Finite Group Databasebeta

← #29570998

Subgroups — #29570998

Order 15616.

534 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 534 conjugacy classes of subgroups — too many to draw. Only its 121 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#21454509C211yesmaximal, characteristic
2C22⋊C4×#92418C212yesmaximal, complemented
3#21444308C212yesmaximal
4#21443706C211yesmaximal, characteristic, complemented
5C61×#1297C211yesmaximal, characteristic, complemented
6C2×#14519785C411yescharacteristic, complemented
7C23×#92418C2211yescharacteristic
8#16840273C2211yescharacteristic
9#16839830—22no—
10#16839825—22no—
11#16839790C411yescharacteristic, complemented
12#16839730C411yescharacteristic, complemented
13C2×C22⋊#92418C2212yes—
14#16839720C411yescharacteristic, complemented
15C2×C4×#92418—22no—
16#16839517—22no—
17#16839498C414yescomplemented
18#16839495C414yescomplemented
19C61×#407C2211yescharacteristic
20C4×C22⋊C4×C61C2212yes—
21C2×#11758222C2×C411yescharacteristic
22#14519785—42no—
23C2×#11758189—21no—
24C22×#92418—22no—
25C22×#92418—42no—
26C22×#92418C2×C411yescharacteristic
27C22×#92418C2×C411yescharacteristic
28C22×#92418D412yes—
29C22×#92418D412yes—
30C2×C8×D61—21no—
31#14519760—21no—
32#14519756C2×C412yes—
33#14519751C2×C412yes—
34#14519746—21no—
35C4×C22⋊D61—22no—
36#14519736C2×C411yescharacteristic
37#14519706—22no—
38C22⋊#92418—22no—
39C22⋊#92418C2×C414yes—
40#14519689—22no—
41#14519687—21no—
42C4×#92418—44no—
43C8×Dic61—21no—
44C23×C4×C61C2311yescharacteristic
45C2×M16×C61C2×C411yescharacteristic
46C2×M16×C61C2×C411yescharacteristic
47C2×C22⋊C4×C61—22no—
48C2×C42×C61—22no—
49C22⋊C8×C61—22no—
50#95×C61C2×C414yes—
51C24×C61#4111yescharacteristic
52C22×C4×C61—24no—
53C22×C4×C61—41no—
54C22×C4×C61—41no—
55C22×C4×C61C22×C411yescharacteristic
56C22×C4×C61C22×C412yes—
57C22×C4×C61C2×D412yes—
58C22×C4×C61#4111yescharacteristic
59C2×C22⋊D61—21no—
60C2×C22⋊D61—22no—
61#11758222—41no—
62#11758222—41no—
63C2×D244C4211yescharacteristic
64C2×C4×D61—21no—
65C2×Dic122C4211yescharacteristic
66M16×C61—41no—
67M16×C61—41no—
68C2×C8×C61—21no—
69C2×C8×C61—21no—
70C22⋊C4×C61—28no—
71C42×C61—42no—
72C42×C61—42no—
73C22⋊Dic61—21no—
74C22⋊Dic61—22no—
75#11758198—22no—
76C4⋊Dic61C4212yes—
77#11758196—22no—
78C4×Dic61—21no—
79C2×#92418—24no—
80C2×#92418—22no—
81C2×#92418—24no—
82C2×#92418—41no—
83C2×#92418—42no—
84C2×#92418—42no—
85C2×#92418—42no—
86C2×#92418C22⋊C411yescharacteristic
87C2×#92418C22⋊C412yes—
88C2×#92418C22⋊C411yescharacteristic
89#11758189—42no—
90C8×D61—42no—
91C23×C61—24no—
92C23×C61—41no—
93C23×C61#11711yescharacteristic
94C23×C61C4×D412yes—
95C22×D61—21no—
96C2×C4×C61—22no—
97C2×C4×C61—21no—
98C2×C4×C61—22no—
99C2×C4×C61—21no—
100C2×C4×C61—28no—
101C2×C4×C61—42no—
102C2×C4×C61—41no—
103C2×C4×C61—44no—
104C2×C4×C61—44no—
105C2×C4×C61C2×C4211yescharacteristic
106C2×C4×C61C2×C22⋊C411yescharacteristic
107C2×C4×C61C4×D412yes—
108C22⋊D61—42no—
109C22⋊D61—44no—
110C2×Dic61—22no—
111C2×Dic61—21no—
112D244—41no—
113C4×D61—41no—
114C4×D61—41no—
115Dic122—41no—
116C8×C61—41no—
117C8×C61—41no—
118#92418—21no—
119#92418—22no—
120#92418—44no—
121#92418#9912yes—
122#8238—611nomaximal, Sylow
123C22×C61—22no—
124C22×C61—22no—
125C22×C61—21no—
126C22×C61—22no—
127C22×C61—44no—
128C22×C61C4×C22⋊C411yescharacteristic
129C22×C61#44314yes—
130C2×D61—41no—
131C2×D61—42no—
132C4×C61—22no—
133C4×C61—21no—
134C4×C61—48no—
135C4×C61C2×#9911yescharacteristic
136C4×C61#41011yescharacteristic
137Dic61—41no—
138Dic61—42no—
139#2929—611no—
140C8×C22⋊C4—612no—
141#1501—612no—
142#1298—611no—
143#1297D6111yescharacteristic, complemented
144C2×C61—24no—
145C2×C61—41no—
146C2×C61C4×#9911yescharacteristic
147C2×C61#176412yes—
148D61—81no—
149C2×#131—611no—
150C23×C8—611no—
151#525—611no—
152#435—1222no—
153C8×D4—1222no—
154#424—611no—
155#408—611no—
156#407C2×D6111yescharacteristic
157C2×C22⋊C8—612no—
158#405—611no—
159C2×C4×C8—1222no—
160C4×C22⋊C4C2×D6112yes—
161#336—1222no—
162#328—614no—
163#327—614no—
164C61#823811yescharacteristic, complemented, Sylow
165C2×#41—611no—
166C23×C4C22×D6111yescharacteristic
167#131—2442no—
168C2×M16—1221no—
169C2×M16C4×D6111yescharacteristic
170C2×M16C4×D6111yescharacteristic
171C22×C8—611no—
172C22×C8—612no—
173C22×C8—611no—
174C22×C8—612no—
175C22×C8—1221no—
176C22×C8—1222no—
177C22×C8—2442no—
178#123—1221no—
179C22⋊Q8—612no—
180#121—612no—
181#120—1221no—
182C4×D4—1222no—
183#117—611no—
184C2×C22⋊C4—22no—
185C2×C42—22no—
186C4⋊C8—1222no—
187C22⋊C8—22no—
188C22⋊C8—614no—
189C22⋊C8—1222no—
190C22⋊C8—1222no—
191#97—1221no—
192C4×C8—1221no—
193C4×C8—2444no—
194#95C4×D6114yes—
195C24#1175822411yescharacteristic
196#41—2441no—
197#41—2441no—
198C2×Q8—611no—
199C2×D4—611no—
200C2×D4—1221no—
201C2×D4—1222no—
202C22×C4—24no—
203C22×C4—41no—
204C22×C4—41no—
205C22×C4—1221no—
206C22×C4C2×C4×D6111yescharacteristic
207C22×C4C2×C4×D6112yes—
208C22×C4D4×D6112yes—
209C22×C4#1175822611yescharacteristic
210M16—41no—
211M16—41no—
212M16—2442no—
213C2×C8—21no—
214C2×C8—21no—
215C2×C8—611no—
216C2×C8—611no—
217C2×C8—612no—
218C2×C8—1224no—
219C2×C8—1222no—
220C2×C8—1224no—
221C2×C8—2442no—
222C2×C8—2441no—
223C2×C8—2442no—
224C2×C8—2442no—
225C2×C8—2442no—
226C4⋊C4—612no—
227C4⋊C4—1222no—
228C22⋊C4—28no—
229C22⋊C4—1221no—
230C22⋊C4—1222no—
231C22⋊C4—1222no—
232C42—42no—
233C42—42no—
234C42—1221no—
235C23—24no—
236C23—41no—
237C23—1221no—
238C23#1451973511yescharacteristic
239C23#1451973712yes—
240Q8—2441no—
241D4—2441no—
242D4—2442no—
243D4—2444no—
244C2×C4—22no—
245C2×C4—21no—
246C2×C4—22no—
247C2×C4—21no—
248C2×C4—28no—
249C2×C4—42no—
250C2×C4—41no—
251C2×C4—44no—
252C2×C4—44no—
253C2×C4—1222no—
254C2×C4—1221no—
255C2×C4—2441no—
256C2×C4—2441no—
257C2×C4C42×D6111yescharacteristic
258C2×C4C22⋊C4×D6111yescharacteristic
259C2×C4#1451973912yes—
260C8—41no—
261C8—41no—
262C8—612no—
263C8—1222no—
264C8—1221no—
265C8—2444no—
266C22—22no—
267C22—22no—
268C22—22no—
269C22—21no—
270C22—44no—
271C22—2442no—
272C22—2441no—
273C22#1683960911yescharacteristic
274C22#1683987614yes—
275C4—22no—
276C4—21no—
277C4—48no—
278C4—2442no—
279C4—2441no—
280C4#99×D6111yescharacteristic
281C4#1683973411yescharacteristic
282C2—24no—
283C2—41no—
284C2—4881no—
285C2#2144560611yescharacteristic
286C2#2144565312yes—
subgroupG/H
centerC2×C4C22⋊C4×D61
commutatorC2×C4×C61C2×C42
FrattiniC23×C4C22×D61
FittingC61×#1297C2
socleC22×C61C4×C22⋊C4
prime radical#16840273C22
cosocleC23×C4×C61C23
hypercenter#1297D61
hypocenterC61#8238
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1297

Complements

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

NH ≅ G/Ntype
2. C22⋊C4×#92418C2semidirect
4. #21443706C2semidirect
5. C61×#1297C2semidirect
6. C2×#14519785C4semidirect
11. #16839790C4semidirect
12. #16839730C4semidirect
14. #16839720C4semidirect
17. #16839498C4semidirect
18. #16839495C4semidirect
143. #1297D61semidirect
164. C61#8238semidirect

Maximal subgroups

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

subgroupindex
#214545092
C22⋊C4×#924182
#214443082
#214437062
C61×#12972
#823861