Finite Group Databasebeta

← #21447685

Subgroups — #21447685

Order 7808.

160 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 61 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
1C2×#14519722C211yesmaximal, characteristic
2C4×Dic244C211yesmaximal, characteristic, complemented
3C4×D488C211yesmaximal, characteristic
4#16839588C211yesmaximal, characteristic, complemented
5#16839567C211yesmaximal, characteristic, complemented
6#16839564C211yesmaximal, characteristic
7C61×#346C211yesmaximal, characteristic, complemented
8C2×Dic244C2211yescharacteristic
9C2×D488C2211yescharacteristic
10C4×Dic122—21no—
11C4×D244—21no—
12#14519722C414yescomplemented
13#14519711C2211yescharacteristic
14#14519711C2211yescharacteristic
15#14519702—21no—
16#14519699—21no—
17C2×C16×C61C2211yescharacteristic
18C2×C16×C61C2211yescharacteristic
19C4×C8×C61C2211yescharacteristic
20C2×D244—21no—
21C2×C4×D61—41no—
22C2×Dic122—21no—
23C2×C8×C61D411yescharacteristic
24C2×C8×C61C2311yescharacteristic
25C42×C61D411yescharacteristic
26#11758198—41no—
27C4⋊Dic61—21no—
28C4⋊Dic61—21no—
29#11758196—41no—
30C4×Dic61—41no—
31Dic244—21no—
32Dic244C2×C412yescomplemented
33D488—21no—
34D488C2×C412yes—
35C16×C61—21no—
36C16×C61C2×C412yescomplemented
37C22×D61—41no—
38C2×C4×C61D811yescharacteristic
39C2×C4×C61D811yescharacteristic
40C2×C4×C61C2×D411yescharacteristic
41C2×Dic61—41no—
42C2×Dic61—41no—
43C2×Dic61—41no—
44D244—22no—
45D244—41no—
46C4×D61—82no—
47Dic122—22no—
48Dic122—41no—
49C8×C61—21no—
50C8×C61C22×C411yescharacteristic
51C8×C61#4111yescharacteristic
52C22×C61C2×D811yescharacteristic
53C2×D61—42no—
54C2×D61—81no—
55C2×D61—81no—
56C4×C61—21no—
57C4×C61—21no—
58C4×C61C4×D411yescharacteristic
59C4×C61#13511yescharacteristic
60Dic61—42no—
61Dic61—81no—
62Dic61—81no—
63#2175—611nomaximal, Sylow
64C2×C61C4×D811yescharacteristic
65C2×C61#50911yescharacteristic
66C2×C61#51011yescharacteristic
67D61—82no—
68C2×SD32—611no—
69C4×Q16—611no—
70C4×D8—611no—
71#366—611no—
72#358—611no—
73#357—611no—
74#346D6111yescharacteristic, complemented
75C61#217511yescharacteristic, complemented, Sylow
76C2×Q16—611no—
77C2×D8—611no—
78C4×Q8—1221no—
79C4×D4—1221no—
80SD32—614no—
81C2×C16C2×D6111yescharacteristic
82C2×C16C2×D6111yescharacteristic
83#107—611no—
84#107—611no—
85#103—1221no—
86#102—1221no—
87C4×C8C2×D6111yescharacteristic
88C2×Q8—1221no—
89C2×D4—1221no—
90C22×C4—2441no—
91Q16—612no—
92Q16—1221no—
93D8—612no—
94D8—1221no—
95C2×C8D24411yescharacteristic
96C2×C8C22×D6111yescharacteristic
97C4⋊C4—1221no—
98C4⋊C4—1221no—
99C4⋊C4—2441no—
100C22⋊C4—2441no—
101C42—2441no—
102C42D24411yescharacteristic
103C16—21no—
104C16C4×D6112yescomplemented
105C23—2441no—
106Q8—1222no—
107Q8—2441no—
108D4—1222no—
109D4—2441no—
110C2×C4—4882no—
111C2×C4—2441no—
112C2×C4—2441no—
113C2×C4—2441no—
114C2×C4D48811yescharacteristic
115C2×C4D48811yescharacteristic
116C2×C4C2×D24411yescharacteristic
117C8—21no—
118C8C2×C4×D6111yescharacteristic
119C8#1175822211yescharacteristic
120C22—4881no—
121C22—4881no—
122C22—2442no—
123C22C2×D48811yescharacteristic
124C4—21no—
125C4—21no—
126C4—4881no—
127C4—4881no—
128C4—2442no—
129C4C4×D24411yescharacteristic
130C4#1451979911yescharacteristic
131C2—4882no—
132C2C4×D48811yescharacteristic
133C2#1684020011yescharacteristic
134C2#1684020511yescharacteristic
subgroupG/H
centerC22C2×D488
commutatorC8×C61C22×C4
FrattiniC2×C8C22×D61
FittingC61×#346C2
socleC22×C61C2×D8
hypercenter#346D61
hypocenterC61#2175
LCSG ▷ C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #346

Complements

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

NH ≅ G/Ntype
2. C4×Dic244C2semidirect
4. #16839588C2semidirect
5. #16839567C2semidirect
7. C61×#346C2semidirect
12. #14519722C4semidirect
32. Dic244C2×C4semidirect
36. C16×C61C2×C4semidirect
74. #346D61semidirect
75. C61#2175semidirect
104. C16C4×D61semidirect