Finite Group Databasebeta

← #46784053

Subgroups — #46784053

Order 33664.

264 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 65 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#30681935C212yesmaximal, complemented
3#30681911C212yesmaximal, complemented
4#30681695C211yesmaximal, characteristic, complemented
5#424×C263C211yesmaximal, characteristic, complemented
6C2×#16862376C2212yes—
7#22554503—22no—
8#22554498—22no—
9#22554492—22no—
10#22554429C2212yes—
11#22554395—22no—
12#22554392—22no—
13#22554384—24no—
14C2×M16×C263C2211yescharacteristic
15C22×C8×C263C2211yescharacteristic
16#117×C263C2211yescharacteristic
17C4⋊C8×C263—22no—
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—
29C4⋊Dic263—22no—
30C22⋊Dic263—22no—
31C4×Dic263—22no—
32C22×C4×C263C2311yescharacteristic
33M16×C263—22no—
34C2×C8×C263—22no—
35C2×C8×C263—21no—
36C2×C8×C263D412yes—
37C4⋊C4×C263—21no—
38C22⋊C4×C263D412yes—
39C42×C263—21no—
40C22×D263—22no—
41Dic526—22no—
42Dic526—22no—
43D1052—22no—
44D1052—22no—
45C22⋊D263—42no—
46C22⋊D263—42no—
47C2×Dic263—22no—
48C2×Dic263—42no—
49C4×D263—42no—
50C4×D263—42no—
51C23×C263C2×D411yescharacteristic
52C2×C4×C263—22no—
53C2×C4×C263C2×D412yes—
54C2×C4×C263C2×D411yescharacteristic
55C2×C4×C263#4111yescharacteristic
56C2×C4×C263#4112yes—
57C8×C263—22no—
58C8×C263—41no—
59C22×C263—41no—
60C22×C263#12111yescharacteristic
61C22×C263#12112yes—
62C2×D263—42no—
63C2×D263—82no—
64C4×C263—42no—
65C4×C263#12011yescharacteristic
66C4×C263#12312yes—
67C4×C263#12411yescharacteristic
68Dic263—42no—
69Dic263—82no—
70C2×C263—22no—
71C2×C263—21no—
72C2×C263#39411yescharacteristic
73D263—82no—
74C263#205311yescharacteristic, complemented, Sylow
75#2053—2631nomaximal, Sylow
76#575—2631no—
77#424D26311yescharacteristic, complemented
78#416—2632no—
79#410—2632no—
80H(3,ℤ/4)—2631no—
81C2×#41—2632no—
82#137—5262no—
83AGL(1,ℤ/8)—5262no—
84#135—5262no—
85C2×M16C2×D26311yescharacteristic
86C22×C8C2×D26311yescharacteristic
87#117—2632no—
88#117C2×D26311yescharacteristic
89C4⋊C8—22no—
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—22no—
107C2×C8—21no—
108C2×C8C22⋊D26312yes—
109C4⋊C4—21no—
110C4⋊C4—5262no—
111C22⋊C4—5262no—
112C22⋊C4D105212yes—
113C42—21no—
114C42—5262no—
115C23—5262no—
116C23C2×D105211yescharacteristic
117Q8—5262no—
118Q8—5262no—
119D4—5262no—
120D4—5262no—
121D4—10522no—
122D4—10522no—
123C2×C4—22no—
124C2×C4—5262no—
125C2×C4—10522no—
126C2×C4—10522no—
127C2×C4—10522no—
128C2×C4D4×D26312yes—
129C2×C4C2×C22⋊D26311yescharacteristic
130C2×C4#1686237611yescharacteristic
131C2×C4#1686237712yes—
132C8—22no—
133C8—41no—
134C22—41no—
135C22—10522no—
136C22—21042no—
137C22#2255444411yescharacteristic
138C22#2255444512yes—
139C4—42no—
140C4—10522no—
141C4—21042no—
142C4#2255443811yescharacteristic
143C4#2255445512yes—
144C4#2255445911yescharacteristic
145C2—21no—
146C2—22no—
147C2—21042no—
148C2#3068185511yescharacteristic
subgroupG/H
centerC4#22554459
commutator, cosocleC22×C4×C263C23
FrattiniC22×C4C22×D263
Fitting#424×C263C2
socleC2×C263#394
prime radical#30682738C2
hypercenter#424D263
hypocenterC263#2053
LCSG ▷ C22×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C4 ◁ C22×C4 ◁ #424

Complements

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

NH ≅ G/Ntype
2. #30681935C2semidirect
3. #30681911C2semidirect
4. #30681695C2semidirect
5. #424×C263C2semidirect
74. C263#2053semidirect
77. #424D263semidirect

Maximal subgroups

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

subgroupindex
#306827382
#306819352
#306819112
#306816952
#424×C2632
#2053263