Finite Group Databasebeta

← #21447900

Subgroups — #21447900

Order 7808.

150 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 150 conjugacy classes of subgroups — too many to draw. Only its 49 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#16840202C212yesmaximal
2#16840142C211yesmaximal, characteristic, complemented
3#16839583C211yesmaximal, characteristic, complemented
4#16839577C212yesmaximal, complemented
5C61×#443C211yesmaximal, characteristic
6C2×Dic244—21no—
7C2×Dic244C2212yes—
8#14519777—21no—
9#14519723—22no—
10#14519721—22no—
11#14519717C2212yes—
12#135×C61C2211yescharacteristic
13#131×C61—21no—
14#108×C61C2211yescharacteristic
15#104×C61—21no—
16C4×C8×C61C2211yescharacteristic
17#41×C61—21no—
18C2×Dic122—22no—
19Q16×C61D411yescharacteristic
20SD16×C61—21no—
21D8×C61D411yescharacteristic
22M16×C61—21no—
23M16×C61—41no—
24C2×C8×C61—41no—
25C2×C8×C61D411yescharacteristic
26C2×C8×C61C2311yescharacteristic
27C42×C61D411yescharacteristic
28C4⋊Dic61—42no—
29Dic244—22no—
30Dic244—22no—
31Dic244—41no—
32Dic244—41no—
33#11758185—22no—
34Q8×C61—21no—
35D4×C61—21no—
36D4×C61—41no—
37C2×C4×C61—21no—
38C2×C4×C61—41no—
39C2×C4×C61C2×D411yescharacteristic
40C2×Dic61—42no—
41Dic122—42no—
42Dic122—42no—
43C8×C61—41no—
44C8×C61D811yescharacteristic
45C8×C61D811yescharacteristic
46C8×C61C2×D411yescharacteristic
47C8×C61#4111yescharacteristic
48C22×C61—41no—
49C22×C61AGL(1,ℤ/8)11yescharacteristic
50C4×C61—22no—
51C4×C61—41no—
52C4×C61#12111yescharacteristic
53C4×C61C2×D811yescharacteristic
54Dic61—82no—
55#2214—611nomaximal, Sylow
56C2×C61—21no—
57C2×C61—81no—
58C2×C61#45911yescharacteristic
59#510—612no—
60#494—611no—
61#443D6111yescharacteristic
62#364—611no—
63#362—612no—
64C61#221411yescharacteristic, complemented, Sylow
65#135C2×D6111yescharacteristic
66C2×Q16—612no—
67C2×Q16—1221no—
68#131—21no—
69C4⋊Q8—1221no—
70Q32—1222no—
71SD32—1222no—
72M32—612no—
73#108C2×D6111yescharacteristic
74#104—21no—
75C4×C8C2×D6111yescharacteristic
76#41—21no—
77C2×Q8—1222no—
78Q16—1222no—
79Q16—1222no—
80Q16—2441no—
81Q16—2441no—
82Q16D24411yescharacteristic
83SD16—21no—
84D8D24411yescharacteristic
85M16—21no—
86M16—41no—
87C2×C8—41no—
88C2×C8C22⋊D6111yescharacteristic
89C2×C8C22×D6111yescharacteristic
90C4⋊C4—2442no—
91C42C22⋊D6111yescharacteristic
92C16—1222no—
93Q8—21no—
94Q8—2442no—
95Q8—2442no—
96D4—21no—
97D4—41no—
98C2×C4—21no—
99C2×C4—41no—
100C2×C4—2442no—
101C2×C4C2×C22⋊D6111yescharacteristic
102C8—41no—
103C8#1175819911yescharacteristic
104C8#1175819911yescharacteristic
105C8C2×D24411yescharacteristic
106C8#1175822211yescharacteristic
107C22—41no—
108C22#1451980211yescharacteristic
109C4—22no—
110C4—41no—
111C4—4882no—
112C4#1451975111yescharacteristic
113C4C2×#1175819911yescharacteristic
114C2—21no—
115C2—81no—
116C2#1683995711yescharacteristic
subgroupG/H
centerC2#16839957
commutatorC2×C8×C61C23
FrattiniC2×C8C22×D61
FittingC61×#443C2
socleC2×C61#459
hypercenter#443D61
hypocenterC61#2214
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #443

Complements

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

NH ≅ G/Ntype
2. #16840142C2semidirect
3. #16839583C2semidirect
4. #16839577C2semidirect
64. C61#2214semidirect