Finite Group Databasebeta

← C3×D49×D55 #44568384

Subgroups — C3×D49×D55 #44568384

Order 32340.

120 conjugacy classes of subgroups; only the 42 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 42 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
1C3×D2695C211yesmaximal, characteristic, complemented
2C3×C49×D55C211yesmaximal, characteristic, complemented
3C3×C5×C11×D49C211yesmaximal, characteristic, complemented
4D49×D55C311yesmaximal, characteristic, direct product factor, Hall
5C3×C5×C11×C49C2211yescharacteristic, complemented, Hall
6C3×D11×D49—51nomaximal, Hall
7D2695C2×C311yescharacteristic, complemented
8C49×D55C2×C311yescharacteristic, complemented
9C5×C11×D49C2×C311yescharacteristic, complemented
10C3×D7×D55—71nomaximal
11C3×D539—51no—
12C3×C11×D49D511yescharacteristic, complemented
13C3×D11×C49—51no—
14C3×D5×D49—111nomaximal, Hall
15C5×C11×C49C22×C311yescharacteristic, complemented, Hall
16C3×D385—71no—
17C3×C7×D55D711yescharacteristic
18C3×C5×C11×D7—71no—
19D11×D49—51noHall
20C3×C11×C49C2×D511yescharacteristic, complemented, Hall
21D7×D55—71no—
22C3×D245—111no—
23C3×D5×C49—111no—
24C3×C5×D49D1111yescharacteristic, complemented
25C3×C5×C7×C11C2×D711yescharacteristic
26D539—51no—
27D11×C49—51no—
28C11×D49C3×D511yescharacteristic, complemented
29D5×D49—111noHall
30C3×D7×D11—351no—
31D385—71no—
32C7×D55C3×D711yescharacteristic
33C5×C11×D7—71no—
34C3×C5×C49C2×D1111yescharacteristic, complemented, Hall
35C2×C3×D55—491noHall
36C2×C3×D49—551noHall
37C11×C49C2×C3×D511yescharacteristic, complemented, Hall
38D245—111no—
39C5×D49C3×D1111yescharacteristic, complemented
40D5×C49—111no—
41C3×D77—351no—
42C3×C11×D7—71no—
43C3×C7×D11—51no—
44C3×D5×D7—771no—
45C5×C7×C11C2×C3×D711yescharacteristic
46C2×C3×C5×C11—491no—
47C3×D55—491no—
48C3×D55D4911yescharacteristic, direct product factor
49D7×D11—351no—
50C2×C3×C49—551no—
51C3×D49—551no—
52C3×D49D5511yescharacteristic, direct product factor
53C5×C49C2×C3×D1111yescharacteristic, complemented, Hall
54C3×C7×C11D5×D711yescharacteristic
55C2×D55—491noHall
56C3×D35—771no—
57C3×C7×D5—111no—
58C3×C5×D7—71no—
59C2×D49—551noHall
60C3×C5×C11C2×D4911yescharacteristic, complemented, Hall
61D77—351no—
62C7×D11—51no—
63C11×D7—71no—
64C3×C49C2×D5511yescharacteristic, complemented, Hall
65D5×D7—771no—
66C2×C3×D11—2451noHall
67C2×C5×C11—491no—
68D55—491no—
69D55C3×D4911yescharacteristic, direct product factor
70C3×C5×C7D7×D1111yescharacteristic
71C2×C49—551no—
72D49—551no—
73D49C3×D5511yescharacteristic, direct product factor
74C2×C3×D7—3851no—
75C7×C11C3×D5×D711yescharacteristic
76D35—771no—
77C5×D7—71no—
78C7×D5—111no—
79C2×C3×C11—491no—
80C3×D11—51no—
81C3×D11—2451no—
82C2×C3×D5—5391noHall
83C5×C11C2×C3×D4911yescharacteristic, complemented, Hall
84C49C2×C3×D5511yescharacteristic, complemented, Sylow
85C2×D11—2451noHall
86C2×C3×C7—551no—
87C3×D7—71no—
88C3×D7—3851no—
89C5×C7C3×D7×D1111yescharacteristic
90C3×C11D5×D4911yescharacteristic, complemented, Hall
91C2×C3×C5—491no—
92C3×D5—111no—
93C3×D5—5391no—
94C2×D7—3851no—
95C2×C11—491no—
96D11—51no—
97D11—2451no—
98C3×C7D7×D5511yescharacteristic
99C2×D5—5391noHall
100C3×C5D11×D4911yescharacteristic, complemented, Hall
101C2×C7—551no—
102D7—71no—
103D7—3851no—
104C22×C3—26951noHall
105C11C3×D5×D4911yescharacteristic, complemented, Sylow
106C2×C5—491no—
107D5—111no—
108D5—5391no—
109C7C3×D7×D5511yescharacteristic
110C2×C3—491no—
111C2×C3—551no—
112C2×C3—26951no—
113C5C3×D11×D4911yescharacteristic, complemented, Sylow
114C22—26951noSylow
115C3D49×D5511yescharacteristic, direct product factor, Sylow
116C2—491no—
117C2—551no—
118C2—26951no—
subgroupG/H
center, hypercenterC3D49×D55
commutator, cosocle, hypocenterC5×C11×C49C22×C3
FrattiniC7C3×D7×D55
FittingC3×C5×C11×C49C22
socleC3×C5×C7×C11C2×D7
LCSG ▷ C5×C11×C49
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
1. C3×D2695C2semidirect
2. C3×C49×D55C2semidirect
3. C3×C5×C11×D49C2semidirect
4. D49×D55C3direct (N × H)
5. C3×C5×C11×C49C22semidirect
7. D2695C2×C3semidirect
8. C49×D55C2×C3semidirect
9. C5×C11×D49C2×C3semidirect
12. C3×C11×D49D5semidirect
15. C5×C11×C49C22×C3semidirect
20. C3×C11×C49C2×D5semidirect
24. C3×C5×D49D11semidirect
28. C11×D49C3×D5semidirect
34. C3×C5×C49C2×D11semidirect
37. C11×C49C2×C3×D5semidirect
39. C5×D49C3×D11semidirect
48. C3×D55D49direct (N × H)
52. C3×D49D55direct (N × H)
53. C5×C49C2×C3×D11semidirect
60. C3×C5×C11C2×D49semidirect
64. C3×C49C2×D55semidirect
69. D55C3×D49direct (N × H)
73. D49C3×D55direct (N × H)
83. C5×C11C2×C3×D49semidirect
84. C49C2×C3×D55semidirect
90. C3×C11D5×D49semidirect
100. C3×C5D11×D49semidirect
105. C11C3×D5×D49semidirect
113. C5C3×D11×D49semidirect
115. C3D49×D55direct (N × H)

Maximal subgroups

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

subgroupindex
C3×D26952
C3×C49×D552
C3×C5×C11×D492
D49×D553
C3×D11×D495
C3×D7×D557
C3×D5×D4911