Finite Group Databasebeta

← #30604185

Subgroups — #30604185

Order 15616.

460 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 76 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#21461075C212yesmaximal
2#21460759C212yesmaximal, complemented
3#21460749C212yesmaximal, complemented
4#124×Dic61C211yesmaximal, characteristic
5#16840732—22no—
6#16840607C2214yes—
7#16840605—22no—
8C2×Q8×Dic61C411yescharacteristic
9C2×D4×Dic61C2211yescharacteristic
10#16839669C2211yescharacteristic
11#16839665C411yescharacteristic
12#16839655—22no—
13#16839628C2211yescharacteristic
14C22⋊C4×Dic61—22no—
15C42×Dic61C411yescharacteristic
16C2×#124×C61C411yescharacteristic
17C2×#11758217—42no—
18C22⋊#92420—24no—
19C22⋊#92420—42no—
20C23×Dic61D412yes—
21Q8×Dic61—41no—
22Q8×Dic61—41no—
23D4×Dic61—41no—
24D4×Dic61—41no—
25C2×C4⋊Dic61—21no—
26C2×C4⋊Dic61C2×C411yescharacteristic
27C2×C4⋊Dic61C2311yescharacteristic
28C2×C22⋊Dic61—22no—
29C2×C22⋊Dic61D412yes—
30C2×C4×Dic61—21no—
31C2×C4×Dic61—21no—
32C2×C4×Dic61—21no—
33C2×C4×Dic61C2×C411yescharacteristic
34C2×C4×Dic61C2×C411yescharacteristic
35#14519684—22no—
36#14519684—22no—
37C22×Q8×C61C2×C411yescharacteristic
38C22×D4×C61C2×C411yescharacteristic
39#124×C61—22no—
40#124×C61—22no—
41C2×C22⋊C4×C61—22no—
42C2×C42×C61C2×C411yescharacteristic
43C24×C61C22⋊C412yes—
44C2×Q8×C61—21no—
45C2×Q8×C61—41no—
46C2×Q8×C61—41no—
47C2×Q8×C61M1612yescomplemented
48C2×D4×C61—21no—
49C2×D4×C61—21no—
50C2×D4×C61—41no—
51C2×D4×C61—41no—
52C22×C4×C61—21no—
53C22×C4×C61—21no—
54C22×C4×C61C22×C411yescharacteristic
55C22×Dic61—21no—
56C22×Dic61—22no—
57C22×Dic61—22no—
58C22×Dic61—21no—
59C22×Dic61—44no—
60C22×Dic61C22⋊C411yescharacteristic
61C22×Dic61C22⋊C411yescharacteristic
62C22×Dic61C2×D412yes—
63#11758217—84no—
64C2×#92420—44no—
65C22⋊C4×C61—28no—
66C42×C61—21no—
67C42×C61M1612yescomplemented
68C22⋊Dic61—42no—
69C22⋊Dic61—44no—
70C4⋊Dic61—41no—
71C4⋊Dic61—42no—
72C4⋊Dic61—41no—
73C4×Dic61—21no—
74C4×Dic61—21no—
75C4×Dic61—42no—
76C4×Dic61—42no—
77C4×Dic61—41no—
78C4×Dic61—41no—
79C4×Dic61—41no—
80C23×C61—22no—
81C23×C61—22no—
82C23×C61—22no—
83C23×C61—42no—
84C23×C61—42no—
85C23×C61C2×C22⋊C411yescharacteristic
86Q8×C61—42no—
87Q8×C61—42no—
88D4×C61—42no—
89D4×C61—42no—
90C2×C4×C61—21no—
91C2×C4×C61—21no—
92C2×C4×C61—22no—
93C2×C4×C61—22no—
94C2×C4×C61—41no—
95C2×C4×C61—41no—
96C2×C4×C61—41no—
97C2×C4×C61—41no—
98C2×C4×C61C2×M1611yescharacteristic
99C2×C4×C61C2×M1611yescharacteristic
100C2×Dic61—22no—
101C2×Dic61—22no—
102C2×Dic61—21no—
103C2×Dic61—22no—
104C2×Dic61—41no—
105C2×Dic61—41no—
106C2×Dic61—44no—
107C2×Dic61—41no—
108C2×Dic61—42no—
109C2×Dic61—42no—
110C2×Dic61—41no—
111C2×Dic61—82no—
112C2×Dic61#9911yescharacteristic
113C2×Dic61#9911yescharacteristic
114#92420—84no—
115#11531—611nomaximal, Sylow
116C22×C61—21no—
117C22×C61—21no—
118C22×C61—44no—
119C22×C61—42no—
120C22×C61—42no—
121C22×C61—42no—
122C22×C61—82no—
123C22×C61#40711yescharacteristic
124C22×C61C2×#9911yescharacteristic
125C22×C61#41311yescharacteristic
126C4×C61—21no—
127C4×C61—21no—
128C4×C61—42no—
129C4×C61—42no—
130Dic61—21no—
131Dic61—42no—
132Dic61—42no—
133Dic61—41no—
134Dic61—81no—
135Dic61#35412yes—
136C4×#124—611no—
137#1465—612no—
138#1324—612no—
139#1319—612no—
140C2×C61—21no—
141C2×C61—21no—
142C2×C61—82no—
143C2×C61#146511yescharacteristic
144C2×C61C2×#35411yescharacteristic
145C2×C61#213211yescharacteristic
146C2×#124#692311yescharacteristic
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—611no—
156#324—614no—
157#323—1222no—
158C61#1153111yescharacteristic, complemented, Sylow
159C22×Q8C2×#692311yescharacteristic
160C22×D4C2×#692311yescharacteristic
161C23×C4—612no—
162C2×M16—2442no—
163#124—22no—
164#124—22no—
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—22no—
173C2×C22⋊C4—612no—
174C2×C22⋊C4—1222no—
175C2×C42—611no—
176C2×C42—611no—
177C2×C42—1221no—
178C2×C42—1221no—
179C2×C42—1221no—
180C2×C42C2×#692311yescharacteristic
181C22⋊C8—1224no—
182C22⋊C8—2442no—
183#95—1222no—
184#95—1222no—
185C24C22⋊#692312yes—
186C2×Q8—21no—
187C2×Q8—41no—
188C2×Q8—41no—
189C2×Q8#1175821712yescomplemented
190C2×D4—21no—
191C2×D4—21no—
192C2×D4—41no—
193C2×D4—41no—
194C22×C4—21no—
195C22×C4—21no—
196C22×C4—611no—
197C22×C4—612no—
198C22×C4—611no—
199C22×C4—1222no—
200C22×C4—1222no—
201C22×C4—1221no—
202C22×C4—1221no—
203C22×C4—2444no—
204C22×C4C22×#692311yescharacteristic
205M16—4884no—
206C2×C8—2444no—
207C4⋊C4—2441no—
208C4⋊C4—2441no—
209C4⋊C4—2442no—
210C22⋊C4—28no—
211C22⋊C4—2442no—
212C22⋊C4—2444no—
213C42—21no—
214C42—1221no—
215C42—1221no—
216C42—2441no—
217C42—2441no—
218C42—2441no—
219C42—2442no—
220C42—2442no—
221C42#1175821712yescomplemented
222C23—22no—
223C23—22no—
224C23—22no—
225C23—42no—
226C23—42no—
227C23C2×C22⋊#692311yescharacteristic
228Q8—42no—
229Q8—42no—
230D4—42no—
231D4—42no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—22no—
235C2×C4—22no—
236C2×C4—41no—
237C2×C4—41no—
238C2×C4—41no—
239C2×C4—41no—
240C2×C4—611no—
241C2×C4—611no—
242C2×C4—1222no—
243C2×C4—1222no—
244C2×C4—1221no—
245C2×C4—1222no—
246C2×C4—4882no—
247C2×C4—2444no—
248C2×C4—2442no—
249C2×C4—2441no—
250C2×C4—2441no—
251C2×C4—2441no—
252C2×C4—2441no—
253C2×C4—2442no—
254C2×C4C2×#1175821711yescharacteristic
255C2×C4C2×#1175821711yescharacteristic
256C8—4884no—
257C22—21no—
258C22—21no—
259C22—44no—
260C22—42no—
261C22—42no—
262C22—42no—
263C22—82no—
264C22#1684073211yescharacteristic
265C22D61⋊#9911yescharacteristic
266C22#1684074911yescharacteristic
267C4—21no—
268C4—21no—
269C4—42no—
270C4—42no—
271C4—612no—
272C4—1221no—
273C4—4881no—
274C4—2442no—
275C4—2442no—
276C4—2441no—
277C2—21no—
278C2—21no—
279C2—82no—
280C2#2146107511yescharacteristic
281C2D61⋊#35411yescharacteristic
282C2#2146211311yescharacteristic
subgroupG/H
centerC22D61⋊#99
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC2×#124×C61C4
socleC22×C61C2×#99
prime radicalC22×D4×C61C2×C4
cosocleC2×C4⋊Dic61C23
hypercenterC2×#124#6923
hypocenterC61#11531
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
2. #21460759C2semidirect
3. #21460749C2semidirect
47. C2×Q8×C61M16semidirect
67. C42×C61M16semidirect
158. C61#11531semidirect
189. C2×Q8#11758217semidirect
221. C42#11758217semidirect

Maximal subgroups

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

subgroupindex
#214610752
#214607592
#214607492
#124×Dic612
#1153161