Finite Group Databasebeta

← #46782054

Subgroups — #46782054

Order 33664.

228 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 45 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#30682680C211yesmaximal, characteristic
2#30682333C211yesmaximal, characteristic, complemented
3#30682298C212yesmaximal, complemented
4#30681677C212yesmaximal, complemented
5#329×C263C211yesmaximal, characteristic, complemented
6C2×#16862366—21no—
7C2×#16862364—21no—
8#22554470C2211yescharacteristic, complemented
9#22554459—21no—
10#22554458C2212yes—
11#22554456—22no—
12#22554440—22no—
13#22554438—21no—
14#22554395—22no—
15#22554392—22no—
16#22554381C2211yescharacteristic, complemented
17#124×C263C2211yescharacteristic
18#97×C263C2212yescomplemented
19C23×D263—21no—
20C2×Dic526—21no—
21C2×Dic526D412yes—
22C2×D1052—21no—
23C2×D1052D412yes—
24C2×C22⋊D263—22no—
25#16862366—42no—
26#16862364—42no—
27C2×C263⋊C8—21no—
28C4⋊Dic263—22no—
29C22⋊Dic263—21no—
30(C2×D263)⋊C4—22no—
31(C2×D263)⋊C4—22no—
32(C2×D263)⋊C4—22no—
33C4×Dic263—21no—
34C2×Q8×C263D411yescharacteristic
35C2×D4×C263D411yescharacteristic
36C2×C8×C263—22no—
37C22⋊C4×C263—22no—
38C42×C263C2311yescharacteristic
39C22×D263—22no—
40C22×D263—81no—
41C22×D263—82no—
42Dic526—42no—
43Dic526—41no—
44Dic526—41no—
45D1052—42no—
46D1052—81no—
47C22⋊D263—82no—
48C2×Dic263—22no—
49C2×Dic263—41no—
50C263⋊C8—22no—
51C23×C263—21no—
52Q8×C263—41no—
53D4×C263—41no—
54C2×C4×C263—21no—
55C2×C4×C263C2×D412yes—
56C2×C4×C263C2×D411yescharacteristic
57C8×C263—42no—
58C22×C263—41no—
59C22×C263—42no—
60C22×C263#12011yescharacteristic
61C2×D263—42no—
62C2×D263—42no—
63C2×D263—42no—
64C2×D263—84no—
65C4×C263—21no—
66C4×C263—22no—
67C4×C263—41no—
68Dic263—42no—
69Dic263—81no—
70C2×C263—81no—
71C2×C263#45311yescharacteristic
72C2×C263#45512yes—
73D263—82no—
74C263#165911yescharacteristic, complemented, Sylow
75#1659—2631nomaximal, Sylow
76H(3,𝔽4)—2631no—
77#497—2631no—
78#489—2632no—
79#329—2632no—
80#329D26311yescharacteristic, complemented
81C2×Q16—5261no—
82C2×SD16—5261no—
83C4⋊Q8—2631no—
84#124—2632no—
85#124—5262no—
86#124—5261no—
87#124C2×D26311yescharacteristic
88#120—5262no—
89#120—5261no—
90#103—5262no—
91#102—5262no—
92#97—2631no—
93#97C2×D26312yescomplemented
94C24—5261no—
95C2×Q8—2632no—
96C2×Q8—5261no—
97C2×Q8D105211yescharacteristic
98C2×D4—2632no—
99C2×D4—5261no—
100C2×D4—5262no—
101C2×D4D105211yescharacteristic
102Q16—10522no—
103SD16—10522no—
104C2×C8—22no—
105C2×C8—5261no—
106C4⋊C4—5262no—
107C22⋊C4—22no—
108C22⋊C4—5262no—
109C22⋊C4—5261no—
110C22⋊C4—5262no—
111C22⋊C4—5262no—
112C42—5261no—
113C42C22×D26311yescharacteristic
114C23—21no—
115C23—5262no—
116C23—21042no—
117C23—21041no—
118Q8—41no—
119Q8—10522no—
120Q8—10521no—
121Q8—10521no—
122D4—41no—
123D4—10522no—
124D4—21041no—
125D4—21042no—
126C2×C4—21no—
127C2×C4—5262no—
128C2×C4—10521no—
129C2×C4D4×D26312yes—
130C2×C4C2×D105211yescharacteristic
131C8—42no—
132C8—5262no—
133C22—42no—
134C22—41no—
135C22—10522no—
136C22—10522no—
137C22—10522no—
138C22—21044no—
139C22#2255444011yescharacteristic
140C4—22no—
141C4—21no—
142C4—41no—
143C4—10522no—
144C4—21041no—
145C2—81no—
146C2—21042no—
147C2#3068210811yescharacteristic
148C2#3068211712yes—
subgroupG/H
centerC22#22554440
commutator, cosocleC42×C263C23
FrattiniC42C22×D263
Fitting#329×C263C2
socleC22×C263#120
prime radical#30682680C2
hypercenter#329D263
hypocenterC263#1659
LCSG ▷ C42×C263 ▷ C22×C263 ▷ C263
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
2. #30682333C2semidirect
3. #30682298C2semidirect
4. #30681677C2semidirect
5. #329×C263C2semidirect
8. #22554470C22semidirect
16. #22554381C22semidirect
18. #97×C263C22semidirect
74. C263#1659semidirect
80. #329D263semidirect
93. #97C2×D263semidirect

Maximal subgroups

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

subgroupindex
#306826802
#306823332
#306822982
#306816772
#329×C2632
#1659263