Finite Group Databasebeta

← #46782550

Subgroups — #46782550

Order 33664.

284 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 113 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#30681912C211yesmaximal, characteristic
3#30681896C212yesmaximal, complemented
4#30681710C212yesmaximal, complemented
5#413×C263C211yesmaximal, characteristic
6#22554477—22no—
7#22554477—22no—
8C2×#16862360C412yescomplemented
9C2×#16862360C2211yescharacteristic
10C22×C263⋊C8C412yescomplemented
11C22×C263⋊C8C2211yescharacteristic
12#22554429C2212yes—
13#22554385C414yes—
14#22554380—22no—
15C8×Dic263—22no—
16C2×#41×C263C2211yescharacteristic
17C2×M16×C263C2212yes—
18#101×C263C412yescomplemented
19#100×C263C412yescomplemented
20#16862360—24no—
21#16862360—22no—
22C2×C263⋊C8—22no—
23C2×C263⋊C8—22no—
24C2×C263⋊C8C2×C412yes—
25C2×C263⋊C8C2×C411yescharacteristic
26C2×C263⋊C8C2×C411yescharacteristic
27C2×C263⋊C8D412yes—
28C2×C263⋊C8D412yes—
29C4⋊Dic263—22no—
30C22⋊Dic263C2×C414yes—
31C4×Dic263—22no—
32#41×C263—22no—
33#41×C263—22no—
34C2×Q8×C263C2×C411yescharacteristic
35C2×D4×C263C2×C412yes—
36C2×D4×C263C2×C411yescharacteristic
37C22×C4×C263C2×C412yes—
38C22×C4×C263C2311yescharacteristic
39M16×C263—22no—
40M16×C263C2×C414yes—
41C2×C8×C263—22no—
42C2×Dic263—24no—
43C263⋊C8—22no—
44C263⋊C8C22⋊C411yescharacteristic
45C263⋊C8C22⋊C411yescharacteristic
46C263⋊C8C22⋊C412yes—
47C23×C263C4212yes—
48C23×C263C22×C411yescharacteristic
49Q8×C263—22no—
50D4×C263—24no—
51D4×C263—22no—
52C2×C4×C263—22no—
53C2×C4×C263—22no—
54C2×C4×C263C4212yes—
55C2×C4×C263C22×C411yescharacteristic
56C2×C4×C263C22×C411yescharacteristic
57C2×C4×C263C2×D412yes—
58C2×C4×C263#4112yes—
59C8×C263—24no—
60C22×C263—22no—
61C22×C263—41no—
62C22×C263—42no—
63C22×C263C2×C4211yescharacteristic
64C22×C263C4×D412yes—
65C4×C263—22no—
66C4×C263C2×C22⋊C411yescharacteristic
67C4×C263#11711yescharacteristic
68C4×C263C4×D412yes—
69Dic263—44no—
70C2×C263—22no—
71C2×C263—21no—
72C2×C263—42no—
73C2×C263C4×C22⋊C411yescharacteristic
74C263#175711yescharacteristic, complemented, Sylow
75#1757—2631nomaximal, Sylow
76C2×#131—2631no—
77#413D26311yescharacteristic
78#410—2631no—
79#405—2632no—
80#344—2632no—
81C2×#41C2×D26311yescharacteristic
82#131—5262no—
83#131—5262no—
84C2×M16—2632no—
85C2×M16—2631no—
86C2×M16C2×D26312yes—
87C22×C8—2631no—
88C22×C8—2632no—
89#117—2632no—
90#101Dic26312yescomplemented
91#100Dic26312yescomplemented
92#99—2634no—
93#97—5262no—
94C4×C8—5262no—
95#41—22no—
96#41—22no—
97C2×Q8C2×Dic26311yescharacteristic
98C2×D4C4×D26312yes—
99C2×D4C2×Dic26311yescharacteristic
100C22×C4C4×D26312yes—
101C22×C4C22×D26311yescharacteristic
102M16—22no—
103M16—5264no—
104M16—5262no—
105M16C2×Dic26314yes—
106C2×C8—22no—
107C2×C8—2631no—
108C2×C8—2631no—
109C2×C8—2632no—
110C2×C8—2632no—
111C2×C8—2632no—
112C2×C8—5262no—
113C2×C8—5262no—
114C4⋊C4—5262no—
115C22⋊C4—2634no—
116C42—5262no—
117C23C4×Dic26312yes—
118C23C2×C4×D26311yescharacteristic
119Q8—22no—
120D4—24no—
121D4—22no—
122C2×C4—22no—
123C2×C4—22no—
124C2×C4—5264no—
125C2×C4C4×Dic26312yes—
126C2×C4C2×C4×D26311yescharacteristic
127C2×C4C22×Dic26311yescharacteristic
128C2×C4D4×D26312yes—
129C2×C4#1686237512yes—
130C8—24no—
131C8—2631no—
132C8—2631no—
133C8—2632no—
134C8—5262no—
135C22—22no—
136C22—41no—
137C22—42no—
138C22C2×C4×Dic26311yescharacteristic
139C22(C22⋊D263)⋊C412yes—
140C4—22no—
141C4—10524no—
142C4C22⋊C4×D26311yescharacteristic
143C4#2255442611yescharacteristic
144C4D4×Dic26312yes—
145C2—22no—
146C2—21no—
147C2—42no—
148C2C22⋊C4×Dic26311yescharacteristic
subgroupG/H
centerC4C22⋊C4×D263
commutatorC22×C263C2×C42
FrattiniC22×C4C22×D263
Fitting#413×C263C2
socleC2×C263C4×C22⋊C4
prime radicalC2×#41×C263C22
cosocleC22×C4×C263C23
hypercenter#413D263
hypocenterC263#1757
LCSG ▷ C22×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C4 ◁ C22×C4 ◁ #413

Complements

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

NH ≅ G/Ntype
3. #30681896C2semidirect
4. #30681710C2semidirect
8. C2×#16862360C4semidirect
10. C22×C263⋊C8C4semidirect
18. #101×C263C4semidirect
19. #100×C263C4semidirect
74. C263#1757semidirect
90. #101Dic263semidirect
91. #100Dic263semidirect

Maximal subgroups

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

subgroupindex
C2×#225544772
#306819122
#306818962
#306817102
#413×C2632
#1757263