Finite Group Databasebeta

← #41011568

Subgroups — #41011568

Order 27008.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#27213510C211yesmaximal, characteristic
2#27212939C211yesmaximal, characteristic
3#353×C211C211yesmaximal, characteristic
4#20269969C411yescharacteristic, complemented
5#20269898—21no—
6#20269898—21no—
7#20269892—21no—
8#20269888C411yescharacteristic, complemented
9#127×C211C2211yescharacteristic
10#99×C211—21no—
11C2×C211⋊C8—21no—
12C4⋊Dic211—21no—
13Dic211⋊C4—41no—
14C22⋊Dic211—41no—
15C2×D4×C211—41no—
16C2×D4×C211D411yescharacteristic
17C2×D4×C211D411yescharacteristic
18C22⋊C4×C211—41no—
19C42×C211C2×C411yescharacteristic
20C2×Dic211—41no—
21C2×Dic211—81no—
22C211⋊C8—41no—
23C23×C211—21no—
24C23×C211—21no—
25D4×C211—41no—
26D4×C211—41no—
27D4×C211—82no—
28C2×C4×C211—21no—
29C2×C4×C211—81no—
30C2×C4×C211C22⋊C411yescharacteristic
31C22×C211—41no—
32C22×C211—41no—
33C22×C211—81no—
34C22×C211—81no—
35C22×C211#9911yescharacteristic
36C4×C211—21no—
37C4×C211—41no—
38C4×C211—161no—
39Dic211—81no—
40Dic211—161no—
41C2×C211—21no—
42C2×C211—81no—
43C2×C211—81no—
44C2×C211#35411yescharacteristic
45C211#141211yescharacteristic, complemented, Sylow
46#1412—2111nomaximal, Sylow
47#490—2111no—
48#353—2111no—
49#353D21111yescharacteristic
50#127C2×D21111yescharacteristic
51#125—2111no—
52#102—4221no—
53#102—4221no—
54#99—21no—
55#99—4221no—
56#97—2111no—
57C2×D4—41no—
58C2×D4C22⋊D21111yescharacteristic
59C2×D4D84411yescharacteristic
60C2×C8—4221no—
61C4⋊C4—8441no—
62C4⋊C4—4221no—
63C22⋊C4—41no—
64C22⋊C4—8441no—
65C42C4×D21111yescharacteristic
66C23—21no—
67C23—21no—
68D4—41no—
69D4—41no—
70D4—82no—
71C2×C4—21no—
72C2×C4—81no—
73C2×C4—8441no—
74C2×C4—16881no—
75C2×C4(C2×D211)⋊C411yescharacteristic
76C8—8441no—
77C22—41no—
78C22—41no—
79C22—81no—
80C22—81no—
81C22#2026989111yescharacteristic
82C4—21no—
83C4—41no—
84C4—161no—
85C4—33761no—
86C4—16881no—
87C2—21no—
88C2—81no—
89C2—81no—
90C2#2721294011yescharacteristic
subgroupG/H
centerC2#27212940
commutatorC42×C211C2×C4
Frattini#127C2×D211
Fitting#353×C211C2
socleC2×C211#354
prime radical, cosocle#127×C211C22
hypercenter#353D211
hypocenterC211#1412
LCSG ▷ C42×C211 ▷ C2×C4×C211 ▷ C22×C211 ▷ C2×C211 ▷ C211
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ #127 ◁ #353

Complements

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

NH ≅ G/Ntype
4. #20269969C4semidirect
8. #20269888C4semidirect
45. C211#1412semidirect

Maximal subgroups

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

subgroupindex
#272135102
#272129392
#353×C2112
#1412211