Finite Group Databasebeta

← #44399026

Subgroups — #44399026

Order 29056.

230 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 45 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#28409780C211yesmaximal, characteristic, complemented
2#28409419C212yesmaximal, complemented
3#28408774C211yesmaximal, characteristic, complemented
4#28408771C212yesmaximal, complemented
5#490×C227C211yesmaximal, characteristic, complemented
6C2×#16813872—22no—
7C2×#16813869—22no—
8#20300276C2212yes—
9#20300273—22no—
10#20300266—22no—
11#20300263—22no—
12#20300199C2212yes—
13#127×C227C2211yescharacteristic
14#125×C227C2211yescharacteristic
15#102×C227—22no—
16#97×C227C2211yescharacteristic
17C2×Dic454D412yes—
18C2×D908—22no—
19C2×D908D412yes—
20C2×C4×D227—22no—
21#16813872—44no—
22#16813869—44no—
23C2×C227⋊C8—22no—
24Dic227⋊C4—22no—
25(C2×D227)⋊C4—22no—
26(C2×D227)⋊C4—22no—
27(C2×D227)⋊C4—22no—
28C2×D4×C227—22no—
29C2×D4×C227—21no—
30C2×C8×C227—21no—
31C4⋊C4×C227—22no—
32C4⋊C4×C227D412yes—
33C42×C227C2311yescharacteristic
34C22×D227—22no—
35Dic454—42no—
36D908—42no—
37D908—82no—
38C2×Dic227—22no—
39C4×D227—82no—
40C227⋊C8—24no—
41C23×C227—41no—
42D4×C227—42no—
43D4×C227—42no—
44D4×C227—42no—
45C2×C4×C227—22no—
46C2×C4×C227C2×D412yes—
47C2×C4×C227C2×D411yescharacteristic
48C8×C227—41no—
49C22×C227—82no—
50C22×C227—81no—
51C22×C227#12011yescharacteristic
52C2×D227—42no—
53C2×D227—42no—
54C2×D227—42no—
55C4×C227—22no—
56C4×C227—21no—
57C4×C227—42no—
58Dic227—42no—
59C2×C227—161no—
60C2×C227#45312yes—
61C2×C227#45411yescharacteristic
62D227—82no—
63C227#165611yescharacteristic, complemented, Sylow
64#1656—2271nomaximal, Sylow
65#562—2271no—
66#496—2272no—
67#490D22711yescharacteristic, complemented
68#330—2271no—
69#329—2272no—
70C2×SD16—4542no—
71C2×D8—4542no—
72#127C2×D22711yescharacteristic
73#125C2×D22711yescharacteristic
74#124—2272no—
75#123—4542no—
76C22⋊Q8—4542no—
77#121—4542no—
78#102—22no—
79#97—2272no—
80#97C2×D22711yescharacteristic
81C2×Q8—2272no—
82C2×D4—22no—
83C2×D4—21no—
84C2×D4—4542no—
85C2×D4—2272no—
86C22×C4—4542no—
87SD16—9084no—
88D8—9084no—
89C2×C8—21no—
90C2×C8—4542no—
91C4⋊C4—22no—
92C4⋊C4—4542no—
93C4⋊C4C22⋊D22712yes—
94C22⋊C4—4542no—
95C22⋊C4—4542no—
96C22⋊C4—4542no—
97C42C22×D22711yescharacteristic
98C23—41no—
99C23—4542no—
100Q8—9082no—
101D4—42no—
102D4—42no—
103D4—42no—
104D4—18162no—
105D4—9082no—
106C2×C4—22no—
107C2×C4—18162no—
108C2×C4—4542no—
109C2×C4D4×D22712yes—
110C2×C4C2×C22⋊D22711yescharacteristic
111C8—41no—
112C8—4544no—
113C22—82no—
114C22—81no—
115C22—9082no—
116C22—9082no—
117C22—9082no—
118C22#2030025611yescharacteristic
119C4—22no—
120C4—21no—
121C4—42no—
122C4—9082no—
123C2—161no—
124C2—18162no—
125C2#2840919812yes—
126C2#2840920411yescharacteristic
subgroupG/H
centerC22#20300256
commutator, cosocleC42×C227C23
FrattiniC42C22×D227
Fitting#490×C227C2
socleC22×C227#120
hypercenter#490D227
hypocenterC227#1656
LCSG ▷ C42×C227 ▷ C22×C227 ▷ C227
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
1. #28409780C2semidirect
2. #28409419C2semidirect
3. #28408774C2semidirect
4. #28408771C2semidirect
5. #490×C227C2semidirect
63. C227#1656semidirect
67. #490D227semidirect

Maximal subgroups

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

subgroupindex
#284097802
#284094192
#284087742
#284087712
#490×C2272
#1656227