Finite Group Databasebeta

← #27194453

Subgroups — #27194453

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#20268541C211yesmaximal, characteristic
2#20268197C212yesmaximal, complemented
3#20267532C212yesmaximal, complemented
4#20267531C211yesmaximal, characteristic
5#497×C103C211yesmaximal, characteristic
6#15693019—21no—
7#15693014—22no—
8#15693013C2212yes—
9#15693002—21no—
10#15692998—22no—
11#15692954—22no—
12#15692952—22no—
13#15692932C2212yes—
14C2×Q16×C103—21no—
15C2×SD16×C103—21no—
16C4⋊Q8×C103C2211yescharacteristic
17#124×C103C2211yescharacteristic
18#97×C103C2211yescharacteristic
19C2×Dic206—21no—
20C22×Dic103—21no—
21C2×C103⋊C8—22no—
22C4⋊Dic103D412yes—
23C4⋊Dic103D412yes—
24Dic103⋊C4—22no—
25Dic103⋊C4—22no—
26Dic103⋊C4—22no—
27C22⋊Dic103—22no—
28C22⋊Dic103—21no—
29C4×Dic103—21no—
30C2×Q8×C103—21no—
31C2×Q8×C103D411yescharacteristic
32C2×D4×C103D411yescharacteristic
33Q16×C103—42no—
34SD16×C103—42no—
35C2×C8×C103—21no—
36C4⋊C4×C103—22no—
37C22⋊C4×C103—22no—
38C42×C103C2311yescharacteristic
39C23×C103—21no—
40Q8×C103—41no—
41Q8×C103—41no—
42Q8×C103—41no—
43D4×C103—41no—
44C2×C4×C103—21no—
45C2×C4×C103—41no—
46C2×C4×C103C2×D412yes—
47C2×C4×C103C2×D411yescharacteristic
48C2×Dic103—22no—
49C2×Dic103—22no—
50C2×Dic103—81no—
51Dic206—81no—
52C8×C103—22no—
53C103⋊C8—24no—
54C22×C103—41no—
55C22×C103—42no—
56C22×C103#12011yescharacteristic
57C4×C103—21no—
58C4×C103—22no—
59C4×C103—41no—
60C4×C103—81no—
61Dic103—42no—
62Dic103—42no—
63C2×C103—81no—
64C2×C103#45311yescharacteristic
65C2×C103#45612yes—
66#1660—1031nomaximal, Sylow
67C103#166011yescharacteristic, complemented, Sylow
68#563—1031no—
69#501—1032no—
70#497D10311yescharacteristic
71#330—1032no—
72#329—1031no—
73C2×Q16—21no—
74C2×SD16—21no—
75C4⋊Q8—2061no—
76C4⋊Q8C2×D10311yescharacteristic
77#126—2062no—
78#125—1032no—
79#124C2×D10311yescharacteristic
80#123—2061no—
81C22⋊Q8—2062no—
82#107—2062no—
83#106—2062no—
84#97—1032no—
85#97C2×D10311yescharacteristic
86C2×Q8—21no—
87C2×Q8—2061no—
88C2×Q8C22⋊D10311yescharacteristic
89C2×D4C22⋊D10311yescharacteristic
90C22×C4—2061no—
91Q16—42no—
92SD16—42no—
93C2×C8—21no—
94C2×C8—2062no—
95C4⋊C4—22no—
96C4⋊C4—1032no—
97C4⋊C4—1032no—
98C4⋊C4—2062no—
99C4⋊C4—2062no—
100C4⋊C4—2062no—
101C22⋊C4—22no—
102C22⋊C4—2062no—
103C22⋊C4—2061no—
104C42—2061no—
105C42C22×D10311yescharacteristic
106C23—21no—
107Q8—41no—
108Q8—41no—
109Q8—41no—
110Q8—8241no—
111D4—41no—
112C2×C4—21no—
113C2×C4—41no—
114C2×C4—8241no—
115C2×C4—2062no—
116C2×C4—2062no—
117C2×C4D4×D10312yes—
118C2×C4C2×C22⋊D10311yescharacteristic
119C8—22no—
120C8—2064no—
121C22—41no—
122C22—42no—
123C22#1569298911yescharacteristic
124C4—21no—
125C4—22no—
126C4—41no—
127C4—81no—
128C4—4122no—
129C4—4122no—
130C2—81no—
131C2#2026795811yescharacteristic
132C2#2026797212yes—
subgroupG/H
centerC22#15692989
commutator, cosocleC42×C103C23
FrattiniC42C22×D103
Fitting#497×C103C2
socleC22×C103#120
prime radicalC2×D4×C103D4
hypercenter#497D103
hypocenterC103#1660
LCSG ▷ C42×C103 ▷ C22×C103 ▷ C103
UCSC1 ◁ C22 ◁ C42 ◁ #497

Complements

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

NH ≅ G/Ntype
2. #20268197C2semidirect
3. #20267532C2semidirect
67. C103#1660semidirect

Maximal subgroups

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

subgroupindex
#202685412
#202681972
#202675322
#202675312
#497×C1032
#1660103