Group #11927356 — subgroups

Subgroups — #11927356

Order 1216.

258 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 107 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	#10597436	C₂	1	1	yes	maximal, characteristic, complemented
2	#10597435	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#131	C₂	1	1	yes	maximal, characteristic, complemented
4	#10597355	C₂	1	3	yes	maximal, complemented
5	#10597354	C₂	1	3	yes	maximal, complemented
6	#10597350	C₂	1	3	yes	maximal, complemented
7	C₂×#64516	C₂	1	3	yes	maximal, complemented
8	#41×C₁₉	C₂²	1	1	yes	characteristic
9	#64545	—	2	1	no	—
10	Q₈×D₁₉	—	2	1	no	—
11	#64543	—	2	3	no	—
12	D₄×D₁₉	—	2	3	no	—
13	#64541	C₂²	1	3	yes	—
14	#64541	C₂²	1	3	yes	complemented
15	C₂×D₇₆	C₂²	1	3	yes	—
16	C₂×Dic₃₈	C₂²	1	3	yes	complemented
17	M₁₆×C₁₉	C₂²	1	3	yes	complemented
18	C₂×C₈×C₁₉	C₂²	1	3	yes	complemented
19	Dic₇₆	C₂²	1	3	yes	complemented
20	D₁₅₂	C₂²	1	3	yes	complemented
21	#64516	C₂²	1	3	yes	complemented
22	#64516	C₂²	1	6	yes	complemented
23	#64516	C₂²	1	1	yes	characteristic, complemented
24	C₂²×D₁₉	—	2	3	no	—
25	Q₈×C₁₉	D₄	1	1	yes	characteristic
26	D₄×C₁₉	D₄	1	3	yes	—
27	C₂×C₄×C₁₉	C₂³	1	3	yes	—
28	C₂²⋊D₁₉	—	2	3	no	—
29	C₂²⋊D₁₉	—	2	3	no	—
30	C₂×Dic₁₉	—	2	3	no	—
31	D₇₆	—	2	3	no	—
32	D₇₆	C₂³	1	3	yes	—
33	D₇₆	C₂³	1	1	yes	characteristic
34	C₄×D₁₉	—	2	3	no	—
35	C₄×D₁₉	—	2	3	no	—
36	Dic₃₈	—	2	3	no	—
37	Dic₃₈	C₂³	1	3	yes	—
38	Dic₃₈	C₂³	1	1	yes	characteristic
39	C₈×C₁₉	C₂³	1	1	yes	characteristic
40	C₈×C₁₉	C₂³	1	3	yes	—
41	C₂²×C₁₉	C₂×D₄	1	3	yes	—
42	C₂×D₁₉	—	2	1	no	—
43	C₂×D₁₉	—	2	3	no	—
44	C₂×D₁₉	—	8	3	no	—
45	C₄×C₁₉	C₂×D₄	1	3	yes	—
46	C₄×C₁₉	C₂⁴	1	1	yes	characteristic
47	Dic₁₉	—	2	3	no	—
48	Dic₁₉	—	2	1	no	—
49	#577	—	19	1	no	maximal, Sylow
50	C₂×C₁₉	—	2	3	no	—
51	C₂×C₁₉	C₂²×D₄	1	1	yes	characteristic
52	D₁₉	—	4	1	no	—
53	D₁₉	—	4	3	no	—
54	2₋¹⁺⁴	—	19	1	no	—
55	H(5,𝔽₂)	—	19	1	no	—
56	#137	—	19	3	no	—
57	AGL(1,ℤ/8)	—	19	3	no	—
58	#135	—	19	3	no	—
59	C₂×SD₁₆	—	19	3	no	—
60	#131	D₁₉	1	1	yes	characteristic, complemented
61	C₁₉	#577	1	1	yes	characteristic, complemented, Sylow
62	#41	—	19	3	no	—
63	#41	—	19	3	no	—
64	#41	—	38	1	no	—
65	#41	—	38	3	no	—
66	#41	C₂×D₁₉	1	1	yes	characteristic
67	C₂×Q₈	—	19	3	no	—
68	C₂×Q₈	—	38	1	no	—
69	C₂×D₄	—	19	3	no	—
70	C₂×D₄	—	38	3	no	—
71	Q₁₆	—	19	3	no	—
72	SD₁₆	—	19	3	no	—
73	SD₁₆	—	19	6	no	—
74	SD₁₆	—	19	1	no	—
75	D₈	—	19	3	no	—
76	M₁₆	C₂×D₁₉	1	3	yes	complemented
77	C₂×C₈	C₂×D₁₉	1	3	yes	complemented
78	C₂³	—	38	3	no	—
79	Q₈	—	19	3	no	—
80	Q₈	—	19	1	no	—
81	Q₈	—	38	3	no	—
82	Q₈	D₇₆	1	1	yes	characteristic
83	D₄	—	19	1	no	—
84	D₄	—	19	3	no	—
85	D₄	—	38	3	no	—
86	D₄	—	38	3	no	—
87	D₄	—	38	3	no	—
88	D₄	D₇₆	1	3	yes	—
89	C₂×C₄	—	38	3	no	—
90	C₂×C₄	—	38	3	no	—
91	C₂×C₄	—	38	3	no	—
92	C₂×C₄	C₂²×D₁₉	1	3	yes	—
93	C₈	C₂²×D₁₉	1	1	yes	characteristic
94	C₈	C₂²×D₁₉	1	3	yes	—
95	C₂²	—	38	1	no	—
96	C₂²	—	38	3	no	—
97	C₂²	—	152	3	no	—
98	C₂²	C₂×D₇₆	1	3	yes	—
99	C₄	—	38	1	no	—
100	C₄	—	38	3	no	—
101	C₄	C₂×D₇₆	1	3	yes	—
102	C₄	C₂³×D₁₉	1	1	yes	characteristic
103	C₂	—	2	3	no	—
104	C₂	—	76	3	no	—
105	C₂	—	76	1	no	—
106	C₂	C₂²×D₇₆	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#10597436

C₂

yes

maximal, characteristic, complemented

#10597435

C₂

yes

maximal, characteristic, complemented

C₁₉×#131

C₂

yes

maximal, characteristic, complemented

#10597355

C₂

yes

maximal, complemented

#10597354

C₂

yes

maximal, complemented

#10597350

C₂

yes

maximal, complemented

C₂×#64516

C₂

yes

maximal, complemented

#41×C₁₉

C₂²

yes

characteristic

#64545

—

Q₈×D₁₉

—

#64543

—

D₄×D₁₉

—

#64541

C₂²

yes

—

#64541

C₂²

yes

complemented

C₂×D₇₆

C₂²

yes

—

C₂×Dic₃₈

C₂²

yes

complemented

M₁₆×C₁₉

C₂²

yes

complemented

C₂×C₈×C₁₉

C₂²

yes

complemented

Dic₇₆

C₂²

yes

complemented

D₁₅₂

C₂²

yes

complemented

#64516

C₂²

yes

complemented

#64516

C₂²

yes

complemented

#64516

C₂²

yes

characteristic, complemented

C₂²×D₁₉

—

Q₈×C₁₉

D₄

yes

characteristic

D₄×C₁₉

D₄

yes

—

C₂×C₄×C₁₉

C₂³

yes

—

C₂²⋊D₁₉

—

C₂²⋊D₁₉

—

C₂×Dic₁₉

—

D₇₆

—

D₇₆

C₂³

yes

—

D₇₆

C₂³

yes

characteristic

C₄×D₁₉

—

C₄×D₁₉

—

Dic₃₈

—

Dic₃₈

C₂³

yes

—

Dic₃₈

C₂³

yes

characteristic

C₈×C₁₉

C₂³

yes

characteristic

C₈×C₁₉

C₂³

yes

—

C₂²×C₁₉

C₂×D₄

yes

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

C₂×D₄

yes

—

C₄×C₁₉

C₂⁴

yes

characteristic

Dic₁₉

—

Dic₁₉

—

#577

—

maximal, Sylow

C₂×C₁₉

—

C₂×C₁₉

C₂²×D₄

yes

characteristic

D₁₉

—

D₁₉

—

2₋¹⁺⁴

—

—

—

—

—

C₂×SD₁₆

—

#131

D₁₉

yes

characteristic, complemented

C₁₉

#577

yes

characteristic, complemented, Sylow

—

—

—

—

C₂×D₁₉

yes

characteristic

C₂×Q₈

—

C₂×Q₈

—

C₂×D₄

—

C₂×D₄

—

Q₁₆

—

SD₁₆

—

SD₁₆

—

SD₁₆

—

D₈

—

M₁₆

C₂×D₁₉

yes

complemented

C₂×C₈

C₂×D₁₉

yes

complemented

C₂³

—

Q₈

—

Q₈

—

Q₈

—

Q₈

D₇₆

yes

characteristic

D₄

—

D₄

—

D₄

—

D₄

—

D₄

—

D₄

D₇₆

yes

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂²×D₁₉

yes

—

C₈

C₂²×D₁₉

yes

characteristic

C₈

C₂²×D₁₉

yes

—

C₂²

—

C₂²

—

C₂²

—

152

—

C₂²

C₂×D₇₆

yes

—

C₄

—

100

C₄

—

101

C₄

C₂×D₇₆

yes

—

102

C₄

C₂³×D₁₉

yes

characteristic

103

C₂

—

104

C₂

—

105

C₂

—

106

C₂

C₂²×D₇₆

yes

characteristic

	subgroup	G/H
center	C₂	C₂²×D₇₆
commutator, cosocle	C₄×C₁₉	C₂⁴
Frattini	C₄	C₂³×D₁₉
Fitting	C₁₉×#131	C₂
socle	C₂×C₁₉	C₂²×D₄
hypercenter	#131	D₁₉
hypocenter	C₁₉	#577
LCS	G ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂ ◁ #41 ◁ #131

subgroup

G/H

center

C₂

C₂²×D₇₆

commutator, cosocle

C₄×C₁₉

C₂⁴

Frattini

C₄

C₂³×D₁₉

Fitting

C₁₉×#131

C₂

socle

C₂×C₁₉

C₂²×D₄

D₁₉

C₁₉

G ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂ ◁ #41 ◁ #131

N	H ≅ G/N	type
1. #10597436	C₂	semidirect
2. #10597435	C₂	semidirect
3. C₁₉×#131	C₂	semidirect
4. #10597355	C₂	semidirect
5. #10597354	C₂	semidirect
6. #10597350	C₂	semidirect
7. C₂×#64516	C₂	semidirect
14. #64541	C₂²	semidirect
16. C₂×Dic₃₈	C₂²	semidirect
17. M₁₆×C₁₉	C₂²	semidirect
18. C₂×C₈×C₁₉	C₂²	semidirect
19. Dic₇₆	C₂²	semidirect
20. D₁₅₂	C₂²	semidirect
21. #64516	C₂²	semidirect
22. #64516	C₂²	semidirect
23. #64516	C₂²	semidirect
60. #131	D₁₉	semidirect
61. C₁₉	#577	semidirect
76. M₁₆	C₂×D₁₉	semidirect
77. C₂×C₈	C₂×D₁₉	semidirect

H ≅ G/N

type

1. #10597436

C₂

semidirect

2. #10597435

C₂

semidirect

3. C₁₉×#131

C₂

semidirect

4. #10597355

C₂

semidirect

5. #10597354

C₂

semidirect

6. #10597350

C₂

semidirect

7. C₂×#64516

C₂

semidirect

14. #64541

C₂²

semidirect

16. C₂×Dic₃₈

C₂²

semidirect

17. M₁₆×C₁₉

C₂²

semidirect

18. C₂×C₈×C₁₉

C₂²

semidirect

19. Dic₇₆

C₂²

semidirect

20. D₁₅₂

C₂²

semidirect

21. #64516

C₂²

semidirect

22. #64516

C₂²

semidirect

23. #64516

C₂²

semidirect

60. #131

D₁₉

semidirect

61. C₁₉

#577

semidirect

76. M₁₆

C₂×D₁₉

semidirect

77. C₂×C₈

C₂×D₁₉

semidirect

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

subgroup	index
#10597436	2
#10597435	2
C₁₉×#131	2
#10597355	2
#10597354	2
#10597350	2
C₂×#64516	2
#577	19

subgroup

index

C₁₉×#131

Subgroups — #11927356

Conjugacy classes of subgroups

Complements

Maximal subgroups