Finite Group Databasebeta

← #26018282

Subgroups — #26018282

Order 11392.

140 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 140 conjugacy classes of subgroups — too many to draw. Only its 37 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
1#19151367C211yesmaximal, characteristic
2#19151324C211yesmaximal, characteristic
3#395×C89C211yesmaximal, characteristic
4C2×#13083558—21no—
5C22⋊#10623494—21no—
6C22×Q8×C89C411yescharacteristic
7C2×C4⋊C4×C89—21no—
8C2×C4⋊C4×C89C2211yescharacteristic
9#95×C89—21no—
10#95×C89C411yescharacteristic
11#13083558—22no—
12#13083558—41no—
13C2×#10623494—41no—
14C2×#10623494—41no—
15C2×Q8×C89—42no—
16C2×Q8×C89—41no—
17C22×C4×C89—21no—
18C22×C4×C89—21no—
19C22×C4×C89C2×C411yescharacteristic
20C22×C4×C89D411yescharacteristic
21C22×C4×C89D411yescharacteristic
22C4⋊C4×C89—41no—
23C4⋊C4×C89—42no—
24C23×C89C22⋊C411yescharacteristic
25Q8×C89—42no—
26Q8×C89—42no—
27C2×C4×C89—21no—
28C2×C4×C89—21no—
29C2×C4×C89—22no—
30C2×C4×C89—22no—
31C2×C4×C89—21no—
32C2×C4×C89—21no—
33C2×C4×C89—41no—
34C2×C4×C89—41no—
35C2×C4×C89—41no—
36C2×C4×C89—41no—
37C2×C4×C89—41no—
38C2×C4×C89—41no—
39C2×C4×C89SD1611yescharacteristic
40C2×C4×C89Q1611yescharacteristic
41#10623494—42no—
42#10623494—81no—
43C22×C89—21no—
44C22×C89—21no—
45C22×C89#9911yescharacteristic
46C22×C89#10311yescharacteristic
47C22×C89#10411yescharacteristic
48C4×C89—21no—
49C4×C89—21no—
50C4×C89—42no—
51C4×C89—41no—
52C4×C89—42no—
53C4×C89—41no—
54C2×C89—21no—
55C2×C89—21no—
56C2×C89#32811yescharacteristic
57C2×C89AΣL(1,𝔽16)11yescharacteristic
58C2×C89#35611yescharacteristic
59#1354—891nomaximal, Sylow
60C89#135411yescharacteristic, complemented, Sylow
61#395D8911yescharacteristic
62#343—891no—
63#324—891no—
64C22×Q8Dic8911yescharacteristic
65C2×M16—1781no—
66C2×C4⋊C4—21no—
67C2×C4⋊C4C2×D8911yescharacteristic
68C22⋊C8—1781no—
69#95—21no—
70#95Dic8911yescharacteristic
71C2×Q8—42no—
72C2×Q8—41no—
73C22×C4—21no—
74C22×C4—21no—
75C22×C4C2×Dic8911yescharacteristic
76C22×C4C22⋊D8911yescharacteristic
77C22×C4C22⋊D8911yescharacteristic
78M16—3561no—
79M16—1782no—
80C2×C8—3561no—
81C2×C8—3561no—
82C4⋊C4—41no—
83C4⋊C4—42no—
84C23C22⋊Dic8911yescharacteristic
85Q8—42no—
86Q8—42no—
87C2×C4—21no—
88C2×C4—21no—
89C2×C4—22no—
90C2×C4—22no—
91C2×C4—21no—
92C2×C4—21no—
93C2×C4—41no—
94C2×C4—41no—
95C2×C4—41no—
96C2×C4—41no—
97C2×C4—41no—
98C2×C4—41no—
99C2×C4#1308356111yescharacteristic
100C2×C4#1308356411yescharacteristic
101C8—3562no—
102C8—7121no—
103C22—21no—
104C22—21no—
105C22#1566792711yescharacteristic
106C22#1566793611yescharacteristic
107C22#1566793911yescharacteristic
108C4—21no—
109C4—21no—
110C4—42no—
111C4—41no—
112C4—42no—
113C4—41no—
114C2—21no—
115C2—21no—
116C2#1915133511yescharacteristic
117C2#1915138511yescharacteristic
118C2#1915139711yescharacteristic
subgroupG/H
centerC22#15667927
commutatorC22×C4×C89C2×C4
FrattiniC2×C4⋊C4C2×D89
Fitting#395×C89C2
socleC22×C89#99
prime radicalC23×C89C22⋊C4
cosocleC2×C4⋊C4×C89C22
hypercenter#395D89
hypocenterC89#1354
LCSG ▷ C22×C4×C89 ▷ C23×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #395

Complements

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

NH ≅ G/Ntype
60. C89#1354semidirect

Maximal subgroups

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

subgroupindex
#191513672
#191513242
#395×C892
#135489