Finite Group Databasebeta

← C11×#24209 #14601402

Subgroups — C11×#24209 #14601402

Order 2816.

1514 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×C4⋊Q8C211yesmaximal, characteristic, complemented
2C2×C11×#461C212yesmaximal, complemented
3C2×C11×#448C212yesmaximal
4C4×C11×#121C211yesmaximal, characteristic
5C11×#2043C212yesmaximal, complemented
6C11×#2013C212yesmaximal, complemented
7C11×#1981C212yesmaximal, complemented
8C11×#1797C211yesmaximal, characteristic, complemented
9C11×#1787C212yesmaximal, complemented
10C23×Q8×C11C2212yes—
11C22×C11×SD16C2214yes—
12C2×C11×C4⋊Q8—28no—
13C2×C11×C4⋊Q8—21no—
14C2×C11×C4⋊Q8—21no—
15C2×C11×C4⋊Q8C2212yes—
16C2×C11×C4⋊Q8C2212yes—
17C2×C11×#121C2211yescharacteristic
18C2×C4×D4×C11—21no—
19C2×C4×D4×C11C2211yescharacteristic
20C22×C11×C4⋊C4—21no—
21C22×C11×C4⋊C4—21no—
22C22×C42×C11C2211yescharacteristic
23C11×#461—28no—
24C11×#448—28no—
25C2×C11×C4⋊C8C2212yes—
26C2×C11×#103C2214yes—
27C2×C11×#103C2214yes—
28C2×C11×#103C2214yes—
29C2×C11×C22⋊C8C2212yes—
30C11×#390C2211yescharacteristic
31C11×#389C2211yescharacteristic
32C11×#388—21no—
33C11×#386—21no—
34C11×#380C2211yescharacteristic
35C4×C11×C4⋊C4C2211yescharacteristic
36C4×C11×C22⋊C4—21no—
37C11×#336C2212yes—
38C22×Q8×C11—28no—
39C22×Q8×C11—22no—
40C22×Q8×C11—24no—
41C22×Q8×C11—24no—
42C22×Q8×C11—44no—
43C22×Q8×C11C2314yes—
44C22×D4×C11—21no—
45C22×D4×C11C2311yescharacteristic
46C23×C4×C11—22no—
47C23×C4×C11—21no—
48C23×C4×C11D411yescharacteristic
49C23×C4×C11D411yescharacteristic
50C23×C4×C11C2311yescharacteristic
51C2×C11×SD16—28no—
52C2×C11×SD16—28no—
53C2×C11×SD16—44no—
54C22×C8×C11C2314yes—
55C11×C4⋊Q8—28no—
56C11×C4⋊Q8—28no—
57C11×C4⋊Q8—28no—
58C11×C4⋊Q8—24no—
59C11×C4⋊Q8D418yescomplemented
60C11×#121—22no—
61C11×#121D414yes—
62C4×D4×C11—24no—
63C4×D4×C11—44no—
64C2×C11×C4⋊C4—28no—
65C2×C11×C4⋊C4—28no—
66C2×C11×C4⋊C4—22no—
67C2×C11×C4⋊C4—22no—
68C2×C11×C4⋊C4—22no—
69C2×C11×C4⋊C4—22no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C22⋊C4—21no—
75C2×C11×C22⋊C4—21no—
76C2×C11×C22⋊C4—21no—
77C2×C11×C22⋊C4—21no—
78C2×C11×C22⋊C4—21no—
79C2×C42×C11—24no—
80C2×C42×C11—21no—
81C2×C42×C11D411yescharacteristic
82C2×C42×C11D411yescharacteristic
83C2×C42×C11C2311yescharacteristic
84C2×C42×C11C2311yescharacteristic
85C11×C4⋊C8—24no—
86C11×#103—28no—
87C11×#103—28no—
88C11×#103—44no—
89C11×C22⋊C8—24no—
90C11×#95—21no—
91C11×#95—21no—
92C11×#95—21no—
93#24209C1111yesmaximal, characteristic, direct product factor, Sylow
94C24×C11—21no—
95C24×C11C2×D411yescharacteristic
96C2×Q8×C11—28no—
97C2×Q8×C11—24no—
98C2×Q8×C11—24no—
99C2×Q8×C11—24no—
100C2×Q8×C11—24no—
101C2×Q8×C11—24no—
102C2×Q8×C11—416no—
103C2×Q8×C11—416no—
104C2×Q8×C11—44no—
105C2×Q8×C11—44no—
106C2×Q8×C11C2×D418yes—
107C2×D4×C11—24no—
108C2×D4×C11—22no—
109C2×D4×C11—21no—
110C2×D4×C11—22no—
111C2×D4×C11—42no—
112C2×D4×C11—42no—
113C2×D4×C11C2×D412yes—
114C22×C4×C11—22no—
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—22no—
120C22×C4×C11—22no—
121C22×C4×C11—28no—
122C22×C4×C11—21no—
123C22×C4×C11—24no—
124C22×C4×C11—21no—
125C22×C4×C11—21no—
126C22×C4×C11—44no—
127C22×C4×C11—44no—
128C22×C4×C11—42no—
129C22×C4×C11—42no—
130C22×C4×C11—42no—
131C22×C4×C11SD1614yescomplemented
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11C2×D412yes—
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11#4112yes—
139C22×C4×C11C2411yescharacteristic
140C11×SD16—416no—
141C2×C8×C11—24no—
142C2×C8×C11—24no—
143C2×C8×C11—24no—
144C11×C4⋊C4—28no—
145C11×C4⋊C4—28no—
146C11×C4⋊C4—28no—
147C11×C4⋊C4—28no—
148C11×C4⋊C4—21no—
149C11×C4⋊C4—22no—
150C11×C4⋊C4—22no—
151C11×C4⋊C4—42no—
152C11×C4⋊C4C2×D412yes—
153C11×C22⋊C4—24no—
154C11×C22⋊C4—42no—
155C11×C22⋊C4—42no—
156C11×C22⋊C4—42no—
157C11×C22⋊C4—42no—
158C42×C11—22no—
159C42×C11—22no—
160C42×C11—22no—
161C42×C11—42no—
162C42×C11C2×D414yes—
163C22×C4⋊Q8C2×C1111yescharacteristic, complemented
164C2×#461C2×C1112yescomplemented
165C2×#448C2×C1112yes—
166C4×#121C2×C1111yescharacteristic
167#2043C2×C1112yescomplemented
168#2013C2×C1112yescomplemented
169#1981C2×C1112yescomplemented
170#1797C2×C1111yescharacteristic, complemented
171#1787C2×C1112yescomplemented
172C23×C11—21no—
173C23×C11—21no—
174C23×C11—21no—
175C23×C11—21no—
176C23×C11—22no—
177C23×C11—41no—
178C23×C11—41no—
179C23×C11—41no—
180C23×C11—41no—
181C23×C11—41no—
182C23×C11—41no—
183C23×C11#12112yes—
184C23×C11C2×SD1612yes—
185C23×C11#13712yes—
186C23×C11C22×D411yescharacteristic
187Q8×C11—28no—
188Q8×C11—28no—
189Q8×C11—416no—
190Q8×C11—44no—
191Q8×C11—44no—
192D4×C11—24no—
193D4×C11—48no—
194D4×C11—42no—
195C2×C4×C11—28no—
196C2×C4×C11—21no—
197C2×C4×C11—21no—
198C2×C4×C11—21no—
199C2×C4×C11—21no—
200C2×C4×C11—21no—
201C2×C4×C11—21no—
202C2×C4×C11—21no—
203C2×C4×C11—21no—
204C2×C4×C11—24no—
205C2×C4×C11—24no—
206C2×C4×C11—28no—
207C2×C4×C11—28no—
208C2×C4×C11—22no—
209C2×C4×C11—416no—
210C2×C4×C11—44no—
211C2×C4×C11—44no—
212C2×C4×C11—41no—
213C2×C4×C11—41no—
214C2×C4×C11—41no—
215C2×C4×C11—41no—
216C2×C4×C11—41no—
217C2×C4×C11—41no—
218C2×C4×C11—41no—
219C2×C4×C11—41no—
220C2×C4×C11—84no—
221C2×C4×C11#12012yes—
222C2×C4×C11#12012yes—
223C2×C4×C11#12112yes—
224C2×C4×C11C2×SD1612yes—
225C2×C4×C11C2×SD1612yes—
226C2×C4×C11#13712yes—
227C2×C4×C11#13712yes—
228C2×C4×C11C22×D411yescharacteristic
229C2×C4×C11C22×D412yes—
230C2×C4×C11C2×#4111yescharacteristic
231C2×C4×C11H(5,𝔽2)12yes—
232C8×C11—44no—
233C23×Q8C22×C1112yes—
234C22×SD16C22×C1114yes—
235C2×C4⋊Q8—28no—
236C2×C4⋊Q8—21no—
237C2×C4⋊Q8—21no—
238C2×C4⋊Q8C22×C1112yes—
239C2×C4⋊Q8C22×C1112yes—
240C2×#121C22×C1111yescharacteristic
241C2×C4×D4—21no—
242C2×C4×D4C22×C1111yescharacteristic
243C22×C4⋊C4—21no—
244C22×C4⋊C4—21no—
245C22×C42C22×C1111yescharacteristic
246#461—28no—
247#448—28no—
248C2×C4⋊C8C22×C1112yes—
249C2×#103C22×C1114yes—
250C2×#103C22×C1114yes—
251C2×#103C22×C1114yes—
252C2×C22⋊C8C22×C1112yes—
253#390C22×C1111yescharacteristic
254#389C22×C1111yescharacteristic
255#388—21no—
256#386—21no—
257#380C22×C1111yescharacteristic
258C4×C4⋊C4C22×C1111yescharacteristic
259C4×C22⋊C4—21no—
260#336C22×C1112yes—
261C22×C11—22no—
262C22×C11—22no—
263C22×C11—22no—
264C22×C11—22no—
265C22×C11—22no—
266C22×C11—22no—
267C22×C11—42no—
268C22×C11—42no—
269C22×C11—42no—
270C22×C11—81no—
271C22×C11—81no—
272C22×C11—81no—
273C22×C11—81no—
274C22×C11#46114yescomplemented
275C22×C11C2×#12011yescharacteristic
276C22×C11C2×#12111yescharacteristic
277C22×C11#53511yescharacteristic
278C22×C11C22×SD1611yescharacteristic
279C22×C11C2×#13711yescharacteristic
280C22×C11C2×#13711yescharacteristic
281C22×C11C2×#13711yescharacteristic
282C4×C11—22no—
283C4×C11—22no—
284C4×C11—22no—
285C4×C11—22no—
286C4×C11—48no—
287C4×C11—42no—
288C4×C11—81no—
289C4×C11—81no—
290C4×C11#44814yescomplemented
291C4×C11D4212yes—
292C4×C11#54612yes—
293C22×Q8—28no—
294C22×Q8—22no—
295C22×Q8—24no—
296C22×Q8—24no—
297C22×Q8—44no—
298C22×Q8C23×C1114yes—
299C22×D4—21no—
300C22×D4C23×C1111yescharacteristic
301C23×C4—22no—
302C23×C4—21no—
303C23×C4D4×C1111yescharacteristic
304C23×C4D4×C1111yescharacteristic
305C23×C4C23×C1111yescharacteristic
306C2×SD16—28no—
307C2×SD16—28no—
308C2×SD16—44no—
309C22×C8C23×C1114yes—
310C4⋊Q8—28no—
311C4⋊Q8—28no—
312C4⋊Q8—28no—
313C4⋊Q8—24no—
314C4⋊Q8D4×C1118yescomplemented
315#121—22no—
316#121D4×C1114yes—
317C4×D4—24no—
318C4×D4—44no—
319C2×C4⋊C4—28no—
320C2×C4⋊C4—28no—
321C2×C4⋊C4—22no—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—22no—
324C2×C4⋊C4—22no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4C23×C1111yescharacteristic
327C2×C4⋊C4C23×C1111yescharacteristic
328C2×C4⋊C4C23×C1111yescharacteristic
329C2×C22⋊C4—21no—
330C2×C22⋊C4—21no—
331C2×C22⋊C4—21no—
332C2×C22⋊C4—21no—
333C2×C22⋊C4—21no—
334C2×C42—24no—
335C2×C42—21no—
336C2×C42D4×C1111yescharacteristic
337C2×C42D4×C1111yescharacteristic
338C2×C42C23×C1111yescharacteristic
339C2×C42C23×C1111yescharacteristic
340C4⋊C8—24no—
341#103—28no—
342#103—28no—
343#103—44no—
344C22⋊C8—24no—
345#95—21no—
346#95—21no—
347#95—21no—
348C2×C11—24no—
349C2×C11—82no—
350C2×C11#240811yescharacteristic
351C2×C11C2×#44811yescharacteristic
352C2×C11#300411yescharacteristic
353C2×C11C2×#46111yescharacteristic
354C2×C11#303911yescharacteristic
355C2×C11#320611yescharacteristic
356C2×C11#321811yescharacteristic
357C24—21no—
358C24C2×D4×C1111yescharacteristic
359C2×Q8—28no—
360C2×Q8—24no—
361C2×Q8—24no—
362C2×Q8—24no—
363C2×Q8—24no—
364C2×Q8—24no—
365C2×Q8—416no—
366C2×Q8—416no—
367C2×Q8—44no—
368C2×Q8—44no—
369C2×Q8C2×D4×C1118yes—
370C2×D4—24no—
371C2×D4—22no—
372C2×D4—21no—
373C2×D4—22no—
374C2×D4—42no—
375C2×D4—42no—
376C2×D4C2×D4×C1112yes—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—28no—
385C22×C4—21no—
386C22×C4—24no—
387C22×C4—21no—
388C22×C4—21no—
389C22×C4—44no—
390C22×C4—44no—
391C22×C4—42no—
392C22×C4—42no—
393C22×C4—42no—
394C22×C4C11×SD1614yescomplemented
395C22×C4C2×D4×C1111yescharacteristic
396C22×C4C2×D4×C1111yescharacteristic
397C22×C4C2×D4×C1112yes—
398C22×C4C2×D4×C1111yescharacteristic
399C22×C4C2×D4×C1111yescharacteristic
400C22×C4C2×D4×C1111yescharacteristic
401C22×C4C11×#4112yes—
402C22×C4C24×C1111yescharacteristic
403SD16—416no—
404C2×C8—24no—
405C2×C8—24no—
406C2×C8—24no—
407C4⋊C4—28no—
408C4⋊C4—28no—
409C4⋊C4—28no—
410C4⋊C4—28no—
411C4⋊C4—21no—
412C4⋊C4—22no—
413C4⋊C4—22no—
414C4⋊C4—42no—
415C4⋊C4C2×D4×C1112yes—
416C22⋊C4—24no—
417C22⋊C4—42no—
418C22⋊C4—42no—
419C22⋊C4—42no—
420C22⋊C4—42no—
421C42—22no—
422C42—22no—
423C42—22no—
424C42—42no—
425C42C2×D4×C1114yes—
426C11#2420911yescharacteristic, direct product factor, Sylow
427C23—21no—
428C23—21no—
429C23—21no—
430C23—21no—
431C23—22no—
432C23—41no—
433C23—41no—
434C23—41no—
435C23—41no—
436C23—41no—
437C23—41no—
438C23C11×#12112yes—
439C23C2×C11×SD1612yes—
440C23C11×#13712yes—
441C23C22×D4×C1111yescharacteristic
442Q8—28no—
443Q8—28no—
444Q8—416no—
445Q8—44no—
446Q8—44no—
447D4—24no—
448D4—48no—
449D4—42no—
450C2×C4—28no—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—21no—
457C2×C4—21no—
458C2×C4—21no—
459C2×C4—24no—
460C2×C4—24no—
461C2×C4—28no—
462C2×C4—28no—
463C2×C4—22no—
464C2×C4—416no—
465C2×C4—44no—
466C2×C4—44no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—41no—
475C2×C4—84no—
476C2×C4C11×#12012yes—
477C2×C4C11×#12012yes—
478C2×C4C11×#12112yes—
479C2×C4C2×C11×SD1612yes—
480C2×C4C2×C11×SD1612yes—
481C2×C4C11×#13712yes—
482C2×C4C11×#13712yes—
483C2×C4C22×D4×C1111yescharacteristic
484C2×C4C22×D4×C1112yes—
485C2×C4C2×C11×#4111yescharacteristic
486C2×C4C11×H(5,𝔽2)12yes—
487C8—44no—
488C22—22no—
489C22—22no—
490C22—22no—
491C22—22no—
492C22—22no—
493C22—22no—
494C22—42no—
495C22—42no—
496C22—42no—
497C22—81no—
498C22—81no—
499C22—81no—
500C22—81no—
501C22C11×#46114yescomplemented
502C22C2×C11×#12011yescharacteristic
503C22C2×C11×#12111yescharacteristic
504C22C11×#53511yescharacteristic
505C22C22×C11×SD1611yescharacteristic
506C22C2×C11×#13711yescharacteristic
507C22C2×C11×#13711yescharacteristic
508C22C2×C11×#13711yescharacteristic
509C4—22no—
510C4—22no—
511C4—22no—
512C4—22no—
513C4—48no—
514C4—42no—
515C4—81no—
516C4—81no—
517C4C11×#44814yescomplemented
518C4D42×C1112yes—
519C4C11×#54612yes—
520C2—24no—
521C2—82no—
522C2C11×#240811yescharacteristic
523C2C2×C11×#44811yescharacteristic
524C2C11×#300411yescharacteristic
525C2C2×C11×#46111yescharacteristic
526C2C11×#303911yescharacteristic
527C2C11×#320611yescharacteristic
528C2C11×#321811yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#121C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C22×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C11×C4⋊Q8C2semidirect
2. C2×C11×#461C2semidirect
5. C11×#2043C2semidirect
6. C11×#2013C2semidirect
7. C11×#1981C2semidirect
8. C11×#1797C2semidirect
9. C11×#1787C2semidirect
59. C11×C4⋊Q8D4semidirect
93. #24209C11direct (N × H)
131. C22×C4×C11SD16semidirect
163. C22×C4⋊Q8C2×C11semidirect
164. C2×#461C2×C11semidirect
167. #2043C2×C11semidirect
168. #2013C2×C11semidirect
169. #1981C2×C11semidirect
170. #1797C2×C11semidirect
171. #1787C2×C11semidirect
274. C22×C11#461semidirect
290. C4×C11#448semidirect
314. C4⋊Q8D4×C11semidirect
394. C22×C4C11×SD16semidirect
426. C11#24209direct (N × H)
501. C22C11×#461semidirect
517. C4C11×#448semidirect

Maximal subgroups

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

subgroupindex
C22×C11×C4⋊Q82
C2×C11×#4612
C2×C11×#4482
C4×C11×#1212
C11×#20432
C11×#20132
C11×#19812
C11×#17972
C11×#17872
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