Finite Group Databasebeta

← #14543910

Subgroups — #14543910

Order 2176.

106 conjugacy classes of subgroups; only the 20 normal subgroups are shown.

normal subgroups only

This group has 106 conjugacy classes of subgroups — too many to draw. Only its 20 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11763719C211yesmaximal, characteristic, complemented
2#11763669C211yesmaximal, characteristic, complemented
3#11762994C211yesmaximal, characteristic
4#10587694C411yescharacteristic
5#10587630C2211yescharacteristic
6#10587595—21no—
7#10587545—21no—
8#10587544—21no—
9C17×#101C411yescharacteristic
10#10587496—21no—
11C2×Q8×C17C2×C411yescharacteristic
12#63256—41no—
13Q8×D17—41no—
14#63252—21no—
15#63252—41no—
16C2×Dic34D411yescharacteristic
17#63247—41no—
18C2×#3624—41no—
19M16×C17—21no—
20#63225—41no—
21C4×Dic17D411yescharacteristic
22Dic68—41no—
23#63219—41no—
24Q8×C17—41no—
25C2×C4×C17—21no—
26C2×C4×C17C22⋊C411yescharacteristic
27C22⋊D17—41no—
28C2×Dic17—21no—
29C2×Dic17—21no—
30D68—21no—
31D68—41no—
32C4×D17—41no—
33C4×D17—42no—
34Dic34—21no—
35Dic34—41no—
36Dic34—41no—
37#3624—81no—
38#3624—81no—
39C8×C17—41no—
40#1405—171nomaximal, Sylow
41C22×C17#9911yescharacteristic
42C2×D17—41no—
43C4×C17—21no—
44C4×C17—41no—
45Dic17—21no—
46Dic17—21no—
47Dic17—41no—
48Dic17—41no—
49#456—171no—
50#356—171no—
51#333—171no—
52C2×C17—21no—
53C2×C17AΣL(1,𝔽16)11yescharacteristic
54D17—81no—
552−1+4—171no—
56#137—341no—
57C4⋊Q8—171no—
58C4⋊C8—341no—
59#104—341no—
60#101—341no—
61#101#59511yescharacteristic
62C17#140511yescharacteristic, complemented, Sylow
63#41—341no—
64#41—681no—
65#41—681no—
66C2×Q8—171no—
67C2×Q8—681no—
68C2×Q8C2×#59511yescharacteristic
69Q16—681no—
70SD16—681no—
71M16—21no—
72M16—681no—
73C2×C8—681no—
74C4⋊C4—681no—
75C42—171no—
76Q8—41no—
77Q8—341no—
78Q8—681no—
79Q8—681no—
80D4—341no—
81D4—681no—
82D4—681no—
83C2×C4—21no—
84C2×C4—341no—
85C2×C4—341no—
86C2×C4—681no—
87C2×C4—682no—
88C2×C4C22⋊#59511yescharacteristic
89C8—41no—
90C8—1361no—
91C8—1361no—
92C22—681no—
93C22#1058753911yescharacteristic
94C4—21no—
95C4—41no—
96C4—341no—
97C4—341no—
98C4—681no—
99C4—681no—
100C2—21no—
101C2—1361no—
102C2#1176371011yescharacteristic
subgroupG/H
centerC2#11763710
commutatorC2×Q8×C17C2×C4
FrattiniC2×Q8C2×#595
FittingC17×#101C4
socleC2×C17AΣL(1,𝔽16)
prime radical#10587694C4
cosocle#10587630C22
hypercenter#101#595
hypocenterC17#1405
LCSG ▷ C2×Q8×C17 ▷ C2×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C2×Q8 ◁ #101

Complements

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

NH ≅ G/Ntype
1. #11763719C2semidirect
2. #11763669C2semidirect
62. C17#1405semidirect

Maximal subgroups

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

subgroupindex
#117637192
#117636692
#117629942
#140517