Finite Group Databasebeta

← C3×C7×C7⋊(Dic11⋊C5) #44568461

Subgroups — C3×C7×C7⋊(Dic11⋊C5) #44568461

Order 32340.

144 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 144 conjugacy classes of subgroups — too many to draw. Only its 56 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
1C2×C3×C72×C11⋊C5C211yesmaximal, characteristic
2C7×C7⋊(Dic11⋊C5)C311yesmaximal, characteristic, direct product factor, Hall
3C3×C72×C11⋊C5C411yescharacteristic, complemented, Hall
4C3×C7×Dic77C511yesmaximal, characteristic, complemented, Hall
5C2×C72×C11⋊C5C2×C311yescharacteristic
6C3×C7⋊(Dic11⋊C5)C711yesmaximal, characteristic, direct product factor
7C3×C7×Dic11⋊C5—71nomaximal
8C2×C3×C72×C11C2×C511yescharacteristic
9C3×C5×C7×Dic7—111nomaximal, Hall
10C72×C11⋊C5C3×C411yescharacteristic, complemented, Hall
11C2×C3×C7×C11⋊C5—23no—
12C2×C3×C7×C11⋊C5D711yescharacteristic
13C2×C3×C7×C11⋊C5C2×C711yescharacteristic
14C7×Dic77C3×C511yescharacteristic, complemented, Hall
15C3×C72×C11C4×C511yescharacteristic, complemented, Hall
16C7⋊(Dic11⋊C5)C3×C711yescharacteristic, direct product factor
17C7×Dic11⋊C5—71no—
18C2×C3×C5×C72—111no—
19C3×C7×C11⋊C5—23no—
20C3×C7×C11⋊C5Dic711yescharacteristic, complemented
21C3×C7×C11⋊C5C4×C711yescharacteristic, complemented
22C2×C72×C11C2×C3×C511yescharacteristic
23C5×C7×Dic7—111noHall
24C3×Dic77C5×C711yescharacteristic, complemented
25C3×C7×Dic11—71no—
26C2×C7×C11⋊C5—23no—
27C2×C7×C11⋊C5C3×D711yescharacteristic
28C2×C7×C11⋊C5C2×C3×C711yescharacteristic
29C3×C5×C72—111noHall
30C3×Dic11⋊C5—71noHall
31C3×C7×Dic7—551noHall
32C72×C11C3×C4×C511yescharacteristic, complemented, Hall
33C2×C5×C72—111no—
34C2×C3×C7×C11—23no—
35C2×C3×C7×C11C5×D711yescharacteristic
36C2×C3×C7×C11C2×C5×C711yescharacteristic
37C3×C4×C5×C7—771no—
38C3×C5×Dic7—111no—
39C7×C11⋊C5—23no—
40C7×C11⋊C5C3×Dic711yescharacteristic, complemented
41C7×C11⋊C5C3×C4×C711yescharacteristic, complemented
42C2×C3×C11⋊C5C7×D711yescharacteristic
43Dic77C3×C5×C711yescharacteristic, complemented
44C7×Dic11—71no—
45C2×C3×C72AGL(1,𝔽11)11yescharacteristic
46C5×C72—111noHall
47C3×C7×C11—23no—
48C3×C7×C11C5×Dic711yescharacteristic, complemented
49C3×C7×C11C4×C5×C711yescharacteristic, complemented
50Dic11⋊C5—71noHall
51C2×C3×C5×C7—111no—
52C2×C3×C5×C7—111no—
53C2×C3×C5×C7—223no—
54C7×Dic7—551noHall
55C3×C11⋊C5C7×Dic711yescharacteristic, complemented, Hall
56C2×C7×C11—23no—
57C2×C7×C11C3×C5×D711yescharacteristic
58C2×C7×C11C2×C3×C5×C711yescharacteristic
59C3×C72Dic11⋊C511yescharacteristic, complemented, Hall
60C4×C5×C7—771no—
61C5×Dic7—111no—
62C3×Dic11—71noHall
63C2×C11⋊C5C3×C7×D711yescharacteristic
64C3×C5×C7—111no—
65C3×C5×C7—111no—
66C3×C5×C7—223no—
67C2×C72C3×AGL(1,𝔽11)11yescharacteristic
68C3×C4×C7—3851no—
69C3×Dic7—551no—
70C7×C11—23no—
71C7×C11C3×C5×Dic711yescharacteristic, complemented
72C7×C11C3×C4×C5×C711yescharacteristic, complemented
73C2×C5×C7—111no—
74C2×C5×C7—111no—
75C2×C5×C7—223no—
76C2×C3×C11C5×C7×D711yescharacteristic
77C3×C4×C5—771noHall
78C11⋊C5C3×C7×Dic711yescharacteristic, complemented, Hall
79C72C3×Dic11⋊C511yescharacteristic, complemented, Sylow
80Dic11—71noHall
81C2×C3×C7—23no—
82C2×C3×C7C7×AGL(1,𝔽11)11yescharacteristic
83C2×C3×C7C7⋊AGL(1,𝔽11)11yescharacteristic
84C5×C7—111no—
85C5×C7—111no—
86C5×C7—223no—
87C3×C11C5×C7×Dic711yescharacteristic, complemented, Hall
88C2×C3×C5—111no—
89C4×C7—3851no—
90Dic7—551no—
91C2×C11C3×C5×C7×D711yescharacteristic
92C3×C7—23no—
93C3×C7C7×Dic11⋊C511yescharacteristic, complemented
94C3×C7C7⋊(Dic11⋊C5)11yescharacteristic, direct product factor
95C4×C5—771noHall
96C3×C5—111noHall
97C2×C7—23no—
98C2×C7C3×C7×AGL(1,𝔽11)11yescharacteristic
99C2×C7C3×C7⋊AGL(1,𝔽11)11yescharacteristic
100C3×C4—3851noHall
101C11C3×C5×C7×Dic711yescharacteristic, complemented, Sylow
102C2×C5—111no—
103C7—23no—
104C7C3×C7×Dic11⋊C511yescharacteristic, complemented
105C7C3×C7⋊(Dic11⋊C5)11yescharacteristic, direct product factor
106C2×C3C7×C7⋊AGL(1,𝔽11)11yescharacteristic
107C5—111noSylow
108C4—771noSylow
109C3C7×C7⋊(Dic11⋊C5)11yescharacteristic, direct product factor, Sylow
110C2C3×C7×C7⋊AGL(1,𝔽11)11yescharacteristic
subgroupG/H
center, hypercenterC2×C3×C7C7⋊AGL(1,𝔽11)
commutator, hypocenterC7×C11C3×C4×C5×C7
FrattiniC2C3×C7×C7⋊AGL(1,𝔽11)
Fitting, socleC2×C3×C72×C11C2×C5
prime radicalC2×C3×C72×C11⋊C5C2
cosocleC2×C7×C11C2×C3×C5×C7
LCSG ▷ C7×C11
UCSC1 ◁ C2×C3×C7

Complements

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

NH ≅ G/Ntype
2. C7×C7⋊(Dic11⋊C5)C3direct (N × H)
3. C3×C72×C11⋊C5C4semidirect
4. C3×C7×Dic77C5semidirect
6. C3×C7⋊(Dic11⋊C5)C7direct (N × H)
10. C72×C11⋊C5C3×C4semidirect
14. C7×Dic77C3×C5semidirect
15. C3×C72×C11C4×C5semidirect
16. C7⋊(Dic11⋊C5)C3×C7direct (N × H)
20. C3×C7×C11⋊C5Dic7semidirect
21. C3×C7×C11⋊C5C4×C7semidirect
24. C3×Dic77C5×C7semidirect
32. C72×C11C3×C4×C5semidirect
40. C7×C11⋊C5C3×Dic7semidirect
41. C7×C11⋊C5C3×C4×C7semidirect
43. Dic77C3×C5×C7semidirect
48. C3×C7×C11C5×Dic7semidirect
49. C3×C7×C11C4×C5×C7semidirect
55. C3×C11⋊C5C7×Dic7semidirect
59. C3×C72Dic11⋊C5semidirect
71. C7×C11C3×C5×Dic7semidirect
72. C7×C11C3×C4×C5×C7semidirect
78. C11⋊C5C3×C7×Dic7semidirect
79. C72C3×Dic11⋊C5semidirect
87. C3×C11C5×C7×Dic7semidirect
93. C3×C7C7×Dic11⋊C5semidirect
94. C3×C7C7⋊(Dic11⋊C5)direct (N × H)
101. C11C3×C5×C7×Dic7semidirect
104. C7C3×C7×Dic11⋊C5semidirect
105. C7C3×C7⋊(Dic11⋊C5)direct (N × H)
109. C3C7×C7⋊(Dic11⋊C5)direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C72×C11⋊C52
C7×C7⋊(Dic11⋊C5)3
C3×C7×Dic775
C3×C7⋊(Dic11⋊C5)7
C3×C7×Dic11⋊C57
C3×C5×C7×Dic711