Group #14563312 — subgroups

Subgroups — #14563312

Order 2432.

176 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 69 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	#11926949	C₂	1	1	yes	maximal, characteristic
2	#11926949	C₂	1	1	yes	maximal, characteristic
3	#11926942	C₂	1	1	yes	maximal, characteristic
4	#11926924	C₂	1	1	yes	maximal, characteristic
5	#11926895	C₂	1	1	yes	maximal, characteristic
6	#11926895	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#322	C₂	1	1	yes	maximal, characteristic
8	C₂×Dic₇₆	—	2	2	no	—
9	#10597315	C₂²	1	1	yes	characteristic
10	#10597315	C₂²	1	1	yes	characteristic
11	#10597315	C₂²	1	1	yes	characteristic
12	#10597315	C₂²	1	1	yes	characteristic
13	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
14	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
15	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
16	#10597275	—	2	2	no	—
17	#10597275	—	2	2	no	—
18	#10597274	—	2	2	no	—
19	#10597273	—	2	2	no	—
20	#10597273	—	2	2	no	—
21	C₂×Dic₃₈	—	2	1	no	—
22	C₂×Dic₃₈	—	2	1	no	—
23	C₂×Dic₃₈	—	2	1	no	—
24	C₂×Dic₃₈	—	2	1	no	—
25	C₂×C₈×C₁₉	D₄	1	2	yes	—
26	C₂×C₈×C₁₉	D₄	1	2	yes	—
27	C₂×C₈×C₁₉	D₄	1	2	yes	—
28	C₄²×C₁₉	C₂³	1	1	yes	characteristic
29	C₄⋊Dic₁₉	—	2	1	no	—
30	C₄⋊Dic₁₉	—	2	1	no	—
31	C₄⋊Dic₁₉	—	2	1	no	—
32	C₄⋊Dic₁₉	—	2	1	no	—
33	C₄⋊Dic₁₉	—	2	1	no	—
34	C₄⋊Dic₁₉	—	2	1	no	—
35	C₄⋊Dic₁₉	—	2	1	no	—
36	C₄⋊Dic₁₉	—	2	1	no	—
37	Dic₇₆	—	4	4	no	—
38	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
39	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
40	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
41	C₂×Dic₁₉	—	4	1	no	—
42	C₂×Dic₁₉	—	4	1	no	—
43	C₂×Dic₁₉	—	4	1	no	—
44	C₂×Dic₁₉	—	4	1	no	—
45	Dic₃₈	—	4	2	no	—
46	Dic₃₈	—	4	2	no	—
47	Dic₃₈	—	4	2	no	—
48	Dic₃₈	—	4	2	no	—
49	C₈×C₁₉	—	2	2	no	—
50	C₈×C₁₉	—	2	2	no	—
51	C₈×C₁₉	Q₁₆	1	4	yes	complemented
52	#1723	—	19	1	no	maximal, Sylow
53	C₂²×C₁₉	#127	1	1	yes	characteristic
54	C₄×C₁₉	C₂×Q₁₆	1	2	yes	—
55	C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
56	C₄×C₁₉	#137	1	2	yes	—
57	Dic₁₉	—	8	1	no	—
58	Dic₁₉	—	8	1	no	—
59	Dic₁₉	—	8	1	no	—
60	Dic₁₉	—	8	1	no	—
61	#500	—	19	1	no	—
62	#500	—	19	1	no	—
63	#498	—	19	1	no	—
64	#494	—	19	1	no	—
65	#487	—	19	1	no	—
66	#487	—	19	1	no	—
67	#322	D₁₉	1	1	yes	characteristic
68	C₂×C₁₉	#494	1	1	yes	characteristic
69	C₂×C₁₉	#496	1	1	yes	characteristic
70	C₂×C₁₉	#497	1	1	yes	characteristic
71	C₂×Q₁₆	—	38	2	no	—
72	C₄⋊Q₈	—	19	1	no	—
73	C₄⋊Q₈	—	19	1	no	—
74	C₄⋊Q₈	—	19	1	no	—
75	C₄⋊Q₈	—	19	1	no	—
76	#107	—	38	2	no	—
77	#107	—	38	2	no	—
78	#106	—	38	2	no	—
79	#103	—	38	2	no	—
80	#103	—	38	2	no	—
81	C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
82	C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
83	C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
84	C₁₉	#1723	1	1	yes	characteristic, complemented, Sylow
85	C₂×Q₈	—	38	1	no	—
86	C₂×Q₈	—	38	1	no	—
87	C₂×Q₈	—	38	1	no	—
88	C₂×Q₈	—	38	1	no	—
89	Q₁₆	—	76	4	no	—
90	C₂×C₈	D₇₆	1	2	yes	—
91	C₂×C₈	D₇₆	1	2	yes	—
92	C₂×C₈	D₇₆	1	2	yes	—
93	C₄⋊C₄	—	38	1	no	—
94	C₄⋊C₄	—	38	1	no	—
95	C₄⋊C₄	—	38	1	no	—
96	C₄⋊C₄	—	38	1	no	—
97	C₄⋊C₄	—	38	1	no	—
98	C₄⋊C₄	—	38	1	no	—
99	C₄⋊C₄	—	38	1	no	—
100	C₄⋊C₄	—	38	1	no	—
101	C₄²	C₂²×D₁₉	1	1	yes	characteristic
102	Q₈	—	76	2	no	—
103	Q₈	—	76	2	no	—
104	Q₈	—	76	2	no	—
105	Q₈	—	76	2	no	—
106	C₂×C₄	—	76	1	no	—
107	C₂×C₄	—	76	1	no	—
108	C₂×C₄	—	76	1	no	—
109	C₂×C₄	—	76	1	no	—
110	C₂×C₄	C₂×D₇₆	1	1	yes	characteristic
111	C₂×C₄	C₂×D₇₆	1	1	yes	characteristic
112	C₂×C₄	C₂×D₇₆	1	1	yes	characteristic
113	C₈	—	2	2	no	—
114	C₈	—	2	2	no	—
115	C₈	Dic₇₆	1	4	yes	complemented
116	C₂²	#10597320	1	1	yes	characteristic
117	C₄	—	152	1	no	—
118	C₄	—	152	1	no	—
119	C₄	—	152	1	no	—
120	C₄	—	152	1	no	—
121	C₄	C₂×Dic₇₆	1	2	yes	—
122	C₄	#10597354	1	2	yes	—
123	C₄	#10597355	1	2	yes	—
124	C₂	#11926924	1	1	yes	characteristic
125	C₂	#11926933	1	1	yes	characteristic
126	C₂	#11926938	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11926949

C₂

yes

maximal, characteristic

#11926949

C₂

yes

maximal, characteristic

#11926942

C₂

yes

maximal, characteristic

#11926924

C₂

yes

maximal, characteristic

#11926895

C₂

yes

maximal, characteristic

#11926895

C₂

yes

maximal, characteristic

C₁₉×#322

C₂

yes

maximal, characteristic

C₂×Dic₇₆

—

#10597315

C₂²

yes

characteristic

#10597315

C₂²

yes

characteristic

#10597315

C₂²

yes

characteristic

#10597315

C₂²

yes

characteristic

C₄×C₈×C₁₉

C₂²

yes

characteristic

C₄×C₈×C₁₉

C₂²

yes

characteristic

C₄×C₈×C₁₉

C₂²

yes

—

—

—

—

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×C₈×C₁₉

D₄

yes

—

C₂×C₈×C₁₉

D₄

yes

—

C₂×C₈×C₁₉

D₄

yes

—

C₄²×C₁₉

C₂³

yes

characteristic

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

Dic₇₆

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

Dic₃₈

—

Dic₃₈

—

Dic₃₈

—

Dic₃₈

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

Q₁₆

yes

—

C₂²×C₁₉

yes

C₄×C₁₉

C₂×Q₁₆

yes

—

C₄×C₁₉

AGL(1,ℤ/8)

yes

—

C₄×C₁₉

#137

yes

—

Dic₁₉

—

Dic₁₉

—

Dic₁₉

—

Dic₁₉

—

—

—

—

—

—

—

D₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×Q₁₆

—

C₄⋊Q₈

—

C₄⋊Q₈

—

C₄⋊Q₈

—

C₄⋊Q₈

—

—

—

—

—

—

C₄×C₈

C₂×D₁₉

yes

characteristic

C₄×C₈

C₂×D₁₉

yes

characteristic

C₄×C₈

C₂×D₁₉

yes

characteristic

C₁₉

#1723

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

Q₁₆

—

C₂×C₈

D₇₆

yes

—

C₂×C₈

D₇₆

yes

—

C₂×C₈

D₇₆

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

100

C₄⋊C₄

—

101

C₄²

C₂²×D₁₉

yes

characteristic

102

Q₈

—

103

Q₈

—

104

Q₈

—

105

Q₈

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

C₂×D₇₆

yes

characteristic

111

C₂×C₄

C₂×D₇₆

yes

characteristic

112

C₂×C₄

C₂×D₇₆

yes

characteristic

113

C₈

—

114

C₈

—

115

C₈

Dic₇₆

yes

complemented

116

C₂²

#10597320

yes

characteristic

117

C₄

—

152

—

118

C₄

—

152

—

119

C₄

—

152

—

120

C₄

—

152

—

121

C₄

C₂×Dic₇₆

yes

—

122

C₄

#10597354

yes

—

123

C₄

#10597355

yes

—

124

C₂

#11926924

yes

characteristic

125

C₂

#11926933

yes

characteristic

126

C₂

#11926938

yes

characteristic

	subgroup	G/H
center	C₂²	#10597320
commutator, cosocle	C₄²×C₁₉	C₂³
Frattini	C₄²	C₂²×D₁₉
Fitting	C₁₉×#322	C₂
socle, prime radical	C₂²×C₁₉	#127
hypercenter	#322	D₁₉
hypocenter	C₁₉	#1723
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #322

subgroup

G/H

center

C₂²

#10597320

commutator, cosocle

C₄²×C₁₉

C₂³

Frattini

C₄²

C₂²×D₁₉

Fitting

C₁₉×#322

C₂

C₂²×C₁₉

D₁₉

C₁₉

G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #322

N	H ≅ G/N	type
51. C₈×C₁₉	Q₁₆	semidirect
84. C₁₉	#1723	semidirect
115. C₈	Dic₇₆	semidirect

H ≅ G/N

type

51. C₈×C₁₉

Q₁₆

semidirect

84. C₁₉

#1723

semidirect

115. C₈

Dic₇₆

semidirect

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

subgroup	index
#11926949	2
#11926942	2
#11926924	2
#11926895	2
C₁₉×#322	2
#1723	19

subgroup

index

C₁₉×#322

Subgroups — #14563312

Conjugacy classes of subgroups

Complements

Maximal subgroups