Finite Group Databasebeta

← #30607261

Subgroups — #30607261

Order 15616.

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

normal subgroups only

This group has 642 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#21461656C212yesmaximal
2#21460917C212yesmaximal, complemented
3#21460916C212yesmaximal, complemented
4#21448306C211yesmaximal, characteristic
5C2×#14519838C2214yes—
6C2×#14519837—22no—
7#16840732—22no—
8C22×#11758224C2211yescharacteristic
9C2×#14519735C411yescharacteristic
10C2×C42×D61C411yescharacteristic
11#16839668C2211yescharacteristic
12#16839667C2211yescharacteristic
13#16839665C411yescharacteristic
14#16839638—22no—
15C22⋊C4×Dic61—22no—
16C61×#390C411yescharacteristic
17C2×#11758217—24no—
18#14519838—28no—
19#14519837—44no—
20C22⋊#92420—44no—
21C2×#11758224—24no—
22C2×#11758224—42no—
23C2×#11758224—42no—
24C22×Dic122C2311yescharacteristic
25C22×C22⋊D61D412yes—
26C23×Dic61D412yes—
27C22×C4×D61—21no—
28C22×C4×D61C2×C411yescharacteristic
29#14519735—42no—
30C2×C4⋊Dic61C2×C411yescharacteristic
31C2×C22⋊Dic61—22no—
32C2×#11758198—21no—
33C2×C4×Dic61—21no—
34C2×C4×Dic61—21no—
35C2×C4×Dic61C2×C411yescharacteristic
36C42×D61—42no—
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—
44C23×D61C22⋊C411yescharacteristic
45C2×D4×C61—22no—
46C2×D4×C61—41no—
47C2×D4×C61—41no—
48C22×C4×C61—21no—
49C22×C4×C61—21no—
50C22×C4×C61C22×C411yescharacteristic
51C2×C22⋊D61—24no—
52C2×C22⋊D61—24no—
53C2×C22⋊D61—42no—
54C22×Dic61—21no—
55C22×Dic61—24no—
56C22×Dic61—24no—
57C22×Dic61—21no—
58C22×Dic61—42no—
59C22×Dic61C22⋊C411yescharacteristic
60C22×Dic61C2×D412yes—
61#11758224—416no—
62C2×C4×D61—22no—
63C2×C4×D61—22no—
64C2×C4×D61—22no—
65C2×C4×D61—42no—
66C2×C4×D61—42no—
67C2×C4×D61—42no—
68C2×Dic122—41no—
69C2×Dic122—41no—
70C2×Dic122#4114yes—
71#11758217—44no—
72#11758217—44no—
73C2×#92420—44no—
74C4⋊C4×C61—41no—
75C22⋊C4×C61—44no—
76C42×C61—41no—
77C22⋊Dic61—44no—
78#11758198—42no—
79C4⋊Dic61—41no—
80C4×Dic61—42no—
81C4×Dic61—42no—
82C4×Dic61—41no—
83C23×C61—22no—
84C23×C61—22no—
85C23×C61—22no—
86C23×C61—42no—
87C23×C61—42no—
88C23×C61C2×C22⋊C411yescharacteristic
89C22×D61—21no—
90C22×D61—21no—
91C22×D61—41no—
92C22×D61—41no—
93C22×D61#9912yes—
94D4×C61—44no—
95C2×C4×C61—21no—
96C2×C4×C61—21no—
97C2×C4×C61—22no—
98C2×C4×C61—41no—
99C2×C4×C61—41no—
100C2×C4×C61—42no—
101C2×C4×C61—41no—
102C2×C4×C61#11712yes—
103C22⋊D61—48no—
104C2×Dic61—21no—
105C2×Dic61—21no—
106C2×Dic61—22no—
107C2×Dic61—22no—
108C2×Dic61—22no—
109C2×Dic61—48no—
110C2×Dic61—41no—
111C2×Dic61—41no—
112C2×Dic61—42no—
113C2×Dic61—41no—
114C2×Dic61#9912yes—
115C2×Dic61#12314yes—
116C4×D61—28no—
117C4×D61—48no—
118Dic122—44no—
119#92420—84no—
120#12861—611nomaximal, Sylow
121C22×C61—21no—
122C22×C61—21no—
123C22×C61—44no—
124C22×C61—42no—
125C22×C61—42no—
126C22×C61—42no—
127C22×C61—82no—
128C22×C61#38111yescharacteristic
129C22×C61C2×#9911yescharacteristic
130C22×C61C2×#9911yescharacteristic
131C2×D61—22no—
132C2×D61—42no—
133C2×D61—41no—
134C2×D61—41no—
135C2×D61—42no—
136C4×C61—22no—
137C4×C61—42no—
138C4×C61—81no—
139Dic61—24no—
140Dic61—22no—
141Dic61—42no—
142Dic61—81no—
143#2297—611no—
144#1785—612no—
145#1394—612no—
146#1394—612no—
147C2×C61—21no—
148C2×C61—21no—
149C2×C61—82no—
150C2×C61#181911yescharacteristic
151C2×C61#213211yescharacteristic
152C2×C61#213211yescharacteristic
153D61—42no—
154C22×#41—611no—
155C2×#117—611no—
156C22×C42—611no—
157C2×#101—614no—
158C2×#100—1222no—
159#407—1222no—
160#391—611no—
161#391—611no—
162#390—611no—
163#390#692311yescharacteristic
164#386—1222no—
165C4×C22⋊C4—1222no—
166C61#1286111yescharacteristic, complemented, Sylow
167C2×#41—1224no—
168C2×#41—2442no—
169C2×#41—2442no—
170C22×Q8—611no—
171C22×D4—612no—
172C22×D4C2×#692311yescharacteristic
173C23×C4—612no—
174C23×C4—611no—
175C23×C4—1221no—
176C2×M16—1224no—
177#117—2442no—
178C2×C4⋊C4—611no—
179C2×C4⋊C4C2×#692311yescharacteristic
180C2×C22⋊C4—22no—
181C2×C22⋊C4—1221no—
182C2×C22⋊C4—1222no—
183C2×C42—611no—
184C2×C42—1221no—
185C2×C42—1221no—
186C2×C42—2442no—
187C2×C42C2×#692311yescharacteristic
188#101—1228no—
189#100—2444no—
190C22⋊C8—2444no—
191#95—1222no—
192#95—1222no—
193C24—611no—
194C24C22⋊#692312yes—
195#41—24416no—
196C2×Q8—614no—
197C2×Q8—2441no—
198C2×Q8—2441no—
199C2×D4—22no—
200C2×D4—41no—
201C2×D4—41no—
202C2×D4—1224no—
203C2×D4—1224no—
204C2×D4—2442no—
205C22×C4—21no—
206C22×C4—21no—
207C22×C4—612no—
208C22×C4—611no—
209C22×C4—1222no—
210C22×C4—1222no—
211C22×C4—1224no—
212C22×C4—1224no—
213C22×C4—1222no—
214C22×C4—1221no—
215C22×C4—1221no—
216C22×C4—2442no—
217C22×C4—2442no—
218C22×C4—2442no—
219C22×C4—2442no—
220C22×C4C22×#692311yescharacteristic
221M16—2444no—
222M16—2444no—
223C2×C8—2444no—
224C4⋊C4—41no—
225C4⋊C4—2441no—
226C22⋊C4—44no—
227C22⋊C4—2442no—
228C22⋊C4—2444no—
229C42—41no—
230C42—2441no—
231C42—2442no—
232C42—2442no—
233C23—22no—
234C23—22no—
235C23—22no—
236C23—42no—
237C23—42no—
238C23—612no—
239C23—1221no—
240C23—1221no—
241C23—2441no—
242C23—2441no—
243C23C2×C22⋊#692311yescharacteristic
244Q8—2444no—
245D4—44no—
246D4—2448no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—22no—
250C2×C4—41no—
251C2×C4—41no—
252C2×C4—42no—
253C2×C4—41no—
254C2×C4—614no—
255C2×C4—612no—
256C2×C4—1228no—
257C2×C4—1221no—
258C2×C4—1221no—
259C2×C4—1222no—
260C2×C4—1222no—
261C2×C4—1222no—
262C2×C4—2448no—
263C2×C4—2448no—
264C2×C4—2442no—
265C2×C4—2441no—
266C2×C4—2441no—
267C2×C4—2441no—
268C2×C4#1451985612yes—
269C8—4884no—
270C22—21no—
271C22—21no—
272C22—44no—
273C22—42no—
274C22—42no—
275C22—42no—
276C22—82no—
277C22—1222no—
278C22—2442no—
279C22—2442no—
280C22—2441no—
281C22—2441no—
282C22#1684070511yescharacteristic
283C22D61⋊#9911yescharacteristic
284C22D61⋊#9911yescharacteristic
285C4—22no—
286C4—42no—
287C4—81no—
288C4—1224no—
289C4—1222no—
290C4—4881no—
291C4—2442no—
292C2—21no—
293C2—21no—
294C2—82no—
295C2—2442no—
296C2#2146171511yescharacteristic
297C2#2146211111yescharacteristic
298C2#2146211311yescharacteristic
subgroupG/H
centerC22D61⋊#99
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#390C4
socleC22×C61C2×#99
prime radicalC22×#11758224C22
cosocleC22×Dic122C23
hypercenter#390#6923
hypocenterC61#12861
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. #21460917C2semidirect
3. #21460916C2semidirect
166. C61#12861semidirect

Maximal subgroups

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

subgroupindex
#214616562
#214609172
#214609162
#214483062
#1286161