Finite Group Databasebeta

← #44483632

Subgroups — #44483632

Order 30592.

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#29505488C211yesmaximal, characteristic, complemented
2#29505146C211yesmaximal, characteristic, complemented
3#29504968C212yesmaximal, complemented
4#29504499C212yesmaximal, complemented
5#333×C239C211yesmaximal, characteristic, complemented
6C2×#16838535—22no—
7C2×D1912—22no—
8#21439957C2211yescharacteristic
9#21439949—22no—
10#21439935—22no—
11C4×D956C2212yes—
12#21439918—22no—
13#21439882—22no—
14C4×C239⋊C8C2211yescharacteristic
15C4⋊Q8×C239C2211yescharacteristic
16C4⋊C8×C239C2212yes—
17C2×D956—22no—
18C2×D956—22no—
19C2×D956—21no—
20C2×D956D412yes—
21C2×C4×D239—22no—
22#16838535—44no—
23D1912—44no—
24C2×C239⋊C8—21no—
25C4⋊Dic239D412yes—
26(C2×D239)⋊C4—24no—
27(C2×D239)⋊C4—22no—
28C4×Dic239—22no—
29C2×Q8×C239D412yes—
30C2×C8×C239—22no—
31C4⋊C4×C239—22no—
32C42×C239C2311yescharacteristic
33C22×D239—22no—
34C22×D239—41no—
35D956—22no—
36D956—22no—
37D956—42no—
38D956—42no—
39D956—42no—
40D956—82no—
41C2×Dic239—22no—
42C4×D239—42no—
43C4×D239—42no—
44C239⋊C8—22no—
45Q8×C239—42no—
46C2×C4×C239—22no—
47C2×C4×C239C2×D411yescharacteristic
48C2×C4×C239C2×D412yes—
49C8×C239—42no—
50C22×C239#12011yescharacteristic
51C2×D239—42no—
52C2×D239—42no—
53C2×D239—42no—
54C2×D239—82no—
55C2×D239—81no—
56C4×C239—21no—
57C4×C239—42no—
58C4×C239#13512yes—
59C4×C239AGL(1,ℤ/8)12yes—
60Dic239—42no—
61C2×C239#44912yes—
62C2×C239#45311yescharacteristic
63D239—82no—
64D239—161no—
65C239#162411yescharacteristic, complemented, Sylow
66#1624—2391nomaximal, Sylow
67#555—2391no—
68#492—2391no—
69#459—2392no—
70#333D23911yescharacteristic, complemented
71D4⋊C8—2392no—
72C2×SD16—4782no—
73C2×D8—4782no—
74C4⋊Q8C2×D23911yescharacteristic
75#127—2391no—
76#124—4782no—
77#121—4782no—
78C4×D4—2392no—
79#117—4782no—
80C4⋊C8C2×D23912yes—
81#102—4782no—
82C4×C8—2391no—
83C2×Q8D95612yes—
84C2×D4—4782no—
85C2×D4—4782no—
86C2×D4—4781no—
87C2×D4—2392no—
88C22×C4—4782no—
89SD16—9564no—
90D8—9564no—
91C2×C8—22no—
92C2×C8—4781no—
93C4⋊C4—22no—
94C4⋊C4—2392no—
95C22⋊C4—4784no—
96C22⋊C4—4782no—
97C42—4782no—
98C42C22×D23911yescharacteristic
99C23—9561no—
100C23—4782no—
101Q8—42no—
102D4—19122no—
103D4—9562no—
104D4—9562no—
105D4—9562no—
106D4—4782no—
107D4—4782no—
108C2×C4—22no—
109C2×C4—9562no—
110C2×C4—9562no—
111C2×C4—4782no—
112C2×C4D4×D23912yes—
113C2×C4C2×D95611yescharacteristic
114C8—42no—
115C8—4782no—
116C22—19122no—
117C22—19121no—
118C22—9562no—
119C22—9562no—
120C22—9562no—
121C22#2143993011yescharacteristic
122C4—21no—
123C4—42no—
124C4—9562no—
125C4#2143998312yes—
126C4#2143998712yes—
127C2—19122no—
128C2—38241no—
129C2#2950492012yes—
130C2#2950494211yescharacteristic
subgroupG/H
centerC22#21439930
commutator, cosocleC42×C239C23
FrattiniC42C22×D239
Fitting#333×C239C2
socleC22×C239#120
hypercenter#333D239
hypocenterC239#1624
LCSG ▷ C42×C239 ▷ C22×C239 ▷ C239
UCSC1 ◁ C22 ◁ C42 ◁ #333

Complements

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

NH ≅ G/Ntype
1. #29505488C2semidirect
2. #29505146C2semidirect
3. #29504968C2semidirect
4. #29504499C2semidirect
5. #333×C239C2semidirect
65. C239#1624semidirect
70. #333D239semidirect

Maximal subgroups

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

subgroupindex
#295054882
#295051462
#295049682
#295044992
#333×C2392
#1624239