Finite Group Databasebeta

← #13078241

Subgroups — #13078241

Order 1408.

496 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#66968C211yesmaximal, characteristic, complemented
2C2×M16×D11C211yesmaximal, characteristic, complemented
3D11×C22⋊Q8C211yesmaximal, characteristic, complemented
4#10623137C211yesmaximal, characteristic
5C11×#468C211yesmaximal, characteristic, complemented
6#10622784C211yesmaximal, characteristic, complemented
7#10622750C211yesmaximal, characteristic, complemented
8#10622665C211yesmaximal, characteristic, complemented
9#10622655C211yesmaximal, characteristic, complemented
10#10622500C211yesmaximal, characteristic, complemented
11#10622494C211yesmaximal, characteristic, complemented
12#10622426C211yesmaximal, characteristic, complemented
13#10622415C211yesmaximal, characteristic, complemented
14#10622391C211yesmaximal, characteristic, complemented
15#10622384C211yesmaximal, characteristic, complemented
16C2×Q8×D11C2211yescharacteristic
17C2×#4341C2211yescharacteristic
18C22×C4×D11C2211yescharacteristic
19C2×C11×SD16C2211yescharacteristic, complemented
20C2×C11×M16C2211yescharacteristic
21C11×C22⋊Q8C2211yescharacteristic
22C11×#121C2211yescharacteristic
23#66999C2211yescharacteristic
24C2×#4326C2211yescharacteristic, complemented
25#66991C2211yescharacteristic
26#66990—21no—
27D4×Dic11—21no—
28C2×#4324C2211yescharacteristic, complemented
29#66977C2211yescharacteristic
30#66977C2211yescharacteristic
31C2×#4318C2211yescharacteristic
32#66968—24no—
33M16×D11—24no—
34C2×Dic44C2211yescharacteristic, complemented
35C2×#4313C2211yescharacteristic
36C2×#4313C2211yescharacteristic
37C2×C8×D11C2211yescharacteristic
38C2×C8×D11C2211yescharacteristic
39#66950C2211yescharacteristic
40#66950C2211yescharacteristic
41#66949—21no—
42#66945C2211yescharacteristic
43C4⋊C4×D11—21no—
44C4⋊C4×D11C2211yescharacteristic
45#66936—21no—
46(C22⋊D11)⋊C4—21no—
47C22⋊C4×D11—21no—
48#66931—21no—
49C11×#107C2211yescharacteristic, complemented
50C11×#103C2211yescharacteristic, complemented
51C11×#102C2211yescharacteristic, complemented
52#66899C2211yescharacteristic, complemented
53#66896C2211yescharacteristic, complemented
54#66881C2211yescharacteristic, complemented
55#66880C2211yescharacteristic, complemented
56#66880C2211yescharacteristic, complemented
57#66874C2211yescharacteristic, complemented
58#66874C2211yescharacteristic, complemented
59#66872C2211yescharacteristic, complemented
60#66871C2211yescharacteristic, complemented
61C23×D11D411yescharacteristic
62C2×Q8×C11C2311yescharacteristic
63C2×D4×C11—21no—
64C2×D4×C11C2311yescharacteristic
65C22×C4×C11C2311yescharacteristic
66C2×C22⋊D11—21no—
67C2×C22⋊D11—21no—
68C22×Dic11—21no—
69C22×Dic11D411yescharacteristic
70Q8×D11—22no—
71Q8×D11—22no—
72#4341—22no—
73#4341—22no—
74C2×C4×D11—22no—
75C2×C4×D11—22no—
76C2×C4×D11—21no—
77C2×C4×D11—21no—
78C2×C4×D11D411yescharacteristic
79C2×C4×D11D411yescharacteristic
80C2×C4×D11C2311yescharacteristic
81C2×C4×D11C2311yescharacteristic
82C2×Dic22—21no—
83C2×Dic22C2311yescharacteristic
84C2×Dic22C2311yescharacteristic
85C11×SD16—22no—
86C11×M16—22no—
87C2×C8×C11C2311yescharacteristic
88C2×C8×C11C2311yescharacteristic
89C11×C4⋊C4—21no—
90C11×C4⋊C4C2311yescharacteristic
91C11×C4⋊C4C2311yescharacteristic
92C11×C22⋊C4—21no—
93C11×C22⋊C4—21no—
94C22⋊Dic11—21no—
95C22⋊Dic11—21no—
96C22⋊Dic11—21no—
97#4326—22no—
98#4324—22no—
99(C2×D11)⋊C4—21no—
100(C2×D11)⋊C4—21no—
101(C2×D11)⋊C4—21no—
102(C2×D11)⋊C4—21no—
103C4⋊Dic11—21no—
104C4⋊Dic11—21no—
105C4⋊Dic11C2311yescharacteristic
106C4⋊Dic11C2311yescharacteristic
107Dic11⋊C4—21no—
108Dic11⋊C4—21no—
109Dic11⋊C4—21no—
110Dic11⋊C4—21no—
111C4×Dic11—21no—
112#4318—22no—
113C2×C11⋊C8C2311yescharacteristic
114C2×C11⋊C8C2311yescharacteristic
115Dic44—22no—
116#4313—22no—
117#4313D414yescomplemented
118C8×D11—22no—
119C8×D11—22no—
120#3056—111nomaximal, Sylow
121C23×C11—21no—
122C23×C11C2×D411yescharacteristic
123C22×D11—22no—
124C22×D11—22no—
125C22×D11—41no—
126C22×D11C2×D411yescharacteristic
127C22×D11C2×D411yescharacteristic
128Q8×C11—21no—
129Q8×C11—21no—
130D4×C11—21no—
131D4×C11—21no—
132D4×C11—42no—
133C2×C4×C11—21no—
134C2×C4×C11—21no—
135C2×C4×C11—21no—
136C2×C4×C11—21no—
137C2×C4×C11—21no—
138C2×C4×C11C2×D411yescharacteristic
139C2×C4×C11C2411yescharacteristic
140C22⋊D11—42no—
141C22⋊D11—42no—
142C2×Dic11—22no—
143C2×Dic11—21no—
144C2×Dic11—21no—
145C2×Dic11—21no—
146C2×Dic11—21no—
147C2×Dic11—42no—
148C2×Dic11C2×D411yescharacteristic
149C2×Dic11C2×D411yescharacteristic
150C4×D11—22no—
151C4×D11—21no—
152C4×D11—21no—
153C4×D11—22no—
154C4×D11—42no—
155C4×D11—42no—
156C4×D11C2×D412yes—
157C4×D11#4112yes—
158Dic22—21no—
159Dic22—21no—
160Dic22—21no—
161Dic22—21no—
162Dic22—42no—
163C8×C11—21no—
164C8×C11C2×D412yes—
165C11⋊C8—21no—
166C11⋊C8C2×D412yes—
167C2×#137—111no—
168C22×M16—111no—
169#525—111no—
170C2×C22⋊Q8—111no—
171#470—111no—
172#470—111no—
173#468—111no—
174#468D1111yescharacteristic, complemented
175#467—111no—
176#467—111no—
177#465—111no—
178#465—111no—
179#428—111no—
180#419—111no—
181#417—111no—
182C22×C11—21no—
183C22×C11—21no—
184C22×C11—21no—
185C22×C11—41no—
186C22×C11—41no—
187C22×C11—41no—
188C22×C11C22×D411yescharacteristic
189C2×D11—21no—
190C2×D11—21no—
191C2×D11—21no—
192C2×D11—21no—
193C2×D11—44no—
194C2×D11#12112yes—
195C2×D11#13712yescomplemented
196C4×C11—21no—
197C4×C11—41no—
198C4×C11—41no—
199C4×C11—41no—
200C4×C11C22×D411yescharacteristic
201C4×C11C2×#4111yescharacteristic
202Dic11—21no—
203Dic11—41no—
204Dic11—41no—
205Dic11—41no—
206Dic11—41no—
207Dic11#12112yes—
208C2×#41—111no—
209C22×Q8—111no—
210C23×C4—111no—
211#137—224no—
212C2×Q16—111no—
213C2×Q16—111no—
214C2×SD16—111no—
215C2×SD16C2×D1111yescharacteristic, complemented
216C2×M16—111no—
217C2×M16—111no—
218C2×M16—111no—
219C2×M16—224no—
220C2×M16C2×D1111yescharacteristic
221C22×C8—111no—
222C22×C8—111no—
223#123—221no—
224C22⋊Q8—111no—
225C22⋊Q8—111no—
226C22⋊Q8—111no—
227C22⋊Q8—111no—
228C22⋊Q8—111no—
229C22⋊Q8—221no—
230C22⋊Q8—221no—
231C22⋊Q8C2×D1111yescharacteristic
232#121—111no—
233#121C2×D1111yescharacteristic
234#120—221no—
235C4×D4—221no—
236C4×D4—221no—
237#117—111no—
238C2×C4⋊C4—111no—
239C2×C4⋊C4—221no—
240C2×C22⋊C4—221no—
241#107—111no—
242#107C2×D1111yescharacteristic, complemented
243#106—111no—
244#106—111no—
245#103—111no—
246#103—111no—
247#103—111no—
248#103—111no—
249#103—111no—
250#103C2×D1111yescharacteristic, complemented
251#102—111no—
252#102C2×D1111yescharacteristic, complemented
253C2×C11—41no—
254C2×C11—81no—
255C2×C11C2×#12111yescharacteristic
256C2×C11C2×#13711yescharacteristic
257C2×C11#57511yescharacteristic
258D11—22no—
259D11—22no—
260C24—111no—
261#41—222no—
262#41—222no—
263C2×Q8—111no—
264C2×Q8—111no—
265C2×Q8—221no—
266C2×Q8—222no—
267C2×Q8—222no—
268C2×Q8C22×D1111yescharacteristic
269C2×D4—21no—
270C2×D4—221no—
271C2×D4—221no—
272C2×D4C22×D1111yescharacteristic
273C22×C4—111no—
274C22×C4—111no—
275C22×C4—111no—
276C22×C4—111no—
277C22×C4—111no—
278C22×C4—222no—
279C22×C4—222no—
280C22×C4—221no—
281C22×C4—221no—
282C22×C4—221no—
283C22×C4C22×D1111yescharacteristic
284Q16—222no—
285Q16—222no—
286SD16—22no—
287SD16—222no—
288M16—22no—
289M16—114no—
290M16—222no—
291M16—222no—
292C2×C8—111no—
293C2×C8—111no—
294C2×C8—222no—
295C2×C8—222no—
296C2×C8C22×D1111yescharacteristic
297C2×C8C22×D1111yescharacteristic
298C4⋊C4—21no—
299C4⋊C4—111no—
300C4⋊C4—111no—
301C4⋊C4—221no—
302C4⋊C4—221no—
303C4⋊C4—221no—
304C4⋊C4—221no—
305C4⋊C4—221no—
306C4⋊C4—221no—
307C4⋊C4C22×D1111yescharacteristic
308C4⋊C4C22×D1111yescharacteristic
309C22⋊C4—21no—
310C22⋊C4—21no—
311C22⋊C4—221no—
312C22⋊C4—221no—
313C22⋊C4—221no—
314C22⋊C4—221no—
315C22⋊C4—221no—
316C22⋊C4—221no—
317C22⋊C4—221no—
318C42—221no—
319C11#305611yescharacteristic, complemented, Sylow
320C23—21no—
321C23—111no—
322C23—111no—
323C23—222no—
324C23—222no—
325C23—441no—
326C23D4×D1111yescharacteristic
327Q8—21no—
328Q8—21no—
329Q8—221no—
330Q8—221no—
331Q8—221no—
332Q8—221no—
333Q8—442no—
334D4—21no—
335D4—21no—
336D4—42no—
337D4—442no—
338D4—442no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—111no—
345C2×C4—112no—
346C2×C4—112no—
347C2×C4—111no—
348C2×C4—222no—
349C2×C4—222no—
350C2×C4—222no—
351C2×C4—221no—
352C2×C4—221no—
353C2×C4—221no—
354C2×C4—221no—
355C2×C4—221no—
356C2×C4—221no—
357C2×C4—442no—
358C2×C4—442no—
359C2×C4—442no—
360C2×C4D4×D1111yescharacteristic
361C2×C4C23×D1111yescharacteristic
362C8—21no—
363C8—112no—
364C8—221no—
365C8D4×D1112yes—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—41no—
370C22—41no—
371C22—41no—
372C22—112no—
373C22—112no—
374C22—221no—
375C22—221no—
376C22—221no—
377C22—221no—
378C22—444no—
379C22C2×D4×D1111yescharacteristic
380C4—21no—
381C4—41no—
382C4—41no—
383C4—41no—
384C4—112no—
385C4—221no—
386C4—441no—
387C4—441no—
388C4—441no—
389C4—441no—
390C4C2×D4×D1111yescharacteristic
391C4#41×D1111yescharacteristic
392C2—41no—
393C2—81no—
394C2—222no—
395C2—222no—
396C2D11×#12111yescharacteristic
397C2#1062330411yescharacteristic
398C2D11×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#468C2
socleC22×C11C22×D4
prime radical#10623137C2
hypercenter#468D11
hypocenterC11#3056
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
1. C2×#66968C2semidirect
2. C2×M16×D11C2semidirect
3. D11×C22⋊Q8C2semidirect
5. C11×#468C2semidirect
6. #10622784C2semidirect
7. #10622750C2semidirect
8. #10622665C2semidirect
9. #10622655C2semidirect
10. #10622500C2semidirect
11. #10622494C2semidirect
12. #10622426C2semidirect
13. #10622415C2semidirect
14. #10622391C2semidirect
15. #10622384C2semidirect
19. C2×C11×SD16C22semidirect
24. C2×#4326C22semidirect
28. C2×#4324C22semidirect
34. C2×Dic44C22semidirect
49. C11×#107C22semidirect
50. C11×#103C22semidirect
51. C11×#102C22semidirect
52. #66899C22semidirect
53. #66896C22semidirect
54. #66881C22semidirect
55. #66880C22semidirect
56. #66880C22semidirect
57. #66874C22semidirect
58. #66874C22semidirect
59. #66872C22semidirect
60. #66871C22semidirect
117. #4313D4semidirect
174. #468D11semidirect
195. C2×D11#137semidirect
215. C2×SD16C2×D11semidirect
242. #107C2×D11semidirect
250. #103C2×D11semidirect
252. #102C2×D11semidirect
319. C11#3056semidirect

Maximal subgroups

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

subgroupindex
C2×#669682
C2×M16×D112
D11×C22⋊Q82
#106231372
C11×#4682
#106227842
#106227502
#106226652
#106226552
#106225002
#106224942
#106224262
#106224152
#106223912
#106223842
#305611