Finite Group Databasebeta

← #44486240

Subgroups — #44486240

Order 30592.

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#29504756C212yesmaximal, complemented
2#29504569C214yesmaximal, complemented
3#535×C239C211yesmaximal, characteristic
4C2×#16838532—22no—
5#21439879C2214yescomplemented
6#21439877—22no—
7C2×#41×C239C2211yescharacteristic
8C22×D4×C239C411yescharacteristic
9#127×C239C412yes—
10#124×C239C2212yes—
11#121×C239—22no—
12#120×C239—22no—
13#117×C239C411yescharacteristic
14#16838532—24no—
15#16838532—42no—
16C2×C239⋊C8—42no—
17C24×C239—21no—
18#41×C239—42no—
19C2×Q8×C239C2311yescharacteristic
20C2×D4×C239—24no—
21C2×D4×C239—21no—
22C2×D4×C239—42no—
23C2×D4×C239C2×C412yes—
24C2×D4×C239C2×C411yescharacteristic
25C2×D4×C239D412yes—
26C22×C4×C239C2×C411yescharacteristic
27C22×C4×C239D412yes—
28C4⋊C4×C239—21no—
29C22⋊C4×C239—21no—
30C22⋊C4×C239—24no—
31C42×C239C2×C412yes—
32C239⋊C8—44no—
33C23×C239—22no—
34C23×C239—42no—
35C23×C239—82no—
36C23×C239C22⋊C411yescharacteristic
37C23×C239C22⋊C412yes—
38Q8×C239—41no—
39D4×C239—41no—
40D4×C239—42no—
41D4×C239—42no—
42D4×C239—42no—
43D4×C239—84no—
44C2×C4×C239—22no—
45C2×C4×C239—22no—
46C2×C4×C239—22no—
47C2×C4×C239—22no—
48C2×C4×C239C22⋊C411yescharacteristic
49C2×C4×C239C22×C411yescharacteristic
50C2×C4×C239C2×D412yes—
51C22×C239—21no—
52C22×C239—22no—
53C22×C239—42no—
54C22×C239—41no—
55C22×C239—44no—
56C22×C239—42no—
57C22×C239—84no—
58C22×C239C2×C22⋊C411yescharacteristic
59C4×C239—21no—
60C4×C239—22no—
61C4×C239—42no—
62C4×C239#9912yes—
63C2×C239—21no—
64C2×C239—42no—
65C2×C239—41no—
66C2×C239—82no—
67C2×C239C2×#9911yescharacteristic
68C239#213411yescharacteristic, complemented, Sylow
69#2134—2391nomaximal, Sylow
70#535D23911yescharacteristic
71#413—2392no—
72#355—2394no—
73C2×#41C2×D23911yescharacteristic
74C22×D4Dic23911yescharacteristic
75C2×M16—4782no—
76#127Dic23912yes—
77#124C2×D23912yes—
78#121—22no—
79#120—22no—
80#117Dic23911yescharacteristic
81#101—2394no—
82#100—4782no—
83C24—21no—
84#41—42no—
85C2×Q8C22×D23911yescharacteristic
86C2×D4—24no—
87C2×D4—21no—
88C2×D4—42no—
89C2×D4C2×Dic23912yes—
90C2×D4C2×Dic23911yescharacteristic
91C2×D4C22⋊D23912yes—
92C22×C4C2×Dic23911yescharacteristic
93C22×C4C22⋊D23912yes—
94M16—9562no—
95M16—4784no—
96C2×C8—9562no—
97C4⋊C4—21no—
98C22⋊C4—21no—
99C22⋊C4—24no—
100C42C2×Dic23912yes—
101C23—22no—
102C23—42no—
103C23—82no—
104C23C22⋊Dic23911yescharacteristic
105C23C22⋊Dic23912yes—
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⋊Dic23911yescharacteristic
117C2×C4C22×Dic23911yescharacteristic
118C2×C4C2×C22⋊D23912yes—
119C8—9564no—
120C22—21no—
121C22—22no—
122C22—42no—
123C22—41no—
124C22—44no—
125C22—42no—
126C22—84no—
127C22C2×C22⋊Dic23911yescharacteristic
128C4—22no—
129C4—21no—
130C4—42no—
131C4#2143987512yes—
132C2—21no—
133C2—41no—
134C2—42no—
135C2—82no—
136C2C2×#2143987511yescharacteristic
subgroupG/H
centerC2C2×#21439875
commutatorC2×C4×C239C22×C4
FrattiniC2×Q8C22×D239
Fitting, prime radical#535×C239C2
socleC2×C239C2×#99
cosocleC2×Q8×C239C23
hypercenter#535D239
hypocenterC239#2134
LCSG ▷ C2×C4×C239 ▷ C22×C239 ▷ C2×C239 ▷ C239
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#41 ◁ #535

Complements

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

NH ≅ G/Ntype
1. #29504756C2semidirect
2. #29504569C2semidirect
5. #21439879C22semidirect
68. C239#2134semidirect

Maximal subgroups

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

subgroupindex
#295047562
#295045692
#535×C2392
#2134239