Finite Group Databasebeta

← C28×C121 #72207751

Subgroups — C28×C121 #72207751

Order 30976.

1251597 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C27×C121C21255yesmaximal, direct product factor
2C26×C121C22110795yesdirect product factor
3C25×C121C23197155yesdirect product factor
4C28×C11C1111yesmaximal, characteristic
5C24×C121C241200787yesdirect product factor
6C27×C11C2×C111255yes—
7C23×C121C25197155yesdirect product factor
8C26×C11C22×C11110795yes—
9C22×C121C26110795yesdirect product factor
10C25×C11C23×C11197155yes—
11C28C12111yescharacteristic, direct product factor, Sylow
12C2×C121C271255yesdirect product factor
13C24×C11C24×C111200787yes—
14C27C2×C1211255yesdirect product factor
15C121C2811yescharacteristic, direct product factor, Sylow
16C23×C11C25×C11197155yes—
17C26C22×C121110795yesdirect product factor
18C22×C11C26×C11110795yes—
19C25C23×C121197155yesdirect product factor
20C2×C11C27×C111255yes—
21C24C24×C1211200787yesdirect product factor
22C11C28×C1111yescharacteristic
23C23C25×C121197155yesdirect product factor
24C22C26×C121110795yesdirect product factor
25C2C27×C1211255yesdirect product factor
subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC11C28×C11
socle, prime radicalC28×C11C11
LCSG ▷ C1
UCSC1 ◁ G

Complements

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

NH ≅ G/Ntype
1. C27×C121C2direct (N × H)
2. C26×C121C22direct (N × H)
3. C25×C121C23direct (N × H)
5. C24×C121C24direct (N × H)
7. C23×C121C25direct (N × H)
9. C22×C121C26direct (N × H)
11. C28C121direct (N × H)
12. C2×C121C27direct (N × H)
14. C27C2×C121direct (N × H)
15. C121C28direct (N × H)
17. C26C22×C121direct (N × H)
19. C25C23×C121direct (N × H)
21. C24C24×C121direct (N × H)
23. C23C25×C121direct (N × H)
24. C22C26×C121direct (N × H)
25. C2C27×C121direct (N × H)

Maximal subgroups

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

subgroupindex
C27×C1212
C28×C1111