Finite Group Databasebeta

← #36442275

Subgroups — #36442275

Order 22784.

138 conjugacy classes of subgroups; only the 25 normal subgroups are shown.

normal subgroups only

This group has 138 conjugacy classes of subgroups — too many to draw. Only its 25 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#26019573C211yesmaximal, characteristic
2#26018425C211yesmaximal, characteristic, complemented
3C89×#1356C211yesmaximal, characteristic, complemented
4#19152346C411yescharacteristic
5#19151960—21no—
6#19151397—21no—
7#19151340C411yescharacteristic
8#19151337—21no—
9#491×C89C2211yescharacteristic
10#347×C89—21no—
11#15668000—21no—
12#15667997—41no—
13#15667990—41no—
14#15667987—41no—
15#15667935—41no—
16#15667932—41no—
17#15667931—41no—
18#15667923—21no—
19C4⋊Q8×C89D411yescharacteristic
20#125×C89C2×C411yescharacteristic
21M32×C89—41no—
22#103×C89—41no—
23#97×C89D411yescharacteristic
24C2×Dic178—21no—
25C2×D356—21no—
26C2×D356—41no—
27C2×C4×D89—41no—
28#13083558—81no—
29C2×#10623494—41no—
30#13083553—41no—
31#13083551—41no—
32#13083551—41no—
33#13083551—41no—
34C2×Q8×C89—21no—
35C2×C8×C89—21no—
36C4⋊C4×C89—21no—
37C4⋊C4×C89—41no—
38C4⋊C4×C89—41no—
39C42×C89C22⋊C411yescharacteristic
40C16×C89—42no—
41C22×D89—41no—
42Q8×C89—81no—
43C2×C4×C89—21no—
44C2×C4×C89—41no—
45C2×C4×C89—41no—
46C2×C4×C89#9911yescharacteristic
47C2×Dic89—41no—
48D356—81no—
49D356—161no—
50C4×D89—161no—
51Dic178—81no—
52C8×C89—41no—
53#10623494—81no—
54#10623494—161no—
55C22×C89AΣL(1,𝔽16)11yescharacteristic
56C2×D89—81no—
57C2×D89—81no—
58C2×D89—81no—
59C4×C89—21no—
60C4×C89—41no—
61C4×C89—81no—
62C4×C89—81no—
63Dic89—81no—
64#7525—891nomaximal, Sylow
65C2×C89—21no—
66C2×C89#140411yescharacteristic
67D89—161no—
68#1662—891no—
69#1413—891no—
70#1356D8911yescharacteristic, complemented
71C89#752511yescharacteristic, complemented, Sylow
72#562—891no—
73#491C2×D8911yescharacteristic
74#489—1781no—
75#356—1781no—
76#347—21no—
77#330—891no—
78#329—1781no—
79C4⋊Q8D35611yescharacteristic
80#125C4×D8911yescharacteristic
81#124—1781no—
82#123—3561no—
83C22⋊Q8—3561no—
84#121—3561no—
85M32—41no—
86#103—41no—
87#103—3561no—
88#102—3561no—
89#101—3561no—
90#97—1781no—
91#97C22⋊D8911yescharacteristic
92C2×Q8—21no—
93C2×Q8—1781no—
94C2×D4—3561no—
95C2×D4—1781no—
96C22×C4—3561no—
97M16—7121no—
98C2×C8—21no—
99C2×C8—3561no—
100C4⋊C4—21no—
101C4⋊C4—41no—
102C4⋊C4—41no—
103C4⋊C4—3561no—
104C22⋊C4—3561no—
105C22⋊C4—3561no—
106C22⋊C4—3561no—
107C42#1308355111yescharacteristic
108C16—42no—
109C23—3561no—
110Q8—81no—
111Q8—7121no—
112D4—14241no—
113D4—7121no—
114C2×C4—21no—
115C2×C4—41no—
116C2×C4—41no—
117C2×C4—3561no—
118C2×C4—14241no—
119C2×C4#1566792611yescharacteristic
120C8—41no—
121C8—14241no—
122C8—7121no—
123C22—7121no—
124C22—7121no—
125C22—7121no—
126C22#1915138611yescharacteristic
127C4—21no—
128C4—41no—
129C4—81no—
130C4—81no—
131C4—7121no—
132C2—21no—
133C2—14241no—
134C2#2601840411yescharacteristic
subgroupG/H
centerC2#26018404
commutator#125×C89C2×C4
Frattini#491C2×D89
FittingC89×#1356C2
socleC2×C89#1404
prime radical#19152346C4
cosocle#491×C89C22
hypercenter#1356D89
hypocenterC89#7525
LCSG ▷ #125×C89 ▷ C42×C89 ▷ C2×C4×C89 ▷ C22×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C42 ◁ #491 ◁ #1356

Complements

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

NH ≅ G/Ntype
2. #26018425C2semidirect
3. C89×#1356C2semidirect
70. #1356D89semidirect
71. C89#7525semidirect

Maximal subgroups

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

subgroupindex
#260195732
#260184252
C89×#13562
#752589