Subgroups — C₂₃×#19382 #19167008

Order 5888.

594 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3251	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#3238	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3141	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#2969	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#1704	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#1703	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#1698	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#1697	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#1684	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#1683	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#1678	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#1677	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#1569	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#1553	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#1548	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₃×#532	C₂²	1	1	yes	characteristic
17	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
18	C₂₃×#529	C₂²	1	1	yes	characteristic
19	C₂₃×#501	—	2	1	no	—
20	C₂₃×#489	—	2	1	no	—
21	C₂₃×#489	—	2	1	no	—
22	C₂₃×#489	—	2	1	no	—
23	C₂₃×#487	C₂²	1	1	yes	characteristic
24	C₂₃×#487	C₂²	1	1	yes	characteristic
25	C₂₃×#486	C₂²	1	1	yes	characteristic
26	C₂₃×#486	C₂²	1	1	yes	characteristic
27	C₂₃×#483	—	2	1	no	—
28	C₂₃×#480	—	2	1	no	—
29	C₂₃×#478	—	2	1	no	—
30	C₂₃×#477	C₂²	1	1	yes	characteristic
31	C₂₃×#477	C₂²	1	1	yes	characteristic
32	C₂₃×#476	C₂²	1	1	yes	characteristic
33	C₂₃×#476	C₂²	1	1	yes	characteristic
34	C₂₃×#475	C₂²	1	1	yes	characteristic
35	C₂₃×#474	C₂²	1	1	yes	characteristic
36	C₂₃×#469	—	2	1	no	—
37	C₂₃×#468	—	2	1	no	—
38	C₂₃×#463	—	2	1	no	—
39	C₂₃×#460	C₂²	1	1	yes	characteristic
40	C₂₃×#459	C₂²	1	1	yes	characteristic
41	C₂₃×#446	C₂²	1	1	yes	characteristic
42	C₈×Q₈×C₂₃	C₂²	1	1	yes	characteristic
43	C₂₃×#436	—	2	1	no	—
44	C₂₃×#436	C₂²	1	1	yes	characteristic
45	C₂₃×#435	—	2	1	no	—
46	C₈×D₄×C₂₃	C₂²	1	1	yes	characteristic
47	C₂₃×#433	—	2	1	no	—
48	C₂₃×#432	C₂²	1	1	yes	characteristic
49	C₂₃×#431	C₂²	1	1	yes	characteristic
50	C₂₃×#423	C₂²	1	1	yes	characteristic
51	C₂₃×#417	—	2	1	no	—
52	C₂₃×#417	—	2	1	no	—
53	C₂₃×#405	—	2	1	no	—
54	C₄×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
55	C₂₃×#335	C₂²	1	1	yes	characteristic
56	C₂₃×#335	C₂²	1	1	yes	characteristic
57	C₂₃×#334	C₂²	1	1	yes	characteristic
58	C₂₃×#334	C₂²	1	1	yes	characteristic
59	C₂₃×#333	C₂²	1	1	yes	characteristic
60	C₂₃×#333	C₂²	1	1	yes	characteristic
61	C₂₃×#333	C₂²	1	1	yes	characteristic
62	C₂₃×#333	C₂²	1	1	yes	characteristic
63	C₂₃×#332	C₂²	1	1	yes	characteristic
64	C₂₃×#332	C₂²	1	1	yes	characteristic
65	C₂₃×#331	C₂²	1	1	yes	characteristic
66	C₂₃×#331	C₂²	1	1	yes	characteristic
67	C₂×#41×C₂₃	—	2	1	no	—
68	C₂²×Q₈×C₂₃	—	2	1	no	—
69	C₂×SD₁₆×C₂₃	—	2	1	no	—
70	C₂×D₈×C₂₃	—	2	1	no	—
71	C₂×M₁₆×C₂₃	—	2	1	no	—
72	C₂×M₁₆×C₂₃	—	2	1	no	—
73	C₂×M₁₆×C₂₃	D₄	1	1	yes	characteristic
74	C₂×M₁₆×C₂₃	D₄	1	1	yes	characteristic
75	C₂²×C₈×C₂₃	—	2	1	no	—
76	C₂₃×C₄⋊Q₈	—	2	1	no	—
77	C₂₃×C₄⋊Q₈	—	2	1	no	—
78	C₂₃×C₄⋊Q₈	—	2	1	no	—
79	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
80	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
81	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
82	C₂₃×#127	C₂³	1	1	yes	characteristic
83	C₂₃×#126	—	2	1	no	—
84	C₂₃×#125	D₄	1	1	yes	characteristic
85	C₂₃×#124	—	2	1	no	—
86	C₂₃×#124	D₄	1	1	yes	characteristic
87	C₂₃×#123	—	2	1	no	—
88	C₂₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
89	C₂₃×#121	—	2	1	no	—
90	C₂₃×#121	—	2	1	no	—
91	C₂₃×#121	D₄	1	1	yes	characteristic
92	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
93	C₄×D₄×C₂₃	—	2	1	no	—
94	C₄×D₄×C₂₃	—	2	1	no	—
95	C₄×D₄×C₂₃	—	2	1	no	—
96	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
97	C₂₃×#117	—	2	1	no	—
98	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
99	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
100	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
101	C₂₃×#107	—	2	1	no	—
102	C₂₃×#107	—	2	1	no	—
103	C₂₃×#107	—	2	1	no	—
104	C₂₃×#106	—	2	1	no	—
105	C₂₃×#106	—	2	1	no	—
106	C₂₃×#106	—	2	1	no	—
107	C₂₃×C₄⋊C₈	—	2	1	no	—
108	C₂₃×C₄⋊C₈	—	2	1	no	—
109	C₂₃×C₄⋊C₈	—	2	1	no	—
110	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
111	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
112	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
113	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
114	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
115	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
116	C₂₃×#103	—	2	1	no	—
117	C₂₃×#103	—	2	1	no	—
118	C₂₃×#103	—	2	1	no	—
119	C₂₃×#103	—	2	1	no	—
120	C₂₃×#103	—	2	1	no	—
121	C₂₃×#103	—	2	1	no	—
122	C₂₃×#103	—	2	1	no	—
123	C₂₃×#102	—	2	1	no	—
124	C₂₃×#102	—	2	1	no	—
125	C₂₃×#102	—	2	1	no	—
126	C₂₃×#102	—	2	1	no	—
127	C₂₃×#102	—	2	1	no	—
128	C₂₃×#102	—	2	1	no	—
129	C₂₃×#102	—	2	1	no	—
130	C₂₃×#102	—	2	1	no	—
131	C₂₃×#102	—	2	1	no	—
132	C₂₃×C₂²⋊C₈	—	2	1	no	—
133	C₂₃×C₂²⋊C₈	—	2	1	no	—
134	C₂₃×C₂²⋊C₈	—	2	1	no	—
135	C₂₃×C₂²⋊C₈	—	2	1	no	—
136	C₂₃×#97	—	2	1	no	—
137	C₂₃×#97	—	2	1	no	—
138	C₂₃×#97	D₄	1	1	yes	characteristic
139	C₂₃×#97	D₄	1	1	yes	characteristic
140	C₄×C₈×C₂₃	—	2	1	no	—
141	C₄×C₈×C₂₃	—	2	1	no	—
142	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
143	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
144	#41×C₂₃	—	4	2	no	—
145	#41×C₂₃	—	4	2	no	—
146	C₂×Q₈×C₂₃	—	2	1	no	—
147	C₂×Q₈×C₂₃	—	2	1	no	—
148	C₂×Q₈×C₂₃	—	2	1	no	—
149	C₂×Q₈×C₂₃	—	4	1	no	—
150	C₂×Q₈×C₂₃	—	8	2	no	—
151	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
152	C₂×D₄×C₂₃	—	2	1	no	—
153	C₂×D₄×C₂₃	—	2	1	no	—
154	C₂×D₄×C₂₃	—	2	1	no	—
155	C₂×D₄×C₂₃	—	2	1	no	—
156	C₂×D₄×C₂₃	—	4	1	no	—
157	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
158	C₂²×C₄×C₂₃	—	2	1	no	—
159	C₂²×C₄×C₂₃	—	4	1	no	—
160	C₂²×C₄×C₂₃	—	4	1	no	—
161	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
162	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
163	C₂²×C₄×C₂₃	#41	1	1	yes	characteristic
164	SD₁₆×C₂₃	—	8	1	no	—
165	D₈×C₂₃	—	8	1	no	—
166	M₁₆×C₂₃	—	4	1	no	—
167	M₁₆×C₂₃	—	4	1	no	—
168	M₁₆×C₂₃	—	4	2	no	—
169	M₁₆×C₂₃	—	8	1	no	—
170	C₂×C₈×C₂₃	—	2	1	no	—
171	C₂×C₈×C₂₃	—	2	1	no	—
172	C₂×C₈×C₂₃	—	2	1	no	—
173	C₂×C₈×C₂₃	—	2	1	no	—
174	C₂×C₈×C₂₃	—	2	1	no	—
175	C₂×C₈×C₂₃	—	2	1	no	—
176	C₂×C₈×C₂₃	—	4	2	no	—
177	C₂×C₈×C₂₃	C₂×D₄	1	1	yes	characteristic
178	C₂×C₈×C₂₃	C₂×D₄	1	1	yes	characteristic
179	C₂×C₈×C₂₃	C₂×D₄	1	1	yes	characteristic
180	C₂×C₈×C₂₃	C₂×D₄	1	1	yes	characteristic
181	C₄⋊C₄×C₂₃	—	2	1	no	—
182	C₄⋊C₄×C₂₃	—	2	1	no	—
183	C₄⋊C₄×C₂₃	—	2	1	no	—
184	C₄⋊C₄×C₂₃	—	2	1	no	—
185	C₄⋊C₄×C₂₃	—	2	1	no	—
186	C₄⋊C₄×C₂₃	—	2	1	no	—
187	C₄⋊C₄×C₂₃	—	2	1	no	—
188	C₄⋊C₄×C₂₃	—	2	1	no	—
189	C₄⋊C₄×C₂₃	—	2	1	no	—
190	C₄⋊C₄×C₂₃	—	2	1	no	—
191	C₄⋊C₄×C₂₃	—	4	1	no	—
192	C₄⋊C₄×C₂₃	—	4	1	no	—
193	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
194	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
195	C₂²⋊C₄×C₂₃	—	2	1	no	—
196	C₂²⋊C₄×C₂₃	—	2	1	no	—
197	C₂²⋊C₄×C₂₃	—	2	1	no	—
198	C₂²⋊C₄×C₂₃	—	2	1	no	—
199	C₂²⋊C₄×C₂₃	—	2	1	no	—
200	C₂²⋊C₄×C₂₃	—	4	1	no	—
201	C₂²⋊C₄×C₂₃	—	4	1	no	—
202	C₄²×C₂₃	—	2	1	no	—
203	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
204	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
205	C₄²×C₂₃	#41	1	1	yes	characteristic
206	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
207	#19382	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
208	C₂³×C₂₃	—	2	1	no	—
209	C₂³×C₂₃	—	4	1	no	—
210	C₂³×C₂₃	#121	1	1	yes	characteristic
211	Q₈×C₂₃	—	2	1	no	—
212	Q₈×C₂₃	—	2	1	no	—
213	Q₈×C₂₃	—	4	1	no	—
214	Q₈×C₂₃	—	4	1	no	—
215	Q₈×C₂₃	—	8	1	no	—
216	Q₈×C₂₃	—	8	1	no	—
217	Q₈×C₂₃	—	8	2	no	—
218	D₄×C₂₃	—	2	1	no	—
219	D₄×C₂₃	—	2	1	no	—
220	D₄×C₂₃	—	4	1	no	—
221	D₄×C₂₃	—	4	1	no	—
222	D₄×C₂₃	—	4	1	no	—
223	D₄×C₂₃	—	4	1	no	—
224	D₄×C₂₃	—	8	1	no	—
225	D₄×C₂₃	—	8	1	no	—
226	D₄×C₂₃	—	8	2	no	—
227	C₂×C₄×C₂₃	—	2	1	no	—
228	C₂×C₄×C₂₃	—	2	1	no	—
229	C₂×C₄×C₂₃	—	2	1	no	—
230	C₂×C₄×C₂₃	—	2	1	no	—
231	C₂×C₄×C₂₃	—	2	1	no	—
232	C₂×C₄×C₂₃	—	2	1	no	—
233	C₂×C₄×C₂₃	—	2	1	no	—
234	C₂×C₄×C₂₃	—	4	1	no	—
235	C₂×C₄×C₂₃	—	4	1	no	—
236	C₂×C₄×C₂₃	—	4	1	no	—
237	C₂×C₄×C₂₃	—	4	1	no	—
238	C₂×C₄×C₂₃	—	4	1	no	—
239	C₂×C₄×C₂₃	—	4	1	no	—
240	C₂×C₄×C₂₃	—	8	2	no	—
241	C₂×C₄×C₂₃	—	8	2	no	—
242	C₂×C₄×C₂₃	#121	1	1	yes	characteristic
243	C₂×C₄×C₂₃	#121	1	1	yes	characteristic
244	C₂×C₄×C₂₃	#121	1	1	yes	characteristic
245	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
246	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
247	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
248	C₈×C₂₃	—	2	1	no	—
249	C₈×C₂₃	—	2	1	no	—
250	C₈×C₂₃	—	2	1	no	—
251	C₈×C₂₃	—	2	1	no	—
252	C₈×C₂₃	—	4	1	no	—
253	C₈×C₂₃	—	4	1	no	—
254	C₈×C₂₃	—	4	1	no	—
255	C₈×C₂₃	—	4	1	no	—
256	C₈×C₂₃	—	4	1	no	—
257	C₈×C₂₃	—	4	1	no	—
258	#3251	C₂×C₂₃	1	1	yes	characteristic
259	#3238	C₂×C₂₃	1	1	yes	characteristic, complemented
260	#3141	C₂×C₂₃	1	1	yes	characteristic, complemented
261	#2969	C₂×C₂₃	1	1	yes	characteristic, complemented
262	#1704	C₂×C₂₃	1	1	yes	characteristic, complemented
263	#1703	C₂×C₂₃	1	1	yes	characteristic, complemented
264	#1698	C₂×C₂₃	1	1	yes	characteristic, complemented
265	#1697	C₂×C₂₃	1	1	yes	characteristic, complemented
266	#1684	C₂×C₂₃	1	1	yes	characteristic, complemented
267	#1683	C₂×C₂₃	1	1	yes	characteristic, complemented
268	#1678	C₂×C₂₃	1	1	yes	characteristic, complemented
269	#1677	C₂×C₂₃	1	1	yes	characteristic, complemented
270	#1569	C₂×C₂₃	1	1	yes	characteristic, complemented
271	#1553	C₂×C₂₃	1	1	yes	characteristic, complemented
272	#1548	C₂×C₂₃	1	1	yes	characteristic, complemented
273	C₂²×C₂₃	—	2	1	no	—
274	C₂²×C₂₃	—	2	1	no	—
275	C₂²×C₂₃	—	2	1	no	—
276	C₂²×C₂₃	—	4	1	no	—
277	C₂²×C₂₃	—	4	1	no	—
278	C₂²×C₂₃	—	4	1	no	—
279	C₂²×C₂₃	—	8	1	no	—
280	C₂²×C₂₃	—	8	1	no	—
281	C₂²×C₂₃	—	8	1	no	—
282	C₂²×C₂₃	C₂×#121	1	1	yes	characteristic
283	C₄×C₂₃	—	2	1	no	—
284	C₄×C₂₃	—	2	1	no	—
285	C₄×C₂₃	—	2	1	no	—
286	C₄×C₂₃	—	2	1	no	—
287	C₄×C₂₃	—	4	1	no	—
288	C₄×C₂₃	—	4	1	no	—
289	C₄×C₂₃	—	4	1	no	—
290	C₄×C₂₃	—	8	1	no	—
291	C₄×C₂₃	—	8	1	no	—
292	C₄×C₂₃	—	8	1	no	—
293	C₄×C₂₃	#575	1	1	yes	characteristic
294	C₄×C₂₃	#575	1	1	yes	characteristic
295	C₄×C₂₃	#577	1	1	yes	characteristic
296	C₄×C₂₃	#578	1	1	yes	characteristic
297	#532	C₂²×C₂₃	1	1	yes	characteristic
298	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
299	#529	C₂²×C₂₃	1	1	yes	characteristic
300	#501	—	2	1	no	—
301	#489	—	2	1	no	—
302	#489	—	2	1	no	—
303	#489	—	2	1	no	—
304	#487	C₂²×C₂₃	1	1	yes	characteristic
305	#487	C₂²×C₂₃	1	1	yes	characteristic
306	#486	C₂²×C₂₃	1	1	yes	characteristic
307	#486	C₂²×C₂₃	1	1	yes	characteristic
308	#483	—	2	1	no	—
309	#480	—	2	1	no	—
310	#478	—	2	1	no	—
311	#477	C₂²×C₂₃	1	1	yes	characteristic
312	#477	C₂²×C₂₃	1	1	yes	characteristic
313	#476	C₂²×C₂₃	1	1	yes	characteristic
314	#476	C₂²×C₂₃	1	1	yes	characteristic
315	#475	C₂²×C₂₃	1	1	yes	characteristic
316	#474	C₂²×C₂₃	1	1	yes	characteristic
317	#469	—	2	1	no	—
318	#468	—	2	1	no	—
319	#463	—	2	1	no	—
320	#460	C₂²×C₂₃	1	1	yes	characteristic
321	#459	C₂²×C₂₃	1	1	yes	characteristic
322	#446	C₂²×C₂₃	1	1	yes	characteristic
323	C₈×Q₈	C₂²×C₂₃	1	1	yes	characteristic
324	#436	—	2	1	no	—
325	#436	C₂²×C₂₃	1	1	yes	characteristic
326	#435	—	2	1	no	—
327	C₈×D₄	C₂²×C₂₃	1	1	yes	characteristic
328	#433	—	2	1	no	—
329	#432	C₂²×C₂₃	1	1	yes	characteristic
330	#431	C₂²×C₂₃	1	1	yes	characteristic
331	#423	C₂²×C₂₃	1	1	yes	characteristic
332	#417	—	2	1	no	—
333	#417	—	2	1	no	—
334	#405	—	2	1	no	—
335	C₄×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
336	#335	C₂²×C₂₃	1	1	yes	characteristic
337	#335	C₂²×C₂₃	1	1	yes	characteristic
338	#334	C₂²×C₂₃	1	1	yes	characteristic
339	#334	C₂²×C₂₃	1	1	yes	characteristic
340	#333	C₂²×C₂₃	1	1	yes	characteristic
341	#333	C₂²×C₂₃	1	1	yes	characteristic
342	#333	C₂²×C₂₃	1	1	yes	characteristic
343	#333	C₂²×C₂₃	1	1	yes	characteristic
344	#332	C₂²×C₂₃	1	1	yes	characteristic
345	#332	C₂²×C₂₃	1	1	yes	characteristic
346	#331	C₂²×C₂₃	1	1	yes	characteristic
347	#331	C₂²×C₂₃	1	1	yes	characteristic
348	C₂×C₂₃	—	4	1	no	—
349	C₂×C₂₃	—	8	1	no	—
350	C₂×C₂₃	—	16	1	no	—
351	C₂×C₂₃	#3040	1	1	yes	characteristic
352	C₂×C₂₃	#3063	1	1	yes	characteristic
353	C₂×C₂₃	#3068	1	1	yes	characteristic
354	C₂×#41	—	2	1	no	—
355	C₂²×Q₈	—	2	1	no	—
356	C₂×SD₁₆	—	2	1	no	—
357	C₂×D₈	—	2	1	no	—
358	C₂×M₁₆	—	2	1	no	—
359	C₂×M₁₆	—	2	1	no	—
360	C₂×M₁₆	D₄×C₂₃	1	1	yes	characteristic
361	C₂×M₁₆	D₄×C₂₃	1	1	yes	characteristic
362	C₂²×C₈	—	2	1	no	—
363	C₄⋊Q₈	—	2	1	no	—
364	C₄⋊Q₈	—	2	1	no	—
365	C₄⋊Q₈	—	2	1	no	—
366	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
367	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
368	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
369	#127	C₂³×C₂₃	1	1	yes	characteristic
370	#126	—	2	1	no	—
371	#125	D₄×C₂₃	1	1	yes	characteristic
372	#124	—	2	1	no	—
373	#124	D₄×C₂₃	1	1	yes	characteristic
374	#123	—	2	1	no	—
375	C₂²⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
376	#121	—	2	1	no	—
377	#121	—	2	1	no	—
378	#121	D₄×C₂₃	1	1	yes	characteristic
379	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
380	C₄×D₄	—	2	1	no	—
381	C₄×D₄	—	2	1	no	—
382	C₄×D₄	—	2	1	no	—
383	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
384	#117	—	2	1	no	—
385	C₂×C₄⋊C₄	—	2	1	no	—
386	C₂×C₄⋊C₄	—	2	1	no	—
387	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
388	#107	—	2	1	no	—
389	#107	—	2	1	no	—
390	#107	—	2	1	no	—
391	#106	—	2	1	no	—
392	#106	—	2	1	no	—
393	#106	—	2	1	no	—
394	C₄⋊C₈	—	2	1	no	—
395	C₄⋊C₈	—	2	1	no	—
396	C₄⋊C₈	—	2	1	no	—
397	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
398	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
399	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
400	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
401	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
402	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
403	#103	—	2	1	no	—
404	#103	—	2	1	no	—
405	#103	—	2	1	no	—
406	#103	—	2	1	no	—
407	#103	—	2	1	no	—
408	#103	—	2	1	no	—
409	#103	—	2	1	no	—
410	#102	—	2	1	no	—
411	#102	—	2	1	no	—
412	#102	—	2	1	no	—
413	#102	—	2	1	no	—
414	#102	—	2	1	no	—
415	#102	—	2	1	no	—
416	#102	—	2	1	no	—
417	#102	—	2	1	no	—
418	#102	—	2	1	no	—
419	C₂²⋊C₈	—	2	1	no	—
420	C₂²⋊C₈	—	2	1	no	—
421	C₂²⋊C₈	—	2	1	no	—
422	C₂²⋊C₈	—	2	1	no	—
423	#97	—	2	1	no	—
424	#97	—	2	1	no	—
425	#97	D₄×C₂₃	1	1	yes	characteristic
426	#97	D₄×C₂₃	1	1	yes	characteristic
427	C₄×C₈	—	2	1	no	—
428	C₄×C₈	—	2	1	no	—
429	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
430	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
431	C₂₃	#19382	1	1	yes	characteristic, direct product factor, Sylow
432	#41	—	4	2	no	—
433	#41	—	4	2	no	—
434	C₂×Q₈	—	2	1	no	—
435	C₂×Q₈	—	2	1	no	—
436	C₂×Q₈	—	2	1	no	—
437	C₂×Q₈	—	4	1	no	—
438	C₂×Q₈	—	8	2	no	—
439	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
440	C₂×D₄	—	2	1	no	—
441	C₂×D₄	—	2	1	no	—
442	C₂×D₄	—	2	1	no	—
443	C₂×D₄	—	2	1	no	—
444	C₂×D₄	—	4	1	no	—
445	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
446	C₂²×C₄	—	2	1	no	—
447	C₂²×C₄	—	4	1	no	—
448	C₂²×C₄	—	4	1	no	—
449	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
450	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
451	C₂²×C₄	#41×C₂₃	1	1	yes	characteristic
452	SD₁₆	—	8	1	no	—
453	D₈	—	8	1	no	—
454	M₁₆	—	4	1	no	—
455	M₁₆	—	4	1	no	—
456	M₁₆	—	4	2	no	—
457	M₁₆	—	8	1	no	—
458	C₂×C₈	—	2	1	no	—
459	C₂×C₈	—	2	1	no	—
460	C₂×C₈	—	2	1	no	—
461	C₂×C₈	—	2	1	no	—
462	C₂×C₈	—	2	1	no	—
463	C₂×C₈	—	2	1	no	—
464	C₂×C₈	—	4	2	no	—
465	C₂×C₈	C₂×D₄×C₂₃	1	1	yes	characteristic
466	C₂×C₈	C₂×D₄×C₂₃	1	1	yes	characteristic
467	C₂×C₈	C₂×D₄×C₂₃	1	1	yes	characteristic
468	C₂×C₈	C₂×D₄×C₂₃	1	1	yes	characteristic
469	C₄⋊C₄	—	2	1	no	—
470	C₄⋊C₄	—	2	1	no	—
471	C₄⋊C₄	—	2	1	no	—
472	C₄⋊C₄	—	2	1	no	—
473	C₄⋊C₄	—	2	1	no	—
474	C₄⋊C₄	—	2	1	no	—
475	C₄⋊C₄	—	2	1	no	—
476	C₄⋊C₄	—	2	1	no	—
477	C₄⋊C₄	—	2	1	no	—
478	C₄⋊C₄	—	2	1	no	—
479	C₄⋊C₄	—	4	1	no	—
480	C₄⋊C₄	—	4	1	no	—
481	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
482	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
483	C₂²⋊C₄	—	2	1	no	—
484	C₂²⋊C₄	—	2	1	no	—
485	C₂²⋊C₄	—	2	1	no	—
486	C₂²⋊C₄	—	2	1	no	—
487	C₂²⋊C₄	—	2	1	no	—
488	C₂²⋊C₄	—	4	1	no	—
489	C₂²⋊C₄	—	4	1	no	—
490	C₄²	—	2	1	no	—
491	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
492	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
493	C₄²	#41×C₂₃	1	1	yes	characteristic
494	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
495	C₂³	—	2	1	no	—
496	C₂³	—	4	1	no	—
497	C₂³	C₂₃×#121	1	1	yes	characteristic
498	Q₈	—	2	1	no	—
499	Q₈	—	2	1	no	—
500	Q₈	—	4	1	no	—
501	Q₈	—	4	1	no	—
502	Q₈	—	8	1	no	—
503	Q₈	—	8	1	no	—
504	Q₈	—	8	2	no	—
505	D₄	—	2	1	no	—
506	D₄	—	2	1	no	—
507	D₄	—	4	1	no	—
508	D₄	—	4	1	no	—
509	D₄	—	4	1	no	—
510	D₄	—	4	1	no	—
511	D₄	—	8	1	no	—
512	D₄	—	8	1	no	—
513	D₄	—	8	2	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	2	1	no	—
517	C₂×C₄	—	2	1	no	—
518	C₂×C₄	—	2	1	no	—
519	C₂×C₄	—	2	1	no	—
520	C₂×C₄	—	2	1	no	—
521	C₂×C₄	—	4	1	no	—
522	C₂×C₄	—	4	1	no	—
523	C₂×C₄	—	4	1	no	—
524	C₂×C₄	—	4	1	no	—
525	C₂×C₄	—	4	1	no	—
526	C₂×C₄	—	4	1	no	—
527	C₂×C₄	—	8	2	no	—
528	C₂×C₄	—	8	2	no	—
529	C₂×C₄	C₂₃×#121	1	1	yes	characteristic
530	C₂×C₄	C₂₃×#121	1	1	yes	characteristic
531	C₂×C₄	C₂₃×#121	1	1	yes	characteristic
532	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
533	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
534	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
535	C₈	—	2	1	no	—
536	C₈	—	2	1	no	—
537	C₈	—	2	1	no	—
538	C₈	—	2	1	no	—
539	C₈	—	4	1	no	—
540	C₈	—	4	1	no	—
541	C₈	—	4	1	no	—
542	C₈	—	4	1	no	—
543	C₈	—	4	1	no	—
544	C₈	—	4	1	no	—
545	C₂²	—	2	1	no	—
546	C₂²	—	2	1	no	—
547	C₂²	—	2	1	no	—
548	C₂²	—	4	1	no	—
549	C₂²	—	4	1	no	—
550	C₂²	—	4	1	no	—
551	C₂²	—	8	1	no	—
552	C₂²	—	8	1	no	—
553	C₂²	—	8	1	no	—
554	C₂²	C₂×C₂₃×#121	1	1	yes	characteristic
555	C₄	—	2	1	no	—
556	C₄	—	2	1	no	—
557	C₄	—	2	1	no	—
558	C₄	—	2	1	no	—
559	C₄	—	4	1	no	—
560	C₄	—	4	1	no	—
561	C₄	—	4	1	no	—
562	C₄	—	8	1	no	—
563	C₄	—	8	1	no	—
564	C₄	—	8	1	no	—
565	C₄	C₂₃×#575	1	1	yes	characteristic
566	C₄	C₂₃×#575	1	1	yes	characteristic
567	C₄	C₂₃×#577	1	1	yes	characteristic
568	C₄	C₂₃×#578	1	1	yes	characteristic
569	C₂	—	4	1	no	—
570	C₂	—	8	1	no	—
571	C₂	—	16	1	no	—
572	C₂	C₂₃×#3040	1	1	yes	characteristic
573	C₂	C₂₃×#3063	1	1	yes	characteristic
574	C₂	C₂₃×#3068	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₂₃
prime radical	C₂₃×#3251	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂×C₄²×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂₃×#3238	C₂	semidirect
3. C₂₃×#3141	C₂	semidirect
4. C₂₃×#2969	C₂	semidirect
5. C₂₃×#1704	C₂	semidirect
6. C₂₃×#1703	C₂	semidirect
7. C₂₃×#1698	C₂	semidirect
8. C₂₃×#1697	C₂	semidirect
9. C₂₃×#1684	C₂	semidirect
10. C₂₃×#1683	C₂	semidirect
11. C₂₃×#1678	C₂	semidirect
12. C₂₃×#1677	C₂	semidirect
13. C₂₃×#1569	C₂	semidirect
14. C₂₃×#1553	C₂	semidirect
15. C₂₃×#1548	C₂	semidirect
207. #19382	C₂₃	direct (N × H)
259. #3238	C₂×C₂₃	semidirect
260. #3141	C₂×C₂₃	semidirect
261. #2969	C₂×C₂₃	semidirect
262. #1704	C₂×C₂₃	semidirect
263. #1703	C₂×C₂₃	semidirect
264. #1698	C₂×C₂₃	semidirect
265. #1697	C₂×C₂₃	semidirect
266. #1684	C₂×C₂₃	semidirect
267. #1683	C₂×C₂₃	semidirect
268. #1678	C₂×C₂₃	semidirect
269. #1677	C₂×C₂₃	semidirect
270. #1569	C₂×C₂₃	semidirect
271. #1553	C₂×C₂₃	semidirect
272. #1548	C₂×C₂₃	semidirect
431. C₂₃	#19382	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×#3251	2
C₂₃×#3238	2
C₂₃×#3141	2
C₂₃×#2969	2
C₂₃×#1704	2
C₂₃×#1703	2
C₂₃×#1698	2
C₂₃×#1697	2
C₂₃×#1684	2
C₂₃×#1683	2
C₂₃×#1678	2
C₂₃×#1677	2
C₂₃×#1569	2
C₂₃×#1553	2
C₂₃×#1548	2
#19382	23

Subgroups — C23×#19382 #19167008

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#19382 #19167008