Finite Group Databasebeta

← #21448035

Subgroups — #21448035

Order 7808.

134 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 134 conjugacy classes of subgroups — too many to draw. Only its 41 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#16840016C211yesmaximal, characteristic
2#16839809C211yesmaximal, characteristic, complemented
3#16839584C211yesmaximal, characteristic, complemented
4#16839576C211yesmaximal, characteristic, complemented
5#16839574C211yesmaximal, characteristic, complemented
6#16839543C211yesmaximal, characteristic, complemented
7C61×#365C211yesmaximal, characteristic, complemented
8C2×D488C2211yescharacteristic
9C2×#11758189C2211yescharacteristic
10M16×D61—21no—
11#14519752—21no—
12#14519717C2211yescharacteristic
13#14519713C2211yescharacteristic
14#14519712—21no—
15#14519697—21no—
16M32×C61C2211yescharacteristic
17#108×C61C2211yescharacteristic
18#106×C61C2211yescharacteristic
19C2×D244—21no—
20C2×D244—41no—
21C2×C4×D61D411yescharacteristic
22M16×C61—21no—
23C2×C8×C61C2311yescharacteristic
24C4⋊C4×C61—21no—
25#11758198—41no—
26#11758194—21no—
27C2×#92418D411yescharacteristic
28D488—21no—
29D488—21no—
30#11758189—21no—
31#11758189—21no—
32#11758189—41no—
33C8×D61—41no—
34C16×C61—21no—
35#11758185—21no—
36C22×D61—41no—
37C22×D61SD1611yescharacteristic
38C2×C4×C61—41no—
39C2×C4×C61C2×D411yescharacteristic
40C2×Dic61SD1611yescharacteristic
41D244—41no—
42D244—41no—
43D244—82no—
44C4×D61—21no—
45C4×D61—21no—
46C8×C61—41no—
47C8×C61#4111yescharacteristic
48C8×C61#4111yescharacteristic
49#92418—21no—
50#92418—41no—
51C22×C61C2×SD1611yescharacteristic
52C2×D61—21no—
53C2×D61—41no—
54C2×D61—81no—
55C2×D61—81no—
56C2×D61—81no—
57C4×C61—81no—
58C4×C61#12311yescharacteristic
59C4×C61AGL(1,ℤ/8)11yescharacteristic
60Dic61—21no—
61#2238—611nomaximal, Sylow
62C2×C61—21no—
63C2×C61#48111yescharacteristic
64D61—41no—
65D61—161no—
66#469—611no—
67#430—611no—
68#365—611no—
69#365D6111yescharacteristic, complemented
70#361—611no—
71#361—611no—
72#349—611no—
73C61#223811yescharacteristic, complemented, Sylow
74C2×D8—611no—
75C2×M16—611no—
76C2×M16—1221no—
77#121—1221no—
78M32—611no—
79M32C2×D6111yescharacteristic
80#108—611no—
81#108—1221no—
82#108C2×D6111yescharacteristic
83#106C2×D6111yescharacteristic
84#102—1221no—
85C2×D4—1221no—
86C2×D4—2441no—
87C22×C4—611no—
88D8—1221no—
89D8—1221no—
90M16—21no—
91M16—1221no—
92M16—1221no—
93M16—1221no—
94M16—2441no—
95C2×C8—611no—
96C2×C8—2441no—
97C2×C8C22×D6111yescharacteristic
98C4⋊C4—21no—
99C22⋊C4—2441no—
100C16—21no—
101C16—1221no—
102C23—611no—
103C23—2441no—
104D4—4882no—
105D4—2441no—
106D4—2441no—
107C2×C4—41no—
108C2×C4—611no—
109C2×C4—1221no—
110C2×C4—1221no—
111C2×C4D4×D6111yescharacteristic
112C8—41no—
113C8—1221no—
114C8—2441no—
115C8#1175822211yescharacteristic
116C8#1175822611yescharacteristic
117C22—1221no—
118C22—4881no—
119C22—4881no—
120C22—4881no—
121C22—2441no—
122C22SD16×D6111yescharacteristic
123C4—81no—
124C4—1221no—
125C4#1451976211yescharacteristic
126C4#1451980411yescharacteristic
127C2—21no—
128C2—9761no—
129C2—2441no—
130C2#1684008211yescharacteristic
subgroupG/H
centerC2#16840082
commutatorC2×C8×C61C23
FrattiniC2×C8C22×D61
FittingC61×#365C2
socleC2×C61#481
hypercenter#365D61
hypocenterC61#2238
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #365

Complements

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

NH ≅ G/Ntype
2. #16839809C2semidirect
3. #16839584C2semidirect
4. #16839576C2semidirect
5. #16839574C2semidirect
6. #16839543C2semidirect
7. C61×#365C2semidirect
69. #365D61semidirect
73. C61#2238semidirect