Finite Group Databasebeta

← #13082407

Subgroups — #13082407

Order 1408.

1540 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#67042C211yesmaximal, characteristic, complemented
2C2×#67040C211yesmaximal, characteristic, complemented
3C11×#548C211yesmaximal, characteristic, complemented
4#10623362C211yesmaximal, characteristic, complemented
5#10623348C211yesmaximal, characteristic, complemented
6#10623207C213yesmaximal, complemented
7D11×#124C213yesmaximal, complemented
8#10623161C213yesmaximal, complemented
9#10623159C213yesmaximal, complemented
10#10623143C213yesmaximal, complemented
11#10623138C213yesmaximal, complemented
12#10623107C211yesmaximal, characteristic, complemented
13C4×#4343C211yesmaximal, characteristic, complemented
14#10623081C213yesmaximal, complemented
15#10623079C213yesmaximal, complemented
16C2×C11×#41C2211yescharacteristic
17C22×Q8×C11C2211yescharacteristic, complemented
18#67042—28no—
19#67040—28no—
20C2×#4343C2211yescharacteristic
21C2×#4343C2211yescharacteristic
22C2×#4343C2213yescomplemented
23C2×Q8×D11C2211yescharacteristic, complemented
24C2×Q8×D11C2213yescomplemented
25C2×D4×D11C2213yes—
26C2×D4×D11C2213yes—
27C2×#4339C2213yes—
28C2×#4339C2213yescomplemented
29C2×#4339C2213yescomplemented
30C22×D44C2213yes—
31C11×#124C2213yescomplemented
32C11×C22⋊Q8C2213yescomplemented
33C11×#121C2213yescomplemented
34C4×Q8×C11C2211yescharacteristic, complemented
35C4×D4×C11C2213yescomplemented
36#67000C2213yescomplemented
37#66999C2213yescomplemented
38Q8×Dic11C2211yescharacteristic, complemented
39#66993C2213yescomplemented
40#66991C2213yescomplemented
41#66991C2213yescomplemented
42#66990C2216yescomplemented
43#66989C2213yescomplemented
44#66983C2213yescomplemented
45C4×C22⋊D11C2213yescomplemented
46C4×C22⋊D11C2213yescomplemented
47#66977C2213yescomplemented
48#66950C2213yescomplemented
49#66948C2213yescomplemented
50#66948C2213yescomplemented
51#66947C2216yescomplemented
52#66946C2213yescomplemented
53#66945C2213yescomplemented
54#66941C2213yescomplemented
55#66938C2211yescharacteristic, complemented
56#66938C2213yescomplemented
57#66938C2216yescomplemented
58#66937C2213yescomplemented
59#66937C2213yescomplemented
60#66936C2216yescomplemented
61#66935C2216yescomplemented
62C22⋊C4×D11C2216yescomplemented
63C22⋊C4×D11C2216yescomplemented
64#66928C2213yescomplemented
65C4×D44C2213yescomplemented
66C4×D44C2213yescomplemented
67C42×D11C2213yescomplemented
68C23×D11C2316yes—
69C11×#41—24no—
70C2×Q8×C11—24no—
71C2×Q8×C11C2313yes—
72C2×Q8×C11C2311yescharacteristic
73C2×D4×C11C2313yes—
74C2×D4×C11C2313yes—
75C22×C4×C11C2313yes—
76C22×C4×C11C2313yes—
77C2×C22⋊D11C2313yes—
78C2×C22⋊D11C2313yes—
79C2×C22⋊D11C2313yes—
80C2×C22⋊D11C2311yescharacteristic
81C2×C22⋊D11C2313yes—
82C2×C22⋊D11C2313yes—
83#4343—212no—
84#4343—24no—
85#4343D418yescomplemented
86Q8×D11—212no—
87Q8×D11—24no—
88D4×D11—212no—
89D4×D11—212no—
90#4339—212no—
91#4339—212no—
92#4339—212no—
93C2×D44—212no—
94C2×D44C2313yes—
95C2×D44C2313yes—
96C2×D44C2313yes—
97C2×D44C2313yes—
98C2×D44C2313yes—
99C2×C4×D11C2313yes—
100C2×C4×D11C2313yes—
101C2×C4×D11C2316yes—
102C2×C4×D11C2313yes—
103C2×C4×D11C2313yes—
104C2×C4×D11C2313yes—
105C2×Dic22C2313yes—
106C2×Dic22C2313yes—
107C2×Dic22C2311yescharacteristic
108C11×C4⋊C4C2313yes—
109C11×C4⋊C4C2313yes—
110C11×C22⋊C4C2313yes—
111C11×C22⋊C4C2316yes—
112C11×C22⋊C4C2311yescharacteristic
113C42×C11C2313yes—
114C22⋊Dic11C2313yes—
115C22⋊Dic11C2316yes—
116C22⋊Dic11C2311yescharacteristic
117(C2×D11)⋊C4C2311yescharacteristic
118(C2×D11)⋊C4C2313yes—
119(C2×D11)⋊C4C2316yes—
120(C2×D11)⋊C4C2316yes—
121(C2×D11)⋊C4C2313yes—
122(C2×D11)⋊C4C2316yes—
123(C2×D11)⋊C4C2311yescharacteristic
124C4⋊Dic11C2313yes—
125C4⋊Dic11C2313yes—
126Dic11⋊C4C2313yes—
127Dic11⋊C4C2313yes—
128C4×Dic11C2311yescharacteristic
129C4×Dic11C2313yes—
130C4×Dic11C2313yes—
131#3500—111nomaximal, Sylow
132C23×C11C2413yes—
133C23×C11C2411yescharacteristic
134C22×D11—212no—
135C22×D11—46no—
136C22×D11—46no—
137C22×D11C2413yes—
138C22×D11C2411yescharacteristic
139C22×D11C2413yes—
140Q8×C11—26no—
141Q8×C11C2×D414yes—
142D4×C11—26no—
143D4×C11—43no—
144C2×C4×C11—26no—
145C2×C4×C11—26no—
146C2×C4×C11C2413yes—
147C2×C4×C11C2411yescharacteristic
148C2×C4×C11C2411yescharacteristic
149C2×C4×C11C2413yes—
150C2×C4×C11C2413yes—
151C22⋊D11—26no—
152C22⋊D11—26no—
153C22⋊D11—22no—
154C22⋊D11—26no—
155C22⋊D11—43no—
156C22⋊D11—43no—
157C2×Dic11C2411yescharacteristic
158C2×Dic11C2413yes—
159C2×Dic11C2411yescharacteristic
160C2×Dic11C2413yes—
161C2×Dic11C2411yescharacteristic
162D44—26no—
163D44—26no—
164D44—26no—
165D44—43no—
166D44C2×D4112yes—
167C4×D11—212no—
168C4×D11—26no—
169C4×D11—26no—
170C4×D11—43no—
171C4×D11—43no—
172C4×D11C2×D4112yes—
173Dic22—26no—
174Dic22—22no—
175Dic22—26no—
176C2×2−1+4—111no—
177C2×H(5,𝔽2)—111no—
178#548—111no—
179#548—111no—
180#548—111no—
181#548D1111yescharacteristic, complemented
182#546—113no—
183#546—113no—
184#546—113no—
185#546—113no—
186#536—113no—
187#535—113no—
188#532—113no—
189C2×#124—113no—
190C4×#41—111no—
191C22×C11—21no—
192C22×C11—23no—
193C22×C11—21no—
194C22×C11—23no—
195C22×C11—23no—
196C22×C11—21no—
197C22×C11C2511yescharacteristic
198C2×D11—23no—
199C2×D11—23no—
200C2×D11—23no—
201C2×D11—21no—
202C2×D11—23no—
203C2×D11—23no—
204C2×D11—21no—
205C2×D11—21no—
206C2×D11—812no—
207C2×D11C22×D416yes—
208C4×C11—21no—
209C4×C11—23no—
210C4×C11—23no—
211C4×C11—21no—
212C4×C11C22×D416yes—
213Dic11—23no—
214Dic11—21no—
215Dic11—21no—
216Dic11—23no—
217Dic11C22×D412yes—
2182−1+4—228no—
219H(5,𝔽2)—228no—
220C2×#41—111no—
221C2×#41—113no—
222C2×#41—111no—
223C2×#41—113no—
224C2×#41—113no—
225C2×#41—113no—
226C2×#41C2×D1111yescharacteristic
227C22×Q8—113no—
228C22×Q8—111no—
229C22×Q8C2×D1111yescharacteristic, complemented
230C22×D4—113no—
231C22×D4—113no—
232C22×D4—113no—
233C4⋊Q8—113no—
234#127—113no—
235#124—113no—
236#124—113no—
237#124—113no—
238#124—116no—
239#124—111no—
240#124—113no—
241#124C2×D1113yescomplemented
242#123—116no—
243#123—116no—
244C22⋊Q8—113no—
245C22⋊Q8—113no—
246C22⋊Q8—113no—
247C22⋊Q8C2×D1113yescomplemented
248#121—113no—
249#121—113no—
250#121—113no—
251#121—113no—
252#121—113no—
253#121—113no—
254#121—113no—
255#121C2×D1113yescomplemented
256#120—116no—
257#120—116no—
258C4×Q8—111no—
259C4×Q8C2×D1111yescharacteristic, complemented
260C4×D4—113no—
261C4×D4—113no—
262C4×D4—113no—
263C4×D4—113no—
264C4×D4—113no—
265C4×D4C2×D1113yescomplemented
266#117—113no—
267C2×C22⋊C4—116no—
268C2×C22⋊C4—116no—
269C2×C42—113no—
270C2×C11—43no—
271C2×C11—41no—
272C2×C11C23×D411yescharacteristic
273C2×C11#58511yescharacteristic
274C2×C11#58511yescharacteristic
275D11—26no—
276D11—41no—
277D11—43no—
278C24—116no—
279#41—24no—
280#41—118no—
281#41—2212no—
282#41—2212no—
283#41—2212no—
284#41—2212no—
285#41—224no—
286C2×Q8—24no—
287C2×Q8—113no—
288C2×Q8—113no—
289C2×Q8—111no—
290C2×Q8—2212no—
291C2×Q8—224no—
292C2×Q8C22×D1113yes—
293C2×Q8C22×D1111yescharacteristic
294C2×D4—113no—
295C2×D4—113no—
296C2×D4—113no—
297C2×D4—111no—
298C2×D4—113no—
299C2×D4—113no—
300C2×D4—113no—
301C2×D4—113no—
302C2×D4—113no—
303C2×D4—113no—
304C2×D4—113no—
305C2×D4—2212no—
306C2×D4—2212no—
307C2×D4—2212no—
308C2×D4C22×D1113yes—
309C2×D4C22×D1113yes—
310C22×C4—113no—
311C22×C4—116no—
312C22×C4—113no—
313C22×C4—113no—
314C22×C4—113no—
315C22×C4—113no—
316C22×C4C22×D1113yes—
317C22×C4C22×D1113yes—
318C4⋊C4—113no—
319C4⋊C4—113no—
320C4⋊C4—113no—
321C4⋊C4—113no—
322C4⋊C4C22×D1113yes—
323C4⋊C4C22×D1113yes—
324C22⋊C4—113no—
325C22⋊C4—116no—
326C22⋊C4—111no—
327C22⋊C4—113no—
328C22⋊C4—113no—
329C22⋊C4—116no—
330C22⋊C4—116no—
331C22⋊C4—116no—
332C22⋊C4—111no—
333C22⋊C4—111no—
334C22⋊C4C22×D1113yes—
335C22⋊C4C22×D1116yes—
336C22⋊C4C22×D1111yescharacteristic
337C42—111no—
338C42—113no—
339C42—113no—
340C42C22×D1113yes—
341C11#350011yescharacteristic, complemented, Sylow
342C23—113no—
343C23—113no—
344C23—111no—
345C23—2212no—
346C23—446no—
347C23—446no—
348C23C23×D1113yes—
349C23C23×D1111yescharacteristic
350Q8—26no—
351Q8—226no—
352Q8—222no—
353Q8—226no—
354Q8D4×D1114yes—
355D4—26no—
356D4—43no—
357D4—1112no—
358D4—226no—
359D4—226no—
360D4—226no—
361D4—222no—
362D4—226no—
363D4—226no—
364D4—226no—
365D4—443no—
366D4—443no—
367D4—443no—
368C2×C4—26no—
369C2×C4—26no—
370C2×C4—111no—
371C2×C4—1112no—
372C2×C4—111no—
373C2×C4—113no—
374C2×C4—113no—
375C2×C4—111no—
376C2×C4—2212no—
377C2×C4—226no—
378C2×C4—226no—
379C2×C4—443no—
380C2×C4—443no—
381C2×C4C23×D1111yescharacteristic
382C2×C4C23×D1113yes—
383C2×C4C23×D1113yes—
384C2×C4C23×D1111yescharacteristic
385C2×C4C23×D1113yes—
386C22—21no—
387C22—23no—
388C22—21no—
389C22—23no—
390C22—21no—
391C22—23no—
392C22—116no—
393C22—223no—
394C22—223no—
395C22—221no—
396C22—223no—
397C22—221no—
398C22—223no—
399C22—221no—
400C22—223no—
401C22—8812no—
402C22C24×D1111yescharacteristic
403C4—21no—
404C4—23no—
405C4—23no—
406C4—21no—
407C4—112no—
408C4—221no—
409C4—223no—
410C4—221no—
411C4—223no—
412C4C2×D4×D1116yes—
413C2—43no—
414C2—41no—
415C2—226no—
416C2—443no—
417C2—441no—
418C2C22×D4×D1111yescharacteristic
419C2#1062345311yescharacteristic
420C2#1062345711yescharacteristic
subgroupG/H
center, FrattiniC22C24×D11
commutator, socle, cosocleC22×C11C25
FittingC11×#548C2
hypercenter#548D11
hypocenterC11#3500
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ #548

Complements

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

NH ≅ G/Ntype
1. C2×#67042C2semidirect
2. C2×#67040C2semidirect
3. C11×#548C2semidirect
4. #10623362C2semidirect
5. #10623348C2semidirect
6. #10623207C2semidirect
7. D11×#124C2semidirect
8. #10623161C2semidirect
9. #10623159C2semidirect
10. #10623143C2semidirect
11. #10623138C2semidirect
12. #10623107C2semidirect
13. C4×#4343C2semidirect
14. #10623081C2semidirect
15. #10623079C2semidirect
17. C22×Q8×C11C22semidirect
22. C2×#4343C22semidirect
23. C2×Q8×D11C22semidirect
24. C2×Q8×D11C22semidirect
28. C2×#4339C22semidirect
29. C2×#4339C22semidirect
31. C11×#124C22semidirect
32. C11×C22⋊Q8C22semidirect
33. C11×#121C22semidirect
34. C4×Q8×C11C22semidirect
35. C4×D4×C11C22semidirect
36. #67000C22semidirect
37. #66999C22semidirect
38. Q8×Dic11C22semidirect
39. #66993C22semidirect
40. #66991C22semidirect
41. #66991C22semidirect
42. #66990C22semidirect
43. #66989C22semidirect
44. #66983C22semidirect
45. C4×C22⋊D11C22semidirect
46. C4×C22⋊D11C22semidirect
47. #66977C22semidirect
48. #66950C22semidirect
49. #66948C22semidirect
50. #66948C22semidirect
51. #66947C22semidirect
52. #66946C22semidirect
53. #66945C22semidirect
54. #66941C22semidirect
55. #66938C22semidirect
56. #66938C22semidirect
57. #66938C22semidirect
58. #66937C22semidirect
59. #66937C22semidirect
60. #66936C22semidirect
61. #66935C22semidirect
62. C22⋊C4×D11C22semidirect
63. C22⋊C4×D11C22semidirect
64. #66928C22semidirect
65. C4×D44C22semidirect
66. C4×D44C22semidirect
67. C42×D11C22semidirect
85. #4343D4semidirect
181. #548D11semidirect
229. C22×Q8C2×D11semidirect
241. #124C2×D11semidirect
247. C22⋊Q8C2×D11semidirect
255. #121C2×D11semidirect
259. C4×Q8C2×D11semidirect
265. C4×D4C2×D11semidirect
341. C11#3500semidirect

Maximal subgroups

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

subgroupindex
C2×#670422
C2×#670402
C11×#5482
#106233622
#106233482
#106232072
D11×#1242
#106231612
#106231592
#106231432
#106231382
#106231072
C4×#43432
#106230812
#106230792
#350011