Finite Group Databasebeta

← #28378157

Subgroups — #28378157

Order 13952.

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

normal subgroups only

This group has 106 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#20295936C211yesmaximal, characteristic, complemented
2#20295886C211yesmaximal, characteristic, complemented
3#20295209C211yesmaximal, characteristic
4#16812766—21no—
5#16812760—21no—
6#16812729—21no—
7#16812697C2211yescharacteristic
8#16812626—21no—
9#16812618C411yescharacteristic
102−1+4×C109C411yescharacteristic
11#13182038—41no—
12C2×#11724786—41no—
13C2×Dic218D411yescharacteristic
14#13182019—41no—
15#13182017—41no—
16#13182013—21no—
17#13182008—41no—
18C4×Dic109D411yescharacteristic
19#41×C109—21no—
20#41×C109—41no—
21#41×C109—41no—
22C2×Q8×C109—41no—
23C2×Q8×C109C2×C411yescharacteristic
24Q8×C109—21no—
25Q8×C109—41no—
26Q8×C109—41no—
27D4×C109—21no—
28D4×C109—41no—
29D4×C109—41no—
30C2×C4×C109—21no—
31C2×C4×C109—41no—
32C2×C4×C109—42no—
33C2×C4×C109C22⋊C411yescharacteristic
34C2×Dic109—21no—
35C2×Dic109—21no—
36Dic218—41no—
37#11724786—81no—
38#11724786—81no—
39#11724784—41no—
40C22×C109—41no—
41C22×C109#9911yescharacteristic
42C4×C109—21no—
43C4×C109—41no—
44C4×C109—41no—
45Dic109—21no—
46Dic109—21no—
47Dic109—41no—
48C2×C109—21no—
49C2×C109—81no—
50C2×C109AΣL(1,𝔽16)11yescharacteristic
51#1405—1091nomaximal, Sylow
52C109#140511yescharacteristic, complemented, Sylow
53#456—1091no—
54#356—1091no—
55#333—1091no—
562−1+4#8913711yescharacteristic
57#137—2181no—
58C4⋊Q8—1091no—
59C4⋊C8—2181no—
60#104—2181no—
61#101—1091no—
62#101—2181no—
63#41—21no—
64#41—41no—
65#41—41no—
66C2×Q8—41no—
67C2×Q8—1091no—
68C2×Q8C2×#8913711yescharacteristic
69Q16—4361no—
70SD16—4361no—
71M16—4361no—
72M16—2181no—
73C2×C8—4361no—
74C4⋊C4—4361no—
75C42—1091no—
76Q8—21no—
77Q8—41no—
78Q8—41no—
79Q8—4361no—
80D4—21no—
81D4—41no—
82D4—41no—
83C2×C4—21no—
84C2×C4—41no—
85C2×C4—42no—
86C2×C4—2181no—
87C2×C4—2181no—
88C2×C4C22⋊#8913711yescharacteristic
89C8—8721no—
90C8—8721no—
91C8—4361no—
92C22—41no—
93C22#1681275711yescharacteristic
94C4—21no—
95C4—41no—
96C4—41no—
97C4—4361no—
98C4—2181no—
99C4—2181no—
100C2—21no—
101C2—81no—
102C2#2029592611yescharacteristic
subgroupG/H
centerC2#20295926
commutatorC2×Q8×C109C2×C4
FrattiniC2×Q8C2×#89137
Fitting, prime radical2−1+4×C109C4
socleC2×C109AΣL(1,𝔽16)
cosocle#16812697C22
hypercenter2−1+4#89137
hypocenterC109#1405
LCSG ▷ C2×Q8×C109 ▷ C2×C4×C109 ▷ C22×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C2×Q8 ◁ 2−1+4

Complements

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

NH ≅ G/Ntype
1. #20295936C2semidirect
2. #20295886C2semidirect
52. C109#1405semidirect

Maximal subgroups

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

subgroupindex
#202959362
#202958862
#202952092
#1405109