Finite Group Databasebeta

← #29573409

Subgroups — #29573409

Order 15616.

588 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21448226C211yesmaximal, characteristic
2#21444046C211yesmaximal, characteristic
3#21443699C214yesmaximal
4C61×#1817C211yesmaximal, characteristic
5C2×#14519736—21no—
6#16839632C411yescharacteristic, complemented
7#16839632C411yescharacteristic, complemented
8#16839628—21no—
9#16839622—21no—
10#16839622C2212yes—
11C4×C4⋊Dic61—21no—
12C4×C4⋊Dic61C412yescomplemented
13C2×#14519684—21no—
14C2×#14519684—21no—
15C2×#14519684C2212yes—
16C22×C42×C61C2211yescharacteristic
17C2×C22⋊C8×C61C2212yes—
18C61×#336—21no—
19C61×#336—21no—
20C23×Dic61—22no—
21#14519736—44no—
22C2×C4⋊Dic61—21no—
23C2×C4⋊Dic61—21no—
24C2×C4⋊Dic61—21no—
25C2×C4⋊Dic61—21no—
26C2×C4⋊Dic61C2×C412yes—
27C2×C4⋊Dic61C2×C412yes—
28C2×C22⋊Dic61—22no—
29C2×C4×Dic61—22no—
30#14519684—24no—
31#14519684—22no—
32#14519684—22no—
33#14519684—24no—
34#14519684—42no—
35C23×C4×C61D411yescharacteristic
36C23×C4×C61D411yescharacteristic
37C23×C4×C61C2311yescharacteristic
38C22×C8×C61—22no—
39C2×C42×C61—24no—
40C2×C42×C61C2×C411yescharacteristic
41C2×C42×C61C2×C411yescharacteristic
42C2×C42×C61D411yescharacteristic
43C2×C42×C61D411yescharacteristic
44C22⋊C8×C61—24no—
45C24×C61C2×D411yescharacteristic
46C22×C4×C61—22no—
47C22×C4×C61—22no—
48C22×C4×C61—22no—
49C22×C4×C61—22no—
50C22×C4×C61—41no—
51C22×C4×C61—41no—
52C22×C4×C61—41no—
53C22×C4×C61C22⋊C411yescharacteristic
54C22×C4×C61C22⋊C411yescharacteristic
55C22×C4×C61C22⋊C411yescharacteristic
56C22×C4×C61C22⋊C411yescharacteristic
57C22×C4×C61SD1612yes—
58C22×C4×C61Q1612yes—
59C22×C4×C61C22×C411yescharacteristic
60C22×C4×C61C2×D411yescharacteristic
61C22×C4×C61#4114yes—
62C22×Dic61—24no—
63C22×Dic61—22no—
64C22×Dic61—22no—
65C22×Dic61—42no—
66C22×Dic61—42no—
67C22×Dic61—42no—
68C22×Dic61—42no—
69C22×Dic61—42no—
70C22×Dic61—42no—
71C2×C8×C61—42no—
72C2×C8×C61—42no—
73C2×C8×C61—42no—
74C42×C61—22no—
75C42×C61—22no—
76C42×C61—22no—
77C42×C61—22no—
78C22⋊Dic61—44no—
79C4⋊Dic61—42no—
80C4⋊Dic61—42no—
81C4⋊Dic61—42no—
82C4⋊Dic61—42no—
83C4⋊Dic61—42no—
84C4⋊Dic61—42no—
85C4×Dic61—44no—
86C23×C61—21no—
87C23×C61—21no—
88C23×C61—21no—
89C23×C61—21no—
90C23×C61C2×C22⋊C411yescharacteristic
91C23×C61#12312yes—
92C23×C61C2×SD1611yescharacteristic
93C23×C61C2×Q1611yescharacteristic
94C23×C61AGL(1,ℤ/8)12yes—
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×C61—24no—
106C2×C4×C61—24no—
107C2×C4×C61—21no—
108C2×C4×C61—21no—
109C2×C4×C61—21no—
110C2×C4×C61—44no—
111C2×C4×C61—44no—
112C2×C4×C61#10312yes—
113C2×C4×C61#10312yes—
114C2×C4×C61#10412yes—
115C2×C4×C61#11712yes—
116C2×C4×C61#12312yes—
117C2×Dic61—44no—
118C2×Dic61—44no—
119C2×Dic61—44no—
120C2×Dic61—42no—
121C2×Dic61—42no—
122C2×Dic61—42no—
123C2×Dic61—42no—
124C2×Dic61—42no—
125C2×Dic61—42no—
126C2×Dic61—82no—
127C2×Dic61—82no—
128C2×Dic61—82no—
129C2×Dic61—82no—
130C8×C61—82no—
131#8717—611nomaximal, Sylow
132C22×C61—22no—
133C22×C61—22no—
134C22×C61—21no—
135C22×C61—21no—
136C22×C61—22no—
137C22×C61—22no—
138C22×C61—21no—
139C22×C61—21no—
140C22×C61#38111yescharacteristic
141C22×C61#41011yescharacteristic
142C22×C61#41011yescharacteristic
143C22×C61C2×#10311yescharacteristic
144C22×C61#41811yescharacteristic
145C22×C61C2×#10411yescharacteristic
146C22×C61#42111yescharacteristic
147C22×C61#48112yes—
148C22×C61#48412yes—
149C4×C61—22no—
150C4×C61—22no—
151C4×C61—22no—
152C4×C61—22no—
153C4×C61—22no—
154C4×C61—41no—
155Dic61—84no—
156Dic61—82no—
157Dic61—82no—
158#2285—611no—
159#1817D6111yescharacteristic
160#1434—611no—
161#1294—614no—
162C2×C61—22no—
163C2×C61—22no—
164C2×C61#150311yescharacteristic
165C2×C61#150511yescharacteristic
166C2×C61#151411yescharacteristic
167C2×C61#151811yescharacteristic
168C2×C61#182011yescharacteristic
169C2×C61#182411yescharacteristic
170C2×C61#182611yescharacteristic
171C2×#117—1221no—
172C22×C42C2×D6111yescharacteristic
173C2×C22⋊C8C2×D6112yes—
174#384—611no—
175#384—611no—
176#382—1221no—
177#380—612no—
178#380—1221no—
179C4×C4⋊C4—612no—
180C4×C4⋊C4—1221no—
181C2×#95—612no—
182C2×#95—1221no—
183C2×#95—1221no—
184#336—21no—
185#336—21no—
186C61#871711yescharacteristic, complemented, Sylow
187C23×C4—1222no—
188C23×C4D24411yescharacteristic
189C23×C4D24411yescharacteristic
190C23×C4C22×D6111yescharacteristic
191C22×C8—22no—
192#117—2444no—
193C2×C4⋊C4—612no—
194C2×C4⋊C4—612no—
195C2×C4⋊C4—1221no—
196C2×C4⋊C4—1221no—
197C2×C4⋊C4—1221no—
198C2×C4⋊C4—1221no—
199C2×C22⋊C4—1222no—
200C2×C42—24no—
201C2×C42—1222no—
202C2×C42C4×D6111yescharacteristic
203C2×C42C4×D6111yescharacteristic
204C2×C42C22⋊D6111yescharacteristic
205C2×C42C22⋊D6111yescharacteristic
206C22⋊C8—24no—
207#95—1224no—
208#95—1222no—
209#95—1222no—
210#95—1224no—
211#95—2442no—
212C24C2×D24411yescharacteristic
213C22×C4—22no—
214C22×C4—22no—
215C22×C4—22no—
216C22×C4—22no—
217C22×C4—41no—
218C22×C4—41no—
219C22×C4—41no—
220C22×C4—1224no—
221C22×C4—1222no—
222C22×C4—1222no—
223C22×C4—2442no—
224C22×C4—2442no—
225C22×C4—2442no—
226C22×C4—2442no—
227C22×C4—2442no—
228C22×C4—2442no—
229C22×C4#1175819012yes—
230C22×C4Dic24412yes—
231C22×C4#1175819811yescharacteristic
232C22×C4#1175819811yescharacteristic
233C22×C4#1175819811yescharacteristic
234C22×C4#1175819811yescharacteristic
235C22×C4C2×C4×D6111yescharacteristic
236C22×C4#1175822414yes—
237C22×C4C2×C22⋊D6111yescharacteristic
238C2×C8—42no—
239C2×C8—42no—
240C2×C8—42no—
241C4⋊C4—2442no—
242C4⋊C4—2442no—
243C4⋊C4—2442no—
244C4⋊C4—2442no—
245C4⋊C4—2442no—
246C4⋊C4—2442no—
247C22⋊C4—2444no—
248C42—22no—
249C42—22no—
250C42—22no—
251C42—22no—
252C42—2444no—
253C23—21no—
254C23—21no—
255C23—21no—
256C23—21no—
257C23C2×#1175819811yescharacteristic
258C23#1451976112yes—
259C23C2×#1175819011yescharacteristic
260C23C2×Dic24411yescharacteristic
261C23#1451980512yes—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—24no—
270C2×C4—24no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—44no—
278C2×C4—44no—
279C2×C4—4882no—
280C2×C4—4882no—
281C2×C4—4882no—
282C2×C4—4882no—
283C2×C4—2444no—
284C2×C4—2444no—
285C2×C4—2444no—
286C2×C4—2442no—
287C2×C4—2442no—
288C2×C4—2442no—
289C2×C4—2442no—
290C2×C4—2442no—
291C2×C4—2442no—
292C2×C4#1451970212yes—
293C2×C4#1451970212yes—
294C2×C4#1451970312yes—
295C2×C4#1451973312yes—
296C2×C4#1451975812yes—
297C8—82no—
298C22—22no—
299C22—22no—
300C22—22no—
301C22—21no—
302C22—21no—
303C22—21no—
304C22—21no—
305C22—22no—
306C22#1683962311yescharacteristic
307C22#1683973511yescharacteristic
308C22#1683973511yescharacteristic
309C22C2×#1451970211yescharacteristic
310C22#1683976811yescharacteristic
311C22C2×#1451970311yescharacteristic
312C22#1683977811yescharacteristic
313C22#1684008112yes—
314C22#1684009812yes—
315C4—22no—
316C4—22no—
317C4—22no—
318C4—22no—
319C4—22no—
320C4—41no—
321C4—4884no—
322C4—4882no—
323C4—4882no—
324C2—22no—
325C2—22no—
326C2#2144431911yescharacteristic
327C2#2144432811yescharacteristic
328C2#2144436711yescharacteristic
329C2#2144438411yescharacteristic
330C2#2144589411yescharacteristic
331C2#2144591011yescharacteristic
332C2#2144591611yescharacteristic
subgroupG/H
centerC23C2×#11758198
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#1817C2
socleC23×C61C2×C22⋊C4
prime radicalC24×C61C2×D4
cosocleC23×C4×C61C23
hypercenter#1817D61
hypocenterC61#8717
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1817

Complements

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

NH ≅ G/Ntype
6. #16839632C4semidirect
7. #16839632C4semidirect
12. C4×C4⋊Dic61C4semidirect
186. C61#8717semidirect

Maximal subgroups

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

subgroupindex
#214482262
#214440462
#214436992
C61×#18172
#871761