Finite Group Databasebeta

← #46780901

Subgroups — #46780901

Order 33664.

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

normal subgroups only

This group has 106 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#30681737C211yesmaximal, characteristic, complemented
2#30681687C211yesmaximal, characteristic, complemented
3#456×C263C211yesmaximal, characteristic
4C4⋊(C263⋊C8)—21no—
5#22554389—21no—
62−1+4×C263C411yescharacteristic
7#137×C263—21no—
8C4⋊Q8×C263C2211yescharacteristic
9#104×C263—21no—
10#101×C263C411yescharacteristic
11#16862360—41no—
12C2×C263⋊C8—41no—
13#41×C263—21no—
14#41×C263—41no—
15#41×C263—41no—
16C2×Q8×C263—41no—
17C2×Q8×C263C2×C411yescharacteristic
18C2×Q8×C263D411yescharacteristic
19Q16×C263—41no—
20SD16×C263—41no—
21M16×C263—21no—
22C4⋊C4×C263—41no—
23C42×C263D411yescharacteristic
24C263⋊C8—81no—
25C263⋊C8—81no—
26Q8×C263—21no—
27Q8×C263—41no—
28Q8×C263—41no—
29Q8×C263—41no—
30D4×C263—21no—
31D4×C263—41no—
32D4×C263—41no—
33C2×C4×C263—21no—
34C2×C4×C263—21no—
35C2×C4×C263—21no—
36C2×C4×C263—41no—
37C2×C4×C263—42no—
38C2×C4×C263C22⋊C411yescharacteristic
39C8×C263—41no—
40C22×C263—41no—
41C22×C263#9911yescharacteristic
42C4×C263—21no—
43C4×C263—21no—
44C4×C263—21no—
45C4×C263—41no—
46C4×C263—41no—
47C4×C263—41no—
48C2×C263—21no—
49C2×C263—81no—
50C2×C263AΣL(1,𝔽16)11yescharacteristic
51C263#140511yescharacteristic, complemented, Sylow
52#1405—2631nomaximal, Sylow
53#456D26311yescharacteristic
54#356—2631no—
55#333—2631no—
562−1+4Dic26311yescharacteristic
57#137—21no—
58C4⋊Q8C2×D26311yescharacteristic
59C4⋊C8—5261no—
60#104—21no—
61#101—5261no—
62#101Dic26311yescharacteristic
63#41—21no—
64#41—41no—
65#41—41no—
66C2×Q8—41no—
67C2×Q8C2×Dic26311yescharacteristic
68C2×Q8C22⋊D26311yescharacteristic
69Q16—41no—
70SD16—41no—
71M16—21no—
72M16—10521no—
73C2×C8—10521no—
74C4⋊C4—41no—
75C42C22⋊D26311yescharacteristic
76Q8—21no—
77Q8—41no—
78Q8—41no—
79Q8—41no—
80D4—21no—
81D4—41no—
82D4—41no—
83C2×C4—21no—
84C2×C4—21no—
85C2×C4—21no—
86C2×C4—41no—
87C2×C4—42no—
88C2×C4C22⋊Dic26311yescharacteristic
89C8—41no—
90C8—21041no—
91C8—21041no—
92C22—41no—
93C22#2255438511yescharacteristic
94C4—21no—
95C4—21no—
96C4—21no—
97C4—41no—
98C4—41no—
99C4—41no—
100C2—21no—
101C2—81no—
102C2#3068172511yescharacteristic
subgroupG/H
centerC2#30681725
commutatorC2×Q8×C263C2×C4
FrattiniC4⋊Q8C2×D263
Fitting#456×C263C2
socleC2×C263AΣL(1,𝔽16)
prime radical2−1+4×C263C4
cosocleC4⋊Q8×C263C22
hypercenter#456D263
hypocenterC263#1405
LCSG ▷ C2×Q8×C263 ▷ C2×C4×C263 ▷ C22×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C4⋊Q8 ◁ #456

Complements

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

NH ≅ G/Ntype
1. #30681737C2semidirect
2. #30681687C2semidirect
51. C263#1405semidirect

Maximal subgroups

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

subgroupindex
#306817372
#306816872
#456×C2632
#1405263