Subgroups — #18076286

Order 4864.

418 conjugacy classes of subgroups.

The subgroup lattice has 208 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14563752	C₂	1	1	yes	maximal, characteristic
2	C₄×#10597260	C₂	1	1	yes	maximal, characteristic
3	C₂×#11926296	C₂	1	2	yes	maximal
4	C₂×#11926294	C₂	1	2	yes	maximal
5	C₁₉×#1842	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
7	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
8	C₂×#10597260	C₄	1	2	yes	—
9	C₂×#10597260	C₄	1	1	yes	characteristic
10	C₂×#10597260	C₄	1	1	yes	characteristic
11	C₂×C₄×C₁₉⋊C₈	C₂²	1	2	yes	—
12	#11926299	—	2	2	no	—
13	#11926296	—	2	4	no	—
14	#11926294	—	2	4	no	—
15	C₂×C₁₉×C₄⋊C₈	—	2	2	no	—
16	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
17	C₄³×C₁₉	C₂²	1	1	yes	characteristic
18	C₂²×C₈×C₁₉	—	2	2	no	—
19	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
20	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
21	C₂×C₄²×C₁₉	D₄	1	2	yes	—
22	C₂×C₄²×C₁₉	Q₈	1	2	yes	—
23	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
24	C₂²×C₁₉⋊C₈	—	2	1	no	—
25	C₂²×C₁₉⋊C₈	—	2	1	no	—
26	C₂²×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
27	C₂²×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
28	C₁₉×C₄⋊C₈	—	2	2	no	—
29	C₁₉×C₄⋊C₈	—	2	2	no	—
30	C₁₉×C₄⋊C₈	—	4	4	no	—
31	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
32	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
33	#10597260	—	2	2	no	—
34	#10597260	—	2	4	no	—
35	#10597260	C₈	1	4	yes	complemented
36	C₄×C₁₉⋊C₈	D₄	1	4	yes	—
37	C₄×C₁₉⋊C₈	Q₈	1	4	yes	—
38	C₂²×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
39	C₂²×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
40	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
41	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
42	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
43	C₂×C₈×C₁₉	—	4	2	no	—
44	C₂×C₈×C₁₉	—	4	4	no	—
45	C₄²×C₁₉	—	2	2	no	—
46	C₄²×C₁₉	—	2	2	no	—
47	C₄²×C₁₉	—	2	2	no	—
48	C₄²×C₁₉	—	4	2	no	—
49	C₄²×C₁₉	C₂×C₈	1	2	yes	—
50	C₄²×C₁₉	M₁₆	1	2	yes	—
51	C₄²×C₁₉	C₂×D₄	1	2	yes	—
52	C₄²×C₁₉	C₂×Q₈	1	2	yes	—
53	C₂×C₁₉⋊C₈	—	2	2	no	—
54	C₂×C₁₉⋊C₈	—	2	2	no	—
55	C₂×C₁₉⋊C₈	—	4	1	no	—
56	C₂×C₁₉⋊C₈	—	4	1	no	—
57	C₂×C₁₉⋊C₈	—	4	2	no	—
58	C₂×C₁₉⋊C₈	—	4	2	no	—
59	C₂×C₁₉⋊C₈	C₄⋊C₄	1	4	yes	—
60	C₂×C₁₉⋊C₈	C₄⋊C₄	1	4	yes	—
61	C₂×C₁₉⋊C₈	C₂×C₈	1	4	yes	—
62	C₂×C₁₉⋊C₈	M₁₆	1	4	yes	—
63	#8808	—	19	1	no	maximal, Sylow
64	C₂³×C₁₉	C₂×C₄⋊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	C₄⋊C₈	1	4	yes	—
72	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	2	yes	—
73	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
74	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
75	C₂×C₄×C₁₉	C₄⋊Q₈	1	2	yes	—
76	C₂×C₄×C₁₉	C₂²×C₈	1	1	yes	characteristic
77	C₂×C₄×C₁₉	C₂×M₁₆	1	1	yes	characteristic
78	C₂×C₄×C₁₉	C₂×M₁₆	1	2	yes	—
79	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
80	C₂×C₄×C₁₉	#137	1	2	yes	—
81	C₈×C₁₉	—	8	2	no	—
82	C₁₉⋊C₈	—	2	4	no	—
83	C₁₉⋊C₈	—	8	1	no	—
84	C₁₉⋊C₈	—	8	1	no	—
85	C₁₉⋊C₈	C₄⋊C₈	1	8	yes	complemented
86	#1842	D₁₉	1	1	yes	characteristic
87	#1831	—	19	1	no	—
88	C₄×#97	—	19	1	no	—
89	C₂×#335	—	19	2	no	—
90	C₂×#334	—	19	2	no	—
91	C₂²×C₁₉	#384	1	1	yes	characteristic
92	C₂²×C₁₉	C₂×C₄⋊C₈	1	1	yes	characteristic
93	C₂²×C₁₉	#423	1	1	yes	characteristic
94	C₂²×C₁₉	#428	1	2	yes	—
95	C₂²×C₁₉	#430	1	2	yes	—
96	C₄×C₁₉	—	2	4	no	—
97	C₄×C₁₉	—	2	2	no	—
98	C₄×C₁₉	—	4	2	no	—
99	C₄×C₁₉	C₂×C₄⋊C₈	1	2	yes	—
100	C₄×C₁₉	#423	1	2	yes	—
101	C₄×C₁₉	#496	1	1	yes	characteristic
102	C₄×C₁₉	#497	1	1	yes	characteristic
103	C₄×C₁₉	#501	1	2	yes	—
104	C₂×C₄⋊C₈	—	2	2	no	—
105	C₂×C₄⋊C₈	—	19	1	no	—
106	C₂×C₄⋊C₈	—	19	1	no	—
107	C₂×C₄⋊C₈	C₂×D₁₉	1	2	yes	—
108	C₂×#97	—	19	1	no	—
109	C₂×#97	—	19	2	no	—
110	C₂×#97	—	19	1	no	—
111	C₂×C₄×C₈	—	19	2	no	—
112	C₄³	C₂×D₁₉	1	1	yes	characteristic
113	#336	—	38	2	no	—
114	#335	—	38	4	no	—
115	#334	—	38	4	no	—
116	C₂×C₁₉	#1565	1	2	yes	—
117	C₂×C₁₉	#1569	1	2	yes	—
118	C₂×C₁₉	#1842	1	1	yes	characteristic
119	C₂×C₁₉	#1847	1	1	yes	characteristic
120	C₂×C₁₉	#1849	1	1	yes	characteristic
121	C₂²×C₈	—	2	2	no	—
122	C₂²×C₈	—	19	2	no	—
123	C₂²×C₈	—	19	2	no	—
124	C₂²×C₈	—	38	1	no	—
125	C₂²×C₈	—	38	1	no	—
126	C₂×C₄²	Dic₃₈	1	2	yes	—
127	C₂×C₄²	C₄×D₁₉	1	1	yes	characteristic
128	C₂×C₄²	C₄×D₁₉	1	1	yes	characteristic
129	C₂×C₄²	C₂²⋊D₁₉	1	2	yes	—
130	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
131	C₄⋊C₈	—	2	2	no	—
132	C₄⋊C₈	—	2	2	no	—
133	C₄⋊C₈	—	4	4	no	—
134	C₄⋊C₈	—	38	2	no	—
135	C₄⋊C₈	—	38	2	no	—
136	#97	—	19	4	no	—
137	#97	—	38	4	no	—
138	#97	—	38	2	no	—
139	C₄×C₈	—	19	4	no	—
140	C₄×C₈	—	19	4	no	—
141	C₁₉	#8808	1	1	yes	characteristic, complemented, Sylow
142	C₂²×C₄	Dic₁₉⋊C₄	1	2	yes	—
143	C₂²×C₄	Dic₁₉⋊C₄	1	2	yes	—
144	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
145	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
146	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
147	C₂×C₈	—	4	4	no	—
148	C₂×C₈	—	4	2	no	—
149	C₂×C₈	—	19	4	no	—
150	C₂×C₈	—	19	4	no	—
151	C₂×C₈	—	19	4	no	—
152	C₂×C₈	—	19	4	no	—
153	C₂×C₈	—	38	2	no	—
154	C₂×C₈	—	38	2	no	—
155	C₂×C₈	—	76	2	no	—
156	C₂×C₈	—	76	1	no	—
157	C₂×C₈	—	76	1	no	—
158	C₂×C₈	—	76	2	no	—
159	C₄²	—	2	2	no	—
160	C₄²	—	2	2	no	—
161	C₄²	—	2	2	no	—
162	C₄²	—	4	2	no	—
163	C₄²	C₈×D₁₉	1	2	yes	—
164	C₄²	#64515	1	2	yes	—
165	C₄²	D₄×D₁₉	1	2	yes	—
166	C₄²	Q₈×D₁₉	1	2	yes	—
167	C₂³	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
168	C₂×C₄	—	2	2	no	—
169	C₂×C₄	—	2	2	no	—
170	C₂×C₄	—	2	2	no	—
171	C₂×C₄	—	2	2	no	—
172	C₂×C₄	—	2	2	no	—
173	C₂×C₄	—	2	2	no	—
174	C₂×C₄	Dic₁₉⋊C₈	1	4	yes	—
175	C₂×C₄	#10597334	1	2	yes	—
176	C₂×C₄	C₄⋊C₄×D₁₉	1	2	yes	—
177	C₂×C₄	C₂×C₈×D₁₉	1	1	yes	characteristic
178	C₂×C₄	C₂×#64515	1	1	yes	characteristic
179	C₂×C₄	M₁₆×D₁₉	1	2	yes	—
180	C₂×C₄	#10597378	1	2	yes	—
181	C₂×C₄	#10597386	1	1	yes	characteristic
182	C₂×C₄	#10597388	1	2	yes	—
183	C₂×C₄	#10597390	1	1	yes	characteristic
184	C₈	—	8	2	no	—
185	C₈	—	19	8	no	—
186	C₈	—	38	4	no	—
187	C₈	—	152	1	no	—
188	C₈	—	152	1	no	—
189	C₂²	#11926413	1	1	yes	characteristic
190	C₂²	C₂×Dic₁₉⋊C₈	1	1	yes	characteristic
191	C₂²	#11926567	1	1	yes	characteristic
192	C₂²	#11926584	1	2	yes	—
193	C₂²	#11926592	1	2	yes	—
194	C₄	—	2	4	no	—
195	C₄	—	2	2	no	—
196	C₄	—	4	2	no	—
197	C₄	C₄⋊C₈×D₁₉	1	2	yes	—
198	C₄	#11926566	1	2	yes	—
199	C₄	#11926931	1	1	yes	characteristic
200	C₄	#11926936	1	1	yes	characteristic
201	C₄	#11926950	1	2	yes	—
202	C₂	#14562385	1	2	yes	—
203	C₂	#14562400	1	2	yes	—
204	C₂	#14563786	1	1	yes	characteristic
205	C₂	#14563801	1	1	yes	characteristic
206	C₂	#14563809	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×C₄⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1842	D₁₉
hypocenter	C₁₉	#8808
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
35. #10597260	C₈	semidirect
85. C₁₉⋊C₈	C₄⋊C₈	semidirect
141. C₁₉	#8808	semidirect

Maximal subgroups

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

subgroup	index
#14563752	2
C₄×#10597260	2
C₂×#11926296	2
C₂×#11926294	2
C₁₉×#1842	2
#8808	19