Subgroups — C₂₃×#22736 #19170362

Order 5888.

812 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#446	C₂	1	2	yes	maximal
2	C₄²×Q₈×C₂₃	C₂	1	1	yes	maximal, characteristic
3	C₂₃×#1940	C₂	1	4	yes	maximal
4	C₂₃×#1939	C₂	1	2	yes	maximal
5	C₂₃×#1831	C₂	1	2	yes	maximal
6	C₂₃×#1831	C₂	1	1	yes	maximal, characteristic
7	C₂₃×#1767	C₂	1	2	yes	maximal
8	C₄×C₂₃×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
9	C₂×C₄×Q₈×C₂₃	C₄	1	1	yes	characteristic
10	C₂×C₄×Q₈×C₂₃	C₄	1	1	yes	characteristic
11	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
12	C₂₃×#446	—	2	8	no	—
13	C₂×C₂₃×C₄⋊C₈	C₂²	1	2	yes	—
14	C₂×C₂₃×C₄⋊C₈	C₂²	1	4	yes	—
15	C₂×C₂₃×C₄⋊C₈	C₂²	1	4	yes	—
16	C₂×C₂₃×C₄⋊C₈	C₂²	1	2	yes	—
17	C₂×C₂₃×#97	C₂²	1	4	yes	—
18	C₂×C₄×C₈×C₂₃	C₂²	1	2	yes	—
19	C₄×C₄⋊C₄×C₂₃	C₄	1	1	yes	characteristic
20	C₄×C₄⋊C₄×C₂₃	C₄	1	2	yes	—
21	C₄×C₄⋊C₄×C₂₃	C₄	1	2	yes	—
22	C₄×C₄⋊C₄×C₂₃	C₄	1	1	yes	characteristic
23	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
24	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
25	C₄³×C₂₃	C₂²	1	1	yes	characteristic
26	C₄³×C₂₃	C₂²	1	2	yes	—
27	C₂₃×#336	C₂²	1	4	yes	—
28	C₂₃×#336	C₂²	1	2	yes	—
29	C₂₃×#336	C₂²	1	1	yes	characteristic
30	C₂₃×#336	C₂²	1	1	yes	characteristic
31	C₂₃×#336	C₂²	1	2	yes	—
32	C₂²×Q₈×C₂₃	C₂×C₄	1	1	yes	characteristic
33	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
34	C₂²×C₈×C₂₃	C₂³	1	4	yes	—
35	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
36	C₄×Q₈×C₂₃	—	2	4	no	—
37	C₄×Q₈×C₂₃	—	2	4	no	—
38	C₄×Q₈×C₂₃	D₄	1	4	yes	—
39	C₄×Q₈×C₂₃	Q₈	1	4	yes	—
40	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
41	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
42	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
43	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
44	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
45	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
46	C₂×C₄²×C₂₃	C₂×C₄	1	2	yes	—
47	C₂×C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
48	C₂×C₄²×C₂₃	C₂×C₄	1	2	yes	—
49	C₂×C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
50	C₂×C₄²×C₂₃	C₂×C₄	1	2	yes	—
51	C₂×C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
52	C₂×C₄²×C₂₃	C₂×C₄	1	2	yes	—
53	C₂×C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
54	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
55	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
56	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
57	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
58	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
59	C₂₃×C₄⋊C₈	—	2	8	no	—
60	C₂₃×C₄⋊C₈	—	2	4	no	—
61	C₂₃×C₄⋊C₈	—	2	4	no	—
62	C₂₃×C₄⋊C₈	—	2	8	no	—
63	C₂₃×#97	—	2	8	no	—
64	C₄×C₈×C₂₃	—	2	4	no	—
65	C₂₃×#95	C₂×C₄	1	2	yes	—
66	C₂₃×#95	C₂×C₄	1	2	yes	—
67	C₂₃×#95	C₂×C₄	1	2	yes	—
68	C₂×Q₈×C₂₃	—	2	2	no	—
69	C₂×Q₈×C₂₃	—	2	2	no	—
70	C₂×Q₈×C₂₃	C₄⋊C₄	1	4	yes	—
71	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
72	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
73	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
74	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
75	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
76	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
77	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
78	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
79	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
80	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
81	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
82	C₂×C₈×C₂₃	—	2	2	no	—
83	C₂×C₈×C₂₃	—	2	2	no	—
84	C₂×C₈×C₂₃	—	2	2	no	—
85	C₂×C₈×C₂₃	—	2	4	no	—
86	C₂×C₈×C₂₃	—	2	2	no	—
87	C₂×C₈×C₂₃	—	2	4	no	—
88	C₂×C₈×C₂₃	—	2	2	no	—
89	C₂×C₈×C₂₃	—	2	4	no	—
90	C₂×C₈×C₂₃	#41	1	4	yes	—
91	C₄⋊C₄×C₂₃	—	2	4	no	—
92	C₄⋊C₄×C₂₃	—	2	4	no	—
93	C₄⋊C₄×C₂₃	—	2	2	no	—
94	C₄⋊C₄×C₂₃	C₄⋊C₄	1	8	yes	—
95	C₄⋊C₄×C₂₃	C₄⋊C₄	1	4	yes	—
96	C₄⋊C₄×C₂₃	M₁₆	1	4	yes	—
97	C₄²×C₂₃	—	2	4	no	—
98	C₄²×C₂₃	—	2	2	no	—
99	C₄²×C₂₃	—	2	4	no	—
100	C₄²×C₂₃	—	2	2	no	—
101	C₄²×C₂₃	—	2	4	no	—
102	C₄²×C₂₃	—	2	2	no	—
103	C₄²×C₂₃	—	2	4	no	—
104	C₄²×C₂₃	—	2	2	no	—
105	C₄²×C₂₃	—	4	2	no	—
106	C₄²×C₂₃	—	4	1	no	—
107	C₄²×C₂₃	M₁₆	1	4	yes	—
108	C₄²×C₂₃	C₂×D₄	1	2	yes	—
109	C₄²×C₂₃	C₂×D₄	1	4	yes	—
110	C₄²×C₂₃	C₂×Q₈	1	4	yes	—
111	C₄²×C₂₃	C₂×Q₈	1	2	yes	—
112	#22736	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
113	C₂³×C₂₃	C₂³×C₄	1	1	yes	characteristic
114	Q₈×C₂₃	—	2	8	no	—
115	C₂×C₄×C₂₃	—	2	1	no	—
116	C₂×C₄×C₂₃	—	2	2	no	—
117	C₂×C₄×C₂₃	—	2	1	no	—
118	C₂×C₄×C₂₃	—	2	1	no	—
119	C₂×C₄×C₂₃	—	2	1	no	—
120	C₂×C₄×C₂₃	—	2	2	no	—
121	C₂×C₄×C₂₃	—	2	2	no	—
122	C₂×C₄×C₂₃	—	2	1	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	1	no	—
128	C₂×C₄×C₂₃	—	2	2	no	—
129	C₂×C₄×C₂₃	—	2	2	no	—
130	C₂×C₄×C₂₃	—	2	1	no	—
131	C₂×C₄×C₂₃	—	2	2	no	—
132	C₂×C₄×C₂₃	—	2	1	no	—
133	C₂×C₄×C₂₃	—	2	2	no	—
134	C₂×C₄×C₂₃	—	2	1	no	—
135	C₂×C₄×C₂₃	C₂×C₄⋊C₄	1	2	yes	—
136	C₂×C₄×C₂₃	C₂×C₄⋊C₄	1	4	yes	—
137	C₂×C₄×C₂₃	C₂×C₄⋊C₄	1	4	yes	—
138	C₂×C₄×C₂₃	C₂×C₄⋊C₄	1	2	yes	—
139	C₂×C₄×C₂₃	C₂×M₁₆	1	2	yes	—
140	C₂×C₄×C₂₃	C₂×M₁₆	1	4	yes	—
141	C₂×C₄×C₂₃	C₂×M₁₆	1	2	yes	—
142	C₂×C₄×C₂₃	C₂×M₁₆	1	2	yes	—
143	C₂×C₄×C₂₃	C₂×M₁₆	1	2	yes	—
144	C₂×C₄×C₂₃	#131	1	2	yes	—
145	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
146	C₂×C₄×C₂₃	C₂²×Q₈	1	1	yes	characteristic
147	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
148	C₂×C₄×C₂₃	2₋¹⁺⁴	1	2	yes	—
149	C₈×C₂₃	—	2	4	no	—
150	C₈×C₂₃	—	4	2	no	—
151	C₈×C₂₃	—	4	4	no	—
152	C₂×#446	C₂×C₂₃	1	2	yes	—
153	C₄²×Q₈	C₂×C₂₃	1	1	yes	characteristic
154	#1940	C₂×C₂₃	1	4	yes	—
155	#1939	C₂×C₂₃	1	2	yes	—
156	#1831	C₂×C₂₃	1	2	yes	—
157	#1831	C₂×C₂₃	1	1	yes	characteristic
158	#1767	C₂×C₂₃	1	2	yes	—
159	C₄×C₄⋊C₈	C₂×C₂₃	1	1	yes	characteristic
160	C₂²×C₂₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
161	C₂²×C₂₃	C₄×#41	1	1	yes	characteristic
162	C₂²×C₂₃	#519	1	1	yes	characteristic
163	C₂²×C₂₃	C₂²×M₁₆	1	1	yes	characteristic
164	C₂²×C₂₃	C₂²×M₁₆	1	1	yes	characteristic
165	C₂²×C₂₃	C₂×#131	1	1	yes	characteristic
166	C₂²×C₂₃	#568	1	1	yes	characteristic
167	C₄×C₂₃	—	2	4	no	—
168	C₄×C₂₃	—	2	2	no	—
169	C₄×C₂₃	—	2	4	no	—
170	C₄×C₂₃	—	2	2	no	—
171	C₄×C₂₃	—	2	4	no	—
172	C₄×C₂₃	—	2	2	no	—
173	C₄×C₂₃	—	2	2	no	—
174	C₄×C₂₃	—	4	2	no	—
175	C₄×C₂₃	—	4	1	no	—
176	C₄×C₂₃	#423	1	4	yes	—
177	C₄×C₂₃	#548	1	2	yes	—
178	C₄×C₂₃	#557	1	2	yes	—
179	C₂×C₄×Q₈	C₄×C₂₃	1	1	yes	characteristic
180	C₂×C₄×Q₈	C₄×C₂₃	1	1	yes	characteristic
181	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
182	#446	—	2	8	no	—
183	C₂×C₄⋊C₈	C₂²×C₂₃	1	2	yes	—
184	C₂×C₄⋊C₈	C₂²×C₂₃	1	4	yes	—
185	C₂×C₄⋊C₈	C₂²×C₂₃	1	4	yes	—
186	C₂×C₄⋊C₈	C₂²×C₂₃	1	2	yes	—
187	C₂×#97	C₂²×C₂₃	1	4	yes	—
188	C₂×C₄×C₈	C₂²×C₂₃	1	2	yes	—
189	C₄×C₄⋊C₄	C₄×C₂₃	1	1	yes	characteristic
190	C₄×C₄⋊C₄	C₄×C₂₃	1	2	yes	—
191	C₄×C₄⋊C₄	C₄×C₂₃	1	2	yes	—
192	C₄×C₄⋊C₄	C₄×C₂₃	1	1	yes	characteristic
193	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
194	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
195	C₄³	C₂²×C₂₃	1	1	yes	characteristic
196	C₄³	C₂²×C₂₃	1	2	yes	—
197	#336	C₂²×C₂₃	1	1	yes	characteristic
198	#336	C₂²×C₂₃	1	2	yes	—
199	#336	C₂²×C₂₃	1	4	yes	—
200	#336	C₂²×C₂₃	1	2	yes	—
201	#336	C₂²×C₂₃	1	1	yes	characteristic
202	C₂×C₂₃	#2351	1	1	yes	characteristic
203	C₂×C₂₃	C₂×#423	1	1	yes	characteristic
204	C₂×C₂₃	#2906	1	1	yes	characteristic
205	C₂×C₂₃	#2965	1	1	yes	characteristic
206	C₂×C₂₃	#2970	1	1	yes	characteristic
207	C₂×C₂₃	#2983	1	1	yes	characteristic
208	C₂×C₂₃	#2984	1	1	yes	characteristic
209	C₂²×Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
210	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
211	C₂²×C₈	C₂³×C₂₃	1	4	yes	—
212	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
213	C₄×Q₈	—	2	4	no	—
214	C₄×Q₈	—	2	4	no	—
215	C₄×Q₈	D₄×C₂₃	1	4	yes	—
216	C₄×Q₈	Q₈×C₂₃	1	4	yes	—
217	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
218	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
219	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
220	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
221	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
222	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
223	C₂×C₄²	C₂×C₄×C₂₃	1	2	yes	—
224	C₂×C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic
225	C₂×C₄²	C₂×C₄×C₂₃	1	2	yes	—
226	C₂×C₄²	C₂×C₄×C₂₃	1	2	yes	—
227	C₂×C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic
228	C₂×C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic
229	C₂×C₄²	C₂×C₄×C₂₃	1	2	yes	—
230	C₂×C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic
231	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
232	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
233	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
234	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
235	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
236	C₄⋊C₈	—	2	8	no	—
237	C₄⋊C₈	—	2	4	no	—
238	C₄⋊C₈	—	2	4	no	—
239	C₄⋊C₈	—	2	8	no	—
240	#97	—	2	8	no	—
241	C₄×C₈	—	2	4	no	—
242	#95	C₂×C₄×C₂₃	1	2	yes	—
243	#95	C₂×C₄×C₂₃	1	2	yes	—
244	#95	C₂×C₄×C₂₃	1	2	yes	—
245	C₂₃	#22736	1	1	yes	characteristic, direct product factor, Sylow
246	C₂×Q₈	—	2	2	no	—
247	C₂×Q₈	—	2	2	no	—
248	C₂×Q₈	C₄⋊C₄×C₂₃	1	4	yes	—
249	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
250	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
251	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
252	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
253	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
254	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
255	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
256	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
257	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
258	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
259	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
260	C₂×C₈	—	2	2	no	—
261	C₂×C₈	—	2	2	no	—
262	C₂×C₈	—	2	2	no	—
263	C₂×C₈	—	2	4	no	—
264	C₂×C₈	—	2	2	no	—
265	C₂×C₈	—	2	4	no	—
266	C₂×C₈	—	2	2	no	—
267	C₂×C₈	—	2	4	no	—
268	C₂×C₈	#41×C₂₃	1	4	yes	—
269	C₄⋊C₄	—	2	4	no	—
270	C₄⋊C₄	—	2	4	no	—
271	C₄⋊C₄	—	2	2	no	—
272	C₄⋊C₄	C₄⋊C₄×C₂₃	1	8	yes	—
273	C₄⋊C₄	C₄⋊C₄×C₂₃	1	4	yes	—
274	C₄⋊C₄	M₁₆×C₂₃	1	4	yes	—
275	C₄²	—	2	4	no	—
276	C₄²	—	2	2	no	—
277	C₄²	—	2	4	no	—
278	C₄²	—	2	2	no	—
279	C₄²	—	2	4	no	—
280	C₄²	—	2	2	no	—
281	C₄²	—	2	4	no	—
282	C₄²	—	2	2	no	—
283	C₄²	—	4	2	no	—
284	C₄²	—	4	1	no	—
285	C₄²	M₁₆×C₂₃	1	4	yes	—
286	C₄²	C₂×D₄×C₂₃	1	2	yes	—
287	C₄²	C₂×D₄×C₂₃	1	4	yes	—
288	C₄²	C₂×Q₈×C₂₃	1	4	yes	—
289	C₄²	C₂×Q₈×C₂₃	1	2	yes	—
290	C₂³	C₂³×C₄×C₂₃	1	1	yes	characteristic
291	Q₈	—	2	8	no	—
292	C₂×C₄	—	2	1	no	—
293	C₂×C₄	—	2	2	no	—
294	C₂×C₄	—	2	2	no	—
295	C₂×C₄	—	2	1	no	—
296	C₂×C₄	—	2	1	no	—
297	C₂×C₄	—	2	2	no	—
298	C₂×C₄	—	2	1	no	—
299	C₂×C₄	—	2	2	no	—
300	C₂×C₄	—	2	2	no	—
301	C₂×C₄	—	2	1	no	—
302	C₂×C₄	—	2	1	no	—
303	C₂×C₄	—	2	2	no	—
304	C₂×C₄	—	2	1	no	—
305	C₂×C₄	—	2	1	no	—
306	C₂×C₄	—	2	2	no	—
307	C₂×C₄	—	2	1	no	—
308	C₂×C₄	—	2	2	no	—
309	C₂×C₄	—	2	1	no	—
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	2	1	no	—
312	C₂×C₄	C₂×C₄⋊C₄×C₂₃	1	2	yes	—
313	C₂×C₄	C₂×C₄⋊C₄×C₂₃	1	4	yes	—
314	C₂×C₄	C₂×C₄⋊C₄×C₂₃	1	4	yes	—
315	C₂×C₄	C₂×C₄⋊C₄×C₂₃	1	2	yes	—
316	C₂×C₄	C₂×M₁₆×C₂₃	1	2	yes	—
317	C₂×C₄	C₂×M₁₆×C₂₃	1	4	yes	—
318	C₂×C₄	C₂×M₁₆×C₂₃	1	2	yes	—
319	C₂×C₄	C₂×M₁₆×C₂₃	1	2	yes	—
320	C₂×C₄	C₂×M₁₆×C₂₃	1	2	yes	—
321	C₂×C₄	C₂₃×#131	1	2	yes	—
322	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
323	C₂×C₄	C₂²×Q₈×C₂₃	1	1	yes	characteristic
324	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
325	C₂×C₄	C₂₃×2₋¹⁺⁴	1	2	yes	—
326	C₈	—	2	4	no	—
327	C₈	—	4	2	no	—
328	C₈	—	4	4	no	—
329	C₂²	C₂²×C₄⋊C₄×C₂₃	1	1	yes	characteristic
330	C₂²	C₄×#41×C₂₃	1	1	yes	characteristic
331	C₂²	C₂₃×#519	1	1	yes	characteristic
332	C₂²	C₂²×M₁₆×C₂₃	1	1	yes	characteristic
333	C₂²	C₂²×M₁₆×C₂₃	1	1	yes	characteristic
334	C₂²	C₂×C₂₃×#131	1	1	yes	characteristic
335	C₂²	C₂₃×#568	1	1	yes	characteristic
336	C₄	—	2	2	no	—
337	C₄	—	2	4	no	—
338	C₄	—	2	2	no	—
339	C₄	—	2	2	no	—
340	C₄	—	2	4	no	—
341	C₄	—	2	2	no	—
342	C₄	—	2	4	no	—
343	C₄	—	4	2	no	—
344	C₄	—	4	1	no	—
345	C₄	C₂₃×#423	1	4	yes	—
346	C₄	C₂₃×#548	1	2	yes	—
347	C₄	C₂₃×#557	1	2	yes	—
348	C₂	C₂₃×#2351	1	1	yes	characteristic
349	C₂	C₂×C₂₃×#423	1	1	yes	characteristic
350	C₂	C₂₃×#2906	1	1	yes	characteristic
351	C₂	C₂₃×#2965	1	1	yes	characteristic
352	C₂	C₂₃×#2970	1	1	yes	characteristic
353	C₂	C₂₃×#2983	1	1	yes	characteristic
354	C₂	C₂₃×#2984	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
112. #22736	C₂₃	direct (N × H)
245. C₂₃	#22736	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×#446	2
C₄²×Q₈×C₂₃	2
C₂₃×#1940	2
C₂₃×#1939	2
C₂₃×#1831	2
C₂₃×#1767	2
C₄×C₂₃×C₄⋊C₈	2
#22736	23

Subgroups — C23×#22736 #19170362

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#22736 #19170362