Finite Group Databasebeta

← #30594016

Subgroups — #30594016

Order 15616.

240 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 50 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#21460739C212yesmaximal
2#21445885C211yesmaximal, characteristic
3C22⋊#11758187—22no—
4C22×C4×Dic61C411yescharacteristic
5C2×C22⋊#92418C2211yescharacteristic
6#16839516—22no—
7C2×C22⋊C8×C61C411yescharacteristic
8C2×#11758187—42no—
9C23×Dic61C811yescharacteristic
10C23×Dic61C811yescharacteristic
11C22×#92418D412yes—
12C2×C4×Dic61—21no—
13C2×C4×Dic61—21no—
14C2×C4×Dic61—41no—
15C2×C4×Dic61—41no—
16C22⋊#92418—41no—
17C23×C4×C61C2×C411yescharacteristic
18C22×C8×C61—21no—
19C22⋊C8×C61—41no—
20C24×C61C2×C811yescharacteristic
21C22×C4×C61—21no—
22C22×C4×C61—21no—
23C22×C4×C61—42no—
24C22×C4×C61C22⋊C411yescharacteristic
25C22×C4×C61M1611yescharacteristic
26C22×Dic61—21no—
27C22×Dic61—21no—
28C22×Dic61—21no—
29C22×Dic61—42no—
30C22×Dic61—41no—
31C22×Dic61—41no—
32C22×Dic61—41no—
33C22×Dic61C1612yescomplemented
34C2×C8×C61—42no—
35C2×C8×C61—41no—
36C4×Dic61—42no—
37C4×Dic61—41no—
38C4×Dic61—41no—
39C2×#92418—22no—
40C2×#92418—42no—
41#11758187—82no—
42C23×C61—21no—
43C23×C61—21no—
44C23×C61—41no—
45C23×C61—41no—
46C23×C61C22⋊C811yescharacteristic
47C23×C61C2×C1611yescharacteristic
48C23×C61M3211yescharacteristic
49C2×C4×C61—22no—
50C2×C4×C61—21no—
51C2×C4×C61—42no—
52C2×C4×C61—42no—
53C2×C4×C61—41no—
54C2×C4×C61#9911yescharacteristic
55C2×C4×C61#10011yescharacteristic
56C2×Dic61—22no—
57C2×Dic61—22no—
58C2×Dic61—42no—
59C2×Dic61—41no—
60C2×Dic61—42no—
61C2×Dic61—41no—
62C2×Dic61—41no—
63C2×Dic61—41no—
64C2×Dic61—42no—
65C2×Dic61—42no—
66C8×C61—81no—
67#92418—42no—
68#7055—611nomaximal, Sylow
69C22×C61—21no—
70C22×C61—21no—
71C22×C61—21no—
72C22×C61—21no—
73C22×C61—41no—
74C22×C61—41no—
75C22×C61—42no—
76C22×C61—41no—
77C22×C61—41no—
78C22×C61#32311yescharacteristic
79C22×C61C22⋊C1611yescharacteristic
80C22×C61#34911yescharacteristic
81C4×C61—21no—
82C4×C61—41no—
83C4×C61#35212yes—
84Dic61—42no—
85Dic61—42no—
86#1817—611no—
87#1314—612no—
88C2×C61—21no—
89C2×C61—21no—
90C2×C61—41no—
91C2×C61—41no—
92C2×C61#131411yescharacteristic
93C2×C61#131711yescharacteristic
94C2×C61#132011yescharacteristic
95C22×C42—611no—
96C2×C22⋊C8—611no—
97C2×C22⋊C8#692311yescharacteristic
98C22⋊C16—1222no—
99#336—1222no—
100C61#705511yescharacteristic, complemented, Sylow
101C23×C4—611no—
102C23×C4—611no—
103C23×C4C2×#692311yescharacteristic
104C22×C8—21no—
105C22×C8—612no—
106C2×C42—1221no—
107C2×C42—1221no—
108C2×C42—2441no—
109C2×C42—2441no—
110C2×C16—2442no—
111C22⋊C8—41no—
112C22⋊C8—2441no—
113C24D61⋊C811yescharacteristic
114C22×C4—21no—
115C22×C4—21no—
116C22×C4—42no—
117C22×C4—612no—
118C22×C4—1221no—
119C22×C4—1221no—
120C22×C4—1221no—
121C22×C4—2442no—
122C22×C4—2441no—
123C22×C4—2441no—
124C22×C4—2441no—
125C22×C4#1175821311yescharacteristic
126C22×C4C22⋊#692311yescharacteristic
127C2×C8—42no—
128C2×C8—41no—
129C2×C8—1222no—
130C2×C8—2442no—
131C42—2442no—
132C42—2441no—
133C42—2441no—
134C16—4882no—
135C23—21no—
136C23—21no—
137C23—41no—
138C23—41no—
139C23#1451983411yescharacteristic
140C23D61⋊C1611yescharacteristic
141C23#1451985211yescharacteristic
142C2×C4—22no—
143C2×C4—21no—
144C2×C4—42no—
145C2×C4—42no—
146C2×C4—41no—
147C2×C4—1222no—
148C2×C4—1222no—
149C2×C4—2442no—
150C2×C4—2441no—
151C2×C4—2442no—
152C2×C4—2441no—
153C2×C4—2441no—
154C2×C4—2441no—
155C2×C4—2442no—
156C2×C4—2442no—
157C2×C4#1451983611yescharacteristic
158C2×C4#1451983711yescharacteristic
159C8—81no—
160C8—2442no—
161C22—21no—
162C22—21no—
163C22—21no—
164C22—21no—
165C22—41no—
166C22—41no—
167C22—42no—
168C22—41no—
169C22—41no—
170C22#1684060611yescharacteristic
171C22#1684065711yescharacteristic
172C22#1684065911yescharacteristic
173C4—21no—
174C4—41no—
175C4—2442no—
176C4—2442no—
177C4#1684066512yes—
178C2—21no—
179C2—21no—
180C2—41no—
181C2—41no—
182C2#2146074011yescharacteristic
183C2#2146074611yescharacteristic
184C2#2146075211yescharacteristic
subgroupG/H
centerC2×C4#14519836
commutatorC23×C61C2×C16
FrattiniC23×C4C2×#6923
FittingC2×C22⋊C8×C61C4
socleC22×C61#323
prime radicalC24×C61C2×C8
cosocleC2×C22⋊#92418C22
hypercenterC2×C22⋊C8#6923
hypocenterC61#7055
LCSG ▷ C23×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C23×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
33. C22×Dic61C16semidirect
100. C61#7055semidirect

Maximal subgroups

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

subgroupindex
#214607392
#214458852
#705561