Finite Group Databasebeta

← #26021830

Subgroups — #26021830

Order 11392.

158 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 158 conjugacy classes of subgroups — too many to draw. Only its 59 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#19151646C211yesmaximal, characteristic
2#19151622C211yesmaximal, characteristic
3#19151369C211yesmaximal, characteristic
4#19151368C211yesmaximal, characteristic
5#19151358C211yesmaximal, characteristic
6#19151354C211yesmaximal, characteristic
7#339×C89C211yesmaximal, characteristic
8C2×#13083558C2211yescharacteristic
9C2×#13083558C2211yescharacteristic
10C2×#13083558C2211yescharacteristic
11#15667971C2211yescharacteristic
12#15667947—22no—
13C4⋊#10623494—22no—
14C2×M16×C89C2211yescharacteristic
15#117×C89C2211yescharacteristic
16C2×C42×C89C2211yescharacteristic
17#13083558—21no—
18#13083558—21no—
19#13083558—21no—
20#13083558—21no—
21#13083558—21no—
22#13083558—21no—
23C2×#10623494—21no—
24C2×#10623494—21no—
25C2×#10623494D412yes—
26C4⋊Dic89—21no—
27C22⋊Dic89—21no—
28C4×Dic89—21no—
29C22×C4×C89—21no—
30C22×C4×C89C2311yescharacteristic
31M16×C89—21no—
32M16×C89—21no—
33C2×C8×C89—21no—
34C4⋊C4×C89—21no—
35C22⋊C4×C89—21no—
36C42×C89—21no—
37C42×C89—21no—
38C42×C89Q811yescharacteristic
39C42×C89Q811yescharacteristic
40C23×C89#4111yescharacteristic
41C2×C4×C89—21no—
42C2×C4×C89—21no—
43C2×C4×C89—42no—
44C2×C4×C89—41no—
45C2×C4×C89C2×D411yescharacteristic
46C2×C4×C89C2×Q811yescharacteristic
47C2×C4×C89#4111yescharacteristic
48C2×C4×C89#4111yescharacteristic
49C2×C4×C89#4111yescharacteristic
50C2×C4×C89#4111yescharacteristic
51C2×Dic89—41no—
52C8×C89—41no—
53#10623494—22no—
54#10623494—41no—
55#10623494—41no—
56C22×C89—41no—
57C22×C89C22⋊Q811yescharacteristic
58C22×C89#12611yescharacteristic
59C22×C89#12611yescharacteristic
60C4×C89—22no—
61C4×C89—41no—
62C4×C89—81no—
63C4×C89#12311yescharacteristic
64C4×C89#12411yescharacteristic
65C4×C89#12511yescharacteristic
66C4×C89#12511yescharacteristic
67Dic89—81no—
68C2×C89—21no—
69C2×C89—21no—
70C2×C89—21no—
71C2×C89#40011yescharacteristic
72#2102—891nomaximal, Sylow
73C89#210211yescharacteristic, complemented, Sylow
74#430—891no—
75#423—891no—
76#344—891no—
77#344—891no—
78#339—891no—
79#339D8911yescharacteristic
80H(3,ℤ/4)—891no—
81C2×M16—891no—
82C2×M16—891no—
83C2×M16—891no—
84C2×M16C2×D8911yescharacteristic
85#117—891no—
86#117C2×D8911yescharacteristic
87C2×C42C2×D8911yescharacteristic
88#108—1782no—
89C4⋊C8—1782no—
90C22×C4—21no—
91C22×C4C22×D8911yescharacteristic
92M16—21no—
93M16—21no—
94M16—1781no—
95M16—1781no—
96M16—1781no—
97M16—1781no—
98M16—1781no—
99M16—1781no—
100C2×C8—21no—
101C2×C8—892no—
102C2×C8—1781no—
103C2×C8—1781no—
104C4⋊C4—21no—
105C4⋊C4—1781no—
106C22⋊C4—21no—
107C22⋊C4—1781no—
108C42—21no—
109C42—21no—
110C42—1781no—
111C42Dic17811yescharacteristic
112C42Dic17811yescharacteristic
113C23#1308357311yescharacteristic
114C2×C4—21no—
115C2×C4—21no—
116C2×C4—42no—
117C2×C4—41no—
118C2×C4—3561no—
119C2×C4D4×D8911yescharacteristic
120C2×C4C2×Dic17811yescharacteristic
121C2×C4#1308357311yescharacteristic
122C2×C4#1308357411yescharacteristic
123C2×C4#1308357411yescharacteristic
124C2×C4#1308357511yescharacteristic
125C8—41no—
126C8—3561no—
127C8—3561no—
128C8—1782no—
129C22—41no—
130C22#1566798911yescharacteristic
131C22#1566800511yescharacteristic
132C22#1566800711yescharacteristic
133C4—22no—
134C4—41no—
135C4—81no—
136C4—7121no—
137C4#1566799711yescharacteristic
138C4#1566799811yescharacteristic
139C4#1566800311yescharacteristic
140C4#1566800411yescharacteristic
141C2—21no—
142C2—21no—
143C2—21no—
144C2#1915154011yescharacteristic
subgroupG/H
centerC4#15667998
commutator, cosocleC22×C4×C89C23
FrattiniC22×C4C22×D89
Fitting#339×C89C2
socleC2×C89#400
prime radicalC23×C89#41
hypercenter#339D89
hypocenterC89#2102
LCSG ▷ C22×C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C4 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
73. C89#2102semidirect

Maximal subgroups

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

subgroupindex
#191516462
#191516222
#191513692
#191513682
#191513582
#191513542
#339×C892
#210289