Finite Group Databasebeta

← #21444878

Subgroups — #21444878

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#16840138C211yesmaximal, characteristic
2#16839962C212yesmaximal, complemented
3#16839506C211yesmaximal, characteristic, complemented
4Q8⋊#92418C212yesmaximal, complemented
5C61×#559C211yesmaximal, characteristic, complemented
6C2×#11758201—22no—
7C2×#11758199—22no—
8#14519774C2211yescharacteristic
9C4⋊#92418C2212yes—
10#14519697—22no—
11C4×#92418C2211yescharacteristic
12#127×C61C2211yescharacteristic
13#124×C61—22no—
14#123×C61—22no—
15C4×Q8×C61C2212yes—
16C4×D4×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—22no—
36Q8×C61—22no—
37D4×C61—42no—
38D4×C61—42no—
39D4×C61—42no—
40C2×C4×C61—22no—
41C2×C4×C61—22no—
42C2×C4×C61—82no—
43C2×C4×C61C2×D411yescharacteristic
44C2×C4×C61C2×D412yes—
45D244—42no—
46D244—42no—
47D244—42no—
48#92418—22no—
49#92418—42no—
50C22×C61—44no—
51C22×C61—42no—
52C22×C61#12011yescharacteristic
53C2×D61—82no—
54C2×D61—81no—
55C4×C61—21no—
56C4×C61—42no—
57C4×C61—42no—
58C4×C61#13512yes—
59C4×C61AGL(1,ℤ/8)12yes—
60#1620—611nomaximal, Sylow
61C2×C61—82no—
62C2×C61#44912yes—
63C2×C61#45311yescharacteristic
64D61—161no—
65#559D6111yescharacteristic, complemented
66#493—611no—
67#460—612no—
68#331—611no—
69Q8⋊C8—612no—
70C61#162011yescharacteristic, complemented, Sylow
71C2×SD16—1222no—
72C2×D8—1222no—
73#127—611no—
74#127C2×D6111yescharacteristic
75#124—22no—
76#123—22no—
77C4×Q8C2×D6112yes—
78C4×D4—22no—
79C4⋊C8—612no—
80#102—1222no—
81C4×C8—611no—
82C2×Q8C22⋊D6112yes—
83C2×D4—22no—
84C2×D4—1222no—
85C2×D4—1221no—
86C2×D4C22⋊D6112yes—
87C22×C4—22no—
88SD16—2444no—
89D8—2444no—
90C2×C8—1221no—
91C2×C8—1222no—
92C4⋊C4—22no—
93C4⋊C4C22⋊D6112yes—
94C22⋊C4—24no—
95C22⋊C4—22no—
96C42—22no—
97C42C22×D6111yescharacteristic
98C23—22no—
99C23—2441no—
100Q8—22no—
101Q8—22no—
102D4—42no—
103D4—42no—
104D4—42no—
105D4—2442no—
106D4—2442no—
107D4—2442no—
108C2×C4—22no—
109C2×C4—22no—
110C2×C4—82no—
111C2×C4C2×C22⋊D6111yescharacteristic
112C2×C4C2×C22⋊D6112yes—
113C8—1222no—
114C8—2442no—
115C22—44no—
116C22—42no—
117C22—4882no—
118C22—4881no—
119C22#1451974611yescharacteristic
120C4—21no—
121C4—42no—
122C4—42no—
123C4#1451979712yes—
124C4#1451980212yes—
125C2—82no—
126C2—9761no—
127C2#1683990712yes—
128C2#1683993011yescharacteristic
subgroupG/H
centerC22#14519746
commutatorC42×C61C23
FrattiniC42C22×D61
FittingC61×#559C2
socleC22×C61#120
hypercenter#559D61
hypocenterC61#1620
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #559

Complements

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

NH ≅ G/Ntype
2. #16839962C2semidirect
3. #16839506C2semidirect
4. Q8⋊#92418C2semidirect
5. C61×#559C2semidirect
65. #559D61semidirect
70. C61#1620semidirect