Finite Group Databasebeta

← #14526937

Subgroups — #14526937

Order 2176.

106 conjugacy classes of subgroups; only the 23 normal subgroups are shown.

normal subgroups only

This group has 106 conjugacy classes of subgroups — too many to draw. Only its 23 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#11762991C211yesmaximal, characteristic
2#11762558C211yesmaximal, characteristic, complemented
3C17×#356C211yesmaximal, characteristic, complemented
4#10587694C411yescharacteristic
5C17×C4⋊Q8C2211yescharacteristic
6#10587628—21no—
7C17×#101—21no—
8#10587507C411yescharacteristic
9#10587476—21no—
10C4⋊#3622—21no—
11C2×Q8×C17C2×C411yescharacteristic
12C2×Q8×C17D411yescharacteristic
13#63256—41no—
14Q8×D17—41no—
15#63252—21no—
16#63252—41no—
17M16×C17—41no—
18C4⋊C4×C17—41no—
19C42×C17D411yescharacteristic
20#63231—41no—
21#63230—41no—
22#63223—21no—
23C2×#3622—41no—
24Q8×C17—41no—
25Q8×C17—41no—
26C2×C4×C17—21no—
27C2×C4×C17—21no—
28C2×C4×C17—21no—
29C2×C4×C17C22⋊C411yescharacteristic
30C22⋊D17—41no—
31D68—21no—
32D68—41no—
33C4×D17—41no—
34C4×D17—42no—
35Dic34—21no—
36Dic34—41no—
37C8×C17—81no—
38#3622—41no—
39#3622—81no—
40#1405—171nomaximal, Sylow
41C22×C17#9911yescharacteristic
42C2×D17—41no—
43C4×C17—21no—
44C4×C17—21no—
45C4×C17—21no—
46C4×C17—41no—
47C4×C17—41no—
48Dic17—41no—
49#456—171no—
50#356D1711yescharacteristic, complemented
51#333—171no—
52C2×C17—21no—
53C2×C17AΣL(1,𝔽16)11yescharacteristic
54D17—81no—
552−1+4—171no—
56#137—341no—
57C4⋊Q8C2×D1711yescharacteristic
58C4⋊C8—341no—
59#104—341no—
60#101—21no—
61#101—171no—
62C17#140511yescharacteristic, complemented, Sylow
63#41—341no—
64#41—681no—
65#41—681no—
66C2×Q8—681no—
67C2×Q8C4×D1711yescharacteristic
68C2×Q8C22⋊D1711yescharacteristic
69Q16—681no—
70SD16—681no—
71M16—41no—
72M16—341no—
73C2×C8—681no—
74C4⋊C4—41no—
75C42D6811yescharacteristic
76Q8—41no—
77Q8—41no—
78Q8—341no—
79Q8—681no—
80D4—341no—
81D4—681no—
82D4—681no—
83C2×C4—21no—
84C2×C4—21no—
85C2×C4—21no—
86C2×C4—681no—
87C2×C4—682no—
88C2×C4#6322711yescharacteristic
89C8—81no—
90C8—681no—
91C8—1361no—
92C22—681no—
93C22#1058747711yescharacteristic
94C4—21no—
95C4—21no—
96C4—21no—
97C4—41no—
98C4—41no—
99C4—681no—
100C2—21no—
101C2—1361no—
102C2#1176259511yescharacteristic
subgroupG/H
centerC2#11762595
commutatorC2×Q8×C17C2×C4
FrattiniC4⋊Q8C2×D17
FittingC17×#356C2
socleC2×C17AΣL(1,𝔽16)
prime radical#10587694C4
cosocleC17×C4⋊Q8C22
hypercenter#356D17
hypocenterC17#1405
LCSG ▷ C2×Q8×C17 ▷ C2×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C4⋊Q8 ◁ #356

Complements

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

NH ≅ G/Ntype
2. #11762558C2semidirect
3. C17×#356C2semidirect
50. #356D17semidirect
62. C17#1405semidirect

Maximal subgroups

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

subgroupindex
#117629912
#117625582
C17×#3562
#140517