Finite Group Databasebeta

← #46780778

Subgroups — #46780778

Order 33664.

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

normal subgroups only

This group has 140 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#30681858C211yesmaximal, characteristic
2#30681707C211yesmaximal, characteristic
3#324×C263C211yesmaximal, characteristic
4C22×Dic526C411yescharacteristic
5C2×#16862360—21no—
6C2×Dic263⋊C4—21no—
7C263⋊#95—21no—
8C263⋊#95C411yescharacteristic
9C2×C4⋊C4×C263C2211yescharacteristic
10C22⋊C8×C263—21no—
11C2×Dic526—41no—
12C2×Dic526—42no—
13C22×Dic263—21no—
14C22×Dic263—21no—
15#16862360—22no—
16#16862360—41no—
17C2×C263⋊C8—41no—
18Dic263⋊C4—42no—
19C22×C4×C263C2×C411yescharacteristic
20C22×C4×C263D411yescharacteristic
21C22×C4×C263D411yescharacteristic
22C2×C8×C263—41no—
23C4⋊C4×C263—41no—
24Dic526—42no—
25Dic526—42no—
26C2×Dic263—22no—
27C2×Dic263—22no—
28C2×Dic263—41no—
29C2×Dic263—41no—
30C2×Dic263—41no—
31C2×Dic263—41no—
32C263⋊C8—42no—
33C23×C263C22⋊C411yescharacteristic
34C2×C4×C263—21no—
35C2×C4×C263—21no—
36C2×C4×C263—21no—
37C2×C4×C263—21no—
38C2×C4×C263—41no—
39C2×C4×C263—41no—
40C2×C4×C263SD1611yescharacteristic
41C2×C4×C263Q1611yescharacteristic
42C8×C263—81no—
43C22×C263—21no—
44C22×C263—21no—
45C22×C263#9911yescharacteristic
46C22×C263#10311yescharacteristic
47C22×C263#10411yescharacteristic
48C4×C263—21no—
49C4×C263—21no—
50C4×C263—41no—
51C4×C263—41no—
52Dic263—42no—
53Dic263—42no—
54C2×C263—21no—
55C2×C263—21no—
56C2×C263#32811yescharacteristic
57C2×C263AΣL(1,𝔽16)11yescharacteristic
58C2×C263#35611yescharacteristic
59C263#135411yescharacteristic, complemented, Sylow
60#1354—2631nomaximal, Sylow
61#395—2631no—
62#343—2631no—
63#324D26311yescharacteristic
64C22×Q8—2631no—
65C2×M16—5261no—
66C2×C4⋊C4—5261no—
67C2×C4⋊C4C2×D26311yescharacteristic
68C22⋊C8—21no—
69#95—2631no—
70#95—5261no—
71C2×Q8—10521no—
72C2×Q8—10522no—
73C22×C4—5261no—
74C22×C4—5261no—
75C22×C4C4×D26311yescharacteristic
76C22×C4C22⋊D26311yescharacteristic
77C22×C4D105211yescharacteristic
78M16—5262no—
79M16—10521no—
80C2×C8—41no—
81C2×C8—10521no—
82C4⋊C4—41no—
83C4⋊C4—10522no—
84C23(C2×D263)⋊C411yescharacteristic
85Q8—10522no—
86Q8—10522no—
87C2×C4—21no—
88C2×C4—21no—
89C2×C4—21no—
90C2×C4—21no—
91C2×C4—41no—
92C2×C4—41no—
93C2×C4—5262no—
94C2×C4—5262no—
95C2×C4—10521no—
96C2×C4—10521no—
97C2×C4—10521no—
98C2×C4—10521no—
99C2×C4#1686236511yescharacteristic
100C2×C4Dic105211yescharacteristic
101C8—81no—
102C8—10522no—
103C22—21no—
104C22—21no—
105C22#2255438411yescharacteristic
106C22#2255439511yescharacteristic
107C22#2255439611yescharacteristic
108C4—21no—
109C4—21no—
110C4—41no—
111C4—41no—
112C4—10522no—
113C4—10522no—
114C2—21no—
115C2—21no—
116C2#3068167611yescharacteristic
117C2#3068172411yescharacteristic
118C2#3068173611yescharacteristic
subgroupG/H
centerC22#22554384
commutatorC22×C4×C263C2×C4
FrattiniC2×C4⋊C4C2×D263
Fitting#324×C263C2
socleC22×C263#99
prime radicalC23×C263C22⋊C4
cosocleC2×C4⋊C4×C263C22
hypercenter#324D263
hypocenterC263#1354
LCSG ▷ C22×C4×C263 ▷ C23×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #324

Complements

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

NH ≅ G/Ntype
59. C263#1354semidirect

Maximal subgroups

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

subgroupindex
#306818582
#306817072
#324×C2632
#1354263