Finite Group Databasebeta

← C11×D15⋊D49 #44568415

Subgroups — C11×D15⋊D49 #44568415

Order 32340.

120 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 40 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
1C11×D15×C49C211yesmaximal, characteristic, complemented
2C5×C11×D147C211yesmaximal, characteristic, complemented
3C3×C11×D245C211yesmaximal, characteristic, complemented
4D5×C11×D49—31nomaximal, Hall
5C3×C5×C11×C49C2211yescharacteristic, complemented, Hall
6D3×C11×D49—51nomaximal, Hall
7C11×D245D311yescharacteristic, complemented
8D5×C11×C49—31no—
9C5×C11×D49—31no—
10C11×D15⋊D7—71nomaximal
11C11×D147D511yescharacteristic, complemented
12D3×C11×C49—51no—
13C3×C11×D49—51no—
14D15⋊D49C1111yesmaximal, characteristic, direct product factor, Hall
15C5×C11×C49C2×D311yescharacteristic, complemented, Hall
16C7×C11×D15D711yescharacteristic
17C5×C11×D21—71no—
18C3×C11×D35—71no—
19C2×C11×D49—151noHall
20C3×C11×C49C2×D511yescharacteristic, complemented, Hall
21D5×C11×D7—211no—
22D15×C49C2×C1111yescharacteristic, complemented
23C5×D147C2×C1111yescharacteristic, complemented
24C3×D245C2×C1111yescharacteristic, complemented
25C3×C5×C7×C11C2×D711yescharacteristic
26C2×C11×C49—151no—
27C11×D49—31no—
28C11×D49—51no—
29D5×D49—31noHall
30D3×C11×D7—351no—
31C11×D35—71no—
32C7×D5×C11—31no—
33C5×C11×D7—211no—
34C3×C5×C49C22×C1111yescharacteristic, complemented, Hall
35D3×D5×C11—491noHall
36D3×D49—51noHall
37C11×C49D3×D511yescharacteristic, complemented, Hall
38D245D3×C1111yescharacteristic, complemented
39C5×D49—31no—
40D5×C49—31no—
41C11×D21—71no—
42D3×C7×C11—51no—
43C3×C11×D7—351no—
44D15⋊D7—71no—
45C5×C7×C11D3×D711yescharacteristic
46C11×D15D4911yescharacteristic, complemented
47C5×D3×C11—491no—
48C3×D5×C11—491no—
49C2×C11×D7—1051no—
50D147D5×C1111yescharacteristic, complemented
51C3×D49—51no—
52D3×C49—51no—
53C5×C49C2×D3×C1111yescharacteristic, complemented, Hall
54C3×C7×C11D5×D711yescharacteristic
55C2×D5×C11—1471noHall
56C7×D15C11×D711yescharacteristic
57C5×D21—71no—
58C3×D35—71no—
59C2×D49—151noHall
60C3×C5×C11C2×D4911yescharacteristic, complemented, Hall
61C2×C7×C11—151no—
62C11×D7—211no—
63C11×D7—351no—
64C3×C49C2×D5×C1111yescharacteristic, complemented, Hall
65D5×D7—211no—
66C2×D3×C11—2451noHall
67C2×C5×C11—1471no—
68D5×C11—31no—
69D5×C11—491no—
70C3×C5×C7C2×C11×D711yescharacteristic
71C2×C49—151no—
72D49—31no—
73D49—51no—
74D3×D7—351no—
75C7×C11D15⋊D711yescharacteristic
76D35—71no—
77C5×D7—211no—
78C7×D5—31no—
79C2×C3×C11—2451no—
80D3×C11—51no—
81D3×C11—491no—
82D3×D5—491noHall
83C5×C11D3×D4911yescharacteristic, complemented, Hall
84C49D3×D5×C1111yescharacteristic, complemented, Sylow
85C22×C11—7351noHall
86D21—71no—
87C3×D7—351no—
88D3×C7—51no—
89C5×C7D3×C11×D711yescharacteristic
90C3×C11D5×D4911yescharacteristic, complemented, Hall
91D15C11×D4911yescharacteristic, complemented
92C3×D5—491no—
93C5×D3—491no—
94C2×D7—1051no—
95C2×C11—151no—
96C2×C11—1471no—
97C2×C11—2451no—
98C3×C7D5×C11×D711yescharacteristic
99C2×D5—1471noHall
100C3×C5C2×C11×D4911yescharacteristic, complemented, Hall
101C2×C7—151no—
102D7—211no—
103D7—351no—
104C2×D3—2451noHall
105C11D15⋊D4911yescharacteristic, direct product factor, Sylow
106C2×C5—1471no—
107D5—31no—
108D5—491no—
109C7C11×D15⋊D711yescharacteristic
110C2×C3—2451no—
111D3—51no—
112D3—491no—
113C5D3×C11×D4911yescharacteristic, complemented, Sylow
114C22—7351noSylow
115C3D5×C11×D4911yescharacteristic, complemented, Sylow
116C2—151no—
117C2—1471no—
118C2—2451no—
subgroupG/H
center, hypercenterC11D15⋊D49
commutator, cosocle, hypocenterC3×C5×C49C22×C11
FrattiniC7C11×D15⋊D7
FittingC3×C5×C11×C49C22
socleC3×C5×C7×C11C2×D7
LCSG ▷ C3×C5×C49
UCSC1 ◁ C11

Complements

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

NH ≅ G/Ntype
1. C11×D15×C49C2semidirect
2. C5×C11×D147C2semidirect
3. C3×C11×D245C2semidirect
5. C3×C5×C11×C49C22semidirect
7. C11×D245D3semidirect
11. C11×D147D5semidirect
14. D15⋊D49C11direct (N × H)
15. C5×C11×C49C2×D3semidirect
20. C3×C11×C49C2×D5semidirect
22. D15×C49C2×C11semidirect
23. C5×D147C2×C11semidirect
24. C3×D245C2×C11semidirect
34. C3×C5×C49C22×C11semidirect
37. C11×C49D3×D5semidirect
38. D245D3×C11semidirect
46. C11×D15D49semidirect
50. D147D5×C11semidirect
53. C5×C49C2×D3×C11semidirect
60. C3×C5×C11C2×D49semidirect
64. C3×C49C2×D5×C11semidirect
83. C5×C11D3×D49semidirect
84. C49D3×D5×C11semidirect
90. C3×C11D5×D49semidirect
91. D15C11×D49semidirect
100. C3×C5C2×C11×D49semidirect
105. C11D15⋊D49direct (N × H)
113. C5D3×C11×D49semidirect
115. C3D5×C11×D49semidirect

Maximal subgroups

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

subgroupindex
C11×D15×C492
C5×C11×D1472
C3×C11×D2452
D5×C11×D493
D3×C11×D495
C11×D15⋊D77
D15⋊D4911