Subgroups — #18071915

Order 4864.

582 conjugacy classes of subgroups.

The subgroup lattice has 146 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#10597260	C₂	1	2	yes	maximal
2	C₂×#11926266	C₂	1	2	yes	maximal
3	C₂×#11926265	C₂	1	1	yes	maximal, characteristic
4	C₂×C₈×C₁₉⋊C₈	C₂	1	1	yes	maximal, characteristic
5	C₄×C₁₉×#97	C₂	1	1	yes	maximal, characteristic
6	C₂×#10597260	C₄	1	8	yes	—
7	C₂×C₄×C₁₉⋊C₈	C₂²	1	2	yes	—
8	C₂×C₄×C₁₉⋊C₈	C₂²	1	2	yes	—
9	#11926266	C₄	1	8	yes	complemented
10	#11926265	C₄	1	4	yes	complemented
11	C₈×C₁₉⋊C₈	C₄	1	4	yes	complemented
12	C₂×C₁₉×#97	C₄	1	4	yes	—
13	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
14	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
15	C₄³×C₁₉	C₂²	1	1	yes	characteristic
16	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
17	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
18	C₂×C₄²×C₁₉	C₂×C₄	1	4	yes	—
19	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
20	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
21	C₂²×C₁₉⋊C₈	C₂×C₄	1	4	yes	—
22	C₂²×C₁₉⋊C₈	C₂×C₄	1	4	yes	—
23	C₁₉×#97	—	2	8	no	—
24	C₄×C₈×C₁₉	C₂×C₄	1	2	yes	—
25	C₄×C₈×C₁₉	C₂×C₄	1	2	yes	—
26	C₄×C₈×C₁₉	C₂×C₄	1	4	yes	—
27	#10597260	—	2	16	no	—
28	C₄×C₁₉⋊C₈	C₂×C₄	1	4	yes	—
29	C₄×C₁₉⋊C₈	C₂×C₄	1	4	yes	—
30	C₄×C₁₉⋊C₈	C₂×C₄	1	4	yes	—
31	C₄×C₁₉⋊C₈	C₂×C₄	1	4	yes	—
32	C₂²×C₄×C₁₉	C₄²	1	4	yes	—
33	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
34	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
35	C₂×C₈×C₁₉	—	2	4	no	—
36	C₂×C₈×C₁₉	C₄²	1	4	yes	—
37	C₂×C₈×C₁₉	C₄²	1	4	yes	—
38	C₂×C₈×C₁₉	M₁₆	1	8	yes	—
39	C₄²×C₁₉	—	2	8	no	—
40	C₄²×C₁₉	—	2	4	no	—
41	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
42	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
43	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
44	C₂×C₁₉⋊C₈	—	2	8	no	—
45	C₂×C₁₉⋊C₈	C₄²	1	8	yes	—
46	C₂×C₁₉⋊C₈	C₄²	1	8	yes	—
47	C₂×C₁₉⋊C₈	M₁₆	1	16	yes	—
48	#7846	—	19	1	no	maximal, Sylow
49	C₂³×C₁₉	C₂×C₄²	1	1	yes	characteristic
50	C₂×C₄×C₁₉	—	2	8	no	—
51	C₂×C₄×C₁₉	—	2	4	no	—
52	C₂×C₄×C₁₉	C₂×C₄²	1	2	yes	—
53	C₂×C₄×C₁₉	C₂×C₄²	1	2	yes	—
54	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
55	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
56	C₂×C₄×C₁₉	C₂×M₁₆	1	8	yes	—
57	C₂×C₄×C₁₉	C₂×M₁₆	1	4	yes	—
58	C₈×C₁₉	—	2	4	no	—
59	C₈×C₁₉	#97	1	8	yes	complemented
60	C₁₉⋊C₈	—	2	8	no	—
61	C₁₉⋊C₈	#97	1	16	yes	complemented
62	C₄×#97	—	19	2	no	—
63	C₄×#97	D₁₉	1	1	yes	characteristic
64	C₂×#322	—	19	1	no	—
65	C₂×#322	—	19	2	no	—
66	C₂×C₈²	—	19	1	no	—
67	C₂²×C₁₉	C₄³	1	1	yes	characteristic
68	C₂²×C₁₉	C₄×M₁₆	1	4	yes	—
69	C₂²×C₁₉	C₄×M₁₆	1	2	yes	—
70	C₄×C₁₉	—	4	4	no	—
71	C₄×C₁₉	C₂×#97	1	4	yes	—
72	C₄×C₁₉	C₂×#97	1	2	yes	—
73	C₄×C₁₉	C₄×M₁₆	1	4	yes	—
74	C₄×C₁₉	C₄×M₁₆	1	2	yes	—
75	C₂×#97	—	19	8	no	—
76	C₂×#97	Dic₁₉	1	4	yes	—
77	C₂×C₄×C₈	—	19	2	no	—
78	C₂×C₄×C₈	—	19	2	no	—
79	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
80	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
81	C₄³	C₂×D₁₉	1	1	yes	characteristic
82	#322	—	19	4	no	—
83	#322	—	19	8	no	—
84	C₈²	—	19	4	no	—
85	C₂×C₁₉	#1455	1	4	yes	—
86	C₂×C₁₉	C₄×#97	1	2	yes	—
87	C₂×C₁₉	C₄×#97	1	1	yes	characteristic
88	C₂²×C₈	—	19	4	no	—
89	C₂²×C₈	—	19	4	no	—
90	C₂²×C₈	C₂×Dic₁₉	1	2	yes	—
91	C₂²×C₈	C₂×Dic₁₉	1	2	yes	—
92	C₂×C₄²	C₄×D₁₉	1	4	yes	—
93	C₂×C₄²	C₂×Dic₁₉	1	2	yes	—
94	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
95	#97	—	2	8	no	—
96	#97	—	38	16	no	—
97	C₄×C₈	—	19	4	no	—
98	C₄×C₈	—	19	4	no	—
99	C₄×C₈	—	19	4	no	—
100	C₄×C₈	—	19	4	no	—
101	C₄×C₈	C₄×D₁₉	1	2	yes	—
102	C₄×C₈	C₄×D₁₉	1	4	yes	—
103	C₄×C₈	C₄×D₁₉	1	2	yes	—
104	C₁₉	#7846	1	1	yes	characteristic, complemented, Sylow
105	C₂²×C₄	C₄×Dic₁₉	1	4	yes	—
106	C₂²×C₄	C₂×C₄×D₁₉	1	2	yes	—
107	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
108	C₂×C₈	—	2	4	no	—
109	C₂×C₈	—	19	8	no	—
110	C₂×C₈	—	19	16	no	—
111	C₂×C₈	—	19	8	no	—
112	C₂×C₈	—	38	8	no	—
113	C₂×C₈	#64520	1	8	yes	—
114	C₂×C₈	C₄×Dic₁₉	1	4	yes	—
115	C₂×C₈	C₄×Dic₁₉	1	4	yes	—
116	C₄²	—	2	8	no	—
117	C₄²	—	2	4	no	—
118	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
119	C₄²	C₂×C₄×D₁₉	1	2	yes	—
120	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
121	C₂³	C₂×C₄×Dic₁₉	1	1	yes	characteristic
122	C₂×C₄	—	2	8	no	—
123	C₂×C₄	—	2	4	no	—
124	C₂×C₄	C₄²×D₁₉	1	2	yes	—
125	C₂×C₄	C₄²×D₁₉	1	2	yes	—
126	C₂×C₄	M₁₆×D₁₉	1	8	yes	—
127	C₂×C₄	C₂×#64520	1	4	yes	—
128	C₂×C₄	C₂×C₄×Dic₁₉	1	1	yes	characteristic
129	C₂×C₄	C₂×C₄×Dic₁₉	1	1	yes	characteristic
130	C₈	—	2	4	no	—
131	C₈	—	19	16	no	—
132	C₈	—	38	8	no	—
133	C₈	#10597260	1	8	yes	complemented
134	C₂²	C₄²×Dic₁₉	1	1	yes	characteristic
135	C₂²	M₁₆×Dic₁₉	1	4	yes	—
136	C₂²	C₄×#64520	1	2	yes	—
137	C₄	—	4	4	no	—
138	C₄	#97×D₁₉	1	4	yes	—
139	C₄	C₂×#10597260	1	2	yes	—
140	C₄	#11926496	1	4	yes	—
141	C₄	C₄×#64520	1	2	yes	—
142	C₂	#14561938	1	4	yes	—
143	C₂	#97×Dic₁₉	1	2	yes	—
144	C₂	C₄×#10597260	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄²	C₂²×D₁₉
commutator	C₂²×C₁₉	C₄³
Fitting	C₄×C₁₉×#97	C₂
socle, prime radical	C₂³×C₁₉	C₂×C₄²
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₄×#97	D₁₉
hypocenter	C₁₉	#7846
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄² ◁ C₄×#97

Complements

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

N	H ≅ G/N	type
9. #11926266	C₄	semidirect
10. #11926265	C₄	semidirect
11. C₈×C₁₉⋊C₈	C₄	semidirect
59. C₈×C₁₉	#97	semidirect
61. C₁₉⋊C₈	#97	semidirect
104. C₁₉	#7846	semidirect
133. C₈	#10597260	semidirect

Maximal subgroups

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

subgroup	index
C₄×#10597260	2
C₂×#11926266	2
C₂×#11926265	2
C₂×C₈×C₁₉⋊C₈	2
C₄×C₁₉×#97	2
#7846	19