Subgroups — C₂₃×#60143 #19207769

Order 5888.

2706 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#568	C₂	1	2	yes	maximal, complemented
2	C₂₃×#3449	C₂	1	1	yes	maximal, characteristic
3	C₂₃×#2933	C₂	1	16	yes	maximal, complemented
4	C₂₃×#2932	C₂	1	4	yes	maximal, complemented
5	C₂₃×#2931	C₂	1	4	yes	maximal, complemented
6	C₂₃×#2905	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₂₃×#408	C₂	1	2	yes	maximal, complemented
8	C₂×C₂₃×#405	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#41×C₂₃	C₂²	1	2	yes	—
10	C₂₃×#568	—	2	16	no	—
11	C₂×C₂₃×#131	C₂²	1	8	yes	—
12	C₂×C₂₃×#131	C₂²	1	8	yes	complemented
13	C₂²×M₁₆×C₂₃	C₂²	1	2	yes	—
14	C₂²×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
15	C₂²×M₁₆×C₂₃	C₂²	1	8	yes	complemented
16	C₂³×C₈×C₂₃	C₂²	1	1	yes	characteristic
17	C₂₃×#537	C₄	1	4	yes	—
18	C₂₃×#536	C₄	1	4	yes	—
19	C₂₃×#535	C₄	1	4	yes	—
20	C₂₃×#534	C₄	1	4	yes	—
21	C₂₃×#532	C₂²	1	4	yes	—
22	C₂₃×#525	C₂²	1	8	yes	—
23	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
24	C₂₃×#436	C₂²	1	16	yes	complemented
25	C₂₃×#435	C₂²	1	32	yes	complemented
26	C₈×D₄×C₂₃	C₂²	1	16	yes	complemented
27	C₂₃×#424	C₂²	1	8	yes	complemented
28	C₂₃×#423	C₂²	1	4	yes	complemented
29	C₂₃×#408	C₂²	1	8	yes	—
30	C₂₃×#408	C₂²	1	4	yes	complemented
31	C₂₃×#408	C₂²	1	4	yes	complemented
32	C₂×C₂₃×C₂²⋊C₈	C₂²	1	8	yes	complemented
33	C₂₃×#405	C₂²	1	8	yes	complemented
34	C₂×C₂₃×#97	C₂²	1	2	yes	complemented
35	C₂×C₄×C₈×C₂₃	C₂²	1	2	yes	complemented
36	C₂×#41×C₂₃	—	2	8	no	—
37	C₂×#41×C₂₃	—	2	8	no	—
38	C₂×#41×C₂₃	C₂×C₄	1	4	yes	—
39	C₂×#41×C₂₃	C₂×C₄	1	4	yes	—
40	C₂×#41×C₂₃	C₂³	1	4	yes	—
41	C₂×#41×C₂₃	C₂³	1	4	yes	—
42	C₂²×Q₈×C₂₃	C₂×C₄	1	2	yes	—
43	C₂²×D₄×C₂₃	C₂×C₄	1	4	yes	—
44	C₂²×D₄×C₂₃	C₂×C₄	1	2	yes	—
45	C₂³×C₄×C₂₃	C₂³	1	4	yes	—
46	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
47	C₂₃×#131	—	2	32	no	—
48	C₂₃×#131	—	2	32	no	—
49	C₂×M₁₆×C₂₃	—	2	8	no	—
50	C₂×M₁₆×C₂₃	—	2	32	no	—
51	C₂×M₁₆×C₂₃	D₄	1	8	yes	complemented
52	C₂×M₁₆×C₂₃	C₂³	1	4	yes	—
53	C₂×M₁₆×C₂₃	C₂³	1	4	yes	—
54	C₂×M₁₆×C₂₃	C₂³	1	16	yes	—
55	C₂×M₁₆×C₂₃	C₂³	1	4	yes	—
56	C₂²×C₈×C₂₃	—	2	4	no	—
57	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
58	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
59	C₂²×C₈×C₂₃	C₂³	1	4	yes	—
60	C₂²×C₈×C₂₃	C₂³	1	4	yes	—
61	C₂²×C₈×C₂₃	C₂³	1	16	yes	—
62	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
63	C₂₃×C₄⋊Q₈	C₂×C₄	1	4	yes	—
64	C₂₃×#127	C₂×C₄	1	4	yes	—
65	C₂₃×#124	C₂×C₄	1	8	yes	—
66	C₂₃×#123	C₂×C₄	1	16	yes	—
67	C₂₃×C₂²⋊Q₈	C₂×C₄	1	16	yes	—
68	C₂₃×#121	C₂×C₄	1	16	yes	—
69	C₂₃×#121	C₂×C₄	1	16	yes	—
70	C₂₃×#120	C₂×C₄	1	16	yes	—
71	C₄×D₄×C₂₃	C₂³	1	16	yes	—
72	C₂₃×#117	C₂×C₄	1	4	yes	—
73	C₂₃×#117	C₂³	1	4	yes	—
74	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
75	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
76	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
77	C₂₃×C₄⋊C₈	C₂³	1	16	yes	—
78	C₂₃×C₂²⋊C₈	C₂³	1	16	yes	—
79	C₂₃×C₂²⋊C₈	C₂³	1	16	yes	—
80	C₂₃×#97	C₂³	1	8	yes	—
81	C₄×C₈×C₂₃	C₂³	1	8	yes	—
82	C₂⁴×C₂₃	C₂²×C₄	1	4	yes	—
83	C₂⁴×C₂₃	C₂²×C₄	1	1	yes	characteristic
84	#41×C₂₃	—	2	16	no	—
85	#41×C₂₃	—	2	16	no	—
86	#41×C₂₃	—	2	8	no	—
87	#41×C₂₃	—	2	8	no	—
88	#41×C₂₃	—	2	8	no	—
89	#41×C₂₃	—	2	8	no	—
90	C₂×Q₈×C₂₃	—	2	8	no	—
91	C₂×Q₈×C₂₃	C₂²×C₄	1	4	yes	—
92	C₂×Q₈×C₂₃	C₂²×C₄	1	4	yes	—
93	C₂×D₄×C₂₃	—	2	16	no	—
94	C₂×D₄×C₂₃	—	2	8	no	—
95	C₂×D₄×C₂₃	C₂²×C₄	1	8	yes	—
96	C₂×D₄×C₂₃	C₂²×C₄	1	8	yes	—
97	C₂×D₄×C₂₃	C₂²×C₄	1	4	yes	—
98	C₂×D₄×C₂₃	C₂²×C₄	1	4	yes	—
99	C₂×D₄×C₂₃	C₂²×C₄	1	16	yes	—
100	C₂²×C₄×C₂₃	—	2	8	no	—
101	C₂²×C₄×C₂₃	—	2	8	no	—
102	C₂²×C₄×C₂₃	C₂²×C₄	1	8	yes	—
103	C₂²×C₄×C₂₃	C₂²×C₄	1	4	yes	—
104	C₂²×C₄×C₂₃	C₂²×C₄	1	4	yes	—
105	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
106	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
107	C₂²×C₄×C₂₃	C₂×D₄	1	4	yes	—
108	C₂²×C₄×C₂₃	#41	1	4	yes	—
109	C₂²×C₄×C₂₃	C₂⁴	1	8	yes	—
110	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
111	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
112	M₁₆×C₂₃	—	2	8	no	—
113	M₁₆×C₂₃	—	2	8	no	—
114	M₁₆×C₂₃	—	2	32	no	—
115	M₁₆×C₂₃	C₂×D₄	1	16	yes	—
116	C₂×C₈×C₂₃	—	2	8	no	—
117	C₂×C₈×C₂₃	—	2	8	no	—
118	C₂×C₈×C₂₃	—	2	2	no	—
119	C₂×C₈×C₂₃	—	2	2	no	—
120	C₂×C₈×C₂₃	—	2	32	no	—
121	C₂×C₈×C₂₃	C₂×D₄	1	8	yes	—
122	C₂×C₈×C₂₃	C₂⁴	1	8	yes	—
123	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
124	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
125	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
126	C₄⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
127	C₄⋊C₄×C₂₃	C₂²×C₄	1	16	yes	—
128	C₂²⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
129	C₂²⋊C₄×C₂₃	C₂²×C₄	1	32	yes	—
130	C₄²×C₂₃	C₂²×C₄	1	4	yes	—
131	C₄²×C₂₃	C₂⁴	1	4	yes	—
132	#60143	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
133	C₂³×C₂₃	—	2	8	no	—
134	C₂³×C₂₃	—	4	2	no	—
135	C₂³×C₂₃	—	4	8	no	—
136	C₂³×C₂₃	C₄×D₄	1	4	yes	—
137	C₂³×C₂₃	C₂³×C₄	1	8	yes	—
138	C₂³×C₂₃	C₂³×C₄	1	2	yes	—
139	C₂³×C₂₃	C₂³×C₄	1	1	yes	characteristic
140	Q₈×C₂₃	—	2	8	no	—
141	Q₈×C₂₃	—	2	8	no	—
142	D₄×C₂₃	—	2	16	no	—
143	D₄×C₂₃	—	2	16	no	—
144	D₄×C₂₃	—	2	8	no	—
145	D₄×C₂₃	—	2	8	no	—
146	D₄×C₂₃	—	4	16	no	—
147	C₂×C₄×C₂₃	—	2	8	no	—
148	C₂×C₄×C₂₃	—	2	16	no	—
149	C₂×C₄×C₂₃	—	2	8	no	—
150	C₂×C₄×C₂₃	—	2	8	no	—
151	C₂×C₄×C₂₃	—	4	4	no	—
152	C₂×C₄×C₂₃	C₄×D₄	1	8	yes	—
153	C₂×C₄×C₂₃	C₄×D₄	1	4	yes	—
154	C₂×C₄×C₂₃	C₂³×C₄	1	8	yes	—
155	C₂×C₄×C₂₃	C₂³×C₄	1	8	yes	—
156	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
157	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
158	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
159	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
160	C₂×C₄×C₂₃	C₂×#41	1	4	yes	—
161	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
162	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
163	C₈×C₂₃	—	2	8	no	—
164	C₈×C₂₃	—	2	2	no	—
165	C₈×C₂₃	—	2	2	no	—
166	C₈×C₂₃	C₂²×D₄	1	8	yes	—
167	C₂×#568	C₂×C₂₃	1	2	yes	complemented
168	#3449	C₂×C₂₃	1	1	yes	characteristic
169	#2933	C₂×C₂₃	1	16	yes	complemented
170	#2932	C₂×C₂₃	1	4	yes	complemented
171	#2931	C₂×C₂₃	1	4	yes	complemented
172	#2905	C₂×C₂₃	1	1	yes	characteristic, complemented
173	C₂×#408	C₂×C₂₃	1	2	yes	complemented
174	C₂×#405	C₂×C₂₃	1	1	yes	characteristic, complemented
175	C₂²×C₂₃	—	2	2	no	—
176	C₂²×C₂₃	—	2	4	no	—
177	C₂²×C₂₃	—	2	8	no	—
178	C₂²×C₂₃	—	2	16	no	—
179	C₂²×C₂₃	—	4	4	no	—
180	C₂²×C₂₃	—	8	8	no	—
181	C₂²×C₂₃	C₂×C₄×D₄	1	4	yes	—
182	C₂²×C₂₃	C₂×C₄×D₄	1	2	yes	—
183	C₂²×C₂₃	C₂⁴×C₄	1	1	yes	characteristic
184	C₄×C₂₃	—	2	8	no	—
185	C₄×C₂₃	—	2	8	no	—
186	C₄×C₂₃	C₂×C₄×D₄	1	4	yes	—
187	C₄×C₂₃	C₂×C₄×D₄	1	2	yes	—
188	C₄×C₂₃	C₂³×D₄	1	1	yes	characteristic
189	C₄×C₂₃	C₂²×#41	1	1	yes	characteristic
190	C₂²×#41	C₂²×C₂₃	1	2	yes	—
191	#568	—	2	16	no	—
192	C₂×#131	C₂²×C₂₃	1	8	yes	—
193	C₂×#131	C₂²×C₂₃	1	8	yes	complemented
194	C₂²×M₁₆	C₂²×C₂₃	1	2	yes	—
195	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
196	C₂²×M₁₆	C₂²×C₂₃	1	8	yes	complemented
197	C₂³×C₈	C₂²×C₂₃	1	1	yes	characteristic
198	#537	C₄×C₂₃	1	4	yes	—
199	#536	C₄×C₂₃	1	4	yes	—
200	#535	C₄×C₂₃	1	4	yes	—
201	#534	C₄×C₂₃	1	4	yes	—
202	#532	C₂²×C₂₃	1	4	yes	—
203	#525	C₂²×C₂₃	1	8	yes	—
204	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
205	#436	C₂²×C₂₃	1	16	yes	complemented
206	#435	C₂²×C₂₃	1	32	yes	complemented
207	C₈×D₄	C₂²×C₂₃	1	16	yes	complemented
208	#424	C₂²×C₂₃	1	8	yes	complemented
209	#423	C₂²×C₂₃	1	4	yes	complemented
210	#408	C₂²×C₂₃	1	8	yes	—
211	#408	C₂²×C₂₃	1	4	yes	complemented
212	#408	C₂²×C₂₃	1	4	yes	complemented
213	C₂×C₂²⋊C₈	C₂²×C₂₃	1	8	yes	complemented
214	#405	C₂²×C₂₃	1	8	yes	complemented
215	C₂×#97	C₂²×C₂₃	1	2	yes	complemented
216	C₂×C₄×C₈	C₂²×C₂₃	1	2	yes	complemented
217	C₂×C₂₃	—	2	4	no	—
218	C₂×C₂₃	—	2	2	no	—
219	C₂×C₂₃	—	4	8	no	—
220	C₂×C₂₃	C₂²×C₄×D₄	1	1	yes	characteristic
221	C₂×C₂₃	#3573	1	2	yes	—
222	C₂×#41	—	2	8	no	—
223	C₂×#41	—	2	8	no	—
224	C₂×#41	C₂×C₄×C₂₃	1	4	yes	—
225	C₂×#41	C₂×C₄×C₂₃	1	4	yes	—
226	C₂×#41	C₂³×C₂₃	1	4	yes	—
227	C₂×#41	C₂³×C₂₃	1	4	yes	—
228	C₂²×Q₈	C₂×C₄×C₂₃	1	2	yes	—
229	C₂²×D₄	C₂×C₄×C₂₃	1	4	yes	—
230	C₂²×D₄	C₂×C₄×C₂₃	1	2	yes	—
231	C₂³×C₄	C₂³×C₂₃	1	4	yes	—
232	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
233	#131	—	2	32	no	—
234	#131	—	2	32	no	—
235	C₂×M₁₆	—	2	8	no	—
236	C₂×M₁₆	—	2	32	no	—
237	C₂×M₁₆	D₄×C₂₃	1	8	yes	complemented
238	C₂×M₁₆	C₂³×C₂₃	1	4	yes	—
239	C₂×M₁₆	C₂³×C₂₃	1	4	yes	—
240	C₂×M₁₆	C₂³×C₂₃	1	16	yes	—
241	C₂×M₁₆	C₂³×C₂₃	1	4	yes	—
242	C₂²×C₈	—	2	4	no	—
243	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
244	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
245	C₂²×C₈	C₂³×C₂₃	1	4	yes	—
246	C₂²×C₈	C₂³×C₂₃	1	4	yes	—
247	C₂²×C₈	C₂³×C₂₃	1	16	yes	—
248	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
249	C₄⋊Q₈	C₂×C₄×C₂₃	1	4	yes	—
250	#127	C₂×C₄×C₂₃	1	4	yes	—
251	#124	C₂×C₄×C₂₃	1	8	yes	—
252	#123	C₂×C₄×C₂₃	1	16	yes	—
253	C₂²⋊Q₈	C₂×C₄×C₂₃	1	16	yes	—
254	#121	C₂×C₄×C₂₃	1	16	yes	—
255	#121	C₂×C₄×C₂₃	1	16	yes	—
256	#120	C₂×C₄×C₂₃	1	16	yes	—
257	C₄×D₄	C₂³×C₂₃	1	16	yes	—
258	#117	C₂×C₄×C₂₃	1	4	yes	—
259	#117	C₂³×C₂₃	1	4	yes	—
260	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
261	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
262	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
263	C₄⋊C₈	C₂³×C₂₃	1	16	yes	—
264	C₂²⋊C₈	C₂³×C₂₃	1	16	yes	—
265	C₂²⋊C₈	C₂³×C₂₃	1	16	yes	—
266	#97	C₂³×C₂₃	1	8	yes	—
267	C₄×C₈	C₂³×C₂₃	1	8	yes	—
268	C₂₃	#60143	1	1	yes	characteristic, direct product factor, Sylow
269	C₂⁴	C₂²×C₄×C₂₃	1	4	yes	—
270	C₂⁴	C₂²×C₄×C₂₃	1	1	yes	characteristic
271	#41	—	2	16	no	—
272	#41	—	2	16	no	—
273	#41	—	2	8	no	—
274	#41	—	2	8	no	—
275	#41	—	2	8	no	—
276	#41	—	2	8	no	—
277	C₂×Q₈	—	2	8	no	—
278	C₂×Q₈	C₂²×C₄×C₂₃	1	4	yes	—
279	C₂×Q₈	C₂²×C₄×C₂₃	1	4	yes	—
280	C₂×D₄	—	2	16	no	—
281	C₂×D₄	—	2	8	no	—
282	C₂×D₄	C₂²×C₄×C₂₃	1	8	yes	—
283	C₂×D₄	C₂²×C₄×C₂₃	1	8	yes	—
284	C₂×D₄	C₂²×C₄×C₂₃	1	4	yes	—
285	C₂×D₄	C₂²×C₄×C₂₃	1	4	yes	—
286	C₂×D₄	C₂²×C₄×C₂₃	1	16	yes	—
287	C₂²×C₄	—	2	8	no	—
288	C₂²×C₄	—	2	8	no	—
289	C₂²×C₄	C₂²×C₄×C₂₃	1	8	yes	—
290	C₂²×C₄	C₂²×C₄×C₂₃	1	4	yes	—
291	C₂²×C₄	C₂²×C₄×C₂₃	1	4	yes	—
292	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
293	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
294	C₂²×C₄	C₂×D₄×C₂₃	1	4	yes	—
295	C₂²×C₄	#41×C₂₃	1	4	yes	—
296	C₂²×C₄	C₂⁴×C₂₃	1	8	yes	—
297	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
298	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
299	M₁₆	—	2	8	no	—
300	M₁₆	—	2	8	no	—
301	M₁₆	—	2	32	no	—
302	M₁₆	C₂×D₄×C₂₃	1	16	yes	—
303	C₂×C₈	—	2	8	no	—
304	C₂×C₈	—	2	8	no	—
305	C₂×C₈	—	2	2	no	—
306	C₂×C₈	—	2	2	no	—
307	C₂×C₈	—	2	32	no	—
308	C₂×C₈	C₂×D₄×C₂₃	1	8	yes	—
309	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
310	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
311	C₂×C₈	C₂⁴×C₂₃	1	8	yes	—
312	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
313	C₄⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
314	C₄⋊C₄	C₂²×C₄×C₂₃	1	16	yes	—
315	C₂²⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
316	C₂²⋊C₄	C₂²×C₄×C₂₃	1	32	yes	—
317	C₄²	C₂²×C₄×C₂₃	1	4	yes	—
318	C₄²	C₂⁴×C₂₃	1	4	yes	—
319	C₂³	—	2	8	no	—
320	C₂³	—	4	2	no	—
321	C₂³	—	4	8	no	—
322	C₂³	C₄×D₄×C₂₃	1	4	yes	—
323	C₂³	C₂³×C₄×C₂₃	1	8	yes	—
324	C₂³	C₂³×C₄×C₂₃	1	2	yes	—
325	C₂³	C₂³×C₄×C₂₃	1	1	yes	characteristic
326	Q₈	—	2	8	no	—
327	Q₈	—	2	8	no	—
328	D₄	—	2	16	no	—
329	D₄	—	2	16	no	—
330	D₄	—	2	8	no	—
331	D₄	—	2	8	no	—
332	D₄	—	4	16	no	—
333	C₂×C₄	—	2	8	no	—
334	C₂×C₄	—	2	8	no	—
335	C₂×C₄	—	2	8	no	—
336	C₂×C₄	—	2	16	no	—
337	C₂×C₄	—	4	4	no	—
338	C₂×C₄	C₄×D₄×C₂₃	1	8	yes	—
339	C₂×C₄	C₄×D₄×C₂₃	1	4	yes	—
340	C₂×C₄	C₂³×C₄×C₂₃	1	8	yes	—
341	C₂×C₄	C₂³×C₄×C₂₃	1	8	yes	—
342	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
343	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
344	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
345	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
346	C₂×C₄	C₂×#41×C₂₃	1	4	yes	—
347	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
348	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
349	C₈	—	2	8	no	—
350	C₈	—	2	2	no	—
351	C₈	—	2	2	no	—
352	C₈	C₂²×D₄×C₂₃	1	8	yes	—
353	C₂²	—	2	2	no	—
354	C₂²	—	2	4	no	—
355	C₂²	—	2	8	no	—
356	C₂²	—	2	16	no	—
357	C₂²	—	4	4	no	—
358	C₂²	—	8	8	no	—
359	C₂²	C₂×C₄×D₄×C₂₃	1	4	yes	—
360	C₂²	C₂×C₄×D₄×C₂₃	1	2	yes	—
361	C₂²	C₂⁴×C₄×C₂₃	1	1	yes	characteristic
362	C₄	—	2	8	no	—
363	C₄	—	2	8	no	—
364	C₄	C₂×C₄×D₄×C₂₃	1	4	yes	—
365	C₄	C₂×C₄×D₄×C₂₃	1	2	yes	—
366	C₄	C₂³×D₄×C₂₃	1	1	yes	characteristic
367	C₄	C₂²×#41×C₂₃	1	1	yes	characteristic
368	C₂	—	2	4	no	—
369	C₂	—	2	2	no	—
370	C₂	—	4	8	no	—
371	C₂	C₂²×C₄×D₄×C₂₃	1	1	yes	characteristic
372	C₂	C₂₃×#3573	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₂₃	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₂₃
Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
socle	C₂²×C₂₃	C₂⁴×C₄
prime radical	C₂₃×#3449	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₂₃×#568	C₂	semidirect
3. C₂₃×#2933	C₂	semidirect
4. C₂₃×#2932	C₂	semidirect
5. C₂₃×#2931	C₂	semidirect
6. C₂₃×#2905	C₂	semidirect
7. C₂×C₂₃×#408	C₂	semidirect
8. C₂×C₂₃×#405	C₂	semidirect
12. C₂×C₂₃×#131	C₂²	semidirect
15. C₂²×M₁₆×C₂₃	C₂²	semidirect
24. C₂₃×#436	C₂²	semidirect
25. C₂₃×#435	C₂²	semidirect
26. C₈×D₄×C₂₃	C₂²	semidirect
27. C₂₃×#424	C₂²	semidirect
28. C₂₃×#423	C₂²	semidirect
30. C₂₃×#408	C₂²	semidirect
31. C₂₃×#408	C₂²	semidirect
32. C₂×C₂₃×C₂²⋊C₈	C₂²	semidirect
33. C₂₃×#405	C₂²	semidirect
34. C₂×C₂₃×#97	C₂²	semidirect
35. C₂×C₄×C₈×C₂₃	C₂²	semidirect
51. C₂×M₁₆×C₂₃	D₄	semidirect
132. #60143	C₂₃	direct (N × H)
167. C₂×#568	C₂×C₂₃	semidirect
169. #2933	C₂×C₂₃	semidirect
170. #2932	C₂×C₂₃	semidirect
171. #2931	C₂×C₂₃	semidirect
172. #2905	C₂×C₂₃	semidirect
173. C₂×#408	C₂×C₂₃	semidirect
174. C₂×#405	C₂×C₂₃	semidirect
193. C₂×#131	C₂²×C₂₃	semidirect
196. C₂²×M₁₆	C₂²×C₂₃	semidirect
205. #436	C₂²×C₂₃	semidirect
206. #435	C₂²×C₂₃	semidirect
207. C₈×D₄	C₂²×C₂₃	semidirect
208. #424	C₂²×C₂₃	semidirect
209. #423	C₂²×C₂₃	semidirect
211. #408	C₂²×C₂₃	semidirect
212. #408	C₂²×C₂₃	semidirect
213. C₂×C₂²⋊C₈	C₂²×C₂₃	semidirect
214. #405	C₂²×C₂₃	semidirect
215. C₂×#97	C₂²×C₂₃	semidirect
216. C₂×C₄×C₈	C₂²×C₂₃	semidirect
237. C₂×M₁₆	D₄×C₂₃	semidirect
268. C₂₃	#60143	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×#568	2
C₂₃×#3449	2
C₂₃×#2933	2
C₂₃×#2932	2
C₂₃×#2931	2
C₂₃×#2905	2
C₂×C₂₃×#408	2
C₂×C₂₃×#405	2
#60143	23

Subgroups — C23×#60143 #19207769

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#60143 #19207769