Finite Group Databasebeta

← #28379430

Subgroups — #28379430

Order 13952.

172 conjugacy classes of subgroups; only the 48 normal subgroups are shown.

normal subgroups only

This group has 172 conjugacy classes of subgroups — too many to draw. Only its 48 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
1D8×#89137C212yesmaximal, complemented
2#20295953C211yesmaximal, characteristic, complemented
3#20295938C212yesmaximal, complemented
4#20295913C211yesmaximal, characteristic, complemented
5D16×D109C211yesmaximal, characteristic
6D4×#89137—22no—
7D109⋊C16C2211yescharacteristic
8#16812768C2212yes—
9#16812761—22no—
10C8×#89137C2211yescharacteristic
11D8×D109C2212yes—
12D1744C411yescharacteristic, complemented
13#16812640C412yescomplemented
14C16×D109C2211yescharacteristic
15D16×C109C411yescharacteristic, complemented
16C22×#89137—42no—
17D109⋊C8D411yescharacteristic
18C4⋊#89137—22no—
19C22⋊#89137—42no—
20C4×#89137D411yescharacteristic
21#13182032—21no—
22D4×D109—22no—
23D872C2×C412yescomplemented
24#13182014—22no—
25C8×D109C2311yescharacteristic
26#13182004C2×C411yescharacteristic, complemented
27D8×C109C2×C412yescomplemented
28C16×C109C2×C411yescharacteristic, complemented
29C22×D109—42no—
30C2×#89137—42no—
31C2×#89137—84no—
32C2×#89137D812yes—
33D4×C109—22no—
34C22⋊D109—42no—
35D436—22no—
36C4×D109C2×D411yescharacteristic
37#11724786—21no—
38C8×C109C22×C411yescharacteristic
39#11724784#4111yescharacteristic
40C22×C109—42no—
41C2×D109—42no—
42C2×D109—82no—
43C2×D109—82no—
44C2×D109C2×D811yescharacteristic
45#89137—22no—
46#89137—82no—
47C4×C109C4×D411yescharacteristic
48Dic109#13511yescharacteristic
49C2×C109—82no—
50C2×C109C4×D811yescharacteristic
51D109—82no—
52D109#50912yes—
53#2177—1091nomaximal, Sylow
54C109#217711yescharacteristic, complemented, Sylow
55C2×D16—1091no—
56C4×D8—1092no—
57#367—1091no—
58#357—1092no—
59#346—1091no—
60C2×D8—1092no—
61C4×D4—2182no—
62D16—1092no—
63D16—1091no—
64D16#8913711yescharacteristic, complemented
65C2×C16—1091no—
66C2×C16—1091no—
67#107—1092no—
68#102—2182no—
69C4×C8—1091no—
70C2×D4—2182no—
71C22×C4—4362no—
72D8—1092no—
73D8—2182no—
74D8C2×#8913712yescomplemented
75C2×C8—1091no—
76C2×C8—1091no—
77C4⋊C4—2182no—
78C22⋊C4—4362no—
79C42—1091no—
80C16—1091no—
81C16—2181no—
82C16C2×#8913711yescharacteristic, complemented
83C23—4362no—
84D4—22no—
85D4—4362no—
86D4—2182no—
87C2×C4—8724no—
88C2×C4—1091no—
89C2×C4—1092no—
90C2×C4—4362no—
91C8—1091no—
92C8—2181no—
93C8C22×#8913711yescharacteristic
94C22—42no—
95C22—8722no—
96C22—8722no—
97C22—1091no—
98C22—4362no—
99C4—8722no—
100C4—1091no—
101C4—2182no—
102C4D4×#8913711yescharacteristic
103C2—82no—
104C2—8722no—
105C2—1092no—
106C2D8×#8913711yescharacteristic
subgroupG/H
centerC2D8×#89137
commutatorC8×C109C22×C4
FrattiniC8C22×#89137
FittingD16×C109C4
socleC2×C109C4×D8
prime radicalD16×D109C2
cosocleC8×D109C23
hypercenterD16#89137
hypocenterC109#2177
LCSG ▷ C8×C109 ▷ C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C2 ◁ C4 ◁ C8 ◁ D16

Complements

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

NH ≅ G/Ntype
1. D8×#89137C2semidirect
2. #20295953C2semidirect
3. #20295938C2semidirect
4. #20295913C2semidirect
12. D1744C4semidirect
13. #16812640C4semidirect
15. D16×C109C4semidirect
23. D872C2×C4semidirect
26. #13182004C2×C4semidirect
27. D8×C109C2×C4semidirect
28. C16×C109C2×C4semidirect
54. C109#2177semidirect
64. D16#89137semidirect
74. D8C2×#89137semidirect
82. C16C2×#89137semidirect

Maximal subgroups

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

subgroupindex
D8×#891372
#202959532
#202959382
#202959132
D16×D1092
#2177109