Finite Group Databasebeta

← #27194467

Subgroups — #27194467

Order 13184.

196 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 49 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#20268161C211yesmaximal, characteristic, complemented
2#20268150C212yesmaximal, complemented
3#20267533C211yesmaximal, characteristic, complemented
4#20267531C212yesmaximal, complemented
5#562×C103C211yesmaximal, characteristic
6#15693021C2211yescharacteristic
7#15692945—22no—
8#15692944—22no—
9#15692942—22no—
10#15692932C2211yescharacteristic
11#15692932C2212yes—
12#125×C103C2211yescharacteristic
13#124×C103C2212yes—
14#123×C103—22no—
15C22⋊Q8×C103—22no—
16#121×C103—22no—
17C2×Dic206—21no—
18C2×C103⋊C8—22no—
19C2×C103⋊C8—21no—
20C4⋊Dic103—22no—
21C2×Q8×C103D412yes—
22C2×D4×C103—22no—
23C2×D4×C103D412yes—
24C22×C4×C103—22no—
25C4⋊C4×C103—22no—
26C4⋊C4×C103—22no—
27C4⋊C4×C103D412yes—
28C22⋊C4×C103—22no—
29C22⋊C4×C103—22no—
30C22⋊C4×C103—22no—
31C42×C103C2311yescharacteristic
32C23×C103—22no—
33Q8×C103—42no—
34D4×C103—42no—
35D4×C103—82no—
36C2×C4×C103—22no—
37C2×C4×C103—22no—
38C2×C4×C103—82no—
39C2×C4×C103C2×D411yescharacteristic
40C2×C4×C103C2×D412yes—
41C2×Dic103—41no—
42Dic206—42no—
43C103⋊C8—41no—
44C103⋊C8—42no—
45C22×C103—42no—
46C22×C103—42no—
47C22×C103—42no—
48C22×C103#12011yescharacteristic
49C4×C103—21no—
50C4×C103—22no—
51C4×C103—42no—
52C4×C103—42no—
53Dic103—81no—
54C2×C103—82no—
55C2×C103#45411yescharacteristic
56C2×C103#45512yes—
57#1662—1031nomaximal, Sylow
58C103#166211yescharacteristic, complemented, Sylow
59#562D10311yescharacteristic
60#491—1031no—
61#489—1032no—
62#330—1031no—
63#329—1032no—
64C4⋊Q8—1031no—
65#125C2×D10311yescharacteristic
66#124C2×D10312yes—
67#123—22no—
68C22⋊Q8—22no—
69#121—22no—
70#103—2062no—
71#103—2062no—
72#102—2062no—
73#97—1031no—
74#97—1032no—
75C2×Q8—2061no—
76C2×Q8C22⋊D10312yes—
77C2×D4—22no—
78C2×D4C22⋊D10312yes—
79C22×C4—22no—
80C2×C8—2062no—
81C2×C8—2061no—
82C4⋊C4—22no—
83C4⋊C4—22no—
84C4⋊C4—2062no—
85C4⋊C4C22⋊D10312yes—
86C22⋊C4—22no—
87C22⋊C4—22no—
88C22⋊C4—22no—
89C42C22×D10311yescharacteristic
90C23—22no—
91Q8—42no—
92Q8—4122no—
93D4—42no—
94D4—82no—
95C2×C4—22no—
96C2×C4—22no—
97C2×C4—82no—
98C2×C4—4121no—
99C2×C4C2×C22⋊D10311yescharacteristic
100C2×C4C2×C22⋊D10312yes—
101C8—4121no—
102C8—4122no—
103C22—42no—
104C22—42no—
105C22—42no—
106C22#1569299011yescharacteristic
107C4—21no—
108C4—22no—
109C4—42no—
110C4—42no—
111C4—8241no—
112C2—82no—
113C2#2026796411yescharacteristic
114C2#2026796912yes—
subgroupG/H
centerC22#15692990
commutator, cosocleC42×C103C23
FrattiniC42C22×D103
Fitting, prime radical#562×C103C2
socleC22×C103#120
hypercenter#562D103
hypocenterC103#1662
LCSG ▷ C42×C103 ▷ C22×C103 ▷ C103
UCSC1 ◁ C22 ◁ C42 ◁ #562

Complements

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

NH ≅ G/Ntype
1. #20268161C2semidirect
2. #20268150C2semidirect
3. #20267533C2semidirect
4. #20267531C2semidirect
58. C103#1662semidirect

Maximal subgroups

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

subgroupindex
#202681612
#202681502
#202675332
#202675312
#562×C1032
#1662103