Finite Group Databasebeta

← #21448019

Subgroups — #21448019

Order 7808.

140 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 140 conjugacy classes of subgroups — too many to draw. Only its 53 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×#14519711C211yesmaximal, characteristic
2#16839587C212yesmaximal, complemented
3#16839566C212yesmaximal, complemented
4C22⋊#11758185C211yesmaximal, characteristic
5C61×#467C211yesmaximal, characteristic
6C2×C4⋊Dic61—21no—
7C2×#11758185C2212yes—
8#14519711—21no—
9#14519711C2212yes—
10C2×Q16×C61C2211yescharacteristic
11C22×C8×C61C2211yescharacteristic
12C22⋊Q8×C61—21no—
13#107×C61C2211yescharacteristic
14#103×C61—21no—
15C2×Q8×C61—21no—
16C22×C4×C61D411yescharacteristic
17C22×Dic61—41no—
18Q16×C61—22no—
19C2×C8×C61—22no—
20C2×C8×C61D411yescharacteristic
21C2×C8×C61C2311yescharacteristic
22C4⋊C4×C61—21no—
23C4⋊C4×C61—41no—
24C22⋊C4×C61—41no—
25C4⋊Dic61—22no—
26C4⋊Dic61—41no—
27#11758185—22no—
28C23×C61D811yescharacteristic
29Q8×C61—41no—
30Q8×C61—41no—
31C2×C4×C61—21no—
32C2×C4×C61—21no—
33C2×C4×C61—41no—
34C2×C4×C61—41no—
35C2×C4×C61D811yescharacteristic
36C2×C4×C61C2×D411yescharacteristic
37C2×Dic61—42no—
38C2×Dic61—82no—
39C8×C61—21no—
40C8×C61#4112yes—
41C22×C61—21no—
42C22×C61—21no—
43C22×C61Q3212yes—
44C22×C61C2×D811yescharacteristic
45C4×C61—21no—
46C4×C61—81no—
47C4×C61—81no—
48C4×C61#12311yescharacteristic
49C4×C61#13711yescharacteristic
50Dic61—82no—
51#2236—611nomaximal, Sylow
52C2×C61—22no—
53C2×C61#48011yescharacteristic
54C2×C61C2×Q3211yescharacteristic
55C2×C61#50911yescharacteristic
56#467D6111yescharacteristic
57C2×#107—611no—
58#366—612no—
59#358—612no—
60C22⋊C16—611no—
61C61#223611yescharacteristic, complemented, Sylow
62C2×Q16C2×D6111yescharacteristic
63C22×C8C2×D6111yescharacteristic
64C22⋊Q8—21no—
65C2×C4⋊C4—1221no—
66C2×C16—612no—
67#107—612no—
68#107—1221no—
69#107C2×D6111yescharacteristic
70#103—21no—
71C2×Q8—21no—
72C22×C4—2441no—
73C22×C4C22⋊D6111yescharacteristic
74Q16—22no—
75C2×C8—22no—
76C2×C8C22⋊D6111yescharacteristic
77C2×C8C22×D6111yescharacteristic
78C4⋊C4—21no—
79C4⋊C4—41no—
80C4⋊C4—1222no—
81C4⋊C4—2441no—
82C22⋊C4—41no—
83C16—1222no—
84C23#1175819911yescharacteristic
85Q8—41no—
86Q8—41no—
87C2×C4—21no—
88C2×C4—21no—
89C2×C4—41no—
90C2×C4—41no—
91C2×C4—4882no—
92C2×C4—2442no—
93C2×C4#1175819911yescharacteristic
94C2×C4C2×C22⋊D6111yescharacteristic
95C8—21no—
96C8#1175822412yes—
97C22—21no—
98C22—21no—
99C22#1451972312yes—
100C22C2×#1175819911yescharacteristic
101C4—21no—
102C4—81no—
103C4—81no—
104C4—4882no—
105C4#1451975811yescharacteristic
106C4#1451980711yescharacteristic
107C2—22no—
108C2#1684007311yescharacteristic
109C2C2×#1451972311yescharacteristic
110C2#1684019711yescharacteristic
subgroupG/H
centerC22C2×#11758199
commutatorC2×C8×C61C23
FrattiniC2×C8C22×D61
FittingC61×#467C2
socleC22×C61C2×D8
hypercenter#467D61
hypocenterC61#2236
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #467

Complements

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

NH ≅ G/Ntype
2. #16839587C2semidirect
3. #16839566C2semidirect
61. C61#2236semidirect