Finite Group Databasebeta

← #28378016

Subgroups — #28378016

Order 13952.

124 conjugacy classes of subgroups; only the 30 normal subgroups are shown.

normal subgroups only

This group has 124 conjugacy classes of subgroups — too many to draw. Only its 30 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#20295906C211yesmaximal, characteristic
2#20295872C211yesmaximal, characteristic
3#20294957C211yesmaximal, characteristic
4C2×#13182038—21no—
5C22⋊#11724786—21no—
6C2×#13182008—21no—
7C2×#13182008C2211yescharacteristic
8#16812606—21no—
9#16812606C411yescharacteristic
10C2×C4⋊C4×C109C411yescharacteristic
11#13182038—22no—
12#13182038—41no—
13C2×#11724786—41no—
14C2×#11724786—41no—
15C22×Dic109—21no—
16C22×Dic109D411yescharacteristic
17C22×Dic109D411yescharacteristic
18#13182008—41no—
19#13182008—41no—
20#13182008—41no—
21C22×C4×C109—21no—
22C22×C4×C109C2×C411yescharacteristic
23C4⋊C4×C109—41no—
24C23×C109C22⋊C411yescharacteristic
25C2×C4×C109—21no—
26C2×C4×C109—41no—
27C2×C4×C109—41no—
28C2×C4×C109—41no—
29C2×C4×C109—41no—
30C2×Dic109—21no—
31C2×Dic109—21no—
32C2×Dic109—22no—
33C2×Dic109—21no—
34C2×Dic109—41no—
35C2×Dic109—41no—
36C2×Dic109—41no—
37C2×Dic109D811yescharacteristic
38C2×Dic109SD1611yescharacteristic
39#11724786—42no—
40#11724786—81no—
41C22×C109—21no—
42C22×C109—21no—
43C22×C109#9911yescharacteristic
44C22×C109#10211yescharacteristic
45C22×C109#10411yescharacteristic
46C4×C109—41no—
47C4×C109—81no—
48Dic109—21no—
49Dic109—21no—
50Dic109—42no—
51Dic109—41no—
52C2×C109—21no—
53C2×C109—21no—
54C2×C109#32711yescharacteristic
55C2×C109#35211yescharacteristic
56C2×C109#35611yescharacteristic
57#1346—1091nomaximal, Sylow
58C109#134611yescharacteristic, complemented, Sylow
59#398—1091no—
60#343—1091no—
61#324—1091no—
62C2×M16—2181no—
63C2×C4⋊C4—1091no—
64C2×C4⋊C4—2181no—
65C2×C4⋊C4#8913711yescharacteristic
66C22⋊C8—2181no—
67#95—1091no—
68#95—2181no—
69C22×C4—21no—
70C22×C4—1091no—
71C22×C4—1091no—
72C22×C4—2181no—
73C22×C4C2×#8913711yescharacteristic
74M16—4361no—
75M16—2182no—
76C2×C8—4361no—
77C2×C8—4361no—
78C4⋊C4—41no—
79C4⋊C4—4361no—
80C4⋊C4—4361no—
81C4⋊C4—4361no—
82C23C22⋊#8913711yescharacteristic
83C2×C4—21no—
84C2×C4—41no—
85C2×C4—41no—
86C2×C4—41no—
87C2×C4—41no—
88C2×C4—1091no—
89C2×C4—1091no—
90C2×C4—4361no—
91C2×C4—4361no—
92C2×C4—4361no—
93C2×C4—2182no—
94C2×C4—2181no—
95C2×C4—2181no—
96C2×C4—2181no—
97C8—8721no—
98C8—4362no—
99C22—21no—
100C22—21no—
101C22#1681275711yescharacteristic
102C22#1681276111yescharacteristic
103C22#1681276311yescharacteristic
104C4—41no—
105C4—81no—
106C4—4362no—
107C4—4361no—
108C4—2181no—
109C4—2181no—
110C2—21no—
111C2—21no—
112C2#2029587711yescharacteristic
113C2#2029592811yescharacteristic
114C2#2029593611yescharacteristic
subgroupG/H
centerC22#16812757
commutatorC22×C4×C109C2×C4
FrattiniC22×C4C2×#89137
FittingC2×C4⋊C4×C109C4
socleC22×C109#99
prime radicalC23×C109C22⋊C4
cosocleC2×#13182008C22
hypercenterC2×C4⋊C4#89137
hypocenterC109#1346
LCSG ▷ C22×C4×C109 ▷ C23×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
58. C109#1346semidirect

Maximal subgroups

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

subgroupindex
#202959062
#202958722
#202949572
#1346109