Finite Group Databasebeta

← #26022413

Subgroups — #26022413

Order 11392.

124 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 124 conjugacy classes of subgroups — too many to draw. Only its 51 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×Dic356C211yesmaximal, characteristic
2#19151425C211yesmaximal, characteristic
3#19151423C211yesmaximal, characteristic
4C4⋊#13083549C211yesmaximal, characteristic
5#19151401C211yesmaximal, characteristic
6#19151401C211yesmaximal, characteristic
7#499×C89C211yesmaximal, characteristic
8C2×Dic356C2211yescharacteristic
9C4×Dic178—21no—
10C2×#13083549C2211yescharacteristic
11C2×#13083549C2211yescharacteristic
12#15667946C2211yescharacteristic
13#15667937—21no—
14#125×C89—21no—
15#107×C89C2211yescharacteristic
16#107×C89C2211yescharacteristic
17#106×C89—21no—
18C4×C8×C89C2211yescharacteristic
19C2×Dic178—21no—
20Dic356—21no—
21Dic356Q812yes—
22C4⋊Dic89—21no—
23#13083553—41no—
24C4×Dic89—41no—
25#13083549—21no—
26#13083549—21no—
27C2×C8×C89D411yescharacteristic
28C2×C8×C89C2311yescharacteristic
29C4⋊C4×C89—21no—
30C4⋊C4×C89—21no—
31C4⋊C4×C89—41no—
32C4⋊C4×C89—41no—
33C42×C89D411yescharacteristic
34C2×C4×C89—41no—
35C2×C4×C89—41no—
36C2×C4×C89D811yescharacteristic
37C2×C4×C89D811yescharacteristic
38C2×C4×C89C2×D411yescharacteristic
39C2×Dic89—41no—
40C2×Dic89—41no—
41Dic178—22no—
42Dic178—41no—
43C8×C89—21no—
44C8×C89C2×Q811yescharacteristic
45C8×C89#4111yescharacteristic
46C22×C89C2×D811yescharacteristic
47C4×C89—21no—
48C4×C89—21no—
49C4×C89—81no—
50C4×C89—81no—
51C4×C89C22⋊Q811yescharacteristic
52C4×C89#13711yescharacteristic
53Dic89—42no—
54Dic89—81no—
55C2×C89#47411yescharacteristic
56C2×C89#50811yescharacteristic
57C2×C89#51011yescharacteristic
58#2229—891nomaximal, Sylow
59C89#222911yescharacteristic, complemented, Sylow
60#499D8911yescharacteristic
61C4×Q16—891no—
62#367—891no—
63#366—891no—
64C4⋊C16—891no—
65#358—891no—
66#358—891no—
67C2×Q16—891no—
68#125—21no—
69C4×Q8—1781no—
70C2×C16—891no—
71C2×C16—891no—
72#107—891no—
73#107C2×D8911yescharacteristic
74#107C2×D8911yescharacteristic
75#106—21no—
76#103—1781no—
77C4×C8C2×D8911yescharacteristic
78C2×Q8—1781no—
79Q16—892no—
80Q16—1781no—
81C2×C8C22⋊D8911yescharacteristic
82C2×C8C22×D8911yescharacteristic
83C4⋊C4—21no—
84C4⋊C4—21no—
85C4⋊C4—41no—
86C4⋊C4—41no—
87C4⋊C4—3561no—
88C4⋊C4—1781no—
89C42—3561no—
90C42C22⋊D8911yescharacteristic
91C16—1781no—
92C16—1781no—
93Q8—3561no—
94Q8—1782no—
95C2×C4—41no—
96C2×C4—41no—
97C2×C4—3561no—
98C2×C4—3561no—
99C2×C4#1308355911yescharacteristic
100C2×C4#1308355911yescharacteristic
101C2×C4C2×C22⋊D8911yescharacteristic
102C8—21no—
103C8Q8×D8911yescharacteristic
104C8#1308357511yescharacteristic
105C22C2×#1308355911yescharacteristic
106C4—21no—
107C4—21no—
108C4—81no—
109C4—81no—
110C4—3562no—
111C4—7121no—
112C4#1566798811yescharacteristic
113C4#1566804311yescharacteristic
114C2#1915187511yescharacteristic
115C2#1915202811yescharacteristic
116C2#1915203811yescharacteristic
subgroupG/H
centerC22C2×#13083559
commutator, cosocleC2×C8×C89C23
FrattiniC2×C8C22×D89
Fitting#499×C89C2
socle, prime radicalC22×C89C2×D8
hypercenter#499D89
hypocenterC89#2229
LCSG ▷ C2×C8×C89 ▷ C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #499

Complements

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

NH ≅ G/Ntype
59. C89#2229semidirect

Maximal subgroups

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

subgroupindex
C4×Dic3562
#191514252
#191514232
C4⋊#130835492
#191514012
#499×C892
#222989