Finite Group Databasebeta

← #30604187

Subgroups — #30604187

Order 15616.

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

normal subgroups only

This group has 460 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#21461075C212yesmaximal
2#21460760C212yesmaximal, complemented
3#21460750C212yesmaximal, complemented
4#21448366C211yesmaximal, characteristic
5#16840732—22no—
6#16840607C2214yes—
7#16840605—22no—
8C2×#14519764C411yescharacteristic
9C2×#14519742C411yescharacteristic
10C2×D4×Dic61C2211yescharacteristic
11#16839668C2211yescharacteristic
12#16839650—22no—
13#16839627C2211yescharacteristic
14C22⋊C4×Dic61—22no—
15C42×Dic61C411yescharacteristic
16C61×#390C411yescharacteristic
17C2×#11758217—42no—
18C22⋊#92420—24no—
19C22⋊#92420—42no—
20C22×Dic122C2×C411yescharacteristic
21C23×Dic61D412yes—
22#14519764—22no—
23#14519764—22no—
24#14519742—41no—
25#14519742—41no—
26D4×Dic61—41no—
27D4×Dic61—41no—
28C2×C4⋊Dic61C2311yescharacteristic
29C2×#11758196—21no—
30C2×C22⋊Dic61—22no—
31C2×C22⋊Dic61D412yes—
32C2×C4×Dic61—21no—
33C2×C4×Dic61—21no—
34C2×C4×Dic61—21no—
35C2×C4×Dic61C2×C411yescharacteristic
36C2×C4×Dic61C2×C411yescharacteristic
37#14519684—22no—
38#14519684—22no—
39C22×D4×C61C2×C411yescharacteristic
40C2×C4⋊C4×C61C2×C411yescharacteristic
41C2×C22⋊C4×C61—22no—
42C2×C42×C61C2×C411yescharacteristic
43C24×C61C22⋊C412yes—
44C2×D4×C61—21no—
45C2×D4×C61—21no—
46C2×D4×C61—41no—
47C2×D4×C61—41no—
48C22×C4×C61—21no—
49C22×C4×C61—21no—
50C22×C4×C61C22×C411yescharacteristic
51C22×Dic61—21no—
52C22×Dic61—21no—
53C22×Dic61—22no—
54C22×Dic61—22no—
55C22×Dic61—44no—
56C22×Dic61C22⋊C411yescharacteristic
57C22×Dic61C22⋊C411yescharacteristic
58C22×Dic61C2×D412yes—
59C2×Dic122—21no—
60C2×Dic122—41no—
61C2×Dic122—41no—
62C2×Dic122M1612yescomplemented
63#11758217—84no—
64C2×#92420—44no—
65C4⋊C4×C61—41no—
66C22⋊C4×C61—44no—
67C42×C61—41no—
68C22⋊Dic61—28no—
69C22⋊Dic61—42no—
70C4⋊Dic61—41no—
71#11758196—42no—
72C4×Dic61—21no—
73C4×Dic61—21no—
74C4×Dic61—21no—
75C4×Dic61—42no—
76C4×Dic61—42no—
77C4×Dic61—41no—
78C4×Dic61—41no—
79C4×Dic61M1612yescomplemented
80C23×C61—22no—
81C23×C61—22no—
82C23×C61—22no—
83C23×C61—42no—
84C23×C61—42no—
85C23×C61C2×C22⋊C411yescharacteristic
86D4×C61—42no—
87D4×C61—42no—
88C2×C4×C61—21no—
89C2×C4×C61—21no—
90C2×C4×C61—22no—
91C2×C4×C61—41no—
92C2×C4×C61—41no—
93C2×C4×C61—42no—
94C2×C4×C61—41no—
95C2×C4×C61C2×M1611yescharacteristic
96C2×C4×C61C2×M1611yescharacteristic
97C2×Dic61—22no—
98C2×Dic61—22no—
99C2×Dic61—22no—
100C2×Dic61—21no—
101C2×Dic61—22no—
102C2×Dic61—41no—
103C2×Dic61—41no—
104C2×Dic61—41no—
105C2×Dic61—41no—
106C2×Dic61—44no—
107C2×Dic61—41no—
108C2×Dic61—42no—
109C2×Dic61—82no—
110C2×Dic61#9911yescharacteristic
111C2×Dic61#9911yescharacteristic
112Dic122—42no—
113Dic122—42no—
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—81no—
130Dic61—21no—
131Dic61—42no—
132Dic61—42no—
133Dic61—41no—
134Dic61—42no—
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—611no—
147C2×C4×Q8—611no—
148C2×C4×D4—611no—
149#407—1222no—
150#391—611no—
151#390#692311yescharacteristic
152#388—1222no—
153#382—611no—
154C4×C22⋊C4—1222no—
155C43—611no—
156#324—614no—
157#323—1222no—
158C61#1153111yescharacteristic, complemented, Sylow
159C22×Q8—611no—
160C22×D4C2×#692311yescharacteristic
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—1221no—
171C2×C4⋊C4C2×#692311yescharacteristic
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—612no—
187C2×Q8—1221no—
188C2×Q8—2441no—
189C2×Q8—2441no—
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—41no—
208C4⋊C4—2441no—
209C4⋊C4—2442no—
210C22⋊C4—44no—
211C22⋊C4—1228no—
212C22⋊C4—2442no—
213C42—41no—
214C42—612no—
215C42—1221no—
216C42—1221no—
217C42—1221no—
218C42—2442no—
219C42—2441no—
220C42—2441no—
221C42—2442no—
222C23—22no—
223C23—22no—
224C23—22no—
225C23—42no—
226C23—42no—
227C23C2×C22⋊#692311yescharacteristic
228Q8—2442no—
229Q8—2442no—
230D4—42no—
231D4—42no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—22no—
235C2×C4—41no—
236C2×C4—41no—
237C2×C4—42no—
238C2×C4—41no—
239C2×C4—611no—
240C2×C4—611no—
241C2×C4—1222no—
242C2×C4—1222no—
243C2×C4—1222no—
244C2×C4—1221no—
245C2×C4—1222no—
246C2×C4—4882no—
247C2×C4—2444no—
248C2×C4—2441no—
249C2×C4—2441no—
250C2×C4—2441no—
251C2×C4—2441no—
252C2×C4—2441no—
253C2×C4—2442no—
254C2×C4D61⋊M1611yescharacteristic
255C2×C4D61⋊M1611yescharacteristic
256C8—4884no—
257C22—21no—
258C22—21no—
259C22—44no—
260C22—42no—
261C22—42no—
262C22—42no—
263C22—82no—
264C22#1684073411yescharacteristic
265C22D61⋊#9911yescharacteristic
266C22#1684074911yescharacteristic
267C4—21no—
268C4—21no—
269C4—42no—
270C4—81no—
271C4—612no—
272C4—1221no—
273C4—2442no—
274C4—2442no—
275C4—2442no—
276C4—2441no—
277C2—21no—
278C2—21no—
279C2—82no—
280C2#2146107711yescharacteristic
281C2D61⋊#35411yescharacteristic
282C2#2146211111yescharacteristic
subgroupG/H
centerC22D61⋊#99
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#390C4
socleC22×C61C2×#99
prime radicalC22×D4×C61C2×C4
cosocleC2×C4⋊Dic61C23
hypercenter#390#6923
hypocenterC61#11531
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ #390

Complements

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

NH ≅ G/Ntype
2. #21460760C2semidirect
3. #21460750C2semidirect
62. C2×Dic122M16semidirect
79. C4×Dic61M16semidirect
158. C61#11531semidirect

Maximal subgroups

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

subgroupindex
#214610752
#214607602
#214607502
#214483662
#1153161