Finite Group Databasebeta

← #13082282

Subgroups — #13082282

Order 1408.

1658 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#67042C211yesmaximal, characteristic, complemented
2C22×#4343C211yesmaximal, characteristic, complemented
3C11×#548C211yesmaximal, characteristic, complemented
4#10623365C211yesmaximal, characteristic, complemented
5#10623348C211yesmaximal, characteristic, complemented
6#10623207C213yesmaximal, complemented
7#10623205C213yesmaximal, complemented
8#10623161C213yesmaximal, complemented
9#10623160C213yesmaximal, complemented
10#10623140C213yesmaximal, complemented
11D11×#121C213yesmaximal, complemented
12#10623108C211yesmaximal, characteristic, complemented
13#10623105C211yesmaximal, characteristic, complemented
14D4×D44C213yesmaximal, complemented
15#10623078C213yesmaximal, complemented
16C2×C11×#41C2211yescharacteristic, complemented
17C22×Q8×C11C2211yescharacteristic, complemented
18#67042—28no—
19C2×#4343—28no—
20C2×#4343C2211yescharacteristic
21C2×#4343C2211yescharacteristic, complemented
22C2×#4343C2211yescharacteristic, complemented
23C2×#4343C2213yescomplemented
24C2×#4343C2213yescomplemented
25C2×D4×D11C2213yescomplemented
26C2×D4×D11C2213yescomplemented
27C2×D4×D11C2216yescomplemented
28C2×#4339C2213yescomplemented
29C22×D44C2213yescomplemented
30C22×D44C2213yescomplemented
31C22×C4×D11C2213yescomplemented
32C11×#124C2213yescomplemented
33C11×C22⋊Q8C2213yescomplemented
34C11×#121C2213yescomplemented
35C4×Q8×C11C2211yescharacteristic, complemented
36C4×D4×C11C2213yescomplemented
37#67000C2213yescomplemented
38#66999C2213yescomplemented
39Q8×Dic11C2211yescharacteristic, complemented
40#66993C2213yescomplemented
41#66992C2213yescomplemented
42#66991C2213yescomplemented
43#66990C2213yescomplemented
44#66983C2213yescomplemented
45#66983C2213yescomplemented
46C4×C22⋊D11C2213yescomplemented
47C4×C22⋊D11C2213yescomplemented
48#66949C2213yescomplemented
49#66948C2216yescomplemented
50#66948C2213yescomplemented
51#66948C2213yescomplemented
52#66947C2213yescomplemented
53#66946C2213yescomplemented
54C4⋊C4×D11C2213yescomplemented
55#66937C2213yescomplemented
56#66937C2216yescomplemented
57#66937C2216yescomplemented
58#66936C2213yescomplemented
59#66935C2213yescomplemented
60#66935C2216yescomplemented
61#66935C2216yescomplemented
62C22⋊C4×D11C2216yescomplemented
63#66931C2211yescharacteristic, complemented
64#66927C2213yescomplemented
65C4×D44C2213yescomplemented
66C4×D44C2213yescomplemented
67#66925C2213yescomplemented
68C23×D11C2313yes—
69C23×D11C2316yes—
70C11×#41—24no—
71C2×Q8×C11—24no—
72C2×Q8×C11C2313yes—
73C2×Q8×C11C2311yescharacteristic
74C2×D4×C11C2313yes—
75C2×D4×C11C2313yes—
76C22×C4×C11C2313yes—
77C22×C4×C11C2313yes—
78C2×C22⋊D11C2313yes—
79C2×C22⋊D11C2313yes—
80C2×C22⋊D11C2313yes—
81C2×C22⋊D11C2313yes—
82C2×C22⋊D11C2316yes—
83C22×Dic11C2311yescharacteristic
84#4343—212no—
85#4343—212no—
86#4343—24no—
87#4343—24no—
88#4343D418yescomplemented
89D4×D11—212no—
90D4×D11—212no—
91D4×D11—412no—
92#4339—212no—
93C2×D44—212no—
94C2×D44—212no—
95C2×D44C2313yes—
96C2×D44C2313yes—
97C2×D44C2316yes—
98C2×D44C2313yes—
99C2×D44C2313yes—
100C2×D44C2316yes—
101C2×D44C2313yes—
102C2×C4×D11—212no—
103C2×C4×D11C2313yes—
104C2×C4×D11C2313yes—
105C2×C4×D11C2313yes—
106C2×C4×D11C2313yes—
107C2×C4×D11C2316yes—
108C2×C4×D11C2313yes—
109C2×Dic22C2311yescharacteristic
110C11×C4⋊C4C2313yes—
111C11×C4⋊C4C2313yes—
112C11×C22⋊C4C2311yescharacteristic
113C11×C22⋊C4C2316yes—
114C11×C22⋊C4C2313yes—
115C42×C11C2313yes—
116C22⋊Dic11C2311yescharacteristic
117C22⋊Dic11C2313yes—
118(C2×D11)⋊C4C2313yes—
119(C2×D11)⋊C4C2313yes—
120(C2×D11)⋊C4C2313yes—
121(C2×D11)⋊C4C2313yes—
122(C2×D11)⋊C4C2316yes—
123(C2×D11)⋊C4C2313yes—
124(C2×D11)⋊C4C2313yes—
125C4⋊Dic11C2311yescharacteristic
126C4⋊Dic11C2313yes—
127Dic11⋊C4C2311yescharacteristic
128Dic11⋊C4C2313yes—
129Dic11⋊C4C2311yescharacteristic
130Dic11⋊C4C2313yes—
131C4×Dic11C2313yes—
132#3488—111nomaximal, Sylow
133C23×C11C2413yes—
134C23×C11C2411yescharacteristic
135C22×D11—26no—
136C22×D11—26no—
137C22×D11—212no—
138C22×D11—43no—
139C22×D11—46no—
140C22×D11—46no—
141C22×D11C2413yes—
142C22×D11C2413yes—
143C22×D11C2413yes—
144Q8×C11—26no—
145Q8×C11C2×D414yescomplemented
146D4×C11—26no—
147D4×C11—26no—
148C2×C4×C11—26no—
149C2×C4×C11—26no—
150C2×C4×C11C2411yescharacteristic
151C2×C4×C11C2413yes—
152C2×C4×C11C2413yes—
153C2×C4×C11C2411yescharacteristic
154C2×C4×C11C2413yes—
155C22⋊D11—26no—
156C22⋊D11—26no—
157C22⋊D11—26no—
158C22⋊D11—46no—
159C22⋊D11—43no—
160C2×Dic11—22no—
161C2×Dic11C2411yescharacteristic
162C2×Dic11C2413yes—
163C2×Dic11C2411yescharacteristic
164C2×Dic11C2411yescharacteristic
165C2×Dic11C2411yescharacteristic
166D44—26no—
167D44—212no—
168D44—26no—
169D44—26no—
170D44—43no—
171D44—46no—
172D44C2×D4112yescomplemented
173C4×D11—26no—
174C4×D11—26no—
175C4×D11—26no—
176C4×D11—26no—
177C4×D11—46no—
178C4×D11C2×D4112yescomplemented
179Dic22—22no—
180C2×H(5,𝔽2)—111no—
181C22×#41—111no—
182#550—111no—
183#550—111no—
184#548—111no—
185#548D1111yescharacteristic, complemented
186#546—113no—
187#546—113no—
188D42—113no—
189D42—113no—
190#537—113no—
191#535—113no—
192#525—113no—
193C2×#121—113no—
194#520—111no—
195C22×C11—21no—
196C22×C11—21no—
197C22×C11—23no—
198C22×C11—23no—
199C22×C11—23no—
200C22×C11H(5,𝔽2)12yescomplemented
201C22×C11C2511yescharacteristic
202C2×D11—23no—
203C2×D11—23no—
204C2×D11—23no—
205C2×D11—23no—
206C2×D11—23no—
207C2×D11—23no—
208C2×D11—23no—
209C2×D11—23no—
210C2×D11—412no—
211C2×D11—812no—
212C2×D11C22×D416yes—
213C4×C11—21no—
214C4×C11—23no—
215C4×C11—23no—
216C4×C11—21no—
217C4×C11C22×D416yes—
218Dic11—21no—
219Dic11—21no—
220Dic11—23no—
221Dic11—21no—
222Dic11C22×D412yes—
223H(5,𝔽2)—228no—
224C2×#41—111no—
225C2×#41—113no—
226C2×#41—113no—
227C2×#41—111no—
228C2×#41—111no—
229C2×#41—113no—
230C2×#41—228no—
231C2×#41C2×D1111yescharacteristic, complemented
232C22×Q8C2×D1111yescharacteristic, complemented
233C22×D4—113no—
234C22×D4—113no—
235C22×D4—116no—
236C22×D4—113no—
237C22×D4—113no—
238C23×C4—113no—
239#127—113no—
240#127—113no—
241#124—113no—
242#124C2×D1113yescomplemented
243#123—113no—
244#123—113no—
245C22⋊Q8—113no—
246C22⋊Q8—113no—
247C22⋊Q8—111no—
248C22⋊Q8C2×D1113yescomplemented
249#121—113no—
250#121—113no—
251#121—113no—
252#121—113no—
253#121—113no—
254#121—116no—
255#121—113no—
256#121—116no—
257#121—113no—
258#121—116no—
259#121C2×D1113yescomplemented
260#120—113no—
261#120—113no—
262#120—116no—
263#120—116no—
264C4×Q8—111no—
265C4×Q8C2×D1111yescharacteristic, complemented
266C4×D4—113no—
267C4×D4—113no—
268C4×D4—113no—
269C4×D4—113no—
270C4×D4—113no—
271C4×D4C2×D1113yescomplemented
272#117—113no—
273C2×C4⋊C4—113no—
274C2×C22⋊C4—116no—
275C2×C11—22no—
276C2×C11—43no—
277C2×C11C23×D411yescharacteristic
278C2×C11C2×H(5,𝔽2)11yescharacteristic
279C2×C11#58511yescharacteristic
280D11—26no—
281D11—43no—
282D11—43no—
283C24—113no—
284C24—116no—
285#41—24no—
286#41—118no—
287#41—2212no—
288#41—2212no—
289#41—2212no—
290#41—224no—
291#41—224no—
292C2×Q8—24no—
293C2×Q8—111no—
294C2×Q8C22×D1113yes—
295C2×Q8C22×D1111yescharacteristic
296C2×D4—113no—
297C2×D4—113no—
298C2×D4—113no—
299C2×D4—113no—
300C2×D4—116no—
301C2×D4—113no—
302C2×D4—116no—
303C2×D4—113no—
304C2×D4—113no—
305C2×D4—113no—
306C2×D4—113no—
307C2×D4—116no—
308C2×D4—2212no—
309C2×D4—2212no—
310C2×D4—2212no—
311C2×D4—2212no—
312C2×D4—4412no—
313C2×D4C22×D1113yes—
314C2×D4C22×D1113yes—
315C22×C4—113no—
316C22×C4—111no—
317C22×C4—113no—
318C22×C4—113no—
319C22×C4—113no—
320C22×C4—113no—
321C22×C4—116no—
322C22×C4—2212no—
323C22×C4C22×D1113yes—
324C22×C4C22×D1113yes—
325C4⋊C4—113no—
326C4⋊C4—113no—
327C4⋊C4—111no—
328C4⋊C4—111no—
329C4⋊C4—111no—
330C4⋊C4—113no—
331C4⋊C4C22×D1113yes—
332C4⋊C4C22×D1113yes—
333C22⋊C4—113no—
334C22⋊C4—111no—
335C22⋊C4—113no—
336C22⋊C4—116no—
337C22⋊C4—113no—
338C22⋊C4—113no—
339C22⋊C4—113no—
340C22⋊C4—113no—
341C22⋊C4—113no—
342C22⋊C4C22×D1116yes—
343C22⋊C4C22×D1111yescharacteristic
344C22⋊C4C22×D1113yes—
345C42—113no—
346C42C22×D1113yes—
347C11#348811yescharacteristic, complemented, Sylow
348C23—113no—
349C23—113no—
350C23—113no—
351C23—226no—
352C23—2212no—
353C23—226no—
354C23—443no—
355C23—446no—
356C23—446no—
357C23C23×D1113yes—
358C23C23×D1111yescharacteristic
359Q8—26no—
360Q8—222no—
361Q8D4×D1114yescomplemented
362D4—26no—
363D4—26no—
364D4—1112no—
365D4—226no—
366D4—2212no—
367D4—226no—
368D4—226no—
369D4—226no—
370D4—226no—
371D4—226no—
372D4—446no—
373D4—443no—
374D4—446no—
375D4—443no—
376C2×C4—26no—
377C2×C4—26no—
378C2×C4—111no—
379C2×C4—1112no—
380C2×C4—111no—
381C2×C4—113no—
382C2×C4—111no—
383C2×C4—111no—
384C2×C4—226no—
385C2×C4—226no—
386C2×C4—222no—
387C2×C4—226no—
388C2×C4—226no—
389C2×C4—446no—
390C2×C4C23×D1111yescharacteristic
391C2×C4C23×D1113yes—
392C2×C4C23×D1113yes—
393C2×C4C23×D1111yescharacteristic
394C2×C4C23×D1113yes—
395C22—21no—
396C22—21no—
397C22—23no—
398C22—23no—
399C22—23no—
400C22—116no—
401C22—223no—
402C22—223no—
403C22—223no—
404C22—223no—
405C22—223no—
406C22—223no—
407C22—223no—
408C22—223no—
409C22—4412no—
410C22—8812no—
411C22#6704212yescomplemented
412C22C24×D1111yescharacteristic
413C4—21no—
414C4—23no—
415C4—23no—
416C4—21no—
417C4—112no—
418C4—221no—
419C4—221no—
420C4—223no—
421C4—221no—
422C4C2×D4×D1116yes—
423C2—22no—
424C2—43no—
425C2—226no—
426C2—443no—
427C2—443no—
428C2C22×D4×D1111yescharacteristic
429C2C2×#6704211yescharacteristic
430C2#1062345711yescharacteristic
subgroupG/H
center, FrattiniC22C24×D11
commutator, socle, cosocleC22×C11C25
FittingC11×#548C2
hypercenter#548D11
hypocenterC11#3488
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. C22×#4343C2semidirect
3. C11×#548C2semidirect
4. #10623365C2semidirect
5. #10623348C2semidirect
6. #10623207C2semidirect
7. #10623205C2semidirect
8. #10623161C2semidirect
9. #10623160C2semidirect
10. #10623140C2semidirect
11. D11×#121C2semidirect
12. #10623108C2semidirect
13. #10623105C2semidirect
14. D4×D44C2semidirect
15. #10623078C2semidirect
16. C2×C11×#41C22semidirect
17. C22×Q8×C11C22semidirect
21. C2×#4343C22semidirect
22. C2×#4343C22semidirect
23. C2×#4343C22semidirect
24. C2×#4343C22semidirect
25. C2×D4×D11C22semidirect
26. C2×D4×D11C22semidirect
27. C2×D4×D11C22semidirect
28. C2×#4339C22semidirect
29. C22×D44C22semidirect
30. C22×D44C22semidirect
31. C22×C4×D11C22semidirect
32. C11×#124C22semidirect
33. C11×C22⋊Q8C22semidirect
34. C11×#121C22semidirect
35. C4×Q8×C11C22semidirect
36. C4×D4×C11C22semidirect
37. #67000C22semidirect
38. #66999C22semidirect
39. Q8×Dic11C22semidirect
40. #66993C22semidirect
41. #66992C22semidirect
42. #66991C22semidirect
43. #66990C22semidirect
44. #66983C22semidirect
45. #66983C22semidirect
46. C4×C22⋊D11C22semidirect
47. C4×C22⋊D11C22semidirect
48. #66949C22semidirect
49. #66948C22semidirect
50. #66948C22semidirect
51. #66948C22semidirect
52. #66947C22semidirect
53. #66946C22semidirect
54. C4⋊C4×D11C22semidirect
55. #66937C22semidirect
56. #66937C22semidirect
57. #66937C22semidirect
58. #66936C22semidirect
59. #66935C22semidirect
60. #66935C22semidirect
61. #66935C22semidirect
62. C22⋊C4×D11C22semidirect
63. #66931C22semidirect
64. #66927C22semidirect
65. C4×D44C22semidirect
66. C4×D44C22semidirect
67. #66925C22semidirect
88. #4343D4semidirect
145. Q8×C11C2×D4semidirect
172. D44C2×D4semidirect
178. C4×D11C2×D4semidirect
185. #548D11semidirect
200. C22×C11H(5,𝔽2)semidirect
231. C2×#41C2×D11semidirect
232. C22×Q8C2×D11semidirect
242. #124C2×D11semidirect
248. C22⋊Q8C2×D11semidirect
259. #121C2×D11semidirect
265. C4×Q8C2×D11semidirect
271. C4×D4C2×D11semidirect
347. C11#3488semidirect
361. Q8D4×D11semidirect
411. C22#67042semidirect

Maximal subgroups

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

subgroupindex
C2×#670422
C22×#43432
C11×#5482
#106233652
#106233482
#106232072
#106232052
#106231612
#106231602
#106231402
D11×#1212
#106231082
#106231052
D4×D442
#106230782
#348811