Finite Group Databasebeta

← C11×#22272 #14599465

Subgroups — C11×#22272 #14599465

Order 2816.

1074 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#496C211yesmaximal, characteristic
2C4×C11×#127C211yesmaximal, characteristic, complemented
3C4×C11×#124C211yesmaximal, characteristic, complemented
4C11×#1961C211yesmaximal, characteristic, complemented
5C11×#1959C211yesmaximal, characteristic, complemented
6C11×#1880C212yesmaximal, complemented
7C11×#1879C212yesmaximal, complemented
8C11×#1879C212yesmaximal, complemented
9C11×#1877C212yesmaximal, complemented
10C11×#1836C211yesmaximal, characteristic, complemented
11C11×#1745C211yesmaximal, characteristic, complemented
12C22×C11×SD16C2212yes—
13C22×C11×D8C2212yes—
14C2×C11×#127C2211yescharacteristic
15C2×C11×#124C2211yescharacteristic
16C2×C4×Q8×C11C2211yescharacteristic
17C2×C4×D4×C11—21no—
18C2×C4×D4×C11—21no—
19C2×C4×D4×C11C2212yes—
20C2×C4×D4×C11C2211yescharacteristic
21C11×#496C418yescomplemented
22C2×C11×#103C2212yes—
23C2×C11×#102C2212yes—
24C2×C11×#102C2212yes—
25C2×C11×#102C2212yes—
26C2×C11×#97C2211yescharacteristic
27C2×C11×#97C2211yescharacteristic
28C11×#391C2211yescharacteristic
29C11×#390—21no—
30C11×#390—21no—
31C11×#390C2211yescharacteristic
32C11×#390C2212yes—
33C11×#388—21no—
34C11×#388—21no—
35C11×#384C2211yescharacteristic
36C11×#382C2211yescharacteristic
37C4×C11×C22⋊C4—21no—
38C4×C11×C22⋊C4—21no—
39C43×C11C2211yescharacteristic
40C11×#340C2212yes—
41C11×#340C2212yes—
42C11×#336C2212yes—
43C11×#336C2212yes—
44C22×Q8×C11C2311yescharacteristic
45C22×D4×C11—21no—
46C22×D4×C11—21no—
47C22×D4×C11C2311yescharacteristic
48C22×D4×C11C2312yes—
49C23×C4×C11—21no—
50C23×C4×C11—22no—
51C2×C11×SD16—42no—
52C2×C11×SD16—42no—
53C2×C11×SD16C2×C418yescomplemented
54C2×C11×D8—42no—
55C2×C11×D8—42no—
56C2×C11×D8C2×C418yescomplemented
57C22×C8×C11C2312yes—
58C22×C8×C11C2312yes—
59C11×#127—22no—
60C11×#127C2×C414yescomplemented
61C11×#124—22no—
62C11×#124C2×C414yescomplemented
63C4×Q8×C11—42no—
64C4×D4×C11—42no—
65C4×D4×C11—42no—
66C4×D4×C11—42no—
67C4×D4×C11—44no—
68C4×D4×C11—44no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2312yes—
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C22⋊C4—21no—
76C2×C11×C22⋊C4—21no—
77C2×C11×C22⋊C4—21no—
78C2×C11×C22⋊C4—21no—
79C2×C11×C22⋊C4—22no—
80C2×C11×C22⋊C4—22no—
81C2×C11×C22⋊C4—21no—
82C2×C11×C22⋊C4—22no—
83C2×C42×C11—21no—
84C2×C42×C11D411yescharacteristic
85C2×C42×C11D411yescharacteristic
86C2×C42×C11D411yescharacteristic
87C2×C42×C11D411yescharacteristic
88C2×C42×C11C2311yescharacteristic
89C2×C42×C11C2311yescharacteristic
90C2×C42×C11C2311yescharacteristic
91C11×#103—42no—
92C11×#102—42no—
93C11×#102—42no—
94C11×#102—42no—
95C11×#97—22no—
96C11×#97C2×C414yescomplemented
97C11×#95—21no—
98C11×#95—21no—
99C11×#95—21no—
100C11×#95—21no—
101#22272C1111yesmaximal, characteristic, direct product factor, Sylow
102C24×C11—21no—
103C24×C11—22no—
104C2×Q8×C11—21no—
105C2×Q8×C11—22no—
106C2×Q8×C11—22no—
107C2×Q8×C11C22×C412yes—
108C2×D4×C11—24no—
109C2×D4×C11—24no—
110C2×D4×C11—21no—
111C2×D4×C11—22no—
112C2×D4×C11—22no—
113C2×D4×C11—22no—
114C2×D4×C11—22no—
115C2×D4×C11—22no—
116C2×D4×C11—22no—
117C2×D4×C11—22no—
118C2×D4×C11—42no—
119C2×D4×C11—42no—
120C2×D4×C11—42no—
121C2×D4×C11—42no—
122C2×D4×C11C22×C412yes—
123C2×D4×C11C22×C414yes—
124C22×C4×C11—21no—
125C22×C4×C11—21no—
126C22×C4×C11—21no—
127C22×C4×C11—22no—
128C22×C4×C11—42no—
129C22×C4×C11—44no—
130C22×C4×C11—44no—
131C22×C4×C11—42no—
132C22×C4×C11—44no—
133C22×C4×C11—42no—
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2411yescharacteristic
141C11×SD16—48no—
142C11×D8—48no—
143C2×C8×C11—22no—
144C2×C8×C11—22no—
145C2×C8×C11—22no—
146C2×C8×C11—22no—
147C2×C8×C11—22no—
148C2×C8×C11C22×C414yes—
149C11×C4⋊C4—22no—
150C11×C4⋊C4—22no—
151C11×C4⋊C4—22no—
152C11×C4⋊C4—22no—
153C11×C4⋊C4—42no—
154C11×C4⋊C4—42no—
155C11×C4⋊C4—42no—
156C11×C22⋊C4—24no—
157C11×C22⋊C4—24no—
158C11×C22⋊C4—42no—
159C11×C22⋊C4—44no—
160C11×C22⋊C4—42no—
161C11×C22⋊C4—44no—
162C11×C22⋊C4—42no—
163C11×C22⋊C4—44no—
164C42×C11—22no—
165C42×C11—22no—
166C42×C11—22no—
167C42×C11—22no—
168C42×C11—41no—
169C42×C11—41no—
170C42×C11—42no—
171C42×C11C22×C412yes—
172C42×C11#4112yes—
173C2×#496C2×C1111yescharacteristic
174C4×#127C2×C1111yescharacteristic, complemented
175C4×#124C2×C1111yescharacteristic, complemented
176#1961C2×C1111yescharacteristic, complemented
177#1959C2×C1111yescharacteristic, complemented
178#1880C2×C1112yescomplemented
179#1879C2×C1112yescomplemented
180#1879C2×C1112yescomplemented
181#1877C2×C1112yescomplemented
182#1836C2×C1111yescharacteristic, complemented
183#1745C2×C1111yescharacteristic, complemented
184C23×C11—22no—
185C23×C11—24no—
186C23×C11—41no—
187C23×C11—42no—
188C23×C11—42no—
189C23×C11—41no—
190C23×C11—42no—
191C23×C11—42no—
192C23×C11—41no—
193C23×C11—41no—
194C23×C11—41no—
195C23×C11—41no—
196C23×C11—42no—
197C23×C11—42no—
198C23×C11C22×D411yescharacteristic
199Q8×C11—24no—
200Q8×C11—42no—
201D4×C11—24no—
202D4×C11—24no—
203D4×C11—24no—
204D4×C11—48no—
205D4×C11—48no—
206D4×C11—42no—
207D4×C11—42no—
208D4×C11—42no—
209C2×C4×C11—21no—
210C2×C4×C11—21no—
211C2×C4×C11—21no—
212C2×C4×C11—21no—
213C2×C4×C11—21no—
214C2×C4×C11—21no—
215C2×C4×C11—21no—
216C2×C4×C11—21no—
217C2×C4×C11—22no—
218C2×C4×C11—21no—
219C2×C4×C11—21no—
220C2×C4×C11—21no—
221C2×C4×C11—21no—
222C2×C4×C11—21no—
223C2×C4×C11—21no—
224C2×C4×C11—41no—
225C2×C4×C11—41no—
226C2×C4×C11—41no—
227C2×C4×C11—41no—
228C2×C4×C11—42no—
229C2×C4×C11—42no—
230C2×C4×C11—42no—
231C2×C4×C11—41no—
232C2×C4×C11—41no—
233C2×C4×C11—41no—
234C2×C4×C11—41no—
235C2×C4×C11—84no—
236C2×C4×C11—88no—
237C2×C4×C11C4×D412yes—
238C2×C4×C11C4×D412yes—
239C2×C4×C11AGL(1,ℤ/8)12yes—
240C2×C4×C11AGL(1,ℤ/8)12yes—
241C2×C4×C11C23×C411yescharacteristic
242C2×C4×C11C2×#4111yescharacteristic
243C2×C4×C11H(5,𝔽2)12yes—
244C2×C4×C11H(5,𝔽2)12yes—
245C8×C11—24no—
246C8×C11—42no—
247C22×SD16C22×C1112yes—
248C22×D8C22×C1112yes—
249C2×#127C22×C1111yescharacteristic
250C2×#124C22×C1111yescharacteristic
251C2×C4×Q8C22×C1111yescharacteristic
252C2×C4×D4—21no—
253C2×C4×D4—21no—
254C2×C4×D4C22×C1112yes—
255C2×C4×D4C22×C1111yescharacteristic
256#496C4×C1118yescomplemented
257C2×#103C22×C1112yes—
258C2×#102C22×C1112yes—
259C2×#102C22×C1112yes—
260C2×#102C22×C1112yes—
261C2×#97C22×C1111yescharacteristic
262C2×#97C22×C1111yescharacteristic
263#391C22×C1111yescharacteristic
264#390—21no—
265#390—21no—
266#390C22×C1112yes—
267#390C22×C1111yescharacteristic
268#388—21no—
269#388—21no—
270#384C22×C1111yescharacteristic
271#382C22×C1111yescharacteristic
272C4×C22⋊C4—21no—
273C4×C22⋊C4—21no—
274C43C22×C1111yescharacteristic
275#340C22×C1112yes—
276#340C22×C1112yes—
277#336C22×C1112yes—
278#336C22×C1112yes—
279C22×C11—42no—
280C22×C11—44no—
281C22×C11—44no—
282C22×C11—44no—
283C22×C11—42no—
284C22×C11—42no—
285C22×C11—81no—
286C22×C11—82no—
287C22×C11—81no—
288C22×C11—82no—
289C22×C11—82no—
290C22×C11—81no—
291C22×C11—82no—
292C22×C11—81no—
293C22×C11C2×C4×D411yescharacteristic
294C22×C11#53511yescharacteristic
295C22×C11#53511yescharacteristic
296C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
297C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
298C22×C11#57511yescharacteristic
299C22×C11#57511yescharacteristic
300C4×C11—22no—
301C4×C11—22no—
302C4×C11—22no—
303C4×C11—22no—
304C4×C11—42no—
305C4×C11—41no—
306C4×C11—41no—
307C4×C11—81no—
308C4×C11—81no—
309C4×C11—82no—
310C4×C11#51812yes—
311C4×C11#54012yes—
312C22×Q8C23×C1111yescharacteristic
313C22×D4—21no—
314C22×D4—21no—
315C22×D4C23×C1111yescharacteristic
316C22×D4C23×C1112yes—
317C23×C4—22no—
318C23×C4—21no—
319C2×SD16—42no—
320C2×SD16—42no—
321C2×SD16C2×C4×C1118yescomplemented
322C2×D8—42no—
323C2×D8—42no—
324C2×D8C2×C4×C1118yescomplemented
325C22×C8C23×C1112yes—
326C22×C8C23×C1112yes—
327#127—22no—
328#127C2×C4×C1114yescomplemented
329#124—22no—
330#124C2×C4×C1114yescomplemented
331C4×Q8—42no—
332C4×D4—42no—
333C4×D4—42no—
334C4×D4—42no—
335C4×D4—44no—
336C4×D4—44no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4C23×C1111yescharacteristic
341C2×C4⋊C4C23×C1112yes—
342C2×C4⋊C4C23×C1111yescharacteristic
343C2×C22⋊C4—21no—
344C2×C22⋊C4—21no—
345C2×C22⋊C4—22no—
346C2×C22⋊C4—22no—
347C2×C22⋊C4—21no—
348C2×C22⋊C4—22no—
349C2×C22⋊C4—21no—
350C2×C22⋊C4—21no—
351C2×C42—21no—
352C2×C42D4×C1111yescharacteristic
353C2×C42D4×C1111yescharacteristic
354C2×C42D4×C1111yescharacteristic
355C2×C42D4×C1111yescharacteristic
356C2×C42C23×C1111yescharacteristic
357C2×C42C23×C1111yescharacteristic
358C2×C42C23×C1111yescharacteristic
359#103—42no—
360#102—42no—
361#102—42no—
362#102—42no—
363#97—22no—
364#97C2×C4×C1114yescomplemented
365#95—21no—
366#95—21no—
367#95—21no—
368#95—21no—
369C2×C11—84no—
370C2×C11—82no—
371C2×C11#232811yescharacteristic
372C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
373C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
374C2×C11#321311yescharacteristic
375C2×C11#321411yescharacteristic
376C2×C11#321711yescharacteristic
377C2×C11#321911yescharacteristic
378C24—21no—
379C24—22no—
380C2×Q8—21no—
381C2×Q8—22no—
382C2×Q8—22no—
383C2×Q8C22×C4×C1112yes—
384C2×D4—24no—
385C2×D4—24no—
386C2×D4—21no—
387C2×D4—22no—
388C2×D4—22no—
389C2×D4—22no—
390C2×D4—22no—
391C2×D4—22no—
392C2×D4—22no—
393C2×D4—22no—
394C2×D4—42no—
395C2×D4—42no—
396C2×D4—42no—
397C2×D4—42no—
398C2×D4C22×C4×C1112yes—
399C2×D4C22×C4×C1114yes—
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—21no—
403C22×C4—22no—
404C22×C4—42no—
405C22×C4—44no—
406C22×C4—44no—
407C22×C4—42no—
408C22×C4—44no—
409C22×C4—42no—
410C22×C4C2×D4×C1111yescharacteristic
411C22×C4C2×D4×C1111yescharacteristic
412C22×C4C2×D4×C1111yescharacteristic
413C22×C4C2×D4×C1111yescharacteristic
414C22×C4C2×D4×C1111yescharacteristic
415C22×C4C2×D4×C1111yescharacteristic
416C22×C4C24×C1111yescharacteristic
417SD16—48no—
418D8—48no—
419C2×C8—22no—
420C2×C8—22no—
421C2×C8—22no—
422C2×C8—22no—
423C2×C8—22no—
424C2×C8C22×C4×C1114yes—
425C4⋊C4—22no—
426C4⋊C4—22no—
427C4⋊C4—22no—
428C4⋊C4—22no—
429C4⋊C4—42no—
430C4⋊C4—42no—
431C4⋊C4—42no—
432C22⋊C4—24no—
433C22⋊C4—24no—
434C22⋊C4—44no—
435C22⋊C4—42no—
436C22⋊C4—44no—
437C22⋊C4—42no—
438C22⋊C4—44no—
439C22⋊C4—42no—
440C42—22no—
441C42—22no—
442C42—22no—
443C42—22no—
444C42—41no—
445C42—41no—
446C42—42no—
447C42C22×C4×C1112yes—
448C42C11×#4112yes—
449C11#2227211yescharacteristic, direct product factor, Sylow
450C23—22no—
451C23—24no—
452C23—41no—
453C23—42no—
454C23—42no—
455C23—41no—
456C23—42no—
457C23—42no—
458C23—41no—
459C23—41no—
460C23—41no—
461C23—41no—
462C23—42no—
463C23—42no—
464C23C22×D4×C1111yescharacteristic
465Q8—24no—
466Q8—42no—
467D4—24no—
468D4—24no—
469D4—24no—
470D4—48no—
471D4—48no—
472D4—42no—
473D4—42no—
474D4—42no—
475C2×C4—21no—
476C2×C4—21no—
477C2×C4—21no—
478C2×C4—21no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—21no—
483C2×C4—22no—
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—21no—
487C2×C4—21no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—41no—
491C2×C4—41no—
492C2×C4—41no—
493C2×C4—41no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—84no—
502C2×C4—88no—
503C2×C4C4×D4×C1112yes—
504C2×C4C4×D4×C1112yes—
505C2×C4C11×AGL(1,ℤ/8)12yes—
506C2×C4C11×AGL(1,ℤ/8)12yes—
507C2×C4C23×C4×C1111yescharacteristic
508C2×C4C2×C11×#4111yescharacteristic
509C2×C4C11×H(5,𝔽2)12yes—
510C2×C4C11×H(5,𝔽2)12yes—
511C8—24no—
512C8—42no—
513C22—44no—
514C22—44no—
515C22—42no—
516C22—42no—
517C22—42no—
518C22—44no—
519C22—81no—
520C22—82no—
521C22—81no—
522C22—82no—
523C22—82no—
524C22—81no—
525C22—82no—
526C22—81no—
527C22C2×C4×D4×C1111yescharacteristic
528C22C11×#53511yescharacteristic
529C22C11×#53511yescharacteristic
530C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
531C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
532C22C11×#57511yescharacteristic
533C22C11×#57511yescharacteristic
534C4—22no—
535C4—22no—
536C4—22no—
537C4—22no—
538C4—41no—
539C4—41no—
540C4—42no—
541C4—81no—
542C4—81no—
543C4—82no—
544C4C11×#51812yes—
545C4C11×#54012yes—
546C2—84no—
547C2—82no—
548C2C11×#232811yescharacteristic
549C2C4×C11×AGL(1,ℤ/8)11yescharacteristic
550C2C4×C11×AGL(1,ℤ/8)11yescharacteristic
551C2C11×#321311yescharacteristic
552C2C11×#321411yescharacteristic
553C2C11×#321711yescharacteristic
554C2C11×#321911yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#496C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C43×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C4×C11×#127C2semidirect
3. C4×C11×#124C2semidirect
4. C11×#1961C2semidirect
5. C11×#1959C2semidirect
6. C11×#1880C2semidirect
7. C11×#1879C2semidirect
8. C11×#1879C2semidirect
9. C11×#1877C2semidirect
10. C11×#1836C2semidirect
11. C11×#1745C2semidirect
21. C11×#496C4semidirect
53. C2×C11×SD16C2×C4semidirect
56. C2×C11×D8C2×C4semidirect
60. C11×#127C2×C4semidirect
62. C11×#124C2×C4semidirect
96. C11×#97C2×C4semidirect
101. #22272C11direct (N × H)
174. C4×#127C2×C11semidirect
175. C4×#124C2×C11semidirect
176. #1961C2×C11semidirect
177. #1959C2×C11semidirect
178. #1880C2×C11semidirect
179. #1879C2×C11semidirect
180. #1879C2×C11semidirect
181. #1877C2×C11semidirect
182. #1836C2×C11semidirect
183. #1745C2×C11semidirect
256. #496C4×C11semidirect
321. C2×SD16C2×C4×C11semidirect
324. C2×D8C2×C4×C11semidirect
328. #127C2×C4×C11semidirect
330. #124C2×C4×C11semidirect
364. #97C2×C4×C11semidirect
449. C11#22272direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4962
C4×C11×#1272
C4×C11×#1242
C11×#19612
C11×#19592
C11×#18802
C11×#18792
C11×#18772
C11×#18362
C11×#17452
#2227211