Subgroups — #18087445

Order 4864.

350 conjugacy classes of subgroups.

The subgroup lattice has 238 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14564393	C₂	1	2	yes	maximal
2	#14563795	C₂	1	1	yes	maximal, characteristic
3	#14561519	C₂	1	2	yes	maximal
4	#14561470	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1939	C₂	1	1	yes	maximal, characteristic
6	C₂×#10597275	—	2	1	no	—
7	C₂×#10597275	—	2	1	no	—
8	C₂×#10597264	—	2	2	no	—
9	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
10	#11926414	C₂²	1	2	yes	—
11	#11926306	—	2	2	no	—
12	C₂×C₁₉×C₄⋊C₈	—	2	1	no	—
13	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
14	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
15	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
16	C₁₉×#336	—	2	1	no	—
17	C₂²×C₈×C₁₉	—	2	1	no	—
18	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
19	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
20	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
21	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
22	C₂×C₄²×C₁₉	—	2	1	no	—
23	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
24	C₂×C₄⋊Dic₁₉	—	2	2	no	—
25	C₂×C₄⋊Dic₁₉	—	2	2	no	—
26	C₂×C₄⋊Dic₁₉	—	2	2	no	—
27	C₂²×C₁₉⋊C₈	—	2	2	no	—
28	C₁₉×C₄⋊C₈	—	2	2	no	—
29	C₁₉×C₄⋊C₈	—	4	2	no	—
30	C₄×C₈×C₁₉	—	2	2	no	—
31	C₁₉×#95	—	2	1	no	—
32	#10597275	—	4	2	no	—
33	#10597275	—	4	2	no	—
34	#10597264	—	4	4	no	—
35	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
36	C₄⋊(C₁₉⋊C₈)	Q₈	1	4	yes	—
37	C₂²×C₄×C₁₉	—	2	1	no	—
38	C₂²×C₄×C₁₉	—	2	1	no	—
39	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
40	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
41	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
42	C₂²×Dic₁₉	—	4	2	no	—
43	C₂×C₈×C₁₉	—	2	1	no	—
44	C₂×C₈×C₁₉	—	2	1	no	—
45	C₂×C₈×C₁₉	—	2	1	no	—
46	C₂×C₈×C₁₉	—	2	1	no	—
47	C₂×C₈×C₁₉	—	4	1	no	—
48	C₂×C₈×C₁₉	—	4	1	no	—
49	C₂×C₈×C₁₉	—	4	1	no	—
50	C₂×C₈×C₁₉	D₈	1	2	yes	—
51	C₂×C₈×C₁₉	Q₁₆	1	2	yes	—
52	C₄⋊C₄×C₁₉	—	2	1	no	—
53	C₄⋊C₄×C₁₉	—	2	2	no	—
54	C₄⋊C₄×C₁₉	D₈	1	2	yes	—
55	C₄²×C₁₉	—	4	1	no	—
56	C₄²×C₁₉	—	4	1	no	—
57	C₄²×C₁₉	C₂×Q₈	1	2	yes	—
58	C₄²×C₁₉	#41	1	2	yes	—
59	C₄⋊Dic₁₉	—	4	2	no	—
60	C₄⋊Dic₁₉	—	4	2	no	—
61	C₄⋊Dic₁₉	—	4	2	no	—
62	C₄⋊Dic₁₉	—	4	2	no	—
63	C₄⋊Dic₁₉	—	8	2	no	—
64	C₂×C₁₉⋊C₈	—	2	4	no	—
65	C₂×C₁₉⋊C₈	—	4	2	no	—
66	C₂×C₁₉⋊C₈	—	4	2	no	—
67	#10649	—	19	1	no	maximal, Sylow
68	C₂³×C₁₉	#121	1	1	yes	characteristic
69	C₂×C₄×C₁₉	—	2	1	no	—
70	C₂×C₄×C₁₉	—	2	1	no	—
71	C₂×C₄×C₁₉	—	2	2	no	—
72	C₂×C₄×C₁₉	—	4	1	no	—
73	C₂×C₄×C₁₉	—	4	1	no	—
74	C₂×C₄×C₁₉	—	4	1	no	—
75	C₂×C₄×C₁₉	—	4	1	no	—
76	C₂×C₄×C₁₉	—	4	1	no	—
77	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
78	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
79	C₂×C₄×C₁₉	#125	1	2	yes	—
80	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
81	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
82	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
83	C₂×C₄×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
84	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
85	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
86	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
87	C₂×C₄×C₁₉	#137	1	2	yes	—
88	C₂×Dic₁₉	—	8	2	no	—
89	C₂×Dic₁₉	—	8	2	no	—
90	C₂×Dic₁₉	—	8	2	no	—
91	C₈×C₁₉	—	2	2	no	—
92	C₈×C₁₉	—	2	2	no	—
93	C₈×C₁₉	—	8	1	no	—
94	C₁₉⋊C₈	—	4	4	no	—
95	#1947	—	19	2	no	—
96	#1939	D₁₉	1	1	yes	characteristic
97	#1845	—	19	1	no	—
98	#1296	—	19	2	no	—
99	#1277	—	19	1	no	—
100	C₂²×C₁₉	#398	1	1	yes	characteristic
101	C₂²×C₁₉	#459	1	1	yes	characteristic
102	C₂²×C₁₉	#462	1	1	yes	characteristic
103	C₂²×C₁₉	#466	1	1	yes	characteristic
104	C₂²×C₁₉	#470	1	1	yes	characteristic
105	C₂²×C₁₉	#472	1	1	yes	characteristic
106	C₂²×C₁₉	#473	1	1	yes	characteristic
107	C₄×C₁₉	—	2	2	no	—
108	C₄×C₁₉	—	4	2	no	—
109	C₄×C₁₉	—	8	1	no	—
110	C₄×C₁₉	#474	1	2	yes	—
111	C₄×C₁₉	#479	1	2	yes	—
112	C₄×C₁₉	#480	1	1	yes	characteristic
113	C₄×C₁₉	#484	1	1	yes	characteristic
114	C₄×C₁₉	#500	1	1	yes	characteristic
115	C₄×C₁₉	#501	1	1	yes	characteristic
116	Dic₁₉	—	16	2	no	—
117	C₂×#107	—	38	1	no	—
118	C₂×#107	—	38	1	no	—
119	C₂×#107	—	38	2	no	—
120	C₂×C₄⋊C₈	—	2	1	no	—
121	C₂×C₄⋊C₈	—	19	2	no	—
122	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
123	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
124	#384	—	19	2	no	—
125	C₄×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
126	#340	—	38	2	no	—
127	#336	—	2	1	no	—
128	C₂×C₁₉	#1667	1	1	yes	characteristic
129	C₂×C₁₉	#1674	1	1	yes	characteristic
130	C₂×C₁₉	#1689	1	1	yes	characteristic
131	C₂×C₁₉	#1696	1	1	yes	characteristic
132	C₂×C₁₉	#2083	1	1	yes	characteristic
133	C₂×C₁₉	#2086	1	1	yes	characteristic
134	C₂×C₁₉	#2089	1	1	yes	characteristic
135	C₂²×C₈	—	2	1	no	—
136	C₂²×C₈	—	38	2	no	—
137	C₂²×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
138	C₂²×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
139	C₂×C₄⋊C₄	—	38	2	no	—
140	C₂×C₄⋊C₄	—	38	2	no	—
141	C₂×C₄⋊C₄	—	38	2	no	—
142	C₂×C₄⋊C₄	D₇₆	1	1	yes	characteristic
143	C₂×C₄⋊C₄	D₇₆	1	1	yes	characteristic
144	C₂×C₄²	—	2	1	no	—
145	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
146	#107	—	76	2	no	—
147	#107	—	76	2	no	—
148	#107	—	76	4	no	—
149	C₄⋊C₈	—	2	2	no	—
150	C₄⋊C₈	—	4	2	no	—
151	C₄⋊C₈	—	19	4	no	—
152	C₄⋊C₈	—	38	2	no	—
153	C₄×C₈	—	2	2	no	—
154	#95	—	2	1	no	—
155	C₁₉	#10649	1	1	yes	characteristic, complemented, Sylow
156	C₂²×C₄	—	2	1	no	—
157	C₂²×C₄	—	2	1	no	—
158	C₂²×C₄	—	76	2	no	—
159	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
160	C₂²×C₄	#64541	1	1	yes	characteristic
161	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
162	C₂×C₈	—	2	1	no	—
163	C₂×C₈	—	2	1	no	—
164	C₂×C₈	—	2	1	no	—
165	C₂×C₈	—	2	1	no	—
166	C₂×C₈	—	4	1	no	—
167	C₂×C₈	—	4	1	no	—
168	C₂×C₈	—	4	1	no	—
169	C₂×C₈	—	38	4	no	—
170	C₂×C₈	—	76	2	no	—
171	C₂×C₈	—	76	2	no	—
172	C₂×C₈	#64525	1	2	yes	—
173	C₂×C₈	#64528	1	2	yes	—
174	C₄⋊C₄	—	2	1	no	—
175	C₄⋊C₄	—	2	2	no	—
176	C₄⋊C₄	—	76	2	no	—
177	C₄⋊C₄	—	76	2	no	—
178	C₄⋊C₄	—	76	2	no	—
179	C₄⋊C₄	—	76	2	no	—
180	C₄⋊C₄	—	152	2	no	—
181	C₄⋊C₄	D₁₅₂	1	2	yes	—
182	C₄²	—	4	1	no	—
183	C₄²	—	4	1	no	—
184	C₄²	#64543	1	2	yes	—
185	C₄²	Q₈×D₁₉	1	2	yes	—
186	C₂³	#10597376	1	1	yes	characteristic
187	C₂×C₄	—	2	1	no	—
188	C₂×C₄	—	2	1	no	—
189	C₂×C₄	—	2	2	no	—
190	C₂×C₄	—	4	1	no	—
191	C₂×C₄	—	4	1	no	—
192	C₂×C₄	—	4	1	no	—
193	C₂×C₄	—	4	1	no	—
194	C₂×C₄	—	4	1	no	—
195	C₂×C₄	—	152	2	no	—
196	C₂×C₄	—	152	2	no	—
197	C₂×C₄	—	152	2	no	—
198	C₂×C₄	#10597335	1	2	yes	—
199	C₂×C₄	#10597343	1	2	yes	—
200	C₂×C₄	C₂×D₁₅₂	1	1	yes	characteristic
201	C₂×C₄	#10597350	1	1	yes	characteristic
202	C₂×C₄	#10597355	1	2	yes	—
203	C₂×C₄	C₂×#64525	1	1	yes	characteristic
204	C₂×C₄	#10597381	1	1	yes	characteristic
205	C₂×C₄	C₂×#64528	1	1	yes	characteristic
206	C₂×C₄	#10597390	1	1	yes	characteristic
207	C₂×C₄	#10597395	1	1	yes	characteristic
208	C₂×C₄	#10597397	1	1	yes	characteristic
209	C₈	—	2	2	no	—
210	C₈	—	2	2	no	—
211	C₈	—	8	1	no	—
212	C₈	—	76	4	no	—
213	C₂²	#11926474	1	1	yes	characteristic
214	C₂²	#11926739	1	1	yes	characteristic
215	C₂²	#11926754	1	1	yes	characteristic
216	C₂²	#11926780	1	1	yes	characteristic
217	C₂²	#11926802	1	1	yes	characteristic
218	C₂²	#11926814	1	1	yes	characteristic
219	C₂²	#11926819	1	1	yes	characteristic
220	C₄	—	2	2	no	—
221	C₄	—	4	2	no	—
222	C₄	—	8	1	no	—
223	C₄	—	304	2	no	—
224	C₄	#11926825	1	2	yes	—
225	C₄	#11926852	1	2	yes	—
226	C₄	#11926855	1	1	yes	characteristic
227	C₄	#11926877	1	1	yes	characteristic
228	C₄	#11926947	1	1	yes	characteristic
229	C₄	#11926954	1	1	yes	characteristic
230	C₂	#14562990	1	1	yes	characteristic
231	C₂	#14563029	1	1	yes	characteristic
232	C₂	#14563124	1	1	yes	characteristic
233	C₂	#14563163	1	1	yes	characteristic
234	C₂	#14565106	1	1	yes	characteristic
235	C₂	#14565123	1	1	yes	characteristic
236	C₂	#14565140	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#10597376
commutator, cosocle	C₂×C₄²×C₁₉	C₂³
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1939	C₂
socle, prime radical	C₂³×C₁₉	#121
hypercenter	#1939	D₁₉
hypocenter	C₁₉	#10649
LCS	G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1939

Complements

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

N	H ≅ G/N	type
155. C₁₉	#10649	semidirect

Maximal subgroups

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

subgroup	index
#14564393	2
#14563795	2
#14561519	2
#14561470	2
C₁₉×#1939	2
#10649	19