Group #11919630 — subgroups

Subgroups — C₃×#3415⋊C₃ #11919630

Order 1152.

246 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 58 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	C₃×#576⋊C₃	C₂	1	2	yes	maximal, complemented
2	C₃×#504⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#3415	C₃	1	1	yes	maximal, characteristic, complemented
4	#3415⋊C₃	C₃	1	3	yes	maximal, direct product factor
5	C₃×#994	—	2	2	no	—
6	C₃×#131⋊C₃	C₂²	1	1	yes	characteristic
7	C₃²×Q₃₂	—	4	1	no	maximal
8	C₃×#576	C₂×C₃	1	2	yes	—
9	#576⋊C₃	C₂×C₃	1	6	yes	complemented
10	C₃×#509	—	3	2	no	—
11	C₃×#508	—	3	1	no	—
12	C₂×C₃×D₁₆	—	3	1	no	—
13	C₃×#504	C₂×C₃	1	1	yes	characteristic
14	#504⋊C₃	C₂×C₃	1	3	yes	complemented
15	C₃×#41⋊C₃	—	4	2	no	—
16	C₃×#41⋊C₃	D₄	1	1	yes	characteristic
17	C₃²×Q₁₆	—	4	2	no	—
18	C₃²×C₁₆	—	4	1	no	—
19	#3415	C₃²	1	1	yes	characteristic, complemented, Sylow
20	C₃×H(5,𝔽₂)	—	2	2	no	—
21	#994	—	2	6	no	—
22	C₃×AGL(1,ℤ/8)	—	6	2	no	—
23	C₃×#135	—	3	2	no	—
24	C₂×C₃×D₈	—	3	2	no	—
25	C₃×#131	C₂²×C₃	1	1	yes	characteristic
26	#131⋊C₃	C₂²×C₃	1	3	yes	—
27	C₃×Q₃₂	—	4	3	no	—
28	C₃×Q₃₂	A₄	1	1	yes	characteristic
29	C₃×SD₃₂	—	3	2	no	—
30	C₃×D₁₆	—	3	2	no	—
31	C₃×D₁₆	—	3	1	no	—
32	C₃×M₃₂	—	3	1	no	—
33	C₂×C₃×C₁₆	—	3	1	no	—
34	C₃²×Q₈	—	8	2	no	—
35	C₃×SL(2,𝔽₃)	D₈	1	1	yes	characteristic
36	C₃²×C₈	—	4	1	no	—
37	#576	C₂×C₃²	1	2	yes	—
38	#509	—	3	2	no	—
39	#508	—	3	1	no	—
40	C₂×D₁₆	—	3	1	no	—
41	#504	C₂×C₃²	1	1	yes	characteristic
42	C₃×#41	—	4	2	no	—
43	C₃×#41	—	6	2	no	—
44	C₃×#41	C₃×D₄	1	1	yes	characteristic
45	C₂×C₃×D₄	—	6	2	no	—
46	C₂×C₃×D₄	—	12	2	no	—
47	#41⋊C₃	—	4	6	no	—
48	#41⋊C₃	C₃×D₄	1	3	yes	—
49	C₃×Q₁₆	—	4	6	no	—
50	C₃×Q₁₆	C₂×A₄	1	2	yes	—
51	C₃×SD₁₆	—	6	2	no	—
52	C₃×D₈	—	3	2	no	—
53	C₃×D₈	—	6	2	no	—
54	C₃×M₁₆	—	3	1	no	—
55	C₂×C₃×C₈	—	3	1	no	—
56	C₃×C₁₆	—	3	1	no	—
57	C₃×C₁₆	—	4	3	no	—
58	C₃×C₁₆	C₂×A₄	1	1	yes	characteristic
59	C₃²×C₄	—	4	1	no	—
60	C₃²×C₄	—	16	2	no	—
61	H(5,𝔽₂)	—	2	2	no	—
62	AGL(1,ℤ/8)	—	6	2	no	—
63	#135	—	3	2	no	—
64	C₂×D₈	—	3	2	no	—
65	#131	C₂²×C₃²	1	1	yes	characteristic
66	Q₃₂	C₃×A₄	1	1	yes	characteristic
67	SD₃₂	—	3	2	no	—
68	D₁₆	—	3	2	no	—
69	D₁₆	—	3	1	no	—
70	M₃₂	—	3	1	no	—
71	C₂×C₁₆	—	3	1	no	—
72	C₂³×C₃	—	12	2	no	—
73	C₃×Q₈	—	2	2	no	—
74	C₃×Q₈	—	8	6	no	—
75	C₃×Q₈	C₃×D₈	1	1	yes	characteristic
76	C₃×D₄	—	3	1	no	—
77	C₃×D₄	—	6	2	no	—
78	C₃×D₄	—	12	2	no	—
79	C₃×D₄	—	12	2	no	—
80	C₂×C₃×C₄	—	3	1	no	—
81	C₂×C₃×C₄	—	12	2	no	—
82	SL(2,𝔽₃)	C₃×D₈	1	3	yes	—
83	C₃×C₈	—	3	1	no	—
84	C₃×C₈	—	4	3	no	—
85	C₃×C₈	C₂²×A₄	1	1	yes	characteristic
86	C₂×C₃²	—	4	1	no	—
87	#41	—	4	2	no	—
88	#41	—	6	2	no	—
89	#41	C₃²×D₄	1	1	yes	characteristic
90	C₂×D₄	—	6	2	no	—
91	C₂×D₄	—	12	2	no	—
92	Q₁₆	C₂×C₃×A₄	1	2	yes	—
93	SD₁₆	—	6	2	no	—
94	D₈	—	3	2	no	—
95	D₈	—	6	2	no	—
96	M₁₆	—	3	1	no	—
97	C₂×C₈	—	3	1	no	—
98	C₁₆	—	3	1	no	—
99	C₁₆	C₂×C₃×A₄	1	1	yes	characteristic
100	C₂²×C₃	—	3	1	no	—
101	C₂²×C₃	—	12	2	no	—
102	C₂²×C₃	—	48	2	no	—
103	C₃×C₄	—	3	1	no	—
104	C₃×C₄	—	4	2	no	—
105	C₃×C₄	—	4	3	no	—
106	C₃×C₄	—	16	6	no	—
107	C₃×C₄	D₄×A₄	1	1	yes	characteristic
108	C₃²	—	4	1	no	Sylow
109	C₂³	—	12	2	no	—
110	Q₈	—	2	2	no	—
111	Q₈	C₃²×D₈	1	1	yes	characteristic
112	D₄	—	3	1	no	—
113	D₄	—	6	2	no	—
114	D₄	—	12	2	no	—
115	D₄	—	12	2	no	—
116	C₂×C₄	—	3	1	no	—
117	C₂×C₄	—	12	2	no	—
118	C₈	—	3	1	no	—
119	C₈	C₂²×C₃×A₄	1	1	yes	characteristic
120	C₂×C₃	—	4	3	no	—
121	C₂×C₃	—	6	1	no	—
122	C₂×C₃	—	24	2	no	—
123	C₂×C₃	A₄×D₈	1	1	yes	characteristic
124	C₂²	—	3	1	no	—
125	C₂²	—	12	2	no	—
126	C₂²	—	48	2	no	—
127	C₄	—	3	1	no	—
128	C₄	—	4	2	no	—
129	C₄	C₃×D₄×A₄	1	1	yes	characteristic
130	C₃	—	4	3	no	—
131	C₃	#3415⋊C₃	1	1	yes	characteristic, direct product factor
132	C₂	—	6	1	no	—
133	C₂	—	24	2	no	—
134	C₂	C₃×A₄×D₈	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₃×#576⋊C₃

C₂

yes

maximal, complemented

C₃×#504⋊C₃

C₂

yes

maximal, characteristic, complemented

C₃×#3415

C₃

yes

maximal, characteristic, complemented

#3415⋊C₃

C₃

yes

maximal, direct product factor

C₃×#994

—

C₃×#131⋊C₃

C₂²

yes

characteristic

C₃²×Q₃₂

—

maximal

C₃×#576

C₂×C₃

yes

—

#576⋊C₃

C₂×C₃

yes

complemented

C₃×#509

—

C₃×#508

—

C₂×C₃×D₁₆

—

C₃×#504

C₂×C₃

yes

characteristic

#504⋊C₃

C₂×C₃

yes

complemented

C₃×#41⋊C₃

—

C₃×#41⋊C₃

D₄

yes

characteristic

C₃²×Q₁₆

—

C₃²×C₁₆

—

#3415

C₃²

yes

characteristic, complemented, Sylow

C₃×H(5,𝔽₂)

—

#994

—

C₃×AGL(1,ℤ/8)

—

C₃×#135

—

C₂×C₃×D₈

—

C₃×#131

C₂²×C₃

yes

characteristic

#131⋊C₃

C₂²×C₃

yes

—

C₃×Q₃₂

—

C₃×Q₃₂

A₄

yes

characteristic

C₃×SD₃₂

—

C₃×D₁₆

—

C₃×D₁₆

—

C₃×M₃₂

—

C₂×C₃×C₁₆

—

C₃²×Q₈

—

C₃×SL(2,𝔽₃)

D₈

yes

characteristic

C₃²×C₈

—

#576

C₂×C₃²

yes

—

#509

—

#508

—

C₂×D₁₆

—

#504

C₂×C₃²

yes

characteristic

C₃×#41

—

C₃×#41

—

C₃×#41

C₃×D₄

yes

characteristic

C₂×C₃×D₄

—

C₂×C₃×D₄

—

#41⋊C₃

—

#41⋊C₃

C₃×D₄

yes

—

C₃×Q₁₆

—

C₃×Q₁₆

C₂×A₄

yes

—

C₃×SD₁₆

—

C₃×D₈

—

C₃×D₈

—

C₃×M₁₆

—

C₂×C₃×C₈

—

C₃×C₁₆

—

C₃×C₁₆

—

C₃×C₁₆

C₂×A₄

yes

characteristic

C₃²×C₄

—

C₃²×C₄

—

H(5,𝔽₂)

—

AGL(1,ℤ/8)

—

#135

—

C₂×D₈

—

#131

C₂²×C₃²

yes

characteristic

Q₃₂

C₃×A₄

yes

characteristic

SD₃₂

—

D₁₆

—

D₁₆

—

M₃₂

—

C₂×C₁₆

—

C₂³×C₃

—

C₃×Q₈

—

C₃×Q₈

—

C₃×Q₈

C₃×D₈

yes

characteristic

C₃×D₄

—

C₃×D₄

—

C₃×D₄

—

C₃×D₄

—

C₂×C₃×C₄

—

C₂×C₃×C₄

—

SL(2,𝔽₃)

C₃×D₈

yes

—

C₃×C₈

—

C₃×C₈

—

C₃×C₈

C₂²×A₄

yes

characteristic

C₂×C₃²

—

#41

—

#41

—

#41

C₃²×D₄

yes

characteristic

C₂×D₄

—

C₂×D₄

—

Q₁₆

C₂×C₃×A₄

yes

—

SD₁₆

—

D₈

—

D₈

—

M₁₆

—

C₂×C₈

—

C₁₆

—

C₁₆

C₂×C₃×A₄

yes

characteristic

100

C₂²×C₃

—

101

C₂²×C₃

—

102

C₂²×C₃

—

103

C₃×C₄

—

104

C₃×C₄

—

105

C₃×C₄

—

106

C₃×C₄

—

107

C₃×C₄

D₄×A₄

yes

characteristic

108

C₃²

—

Sylow

109

C₂³

—

110

Q₈

—

111

Q₈

C₃²×D₈

yes

characteristic

112

D₄

—

113

D₄

—

114

D₄

—

115

D₄

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₈

—

119

C₈

C₂²×C₃×A₄

yes

characteristic

120

C₂×C₃

—

121

C₂×C₃

—

122

C₂×C₃

—

123

C₂×C₃

A₄×D₈

yes

characteristic

124

C₂²

—

125

C₂²

—

126

C₂²

—

127

C₄

—

128

C₄

—

129

C₄

C₃×D₄×A₄

yes

characteristic

130

C₃

—

131

C₃

#3415⋊C₃

yes

characteristic, direct product factor

132

C₂

—

133

C₂

—

134

C₂

C₃×A₄×D₈

yes

characteristic

	subgroup	G/H
center, socle	C₂×C₃	A₄×D₈
commutator, cosocle	#131	C₂²×C₃²
Frattini	C₈	C₂²×C₃×A₄
Fitting	C₃×#3415	C₃
hypercenter	C₃×Q₃₂	A₄
hypocenter	Q₈	C₃²×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, cosocle

#131

C₂²×C₃²

Frattini

C₈

C₂²×C₃×A₄

Fitting

C₃×#3415

C₃

hypercenter

C₃×Q₃₂

A₄

hypocenter

Q₈

C₃²×D₈

LCS

G ▷ #131 ▷ #41 ▷ Q₈

UCS

C₁ ◁ C₂×C₃ ◁ C₃×C₄ ◁ C₃×C₈ ◁ C₃×Q₃₂

N	H ≅ G/N	type
1. C₃×#576⋊C₃	C₂	semidirect
2. C₃×#504⋊C₃	C₂	semidirect
3. C₃×#3415	C₃	semidirect
4. #3415⋊C₃	C₃	direct (N × H)
9. #576⋊C₃	C₂×C₃	semidirect
14. #504⋊C₃	C₂×C₃	semidirect
19. #3415	C₃²	semidirect
131. C₃	#3415⋊C₃	direct (N × H)

H ≅ G/N

type

1. C₃×#576⋊C₃

C₂

semidirect

2. C₃×#504⋊C₃

C₂

semidirect

3. C₃×#3415

C₃

semidirect

4. #3415⋊C₃

C₃

direct (N × H)

9. #576⋊C₃

C₂×C₃

semidirect

14. #504⋊C₃

C₂×C₃

semidirect

19. #3415

C₃²

semidirect

131. C₃

#3415⋊C₃

direct (N × H)

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

subgroup	index
C₃×#576⋊C₃	2
C₃×#504⋊C₃	2
C₃×#3415	3
#3415⋊C₃	3
C₃²×Q₃₂	4

subgroup

index

C₃×#576⋊C₃

C₃×#504⋊C₃

C₃×#3415

#3415⋊C₃

C₃²×Q₃₂

Subgroups — C₃×#3415⋊C₃ #11919630

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C3×#3415⋊C3 #11919630

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#3415⋊C₃ #11919630