Finite Group Databasebeta

← #13080247

Subgroups — #13080247

Order 1408.

498 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×AGL(1,ℤ/8)C211yesmaximal, characteristic, complemented
2#10623362C211yesmaximal, characteristic, complemented
3#10623337C211yesmaximal, characteristic, complemented
4C2×#66968C211yesmaximal, characteristic, complemented
5#10622852C211yesmaximal, characteristic, complemented
6#10622831C211yesmaximal, characteristic, complemented
7#10622783C211yesmaximal, characteristic, complemented
8#10622779C211yesmaximal, characteristic, complemented
9SD16×Dic11C211yesmaximal, characteristic, complemented
10#10622772C211yesmaximal, characteristic, complemented
11#10622771C211yesmaximal, characteristic, complemented
12#10622768C211yesmaximal, characteristic, complemented
13#10622766C211yesmaximal, characteristic, complemented
14#10622750C211yesmaximal, characteristic, complemented
15#10622741C211yesmaximal, characteristic, complemented
16C2×C11×#41C2211yescharacteristic
17C22×D4×C11C2211yescharacteristic
18C2×Q8×D11C2211yescharacteristic, complemented
19C2×#4341C2211yescharacteristic
20C11×AGL(1,ℤ/8)—24no—
21C2×C11×SD16C2211yescharacteristic
22C2×C11×SD16C2211yescharacteristic
23C2×C11×D8C2211yescharacteristic
24C2×C11×D8C2211yescharacteristic
25C2×C11×M16C2211yescharacteristic
26#67006—21no—
27C2×C22⋊Dic11—21no—
28Q8×Dic11C2211yescharacteristic, complemented
29C2×#4326C2211yescharacteristic, complemented
30#66992—21no—
31#66991—21no—
32#66991C2211yescharacteristic
33#66991C2211yescharacteristic, complemented
34#66989—21no—
35#66989C2211yescharacteristic
36#66989C2211yescharacteristic, complemented
37#66988—21no—
38D4×Dic11C2211yescharacteristic
39C2×#4324C2211yescharacteristic
40C2×#4324C2211yescharacteristic
41C2×#4324C2211yescharacteristic, complemented
42C4×C22⋊D11—21no—
43C4×C22⋊D11C2211yescharacteristic
44#66977—21no—
45#66977C2211yescharacteristic
46#66977C2211yescharacteristic
47#66968—24no—
48C2×Dic44C2211yescharacteristic, complemented
49C2×#4313C2211yescharacteristic, complemented
50#66899C2211yescharacteristic, complemented
51#66896C2211yescharacteristic
52#66896C2211yescharacteristic
53#66896C2211yescharacteristic, complemented
54C22⋊(C11⋊C8)C2211yescharacteristic
55(C2×D11)⋊C8C2211yescharacteristic, complemented
56#66881C2211yescharacteristic, complemented
57#66880C2211yescharacteristic, complemented
58#66880C2211yescharacteristic, complemented
59Dic11⋊C8C2211yescharacteristic, complemented
60C8×Dic11C2211yescharacteristic, complemented
61C24×C11—21no—
62C11×#41—22no—
63C11×#41—41no—
64C2×Q8×C11C2311yescharacteristic
65C2×D4×C11—22no—
66C2×D4×C11—21no—
67C2×D4×C11—21no—
68C2×D4×C11—41no—
69C2×D4×C11C2311yescharacteristic
70C2×D4×C11C2311yescharacteristic
71C2×D4×C11C2311yescharacteristic
72C22×C4×C11—21no—
73C22×C4×C11C2311yescharacteristic
74C2×C22⋊D11—21no—
75C2×C22⋊D11—21no—
76C2×C22⋊D11—21no—
77C2×C22⋊D11D411yescharacteristic
78C22×Dic11—21no—
79C22×Dic11—21no—
80Q8×D11—22no—
81Q8×D11—41no—
82#4341—22no—
83#4341—41no—
84C2×C4×D11—21no—
85C2×C4×D11C2311yescharacteristic
86C2×Dic22—21no—
87C2×Dic22C2311yescharacteristic
88C2×Dic22C2311yescharacteristic
89C11×SD16—22no—
90C11×SD16D414yescomplemented
91C11×D8—22no—
92C11×D8—22no—
93C11×M16—22no—
94C2×C8×C11C2311yescharacteristic
95C2×C8×C11C2311yescharacteristic
96C22⋊Dic11—21no—
97C22⋊Dic11—21no—
98C22⋊Dic11—21no—
99C22⋊Dic11—21no—
100C22⋊Dic11—21no—
101C22⋊Dic11—21no—
102C22⋊Dic11—21no—
103C22⋊Dic11—21no—
104C22⋊Dic11—21no—
105C22⋊Dic11D411yescharacteristic
106#4326—22no—
107#4324—22no—
108#4324—41no—
109#4324—41no—
110(C2×D11)⋊C4D411yescharacteristic
111C4⋊Dic11—21no—
112C4⋊Dic11C2311yescharacteristic
113C4⋊Dic11C2311yescharacteristic
114Dic11⋊C4—21no—
115Dic11⋊C4—21no—
116Dic11⋊C4D411yescharacteristic
117C4×Dic11—21no—
118C4×Dic11C2311yescharacteristic
119C2×C11⋊C8C2311yescharacteristic
120C2×C11⋊C8C2311yescharacteristic
121Dic44—22no—
122#4313—22no—
123#3275—111nomaximal, Sylow
124C23×C11—21no—
125C23×C11—21no—
126C23×C11—21no—
127C23×C11—42no—
128C23×C11—42no—
129C23×C11—81no—
130C23×C11C2×D411yescharacteristic
131C22×D11C2×D411yescharacteristic
132Q8×C11—21no—
133Q8×C11C2×D412yes—
134D4×C11—21no—
135D4×C11—21no—
136D4×C11—21no—
137D4×C11—21no—
138D4×C11—21no—
139D4×C11—42no—
140D4×C11—42no—
141D4×C11C2×D412yes—
142C2×C4×C11—21no—
143C2×C4×C11—21no—
144C2×C4×C11—21no—
145C2×C4×C11—42no—
146C2×C4×C11C2×D411yescharacteristic
147C2×C4×C11C2411yescharacteristic
148C22⋊D11—41no—
149C22⋊D11—42no—
150C22⋊D11—42no—
151C22⋊D11—81no—
152C2×Dic11—21no—
153C2×Dic11—21no—
154C2×Dic11—21no—
155C2×Dic11—21no—
156C2×Dic11—42no—
157C2×Dic11—81no—
158C2×Dic11C2×D411yescharacteristic
159C2×Dic11C2×D411yescharacteristic
160C2×Dic11C2×D411yescharacteristic
161C4×D11—21no—
162C4×D11—21no—
163C4×D11—42no—
164Dic22—21no—
165Dic22—21no—
166Dic22—21no—
167Dic22—21no—
168Dic22—42no—
169C8×C11—21no—
170C8×C11C2×D412yes—
171C11⋊C8—21no—
172C11⋊C8—21no—
173C2×#137—111no—
174C2×AGL(1,ℤ/8)D1111yescharacteristic, complemented
175#548—111no—
176#546—111no—
177#495—111no—
178#470—111no—
179#469—111no—
180#464—111no—
181#463—111no—
182#452—111no—
183#450—111no—
184#449—111no—
185#448—111no—
186C4×SD16—111no—
187#436—111no—
188C22×C11—21no—
189C22×C11—22no—
190C22×C11—21no—
191C22×C11—21no—
192C22×C11—41no—
193C22×C11—41no—
194C22×C11—41no—
195C22×C11—41no—
196C22×C11—41no—
197C22×C11—41no—
198C22×C11—41no—
199C22×C11—41no—
200C22×C11—84no—
201C22×C11C22×D411yescharacteristic
202C2×D11—21no—
203C2×D11—21no—
204C2×D11—21no—
205C4×C11—21no—
206C4×C11—22no—
207C4×C11C22×D411yescharacteristic
208C4×C11H(5,𝔽2)11yescharacteristic
209Dic11—21no—
210Dic11—21no—
211Dic11—21no—
212Dic11—41no—
213Dic11—41no—
214Dic11—41no—
215Dic11—41no—
216C2×#41—111no—
217C2×#41C2×D1111yescharacteristic
218C22×Q8—111no—
219C22×D4C2×D1111yescharacteristic
220#137—224no—
221AGL(1,ℤ/8)—24no—
222C2×Q16—111no—
223C2×Q16—111no—
224C2×SD16—111no—
225C2×SD16—111no—
226C2×SD16—111no—
227C2×SD16C2×D1111yescharacteristic
228C2×SD16C2×D1111yescharacteristic
229C2×D8C2×D1111yescharacteristic
230C2×D8C2×D1111yescharacteristic
231C2×M16—111no—
232C2×M16C2×D1111yescharacteristic
233#124—111no—
234#124—111no—
235#124—221no—
236#123—221no—
237C22⋊Q8—111no—
238C22⋊Q8—111no—
239C22⋊Q8—221no—
240#121—111no—
241#121—111no—
242#121—221no—
243#121—221no—
244#120—221no—
245C4×Q8—111no—
246C4×D4—111no—
247C4×D4—111no—
248C4×D4—221no—
249C2×C22⋊C4—221no—
250#106—111no—
251C4⋊C8—111no—
252#103—111no—
253#103—111no—
254#103—111no—
255#102—111no—
256#102—111no—
257#102—111no—
258C22⋊C8—111no—
259C22⋊C8—111no—
260C4×C8—111no—
261C2×C11—41no—
262C2×C11—42no—
263C2×C11—81no—
264C2×C11—81no—
265C2×C11D4211yescharacteristic
266C2×C11#57511yescharacteristic
267C2×C11#57711yescharacteristic
268D11—41no—
269C24—21no—
270#41—22no—
271#41—41no—
272#41—222no—
273#41—441no—
274C2×Q8—111no—
275C2×Q8—111no—
276C2×Q8—221no—
277C2×Q8—222no—
278C2×Q8—441no—
279C2×Q8C22×D1111yescharacteristic
280C2×D4—22no—
281C2×D4—21no—
282C2×D4—21no—
283C2×D4—41no—
284C2×D4—111no—
285C2×D4—221no—
286C2×D4—221no—
287C2×D4—221no—
288C2×D4C22×D1111yescharacteristic
289C2×D4C22×D1111yescharacteristic
290C2×D4C22×D1111yescharacteristic
291C22×C4—21no—
292C22×C4—111no—
293C22×C4—221no—
294C22×C4—221no—
295C22×C4—221no—
296C22×C4C22×D1111yescharacteristic
297Q16—222no—
298Q16—222no—
299SD16—22no—
300SD16—222no—
301SD16—441no—
302SD16—441no—
303SD16C22⋊D1114yescomplemented
304D8—22no—
305D8—22no—
306M16—22no—
307M16—222no—
308C2×C8—111no—
309C2×C8—111no—
310C2×C8C22×D1111yescharacteristic
311C2×C8C22×D1111yescharacteristic
312C4⋊C4—111no—
313C4⋊C4—111no—
314C4⋊C4—111no—
315C4⋊C4—221no—
316C4⋊C4—221no—
317C4⋊C4—221no—
318C22⋊C4—111no—
319C22⋊C4—111no—
320C22⋊C4—221no—
321C22⋊C4—221no—
322C22⋊C4—221no—
323C22⋊C4—221no—
324C22⋊C4—221no—
325C22⋊C4—221no—
326C22⋊C4—221no—
327C22⋊C4—221no—
328C22⋊C4—221no—
329C42—111no—
330C42—221no—
331C11#327511yescharacteristic, complemented, Sylow
332C23—21no—
333C23—21no—
334C23—21no—
335C23—42no—
336C23—42no—
337C23—81no—
338C23—111no—
339C23D4×D1111yescharacteristic
340Q8—21no—
341Q8—221no—
342Q8—221no—
343Q8—221no—
344Q8—221no—
345Q8—442no—
346Q8C2×C22⋊D1112yes—
347D4—21no—
348D4—21no—
349D4—21no—
350D4—21no—
351D4—21no—
352D4—42no—
353D4—42no—
354D4—441no—
355D4—442no—
356D4—442no—
357D4—881no—
358D4C2×C22⋊D1112yes—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—42no—
363C2×C4—111no—
364C2×C4—111no—
365C2×C4—111no—
366C2×C4—221no—
367C2×C4—221no—
368C2×C4—221no—
369C2×C4—221no—
370C2×C4—221no—
371C2×C4—221no—
372C2×C4—442no—
373C2×C4—442no—
374C2×C4—881no—
375C2×C4D4×D1111yescharacteristic
376C2×C4C23×D1111yescharacteristic
377C8—21no—
378C8—221no—
379C8—221no—
380C8C2×C22⋊D1112yes—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—22no—
385C22—41no—
386C22—41no—
387C22—41no—
388C22—41no—
389C22—41no—
390C22—41no—
391C22—41no—
392C22—41no—
393C22—84no—
394C22—221no—
395C22—221no—
396C22—221no—
397C22C2×D4×D1111yescharacteristic
398C4—21no—
399C4—22no—
400C4—221no—
401C4—221no—
402C4—221no—
403C4—441no—
404C4—441no—
405C4—441no—
406C4—441no—
407C4#6703711yescharacteristic
408C4C22×C22⋊D1111yescharacteristic
409C2—41no—
410C2—42no—
411C2—81no—
412C2—81no—
413C2—441no—
414C2#1062330411yescharacteristic
415C2#1062330611yescharacteristic
416C2D4×C22⋊D1111yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC2×C11×AGL(1,ℤ/8)C2
socleC22×C11C22×D4
hypercenterC2×AGL(1,ℤ/8)D11
hypocenterC11#3275
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. C2×C11×AGL(1,ℤ/8)C2semidirect
2. #10623362C2semidirect
3. #10623337C2semidirect
4. C2×#66968C2semidirect
5. #10622852C2semidirect
6. #10622831C2semidirect
7. #10622783C2semidirect
8. #10622779C2semidirect
9. SD16×Dic11C2semidirect
10. #10622772C2semidirect
11. #10622771C2semidirect
12. #10622768C2semidirect
13. #10622766C2semidirect
14. #10622750C2semidirect
15. #10622741C2semidirect
18. C2×Q8×D11C22semidirect
28. Q8×Dic11C22semidirect
29. C2×#4326C22semidirect
33. #66991C22semidirect
36. #66989C22semidirect
41. C2×#4324C22semidirect
48. C2×Dic44C22semidirect
49. C2×#4313C22semidirect
50. #66899C22semidirect
53. #66896C22semidirect
55. (C2×D11)⋊C8C22semidirect
56. #66881C22semidirect
57. #66880C22semidirect
58. #66880C22semidirect
59. Dic11⋊C8C22semidirect
60. C8×Dic11C22semidirect
90. C11×SD16D4semidirect
174. C2×AGL(1,ℤ/8)D11semidirect
303. SD16C22⋊D11semidirect
331. C11#3275semidirect

Maximal subgroups

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

subgroupindex
C2×C11×AGL(1,ℤ/8)2
#106233622
#106233372
C2×#669682
#106228522
#106228312
#106227832
#106227792
SD16×Dic112
#106227722
#106227712
#106227682
#106227662
#106227502
#106227412
#327511