Finite Group Databasebeta

← #13080246

Subgroups — #13080246

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×#66971C211yesmaximal, characteristic, complemented
2C2×#66964C211yesmaximal, characteristic, complemented
3#10623208C211yesmaximal, characteristic, complemented
4#10623207C211yesmaximal, characteristic, complemented
5C11×#495C211yesmaximal, characteristic, complemented
6#10622802C211yesmaximal, characteristic, complemented
7#10622786C211yesmaximal, characteristic, complemented
8#10622785C211yesmaximal, characteristic, complemented
9#10622783C211yesmaximal, characteristic, complemented
10#10622782C211yesmaximal, characteristic, complemented
11#10622772C211yesmaximal, characteristic, complemented
12#10622670C211yesmaximal, characteristic, complemented
13#10622667C211yesmaximal, characteristic, complemented
14C4×#4314C211yesmaximal, characteristic, complemented
15#10622301C211yesmaximal, characteristic, complemented
16C2×#4343C2211yescharacteristic
17C2×Q8×D11C2211yescharacteristic, complemented
18C2×#4341C2211yescharacteristic
19C2×D4×D11C2211yescharacteristic
20C2×C11×Q16C2211yescharacteristic, complemented
21C2×C11×SD16C2211yescharacteristic
22C2×C11×SD16C2211yescharacteristic, complemented
23C2×C11×D8C2211yescharacteristic
24C11×#124C2211yescharacteristic
25C11×#124C2211yescharacteristic, complemented
26#66999C2211yescharacteristic
27#66999C2211yescharacteristic
28C2×#4326C2211yescharacteristic, complemented
29C2×#4325C2211yescharacteristic
30#66991C2211yescharacteristic
31#66991C2211yescharacteristic, complemented
32C2×#4324C2211yescharacteristic
33C2×#4323C2211yescharacteristic
34#66971—24no—
35#66964—24no—
36C2×#4314C2211yescharacteristic
37C2×#4313C2211yescharacteristic
38C2×#4313C2211yescharacteristic, complemented
39#66938—21no—
40#66937—21no—
41#66937—21no—
42#66936—21no—
43#66935—21no—
44(C22⋊D11)⋊C4—21no—
45C22⋊C4×D11—21no—
46#66931—21no—
47C4×D44C2211yescharacteristic
48C4×D44C2211yescharacteristic
49C4×Dic22C2211yescharacteristic, complemented
50C4×C8×C11C2211yescharacteristic, complemented
51#66899C2211yescharacteristic, complemented
52#66899C2211yescharacteristic, complemented
53#66896C2211yescharacteristic
54#66896C2211yescharacteristic, complemented
55#66885C2211yescharacteristic
56(C2×D11)⋊C8C2211yescharacteristic
57(C2×D11)⋊C8C2211yescharacteristic, complemented
58#66881C2211yescharacteristic, complemented
59#66880C2211yescharacteristic, complemented
60C4⋊(C11⋊C8)C2211yescharacteristic, complemented
61C23×D11—21no—
62C2×Q8×C11C2311yescharacteristic
63C2×Q8×C11C2311yescharacteristic
64C2×D4×C11C2311yescharacteristic
65C2×D4×C11C2311yescharacteristic
66C2×C22⋊D11—21no—
67C2×C22⋊D11—21no—
68C2×C22⋊D11—21no—
69C2×C22⋊D11—21no—
70C22×Dic11—21no—
71#4343—22no—
72#4343—41no—
73Q8×D11—22no—
74Q8×D11—41no—
75#4341—22no—
76#4341—41no—
77D4×D11—22no—
78D4×D11—41no—
79C2×D44—21no—
80C2×D44D411yescharacteristic
81C2×D44C2311yescharacteristic
82C2×C4×D11—21no—
83C2×C4×D11—21no—
84C2×C4×D11—21no—
85C2×C4×D11C2311yescharacteristic
86C2×C4×D11C2311yescharacteristic
87C2×Dic22—21no—
88C2×Dic22C2311yescharacteristic
89C11×Q16—22no—
90C11×SD16—41no—
91C11×SD16—41no—
92C11×D8—22no—
93C2×C8×C11C2311yescharacteristic
94C2×C8×C11C2311yescharacteristic
95C11×C22⋊C4—21no—
96C11×C22⋊C4—21no—
97C11×C22⋊C4—21no—
98C11×C22⋊C4—21no—
99C42×C11C2311yescharacteristic
100C22⋊Dic11—21no—
101C22⋊Dic11—21no—
102#4326—22no—
103#4325—22no—
104#4324—22no—
105#4323—22no—
106(C2×D11)⋊C4—21no—
107(C2×D11)⋊C4—21no—
108(C2×D11)⋊C4—21no—
109(C2×D11)⋊C4D411yescharacteristic
110(C2×D11)⋊C4D411yescharacteristic
111C4⋊Dic11D411yescharacteristic
112C4⋊Dic11C2311yescharacteristic
113C4⋊Dic11C2311yescharacteristic
114Dic11⋊C4—21no—
115Dic11⋊C4—21no—
116Dic11⋊C4—21no—
117C4×Dic11—21no—
118C2×C11⋊C8C2311yescharacteristic
119C2×C11⋊C8C2311yescharacteristic
120#4314D414yescomplemented
121#4313—22no—
122#4313—22no—
123#3275—111nomaximal, Sylow
124C23×C11—21no—
125C23×C11—21no—
126C22×D11—21no—
127C22×D11—42no—
128C22×D11—42no—
129C22×D11—81no—
130C22×D11C2×D411yescharacteristic
131C22×D11C2×D411yescharacteristic
132Q8×C11—21no—
133Q8×C11—21no—
134Q8×C11—21no—
135Q8×C11—21no—
136D4×C11—21no—
137D4×C11—21no—
138D4×C11—21no—
139D4×C11—21no—
140C2×C4×C11—21no—
141C2×C4×C11—21no—
142C2×C4×C11C2×D411yescharacteristic
143C2×C4×C11C2×D411yescharacteristic
144C2×C4×C11C2411yescharacteristic
145C22⋊D11—42no—
146C22⋊D11—42no—
147C22⋊D11—42no—
148C22⋊D11—81no—
149C2×Dic11—21no—
150C2×Dic11—21no—
151C2×Dic11—21no—
152C2×Dic11—42no—
153C2×Dic11C2×D411yescharacteristic
154C2×Dic11C2×D411yescharacteristic
155D44—21no—
156D44—41no—
157D44—42no—
158D44C2×D412yes—
159C4×D11—21no—
160C4×D11—21no—
161C4×D11—21no—
162C4×D11—21no—
163C4×D11—42no—
164C4×D11—42no—
165C4×D11—81no—
166Dic22—21no—
167Dic22—42no—
168Dic22C2×D412yes—
169C8×C11—21no—
170C8×C11C2×D412yes—
171C11⋊C8—21no—
172C11⋊C8—21no—
173C2×#137—111no—
174C2×AGL(1,ℤ/8)—111no—
175#548—111no—
176#546—111no—
177#495D1111yescharacteristic, complemented
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—41no—
189C22×C11—41no—
190C22×C11—41no—
191C22×C11—41no—
192C22×C11—41no—
193C22×C11—41no—
194C22×C11C22×D411yescharacteristic
195C2×D11—22no—
196C2×D11—21no—
197C2×D11—21no—
198C2×D11—21no—
199C2×D11—21no—
200C2×D11—21no—
201C2×D11—21no—
202C2×D11—41no—
203C2×D11—41no—
204C2×D11—84no—
205C4×C11—21no—
206C4×C11—21no—
207C4×C11—41no—
208C4×C11—41no—
209C4×C11C22×D411yescharacteristic
210C4×C11H(5,𝔽2)11yescharacteristic
211Dic11—22no—
212Dic11—21no—
213Dic11—21no—
214Dic11—41no—
215Dic11—41no—
216C2×#41—111no—
217C2×#41—111no—
218C22×Q8—111no—
219C22×D4—111no—
220#137—224no—
221AGL(1,ℤ/8)—224no—
222C2×Q16—111no—
223C2×Q16C2×D1111yescharacteristic, complemented
224C2×SD16—111no—
225C2×SD16—111no—
226C2×SD16—111no—
227C2×SD16C2×D1111yescharacteristic
228C2×SD16C2×D1111yescharacteristic, complemented
229C2×D8—111no—
230C2×D8C2×D1111yescharacteristic
231C2×M16—111no—
232C2×M16—111no—
233#124—221no—
234#124C2×D1111yescharacteristic
235#124C2×D1111yescharacteristic, complemented
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×C8C2×D1111yescharacteristic, complemented
261C2×C11—81no—
262C2×C11—81no—
263C2×C11D4211yescharacteristic
264C2×C11#57511yescharacteristic
265C2×C11#57711yescharacteristic
266D11—41no—
267D11—41no—
268D11—42no—
269C24—221no—
270#41—222no—
271#41—222no—
272#41—441no—
273#41—441no—
274C2×Q8—111no—
275C2×Q8—221no—
276C2×Q8—222no—
277C2×Q8—441no—
278C2×Q8C22×D1111yescharacteristic
279C2×Q8C22×D1111yescharacteristic
280C2×D4—111no—
281C2×D4—111no—
282C2×D4—221no—
283C2×D4—221no—
284C2×D4—222no—
285C2×D4—221no—
286C2×D4—221no—
287C2×D4—221no—
288C2×D4—441no—
289C2×D4C22×D1111yescharacteristic
290C2×D4C22×D1111yescharacteristic
291C22×C4—111no—
292C22×C4—111no—
293C22×C4—221no—
294C22×C4—221no—
295C22×C4—221no—
296C22×C4—221no—
297Q16—22no—
298Q16—222no—
299SD16—41no—
300SD16—41no—
301SD16—114no—
302SD16—222no—
303SD16—222no—
304D8—22no—
305D8—222no—
306M16—222no—
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—21no—
319C22⋊C4—21no—
320C22⋊C4—21no—
321C22⋊C4—21no—
322C22⋊C4—111no—
323C22⋊C4—111no—
324C22⋊C4—221no—
325C22⋊C4—221no—
326C22⋊C4—221no—
327C22⋊C4—221no—
328C22⋊C4—221no—
329C42—221no—
330C42C22×D1111yescharacteristic
331C11#327511yescharacteristic, complemented, Sylow
332C23—21no—
333C23—21no—
334C23—111no—
335C23—111no—
336C23—221no—
337C23—442no—
338C23—442no—
339C23—881no—
340Q8—21no—
341Q8—21no—
342Q8—21no—
343Q8—21no—
344Q8—112no—
345Q8—221no—
346Q8—442no—
347D4—21no—
348D4—21no—
349D4—21no—
350D4—21no—
351D4—112no—
352D4—221no—
353D4—441no—
354D4—442no—
355D4—442no—
356D4—442no—
357D4—442no—
358D4—881no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—111no—
362C2×C4—111no—
363C2×C4—221no—
364C2×C4—221no—
365C2×C4—221no—
366C2×C4—221no—
367C2×C4—221no—
368C2×C4—221no—
369C2×C4—221no—
370C2×C4—442no—
371C2×C4—442no—
372C2×C4—442no—
373C2×C4—881no—
374C2×C4D4×D1111yescharacteristic
375C2×C4D4×D1111yescharacteristic
376C2×C4C23×D1111yescharacteristic
377C8—21no—
378C8—221no—
379C8—221no—
380C8D4×D1112yes—
381C22—41no—
382C22—41no—
383C22—41no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—221no—
388C22—221no—
389C22—222no—
390C22—221no—
391C22—221no—
392C22—221no—
393C22—221no—
394C22—441no—
395C22—441no—
396C22—884no—
397C22C2×D4×D1111yescharacteristic
398C4—21no—
399C4—21no—
400C4—41no—
401C4—41no—
402C4—221no—
403C4—221no—
404C4—222no—
405C4—441no—
406C4—441no—
407C4C2×D4×D1111yescharacteristic
408C4#6703711yescharacteristic
409C2—81no—
410C2—81no—
411C2—441no—
412C2—441no—
413C2—442no—
414C2#1062324811yescharacteristic
415C2#1062329911yescharacteristic
416C2#1062330111yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#495C2
socleC22×C11C22×D4
hypercenter#495D11
hypocenterC11#3275
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #495

Complements

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

NH ≅ G/Ntype
1. C2×#66971C2semidirect
2. C2×#66964C2semidirect
3. #10623208C2semidirect
4. #10623207C2semidirect
5. C11×#495C2semidirect
6. #10622802C2semidirect
7. #10622786C2semidirect
8. #10622785C2semidirect
9. #10622783C2semidirect
10. #10622782C2semidirect
11. #10622772C2semidirect
12. #10622670C2semidirect
13. #10622667C2semidirect
14. C4×#4314C2semidirect
15. #10622301C2semidirect
17. C2×Q8×D11C22semidirect
20. C2×C11×Q16C22semidirect
22. C2×C11×SD16C22semidirect
25. C11×#124C22semidirect
28. C2×#4326C22semidirect
31. #66991C22semidirect
38. C2×#4313C22semidirect
49. C4×Dic22C22semidirect
50. C4×C8×C11C22semidirect
51. #66899C22semidirect
52. #66899C22semidirect
54. #66896C22semidirect
57. (C2×D11)⋊C8C22semidirect
58. #66881C22semidirect
59. #66880C22semidirect
60. C4⋊(C11⋊C8)C22semidirect
120. #4314D4semidirect
177. #495D11semidirect
223. C2×Q16C2×D11semidirect
228. C2×SD16C2×D11semidirect
235. #124C2×D11semidirect
260. C4×C8C2×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×#669712
C2×#669642
#106232082
#106232072
C11×#4952
#106228022
#106227862
#106227852
#106227832
#106227822
#106227722
#106226702
#106226672
C4×#43142
#106223012
#327511