Finite Group Databasebeta

← #26018353

Subgroups — #26018353

Order 11392.

132 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 132 conjugacy classes of subgroups — too many to draw. Only its 69 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
1C2×#15667952C211yesmaximal, characteristic
2#19151636C211yesmaximal, characteristic
3#427×C89C211yesmaximal, characteristic
4#15667971—21no—
5#15667952—21no—
6#15667952—21no—
7C2×#13083549C412yescomplemented
8#15667946—21no—
9#15667944C412yescomplemented
10C22×C8×C89C2211yescharacteristic
11#117×C89—21no—
12#107×C89—21no—
13#106×C89C412yescomplemented
14C4⋊Dic89—22no—
15C22⋊Dic89—41no—
16C4×Dic89—41no—
17#13083549—22no—
18C22×C4×C89D411yescharacteristic
19C2×C8×C89C2×C411yescharacteristic
20C2×C8×C89C2×C411yescharacteristic
21C2×C8×C89C2×C411yescharacteristic
22C2×C8×C89D411yescharacteristic
23C2×C8×C89D411yescharacteristic
24C2×C8×C89Q811yescharacteristic
25C4⋊C4×C89—22no—
26C22⋊C4×C89—41no—
27C42×C89—41no—
28C23×C89D811yescharacteristic
29C2×C4×C89—42no—
30C2×C4×C89C22⋊C411yescharacteristic
31C2×C4×C89C22⋊C411yescharacteristic
32C2×C4×C89C4⋊C411yescharacteristic
33C2×C4×C89SD1611yescharacteristic
34C2×C4×C89SD1611yescharacteristic
35C2×C4×C89Q1611yescharacteristic
36C2×Dic89—42no—
37C8×C89C4211yescharacteristic
38C8×C89C22⋊C411yescharacteristic
39C8×C89C4⋊C411yescharacteristic
40C8×C89C4⋊C411yescharacteristic
41C22×C89—41no—
42C22×C89#10211yescharacteristic
43C22×C89#10211yescharacteristic
44C22×C89#10711yescharacteristic
45C4×C89—82no—
46C4×C89#9511yescharacteristic
47C4×C89#10311yescharacteristic
48C4×C89#10311yescharacteristic
49C4×C89#10611yescharacteristic
50Dic89—82no—
51C2×C89—21no—
52C2×C89—21no—
53C2×C89—21no—
54C2×C89#34011yescharacteristic
55#1384—891nomaximal, Sylow
56C89#138411yescharacteristic, complemented, Sylow
57C2×M32—891no—
58#427—891no—
59#427D8911yescharacteristic
60C22×C8C2×D8911yescharacteristic
61#117—21no—
62#117—1781no—
63M32—1781no—
64M32—1781no—
65C2×C16—892no—
66#107—21no—
67#107—1781no—
68#106—892no—
69#106Dic8912yescomplemented
70C22×C4C22⋊D8911yescharacteristic
71C2×C8Dic17811yescharacteristic
72C2×C8C4×D8911yescharacteristic
73C2×C8C4×D8911yescharacteristic
74C2×C8D35611yescharacteristic
75C2×C8C2×Dic8911yescharacteristic
76C2×C8C22⋊D8911yescharacteristic
77C4⋊C4—22no—
78C4⋊C4—1782no—
79C22⋊C4—41no—
80C22⋊C4—3561no—
81C42—41no—
82C42—3561no—
83C16—1782no—
84C23#1308355911yescharacteristic
85C2×C4—42no—
86C2×C4—3562no—
87C2×C4#1308355111yescharacteristic
88C2×C4C22⋊Dic8911yescharacteristic
89C2×C4#1308355311yescharacteristic
90C2×C4#1308356111yescharacteristic
91C2×C4#1308356211yescharacteristic
92C2×C4#1308356411yescharacteristic
93C8C4×Dic8911yescharacteristic
94C8#1308355111yescharacteristic
95C8#1308355311yescharacteristic
96C8C4⋊Dic8911yescharacteristic
97C22—41no—
98C22#1566793211yescharacteristic
99C22#1566793311yescharacteristic
100C22#1566794511yescharacteristic
101C4—82no—
102C4—7122no—
103C4#1566791911yescharacteristic
104C4#1566793511yescharacteristic
105C4#1566793611yescharacteristic
106C4#1566794311yescharacteristic
107C2—21no—
108C2—21no—
109C2—21no—
110C2#1915136011yescharacteristic
subgroupG/H
centerC4#15667943
commutatorC8×C89C42
FrattiniC22×C8C2×D89
Fitting#427×C89C2
socleC2×C89#340
prime radicalC23×C89D8
cosocleC22×C8×C89C22
hypercenter#427D89
hypocenterC89#1384
LCSG ▷ C8×C89 ▷ C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C4 ◁ C22×C4 ◁ C22×C8 ◁ #427

Complements

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

NH ≅ G/Ntype
7. C2×#13083549C4semidirect
9. #15667944C4semidirect
13. #106×C89C4semidirect
56. C89#1384semidirect
69. #106Dic89semidirect

Maximal subgroups

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

subgroupindex
C2×#156679522
#191516362
#427×C892
#138489