Finite Group Databasebeta

← #30595277

Subgroups — #30595277

Order 15616.

164 conjugacy classes of subgroups; only the 22 normal subgroups are shown.

normal subgroups only

This group has 164 conjugacy classes of subgroups — too many to draw. Only its 22 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#21460955C211yesmaximal, characteristic, complemented
2#21460953C211yesmaximal, characteristic, complemented
3#21445486C211yesmaximal, characteristic
4#16840673—21no—
5#16840667—21no—
6#16840138—21no—
7#16840135C2211yescharacteristic
8#16840108—21no—
9#16839483C411yescharacteristic, complemented
10C61×#493C411yescharacteristic, complemented
11#14519838—41no—
12#14519836—41no—
13C2×#11758190—41no—
14C2×#11758199—42no—
15#14519777D411yescharacteristic
16#14519774D411yescharacteristic
17#14519698—42no—
18C4×#92418—21no—
19C2×D8×C61—41no—
20#127×C61—21no—
21C4×C8×C61C2×C411yescharacteristic
22C2×D4×C61—41no—
23C2×D4×C61—41no—
24C2×D4×C61—41no—
25C2×D244—21no—
26C2×D244—41no—
27C2×Dic122—21no—
28C22⋊#6923—81no—
29#11758217—81no—
30D8×C61—82no—
31C2×C8×C61—21no—
32C42×C61C22⋊C411yescharacteristic
33#11758199—84no—
34C4⋊Dic61—41no—
35C2×#92418—22no—
36#11758190—82no—
37C23×C61—81no—
38C22×D61—41no—
39C2×#6923—161no—
40D4×C61—82no—
41D4×C61—82no—
42D4×C61—82no—
43C2×C4×C61—21no—
44C2×C4×C61#9911yescharacteristic
45C2×Dic61—41no—
46D244—81no—
47D244—82no—
48Dic122—81no—
49#92420—161no—
50C8×C61—22no—
51#92418—42no—
52#7527—611nomaximal, Sylow
53C22×C61—161no—
54C22×C61—161no—
55C22×C61—161no—
56C22×C61#35311yescharacteristic
57C2×D61—81no—
58C2×D61—161no—
59#6923—321no—
60C4×C61—22no—
61C4×C61—21no—
62Dic61—81no—
63#1721—611no—
64#1410—611no—
65#1409—611no—
66C2×C61—21no—
67C2×C61—321no—
68C2×C61#140811yescharacteristic
69D61—161no—
70#493—1221no—
71#493#692311yescharacteristic, complemented
72#492—611no—
73#486—1221no—
74#356—1221no—
75#353—1221no—
76#322—611no—
77C61#752711yescharacteristic, complemented, Sylow
78C2×SD16—2441no—
79C2×D8—41no—
80C2×D8—2442no—
81C4⋊Q8—611no—
82#127—21no—
83#127—611no—
84#102—2442no—
85#101—2441no—
86#99—2441no—
87C4×C8—1221no—
88C4×C8C2×#692311yescharacteristic
89C2×Q8—1221no—
90C2×D4—41no—
91C2×D4—41no—
92C2×D4—41no—
93C2×D4—1221no—
94C2×D4—2441no—
95SD16—4882no—
96D8—82no—
97D8—4884no—
98M16—4881no—
99C2×C8—21no—
100C2×C8—1222no—
101C4⋊C4—2441no—
102C22⋊C4—4881no—
103C42C22⋊#692311yescharacteristic
104C23—81no—
105C23—2441no—
106Q8—4881no—
107D4—82no—
108D4—82no—
109D4—82no—
110D4—4882no—
111D4—4881no—
112C2×C4—21no—
113C2×C4—9761no—
114C2×C4—2441no—
115C2×C4#1451983511yescharacteristic
116C8—22no—
117C8—9761no—
118C8—2442no—
119C22—161no—
120C22—161no—
121C22—161no—
122C22—9761no—
123C22—4881no—
124C22#1684066611yescharacteristic
125C4—22no—
126C4—21no—
127C4—19521no—
128C4—4881no—
129C2—21no—
130C2—321no—
131C2—9761no—
132C2#2146095011yescharacteristic
subgroupG/H
centerC2#21460950
commutatorC4×C8×C61C2×C4
FrattiniC4×C8C2×#6923
FittingC61×#493C4
socleC2×C61#1408
prime radical#21445486C2
cosocle#16840135C22
hypercenter#493#6923
hypocenterC61#7527
LCSG ▷ C4×C8×C61 ▷ C42×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C42 ◁ C4×C8 ◁ #493

Complements

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

NH ≅ G/Ntype
1. #21460955C2semidirect
2. #21460953C2semidirect
9. #16839483C4semidirect
10. C61×#493C4semidirect
71. #493#6923semidirect
77. C61#7527semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#214609552
#214609532
#214454862
#752761