Finite Group Databasebeta

← #27195947

Subgroups — #27195947

Order 13184.

332 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 145 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
1C2×#15692945C214yesmaximal
2C2×C4×C103⋊C8C211yesmaximal, characteristic
3#20267661C211yesmaximal, characteristic
4C2×C4⋊Q8×C103C211yesmaximal, characteristic
5C22×C103⋊C8C2212yes—
6C2×C4⋊Dic103—22no—
7C2×C4⋊Dic103C2212yes—
8#15692945—28no—
9C4×C103⋊C8—22no—
10C22×Q8×C103C2212yes—
11C4⋊Q8×C103—22no—
12C4⋊Q8×C103C414yescomplemented
13C2×C4⋊C4×C103—22no—
14C2×C42×C103C2211yescharacteristic
15C22×Dic103—22no—
16C2×C103⋊C8—22no—
17C2×C103⋊C8—22no—
18C2×C103⋊C8D414yes—
19C4⋊Dic103—24no—
20C4⋊Dic103—44no—
21C2×Q8×C103—22no—
22C2×Q8×C103—24no—
23C2×Q8×C103—24no—
24C2×Q8×C103C2×C414yes—
25C22×C4×C103—22no—
26C22×C4×C103D412yes—
27C22×C4×C103C2311yescharacteristic
28C4⋊C4×C103—28no—
29C42×C103C2×C412yes—
30C42×C103D412yes—
31C23×C103C2×D411yescharacteristic
32Q8×C103—28no—
33Q8×C103—44no—
34C2×C4×C103—24no—
35C2×C4×C103—42no—
36C2×C4×C103—42no—
37C2×C4×C103C22⋊C414yes—
38C2×C4×C103SD1614yes—
39C2×C4×C103Q1614yes—
40C2×C4×C103C22×C411yescharacteristic
41C2×C4×C103C2×D412yes—
42C2×C4×C103C2×D411yescharacteristic
43C2×C4×C103#4112yes—
44C2×Dic103—42no—
45C2×Dic103—44no—
46C103⋊C8—24no—
47C22×C103C2×C22⋊C411yescharacteristic
48C22×C103#12411yescharacteristic
49C22×C103#12711yescharacteristic
50C22×C103C2×SD1612yes—
51C22×C103C2×Q1612yes—
52C4×C103—44no—
53C4×C103#10318yescomplemented
54C4×C103C4×D412yes—
55C4×C103#12112yes—
56Dic103—82no—
57C2×C103#39011yescharacteristic
58C2×C103C2×#10312yes—
59C2×C103#48712yes—
60C2×C103#49211yescharacteristic
61C2×C103#49411yescharacteristic
62#1956—1031nomaximal, Sylow
63C103#195611yescharacteristic, complemented, Sylow
64C2×C4⋊Q8D10311yescharacteristic
65C2×#103—1034no—
66C2×C4×C8—1031no—
67#384—1031no—
68C22×Q8C2×D10312yes—
69C22×C8—1032no—
70C4⋊Q8—22no—
71C4⋊Q8Dic10314yescomplemented
72C2×C4⋊C4—22no—
73C2×C4⋊C4—1032no—
74C2×C4⋊C4—2062no—
75C2×C42C2×D10311yescharacteristic
76#103—2068no—
77C4×C8—2062no—
78C2×Q8—22no—
79C2×Q8—24no—
80C2×Q8—24no—
81C2×Q8C2×Dic10314yes—
82C22×C4—22no—
83C22×C4—2062no—
84C22×C4C22⋊D10312yes—
85C22×C4C22×D10311yescharacteristic
86C2×C8—1034no—
87C2×C8—2062no—
88C2×C8—2062no—
89C4⋊C4—28no—
90C4⋊C4—4124no—
91C4⋊C4—2064no—
92C42C2×Dic10312yes—
93C42C22⋊D10312yes—
94C23C2×C22⋊D10311yescharacteristic
95Q8—28no—
96Q8—44no—
97C2×C4—24no—
98C2×C4—42no—
99C2×C4—42no—
100C2×C4—4122no—
101C2×C4—4124no—
102C2×C4C22⋊Dic10314yes—
103C2×C4#1311009214yes—
104C2×C4#1311009514yes—
105C2×C4C22×Dic10311yescharacteristic
106C2×C4D4×D10312yes—
107C2×C4C2×C22⋊D10311yescharacteristic
108C2×C4#1311010412yes—
109C8—2064no—
110C22C2×C22⋊Dic10311yescharacteristic
111C22#1569300811yescharacteristic
112C22#1569301711yescharacteristic
113C22C2×#1311009212yes—
114C22C2×#1311009512yes—
115C4—44no—
116C4—8242no—
117C4#1569294518yescomplemented
118C4D4×Dic10312yes—
119C4#1569299212yes—
120C2#2026769411yescharacteristic
121C2C2×#1569294512yes—
122C2#2026814112yes—
123C2#2026816511yescharacteristic
124C2#2026817011yescharacteristic
subgroupG/H
centerC23C2×C22⋊D103
commutatorC2×C4×C103C22×C4
FrattiniC22×C4C22×D103
FittingC2×C4⋊Q8×C103C2
socle, prime radicalC23×C103C2×D4
cosocleC22×C4×C103C23
hypercenterC2×C4⋊Q8D103
hypocenterC103#1956
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
12. C4⋊Q8×C103C4semidirect
53. C4×C103#103semidirect
63. C103#1956semidirect
71. C4⋊Q8Dic103semidirect
117. C4#15692945semidirect

Maximal subgroups

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

subgroupindex
C2×#156929452
C2×C4×C103⋊C82
#202676612
C2×C4⋊Q8×C1032
#1956103