Finite Group Databasebeta

← #28378151

Subgroups — #28378151

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#20295194C211yesmaximal, characteristic
4#16812766—21no—
5#16812758—21no—
6#16812724—21no—
7#16812695C2211yescharacteristic
8#16812626—21no—
9#16812616C411yescharacteristic, complemented
10H(5,𝔽2)×C109C411yescharacteristic, complemented
11C2×#11724786—41no—
12C22⋊#89137—41no—
13C2×D436D411yescharacteristic
14C2×C22⋊D109—41no—
15#13182016—41no—
16#13182014—41no—
17#13182013—21no—
18C4×Dic109D411yescharacteristic
19#41×C109—21no—
20#41×C109—41no—
21C2×D4×C109—41no—
22C2×D4×C109—41no—
23C2×D4×C109C2×C411yescharacteristic
24C23×C109—21no—
25C23×C109—41no—
26C22×D109—21no—
27C2×#89137—81no—
28Q8×C109—21no—
29D4×C109—21no—
30D4×C109—41no—
31D4×C109—42no—
32D4×C109—41no—
33C2×C4×C109—41no—
34C2×C4×C109—41no—
35C2×C4×C109C22⋊C411yescharacteristic
36C22⋊D109—81no—
37C22⋊D109—81no—
38C2×Dic109—21no—
39D436—41no—
40#11724786—81no—
41#11724784—41no—
42C22×C109—41no—
43C22×C109—41no—
44C22×C109—81no—
45C22×C109—161no—
46C22×C109#9911yescharacteristic
47C2×D109—41no—
48C2×D109—81no—
49#89137—161no—
50C4×C109—21no—
51C4×C109—41no—
52Dic109—21no—
53Dic109—21no—
54C2×C109—21no—
55C2×C109—81no—
56C2×C109—81no—
57C2×C109AΣL(1,𝔽16)11yescharacteristic
58D109—81no—
59#1402—1091nomaximal, Sylow
60C109#140211yescharacteristic, complemented, Sylow
61#453—1091no—
62#353—1091no—
63#331—1091no—
64H(5,𝔽2)#8913711yescharacteristic, complemented
65AGL(1,ℤ/8)—2181no—
66#127—1091no—
67C4⋊C8—2181no—
68#104—2181no—
69#100—1091no—
70#99—2181no—
71#41—21no—
72#41—41no—
73C2×D4—41no—
74C2×D4—41no—
75C2×D4—1091no—
76C2×D4—4361no—
77C2×D4C2×#8913711yescharacteristic
78SD16—4361no—
79D8—4361no—
80M16—2181no—
81C2×C8—4361no—
82C22⋊C4—4361no—
83C42—1091no—
84C23—21no—
85C23—41no—
86C23—2181no—
87Q8—21no—
88D4—21no—
89D4—41no—
90D4—42no—
91D4—41no—
92D4—8721no—
93D4—8721no—
94D4—4361no—
95C2×C4—41no—
96C2×C4—41no—
97C2×C4—8721no—
98C2×C4—2181no—
99C2×C4C22⋊#8913711yescharacteristic
100C8—8721no—
101C8—4361no—
102C22—41no—
103C22—41no—
104C22—81no—
105C22—161no—
106C22—8721no—
107C22—4361no—
108C22#1681275711yescharacteristic
109C4—21no—
110C4—41no—
111C4—17441no—
112C4—2181no—
113C4—2181no—
114C2—21no—
115C2—81no—
116C2—81no—
117C2—8721no—
118C2#2029592611yescharacteristic
subgroupG/H
centerC2#20295926
commutatorC2×D4×C109C2×C4
FrattiniC2×D4C2×#89137
FittingH(5,𝔽2)×C109C4
socleC2×C109AΣL(1,𝔽16)
prime radical#20295194C2
cosocle#16812695C22
hypercenterH(5,𝔽2)#89137
hypocenterC109#1402
LCSG ▷ C2×D4×C109 ▷ C2×C4×C109 ▷ C22×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C2×D4 ◁ H(5,𝔽2)

Complements

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

NH ≅ G/Ntype
1. #20295930C2semidirect
2. #20295884C2semidirect
9. #16812616C4semidirect
10. H(5,𝔽2)×C109C4semidirect
60. C109#1402semidirect
64. H(5,𝔽2)#89137semidirect

Maximal subgroups

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

subgroupindex
#202959302
#202958842
#202951942
#1402109