Finite Group Databasebeta

← #28362333

Subgroups — #28362333

Order 13952.

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

normal subgroups only

This group has 182 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
1C109⋊#564C211yesmaximal, characteristic, complemented
2#20295390C212yesmaximal
3#20294768C211yesmaximal, characteristic, complemented
4#20294767C212yesmaximal, complemented
5#490×C109C211yesmaximal, characteristic
6#16812691C2212yes—
7#16812690—22no—
8#16812689—22no—
9#16812689—22no—
10#16812620—22no—
11#16812620—22no—
12#16812610C2212yes—
13#127×C109C2211yescharacteristic
14#125×C109C2211yescharacteristic
15#102×C109—22no—
16#97×C109C2211yescharacteristic
17C2×#11724784—22no—
18C4⋊Dic109—22no—
19C4⋊Dic109D412yes—
20C4⋊Dic109D412yes—
21#13182008—22no—
22#13182008—22no—
23#13182008—22no—
24#13182008—22no—
25C4×Dic109—22no—
26C2×D4×C109—21no—
27C2×D4×C109—22no—
28C2×C8×C109—21no—
29C4⋊C4×C109—22no—
30C4⋊C4×C109D412yes—
31C42×C109C2311yescharacteristic
32C23×C109—41no—
33D4×C109—44no—
34D4×C109—42no—
35C2×C4×C109—22no—
36C2×C4×C109C2×D412yes—
37C2×C4×C109C2×D411yescharacteristic
38C2×Dic109—22no—
39C2×Dic109—22no—
40C8×C109—41no—
41#11724784—42no—
42C22×C109—82no—
43C22×C109—81no—
44C22×C109#12011yescharacteristic
45C4×C109—22no—
46C4×C109—21no—
47C4×C109—42no—
48Dic109—42no—
49Dic109—42no—
50C2×C109—161no—
51C2×C109#45412yes—
52C2×C109#45411yescharacteristic
53#1658—1091nomaximal, Sylow
54C109#165811yescharacteristic, complemented, Sylow
55#564—1091no—
56#490—1092no—
57#490D10911yescharacteristic
58#330—1091no—
59#330—1092no—
60#127C2×D10911yescharacteristic
61#125—1092no—
62#125—2182no—
63#125—2182no—
64#125—2182no—
65#125C2×D10911yescharacteristic
66#102—22no—
67#102—2182no—
68#102—2182no—
69#97—1092no—
70#97C2×D10911yescharacteristic
71C2×D4—22no—
72C2×D4—21no—
73C2×C8—21no—
74C2×C8—2182no—
75C4⋊C4—22no—
76C4⋊C4—1092no—
77C4⋊C4—1092no—
78C4⋊C4—2182no—
79C4⋊C4—2182no—
80C4⋊C4—2182no—
81C4⋊C4—2182no—
82C4⋊C4—2182no—
83C4⋊C4C22⋊D10912yes—
84C42—2182no—
85C42C22×D10911yescharacteristic
86C23—41no—
87D4—44no—
88D4—42no—
89C2×C4—22no—
90C2×C4—2182no—
91C2×C4—2182no—
92C2×C4D4×D10912yes—
93C2×C4C2×C22⋊D10911yescharacteristic
94C8—41no—
95C8—4362no—
96C22—82no—
97C22—81no—
98C22#1681266711yescharacteristic
99C4—22no—
100C4—21no—
101C4—42no—
102C4—4362no—
103C4—4362no—
104C2—161no—
105C2#2029519712yes—
106C2#2029519811yescharacteristic
subgroupG/H
centerC22#16812667
commutator, cosocleC42×C109C23
FrattiniC42C22×D109
Fitting#490×C109C2
socleC22×C109#120
prime radical#127×C109C22
hypercenter#490D109
hypocenterC109#1658
LCSG ▷ C42×C109 ▷ C22×C109 ▷ C109
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
1. C109⋊#564C2semidirect
3. #20294768C2semidirect
4. #20294767C2semidirect
54. C109#1658semidirect

Maximal subgroups

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

subgroupindex
C109⋊#5642
#202953902
#202947682
#202947672
#490×C1092
#1658109