Finite Group Databasebeta

← #11772284

Subgroups — #11772284

Order 1152.

194 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 194 conjugacy classes of subgroups — too many to draw. Only its 51 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#10596481C212yesmaximal
2#10593723C211yesmaximal, characteristic
3C2×#3787C411yescharacteristic
4C2×#3787C2211yescharacteristic
5#64218—22no—
6#64214—22no—
7#64213C414yescomplemented
8C42×C3⋊D3C411yescharacteristic
9#63777—22no—
10C2×C4×C3⋊D3—21no—
11C2×C4×C3⋊D3C2×C411yescharacteristic
12C2×#622—21no—
13C2×#622D412yes—
14#3787—21no—
15#3787C812yes—
16#3787C2×C412yes—
17#3787D411yescharacteristic
18#3787Q811yescharacteristic
19#3771—24no—
20C32×C42C811yescharacteristic
21C4×C3⋊Dic3—21no—
22C4×C3⋊Dic3C811yescharacteristic
23#1375—91nomaximal, Sylow
24C42×D3—121no—
25C22×C3⋊D3M1611yescharacteristic
26C2×C32×C4—21no—
27C2×C32×C4C2×C811yescharacteristic
28C2×C3⋊Dic3—21no—
29C2×C3⋊Dic3C22⋊C411yescharacteristic
30C4×C3⋊D3—42no—
31C4×C3⋊D3C4211yescharacteristic
32C4×C3⋊D3C4⋊C411yescharacteristic
33C4×C3⋊D3C2×C811yescharacteristic
34C4×C3⋊D3M1611yescharacteristic
35#622—22no—
36#622C22⋊C412yes—
37#622C4⋊C412yes—
38C2×M32—92no—
39C2×#97—91no—
40C2×C4×D3—121no—
41C2×C4×D3—122no—
42C3×C42—41no—
43C4×Dic3—121no—
44C4×Dic3—122no—
45C22×C32C22⋊C811yescharacteristic
46C2×C3⋊D3—22no—
47C2×C3⋊D3#9711yescharacteristic
48C2×C3⋊D3C4⋊C811yescharacteristic
49C32×C4—41no—
50C32×C4C4×C811yescharacteristic
51C32×C4C4⋊C811yescharacteristic
52C3⋊Dic3—41no—
53C3⋊Dic3#9511yescharacteristic
54C3⋊Dic3C22⋊C811yescharacteristic
55C22×C8—91no—
56C22×C8—91no—
57C2×C42—91no—
58M32—182no—
59M32—182no—
60C2×C16—94no—
61#97—182no—
62C22×D3—121no—
63C2×C3×C4—42no—
64C2×C3×C4—41no—
65C2×Dic3—121no—
66C2×Dic3—122no—
67C4×D3—121no—
68C4×D3—121no—
69C4×D3—121no—
70C4×D3—121no—
71C4×D3—128no—
72C2×C32—21no—
73C2×C32#33611yescharacteristic
74C3⋊D3—21no—
75C3⋊D3#34712yes—
76C22×C4—91no—
77C22×C4—181no—
78C2×C8—92no—
79C2×C8—92no—
80C2×C8—91no—
81C2×C8—91no—
82C2×C8—92no—
83C2×C8—181no—
84C2×C8—181no—
85C42—91no—
86C42—181no—
87C42AGL(1,𝔽9)11yescharacteristic
88C16—184no—
89C22×C3—41no—
90C2×D3—121no—
91C2×D3—121no—
92C2×D3—124no—
93C3×C4—44no—
94C3×C4—41no—
95C3×C4—41no—
96Dic3—121no—
97Dic3—121no—
98Dic3—124no—
99C32#137511yescharacteristic, complemented, Sylow
100C23—91no—
101C2×C4—21no—
102C2×C4—91no—
103C2×C4—91no—
104C2×C4—91no—
105C2×C4—91no—
106C2×C4—91no—
107C2×C4—181no—
108C2×C4—362no—
109C2×C4C2×AGL(1,𝔽9)11yescharacteristic
110C8—92no—
111C8—92no—
112C8—182no—
113C2×C3—42no—
114C2×C3—41no—
115D3—122no—
116D3—122no—
117C22—91no—
118C22—91no—
119C22—182no—
120C22C22⋊AGL(1,𝔽9)11yescharacteristic
121C4—41no—
122C4—91no—
123C4—91no—
124C4—361no—
125C4C4×AGL(1,𝔽9)11yescharacteristic
126C4C4⋊AGL(1,𝔽9)11yescharacteristic
127C3—41no—
128C2—21no—
129C2—92no—
130C2—181no—
131C2#1059326711yescharacteristic
subgroupG/H
centerC4C4×AGL(1,𝔽9)
commutatorC32×C4C4×C8
FrattiniC2×C4C2×AGL(1,𝔽9)
FittingC32×C42C8
socleC2×C32#336
prime radicalC22×C3⋊D3M16
cosocleC2×#3787C22
hypercenterC42AGL(1,𝔽9)
hypocenterC32#1375
LCSG ▷ C32×C4 ▷ C32
UCSC1 ◁ C4 ◁ C42

Complements

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

NH ≅ G/Ntype
7. #64213C4semidirect
99. C32#1375semidirect

Maximal subgroups

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

subgroupindex
#105964812
#105937232
#13759