Finite Group Databasebeta

← #14543909

Subgroups — #14543909

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#11762992C211yesmaximal, characteristic
4C17×2−1+4C411yescharacteristic
5#10587637—21no—
6#10587630C2211yescharacteristic
7#10587545—21no—
8#10587544—21no—
9#10587508—21no—
10#10587507C411yescharacteristic
11#41×C17—21no—
12#41×C17—41no—
13#41×C17—41no—
14C2×Q8×C17—41no—
15C2×Q8×C17C2×C411yescharacteristic
16C2×Dic34D411yescharacteristic
17#63247—41no—
18C2×#3624—41no—
19#63231—41no—
20#63229—41no—
21#63225—41no—
22C4×Dic17D411yescharacteristic
23#63223—21no—
24Q8×C17—21no—
25Q8×C17—41no—
26Q8×C17—41no—
27D4×C17—21no—
28D4×C17—41no—
29D4×C17—41no—
30C2×C4×C17—21no—
31C2×C4×C17—41no—
32C2×C4×C17—42no—
33C2×C4×C17C22⋊C411yescharacteristic
34C2×Dic17—21no—
35C2×Dic17—21no—
36Dic34—41no—
37#3624—81no—
38#3624—81no—
39#3622—41no—
40#1405—171nomaximal, Sylow
41C22×C17—41no—
42C22×C17#9911yescharacteristic
43C4×C17—21no—
44C4×C17—41no—
45C4×C17—41no—
46Dic17—21no—
47Dic17—21no—
48Dic17—41no—
49#456—171no—
50#356—171no—
51#333—171no—
52C2×C17—21no—
53C2×C17—81no—
54C2×C17AΣL(1,𝔽16)11yescharacteristic
552−1+4#59511yescharacteristic
56#137—341no—
57C4⋊Q8—171no—
58C4⋊C8—341no—
59#104—341no—
60#101—171no—
61#101—341no—
62C17#140511yescharacteristic, complemented, Sylow
63#41—21no—
64#41—41no—
65#41—41no—
66C2×Q8—41no—
67C2×Q8—171no—
68C2×Q8C2×#59511yescharacteristic
69Q16—681no—
70SD16—681no—
71M16—341no—
72M16—681no—
73C2×C8—681no—
74C4⋊C4—681no—
75C42—171no—
76Q8—21no—
77Q8—41no—
78Q8—41no—
79Q8—681no—
80D4—21no—
81D4—41no—
82D4—41no—
83C2×C4—21no—
84C2×C4—41no—
85C2×C4—42no—
86C2×C4—341no—
87C2×C4—341no—
88C2×C4C22⋊#59511yescharacteristic
89C8—681no—
90C8—1361no—
91C8—1361no—
92C22—41no—
93C22#1058755111yescharacteristic
94C4—21no—
95C4—41no—
96C4—41no—
97C4—341no—
98C4—341no—
99C4—681no—
100C2—21no—
101C2—81no—
102C2#1176370911yescharacteristic
subgroupG/H
centerC2#11763709
commutatorC2×Q8×C17C2×C4
FrattiniC2×Q8C2×#595
Fitting, prime radicalC17×2−1+4C4
socleC2×C17AΣL(1,𝔽16)
cosocle#10587630C22
hypercenter2−1+4#595
hypocenterC17#1405
LCSG ▷ C2×Q8×C17 ▷ C2×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C2×Q8 ◁ 2−1+4

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
#117629922
#140517