Finite Group Databasebeta

← #21447963

Subgroups — #21447963

Order 7808.

142 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 142 conjugacy classes of subgroups — too many to draw. Only its 55 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
1C4×D488C211yesmaximal, characteristic
2#16839589C212yesmaximal, complemented
3C4⋊#11758185C211yesmaximal, characteristic, complemented
4#16839562C212yesmaximal
5C61×#500C211yesmaximal, characteristic, complemented
6C2×D488C2211yescharacteristic
7C4×D244—21no—
8C2×#11758185C2212yes—
9#14519711C2211yescharacteristic
10#14519699—21no—
11C4⋊Q8×C61—21no—
12#107×C61—21no—
13#107×C61C2212yes—
14C4×C8×C61C2211yescharacteristic
15C2×Q8×C61—41no—
16C2×D244—21no—
17C2×C4×D61—41no—
18C2×C8×C61D411yescharacteristic
19C2×C8×C61C2311yescharacteristic
20C4⋊C4×C61—22no—
21C4⋊C4×C61—41no—
22C42×C61D411yescharacteristic
23#11758198—41no—
24C4⋊Dic61—21no—
25D488—21no—
26D488Q812yescomplemented
27#11758185—22no—
28C22×D61—41no—
29Q8×C61—82no—
30C2×C4×C61—42no—
31C2×C4×C61D811yescharacteristic
32C2×C4×C61D811yescharacteristic
33C2×C4×C61C2×D411yescharacteristic
34C2×Dic61—41no—
35D244—22no—
36D244—41no—
37C4×D61—82no—
38C8×C61—21no—
39C8×C61C2×Q811yescharacteristic
40C8×C61#4111yescharacteristic
41C22×C61C2×D811yescharacteristic
42C2×D61—42no—
43C2×D61—81no—
44C2×D61—81no—
45C4×C61—21no—
46C4×C61—82no—
47C4×C61SD3212yes—
48C4×C61C22⋊Q811yescharacteristic
49C4×C61#13711yescharacteristic
50Dic61—81no—
51#2226—611nomaximal, Sylow
52C2×C61#47411yescharacteristic
53C2×C61C2×SD3211yescharacteristic
54C2×C61#50911yescharacteristic
55D61—82no—
56#500D6111yescharacteristic, complemented
57C4×D8—611no—
58#367—612no—
59C4⋊C16—611no—
60#357—612no—
61C61#222611yescharacteristic, complemented, Sylow
62C2×D8—611no—
63C4⋊Q8—21no—
64C4×D4—1221no—
65C2×C16—612no—
66#107—21no—
67#107—611no—
68#107C2×D6112yes—
69#102—1221no—
70C4×C8C2×D6111yescharacteristic
71C2×Q8—41no—
72C2×D4—1221no—
73C22×C4—2441no—
74D8—612no—
75D8—1221no—
76C2×C8C22⋊D6111yescharacteristic
77C2×C8C22×D6111yescharacteristic
78C4⋊C4—22no—
79C4⋊C4—41no—
80C4⋊C4—1221no—
81C22⋊C4—2441no—
82C42C22⋊D6111yescharacteristic
83C16—1222no—
84C23—2441no—
85Q8—82no—
86D4—1222no—
87D4—2441no—
88C2×C4—42no—
89C2×C4—4882no—
90C2×C4—2441no—
91C2×C4#1175819911yescharacteristic
92C2×C4#1175819911yescharacteristic
93C2×C4C2×C22⋊D6111yescharacteristic
94C8—21no—
95C8Q8×D6111yescharacteristic
96C8#1175822611yescharacteristic
97C22—4881no—
98C22—4881no—
99C22—2442no—
100C22C2×#1175819911yescharacteristic
101C4—21no—
102C4—82no—
103C4—4881no—
104C4#1451972012yes—
105C4#1451975311yescharacteristic
106C4#1451980811yescharacteristic
107C2—4882no—
108C2#1684003911yescharacteristic
109C2C2×#1451972011yescharacteristic
110C2#1684019811yescharacteristic
subgroupG/H
centerC22C2×#11758199
commutatorC2×C8×C61C23
FrattiniC2×C8C22×D61
FittingC61×#500C2
socleC22×C61C2×D8
hypercenter#500D61
hypocenterC61#2226
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #500

Complements

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

NH ≅ G/Ntype
2. #16839589C2semidirect
3. C4⋊#11758185C2semidirect
5. C61×#500C2semidirect
26. D488Q8semidirect
56. #500D61semidirect
61. C61#2226semidirect