Subgroups — #18087239

Order 4864.

418 conjugacy classes of subgroups.

The subgroup lattice has 292 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14563795	C₂	1	1	yes	maximal, characteristic, complemented
2	#14563635	C₂	1	2	yes	maximal
3	#14561519	C₂	1	2	yes	maximal, complemented
4	#14561470	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1954	C₂	1	1	yes	maximal, characteristic
6	C₂×#10597275	—	2	1	no	—
7	C₂×#10597275	—	2	1	no	—
8	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
9	C₂×#10597289	—	2	2	no	—
10	#11926414	C₂²	1	2	yes	—
11	#11926306	—	2	2	no	—
12	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
13	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
14	C₂×C₁₉×C₂²⋊C₈	—	2	1	no	—
15	C₂×C₁₉×C₂²⋊C₈	—	2	1	no	—
16	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
17	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
18	C₂³×C₄×C₁₉	—	2	1	no	—
19	C₂²×C₈×C₁₉	—	2	1	no	—
20	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
21	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
22	C₄×D₄×C₁₉	—	2	2	no	—
23	C₄×D₄×C₁₉	—	2	2	no	—
24	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
25	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
26	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
27	C₂×C₄⋊Dic₁₉	—	2	2	no	—
28	C₂×C₄⋊Dic₁₉	—	2	2	no	—
29	C₂×C₄⋊Dic₁₉	—	2	2	no	—
30	C₂²×C₁₉⋊C₈	—	2	2	no	—
31	C₁₉×C₄⋊C₈	—	2	2	no	—
32	C₁₉×C₂²⋊C₈	—	4	2	no	—
33	C₁₉×C₂²⋊C₈	—	4	2	no	—
34	C₄×C₈×C₁₉	—	2	2	no	—
35	#10597289	—	4	4	no	—
36	#10597275	—	4	2	no	—
37	#10597275	—	4	2	no	—
38	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
39	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
40	C₂⁴×C₁₉	—	2	1	no	—
41	C₂×D₄×C₁₉	—	2	2	no	—
42	C₂×D₄×C₁₉	—	2	1	no	—
43	C₂×D₄×C₁₉	—	2	2	no	—
44	C₂×D₄×C₁₉	D₈	1	2	yes	—
45	C₂²×C₄×C₁₉	—	2	1	no	—
46	C₂²×C₄×C₁₉	—	4	1	no	—
47	C₂²×C₄×C₁₉	—	4	1	no	—
48	C₂²×C₄×C₁₉	—	4	1	no	—
49	C₂²×C₄×C₁₉	—	4	1	no	—
50	C₂²×C₄×C₁₉	—	4	1	no	—
51	C₂²×C₄×C₁₉	—	4	1	no	—
52	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
53	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
54	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
55	C₂²×Dic₁₉	—	4	2	no	—
56	C₂×C₈×C₁₉	—	2	1	no	—
57	C₂×C₈×C₁₉	—	2	1	no	—
58	C₂×C₈×C₁₉	—	2	1	no	—
59	C₂×C₈×C₁₉	—	2	1	no	—
60	C₂×C₈×C₁₉	—	4	1	no	—
61	C₂×C₈×C₁₉	—	4	1	no	—
62	C₂×C₈×C₁₉	—	4	1	no	—
63	C₂×C₈×C₁₉	D₈	1	2	yes	—
64	C₂×C₈×C₁₉	SD₁₆	1	2	yes	—
65	C₄⋊C₄×C₁₉	—	2	2	no	—
66	C₂²⋊C₄×C₁₉	—	4	2	no	—
67	C₄²×C₁₉	#41	1	2	yes	—
68	C₄²×C₁₉	#41	1	2	yes	—
69	C₄⋊Dic₁₉	—	4	2	no	—
70	C₄⋊Dic₁₉	—	4	2	no	—
71	C₄⋊Dic₁₉	—	4	2	no	—
72	C₄⋊Dic₁₉	—	4	2	no	—
73	C₄⋊Dic₁₉	—	8	2	no	—
74	C₂×C₁₉⋊C₈	—	4	2	no	—
75	C₂×C₁₉⋊C₈	—	4	2	no	—
76	C₂×C₁₉⋊C₈	—	4	2	no	—
77	#10615	—	19	1	no	maximal, Sylow
78	C₂³×C₁₉	—	2	2	no	—
79	C₂³×C₁₉	—	4	1	no	—
80	C₂³×C₁₉	—	4	1	no	—
81	C₂³×C₁₉	—	4	1	no	—
82	C₂³×C₁₉	—	4	1	no	—
83	C₂³×C₁₉	—	4	1	no	—
84	C₂³×C₁₉	—	4	1	no	—
85	C₂³×C₁₉	#121	1	1	yes	characteristic
86	D₄×C₁₉	—	2	4	no	—
87	D₄×C₁₉	—	4	2	no	—
88	C₂×C₄×C₁₉	—	2	1	no	—
89	C₂×C₄×C₁₉	—	2	1	no	—
90	C₂×C₄×C₁₉	—	4	1	no	—
91	C₂×C₄×C₁₉	—	4	1	no	—
92	C₂×C₄×C₁₉	—	4	1	no	—
93	C₂×C₄×C₁₉	—	8	1	no	—
94	C₂×C₄×C₁₉	—	8	1	no	—
95	C₂×C₄×C₁₉	—	8	1	no	—
96	C₂×C₄×C₁₉	—	8	1	no	—
97	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
98	C₂×C₄×C₁₉	#123	1	2	yes	—
99	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
100	C₂×C₄×C₁₉	#126	1	2	yes	—
101	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
102	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
103	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
104	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
105	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
106	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
107	C₂×C₄×C₁₉	#137	1	2	yes	—
108	C₂×Dic₁₉	—	8	2	no	—
109	C₂×Dic₁₉	—	8	2	no	—
110	C₂×Dic₁₉	—	8	2	no	—
111	C₈×C₁₉	—	2	2	no	—
112	C₈×C₁₉	—	2	2	no	—
113	C₈×C₁₉	—	8	1	no	—
114	C₁₉⋊C₈	—	8	2	no	—
115	#1954	D₁₉	1	1	yes	characteristic
116	#1845	—	19	1	no	—
117	#1802	—	19	2	no	—
118	#1296	—	19	2	no	—
119	#1277	—	19	1	no	—
120	C₂²×C₁₉	—	4	2	no	—
121	C₂²×C₁₉	—	4	2	no	—
122	C₂²×C₁₉	—	4	2	no	—
123	C₂²×C₁₉	—	8	1	no	—
124	C₂²×C₁₉	—	8	1	no	—
125	C₂²×C₁₉	—	8	1	no	—
126	C₂²×C₁₉	—	8	1	no	—
127	C₂²×C₁₉	#397	1	1	yes	characteristic
128	C₂²×C₁₉	#459	1	1	yes	characteristic
129	C₂²×C₁₉	#461	1	1	yes	characteristic
130	C₂²×C₁₉	#466	1	1	yes	characteristic
131	C₂²×C₁₉	#470	1	1	yes	characteristic
132	C₂²×C₁₉	#472	1	1	yes	characteristic
133	C₂²×C₁₉	#473	1	1	yes	characteristic
134	C₄×C₁₉	—	2	2	no	—
135	C₄×C₁₉	—	8	1	no	—
136	C₄×C₁₉	#480	1	1	yes	characteristic
137	C₄×C₁₉	#480	1	2	yes	—
138	C₄×C₁₉	#481	1	1	yes	characteristic
139	C₄×C₁₉	#485	1	2	yes	—
140	C₄×C₁₉	#486	1	1	yes	characteristic
141	C₄×C₁₉	#489	1	1	yes	characteristic
142	Dic₁₉	—	16	2	no	—
143	C₂×C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
144	C₂×#107	—	38	1	no	—
145	C₂×#107	—	38	1	no	—
146	C₂×C₄⋊C₈	—	19	2	no	—
147	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
148	C₂×#102	—	38	2	no	—
149	C₂×C₂²⋊C₈	—	2	1	no	—
150	C₂×C₂²⋊C₈	—	2	1	no	—
151	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
152	#384	—	19	2	no	—
153	#340	—	38	2	no	—
154	C₂×C₁₉	—	8	2	no	—
155	C₂×C₁₉	#1667	1	1	yes	characteristic
156	C₂×C₁₉	#1673	1	1	yes	characteristic
157	C₂×C₁₉	#1689	1	1	yes	characteristic
158	C₂×C₁₉	#1695	1	1	yes	characteristic
159	C₂×C₁₉	#2071	1	1	yes	characteristic
160	C₂×C₁₉	#2075	1	1	yes	characteristic
161	C₂×C₁₉	#2078	1	1	yes	characteristic
162	C₂²×D₄	D₇₆	1	1	yes	characteristic
163	C₂³×C₄	—	2	1	no	—
164	C₂²×C₈	—	2	1	no	—
165	C₂²×C₈	—	38	2	no	—
166	C₂²×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
167	C₂²×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
168	C₄×D₄	—	2	2	no	—
169	C₄×D₄	—	2	2	no	—
170	C₂×C₄⋊C₄	—	38	2	no	—
171	C₂×C₄⋊C₄	—	38	2	no	—
172	C₂×C₄⋊C₄	—	38	2	no	—
173	C₂×C₄⋊C₄	D₇₆	1	1	yes	characteristic
174	C₂×C₂²⋊C₄	—	2	1	no	—
175	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
176	#107	—	76	2	no	—
177	#107	—	76	2	no	—
178	C₄⋊C₈	—	2	2	no	—
179	C₄⋊C₈	—	38	2	no	—
180	C₄⋊C₈	—	38	2	no	—
181	#102	—	76	4	no	—
182	C₂²⋊C₈	—	4	2	no	—
183	C₂²⋊C₈	—	4	2	no	—
184	C₄×C₈	—	2	2	no	—
185	C₁₉	#10615	1	1	yes	characteristic, complemented, Sylow
186	C₂⁴	—	2	1	no	—
187	C₂×D₄	—	2	2	no	—
188	C₂×D₄	—	2	1	no	—
189	C₂×D₄	—	2	2	no	—
190	C₂×D₄	D₁₅₂	1	2	yes	—
191	C₂²×C₄	—	2	1	no	—
192	C₂²×C₄	—	4	1	no	—
193	C₂²×C₄	—	4	1	no	—
194	C₂²×C₄	—	4	1	no	—
195	C₂²×C₄	—	4	1	no	—
196	C₂²×C₄	—	4	1	no	—
197	C₂²×C₄	—	4	1	no	—
198	C₂²×C₄	—	76	2	no	—
199	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
200	C₂²×C₄	#64541	1	1	yes	characteristic
201	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
202	C₂×C₈	—	2	1	no	—
203	C₂×C₈	—	2	1	no	—
204	C₂×C₈	—	2	1	no	—
205	C₂×C₈	—	2	1	no	—
206	C₂×C₈	—	4	1	no	—
207	C₂×C₈	—	4	1	no	—
208	C₂×C₈	—	4	1	no	—
209	C₂×C₈	—	76	2	no	—
210	C₂×C₈	—	76	2	no	—
211	C₂×C₈	—	76	2	no	—
212	C₂×C₈	#64525	1	2	yes	—
213	C₂×C₈	#64526	1	2	yes	—
214	C₄⋊C₄	—	2	2	no	—
215	C₄⋊C₄	—	76	2	no	—
216	C₄⋊C₄	—	76	2	no	—
217	C₄⋊C₄	—	76	2	no	—
218	C₄⋊C₄	—	76	2	no	—
219	C₄⋊C₄	—	152	2	no	—
220	C₂²⋊C₄	—	4	2	no	—
221	C₄²	#64543	1	2	yes	—
222	C₄²	#64543	1	2	yes	—
223	C₂³	—	2	2	no	—
224	C₂³	—	4	1	no	—
225	C₂³	—	4	1	no	—
226	C₂³	—	4	1	no	—
227	C₂³	—	4	1	no	—
228	C₂³	—	4	1	no	—
229	C₂³	—	4	1	no	—
230	C₂³	#10597376	1	1	yes	characteristic
231	D₄	—	2	4	no	—
232	D₄	—	4	2	no	—
233	C₂×C₄	—	2	1	no	—
234	C₂×C₄	—	2	1	no	—
235	C₂×C₄	—	4	1	no	—
236	C₂×C₄	—	4	1	no	—
237	C₂×C₄	—	4	1	no	—
238	C₂×C₄	—	8	1	no	—
239	C₂×C₄	—	8	1	no	—
240	C₂×C₄	—	8	1	no	—
241	C₂×C₄	—	8	1	no	—
242	C₂×C₄	—	152	2	no	—
243	C₂×C₄	—	152	2	no	—
244	C₂×C₄	—	152	2	no	—
245	C₂×C₄	#10597325	1	2	yes	—
246	C₂×C₄	#10597332	1	2	yes	—
247	C₂×C₄	C₂×D₁₅₂	1	1	yes	characteristic
248	C₂×C₄	#10597350	1	1	yes	characteristic
249	C₂×C₄	#10597355	1	2	yes	—
250	C₂×C₄	C₂×#64525	1	1	yes	characteristic
251	C₂×C₄	C₂×#64526	1	1	yes	characteristic
252	C₂×C₄	#10597381	1	1	yes	characteristic
253	C₂×C₄	#10597382	1	1	yes	characteristic
254	C₂×C₄	#10597395	1	1	yes	characteristic
255	C₂×C₄	#10597397	1	1	yes	characteristic
256	C₈	—	2	2	no	—
257	C₈	—	2	2	no	—
258	C₈	—	8	1	no	—
259	C₈	—	152	2	no	—
260	C₂²	—	4	2	no	—
261	C₂²	—	4	2	no	—
262	C₂²	—	4	2	no	—
263	C₂²	—	8	1	no	—
264	C₂²	—	8	1	no	—
265	C₂²	—	8	1	no	—
266	C₂²	—	8	1	no	—
267	C₂²	#11926469	1	1	yes	characteristic
268	C₂²	#11926739	1	1	yes	characteristic
269	C₂²	#11926749	1	1	yes	characteristic
270	C₂²	#11926780	1	1	yes	characteristic
271	C₂²	#11926802	1	1	yes	characteristic
272	C₂²	#11926814	1	1	yes	characteristic
273	C₂²	#11926819	1	1	yes	characteristic
274	C₄	—	2	2	no	—
275	C₄	—	8	1	no	—
276	C₄	—	304	2	no	—
277	C₄	#11926855	1	1	yes	characteristic
278	C₄	#11926858	1	2	yes	—
279	C₄	#11926860	1	1	yes	characteristic
280	C₄	#11926886	1	2	yes	—
281	C₄	#11926890	1	1	yes	characteristic
282	C₄	#11926903	1	1	yes	characteristic
283	C₂	—	8	2	no	—
284	C₂	#14562990	1	1	yes	characteristic
285	C₂	#14563024	1	1	yes	characteristic
286	C₂	#14563124	1	1	yes	characteristic
287	C₂	#14563158	1	1	yes	characteristic
288	C₂	#14565038	1	1	yes	characteristic
289	C₂	#14565058	1	1	yes	characteristic
290	C₂	#14565075	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#10597376
commutator, cosocle	C₂×C₄²×C₁₉	C₂³
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1954	C₂
socle	C₂³×C₁₉	#121
prime radical	C₂²×D₄×C₁₉	D₄
hypercenter	#1954	D₁₉
hypocenter	C₁₉	#10615
LCS	G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1954

Complements

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

N	H ≅ G/N	type
1. #14563795	C₂	semidirect
3. #14561519	C₂	semidirect
4. #14561470	C₂	semidirect
185. C₁₉	#10615	semidirect

Maximal subgroups

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

subgroup	index
#14563795	2
#14563635	2
#14561519	2
#14561470	2
C₁₉×#1954	2
#10615	19