Finite Group Databasebeta

← #11771554

Subgroups — #11771554

Order 1152.

222 conjugacy classes of subgroups; only the 36 normal subgroups are shown.

normal subgroups only

This group has 222 conjugacy classes of subgroups — too many to draw. Only its 36 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#10592537C211yesmaximal, characteristic
2#10590148C211yesmaximal, characteristic, complemented
3C4⋊#3708C211yesmaximal, characteristic, complemented
4C2×#3743—21no—
5C4×C4⋊(C3⋊D3)C411yescharacteristic
6C2×#3708—21no—
7C2×#3708—21no—
8C32×C4⋊C8C411yescharacteristic
9#63647—21no—
10C4×C3⋊(C3⋊C8)C2211yescharacteristic
11#4838—62no—
12C2×C4⋊(C3⋊D3)C811yescharacteristic
13C2×C4×C3⋊D3—21no—
14C2×C32×C8—21no—
15C32×C42C2×C411yescharacteristic
16#3752—21no—
17C4⋊(C3⋊Dic3)C811yescharacteristic
18C2×C3⋊(C3⋊C8)D411yescharacteristic
19C2×C3⋊(C3⋊C8)D411yescharacteristic
20#3743—41no—
21#3743—41no—
22#3708—22no—
23#3708—41no—
24#1330—91nomaximal, Sylow
25C2×ΓL(1,𝔽25)—64no—
26C4×D12—62no—
27C3×C4⋊C8—22no—
28(C2×D3)⋊C8—64no—
29C4×C3⋊C8—62no—
30C22×C3⋊D3—21no—
31C2×C32×C4C22⋊C411yescharacteristic
32C2×C32×C4C2×C811yescharacteristic
33C2×C32×C4M1611yescharacteristic
34C2×C3⋊Dic3—21no—
35C4⋊(C3⋊D3)—41no—
36C4×C3⋊D3—41no—
37C4×C3⋊D3—41no—
38C32×C8—41no—
39C3⋊(C3⋊C8)—21no—
40C3⋊(C3⋊C8)D811yescharacteristic
41C3⋊(C3⋊C8)SD1611yescharacteristic
42#436—91no—
43C4⋊C16—91no—
44#346—91no—
45C2×D12—62no—
46C2×C4×D3—64no—
47C2×C3×C8—24no—
48C3×C42—22no—
49(C2×D3)⋊C4—64no—
50C4⋊Dic3—62no—
51C2×C3⋊C8—62no—
52C2×C3⋊C8—62no—
53ΓL(1,𝔽25)—124no—
54ΓL(1,𝔽25)—124no—
55C22×C32C22⋊C811yescharacteristic
56C2×C3⋊D3—41no—
57C2×C3⋊D3—41no—
58C2×C3⋊D3—41no—
59C32×C4—21no—
60C32×C4—21no—
61C32×C4#10211yescharacteristic
62C32×C4#10411yescharacteristic
63C3⋊Dic3—41no—
64C2×M16—181no—
65C4×D4—91no—
66C2×C16—181no—
67C2×C16—181no—
68C4⋊C8#15711yescharacteristic
69C22⋊C8—181no—
70C4×C8—91no—
71C22×D3—64no—
72C2×C3×C4—22no—
73C2×C3×C4—22no—
74C2×C3×C4—22no—
75C2×Dic3—64no—
76D12—124no—
77C4×D3—124no—
78C4×D3—124no—
79C3×C8—44no—
80C3⋊C8—62no—
81C3⋊C8—62no—
82C3⋊C8—122no—
83C2×C32D4⋊C811yescharacteristic
84C2×C32#34911yescharacteristic
85C2×C32#35011yescharacteristic
86C3⋊D3—81no—
87C2×D4—91no—
88C22×C4—181no—
89M16—361no—
90M16—361no—
91C2×C8—21no—
92C2×C8—91no—
93C2×C8—91no—
94C4⋊C4—91no—
95C22⋊C4—181no—
96C42C2×#15711yescharacteristic
97C16—182no—
98C16—361no—
99C22×C3—22no—
100C2×D3—124no—
101C2×D3—124no—
102C2×D3—124no—
103C3×C4—24no—
104C3×C4—22no—
105C3×C4—22no—
106C3×C4—42no—
107Dic3—124no—
108C32#133011yescharacteristic, complemented, Sylow
109C23—181no—
110D4—361no—
111C2×C4—181no—
112C2×C4—361no—
113C2×C4—361no—
114C2×C4#378711yescharacteristic
115C2×C4#378811yescharacteristic
116C2×C4C22⋊#15711yescharacteristic
117C8—41no—
118C8—91no—
119C8—91no—
120C8—181no—
121C2×C3—22no—
122C2×C3—22no—
123C2×C3—22no—
124D3—244no—
125C22—361no—
126C22—361no—
127C22—361no—
128C22#6377811yescharacteristic
129C4—21no—
130C4—21no—
131C4—361no—
132C4#6378211yescharacteristic
133C4#6378511yescharacteristic
134C3—22no—
135C2—721no—
136C2#1059016011yescharacteristic
137C2#1059018011yescharacteristic
138C2#1059018711yescharacteristic
subgroupG/H
centerC2×C4C22⋊#157
commutatorC2×C32×C4C2×C8
FrattiniC42C2×#157
FittingC32×C4⋊C8C4
socleC22×C32C22⋊C8
prime radicalC2×C4⋊(C3⋊D3)C8
cosocleC4×C3⋊(C3⋊C8)C22
hypercenterC4⋊C8#157
hypocenterC32#1330
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
2. #10590148C2semidirect
3. C4⋊#3708C2semidirect
108. C32#1330semidirect

Maximal subgroups

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

subgroupindex
#105925372
#105901482
C4⋊#37082
#13309