Finite Group Databasebeta

← #13082295

Subgroups — #13082295

Order 1408.

1522 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#41×D11C211yesmaximal, characteristic, complemented
2C2×#67040C211yesmaximal, characteristic, complemented
3C11×#548C211yesmaximal, characteristic, complemented
4#10623362C211yesmaximal, characteristic, complemented
5Q8×C22⋊D11C211yesmaximal, characteristic, complemented
6#10623207C213yesmaximal, complemented
7#10623206C213yesmaximal, complemented
8#10623162C213yesmaximal, complemented
9D11×C22⋊Q8C213yesmaximal, complemented
10#10623143C213yesmaximal, complemented
11#10623139C213yesmaximal, complemented
12Q8×D44C211yesmaximal, characteristic, complemented
13#10623105C211yesmaximal, characteristic, complemented
14#10623082C213yesmaximal, complemented
15#10623078C213yesmaximal, complemented
16C2×C11×#41C2211yescharacteristic
17C22×Q8×C11C2211yescharacteristic, complemented
18#41×D11—28no—
19#67040—28no—
20C2×#4343C2211yescharacteristic
21C2×#4343C2213yescomplemented
22C2×Q8×D11C2211yescharacteristic
23C2×Q8×D11C2211yescharacteristic, complemented
24C2×Q8×D11C2213yescomplemented
25C2×#4341C2213yes—
26C2×D4×D11C2213yes—
27C2×#4339C2213yes—
28C2×#4339C2213yescomplemented
29C2×#4339C2213yescomplemented
30C22×C4×D11C2213yes—
31C11×#124C2213yescomplemented
32C11×C22⋊Q8C2213yescomplemented
33C11×#121C2213yescomplemented
34C4×Q8×C11C2211yescharacteristic, complemented
35C4×D4×C11C2213yescomplemented
36#66999C2213yes—
37Q8×Dic11C2211yescharacteristic, complemented
38#66997C2213yescomplemented
39#66992C2213yescomplemented
40#66991C2216yescomplemented
41#66991C2213yescomplemented
42#66990C2213yes—
43#66989C2213yescomplemented
44C4×C22⋊D11C2213yes—
45C4×C22⋊D11C2213yescomplemented
46#66977C2213yescomplemented
47#66977C2213yescomplemented
48#66950C2213yes—
49#66950C2213yescomplemented
50#66949C2213yes—
51#66947C2213yescomplemented
52#66946C2213yescomplemented
53C4⋊C4×D11C2216yescomplemented
54C4⋊C4×D11C2213yescomplemented
55#66937C2211yescharacteristic
56#66937C2216yescomplemented
57#66936C2213yescomplemented
58#66936C2216yescomplemented
59#66936C2216yescomplemented
60#66935C2213yes—
61C22⋊C4×D11C2216yes—
62#66931C2213yescomplemented
63#66931C2216yescomplemented
64C4×D44C2213yes—
65C4×D44C2213yescomplemented
66#66925C2213yescomplemented
67#66922C2213yescomplemented
68C23×D11C2313yes—
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⋊D11C2316yes—
78C2×C22⋊D11C2313yes—
79C2×C22⋊D11C2311yescharacteristic
80C2×C22⋊D11C2311yescharacteristic
81C2×C22⋊D11C2313yes—
82C22×Dic11C2313yes—
83#4343—212no—
84#4343D418yescomplemented
85Q8×D11—212no—
86Q8×D11—24no—
87Q8×D11—24no—
88#4341—212no—
89D4×D11—212no—
90#4339—212no—
91#4339—212no—
92#4339—212no—
93C2×D44C2311yescharacteristic
94C2×D44C2313yes—
95C2×D44C2313yes—
96C2×C4×D11—212no—
97C2×C4×D11C2313yes—
98C2×C4×D11C2313yes—
99C2×C4×D11C2316yes—
100C2×C4×D11C2313yes—
101C2×C4×D11C2311yescharacteristic
102C2×C4×D11C2316yes—
103C2×C4×D11C2313yes—
104C2×Dic22C2313yes—
105C2×Dic22C2313yes—
106C2×Dic22C2313yes—
107C11×C4⋊C4C2313yes—
108C11×C4⋊C4C2313yes—
109C11×C22⋊C4C2316yes—
110C11×C22⋊C4C2313yes—
111C11×C22⋊C4C2311yescharacteristic
112C42×C11C2313yes—
113C22⋊Dic11C2316yes—
114C22⋊Dic11C2313yes—
115C22⋊Dic11C2313yes—
116(C2×D11)⋊C4C2313yes—
117(C2×D11)⋊C4C2313yes—
118(C2×D11)⋊C4C2313yes—
119(C2×D11)⋊C4C2313yes—
120(C2×D11)⋊C4C2313yes—
121(C2×D11)⋊C4C2311yescharacteristic
122C4⋊Dic11C2313yes—
123C4⋊Dic11C2316yes—
124C4⋊Dic11C2313yes—
125Dic11⋊C4C2311yescharacteristic
126Dic11⋊C4C2313yes—
127Dic11⋊C4C2313yes—
128Dic11⋊C4C2316yes—
129Dic11⋊C4C2313yes—
130C4×Dic11C2313yes—
131#3489—111nomaximal, Sylow
132C23×C11C2413yes—
133C23×C11C2411yescharacteristic
134C22×D11—26no—
135C22×D11—26no—
136C22×D11—43no—
137C22×D11C2411yescharacteristic
138C22×D11C2413yes—
139C22×D11C2411yescharacteristic
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—212no—
153C22⋊D11—22no—
154C22⋊D11—22no—
155C22⋊D11—43no—
156C2×Dic11—26no—
157C2×Dic11C2411yescharacteristic
158C2×Dic11C2413yes—
159C2×Dic11C2413yes—
160C2×Dic11C2413yes—
161C2×Dic11C2411yescharacteristic
162D44—26no—
163D44—22no—
164D44C2×D4112yes—
165C4×D11—26no—
166C4×D11—212no—
167C4×D11—26no—
168C4×D11—26no—
169C4×D11—22no—
170C4×D11—46no—
171C4×D11C2×D4112yes—
172Dic22—26no—
173Dic22—26no—
174Dic22—26no—
175C2×2−1+4—111no—
176C22×#41—111no—
177D4×Q8—111no—
178D4×Q8—111no—
179#548—111no—
180#548D1111yescharacteristic, complemented
181#547—113no—
182#547—113no—
183#546—113no—
184#546—113no—
185#537—113no—
186#536—113no—
187#525—113no—
188C2×C22⋊Q8—113no—
189#520—111no—
190C22×C11—21no—
191C22×C11—23no—
192C22×C11—23no—
193C22×C11—21no—
194C22×C11—21no—
195C22×C11—23no—
196C22×C11C2511yescharacteristic
197C2×D11—21no—
198C2×D11—23no—
199C2×D11—21no—
200C2×D11—23no—
201C2×D11—21no—
202C2×D11—21no—
203C2×D11—21no—
204C2×D11—412no—
205C2×D11C22×D416yes—
206C2×D112−1+412yescomplemented
207C4×C11—21no—
208C4×C11—23no—
209C4×C11—21no—
210C4×C11—23no—
211C4×C11C22×D416yes—
212Dic11—23no—
213Dic11—23no—
214Dic11—21no—
215Dic11—23no—
216Dic11C22×D412yes—
2172−1+4—228no—
218C2×#41—111no—
219C2×#41—113no—
220C2×#41—113no—
221C2×#41—113no—
222C2×#41—113no—
223C2×#41—113no—
224C2×#41—228no—
225C2×#41C2×D1111yescharacteristic
226C22×Q8—113no—
227C22×Q8—111no—
228C22×Q8—111no—
229C22×Q8C2×D1111yescharacteristic, complemented
230C22×D4—113no—
231C23×C4—113no—
232C4⋊Q8—113no—
233C4⋊Q8—113no—
234#124—113no—
235#124C2×D1113yescomplemented
236#123—113no—
237#123—113no—
238#123—116no—
239#123—116no—
240C22⋊Q8—113no—
241C22⋊Q8—113no—
242C22⋊Q8—113no—
243C22⋊Q8—113no—
244C22⋊Q8—113no—
245C22⋊Q8—113no—
246C22⋊Q8—116no—
247C22⋊Q8—113no—
248C22⋊Q8C2×D1113yescomplemented
249#121—113no—
250#121—116no—
251#121—113no—
252#121—111no—
253#121—116no—
254#121C2×D1113yescomplemented
255#120—113no—
256#120—113no—
257C4×Q8—111no—
258C4×Q8C2×D1111yescharacteristic, complemented
259C4×D4—113no—
260C4×D4—113no—
261C4×D4—113no—
262C4×D4—113no—
263C4×D4—113no—
264C4×D4C2×D1113yescomplemented
265#117—113no—
266C2×C4⋊C4—113no—
267C2×C4⋊C4—116no—
268C2×C22⋊C4—116no—
269C2×C11—43no—
270C2×C11—41no—
271C2×C11C23×D411yescharacteristic
272C2×C11C2×2−1+411yescharacteristic
273C2×C11#58511yescharacteristic
274D11—22no—
275D11—26no—
276D11—41no—
277C24—113no—
278#41—24no—
279#41—118no—
280#41—2212no—
281#41—2212no—
282#41—2212no—
283#41—2212no—
284#41—2212no—
285C2×Q8—24no—
286C2×Q8—113no—
287C2×Q8—113no—
288C2×Q8—113no—
289C2×Q8—2212no—
290C2×Q8—224no—
291C2×Q8—224no—
292C2×Q8C22×D1113yes—
293C2×Q8C22×D1111yescharacteristic
294C2×D4—111no—
295C2×D4—113no—
296C2×D4—111no—
297C2×D4—116no—
298C2×D4—113no—
299C2×D4—113no—
300C2×D4—111no—
301C2×D4—113no—
302C2×D4—2212no—
303C2×D4C22×D1113yes—
304C2×D4C22×D1113yes—
305C22×C4—113no—
306C22×C4—113no—
307C22×C4—116no—
308C22×C4—113no—
309C22×C4—113no—
310C22×C4—113no—
311C22×C4—111no—
312C22×C4—116no—
313C22×C4—2212no—
314C22×C4C22×D1113yes—
315C22×C4C22×D1113yes—
316C4⋊C4—113no—
317C4⋊C4—113no—
318C4⋊C4—113no—
319C4⋊C4—116no—
320C4⋊C4—116no—
321C4⋊C4—111no—
322C4⋊C4—113no—
323C4⋊C4—113no—
324C4⋊C4C22×D1113yes—
325C4⋊C4C22×D1113yes—
326C22⋊C4—116no—
327C22⋊C4—113no—
328C22⋊C4—113no—
329C22⋊C4—113no—
330C22⋊C4—113no—
331C22⋊C4—113no—
332C22⋊C4—113no—
333C22⋊C4—111no—
334C22⋊C4—113no—
335C22⋊C4C22×D1116yes—
336C22⋊C4C22×D1111yescharacteristic
337C22⋊C4C22×D1113yes—
338C42—113no—
339C42C22×D1113yes—
340C11#348911yescharacteristic, complemented, Sylow
341C23—111no—
342C23—113no—
343C23—111no—
344C23—226no—
345C23—226no—
346C23—443no—
347C23C23×D1113yes—
348C23C23×D1111yescharacteristic
349Q8—26no—
350Q8—226no—
351Q8—226no—
352Q8—226no—
353Q8D4×D1114yes—
354D4—26no—
355D4—43no—
356D4—1112no—
357D4—226no—
358D4—222no—
359D4—222no—
360D4—2212no—
361D4—226no—
362D4—222no—
363D4—443no—
364C2×C4—26no—
365C2×C4—26no—
366C2×C4—111no—
367C2×C4—1112no—
368C2×C4—111no—
369C2×C4—113no—
370C2×C4—113no—
371C2×C4—113no—
372C2×C4—222no—
373C2×C4—226no—
374C2×C4—2212no—
375C2×C4—226no—
376C2×C4—226no—
377C2×C4—226no—
378C2×C4—446no—
379C2×C4C23×D1111yescharacteristic
380C2×C4C23×D1113yes—
381C2×C4C23×D1113yes—
382C2×C4C23×D1111yescharacteristic
383C2×C4C23×D1113yes—
384C22—21no—
385C22—23no—
386C22—21no—
387C22—23no—
388C22—21no—
389C22—23no—
390C22—116no—
391C22—112no—
392C22—221no—
393C22—223no—
394C22—221no—
395C22—223no—
396C22—221no—
397C22—221no—
398C22—221no—
399C22—4412no—
400C22C24×D1111yescharacteristic
401C4—21no—
402C4—23no—
403C4—23no—
404C4—21no—
405C4—112no—
406C4—223no—
407C4—223no—
408C4—223no—
409C4—221no—
410C4C2×D4×D1116yes—
411C2—43no—
412C2—41no—
413C2—222no—
414C2—226no—
415C2—441no—
416C2C22×D4×D1111yescharacteristic
417C2#1062345311yescharacteristic
418C2D11×2−1+411yescharacteristic
subgroupG/H
center, FrattiniC22C24×D11
commutator, socle, cosocleC22×C11C25
FittingC11×#548C2
hypercenter#548D11
hypocenterC11#3489
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ #548

Complements

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

NH ≅ G/Ntype
1. C2×#41×D11C2semidirect
2. C2×#67040C2semidirect
3. C11×#548C2semidirect
4. #10623362C2semidirect
5. Q8×C22⋊D11C2semidirect
6. #10623207C2semidirect
7. #10623206C2semidirect
8. #10623162C2semidirect
9. D11×C22⋊Q8C2semidirect
10. #10623143C2semidirect
11. #10623139C2semidirect
12. Q8×D44C2semidirect
13. #10623105C2semidirect
14. #10623082C2semidirect
15. #10623078C2semidirect
17. C22×Q8×C11C22semidirect
21. 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
37. Q8×Dic11C22semidirect
38. #66997C22semidirect
39. #66992C22semidirect
40. #66991C22semidirect
41. #66991C22semidirect
43. #66989C22semidirect
45. C4×C22⋊D11C22semidirect
46. #66977C22semidirect
47. #66977C22semidirect
49. #66950C22semidirect
51. #66947C22semidirect
52. #66946C22semidirect
53. C4⋊C4×D11C22semidirect
54. C4⋊C4×D11C22semidirect
56. #66937C22semidirect
57. #66936C22semidirect
58. #66936C22semidirect
59. #66936C22semidirect
62. #66931C22semidirect
63. #66931C22semidirect
65. C4×D44C22semidirect
66. #66925C22semidirect
67. #66922C22semidirect
84. #4343D4semidirect
180. #548D11semidirect
206. C2×D112−1+4semidirect
229. C22×Q8C2×D11semidirect
235. #124C2×D11semidirect
248. C22⋊Q8C2×D11semidirect
254. #121C2×D11semidirect
258. C4×Q8C2×D11semidirect
264. C4×D4C2×D11semidirect
340. C11#3489semidirect

Maximal subgroups

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

subgroupindex
C2×#41×D112
C2×#670402
C11×#5482
#106233622
Q8×C22⋊D112
#106232072
#106232062
#106231622
D11×C22⋊Q82
#106231432
#106231392
Q8×D442
#106231052
#106230822
#106230782
#348911