Finite Group Databasebeta

← #26018295

Subgroups — #26018295

Order 11392.

102 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 102 conjugacy classes of subgroups — too many to draw. Only its 41 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⋊#13083549C211yesmaximal, characteristic, complemented
2#19151349C211yesmaximal, characteristic, complemented
3#495×C89C211yesmaximal, characteristic
4C2×#13083549—21no—
5C4⋊#10623494—21no—
6C2×Q16×C89C411yescharacteristic
7C2×SD16×C89—21no—
8C2×D8×C89C411yescharacteristic
9#124×C89—21no—
10C4×C8×C89C2211yescharacteristic
11C2×#10623494—41no—
12#13083549—41no—
13C2×Q8×C89—21no—
14C2×D4×C89—21no—
15Q16×C89—41no—
16SD16×C89—41no—
17SD16×C89—41no—
18D8×C89—41no—
19C2×C8×C89C2×C411yescharacteristic
20C2×C8×C89D411yescharacteristic
21C22⋊C4×C89—41no—
22C22⋊C4×C89—41no—
23C42×C89D411yescharacteristic
24C23×C89—41no—
25Q8×C89—41no—
26Q8×C89—41no—
27D4×C89—41no—
28D4×C89—41no—
29C2×C4×C89—41no—
30C2×C4×C89C22⋊C411yescharacteristic
31C2×C4×C89D811yescharacteristic
32C2×C4×C89SD1611yescharacteristic
33C8×C89—21no—
34C8×C89D811yescharacteristic
35C8×C89SD1611yescharacteristic
36#10623494—81no—
37C22×C89—81no—
38C22×C89—81no—
39C22×C89—81no—
40C22×C89#10211yescharacteristic
41C4×C89—21no—
42C4×C89—21no—
43C4×C89—81no—
44C4×C89#10011yescharacteristic
45C4×C89#10211yescharacteristic
46C2×C89—161no—
47C2×C89#33111yescharacteristic
48C2×C89#35911yescharacteristic
49C2×C89#36011yescharacteristic
50#1360—891nomaximal, Sylow
51C89#136011yescharacteristic, complemented, Sylow
52#495D8911yescharacteristic
53C4⋊C16—891no—
54#334—891no—
55C2×Q16Dic8911yescharacteristic
56C2×SD16—21no—
57C2×D8Dic8911yescharacteristic
58#124—21no—
59C2×C16—1781no—
60C4⋊C8—1781no—
61C4×C8C2×D8911yescharacteristic
62C2×Q8—21no—
63C2×D4—21no—
64Q16—41no—
65SD16—41no—
66SD16—41no—
67D8—41no—
68C2×C8—3561no—
69C2×C8C2×Dic8911yescharacteristic
70C2×C8C22⋊D8911yescharacteristic
71C22⋊C4—41no—
72C22⋊C4—41no—
73C42C22⋊D8911yescharacteristic
74C16—3561no—
75C23—41no—
76Q8—41no—
77Q8—41no—
78D4—41no—
79D4—41no—
80C2×C4—41no—
81C2×C4C22⋊Dic8911yescharacteristic
82C2×C4#1308355911yescharacteristic
83C2×C4#1308356211yescharacteristic
84C8—21no—
85C8—7121no—
86C8#1308355911yescharacteristic
87C8#1308356211yescharacteristic
88C22—81no—
89C22—81no—
90C22—81no—
91C22#1566793311yescharacteristic
92C4—21no—
93C4—21no—
94C4—81no—
95C4#1566792911yescharacteristic
96C4#1566793311yescharacteristic
97C2—161no—
98C2#1915134211yescharacteristic
99C2#1915140511yescharacteristic
100C2#1915140811yescharacteristic
subgroupG/H
centerC22#15667933
commutatorC2×C8×C89C2×C4
FrattiniC4×C8C2×D89
Fitting#495×C89C2
socleC22×C89#102
prime radicalC2×D8×C89C4
cosocleC4×C8×C89C22
hypercenter#495D89
hypocenterC89#1360
LCSG ▷ C2×C8×C89 ▷ C2×C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #495

Complements

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

NH ≅ G/Ntype
1. C4⋊#13083549C2semidirect
2. #19151349C2semidirect
51. C89#1360semidirect

Maximal subgroups

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

subgroupindex
C4⋊#130835492
#191513492
#495×C892
#136089