Finite Group Databasebeta

← #27172824

Subgroups — #27172824

Order 12928.

262 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 73 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#20265161C212yesmaximal, complemented
2#20264974C214yesmaximal, complemented
3#535×C101C211yesmaximal, characteristic
4C2×#13108058—22no—
5#15692174C2214yescomplemented
6#15692172—22no—
7C2×#41×C101C2211yescharacteristic
8C22×D4×C101C411yescharacteristic
9#127×C101C412yes—
10#124×C101C2212yes—
11#121×C101—22no—
12#120×C101—22no—
13#117×C101C411yescharacteristic
14#13108058—24no—
15#13108058—42no—
16C2×#11717579—42no—
17C24×C101—21no—
18#41×C101—42no—
19C2×Q8×C101C2311yescharacteristic
20C2×D4×C101—24no—
21C2×D4×C101—21no—
22C2×D4×C101—42no—
23C2×D4×C101C2×C412yes—
24C2×D4×C101C2×C411yescharacteristic
25C2×D4×C101D412yes—
26C22×C4×C101C2×C411yescharacteristic
27C22×C4×C101D412yes—
28C4⋊C4×C101—21no—
29C22⋊C4×C101—21no—
30C22⋊C4×C101—24no—
31C42×C101C2×C412yes—
32C23×C101—22no—
33C23×C101—42no—
34C23×C101—82no—
35C23×C101C22⋊C411yescharacteristic
36C23×C101C22⋊C412yes—
37Q8×C101—41no—
38D4×C101—41no—
39D4×C101—42no—
40D4×C101—42no—
41D4×C101—42no—
42D4×C101—84no—
43C2×C4×C101—22no—
44C2×C4×C101—22no—
45C2×C4×C101—22no—
46C2×C4×C101—22no—
47C2×C4×C101C22⋊C411yescharacteristic
48C2×C4×C101C22×C411yescharacteristic
49C2×C4×C101C2×D412yes—
50#11717579—44no—
51C22×C101—21no—
52C22×C101—22no—
53C22×C101—42no—
54C22×C101—41no—
55C22×C101—44no—
56C22×C101—42no—
57C22×C101—84no—
58C22×C101C2×C22⋊C411yescharacteristic
59C4×C101—22no—
60C4×C101—21no—
61C4×C101—42no—
62C4×C101#9912yes—
63C2×C101—21no—
64C2×C101—42no—
65C2×C101—41no—
66C2×C101—82no—
67C2×C101C2×#9911yescharacteristic
68#2134—1011nomaximal, Sylow
69C101#213411yescharacteristic, complemented, Sylow
70#535D10111yescharacteristic
71#413—1012no—
72#355—1014no—
73C2×#41C2×D10111yescharacteristic
74C22×D4Dic10111yescharacteristic
75C2×M16—2022no—
76#127Dic10112yes—
77#124C2×D10112yes—
78#121—22no—
79#120—22no—
80#117Dic10111yescharacteristic
81#101—1014no—
82#100—2022no—
83C24—21no—
84#41—42no—
85C2×Q8C22×D10111yescharacteristic
86C2×D4—24no—
87C2×D4—21no—
88C2×D4—42no—
89C2×D4C2×Dic10112yes—
90C2×D4C2×Dic10111yescharacteristic
91C2×D4C22⋊D10112yes—
92C22×C4C2×Dic10111yescharacteristic
93C22×C4C22⋊D10112yes—
94M16—4042no—
95M16—2024no—
96C2×C8—4042no—
97C4⋊C4—21no—
98C22⋊C4—21no—
99C22⋊C4—24no—
100C42C2×Dic10112yes—
101C23—22no—
102C23—42no—
103C23—82no—
104C23C22⋊Dic10111yescharacteristic
105C23C22⋊Dic10112yes—
106Q8—41no—
107D4—41no—
108D4—42no—
109D4—42no—
110D4—42no—
111D4—84no—
112C2×C4—22no—
113C2×C4—22no—
114C2×C4—22no—
115C2×C4—22no—
116C2×C4C22⋊Dic10111yescharacteristic
117C2×C4C22×Dic10111yescharacteristic
118C2×C4C2×C22⋊D10112yes—
119C8—4044no—
120C22—21no—
121C22—22no—
122C22—42no—
123C22—41no—
124C22—44no—
125C22—42no—
126C22—84no—
127C22C2×C22⋊Dic10111yescharacteristic
128C4—22no—
129C4—21no—
130C4—42no—
131C4#1569217012yes—
132C2—21no—
133C2—41no—
134C2—42no—
135C2—82no—
136C2C2×#1569217011yescharacteristic
subgroupG/H
centerC2C2×#15692170
commutatorC2×C4×C101C22×C4
FrattiniC2×Q8C22×D101
Fitting, prime radical#535×C101C2
socleC2×C101C2×#99
cosocleC2×Q8×C101C23
hypercenter#535D101
hypocenterC101#2134
LCSG ▷ C2×C4×C101 ▷ C22×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#41 ◁ #535

Complements

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

NH ≅ G/Ntype
1. #20265161C2semidirect
2. #20264974C2semidirect
5. #15692174C22semidirect
69. C101#2134semidirect

Maximal subgroups

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

subgroupindex
#202651612
#202649742
#535×C1012
#2134101