Finite Group Databasebeta

← #46784050

Subgroups — #46784050

Order 33664.

264 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 67 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#30681966C211yesmaximal, characteristic, complemented
2#30681934C212yesmaximal, complemented
3#30681912C212yesmaximal, complemented
4#30681695C211yesmaximal, characteristic, complemented
5#575×C263C211yesmaximal, characteristic
6C22×C263⋊C8C2211yescharacteristic
7#22554429C2212yes—
8#22554429C2211yescharacteristic
9Dic263⋊C8—22no—
10#22554394—22no—
11#22554391—22no—
12#22554385—24no—
13C2×#41×C263C2212yes—
14#137×C263—22no—
15AGL(1,ℤ/8)×C263—22no—
16#135×C263—22no—
17C2×M16×C263C2211yescharacteristic
18C2×C263⋊C8—22no—
19C2×C263⋊C8—21no—
20C4⋊Dic263—22no—
21C4⋊Dic263—21no—
22C22⋊Dic263—22no—
23C22⋊Dic263D412yes—
24C4×Dic263—21no—
25C4×Dic263—22no—
26#41×C263—22no—
27#41×C263—22no—
28#41×C263—22no—
29#41×C263—22no—
30C2×Q8×C263D412yes—
31C2×D4×C263—22no—
32C2×D4×C263D412yes—
33C22×C4×C263—22no—
34C22×C4×C263C2311yescharacteristic
35Q16×C263—22no—
36SD16×C263—24no—
37D8×C263—22no—
38M16×C263—22no—
39C2×C8×C263D412yes—
40C2×Dic263—22no—
41C2×Dic263—42no—
42C263⋊C8—41no—
43C23×C263—22no—
44C23×C263C2×D411yescharacteristic
45Q8×C263—22no—
46Q8×C263—22no—
47D4×C263—22no—
48D4×C263—22no—
49D4×C263—42no—
50D4×C263—42no—
51C2×C4×C263—22no—
52C2×C4×C263—42no—
53C2×C4×C263—42no—
54C2×C4×C263C2×D412yes—
55C2×C4×C263C2×D411yescharacteristic
56C2×C4×C263#4111yescharacteristic
57C2×C4×C263#4112yes—
58C8×C263—22no—
59C22×C263—41no—
60C22×C263—42no—
61C22×C263—82no—
62C22×C263#12111yescharacteristic
63C22×C263#12112yes—
64C4×C263—42no—
65C4×C263#12011yescharacteristic
66C4×C263#12312yes—
67C4×C263#12411yescharacteristic
68Dic263—42no—
69Dic263—82no—
70C2×C263—21no—
71C2×C263—22no—
72C2×C263—82no—
73C2×C263#39411yescharacteristic
74C263#205311yescharacteristic, complemented, Sylow
75#2053—2631nomaximal, Sylow
76#575D26311yescharacteristic
77#424—2631no—
78#416—2632no—
79#410—2632no—
80H(3,ℤ/4)—2631no—
81C2×#41C2×D26312yes—
82#137—22no—
83AGL(1,ℤ/8)—22no—
84#135—22no—
85C2×M16C2×D26311yescharacteristic
86C22×C8—2631no—
87#117—2631no—
88#117—2632no—
89C4⋊C8—5262no—
90#103—5262no—
91#102—5262no—
92#99—5264no—
93#41—22no—
94#41—22no—
95#41—22no—
96#41—22no—
97C2×Q8C22⋊D26312yes—
98C2×D4—22no—
99C2×D4C22⋊D26312yes—
100C22×C4—22no—
101C22×C4C22×D26311yescharacteristic
102Q16—22no—
103SD16—24no—
104D8—22no—
105M16—22no—
106C2×C8—5262no—
107C2×C8—5261no—
108C2×C8C22⋊D26312yes—
109C4⋊C4—5261no—
110C4⋊C4—5262no—
111C22⋊C4—2632no—
112C22⋊C4—5262no—
113C42—5261no—
114C42—5262no—
115C23—22no—
116C23D4×D26311yescharacteristic
117Q8—22no—
118Q8—22no—
119D4—22no—
120D4—22no—
121D4—42no—
122D4—42no—
123C2×C4—22no—
124C2×C4—42no—
125C2×C4—42no—
126C2×C4—5262no—
127C2×C4—10522no—
128C2×C4C2×C22⋊D26312yes—
129C2×C4C2×C22⋊D26311yescharacteristic
130C2×C4#1686237511yescharacteristic
131C2×C4#1686237512yes—
132C8—22no—
133C8—10521no—
134C22—41no—
135C22—42no—
136C22—82no—
137C22#2255444111yescharacteristic
138C22#2255444212yes—
139C4—42no—
140C4—10522no—
141C4—21042no—
142C4#2255443911yescharacteristic
143C4#2255445112yes—
144C4#2255445711yescharacteristic
145C2—21no—
146C2—22no—
147C2—82no—
148C2#3068185211yescharacteristic
subgroupG/H
centerC4#22554457
commutator, cosocleC22×C4×C263C23
FrattiniC22×C4C22×D263
Fitting, prime radical#575×C263C2
socleC2×C263#394
hypercenter#575D263
hypocenterC263#2053
LCSG ▷ C22×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C4 ◁ C22×C4 ◁ #575

Complements

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

NH ≅ G/Ntype
1. #30681966C2semidirect
2. #30681934C2semidirect
3. #30681912C2semidirect
4. #30681695C2semidirect
74. C263#2053semidirect

Maximal subgroups

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

subgroupindex
#306819662
#306819342
#306819122
#306816952
#575×C2632
#2053263