Finite Group Databasebeta

← #21448004

Subgroups — #21448004

Order 7808.

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

normal subgroups only

This group has 150 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
1#16839998C211yesmaximal, characteristic
2#16839589C212yesmaximal, complemented
3#16839562C212yesmaximal, complemented
4C22⋊#11758185C211yesmaximal, characteristic, complemented
5C2×#107×C61C211yesmaximal, characteristic, complemented
6C2×D488C2211yescharacteristic
7#14519751—21no—
8C2×#11758185C2212yes—
9#14519711C2211yescharacteristic
10#14519699—21no—
11C22×C8×C61C2211yescharacteristic
12C2×C4⋊C4×C61—21no—
13#107×C61—21no—
14#107×C61C2212yes—
15C22×C4×C61—41no—
16C22×C4×C61D411yescharacteristic
17C2×C22⋊D61—41no—
18C2×D244—21no—
19C2×C8×C61—22no—
20C2×C8×C61D411yescharacteristic
21C2×C8×C61C2311yescharacteristic
22C4⋊C4×C61—22no—
23C4⋊C4×C61—41no—
24#11758198—41no—
25C4⋊Dic61—21no—
26D488—22no—
27#11758185—22no—
28C23×C61D811yescharacteristic
29C22×D61—41no—
30C2×C4×C61—21no—
31C2×C4×C61—21no—
32C2×C4×C61—42no—
33C2×C4×C61—82no—
34C2×C4×C61D811yescharacteristic
35C2×C4×C61C2×D411yescharacteristic
36C22⋊D61—82no—
37C2×Dic61—41no—
38D244—41no—
39D244—41no—
40C8×C61—21no—
41C8×C61#4112yes—
42C22×C61—21no—
43C22×C61—21no—
44C22×C61SD3212yes—
45C22×C61C2×D811yescharacteristic
46C2×D61—81no—
47C2×D61—81no—
48C2×D61—81no—
49C4×C61—21no—
50C4×C61—82no—
51C4×C61#12311yescharacteristic
52C4×C61#13711yescharacteristic
53Dic61—81no—
54#2233—611nomaximal, Sylow
55C2×C61—22no—
56C2×C61#48011yescharacteristic
57C2×C61C2×SD3211yescharacteristic
58C2×C61#50911yescharacteristic
59D61—161no—
60#466—611no—
61C2×#107D6111yescharacteristic, complemented
62#367—612no—
63#357—612no—
64C22⋊C16—611no—
65C61#223311yescharacteristic, complemented, Sylow
66C2×D8—611no—
67C22×C8C2×D6111yescharacteristic
68#121—1221no—
69C2×C4⋊C4—21no—
70C2×C16—612no—
71#107—21no—
72#107—611no—
73#107C2×D6112yes—
74#102—1221no—
75C2×D4—1221no—
76C2×D4—2441no—
77C22×C4—41no—
78C22×C4C22⋊D6111yescharacteristic
79D8—1222no—
80C2×C8—22no—
81C2×C8C22⋊D6111yescharacteristic
82C2×C8C22×D6111yescharacteristic
83C4⋊C4—22no—
84C4⋊C4—41no—
85C4⋊C4—1221no—
86C22⋊C4—2441no—
87C16—1222no—
88C23—2441no—
89C23#1175819911yescharacteristic
90D4—4882no—
91D4—2441no—
92D4—2441no—
93C2×C4—21no—
94C2×C4—21no—
95C2×C4—42no—
96C2×C4—82no—
97C2×C4—2441no—
98C2×C4#1175819911yescharacteristic
99C2×C4C2×C22⋊D6111yescharacteristic
100C8—21no—
101C8#1175822212yes—
102C22—21no—
103C22—21no—
104C22—4881no—
105C22—4881no—
106C22—4881no—
107C22#1451972012yes—
108C22C2×#1175819911yescharacteristic
109C4—21no—
110C4—82no—
111C4—4881no—
112C4#1451976011yescharacteristic
113C4#1451980811yescharacteristic
114C2—22no—
115C2—9761no—
116C2#1684007511yescharacteristic
117C2C2×#1451972011yescharacteristic
118C2#1684019811yescharacteristic
subgroupG/H
centerC22C2×#11758199
commutatorC2×C8×C61C23
FrattiniC2×C8C22×D61
FittingC2×#107×C61C2
socleC22×C61C2×D8
hypercenterC2×#107D61
hypocenterC61#2233
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
2. #16839589C2semidirect
3. #16839562C2semidirect
4. C22⋊#11758185C2semidirect
5. C2×#107×C61C2semidirect
61. C2×#107D61semidirect
65. C61#2233semidirect