Finite Group Databasebeta

← #21444902

Subgroups — #21444902

Order 7808.

240 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 57 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#16840136C211yesmaximal, characteristic, complemented
2#16839957C212yesmaximal, complemented
3#16839511C211yesmaximal, characteristic, complemented
4D4⋊#92418C212yesmaximal, complemented
5C61×#555C211yesmaximal, characteristic, complemented
6C2×#11758201—22no—
7C2×#11758199—22no—
8#14519774C2211yescharacteristic
9C4⋊#92418C2212yes—
10#14519697—22no—
11C4×#92418C2211yescharacteristic
12C4⋊Q8×C61C2211yescharacteristic
13#124×C61—22no—
14#121×C61—22no—
15C4×D4×C61C2212yes—
16#117×C61—22no—
17C2×Q8×C61D412yes—
18C2×D4×C61—22no—
19C2×D4×C61D412yes—
20C22×C4×C61—22no—
21C2×D244—22no—
22C2×D244—21no—
23C4⋊C4×C61—22no—
24C4⋊C4×C61D412yes—
25C22⋊C4×C61—24no—
26C22⋊C4×C61—22no—
27C42×C61—22no—
28C42×C61C2311yescharacteristic
29#11758201—44no—
30#11758199—44no—
31C2×#92418—21no—
32C2×#92418—22no—
33C23×C61—22no—
34C22×D61—41no—
35Q8×C61—42no—
36D4×C61—22no—
37D4×C61—22no—
38D4×C61—82no—
39C2×C4×C61—22no—
40C2×C4×C61—22no—
41C2×C4×C61—42no—
42C2×C4×C61—42no—
43C2×C4×C61C2×D411yescharacteristic
44C2×C4×C61C2×D412yes—
45D244—42no—
46D244—42no—
47D244—42no—
48#92418—22no—
49#92418—42no—
50C22×C61—42no—
51C22×C61—42no—
52C22×C61—42no—
53C22×C61#12011yescharacteristic
54C2×D61—82no—
55C2×D61—81no—
56C4×C61—21no—
57C4×C61—42no—
58C4×C61—42no—
59C4×C61#13512yes—
60C4×C61AGL(1,ℤ/8)12yes—
61#1624—611nomaximal, Sylow
62C2×C61—82no—
63C2×C61#44912yes—
64C2×C61#45311yescharacteristic
65D61—161no—
66#555D6111yescharacteristic, complemented
67#492—611no—
68#459—612no—
69#333—611no—
70D4⋊C8—612no—
71C61#162411yescharacteristic, complemented, Sylow
72C2×SD16—1222no—
73C2×D8—1222no—
74C4⋊Q8C2×D6111yescharacteristic
75#127—611no—
76#124—22no—
77#121—22no—
78C4×D4C2×D6112yes—
79#117—22no—
80C4⋊C8—612no—
81#102—1222no—
82C4×C8—611no—
83C2×Q8C22⋊D6112yes—
84C2×D4—22no—
85C2×D4—1222no—
86C2×D4—1221no—
87C2×D4C22⋊D6112yes—
88C22×C4—22no—
89SD16—2444no—
90D8—2444no—
91C2×C8—1221no—
92C2×C8—1222no—
93C4⋊C4—22no—
94C4⋊C4C22⋊D6112yes—
95C22⋊C4—24no—
96C22⋊C4—22no—
97C42—22no—
98C42C22×D6111yescharacteristic
99C23—22no—
100C23—2441no—
101Q8—42no—
102D4—22no—
103D4—22no—
104D4—82no—
105D4—2442no—
106D4—2442no—
107D4—2442no—
108C2×C4—22no—
109C2×C4—22no—
110C2×C4—42no—
111C2×C4—42no—
112C2×C4C2×C22⋊D6111yescharacteristic
113C2×C4C2×C22⋊D6112yes—
114C8—1222no—
115C8—2442no—
116C22—42no—
117C22—42no—
118C22—42no—
119C22—4882no—
120C22—4881no—
121C22#1451974611yescharacteristic
122C4—21no—
123C4—42no—
124C4—42no—
125C4#1451979712yes—
126C4#1451980212yes—
127C2—82no—
128C2—9761no—
129C2#1683990712yes—
130C2#1683993011yescharacteristic
subgroupG/H
centerC22#14519746
commutatorC42×C61C23
FrattiniC42C22×D61
FittingC61×#555C2
socleC22×C61#120
hypercenter#555D61
hypocenterC61#1624
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #555

Complements

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

NH ≅ G/Ntype
1. #16840136C2semidirect
2. #16839957C2semidirect
3. #16839511C2semidirect
4. D4⋊#92418C2semidirect
5. C61×#555C2semidirect
66. #555D61semidirect
71. C61#1624semidirect