Finite Group Databasebeta

← C3×A4⋊AGL(1,𝔽13) #72242046

Subgroups — C3×A4⋊AGL(1,𝔽13) #72242046

Order 5616.

292 conjugacy classes of subgroups; only the 48 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 48 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×A4×D13⋊C3C211yesmaximal, characteristic
2C3×A4⋊#261C311yesmaximal, characteristic, complemented
3A4⋊AGL(1,𝔽13)C313yesmaximal, direct product factor
4C3×(C22⋊#261)⋊C3—31nomaximal
5C3×A4×C13⋊C3C411yescharacteristic, complemented
6C3×C3⋊AGL(1,𝔽13)—41nomaximal
7C3×D13⋊A4—21no—
8C3×A4×D13C2×C311yescharacteristic
9C22×C3×D13⋊C3D311yescharacteristic
10C2×C3×AGL(1,𝔽13)—31no—
11C2×C3×AGL(1,𝔽13)—31no—
12A4×D13⋊C3—23no—
13A4×D13⋊C3C2×C313yes—
14C32×D13⋊C3—41no—
15A4⋊#261C3211yescharacteristic, complemented
16C3×C22⋊#261—31no—
17(C22⋊#261)⋊C3—33no—
18C3×C22⋊(C13⋊C3)—21no—
19C3×A4×C13C3×C411yescharacteristic, complemented
20C22×C3×C13⋊C3Dic311yescharacteristic, complemented
21C3×C3⋊#261—41no—
22C2×C3×D13⋊C3—31no—
23C2×C3×D13⋊C3—31no—
24A4×C13⋊C3—23no—
25A4×C13⋊C3C3×C413yescomplemented
26C3⋊AGL(1,𝔽13)—43no—
27C3×AGL(1,𝔽13)—61no—
28C3×AGL(1,𝔽13)—61no—
29C32×SL(2,ℤ/4)—131nomaximal, Hall
30C32×C13⋊C3—41noHall
31C22×C3×D13C3×D311yescharacteristic
32C2×C3×#261—31no—
33C2×C3×#261—31no—
34D13⋊A4—23no—
35A4×D13—21no—
36A4×D13C2×C3211yescharacteristic
37C22×D13⋊C3C3×D313yes—
38C2×AGL(1,𝔽13)—33no—
39C2×AGL(1,𝔽13)—33no—
40C32×D13—41no—
41C2×C3×C13⋊C3—31no—
42C3×D13⋊C3—31no—
43C3×D13⋊C3—43no—
44C3×D13⋊C3—81no—
45C3×D13⋊C3—83no—
46C3×D13⋊C3S411yescharacteristic
47C2×C32×A4—131no—
48C22⋊#261—31noHall
49C22×C3×C13C3×Dic311yescharacteristic, complemented
50C2×C3×D13—31no—
51C2×C3×D13—31no—
52C22⋊(C13⋊C3)—23no—
53A4×C13—21no—
54A4×C13C32×C411yescharacteristic, complemented
55C22×C13⋊C3C3×Dic313yescomplemented
56C3⋊#261—41no—
57C3×#261—61no—
58C3×#261—61no—
59C2×D13⋊C3—33no—
60C2×D13⋊C3—33no—
61AGL(1,𝔽13)—63no—
62AGL(1,𝔽13)—63no—
63C3×SL(2,ℤ/4)—133no—
64C3×SL(2,ℤ/4)—131no—
65C32×C22⋊C4—391no—
66C32×C13—41no—
67C3×C13⋊C3—43no—
68C3×C13⋊C3—81no—
69C3×C13⋊C3—83no—
70C3×C13⋊C3SL(2,ℤ/4)11yescharacteristic, complemented
71C32×A4—131no—
72C32×Dic3—521no—
73C22×D13C32×D311yescharacteristic
74C2×#261—31no—
75C2×#261—31no—
76C2×C3×C13—31no—
77C3×D13—31no—
78C3×D13—41no—
79C3×D13—81no—
80C3×D13C3×S411yescharacteristic
81C2×C13⋊C3—33no—
82D13⋊C3—33no—
83D13⋊C3—83no—
84D13⋊C3C3×S413yes—
85C23×C32—131no—
86C2×C3×A4—133no—
87C2×C3×A4—131no—
88C2×C3×A4—263no—
89C2×C3×A4—261no—
90C2×C32×C4—391no—
91C2×C32×C4—391no—
92C2×C33—521no—
93C22×C13C32×Dic311yescharacteristic, complemented
94C2×D13—31no—
95C2×D13—31no—
96#261—61no—
97#261—61no—
98SL(2,ℤ/4)—131no—
99C3×C22⋊C4—393no—
100C3×C22⋊C4—391no—
101C3×C13—41no—
102C3×C13—81no—
103C3×C13C3×SL(2,ℤ/4)11yescharacteristic, complemented
104C13⋊C3—83no—
105C13⋊C3C3×SL(2,ℤ/4)13yescomplemented
106C22×C32—131no—
107C22×C32—391no—
108C22×C32—391no—
109C3×A4—133no—
110C3×A4—263no—
111C3×A4—261no—
112C3×A4AGL(1,𝔽13)11yescharacteristic, complemented
113C32×C4—781no—
114C32×C4—781no—
115C3×Dic3—523no—
116C3×Dic3—521no—
117C33—521noSylow
118C2×C13—31no—
119D13—31no—
120D13C32×S411yescharacteristic
121C23×C3—133no—
122C23×C3—131no—
123C2×A4—131no—
124C2×A4—261no—
125C2×A4—263no—
126C2×C3×C4—393no—
127C2×C3×C4—393no—
128C2×C3×C4—391no—
129C2×C3×C4—391no—
130C2×C32—131no—
131C2×C32—391no—
132C2×C32—391no—
133C2×C32—521no—
134C2×C32—523no—
135C2×C32—1043no—
136C2×C32—1041no—
137C22⋊C4—391noSylow
138C13C32×SL(2,ℤ/4)11yescharacteristic, complemented, Sylow
139C22×C3—133no—
140C22×C3—391no—
141C22×C3—391no—
142C22×C3—393no—
143C22×C3—393no—
144C22×C3C3⋊AGL(1,𝔽13)11yescharacteristic, complemented
145A4—21no—
146A4—263no—
147A4C3×AGL(1,𝔽13)11yescharacteristic, complemented
148C3×C4—783no—
149C3×C4—781no—
150C3×C4—783no—
151C3×C4—781no—
152Dic3—521no—
153C32—41no—
154C32—131no—
155C32—523no—
156C32—1043no—
157C32—1041no—
158C23—131no—
159C2×C4—391no—
160C2×C4—391no—
161C2×C3—31no—
162C2×C3—133no—
163C2×C3—131no—
164C2×C3—393no—
165C2×C3—393no—
166C2×C3—391no—
167C2×C3—521no—
168C2×C3—1041no—
169C2×C3—1043no—
170C22—391no—
171C22—391no—
172C22C3×C3⋊AGL(1,𝔽13)11yescharacteristic, complemented
173C4—781no—
174C4—781no—
175C3—41no—
176C3—81no—
177C3—133no—
178C3—1043no—
179C3A4⋊AGL(1,𝔽13)11yescharacteristic, direct product factor
180C2—31no—
181C2—131no—
182C2—391no—
subgroupG/H
center, hypercenterC3A4⋊AGL(1,𝔽13)
commutator, hypocenterA4×C13C32×C4
FrattiniC1G
Fitting, socleC22×C3×C13C3×Dic3
prime radicalC3×A4×D13⋊C3C2
cosocleA4×D13C2×C32
LCSG ▷ A4×C13
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
2. C3×A4⋊#261C3semidirect
3. A4⋊AGL(1,𝔽13)C3direct (N × H)
5. C3×A4×C13⋊C3C4semidirect
15. A4⋊#261C32semidirect
19. C3×A4×C13C3×C4semidirect
20. C22×C3×C13⋊C3Dic3semidirect
25. A4×C13⋊C3C3×C4semidirect
49. C22×C3×C13C3×Dic3semidirect
54. A4×C13C32×C4semidirect
55. C22×C13⋊C3C3×Dic3semidirect
70. C3×C13⋊C3SL(2,ℤ/4)semidirect
93. C22×C13C32×Dic3semidirect
103. C3×C13C3×SL(2,ℤ/4)semidirect
105. C13⋊C3C3×SL(2,ℤ/4)semidirect
112. C3×A4AGL(1,𝔽13)semidirect
138. C13C32×SL(2,ℤ/4)semidirect
144. C22×C3C3⋊AGL(1,𝔽13)semidirect
147. A4C3×AGL(1,𝔽13)semidirect
172. C22C3×C3⋊AGL(1,𝔽13)semidirect
179. C3A4⋊AGL(1,𝔽13)direct (N × H)

Maximal subgroups

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

subgroupindex
C3×A4×D13⋊C32
C3×A4⋊#2613
A4⋊AGL(1,𝔽13)3
C3×(C22⋊#261)⋊C33
C3×C3⋊AGL(1,𝔽13)4
C32×SL(2,ℤ/4)13