Finite Group Databasebeta

← #11771650

Subgroups — #11771650

Order 1152.

131 conjugacy classes of subgroups; only the 27 normal subgroups are shown.

normal subgroups only

This group has 131 conjugacy classes of subgroups — too many to draw. Only its 27 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
1#10593787C211yesmaximal, characteristic
2#10593257C211yesmaximal, characteristic, complemented
3C8×AGL(1,𝔽9)C211yesmaximal, characteristic, complemented
4#64289—21no—
5C4×AGL(1,𝔽9)—21no—
6#64214—21no—
7#64128C411yescharacteristic
8#63785—21no—
9#63771C411yescharacteristic
10C8×#157C2211yescharacteristic
11C2×AGL(1,𝔽9)—22no—
12#3832—21no—
13C4×#157D411yescharacteristic
14#3788—21no—
15#3788—41no—
16#3787—41no—
17#3787D411yescharacteristic
18#3771—41no—
19C32×Q16C811yescharacteristic, complemented
20#3755—21no—
21#3745C811yescharacteristic, complemented
22C8×C3⋊D3C2×C411yescharacteristic
23#1335—91nomaximal, Sylow
24#919—121no—
25C2×#157—21no—
26AGL(1,𝔽9)—24no—
27C32×Q8—21no—
28C4⋊(C3⋊D3)—21no—
29C4⋊(C3⋊D3)—41no—
30C4×C3⋊D3—41no—
31C4×C3⋊D3C22⋊C411yescharacteristic
32#622—41no—
33#622D811yescharacteristic
34#622SD1611yescharacteristic
35C32×C8C2×C811yescharacteristic
36C3⋊(C3⋊C8)M1611yescharacteristic
37#443—91no—
38#364—91no—
39C82—91no—
40#239—122no—
41C3×Q16—41no—
42#215—122no—
43D24—121no—
44D3×C8—121no—
45C2×C3⋊D3—41no—
46C2×C3⋊D3#10411yescharacteristic
47#157—22no—
48C32×C4—41no—
49C32×C4C22⋊C811yescharacteristic
50C3⋊Dic3#10211yescharacteristic
51#135—91no—
52#131—181no—
53M32—181no—
54#108—91no—
55#104—181no—
56C4×C8—91no—
57C4×C8—181no—
58C3×Q8—42no—
59D12—122no—
60D12—242no—
61C4×D3—121no—
62C4×D3—242no—
63C3×C8—41no—
64C3⋊C8—121no—
65C2×C32D4⋊C811yescharacteristic
66C3⋊D3—21no—
67C3⋊D3—81no—
68#41—181no—
69Q16AGL(1,𝔽9)11yescharacteristic, complemented
70SD16—181no—
71D8—91no—
72M16—181no—
73M16—361no—
74C2×C8—91no—
75C2×C8—91no—
76C2×C8—182no—
77C2×C8—361no—
78C42—91no—
79C16—361no—
80C2×D3—121no—
81C2×D3—242no—
82C3×C4—41no—
83C3×C4—82no—
84Dic3—121no—
85C32#133511yescharacteristic, complemented, Sylow
86Q8—21no—
87D4—181no—
88D4—361no—
89C2×C4—91no—
90C2×C4—181no—
91C2×C4—361no—
92C8—91no—
93C8—91no—
94C8—91no—
95C8—184no—
96C8—361no—
97C8C2×AGL(1,𝔽9)11yescharacteristic
98C2×C3—41no—
99D3—241no—
100D3—482no—
101C22—91no—
102C22—361no—
103C4—41no—
104C4—91no—
105C4—182no—
106C4C22⋊AGL(1,𝔽9)11yescharacteristic
107C3—41no—
108C2—181no—
109C2—721no—
110C2D4⋊AGL(1,𝔽9)11yescharacteristic
subgroupG/H
centerC2D4⋊AGL(1,𝔽9)
commutatorC32×C8C2×C8
FrattiniC8C2×AGL(1,𝔽9)
FittingC32×Q16C8
socleC2×C32D4⋊C8
prime radical#64128C4
cosocleC8×#157C22
hypercenterQ16AGL(1,𝔽9)
hypocenterC32#1335
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C4 ◁ C8 ◁ Q16

Complements

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

NH ≅ G/Ntype
2. #10593257C2semidirect
3. C8×AGL(1,𝔽9)C2semidirect
19. C32×Q16C8semidirect
21. #3745C8semidirect
69. Q16AGL(1,𝔽9)semidirect
85. C32#1335semidirect

Maximal subgroups

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

subgroupindex
#105937872
#105932572
C8×AGL(1,𝔽9)2
#13359