Finite Group Databasebeta

← #14543906

Subgroups — #14543906

Order 2176.

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

normal subgroups only

This group has 112 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#11763717C211yesmaximal, characteristic, complemented
2#11763664C211yesmaximal, characteristic, complemented
3#11762989C211yesmaximal, characteristic
4#10587691C411yescharacteristic
5#10587622C2211yescharacteristic
6#10587595—21no—
7#10587545—21no—
8#10587542—21no—
9C17×#100C411yescharacteristic
10#10587496—21no—
11C2×D4×C17C2×C411yescharacteristic
12C2×C22⋊D17—41no—
13#63254—41no—
14D4×D17—41no—
15#63252—21no—
16C2×Dic34D411yescharacteristic
17#63247—41no—
18C2×#3624—41no—
19M16×C17—21no—
20C22⋊Dic17—41no—
21C4×Dic17D411yescharacteristic
22Dic68—41no—
23#63219—41no—
24C23×C17—21no—
25C22×D17—41no—
26D4×C17—41no—
27C2×C4×C17C22⋊C411yescharacteristic
28C22⋊D17—42no—
29C22⋊D17—41no—
30C2×Dic17—21no—
31C2×Dic17—21no—
32C2×Dic17—41no—
33D68—21no—
34C4×D17—41no—
35Dic34—21no—
36Dic34—41no—
37#3624—42no—
38#3624—81no—
39C8×C17—41no—
40#1403—171nomaximal, Sylow
41C22×C17—41no—
42C22×C17—81no—
43C22×C17#9911yescharacteristic
44C2×D17—41no—
45C2×D17—161no—
46C4×C17—21no—
47Dic17—41no—
48Dic17—41no—
49Dic17—41no—
50#455—171no—
51#355—171no—
52#329—171no—
53C2×C17—21no—
54C2×C17—81no—
55C2×C17AΣL(1,𝔽16)11yescharacteristic
56D17—81no—
57H(5,𝔽2)—171no—
58#137—341no—
59#124—171no—
60#104—341no—
61#101—341no—
62#100#59511yescharacteristic
63#97—341no—
64C17#140311yescharacteristic, complemented, Sylow
65#41—341no—
66#41—681no—
67C2×Q8—171no—
68C2×D4—681no—
69C2×D4—681no—
70C2×D4C2×#59511yescharacteristic
71Q16—681no—
72SD16—681no—
73M16—21no—
74M16—681no—
75C2×C8—681no—
76C22⋊C4—681no—
77C42—171no—
78C23—21no—
79C23—681no—
80Q8—341no—
81Q8—681no—
82D4—41no—
83D4—341no—
84D4—682no—
85D4—681no—
86C2×C4—341no—
87C2×C4—341no—
88C2×C4—681no—
89C2×C4—681no—
90C2×C4C22⋊#59511yescharacteristic
91C8—41no—
92C8—682no—
93C8—1361no—
94C22—41no—
95C22—81no—
96C22—2721no—
97C22—681no—
98C22#1058753911yescharacteristic
99C4—21no—
100C4—681no—
101C4—681no—
102C4—681no—
103C2—21no—
104C2—81no—
105C2—1361no—
106C2#1176371011yescharacteristic
subgroupG/H
centerC2#11763710
commutatorC2×D4×C17C2×C4
FrattiniC2×D4C2×#595
FittingC17×#100C4
socleC2×C17AΣL(1,𝔽16)
prime radical#10587691C4
cosocle#10587622C22
hypercenter#100#595
hypocenterC17#1403
LCSG ▷ C2×D4×C17 ▷ C2×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C2×D4 ◁ #100

Complements

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

NH ≅ G/Ntype
1. #11763717C2semidirect
2. #11763664C2semidirect
64. C17#1403semidirect

Maximal subgroups

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

subgroupindex
#117637172
#117636642
#117629892
#140317