Finite Group Databasebeta

← #11921471

Subgroups — #11921471

Order 1152.

251 conjugacy classes of subgroups; only the 26 normal subgroups are shown.

normal subgroups only

This group has 251 conjugacy classes of subgroups — too many to draw. Only its 26 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Ω+(4,𝔽3)C211yesmaximal, characteristic
2#85565—32nomaximal
3#73153—32nomaximal
4Ω+(4,𝔽3)C411yescharacteristic, complemented
5C3⋊#859—42nomaximal
6C2×#997D312yes—
7C2×#994D312yes—
8#5426—32no—
9C2×GU(2,𝔽3)—32no—
10C2×C3×SL(2,𝔽3)—42no—
11#1792—91noSylow
12#997Dic312yescomplemented
13#994—32no—
14#994Dic312yescomplemented
15C2×#41⋊C3—32no—
16C2×SL(2,ℤ/4)—122no—
17GU(2,𝔽3)—62no—
18#859—62no—
19#859—124no—
20#835—122no—
21C2×C3⋊Dic3—161no—
22C3×SL(2,𝔽3)—42no—
23C2×H(5,𝔽2)C3⋊D311yescharacteristic
24C2×#104—92no—
25#417—92no—
26C2×#100—91no—
27#390—91no—
28C22×A4—122no—
29C2×C3×Q8—42no—
30#41⋊C3—32no—
31#41⋊C3—32no—
32C2×SL(2,𝔽3)—44no—
33C2×SL(2,𝔽3)S412yes—
34SL(2,ℤ/4)—124no—
35C4⋊Dic3—122no—
36C2×C3⋊C8—122no—
37C22×C32—161no—
38C3⋊Dic3—162no—
39H(5,𝔽2)—32no—
40H(5,𝔽2)—91no—
41H(5,𝔽2)C3⋊Dic311yescharacteristic, complemented
42C2×#41—32no—
43C22×D4—91no—
44C2×M16—92no—
45C2×C4⋊C4—91no—
46C2×C22⋊C4—182no—
47C2×C42—91no—
48#104—182no—
49#104—182no—
50#103—182no—
51#102—182no—
52#100—182no—
53C2×A4—122no—
54C2×A4—122no—
55C2×A4—122no—
56C3×Q8—42no—
57C3×Q8—122no—
58C2×C3×C4—122no—
59C2×Dic3—242no—
60C2×Dic3—482no—
61SL(2,𝔽3)—44no—
62SL(2,𝔽3)SL(2,ℤ/4)12yescomplemented
63C3⋊C8—242no—
64C2×C32—161no—
65C2×C32—161no—
66C2×C32—161no—
67C24—32no—
68#41—32no—
69#41—32no—
70#41—92no—
71#41—92no—
72C2×Q8C3⋊S412yes—
73C2×D4—92no—
74C2×D4—91no—
75C2×D4—91no—
76C2×D4—92no—
77C2×D4—182no—
78C22×C4—91no—
79C22×C4—181no—
80C22×C4—181no—
81M16—182no—
82M16—182no—
83C2×C8—182no—
84C4⋊C4—182no—
85C22⋊C4—364no—
86C42—182no—
87C22×C3—42no—
88C22×C3—162no—
89A4—122no—
90C3×C4—122no—
91C3×C4—122no—
92Dic3—482no—
93Dic3—484no—
94C32—161noSylow
95C23—32no—
96C23—91no—
97C23—92no—
98C23—122no—
99C23—122no—
100Q8—32no—
101Q8C3⋊SL(2,ℤ/4)12yes—
102D4—92no—
103D4—92no—
104D4—182no—
105C2×C4—32no—
106C2×C4—92no—
107C2×C4—91no—
108C2×C4—91no—
109C2×C4—182no—
110C2×C4—361no—
111C2×C4—361no—
112C2×C4—362no—
113C2×C4—361no—
114C8—362no—
115C2×C3—42no—
116C2×C3—42no—
117C2×C3—42no—
118C2×C3—162no—
119C2×C3—162no—
120C2×C3—162no—
121C22—91no—
122C22—91no—
123C22—122no—
124C22—181no—
125C22—181no—
126C22—362no—
127C22A4⋊S411yescharacteristic
128C4—32no—
129C4—32no—
130C4—362no—
131C4—721no—
132C3—42no—
133C3—162no—
134C2—181no—
135C2—181no—
136C2#1059639911yescharacteristic
137C2SO+(4,𝔽3)11yescharacteristic
138C2A4⋊SL(2,ℤ/4)11yescharacteristic
subgroupG/H
center, Frattini, socle, hypercenterC22A4⋊S4
commutator, hypocenterΩ+(4,𝔽3)C4
FittingC2×H(5,𝔽2)C3⋊D3
prime radical, cosocleC2×Ω+(4,𝔽3)C2
LCSG ▷ Ω+(4,𝔽3)
UCSC1 ◁ C22

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
4. Ω+(4,𝔽3)C4semidirect
12. #997Dic3semidirect
14. #994Dic3semidirect
41. H(5,𝔽2)C3⋊Dic3semidirect
62. SL(2,𝔽3)SL(2,ℤ/4)semidirect

Maximal subgroups

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

subgroupindex
C2×Ω+(4,𝔽3)2
#855653
#731533
C3⋊#8594