Finite Group Databasebeta

← #44486718

Subgroups — #44486718

Order 30592.

126 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 126 conjugacy classes of subgroups — too many to draw. Only its 43 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#29505169C211yesmaximal, characteristic, complemented
2#29504888C211yesmaximal, characteristic
3#29504596C211yesmaximal, characteristic, complemented
4#29504592C211yesmaximal, characteristic, complemented
5#29504583C211yesmaximal, characteristic
6#29504581C211yesmaximal, characteristic
7#365×C239C211yesmaximal, characteristic, complemented
8#21439982C2211yescharacteristic
9#21439968—21no—
10#21439959—21no—
11#21439900C2211yescharacteristic
12#21439892C2211yescharacteristic
13#21439891—21no—
14#21439886—21no—
15C8×Dic239C2211yescharacteristic
16M32×C239C2211yescharacteristic
17#108×C239C2211yescharacteristic
18#106×C239C2211yescharacteristic
19#16838548—21no—
20C2×Dic478—41no—
21Dic956Q811yescharacteristic, complemented
22#16838537—21no—
23D1912Q811yescharacteristic, complemented
24#16838531—41no—
25C2×C239⋊C8D411yescharacteristic
26C8×D239—41no—
27C4⋊Dic239—21no—
28Dic239⋊C4—41no—
29C4×Dic239D411yescharacteristic
30C239⋊C16—21no—
31M16×C239—21no—
32C2×C8×C239C2311yescharacteristic
33C4⋊C4×C239—21no—
34C16×C239—21no—
35Dic478—21no—
36Dic478—82no—
37D956—21no—
38C22⋊D239—41no—
39C2×Dic239—21no—
40C2×Dic239—41no—
41C4×D239—41no—
42C239⋊C8SD1611yescharacteristic
43C239⋊C8SD1611yescharacteristic
44C2×C4×C239—41no—
45C2×C4×C239C2×D411yescharacteristic
46C8×C239—41no—
47C8×C239C2×Q811yescharacteristic
48C8×C239#4111yescharacteristic
49C22×C239AGL(1,ℤ/8)11yescharacteristic
50C2×D239—41no—
51C4×C239—81no—
52C4×C239C22⋊Q811yescharacteristic
53C4×C239C2×SD1611yescharacteristic
54Dic239—22no—
55Dic239—41no—
56Dic239—81no—
57C2×C239—21no—
58C2×C239#47611yescharacteristic
59D239—81no—
60C239#223011yescharacteristic, complemented, Sylow
61#2230—2391nomaximal, Sylow
62#498—2391no—
63#443—2391no—
64#365—2391no—
65#365D23911yescharacteristic, complemented
66#364—2391no—
67#360—2391no—
68#360—2391no—
69#135—2391no—
70#131—4781no—
71C4⋊Q8—4781no—
72M32—2391no—
73M32C2×D23911yescharacteristic
74#108C2×D23911yescharacteristic
75#106—4781no—
76#106—2391no—
77#106C2×D23911yescharacteristic
78#104—4781no—
79C4×C8—2391no—
80#41—4781no—
81C2×Q8—9561no—
82Q16—2391no—
83SD16—4781no—
84D8—2391no—
85M16—21no—
86M16—9561no—
87C2×C8—9561no—
88C2×C8—2391no—
89C2×C8C22×D23911yescharacteristic
90C4⋊C4—21no—
91C4⋊C4—9561no—
92C4⋊C4—4781no—
93C42—2391no—
94C16—21no—
95C16—4781no—
96Q8—19122no—
97Q8—4781no—
98D4—9561no—
99D4—4781no—
100C2×C4—41no—
101C2×C4—9561no—
102C2×C4—9561no—
103C2×C4—4781no—
104C2×C4D4×D23911yescharacteristic
105C8—41no—
106C8—2391no—
107C8—2391no—
108C8Q8×D23911yescharacteristic
109C8#1683854811yescharacteristic
110C22—9561no—
111C22#2143998711yescharacteristic
112C4—81no—
113C4—19121no—
114C4—9561no—
115C4—4782no—
116C4#2143993811yescharacteristic
117C4SD16×D23911yescharacteristic
118C2—21no—
119C2—19121no—
120C2#2950506111yescharacteristic
subgroupG/H
centerC2#29505061
commutator, cosocleC2×C8×C239C23
FrattiniC2×C8C22×D239
Fitting#365×C239C2
socleC2×C239#476
prime radical#21439982C22
hypercenter#365D239
hypocenterC239#2230
LCSG ▷ C2×C8×C239 ▷ C4×C239 ▷ C2×C239 ▷ C239
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #365

Complements

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

NH ≅ G/Ntype
1. #29505169C2semidirect
3. #29504596C2semidirect
4. #29504592C2semidirect
7. #365×C239C2semidirect
21. Dic956Q8semidirect
23. D1912Q8semidirect
60. C239#2230semidirect
65. #365D239semidirect

Maximal subgroups

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

subgroupindex
#295051692
#295048882
#295045962
#295045922
#295045832
#295045812
#365×C2392
#2230239