Finite Group Databasebeta

← #17949603

Subgroups — #17949603

Order 4352.

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

normal subgroups only

This group has 128 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#14543922C211yesmaximal, characteristic
2#14543922C211yesmaximal, characteristic
3#14528417C211yesmaximal, characteristic
4#11763720—21no—
5#11763720—21no—
6#11763207—21no—
7#11763207C411yescharacteristic
8#11763189C2211yescharacteristic
9#11763160—21no—
10C17×#322C411yescharacteristic
11C2×Dic68—41no—
12#10587555—21no—
13#10587555D411yescharacteristic
14#10587555D411yescharacteristic
15#10587545—41no—
16#10587545—41no—
17C4×C8×C17—21no—
18C4×C8×C17C2×C411yescharacteristic
19#10587488—41no—
20#10587488—42no—
21#10587487—42no—
22C2×Dic34—21no—
23C2×Dic34—21no—
24C2×Dic34—41no—
25#63247—81no—
26#63247—81no—
27C2×C8×C17—21no—
28C2×C8×C17—22no—
29C42×C17C22⋊C411yescharacteristic
30C4⋊Dic17—41no—
31C4⋊Dic17—41no—
32C4⋊Dic17—41no—
33C4⋊Dic17—41no—
34Dic68—82no—
35#7534—171nomaximal, Sylow
36C2×C4×C17—21no—
37C2×C4×C17#9911yescharacteristic
38C2×Dic17—41no—
39C2×Dic17—41no—
40C2×Dic17—81no—
41Dic34—81no—
42Dic34—81no—
43Dic34—82no—
44#3624—161no—
45#3624—161no—
46C8×C17—22no—
47C8×C17—42no—
48#1716—171no—
49#1411—171no—
50#1411—171no—
51C22×C17#35311yescharacteristic
52C4×C17—22no—
53C4×C17—21no—
54Dic17—81no—
55Dic17—81no—
56Dic17—161no—
57#498—171no—
58#498—341no—
59#494—171no—
60#487—341no—
61#356—341no—
62#356—341no—
63#322#59511yescharacteristic
64C2×C17—21no—
65C2×C17#140911yescharacteristic
66C2×Q16—681no—
67C4⋊Q8—171no—
68C4⋊Q8—171no—
69C4⋊Q8—341no—
70#106—682no—
71#106—681no—
72#103—682no—
73#101—681no—
74#101—681no—
75C4×C8—21no—
76C4×C8C2×#59511yescharacteristic
77C17#753411yescharacteristic, complemented, Sylow
78C2×Q8—341no—
79C2×Q8—341no—
80C2×Q8—681no—
81Q16—1362no—
82M16—1361no—
83M16—1361no—
84C2×C8—21no—
85C2×C8—22no—
86C4⋊C4—681no—
87C4⋊C4—681no—
88C4⋊C4—681no—
89C4⋊C4—681no—
90C42C22⋊#59511yescharacteristic
91Q8—1362no—
92Q8—1361no—
93Q8—1361no—
94C2×C4—21no—
95C2×C4—681no—
96C2×C4—681no—
97C2×C4—1361no—
98C2×C4#1058753911yescharacteristic
99C8—22no—
100C8—42no—
101C8—2721no—
102C8—2721no—
103C22#1176371411yescharacteristic
104C4—22no—
105C4—21no—
106C4—2721no—
107C4—1361no—
108C4—1361no—
109C2—21no—
110C2#1454391811yescharacteristic
subgroupG/H
centerC2#14543918
commutatorC4×C8×C17C2×C4
FrattiniC4×C8C2×#595
FittingC17×#322C4
socleC2×C17#1409
prime radicalC22×C17#353
cosocle#11763189C22
hypercenter#322#595
hypocenterC17#7534
LCSG ▷ C4×C8×C17 ▷ C42×C17 ▷ C2×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C42 ◁ C4×C8 ◁ #322

Complements

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

NH ≅ G/Ntype
77. C17#7534semidirect

Maximal subgroups

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

subgroupindex
#145439222
#145284172
#753417