Finite Group Databasebeta

← #13116913

Subgroups — #13116913

Order 1664.

170 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 170 conjugacy classes of subgroups — too many to draw. Only its 47 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#11718569C212yesmaximal, complemented
2#11718361C211yesmaximal, characteristic, complemented
3#11718356C211yesmaximal, characteristic, complemented
4C13×#364C211yesmaximal, characteristic, complemented
5#11718108C212yesmaximal, complemented
6#88158C2211yescharacteristic
7C2×D104—21no—
8C2×D104C2212yes—
9#88155—21no—
10#88128—21no—
11C13×M32C2212yes—
12C4×C8×C13C2211yescharacteristic
13#88059C2211yescharacteristic
14#88045—21no—
15#88040—22no—
16D208—22no—
17#6127—21no—
18C2×D52—22no—
19C2×D52—42no—
20C2×C8×C13D411yescharacteristic
21C2×C8×C13C2311yescharacteristic
22C42×C13D411yescharacteristic
23#6099—21no—
24Dic52D411yescharacteristic, complemented
25D104—22no—
26D104—22no—
27D104—41no—
28D104—41no—
29D104D411yescharacteristic, complemented
30#6095—21no—
31#6094—41no—
32C8×D13—41no—
33C13×C16—22no—
34#2213—131nomaximal, Sylow
35C22×D13—42no—
36C2×C4×C13—21no—
37C2×C4×C13C2×D411yescharacteristic
38C22⋊D13—41no—
39D52—21no—
40D52—42no—
41D52—42no—
42D52—84no—
43C4×D13—41no—
44Dic26—21no—
45C8×C13D811yescharacteristic
46C8×C13D811yescharacteristic
47C8×C13C2×D411yescharacteristic
48C8×C13#4111yescharacteristic
49#1055—41no—
50#509—132no—
51#493—131no—
52#443—131no—
53#364D1311yescharacteristic, complemented
54#361—132no—
55C22×C13AGL(1,ℤ/8)11yescharacteristic
56C2×D13—41no—
57C2×D13—84no—
58C2×D13—82no—
59C4×C13—22no—
60C4×C13#12111yescharacteristic
61C4×C13C2×D811yescharacteristic
62Dic13—41no—
63#135—131no—
64C2×D8—132no—
65C2×D8—261no—
66#131—261no—
67#127—261no—
68SD32—262no—
69D16—262no—
70M32C2×D1312yes—
71#108—131no—
72#104—261no—
73C4×C8C2×D1311yescharacteristic
74C2×C13—21no—
75C2×C13#45911yescharacteristic
76D13—81no—
77D13—162no—
78#41—261no—
79C2×D4—262no—
80C2×D4—522no—
81Q16—131no—
82SD16—261no—
83D8—131no—
84D8—262no—
85D8—262no—
86D8—521no—
87D8—521no—
88M16—261no—
89M16—521no—
90C2×C8—521no—
91C2×C8D5211yescharacteristic
92C2×C8C22×D1311yescharacteristic
93C42D5211yescharacteristic
94C16—22no—
95C13#221311yescharacteristic, complemented, Sylow
96C23—522no—
97Q8—261no—
98D4—261no—
99D4—521no—
100D4—522no—
101D4—522no—
102D4—1044no—
103C2×C4—21no—
104C2×C4—521no—
105C2×C4C2×D5211yescharacteristic
106C8—521no—
107C8D10411yescharacteristic
108C8D10411yescharacteristic
109C8D4×D1311yescharacteristic
110C8#613111yescharacteristic
111C22—521no—
112C22—1044no—
113C22—1042no—
114C22#8816211yescharacteristic
115C4—22no—
116C4—521no—
117C4#8814911yescharacteristic
118C4C2×D10411yescharacteristic
119C2—21no—
120C2—1041no—
121C2—2082no—
122C2#1171850411yescharacteristic
subgroupG/H
centerC2#11718504
commutator, cosocleC2×C8×C13C23
FrattiniC2×C8C22×D13
FittingC13×#364C2
socleC2×C13#459
hypercenter#364D13
hypocenterC13#2213
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #364

Complements

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

NH ≅ G/Ntype
1. #11718569C2semidirect
2. #11718361C2semidirect
3. #11718356C2semidirect
4. C13×#364C2semidirect
5. #11718108C2semidirect
24. Dic52D4semidirect
29. D104D4semidirect
53. #364D13semidirect
95. C13#2213semidirect

Maximal subgroups

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

subgroupindex
#117185692
#117183612
#117183562
C13×#3642
#117181082
#221313