Finite Group Databasebeta

← #13078969

Subgroups — #13078969

Order 1408.

404 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623220C211yesmaximal, characteristic, complemented
2#10623205C211yesmaximal, characteristic
3C11×#488C211yesmaximal, characteristic, complemented
4#10622680C211yesmaximal, characteristic, complemented
5#10622668C211yesmaximal, characteristic, complemented
6#10622417C211yesmaximal, characteristic, complemented
7#10622416C211yesmaximal, characteristic, complemented
8#10622413C211yesmaximal, characteristic, complemented
9#10622408C211yesmaximal, characteristic, complemented
10#10622383C211yesmaximal, characteristic, complemented
11D11×#102C211yesmaximal, characteristic, complemented
12#10622377C211yesmaximal, characteristic, complemented
13#10622373C211yesmaximal, characteristic, complemented
14#10622307C211yesmaximal, characteristic, complemented
15#10622302C211yesmaximal, characteristic, complemented
16C2×#4343C2211yescharacteristic
17C2×D4×D11C2211yescharacteristic
18C11×#125C2211yescharacteristic, complemented
19C11×#124C2211yescharacteristic
20#67000C2211yescharacteristic
21#66993C2211yescharacteristic
22C2×#4313C2211yescharacteristic
23C2×C8×D11C2211yescharacteristic
24#66950—21no—
25#66949—21no—
26#66945C2211yescharacteristic
27C4⋊C4×D11C2211yescharacteristic
28#66943C2211yescharacteristic, complemented
29#66942—21no—
30#66941—21no—
31#66941C2211yescharacteristic, complemented
32#66937—21no—
33#66937—21no—
34#66935—21no—
35#66935—21no—
36#66927C2211yescharacteristic
37#66925C2211yescharacteristic
38#66922C2211yescharacteristic, complemented
39C11×#103C2211yescharacteristic, complemented
40C11×#103C2211yescharacteristic, complemented
41C11×#102C2211yescharacteristic
42C11×#102C2211yescharacteristic
43C4×C8×C11C2211yescharacteristic, complemented
44#66899C2211yescharacteristic, complemented
45#66899C2211yescharacteristic, complemented
46#66896C2211yescharacteristic
47#66896C2211yescharacteristic
48#66885C2211yescharacteristic
49#66885C2211yescharacteristic
50#66885C2211yescharacteristic, complemented
51#66885C2211yescharacteristic, complemented
52#66879C2211yescharacteristic, complemented
53C8×Dic11C2211yescharacteristic, complemented
54#66873C2211yescharacteristic
55#66873C2211yescharacteristic
56#66873C2211yescharacteristic, complemented
57#66873C2211yescharacteristic, complemented
58#66867C2211yescharacteristic, complemented
59C23×D11—21no—
60C2×Q8×C11C2311yescharacteristic
61C2×D4×C11C2311yescharacteristic
62C2×C22⋊D11—21no—
63C2×C22⋊D11—21no—
64C2×C22⋊D11—21no—
65#4343—22no—
66#4343—22no—
67D4×D11—22no—
68D4×D11—22no—
69C2×D44—21no—
70C2×D44—21no—
71C2×D44—21no—
72C2×D44C2311yescharacteristic
73C2×D44C2311yescharacteristic
74C2×C4×D11—21no—
75C2×C4×D11—21no—
76C2×C4×D11C2311yescharacteristic
77C2×Dic22—21no—
78C2×Dic22—21no—
79C2×C8×C11C2311yescharacteristic
80C2×C8×C11C2311yescharacteristic
81C11×C4⋊C4—21no—
82C11×C4⋊C4—21no—
83C11×C4⋊C4C2311yescharacteristic
84C11×C4⋊C4C2311yescharacteristic
85C11×C22⋊C4—21no—
86C11×C22⋊C4—21no—
87C42×C11C2311yescharacteristic
88(C2×D11)⋊C4—21no—
89(C2×D11)⋊C4—21no—
90(C2×D11)⋊C4—21no—
91(C2×D11)⋊C4D411yescharacteristic
92(C2×D11)⋊C4D411yescharacteristic
93C4⋊Dic11—21no—
94C4⋊Dic11—21no—
95C4⋊Dic11C2311yescharacteristic
96C4⋊Dic11C2311yescharacteristic
97Dic11⋊C4—21no—
98Dic11⋊C4—21no—
99Dic11⋊C4—21no—
100Dic11⋊C4D411yescharacteristic
101Dic11⋊C4D411yescharacteristic
102C4×Dic11—21no—
103C4×Dic11C2311yescharacteristic
104C2×C11⋊C8C2311yescharacteristic
105C2×C11⋊C8C2311yescharacteristic
106#4313—22no—
107C8×D11—22no—
108#3136—111nomaximal, Sylow
109C23×C11—21no—
110C22×D11—21no—
111C22×D11—21no—
112C22×D11—42no—
113C22×D11—81no—
114C22×D11—81no—
115C22×D11C2×D411yescharacteristic
116Q8×C11—21no—
117Q8×C11—21no—
118D4×C11—21no—
119D4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11C2×D411yescharacteristic
124C2×C4×C11C2×D411yescharacteristic
125C2×C4×C11C2411yescharacteristic
126C22⋊D11—42no—
127C22⋊D11—81no—
128C22⋊D11—81no—
129C2×Dic11—21no—
130C2×Dic11—21no—
131C2×Dic11C2×D411yescharacteristic
132C2×Dic11C2×D411yescharacteristic
133C2×Dic11C2×D411yescharacteristic
134D44—21no—
135D44—21no—
136D44—21no—
137D44—21no—
138D44—42no—
139D44—81no—
140D44—81no—
141C4×D11—42no—
142C4×D11—81no—
143C4×D11#4112yes—
144C4×D11#4112yes—
145Dic22—81no—
146Dic22—81no—
147C8×C11—21no—
148C8×C11—21no—
149C11⋊C8—21no—
150C11⋊C8—21no—
151#544—111no—
152#535—111no—
153#490—111no—
154#490—111no—
155#489—111no—
156#489—111no—
157#488—111no—
158#488D1111yescharacteristic, complemented
159#486—111no—
160#486—111no—
161#418—111no—
162#417—111no—
163#416—111no—
164C2×#102—111no—
165#405—111no—
166C22×C11—41no—
167C22×C11—41no—
168C22×C11—41no—
169C22×C11C22×D411yescharacteristic
170C2×D11—21no—
171C2×D11—21no—
172C2×D11—41no—
173C2×D11—41no—
174C2×D11—41no—
175C2×D11—41no—
176C2×D11—41no—
177C2×D11—41no—
178C2×D11—84no—
179C2×D11#12412yes—
180C4×C11—21no—
181C4×C11—21no—
182C4×C11—41no—
183C4×C11—41no—
184C4×C11—41no—
185C4×C11C2×#4111yescharacteristic
186C4×C11C2×#4111yescharacteristic
187Dic11—21no—
188Dic11—21no—
189Dic11—41no—
190Dic11—41no—
191Dic11#12412yes—
192C2×#41—111no—
193C22×D4—111no—
194C2×M16—111no—
195C22×C8—111no—
196C4⋊Q8—111no—
197C4⋊Q8—111no—
198C4⋊Q8—221no—
199#127—111no—
200#127—111no—
201#125—111no—
202#125—221no—
203#125C2×D1111yescharacteristic, complemented
204#124—111no—
205#124C2×D1111yescharacteristic
206C22⋊Q8—221no—
207C22⋊Q8—221no—
208#121—221no—
209#121—221no—
210#120—221no—
211#120—221no—
212#117—111no—
213#117—111no—
214C2×C4⋊C4—111no—
215#103—111no—
216#103—111no—
217#103C2×D1111yescharacteristic, complemented
218#103C2×D1111yescharacteristic, complemented
219#102—111no—
220#102—111no—
221#102—111no—
222#102—111no—
223#102—111no—
224#102—111no—
225#102—111no—
226#102—111no—
227#102—111no—
228#102—111no—
229#102C2×D1111yescharacteristic
230#102C2×D1111yescharacteristic
231#97—111no—
232#97—111no—
233C4×C8—111no—
234C4×C8C2×D1111yescharacteristic, complemented
235C2×C11—81no—
236C2×C11C2×#12411yescharacteristic
237C2×C11#57611yescharacteristic
238C2×C11#57711yescharacteristic
239D11—22no—
240D11—81no—
241D11—81no—
242C24—221no—
243#41—222no—
244#41—222no—
245C2×Q8—221no—
246C2×Q8—221no—
247C2×Q8C22×D1111yescharacteristic
248C2×D4—111no—
249C2×D4—111no—
250C2×D4—221no—
251C2×D4—222no—
252C2×D4—222no—
253C2×D4—221no—
254C2×D4—221no—
255C2×D4—221no—
256C2×D4—221no—
257C2×D4—221no—
258C2×D4C22×D1111yescharacteristic
259C22×C4—111no—
260C22×C4—221no—
261C22×C4—221no—
262M16—222no—
263C2×C8—111no—
264C2×C8—111no—
265C2×C8—222no—
266C2×C8C22×D1111yescharacteristic
267C2×C8C22×D1111yescharacteristic
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—111no—
271C4⋊C4—111no—
272C4⋊C4—111no—
273C4⋊C4—111no—
274C4⋊C4—221no—
275C4⋊C4—221no—
276C4⋊C4—221no—
277C4⋊C4—221no—
278C4⋊C4—221no—
279C4⋊C4C22×D1111yescharacteristic
280C4⋊C4C22×D1111yescharacteristic
281C22⋊C4—21no—
282C22⋊C4—21no—
283C22⋊C4—111no—
284C22⋊C4—111no—
285C22⋊C4—221no—
286C22⋊C4—221no—
287C22⋊C4—221no—
288C42—111no—
289C42—221no—
290C42C22×D1111yescharacteristic
291C11#313611yescharacteristic, complemented, Sylow
292C23—21no—
293C23—111no—
294C23—221no—
295C23—221no—
296C23—442no—
297C23—881no—
298C23—881no—
299Q8—21no—
300Q8—21no—
301Q8—881no—
302Q8—881no—
303D4—21no—
304D4—21no—
305D4—221no—
306D4—221no—
307D4—221no—
308D4—221no—
309D4—442no—
310D4—442no—
311D4—881no—
312D4—881no—
313D4—881no—
314D4—881no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—111no—
319C2×C4—112no—
320C2×C4—112no—
321C2×C4—111no—
322C2×C4—111no—
323C2×C4—221no—
324C2×C4—221no—
325C2×C4—442no—
326C2×C4—881no—
327C2×C4D4×D1111yescharacteristic
328C2×C4D4×D1111yescharacteristic
329C2×C4C23×D1111yescharacteristic
330C8—21no—
331C8—21no—
332C8—221no—
333C8—221no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—112no—
338C22—221no—
339C22—221no—
340C22—441no—
341C22—441no—
342C22—441no—
343C22—441no—
344C22—441no—
345C22—441no—
346C22—884no—
347C22C2×D4×D1111yescharacteristic
348C4—21no—
349C4—21no—
350C4—41no—
351C4—41no—
352C4—41no—
353C4—112no—
354C4—221no—
355C4—221no—
356C4—441no—
357C4—441no—
358C4#41×D1111yescharacteristic
359C4#41×D1111yescharacteristic
360C2—81no—
361C2—222no—
362C2—881no—
363C2—881no—
364C2D11×#12411yescharacteristic
365C2#1062330011yescharacteristic
366C2#1062330111yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#488C2
socleC22×C11C22×D4
prime radical#10623205C2
hypercenter#488D11
hypocenterC11#3136
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #488

Complements

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

NH ≅ G/Ntype
1. #10623220C2semidirect
3. C11×#488C2semidirect
4. #10622680C2semidirect
5. #10622668C2semidirect
6. #10622417C2semidirect
7. #10622416C2semidirect
8. #10622413C2semidirect
9. #10622408C2semidirect
10. #10622383C2semidirect
11. D11×#102C2semidirect
12. #10622377C2semidirect
13. #10622373C2semidirect
14. #10622307C2semidirect
15. #10622302C2semidirect
18. C11×#125C22semidirect
28. #66943C22semidirect
31. #66941C22semidirect
38. #66922C22semidirect
39. C11×#103C22semidirect
40. C11×#103C22semidirect
43. C4×C8×C11C22semidirect
44. #66899C22semidirect
45. #66899C22semidirect
50. #66885C22semidirect
51. #66885C22semidirect
52. #66879C22semidirect
53. C8×Dic11C22semidirect
56. #66873C22semidirect
57. #66873C22semidirect
58. #66867C22semidirect
158. #488D11semidirect
203. #125C2×D11semidirect
217. #103C2×D11semidirect
218. #103C2×D11semidirect
234. C4×C8C2×D11semidirect
291. C11#3136semidirect

Maximal subgroups

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

subgroupindex
#106232202
#106232052
C11×#4882
#106226802
#106226682
#106224172
#106224162
#106224132
#106224082
#106223832
D11×#1022
#106223772
#106223732
#106223072
#106223022
#313611