Finite Group Databasebeta

← #46781823

Subgroups — #46781823

Order 33664.

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

normal subgroups only

This group has 228 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, complemented
2#30682135C212yesmaximal
3#30681687C211yesmaximal, characteristic, complemented
4#30681670C212yesmaximal, complemented
5#492×C263C211yesmaximal, characteristic
6C2×#16862364—22no—
7#22554469—22no—
8#22554468—22no—
9C4×Dic526C2212yes—
10#22554435—22no—
11C4⋊(C263⋊C8)C2212yes—
12#22554391—22no—
13C2×SD16×C263—22no—
14C4⋊Q8×C263C2211yescharacteristic
15#127×C263C2211yescharacteristic
16C4×C8×C263C2211yescharacteristic
17C2×Dic526—22no—
18C2×Dic526D412yes—
19#16862364—44no—
20C2×C263⋊C8—22no—
21C4⋊Dic263D412yes—
22Dic263⋊C4—24no—
23Dic263⋊C4—22no—
24C4×Dic263—22no—
25C4×Dic263—22no—
26C2×Q8×C263D412yes—
27C2×D4×C263—22no—
28C2×D4×C263—21no—
29SD16×C263—44no—
30C2×C8×C263—21no—
31C4⋊C4×C263—22no—
32C42×C263C2311yescharacteristic
33Dic526—22no—
34Dic526—82no—
35Dic526SD1614yescomplemented
36C2×Dic263—22no—
37C2×Dic263—22no—
38C263⋊C8—42no—
39C23×C263—41no—
40Q8×C263—42no—
41D4×C263—42no—
42D4×C263—42no—
43D4×C263—42no—
44C2×C4×C263—22no—
45C2×C4×C263C2×D412yes—
46C2×C4×C263C2×D411yescharacteristic
47C8×C263—22no—
48C22×C263—82no—
49C22×C263—81no—
50C22×C263#12011yescharacteristic
51C4×C263—21no—
52C4×C263—42no—
53C4×C263C2×SD1612yes—
54C4×C263#13712yes—
55Dic263—24no—
56Dic263—42no—
57C2×C263—161no—
58C2×C263#44812yes—
59C2×C263#45311yescharacteristic
60C263#162311yescharacteristic, complemented, Sylow
61#1623—2631nomaximal, Sylow
62Q82—2631no—
63#492D26311yescharacteristic
64#460—2632no—
65#333—2631no—
66Q8⋊C8—2632no—
67C2×SD16—22no—
68C2×SD16—5262no—
69C4⋊Q8—5262no—
70C4⋊Q8—5262no—
71C4⋊Q8C2×D26311yescharacteristic
72#127C2×D26311yescharacteristic
73C4×Q8—2632no—
74C4×Q8—5262no—
75C4⋊C8—2632no—
76#102—5262no—
77C4×C8C2×D26311yescharacteristic
78C2×Q8—2632no—
79C2×Q8—5262no—
80C2×Q8C22⋊D26312yes—
81C2×D4—22no—
82C2×D4—21no—
83SD16—44no—
84SD16—10524no—
85C2×C8—21no—
86C2×C8—5262no—
87C4⋊C4—22no—
88C4⋊C4—2632no—
89C4⋊C4—5264no—
90C4⋊C4—5262no—
91C42—5262no—
92C42—5262no—
93C42C22×D26311yescharacteristic
94C23—41no—
95Q8—42no—
96Q8—2634no—
97Q8—5262no—
98Q8—21042no—
99D4—42no—
100D4—42no—
101D4—42no—
102C2×C4—22no—
103C2×C4—5262no—
104C2×C4—5262no—
105C2×C4D4×D26312yes—
106C2×C4C2×C22⋊D26311yescharacteristic
107C8—22no—
108C8—10522no—
109C22—82no—
110C22—81no—
111C22#2255443811yescharacteristic
112C4—21no—
113C4—42no—
114C4—5264no—
115C4—10522no—
116C4SD16×D26312yes—
117C4#2255449912yes—
118C2—161no—
119C2#3068207512yes—
120C2#3068210511yescharacteristic
subgroupG/H
centerC22#22554438
commutator, cosocleC42×C263C23
FrattiniC42C22×D263
Fitting#492×C263C2
socleC22×C263#120
prime radical#127×C263C22
hypercenter#492D263
hypocenterC263#1623
LCSG ▷ C42×C263 ▷ C22×C263 ▷ C263
UCSC1 ◁ C22 ◁ C42 ◁ #492

Complements

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

NH ≅ G/Ntype
1. #30682668C2semidirect
3. #30681687C2semidirect
4. #30681670C2semidirect
35. Dic526SD16semidirect
60. C263#1623semidirect

Maximal subgroups

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

subgroupindex
#306826682
#306821352
#306816872
#306816702
#492×C2632
#1623263