Finite Group Databasebeta

← #30594476

Subgroups — #30594476

Order 15616.

180 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 180 conjugacy classes of subgroups — too many to draw. Only its 44 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#21462191C211yesmaximal, characteristic
2#21461749C211yesmaximal, characteristic
3#21444113C211yesmaximal, characteristic
4#16840685—21no—
5#16840659—21no—
6#16840655C412yescomplemented
7#16840644—21no—
8#16840633—21no—
9#16840631C411yescharacteristic
10#16840630C411yescharacteristic
11#16839813—21no—
12C4×#11758189C2211yescharacteristic
13#16839484—21no—
14#16839483C411yescharacteristic, complemented
15C82×C61C411yescharacteristic, complemented
16D61⋊M16—21no—
17#14519856—21no—
18#14519851—22no—
19C2×#11758189C2×C411yescharacteristic
20C2×#11758189D411yescharacteristic
21C42×D61D411yescharacteristic
22#14519706—22no—
23#14519689—22no—
24#14519687C2×C411yescharacteristic
25#14519687Q811yescharacteristic
26C4×#92418—21no—
27C4×#92418D411yescharacteristic
28C4×C8×C61—21no—
29C4×C8×C61C2×C411yescharacteristic
30C2×C4×D61—21no—
31C2×C4×D61C22⋊C411yescharacteristic
32C22⋊#6923—41no—
33#11758217—41no—
34C4⋊#6923—41no—
35C4×#6923—41no—
36#11758213—41no—
37D61⋊C8—41no—
38C2×C8×C61—22no—
39C2×C8×C61C4211yescharacteristic
40C2×C8×C61C4⋊C411yescharacteristic
41C42×C61C22⋊C411yescharacteristic
42C4×Dic61—21no—
43C4×Dic61C4⋊C411yescharacteristic
44C2×#92418—22no—
45C2×#92418C22⋊C411yescharacteristic
46C2×#92418C4⋊C411yescharacteristic
47#11758189—41no—
48#11758189—41no—
49#11758187—42no—
50C22×D61#10411yescharacteristic
51C2×#6923—81no—
52C2×C4×C61—21no—
53C2×C4×C61#9511yescharacteristic
54C2×Dic61—21no—
55C2×Dic61#10411yescharacteristic
56C4×D61—21no—
57C4×D61—21no—
58C4×D61—42no—
59#92420—81no—
60C8×C61—21no—
61C8×C61—21no—
62C8×C61—42no—
63#92418—21no—
64#92418—21no—
65#92418—42no—
66#7226—611nomaximal, Sylow
67C22×C61#33911yescharacteristic
68C2×D61—21no—
69C2×D61—41no—
70#6923—161no—
71C4×C61—22no—
72C4×C61H(3,ℤ/4)11yescharacteristic
73C4×C61#34411yescharacteristic
74Dic61—21no—
75Dic61—41no—
76#2165—611no—
77#1841—611no—
78#1453—611no—
79C2×C61—21no—
80C2×C61#128811yescharacteristic
81D61—41no—
82#431—1221no—
83C4×M16—611no—
84#364—1221no—
85#349—1221no—
86#347—612no—
87#344—1221no—
88#339—1221no—
89#338—611no—
90H(3,ℤ/4)—611no—
91#322—611no—
92#322—1221no—
93C82#692311yescharacteristic, complemented
94C61#722611yescharacteristic, complemented, Sylow
95C2×M16—611no—
96C2×M16—611no—
97C2×M16—1221no—
98#117—1221no—
99C2×C42—611no—
100M32—1222no—
101C4⋊C8—1222no—
102C22⋊C8—1222no—
103#97—611no—
104#97—611no—
105C4×C8—21no—
106C4×C8—611no—
107C4×C8—1221no—
108C4×C8C2×#692311yescharacteristic
109C22×C4—611no—
110C22×C4—1221no—
111M16—2441no—
112M16—2441no—
113M16—2441no—
114M16—2441no—
115C2×C8—22no—
116C2×C8—611no—
117C2×C8—611no—
118C2×C8—1222no—
119C2×C8—2441no—
120C2×C8C4×#692311yescharacteristic
121C2×C8C4⋊#692311yescharacteristic
122C4⋊C4—2441no—
123C22⋊C4—2441no—
124C42—611no—
125C42—1221no—
126C42—2441no—
127C42C22⋊#692311yescharacteristic
128C16—2442no—
129C23—611no—
130C2×C4—21no—
131C2×C4—611no—
132C2×C4—1221no—
133C2×C4—1221no—
134C2×C4—1221no—
135C2×C4—4881no—
136C2×C4—2442no—
137C2×C4(C2×#6923)⋊C411yescharacteristic
138C8—21no—
139C8—21no—
140C8—42no—
141C8—1221no—
142C8—1221no—
143C8—4881no—
144C8—2442no—
145C22—1221no—
146C22—2441no—
147C22#1684063311yescharacteristic
148C4—22no—
149C4—1221no—
150C4—9761no—
151C4—2441no—
152C4#1684063011yescharacteristic
153C4#1684064411yescharacteristic
154C2—21no—
155C2—2441no—
156C2#2146067911yescharacteristic
subgroupG/H
centerC4#16840630
commutatorC2×C8×C61C42
FrattiniC4×C8C2×#6923
FittingC82×C61C4
socleC2×C61#1288
prime radicalC22×D61#104
cosocleC4×#11758189C22
hypercenterC82#6923
hypocenterC61#7226
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C61
UCSC1 ◁ C4 ◁ C2×C8 ◁ C82

Complements

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

NH ≅ G/Ntype
6. #16840655C4semidirect
14. #16839483C4semidirect
15. C82×C61C4semidirect
93. C82#6923semidirect
94. C61#7226semidirect

Maximal subgroups

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

subgroupindex
#214621912
#214617492
#214441132
#722661