Finite Group Databasebeta

← #13080243

Subgroups — #13080243

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
1C11×#546C211yesmaximal, characteristic, complemented
2C2×#67004C211yesmaximal, characteristic, complemented
3C2×#66985C211yesmaximal, characteristic, complemented
4#10623083C211yesmaximal, characteristic, complemented
5#10622851C211yesmaximal, characteristic, complemented
6#10622831C211yesmaximal, characteristic, complemented
7#10622672C211yesmaximal, characteristic, complemented
8#10622667C211yesmaximal, characteristic, complemented
9#10622665C211yesmaximal, characteristic, complemented
10#10622660C211yesmaximal, characteristic, complemented
11#10622653C211yesmaximal, characteristic, complemented
12#10622652C211yesmaximal, characteristic, complemented
13C4×#4324C211yesmaximal, characteristic, complemented
14#10622629C211yesmaximal, characteristic, complemented
15#10622625C211yesmaximal, characteristic, complemented
16C2×C11×#41C2211yescharacteristic
17C22×D4×C11C2211yescharacteristic
18C2×#4339C2211yescharacteristic
19C22×Dic22C2211yescharacteristic, complemented
20C11×#124C2211yescharacteristic
21C11×#123—21no—
22C11×C22⋊Q8C2211yescharacteristic
23C11×#121—21no—
24C11×#121C2211yescharacteristic
25C11×#120—21no—
26C4×D4×C11C2211yescharacteristic
27C4×D4×C11C2211yescharacteristic
28C2×C11×C22⋊C4—21no—
29#67004—24no—
30C2×#4326C2211yescharacteristic, complemented
31C2×#4326C2211yescharacteristic, complemented
32C2×#4325C2211yescharacteristic, complemented
33#66992—21no—
34C2×#4324C2211yescharacteristic
35C2×#4324C2211yescharacteristic
36C2×#4324C2211yescharacteristic
37C2×#4324C2211yescharacteristic
38#66985—24no—
39C2×#4323C2211yescharacteristic
40C2×#4323C2211yescharacteristic
41#66983C2211yescharacteristic, complemented
42#66977C2211yescharacteristic
43C2×#4318C2211yescharacteristic
44C2×#4318C2211yescharacteristic, complemented
45#66949—21no—
46#66938—21no—
47(C22⋊D11)⋊C4—21no—
48#66928C2211yescharacteristic, complemented
49C4×Dic22C2211yescharacteristic, complemented
50#66899C2211yescharacteristic, complemented
51#66896C2211yescharacteristic
52#66896C2211yescharacteristic
53C22⋊(C11⋊C8)C2211yescharacteristic
54C22⋊(C11⋊C8)C2211yescharacteristic, complemented
55#66874C2211yescharacteristic, complemented
56#66874C2211yescharacteristic, complemented
57#66873C2211yescharacteristic, complemented
58#66872C2211yescharacteristic, complemented
59C4⋊(C11⋊C8)C2211yescharacteristic, complemented
60C4×C11⋊C8C2211yescharacteristic, 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—21no—
69C2×D4×C11—41no—
70C2×D4×C11D411yescharacteristic
71C2×D4×C11C2311yescharacteristic
72C2×D4×C11C2311yescharacteristic
73C22×C4×C11—21no—
74C22×C4×C11—21no—
75C22×C4×C11C2311yescharacteristic
76C22×C4×C11C2311yescharacteristic
77C2×C22⋊D11—21no—
78C2×C22⋊D11—21no—
79C22×Dic11—21no—
80#4339—22no—
81#4339—41no—
82C2×D44C2311yescharacteristic
83C2×C4×D11—21no—
84C2×Dic22—22no—
85C2×Dic22—21no—
86C2×Dic22—41no—
87C2×Dic22C2311yescharacteristic
88C2×Dic22C2311yescharacteristic
89C11×C4⋊C4—21no—
90C11×C4⋊C4D411yescharacteristic
91C11×C4⋊C4C2311yescharacteristic
92C11×C22⋊C4—21no—
93C11×C22⋊C4—21no—
94C11×C22⋊C4—21no—
95C11×C22⋊C4—21no—
96C11×C22⋊C4—21no—
97C11×C22⋊C4D411yescharacteristic
98C11×C22⋊C4D411yescharacteristic
99C42×C11C2311yescharacteristic
100C22⋊Dic11—21no—
101#4326—22no—
102#4326—22no—
103#4325—41no—
104#4324—22no—
105#4324—22no—
106#4324—41no—
107#4324D414yescomplemented
108#4323—22no—
109#4323—22no—
110(C2×D11)⋊C4—21no—
111(C2×D11)⋊C4—21no—
112(C2×D11)⋊C4—21no—
113C4⋊Dic11C2311yescharacteristic
114Dic11⋊C4—21no—
115Dic11⋊C4—21no—
116C4×Dic11—21no—
117#4318—22no—
118#4318—22no—
119C2×C11⋊C8C2311yescharacteristic
120C2×C11⋊C8C2311yescharacteristic
121C2×C11⋊C8C2311yescharacteristic
122C2×C11⋊C8C2311yescharacteristic
123#3275—111nomaximal, Sylow
124C23×C11—21no—
125C23×C11—21no—
126C23×C11—42no—
127C23×C11—42no—
128C23×C11—81no—
129C23×C11C2×D411yescharacteristic
130C23×C11C2×D411yescharacteristic
131C22×D11—21no—
132Q8×C11—21no—
133Q8×C11—21no—
134D4×C11—21no—
135D4×C11—21no—
136D4×C11—21no—
137D4×C11—41no—
138D4×C11—42no—
139D4×C11—42no—
140D4×C11—81no—
141D4×C11C2×D412yes—
142C2×C4×C11—21no—
143C2×C4×C11—21no—
144C2×C4×C11—21no—
145C2×C4×C11—21no—
146C2×C4×C11—21no—
147C2×C4×C11—21no—
148C2×C4×C11—42no—
149C2×C4×C11—81no—
150C2×C4×C11C2×D411yescharacteristic
151C2×C4×C11C2×D411yescharacteristic
152C2×C4×C11C2×D411yescharacteristic
153C2×C4×C11C2×D411yescharacteristic
154C2×C4×C11C2411yescharacteristic
155C22⋊D11—42no—
156C22⋊D11—42no—
157C2×Dic11—21no—
158C2×Dic11—21no—
159C2×Dic11—21no—
160C2×Dic11—42no—
161D44—21no—
162D44—21no—
163C4×D11—42no—
164Dic22—21no—
165Dic22—21no—
166Dic22—21no—
167Dic22—42no—
168Dic22C2×D412yes—
169C11⋊C8—21no—
170C11⋊C8—21no—
171C11⋊C8—21no—
172C11⋊C8C2×D412yes—
173C2×#137—111no—
174C2×AGL(1,ℤ/8)—111no—
175#548—111no—
176#546D1111yescharacteristic, complemented
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—21no—
190C22×C11—22no—
191C22×C11—21no—
192C22×C11—21no—
193C22×C11—21no—
194C22×C11—21no—
195C22×C11—41no—
196C22×C11—41no—
197C22×C11—41no—
198C22×C11—41no—
199C22×C11—41no—
200C22×C11—84no—
201C22×C11C22×D411yescharacteristic
202C2×D11—41no—
203C2×D11—41no—
204C2×D11—41no—
205C4×C11—21no—
206C4×C11—21no—
207C4×C11—21no—
208C4×C11—21no—
209C4×C11—41no—
210C4×C11—41no—
211C4×C11C22×D411yescharacteristic
212C4×C11H(5,𝔽2)11yescharacteristic
213Dic11—22no—
214Dic11—41no—
215Dic11—41no—
216C2×#41—111no—
217C2×#41C2×D1111yescharacteristic
218C22×Q8—111no—
219C22×D4C2×D1111yescharacteristic
220#137—224no—
221AGL(1,ℤ/8)—224no—
222C2×Q16—111no—
223C2×Q16—111no—
224C2×SD16—111no—
225C2×SD16—111no—
226C2×SD16—111no—
227C2×SD16—111no—
228C2×SD16—111no—
229C2×D8—111no—
230C2×D8—111no—
231C2×M16—111no—
232C2×M16—111no—
233#124—111no—
234#124—221no—
235#124C2×D1111yescharacteristic
236#123—21no—
237C22⋊Q8—111no—
238C22⋊Q8—221no—
239C22⋊Q8C2×D1111yescharacteristic
240#121—21no—
241#121—111no—
242#121—221no—
243#121C2×D1111yescharacteristic
244#120—21no—
245C4×Q8—111no—
246C4×D4—221no—
247C4×D4C2×D1111yescharacteristic
248C4×D4C2×D1111yescharacteristic
249C2×C22⋊C4—21no—
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—41no—
263C2×C11—42no—
264C2×C11—81no—
265C2×C11D4211yescharacteristic
266C2×C11#57511yescharacteristic
267C2×C11#57711yescharacteristic
268D11—81no—
269C24—21no—
270#41—22no—
271#41—41no—
272#41—222no—
273#41—441no—
274C2×Q8—111no—
275C2×Q8—111no—
276C2×Q8—222no—
277C2×Q8—221no—
278C2×Q8—441no—
279C2×Q8C22×D1111yescharacteristic
280C2×D4—22no—
281C2×D4—21no—
282C2×D4—21no—
283C2×D4—21no—
284C2×D4—41no—
285C2×D4—111no—
286C2×D4—221no—
287C2×D4—221no—
288C2×D4C22⋊D1111yescharacteristic
289C2×D4C22×D1111yescharacteristic
290C2×D4C22×D1111yescharacteristic
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—221no—
294C22×C4—221no—
295C22×C4C22×D1111yescharacteristic
296C22×C4C22×D1111yescharacteristic
297Q16—222no—
298Q16—222no—
299SD16—114no—
300SD16—222no—
301SD16—222no—
302SD16—441no—
303SD16—441no—
304D8—222no—
305D8—222no—
306M16—222no—
307M16—222no—
308C2×C8—111no—
309C2×C8—111no—
310C2×C8—111no—
311C2×C8—111no—
312C4⋊C4—21no—
313C4⋊C4—111no—
314C4⋊C4—221no—
315C4⋊C4—221no—
316C4⋊C4C22⋊D1111yescharacteristic
317C4⋊C4C22×D1111yescharacteristic
318C22⋊C4—21no—
319C22⋊C4—21no—
320C22⋊C4—21no—
321C22⋊C4—21no—
322C22⋊C4—21no—
323C22⋊C4—221no—
324C22⋊C4—221no—
325C22⋊C4—221no—
326C22⋊C4—221no—
327C22⋊C4C22⋊D1111yescharacteristic
328C22⋊C4C22⋊D1111yescharacteristic
329C42—221no—
330C42C22×D1111yescharacteristic
331C11#327511yescharacteristic, complemented, Sylow
332C23—21no—
333C23—21no—
334C23—42no—
335C23—42no—
336C23—81no—
337C23—221no—
338C23C2×C22⋊D1111yescharacteristic
339C23C2×C22⋊D1111yescharacteristic
340Q8—21no—
341Q8—21no—
342Q8—112no—
343Q8—221no—
344Q8—221no—
345Q8—221no—
346Q8—442no—
347D4—21no—
348D4—21no—
349D4—21no—
350D4—41no—
351D4—42no—
352D4—42no—
353D4—81no—
354D4—221no—
355D4—221no—
356D4—442no—
357D4—442no—
358D4D4×D1112yes—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—42no—
366C2×C4—81no—
367C2×C4—221no—
368C2×C4—221no—
369C2×C4—221no—
370C2×C4—442no—
371C2×C4—442no—
372C2×C4C2×C22⋊D1111yescharacteristic
373C2×C4C2×C22⋊D1111yescharacteristic
374C2×C4C2×C22⋊D1111yescharacteristic
375C2×C4C2×C22⋊D1111yescharacteristic
376C2×C4C23×D1111yescharacteristic
377C8—112no—
378C8—221no—
379C8—221no—
380C8—221no—
381C22—21no—
382C22—21no—
383C22—22no—
384C22—21no—
385C22—21no—
386C22—21no—
387C22—21no—
388C22—41no—
389C22—41no—
390C22—41no—
391C22—41no—
392C22—41no—
393C22—84no—
394C22—441no—
395C22—441no—
396C22—441no—
397C22C22×C22⋊D1111yescharacteristic
398C4—21no—
399C4—21no—
400C4—21no—
401C4—21no—
402C4—41no—
403C4—41no—
404C4—222no—
405C4—441no—
406C4—441no—
407C4C2×D4×D1111yescharacteristic
408C4#6703711yescharacteristic
409C2—41no—
410C2—41no—
411C2—42no—
412C2—81no—
413C2—881no—
414C2D4×C22⋊D1111yescharacteristic
415C2#1062335311yescharacteristic
416C2#1062336711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#546C2
socleC22×C11C22×D4
hypercenter#546D11
hypocenterC11#3275
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×D4 ◁ #546

Complements

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

NH ≅ G/Ntype
1. C11×#546C2semidirect
2. C2×#67004C2semidirect
3. C2×#66985C2semidirect
4. #10623083C2semidirect
5. #10622851C2semidirect
6. #10622831C2semidirect
7. #10622672C2semidirect
8. #10622667C2semidirect
9. #10622665C2semidirect
10. #10622660C2semidirect
11. #10622653C2semidirect
12. #10622652C2semidirect
13. C4×#4324C2semidirect
14. #10622629C2semidirect
15. #10622625C2semidirect
19. C22×Dic22C22semidirect
30. C2×#4326C22semidirect
31. C2×#4326C22semidirect
32. C2×#4325C22semidirect
41. #66983C22semidirect
44. C2×#4318C22semidirect
48. #66928C22semidirect
49. C4×Dic22C22semidirect
50. #66899C22semidirect
54. C22⋊(C11⋊C8)C22semidirect
55. #66874C22semidirect
56. #66874C22semidirect
57. #66873C22semidirect
58. #66872C22semidirect
59. C4⋊(C11⋊C8)C22semidirect
60. C4×C11⋊C8C22semidirect
107. #4324D4semidirect
176. #546D11semidirect
331. C11#3275semidirect

Maximal subgroups

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

subgroupindex
C11×#5462
C2×#670042
C2×#669852
#106230832
#106228512
#106228312
#106226722
#106226672
#106226652
#106226602
#106226532
#106226522
C4×#43242
#106226292
#106226252
#327511