Finite Group Databasebeta

← #11763000

Subgroups — #11763000

Order 1088.

160 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 39 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#10587691C211yesmaximal, characteristic
2#10587621C211yesmaximal, characteristic, complemented
3#10587572C212yesmaximal, complemented
4C17×#99C211yesmaximal, characteristic, complemented
5#10587477C212yesmaximal, complemented
6C2×D4×C17C2211yescharacteristic
7C2×C22⋊D17—21no—
8C2×C22⋊D17C2212yes—
9C22×Dic17C2211yescharacteristic, complemented
10#63254—22no—
11D4×D17—22no—
12#63252—21no—
13C22⋊C4×C17C2212yescomplemented
14C22⋊Dic17—21no—
15C22⋊Dic17C2211yescharacteristic, complemented
16#63227—22no—
17C4⋊Dic17—22no—
18#63225—21no—
19C23×C17D411yescharacteristic
20C23×C17C2311yescharacteristic
21C22×D17—21no—
22C22×D17D412yes—
23D4×C17—22no—
24C2×C4×C17—22no—
25C2×C4×C17D411yescharacteristic
26C22⋊D17—22no—
27C22⋊D17—22no—
28C22⋊D17—22no—
29C2×Dic17—21no—
30C2×Dic17—21no—
31C2×Dic17—21no—
32C2×Dic17—22no—
33C2×Dic17D412yes—
34D68—21no—
35C4×D17—22no—
36Dic34—21no—
37C22×C17—21no—
38C22×C17—41no—
39C22×C17—41no—
40C22×C17C2×D411yescharacteristic
41C22×C17C2×D412yes—
42C2×D17—22no—
43C2×D17—42no—
44C2×D17—81no—
45C4×C17—21no—
46C4×C17—42no—
47Dic17—22no—
48Dic17—41no—
49Dic17—41no—
50#458—171nomaximal, Sylow
51C2×C17—21no—
52C2×C17—22no—
53C2×C17—41no—
54C2×C17#12011yescharacteristic
55D17—42no—
56H(5,𝔽2)—171no—
57#123—171no—
58#123—172no—
59#99—172no—
60#99D1711yescharacteristic, complemented
61C17#45811yescharacteristic, complemented, Sylow
62#41—342no—
63#41—341no—
64C2×D4—172no—
65C2×D4—342no—
66C2×D4—341no—
67C2×D4C2×D1711yescharacteristic
68C22×C4—171no—
69C4⋊C4—342no—
70C4⋊C4—341no—
71C22⋊C4—171no—
72C22⋊C4—342no—
73C22⋊C4—341no—
74C22⋊C4C2×D1712yescomplemented
75C23—172no—
76C23—341no—
77C23D6811yescharacteristic
78C23C22×D1711yescharacteristic
79Q8—341no—
80D4—22no—
81D4—341no—
82D4—342no—
83D4—342no—
84D4—342no—
85C2×C4—22no—
86C2×C4—172no—
87C2×C4—342no—
88C2×C4—341no—
89C2×C4—341no—
90C2×C4—341no—
91C2×C4—342no—
92C2×C4D6811yescharacteristic
93C22—21no—
94C22—41no—
95C22—41no—
96C22—342no—
97C22—682no—
98C22—1361no—
99C22C2×D6811yescharacteristic
100C22D4×D1712yes—
101C4—21no—
102C4—42no—
103C4—342no—
104C4—681no—
105C4—681no—
106C2—22no—
107C2—21no—
108C2—41no—
109C2—682no—
110C2#1058756811yescharacteristic
subgroupG/H
centerC2#10587568
commutator, cosocleC23×C17C23
FrattiniC23C22×D17
FittingC17×#99C2
socleC2×C17#120
prime radical#10587691C2
hypercenter#99D17
hypocenterC17#458
LCSG ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2 ◁ C23 ◁ #99

Complements

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

NH ≅ G/Ntype
2. #10587621C2semidirect
3. #10587572C2semidirect
4. C17×#99C2semidirect
5. #10587477C2semidirect
9. C22×Dic17C22semidirect
13. C22⋊C4×C17C22semidirect
15. C22⋊Dic17C22semidirect
60. #99D17semidirect
61. C17#458semidirect
74. C22⋊C4C2×D17semidirect

Maximal subgroups

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

subgroupindex
#105876912
#105876212
#105875722
C17×#992
#105874772
#45817