Group #11926915 — subgroups

Subgroups — #11926915

Order 1216.

142 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 142 conjugacy classes of subgroups — too many to draw. Only its 47 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×SD₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
2	#10597390	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#64527	C₂	1	1	yes	maximal, characteristic, complemented
4	#10597386	C₂	1	1	yes	maximal, characteristic
5	C₂×#64526	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#64516	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈×Dic₁₉	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×Q₈×C₁₉	C₂²	1	1	yes	characteristic
9	C₂×D₄×C₁₉	C₂²	1	1	yes	characteristic
10	C₂×C₂²⋊D₁₉	—	2	2	no	—
11	C₂×D₇₆	C₂²	1	1	yes	characteristic
12	C₂×Dic₃₈	C₂²	1	1	yes	characteristic
13	SD₁₆×C₁₉	—	2	2	no	—
14	C₂×C₈×C₁₉	C₂²	1	1	yes	characteristic
15	#64527	—	2	2	no	—
16	#64526	—	2	2	no	—
17	Dic₁₉⋊C₄	—	2	2	no	—
18	C₄×Dic₁₉	C₂²	1	1	yes	characteristic
19	C₂×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
20	#64516	—	2	2	no	—
21	C₂³×C₁₉	—	2	1	no	—
22	C₂²×D₁₉	—	2	1	no	—
23	Q₈×C₁₉	—	2	1	no	—
24	Q₈×C₁₉	—	2	1	no	—
25	D₄×C₁₉	—	2	1	no	—
26	D₄×C₁₉	—	2	1	no	—
27	C₂×C₄×C₁₉	—	2	1	no	—
28	C₂×C₄×C₁₉	C₂³	1	1	yes	characteristic
29	C₂²⋊D₁₉	—	4	4	no	—
30	C₂×Dic₁₉	—	2	1	no	—
31	C₂×Dic₁₉	D₄	1	2	yes	—
32	D₇₆	—	2	1	no	—
33	D₇₆	—	2	1	no	—
34	Dic₃₈	—	2	1	no	—
35	Dic₃₈	—	2	1	no	—
36	C₈×C₁₉	D₄	1	2	yes	complemented
37	C₁₉⋊C₈	D₄	1	2	yes	complemented
38	C₂²×C₁₉	—	4	1	no	—
39	C₂²×C₁₉	—	4	2	no	—
40	C₂²×C₁₉	C₂×D₄	1	1	yes	characteristic
41	C₂×D₁₉	—	4	1	no	—
42	C₂×D₁₉	—	4	2	no	—
43	C₄×C₁₉	—	4	1	no	—
44	C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
45	C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
46	Dic₁₉	—	4	1	no	—
47	Dic₁₉	SD₁₆	1	4	yes	complemented
48	#492	—	19	1	no	maximal, Sylow
49	C₂×C₁₉	—	8	1	no	—
50	C₂×C₁₉	#127	1	1	yes	characteristic
51	C₂×C₁₉	C₂×SD₁₆	1	2	yes	—
52	D₁₉	—	8	1	no	—
53	C₂×SD₁₆	—	19	1	no	—
54	C₂×SD₁₆	—	19	1	no	—
55	C₂×SD₁₆	—	19	1	no	—
56	C₂×SD₁₆	D₁₉	1	1	yes	characteristic, complemented
57	C₄⋊Q₈	—	19	1	no	—
58	#127	—	19	1	no	—
59	C₄×C₈	—	19	1	no	—
60	C₁₉	#492	1	1	yes	characteristic, complemented, Sylow
61	C₂×Q₈	—	19	1	no	—
62	C₂×Q₈	C₂×D₁₉	1	1	yes	characteristic
63	C₂×D₄	—	19	1	no	—
64	C₂×D₄	—	38	2	no	—
65	C₂×D₄	C₂×D₁₉	1	1	yes	characteristic
66	SD₁₆	—	2	2	no	—
67	SD₁₆	—	38	2	no	—
68	SD₁₆	—	38	2	no	—
69	SD₁₆	—	38	2	no	—
70	C₂×C₈	—	19	1	no	—
71	C₂×C₈	C₂×D₁₉	1	1	yes	characteristic
72	C₄⋊C₄	—	38	2	no	—
73	C₄²	—	19	1	no	—
74	C₂³	—	2	1	no	—
75	C₂³	—	38	1	no	—
76	Q₈	—	2	1	no	—
77	Q₈	—	2	1	no	—
78	Q₈	—	38	1	no	—
79	Q₈	—	38	1	no	—
80	D₄	—	2	1	no	—
81	D₄	—	2	1	no	—
82	D₄	—	38	1	no	—
83	D₄	—	38	1	no	—
84	D₄	—	76	4	no	—
85	C₂×C₄	—	2	1	no	—
86	C₂×C₄	—	19	2	no	—
87	C₂×C₄	—	38	1	no	—
88	C₂×C₄	C₂²×D₁₉	1	1	yes	characteristic
89	C₈	—	19	2	no	—
90	C₈	C₂²⋊D₁₉	1	2	yes	complemented
91	C₂²	—	4	1	no	—
92	C₂²	—	4	2	no	—
93	C₂²	—	76	1	no	—
94	C₂²	—	76	2	no	—
95	C₂²	D₄×D₁₉	1	1	yes	characteristic
96	C₄	—	4	1	no	—
97	C₄	—	19	4	no	—
98	C₄	—	76	1	no	—
99	C₄	D₄×D₁₉	1	1	yes	characteristic
100	C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
101	C₂	—	8	1	no	—
102	C₂	—	152	1	no	—
103	C₂	SD₁₆×D₁₉	1	2	yes	—
104	C₂	#10597386	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×SD₁₆×C₁₉

C₂

yes

maximal, characteristic, complemented

#10597390

C₂

yes

maximal, characteristic, complemented

C₂×#64527

C₂

yes

maximal, characteristic, complemented

#10597386

C₂

yes

maximal, characteristic

C₂×#64526

C₂

yes

maximal, characteristic, complemented

C₂×#64516

C₂

yes

maximal, characteristic, complemented

C₈×Dic₁₉

C₂

yes

maximal, characteristic, complemented

C₂×Q₈×C₁₉

C₂²

yes

characteristic

C₂×D₄×C₁₉

C₂²

yes

characteristic

C₂×C₂²⋊D₁₉

—

C₂×D₇₆

C₂²

yes

characteristic

C₂×Dic₃₈

C₂²

yes

characteristic

SD₁₆×C₁₉

—

C₂×C₈×C₁₉

C₂²

yes

characteristic

#64527

—

#64526

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

C₂²

yes

characteristic

C₂×C₁₉⋊C₈

C₂²

yes

characteristic

#64516

—

C₂³×C₁₉

—

C₂²×D₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂³

yes

characteristic

C₂²⋊D₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

D₄

yes

—

D₇₆

—

D₇₆

—

Dic₃₈

—

Dic₃₈

—

C₈×C₁₉

D₄

yes

complemented

C₁₉⋊C₈

D₄

yes

complemented

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂×D₄

yes

characteristic

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₂×D₄

yes

characteristic

C₄×C₁₉

C₂×D₄

yes

characteristic

Dic₁₉

—

Dic₁₉

SD₁₆

yes

complemented

#492

—

maximal, Sylow

C₂×C₁₉

—

C₂×C₁₉

#127

yes

characteristic

C₂×C₁₉

C₂×SD₁₆

yes

—

D₁₉

—

C₂×SD₁₆

—

C₂×SD₁₆

—

C₂×SD₁₆

—

C₂×SD₁₆

D₁₉

yes

characteristic, complemented

C₄⋊Q₈

—

#127

—

C₄×C₈

—

C₁₉

#492

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

C₂×D₁₉

yes

characteristic

C₂×D₄

—

C₂×D₄

—

C₂×D₄

C₂×D₁₉

yes

characteristic

SD₁₆

—

SD₁₆

—

SD₁₆

—

SD₁₆

—

C₂×C₈

—

C₂×C₈

C₂×D₁₉

yes

characteristic

C₄⋊C₄

—

C₄²

—

C₂³

—

C₂³

—

Q₈

—

Q₈

—

Q₈

—

Q₈

—

D₄

—

D₄

—

D₄

—

D₄

—

D₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂²×D₁₉

yes

characteristic

C₈

—

C₈

C₂²⋊D₁₉

yes

complemented

C₂²

—

C₂²

—

C₂²

—

C₂²

—

C₂²

D₄×D₁₉

yes

characteristic

C₄

—

C₄

—

C₄

—

C₄

D₄×D₁₉

yes

characteristic

100

C₄

C₂×C₂²⋊D₁₉

yes

characteristic

101

C₂

—

102

C₂

—

152

—

103

C₂

SD₁₆×D₁₉

yes

—

104

C₂

#10597386

yes

characteristic

	subgroup	G/H
center	C₂²	D₄×D₁₉
commutator, cosocle	C₂×C₄×C₁₉	C₂³
Frattini	C₂×C₄	C₂²×D₁₉
Fitting	C₂×SD₁₆×C₁₉	C₂
socle	C₂²×C₁₉	C₂×D₄
prime radical	#10597386	C₂
hypercenter	C₂×SD₁₆	D₁₉
hypocenter	C₁₉	#492
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×SD₁₆

subgroup

G/H

center

C₂²

D₄×D₁₉

commutator, cosocle

C₂×C₄×C₁₉

C₂³

Frattini

C₂×C₄

C₂²×D₁₉

Fitting

C₂×SD₁₆×C₁₉

C₂

socle

C₂²×C₁₉

C₂×D₄

prime radical

#10597386

C₂

hypercenter

C₂×SD₁₆

D₁₉

hypocenter

C₁₉

#492

LCS

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×SD₁₆

N	H ≅ G/N	type
1. C₂×SD₁₆×C₁₉	C₂	semidirect
2. #10597390	C₂	semidirect
3. C₂×#64527	C₂	semidirect
5. C₂×#64526	C₂	semidirect
6. C₂×#64516	C₂	semidirect
7. C₈×Dic₁₉	C₂	semidirect
36. C₈×C₁₉	D₄	semidirect
37. C₁₉⋊C₈	D₄	semidirect
47. Dic₁₉	SD₁₆	semidirect
56. C₂×SD₁₆	D₁₉	semidirect
60. C₁₉	#492	semidirect
90. C₈	C₂²⋊D₁₉	semidirect

H ≅ G/N

type

1. C₂×SD₁₆×C₁₉

C₂

semidirect

2. #10597390

C₂

semidirect

3. C₂×#64527

C₂

semidirect

5. C₂×#64526

C₂

semidirect

6. C₂×#64516

C₂

semidirect

7. C₈×Dic₁₉

C₂

semidirect

36. C₈×C₁₉

D₄

semidirect

37. C₁₉⋊C₈

D₄

semidirect

47. Dic₁₉

SD₁₆

semidirect

56. C₂×SD₁₆

D₁₉

semidirect

60. C₁₉

#492

semidirect

90. C₈

C₂²⋊D₁₉

semidirect

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

subgroup	index
C₂×SD₁₆×C₁₉	2
#10597390	2
C₂×#64527	2
#10597386	2
C₂×#64526	2
C₂×#64516	2
C₈×Dic₁₉	2
#492	19

subgroup

index

C₂×SD₁₆×C₁₉

C₈×Dic₁₉

Subgroups — #11926915

Conjugacy classes of subgroups

Complements

Maximal subgroups