Subgroups — #18087249

Order 4864.

366 conjugacy classes of subgroups.

The subgroup lattice has 250 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
2	#14563640	C₂	1	2	yes	maximal
3	#14561519	C₂	1	2	yes	maximal
4	#14561470	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1984	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×#10597292	—	2	2	no	—
10	#11926414	C₂²	1	2	yes	—
11	#11926306	—	2	2	no	—
12	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
13	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
14	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
15	C₁₉×#336	—	2	1	no	—
16	C₁₉×#336	—	2	1	no	—
17	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
18	C₂²×C₈×C₁₉	—	2	1	no	—
19	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
20	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
21	C₄×Q₈×C₁₉	—	2	2	no	—
22	C₄×Q₈×C₁₉	—	2	2	no	—
23	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
24	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
25	C₂×C₄²×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	C₄×C₈×C₁₉	—	2	2	no	—
33	#10597292	—	4	4	no	—
34	#10597275	—	4	2	no	—
35	#10597275	—	4	2	no	—
36	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
37	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
38	C₂×Q₈×C₁₉	—	2	1	no	—
39	C₂×Q₈×C₁₉	—	2	2	no	—
40	C₂×Q₈×C₁₉	—	2	2	no	—
41	C₂×Q₈×C₁₉	D₈	1	2	yes	—
42	C₂²×C₄×C₁₉	—	2	1	no	—
43	C₂²×C₄×C₁₉	—	2	1	no	—
44	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
45	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
46	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
47	C₂²×Dic₁₉	—	4	2	no	—
48	C₂×C₈×C₁₉	—	2	1	no	—
49	C₂×C₈×C₁₉	—	2	1	no	—
50	C₂×C₈×C₁₉	—	2	1	no	—
51	C₂×C₈×C₁₉	—	2	1	no	—
52	C₂×C₈×C₁₉	—	4	1	no	—
53	C₂×C₈×C₁₉	—	4	1	no	—
54	C₂×C₈×C₁₉	—	4	1	no	—
55	C₂×C₈×C₁₉	SD₁₆	1	2	yes	—
56	C₂×C₈×C₁₉	Q₁₆	1	2	yes	—
57	C₄⋊C₄×C₁₉	—	2	2	no	—
58	C₄⋊C₄×C₁₉	—	4	2	no	—
59	C₄²×C₁₉	—	4	1	no	—
60	C₄²×C₁₉	—	4	1	no	—
61	C₄²×C₁₉	#41	1	2	yes	—
62	C₄²×C₁₉	#41	1	2	yes	—
63	C₄⋊Dic₁₉	—	4	2	no	—
64	C₄⋊Dic₁₉	—	4	2	no	—
65	C₄⋊Dic₁₉	—	4	2	no	—
66	C₄⋊Dic₁₉	—	4	2	no	—
67	C₄⋊Dic₁₉	—	8	2	no	—
68	C₂×C₁₉⋊C₈	—	4	2	no	—
69	C₂×C₁₉⋊C₈	—	4	2	no	—
70	C₂×C₁₉⋊C₈	—	4	2	no	—
71	#10617	—	19	1	no	maximal, Sylow
72	C₂³×C₁₉	#121	1	1	yes	characteristic
73	Q₈×C₁₉	—	2	4	no	—
74	Q₈×C₁₉	—	4	2	no	—
75	C₂×C₄×C₁₉	—	2	1	no	—
76	C₂×C₄×C₁₉	—	2	1	no	—
77	C₂×C₄×C₁₉	—	2	2	no	—
78	C₂×C₄×C₁₉	—	4	1	no	—
79	C₂×C₄×C₁₉	—	4	1	no	—
80	C₂×C₄×C₁₉	—	4	1	no	—
81	C₂×C₄×C₁₉	—	4	1	no	—
82	C₂×C₄×C₁₉	—	4	1	no	—
83	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
84	C₂×C₄×C₁₉	#123	1	2	yes	—
85	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
86	C₂×C₄×C₁₉	#126	1	2	yes	—
87	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
88	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
89	C₂×C₄×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
90	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
91	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
92	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
93	C₂×C₄×C₁₉	#137	1	2	yes	—
94	C₂×Dic₁₉	—	8	2	no	—
95	C₂×Dic₁₉	—	8	2	no	—
96	C₂×Dic₁₉	—	8	2	no	—
97	C₈×C₁₉	—	2	2	no	—
98	C₈×C₁₉	—	2	2	no	—
99	C₈×C₁₉	—	8	1	no	—
100	C₁₉⋊C₈	—	8	2	no	—
101	#1984	D₁₉	1	1	yes	characteristic
102	#1845	—	19	1	no	—
103	#1803	—	19	2	no	—
104	#1296	—	19	2	no	—
105	#1277	—	19	1	no	—
106	C₂²×C₁₉	#397	1	1	yes	characteristic
107	C₂²×C₁₉	#460	1	1	yes	characteristic
108	C₂²×C₁₉	#462	1	1	yes	characteristic
109	C₂²×C₁₉	#466	1	1	yes	characteristic
110	C₂²×C₁₉	#470	1	1	yes	characteristic
111	C₂²×C₁₉	#472	1	1	yes	characteristic
112	C₂²×C₁₉	#473	1	1	yes	characteristic
113	C₄×C₁₉	—	2	2	no	—
114	C₄×C₁₉	—	4	2	no	—
115	C₄×C₁₉	—	8	1	no	—
116	C₄×C₁₉	#480	1	2	yes	—
117	C₄×C₁₉	#483	1	1	yes	characteristic
118	C₄×C₁₉	#484	1	1	yes	characteristic
119	C₄×C₁₉	#485	1	2	yes	—
120	C₄×C₁₉	#487	1	1	yes	characteristic
121	C₄×C₁₉	#489	1	1	yes	characteristic
122	Dic₁₉	—	16	2	no	—
123	C₂×C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic
124	C₂×#107	—	38	1	no	—
125	C₂×#107	—	38	1	no	—
126	C₂×C₄⋊C₈	—	19	2	no	—
127	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
128	C₂×#103	—	38	2	no	—
129	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
130	#384	—	19	2	no	—
131	#340	—	38	2	no	—
132	#336	—	2	1	no	—
133	#336	—	2	1	no	—
134	C₂×C₁₉	#1668	1	1	yes	characteristic
135	C₂×C₁₉	#1674	1	1	yes	characteristic
136	C₂×C₁₉	#1690	1	1	yes	characteristic
137	C₂×C₁₉	#1696	1	1	yes	characteristic
138	C₂×C₁₉	#2072	1	1	yes	characteristic
139	C₂×C₁₉	#2075	1	1	yes	characteristic
140	C₂×C₁₉	#2078	1	1	yes	characteristic
141	C₂²×Q₈	D₇₆	1	1	yes	characteristic
142	C₂²×C₈	—	2	1	no	—
143	C₂²×C₈	—	38	2	no	—
144	C₂²×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
145	C₂²×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
146	C₄×Q₈	—	2	2	no	—
147	C₄×Q₈	—	2	2	no	—
148	C₂×C₄⋊C₄	—	2	1	no	—
149	C₂×C₄⋊C₄	—	38	2	no	—
150	C₂×C₄⋊C₄	—	38	2	no	—
151	C₂×C₄⋊C₄	—	38	2	no	—
152	C₂×C₄⋊C₄	D₇₆	1	1	yes	characteristic
153	C₂×C₄²	—	2	1	no	—
154	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
155	#107	—	76	2	no	—
156	#107	—	76	2	no	—
157	C₄⋊C₈	—	2	2	no	—
158	C₄⋊C₈	—	38	2	no	—
159	C₄⋊C₈	—	38	2	no	—
160	#103	—	76	4	no	—
161	C₄×C₈	—	2	2	no	—
162	C₁₉	#10617	1	1	yes	characteristic, complemented, Sylow
163	C₂×Q₈	—	2	1	no	—
164	C₂×Q₈	—	2	2	no	—
165	C₂×Q₈	—	2	2	no	—
166	C₂×Q₈	D₁₅₂	1	2	yes	—
167	C₂²×C₄	—	2	1	no	—
168	C₂²×C₄	—	2	1	no	—
169	C₂²×C₄	—	76	2	no	—
170	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
171	C₂²×C₄	#64541	1	1	yes	characteristic
172	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
173	C₂×C₈	—	2	1	no	—
174	C₂×C₈	—	2	1	no	—
175	C₂×C₈	—	2	1	no	—
176	C₂×C₈	—	2	1	no	—
177	C₂×C₈	—	4	1	no	—
178	C₂×C₈	—	4	1	no	—
179	C₂×C₈	—	4	1	no	—
180	C₂×C₈	—	76	2	no	—
181	C₂×C₈	—	76	2	no	—
182	C₂×C₈	—	76	2	no	—
183	C₂×C₈	#64527	1	2	yes	—
184	C₂×C₈	#64528	1	2	yes	—
185	C₄⋊C₄	—	2	2	no	—
186	C₄⋊C₄	—	4	2	no	—
187	C₄⋊C₄	—	76	2	no	—
188	C₄⋊C₄	—	76	2	no	—
189	C₄⋊C₄	—	76	2	no	—
190	C₄⋊C₄	—	76	2	no	—
191	C₄⋊C₄	—	152	2	no	—
192	C₄²	—	4	1	no	—
193	C₄²	—	4	1	no	—
194	C₄²	#64543	1	2	yes	—
195	C₄²	#64543	1	2	yes	—
196	C₂³	#10597376	1	1	yes	characteristic
197	Q₈	—	2	4	no	—
198	Q₈	—	4	2	no	—
199	C₂×C₄	—	2	1	no	—
200	C₂×C₄	—	2	1	no	—
201	C₂×C₄	—	2	2	no	—
202	C₂×C₄	—	4	1	no	—
203	C₂×C₄	—	4	1	no	—
204	C₂×C₄	—	4	1	no	—
205	C₂×C₄	—	4	1	no	—
206	C₂×C₄	—	4	1	no	—
207	C₂×C₄	—	152	2	no	—
208	C₂×C₄	—	152	2	no	—
209	C₂×C₄	—	152	2	no	—
210	C₂×C₄	#10597325	1	2	yes	—
211	C₂×C₄	#10597332	1	2	yes	—
212	C₂×C₄	C₂×D₁₅₂	1	1	yes	characteristic
213	C₂×C₄	#10597350	1	1	yes	characteristic
214	C₂×C₄	#10597355	1	2	yes	—
215	C₂×C₄	#10597381	1	1	yes	characteristic
216	C₂×C₄	#10597382	1	1	yes	characteristic
217	C₂×C₄	C₂×#64527	1	1	yes	characteristic
218	C₂×C₄	C₂×#64528	1	1	yes	characteristic
219	C₂×C₄	#10597395	1	1	yes	characteristic
220	C₂×C₄	#10597397	1	1	yes	characteristic
221	C₈	—	2	2	no	—
222	C₈	—	2	2	no	—
223	C₈	—	8	1	no	—
224	C₈	—	152	2	no	—
225	C₂²	#11926469	1	1	yes	characteristic
226	C₂²	#11926744	1	1	yes	characteristic
227	C₂²	#11926754	1	1	yes	characteristic
228	C₂²	#11926780	1	1	yes	characteristic
229	C₂²	#11926802	1	1	yes	characteristic
230	C₂²	#11926814	1	1	yes	characteristic
231	C₂²	#11926819	1	1	yes	characteristic
232	C₄	—	2	2	no	—
233	C₄	—	4	2	no	—
234	C₄	—	8	1	no	—
235	C₄	—	304	2	no	—
236	C₄	#11926858	1	2	yes	—
237	C₄	#11926872	1	1	yes	characteristic
238	C₄	#11926877	1	1	yes	characteristic
239	C₄	#11926886	1	2	yes	—
240	C₄	#11926894	1	1	yes	characteristic
241	C₄	#11926903	1	1	yes	characteristic
242	C₂	#14562995	1	1	yes	characteristic
243	C₂	#14563029	1	1	yes	characteristic
244	C₂	#14563129	1	1	yes	characteristic
245	C₂	#14563163	1	1	yes	characteristic
246	C₂	#14565043	1	1	yes	characteristic
247	C₂	#14565058	1	1	yes	characteristic
248	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×#1984	C₂
socle, prime radical	C₂³×C₁₉	#121
hypercenter	#1984	D₁₉
hypocenter	C₁₉	#10617
LCS	G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1984

Complements

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

N	H ≅ G/N	type
162. C₁₉	#10617	semidirect

Maximal subgroups

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

subgroup	index
#14563795	2
#14563640	2
#14561519	2
#14561470	2
C₁₉×#1984	2
#10617	19