Finite Group Databasebeta

← #14738954

Subgroups — #14738954

Order 2816.

792 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079531C211yesmaximal, characteristic, complemented
2#13078076C211yesmaximal, characteristic, complemented
3C2×#10622456C211yesmaximal, characteristic, complemented
4#13077639C211yesmaximal, characteristic, complemented
5#13068056C214yesmaximal, complemented
6#13067970C214yesmaximal, complemented
7#13067390C211yesmaximal, characteristic, complemented
8#13067283C211yesmaximal, characteristic, complemented
9C11×#1540C211yesmaximal, characteristic, complemented
10C11×#532C2211yescharacteristic
11C2×#67002—21no—
12C22×D88—21no—
13C2×#66927C2211yescharacteristic
14C2×C4×D44C2211yescharacteristic
15C11×#431C2211yescharacteristic
16C2×C11×C4⋊C8C2211yescharacteristic
17#10622845—21no—
18C2×#66885—21no—
19#10622701C2212yescomplemented
20#10622696C2212yescomplemented
21#10622686C2212yescomplemented
22#10622685C2212yescomplemented
23#10622670—22no—
24#10622649—22no—
25#10622628—22no—
26#10622538C2211yescharacteristic
27#10622537C2211yescharacteristic
28#10622456—22no—
29#10622456C2214yes—
30#10622447C2214yescomplemented
31D11×C22⋊C8—22no—
32C8×D44—22no—
33C11×#332C2212yescomplemented
34C11×#331C2212yescomplemented
35#10622123C2214yescomplemented
36#10622117C2214yescomplemented
37C2×C11×#41—21no—
38C22×D44—21no—
39C22×D44—21no—
40C22×D44—21no—
41C22×D44D411yescharacteristic
42C22×C4×D11—21no—
43C22×C8×C11—21no—
44C11×C4⋊Q8C2311yescharacteristic
45C11×#127C2311yescharacteristic
46C11×#124—21no—
47C11×#121—21no—
48C11×#121—21no—
49C4×D4×C11—21no—
50C4×D4×C11—21no—
51C2×C42×C11C2311yescharacteristic
52#67002—44no—
53C2×#4325—22no—
54C2×#4323—22no—
55C2×#4323—24no—
56C2×(C2×D11)⋊C4—21no—
57C2×C4⋊Dic11D411yescharacteristic
58C2×#4318—21no—
59C2×D88—24no—
60C2×D88—44no—
61C2×C8×D11—24no—
62#66927—21no—
63#66927—21no—
64#66927—21no—
65#66927C2312yes—
66C4×D44—21no—
67C4×D44—21no—
68C4×D44D412yes—
69C4×D44C2312yes—
70C11×C4⋊C8—21no—
71C11×C4⋊C8C2312yes—
72C11×C4⋊C8C2312yes—
73C11×C22⋊C8—21no—
74C4×C8×C11—21no—
75#66899—22no—
76#66896—22no—
77C22⋊(C11⋊C8)D412yes—
78#66885—24no—
79(C2×D11)⋊C8—24no—
80#66873—24no—
81C4⋊(C11⋊C8)—21no—
82C4⋊(C11⋊C8)D412yes—
83C4⋊(C11⋊C8)C2312yes—
84C4×C11⋊C8C2312yes—
85#19386—111nomaximal, Sylow
86C23×D11—21no—
87C23×D11—41no—
88C11×#41—42no—
89C11×#41—42no—
90C2×Q8×C11—21no—
91C2×D4×C11—21no—
92C2×D4×C11—21no—
93C2×D4×C11—21no—
94C2×D4×C11—41no—
95C22×C4×C11—41no—
96C22×C4×C11C2×D411yescharacteristic
97C22×C4×C11C2×D411yescharacteristic
98C22×C4×C11#4111yescharacteristic
99C22×Dic11—21no—
100C2×D44—21no—
101C2×D44—22no—
102C2×D44—22no—
103C2×D44—22no—
104C2×D44—22no—
105C2×D44—41no—
106C2×D44—41no—
107C2×D44—41no—
108C2×D44—42no—
109C2×D44—42no—
110C2×D44—82no—
111C2×D44—82no—
112C2×D44D814yescomplemented
113C2×D44C2×D412yes—
114C2×C4×D11—22no—
115C2×C4×D11—22no—
116C2×C4×D11—82no—
117C2×C8×C11—22no—
118C2×C8×C11—22no—
119C2×C8×C11—42no—
120C11×C4⋊C4—21no—
121C11×C4⋊C4—21no—
122C11×C22⋊C4—41no—
123C11×C22⋊C4—41no—
124C42×C11C2×D411yescharacteristic
125C42×C11C2×D411yescharacteristic
126C42×C11#4111yescharacteristic
127C42×C11C2411yescharacteristic
128#4325—44no—
129#4323—44no—
130#4323—84no—
131(C2×D11)⋊C4—22no—
132(C2×D11)⋊C4—22no—
133C4⋊Dic11—21no—
134C4⋊Dic11C2×D412yes—
135#4318—42no—
136C2×C11⋊C8—22no—
137C2×C11⋊C8C2×D414yes—
138D88—48no—
139C8×D11—84no—
140#3205—111no—
141#3036—111no—
142C2×#459—111no—
143#2972—111no—
144#1681—114no—
145#1667—114no—
146#1571—111no—
147#1545—111no—
148#1540D1111yescharacteristic, complemented
149C23×C11—41no—
150C23×C11#12111yescharacteristic
151C22×D11—22no—
152C22×D11—24no—
153C22×D11—42no—
154C22×D11—81no—
155C22×D11—81no—
156C22×D11—82no—
157C22×D11—82no—
158C22×D11—82no—
159Q8×C11—41no—
160Q8×C11—41no—
161D4×C11—41no—
162D4×C11—41no—
163D4×C11—42no—
164D4×C11—81no—
165D4×C11—82no—
166C2×C4×C11—22no—
167C2×C4×C11—41no—
168C2×C4×C11—41no—
169C2×C4×C11—82no—
170C2×C4×C11#12111yescharacteristic
171C2×C4×C11#12111yescharacteristic
172C2×C4×C11#12111yescharacteristic
173C2×C4×C11C2×D812yes—
174C2×C4×C11#13512yes—
175C2×C4×C11C22×D411yescharacteristic
176C2×C4×C11C22×D411yescharacteristic
177C2×C4×C11C2×#4111yescharacteristic
178C2×Dic11—22no—
179C2×Dic11—81no—
180D44—22no—
181D44—24no—
182D44—42no—
183D44—42no—
184D44—44no—
185D44—82no—
186D44—82no—
187D44—82no—
188D44—82no—
189D44C2×D814yes—
190C4×D11—44no—
191C4×D11—82no—
192C8×C11—42no—
193C8×C11—42no—
194C11⋊C8—24no—
195C11⋊C8—42no—
196C2×AGL(1,ℤ/8)—221no—
197C22×D8—221no—
198#532C2×D1111yescharacteristic
199C2×#127—111no—
200C2×C4×D4—111no—
201#493—112no—
202#486—112no—
203#463—222no—
204#461—112no—
205#459—112no—
206#459—114no—
207#459—222no—
208#459—222no—
209#447—222no—
210C8×D4—114no—
211C8×D4—222no—
212#431—111no—
213#431C2×D1111yescharacteristic
214#423—111no—
215C2×C4⋊C8C2×D1111yescharacteristic
216#417—221no—
217C2×#102—221no—
218C2×C22⋊C8—222no—
219#335—114no—
220#332C2×D1112yescomplemented
221#331—114no—
222#331C2×D1112yescomplemented
223C22×C11—21no—
224C22×C11—21no—
225C22×C11—81no—
226C22×C11—81no—
227C22×C11—81no—
228C22×C11#46612yes—
229C22×C11C2×#12111yescharacteristic
230C2×D11—24no—
231C2×D11—42no—
232C2×D11—42no—
233C2×D11—84no—
234C2×D11—82no—
235C2×D11—82no—
236C2×D11—82no—
237C2×D11—164no—
238C4×C11—21no—
239C4×C11—21no—
240C4×C11—21no—
241C4×C11—81no—
242C4×C11#46612yes—
243C4×C11C22×D811yescharacteristic
244C4×C11C2×#13511yescharacteristic
245C4×C11#57612yes—
246Dic11—42no—
247C2×#41—21no—
248C22×D4—111no—
249C22×D4—221no—
250C22×D4—221no—
251C22×D4—221no—
252C23×C4—221no—
253AGL(1,ℤ/8)—444no—
254C2×SD16—222no—
255C2×D8—224no—
256C2×D8—224no—
257C2×D8—222no—
258C2×D8—444no—
259C2×M16—221no—
260C22×C8—21no—
261C22×C8—224no—
262C4⋊Q8C22×D1111yescharacteristic
263#127—112no—
264#127—221no—
265#127—221no—
266#127—221no—
267#127C22×D1111yescharacteristic
268#124—21no—
269#121—21no—
270#121—21no—
271C4×D4—21no—
272C4×D4—21no—
273C4×D4—112no—
274C4×D4—112no—
275C4×D4—221no—
276C4×D4—221no—
277C2×C4⋊C4—111no—
278C2×C22⋊C4—221no—
279C2×C42C22×D1111yescharacteristic
280C4⋊C8—21no—
281C4⋊C8—112no—
282C4⋊C8—112no—
283C4⋊C8—221no—
284C4⋊C8C22×D1112yes—
285C4⋊C8C22×D1112yes—
286#103—222no—
287#102—224no—
288#102—224no—
289#102—222no—
290C22⋊C8—21no—
291C22⋊C8—112no—
292C22⋊C8—224no—
293C4×C8—21no—
294C4×C8—112no—
295C2×C11—22no—
296C2×C11—161no—
297C2×C11#304111yescharacteristic
298C2×C11C2×#46611yescharacteristic
299C2×C11#306811yescharacteristic
300D11—44no—
301D11—162no—
302C24—221no—
303C24—441no—
304#41—42no—
305#41—42no—
306C2×Q8—21no—
307C2×D4—21no—
308C2×D4—21no—
309C2×D4—21no—
310C2×D4—41no—
311C2×D4—114no—
312C2×D4—112no—
313C2×D4—221no—
314C2×D4—222no—
315C2×D4—222no—
316C2×D4—222no—
317C2×D4—222no—
318C2×D4—441no—
319C2×D4—441no—
320C2×D4—441no—
321C2×D4—442no—
322C2×D4—442no—
323C2×D4—882no—
324C2×D4—882no—
325C22×C4—41no—
326C22×C4—221no—
327C22×C4—222no—
328C22×C4—222no—
329C22×C4—882no—
330C22×C4#433911yescharacteristic
331C22×C4D4×D1111yescharacteristic
332C22×C4D4×D1111yescharacteristic
333SD16—444no—
334D8—448no—
335D8—444no—
336D8—884no—
337M16—442no—
338C2×C8—22no—
339C2×C8—22no—
340C2×C8—42no—
341C2×C8—114no—
342C2×C8—222no—
343C2×C8—884no—
344C4⋊C4—21no—
345C4⋊C4—21no—
346C4⋊C4—112no—
347C4⋊C4—221no—
348C22⋊C4—41no—
349C22⋊C4—41no—
350C22⋊C4—222no—
351C22⋊C4—222no—
352C42#433911yescharacteristic
353C42D4×D1111yescharacteristic
354C42D4×D1111yescharacteristic
355C42C23×D1111yescharacteristic
356C11#1938611yescharacteristic, complemented, Sylow
357C23—41no—
358C23—222no—
359C23—224no—
360C23—442no—
361C23—881no—
362C23—881no—
363C23—882no—
364C23—882no—
365C23—882no—
366C23#6693711yescharacteristic
367Q8—41no—
368Q8—41no—
369D4—41no—
370D4—41no—
371D4—42no—
372D4—81no—
373D4—82no—
374D4—114no—
375D4—222no—
376D4—224no—
377D4—442no—
378D4—442no—
379D4—444no—
380D4—882no—
381D4—882no—
382D4—882no—
383D4—882no—
384C2×C4—22no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—82no—
388C2×C4—222no—
389C2×C4—444no—
390C2×C4—882no—
391C2×C4—881no—
392C2×C4#6693711yescharacteristic
393C2×C4#6693711yescharacteristic
394C2×C4#6693711yescharacteristic
395C2×C4D8×D1112yes—
396C2×C4#6696912yes—
397C2×C4C2×#433911yescharacteristic
398C2×C4C2×D4×D1111yescharacteristic
399C2×C4C2×D4×D1111yescharacteristic
400C8—42no—
401C8—42no—
402C8—224no—
403C8—442no—
404C22—21no—
405C22—21no—
406C22—81no—
407C22—81no—
408C22—81no—
409C22—224no—
410C22—442no—
411C22—442no—
412C22—884no—
413C22—882no—
414C22—882no—
415C22—882no—
416C22—1764no—
417C22#1062238812yes—
418C22C2×#6693711yescharacteristic
419C4—21no—
420C4—21no—
421C4—21no—
422C4—81no—
423C4—442no—
424C4#1062238812yes—
425C4C2×D8×D1111yescharacteristic
426C4C2×#6696911yescharacteristic
427C4#1062330012yes—
428C2—22no—
429C2—161no—
430C2—444no—
431C2—1762no—
432C2#1307812211yescharacteristic
433C2C2×#1062238811yescharacteristic
434C2#1307834711yescharacteristic
subgroupG/H
centerC22C2×#66937
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#1540C2
socleC22×C11C2×#121
hypercenter#1540D11
hypocenterC11#19386
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1540

Complements

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

NH ≅ G/Ntype
1. #13079531C2semidirect
2. #13078076C2semidirect
3. C2×#10622456C2semidirect
4. #13077639C2semidirect
5. #13068056C2semidirect
6. #13067970C2semidirect
7. #13067390C2semidirect
8. #13067283C2semidirect
9. C11×#1540C2semidirect
19. #10622701C22semidirect
20. #10622696C22semidirect
21. #10622686C22semidirect
22. #10622685C22semidirect
30. #10622447C22semidirect
33. C11×#332C22semidirect
34. C11×#331C22semidirect
35. #10622123C22semidirect
36. #10622117C22semidirect
112. C2×D44D8semidirect
148. #1540D11semidirect
220. #332C2×D11semidirect
222. #331C2×D11semidirect
356. C11#19386semidirect

Maximal subgroups

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

subgroupindex
#130795312
#130780762
C2×#106224562
#130776392
#130680562
#130679702
#130673902
#130672832
C11×#15402
#1938611