Finite Group Databasebeta

← #27186258

Subgroups — #27186258

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#20265362C211yesmaximal, characteristic
4#15692322—21no—
5#15692316—21no—
6#15692303C411yescharacteristic
7#15692288—21no—
8#15692253C2211yescharacteristic
9#15692181—21no—
10#101×C101C411yescharacteristic
11#13108083—41no—
12C2×#11717581—41no—
13#13108075—41no—
14#13108074—21no—
15#13108074—41no—
16C2×Dic202D411yescharacteristic
17Q8×D101—41no—
18Dic404—41no—
19#13108063—41no—
20#13108053—41no—
21C4×Dic101D411yescharacteristic
22C2×Q8×C101C2×C411yescharacteristic
23M16×C101—21no—
24Q8×C101—41no—
25C2×C4×C101—21no—
26C2×C4×C101C22⋊C411yescharacteristic
27C22⋊D101—41no—
28C2×Dic101—21no—
29C2×Dic101—21no—
30D404—21no—
31D404—41no—
32C4×D101—41no—
33C4×D101—42no—
34Dic202—21no—
35Dic202—41no—
36Dic202—41no—
37#11717581—81no—
38#11717581—81no—
39C8×C101—41no—
40C22×C101#9911yescharacteristic
41C2×D101—41no—
42C4×C101—21no—
43C4×C101—41no—
44Dic101—21no—
45Dic101—21no—
46Dic101—41no—
47Dic101—41no—
48C2×C101—21no—
49C2×C101AΣL(1,𝔽16)11yescharacteristic
50D101—81no—
51#1405—1011nomaximal, Sylow
52C101#140511yescharacteristic, complemented, Sylow
53#456—1011no—
54#356—1011no—
55#333—1011no—
562−1+4—1011no—
57#137—2021no—
58C4⋊Q8—1011no—
59C4⋊C8—2021no—
60#104—2021no—
61#101—2021no—
62#101#8793811yescharacteristic
63#41—4041no—
64#41—4041no—
65#41—2021no—
66C2×Q8—1011no—
67C2×Q8—4041no—
68C2×Q8C2×#8793811yescharacteristic
69Q16—4041no—
70SD16—4041no—
71M16—21no—
72M16—4041no—
73C2×C8—4041no—
74C4⋊C4—4041no—
75C42—1011no—
76Q8—41no—
77Q8—4041no—
78Q8—4041no—
79Q8—2021no—
80D4—4041no—
81D4—4041no—
82D4—2021no—
83C2×C4—21no—
84C2×C4—4041no—
85C2×C4—4042no—
86C2×C4—2021no—
87C2×C4—2021no—
88C2×C4C22⋊#8793811yescharacteristic
89C8—41no—
90C8—8081no—
91C8—8081no—
92C22—4041no—
93C22#1569231411yescharacteristic
94C4—21no—
95C4—41no—
96C4—4041no—
97C4—4041no—
98C4—2021no—
99C4—2021no—
100C2—21no—
101C2—8081no—
102C2#2026607811yescharacteristic
subgroupG/H
centerC2#20266078
commutatorC2×Q8×C101C2×C4
FrattiniC2×Q8C2×#87938
Fitting#101×C101C4
socleC2×C101AΣL(1,𝔽16)
prime radical#15692303C4
cosocle#15692253C22
hypercenter#101#87938
hypocenterC101#1405
LCSG ▷ C2×Q8×C101 ▷ C2×C4×C101 ▷ C22×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C2×Q8 ◁ #101

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
#202653622
#1405101