Finite Group Databasebeta

← #27194054

Subgroups — #27194054

Order 13184.

148 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 148 conjugacy classes of subgroups — too many to draw. Only its 65 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#20267921C212yesmaximal
2C4×Dic412C211yesmaximal, characteristic
3#20267542C211yesmaximal, characteristic
4#20267523C212yesmaximal
5#322×C103C211yesmaximal, characteristic
6C2×Dic412C411yescharacteristic
7C4×Dic206C2212yes—
8#15692955C411yescharacteristic
9C4⋊(C103⋊C8)C2212yes—
10Dic103⋊C8—22no—
11#15692946C412yes—
12#15692931—22no—
13C4×C8×C103C2211yescharacteristic
14C4×C8×C103C2211yescharacteristic
15C4×C8×C103C2211yescharacteristic
16C2×Dic206C2×C412yes—
17Dic412—22no—
18C2×C103⋊C8—22no—
19C4⋊Dic103C2×C412yes—
20Dic103⋊C4—22no—
21C4×Dic103—22no—
22C2×C8×C103—21no—
23C2×C8×C103C2×C411yescharacteristic
24C2×C8×C103C2×C411yescharacteristic
25C2×C8×C103D412yes—
26C42×C103C2311yescharacteristic
27C2×C4×C103C22×C411yescharacteristic
28C2×C4×C103C2×D411yescharacteristic
29C2×C4×C103#4111yescharacteristic
30C2×Dic103—22no—
31C2×Dic103—22no—
32Dic206—22no—
33Dic206—22no—
34C8×C103—21no—
35C8×C103—22no—
36C8×C103—41no—
37C8×C103M1612yes—
38C103⋊C8—42no—
39C22×C103C4×D411yescharacteristic
40C4×C103—21no—
41C4×C103C2×M1611yescharacteristic
42C4×C103#13111yescharacteristic
43C4×C103#13712yes—
44Dic103—42no—
45Dic103—42no—
46C2×C103#43611yescharacteristic
47C2×C103#44111yescharacteristic
48C2×C103#44411yescharacteristic
49#1593—1031nomaximal, Sylow
50C103#159311yescharacteristic, complemented, Sylow
51#446—1032no—
52C4×Q16—1031no—
53#334—1031no—
54Q8⋊C8—1032no—
55#322D10311yescharacteristic
56C2×Q16—1031no—
57C4×Q8—1032no—
58#107—1031no—
59C4⋊C8—1032no—
60C4⋊C8—2062no—
61#103—1032no—
62#97—2062no—
63C4×C8C2×D10311yescharacteristic
64C4×C8C2×D10311yescharacteristic
65C4×C8C2×D10311yescharacteristic
66C2×Q8—1032no—
67Q16—2062no—
68C2×C8—21no—
69C2×C8—2062no—
70C2×C8C4×D10311yescharacteristic
71C2×C8C4×D10311yescharacteristic
72C2×C8D41212yes—
73C4⋊C4—1032no—
74C4⋊C4—2062no—
75C42—2062no—
76C42C22×D10311yescharacteristic
77Q8—2062no—
78Q8—2062no—
79C2×C4—2062no—
80C2×C4—2062no—
81C2×C4C2×C4×D10311yescharacteristic
82C2×C4C2×D41211yescharacteristic
83C2×C4#1311010511yescharacteristic
84C8—21no—
85C8—22no—
86C8—41no—
87C8—4122no—
88C8#1311008812yes—
89C22C4×D41211yescharacteristic
90C4—21no—
91C4—4122no—
92C4—4122no—
93C4C2×#1311008811yescharacteristic
94C4#1569302711yescharacteristic
95C4#1569305412yes—
96C2#2026787011yescharacteristic
97C2#2026789911yescharacteristic
98C2#2026791411yescharacteristic
subgroupG/H
centerC2×C4C2×D412
commutatorC2×C4×C103C22×C4
FrattiniC42C22×D103
Fitting#322×C103C2
socle, prime radicalC22×C103C4×D4
cosocleC42×C103C23
hypercenter#322D103
hypocenterC103#1593
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #322

Complements

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

NH ≅ G/Ntype
50. C103#1593semidirect

Maximal subgroups

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

subgroupindex
#202679212
C4×Dic4122
#202675422
#202675232
#322×C1032
#1593103