Finite Group Databasebeta

← #21461730

Subgroups — #21461730

Order 7808.

296 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 296 conjugacy classes of subgroups — too many to draw. Only its 62 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×#14519835C212yesmaximal
2#16840639C214yesmaximal, complemented
3#16840235C211yesmaximal, characteristic
4C2×C22⋊#6923C2214yes—
5#14519835—22no—
6#14519835—22no—
7C22×C22⋊D61C2211yescharacteristic
8C4×C22⋊D61—22no—
9#14519737—22no—
10#14519733C412yescomplemented
11C2×C22⋊Dic61C411yescharacteristic, complemented
12C22⋊C4×D61C2212yes—
13C2×C22⋊C4×C61C411yescharacteristic, complemented
14C24×C61C2×C411yescharacteristic
15C23×D61C2311yescharacteristic
16C22×#6923—24no—
17C22×C4×C61—21no—
18C2×C22⋊D61—24no—
19C2×C22⋊D61D412yes—
20C2×C22⋊D61D412yes—
21C22×Dic61—21no—
22C22×Dic61C2×C411yescharacteristic
23C2×C4×D61—22no—
24C22⋊#6923—24no—
25C22⋊#6923—24no—
26C22⋊C4×C61—21no—
27C22⋊C4×C61C2×C412yes—
28C22⋊Dic61—21no—
29C22⋊Dic61C2×C412yes—
30#11758198—22no—
31#11758196—22no—
32C4×Dic61—22no—
33C23×C61—22no—
34C23×C61—81no—
35C23×C61C22⋊C411yescharacteristic
36C23×C61C22⋊C411yescharacteristic
37C23×C61C22×C411yescharacteristic
38C22×D61—81no—
39C22×D61C2×D412yes—
40C22×D61#4114yes—
41C2×#6923—44no—
42C2×#6923—84no—
43C2×C4×C61—22no—
44C2×C4×C61—81no—
45C22⋊D61—24no—
46C22⋊D61—24no—
47C2×Dic61—22no—
48C2×Dic61—22no—
49C2×Dic61—81no—
50C2×Dic61C22⋊C412yes—
51C4×D61—82no—
52C22×C61—21no—
53C22×C61—21no—
54C22×C61—41no—
55C22×C61—41no—
56C22×C61—41no—
57C22×C61—82no—
58C22×C61C2×C22⋊C411yescharacteristic
59C22×C61#11712yes—
60C2×D61—42no—
61C2×D61—44no—
62C2×D61#12314yes—
63#6923—84no—
64C4×C61—42no—
65Dic61—22no—
66Dic61—42no—
67#1828—611nomaximal, Sylow
68C2×C61—21no—
69C2×C61—22no—
70C2×C61—41no—
71C2×C61—41no—
72C2×C61#38111yescharacteristic
73D61—24no—
74#518—611no—
75C2×#99—612no—
76#342—614no—
77C61#182811yescharacteristic, complemented, Sylow
78C22×D4—611no—
79C4×D4—1222no—
80C4×D4—1222no—
81#117—612no—
82C2×C22⋊C4—611no—
83C2×C22⋊C4—612no—
84C2×C22⋊C4—614no—
85C2×C22⋊C4#692311yescharacteristic, complemented
86#99—1222no—
87#99—1222no—
88C24—611no—
89C24C2×#692311yescharacteristic
90C2×D4—612no—
91C2×D4—612no—
92C2×D4—1224no—
93C22×C4—21no—
94C22×C4—611no—
95C22×C4—1222no—
96C22×C4—1221no—
97C22×C4—1224no—
98C4⋊C4—1222no—
99C22⋊C4—21no—
100C22⋊C4—612no—
101C22⋊C4—1222no—
102C22⋊C4—1221no—
103C22⋊C4—1224no—
104C22⋊C4—1224no—
105C22⋊C4C2×#692312yes—
106C42—1222no—
107C23—22no—
108C23—81no—
109C23—612no—
110C23—614no—
111C23—4881no—
112C23C22⋊#692311yescharacteristic
113C23C22⋊#692311yescharacteristic
114C23C22×#692311yescharacteristic
115D4—1224no—
116D4—1224no—
117C2×C4—22no—
118C2×C4—81no—
119C2×C4—612no—
120C2×C4—1222no—
121C2×C4—1222no—
122C2×C4—4882no—
123C2×C4—4884no—
124C2×C4—4881no—
125C2×C4—2444no—
126C22—21no—
127C22—21no—
128C22—41no—
129C22—41no—
130C22—41no—
131C22—82no—
132C22—614no—
133C22—2442no—
134C22—2444no—
135C22C2×C22⋊#692311yescharacteristic
136C22#1451985612yes—
137C4—42no—
138C4—1222no—
139C4—4884no—
140C4—2442no—
141C2—21no—
142C2—22no—
143C2—41no—
144C2—41no—
145C2—1224no—
146C2#1684070511yescharacteristic
subgroupG/H
centerC2#16840705
commutatorC23×C61C22×C4
FrattiniC23C22×#6923
FittingC2×C22⋊C4×C61C4
socleC2×C61#381
hypercenterC2×C22⋊C4#6923
hypocenterC61#1828
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #16840639C2semidirect
10. #14519733C4semidirect
11. C2×C22⋊Dic61C4semidirect
13. C2×C22⋊C4×C61C4semidirect
77. C61#1828semidirect
85. C2×C22⋊C4#6923semidirect