Finite Group Databasebeta

← #21447715

Subgroups — #21447715

Order 7808.

154 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 154 conjugacy classes of subgroups — too many to draw. Only its 53 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#16840198C211yesmaximal, characteristic
2#16839885C211yesmaximal, characteristic, complemented
3#16839584C211yesmaximal, characteristic, complemented
4#16839575C211yesmaximal, characteristic, complemented
5#16839571C211yesmaximal, characteristic, complemented
6#16839540C211yesmaximal, characteristic, complemented
7C61×#442C211yesmaximal, characteristic, complemented
8#14519799C2211yescharacteristic
9#14519783—21no—
10#14519721C412yescomplemented
11#14519718C412yescomplemented
12#14519717C2211yescharacteristic
13#14519717C2211yescharacteristic
14#14519713C2211yescharacteristic
15#14519705—21no—
16C2×D8×C61C2211yescharacteristic
17C4×D4×C61—21no—
18#106×C61C2211yescharacteristic
19#102×C61—21no—
20#97×C61C2211yescharacteristic
21C2×D4×C61—21no—
22C22×C4×C61—41no—
23#11758222—21no—
24D8×C61—21no—
25D8×C61C2×C412yes—
26C2×C8×C61D411yescharacteristic
27C2×C8×C61C2311yescharacteristic
28C4⋊C4×C61—21no—
29C22⋊C4×C61—41no—
30C42×C61D411yescharacteristic
31#11758194—21no—
32Dic244C2×C411yescharacteristic, complemented
33D488C2×C411yescharacteristic, complemented
34#11758190—21no—
35#11758189—41no—
36C8×D61—41no—
37#11758185—21no—
38#11758185C2×C412yescomplemented
39C23×C61—41no—
40D4×C61—22no—
41D4×C61—41no—
42C2×C4×C61—21no—
43C2×C4×C61—41no—
44C2×C4×C61—82no—
45C2×C4×C61C2×D411yescharacteristic
46C22⋊D61—41no—
47D244—21no—
48C4×D61—41no—
49Dic122—21no—
50C8×C61—21no—
51C8×C61C22×C411yescharacteristic
52C8×C61#4111yescharacteristic
53#92418—41no—
54C22×C61—42no—
55C22×C61—81no—
56C22×C61—81no—
57C22×C61AGL(1,ℤ/8)11yescharacteristic
58C2×D61—41no—
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—82no—
67C2×C61#44211yescharacteristic
68D61—81no—
69#509—611no—
70#444—611no—
71#442D6111yescharacteristic, complemented
72#365—611no—
73#361—611no—
74#360—611no—
75#347—611no—
76C61AGL(1,ℤ/16)11yescharacteristic, complemented, Sylow
77#135—611no—
78C2×D8C2×D6111yescharacteristic
79#131—1221no—
80C4×D4—21no—
81SD32—612no—
82D16—612no—
83M32—611no—
84M32—611no—
85#108—611no—
86#106C2×D6111yescharacteristic
87#104—1221no—
88#102—21no—
89#97C2×D6111yescharacteristic
90#41—1221no—
91C2×D4—21no—
92C22×C4—41no—
93Q16—611no—
94SD16—1221no—
95D8—21no—
96D8—611no—
97D8C4×D6112yes—
98M16—1221no—
99M16—2441no—
100C2×C8—2441no—
101C2×C8C22⋊D6111yescharacteristic
102C2×C8C22×D6111yescharacteristic
103C4⋊C4—21no—
104C22⋊C4—41no—
105C42C22⋊D6111yescharacteristic
106C16—612no—
107C16—1221no—
108C23—41no—
109Q8—1221no—
110D4—22no—
111D4—41no—
112D4—1221no—
113D4—2441no—
114C2×C4—21no—
115C2×C4—41no—
116C2×C4—82no—
117C2×C4—2441no—
118C2×C4C2×C22⋊D6111yescharacteristic
119C8—21no—
120C8—2441no—
121C8C2×C4×D6111yescharacteristic
122C8#1175822211yescharacteristic
123C22—42no—
124C22—81no—
125C22—81no—
126C22—2441no—
127C22#1451980311yescharacteristic
128C4—41no—
129C4—81no—
130C4—2441no—
131C4C4×C22⋊D6111yescharacteristic
132C4#1451980211yescharacteristic
133C2—21no—
134C2—82no—
135C2—4881no—
136C2#1683987211yescharacteristic
subgroupG/H
centerC2#16839872
commutatorC8×C61C22×C4
FrattiniC2×C8C22×D61
FittingC61×#442C2
socleC2×C61#442
hypercenter#442D61
hypocenterC61AGL(1,ℤ/16)
LCSG ▷ C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ #97 ◁ #442

Complements

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

NH ≅ G/Ntype
2. #16839885C2semidirect
3. #16839584C2semidirect
4. #16839575C2semidirect
5. #16839571C2semidirect
6. #16839540C2semidirect
7. C61×#442C2semidirect
10. #14519721C4semidirect
11. #14519718C4semidirect
32. Dic244C2×C4semidirect
33. D488C2×C4semidirect
38. #11758185C2×C4semidirect
71. #442D61semidirect
76. C61AGL(1,ℤ/16)semidirect