Finite Group Databasebeta

← #28378153

Subgroups — #28378153

Order 13952.

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

normal subgroups only

This group has 112 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#20295934C211yesmaximal, characteristic, complemented
2#20295881C211yesmaximal, characteristic, complemented
3#20295204C211yesmaximal, characteristic
4#16812760—21no—
5#16812754—21no—
6#16812729—21no—
7#16812686C2211yescharacteristic
8#16812626—21no—
9#16812616C411yescharacteristic
10H(5,𝔽2)×C109C411yescharacteristic
11#13182038—41no—
12C2×#11724786—41no—
13C2×Dic218D411yescharacteristic
14#13182019—41no—
15#13182017—41no—
16#13182013—21no—
17C22⋊Dic109—41no—
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—
26Q8×C109—21no—
27D4×C109—21no—
28D4×C109—41no—
29D4×C109—42no—
30D4×C109—41no—
31C2×C4×C109—41no—
32C2×C4×C109—41no—
33C2×C4×C109C22⋊C411yescharacteristic
34C2×Dic109—21no—
35C2×Dic109—21no—
36Dic218—41no—
37#11724786—42no—
38#11724786—81no—
39#11724784—41no—
40C22×C109—41no—
41C22×C109—41no—
42C22×C109—81no—
43C22×C109—161no—
44C22×C109#9911yescharacteristic
45C4×C109—21no—
46C4×C109—41no—
47Dic109—41no—
48Dic109—41no—
49C2×C109—21no—
50C2×C109—81no—
51C2×C109—81no—
52C2×C109AΣL(1,𝔽16)11yescharacteristic
53#1403—1091nomaximal, Sylow
54C109#140311yescharacteristic, complemented, Sylow
55#455—1091no—
56#355—1091no—
57#329—1091no—
58H(5,𝔽2)#8913711yescharacteristic
59#137—2181no—
60#124—1091no—
61#104—2181no—
62#101—2181no—
63#100—1091no—
64#97—2181no—
65#41—21no—
66#41—41no—
67C2×Q8—1091no—
68C2×D4—41no—
69C2×D4—41no—
70C2×D4C2×#8913711yescharacteristic
71Q16—4361no—
72SD16—4361no—
73M16—4361no—
74M16—2181no—
75C2×C8—4361no—
76C22⋊C4—4361no—
77C42—1091no—
78C23—21no—
79C23—41no—
80Q8—21no—
81Q8—4361no—
82D4—21no—
83D4—41no—
84D4—42no—
85D4—41no—
86C2×C4—41no—
87C2×C4—41no—
88C2×C4—2181no—
89C2×C4—2181no—
90C2×C4C22⋊#8913711yescharacteristic
91C8—8721no—
92C8—4361no—
93C8—4362no—
94C22—41no—
95C22—41no—
96C22—81no—
97C22—161no—
98C22#1681275711yescharacteristic
99C4—21no—
100C4—41no—
101C4—4361no—
102C4—4361no—
103C2—21no—
104C2—81no—
105C2—81no—
106C2#2029592611yescharacteristic
subgroupG/H
centerC2#20295926
commutatorC2×D4×C109C2×C4
FrattiniC2×D4C2×#89137
Fitting, prime radicalH(5,𝔽2)×C109C4
socleC2×C109AΣL(1,𝔽16)
cosocle#16812686C22
hypercenterH(5,𝔽2)#89137
hypocenterC109#1403
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. #20295934C2semidirect
2. #20295881C2semidirect
54. C109#1403semidirect

Maximal subgroups

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

subgroupindex
#202959342
#202958812
#202952042
#1403109