Finite Group Databasebeta

← #44486621

Subgroups — #44486621

Order 30592.

170 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 170 conjugacy classes of subgroups — too many to draw. Only its 47 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#29505208C212yesmaximal, complemented
2#29504890C211yesmaximal, characteristic, complemented
3#29504593C211yesmaximal, characteristic, complemented
4#29504585C212yesmaximal, complemented
5#493×C239C211yesmaximal, characteristic, complemented
6#21439982C2211yescharacteristic
7#21439966—21no—
8#21439904—22no—
9#21439901—22no—
10#21439900C2212yes—
11#21439896C2211yescharacteristic
12#21439888—21no—
13C2×D8×C239—21no—
14C2×D8×C239C2212yes—
15#127×C239—21no—
16C4×C8×C239C2211yescharacteristic
17#16838548—21no—
18Dic956D411yescharacteristic, complemented
19#16838537—21no—
20D1912D411yescharacteristic, complemented
21#16838532—21no—
22#16838531—41no—
23C8×D239—41no—
24C239⋊C16—22no—
25C2×D4×C239—22no—
26C2×D4×C239—42no—
27D8×C239—22no—
28D8×C239—22no—
29D8×C239—41no—
30D8×C239—41no—
31C2×C8×C239D411yescharacteristic
32C2×C8×C239C2311yescharacteristic
33C42×C239D411yescharacteristic
34Dic478—21no—
35D956—21no—
36C22⋊D239—41no—
37C4×D239—41no—
38C239⋊C8—41no—
39C23×C239—42no—
40D4×C239—42no—
41D4×C239—42no—
42D4×C239—84no—
43C2×C4×C239—21no—
44C2×C4×C239C2×D411yescharacteristic
45C8×C239D811yescharacteristic
46C8×C239D811yescharacteristic
47C8×C239C2×D411yescharacteristic
48C8×C239#4111yescharacteristic
49C22×C239—84no—
50C22×C239—82no—
51C22×C239AGL(1,ℤ/8)11yescharacteristic
52C2×D239—41no—
53C4×C239—22no—
54C4×C239#12111yescharacteristic
55C4×C239C2×D811yescharacteristic
56Dic239—41no—
57C2×C239—21no—
58C2×C239—162no—
59C2×C239#45911yescharacteristic
60D239—81no—
61C239#221311yescharacteristic, complemented, Sylow
62#2213—2391nomaximal, Sylow
63#509—2392no—
64#493D23911yescharacteristic, complemented
65#443—2391no—
66#364—2391no—
67#361—2392no—
68#135—2391no—
69C2×D8—21no—
70C2×D8C2×D23912yes—
71#131—4781no—
72#127—21no—
73SD32—4782no—
74D16—4782no—
75M32—2392no—
76#108—2391no—
77#104—4781no—
78C4×C8C2×D23911yescharacteristic
79#41—4781no—
80C2×D4—22no—
81C2×D4—42no—
82Q16—2391no—
83SD16—4781no—
84D8—22no—
85D8—22no—
86D8—41no—
87D8—41no—
88D8—2391no—
89M16—9561no—
90M16—4781no—
91C2×C8—9561no—
92C2×C8C22⋊D23911yescharacteristic
93C2×C8C22×D23911yescharacteristic
94C42C22⋊D23911yescharacteristic
95C16—4782no—
96C23—42no—
97Q8—4781no—
98D4—42no—
99D4—42no—
100D4—84no—
101D4—9561no—
102D4—4781no—
103C2×C4—21no—
104C2×C4—9561no—
105C2×C4C2×C22⋊D23911yescharacteristic
106C8—9561no—
107C8#1683853311yescharacteristic
108C8#1683853311yescharacteristic
109C8D4×D23911yescharacteristic
110C8#1683854711yescharacteristic
111C22—84no—
112C22—82no—
113C22—9561no—
114C22#2143998611yescharacteristic
115C4—22no—
116C4—9561no—
117C4#2143993111yescharacteristic
118C4C2×#1683853311yescharacteristic
119C2—21no—
120C2—162no—
121C2—19121no—
122C2#2950496411yescharacteristic
subgroupG/H
centerC2#29504964
commutator, cosocleC2×C8×C239C23
FrattiniC2×C8C22×D239
Fitting#493×C239C2
socleC2×C239#459
hypercenter#493D239
hypocenterC239#2213
LCSG ▷ C2×C8×C239 ▷ C4×C239 ▷ C2×C239 ▷ C239
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #493

Complements

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

NH ≅ G/Ntype
1. #29505208C2semidirect
2. #29504890C2semidirect
3. #29504593C2semidirect
4. #29504585C2semidirect
5. #493×C239C2semidirect
18. Dic956D4semidirect
20. D1912D4semidirect
61. C239#2213semidirect
64. #493D239semidirect

Maximal subgroups

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

subgroupindex
#295052082
#295048902
#295045932
#295045852
#493×C2392
#2213239