Finite Group Databasebeta

← #46780694

Subgroups — #46780694

Order 33664.

158 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 158 conjugacy classes of subgroups — too many to draw. Only its 37 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#30681810C211yesmaximal, characteristic
2#30681662C211yesmaximal, characteristic
3#323×C263C211yesmaximal, characteristic
4C23×Dic263C411yescharacteristic
5C2×Dic263⋊C4—21no—
6C2×C22⋊Dic263C411yescharacteristic
7C22⋊(C263⋊C8)—21no—
8C263⋊#95—21no—
9C2×C22⋊C4×C263C2211yescharacteristic
10C22⋊C8×C263—21no—
11C22×Dic263—21no—
12C22×Dic263—21no—
13C22×Dic263—41no—
14C22×Dic263—42no—
15C2×C263⋊C8—41no—
16Dic263⋊C4—42no—
17C22⋊Dic263—21no—
18C22⋊Dic263C812yescomplemented
19C24×C263C2×C411yescharacteristic
20C22×C4×C263D411yescharacteristic
21C22×C4×C263D411yescharacteristic
22C2×C8×C263—41no—
23C22⋊C4×C263—41no—
24C2×Dic263—22no—
25C2×Dic263—22no—
26C2×Dic263—41no—
27C2×Dic263—41no—
28C2×Dic263—41no—
29C2×Dic263—42no—
30C2×Dic263—41no—
31C2×Dic263—42no—
32C263⋊C8—81no—
33C23×C263—21no—
34C23×C263—21no—
35C23×C263—41no—
36C23×C263—41no—
37C23×C263C22⋊C411yescharacteristic
38C23×C263C2×C811yescharacteristic
39C23×C263M1611yescharacteristic
40C2×C4×C263—21no—
41C2×C4×C263—21no—
42C2×C4×C263—41no—
43C2×C4×C263—41no—
44C8×C263—81no—
45C22×C263—21no—
46C22×C263—21no—
47C22×C263—21no—
48C22×C263—21no—
49C22×C263—41no—
50C22×C263—41no—
51C22×C263—42no—
52C22×C263—41no—
53C22×C263—41no—
54C22×C263C22⋊C811yescharacteristic
55C22×C263#9911yescharacteristic
56C22×C263#10111yescharacteristic
57C4×C263—41no—
58C4×C263—41no—
59Dic263—42no—
60Dic263—42no—
61C2×C263—21no—
62C2×C263—21no—
63C2×C263—41no—
64C2×C263—41no—
65C2×C263#32411yescharacteristic
66C2×C263AΣL(1,𝔽16)11yescharacteristic
67C2×C263#35211yescharacteristic
68C263#132611yescharacteristic, complemented, Sylow
69#1326—2631nomaximal, Sylow
70#385—2631no—
71#323—2631no—
72#323D26311yescharacteristic
73C23×C4—2631no—
74C2×C4⋊C4—5261no—
75C2×C22⋊C4—2631no—
76C2×C22⋊C4C2×D26311yescharacteristic
77C22⋊C8—21no—
78C22⋊C8—5261no—
79#95—5261no—
80C24C4×D26311yescharacteristic
81C22×C4—5261no—
82C22×C4—5261no—
83C22×C4—10522no—
84C22×C4—10521no—
85C22×C4C22⋊D26311yescharacteristic
86C22×C4D105211yescharacteristic
87C2×C8—41no—
88C2×C8—10521no—
89C4⋊C4—10522no—
90C22⋊C4—41no—
91C22⋊C4—2632no—
92C22⋊C4—5261no—
93C23—21no—
94C23—21no—
95C23—41no—
96C23—41no—
97C23(C2×D263)⋊C411yescharacteristic
98C23C8×D26311yescharacteristic
99C23#1686235911yescharacteristic
100C2×C4—21no—
101C2×C4—21no—
102C2×C4—41no—
103C2×C4—41no—
104C2×C4—5262no—
105C2×C4—5262no—
106C2×C4—10521no—
107C2×C4—10521no—
108C2×C4—10521no—
109C2×C4—10522no—
110C2×C4—10521no—
111C2×C4—10522no—
112C8—81no—
113C8—21041no—
114C22—21no—
115C22—21no—
116C22—21no—
117C22—21no—
118C22—41no—
119C22—41no—
120C22—42no—
121C22—41no—
122C22—41no—
123C22(C2×D263)⋊C811yescharacteristic
124C22#2255438411yescharacteristic
125C22#2255438811yescharacteristic
126C4—41no—
127C4—41no—
128C4—10522no—
129C4—10522no—
130C2—21no—
131C2—21no—
132C2—41no—
133C2—41no—
134C2#3068166311yescharacteristic
135C2#3068172411yescharacteristic
136C2#3068172911yescharacteristic
subgroupG/H
centerC22#22554384
commutatorC23×C263C2×C8
FrattiniC2×C22⋊C4C2×D263
Fitting#323×C263C2
socleC22×C263#99
prime radicalC24×C263C2×C4
cosocleC2×C22⋊C4×C263C22
hypercenter#323D263
hypocenterC263#1326
LCSG ▷ C23×C263 ▷ C22×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #323

Complements

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

NH ≅ G/Ntype
18. C22⋊Dic263C8semidirect
68. C263#1326semidirect

Maximal subgroups

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

subgroupindex
#306818102
#306816622
#323×C2632
#1326263