Finite Group Databasebeta

← D11×#2079 #14782668

Subgroups — D11×#2079 #14782668

Order 2816.

950 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×#106C211yesmaximal, characteristic, complemented
2D11×#417C212yesmaximal
3D11×#408C211yesmaximal, characteristic
4#13070065C212yesmaximal, complemented
5#13070064C212yesmaximal, complemented
6#13070063C211yesmaximal, characteristic, complemented
7#13070062C211yesmaximal, characteristic, complemented
8#13070061C211yesmaximal, characteristic, complemented
9D11×#343C212yesmaximal, complemented
10D11×#341C211yesmaximal, characteristic, complemented
11C11×#2079C211yesmaximal, characteristic, complemented
12C2×#41×D11C2211yescharacteristic
13C2×M16×D11C2212yes—
14C2×M16×D11C2211yescharacteristic
15C22×C8×D11C2211yescharacteristic
16C2×C4⋊C4×D11C2212yes—
17C2×C11×#106C2211yescharacteristic, complemented
18C11×#417C2212yes—
19C11×#408C2211yescharacteristic
20#10622847C2211yescharacteristic
21#10622845C2212yes—
22#10622746C2212yes—
23#10622742C2211yescharacteristic
24#10622723C2211yescharacteristic
25C2×#66881C2211yescharacteristic, complemented
26#10622579C2212yes—
27C2×#66872C2212yescomplemented
28D11×#106—22no—
29D11×#106—22no—
30#10622416—22no—
31D11×#103—22no—
32#10622384—22no—
33D11×#102—22no—
34#10622340—22no—
35D11×C22⋊C8—22no—
36C11×#343C2212yescomplemented
37C11×#341C2211yescharacteristic, complemented
38#10622196C2212yescomplemented
39#10622192C2212yescomplemented
40#10622192C2212yescomplemented
41#10622190C2211yescharacteristic, complemented
42#10622168C2212yescomplemented
43C2×C11×#41C2311yescharacteristic
44#41×D11—24no—
45#41×D11—24no—
46C2×#4343D411yescharacteristic
47C2×Q8×D11D411yescharacteristic
48C2×#4341—21no—
49C2×#4341D411yescharacteristic
50C2×D4×D11—21no—
51C2×D4×D11D411yescharacteristic
52C2×#4339—21no—
53C2×#4339C2311yescharacteristic
54C22×C4×D11—21no—
55C22×C4×D11—22no—
56C22×C4×D11C2311yescharacteristic
57C2×C11×M16C2312yes—
58C2×C11×M16C2311yescharacteristic
59C22×C8×C11C2311yescharacteristic
60C2×C11×C4⋊C4C2312yes—
61C2×C4⋊Dic11C2312yes—
62C2×Dic11⋊C4—22no—
63C2×#4318C2311yescharacteristic
64C2×#4318C2312yes—
65C22×C11⋊C8C2311yescharacteristic
66M16×D11—24no—
67M16×D11—24no—
68M16×D11—24no—
69C2×#4313—21no—
70C2×#4313—22no—
71C2×C8×D11—24no—
72C2×C8×D11—21no—
73C2×C8×D11—22no—
74C2×C8×D11D412yes—
75C2×C8×D11D412yes—
76C4⋊C4×D11—22no—
77C4⋊C4×D11—22no—
78C4⋊C4×D11—22no—
79C4⋊C4×D11—22no—
80C11×#106—22no—
81C11×#103—22no—
82C11×#102—22no—
83C11×C22⋊C8—22no—
84#66899—22no—
85#66896—22no—
86C22⋊(C11⋊C8)—22no—
87#66885—22no—
88(C2×D11)⋊C8—22no—
89(C2×D11)⋊C8—22no—
90#66881—22no—
91#66880—22no—
92#66874—22no—
93#66873—22no—
94#66872—24no—
95C2×#2079—111nomaximal, Sylow
96C23×D11—21no—
97C23×D11#4111yescharacteristic
98C11×#41—22no—
99C11×#41—22no—
100C2×Q8×C11C2×D411yescharacteristic
101C2×D4×C11—21no—
102C2×D4×C11C2×D411yescharacteristic
103C22×C4×C11—21no—
104C22×C4×C11—22no—
105C22×C4×C11C2411yescharacteristic
106C2×C22⋊D11—21no—
107C2×C22⋊D11—21no—
108C2×C22⋊D11—21no—
109C22×Dic11—21no—
110C22×Dic11—22no—
111C22×Dic11#4111yescharacteristic
112#4343—24no—
113Q8×D11—24no—
114#4341—24no—
115#4341—44no—
116D4×D11—24no—
117D4×D11—44no—
118#4339—22no—
119#4339—22no—
120#4339—42no—
121#4339—42no—
122C2×D44—21no—
123C2×D44C2×D411yescharacteristic
124C2×C4×D11—21no—
125C2×C4×D11—21no—
126C2×C4×D11—21no—
127C2×C4×D11—42no—
128C2×C4×D11—42no—
129C2×C4×D11—42no—
130C2×C4×D11—42no—
131C2×C4×D11—84no—
132C2×C4×D11C2×D411yescharacteristic
133C2×C4×D11C2×D411yescharacteristic
134C2×C4×D11C2×D411yescharacteristic
135C2×C4×D11C2×D411yescharacteristic
136C2×C4×D11#4114yes—
137C2×C4×D11#4114yes—
138C2×Dic22—21no—
139C2×Dic22C2×D411yescharacteristic
140C11×M16—22no—
141C11×M16—22no—
142C11×M16—22no—
143C2×C8×C11—22no—
144C2×C8×C11—21no—
145C2×C8×C11—22no—
146C2×C8×C11C2×D412yes—
147C11×C4⋊C4—22no—
148C11×C4⋊C4—22no—
149C4⋊Dic11—22no—
150C4⋊Dic11—22no—
151Dic11⋊C4—42no—
152Dic11⋊C4—42no—
153#4318—22no—
154#4318—22no—
155#4318—22no—
156C2×C11⋊C8—22no—
157C2×C11⋊C8—21no—
158C2×C11⋊C8—22no—
159C2×C11⋊C8C2×D412yes—
160#4313—44no—
161#4313—42no—
162C8×D11—24no—
163C8×D11—24no—
164C8×D11—44no—
165C8×D11—42no—
166C22×#106—111no—
167C2×#417—112no—
168C2×#408—111no—
169#2079—111no—
170#2079—112no—
171#2079—111no—
172#2079—112no—
173#2079—111no—
174#2079D1111yescharacteristic, direct product factor
175C2×#343—112no—
176C2×#341—111no—
177C23×C11—21no—
178C23×C11C2×#4111yescharacteristic
179C22×D11—24no—
180C22×D11—21no—
181C22×D11—42no—
182C22×D11—44no—
183C22×D11#12111yescharacteristic
184C22×D11#12111yescharacteristic
185C22×D11#12614yes—
186Q8×C11—22no—
187D4×C11—22no—
188D4×C11—42no—
189C2×C4×C11—21no—
190C2×C4×C11—41no—
191C2×C4×C11—41no—
192C2×C4×C11—42no—
193C2×C4×C11—82no—
194C2×C4×C11C22×D411yescharacteristic
195C2×C4×C11C22×D411yescharacteristic
196C2×C4×C11C2×#4112yes—
197C2×C4×C11C2×#4112yes—
198C22⋊D11—42no—
199C22⋊D11—42no—
200C22⋊D11—42no—
201C2×Dic11—21no—
202C2×Dic11—42no—
203C2×Dic11—42no—
204C2×Dic11—82no—
205C2×Dic11#12111yescharacteristic
206C2×Dic11#12111yescharacteristic
207C2×Dic11#12614yes—
208D44—22no—
209D44—42no—
210C4×D11—42no—
211C4×D11—41no—
212C4×D11—41no—
213C4×D11—42no—
214C4×D11—84no—
215C4×D11—84no—
216C4×D11#12312yes—
217C4×D11#12312yes—
218C4×D11#12314yes—
219C4×D11#12314yes—
220C4×D11#12412yes—
221C4×D11#12412yes—
222Dic22—22no—
223Dic22—42no—
224C8×C11—22no—
225C8×C11—42no—
226C8×C11—41no—
227C11⋊C8—22no—
228C11⋊C8—42no—
229C11⋊C8—41no—
230C22×#41—111no—
231C22×M16—111no—
232C22×M16—112no—
233C23×C8—111no—
234C22×C4⋊C4—112no—
235C2×#106—111no—
236C2×#106—112no—
237C2×#106—222no—
238C2×#106—222no—
239C2×#106C2×D1111yescharacteristic, complemented
240#417—112no—
241#417—112no—
242#417—112no—
243#417—222no—
244#417—222no—
245#417C2×D1112yes—
246C2×#103—222no—
247C2×#102—222no—
248#408—111no—
249#408—111no—
250#408—111no—
251#408—222no—
252#408C2×D1111yescharacteristic
253C2×C22⋊C8—222no—
254#343—112no—
255#343—112no—
256#343—112no—
257#343C2×D1112yescomplemented
258#341—112no—
259#341—111no—
260#341C2×D1111yescharacteristic, complemented
261C22×C11—22no—
262C22×C11—41no—
263C22×C11—42no—
264C22×C11C2×#12111yescharacteristic
265C22×C11C2×#12612yes—
266C2×D11—22no—
267C2×D11—28no—
268C2×D11—41no—
269C2×D11—42no—
270C2×D11—84no—
271C2×D11#39712yes—
272C2×D11#39712yes—
273C2×D11#47114yes—
274C4×C11—41no—
275C4×C11—82no—
276C4×C11C2×#12311yescharacteristic
277C4×C11C2×#12312yes—
278C4×C11C2×#12411yescharacteristic
279Dic11—41no—
280Dic11—82no—
281Dic11#39712yes—
282Dic11#39712yes—
283C2×#41—111no—
284C2×#41—111no—
285C2×#41—111no—
286C2×#41—221no—
287C2×#41—221no—
288C2×#41—224no—
289C2×#41—224no—
290C2×#41C22×D1111yescharacteristic
291C22×Q8—111no—
292C22×D4—111no—
293C22×D4—221no—
294C23×C4—111no—
295C23×C4—221no—
296C23×C4—222no—
297C2×M16—112no—
298C2×M16—111no—
299C2×M16—221no—
300C2×M16—222no—
301C2×M16—224no—
302C2×M16—224no—
303C2×M16—224no—
304C2×M16C22×D1112yes—
305C2×M16C22×D1111yescharacteristic
306C22×C8—111no—
307C22×C8—112no—
308C22×C8—112no—
309C22×C8—224no—
310C22×C8—221no—
311C22×C8—222no—
312C22×C8C22×D1111yescharacteristic
313C2×C4⋊C4—112no—
314C2×C4⋊C4—222no—
315C2×C4⋊C4—222no—
316C2×C4⋊C4—222no—
317C2×C4⋊C4—222no—
318C2×C4⋊C4—222no—
319C2×C4⋊C4C22×D1112yes—
320#106—22no—
321#106—224no—
322#106—222no—
323#103—22no—
324#103—222no—
325#103—222no—
326#103—222no—
327#102—22no—
328#102—222no—
329#102—222no—
330#102—222no—
331C22⋊C8—22no—
332C22⋊C8—222no—
333C22⋊C8—222no—
334C22⋊C8—222no—
335C2×C11—22no—
336C2×C11—81no—
337C2×C11C2×#39711yescharacteristic
338C2×C11C2×#47112yes—
339D11—22no—
340D11—81no—
341D11#207914yesdirect product factor
342C24—111no—
343C24—221no—
344#41—22no—
345#41—22no—
346#41—224no—
347#41—224no—
348#41—222no—
349#41—222no—
350#41—442no—
351#41—442no—
352#41—444no—
353C2×Q8—111no—
354C2×Q8—221no—
355C2×Q8—224no—
356C2×Q8D4×D1111yescharacteristic
357C2×D4—21no—
358C2×D4—111no—
359C2×D4—221no—
360C2×D4—224no—
361C2×D4—221no—
362C2×D4—221no—
363C2×D4—221no—
364C2×D4—444no—
365C2×D4D4×D1111yescharacteristic
366C22×C4—21no—
367C22×C4—22no—
368C22×C4—111no—
369C22×C4—111no—
370C22×C4—111no—
371C22×C4—111no—
372C22×C4—111no—
373C22×C4—114no—
374C22×C4—114no—
375C22×C4—221no—
376C22×C4—221no—
377C22×C4—221no—
378C22×C4—221no—
379C22×C4—222no—
380C22×C4—442no—
381C22×C4—442no—
382C22×C4—442no—
383C22×C4—442no—
384C22×C4—884no—
385C22×C4C23×D1111yescharacteristic
386M16—22no—
387M16—22no—
388M16—22no—
389M16—222no—
390M16—222no—
391M16—222no—
392M16—444no—
393M16—442no—
394C2×C8—22no—
395C2×C8—21no—
396C2×C8—22no—
397C2×C8—112no—
398C2×C8—224no—
399C2×C8—224no—
400C2×C8—222no—
401C2×C8—221no—
402C2×C8—222no—
403C2×C8—444no—
404C2×C8—442no—
405C2×C8D4×D1112yes—
406C4⋊C4—22no—
407C4⋊C4—22no—
408C4⋊C4—222no—
409C4⋊C4—222no—
410C4⋊C4—442no—
411C4⋊C4—442no—
412C11C2×#207911yescharacteristic, complemented, Sylow
413C23—21no—
414C23—111no—
415C23—114no—
416C23—111no—
417C23—224no—
418C23—221no—
419C23—442no—
420C23—444no—
421C23#41×D1111yescharacteristic
422Q8—22no—
423Q8—222no—
424Q8—442no—
425D4—22no—
426D4—42no—
427D4—222no—
428D4—442no—
429D4—442no—
430D4—442no—
431D4—442no—
432C2×C4—21no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—42no—
436C2×C4—82no—
437C2×C4—114no—
438C2×C4—111no—
439C2×C4—111no—
440C2×C4—112no—
441C2×C4—112no—
442C2×C4—114no—
443C2×C4—114no—
444C2×C4—112no—
445C2×C4—112no—
446C2×C4—221no—
447C2×C4—442no—
448C2×C4—442no—
449C2×C4—442no—
450C2×C4—441no—
451C2×C4—441no—
452C2×C4—442no—
453C2×C4—884no—
454C2×C4—884no—
455C2×C4—882no—
456C2×C4C2×D4×D1111yescharacteristic
457C2×C4C2×D4×D1111yescharacteristic
458C2×C4#41×D1112yes—
459C2×C4#41×D1112yes—
460C8—22no—
461C8—42no—
462C8—41no—
463C8—222no—
464C8—442no—
465C8—441no—
466C22—22no—
467C22—42no—
468C22—41no—
469C22—114no—
470C22—112no—
471C22—112no—
472C22—228no—
473C22—222no—
474C22—442no—
475C22—441no—
476C22—884no—
477C22D11×#12111yescharacteristic
478C22D11×#12612yes—
479C4—41no—
480C4—82no—
481C4—112no—
482C4—112no—
483C4—441no—
484C4—882no—
485C4D11×#12311yescharacteristic
486C4D11×#12312yes—
487C4D11×#12411yescharacteristic
488C2—22no—
489C2—81no—
490C2—114no—
491C2—222no—
492C2—881no—
493C2D11×#39711yescharacteristic
494C2D11×#47112yes—
subgroupG/H
centerC22D11×#121
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2079C2
socleC22×C11C2×#121
prime radicalC2×#41×D11C22
hypercenter#2079D11
hypocenterC11C2×#2079
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #2079

Complements

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

NH ≅ G/Ntype
1. C2×D11×#106C2semidirect
4. #13070065C2semidirect
5. #13070064C2semidirect
6. #13070063C2semidirect
7. #13070062C2semidirect
8. #13070061C2semidirect
9. D11×#343C2semidirect
10. D11×#341C2semidirect
11. C11×#2079C2semidirect
17. C2×C11×#106C22semidirect
25. C2×#66881C22semidirect
27. C2×#66872C22semidirect
36. C11×#343C22semidirect
37. C11×#341C22semidirect
38. #10622196C22semidirect
39. #10622192C22semidirect
40. #10622192C22semidirect
41. #10622190C22semidirect
42. #10622168C22semidirect
174. #2079D11direct (N × H)
239. C2×#106C2×D11semidirect
257. #343C2×D11semidirect
260. #341C2×D11semidirect
341. D11#2079direct (N × H)
412. C11C2×#2079semidirect

Maximal subgroups

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

subgroupindex
C2×D11×#1062
D11×#4172
D11×#4082
#130700652
#130700642
#130700632
#130700622
#130700612
D11×#3432
D11×#3412
C11×#20792
C2×#207911