Finite Group Databasebeta

← #20259342

Subgroups — #20259342

Order 6112.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15690287C211yesmaximal, characteristic, complemented
2#15690277C211yesmaximal, characteristic, complemented
3#15690275C211yesmaximal, characteristic, complemented
4#15690274C211yesmaximal, characteristic, complemented
5#15690272C211yesmaximal, characteristic, complemented
6C2×C191⋊C8C211yesmaximal, characteristic, complemented
7#41×C191C211yesmaximal, characteristic, complemented
8Dic382C2211yescharacteristic
9D764C2211yescharacteristic
10C22⋊D191—21no—
11C4×D191—21no—
12C191⋊C8C2211yescharacteristic
13C191⋊C8C2211yescharacteristic
14Q8×C191C2211yescharacteristic
15D4×C191—21no—
16D4×C191C2211yescharacteristic
17C2×C4×C191—21no—
18C2×C4×C191C2211yescharacteristic
19C22×C191—21no—
20C22×C191D411yescharacteristic
21C2×D191—21no—
22C4×C191—21no—
23C4×C191D411yescharacteristic
24C4×C191C2311yescharacteristic
25Dic191—21no—
26C2×C191—21no—
27C2×C191—41no—
28C2×C191C2×D411yescharacteristic
29D191—41no—
30C191#13511yescharacteristic, complemented, Sylow
31#135—1911nomaximal, Sylow
32#41—1911no—
33#41D19111yescharacteristic, complemented
34Q16—1911no—
35SD16—1911no—
36SD16—1911no—
37D8—1911no—
38C2×C8—1911no—
39Q8—1911no—
40Q8C2×D19111yescharacteristic
41D4—21no—
42D4—3821no—
43D4—1911no—
44D4C2×D19111yescharacteristic
45C2×C4—21no—
46C2×C4—3821no—
47C2×C4C2×D19111yescharacteristic
48C8—1911no—
49C8—1911no—
50C22—21no—
51C22—3821no—
52C22C22⋊D19111yescharacteristic
53C4—21no—
54C4—3821no—
55C4C22⋊D19111yescharacteristic
56C4C22×D19111yescharacteristic
57C2—21no—
58C2—41no—
59C2—7641no—
60C2C2×C22⋊D19111yescharacteristic
subgroupG/H
centerC4C22⋊D191
commutatorC4×C191C23
FrattiniC4C22×D191
Fitting#41×C191C2
socleC2×C191C2×D4
hypercenter#41D191
hypocenterC191#135
LCSG ▷ C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C4 ◁ C2×C4 ◁ #41

Complements

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

NH ≅ G/Ntype
1. #15690287C2semidirect
2. #15690277C2semidirect
3. #15690275C2semidirect
4. #15690274C2semidirect
5. #15690272C2semidirect
6. C2×C191⋊C8C2semidirect
7. #41×C191C2semidirect
30. C191#135semidirect
33. #41D191semidirect