Subgroups — C₂₃×#17803 #19165429

Order 5888.

668 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	C₂₃×#2920	C₂	1	1	yes	maximal, characteristic
2	C₂×C₂₃×#431	C₂	1	1	yes	maximal, characteristic
3	C₂×C₂₃×#431	C₂	1	1	yes	maximal, characteristic
4	C₂₃×#1572	C₂	1	4	yes	maximal, complemented
5	C₂₃×#1571	C₂	1	2	yes	maximal, complemented
6	C₂₃×#1570	C₂	1	2	yes	maximal, complemented
7	C₂₃×#1564	C₂	1	4	yes	maximal, complemented
8	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
9	C₂₃×#432	—	2	1	no	—
10	C₂₃×#432	C₂²	1	2	yes	—
11	C₂₃×#431	—	2	1	no	—
12	C₂₃×#431	—	2	1	no	—
13	C₂₃×#431	—	2	1	no	—
14	C₂₃×#431	C₄	1	2	yes	—
15	C₂₃×#431	C₄	1	2	yes	—
16	C₂₃×#431	C₂²	1	1	yes	characteristic
17	C₂₃×#431	C₂²	1	1	yes	characteristic
18	C₂₃×#431	C₂²	1	2	yes	—
19	C₂₃×#431	C₂²	1	2	yes	—
20	C₂₃×#431	C₂²	1	2	yes	—
21	C₂₃×#431	C₂²	1	2	yes	—
22	C₂₃×#423	C₂²	1	2	yes	—
23	C₂×C₂₃×C₄⋊C₈	C₄	1	2	yes	—
24	C₂×C₂₃×C₄⋊C₈	C₂²	1	2	yes	—
25	C₂₃×#407	—	2	1	no	—
26	C₂×C₂₃×C₂²⋊C₈	—	2	1	no	—
27	C₂×C₂₃×C₂²⋊C₈	C₄	1	2	yes	—
28	C₄×M₁₆×C₂₃	—	2	1	no	—
29	C₂×C₄×C₈×C₂₃	—	2	1	no	—
30	C₂×C₄×C₈×C₂₃	C₂²	1	2	yes	—
31	C₂₃×#335	C₂²	1	8	yes	complemented
32	C₂₃×#334	C₂²	1	8	yes	complemented
33	C₂³×C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
34	C₂³×C₄×C₂₃	D₄	1	1	yes	characteristic
35	C₂³×C₄×C₂₃	Q₈	1	1	yes	characteristic
36	C₂×M₁₆×C₂₃	—	2	2	no	—
37	C₂²×C₈×C₂₃	—	2	2	no	—
38	C₂²×C₈×C₂₃	C₂×C₄	1	4	yes	—
39	C₂×C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
40	C₂×C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
41	C₂×C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
42	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
43	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
44	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
45	C₂×C₄²×C₂₃	Q₈	1	1	yes	characteristic
46	C₂×C₄²×C₂₃	Q₈	1	1	yes	characteristic
47	C₂×C₄²×C₂₃	Q₈	1	1	yes	characteristic
48	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
49	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
50	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
51	C₂₃×C₄⋊C₈	—	2	2	no	—
52	C₂₃×C₄⋊C₈	—	2	2	no	—
53	C₂₃×C₄⋊C₈	C₂×C₄	1	2	yes	—
54	C₂₃×C₄⋊C₈	C₂×C₄	1	2	yes	—
55	C₂₃×C₄⋊C₈	C₂×C₄	1	4	yes	—
56	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
57	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
58	C₂₃×C₂²⋊C₈	—	2	2	no	—
59	C₂₃×C₂²⋊C₈	—	2	2	no	—
60	C₂₃×C₂²⋊C₈	—	2	2	no	—
61	C₂₃×C₂²⋊C₈	—	2	2	no	—
62	C₂₃×C₂²⋊C₈	C₂×C₄	1	2	yes	—
63	C₂₃×C₂²⋊C₈	C₂×C₄	1	2	yes	—
64	C₂₃×C₂²⋊C₈	C₂×C₄	1	4	yes	—
65	C₂₃×#97	—	2	2	no	—
66	C₄×C₈×C₂₃	—	2	2	no	—
67	C₄×C₈×C₂₃	—	2	2	no	—
68	C₄×C₈×C₂₃	—	2	2	no	—
69	C₄×C₈×C₂₃	C₂×C₄	1	4	yes	—
70	C₄×C₈×C₂₃	C₂³	1	2	yes	—
71	C₄×C₈×C₂₃	C₂³	1	2	yes	—
72	C₂⁴×C₂₃	C₄⋊C₄	1	1	yes	characteristic
73	C₂²×C₄×C₂₃	—	2	4	no	—
74	C₂²×C₄×C₂₃	—	2	4	no	—
75	C₂²×C₄×C₂₃	—	4	2	no	—
76	C₂²×C₄×C₂₃	C₄⋊C₄	1	1	yes	characteristic
77	C₂²×C₄×C₂₃	C₄⋊C₄	1	1	yes	characteristic
78	C₂²×C₄×C₂₃	C₄⋊C₄	1	1	yes	characteristic
79	C₂²×C₄×C₂₃	C₄⋊C₄	1	1	yes	characteristic
80	C₂²×C₄×C₂₃	C₄⋊C₄	1	1	yes	characteristic
81	C₂²×C₄×C₂₃	C₄⋊C₄	1	1	yes	characteristic
82	C₂²×C₄×C₂₃	C₄⋊C₄	1	1	yes	characteristic
83	C₂²×C₄×C₂₃	C₄⋊C₄	1	1	yes	characteristic
84	C₂²×C₄×C₂₃	C₄⋊C₄	1	1	yes	characteristic
85	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
86	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
87	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
88	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
89	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
91	C₂²×C₄×C₂₃	C₂×Q₈	1	1	yes	characteristic
92	C₂²×C₄×C₂₃	C₂×Q₈	1	1	yes	characteristic
93	C₂²×C₄×C₂₃	C₂×Q₈	1	1	yes	characteristic
94	M₁₆×C₂₃	—	4	4	no	—
95	C₂×C₈×C₂₃	—	2	8	no	—
96	C₂×C₈×C₂₃	—	2	4	no	—
97	C₂×C₈×C₂₃	—	2	4	no	—
98	C₂×C₈×C₂₃	—	4	4	no	—
99	C₂×C₈×C₂₃	C₂²×C₄	1	4	yes	—
100	C₂×C₈×C₂₃	C₂²×C₄	1	4	yes	—
101	C₄²×C₂₃	C₄⋊C₄	1	1	yes	characteristic
102	C₄²×C₂₃	C₄⋊C₄	1	1	yes	characteristic
103	C₄²×C₂₃	C₄⋊C₄	1	1	yes	characteristic
104	C₄²×C₂₃	C₄⋊C₄	1	1	yes	characteristic
105	C₄²×C₂₃	C₄⋊C₄	1	1	yes	characteristic
106	C₄²×C₂₃	C₄⋊C₄	1	1	yes	characteristic
107	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
108	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
109	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
110	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
111	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
112	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
113	C₄²×C₂₃	C₂×Q₈	1	1	yes	characteristic
114	C₄²×C₂₃	C₂×Q₈	1	1	yes	characteristic
115	C₄²×C₂₃	C₂×Q₈	1	1	yes	characteristic
116	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
117	#17803	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
118	C₂³×C₂₃	—	2	2	no	—
119	C₂³×C₂₃	—	2	2	no	—
120	C₂³×C₂₃	—	4	1	no	—
121	C₂³×C₂₃	C₂×C₄⋊C₄	1	1	yes	characteristic
122	C₂³×C₂₃	C₂×C₄⋊C₄	1	1	yes	characteristic
123	C₂³×C₂₃	C₂×C₄⋊C₄	1	1	yes	characteristic
124	C₂×C₄×C₂₃	—	2	2	no	—
125	C₂×C₄×C₂₃	—	2	2	no	—
126	C₂×C₄×C₂₃	—	2	2	no	—
127	C₂×C₄×C₂₃	—	2	2	no	—
128	C₂×C₄×C₂₃	—	2	2	no	—
129	C₂×C₄×C₂₃	—	2	2	no	—
130	C₂×C₄×C₂₃	—	2	2	no	—
131	C₂×C₄×C₂₃	—	2	2	no	—
132	C₂×C₄×C₂₃	—	2	2	no	—
133	C₂×C₄×C₂₃	—	2	2	no	—
134	C₂×C₄×C₂₃	—	2	2	no	—
135	C₂×C₄×C₂₃	—	2	2	no	—
136	C₂×C₄×C₂₃	—	2	2	no	—
137	C₂×C₄×C₂₃	—	4	1	no	—
138	C₂×C₄×C₂₃	—	4	1	no	—
139	C₂×C₄×C₂₃	—	4	1	no	—
140	C₂×C₄×C₂₃	C₂×C₄⋊C₄	1	1	yes	characteristic
141	C₂×C₄×C₂₃	C₂×C₄⋊C₄	1	1	yes	characteristic
142	C₂×C₄×C₂₃	C₂×C₄⋊C₄	1	1	yes	characteristic
143	C₂×C₄×C₂₃	C₂×C₄⋊C₄	1	1	yes	characteristic
144	C₂×C₄×C₂₃	C₂×C₄⋊C₄	1	1	yes	characteristic
145	C₂×C₄×C₂₃	C₂×C₄⋊C₄	1	1	yes	characteristic
146	C₂×C₄×C₂₃	C₂×C₄⋊C₄	1	1	yes	characteristic
147	C₂×C₄×C₂₃	C₂×C₄⋊C₄	1	1	yes	characteristic
148	C₂×C₄×C₂₃	C₂×C₄⋊C₄	1	1	yes	characteristic
149	C₂×C₄×C₂₃	#131	1	4	yes	—
150	C₂×C₄×C₂₃	#135	1	4	yes	—
151	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
152	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
153	C₂×C₄×C₂₃	C₂²×Q₈	1	1	yes	characteristic
154	C₈×C₂₃	—	2	4	no	—
155	C₈×C₂₃	—	2	4	no	—
156	C₈×C₂₃	—	4	4	no	—
157	C₈×C₂₃	—	4	4	no	—
158	#2920	C₂×C₂₃	1	1	yes	characteristic
159	C₂×#431	C₂×C₂₃	1	1	yes	characteristic
160	C₂×#431	C₂×C₂₃	1	1	yes	characteristic
161	#1572	C₂×C₂₃	1	4	yes	complemented
162	#1571	C₂×C₂₃	1	2	yes	complemented
163	#1570	C₂×C₂₃	1	2	yes	complemented
164	#1564	C₂×C₂₃	1	4	yes	complemented
165	C₂²×C₂₃	—	2	1	no	—
166	C₂²×C₂₃	—	2	1	no	—
167	C₂²×C₂₃	—	2	1	no	—
168	C₂²×C₂₃	—	2	1	no	—
169	C₂²×C₂₃	—	2	1	no	—
170	C₂²×C₂₃	—	2	1	no	—
171	C₂²×C₂₃	—	2	1	no	—
172	C₂²×C₂₃	—	4	4	no	—
173	C₂²×C₂₃	#424	1	2	yes	—
174	C₂²×C₂₃	#427	1	2	yes	—
175	C₂²×C₂₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
176	C₄×C₂₃	—	2	1	no	—
177	C₄×C₂₃	—	2	1	no	—
178	C₄×C₂₃	—	2	1	no	—
179	C₄×C₂₃	—	2	1	no	—
180	C₄×C₂₃	—	2	1	no	—
181	C₄×C₂₃	—	2	1	no	—
182	C₄×C₂₃	—	2	1	no	—
183	C₄×C₂₃	#424	1	2	yes	—
184	C₄×C₂₃	#427	1	2	yes	—
185	C₄×C₂₃	#430	1	2	yes	—
186	C₄×C₂₃	C₂×#131	1	2	yes	—
187	C₄×C₂₃	C₂×#135	1	2	yes	—
188	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
189	#432	—	2	1	no	—
190	#432	C₂²×C₂₃	1	2	yes	—
191	#431	—	2	1	no	—
192	#431	—	2	1	no	—
193	#431	—	2	1	no	—
194	#431	C₄×C₂₃	1	2	yes	—
195	#431	C₄×C₂₃	1	2	yes	—
196	#431	C₂²×C₂₃	1	2	yes	—
197	#431	C₂²×C₂₃	1	2	yes	—
198	#431	C₂²×C₂₃	1	2	yes	—
199	#431	C₂²×C₂₃	1	1	yes	characteristic
200	#431	C₂²×C₂₃	1	1	yes	characteristic
201	#431	C₂²×C₂₃	1	2	yes	—
202	#423	C₂²×C₂₃	1	2	yes	—
203	C₂×C₄⋊C₈	C₄×C₂₃	1	2	yes	—
204	C₂×C₄⋊C₈	C₂²×C₂₃	1	2	yes	—
205	#407	—	2	1	no	—
206	C₂×C₂²⋊C₈	—	2	1	no	—
207	C₂×C₂²⋊C₈	C₄×C₂₃	1	2	yes	—
208	C₄×M₁₆	—	2	1	no	—
209	C₂×C₄×C₈	—	2	1	no	—
210	C₂×C₄×C₈	C₂²×C₂₃	1	2	yes	—
211	#335	C₂²×C₂₃	1	8	yes	complemented
212	#334	C₂²×C₂₃	1	8	yes	complemented
213	C₂×C₂₃	—	2	2	no	—
214	C₂×C₂₃	—	2	2	no	—
215	C₂×C₂₃	—	4	1	no	—
216	C₂×C₂₃	C₂×#424	1	1	yes	characteristic
217	C₂×C₂₃	C₂×#427	1	1	yes	characteristic
218	C₂×C₂₃	C₂×#430	1	1	yes	characteristic
219	C₂³×C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
220	C₂³×C₄	D₄×C₂₃	1	1	yes	characteristic
221	C₂³×C₄	Q₈×C₂₃	1	1	yes	characteristic
222	C₂×M₁₆	—	2	2	no	—
223	C₂²×C₈	—	2	2	no	—
224	C₂²×C₈	C₂×C₄×C₂₃	1	4	yes	—
225	C₂×C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic
226	C₂×C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic
227	C₂×C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic
228	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
229	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
230	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
231	C₂×C₄²	Q₈×C₂₃	1	1	yes	characteristic
232	C₂×C₄²	Q₈×C₂₃	1	1	yes	characteristic
233	C₂×C₄²	Q₈×C₂₃	1	1	yes	characteristic
234	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
235	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
236	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
237	C₄⋊C₈	—	2	2	no	—
238	C₄⋊C₈	—	2	2	no	—
239	C₄⋊C₈	C₂×C₄×C₂₃	1	2	yes	—
240	C₄⋊C₈	C₂×C₄×C₂₃	1	2	yes	—
241	C₄⋊C₈	C₂×C₄×C₂₃	1	4	yes	—
242	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
243	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
244	C₂²⋊C₈	—	2	2	no	—
245	C₂²⋊C₈	—	2	2	no	—
246	C₂²⋊C₈	—	2	2	no	—
247	C₂²⋊C₈	—	2	2	no	—
248	C₂²⋊C₈	C₂×C₄×C₂₃	1	2	yes	—
249	C₂²⋊C₈	C₂×C₄×C₂₃	1	2	yes	—
250	C₂²⋊C₈	C₂×C₄×C₂₃	1	4	yes	—
251	#97	—	2	2	no	—
252	C₄×C₈	—	2	2	no	—
253	C₄×C₈	—	2	2	no	—
254	C₄×C₈	—	2	2	no	—
255	C₄×C₈	C₂×C₄×C₂₃	1	4	yes	—
256	C₄×C₈	C₂³×C₂₃	1	2	yes	—
257	C₄×C₈	C₂³×C₂₃	1	2	yes	—
258	C₂₃	#17803	1	1	yes	characteristic, direct product factor, Sylow
259	C₂⁴	C₄⋊C₄×C₂₃	1	1	yes	characteristic
260	C₂²×C₄	—	2	4	no	—
261	C₂²×C₄	—	2	4	no	—
262	C₂²×C₄	—	4	2	no	—
263	C₂²×C₄	C₄⋊C₄×C₂₃	1	1	yes	characteristic
264	C₂²×C₄	C₄⋊C₄×C₂₃	1	1	yes	characteristic
265	C₂²×C₄	C₄⋊C₄×C₂₃	1	1	yes	characteristic
266	C₂²×C₄	C₄⋊C₄×C₂₃	1	1	yes	characteristic
267	C₂²×C₄	C₄⋊C₄×C₂₃	1	1	yes	characteristic
268	C₂²×C₄	C₄⋊C₄×C₂₃	1	1	yes	characteristic
269	C₂²×C₄	C₄⋊C₄×C₂₃	1	1	yes	characteristic
270	C₂²×C₄	C₄⋊C₄×C₂₃	1	1	yes	characteristic
271	C₂²×C₄	C₄⋊C₄×C₂₃	1	1	yes	characteristic
272	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
273	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
274	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
275	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
276	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
277	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
278	C₂²×C₄	C₂×Q₈×C₂₃	1	1	yes	characteristic
279	C₂²×C₄	C₂×Q₈×C₂₃	1	1	yes	characteristic
280	C₂²×C₄	C₂×Q₈×C₂₃	1	1	yes	characteristic
281	M₁₆	—	4	4	no	—
282	C₂×C₈	—	2	8	no	—
283	C₂×C₈	—	2	4	no	—
284	C₂×C₈	—	2	4	no	—
285	C₂×C₈	—	4	4	no	—
286	C₂×C₈	C₂²×C₄×C₂₃	1	4	yes	—
287	C₂×C₈	C₂²×C₄×C₂₃	1	4	yes	—
288	C₄²	C₄⋊C₄×C₂₃	1	1	yes	characteristic
289	C₄²	C₄⋊C₄×C₂₃	1	1	yes	characteristic
290	C₄²	C₄⋊C₄×C₂₃	1	1	yes	characteristic
291	C₄²	C₄⋊C₄×C₂₃	1	1	yes	characteristic
292	C₄²	C₄⋊C₄×C₂₃	1	1	yes	characteristic
293	C₄²	C₄⋊C₄×C₂₃	1	1	yes	characteristic
294	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
295	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
296	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
297	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
298	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
299	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
300	C₄²	C₂×Q₈×C₂₃	1	1	yes	characteristic
301	C₄²	C₂×Q₈×C₂₃	1	1	yes	characteristic
302	C₄²	C₂×Q₈×C₂₃	1	1	yes	characteristic
303	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
304	C₂³	—	2	2	no	—
305	C₂³	—	2	2	no	—
306	C₂³	—	4	1	no	—
307	C₂³	C₂×C₄⋊C₄×C₂₃	1	1	yes	characteristic
308	C₂³	C₂×C₄⋊C₄×C₂₃	1	1	yes	characteristic
309	C₂³	C₂×C₄⋊C₄×C₂₃	1	1	yes	characteristic
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	2	2	no	—
312	C₂×C₄	—	2	2	no	—
313	C₂×C₄	—	2	2	no	—
314	C₂×C₄	—	2	2	no	—
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	2	2	no	—
318	C₂×C₄	—	2	2	no	—
319	C₂×C₄	—	2	2	no	—
320	C₂×C₄	—	2	2	no	—
321	C₂×C₄	—	2	2	no	—
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	—	4	1	no	—
324	C₂×C₄	—	4	1	no	—
325	C₂×C₄	—	4	1	no	—
326	C₂×C₄	C₂×C₄⋊C₄×C₂₃	1	1	yes	characteristic
327	C₂×C₄	C₂×C₄⋊C₄×C₂₃	1	1	yes	characteristic
328	C₂×C₄	C₂×C₄⋊C₄×C₂₃	1	1	yes	characteristic
329	C₂×C₄	C₂×C₄⋊C₄×C₂₃	1	1	yes	characteristic
330	C₂×C₄	C₂×C₄⋊C₄×C₂₃	1	1	yes	characteristic
331	C₂×C₄	C₂×C₄⋊C₄×C₂₃	1	1	yes	characteristic
332	C₂×C₄	C₂×C₄⋊C₄×C₂₃	1	1	yes	characteristic
333	C₂×C₄	C₂×C₄⋊C₄×C₂₃	1	1	yes	characteristic
334	C₂×C₄	C₂×C₄⋊C₄×C₂₃	1	1	yes	characteristic
335	C₂×C₄	C₂₃×#131	1	4	yes	—
336	C₂×C₄	C₂₃×#135	1	4	yes	—
337	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
338	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
339	C₂×C₄	C₂²×Q₈×C₂₃	1	1	yes	characteristic
340	C₈	—	2	4	no	—
341	C₈	—	2	4	no	—
342	C₈	—	4	4	no	—
343	C₈	—	4	4	no	—
344	C₂²	—	2	1	no	—
345	C₂²	—	2	1	no	—
346	C₂²	—	2	1	no	—
347	C₂²	—	2	1	no	—
348	C₂²	—	2	1	no	—
349	C₂²	—	2	1	no	—
350	C₂²	—	2	1	no	—
351	C₂²	—	4	4	no	—
352	C₂²	C₂₃×#424	1	2	yes	—
353	C₂²	C₂₃×#427	1	2	yes	—
354	C₂²	C₂²×C₄⋊C₄×C₂₃	1	1	yes	characteristic
355	C₄	—	2	1	no	—
356	C₄	—	2	1	no	—
357	C₄	—	2	1	no	—
358	C₄	—	2	1	no	—
359	C₄	—	2	1	no	—
360	C₄	—	2	1	no	—
361	C₄	—	2	1	no	—
362	C₄	C₂₃×#424	1	2	yes	—
363	C₄	C₂₃×#427	1	2	yes	—
364	C₄	C₂₃×#430	1	2	yes	—
365	C₄	C₂×C₂₃×#131	1	2	yes	—
366	C₄	C₂×C₂₃×#135	1	2	yes	—
367	C₂	—	2	2	no	—
368	C₂	—	2	2	no	—
369	C₂	—	4	1	no	—
370	C₂	C₂×C₂₃×#424	1	1	yes	characteristic
371	C₂	C₂×C₂₃×#427	1	1	yes	characteristic
372	C₂	C₂×C₂₃×#430	1	1	yes	characteristic

	subgroup	G/H
center	C₄²×C₂₃	C₂×D₄
commutator	C₂×C₄	C₂³×C₄×C₂₃
Frattini, cosocle	C₄²	C₂⁴×C₂₃
socle	C₂²×C₂₃	C₂²×C₄⋊C₄
prime radical	C₂⁴×C₂₃	C₄⋊C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄²×C₂₃ ◁ C₂²×C₄²×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₂₃×#1572	C₂	semidirect
5. C₂₃×#1571	C₂	semidirect
6. C₂₃×#1570	C₂	semidirect
7. C₂₃×#1564	C₂	semidirect
31. C₂₃×#335	C₂²	semidirect
32. C₂₃×#334	C₂²	semidirect
117. #17803	C₂₃	direct (N × H)
161. #1572	C₂×C₂₃	semidirect
162. #1571	C₂×C₂₃	semidirect
163. #1570	C₂×C₂₃	semidirect
164. #1564	C₂×C₂₃	semidirect
211. #335	C₂²×C₂₃	semidirect
212. #334	C₂²×C₂₃	semidirect
258. C₂₃	#17803	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×#2920	2
C₂×C₂₃×#431	2
C₂₃×#1572	2
C₂₃×#1571	2
C₂₃×#1570	2
C₂₃×#1564	2
#17803	23

Subgroups — C23×#17803 #19165429

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#17803 #19165429