Finite Group Databasebeta

← #46781885

Subgroups — #46781885

Order 33664.

206 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 206 conjugacy classes of subgroups — too many to draw. Only its 57 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#30682668C211yesmaximal, characteristic
2#30682230C212yesmaximal
3#30681687C211yesmaximal, characteristic
4#30681670C212yesmaximal
5#494×C263C211yesmaximal, characteristic
6#22554469—22no—
7#22554468—22no—
8C4×Dic526C2212yes—
9#22554435—22no—
10#22554403—22no—
11C4⋊(C263⋊C8)C2212yes—
12#22554393—22no—
13C2×Q16×C263—22no—
14C4⋊Q8×C263C2211yescharacteristic
15C4⋊Q8×C263C2211yescharacteristic
16C4×C8×C263C2211yescharacteristic
17C2×Dic526—22no—
18C2×Dic526D412yes—
19C2×C263⋊C8—22no—
20C4⋊Dic263D412yes—
21Dic263⋊C4—24no—
22Dic263⋊C4—22no—
23C4×Dic263—22no—
24C4×Dic263—22no—
25C2×Q8×C263—21no—
26C2×Q8×C263D412yes—
27Q16×C263—44no—
28C2×C8×C263—21no—
29C4⋊C4×C263—22no—
30C4⋊C4×C263—22no—
31C42×C263C2311yescharacteristic
32Dic526—22no—
33Dic526—82no—
34Dic526Q1614yescomplemented
35C2×Dic263—22no—
36C2×Dic263—22no—
37C263⋊C8—42no—
38Q8×C263—42no—
39Q8×C263—42no—
40C2×C4×C263—22no—
41C2×C4×C263—41no—
42C2×C4×C263C2×D412yes—
43C2×C4×C263C2×D411yescharacteristic
44C8×C263—22no—
45C22×C263#12011yescharacteristic
46C4×C263—21no—
47C4×C263—42no—
48C4×C263—81no—
49C4×C263C2×Q1612yes—
50C4×C263#13712yes—
51Dic263—24no—
52Dic263—42no—
53C2×C263#45112yes—
54C2×C263#45311yescharacteristic
55C263#163311yescharacteristic, complemented, Sylow
56#1633—2631nomaximal, Sylow
57Q82—2631no—
58#494D26311yescharacteristic
59#477—2632no—
60#333—2631no—
61Q8⋊C8—2632no—
62C2×Q16—22no—
63C4⋊Q8—5262no—
64C4⋊Q8—5262no—
65C4⋊Q8C2×D26311yescharacteristic
66C4⋊Q8C2×D26311yescharacteristic
67C4×Q8—2632no—
68C4×Q8—5262no—
69#107—5262no—
70C4⋊C8—2632no—
71#103—5262no—
72C4×C8C2×D26311yescharacteristic
73C2×Q8—21no—
74C2×Q8—2632no—
75C2×Q8—5262no—
76C2×Q8C22⋊D26312yes—
77Q16—44no—
78C2×C8—21no—
79C2×C8—5262no—
80C4⋊C4—22no—
81C4⋊C4—22no—
82C4⋊C4—2632no—
83C4⋊C4—5264no—
84C4⋊C4—5262no—
85C42—5262no—
86C42—5262no—
87C42C22×D26311yescharacteristic
88Q8—42no—
89Q8—42no—
90Q8—2634no—
91Q8—5262no—
92Q8—21042no—
93C2×C4—22no—
94C2×C4—41no—
95C2×C4—5262no—
96C2×C4—5262no—
97C2×C4D4×D26312yes—
98C2×C4C2×C22⋊D26311yescharacteristic
99C8—22no—
100C8—10522no—
101C22#2255443811yescharacteristic
102C4—21no—
103C4—42no—
104C4—81no—
105C4—5264no—
106C4—10522no—
107C4Q16×D26312yes—
108C4#2255450212yes—
109C2#3068209212yes—
110C2#3068210511yescharacteristic
subgroupG/H
centerC22#22554438
commutator, cosocleC42×C263C23
FrattiniC42C22×D263
Fitting#494×C263C2
socle, prime radicalC22×C263#120
hypercenter#494D263
hypocenterC263#1633
LCSG ▷ C42×C263 ▷ C22×C263 ▷ C263
UCSC1 ◁ C22 ◁ C42 ◁ #494

Complements

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

NH ≅ G/Ntype
34. Dic526Q16semidirect
55. C263#1633semidirect

Maximal subgroups

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

subgroupindex
#306826682
#306822302
#306816872
#306816702
#494×C2632
#1633263