Subgroups — #18082553

Order 4864.

458 conjugacy classes of subgroups.

The subgroup lattice has 218 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#10597316	C₂	1	1	yes	maximal, characteristic
2	#14563381	C₂	1	1	yes	maximal, characteristic
3	#14561474	C₂	1	4	yes	maximal
4	C₁₉×#1842	C₂	1	1	yes	maximal, characteristic
5	C₂×#10597316	C₄	1	1	yes	characteristic
6	C₂×C₄×C₁₉⋊C₈	C₂²	1	2	yes	—
7	#11926442	C₄	1	2	yes	—
8	#11926428	—	2	2	no	—
9	#11926410	C₄	1	1	yes	characteristic
10	C₄×Dic₁₉⋊C₄	—	2	2	no	—
11	C₄×C₄⋊Dic₁₉	C₂²	1	2	yes	—
12	#11926299	—	2	2	no	—
13	C₂×C₁₉×C₄⋊C₈	—	2	2	no	—
14	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
15	C₄³×C₁₉	C₂²	1	1	yes	characteristic
16	C₂²×C₈×C₁₉	—	2	2	no	—
17	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
18	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
19	C₂×C₄²×C₁₉	D₄	1	2	yes	—
20	C₂×C₄²×C₁₉	D₄	1	2	yes	—
21	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
22	C₂×C₄⋊Dic₁₉	C₂×C₄	1	2	yes	—
23	C₂×C₄⋊Dic₁₉	C₂×C₄	1	2	yes	—
24	C₂×Dic₁₉⋊C₄	—	2	2	no	—
25	C₂×Dic₁₉⋊C₄	—	2	2	no	—
26	C₂×C₄×Dic₁₉	—	2	2	no	—
27	C₂²×C₁₉⋊C₈	—	2	2	no	—
28	#10597316	—	2	2	no	—
29	#10597316	C₈	1	4	yes	complemented
30	C₁₉×C₄⋊C₈	—	2	4	no	—
31	C₁₉×C₄⋊C₈	—	4	4	no	—
32	C₁₉⋊#95	—	2	2	no	—
33	C₁₉⋊#95	—	2	2	no	—
34	C₁₉⋊#95	—	2	2	no	—
35	C₄×C₁₉⋊C₈	—	2	2	no	—
36	C₄×C₁₉⋊C₈	Q₈	1	4	yes	—
37	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
38	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
39	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
40	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
41	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
42	C₂²×Dic₁₉	—	2	2	no	—
43	C₂²×Dic₁₉	—	2	2	no	—
44	C₂×C₈×C₁₉	—	4	2	no	—
45	C₂×C₈×C₁₉	—	4	4	no	—
46	C₄²×C₁₉	—	2	2	no	—
47	C₄²×C₁₉	—	2	2	no	—
48	C₄²×C₁₉	—	2	2	no	—
49	C₄²×C₁₉	—	4	2	no	—
50	C₄²×C₁₉	C₂×C₈	1	2	yes	—
51	C₄²×C₁₉	M₁₆	1	2	yes	—
52	C₄²×C₁₉	C₂×Q₈	1	2	yes	—
53	C₄²×C₁₉	#41	1	2	yes	—
54	C₄⋊Dic₁₉	—	2	2	no	—
55	C₄⋊Dic₁₉	—	2	4	no	—
56	C₄⋊Dic₁₉	C₂×C₈	1	4	yes	—
57	Dic₁₉⋊C₄	—	2	8	no	—
58	Dic₁₉⋊C₄	—	4	4	no	—
59	C₄×Dic₁₉	—	4	2	no	—
60	C₄×Dic₁₉	—	4	2	no	—
61	C₂×C₁₉⋊C₈	—	2	4	no	—
62	C₂×C₁₉⋊C₈	—	4	4	no	—
63	#9872	—	19	1	no	maximal, Sylow
64	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
65	C₂×C₄×C₁₉	—	2	2	no	—
66	C₂×C₄×C₁₉	—	2	2	no	—
67	C₂×C₄×C₁₉	—	2	2	no	—
68	C₂×C₄×C₁₉	—	2	2	no	—
69	C₂×C₄×C₁₉	—	2	2	no	—
70	C₂×C₄×C₁₉	—	2	2	no	—
71	C₂×C₄×C₁₉	C₂²⋊C₈	1	4	yes	—
72	C₂×C₄×C₁₉	C₄×Q₈	1	2	yes	—
73	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
74	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
75	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
76	C₂×C₄×C₁₉	C₂²×C₈	1	1	yes	characteristic
77	C₂×C₄×C₁₉	C₂×M₁₆	1	1	yes	characteristic
78	C₂×C₄×C₁₉	#131	1	2	yes	—
79	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
80	C₂×C₄×C₁₉	#137	1	2	yes	—
81	C₂×Dic₁₉	—	2	4	no	—
82	C₂×Dic₁₉	—	4	2	no	—
83	C₂×Dic₁₉	—	4	2	no	—
84	C₂×Dic₁₉	—	4	2	no	—
85	C₂×Dic₁₉	—	4	2	no	—
86	C₂×Dic₁₉	—	4	2	no	—
87	C₈×C₁₉	—	8	2	no	—
88	C₁₉⋊C₈	—	4	4	no	—
89	C₄×#125	—	19	1	no	—
90	#1842	D₁₉	1	1	yes	characteristic
91	#1744	—	19	1	no	—
92	#1279	—	19	4	no	—
93	C₂²×C₁₉	#391	1	1	yes	characteristic
94	C₂²×C₁₉	C₂×C₂²⋊C₈	1	1	yes	characteristic
95	C₂²×C₁₉	#408	1	1	yes	characteristic
96	C₂²×C₁₉	#417	1	2	yes	—
97	C₂²×C₁₉	#421	1	2	yes	—
98	C₄×C₁₉	—	2	4	no	—
99	C₄×C₁₉	—	2	2	no	—
100	C₄×C₁₉	—	4	2	no	—
101	C₄×C₁₉	C₈×Q₈	1	2	yes	—
102	C₄×C₁₉	#446	1	2	yes	—
103	C₄×C₁₉	#490	1	1	yes	characteristic
104	C₄×C₁₉	#491	1	1	yes	characteristic
105	C₄×C₁₉	#501	1	2	yes	—
106	Dic₁₉	—	4	4	no	—
107	Dic₁₉	—	8	2	no	—
108	C₂×#125	—	19	1	no	—
109	C₂×C₄⋊C₈	—	2	2	no	—
110	C₂×C₄⋊C₈	C₂×D₁₉	1	2	yes	—
111	C₂×C₄×C₈	—	19	2	no	—
112	#389	—	19	2	no	—
113	#387	—	38	2	no	—
114	#382	—	19	1	no	—
115	C₄×C₄⋊C₄	—	19	2	no	—
116	C₄×C₄⋊C₄	—	38	2	no	—
117	C₄³	C₂×D₁₉	1	1	yes	characteristic
118	#336	—	38	2	no	—
119	C₂×C₁₉	#1477	1	2	yes	—
120	C₂×C₁₉	#1495	1	2	yes	—
121	C₂×C₁₉	#1984	1	1	yes	characteristic
122	C₂×C₁₉	#1992	1	1	yes	characteristic
123	C₂×C₁₉	#1995	1	1	yes	characteristic
124	C₂²×C₈	—	2	2	no	—
125	C₂²×C₈	—	38	2	no	—
126	#125	—	19	4	no	—
127	#125	—	38	2	no	—
128	C₂×C₄⋊C₄	—	19	2	no	—
129	C₂×C₄⋊C₄	—	19	2	no	—
130	C₂×C₄⋊C₄	—	38	2	no	—
131	C₂×C₄⋊C₄	—	38	2	no	—
132	C₂×C₄²	—	38	2	no	—
133	C₂×C₄²	C₄×D₁₉	1	1	yes	characteristic
134	C₂×C₄²	C₄×D₁₉	1	1	yes	characteristic
135	C₂×C₄²	D₇₆	1	2	yes	—
136	C₂×C₄²	C₂²⋊D₁₉	1	2	yes	—
137	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
138	C₄⋊C₈	—	2	4	no	—
139	C₄⋊C₈	—	4	4	no	—
140	C₄×C₈	—	19	4	no	—
141	C₄×C₈	—	38	2	no	—
142	#95	—	38	2	no	—
143	#95	—	38	2	no	—
144	#95	—	38	2	no	—
145	C₁₉	#9872	1	1	yes	characteristic, complemented, Sylow
146	C₂²×C₄	—	38	2	no	—
147	C₂²×C₄	—	38	2	no	—
148	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
149	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
150	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
151	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
152	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
153	C₂×C₈	—	4	4	no	—
154	C₂×C₈	—	4	2	no	—
155	C₂×C₈	—	38	4	no	—
156	C₂×C₈	—	76	4	no	—
157	C₄⋊C₄	—	19	4	no	—
158	C₄⋊C₄	—	38	8	no	—
159	C₄⋊C₄	—	38	2	no	—
160	C₄⋊C₄	—	38	4	no	—
161	C₄⋊C₄	—	76	4	no	—
162	C₄²	—	2	2	no	—
163	C₄²	—	2	2	no	—
164	C₄²	—	2	2	no	—
165	C₄²	—	4	2	no	—
166	C₄²	—	76	2	no	—
167	C₄²	—	76	2	no	—
168	C₄²	C₈×D₁₉	1	2	yes	—
169	C₄²	#64515	1	2	yes	—
170	C₄²	#64543	1	2	yes	—
171	C₄²	Q₈×D₁₉	1	2	yes	—
172	C₂³	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
173	C₂×C₄	—	2	2	no	—
174	C₂×C₄	—	2	2	no	—
175	C₂×C₄	—	2	2	no	—
176	C₂×C₄	—	2	2	no	—
177	C₂×C₄	—	2	2	no	—
178	C₂×C₄	—	2	2	no	—
179	C₂×C₄	—	38	4	no	—
180	C₂×C₄	—	76	2	no	—
181	C₂×C₄	—	76	2	no	—
182	C₂×C₄	—	76	2	no	—
183	C₂×C₄	—	76	2	no	—
184	C₂×C₄	—	76	2	no	—
185	C₂×C₄	(C₂×D₁₉)⋊C₈	1	4	yes	—
186	C₂×C₄	#10597333	1	2	yes	—
187	C₂×C₄	#10597343	1	2	yes	—
188	C₂×C₄	C₂×C₈×D₁₉	1	1	yes	characteristic
189	C₂×C₄	C₂×#64515	1	1	yes	characteristic
190	C₂×C₄	#10597353	1	2	yes	—
191	C₂×C₄	#10597378	1	2	yes	—
192	C₂×C₄	#10597382	1	1	yes	characteristic
193	C₂×C₄	#10597388	1	2	yes	—
194	C₂×C₄	#10597390	1	1	yes	characteristic
195	C₈	—	8	2	no	—
196	C₈	—	76	4	no	—
197	C₂²	#11926449	1	1	yes	characteristic
198	C₂²	C₂×(C₂×D₁₉)⋊C₈	1	1	yes	characteristic
199	C₂²	#11926512	1	1	yes	characteristic
200	C₂²	#11926543	1	2	yes	—
201	C₂²	#11926560	1	2	yes	—
202	C₄	—	2	2	no	—
203	C₄	—	2	4	no	—
204	C₄	—	4	2	no	—
205	C₄	—	76	4	no	—
206	C₄	—	152	2	no	—
207	C₄	#11926668	1	2	yes	—
208	C₄	#11926671	1	2	yes	—
209	C₄	#11926908	1	1	yes	characteristic
210	C₄	#11926912	1	1	yes	characteristic
211	C₄	#11926950	1	2	yes	—
212	C₂	#14562020	1	2	yes	—
213	C₂	#14562098	1	2	yes	—
214	C₂	#14564570	1	1	yes	characteristic
215	C₂	#14564603	1	1	yes	characteristic
216	C₂	#14564615	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×C₂²⋊D₁₉
commutator	C₂×C₄×C₁₉	C₂²×C₈
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1842	C₂
socle, prime radical	C₂³×C₁₉	C₂×C₂²⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1842	D₁₉
hypocenter	C₁₉	#9872
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₄³ ◁ #1842

Complements

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

N	H ≅ G/N	type
29. #10597316	C₈	semidirect
145. C₁₉	#9872	semidirect

Maximal subgroups

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

subgroup	index
C₄×#10597316	2
#14563381	2
#14561474	2
C₁₉×#1842	2
#9872	19