Finite Group Databasebeta

← C11×#24837 #14602030

Subgroups — C11×#24837 #14602030

Order 2816.

904 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#477C211yesmaximal, characteristic, complemented
2C22×C11×C4⋊C8C211yesmaximal, characteristic
3C11×#2857C211yesmaximal, characteristic
4C4×C11×C22⋊Q8C211yesmaximal, characteristic
5C11×#2087C212yesmaximal, complemented
6C11×#2068C212yesmaximal, complemented
7C11×#1987C211yesmaximal, characteristic, complemented
8C11×#1947C211yesmaximal, characteristic, complemented
9C11×#1892C212yesmaximal
10C11×#1808C212yesmaximal
11C11×#1803C211yesmaximal, characteristic, complemented
12C23×C8×C11C2212yes—
13C2×C11×C4⋊Q8C2211yescharacteristic
14C2×C11×C22⋊Q8—21no—
15C2×C11×C22⋊Q8C2211yescharacteristic
16C2×C4×Q8×C11C2211yescharacteristic
17C22×C42×C11C2211yescharacteristic
18C11×#477—24no—
19C2×C11×#107C2212yes—
20C2×C11×#107C2212yes—
21C2×C11×C4⋊C8—24no—
22C2×C11×C4⋊C8C2211yescharacteristic
23C2×C11×C4⋊C8C2212yes—
24C2×C11×C4⋊C8C2211yescharacteristic
25C2×C11×#103C2212yes—
26C2×C11×#103C2212yes—
27C11×#391—21no—
28C11×#391C2211yescharacteristic
29C11×#389—21no—
30C11×#389C2211yescharacteristic
31C11×#389C2212yes—
32C11×#387—21no—
33C11×#385—21no—
34C11×#384C2211yescharacteristic
35C11×#380—21no—
36C11×#380C2212yes—
37C11×#380C2211yescharacteristic
38C4×C11×C4⋊C4—21no—
39C4×C11×C4⋊C4C2211yescharacteristic
40C4×C11×C22⋊C4—21no—
41C11×#340C2212yes—
42C11×#340C2212yes—
43C11×#340C2212yes—
44C11×#340C2212yes—
45C22×Q8×C11—21no—
46C22×Q8×C11C2311yescharacteristic
47C23×C4×C11D411yescharacteristic
48C23×C4×C11D411yescharacteristic
49C23×C4×C11C2311yescharacteristic
50C22×C8×C11—24no—
51C22×C8×C11—24no—
52C22×C8×C11—42no—
53C22×C8×C11C2312yes—
54C22×C8×C11C2312yes—
55C11×C4⋊Q8—22no—
56C11×C4⋊Q8—22no—
57C11×C22⋊Q8—22no—
58C11×C22⋊Q8—44no—
59C11×C22⋊Q8Q814yescomplemented
60C4×Q8×C11—22no—
61C4×Q8×C11—22no—
62C2×C11×C4⋊C4—21no—
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4—21no—
68C2×C11×C4⋊C4—22no—
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C4⋊C4C2312yes—
72C2×C11×C4⋊C4C2312yes—
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C22⋊C4—21no—
75C2×C11×C22⋊C4—21no—
76C2×C11×C22⋊C4—22no—
77C2×C42×C11—22no—
78C2×C42×C11—22no—
79C2×C42×C11—21no—
80C2×C42×C11—21no—
81C2×C42×C11D411yescharacteristic
82C2×C42×C11D411yescharacteristic
83C2×C42×C11C2311yescharacteristic
84C2×C42×C11C2311yescharacteristic
85C11×#107—24no—
86C11×#107—42no—
87C11×C4⋊C8—24no—
88C11×C4⋊C8—22no—
89C11×C4⋊C8D414yes—
90C11×#103—24no—
91C11×#103—42no—
92C11×#95—21no—
93C11×#95—21no—
94C11×#95—21no—
95C11×#95—21no—
96C11×#95—21no—
97C11×#95—22no—
98C11×#95—22no—
99#24837C1111yesmaximal, characteristic, direct product factor, Sylow
100C24×C11C2×D411yescharacteristic
101C2×Q8×C11—21no—
102C2×Q8×C11—21no—
103C2×Q8×C11—21no—
104C2×Q8×C11—21no—
105C2×Q8×C11—21no—
106C2×Q8×C11—42no—
107C2×Q8×C11—42no—
108C2×Q8×C11—42no—
109C2×Q8×C11C2×Q812yes—
110C22×C4×C11—22no—
111C22×C4×C11—22no—
112C22×C4×C11—21no—
113C22×C4×C11—21no—
114C22×C4×C11—21no—
115C22×C4×C11—21no—
116C22×C4×C11—22no—
117C22×C4×C11—21no—
118C22×C4×C11—21no—
119C22×C4×C11—22no—
120C22×C4×C11—21no—
121C22×C4×C11—21no—
122C22×C4×C11—22no—
123C22×C4×C11—22no—
124C22×C4×C11—41no—
125C22×C4×C11Q1614yes—
126C22×C4×C11C2×D411yescharacteristic
127C22×C4×C11C2×D411yescharacteristic
128C22×C4×C11C2×D411yescharacteristic
129C22×C4×C11C2×D411yescharacteristic
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11C2×Q812yes—
132C22×C4×C11#4112yes—
133C22×C4×C11C2411yescharacteristic
134C2×C8×C11—22no—
135C2×C8×C11—22no—
136C2×C8×C11—22no—
137C2×C8×C11—22no—
138C2×C8×C11—22no—
139C2×C8×C11—48no—
140C2×C8×C11C2×D414yes—
141C11×C4⋊C4—24no—
142C11×C4⋊C4—21no—
143C11×C4⋊C4—22no—
144C11×C4⋊C4—21no—
145C11×C4⋊C4—21no—
146C11×C4⋊C4—22no—
147C11×C4⋊C4—22no—
148C11×C4⋊C4—21no—
149C11×C4⋊C4—21no—
150C11×C4⋊C4—22no—
151C11×C4⋊C4—42no—
152C11×C4⋊C4—42no—
153C11×C4⋊C4—44no—
154C11×C4⋊C4—42no—
155C11×C4⋊C4—42no—
156C11×C4⋊C4—42no—
157C11×C4⋊C4C2×Q812yes—
158C11×C22⋊C4—24no—
159C11×C22⋊C4—42no—
160C11×C22⋊C4—44no—
161C42×C11—22no—
162C42×C11—22no—
163C42×C11—21no—
164C42×C11—21no—
165C42×C11—42no—
166C42×C11—42no—
167C42×C11C2×D412yes—
168C42×C11#4112yes—
169C2×#477C2×C1111yescharacteristic, complemented
170C22×C4⋊C8C2×C1111yescharacteristic
171#2857C2×C1111yescharacteristic
172C4×C22⋊Q8C2×C1111yescharacteristic
173#2087C2×C1112yescomplemented
174#2068C2×C1112yescomplemented
175#1987C2×C1111yescharacteristic, complemented
176#1947C2×C1111yescharacteristic, complemented
177#1892C2×C1112yes—
178#1808C2×C1112yes—
179#1803C2×C1111yescharacteristic, complemented
180C23×C11—21no—
181C23×C11—21no—
182C23×C11—21no—
183C23×C11—21no—
184C23×C11C22⋊Q812yes—
185C23×C11C2×Q1612yes—
186C23×C11AGL(1,ℤ/8)12yes—
187C23×C11C22×D411yescharacteristic
188Q8×C11—22no—
189Q8×C11—22no—
190Q8×C11—41no—
191Q8×C11—41no—
192Q8×C11—84no—
193C2×C4×C11—21no—
194C2×C4×C11—21no—
195C2×C4×C11—21no—
196C2×C4×C11—21no—
197C2×C4×C11—21no—
198C2×C4×C11—21no—
199C2×C4×C11—22no—
200C2×C4×C11—22no—
201C2×C4×C11—22no—
202C2×C4×C11—22no—
203C2×C4×C11—28no—
204C2×C4×C11—21no—
205C2×C4×C11—22no—
206C2×C4×C11—22no—
207C2×C4×C11—21no—
208C2×C4×C11—21no—
209C2×C4×C11—44no—
210C2×C4×C11—41no—
211C2×C4×C11—41no—
212C2×C4×C11—41no—
213C2×C4×C11—41no—
214C2×C4×C11—41no—
215C2×C4×C11—42no—
216C2×C4×C11—42no—
217C2×C4×C11—41no—
218C2×C4×C11—41no—
219C2×C4×C11—42no—
220C2×C4×C11—42no—
221C2×C4×C11—42no—
222C2×C4×C11—41no—
223C2×C4×C11—41no—
224C2×C4×C11—41no—
225C2×C4×C11—42no—
226C2×C4×C11#12112yes—
227C2×C4×C11#12112yes—
228C2×C4×C11C22⋊Q812yes—
229C2×C4×C11C2×Q1612yes—
230C2×C4×C11C2×Q1612yes—
231C2×C4×C11#13512yes—
232C2×C4×C11C22×D411yescharacteristic
233C2×C4×C11C22×Q811yescharacteristic
234C2×C4×C11C2×#4111yescharacteristic
235C2×C4×C11C2×#4111yescharacteristic
236C2×C4×C11H(5,𝔽2)11yescharacteristic
237C2×C4×C112−1+411yescharacteristic
238C8×C11—24no—
239C8×C11—42no—
240C23×C8C22×C1112yes—
241C2×C4⋊Q8C22×C1111yescharacteristic
242C2×C22⋊Q8—21no—
243C2×C22⋊Q8C22×C1111yescharacteristic
244C2×C4×Q8C22×C1111yescharacteristic
245C22×C42C22×C1111yescharacteristic
246#477—24no—
247C2×#107C22×C1112yes—
248C2×#107C22×C1112yes—
249C2×C4⋊C8—24no—
250C2×C4⋊C8C22×C1111yescharacteristic
251C2×C4⋊C8C22×C1112yes—
252C2×C4⋊C8C22×C1111yescharacteristic
253C2×#103C22×C1112yes—
254C2×#103C22×C1112yes—
255#391—21no—
256#391C22×C1111yescharacteristic
257#389—21no—
258#389C22×C1112yes—
259#389C22×C1111yescharacteristic
260#387—21no—
261#385—21no—
262#384C22×C1111yescharacteristic
263#380—21no—
264#380C22×C1111yescharacteristic
265#380C22×C1112yes—
266C4×C4⋊C4—21no—
267C4×C4⋊C4C22×C1111yescharacteristic
268C4×C22⋊C4—21no—
269#340C22×C1112yes—
270#340C22×C1112yes—
271#340C22×C1112yes—
272#340C22×C1112yes—
273C22×C11—22no—
274C22×C11—22no—
275C22×C11—22no—
276C22×C11—22no—
277C22×C11—22no—
278C22×C11—22no—
279C22×C11#47714yescomplemented
280C22×C11C2×#12111yescharacteristic
281C22×C11C2×C22⋊Q811yescharacteristic
282C22×C11#53711yescharacteristic
283C22×C11C22×Q1611yescharacteristic
284C22×C11C2×#13511yescharacteristic
285C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
286C22×C11#57511yescharacteristic
287C4×C11—22no—
288C4×C11—22no—
289C4×C11—22no—
290C4×C11—42no—
291C4×C11—42no—
292C4×C11—41no—
293C4×C11—81no—
294C4×C11—82no—
295C4×C11—81no—
296C4×C11—82no—
297C4×C11#46714yes—
298C4×C11#54611yescharacteristic
299C4×C11D4×Q811yescharacteristic
300C4×C11#55211yescharacteristic
301C4×C11#55411yescharacteristic
302C22×Q8—21no—
303C22×Q8C23×C1111yescharacteristic
304C23×C4D4×C1111yescharacteristic
305C23×C4D4×C1111yescharacteristic
306C23×C4C23×C1111yescharacteristic
307C22×C8—24no—
308C22×C8—24no—
309C22×C8—42no—
310C22×C8C23×C1112yes—
311C22×C8C23×C1112yes—
312C4⋊Q8—22no—
313C4⋊Q8—22no—
314C22⋊Q8—22no—
315C22⋊Q8—44no—
316C22⋊Q8Q8×C1114yescomplemented
317C4×Q8—22no—
318C4×Q8—22no—
319C2×C4⋊C4—21no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—21no—
324C2×C4⋊C4—21no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4C23×C1111yescharacteristic
327C2×C4⋊C4C23×C1112yes—
328C2×C4⋊C4C23×C1111yescharacteristic
329C2×C4⋊C4C23×C1112yes—
330C2×C4⋊C4C23×C1111yescharacteristic
331C2×C22⋊C4—21no—
332C2×C22⋊C4—22no—
333C2×C22⋊C4—21no—
334C2×C42—22no—
335C2×C42—22no—
336C2×C42—21no—
337C2×C42—21no—
338C2×C42D4×C1111yescharacteristic
339C2×C42D4×C1111yescharacteristic
340C2×C42C23×C1111yescharacteristic
341C2×C42C23×C1111yescharacteristic
342#107—24no—
343#107—42no—
344C4⋊C8—24no—
345C4⋊C8—22no—
346C4⋊C8D4×C1114yes—
347#103—24no—
348#103—42no—
349#95—21no—
350#95—21no—
351#95—21no—
352#95—21no—
353#95—21no—
354#95—22no—
355#95—22no—
356C2×C11—24no—
357C2×C11#241711yescharacteristic
358C2×C11C2×#46711yescharacteristic
359C2×C11#305511yescharacteristic
360C2×C11C2×#47711yescharacteristic
361C2×C11#307611yescharacteristic
362C2×C11#324711yescharacteristic
363C2×C11#324911yescharacteristic
364C24C2×D4×C1111yescharacteristic
365C2×Q8—21no—
366C2×Q8—21no—
367C2×Q8—21no—
368C2×Q8—21no—
369C2×Q8—21no—
370C2×Q8—42no—
371C2×Q8—42no—
372C2×Q8—42no—
373C2×Q8C2×Q8×C1112yes—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—21no—
377C22×C4—21no—
378C22×C4—21no—
379C22×C4—21no—
380C22×C4—22no—
381C22×C4—21no—
382C22×C4—21no—
383C22×C4—22no—
384C22×C4—21no—
385C22×C4—21no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—41no—
389C22×C4C11×Q1614yes—
390C22×C4C2×D4×C1111yescharacteristic
391C22×C4C2×D4×C1111yescharacteristic
392C22×C4C2×D4×C1111yescharacteristic
393C22×C4C2×D4×C1111yescharacteristic
394C22×C4C2×D4×C1111yescharacteristic
395C22×C4C2×Q8×C1112yes—
396C22×C4C11×#4112yes—
397C22×C4C24×C1111yescharacteristic
398C2×C8—22no—
399C2×C8—22no—
400C2×C8—22no—
401C2×C8—22no—
402C2×C8—22no—
403C2×C8—48no—
404C2×C8C2×D4×C1114yes—
405C4⋊C4—24no—
406C4⋊C4—21no—
407C4⋊C4—22no—
408C4⋊C4—21no—
409C4⋊C4—21no—
410C4⋊C4—22no—
411C4⋊C4—22no—
412C4⋊C4—21no—
413C4⋊C4—21no—
414C4⋊C4—22no—
415C4⋊C4—42no—
416C4⋊C4—44no—
417C4⋊C4—42no—
418C4⋊C4—42no—
419C4⋊C4—42no—
420C4⋊C4—42no—
421C4⋊C4C2×Q8×C1112yes—
422C22⋊C4—24no—
423C22⋊C4—44no—
424C22⋊C4—42no—
425C42—22no—
426C42—22no—
427C42—21no—
428C42—21no—
429C42—42no—
430C42—42no—
431C42C2×D4×C1112yes—
432C42C11×#4112yes—
433C11#2483711yescharacteristic, direct product factor, Sylow
434C23—21no—
435C23—21no—
436C23—21no—
437C23—21no—
438C23C11×C22⋊Q812yes—
439C23C2×C11×Q1612yes—
440C23C11×AGL(1,ℤ/8)12yes—
441C23C22×D4×C1111yescharacteristic
442Q8—22no—
443Q8—22no—
444Q8—41no—
445Q8—41no—
446Q8—84no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—22no—
454C2×C4—22no—
455C2×C4—22no—
456C2×C4—22no—
457C2×C4—28no—
458C2×C4—21no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—21no—
462C2×C4—21no—
463C2×C4—44no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—42no—
470C2×C4—42no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—42no—
474C2×C4—42no—
475C2×C4—42no—
476C2×C4—41no—
477C2×C4—41no—
478C2×C4—41no—
479C2×C4—42no—
480C2×C4C11×#12112yes—
481C2×C4C11×#12112yes—
482C2×C4C11×C22⋊Q812yes—
483C2×C4C2×C11×Q1612yes—
484C2×C4C2×C11×Q1612yes—
485C2×C4C11×#13512yes—
486C2×C4C22×D4×C1111yescharacteristic
487C2×C4C22×Q8×C1111yescharacteristic
488C2×C4C2×C11×#4111yescharacteristic
489C2×C4C2×C11×#4111yescharacteristic
490C2×C4C11×H(5,𝔽2)11yescharacteristic
491C2×C4C11×2−1+411yescharacteristic
492C8—24no—
493C8—42no—
494C22—22no—
495C22—22no—
496C22—22no—
497C22—22no—
498C22—22no—
499C22—22no—
500C22C11×#47714yescomplemented
501C22C2×C11×#12111yescharacteristic
502C22C2×C11×C22⋊Q811yescharacteristic
503C22C11×#53711yescharacteristic
504C22C22×C11×Q1611yescharacteristic
505C22C2×C11×#13511yescharacteristic
506C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
507C22C11×#57511yescharacteristic
508C4—22no—
509C4—22no—
510C4—22no—
511C4—42no—
512C4—41no—
513C4—42no—
514C4—81no—
515C4—82no—
516C4—82no—
517C4—81no—
518C4C11×#46714yes—
519C4C11×#54611yescharacteristic
520C4D4×Q8×C1111yescharacteristic
521C4C11×#55211yescharacteristic
522C4C11×#55411yescharacteristic
523C2—24no—
524C2C11×#241711yescharacteristic
525C2C2×C11×#46711yescharacteristic
526C2C11×#305511yescharacteristic
527C2C2×C11×#47711yescharacteristic
528C2C11×#307611yescharacteristic
529C2C11×#324711yescharacteristic
530C2C11×#324911yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC24×C11C2×D4
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. C2×C11×#477C2semidirect
5. C11×#2087C2semidirect
6. C11×#2068C2semidirect
7. C11×#1987C2semidirect
8. C11×#1947C2semidirect
11. C11×#1803C2semidirect
59. C11×C22⋊Q8Q8semidirect
99. #24837C11direct (N × H)
169. C2×#477C2×C11semidirect
173. #2087C2×C11semidirect
174. #2068C2×C11semidirect
175. #1987C2×C11semidirect
176. #1947C2×C11semidirect
179. #1803C2×C11semidirect
279. C22×C11#477semidirect
316. C22⋊Q8Q8×C11semidirect
433. C11#24837direct (N × H)
500. C22C11×#477semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#4772
C22×C11×C4⋊C82
C11×#28572
C4×C11×C22⋊Q82
C11×#20872
C11×#20682
C11×#19872
C11×#19472
C11×#18922
C11×#18082
C11×#18032
#2483711