Finite Group Databasebeta

← #27194450

Subgroups — #27194450

Order 13184.

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

normal subgroups only

This group has 228 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#20268186C211yesmaximal, characteristic, complemented
2#20268150C212yesmaximal, complemented
3#20267531C212yesmaximal, complemented
4#20267531C211yesmaximal, characteristic, complemented
5H(3,𝔽4)×C103C211yesmaximal, characteristic
6C2×#13110095—21no—
7C2×#13110093—21no—
8#15693021C2211yescharacteristic, complemented
9#15692945—22no—
10#15692942—22no—
11#15692932C2212yescomplemented
12#15692932C2211yescharacteristic, complemented
13#124×C103—22no—
14#124×C103—21no—
15#124×C103C2212yes—
16#124×C103C2211yescharacteristic
17#120×C103—22no—
18#120×C103—21no—
19C2×Dic206—21no—
20#13110095—42no—
21#13110093—42no—
22C2×C103⋊C8—21no—
23C2×C103⋊C8—22no—
24C4⋊Dic103—22no—
25C24×C103—21no—
26C2×Q8×C103D412yes—
27C2×Q8×C103D411yescharacteristic
28C2×D4×C103—21no—
29C2×D4×C103—22no—
30C2×D4×C103D412yes—
31C2×D4×C103D411yescharacteristic
32C22⋊C4×C103—22no—
33C22⋊C4×C103—21no—
34C22⋊C4×C103—22no—
35C22⋊C4×C103—22no—
36C22⋊C4×C103—22no—
37C42×C103—21no—
38C42×C103C2311yescharacteristic
39C23×C103—21no—
40C23×C103—22no—
41C23×C103—81no—
42C23×C103—82no—
43Q8×C103—42no—
44Q8×C103—41no—
45D4×C103—42no—
46D4×C103—41no—
47D4×C103—81no—
48D4×C103—82no—
49C2×C4×C103—21no—
50C2×C4×C103—22no—
51C2×C4×C103C2×D412yes—
52C2×C4×C103C2×D411yescharacteristic
53C2×Dic103—41no—
54Dic206—41no—
55Dic206—41no—
56C103⋊C8—22no—
57C103⋊C8—42no—
58C22×C103—41no—
59C22×C103—42no—
60C22×C103—42no—
61C22×C103—42no—
62C22×C103—42no—
63C22×C103—84no—
64C22×C103#12011yescharacteristic
65C4×C103—21no—
66C4×C103—22no—
67C4×C103—41no—
68C4×C103—42no—
69Dic103—81no—
70C2×C103—81no—
71C2×C103—82no—
72C2×C103#45311yescharacteristic
73C2×C103#45512yes—
74#1659—1031nomaximal, Sylow
75C103#165911yescharacteristic, complemented, Sylow
76H(3,𝔽4)D10311yescharacteristic
77#497—1031no—
78#489—1032no—
79#329—1031no—
80#329—1032no—
81C2×Q16—2061no—
82C2×SD16—2061no—
83C4⋊Q8—1031no—
84#124—22no—
85#124—21no—
86#124C2×D10312yes—
87#124C2×D10311yescharacteristic
88#120—22no—
89#120—21no—
90#103—2062no—
91#102—2062no—
92#97—1032no—
93#97—1031no—
94C24—21no—
95C2×Q8—2061no—
96C2×Q8C22⋊D10312yes—
97C2×Q8C22⋊D10311yescharacteristic
98C2×D4—21no—
99C2×D4—22no—
100C2×D4C22⋊D10312yes—
101C2×D4C22⋊D10311yescharacteristic
102Q16—4122no—
103SD16—4122no—
104C2×C8—2062no—
105C2×C8—2061no—
106C4⋊C4—2062no—
107C22⋊C4—22no—
108C22⋊C4—21no—
109C22⋊C4—22no—
110C22⋊C4—22no—
111C22⋊C4—22no—
112C42—21no—
113C42C22×D10311yescharacteristic
114C23—21no—
115C23—22no—
116C23—81no—
117C23—82no—
118Q8—41no—
119Q8—42no—
120Q8—4121no—
121Q8—4121no—
122D4—41no—
123D4—42no—
124D4—81no—
125D4—82no—
126C2×C4—21no—
127C2×C4—22no—
128C2×C4—4121no—
129C2×C4C2×C22⋊D10312yes—
130C2×C4C2×C22⋊D10311yescharacteristic
131C8—4122no—
132C8—2062no—
133C22—41no—
134C22—42no—
135C22—42no—
136C22—42no—
137C22—42no—
138C22—84no—
139C22#1569299011yescharacteristic
140C4—21no—
141C4—22no—
142C4—41no—
143C4—42no—
144C4—8241no—
145C2—81no—
146C2—82no—
147C2#2026795911yescharacteristic
148C2#2026796912yes—
subgroupG/H
centerC22#15692990
commutator, cosocleC42×C103C23
FrattiniC42C22×D103
Fitting, prime radicalH(3,𝔽4)×C103C2
socleC22×C103#120
hypercenterH(3,𝔽4)D103
hypocenterC103#1659
LCSG ▷ C42×C103 ▷ C22×C103 ▷ C103
UCSC1 ◁ C22 ◁ C42 ◁ H(3,𝔽4)

Complements

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

NH ≅ G/Ntype
1. #20268186C2semidirect
2. #20268150C2semidirect
3. #20267531C2semidirect
4. #20267531C2semidirect
8. #15693021C22semidirect
11. #15692932C22semidirect
12. #15692932C22semidirect
75. C103#1659semidirect

Maximal subgroups

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

subgroupindex
#202681862
#202681502
#202675312
H(3,𝔽4)×C1032
#1659103