Finite Group Databasebeta

← C3×#16838414⋊C2 #37524191

Subgroups — C3×#16838414⋊C2 #37524191

Order 22932.

180 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 180 conjugacy classes of subgroups — too many to draw. Only its 46 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×#16838420C211yesmaximal, characteristic, complemented
2C3×#16838418C211yesmaximal, characteristic, complemented
3C3×#16838414C211yesmaximal, characteristic, complemented
4C3×D13×D49C311yesmaximal, characteristic, complemented
5#16838414⋊C2C313yesmaximal, direct product factor
6C3×#14274255C2211yescharacteristic, complemented, Hall
7C3×D637C2×C311yescharacteristic, complemented
8C3×C13×D49C2×C311yescharacteristic, complemented
9C3×D13×C49C2×C311yescharacteristic, complemented
10#16838420C2×C313yescomplemented
11#16838418C2×C313yescomplemented
12#16838414C2×C313yescomplemented
13C3×#10587717⋊C2—71nomaximal
14D13×D49C3211yescharacteristic, complemented, Hall
15C3×C13×C49C22×C311yescharacteristic, complemented
16#14274255C22×C313yescomplemented
17C2×C3×D49⋊C3—131nomaximal, Hall
18C3×#10587723—71no—
19C3×#10587721—71no—
20C3×#10587717—71no—
21D637C2×C3211yescharacteristic, complemented
22D13×C49C2×C3211yescharacteristic, complemented
23C13×D49C2×C3211yescharacteristic, complemented
24C3×D7×D13—211no—
25#10587717⋊C2—73no—
26C2×C3×C49⋊C3—131no—
27C3×D49⋊C3—131no—
28C3×D49⋊C3—131no—
29C3×#63271—71no—
30C13×C49C22×C3211yescharacteristic, complemented, Hall
31C2×C3×D49—391no—
32C2×D49⋊C3—133no—
33C3×D91—211no—
34C3×C13×D7—211no—
35C3×C7×D13AGL(1,𝔽7)11yescharacteristic
36#10587723—73no—
37#10587721—73no—
38#10587717—73no—
39C2×C3×D13⋊C3—491noHall
40C3×C49⋊C3—131noHall
41D7×D13—211no—
42C2×C3×C49—391no—
43C3×D49—391no—
44C3×D49D13⋊C311yescharacteristic, complemented
45C2×C49⋊C3—133no—
46D49⋊C3—133no—
47D49⋊C3—133no—
48C3×C7×C13C2×AGL(1,𝔽7)11yescharacteristic
49#63271—73no—
50C2×C3×AGL(1,𝔽7)—911no—
51C2×C3×C13⋊C3—491no—
52C3×D13⋊C3—491no—
53C3×D13⋊C3—491no—
54C2×D49—391noHall
55D91—211no—
56C7×D13C3×AGL(1,𝔽7)11yescharacteristic
57C13×D7—211no—
58C2×C3×D13—1471no—
59C2×D13⋊C3—493no—
60C3×C49C2×D13⋊C311yescharacteristic, complemented
61C49⋊C3—133no—
62C2×C3×ΓL(1,𝔽8)—911no—
63C3×AGL(1,𝔽7)—911no—
64C3×AGL(1,𝔽7)—911no—
65C3×C13⋊C3—491noHall
66C2×C49—391no—
67D49—391no—
68D49C3×D13⋊C311yescharacteristic, complemented
69C7×C13C2×C3×AGL(1,𝔽7)11yescharacteristic
70C2×C3×D7—2731no—
71C2×AGL(1,𝔽7)—913no—
72C2×C3×C13—1471no—
73C3×D13—491no—
74C3×D13D49⋊C311yescharacteristic, complemented
75C2×C13⋊C3—493no—
76D13⋊C3—493no—
77D13⋊C3—493no—
78C3×ΓL(1,𝔽8)—911no—
79C2×D13—1471noHall
80C49C2×C3×D13⋊C311yescharacteristic, complemented, Sylow
81C2×C3×C7—391no—
82C3×D7—2731no—
83C3×D7—211no—
84C2×ΓL(1,𝔽8)—913no—
85AGL(1,𝔽7)—913no—
86AGL(1,𝔽7)—913no—
87C3×C13C2×D49⋊C311yescharacteristic, complemented
88C13⋊C3—493no—
89C22×C32—6371noHall
90C2×D7—2731no—
91C2×C13—1471no—
92D13—491no—
93D13C3×D49⋊C311yescharacteristic, complemented
94C3×C7#10587717⋊C211yescharacteristic
95ΓL(1,𝔽8)—913no—
96C2×C32—6371no—
97C2×C32—6371no—
98C2×C32—6371no—
99C2×C7—391no—
100D7—2731no—
101D7—211no—
102C13C2×C3×D49⋊C311yescharacteristic, complemented, Sylow
103C22×C3—19111no—
104C22×C3—6373no—
105C32—6371noSylow
106C7C3×#10587717⋊C211yescharacteristic
107C2×C3—391no—
108C2×C3—19111no—
109C2×C3—6373no—
110C2×C3—6373no—
111C2×C3—6373no—
112C2×C3—1471no—
113C22—19111noSylow
114C3—6373no—
115C3#16838414⋊C211yescharacteristic, direct product factor
116C2—391no—
117C2—19111no—
118C2—1471no—
subgroupG/H
center, hypercenterC3#16838414⋊C2
commutator, cosocle, hypocenterC13×C49C22×C32
FrattiniC7C3×#10587717⋊C2
FittingC3×C13×C49C22×C3
socleC3×C7×C13C2×AGL(1,𝔽7)
LCSG ▷ C13×C49
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
1. C3×#16838420C2semidirect
2. C3×#16838418C2semidirect
3. C3×#16838414C2semidirect
4. C3×D13×D49C3semidirect
5. #16838414⋊C2C3direct (N × H)
6. C3×#14274255C22semidirect
7. C3×D637C2×C3semidirect
8. C3×C13×D49C2×C3semidirect
9. C3×D13×C49C2×C3semidirect
10. #16838420C2×C3semidirect
11. #16838418C2×C3semidirect
12. #16838414C2×C3semidirect
14. D13×D49C32semidirect
15. C3×C13×C49C22×C3semidirect
16. #14274255C22×C3semidirect
21. D637C2×C32semidirect
22. D13×C49C2×C32semidirect
23. C13×D49C2×C32semidirect
30. C13×C49C22×C32semidirect
44. C3×D49D13⋊C3semidirect
60. C3×C49C2×D13⋊C3semidirect
68. D49C3×D13⋊C3semidirect
74. C3×D13D49⋊C3semidirect
80. C49C2×C3×D13⋊C3semidirect
87. C3×C13C2×D49⋊C3semidirect
93. D13C3×D49⋊C3semidirect
102. C13C2×C3×D49⋊C3semidirect
115. C3#16838414⋊C2direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#168384202
C3×#168384182
C3×#168384142
C3×D13×D493
#16838414⋊C23
C3×#10587717⋊C27
C2×C3×D49⋊C313