Subgroups — #18073775

Order 4864.

414 conjugacy classes of subgroups.

The subgroup lattice has 216 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14563504	C₂	1	2	yes	maximal
2	C₂×#11926297	C₂	1	1	yes	maximal, characteristic
3	C₂×C₈×C₁₉⋊C₈	C₂	1	1	yes	maximal, characteristic
4	#14561476	C₂	1	2	yes	maximal
5	C₄×C₁₉×#107	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
7	C₂×#10597260	—	2	2	no	—
8	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
9	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
10	#11926299	—	2	2	no	—
11	#11926297	C₄	1	4	yes	complemented
12	C₈×C₁₉⋊C₈	C₄	1	4	yes	complemented
13	C₂×C₁₉×#107	C₄	1	2	yes	—
14	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
15	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
16	C₁₉×#340	C₄	1	2	yes	—
17	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
18	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
19	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
20	C₂×C₄²×C₁₉	—	2	2	no	—
21	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
22	C₂²×C₁₉⋊C₈	—	2	1	no	—
23	C₂²×C₁₉⋊C₈	—	2	2	no	—
24	C₂²×C₁₉⋊C₈	D₄	1	1	yes	characteristic
25	C₂²×C₁₉⋊C₈	D₄	1	1	yes	characteristic
26	C₁₉×#107	—	2	4	no	—
27	C₄×C₈×C₁₉	C₂×C₄	1	2	yes	—
28	C₄×C₈×C₁₉	C₂×C₄	1	2	yes	—
29	C₁₉×#95	—	2	2	no	—
30	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
31	C₄⋊(C₁₉⋊C₈)	C₂×C₄	1	4	yes	—
32	#10597260	—	4	4	no	—
33	C₄×C₁₉⋊C₈	—	2	1	no	—
34	C₄×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
35	C₄×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
36	C₄×C₁₉⋊C₈	Q₈	1	2	yes	—
37	C₂²×C₄×C₁₉	—	2	4	no	—
38	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
39	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
40	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
41	C₂×C₈×C₁₉	—	2	2	no	—
42	C₂×C₈×C₁₉	C₄²	1	2	yes	—
43	C₂×C₈×C₁₉	C₄²	1	2	yes	—
44	C₂×C₈×C₁₉	M₁₆	1	4	yes	—
45	C₄⋊C₄×C₁₉	—	2	4	no	—
46	C₄⋊C₄×C₁₉	—	2	4	no	—
47	C₄²×C₁₉	—	4	2	no	—
48	C₄²×C₁₉	—	4	2	no	—
49	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
50	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
51	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
52	C₄²×C₁₉	#41	1	1	yes	characteristic
53	C₂×C₁₉⋊C₈	—	2	4	no	—
54	C₂×C₁₉⋊C₈	—	2	2	no	—
55	C₂×C₁₉⋊C₈	—	2	1	no	—
56	C₂×C₁₉⋊C₈	—	2	1	no	—
57	C₂×C₁₉⋊C₈	—	2	4	no	—
58	C₂×C₁₉⋊C₈	—	4	2	no	—
59	C₂×C₁₉⋊C₈	—	4	2	no	—
60	C₂×C₁₉⋊C₈	C₄⋊C₄	1	2	yes	—
61	C₂×C₁₉⋊C₈	C₄⋊C₄	1	2	yes	—
62	C₂×C₁₉⋊C₈	D₈	1	2	yes	—
63	C₂×C₁₉⋊C₈	Q₁₆	1	2	yes	—
64	#8282	—	19	1	no	maximal, Sylow
65	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
66	C₂×C₄×C₁₉	—	2	2	no	—
67	C₂×C₄×C₁₉	—	4	4	no	—
68	C₂×C₄×C₁₉	—	4	4	no	—
69	C₂×C₄×C₁₉	—	4	4	no	—
70	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
71	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
72	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
73	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
74	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
75	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
76	C₂×C₄×C₁₉	C₂×M₁₆	1	2	yes	—
77	C₂×C₄×C₁₉	#131	1	2	yes	—
78	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
79	C₂×C₄×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
80	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
81	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
82	C₈×C₁₉	—	2	2	no	—
83	C₈×C₁₉	#97	1	4	yes	complemented
84	C₁₉⋊C₈	—	2	4	no	—
85	C₁₉⋊C₈	—	2	2	no	—
86	C₁₉⋊C₈	—	4	4	no	—
87	C₁₉⋊C₈	#107	1	4	yes	complemented
88	C₄×#107	D₁₉	1	1	yes	characteristic
89	#1770	—	19	2	no	—
90	C₂×#335	—	19	1	no	—
91	C₂×C₈²	—	19	1	no	—
92	#1279	—	19	2	no	—
93	C₂²×C₁₉	C₄×C₄⋊C₄	1	1	yes	characteristic
94	C₂²×C₁₉	#436	1	2	yes	—
95	C₂²×C₁₉	C₄×D₈	1	1	yes	characteristic
96	C₂²×C₁₉	C₄×Q₁₆	1	1	yes	characteristic
97	C₂²×C₁₉	#443	1	2	yes	—
98	C₄×C₁₉	—	2	1	no	—
99	C₄×C₁₉	—	2	1	no	—
100	C₄×C₁₉	—	8	4	no	—
101	C₄×C₁₉	C₂×#97	1	1	yes	characteristic
102	C₄×C₁₉	#405	1	1	yes	characteristic
103	C₄×C₁₉	C₂×#107	1	1	yes	characteristic
104	C₄×C₁₉	#427	1	1	yes	characteristic
105	C₄×C₁₉	C₄×D₈	1	1	yes	characteristic
106	C₄×C₁₉	C₄×Q₁₆	1	1	yes	characteristic
107	C₄×C₁₉	#446	1	2	yes	—
108	C₂×#107	Dic₁₉	1	2	yes	—
109	C₂×C₄⋊C₈	—	19	2	no	—
110	C₂×#97	—	38	2	no	—
111	C₂×C₄×C₈	—	19	1	no	—
112	C₂×C₄×C₈	—	19	1	no	—
113	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
114	C₄×C₄⋊C₄	C₂×D₁₉	1	2	yes	—
115	#340	Dic₁₉	1	2	yes	—
116	#336	—	38	2	no	—
117	#335	—	19	4	no	—
118	C₈²	—	19	4	no	—
119	C₂×C₁₉	#1589	1	2	yes	—
120	C₂×C₁₉	#1591	1	2	yes	—
121	C₂×C₁₉	#1770	1	1	yes	characteristic
122	C₂×C₁₉	#1772	1	1	yes	characteristic
123	C₂×C₁₉	C₄×#107	1	1	yes	characteristic
124	C₂²×C₈	—	19	1	no	—
125	C₂²×C₈	—	19	1	no	—
126	C₂²×C₈	—	38	1	no	—
127	C₂²×C₈	—	38	2	no	—
128	C₂²×C₈	C₂×Dic₁₉	1	1	yes	characteristic
129	C₂²×C₈	C₂×Dic₁₉	1	1	yes	characteristic
130	C₂×C₄⋊C₄	C₂×Dic₁₉	1	4	yes	—
131	C₂×C₄²	—	2	2	no	—
132	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
133	#107	—	2	4	no	—
134	C₄⋊C₈	—	19	4	no	—
135	C₄⋊C₈	—	38	2	no	—
136	#97	—	76	4	no	—
137	C₄×C₈	—	19	2	no	—
138	C₄×C₈	—	19	2	no	—
139	C₄×C₈	—	19	2	no	—
140	C₄×C₈	—	38	1	no	—
141	C₄×C₈	C₄×D₁₉	1	2	yes	—
142	C₄×C₈	C₄×D₁₉	1	2	yes	—
143	#95	—	2	2	no	—
144	C₁₉	#8282	1	1	yes	characteristic, complemented, Sylow
145	C₂²×C₄	—	2	4	no	—
146	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
147	C₂²×C₄	#64543	1	1	yes	characteristic
148	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
149	C₂×C₈	—	2	2	no	—
150	C₂×C₈	—	19	2	no	—
151	C₂×C₈	—	19	2	no	—
152	C₂×C₈	—	19	2	no	—
153	C₂×C₈	—	19	2	no	—
154	C₂×C₈	—	38	4	no	—
155	C₂×C₈	—	38	2	no	—
156	C₂×C₈	—	38	1	no	—
157	C₂×C₈	—	38	1	no	—
158	C₂×C₈	—	38	4	no	—
159	C₂×C₈	—	76	2	no	—
160	C₂×C₈	—	76	2	no	—
161	C₂×C₈	#64520	1	4	yes	—
162	C₂×C₈	C₄×Dic₁₉	1	2	yes	—
163	C₂×C₈	C₄×Dic₁₉	1	2	yes	—
164	C₄⋊C₄	—	2	4	no	—
165	C₄⋊C₄	—	2	4	no	—
166	C₄²	—	4	2	no	—
167	C₄²	—	4	2	no	—
168	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
169	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
170	C₄²	Q₈×D₁₉	1	1	yes	characteristic
171	C₄²	#64545	1	1	yes	characteristic
172	C₂³	D₄×Dic₁₉	1	1	yes	characteristic
173	C₂×C₄	—	2	2	no	—
174	C₂×C₄	—	4	4	no	—
175	C₂×C₄	—	4	4	no	—
176	C₂×C₄	—	4	4	no	—
177	C₂×C₄	#10597333	1	1	yes	characteristic
178	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
179	C₂×C₄	#10597338	1	1	yes	characteristic
180	C₂×C₄	#10597339	1	1	yes	characteristic
181	C₂×C₄	D₈×D₁₉	1	1	yes	characteristic
182	C₂×C₄	#10597358	1	1	yes	characteristic
183	C₂×C₄	Q₁₆×D₁₉	1	1	yes	characteristic
184	C₂×C₄	#10597365	1	1	yes	characteristic
185	C₂×C₄	C₂×#64520	1	2	yes	—
186	C₂×C₄	C₂×C₄×Dic₁₉	1	1	yes	characteristic
187	C₂×C₄	Q₈×Dic₁₉	1	1	yes	characteristic
188	C₂×C₄	#10597394	1	2	yes	—
189	C₈	—	2	2	no	—
190	C₈	—	19	4	no	—
191	C₈	—	38	4	no	—
192	C₈	—	38	2	no	—
193	C₈	—	76	4	no	—
194	C₈	#10597260	1	4	yes	complemented
195	C₂²	C₄⋊C₄×Dic₁₉	1	1	yes	characteristic
196	C₂²	#11926622	1	2	yes	—
197	C₂²	D₈×Dic₁₉	1	1	yes	characteristic
198	C₂²	Q₁₆×Dic₁₉	1	1	yes	characteristic
199	C₂²	#11926661	1	2	yes	—
200	C₄	—	2	1	no	—
201	C₄	—	2	1	no	—
202	C₄	—	8	4	no	—
203	C₄	C₂×#10597260	1	1	yes	characteristic
204	C₄	#11926500	1	1	yes	characteristic
205	C₄	#107×D₁₉	1	1	yes	characteristic
206	C₄	#11926581	1	1	yes	characteristic
207	C₄	#11926626	1	1	yes	characteristic
208	C₄	#11926638	1	1	yes	characteristic
209	C₄	#11926675	1	2	yes	—
210	C₂	#14562520	1	2	yes	—
211	C₂	#14562532	1	2	yes	—
212	C₂	#14563504	1	1	yes	characteristic
213	C₂	#14563516	1	1	yes	characteristic
214	C₂	#107×Dic₁₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	D₄×D₁₉
commutator	C₂×C₄×C₁₉	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₄×C₁₉×#107	C₂
socle, prime radical	C₂³×C₁₉	C₄×D₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₄×#107	D₁₉
hypocenter	C₁₉	#8282
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ C₄×#107

Complements

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

N	H ≅ G/N	type
11. #11926297	C₄	semidirect
12. C₈×C₁₉⋊C₈	C₄	semidirect
83. C₈×C₁₉	#97	semidirect
87. C₁₉⋊C₈	#107	semidirect
144. C₁₉	#8282	semidirect
194. C₈	#10597260	semidirect

Maximal subgroups

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

subgroup	index
#14563504	2
C₂×#11926297	2
C₂×C₈×C₁₉⋊C₈	2
#14561476	2
C₄×C₁₉×#107	2
#8282	19