Finite Group Databasebeta

← #46780751

Subgroups — #46780751

Order 33664.

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

normal subgroups only

This group has 168 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#30681855C211yesmaximal, characteristic
2#30681707C211yesmaximal, characteristic, complemented
3#324×C263C211yesmaximal, characteristic, complemented
4C22×D1052C411yescharacteristic
5C2×#16862360—21no—
6C2×(C2×D263)⋊C4—21no—
7C2×(C2×D263)⋊C4—21no—
8C263⋊#95C411yescharacteristic
9C2×C4⋊C4×C263C2211yescharacteristic
10C22⋊C8×C263—21no—
11C23×D263—21no—
12C2×D1052—41no—
13C2×D1052—42no—
14C22×Dic263—21no—
15#16862360—22no—
16#16862360—41no—
17C2×C263⋊C8—41no—
18(C2×D263)⋊C4—42no—
19(C2×D263)⋊C4—41no—
20(C2×D263)⋊C4—41no—
21C22×C4×C263C2×C411yescharacteristic
22C22×C4×C263D411yescharacteristic
23C22×C4×C263D411yescharacteristic
24C2×C8×C263—41no—
25C4⋊C4×C263—41no—
26C22×D263—22no—
27C22×D263—41no—
28C22×D263—41no—
29C22×D263—41no—
30C22×D263—41no—
31C22×D263—41no—
32C22×D263—41no—
33D1052—42no—
34D1052—42no—
35C2×Dic263—41no—
36C2×Dic263—41no—
37C2×Dic263—41no—
38C263⋊C8—42no—
39C23×C263C22⋊C411yescharacteristic
40C2×C4×C263—21no—
41C2×C4×C263—21no—
42C2×C4×C263—21no—
43C2×C4×C263—21no—
44C2×C4×C263—41no—
45C2×C4×C263—41no—
46C2×C4×C263D811yescharacteristic
47C2×C4×C263SD1611yescharacteristic
48C8×C263—81no—
49C22×C263—21no—
50C22×C263—21no—
51C22×C263#9911yescharacteristic
52C22×C263#10211yescharacteristic
53C22×C263#10411yescharacteristic
54C2×D263—42no—
55C2×D263—42no—
56C2×D263—42no—
57C2×D263—81no—
58C2×D263—81no—
59C2×D263—81no—
60C2×D263—81no—
61C4×C263—21no—
62C4×C263—21no—
63C4×C263—41no—
64C4×C263—41no—
65Dic263—81no—
66C2×C263—21no—
67C2×C263—21no—
68C2×C263#32711yescharacteristic
69C2×C263AΣL(1,𝔽16)11yescharacteristic
70C2×C263#35511yescharacteristic
71D263—82no—
72C263#134511yescharacteristic, complemented, Sylow
73#1345—2631nomaximal, Sylow
74#394—2631no—
75#343—2631no—
76#324D26311yescharacteristic, complemented
77C22×D4—2631no—
78C2×M16—5261no—
79C2×C4⋊C4C2×D26311yescharacteristic
80C2×C22⋊C4—5261no—
81C2×C22⋊C4—5261no—
82C22⋊C8—21no—
83#95—2631no—
84C24—5261no—
85C2×D4—10521no—
86C2×D4—10522no—
87C22×C4—5261no—
88C22×C4C4×D26311yescharacteristic
89C22×C4C22⋊D26311yescharacteristic
90C22×C4D105211yescharacteristic
91M16—5262no—
92M16—10521no—
93C2×C8—41no—
94C2×C8—10521no—
95C4⋊C4—41no—
96C22⋊C4—10522no—
97C22⋊C4—10521no—
98C22⋊C4—10521no—
99C23—5262no—
100C23—10521no—
101C23—10521no—
102C23—10521no—
103C23—10521no—
104C23—10521no—
105C23—10521no—
106C23(C2×D263)⋊C411yescharacteristic
107D4—10522no—
108D4—10522no—
109C2×C4—21no—
110C2×C4—21no—
111C2×C4—21no—
112C2×C4—21no—
113C2×C4—41no—
114C2×C4—41no—
115C2×C4—10521no—
116C2×C4—10521no—
117C2×C4—10521no—
118C2×C4D210411yescharacteristic
119C2×C4#1686236511yescharacteristic
120C8—81no—
121C8—10522no—
122C22—21no—
123C22—21no—
124C22—10522no—
125C22—10522no—
126C22—10522no—
127C22—21041no—
128C22—21041no—
129C22—21041no—
130C22—21041no—
131C22#2255438411yescharacteristic
132C22#2255439211yescharacteristic
133C22#2255439611yescharacteristic
134C4—21no—
135C4—21no—
136C4—41no—
137C4—41no—
138C4—21041no—
139C2—21no—
140C2—21no—
141C2—21042no—
142C2#3068167311yescharacteristic
143C2#3068172411yescharacteristic
144C2#3068173411yescharacteristic
subgroupG/H
centerC22#22554384
commutatorC22×C4×C263C2×C4
FrattiniC2×C4⋊C4C2×D263
Fitting#324×C263C2
socleC22×C263#99
prime radicalC22×D1052C4
cosocleC2×C4⋊C4×C263C22
hypercenter#324D263
hypocenterC263#1345
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
2. #30681707C2semidirect
3. #324×C263C2semidirect
72. C263#1345semidirect
76. #324D263semidirect

Maximal subgroups

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

subgroupindex
#306818552
#306817072
#324×C2632
#1345263