Finite Group Databasebeta

← #13127974

Subgroups — #13127974

Order 1664.

370 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 113 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#11719474C212yesmaximal, complemented
2C13×#508C211yesmaximal, characteristic, complemented
3#11718854C212yesmaximal, complemented
4#11718580C212yesmaximal, complemented
5#11718575C214yesmaximal, complemented
6D13×D16C212yesmaximal, complemented
7C2×D208C211yesmaximal, characteristic, complemented
8#11718562C211yesmaximal, characteristic, complemented
9#88256—22no—
10C13×#135C2212yescomplemented
11#88203—22no—
12#88173C2214yescomplemented
13#88168—24no—
14D8×D13C2214yescomplemented
15C2×D104C2212yescomplemented
16#88155C2211yescharacteristic
17C13×Q32C2211yescharacteristic, complemented
18C13×SD32C2212yescomplemented
19C13×D16C2211yescharacteristic, complemented
20C2×C13×C16C2211yescharacteristic, complemented
21#88068C2214yescomplemented
22#88066C2214yescomplemented
23#88052C2211yescharacteristic, complemented
24D208C2212yescomplemented
25D208C2212yescomplemented
26#88038C2212yescomplemented
27C16×D13C2212yescomplemented
28C13×#41—22no—
29#6131—24no—
30D4×D13—24no—
31D4×D13—44no—
32#6127—42no—
33#6127D411yescharacteristic
34C2×D52—22no—
35C2×D52—42no—
36C13×Q16C2312yes—
37C13×SD16—22no—
38C13×D8C2312yes—
39C2×C8×C13C2311yescharacteristic
40#6106—24no—
41#6104—24no—
42#6099D411yescharacteristic
43D104—22no—
44D104C2314yes—
45#6094D412yes—
46C8×D13C2312yes—
47C13×C16C2311yescharacteristic
48C13×C16C2311yescharacteristic
49#6090C2312yes—
50#3415—131nomaximal, Sylow
51C22×D13—42no—
52C22×D13—44no—
53Q8×C13—22no—
54D4×C13—22no—
55D4×C13—42no—
56C2×C4×C13—42no—
57C2×C4×C13C2×D411yescharacteristic
58C22⋊D13—44no—
59C22⋊D13D812yes—
60D52—24no—
61D52—44no—
62D52—42no—
63D52D811yescharacteristic
64C4×D13—44no—
65C4×D13C2×D412yes—
66Dic26D811yescharacteristic
67C8×C13C2×D411yescharacteristic
68C8×C13C2411yescharacteristic
69#1055C2×D412yes—
70#576—132no—
71#509—132no—
72#509—134no—
73#508—132no—
74#508D1311yescharacteristic, complemented
75C2×D16—132no—
76C2×D16—131no—
77#504—131no—
78C22×C13—42no—
79C22×C13C2×D811yescharacteristic
80C2×D13—44no—
81C2×D13—164no—
82C2×D13—162no—
83C2×D13C2×D812yes—
84C4×C13—42no—
85C4×C13C2×D811yescharacteristic
86C4×C13C22×D411yescharacteristic
87Dic13C2×D812yes—
88H(5,𝔽2)—262no—
89AGL(1,ℤ/8)—264no—
90AGL(1,ℤ/8)—262no—
91#135—134no—
92#135C2×D1312yescomplemented
93C2×D8—134no—
94C2×D8—132no—
95#131—131no—
96Q32C2×D1311yescharacteristic, complemented
97SD32—134no—
98SD32C2×D1312yescomplemented
99D16—134no—
100D16—132no—
101D16—132no—
102D16C2×D1311yescharacteristic, complemented
103M32—131no—
104M32—132no—
105C2×C16—132no—
106C2×C16C2×D1311yescharacteristic, complemented
107C2×C13—21no—
108C2×C13—82no—
109C2×C13C22×D811yescharacteristic
110D13—22no—
111D13—84no—
112#41—22no—
113#41—131no—
114#41—264no—
115#41—522no—
116C2×D4—264no—
117C2×D4—262no—
118C2×D4—522no—
119C2×D4—524no—
120Q16C22×D1312yes—
121SD16—22no—
122SD16—264no—
123D8—134no—
124D8—264no—
125D8—262no—
126D8C22×D1312yes—
127M16—131no—
128M16—132no—
129C2×C8—132no—
130C2×C8C22×D1311yescharacteristic
131C16—132no—
132C16C22×D1311yescharacteristic
133C16C22×D1311yescharacteristic
134C13#341511yescharacteristic, complemented, Sylow
135C23—524no—
136C23—522no—
137Q8—22no—
138Q8—131no—
139D4—22no—
140D4—42no—
141D4—132no—
142D4—131no—
143D4—264no—
144D4—524no—
145D4—524no—
146D4—522no—
147C2×C4—42no—
148C2×C4—132no—
149C2×C4—524no—
150C2×C4D4×D1311yescharacteristic
151C8—132no—
152C8D4×D1311yescharacteristic
153C8C23×D1311yescharacteristic
154C22—42no—
155C22—132no—
156C22—524no—
157C22—2082no—
158C22—2084no—
159C22D8×D1311yescharacteristic
160C4—42no—
161C4—132no—
162C4D8×D1311yescharacteristic
163C4C2×D4×D1311yescharacteristic
164C2—21no—
165C2—82no—
166C2—262no—
167C2—1044no—
168C2C2×D8×D1311yescharacteristic
subgroupG/H
centerC2C2×D8×D13
commutator, cosocleC8×C13C24
FrattiniC8C23×D13
FittingC13×#508C2
socleC2×C13C22×D8
hypercenter#508D13
hypocenterC13#3415
LCSG ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #508

Complements

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

NH ≅ G/Ntype
1. #11719474C2semidirect
2. C13×#508C2semidirect
3. #11718854C2semidirect
4. #11718580C2semidirect
5. #11718575C2semidirect
6. D13×D16C2semidirect
7. C2×D208C2semidirect
8. #11718562C2semidirect
10. C13×#135C22semidirect
12. #88173C22semidirect
14. D8×D13C22semidirect
15. C2×D104C22semidirect
17. C13×Q32C22semidirect
18. C13×SD32C22semidirect
19. C13×D16C22semidirect
20. C2×C13×C16C22semidirect
21. #88068C22semidirect
22. #88066C22semidirect
23. #88052C22semidirect
24. D208C22semidirect
25. D208C22semidirect
26. #88038C22semidirect
27. C16×D13C22semidirect
74. #508D13semidirect
92. #135C2×D13semidirect
96. Q32C2×D13semidirect
98. SD32C2×D13semidirect
102. D16C2×D13semidirect
106. C2×C16C2×D13semidirect
134. C13#3415semidirect

Maximal subgroups

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

subgroupindex
#117194742
C13×#5082
#117188542
#117185802
#117185752
D13×D162
C2×D2082
#117185622
#341513