Group #14562956 — subgroups

Subgroups — #14562956

Order 2432.

196 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 45 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	#11927292	C₂	1	1	yes	maximal, characteristic
2	#11926906	C₂	1	2	yes	maximal, complemented
3	#11926286	C₂	1	1	yes	maximal, characteristic, complemented
4	#11926283	C₂	1	2	yes	maximal, complemented
5	C₁₉×#491	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
7	C₁₉×#125	C₂²	1	1	yes	characteristic
8	#10597342	—	2	2	no	—
9	#10597341	—	2	2	no	—
10	#10597340	—	2	2	no	—
11	#10597321	C₂²	1	2	yes	—
12	C₁₉×#103	—	2	2	no	—
13	C₁₉×#97	C₂²	1	1	yes	characteristic
14	#10597267	—	2	2	no	—
15	#10597266	—	2	2	no	—
16	#10597260	C₂²	1	2	yes	—
17	C₂×Q₈×C₁₉	—	2	1	no	—
18	C₂×D₇₆	—	2	2	no	—
19	C₂×D₇₆	D₄	1	2	yes	—
20	C₂×C₄×D₁₉	—	2	2	no	—
21	C₂×Dic₃₈	D₄	1	2	yes	—
22	C₂×C₈×C₁₉	—	2	1	no	—
23	C₄⋊C₄×C₁₉	—	2	2	no	—
24	C₄⋊C₄×C₁₉	—	2	2	no	—
25	C₄⋊C₄×C₁₉	D₄	1	2	yes	—
26	C₄²×C₁₉	C₂³	1	1	yes	characteristic
27	(C₂×D₁₉)⋊C₄	—	2	2	no	—
28	(C₂×D₁₉)⋊C₄	—	2	2	no	—
29	(C₂×D₁₉)⋊C₄	—	2	2	no	—
30	Dic₁₉⋊C₄	—	2	2	no	—
31	C₂×C₁₉⋊C₈	—	2	2	no	—
32	C₂²×D₁₉	—	2	2	no	—
33	Q₈×C₁₉	—	4	2	no	—
34	C₂×C₄×C₁₉	—	2	2	no	—
35	C₂×C₄×C₁₉	—	4	1	no	—
36	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
37	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
38	C₂×Dic₁₉	—	2	2	no	—
39	D₇₆	—	4	2	no	—
40	D₇₆	—	8	2	no	—
41	C₄×D₁₉	—	8	2	no	—
42	Dic₃₈	—	4	2	no	—
43	C₈×C₁₉	—	4	1	no	—
44	C₁₉⋊C₈	—	4	2	no	—
45	#1662	—	19	1	no	maximal, Sylow
46	C₂²×C₁₉	#120	1	1	yes	characteristic
47	C₂×D₁₉	—	4	2	no	—
48	C₂×D₁₉	—	4	2	no	—
49	C₂×D₁₉	—	4	2	no	—
50	C₄×C₁₉	—	2	1	no	—
51	C₄×C₁₉	—	2	2	no	—
52	C₄×C₁₉	—	4	2	no	—
53	C₄×C₁₉	—	8	1	no	—
54	Dic₁₉	—	4	2	no	—
55	#562	—	19	1	no	—
56	#491	D₁₉	1	1	yes	characteristic, complemented
57	#489	—	19	2	no	—
58	#330	—	19	1	no	—
59	#329	—	19	2	no	—
60	C₂×C₁₉	#454	1	1	yes	characteristic
61	C₂×C₁₉	#455	1	2	yes	—
62	D₁₉	—	8	2	no	—
63	C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
64	#125	C₂×D₁₉	1	1	yes	characteristic
65	#124	—	19	2	no	—
66	#123	—	38	2	no	—
67	C₂²⋊Q₈	—	38	2	no	—
68	#121	—	38	2	no	—
69	#103	—	2	2	no	—
70	#103	—	38	2	no	—
71	#102	—	38	2	no	—
72	#97	—	19	2	no	—
73	#97	C₂×D₁₉	1	1	yes	characteristic
74	C₁₉	#1662	1	1	yes	characteristic, complemented, Sylow
75	C₂×Q₈	—	2	1	no	—
76	C₂×Q₈	—	19	2	no	—
77	C₂×D₄	—	19	2	no	—
78	C₂×D₄	—	38	2	no	—
79	C₂²×C₄	—	38	2	no	—
80	C₂×C₈	—	2	1	no	—
81	C₂×C₈	—	38	2	no	—
82	C₄⋊C₄	—	2	2	no	—
83	C₄⋊C₄	—	2	2	no	—
84	C₄⋊C₄	—	38	2	no	—
85	C₄⋊C₄	C₂²⋊D₁₉	1	2	yes	—
86	C₂²⋊C₄	—	38	2	no	—
87	C₂²⋊C₄	—	38	2	no	—
88	C₂²⋊C₄	—	38	2	no	—
89	C₄²	C₂²×D₁₉	1	1	yes	characteristic
90	C₂³	—	38	2	no	—
91	Q₈	—	4	2	no	—
92	Q₈	—	76	2	no	—
93	D₄	—	76	2	no	—
94	D₄	—	152	2	no	—
95	C₂×C₄	—	2	2	no	—
96	C₂×C₄	—	4	1	no	—
97	C₂×C₄	—	38	2	no	—
98	C₂×C₄	—	152	2	no	—
99	C₂×C₄	D₄×D₁₉	1	2	yes	—
100	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
101	C₈	—	4	1	no	—
102	C₈	—	76	2	no	—
103	C₂²	—	76	2	no	—
104	C₂²	—	76	2	no	—
105	C₂²	—	76	2	no	—
106	C₂²	#10597383	1	1	yes	characteristic
107	C₄	—	2	1	no	—
108	C₄	—	2	2	no	—
109	C₄	—	4	2	no	—
110	C₄	—	8	1	no	—
111	C₄	—	76	2	no	—
112	C₂	—	152	2	no	—
113	C₂	#11926716	1	1	yes	characteristic
114	C₂	#11926720	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#11927292

C₂

yes

maximal, characteristic

#11926906

C₂

yes

maximal, complemented

#11926286

C₂

yes

maximal, characteristic, complemented

#11926283

C₂

yes

maximal, complemented

C₁₉×#491

C₂

yes

maximal, characteristic, complemented

C₁₉×C₄⋊Q₈

C₂²

yes

characteristic

C₁₉×#125

C₂²

yes

—

—

—

C₂²

yes

—

C₁₉×#103

—

C₁₉×#97

C₂²

yes

—

—

C₂²

yes

—

C₂×Q₈×C₁₉

—

C₂×D₇₆

—

C₂×D₇₆

D₄

yes

—

C₂×C₄×D₁₉

—

C₂×Dic₃₈

D₄

yes

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

D₄

yes

—

C₄²×C₁₉

C₂³

yes

characteristic

(C₂×D₁₉)⋊C₄

—

(C₂×D₁₉)⋊C₄

—

(C₂×D₁₉)⋊C₄

—

Dic₁₉⋊C₄

—

C₂×C₁₉⋊C₈

—

C₂²×D₁₉

—

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×Dic₁₉

—

D₇₆

—

D₇₆

—

C₄×D₁₉

—

Dic₃₈

—

C₈×C₁₉

—

C₁₉⋊C₈

—

—

C₂²×C₁₉

yes

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

Dic₁₉

—

#562

—

#491

D₁₉

yes

characteristic, complemented

#489

—

#330

—

#329

—

C₂×C₁₉

#454

yes

characteristic

C₂×C₁₉

#455

yes

—

D₁₉

—

C₄⋊Q₈

C₂×D₁₉

yes

characteristic

#125

C₂×D₁₉

yes

characteristic

#124

—

#123

—

C₂²⋊Q₈

—

—

—

—

—

—

C₂×D₁₉

yes

characteristic

C₁₉

#1662

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

—

C₂×D₄

—

C₂×D₄

—

C₂²×C₄

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

C₂²⋊D₁₉

yes

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₄²

C₂²×D₁₉

yes

characteristic

C₂³

—

Q₈

—

Q₈

—

D₄

—

D₄

—

152

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

152

—

C₂×C₄

D₄×D₁₉

yes

—

100

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

101

C₈

—

102

C₈

—

103

C₂²

—

104

C₂²

—

105

C₂²

—

106

C₂²

#10597383

yes

characteristic

107

C₄

—

108

C₄

—

109

C₄

—

110

C₄

—

111

C₄

—

112

C₂

—

152

—

113

C₂

#11926716

yes

characteristic

114

C₂

#11926720

yes

—

	subgroup	G/H
center	C₂²	#10597383
commutator, cosocle	C₄²×C₁₉	C₂³
Frattini	C₄²	C₂²×D₁₉
Fitting	C₁₉×#491	C₂
socle	C₂²×C₁₉	#120
prime radical	#11927292	C₂
hypercenter	#491	D₁₉
hypocenter	C₁₉	#1662
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #491

subgroup

G/H

center

C₂²

#10597383

commutator, cosocle

C₄²×C₁₉

C₂³

Frattini

C₄²

C₂²×D₁₉

Fitting

C₁₉×#491

C₂

C₂²×C₁₉

C₂

D₁₉

C₁₉

G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #491

N	H ≅ G/N	type
2. #11926906	C₂	semidirect
3. #11926286	C₂	semidirect
4. #11926283	C₂	semidirect
5. C₁₉×#491	C₂	semidirect
56. #491	D₁₉	semidirect
74. C₁₉	#1662	semidirect

H ≅ G/N

type

2. #11926906

C₂

semidirect

3. #11926286

C₂

semidirect

4. #11926283

C₂

semidirect

5. C₁₉×#491

C₂

semidirect

56. #491

D₁₉

semidirect

74. C₁₉

#1662

semidirect

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

subgroup	index
#11927292	2
#11926906	2
#11926286	2
#11926283	2
C₁₉×#491	2
#1662	19

subgroup

index

C₁₉×#491

Subgroups — #14562956

Conjugacy classes of subgroups

Complements

Maximal subgroups