Finite Group Databasebeta

← #11771701

Subgroups — #11771701

Order 1152.

180 conjugacy classes of subgroups; only the 38 normal subgroups are shown.

normal subgroups only

This group has 180 conjugacy classes of subgroups — too many to draw. Only its 38 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#10592723C211yesmaximal, characteristic
2#10590148C211yesmaximal, characteristic
3C4⋊#3708C211yesmaximal, characteristic
4C32×C4×Q8C411yescharacteristic
5C2×#3708—21no—
6C2×#3708—21no—
7C4⋊(C3⋊(C3⋊C8))—21no—
8C4⋊(C3⋊(C3⋊C8))C411yescharacteristic
9#63630—21no—
10C4×C3⋊(C3⋊C8)C2211yescharacteristic
11#5024—62no—
12C2×C32×Q8C811yescharacteristic
13C32×C4⋊C4—21no—
14C32×C4⋊C4C811yescharacteristic
15C32×C42—21no—
16C32×C42C2×C411yescharacteristic
17C2×C3⋊(C3⋊C8)—21no—
18C2×C3⋊(C3⋊C8)D411yescharacteristic
19C2×C3⋊(C3⋊C8)D411yescharacteristic
20#3708—22no—
21#3708—41no—
22#1338—91nomaximal, Sylow
23C3×C4×Q8—22no—
24C4⋊(C3⋊C8)—62no—
25C4⋊(C3⋊C8)—64no—
26#803—64no—
27C4×C3⋊C8—62no—
28C32×Q8—41no—
29C2×C32×C4—21no—
30C2×C32×C4—21no—
31C2×C32×C4C22⋊C411yescharacteristic
32C2×C32×C4C2×C811yescharacteristic
33C2×C32×C4M1611yescharacteristic
34C3⋊(C3⋊C8)—21no—
35C3⋊(C3⋊C8)—41no—
36C3⋊(C3⋊C8)SD1611yescharacteristic
37C3⋊(C3⋊C8)Q1611yescharacteristic
38#446—91no—
39C4⋊C16—91no—
40#346—91no—
41C2×C3×Q8—22no—
42C3×C4⋊C4—24no—
43C3×C4⋊C4—22no—
44C3×C42—24no—
45C3×C42—22no—
46C2×C3⋊C8—62no—
47C2×C3⋊C8—62no—
48C2×C3⋊C8—64no—
49C22×C32C22⋊C811yescharacteristic
50C32×C4—21no—
51C32×C4—21no—
52C32×C4—41no—
53C32×C4—41no—
54C32×C4#10311yescharacteristic
55C32×C4#10411yescharacteristic
56C4×Q8#15711yescharacteristic
57C2×C16—181no—
58C2×C16—181no—
59C4⋊C8—91no—
60C4⋊C8—181no—
61#97—181no—
62C4×C8—91no—
63C3×Q8—44no—
64C2×C3×C4—24no—
65C2×C3×C4—24no—
66C2×C3×C4—22no—
67C2×C3×C4—22no—
68C2×C3×C4—22no—
69C3⋊C8—62no—
70C3⋊C8—62no—
71C3⋊C8—122no—
72C3⋊C8—124no—
73C2×C32Q8⋊C811yescharacteristic
74C2×C32#34911yescharacteristic
75C2×C32#35011yescharacteristic
76C2×Q8#62211yescharacteristic
77C2×C8—91no—
78C2×C8—91no—
79C2×C8—181no—
80C4⋊C4—21no—
81C4⋊C4#62211yescharacteristic
82C42—21no—
83C42C2×#15711yescharacteristic
84C16—182no—
85C16—361no—
86C22×C3—22no—
87C3×C4—24no—
88C3×C4—22no—
89C3×C4—22no—
90C3×C4—42no—
91C3×C4—44no—
92C3×C4—44no—
93C32#133811yescharacteristic, complemented, Sylow
94Q8—41no—
95C2×C4—21no—
96C2×C4—21no—
97C2×C4C2×#62211yescharacteristic
98C2×C4#379211yescharacteristic
99C2×C4C22⋊#15711yescharacteristic
100C8—91no—
101C8—91no—
102C8—181no—
103C8—361no—
104C2×C3—22no—
105C2×C3—22no—
106C2×C3—22no—
107C22C22⋊#62211yescharacteristic
108C4—21no—
109C4—21no—
110C4—41no—
111C4—41no—
112C4#6378411yescharacteristic
113C4#6378511yescharacteristic
114C3—22no—
115C2#1059020111yescharacteristic
116C2Q8⋊#62211yescharacteristic
117C2#1059022111yescharacteristic
subgroupG/H
centerC2×C4C22⋊#157
commutatorC2×C32×C4C2×C8
FrattiniC42C2×#157
FittingC32×C4×Q8C4
socle, prime radicalC22×C32C22⋊C8
cosocleC4×C3⋊(C3⋊C8)C22
hypercenterC4×Q8#157
hypocenterC32#1338
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
93. C32#1338semidirect

Maximal subgroups

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

subgroupindex
#105927232
#105901482
C4⋊#37082
#13389