Subgroups — C₂₃×#11204 #19158830

Order 5888.

778 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#423	C₂	1	1	yes	maximal, characteristic
2	C₂×C₂₃×#389	C₂	1	1	yes	maximal, characteristic
3	C₂×C₂₃×#343	C₂	1	2	yes	maximal
4	C₂×C₂₃×#343	C₂	1	2	yes	maximal
5	C₂₃×#1728	C₂	1	1	yes	maximal, characteristic
6	C₂²×M₁₆×C₂₃	C₂²	1	2	yes	—
7	C₂²×M₁₆×C₂₃	C₂²	1	2	yes	—
8	C₂²×C₄⋊C₄×C₂₃	C₄	1	2	yes	—
9	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
10	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
11	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
12	C₂₃×#423	—	2	4	no	—
13	C₂×C₂₃×C₄⋊C₈	—	2	1	no	—
14	C₂×C₂₃×C₄⋊C₈	—	2	1	no	—
15	C₂₃×#389	—	2	1	no	—
16	C₂₃×#389	—	2	1	no	—
17	C₂₃×#389	—	2	1	no	—
18	C₂₃×#389	—	2	1	no	—
19	C₂×C₂₃×#95	C₄	1	2	yes	—
20	C₂₃×#343	—	2	4	no	—
21	C₂₃×#343	—	2	4	no	—
22	C₂₃×#336	—	2	1	no	—
23	C₂₃×#336	—	2	1	no	—
24	C₂³×C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
25	C₂³×C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
26	C₂³×C₄×C₂₃	C₂×C₄	1	2	yes	—
27	C₂³×C₄×C₂₃	C₂×C₄	1	2	yes	—
28	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
29	C₂×M₁₆×C₂₃	—	2	2	no	—
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	—	2	2	no	—
34	C₂×M₁₆×C₂₃	—	2	2	no	—
35	C₂×M₁₆×C₂₃	—	2	2	no	—
36	C₂×M₁₆×C₂₃	—	2	2	no	—
37	C₂×M₁₆×C₂₃	—	2	2	no	—
38	C₂×M₁₆×C₂₃	—	2	2	no	—
39	C₂×M₁₆×C₂₃	D₄	1	4	yes	—
40	C₂×M₁₆×C₂₃	Q₈	1	4	yes	—
41	C₂²×C₈×C₂₃	—	2	2	no	—
42	C₂²×C₈×C₂₃	—	2	2	no	—
43	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
44	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
45	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
46	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
47	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
48	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
49	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
50	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
51	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
52	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
53	C₂×C₄⋊C₄×C₂₃	—	4	4	no	—
54	C₂×C₄⋊C₄×C₂₃	D₄	1	2	yes	—
55	C₂×C₄⋊C₄×C₂₃	Q₈	1	2	yes	—
56	C₂×C₄²×C₂₃	—	2	2	no	—
57	C₂×C₄²×C₂₃	—	2	2	no	—
58	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
59	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
60	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
61	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
62	C₂₃×C₄⋊C₈	—	2	4	no	—
63	C₂₃×C₄⋊C₈	—	2	4	no	—
64	C₂₃×#95	—	2	2	no	—
65	C₂₃×#95	—	2	2	no	—
66	C₂⁴×C₂₃	C₂²×C₄	1	1	yes	characteristic
67	C₂²×C₄×C₂₃	—	2	2	no	—
68	C₂²×C₄×C₂₃	—	2	2	no	—
69	C₂²×C₄×C₂₃	—	2	2	no	—
70	C₂²×C₄×C₂₃	—	2	2	no	—
71	C₂²×C₄×C₂₃	—	2	2	no	—
72	C₂²×C₄×C₂₃	—	2	2	no	—
73	C₂²×C₄×C₂₃	—	2	2	no	—
74	C₂²×C₄×C₂₃	—	2	4	no	—
75	C₂²×C₄×C₂₃	—	4	1	no	—
76	C₂²×C₄×C₂₃	—	4	1	no	—
77	C₂²×C₄×C₂₃	—	4	2	no	—
78	C₂²×C₄×C₂₃	—	4	2	no	—
79	C₂²×C₄×C₂₃	—	4	2	no	—
80	C₂²×C₄×C₂₃	—	4	2	no	—
81	C₂²×C₄×C₂₃	C₂²⋊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	C₄⋊C₄	1	4	yes	—
86	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
87	C₂²×C₄×C₂₃	C₂×D₄	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×Q₈	1	2	yes	—
91	C₂²×C₄×C₂₃	C₂×Q₈	1	1	yes	characteristic
92	C₂²×C₄×C₂₃	#41	1	1	yes	characteristic
93	C₂²×C₄×C₂₃	#41	1	1	yes	characteristic
94	C₂²×C₄×C₂₃	#41	1	2	yes	—
95	C₂²×C₄×C₂₃	#41	1	2	yes	—
96	M₁₆×C₂₃	—	2	4	no	—
97	M₁₆×C₂₃	—	2	4	no	—
98	M₁₆×C₂₃	—	2	4	no	—
99	M₁₆×C₂₃	—	2	4	no	—
100	M₁₆×C₂₃	—	4	2	no	—
101	M₁₆×C₂₃	—	4	2	no	—
102	M₁₆×C₂₃	—	4	2	no	—
103	M₁₆×C₂₃	—	4	2	no	—
104	C₂×C₈×C₂₃	—	2	4	no	—
105	C₂×C₈×C₂₃	—	2	4	no	—
106	C₂×C₈×C₂₃	—	4	2	no	—
107	C₂×C₈×C₂₃	—	4	2	no	—
108	C₂×C₈×C₂₃	—	4	2	no	—
109	C₂×C₈×C₂₃	—	4	2	no	—
110	C₄⋊C₄×C₂₃	—	2	2	no	—
111	C₄⋊C₄×C₂₃	—	2	2	no	—
112	C₄⋊C₄×C₂₃	—	2	2	no	—
113	C₄⋊C₄×C₂₃	—	2	2	no	—
114	C₄⋊C₄×C₂₃	—	4	4	no	—
115	C₄⋊C₄×C₂₃	—	4	4	no	—
116	C₄⋊C₄×C₂₃	—	4	1	no	—
117	C₄⋊C₄×C₂₃	—	4	2	no	—
118	C₄⋊C₄×C₂₃	—	4	1	no	—
119	C₄²×C₂₃	—	2	1	no	—
120	C₄²×C₂₃	—	2	1	no	—
121	C₄²×C₂₃	—	2	2	no	—
122	C₄²×C₂₃	—	2	2	no	—
123	C₄²×C₂₃	—	2	1	no	—
124	C₄²×C₂₃	—	2	1	no	—
125	#11204	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
126	C₂³×C₂₃	—	2	1	no	—
127	C₂³×C₂₃	—	2	1	no	—
128	C₂³×C₂₃	—	2	1	no	—
129	C₂³×C₂₃	—	2	1	no	—
130	C₂³×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
131	C₂³×C₂₃	C₂×C₄⋊C₄	1	1	yes	characteristic
132	C₂³×C₂₃	#117	1	1	yes	characteristic
133	C₂³×C₂₃	C₄×D₄	1	2	yes	—
134	C₂³×C₂₃	C₄×Q₈	1	2	yes	—
135	C₂×C₄×C₂₃	—	2	1	no	—
136	C₂×C₄×C₂₃	—	2	1	no	—
137	C₂×C₄×C₂₃	—	2	1	no	—
138	C₂×C₄×C₂₃	—	2	1	no	—
139	C₂×C₄×C₂₃	—	2	4	no	—
140	C₂×C₄×C₂₃	—	2	1	no	—
141	C₂×C₄×C₂₃	—	2	1	no	—
142	C₂×C₄×C₂₃	—	2	1	no	—
143	C₂×C₄×C₂₃	—	2	1	no	—
144	C₂×C₄×C₂₃	—	2	1	no	—
145	C₂×C₄×C₂₃	—	2	1	no	—
146	C₂×C₄×C₂₃	—	4	4	no	—
147	C₂×C₄×C₂₃	—	4	4	no	—
148	C₂×C₄×C₂₃	—	4	4	no	—
149	C₂×C₄×C₂₃	—	4	2	no	—
150	C₂×C₄×C₂₃	—	4	2	no	—
151	C₂×C₄×C₂₃	—	4	4	no	—
152	C₂×C₄×C₂₃	—	4	2	no	—
153	C₂×C₄×C₂₃	—	4	2	no	—
154	C₂×C₄×C₂₃	—	4	2	no	—
155	C₂×C₄×C₂₃	—	8	4	no	—
156	C₂×C₄×C₂₃	#100	1	2	yes	—
157	C₂×C₄×C₂₃	#101	1	2	yes	—
158	C₂×C₄×C₂₃	#120	1	1	yes	characteristic
159	C₂×C₄×C₂₃	#121	1	2	yes	—
160	C₂×C₄×C₂₃	#121	1	1	yes	characteristic
161	C₂×C₄×C₂₃	#121	1	1	yes	characteristic
162	C₂×C₄×C₂₃	#121	1	2	yes	—
163	C₂×C₄×C₂₃	C₂²⋊Q₈	1	2	yes	—
164	C₂×C₄×C₂₃	C₂²⋊Q₈	1	1	yes	characteristic
165	C₂×C₄×C₂₃	C₂²⋊Q₈	1	2	yes	—
166	C₂×C₄×C₂₃	C₂²⋊Q₈	1	2	yes	—
167	C₂×C₄×C₂₃	C₂²⋊Q₈	1	1	yes	characteristic
168	C₂×C₄×C₂₃	#123	1	2	yes	—
169	C₂×C₄×C₂₃	#123	1	1	yes	characteristic
170	C₂×C₄×C₂₃	#124	1	1	yes	characteristic
171	C₂×C₄×C₂₃	#125	1	2	yes	—
172	C₂×C₄×C₂₃	#125	1	2	yes	—
173	C₂×C₄×C₂₃	#126	1	2	yes	—
174	C₂×C₄×C₂₃	C₄⋊Q₈	1	2	yes	—
175	C₂×C₄×C₂₃	C₄⋊Q₈	1	1	yes	characteristic
176	C₈×C₂₃	—	4	4	no	—
177	C₈×C₂₃	—	4	4	no	—
178	C₂×#423	C₂×C₂₃	1	1	yes	characteristic
179	C₂×#389	C₂×C₂₃	1	1	yes	characteristic
180	C₂×#343	C₂×C₂₃	1	2	yes	—
181	C₂×#343	C₂×C₂₃	1	2	yes	—
182	#1728	C₂×C₂₃	1	1	yes	characteristic
183	C₂²×C₂₃	—	2	1	no	—
184	C₂²×C₂₃	—	2	1	no	—
185	C₂²×C₂₃	—	2	1	no	—
186	C₂²×C₂₃	—	2	1	no	—
187	C₂²×C₂₃	—	2	2	no	—
188	C₂²×C₂₃	—	2	2	no	—
189	C₂²×C₂₃	—	2	2	no	—
190	C₂²×C₂₃	—	2	2	no	—
191	C₂²×C₂₃	#380	1	1	yes	characteristic
192	C₂²×C₂₃	#386	1	1	yes	characteristic
193	C₂²×C₂₃	#387	1	2	yes	—
194	C₂²×C₂₃	#389	1	2	yes	—
195	C₂²×C₂₃	#391	1	1	yes	characteristic
196	C₂²×C₂₃	C₂×#100	1	1	yes	characteristic
197	C₂²×C₂₃	C₂×#101	1	1	yes	characteristic
198	C₂²×C₂₃	#413	1	1	yes	characteristic
199	C₂²×C₂₃	#413	1	1	yes	characteristic
200	C₄×C₂₃	—	2	2	no	—
201	C₄×C₂₃	—	2	2	no	—
202	C₄×C₂₃	—	4	4	no	—
203	C₄×C₂₃	—	4	1	no	—
204	C₄×C₂₃	—	4	1	no	—
205	C₄×C₂₃	—	8	2	no	—
206	C₄×C₂₃	#394	1	1	yes	characteristic
207	C₄×C₂₃	#395	1	1	yes	characteristic
208	C₄×C₂₃	#396	1	2	yes	—
209	C₄×C₂₃	#398	1	1	yes	characteristic
210	C₄×C₂₃	#398	1	2	yes	—
211	C₄×C₂₃	#400	1	1	yes	characteristic
212	C₂²×M₁₆	C₂²×C₂₃	1	2	yes	—
213	C₂²×M₁₆	C₂²×C₂₃	1	2	yes	—
214	C₂²×C₄⋊C₄	C₄×C₂₃	1	2	yes	—
215	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
216	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
217	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
218	#423	—	2	4	no	—
219	C₂×C₄⋊C₈	—	2	1	no	—
220	C₂×C₄⋊C₈	—	2	1	no	—
221	#389	—	2	1	no	—
222	#389	—	2	1	no	—
223	#389	—	2	1	no	—
224	#389	—	2	1	no	—
225	C₂×#95	C₄×C₂₃	1	2	yes	—
226	#343	—	2	4	no	—
227	#343	—	2	4	no	—
228	#336	—	2	1	no	—
229	#336	—	2	1	no	—
230	C₂×C₂₃	—	2	2	no	—
231	C₂×C₂₃	—	2	2	no	—
232	C₂×C₂₃	#1441	1	1	yes	characteristic
233	C₂×C₂₃	#1800	1	1	yes	characteristic
234	C₂×C₂₃	#1801	1	1	yes	characteristic
235	C₂×C₂₃	#1900	1	1	yes	characteristic
236	C₂×C₂₃	#1901	1	1	yes	characteristic
237	C₂×C₂₃	#1997	1	1	yes	characteristic
238	C₂×C₂₃	#1998	1	1	yes	characteristic
239	C₂³×C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
240	C₂³×C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
241	C₂³×C₄	C₂×C₄×C₂₃	1	2	yes	—
242	C₂³×C₄	C₂×C₄×C₂₃	1	2	yes	—
243	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
244	C₂×M₁₆	—	2	2	no	—
245	C₂×M₁₆	—	2	2	no	—
246	C₂×M₁₆	—	2	2	no	—
247	C₂×M₁₆	—	2	2	no	—
248	C₂×M₁₆	—	2	2	no	—
249	C₂×M₁₆	—	2	2	no	—
250	C₂×M₁₆	—	2	2	no	—
251	C₂×M₁₆	—	2	2	no	—
252	C₂×M₁₆	—	2	2	no	—
253	C₂×M₁₆	—	2	2	no	—
254	C₂×M₁₆	D₄×C₂₃	1	4	yes	—
255	C₂×M₁₆	Q₈×C₂₃	1	4	yes	—
256	C₂²×C₈	—	2	2	no	—
257	C₂²×C₈	—	2	2	no	—
258	C₂×C₄⋊C₄	—	2	1	no	—
259	C₂×C₄⋊C₄	—	2	1	no	—
260	C₂×C₄⋊C₄	—	2	1	no	—
261	C₂×C₄⋊C₄	—	2	1	no	—
262	C₂×C₄⋊C₄	—	2	2	no	—
263	C₂×C₄⋊C₄	—	2	2	no	—
264	C₂×C₄⋊C₄	—	2	2	no	—
265	C₂×C₄⋊C₄	—	2	1	no	—
266	C₂×C₄⋊C₄	—	2	1	no	—
267	C₂×C₄⋊C₄	—	2	2	no	—
268	C₂×C₄⋊C₄	—	4	4	no	—
269	C₂×C₄⋊C₄	D₄×C₂₃	1	2	yes	—
270	C₂×C₄⋊C₄	Q₈×C₂₃	1	2	yes	—
271	C₂×C₄²	—	2	2	no	—
272	C₂×C₄²	—	2	2	no	—
273	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
274	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
275	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
276	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
277	C₄⋊C₈	—	2	4	no	—
278	C₄⋊C₈	—	2	4	no	—
279	#95	—	2	2	no	—
280	#95	—	2	2	no	—
281	C₂₃	#11204	1	1	yes	characteristic, direct product factor, Sylow
282	C₂⁴	C₂²×C₄×C₂₃	1	1	yes	characteristic
283	C₂²×C₄	—	2	2	no	—
284	C₂²×C₄	—	2	2	no	—
285	C₂²×C₄	—	2	2	no	—
286	C₂²×C₄	—	2	2	no	—
287	C₂²×C₄	—	2	2	no	—
288	C₂²×C₄	—	2	2	no	—
289	C₂²×C₄	—	2	2	no	—
290	C₂²×C₄	—	2	4	no	—
291	C₂²×C₄	—	4	1	no	—
292	C₂²×C₄	—	4	1	no	—
293	C₂²×C₄	—	4	2	no	—
294	C₂²×C₄	—	4	2	no	—
295	C₂²×C₄	—	4	2	no	—
296	C₂²×C₄	—	4	2	no	—
297	C₂²×C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
298	C₂²×C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
299	C₂²×C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
300	C₂²×C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
301	C₂²×C₄	C₄⋊C₄×C₂₃	1	4	yes	—
302	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
303	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
304	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
305	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
306	C₂²×C₄	C₂×Q₈×C₂₃	1	2	yes	—
307	C₂²×C₄	C₂×Q₈×C₂₃	1	1	yes	characteristic
308	C₂²×C₄	#41×C₂₃	1	1	yes	characteristic
309	C₂²×C₄	#41×C₂₃	1	1	yes	characteristic
310	C₂²×C₄	#41×C₂₃	1	2	yes	—
311	C₂²×C₄	#41×C₂₃	1	2	yes	—
312	M₁₆	—	2	4	no	—
313	M₁₆	—	2	4	no	—
314	M₁₆	—	2	4	no	—
315	M₁₆	—	2	4	no	—
316	M₁₆	—	4	2	no	—
317	M₁₆	—	4	2	no	—
318	M₁₆	—	4	2	no	—
319	M₁₆	—	4	2	no	—
320	C₂×C₈	—	2	4	no	—
321	C₂×C₈	—	2	4	no	—
322	C₂×C₈	—	4	2	no	—
323	C₂×C₈	—	4	2	no	—
324	C₂×C₈	—	4	2	no	—
325	C₂×C₈	—	4	2	no	—
326	C₄⋊C₄	—	2	2	no	—
327	C₄⋊C₄	—	2	2	no	—
328	C₄⋊C₄	—	2	2	no	—
329	C₄⋊C₄	—	2	2	no	—
330	C₄⋊C₄	—	4	4	no	—
331	C₄⋊C₄	—	4	4	no	—
332	C₄⋊C₄	—	4	1	no	—
333	C₄⋊C₄	—	4	2	no	—
334	C₄⋊C₄	—	4	1	no	—
335	C₄²	—	2	1	no	—
336	C₄²	—	2	1	no	—
337	C₄²	—	2	2	no	—
338	C₄²	—	2	2	no	—
339	C₄²	—	2	1	no	—
340	C₄²	—	2	1	no	—
341	C₂³	—	2	1	no	—
342	C₂³	—	2	1	no	—
343	C₂³	—	2	1	no	—
344	C₂³	—	2	1	no	—
345	C₂³	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
346	C₂³	C₂×C₄⋊C₄×C₂₃	1	1	yes	characteristic
347	C₂³	C₂₃×#117	1	1	yes	characteristic
348	C₂³	C₄×D₄×C₂₃	1	2	yes	—
349	C₂³	C₄×Q₈×C₂₃	1	2	yes	—
350	C₂×C₄	—	2	1	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	2	1	no	—
354	C₂×C₄	—	2	4	no	—
355	C₂×C₄	—	2	1	no	—
356	C₂×C₄	—	2	1	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	2	1	no	—
361	C₂×C₄	—	4	4	no	—
362	C₂×C₄	—	4	4	no	—
363	C₂×C₄	—	4	4	no	—
364	C₂×C₄	—	4	2	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	4	4	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	8	4	no	—
371	C₂×C₄	C₂₃×#100	1	2	yes	—
372	C₂×C₄	C₂₃×#101	1	2	yes	—
373	C₂×C₄	C₂₃×#120	1	1	yes	characteristic
374	C₂×C₄	C₂₃×#121	1	2	yes	—
375	C₂×C₄	C₂₃×#121	1	1	yes	characteristic
376	C₂×C₄	C₂₃×#121	1	1	yes	characteristic
377	C₂×C₄	C₂₃×#121	1	2	yes	—
378	C₂×C₄	C₂₃×C₂²⋊Q₈	1	2	yes	—
379	C₂×C₄	C₂₃×C₂²⋊Q₈	1	1	yes	characteristic
380	C₂×C₄	C₂₃×C₂²⋊Q₈	1	2	yes	—
381	C₂×C₄	C₂₃×C₂²⋊Q₈	1	2	yes	—
382	C₂×C₄	C₂₃×C₂²⋊Q₈	1	1	yes	characteristic
383	C₂×C₄	C₂₃×#123	1	2	yes	—
384	C₂×C₄	C₂₃×#123	1	1	yes	characteristic
385	C₂×C₄	C₂₃×#124	1	1	yes	characteristic
386	C₂×C₄	C₂₃×#125	1	2	yes	—
387	C₂×C₄	C₂₃×#125	1	2	yes	—
388	C₂×C₄	C₂₃×#126	1	2	yes	—
389	C₂×C₄	C₂₃×C₄⋊Q₈	1	2	yes	—
390	C₂×C₄	C₂₃×C₄⋊Q₈	1	1	yes	characteristic
391	C₈	—	4	4	no	—
392	C₈	—	4	4	no	—
393	C₂²	—	2	2	no	—
394	C₂²	—	2	2	no	—
395	C₂²	—	2	2	no	—
396	C₂²	—	2	2	no	—
397	C₂²	—	2	1	no	—
398	C₂²	—	2	1	no	—
399	C₂²	—	2	1	no	—
400	C₂²	—	2	1	no	—
401	C₂²	C₂₃×#380	1	1	yes	characteristic
402	C₂²	C₂₃×#386	1	1	yes	characteristic
403	C₂²	C₂₃×#387	1	2	yes	—
404	C₂²	C₂₃×#389	1	2	yes	—
405	C₂²	C₂₃×#391	1	1	yes	characteristic
406	C₂²	C₂×C₂₃×#100	1	1	yes	characteristic
407	C₂²	C₂×C₂₃×#101	1	1	yes	characteristic
408	C₂²	C₂₃×#413	1	1	yes	characteristic
409	C₂²	C₂₃×#413	1	1	yes	characteristic
410	C₄	—	2	2	no	—
411	C₄	—	2	2	no	—
412	C₄	—	4	1	no	—
413	C₄	—	4	1	no	—
414	C₄	—	4	4	no	—
415	C₄	—	8	2	no	—
416	C₄	C₂₃×#394	1	1	yes	characteristic
417	C₄	C₂₃×#395	1	1	yes	characteristic
418	C₄	C₂₃×#396	1	2	yes	—
419	C₄	C₂₃×#398	1	1	yes	characteristic
420	C₄	C₂₃×#398	1	2	yes	—
421	C₄	C₂₃×#400	1	1	yes	characteristic
422	C₂	—	2	2	no	—
423	C₂	—	2	2	no	—
424	C₂	C₂₃×#1441	1	1	yes	characteristic
425	C₂	C₂₃×#1800	1	1	yes	characteristic
426	C₂	C₂₃×#1801	1	1	yes	characteristic
427	C₂	C₂₃×#1900	1	1	yes	characteristic
428	C₂	C₂₃×#1901	1	1	yes	characteristic
429	C₂	C₂₃×#1997	1	1	yes	characteristic
430	C₂	C₂₃×#1998	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
125. #11204	C₂₃	direct (N × H)
281. C₂₃	#11204	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×#423	2
C₂×C₂₃×#389	2
C₂×C₂₃×#343	2
C₂₃×#1728	2
#11204	23

Subgroups — C23×#11204 #19158830

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#11204 #19158830