Group #11768879 — subgroups

Subgroups — C₃²×#1830 #11768879

Order 1152.

708 conjugacy classes of subgroups; only the 300 normal subgroups are shown.

normal subgroups only

This group has 708 conjugacy classes of subgroups — too many to draw. Only its 300 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×#519	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃²×#101	C₂	1	2	yes	maximal
3	C₃²×#344	C₂	1	4	yes	maximal
4	C₃×#1830	C₃	1	4	yes	maximal, direct product factor
5	C₂²×C₃²×Q₈	C₂²	1	1	yes	characteristic
6	C₂×C₃²×M₁₆	C₂²	1	4	yes	—
7	C₃²×C₄×Q₈	—	2	4	no	—
8	C₃²×#117	C₄	1	4	yes	—
9	C₃²×#117	C₂²	1	2	yes	—
10	C₃²×#101	—	2	4	no	—
11	C₃×#519	C₂×C₃	1	4	yes	—
12	C₂×C₃×#101	C₂×C₃	1	8	yes	—
13	C₃×#344	C₂×C₃	1	16	yes	—
14	C₂×C₃²×Q₈	—	2	4	no	—
15	C₂×C₃²×Q₈	D₄	1	4	yes	—
16	C₂²×C₃²×C₄	C₂×C₄	1	2	yes	—
17	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
18	C₃²×M₁₆	—	2	4	no	—
19	C₃²×M₁₆	—	2	4	no	—
20	C₂×C₃²×C₈	—	2	4	no	—
21	C₃²×C₄⋊C₄	—	2	4	no	—
22	C₃²×C₄⋊C₄	—	2	2	no	—
23	C₃²×C₂²⋊C₄	C₂×C₄	1	4	yes	—
24	C₃²×C₄²	—	2	4	no	—
25	C₃²×C₄²	—	2	2	no	—
26	#1830	C₃²	1	1	yes	characteristic, direct product factor, Sylow
27	C₂²×C₃×Q₈	C₂²×C₃	1	4	yes	—
28	C₂×C₃×M₁₆	C₂²×C₃	1	16	yes	—
29	C₃×C₄×Q₈	—	2	16	no	—
30	C₃×#117	C₃×C₄	1	16	yes	—
31	C₃×#117	C₂²×C₃	1	8	yes	—
32	C₃×#101	—	2	16	no	—
33	C₂³×C₃²	C₂²×C₄	1	1	yes	characteristic
34	C₃²×Q₈	—	2	8	no	—
35	C₂×C₃²×C₄	—	2	4	no	—
36	C₂×C₃²×C₄	—	2	4	no	—
37	C₂×C₃²×C₄	C₂²⋊C₄	1	4	yes	—
38	C₂×C₃²×C₄	C₂×D₄	1	2	yes	—
39	C₂×C₃²×C₄	#41	1	4	yes	—
40	C₃²×C₈	—	4	4	no	—
41	#519	C₂×C₃²	1	1	yes	characteristic
42	C₂×#101	C₂×C₃²	1	2	yes	—
43	#344	C₂×C₃²	1	4	yes	—
44	C₂×C₃×Q₈	—	2	16	no	—
45	C₂×C₃×Q₈	C₃×D₄	1	16	yes	—
46	C₂²×C₃×C₄	C₂×C₃×C₄	1	8	yes	—
47	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
48	C₃×M₁₆	—	2	16	no	—
49	C₃×M₁₆	—	2	16	no	—
50	C₂×C₃×C₈	—	2	16	no	—
51	C₃×C₄⋊C₄	—	2	16	no	—
52	C₃×C₄⋊C₄	—	2	8	no	—
53	C₃×C₂²⋊C₄	C₂×C₃×C₄	1	16	yes	—
54	C₃×C₄²	—	2	16	no	—
55	C₃×C₄²	—	2	8	no	—
56	C₂²×C₃²	—	4	1	no	—
57	C₂²×C₃²	C₂×C₂²⋊C₄	1	1	yes	characteristic
58	C₂²×C₃²	#117	1	2	yes	—
59	C₃²×C₄	—	2	4	no	—
60	C₃²×C₄	—	4	4	no	—
61	C₃²×C₄	#123	1	4	yes	—
62	C₂²×Q₈	C₂²×C₃²	1	1	yes	characteristic
63	C₂×M₁₆	C₂²×C₃²	1	4	yes	—
64	C₄×Q₈	—	2	4	no	—
65	#117	C₃²×C₄	1	4	yes	—
66	#117	C₂²×C₃²	1	2	yes	—
67	#101	—	2	4	no	—
68	C₂³×C₃	C₂²×C₃×C₄	1	4	yes	—
69	C₃×Q₈	—	2	32	no	—
70	C₂×C₃×C₄	—	2	16	no	—
71	C₂×C₃×C₄	—	2	16	no	—
72	C₂×C₃×C₄	C₃×C₂²⋊C₄	1	16	yes	—
73	C₂×C₃×C₄	C₂×C₃×D₄	1	8	yes	—
74	C₂×C₃×C₄	C₃×#41	1	16	yes	—
75	C₃×C₈	—	4	16	no	—
76	C₂×C₃²	—	2	1	no	—
77	C₂×C₃²	—	2	2	no	—
78	C₂×C₃²	#381	1	1	yes	characteristic
79	C₂×Q₈	—	2	4	no	—
80	C₂×Q₈	C₃²×D₄	1	4	yes	—
81	C₂²×C₄	C₂×C₃²×C₄	1	2	yes	—
82	C₂²×C₄	C₂³×C₃²	1	1	yes	characteristic
83	M₁₆	—	2	4	no	—
84	M₁₆	—	2	4	no	—
85	C₂×C₈	—	2	4	no	—
86	C₄⋊C₄	—	2	4	no	—
87	C₄⋊C₄	—	2	2	no	—
88	C₂²⋊C₄	C₂×C₃²×C₄	1	4	yes	—
89	C₄²	—	2	4	no	—
90	C₄²	—	2	2	no	—
91	C₂²×C₃	—	4	4	no	—
92	C₂²×C₃	C₂×C₃×C₂²⋊C₄	1	4	yes	—
93	C₂²×C₃	C₃×#117	1	8	yes	—
94	C₃×C₄	—	2	16	no	—
95	C₃×C₄	—	4	16	no	—
96	C₃×C₄	C₃×#123	1	16	yes	—
97	C₃²	#1830	1	1	yes	characteristic, direct product factor, Sylow
98	C₂³	C₂²×C₃²×C₄	1	1	yes	characteristic
99	Q₈	—	2	8	no	—
100	C₂×C₄	—	2	4	no	—
101	C₂×C₄	—	2	4	no	—
102	C₂×C₄	C₃²×C₂²⋊C₄	1	4	yes	—
103	C₂×C₄	C₂×C₃²×D₄	1	2	yes	—
104	C₂×C₄	C₃²×#41	1	4	yes	—
105	C₈	—	4	4	no	—
106	C₂×C₃	—	2	4	no	—
107	C₂×C₃	—	2	8	no	—
108	C₂×C₃	C₃×#381	1	4	yes	—
109	C₂²	—	4	1	no	—
110	C₂²	C₂×C₃²×C₂²⋊C₄	1	1	yes	characteristic
111	C₂²	C₃²×#117	1	2	yes	—
112	C₄	—	2	4	no	—
113	C₄	—	4	4	no	—
114	C₄	C₃²×#123	1	4	yes	—
115	C₃	C₃×#1830	1	4	yes	direct product factor
116	C₂	—	2	1	no	—
117	C₂	—	2	2	no	—
118	C₂	C₃²×#381	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₃²×#519

C₂

yes

maximal, characteristic

C₂×C₃²×#101

C₂

yes

maximal

C₃²×#344

C₂

yes

maximal

C₃×#1830

C₃

yes

maximal, direct product factor

C₂²×C₃²×Q₈

C₂²

yes

characteristic

C₂×C₃²×M₁₆

C₂²

yes

—

C₃²×C₄×Q₈

—

C₃²×#117

C₄

yes

—

C₃²×#117

C₂²

yes

—

C₃²×#101

—

C₃×#519

C₂×C₃

yes

—

C₂×C₃×#101

C₂×C₃

yes

—

C₃×#344

C₂×C₃

yes

—

C₂×C₃²×Q₈

—

C₂×C₃²×Q₈

D₄

yes

—

C₂²×C₃²×C₄

C₂×C₄

yes

—

C₂²×C₃²×C₄

C₂³

yes

characteristic

C₃²×M₁₆

—

C₃²×M₁₆

—

C₂×C₃²×C₈

—

C₃²×C₄⋊C₄

—

C₃²×C₄⋊C₄

—

C₃²×C₂²⋊C₄

C₂×C₄

yes

—

C₃²×C₄²

—

C₃²×C₄²

—

#1830

C₃²

yes

characteristic, direct product factor, Sylow

C₂²×C₃×Q₈

C₂²×C₃

yes

—

C₂×C₃×M₁₆

C₂²×C₃

yes

—

C₃×C₄×Q₈

—

C₃×#117

C₃×C₄

yes

—

C₃×#117

C₂²×C₃

yes

—

C₃×#101

—

C₂³×C₃²

C₂²×C₄

yes

characteristic

C₃²×Q₈

—

C₂×C₃²×C₄

—

C₂×C₃²×C₄

—

C₂×C₃²×C₄

C₂²⋊C₄

yes

—

C₂×C₃²×C₄

C₂×D₄

yes

—

C₂×C₃²×C₄

#41

yes

—

C₃²×C₈

—

#519

C₂×C₃²

yes

characteristic

C₂×#101

C₂×C₃²

yes

—

#344

C₂×C₃²

yes

—

C₂×C₃×Q₈

—

C₂×C₃×Q₈

C₃×D₄

yes

—

C₂²×C₃×C₄

C₂×C₃×C₄

yes

—

C₂²×C₃×C₄

C₂³×C₃

yes

—

C₃×M₁₆

—

C₃×M₁₆

—

C₂×C₃×C₈

—

C₃×C₄⋊C₄

—

C₃×C₄⋊C₄

—

C₃×C₂²⋊C₄

C₂×C₃×C₄

yes

—

C₃×C₄²

—

C₃×C₄²

—

C₂²×C₃²

—

C₂²×C₃²

C₂×C₂²⋊C₄

yes

characteristic

C₂²×C₃²

#117

yes

—

C₃²×C₄

—

C₃²×C₄

—

C₃²×C₄

#123

yes

—

C₂²×Q₈

C₂²×C₃²

yes

characteristic

C₂×M₁₆

C₂²×C₃²

yes

—

C₄×Q₈

—

#117

C₃²×C₄

yes

—

#117

C₂²×C₃²

yes

—

#101

—

C₂³×C₃

C₂²×C₃×C₄

yes

—

C₃×Q₈

—

C₂×C₃×C₄

—

C₂×C₃×C₄

—

C₂×C₃×C₄

C₃×C₂²⋊C₄

yes

—

C₂×C₃×C₄

C₂×C₃×D₄

yes

—

C₂×C₃×C₄

C₃×#41

yes

—

C₃×C₈

—

C₂×C₃²

—

C₂×C₃²

—

C₂×C₃²

#381

yes

characteristic

C₂×Q₈

—

C₂×Q₈

C₃²×D₄

yes

—

C₂²×C₄

C₂×C₃²×C₄

yes

—

C₂²×C₄

C₂³×C₃²

yes

characteristic

M₁₆

—

M₁₆

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₂²⋊C₄

C₂×C₃²×C₄

yes

—

C₄²

—

C₄²

—

C₂²×C₃

—

C₂²×C₃

C₂×C₃×C₂²⋊C₄

yes

—

C₂²×C₃

C₃×#117

yes

—

C₃×C₄

—

C₃×C₄

—

C₃×C₄

C₃×#123

yes

—

C₃²

#1830

yes

characteristic, direct product factor, Sylow

C₂³

C₂²×C₃²×C₄

yes

characteristic

Q₈

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

C₃²×C₂²⋊C₄

yes

—

103

C₂×C₄

C₂×C₃²×D₄

yes

—

104

C₂×C₄

C₃²×#41

yes

—

105

C₈

—

106

C₂×C₃

—

107

C₂×C₃

—

108

C₂×C₃

C₃×#381

yes

—

109

C₂²

—

110

C₂²

C₂×C₃²×C₂²⋊C₄

yes

characteristic

111

C₂²

C₃²×#117

yes

—

112

C₄

—

113

C₄

—

114

C₄

C₃²×#123

yes

—

115

C₃

C₃×#1830

yes

direct product factor

116

C₂

—

117

C₂

—

118

C₂

C₃²×#381

yes

characteristic

	subgroup	G/H
center, socle	C₂×C₃²	#381
commutator	C₂³	C₂²×C₃²×C₄
Frattini, cosocle	C₂²×C₄	C₂³×C₃²
prime radical	C₂³×C₃²	C₂²×C₄
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃² ◁ C₂²×C₃²×C₄ ◁ G

subgroup

G/H

center, socle

C₂×C₃²

#381

commutator

C₂³

C₂²×C₃²×C₄

Frattini, cosocle

C₂²×C₄

C₂³×C₃²

prime radical

C₂³×C₃²

C₂²×C₄

LCS

G ▷ C₂³ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂×C₃² ◁ C₂²×C₃²×C₄ ◁ G

N	H ≅ G/N	type
4. C₃×#1830	C₃	direct (N × H)
26. #1830	C₃²	direct (N × H)
97. C₃²	#1830	direct (N × H)
115. C₃	C₃×#1830	direct (N × H)

H ≅ G/N

type

4. C₃×#1830

C₃

direct (N × H)

26. #1830

C₃²

direct (N × H)

97. C₃²

#1830

direct (N × H)

115. C₃

C₃×#1830

direct (N × H)

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

subgroup	index
C₃²×#519	2
C₂×C₃²×#101	2
C₃²×#344	2
C₃×#1830	3

subgroup

index

C₃²×#519

C₂×C₃²×#101

C₃²×#344

C₃×#1830

Subgroups — C₃²×#1830 #11768879

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C32×#1830 #11768879

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×#1830 #11768879