Finite Group Databasebeta

← #27196122

Subgroups — #27196122

Order 13184.

284 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 105 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#20267815C211yesmaximal, characteristic
2C42×Dic103C211yesmaximal, characteristic
3#20267550C214yesmaximal
4#533×C103C211yesmaximal, characteristic
5C2×#13110089C2212yes—
6C2×C4×Dic103—22no—
7C2×C4×Dic103C2212yes—
8C4⋊(C103⋊C8)—22no—
9C4⋊Q8×C103C412yescomplemented
10#125×C103C412yescomplemented
11C22⋊Q8×C103—22no—
12C4×Q8×C103—22no—
13#117×C103C2212yes—
14C2×C42×C103C2211yescharacteristic
15C22×Dic103—22no—
16#13110089—24no—
17C2×C103⋊C8—22no—
18C4×Dic103—28no—
19C4×Dic103—22no—
20C4×Dic103Q814yescomplemented
21C2×Q8×C103—22no—
22C22×C4×C103D412yes—
23C22×C4×C103C2311yescharacteristic
24C4⋊C4×C103—24no—
25C4⋊C4×C103—22no—
26C4⋊C4×C103C2×C414yes—
27C22⋊C4×C103—22no—
28C42×C103—22no—
29C42×C103C2×C411yescharacteristic
30C42×C103C2×C411yescharacteristic
31C42×C103D412yes—
32C23×C103C2×D411yescharacteristic
33Q8×C103—44no—
34C2×C4×C103—24no—
35C2×C4×C103—24no—
36C2×C4×C103C22⋊C412yes—
37C2×C4×C103C22⋊C412yes—
38C2×C4×C103C22×C411yescharacteristic
39C2×C4×C103C2×D411yescharacteristic
40C2×C4×C103C2×Q812yes—
41C2×C4×C103#4112yes—
42C2×Dic103—28no—
43C2×Dic103—24no—
44C103⋊C8—42no—
45C22×C103—22no—
46C22×C103C2×C22⋊C411yescharacteristic
47C22×C103C22⋊Q812yes—
48C4×C103—22no—
49C4×C103—44no—
50C4×C103#10414yes—
51C4×C103C4×Q812yes—
52C4×C103#12411yescharacteristic
53C4×C103C4⋊Q811yescharacteristic
54Dic103—28no—
55C2×C103—22no—
56C2×C103#39111yescharacteristic
57C2×C103C2×#10412yes—
58#1994—1031nomaximal, Sylow
59C103#199411yescharacteristic, complemented, Sylow
60#533D10311yescharacteristic
61#423—1031no—
62C43—1031no—
63#339—1034no—
64C2×M16—1032no—
65C4⋊Q8Dic10312yescomplemented
66#125Dic10312yescomplemented
67C22⋊Q8—22no—
68C4×Q8—22no—
69#117C2×D10312yes—
70C2×C42—1032no—
71C2×C42—2062no—
72C2×C42C2×D10311yescharacteristic
73C4⋊C8—2062no—
74C2×Q8—22no—
75C22×C4—2062no—
76C22×C4C22⋊D10312yes—
77C22×C4C22×D10311yescharacteristic
78M16—2064no—
79C2×C8—2062no—
80C4⋊C4—24no—
81C4⋊C4—22no—
82C4⋊C4C2×Dic10314yes—
83C22⋊C4—22no—
84C42—22no—
85C42—1034no—
86C42—2068no—
87C42—2062no—
88C42C2×Dic10311yescharacteristic
89C42C2×Dic10311yescharacteristic
90C42C22⋊D10312yes—
91C23C2×C22⋊D10311yescharacteristic
92Q8—44no—
93C2×C4—24no—
94C2×C4—24no—
95C2×C4—2068no—
96C2×C4—2064no—
97C2×C4C22⋊Dic10312yes—
98C2×C4C22⋊Dic10312yes—
99C2×C4C22×Dic10311yescharacteristic
100C2×C4C2×C22⋊D10311yescharacteristic
101C2×C4Q8×D10312yes—
102C2×C4#1311010612yes—
103C8—4122no—
104C22—22no—
105C22C2×C22⋊Dic10311yescharacteristic
106C22#1569299712yes—
107C4—22no—
108C4—44no—
109C4—2068no—
110C4#1569294814yes—
111C4Q8×Dic10312yes—
112C4#1569301011yescharacteristic
113C4#1569301911yescharacteristic
114C2—22no—
115C2#2026769811yescharacteristic
116C2C2×#1569294812yes—
subgroupG/H
centerC2×C4C2×C22⋊D103
commutatorC2×C4×C103C22×C4
FrattiniC22×C4C22×D103
Fitting#533×C103C2
socleC22×C103C2×C22⋊C4
prime radicalC23×C103C2×D4
cosocleC22×C4×C103C23
hypercenter#533D103
hypocenterC103#1994
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #533

Complements

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

NH ≅ G/Ntype
9. C4⋊Q8×C103C4semidirect
10. #125×C103C4semidirect
20. C4×Dic103Q8semidirect
59. C103#1994semidirect
65. C4⋊Q8Dic103semidirect
66. #125Dic103semidirect

Maximal subgroups

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

subgroupindex
#202678152
C42×Dic1032
#202675502
#533×C1032
#1994103