Finite Group Databasebeta

← #21444420

Subgroups — #21444420

Order 7808.

212 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 73 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
1C2×#14519769C211yesmaximal, characteristic
2#16839819C211yesmaximal, characteristic
3#16839503C214yesmaximal, complemented
4C4×M16×C61C211yesmaximal, characteristic
5#14519769—21no—
6#14519769—21no—
7#14519769C412yes—
8#14519769C2212yes—
9C2×C4⋊Dic61C411yescharacteristic
10C2×C4⋊Dic61C411yescharacteristic
11C2×#11758196—21no—
12C2×#11758196—21no—
13C4⋊#92418—21no—
14C22⋊#92418—21no—
15#14519688C2212yes—
16C2×M16×C61—21no—
17C2×C42×C61C2211yescharacteristic
18#97×C61C2212yes—
19C4×C8×C61—21no—
20C22×C4×C61C2×C411yescharacteristic
21C22×C4×C61D411yescharacteristic
22C22×C4×C61D411yescharacteristic
23C22×Dic61—21no—
24C22×Dic61—21no—
25M16×C61—24no—
26C2×C8×C61—22no—
27C42×C61C2×C411yescharacteristic
28C42×C61D411yescharacteristic
29C42×C61D411yescharacteristic
30C42×C61C2311yescharacteristic
31C4⋊Dic61—21no—
32C4⋊Dic61—21no—
33C4⋊Dic61C2×C412yes—
34C4⋊Dic61C2×C412yes—
35#11758196—22no—
36#11758196—22no—
37#11758196—22no—
38#11758196—22no—
39C2×#92418—22no—
40C23×C61C22⋊C411yescharacteristic
41C2×C4×C61—22no—
42C2×C4×C61—22no—
43C2×C4×C61—41no—
44C2×C4×C61C22⋊C411yescharacteristic
45C2×C4×C61C22⋊C411yescharacteristic
46C2×C4×C61C22⋊C411yescharacteristic
47C2×C4×C61C22×C411yescharacteristic
48C2×C4×C61C2×D411yescharacteristic
49C2×C4×C61C2×D411yescharacteristic
50C2×Dic61—22no—
51C2×Dic61—22no—
52C2×Dic61—42no—
53C2×Dic61—42no—
54C8×C61—24no—
55#92418—42no—
56C22×C61—21no—
57C22×C61—21no—
58C22×C61#10412yes—
59C22×C61C2×C22⋊C411yescharacteristic
60C4×C61—21no—
61C4×C61—21no—
62C4×C61—21no—
63C4×C61—21no—
64C4×C61—21no—
65C4×C61#10112yes—
66Dic61—42no—
67Dic61—42no—
68#1528—611nomaximal, Sylow
69C2×C61—22no—
70C2×C61C2×#10111yescharacteristic
71C2×C61C2×#10411yescharacteristic
72C2×C61#42111yescharacteristic
73C2×#125—611no—
74#432—611no—
75C4×M16D6111yescharacteristic
76#330—614no—
77C61#152811yescharacteristic, complemented, Sylow
78C2×M16—21no—
79#125—612no—
80#125—612no—
81#125—1221no—
82#125—1221no—
83C2×C4⋊C4—611no—
84C2×C4⋊C4—611no—
85C2×C4⋊C4—1221no—
86C2×C4⋊C4—1221no—
87C2×C42C2×D6111yescharacteristic
88C4⋊C8—1221no—
89C22⋊C8—1221no—
90#97—612no—
91#97C2×D6112yes—
92C4×C8—21no—
93C22×C4—1221no—
94C22×C4—1221no—
95C22×C4C4×D6111yescharacteristic
96C22×C4D24411yescharacteristic
97C22×C4C22⋊D6111yescharacteristic
98M16—24no—
99C2×C8—22no—
100C2×C8—1222no—
101C4⋊C4—612no—
102C4⋊C4—612no—
103C4⋊C4—1221no—
104C4⋊C4—1221no—
105C4⋊C4—1222no—
106C4⋊C4—1222no—
107C4⋊C4—1222no—
108C4⋊C4—1222no—
109C42C4×D6111yescharacteristic
110C42D24411yescharacteristic
111C42C22⋊D6111yescharacteristic
112C42C22×D6111yescharacteristic
113C23#1175819811yescharacteristic
114C2×C4—22no—
115C2×C4—22no—
116C2×C4—41no—
117C2×C4—1222no—
118C2×C4—1222no—
119C2×C4—2442no—
120C2×C4—2442no—
121C2×C4#1175819811yescharacteristic
122C2×C4#1175819811yescharacteristic
123C2×C4#1175819811yescharacteristic
124C2×C4C2×C4×D6111yescharacteristic
125C2×C4C2×D24411yescharacteristic
126C2×C4C2×C22⋊D6111yescharacteristic
127C8—24no—
128C8—2442no—
129C22—21no—
130C22—21no—
131C22#1451970512yes—
132C22C2×#1175819811yescharacteristic
133C4—21no—
134C4—21no—
135C4—21no—
136C4—21no—
137C4—21no—
138C4—2442no—
139C4—2442no—
140C4#1451969512yes—
141C2—22no—
142C2C2×#1451969511yescharacteristic
143C2C2×#1451970511yescharacteristic
144C2#1683977811yescharacteristic
subgroupG/H
centerC22C2×#11758198
commutatorC2×C4×C61C22×C4
FrattiniC42C22×D61
FittingC4×M16×C61C2
socleC22×C61C2×C22⋊C4
hypercenterC4×M16D61
hypocenterC61#1528
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×M16

Complements

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

NH ≅ G/Ntype
3. #16839503C2semidirect
77. C61#1528semidirect