Finite Group Databasebeta

← #21444580

Subgroups — #21444580

Order 7808.

168 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 168 conjugacy classes of subgroups — too many to draw. Only its 81 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#16839819C211yesmaximal, characteristic
2C2×C4×#92418C211yesmaximal, characteristic
3#16839514C212yesmaximal, complemented
4#16839512C212yesmaximal, complemented
5C61×#432C211yesmaximal, characteristic
6C22×#92418C411yescharacteristic
7C22×#92418C411yescharacteristic
8C4⋊#92418C2212yes—
9C22⋊#92418—21no—
10#14519688—21no—
11C4×#92418C411yescharacteristic
12C4×#92418C411yescharacteristic
13C4×#92418C2211yescharacteristic
14C4×#92418C2211yescharacteristic
15C2×C42×C61C2211yescharacteristic
16C4⋊C8×C61C2212yes—
17C22⋊C8×C61—21no—
18#97×C61—21no—
19C22×C4×C61C2×C411yescharacteristic
20C22×C4×C61D411yescharacteristic
21C22×C4×C61Q811yescharacteristic
22C2×C8×C61—22no—
23C42×C61C2×C411yescharacteristic
24C42×C61D411yescharacteristic
25C42×C61Q811yescharacteristic
26C42×C61C2311yescharacteristic
27C2×#92418—22no—
28C2×#92418—22no—
29C2×#92418—22no—
30C2×#92418C2×C411yescharacteristic
31C2×#92418C2×C411yescharacteristic
32C2×#92418C2×C411yescharacteristic
33C2×#92418C2×C411yescharacteristic
34C23×C61C4⋊C411yescharacteristic
35C2×C4×C61—22no—
36C2×C4×C61—21no—
37C2×C4×C61—21no—
38C2×C4×C61—22no—
39C2×C4×C61C4⋊C411yescharacteristic
40C2×C4×C61C4⋊C411yescharacteristic
41C2×C4×C61C4⋊C411yescharacteristic
42C2×C4×C61C22×C411yescharacteristic
43C2×C4×C61C2×D411yescharacteristic
44C2×C4×C61C2×Q811yescharacteristic
45C8×C61—42no—
46#92418—21no—
47#92418—21no—
48#92418—42no—
49#92418M1612yes—
50#92418M1612yes—
51C22×C61—21no—
52C22×C61—21no—
53C22×C61#10812yes—
54C22×C61C2×C4⋊C411yescharacteristic
55C4×C61—21no—
56C4×C61—21no—
57C4×C61—21no—
58C4×C61—21no—
59C4×C61C2×M1611yescharacteristic
60C4×C61C2×M1611yescharacteristic
61C4×C61#13512yes—
62#1568—611nomaximal, Sylow
63C2×C61—22no—
64C2×C61#42311yescharacteristic
65C2×C61#42711yescharacteristic
66C2×C61C2×#10811yescharacteristic
67#432—611no—
68#432D6111yescharacteristic
69C2×C4×C8—611no—
70#335—612no—
71#334—612no—
72C61#156811yescharacteristic, complemented, Sylow
73C22×C8—611no—
74C22×C8—611no—
75C2×C42C2×D6111yescharacteristic
76C4⋊C8—612no—
77C4⋊C8C2×D6112yes—
78C22⋊C8—21no—
79C22⋊C8—1221no—
80#97—21no—
81#97—1221no—
82C4×C8—611no—
83C4×C8—611no—
84C4×C8—611no—
85C4×C8—611no—
86C22×C4Dic12211yescharacteristic
87C22×C4C4×D6111yescharacteristic
88C22×C4C22⋊D6111yescharacteristic
89C2×C8—22no—
90C2×C8—611no—
91C2×C8—611no—
92C2×C8—611no—
93C2×C8—611no—
94C2×C8—1222no—
95C2×C8—1222no—
96C2×C8—1222no—
97C42Dic12211yescharacteristic
98C42C4×D6111yescharacteristic
99C42C22⋊D6111yescharacteristic
100C42C22×D6111yescharacteristic
101C23#1175819611yescharacteristic
102C2×C4—22no—
103C2×C4—21no—
104C2×C4—21no—
105C2×C4—22no—
106C2×C4#1175819611yescharacteristic
107C2×C4#1175819611yescharacteristic
108C2×C4#1175819611yescharacteristic
109C2×C4C2×Dic12211yescharacteristic
110C2×C4C2×C4×D6111yescharacteristic
111C2×C4C2×C22⋊D6111yescharacteristic
112C8—42no—
113C8—612no—
114C8—612no—
115C8—1221no—
116C8—1221no—
117C8—2442no—
118C22—21no—
119C22—21no—
120C22#1451971212yes—
121C22C2×#1175819611yescharacteristic
122C4—21no—
123C4—21no—
124C4—21no—
125C4—21no—
126C4M16×D6111yescharacteristic
127C4M16×D6111yescharacteristic
128C4#1451979712yes—
129C2—22no—
130C2#1683978511yescharacteristic
131C2#1683979811yescharacteristic
132C2C2×#1451971211yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊D61
commutatorC2×C4×C61C22×C4
FrattiniC42C22×D61
FittingC61×#432C2
socleC22×C61C2×C4⋊C4
hypercenter#432D61
hypocenterC61#1568
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
3. #16839514C2semidirect
4. #16839512C2semidirect
72. C61#1568semidirect