Finite Group Databasebeta

← #27194436

Subgroups — #27194436

Order 13184.

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

normal subgroups only

This group has 230 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#20268539C211yesmaximal, characteristic, complemented
2#20268178C212yesmaximal, complemented
3#20267533C211yesmaximal, characteristic, complemented
4#20267530C212yesmaximal, complemented
5#490×C103C211yesmaximal, characteristic, complemented
6C2×#13110093—22no—
7C2×#13110090—22no—
8#15693009C2212yes—
9#15693006—22no—
10#15692999—22no—
11#15692996—22no—
12#15692932C2212yes—
13#127×C103C2211yescharacteristic
14#125×C103C2211yescharacteristic
15#102×C103—22no—
16#97×C103C2211yescharacteristic
17C2×Dic206D412yes—
18C2×D412—22no—
19C2×D412D412yes—
20C2×C4×D103—22no—
21#13110093—44no—
22#13110090—44no—
23C2×C103⋊C8—22no—
24Dic103⋊C4—22no—
25(C2×D103)⋊C4—22no—
26(C2×D103)⋊C4—22no—
27(C2×D103)⋊C4—22no—
28C2×D4×C103—21no—
29C2×D4×C103—22no—
30C2×C8×C103—21no—
31C4⋊C4×C103—22no—
32C4⋊C4×C103D412yes—
33C42×C103C2311yescharacteristic
34C23×C103—41no—
35C22×D103—22no—
36D4×C103—42no—
37D4×C103—42no—
38D4×C103—42no—
39C2×C4×C103—22no—
40C2×C4×C103C2×D412yes—
41C2×C4×C103C2×D411yescharacteristic
42C2×Dic103—22no—
43D412—42no—
44D412—82no—
45C4×D103—82no—
46Dic206—42no—
47C8×C103—41no—
48C103⋊C8—24no—
49C22×C103—82no—
50C22×C103—81no—
51C22×C103#12011yescharacteristic
52C2×D103—42no—
53C2×D103—42no—
54C2×D103—42no—
55C4×C103—22no—
56C4×C103—21no—
57C4×C103—42no—
58Dic103—42no—
59C2×C103—161no—
60C2×C103#45312yes—
61C2×C103#45411yescharacteristic
62D103—82no—
63#1656—1031nomaximal, Sylow
64C103#165611yescharacteristic, complemented, Sylow
65#562—1031no—
66#496—1032no—
67#490D10311yescharacteristic, complemented
68#330—1031no—
69#329—1032no—
70C2×SD16—2062no—
71C2×D8—2062no—
72#127C2×D10311yescharacteristic
73#125C2×D10311yescharacteristic
74#124—1032no—
75#123—2062no—
76C22⋊Q8—2062no—
77#121—2062no—
78#102—22no—
79#97—1032no—
80#97C2×D10311yescharacteristic
81C2×Q8—1032no—
82C2×D4—22no—
83C2×D4—21no—
84C2×D4—1032no—
85C2×D4—2062no—
86C22×C4—2062no—
87SD16—4124no—
88D8—4124no—
89C2×C8—21no—
90C2×C8—2062no—
91C4⋊C4—22no—
92C4⋊C4—2062no—
93C4⋊C4C22⋊D10312yes—
94C22⋊C4—2062no—
95C22⋊C4—2062no—
96C22⋊C4—2062no—
97C42C22×D10311yescharacteristic
98C23—41no—
99C23—2062no—
100Q8—4122no—
101D4—42no—
102D4—42no—
103D4—42no—
104D4—8242no—
105D4—4122no—
106C2×C4—22no—
107C2×C4—8242no—
108C2×C4—2062no—
109C2×C4D4×D10312yes—
110C2×C4C2×C22⋊D10311yescharacteristic
111C8—41no—
112C8—2064no—
113C22—82no—
114C22—81no—
115C22—4122no—
116C22—4122no—
117C22—4122no—
118C22#1569298911yescharacteristic
119C4—22no—
120C4—21no—
121C4—42no—
122C4—4122no—
123C2—161no—
124C2—8242no—
125C2#2026795712yes—
126C2#2026796311yescharacteristic
subgroupG/H
centerC22#15692989
commutator, cosocleC42×C103C23
FrattiniC42C22×D103
Fitting#490×C103C2
socleC22×C103#120
hypercenter#490D103
hypocenterC103#1656
LCSG ▷ C42×C103 ▷ C22×C103 ▷ C103
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
1. #20268539C2semidirect
2. #20268178C2semidirect
3. #20267533C2semidirect
4. #20267530C2semidirect
5. #490×C103C2semidirect
64. C103#1656semidirect
67. #490D103semidirect

Maximal subgroups

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

subgroupindex
#202685392
#202681782
#202675332
#202675302
#490×C1032
#1656103