Finite Group Databasebeta

← #27186257

Subgroups — #27186257

Order 12928.

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#20266087C211yesmaximal, characteristic, complemented
2#20266037C211yesmaximal, characteristic, complemented
3#20265360C211yesmaximal, characteristic
4#15692322—21no—
5#15692316—21no—
6#15692285—21no—
7#15692253C2211yescharacteristic
8#15692182—21no—
9#15692174C411yescharacteristic
102−1+4×C101C411yescharacteristic
11#13108083—41no—
12C2×#11717581—41no—
13C2×Dic202D411yescharacteristic
14#13108064—41no—
15#13108062—41no—
16#13108058—21no—
17#13108053—41no—
18C4×Dic101D411yescharacteristic
19#41×C101—21no—
20#41×C101—41no—
21#41×C101—41no—
22C2×Q8×C101—41no—
23C2×Q8×C101C2×C411yescharacteristic
24Q8×C101—21no—
25Q8×C101—41no—
26Q8×C101—41no—
27D4×C101—21no—
28D4×C101—41no—
29D4×C101—41no—
30C2×C4×C101—21no—
31C2×C4×C101—41no—
32C2×C4×C101—42no—
33C2×C4×C101C22⋊C411yescharacteristic
34C2×Dic101—21no—
35C2×Dic101—21no—
36Dic202—41no—
37#11717581—81no—
38#11717581—81no—
39#11717579—41no—
40C22×C101—41no—
41C22×C101#9911yescharacteristic
42C4×C101—21no—
43C4×C101—41no—
44C4×C101—41no—
45Dic101—21no—
46Dic101—21no—
47Dic101—41no—
48C2×C101—21no—
49C2×C101—81no—
50C2×C101AΣL(1,𝔽16)11yescharacteristic
51#1405—1011nomaximal, Sylow
52C101#140511yescharacteristic, complemented, Sylow
53#456—1011no—
54#356—1011no—
55#333—1011no—
562−1+4#8793811yescharacteristic
57#137—2021no—
58C4⋊Q8—1011no—
59C4⋊C8—2021no—
60#104—2021no—
61#101—1011no—
62#101—2021no—
63#41—21no—
64#41—41no—
65#41—41no—
66C2×Q8—41no—
67C2×Q8—1011no—
68C2×Q8C2×#8793811yescharacteristic
69Q16—4041no—
70SD16—4041no—
71M16—4041no—
72M16—2021no—
73C2×C8—4041no—
74C4⋊C4—4041no—
75C42—1011no—
76Q8—21no—
77Q8—41no—
78Q8—41no—
79Q8—4041no—
80D4—21no—
81D4—41no—
82D4—41no—
83C2×C4—21no—
84C2×C4—41no—
85C2×C4—42no—
86C2×C4—2021no—
87C2×C4—2021no—
88C2×C4C22⋊#8793811yescharacteristic
89C8—8081no—
90C8—8081no—
91C8—4041no—
92C22—41no—
93C22#1569231311yescharacteristic
94C4—21no—
95C4—41no—
96C4—41no—
97C4—4041no—
98C4—2021no—
99C4—2021no—
100C2—21no—
101C2—81no—
102C2#2026607711yescharacteristic
subgroupG/H
centerC2#20266077
commutatorC2×Q8×C101C2×C4
FrattiniC2×Q8C2×#87938
Fitting, prime radical2−1+4×C101C4
socleC2×C101AΣL(1,𝔽16)
cosocle#15692253C22
hypercenter2−1+4#87938
hypocenterC101#1405
LCSG ▷ C2×Q8×C101 ▷ C2×C4×C101 ▷ C22×C101 ▷ C2×C101 ▷ C101
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. #20266087C2semidirect
2. #20266037C2semidirect
52. C101#1405semidirect

Maximal subgroups

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

subgroupindex
#202660872
#202660372
#202653602
#1405101