Subgroups — C₂₃×#8097 #19155723

Order 5888.

700 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×#2920	C₂	1	1	yes	maximal, characteristic
2	C₂×C₂₃×#423	C₂	1	1	yes	maximal, characteristic
3	C₄×C₂₃×#117	C₂	1	1	yes	maximal, characteristic
4	C₂₃×#1303	C₂	1	4	yes	maximal, complemented
5	C₂²×M₁₆×C₂₃	—	2	1	no	—
6	C₂×C₂₃×#117	—	2	1	no	—
7	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
8	C₂₃×#432	—	2	1	no	—
9	C₂₃×#432	C₄	1	2	yes	complemented
10	C₂₃×#431	—	2	1	no	—
11	C₂₃×#431	C₂²	1	2	yes	—
12	C₂₃×#423	—	2	1	no	—
13	C₂₃×#423	—	2	1	no	—
14	C₂₃×#423	C₄	1	2	yes	complemented
15	C₂₃×#423	C₄	1	2	yes	complemented
16	C₂₃×#423	C₂²	1	2	yes	—
17	C₂×C₂₃×C₄⋊C₈	—	2	1	no	—
18	C₂×C₂₃×C₄⋊C₈	C₄	1	2	yes	complemented
19	C₂₃×#407	—	2	1	no	—
20	C₄×M₁₆×C₂₃	—	2	1	no	—
21	C₄×C₄⋊C₄×C₂₃	—	2	1	no	—
22	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
23	C₄×C₂²⋊C₄×C₂₃	—	2	1	no	—
24	C₄×C₂²⋊C₄×C₂₃	C₄	1	2	yes	—
25	C₂₃×#376	C₄	1	2	yes	—
26	C₄³×C₂₃	—	2	1	no	—
27	C₂³×C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
28	C₂³×C₄×C₂₃	D₄	1	1	yes	characteristic
29	C₂³×C₄×C₂₃	D₄	1	1	yes	characteristic
30	C₂×M₁₆×C₂₃	—	2	2	no	—
31	C₂×M₁₆×C₂₃	—	2	2	no	—
32	C₂×M₁₆×C₂₃	—	2	2	no	—
33	C₂×M₁₆×C₂₃	—	4	4	no	—
34	C₂²×C₈×C₂₃	—	2	2	no	—
35	C₂₃×#117	—	2	8	no	—
36	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
37	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
38	C₂×C₄²×C₂₃	—	2	2	no	—
39	C₂×C₄²×C₂₃	—	2	2	no	—
40	C₂×C₄²×C₂₃	—	2	2	no	—
41	C₂×C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
42	C₂×C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
43	C₂×C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
44	C₂×C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
45	C₂×C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
46	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
47	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
48	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
49	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
50	C₂×C₄²×C₂₃	Q₈	1	1	yes	characteristic
51	C₂×C₄²×C₂₃	Q₈	1	1	yes	characteristic
52	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
53	C₂₃×C₄⋊C₈	—	2	2	no	—
54	C₂₃×C₄⋊C₈	—	2	2	no	—
55	C₂₃×C₄⋊C₈	—	2	2	no	—
56	C₂₃×C₄⋊C₈	—	2	2	no	—
57	C₂₃×C₄⋊C₈	C₂×C₄	1	4	yes	—
58	C₂₃×C₄⋊C₈	C₂×C₄	1	4	yes	—
59	C₂₃×C₂²⋊C₈	—	2	2	no	—
60	C₂₃×C₂²⋊C₈	—	2	2	no	—
61	C₂₃×#97	—	2	2	no	—
62	C₄×C₈×C₂₃	—	2	2	no	—
63	C₂₃×#95	—	2	2	no	—
64	C₂₃×#95	C₂×C₄	1	4	yes	—
65	C₂⁴×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
66	C₂²×C₄×C₂₃	—	2	4	no	—
67	C₂²×C₄×C₂₃	—	2	2	no	—
68	C₂²×C₄×C₂₃	—	2	2	no	—
69	C₂²×C₄×C₂₃	—	2	4	no	—
70	C₂²×C₄×C₂₃	—	4	2	no	—
71	C₂²×C₄×C₂₃	C₄²	1	1	yes	characteristic
72	C₂²×C₄×C₂₃	C₄²	1	1	yes	characteristic
73	C₂²×C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
74	C₂²×C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
75	C₂²×C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
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	1	yes	characteristic
79	C₂²×C₄×C₂₃	C₂²⋊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	C₄⋊C₄	1	1	yes	characteristic
86	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
87	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
88	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
89	M₁₆×C₂₃	—	4	4	no	—
90	M₁₆×C₂₃	—	4	4	no	—
91	M₁₆×C₂₃	—	4	4	no	—
92	C₂×C₈×C₂₃	—	2	4	no	—
93	C₂×C₈×C₂₃	—	2	4	no	—
94	C₂×C₈×C₂₃	—	4	4	no	—
95	C₄⋊C₄×C₂₃	—	2	8	no	—
96	C₂²⋊C₄×C₂₃	—	2	8	no	—
97	C₄²×C₂₃	—	2	8	no	—
98	C₄²×C₂₃	—	4	4	no	—
99	C₄²×C₂₃	—	4	2	no	—
100	C₄²×C₂₃	—	4	2	no	—
101	C₄²×C₂₃	C₄²	1	1	yes	characteristic
102	C₄²×C₂₃	C₄²	1	1	yes	characteristic
103	C₄²×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
104	C₄²×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
105	C₄²×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
106	C₄²×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
107	C₄²×C₂₃	C₄⋊C₄	1	1	yes	characteristic
108	C₄²×C₂₃	C₄⋊C₄	1	1	yes	characteristic
109	C₄²×C₂₃	C₄⋊C₄	1	1	yes	characteristic
110	C₄²×C₂₃	C₄⋊C₄	1	1	yes	characteristic
111	C₄²×C₂₃	C₄⋊C₄	1	1	yes	characteristic
112	C₄²×C₂₃	C₄⋊C₄	1	1	yes	characteristic
113	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
114	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
115	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
116	C₄²×C₂₃	C₂×Q₈	1	1	yes	characteristic
117	#8097	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	#95	1	1	yes	characteristic
122	C₂³×C₂₃	#95	1	1	yes	characteristic
123	C₂³×C₂₃	C₂×C₂²⋊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	1	no	—
132	C₂×C₄×C₂₃	—	2	1	no	—
133	C₂×C₄×C₂₃	—	2	1	no	—
134	C₂×C₄×C₂₃	—	2	1	no	—
135	C₂×C₄×C₂₃	—	2	2	no	—
136	C₂×C₄×C₂₃	—	2	2	no	—
137	C₂×C₄×C₂₃	—	2	2	no	—
138	C₂×C₄×C₂₃	—	2	2	no	—
139	C₂×C₄×C₂₃	—	2	8	no	—
140	C₂×C₄×C₂₃	—	4	1	no	—
141	C₂×C₄×C₂₃	—	4	1	no	—
142	C₂×C₄×C₂₃	—	4	1	no	—
143	C₂×C₄×C₂₃	—	4	4	no	—
144	C₂×C₄×C₂₃	—	4	4	no	—
145	C₂×C₄×C₂₃	#95	1	1	yes	characteristic
146	C₂×C₄×C₂₃	#95	1	1	yes	characteristic
147	C₂×C₄×C₂₃	#95	1	1	yes	characteristic
148	C₂×C₄×C₂₃	#95	1	1	yes	characteristic
149	C₂×C₄×C₂₃	#95	1	1	yes	characteristic
150	C₂×C₄×C₂₃	#95	1	1	yes	characteristic
151	C₂×C₄×C₂₃	#104	1	4	yes	—
152	C₂×C₄×C₂₃	C₂×C₄²	1	1	yes	characteristic
153	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
154	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
155	C₂×C₄×C₂₃	C₂×C₄⋊C₄	1	1	yes	characteristic
156	C₂×C₄×C₂₃	C₂×C₄⋊C₄	1	1	yes	characteristic
157	C₂×C₄×C₂₃	C₂×C₄⋊C₄	1	1	yes	characteristic
158	C₂×C₄×C₂₃	AGL(1,ℤ/8)	1	2	yes	—
159	C₂×C₄×C₂₃	#137	1	2	yes	—
160	C₈×C₂₃	—	4	4	no	—
161	C₈×C₂₃	—	4	4	no	—
162	#2920	C₂×C₂₃	1	1	yes	characteristic
163	C₂×#423	C₂×C₂₃	1	1	yes	characteristic
164	C₄×#117	C₂×C₂₃	1	1	yes	characteristic
165	#1303	C₂×C₂₃	1	4	yes	complemented
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	—	2	1	no	—
173	C₂²×C₂₃	—	4	4	no	—
174	C₂²×C₂₃	#339	1	2	yes	—
175	C₂²×C₂₃	C₂×#95	1	1	yes	characteristic
176	C₂²×C₂₃	#417	1	2	yes	—
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	—	2	1	no	—
184	C₄×C₂₃	—	4	8	no	—
185	C₄×C₂₃	#339	1	2	yes	—
186	C₄×C₂₃	#344	1	2	yes	—
187	C₄×C₂₃	#418	1	1	yes	characteristic
188	C₄×C₂₃	#419	1	1	yes	characteristic
189	C₄×C₂₃	C₂×#104	1	2	yes	—
190	C₄×C₂₃	#428	1	2	yes	—
191	C₂²×M₁₆	—	2	1	no	—
192	C₂×#117	—	2	1	no	—
193	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
194	#432	—	2	1	no	—
195	#432	C₄×C₂₃	1	2	yes	complemented
196	#431	—	2	1	no	—
197	#431	C₂²×C₂₃	1	2	yes	—
198	#423	—	2	1	no	—
199	#423	—	2	1	no	—
200	#423	C₄×C₂₃	1	2	yes	complemented
201	#423	C₄×C₂₃	1	2	yes	complemented
202	#423	C₂²×C₂₃	1	2	yes	—
203	C₂×C₄⋊C₈	—	2	1	no	—
204	C₂×C₄⋊C₈	C₄×C₂₃	1	2	yes	complemented
205	#407	—	2	1	no	—
206	C₄×M₁₆	—	2	1	no	—
207	C₄×C₄⋊C₄	—	2	1	no	—
208	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
209	C₄×C₂²⋊C₄	—	2	1	no	—
210	C₄×C₂²⋊C₄	C₄×C₂₃	1	2	yes	—
211	#376	C₄×C₂₃	1	2	yes	—
212	C₄³	—	2	1	no	—
213	C₂×C₂₃	—	2	2	no	—
214	C₂×C₂₃	—	2	2	no	—
215	C₂×C₂₃	—	4	1	no	—
216	C₂×C₂₃	C₂×#339	1	1	yes	characteristic
217	C₂×C₂₃	#1736	1	1	yes	characteristic
218	C₂×C₂₃	C₂×#344	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	D₄×C₂₃	1	1	yes	characteristic
222	C₂×M₁₆	—	2	2	no	—
223	C₂×M₁₆	—	2	2	no	—
224	C₂×M₁₆	—	2	2	no	—
225	C₂×M₁₆	—	4	4	no	—
226	C₂²×C₈	—	2	2	no	—
227	#117	—	2	8	no	—
228	C₂×C₄⋊C₄	—	2	2	no	—
229	C₂×C₂²⋊C₄	—	2	2	no	—
230	C₂×C₄²	—	2	2	no	—
231	C₂×C₄²	—	2	2	no	—
232	C₂×C₄²	—	2	2	no	—
233	C₂×C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic
234	C₂×C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic
235	C₂×C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic
236	C₂×C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic
237	C₂×C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic
238	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
239	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
240	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
241	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
242	C₂×C₄²	Q₈×C₂₃	1	1	yes	characteristic
243	C₂×C₄²	Q₈×C₂₃	1	1	yes	characteristic
244	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
245	C₄⋊C₈	—	2	2	no	—
246	C₄⋊C₈	—	2	2	no	—
247	C₄⋊C₈	—	2	2	no	—
248	C₄⋊C₈	—	2	2	no	—
249	C₄⋊C₈	C₂×C₄×C₂₃	1	4	yes	—
250	C₄⋊C₈	C₂×C₄×C₂₃	1	4	yes	—
251	C₂²⋊C₈	—	2	2	no	—
252	C₂²⋊C₈	—	2	2	no	—
253	#97	—	2	2	no	—
254	C₄×C₈	—	2	2	no	—
255	#95	—	2	2	no	—
256	#95	C₂×C₄×C₂₃	1	4	yes	—
257	C₂₃	#8097	1	1	yes	characteristic, direct product factor, Sylow
258	C₂⁴	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
259	C₂²×C₄	—	2	4	no	—
260	C₂²×C₄	—	2	2	no	—
261	C₂²×C₄	—	2	2	no	—
262	C₂²×C₄	—	2	4	no	—
263	C₂²×C₄	—	4	2	no	—
264	C₂²×C₄	C₄²×C₂₃	1	1	yes	characteristic
265	C₂²×C₄	C₄²×C₂₃	1	1	yes	characteristic
266	C₂²×C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
267	C₂²×C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
268	C₂²×C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
269	C₂²×C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
270	C₂²×C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
271	C₂²×C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
272	C₂²×C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
273	C₂²×C₄	C₄⋊C₄×C₂₃	1	1	yes	characteristic
274	C₂²×C₄	C₄⋊C₄×C₂₃	1	1	yes	characteristic
275	C₂²×C₄	C₄⋊C₄×C₂₃	1	1	yes	characteristic
276	C₂²×C₄	C₄⋊C₄×C₂₃	1	1	yes	characteristic
277	C₂²×C₄	C₄⋊C₄×C₂₃	1	1	yes	characteristic
278	C₂²×C₄	C₄⋊C₄×C₂₃	1	1	yes	characteristic
279	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
280	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
281	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
282	M₁₆	—	4	4	no	—
283	M₁₆	—	4	4	no	—
284	M₁₆	—	4	4	no	—
285	C₂×C₈	—	2	4	no	—
286	C₂×C₈	—	2	4	no	—
287	C₂×C₈	—	4	4	no	—
288	C₄⋊C₄	—	2	8	no	—
289	C₂²⋊C₄	—	2	8	no	—
290	C₄²	—	2	8	no	—
291	C₄²	—	4	4	no	—
292	C₄²	—	4	2	no	—
293	C₄²	—	4	2	no	—
294	C₄²	C₄²×C₂₃	1	1	yes	characteristic
295	C₄²	C₄²×C₂₃	1	1	yes	characteristic
296	C₄²	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
297	C₄²	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
298	C₄²	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
299	C₄²	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
300	C₄²	C₄⋊C₄×C₂₃	1	1	yes	characteristic
301	C₄²	C₄⋊C₄×C₂₃	1	1	yes	characteristic
302	C₄²	C₄⋊C₄×C₂₃	1	1	yes	characteristic
303	C₄²	C₄⋊C₄×C₂₃	1	1	yes	characteristic
304	C₄²	C₄⋊C₄×C₂₃	1	1	yes	characteristic
305	C₄²	C₄⋊C₄×C₂₃	1	1	yes	characteristic
306	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
307	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
308	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
309	C₄²	C₂×Q₈×C₂₃	1	1	yes	characteristic
310	C₂³	—	2	2	no	—
311	C₂³	—	2	2	no	—
312	C₂³	—	4	1	no	—
313	C₂³	C₂₃×#95	1	1	yes	characteristic
314	C₂³	C₂₃×#95	1	1	yes	characteristic
315	C₂³	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
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	—	2	1	no	—
324	C₂×C₄	—	2	1	no	—
325	C₂×C₄	—	2	1	no	—
326	C₂×C₄	—	2	1	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	8	no	—
332	C₂×C₄	—	4	1	no	—
333	C₂×C₄	—	4	1	no	—
334	C₂×C₄	—	4	1	no	—
335	C₂×C₄	—	4	4	no	—
336	C₂×C₄	—	4	4	no	—
337	C₂×C₄	C₂₃×#95	1	1	yes	characteristic
338	C₂×C₄	C₂₃×#95	1	1	yes	characteristic
339	C₂×C₄	C₂₃×#95	1	1	yes	characteristic
340	C₂×C₄	C₂₃×#95	1	1	yes	characteristic
341	C₂×C₄	C₂₃×#95	1	1	yes	characteristic
342	C₂×C₄	C₂₃×#95	1	1	yes	characteristic
343	C₂×C₄	C₂₃×#104	1	4	yes	—
344	C₂×C₄	C₂×C₄²×C₂₃	1	1	yes	characteristic
345	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
346	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
347	C₂×C₄	C₂×C₄⋊C₄×C₂₃	1	1	yes	characteristic
348	C₂×C₄	C₂×C₄⋊C₄×C₂₃	1	1	yes	characteristic
349	C₂×C₄	C₂×C₄⋊C₄×C₂₃	1	1	yes	characteristic
350	C₂×C₄	C₂₃×AGL(1,ℤ/8)	1	2	yes	—
351	C₂×C₄	C₂₃×#137	1	2	yes	—
352	C₈	—	4	4	no	—
353	C₈	—	4	4	no	—
354	C₂²	—	2	1	no	—
355	C₂²	—	2	1	no	—
356	C₂²	—	2	1	no	—
357	C₂²	—	2	1	no	—
358	C₂²	—	2	1	no	—
359	C₂²	—	2	1	no	—
360	C₂²	—	2	1	no	—
361	C₂²	—	4	4	no	—
362	C₂²	C₂₃×#339	1	2	yes	—
363	C₂²	C₂×C₂₃×#95	1	1	yes	characteristic
364	C₂²	C₂₃×#417	1	2	yes	—
365	C₄	—	2	1	no	—
366	C₄	—	2	1	no	—
367	C₄	—	2	1	no	—
368	C₄	—	2	1	no	—
369	C₄	—	2	1	no	—
370	C₄	—	2	1	no	—
371	C₄	—	2	1	no	—
372	C₄	—	4	8	no	—
373	C₄	C₂₃×#339	1	2	yes	—
374	C₄	C₂₃×#344	1	2	yes	—
375	C₄	C₂₃×#418	1	1	yes	characteristic
376	C₄	C₂₃×#419	1	1	yes	characteristic
377	C₄	C₂×C₂₃×#104	1	2	yes	—
378	C₄	C₂₃×#428	1	2	yes	—
379	C₂	—	2	2	no	—
380	C₂	—	2	2	no	—
381	C₂	—	4	1	no	—
382	C₂	C₂×C₂₃×#339	1	1	yes	characteristic
383	C₂	C₂₃×#1736	1	1	yes	characteristic
384	C₂	C₂×C₂₃×#344	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₂₃	C₂×C₂²⋊C₄
commutator	C₂×C₄	C₂×C₄²×C₂₃
Frattini, cosocle	C₂×C₄²	C₂³×C₂₃
socle	C₂²×C₂₃	C₂×#95
prime radical	C₂⁴×C₂₃	C₂²⋊C₄
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ 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
4. C₂₃×#1303	C₂	semidirect
9. C₂₃×#432	C₄	semidirect
14. C₂₃×#423	C₄	semidirect
15. C₂₃×#423	C₄	semidirect
18. C₂×C₂₃×C₄⋊C₈	C₄	semidirect
117. #8097	C₂₃	direct (N × H)
165. #1303	C₂×C₂₃	semidirect
195. #432	C₄×C₂₃	semidirect
200. #423	C₄×C₂₃	semidirect
201. #423	C₄×C₂₃	semidirect
204. C₂×C₄⋊C₈	C₄×C₂₃	semidirect
257. C₂₃	#8097	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×#423	2
C₄×C₂₃×#117	2
C₂₃×#1303	2
#8097	23

Subgroups — C23×#8097 #19155723

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#8097 #19155723