Finite Group Databasebeta

← #1414×C211 #41009034

Subgroups — #1414×C211 #41009034

Order 27008.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#488×C211C211yesmaximal, characteristic
2#355×C211C211yesmaximal, characteristic
3#354×C211C211yesmaximal, characteristic
4#125×C211C411yescharacteristic, complemented
5#124×C211C2211yescharacteristic
6#103×C211—21no—
7#102×C211—21no—
8#101×C211—21no—
9#99×C211—21no—
10C4×C8×C211C411yescharacteristic, complemented
11C2×Q8×C211D411yescharacteristic
12C2×D4×C211D411yescharacteristic
13M16×C211—41no—
14C2×C8×C211—21no—
15C4⋊C4×C211—21no—
16C4⋊C4×C211—41no—
17C22⋊C4×C211—41no—
18C22⋊C4×C211—41no—
19C42×C211C2×C411yescharacteristic
20C23×C211—21no—
21Q8×C211—41no—
22D4×C211—41no—
23C2×C4×C211—21no—
24C2×C4×C211—21no—
25C2×C4×C211—41no—
26C2×C4×C211—81no—
27C2×C4×C211C22⋊C411yescharacteristic
28C8×C211—41no—
29C8×C211—81no—
30C22×C211—41no—
31C22×C211—81no—
32C22×C211#9911yescharacteristic
33C4×C211—21no—
34C4×C211—41no—
35C4×C211—41no—
36C4×C211—81no—
37C4×C211—161no—
38C2×C211—21no—
39C2×C211—81no—
40C2×C211#35411yescharacteristic
41C211#141411yescharacteristic, direct product factor, Sylow
42#1414C21111yesmaximal, characteristic, direct product factor, Sylow
43#488C2×C21111yescharacteristic
44#355C2×C21111yescharacteristic
45#354C2×C21111yescharacteristic
46#125C4×C21111yescharacteristic, complemented
47#124C22×C21111yescharacteristic
48#103—21no—
49#102—21no—
50#101—21no—
51#99—21no—
52C4×C8C4×C21111yescharacteristic, complemented
53C2×Q8D4×C21111yescharacteristic
54C2×D4D4×C21111yescharacteristic
55M16—41no—
56C2×C8—21no—
57C4⋊C4—21no—
58C4⋊C4—41no—
59C22⋊C4—41no—
60C22⋊C4—41no—
61C42C2×C4×C21111yescharacteristic
62C23—21no—
63Q8—41no—
64D4—41no—
65C2×C4—21no—
66C2×C4—21no—
67C2×C4—41no—
68C2×C4—81no—
69C2×C4C22⋊C4×C21111yescharacteristic
70C8—41no—
71C8—81no—
72C22—41no—
73C22—81no—
74C22#99×C21111yescharacteristic
75C4—21no—
76C4—41no—
77C4—41no—
78C4—81no—
79C4—161no—
80C2—21no—
81C2—81no—
82C2#354×C21111yescharacteristic
subgroupG/H
center, socleC2×C211#354
commutatorC42C2×C4×C211
Frattini, cosocle#124C22×C211
prime radicalC2×D4×C211D4
LCSG ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C211 ◁ C22×C211 ◁ C2×C4×C211 ◁ #124×C211 ◁ G

Complements

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

NH ≅ G/Ntype
4. #125×C211C4semidirect
10. C4×C8×C211C4semidirect
41. C211#1414direct (N × H)
42. #1414C211direct (N × H)
46. #125C4×C211semidirect
52. C4×C8C4×C211semidirect

Maximal subgroups

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

subgroupindex
#488×C2112
#355×C2112
#354×C2112
#1414211