Group #11920998 — subgroups

Subgroups — #11920998

Order 1152.

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

normal subgroups only

This group has 210 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	#10593637	C₂	1	2	yes	maximal
2	C₃×#504⋊C₃	C₂	1	1	yes	maximal, characteristic
3	#73042	—	3	3	no	maximal
4	#71456	—	3	1	no	maximal
5	#64265	—	2	2	no	—
6	C₃×#131⋊C₃	C₂²	1	1	yes	characteristic
7	#63628	—	4	1	no	maximal
8	#5403	—	3	6	no	—
9	C₃×#504	D₃	1	1	yes	characteristic
10	#5143	—	3	2	no	—
11	C₂×Dic₂₄	—	3	1	no	—
12	#504⋊C₃	D₃	1	3	yes	—
13	#4517	—	3	2	no	—
14	#4506	—	3	1	no	—
15	C₃×#41⋊C₃	D₄	1	1	yes	characteristic
16	C₃⋊#226	—	4	2	no	—
17	#3746	—	4	2	no	—
18	C₃²×C₁₆	—	4	1	no	—
19	#2222	—	9	1	no	Sylow
20	#984	—	6	6	no	—
21	C₃×#131	C₂×D₃	1	1	yes	characteristic
22	#951	—	6	2	no	—
23	C₂×Dic₁₂	—	3	2	no	—
24	#131⋊C₃	C₂×D₃	1	3	yes	—
25	C₃×M₃₂	—	3	1	no	—
26	C₂×C₃×C₁₆	—	3	1	no	—
27	#824	—	6	2	no	—
28	#819	—	3	2	no	—
29	Dic₂₄	—	6	1	no	—
30	Dic₂₄	—	6	1	no	—
31	Dic₂₄	—	12	3	no	—
32	#634	—	8	2	no	—
33	C₃×SL(2,𝔽₃)	D₈	1	1	yes	characteristic
34	C₃²×C₈	—	4	1	no	—
35	C₂×Q₃₂	—	9	1	no	—
36	#504	C₃⋊D₃	1	1	yes	characteristic
37	#473	—	9	2	no	—
38	#368	—	9	1	no	—
39	#362	—	9	2	no	—
40	C₃×#41	D₁₂	1	1	yes	characteristic
41	C₂×Dic₆	—	6	2	no	—
42	#41⋊C₃	D₁₂	1	3	yes	—
43	#226	—	12	6	no	—
44	C₃×M₁₆	—	3	1	no	—
45	C₂×C₃×C₈	—	3	1	no	—
46	#216	—	12	2	no	—
47	#214	—	12	2	no	—
48	#208	—	6	2	no	—
49	Dic₁₂	—	6	2	no	—
50	Dic₁₂	—	6	2	no	—
51	Dic₁₂	—	12	6	no	—
52	C₃×C₁₆	—	3	1	no	—
53	C₃×C₁₆	—	4	3	no	—
54	C₃×C₁₆	S₄	1	1	yes	characteristic
55	C₃²×C₄	—	4	1	no	—
56	C₃⋊Dic₃	—	16	2	no	—
57	#137	—	18	2	no	—
58	C₂×Q₁₆	—	9	2	no	—
59	#131	C₂×C₃⋊D₃	1	1	yes	characteristic
60	Q₃₂	—	18	1	no	—
61	Q₃₂	—	18	1	no	—
62	M₃₂	—	3	1	no	—
63	C₂×C₁₆	—	3	1	no	—
64	#108	—	9	2	no	—
65	#101	—	18	2	no	—
66	C₃×Q₈	D₂₄	1	1	yes	characteristic
67	C₃×D₄	—	3	1	no	—
68	C₂×C₃×C₄	—	3	1	no	—
69	C₂×Dic₃	—	12	2	no	—
70	Dic₆	—	12	2	no	—
71	Dic₆	—	12	2	no	—
72	Dic₆	—	24	6	no	—
73	SL(2,𝔽₃)	D₂₄	1	3	yes	—
74	C₃×C₈	—	3	1	no	—
75	C₃×C₈	—	4	3	no	—
76	C₃×C₈	C₂×S₄	1	1	yes	characteristic
77	C₃⋊C₈	—	12	2	no	—
78	C₂×C₃²	—	4	1	no	—
79	#41	C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
80	C₂×Q₈	—	18	2	no	—
81	Q₁₆	—	18	2	no	—
82	Q₁₆	—	18	2	no	—
83	Q₁₆	—	36	2	no	—
84	SD₁₆	—	36	2	no	—
85	M₁₆	—	3	1	no	—
86	M₁₆	—	18	2	no	—
87	C₂×C₈	—	3	1	no	—
88	C₁₆	—	3	1	no	—
89	C₁₆	C₃⋊S₄	1	1	yes	characteristic
90	C₂²×C₃	—	3	1	no	—
91	C₃×C₄	—	3	1	no	—
92	C₃×C₄	—	4	3	no	—
93	C₃×C₄	C₄⋊S₄	1	1	yes	characteristic
94	Dic₃	—	24	2	no	—
95	Dic₃	—	48	6	no	—
96	C₃²	—	4	1	no	Sylow
97	Q₈	—	36	2	no	—
98	Q₈	—	36	2	no	—
99	Q₈	#3745	1	1	yes	characteristic
100	D₄	—	3	1	no	—
101	C₂×C₄	—	3	1	no	—
102	C₂×C₄	—	36	2	no	—
103	C₈	—	3	1	no	—
104	C₈	—	36	2	no	—
105	C₈	C₂×C₃⋊S₄	1	1	yes	characteristic
106	C₂×C₃	—	4	3	no	—
107	C₂×C₃	—	6	1	no	—
108	C₂×C₃	#5402	1	1	yes	characteristic
109	C₂²	—	3	1	no	—
110	C₄	—	3	1	no	—
111	C₄	—	72	2	no	—
112	C₄	C₄⋊(C₃⋊S₄)	1	1	yes	characteristic
113	C₃	—	4	3	no	—
114	C₃	#73042	1	1	yes	characteristic, complemented
115	C₂	—	6	1	no	—
116	C₂	#10593636	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#10593637

C₂

yes

maximal

C₃×#504⋊C₃

C₂

yes

maximal, characteristic

—

—

—

C₃×#131⋊C₃

C₂²

yes

—

—

D₃

yes

characteristic

#5143

—

C₂×Dic₂₄

—

#504⋊C₃

D₃

yes

—

#4517

—

#4506

—

C₃×#41⋊C₃

D₄

yes

characteristic

C₃⋊#226

—

#3746

—

C₃²×C₁₆

—

—

—

C₂×D₃

yes

characteristic

#951

—

C₂×Dic₁₂

—

#131⋊C₃

C₂×D₃

yes

—

C₃×M₃₂

—

C₂×C₃×C₁₆

—

#824

—

#819

—

Dic₂₄

—

Dic₂₄

—

Dic₂₄

—

#634

—

C₃×SL(2,𝔽₃)

D₈

yes

characteristic

C₃²×C₈

—

C₂×Q₃₂

—

#504

C₃⋊D₃

yes

—

—

—

C₃×#41

D₁₂

yes

characteristic

C₂×Dic₆

—

#41⋊C₃

D₁₂

yes

—

#226

—

C₃×M₁₆

—

C₂×C₃×C₈

—

#216

—

#214

—

#208

—

Dic₁₂

—

Dic₁₂

—

Dic₁₂

—

C₃×C₁₆

—

C₃×C₁₆

—

C₃×C₁₆

S₄

yes

characteristic

C₃²×C₄

—

C₃⋊Dic₃

—

#137

—

C₂×Q₁₆

—

#131

C₂×C₃⋊D₃

yes

characteristic

Q₃₂

—

Q₃₂

—

M₃₂

—

C₂×C₁₆

—

#108

—

#101

—

C₃×Q₈

D₂₄

yes

characteristic

C₃×D₄

—

C₂×C₃×C₄

—

C₂×Dic₃

—

Dic₆

—

Dic₆

—

Dic₆

—

SL(2,𝔽₃)

D₂₄

yes

—

C₃×C₈

—

C₃×C₈

—

C₃×C₈

C₂×S₄

yes

characteristic

C₃⋊C₈

—

C₂×C₃²

—

#41

C₄⋊(C₃⋊D₃)

yes

characteristic

C₂×Q₈

—

Q₁₆

—

Q₁₆

—

Q₁₆

—

SD₁₆

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₁₆

—

C₁₆

C₃⋊S₄

yes

characteristic

C₂²×C₃

—

C₃×C₄

—

C₃×C₄

—

C₃×C₄

C₄⋊S₄

yes

characteristic

Dic₃

—

Dic₃

—

C₃²

—

Sylow

Q₈

—

Q₈

—

Q₈

#3745

yes

characteristic

100

D₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₈

—

104

C₈

—

105

C₈

C₂×C₃⋊S₄

yes

characteristic

106

C₂×C₃

—

107

C₂×C₃

—

108

C₂×C₃

#5402

yes

characteristic

109

C₂²

—

110

C₄

—

111

C₄

—

112

C₄

C₄⋊(C₃⋊S₄)

yes

characteristic

113

C₃

—

114

C₃

#73042

yes

characteristic, complemented

115

C₂

—

116

C₂

#10593636

yes

characteristic

	subgroup	G/H
center	C₂	#10593636
commutator, cosocle	C₃×#131⋊C₃	C₂²
Frattini	C₈	C₂×C₃⋊S₄
Fitting	C₃×#504	D₃
socle	C₂×C₃	#5402
prime radical	C₃×#41⋊C₃	D₄
hypercenter	C₁₆	C₃⋊S₄
hypocenter	C₃×SL(2,𝔽₃)	D₈
LCS	G ▷ C₃×#131⋊C₃ ▷ C₃×#41⋊C₃ ▷ C₃×SL(2,𝔽₃)
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆

subgroup

G/H

center

C₂

#10593636

commutator, cosocle

C₃×#131⋊C₃

C₂²

Frattini

C₈

C₂×C₃⋊S₄

D₃

C₂×C₃

C₃×#41⋊C₃

D₄

hypercenter

C₁₆

C₃⋊S₄

hypocenter

C₃×SL(2,𝔽₃)

D₈

LCS

G ▷ C₃×#131⋊C₃ ▷ C₃×#41⋊C₃ ▷ C₃×SL(2,𝔽₃)

UCS

C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆

N	H ≅ G/N	type
114. C₃	#73042	semidirect

H ≅ G/N

type

114. C₃

#73042

semidirect

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

subgroup	index
#10593637	2
C₃×#504⋊C₃	2
#73042	3
#71456	3
#63628	4

subgroup

index

C₃×#504⋊C₃

Subgroups — #11920998

Conjugacy classes of subgroups

Complements

Maximal subgroups