Finite Group Databasebeta

← #44566455

Subgroups — #44566455

Order 32192.

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#30632911C211yesmaximal, characteristic, complemented
2#30632892C211yesmaximal, characteristic, complemented
3#30632889C211yesmaximal, characteristic, complemented
4#30632852C211yesmaximal, characteristic, complemented
5#30632792C211yesmaximal, characteristic, complemented
6#30632782C211yesmaximal, characteristic, complemented
7#104×C503C211yesmaximal, characteristic, complemented
8#22548883—21no—
9#22548883C2211yescharacteristic
10#22548882—22no—
11#22548882—21no—
12C2×Dic1006—21no—
13C2×Dic1006C2211yescharacteristic
14Q8×D503—21no—
15C2×D2012C2211yescharacteristic
16#22548872—21no—
17#22548870—21no—
18D4024—21no—
19#22548868—21no—
20#22548867C2211yescharacteristic
21(C2×D503)⋊C4—22no—
22#41×C503C2211yescharacteristic
23M16×C503C2211yescharacteristic
24C42×C503C2211yescharacteristic
25C22×D503—21no—
26Dic1006—22no—
27Dic1006—21no—
28Dic1006—21no—
29Dic1006D411yescharacteristic
30D2012—21no—
31D2012—21no—
32D2012D411yescharacteristic
33C22⋊D503—22no—
34C22⋊D503—21no—
35C2×Dic503—22no—
36C2×Dic503D412yes—
37C4×D503—22no—
38C4×D503—21no—
39C503⋊C8—21no—
40Q8×C503D411yescharacteristic
41D4×C503—21no—
42D4×C503D411yescharacteristic
43C2×C4×C503—21no—
44C2×C4×C503—21no—
45C2×C4×C503C2311yescharacteristic
46C8×C503—21no—
47C22×C503—21no—
48C22×C503C2×D411yescharacteristic
49C2×D503—21no—
50C2×D503—42no—
51C2×D503—41no—
52C4×C503—21no—
53C4×C503—41no—
54C4×C503C2×D411yescharacteristic
55C4×C503C2×D411yescharacteristic
56Dic503—21no—
57Dic503—22no—
58C2×C503—21no—
59C2×C503—41no—
60C2×C503#12011yescharacteristic
61D503—41no—
62D503—81no—
63C503#45411yescharacteristic, complemented, Sylow
64#454—5031nomaximal, Sylow
652−1+4—5031no—
66AGL(1,ℤ/8)—5031no—
67AGL(1,ℤ/8)—5031no—
68#124—5031no—
69#104—5031no—
70#104D50311yescharacteristic, complemented
71#101—5031no—
72#41—10061no—
73#41—10061no—
74#41—10062no—
75#41—5031no—
76#41C2×D50311yescharacteristic
77C2×Q8—10061no—
78C2×Q8—10061no—
79C2×Q8—5031no—
80C2×D4—5031no—
81SD16—10061no—
82SD16—10061no—
83D8—10061no—
84D8—10061no—
85M16—5031no—
86M16C2×D50311yescharacteristic
87C22⋊C4—10062no—
88C42C2×D50311yescharacteristic
89C23—10061no—
90Q8—10062no—
91Q8—10061no—
92Q8—10061no—
93Q8—5031no—
94Q8D201211yescharacteristic
95D4—21no—
96D4—10062no—
97D4—10061no—
98D4—10061no—
99D4—10061no—
100D4—5031no—
101D4D201211yescharacteristic
102C2×C4—21no—
103C2×C4—21no—
104C2×C4—10062no—
105C2×C4—10062no—
106C2×C4—10061no—
107C2×C4—5032no—
108C2×C4C22×D50311yescharacteristic
109C8—21no—
110C8—10061no—
111C22—21no—
112C22—20122no—
113C22—20121no—
114C22—10061no—
115C22D4×D50311yescharacteristic
116C4—21no—
117C4—41no—
118C4—10061no—
119C4—10062no—
120C4D4×D50311yescharacteristic
121C4C2×D201211yescharacteristic
122C2—21no—
123C2—41no—
124C2—40241no—
125C2—20121no—
126C2#3063283411yescharacteristic
subgroupG/H
centerC2#30632834
commutator, cosocleC2×C4×C503C23
FrattiniC2×C4C22×D503
Fitting#104×C503C2
socleC2×C503#120
hypercenter#104D503
hypocenterC503#454
LCSG ▷ C2×C4×C503 ▷ C2×C503 ▷ C503
UCSC1 ◁ C2 ◁ C2×C4 ◁ #104

Complements

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

NH ≅ G/Ntype
1. #30632911C2semidirect
2. #30632892C2semidirect
3. #30632889C2semidirect
4. #30632852C2semidirect
5. #30632792C2semidirect
6. #30632782C2semidirect
7. #104×C503C2semidirect
63. C503#454semidirect
70. #104D503semidirect

Maximal subgroups

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

subgroupindex
#306329112
#306328922
#306328892
#306328522
#306327922
#306327822
#104×C5032
#454503