Finite Group Databasebeta

← #14738947

Subgroups — #14738947

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#13078076C211yesmaximal, characteristic, complemented
2C2×#10622685C211yesmaximal, characteristic, complemented
3#13077639C211yesmaximal, characteristic, complemented
4#13068050C214yesmaximal, complemented
5#13067968C214yesmaximal, complemented
6#13067391C211yesmaximal, characteristic, complemented
7#13067284C211yesmaximal, characteristic, complemented
8#13067265C211yesmaximal, characteristic, complemented
9C11×#3205C211yesmaximal, characteristic, complemented
10C11×#532C2211yescharacteristic
11C2×C11×#127C2211yescharacteristic
12C2×#67002—21no—
13C22×#4323—21no—
14C2×C4×D44C2211yescharacteristic
15C11×#493C2212yescomplemented
16C11×#486C2212yescomplemented
17C11×#459—22no—
18C11×#447—22no—
19C11×#431C2211yescharacteristic
20#10622845—21no—
21C2×#66896—21no—
22#10622696C2212yescomplemented
23#10622685—22no—
24#10622685C2214yes—
25#10622685C2212yescomplemented
26#10622670—22no—
27#10622538C2211yescharacteristic
28#10622537C2211yescharacteristic
29C2×C4⋊(C11⋊C8)C2211yescharacteristic
30#10622447—22no—
31D11×C22⋊C8—22no—
32C8×D44C2214yescomplemented
33#10622185C2212yescomplemented
34#10622182C2212yescomplemented
35#10622182C2214yescomplemented
36#10622096C2214yescomplemented
37C2×C11×#41—21no—
38C22×D4×C11—21no—
39C22×D4×C11—21no—
40C22×D4×C11—21no—
41C22×D44D411yescharacteristic
42C22×C4×D11—21no—
43C2×C11×D8—24no—
44C11×C4⋊Q8C2311yescharacteristic
45C11×#127—21no—
46C11×#127—21no—
47C11×#127—21no—
48C11×#127C2311yescharacteristic
49C11×#127C2312yes—
50C11×#124—21no—
51C11×#121—21no—
52C11×#121—21no—
53C4×D4×C11—21no—
54C4×D4×C11—21no—
55C2×C42×C11C2311yescharacteristic
56#67002—44no—
57C2×#4325—22no—
58C2×#4323—24no—
59C2×#4323—22no—
60C2×#4323—44no—
61C2×(C2×D11)⋊C4—21no—
62C2×C4⋊Dic11D411yescharacteristic
63C2×#4318—21no—
64C22×C11⋊C8—21no—
65C2×C8×D11—24no—
66C4×D44—21no—
67C4×D44—21no—
68C4×D44D412yes—
69C4×D44C2312yes—
70C11×C4⋊C8D412yes—
71C11×#102—24no—
72C11×C22⋊C8D412yes—
73C4×C8×C11C2312yes—
74#66899—22no—
75#66896—24no—
76#66896—22no—
77C22⋊(C11⋊C8)—21no—
78(C2×D11)⋊C8—24no—
79C4⋊(C11⋊C8)—21no—
80C4⋊(C11⋊C8)—21no—
81C4⋊(C11⋊C8)C2312yes—
82C4⋊(C11⋊C8)C2312yes—
83C4⋊(C11⋊C8)C2312yes—
84C4×C11⋊C8—21no—
85#19386—111nomaximal, Sylow
86C24×C11—41no—
87C23×D11—21no—
88C11×#41—42no—
89C11×#41—42no—
90C2×Q8×C11—21no—
91C2×D4×C11—21no—
92C2×D4×C11—22no—
93C2×D4×C11—22no—
94C2×D4×C11—21no—
95C2×D4×C11—21no—
96C2×D4×C11—22no—
97C2×D4×C11—41no—
98C2×D4×C11—41no—
99C2×D4×C11—41no—
100C2×D4×C11—41no—
101C2×D4×C11—42no—
102C2×D4×C11—42no—
103C2×D4×C11—82no—
104C2×D4×C11—82no—
105C22×C4×C11—41no—
106C22×C4×C11C2×D411yescharacteristic
107C22×C4×C11C2×D411yescharacteristic
108C22×C4×C11#4111yescharacteristic
109C22×Dic11—21no—
110C2×D44—21no—
111C2×D44—22no—
112C2×D44D814yescomplemented
113C2×D44C2×D412yes—
114C2×C4×D11—22no—
115C2×C4×D11—22no—
116C2×C4×D11—82no—
117C11×D8—84no—
118C2×C8×C11C2×D414yes—
119C11×C4⋊C4—21no—
120C11×C4⋊C4—21no—
121C11×C22⋊C4—41no—
122C11×C22⋊C4—41no—
123C42×C11C2×D411yescharacteristic
124C42×C11C2×D411yescharacteristic
125C42×C11#4111yescharacteristic
126C42×C11C2411yescharacteristic
127#4325—44no—
128#4323—48no—
129#4323—44no—
130(C2×D11)⋊C4—22no—
131(C2×D11)⋊C4—22no—
132C4⋊Dic11—21no—
133C4⋊Dic11C2×D412yes—
134#4318—42no—
135C2×C11⋊C8—22no—
136C2×C11⋊C8—22no—
137C2×C11⋊C8—22no—
138C2×C11⋊C8—42no—
139C8×D11—84no—
140#3205D1111yescharacteristic, complemented
141#3036—111no—
142C2×#459—111no—
143#2972—111no—
144#1681—114no—
145#1667—114no—
146#1571—111no—
147#1545—111no—
148#1540—111no—
149C23×C11—41no—
150C23×C11—42no—
151C23×C11—82no—
152C23×C11—82no—
153C23×C11—82no—
154C23×C11#12111yescharacteristic
155C22×D11—22no—
156C22×D11—24no—
157C22×D11—81no—
158C22×D11—81no—
159Q8×C11—41no—
160Q8×C11—41no—
161D4×C11—42no—
162D4×C11—41no—
163D4×C11—42no—
164D4×C11—41no—
165D4×C11—42no—
166D4×C11—44no—
167D4×C11—81no—
168D4×C11—82no—
169D4×C11—82no—
170D4×C11—82no—
171D4×C11—82no—
172D4×C11—82no—
173C2×C4×C11—22no—
174C2×C4×C11—41no—
175C2×C4×C11—41no—
176C2×C4×C11—82no—
177C2×C4×C11#12111yescharacteristic
178C2×C4×C11#12111yescharacteristic
179C2×C4×C11#12111yescharacteristic
180C2×C4×C11C2×D812yes—
181C2×C4×C11#13512yes—
182C2×C4×C11C22×D411yescharacteristic
183C2×C4×C11C22×D411yescharacteristic
184C2×C4×C11C2×#4111yescharacteristic
185C2×Dic11—22no—
186C2×Dic11—81no—
187D44—22no—
188D44—24no—
189D44C2×D814yes—
190C4×D11—44no—
191C4×D11—82no—
192C8×C11—24no—
193C11⋊C8—42no—
194C11⋊C8—42no—
195C11⋊C8—42no—
196C2×AGL(1,ℤ/8)—221no—
197C22×D8—221no—
198#532C2×D1111yescharacteristic
199C2×#127C2×D1111yescharacteristic
200C2×C4×D4—111no—
201#493C2×D1112yescomplemented
202#486C2×D1112yescomplemented
203#463—222no—
204#461—112no—
205#459—22no—
206#459—112no—
207#459—114no—
208#459—222no—
209#447—22no—
210C8×D4—114no—
211C8×D4—222no—
212#431—111no—
213#431C2×D1111yescharacteristic
214#423—111no—
215C2×C4⋊C8—111no—
216#417—221no—
217C2×#102—221no—
218C2×C22⋊C8—222no—
219#335—114no—
220#332—112no—
221#331—112no—
222#331—114no—
223C22×C11—21no—
224C22×C11—21no—
225C22×C11—82no—
226C22×C11—81no—
227C22×C11—81no—
228C22×C11—82no—
229C22×C11—82no—
230C22×C11—81no—
231C22×C11—164no—
232C22×C11#46612yes—
233C22×C11C2×#12111yescharacteristic
234C2×D11—24no—
235C2×D11—42no—
236C2×D11—42no—
237C2×D11—84no—
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—21no—
249C22×D4—21no—
250C22×D4—21no—
251C22×D4—111no—
252C23×C4—221no—
253AGL(1,ℤ/8)—444no—
254C2×SD16—222no—
255C2×D8—24no—
256C2×D8—224no—
257C2×D8—222no—
258C2×D8—444no—
259C2×M16—221no—
260C22×C8—221no—
261C22×C8—224no—
262C4⋊Q8C22×D1111yescharacteristic
263#127—21no—
264#127—21no—
265#127—21no—
266#127C22×D1112yes—
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—112no—
281C4⋊C8—112no—
282C4⋊C8—112no—
283C4⋊C8—221no—
284C4⋊C8—221no—
285C4⋊C8C22⋊D1112yes—
286#103—222no—
287#102—24no—
288#102—224no—
289#102—222no—
290C22⋊C8—221no—
291C22⋊C8—224no—
292C22⋊C8C22⋊D1112yes—
293C4×C8—221no—
294C4×C8C22×D1112yes—
295C2×C11—22no—
296C2×C11—161no—
297C2×C11—162no—
298C2×C11#304111yescharacteristic
299C2×C11C2×#46611yescharacteristic
300C2×C11#306811yescharacteristic
301D11—44no—
302C24—41no—
303C24—221no—
304#41—42no—
305#41—42no—
306C2×Q8—21no—
307C2×D4—21no—
308C2×D4—22no—
309C2×D4—21no—
310C2×D4—22no—
311C2×D4—22no—
312C2×D4—21no—
313C2×D4—41no—
314C2×D4—42no—
315C2×D4—42no—
316C2×D4—41no—
317C2×D4—41no—
318C2×D4—41no—
319C2×D4—82no—
320C2×D4—82no—
321C2×D4—114no—
322C2×D4—112no—
323C2×D4—222no—
324C2×D4—221no—
325C22×C4—41no—
326C22×C4—221no—
327C22×C4—222no—
328C22×C4—222no—
329C22×C4—882no—
330C22×C4D4×D1111yescharacteristic
331C22×C4#434111yescharacteristic
332C22×C4C2×C22⋊D1111yescharacteristic
333SD16—444no—
334D8—84no—
335D8—448no—
336D8—444no—
337M16—442no—
338C2×C8—222no—
339C2×C8—222no—
340C2×C8—222no—
341C2×C8—442no—
342C2×C8—884no—
343C2×C8C2×C22⋊D1114yes—
344C4⋊C4—21no—
345C4⋊C4—21no—
346C4⋊C4—112no—
347C4⋊C4—221no—
348C22⋊C4—41no—
349C22⋊C4—41no—
350C22⋊C4—222no—
351C22⋊C4—222no—
352C42D4×D1111yescharacteristic
353C42#434111yescharacteristic
354C42C2×C22⋊D1111yescharacteristic
355C42C23×D1111yescharacteristic
356C11#1938611yescharacteristic, complemented, Sylow
357C23—41no—
358C23—42no—
359C23—82no—
360C23—82no—
361C23—82no—
362C23—222no—
363C23—224no—
364C23—881no—
365C23—881no—
366C23#6699111yescharacteristic
367Q8—41no—
368Q8—41no—
369D4—42no—
370D4—41no—
371D4—42no—
372D4—41no—
373D4—42no—
374D4—44no—
375D4—81no—
376D4—82no—
377D4—82no—
378D4—82no—
379D4—82no—
380D4—82no—
381D4—114no—
382D4—224no—
383D4—222no—
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×C4D8×D1112yes—
393C2×C4#6696512yes—
394C2×C4#6699111yescharacteristic
395C2×C4#6699111yescharacteristic
396C2×C4#6699111yescharacteristic
397C2×C4C2×D4×D1111yescharacteristic
398C2×C4C2×#434111yescharacteristic
399C2×C4C22×C22⋊D1111yescharacteristic
400C8—24no—
401C8—442no—
402C8—442no—
403C8—442no—
404C22—21no—
405C22—21no—
406C22—82no—
407C22—81no—
408C22—82no—
409C22—81no—
410C22—81no—
411C22—82no—
412C22—164no—
413C22—224no—
414C22—442no—
415C22—442no—
416C22—884no—
417C22#1062277012yes—
418C22C2×#6699111yescharacteristic
419C4—21no—
420C4—21no—
421C4—21no—
422C4—81no—
423C4—442no—
424C4#1062277012yes—
425C4C2×D8×D1111yescharacteristic
426C4C2×#6696511yescharacteristic
427C4#1062336612yes—
428C2—22no—
429C2—162no—
430C2—161no—
431C2—444no—
432C2#1307811511yescharacteristic
433C2C2×#1062277011yescharacteristic
434C2#1307834011yescharacteristic
subgroupG/H
centerC22C2×#66991
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3205C2
socleC22×C11C2×#121
hypercenter#3205D11
hypocenterC11#19386
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3205

Complements

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

NH ≅ G/Ntype
1. #13078076C2semidirect
2. C2×#10622685C2semidirect
3. #13077639C2semidirect
4. #13068050C2semidirect
5. #13067968C2semidirect
6. #13067391C2semidirect
7. #13067284C2semidirect
8. #13067265C2semidirect
9. C11×#3205C2semidirect
15. C11×#493C22semidirect
16. C11×#486C22semidirect
22. #10622696C22semidirect
25. #10622685C22semidirect
32. C8×D44C22semidirect
33. #10622185C22semidirect
34. #10622182C22semidirect
35. #10622182C22semidirect
36. #10622096C22semidirect
112. C2×D44D8semidirect
140. #3205D11semidirect
201. #493C2×D11semidirect
202. #486C2×D11semidirect
356. C11#19386semidirect

Maximal subgroups

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

subgroupindex
#130780762
C2×#106226852
#130776392
#130680502
#130679682
#130673912
#130672842
#130672652
C11×#32052
#1938611