Finite Group Databasebeta

← #46782056

Subgroups — #46782056

Order 33664.

196 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 45 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#30682688C211yesmaximal, characteristic
2#30682344C212yesmaximal, complemented
3#30681679C212yesmaximal, complemented
4#30681678C211yesmaximal, characteristic
5#497×C263C211yesmaximal, characteristic
6#22554468—21no—
7#22554463—22no—
8#22554462C2212yes—
9#22554451—21no—
10#22554447—22no—
11#22554403—22no—
12#22554401—22no—
13#22554381C2212yes—
14C2×Q16×C263—21no—
15C2×SD16×C263—21no—
16C4⋊Q8×C263C2211yescharacteristic
17#124×C263C2211yescharacteristic
18#97×C263C2211yescharacteristic
19C2×Dic526—21no—
20C22×Dic263—21no—
21C2×C263⋊C8—22no—
22C4⋊Dic263D412yes—
23C4⋊Dic263D412yes—
24Dic263⋊C4—22no—
25Dic263⋊C4—22no—
26Dic263⋊C4—22no—
27C22⋊Dic263—22no—
28C22⋊Dic263—21no—
29C4×Dic263—21no—
30C2×Q8×C263—21no—
31C2×Q8×C263D411yescharacteristic
32C2×D4×C263D411yescharacteristic
33Q16×C263—42no—
34SD16×C263—42no—
35C2×C8×C263—21no—
36C4⋊C4×C263—22no—
37C22⋊C4×C263—22no—
38C42×C263C2311yescharacteristic
39Dic526—81no—
40C2×Dic263—22no—
41C2×Dic263—22no—
42C2×Dic263—81no—
43C263⋊C8—24no—
44C23×C263—21no—
45Q8×C263—41no—
46Q8×C263—41no—
47Q8×C263—41no—
48D4×C263—41no—
49C2×C4×C263—21no—
50C2×C4×C263—41no—
51C2×C4×C263C2×D412yes—
52C2×C4×C263C2×D411yescharacteristic
53C8×C263—22no—
54C22×C263—41no—
55C22×C263—42no—
56C22×C263#12011yescharacteristic
57C4×C263—21no—
58C4×C263—22no—
59C4×C263—41no—
60C4×C263—81no—
61Dic263—42no—
62Dic263—42no—
63C2×C263—81no—
64C2×C263#45311yescharacteristic
65C2×C263#45612yes—
66C263#166011yescharacteristic, complemented, Sylow
67#1660—2631nomaximal, Sylow
68#563—2631no—
69#501—2632no—
70#497D26311yescharacteristic
71#330—2632no—
72#329—2631no—
73C2×Q16—21no—
74C2×SD16—21no—
75C4⋊Q8—5261no—
76C4⋊Q8C2×D26311yescharacteristic
77#126—5262no—
78#125—2632no—
79#124C2×D26311yescharacteristic
80#123—5261no—
81C22⋊Q8—5262no—
82#107—5262no—
83#106—5262no—
84#97—2632no—
85#97C2×D26311yescharacteristic
86C2×Q8—21no—
87C2×Q8—5261no—
88C2×Q8C22⋊D26311yescharacteristic
89C2×D4C22⋊D26311yescharacteristic
90C22×C4—5261no—
91Q16—42no—
92SD16—42no—
93C2×C8—21no—
94C2×C8—5262no—
95C4⋊C4—22no—
96C4⋊C4—2632no—
97C4⋊C4—2632no—
98C4⋊C4—5262no—
99C4⋊C4—5262no—
100C4⋊C4—5262no—
101C22⋊C4—22no—
102C22⋊C4—5262no—
103C22⋊C4—5261no—
104C42—5261no—
105C42C22×D26311yescharacteristic
106C23—21no—
107Q8—41no—
108Q8—41no—
109Q8—41no—
110Q8—21041no—
111D4—41no—
112C2×C4—21no—
113C2×C4—41no—
114C2×C4—5262no—
115C2×C4—5262no—
116C2×C4—21041no—
117C2×C4D4×D26312yes—
118C2×C4C2×C22⋊D26311yescharacteristic
119C8—22no—
120C8—5264no—
121C22—42no—
122C22—41no—
123C22#2255443811yescharacteristic
124C4—22no—
125C4—21no—
126C4—41no—
127C4—81no—
128C4—10522no—
129C4—10522no—
130C2—81no—
131C2#3068210511yescharacteristic
132C2#3068211912yes—
subgroupG/H
centerC22#22554438
commutator, cosocleC42×C263C23
FrattiniC42C22×D263
Fitting#497×C263C2
socleC22×C263#120
prime radicalC2×D4×C263D4
hypercenter#497D263
hypocenterC263#1660
LCSG ▷ C42×C263 ▷ C22×C263 ▷ C263
UCSC1 ◁ C22 ◁ C42 ◁ #497

Complements

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

NH ≅ G/Ntype
2. #30682344C2semidirect
3. #30681679C2semidirect
66. C263#1660semidirect

Maximal subgroups

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

subgroupindex
#306826882
#306823442
#306816792
#306816782
#497×C2632
#1660263