Finite Group Databasebeta

← #27193409

Subgroups — #27193409

Order 13184.

608 conjugacy classes of subgroups; only the 229 normal subgroups are shown.

normal subgroups only

This group has 608 conjugacy classes of subgroups — too many to draw. Only its 229 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
1C22×C4⋊Dic103C213yesmaximal
2C2×C103⋊#95C213yesmaximal
3C2×#95×C103C211yesmaximal, characteristic
4C23×Dic103C2213yes—
5C23×Dic103C2211yescharacteristic
6C2×C4⋊Dic103—212no—
7C2×C4⋊Dic103—26no—
8C103⋊#95—26no—
9C23×C4×C103C2213yes—
10#95×C103C414yescomplemented
11C22×Dic103—23no—
12C22×Dic103—23no—
13C22×Dic103—26no—
14C22×Dic103—26no—
15C22×Dic103—23no—
16C22×Dic103—23no—
17C22×Dic103D416yes—
18C22×Dic103Q812yes—
19C4⋊Dic103—224no—
20C24×C103C2311yescharacteristic
21C22×C4×C103—26no—
22C22×C4×C103—26no—
23C22×C4×C103C2×C416yes—
24C22×C4×C103D416yes—
25C22×C4×C103Q816yes—
26C23×C103C22×C411yescharacteristic
27C23×C103C2×D413yes—
28C23×C103C2×D413yes—
29C23×C103C2×Q811yescharacteristic
30C23×C103C2×Q813yes—
31C23×C103#4113yes—
32C23×C103#4111yescharacteristic
33C2×C4×C103—212no—
34C2×C4×C103—26no—
35C2×C4×C103—212no—
36C2×C4×C103—26no—
37C2×C4×C103C4⋊C4112yescomplemented
38C2×Dic103—212no—
39C2×Dic103—26no—
40C2×Dic103—26no—
41C2×Dic103—43no—
42C2×Dic103—46no—
43C2×Dic103—43no—
44C2×Dic103—43no—
45C2×Dic103—41no—
46C22×C103C2×C4⋊C413yes—
47C22×C103C4×D413yes—
48C22×C103C4×Q811yescharacteristic
49C22×C103#12013yes—
50C22×C103#12113yes—
51C22×C103C22⋊Q816yes—
52C22×C103C22⋊Q813yes—
53C22×C103#12313yes—
54C22×C103#12513yes—
55C22×C103#12711yescharacteristic
56C22×C103C4⋊Q813yes—
57C22×C103C4⋊Q813yes—
58C4×C103—212no—
59Dic103—46no—
60Dic103—42no—
61C2×C103#38411yescharacteristic
62C2×C103#38513yes—
63C2×C103#38913yes—
64C2×C103#39211yescharacteristic
65C2×C103#39513yes—
66C2×C103#39813yes—
67C2×C103#39911yescharacteristic
68#1444—1031nomaximal, Sylow
69C103#144411yescharacteristic, complemented, Sylow
70C22×C4⋊C4—1033no—
71C2×#95—1033no—
72C2×#95D10311yescharacteristic
73C23×C4—1033no—
74C23×C4—1031no—
75C23×C4C2×D10313yes—
76C2×C4⋊C4—20612no—
77C2×C4⋊C4—2066no—
78#95—2066no—
79#95Dic10314yescomplemented
80C24C22×D10311yescharacteristic
81C22×C4—26no—
82C22×C4—26no—
83C22×C4—1036no—
84C22×C4—1032no—
85C22×C4—2066no—
86C22×C4—2063no—
87C22×C4—2063no—
88C22×C4—2066no—
89C22×C4—2063no—
90C22×C4—2063no—
91C22×C4Dic20616yes—
92C22×C4D41216yes—
93C22×C4C2×Dic10316yes—
94C4⋊C4—20624no—
95C23C22×Dic10311yescharacteristic
96C23D4×D10313yes—
97C23C2×D41213yes—
98C23Q8×D10311yescharacteristic
99C23C2×Dic20613yes—
100C23#1311010413yes—
101C23#1311010611yescharacteristic
102C2×C4—212no—
103C2×C4—26no—
104C2×C4—212no—
105C2×C4—26no—
106C2×C4—4123no—
107C2×C4—4126no—
108C2×C4—4123no—
109C2×C4—4123no—
110C2×C4—4121no—
111C2×C4—20612no—
112C2×C4—2066no—
113C2×C4—2066no—
114C2×C4C4⋊Dic103112yescomplemented
115C22C2×C4⋊Dic10313yes—
116C22D4×Dic10313yes—
117C22Q8×Dic10311yescharacteristic
118C22#1569299113yes—
119C22#1569299613yes—
120C22#1569299816yes—
121C22#1569300113yes—
122C22#1569300513yes—
123C22#1569301213yes—
124C22#1569301811yescharacteristic
125C22#1569302013yes—
126C22#1569302113yes—
127C4—212no—
128C4—4126no—
129C4—4122no—
130C2#2026766111yescharacteristic
131C2#2026766613yes—
132C2#2026769013yes—
133C2#2026770111yescharacteristic
134C2#2026771213yes—
135C2#2026772313yes—
136C2#2026772811yescharacteristic
subgroupG/H
center, FrattiniC24C22×D103
commutatorC23×C103C22×C4
FittingC2×#95×C103C2
socle, prime radical, cosocleC24×C103C23
hypercenterC2×#95D103
hypocenterC103#1444
LCSG ▷ C23×C103 ▷ C103
UCSC1 ◁ C24 ◁ C2×#95

Complements

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

NH ≅ G/Ntype
10. #95×C103C4semidirect
37. C2×C4×C103C4⋊C4semidirect
69. C103#1444semidirect
79. #95Dic103semidirect
114. C2×C4C4⋊Dic103semidirect

Maximal subgroups

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

subgroupindex
C22×C4⋊Dic1032
C2×C103⋊#952
C2×#95×C1032
#1444103