Finite Group Databasebeta

← #44548313

Subgroups — #44548313

Order 32128.

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#30631411C211yesmaximal, characteristic
2#30631411C211yesmaximal, characteristic
3#385×C251C211yesmaximal, characteristic
4C22⋊(C251⋊C8)—21no—
5C22⋊(C251⋊C8)—21no—
6C23×C4×C251C411yescharacteristic
7C2×C4⋊C4×C251—21no—
8C2×C22⋊C4×C251C411yescharacteristic
9C2×C22⋊C4×C251C2211yescharacteristic
10#95×C251—21no—
11C2×C251⋊C8—41no—
12C2×C251⋊C8—41no—
13C24×C251C2×C411yescharacteristic
14C22×C4×C251—21no—
15C22×C4×C251—21no—
16C22×C4×C251—42no—
17C22×C4×C251—41no—
18C22×C4×C251D411yescharacteristic
19C22×C4×C251D411yescharacteristic
20C4⋊C4×C251—42no—
21C22⋊C4×C251—21no—
22C22⋊C4×C251—41no—
23C22⋊C4×C251C812yescomplemented
24C251⋊C8—81no—
25C251⋊C8—81no—
26C23×C251—21no—
27C23×C251—21no—
28C23×C251—41no—
29C23×C251—41no—
30C23×C251C22⋊C411yescharacteristic
31C23×C251C2×C811yescharacteristic
32C23×C251M1611yescharacteristic
33C2×C4×C251—22no—
34C2×C4×C251—22no—
35C2×C4×C251—21no—
36C2×C4×C251—21no—
37C2×C4×C251—41no—
38C2×C4×C251—41no—
39C2×C4×C251—41no—
40C2×C4×C251—42no—
41C2×C4×C251—41no—
42C2×C4×C251—41no—
43C2×C4×C251—41no—
44C2×C4×C251—42no—
45C22×C251—21no—
46C22×C251—21no—
47C22×C251—21no—
48C22×C251—21no—
49C22×C251—41no—
50C22×C251—41no—
51C22×C251—42no—
52C22×C251—41no—
53C22×C251—41no—
54C22×C251C22⋊C811yescharacteristic
55C22×C251#9911yescharacteristic
56C22×C251#10111yescharacteristic
57C4×C251—42no—
58C4×C251—42no—
59C4×C251—41no—
60C4×C251—41no—
61C2×C251—21no—
62C2×C251—21no—
63C2×C251—41no—
64C2×C251—41no—
65C2×C251#32411yescharacteristic
66C2×C251AΣL(1,𝔽16)11yescharacteristic
67C2×C251#35211yescharacteristic
68C251#132611yescharacteristic, complemented, Sylow
69#1326—2511nomaximal, Sylow
70#385D25111yescharacteristic
71#323—2511no—
72#323—2511no—
73C23×C4Dic25111yescharacteristic
74C2×C4⋊C4—21no—
75C2×C22⋊C4Dic25111yescharacteristic
76C2×C22⋊C4C2×D25111yescharacteristic
77C22⋊C8—5021no—
78C22⋊C8—5021no—
79#95—21no—
80C24C2×Dic25111yescharacteristic
81C22×C4—21no—
82C22×C4—21no—
83C22×C4—42no—
84C22×C4—41no—
85C22×C4C22⋊D25111yescharacteristic
86C22×C4C22⋊D25111yescharacteristic
87C2×C8—10041no—
88C2×C8—10041no—
89C4⋊C4—42no—
90C22⋊C4—21no—
91C22⋊C4—41no—
92C22⋊C4C251⋊C812yescomplemented
93C23—21no—
94C23—21no—
95C23—41no—
96C23—41no—
97C23C22⋊Dic25111yescharacteristic
98C23C2×C251⋊C811yescharacteristic
99C23#1686079411yescharacteristic
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—20081no—
113C8—20081no—
114C22—21no—
115C22—21no—
116C22—21no—
117C22—21no—
118C22—41no—
119C22—41no—
120C22—42no—
121C22—41no—
122C22—41no—
123C22C22⋊(C251⋊C8)11yescharacteristic
124C22#2254863011yescharacteristic
125C22#2254863411yescharacteristic
126C4—42no—
127C4—41no—
128C4—42no—
129C4—41no—
130C2—21no—
131C2—21no—
132C2—41no—
133C2—41no—
134C2#3063141311yescharacteristic
135C2#3063147411yescharacteristic
136C2#3063147711yescharacteristic
subgroupG/H
centerC22#22548630
commutatorC23×C251C2×C8
FrattiniC2×C22⋊C4C2×D251
Fitting#385×C251C2
socleC22×C251#99
prime radicalC24×C251C2×C4
cosocleC2×C22⋊C4×C251C22
hypercenter#385D251
hypocenterC251#1326
LCSG ▷ C23×C251 ▷ C22×C251 ▷ C2×C251 ▷ C251
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #385

Complements

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

NH ≅ G/Ntype
23. C22⋊C4×C251C8semidirect
68. C251#1326semidirect
92. C22⋊C4C251⋊C8semidirect

Maximal subgroups

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

subgroupindex
#306314112
#385×C2512
#1326251