Finite Group Databasebeta

← #30594841

Subgroups — #30594841

Order 15616.

216 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 40 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#21460761C212yesmaximal
2#21446621C211yesmaximal, characteristic
3#16840607—22no—
4C2×#14519777C411yescharacteristic
5C2×#14519702—22no—
6#16839632C2211yescharacteristic
7C2×C4×C8×C61C411yescharacteristic
8C22⋊#92420—42no—
9C22×Dic122—21no—
10#14519777—21no—
11#14519777—41no—
12#14519777C812yescomplemented
13C2×C4⋊Dic61—41no—
14C2×C4⋊Dic61—41no—
15C2×C4⋊Dic61D412yes—
16#14519702—44no—
17C22×C8×C61—21no—
18C2×C42×C61C2×C411yescharacteristic
19C4×C8×C61—41no—
20C22×C4×C61—21no—
21C22×C4×C61C22⋊C411yescharacteristic
22C22×Dic61—22no—
23C22×Dic61—41no—
24C2×Dic122—22no—
25C2×Dic122—42no—
26C2×Dic122—42no—
27C2×Dic122—41no—
28C2×#92420—82no—
29C2×C8×C61—22no—
30C2×C8×C61—41no—
31C2×C8×C61—41no—
32C42×C61—21no—
33C42×C61C2×C811yescharacteristic
34C42×C61M1611yescharacteristic
35C4⋊Dic61—42no—
36C4⋊Dic61—42no—
37C4⋊Dic61—42no—
38C4⋊Dic61—82no—
39C23×C61#9911yescharacteristic
40C2×C4×C61—22no—
41C2×C4×C61—22no—
42C2×C4×C61—21no—
43C2×C4×C61—21no—
44C2×C4×C61—21no—
45C2×C4×C61—21no—
46C2×C4×C61C22⋊C811yescharacteristic
47C2×C4×C61#10011yescharacteristic
48C2×Dic61—42no—
49C2×Dic61—42no—
50C2×Dic61—81no—
51C2×Dic61—81no—
52C2×Dic61—82no—
53Dic122—44no—
54Dic122—82no—
55#92420—162no—
56C8×C61—42no—
57#7355—611nomaximal, Sylow
58C22×C61—21no—
59C22×C61—21no—
60C22×C61#32311yescharacteristic
61C22×C61#35311yescharacteristic
62C22×C61#35511yescharacteristic
63C4×C61—22no—
64C4×C61—22no—
65C4×C61—21no—
66C4×C61—21no—
67Dic61—82no—
68Dic61—82no—
69#1956—611no—
70#1325—612no—
71C2×C61—21no—
72C2×C61—21no—
73C2×C61#131811yescharacteristic
74C2×C61#140911yescharacteristic
75C2×C61#141111yescharacteristic
76C2×C4⋊Q8—611no—
77C2×#103—1222no—
78C2×C4×C8#692311yescharacteristic
79#384—611no—
80#324—1222no—
81C61#735511yescharacteristic, complemented, Sylow
82C22×Q8—1221no—
83C22×C8—21no—
84C4⋊Q8—612no—
85C4⋊Q8—1221no—
86C4⋊Q8—2441no—
87C2×C4⋊C4—612no—
88C2×C4⋊C4—2441no—
89C2×C4⋊C4—2441no—
90C2×C42C2×#692311yescharacteristic
91#103—2444no—
92C22⋊C8—2442no—
93C4×C8—41no—
94C2×Q8—1222no—
95C2×Q8—2442no—
96C2×Q8—2442no—
97C2×Q8—2441no—
98C22×C4—21no—
99C22×C4—1222no—
100C22×C4—2441no—
101C22×C4C22⋊#692311yescharacteristic
102C2×C8—22no—
103C2×C8—41no—
104C2×C8—41no—
105C2×C8—4882no—
106C4⋊C4—4882no—
107C4⋊C4—2442no—
108C4⋊C4—2442no—
109C4⋊C4—2442no—
110C42—21no—
111C42D61⋊C811yescharacteristic
112C42#1175821311yescharacteristic
113C23#1451983611yescharacteristic
114Q8—4882no—
115Q8—2444no—
116C2×C4—22no—
117C2×C4—22no—
118C2×C4—21no—
119C2×C4—21no—
120C2×C4—21no—
121C2×C4—21no—
122C2×C4—4881no—
123C2×C4—4881no—
124C2×C4—4882no—
125C2×C4—2442no—
126C2×C4—2442no—
127C2×C4#1451983411yescharacteristic
128C2×C4#1451983711yescharacteristic
129C8—42no—
130C8—9762no—
131C22—21no—
132C22—21no—
133C22#1684060611yescharacteristic
134C22#1684066711yescharacteristic
135C22#1684067111yescharacteristic
136C4—22no—
137C4—22no—
138C4—21no—
139C4—21no—
140C4—4882no—
141C4—4882no—
142C2—21no—
143C2—21no—
144C2#2146074811yescharacteristic
145C2#2146095311yescharacteristic
146C2#2146095711yescharacteristic
subgroupG/H
centerC22#16840667
commutatorC42×C61C2×C8
FrattiniC2×C42C2×#6923
FittingC2×C4×C8×C61C4
socleC22×C61#353
prime radicalC23×C61#99
cosocle#16839632C22
hypercenterC2×C4×C8#6923
hypocenterC61#7355
LCSG ▷ C42×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×C8

Complements

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

NH ≅ G/Ntype
12. #14519777C8semidirect
81. C61#7355semidirect

Maximal subgroups

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

subgroupindex
#214607612
#214466212
#735561