Finite Group Databasebeta

← #14908128

Subgroups — #14908128

Order 2816.

726 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622807C211yesmaximal, characteristic, complemented
2#13079097C211yesmaximal, characteristic, complemented
3#13077492C211yesmaximal, characteristic, complemented
4#13070676C212yesmaximal, complemented
5#13070669C212yesmaximal, complemented
6#13070654C212yesmaximal, complemented
7#13070649C212yesmaximal, complemented
8#13070376C211yesmaximal, characteristic, complemented
9#13070329C211yesmaximal, characteristic, complemented
10C2×#10622200C211yesmaximal, characteristic, complemented
11C2×C11×#509C211yesmaximal, characteristic, complemented
12C2×C11×#135C2211yescharacteristic
13C22×C11×D8C2211yescharacteristic
14#10623358—21no—
15#10623336—21no—
16C2×#66985—21no—
17C2×#66957C2211yescharacteristic
18C11×#509—24no—
19C2×C11×SD32C2212yes—
20C2×C11×D16C2212yes—
21C2×C11×M32C2211yescharacteristic
22#10622845—21no—
23#10622807—24no—
24Q16×Dic11C2212yescomplemented
25C2×#66893C2211yescharacteristic, complemented
26C2×#66892C2211yescharacteristic, complemented
27#10622777—22no—
28#10622768C2212yes—
29#10622767—22no—
30#10622764C2212yes—
31D8×Dic11C2212yescomplemented
32C2×#66891C2211yescharacteristic, complemented
33C2×#66890C2211yescharacteristic, complemented
34C2×#66882C2211yescharacteristic
35#10622714C2211yescharacteristic
36C22×C11⋊C16C2211yescharacteristic
37#10622200C2212yes—
38#10622200C2212yes—
39#10622147C2212yescomplemented
40#10622141C2212yescomplemented
41Dic11⋊C16C2212yescomplemented
42Dic11⋊C16C2212yescomplemented
43C2×C11×#41—21no—
44C22×D4×C11—21no—
45C2×#4339—21no—
46C11×#135—22no—
47C11×#135D414yescomplemented
48C2×C11×Q16C2311yescharacteristic
49C2×C11×SD16—21no—
50C2×C11×D8—22no—
51C2×C11×D8—21no—
52C2×C11×D8—22no—
53C2×C11×D8C2312yes—
54C2×C11×D8C2311yescharacteristic
55C22×C8×C11C2311yescharacteristic
56#67006—42no—
57Q8×Dic11—22no—
58#66993—22no—
59#66991—41no—
60#66991—41no—
61#66989—22no—
62D4×Dic11—22no—
63D4×Dic11—42no—
64C2×#4324—22no—
65#66985—44no—
66C2×#4323—22no—
67#66979—41no—
68#66979D411yescharacteristic
69C2×C4⋊Dic11—21no—
70C2×C4⋊Dic11—41no—
71C2×#4318D411yescharacteristic
72C2×Dic44C2311yescharacteristic
73#66957—22no—
74#66957—22no—
75C2×D88C2311yescharacteristic
76C2×#4314—21no—
77C11×SD32—24no—
78C11×D16—24no—
79C11×M32—22no—
80C2×C11×C16C2312yes—
81#66899—22no—
82#66896—22no—
83#66893—22no—
84#66892—22no—
85#66891—22no—
86#66890—22no—
87#66882—21no—
88#66882C2312yes—
89#66879D412yes—
90C8×Dic11C2312yes—
91C2×C11⋊C16—22no—
92C2×C11⋊C16C2311yescharacteristic
93C2×C11⋊C16C2311yescharacteristic
94#33589—111nomaximal, Sylow
95C24×C11—41no—
96C11×#41—24no—
97C11×#41—42no—
98C2×Q8×C11—21no—
99C2×D4×C11—21no—
100C2×D4×C11—22no—
101C2×D4×C11—41no—
102C2×D4×C11—42no—
103C2×D4×C11—41no—
104C2×D4×C11—42no—
105C22×C4×C11—41no—
106C22×C4×C11C2×D411yescharacteristic
107C2×C22⋊D11—42no—
108C2×C22⋊D11—42no—
109C2×C22⋊D11—41no—
110C22×Dic11—42no—
111C22×Dic11—41no—
112#4339—42no—
113#4339—42no—
114C2×D44—21no—
115C2×C4×D11—41no—
116C2×Dic22—21no—
117C11×Q16—21no—
118C11×Q16C2×D412yes—
119C11×SD16—24no—
120C11×D8—21no—
121C11×D8—22no—
122C11×D8—22no—
123C11×D8—42no—
124C11×D8C2×D412yes—
125C2×C8×C11C2×D412yes—
126C2×C8×C11C2×D411yescharacteristic
127C2×C8×C11#4112yes—
128C2×C8×C11C2411yescharacteristic
129C22⋊Dic11—42no—
130C22⋊Dic11—42no—
131C22⋊Dic11—42no—
132C22⋊Dic11D812yes—
133#4324—44no—
134#4323—44no—
135C4⋊Dic11—22no—
136C4⋊Dic11—42no—
137C4⋊Dic11—41no—
138C4⋊Dic11D811yescharacteristic
139C4⋊Dic11D811yescharacteristic
140C4×Dic11—42no—
141C4×Dic11C2×D412yes—
142#4318—22no—
143C2×C11⋊C8C2×D412yes—
144Dic44—21no—
145Dic44—21no—
146D88—21no—
147D88—21no—
148#4314—42no—
149C11×C16—22no—
150C11⋊C16—21no—
151C11⋊C16—21no—
152C2×#509D1111yescharacteristic, complemented
153C2×#508—111no—
154#3155—111no—
155#2951—111no—
156#2211—112no—
157#2210—112no—
158#2207—112no—
159#2206—112no—
160#2151—111no—
161#2139—111no—
162C2×#357—111no—
163C23×C11—41no—
164C23×C11—42no—
165C23×C11—82no—
166C23×C11—161no—
167C23×C11—161no—
168C23×C11C2×D811yescharacteristic
169C22×D11—41no—
170Q8×C11—22no—
171Q8×C11—41no—
172D4×C11—22no—
173D4×C11—44no—
174D4×C11—42no—
175D4×C11—41no—
176D4×C11—42no—
177D4×C11—82no—
178C2×C4×C11—41no—
179C2×C4×C11—44no—
180C2×C4×C11#12112yes—
181C2×C4×C11C2×D811yescharacteristic
182C2×C4×C11AGL(1,ℤ/8)12yes—
183C2×C4×C11C22×D411yescharacteristic
184C22⋊D11—82no—
185C22⋊D11—162no—
186C22⋊D11—162no—
187C2×Dic11—42no—
188C2×Dic11—41no—
189C2×Dic11—162no—
190C2×Dic11—161no—
191C2×Dic11C2×D812yes—
192C2×Dic11C2×D812yes—
193D44—41no—
194D44—41no—
195C4×D11—82no—
196Dic22—41no—
197Dic22—41no—
198C8×C11#12112yes—
199C8×C11C22×D411yescharacteristic
200C8×C11C2×#4111yescharacteristic
201C11⋊C8—22no—
202C2×AGL(1,ℤ/8)—221no—
203C2×#135—111no—
204C2×#135C2×D1111yescharacteristic
205C22×D8C2×D1111yescharacteristic
206#535—221no—
207#520—221no—
208#509—24no—
209#508—224no—
210C2×Q32—111no—
211C2×SD32—111no—
212C2×SD32—111no—
213C2×SD32C2×D1112yes—
214C2×D16—111no—
215C2×D16C2×D1112yes—
216C2×M32C2×D1111yescharacteristic
217C22×C16—111no—
218#496—222no—
219#495—112no—
220#493—112no—
221#440—222no—
222C4×Q16—112no—
223C4×D8—112no—
224C2×#107—111no—
225#417—221no—
226#405—111no—
227C4⋊C16—112no—
228C4⋊C16—112no—
229#358—112no—
230#357—112no—
231#357—112no—
232#357—112no—
233C22×C11—21no—
234C22×C11—21no—
235C22×C11—42no—
236C22×C11—81no—
237C22×C11—81no—
238C22×C11—82no—
239C22×C11—82no—
240C22×C11—82no—
241C22×C11—164no—
242C22×C11#45912yes—
243C22×C11C22×D811yescharacteristic
244C2×D11—81no—
245C2×D11—81no—
246C2×D11—81no—
247C4×C11—42no—
248C4×C11#45912yes—
249C4×C11C2×#12111yescharacteristic
250C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
251Dic11—22no—
252Dic11—22no—
253Dic11—82no—
254Dic11—81no—
255C2×#41—21no—
256C2×#41—221no—
257C22×D4—21no—
258AGL(1,ℤ/8)—444no—
259#135—22no—
260#135—222no—
261#135—222no—
262#135C22⋊D1114yescomplemented
263C2×Q16—111no—
264C2×Q16C22×D1111yescharacteristic
265C2×SD16—21no—
266C2×SD16—222no—
267C2×SD16—221no—
268C2×D8—21no—
269C2×D8—22no—
270C2×D8—22no—
271C2×D8—111no—
272C2×D8—222no—
273C2×D8C22×D1112yes—
274C2×D8C22×D1111yescharacteristic
275C2×M16—111no—
276C22×C8C22×D1111yescharacteristic
277#127—222no—
278#124—222no—
279#121—441no—
280#121—441no—
281#120—442no—
282C4×Q8—222no—
283C4×D4—222no—
284C4×D4—442no—
285#117—111no—
286#117—441no—
287C2×C4⋊C4—221no—
288C2×C4⋊C4—441no—
289Q32—222no—
290SD32—24no—
291SD32—222no—
292SD32—222no—
293D16—24no—
294D16—222no—
295M32—22no—
296C2×C16—111no—
297C2×C16—111no—
298C2×C16—222no—
299C2×C16C22×D1112yes—
300#107—112no—
301#107—221no—
302#103—222no—
303#102—222no—
304#97—112no—
305C4×C8—112no—
306C2×C11—22no—
307C2×C11—82no—
308C2×C11—162no—
309C2×C11C2×#45911yescharacteristic
310C2×C11#341511yescharacteristic
311C2×C11#341611yescharacteristic
312D11—161no—
313C24—41no—
314#41—24no—
315#41—42no—
316#41—442no—
317#41—442no—
318C2×Q8—21no—
319C2×Q8—221no—
320C2×D4—21no—
321C2×D4—22no—
322C2×D4—41no—
323C2×D4—41no—
324C2×D4—42no—
325C2×D4—42no—
326C2×D4—221no—
327C2×D4—442no—
328C2×D4—442no—
329C2×D4—441no—
330C22×C4—41no—
331C22×C4—442no—
332C22×C4—441no—
333C22×C4—441no—
334C22×C4D4×D1111yescharacteristic
335Q16—21no—
336Q16—221no—
337Q16—221no—
338Q16C2×C22⋊D1112yes—
339SD16—24no—
340SD16—444no—
341SD16—442no—
342D8—21no—
343D8—22no—
344D8—22no—
345D8—42no—
346D8—221no—
347D8—221no—
348D8—444no—
349D8C2×C22⋊D1112yes—
350M16—222no—
351C2×C8—112no—
352C2×C8D4×D1111yescharacteristic
353C2×C8#434112yes—
354C2×C8C2×C22⋊D1112yes—
355C2×C8C23×D1111yescharacteristic
356C4⋊C4—111no—
357C4⋊C4—111no—
358C4⋊C4—222no—
359C4⋊C4—442no—
360C4⋊C4—441no—
361C22⋊C4—112no—
362C22⋊C4—442no—
363C22⋊C4—442no—
364C22⋊C4—442no—
365C42—112no—
366C42—442no—
367C16—22no—
368C16—221no—
369C16—221no—
370C11#3358911yescharacteristic, complemented, Sylow
371C23—41no—
372C23—42no—
373C23—82no—
374C23—161no—
375C23—161no—
376C23—441no—
377C23D8×D1111yescharacteristic
378Q8—22no—
379Q8—41no—
380Q8—441no—
381Q8—441no—
382D4—22no—
383D4—44no—
384D4—41no—
385D4—42no—
386D4—42no—
387D4—82no—
388D4—441no—
389D4—441no—
390D4—882no—
391D4—1762no—
392D4—1762no—
393C2×C4—41no—
394C2×C4—44no—
395C2×C4—112no—
396C2×C4—112no—
397C2×C4—442no—
398C2×C4—441no—
399C2×C4—882no—
400C2×C4—1762no—
401C2×C4—1761no—
402C2×C4D8×D1111yescharacteristic
403C2×C4#6696412yes—
404C2×C4#6699212yes—
405C2×C4C2×D4×D1111yescharacteristic
406C8—222no—
407C8#6699212yes—
408C8C2×#434111yescharacteristic
409C8C22×C22⋊D1111yescharacteristic
410C22—21no—
411C22—21no—
412C22—42no—
413C22—81no—
414C22—81no—
415C22—82no—
416C22—82no—
417C22—82no—
418C22—164no—
419C22—881no—
420C22—881no—
421C22—881no—
422C22#1062276312yes—
423C22C2×D8×D1111yescharacteristic
424C4—42no—
425C4—222no—
426C4—222no—
427C4—881no—
428C4—882no—
429C4#1062276312yes—
430C4C2×#6696411yescharacteristic
431C4C2×#6699211yescharacteristic
432C2—22no—
433C2—82no—
434C2—162no—
435C2—1761no—
436C2C2×#1062276311yescharacteristic
437C2#1308175611yescharacteristic
438C2#1308176211yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC2×C11×#509C2
socleC22×C11C22×D8
hypercenterC2×#509D11
hypocenterC11#33589
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#509

Complements

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

NH ≅ G/Ntype
1. C2×#10622807C2semidirect
2. #13079097C2semidirect
3. #13077492C2semidirect
4. #13070676C2semidirect
5. #13070669C2semidirect
6. #13070654C2semidirect
7. #13070649C2semidirect
8. #13070376C2semidirect
9. #13070329C2semidirect
10. C2×#10622200C2semidirect
11. C2×C11×#509C2semidirect
24. Q16×Dic11C22semidirect
25. C2×#66893C22semidirect
26. C2×#66892C22semidirect
31. D8×Dic11C22semidirect
32. C2×#66891C22semidirect
33. C2×#66890C22semidirect
39. #10622147C22semidirect
40. #10622141C22semidirect
41. Dic11⋊C16C22semidirect
42. Dic11⋊C16C22semidirect
47. C11×#135D4semidirect
152. C2×#509D11semidirect
262. #135C22⋊D11semidirect
370. C11#33589semidirect

Maximal subgroups

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

subgroupindex
C2×#106228072
#130790972
#130774922
#130706762
#130706692
#130706542
#130706492
#130703762
#130703292
C2×#106222002
C2×C11×#5092
#3358911