Finite Group Databasebeta

← #30594475

Subgroups — #30594475

Order 15616.

180 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 180 conjugacy classes of subgroups — too many to draw. Only its 46 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#21462189C211yesmaximal, characteristic
2#21461038C211yesmaximal, characteristic
3#21445966C211yesmaximal, characteristic
4#16840779—21no—
5#16840684—21no—
6#16840658—21no—
7#16840655C412yescomplemented
8#92420⋊C8—21no—
9#16840603C411yescharacteristic, complemented
10C8×#92420C411yescharacteristic, complemented
11M16×Dic61C2211yescharacteristic
12#16839532—21no—
13#16839521—21no—
14#16839520C411yescharacteristic
15C61×H(3,ℤ/4)C411yescharacteristic
16#14519851—22no—
17#14519844—22no—
18C22⋊#92420—22no—
19C4×#92420—21no—
20C4×#92420—21no—
21C2×#11758194—21no—
22C2×#11758194D411yescharacteristic
23C2×C4×Dic61D411yescharacteristic
24#14519687C2×C411yescharacteristic
25#14519687Q811yescharacteristic
26C8×Dic61C2×C411yescharacteristic
27C8×Dic61D411yescharacteristic
28C2×M16×C61C2×C411yescharacteristic
29#117×C61—21no—
30C22×C4×C61C22⋊C411yescharacteristic
31C22×Dic61—21no—
32C2×#92420—22no—
33C2×#92420—22no—
34M16×C61—41no—
35C2×C8×C61C4211yescharacteristic
36C2×C8×C61C4⋊C411yescharacteristic
37C4⋊C4×C61—41no—
38C22⋊C4×C61—41no—
39C42×C61—41no—
40C4×Dic61—21no—
41C4×Dic61C22⋊C411yescharacteristic
42C4×Dic61C4⋊C411yescharacteristic
43#11758194—41no—
44#11758194—41no—
45#11758194—41no—
46C2×#92418—41no—
47C2×#92418C22⋊C411yescharacteristic
48C2×#92418C4⋊C411yescharacteristic
49#11758187—42no—
50C23×C61#10411yescharacteristic
51C2×C4×C61—21no—
52C2×C4×C61—21no—
53C2×C4×C61—81no—
54C2×C4×C61#9511yescharacteristic
55C2×C4×C61#10411yescharacteristic
56C2×Dic61—21no—
57C2×Dic61—21no—
58C2×Dic61—42no—
59#92420—42no—
60#92420—42no—
61C8×C61—21no—
62C8×C61—21no—
63#92418—21no—
64#92418—21no—
65#92418—81no—
66#7226—611nomaximal, Sylow
67C22×C61—21no—
68C22×C61—41no—
69C22×C61#33911yescharacteristic
70C4×C61—21no—
71C4×C61—161no—
72C4×C61H(3,ℤ/4)11yescharacteristic
73C4×C61#34411yescharacteristic
74Dic61—22no—
75Dic61—41no—
76#2165—611no—
77#1841—611no—
78#1453—611no—
79C2×C61—21no—
80C2×C61—41no—
81C2×C61#128811yescharacteristic
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)#692311yescharacteristic
91#322—611no—
92#322—1221no—
93C82—611no—
94C61#722611yescharacteristic, complemented, Sylow
95C2×M16—611no—
96C2×M16—1221no—
97C2×M16C2×#692311yescharacteristic
98#117—21no—
99C2×C42—611no—
100M32—1222no—
101C4⋊C8—1222no—
102C22⋊C8—1222no—
103#97—611no—
104#97—611no—
105C4×C8—611no—
106C4×C8—611no—
107C4×C8—1221no—
108C4×C8—1221no—
109C22×C4—1221no—
110C22×C4C22⋊#692311yescharacteristic
111M16—41no—
112M16—2441no—
113M16—2441no—
114M16—2441no—
115C2×C8—611no—
116C2×C8—611no—
117C2×C8—1222no—
118C2×C8—1222no—
119C2×C8—2441no—
120C2×C8C4×#692311yescharacteristic
121C2×C8C4⋊#692311yescharacteristic
122C4⋊C4—41no—
123C22⋊C4—41no—
124C42—41no—
125C42—611no—
126C42—611no—
127C42—1221no—
128C16—2442no—
129C23#1451984111yescharacteristic
130C2×C4—21no—
131C2×C4—21no—
132C2×C4—81no—
133C2×C4—1221no—
134C2×C4—1221no—
135C2×C4—2442no—
136C2×C4(C2×#6923)⋊C411yescharacteristic
137C2×C4#1451984211yescharacteristic
138C8—21no—
139C8—21no—
140C8—1221no—
141C8—1221no—
142C8—4881no—
143C8—2442no—
144C8—2442no—
145C22—21no—
146C22—41no—
147C22#1684063211yescharacteristic
148C4—21no—
149C4—161no—
150C4—1222no—
151C4—2441no—
152C4#1684062911yescharacteristic
153C4#1684064311yescharacteristic
154C2—21no—
155C2—41no—
156C2#2146067811yescharacteristic
subgroupG/H
centerC4#16840629
commutatorC2×C8×C61C42
FrattiniC2×M16C2×#6923
FittingC61×H(3,ℤ/4)C4
socleC2×C61#1288
prime radicalC23×C61#104
cosocleM16×Dic61C22
hypercenterH(3,ℤ/4)#6923
hypocenterC61#7226
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C61
UCSC1 ◁ C4 ◁ C2×C8 ◁ H(3,ℤ/4)

Complements

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

NH ≅ G/Ntype
7. #16840655C4semidirect
9. #16840603C4semidirect
10. C8×#92420C4semidirect
94. C61#7226semidirect

Maximal subgroups

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

subgroupindex
#214621892
#214610382
#214459662
#722661