Subgroups — #18073705

Order 4864.

390 conjugacy classes of subgroups.

The subgroup lattice has 152 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14562383	C₂	1	2	yes	maximal
2	#14561918	C₂	1	2	yes	maximal
3	#14561468	C₂	1	2	yes	maximal
4	C₄×C₁₉×#97	C₂	1	1	yes	maximal, characteristic
5	#11926597	C₂²	1	4	yes	—
6	#11926297	C₄	1	4	yes	complemented
7	#11926295	C₄	1	4	yes	complemented
8	#11926265	—	2	2	no	—
9	C₈×C₁₉⋊C₈	—	2	2	no	—
10	C₂×C₁₉×#97	C₄	1	2	yes	—
11	C₂×C₁₉×#97	C₄	1	2	yes	—
12	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
13	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
14	C₄³×C₁₉	C₂²	1	1	yes	characteristic
15	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
16	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
17	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
18	C₂×C₄²×C₁₉	—	2	2	no	—
19	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
20	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
21	C₁₉×#97	—	2	4	no	—
22	C₁₉×#97	C₈	1	8	yes	complemented
23	C₄×C₈×C₁₉	C₂×C₄	1	2	yes	—
24	C₄×C₈×C₁₉	C₂×C₄	1	2	yes	—
25	C₄×C₈×C₁₉	D₄	1	2	yes	—
26	C₄×C₈×C₁₉	Q₈	1	2	yes	—
27	C₂²⋊(C₁₉⋊C₈)	—	2	4	no	—
28	C₄⋊(C₁₉⋊C₈)	C₂×C₄	1	8	yes	—
29	C₄×C₁₉⋊C₈	—	2	4	no	—
30	C₂²×C₄×C₁₉	—	2	2	no	—
31	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
32	C₂²×C₄×C₁₉	#41	1	2	yes	—
33	C₂×C₈×C₁₉	—	2	2	no	—
34	C₂×C₈×C₁₉	C₄²	1	1	yes	characteristic
35	C₂×C₈×C₁₉	C₄²	1	1	yes	characteristic
36	C₂×C₈×C₁₉	C₄²	1	2	yes	—
37	C₂×C₈×C₁₉	C₄⋊C₄	1	4	yes	—
38	C₂×C₈×C₁₉	C₂×C₈	1	4	yes	—
39	C₂×C₈×C₁₉	C₂×C₈	1	4	yes	—
40	C₂×C₈×C₁₉	M₁₆	1	4	yes	—
41	C₄²×C₁₉	—	2	2	no	—
42	C₄²×C₁₉	—	4	4	no	—
43	C₄²×C₁₉	C₂×C₈	1	4	yes	—
44	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
45	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
46	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
47	C₂×C₁₉⋊C₈	—	2	8	no	—
48	#8268	—	19	1	no	maximal, Sylow
49	C₂³×C₁₉	#117	1	1	yes	characteristic
50	C₂×C₄×C₁₉	—	2	4	no	—
51	C₂×C₄×C₁₉	—	2	4	no	—
52	C₂×C₄×C₁₉	—	4	4	no	—
53	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
54	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
55	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
56	C₂×C₄×C₁₉	C₄×Q₈	1	2	yes	—
57	C₂×C₄×C₁₉	C₂²×C₈	1	2	yes	—
58	C₂×C₄×C₁₉	C₂×M₁₆	1	2	yes	—
59	C₈×C₁₉	—	2	1	no	—
60	C₈×C₁₉	—	2	1	no	—
61	C₈×C₁₉	C₄×C₈	1	4	yes	—
62	C₈×C₁₉	C₄⋊C₈	1	8	yes	—
63	C₁₉⋊C₈	—	4	8	no	—
64	C₄×#97	D₁₉	1	1	yes	characteristic
65	#1564	—	19	2	no	—
66	#1450	—	19	2	no	—
67	#1276	—	19	2	no	—
68	C₂²×C₁₉	—	2	2	no	—
69	C₂²×C₁₉	C₄×C₄⋊C₄	1	1	yes	characteristic
70	C₂²×C₁₉	#431	1	2	yes	—
71	C₄×C₁₉	—	2	2	no	—
72	C₄×C₁₉	—	4	4	no	—
73	C₄×C₁₉	C₂×C₄×C₈	1	1	yes	characteristic
74	C₄×C₁₉	C₄×M₁₆	1	1	yes	characteristic
75	C₄×C₁₉	C₂×C₄⋊C₈	1	2	yes	—
76	C₄×C₁₉	#444	1	4	yes	—
77	#431	—	19	4	no	—
78	C₂×#97	Dic₁₉	1	2	yes	—
79	C₂×#97	Dic₁₉	1	2	yes	—
80	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
81	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
82	C₄³	C₂×D₁₉	1	1	yes	characteristic
83	#335	—	19	4	no	—
84	#334	—	19	4	no	—
85	#322	—	38	2	no	—
86	C₈²	—	38	2	no	—
87	C₂×C₁₉	—	2	2	no	—
88	C₂×C₁₉	C₄×C₄⋊C₈	1	1	yes	characteristic
89	C₂×C₁₉	#1773	1	2	yes	—
90	C₂²×C₈	C₂×Dic₁₉	1	1	yes	characteristic
91	C₂²×C₈	C₂×Dic₁₉	1	1	yes	characteristic
92	C₂²×C₈	C₂×Dic₁₉	1	2	yes	—
93	C₂×C₄²	—	2	2	no	—
94	C₂×C₄²	C₂×Dic₁₉	1	2	yes	—
95	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
96	C₄⋊C₈	—	19	8	no	—
97	C₂²⋊C₈	—	38	4	no	—
98	#97	—	2	4	no	—
99	#97	C₁₉⋊C₈	1	8	yes	complemented
100	C₄×C₈	—	38	4	no	—
101	C₄×C₈	Dic₃₈	1	2	yes	—
102	C₄×C₈	C₄×D₁₉	1	2	yes	—
103	C₄×C₈	C₄×D₁₉	1	2	yes	—
104	C₄×C₈	D₇₆	1	2	yes	—
105	C₁₉	#8268	1	1	yes	characteristic, complemented, Sylow
106	C₂²×C₄	—	2	2	no	—
107	C₂²×C₄	#64541	1	2	yes	—
108	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
109	C₂×C₈	—	2	2	no	—
110	C₂×C₈	—	38	8	no	—
111	C₂×C₈	C₂×C₁₉⋊C₈	1	4	yes	—
112	C₂×C₈	C₂×C₁₉⋊C₈	1	4	yes	—
113	C₂×C₈	#64520	1	4	yes	—
114	C₂×C₈	C₄×Dic₁₉	1	1	yes	characteristic
115	C₂×C₈	C₄×Dic₁₉	1	1	yes	characteristic
116	C₂×C₈	C₄×Dic₁₉	1	2	yes	—
117	C₂×C₈	C₄⋊Dic₁₉	1	4	yes	—
118	C₄²	—	2	2	no	—
119	C₄²	—	4	4	no	—
120	C₄²	C₂×C₁₉⋊C₈	1	4	yes	—
121	C₄²	C₂×Dic₃₈	1	1	yes	characteristic
122	C₄²	C₂×C₄×D₁₉	1	2	yes	—
123	C₄²	C₂×D₇₆	1	1	yes	characteristic
124	C₂³	#10597372	1	1	yes	characteristic
125	C₂×C₄	—	2	4	no	—
126	C₂×C₄	—	2	4	no	—
127	C₂×C₄	—	4	4	no	—
128	C₂×C₄	C₄×Dic₃₈	1	2	yes	—
129	C₂×C₄	C₄×D₇₆	1	2	yes	—
130	C₂×C₄	C₂²×C₁₉⋊C₈	1	2	yes	—
131	C₂×C₄	C₂×#64520	1	2	yes	—
132	C₂×C₄	C₂×C₄×Dic₁₉	1	1	yes	characteristic
133	C₂×C₄	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
134	C₈	—	2	1	no	—
135	C₈	—	2	1	no	—
136	C₈	—	76	8	no	—
137	C₈	C₄×C₁₉⋊C₈	1	4	yes	—
138	C₈	C₄⋊(C₁₉⋊C₈)	1	8	yes	—
139	C₂²	—	2	2	no	—
140	C₂²	C₄×C₄⋊Dic₁₉	1	1	yes	characteristic
141	C₂²	#11926597	1	2	yes	—
142	C₄	—	2	2	no	—
143	C₄	—	4	4	no	—
144	C₄	C₂×C₄×C₁₉⋊C₈	1	1	yes	characteristic
145	C₄	C₄×#64520	1	1	yes	characteristic
146	C₄	C₂×C₄⋊(C₁₉⋊C₈)	1	2	yes	—
147	C₄	#11926667	1	4	yes	—
148	C₂	—	2	2	no	—
149	C₂	C₄×C₄⋊(C₁₉⋊C₈)	1	1	yes	characteristic
150	C₂	#14563519	1	2	yes	—

	subgroup	G/H
center	C₄²	C₂×D₇₆
commutator	C₄×C₁₉	C₂×C₄×C₈
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₄×C₁₉×#97	C₂
socle	C₂²×C₁₉	C₄×C₄⋊C₄
prime radical	C₂³×C₁₉	#117
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₄×#97	D₁₉
hypocenter	C₁₉	#8268
LCS	G ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₄² ◁ C₂×C₄×C₈ ◁ C₄×#97

Complements

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

N	H ≅ G/N	type
6. #11926297	C₄	semidirect
7. #11926295	C₄	semidirect
22. C₁₉×#97	C₈	semidirect
99. #97	C₁₉⋊C₈	semidirect
105. C₁₉	#8268	semidirect

Maximal subgroups

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

subgroup	index
#14562383	2
#14561918	2
#14561468	2
C₄×C₁₉×#97	2
#8268	19