Finite Group Databasebeta

← C11⋊#15668766 #44568668

Subgroups — C11⋊#15668766 #44568668

Order 32340.

120 conjugacy classes of subgroups; only the 32 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 32 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
1D5×C11×#3862C211yesmaximal, characteristic
2C7⋊(C7⋊(C11⋊AGL(1,𝔽5)))C311yesmaximal, characteristic, complemented, Hall
3C5×C11×#3862C411yescharacteristic, complemented, Hall
4C11⋊#10596875—51nomaximal, Hall
5C72×D5×C11C2×C311yescharacteristic
6C11⋊(ΓL(1,𝔽8)⋊AGL(1,𝔽5))—71nomaximal
7C11⋊(ΓL(1,𝔽8)⋊AGL(1,𝔽5))—71nomaximal
8C2×C11×#3862—51no—
9#15668766—111nomaximal, Hall
10C5×C72×C11C3×C411yescharacteristic, complemented, Hall
11D5×C11×ΓL(1,𝔽8)—141no—
12D5×C11×ΓL(1,𝔽8)—141no—
13C7⋊Dic77—51noHall
14C11×#3862AGL(1,𝔽5)11yescharacteristic, complemented, Hall
15C7⋊(C11⋊AGL(1,𝔽5))—71no—
16C7⋊(C11⋊AGL(1,𝔽5))—71no—
17C7⋊(C11⋊AGL(1,𝔽5))—212no—
18D5×#3862D1111yescharacteristic
19C5×C11×ΓL(1,𝔽8)—141no—
20C5×C11×ΓL(1,𝔽8)—141no—
21C2×C72×C11—51no—
22C7⋊(C7⋊AGL(1,𝔽5))—111noHall
23C11⋊(ΓL(1,𝔽8)⋊C4)—351no—
24C11⋊(ΓL(1,𝔽8)⋊C4)—351no—
25C7×D5×C11—32no—
26C7×D5×C11AGL(1,𝔽7)11yescharacteristic
27C7×D5×C11AGL(1,𝔽7)11yescharacteristic
28C5×#3862Dic1111yescharacteristic, complemented, Hall
29C3×C11⋊AGL(1,𝔽5)—491noHall
30#10596875—551noHall
31C72×C11C3×AGL(1,𝔽5)11yescharacteristic, complemented, Hall
32C72×D5C3×D1111yescharacteristic
33C2×C11×ΓL(1,𝔽8)—701no—
34C2×C11×ΓL(1,𝔽8)—701no—
35ΓL(1,𝔽8)⋊AGL(1,𝔽5)—771no—
36ΓL(1,𝔽8)⋊AGL(1,𝔽5)—771no—
37C5×C7×C11—32no—
38C5×C7×C11ΓL(1,𝔽8)⋊C411yescharacteristic, complemented
39C5×C7×C11ΓL(1,𝔽8)⋊C411yescharacteristic, complemented
40C3×D5×C11—981no—
41Dic77—351no—
42Dic77—351no—
43Dic77—1052no—
44C2×#3862—51no—
45C5×C72C3×Dic1111yescharacteristic, complemented, Hall
46C11×ΓL(1,𝔽8)—141no—
47C11×ΓL(1,𝔽8)—141no—
48C11⋊AGL(1,𝔽5)—491noHall
49D5×ΓL(1,𝔽8)—71no—
50D5×ΓL(1,𝔽8)—141no—
51C7⋊Dic7—551noHall
52C3×C5×C11—981noHall
53C2×C7×C11—51no—
54C2×C7×C11—51no—
55C2×C7×C11—152no—
56#3862C11⋊AGL(1,𝔽5)11yescharacteristic, complemented, Hall
57C7⋊AGL(1,𝔽5)—771no—
58C7⋊AGL(1,𝔽5)—771no—
59C7⋊AGL(1,𝔽5)—2312no—
60C3×Dic11—2451noHall
61D5×C11#6442511yescharacteristic
62C5×ΓL(1,𝔽8)—71no—
63C5×ΓL(1,𝔽8)—141no—
64C2×C72—51no—
65ΓL(1,𝔽8)⋊C4—3851no—
66ΓL(1,𝔽8)⋊C4—3851no—
67C7×C11—32no—
68C7×C11ΓL(1,𝔽8)⋊AGL(1,𝔽5)11yescharacteristic, complemented
69C7×C11ΓL(1,𝔽8)⋊AGL(1,𝔽5)11yescharacteristic, complemented
70C7×D5—32no—
71C7×D5C11⋊AGL(1,𝔽7)11yescharacteristic
72C7×D5C11⋊AGL(1,𝔽7)11yescharacteristic
73C2×C3×C11—4901no—
74C3×AGL(1,𝔽5)—5391noHall
75C5×C11#1059687511yescharacteristic, complemented, Hall
76C72C3×C11⋊AGL(1,𝔽5)11yescharacteristic, complemented, Sylow
77Dic11—2451noHall
78C2×ΓL(1,𝔽8)—701no—
79C2×ΓL(1,𝔽8)—701no—
80C5×C7—32no—
81C5×C7C11⋊(ΓL(1,𝔽8)⋊C4)11yescharacteristic, complemented
82C5×C7C11⋊(ΓL(1,𝔽8)⋊C4)11yescharacteristic, complemented
83C3×C11—981noHall
84C3×D5—981no—
85Dic7—3851no—
86Dic7—3851no—
87Dic7—11552no—
88C2×C11—51no—
89ΓL(1,𝔽8)—141no—
90ΓL(1,𝔽8)—141no—
91AGL(1,𝔽5)—5391noHall
92C3×C5—981noHall
93C2×C7—51no—
94C2×C7—51no—
95C2×C7—152no—
96C3×C4—26951noHall
97C11#1566876611yescharacteristic, complemented, Sylow
98D5C11⋊#6442511yescharacteristic
99C7—32no—
100C7C11⋊(ΓL(1,𝔽8)⋊AGL(1,𝔽5))11yescharacteristic, complemented
101C7C11⋊(ΓL(1,𝔽8)⋊AGL(1,𝔽5))11yescharacteristic, complemented
102C2×C3—4901no—
103C5C11⋊#1059687511yescharacteristic, complemented, Sylow
104C4—26951noSylow
105C3—981noSylow
106C2—51no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC5×C72×C11C3×C4
prime radicalD5×C11×#3862C2
cosocleC72×D5×C11C2×C3
LCSG ▷ C5×C72×C11
UCSC1

Complements

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

NH ≅ G/Ntype
2. C7⋊(C7⋊(C11⋊AGL(1,𝔽5)))C3semidirect
3. C5×C11×#3862C4semidirect
10. C5×C72×C11C3×C4semidirect
14. C11×#3862AGL(1,𝔽5)semidirect
28. C5×#3862Dic11semidirect
31. C72×C11C3×AGL(1,𝔽5)semidirect
38. C5×C7×C11ΓL(1,𝔽8)⋊C4semidirect
39. C5×C7×C11ΓL(1,𝔽8)⋊C4semidirect
45. C5×C72C3×Dic11semidirect
56. #3862C11⋊AGL(1,𝔽5)semidirect
68. C7×C11ΓL(1,𝔽8)⋊AGL(1,𝔽5)semidirect
69. C7×C11ΓL(1,𝔽8)⋊AGL(1,𝔽5)semidirect
75. C5×C11#10596875semidirect
76. C72C3×C11⋊AGL(1,𝔽5)semidirect
81. C5×C7C11⋊(ΓL(1,𝔽8)⋊C4)semidirect
82. C5×C7C11⋊(ΓL(1,𝔽8)⋊C4)semidirect
97. C11#15668766semidirect
100. C7C11⋊(ΓL(1,𝔽8)⋊AGL(1,𝔽5))semidirect
101. C7C11⋊(ΓL(1,𝔽8)⋊AGL(1,𝔽5))semidirect
103. C5C11⋊#10596875semidirect

Maximal subgroups

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

subgroupindex
D5×C11×#38622
C7⋊(C7⋊(C11⋊AGL(1,𝔽5)))3
C11⋊#105968755
C11⋊(ΓL(1,𝔽8)⋊AGL(1,𝔽5))7
#1566876611