Finite Group Databasebeta

← #46782053

Subgroups — #46782053

Order 33664.

228 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 49 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#30682333C211yesmaximal, characteristic, complemented
2#30682297C212yesmaximal, complemented
3#30681678C211yesmaximal, characteristic, complemented
4#30681678C212yesmaximal, complemented
5H(3,𝔽4)×C263C211yesmaximal, characteristic
6C2×#16862366—21no—
7C2×#16862364—21no—
8#22554470C2211yescharacteristic, complemented
9#22554394—22no—
10#22554391—22no—
11#22554381C2212yescomplemented
12#22554381C2211yescharacteristic, complemented
13#124×C263—22no—
14#124×C263—21no—
15#124×C263C2212yes—
16#124×C263C2211yescharacteristic
17#120×C263—22no—
18#120×C263—21no—
19C2×Dic526—21no—
20#16862366—42no—
21#16862364—42no—
22C2×C263⋊C8—21no—
23C2×C263⋊C8—22no—
24C4⋊Dic263—22no—
25C24×C263—21no—
26C2×Q8×C263D412yes—
27C2×Q8×C263D411yescharacteristic
28C2×D4×C263—21no—
29C2×D4×C263—22no—
30C2×D4×C263D412yes—
31C2×D4×C263D411yescharacteristic
32C22⋊C4×C263—22no—
33C22⋊C4×C263—21no—
34C22⋊C4×C263—22no—
35C22⋊C4×C263—22no—
36C22⋊C4×C263—22no—
37C42×C263—21no—
38C42×C263C2311yescharacteristic
39Dic526—41no—
40Dic526—41no—
41C2×Dic263—41no—
42C263⋊C8—22no—
43C263⋊C8—42no—
44C23×C263—21no—
45C23×C263—22no—
46C23×C263—81no—
47C23×C263—82no—
48Q8×C263—42no—
49Q8×C263—41no—
50D4×C263—42no—
51D4×C263—41no—
52D4×C263—81no—
53D4×C263—82no—
54C2×C4×C263—21no—
55C2×C4×C263—22no—
56C2×C4×C263C2×D412yes—
57C2×C4×C263C2×D411yescharacteristic
58C22×C263—41no—
59C22×C263—42no—
60C22×C263—42no—
61C22×C263—42no—
62C22×C263—42no—
63C22×C263—84no—
64C22×C263#12011yescharacteristic
65C4×C263—21no—
66C4×C263—22no—
67C4×C263—41no—
68C4×C263—42no—
69Dic263—81no—
70C2×C263—81no—
71C2×C263—82no—
72C2×C263#45311yescharacteristic
73C2×C263#45512yes—
74C263#165911yescharacteristic, complemented, Sylow
75#1659—2631nomaximal, Sylow
76H(3,𝔽4)D26311yescharacteristic
77#497—2631no—
78#489—2632no—
79#329—2631no—
80#329—2632no—
81C2×Q16—5261no—
82C2×SD16—5261no—
83C4⋊Q8—2631no—
84#124—22no—
85#124—21no—
86#124C2×D26312yes—
87#124C2×D26311yescharacteristic
88#120—22no—
89#120—21no—
90#103—5262no—
91#102—5262no—
92#97—2632no—
93#97—2631no—
94C24—21no—
95C2×Q8—5261no—
96C2×Q8C22⋊D26312yes—
97C2×Q8C22⋊D26311yescharacteristic
98C2×D4—22no—
99C2×D4—21no—
100C2×D4C22⋊D26312yes—
101C2×D4C22⋊D26311yescharacteristic
102Q16—10522no—
103SD16—10522no—
104C2×C8—5261no—
105C2×C8—5262no—
106C4⋊C4—5262no—
107C22⋊C4—21no—
108C22⋊C4—22no—
109C22⋊C4—22no—
110C22⋊C4—22no—
111C22⋊C4—22no—
112C42—21no—
113C42C22×D26311yescharacteristic
114C23—22no—
115C23—21no—
116C23—82no—
117C23—81no—
118Q8—41no—
119Q8—42no—
120Q8—10521no—
121Q8—10521no—
122D4—41no—
123D4—42no—
124D4—82no—
125D4—81no—
126C2×C4—22no—
127C2×C4—21no—
128C2×C4—10521no—
129C2×C4C2×C22⋊D26312yes—
130C2×C4C2×C22⋊D26311yescharacteristic
131C8—5262no—
132C8—10522no—
133C22—42no—
134C22—42no—
135C22—42no—
136C22—41no—
137C22—42no—
138C22—84no—
139C22#2255443911yescharacteristic
140C4—22no—
141C4—21no—
142C4—42no—
143C4—41no—
144C4—21041no—
145C2—82no—
146C2—81no—
147C2#3068210611yescharacteristic
148C2#3068211612yes—
subgroupG/H
centerC22#22554439
commutator, cosocleC42×C263C23
FrattiniC42C22×D263
Fitting, prime radicalH(3,𝔽4)×C263C2
socleC22×C263#120
hypercenterH(3,𝔽4)D263
hypocenterC263#1659
LCSG ▷ C42×C263 ▷ C22×C263 ▷ C263
UCSC1 ◁ C22 ◁ C42 ◁ H(3,𝔽4)

Complements

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

NH ≅ G/Ntype
1. #30682333C2semidirect
2. #30682297C2semidirect
3. #30681678C2semidirect
4. #30681678C2semidirect
8. #22554470C22semidirect
11. #22554381C22semidirect
12. #22554381C22semidirect
74. C263#1659semidirect

Maximal subgroups

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

subgroupindex
#306823332
#306822972
#306816782
H(3,𝔽4)×C2632
#1659263