Finite Group Databasebeta

← #11772900

Subgroups — #11772900

Order 1152.

180 conjugacy classes of subgroups; only the 20 normal subgroups are shown.

normal subgroups only

This group has 180 conjugacy classes of subgroups — too many to draw. Only its 20 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#10592767C211yesmaximal, characteristic
2#10590145C211yesmaximal, characteristic
3#10590143C211yesmaximal, characteristic
4C32×#125C411yescharacteristic, complemented
5#64084C2211yescharacteristic
6#63780—21no—
7#63774—21no—
8#63637—21no—
9#63636—21no—
10C4×C3⋊(C3⋊C8)C411yescharacteristic, complemented
11#5068—62no—
12C2×C4⋊(C3⋊D3)D411yescharacteristic
13C2×#634D411yescharacteristic
14C22⋊#157—41no—
15#3792—41no—
16C32×C4⋊C4—21no—
17C32×C4⋊C4—41no—
18C32×C42C2×C411yescharacteristic
19#3752—41no—
20C2×C3⋊(C3⋊C8)—21no—
21#1414—91nomaximal, Sylow
22C3×#125—22no—
23#875—62no—
24#810—64no—
25#809—64no—
26C4×C3⋊C8—62no—
27C22×C3⋊D3—21no—
28C2×#157—81no—
29C2×C32×C4—21no—
30C2×C32×C4—41no—
31C2×C32×C4C22⋊C411yescharacteristic
32C2×C3⋊Dic3—21no—
33C4⋊(C3⋊D3)—41no—
34#634—41no—
35#622—81no—
36C3⋊(C3⋊C8)—41no—
37#488—91no—
38#355—91no—
39#354—91no—
40C2×D12—62no—
41C2×Dic6—62no—
42C3×C4⋊C4—24no—
43C3×C4⋊C4—44no—
44C3×C42—22no—
45(C2×D3)⋊C4—124no—
46C2×C3⋊C8—64no—
47C22×C32#9911yescharacteristic
48C2×C3⋊D3—41no—
49C2×C3⋊D3—81no—
50#157—161no—
51C32×C4—21no—
52C32×C4—41no—
53C32×C4—81no—
54C3⋊Dic3—41no—
55#125#15711yescharacteristic, complemented
56#124—91no—
57#103—181no—
58#102—181no—
59#101—181no—
60#99—181no—
61C4×C8—91no—
62C22×D3—122no—
63C2×C3×C4—24no—
64C2×C3×C4—22no—
65C2×C3×C4—44no—
66C2×Dic3—122no—
67D12—124no—
68Dic6—124no—
69C3⋊C8—124no—
70C2×C32—21no—
71C2×C32#35411yescharacteristic
72C3⋊D3—81no—
73C2×Q8—91no—
74C2×D4—91no—
75M16—361no—
76C2×C8—181no—
77C4⋊C4—21no—
78C4⋊C4—41no—
79C22⋊C4—361no—
80C22⋊C4—361no—
81C42C2×#15711yescharacteristic
82C22×C3—22no—
83C2×D3—242no—
84C2×D3—244no—
85C3×C4—24no—
86C3×C4—44no—
87C3×C4—84no—
88Dic3—242no—
89C32#141411yescharacteristic, complemented, Sylow
90C23—181no—
91Q8—361no—
92D4—361no—
93C2×C4—21no—
94C2×C4—41no—
95C2×C4—181no—
96C2×C4—721no—
97C2×C4C22⋊#15711yescharacteristic
98C8—361no—
99C8—721no—
100C2×C3—24no—
101C2×C3—22no—
102D3—482no—
103C22—361no—
104C22—721no—
105C22#6378611yescharacteristic
106C4—21no—
107C4—41no—
108C4—81no—
109C4—361no—
110C4—1441no—
111C3—22no—
112C2—21no—
113C2—721no—
114C2#1059021711yescharacteristic
subgroupG/H
centerC2#10590217
commutatorC32×C42C2×C4
FrattiniC42C2×#157
FittingC32×#125C4
socleC2×C32#354
prime radicalC2×C4⋊(C3⋊D3)D4
cosocle#64084C22
hypercenter#125#157
hypocenterC32#1414
LCSG ▷ C32×C42 ▷ C2×C32×C4 ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C42 ◁ #125

Complements

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

NH ≅ G/Ntype
4. C32×#125C4semidirect
10. C4×C3⋊(C3⋊C8)C4semidirect
55. #125#157semidirect
89. C32#1414semidirect

Maximal subgroups

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

subgroupindex
#105927672
#105901452
#105901432
#14149