Group #11919635 — subgroups

Subgroups — #3417⋊C₉ #11919635

Order 1152.

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

normal subgroups only

This group has 175 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	#578⋊C₉	C₂	1	2	yes	maximal, complemented
2	#504⋊C₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#3417	C₃	1	1	yes	maximal, characteristic
4	2₋¹⁺⁴⋊C₉	—	2	2	no	—
5	#131⋊C₉	C₂²	1	1	yes	characteristic
6	C₉×D₁₆	—	4	1	no	maximal
7	C₃×#578	C₂×C₃	1	2	yes	—
8	C₃×#510	—	3	2	no	—
9	C₃×#508	—	3	1	no	—
10	C₂×C₃×Q₃₂	—	3	1	no	—
11	C₃×#504	C₂×C₃	1	1	yes	characteristic
12	#41⋊C₉	D₄	1	1	yes	characteristic
13	C₂×Q₈⋊C₉	—	4	2	no	—
14	C₉×D₈	—	4	2	no	—
15	C₉×C₁₆	—	4	1	no	—
16	#3417	C₉	1	1	yes	characteristic, complemented, Sylow
17	C₃×2₋¹⁺⁴	—	2	2	no	—
18	C₃×#137	—	6	2	no	—
19	C₃×#135	—	3	2	no	—
20	C₂×C₃×Q₁₆	—	3	2	no	—
21	C₃×#131	C₂²×C₃	1	1	yes	characteristic
22	C₃×Q₃₂	—	3	2	no	—
23	C₃×Q₃₂	—	3	1	no	—
24	C₃×SD₃₂	—	3	2	no	—
25	C₃×D₁₆	A₄	1	1	yes	characteristic
26	C₃×M₃₂	—	3	1	no	—
27	C₂×C₃×C₁₆	—	3	1	no	—
28	D₄×C₉	—	8	2	no	—
29	Q₈⋊C₉	D₈	1	1	yes	characteristic
30	C₈×C₉	—	4	1	no	—
31	#578	C₂×C₉	1	2	yes	complemented
32	#510	—	3	2	no	—
33	#508	—	3	1	no	—
34	C₂×Q₃₂	—	3	1	no	—
35	#504	C₂×C₉	1	1	yes	characteristic, complemented
36	C₃×#41	—	6	2	no	—
37	C₃×#41	—	12	2	no	—
38	C₃×#41	C₃×D₄	1	1	yes	characteristic
39	C₂×C₃×Q₈	—	4	2	no	—
40	C₂×C₃×Q₈	—	6	2	no	—
41	C₃×Q₁₆	—	3	2	no	—
42	C₃×Q₁₆	—	6	2	no	—
43	C₃×SD₁₆	—	6	2	no	—
44	C₃×D₈	C₂×A₄	1	2	yes	—
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	C₂²×C₉	—	16	2	no	—
50	C₄×C₉	—	4	1	no	—
51	2₋¹⁺⁴	—	2	2	no	—
52	#137	—	6	2	no	—
53	#135	—	3	2	no	—
54	C₂×Q₁₆	—	3	2	no	—
55	#131	C₂²×C₉	1	1	yes	characteristic
56	Q₃₂	—	3	2	no	—
57	Q₃₂	—	3	1	no	—
58	SD₃₂	—	3	2	no	—
59	D₁₆	C₂²⋊C₉	1	1	yes	characteristic
60	M₃₂	—	3	1	no	—
61	C₂×C₁₆	—	3	1	no	—
62	C₃×Q₈	—	6	2	no	—
63	C₃×Q₈	—	12	2	no	—
64	C₃×Q₈	C₃×D₈	1	1	yes	characteristic
65	C₃×D₄	—	2	2	no	—
66	C₃×D₄	—	3	1	no	—
67	C₃×D₄	—	12	2	no	—
68	C₂×C₃×C₄	—	3	1	no	—
69	C₂×C₃×C₄	—	12	2	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	C₂×C₉	—	32	2	no	—
75	#41	—	6	2	no	—
76	#41	—	12	2	no	—
77	#41	D₄×C₉	1	1	yes	characteristic
78	C₂×Q₈	—	4	2	no	—
79	C₂×Q₈	—	6	2	no	—
80	Q₁₆	—	3	2	no	—
81	Q₁₆	—	6	2	no	—
82	SD₁₆	—	6	2	no	—
83	D₈	C₂×C₂²⋊C₉	1	2	yes	—
84	M₁₆	—	3	1	no	—
85	C₂×C₈	—	3	1	no	—
86	C₁₆	—	3	1	no	—
87	C₁₆	C₂×C₂²⋊C₉	1	1	yes	characteristic
88	C₂²×C₃	—	3	1	no	—
89	C₂²×C₃	—	4	2	no	—
90	C₃×C₄	—	3	1	no	—
91	C₃×C₄	—	12	2	no	—
92	C₃×C₄	D₄×A₄	1	1	yes	characteristic
93	C₉	—	4	1	no	Sylow
94	Q₈	—	6	2	no	—
95	Q₈	—	12	2	no	—
96	Q₈	C₉×D₈	1	1	yes	characteristic
97	D₄	—	2	2	no	—
98	D₄	—	3	1	no	—
99	D₄	—	12	2	no	—
100	C₂×C₄	—	3	1	no	—
101	C₂×C₄	—	12	2	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	—	8	2	no	—
107	C₂×C₃	A₄×D₈	1	1	yes	characteristic
108	C₂²	—	3	1	no	—
109	C₂²	—	4	2	no	—
110	C₄	—	3	1	no	—
111	C₄	—	12	2	no	—
112	C₄	D₄×C₂²⋊C₉	1	1	yes	characteristic
113	C₃	#3417⋊C₃	1	1	yes	characteristic
114	C₂	—	6	1	no	—
115	C₂	—	8	2	no	—
116	C₂	D₈×C₂²⋊C₉	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#578⋊C₉

C₂

yes

maximal, complemented

#504⋊C₉

C₂

yes

maximal, characteristic, complemented

C₃×#3417

C₃

yes

maximal, characteristic

2₋¹⁺⁴⋊C₉

—

#131⋊C₉

C₂²

yes

characteristic

C₉×D₁₆

—

maximal

C₃×#578

C₂×C₃

yes

—

C₃×#510

—

C₃×#508

—

C₂×C₃×Q₃₂

—

C₃×#504

C₂×C₃

yes

characteristic

#41⋊C₉

D₄

yes

characteristic

C₂×Q₈⋊C₉

—

C₉×D₈

—

C₉×C₁₆

—

#3417

C₉

yes

characteristic, complemented, Sylow

C₃×2₋¹⁺⁴

—

C₃×#137

—

C₃×#135

—

C₂×C₃×Q₁₆

—

C₃×#131

C₂²×C₃

yes

characteristic

C₃×Q₃₂

—

C₃×Q₃₂

—

C₃×SD₃₂

—

C₃×D₁₆

A₄

yes

characteristic

C₃×M₃₂

—

C₂×C₃×C₁₆

—

D₄×C₉

—

Q₈⋊C₉

D₈

yes

characteristic

C₈×C₉

—

#578

C₂×C₉

yes

complemented

#510

—

#508

—

C₂×Q₃₂

—

#504

C₂×C₉

yes

characteristic, complemented

C₃×#41

—

C₃×#41

—

C₃×#41

C₃×D₄

yes

characteristic

C₂×C₃×Q₈

—

C₂×C₃×Q₈

—

C₃×Q₁₆

—

C₃×Q₁₆

—

C₃×SD₁₆

—

C₃×D₈

C₂×A₄

yes

—

C₃×M₁₆

—

C₂×C₃×C₈

—

C₃×C₁₆

—

C₃×C₁₆

C₂×A₄

yes

characteristic

C₂²×C₉

—

C₄×C₉

—

2₋¹⁺⁴

—

#137

—

#135

—

C₂×Q₁₆

—

#131

C₂²×C₉

yes

characteristic

Q₃₂

—

Q₃₂

—

SD₃₂

—

D₁₆

C₂²⋊C₉

yes

characteristic

M₃₂

—

C₂×C₁₆

—

C₃×Q₈

—

C₃×Q₈

—

C₃×Q₈

C₃×D₈

yes

characteristic

C₃×D₄

—

C₃×D₄

—

C₃×D₄

—

C₂×C₃×C₄

—

C₂×C₃×C₄

—

C₂×C₃×C₄

—

C₃×C₈

—

C₃×C₈

C₂²×A₄

yes

characteristic

C₂×C₉

—

C₂×C₉

—

#41

—

#41

—

#41

D₄×C₉

yes

characteristic

C₂×Q₈

—

C₂×Q₈

—

Q₁₆

—

Q₁₆

—

SD₁₆

—

D₈

C₂×C₂²⋊C₉

yes

—

M₁₆

—

C₂×C₈

—

C₁₆

—

C₁₆

C₂×C₂²⋊C₉

yes

characteristic

C₂²×C₃

—

C₂²×C₃

—

C₃×C₄

—

C₃×C₄

—

C₃×C₄

D₄×A₄

yes

characteristic

C₉

—

Sylow

Q₈

—

Q₈

—

Q₈

C₉×D₈

yes

characteristic

D₄

—

D₄

—

D₄

—

100

C₂×C₄

—

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

C₄

—

111

C₄

—

112

C₄

D₄×C₂²⋊C₉

yes

characteristic

113

C₃

#3417⋊C₃

yes

characteristic

114

C₂

—

115

C₂

—

116

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×#3417	C₃
cosocle	C₃×#131	C₂²×C₃
hypercenter	C₃×D₁₆	A₄
hypocenter	Q₈	C₉×D₈
LCS	G ▷ #131 ▷ #41 ▷ Q₈
UCS	C₁ ◁ C₂×C₃ ◁ C₃×C₄ ◁ C₃×C₈ ◁ C₃×D₁₆

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×D₁₆

A₄

hypocenter

Q₈

C₉×D₈

LCS

G ▷ #131 ▷ #41 ▷ Q₈

UCS

C₁ ◁ C₂×C₃ ◁ C₃×C₄ ◁ C₃×C₈ ◁ C₃×D₁₆

N	H ≅ G/N	type
1. #578⋊C₉	C₂	semidirect
2. #504⋊C₉	C₂	semidirect
16. #3417	C₉	semidirect
31. #578	C₂×C₉	semidirect
35. #504	C₂×C₉	semidirect

H ≅ G/N

type

1. #578⋊C₉

C₂

semidirect

2. #504⋊C₉

C₂

semidirect

16. #3417

C₉

semidirect

31. #578

C₂×C₉

semidirect

35. #504

C₂×C₉

semidirect

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

subgroup	index
#578⋊C₉	2
#504⋊C₉	2
C₃×#3417	3
C₉×D₁₆	4

subgroup

index

#578⋊C₉

#504⋊C₉

C₃×#3417

C₉×D₁₆

Subgroups — #3417⋊C₉ #11919635

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #3417⋊C9 #11919635

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #3417⋊C₉ #11919635