Group #14565853 — subgroups

Subgroups — #14565853

Order 2432.

124 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 124 conjugacy classes of subgroups — too many to draw. Only its 41 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	#11926799	C₂	1	1	yes	maximal, characteristic
2	#11926591	C₂	1	1	yes	maximal, characteristic
3	#11926368	C₂	1	1	yes	maximal, characteristic, complemented
4	#11926367	C₂	1	1	yes	maximal, characteristic, complemented
5	#11926360	C₂	1	1	yes	maximal, characteristic, complemented
6	#11926325	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#362	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
9	#10597392	—	2	1	no	—
10	M₁₆×D₁₉	—	2	1	no	—
11	C₂×#64515	C₂²	1	1	yes	characteristic
12	C₁₉×M₃₂	C₂²	1	1	yes	characteristic
13	C₁₉×#108	C₂²	1	1	yes	characteristic
14	#10597292	—	2	1	no	—
15	#10597279	—	2	1	no	—
16	#10597276	C₂²	1	1	yes	characteristic
17	#10597274	C₂²	1	1	yes	characteristic
18	#10597269	C₂²	1	1	yes	characteristic
19	C₂×Q₈×C₁₉	—	2	1	no	—
20	C₂×C₄×D₁₉	D₄	1	1	yes	characteristic
21	Q₁₆×C₁₉	—	2	1	no	—
22	Q₁₆×C₁₉	—	2	1	no	—
23	M₁₆×C₁₉	—	2	1	no	—
24	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
25	(C₂×D₁₉)⋊C₄	—	4	1	no	—
26	C₄⋊Dic₁₉	—	2	1	no	—
27	Dic₁₉⋊C₄	—	4	1	no	—
28	#64520	—	2	1	no	—
29	C₂×C₁₉⋊C₈	D₄	1	1	yes	characteristic
30	#64515	—	2	1	no	—
31	#64515	—	2	1	no	—
32	#64515	—	4	1	no	—
33	C₈×D₁₉	—	4	1	no	—
34	C₁₆×C₁₉	—	2	1	no	—
35	C₁₉⋊C₁₆	—	2	1	no	—
36	C₂²×D₁₉	SD₁₆	1	1	yes	characteristic
37	Q₈×C₁₉	—	4	1	no	—
38	Q₈×C₁₉	—	4	1	no	—
39	C₂×C₄×C₁₉	—	4	1	no	—
40	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
41	C₂×Dic₁₉	—	4	1	no	—
42	C₂×Dic₁₉	SD₁₆	1	1	yes	characteristic
43	C₄×D₁₉	—	2	1	no	—
44	C₄×D₁₉	—	2	1	no	—
45	C₈×C₁₉	—	4	1	no	—
46	C₈×C₁₉	#41	1	1	yes	characteristic
47	C₈×C₁₉	#41	1	1	yes	characteristic
48	C₁₉⋊C₈	—	2	1	no	—
49	C₁₉⋊C₈	—	4	1	no	—
50	#2239	—	19	1	no	maximal, Sylow
51	C₂²×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
52	C₂×D₁₉	—	2	1	no	—
53	C₂×D₁₉	—	4	1	no	—
54	C₄×C₁₉	—	8	1	no	—
55	C₄×C₁₉	#123	1	1	yes	characteristic
56	C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
57	Dic₁₉	—	2	1	no	—
58	Dic₁₉	—	8	1	no	—
59	#470	—	19	1	no	—
60	#430	—	19	1	no	—
61	#365	—	19	1	no	—
62	#365	—	19	1	no	—
63	#362	—	19	1	no	—
64	#362	D₁₉	1	1	yes	characteristic, complemented
65	#349	—	19	1	no	—
66	C₂×C₁₉	—	2	1	no	—
67	C₂×C₁₉	#481	1	1	yes	characteristic
68	D₁₉	—	4	1	no	—
69	C₂×Q₁₆	C₂×D₁₉	1	1	yes	characteristic
70	C₂×M₁₆	—	19	1	no	—
71	C₂×M₁₆	—	38	1	no	—
72	C₂²⋊Q₈	—	38	1	no	—
73	M₃₂	—	19	1	no	—
74	M₃₂	C₂×D₁₉	1	1	yes	characteristic
75	#108	—	19	1	no	—
76	#108	—	38	1	no	—
77	#108	C₂×D₁₉	1	1	yes	characteristic
78	#106	—	19	1	no	—
79	#103	—	38	1	no	—
80	C₁₉	#2239	1	1	yes	characteristic, complemented, Sylow
81	C₂×Q₈	—	2	1	no	—
82	C₂²×C₄	—	19	1	no	—
83	Q₁₆	—	2	1	no	—
84	Q₁₆	—	2	1	no	—
85	M₁₆	—	2	1	no	—
86	M₁₆	—	38	1	no	—
87	M₁₆	—	38	1	no	—
88	M₁₆	—	38	1	no	—
89	M₁₆	—	76	1	no	—
90	C₂×C₈	—	19	1	no	—
91	C₂×C₈	—	76	1	no	—
92	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
93	C₄⋊C₄	—	38	1	no	—
94	C₄⋊C₄	—	76	1	no	—
95	C₂²⋊C₄	—	76	1	no	—
96	C₁₆	—	2	1	no	—
97	C₁₆	—	38	1	no	—
98	C₂³	—	19	1	no	—
99	Q₈	—	4	1	no	—
100	Q₈	—	4	1	no	—
101	C₂×C₄	—	4	1	no	—
102	C₂×C₄	—	19	1	no	—
103	C₂×C₄	—	38	1	no	—
104	C₂×C₄	—	38	1	no	—
105	C₂×C₄	—	76	1	no	—
106	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
107	C₈	—	4	1	no	—
108	C₈	—	38	1	no	—
109	C₈	—	76	1	no	—
110	C₈	#64541	1	1	yes	characteristic
111	C₈	#64543	1	1	yes	characteristic
112	C₂²	—	38	1	no	—
113	C₂²	—	76	1	no	—
114	C₂²	SD₁₆×D₁₉	1	1	yes	characteristic
115	C₄	—	8	1	no	—
116	C₄	—	38	1	no	—
117	C₄	—	152	1	no	—
118	C₄	#10597329	1	1	yes	characteristic
119	C₄	#10597357	1	1	yes	characteristic
120	C₂	—	2	1	no	—
121	C₂	—	76	1	no	—
122	C₂	#11926861	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11926799

C₂

yes

maximal, characteristic

#11926591

C₂

yes

maximal, characteristic

#11926368

C₂

yes

maximal, characteristic, complemented

#11926367

C₂

yes

maximal, characteristic, complemented

#11926360

C₂

yes

maximal, characteristic, complemented

#11926325

C₂

yes

maximal, characteristic

C₁₉×#362

C₂

yes

maximal, characteristic, complemented

C₂×Q₁₆×C₁₉

C₂²

yes

characteristic

#10597392

—

M₁₆×D₁₉

—

C₂×#64515

C₂²

yes

characteristic

C₁₉×M₃₂

C₂²

yes

characteristic

C₁₉×#108

C₂²

yes

—

—

C₂²

yes

characteristic

#10597274

C₂²

yes

characteristic

#10597269

C₂²

yes

characteristic

C₂×Q₈×C₁₉

—

C₂×C₄×D₁₉

D₄

yes

characteristic

Q₁₆×C₁₉

—

Q₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

C₂³

yes

characteristic

(C₂×D₁₉)⋊C₄

—

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

#64520

—

C₂×C₁₉⋊C₈

D₄

yes

—

—

—

C₈×D₁₉

—

C₁₆×C₁₉

—

C₁₉⋊C₁₆

—

C₂²×D₁₉

SD₁₆

yes

characteristic

Q₈×C₁₉

—

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×Dic₁₉

—

C₂×Dic₁₉

SD₁₆

yes

characteristic

C₄×D₁₉

—

C₄×D₁₉

—

C₈×C₁₉

—

C₈×C₁₉

yes

C₈×C₁₉

yes

C₁₉⋊C₈

—

C₁₉⋊C₈

—

#2239

—

maximal, Sylow

C₂²×C₁₉

C₂×SD₁₆

yes

characteristic

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

Dic₁₉

—

Dic₁₉

—

—

—

—

—

—

D₁₉

yes

characteristic, complemented

#349

—

C₂×C₁₉

—

C₂×C₁₉

#481

yes

characteristic

D₁₉

—

C₂×Q₁₆

C₂×D₁₉

yes

characteristic

C₂×M₁₆

—

C₂×M₁₆

—

C₂²⋊Q₈

—

M₃₂

—

M₃₂

C₂×D₁₉

yes

—

—

C₂×D₁₉

yes

characteristic

#106

—

#103

—

C₁₉

#2239

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂²×C₄

—

Q₁₆

—

Q₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂²×D₁₉

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₁₆

—

C₁₆

—

C₂³

—

Q₈

—

100

Q₈

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

D₄×D₁₉

yes

characteristic

107

C₈

—

108

C₈

—

109

C₈

—

110

C₈

#64541

yes

characteristic

111

C₈

#64543

yes

characteristic

112

C₂²

—

113

C₂²

—

114

C₂²

SD₁₆×D₁₉

yes

characteristic

115

C₄

—

116

C₄

—

117

C₄

—

152

—

118

C₄

#10597329

yes

characteristic

119

C₄

#10597357

yes

characteristic

120

C₂

—

121

C₂

—

122

C₂

#11926861

yes

characteristic

	subgroup	G/H
center	C₂	#11926861
commutator, cosocle	C₂×C₈×C₁₉	C₂³
Frattini	C₂×C₈	C₂²×D₁₉
Fitting	C₁₉×#362	C₂
socle	C₂×C₁₉	#481
prime radical	C₂²×D₁₉	SD₁₆
hypercenter	#362	D₁₉
hypocenter	C₁₉	#2239
LCS	G ▷ C₂×C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #362

subgroup

G/H

center

C₂

#11926861

commutator, cosocle

C₂×C₈×C₁₉

C₂³

Frattini

C₂×C₈

C₂²×D₁₉

Fitting

C₁₉×#362

C₂

socle

C₂×C₁₉

#481

prime radical

C₂²×D₁₉

SD₁₆

D₁₉

C₁₉

G ▷ C₂×C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #362

N	H ≅ G/N	type
3. #11926368	C₂	semidirect
4. #11926367	C₂	semidirect
5. #11926360	C₂	semidirect
7. C₁₉×#362	C₂	semidirect
64. #362	D₁₉	semidirect
80. C₁₉	#2239	semidirect

H ≅ G/N

type

3. #11926368

C₂

semidirect

4. #11926367

C₂

semidirect

5. #11926360

C₂

semidirect

7. C₁₉×#362

C₂

semidirect

64. #362

D₁₉

semidirect

80. C₁₉

#2239

semidirect

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

subgroup	index
#11926799	2
#11926591	2
#11926368	2
#11926367	2
#11926360	2
#11926325	2
C₁₉×#362	2
#2239	19

subgroup

index

C₁₉×#362

Subgroups — #14565853

Conjugacy classes of subgroups

Complements

Maximal subgroups