Finite Group Databasebeta

← C11×#25567 #14602760

Subgroups — C11×#25567 #14602760

Order 2816.

1522 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#547C211yesmaximal, characteristic, complemented
2C2×C11×#486C211yesmaximal, characteristic, complemented
3C2×C11×#459C211yesmaximal, characteristic, complemented
4C11×#2541C211yesmaximal, characteristic, complemented
5C11×#1999C214yesmaximal, complemented
6C11×#1988C211yesmaximal, characteristic, complemented
7C11×#1954C211yesmaximal, characteristic, complemented
8C11×#1874C214yesmaximal, complemented
9C4×C11×#102C211yesmaximal, characteristic, complemented
10C22×C11×#41—21no—
11C22×C11×D8C2212yes—
12C11×#547—24no—
13C11×#547—24no—
14C2×C11×C4⋊Q8C2211yescharacteristic
15C2×C11×#127—21no—
16C2×C11×#127C2211yescharacteristic
17C2×C11×#123—22no—
18C2×C11×C22⋊Q8—21no—
19C2×C11×#121C2212yes—
20C2×C11×#121C2214yes—
21C2×C4×D4×C11C2211yescharacteristic
22C2×C4×D4×C11C2211yescharacteristic
23C22×C11×C4⋊C4C2212yes—
24C11×#486—24no—
25C11×#459—24no—
26C2×C11×C4⋊C8C2211yescharacteristic
27C2×C11×#102C2212yes—
28C2×C11×#102C2214yes—
29C2×C11×#102C2212yes—
30C2×C11×C22⋊C8C2214yes—
31C2×C4×C8×C11C2211yescharacteristic
32C11×#392—22no—
33C11×#390—21no—
34C4×C11×C4⋊C4C2211yescharacteristic
35C11×#340C2212yes—
36C11×#340C2214yes—
37C2×C11×#41—28no—
38C2×C11×#41—44no—
39C2×C11×#41—44no—
40C22×Q8×C11—21no—
41C22×D4×C11—22no—
42C22×D4×C11—24no—
43C22×D4×C11—21no—
44C22×D4×C11—21no—
45C22×D4×C11D411yescharacteristic
46C22×D4×C11C2312yes—
47C22×D4×C11C2311yescharacteristic
48C23×C4×C11—22no—
49C23×C4×C11—21no—
50C23×C4×C11C2312yes—
51C2×C11×D8—24no—
52C2×C11×D8—44no—
53C22×C8×C11C2312yes—
54C22×C8×C11C2312yes—
55C11×C4⋊Q8—22no—
56C11×C4⋊Q8D414yescomplemented
57C11×#127—22no—
58C11×#127—22no—
59C11×#127—44no—
60C11×#123—216no—
61C11×C22⋊Q8—28no—
62C11×#121—24no—
63C11×#121—24no—
64C11×#121—28no—
65C11×#121—44no—
66C4×D4×C11—22no—
67C4×D4×C11—22no—
68C4×D4×C11—22no—
69C4×D4×C11D414yescomplemented
70C2×C11×C4⋊C4—22no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—24no—
73C2×C11×C4⋊C4—24no—
74C2×C11×C4⋊C4D411yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C4⋊C4C2312yes—
77C2×C11×C4⋊C4C2312yes—
78C2×C11×C22⋊C4—21no—
79C2×C11×C22⋊C4—22no—
80C2×C11×C22⋊C4—24no—
81C2×C11×C22⋊C4D412yes—
82C2×C42×C11—21no—
83C2×C42×C11C2311yescharacteristic
84C11×C4⋊C8—22no—
85C11×#102—24no—
86C11×#102—28no—
87C11×#102—24no—
88C11×C22⋊C8—44no—
89C4×C8×C11—22no—
90C11×#95—21no—
91#25567C1111yesmaximal, characteristic, direct product factor, Sylow
92C24×C11—21no—
93C24×C11—22no—
94C24×C11C2×D412yes—
95C11×#41—432no—
96C2×Q8×C11—24no—
97C2×Q8×C11—42no—
98C2×Q8×C11—42no—
99C2×D4×C11—28no—
100C2×D4×C11—22no—
101C2×D4×C11—22no—
102C2×D4×C11—21no—
103C2×D4×C11—22no—
104C2×D4×C11—22no—
105C2×D4×C11—22no—
106C2×D4×C11—24no—
107C2×D4×C11—22no—
108C2×D4×C11—24no—
109C2×D4×C11—48no—
110C2×D4×C11—44no—
111C2×D4×C11—44no—
112C2×D4×C11—48no—
113C2×D4×C11—42no—
114C2×D4×C11—42no—
115C2×D4×C11—42no—
116C2×D4×C11—42no—
117C2×D4×C11—82no—
118C2×D4×C11—84no—
119C2×D4×C11D814yescomplemented
120C2×D4×C11C2×D412yes—
121C22×C4×C11—28no—
122C22×C4×C11—22no—
123C22×C4×C11—21no—
124C22×C4×C11—22no—
125C22×C4×C11—24no—
126C22×C4×C11—22no—
127C22×C4×C11—22no—
128C22×C4×C11—24no—
129C22×C4×C11—24no—
130C22×C4×C11—44no—
131C22×C4×C11—44no—
132C22×C4×C11—42no—
133C22×C4×C11—42no—
134C22×C4×C11C2×D412yes—
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2411yescharacteristic
138C11×D8—48no—
139C2×C8×C11—22no—
140C2×C8×C11—22no—
141C2×C8×C11—22no—
142C2×C8×C11—22no—
143C2×C8×C11—24no—
144C11×C4⋊C4—28no—
145C11×C4⋊C4—24no—
146C11×C4⋊C4—22no—
147C11×C4⋊C4—21no—
148C11×C4⋊C4—22no—
149C11×C4⋊C4—22no—
150C11×C4⋊C4C2×D412yes—
151C11×C4⋊C4C2×D414yes—
152C11×C4⋊C4#4114yescomplemented
153C11×C22⋊C4—28no—
154C11×C22⋊C4—24no—
155C11×C22⋊C4—24no—
156C11×C22⋊C4—48no—
157C42×C11—42no—
158C42×C11C2×D412yes—
159C42×C11C2×D412yes—
160C2×#547C2×C1111yescharacteristic, complemented
161C2×#486C2×C1111yescharacteristic, complemented
162C2×#459C2×C1111yescharacteristic, complemented
163#2541C2×C1111yescharacteristic, complemented
164#1999C2×C1114yescomplemented
165#1988C2×C1111yescharacteristic, complemented
166#1954C2×C1111yescharacteristic, complemented
167#1874C2×C1114yescomplemented
168C4×#102C2×C1111yescharacteristic, complemented
169C23×C11—22no—
170C23×C11—24no—
171C23×C11—22no—
172C23×C11—24no—
173C23×C11—22no—
174C23×C11—42no—
175C23×C11—41no—
176C23×C11—41no—
177C23×C11—42no—
178C23×C11—42no—
179C23×C11—44no—
180C23×C11—42no—
181C23×C11—42no—
182C23×C11—44no—
183C23×C11C2×D814yes—
184C23×C11C22×D411yescharacteristic
185Q8×C11—48no—
186D4×C11—22no—
187D4×C11—22no—
188D4×C11—28no—
189D4×C11—416no—
190D4×C11—42no—
191D4×C11—42no—
192D4×C11—42no—
193D4×C11—44no—
194D4×C11—84no—
195D4×C11—816no—
196D4×C11—84no—
197C2×C4×C11—22no—
198C2×C4×C11—22no—
199C2×C4×C11—22no—
200C2×C4×C11—24no—
201C2×C4×C11—24no—
202C2×C4×C11—24no—
203C2×C4×C11—416no—
204C2×C4×C11—42no—
205C2×C4×C11—41no—
206C2×C4×C11—42no—
207C2×C4×C11—41no—
208C2×C4×C11—42no—
209C2×C4×C11—42no—
210C2×C4×C11—42no—
211C2×C4×C11—42no—
212C2×C4×C11—44no—
213C2×C4×C11—48no—
214C2×C4×C11#12012yes—
215C2×C4×C11#12012yes—
216C2×C4×C11C2×D812yes—
217C2×C4×C11AGL(1,ℤ/8)12yes—
218C2×C4×C11C22×D411yescharacteristic
219C2×C4×C11C22×D411yescharacteristic
220C2×C4×C11C2×#4112yes—
221C2×C4×C11H(5,𝔽2)12yes—
222C8×C11—42no—
223C8×C11—42no—
224C22×#41—21no—
225C22×D8C22×C1112yes—
226#547—24no—
227#547—24no—
228C2×C4⋊Q8C22×C1111yescharacteristic
229C2×#127—21no—
230C2×#127C22×C1111yescharacteristic
231C2×#123—22no—
232C2×C22⋊Q8—21no—
233C2×#121C22×C1112yes—
234C2×#121C22×C1114yes—
235C2×C4×D4C22×C1111yescharacteristic
236C2×C4×D4C22×C1111yescharacteristic
237C22×C4⋊C4C22×C1112yes—
238#486—24no—
239#459—24no—
240C2×C4⋊C8C22×C1111yescharacteristic
241C2×#102C22×C1114yes—
242C2×#102C22×C1112yes—
243C2×#102C22×C1112yes—
244C2×C22⋊C8C22×C1114yes—
245C2×C4×C8C22×C1111yescharacteristic
246#392—22no—
247#390—21no—
248C4×C4⋊C4C22×C1111yescharacteristic
249#340C22×C1112yes—
250#340C22×C1114yes—
251C22×C11—24no—
252C22×C11—28no—
253C22×C11—44no—
254C22×C11—42no—
255C22×C11—42no—
256C22×C11—42no—
257C22×C11—42no—
258C22×C11—42no—
259C22×C11—82no—
260C22×C11—82no—
261C22×C11—84no—
262C22×C11—82no—
263C22×C11—82no—
264C22×C11—82no—
265C22×C11—84no—
266C22×C11C2×#12011yescharacteristic
267C22×C11#54612yes—
268C22×C11C22×D811yescharacteristic
269C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
270C22×C11#57712yes—
271C4×C11—22no—
272C4×C11—42no—
273C4×C11—42no—
274C4×C11—44no—
275C4×C11—44no—
276C4×C11#44714yes—
277C4×C11#53211yescharacteristic
278C4×C11#53511yescharacteristic
279C4×C11#55012yes—
280C2×#41—28no—
281C2×#41—44no—
282C2×#41—44no—
283C22×Q8—21no—
284C22×D4—22no—
285C22×D4—24no—
286C22×D4—21no—
287C22×D4—21no—
288C22×D4D4×C1111yescharacteristic
289C22×D4C23×C1112yes—
290C22×D4C23×C1111yescharacteristic
291C23×C4—22no—
292C23×C4—21no—
293C23×C4C23×C1112yes—
294C2×D8—24no—
295C2×D8—44no—
296C22×C8C23×C1112yes—
297C22×C8C23×C1112yes—
298C4⋊Q8—22no—
299C4⋊Q8D4×C1114yescomplemented
300#127—22no—
301#127—22no—
302#127—44no—
303#123—216no—
304C22⋊Q8—28no—
305#121—24no—
306#121—24no—
307#121—28no—
308#121—44no—
309C4×D4—22no—
310C4×D4—22no—
311C4×D4—22no—
312C4×D4D4×C1114yescomplemented
313C2×C4⋊C4—22no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4—24no—
316C2×C4⋊C4—24no—
317C2×C4⋊C4D4×C1111yescharacteristic
318C2×C4⋊C4C23×C1111yescharacteristic
319C2×C4⋊C4C23×C1112yes—
320C2×C4⋊C4C23×C1112yes—
321C2×C22⋊C4—21no—
322C2×C22⋊C4—22no—
323C2×C22⋊C4—24no—
324C2×C22⋊C4D4×C1112yes—
325C2×C42—21no—
326C2×C42C23×C1111yescharacteristic
327C4⋊C8—22no—
328#102—24no—
329#102—28no—
330#102—24no—
331C22⋊C8—44no—
332C4×C8—22no—
333#95—21no—
334C2×C11—44no—
335C2×C11—82no—
336C2×C11—162no—
337C2×C11#243111yescharacteristic
338C2×C11C2×#44711yescharacteristic
339C2×C11#301011yescharacteristic
340C2×C11#329412yes—
341C2×C11#333212yes—
342C24—21no—
343C24—22no—
344C24C2×D4×C1112yes—
345#41—432no—
346C2×Q8—24no—
347C2×Q8—42no—
348C2×Q8—42no—
349C2×D4—28no—
350C2×D4—22no—
351C2×D4—22no—
352C2×D4—21no—
353C2×D4—22no—
354C2×D4—22no—
355C2×D4—22no—
356C2×D4—24no—
357C2×D4—22no—
358C2×D4—24no—
359C2×D4—48no—
360C2×D4—44no—
361C2×D4—44no—
362C2×D4—48no—
363C2×D4—42no—
364C2×D4—42no—
365C2×D4—42no—
366C2×D4—42no—
367C2×D4—82no—
368C2×D4—84no—
369C2×D4C11×D814yescomplemented
370C2×D4C2×D4×C1112yes—
371C22×C4—28no—
372C22×C4—22no—
373C22×C4—21no—
374C22×C4—22no—
375C22×C4—24no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—24no—
379C22×C4—24no—
380C22×C4—44no—
381C22×C4—44no—
382C22×C4—42no—
383C22×C4—42no—
384C22×C4C2×D4×C1112yes—
385C22×C4C2×D4×C1111yescharacteristic
386C22×C4C2×D4×C1111yescharacteristic
387C22×C4C24×C1111yescharacteristic
388D8—48no—
389C2×C8—22no—
390C2×C8—22no—
391C2×C8—22no—
392C2×C8—22no—
393C2×C8—24no—
394C4⋊C4—28no—
395C4⋊C4—24no—
396C4⋊C4—22no—
397C4⋊C4—21no—
398C4⋊C4—22no—
399C4⋊C4—22no—
400C4⋊C4C2×D4×C1112yes—
401C4⋊C4C2×D4×C1114yes—
402C4⋊C4C11×#4114yescomplemented
403C22⋊C4—28no—
404C22⋊C4—24no—
405C22⋊C4—24no—
406C22⋊C4—48no—
407C42—42no—
408C42C2×D4×C1112yes—
409C42C2×D4×C1112yes—
410C11#2556711yescharacteristic, direct product factor, Sylow
411C23—22no—
412C23—24no—
413C23—22no—
414C23—24no—
415C23—22no—
416C23—42no—
417C23—41no—
418C23—41no—
419C23—42no—
420C23—42no—
421C23—44no—
422C23—42no—
423C23—42no—
424C23—44no—
425C23C2×C11×D814yes—
426C23C22×D4×C1111yescharacteristic
427Q8—48no—
428D4—22no—
429D4—22no—
430D4—28no—
431D4—416no—
432D4—42no—
433D4—42no—
434D4—42no—
435D4—44no—
436D4—84no—
437D4—816no—
438D4—84no—
439C2×C4—22no—
440C2×C4—22no—
441C2×C4—22no—
442C2×C4—24no—
443C2×C4—24no—
444C2×C4—24no—
445C2×C4—416no—
446C2×C4—42no—
447C2×C4—41no—
448C2×C4—42no—
449C2×C4—41no—
450C2×C4—42no—
451C2×C4—42no—
452C2×C4—42no—
453C2×C4—42no—
454C2×C4—44no—
455C2×C4—48no—
456C2×C4C11×#12012yes—
457C2×C4C11×#12012yes—
458C2×C4C2×C11×D812yes—
459C2×C4C11×AGL(1,ℤ/8)12yes—
460C2×C4C22×D4×C1111yescharacteristic
461C2×C4C22×D4×C1111yescharacteristic
462C2×C4C2×C11×#4112yes—
463C2×C4C11×H(5,𝔽2)12yes—
464C8—42no—
465C8—42no—
466C22—24no—
467C22—28no—
468C22—42no—
469C22—42no—
470C22—44no—
471C22—42no—
472C22—42no—
473C22—42no—
474C22—82no—
475C22—82no—
476C22—82no—
477C22—82no—
478C22—82no—
479C22—84no—
480C22—84no—
481C22C2×C11×#12011yescharacteristic
482C22C11×#54612yes—
483C22C22×C11×D811yescharacteristic
484C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
485C22C11×#57712yes—
486C4—22no—
487C4—42no—
488C4—42no—
489C4—44no—
490C4—44no—
491C4C11×#44714yes—
492C4C11×#53211yescharacteristic
493C4C11×#53511yescharacteristic
494C4C11×#55012yes—
495C2—44no—
496C2—82no—
497C2—162no—
498C2C11×#243111yescharacteristic
499C2C2×C11×#44711yescharacteristic
500C2C11×#301011yescharacteristic
501C2C11×#329412yes—
502C2C11×#333212yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C4×D4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#547C2semidirect
2. C2×C11×#486C2semidirect
3. C2×C11×#459C2semidirect
4. C11×#2541C2semidirect
5. C11×#1999C2semidirect
6. C11×#1988C2semidirect
7. C11×#1954C2semidirect
8. C11×#1874C2semidirect
9. C4×C11×#102C2semidirect
56. C11×C4⋊Q8D4semidirect
69. C4×D4×C11D4semidirect
91. #25567C11direct (N × H)
119. C2×D4×C11D8semidirect
152. C11×C4⋊C4#41semidirect
160. C2×#547C2×C11semidirect
161. C2×#486C2×C11semidirect
162. C2×#459C2×C11semidirect
163. #2541C2×C11semidirect
164. #1999C2×C11semidirect
165. #1988C2×C11semidirect
166. #1954C2×C11semidirect
167. #1874C2×C11semidirect
168. C4×#102C2×C11semidirect
299. C4⋊Q8D4×C11semidirect
312. C4×D4D4×C11semidirect
369. C2×D4C11×D8semidirect
402. C4⋊C4C11×#41semidirect
410. C11#25567direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5472
C2×C11×#4862
C2×C11×#4592
C11×#25412
C11×#19992
C11×#19882
C11×#19542
C11×#18742
C4×C11×#1022
#2556711