Finite Group Databasebeta

← C3×C7⋊(C11⋊#1042) #37528613

Subgroups — C3×C7⋊(C11⋊#1042) #37528613

Order 23100.

104 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 104 conjugacy classes of subgroups — too many to draw. Only its 50 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×C7×D5×C11C211yesmaximal, characteristic
2C7⋊(C11⋊#1042)C311yesmaximal, characteristic, direct product factor, Hall
3C3×C52×C7×C11C411yescharacteristic, complemented, Hall
4C3×C7⋊(C11⋊AGL(1,𝔽5))—51nomaximal
5C3×Dic385—51nomaximal
6C5×C7×D5×C11C2×C311yescharacteristic
7C3×C11⋊#1042—71nomaximal, Hall
8C3×C7×D5×C11D511yescharacteristic
9C2×C3×C5×C7×C11—51no—
10C3×C7⋊#1042—111nomaximal, Hall
11C52×C7×C11C3×C411yescharacteristic, complemented, Hall
12C3×C5×D5×C11D711yescharacteristic
13C7⋊(C11⋊AGL(1,𝔽5))—51no—
14Dic385—51no—
15C3×C5×C7×C11—41no—
16C3×C5×C7×C11Dic511yescharacteristic, complemented
17C3×C5×C7×C11AGL(1,𝔽5)11yescharacteristic, complemented
18C11⋊#1042—71noHall
19C3×C5×C7×D5D1111yescharacteristic
20C3×Dic77—251noHall
21C3×C52×C11Dic711yescharacteristic, complemented, Hall
22C2×C5×C7×C11—51no—
23C7×D5×C11C3×D511yescharacteristic
24C7⋊#1042—111noHall
25C3×C11⋊AGL(1,𝔽5)—351no—
26C3×Dic55—351no—
27C5×D5×C11C3×D711yescharacteristic
28C3×C52×C7Dic1111yescharacteristic, complemented, Hall
29C2×C3×C7×C11—51no—
30C3×C7⋊AGL(1,𝔽5)—551no—
31C3×Dic35—551no—
32C5×C7×C11—41no—
33C5×C7×C11C3×Dic511yescharacteristic, complemented
34C5×C7×C11C3×AGL(1,𝔽5)11yescharacteristic, complemented
35C5×C7×D5C3×D1111yescharacteristic
36C2×C3×C5×C11—51no—
37C3×D5×C11D3511yescharacteristic
38Dic77—251noHall
39C3×#1042—771noHall
40C52×C11C3×Dic711yescharacteristic, complemented, Hall
41C3×C7×C11#104211yescharacteristic, complemented, Hall
42C11⋊AGL(1,𝔽5)—351no—
43Dic55—351no—
44C2×C3×C5×C7—51no—
45C3×C7×D5D5511yescharacteristic
46C52×C7C3×Dic1111yescharacteristic, complemented, Hall
47C3×C5×C11—41no—
48C3×C5×C11Dic3511yescharacteristic, complemented
49C3×C5×C11C7⋊AGL(1,𝔽5)11yescharacteristic, complemented
50C2×C7×C11—51no—
51C3×C5×D5D7711yescharacteristic
52C7⋊AGL(1,𝔽5)—551no—
53Dic35—551no—
54C3×Dic11—1751noHall
55C2×C5×C11—51no—
56D5×C11C3×D3511yescharacteristic
57C3×C5×C7—41no—
58C3×C5×C7Dic5511yescharacteristic, complemented
59C3×C5×C7C11⋊AGL(1,𝔽5)11yescharacteristic, complemented
60#1042—771noHall
61C3×Dic7—2751noHall
62C7×C11C3×#104211yescharacteristic, complemented, Hall
63C3×C52Dic7711yescharacteristic, complemented, Hall
64C2×C5×C7—51no—
65C7×D5C3×D5511yescharacteristic
66C2×C3×C11—51no—
67C3×AGL(1,𝔽5)—3851no—
68C3×Dic5—3851no—
69C5×C11—41no—
70C5×C11C3×Dic3511yescharacteristic, complemented
71C5×C11C3×C7⋊AGL(1,𝔽5)11yescharacteristic, complemented
72C5×D5C3×D7711yescharacteristic
73Dic11—1751noHall
74C2×C3×C7—51no—
75C5×C7—41no—
76C5×C7C3×Dic5511yescharacteristic, complemented
77C5×C7C3×C11⋊AGL(1,𝔽5)11yescharacteristic, complemented
78C3×C11C7⋊#104211yescharacteristic, complemented, Hall
79C2×C3×C5—51no—
80C3×D5D38511yescharacteristic
81Dic7—2751noHall
82C52C3×Dic7711yescharacteristic, complemented, Sylow
83C2×C11—51no—
84C3×C7C11⋊#104211yescharacteristic, complemented, Hall
85AGL(1,𝔽5)—3851no—
86Dic5—3851no—
87C3×C5—41no—
88C3×C5Dic38511yescharacteristic, complemented
89C3×C5C7⋊(C11⋊AGL(1,𝔽5))11yescharacteristic, complemented
90C2×C7—51no—
91C3×C4—19251noHall
92C11C3×C7⋊#104211yescharacteristic, complemented, Sylow
93C2×C5—51no—
94D5C3×D38511yescharacteristic
95C7C3×C11⋊#104211yescharacteristic, complemented, Sylow
96C2×C3—51no—
97C5—41no—
98C5C3×Dic38511yescharacteristic, complemented
99C5C3×C7⋊(C11⋊AGL(1,𝔽5))11yescharacteristic, complemented
100C4—19251noSylow
101C3C7⋊(C11⋊#1042)11yescharacteristic, direct product factor, Sylow
102C2—51no—
subgroupG/H
center, hypercenterC3C7⋊(C11⋊#1042)
commutator, hypocenterC52×C7×C11C3×C4
FrattiniC1G
Fitting, socleC3×C52×C7×C11C4
prime radicalC3×C5×C7×D5×C11C2
cosocleC5×C7×D5×C11C2×C3
LCSG ▷ C52×C7×C11
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
2. C7⋊(C11⋊#1042)C3direct (N × H)
3. C3×C52×C7×C11C4semidirect
11. C52×C7×C11C3×C4semidirect
16. C3×C5×C7×C11Dic5semidirect
17. C3×C5×C7×C11AGL(1,𝔽5)semidirect
21. C3×C52×C11Dic7semidirect
28. C3×C52×C7Dic11semidirect
33. C5×C7×C11C3×Dic5semidirect
34. C5×C7×C11C3×AGL(1,𝔽5)semidirect
40. C52×C11C3×Dic7semidirect
41. C3×C7×C11#1042semidirect
46. C52×C7C3×Dic11semidirect
48. C3×C5×C11Dic35semidirect
49. C3×C5×C11C7⋊AGL(1,𝔽5)semidirect
58. C3×C5×C7Dic55semidirect
59. C3×C5×C7C11⋊AGL(1,𝔽5)semidirect
62. C7×C11C3×#1042semidirect
63. C3×C52Dic77semidirect
70. C5×C11C3×Dic35semidirect
71. C5×C11C3×C7⋊AGL(1,𝔽5)semidirect
76. C5×C7C3×Dic55semidirect
77. C5×C7C3×C11⋊AGL(1,𝔽5)semidirect
78. C3×C11C7⋊#1042semidirect
82. C52C3×Dic77semidirect
84. C3×C7C11⋊#1042semidirect
88. C3×C5Dic385semidirect
89. C3×C5C7⋊(C11⋊AGL(1,𝔽5))semidirect
92. C11C3×C7⋊#1042semidirect
95. C7C3×C11⋊#1042semidirect
98. C5C3×Dic385semidirect
99. C5C3×C7⋊(C11⋊AGL(1,𝔽5))semidirect
101. C3C7⋊(C11⋊#1042)direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×C7×D5×C112
C7⋊(C11⋊#1042)3
C3×C7⋊(C11⋊AGL(1,𝔽5))5
C3×Dic3855
C3×C11⋊#10427
C3×C7⋊#104211