Finite Group Databasebeta

← #46780921

Subgroups — #46780921

Order 33664.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#30682292C211yesmaximal, characteristic
2#30681735C211yesmaximal, characteristic
3#354×C263C211yesmaximal, characteristic
4#22554462C411yescharacteristic, complemented
5#22554394—21no—
6#22554391—21no—
7#22554389—21no—
8C4×C263⋊C8C411yescharacteristic, complemented
9#124×C263C2211yescharacteristic
10#99×C263—21no—
11#16862360—41no—
12C2×C263⋊C8—21no—
13C4⋊Dic263—21no—
14Dic263⋊C4—41no—
15C2×Q8×C263D411yescharacteristic
16C2×D4×C263D411yescharacteristic
17C22⋊C4×C263—41no—
18C22⋊C4×C263—41no—
19C42×C263C2×C411yescharacteristic
20C2×Dic263—41no—
21C263⋊C8—41no—
22C263⋊C8—81no—
23C23×C263—21no—
24Q8×C263—41no—
25D4×C263—41no—
26C2×C4×C263—21no—
27C2×C4×C263—21no—
28C2×C4×C263—81no—
29C2×C4×C263C22⋊C411yescharacteristic
30C22×C263—41no—
31C22×C263—81no—
32C22×C263#9911yescharacteristic
33C4×C263—21no—
34C4×C263—41no—
35C4×C263—41no—
36C4×C263—161no—
37Dic263—81no—
38C2×C263—21no—
39C2×C263—81no—
40C2×C263#35411yescharacteristic
41C263#141411yescharacteristic, complemented, Sylow
42#1414—2631nomaximal, Sylow
43#488—2631no—
44#355—2631no—
45#354D26311yescharacteristic
46#125—2631no—
47#124C2×D26311yescharacteristic
48#103—5261no—
49#102—5261no—
50#101—5261no—
51#99—21no—
52C4×C8—2631no—
53C2×Q8D105211yescharacteristic
54C2×D4C22⋊D26311yescharacteristic
55M16—10521no—
56C2×C8—5261no—
57C4⋊C4—5261no—
58C4⋊C4—10521no—
59C22⋊C4—41no—
60C22⋊C4—41no—
61C42C4×D26311yescharacteristic
62C23—21no—
63Q8—41no—
64D4—41no—
65C2×C4—21no—
66C2×C4—21no—
67C2×C4—81no—
68C2×C4—10521no—
69C2×C4(C2×D263)⋊C411yescharacteristic
70C8—10521no—
71C8—21041no—
72C22—41no—
73C22—81no—
74C22#2255438411yescharacteristic
75C4—21no—
76C4—41no—
77C4—41no—
78C4—161no—
79C4—21041no—
80C2—21no—
81C2—81no—
82C2#3068173211yescharacteristic
subgroupG/H
centerC2#30681732
commutatorC42×C263C2×C4
Frattini#124C2×D263
Fitting#354×C263C2
socleC2×C263#354
prime radicalC2×D4×C263D4
cosocle#124×C263C22
hypercenter#354D263
hypocenterC263#1414
LCSG ▷ C42×C263 ▷ C2×C4×C263 ▷ C22×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ #124 ◁ #354

Complements

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

NH ≅ G/Ntype
4. #22554462C4semidirect
8. C4×C263⋊C8C4semidirect
41. C263#1414semidirect

Maximal subgroups

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

subgroupindex
#306822922
#306817352
#354×C2632
#1414263