Finite Group Databasebeta

← #21447712

Subgroups — #21447712

Order 7808.

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

normal subgroups only

This group has 142 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#16840205C211yesmaximal, characteristic
2#16839885C211yesmaximal, characteristic
3#16839870C211yesmaximal, characteristic, complemented
4#16839585C211yesmaximal, characteristic, complemented
5#16839579C211yesmaximal, characteristic, complemented
6#16839573C211yesmaximal, characteristic
7C61×#347C211yesmaximal, characteristic, complemented
8#14519799C2211yescharacteristic
9C2×Dic244C2211yescharacteristic
10#14519783—21no—
11C4×Dic122—21no—
12Dic488C412yescomplemented
13#14519722C412yescomplemented
14#14519713C2211yescharacteristic
15#14519709C2211yescharacteristic
16#14519705—21no—
17#14519702—21no—
18M32×C61C2211yescharacteristic
19M32×C61C2211yescharacteristic
20#97×C61C2211yescharacteristic
21#11758222—21no—
22C2×Dic122—21no—
23C2×C8×C61D411yescharacteristic
24C2×C8×C61C2311yescharacteristic
25C42×C61D411yescharacteristic
26C4⋊Dic61—21no—
27#11758196—41no—
28C4×Dic61—41no—
29#11758194—21no—
30Dic244—21no—
31Dic244C2×C412yes—
32Dic244C2×C411yescharacteristic
33D488C2×C411yescharacteristic
34#11758190—21no—
35#11758189—41no—
36C8×D61—41no—
37C16×C61—21no—
38C16×C61C2×C412yes—
39C2×C4×C61—21no—
40C2×C4×C61C2×D411yescharacteristic
41C22⋊D61—41no—
42C2×Dic61—41no—
43C2×Dic61—41no—
44D244—21no—
45C4×D61—41no—
46Dic122—21no—
47Dic122—22no—
48Dic122—41no—
49C8×C61—21no—
50C8×C61C22×C411yescharacteristic
51C8×C61#4111yescharacteristic
52#92418—41no—
53C22×C61AGL(1,ℤ/8)11yescharacteristic
54C2×D61—41no—
55C4×C61—41no—
56C4×C61C4×D411yescharacteristic
57C4×C61AGL(1,ℤ/8)11yescharacteristic
58Dic61—42no—
59Dic61—41no—
60Dic61—81no—
61#2180—611nomaximal, Sylow
62C2×C61—21no—
63C2×C61#44211yescharacteristic
64D61—81no—
65#510—611no—
66#444—611no—
67#441—611no—
68#365—611no—
69#362—611no—
70#360—611no—
71#347D6111yescharacteristic, complemented
72C61#218011yescharacteristic, complemented, Sylow
73#135—611no—
74C2×Q16—611no—
75#131—1221no—
76C4×Q8—1221no—
77Q32—612no—
78SD32—612no—
79M32C2×D6111yescharacteristic
80M32C2×D6111yescharacteristic
81#108—611no—
82#106—611no—
83#104—1221no—
84#103—1221no—
85#97C2×D6111yescharacteristic
86#41—1221no—
87C2×Q8—1221no—
88Q16—612no—
89Q16—611no—
90Q16—1221no—
91SD16—1221no—
92D8—611no—
93M16—1221no—
94M16—2441no—
95C2×C8—2441no—
96C2×C8D24411yescharacteristic
97C2×C8C22×D6111yescharacteristic
98C4⋊C4—1221no—
99C4⋊C4—2441no—
100C42—2441no—
101C42D24411yescharacteristic
102C16—21no—
103C16C4×D6112yes—
104Q8—1221no—
105Q8—1222no—
106Q8—2441no—
107D4—1221no—
108D4—2441no—
109C2×C4—21no—
110C2×C4—2441no—
111C2×C4—2441no—
112C2×C4—2441no—
113C2×C4C2×D24411yescharacteristic
114C8—21no—
115C8—2441no—
116C8C2×C4×D6111yescharacteristic
117C8#1175822211yescharacteristic
118C22—2441no—
119C22#1451980511yescharacteristic
120C4—41no—
121C4—4881no—
122C4—2441no—
123C4—2442no—
124C4C4×D24411yescharacteristic
125C4#1451980511yescharacteristic
126C2—21no—
127C2—4881no—
128C2#1683987511yescharacteristic
subgroupG/H
centerC2#16839875
commutatorC8×C61C22×C4
FrattiniC2×C8C22×D61
FittingC61×#347C2
socleC2×C61#442
hypercenter#347D61
hypocenterC61#2180
LCSG ▷ C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ #97 ◁ #347

Complements

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

NH ≅ G/Ntype
3. #16839870C2semidirect
4. #16839585C2semidirect
5. #16839579C2semidirect
7. C61×#347C2semidirect
12. Dic488C4semidirect
13. #14519722C4semidirect
71. #347D61semidirect
72. C61#2180semidirect