Finite Group Databasebeta

← #46780768

Subgroups — #46780768

Order 33664.

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

normal subgroups only

This group has 162 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#30681705C211yesmaximal, characteristic
2#30681662C211yesmaximal, characteristic
3#393×C263C211yesmaximal, characteristic
4C2×C22⋊Dic263—21no—
5C22⋊(C263⋊C8)—21no—
6C22×Q8×C263C411yescharacteristic, complemented
7C2×C22⋊C4×C263—21no—
8C2×C22⋊C4×C263C2211yescharacteristic
9#95×C263—21no—
10#95×C263C411yescharacteristic, complemented
11C22×Dic263—41no—
12C2×C263⋊C8—41no—
13C22⋊Dic263—22no—
14C22⋊Dic263—41no—
15C24×C263D411yescharacteristic
16C2×Q8×C263—42no—
17C2×Q8×C263—41no—
18C22×C4×C263—21no—
19C22×C4×C263—21no—
20C22×C4×C263C2×C411yescharacteristic
21C22×C4×C263D411yescharacteristic
22C22⋊C4×C263—41no—
23C22⋊C4×C263—42no—
24C2×Dic263—42no—
25C2×Dic263—81no—
26C2×Dic263—81no—
27C263⋊C8—81no—
28C23×C263—21no—
29C23×C263—21no—
30C23×C263—41no—
31C23×C263—41no—
32C23×C263C22⋊C411yescharacteristic
33C23×C263SD1611yescharacteristic
34C23×C263Q1611yescharacteristic
35Q8×C263—42no—
36Q8×C263—42no—
37C2×C4×C263—22no—
38C2×C4×C263—21no—
39C2×C4×C263—21no—
40C2×C4×C263—41no—
41C2×C4×C263—41no—
42C2×C4×C263—41no—
43C2×C4×C263—41no—
44C2×C4×C263—41no—
45C2×C4×C263—41no—
46C2×C4×C263—41no—
47C22×C263—21no—
48C22×C263—21no—
49C22×C263—21no—
50C22×C263—21no—
51C22×C263—41no—
52C22×C263—41no—
53C22×C263—41no—
54C22×C263—41no—
55C22×C263—81no—
56C22×C263#9911yescharacteristic
57C22×C263#10311yescharacteristic
58C22×C263#10411yescharacteristic
59C4×C263—42no—
60C4×C263—41no—
61C4×C263—41no—
62C4×C263—81no—
63Dic263—82no—
64C2×C263—21no—
65C2×C263—21no—
66C2×C263—41no—
67C2×C263—41no—
68C2×C263#32811yescharacteristic
69C2×C263AΣL(1,𝔽16)11yescharacteristic
70C2×C263#35411yescharacteristic
71C263#135111yescharacteristic, complemented, Sylow
72#1351—2631nomaximal, Sylow
73#393D26311yescharacteristic
74#342—2631no—
75#323—2631no—
76C22×Q8Dic26311yescharacteristic, complemented
77C2×C22⋊C4—21no—
78C2×C22⋊C4—5261no—
79C2×C22⋊C4C2×D26311yescharacteristic
80C22⋊C8—5261no—
81#95—21no—
82#95Dic26311yescharacteristic, complemented
83C24C22⋊D26311yescharacteristic
84C2×Q8—42no—
85C2×Q8—41no—
86C22×C4—21no—
87C22×C4—21no—
88C22×C4—10521no—
89C22×C4C2×Dic26311yescharacteristic
90C22×C4C22⋊D26311yescharacteristic
91C2×C8—10521no—
92C22⋊C4—41no—
93C22⋊C4—42no—
94C22⋊C4—5262no—
95C22⋊C4—10521no—
96C23—21no—
97C23—21no—
98C23—41no—
99C23—41no—
100C23C22⋊Dic26311yescharacteristic
101C23#1686236311yescharacteristic
102C23#1686236611yescharacteristic
103Q8—42no—
104Q8—42no—
105C2×C4—22no—
106C2×C4—21no—
107C2×C4—21no—
108C2×C4—41no—
109C2×C4—41no—
110C2×C4—41no—
111C2×C4—41no—
112C2×C4—41no—
113C2×C4—41no—
114C2×C4—41no—
115C2×C4—10522no—
116C2×C4—21041no—
117C2×C4—21041no—
118C8—21041no—
119C22—21no—
120C22—21no—
121C22—21no—
122C22—21no—
123C22—41no—
124C22—41no—
125C22—41no—
126C22—41no—
127C22—81no—
128C22#2255438511yescharacteristic
129C22#2255439411yescharacteristic
130C22#2255439711yescharacteristic
131C4—42no—
132C4—41no—
133C4—41no—
134C4—81no—
135C4—21042no—
136C2—21no—
137C2—21no—
138C2—41no—
139C2—41no—
140C2#3068167511yescharacteristic
141C2#3068172511yescharacteristic
142C2#3068173311yescharacteristic
subgroupG/H
centerC22#22554385
commutatorC22×C4×C263C2×C4
FrattiniC2×C22⋊C4C2×D263
Fitting#393×C263C2
socleC22×C263#99
prime radicalC24×C263D4
cosocleC2×C22⋊C4×C263C22
hypercenter#393D263
hypocenterC263#1351
LCSG ▷ C22×C4×C263 ▷ C23×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #393

Complements

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

NH ≅ G/Ntype
6. C22×Q8×C263C4semidirect
10. #95×C263C4semidirect
71. C263#1351semidirect
76. C22×Q8Dic263semidirect
82. #95Dic263semidirect

Maximal subgroups

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

subgroupindex
#306817052
#306816622
#393×C2632
#1351263