Finite Group Databasebeta

← #49093169

Subgroups — #49093169

Order 35968.

152 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 152 conjugacy classes of subgroups — too many to draw. Only its 57 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
1C4×#17985122C211yesmaximal, characteristic
2#31823331C211yesmaximal, characteristic
3#432×C281C211yesmaximal, characteristic
4C2×#17985122—21no—
5#22582790—21no—
6C4×#14555886C412yescomplemented
7#22582786—21no—
8#22582786—21no—
9#22582786C412yes—
10C2×C42×C281C2211yescharacteristic
11C4⋊C8×C281—21no—
12C22⋊C8×C281—21no—
13#97×C281C412yescomplemented
14C22×Dic281—22no—
15#17985122—24no—
16C2×#14555886—22no—
17C22×C4×C281C2×C411yescharacteristic
18C22×C4×C281D411yescharacteristic
19C22×C4×C281D411yescharacteristic
20C2×C8×C281—22no—
21C42×C281C2×C411yescharacteristic
22C42×C281C2×C411yescharacteristic
23C42×C281D411yescharacteristic
24C42×C281Q811yescharacteristic
25C2×Dic281—42no—
26C2×Dic281—42no—
27C2×Dic281—42no—
28#14555886—24no—
29C23×C281C22⋊C411yescharacteristic
30C2×C4×C281—22no—
31C2×C4×C281—41no—
32C2×C4×C281—41no—
33C2×C4×C281C4211yescharacteristic
34C2×C4×C281C22⋊C411yescharacteristic
35C2×C4×C281C22⋊C411yescharacteristic
36C2×C4×C281C4⋊C411yescharacteristic
37C2×C4×C281C4⋊C411yescharacteristic
38C2×C4×C281C4⋊C411yescharacteristic
39C8×C281—42no—
40C22×C281—21no—
41C22×C281—21no—
42C22×C281#9511yescharacteristic
43C22×C281#10412yes—
44C4×C281—21no—
45C4×C281—21no—
46C4×C281—21no—
47C4×C281—21no—
48C4×C281—21no—
49C4×C281—21no—
50Dic281—82no—
51C2×C281—22no—
52C2×C281H(3,ℤ/4)11yescharacteristic
53C2×C281#33911yescharacteristic
54C2×C281#34411yescharacteristic
55C281#128811yescharacteristic, complemented, Sylow
56#1288—2811nomaximal, Sylow
57#432D28111yescharacteristic
58C4×M16—2811no—
59#383—2811no—
60C2×M16—5621no—
61C2×C42C2×D28111yescharacteristic
62C4⋊C8—21no—
63C22⋊C8—21no—
64#97—5621no—
65#97Dic28112yescomplemented
66C4×C8—2812no—
67#95—2812no—
68#95—5621no—
69#95—5621no—
70C22×C4—5622no—
71C22×C4C4×D28111yescharacteristic
72C22×C4C22⋊D28111yescharacteristic
73C22×C4D112411yescharacteristic
74M16—5624no—
75C2×C8—22no—
76C2×C8—5622no—
77C42C4×D28111yescharacteristic
78C42C2×Dic28111yescharacteristic
79C42C22⋊D28111yescharacteristic
80C42Dic56211yescharacteristic
81C23#1798511511yescharacteristic
82C2×C4—22no—
83C2×C4—41no—
84C2×C4—41no—
85C2×C4—11242no—
86C2×C4—11242no—
87C2×C4—11242no—
88C2×C4C4×Dic28111yescharacteristic
89C2×C4#1798511511yescharacteristic
90C2×C4C22⋊Dic28111yescharacteristic
91C2×C4#1798511711yescharacteristic
92C2×C4#1798511711yescharacteristic
93C2×C4C4⋊Dic28111yescharacteristic
94C8—42no—
95C8—5624no—
96C22—21no—
97C22—21no—
98C22#2258278611yescharacteristic
99C22#2258280512yes—
100C4—21no—
101C4—21no—
102C4—21no—
103C4—21no—
104C4—21no—
105C4—21no—
106C4—22482no—
107C2—22no—
108C2#3182321911yescharacteristic
109C2#3182322411yescharacteristic
110C2#3182323511yescharacteristic
subgroupG/H
centerC22#22582786
commutatorC2×C4×C281C42
FrattiniC2×C42C2×D281
Fitting#432×C281C2
socleC22×C281#95
prime radicalC23×C281C22⋊C4
cosocleC2×C42×C281C22
hypercenter#432D281
hypocenterC281#1288
LCSG ▷ C2×C4×C281 ▷ C2×C281 ▷ C281
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
6. C4×#14555886C4semidirect
13. #97×C281C4semidirect
55. C281#1288semidirect
65. #97Dic281semidirect

Maximal subgroups

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

subgroupindex
C4×#179851222
#318233312
#432×C2812
#1288281