Finite Group Databasebeta

← #20245584

Subgroups — #20245584

Order 6016.

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

normal subgroups only

This group has 140 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#15689361C211yesmaximal, characteristic
2#107×D47C211yesmaximal, characteristic
3#15688951C211yesmaximal, characteristic, complemented
4#15688950C211yesmaximal, characteristic, complemented
5#15688927C211yesmaximal, characteristic, complemented
6(C2×D47)⋊C16C211yesmaximal, characteristic
7C47×#358C211yesmaximal, characteristic, complemented
8C2×C8×D47C2211yescharacteristic
9#13094000—21no—
10C4⋊C4×D47—21no—
11C2×C47⋊C16C2211yescharacteristic
12#13093958C2211yescharacteristic
13#13093958C2211yescharacteristic
14#13093957—21no—
15#13093948—21no—
16C2×Q16×C47C2211yescharacteristic
17C2×C16×C47C2211yescharacteristic
18#107×C47C2211yescharacteristic
19C2×Q8×C47—21no—
20C2×C4×D47—41no—
21C2×C4×D47D411yescharacteristic
22Q16×C47—21no—
23Q16×C47—21no—
24C2×C8×C47C2311yescharacteristic
25C4⋊C4×C47—21no—
26(C2×D47)⋊C4—41no—
27C4⋊Dic47—21no—
28C4⋊Dic47—21no—
29Dic47⋊C4—41no—
30Dic47⋊C4—41no—
31C2×C47⋊C8D411yescharacteristic
32C8×D47—21no—
33C8×D47—21no—
34C16×C47—21no—
35C47⋊C16—21no—
36C22×D47D811yescharacteristic
37Q8×C47—41no—
38Q8×C47—41no—
39C2×C4×C47—41no—
40C2×C4×C47—41no—
41C2×C4×C47C2×D411yescharacteristic
42C2×Dic47—41no—
43C2×Dic47—41no—
44C2×Dic47D811yescharacteristic
45C4×D47—21no—
46C4×D47—21no—
47C4×D47—82no—
48C8×C47#4111yescharacteristic
49C8×C47#4111yescharacteristic
50C47⋊C8—21no—
51C22×C47C2×D811yescharacteristic
52C2×D47—21no—
53C2×D47—21no—
54C2×D47SD3212yes—
55C4×C47—81no—
56C4×C47—81no—
57C4×C47#12311yescharacteristic
58C4×C47#13711yescharacteristic
59Dic47—21no—
60Dic47—81no—
61Dic47—81no—
62#2235—471nomaximal, Sylow
63C2×C47#48011yescharacteristic
64C2×C47C2×SD3211yescharacteristic
65C2×C47#51011yescharacteristic
66D47—22no—
67#467—471no—
68C2×#107—471no—
69#367—471no—
70#367—471no—
71#358—471no—
72#358D4711yescharacteristic, complemented
73C22⋊C16—471no—
74C47#223511yescharacteristic, complemented, Sylow
75C2×Q16C2×D4711yescharacteristic
76C22×C8—471no—
77C22⋊Q8—941no—
78C2×C4⋊C4—941no—
79C2×C16—471no—
80C2×C16C2×D4711yescharacteristic
81#107—471no—
82#107—471no—
83#107—941no—
84#107C2×D4711yescharacteristic
85#103—941no—
86C2×Q8—21no—
87C22×C4—471no—
88C22×C4—1881no—
89Q16—21no—
90Q16—21no—
91C2×C8—471no—
92C2×C8—941no—
93C2×C8—941no—
94C2×C8C22×D4711yescharacteristic
95C4⋊C4—21no—
96C4⋊C4—941no—
97C4⋊C4—941no—
98C4⋊C4—1881no—
99C4⋊C4—1881no—
100C22⋊C4—1881no—
101C16—21no—
102C16—941no—
103C23—471no—
104Q8—41no—
105Q8—41no—
106C2×C4—41no—
107C2×C4—41no—
108C2×C4—471no—
109C2×C4—941no—
110C2×C4—941no—
111C2×C4—3762no—
112C2×C4—1881no—
113C2×C4—1881no—
114C2×C4D4×D4711yescharacteristic
115C8—941no—
116C8#1062535011yescharacteristic
117C8#1062535211yescharacteristic
118C22—472no—
119C22—941no—
120C22—941no—
121C22D8×D4711yescharacteristic
122C4—81no—
123C4—81no—
124C4—941no—
125C4—3761no—
126C4—3761no—
127C4#1309400611yescharacteristic
128C4#1309405311yescharacteristic
129C2—942no—
130C2#1568943511yescharacteristic
131C2SD32×D4711yescharacteristic
132C2#1568956511yescharacteristic
subgroupG/H
centerC22D8×D47
commutatorC2×C8×C47C23
FrattiniC2×C8C22×D47
FittingC47×#358C2
socleC22×C47C2×D8
hypercenter#358D47
hypocenterC47#2235
LCSG ▷ C2×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #358

Complements

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

NH ≅ G/Ntype
3. #15688951C2semidirect
4. #15688950C2semidirect
5. #15688927C2semidirect
7. C47×#358C2semidirect
72. #358D47semidirect
74. C47#2235semidirect