Subgroups — C₂₃×#7940 #19155566

Order 5888.

696 conjugacy classes of subgroups.

The subgroup lattice has 378 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	C₂₃×#2283	C₂	1	1	yes	maximal, characteristic
3	C₄×C₂₃×#117	C₂	1	1	yes	maximal, characteristic
4	C₂₃×#1284	C₂	1	4	yes	maximal
5	C₂×C₂₃×#117	—	2	1	no	—
6	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
7	C₂₃×#432	—	2	1	no	—
8	C₂₃×#432	C₄	1	2	yes	complemented
9	C₂₃×#431	—	2	1	no	—
10	C₂₃×#431	C₄	1	2	yes	complemented
11	C₂₃×#423	—	2	1	no	—
12	C₂₃×#407	C₂²	1	2	yes	—
13	C₄×M₁₆×C₂₃	—	2	1	no	—
14	C₂₃×#383	—	2	1	no	—
15	C₂₃×#382	C₄	1	2	yes	complemented
16	C₂₃×#381	C₂²	1	2	yes	—
17	C₂₃×#380	—	2	1	no	—
18	C₄×C₄⋊C₄×C₂₃	—	2	1	no	—
19	C₄×C₄⋊C₄×C₂₃	—	2	1	no	—
20	C₄×C₄⋊C₄×C₂₃	C₄	1	2	yes	complemented
21	C₄×C₂²⋊C₄×C₂₃	—	2	1	no	—
22	C₄×C₂²⋊C₄×C₂₃	—	2	1	no	—
23	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
24	C₂₃×#376	—	2	1	no	—
25	C₂₃×#376	C₄	1	2	yes	complemented
26	C₄³×C₂₃	C₄	1	2	yes	complemented
27	C₂³×C₄×C₂₃	D₄	1	1	yes	characteristic
28	C₂³×C₄×C₂₃	D₄	1	1	yes	characteristic
29	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
30	C₂×M₁₆×C₂₃	—	2	2	no	—
31	C₂₃×#117	—	2	8	no	—
32	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
33	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
34	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
35	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
36	C₂×C₄²×C₂₃	—	2	2	no	—
37	C₂×C₄²×C₂₃	—	2	2	no	—
38	C₂×C₄²×C₂₃	—	2	2	no	—
39	C₂×C₄²×C₂₃	C₂×C₄	1	4	yes	—
40	C₂×C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
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	C₂₃×C₄⋊C₈	—	2	2	no	—
53	C₂₃×C₄⋊C₈	—	2	2	no	—
54	C₂₃×C₂²⋊C₈	—	2	2	no	—
55	C₂₃×C₂²⋊C₈	C₂×C₄	1	4	yes	—
56	C₂₃×#97	—	2	2	no	—
57	C₄×C₈×C₂₃	—	2	2	no	—
58	C₂₃×#95	—	2	2	no	—
59	C₂₃×#95	—	2	2	no	—
60	C₂₃×#95	—	2	2	no	—
61	C₂₃×#95	—	2	2	no	—
62	C₂₃×#95	—	2	2	no	—
63	C₂₃×#95	C₂×C₄	1	4	yes	—
64	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
65	C₂²×C₄×C₂₃	—	2	4	no	—
66	C₂²×C₄×C₂₃	—	2	4	no	—
67	C₂²×C₄×C₂₃	—	2	4	no	—
68	C₂²×C₄×C₂₃	—	4	2	no	—
69	C₂²×C₄×C₂₃	—	4	2	no	—
70	C₂²×C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
71	C₂²×C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
72	C₂²×C₄×C₂₃	C₂²⋊C₄	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	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	C₂²×C₄	1	1	yes	characteristic
83	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
84	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
85	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
86	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
87	C₂²×C₄×C₂₃	C₂×Q₈	1	1	yes	characteristic
88	M₁₆×C₂₃	—	4	4	no	—
89	C₂×C₈×C₂₃	—	2	4	no	—
90	C₄⋊C₄×C₂₃	—	2	8	no	—
91	C₄⋊C₄×C₂₃	—	4	4	no	—
92	C₂²⋊C₄×C₂₃	—	2	8	no	—
93	C₂²⋊C₄×C₂₃	—	4	4	no	—
94	C₄²×C₂₃	—	2	8	no	—
95	C₄²×C₂₃	—	4	4	no	—
96	C₄²×C₂₃	—	4	4	no	—
97	C₄²×C₂₃	—	4	4	no	—
98	C₄²×C₂₃	C₄²	1	1	yes	characteristic
99	C₄²×C₂₃	C₄²	1	1	yes	characteristic
100	C₄²×C₂₃	C₄²	1	1	yes	characteristic
101	C₄²×C₂₃	C₄²	1	1	yes	characteristic
102	C₄²×C₂₃	C₂²⋊C₄	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	C₄⋊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	C₄⋊C₄	1	1	yes	characteristic
114	#7940	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
115	C₂³×C₂₃	—	2	2	no	—
116	C₂³×C₂₃	—	2	2	no	—
117	C₂³×C₂₃	—	4	1	no	—
118	C₂³×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
119	C₂³×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
120	C₂³×C₂₃	C₂×C₄⋊C₄	1	1	yes	characteristic
121	C₂×C₄×C₂₃	—	2	2	no	—
122	C₂×C₄×C₂₃	—	2	2	no	—
123	C₂×C₄×C₂₃	—	2	2	no	—
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	8	no	—
132	C₂×C₄×C₂₃	—	4	1	no	—
133	C₂×C₄×C₂₃	—	4	1	no	—
134	C₂×C₄×C₂₃	—	4	1	no	—
135	C₂×C₄×C₂₃	—	4	1	no	—
136	C₂×C₄×C₂₃	—	4	1	no	—
137	C₂×C₄×C₂₃	—	4	1	no	—
138	C₂×C₄×C₂₃	—	4	1	no	—
139	C₂×C₄×C₂₃	—	4	4	no	—
140	C₂×C₄×C₂₃	—	4	4	no	—
141	C₂×C₄×C₂₃	—	4	4	no	—
142	C₂×C₄×C₂₃	—	4	4	no	—
143	C₂×C₄×C₂₃	—	4	4	no	—
144	C₂×C₄×C₂₃	#95	1	1	yes	characteristic
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	#95	1	1	yes	characteristic
152	C₂×C₄×C₂₃	#104	1	4	yes	—
153	C₂×C₄×C₂₃	C₂×C₄²	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	C₈×C₂₃	—	4	4	no	—
158	#2920	C₂×C₂₃	1	1	yes	characteristic
159	#2283	C₂×C₂₃	1	1	yes	characteristic
160	C₄×#117	C₂×C₂₃	1	1	yes	characteristic
161	#1284	C₂×C₂₃	1	4	yes	—
162	C₂²×C₂₃	—	2	1	no	—
163	C₂²×C₂₃	—	2	1	no	—
164	C₂²×C₂₃	—	2	1	no	—
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	—	4	4	no	—
170	C₂²×C₂₃	C₂×#95	1	1	yes	characteristic
171	C₂²×C₂₃	#410	1	2	yes	—
172	C₂²×C₂₃	C₂×#104	1	2	yes	—
173	C₄×C₂₃	—	2	1	no	—
174	C₄×C₂₃	—	2	1	no	—
175	C₄×C₂₃	—	2	1	no	—
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	—	4	8	no	—
183	C₄×C₂₃	—	8	4	no	—
184	C₄×C₂₃	H(3,ℤ/4)	1	2	yes	—
185	C₄×C₂₃	#339	1	2	yes	—
186	C₄×C₂₃	#339	1	2	yes	—
187	C₂×#117	—	2	1	no	—
188	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
189	#432	—	2	1	no	—
190	#432	C₄×C₂₃	1	2	yes	complemented
191	#431	—	2	1	no	—
192	#431	C₄×C₂₃	1	2	yes	complemented
193	#423	—	2	1	no	—
194	#407	C₂²×C₂₃	1	2	yes	—
195	C₄×M₁₆	—	2	1	no	—
196	#383	—	2	1	no	—
197	#382	C₄×C₂₃	1	2	yes	complemented
198	#381	C₂²×C₂₃	1	2	yes	—
199	#380	—	2	1	no	—
200	C₄×C₄⋊C₄	—	2	1	no	—
201	C₄×C₄⋊C₄	—	2	1	no	—
202	C₄×C₄⋊C₄	C₄×C₂₃	1	2	yes	complemented
203	C₄×C₂²⋊C₄	—	2	1	no	—
204	C₄×C₂²⋊C₄	—	2	1	no	—
205	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
206	#376	—	2	1	no	—
207	#376	C₄×C₂₃	1	2	yes	complemented
208	C₄³	C₄×C₂₃	1	2	yes	complemented
209	C₂×C₂₃	—	2	2	no	—
210	C₂×C₂₃	—	2	2	no	—
211	C₂×C₂₃	—	4	1	no	—
212	C₂×C₂₃	C₂×H(3,ℤ/4)	1	1	yes	characteristic
213	C₂×C₂₃	C₂×#339	1	1	yes	characteristic
214	C₂×C₂₃	#1740	1	1	yes	characteristic
215	C₂³×C₄	D₄×C₂₃	1	1	yes	characteristic
216	C₂³×C₄	D₄×C₂₃	1	1	yes	characteristic
217	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
218	C₂×M₁₆	—	2	2	no	—
219	#117	—	2	8	no	—
220	C₂×C₄⋊C₄	—	2	2	no	—
221	C₂×C₄⋊C₄	—	2	2	no	—
222	C₂×C₂²⋊C₄	—	2	2	no	—
223	C₂×C₂²⋊C₄	—	2	2	no	—
224	C₂×C₄²	—	2	2	no	—
225	C₂×C₄²	—	2	2	no	—
226	C₂×C₄²	—	2	2	no	—
227	C₂×C₄²	C₂×C₄×C₂₃	1	4	yes	—
228	C₂×C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic
229	C₂×C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic
230	C₂×C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic
231	C₂×C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic
232	C₂×C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic
233	C₂×C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic
234	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
235	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
236	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
237	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
238	C₂×C₄²	Q₈×C₂₃	1	1	yes	characteristic
239	C₂×C₄²	Q₈×C₂₃	1	1	yes	characteristic
240	C₄⋊C₈	—	2	2	no	—
241	C₄⋊C₈	—	2	2	no	—
242	C₂²⋊C₈	—	2	2	no	—
243	C₂²⋊C₈	C₂×C₄×C₂₃	1	4	yes	—
244	#97	—	2	2	no	—
245	C₄×C₈	—	2	2	no	—
246	#95	—	2	2	no	—
247	#95	—	2	2	no	—
248	#95	—	2	2	no	—
249	#95	—	2	2	no	—
250	#95	—	2	2	no	—
251	#95	C₂×C₄×C₂₃	1	4	yes	—
252	C₂₃	#7940	1	1	yes	characteristic, direct product factor, Sylow
253	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
254	C₂²×C₄	—	2	4	no	—
255	C₂²×C₄	—	2	4	no	—
256	C₂²×C₄	—	2	4	no	—
257	C₂²×C₄	—	4	2	no	—
258	C₂²×C₄	—	4	2	no	—
259	C₂²×C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
260	C₂²×C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
261	C₂²×C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
262	C₂²×C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
263	C₂²×C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
264	C₂²×C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
265	C₂²×C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
266	C₂²×C₄	C₂²⋊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	C₂²×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	C₂×D₄×C₂₃	1	1	yes	characteristic
275	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
276	C₂²×C₄	C₂×Q₈×C₂₃	1	1	yes	characteristic
277	M₁₆	—	4	4	no	—
278	C₂×C₈	—	2	4	no	—
279	C₄⋊C₄	—	2	8	no	—
280	C₄⋊C₄	—	4	4	no	—
281	C₂²⋊C₄	—	2	8	no	—
282	C₂²⋊C₄	—	4	4	no	—
283	C₄²	—	2	8	no	—
284	C₄²	—	4	4	no	—
285	C₄²	—	4	4	no	—
286	C₄²	—	4	4	no	—
287	C₄²	C₄²×C₂₃	1	1	yes	characteristic
288	C₄²	C₄²×C₂₃	1	1	yes	characteristic
289	C₄²	C₄²×C₂₃	1	1	yes	characteristic
290	C₄²	C₄²×C₂₃	1	1	yes	characteristic
291	C₄²	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
292	C₄²	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
293	C₄²	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
294	C₄²	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
295	C₄²	C₄⋊C₄×C₂₃	1	1	yes	characteristic
296	C₄²	C₄⋊C₄×C₂₃	1	1	yes	characteristic
297	C₄²	C₄⋊C₄×C₂₃	1	1	yes	characteristic
298	C₄²	C₄⋊C₄×C₂₃	1	1	yes	characteristic
299	C₄²	C₄⋊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	C₂³	—	2	2	no	—
304	C₂³	—	2	2	no	—
305	C₂³	—	4	1	no	—
306	C₂³	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
307	C₂³	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
308	C₂³	C₂×C₄⋊C₄×C₂₃	1	1	yes	characteristic
309	C₂×C₄	—	2	2	no	—
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	8	no	—
320	C₂×C₄	—	4	1	no	—
321	C₂×C₄	—	4	1	no	—
322	C₂×C₄	—	4	1	no	—
323	C₂×C₄	—	4	1	no	—
324	C₂×C₄	—	4	1	no	—
325	C₂×C₄	—	4	1	no	—
326	C₂×C₄	—	4	1	no	—
327	C₂×C₄	—	4	4	no	—
328	C₂×C₄	—	4	4	no	—
329	C₂×C₄	—	4	4	no	—
330	C₂×C₄	—	4	4	no	—
331	C₂×C₄	—	4	4	no	—
332	C₂×C₄	C₂₃×#95	1	1	yes	characteristic
333	C₂×C₄	C₂₃×#95	1	1	yes	characteristic
334	C₂×C₄	C₂₃×#95	1	1	yes	characteristic
335	C₂×C₄	C₂₃×#95	1	1	yes	characteristic
336	C₂×C₄	C₂₃×#95	1	1	yes	characteristic
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×#104	1	4	yes	—
341	C₂×C₄	C₂×C₄²×C₂₃	1	1	yes	characteristic
342	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
343	C₂×C₄	C₂×C₄⋊C₄×C₂₃	1	1	yes	characteristic
344	C₂×C₄	C₂×C₄⋊C₄×C₂₃	1	1	yes	characteristic
345	C₈	—	4	4	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	—	2	1	no	—
352	C₂²	—	2	1	no	—
353	C₂²	—	4	4	no	—
354	C₂²	C₂×C₂₃×#95	1	1	yes	characteristic
355	C₂²	C₂₃×#410	1	2	yes	—
356	C₂²	C₂×C₂₃×#104	1	2	yes	—
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	—	2	1	no	—
363	C₄	—	2	1	no	—
364	C₄	—	2	1	no	—
365	C₄	—	2	1	no	—
366	C₄	—	4	8	no	—
367	C₄	—	8	4	no	—
368	C₄	C₂₃×H(3,ℤ/4)	1	2	yes	—
369	C₄	C₂₃×#339	1	2	yes	—
370	C₄	C₂₃×#339	1	2	yes	—
371	C₂	—	2	2	no	—
372	C₂	—	2	2	no	—
373	C₂	—	4	1	no	—
374	C₂	C₂×C₂₃×H(3,ℤ/4)	1	1	yes	characteristic
375	C₂	C₂×C₂₃×#339	1	1	yes	characteristic
376	C₂	C₂₃×#1740	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₂₃	#95
commutator	C₂×C₄	C₂×C₄²×C₂₃
Frattini, cosocle	C₂³×C₄	C₂³×C₂₃
socle	C₂²×C₂₃	C₂×#95
prime radical	C₂⁴×C₂₃	C₂×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
8. C₂₃×#432	C₄	semidirect
10. C₂₃×#431	C₄	semidirect
15. C₂₃×#382	C₄	semidirect
20. C₄×C₄⋊C₄×C₂₃	C₄	semidirect
25. C₂₃×#376	C₄	semidirect
26. C₄³×C₂₃	C₄	semidirect
114. #7940	C₂₃	direct (N × H)
190. #432	C₄×C₂₃	semidirect
192. #431	C₄×C₂₃	semidirect
197. #382	C₄×C₂₃	semidirect
202. C₄×C₄⋊C₄	C₄×C₂₃	semidirect
207. #376	C₄×C₂₃	semidirect
208. C₄³	C₄×C₂₃	semidirect
252. C₂₃	#7940	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
C₂₃×#2283	2
C₄×C₂₃×#117	2
C₂₃×#1284	2
#7940	23

Subgroups — C23×#7940 #19155566

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#7940 #19155566