Finite Group Databasebeta

← C3×D5×ΓL(1,𝔽8)×C11⋊C5 #46831541

Subgroups — C3×D5×ΓL(1,𝔽8)×C11⋊C5 #46831541

Order 34650.

240 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 72 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×C5×ΓL(1,𝔽8)×C11⋊C5C211yesmaximal, characteristic, complemented, Hall
2C3×C7×D5×C11⋊C5C311yesmaximal, characteristic, complemented
3D5×ΓL(1,𝔽8)×C11⋊C5C313yesmaximal, direct product factor
4C3×D5×C11×ΓL(1,𝔽8)C511yesmaximal, characteristic, complemented
5C2×C3×ΓL(1,𝔽8)×C11⋊C5—51nomaximal
6C3×C5×C7×C11⋊C5C2×C311yescharacteristic, complemented
7C5×ΓL(1,𝔽8)×C11⋊C5C2×C313yescomplemented
8C32×D5×C11⋊C5—71nomaximal, Hall
9C7×D5×C11⋊C5C3211yescharacteristic, complemented, Hall
10C3×C5×C11×ΓL(1,𝔽8)C2×C511yescharacteristic, complemented
11C3×ΓL(1,𝔽8)×C11⋊C5—22no—
12C3×ΓL(1,𝔽8)×C11⋊C5D511yescharacteristic, direct product factor
13C3×C5×D5×ΓL(1,𝔽8)—111nomaximal, Hall
14C32×C5×C11⋊C5—71noHall
15D5×C11×ΓL(1,𝔽8)C3×C513yescomplemented
16C3×C7×D5×C11C3×C511yescharacteristic, complemented
17C2×ΓL(1,𝔽8)×C11⋊C5—53no—
18C2×C3×C7×C11⋊C5—51no—
19C5×C7×C11⋊C5C2×C3211yescharacteristic, complemented, Hall
20C3×D5×C11⋊C5—73no—
21C3×D5×C11⋊C5ΓL(1,𝔽8)11yescharacteristic, direct product factor
22C3×C52×ΓL(1,𝔽8)—111noHall
23C2×C3×C11×ΓL(1,𝔽8)—51noHall
24C3×C5×C7×C11C2×C3×C511yescharacteristic, complemented
25C5×C11×ΓL(1,𝔽8)C2×C3×C513yescomplemented
26C3×C7×C11⋊C5—22no—
27C3×C7×C11⋊C5C3×D511yescharacteristic, complemented
28ΓL(1,𝔽8)×C11⋊C5—26no—
29ΓL(1,𝔽8)×C11⋊C5C3×D513yesdirect product factor
30C3×C5×C7×D5—111no—
31C5×D5×ΓL(1,𝔽8)—113no—
32C32×D5×C11—71no—
33C2×C32×C11⋊C5—351no—
34C3×C5×C11⋊C5—73no—
35C3×C5×C11⋊C5C2×ΓL(1,𝔽8)11yescharacteristic, complemented
36C7×D5×C11C32×C511yescharacteristic, complemented
37C2×C7×C11⋊C5—51no—
38C3×C11×ΓL(1,𝔽8)C5×D511yescharacteristic, complemented, Hall
39C2×C3×C5×ΓL(1,𝔽8)—551no—
40C3×D5×ΓL(1,𝔽8)C11⋊C511yescharacteristic, direct product factor
41D5×C11⋊C5C3×ΓL(1,𝔽8)11yescharacteristic, direct product factor, Hall
42C3×C52×C7—111no—
43C52×ΓL(1,𝔽8)—113no—
44C32×C5×C11—71no—
45C32×C11⋊C5—71no—
46C32×C11⋊C5—142no—
47C2×C3×C7×C11—51no—
48C2×C11×ΓL(1,𝔽8)—53no—
49C32×C5×D5—771noHall
50C5×C7×C11C2×C32×C511yescharacteristic, complemented
51C7×C11⋊C5—22no—
52C7×C11⋊C5C32×D511yescharacteristic, complemented
53C5×C7×D5—111noHall
54C3×D5×C11—73no—
55C3×D5×C11C5×ΓL(1,𝔽8)11yescharacteristic, complemented
56C2×C3×C11⋊C5—51no—
57C2×C3×C11⋊C5—353no—
58C3×C5×ΓL(1,𝔽8)—111no—
59C3×C5×ΓL(1,𝔽8)—222no—
60C3×C5×ΓL(1,𝔽8)C2×C11⋊C511yescharacteristic, complemented
61C5×C11⋊C5C2×C3×ΓL(1,𝔽8)11yescharacteristic, complemented, Hall
62C3×C7×C11C3×C5×D511yescharacteristic, complemented
63C11×ΓL(1,𝔽8)C3×C5×D513yescomplemented
64C32×C52—771noHall
65C2×C3×C5×C7—551no—
66C3×C7×D5C3×C11⋊C511yescharacteristic, complemented
67C2×C5×ΓL(1,𝔽8)—553no—
68D5×ΓL(1,𝔽8)C3×C11⋊C513yesdirect product factor
69C2×C32×C11—351noHall
70C52×C7—111noHall
71C3×C5×C11—73no—
72C3×C5×C11C2×C5×ΓL(1,𝔽8)11yescharacteristic, complemented
73C3×C11⋊C5—22no—
74C3×C11⋊C5—73no—
75C3×C11⋊C5—146no—
76C3×C11⋊C5D5×ΓL(1,𝔽8)11yescharacteristic, direct product factor
77C2×C7×C11—51noHall
78C3×C5×D5—111no—
79C3×C5×D5—773no—
80C2×C3×ΓL(1,𝔽8)—51noHall
81D5×C11C3×C5×ΓL(1,𝔽8)11yescharacteristic, complemented
82C2×C11⋊C5—51no—
83C3×C5×C7—111no—
84C3×C5×C7—222no—
85C3×C5×C7C2×C3×C11⋊C511yescharacteristic, complemented
86C5×ΓL(1,𝔽8)—113no—
87C5×ΓL(1,𝔽8)—226no—
88C5×ΓL(1,𝔽8)C2×C3×C11⋊C513yescomplemented
89C32×C11—71noHall
90C2×C32×C5—3851no—
91C32×D5—71no—
92C7×C11C32×C5×D511yescharacteristic, complemented, Hall
93C3×C52—111no—
94C3×C52—773no—
95C2×C5×C7—551no—
96C7×D5C32×C11⋊C511yescharacteristic, complemented
97C2×C3×C11—51no—
98C2×C3×C11—353no—
99C3×ΓL(1,𝔽8)D5×C11⋊C511yescharacteristic, direct product factor, Hall
100C5×C11C2×C3×C5×ΓL(1,𝔽8)11yescharacteristic, complemented
101C11⋊C5—22no—
102C11⋊C5C3×D5×ΓL(1,𝔽8)11yescharacteristic, direct product factor
103C5×D5—111noHall
104C32×C5—71no—
105C32×C5—771no—
106C32×C5—1542no—
107C2×C3×C7—51no—
108C2×ΓL(1,𝔽8)—53no—
109C5×C7—111no—
110C5×C7—222no—
111C5×C7C2×C32×C11⋊C511yescharacteristic, complemented
112C3×C11—73no—
113C3×C11C5×D5×ΓL(1,𝔽8)11yescharacteristic, complemented
114C2×C3×C5—551no—
115C2×C3×C5—3853no—
116C3×D5—73no—
117C3×D5ΓL(1,𝔽8)×C11⋊C511yescharacteristic, direct product factor
118C52—111noSylow
119C2×C11—51noHall
120C3×C7C3×D5×C11⋊C511yescharacteristic, complemented
121ΓL(1,𝔽8)C3×D5×C11⋊C513yesdirect product factor
122C2×C32—351noHall
123C3×C5—73no—
124C3×C5—111no—
125C3×C5—222no—
126C3×C5—773no—
127C3×C5—1546no—
128C3×C5C2×ΓL(1,𝔽8)×C11⋊C511yescharacteristic, complemented
129C2×C7—51noHall
130C11C3×C5×D5×ΓL(1,𝔽8)11yescharacteristic, complemented, Sylow
131C2×C5—551no—
132D5C3×ΓL(1,𝔽8)×C11⋊C511yescharacteristic, direct product factor
133C32—71noSylow
134C7C32×D5×C11⋊C511yescharacteristic, complemented, Sylow
135C2×C3—51no—
136C2×C3—353no—
137C5—111no—
138C5—222no—
139C5C2×C3×ΓL(1,𝔽8)×C11⋊C511yescharacteristic, complemented
140C3—73no—
141C3D5×ΓL(1,𝔽8)×C11⋊C511yescharacteristic, direct product factor
142C2—51noSylow
subgroupG/H
center, hypercenterC3D5×ΓL(1,𝔽8)×C11⋊C5
commutator, cosocle, hypocenterC5×C7×C11C2×C32×C5
FrattiniC1G
Fitting, socleC3×C5×C7×C11C2×C3×C5
LCSG ▷ C5×C7×C11
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
1. C3×C5×ΓL(1,𝔽8)×C11⋊C5C2semidirect
2. C3×C7×D5×C11⋊C5C3semidirect
3. D5×ΓL(1,𝔽8)×C11⋊C5C3direct (N × H)
4. C3×D5×C11×ΓL(1,𝔽8)C5semidirect
6. C3×C5×C7×C11⋊C5C2×C3semidirect
7. C5×ΓL(1,𝔽8)×C11⋊C5C2×C3semidirect
9. C7×D5×C11⋊C5C32semidirect
10. C3×C5×C11×ΓL(1,𝔽8)C2×C5semidirect
12. C3×ΓL(1,𝔽8)×C11⋊C5D5direct (N × H)
15. D5×C11×ΓL(1,𝔽8)C3×C5semidirect
16. C3×C7×D5×C11C3×C5semidirect
19. C5×C7×C11⋊C5C2×C32semidirect
21. C3×D5×C11⋊C5ΓL(1,𝔽8)direct (N × H)
24. C3×C5×C7×C11C2×C3×C5semidirect
25. C5×C11×ΓL(1,𝔽8)C2×C3×C5semidirect
27. C3×C7×C11⋊C5C3×D5semidirect
29. ΓL(1,𝔽8)×C11⋊C5C3×D5direct (N × H)
35. C3×C5×C11⋊C5C2×ΓL(1,𝔽8)semidirect
36. C7×D5×C11C32×C5semidirect
38. C3×C11×ΓL(1,𝔽8)C5×D5semidirect
40. C3×D5×ΓL(1,𝔽8)C11⋊C5direct (N × H)
41. D5×C11⋊C5C3×ΓL(1,𝔽8)direct (N × H)
50. C5×C7×C11C2×C32×C5semidirect
52. C7×C11⋊C5C32×D5semidirect
55. C3×D5×C11C5×ΓL(1,𝔽8)semidirect
60. C3×C5×ΓL(1,𝔽8)C2×C11⋊C5semidirect
61. C5×C11⋊C5C2×C3×ΓL(1,𝔽8)semidirect
62. C3×C7×C11C3×C5×D5semidirect
63. C11×ΓL(1,𝔽8)C3×C5×D5semidirect
66. C3×C7×D5C3×C11⋊C5semidirect
68. D5×ΓL(1,𝔽8)C3×C11⋊C5direct (N × H)
72. C3×C5×C11C2×C5×ΓL(1,𝔽8)semidirect
76. C3×C11⋊C5D5×ΓL(1,𝔽8)direct (N × H)
81. D5×C11C3×C5×ΓL(1,𝔽8)semidirect
85. C3×C5×C7C2×C3×C11⋊C5semidirect
88. C5×ΓL(1,𝔽8)C2×C3×C11⋊C5semidirect
92. C7×C11C32×C5×D5semidirect
96. C7×D5C32×C11⋊C5semidirect
99. C3×ΓL(1,𝔽8)D5×C11⋊C5direct (N × H)
100. C5×C11C2×C3×C5×ΓL(1,𝔽8)semidirect
102. C11⋊C5C3×D5×ΓL(1,𝔽8)direct (N × H)
111. C5×C7C2×C32×C11⋊C5semidirect
113. C3×C11C5×D5×ΓL(1,𝔽8)semidirect
117. C3×D5ΓL(1,𝔽8)×C11⋊C5direct (N × H)
120. C3×C7C3×D5×C11⋊C5semidirect
121. ΓL(1,𝔽8)C3×D5×C11⋊C5direct (N × H)
128. C3×C5C2×ΓL(1,𝔽8)×C11⋊C5semidirect
130. C11C3×C5×D5×ΓL(1,𝔽8)semidirect
132. D5C3×ΓL(1,𝔽8)×C11⋊C5direct (N × H)
134. C7C32×D5×C11⋊C5semidirect
139. C5C2×C3×ΓL(1,𝔽8)×C11⋊C5semidirect
141. C3D5×ΓL(1,𝔽8)×C11⋊C5direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×ΓL(1,𝔽8)×C11⋊C52
C3×C7×D5×C11⋊C53
D5×ΓL(1,𝔽8)×C11⋊C53
C3×D5×C11×ΓL(1,𝔽8)5
C2×C3×ΓL(1,𝔽8)×C11⋊C55
C32×D5×C11⋊C57
C3×C5×D5×ΓL(1,𝔽8)11