Finite Group Databasebeta

← #46781340

Subgroups — #46781340

Order 33664.

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

normal subgroups only

This group has 226 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#30682494C211yesmaximal, characteristic
2#30681890C212yesmaximal
3#30681680C211yesmaximal, characteristic, complemented
4#30681679C212yesmaximal, complemented
5#330×C263C211yesmaximal, characteristic, complemented
6C2×#16862359—22no—
7#22554469C412yes—
8#22554462C2211yescharacteristic
9#22554448—22no—
10#22554435—22no—
11#22554428C412yes—
12C42×D263C2211yescharacteristic
13#22554381C2212yes—
14C8×Dic263—22no—
15#125×C263C2211yescharacteristic
16#97×C263C2212yes—
17C2×Dic526—22no—
18C2×C4×D263C2×C411yescharacteristic
19C2×C4×D263D412yes—
20#16862359—28no—
21C2×C263⋊C8—22no—
22C4⋊Dic263C2×C412yes—
23Dic263⋊C4—22no—
24Dic263⋊C4—22no—
25(C2×D263)⋊C4—22no—
26C4×Dic263—22no—
27C4×Dic263C2×C411yescharacteristic
28C4×Dic263D412yes—
29C2×C8×C263—22no—
30C4⋊C4×C263—22no—
31C4⋊C4×C263C2×C412yes—
32C42×C263C2311yescharacteristic
33C22×D263C22⋊C411yescharacteristic
34Dic526—44no—
35C2×Dic263—22no—
36C2×Dic263C22⋊C411yescharacteristic
37C2×Dic263C22⋊C412yes—
38C4×D263—22no—
39C4×D263—24no—
40C263⋊C8—24no—
41C2×C4×C263—22no—
42C2×C4×C263C22×C411yescharacteristic
43C2×C4×C263C2×D412yes—
44C8×C263—24no—
45C22×C263C2×C22⋊C411yescharacteristic
46C2×D263—21no—
47C2×D263—22no—
48C4×C263—21no—
49C4×C263—22no—
50C4×C263—42no—
51Dic263—42no—
52Dic263#10112yes—
53Dic263#10414yes—
54C2×C263C2×#10111yescharacteristic
55C2×C263C2×#10412yes—
56D263—41no—
57C263#152611yescharacteristic, complemented, Sylow
58#1526—2631nomaximal, Sylow
59#533—2631no—
60C4×M16—2632no—
61#330—2631no—
62#330—2632no—
63#330D26311yescharacteristic, complemented
64C2×M16—5262no—
65C4⋊Q8—2632no—
66#125—2631no—
67#125C2×D26311yescharacteristic
68C22⋊Q8—5262no—
69C4×Q8—5262no—
70#117—2632no—
71C2×C42—2631no—
72#97—2632no—
73#97C2×D26312yes—
74C4×C8—5262no—
75C2×Q8—5262no—
76C22×C4—2631no—
77C22×C4—2632no—
78M16—5268no—
79C2×C8—22no—
80C2×C8—5262no—
81C4⋊C4—22no—
82C4⋊C4—2632no—
83C4⋊C4—5262no—
84C4⋊C4—5262no—
85C4⋊C4C4×D26312yes—
86C22⋊C4—5262no—
87C42—2631no—
88C42—2632no—
89C42—5262no—
90C42C22×D26311yescharacteristic
91C23—2631no—
92Q8—10524no—
93C2×C4—22no—
94C2×C4—2631no—
95C2×C4—2632no—
96C2×C4—5264no—
97C2×C4—5262no—
98C2×C4—5262no—
99C2×C4C2×C4×D26311yescharacteristic
100C2×C4D4×D26312yes—
101C8—24no—
102C8—5264no—
103C22—5261no—
104C22—5262no—
105C22C22⋊C4×D26311yescharacteristic
106C4—21no—
107C4—22no—
108C4—42no—
109C4—2632no—
110C4—2634no—
111C4—10522no—
112C2—10521no—
113C2#101×D26311yescharacteristic
114C2#104×D26312yes—
subgroupG/H
centerC22C22⋊C4×D263
commutatorC2×C4×C263C22×C4
FrattiniC42C22×D263
Fitting#330×C263C2
socleC22×C263C2×C22⋊C4
prime radicalC22×D263C22⋊C4
cosocleC42×C263C23
hypercenter#330D263
hypocenterC263#1526
LCSG ▷ C2×C4×C263 ▷ C22×C263 ▷ C263
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
3. #30681680C2semidirect
4. #30681679C2semidirect
5. #330×C263C2semidirect
57. C263#1526semidirect
63. #330D263semidirect

Maximal subgroups

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

subgroupindex
#306824942
#306818902
#306816802
#306816792
#330×C2632
#1526263