Finite Group Databasebeta

← #1407×C211 #41009027

Subgroups — #1407×C211 #41009027

Order 27008.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#497×C211C211yesmaximal, characteristic
2#355×C211C211yesmaximal, characteristic
3#354×C211C211yesmaximal, characteristic
4C2×Q16×C211—21no—
5C2×SD16×C211—21no—
6C4⋊Q8×C211C411yescharacteristic, complemented
7#124×C211C2211yescharacteristic
8#101×C211—21no—
9#99×C211—21no—
10#97×C211C411yescharacteristic, complemented
11C2×Q8×C211—21no—
12C2×Q8×C211D411yescharacteristic
13C2×D4×C211D411yescharacteristic
14Q16×C211—42no—
15SD16×C211—42no—
16M16×C211—41no—
17C2×C8×C211—21no—
18C4⋊C4×C211—41no—
19C22⋊C4×C211—41no—
20C22⋊C4×C211—41no—
21C42×C211C2×C411yescharacteristic
22C23×C211—21no—
23Q8×C211—41no—
24Q8×C211—41no—
25Q8×C211—41no—
26D4×C211—41no—
27C2×C4×C211—21no—
28C2×C4×C211—21no—
29C2×C4×C211—41no—
30C2×C4×C211—81no—
31C2×C4×C211C22⋊C411yescharacteristic
32C8×C211—22no—
33C8×C211—81no—
34C22×C211—41no—
35C22×C211—81no—
36C22×C211#9911yescharacteristic
37C4×C211—21no—
38C4×C211—41no—
39C4×C211—41no—
40C4×C211—81no—
41C4×C211—161no—
42C2×C211—21no—
43C2×C211—81no—
44C2×C211#35311yescharacteristic
45C211#140711yescharacteristic, direct product factor, Sylow
46#1407C21111yesmaximal, characteristic, direct product factor, Sylow
47#497C2×C21111yescharacteristic
48#355C2×C21111yescharacteristic
49#354C2×C21111yescharacteristic
50C2×Q16—21no—
51C2×SD16—21no—
52C4⋊Q8C4×C21111yescharacteristic, complemented
53#124C22×C21111yescharacteristic
54#101—21no—
55#99—21no—
56#97C4×C21111yescharacteristic, complemented
57C2×Q8—21no—
58C2×Q8D4×C21111yescharacteristic
59C2×D4D4×C21111yescharacteristic
60Q16—42no—
61SD16—42no—
62M16—41no—
63C2×C8—21no—
64C4⋊C4—41no—
65C22⋊C4—41no—
66C22⋊C4—41no—
67C42C2×C4×C21111yescharacteristic
68C23—21no—
69Q8—41no—
70Q8—41no—
71Q8—41no—
72D4—41no—
73C2×C4—21no—
74C2×C4—21no—
75C2×C4—41no—
76C2×C4—81no—
77C2×C4C22⋊C4×C21111yescharacteristic
78C8—22no—
79C8—81no—
80C22—41no—
81C22—81no—
82C22#99×C21111yescharacteristic
83C4—21no—
84C4—41no—
85C4—41no—
86C4—81no—
87C4—161no—
88C2—21no—
89C2—81no—
90C2#353×C21111yescharacteristic
subgroupG/H
center, socleC2×C211#353
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
6. C4⋊Q8×C211C4semidirect
10. #97×C211C4semidirect
45. C211#1407direct (N × H)
46. #1407C211direct (N × H)
52. C4⋊Q8C4×C211semidirect
56. #97C4×C211semidirect

Maximal subgroups

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

subgroupindex
#497×C2112
#355×C2112
#354×C2112
#1407211