Finite Group Databasebeta

← #21448057

Subgroups — #21448057

Order 7808.

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

normal subgroups only

This group has 142 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#16840166C211yesmaximal, characteristic, complemented
2#16840147C211yesmaximal, characteristic
3#16839566C211yesmaximal, characteristic, complemented
4#16839564C211yesmaximal, characteristic
5#16839562C211yesmaximal, characteristic
6#16839537C211yesmaximal, characteristic, complemented
7C61×#358C211yesmaximal, characteristic, complemented
8C2×#11758201—21no—
9C2×D488C2211yescharacteristic
10#14519776—21no—
11#14519766—21no—
12C2×#11758185C2211yescharacteristic
13#14519711C2211yescharacteristic
14#14519710—21no—
15C8×Dic61C2211yescharacteristic
16C2×Q16×C61C2211yescharacteristic
17C2×C16×C61C2211yescharacteristic
18#107×C61C2211yescharacteristic
19C2×Q8×C61—21no—
20C2×D244—21no—
21C2×Dic122—41no—
22Q16×C61—21no—
23Q16×C61—21no—
24C2×C8×C61C2311yescharacteristic
25C4⋊C4×C61—21no—
26#11758201—42no—
27#11758198—41no—
28#11758198—41no—
29C4⋊Dic61—21no—
30#11758196—41no—
31C4×Dic61D411yescharacteristic
32C2×#92418D411yescharacteristic
33D488—21no—
34D488—21no—
35C16×C61—21no—
36#11758185—21no—
37C22×D61—41no—
38Q8×C61—41no—
39Q8×C61—41no—
40C2×C4×C61—41no—
41C2×C4×C61—41no—
42C2×C4×C61C2×D411yescharacteristic
43C2×Dic61—41no—
44C2×Dic61D811yescharacteristic
45C2×Dic61D811yescharacteristic
46D244—41no—
47D244—41no—
48Dic122—82no—
49C8×C61#4111yescharacteristic
50C8×C61#4111yescharacteristic
51#92418SD1612yes—
52C22×C61C2×D811yescharacteristic
53C2×D61—81no—
54C2×D61—81no—
55C2×D61—81no—
56C4×C61—81no—
57C4×C61—81no—
58C4×C61#12411yescharacteristic
59C4×C61C2×SD1611yescharacteristic
60Dic61—21no—
61Dic61—21no—
62Dic61—81no—
63#2243—611nomaximal, Sylow
64C2×C61#48611yescharacteristic
65C2×C61#50911yescharacteristic
66C2×C61#51011yescharacteristic
67D61—161no—
68#500—611no—
69#495—611no—
70#358—611no—
71#358D6111yescharacteristic, complemented
72#357—611no—
73#357—611no—
74#346—611no—
75C61#224311yescharacteristic, complemented, Sylow
76C2×Q16C2×D6111yescharacteristic
77C2×SD16—1221no—
78C2×D8—611no—
79C4⋊Q8—1221no—
80#124—1221no—
81C2×C16—611no—
82C2×C16C2×D6111yescharacteristic
83#107—611no—
84#107—1221no—
85#107C2×D6111yescharacteristic
86C4×C8—611no—
87C2×Q8—21no—
88C2×Q8—2441no—
89C2×D4—1221no—
90Q16—21no—
91Q16—21no—
92SD16—2442no—
93D8—1221no—
94D8—1221no—
95C2×C8—611no—
96C2×C8C22×D6111yescharacteristic
97C4⋊C4—21no—
98C4⋊C4—1221no—
99C4⋊C4—2441no—
100C22⋊C4—2441no—
101C22⋊C4—2441no—
102C42—611no—
103C16—21no—
104C16—1221no—
105C23—2441no—
106Q8—41no—
107Q8—41no—
108Q8—4882no—
109D4—2441no—
110D4—2441no—
111C2×C4—41no—
112C2×C4—41no—
113C2×C4—611no—
114C2×C4—611no—
115C2×C4—2441no—
116C2×C4D4×D6111yescharacteristic
117C8—612no—
118C8#1175822211yescharacteristic
119C8#1175822411yescharacteristic
120C22—4881no—
121C22—4881no—
122C22—4881no—
123C22D8×D6111yescharacteristic
124C4—81no—
125C4—81no—
126C4—1221no—
127C4—1221no—
128C4—4881no—
129C4#1451976311yescharacteristic
130C4SD16×D6111yescharacteristic
131C2—9761no—
132C2#1684010711yescharacteristic
133C2#1684019911yescharacteristic
134C2#1684020411yescharacteristic
subgroupG/H
centerC22D8×D61
commutatorC2×C8×C61C23
FrattiniC2×C8C22×D61
FittingC61×#358C2
socleC22×C61C2×D8
hypercenter#358D61
hypocenterC61#2243
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #358

Complements

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

NH ≅ G/Ntype
1. #16840166C2semidirect
3. #16839566C2semidirect
6. #16839537C2semidirect
7. C61×#358C2semidirect
71. #358D61semidirect
75. C61#2243semidirect