Finite Group Databasebeta

← #41011572

Subgroups — #41011572

Order 27008.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#27213500C211yesmaximal, characteristic
2#27212943C211yesmaximal, characteristic
3#354×C211C211yesmaximal, characteristic
4#20269969C411yescharacteristic, complemented
5#20269901—21no—
6#20269898—21no—
7#20269896—21no—
8C4×C211⋊C8C411yescharacteristic, complemented
9#124×C211C2211yescharacteristic
10#99×C211—21no—
11#16809946—41no—
12C2×C211⋊C8—21no—
13C4⋊Dic211—21no—
14Dic211⋊C4—41no—
15C2×Q8×C211D411yescharacteristic
16C2×D4×C211D411yescharacteristic
17C22⋊C4×C211—41no—
18C22⋊C4×C211—41no—
19C42×C211C2×C411yescharacteristic
20C2×Dic211—41no—
21C211⋊C8—41no—
22C211⋊C8—81no—
23C23×C211—21no—
24Q8×C211—41no—
25D4×C211—41no—
26C2×C4×C211—21no—
27C2×C4×C211—21no—
28C2×C4×C211—81no—
29C2×C4×C211C22⋊C411yescharacteristic
30C22×C211—41no—
31C22×C211—81no—
32C22×C211#9911yescharacteristic
33C4×C211—21no—
34C4×C211—41no—
35C4×C211—41no—
36C4×C211—161no—
37Dic211—81no—
38C2×C211—21no—
39C2×C211—81no—
40C2×C211#35411yescharacteristic
41C211#141411yescharacteristic, complemented, Sylow
42#1414—2111nomaximal, Sylow
43#488—2111no—
44#355—2111no—
45#354D21111yescharacteristic
46#125—2111no—
47#124C2×D21111yescharacteristic
48#103—4221no—
49#102—4221no—
50#101—4221no—
51#99—21no—
52C4×C8—2111no—
53C2×Q8D84411yescharacteristic
54C2×D4C22⋊D21111yescharacteristic
55M16—8441no—
56C2×C8—4221no—
57C4⋊C4—8441no—
58C4⋊C4—4221no—
59C22⋊C4—41no—
60C22⋊C4—41no—
61C42C4×D21111yescharacteristic
62C23—21no—
63Q8—41no—
64D4—41no—
65C2×C4—21no—
66C2×C4—21no—
67C2×C4—81no—
68C2×C4—8441no—
69C2×C4(C2×D211)⋊C411yescharacteristic
70C8—8441no—
71C8—16881no—
72C22—41no—
73C22—81no—
74C22#2026989111yescharacteristic
75C4—21no—
76C4—41no—
77C4—41no—
78C4—161no—
79C4—16881no—
80C2—21no—
81C2—81no—
82C2#2721294011yescharacteristic
subgroupG/H
centerC2#27212940
commutatorC42×C211C2×C4
Frattini#124C2×D211
Fitting#354×C211C2
socleC2×C211#354
prime radicalC2×D4×C211D4
cosocle#124×C211C22
hypercenter#354D211
hypocenterC211#1414
LCSG ▷ C42×C211 ▷ C2×C4×C211 ▷ C22×C211 ▷ C2×C211 ▷ C211
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ #124 ◁ #354

Complements

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

NH ≅ G/Ntype
4. #20269969C4semidirect
8. C4×C211⋊C8C4semidirect
41. C211#1414semidirect

Maximal subgroups

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

subgroupindex
#272135002
#272129432
#354×C2112
#1414211