Finite Group Databasebeta

← D11×#2078 #14782662

Subgroups — D11×#2078 #14782662

Order 2816.

950 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×#107C211yesmaximal, characteristic, complemented
2D11×#417C212yesmaximal
3D11×#408C211yesmaximal, characteristic
4#13070060C212yesmaximal, complemented
5#13070059C212yesmaximal, complemented
6#13070058C211yesmaximal, characteristic, complemented
7#13070057C211yesmaximal, characteristic, complemented
8#13070056C211yesmaximal, characteristic, complemented
9D11×#343C212yesmaximal, complemented
10D11×#341C211yesmaximal, characteristic, complemented
11C11×#2078C211yesmaximal, characteristic, complemented
12C2×#41×D11C2211yescharacteristic
13C2×M16×D11C2212yes—
14C2×M16×D11C2211yescharacteristic
15C22×C8×D11C2211yescharacteristic
16C2×C4⋊C4×D11C2212yes—
17C2×C11×#107C2211yescharacteristic, complemented
18C11×#417C2212yes—
19C11×#408C2211yescharacteristic
20#10622847C2211yescharacteristic
21#10622845C2212yes—
22#10622746C2212yes—
23#10622742C2211yescharacteristic
24#10622723C2211yescharacteristic
25C2×#66882C2211yescharacteristic, complemented
26#10622579C2212yes—
27C2×#66871C2212yescomplemented
28D11×#107—22no—
29D11×#107—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×#107—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#66882—22no—
91#66880—22no—
92#66874—22no—
93#66873—22no—
94#66871—24no—
95C2×#2078—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×#107—111no—
167C2×#417—112no—
168C2×#408—111no—
169#2078—111no—
170#2078—112no—
171#2078—111no—
172#2078—112no—
173#2078—111no—
174#2078D1111yescharacteristic, direct product factor
175C2×#343—112no—
176C2×#341—111no—
177C23×C11—21no—
178C23×C11C2×#4111yescharacteristic
179C22×D11—22no—
180C22×D11—22no—
181C22×D11—21no—
182C22×D11—42no—
183C22×D11—42no—
184C22×D11—42no—
185C22×D11#12111yescharacteristic
186C22×D11#12111yescharacteristic
187C22×D11#12614yes—
188Q8×C11—22no—
189D4×C11—22no—
190D4×C11—42no—
191C2×C4×C11—21no—
192C2×C4×C11—41no—
193C2×C4×C11—41no—
194C2×C4×C11—42no—
195C2×C4×C11—82no—
196C2×C4×C11C22×D411yescharacteristic
197C2×C4×C11C22×D411yescharacteristic
198C2×C4×C11C2×#4112yes—
199C2×C4×C11C2×#4112yes—
200C22⋊D11—42no—
201C22⋊D11—42no—
202C22⋊D11—42no—
203C2×Dic11—21no—
204C2×Dic11—42no—
205C2×Dic11—42no—
206C2×Dic11—82no—
207C2×Dic11#12111yescharacteristic
208C2×Dic11#12111yescharacteristic
209C2×Dic11#12614yes—
210D44—22no—
211D44—42no—
212C4×D11—42no—
213C4×D11—41no—
214C4×D11—41no—
215C4×D11—42no—
216C4×D11—84no—
217C4×D11—84no—
218C4×D11#12312yes—
219C4×D11#12312yes—
220C4×D11#12314yes—
221C4×D11#12314yes—
222C4×D11#12412yes—
223C4×D11#12412yes—
224Dic22—22no—
225Dic22—42no—
226C8×C11—22no—
227C8×C11—42no—
228C8×C11—41no—
229C11⋊C8—22no—
230C11⋊C8—42no—
231C11⋊C8—41no—
232C22×#41—111no—
233C22×M16—111no—
234C22×M16—112no—
235C23×C8—111no—
236C22×C4⋊C4—112no—
237C2×#107—111no—
238C2×#107—112no—
239C2×#107—222no—
240C2×#107—222no—
241C2×#107C2×D1111yescharacteristic, complemented
242#417—112no—
243#417—112no—
244#417—112no—
245#417—222no—
246#417—222no—
247#417C2×D1112yes—
248C2×#103—222no—
249C2×#102—222no—
250#408—111no—
251#408—111no—
252#408—111no—
253#408—222no—
254#408C2×D1111yescharacteristic
255C2×C22⋊C8—222no—
256#343—112no—
257#343—112no—
258#343—112no—
259#343C2×D1112yescomplemented
260#341—112no—
261#341—111no—
262#341C2×D1111yescharacteristic, complemented
263C22×C11—21no—
264C22×C11—21no—
265C22×C11—41no—
266C22×C11—41no—
267C22×C11—41no—
268C22×C11C2×#12111yescharacteristic
269C22×C11C2×#12612yes—
270C2×D11—21no—
271C2×D11—21no—
272C2×D11—28no—
273C2×D11—41no—
274C2×D11—41no—
275C2×D11—41no—
276C2×D11—84no—
277C2×D11#39712yes—
278C2×D11#39712yes—
279C2×D11#47212yes—
280C2×D11#47312yes—
281C4×C11—41no—
282C4×C11—82no—
283C4×C11C2×#12311yescharacteristic
284C4×C11C2×#12312yes—
285C4×C11C2×#12411yescharacteristic
286Dic11—41no—
287Dic11—82no—
288Dic11#39712yes—
289Dic11#39712yes—
290C2×#41—111no—
291C2×#41—111no—
292C2×#41—111no—
293C2×#41—221no—
294C2×#41—221no—
295C2×#41—224no—
296C2×#41—224no—
297C2×#41C22×D1111yescharacteristic
298C22×Q8—111no—
299C22×D4—111no—
300C22×D4—221no—
301C23×C4—111no—
302C23×C4—221no—
303C23×C4—222no—
304C2×M16—112no—
305C2×M16—111no—
306C2×M16—221no—
307C2×M16—222no—
308C2×M16—224no—
309C2×M16—224no—
310C2×M16—224no—
311C2×M16C22×D1112yes—
312C2×M16C22×D1111yescharacteristic
313C22×C8—111no—
314C22×C8—112no—
315C22×C8—112no—
316C22×C8—224no—
317C22×C8—221no—
318C22×C8—222no—
319C22×C8C22×D1111yescharacteristic
320C2×C4⋊C4—112no—
321C2×C4⋊C4—222no—
322C2×C4⋊C4—222no—
323C2×C4⋊C4—222no—
324C2×C4⋊C4—222no—
325C2×C4⋊C4—222no—
326C2×C4⋊C4C22×D1112yes—
327#107—22no—
328#107—224no—
329#107—222no—
330#103—22no—
331#103—222no—
332#103—222no—
333#103—222no—
334#102—22no—
335#102—222no—
336#102—222no—
337#102—222no—
338C22⋊C8—22no—
339C22⋊C8—222no—
340C22⋊C8—222no—
341C22⋊C8—222no—
342C2×C11—22no—
343C2×C11—81no—
344C2×C11C2×#39711yescharacteristic
345C2×C11C2×#47211yescharacteristic
346C2×C11C2×#47311yescharacteristic
347D11—22no—
348D11—81no—
349D11#207814yesdirect product factor
350C24—111no—
351C24—221no—
352#41—22no—
353#41—22no—
354#41—224no—
355#41—224no—
356#41—222no—
357#41—222no—
358#41—442no—
359#41—442no—
360#41—444no—
361C2×Q8—111no—
362C2×Q8—221no—
363C2×Q8—224no—
364C2×Q8D4×D1111yescharacteristic
365C2×D4—21no—
366C2×D4—111no—
367C2×D4—221no—
368C2×D4—224no—
369C2×D4—221no—
370C2×D4—221no—
371C2×D4—221no—
372C2×D4—444no—
373C2×D4D4×D1111yescharacteristic
374C22×C4—21no—
375C22×C4—22no—
376C22×C4—111no—
377C22×C4—111no—
378C22×C4—111no—
379C22×C4—111no—
380C22×C4—111no—
381C22×C4—114no—
382C22×C4—114no—
383C22×C4—221no—
384C22×C4—221no—
385C22×C4—221no—
386C22×C4—221no—
387C22×C4—222no—
388C22×C4—442no—
389C22×C4—442no—
390C22×C4—442no—
391C22×C4—442no—
392C22×C4—884no—
393C22×C4C23×D1111yescharacteristic
394M16—22no—
395M16—22no—
396M16—22no—
397M16—222no—
398M16—222no—
399M16—222no—
400M16—444no—
401M16—442no—
402C2×C8—22no—
403C2×C8—21no—
404C2×C8—22no—
405C2×C8—112no—
406C2×C8—224no—
407C2×C8—224no—
408C2×C8—222no—
409C2×C8—221no—
410C2×C8—222no—
411C2×C8—444no—
412C2×C8—442no—
413C2×C8D4×D1112yes—
414C4⋊C4—22no—
415C4⋊C4—22no—
416C4⋊C4—222no—
417C4⋊C4—222no—
418C4⋊C4—442no—
419C4⋊C4—442no—
420C11C2×#207811yescharacteristic, complemented, Sylow
421C23—21no—
422C23—111no—
423C23—114no—
424C23—111no—
425C23—222no—
426C23—222no—
427C23—221no—
428C23—442no—
429C23—442no—
430C23—442no—
431C23#41×D1111yescharacteristic
432Q8—22no—
433Q8—222no—
434Q8—442no—
435D4—22no—
436D4—42no—
437D4—222no—
438D4—442no—
439D4—442no—
440D4—442no—
441D4—442no—
442C2×C4—21no—
443C2×C4—41no—
444C2×C4—41no—
445C2×C4—42no—
446C2×C4—82no—
447C2×C4—114no—
448C2×C4—111no—
449C2×C4—111no—
450C2×C4—112no—
451C2×C4—112no—
452C2×C4—114no—
453C2×C4—114no—
454C2×C4—112no—
455C2×C4—112no—
456C2×C4—221no—
457C2×C4—442no—
458C2×C4—442no—
459C2×C4—442no—
460C2×C4—441no—
461C2×C4—441no—
462C2×C4—442no—
463C2×C4—884no—
464C2×C4—884no—
465C2×C4—882no—
466C2×C4C2×D4×D1111yescharacteristic
467C2×C4C2×D4×D1111yescharacteristic
468C2×C4#41×D1112yes—
469C2×C4#41×D1112yes—
470C8—22no—
471C8—42no—
472C8—41no—
473C8—222no—
474C8—442no—
475C8—441no—
476C22—21no—
477C22—21no—
478C22—41no—
479C22—41no—
480C22—41no—
481C22—112no—
482C22—112no—
483C22—112no—
484C22—112no—
485C22—228no—
486C22—221no—
487C22—221no—
488C22—441no—
489C22—441no—
490C22—441no—
491C22—884no—
492C22D11×#12111yescharacteristic
493C22D11×#12612yes—
494C4—41no—
495C4—82no—
496C4—112no—
497C4—112no—
498C4—441no—
499C4—882no—
500C4D11×#12311yescharacteristic
501C4D11×#12312yes—
502C4D11×#12411yescharacteristic
503C2—22no—
504C2—81no—
505C2—114no—
506C2—222no—
507C2—881no—
508C2D11×#39711yescharacteristic
509C2D11×#47211yescharacteristic
510C2D11×#47311yescharacteristic
subgroupG/H
centerC22D11×#121
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2078C2
socleC22×C11C2×#121
prime radicalC2×#41×D11C22
hypercenter#2078D11
hypocenterC11C2×#2078
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #2078

Complements

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

NH ≅ G/Ntype
1. C2×D11×#107C2semidirect
4. #13070060C2semidirect
5. #13070059C2semidirect
6. #13070058C2semidirect
7. #13070057C2semidirect
8. #13070056C2semidirect
9. D11×#343C2semidirect
10. D11×#341C2semidirect
11. C11×#2078C2semidirect
17. C2×C11×#107C22semidirect
25. C2×#66882C22semidirect
27. C2×#66871C22semidirect
36. C11×#343C22semidirect
37. C11×#341C22semidirect
38. #10622196C22semidirect
39. #10622192C22semidirect
40. #10622192C22semidirect
41. #10622190C22semidirect
42. #10622168C22semidirect
174. #2078D11direct (N × H)
241. C2×#107C2×D11semidirect
259. #343C2×D11semidirect
262. #341C2×D11semidirect
349. D11#2078direct (N × H)
420. C11C2×#2078semidirect

Maximal subgroups

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

subgroupindex
C2×D11×#1072
D11×#4172
D11×#4082
#130700602
#130700592
#130700582
#130700572
#130700562
D11×#3432
D11×#3412
C11×#20782
C2×#207811