Finite Group Databasebeta

← #16922166

Subgroups — #16922166

Order 4352.

134 conjugacy classes of subgroups; only the 25 normal subgroups are shown.

normal subgroups only

This group has 134 conjugacy classes of subgroups — too many to draw. Only its 25 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#14528085C211yesmaximal, characteristic
2#14526817C211yesmaximal, characteristic
3C17×#1412C211yesmaximal, characteristic
4C17⋊#564C411yescharacteristic, complemented
5#11763173—21no—
6#11762587—21no—
7#11762551C411yescharacteristic, complemented
8#11762550—21no—
9C17×#490C2211yescharacteristic
10C17×#353—21no—
11C17×#127D411yescharacteristic
12C17×#125C2×C411yescharacteristic
13#10587576—41no—
14#10587575—41no—
15#10587575—41no—
16#10587556—21no—
17C17×#102—41no—
18C17×#99—41no—
19C17×#97D411yescharacteristic
20#10587503—41no—
21#10587503—41no—
22#10587483—41no—
23#10587474—21no—
24C2×D4×C17—21no—
25C2×D4×C17—41no—
26C2×C8×C17—21no—
27C4⋊C4×C17—21no—
28C4⋊C4×C17—41no—
29C22⋊C4×C17—81no—
30C42×C17C22⋊C411yescharacteristic
31C4⋊Dic17—21no—
32C4⋊Dic17—21no—
33C4⋊Dic17—41no—
34#63225—41no—
35#63225—41no—
36#63225—41no—
37#63225—41no—
38C4×Dic17—41no—
39C2×#3622—41no—
40#63214—42no—
41#7524—171nomaximal, Sylow
42C23×C17—41no—
43D4×C17—81no—
44D4×C17—82no—
45C2×C4×C17—21no—
46C2×C4×C17—41no—
47C2×C4×C17—161no—
48C2×C4×C17#9911yescharacteristic
49C2×Dic17—41no—
50C2×Dic17—41no—
51C8×C17—41no—
52#3622—81no—
53#1658—171no—
54#1412D1711yescharacteristic
55#1355—171no—
56C22×C17—81no—
57C22×C17—161no—
58C22×C17AΣL(1,𝔽16)11yescharacteristic
59C4×C17—21no—
60C4×C17—41no—
61C4×C17—81no—
62C4×C17—321no—
63Dic17—81no—
64Dic17—81no—
65#564—171no—
66#490—341no—
67#490C2×D1711yescharacteristic
68#353—21no—
69#347—341no—
70#330—171no—
71#330—341no—
72C2×C17—21no—
73C2×C17—161no—
74C2×C17#140411yescharacteristic
75#127C22⋊D1711yescharacteristic
76#125—341no—
77#125—681no—
78#125—681no—
79#125—681no—
80#125C4×D1711yescharacteristic
81M32—681no—
82#102—41no—
83#102—681no—
84#102—681no—
85#99—41no—
86#97—341no—
87#97D6811yescharacteristic
88C17#752411yescharacteristic, complemented, Sylow
89C2×D4—21no—
90C2×D4—41no—
91C2×C8—21no—
92C2×C8—681no—
93C4⋊C4—21no—
94C4⋊C4—41no—
95C4⋊C4—341no—
96C4⋊C4—341no—
97C4⋊C4—681no—
98C4⋊C4—681no—
99C4⋊C4—681no—
100C4⋊C4—681no—
101C4⋊C4—681no—
102C22⋊C4—81no—
103C42—681no—
104C42#6322711yescharacteristic
105C16—682no—
106C23—41no—
107D4—81no—
108D4—82no—
109C2×C4—21no—
110C2×C4—41no—
111C2×C4—161no—
112C2×C4—681no—
113C2×C4—681no—
114C2×C4#1058747711yescharacteristic
115C8—41no—
116C8—1361no—
117C22—81no—
118C22—161no—
119C22#1176259511yescharacteristic
120C4—21no—
121C4—41no—
122C4—81no—
123C4—321no—
124C4—1361no—
125C4—1361no—
126C2—21no—
127C2—161no—
128C2#1452693411yescharacteristic
subgroupG/H
centerC2#14526934
commutatorC17×#125C2×C4
Frattini#490C2×D17
FittingC17×#1412C2
socleC2×C17#1404
prime radicalC17×#127D4
cosocleC17×#490C22
hypercenter#1412D17
hypocenterC17#7524
LCSG ▷ C17×#125 ▷ C42×C17 ▷ C2×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C42 ◁ #490 ◁ #1412

Complements

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

NH ≅ G/Ntype
4. C17⋊#564C4semidirect
7. #11762551C4semidirect
88. C17#7524semidirect

Maximal subgroups

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

subgroupindex
#145280852
#145268172
C17×#14122
#752417