Finite Group Databasebeta

← #21447716

Subgroups — #21447716

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#16840200C211yesmaximal, characteristic
2#16839883C211yesmaximal, characteristic, complemented
3#16839873C211yesmaximal, characteristic, complemented
4#16839574C211yesmaximal, characteristic, complemented
5#16839571C211yesmaximal, characteristic, complemented
6#16839539C211yesmaximal, characteristic, complemented
7C61×#365C211yesmaximal, characteristic, complemented
8#14519799C2211yescharacteristic
9C2×D488C2211yescharacteristic
10#14519785—21no—
11#14519739—21no—
12#14519722C412yescomplemented
13D976C412yescomplemented
14#14519717C2211yescharacteristic
15#14519703—21no—
16#14519697—21no—
17#14519687C2211yescharacteristic
18M32×C61C2211yescharacteristic
19#108×C61C2211yescharacteristic
20#106×C61C2211yescharacteristic
21#11758222—21no—
22C2×D244—21no—
23C2×C4×D61—41no—
24M16×C61—21no—
25C2×C8×C61C2311yescharacteristic
26C4⋊C4×C61—21no—
27#11758198—41no—
28C4×Dic61D411yescharacteristic
29C2×#92418D411yescharacteristic
30Dic244C2×C411yescharacteristic, complemented
31D488—21no—
32D488C2×C412yes—
33D488C2×C411yescharacteristic, complemented
34#11758190—21no—
35#11758189—41no—
36C8×D61—41no—
37C16×C61C2×C412yescomplemented
38#11758185—21no—
39C22×D61—41no—
40C2×C4×C61—41no—
41C2×C4×C61C2×D411yescharacteristic
42C22⋊D61—41no—
43C2×Dic61—21no—
44D244—21no—
45D244—22no—
46D244—41no—
47C4×D61—41no—
48C4×D61—82no—
49Dic122—21no—
50C8×C61—41no—
51C8×C61C22×C411yescharacteristic
52C8×C61#4111yescharacteristic
53#92418—21no—
54C22×C61AGL(1,ℤ/8)11yescharacteristic
55C2×D61—41no—
56C2×D61—42no—
57C2×D61—81no—
58C2×D61—81no—
59C4×C61—81no—
60C4×C61C4×D411yescharacteristic
61C4×C61AGL(1,ℤ/8)11yescharacteristic
62Dic61—41no—
63Dic61—41no—
64AGL(1,ℤ/16)—611nomaximal, Sylow
65C2×C61—21no—
66C2×C61#44211yescharacteristic
67D61—81no—
68D61—82no—
69#509—611no—
70#444—611no—
71#442—611no—
72#365D6111yescharacteristic, complemented
73#361—611no—
74#360—611no—
75#347—611no—
76C61AGL(1,ℤ/16)11yescharacteristic, complemented, Sylow
77#135—611no—
78C2×D8—611no—
79#131—1221no—
80C4×D4—1221no—
81SD32—612no—
82D16—612no—
83M32—611no—
84M32C2×D6111yescharacteristic
85#108C2×D6111yescharacteristic
86#106C2×D6111yescharacteristic
87#104—1221no—
88#102—1221no—
89#97—611no—
90#41—1221no—
91C2×D4—1221no—
92C22×C4—2441no—
93Q16—611no—
94SD16—1221no—
95D8—611no—
96D8—612no—
97D8—1221no—
98M16—21no—
99M16—2441no—
100C2×C8—611no—
101C2×C8—2441no—
102C2×C8C22×D6111yescharacteristic
103C4⋊C4—21no—
104C22⋊C4—2441no—
105C42—611no—
106C16—1221no—
107C16C4×D6112yescomplemented
108C23—2441no—
109Q8—1221no—
110D4—1222no—
111D4—1221no—
112D4—2441no—
113D4—2441no—
114C2×C4—41no—
115C2×C4—1221no—
116C2×C4—4882no—
117C2×C4—2441no—
118C2×C4D4×D6111yescharacteristic
119C8—41no—
120C8—1221no—
121C8C2×C4×D6111yescharacteristic
122C8#1175822611yescharacteristic
123C22—4881no—
124C22—4881no—
125C22—2441no—
126C22—2442no—
127C22#1451980411yescharacteristic
128C4—81no—
129C4—2441no—
130C4—2441no—
131C4#1451973911yescharacteristic
132C4#1451980411yescharacteristic
133C2—21no—
134C2—4882no—
135C2—4881no—
136C2#1683987311yescharacteristic
subgroupG/H
centerC2#16839873
commutatorC8×C61C22×C4
FrattiniC2×C8C22×D61
FittingC61×#365C2
socleC2×C61#442
hypercenter#365D61
hypocenterC61AGL(1,ℤ/16)
LCSG ▷ C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #365

Complements

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

NH ≅ G/Ntype
2. #16839883C2semidirect
3. #16839873C2semidirect
4. #16839574C2semidirect
5. #16839571C2semidirect
6. #16839539C2semidirect
7. C61×#365C2semidirect
12. #14519722C4semidirect
13. D976C4semidirect
30. Dic244C2×C4semidirect
33. D488C2×C4semidirect
37. C16×C61C2×C4semidirect
72. #365D61semidirect
76. C61AGL(1,ℤ/16)semidirect
107. C16C4×D61semidirect