Group #11768330 — subgroups

Subgroups — C₃²×#1281 #11768330

Order 1152.

456 conjugacy classes of subgroups; only the 264 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 264 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	C₃²×#431	C₂	1	2	yes	maximal
2	C₂×C₃²×#97	C₂	1	1	yes	maximal, characteristic
3	C₃×#1281	C₃	1	4	yes	maximal, direct product factor
4	C₂²×C₃²×C₈	C₄	1	2	yes	—
5	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
6	C₃²×C₄⋊C₈	—	2	2	no	—
7	C₃²×C₂²⋊C₈	C₄	1	4	yes	—
8	C₃²×#97	—	2	2	no	—
9	C₃²×C₄×C₈	—	2	2	no	—
10	C₃×#431	C₂×C₃	1	8	yes	—
11	C₂×C₃×#97	C₂×C₃	1	4	yes	—
12	C₂²×C₃²×C₄	C₂×C₄	1	2	yes	—
13	C₂²×C₃²×C₄	C₂×C₄	1	1	yes	characteristic
14	C₂×C₃²×C₈	—	2	2	no	—
15	C₂×C₃²×C₈	—	2	2	no	—
16	C₂×C₃²×C₈	—	2	4	no	—
17	C₂×C₃²×C₈	C₈	1	4	yes	complemented
18	C₃²×C₄²	D₄	1	1	yes	characteristic
19	C₃²×C₄²	D₄	1	2	yes	—
20	C₃²×C₄²	Q₈	1	1	yes	characteristic
21	#1281	C₃²	1	1	yes	characteristic, direct product factor, Sylow
22	C₂²×C₃×C₈	C₃×C₄	1	8	yes	—
23	C₂×C₃×C₄²	C₂²×C₃	1	4	yes	—
24	C₃×C₄⋊C₈	—	2	8	no	—
25	C₃×C₂²⋊C₈	C₃×C₄	1	16	yes	—
26	C₃×#97	—	2	8	no	—
27	C₃×C₄×C₈	—	2	8	no	—
28	C₂³×C₃²	C₄²	1	1	yes	characteristic
29	C₂×C₃²×C₄	—	4	2	no	—
30	C₂×C₃²×C₄	C₂²⋊C₄	1	2	yes	—
31	C₂×C₃²×C₄	C₂²⋊C₄	1	1	yes	characteristic
32	C₂×C₃²×C₄	C₄⋊C₄	1	2	yes	—
33	C₂×C₃²×C₄	C₄⋊C₄	1	1	yes	characteristic
34	C₂×C₃²×C₄	C₂×C₈	1	2	yes	—
35	C₂×C₃²×C₄	M₁₆	1	2	yes	—
36	C₃²×C₈	—	2	4	no	—
37	C₃²×C₈	—	4	4	no	—
38	#431	C₂×C₃²	1	2	yes	—
39	C₂×#97	C₂×C₃²	1	1	yes	characteristic
40	C₂²×C₃×C₄	C₂×C₃×C₄	1	8	yes	—
41	C₂²×C₃×C₄	C₂×C₃×C₄	1	4	yes	—
42	C₂×C₃×C₈	—	2	8	no	—
43	C₂×C₃×C₈	—	2	8	no	—
44	C₂×C₃×C₈	—	2	16	no	—
45	C₂×C₃×C₈	C₃×C₈	1	16	yes	complemented
46	C₃×C₄²	C₃×D₄	1	8	yes	—
47	C₃×C₄²	C₃×D₄	1	4	yes	—
48	C₃×C₄²	C₃×Q₈	1	4	yes	—
49	C₂²×C₃²	—	2	2	no	—
50	C₂²×C₃²	#95	1	1	yes	characteristic
51	C₂²×C₃²	C₄×C₈	1	1	yes	characteristic
52	C₂²×C₃²	#97	1	1	yes	characteristic
53	C₃²×C₄	—	2	2	no	—
54	C₃²×C₄	—	2	2	no	—
55	C₃²×C₄	C₂²⋊C₈	1	2	yes	—
56	C₃²×C₄	C₄⋊C₈	1	2	yes	—
57	C₂²×C₈	C₃²×C₄	1	2	yes	—
58	C₂×C₄²	C₂²×C₃²	1	1	yes	characteristic
59	C₄⋊C₈	—	2	2	no	—
60	C₂²⋊C₈	C₃²×C₄	1	4	yes	—
61	#97	—	2	2	no	—
62	C₄×C₈	—	2	2	no	—
63	C₂³×C₃	C₃×C₄²	1	4	yes	—
64	C₂×C₃×C₄	—	4	8	no	—
65	C₂×C₃×C₄	C₃×C₂²⋊C₄	1	8	yes	—
66	C₂×C₃×C₄	C₃×C₂²⋊C₄	1	4	yes	—
67	C₂×C₃×C₄	C₃×C₄⋊C₄	1	8	yes	—
68	C₂×C₃×C₄	C₃×C₄⋊C₄	1	4	yes	—
69	C₂×C₃×C₄	C₂×C₃×C₈	1	8	yes	—
70	C₂×C₃×C₄	C₃×M₁₆	1	8	yes	—
71	C₃×C₈	—	2	16	no	—
72	C₃×C₈	—	4	16	no	—
73	C₂×C₃²	—	2	1	no	—
74	C₂×C₃²	—	2	1	no	—
75	C₂×C₃²	#336	1	1	yes	characteristic
76	C₂×C₃²	#344	1	2	yes	—
77	C₂²×C₄	C₂×C₃²×C₄	1	2	yes	—
78	C₂²×C₄	C₂×C₃²×C₄	1	1	yes	characteristic
79	C₂×C₈	—	2	2	no	—
80	C₂×C₈	—	2	2	no	—
81	C₂×C₈	—	2	4	no	—
82	C₂×C₈	C₃²×C₈	1	4	yes	complemented
83	C₄²	C₃²×D₄	1	2	yes	—
84	C₄²	C₃²×D₄	1	1	yes	characteristic
85	C₄²	C₃²×Q₈	1	1	yes	characteristic
86	C₂²×C₃	—	2	8	no	—
87	C₂²×C₃	C₃×#95	1	4	yes	—
88	C₂²×C₃	C₃×C₄×C₈	1	4	yes	—
89	C₂²×C₃	C₃×#97	1	4	yes	—
90	C₃×C₄	—	2	8	no	—
91	C₃×C₄	—	2	8	no	—
92	C₃×C₄	C₃×C₂²⋊C₈	1	8	yes	—
93	C₃×C₄	C₃×C₄⋊C₈	1	8	yes	—
94	C₃²	#1281	1	1	yes	characteristic, direct product factor, Sylow
95	C₂³	C₃²×C₄²	1	1	yes	characteristic
96	C₂×C₄	—	4	2	no	—
97	C₂×C₄	C₃²×C₂²⋊C₄	1	2	yes	—
98	C₂×C₄	C₃²×C₂²⋊C₄	1	1	yes	characteristic
99	C₂×C₄	C₃²×C₄⋊C₄	1	2	yes	—
100	C₂×C₄	C₃²×C₄⋊C₄	1	1	yes	characteristic
101	C₂×C₄	C₂×C₃²×C₈	1	2	yes	—
102	C₂×C₄	C₃²×M₁₆	1	2	yes	—
103	C₈	—	2	4	no	—
104	C₈	—	4	4	no	—
105	C₂×C₃	—	2	4	no	—
106	C₂×C₃	—	2	4	no	—
107	C₂×C₃	C₃×#336	1	4	yes	—
108	C₂×C₃	C₃×#344	1	8	yes	—
109	C₂²	—	2	2	no	—
110	C₂²	C₃²×#95	1	1	yes	characteristic
111	C₂²	C₃²×C₄×C₈	1	1	yes	characteristic
112	C₂²	C₃²×#97	1	1	yes	characteristic
113	C₄	—	2	2	no	—
114	C₄	—	2	2	no	—
115	C₄	C₃²×C₂²⋊C₈	1	2	yes	—
116	C₄	C₃²×C₄⋊C₈	1	2	yes	—
117	C₃	C₃×#1281	1	4	yes	direct product factor
118	C₂	—	2	1	no	—
119	C₂	—	2	1	no	—
120	C₂	C₃²×#336	1	1	yes	characteristic
121	C₂	C₃²×#344	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₃²×#431

C₂

yes

maximal

C₂×C₃²×#97

C₂

yes

maximal, characteristic

C₃×#1281

C₃

yes

maximal, direct product factor

C₂²×C₃²×C₈

C₄

yes

—

C₂×C₃²×C₄²

C₂²

yes

characteristic

C₃²×C₄⋊C₈

—

C₃²×C₂²⋊C₈

C₄

yes

—

C₃²×#97

—

C₃²×C₄×C₈

—

C₃×#431

C₂×C₃

yes

—

C₂×C₃×#97

C₂×C₃

yes

—

C₂²×C₃²×C₄

C₂×C₄

yes

—

C₂²×C₃²×C₄

C₂×C₄

yes

characteristic

C₂×C₃²×C₈

—

C₂×C₃²×C₈

—

C₂×C₃²×C₈

—

C₂×C₃²×C₈

C₈

yes

complemented

C₃²×C₄²

D₄

yes

characteristic

C₃²×C₄²

D₄

yes

—

C₃²×C₄²

Q₈

yes

characteristic

#1281

C₃²

yes

characteristic, direct product factor, Sylow

C₂²×C₃×C₈

C₃×C₄

yes

—

C₂×C₃×C₄²

C₂²×C₃

yes

—

C₃×C₄⋊C₈

—

C₃×C₂²⋊C₈

C₃×C₄

yes

—

C₃×#97

—

C₃×C₄×C₈

—

C₂³×C₃²

C₄²

yes

characteristic

C₂×C₃²×C₄

—

C₂×C₃²×C₄

C₂²⋊C₄

yes

—

C₂×C₃²×C₄

C₂²⋊C₄

yes

characteristic

C₂×C₃²×C₄

C₄⋊C₄

yes

—

C₂×C₃²×C₄

C₄⋊C₄

yes

characteristic

C₂×C₃²×C₄

C₂×C₈

yes

—

C₂×C₃²×C₄

M₁₆

yes

—

C₃²×C₈

—

C₃²×C₈

—

#431

C₂×C₃²

yes

—

C₂×#97

C₂×C₃²

yes

characteristic

C₂²×C₃×C₄

C₂×C₃×C₄

yes

—

C₂²×C₃×C₄

C₂×C₃×C₄

yes

—

C₂×C₃×C₈

—

C₂×C₃×C₈

—

C₂×C₃×C₈

—

C₂×C₃×C₈

C₃×C₈

yes

complemented

C₃×C₄²

C₃×D₄

yes

—

C₃×C₄²

C₃×D₄

yes

—

C₃×C₄²

C₃×Q₈

yes

—

C₂²×C₃²

—

C₂²×C₃²

#95

yes

characteristic

C₂²×C₃²

C₄×C₈

yes

characteristic

C₂²×C₃²

#97

yes

characteristic

C₃²×C₄

—

C₃²×C₄

—

C₃²×C₄

C₂²⋊C₈

yes

—

C₃²×C₄

C₄⋊C₈

yes

—

C₂²×C₈

C₃²×C₄

yes

—

C₂×C₄²

C₂²×C₃²

yes

characteristic

C₄⋊C₈

—

C₂²⋊C₈

C₃²×C₄

yes

—

#97

—

C₄×C₈

—

C₂³×C₃

C₃×C₄²

yes

—

C₂×C₃×C₄

—

C₂×C₃×C₄

C₃×C₂²⋊C₄

yes

—

C₂×C₃×C₄

C₃×C₂²⋊C₄

yes

—

C₂×C₃×C₄

C₃×C₄⋊C₄

yes

—

C₂×C₃×C₄

C₃×C₄⋊C₄

yes

—

C₂×C₃×C₄

C₂×C₃×C₈

yes

—

C₂×C₃×C₄

C₃×M₁₆

yes

—

C₃×C₈

—

C₃×C₈

—

C₂×C₃²

—

C₂×C₃²

—

C₂×C₃²

#336

yes

characteristic

C₂×C₃²

#344

yes

—

C₂²×C₄

C₂×C₃²×C₄

yes

—

C₂²×C₄

C₂×C₃²×C₄

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₃²×C₈

yes

complemented

C₄²

C₃²×D₄

yes

—

C₄²

C₃²×D₄

yes

characteristic

C₄²

C₃²×Q₈

yes

characteristic

C₂²×C₃

—

C₂²×C₃

C₃×#95

yes

—

C₂²×C₃

C₃×C₄×C₈

yes

—

C₂²×C₃

C₃×#97

yes

—

C₃×C₄

—

C₃×C₄

—

C₃×C₄

C₃×C₂²⋊C₈

yes

—

C₃×C₄

C₃×C₄⋊C₈

yes

—

C₃²

#1281

yes

characteristic, direct product factor, Sylow

C₂³

C₃²×C₄²

yes

characteristic

C₂×C₄

—

C₂×C₄

C₃²×C₂²⋊C₄

yes

—

C₂×C₄

C₃²×C₂²⋊C₄

yes

characteristic

C₂×C₄

C₃²×C₄⋊C₄

yes

—

100

C₂×C₄

C₃²×C₄⋊C₄

yes

characteristic

101

C₂×C₄

C₂×C₃²×C₈

yes

—

102

C₂×C₄

C₃²×M₁₆

yes

—

103

C₈

—

104

C₈

—

105

C₂×C₃

—

106

C₂×C₃

—

107

C₂×C₃

C₃×#336

yes

—

108

C₂×C₃

C₃×#344

yes

—

109

C₂²

—

110

C₂²

C₃²×#95

yes

characteristic

111

C₂²

C₃²×C₄×C₈

yes

characteristic

112

C₂²

C₃²×#97

yes

characteristic

113

C₄

—

114

C₄

—

115

C₄

C₃²×C₂²⋊C₈

yes

—

116

C₄

C₃²×C₄⋊C₈

yes

—

117

C₃

C₃×#1281

yes

direct product factor

118

C₂

—

119

C₂

—

120

C₂

C₃²×#336

yes

characteristic

121

C₂

C₃²×#344

yes

—

	subgroup	G/H
center	C₂×C₃²×C₄	C₂²⋊C₄
commutator	C₂²	C₃²×C₄×C₈
Frattini, cosocle	C₂×C₄²	C₂²×C₃²
socle	C₂²×C₃²	#95
prime radical	C₂³×C₃²	C₄²
LCS	G ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃²×C₄ ◁ C₂×C₃²×C₄² ◁ G

subgroup

G/H

center

C₂×C₃²×C₄

C₂²⋊C₄

commutator

C₂²

C₃²×C₄×C₈

Frattini, cosocle

C₂×C₄²

C₂²×C₃²

socle

C₂²×C₃²

#95

prime radical

C₂³×C₃²

C₄²

LCS

G ▷ C₂² ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂×C₃²×C₄ ◁ C₂×C₃²×C₄² ◁ G

N	H ≅ G/N	type
3. C₃×#1281	C₃	direct (N × H)
17. C₂×C₃²×C₈	C₈	semidirect
21. #1281	C₃²	direct (N × H)
45. C₂×C₃×C₈	C₃×C₈	semidirect
82. C₂×C₈	C₃²×C₈	semidirect
94. C₃²	#1281	direct (N × H)
117. C₃	C₃×#1281	direct (N × H)

H ≅ G/N

type

3. C₃×#1281

C₃

direct (N × H)

17. C₂×C₃²×C₈

C₈

semidirect

21. #1281

C₃²

direct (N × H)

45. C₂×C₃×C₈

C₃×C₈

semidirect

82. C₂×C₈

C₃²×C₈

semidirect

94. C₃²

#1281

direct (N × H)

117. C₃

C₃×#1281

direct (N × H)

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

subgroup	index
C₃²×#431	2
C₂×C₃²×#97	2
C₃×#1281	3

subgroup

index

C₃²×#431

C₂×C₃²×#97

C₃×#1281

Subgroups — C₃²×#1281 #11768330

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C32×#1281 #11768330

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×#1281 #11768330