Finite Group Databasebeta

← #17949576

Subgroups — #17949576

Order 4352.

134 conjugacy classes of subgroups; only the 22 normal subgroups are shown.

normal subgroups only

This group has 134 conjugacy classes of subgroups — too many to draw. Only its 22 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#14543923C211yesmaximal, characteristic
2#14543788C211yesmaximal, characteristic
3#14528086C211yesmaximal, characteristic
4#11763714—21no—
5#11763701—21no—
6#11763175—21no—
7#11763175C2211yescharacteristic
8#11762551—21no—
9#11762551C411yescharacteristic, complemented
10C17×#564C411yescharacteristic, complemented
11C17×#125—21no—
12C17×#125—41no—
13C17×#125—41no—
14C17×#125—41no—
15C17×#125C2×C411yescharacteristic
16#10587560D411yescharacteristic
17#10587539—41no—
18#10587538—41no—
19#10587480—41no—
20#10587480—41no—
21#10587480—41no—
22#10587474—21no—
23#10587474D411yescharacteristic
24C2×D68—21no—
25C2×D68—41no—
26C22⋊#595—81no—
27C4⋊C4×C17—21no—
28C4⋊C4×C17—21no—
29C4⋊C4×C17—21no—
30C4⋊C4×C17—41no—
31C4⋊C4×C17—41no—
32C4⋊C4×C17—41no—
33C4⋊C4×C17—41no—
34C4⋊C4×C17—41no—
35C4⋊C4×C17—41no—
36C42×C17—41no—
37C42×C17C22⋊C411yescharacteristic
38C2×#3622—21no—
39C2×#3622—41no—
40#63216—42no—
41#7524—171nomaximal, Sylow
42C22×D17—41no—
43C2×#595—161no—
44C2×C4×C17—21no—
45C2×C4×C17—41no—
46C2×C4×C17—41no—
47C2×C4×C17—41no—
48C2×C4×C17#9911yescharacteristic
49D68—81no—
50D68—82no—
51#3622—41no—
52#3622—81no—
53#1658—171no—
54#1412—171no—
55#1355—171no—
56C22×C17AΣL(1,𝔽16)11yescharacteristic
57C2×D17—81no—
58C2×D17—161no—
59#595—321no—
60C4×C17—21no—
61C4×C17—41no—
62C4×C17—81no—
63C4×C17—81no—
64C4×C17—81no—
65#564#59511yescharacteristic, complemented
66#490—171no—
67#490—341no—
68#353—341no—
69#347—341no—
70#330—171no—
71#330—341no—
72C2×C17—21no—
73C2×C17#140411yescharacteristic
74D17—161no—
75#127—171no—
76#125—21no—
77#125—41no—
78#125—41no—
79#125—41no—
80#125C2×#59511yescharacteristic
81M32—681no—
82#102—681no—
83#102—681no—
84#102—681no—
85#99—681no—
86#97—171no—
87#97—341no—
88C17#752411yescharacteristic, complemented, Sylow
89C2×D4—341no—
90C2×D4—681no—
91C2×C8—341no—
92C2×C8—681no—
93C4⋊C4—21no—
94C4⋊C4—21no—
95C4⋊C4—21no—
96C4⋊C4—41no—
97C4⋊C4—41no—
98C4⋊C4—41no—
99C4⋊C4—41no—
100C4⋊C4—41no—
101C4⋊C4—41no—
102C22⋊C4—1361no—
103C42—41no—
104C42C22⋊#59511yescharacteristic
105C16—682no—
106C23—681no—
107D4—1361no—
108D4—1362no—
109C2×C4—21no—
110C2×C4—41no—
111C2×C4—41no—
112C2×C4—41no—
113C2×C4—2721no—
114C2×C4#1058755111yescharacteristic
115C8—681no—
116C8—1361no—
117C22—2721no—
118C22—1361no—
119C22#1176370911yescharacteristic
120C4—21no—
121C4—41no—
122C4—81no—
123C4—81no—
124C4—81no—
125C4—5441no—
126C2—21no—
127C2—2721no—
128C2#1454390711yescharacteristic
subgroupG/H
centerC2#14543907
commutatorC17×#125C2×C4
Frattini#125C2×#595
FittingC17×#564C4
socleC2×C17#1404
prime radical#10587560D4
cosocle#11763175C22
hypercenter#564#595
hypocenterC17#7524
LCSG ▷ C17×#125 ▷ C42×C17 ▷ C2×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C42 ◁ #125 ◁ #564

Complements

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

NH ≅ G/Ntype
9. #11762551C4semidirect
10. C17×#564C4semidirect
65. #564#595semidirect
88. C17#7524semidirect

Maximal subgroups

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

subgroupindex
#145439232
#145437882
#145280862
#752417