Finite Group Databasebeta

← #27194468

Subgroups — #27194468

Order 13184.

196 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 45 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#20268539C211yesmaximal, characteristic
2#20268161C211yesmaximal, characteristic, complemented
3#20268151C212yesmaximal, complemented
4#20267530C212yesmaximal, complemented
5#330×C103C211yesmaximal, characteristic, complemented
6#15693021C2211yescharacteristic
7#15693009C2212yes—
8#15693006—22no—
9#15692999—22no—
10#15692996—22no—
11#15692946—22no—
12#15692944—22no—
13#15692943—22no—
14#15692932C2211yescharacteristic
15#125×C103C2211yescharacteristic
16#97×C103C2212yes—
17C2×Dic206—21no—
18C2×Dic206D412yes—
19C2×D412—22no—
20C2×D412D412yes—
21C2×C4×D103—22no—
22C2×C103⋊C8—21no—
23C4⋊Dic103—22no—
24Dic103⋊C4—22no—
25(C2×D103)⋊C4—22no—
26(C2×D103)⋊C4—22no—
27(C2×D103)⋊C4—22no—
28C2×C8×C103—22no—
29C4⋊C4×C103—22no—
30C4⋊C4×C103D412yes—
31C42×C103C2311yescharacteristic
32C22×D103—22no—
33C2×C4×C103—22no—
34C2×C4×C103C2×D412yes—
35C2×C4×C103C2×D411yescharacteristic
36C2×Dic103—22no—
37C2×Dic103—41no—
38D412—42no—
39D412—82no—
40C4×D103—82no—
41Dic206—42no—
42Dic206—42no—
43C8×C103—42no—
44C103⋊C8—41no—
45C22×C103#12011yescharacteristic
46C2×D103—42no—
47C2×D103—42no—
48C2×D103—42no—
49C4×C103—21no—
50C4×C103—22no—
51C4×C103—42no—
52Dic103—42no—
53Dic103—81no—
54C2×C103#45411yescharacteristic
55C2×C103#45512yes—
56D103—82no—
57#1662—1031nomaximal, Sylow
58C103#166211yescharacteristic, complemented, Sylow
59#562—1031no—
60#491—1031no—
61#489—1032no—
62#330D10311yescharacteristic, complemented
63#329—1032no—
64C4⋊Q8—1031no—
65#125C2×D10311yescharacteristic
66#124—1032no—
67#123—2062no—
68C22⋊Q8—2062no—
69#121—2062no—
70#103—2062no—
71#103—2062no—
72#102—2062no—
73#97—1031no—
74#97C2×D10312yes—
75C2×Q8—1032no—
76C2×Q8—2061no—
77C2×D4—1032no—
78C2×D4—2062no—
79C22×C4—2062no—
80C2×C8—22no—
81C2×C8—2061no—
82C4⋊C4—22no—
83C4⋊C4—2062no—
84C4⋊C4—2062no—
85C4⋊C4D41212yes—
86C22⋊C4—2062no—
87C22⋊C4—2062no—
88C22⋊C4—2062no—
89C42C22×D10311yescharacteristic
90C23—2062no—
91Q8—4122no—
92Q8—4122no—
93D4—8242no—
94D4—4122no—
95C2×C4—22no—
96C2×C4—8242no—
97C2×C4—4121no—
98C2×C4—2062no—
99C2×C4D4×D10312yes—
100C2×C4C2×D41211yescharacteristic
101C8—42no—
102C8—4121no—
103C22—4122no—
104C22—4122no—
105C22—4122no—
106C22#1569299111yescharacteristic
107C4—21no—
108C4—22no—
109C4—42no—
110C4—8241no—
111C4—4122no—
112C2—8242no—
113C2#2026796611yescharacteristic
114C2#2026797012yes—
subgroupG/H
centerC22#15692991
commutator, cosocleC42×C103C23
FrattiniC42C22×D103
Fitting#330×C103C2
socleC22×C103#120
prime radical#20268539C2
hypercenter#330D103
hypocenterC103#1662
LCSG ▷ C42×C103 ▷ C22×C103 ▷ C103
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
2. #20268161C2semidirect
3. #20268151C2semidirect
4. #20267530C2semidirect
5. #330×C103C2semidirect
58. C103#1662semidirect
62. #330D103semidirect

Maximal subgroups

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

subgroupindex
#202685392
#202681612
#202681512
#202675302
#330×C1032
#1662103