Finite Group Databasebeta

← #21447708

Subgroups — #21447708

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#16840203C211yesmaximal, characteristic
2#16839885C211yesmaximal, characteristic
3#16839584C211yesmaximal, characteristic, complemented
4#16839578C211yesmaximal, characteristic, complemented
5#16839571C211yesmaximal, characteristic
6#16839540C211yesmaximal, characteristic, complemented
7C61×#441C211yesmaximal, characteristic, complemented
8#14519799C2211yescharacteristic
9#14519783—21no—
10#14519723C412yescomplemented
11#14519720C412yescomplemented
12#14519717C2211yescharacteristic
13#14519717C2211yescharacteristic
14#14519713C2211yescharacteristic
15#14519705—21no—
16C2×Q16×C61C2211yescharacteristic
17C4×Q8×C61—21no—
18#106×C61C2211yescharacteristic
19#103×C61—21no—
20#97×C61C2211yescharacteristic
21C2×Q8×C61—21no—
22#11758222—21no—
23Q16×C61—21no—
24Q16×C61C2×C412yes—
25C2×C8×C61D411yescharacteristic
26C2×C8×C61C2311yescharacteristic
27C4⋊C4×C61—21no—
28C4⋊C4×C61—41no—
29C42×C61—41no—
30C42×C61D411yescharacteristic
31#11758194—21no—
32Dic244C2×C411yescharacteristic
33D488C2×C411yescharacteristic
34#11758190—21no—
35#11758189—41no—
36C8×D61—41no—
37#11758185—21no—
38#11758185C2×C412yes—
39Q8×C61—22no—
40Q8×C61—41no—
41C2×C4×C61—21no—
42C2×C4×C61—41no—
43C2×C4×C61—41no—
44C2×C4×C61C2×D411yescharacteristic
45C22⋊D61—41no—
46D244—21no—
47C4×D61—41no—
48Dic122—21no—
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×C61—42no—
57C4×C61—81no—
58C4×C61C4×D411yescharacteristic
59C4×C61AGL(1,ℤ/8)11yescharacteristic
60Dic61—41no—
61#2180—611nomaximal, Sylow
62C2×C61—21no—
63C2×C61#44211yescharacteristic
64D61—81no—
65#510—611no—
66#444—611no—
67#441D6111yescharacteristic, complemented
68#365—611no—
69#362—611no—
70#360—611no—
71#347—611no—
72C61#218011yescharacteristic, complemented, Sylow
73#135—611no—
74C2×Q16C2×D6111yescharacteristic
75#131—1221no—
76C4×Q8—21no—
77Q32—612no—
78SD32—612no—
79M32—611no—
80M32—611no—
81#108—611no—
82#106C2×D6111yescharacteristic
83#104—1221no—
84#103—21no—
85#97C2×D6111yescharacteristic
86#41—1221no—
87C2×Q8—21no—
88Q16—21no—
89Q16—611no—
90Q16C4×D6112yes—
91SD16—1221no—
92D8—611no—
93M16—1221no—
94M16—2441no—
95C2×C8—2441no—
96C2×C8C22⋊D6111yescharacteristic
97C2×C8C22×D6111yescharacteristic
98C4⋊C4—21no—
99C4⋊C4—41no—
100C42—41no—
101C42C22⋊D6111yescharacteristic
102C16—612no—
103C16—1221no—
104Q8—22no—
105Q8—41no—
106Q8—1221no—
107D4—1221no—
108D4—2441no—
109C2×C4—21no—
110C2×C4—41no—
111C2×C4—41no—
112C2×C4—2441no—
113C2×C4C2×C22⋊D6111yescharacteristic
114C8—21no—
115C8—2441no—
116C8C2×C4×D6111yescharacteristic
117C8#1175822211yescharacteristic
118C22—2441no—
119C22#1451980311yescharacteristic
120C4—41no—
121C4—42no—
122C4—81no—
123C4—2441no—
124C4C4×C22⋊D6111yescharacteristic
125C4#1451980211yescharacteristic
126C2—21no—
127C2—4881no—
128C2#1683987211yescharacteristic
subgroupG/H
centerC2#16839872
commutatorC8×C61C22×C4
FrattiniC2×C8C22×D61
FittingC61×#441C2
socleC2×C61#442
hypercenter#441D61
hypocenterC61#2180
LCSG ▷ C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ #97 ◁ #441

Complements

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

NH ≅ G/Ntype
3. #16839584C2semidirect
4. #16839578C2semidirect
6. #16839540C2semidirect
7. C61×#441C2semidirect
10. #14519723C4semidirect
11. #14519720C4semidirect
67. #441D61semidirect
72. C61#2180semidirect