Finite Group Databasebeta

← #21447670

Subgroups — #21447670

Order 7808.

162 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 162 conjugacy classes of subgroups — too many to draw. Only its 59 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
2#16839856C211yesmaximal, characteristic, complemented
3#16839844C211yesmaximal, characteristic
4#16839565C211yesmaximal, characteristic, complemented
5#16839562C211yesmaximal, characteristic
6C16×Dic61C211yesmaximal, characteristic, complemented
7C61×#367C211yesmaximal, characteristic, complemented
8C2×Dic244C2211yescharacteristic
9C2×D488C2211yescharacteristic
10#14519742—21no—
11#14519739—21no—
12#14519722C414yescomplemented
13C2×#11758185C2211yescharacteristic
14#14519700—21no—
15#14519697—21no—
16C8×Dic61C2211yescharacteristic
17C2×C16×C61C2211yescharacteristic
18#107×C61C2211yescharacteristic
19#107×C61C2211yescharacteristic
20C2×D244—21no—
21C2×C4×D61—41no—
22C2×Dic122—21no—
23C2×C8×C61C2311yescharacteristic
24C4⋊C4×C61—21no—
25C4⋊C4×C61—21no—
26#11758198—41no—
27#11758196—41no—
28C4×Dic61—41no—
29C4×Dic61D411yescharacteristic
30C2×#92418D411yescharacteristic
31Dic244—21no—
32Dic244C2×C412yescomplemented
33D488—21no—
34D488C2×C412yes—
35C16×C61C2×C412yescomplemented
36#11758185—21no—
37C22×D61—41no—
38C2×C4×C61—41no—
39C2×C4×C61—41no—
40C2×C4×C61C2×D411yescharacteristic
41C2×Dic61—41no—
42C2×Dic61D811yescharacteristic
43C2×Dic61D811yescharacteristic
44D244—22no—
45D244—41no—
46C4×D61—82no—
47Dic122—22no—
48Dic122—41no—
49C8×C61C22×C411yescharacteristic
50C8×C61#4111yescharacteristic
51#92418—21no—
52C22×C61C2×D811yescharacteristic
53C2×D61—42no—
54C2×D61—81no—
55C2×D61—81no—
56C4×C61—81no—
57C4×C61—81no—
58C4×C61C4×D411yescharacteristic
59C4×C61#13511yescharacteristic
60Dic61—21no—
61Dic61—42no—
62Dic61SD3212yescomplemented
63C4×SD32—611nomaximal, Sylow
64C2×C61C4×D811yescharacteristic
65C2×C61C2×SD3211yescharacteristic
66C2×C61#50811yescharacteristic
67D61—82no—
68C2×SD32—611no—
69C4×Q16—611no—
70C4×D8—611no—
71#367D6111yescharacteristic, complemented
72#358—611no—
73#357—611no—
74C4×C16—611no—
75C61C4×SD3211yescharacteristic, complemented, Sylow
76C2×Q16—611no—
77C2×D8—611no—
78C4×Q8—1221no—
79C4×D4—1221no—
80SD32—614no—
81C2×C16—611no—
82C2×C16C2×D6111yescharacteristic
83#107C2×D6111yescharacteristic
84#107C2×D6111yescharacteristic
85#103—1221no—
86#102—1221no—
87C4×C8—611no—
88C2×Q8—1221no—
89C2×D4—1221no—
90C22×C4—2441no—
91Q16—612no—
92Q16—1221no—
93D8—612no—
94D8—1221no—
95C2×C8—611no—
96C2×C8C22×D6111yescharacteristic
97C4⋊C4—21no—
98C4⋊C4—21no—
99C4⋊C4—2441no—
100C22⋊C4—2441no—
101C42—611no—
102C42—2441no—
103C16—1221no—
104C16C4×D6112yescomplemented
105C23—2441no—
106Q8—1222no—
107Q8—2441no—
108D4—1222no—
109D4—2441no—
110C2×C4—41no—
111C2×C4—41no—
112C2×C4—611no—
113C2×C4—611no—
114C2×C4—4882no—
115C2×C4—2441no—
116C2×C4D4×D6111yescharacteristic
117C8—1221no—
118C8C2×C4×D6111yescharacteristic
119C8#1175822611yescharacteristic
120C22—4881no—
121C22—4881no—
122C22—2442no—
123C22D8×D6111yescharacteristic
124C4—81no—
125C4—81no—
126C4—612no—
127C4—1221no—
128C4—2442no—
129C4#1451973911yescharacteristic
130C4#1451980011yescharacteristic
131C2—4882no—
132C2#1683984411yescharacteristic
133C2SD32×D6111yescharacteristic
134C2#1684019311yescharacteristic
subgroupG/H
centerC22D8×D61
commutatorC8×C61C22×C4
FrattiniC2×C8C22×D61
FittingC61×#367C2
socleC22×C61C2×D8
hypercenter#367D61
hypocenterC61C4×SD32
LCSG ▷ C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #367

Complements

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

NH ≅ G/Ntype
2. #16839856C2semidirect
4. #16839565C2semidirect
6. C16×Dic61C2semidirect
7. C61×#367C2semidirect
12. #14519722C4semidirect
32. Dic244C2×C4semidirect
35. C16×C61C2×C4semidirect
62. Dic61SD32semidirect
71. #367D61semidirect
75. C61C4×SD32semidirect
104. C16C4×D61semidirect