Group #14565805 — subgroups

Subgroups — #14565805

Order 2432.

126 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 126 conjugacy classes of subgroups — too many to draw. Only its 43 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	#11926941	C₂	1	1	yes	maximal, characteristic, complemented
2	#11926660	C₂	1	1	yes	maximal, characteristic
3	#11926368	C₂	1	1	yes	maximal, characteristic, complemented
4	#11926364	C₂	1	1	yes	maximal, characteristic, complemented
5	#11926355	C₂	1	1	yes	maximal, characteristic
6	#11926353	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#365	C₂	1	1	yes	maximal, characteristic, complemented
8	#10597353	—	2	1	no	—
9	#10597350	C₂²	1	1	yes	characteristic
10	#10597334	—	2	1	no	—
11	C₁₉×M₃₂	C₂²	1	1	yes	characteristic
12	C₁₉×#108	C₂²	1	1	yes	characteristic
13	C₁₉×#106	C₂²	1	1	yes	characteristic
14	#10597282	—	2	1	no	—
15	#10597274	C₂²	1	1	yes	characteristic
16	C₈×Dic₁₉	C₂²	1	1	yes	characteristic
17	#10597269	C₂²	1	1	yes	characteristic
18	#10597265	—	2	1	no	—
19	#64541	—	2	1	no	—
20	C₂×Dic₃₈	—	4	1	no	—
21	M₁₆×C₁₉	—	2	1	no	—
22	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
23	C₄⋊C₄×C₁₉	—	2	1	no	—
24	C₄⋊Dic₁₉	—	2	1	no	—
25	Dic₁₉⋊C₄	—	4	1	no	—
26	C₄×Dic₁₉	D₄	1	1	yes	characteristic
27	C₂×C₁₉⋊C₈	D₄	1	1	yes	characteristic
28	Dic₇₆	Q₈	1	1	yes	characteristic, complemented
29	D₁₅₂	Q₈	1	1	yes	characteristic, complemented
30	#64516	—	2	1	no	—
31	#64515	—	4	1	no	—
32	C₈×D₁₉	—	4	1	no	—
33	C₁₆×C₁₉	—	2	1	no	—
34	C₁₉⋊C₁₆	—	2	1	no	—
35	C₂×C₄×C₁₉	—	4	1	no	—
36	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
37	C₂²⋊D₁₉	—	4	1	no	—
38	C₂×Dic₁₉	—	2	1	no	—
39	C₂×Dic₁₉	—	4	1	no	—
40	D₇₆	—	2	1	no	—
41	C₄×D₁₉	—	4	1	no	—
42	Dic₃₈	—	2	1	no	—
43	Dic₃₈	—	8	2	no	—
44	C₈×C₁₉	—	4	1	no	—
45	C₈×C₁₉	C₂×Q₈	1	1	yes	characteristic
46	C₈×C₁₉	#41	1	1	yes	characteristic
47	C₁₉⋊C₈	SD₁₆	1	1	yes	characteristic
48	C₁₉⋊C₈	SD₁₆	1	1	yes	characteristic
49	#2230	—	19	1	no	maximal, Sylow
50	C₂²×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
51	C₂×D₁₉	—	4	1	no	—
52	C₄×C₁₉	—	8	1	no	—
53	C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
54	C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
55	Dic₁₉	—	2	2	no	—
56	Dic₁₉	—	4	1	no	—
57	Dic₁₉	—	8	1	no	—
58	#498	—	19	1	no	—
59	#443	—	19	1	no	—
60	#365	—	19	1	no	—
61	#365	D₁₉	1	1	yes	characteristic, complemented
62	#364	—	19	1	no	—
63	#360	—	19	1	no	—
64	#360	—	19	1	no	—
65	C₂×C₁₉	—	2	1	no	—
66	C₂×C₁₉	#476	1	1	yes	characteristic
67	D₁₉	—	8	1	no	—
68	#135	—	19	1	no	—
69	#131	—	38	1	no	—
70	C₄⋊Q₈	—	38	1	no	—
71	M₃₂	—	19	1	no	—
72	M₃₂	C₂×D₁₉	1	1	yes	characteristic
73	#108	C₂×D₁₉	1	1	yes	characteristic
74	#106	—	19	1	no	—
75	#106	—	38	1	no	—
76	#106	C₂×D₁₉	1	1	yes	characteristic
77	#104	—	38	1	no	—
78	C₄×C₈	—	19	1	no	—
79	C₁₉	#2230	1	1	yes	characteristic, complemented, Sylow
80	#41	—	38	1	no	—
81	C₂×Q₈	—	76	1	no	—
82	Q₁₆	—	19	1	no	—
83	SD₁₆	—	38	1	no	—
84	D₈	—	19	1	no	—
85	M₁₆	—	2	1	no	—
86	M₁₆	—	76	1	no	—
87	C₂×C₈	—	19	1	no	—
88	C₂×C₈	—	76	1	no	—
89	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
90	C₄⋊C₄	—	2	1	no	—
91	C₄⋊C₄	—	38	1	no	—
92	C₄⋊C₄	—	76	1	no	—
93	C₄²	—	19	1	no	—
94	C₁₆	—	2	1	no	—
95	C₁₆	—	38	1	no	—
96	Q₈	—	38	1	no	—
97	Q₈	—	152	2	no	—
98	D₄	—	38	1	no	—
99	D₄	—	76	1	no	—
100	C₂×C₄	—	4	1	no	—
101	C₂×C₄	—	38	1	no	—
102	C₂×C₄	—	76	1	no	—
103	C₂×C₄	—	76	1	no	—
104	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
105	C₈	—	4	1	no	—
106	C₈	—	19	1	no	—
107	C₈	—	19	1	no	—
108	C₈	#64541	1	1	yes	characteristic
109	C₈	Q₈×D₁₉	1	1	yes	characteristic
110	C₂²	—	76	1	no	—
111	C₂²	#10597360	1	1	yes	characteristic
112	C₄	—	8	1	no	—
113	C₄	—	38	2	no	—
114	C₄	—	76	1	no	—
115	C₄	—	152	1	no	—
116	C₄	#10597342	1	1	yes	characteristic
117	C₄	SD₁₆×D₁₉	1	1	yes	characteristic
118	C₂	—	2	1	no	—
119	C₂	—	152	1	no	—
120	C₂	#11926833	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11926941

C₂

yes

maximal, characteristic, complemented

#11926660

C₂

yes

maximal, characteristic

#11926368

C₂

yes

maximal, characteristic, complemented

#11926364

C₂

yes

maximal, characteristic, complemented

#11926355

C₂

yes

maximal, characteristic

#11926353

C₂

yes

maximal, characteristic

C₁₉×#365

C₂

yes

maximal, characteristic, complemented

#10597353

—

#10597350

C₂²

yes

characteristic

#10597334

—

C₁₉×M₃₂

C₂²

yes

characteristic

C₁₉×#108

C₂²

yes

characteristic

C₁₉×#106

C₂²

yes

characteristic

#10597282

—

#10597274

C₂²

yes

characteristic

C₈×Dic₁₉

C₂²

yes

characteristic

#10597269

C₂²

yes

characteristic

#10597265

—

#64541

—

C₂×Dic₃₈

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

C₂³

yes

characteristic

C₄⋊C₄×C₁₉

—

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

D₄

yes

characteristic

C₂×C₁₉⋊C₈

D₄

yes

characteristic

Dic₇₆

Q₈

yes

characteristic, complemented

D₁₅₂

Q₈

yes

characteristic, complemented

#64516

—

#64515

—

C₈×D₁₉

—

C₁₆×C₁₉

—

C₁₉⋊C₁₆

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²⋊D₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

D₇₆

—

C₄×D₁₉

—

Dic₃₈

—

Dic₃₈

—

C₈×C₁₉

—

C₈×C₁₉

C₂×Q₈

yes

characteristic

C₈×C₁₉

#41

yes

characteristic

C₁₉⋊C₈

SD₁₆

yes

characteristic

C₁₉⋊C₈

SD₁₆

yes

—

C₂²×C₁₉

yes

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₂²⋊Q₈

yes

characteristic

C₄×C₁₉

C₂×SD₁₆

yes

characteristic

Dic₁₉

—

Dic₁₉

—

Dic₁₉

—

—

—

—

D₁₉

yes

characteristic, complemented

#364

—

#360

—

#360

—

C₂×C₁₉

—

C₂×C₁₉

#476

yes

characteristic

D₁₉

—

#135

—

#131

—

C₄⋊Q₈

—

M₃₂

—

M₃₂

C₂×D₁₉

yes

characteristic

#108

C₂×D₁₉

yes

—

—

C₂×D₁₉

yes

characteristic

#104

—

C₄×C₈

—

C₁₉

#2230

yes

characteristic, complemented, Sylow

#41

—

C₂×Q₈

—

Q₁₆

—

SD₁₆

—

D₈

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂²×D₁₉

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

C₁₆

—

C₁₆

—

Q₈

—

Q₈

—

152

—

D₄

—

D₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

D₄×D₁₉

yes

characteristic

105

C₈

—

106

C₈

—

107

C₈

—

108

C₈

#64541

yes

characteristic

109

C₈

Q₈×D₁₉

yes

characteristic

110

C₂²

—

111

C₂²

#10597360

yes

characteristic

112

C₄

—

113

C₄

—

114

C₄

—

115

C₄

—

152

—

116

C₄

#10597342

yes

characteristic

117

C₄

SD₁₆×D₁₉

yes

characteristic

118

C₂

—

119

C₂

—

152

—

120

C₂

#11926833

yes

characteristic

	subgroup	G/H
center	C₂	#11926833
commutator, cosocle	C₂×C₈×C₁₉	C₂³
Frattini	C₂×C₈	C₂²×D₁₉
Fitting	C₁₉×#365	C₂
socle	C₂×C₁₉	#476
prime radical	#10597350	C₂²
hypercenter	#365	D₁₉
hypocenter	C₁₉	#2230
LCS	G ▷ C₂×C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #365

subgroup

G/H

center

C₂

#11926833

commutator, cosocle

C₂×C₈×C₁₉

C₂³

Frattini

C₂×C₈

C₂²×D₁₉

Fitting

C₁₉×#365

C₂

C₂×C₁₉

C₂²

D₁₉

C₁₉

G ▷ C₂×C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #365

N	H ≅ G/N	type
1. #11926941	C₂	semidirect
3. #11926368	C₂	semidirect
4. #11926364	C₂	semidirect
7. C₁₉×#365	C₂	semidirect
28. Dic₇₆	Q₈	semidirect
29. D₁₅₂	Q₈	semidirect
61. #365	D₁₉	semidirect
79. C₁₉	#2230	semidirect

H ≅ G/N

type

1. #11926941

C₂

semidirect

3. #11926368

C₂

semidirect

4. #11926364

C₂

semidirect

7. C₁₉×#365

C₂

semidirect

28. Dic₇₆

Q₈

semidirect

29. D₁₅₂

Q₈

semidirect

61. #365

D₁₉

semidirect

79. C₁₉

#2230

semidirect

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

subgroup	index
#11926941	2
#11926660	2
#11926368	2
#11926364	2
#11926355	2
#11926353	2
C₁₉×#365	2
#2230	19

subgroup

index

C₁₉×#365

Subgroups — #14565805

Conjugacy classes of subgroups

Complements

Maximal subgroups