Subgroups — C₂₃×#21417 #19169043

Order 5888.

1214 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3444	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#2920	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₂₃×#376	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#1995	C₂	1	2	yes	maximal, complemented
5	C₂₃×#1963	C₂	1	2	yes	maximal, complemented
6	C₂₃×#1896	C₂	1	4	yes	maximal, complemented
7	C₂₃×#1759	C₂	1	4	yes	maximal, complemented
8	C₂₃×#533	C₄	1	2	yes	complemented
9	C₂₃×#533	C₂²	1	1	yes	characteristic
10	C₂₃×#532	C₄	1	2	yes	complemented
11	C₂₃×#532	C₂²	1	1	yes	characteristic
12	C₂₃×#529	—	2	2	no	—
13	C₂₃×#529	—	2	2	no	—
14	C₂₃×#529	C₄	1	4	yes	complemented
15	C₂₃×#525	—	2	2	no	—
16	C₂₃×#525	C₂²	1	2	yes	—
17	C₄×#41×C₂₃	—	2	2	no	—
18	C₄×#41×C₂₃	C₂²	1	2	yes	—
19	C₂²×C₄²×C₂₃	C₂²	1	2	yes	—
20	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
21	C₂₃×#432	—	2	2	no	—
22	C₂₃×#431	—	2	2	no	—
23	C₂₃×#423	C₂²	1	2	yes	—
24	C₂×C₂₃×#104	C₂²	1	8	yes	—
25	C₂₃×#407	C₂²	1	2	yes	—
26	C₄×M₁₆×C₂₃	C₂²	1	2	yes	—
27	C₂₃×#376	—	2	2	no	—
28	C₂₃×#376	C₂²	1	2	yes	—
29	C₂₃×#376	C₂²	1	2	yes	—
30	C₂×C₂₃×#95	—	2	2	no	—
31	C₂₃×#339	C₂²	1	8	yes	—
32	C₂×#41×C₂₃	—	2	2	no	—
33	C₂×#41×C₂₃	C₂³	1	2	yes	—
34	C₂³×C₄×C₂₃	—	2	2	no	—
35	C₂³×C₄×C₂₃	D₄	1	2	yes	—
36	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
37	C₂×M₁₆×C₂₃	C₂³	1	4	yes	—
38	C₂₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic, complemented
39	C₂₃×C₄⋊Q₈	C₂×C₄	1	2	yes	complemented
40	C₂₃×#127	C₂×C₄	1	1	yes	characteristic, complemented
41	C₂₃×#126	—	2	4	no	—
42	C₂₃×#125	—	2	2	no	—
43	C₂₃×#125	C₂×C₄	1	2	yes	complemented
44	C₂₃×#124	—	2	2	no	—
45	C₂₃×#124	C₂×C₄	1	2	yes	complemented
46	C₂₃×#123	—	2	4	no	—
47	C₂₃×#123	—	2	2	no	—
48	C₂₃×C₂²⋊Q₈	—	2	2	no	—
49	C₂₃×C₂²⋊Q₈	—	2	2	no	—
50	C₂₃×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
51	C₂₃×#121	—	2	2	no	—
52	C₂₃×#121	—	2	2	no	—
53	C₂₃×#121	C₂×C₄	1	4	yes	—
54	C₂₃×#120	—	2	2	no	—
55	C₄×Q₈×C₂₃	—	2	2	no	—
56	C₄×Q₈×C₂₃	—	2	2	no	—
57	C₄×Q₈×C₂₃	C₂×C₄	1	4	yes	complemented
58	C₄×D₄×C₂₃	—	2	4	no	—
59	C₄×D₄×C₂₃	—	2	4	no	—
60	C₄×D₄×C₂₃	—	2	4	no	—
61	C₄×D₄×C₂₃	—	2	2	no	—
62	C₄×D₄×C₂₃	—	2	2	no	—
63	C₄×D₄×C₂₃	C₂×C₄	1	4	yes	complemented
64	C₂₃×#117	—	2	2	no	—
65	C₂₃×#117	—	2	4	no	—
66	C₂₃×#117	—	2	2	no	—
67	C₂₃×#117	C₂³	1	2	yes	—
68	C₂×C₄²×C₂₃	—	2	2	no	—
69	C₂×C₄²×C₂₃	—	2	2	no	—
70	C₂×C₄²×C₂₃	—	2	8	no	—
71	C₂×C₄²×C₂₃	C₂×C₄	1	2	yes	—
72	C₂×C₄²×C₂₃	C₂×C₄	1	2	yes	—
73	C₂×C₄²×C₂₃	D₄	1	2	yes	—
74	C₂×C₄²×C₂₃	D₄	1	2	yes	—
75	C₂×C₄²×C₂₃	D₄	1	2	yes	—
76	C₂×C₄²×C₂₃	C₂³	1	4	yes	—
77	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
78	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
79	C₂₃×C₄⋊C₈	—	2	4	no	—
80	C₂₃×#104	—	2	16	no	—
81	C₂₃×C₂²⋊C₈	—	2	4	no	—
82	C₂₃×#97	—	2	2	no	—
83	C₄×C₈×C₂₃	—	2	2	no	—
84	C₂₃×#95	—	2	4	no	—
85	C₂₃×#95	—	2	4	no	—
86	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
87	#41×C₂₃	—	2	8	no	—
88	#41×C₂₃	—	4	8	no	—
89	C₂×Q₈×C₂₃	—	2	2	no	—
90	C₂×Q₈×C₂₃	C₂²×C₄	1	2	yes	—
91	C₂×D₄×C₂₃	—	2	4	no	—
92	C₂×D₄×C₂₃	—	2	2	no	—
93	C₂×D₄×C₂₃	—	2	2	no	—
94	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
95	C₂²×C₄×C₂₃	—	2	4	no	—
96	C₂²×C₄×C₂₃	—	2	8	no	—
97	C₂²×C₄×C₂₃	—	2	4	no	—
98	C₂²×C₄×C₂₃	—	2	4	no	—
99	C₂²×C₄×C₂₃	—	2	2	no	—
100	C₂²×C₄×C₂₃	—	4	4	no	—
101	C₂²×C₄×C₂₃	—	4	8	no	—
102	C₂²×C₄×C₂₃	C₂²⋊C₄	1	2	yes	—
103	C₂²×C₄×C₂₃	C₂²⋊C₄	1	2	yes	—
104	C₂²×C₄×C₂₃	C₂²⋊C₄	1	2	yes	—
105	C₂²×C₄×C₂₃	C₂²⋊C₄	1	2	yes	—
106	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
107	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
109	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
110	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
111	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
112	M₁₆×C₂₃	—	2	8	no	—
113	C₂×C₈×C₂₃	—	2	4	no	—
114	C₄⋊C₄×C₂₃	—	2	2	no	—
115	C₄⋊C₄×C₂₃	—	2	2	no	—
116	C₄⋊C₄×C₂₃	—	2	4	no	—
117	C₄⋊C₄×C₂₃	—	2	4	no	—
118	C₄⋊C₄×C₂₃	—	2	4	no	—
119	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
120	C₂²⋊C₄×C₂₃	—	2	4	no	—
121	C₂²⋊C₄×C₂₃	—	2	2	no	—
122	C₂²⋊C₄×C₂₃	—	2	4	no	—
123	C₂²⋊C₄×C₂₃	—	2	4	no	—
124	C₂²⋊C₄×C₂₃	—	2	4	no	—
125	C₄²×C₂₃	—	2	8	no	—
126	C₄²×C₂₃	—	2	4	no	—
127	C₄²×C₂₃	—	2	2	no	—
128	C₄²×C₂₃	—	2	4	no	—
129	C₄²×C₂₃	C₂²⋊C₄	1	2	yes	—
130	C₄²×C₂₃	C₂²⋊C₄	1	2	yes	—
131	C₄²×C₂₃	C₂²⋊C₄	1	2	yes	—
132	C₄²×C₂₃	C₂²⋊C₄	1	2	yes	—
133	C₄²×C₂₃	C₂²×C₄	1	2	yes	—
134	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
135	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
136	C₄²×C₂₃	C₂×D₄	1	2	yes	—
137	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
138	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
139	C₄²×C₂₃	#41	1	8	yes	complemented
140	#21417	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
141	C₂³×C₂₃	—	2	2	no	—
142	C₂³×C₂₃	—	2	4	no	—
143	C₂³×C₂₃	—	2	2	no	—
144	C₂³×C₂₃	C₂×C₂²⋊C₄	1	2	yes	—
145	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
146	Q₈×C₂₃	—	2	4	no	—
147	Q₈×C₂₃	—	4	4	no	—
148	D₄×C₂₃	—	2	4	no	—
149	D₄×C₂₃	—	4	4	no	—
150	D₄×C₂₃	—	4	4	no	—
151	D₄×C₂₃	—	4	8	no	—
152	C₂×C₄×C₂₃	—	2	2	no	—
153	C₂×C₄×C₂₃	—	2	4	no	—
154	C₂×C₄×C₂₃	—	2	4	no	—
155	C₂×C₄×C₂₃	—	2	4	no	—
156	C₂×C₄×C₂₃	—	2	4	no	—
157	C₂×C₄×C₂₃	—	2	2	no	—
158	C₂×C₄×C₂₃	—	2	4	no	—
159	C₂×C₄×C₂₃	—	2	8	no	—
160	C₂×C₄×C₂₃	—	4	2	no	—
161	C₂×C₄×C₂₃	—	4	2	no	—
162	C₂×C₄×C₂₃	—	4	2	no	—
163	C₂×C₄×C₂₃	—	4	2	no	—
164	C₂×C₄×C₂₃	—	4	8	no	—
165	C₂×C₄×C₂₃	—	4	16	no	—
166	C₂×C₄×C₂₃	—	4	8	no	—
167	C₂×C₄×C₂₃	—	4	4	no	—
168	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	2	yes	—
169	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	2	yes	—
170	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	2	yes	—
171	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	2	yes	—
172	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	2	yes	—
173	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
174	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
175	C₂×C₄×C₂₃	C₂×#41	1	4	yes	—
176	C₈×C₂₃	—	4	4	no	—
177	#3444	C₂×C₂₃	1	1	yes	characteristic
178	#2920	C₂×C₂₃	1	1	yes	characteristic, complemented
179	C₂×#376	C₂×C₂₃	1	1	yes	characteristic, complemented
180	#1995	C₂×C₂₃	1	2	yes	complemented
181	#1963	C₂×C₂₃	1	2	yes	complemented
182	#1896	C₂×C₂₃	1	4	yes	complemented
183	#1759	C₂×C₂₃	1	4	yes	complemented
184	C₂²×C₂₃	—	2	8	no	—
185	C₂²×C₂₃	—	2	2	no	—
186	C₂²×C₂₃	—	2	2	no	—
187	C₂²×C₂₃	—	2	2	no	—
188	C₂²×C₂₃	—	4	4	no	—
189	C₂²×C₂₃	—	4	2	no	—
190	C₂²×C₂₃	#421	1	4	yes	—
191	C₂²×C₂₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
192	C₂²×C₂₃	#525	1	2	yes	—
193	C₄×C₂₃	—	2	2	no	—
194	C₄×C₂₃	—	2	2	no	—
195	C₄×C₂₃	—	2	2	no	—
196	C₄×C₂₃	—	2	2	no	—
197	C₄×C₂₃	—	2	2	no	—
198	C₄×C₂₃	—	4	8	no	—
199	C₄×C₂₃	—	4	4	no	—
200	C₄×C₂₃	—	4	2	no	—
201	C₄×C₂₃	C₄×#41	1	2	yes	—
202	C₄×C₂₃	#532	1	2	yes	—
203	#533	C₄×C₂₃	1	2	yes	complemented
204	#533	C₂²×C₂₃	1	1	yes	characteristic
205	#532	C₄×C₂₃	1	2	yes	complemented
206	#532	C₂²×C₂₃	1	1	yes	characteristic
207	#529	—	2	2	no	—
208	#529	—	2	2	no	—
209	#529	C₄×C₂₃	1	4	yes	complemented
210	#525	—	2	2	no	—
211	#525	C₂²×C₂₃	1	2	yes	—
212	C₄×#41	—	2	2	no	—
213	C₄×#41	C₂²×C₂₃	1	2	yes	—
214	C₂²×C₄²	C₂²×C₂₃	1	2	yes	—
215	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
216	#432	—	2	2	no	—
217	#431	—	2	2	no	—
218	#423	C₂²×C₂₃	1	2	yes	—
219	C₂×#104	C₂²×C₂₃	1	8	yes	—
220	#407	C₂²×C₂₃	1	2	yes	—
221	C₄×M₁₆	C₂²×C₂₃	1	2	yes	—
222	#376	—	2	2	no	—
223	#376	C₂²×C₂₃	1	2	yes	—
224	#376	C₂²×C₂₃	1	2	yes	—
225	C₂×#95	—	2	2	no	—
226	#339	C₂²×C₂₃	1	8	yes	—
227	C₂×C₂₃	—	2	2	no	—
228	C₂×C₂₃	—	2	4	no	—
229	C₂×C₂₃	—	8	2	no	—
230	C₂×C₂₃	#2297	1	1	yes	characteristic
231	C₂×C₂₃	C₂×#421	1	2	yes	—
232	C₂×#41	—	2	2	no	—
233	C₂×#41	C₂³×C₂₃	1	2	yes	—
234	C₂³×C₄	—	2	2	no	—
235	C₂³×C₄	D₄×C₂₃	1	2	yes	—
236	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
237	C₂×M₁₆	C₂³×C₂₃	1	4	yes	—
238	C₄⋊Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic, complemented
239	C₄⋊Q₈	C₂×C₄×C₂₃	1	2	yes	complemented
240	#127	C₂×C₄×C₂₃	1	1	yes	characteristic, complemented
241	#126	—	2	4	no	—
242	#125	—	2	2	no	—
243	#125	C₂×C₄×C₂₃	1	2	yes	complemented
244	#124	—	2	2	no	—
245	#124	C₂×C₄×C₂₃	1	2	yes	complemented
246	#123	—	2	4	no	—
247	#123	—	2	2	no	—
248	C₂²⋊Q₈	—	2	2	no	—
249	C₂²⋊Q₈	—	2	2	no	—
250	C₂²⋊Q₈	C₂×C₄×C₂₃	1	4	yes	—
251	#121	—	2	2	no	—
252	#121	—	2	2	no	—
253	#121	C₂×C₄×C₂₃	1	4	yes	—
254	#120	—	2	2	no	—
255	C₄×Q₈	—	2	2	no	—
256	C₄×Q₈	—	2	2	no	—
257	C₄×Q₈	C₂×C₄×C₂₃	1	4	yes	complemented
258	C₄×D₄	—	2	4	no	—
259	C₄×D₄	—	2	4	no	—
260	C₄×D₄	—	2	4	no	—
261	C₄×D₄	—	2	2	no	—
262	C₄×D₄	—	2	2	no	—
263	C₄×D₄	C₂×C₄×C₂₃	1	4	yes	complemented
264	#117	—	2	2	no	—
265	#117	—	2	4	no	—
266	#117	—	2	2	no	—
267	#117	C₂³×C₂₃	1	2	yes	—
268	C₂×C₄²	—	2	2	no	—
269	C₂×C₄²	—	2	2	no	—
270	C₂×C₄²	—	2	8	no	—
271	C₂×C₄²	C₂×C₄×C₂₃	1	2	yes	—
272	C₂×C₄²	C₂×C₄×C₂₃	1	2	yes	—
273	C₂×C₄²	D₄×C₂₃	1	2	yes	—
274	C₂×C₄²	D₄×C₂₃	1	2	yes	—
275	C₂×C₄²	D₄×C₂₃	1	2	yes	—
276	C₂×C₄²	C₂³×C₂₃	1	4	yes	—
277	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
278	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
279	C₄⋊C₈	—	2	4	no	—
280	#104	—	2	16	no	—
281	C₂²⋊C₈	—	2	4	no	—
282	#97	—	2	2	no	—
283	C₄×C₈	—	2	2	no	—
284	#95	—	2	4	no	—
285	#95	—	2	4	no	—
286	C₂₃	#21417	1	1	yes	characteristic, direct product factor, Sylow
287	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
288	#41	—	2	8	no	—
289	#41	—	4	8	no	—
290	C₂×Q₈	—	2	2	no	—
291	C₂×Q₈	C₂²×C₄×C₂₃	1	2	yes	—
292	C₂×D₄	—	2	4	no	—
293	C₂×D₄	—	2	2	no	—
294	C₂×D₄	—	2	2	no	—
295	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
296	C₂²×C₄	—	2	4	no	—
297	C₂²×C₄	—	2	8	no	—
298	C₂²×C₄	—	2	4	no	—
299	C₂²×C₄	—	2	4	no	—
300	C₂²×C₄	—	2	2	no	—
301	C₂²×C₄	—	4	4	no	—
302	C₂²×C₄	—	4	8	no	—
303	C₂²×C₄	C₂²⋊C₄×C₂₃	1	2	yes	—
304	C₂²×C₄	C₂²⋊C₄×C₂₃	1	2	yes	—
305	C₂²×C₄	C₂²⋊C₄×C₂₃	1	2	yes	—
306	C₂²×C₄	C₂²⋊C₄×C₂₃	1	2	yes	—
307	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
308	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
309	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
310	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
311	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
312	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
313	M₁₆	—	2	8	no	—
314	C₂×C₈	—	2	4	no	—
315	C₄⋊C₄	—	2	2	no	—
316	C₄⋊C₄	—	2	2	no	—
317	C₄⋊C₄	—	2	4	no	—
318	C₄⋊C₄	—	2	4	no	—
319	C₄⋊C₄	—	2	4	no	—
320	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
321	C₂²⋊C₄	—	2	4	no	—
322	C₂²⋊C₄	—	2	2	no	—
323	C₂²⋊C₄	—	2	4	no	—
324	C₂²⋊C₄	—	2	4	no	—
325	C₂²⋊C₄	—	2	4	no	—
326	C₄²	—	2	8	no	—
327	C₄²	—	2	4	no	—
328	C₄²	—	2	2	no	—
329	C₄²	—	2	4	no	—
330	C₄²	C₂²⋊C₄×C₂₃	1	2	yes	—
331	C₄²	C₂²⋊C₄×C₂₃	1	2	yes	—
332	C₄²	C₂²⋊C₄×C₂₃	1	2	yes	—
333	C₄²	C₂²⋊C₄×C₂₃	1	2	yes	—
334	C₄²	C₂²×C₄×C₂₃	1	2	yes	—
335	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
336	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
337	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
338	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
339	C₄²	C₂×D₄×C₂₃	1	2	yes	—
340	C₄²	#41×C₂₃	1	8	yes	complemented
341	C₂³	—	2	4	no	—
342	C₂³	—	2	2	no	—
343	C₂³	—	2	2	no	—
344	C₂³	C₂×C₂²⋊C₄×C₂₃	1	2	yes	—
345	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
346	Q₈	—	2	4	no	—
347	Q₈	—	4	4	no	—
348	D₄	—	2	4	no	—
349	D₄	—	4	4	no	—
350	D₄	—	4	8	no	—
351	D₄	—	4	4	no	—
352	C₂×C₄	—	2	4	no	—
353	C₂×C₄	—	2	4	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	4	no	—
356	C₂×C₄	—	2	4	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	4	no	—
359	C₂×C₄	—	2	8	no	—
360	C₂×C₄	—	4	2	no	—
361	C₂×C₄	—	4	2	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	—	4	2	no	—
364	C₂×C₄	—	4	8	no	—
365	C₂×C₄	—	4	16	no	—
366	C₂×C₄	—	4	8	no	—
367	C₂×C₄	—	4	4	no	—
368	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	2	yes	—
369	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	2	yes	—
370	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	2	yes	—
371	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	2	yes	—
372	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	2	yes	—
373	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
374	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
375	C₂×C₄	C₂×#41×C₂₃	1	4	yes	—
376	C₈	—	4	4	no	—
377	C₂²	—	2	8	no	—
378	C₂²	—	2	2	no	—
379	C₂²	—	2	2	no	—
380	C₂²	—	2	2	no	—
381	C₂²	—	4	2	no	—
382	C₂²	—	4	4	no	—
383	C₂²	C₂₃×#421	1	4	yes	—
384	C₂²	C₂²×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
385	C₂²	C₂₃×#525	1	2	yes	—
386	C₄	—	2	2	no	—
387	C₄	—	2	2	no	—
388	C₄	—	2	2	no	—
389	C₄	—	2	2	no	—
390	C₄	—	2	2	no	—
391	C₄	—	4	8	no	—
392	C₄	—	4	2	no	—
393	C₄	—	4	4	no	—
394	C₄	C₄×#41×C₂₃	1	2	yes	—
395	C₄	C₂₃×#532	1	2	yes	—
396	C₂	—	2	2	no	—
397	C₂	—	2	4	no	—
398	C₂	—	8	2	no	—
399	C₂	C₂₃×#2297	1	1	yes	characteristic
400	C₂	C₂×C₂₃×#421	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₂₃	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₂₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₃
socle	C₂²×C₂₃	C₂²×C₂²⋊C₄
prime radical	C₂₃×#3444	C₂
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
2. C₂₃×#2920	C₂	semidirect
3. C₂×C₂₃×#376	C₂	semidirect
4. C₂₃×#1995	C₂	semidirect
5. C₂₃×#1963	C₂	semidirect
6. C₂₃×#1896	C₂	semidirect
7. C₂₃×#1759	C₂	semidirect
8. C₂₃×#533	C₄	semidirect
10. C₂₃×#532	C₄	semidirect
14. C₂₃×#529	C₄	semidirect
38. C₂₃×C₄⋊Q₈	C₂×C₄	semidirect
39. C₂₃×C₄⋊Q₈	C₂×C₄	semidirect
40. C₂₃×#127	C₂×C₄	semidirect
43. C₂₃×#125	C₂×C₄	semidirect
45. C₂₃×#124	C₂×C₄	semidirect
57. C₄×Q₈×C₂₃	C₂×C₄	semidirect
63. C₄×D₄×C₂₃	C₂×C₄	semidirect
139. C₄²×C₂₃	#41	semidirect
140. #21417	C₂₃	direct (N × H)
178. #2920	C₂×C₂₃	semidirect
179. C₂×#376	C₂×C₂₃	semidirect
180. #1995	C₂×C₂₃	semidirect
181. #1963	C₂×C₂₃	semidirect
182. #1896	C₂×C₂₃	semidirect
183. #1759	C₂×C₂₃	semidirect
203. #533	C₄×C₂₃	semidirect
205. #532	C₄×C₂₃	semidirect
209. #529	C₄×C₂₃	semidirect
238. C₄⋊Q₈	C₂×C₄×C₂₃	semidirect
239. C₄⋊Q₈	C₂×C₄×C₂₃	semidirect
240. #127	C₂×C₄×C₂₃	semidirect
243. #125	C₂×C₄×C₂₃	semidirect
245. #124	C₂×C₄×C₂₃	semidirect
257. C₄×Q₈	C₂×C₄×C₂₃	semidirect
263. C₄×D₄	C₂×C₄×C₂₃	semidirect
286. C₂₃	#21417	direct (N × H)
340. C₄²	#41×C₂₃	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂₃×#3444	2
C₂₃×#2920	2
C₂×C₂₃×#376	2
C₂₃×#1995	2
C₂₃×#1963	2
C₂₃×#1896	2
C₂₃×#1759	2
#21417	23

Subgroups — C23×#21417 #19169043

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#21417 #19169043