Finite Group Databasebeta

← #46784054

Subgroups — #46784054

Order 33664.

264 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 63 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#30682738C211yesmaximal, characteristic
2#30681966C211yesmaximal, characteristic, complemented
3#30681932C212yesmaximal, complemented
4#30681911C212yesmaximal, complemented
5H(3,ℤ/4)×C263C211yesmaximal, characteristic, complemented
6C2×#16862376C2212yes—
7#22554503—22no—
8#22554498—22no—
9#22554492—22no—
10C22×C263⋊C8C2211yescharacteristic
11#22554429C2211yescharacteristic
12Dic263⋊C8—22no—
13#22554393—22no—
14#22554390—22no—
15#22554384—24no—
16C2×M16×C263C2211yescharacteristic
17#117×C263C2212yes—
18#16862376—22no—
19#16862376—22no—
20#16862376—22no—
21#16862376—22no—
22C2×Dic526D412yes—
23C2×D1052D412yes—
24C2×C22⋊D263—22no—
25C2×C4×D263—22no—
26Dic1052—22no—
27#16862365—24no—
28D2104—22no—
29C2×C263⋊C8—22no—
30C2×C263⋊C8—21no—
31C4⋊Dic263—21no—
32C22⋊Dic263D412yes—
33C4×Dic263—21no—
34C22×C4×C263C2311yescharacteristic
35M16×C263—22no—
36C2×C8×C263D412yes—
37C4⋊C4×C263—22no—
38C22⋊C4×C263—22no—
39C42×C263—22no—
40C22×D263—22no—
41Dic526—22no—
42Dic526—22no—
43D1052—22no—
44D1052—22no—
45C22⋊D263—42no—
46C22⋊D263—42no—
47C2×Dic263—22no—
48C2×Dic263—22no—
49C4×D263—42no—
50C4×D263—42no—
51C263⋊C8—41no—
52C23×C263C2×D411yescharacteristic
53C2×C4×C263—42no—
54C2×C4×C263C2×D412yes—
55C2×C4×C263C2×D411yescharacteristic
56C2×C4×C263#4112yes—
57C2×C4×C263#4111yescharacteristic
58C8×C263—22no—
59C22×C263—41no—
60C22×C263#12112yes—
61C22×C263#12111yescharacteristic
62C2×D263—42no—
63C2×D263—82no—
64C4×C263—82no—
65C4×C263#12011yescharacteristic
66C4×C263#12312yes—
67C4×C263#12411yescharacteristic
68Dic263—42no—
69Dic263—42no—
70C2×C263—21no—
71C2×C263—22no—
72C2×C263#39411yescharacteristic
73D263—82no—
74C263#205311yescharacteristic, complemented, Sylow
75#2053—2631nomaximal, Sylow
76#575—2631no—
77#424—2631no—
78#416—2632no—
79#410—2632no—
80H(3,ℤ/4)D26311yescharacteristic, complemented
81C2×#41—2632no—
82#137—5262no—
83AGL(1,ℤ/8)—5262no—
84#135—5262no—
85C2×M16C2×D26311yescharacteristic
86C22×C8—2631no—
87#117—2631no—
88#117C2×D26312yes—
89C4⋊C8—5262no—
90#103—5262no—
91#102—5262no—
92#99—5264no—
93#41—5262no—
94#41—5262no—
95#41—5262no—
96#41—5262no—
97C2×Q8—2632no—
98C2×D4—2632no—
99C2×D4—5262no—
100C22×C4—5262no—
101C22×C4C22×D26311yescharacteristic
102Q16—5262no—
103SD16—5264no—
104D8—5262no—
105M16—22no—
106C2×C8—5262no—
107C2×C8—5261no—
108C2×C8D105212yes—
109C4⋊C4—22no—
110C4⋊C4—5261no—
111C22⋊C4—22no—
112C22⋊C4—2632no—
113C42—22no—
114C42—5261no—
115C23—5262no—
116C23D4×D26311yescharacteristic
117Q8—5262no—
118Q8—5262no—
119D4—5262no—
120D4—5262no—
121D4—10522no—
122D4—10522no—
123C2×C4—42no—
124C2×C4—5262no—
125C2×C4—5262no—
126C2×C4—10522no—
127C2×C4—10522no—
128C2×C4D4×D26312yes—
129C2×C4C2×D105211yescharacteristic
130C2×C4#1686237612yes—
131C2×C4#1686237711yescharacteristic
132C8—22no—
133C8—10521no—
134C22—41no—
135C22—10522no—
136C22—21042no—
137C22#2255444312yes—
138C22#2255444511yescharacteristic
139C4—82no—
140C4—10522no—
141C4—10522no—
142C4#2255444011yescharacteristic
143C4#2255445512yes—
144C4#2255445811yescharacteristic
145C2—22no—
146C2—21no—
147C2—21042no—
148C2#3068185611yescharacteristic
subgroupG/H
centerC4#22554458
commutator, cosocleC22×C4×C263C23
FrattiniC22×C4C22×D263
FittingH(3,ℤ/4)×C263C2
socleC2×C263#394
prime radical#30682738C2
hypercenterH(3,ℤ/4)D263
hypocenterC263#2053
LCSG ▷ C22×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C4 ◁ C22×C4 ◁ H(3,ℤ/4)

Complements

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

NH ≅ G/Ntype
2. #30681966C2semidirect
3. #30681932C2semidirect
4. #30681911C2semidirect
5. H(3,ℤ/4)×C263C2semidirect
74. C263#2053semidirect
80. H(3,ℤ/4)D263semidirect

Maximal subgroups

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

subgroupindex
#306827382
#306819662
#306819322
#306819112
H(3,ℤ/4)×C2632
#2053263