Finite Group Databasebeta

← D4⋊#3708 #11771534

Subgroups — D4⋊#3708 #11771534

Order 1152.

244 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 244 conjugacy classes of subgroups — too many to draw. Only its 46 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
1D4×C3⋊(C3⋊C8)C211yesmaximal, characteristic
2C4⋊#3708C211yesmaximal, characteristic, complemented
3C4×#3708C211yesmaximal, characteristic, complemented
4C32×C4×D4C411yescharacteristic
5C22×C3⋊(C3⋊C8)—21no—
6C2×#3708—21no—
7C2×#3708—21no—
8#63657—21no—
9C4⋊(C3⋊(C3⋊C8))C411yescharacteristic
10C4×C3⋊(C3⋊C8)C2211yescharacteristic
11D4×C3⋊C8—62no—
12C2×C32×D4C811yescharacteristic
13C22×C32×C4—21no—
14C32×C4⋊C4C811yescharacteristic
15C32×C22⋊C4—21no—
16C32×C42C2×C411yescharacteristic
17C2×C3⋊(C3⋊C8)—21no—
18C2×C3⋊(C3⋊C8)—41no—
19C2×C3⋊(C3⋊C8)—41no—
20C2×C3⋊(C3⋊C8)D411yescharacteristic
21C2×C3⋊(C3⋊C8)D411yescharacteristic
22#3708—22no—
23#3708—41no—
24D4⋊C16—91nomaximal, Sylow
25C3×C4×D4—22no—
26C22×C3⋊C8—64no—
27#830—64no—
28C4⋊(C3⋊C8)—62no—
29C4×C3⋊C8—62no—
30C23×C32—21no—
31C32×D4—21no—
32C32×D4C1612yescomplemented
33C2×C32×C4—21no—
34C2×C32×C4—41no—
35C2×C32×C4—41no—
36C2×C32×C4C22⋊C411yescharacteristic
37C2×C32×C4C2×C811yescharacteristic
38C2×C32×C4M1611yescharacteristic
39C3⋊(C3⋊C8)—21no—
40C3⋊(C3⋊C8)—41no—
41C3⋊(C3⋊C8)D811yescharacteristic
42C3⋊(C3⋊C8)SD1611yescharacteristic
43C8×D4—91no—
44C4⋊C16—91no—
45C4×C16—91no—
46C2×C3×D4—22no—
47C22×C3×C4—24no—
48C3×C4⋊C4—22no—
49C3×C22⋊C4—24no—
50C3×C42—22no—
51C2×C3⋊C8—62no—
52C2×C3⋊C8—62no—
53C2×C3⋊C8—64no—
54C2×C3⋊C8—124no—
55C2×C3⋊C8—124no—
56C22×C32—22no—
57C22×C32—41no—
58C22×C32—41no—
59C22×C32C22⋊C811yescharacteristic
60C32×C4—21no—
61C32×C4—41no—
62C32×C4#10211yescharacteristic
63C32×C4#10411yescharacteristic
64C32×C4C2×C1611yescharacteristic
65C32×C4M3211yescharacteristic
66C22×C8—181no—
67C4×D4#15711yescharacteristic
68C2×C16—181no—
69C2×C16—181no—
70C4⋊C8—91no—
71C22⋊C8—181no—
72C4×C8—91no—
73C23×C3—24no—
74C3×D4—24no—
75C3×D4—24no—
76C2×C3×C4—24no—
77C2×C3×C4—22no—
78C2×C3×C4—22no—
79C2×C3×C4—22no—
80C2×C3×C4—44no—
81C2×C3×C4—44no—
82C3⋊C8—62no—
83C3⋊C8—62no—
84C3⋊C8—122no—
85C3⋊C8—124no—
86C2×C32—42no—
87C2×C32D4⋊C811yescharacteristic
88C2×C32C22⋊C1611yescharacteristic
89C2×C32#35011yescharacteristic
90C2×D4#62211yescharacteristic
91C22×C4—21no—
92C2×C8—91no—
93C2×C8—91no—
94C2×C8—181no—
95C2×C8—361no—
96C2×C8—361no—
97C4⋊C4#62211yescharacteristic
98C22⋊C4—21no—
99C42C2×#15711yescharacteristic
100C16—182no—
101C16—361no—
102C22×C3—28no—
103C22×C3—22no—
104C22×C3—44no—
105C22×C3—44no—
106C3×C4—22no—
107C3×C4—22no—
108C3×C4—22no—
109C3×C4—22no—
110C3×C4—42no—
111C3×C4—44no—
112C32D4⋊C1611yescharacteristic, complemented, Sylow
113C23—21no—
114D4—21no—
115D4#370812yescomplemented
116C2×C4—21no—
117C2×C4—41no—
118C2×C4—41no—
119C2×C4C2×#62211yescharacteristic
120C2×C4#379211yescharacteristic
121C2×C4C22⋊#15711yescharacteristic
122C8—91no—
123C8—91no—
124C8—181no—
125C8—361no—
126C2×C3—22no—
127C2×C3—22no—
128C2×C3—22no—
129C2×C3—48no—
130C22—22no—
131C22—41no—
132C22—41no—
133C22C22⋊#62211yescharacteristic
134C4—21no—
135C4—41no—
136C4C2×#370811yescharacteristic
137C4#6377311yescharacteristic
138C4#6378211yescharacteristic
139C4#6378311yescharacteristic
140C3—22no—
141C2—42no—
142C2C22⋊#370811yescharacteristic
143C2D4⋊#62211yescharacteristic
144C2#1059022111yescharacteristic
subgroupG/H
centerC2×C4C22⋊#157
commutatorC32×C4C2×C16
FrattiniC42C2×#157
FittingC32×C4×D4C4
socleC22×C32C22⋊C8
prime radicalC2×C32×D4C8
cosocleC4×C3⋊(C3⋊C8)C22
hypercenterC4×D4#157
hypocenterC32D4⋊C16
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
2. C4⋊#3708C2semidirect
3. C4×#3708C2semidirect
32. C32×D4C16semidirect
112. C32D4⋊C16semidirect
115. D4#3708semidirect

Maximal subgroups

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

subgroupindex
D4×C3⋊(C3⋊C8)2
C4⋊#37082
C4×#37082
D4⋊C169