Finite Group Databasebeta

← #13125209

Subgroups — #13125209

Order 1664.

484 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 121 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
1D13×#127C211yesmaximal, characteristic
2#11719393C211yesmaximal, characteristic, complemented
3C13×#490C211yesmaximal, characteristic, complemented
4#11718732C211yesmaximal, characteristic, complemented
5#11718728C211yesmaximal, characteristic, complemented
6#11718431C214yesmaximal, complemented
7#11718421C214yesmaximal, complemented
8#11718374C211yesmaximal, characteristic, complemented
9#11718368C211yesmaximal, characteristic, complemented
10C2×D4×D13—22no—
11C2×D4×D13C2212yes—
12C13×#127C2211yescharacteristic
13C13×#125C2211yescharacteristic, complemented
14#88194—22no—
15#88194C2212yes—
16C2×#6094C2212yes—
17#88150—22no—
18#88146C2212yes—
19#88142C2212yescomplemented
20#88141—22no—
21#88128C2211yescharacteristic
22C42×D13C2211yescharacteristic
23#88124C2211yescharacteristic, complemented
24C13×#102C2214yescomplemented
25C13×#97C2211yescharacteristic, complemented
26#88072C2214yescomplemented
27#88061C2214yescomplemented
28C8×Dic13C2212yescomplemented
29#88049C2214yescomplemented
30#88043C2211yescharacteristic, complemented
31C23×D13—22no—
32C2×D4×C13—22no—
33C2×D4×C13C2312yes—
34C2×C22⋊D13—22no—
35C2×C22⋊D13—24no—
36D4×D13—28no—
37D4×D13—48no—
38C2×D52—22no—
39C2×D52C2312yes—
40C2×C4×D13D412yes—
41C2×C4×D13C2311yescharacteristic
42C2×Dic26—22no—
43C2×C8×C13C2312yes—
44C13×C4⋊C4—22no—
45C13×C4⋊C4C2312yes—
46C42×C13C2311yescharacteristic
47#6103—22no—
48C4⋊Dic13C2312yes—
49#6101—22no—
50#6101—22no—
51C4×Dic13—22no—
52C4×Dic13D412yes—
53C4×Dic13C2311yescharacteristic
54C2×#1055C2312yes—
55#6094—24no—
56#3138—131nomaximal, Sylow
57C23×C13—22no—
58C22×D13—22no—
59C22×D13—48no—
60C22×D13—44no—
61C22×D13C2×D411yescharacteristic
62D4×C13—24no—
63D4×C13—44no—
64C2×C4×C13—22no—
65C2×C4×C13C2×D412yes—
66C2×C4×C13C2411yescharacteristic
67C22⋊D13—44no—
68C22⋊D13—48no—
69C2×Dic13—22no—
70C2×Dic13C2×D411yescharacteristic
71C2×Dic13C2×D412yes—
72D52—24no—
73D52—44no—
74C4×D13—24no—
75C4×D13#4114yes—
76Dic26—44no—
77C8×C13—22no—
78#1055—22no—
79#533—131no—
80C2×#127—131no—
81#490—131no—
82#490—131no—
83#490—131no—
84#490D1311yescharacteristic, complemented
85#486—134no—
86#418—134no—
87C4×M16—131no—
88C22×C13—42no—
89C22×C13—44no—
90C22×C13C22×D411yescharacteristic
91C2×D13—22no—
92C2×D13—42no—
93C2×D13—44no—
94C2×D13—88no—
95C2×D13#12412yes—
96C4×C13—22no—
97C4×C13—42no—
98C4×C13C2×#4112yes—
99Dic13—42no—
100Dic13#12412yes—
101Dic13AGL(1,ℤ/8)14yes—
102C22×D4—132no—
103C22×D4—262no—
104C2×M16—132no—
105C4⋊Q8—132no—
106#127—132no—
107#127—131no—
108#127—262no—
109#127C2×D1311yescharacteristic
110#125—131no—
111#125C2×D1311yescharacteristic, complemented
112C22⋊Q8—262no—
113C4×Q8—262no—
114#117—132no—
115C2×C42—131no—
116#102—134no—
117#102—134no—
118#102—134no—
119#102C2×D1314yescomplemented
120#97—131no—
121#97C2×D1311yescharacteristic, complemented
122C4×C8—132no—
123C2×C13—82no—
124C2×C13C2×#12411yescharacteristic
125C2×C13C2×AGL(1,ℤ/8)12yes—
126D13—22no—
127D13—82no—
128C24—262no—
129C2×Q8—262no—
130C2×D4—22no—
131C2×D4—132no—
132C2×D4—268no—
133C2×D4—264no—
134C2×D4—262no—
135C2×D4—262no—
136C2×D4—528no—
137C2×D4C22×D1312yes—
138C22×C4—131no—
139C22×C4—132no—
140M16—264no—
141C2×C8—132no—
142C2×C8C22×D1312yes—
143C4⋊C4—22no—
144C4⋊C4—132no—
145C4⋊C4—262no—
146C4⋊C4—262no—
147C4⋊C4C22×D1312yes—
148C22⋊C4—262no—
149C42—132no—
150C42—131no—
151C42—262no—
152C42C22×D1311yescharacteristic
153C13#313811yescharacteristic, complemented, Sylow
154C23—22no—
155C23—131no—
156C23—262no—
157C23—524no—
158C23—528no—
159Q8—524no—
160D4—24no—
161D4—44no—
162D4—264no—
163D4—524no—
164D4—524no—
165D4—528no—
166C2×C4—22no—
167C2×C4—131no—
168C2×C4—132no—
169C2×C4—134no—
170C2×C4—264no—
171C2×C4—262no—
172C2×C4D4×D1312yes—
173C2×C4C23×D1311yescharacteristic
174C8—22no—
175C8—262no—
176C22—44no—
177C22—42no—
178C22—132no—
179C22—262no—
180C22—524no—
181C22—522no—
182C22—1048no—
183C22C2×D4×D1311yescharacteristic
184C4—22no—
185C4—42no—
186C4—134no—
187C4—132no—
188C4—522no—
189C4#41×D1312yes—
190C2—82no—
191C2—262no—
192C2—1042no—
193C2D13×#12411yescharacteristic
194C2D13×AGL(1,ℤ/8)12yes—
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#490C2
socleC22×C13C22×D4
prime radicalD13×#127C2
hypercenter#490D13
hypocenterC13#3138
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
2. #11719393C2semidirect
3. C13×#490C2semidirect
4. #11718732C2semidirect
5. #11718728C2semidirect
6. #11718431C2semidirect
7. #11718421C2semidirect
8. #11718374C2semidirect
9. #11718368C2semidirect
13. C13×#125C22semidirect
19. #88142C22semidirect
23. #88124C22semidirect
24. C13×#102C22semidirect
25. C13×#97C22semidirect
26. #88072C22semidirect
27. #88061C22semidirect
28. C8×Dic13C22semidirect
29. #88049C22semidirect
30. #88043C22semidirect
84. #490D13semidirect
111. #125C2×D13semidirect
119. #102C2×D13semidirect
121. #97C2×D13semidirect
153. C13#3138semidirect

Maximal subgroups

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

subgroupindex
D13×#1272
#117193932
C13×#4902
#117187322
#117187282
#117184312
#117184212
#117183742
#117183682
#313813