Finite Group Databasebeta

← #21447996

Subgroups — #21447996

Order 7808.

120 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 47 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#16840164C211yesmaximal, characteristic, complemented
2#16839880C211yesmaximal, characteristic
3#16839585C212yesmaximal, complemented
4#16839573C212yesmaximal
5C61×#364C211yesmaximal, characteristic, complemented
6#14519799C2211yescharacteristic
7#14519783—21no—
8#14519769—21no—
9#14519713C2211yescharacteristic
10#14519711—21no—
11#14519709C2212yes—
12#14519705—21no—
13M32×C61C2212yes—
14C4×C8×C61C2211yescharacteristic
15#11758222—21no—
16C2×C8×C61D411yescharacteristic
17C2×C8×C61C2311yescharacteristic
18C42×C61D411yescharacteristic
19C4⋊Dic61—22no—
20#11758196—42no—
21#11758194—21no—
22Dic244Q811yescharacteristic
23D488Q811yescharacteristic
24#11758190—21no—
25#11758189—41no—
26C8×D61—41no—
27C16×C61—22no—
28C2×C4×C61—21no—
29C2×C4×C61C2×D411yescharacteristic
30C22⋊D61—41no—
31C2×Dic61—42no—
32D244—21no—
33C4×D61—41no—
34Dic122—21no—
35C8×C61SD1611yescharacteristic
36C8×C61SD1611yescharacteristic
37C8×C61C2×Q811yescharacteristic
38C8×C61#4111yescharacteristic
39#92418—41no—
40C22×C61AGL(1,ℤ/8)11yescharacteristic
41C2×D61—41no—
42C4×C61—41no—
43C4×C61C22⋊Q811yescharacteristic
44C4×C61C2×SD1611yescharacteristic
45Dic61—41no—
46Dic61—82no—
47#2231—611nomaximal, Sylow
48C2×C61—21no—
49C2×C61#47611yescharacteristic
50D61—81no—
51#499—611no—
52#443—611no—
53#365—612no—
54#364D6111yescharacteristic, complemented
55#360—612no—
56C61#223111yescharacteristic, complemented, Sylow
57#135—611no—
58#131—1221no—
59#125—1221no—
60M32C2×D6112yes—
61#108—611no—
62#107—1221no—
63#106—612no—
64#104—1221no—
65C4×C8C2×D6111yescharacteristic
66#41—1221no—
67Q16—611no—
68SD16—1221no—
69D8—611no—
70M16—1221no—
71M16—2441no—
72C2×C8—2441no—
73C2×C8D24411yescharacteristic
74C2×C8C22×D6111yescharacteristic
75C4⋊C4—1222no—
76C4⋊C4—2442no—
77C42D24411yescharacteristic
78C16—22no—
79Q8—1221no—
80D4—1221no—
81D4—2441no—
82C2×C4—21no—
83C2×C4—2442no—
84C2×C4—2441no—
85C2×C4C2×D24411yescharacteristic
86C8—2441no—
87C8#1175819011yescharacteristic
88C8#1175819011yescharacteristic
89C8#1175822411yescharacteristic
90C8Q8×D6111yescharacteristic
91C22—2441no—
92C22#1451980511yescharacteristic
93C4—41no—
94C4—4882no—
95C4—2441no—
96C4#1451975711yescharacteristic
97C4C2×#1175819011yescharacteristic
98C2—21no—
99C2—4881no—
100C2#1684005311yescharacteristic
subgroupG/H
centerC2#16840053
commutatorC2×C8×C61C23
FrattiniC2×C8C22×D61
FittingC61×#364C2
socleC2×C61#476
hypercenter#364D61
hypocenterC61#2231
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #364

Complements

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

NH ≅ G/Ntype
1. #16840164C2semidirect
3. #16839585C2semidirect
5. C61×#364C2semidirect
54. #364D61semidirect
56. C61#2231semidirect