Finite Group Databasebeta

← #27186254

Subgroups — #27186254

Order 12928.

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#20266085C211yesmaximal, characteristic, complemented
2#20266032C211yesmaximal, characteristic, complemented
3#20265357C211yesmaximal, characteristic
4#15692316—21no—
5#15692310—21no—
6#15692300C411yescharacteristic
7#15692288—21no—
8#15692242C2211yescharacteristic
9#15692181—21no—
10#100×C101C411yescharacteristic
11#13108083—41no—
12C2×#11717581—41no—
13#13108074—21no—
14#13108073—41no—
15C2×Dic202D411yescharacteristic
16C2×C22⋊D101—41no—
17D4×D101—41no—
18Dic404—41no—
19#13108063—41no—
20C22⋊Dic101—41no—
21C4×Dic101D411yescharacteristic
22C2×D4×C101C2×C411yescharacteristic
23M16×C101—21no—
24C23×C101—21no—
25C22×D101—41no—
26D4×C101—41no—
27C2×C4×C101C22⋊C411yescharacteristic
28C22⋊D101—42no—
29C22⋊D101—41no—
30C2×Dic101—21no—
31C2×Dic101—21no—
32C2×Dic101—41no—
33D404—21no—
34C4×D101—41no—
35Dic202—21no—
36Dic202—41no—
37#11717581—42no—
38#11717581—81no—
39C8×C101—41no—
40C22×C101—41no—
41C22×C101—81no—
42C22×C101#9911yescharacteristic
43C2×D101—41no—
44C2×D101—161no—
45C4×C101—21no—
46Dic101—41no—
47Dic101—41no—
48Dic101—41no—
49C2×C101—21no—
50C2×C101—81no—
51C2×C101AΣL(1,𝔽16)11yescharacteristic
52D101—81no—
53#1403—1011nomaximal, Sylow
54C101#140311yescharacteristic, complemented, Sylow
55#455—1011no—
56#355—1011no—
57#329—1011no—
58H(5,𝔽2)—1011no—
59#137—2021no—
60#124—1011no—
61#104—2021no—
62#101—2021no—
63#100#8793811yescharacteristic
64#97—2021no—
65#41—4041no—
66#41—2021no—
67C2×Q8—1011no—
68C2×D4—4041no—
69C2×D4—4041no—
70C2×D4C2×#8793811yescharacteristic
71Q16—4041no—
72SD16—4041no—
73M16—21no—
74M16—4041no—
75C2×C8—4041no—
76C22⋊C4—4041no—
77C42—1011no—
78C23—21no—
79C23—4041no—
80Q8—4041no—
81Q8—2021no—
82D4—41no—
83D4—4042no—
84D4—4041no—
85D4—2021no—
86C2×C4—4041no—
87C2×C4—4041no—
88C2×C4—2021no—
89C2×C4—2021no—
90C2×C4C22⋊#8793811yescharacteristic
91C8—41no—
92C8—8081no—
93C8—4042no—
94C22—41no—
95C22—81no—
96C22—16161no—
97C22—4041no—
98C22#1569231411yescharacteristic
99C4—21no—
100C4—4041no—
101C4—4041no—
102C4—4041no—
103C2—21no—
104C2—81no—
105C2—8081no—
106C2#2026607811yescharacteristic
subgroupG/H
centerC2#20266078
commutatorC2×D4×C101C2×C4
FrattiniC2×D4C2×#87938
Fitting#100×C101C4
socleC2×C101AΣL(1,𝔽16)
prime radical#15692300C4
cosocle#15692242C22
hypercenter#100#87938
hypocenterC101#1403
LCSG ▷ C2×D4×C101 ▷ C2×C4×C101 ▷ C22×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C2×D4 ◁ #100

Complements

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

NH ≅ G/Ntype
1. #20266085C2semidirect
2. #20266032C2semidirect
54. C101#1403semidirect

Maximal subgroups

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

subgroupindex
#202660852
#202660322
#202653572
#1403101