Finite Group Databasebeta

← #352×C499 #44542582

Subgroups — #352×C499 #44542582

Order 31936.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#123×C499C211yesmaximal, characteristic
2#100×C499C211yesmaximal, characteristic
3#99×C499C211yesmaximal, characteristic
4C2×D4×C499C2211yescharacteristic
5C22×C4×C499C411yescharacteristic, complemented
6M16×C499—21no—
7C4⋊C4×C499—21no—
8C22⋊C4×C499—21no—
9C22⋊C4×C499—21no—
10C22⋊C4×C499C411yescharacteristic, complemented
11C23×C499C2×C411yescharacteristic
12C23×C499D411yescharacteristic
13D4×C499—41no—
14C2×C4×C499—21no—
15C2×C4×C499—21no—
16C2×C4×C499—41no—
17C2×C4×C499—41no—
18C2×C4×C499D411yescharacteristic
19C8×C499—41no—
20C22×C499—21no—
21C22×C499—21no—
22C22×C499—41no—
23C22×C499—41no—
24C22×C499C22⋊C411yescharacteristic
25C4×C499—21no—
26C4×C499—41no—
27C4×C499—41no—
28C4×C499—81no—
29C2×C499—21no—
30C2×C499—41no—
31C2×C499—41no—
32C2×C499#9911yescharacteristic
33C499#35211yescharacteristic, direct product factor, Sylow
34#352C49911yesmaximal, characteristic, direct product factor, Sylow
35#123C2×C49911yescharacteristic
36#100C2×C49911yescharacteristic
37#99C2×C49911yescharacteristic
38C2×D4C22×C49911yescharacteristic
39C22×C4C4×C49911yescharacteristic, complemented
40M16—21no—
41C4⋊C4—21no—
42C22⋊C4—21no—
43C22⋊C4—21no—
44C22⋊C4C4×C49911yescharacteristic, complemented
45C23C2×C4×C49911yescharacteristic
46C23D4×C49911yescharacteristic
47D4—41no—
48C2×C4—21no—
49C2×C4—21no—
50C2×C4—41no—
51C2×C4—41no—
52C2×C4D4×C49911yescharacteristic
53C8—41no—
54C22—21no—
55C22—21no—
56C22—41no—
57C22—41no—
58C22C22⋊C4×C49911yescharacteristic
59C4—21no—
60C4—41no—
61C4—41no—
62C4—81no—
63C2—21no—
64C2—41no—
65C2—41no—
66C2#99×C49911yescharacteristic
subgroupG/H
center, socleC2×C499#99
commutatorC23C2×C4×C499
Frattini, cosocleC2×D4C22×C499
prime radicalC2×D4×C499C22
LCSG ▷ C23 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C499 ◁ C22×C499 ◁ C2×D4×C499 ◁ G

Complements

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

NH ≅ G/Ntype
5. C22×C4×C499C4semidirect
10. C22⋊C4×C499C4semidirect
33. C499#352direct (N × H)
34. #352C499direct (N × H)
39. C22×C4C4×C499semidirect
44. C22⋊C4C4×C499semidirect

Maximal subgroups

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

subgroupindex
#123×C4992
#100×C4992
#99×C4992
#352499