Subgroups — C₂₃×#21629 #19169255

Order 5888.

730 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3076	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#2961	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#2875	C₂	1	1	yes	maximal, characteristic
4	C₂₃×#1986	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#1950	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#1922	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#1922	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#1866	C₂	1	1	yes	maximal, characteristic
9	C₂₃×#1866	C₂	1	1	yes	maximal, characteristic
10	C₂₃×#1806	C₂	1	1	yes	maximal, characteristic
11	C₂₃×#1773	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#1772	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#1771	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#1765	C₂	1	1	yes	maximal, characteristic
15	C₂₃×#1764	C₂	1	1	yes	maximal, characteristic
16	C₂×C₂₃×#131	C₂²	1	1	yes	characteristic
17	C₂×C₂₃×#131	C₂²	1	1	yes	characteristic
18	C₂₃×#533	C₂²	1	1	yes	characteristic
19	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
20	C₂₃×#479	C₄	1	1	yes	characteristic, complemented
21	C₂₃×#479	C₄	1	1	yes	characteristic, complemented
22	C₂₃×#478	C₄	1	1	yes	characteristic, complemented
23	C₂₃×#478	C₄	1	1	yes	characteristic, complemented
24	C₂₃×#477	C₄	1	1	yes	characteristic, complemented
25	C₂₃×#476	C₄	1	1	yes	characteristic, complemented
26	C₂₃×#475	C₄	1	1	yes	characteristic, complemented
27	C₂₃×#474	C₄	1	1	yes	characteristic, complemented
28	C₂₃×#446	—	2	1	no	—
29	C₂₃×#446	—	2	1	no	—
30	C₂₃×#446	—	2	1	no	—
31	C₂₃×#446	—	2	1	no	—
32	C₂×C₂₃×#108	C₂²	1	1	yes	characteristic
33	C₂×C₂₃×#108	C₂²	1	1	yes	characteristic
34	C₂₃×#427	C₂²	1	1	yes	characteristic
35	C₂₃×#427	C₂²	1	1	yes	characteristic
36	C₂₃×#424	C₂²	1	1	yes	characteristic
37	C₂₃×#424	C₂²	1	1	yes	characteristic
38	C₂₃×#423	C₂²	1	1	yes	characteristic
39	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
40	C₂×C₂₃×#104	C₂²	1	1	yes	characteristic
41	C₂×C₂₃×#104	C₂²	1	1	yes	characteristic
42	C₂₃×#416	C₂²	1	1	yes	characteristic
43	C₂₃×#416	C₂²	1	1	yes	characteristic
44	C₂₃×#405	—	2	1	no	—
45	C₂₃×#405	—	2	1	no	—
46	C₂₃×#405	C₂²	1	1	yes	characteristic
47	C₂₃×#405	C₂²	1	1	yes	characteristic
48	C₂₃×#405	C₂²	1	1	yes	characteristic
49	C₂₃×#405	C₂²	1	1	yes	characteristic
50	C₄×M₁₆×C₂₃	—	2	1	no	—
51	C₄×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
52	C₂×C₂₃×#97	—	2	1	no	—
53	C₂×C₂₃×#97	C₂²	1	1	yes	characteristic
54	C₂×C₂₃×#97	C₂²	1	1	yes	characteristic
55	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
56	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
57	C₂₃×#341	C₂²	1	1	yes	characteristic
58	C₂₃×#341	C₂²	1	1	yes	characteristic
59	C₂₃×#339	C₂²	1	1	yes	characteristic
60	C₂₃×#339	C₂²	1	1	yes	characteristic
61	C₂₃×#339	C₂²	1	1	yes	characteristic
62	C₂₃×#339	C₂²	1	1	yes	characteristic
63	C₂₃×#339	C₂²	1	1	yes	characteristic
64	C₂₃×#339	C₂²	1	1	yes	characteristic
65	C₂₃×#336	C₂²	1	1	yes	characteristic
66	C₂₃×#336	C₂²	1	1	yes	characteristic
67	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
68	C₂₃×#131	—	2	2	no	—
69	C₂₃×#131	—	2	2	no	—
70	C₂₃×#131	—	2	2	no	—
71	C₂₃×#131	Q₈	1	4	yes	complemented
72	C₂×M₁₆×C₂₃	—	2	1	no	—
73	C₂×M₁₆×C₂₃	—	2	1	no	—
74	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
75	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
76	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
77	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
78	C₂²×C₈×C₂₃	—	2	1	no	—
79	C₂²×C₈×C₂₃	—	2	1	no	—
80	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
81	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
82	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
83	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
84	C₂₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
85	C₂₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
86	C₂₃×#125	C₂×C₄	1	1	yes	characteristic
87	C₂₃×#125	C₂×C₄	1	1	yes	characteristic
88	C₂₃×C₂²⋊Q₈	—	2	1	no	—
89	C₂₃×C₂²⋊Q₈	—	2	1	no	—
90	C₄×Q₈×C₂₃	—	2	1	no	—
91	C₄×Q₈×C₂₃	—	2	1	no	—
92	C₄×Q₈×C₂₃	C₂×C₄	1	1	yes	characteristic
93	C₄×Q₈×C₂₃	C₂×C₄	1	1	yes	characteristic
94	C₄×D₄×C₂₃	—	2	1	no	—
95	C₄×D₄×C₂₃	—	2	1	no	—
96	C₄×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic
97	C₄×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic
98	C₂₃×#117	—	2	1	no	—
99	C₂₃×#117	C₂³	1	1	yes	characteristic
100	C₂₃×#117	C₂³	1	1	yes	characteristic
101	C₂₃×#117	C₂³	1	1	yes	characteristic
102	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
103	C₂×C₄²×C₂₃	—	2	1	no	—
104	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
105	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
106	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
107	C₂₃×#108	—	2	2	no	—
108	C₂₃×#108	—	2	2	no	—
109	C₂₃×#107	C₂×C₄	1	1	yes	characteristic
110	C₂₃×#107	C₂×C₄	1	1	yes	characteristic
111	C₂₃×#107	C₂×C₄	1	1	yes	characteristic
112	C₂₃×#107	C₂×C₄	1	1	yes	characteristic
113	C₂₃×#106	C₂×C₄	1	1	yes	characteristic
114	C₂₃×#106	C₂×C₄	1	1	yes	characteristic
115	C₂₃×#106	C₂×C₄	1	1	yes	characteristic
116	C₂₃×#106	C₂×C₄	1	1	yes	characteristic
117	C₂₃×C₄⋊C₈	—	2	1	no	—
118	C₂₃×C₄⋊C₈	—	2	1	no	—
119	C₂₃×C₄⋊C₈	—	2	1	no	—
120	C₂₃×C₄⋊C₈	—	2	1	no	—
121	C₂₃×C₄⋊C₈	—	2	1	no	—
122	C₂₃×C₄⋊C₈	—	2	1	no	—
123	C₂₃×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
124	C₂₃×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
125	C₂₃×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
126	C₂₃×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
127	C₂₃×#104	—	2	2	no	—
128	C₂₃×#104	—	2	2	no	—
129	C₂₃×#103	C₂×C₄	1	1	yes	characteristic
130	C₂₃×#103	C₂×C₄	1	1	yes	characteristic
131	C₂₃×#103	C₂×C₄	1	1	yes	characteristic
132	C₂₃×#103	C₂×C₄	1	1	yes	characteristic
133	C₂₃×#102	C₂×C₄	1	1	yes	characteristic
134	C₂₃×#102	C₂×C₄	1	1	yes	characteristic
135	C₂₃×#102	C₂×C₄	1	1	yes	characteristic
136	C₂₃×#102	C₂×C₄	1	1	yes	characteristic
137	C₂₃×#97	—	2	1	no	—
138	C₂₃×#97	—	2	1	no	—
139	C₂₃×#97	—	2	1	no	—
140	C₂₃×#97	—	2	1	no	—
141	C₂₃×#97	—	2	2	no	—
142	C₂₃×#97	—	2	1	no	—
143	C₂₃×#97	D₄	1	1	yes	characteristic
144	C₂₃×#97	D₄	1	1	yes	characteristic
145	C₂₃×#97	D₄	1	1	yes	characteristic
146	C₂₃×#97	D₄	1	1	yes	characteristic
147	C₄×C₈×C₂₃	—	2	1	no	—
148	C₄×C₈×C₂₃	—	2	1	no	—
149	C₄×C₈×C₂₃	—	2	1	no	—
150	C₄×C₈×C₂₃	—	2	1	no	—
151	C₄×C₈×C₂₃	—	2	2	no	—
152	C₄×C₈×C₂₃	—	2	1	no	—
153	C₂₃×#95	—	2	1	no	—
154	#41×C₂₃	—	2	1	no	—
155	#41×C₂₃	—	2	1	no	—
156	#41×C₂₃	C₂×Q₈	1	2	yes	—
157	#41×C₂₃	#41	1	2	yes	—
158	C₂×Q₈×C₂₃	—	2	1	no	—
159	C₂×Q₈×C₂₃	—	2	1	no	—
160	C₂×Q₈×C₂₃	C₂²×C₄	1	1	yes	characteristic
161	C₂×D₄×C₂₃	—	2	1	no	—
162	C₂×D₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
163	C₂²×C₄×C₂₃	—	2	1	no	—
164	C₂²×C₄×C₂₃	—	2	1	no	—
165	C₂²×C₄×C₂₃	—	2	1	no	—
166	C₂²×C₄×C₂₃	—	2	1	no	—
167	C₂²×C₄×C₂₃	—	2	1	no	—
168	C₂²×C₄×C₂₃	#41	1	1	yes	characteristic
169	C₂²×C₄×C₂₃	#41	1	1	yes	characteristic
170	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
171	M₁₆×C₂₃	—	2	4	no	—
172	M₁₆×C₂₃	—	2	1	no	—
173	M₁₆×C₂₃	—	2	1	no	—
174	M₁₆×C₂₃	—	2	4	no	—
175	M₁₆×C₂₃	—	2	1	no	—
176	M₁₆×C₂₃	—	2	1	no	—
177	M₁₆×C₂₃	—	2	1	no	—
178	M₁₆×C₂₃	—	2	1	no	—
179	M₁₆×C₂₃	C₂×Q₈	1	2	yes	—
180	M₁₆×C₂₃	#41	1	2	yes	—
181	C₂×C₈×C₂₃	—	2	4	no	—
182	C₂×C₈×C₂₃	—	2	1	no	—
183	C₂×C₈×C₂₃	—	2	1	no	—
184	C₂×C₈×C₂₃	—	2	1	no	—
185	C₂×C₈×C₂₃	—	2	1	no	—
186	C₂×C₈×C₂₃	—	2	1	no	—
187	C₂×C₈×C₂₃	—	2	1	no	—
188	C₂×C₈×C₂₃	—	2	1	no	—
189	C₂×C₈×C₂₃	—	2	1	no	—
190	C₂×C₈×C₂₃	—	2	4	no	—
191	C₂×C₈×C₂₃	—	2	1	no	—
192	C₂×C₈×C₂₃	—	2	1	no	—
193	C₂×C₈×C₂₃	C₂²×C₄	1	1	yes	characteristic
194	C₂×C₈×C₂₃	C₂²×C₄	1	1	yes	characteristic
195	C₂×C₈×C₂₃	C₂²×C₄	1	1	yes	characteristic
196	C₂×C₈×C₂₃	C₂²×C₄	1	1	yes	characteristic
197	C₂×C₈×C₂₃	C₂×D₄	1	1	yes	characteristic
198	C₂×C₈×C₂₃	C₂×D₄	1	1	yes	characteristic
199	C₂×C₈×C₂₃	C₂×D₄	1	1	yes	characteristic
200	C₂×C₈×C₂₃	C₂×D₄	1	1	yes	characteristic
201	C₂×C₈×C₂₃	C₂×Q₈	1	2	yes	—
202	C₂×C₈×C₂₃	#41	1	2	yes	—
203	C₄⋊C₄×C₂₃	—	2	1	no	—
204	C₄⋊C₄×C₂₃	—	2	1	no	—
205	C₄⋊C₄×C₂₃	—	2	1	no	—
206	C₄⋊C₄×C₂₃	—	2	1	no	—
207	C₄⋊C₄×C₂₃	—	2	1	no	—
208	C₄⋊C₄×C₂₃	—	2	1	no	—
209	C₄⋊C₄×C₂₃	—	2	1	no	—
210	C₄⋊C₄×C₂₃	—	2	1	no	—
211	C₄⋊C₄×C₂₃	—	4	2	no	—
212	C₄⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
213	C₄⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
214	C₄⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
215	C₄⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
216	C₄⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
217	C₄⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
218	C₂²⋊C₄×C₂₃	—	2	1	no	—
219	C₂²⋊C₄×C₂₃	—	2	1	no	—
220	C₂²⋊C₄×C₂₃	—	2	1	no	—
221	C₂²⋊C₄×C₂₃	—	2	1	no	—
222	C₂²⋊C₄×C₂₃	—	2	1	no	—
223	C₄²×C₂₃	—	2	1	no	—
224	C₄²×C₂₃	—	2	1	no	—
225	C₄²×C₂₃	—	2	1	no	—
226	C₄²×C₂₃	—	2	1	no	—
227	C₄²×C₂₃	—	2	1	no	—
228	C₄²×C₂₃	—	2	1	no	—
229	C₄²×C₂₃	—	2	1	no	—
230	C₄²×C₂₃	—	2	1	no	—
231	C₄²×C₂₃	—	2	1	no	—
232	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
233	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
234	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
235	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
236	#21629	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
237	C₂³×C₂₃	—	2	1	no	—
238	C₂³×C₂₃	C₂×#41	1	1	yes	characteristic
239	Q₈×C₂₃	—	2	1	no	—
240	Q₈×C₂₃	—	8	1	no	—
241	Q₈×C₂₃	—	8	1	no	—
242	Q₈×C₂₃	C₄×Q₈	1	2	yes	—
243	D₄×C₂₃	—	2	2	no	—
244	D₄×C₂₃	—	2	2	no	—
245	D₄×C₂₃	—	2	1	no	—
246	D₄×C₂₃	C₄×Q₈	1	2	yes	—
247	C₂×C₄×C₂₃	—	2	1	no	—
248	C₂×C₄×C₂₃	—	2	2	no	—
249	C₂×C₄×C₂₃	—	2	2	no	—
250	C₂×C₄×C₂₃	—	2	2	no	—
251	C₂×C₄×C₂₃	—	2	1	no	—
252	C₂×C₄×C₂₃	—	2	1	no	—
253	C₂×C₄×C₂₃	—	2	1	no	—
254	C₂×C₄×C₂₃	—	2	1	no	—
255	C₂×C₄×C₂₃	—	2	1	no	—
256	C₂×C₄×C₂₃	—	2	1	no	—
257	C₂×C₄×C₂₃	—	4	1	no	—
258	C₂×C₄×C₂₃	—	4	1	no	—
259	C₂×C₄×C₂₃	—	4	1	no	—
260	C₂×C₄×C₂₃	—	4	1	no	—
261	C₂×C₄×C₂₃	—	4	1	no	—
262	C₂×C₄×C₂₃	—	4	1	no	—
263	C₂×C₄×C₂₃	—	4	1	no	—
264	C₂×C₄×C₂₃	—	8	1	no	—
265	C₂×C₄×C₂₃	—	8	1	no	—
266	C₂×C₄×C₂₃	C₄×D₄	1	1	yes	characteristic
267	C₂×C₄×C₂₃	C₄×D₄	1	1	yes	characteristic
268	C₂×C₄×C₂₃	C₄×D₄	1	1	yes	characteristic
269	C₂×C₄×C₂₃	C₄×D₄	1	1	yes	characteristic
270	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
271	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
272	C₂×C₄×C₂₃	C₂²×Q₈	1	1	yes	characteristic
273	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
274	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
275	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
276	C₈×C₂₃	—	2	1	no	—
277	C₈×C₂₃	—	2	1	no	—
278	C₈×C₂₃	—	2	1	no	—
279	C₈×C₂₃	—	2	1	no	—
280	C₈×C₂₃	—	2	2	no	—
281	C₈×C₂₃	—	2	1	no	—
282	C₈×C₂₃	—	2	2	no	—
283	C₈×C₂₃	—	2	1	no	—
284	C₈×C₂₃	—	4	1	no	—
285	C₈×C₂₃	—	4	1	no	—
286	C₈×C₂₃	C₂²⋊Q₈	1	2	yes	—
287	C₈×C₂₃	C₂²⋊Q₈	1	2	yes	—
288	#3076	C₂×C₂₃	1	1	yes	characteristic
289	#2961	C₂×C₂₃	1	1	yes	characteristic, complemented
290	#2875	C₂×C₂₃	1	1	yes	characteristic
291	#1986	C₂×C₂₃	1	1	yes	characteristic, complemented
292	#1950	C₂×C₂₃	1	1	yes	characteristic, complemented
293	#1922	C₂×C₂₃	1	1	yes	characteristic, complemented
294	#1922	C₂×C₂₃	1	1	yes	characteristic, complemented
295	#1866	C₂×C₂₃	1	1	yes	characteristic
296	#1866	C₂×C₂₃	1	1	yes	characteristic
297	#1806	C₂×C₂₃	1	1	yes	characteristic
298	#1773	C₂×C₂₃	1	1	yes	characteristic, complemented
299	#1772	C₂×C₂₃	1	1	yes	characteristic, complemented
300	#1771	C₂×C₂₃	1	1	yes	characteristic, complemented
301	#1765	C₂×C₂₃	1	1	yes	characteristic
302	#1764	C₂×C₂₃	1	1	yes	characteristic
303	C₂²×C₂₃	—	2	1	no	—
304	C₂²×C₂₃	—	2	1	no	—
305	C₂²×C₂₃	—	2	2	no	—
306	C₂²×C₂₃	—	4	1	no	—
307	C₂²×C₂₃	—	4	1	no	—
308	C₂²×C₂₃	C₂×C₄×D₄	1	1	yes	characteristic
309	C₂²×C₂₃	#529	1	1	yes	characteristic
310	C₂²×C₂₃	#533	1	1	yes	characteristic
311	C₄×C₂₃	—	2	1	no	—
312	C₄×C₂₃	—	2	1	no	—
313	C₄×C₂₃	—	2	1	no	—
314	C₄×C₂₃	—	2	1	no	—
315	C₄×C₂₃	—	2	2	no	—
316	C₄×C₂₃	—	4	2	no	—
317	C₄×C₂₃	—	4	1	no	—
318	C₄×C₂₃	—	4	1	no	—
319	C₄×C₂₃	—	4	1	no	—
320	C₄×C₂₃	—	4	1	no	—
321	C₄×C₂₃	—	4	1	no	—
322	C₄×C₂₃	—	4	1	no	—
323	C₄×C₂₃	—	8	1	no	—
324	C₄×C₂₃	C₂×C₄×Q₈	1	1	yes	characteristic
325	C₄×C₂₃	C₄×#41	1	1	yes	characteristic
326	C₄×C₂₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
327	C₄×C₂₃	#525	1	1	yes	characteristic
328	C₂×#131	C₂²×C₂₃	1	1	yes	characteristic
329	C₂×#131	C₂²×C₂₃	1	1	yes	characteristic
330	#533	C₂²×C₂₃	1	1	yes	characteristic
331	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
332	#479	C₄×C₂₃	1	1	yes	characteristic, complemented
333	#479	C₄×C₂₃	1	1	yes	characteristic, complemented
334	#478	C₄×C₂₃	1	1	yes	characteristic, complemented
335	#478	C₄×C₂₃	1	1	yes	characteristic, complemented
336	#477	C₄×C₂₃	1	1	yes	characteristic, complemented
337	#476	C₄×C₂₃	1	1	yes	characteristic, complemented
338	#475	C₄×C₂₃	1	1	yes	characteristic, complemented
339	#474	C₄×C₂₃	1	1	yes	characteristic, complemented
340	#446	—	2	1	no	—
341	#446	—	2	1	no	—
342	#446	—	2	1	no	—
343	#446	—	2	1	no	—
344	C₂×#108	C₂²×C₂₃	1	1	yes	characteristic
345	C₂×#108	C₂²×C₂₃	1	1	yes	characteristic
346	#427	C₂²×C₂₃	1	1	yes	characteristic
347	#427	C₂²×C₂₃	1	1	yes	characteristic
348	#424	C₂²×C₂₃	1	1	yes	characteristic
349	#424	C₂²×C₂₃	1	1	yes	characteristic
350	#423	C₂²×C₂₃	1	1	yes	characteristic
351	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
352	C₂×#104	C₂²×C₂₃	1	1	yes	characteristic
353	C₂×#104	C₂²×C₂₃	1	1	yes	characteristic
354	#416	C₂²×C₂₃	1	1	yes	characteristic
355	#416	C₂²×C₂₃	1	1	yes	characteristic
356	#405	—	2	1	no	—
357	#405	—	2	1	no	—
358	#405	C₂²×C₂₃	1	1	yes	characteristic
359	#405	C₂²×C₂₃	1	1	yes	characteristic
360	#405	C₂²×C₂₃	1	1	yes	characteristic
361	#405	C₂²×C₂₃	1	1	yes	characteristic
362	C₄×M₁₆	—	2	1	no	—
363	C₄×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
364	C₂×#97	—	2	1	no	—
365	C₂×#97	C₂²×C₂₃	1	1	yes	characteristic
366	C₂×#97	C₂²×C₂₃	1	1	yes	characteristic
367	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
368	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
369	#341	C₂²×C₂₃	1	1	yes	characteristic
370	#341	C₂²×C₂₃	1	1	yes	characteristic
371	#339	C₂²×C₂₃	1	1	yes	characteristic
372	#339	C₂²×C₂₃	1	1	yes	characteristic
373	#339	C₂²×C₂₃	1	1	yes	characteristic
374	#339	C₂²×C₂₃	1	1	yes	characteristic
375	#339	C₂²×C₂₃	1	1	yes	characteristic
376	#339	C₂²×C₂₃	1	1	yes	characteristic
377	#336	C₂²×C₂₃	1	1	yes	characteristic
378	#336	C₂²×C₂₃	1	1	yes	characteristic
379	C₂×C₂₃	—	2	1	no	—
380	C₂×C₂₃	—	2	1	no	—
381	C₂×C₂₃	—	4	2	no	—
382	C₂×C₂₃	C₄×C₂²⋊Q₈	1	1	yes	characteristic
383	C₂×C₂₃	#2956	1	1	yes	characteristic
384	C₂×C₂₃	#2957	1	1	yes	characteristic
385	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
386	#131	—	2	2	no	—
387	#131	—	2	2	no	—
388	#131	—	2	2	no	—
389	#131	Q₈×C₂₃	1	4	yes	complemented
390	C₂×M₁₆	—	2	1	no	—
391	C₂×M₁₆	—	2	1	no	—
392	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
393	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
394	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
395	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
396	C₂²×C₈	—	2	1	no	—
397	C₂²×C₈	—	2	1	no	—
398	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
399	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
400	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
401	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
402	C₄⋊Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
403	C₄⋊Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
404	#125	C₂×C₄×C₂₃	1	1	yes	characteristic
405	#125	C₂×C₄×C₂₃	1	1	yes	characteristic
406	C₂²⋊Q₈	—	2	1	no	—
407	C₂²⋊Q₈	—	2	1	no	—
408	C₄×Q₈	—	2	1	no	—
409	C₄×Q₈	—	2	1	no	—
410	C₄×Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
411	C₄×Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
412	C₄×D₄	—	2	1	no	—
413	C₄×D₄	—	2	1	no	—
414	C₄×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
415	C₄×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
416	#117	—	2	1	no	—
417	#117	C₂³×C₂₃	1	1	yes	characteristic
418	#117	C₂³×C₂₃	1	1	yes	characteristic
419	#117	C₂³×C₂₃	1	1	yes	characteristic
420	C₂×C₄⋊C₄	—	2	1	no	—
421	C₂×C₄²	—	2	1	no	—
422	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
423	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
424	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
425	#108	—	2	2	no	—
426	#108	—	2	2	no	—
427	#107	C₂×C₄×C₂₃	1	1	yes	characteristic
428	#107	C₂×C₄×C₂₃	1	1	yes	characteristic
429	#107	C₂×C₄×C₂₃	1	1	yes	characteristic
430	#107	C₂×C₄×C₂₃	1	1	yes	characteristic
431	#106	C₂×C₄×C₂₃	1	1	yes	characteristic
432	#106	C₂×C₄×C₂₃	1	1	yes	characteristic
433	#106	C₂×C₄×C₂₃	1	1	yes	characteristic
434	#106	C₂×C₄×C₂₃	1	1	yes	characteristic
435	C₄⋊C₈	—	2	1	no	—
436	C₄⋊C₈	—	2	1	no	—
437	C₄⋊C₈	—	2	1	no	—
438	C₄⋊C₈	—	2	1	no	—
439	C₄⋊C₈	—	2	1	no	—
440	C₄⋊C₈	—	2	1	no	—
441	C₄⋊C₈	C₂×C₄×C₂₃	1	1	yes	characteristic
442	C₄⋊C₈	C₂×C₄×C₂₃	1	1	yes	characteristic
443	C₄⋊C₈	C₂×C₄×C₂₃	1	1	yes	characteristic
444	C₄⋊C₈	C₂×C₄×C₂₃	1	1	yes	characteristic
445	#104	—	2	2	no	—
446	#104	—	2	2	no	—
447	#103	C₂×C₄×C₂₃	1	1	yes	characteristic
448	#103	C₂×C₄×C₂₃	1	1	yes	characteristic
449	#103	C₂×C₄×C₂₃	1	1	yes	characteristic
450	#103	C₂×C₄×C₂₃	1	1	yes	characteristic
451	#102	C₂×C₄×C₂₃	1	1	yes	characteristic
452	#102	C₂×C₄×C₂₃	1	1	yes	characteristic
453	#102	C₂×C₄×C₂₃	1	1	yes	characteristic
454	#102	C₂×C₄×C₂₃	1	1	yes	characteristic
455	#97	—	2	1	no	—
456	#97	—	2	1	no	—
457	#97	—	2	1	no	—
458	#97	—	2	1	no	—
459	#97	—	2	2	no	—
460	#97	—	2	1	no	—
461	#97	D₄×C₂₃	1	1	yes	characteristic
462	#97	D₄×C₂₃	1	1	yes	characteristic
463	#97	D₄×C₂₃	1	1	yes	characteristic
464	#97	D₄×C₂₃	1	1	yes	characteristic
465	C₄×C₈	—	2	1	no	—
466	C₄×C₈	—	2	1	no	—
467	C₄×C₈	—	2	1	no	—
468	C₄×C₈	—	2	1	no	—
469	C₄×C₈	—	2	2	no	—
470	C₄×C₈	—	2	1	no	—
471	#95	—	2	1	no	—
472	C₂₃	#21629	1	1	yes	characteristic, direct product factor, Sylow
473	#41	—	2	1	no	—
474	#41	—	2	1	no	—
475	#41	C₂×Q₈×C₂₃	1	2	yes	—
476	#41	#41×C₂₃	1	2	yes	—
477	C₂×Q₈	—	2	1	no	—
478	C₂×Q₈	—	2	1	no	—
479	C₂×Q₈	C₂²×C₄×C₂₃	1	1	yes	characteristic
480	C₂×D₄	—	2	1	no	—
481	C₂×D₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
482	C₂²×C₄	—	2	1	no	—
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	#41×C₂₃	1	1	yes	characteristic
488	C₂²×C₄	#41×C₂₃	1	1	yes	characteristic
489	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
490	M₁₆	—	2	4	no	—
491	M₁₆	—	2	1	no	—
492	M₁₆	—	2	1	no	—
493	M₁₆	—	2	4	no	—
494	M₁₆	—	2	1	no	—
495	M₁₆	—	2	1	no	—
496	M₁₆	—	2	1	no	—
497	M₁₆	—	2	1	no	—
498	M₁₆	C₂×Q₈×C₂₃	1	2	yes	—
499	M₁₆	#41×C₂₃	1	2	yes	—
500	C₂×C₈	—	2	4	no	—
501	C₂×C₈	—	2	1	no	—
502	C₂×C₈	—	2	1	no	—
503	C₂×C₈	—	2	1	no	—
504	C₂×C₈	—	2	1	no	—
505	C₂×C₈	—	2	1	no	—
506	C₂×C₈	—	2	1	no	—
507	C₂×C₈	—	2	1	no	—
508	C₂×C₈	—	2	1	no	—
509	C₂×C₈	—	2	4	no	—
510	C₂×C₈	—	2	1	no	—
511	C₂×C₈	—	2	1	no	—
512	C₂×C₈	C₂²×C₄×C₂₃	1	1	yes	characteristic
513	C₂×C₈	C₂²×C₄×C₂₃	1	1	yes	characteristic
514	C₂×C₈	C₂²×C₄×C₂₃	1	1	yes	characteristic
515	C₂×C₈	C₂²×C₄×C₂₃	1	1	yes	characteristic
516	C₂×C₈	C₂×D₄×C₂₃	1	1	yes	characteristic
517	C₂×C₈	C₂×D₄×C₂₃	1	1	yes	characteristic
518	C₂×C₈	C₂×D₄×C₂₃	1	1	yes	characteristic
519	C₂×C₈	C₂×D₄×C₂₃	1	1	yes	characteristic
520	C₂×C₈	C₂×Q₈×C₂₃	1	2	yes	—
521	C₂×C₈	#41×C₂₃	1	2	yes	—
522	C₄⋊C₄	—	2	1	no	—
523	C₄⋊C₄	—	2	1	no	—
524	C₄⋊C₄	—	2	1	no	—
525	C₄⋊C₄	—	2	1	no	—
526	C₄⋊C₄	—	2	1	no	—
527	C₄⋊C₄	—	2	1	no	—
528	C₄⋊C₄	—	2	1	no	—
529	C₄⋊C₄	—	2	1	no	—
530	C₄⋊C₄	—	4	2	no	—
531	C₄⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
532	C₄⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
533	C₄⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
534	C₄⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
535	C₄⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
536	C₄⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
537	C₂²⋊C₄	—	2	1	no	—
538	C₂²⋊C₄	—	2	1	no	—
539	C₂²⋊C₄	—	2	1	no	—
540	C₂²⋊C₄	—	2	1	no	—
541	C₂²⋊C₄	—	2	1	no	—
542	C₄²	—	2	1	no	—
543	C₄²	—	2	1	no	—
544	C₄²	—	2	1	no	—
545	C₄²	—	2	1	no	—
546	C₄²	—	2	1	no	—
547	C₄²	—	2	1	no	—
548	C₄²	—	2	1	no	—
549	C₄²	—	2	1	no	—
550	C₄²	—	2	1	no	—
551	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
552	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
553	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
554	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
555	C₂³	—	2	1	no	—
556	C₂³	C₂×#41×C₂₃	1	1	yes	characteristic
557	Q₈	—	2	1	no	—
558	Q₈	—	8	1	no	—
559	Q₈	—	8	1	no	—
560	Q₈	C₄×Q₈×C₂₃	1	2	yes	—
561	D₄	—	2	2	no	—
562	D₄	—	2	2	no	—
563	D₄	—	2	1	no	—
564	D₄	C₄×Q₈×C₂₃	1	2	yes	—
565	C₂×C₄	—	2	1	no	—
566	C₂×C₄	—	2	2	no	—
567	C₂×C₄	—	2	2	no	—
568	C₂×C₄	—	2	2	no	—
569	C₂×C₄	—	2	1	no	—
570	C₂×C₄	—	2	1	no	—
571	C₂×C₄	—	2	1	no	—
572	C₂×C₄	—	2	1	no	—
573	C₂×C₄	—	2	1	no	—
574	C₂×C₄	—	2	1	no	—
575	C₂×C₄	—	4	1	no	—
576	C₂×C₄	—	4	1	no	—
577	C₂×C₄	—	4	1	no	—
578	C₂×C₄	—	4	1	no	—
579	C₂×C₄	—	4	1	no	—
580	C₂×C₄	—	4	1	no	—
581	C₂×C₄	—	4	1	no	—
582	C₂×C₄	—	8	1	no	—
583	C₂×C₄	—	8	1	no	—
584	C₂×C₄	C₄×D₄×C₂₃	1	1	yes	characteristic
585	C₂×C₄	C₄×D₄×C₂₃	1	1	yes	characteristic
586	C₂×C₄	C₄×D₄×C₂₃	1	1	yes	characteristic
587	C₂×C₄	C₄×D₄×C₂₃	1	1	yes	characteristic
588	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
589	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
590	C₂×C₄	C₂²×Q₈×C₂₃	1	1	yes	characteristic
591	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
592	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
593	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
594	C₈	—	2	1	no	—
595	C₈	—	2	1	no	—
596	C₈	—	2	1	no	—
597	C₈	—	2	1	no	—
598	C₈	—	2	2	no	—
599	C₈	—	2	1	no	—
600	C₈	—	2	2	no	—
601	C₈	—	2	1	no	—
602	C₈	—	4	1	no	—
603	C₈	—	4	1	no	—
604	C₈	C₂₃×C₂²⋊Q₈	1	2	yes	—
605	C₈	C₂₃×C₂²⋊Q₈	1	2	yes	—
606	C₂²	—	2	1	no	—
607	C₂²	—	2	1	no	—
608	C₂²	—	2	2	no	—
609	C₂²	—	4	1	no	—
610	C₂²	—	4	1	no	—
611	C₂²	C₂×C₄×D₄×C₂₃	1	1	yes	characteristic
612	C₂²	C₂₃×#529	1	1	yes	characteristic
613	C₂²	C₂₃×#533	1	1	yes	characteristic
614	C₄	—	2	1	no	—
615	C₄	—	2	1	no	—
616	C₄	—	2	1	no	—
617	C₄	—	2	1	no	—
618	C₄	—	2	2	no	—
619	C₄	—	4	2	no	—
620	C₄	—	4	1	no	—
621	C₄	—	4	1	no	—
622	C₄	—	4	1	no	—
623	C₄	—	4	1	no	—
624	C₄	—	4	1	no	—
625	C₄	—	4	1	no	—
626	C₄	—	8	1	no	—
627	C₄	C₂×C₄×Q₈×C₂₃	1	1	yes	characteristic
628	C₄	C₄×#41×C₂₃	1	1	yes	characteristic
629	C₄	C₂×C₂₃×C₂²⋊Q₈	1	1	yes	characteristic
630	C₄	C₂₃×#525	1	1	yes	characteristic
631	C₂	—	2	1	no	—
632	C₂	—	2	1	no	—
633	C₂	—	4	2	no	—
634	C₂	C₄×C₂₃×C₂²⋊Q₈	1	1	yes	characteristic
635	C₂	C₂₃×#2956	1	1	yes	characteristic
636	C₂	C₂₃×#2957	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₂₃	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₂₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₃
socle	C₂²×C₂₃	C₂×C₄×D₄
prime radical	C₂×#41×C₂₃	C₂³
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₃ ◁ C₂×C₂₃×#97 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂₃×#2961	C₂	semidirect
4. C₂₃×#1986	C₂	semidirect
5. C₂₃×#1950	C₂	semidirect
6. C₂₃×#1922	C₂	semidirect
7. C₂₃×#1922	C₂	semidirect
11. C₂₃×#1773	C₂	semidirect
12. C₂₃×#1772	C₂	semidirect
13. C₂₃×#1771	C₂	semidirect
20. C₂₃×#479	C₄	semidirect
21. C₂₃×#479	C₄	semidirect
22. C₂₃×#478	C₄	semidirect
23. C₂₃×#478	C₄	semidirect
24. C₂₃×#477	C₄	semidirect
25. C₂₃×#476	C₄	semidirect
26. C₂₃×#475	C₄	semidirect
27. C₂₃×#474	C₄	semidirect
71. C₂₃×#131	Q₈	semidirect
236. #21629	C₂₃	direct (N × H)
289. #2961	C₂×C₂₃	semidirect
291. #1986	C₂×C₂₃	semidirect
292. #1950	C₂×C₂₃	semidirect
293. #1922	C₂×C₂₃	semidirect
294. #1922	C₂×C₂₃	semidirect
298. #1773	C₂×C₂₃	semidirect
299. #1772	C₂×C₂₃	semidirect
300. #1771	C₂×C₂₃	semidirect
332. #479	C₄×C₂₃	semidirect
333. #479	C₄×C₂₃	semidirect
334. #478	C₄×C₂₃	semidirect
335. #478	C₄×C₂₃	semidirect
336. #477	C₄×C₂₃	semidirect
337. #476	C₄×C₂₃	semidirect
338. #475	C₄×C₂₃	semidirect
339. #474	C₄×C₂₃	semidirect
389. #131	Q₈×C₂₃	semidirect
472. C₂₃	#21629	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×#3076	2
C₂₃×#2961	2
C₂₃×#2875	2
C₂₃×#1986	2
C₂₃×#1950	2
C₂₃×#1922	2
C₂₃×#1866	2
C₂₃×#1806	2
C₂₃×#1773	2
C₂₃×#1772	2
C₂₃×#1771	2
C₂₃×#1765	2
C₂₃×#1764	2
#21629	23

Subgroups — C23×#21629 #19169255

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#21629 #19169255