Finite Group Databasebeta

← #41011555

Subgroups — #41011555

Order 27008.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#27212943C211yesmaximal, characteristic, complemented
2#27212941C211yesmaximal, characteristic, complemented
3#496×C211C211yesmaximal, characteristic
4#20269896—21no—
5#20269892—21no—
6C2×SD16×C211—21no—
7C2×D8×C211—21no—
8#127×C211C411yescharacteristic, complemented
9#124×C211C2211yescharacteristic
10#97×C211C411yescharacteristic, complemented
11#16809946—41no—
12C22⋊Dic211—41no—
13C2×Q8×C211D411yescharacteristic
14C2×D4×C211—21no—
15C2×D4×C211—41no—
16C2×D4×C211D411yescharacteristic
17SD16×C211—42no—
18D8×C211—42no—
19C2×C8×C211—21no—
20C22⋊C4×C211—41no—
21C42×C211C2×C411yescharacteristic
22C2×Dic211—81no—
23C211⋊C8—81no—
24C23×C211—21no—
25C23×C211—41no—
26Q8×C211—41no—
27D4×C211—41no—
28D4×C211—41no—
29D4×C211—41no—
30D4×C211—82no—
31C2×C4×C211—21no—
32C2×C4×C211—21no—
33C2×C4×C211C22⋊C411yescharacteristic
34C8×C211—22no—
35C22×C211—41no—
36C22×C211—81no—
37C22×C211—82no—
38C22×C211—81no—
39C22×C211#9911yescharacteristic
40C4×C211—21no—
41C4×C211—41no—
42C4×C211—41no—
43Dic211—161no—
44C2×C211—21no—
45C2×C211—81no—
46C2×C211—161no—
47C2×C211#35311yescharacteristic
48C211#140611yescharacteristic, complemented, Sylow
49#1406—2111nomaximal, Sylow
50#496D21111yescharacteristic
51#355—2111no—
52#354—2111no—
53C2×SD16—21no—
54C2×D8—21no—
55#127Dic21111yescharacteristic, complemented
56#124C2×D21111yescharacteristic
57#101—4221no—
58#99—4221no—
59#97Dic21111yescharacteristic, complemented
60C2×Q8C22⋊D21111yescharacteristic
61C2×D4—21no—
62C2×D4—41no—
63C2×D4C22⋊D21111yescharacteristic
64SD16—42no—
65D8—42no—
66M16—8441no—
67C2×C8—21no—
68C22⋊C4—41no—
69C22⋊C4—8441no—
70C42C2×Dic21111yescharacteristic
71C23—21no—
72C23—41no—
73Q8—41no—
74D4—41no—
75D4—41no—
76D4—41no—
77D4—82no—
78C2×C4—21no—
79C2×C4—21no—
80C2×C4—16881no—
81C2×C4C22⋊Dic21111yescharacteristic
82C8—22no—
83C8—16881no—
84C22—41no—
85C22—81no—
86C22—82no—
87C22—81no—
88C22#2026989211yescharacteristic
89C4—21no—
90C4—41no—
91C4—41no—
92C4—33761no—
93C2—21no—
94C2—81no—
95C2—161no—
96C2#2721293911yescharacteristic
subgroupG/H
centerC2#27212939
commutatorC42×C211C2×C4
Frattini#124C2×D211
Fitting, prime radical#496×C211C2
socleC2×C211#353
cosocle#124×C211C22
hypercenter#496D211
hypocenterC211#1406
LCSG ▷ C42×C211 ▷ C2×C4×C211 ▷ C22×C211 ▷ C2×C211 ▷ C211
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ #124 ◁ #496

Complements

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

NH ≅ G/Ntype
1. #27212943C2semidirect
2. #27212941C2semidirect
8. #127×C211C4semidirect
10. #97×C211C4semidirect
48. C211#1406semidirect
55. #127Dic211semidirect
59. #97Dic211semidirect

Maximal subgroups

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

subgroupindex
#272129432
#272129412
#496×C2112
#1406211