Finite Group Databasebeta

← #30599351

Subgroups — #30599351

Order 15616.

538 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 538 conjugacy classes of subgroups — too many to draw. Only its 72 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#21461714C212yesmaximal
2#21460718C214yesmaximal
3#21448414C211yesmaximal, characteristic
4#16840703C2214yes—
5#16840640—22no—
6#16840640—22no—
7C22×#11758198C2211yescharacteristic
8#16839653—22no—
9#16839651—22no—
10#16839620C412yescomplemented
11#16839617C2212yes—
12C4×C22⋊Dic61C411yescharacteristic, complemented
13C4×C22⋊C4×C61C411yescharacteristic, complemented
14C2×C22⋊#6923—24no—
15C2×C22⋊#6923—24no—
16C2×C22⋊#6923—24no—
17C24×D61C2311yescharacteristic
18C23×Dic61C2×C411yescharacteristic
19C2×#11758196—22no—
20C2×C22⋊Dic61C2×C412yes—
21C2×#11758198—24no—
22C2×#11758198—22no—
23C2×#11758198—22no—
24C2×#11758198D412yes—
25C2×#11758198D412yes—
26C2×C4×Dic61—21no—
27#14519684—21no—
28#14519684—22no—
29C23×C4×C61C2×C411yescharacteristic
30C2×C22⋊C4×C61C2×C412yes—
31C2×C42×C61—21no—
32#95×C61—21no—
33C24×C61C22×C411yescharacteristic
34C23×D61—42no—
35C23×D61—81no—
36C23×D61—81no—
37C23×D61C2×D412yes—
38C23×D61#4114yes—
39C22×#6923—44no—
40C22×C4×C61—22no—
41C22×C4×C61—22no—
42C22×C4×C61—81no—
43C22×C4×C61C22⋊C411yescharacteristic
44C22×C4×C61C22⋊C411yescharacteristic
45C22×Dic61—22no—
46C22×Dic61—22no—
47C22×Dic61—81no—
48C22×Dic61C22⋊C412yes—
49C22⋊#6923—48no—
50C22⋊#6923—84no—
51C22⋊#6923—84no—
52C22⋊C4×C61—42no—
53C42×C61—81no—
54C22⋊Dic61—42no—
55#11758198—24no—
56#11758198—24no—
57#11758198—82no—
58#11758198—82no—
59#11758196—82no—
60C4×Dic61—81no—
61C23×C61—22no—
62C23×C61—41no—
63C23×C61—41no—
64C23×C61C2×C22⋊C411yescharacteristic
65C23×C61#11712yes—
66C22×D61—24no—
67C22×D61—42no—
68C22×D61—42no—
69C22×D61—44no—
70C22×D61—44no—
71C22×D61—44no—
72C22×D61—88no—
73C22×D61#12314yes—
74C2×#6923—84no—
75C2×#6923—84no—
76C2×#6923—84no—
77C2×C4×C61—21no—
78C2×C4×C61—21no—
79C2×C4×C61—41no—
80C2×C4×C61—41no—
81C2×C4×C61—42no—
82C2×C4×C61—42no—
83C2×C4×C61—42no—
84C2×C4×C61—82no—
85C2×Dic61—22no—
86C2×Dic61—42no—
87C2×Dic61—42no—
88C2×Dic61—42no—
89C2×Dic61—42no—
90C2×Dic61—82no—
91#8750—611nomaximal, Sylow
92C22×C61—21no—
93C22×C61—21no—
94C22×C61—22no—
95C22×C61—22no—
96C22×C61—22no—
97C22×C61—44no—
98C22×C61#38111yescharacteristic
99C22×C61#41012yes—
100C2×D61—24no—
101C2×D61—24no—
102C2×D61—24no—
103C2×D61—84no—
104C2×D61—88no—
105#6923—164no—
106C4×C61—41no—
107C4×C61—41no—
108C4×C61—82no—
109Dic61—42no—
110Dic61—82no—
111#2312—611no—
112#1819—612no—
113#1304—614no—
114C2×C61—22no—
115C2×C61—42no—
116C2×C61#182011yescharacteristic
117C2×C61#182811yescharacteristic
118C2×C61#182811yescharacteristic
119D61—44no—
120C22×C22⋊C4—611no—
121#388—1222no—
122#388—1222no—
123#380—612no—
124#379—612no—
125#379—614no—
126C4×C22⋊C4—611no—
127C4×C22⋊C4#692311yescharacteristic, complemented
128#342—1222no—
129#342—1222no—
130C61#875011yescharacteristic, complemented, Sylow
131C25—611no—
132C23×C4—611no—
133C23×C4C2×#692311yescharacteristic
134C2×C4⋊C4—1222no—
135C2×C22⋊C4—612no—
136C2×C22⋊C4—612no—
137C2×C22⋊C4—612no—
138C2×C22⋊C4—1224no—
139C2×C22⋊C4—1222no—
140C2×C22⋊C4—1222no—
141C2×C22⋊C4—1224no—
142C2×C22⋊C4—1224no—
143C2×C22⋊C4—1224no—
144C2×C22⋊C4C2×#692312yes—
145C2×C42—21no—
146C2×C42—1221no—
147#95—21no—
148#95—1222no—
149#95—1221no—
150C24—612no—
151C24—614no—
152C24—4881no—
153C24—4881no—
154C24—2442no—
155C24C22×#692311yescharacteristic
156C22×C4—22no—
157C22×C4—22no—
158C22×C4—81no—
159C22×C4—612no—
160C22×C4—1222no—
161C22×C4—1222no—
162C22×C4—4881no—
163C22×C4—2444no—
164C22×C4C22⋊#692311yescharacteristic
165C22×C4C22⋊#692311yescharacteristic
166C4⋊C4—4882no—
167C22⋊C4—42no—
168C22⋊C4—1224no—
169C22⋊C4—1224no—
170C22⋊C4—4882no—
171C22⋊C4—4882no—
172C22⋊C4—4884no—
173C22⋊C4—4884no—
174C22⋊C4—2448no—
175C22⋊C4—2442no—
176C42—81no—
177C42—4881no—
178C23—22no—
179C23—41no—
180C23—41no—
181C23—614no—
182C23—1224no—
183C23—4888no—
184C23—2442no—
185C23—2442no—
186C23—2444no—
187C23—2444no—
188C23—2444no—
189C23C2×C22⋊#692311yescharacteristic
190C23#1451985612yes—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—41no—
194C2×C4—41no—
195C2×C4—42no—
196C2×C4—42no—
197C2×C4—42no—
198C2×C4—82no—
199C2×C4—1222no—
200C2×C4—4884no—
201C2×C4—4884no—
202C2×C4—4884no—
203C2×C4—4882no—
204C2×C4—2442no—
205C2×C4—2442no—
206C2×C4—2442no—
207C2×C4—2442no—
208C22—21no—
209C22—21no—
210C22—22no—
211C22—22no—
212C22—22no—
213C22—44no—
214C22—1224no—
215C22—1224no—
216C22—1224no—
217C22—4884no—
218C22—4888no—
219C22#1684070511yescharacteristic
220C22#1684074112yes—
221C4—41no—
222C4—41no—
223C4—82no—
224C4—9764no—
225C4—4882no—
226C4—2442no—
227C2—22no—
228C2—42no—
229C2—2444no—
230C2#2146171611yescharacteristic
231C2#2146173011yescharacteristic
232C2#2146173111yescharacteristic
subgroupG/H
centerC22#16840705
commutatorC24×C61C22×C4
FrattiniC24C22×#6923
FittingC4×C22⋊C4×C61C4
socleC22×C61#381
prime radical, cosocleC24×D61C23
hypercenterC4×C22⋊C4#6923
hypocenterC61#8750
LCSG ▷ C24×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C24 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
10. #16839620C4semidirect
12. C4×C22⋊Dic61C4semidirect
13. C4×C22⋊C4×C61C4semidirect
127. C4×C22⋊C4#6923semidirect
130. C61#8750semidirect

Maximal subgroups

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

subgroupindex
#214617142
#214607182
#214484142
#875061