Finite Group Databasebeta

← #30604202

Subgroups — #30604202

Order 15616.

440 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 74 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#21460761C212yesmaximal, complemented
3#21460750C212yesmaximal, complemented
4#21448530C211yesmaximal, characteristic
5#16840733—22no—
6#16840607C2214yes—
7#16840606—22no—
8C2×#14519765C411yescharacteristic
9C2×C4×Dic122C411yescharacteristic
10C2×C4×D244C2211yescharacteristic
11#16839668C2211yescharacteristic
12#16839664C411yescharacteristic
13#16839654—22no—
14#16839636—22no—
15#16839632C2211yescharacteristic
16C61×#376C411yescharacteristic
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—42no—
26C4×D244—42no—
27C2×C4⋊Dic61—22no—
28C2×C4⋊Dic61C2×C411yescharacteristic
29C2×C4⋊Dic61C2311yescharacteristic
30C2×#11758196—21no—
31C2×#11758198—22no—
32C2×#11758198—22no—
33C2×#11758198D412yes—
34C2×C4×Dic61—21no—
35#14519684—22no—
36C2×C42×C61C2×C411yescharacteristic
37C2×C42×C61C2×C411yescharacteristic
38C2×C42×C61C2×C411yescharacteristic
39#95×C61—21no—
40#95×C61—21no—
41C23×D61C22⋊C412yes—
42C22×C4×C61—21no—
43C22×C4×C61—21no—
44C22×C4×C61C22⋊C411yescharacteristic
45C22×C4×C61C22⋊C411yescharacteristic
46C22×C4×C61C22×C411yescharacteristic
47C22×Dic61—21no—
48C22×Dic61—21no—
49C22×Dic61C2×D412yes—
50C2×D244—21no—
51C2×D244—21no—
52C2×D244—41no—
53C2×D244—41no—
54C2×C4×D61—22no—
55C2×C4×D61—22no—
56C2×C4×D61—82no—
57C2×Dic122—21no—
58C2×Dic122—41no—
59C2×Dic122—41no—
60C2×Dic122M1612yescomplemented
61C2×#92420—44no—
62#11758213—84no—
63C42×C61—22no—
64C42×C61—21no—
65C42×C61—41no—
66C42×C61M1612yescomplemented
67#11758198—28no—
68#11758198—42no—
69#11758198—82no—
70C4⋊Dic61—41no—
71C4⋊Dic61—41no—
72C4⋊Dic61—82no—
73#11758196—42no—
74C4×Dic61—42no—
75C23×C61C2×C22⋊C411yescharacteristic
76C22×D61—22no—
77C22×D61—22no—
78C22×D61—22no—
79C22×D61—42no—
80C22×D61—42no—
81C2×C4×C61—21no—
82C2×C4×C61—21no—
83C2×C4×C61—22no—
84C2×C4×C61—21no—
85C2×C4×C61—41no—
86C2×C4×C61—41no—
87C2×C4×C61—41no—
88C2×C4×C61—41no—
89C2×C4×C61—41no—
90C2×C4×C61—41no—
91C2×C4×C61—41no—
92C2×C4×C61#9912yes—
93C2×C4×C61C2×M1611yescharacteristic
94C2×C4×C61C2×M1611yescharacteristic
95C2×Dic61—22no—
96C2×Dic61—22no—
97C2×Dic61—41no—
98C2×Dic61—41no—
99C2×Dic61—42no—
100C2×Dic61—42no—
101C2×Dic61—41no—
102D244—42no—
103D244—42no—
104C4×D61—44no—
105C4×D61—82no—
106Dic122—42no—
107Dic122—42no—
108#92420—84no—
109#11535—611nomaximal, Sylow
110C22×C61—21no—
111C22×C61—21no—
112C22×C61#40711yescharacteristic
113C22×C61C2×#9911yescharacteristic
114C22×C61#41311yescharacteristic
115C2×D61—44no—
116C2×D61—42no—
117C2×D61—42no—
118C2×D61—42no—
119C2×D61—82no—
120C4×C61—22no—
121C4×C61—21no—
122C4×C61—21no—
123C4×C61—42no—
124C4×C61—41no—
125C4×C61—81no—
126Dic61—42no—
127Dic61—42no—
128Dic61—81no—
129#2326—611no—
130#1465—612no—
131#1325—612no—
132#1319—612no—
133C2×C61—21no—
134C2×C61—21no—
135C2×C61#146511yescharacteristic
136C2×C61#212711yescharacteristic
137C2×C61#213511yescharacteristic
138D61—82no—
139C2×#124—611no—
140C2×C4×Q8—611no—
141C2×C4×D4—611no—
142#407—1222no—
143#391—611no—
144#390—611no—
145#388—1222no—
146#385—1222no—
147#384—611no—
148#376#692311yescharacteristic
149#324—614no—
150#323—1222no—
151C61#1153511yescharacteristic, complemented, Sylow
152C22×Q8—611no—
153C22×D4—611no—
154C23×C4—612no—
155C2×M16—2442no—
156#124—1222no—
157#124—1222no—
158C4×Q8—2442no—
159C4×D4—2442no—
160C2×C4⋊C4—611no—
161C2×C4⋊C4—611no—
162C2×C4⋊C4—1222no—
163C2×C4⋊C4—1221no—
164C2×C22⋊C4—612no—
165C2×C22⋊C4—1222no—
166C2×C22⋊C4—1222no—
167C2×C42—1221no—
168C2×C42C2×#692311yescharacteristic
169C2×C42C2×#692311yescharacteristic
170C2×C42C2×#692311yescharacteristic
171C22⋊C8—1224no—
172C22⋊C8—2442no—
173#95—21no—
174#95—21no—
175#95—1222no—
176C24—612no—
177C2×Q8—612no—
178C2×Q8—1221no—
179C2×Q8—2441no—
180C2×Q8—2441no—
181C2×D4—1221no—
182C2×D4—1221no—
183C2×D4—2441no—
184C2×D4—2441no—
185C22×C4—21no—
186C22×C4—21no—
187C22×C4—612no—
188C22×C4—1221no—
189C22×C4—1222no—
190C22×C4—1222no—
191C22×C4—1221no—
192C22×C4—4882no—
193C22×C4C22⋊#692311yescharacteristic
194C22×C4C22⋊#692311yescharacteristic
195C22×C4C22×#692311yescharacteristic
196M16—4884no—
197C2×C8—2444no—
198C4⋊C4—4882no—
199C4⋊C4—2441no—
200C4⋊C4—2441no—
201C4⋊C4—2442no—
202C22⋊C4—1228no—
203C22⋊C4—4882no—
204C22⋊C4—2442no—
205C42—22no—
206C42—21no—
207C42—41no—
208C42—2442no—
209C42#1175821312yescomplemented
210C23—1222no—
211C23—1222no—
212C23—1222no—
213C23—2442no—
214C23—2442no—
215C23C2×C22⋊#692311yescharacteristic
216Q8—2442no—
217Q8—2442no—
218D4—2442no—
219D4—2442no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—22no—
223C2×C4—21no—
224C2×C4—41no—
225C2×C4—41no—
226C2×C4—41no—
227C2×C4—41no—
228C2×C4—41no—
229C2×C4—41no—
230C2×C4—41no—
231C2×C4—1222no—
232C2×C4—1222no—
233C2×C4—4882no—
234C2×C4—2444no—
235C2×C4—2442no—
236C2×C4—2441no—
237C2×C4—2441no—
238C2×C4—2441no—
239C2×C4—2442no—
240C2×C4#1451983612yes—
241C2×C4D61⋊M1611yescharacteristic
242C2×C4C2×#1175821311yescharacteristic
243C8—4884no—
244C22—21no—
245C22—21no—
246C22—4882no—
247C22—2444no—
248C22—2442no—
249C22—2442no—
250C22—2442no—
251C22#1684073311yescharacteristic
252C22C2×#1451983611yescharacteristic
253C22#1684074811yescharacteristic
254C4—22no—
255C4—21no—
256C4—21no—
257C4—42no—
258C4—41no—
259C4—81no—
260C4—4881no—
261C4—2442no—
262C4—2442no—
263C2—21no—
264C2—21no—
265C2—4882no—
266C2#2146107611yescharacteristic
267C2#2146209611yescharacteristic
268C2#2146212311yescharacteristic
subgroupG/H
centerC22C2×#14519836
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#376C4
socleC22×C61C2×#99
prime radicalC22×D244C2×C4
cosocleC2×C4⋊Dic61C23
hypercenter#376#6923
hypocenterC61#11535
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42 ◁ #376

Complements

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

NH ≅ G/Ntype
2. #21460761C2semidirect
3. #21460750C2semidirect
60. C2×Dic122M16semidirect
66. C42×C61M16semidirect
151. C61#11535semidirect
209. C42#11758213semidirect

Maximal subgroups

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

subgroupindex
#214610762
#214607612
#214607502
#214485302
#1153561