Finite Group Databasebeta

← D13⋊C3×D49⋊C3 #37524182

Subgroups — D13⋊C3×D49⋊C3 #37524182

Order 22932.

180 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 180 conjugacy classes of subgroups — too many to draw. Only its 44 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(C13⋊C3)⋊(D49⋊C3)C211yesmaximal, characteristic, complemented
2C13⋊C3×D49⋊C3C211yesmaximal, characteristic, complemented
3D13⋊C3×C49⋊C3C211yesmaximal, characteristic, complemented
4#16838413⋊C2C311yesmaximal, characteristic, complemented
5#16838414⋊C2C311yesmaximal, characteristic, complemented
6D13×D49⋊C3C311yesmaximal, characteristic, complemented
7D13⋊C3×D49C311yesmaximal, characteristic, complemented
8C13⋊C3×C49⋊C3C2211yescharacteristic, complemented, Hall
9#16838420C2×C311yescharacteristic, complemented
10#16838419C2×C311yescharacteristic, complemented
11#16838418C2×C311yescharacteristic, complemented
12#16838417C2×C311yescharacteristic, complemented
13(C49⋊C3)⋊D13C2×C311yescharacteristic, complemented
14C13×D49⋊C3C2×C311yescharacteristic, complemented
15#16838414C2×C311yescharacteristic, complemented
16#16838413C2×C311yescharacteristic, complemented
17D13×C49⋊C3C2×C311yescharacteristic, complemented
18(C13⋊C3)⋊D49C2×C311yescharacteristic, complemented
19C13⋊C3×D49C2×C311yescharacteristic, complemented
20C49×D13⋊C3C2×C311yescharacteristic, complemented
21AGL(1,𝔽7)×D13⋊C3—71nomaximal
22D13×D49C3211yescharacteristic, complemented, Hall
23#14274255C22×C311yescharacteristic, complemented
24#14274254C22×C311yescharacteristic, complemented
25C13⋊C3×C49C22×C311yescharacteristic, complemented
26C13×C49⋊C3C22×C311yescharacteristic, complemented
27C2×C3×D49⋊C3—131nomaximal, Hall
28ΓL(1,𝔽8)⋊(D13⋊C3)—71no—
29C13⋊C3×AGL(1,𝔽7)—71no—
30ΓL(1,𝔽8)×D13⋊C3—71no—
31D637C2×C3211yescharacteristic, complemented
32D13×C49C2×C3211yescharacteristic, complemented
33C13×D49C2×C3211yescharacteristic, complemented
34#10587716⋊C2—71no—
35#10587717⋊C2—71no—
36D13×AGL(1,𝔽7)—71no—
37D7×D13⋊C3—211no—
38C2×C3×C49⋊C3—131no—
39C3×D49⋊C3—131no—
40C3×D49⋊C3—131no—
41ΓL(1,𝔽8)×C13⋊C3—71no—
42C13×C49C22×C3211yescharacteristic, complemented, Hall
43C2×C3×D49—131no—
44C2×D49⋊C3—131no—
45C2×D49⋊C3—131no—
46C2×D49⋊C3—391no—
47#10587723—71no—
48#10587722—71no—
49#10587721—71no—
50#10587720—71no—
51ΓL(1,𝔽8)⋊D13—71no—
52C13×AGL(1,𝔽7)—71no—
53#10587717—71no—
54#10587716—71no—
55ΓL(1,𝔽8)×D13—71no—
56(C13⋊C3)⋊D7—211no—
57D7×C13⋊C3—211no—
58C7×D13⋊C3AGL(1,𝔽7)11yescharacteristic
59C2×C3×D13⋊C3—491noHall
60C3×C49⋊C3—131noHall
61D7×D13—211no—
62C2×C3×C49—131no—
63C3×D49—131no—
64C3×D49—131no—
65C2×C49⋊C3—131no—
66C2×C49⋊C3—131no—
67C2×C49⋊C3—391no—
68D49⋊C3—131no—
69D49⋊C3—131no—
70D49⋊C3—131no—
71D49⋊C3—131no—
72D49⋊C3—391no—
73D49⋊C3D13⋊C311yescharacteristic, direct product factor
74#63271—71no—
75#63270—71no—
76C7×C13⋊C3C2×AGL(1,𝔽7)11yescharacteristic
77C13×ΓL(1,𝔽8)—71no—
78C2×C3×AGL(1,𝔽7)—911no—
79C2×C3×C13⋊C3—491no—
80C3×D13⋊C3—491no—
81C3×D13⋊C3—491no—
82C2×D49—391noHall
83D91—211no—
84C7×D13C3×AGL(1,𝔽7)11yescharacteristic
85C13×D7—211no—
86C2×C3×D13—491no—
87C2×D13⋊C3—491no—
88C2×D13⋊C3—491no—
89C2×D13⋊C3—1471no—
90C3×C49—131no—
91C49⋊C3—131no—
92C49⋊C3—131no—
93C49⋊C3C2×D13⋊C311yescharacteristic, complemented
94C2×C3×ΓL(1,𝔽8)—911no—
95C3×AGL(1,𝔽7)—911no—
96C3×AGL(1,𝔽7)—911no—
97C3×C13⋊C3—491noHall
98C2×C49—391no—
99D49—391no—
100D49C3×D13⋊C311yescharacteristic, complemented
101C7×C13C2×C3×AGL(1,𝔽7)11yescharacteristic
102C2×C3×D7—2731no—
103C2×AGL(1,𝔽7)—2731no—
104C2×AGL(1,𝔽7)—911no—
105C2×AGL(1,𝔽7)—911no—
106C2×C3×C13—491no—
107C3×D13—491no—
108C3×D13—491no—
109C2×C13⋊C3—491no—
110C2×C13⋊C3—491no—
111C2×C13⋊C3—1471no—
112D13⋊C3—491no—
113D13⋊C3—491no—
114D13⋊C3—491no—
115D13⋊C3—491no—
116D13⋊C3—1471no—
117D13⋊C3D49⋊C311yescharacteristic, direct product factor
118C3×ΓL(1,𝔽8)—911no—
119C2×D13—1471noHall
120C49C2×C3×D13⋊C311yescharacteristic, complemented, Sylow
121C2×C3×C7—131no—
122C3×D7—2731no—
123C3×D7—2731no—
124C2×ΓL(1,𝔽8)—2731no—
125C2×ΓL(1,𝔽8)—911no—
126C2×ΓL(1,𝔽8)—911no—
127AGL(1,𝔽7)—71no—
128AGL(1,𝔽7)—2731no—
129AGL(1,𝔽7)—911no—
130AGL(1,𝔽7)—911no—
131AGL(1,𝔽7)—911no—
132AGL(1,𝔽7)—911no—
133C3×C13—491no—
134C13⋊C3—491no—
135C13⋊C3—491no—
136C13⋊C3C2×D49⋊C311yescharacteristic, complemented
137C22×C32—6371noHall
138C2×D7—8191no—
139C2×C13—1471no—
140D13—1471no—
141D13C3×D49⋊C311yescharacteristic, complemented
142C3×C7—131no—
143ΓL(1,𝔽8)—71no—
144ΓL(1,𝔽8)—911no—
145ΓL(1,𝔽8)—911no—
146C2×C32—6371no—
147C2×C32—6371no—
148C2×C32—6371no—
149C2×C7—391no—
150D7—211no—
151D7—8191no—
152C13C2×C3×D49⋊C311yescharacteristic, complemented, Sylow
153C22×C3—19111no—
154C22×C3—19111no—
155C22×C3—6371no—
156C22×C3—6371no—
157C32—6371noSylow
158C7AGL(1,𝔽7)×D13⋊C311yescharacteristic
159C2×C3—131no—
160C2×C3—491no—
161C2×C3—19111no—
162C2×C3—19111no—
163C2×C3—19111no—
164C2×C3—19111no—
165C2×C3—6371no—
166C2×C3—6371no—
167C2×C3—6371no—
168C2×C3—6371no—
169C2×C3—6371no—
170C2×C3—6371no—
171C22—57331noSylow
172C3—131no—
173C3—491no—
174C3—6371no—
175C3—6371no—
176C2—391no—
177C2—57331no—
178C2—1471no—
subgroupG/H
center, hypercenterC1G
commutator, Fitting, cosocle, hypocenterC13×C49C22×C32
FrattiniC7AGL(1,𝔽7)×D13⋊C3
socleC7×C13C2×C3×AGL(1,𝔽7)
LCSG ▷ C13×C49
UCSC1

Complements

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

NH ≅ G/Ntype
1. (C13⋊C3)⋊(D49⋊C3)C2semidirect
2. C13⋊C3×D49⋊C3C2semidirect
3. D13⋊C3×C49⋊C3C2semidirect
4. #16838413⋊C2C3semidirect
5. #16838414⋊C2C3semidirect
6. D13×D49⋊C3C3semidirect
7. D13⋊C3×D49C3semidirect
8. C13⋊C3×C49⋊C3C22semidirect
9. #16838420C2×C3semidirect
10. #16838419C2×C3semidirect
11. #16838418C2×C3semidirect
12. #16838417C2×C3semidirect
13. (C49⋊C3)⋊D13C2×C3semidirect
14. C13×D49⋊C3C2×C3semidirect
15. #16838414C2×C3semidirect
16. #16838413C2×C3semidirect
17. D13×C49⋊C3C2×C3semidirect
18. (C13⋊C3)⋊D49C2×C3semidirect
19. C13⋊C3×D49C2×C3semidirect
20. C49×D13⋊C3C2×C3semidirect
22. D13×D49C32semidirect
23. #14274255C22×C3semidirect
24. #14274254C22×C3semidirect
25. C13⋊C3×C49C22×C3semidirect
26. C13×C49⋊C3C22×C3semidirect
31. D637C2×C32semidirect
32. D13×C49C2×C32semidirect
33. C13×D49C2×C32semidirect
42. C13×C49C22×C32semidirect
73. D49⋊C3D13⋊C3direct (N × H)
93. C49⋊C3C2×D13⋊C3semidirect
100. D49C3×D13⋊C3semidirect
117. D13⋊C3D49⋊C3direct (N × H)
120. C49C2×C3×D13⋊C3semidirect
136. C13⋊C3C2×D49⋊C3semidirect
141. D13C3×D49⋊C3semidirect
152. C13C2×C3×D49⋊C3semidirect

Maximal subgroups

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

subgroupindex
(C13⋊C3)⋊(D49⋊C3)2
C13⋊C3×D49⋊C32
D13⋊C3×C49⋊C32
#16838413⋊C23
#16838414⋊C23
D13×D49⋊C33
D13⋊C3×D493
AGL(1,𝔽7)×D13⋊C37
C2×C3×D49⋊C313