Finite Group Databasebeta

← C11×#22050 #14599243

Subgroups — C11×#22050 #14599243

Order 2816.

996 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#451C211yesmaximal, characteristic
2C4×C11×C22⋊Q8C211yesmaximal, characteristic
3C2×C11×#391C211yesmaximal, characteristic
4C11×#1971C212yesmaximal, complemented
5C11×#1935C212yesmaximal, complemented
6C11×#1927C212yesmaximal, complemented
7C11×#1878C212yesmaximal, complemented
8C11×#1872C211yesmaximal, characteristic
9C11×#1853C211yesmaximal, characteristic
10C11×#1787C211yesmaximal, characteristic
11C11×#1749C211yesmaximal, characteristic
12C23×Q8×C11C2211yescharacteristic
13C22×C11×Q16C2212yes—
14C2×C11×C22⋊Q8C2211yescharacteristic
15C2×C4×Q8×C11C2211yescharacteristic
16C22×C11×C4⋊C4C2211yescharacteristic
17C22×C42×C11C2211yescharacteristic
18C11×#451C418yescomplemented
19C2×C11×#106C2212yes—
20C2×C11×#103C2212yes—
21C2×C11×#103C2212yes—
22C2×C11×#103C2212yes—
23C2×C11×#103C2212yes—
24C2×C11×C22⋊C8C2211yescharacteristic
25C2×C11×C22⋊C8C2211yescharacteristic
26C2×C11×#97C2212yes—
27C11×#391—21no—
28C11×#391—21no—
29C11×#391C2212yes—
30C11×#391C2212yes—
31C11×#391C2211yescharacteristic
32C11×#389C2211yescharacteristic
33C11×#387—21no—
34C11×#385—21no—
35C11×#380C2211yescharacteristic
36C4×C11×C4⋊C4—21no—
37C4×C11×C4⋊C4C2211yescharacteristic
38C4×C11×C22⋊C4—21no—
39C2×C11×#95—21no—
40C2×C11×#95—21no—
41C11×#340C2212yes—
42C11×#340C2212yes—
43C11×#336C2212yes—
44C22×Q8×C11—21no—
45C22×Q8×C11—22no—
46C22×Q8×C11—42no—
47C22×Q8×C11—42no—
48C22×Q8×C11C2×C414yes—
49C22×Q8×C11C2311yescharacteristic
50C22×Q8×C11C2312yes—
51C23×C4×C11—21no—
52C23×C4×C11—21no—
53C23×C4×C11D411yescharacteristic
54C23×C4×C11D411yescharacteristic
55C23×C4×C11C2311yescharacteristic
56C2×C11×Q16—42no—
57C2×C11×Q16—42no—
58C2×C11×Q16C2×C418yescomplemented
59C22×C8×C11C2312yes—
60C22×C8×C11C2312yes—
61C11×C22⋊Q8—22no—
62C11×C22⋊Q8C2×C414yes—
63C4×Q8×C11—42no—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4—21no—
68C2×C11×C4⋊C4—42no—
69C2×C11×C4⋊C4C2312yes—
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C22⋊C4—21no—
74C2×C11×C22⋊C4—21no—
75C2×C42×C11—21no—
76C2×C42×C11—21no—
77C2×C42×C11—42no—
78C2×C42×C11D411yescharacteristic
79C2×C42×C11D411yescharacteristic
80C2×C42×C11C2311yescharacteristic
81C2×C42×C11C2311yescharacteristic
82C11×#106—42no—
83C11×#103—42no—
84C11×#103—42no—
85C11×#103—42no—
86C11×#103C2×C418yescomplemented
87C11×C22⋊C8—22no—
88C11×C22⋊C8C2×C414yes—
89C11×#97—42no—
90C11×#95—22no—
91C11×#95—22no—
92C11×#95—22no—
93C11×#95—22no—
94C11×#95—21no—
95C11×#95—21no—
96C11×#95—21no—
97C11×#95—21no—
98C11×#95—21no—
99#22050C1111yesmaximal, characteristic, direct product factor, Sylow
100C24×C11C2×D411yescharacteristic
101C2×Q8×C11—24no—
102C2×Q8×C11—21no—
103C2×Q8×C11—22no—
104C2×Q8×C11—22no—
105C2×Q8×C11—22no—
106C2×Q8×C11—22no—
107C2×Q8×C11—22no—
108C2×Q8×C11—22no—
109C2×Q8×C11—22no—
110C2×Q8×C11—48no—
111C2×Q8×C11—42no—
112C2×Q8×C11—42no—
113C2×Q8×C11—48no—
114C2×Q8×C11C22×C414yes—
115C2×Q8×C11C22×C412yes—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—24no—
119C22×C4×C11—22no—
120C22×C4×C11—22no—
121C22×C4×C11—22no—
122C22×C4×C11—21no—
123C22×C4×C11—21no—
124C22×C4×C11—22no—
125C22×C4×C11—21no—
126C22×C4×C11—22no—
127C22×C4×C11—21no—
128C22×C4×C11—41no—
129C22×C4×C11—41no—
130C22×C4×C11—41no—
131C22×C4×C11—42no—
132C22×C4×C11—42no—
133C22×C4×C11—42no—
134C22×C4×C11—42no—
135C22×C4×C11—42no—
136C22×C4×C11C22×C412yes—
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11#4112yes—
143C22×C4×C11C2411yescharacteristic
144C11×Q16—48no—
145C2×C8×C11—22no—
146C2×C8×C11—22no—
147C2×C8×C11—22no—
148C2×C8×C11—22no—
149C2×C8×C11—22no—
150C2×C8×C11C22×C414yes—
151C11×C4⋊C4—24no—
152C11×C4⋊C4—21no—
153C11×C4⋊C4—22no—
154C11×C4⋊C4—22no—
155C11×C4⋊C4—22no—
156C11×C4⋊C4—22no—
157C11×C4⋊C4—42no—
158C11×C4⋊C4—42no—
159C11×C4⋊C4—42no—
160C11×C4⋊C4C22×C412yes—
161C11×C22⋊C4—24no—
162C11×C22⋊C4—42no—
163C42×C11—22no—
164C42×C11—22no—
165C42×C11—41no—
166C42×C11—41no—
167C42×C11—42no—
168C42×C11—42no—
169C2×#451C2×C1111yescharacteristic
170C4×C22⋊Q8C2×C1111yescharacteristic
171C2×#391C2×C1111yescharacteristic
172#1971C2×C1112yescomplemented
173#1935C2×C1112yescomplemented
174#1927C2×C1112yescomplemented
175#1878C2×C1112yescomplemented
176#1872C2×C1111yescharacteristic
177#1853C2×C1111yescharacteristic
178#1787C2×C1111yescharacteristic
179#1749C2×C1111yescharacteristic
180C23×C11—21no—
181C23×C11—21no—
182C23×C11—21no—
183C23×C11—21no—
184C23×C11C4×D412yes—
185C23×C11#13712yes—
186C23×C11#13712yes—
187C23×C11C22×D411yescharacteristic
188Q8×C11—24no—
189Q8×C11—24no—
190Q8×C11—24no—
191Q8×C11—48no—
192Q8×C11—42no—
193Q8×C11—42no—
194Q8×C11—42no—
195C2×C4×C11—21no—
196C2×C4×C11—21no—
197C2×C4×C11—21no—
198C2×C4×C11—21no—
199C2×C4×C11—24no—
200C2×C4×C11—24no—
201C2×C4×C11—22no—
202C2×C4×C11—22no—
203C2×C4×C11—24no—
204C2×C4×C11—21no—
205C2×C4×C11—21no—
206C2×C4×C11—21no—
207C2×C4×C11—21no—
208C2×C4×C11—21no—
209C2×C4×C11—21no—
210C2×C4×C11—21no—
211C2×C4×C11—21no—
212C2×C4×C11—21no—
213C2×C4×C11—44no—
214C2×C4×C11—44no—
215C2×C4×C11—48no—
216C2×C4×C11—41no—
217C2×C4×C11—42no—
218C2×C4×C11—42no—
219C2×C4×C11—41no—
220C2×C4×C11—41no—
221C2×C4×C11—41no—
222C2×C4×C11—41no—
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—41no—
230C2×C4×C11—42no—
231C2×C4×C11—84no—
232C2×C4×C11C4×D412yes—
233C2×C4×C11#13712yes—
234C2×C4×C11C23×C411yescharacteristic
235C2×C4×C11C2×#4111yescharacteristic
236C2×C4×C11H(5,𝔽2)12yes—
237C2×C4×C11H(5,𝔽2)12yes—
238C8×C11—24no—
239C8×C11—42no—
240C23×Q8C22×C1111yescharacteristic
241C22×Q16C22×C1112yes—
242C2×C22⋊Q8C22×C1111yescharacteristic
243C2×C4×Q8C22×C1111yescharacteristic
244C22×C4⋊C4C22×C1111yescharacteristic
245C22×C42C22×C1111yescharacteristic
246#451C4×C1118yescomplemented
247C2×#106C22×C1112yes—
248C2×#103C22×C1112yes—
249C2×#103C22×C1112yes—
250C2×#103C22×C1112yes—
251C2×#103C22×C1112yes—
252C2×C22⋊C8C22×C1111yescharacteristic
253C2×C22⋊C8C22×C1111yescharacteristic
254C2×#97C22×C1112yes—
255#391—21no—
256#391—21no—
257#391C22×C1112yes—
258#391C22×C1112yes—
259#391C22×C1111yescharacteristic
260#389C22×C1111yescharacteristic
261#387—21no—
262#385—21no—
263#380C22×C1111yescharacteristic
264C4×C4⋊C4—21no—
265C4×C4⋊C4C22×C1111yescharacteristic
266C4×C22⋊C4—21no—
267C2×#95—21no—
268C2×#95—21no—
269#340C22×C1112yes—
270#340C22×C1112yes—
271#336C22×C1112yes—
272C22×C11—22no—
273C22×C11—22no—
274C22×C11—22no—
275C22×C11—22no—
276C22×C11—22no—
277C22×C11—22no—
278C22×C11#44114yes—
279C22×C11C2×C4×D411yescharacteristic
280C22×C11#53411yescharacteristic
281C22×C11#53511yescharacteristic
282C22×C11C2×#13711yescharacteristic
283C22×C11C2×#13711yescharacteristic
284C22×C11C2×#13711yescharacteristic
285C22×C11#57511yescharacteristic
286C4×C11—22no—
287C4×C11—22no—
288C4×C11—44no—
289C4×C11—42no—
290C4×C11—41no—
291C4×C11—41no—
292C4×C11—41no—
293C4×C11—42no—
294C4×C11—81no—
295C4×C11—82no—
296C4×C11—81no—
297C4×C11#51812yes—
298C4×C11#53812yes—
299C22×Q8—21no—
300C22×Q8—22no—
301C22×Q8—42no—
302C22×Q8—42no—
303C22×Q8C2×C4×C1114yes—
304C22×Q8C23×C1111yescharacteristic
305C22×Q8C23×C1112yes—
306C23×C4—21no—
307C23×C4—21no—
308C23×C4D4×C1111yescharacteristic
309C23×C4D4×C1111yescharacteristic
310C23×C4C23×C1111yescharacteristic
311C2×Q16—42no—
312C2×Q16—42no—
313C2×Q16C2×C4×C1118yescomplemented
314C22×C8C23×C1112yes—
315C22×C8C23×C1112yes—
316C22⋊Q8—22no—
317C22⋊Q8C2×C4×C1114yes—
318C4×Q8—42no—
319C2×C4⋊C4—21no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4—21no—
323C2×C4⋊C4—42no—
324C2×C4⋊C4C23×C1112yes—
325C2×C4⋊C4C23×C1111yescharacteristic
326C2×C4⋊C4C23×C1111yescharacteristic
327C2×C4⋊C4C23×C1111yescharacteristic
328C2×C22⋊C4—21no—
329C2×C22⋊C4—21no—
330C2×C42—21no—
331C2×C42—21no—
332C2×C42—42no—
333C2×C42D4×C1111yescharacteristic
334C2×C42D4×C1111yescharacteristic
335C2×C42C23×C1111yescharacteristic
336C2×C42C23×C1111yescharacteristic
337#106—42no—
338#103—42no—
339#103—42no—
340#103—42no—
341#103C2×C4×C1118yescomplemented
342C22⋊C8—22no—
343C22⋊C8C2×C4×C1114yes—
344#97—42no—
345#95—22no—
346#95—22no—
347#95—22no—
348#95—22no—
349#95—21no—
350#95—21no—
351#95—21no—
352#95—21no—
353#95—21no—
354C2×C11—24no—
355C2×C11#232111yescharacteristic
356C2×C11C2×#44111yescharacteristic
357C2×C11C4×#13711yescharacteristic
358C2×C11#319511yescharacteristic
359C2×C11#319611yescharacteristic
360C2×C11#321511yescharacteristic
361C2×C11#321811yescharacteristic
362C24C2×D4×C1111yescharacteristic
363C2×Q8—24no—
364C2×Q8—21no—
365C2×Q8—22no—
366C2×Q8—22no—
367C2×Q8—22no—
368C2×Q8—22no—
369C2×Q8—22no—
370C2×Q8—22no—
371C2×Q8—22no—
372C2×Q8—48no—
373C2×Q8—42no—
374C2×Q8—42no—
375C2×Q8—48no—
376C2×Q8C22×C4×C1114yes—
377C2×Q8C22×C4×C1112yes—
378C22×C4—22no—
379C22×C4—22no—
380C22×C4—24no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—21no—
385C22×C4—21no—
386C22×C4—22no—
387C22×C4—21no—
388C22×C4—22no—
389C22×C4—21no—
390C22×C4—41no—
391C22×C4—41no—
392C22×C4—41no—
393C22×C4—42no—
394C22×C4—42no—
395C22×C4—42no—
396C22×C4—42no—
397C22×C4—42no—
398C22×C4C22×C4×C1112yes—
399C22×C4C2×D4×C1111yescharacteristic
400C22×C4C2×D4×C1111yescharacteristic
401C22×C4C2×D4×C1111yescharacteristic
402C22×C4C2×D4×C1111yescharacteristic
403C22×C4C2×D4×C1111yescharacteristic
404C22×C4C11×#4112yes—
405C22×C4C24×C1111yescharacteristic
406Q16—48no—
407C2×C8—22no—
408C2×C8—22no—
409C2×C8—22no—
410C2×C8—22no—
411C2×C8—22no—
412C2×C8C22×C4×C1114yes—
413C4⋊C4—24no—
414C4⋊C4—21no—
415C4⋊C4—22no—
416C4⋊C4—22no—
417C4⋊C4—22no—
418C4⋊C4—22no—
419C4⋊C4—42no—
420C4⋊C4—42no—
421C4⋊C4—42no—
422C4⋊C4C22×C4×C1112yes—
423C22⋊C4—24no—
424C22⋊C4—42no—
425C42—22no—
426C42—22no—
427C42—41no—
428C42—41no—
429C42—42no—
430C42—42no—
431C11#2205011yescharacteristic, direct product factor, Sylow
432C23—21no—
433C23—21no—
434C23—21no—
435C23—21no—
436C23C4×D4×C1112yes—
437C23C11×#13712yes—
438C23C11×#13712yes—
439C23C22×D4×C1111yescharacteristic
440Q8—24no—
441Q8—24no—
442Q8—24no—
443Q8—48no—
444Q8—42no—
445Q8—42no—
446Q8—42no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—24no—
452C2×C4—24no—
453C2×C4—22no—
454C2×C4—22no—
455C2×C4—24no—
456C2×C4—21no—
457C2×C4—21no—
458C2×C4—21no—
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—21no—
463C2×C4—21no—
464C2×C4—21no—
465C2×C4—44no—
466C2×C4—44no—
467C2×C4—48no—
468C2×C4—41no—
469C2×C4—42no—
470C2×C4—42no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—41no—
475C2×C4—42no—
476C2×C4—41no—
477C2×C4—41no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—42no—
481C2×C4—41no—
482C2×C4—42no—
483C2×C4—84no—
484C2×C4C4×D4×C1112yes—
485C2×C4C11×#13712yes—
486C2×C4C23×C4×C1111yescharacteristic
487C2×C4C2×C11×#4111yescharacteristic
488C2×C4C11×H(5,𝔽2)12yes—
489C2×C4C11×H(5,𝔽2)12yes—
490C8—24no—
491C8—42no—
492C22—22no—
493C22—22no—
494C22—22no—
495C22—22no—
496C22—22no—
497C22—22no—
498C22C11×#44114yes—
499C22C2×C4×D4×C1111yescharacteristic
500C22C11×#53411yescharacteristic
501C22C11×#53511yescharacteristic
502C22C2×C11×#13711yescharacteristic
503C22C2×C11×#13711yescharacteristic
504C22C2×C11×#13711yescharacteristic
505C22C11×#57511yescharacteristic
506C4—22no—
507C4—22no—
508C4—41no—
509C4—41no—
510C4—41no—
511C4—42no—
512C4—44no—
513C4—42no—
514C4—81no—
515C4—82no—
516C4—81no—
517C4C11×#51812yes—
518C4C11×#53812yes—
519C2—24no—
520C2C11×#232111yescharacteristic
521C2C2×C11×#44111yescharacteristic
522C2C4×C11×#13711yescharacteristic
523C2C11×#319511yescharacteristic
524C2C11×#319611yescharacteristic
525C2C11×#321511yescharacteristic
526C2C11×#321811yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC24×C11C2×D4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C22×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
4. C11×#1971C2semidirect
5. C11×#1935C2semidirect
6. C11×#1927C2semidirect
7. C11×#1878C2semidirect
18. C11×#451C4semidirect
58. C2×C11×Q16C2×C4semidirect
86. C11×#103C2×C4semidirect
99. #22050C11direct (N × H)
172. #1971C2×C11semidirect
173. #1935C2×C11semidirect
174. #1927C2×C11semidirect
175. #1878C2×C11semidirect
246. #451C4×C11semidirect
313. C2×Q16C2×C4×C11semidirect
341. #103C2×C4×C11semidirect
431. C11#22050direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4512
C4×C11×C22⋊Q82
C2×C11×#3912
C11×#19712
C11×#19352
C11×#19272
C11×#18782
C11×#18722
C11×#18532
C11×#17872
C11×#17492
#2205011