Finite Group Databasebeta

← #46784094

Subgroups — #46784094

Order 33664.

230 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 75 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#30681981C212yesmaximal
2#30681803C211yesmaximal, characteristic
3#30681707C211yesmaximal, characteristic
4#30681697C212yesmaximal
5#544×C263C211yesmaximal, characteristic
6C2×#16862360C2212yes—
7C2×C4⋊Dic263C2211yescharacteristic
8C2×C4×Dic263C2211yescharacteristic
9#22554403—22no—
10#22554401—22no—
11C263⋊#95—22no—
12C4⋊Q8×C263—22no—
13#125×C263—22no—
14C22⋊Q8×C263—22no—
15#117×C263C2212yes—
16C2×C4⋊C4×C263C2211yescharacteristic
17C22×Dic263—21no—
18C22×Dic263—21no—
19#16862360—22no—
20#16862360Q814yescomplemented
21C2×C263⋊C8—22no—
22C4⋊Dic263—22no—
23C4×Dic263—21no—
24C4×Dic263Q812yescomplemented
25C2×Q8×C263—22no—
26C22×C4×C263D412yes—
27C22×C4×C263C2311yescharacteristic
28C4⋊C4×C263—22no—
29C4⋊C4×C263—24no—
30C4⋊C4×C263—22no—
31C4⋊C4×C263D412yes—
32C4⋊C4×C263D412yes—
33C22⋊C4×C263—22no—
34C42×C263—22no—
35C2×Dic263—22no—
36C2×Dic263—41no—
37C2×Dic263—41no—
38C2×Dic263—42no—
39C2×Dic263—41no—
40C263⋊C8—24no—
41C23×C263C2×D411yescharacteristic
42Q8×C263—82no—
43C2×C4×C263—22no—
44C2×C4×C263—22no—
45C2×C4×C263—22no—
46C2×C4×C263—42no—
47C2×C4×C263C2×D412yes—
48C2×C4×C263C2×Q812yes—
49C2×C4×C263C2×Q811yescharacteristic
50C2×C4×C263#4111yescharacteristic
51C22×C263—21no—
52C22×C263—21no—
53C22×C263#12011yescharacteristic
54C22×C263C22⋊Q811yescharacteristic
55C22×C263C4⋊Q811yescharacteristic
56C4×C263—42no—
57C4×C263—42no—
58C4×C263—42no—
59C4×C263C22⋊Q812yes—
60C4×C263C4⋊Q812yes—
61Dic263—42no—
62Dic263—81no—
63C2×C263—21no—
64C2×C263—21no—
65C2×C263#39511yescharacteristic
66C2×C263#45411yescharacteristic
67C2×C263#45511yescharacteristic
68C263#206111yescharacteristic, complemented, Sylow
69#2061—2631nomaximal, Sylow
70#544D26311yescharacteristic
71#428—2632no—
72#382—2631no—
73#343—2631no—
74#339—2632no—
75C2×M16—2632no—
76C4⋊Q8—22no—
77#125—22no—
78C22⋊Q8—22no—
79#117C2×D26312yes—
80C2×C4⋊C4—2631no—
81C2×C4⋊C4C2×D26311yescharacteristic
82C2×C42—2631no—
83#107—5262no—
84#106—5262no—
85#95—5262no—
86C2×Q8—22no—
87C22×C4—5261no—
88C22×C4—5261no—
89C22×C4C22⋊D26312yes—
90C22×C4C22×D26311yescharacteristic
91M16—2634no—
92M16—5262no—
93C2×C8—5262no—
94C4⋊C4—22no—
95C4⋊C4—24no—
96C4⋊C4—22no—
97C4⋊C4—5262no—
98C4⋊C4C22⋊D26312yes—
99C4⋊C4C22⋊D26312yes—
100C22⋊C4—22no—
101C42—22no—
102C42—2632no—
103C42—5261no—
104C23C2×C22⋊D26311yescharacteristic
105Q8—82no—
106C2×C4—22no—
107C2×C4—22no—
108C2×C4—22no—
109C2×C4—42no—
110C2×C4—5262no—
111C2×C4—10521no—
112C2×C4—10521no—
113C2×C4—10522no—
114C2×C4—10521no—
115C2×C4C2×C22⋊D26312yes—
116C2×C4Q8×D26312yes—
117C2×C4Q8×D26311yescharacteristic
118C2×C4#1686237711yescharacteristic
119C8—5264no—
120C22—21no—
121C22—21no—
122C22#2255443911yescharacteristic
123C22#2255444611yescharacteristic
124C22#2255446811yescharacteristic
125C4—42no—
126C4—42no—
127C4—42no—
128C4—10522no—
129C4—21041no—
130C4#2255444612yes—
131C4#2255446812yes—
132C2—21no—
133C2—21no—
134C2#3068185711yescharacteristic
135C2#3068211111yescharacteristic
136C2#3068211611yescharacteristic
subgroupG/H
centerC22#22554439
commutator, cosocleC22×C4×C263C23
FrattiniC22×C4C22×D263
Fitting#544×C263C2
socleC22×C263#120
prime radicalC23×C263C2×D4
hypercenter#544D263
hypocenterC263#2061
LCSG ▷ C22×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C22 ◁ C22×C4 ◁ #544

Complements

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

NH ≅ G/Ntype
20. #16862360Q8semidirect
24. C4×Dic263Q8semidirect
68. C263#2061semidirect

Maximal subgroups

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

subgroupindex
#306819812
#306818032
#306817072
#306816972
#544×C2632
#2061263