Finite Group Databasebeta

← #11771354

Subgroups — #11771354

Order 1152.

274 conjugacy classes of subgroups; only the 34 normal subgroups are shown.

normal subgroups only

This group has 274 conjugacy classes of subgroups — too many to draw. Only its 34 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#10592828C211yesmaximal, characteristic
2C22⋊#3708C212yesmaximal, complemented
3C2×#3828C411yescharacteristic
4C2×C32×M16C411yescharacteristic
5C22×C3⋊(C3⋊C8)C2211yescharacteristic
6C2×#3708—22no—
7#63647—22no—
8#5129—62no—
9C22×C32×C4C2×C411yescharacteristic
10C2×#638—21no—
11#3828—41no—
12#3828—41no—
13C2×C4⋊(C3⋊D3)C811yescharacteristic
14C2×C4×C3⋊D3—21no—
15C2×#634C811yescharacteristic
16C32×M16—41no—
17C2×C32×C8—21no—
18C2×C3⋊(C3⋊C8)—41no—
19C2×C3⋊(C3⋊C8)D412yes—
20#3708—42no—
21#1315—91nomaximal, Sylow
22C2×#235—62no—
23C2×C3×M16—22no—
24C22×C3⋊C8—62no—
25(C2×D3)⋊C8—68no—
26C23×C32M1611yescharacteristic
27C22×C3⋊D3—21no—
28C2×C32×C4—21no—
29C2×C32×C4—21no—
30C2×C32×C4C22⋊C411yescharacteristic
31C2×C32×C4C2×C811yescharacteristic
32#638—42no—
33C2×C3⋊Dic3—21no—
34C4⋊(C3⋊D3)—41no—
35C4×C3⋊D3—41no—
36C4×C3⋊D3—41no—
37#634—41no—
38C32×C8—41no—
39C3⋊(C3⋊C8)—22no—
40#408—91no—
41C22⋊C16—92no—
42C22×C3×C4—22no—
43C2×#67—64no—
44#235—124no—
45#235—124no—
46C2×D12—62no—
47C2×C4×D3—64no—
48C2×Dic6—62no—
49C3×M16—44no—
50C2×C3×C8—24no—
51C2×C3⋊C8—64no—
52C2×C3⋊C8—124no—
53C22×C32—21no—
54C22×C32—22no—
55C22×C32C22⋊C811yescharacteristic
56C2×C3⋊D3—41no—
57C2×C3⋊D3—42no—
58C32×C4—21no—
59C32×C4#9911yescharacteristic
60C32×C4#10011yescharacteristic
61C3⋊Dic3—41no—
62C2×#41—91no—
63C2×M16#15711yescharacteristic
64C22×C8—91no—
65C2×C16—182no—
66C22⋊C8—182no—
67C23×C3—22no—
68C22×D3—64no—
69C2×C3×C4—24no—
70C2×C3×C4—24no—
71C2×C3×C4—22no—
72C2×C3×C4—22no—
73#67—128no—
74C2×Dic3—64no—
75D12—124no—
76C4×D3—124no—
77C4×D3—124no—
78Dic6—124no—
79C3×C8—44no—
80C3⋊C8—124no—
81C2×C32—41no—
82C2×C32#32311yescharacteristic
83C2×C32#35012yes—
84C3⋊D3—81no—
85#41—361no—
86#41—361no—
87C2×Q8—91no—
88C2×D4—91no—
89C2×D4—181no—
90C22×C4—181no—
91C22×C4C2×#15711yescharacteristic
92M16—41no—
93C2×C8—21no—
94C2×C8—92no—
95C2×C8—361no—
96C16—362no—
97C22×C3—24no—
98C22×C3—22no—
99C22×C3—44no—
100C2×D3—124no—
101C2×D3—128no—
102C3×C4—24no—
103C3×C4—22no—
104C3×C4—22no—
105Dic3—124no—
106C32#131511yescharacteristic, complemented, Sylow
107C23—181no—
108C23#378811yescharacteristic
109Q8—361no—
110D4—361no—
111D4—362no—
112C2×C4—21no—
113C2×C4—21no—
114C2×C4—181no—
115C2×C4—361no—
116C2×C4—361no—
117C2×C4#378711yescharacteristic
118C2×C4C22⋊#15711yescharacteristic
119C8—41no—
120C8—182no—
121C2×C3—24no—
122C2×C3—22no—
123C2×C3—44no—
124D3—244no—
125C22—22no—
126C22—21no—
127C22—362no—
128C22—361no—
129C22#6377811yescharacteristic
130C4—21no—
131C4—361no—
132C4#6377411yescharacteristic
133C4#6378811yescharacteristic
134C3—22no—
135C2—41no—
136C2—721no—
137C2#1059018712yes—
138C2#1059020411yescharacteristic
subgroupG/H
centerC2×C4C22⋊#157
commutatorC2×C32×C4C2×C8
FrattiniC22×C4C2×#157
FittingC2×C32×M16C4
socleC22×C32C22⋊C8
prime radicalC2×#3828C4
cosocleC22×C3⋊(C3⋊C8)C22
hypercenterC2×M16#157
hypocenterC32#1315
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
2. C22⋊#3708C2semidirect
106. C32#1315semidirect

Maximal subgroups

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

subgroupindex
#105928282
C22⋊#37082
#13159