Finite Group Databasebeta

← #14807172

Subgroups — #14807172

Order 2816.

1448 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078992C211yesmaximal, characteristic, complemented
2#13078096C211yesmaximal, characteristic, complemented
3#13077010C211yesmaximal, characteristic, complemented
4#13069629C214yesmaximal, complemented
5#13069594C211yesmaximal, characteristic, complemented
6#13069457C211yesmaximal, characteristic, complemented
7#13069014C214yesmaximal, complemented
8C4×#66901C211yesmaximal, characteristic, complemented
9C11×#3508C211yesmaximal, characteristic, complemented
10C11×#559—22no—
11C11×#550—22no—
12C11×#546—24no—
13C11×#540—22no—
14C11×#535C2212yes—
15C11×#533C2211yescharacteristic
16C11×#532—22no—
17C2×C11×#127C2211yescharacteristic
18C11×#518C2212yes—
19C4×C11×#41C2211yescharacteristic
20C2×#67002C2212yes—
21C2×#66993—24no—
22C2×#66993C2214yes—
23C2×#66927C2211yescharacteristic
24C2×#66901C2212yes—
25C2×#66897C2214yes—
26#10622701—22no—
27#10622680—22no—
28#10622640—22no—
29#10622628—22no—
30#10622614C2214yes—
31#10622614C2212yes—
32C42×Dic11C2211yescharacteristic
33#10622537C2211yescharacteristic
34C4×#4318C2211yescharacteristic
35#10622170C2214yes—
36#10622170C2212yes—
37C2×C11×#41—24no—
38C2×C11×#41C2311yescharacteristic
39C22×D4×C11D414yes—
40C22×D4×C11C2312yes—
41C22×C22⋊D11—28no—
42C22×D44—22no—
43C22×D44C2312yes—
44C11×C4⋊Q8D412yescomplemented
45C11×#127—22no—
46C11×#127—21no—
47C11×#127—21no—
48C11×#127—22no—
49C11×#125D412yescomplemented
50C11×#124—24no—
51C11×#124—22no—
52C11×#123—28no—
53C11×C22⋊Q8—22no—
54C11×#121—24no—
55C11×#121—28no—
56C11×#121—24no—
57C11×#120—24no—
58C4×Q8×C11—22no—
59C4×Q8×C11D412yescomplemented
60C4×D4×C11—24no—
61C4×D4×C11—22no—
62C4×D4×C11—24no—
63C4×D4×C11—24no—
64C4×D4×C11D412yescomplemented
65C11×#117—21no—
66C11×#117C2311yescharacteristic
67C11×#117C2312yes—
68C2×C11×C22⋊C4—24no—
69C2×C42×C11—21no—
70C2×C42×C11C2311yescharacteristic
71#67002—44no—
72C2×#4325—22no—
73#66993—28no—
74#66993—44no—
75#66993—416no—
76C2×#4323—22no—
77C2×C4×Dic11—22no—
78C2×C4×Dic11C2312yes—
79C2×#4318C2312yes—
80C2×#4318C2312yes—
81#66927—22no—
82#66927—21no—
83#66927—21no—
84#66901—24no—
85#66897—44no—
86#66873—24no—
87#66873—28no—
88C4⋊(C11⋊C8)—22no—
89#66867—21no—
90C4×C11⋊C8—21no—
91#25588—111nomaximal, Sylow
92C24×C11C2×D414yes—
93C23×D11—22no—
94C11×#41—22no—
95C11×#41—22no—
96C11×#41—88no—
97C2×Q8×C11—22no—
98C2×Q8×C11C2×D411yescharacteristic
99C2×D4×C11—21no—
100C2×D4×C11—28no—
101C2×D4×C11—24no—
102C2×D4×C11—24no—
103C2×D4×C11—22no—
104C2×D4×C11—22no—
105C2×D4×C11—24no—
106C2×D4×C11—24no—
107C2×D4×C11—48no—
108C2×D4×C11C2×D411yescharacteristic
109C22×C4×C11—28no—
110C22×C4×C11—22no—
111C22×C4×C11—21no—
112C22×C4×C11C2×D412yes—
113C22×C4×C11C2411yescharacteristic
114C2×C22⋊D11—416no—
115C2×C22⋊D11—432no—
116C22×Dic11—22no—
117C2×D44—22no—
118C2×D44—22no—
119C2×D44—24no—
120C2×D44—24no—
121C2×D44—48no—
122C2×D44—42no—
123C2×D44—42no—
124C11×C4⋊C4—22no—
125C11×C4⋊C4—22no—
126C11×C4⋊C4—24no—
127C11×C4⋊C4C2×D412yes—
128C11×C4⋊C4C2×D414yes—
129C11×C22⋊C4—28no—
130C11×C22⋊C4—28no—
131C11×C22⋊C4—21no—
132C11×C22⋊C4—22no—
133C11×C22⋊C4—22no—
134C42×C11—22no—
135C42×C11—21no—
136C42×C11—22no—
137C42×C11C2×D411yescharacteristic
138C42×C11C2×D411yescharacteristic
139C42×C11C2×D412yes—
140#4325—44no—
141#4323—44no—
142C4×Dic11—28no—
143C4×Dic11—22no—
144C4×Dic11#4114yescomplemented
145#4318—22no—
146#4318—22no—
147#4318—24no—
148C2×C11⋊C8—22no—
149C2×C11⋊C8—22no—
150#3508D1111yescharacteristic, complemented
151#3138—111no—
152#3038—111no—
153#2867—111no—
154#2002—114no—
155#1994—111no—
156#1965—111no—
157#1887—114no—
158C4×#104—111no—
159C23×C11—24no—
160C23×C11—21no—
161C23×C11—28no—
162C23×C11—48no—
163C23×C11C22×D411yescharacteristic
164C22×D11—48no—
165C22×D11—42no—
166C22×D11—44no—
167Q8×C11—21no—
168Q8×C11—21no—
169Q8×C11—44no—
170D4×C11—21no—
171D4×C11—21no—
172D4×C11—42no—
173D4×C11—42no—
174D4×C11—42no—
175D4×C11—44no—
176D4×C11—48no—
177D4×C11—84no—
178D4×C11—88no—
179C2×C4×C11—24no—
180C2×C4×C11—21no—
181C2×C4×C11—22no—
182C2×C4×C11—24no—
183C2×C4×C11—42no—
184C2×C4×C11—44no—
185C2×C4×C11—88no—
186C2×C4×C11#12012yes—
187C2×C4×C11#12012yes—
188C2×C4×C11C22×D411yescharacteristic
189C2×C4×C11C22×D411yescharacteristic
190C2×C4×C11C2×#4112yes—
191C2×C4×C11H(5,𝔽2)12yes—
192C22⋊D11—832no—
193C2×Dic11—28no—
194C2×Dic11—24no—
195D44—42no—
196D44—42no—
197D44—44no—
198D44—84no—
199D44—84no—
200C11⋊C8—42no—
201C11⋊C8—42no—
202C2×AGL(1,ℤ/8)—112no—
203#559—22no—
204#550—22no—
205#546—24no—
206#540—22no—
207#535C2×D1112yes—
208#533C2×D1111yescharacteristic
209#532—22no—
210C2×#127—114no—
211C2×#127—111no—
212C2×#127—224no—
213C2×#127C2×D1111yescharacteristic
214#518C2×D1112yes—
215C4×#41C2×D1111yescharacteristic
216#490—222no—
217#486—222no—
218#460—222no—
219#459—222no—
220#423—111no—
221C2×#104—112no—
222#418—114no—
223#418—112no—
224C2×#100—114no—
225C4×M16—111no—
226C43—111no—
227#339—112no—
228#339—114no—
229C22×C11—22no—
230C22×C11—41no—
231C22×C11—44no—
232C22×C11—42no—
233C22×C11—48no—
234C22×C11—88no—
235C22×C11C2×#12011yescharacteristic
236C22×C11#54612yes—
237C2×D11—88no—
238C2×D11—82no—
239C2×D11—84no—
240C4×C11—22no—
241C4×C11—41no—
242C4×C11—42no—
243C4×C11—44no—
244C4×C11#45314yes—
245C4×C11#53211yescharacteristic
246C4×C11#53511yescharacteristic
247C4×C11#55012yes—
248Dic11—28no—
249C2×#41—24no—
250C2×#41C22×D1111yescharacteristic
251C22×D4—112no—
252C22×D4—228no—
253C22×D4—222no—
254C22×D4C22⋊D1114yes—
255C22×D4C22×D1112yes—
256AGL(1,ℤ/8)—444no—
257C2×SD16—222no—
258C2×D8—222no—
259C2×M16—112no—
260C2×M16—112no—
261C4⋊Q8C22⋊D1112yescomplemented
262#127—22no—
263#127—21no—
264#127—21no—
265#127—22no—
266#127—228no—
267#127—222no—
268#127—221no—
269#127—221no—
270#127—444no—
271#127—4416no—
272#125C22⋊D1112yescomplemented
273#124—24no—
274#124—22no—
275#123—28no—
276C22⋊Q8—22no—
277#121—24no—
278#121—28no—
279#121—24no—
280#120—24no—
281C4×Q8—22no—
282C4×Q8C22⋊D1112yescomplemented
283C4×D4—24no—
284C4×D4—22no—
285C4×D4—24no—
286C4×D4—24no—
287C4×D4C22⋊D1112yescomplemented
288#117—21no—
289#117C22×D1111yescharacteristic
290#117C22×D1112yes—
291C2×C22⋊C4—24no—
292C2×C42—21no—
293C2×C42—112no—
294C2×C42—222no—
295C2×C42C22×D1111yescharacteristic
296C4⋊C8—222no—
297#104—224no—
298#102—224no—
299#102—228no—
300#100—444no—
301#97—221no—
302C4×C8—221no—
303C2×C11—22no—
304C2×C11—81no—
305C2×C11—84no—
306C2×C11#243111yescharacteristic
307C2×C11C2×#45312yes—
308D11—162no—
309C24—222no—
310C24C2×C22⋊D1114yes—
311#41—22no—
312#41—22no—
313#41—88no—
314C2×Q8—22no—
315C2×Q8C2×C22⋊D1111yescharacteristic
316C2×D4—21no—
317C2×D4—28no—
318C2×D4—24no—
319C2×D4—24no—
320C2×D4—24no—
321C2×D4—24no—
322C2×D4—22no—
323C2×D4—22no—
324C2×D4—48no—
325C2×D4—224no—
326C2×D4—224no—
327C2×D4—222no—
328C2×D4—222no—
329C2×D4—448no—
330C2×D4—4416no—
331C2×D4—4432no—
332C2×D4—442no—
333C2×D4—442no—
334C2×D4C2×C22⋊D1111yescharacteristic
335C22×C4—28no—
336C22×C4—22no—
337C22×C4—21no—
338C22×C4—222no—
339C22×C4C2×C22⋊D1112yes—
340C22×C4C23×D1111yescharacteristic
341SD16—444no—
342D8—444no—
343M16—222no—
344M16—222no—
345M16—224no—
346C2×C8—222no—
347C2×C8—222no—
348C4⋊C4—22no—
349C4⋊C4—22no—
350C4⋊C4—24no—
351C4⋊C4C2×C22⋊D1112yes—
352C4⋊C4C2×C22⋊D1114yes—
353C22⋊C4—28no—
354C22⋊C4—28no—
355C22⋊C4—21no—
356C22⋊C4—22no—
357C22⋊C4—22no—
358C42—22no—
359C42—21no—
360C42—22no—
361C42—114no—
362C42—228no—
363C42—222no—
364C42C2×C22⋊D1111yescharacteristic
365C42C2×C22⋊D1111yescharacteristic
366C42C2×C22⋊D1112yes—
367C11#2558811yescharacteristic, complemented, Sylow
368C23—24no—
369C23—21no—
370C23—28no—
371C23—48no—
372C23—448no—
373C23—444no—
374C23—442no—
375C23C22×C22⋊D1111yescharacteristic
376Q8—21no—
377Q8—21no—
378Q8—44no—
379D4—21no—
380D4—21no—
381D4—42no—
382D4—42no—
383D4—42no—
384D4—44no—
385D4—48no—
386D4—84no—
387D4—88no—
388D4—442no—
389D4—442no—
390D4—444no—
391D4—884no—
392D4—8832no—
393D4—884no—
394C2×C4—24no—
395C2×C4—21no—
396C2×C4—22no—
397C2×C4—24no—
398C2×C4—42no—
399C2×C4—44no—
400C2×C4—88no—
401C2×C4—228no—
402C2×C4—224no—
403C2×C4#6700612yes—
404C2×C4#6700612yes—
405C2×C4#41×D1112yes—
406C2×C4#6704212yes—
407C2×C4C22×C22⋊D1111yescharacteristic
408C2×C4C22×C22⋊D1111yescharacteristic
409C8—442no—
410C8—442no—
411C22—22no—
412C22—41no—
413C22—44no—
414C22—42no—
415C22—48no—
416C22—88no—
417C22—888no—
418C22—882no—
419C22—884no—
420C22#1062336012yes—
421C22C2×#6700611yescharacteristic
422C4—22no—
423C4—41no—
424C4—42no—
425C4—44no—
426C4—228no—
427C4#1062285414yes—
428C4#1062336111yescharacteristic
429C4#1062336311yescharacteristic
430C4#1062336512yes—
431C2—22no—
432C2—84no—
433C2—81no—
434C2—1762no—
435C2#1307223111yescharacteristic
436C2C2×#1062285412yes—
subgroupG/H
centerC22C2×#67006
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#3508C2
socleC22×C11C2×#120
hypercenter#3508D11
hypocenterC11#25588
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3508

Complements

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

NH ≅ G/Ntype
1. #13078992C2semidirect
2. #13078096C2semidirect
3. #13077010C2semidirect
4. #13069629C2semidirect
5. #13069594C2semidirect
6. #13069457C2semidirect
7. #13069014C2semidirect
8. C4×#66901C2semidirect
9. C11×#3508C2semidirect
44. C11×C4⋊Q8D4semidirect
49. C11×#125D4semidirect
59. C4×Q8×C11D4semidirect
64. C4×D4×C11D4semidirect
144. C4×Dic11#41semidirect
150. #3508D11semidirect
261. C4⋊Q8C22⋊D11semidirect
272. #125C22⋊D11semidirect
282. C4×Q8C22⋊D11semidirect
287. C4×D4C22⋊D11semidirect
367. C11#25588semidirect

Maximal subgroups

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

subgroupindex
#130789922
#130780962
#130770102
#130696292
#130695942
#130694572
#130690142
C4×#669012
C11×#35082
#2558811