Finite Group Databasebeta

← #41011573

Subgroups — #41011573

Order 27008.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#27212943C211yesmaximal, characteristic
2#27212941C211yesmaximal, characteristic
3#488×C211C211yesmaximal, characteristic
4#20269896—21no—
5#20269892—21no—
6#125×C211C411yescharacteristic, complemented
7#124×C211C2211yescharacteristic
8#103×C211—21no—
9#102×C211—21no—
10C4×C8×C211C411yescharacteristic, complemented
11#16809946—41no—
12C22⋊Dic211—41no—
13C2×Q8×C211D411yescharacteristic
14C2×D4×C211D411yescharacteristic
15C2×C8×C211—21no—
16C4⋊C4×C211—21no—
17C4⋊C4×C211—41no—
18C22⋊C4×C211—41no—
19C42×C211C2×C411yescharacteristic
20C2×Dic211—81no—
21C211⋊C8—81no—
22C23×C211—21no—
23Q8×C211—41no—
24D4×C211—41no—
25C2×C4×C211—21no—
26C2×C4×C211—21no—
27C2×C4×C211—41no—
28C2×C4×C211C22⋊C411yescharacteristic
29C8×C211—41no—
30C22×C211—41no—
31C22×C211—81no—
32C22×C211#9911yescharacteristic
33C4×C211—21no—
34C4×C211—41no—
35C4×C211—41no—
36C4×C211—81no—
37Dic211—161no—
38C2×C211—21no—
39C2×C211—81no—
40C2×C211#35411yescharacteristic
41C211#141411yescharacteristic, complemented, Sylow
42#1414—2111nomaximal, Sylow
43#488D21111yescharacteristic
44#355—2111no—
45#354—2111no—
46#125Dic21111yescharacteristic, complemented
47#124C2×D21111yescharacteristic
48#103—21no—
49#102—21no—
50#101—4221no—
51#99—4221no—
52C4×C8Dic21111yescharacteristic, complemented
53C2×Q8C22⋊D21111yescharacteristic
54C2×D4C22⋊D21111yescharacteristic
55M16—8441no—
56C2×C8—21no—
57C4⋊C4—21no—
58C4⋊C4—41no—
59C22⋊C4—41no—
60C22⋊C4—8441no—
61C42C2×Dic21111yescharacteristic
62C23—21no—
63Q8—41no—
64D4—41no—
65C2×C4—21no—
66C2×C4—21no—
67C2×C4—41no—
68C2×C4—16881no—
69C2×C4C22⋊Dic21111yescharacteristic
70C8—41no—
71C8—16881no—
72C22—41no—
73C22—81no—
74C22#2026989211yescharacteristic
75C4—21no—
76C4—41no—
77C4—41no—
78C4—81no—
79C4—33761no—
80C2—21no—
81C2—81no—
82C2#2721294111yescharacteristic
subgroupG/H
centerC2#27212941
commutatorC42×C211C2×C4
Frattini#124C2×D211
Fitting#488×C211C2
socleC2×C211#354
prime radicalC2×D4×C211D4
cosocle#124×C211C22
hypercenter#488D211
hypocenterC211#1414
LCSG ▷ C42×C211 ▷ C2×C4×C211 ▷ C22×C211 ▷ C2×C211 ▷ C211
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ #124 ◁ #488

Complements

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

NH ≅ G/Ntype
6. #125×C211C4semidirect
10. C4×C8×C211C4semidirect
41. C211#1414semidirect
46. #125Dic211semidirect
52. C4×C8Dic211semidirect

Maximal subgroups

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

subgroupindex
#272129432
#272129412
#488×C2112
#1414211