Finite Group Databasebeta

← D3×#16838419 #37524210

Subgroups — D3×#16838419 #37524210

Order 22932.

132 conjugacy classes of subgroups; only the 29 normal subgroups are shown.

normal subgroups only

This group has 132 conjugacy classes of subgroups — too many to draw. Only its 29 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⋊#16838419C211yesmaximal, characteristic, complemented
2D3×#14274254C211yesmaximal, characteristic, complemented
3C3×#16838419C211yesmaximal, characteristic, complemented
4D3×D637C311yesmaximal, characteristic, complemented
5C2×#16838419—31nomaximal
6C3×#14274254C2211yescharacteristic, complemented, Hall
7D1911C2×C311yescharacteristic, complemented
8D3×C13×C49C2×C311yescharacteristic, complemented
9C3×D637C2×C311yescharacteristic, complemented
10C2×#14274254—31no—
11#16838419—21no—
12#16838419—31no—
13#16838419D311yescharacteristic, direct product factor
14D3×#10587722—71nomaximal
15C2×D637—31noHall
16C3×C13×C49C22×C311yescharacteristic, complemented
17#14274254—21no—
18#14274254C2×D311yescharacteristic, complemented
19D3×D49⋊C3—131nomaximal, Hall
20C3⋊#10587722—71no—
21D3×#63270—141no—
22C3×#10587722—71no—
23C2×C13×C49—31no—
24D637—31no—
25D637C3×D311yescharacteristic, complemented
26D3×D91—71no—
27C2×#10587722—211no—
28C3⋊(D49⋊C3)—131no—
29D3×C49⋊C3—261no—
30C3×D49⋊C3—131no—
31C3×#63270—141no—
32C13×C49C2×C3×D311yescharacteristic, complemented, Hall
33D3×D49—131no—
34C2×D49⋊C3—391no—
35D273—71no—
36D3×C7×C13AGL(1,𝔽7)11yescharacteristic
37C3×D91—71no—
38C2×#63270—421no—
39#10587722—71no—
40#10587722—141no—
41#10587722—211no—
42D3×D13⋊C3—491noHall
43C3×C49⋊C3—261noHall
44C2×D91—211no—
45D147—131no—
46C3×D49—131no—
47D3×C49D13⋊C311yescharacteristic, complemented
48C2×C49⋊C3—781no—
49D49⋊C3—131no—
50D49⋊C3—261no—
51D49⋊C3—391no—
52C3×C7×C13C2×AGL(1,𝔽7)11yescharacteristic
53#63270—141no—
54#63270—281no—
55D3×AGL(1,𝔽7)—911no—
56C3⋊(D13⋊C3)—491no—
57D3×C13⋊C3—981no—
58C3×D13⋊C3—491no—
59C2×D49—391noHall
60C2×C7×C13—31no—
61D91—71no—
62D91—211no—
63D3×D13—491no—
64C2×D13⋊C3—1471no—
65C3×C49C2×D13⋊C311yescharacteristic, complemented
66C49⋊C3—261no—
67C49⋊C3—521no—
68C3⋊AGL(1,𝔽7)—911no—
69D3×ΓL(1,𝔽8)—1821no—
70C3×AGL(1,𝔽7)—911no—
71C3×C13⋊C3—981noHall
72C2×C49—31no—
73D49—131no—
74D49—391no—
75C7×C13D3×AGL(1,𝔽7)11yescharacteristic
76D3×D7—911no—
77C2×AGL(1,𝔽7)—2731no—
78D39—491no—
79C3×D13—491no—
80D3×C13D49⋊C311yescharacteristic, complemented
81C2×C13⋊C3—2941no—
82D13⋊C3—491no—
83D13⋊C3—981no—
84D13⋊C3—1471no—
85C3×ΓL(1,𝔽8)—1821no—
86C2×D13—1471noHall
87C49D3×D13⋊C311yescharacteristic, complemented, Sylow
88D21—911no—
89C3×D7—911no—
90D3×C7#1058772211yescharacteristic
91C2×ΓL(1,𝔽8)—5461no—
92AGL(1,𝔽7)—2731no—
93AGL(1,𝔽7)—911no—
94AGL(1,𝔽7)—1821no—
95C3×C13C2×D49⋊C311yescharacteristic, complemented
96C13⋊C3—981no—
97C13⋊C3—1961no—
98C2×C3×D3—6371noHall
99C2×D7—2731no—
100C2×C13—31no—
101D13—491no—
102D13—1471no—
103C3×C7C2×#1058772211yescharacteristic
104ΓL(1,𝔽8)—3641no—
105ΓL(1,𝔽8)—1821no—
106C2×C32—6371no—
107C3×D3—6371no—
108C3×D3—12741no—
109C2×C7—31no—
110D7—2731no—
111D7—911no—
112C13D3×D49⋊C311yescharacteristic, complemented, Sylow
113C22×C3—19111no—
114C2×D3—6371no—
115C32—12741noSylow
116C7D3×#1058772211yescharacteristic
117C2×C3—19111no—
118C2×C3—6371no—
119C2×C3—6371no—
120C2×C3—38221no—
121C2×C3—12741no—
122D3—6371no—
123D3#1683841911yescharacteristic, direct product factor
124C22—19111noSylow
125C3—25481no—
126C3—12741no—
127C3C2×#1683841911yescharacteristic, complemented
128C2—31no—
129C2—19111no—
130C2—6371no—
subgroupG/H
center, hypercenterC1G
commutator, Fitting, cosocle, hypocenterC3×C13×C49C22×C3
FrattiniC7D3×#10587722
socleC3×C7×C13C2×AGL(1,𝔽7)
LCSG ▷ C3×C13×C49
UCSC1

Complements

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

NH ≅ G/Ntype
1. C3⋊#16838419C2semidirect
2. D3×#14274254C2semidirect
3. C3×#16838419C2semidirect
4. D3×D637C3semidirect
6. C3×#14274254C22semidirect
7. D1911C2×C3semidirect
8. D3×C13×C49C2×C3semidirect
9. C3×D637C2×C3semidirect
13. #16838419D3direct (N × H)
16. C3×C13×C49C22×C3semidirect
18. #14274254C2×D3semidirect
25. D637C3×D3semidirect
32. C13×C49C2×C3×D3semidirect
47. D3×C49D13⋊C3semidirect
65. C3×C49C2×D13⋊C3semidirect
80. D3×C13D49⋊C3semidirect
87. C49D3×D13⋊C3semidirect
95. C3×C13C2×D49⋊C3semidirect
112. C13D3×D49⋊C3semidirect
123. D3#16838419direct (N × H)
127. C3C2×#16838419semidirect

Maximal subgroups

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

subgroupindex
C3⋊#168384192
D3×#142742542
C3×#168384192
D3×D6373
C2×#168384193
D3×#105877227
D3×D49⋊C313