Finite Group Databasebeta

← #27169080

Subgroups — #27169080

Order 12928.

158 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 158 conjugacy classes of subgroups — too many to draw. Only its 41 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#20264901C211yesmaximal, characteristic
2#20264901C211yesmaximal, characteristic
3#385×C101C211yesmaximal, characteristic
4C22⋊#11717579—21no—
5C22⋊#11717579—21no—
6C23×C4×C101C411yescharacteristic
7C2×C4⋊C4×C101—21no—
8C2×C22⋊C4×C101C411yescharacteristic
9C2×C22⋊C4×C101C2211yescharacteristic
10#95×C101—21no—
11C2×#11717579—41no—
12C2×#11717579—41no—
13C24×C101C2×C411yescharacteristic
14C22×C4×C101—21no—
15C22×C4×C101—21no—
16C22×C4×C101—42no—
17C22×C4×C101—41no—
18C22×C4×C101D411yescharacteristic
19C22×C4×C101D411yescharacteristic
20C4⋊C4×C101—42no—
21C22⋊C4×C101—21no—
22C22⋊C4×C101—41no—
23C22⋊C4×C101C812yescomplemented
24C23×C101—21no—
25C23×C101—21no—
26C23×C101—41no—
27C23×C101—41no—
28C23×C101C22⋊C411yescharacteristic
29C23×C101C2×C811yescharacteristic
30C23×C101M1611yescharacteristic
31C2×C4×C101—22no—
32C2×C4×C101—22no—
33C2×C4×C101—21no—
34C2×C4×C101—21no—
35C2×C4×C101—41no—
36C2×C4×C101—41no—
37C2×C4×C101—41no—
38C2×C4×C101—42no—
39C2×C4×C101—41no—
40C2×C4×C101—41no—
41C2×C4×C101—41no—
42C2×C4×C101—42no—
43#11717579—81no—
44#11717579—81no—
45C22×C101—21no—
46C22×C101—21no—
47C22×C101—21no—
48C22×C101—21no—
49C22×C101—41no—
50C22×C101—41no—
51C22×C101—42no—
52C22×C101—41no—
53C22×C101—41no—
54C22×C101C22⋊C811yescharacteristic
55C22×C101#9911yescharacteristic
56C22×C101#10111yescharacteristic
57C4×C101—42no—
58C4×C101—41no—
59C4×C101—42no—
60C4×C101—41no—
61C2×C101—21no—
62C2×C101—21no—
63C2×C101—41no—
64C2×C101—41no—
65C2×C101#32411yescharacteristic
66C2×C101AΣL(1,𝔽16)11yescharacteristic
67C2×C101#35211yescharacteristic
68#1326—1011nomaximal, Sylow
69C101#132611yescharacteristic, complemented, Sylow
70#385D10111yescharacteristic
71#323—1011no—
72#323—1011no—
73C23×C4Dic10111yescharacteristic
74C2×C4⋊C4—21no—
75C2×C22⋊C4Dic10111yescharacteristic
76C2×C22⋊C4C2×D10111yescharacteristic
77C22⋊C8—2021no—
78C22⋊C8—2021no—
79#95—21no—
80C24C2×Dic10111yescharacteristic
81C22×C4—21no—
82C22×C4—21no—
83C22×C4—42no—
84C22×C4—41no—
85C22×C4C22⋊D10111yescharacteristic
86C22×C4C22⋊D10111yescharacteristic
87C2×C8—4041no—
88C2×C8—4041no—
89C4⋊C4—42no—
90C22⋊C4—21no—
91C22⋊C4—41no—
92C22⋊C4#1171757912yescomplemented
93C23—21no—
94C23—21no—
95C23—41no—
96C23—41no—
97C23C22⋊Dic10111yescharacteristic
98C23C2×#1171757911yescharacteristic
99C23#1310805811yescharacteristic
100C2×C4—22no—
101C2×C4—22no—
102C2×C4—21no—
103C2×C4—21no—
104C2×C4—41no—
105C2×C4—41no—
106C2×C4—41no—
107C2×C4—42no—
108C2×C4—41no—
109C2×C4—41no—
110C2×C4—41no—
111C2×C4—42no—
112C8—8081no—
113C8—8081no—
114C22—21no—
115C22—21no—
116C22—21no—
117C22—21no—
118C22—41no—
119C22—41no—
120C22—42no—
121C22—41no—
122C22—41no—
123C22C22⋊#1171757911yescharacteristic
124C22#1569217011yescharacteristic
125C22#1569217411yescharacteristic
126C4—42no—
127C4—41no—
128C4—42no—
129C4—41no—
130C2—21no—
131C2—21no—
132C2—41no—
133C2—41no—
134C2#2026490311yescharacteristic
135C2#2026496411yescharacteristic
136C2#2026496711yescharacteristic
subgroupG/H
centerC22#15692170
commutatorC23×C101C2×C8
FrattiniC2×C22⋊C4C2×D101
Fitting#385×C101C2
socleC22×C101#99
prime radicalC24×C101C2×C4
cosocleC2×C22⋊C4×C101C22
hypercenter#385D101
hypocenterC101#1326
LCSG ▷ C23×C101 ▷ C22×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #385

Complements

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

NH ≅ G/Ntype
23. C22⋊C4×C101C8semidirect
69. C101#1326semidirect
92. C22⋊C4#11717579semidirect

Maximal subgroups

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

subgroupindex
#202649012
#385×C1012
#1326101