Finite Group Databasebeta

← #30599363

Subgroups — #30599363

Order 15616.

546 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 546 conjugacy classes of subgroups — too many to draw. Only its 80 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#21461064C212yesmaximal
2#21460720C214yesmaximal, complemented
3#21448431C211yesmaximal, characteristic
4#16840732C2214yes—
5#16840605—22no—
6#16840605—22no—
7C22×C22⋊Dic61C411yescharacteristic
8C22×C22⋊Dic61C2211yescharacteristic
9#16839635—22no—
10#16839634—22no—
11#16839620C412yes—
12#16839620C2212yes—
13C22×C22⋊C4×C61C411yescharacteristic
14C2×#11758217—24no—
15C22⋊#92420—24no—
16C22⋊#92420—24no—
17C23×Dic61—21no—
18C23×Dic61C2×C411yescharacteristic
19C23×Dic61C2311yescharacteristic
20C2×#11758196—22no—
21C2×#11758196—22no—
22C2×C22⋊Dic61—24no—
23C2×C22⋊Dic61—21no—
24C2×C22⋊Dic61—42no—
25C2×C22⋊Dic61C2×C412yes—
26C2×C22⋊Dic61D412yes—
27C2×C22⋊Dic61D412yes—
28#14519684—22no—
29#14519684—22no—
30C25×C61C2×C411yescharacteristic
31C23×C4×C61—21no—
32C2×C22⋊C4×C61—21no—
33C2×C22⋊C4×C61—42no—
34C2×C22⋊C4×C61C2×C412yes—
35C24×C61—22no—
36C24×C61—22no—
37C24×C61—22no—
38C24×C61—81no—
39C24×C61—81no—
40C24×C61C22⋊C411yescharacteristic
41C24×C61C22⋊C411yescharacteristic
42C24×C61C22×C411yescharacteristic
43C22×C4×C61—22no—
44C22×C4×C61—42no—
45C22×C4×C61—81no—
46C22×C4×C61—81no—
47C22×Dic61—22no—
48C22×Dic61—22no—
49C22×Dic61—42no—
50C22×Dic61—81no—
51C22×Dic61—81no—
52C22×Dic61—81no—
53C22×Dic61—81no—
54C22×Dic61C22⋊C412yes—
55C22×Dic61C2×D412yes—
56C22×Dic61#4114yes—
57#11758217—84no—
58C2×#92420—44no—
59C22⋊C4×C61—42no—
60C22⋊C4×C61—42no—
61C22⋊Dic61—24no—
62C22⋊Dic61—24no—
63C22⋊Dic61—42no—
64C22⋊Dic61—42no—
65#11758196—82no—
66#11758196—82no—
67C23×C61—28no—
68C23×C61—21no—
69C23×C61—21no—
70C23×C61—21no—
71C23×C61—21no—
72C23×C61—21no—
73C23×C61—21no—
74C23×C61—41no—
75C23×C61—41no—
76C23×C61—41no—
77C23×C61—41no—
78C23×C61—41no—
79C23×C61—41no—
80C23×C61—82no—
81C23×C61—82no—
82C23×C61—84no—
83C23×C61—84no—
84C23×C61#10012yes—
85C23×C61#10112yes—
86C23×C61C2×C22⋊C411yescharacteristic
87C23×C61#11712yes—
88C2×C4×C61—42no—
89C2×C4×C61—42no—
90C2×C4×C61—42no—
91C2×C4×C61—84no—
92C2×Dic61—22no—
93C2×Dic61—42no—
94C2×Dic61—44no—
95C2×Dic61—42no—
96C2×Dic61—42no—
97C2×Dic61—42no—
98C2×Dic61—42no—
99C2×Dic61—82no—
100C2×Dic61—84no—
101C2×Dic61#12314yes—
102#92420—84no—
103#8756—611nomaximal, Sylow
104C22×C61—21no—
105C22×C61—21no—
106C22×C61—22no—
107C22×C61—22no—
108C22×C61—22no—
109C22×C61—22no—
110C22×C61—22no—
111C22×C61—42no—
112C22×C61—42no—
113C22×C61—42no—
114C22×C61—42no—
115C22×C61—42no—
116C22×C61—42no—
117C22×C61—41no—
118C22×C61—41no—
119C22×C61—41no—
120C22×C61—41no—
121C22×C61—88no—
122C22×C61#38111yescharacteristic
123C22×C61C2×#10011yescharacteristic
124C22×C61C2×#10111yescharacteristic
125C4×C61—82no—
126Dic61—24no—
127Dic61—42no—
128Dic61—82no—
129#2315—611no—
130#1462—612no—
131#1305—614no—
132C2×C61—21no—
133C2×C61—21no—
134C2×C61—42no—
135C2×C61—42no—
136C2×C61—42no—
137C2×C61#182111yescharacteristic
138C2×C61#182811yescharacteristic
139C2×C61#182911yescharacteristic
140C22×C22⋊C4—611no—
141C22×C22⋊C4—611no—
142C22×C22⋊C4#692311yescharacteristic
143#407—614no—
144#385—1222no—
145#385—1222no—
146#380—612no—
147#380—612no—
148#323—1222no—
149#323—1222no—
150C61#875611yescharacteristic, complemented, Sylow
151C25C2×#692311yescharacteristic
152C23×C4—21no—
153C23×C4—611no—
154C23×C4—611no—
155C23×C4—1221no—
156C2×M16—1224no—
157C2×C4⋊C4—1222no—
158C2×C4⋊C4—1222no—
159C2×C22⋊C4—21no—
160C2×C22⋊C4—42no—
161C2×C22⋊C4—612no—
162C2×C22⋊C4—612no—
163C2×C22⋊C4—612no—
164C2×C22⋊C4—1224no—
165C2×C22⋊C4—1221no—
166C2×C22⋊C4—2442no—
167C2×C22⋊C4C2×#692312yes—
168C22⋊C8—1224no—
169C22⋊C8—1224no—
170#95—1222no—
171#95—1222no—
172C24—22no—
173C24—22no—
174C24—22no—
175C24—81no—
176C24—81no—
177C24C22⋊#692311yescharacteristic
178C24C22⋊#692311yescharacteristic
179C24C22×#692311yescharacteristic
180C22×C4—22no—
181C22×C4—42no—
182C22×C4—81no—
183C22×C4—81no—
184C22×C4—612no—
185C22×C4—614no—
186C22×C4—612no—
187C22×C4—1222no—
188C22×C4—1222no—
189C22×C4—4881no—
190C22×C4—4881no—
191C22×C4—4881no—
192C22×C4—4881no—
193C22×C4—2442no—
194M16—4884no—
195C2×C8—2444no—
196C4⋊C4—4882no—
197C4⋊C4—4882no—
198C22⋊C4—42no—
199C22⋊C4—42no—
200C22⋊C4—1224no—
201C22⋊C4—1224no—
202C22⋊C4—2442no—
203C22⋊C4—2442no—
204C23—28no—
205C23—21no—
206C23—21no—
207C23—21no—
208C23—21no—
209C23—21no—
210C23—21no—
211C23—41no—
212C23—41no—
213C23—41no—
214C23—41no—
215C23—41no—
216C23—41no—
217C23—82no—
218C23—82no—
219C23—84no—
220C23—84no—
221C23#1451983712yes—
222C23#1451983812yes—
223C23C2×C22⋊#692311yescharacteristic
224C23#1451985612yes—
225C2×C4—42no—
226C2×C4—42no—
227C2×C4—42no—
228C2×C4—84no—
229C2×C4—614no—
230C2×C4—1222no—
231C2×C4—4884no—
232C2×C4—4882no—
233C2×C4—2442no—
234C2×C4—2444no—
235C2×C4—2442no—
236C2×C4—2442no—
237C2×C4—2442no—
238C2×C4—2442no—
239C8—4884no—
240C22—21no—
241C22—21no—
242C22—22no—
243C22—22no—
244C22—22no—
245C22—22no—
246C22—22no—
247C22—42no—
248C22—42no—
249C22—42no—
250C22—42no—
251C22—42no—
252C22—42no—
253C22—41no—
254C22—41no—
255C22—41no—
256C22—41no—
257C22—88no—
258C22#1684070511yescharacteristic
259C22C2×#1451983711yescharacteristic
260C22C2×#1451983811yescharacteristic
261C4—82no—
262C4—1224no—
263C4—4882no—
264C4—2442no—
265C2—21no—
266C2—21no—
267C2—42no—
268C2—42no—
269C2—42no—
270C2#2146171811yescharacteristic
271C2#2146173011yescharacteristic
272C2#2146173211yescharacteristic
subgroupG/H
centerC22#16840705
commutatorC24×C61C22×C4
FrattiniC24C22×#6923
FittingC22×C22⋊C4×C61C4
socleC22×C61#381
prime radicalC25×C61C2×C4
cosocleC23×Dic61C23
hypercenterC22×C22⋊C4#6923
hypocenterC61#8756
LCSG ▷ C24×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C24 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #21460720C2semidirect
150. C61#8756semidirect

Maximal subgroups

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

subgroupindex
#214610642
#214607202
#214484312
#875661