Finite Group Databasebeta

← #30604186

Subgroups — #30604186

Order 15616.

460 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 78 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#21461076C212yesmaximal
2#21460759C212yesmaximal, complemented
3#21460750C212yesmaximal, complemented
4C4×#14519765C211yesmaximal, characteristic
5#16840733—22no—
6#16840607C2214yes—
7#16840606—22no—
8C2×#14519765C411yescharacteristic
9C2×C4×Dic122C411yescharacteristic
10C2×C4×D244C2211yescharacteristic
11#16839668C2211yescharacteristic
12#16839664C411yescharacteristic
13#16839653—22no—
14#16839628C2211yescharacteristic
15C4×#11758198—22no—
16C43×C61C411yescharacteristic
17C2×#11758213—42no—
18#14519834—42no—
19C22⋊#92420—24no—
20C22×Dic122C2×C411yescharacteristic
21C22×D244C2×C411yescharacteristic
22C22×C4×D61D412yes—
23#14519765—22no—
24#14519765—22no—
25C4×Dic122—41no—
26C4×Dic122—41no—
27C4×D244—41no—
28C4×D244—41no—
29C2×C4⋊Dic61C2×C411yescharacteristic
30C2×C4⋊Dic61C2311yescharacteristic
31C2×#11758196—21no—
32C2×#11758198—22no—
33C2×#11758198—22no—
34C2×#11758198D412yes—
35C2×C4×Dic61—21no—
36#14519684—22no—
37#14519684—22no—
38C2×C42×C61—21no—
39C2×C42×C61—21no—
40C2×C42×C61C2×C411yescharacteristic
41C2×C42×C61C2×C411yescharacteristic
42C2×C42×C61C2×C411yescharacteristic
43C23×D61C22⋊C412yes—
44C22×C4×C61—21no—
45C22×C4×C61—21no—
46C22×C4×C61C22⋊C411yescharacteristic
47C22×C4×C61C22⋊C411yescharacteristic
48C22×C4×C61C22×C411yescharacteristic
49C22×Dic61—21no—
50C22×Dic61—21no—
51C22×Dic61C2×D412yes—
52C2×D244—21no—
53C2×D244—21no—
54C2×D244—41no—
55C2×D244—41no—
56C2×C4×D61—22no—
57C2×C4×D61—22no—
58C2×C4×D61—44no—
59C2×Dic122—21no—
60C2×Dic122—41no—
61C2×Dic122—41no—
62C2×Dic122M1612yescomplemented
63C2×#92420—44no—
64#11758213—84no—
65C42×C61—21no—
66C42×C61—21no—
67C42×C61—21no—
68C42×C61—42no—
69C42×C61—42no—
70C42×C61—41no—
71C42×C61M1612yescomplemented
72#11758198—28no—
73#11758198—42no—
74#11758198—44no—
75C4⋊Dic61—41no—
76C4⋊Dic61—41no—
77#11758196—42no—
78C4×Dic61—41no—
79C4×Dic61—41no—
80C23×C61C2×C22⋊C411yescharacteristic
81C22×D61—22no—
82C22×D61—22no—
83C22×D61—22no—
84C22×D61—42no—
85C22×D61—42no—
86C2×C4×C61—21no—
87C2×C4×C61—21no—
88C2×C4×C61—22no—
89C2×C4×C61—22no—
90C2×C4×C61—22no—
91C2×C4×C61—21no—
92C2×C4×C61—41no—
93C2×C4×C61—41no—
94C2×C4×C61—41no—
95C2×C4×C61—41no—
96C2×C4×C61—41no—
97C2×C4×C61#9911yescharacteristic
98C2×C4×C61#9911yescharacteristic
99C2×C4×C61C2×M1611yescharacteristic
100C2×C4×C61C2×M1611yescharacteristic
101C2×Dic61—22no—
102C2×Dic61—22no—
103C2×Dic61—41no—
104C2×Dic61—41no—
105C2×Dic61—42no—
106C2×Dic61—42no—
107C2×Dic61—41no—
108D244—42no—
109D244—42no—
110C4×D61—44no—
111C4×D61—82no—
112Dic122—42no—
113Dic122—42no—
114#92420—84no—
115#11531—611nomaximal, Sylow
116C22×C61—21no—
117C22×C61—21no—
118C22×C61#40711yescharacteristic
119C22×C61C2×#9911yescharacteristic
120C22×C61#41311yescharacteristic
121C2×D61—44no—
122C2×D61—42no—
123C2×D61—42no—
124C2×D61—42no—
125C2×D61—82no—
126C4×C61—21no—
127C4×C61—21no—
128C4×C61—21no—
129C4×C61—42no—
130C4×C61—42no—
131C4×C61—41no—
132C4×C61#35412yes—
133Dic61—42no—
134Dic61—42no—
135Dic61—81no—
136C4×#124—611no—
137#1465—612no—
138#1324—612no—
139#1319—612no—
140C2×C61—21no—
141C2×C61—21no—
142C2×C61#146511yescharacteristic
143C2×C61C2×#35411yescharacteristic
144C2×C61#213211yescharacteristic
145D61—82no—
146C2×#124—611no—
147C2×C4×Q8—611no—
148C2×C4×D4—611no—
149#407—1222no—
150#391—611no—
151#390—611no—
152#388—1222no—
153#382—611no—
154C4×C22⋊C4—1222no—
155C43#692311yescharacteristic
156#324—614no—
157#323—1222no—
158C61#1153111yescharacteristic, complemented, Sylow
159C22×Q8—611no—
160C22×D4—611no—
161C23×C4—612no—
162C2×M16—2442no—
163#124—1222no—
164#124—1222no—
165C4×Q8—2441no—
166C4×Q8—2441no—
167C4×D4—2441no—
168C4×D4—2441no—
169C2×C4⋊C4—611no—
170C2×C4⋊C4—611no—
171C2×C4⋊C4—1221no—
172C2×C22⋊C4—612no—
173C2×C22⋊C4—1222no—
174C2×C22⋊C4—1222no—
175C2×C42—21no—
176C2×C42—21no—
177C2×C42—1221no—
178C2×C42C2×#692311yescharacteristic
179C2×C42C2×#692311yescharacteristic
180C2×C42C2×#692311yescharacteristic
181C22⋊C8—1224no—
182C22⋊C8—2442no—
183#95—1222no—
184#95—1222no—
185C24—612no—
186C2×Q8—612no—
187C2×Q8—1221no—
188C2×Q8—2441no—
189C2×Q8—2441no—
190C2×D4—1221no—
191C2×D4—1221no—
192C2×D4—2441no—
193C2×D4—2441no—
194C22×C4—21no—
195C22×C4—21no—
196C22×C4—612no—
197C22×C4—1221no—
198C22×C4—1222no—
199C22×C4—1222no—
200C22×C4—1221no—
201C22×C4—2444no—
202C22×C4C22⋊#692311yescharacteristic
203C22×C4C22⋊#692311yescharacteristic
204C22×C4C22×#692311yescharacteristic
205M16—4884no—
206C2×C8—2444no—
207C4⋊C4—2441no—
208C4⋊C4—2441no—
209C4⋊C4—2442no—
210C22⋊C4—1228no—
211C22⋊C4—2442no—
212C22⋊C4—2444no—
213C42—21no—
214C42—21no—
215C42—21no—
216C42—41no—
217C42—42no—
218C42—42no—
219C42—2441no—
220C42—2441no—
221C42#1175821312yescomplemented
222C23—1222no—
223C23—1222no—
224C23—1222no—
225C23—2442no—
226C23—2442no—
227C23C2×C22⋊#692311yescharacteristic
228Q8—2442no—
229Q8—2442no—
230D4—2442no—
231D4—2442no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—22no—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—21no—
238C2×C4—41no—
239C2×C4—41no—
240C2×C4—41no—
241C2×C4—41no—
242C2×C4—41no—
243C2×C4—1222no—
244C2×C4—1222no—
245C2×C4—4882no—
246C2×C4—2442no—
247C2×C4—2441no—
248C2×C4—2441no—
249C2×C4—2441no—
250C2×C4—2444no—
251C2×C4—2442no—
252C2×C4#1451983611yescharacteristic
253C2×C4#1451983611yescharacteristic
254C2×C4D61⋊M1611yescharacteristic
255C2×C4C2×#1175821311yescharacteristic
256C8—4884no—
257C22—21no—
258C22—21no—
259C22—4882no—
260C22—2444no—
261C22—2442no—
262C22—2442no—
263C22—2442no—
264C22#1684073311yescharacteristic
265C22C2×#1451983611yescharacteristic
266C22#1684074811yescharacteristic
267C4—21no—
268C4—21no—
269C4—21no—
270C4—42no—
271C4—42no—
272C4—41no—
273C4—4881no—
274C4—2442no—
275C4—2442no—
276C4#1684066912yes—
277C2—21no—
278C2—21no—
279C2—4882no—
280C2#2146107611yescharacteristic
281C2C2×#1684066911yescharacteristic
282C2#2146211211yescharacteristic
subgroupG/H
centerC22C2×#14519836
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC43×C61C4
socleC22×C61C2×#99
prime radicalC22×D244C2×C4
cosocleC2×C4⋊Dic61C23
hypercenterC43#6923
hypocenterC61#11531
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42 ◁ C43

Complements

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

NH ≅ G/Ntype
2. #21460759C2semidirect
3. #21460750C2semidirect
62. C2×Dic122M16semidirect
71. C42×C61M16semidirect
158. C61#11531semidirect
221. C42#11758213semidirect

Maximal subgroups

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

subgroupindex
#214610762
#214607592
#214607502
C4×#145197652
#1153161