Finite Group Databasebeta

← #29568038

Subgroups — #29568038

Order 15616.

424 conjugacy classes of subgroups.

The subgroup lattice has 310 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21448296C211yesmaximal, characteristic
2#21445962C211yesmaximal, characteristic
3#21443644C212yesmaximal
4#21443641C212yesmaximal
5C61×#1744C211yesmaximal, characteristic
6C2×C4×Dic122C411yescharacteristic
7#16839668C411yescharacteristic
8#16839668C2211yescharacteristic
9#16839660C411yescharacteristic
10#16839660C2211yescharacteristic
11#16839646—21no—
12#16839646—21no—
13C4×#11758196—21no—
14C4×C4⋊Dic61C411yescharacteristic
15#16839608—21no—
16#16839517—21no—
17#16839517—21no—
18#16839517C2212yes—
19C2×C4×C8×C61—21no—
20C43×C61C2211yescharacteristic
21C61×#336—21no—
22C61×#336C2212yes—
23C22×Dic122C2×C411yescharacteristic
24C22×#92418—22no—
25C4×Dic122—22no—
26C4×Dic122C814yescomplemented
27C2×C4⋊Dic61C2×C411yescharacteristic
28C2×C4⋊Dic61C2×C411yescharacteristic
29C2×C4⋊Dic61C2×C411yescharacteristic
30C2×#11758196—21no—
31C2×#11758196—21no—
32C2×#11758196—21no—
33C2×C4×Dic61—21no—
34C2×C4×Dic61—21no—
35#14519684—21no—
36#14519684—21no—
37#14519684—21no—
38#14519684—21no—
39#14519684—21no—
40#14519684—21no—
41#14519684—21no—
42C22×C8×C61—22no—
43C2×C42×C61C2×C411yescharacteristic
44C2×C42×C61C2×C411yescharacteristic
45C2×C42×C61D411yescharacteristic
46C2×C42×C61D411yescharacteristic
47C2×C42×C61D411yescharacteristic
48C2×C42×C61D411yescharacteristic
49C2×C42×C61C2311yescharacteristic
50C4×C8×C61—24no—
51C22×C4×C61C22⋊C411yescharacteristic
52C22×C4×C61C22⋊C411yescharacteristic
53C22×C4×C61C22⋊C411yescharacteristic
54C22×C4×C61C22⋊C411yescharacteristic
55C22×C4×C61C22×C411yescharacteristic
56C22×C4×C61C2×D411yescharacteristic
57C22×C4×C61C2×D411yescharacteristic
58C22×Dic61—21no—
59C22×Dic61—21no—
60C22×Dic61—21no—
61C22×Dic61—21no—
62C2×Dic122—21no—
63C2×Dic122—41no—
64C2×Dic122—41no—
65C2×Dic122C2×C812yes—
66C2×C8×C61—24no—
67C2×C8×C61—42no—
68C2×C8×C61—42no—
69C42×C61—22no—
70C42×C61—22no—
71C42×C61—22no—
72C42×C61—41no—
73C42×C61—41no—
74C42×C61—41no—
75C42×C61C2×C812yes—
76C42×C61M1612yes—
77C4⋊Dic61—21no—
78C4⋊Dic61—41no—
79C4⋊Dic61—41no—
80C4⋊Dic61C2×C812yes—
81#11758196—24no—
82#11758196—42no—
83#11758196—42no—
84C4×Dic61—24no—
85C4×Dic61—42no—
86C2×#92418—42no—
87C2×#92418—42no—
88C2×#92418—42no—
89C23×C61C2×C22⋊C411yescharacteristic
90C2×C4×C61—21no—
91C2×C4×C61—21no—
92C2×C4×C61—21no—
93C2×C4×C61—21no—
94C2×C4×C61—21no—
95C2×C4×C61—21no—
96C2×C4×C61—21no—
97C2×C4×C61—21no—
98C2×C4×C61—21no—
99C2×C4×C61—21no—
100C2×C4×C61—21no—
101C2×C4×C61—21no—
102C2×C4×C61—21no—
103C2×C4×C61—21no—
104C2×C4×C61—21no—
105C2×C4×C61C22⋊C812yes—
106C2×C4×C61C22⋊C812yes—
107C2×C4×C61#10412yes—
108C2×C4×C61C22×C811yescharacteristic
109C2×C4×C61C2×M1611yescharacteristic
110C2×C4×C61#13512yes—
111C2×C4×C61#13712yes—
112C2×Dic61—22no—
113C2×Dic61—22no—
114C2×Dic61—41no—
115C2×Dic61—41no—
116C2×Dic61—41no—
117C2×Dic61—41no—
118C2×Dic61—41no—
119C2×Dic61—41no—
120C2×Dic61—41no—
121C2×Dic61—41no—
122C2×Dic61—41no—
123C2×Dic61—41no—
124Dic122—42no—
125Dic122—42no—
126C8×C61—44no—
127#92418—82no—
128#7581—611nomaximal, Sylow
129C22×C61C2×C22⋊C811yescharacteristic
130C22×C61#41011yescharacteristic
131C22×C61#41311yescharacteristic
132C22×C61#41611yescharacteristic
133C22×C61#41911yescharacteristic
134C22×C61C2×#10411yescharacteristic
135C22×C61#42111yescharacteristic
136C4×C61—21no—
137C4×C61—21no—
138C4×C61—22no—
139C4×C61—22no—
140C4×C61—22no—
141C4×C61—22no—
142C4×C61—22no—
143C4×C61—41no—
144Dic61—42no—
145Dic61—42no—
146Dic61—81no—
147Dic61—81no—
148#2295—611no—
149#1839—611no—
150#1744D6111yescharacteristic
151#1272—612no—
152#1271—612no—
153C2×C61#145811yescharacteristic
154C2×C61#147611yescharacteristic
155C2×C61#147911yescharacteristic
156C2×C61#150611yescharacteristic
157C2×C61#152111yescharacteristic
158C2×C61#153211yescharacteristic
159C2×C61#155411yescharacteristic
160C2×C4×Q8—611no—
161C2×C4×C8—21no—
162#391—611no—
163#391—611no—
164#389—611no—
165#389—611no—
166#387—1221no—
167#387—1221no—
168C4×C4⋊C4—611no—
169C4×C4⋊C4—1221no—
170#376—1221no—
171C43C2×D6111yescharacteristic
172#336—21no—
173#336—612no—
174#336—1221no—
175#336—1221no—
176#336C2×D6112yes—
177C61#758111yescharacteristic, complemented, Sylow
178C22×Q8—611no—
179C22×C8—22no—
180C22×C8—1222no—
181C4×Q8—614no—
182C4×Q8—1222no—
183C2×C4⋊C4—611no—
184C2×C4⋊C4—611no—
185C2×C4⋊C4—611no—
186C2×C4⋊C4—1221no—
187C2×C4⋊C4—1221no—
188C2×C4⋊C4—1221no—
189C2×C42—1221no—
190C2×C42—1221no—
191C2×C42C4×D6111yescharacteristic
192C2×C42C4×D6111yescharacteristic
193C2×C42D24411yescharacteristic
194C2×C42D24411yescharacteristic
195C2×C42C22⋊D6111yescharacteristic
196C2×C42C22⋊D6111yescharacteristic
197C2×C42C22×D6111yescharacteristic
198C4×C8—24no—
199#95—1221no—
200#95—1221no—
201#95—1221no—
202#95—1221no—
203#95—1221no—
204#95—1221no—
205#95—1221no—
206C2×Q8—612no—
207C2×Q8—1221no—
208C2×Q8—2441no—
209C2×Q8—2441no—
210C22×C4—1221no—
211C22×C4—1221no—
212C22×C4—1221no—
213C22×C4—1221no—
214C22×C4#1175819811yescharacteristic
215C22×C4#1175819811yescharacteristic
216C22×C4#1175819811yescharacteristic
217C22×C4#1175819811yescharacteristic
218C22×C4C2×C4×D6111yescharacteristic
219C22×C4C2×D24411yescharacteristic
220C22×C4C2×C22⋊D6111yescharacteristic
221C2×C8—24no—
222C2×C8—42no—
223C2×C8—42no—
224C2×C8—2442no—
225C2×C8—2442no—
226C2×C8—2442no—
227C4⋊C4—612no—
228C4⋊C4—1224no—
229C4⋊C4—1221no—
230C4⋊C4—2441no—
231C4⋊C4—2441no—
232C4⋊C4—2442no—
233C4⋊C4—2442no—
234C42—22no—
235C42—22no—
236C42—22no—
237C42—41no—
238C42—41no—
239C42—41no—
240C42—1224no—
241C42—2442no—
242C42C8×D6112yes—
243C42#1175818912yes—
244C23C2×#1175819811yescharacteristic
245Q8—2442no—
246Q8—2442no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—1222no—
263C2×C4—1222no—
264C2×C4—2441no—
265C2×C4—2441no—
266C2×C4—2441no—
267C2×C4—2441no—
268C2×C4—2441no—
269C2×C4—2441no—
270C2×C4—2441no—
271C2×C4—2441no—
272C2×C4—2441no—
273C2×C4—2441no—
274C2×C4#1451968912yes—
275C2×C4#1451968912yes—
276C2×C4#1451970512yes—
277C2×C4C2×C8×D6111yescharacteristic
278C2×C4C2×#1175818911yescharacteristic
279C2×C4#1451979912yes—
280C2×C4#1451980712yes—
281C8—44no—
282C8—4882no—
283C22C2×#1451968911yescharacteristic
284C22#1683973511yescharacteristic
285C22#1683974411yescharacteristic
286C22#1683975911yescharacteristic
287C22#1683977011yescharacteristic
288C22C2×#1451970511yescharacteristic
289C22#1683977811yescharacteristic
290C4—21no—
291C4—21no—
292C4—22no—
293C4—22no—
294C4—22no—
295C4—22no—
296C4—22no—
297C4—41no—
298C4—4881no—
299C4—4881no—
300C4—2442no—
301C4—2442no—
302C2#2144413111yescharacteristic
303C2#2144420211yescharacteristic
304C2#2144421311yescharacteristic
305C2#2144433011yescharacteristic
306C2#2144439711yescharacteristic
307C2#2144443711yescharacteristic
308C2#2144452711yescharacteristic
subgroupG/H
centerC23C2×#11758198
commutatorC2×C4×C61C22×C8
FrattiniC2×C42C22×D61
FittingC61×#1744C2
socle, prime radicalC23×C61C2×C22⋊C4
cosocleC2×C42×C61C23
hypercenter#1744D61
hypocenterC61#7581
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C43 ◁ #1744

Complements

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

NH ≅ G/Ntype
26. C4×Dic122C8semidirect
177. C61#7581semidirect

Maximal subgroups

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

subgroupindex
#214482962
#214459622
#214436442
#214436412
C61×#17442
#758161