Group #14569008 — subgroups

Subgroups — #14569008

Order 2432.

484 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 181 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×Dic₃₈	C₂	1	2	yes	maximal
2	#11926474	C₂	1	4	yes	maximal
3	#11926449	C₂	1	4	yes	maximal
4	#11926443	C₂	1	4	yes	maximal
5	C₁₉×#384	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₃₈	C₂²	1	2	yes	—
7	C₂×C₄⋊C₄×C₁₉	C₂²	1	4	yes	—
8	C₂×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
9	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊Dic₁₉	C₂²	1	2	yes	—
11	C₂×C₄⋊Dic₁₉	C₂²	1	4	yes	—
12	C₂×Dic₁₉⋊C₄	C₂²	1	4	yes	—
13	C₂×C₄×Dic₁₉	C₂²	1	4	yes	—
14	C₄×Dic₃₈	—	2	8	no	—
15	C₁₉⋊#95	C₂²	1	8	yes	—
16	C₁₉⋊#95	C₂²	1	4	yes	—
17	C₂²×C₄×C₁₉	C₂³	1	4	yes	—
18	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
19	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
20	C₂²×Dic₁₉	C₂³	1	4	yes	—
21	C₂²×Dic₁₉	C₂³	1	4	yes	—
22	C₂×Dic₃₈	—	2	4	no	—
23	C₂×Dic₃₈	—	2	4	no	—
24	C₂×Dic₃₈	Q₈	1	8	yes	complemented
25	C₄⋊C₄×C₁₉	—	2	8	no	—
26	C₄⋊C₄×C₁₉	—	4	2	no	—
27	C₄²×C₁₉	D₄	1	4	yes	—
28	C₄⋊Dic₁₉	—	2	4	no	—
29	C₄⋊Dic₁₉	—	4	4	no	—
30	Dic₁₉⋊C₄	—	2	8	no	—
31	C₄×Dic₁₉	—	2	8	no	—
32	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
33	C₂×C₄×C₁₉	—	2	1	no	—
34	C₂×C₄×C₁₉	—	2	1	no	—
35	C₂×C₄×C₁₉	—	2	8	no	—
36	C₂×C₄×C₁₉	—	2	4	no	—
37	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
38	C₂×C₄×C₁₉	C₂×D₄	1	4	yes	—
39	C₂×C₄×C₁₉	C₂×Q₈	1	4	yes	—
40	C₂×C₄×C₁₉	#41	1	4	yes	—
41	C₂×Dic₁₉	—	2	4	no	—
42	C₂×Dic₁₉	—	2	4	no	—
43	C₂×Dic₁₉	—	2	4	no	—
44	C₂×Dic₁₉	—	2	4	no	—
45	C₂×Dic₁₉	—	2	4	no	—
46	C₂×Dic₁₉	C₂×Q₈	1	8	yes	—
47	Dic₃₈	—	2	16	no	—
48	#2582	—	19	1	no	maximal, Sylow
49	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
50	C₂²×C₁₉	C₂²×Q₈	1	2	yes	—
51	C₂²×C₁₉	C₂×#41	1	2	yes	—
52	C₂²×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
53	C₂²×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
54	C₄×C₁₉	—	2	2	no	—
55	C₄×C₁₉	—	4	4	no	—
56	C₄×C₁₉	C₂²⋊Q₈	1	8	yes	—
57	Dic₁₉	—	2	8	no	—
58	Dic₁₉	—	4	4	no	—
59	C₂×C₄×Q₈	—	19	2	no	—
60	#398	—	19	4	no	—
61	#391	—	19	4	no	—
62	#389	—	19	4	no	—
63	#384	D₁₉	1	1	yes	characteristic
64	C₂×C₁₉	C₂×C₂²⋊Q₈	1	2	yes	—
65	C₂×C₁₉	#537	1	1	yes	characteristic
66	C₂×C₁₉	#557	1	2	yes	—
67	C₂×C₁₉	Q₈²	1	1	yes	characteristic
68	C₂×C₁₉	#559	1	1	yes	characteristic
69	C₂²×Q₈	—	19	2	no	—
70	C₄×Q₈	—	38	8	no	—
71	C₂×C₄⋊C₄	—	19	2	no	—
72	C₂×C₄⋊C₄	—	19	4	no	—
73	C₂×C₄⋊C₄	—	19	4	no	—
74	C₂×C₄⋊C₄	C₂×D₁₉	1	4	yes	—
75	C₂×C₄⋊C₄	C₂×D₁₉	1	2	yes	—
76	C₂×C₄²	—	19	4	no	—
77	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
78	#95	—	19	8	no	—
79	#95	—	19	4	no	—
80	C₁₉	#2582	1	1	yes	characteristic, complemented, Sylow
81	C₂×Q₈	—	19	8	no	—
82	C₂×Q₈	—	38	4	no	—
83	C₂×Q₈	—	38	4	no	—
84	C₂²×C₄	—	19	4	no	—
85	C₂²×C₄	—	19	4	no	—
86	C₂²×C₄	C₂²×D₁₉	1	4	yes	—
87	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
88	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
89	C₄⋊C₄	—	2	8	no	—
90	C₄⋊C₄	—	4	2	no	—
91	C₄⋊C₄	—	38	8	no	—
92	C₄⋊C₄	—	38	4	no	—
93	C₄⋊C₄	—	76	4	no	—
94	C₄²	—	38	8	no	—
95	C₄²	D₇₆	1	4	yes	—
96	C₂³	C₂³×D₁₉	1	1	yes	characteristic
97	Q₈	—	38	16	no	—
98	C₂×C₄	—	2	1	no	—
99	C₂×C₄	—	2	1	no	—
100	C₂×C₄	—	2	8	no	—
101	C₂×C₄	—	2	4	no	—
102	C₂×C₄	—	19	8	no	—
103	C₂×C₄	—	38	4	no	—
104	C₂×C₄	—	38	4	no	—
105	C₂×C₄	—	38	4	no	—
106	C₂×C₄	—	38	4	no	—
107	C₂×C₄	—	38	4	no	—
108	C₂×C₄	C₂×D₇₆	1	2	yes	—
109	C₂×C₄	C₂×D₇₆	1	4	yes	—
110	C₂×C₄	#64543	1	4	yes	—
111	C₂×C₄	Q₈×D₁₉	1	4	yes	—
112	C₂²	C₂²×D₇₆	1	1	yes	characteristic
113	C₂²	C₂×#64543	1	2	yes	—
114	C₂²	#10597430	1	1	yes	characteristic
115	C₂²	C₂×Q₈×D₁₉	1	2	yes	—
116	C₂²	#10597433	1	1	yes	characteristic
117	C₄	—	2	2	no	—
118	C₄	—	4	4	no	—
119	C₄	—	38	8	no	—
120	C₄	—	76	4	no	—
121	C₄	#10597343	1	8	yes	—
122	C₂	C₂×#10597343	1	2	yes	—
123	C₂	#11927125	1	1	yes	characteristic
124	C₂	#11927269	1	2	yes	—
125	C₂	#11927274	1	1	yes	characteristic
126	C₂	#11927280	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₄×Dic₃₈

C₂

yes

maximal

#11926474

C₂

yes

maximal

#11926449

C₂

yes

maximal

#11926443

C₂

yes

maximal

C₁₉×#384

C₂

yes

maximal, characteristic

C₂²×Dic₃₈

C₂²

yes

—

C₂×C₄⋊C₄×C₁₉

C₂²

yes

—

C₂×C₄⋊C₄×C₁₉

C₂²

yes

—

C₂×C₄²×C₁₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₁₉

C₂²

yes

—

C₂×C₄⋊Dic₁₉

C₂²

yes

—

C₂×Dic₁₉⋊C₄

C₂²

yes

—

C₂×C₄×Dic₁₉

C₂²

yes

—

C₄×Dic₃₈

—

C₁₉⋊#95

C₂²

yes

—

C₁₉⋊#95

C₂²

yes

—

C₂²×C₄×C₁₉

C₂³

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×C₄×C₁₉

C₂³

yes

—

C₂²×Dic₁₉

C₂³

yes

—

C₂²×Dic₁₉

C₂³

yes

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

Q₈

yes

complemented

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

D₄

yes

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₂³×C₁₉

C₂⁴

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×Q₈

yes

—

C₂×C₄×C₁₉

#41

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

C₂×Q₈

yes

—

Dic₃₈

—

#2582

—

maximal, Sylow

C₂²×C₁₉

C₂²×D₄

yes

characteristic

C₂²×C₁₉

C₂²×Q₈

yes

—

C₂²×C₁₉

C₂×#41

yes

—

C₂²×C₁₉

H(5,𝔽₂)

yes

characteristic

C₂²×C₁₉

2₋¹⁺⁴

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₂²⋊Q₈

yes

—

Dic₁₉

—

Dic₁₉

—

C₂×C₄×Q₈

—

—

—

—

D₁₉

yes

characteristic

C₂×C₁₉

C₂×C₂²⋊Q₈

yes

—

C₂×C₁₉

#537

yes

characteristic

C₂×C₁₉

#557

yes

—

C₂×C₁₉

Q₈²

yes

characteristic

C₂×C₁₉

#559

yes

characteristic

C₂²×Q₈

—

C₄×Q₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₁₉

yes

—

C₂×C₄⋊C₄

C₂×D₁₉

yes

—

C₂×C₄²

—

C₂×C₄²

C₂×D₁₉

yes

characteristic

#95

—

#95

—

C₁₉

#2582

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₁₉

yes

—

C₂²×C₄

C₂²×D₁₉

yes

characteristic

C₂²×C₄

C₂²×D₁₉

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

C₄²

D₇₆

yes

—

C₂³

C₂³×D₁₉

yes

characteristic

Q₈

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

C₂×D₇₆

yes

—

109

C₂×C₄

C₂×D₇₆

yes

—

110

C₂×C₄

#64543

yes

—

111

C₂×C₄

Q₈×D₁₉

yes

—

112

C₂²

C₂²×D₇₆

yes

characteristic

113

C₂²

C₂×#64543

yes

—

114

C₂²

#10597430

yes

characteristic

115

C₂²

C₂×Q₈×D₁₉

yes

—

116

C₂²

#10597433

yes

characteristic

117

C₄

—

118

C₄

—

119

C₄

—

120

C₄

—

121

C₄

#10597343

yes

—

122

C₂

C₂×#10597343

yes

—

123

C₂

#11927125

yes

characteristic

124

C₂

#11927269

yes

—

125

C₂

#11927274

yes

characteristic

126

C₂

#11927280

yes

characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₉
commutator, socle, prime radical, cosocle	C₂³×C₁₉	C₂⁴
Fitting	C₁₉×#384	C₂
hypercenter	#384	D₁₉
hypocenter	C₁₉	#2582
LCS	G ▷ C₂³×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ #384

subgroup

G/H

center, Frattini

C₂³

C₂³×D₁₉

commutator, socle, prime radical, cosocle

C₂³×C₁₉

C₂⁴

Fitting

C₁₉×#384

C₂

D₁₉

C₁₉

G ▷ C₂³×C₁₉ ▷ C₁₉

C₁ ◁ C₂³ ◁ #384

N	H ≅ G/N	type
24. C₂×Dic₃₈	Q₈	semidirect
80. C₁₉	#2582	semidirect

H ≅ G/N

type

24. C₂×Dic₃₈

Q₈

semidirect

80. C₁₉

#2582

semidirect

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

subgroup	index
C₂×C₄×Dic₃₈	2
#11926474	2
#11926449	2
#11926443	2
C₁₉×#384	2
#2582	19

subgroup

index

C₂×C₄×Dic₃₈

C₁₉×#384

Subgroups — #14569008

Conjugacy classes of subgroups

Complements

Maximal subgroups