Finite Group Databasebeta

← C11×#24187 #14601380

Subgroups — C11×#24187 #14601380

Order 2816.

1118 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#557C211yesmaximal, characteristic, complemented
2C2×C11×#461C211yesmaximal, characteristic
3C2×C4×C11×SD16C211yesmaximal, characteristic
4C11×#2538C211yesmaximal, characteristic
5C11×#2043C212yesmaximal, complemented
6C11×#2013C212yesmaximal
7C11×#1984C211yesmaximal, characteristic, complemented
8C11×#1956C211yesmaximal, characteristic, complemented
9C11×#1880C212yesmaximal
10C11×#1865C212yesmaximal, complemented
11C11×#1803C211yesmaximal, characteristic, complemented
12C22×C11×SD16C2211yescharacteristic
13C22×C11×SD16C2212yes—
14C11×#557—24no—
15C11×#557—24no—
16C2×C11×C4⋊Q8C2212yes—
17C2×C11×C4⋊Q8C2211yescharacteristic
18C2×C11×#125—21no—
19C2×C11×#125—22no—
20C2×C11×C22⋊Q8—21no—
21C2×C4×Q8×C11—21no—
22C2×C4×Q8×C11C2212yes—
23C2×C4×Q8×C11C2211yescharacteristic
24C2×C4×Q8×C11C2211yescharacteristic
25C2×C4×D4×C11C2211yescharacteristic
26C11×#461—24no—
27C4×C11×SD16—24no—
28C2×C11×#106C2211yescharacteristic
29C2×C11×C4⋊C8C2211yescharacteristic
30C2×C11×#103C2211yescharacteristic
31C2×C11×#103C2212yes—
32C2×C11×#103C2212yes—
33C2×C11×#103C2212yes—
34C2×C11×#103C2212yes—
35C2×C11×#102C2211yescharacteristic
36C2×C4×C8×C11C2211yescharacteristic
37C11×#396—22no—
38C11×#390C2212yes—
39C11×#389C2212yes—
40C11×#384C2211yescharacteristic
41C11×#380—21no—
42C11×#340C2212yes—
43C11×#336C2212yes—
44C11×#336C2212yes—
45C22×Q8×C11D411yescharacteristic
46C22×Q8×C11C2312yes—
47C22×Q8×C11C2311yescharacteristic
48C22×D4×C11C2311yescharacteristic
49C23×C4×C11—21no—
50C2×C11×SD16—22no—
51C2×C11×SD16—22no—
52C2×C11×SD16—24no—
53C2×C11×SD16—24no—
54C2×C11×SD16—22no—
55C2×C11×SD16—42no—
56C22×C8×C11C2312yes—
57C22×C8×C11C2311yescharacteristic
58C22×C8×C11C2311yescharacteristic
59C11×C4⋊Q8—24no—
60C11×C4⋊Q8—24no—
61C11×C4⋊Q8—22no—
62C11×C4⋊Q8D414yes—
63C11×#125—216no—
64C11×#125—28no—
65C11×C22⋊Q8—44no—
66C4×Q8×C11—28no—
67C4×Q8×C11—24no—
68C4×Q8×C11—24no—
69C4×Q8×C11—22no—
70C4×Q8×C11—22no—
71C4×Q8×C11—22no—
72C4×Q8×C11D414yes—
73C4×D4×C11—22no—
74C4×D4×C11—22no—
75C2×C11×C4⋊C4—22no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4—22no—
78C2×C11×C4⋊C4—21no—
79C2×C11×C4⋊C4—22no—
80C2×C11×C4⋊C4—21no—
81C2×C11×C4⋊C4—21no—
82C2×C11×C4⋊C4—22no—
83C2×C11×C4⋊C4—21no—
84C2×C11×C4⋊C4D411yescharacteristic
85C2×C11×C4⋊C4D412yes—
86C2×C11×C4⋊C4C2312yes—
87C2×C11×C4⋊C4C2311yescharacteristic
88C2×C11×C4⋊C4C2311yescharacteristic
89C2×C11×C22⋊C4—21no—
90C2×C11×C22⋊C4—22no—
91C2×C11×C22⋊C4—22no—
92C2×C42×C11—22no—
93C2×C42×C11—21no—
94C2×C42×C11C2312yes—
95C2×C42×C11C2311yescharacteristic
96C11×#106—22no—
97C11×C4⋊C8—22no—
98C11×#103—22no—
99C11×#103—24no—
100C11×#103—24no—
101C11×#103—42no—
102C11×#103—42no—
103C11×#102—22no—
104C4×C8×C11—22no—
105C11×#95—22no—
106#24187C1111yesmaximal, characteristic, direct product factor, Sylow
107C24×C11—21no—
108C2×Q8×C11—22no—
109C2×Q8×C11—22no—
110C2×Q8×C11—22no—
111C2×Q8×C11—21no—
112C2×Q8×C11—22no—
113C2×Q8×C11—21no—
114C2×Q8×C11—22no—
115C2×Q8×C11—21no—
116C2×Q8×C11—21no—
117C2×Q8×C11—22no—
118C2×Q8×C11—21no—
119C2×Q8×C11—22no—
120C2×Q8×C11SD1614yescomplemented
121C2×Q8×C11C2×D414yes—
122C2×Q8×C11C2×D412yes—
123C2×D4×C11—21no—
124C2×D4×C11—21no—
125C2×D4×C11—21no—
126C2×D4×C11—21no—
127C2×D4×C11—21no—
128C2×D4×C11#4112yes—
129C22×C4×C11—21no—
130C22×C4×C11—22no—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—22no—
134C22×C4×C11—42no—
135C22×C4×C11—42no—
136C22×C4×C11—42no—
137C22×C4×C11C2×D412yes—
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2×D412yes—
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2411yescharacteristic
142C11×SD16—28no—
143C11×SD16—48no—
144C2×C8×C11—21no—
145C2×C8×C11—21no—
146C2×C8×C11—22no—
147C2×C8×C11—21no—
148C2×C8×C11—22no—
149C2×C8×C11—21no—
150C2×C8×C11—22no—
151C2×C8×C11—21no—
152C2×C8×C11#4112yes—
153C11×C4⋊C4—28no—
154C11×C4⋊C4—28no—
155C11×C4⋊C4—28no—
156C11×C4⋊C4—24no—
157C11×C4⋊C4—24no—
158C11×C4⋊C4—24no—
159C11×C4⋊C4—24no—
160C11×C4⋊C4—22no—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—22no—
165C11×C4⋊C4—22no—
166C11×C4⋊C4—42no—
167C11×C4⋊C4—44no—
168C11×C4⋊C4—81no—
169C11×C4⋊C4C2×D412yes—
170C11×C22⋊C4—42no—
171C11×C22⋊C4—44no—
172C11×C22⋊C4—82no—
173C42×C11—28no—
174C42×C11—24no—
175C42×C11—22no—
176C42×C11—22no—
177C42×C11C2×D412yes—
178C42×C11C2×D412yes—
179C2×#557C2×C1111yescharacteristic, complemented
180C2×#461C2×C1111yescharacteristic
181C2×C4×SD16C2×C1111yescharacteristic
182#2538C2×C1111yescharacteristic
183#2043C2×C1112yescomplemented
184#2013C2×C1112yes—
185#1984C2×C1111yescharacteristic, complemented
186#1956C2×C1111yescharacteristic, complemented
187#1880C2×C1112yes—
188#1865C2×C1112yescomplemented
189#1803C2×C1111yescharacteristic, complemented
190C23×C11—22no—
191C23×C11—41no—
192C23×C11—41no—
193C23×C11—41no—
194C23×C11—41no—
195C23×C11—41no—
196C23×C11—41no—
197C23×C11C22×D411yescharacteristic
198Q8×C11—28no—
199Q8×C11—22no—
200Q8×C11—22no—
201Q8×C11—24no—
202Q8×C11—24no—
203Q8×C11—42no—
204Q8×C11—42no—
205Q8×C11—41no—
206Q8×C11—41no—
207D4×C11—22no—
208D4×C11—22no—
209D4×C11—41no—
210D4×C11—41no—
211C2×C4×C11—22no—
212C2×C4×C11—22no—
213C2×C4×C11—21no—
214C2×C4×C11—21no—
215C2×C4×C11—22no—
216C2×C4×C11—22no—
217C2×C4×C11—24no—
218C2×C4×C11—22no—
219C2×C4×C11—22no—
220C2×C4×C11—22no—
221C2×C4×C11—41no—
222C2×C4×C11—42no—
223C2×C4×C11—42no—
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—41no—
231C2×C4×C11—41no—
232C2×C4×C11—42no—
233C2×C4×C11—84no—
234C2×C4×C11#12012yes—
235C2×C4×C11#12012yes—
236C2×C4×C11C2×SD1614yes—
237C2×C4×C11C2×SD1612yes—
238C2×C4×C11#13712yes—
239C2×C4×C11C22×D411yescharacteristic
240C2×C4×C11C22×D411yescharacteristic
241C2×C4×C11C2×#4111yescharacteristic
242C2×C4×C11C2×#4111yescharacteristic
243C2×C4×C11H(5,𝔽2)11yescharacteristic
244C2×C4×C112−1+411yescharacteristic
245C8×C11—22no—
246C8×C11—41no—
247C8×C11—42no—
248C22×SD16C22×C1111yescharacteristic
249C22×SD16C22×C1112yes—
250#557—24no—
251#557—24no—
252C2×C4⋊Q8C22×C1112yes—
253C2×C4⋊Q8C22×C1111yescharacteristic
254C2×#125—21no—
255C2×#125—22no—
256C2×C22⋊Q8—21no—
257C2×C4×Q8—21no—
258C2×C4×Q8C22×C1112yes—
259C2×C4×Q8C22×C1111yescharacteristic
260C2×C4×Q8C22×C1111yescharacteristic
261C2×C4×D4C22×C1111yescharacteristic
262#461—24no—
263C4×SD16—24no—
264C2×#106C22×C1111yescharacteristic
265C2×C4⋊C8C22×C1111yescharacteristic
266C2×#103C22×C1112yes—
267C2×#103C22×C1112yes—
268C2×#103C22×C1111yescharacteristic
269C2×#103C22×C1112yes—
270C2×#103C22×C1112yes—
271C2×#102C22×C1111yescharacteristic
272C2×C4×C8C22×C1111yescharacteristic
273#396—22no—
274#390C22×C1112yes—
275#389C22×C1112yes—
276#384C22×C1111yescharacteristic
277#380—21no—
278#340C22×C1112yes—
279#336C22×C1112yes—
280#336C22×C1112yes—
281C22×C11—42no—
282C22×C11—42no—
283C22×C11—42no—
284C22×C11—81no—
285C22×C11—81no—
286C22×C11—81no—
287C22×C11—81no—
288C22×C11C2×#12011yescharacteristic
289C22×C11#54811yescharacteristic
290C22×C11#55011yescharacteristic
291C22×C11C22×SD1611yescharacteristic
292C22×C11C2×#13711yescharacteristic
293C22×C11#57711yescharacteristic
294C22×C11#57811yescharacteristic
295C4×C11—24no—
296C4×C11—22no—
297C4×C11—42no—
298C4×C11—44no—
299C4×C11—42no—
300C4×C11—42no—
301C4×C11—82no—
302C4×C11—81no—
303C4×C11#44814yes—
304C4×C11#52511yescharacteristic
305C4×C11#53711yescharacteristic
306C4×C11#54611yescharacteristic
307C4×C11#54711yescharacteristic
308C22×Q8D4×C1111yescharacteristic
309C22×Q8C23×C1112yes—
310C22×Q8C23×C1111yescharacteristic
311C22×D4C23×C1111yescharacteristic
312C23×C4—21no—
313C2×SD16—22no—
314C2×SD16—22no—
315C2×SD16—24no—
316C2×SD16—24no—
317C2×SD16—22no—
318C2×SD16—42no—
319C22×C8C23×C1112yes—
320C22×C8C23×C1111yescharacteristic
321C22×C8C23×C1111yescharacteristic
322C4⋊Q8—24no—
323C4⋊Q8—24no—
324C4⋊Q8—22no—
325C4⋊Q8D4×C1114yes—
326#125—216no—
327#125—28no—
328C22⋊Q8—44no—
329C4×Q8—28no—
330C4×Q8—24no—
331C4×Q8—24no—
332C4×Q8—22no—
333C4×Q8—22no—
334C4×Q8—22no—
335C4×Q8D4×C1114yes—
336C4×D4—22no—
337C4×D4—22no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—22no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4D4×C1111yescharacteristic
348C2×C4⋊C4D4×C1112yes—
349C2×C4⋊C4C23×C1111yescharacteristic
350C2×C4⋊C4C23×C1112yes—
351C2×C4⋊C4C23×C1111yescharacteristic
352C2×C22⋊C4—21no—
353C2×C22⋊C4—22no—
354C2×C22⋊C4—22no—
355C2×C42—22no—
356C2×C42—21no—
357C2×C42C23×C1112yes—
358C2×C42C23×C1111yescharacteristic
359#106—22no—
360C4⋊C8—22no—
361#103—22no—
362#103—24no—
363#103—24no—
364#103—42no—
365#103—42no—
366#102—22no—
367C4×C8—22no—
368#95—22no—
369C2×C11—82no—
370C2×C11#240711yescharacteristic
371C2×C11C2×#44811yescharacteristic
372C2×C11#301311yescharacteristic
373C2×C11#335911yescharacteristic
374C2×C11#337211yescharacteristic
375C2×C11#339211yescharacteristic
376C2×C11#339811yescharacteristic
377C24—21no—
378C2×Q8—22no—
379C2×Q8—22no—
380C2×Q8—22no—
381C2×Q8—21no—
382C2×Q8—22no—
383C2×Q8—21no—
384C2×Q8—22no—
385C2×Q8—21no—
386C2×Q8—21no—
387C2×Q8—22no—
388C2×Q8—21no—
389C2×Q8—22no—
390C2×Q8C11×SD1614yescomplemented
391C2×Q8C2×D4×C1114yes—
392C2×Q8C2×D4×C1112yes—
393C2×D4—21no—
394C2×D4—21no—
395C2×D4—21no—
396C2×D4—21no—
397C2×D4—21no—
398C2×D4C11×#4112yes—
399C22×C4—21no—
400C22×C4—22no—
401C22×C4—21no—
402C22×C4—21no—
403C22×C4—22no—
404C22×C4—42no—
405C22×C4—42no—
406C22×C4—42no—
407C22×C4C2×D4×C1112yes—
408C22×C4C2×D4×C1111yescharacteristic
409C22×C4C2×D4×C1112yes—
410C22×C4C2×D4×C1111yescharacteristic
411C22×C4C24×C1111yescharacteristic
412SD16—28no—
413SD16—48no—
414C2×C8—21no—
415C2×C8—21no—
416C2×C8—21no—
417C2×C8—22no—
418C2×C8—22no—
419C2×C8—21no—
420C2×C8—22no—
421C2×C8—21no—
422C2×C8C11×#4112yes—
423C4⋊C4—28no—
424C4⋊C4—28no—
425C4⋊C4—28no—
426C4⋊C4—24no—
427C4⋊C4—24no—
428C4⋊C4—24no—
429C4⋊C4—24no—
430C4⋊C4—22no—
431C4⋊C4—21no—
432C4⋊C4—21no—
433C4⋊C4—21no—
434C4⋊C4—22no—
435C4⋊C4—22no—
436C4⋊C4—42no—
437C4⋊C4—44no—
438C4⋊C4—81no—
439C4⋊C4C2×D4×C1112yes—
440C22⋊C4—42no—
441C22⋊C4—44no—
442C22⋊C4—82no—
443C42—28no—
444C42—24no—
445C42—22no—
446C42—22no—
447C42C2×D4×C1112yes—
448C42C2×D4×C1112yes—
449C11#2418711yescharacteristic, direct product factor, Sylow
450C23—22no—
451C23—41no—
452C23—41no—
453C23—41no—
454C23—41no—
455C23—41no—
456C23—41no—
457C23C22×D4×C1111yescharacteristic
458Q8—28no—
459Q8—22no—
460Q8—22no—
461Q8—24no—
462Q8—24no—
463Q8—42no—
464Q8—42no—
465Q8—41no—
466Q8—41no—
467D4—22no—
468D4—22no—
469D4—41no—
470D4—41no—
471C2×C4—22no—
472C2×C4—22no—
473C2×C4—21no—
474C2×C4—21no—
475C2×C4—22no—
476C2×C4—22no—
477C2×C4—24no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—41no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—41no—
485C2×C4—41no—
486C2×C4—41no—
487C2×C4—41no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—41no—
491C2×C4—41no—
492C2×C4—42no—
493C2×C4—84no—
494C2×C4C11×#12012yes—
495C2×C4C11×#12012yes—
496C2×C4C2×C11×SD1614yes—
497C2×C4C2×C11×SD1612yes—
498C2×C4C11×#13712yes—
499C2×C4C22×D4×C1111yescharacteristic
500C2×C4C22×D4×C1111yescharacteristic
501C2×C4C2×C11×#4111yescharacteristic
502C2×C4C2×C11×#4111yescharacteristic
503C2×C4C11×H(5,𝔽2)11yescharacteristic
504C2×C4C11×2−1+411yescharacteristic
505C8—22no—
506C8—41no—
507C8—42no—
508C22—42no—
509C22—42no—
510C22—42no—
511C22—81no—
512C22—81no—
513C22—81no—
514C22—81no—
515C22C2×C11×#12011yescharacteristic
516C22C11×#54811yescharacteristic
517C22C11×#55011yescharacteristic
518C22C22×C11×SD1611yescharacteristic
519C22C2×C11×#13711yescharacteristic
520C22C11×#57711yescharacteristic
521C22C11×#57811yescharacteristic
522C4—24no—
523C4—22no—
524C4—42no—
525C4—44no—
526C4—42no—
527C4—42no—
528C4—81no—
529C4—82no—
530C4C11×#44814yes—
531C4C11×#52511yescharacteristic
532C4C11×#53711yescharacteristic
533C4C11×#54611yescharacteristic
534C4C11×#54711yescharacteristic
535C2—82no—
536C2C11×#240711yescharacteristic
537C2C2×C11×#44811yescharacteristic
538C2C11×#301311yescharacteristic
539C2C11×#335911yescharacteristic
540C2C11×#337211yescharacteristic
541C2C11×#339211yescharacteristic
542C2C11×#339811yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC22×D4×C11C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C4×Q8×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#557C2semidirect
5. C11×#2043C2semidirect
7. C11×#1984C2semidirect
8. C11×#1956C2semidirect
10. C11×#1865C2semidirect
11. C11×#1803C2semidirect
106. #24187C11direct (N × H)
120. C2×Q8×C11SD16semidirect
179. C2×#557C2×C11semidirect
183. #2043C2×C11semidirect
185. #1984C2×C11semidirect
186. #1956C2×C11semidirect
188. #1865C2×C11semidirect
189. #1803C2×C11semidirect
390. C2×Q8C11×SD16semidirect
449. C11#24187direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5572
C2×C11×#4612
C2×C4×C11×SD162
C11×#25382
C11×#20432
C11×#20132
C11×#19842
C11×#19562
C11×#18802
C11×#18652
C11×#18032
#2418711