Finite Group Databasebeta

← #21447714

Subgroups — #21447714

Order 7808.

154 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 154 conjugacy classes of subgroups — too many to draw. Only its 51 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#16840197C211yesmaximal, characteristic
2#16839884C211yesmaximal, characteristic, complemented
3#16839873C211yesmaximal, characteristic, complemented
4#16839584C211yesmaximal, characteristic, complemented
5#16839576C211yesmaximal, characteristic, complemented
6#16839539C211yesmaximal, characteristic, complemented
7C61×#360C211yesmaximal, characteristic, complemented
8C2×D488C2211yescharacteristic
9#14519784—21no—
10#14519739—21no—
11#14519720C412yescomplemented
12#14519718C412yescomplemented
13#14519717C2211yescharacteristic
14#14519713C2211yescharacteristic
15#14519704—21no—
16#14519697—21no—
17#14519687C2211yescharacteristic
18#135×C61C2211yescharacteristic
19M32×C61C2211yescharacteristic
20#106×C61C2211yescharacteristic
21#41×C61—21no—
22C2×D244—21no—
23C2×C4×D61—41no—
24Q16×C61C2×C411yescharacteristic, complemented
25SD16×C61—21no—
26D8×C61C2×C411yescharacteristic, complemented
27C2×C8×C61C2311yescharacteristic
28C4⋊C4×C61—21no—
29#11758198—41no—
30C4×Dic61D411yescharacteristic
31#11758194—21no—
32#11758194—41no—
33C2×#92418—41no—
34C2×#92418D411yescharacteristic
35D488—21no—
36D488C2×C412yes—
37C16×C61—21no—
38#11758185C2×C412yescomplemented
39C22×D61—41no—
40Q8×C61—21no—
41D4×C61—21no—
42D4×C61—41no—
43C2×C4×C61—41no—
44C2×C4×C61—41no—
45C2×C4×C61C2×D411yescharacteristic
46C2×Dic61—21no—
47D244—22no—
48D244—41no—
49C4×D61—82no—
50C8×C61C22×C411yescharacteristic
51C8×C61#4111yescharacteristic
52#92418—21no—
53#92418—41no—
54C22×C61—41no—
55C22×C61AGL(1,ℤ/8)11yescharacteristic
56C2×D61—42no—
57C2×D61—81no—
58C2×D61—81no—
59C4×C61—41no—
60C4×C61—81no—
61C4×C61C4×D411yescharacteristic
62C4×C61AGL(1,ℤ/8)11yescharacteristic
63Dic61—41no—
64AGL(1,ℤ/16)—611nomaximal, Sylow
65C2×C61—21no—
66C2×C61—81no—
67C2×C61#44211yescharacteristic
68D61—82no—
69#509—611no—
70#444—611no—
71#442—611no—
72#365—611no—
73#361—611no—
74#360D6111yescharacteristic, complemented
75#347—611no—
76C61AGL(1,ℤ/16)11yescharacteristic, complemented, Sylow
77#135C2×D6111yescharacteristic
78C2×D8—611no—
79#131—1221no—
80C4×D4—1221no—
81SD32—612no—
82D16—612no—
83M32—611no—
84M32C2×D6111yescharacteristic
85#108—611no—
86#106C2×D6111yescharacteristic
87#104—1221no—
88#102—1221no—
89#97—611no—
90#41—21no—
91C2×D4—1221no—
92C22×C4—2441no—
93Q16C4×D6111yescharacteristic, complemented
94SD16—21no—
95D8—612no—
96D8—1221no—
97D8C4×D6111yescharacteristic, complemented
98M16—1221no—
99M16—2441no—
100C2×C8—611no—
101C2×C8—2441no—
102C2×C8C22×D6111yescharacteristic
103C4⋊C4—21no—
104C22⋊C4—2441no—
105C42—611no—
106C16—21no—
107C16—612no—
108C23—2441no—
109Q8—21no—
110D4—21no—
111D4—41no—
112D4—1222no—
113D4—2441no—
114C2×C4—41no—
115C2×C4—41no—
116C2×C4—1221no—
117C2×C4—4882no—
118C2×C4D4×D6111yescharacteristic
119C8—1221no—
120C8—2441no—
121C8C2×C4×D6111yescharacteristic
122C8#1175822411yescharacteristic
123C22—41no—
124C22—4881no—
125C22—4881no—
126C22—2442no—
127C22#1451980111yescharacteristic
128C4—41no—
129C4—81no—
130C4—2441no—
131C4#1451973711yescharacteristic
132C4#1451980411yescharacteristic
133C2—21no—
134C2—81no—
135C2—4882no—
136C2#1683987111yescharacteristic
subgroupG/H
centerC2#16839871
commutatorC8×C61C22×C4
FrattiniC2×C8C22×D61
FittingC61×#360C2
socleC2×C61#442
hypercenter#360D61
hypocenterC61AGL(1,ℤ/16)
LCSG ▷ C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #360

Complements

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

NH ≅ G/Ntype
2. #16839884C2semidirect
3. #16839873C2semidirect
4. #16839584C2semidirect
5. #16839576C2semidirect
6. #16839539C2semidirect
7. C61×#360C2semidirect
11. #14519720C4semidirect
12. #14519718C4semidirect
24. Q16×C61C2×C4semidirect
26. D8×C61C2×C4semidirect
38. #11758185C2×C4semidirect
74. #360D61semidirect
76. C61AGL(1,ℤ/16)semidirect
93. Q16C4×D61semidirect
97. D8C4×D61semidirect