Group #11919631 — subgroups

Subgroups — #3415⋊C₉ #11919631

Order 1152.

177 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 177 conjugacy classes of subgroups — too many to draw. Only its 37 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	#576⋊C₉	C₂	1	2	yes	maximal, complemented
2	#504⋊C₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#3415	C₃	1	1	yes	maximal, characteristic
4	#63700	—	2	2	no	—
5	#131⋊C₉	C₂²	1	1	yes	characteristic
6	C₉×Q₃₂	—	4	1	no	maximal
7	C₃×#576	C₂×C₃	1	2	yes	—
8	C₃×#509	—	3	2	no	—
9	C₃×#508	—	3	1	no	—
10	C₂×C₃×D₁₆	—	3	1	no	—
11	C₃×#504	C₂×C₃	1	1	yes	characteristic
12	#41⋊C₉	—	4	2	no	—
13	#41⋊C₉	D₄	1	1	yes	characteristic
14	C₉×Q₁₆	—	4	2	no	—
15	C₉×C₁₆	—	4	1	no	—
16	#3415	C₉	1	1	yes	characteristic, complemented, Sylow
17	C₃×H(5,𝔽₂)	—	2	2	no	—
18	C₃×AGL(1,ℤ/8)	—	6	2	no	—
19	C₃×#135	—	3	2	no	—
20	C₂×C₃×D₈	—	3	2	no	—
21	C₃×#131	C₂²×C₃	1	1	yes	characteristic
22	C₃×Q₃₂	A₄	1	1	yes	characteristic
23	C₃×SD₃₂	—	3	2	no	—
24	C₃×D₁₆	—	3	2	no	—
25	C₃×D₁₆	—	3	1	no	—
26	C₃×M₃₂	—	3	1	no	—
27	C₂×C₃×C₁₆	—	3	1	no	—
28	Q₈×C₉	—	8	2	no	—
29	Q₈⋊C₉	D₈	1	1	yes	characteristic
30	C₈×C₉	—	4	1	no	—
31	#576	C₂×C₉	1	2	yes	—
32	#509	—	3	2	no	—
33	#508	—	3	1	no	—
34	C₂×D₁₆	—	3	1	no	—
35	#504	C₂×C₉	1	1	yes	characteristic
36	C₃×#41	—	4	2	no	—
37	C₃×#41	—	6	2	no	—
38	C₃×#41	C₃×D₄	1	1	yes	characteristic
39	C₂×C₃×D₄	—	6	2	no	—
40	C₂×C₃×D₄	—	12	2	no	—
41	C₃×Q₁₆	C₂×A₄	1	2	yes	—
42	C₃×SD₁₆	—	6	2	no	—
43	C₃×D₈	—	3	2	no	—
44	C₃×D₈	—	6	2	no	—
45	C₃×M₁₆	—	3	1	no	—
46	C₂×C₃×C₈	—	3	1	no	—
47	C₃×C₁₆	—	3	1	no	—
48	C₃×C₁₆	C₂×A₄	1	1	yes	characteristic
49	C₄×C₉	—	4	1	no	—
50	C₄×C₉	—	16	2	no	—
51	H(5,𝔽₂)	—	2	2	no	—
52	AGL(1,ℤ/8)	—	6	2	no	—
53	#135	—	3	2	no	—
54	C₂×D₈	—	3	2	no	—
55	#131	C₂²×C₉	1	1	yes	characteristic
56	Q₃₂	C₂²⋊C₉	1	1	yes	characteristic
57	SD₃₂	—	3	2	no	—
58	D₁₆	—	3	2	no	—
59	D₁₆	—	3	1	no	—
60	M₃₂	—	3	1	no	—
61	C₂×C₁₆	—	3	1	no	—
62	C₂³×C₃	—	12	2	no	—
63	C₃×Q₈	—	2	2	no	—
64	C₃×Q₈	C₃×D₈	1	1	yes	characteristic
65	C₃×D₄	—	3	1	no	—
66	C₃×D₄	—	6	2	no	—
67	C₃×D₄	—	12	2	no	—
68	C₃×D₄	—	12	2	no	—
69	C₂×C₃×C₄	—	3	1	no	—
70	C₂×C₃×C₄	—	12	2	no	—
71	C₃×C₈	—	3	1	no	—
72	C₃×C₈	C₂²×A₄	1	1	yes	characteristic
73	C₂×C₉	—	4	1	no	—
74	#41	—	4	2	no	—
75	#41	—	6	2	no	—
76	#41	D₄×C₉	1	1	yes	characteristic
77	C₂×D₄	—	6	2	no	—
78	C₂×D₄	—	12	2	no	—
79	Q₁₆	C₂×C₂²⋊C₉	1	2	yes	—
80	SD₁₆	—	6	2	no	—
81	D₈	—	3	2	no	—
82	D₈	—	6	2	no	—
83	M₁₆	—	3	1	no	—
84	C₂×C₈	—	3	1	no	—
85	C₁₆	—	3	1	no	—
86	C₁₆	C₂×C₂²⋊C₉	1	1	yes	characteristic
87	C₂²×C₃	—	3	1	no	—
88	C₂²×C₃	—	12	2	no	—
89	C₂²×C₃	—	48	2	no	—
90	C₃×C₄	—	3	1	no	—
91	C₃×C₄	—	4	2	no	—
92	C₃×C₄	D₄×A₄	1	1	yes	characteristic
93	C₉	—	4	1	no	Sylow
94	C₂³	—	12	2	no	—
95	Q₈	—	2	2	no	—
96	Q₈	C₉×D₈	1	1	yes	characteristic
97	D₄	—	3	1	no	—
98	D₄	—	6	2	no	—
99	D₄	—	12	2	no	—
100	D₄	—	12	2	no	—
101	C₂×C₄	—	3	1	no	—
102	C₂×C₄	—	12	2	no	—
103	C₈	—	3	1	no	—
104	C₈	C₂²×C₂²⋊C₉	1	1	yes	characteristic
105	C₂×C₃	—	6	1	no	—
106	C₂×C₃	—	24	2	no	—
107	C₂×C₃	A₄×D₈	1	1	yes	characteristic
108	C₂²	—	3	1	no	—
109	C₂²	—	12	2	no	—
110	C₂²	—	48	2	no	—
111	C₄	—	3	1	no	—
112	C₄	—	4	2	no	—
113	C₄	D₄×C₂²⋊C₉	1	1	yes	characteristic
114	C₃	#3415⋊C₃	1	1	yes	characteristic
115	C₂	—	6	1	no	—
116	C₂	—	24	2	no	—
117	C₂	D₈×C₂²⋊C₉	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#576⋊C₉

C₂

yes

maximal, complemented

#504⋊C₉

C₂

yes

maximal, characteristic, complemented

C₃×#3415

C₃

yes

maximal, characteristic

#63700

—

#131⋊C₉

C₂²

yes

characteristic

C₉×Q₃₂

—

maximal

C₃×#576

C₂×C₃

yes

—

C₃×#509

—

C₃×#508

—

C₂×C₃×D₁₆

—

C₃×#504

C₂×C₃

yes

characteristic

#41⋊C₉

—

#41⋊C₉

D₄

yes

characteristic

C₉×Q₁₆

—

C₉×C₁₆

—

#3415

C₉

yes

characteristic, complemented, Sylow

C₃×H(5,𝔽₂)

—

C₃×AGL(1,ℤ/8)

—

C₃×#135

—

C₂×C₃×D₈

—

C₃×#131

C₂²×C₃

yes

characteristic

C₃×Q₃₂

A₄

yes

characteristic

C₃×SD₃₂

—

C₃×D₁₆

—

C₃×D₁₆

—

C₃×M₃₂

—

C₂×C₃×C₁₆

—

Q₈×C₉

—

Q₈⋊C₉

D₈

yes

characteristic

C₈×C₉

—

#576

C₂×C₉

yes

—

#509

—

#508

—

C₂×D₁₆

—

#504

C₂×C₉

yes

characteristic

C₃×#41

—

C₃×#41

—

C₃×#41

C₃×D₄

yes

characteristic

C₂×C₃×D₄

—

C₂×C₃×D₄

—

C₃×Q₁₆

C₂×A₄

yes

—

C₃×SD₁₆

—

C₃×D₈

—

C₃×D₈

—

C₃×M₁₆

—

C₂×C₃×C₈

—

C₃×C₁₆

—

C₃×C₁₆

C₂×A₄

yes

characteristic

C₄×C₉

—

C₄×C₉

—

H(5,𝔽₂)

—

AGL(1,ℤ/8)

—

#135

—

C₂×D₈

—

#131

C₂²×C₉

yes

characteristic

Q₃₂

C₂²⋊C₉

yes

characteristic

SD₃₂

—

D₁₆

—

D₁₆

—

M₃₂

—

C₂×C₁₆

—

C₂³×C₃

—

C₃×Q₈

—

C₃×Q₈

C₃×D₈

yes

characteristic

C₃×D₄

—

C₃×D₄

—

C₃×D₄

—

C₃×D₄

—

C₂×C₃×C₄

—

C₂×C₃×C₄

—

C₃×C₈

—

C₃×C₈

C₂²×A₄

yes

characteristic

C₂×C₉

—

#41

—

#41

—

#41

D₄×C₉

yes

characteristic

C₂×D₄

—

C₂×D₄

—

Q₁₆

C₂×C₂²⋊C₉

yes

—

SD₁₆

—

D₈

—

D₈

—

M₁₆

—

C₂×C₈

—

C₁₆

—

C₁₆

C₂×C₂²⋊C₉

yes

characteristic

C₂²×C₃

—

C₂²×C₃

—

C₂²×C₃

—

C₃×C₄

—

C₃×C₄

—

C₃×C₄

D₄×A₄

yes

characteristic

C₉

—

Sylow

C₂³

—

Q₈

—

Q₈

C₉×D₈

yes

characteristic

D₄

—

D₄

—

D₄

—

100

D₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₈

—

104

C₈

C₂²×C₂²⋊C₉

yes

characteristic

105

C₂×C₃

—

106

C₂×C₃

—

107

C₂×C₃

A₄×D₈

yes

characteristic

108

C₂²

—

109

C₂²

—

110

C₂²

—

111

C₄

—

112

C₄

—

113

C₄

D₄×C₂²⋊C₉

yes

characteristic

114

C₃

#3415⋊C₃

yes

characteristic

115

C₂

—

116

C₂

—

117

C₂

D₈×C₂²⋊C₉

yes

characteristic

	subgroup	G/H
center, socle	C₂×C₃	A₄×D₈
commutator	#131	C₂²×C₉
Frattini	C₃×C₈	C₂²×A₄
Fitting, prime radical	C₃×#3415	C₃
cosocle	C₃×#131	C₂²×C₃
hypercenter	C₃×Q₃₂	A₄
hypocenter	Q₈	C₉×D₈
LCS	G ▷ #131 ▷ #41 ▷ Q₈
UCS	C₁ ◁ C₂×C₃ ◁ C₃×C₄ ◁ C₃×C₈ ◁ C₃×Q₃₂

subgroup

G/H

center, socle

C₂×C₃

A₄×D₈

commutator

#131

C₂²×C₉

Frattini

C₃×C₈

C₂²×A₄

Fitting, prime radical

C₃

C₂²×C₃

C₃×Q₃₂

A₄

hypocenter

Q₈

C₉×D₈

LCS

G ▷ #131 ▷ #41 ▷ Q₈

UCS

C₁ ◁ C₂×C₃ ◁ C₃×C₄ ◁ C₃×C₈ ◁ C₃×Q₃₂

N	H ≅ G/N	type
1. #576⋊C₉	C₂	semidirect
2. #504⋊C₉	C₂	semidirect
16. #3415	C₉	semidirect

H ≅ G/N

type

1. #576⋊C₉

C₂

semidirect

2. #504⋊C₉

C₂

semidirect

16. #3415

C₉

semidirect

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

subgroup	index
#576⋊C₉	2
#504⋊C₉	2
C₃×#3415	3
C₉×Q₃₂	4

subgroup

index

#576⋊C₉

#504⋊C₉

C₃×#3415

C₉×Q₃₂

Subgroups — #3415⋊C₉ #11919631

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #3415⋊C9 #11919631

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #3415⋊C₉ #11919631