Subgroups — C₄×C₂₃×#461 #19169124

Order 5888.

1104 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#461	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×SD₁₆×C₂₃	C₂	1	2	yes	maximal
3	C₄×C₂₃×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄²×D₄×C₂₃	C₂	1	1	yes	maximal, characteristic
5	C₂₃×#1981	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#1948	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#1927	C₂	1	2	yes	maximal, complemented
8	C₂₃×#1877	C₂	1	2	yes	maximal
9	C₂₃×#1802	C₂	1	1	yes	maximal, characteristic
10	C₄×C₂₃×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₂₃×#103	C₂	1	2	yes	maximal, complemented
12	C₂²×SD₁₆×C₂₃	C₂²	1	2	yes	—
13	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₂×C₄×Q₈×C₂₃	C₂²	1	2	yes	—
15	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
16	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
17	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
18	C₂²×C₄²×C₂₃	—	2	1	no	—
19	C₂₃×#461	C₄	1	8	yes	direct product factor
20	C₄×SD₁₆×C₂₃	—	2	8	no	—
21	C₂×C₂₃×#106	C₂²	1	2	yes	—
22	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₂₃×#103	C₂²	1	2	yes	—
25	C₂×C₂₃×#103	C₂²	1	2	yes	—
26	C₂×C₂₃×#103	C₂²	1	2	yes	—
27	C₂×C₂₃×#102	C₂²	1	2	yes	—
28	C₂×C₄×C₈×C₂₃	C₂²	1	2	yes	—
29	C₂₃×#391	C₂²	1	2	yes	—
30	C₂₃×#389	—	2	1	no	—
31	C₂₃×#389	—	2	1	no	—
32	C₂₃×#384	C₂²	1	1	yes	characteristic
33	C₄×C₄⋊C₄×C₂₃	—	2	1	no	—
34	C₄×C₄⋊C₄×C₂₃	—	2	1	no	—
35	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
36	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
37	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
38	C₄×C₂²⋊C₄×C₂₃	—	2	1	no	—
39	C₄×C₂²⋊C₄×C₂₃	—	2	1	no	—
40	C₄×C₂²⋊C₄×C₂₃	—	2	1	no	—
41	C₄³×C₂₃	C₂²	1	1	yes	characteristic
42	C₂₃×#340	C₂²	1	2	yes	—
43	C₂₃×#340	C₂²	1	2	yes	—
44	C₂₃×#336	C₂²	1	2	yes	—
45	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
46	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
47	C₂³×C₄×C₂₃	—	2	1	no	—
48	C₂³×C₄×C₂₃	—	2	1	no	—
49	C₂³×C₄×C₂₃	—	2	1	no	—
50	C₂×SD₁₆×C₂₃	—	2	4	no	—
51	C₂×SD₁₆×C₂₃	—	2	4	no	—
52	C₂×SD₁₆×C₂₃	C₂×C₄	1	8	yes	—
53	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
54	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
55	C₂₃×C₄⋊Q₈	—	2	2	no	—
56	C₂₃×C₄⋊Q₈	C₂×C₄	1	4	yes	complemented
57	C₄×Q₈×C₂₃	—	2	4	no	—
58	C₄×Q₈×C₂₃	—	2	4	no	—
59	C₄×D₄×C₂₃	—	2	2	no	—
60	C₄×D₄×C₂₃	—	2	2	no	—
61	C₄×D₄×C₂₃	—	2	2	no	—
62	C₄×D₄×C₂₃	—	2	2	no	—
63	C₄×D₄×C₂₃	C₂×C₄	1	4	yes	—
64	C₄×D₄×C₂₃	D₄	1	4	yes	—
65	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
66	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
67	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
68	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
69	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
70	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
71	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
72	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
73	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
74	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
75	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
76	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
77	C₂×C₄²×C₂₃	—	2	1	no	—
78	C₂×C₄²×C₂₃	—	2	1	no	—
79	C₂×C₄²×C₂₃	—	2	1	no	—
80	C₂×C₄²×C₂₃	—	2	2	no	—
81	C₂×C₄²×C₂₃	—	4	4	no	—
82	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
83	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
84	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
85	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
86	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
87	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
88	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
89	C₂₃×#106	—	2	4	no	—
90	C₂₃×C₄⋊C₈	—	2	2	no	—
91	C₂₃×C₄⋊C₈	C₂×C₄	1	4	yes	complemented
92	C₂₃×#103	—	2	4	no	—
93	C₂₃×#103	—	2	4	no	—
94	C₂₃×#103	C₂×C₄	1	8	yes	complemented
95	C₂₃×#102	—	2	4	no	—
96	C₄×C₈×C₂₃	—	2	4	no	—
97	C₂₃×#95	—	2	1	no	—
98	C₂₃×#95	—	2	1	no	—
99	C₂₃×#95	—	2	1	no	—
100	C₂₃×#95	—	2	2	no	—
101	C₂₃×#95	—	2	2	no	—
102	C₂⁴×C₂₃	—	2	1	no	—
103	C₂×Q₈×C₂₃	—	2	2	no	—
104	C₂×Q₈×C₂₃	—	2	2	no	—
105	C₂×Q₈×C₂₃	—	2	2	no	—
106	C₂×Q₈×C₂₃	—	2	2	no	—
107	C₂×Q₈×C₂₃	—	2	2	no	—
108	C₂×Q₈×C₂₃	C₂²×C₄	1	4	yes	—
109	C₂×D₄×C₂₃	—	2	1	no	—
110	C₂×D₄×C₂₃	—	2	1	no	—
111	C₂×D₄×C₂₃	—	2	1	no	—
112	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
113	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
114	C₂×D₄×C₂₃	#41	1	2	yes	—
115	C₂²×C₄×C₂₃	—	2	4	no	—
116	C₂²×C₄×C₂₃	—	2	1	no	—
117	C₂²×C₄×C₂₃	—	2	1	no	—
118	C₂²×C₄×C₂₃	—	2	1	no	—
119	C₂²×C₄×C₂₃	—	2	2	no	—
120	C₂²×C₄×C₂₃	—	2	4	no	—
121	C₂²×C₄×C₂₃	—	2	4	no	—
122	C₂²×C₄×C₂₃	—	2	2	no	—
123	C₂²×C₄×C₂₃	—	4	2	no	—
124	C₂²×C₄×C₂₃	—	4	2	no	—
125	C₂²×C₄×C₂₃	—	4	2	no	—
126	C₂²×C₄×C₂₃	—	4	2	no	—
127	C₂²×C₄×C₂₃	—	4	2	no	—
128	C₂²×C₄×C₂₃	—	4	2	no	—
129	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
136	SD₁₆×C₂₃	—	2	16	no	—
137	C₂×C₈×C₂₃	—	2	2	no	—
138	C₂×C₈×C₂₃	—	2	2	no	—
139	C₂×C₈×C₂₃	—	2	2	no	—
140	C₂×C₈×C₂₃	—	2	2	no	—
141	C₂×C₈×C₂₃	—	2	2	no	—
142	C₂×C₈×C₂₃	C₂²×C₄	1	4	yes	—
143	C₄⋊C₄×C₂₃	—	2	4	no	—
144	C₄⋊C₄×C₂₃	—	2	4	no	—
145	C₄⋊C₄×C₂₃	—	2	1	no	—
146	C₄⋊C₄×C₂₃	—	2	1	no	—
147	C₄⋊C₄×C₂₃	—	2	1	no	—
148	C₄⋊C₄×C₂₃	—	2	2	no	—
149	C₄⋊C₄×C₂₃	—	2	2	no	—
150	C₄⋊C₄×C₂₃	—	4	2	no	—
151	C₄⋊C₄×C₂₃	—	4	4	no	—
152	C₄⋊C₄×C₂₃	—	4	2	no	—
153	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
154	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
155	C₄⋊C₄×C₂₃	#41	1	2	yes	—
156	C₂²⋊C₄×C₂₃	—	2	4	no	—
157	C₂²⋊C₄×C₂₃	—	2	4	no	—
158	C₂²⋊C₄×C₂₃	—	2	4	no	—
159	C₄²×C₂₃	—	2	2	no	—
160	C₄²×C₂₃	—	2	2	no	—
161	C₄²×C₂₃	—	2	1	no	—
162	C₄²×C₂₃	—	2	1	no	—
163	C₄²×C₂₃	—	4	1	no	—
164	C₄²×C₂₃	—	4	4	no	—
165	C₄²×C₂₃	—	4	2	no	—
166	C₄²×C₂₃	—	4	2	no	—
167	C₄²×C₂₃	—	4	2	no	—
168	C₄²×C₂₃	SD₁₆	1	4	yes	complemented
169	C₄²×C₂₃	C₂²×C₄	1	2	yes	—
170	C₄²×C₂₃	C₂×D₄	1	2	yes	—
171	C₄²×C₂₃	#41	1	2	yes	—
172	C₄²×C₂₃	#41	1	2	yes	—
173	C₄×#461	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
174	C₂³×C₂₃	—	2	2	no	—
175	C₂³×C₂₃	—	2	2	no	—
176	C₂³×C₂₃	—	2	2	no	—
177	C₂³×C₂₃	—	4	1	no	—
178	C₂³×C₂₃	—	4	1	no	—
179	C₂³×C₂₃	—	4	1	no	—
180	C₂³×C₂₃	—	4	1	no	—
181	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
182	Q₈×C₂₃	—	2	4	no	—
183	Q₈×C₂₃	—	2	4	no	—
184	Q₈×C₂₃	—	4	2	no	—
185	Q₈×C₂₃	—	4	2	no	—
186	D₄×C₂₃	—	2	2	no	—
187	D₄×C₂₃	—	2	2	no	—
188	D₄×C₂₃	—	2	2	no	—
189	D₄×C₂₃	C₄×D₄	1	4	yes	—
190	C₂×C₄×C₂₃	—	2	1	no	—
191	C₂×C₄×C₂₃	—	2	1	no	—
192	C₂×C₄×C₂₃	—	2	1	no	—
193	C₂×C₄×C₂₃	—	2	1	no	—
194	C₂×C₄×C₂₃	—	2	1	no	—
195	C₂×C₄×C₂₃	—	2	1	no	—
196	C₂×C₄×C₂₃	—	2	2	no	—
197	C₂×C₄×C₂₃	—	2	4	no	—
198	C₂×C₄×C₂₃	—	2	2	no	—
199	C₂×C₄×C₂₃	—	2	1	no	—
200	C₂×C₄×C₂₃	—	2	2	no	—
201	C₂×C₄×C₂₃	—	2	1	no	—
202	C₂×C₄×C₂₃	—	2	1	no	—
203	C₂×C₄×C₂₃	—	4	8	no	—
204	C₂×C₄×C₂₃	—	4	2	no	—
205	C₂×C₄×C₂₃	—	4	2	no	—
206	C₂×C₄×C₂₃	—	4	1	no	—
207	C₂×C₄×C₂₃	—	4	1	no	—
208	C₂×C₄×C₂₃	—	4	1	no	—
209	C₂×C₄×C₂₃	—	4	1	no	—
210	C₂×C₄×C₂₃	—	4	1	no	—
211	C₂×C₄×C₂₃	—	4	1	no	—
212	C₂×C₄×C₂₃	—	4	8	no	—
213	C₂×C₄×C₂₃	—	4	8	no	—
214	C₂×C₄×C₂₃	—	4	2	no	—
215	C₂×C₄×C₂₃	—	4	2	no	—
216	C₂×C₄×C₂₃	—	4	2	no	—
217	C₂×C₄×C₂₃	C₄×D₄	1	2	yes	—
218	C₂×C₄×C₂₃	C₄×D₄	1	2	yes	—
219	C₂×C₄×C₂₃	#121	1	2	yes	—
220	C₂×C₄×C₂₃	#121	1	2	yes	—
221	C₂×C₄×C₂₃	C₂×SD₁₆	1	2	yes	—
222	C₂×C₄×C₂₃	C₂×SD₁₆	1	2	yes	—
223	C₂×C₄×C₂₃	C₂×SD₁₆	1	2	yes	—
224	C₂×C₄×C₂₃	#135	1	2	yes	—
225	C₂×C₄×C₂₃	#137	1	2	yes	—
226	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
227	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
228	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
229	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
230	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
231	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
232	C₈×C₂₃	—	2	4	no	—
233	C₈×C₂₃	—	4	2	no	—
234	C₂×#461	C₂×C₂₃	1	1	yes	characteristic
235	C₂×C₄×SD₁₆	C₂×C₂₃	1	2	yes	—
236	C₄×C₄⋊Q₈	C₂×C₂₃	1	1	yes	characteristic, complemented
237	C₄²×D₄	C₂×C₂₃	1	1	yes	characteristic
238	#1981	C₂×C₂₃	1	1	yes	characteristic, complemented
239	#1948	C₂×C₂₃	1	1	yes	characteristic, complemented
240	#1927	C₂×C₂₃	1	2	yes	complemented
241	#1877	C₂×C₂₃	1	2	yes	—
242	#1802	C₂×C₂₃	1	1	yes	characteristic
243	C₄×C₄⋊C₈	C₂×C₂₃	1	1	yes	characteristic, complemented
244	C₄×#103	C₂×C₂₃	1	2	yes	complemented
245	C₂²×C₂₃	—	2	4	no	—
246	C₂²×C₂₃	—	4	2	no	—
247	C₂²×C₂₃	—	4	2	no	—
248	C₂²×C₂₃	—	4	2	no	—
249	C₂²×C₂₃	—	4	2	no	—
250	C₂²×C₂₃	—	4	2	no	—
251	C₂²×C₂₃	—	4	2	no	—
252	C₂²×C₂₃	C₂×C₄×D₄	1	1	yes	characteristic
253	C₂²×C₂₃	C₂×#121	1	1	yes	characteristic
254	C₂²×C₂₃	#525	1	1	yes	characteristic
255	C₂²×C₂₃	C₂²×SD₁₆	1	1	yes	characteristic
256	C₂²×C₂₃	C₂×#135	1	1	yes	characteristic
257	C₂²×C₂₃	C₂×#137	1	1	yes	characteristic
258	C₂²×C₂₃	#575	1	1	yes	characteristic
259	C₄×C₂₃	—	2	2	no	—
260	C₄×C₂₃	—	2	2	no	—
261	C₄×C₂₃	—	2	2	no	—
262	C₄×C₂₃	—	4	2	no	—
263	C₄×C₂₃	—	4	1	no	—
264	C₄×C₂₃	—	4	2	no	—
265	C₄×C₂₃	—	4	2	no	—
266	C₄×C₂₃	—	4	4	no	—
267	C₄×C₂₃	—	8	2	no	—
268	C₄×C₂₃	C₄×SD₁₆	1	4	yes	complemented
269	C₄×C₂₃	#461	1	4	yes	direct product factor
270	C₄×C₂₃	C₂×C₄×D₄	1	1	yes	characteristic
271	C₄×C₂₃	C₄×#41	1	1	yes	characteristic
272	C₄×C₂₃	#529	1	1	yes	characteristic
273	C₄×C₂₃	#532	1	1	yes	characteristic
274	C₂²×SD₁₆	C₂²×C₂₃	1	2	yes	—
275	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
276	C₂×C₄×Q₈	C₂²×C₂₃	1	2	yes	—
277	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
278	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
279	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
280	C₂²×C₄²	—	2	1	no	—
281	#461	C₄×C₂₃	1	8	yes	direct product factor
282	C₄×SD₁₆	—	2	8	no	—
283	C₂×#106	C₂²×C₂₃	1	2	yes	—
284	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
285	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
286	C₂×#103	C₂²×C₂₃	1	2	yes	—
287	C₂×#103	C₂²×C₂₃	1	2	yes	—
288	C₂×#103	C₂²×C₂₃	1	2	yes	—
289	C₂×#102	C₂²×C₂₃	1	2	yes	—
290	C₂×C₄×C₈	C₂²×C₂₃	1	2	yes	—
291	#391	C₂²×C₂₃	1	2	yes	—
292	#389	—	2	1	no	—
293	#389	—	2	1	no	—
294	#384	C₂²×C₂₃	1	1	yes	characteristic
295	C₄×C₄⋊C₄	—	2	1	no	—
296	C₄×C₄⋊C₄	—	2	1	no	—
297	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
298	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
299	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
300	C₄×C₂²⋊C₄	—	2	1	no	—
301	C₄×C₂²⋊C₄	—	2	1	no	—
302	C₄×C₂²⋊C₄	—	2	1	no	—
303	C₄³	C₂²×C₂₃	1	1	yes	characteristic
304	#340	C₂²×C₂₃	1	2	yes	—
305	#340	C₂²×C₂₃	1	2	yes	—
306	#336	C₂²×C₂₃	1	2	yes	—
307	C₂×C₂₃	—	4	4	no	—
308	C₂×C₂₃	C₄×#121	1	1	yes	characteristic
309	C₂×C₂₃	C₂×C₄×SD₁₆	1	1	yes	characteristic
310	C₂×C₂₃	C₄×#137	1	1	yes	characteristic
311	C₂×C₂₃	C₂×#461	1	1	yes	characteristic
312	C₂×C₂₃	#3035	1	1	yes	characteristic
313	C₂×C₂₃	#3101	1	1	yes	characteristic
314	C₂×C₂₃	#3107	1	1	yes	characteristic
315	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
316	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
317	C₂³×C₄	—	2	1	no	—
318	C₂³×C₄	—	2	1	no	—
319	C₂³×C₄	—	2	1	no	—
320	C₂×SD₁₆	—	2	4	no	—
321	C₂×SD₁₆	—	2	4	no	—
322	C₂×SD₁₆	C₂×C₄×C₂₃	1	8	yes	—
323	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
324	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
325	C₄⋊Q₈	—	2	2	no	—
326	C₄⋊Q₈	C₂×C₄×C₂₃	1	4	yes	complemented
327	C₄×Q₈	—	2	4	no	—
328	C₄×Q₈	—	2	4	no	—
329	C₄×D₄	—	2	2	no	—
330	C₄×D₄	—	2	2	no	—
331	C₄×D₄	—	2	2	no	—
332	C₄×D₄	—	2	2	no	—
333	C₄×D₄	C₂×C₄×C₂₃	1	4	yes	—
334	C₄×D₄	D₄×C₂₃	1	4	yes	—
335	C₂×C₄⋊C₄	—	2	1	no	—
336	C₂×C₄⋊C₄	—	2	1	no	—
337	C₂×C₄⋊C₄	—	2	2	no	—
338	C₂×C₄⋊C₄	—	2	1	no	—
339	C₂×C₄⋊C₄	—	2	1	no	—
340	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
341	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
342	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
343	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
344	C₂×C₂²⋊C₄	—	2	1	no	—
345	C₂×C₂²⋊C₄	—	2	1	no	—
346	C₂×C₂²⋊C₄	—	2	1	no	—
347	C₂×C₄²	—	2	2	no	—
348	C₂×C₄²	—	2	1	no	—
349	C₂×C₄²	—	2	1	no	—
350	C₂×C₄²	—	2	1	no	—
351	C₂×C₄²	—	4	4	no	—
352	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
353	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
354	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
355	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
356	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
357	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
358	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
359	#106	—	2	4	no	—
360	C₄⋊C₈	—	2	2	no	—
361	C₄⋊C₈	C₂×C₄×C₂₃	1	4	yes	complemented
362	#103	—	2	4	no	—
363	#103	—	2	4	no	—
364	#103	C₂×C₄×C₂₃	1	8	yes	complemented
365	#102	—	2	4	no	—
366	C₄×C₈	—	2	4	no	—
367	#95	—	2	1	no	—
368	#95	—	2	1	no	—
369	#95	—	2	1	no	—
370	#95	—	2	2	no	—
371	#95	—	2	2	no	—
372	C₂₃	C₄×#461	1	1	yes	characteristic, direct product factor, Sylow
373	C₂⁴	—	2	1	no	—
374	C₂×Q₈	—	2	2	no	—
375	C₂×Q₈	—	2	2	no	—
376	C₂×Q₈	—	2	2	no	—
377	C₂×Q₈	—	2	2	no	—
378	C₂×Q₈	—	2	2	no	—
379	C₂×Q₈	C₂²×C₄×C₂₃	1	4	yes	—
380	C₂×D₄	—	2	1	no	—
381	C₂×D₄	—	2	1	no	—
382	C₂×D₄	—	2	1	no	—
383	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
384	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
385	C₂×D₄	#41×C₂₃	1	2	yes	—
386	C₂²×C₄	—	2	4	no	—
387	C₂²×C₄	—	2	1	no	—
388	C₂²×C₄	—	2	1	no	—
389	C₂²×C₄	—	2	1	no	—
390	C₂²×C₄	—	2	2	no	—
391	C₂²×C₄	—	2	4	no	—
392	C₂²×C₄	—	2	4	no	—
393	C₂²×C₄	—	2	2	no	—
394	C₂²×C₄	—	4	2	no	—
395	C₂²×C₄	—	4	2	no	—
396	C₂²×C₄	—	4	2	no	—
397	C₂²×C₄	—	4	2	no	—
398	C₂²×C₄	—	4	2	no	—
399	C₂²×C₄	—	4	2	no	—
400	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
401	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
402	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
403	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
404	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
405	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
406	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
407	SD₁₆	—	2	16	no	—
408	C₂×C₈	—	2	2	no	—
409	C₂×C₈	—	2	2	no	—
410	C₂×C₈	—	2	2	no	—
411	C₂×C₈	—	2	2	no	—
412	C₂×C₈	—	2	2	no	—
413	C₂×C₈	C₂²×C₄×C₂₃	1	4	yes	—
414	C₄⋊C₄	—	2	4	no	—
415	C₄⋊C₄	—	2	4	no	—
416	C₄⋊C₄	—	2	1	no	—
417	C₄⋊C₄	—	2	1	no	—
418	C₄⋊C₄	—	2	1	no	—
419	C₄⋊C₄	—	2	2	no	—
420	C₄⋊C₄	—	2	2	no	—
421	C₄⋊C₄	—	4	2	no	—
422	C₄⋊C₄	—	4	4	no	—
423	C₄⋊C₄	—	4	2	no	—
424	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
425	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
426	C₄⋊C₄	#41×C₂₃	1	2	yes	—
427	C₂²⋊C₄	—	2	4	no	—
428	C₂²⋊C₄	—	2	4	no	—
429	C₂²⋊C₄	—	2	4	no	—
430	C₄²	—	2	2	no	—
431	C₄²	—	2	2	no	—
432	C₄²	—	2	1	no	—
433	C₄²	—	2	1	no	—
434	C₄²	—	4	1	no	—
435	C₄²	—	4	4	no	—
436	C₄²	—	4	2	no	—
437	C₄²	—	4	2	no	—
438	C₄²	—	4	2	no	—
439	C₄²	SD₁₆×C₂₃	1	4	yes	complemented
440	C₄²	C₂²×C₄×C₂₃	1	2	yes	—
441	C₄²	C₂×D₄×C₂₃	1	2	yes	—
442	C₄²	#41×C₂₃	1	2	yes	—
443	C₄²	#41×C₂₃	1	2	yes	—
444	C₂³	—	2	2	no	—
445	C₂³	—	2	2	no	—
446	C₂³	—	2	2	no	—
447	C₂³	—	4	1	no	—
448	C₂³	—	4	1	no	—
449	C₂³	—	4	1	no	—
450	C₂³	—	4	1	no	—
451	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
452	Q₈	—	2	4	no	—
453	Q₈	—	2	4	no	—
454	Q₈	—	4	2	no	—
455	Q₈	—	4	2	no	—
456	D₄	—	2	2	no	—
457	D₄	—	2	2	no	—
458	D₄	—	2	2	no	—
459	D₄	C₄×D₄×C₂₃	1	4	yes	—
460	C₂×C₄	—	2	1	no	—
461	C₂×C₄	—	2	1	no	—
462	C₂×C₄	—	2	1	no	—
463	C₂×C₄	—	2	1	no	—
464	C₂×C₄	—	2	1	no	—
465	C₂×C₄	—	2	1	no	—
466	C₂×C₄	—	2	1	no	—
467	C₂×C₄	—	2	1	no	—
468	C₂×C₄	—	2	2	no	—
469	C₂×C₄	—	2	4	no	—
470	C₂×C₄	—	2	2	no	—
471	C₂×C₄	—	2	1	no	—
472	C₂×C₄	—	2	2	no	—
473	C₂×C₄	—	4	8	no	—
474	C₂×C₄	—	4	1	no	—
475	C₂×C₄	—	4	1	no	—
476	C₂×C₄	—	4	1	no	—
477	C₂×C₄	—	4	1	no	—
478	C₂×C₄	—	4	1	no	—
479	C₂×C₄	—	4	1	no	—
480	C₂×C₄	—	4	2	no	—
481	C₂×C₄	—	4	2	no	—
482	C₂×C₄	—	4	8	no	—
483	C₂×C₄	—	4	8	no	—
484	C₂×C₄	—	4	2	no	—
485	C₂×C₄	—	4	2	no	—
486	C₂×C₄	—	4	2	no	—
487	C₂×C₄	C₄×D₄×C₂₃	1	2	yes	—
488	C₂×C₄	C₄×D₄×C₂₃	1	2	yes	—
489	C₂×C₄	C₂₃×#121	1	2	yes	—
490	C₂×C₄	C₂₃×#121	1	2	yes	—
491	C₂×C₄	C₂×SD₁₆×C₂₃	1	2	yes	—
492	C₂×C₄	C₂×SD₁₆×C₂₃	1	2	yes	—
493	C₂×C₄	C₂×SD₁₆×C₂₃	1	2	yes	—
494	C₂×C₄	C₂₃×#135	1	2	yes	—
495	C₂×C₄	C₂₃×#137	1	2	yes	—
496	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
497	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
498	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
499	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
500	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
501	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
502	C₈	—	2	4	no	—
503	C₈	—	4	2	no	—
504	C₂²	—	2	4	no	—
505	C₂²	—	4	2	no	—
506	C₂²	—	4	2	no	—
507	C₂²	—	4	2	no	—
508	C₂²	—	4	2	no	—
509	C₂²	—	4	2	no	—
510	C₂²	—	4	2	no	—
511	C₂²	C₂×C₄×D₄×C₂₃	1	1	yes	characteristic
512	C₂²	C₂×C₂₃×#121	1	1	yes	characteristic
513	C₂²	C₂₃×#525	1	1	yes	characteristic
514	C₂²	C₂²×SD₁₆×C₂₃	1	1	yes	characteristic
515	C₂²	C₂×C₂₃×#135	1	1	yes	characteristic
516	C₂²	C₂×C₂₃×#137	1	1	yes	characteristic
517	C₂²	C₂₃×#575	1	1	yes	characteristic
518	C₄	—	2	2	no	—
519	C₄	—	2	2	no	—
520	C₄	—	2	2	no	—
521	C₄	—	4	2	no	—
522	C₄	—	4	2	no	—
523	C₄	—	4	4	no	—
524	C₄	—	4	2	no	—
525	C₄	—	4	1	no	—
526	C₄	—	8	2	no	—
527	C₄	C₄×SD₁₆×C₂₃	1	4	yes	complemented
528	C₄	C₂₃×#461	1	4	yes	direct product factor
529	C₄	C₂×C₄×D₄×C₂₃	1	1	yes	characteristic
530	C₄	C₄×#41×C₂₃	1	1	yes	characteristic
531	C₄	C₂₃×#529	1	1	yes	characteristic
532	C₄	C₂₃×#532	1	1	yes	characteristic
533	C₂	—	4	4	no	—
534	C₂	C₄×C₂₃×#121	1	1	yes	characteristic
535	C₂	C₂×C₄×SD₁₆×C₂₃	1	1	yes	characteristic
536	C₂	C₄×C₂₃×#137	1	1	yes	characteristic
537	C₂	C₂×C₂₃×#461	1	1	yes	characteristic
538	C₂	C₂₃×#3035	1	1	yes	characteristic
539	C₂	C₂₃×#3101	1	1	yes	characteristic
540	C₂	C₂₃×#3107	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₂₃	C₂×D₄
commutator	C₂×C₄	C₂³×C₄×C₂₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₃
socle	C₂³×C₂₃	C₂²×D₄
prime radical	C₂²×D₄×C₂₃	C₂³
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₂₃ ◁ C₄³×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₄×C₂₃×C₄⋊Q₈	C₂	semidirect
5. C₂₃×#1981	C₂	semidirect
6. C₂₃×#1948	C₂	semidirect
7. C₂₃×#1927	C₂	semidirect
10. C₄×C₂₃×C₄⋊C₈	C₂	semidirect
11. C₄×C₂₃×#103	C₂	semidirect
19. C₂₃×#461	C₄	direct (N × H)
56. C₂₃×C₄⋊Q₈	C₂×C₄	semidirect
91. C₂₃×C₄⋊C₈	C₂×C₄	semidirect
94. C₂₃×#103	C₂×C₄	semidirect
168. C₄²×C₂₃	SD₁₆	semidirect
173. C₄×#461	C₂₃	direct (N × H)
236. C₄×C₄⋊Q₈	C₂×C₂₃	semidirect
238. #1981	C₂×C₂₃	semidirect
239. #1948	C₂×C₂₃	semidirect
240. #1927	C₂×C₂₃	semidirect
243. C₄×C₄⋊C₈	C₂×C₂₃	semidirect
244. C₄×#103	C₂×C₂₃	semidirect
268. C₄×C₂₃	C₄×SD₁₆	semidirect
269. C₄×C₂₃	#461	direct (N × H)
281. #461	C₄×C₂₃	direct (N × H)
326. C₄⋊Q₈	C₂×C₄×C₂₃	semidirect
361. C₄⋊C₈	C₂×C₄×C₂₃	semidirect
364. #103	C₂×C₄×C₂₃	semidirect
372. C₂₃	C₄×#461	direct (N × H)
439. C₄²	SD₁₆×C₂₃	semidirect
527. C₄	C₄×SD₁₆×C₂₃	semidirect
528. C₄	C₂₃×#461	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×#461	2
C₂×C₄×SD₁₆×C₂₃	2
C₄×C₂₃×C₄⋊Q₈	2
C₄²×D₄×C₂₃	2
C₂₃×#1981	2
C₂₃×#1948	2
C₂₃×#1927	2
C₂₃×#1877	2
C₂₃×#1802	2
C₄×C₂₃×C₄⋊C₈	2
C₄×C₂₃×#103	2
C₄×#461	23

Subgroups — C4×C23×#461 #19169124

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₂₃×#461 #19169124