Finite Group Databasebeta

← C11×#24642 #14601835

Subgroups — C11×#24642 #14601835

Order 2816.

1068 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#459C211yesmaximal, characteristic, complemented
2C2×C11×#442C211yesmaximal, characteristic, complemented
3C11×#2541C211yesmaximal, characteristic, complemented
4C11×#2357C211yesmaximal, characteristic, complemented
5C11×#2054C212yesmaximal, complemented
6C11×#2011C212yesmaximal, complemented
7C11×#1982C212yesmaximal, complemented
8C11×#1961C211yesmaximal, characteristic, complemented
9C11×#1940C211yesmaximal, characteristic, complemented
10C11×#1926C212yesmaximal, complemented
11C11×#1804C211yesmaximal, characteristic, complemented
12C22×C11×D8C2211yescharacteristic
13C22×C11×D8C2212yes—
14C2×C11×#127C2211yescharacteristic
15C2×C11×#127C2212yes—
16C2×C11×#121—22no—
17C2×C4×D4×C11C2211yescharacteristic
18C2×C4×D4×C11C2211yescharacteristic
19C11×#459—24no—
20C11×#442—24no—
21C2×C11×#106C2211yescharacteristic
22C2×C11×C4⋊C8C2211yescharacteristic
23C2×C11×C4⋊C8C2212yes—
24C2×C11×#102C2211yescharacteristic
25C2×C11×#102C2211yescharacteristic
26C2×C11×#102C2212yes—
27C2×C11×#102C2212yes—
28C2×C11×#102C2212yes—
29C2×C11×#102C2212yes—
30C2×C11×#97C2211yescharacteristic
31C11×#392—21no—
32C11×#392—21no—
33C11×#390C2212yes—
34C11×#390C2212yes—
35C11×#388—22no—
36C11×#382C2211yescharacteristic
37C11×#381—21no—
38C4×C11×C4⋊C4C2212yes—
39C4×C11×C4⋊C4C2211yescharacteristic
40C4×C11×C22⋊C4—21no—
41C11×#340C2212yes—
42C11×#336C2212yes—
43C22×D4×C11—21no—
44C22×D4×C11—22no—
45C22×D4×C11—22no—
46C22×D4×C11—21no—
47C22×D4×C11C2312yes—
48C22×D4×C11C2311yescharacteristic
49C22×D4×C11C2311yescharacteristic
50C23×C4×C11—21no—
51C23×C4×C11—21no—
52C2×C11×D8—22no—
53C2×C11×D8—22no—
54C2×C11×D8—24no—
55C2×C11×D8—22no—
56C2×C11×D8—42no—
57C2×C11×D8—42no—
58C22×C8×C11C2312yes—
59C22×C8×C11C2311yescharacteristic
60C22×C8×C11C2311yescharacteristic
61C11×#127—24no—
62C11×#127—22no—
63C11×#127—22no—
64C11×#127—42no—
65C11×#121—48no—
66C4×D4×C11—22no—
67C4×D4×C11—22no—
68C4×D4×C11—22no—
69C4×D4×C11D414yescomplemented
70C2×C11×C4⋊C4D412yes—
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2312yes—
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C22⋊C4—21no—
75C2×C11×C22⋊C4—22no—
76C2×C11×C22⋊C4—21no—
77C2×C11×C22⋊C4—22no—
78C2×C11×C22⋊C4—22no—
79C2×C11×C22⋊C4—22no—
80C2×C42×C11—22no—
81C2×C42×C11C2312yes—
82C2×C42×C11C2311yescharacteristic
83C11×#106—22no—
84C11×C4⋊C8—22no—
85C11×C4⋊C8—42no—
86C11×#102—22no—
87C11×#102—24no—
88C11×#102—22no—
89C11×#102—24no—
90C11×#102—42no—
91C11×#102—42no—
92C11×#97—22no—
93C11×#95—21no—
94C11×#95—22no—
95C11×#95—21no—
96C11×#95D411yescharacteristic
97C11×#95D411yescharacteristic
98#24642C1111yesmaximal, characteristic, direct product factor, Sylow
99C24×C11—21no—
100C24×C11—21no—
101C24×C11—22no—
102C2×D4×C11—21no—
103C2×D4×C11—22no—
104C2×D4×C11—21no—
105C2×D4×C11—21no—
106C2×D4×C11—21no—
107C2×D4×C11—21no—
108C2×D4×C11—21no—
109C2×D4×C11—22no—
110C2×D4×C11—22no—
111C2×D4×C11—22no—
112C2×D4×C11—21no—
113C2×D4×C11—21no—
114C2×D4×C11—21no—
115C2×D4×C11—21no—
116C2×D4×C11—22no—
117C2×D4×C11—22no—
118C2×D4×C11—44no—
119C2×D4×C11—44no—
120C2×D4×C11—44no—
121C2×D4×C11—44no—
122C2×D4×C11—42no—
123C2×D4×C11—42no—
124C2×D4×C11—44no—
125C2×D4×C11—82no—
126C2×D4×C11—82no—
127C2×D4×C11—82no—
128C2×D4×C11C2×D412yes—
129C2×D4×C11#4112yes—
130C22×C4×C11—21no—
131C22×C4×C11—24no—
132C22×C4×C11—22no—
133C22×C4×C11—21no—
134C22×C4×C11—44no—
135C22×C4×C11—42no—
136C22×C4×C11—82no—
137C22×C4×C11C2×D412yes—
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2×D412yes—
141C22×C4×C11C2411yescharacteristic
142C11×D8—28no—
143C11×D8—48no—
144C2×C8×C11—21no—
145C2×C8×C11—21no—
146C2×C8×C11—22no—
147C2×C8×C11—21no—
148C2×C8×C11—21no—
149C2×C8×C11—22no—
150C2×C8×C11—21no—
151C2×C8×C11—22no—
152C2×C8×C11#4112yes—
153C11×C4⋊C4—24no—
154C11×C4⋊C4—21no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4—22no—
157C11×C4⋊C4—21no—
158C11×C4⋊C4—22no—
159C11×C4⋊C4C2×D412yes—
160C11×C22⋊C4—24no—
161C11×C22⋊C4—44no—
162C11×C22⋊C4—42no—
163C11×C22⋊C4—44no—
164C11×C22⋊C4—44no—
165C11×C22⋊C4—82no—
166C42×C11—22no—
167C42×C11—22no—
168C42×C11—82no—
169C42×C11C2×D412yes—
170C42×C11#4112yes—
171C2×#459C2×C1111yescharacteristic, complemented
172C2×#442C2×C1111yescharacteristic, complemented
173#2541C2×C1111yescharacteristic, complemented
174#2357C2×C1111yescharacteristic, complemented
175#2054C2×C1112yescomplemented
176#2011C2×C1112yescomplemented
177#1982C2×C1112yescomplemented
178#1961C2×C1111yescharacteristic, complemented
179#1940C2×C1111yescharacteristic, complemented
180#1926C2×C1112yescomplemented
181#1804C2×C1111yescharacteristic, complemented
182C23×C11—22no—
183C23×C11—22no—
184C23×C11—41no—
185C23×C11—41no—
186C23×C11—41no—
187C23×C11—41no—
188C23×C11—42no—
189C23×C11—42no—
190C23×C11—42no—
191C23×C11—42no—
192C23×C11—42no—
193C23×C11—42no—
194C23×C11—42no—
195C23×C11—42no—
196C23×C11—42no—
197C23×C11—42no—
198C23×C11—42no—
199C23×C11C22×D411yescharacteristic
200D4×C11—22no—
201D4×C11—22no—
202D4×C11—22no—
203D4×C11—22no—
204D4×C11—42no—
205D4×C11—41no—
206D4×C11—42no—
207D4×C11—41no—
208D4×C11—42no—
209D4×C11—41no—
210D4×C11—41no—
211D4×C11—42no—
212D4×C11—88no—
213D4×C11—84no—
214D4×C11—84no—
215D4×C11—88no—
216C2×C4×C11—22no—
217C2×C4×C11—22no—
218C2×C4×C11—22no—
219C2×C4×C11—22no—
220C2×C4×C11—22no—
221C2×C4×C11—22no—
222C2×C4×C11—22no—
223C2×C4×C11—22no—
224C2×C4×C11—42no—
225C2×C4×C11—41no—
226C2×C4×C11—42no—
227C2×C4×C11—42no—
228C2×C4×C11—42no—
229C2×C4×C11—42no—
230C2×C4×C11—84no—
231C2×C4×C11—84no—
232C2×C4×C11#12112yes—
233C2×C4×C11#12112yes—
234C2×C4×C11AGL(1,ℤ/8)14yes—
235C2×C4×C11C22×D411yescharacteristic
236C2×C4×C11C2×#4111yescharacteristic
237C2×C4×C11C2×#4111yescharacteristic
238C2×C4×C11C2×#4111yescharacteristic
239C2×C4×C11H(5,𝔽2)11yescharacteristic
240C2×C4×C11H(5,𝔽2)11yescharacteristic
241C8×C11—22no—
242C8×C11—41no—
243C8×C11—42no—
244C22×D8C22×C1111yescharacteristic
245C22×D8C22×C1112yes—
246C2×#127C22×C1111yescharacteristic
247C2×#127C22×C1112yes—
248C2×#121—22no—
249C2×C4×D4C22×C1111yescharacteristic
250C2×C4×D4C22×C1111yescharacteristic
251#459—24no—
252#442—24no—
253C2×#106C22×C1111yescharacteristic
254C2×C4⋊C8C22×C1111yescharacteristic
255C2×C4⋊C8C22×C1112yes—
256C2×#102C22×C1111yescharacteristic
257C2×#102C22×C1111yescharacteristic
258C2×#102C22×C1112yes—
259C2×#102C22×C1112yes—
260C2×#102C22×C1112yes—
261C2×#102C22×C1112yes—
262C2×#97C22×C1111yescharacteristic
263#392—21no—
264#392—21no—
265#390C22×C1112yes—
266#390C22×C1112yes—
267#388—22no—
268#382C22×C1111yescharacteristic
269#381—21no—
270C4×C4⋊C4C22×C1112yes—
271C4×C4⋊C4C22×C1111yescharacteristic
272C4×C22⋊C4—21no—
273#340C22×C1112yes—
274#336C22×C1112yes—
275C22×C11—42no—
276C22×C11—42no—
277C22×C11—42no—
278C22×C11—42no—
279C22×C11—44no—
280C22×C11—82no—
281C22×C11—82no—
282C22×C11—81no—
283C22×C11—81no—
284C22×C11—82no—
285C22×C11—82no—
286C22×C11—82no—
287C22×C11—82no—
288C22×C11—82no—
289C22×C11—82no—
290C22×C11—82no—
291C22×C11—82no—
292C22×C11C2×#12111yescharacteristic
293C22×C11#54611yescharacteristic
294C22×C11#55011yescharacteristic
295C22×C11C2×AGL(1,ℤ/8)12yes—
296C22×C11#57612yes—
297C4×C11—22no—
298C4×C11—22no—
299C4×C11—24no—
300C4×C11—42no—
301C4×C11—42no—
302C4×C11—82no—
303C4×C11—81no—
304C4×C11#52511yescharacteristic
305C4×C11#53511yescharacteristic
306C4×C11#55311yescharacteristic
307C4×C11#55511yescharacteristic
308C22×D4—21no—
309C22×D4—22no—
310C22×D4—22no—
311C22×D4—21no—
312C22×D4C23×C1112yes—
313C22×D4C23×C1111yescharacteristic
314C22×D4C23×C1111yescharacteristic
315C23×C4—21no—
316C23×C4—21no—
317C2×D8—22no—
318C2×D8—22no—
319C2×D8—24no—
320C2×D8—22no—
321C2×D8—42no—
322C2×D8—42no—
323C22×C8C23×C1112yes—
324C22×C8C23×C1111yescharacteristic
325C22×C8C23×C1111yescharacteristic
326#127—24no—
327#127—22no—
328#127—22no—
329#127—42no—
330#121—48no—
331C4×D4—22no—
332C4×D4—22no—
333C4×D4—22no—
334C4×D4D4×C1114yescomplemented
335C2×C4⋊C4D4×C1112yes—
336C2×C4⋊C4C23×C1111yescharacteristic
337C2×C4⋊C4C23×C1112yes—
338C2×C4⋊C4C23×C1111yescharacteristic
339C2×C22⋊C4—21no—
340C2×C22⋊C4—21no—
341C2×C22⋊C4—22no—
342C2×C22⋊C4—22no—
343C2×C22⋊C4—22no—
344C2×C22⋊C4—22no—
345C2×C42—22no—
346C2×C42C23×C1112yes—
347C2×C42C23×C1111yescharacteristic
348#106—22no—
349C4⋊C8—22no—
350C4⋊C8—42no—
351#102—22no—
352#102—24no—
353#102—22no—
354#102—24no—
355#102—42no—
356#102—42no—
357#97—22no—
358#95—21no—
359#95—22no—
360#95—21no—
361#95D4×C1111yescharacteristic
362#95D4×C1111yescharacteristic
363C2×C11—82no—
364C2×C11—82no—
365C2×C11—162no—
366C2×C11#241411yescharacteristic
367C2×C11#303811yescharacteristic
368C2×C11#304111yescharacteristic
369C2×C11#331812yes—
370C2×C11#339912yes—
371C24—21no—
372C24—21no—
373C24—22no—
374C2×D4—21no—
375C2×D4—22no—
376C2×D4—21no—
377C2×D4—21no—
378C2×D4—21no—
379C2×D4—21no—
380C2×D4—21no—
381C2×D4—22no—
382C2×D4—22no—
383C2×D4—22no—
384C2×D4—21no—
385C2×D4—21no—
386C2×D4—21no—
387C2×D4—21no—
388C2×D4—22no—
389C2×D4—22no—
390C2×D4—44no—
391C2×D4—44no—
392C2×D4—44no—
393C2×D4—44no—
394C2×D4—42no—
395C2×D4—42no—
396C2×D4—44no—
397C2×D4—82no—
398C2×D4—82no—
399C2×D4—82no—
400C2×D4C2×D4×C1112yes—
401C2×D4C11×#4112yes—
402C22×C4—21no—
403C22×C4—24no—
404C22×C4—22no—
405C22×C4—21no—
406C22×C4—44no—
407C22×C4—42no—
408C22×C4—82no—
409C22×C4C2×D4×C1112yes—
410C22×C4C2×D4×C1111yescharacteristic
411C22×C4C2×D4×C1111yescharacteristic
412C22×C4C2×D4×C1112yes—
413C22×C4C24×C1111yescharacteristic
414D8—28no—
415D8—48no—
416C2×C8—21no—
417C2×C8—21no—
418C2×C8—21no—
419C2×C8—22no—
420C2×C8—21no—
421C2×C8—22no—
422C2×C8—21no—
423C2×C8—22no—
424C2×C8C11×#4112yes—
425C4⋊C4—24no—
426C4⋊C4—21no—
427C4⋊C4—21no—
428C4⋊C4—22no—
429C4⋊C4—21no—
430C4⋊C4—22no—
431C4⋊C4C2×D4×C1112yes—
432C22⋊C4—24no—
433C22⋊C4—44no—
434C22⋊C4—42no—
435C22⋊C4—44no—
436C22⋊C4—44no—
437C22⋊C4—82no—
438C42—22no—
439C42—22no—
440C42—82no—
441C42C2×D4×C1112yes—
442C42C11×#4112yes—
443C11#2464211yescharacteristic, direct product factor, Sylow
444C23—22no—
445C23—22no—
446C23—41no—
447C23—41no—
448C23—41no—
449C23—41no—
450C23—42no—
451C23—42no—
452C23—42no—
453C23—42no—
454C23—42no—
455C23—42no—
456C23—42no—
457C23—42no—
458C23—42no—
459C23—42no—
460C23—42no—
461C23C22×D4×C1111yescharacteristic
462D4—22no—
463D4—22no—
464D4—22no—
465D4—22no—
466D4—42no—
467D4—41no—
468D4—42no—
469D4—41no—
470D4—42no—
471D4—41no—
472D4—41no—
473D4—42no—
474D4—88no—
475D4—84no—
476D4—84no—
477D4—88no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—22no—
486C2×C4—42no—
487C2×C4—41no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—84no—
493C2×C4—84no—
494C2×C4C11×#12112yes—
495C2×C4C11×#12112yes—
496C2×C4C11×AGL(1,ℤ/8)14yes—
497C2×C4C22×D4×C1111yescharacteristic
498C2×C4C2×C11×#4111yescharacteristic
499C2×C4C2×C11×#4111yescharacteristic
500C2×C4C2×C11×#4111yescharacteristic
501C2×C4C11×H(5,𝔽2)11yescharacteristic
502C2×C4C11×H(5,𝔽2)11yescharacteristic
503C8—22no—
504C8—42no—
505C8—41no—
506C22—42no—
507C22—42no—
508C22—42no—
509C22—42no—
510C22—44no—
511C22—81no—
512C22—81no—
513C22—82no—
514C22—82no—
515C22—82no—
516C22—82no—
517C22—82no—
518C22—82no—
519C22—82no—
520C22—82no—
521C22—82no—
522C22—82no—
523C22C2×C11×#12111yescharacteristic
524C22C11×#54611yescharacteristic
525C22C11×#55011yescharacteristic
526C22C2×C11×AGL(1,ℤ/8)12yes—
527C22C11×#57612yes—
528C4—22no—
529C4—22no—
530C4—24no—
531C4—42no—
532C4—42no—
533C4—81no—
534C4—82no—
535C4C11×#52511yescharacteristic
536C4C11×#53511yescharacteristic
537C4C11×#55311yescharacteristic
538C4C11×#55511yescharacteristic
539C2—82no—
540C2—82no—
541C2—162no—
542C2C11×#241411yescharacteristic
543C2C11×#303811yescharacteristic
544C2C11×#304111yescharacteristic
545C2C11×#331812yes—
546C2C11×#339912yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C4×C11×C4⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#459C2semidirect
2. C2×C11×#442C2semidirect
3. C11×#2541C2semidirect
4. C11×#2357C2semidirect
5. C11×#2054C2semidirect
6. C11×#2011C2semidirect
7. C11×#1982C2semidirect
8. C11×#1961C2semidirect
9. C11×#1940C2semidirect
10. C11×#1926C2semidirect
11. C11×#1804C2semidirect
69. C4×D4×C11D4semidirect
98. #24642C11direct (N × H)
171. C2×#459C2×C11semidirect
172. C2×#442C2×C11semidirect
173. #2541C2×C11semidirect
174. #2357C2×C11semidirect
175. #2054C2×C11semidirect
176. #2011C2×C11semidirect
177. #1982C2×C11semidirect
178. #1961C2×C11semidirect
179. #1940C2×C11semidirect
180. #1926C2×C11semidirect
181. #1804C2×C11semidirect
334. C4×D4D4×C11semidirect
443. C11#24642direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4592
C2×C11×#4422
C11×#25412
C11×#23572
C11×#20542
C11×#20112
C11×#19822
C11×#19612
C11×#19402
C11×#19262
C11×#18042
#2464211