Finite Group Databasebeta

← #46780752

Subgroups — #46780752

Order 33664.

124 conjugacy classes of subgroups; only the 35 normal subgroups are shown.

normal subgroups only

This group has 124 conjugacy classes of subgroups — too many to draw. Only its 35 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#30681868C211yesmaximal, characteristic
2#30681664C211yesmaximal, characteristic
3#343×C263C211yesmaximal, characteristic
4C2×C4⋊Dic263C411yescharacteristic
5C2×Dic263⋊C4—21no—
6C22⋊(C263⋊C8)—21no—
7C263⋊#95—21no—
8C263⋊#95C411yescharacteristic
9C2×M16×C263—21no—
10C2×C4⋊C4×C263C2211yescharacteristic
11C22×Dic263—21no—
12C22×Dic263—21no—
13C2×C263⋊C8—41no—
14C4⋊Dic263—41no—
15Dic263⋊C4—41no—
16Dic263⋊C4—41no—
17C22×C4×C263C2×C411yescharacteristic
18C22×C4×C263D411yescharacteristic
19C22×C4×C263D411yescharacteristic
20M16×C263—22no—
21M16×C263—41no—
22C2×C8×C263—41no—
23C4⋊C4×C263—41no—
24C2×Dic263—22no—
25C2×Dic263—41no—
26C2×Dic263—41no—
27C2×Dic263—41no—
28C2×Dic263—41no—
29C2×Dic263—41no—
30C263⋊C8—81no—
31C23×C263C22⋊C411yescharacteristic
32C2×C4×C263—21no—
33C2×C4×C263—21no—
34C2×C4×C263—21no—
35C2×C4×C263—21no—
36C2×C4×C263—41no—
37C2×C4×C263—41no—
38C2×C4×C263D811yescharacteristic
39C2×C4×C263SD1611yescharacteristic
40C8×C263—42no—
41C22×C263—21no—
42C22×C263—21no—
43C22×C263#9911yescharacteristic
44C22×C263#10211yescharacteristic
45C22×C263#10411yescharacteristic
46C4×C263—21no—
47C4×C263—21no—
48C4×C263—41no—
49C4×C263—41no—
50Dic263—42no—
51Dic263—81no—
52C2×C263—21no—
53C2×C263—21no—
54C2×C263#32711yescharacteristic
55C2×C263#35211yescharacteristic
56C2×C263#35611yescharacteristic
57C263#134611yescharacteristic, complemented, Sylow
58#1346—2631nomaximal, Sylow
59#398—2631no—
60#343D26311yescharacteristic
61#324—2631no—
62C2×M16—21no—
63C2×C4⋊C4—2631no—
64C2×C4⋊C4—5261no—
65C2×C4⋊C4C2×D26311yescharacteristic
66C22⋊C8—5261no—
67#95—2631no—
68#95—5261no—
69C22×C4—5261no—
70C22×C4—5261no—
71C22×C4C4×D26311yescharacteristic
72C22×C4C22⋊D26311yescharacteristic
73C22×C4D105211yescharacteristic
74M16—22no—
75M16—41no—
76C2×C8—41no—
77C2×C8—10521no—
78C4⋊C4—41no—
79C4⋊C4—10521no—
80C4⋊C4—10521no—
81C4⋊C4—10521no—
82C23(C2×D263)⋊C411yescharacteristic
83C2×C4—21no—
84C2×C4—21no—
85C2×C4—21no—
86C2×C4—21no—
87C2×C4—41no—
88C2×C4—41no—
89C2×C4—5262no—
90C2×C4—10521no—
91C2×C4—10521no—
92C2×C4—10521no—
93C2×C4—10521no—
94C2×C4—10521no—
95C2×C4#1686236111yescharacteristic
96C2×C4#1686236311yescharacteristic
97C8—42no—
98C8—21041no—
99C22—21no—
100C22—21no—
101C22#2255438411yescharacteristic
102C22#2255439011yescharacteristic
103C22#2255439811yescharacteristic
104C4—21no—
105C4—21no—
106C4—41no—
107C4—41no—
108C4—10522no—
109C4—21041no—
110C2—21no—
111C2—21no—
112C2#3068167111yescharacteristic
113C2#3068172911yescharacteristic
114C2#3068173611yescharacteristic
subgroupG/H
centerC22#22554384
commutatorC22×C4×C263C2×C4
FrattiniC2×C4⋊C4C2×D263
Fitting#343×C263C2
socleC22×C263#99
prime radicalC23×C263C22⋊C4
cosocleC2×C4⋊C4×C263C22
hypercenter#343D263
hypocenterC263#1346
LCSG ▷ C22×C4×C263 ▷ C23×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #343

Complements

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

NH ≅ G/Ntype
57. C263#1346semidirect

Maximal subgroups

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

subgroupindex
#306818682
#306816642
#343×C2632
#1346263