Finite Group Databasebeta

← #30599285

Subgroups — #30599285

Order 15616.

630 conjugacy classes of subgroups; only the 140 normal subgroups are shown.

normal subgroups only

This group has 630 conjugacy classes of subgroups — too many to draw. Only its 140 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#21461675C212yesmaximal
2#21460697C214yesmaximal, complemented
3C2×#16839631C211yesmaximal, characteristic
4C2×#14519844C2214yes—
5C2×C22⋊#92420—22no—
6#16840628—22no—
7C22×C4⋊Dic61C411yescharacteristic
8C22×#11758196—22no—
9C22×C4×Dic61C2211yescharacteristic
10#16839631—22no—
11#16839631C412yes—
12#16839631C2212yes—
13C22×C4⋊C4×C61C411yescharacteristic
14C22×#92420—24no—
15#14519844—28no—
16C22⋊#92420—44no—
17C23×Dic61—21no—
18C23×Dic61D412yes—
19C2×C4⋊Dic61—21no—
20C2×C4⋊Dic61—42no—
21C2×C4⋊Dic61C2×C412yes—
22C2×#11758196—24no—
23C2×#11758196—24no—
24C2×#11758196—48no—
25C2×C4×Dic61—24no—
26C2×C4×Dic61C2×C411yescharacteristic
27C2×C4×Dic61D412yes—
28C2×C4×Dic61C2311yescharacteristic
29C23×C4×C61—21no—
30C23×C4×C61C2×C411yescharacteristic
31C2×C4⋊C4×C61—21no—
32C2×C4⋊C4×C61—42no—
33C2×C4⋊C4×C61C2×C412yes—
34C24×C61C22⋊C411yescharacteristic
35C22×C4×C61—22no—
36C22×C4×C61—22no—
37C22×C4×C61—22no—
38C22×C4×C61—22no—
39C22×C4×C61—44no—
40C22×C4×C61—42no—
41C22×C4×C61C22⋊C411yescharacteristic
42C22×C4×C61C22×C411yescharacteristic
43C22×Dic61—24no—
44C22×Dic61—24no—
45C22×Dic61—22no—
46C22×Dic61—44no—
47C22×Dic61—42no—
48C22×Dic61C22⋊C412yes—
49C22×Dic61SD1614yes—
50C22×Dic61Q1614yes—
51C22×Dic61C2×D412yes—
52C2×#92420—44no—
53C2×#92420—44no—
54C2×#92420—44no—
55C4⋊C4×C61—42no—
56C4⋊C4×C61—42no—
57C4⋊Dic61—42no—
58C4⋊Dic61—42no—
59#11758196—48no—
60#11758196—48no—
61C4×Dic61—22no—
62C4×Dic61—24no—
63C4×Dic61#4114yes—
64C23×C61—21no—
65C23×C61—21no—
66C23×C61—22no—
67C23×C61#10012yes—
68C23×C61#10314yes—
69C23×C61C2×C22⋊C411yescharacteristic
70C2×C4×C61—28no—
71C2×C4×C61—21no—
72C2×C4×C61—21no—
73C2×C4×C61—21no—
74C2×C4×C61—21no—
75C2×C4×C61—42no—
76C2×C4×C61—44no—
77C2×C4×C61—84no—
78C2×C4×C61#10112yes—
79C2×C4×C61#11712yes—
80C2×Dic61—22no—
81C2×Dic61—22no—
82C2×Dic61—28no—
83C2×Dic61—28no—
84C2×Dic61—42no—
85C2×Dic61—44no—
86C2×Dic61—84no—
87C2×Dic61#10314yes—
88C2×Dic61#12314yes—
89C2×Dic61C2×SD1612yes—
90C2×Dic61C2×Q1612yes—
91C2×Dic61AGL(1,ℤ/8)14yes—
92#92420—84no—
93#8725—611nomaximal, Sylow
94C22×C61—24no—
95C22×C61—22no—
96C22×C61—22no—
97C22×C61—24no—
98C22×C61#33314yes—
99C22×C61#38111yescharacteristic
100C22×C61C2×#10011yescharacteristic
101C22×C61C2×#10111yescharacteristic
102C22×C61C2×#10312yes—
103C22×C61#41812yes—
104C4×C61—22no—
105C4×C61—22no—
106C4×C61—82no—
107Dic61—24no—
108Dic61—82no—
109Dic61#48114yes—
110Dic61#48414yes—
111C2×#384—611no—
112#1797—612no—
113#1296—614no—
114C2×C61—24no—
115C2×C61C2×#33311yescharacteristic
116C2×C61#154912yes—
117C2×C61#155511yescharacteristic
118C2×C61#182111yescharacteristic
119C2×C61#182412yes—
120C22×C4⋊C4—611no—
121C22×C4⋊C4—1222no—
122C22×C4⋊C4#692311yescharacteristic
123C22×C42—611no—
124C2×C4⋊C8—614no—
125C2×C22⋊C8—1222no—
126#384—612no—
127#384—612no—
128#384—1222no—
129#336—1222no—
130C61#872511yescharacteristic, complemented, Sylow
131C23×C4—21no—
132C23×C4—612no—
133C23×C4—1221no—
134C23×C4C2×#692311yescharacteristic
135C22×C8—1224no—
136C2×C4⋊C4—21no—
137C2×C4⋊C4—42no—
138C2×C4⋊C4—612no—
139C2×C4⋊C4—1224no—
140C2×C4⋊C4—1224no—
141C2×C4⋊C4—1221no—
142C2×C4⋊C4—2442no—
143C2×C4⋊C4—2448no—
144C2×C4⋊C4C2×#692312yes—
145C2×C42—611no—
146C2×C42—612no—
147C2×C42—611no—
148C2×C42—1224no—
149C4⋊C8—1228no—
150C22⋊C8—2444no—
151C24C22⋊#692311yescharacteristic
152C22×C4—22no—
153C22×C4—22no—
154C22×C4—22no—
155C22×C4—22no—
156C22×C4—44no—
157C22×C4—42no—
158C22×C4—612no—
159C22×C4—614no—
160C22×C4—614no—
161C22×C4—612no—
162C22×C4—1224no—
163C22×C4—1224no—
164C22×C4—1222no—
165C22×C4—2444no—
166C22×C4—2442no—
167C22×C4C22⋊#692311yescharacteristic
168C22×C4C22×#692311yescharacteristic
169C2×C8—2444no—
170C2×C8—2444no—
171C2×C8—2444no—
172C4⋊C4—42no—
173C4⋊C4—42no—
174C4⋊C4—2442no—
175C4⋊C4—2442no—
176C4⋊C4—2448no—
177C4⋊C4—2448no—
178C42—614no—
179C42—1224no—
180C42—1222no—
181C23—21no—
182C23—21no—
183C23—22no—
184C23#1451983712yes—
185C23#1451984014yes—
186C23C2×C22⋊#692311yescharacteristic
187C2×C4—28no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—21no—
192C2×C4—42no—
193C2×C4—44no—
194C2×C4—84no—
195C2×C4—614no—
196C2×C4—612no—
197C2×C4—612no—
198C2×C4—614no—
199C2×C4—614no—
200C2×C4—1228no—
201C2×C4—1228no—
202C2×C4—1222no—
203C2×C4—1222no—
204C2×C4—4884no—
205C2×C4—2442no—
206C2×C4—2444no—
207C2×C4#1451983812yes—
208C2×C4#1451985612yes—
209C8—4884no—
210C22—24no—
211C22—22no—
212C22—22no—
213C22—24no—
214C22#1684062214yes—
215C22#1684070511yescharacteristic
216C22C2×#1451983711yescharacteristic
217C22C2×#1451983811yescharacteristic
218C22C2×#1451984012yes—
219C22#1684075412yes—
220C4—22no—
221C4—22no—
222C4—82no—
223C4—614no—
224C4—614no—
225C4—1224no—
226C4—4882no—
227C2—24no—
228C2C2×#1684062211yescharacteristic
229C2#2146133412yes—
230C2#2146134611yescharacteristic
231C2#2146171811yescharacteristic
232C2#2146172312yes—
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC22×C4⋊C4×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC24×C61C22⋊C4
cosocleC2×C4×Dic61C23
hypercenterC22×C4⋊C4#6923
hypocenterC61#8725
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #21460697C2semidirect
130. C61#8725semidirect

Maximal subgroups

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

subgroupindex
#214616752
#214606972
C2×#168396312
#872561