Finite Group Databasebeta

← #28299370

Subgroups — #28299370

Order 13568.

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#20289853C211yesmaximal, characteristic
2#20289853C211yesmaximal, characteristic
3#20274349C211yesmaximal, characteristic
4#16811534—21no—
5#16811534—21no—
6#16811019—21no—
7#16811003C2211yescharacteristic
8#16810973—21no—
9#16810344C411yescharacteristic
10C53×#498C411yescharacteristic
11#13133278—41no—
12#13133278—41no—
13C2×Dic212—41no—
14#13133217D411yescharacteristic
15#13133217D411yescharacteristic
16#13133148—42no—
17#13133141—42no—
18C4×#88322—21no—
19C4⋊Q8×C53—21no—
20#106×C53—41no—
21C4×C8×C53C2×C411yescharacteristic
22C2×Q8×C53—41no—
23C2×Dic106—21no—
24C2×Dic106—21no—
25#11719940—81no—
26#11719940—81no—
27C2×C8×C53—21no—
28C4⋊C4×C53—41no—
29C4⋊C4×C53—41no—
30C42×C53C22⋊C411yescharacteristic
31C4⋊Dic53—41no—
32C4⋊Dic53—41no—
33C2×#88322—22no—
34Dic212—82no—
35Q8×C53—82no—
36C2×C4×C53—21no—
37C2×C4×C53—81no—
38C2×C4×C53#9911yescharacteristic
39C2×Dic53—41no—
40C2×Dic53—41no—
41Dic106—81no—
42Dic106—81no—
43#88324—161no—
44#88324—161no—
45C8×C53—22no—
46#88322—42no—
47#7534—531nomaximal, Sylow
48C22×C53#35311yescharacteristic
49C4×C53—22no—
50C4×C53—21no—
51C4×C53—161no—
52Dic53—81no—
53Dic53—81no—
54#1716—531no—
55#1411—531no—
56#1411—531no—
57C2×C53—21no—
58C2×C53#140911yescharacteristic
59#498—1061no—
60#498#615711yescharacteristic
61#494—531no—
62#487—1061no—
63#356—1061no—
64#356—1061no—
65#322—531no—
66C53#753411yescharacteristic, complemented, Sylow
67C2×Q16—2121no—
68C4⋊Q8—21no—
69C4⋊Q8—531no—
70C4⋊Q8—531no—
71#106—41no—
72#106—2122no—
73#103—2122no—
74#101—2121no—
75#101—2121no—
76C4×C8—1061no—
77C4×C8C2×#615711yescharacteristic
78C2×Q8—41no—
79C2×Q8—1061no—
80C2×Q8—1061no—
81Q16—4242no—
82M16—4241no—
83M16—4241no—
84C2×C8—21no—
85C2×C8—1062no—
86C4⋊C4—41no—
87C4⋊C4—41no—
88C4⋊C4—2121no—
89C4⋊C4—2121no—
90C42C22⋊#615711yescharacteristic
91Q8—82no—
92Q8—4241no—
93Q8—4241no—
94C2×C4—21no—
95C2×C4—81no—
96C2×C4—2121no—
97C2×C4—2121no—
98C2×C4#1313327511yescharacteristic
99C8—22no—
100C8—8481no—
101C8—8481no—
102C8—2122no—
103C22#1681152711yescharacteristic
104C4—22no—
105C4—21no—
106C4—161no—
107C4—4241no—
108C4—4241no—
109C2—21no—
110C2#2028984811yescharacteristic
subgroupG/H
centerC2#20289848
commutatorC4×C8×C53C2×C4
FrattiniC4×C8C2×#6157
FittingC53×#498C4
socleC2×C53#1409
prime radicalC22×C53#353
cosocle#16811003C22
hypercenter#498#6157
hypocenterC53#7534
LCSG ▷ C4×C8×C53 ▷ C42×C53 ▷ C2×C4×C53 ▷ C22×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C42 ◁ C4×C8 ◁ #498

Complements

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

NH ≅ G/Ntype
66. C53#7534semidirect

Maximal subgroups

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

subgroupindex
#202898532
#202743492
#753453