²	1	4	yes	—
21	C₄×#41×C₂₃	—	2	4	no	—
22	C₄×#41×C₂₃	C₂²	1	4	yes	—
23	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
24	C₂₃×#501	C₂²	1	8	yes	complemented
25	C₂₃×#497	C₂²	1	4	yes	complemented
26	C₂₃×#496	C₂²	1	4	yes	complemented
27	C₂₃×#491	C₂²	1	4	yes	complemented
28	C₂₃×#490	C₂²	1	4	yes	complemented
29	C₂₃×#489	C₂²	1	8	yes	complemented
30	C₂₃×#467	C₂²	1	8	yes	—
31	C₂₃×#466	C₂²	1	8	yes	—
32	C₂₃×#465	C₂²	1	16	yes	—
33	C₂₃×#442	C₂²	1	8	yes	complemented
34	C₂₃×#441	C₂²	1	8	yes	complemented
35	C₂₃×#440	C₂²	1	16	yes	complemented
36	C₂₃×#427	C₂²	1	4	yes	—
37	C₂₃×#416	C₂²	1	8	yes	—
38	C₂×C₂₃×#97	C₂²	1	8	yes	—
39	C₂×C₂₃×#97	C₂²	1	2	yes	—
40	C₂×C₂₃×#97	C₂²	1	1	yes	characteristic
41	C₂×C₂₃×#97	C₂²	1	1	yes	characteristic
42	C₂×#41×C₂₃	—	2	4	no	—
43	C₂×#41×C₂₃	C₂³	1	4	yes	—
44	C₂³×C₄×C₂₃	D₄	1	2	yes	—
45	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
46	C₂₃×#135	—	2	16	no	—
47	C₂×Q₁₆×C₂₃	C₂³	1	4	yes	—
48	C₂×SD₁₆×C₂₃	C₂³	1	8	yes	—
49	C₂×D₈×C₂₃	C₂³	1	4	yes	—
50	C₂²×C₈×C₂₃	—	2	8	no	—
51	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
52	C₂²×C₈×C₂₃	C₂³	1	8	yes	—
53	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
54	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
55	C₂₃×C₄⋊Q₈	C₂³	1	4	yes	—
56	C₂₃×#127	C₂³	1	2	yes	—
57	C₂₃×#126	—	2	8	no	—
58	C₂₃×#125	—	2	4	no	—
59	C₂₃×#125	C₂³	1	4	yes	—
60	C₂₃×#124	—	2	4	no	—
61	C₂₃×#124	C₂³	1	4	yes	—
62	C₂₃×#123	—	2	8	no	—
63	C₂₃×#123	—	2	4	no	—
64	C₂₃×C₂²⋊Q₈	—	2	4	no	—
65	C₂₃×C₂²⋊Q₈	—	2	4	no	—
66	C₂₃×C₂²⋊Q₈	C₂³	1	8	yes	—
67	C₂₃×#121	—	2	4	no	—
68	C₂₃×#121	—	2	4	no	—
69	C₂₃×#121	C₂³	1	8	yes	—
70	C₂₃×#120	—	2	4	no	—
71	C₄×Q₈×C₂₃	—	2	4	no	—
72	C₄×Q₈×C₂₃	—	2	4	no	—
73	C₄×Q₈×C₂₃	C₂³	1	8	yes	—
74	C₄×D₄×C₂₃	—	2	8	no	—
75	C₄×D₄×C₂₃	—	2	8	no	—
76	C₄×D₄×C₂₃	—	2	8	no	—
77	C₄×D₄×C₂₃	—	2	4	no	—
78	C₄×D₄×C₂₃	—	2	4	no	—
79	C₄×D₄×C₂₃	C₂³	1	8	yes	—
80	C₂₃×#117	—	2	4	no	—
81	C₂₃×#117	—	2	8	no	—
82	C₂₃×#117	—	2	4	no	—
83	C₂₃×#117	C₂³	1	4	yes	—
84	C₂×C₄²×C₂₃	—	2	4	no	—
85	C₂×C₄²×C₂₃	D₄	1	4	yes	—
86	C₂×C₄²×C₂₃	D₄	1	2	yes	—
87	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
88	C₂×C₄²×C₂₃	C₂³	1	4	yes	—
89	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
90	C₂₃×#107	C₂³	1	8	yes	—
91	C₂₃×#106	C₂³	1	8	yes	—
92	C₂₃×#103	C₂³	1	16	yes	—
93	C₂₃×#102	C₂³	1	16	yes	—
94	C₂₃×#97	C₂³	1	8	yes	—
95	C₂₃×#97	C₂³	1	4	yes	—
96	C₂₃×#97	C₂³	1	4	yes	—
97	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
98	#41×C₂₃	—	2	16	no	—
99	#41×C₂₃	—	4	16	no	—
100	C₂×Q₈×C₂₃	—	2	4	no	—
101	C₂×Q₈×C₂₃	C₂⁴	1	4	yes	—
102	C₂×D₄×C₂₃	—	2	4	no	—
103	C₂×D₄×C₂₃	—	2	8	no	—
104	C₂×D₄×C₂₃	—	2	4	no	—
105	C₂×D₄×C₂₃	C₂⁴	1	4	yes	—
106	C₂²×C₄×C₂₃	—	2	4	no	—
107	C₂²×C₄×C₂₃	—	2	8	no	—
108	C₂²×C₄×C₂₃	—	2	4	no	—
109	C₂²×C₄×C₂₃	—	4	4	no	—
110	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₂₃	C₂×D₄	1	4	yes	—
112	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
113	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
114	C₂²×C₄×C₂₃	C₂×D₄	1	4	yes	—
115	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
116	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
117	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
118	Q₁₆×C₂₃	—	2	8	no	—
119	SD₁₆×C₂₃	—	2	16	no	—
120	D₈×C₂₃	—	2	8	no	—
121	C₂×C₈×C₂₃	—	2	4	no	—
122	C₂×C₈×C₂₃	—	2	16	no	—
123	C₂×C₈×C₂₃	#41	1	8	yes	complemented
124	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
125	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
126	C₄⋊C₄×C₂₃	—	2	4	no	—
127	C₄⋊C₄×C₂₃	—	2	4	no	—
128	C₄⋊C₄×C₂₃	—	2	8	no	—
129	C₄⋊C₄×C₂₃	—	2	8	no	—
130	C₄⋊C₄×C₂₃	—	2	8	no	—
131	C₄⋊C₄×C₂₃	C₂⁴	1	8	yes	—
132	C₂²⋊C₄×C₂₃	—	2	8	no	—
133	C₂²⋊C₄×C₂₃	—	2	4	no	—
134	C₂²⋊C₄×C₂₃	—	2	8	no	—
135	C₂²⋊C₄×C₂₃	—	2	8	no	—
136	C₂²⋊C₄×C₂₃	—	2	8	no	—
137	C₄²×C₂₃	—	2	8	no	—
138	C₄²×C₂₃	—	2	4	no	—
139	C₄²×C₂₃	C₂×D₄	1	4	yes	—
140	C₄²×C₂₃	C₂×D₄	1	4	yes	—
141	C₄²×C₂₃	C₂×D₄	1	2	yes	—
142	C₄²×C₂₃	C₂×D₄	1	2	yes	—
143	C₄²×C₂₃	C₂⁴	1	2	yes	—
144	C₄²×C₂₃	C₂⁴	1	2	yes	—
145	#60688	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
146	C₂³×C₂₃	—	2	2	no	—
147	C₂³×C₂₃	—	2	4	no	—
148	C₂³×C₂₃	—	2	4	no	—
149	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
150	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
151	Q₈×C₂₃	—	2	8	no	—
152	Q₈×C₂₃	—	4	8	no	—
153	D₄×C₂₃	—	2	8	no	—
154	D₄×C₂₃	—	4	8	no	—
155	D₄×C₂₃	—	4	8	no	—
156	D₄×C₂₃	—	4	16	no	—
157	C₂×C₄×C₂₃	—	2	2	no	—
158	C₂×C₄×C₂₃	—	2	8	no	—
159	C₂×C₄×C₂₃	—	2	4	no	—
160	C₂×C₄×C₂₃	—	2	4	no	—
161	C₂×C₄×C₂₃	—	2	4	no	—
162	C₂×C₄×C₂₃	—	2	8	no	—
163	C₂×C₄×C₂₃	—	4	2	no	—
164	C₂×C₄×C₂₃	—	4	4	no	—
165	C₂×C₄×C₂₃	—	4	2	no	—
166	C₂×C₄×C₂₃	—	4	16	no	—
167	C₂×C₄×C₂₃	—	4	8	no	—
168	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
169	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
170	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
171	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
172	C₂×C₄×C₂₃	C₂×#41	1	4	yes	—
173	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
174	C₈×C₂₃	—	2	4	no	—
175	C₈×C₂₃	C₂×#41	1	8	yes	—
176	#3444	C₂×C₂₃	1	2	yes	complemented
177	#3181	C₂×C₂₃	1	8	yes	complemented
178	#3180	C₂×C₂₃	1	8	yes	complemented
179	#3162	C₂×C₂₃	1	1	yes	characteristic, complemented
180	#3150	C₂×C₂₃	1	1	yes	characteristic, complemented
181	#3135	C₂×C₂₃	1	2	yes	complemented
182	#3050	C₂×C₂₃	1	4	yes	complemented
183	#2943	C₂×C₂₃	1	4	yes	complemented
184	C₂²×#97	C₂×C₂₃	1	1	yes	characteristic, complemented
185	C₂²×C₂₃	—	2	8	no	—
186	C₂²×C₂₃	—	2	2	no	—
187	C₂²×C₂₃	—	2	2	no	—
188	C₂²×C₂₃	—	2	2	no	—
189	C₂²×C₂₃	—	4	4	no	—
190	C₂²×C₂₃	—	4	8	no	—
191	C₂²×C₂₃	#532	1	2	yes	—
192	C₂²×C₂₃	#575	1	4	yes	—
193	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
194	C₄×C₂₃	—	2	2	no	—
195	C₄×C₂₃	—	2	4	no	—
196	C₄×C₂₃	—	2	4	no	—
197	C₄×C₂₃	—	4	4	no	—
198	C₄×C₂₃	—	4	8	no	—
199	C₄×C₂₃	#532	1	2	yes	—
200	C₄×C₂₃	C₂²×#41	1	2	yes	—
201	C₂×#135	C₂²×C₂₃	1	4	yes	—
202	C₂³×C₈	C₂²×C₂₃	1	2	yes	—
203	#533	C₂²×C₂₃	1	4	yes	—
204	#533	C₂²×C₂₃	1	2	yes	—
205	#532	C₂²×C₂₃	1	2	yes	—
206	#532	C₂²×C₂₃	1	4	yes	—
207	#529	—	2	4	no	—
208	#529	—	2	4	no	—
209	#529	C₂²×C₂₃	1	8	yes	—
210	#525	—	2	4	no	—
211	#525	C₂²×C₂₃	1	4	yes	—
212	C₄×#41	—	2	4	no	—
213	C₄×#41	C₂²×C₂₃	1	4	yes	—
214	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
215	#501	C₂²×C₂₃	1	8	yes	complemented
216	#497	C₂²×C₂₃	1	4	yes	complemented
217	#496	C₂²×C₂₃	1	4	yes	complemented
218	#491	C₂²×C₂₃	1	4	yes	complemented
219	#490	C₂²×C₂₃	1	4	yes	complemented
220	#489	C₂²×C₂₃	1	8	yes	complemented
221	#467	C₂²×C₂₃	1	8	yes	—
222	#466	C₂²×C₂₃	1	8	yes	—
223	#465	C₂²×C₂₃	1	16	yes	—
224	#442	C₂²×C₂₃	1	8	yes	complemented
225	#441	C₂²×C₂₃	1	8	yes	complemented
226	#440	C₂²×C₂₃	1	16	yes	complemented
227	#427	C₂²×C₂₃	1	4	yes	—
228	#416	C₂²×C₂₃	1	8	yes	—
229	C₂×#97	C₂²×C₂₃	1	1	yes	characteristic
230	C₂×#97	C₂²×C₂₃	1	1	yes	characteristic
231	C₂×#97	C₂²×C₂₃	1	8	yes	—
232	C₂×#97	C₂²×C₂₃	1	2	yes	—
233	C₂×C₂₃	—	2	2	no	—
234	C₂×C₂₃	—	2	4	no	—
235	C₂×C₂₃	—	8	4	no	—
236	C₂×C₂₃	C₂×#532	1	1	yes	characteristic
237	C₂×C₂₃	C₂×#575	1	2	yes	—
238	C₂×#41	—	2	4	no	—
239	C₂×#41	C₂³×C₂₃	1	4	yes	—
240	C₂³×C₄	D₄×C₂₃	1	2	yes	—
241	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
242	#135	—	2	16	no	—
243	C₂×Q₁₆	C₂³×C₂₃	1	4	yes	—
244	C₂×SD₁₆	C₂³×C₂₃	1	8	yes	—
245	C₂×D₈	C₂³×C₂₃	1	4	yes	—
246	C₂²×C₈	—	2	8	no	—
247	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
248	C₂²×C₈	C₂³×C₂₃	1	8	yes	—
249	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
250	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
251	C₄⋊Q₈	C₂³×C₂₃	1	4	yes	—
252	#127	C₂³×C₂₃	1	2	yes	—
253	#126	—	2	8	no	—
254	#125	—	2	4	no	—
255	#125	C₂³×C₂₃	1	4	yes	—
256	#124	—	2	4	no	—
257	#124	C₂³×C₂₃	1	4	yes	—
258	#123	—	2	8	no	—
259	#123	—	2	4	no	—
260	C₂²⋊Q₈	—	2	4	no	—
261	C₂²⋊Q₈	—	2	4	no	—
262	C₂²⋊Q₈	C₂³×C₂₃	1	8	yes	—
263	#121	—	2	4	no	—
264	#121	—	2	4	no	—
265	#121	C₂³×C₂₃	1	8	yes	—
266	#120	—	2	4	no	—
267	C₄×Q₈	—	2	4	no	—
268	C₄×Q₈	—	2	4	no	—
269	C₄×Q₈	C₂³×C₂₃	1	8	yes	—
270	C₄×D₄	—	2	8	no	—
271	C₄×D₄	—	2	8	no	—
272	C₄×D₄	—	2	8	no	—
273	C₄×D₄	—	2	4	no	—
274	C₄×D₄	—	2	4	no	—
275	C₄×D₄	C₂³×C₂₃	1	8	yes	—
276	#117	—	2	4	no	—
277	#117	—	2	8	no	—
278	#117	—	2	4	no	—
279	#117	C₂³×C₂₃	1	4	yes	—
280	C₂×C₄²	—	2	4	no	—
281	C₂×C₄²	D₄×C₂₃	1	4	yes	—
282	C₂×C₄²	D₄×C₂₃	1	2	yes	—
283	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
284	C₂×C₄²	C₂³×C₂₃	1	4	yes	—
285	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
286	#107	C₂³×C₂₃	1	8	yes	—
287	#106	C₂³×C₂₃	1	8	yes	—
288	#103	C₂³×C₂₃	1	16	yes	—
289	#102	C₂³×C₂₃	1	16	yes	—
290	#97	C₂³×C₂₃	1	8	yes	—
291	#97	C₂³×C₂₃	1	4	yes	—
292	#97	C₂³×C₂₃	1	4	yes	—
293	C₂₃	#60688	1	1	yes	characteristic, direct product factor, Sylow
294	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
295	#41	—	2	16	no	—
296	#41	—	4	16	no	—
297	C₂×Q₈	—	2	4	no	—
298	C₂×Q₈	C₂⁴×C₂₃	1	4	yes	—
299	C₂×D₄	—	2	4	no	—
300	C₂×D₄	—	2	8	no	—
301	C₂×D₄	—	2	4	no	—
302	C₂×D₄	C₂⁴×C₂₃	1	4	yes	—
303	C₂²×C₄	—	2	4	no	—
304	C₂²×C₄	—	2	4	no	—
305	C₂²×C₄	—	2	8	no	—
306	C₂²×C₄	—	4	4	no	—
307	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
308	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
309	C₂²×C₄	C₂×D₄×C₂₃	1	4	yes	—
310	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
311	C₂²×C₄	C₂×D₄×C₂₃	1	4	yes	—
312	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
313	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
314	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
315	Q₁₆	—	2	8	no	—
316	SD₁₆	—	2	16	no	—
317	D₈	—	2	8	no	—
318	C₂×C₈	—	2	4	no	—
319	C₂×C₈	—	2	16	no	—
320	C₂×C₈	#41×C₂₃	1	8	yes	complemented
321	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
322	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
323	C₄⋊C₄	—	2	4	no	—
324	C₄⋊C₄	—	2	4	no	—
325	C₄⋊C₄	—	2	8	no	—
326	C₄⋊C₄	—	2	8	no	—
327	C₄⋊C₄	—	2	8	no	—
328	C₄⋊C₄	C₂⁴×C₂₃	1	8	yes	—
329	C₂²⋊C₄	—	2	8	no	—
330	C₂²⋊C₄	—	2	4	no	—
331	C₂²⋊C₄	—	2	8	no	—
332	C₂²⋊C₄	—	2	8	no	—
333	C₂²⋊C₄	—	2	8	no	—
334	C₄²	—	2	8	no	—
335	C₄²	—	2	4	no	—
336	C₄²	C₂×D₄×C₂₃	1	2	yes	—
337	C₄²	C₂×D₄×C₂₃	1	4	yes	—
338	C₄²	C₂×D₄×C₂₃	1	2	yes	—
339	C₄²	C₂×D₄×C₂₃	1	4	yes	—
340	C₄²	C₂⁴×C₂₃	1	2	yes	—
341	C₄²	C₂⁴×C₂₃	1	2	yes	—
342	C₂³	—	2	4	no	—
343	C₂³	—	2	2	no	—
344	C₂³	—	2	4	no	—
345	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
346	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
347	Q₈	—	2	8	no	—
348	Q₈	—	4	8	no	—
349	D₄	—	2	8	no	—
350	D₄	—	4	8	no	—
351	D₄	—	4	16	no	—
352	D₄	—	4	8	no	—
353	C₂×C₄	—	2	8	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	4	no	—
356	C₂×C₄	—	2	4	no	—
357	C₂×C₄	—	2	4	no	—
358	C₂×C₄	—	2	8	no	—
359	C₂×C₄	—	4	2	no	—
360	C₂×C₄	—	4	4	no	—
361	C₂×C₄	—	4	2	no	—
362	C₂×C₄	—	4	16	no	—
363	C₂×C₄	—	4	8	no	—
364	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
365	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
366	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
367	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
368	C₂×C₄	C₂×#41×C₂₃	1	4	yes	—
369	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
370	C₈	—	2	4	no	—
371	C₈	C₂×#41×C₂₃	1	8	yes	—
372	C₂²	—	2	8	no	—
373	C₂²	—	2	2	no	—
374	C₂²	—	2	2	no	—
375	C₂²	—	2	2	no	—
376	C₂²	—	4	4	no	—
377	C₂²	—	4	8	no	—
378	C₂²	C₂₃×#532	1	2	yes	—
379	C₂²	C₂₃×#575	1	4	yes	—
380	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
381	C₄	—	2	2	no	—
382	C₄	—	2	4	no	—
383	C₄	—	2	4	no	—
384	C₄	—	4	4	no	—
385	C₄	—	4	8	no	—
386	C₄	C₂₃×#532	1	2	yes	—
387	C₄	C₂²×#41×C₂₃	1	2	yes	—
388	C₂	—	2	4	no	—
389	C₂	—	2	2	no	—
390	C₂	—	8	4	no	—
391	C₂	C₂×C₂₃×#532	1	1	yes	characteristic
392	C₂	C₂×C₂₃×#575	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₂₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
socle	C₂²×C₂₃	C₂³×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₃ ◁ C₂²×C₄²×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₃×#3444	C₂	semidirect
2. C₂₃×#3181	C₂	semidirect
3. C₂₃×#3180	C₂	semidirect
4. C₂₃×#3162	C₂	semidirect
5. C₂₃×#3150	C₂	semidirect
6. C₂₃×#3135	C₂	semidirect
7. C₂₃×#3050	C₂	semidirect
8. C₂₃×#2943	C₂	semidirect
9. C₂²×C₂₃×#97	C₂	semidirect
24. C₂₃×#501	C₂²	semidirect
25. C₂₃×#497	C₂²	semidirect
26. C₂₃×#496	C₂²	semidirect
27. C₂₃×#491	C₂²	semidirect
28. C₂₃×#490	C₂²	semidirect
29. C₂₃×#489	C₂²	semidirect
33. C₂₃×#442	C₂²	semidirect
34. C₂₃×#441	C₂²	semidirect
35. C₂₃×#440	C₂²	semidirect
123. C₂×C₈×C₂₃	#41	semidirect
145. #60688	C₂₃	direct (N × H)
176. #3444	C₂×C₂₃	semidirect
177. #3181	C₂×C₂₃	semidirect
178. #3180	C₂×C₂₃	semidirect
179. #3162	C₂×C₂₃	semidirect
180. #3150	C₂×C₂₃	semidirect
181. #3135	C₂×C₂₃	semidirect
182. #3050	C₂×C₂₃	semidirect
183. #2943	C₂×C₂₃	semidirect
184. C₂²×#97	C₂×C₂₃	semidirect
215. #501	C₂²×C₂₃	semidirect
216. #497	C₂²×C₂₃	semidirect
217. #496	C₂²×C₂₃	semidirect
218. #491	C₂²×C₂₃	semidirect
219. #490	C₂²×C₂₃	semidirect
220. #489	C₂²×C₂₃	semidirect
224. #442	C₂²×C₂₃	semidirect
225. #441	C₂²×C₂₃	semidirect
226. #440	C₂²×C₂₃	semidirect
293. C₂₃	#60688	direct (N × H)
320. C₂×C₈	#41×C₂₃	semidirect

Maximal subgroups

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

subgroup	index
C₂₃×#3444	2
C₂₃×#3181	2
C₂₃×#3180	2
C₂₃×#3162	2
C₂₃×#3150	2
C₂₃×#3135	2
C₂₃×#3050	2
C₂₃×#2943	2
C₂²×C₂₃×#97	2
#60688	23

Subgroups — C23×#60688 #19208314

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#60688 #19208314