Finite Group Databasebeta

← #46782791

Subgroups — #46782791

Order 33664.

260 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 89 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
1C2×#22554477C211yesmaximal, characteristic
2#30681974C212yesmaximal, complemented
3#30681912C211yesmaximal, characteristic
4#30681694C212yesmaximal, complemented
5#410×C263C211yesmaximal, characteristic
6#22554477—22no—
7#22554477—22no—
8C2×#16862360C412yescomplemented
9C2×#16862360C2211yescharacteristic
10C22×C263⋊C8C412yescomplemented
11C22×C263⋊C8C2211yescharacteristic
12#22554429C2212yes—
13#22554403—22no—
14#22554401—22no—
15#22554385—22no—
16C2×#41×C263C2211yescharacteristic
17#117×C263C2212yes—
18#99×C263—22no—
19#16862360—24no—
20#16862360—22no—
21C2×C263⋊C8—22no—
22C2×C263⋊C8—22no—
23C2×C263⋊C8C2×C412yes—
24C2×C263⋊C8C2×C411yescharacteristic
25C2×C263⋊C8C2×C411yescharacteristic
26C2×C263⋊C8D412yes—
27C2×C263⋊C8D412yes—
28C4⋊Dic263—22no—
29C22⋊Dic263—22no—
30C4×Dic263—22no—
31#41×C263—22no—
32#41×C263—22no—
33C2×Q8×C263Q811yescharacteristic
34C2×D4×C263D412yes—
35C2×D4×C263Q811yescharacteristic
36C22×C4×C263C2×C412yes—
37C22×C4×C263C2311yescharacteristic
38C4⋊C4×C263—22no—
39C22⋊C4×C263—22no—
40C42×C263—22no—
41C2×Dic263—42no—
42C263⋊C8—22no—
43C263⋊C8C22⋊C411yescharacteristic
44C263⋊C8C22⋊C411yescharacteristic
45C263⋊C8C22⋊C412yes—
46C23×C263C4⋊C412yes—
47C23×C263C2×D411yescharacteristic
48Q8×C263—22no—
49D4×C263—24no—
50D4×C263—22no—
51C2×C4×C263—22no—
52C2×C4×C263—22no—
53C2×C4×C263—42no—
54C2×C4×C263C4⋊C412yes—
55C2×C4×C263C22×C411yescharacteristic
56C2×C4×C263C2×D412yes—
57C2×C4×C263C2×Q811yescharacteristic
58C2×C4×C263#4112yes—
59C22×C263—22no—
60C22×C263—41no—
61C22×C263—42no—
62C22×C263C2×C4⋊C411yescharacteristic
63C22×C263#12112yes—
64C4×C263—22no—
65C4×C263—82no—
66C4×C263C2×C22⋊C411yescharacteristic
67C4×C263#11711yescharacteristic
68C4×C263C22⋊Q812yes—
69Dic263—82no—
70C2×C263—22no—
71C2×C263—21no—
72C2×C263—42no—
73C2×C263#38011yescharacteristic
74C263#181211yescharacteristic, complemented, Sylow
75#1812—2631nomaximal, Sylow
76C2×#131—2631no—
77#427—2632no—
78#410—2631no—
79#410D26311yescharacteristic
80H(3,ℤ/4)—2632no—
81C2×#41C2×D26311yescharacteristic
82#131—5262no—
83#131—5262no—
84C2×M16—2632no—
85C2×M16—2631no—
86C22×C8—2631no—
87C22×C8—2632no—
88#117—2632no—
89#117C2×D26312yes—
90#107—5262no—
91#106—5262no—
92#99—22no—
93#99—5262no—
94#41—22no—
95#41—22no—
96C2×Q8Dic52611yescharacteristic
97C2×D4C22⋊D26312yes—
98C2×D4Dic52611yescharacteristic
99C22×C4C4×D26312yes—
100C22×C4C22×D26311yescharacteristic
101M16—5264no—
102M16—5262no—
103C2×C8—2631no—
104C2×C8—2631no—
105C2×C8—2632no—
106C2×C8—2632no—
107C2×C8—2632no—
108C2×C8—5262no—
109C2×C8—5262no—
110C4⋊C4—22no—
111C4⋊C4—5262no—
112C22⋊C4—22no—
113C22⋊C4—5262no—
114C42—22no—
115C42—5262no—
116C23Dic263⋊C412yes—
117C23C2×C22⋊D26311yescharacteristic
118Q8—22no—
119D4—24no—
120D4—22no—
121C2×C4—22no—
122C2×C4—22no—
123C2×C4—42no—
124C2×C4—10522no—
125C2×C4Dic263⋊C412yes—
126C2×C4C2×C4×D26311yescharacteristic
127C2×C4D4×D26312yes—
128C2×C4C2×Dic52611yescharacteristic
129C2×C4#1686237512yes—
130C8—2631no—
131C8—2631no—
132C8—2632no—
133C8—5262no—
134C22—22no—
135C22—41no—
136C22—42no—
137C22C2×Dic263⋊C411yescharacteristic
138C22#2255444212yes—
139C4—22no—
140C4—82no—
141C4—21042no—
142C4C22⋊C4×D26311yescharacteristic
143C4#2255442611yescharacteristic
144C4#2255444712yes—
145C2—22no—
146C2—21no—
147C2—42no—
148C2#3068179611yescharacteristic
subgroupG/H
centerC4#22554426
commutatorC2×C4×C263C22×C4
FrattiniC22×C4C22×D263
Fitting#410×C263C2
socleC2×C263#380
prime radicalC2×#41×C263C22
cosocleC22×C4×C263C23
hypercenter#410D263
hypocenterC263#1812
LCSG ▷ C2×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C4 ◁ C22×C4 ◁ #410

Complements

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

NH ≅ G/Ntype
2. #30681974C2semidirect
4. #30681694C2semidirect
8. C2×#16862360C4semidirect
10. C22×C263⋊C8C4semidirect
74. C263#1812semidirect

Maximal subgroups

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

subgroupindex
C2×#225544772
#306819742
#306819122
#306816942
#410×C2632
#1812263