Finite Group Databasebeta

← #14531095

Subgroups — #14531095

Order 2176.

112 conjugacy classes of subgroups; only the 35 normal subgroups are shown.

normal subgroups only

This group has 112 conjugacy classes of subgroups — too many to draw. Only its 35 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#11763238C211yesmaximal, characteristic, complemented
2D16×D17C211yesmaximal, characteristic, complemented
3#11762648C211yesmaximal, characteristic, complemented
4#11762647C211yesmaximal, characteristic, complemented
5#11762644C211yesmaximal, characteristic, complemented
6#11762642C211yesmaximal, characteristic, complemented
7C17×D32C211yesmaximal, characteristic, complemented
8#10587598—21no—
9D8×D17—21no—
10C17×D16C2211yescharacteristic
11C17×D16C2211yescharacteristic, complemented
12#10587498—21no—
13#10587497—21no—
14Dic136C2211yescharacteristic, complemented
15D272C2211yescharacteristic
16C16×D17C2211yescharacteristic
17C17×C32C2211yescharacteristic, complemented
18#10587465C2211yescharacteristic, complemented
19#63254—41no—
20D4×D17—41no—
21D8×C17—21no—
22D8×C17—21no—
23#63229—41no—
24#63228—41no—
25Dic68—21no—
26D136—21no—
27C8×D17D411yescharacteristic
28C16×C17C2311yescharacteristic
29#63214D411yescharacteristic
30C22×D17—81no—
31D4×C17—41no—
32D4×C17—41no—
33C22⋊D17—81no—
34C22⋊D17—81no—
35C2×Dic17—81no—
36D68—41no—
37C4×D17D811yescharacteristic
38Dic34—41no—
39C8×C17C2×D411yescharacteristic
40#3622D811yescharacteristic
41#2263—171nomaximal, Sylow
42C22×C17—81no—
43C22×C17—81no—
44C2×D17—81no—
45C2×D17—162no—
46C2×D17D1611yescharacteristic
47C4×C17C2×D811yescharacteristic
48Dic17—81no—
49Dic17D1611yescharacteristic
50#508—171no—
51C2×D16—171no—
52SD64—171no—
53SD64—171no—
54D32—171no—
55D32D1711yescharacteristic, complemented
56M64—171no—
57C2×C17—161no—
58C2×C17—161no—
59C2×C17C2×D1611yescharacteristic
60D17—21no—
61D17—161no—
62#135—341no—
63C2×D8—341no—
64Q32—171no—
65SD32—341no—
66D16—171no—
67D16—341no—
68D16C2×D1711yescharacteristic
69D16C2×D1711yescharacteristic, complemented
70C2×C16—171no—
71C32—171no—
72C32C2×D1711yescharacteristic, complemented
73C17#226311yescharacteristic, complemented, Sylow
74#41—681no—
75C2×D4—681no—
76Q16—341no—
77SD16—681no—
78D8—21no—
79D8—21no—
80D8—341no—
81D8—681no—
82C2×C8—171no—
83C16—171no—
84C16C22×D1711yescharacteristic
85C23—1361no—
86Q8—681no—
87D4—41no—
88D4—41no—
89D4—681no—
90D4—1361no—
91D4—1361no—
92C2×C4—171no—
93C2×C4—1361no—
94C8—171no—
95C8D4×D1711yescharacteristic
96C22—81no—
97C22—81no—
98C22—2722no—
99C22—171no—
100C22—1361no—
101C4—171no—
102C4—1361no—
103C4D8×D1711yescharacteristic
104C2—161no—
105C2—161no—
106C2—2721no—
107C2—341no—
108C2D16×D1711yescharacteristic
subgroupG/H
centerC2D16×D17
commutator, cosocleC16×C17C23
FrattiniC16C22×D17
FittingC17×D32C2
socleC2×C17C2×D16
hypercenterD32D17
hypocenterC17#2263
LCSG ▷ C16×C17 ▷ C8×C17 ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2 ◁ C4 ◁ C8 ◁ C16 ◁ D32

Complements

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

NH ≅ G/Ntype
1. #11763238C2semidirect
2. D16×D17C2semidirect
3. #11762648C2semidirect
4. #11762647C2semidirect
5. #11762644C2semidirect
6. #11762642C2semidirect
7. C17×D32C2semidirect
11. C17×D16C22semidirect
14. Dic136C22semidirect
17. C17×C32C22semidirect
18. #10587465C22semidirect
55. D32D17semidirect
69. D16C2×D17semidirect
72. C32C2×D17semidirect
73. C17#2263semidirect

Maximal subgroups

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

subgroupindex
#117632382
D16×D172
#117626482
#117626472
#117626442
#117626422
C17×D322
#226317