Finite Group Databasebeta

← #31823634

Subgroups — #31823634

Order 17984.

146 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 146 conjugacy classes of subgroups — too many to draw. Only its 39 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#22582926C211yesmaximal, characteristic, complemented
2#22582905C211yesmaximal, characteristic, complemented
3#22582866C211yesmaximal, characteristic, complemented
4#22582806C211yesmaximal, characteristic, complemented
5#22582805C211yesmaximal, characteristic, complemented
6#22582797C211yesmaximal, characteristic, complemented
7AGL(1,ℤ/8)×C281C211yesmaximal, characteristic, complemented
8#17985138—21no—
9#17985138C2211yescharacteristic
10#17985137—22no—
11#17985137—21no—
12C2×Dic562—21no—
13C2×Dic562C2211yescharacteristic
14Q8×D281—21no—
15#17985126—21no—
16#17985123—21no—
17#17985122C2211yescharacteristic
18C22⋊Dic281—22no—
19C4×Dic281C2211yescharacteristic
20#41×C281C2211yescharacteristic
21C2×D4×C281C2211yescharacteristic
22SD16×C281—21no—
23D8×C281—21no—
24M16×C281C2211yescharacteristic
25Dic562—22no—
26Dic562—21no—
27Dic562—21no—
28Dic562D411yescharacteristic
29D1124D411yescharacteristic
30C22⋊D281—22no—
31C22⋊D281—21no—
32C2×Dic281—22no—
33C2×Dic281—21no—
34C2×Dic281D412yes—
35C4×D281—22no—
36C4×D281—21no—
37#14555886—21no—
38C23×C281—21no—
39Q8×C281D411yescharacteristic
40D4×C281—21no—
41D4×C281—21no—
42D4×C281—21no—
43D4×C281D411yescharacteristic
44C2×C4×C281—21no—
45C2×C4×C281C2311yescharacteristic
46C8×C281—21no—
47C22×C281—21no—
48C22×C281—42no—
49C22×C281—41no—
50C22×C281C2×D411yescharacteristic
51C2×D281—21no—
52C4×C281—21no—
53C4×C281C2×D411yescharacteristic
54C4×C281C2×D411yescharacteristic
55Dic281—21no—
56Dic281—22no—
57Dic281—41no—
58C2×C281—21no—
59C2×C281—41no—
60C2×C281—81no—
61C2×C281#12011yescharacteristic
62D281—41no—
63C281#45411yescharacteristic, complemented, Sylow
64#454—2811nomaximal, Sylow
652−1+4—2811no—
66AGL(1,ℤ/8)—2811no—
67AGL(1,ℤ/8)D28111yescharacteristic, complemented
68#124—2811no—
69#104—2811no—
70#104—2811no—
71#101—2811no—
72#41—2811no—
73#41—5621no—
74#41—5622no—
75#41—5621no—
76#41C2×D28111yescharacteristic
77C2×Q8—2811no—
78C2×Q8—5621no—
79C2×Q8—5621no—
80C2×D4C2×D28111yescharacteristic
81SD16—21no—
82SD16—5621no—
83D8—21no—
84D8—5621no—
85M16—2811no—
86M16C2×D28111yescharacteristic
87C22⋊C4—5622no—
88C42—2811no—
89C23—21no—
90Q8—2811no—
91Q8—5622no—
92Q8—5621no—
93Q8—5621no—
94Q8C22⋊D28111yescharacteristic
95D4—21no—
96D4—21no—
97D4—21no—
98D4—2811no—
99D4—5622no—
100D4—5621no—
101D4C22⋊D28111yescharacteristic
102C2×C4—21no—
103C2×C4—2812no—
104C2×C4—5622no—
105C2×C4—5622no—
106C2×C4—5621no—
107C2×C4—5621no—
108C2×C4C22×D28111yescharacteristic
109C8—21no—
110C8—5621no—
111C22—21no—
112C22—42no—
113C22—41no—
114C22—5621no—
115C22D4×D28111yescharacteristic
116C4—21no—
117C4—5622no—
118C4—5621no—
119C4—11241no—
120C4D4×D28111yescharacteristic
121C4C2×C22⋊D28111yescharacteristic
122C2—21no—
123C2—41no—
124C2—81no—
125C2—11241no—
126C2#2258284711yescharacteristic
subgroupG/H
centerC2#22582847
commutator, cosocleC2×C4×C281C23
FrattiniC2×C4C22×D281
FittingAGL(1,ℤ/8)×C281C2
socleC2×C281#120
hypercenterAGL(1,ℤ/8)D281
hypocenterC281#454
LCSG ▷ C2×C4×C281 ▷ C2×C281 ▷ C281
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. #22582926C2semidirect
2. #22582905C2semidirect
3. #22582866C2semidirect
4. #22582806C2semidirect
5. #22582805C2semidirect
6. #22582797C2semidirect
7. AGL(1,ℤ/8)×C281C2semidirect
63. C281#454semidirect
67. AGL(1,ℤ/8)D281semidirect

Maximal subgroups

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

subgroupindex
#225829262
#225829052
#225828662
#225828062
#225828052
#225827972
AGL(1,ℤ/8)×C2812
#454281