Finite Group Databasebeta

← #27193803

Subgroups — #27193803

Order 13184.

246 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 67 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#20268339C211yesmaximal, characteristic
2#20267843C212yesmaximal, complemented
3#20267539C212yesmaximal, complemented
4#20267535C211yesmaximal, characteristic, complemented
5#331×C103C211yesmaximal, characteristic, complemented
6C2×#13110104C412yes—
7#15693021C2211yescharacteristic
8#15693008C412yes—
9#15692992—22no—
10D4×Dic103—22no—
11C42×D103C2211yescharacteristic
12C4⋊(C103⋊C8)C2212yes—
13(C2×D103)⋊C8—22no—
14C8×Dic103—22no—
15#127×C103C2211yescharacteristic
16C4⋊C8×C103C2212yes—
17#13110104—44no—
18C2×Dic206C2×C412yes—
19C2×C22⋊D103—22no—
20C22×Dic103—22no—
21C2×C4×D103C2×C411yescharacteristic
22C2×C4×D103D412yes—
23C2×C103⋊C8—22no—
24C4⋊Dic103—22no—
25C22⋊Dic103—24no—
26C4×Dic103C2×C411yescharacteristic
27C4×Dic103D412yes—
28C2×D4×C103—22no—
29C2×D4×C103C2×C412yes—
30C2×C8×C103—22no—
31C42×C103C2311yescharacteristic
32C23×C103—22no—
33C22×D103C22⋊C411yescharacteristic
34D4×C103—42no—
35D4×C103—42no—
36D4×C103—42no—
37C2×C4×C103C22×C411yescharacteristic
38C2×C4×C103C2×D412yes—
39C22⋊D103—44no—
40C2×Dic103—22no—
41C2×Dic103—44no—
42C2×Dic103C22⋊C412yes—
43C2×Dic103C22⋊C411yescharacteristic
44C4×D103—22no—
45C4×D103—22no—
46C4×D103—22no—
47Dic206—42no—
48C8×C103—42no—
49C103⋊C8—42no—
50C22×C103—42no—
51C22×C103—44no—
52C22×C103C2×C22⋊C411yescharacteristic
53C2×D103—21no—
54C2×D103—22no—
55C4×C103—21no—
56C4×C103#13512yes—
57C4×C103#13512yes—
58Dic103—22no—
59Dic103—42no—
60Dic103#10012yes—
61C2×C103—82no—
62C2×C103C2×#10011yescharacteristic
63C2×C103#41612yes—
64D103—41no—
65#1543—1031nomaximal, Sylow
66C103#154311yescharacteristic, complemented, Sylow
67#532—1031no—
68#431—1032no—
69#333—1032no—
70#331—1031no—
71#331D10311yescharacteristic, complemented
72C2×#41—1032no—
73C4⋊Q8—1031no—
74#127C2×D10311yescharacteristic
75#124—1032no—
76#121—2062no—
77C4×D4—2062no—
78C2×C42—1031no—
79C4⋊C8—1032no—
80C4⋊C8C2×D10312yes—
81C22⋊C8—2062no—
82C4×C8—2062no—
83#41—4124no—
84C2×Q8—1032no—
85C2×D4—22no—
86C2×D4—2062no—
87C2×D4C4×D10312yes—
88C22×C4—1031no—
89C22×C4—1032no—
90C22×C4—2062no—
91C2×C8—22no—
92C2×C8—2062no—
93C4⋊C4—2062no—
94C22⋊C4—2064no—
95C42—1031no—
96C42—1032no—
97C42C22×D10311yescharacteristic
98C23—22no—
99C23—1031no—
100Q8—4122no—
101D4—42no—
102D4—42no—
103D4—42no—
104D4—4124no—
105C2×C4—1031no—
106C2×C4—1032no—
107C2×C4—4124no—
108C2×C4—2062no—
109C2×C4—2062no—
110C2×C4—2062no—
111C2×C4—2062no—
112C2×C4C2×C4×D10311yescharacteristic
113C2×C4D4×D10312yes—
114C8—42no—
115C8—4122no—
116C22—44no—
117C22—42no—
118C22—2062no—
119C22—2061no—
120C22C22⋊C4×D10311yescharacteristic
121C4—21no—
122C4—1032no—
123C4—4122no—
124C4—2062no—
125C4#1569304012yes—
126C4#1569304212yes—
127C2—82no—
128C2—4121no—
129C2#100×D10311yescharacteristic
130C2#2026778412yes—
subgroupG/H
centerC22C22⋊C4×D103
commutatorC2×C4×C103C22×C4
FrattiniC42C22×D103
Fitting#331×C103C2
socleC22×C103C2×C22⋊C4
prime radical#20268339C2
cosocleC42×C103C23
hypercenter#331D103
hypocenterC103#1543
LCSG ▷ C2×C4×C103 ▷ C22×C103 ▷ C103
UCSC1 ◁ C22 ◁ C42 ◁ #331

Complements

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

NH ≅ G/Ntype
2. #20267843C2semidirect
3. #20267539C2semidirect
4. #20267535C2semidirect
5. #331×C103C2semidirect
66. C103#1543semidirect
71. #331D103semidirect

Maximal subgroups

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

subgroupindex
#202683392
#202678432
#202675392
#202675352
#331×C1032
#1543103