Finite Group Databasebeta

← #13126629

Subgroups — #13126629

Order 1664.

460 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 117 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#11719467C214yesmaximal, complemented
2C13×#492C211yesmaximal, characteristic, complemented
3#11718838C214yesmaximal, complemented
4#11718756C212yesmaximal, complemented
5#11718738C212yesmaximal, complemented
6#11718361C212yesmaximal, complemented
7#88254C2212yes—
8#88251C2212yescomplemented
9C2×C13×SD16C2214yescomplemented
10C13×C4⋊Q8C2211yescharacteristic, complemented
11C13×#127C2211yescharacteristic
12#88196C2214yescomplemented
13#88186C2214yes—
14#88170—24no—
15#88169—24no—
16#88168—24no—
17SD16×D13—24no—
18#88158C2212yes—
19#88155C2214yescomplemented
20C4×C8×C13C2211yescharacteristic, complemented
21#88076C2212yescomplemented
22#88073C2212yescomplemented
23#88059C2212yescomplemented
24#88045C2214yescomplemented
25C2×Q8×C13C2312yes—
26C2×D4×C13—41no—
27C2×D4×C13C2312yes—
28C2×C22⋊D13—42no—
29#6131—24no—
30Q8×D13—24no—
31#6129—24no—
32D4×D13—24no—
33#6127—42no—
34#6127C2314yes—
35C13×SD16—24no—
36C13×SD16—24no—
37C2×C8×C13C2312yes—
38C13×C4⋊C4—41no—
39C42×C13C2311yescharacteristic
40#6107—24no—
41#6106—24no—
42#6105—24no—
43#6104—24no—
44#6099C2314yes—
45Dic52D412yescomplemented
46D104D412yescomplemented
47#6095D414yescomplemented
48#6094—24no—
49C8×D13—24no—
50#3291—131nomaximal, Sylow
51C23×C13—22no—
52C22×D13—42no—
53Q8×C13—24no—
54D4×C13—24no—
55D4×C13—82no—
56C2×C4×C13—21no—
57C2×C4×C13—22no—
58C2×C4×C13C2411yescharacteristic
59C22⋊D13—24no—
60C22⋊D13—44no—
61C2×Dic13—42no—
62D52—42no—
63D52C2×D414yes—
64C4×D13—24no—
65C4×D13—44no—
66Dic26—42no—
67Dic26C2×D414yes—
68C8×C13C2×D412yes—
69C8×C13C2×D412yes—
70#1055—24no—
71#577—134no—
72#492D1311yescharacteristic, complemented
73#471—134no—
74#456—132no—
75#453—132no—
76#443—132no—
77C22×C13—42no—
78C22×C13—82no—
79C22×C13H(5,𝔽2)11yescharacteristic
80C2×D13—24no—
81C2×D13—162no—
82C4×C13—22no—
83C4×C13—42no—
84C4×C13C22×D412yes—
85Dic13—24no—
862−1+4—132no—
87H(5,𝔽2)—132no—
88#137—134no—
89#137—264no—
90AGL(1,ℤ/8)—134no—
91AGL(1,ℤ/8)—264no—
92#135—132no—
93#135—264no—
94C2×SD16—264no—
95C2×SD16C2×D1314yescomplemented
96#131—134no—
97C4⋊Q8C2×D1311yescharacteristic, complemented
98#127C2×D1311yescharacteristic
99#108—132no—
100#104—134no—
101#101—132no—
102#100—132no—
103C4×C8C2×D1311yescharacteristic, complemented
104C2×C13—21no—
105C2×C13—82no—
106C2×C13D4211yescharacteristic
107D13—44no—
108#41—134no—
109#41—264no—
110#41—264no—
111#41—522no—
112C2×Q8—264no—
113C2×Q8C22×D1312yes—
114C2×D4—41no—
115C2×D4—264no—
116C2×D4—522no—
117C2×D4C22×D1312yes—
118Q16—132no—
119Q16—264no—
120SD16—24no—
121SD16—24no—
122SD16—134no—
123SD16—264no—
124SD16—264no—
125D8—132no—
126D8—264no—
127M16—134no—
128M16—264no—
129C2×C8—264no—
130C2×C8C22×D1312yes—
131C4⋊C4—41no—
132C42C22×D1311yescharacteristic
133C13#329111yescharacteristic, complemented, Sylow
134C23—22no—
135C23—522no—
136Q8—24no—
137Q8—134no—
138Q8—522no—
139D4—24no—
140D4—82no—
141D4—134no—
142D4—264no—
143D4—522no—
144D4—524no—
145C2×C4—21no—
146C2×C4—22no—
147C2×C4—264no—
148C2×C4—524no—
149C2×C4—522no—
150C2×C4C23×D1311yescharacteristic
151C8—264no—
152C8D4×D1312yes—
153C8D4×D1312yes—
154C22—42no—
155C22—82no—
156C22—264no—
157C22—2082no—
158C22#8825111yescharacteristic
159C4—22no—
160C4—42no—
161C4—264no—
162C4C2×D4×D1312yes—
163C2—21no—
164C2—82no—
165C2—524no—
166C2#1171942211yescharacteristic
subgroupG/H
centerC2#11719422
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#492C2
socleC2×C13D42
hypercenter#492D13
hypocenterC13#3291
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C2×C4 ◁ #492

Complements

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

NH ≅ G/Ntype
1. #11719467C2semidirect
2. C13×#492C2semidirect
3. #11718838C2semidirect
4. #11718756C2semidirect
5. #11718738C2semidirect
6. #11718361C2semidirect
8. #88251C22semidirect
9. C2×C13×SD16C22semidirect
10. C13×C4⋊Q8C22semidirect
12. #88196C22semidirect
19. #88155C22semidirect
20. C4×C8×C13C22semidirect
21. #88076C22semidirect
22. #88073C22semidirect
23. #88059C22semidirect
24. #88045C22semidirect
45. Dic52D4semidirect
46. D104D4semidirect
47. #6095D4semidirect
72. #492D13semidirect
95. C2×SD16C2×D13semidirect
97. C4⋊Q8C2×D13semidirect
103. C4×C8C2×D13semidirect
133. C13#3291semidirect

Maximal subgroups

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

subgroupindex
#117194672
C13×#4922
#117188382
#117187562
#117187382
#117183612
#329113