Finite Group Databasebeta

← #13078752

Subgroups — #13078752

Order 1408.

450 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623088C211yesmaximal, characteristic, complemented
2C4×D4×D11C211yesmaximal, characteristic, complemented
3C11×#442C211yesmaximal, characteristic, complemented
4#10622769C211yesmaximal, characteristic
5#10622766C211yesmaximal, characteristic, complemented
6#10622631C211yesmaximal, characteristic, complemented
7#10622627C211yesmaximal, characteristic, complemented
8#10622484C211yesmaximal, characteristic, complemented
9#10622475C211yesmaximal, characteristic, complemented
10#10622400C211yesmaximal, characteristic, complemented
11#10622389C211yesmaximal, characteristic, complemented
12#10622387C211yesmaximal, characteristic, complemented
13#10622379C211yesmaximal, characteristic, complemented
14#10622323C211yesmaximal, characteristic, complemented
15#10622318C211yesmaximal, characteristic, complemented
16C2×D4×D11C2211yescharacteristic
17C22×C4×D11—21no—
18C2×C11×D8C2211yescharacteristic
19C4×D4×C11C2211yescharacteristic
20C4×D4×C11C2211yescharacteristic, complemented
21#66991C2211yescharacteristic
22#66989C2211yescharacteristic, complemented
23D4×Dic11C2211yescharacteristic
24C2×#4324C2211yescharacteristic
25C2×#4323C2211yescharacteristic
26C4×C22⋊D11—21no—
27C4×C22⋊D11—21no—
28#66979—21no—
29C2×#4314C2211yescharacteristic
30#66950C2211yescharacteristic
31#66946C2211yescharacteristic
32C4⋊C4×D11C2211yescharacteristic
33#66943C2211yescharacteristic, complemented
34#66936—21no—
35(C22⋊D11)⋊C4—21no—
36C22⋊C4×D11—21no—
37#66932—21no—
38C4×D44C2211yescharacteristic
39C42×D11C2211yescharacteristic
40C4×Dic22C2211yescharacteristic, complemented
41C11×#106C2211yescharacteristic, complemented
42C11×#102C2211yescharacteristic
43C11×#102C2211yescharacteristic, complemented
44C11×#97C2211yescharacteristic, complemented
45#66896C2211yescharacteristic
46#66896C2211yescharacteristic, complemented
47#66885C2211yescharacteristic
48(C2×D11)⋊C8C2211yescharacteristic
49(C2×D11)⋊C8C2211yescharacteristic
50#66882C2211yescharacteristic, complemented
51#66880C2211yescharacteristic, complemented
52Dic11⋊C8C2211yescharacteristic, complemented
53Dic11⋊C8C2211yescharacteristic, complemented
54#66874C2211yescharacteristic, complemented
55#66873C2211yescharacteristic
56#66872C2211yescharacteristic, complemented
57#66871C2211yescharacteristic, complemented
58#66867C2211yescharacteristic, complemented
59C23×D11—21no—
60C2×D4×C11C2311yescharacteristic
61C2×D4×C11C2311yescharacteristic
62C22×C4×C11—21no—
63C22×C4×C11—21no—
64C2×C22⋊D11—21no—
65C2×C22⋊D11—21no—
66C22×Dic11—21no—
67D4×D11—22no—
68D4×D11—22no—
69C2×D44C2311yescharacteristic
70C2×C4×D11—21no—
71C2×C4×D11—21no—
72C2×C4×D11—21no—
73C2×C4×D11—44no—
74C2×C4×D11D411yescharacteristic
75C2×C4×D11D411yescharacteristic
76C2×C4×D11C2311yescharacteristic
77C2×Dic22C2311yescharacteristic
78C11×D8—22no—
79C2×C8×C11C2311yescharacteristic
80C2×C8×C11C2311yescharacteristic
81C11×C4⋊C4C2311yescharacteristic
82C11×C4⋊C4C2311yescharacteristic
83C11×C22⋊C4—21no—
84C11×C22⋊C4—21no—
85C42×C11C2311yescharacteristic
86C22⋊Dic11—21no—
87C22⋊Dic11—21no—
88C22⋊Dic11—21no—
89C22⋊Dic11—21no—
90#4324—22no—
91#4323—22no—
92(C2×D11)⋊C4—21no—
93(C2×D11)⋊C4—21no—
94(C2×D11)⋊C4—21no—
95C4⋊Dic11—21no—
96C4⋊Dic11—21no—
97C4⋊Dic11C2311yescharacteristic
98C4⋊Dic11C2311yescharacteristic
99Dic11⋊C4—21no—
100Dic11⋊C4—21no—
101Dic11⋊C4—21no—
102C4×Dic11—21no—
103C4×Dic11D411yescharacteristic
104C4×Dic11D411yescharacteristic
105C4×Dic11C2311yescharacteristic
106C2×C11⋊C8C2311yescharacteristic
107C2×C11⋊C8C2311yescharacteristic
108#4314—22no—
109#3114—111nomaximal, Sylow
110C23×C11—21no—
111C23×C11—21no—
112C22×D11—24no—
113C22×D11—21no—
114C22×D11—42no—
115C22×D11—42no—
116C22×D11C2×D411yescharacteristic
117D4×C11—21no—
118D4×C11—21no—
119D4×C11—21no—
120D4×C11#4112yes—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—42no—
124C2×C4×C11—42no—
125C2×C4×C11C2×D411yescharacteristic
126C2×C4×C11C2×D411yescharacteristic
127C2×C4×C11C2411yescharacteristic
128C22⋊D11—24no—
129C22⋊D11—42no—
130C2×Dic11—21no—
131C2×Dic11—21no—
132C2×Dic11—21no—
133C2×Dic11—42no—
134C2×Dic11C2×D411yescharacteristic
135C2×Dic11C2×D411yescharacteristic
136C2×Dic11C2×D411yescharacteristic
137D44—21no—
138D44#4112yes—
139C4×D11—22no—
140C4×D11—21no—
141C4×D11—21no—
142C4×D11—41no—
143C4×D11—42no—
144C4×D11—42no—
145C4×D11—42no—
146Dic22—21no—
147Dic22—21no—
148C8×C11—21no—
149C8×C11—21no—
150C11⋊C8—21no—
151C11⋊C8—21no—
152#529—111no—
153C2×C4×D4—111no—
154#483—111no—
155#480—111no—
156#478—111no—
157#478—111no—
158#463—111no—
159#463—111no—
160#450—111no—
161#447—111no—
162#442—111no—
163#442D1111yescharacteristic, complemented
164#440—111no—
165#440—111no—
166#432—111no—
167C22×C11—22no—
168C22×C11—41no—
169C22×C11—41no—
170C22×C11—41no—
171C22×C11—41no—
172C22×C11—41no—
173C22×C11C22×D411yescharacteristic
174C2×D11—21no—
175C2×D11—21no—
176C2×D11—22no—
177C2×D11—48no—
178C2×D11—41no—
179C2×D11—41no—
180C2×D11AGL(1,ℤ/8)12yes—
181C4×C11—21no—
182C4×C11—21no—
183C4×C11—41no—
184C4×C11—41no—
185C4×C11C2×#4111yescharacteristic
186C4×C11C2×#4111yescharacteristic
187Dic11—21no—
188Dic11—21no—
189Dic11—21no—
190Dic11—41no—
191Dic11—41no—
192Dic11—41no—
193C22×D4—111no—
194C23×C4—221no—
195C2×SD16—111no—
196C2×SD16—111no—
197C2×D8—111no—
198C2×D8C2×D1111yescharacteristic
199#126—221no—
200#125—111no—
201#124—111no—
202#123—221no—
203C22⋊Q8—111no—
204#121—111no—
205C4×Q8—111no—
206C4×D4—111no—
207C4×D4—111no—
208C4×D4—111no—
209C4×D4—221no—
210C4×D4—221no—
211C4×D4—221no—
212C4×D4C2×D1111yescharacteristic
213C4×D4C2×D1111yescharacteristic, complemented
214#117—221no—
215C2×C4⋊C4—111no—
216C2×C22⋊C4—221no—
217C2×C42—111no—
218#107—111no—
219#107—111no—
220#106—111no—
221#106C2×D1111yescharacteristic, complemented
222C4⋊C8—111no—
223C4⋊C8—111no—
224#103—111no—
225#103—111no—
226#102—111no—
227#102—111no—
228#102—111no—
229#102—111no—
230#102C2×D1111yescharacteristic
231#102C2×D1111yescharacteristic, complemented
232C22⋊C8—111no—
233C22⋊C8—111no—
234#97—111no—
235#97C2×D1111yescharacteristic, complemented
236C2×C11—42no—
237C2×C11—81no—
238C2×C11#52511yescharacteristic
239C2×C11C2×AGL(1,ℤ/8)11yescharacteristic
240C2×C11#57511yescharacteristic
241D11—22no—
242D11—42no—
243C24—221no—
244C2×Q8—111no—
245C2×D4—111no—
246C2×D4—221no—
247C2×D4—222no—
248C2×D4—222no—
249C2×D4—221no—
250C2×D4C22×D1111yescharacteristic
251C2×D4C22×D1111yescharacteristic
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—111no—
255C22×C4—111no—
256C22×C4—111no—
257C22×C4—221no—
258C22×C4—221no—
259C22×C4—221no—
260C22×C4—221no—
261C22×C4—444no—
262SD16—222no—
263SD16—222no—
264D8—22no—
265D8—222no—
266C2×C8—111no—
267C2×C8—111no—
268C2×C8C22×D1111yescharacteristic
269C2×C8C22×D1111yescharacteristic
270C4⋊C4—111no—
271C4⋊C4—111no—
272C4⋊C4—221no—
273C4⋊C4—221no—
274C4⋊C4—221no—
275C4⋊C4—221no—
276C4⋊C4—221no—
277C4⋊C4C22×D1111yescharacteristic
278C4⋊C4C22×D1111yescharacteristic
279C22⋊C4—21no—
280C22⋊C4—21no—
281C22⋊C4—221no—
282C22⋊C4—221no—
283C22⋊C4—221no—
284C22⋊C4—221no—
285C22⋊C4—221no—
286C22⋊C4—221no—
287C22⋊C4—221no—
288C42—111no—
289C42—111no—
290C42—111no—
291C42—221no—
292C42C22×D1111yescharacteristic
293C11#311411yescharacteristic, complemented, Sylow
294C23—21no—
295C23—21no—
296C23—111no—
297C23—224no—
298C23—221no—
299C23—442no—
300C23—442no—
301Q8—221no—
302Q8—221no—
303D4—21no—
304D4—21no—
305D4—21no—
306D4—112no—
307D4—224no—
308D4—221no—
309D4—442no—
310D4#433912yes—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—111no—
316C2×C4—111no—
317C2×C4—111no—
318C2×C4—222no—
319C2×C4—221no—
320C2×C4—221no—
321C2×C4—221no—
322C2×C4—221no—
323C2×C4—221no—
324C2×C4—441no—
325C2×C4—442no—
326C2×C4—442no—
327C2×C4—442no—
328C2×C4—442no—
329C2×C4D4×D1111yescharacteristic
330C2×C4D4×D1111yescharacteristic
331C2×C4C23×D1111yescharacteristic
332C8—21no—
333C8—21no—
334C8—221no—
335C8—221no—
336C22—22no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—41no—
342C22—112no—
343C22—221no—
344C22—221no—
345C22—222no—
346C22—448no—
347C22—441no—
348C22—441no—
349C22C2×D4×D1111yescharacteristic
350C4—21no—
351C4—21no—
352C4—41no—
353C4—41no—
354C4—221no—
355C4—221no—
356C4—221no—
357C4—441no—
358C4—441no—
359C4—441no—
360C4C2×#433911yescharacteristic
361C4#41×D1111yescharacteristic
362C2—42no—
363C2—81no—
364C2—222no—
365C2—442no—
366C2#1062307811yescharacteristic
367C2D11×AGL(1,ℤ/8)11yescharacteristic
368C2#1062330411yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#442C2
socleC22×C11C22×D4
prime radical#10622769C2
hypercenter#442D11
hypocenterC11#3114
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
1. #10623088C2semidirect
2. C4×D4×D11C2semidirect
3. C11×#442C2semidirect
5. #10622766C2semidirect
6. #10622631C2semidirect
7. #10622627C2semidirect
8. #10622484C2semidirect
9. #10622475C2semidirect
10. #10622400C2semidirect
11. #10622389C2semidirect
12. #10622387C2semidirect
13. #10622379C2semidirect
14. #10622323C2semidirect
15. #10622318C2semidirect
20. C4×D4×C11C22semidirect
22. #66989C22semidirect
33. #66943C22semidirect
40. C4×Dic22C22semidirect
41. C11×#106C22semidirect
43. C11×#102C22semidirect
44. C11×#97C22semidirect
46. #66896C22semidirect
50. #66882C22semidirect
51. #66880C22semidirect
52. Dic11⋊C8C22semidirect
53. Dic11⋊C8C22semidirect
54. #66874C22semidirect
56. #66872C22semidirect
57. #66871C22semidirect
58. #66867C22semidirect
163. #442D11semidirect
213. C4×D4C2×D11semidirect
221. #106C2×D11semidirect
231. #102C2×D11semidirect
235. #97C2×D11semidirect
293. C11#3114semidirect

Maximal subgroups

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

subgroupindex
#106230882
C4×D4×D112
C11×#4422
#106227692
#106227662
#106226312
#106226272
#106224842
#106224752
#106224002
#106223892
#106223872
#106223792
#106223232
#106223182
#311411