Finite Group Databasebeta

← #28378152

Subgroups — #28378152

Order 13952.

122 conjugacy classes of subgroups; only the 20 normal subgroups are shown.

normal subgroups only

This group has 122 conjugacy classes of subgroups — too many to draw. Only its 20 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#20295930C211yesmaximal, characteristic, complemented
2#20295884C211yesmaximal, characteristic, complemented
3#20295196C211yesmaximal, characteristic
4#16812766—21no—
5#16812758—21no—
6#16812744C411yescharacteristic, complemented
7#16812727—21no—
8#16812695C2211yescharacteristic
9#16812625—21no—
10#100×C109C411yescharacteristic, complemented
11C2×#11724786—41no—
12C22⋊#89137—41no—
13#13182029—21no—
14#13182028—41no—
15C2×D436D411yescharacteristic
16C2×C22⋊D109—41no—
17C2×C22⋊D109—41no—
18D4×D109—41no—
19#13182018—41no—
20D872—41no—
21C4×Dic109D411yescharacteristic
22C2×D4×C109C2×C411yescharacteristic
23M16×C109—21no—
24C23×C109—21no—
25C22×D109—21no—
26C22×D109—41no—
27C2×#89137—81no—
28D4×C109—41no—
29C2×C4×C109C22⋊C411yescharacteristic
30C22⋊D109—42no—
31C22⋊D109—41no—
32C22⋊D109—81no—
33C22⋊D109—81no—
34C2×Dic109—21no—
35C2×Dic109—41no—
36D436—21no—
37D436—41no—
38C4×D109—41no—
39Dic218—21no—
40#11724786—81no—
41C8×C109—41no—
42C22×C109—41no—
43C22×C109—81no—
44C22×C109#9911yescharacteristic
45C2×D109—41no—
46C2×D109—41no—
47C2×D109—81no—
48C2×D109—161no—
49#89137—161no—
50C4×C109—21no—
51Dic109—21no—
52Dic109—21no—
53Dic109—41no—
54C2×C109—21no—
55C2×C109—81no—
56C2×C109AΣL(1,𝔽16)11yescharacteristic
57D109—81no—
58D109—81no—
59#1402—1091nomaximal, Sylow
60C109#140211yescharacteristic, complemented, Sylow
61#453—1091no—
62#353—1091no—
63#331—1091no—
64H(5,𝔽2)—1091no—
65AGL(1,ℤ/8)—2181no—
66#127—1091no—
67C4⋊C8—2181no—
68#104—2181no—
69#100#8913711yescharacteristic, complemented
70#99—2181no—
71#41—4361no—
72#41—2181no—
73C2×D4—1091no—
74C2×D4—4361no—
75C2×D4—4361no—
76C2×D4—4361no—
77C2×D4C2×#8913711yescharacteristic
78SD16—4361no—
79D8—4361no—
80M16—21no—
81C2×C8—4361no—
82C22⋊C4—4361no—
83C42—1091no—
84C23—21no—
85C23—4361no—
86C23—2181no—
87Q8—2181no—
88D4—41no—
89D4—8721no—
90D4—8721no—
91D4—4361no—
92D4—4362no—
93D4—4361no—
94D4—2181no—
95C2×C4—8721no—
96C2×C4—4361no—
97C2×C4—4361no—
98C2×C4—2181no—
99C2×C4C22⋊#8913711yescharacteristic
100C8—41no—
101C8—8721no—
102C22—41no—
103C22—81no—
104C22—8721no—
105C22—4361no—
106C22—4361no—
107C22—17441no—
108C22#1681275811yescharacteristic
109C4—21no—
110C4—4361no—
111C4—17441no—
112C4—2181no—
113C4—2181no—
114C2—21no—
115C2—81no—
116C2—8721no—
117C2—8721no—
118C2#2029592711yescharacteristic
subgroupG/H
centerC2#20295927
commutatorC2×D4×C109C2×C4
FrattiniC2×D4C2×#89137
Fitting#100×C109C4
socleC2×C109AΣL(1,𝔽16)
prime radical#20295196C2
cosocle#16812695C22
hypercenter#100#89137
hypocenterC109#1402
LCSG ▷ C2×D4×C109 ▷ C2×C4×C109 ▷ C22×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C2×D4 ◁ #100

Complements

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

NH ≅ G/Ntype
1. #20295930C2semidirect
2. #20295884C2semidirect
6. #16812744C4semidirect
10. #100×C109C4semidirect
60. C109#1402semidirect
69. #100#89137semidirect

Maximal subgroups

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

subgroupindex
#202959302
#202958842
#202951962
#1402109