Finite Group Databasebeta

← Dic11×#509 #14907093

Subgroups — Dic11×#509 #14907093

Order 2816.

738 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#135×Dic11C211yesmaximal, characteristic, complemented
2C2×D8×Dic11C211yesmaximal, characteristic, complemented
3#13070492C212yesmaximal, complemented
4#13070481C212yesmaximal, complemented
5SD32×Dic11C212yesmaximal, complemented
6D16×Dic11C212yesmaximal, complemented
7#13070404C211yesmaximal, characteristic, complemented
8#13070332C211yesmaximal, characteristic, complemented
9#13070328C211yesmaximal, characteristic, complemented
10M32×Dic11C211yesmaximal, characteristic, complemented
11C2×C11×#509C211yesmaximal, characteristic
12C2×C11×#135C2211yescharacteristic
13C22×C11×D8C2211yescharacteristic
14#41×Dic11—21no—
15C2×D4×Dic11—21no—
16C11×#509C418yescomplemented
17C2×C11×SD32C2212yes—
18C2×C11×D16C2212yes—
19C2×C11×M32C2211yescharacteristic
20#10622846—21no—
21C2×#66896—21no—
22Q16×Dic11C2211yescharacteristic, complemented
23Q16×Dic11C2211yescharacteristic, complemented
24SD16×Dic11—21no—
25SD16×Dic11—21no—
26D8×Dic11—21no—
27D8×Dic11—21no—
28D8×Dic11C2212yes—
29D8×Dic11C2212yes—
30D8×Dic11C2211yescharacteristic, complemented
31D8×Dic11C2211yescharacteristic, complemented
32#10622719C2211yescharacteristic
33C2×#66882C2211yescharacteristic
34C2×C8×Dic11C2211yescharacteristic
35C2×#66876C2211yescharacteristic
36#10622202C2212yescomplemented
37#10622200C2212yes—
38#10622200C2212yes—
39#10622200C2212yescomplemented
40#10622143C2212yescomplemented
41#10622142C2212yescomplemented
42#10622140C2212yescomplemented
43C16×Dic11C2212yescomplemented
44C2×C11×#41—21no—
45C22×D4×C11—21no—
46C23×Dic11—41no—
47C11×#135—22no—
48C11×#135C2×C414yescomplemented
49C2×C11×Q16C2311yescharacteristic
50C2×C11×SD16—21no—
51C2×C11×D8—21no—
52C2×C11×D8—22no—
53C2×C11×D8C2×C414yescomplemented
54C2×C11×D8C2312yes—
55C2×C11×D8C2311yescharacteristic
56C22×C8×C11C2311yescharacteristic
57C2×C22⋊Dic11—41no—
58Q8×Dic11—21no—
59Q8×Dic11—21no—
60D4×Dic11—22no—
61D4×Dic11—22no—
62D4×Dic11—21no—
63D4×Dic11—21no—
64D4×Dic11—41no—
65D4×Dic11—41no—
66D4×Dic11—41no—
67D4×Dic11—41no—
68#66979—21no—
69#66979—41no—
70C2×C4⋊Dic11—21no—
71C2×C4×Dic11—41no—
72C2×C4×Dic11D411yescharacteristic
73C22×C11⋊C8D411yescharacteristic
74C11×SD32C2×C418yescomplemented
75C11×D16C2×C418yescomplemented
76C11×M32C2×C414yescomplemented
77C2×C11×C16C2312yes—
78#66899—21no—
79#66899—21no—
80#66896—22no—
81#66896—22no—
82#66896—21no—
83#66896—21no—
84#66882—21no—
85#66882C2312yes—
86#66882C2311yescharacteristic
87#66882C2311yescharacteristic
88#66881—21no—
89C8×Dic11D411yescharacteristic
90C8×Dic11D411yescharacteristic
91C8×Dic11C2311yescharacteristic
92C8×Dic11C2311yescharacteristic
93#66876—22no—
94C2×C11⋊C16C2312yes—
95C4×#509—111nomaximal, Sylow
96C24×C11—41no—
97C11×#41—24no—
98C11×#41—42no—
99C2×Q8×C11—21no—
100C2×D4×C11—24no—
101C2×D4×C11—22no—
102C2×D4×C11—21no—
103C2×D4×C11—41no—
104C2×D4×C11—41no—
105C2×D4×C11—42no—
106C22×C4×C11—41no—
107C22×C4×C11C2×D411yescharacteristic
108C22×Dic11—41no—
109C22×Dic11—41no—
110C22×Dic11—42no—
111C22×Dic11—42no—
112C22×Dic11—41no—
113C22×Dic11—84no—
114C22×Dic11D811yescharacteristic
115C22×Dic11D811yescharacteristic
116C11×Q16—21no—
117C11×Q16C22×C412yescomplemented
118C11×SD16—24no—
119C11×D8—24no—
120C11×D8—22no—
121C11×D8—21no—
122C11×D8C22×C414yes—
123C11×D8C22×C412yescomplemented
124C2×C8×C11C22×C412yes—
125C2×C8×C11C2×D411yescharacteristic
126C2×C8×C11#4112yes—
127C2×C8×C11C2411yescharacteristic
128C22⋊Dic11—41no—
129C22⋊Dic11—41no—
130C22⋊Dic11—42no—
131C22⋊Dic11—42no—
132C22⋊Dic11—41no—
133C4⋊Dic11—21no—
134C4⋊Dic11—21no—
135C4⋊Dic11—22no—
136C4⋊Dic11—41no—
137C4⋊Dic11—41no—
138C4⋊Dic11—41no—
139C4×Dic11—41no—
140C4×Dic11—41no—
141C4×Dic11—41no—
142C4×Dic11D811yescharacteristic
143C4×Dic11D811yescharacteristic
144C4×Dic11C2×D411yescharacteristic
145C4×Dic11C2×D411yescharacteristic
146C2×C11⋊C8—22no—
147C2×C11⋊C8C2×D411yescharacteristic
148C2×C11⋊C8C2×D411yescharacteristic
149C11×C16C22×C414yescomplemented
150C11⋊C16—22no—
151C2×#509D1111yescharacteristic
152C4×#135—111no—
153C2×C4×D8—111no—
154#2177—112no—
155#2175—112no—
156C4×SD32—112no—
157C4×D16—112no—
158#2159—111no—
159#2140—111no—
160#2139—111no—
161C4×M32—111no—
162C23×C11—41no—
163C23×C11—42no—
164C23×C11—44no—
165C23×C11—82no—
166C23×C11—82no—
167C23×C11C2×D811yescharacteristic
168Q8×C11—22no—
169Q8×C11—41no—
170D4×C11—24no—
171D4×C11—22no—
172D4×C11—44no—
173D4×C11—42no—
174D4×C11—41no—
175D4×C11—44no—
176C2×C4×C11—41no—
177C2×C4×C11—44no—
178C2×C4×C11C4×D412yes—
179C2×C4×C11C2×D811yescharacteristic
180C2×C4×C11#13512yes—
181C2×C4×C11C22×D411yescharacteristic
182C2×Dic11—22no—
183C2×Dic11—41no—
184C2×Dic11—41no—
185C2×Dic11—41no—
186C2×Dic11—42no—
187C2×Dic11—82no—
188C2×Dic11—84no—
189C2×Dic11—82no—
190C2×Dic11—82no—
191C2×Dic11—84no—
192C2×Dic11C2×D811yescharacteristic
193C2×Dic11C2×D811yescharacteristic
194C2×Dic11C2×D811yescharacteristic
195C2×Dic11C2×D811yescharacteristic
196C8×C11C4×D412yes—
197C8×C11C23×C411yescharacteristic
198C8×C11C2×#4111yescharacteristic
199C11⋊C8—21no—
200C11⋊C8—21no—
201C2×#135C2×D1111yescharacteristic
202C22×D8C2×D1111yescharacteristic
203C4×#41—221no—
204C2×C4×D4—221no—
205#509Dic1118yesdirect product factor
206C2×SD32C2×D1112yes—
207C2×D16C2×D1112yes—
208C2×M32—111no—
209C2×M32C2×D1111yescharacteristic
210C4×Q16—111no—
211C4×Q16—111no—
212C4×SD16—221no—
213C4×SD16—221no—
214C4×D8—112no—
215C4×D8—112no—
216C4×D8—111no—
217C4×D8—111no—
218C4×D8—221no—
219C4×D8—221no—
220#427—111no—
221C2×#107—111no—
222#416—221no—
223C2×#102—221no—
224C2×C4×C8—111no—
225#367—112no—
226#366—112no—
227#358—112no—
228#357—112no—
229#357—112no—
230#357—112no—
231#346—112no—
232C4×C16—112no—
233C22×C11—21no—
234C22×C11—21no—
235C22×C11—42no—
236C22×C11—44no—
237C22×C11—88no—
238C22×C11—82no—
239C22×C11—81no—
240C22×C11—82no—
241C22×C11—81no—
242C22×C11C4×D812yes—
243C22×C11C22×D811yescharacteristic
244C4×C11—42no—
245C4×C11C4×D812yes—
246C4×C11C2×C4×D411yescharacteristic
247C4×C11C2×#13511yescharacteristic
248Dic11—21no—
249Dic11—21no—
250Dic11—21no—
251Dic11—81no—
252Dic11—82no—
253Dic11—81no—
254Dic11#50912yesdirect product factor
255C2×#41—21no—
256C22×D4—21no—
257C23×C4—441no—
258#135—22no—
259#135C2×Dic1114yescomplemented
260C2×Q16C22×D1111yescharacteristic
261C2×SD16—21no—
262C2×D8—21no—
263C2×D8—22no—
264C2×D8C2×Dic1114yescomplemented
265C2×D8C22×D1112yes—
266C2×D8C22×D1111yescharacteristic
267C22×C8—111no—
268C22×C8C22×D1111yescharacteristic
269C4×Q8—221no—
270C4×Q8—221no—
271C4×D4—222no—
272C4×D4—222no—
273C4×D4—221no—
274C4×D4—221no—
275C4×D4—441no—
276C4×D4—441no—
277C4×D4—441no—
278C4×D4—441no—
279#117—221no—
280#117—441no—
281C2×C4⋊C4—221no—
282C2×C22⋊C4—441no—
283C2×C42—111no—
284C2×C42—441no—
285SD32C2×Dic1118yescomplemented
286D16C2×Dic1118yescomplemented
287M32—222no—
288M32C2×Dic1114yescomplemented
289C2×C16—112no—
290C2×C16C22×D1112yes—
291#107—111no—
292#107—111no—
293#107—112no—
294#107—221no—
295#106—221no—
296#103—221no—
297#103—221no—
298#102—222no—
299#102—222no—
300#102—221no—
301#102—221no—
302C4×C8—111no—
303C4×C8—111no—
304C4×C8—111no—
305C4×C8—111no—
306C2×C11—22no—
307C2×C11—82no—
308C2×C11—84no—
309C2×C11C2×C4×D811yescharacteristic
310C2×C11C2×#50911yescharacteristic
311C2×C11#341411yescharacteristic
312C24—41no—
313#41—24no—
314#41—42no—
315C2×Q8—21no—
316C2×D4—24no—
317C2×D4—22no—
318C2×D4—21no—
319C2×D4—41no—
320C2×D4—41no—
321C2×D4—42no—
322C22×C4—41no—
323C22×C4—111no—
324C22×C4—111no—
325C22×C4—441no—
326C22×C4—441no—
327C22×C4—442no—
328C22×C4—442no—
329C22×C4—441no—
330C22×C4—884no—
331C22×C4D4×D1111yescharacteristic
332Q16—21no—
333Q16C22×Dic1112yescomplemented
334SD16—24no—
335D8—24no—
336D8—22no—
337D8—21no—
338D8C22×Dic1114yes—
339D8C22×Dic1112yescomplemented
340C2×C8—111no—
341C2×C8—111no—
342C2×C8—222no—
343C2×C8D4×D1111yescharacteristic
344C2×C8#434112yes—
345C2×C8C22×Dic1112yes—
346C2×C8C23×D1111yescharacteristic
347C4⋊C4—222no—
348C4⋊C4—221no—
349C4⋊C4—221no—
350C4⋊C4—441no—
351C4⋊C4—441no—
352C4⋊C4—441no—
353C22⋊C4—442no—
354C22⋊C4—442no—
355C22⋊C4—441no—
356C22⋊C4—441no—
357C22⋊C4—441no—
358C42—111no—
359C42—111no—
360C42—111no—
361C42—111no—
362C42—441no—
363C42—441no—
364C42—441no—
365C16—222no—
366C16C22×Dic1114yescomplemented
367C11C4×#50911yescharacteristic, complemented, Sylow
368C23—44no—
369C23—41no—
370C23—42no—
371C23—82no—
372C23—82no—
373C23D8×D1111yescharacteristic
374Q8—22no—
375Q8—41no—
376D4—24no—
377D4—22no—
378D4—44no—
379D4—44no—
380D4—42no—
381D4—41no—
382C2×C4—41no—
383C2×C4—44no—
384C2×C4—111no—
385C2×C4—111no—
386C2×C4—111no—
387C2×C4—111no—
388C2×C4—222no—
389C2×C4—441no—
390C2×C4—441no—
391C2×C4—441no—
392C2×C4—442no—
393C2×C4—884no—
394C2×C4—882no—
395C2×C4—884no—
396C2×C4—882no—
397C2×C4—882no—
398C2×C4D8×D1111yescharacteristic
399C2×C4#6696512yes—
400C2×C4D4×Dic1112yes—
401C2×C4C2×D4×D1111yescharacteristic
402C8—221no—
403C8—221no—
404C8D4×Dic1112yes—
405C8C2×#434111yescharacteristic
406C8C23×Dic1111yescharacteristic
407C22—21no—
408C22—21no—
409C22—42no—
410C22—44no—
411C22—88no—
412C22—82no—
413C22—81no—
414C22—81no—
415C22—82no—
416C22D8×Dic1112yes—
417C22C2×D8×D1111yescharacteristic
418C4—42no—
419C4—112no—
420C4—221no—
421C4—221no—
422C4—221no—
423C4—882no—
424C4—881no—
425C4—881no—
426C4D8×Dic1112yes—
427C4C2×#6696511yescharacteristic
428C4C2×D4×Dic1111yescharacteristic
429C2—22no—
430C2—84no—
431C2—82no—
432C2C2×D8×Dic1111yescharacteristic
433C2D11×#50911yescharacteristic
434C2#1308174811yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutatorC8×C11C23×C4
FrattiniC2×C8C23×D11
Fitting, prime radicalC2×C11×#509C2
socleC22×C11C22×D8
cosocleC2×C8×C11C24
hypercenterC2×#509D11
hypocenterC11C4×#509
LCSG ▷ 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. #135×Dic11C2semidirect
2. C2×D8×Dic11C2semidirect
3. #13070492C2semidirect
4. #13070481C2semidirect
5. SD32×Dic11C2semidirect
6. D16×Dic11C2semidirect
7. #13070404C2semidirect
8. #13070332C2semidirect
9. #13070328C2semidirect
10. M32×Dic11C2semidirect
16. C11×#509C4semidirect
22. Q16×Dic11C22semidirect
23. Q16×Dic11C22semidirect
30. D8×Dic11C22semidirect
31. D8×Dic11C22semidirect
36. #10622202C22semidirect
39. #10622200C22semidirect
40. #10622143C22semidirect
41. #10622142C22semidirect
42. #10622140C22semidirect
43. C16×Dic11C22semidirect
48. C11×#135C2×C4semidirect
53. C2×C11×D8C2×C4semidirect
74. C11×SD32C2×C4semidirect
75. C11×D16C2×C4semidirect
76. C11×M32C2×C4semidirect
117. C11×Q16C22×C4semidirect
123. C11×D8C22×C4semidirect
149. C11×C16C22×C4semidirect
205. #509Dic11direct (N × H)
254. Dic11#509direct (N × H)
259. #135C2×Dic11semidirect
264. C2×D8C2×Dic11semidirect
285. SD32C2×Dic11semidirect
286. D16C2×Dic11semidirect
288. M32C2×Dic11semidirect
333. Q16C22×Dic11semidirect
339. D8C22×Dic11semidirect
366. C16C22×Dic11semidirect
367. C11C4×#509semidirect

Maximal subgroups

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

subgroupindex
#135×Dic112
C2×D8×Dic112
#130704922
#130704812
SD32×Dic112
D16×Dic112
#130704042
#130703322
#130703282
M32×Dic112
C2×C11×#5092
C4×#50911