Finite Group Databasebeta

← #45692004

Subgroups — #45692004

Order 33516.

152 conjugacy classes of subgroups; only the 20 normal subgroups are shown.

normal subgroups only

This group has 152 conjugacy classes of subgroups — too many to draw. Only its 20 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
1#30660725C212yesmaximal, complemented
2#30660666C211yesmaximal, characteristic, complemented
3#26013935C311yesmaximal, characteristic, complemented
4#26013893—31nomaximal
5#22552727C2211yescharacteristic, complemented, Hall
6C19⋊#64418C2×C312yescomplemented
7#19150308—21no—
8#19150295—32no—
9C19×#64425C2×C311yescharacteristic, complemented
10#19150287D311yescharacteristic, complemented
11(C7⋊D7)⋊D19—31noHall
12C19×#3862C22×C311yescharacteristic, complemented
13#14584116C2×D311yescharacteristic, complemented
14C7×#87704—21no—
15AGL(1,𝔽7)×C19⋊C3—141no—
16C19×C7⋊D7C3×D311yescharacteristic, complemented
17C7×D133—32no—
18(#64418⋊C2)⋊C3—191nomaximal, Hall
19#11716322⋊C2—212no—
20ΓL(1,𝔽8)×C19⋊C3—141no—
21C72×C19C2×C3×D311yescharacteristic, complemented, Hall
22ΓL(1,𝔽8)⋊AGL(1,𝔽7)—191no—
23#64418⋊C3—192no—
24#11716328—212no—
25#11716326—141no—
26#11716326—212no—
27#11716325—141no—
28C19×AGL(1,𝔽7)—141no—
29#11716322—212no—
30D7×C19⋊C3—141no—
31C2×C3⋊(D19⋊C3)—491nomaximal, Hall
32#64423⋊C2—571no—
33#64418⋊C2—191no—
34D7×D19—212no—
35ΓL(1,𝔽8)2—191noHall
36#87705—141no—
37#87705—212no—
38#87704—21no—
39C7×C19⋊C3—141no—
40C19×ΓL(1,𝔽8)—141no—
41C2×C3×C19⋊C3—491no—
42C3⋊(D19⋊C3)—492no—
43#64425D19⋊C311yescharacteristic, complemented
44#64424—191no—
45#64423—572no—
46ΓL(1,𝔽8)⋊D7—381no—
47#64418—192no—
48D133—32no—
49C7×D19—212no—
50D7×C19—141no—
51D7×C19—212no—
52C2×D57—491no—
53C2×D19⋊C3—1471no—
54D72—571noHall
55C3×C19⋊C3—491noHall
56#3862C2×D19⋊C311yescharacteristic, complemented
57#3861—191no—
58C7×ΓL(1,𝔽8)—381no—
59C7×C19—21no—
60C7×C19—32no—
61C3×AGL(1,𝔽7)—2661no—
62C2×C3×C19—491no—
63D57—492no—
64C2×C19⋊C3—491no—
65C2×C19⋊C3—981no—
66D19⋊C3—1472no—
67C7⋊D7C3⋊(D19⋊C3)11yescharacteristic, complemented
68C7×D7—572no—
69C2×AGL(1,𝔽7)—3992no—
70C2×D19—1471noHall
71C3×ΓL(1,𝔽8)—2661no—
72C3×C19—491no—
73C19⋊C3—141no—
74C19⋊C3—491no—
75C72C2×C3⋊(D19⋊C3)11yescharacteristic, complemented, Sylow
76C3×D7—2661no—
77C2×ΓL(1,𝔽8)—3992no—
78AGL(1,𝔽7)—2661no—
79AGL(1,𝔽7)—2661no—
80AGL(1,𝔽7)—141no—
81AGL(1,𝔽7)—3992no—
82AGL(1,𝔽7)—3992no—
83C2×C19—491no—
84D19—212no—
85C2×C3×D3—9311noHall
86C2×D7—3992no—
87C3×C7—2661no—
88ΓL(1,𝔽8)—2661no—
89ΓL(1,𝔽8)—141no—
90ΓL(1,𝔽8)—381no—
91ΓL(1,𝔽8)—3992no—
92C19(#64418⋊C2)⋊C311yescharacteristic, complemented, Sylow
93C2×C32—9311no—
94C3×D3—9312no—
95C2×C7—3992no—
96D7—141no—
97D7—212no—
98D7—572no—
99C22×C3—27931no—
100C2×D3—9311no—
101C32—9311noSylow
102C7—21no—
103C7—32no—
104C2×C3—491no—
105C2×C3—18621no—
106C2×C3—9311no—
107C2×C3—27932no—
108D3—9312no—
109C22—27931noSylow
110C3—2661no—
111C3—491no—
112C3—9311no—
113C2—491no—
114C2—3992no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, cosocle, hypocenterC19×#3862C22×C3
Fitting, socleC72×C19C2×C3×D3
LCSG ▷ C19×#3862
UCSC1

Complements

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

NH ≅ G/Ntype
1. #30660725C2semidirect
2. #30660666C2semidirect
3. #26013935C3semidirect
5. #22552727C22semidirect
6. C19⋊#64418C2×C3semidirect
9. C19×#64425C2×C3semidirect
10. #19150287D3semidirect
12. C19×#3862C22×C3semidirect
13. #14584116C2×D3semidirect
16. C19×C7⋊D7C3×D3semidirect
21. C72×C19C2×C3×D3semidirect
43. #64425D19⋊C3semidirect
56. #3862C2×D19⋊C3semidirect
67. C7⋊D7C3⋊(D19⋊C3)semidirect
75. C72C2×C3⋊(D19⋊C3)semidirect
92. C19(#64418⋊C2)⋊C3semidirect

Maximal subgroups

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

subgroupindex
#306607252
#306606662
#260139353
#260138933
(#64418⋊C2)⋊C319
C2×C3⋊(D19⋊C3)49