Finite Group Databasebeta

← C19⋊C3×#10596868 #45691815

Subgroups — C19⋊C3×#10596868 #45691815

Order 33516.

104 conjugacy classes of subgroups; only the 21 normal subgroups are shown.

normal subgroups only

This group has 104 conjugacy classes of subgroups — too many to draw. Only its 21 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×C19⋊C3×#3862C211yesmaximal, characteristic
2C19×#10596868C311yesmaximal, characteristic, complemented
3C7×Dic7×C19⋊C3—31nomaximal
4C19⋊C3×#3862C411yescharacteristic, complemented, Hall
5C2×C19⋊#3862—21no—
6C2×C19×#3862C2×C311yescharacteristic
7C2×C72×C19⋊C3D311yescharacteristic
8C7×C19×Dic7—31noHall
9C19⋊#3862—21no—
10C19×#3862C3×C411yescharacteristic, complemented
11C72×C19⋊C3Dic311yescharacteristic, complemented
12C2×ΓL(1,𝔽8)×C19⋊C3—141no—
13C2×C72×C19C3×D311yescharacteristic
14C3×#10596868—191nomaximal, Hall
15C4×C7×C19⋊C3—211no—
16Dic7×C19⋊C3—31no—
17ΓL(1,𝔽8)×C19⋊C3—141no—
18C72×C19C3×Dic311yescharacteristic, complemented, Hall
19C2×C3×#3862—191no—
20C2×#87705—141no—
21C2×#87704—141no—
22C2×C19×ΓL(1,𝔽8)—141no—
23C2×C7×C19⋊C3—21no—
24C2×C7×C19⋊C3—31no—
25C2×C7×C19⋊C3—31no—
26Dic3×C19⋊C3—491nomaximal, Hall
27C3×C7×Dic7—571no—
28#10596868C19⋊C311yescharacteristic, direct product factor
29C4×C7×C19—211no—
30C19×Dic7—31no—
31C3×#3862—191noHall
32#87705—141no—
33#87704—141no—
34C7×C19⋊C3—21no—
35C7×C19⋊C3—31no—
36C7×C19⋊C3—31no—
37C19×ΓL(1,𝔽8)—141no—
38C2×C3×C19⋊C3—491no—
39C2×C3×C72—191no—
40C2×#3862—381no—
41C2×#3862C2×C19⋊C311yescharacteristic
42C2×C7×C19—21no—
43C2×C7×C19—31no—
44C2×C7×C19—31no—
45Dic3×C19—491no—
46C4×C19⋊C3—211no—
47C7×Dic7—31noHall
48C3×C19⋊C3—491noHall
49C3×C72—191no—
50#3862—381no—
51#3862C4×C19⋊C311yescharacteristic, complemented
52C7×C19—21no—
53C7×C19—31no—
54C7×C19—31no—
55C2×C3×ΓL(1,𝔽8)—2661no—
56C2×C3×C19—491no—
57C2×C19⋊C3—981no—
58C2×C19⋊C3#6441811yescharacteristic
59C2×C72D3×C19⋊C311yescharacteristic
60C3×C4×C7—3991no—
61C3×Dic7—571no—
62C4×C19—211noHall
63C3×ΓL(1,𝔽8)—2661no—
64C3×C19—491no—
65C19⋊C3—981no—
66C19⋊C3#1059686811yescharacteristic, direct product factor
67C72Dic3×C19⋊C311yescharacteristic, complemented, Sylow
68C2×C3×C7—381no—
69C2×C3×C7—571no—
70C2×C3×C7—571no—
71C2×ΓL(1,𝔽8)—2661no—
72C2×ΓL(1,𝔽8)—2661no—
73C2×ΓL(1,𝔽8)—141no—
74C2×C19C3×#6441811yescharacteristic
75C3×Dic3—9311noHall
76C4×C7—211no—
77Dic7—31no—
78C3×C7—381no—
79C3×C7—571no—
80C3×C7—571no—
81ΓL(1,𝔽8)—2661no—
82ΓL(1,𝔽8)—2661no—
83ΓL(1,𝔽8)—141no—
84C19C3×#1059686811yescharacteristic, complemented, Sylow
85C2×C32—9311no—
86C2×C7—21no—
87C2×C7—31no—
88C2×C7—31no—
89C3×C4—3991no—
90Dic3—491no—
91C32—9311noSylow
92C7—21no—
93C7—31no—
94C7—31no—
95C2×C3—191no—
96C2×C3—491no—
97C2×C3—18621no—
98C4—211noSylow
99C3—191no—
100C3—491no—
101C3—18621no—
102C2C19⋊C3×#6441811yescharacteristic
subgroupG/H
center, Frattini, hypercenterC2C19⋊C3×#64418
commutator, hypocenterC19×#3862C3×C4
Fitting, socleC2×C72×C19C3×D3
prime radicalC2×C19⋊C3×#3862C2
cosocleC2×C19×#3862C2×C3
LCSG ▷ C19×#3862
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
2. C19×#10596868C3semidirect
4. C19⋊C3×#3862C4semidirect
10. C19×#3862C3×C4semidirect
11. C72×C19⋊C3Dic3semidirect
18. C72×C19C3×Dic3semidirect
28. #10596868C19⋊C3direct (N × H)
51. #3862C4×C19⋊C3semidirect
66. C19⋊C3#10596868direct (N × H)
67. C72Dic3×C19⋊C3semidirect
84. C19C3×#10596868semidirect

Maximal subgroups

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

subgroupindex
C2×C19⋊C3×#38622
C19×#105968683
C7×Dic7×C19⋊C33
C3×#1059686819
Dic3×C19⋊C349