Finite Group Databasebeta

← #44398818

Subgroups — #44398818

Order 29056.

240 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 53 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#28409748C211yesmaximal, characteristic, complemented
2#28409406C211yesmaximal, characteristic, complemented
3#28409228C212yesmaximal, complemented
4#28408759C212yesmaximal, complemented
5#333×C227C211yesmaximal, characteristic, complemented
6C2×#16813871—22no—
7C2×D1816—22no—
8#20300285C2211yescharacteristic
9#20300277—22no—
10#20300263—22no—
11C4×D908C2212yes—
12#20300246—22no—
13#20300210—22no—
14C4×C227⋊C8C2211yescharacteristic
15C4⋊Q8×C227C2211yescharacteristic
16C4⋊C8×C227C2212yes—
17C2×D908—22no—
18C2×D908—22no—
19C2×D908—21no—
20C2×D908D412yes—
21C2×C4×D227—22no—
22#16813871—44no—
23D1816—44no—
24C2×C227⋊C8—21no—
25C4⋊Dic227D412yes—
26(C2×D227)⋊C4—24no—
27(C2×D227)⋊C4—22no—
28C4×Dic227—22no—
29C2×Q8×C227D412yes—
30C2×C8×C227—22no—
31C4⋊C4×C227—22no—
32C42×C227C2311yescharacteristic
33C22×D227—22no—
34C22×D227—41no—
35D908—22no—
36D908—22no—
37D908—42no—
38D908—42no—
39D908—42no—
40D908—82no—
41C2×Dic227—22no—
42C4×D227—42no—
43C4×D227—42no—
44C227⋊C8—22no—
45Q8×C227—42no—
46C2×C4×C227—22no—
47C2×C4×C227C2×D411yescharacteristic
48C2×C4×C227C2×D412yes—
49C8×C227—42no—
50C22×C227#12011yescharacteristic
51C2×D227—42no—
52C2×D227—42no—
53C2×D227—42no—
54C2×D227—82no—
55C2×D227—81no—
56C4×C227—21no—
57C4×C227—42no—
58C4×C227#13512yes—
59C4×C227AGL(1,ℤ/8)12yes—
60Dic227—42no—
61C2×C227#44912yes—
62C2×C227#45311yescharacteristic
63D227—82no—
64D227—161no—
65C227#162411yescharacteristic, complemented, Sylow
66#1624—2271nomaximal, Sylow
67#555—2271no—
68#492—2271no—
69#459—2272no—
70#333D22711yescharacteristic, complemented
71D4⋊C8—2272no—
72C2×SD16—4542no—
73C2×D8—4542no—
74C4⋊Q8C2×D22711yescharacteristic
75#127—2271no—
76#124—4542no—
77#121—4542no—
78C4×D4—2272no—
79#117—4542no—
80C4⋊C8C2×D22712yes—
81#102—4542no—
82C4×C8—2271no—
83C2×Q8D90812yes—
84C2×D4—4542no—
85C2×D4—4542no—
86C2×D4—4541no—
87C2×D4—2272no—
88C22×C4—4542no—
89SD16—9084no—
90D8—9084no—
91C2×C8—22no—
92C2×C8—4541no—
93C4⋊C4—22no—
94C4⋊C4—2272no—
95C22⋊C4—4544no—
96C22⋊C4—4542no—
97C42—4542no—
98C42C22×D22711yescharacteristic
99C23—9081no—
100C23—4542no—
101Q8—42no—
102D4—18162no—
103D4—9082no—
104D4—9082no—
105D4—9082no—
106D4—4542no—
107D4—4542no—
108C2×C4—22no—
109C2×C4—9082no—
110C2×C4—9082no—
111C2×C4—4542no—
112C2×C4D4×D22712yes—
113C2×C4C2×D90811yescharacteristic
114C8—42no—
115C8—4542no—
116C22—18162no—
117C22—18161no—
118C22—9082no—
119C22—9082no—
120C22—9082no—
121C22#2030025811yescharacteristic
122C4—21no—
123C4—42no—
124C4—9082no—
125C4#2030031112yes—
126C4#2030031512yes—
127C2—18162no—
128C2—36321no—
129C2#2840918012yes—
130C2#2840920211yescharacteristic
subgroupG/H
centerC22#20300258
commutator, cosocleC42×C227C23
FrattiniC42C22×D227
Fitting#333×C227C2
socleC22×C227#120
hypercenter#333D227
hypocenterC227#1624
LCSG ▷ C42×C227 ▷ C22×C227 ▷ C227
UCSC1 ◁ C22 ◁ C42 ◁ #333

Complements

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

NH ≅ G/Ntype
1. #28409748C2semidirect
2. #28409406C2semidirect
3. #28409228C2semidirect
4. #28408759C2semidirect
5. #333×C227C2semidirect
65. C227#1624semidirect
70. #333D227semidirect

Maximal subgroups

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

subgroupindex
#284097482
#284094062
#284092282
#284087592
#333×C2272
#1624227