Finite Group Databasebeta

← C11×#24543 #14601736

Subgroups — C11×#24543 #14601736

Order 2816.

980 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#452C211yesmaximal, characteristic
2C2×C11×#417C211yesmaximal, characteristic
3C11×#2503C211yesmaximal, characteristic, complemented
4C11×#2341C211yesmaximal, characteristic
5C11×#2073C212yesmaximal, complemented
6C11×#2055C212yesmaximal, complemented
7C11×#1894C211yesmaximal, characteristic, complemented
8C11×#1878C212yesmaximal, complemented
9C11×#1851C211yesmaximal, characteristic, complemented
10C11×#1824C211yesmaximal, characteristic, complemented
11C11×#1805C212yesmaximal, complemented
12C22×C11×#41C2211yescharacteristic
13C22×C11×Q16C2211yescharacteristic
14C22×C11×SD16C2211yescharacteristic
15C22×C11×M16C2211yescharacteristic
16C2×C11×C22⋊Q8C2211yescharacteristic
17C2×C4×Q8×C11C2212yes—
18C22×C11×C4⋊C4C2211yescharacteristic
19C11×#452—24no—
20C2×C11×C4⋊C8C2212yes—
21C11×#417—24no—
22C2×C11×#103C2212yes—
23C2×C11×#103C2211yescharacteristic
24C2×C11×#103C2212yes—
25C2×C11×#102C2212yes—
26C2×C11×#102C2211yescharacteristic
27C2×C11×C22⋊C8C2211yescharacteristic
28C11×#400—21no—
29C11×#400—21no—
30C11×#391C2212yes—
31C11×#390—22no—
32C11×#390C2212yes—
33C11×#382C2212yes—
34C11×#381—22no—
35C11×#380—21no—
36C11×#380C2211yescharacteristic
37C4×C11×C22⋊C4—21no—
38C4×C11×C22⋊C4C2211yescharacteristic
39C11×#340C2212yes—
40C11×#340C2212yes—
41C11×#340C2212yes—
42C11×#336C2212yes—
43C2×C11×#41—22no—
44C2×C11×#41—24no—
45C2×C11×#41—42no—
46C2×C11×#41D414yes—
47C22×Q8×C11C2311yescharacteristic
48C22×Q8×C11C2311yescharacteristic
49C22×D4×C11—21no—
50C22×D4×C11C2311yescharacteristic
51C23×C4×C11—21no—
52C23×C4×C11—21no—
53C23×C4×C11C2311yescharacteristic
54C2×C11×Q16—22no—
55C2×C11×Q16—24no—
56C2×C11×SD16—22no—
57C2×C11×SD16—42no—
58C2×C11×M16—22no—
59C2×C11×M16—42no—
60C22×C8×C11C2311yescharacteristic
61C22×C8×C11C2312yes—
62C22×C8×C11C2311yescharacteristic
63C11×C22⋊Q8—22no—
64C11×C22⋊Q8—22no—
65C4×Q8×C11—24no—
66C4×Q8×C11—42no—
67C2×C11×C4⋊C4—22no—
68C2×C11×C4⋊C4—22no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4—22no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4C2312yes—
73C2×C11×C4⋊C4C2312yes—
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C22⋊C4—21no—
76C2×C11×C22⋊C4—22no—
77C2×C11×C22⋊C4—21no—
78C2×C11×C22⋊C4—22no—
79C2×C11×C22⋊C4D412yes—
80C2×C42×C11—22no—
81C2×C42×C11C2312yes—
82C11×C4⋊C8—42no—
83C11×#103—24no—
84C11×#103—22no—
85C11×#103—42no—
86C11×#102—24no—
87C11×#102—22no—
88C11×C22⋊C8—22no—
89C11×#95—21no—
90C11×#95—22no—
91C11×#95—22no—
92C11×#95—22no—
93C11×#95—22no—
94C11×#95D411yescharacteristic
95C11×#95D411yescharacteristic
96#24543C1111yesmaximal, characteristic, direct product factor, Sylow
97C24×C11—21no—
98C24×C11C2×D411yescharacteristic
99C11×#41—28no—
100C11×#41—44no—
101C11×#41—48no—
102C2×Q8×C11—21no—
103C2×Q8×C11—22no—
104C2×Q8×C11—21no—
105C2×Q8×C11—21no—
106C2×Q8×C11—22no—
107C2×Q8×C11—22no—
108C2×Q8×C11C2×D412yes—
109C2×Q8×C11#4114yes—
110C2×D4×C11—24no—
111C2×D4×C11—22no—
112C2×D4×C11—21no—
113C2×D4×C11—22no—
114C2×D4×C11—44no—
115C2×D4×C11C2×D412yes—
116C22×C4×C11—21no—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—24no—
120C22×C4×C11—21no—
121C22×C4×C11—21no—
122C22×C4×C11—22no—
123C22×C4×C11—22no—
124C22×C4×C11—44no—
125C22×C4×C11—44no—
126C22×C4×C11—42no—
127C22×C4×C11C2×D412yes—
128C22×C4×C11C2×D412yes—
129C22×C4×C11C2×D411yescharacteristic
130C22×C4×C11C2×D412yes—
131C22×C4×C11#4112yes—
132C22×C4×C11C2411yescharacteristic
133C11×Q16—44no—
134C11×SD16—44no—
135C11×M16—44no—
136C2×C8×C11—21no—
137C2×C8×C11—21no—
138C2×C8×C11—22no—
139C2×C8×C11—22no—
140C2×C8×C11—22no—
141C2×C8×C11—22no—
142C2×C8×C11—22no—
143C11×C4⋊C4—22no—
144C11×C4⋊C4—21no—
145C11×C4⋊C4—22no—
146C11×C4⋊C4—22no—
147C11×C4⋊C4—21no—
148C11×C4⋊C4—22no—
149C11×C4⋊C4—44no—
150C11×C4⋊C4—42no—
151C11×C4⋊C4—42no—
152C11×C22⋊C4—42no—
153C11×C22⋊C4—44no—
154C11×C22⋊C4—42no—
155C11×C22⋊C4—82no—
156C11×C22⋊C4—81no—
157C42×C11—22no—
158C42×C11—22no—
159C42×C11—44no—
160C2×#452C2×C1111yescharacteristic
161C2×#417C2×C1111yescharacteristic
162#2503C2×C1111yescharacteristic, complemented
163#2341C2×C1111yescharacteristic
164#2073C2×C1112yescomplemented
165#2055C2×C1112yescomplemented
166#1894C2×C1111yescharacteristic, complemented
167#1878C2×C1112yescomplemented
168#1851C2×C1111yescharacteristic, complemented
169#1824C2×C1111yescharacteristic, complemented
170#1805C2×C1112yescomplemented
171C23×C11—22no—
172C23×C11—22no—
173C23×C11—21no—
174C23×C11—21no—
175C23×C11—22no—
176C23×C11—42no—
177C23×C11—42no—
178C23×C11—41no—
179C23×C11—41no—
180C23×C11#12112yes—
181C23×C11C22×D411yescharacteristic
182Q8×C11—22no—
183Q8×C11—24no—
184Q8×C11—41no—
185Q8×C11—41no—
186Q8×C11—42no—
187Q8×C11#12314yes—
188D4×C11—22no—
189D4×C11—22no—
190D4×C11—48no—
191D4×C11—42no—
192C2×C4×C11—22no—
193C2×C4×C11—24no—
194C2×C4×C11—22no—
195C2×C4×C11—22no—
196C2×C4×C11—22no—
197C2×C4×C11—24no—
198C2×C4×C11—22no—
199C2×C4×C11—22no—
200C2×C4×C11—22no—
201C2×C4×C11—22no—
202C2×C4×C11—22no—
203C2×C4×C11—22no—
204C2×C4×C11—48no—
205C2×C4×C11—41no—
206C2×C4×C11—41no—
207C2×C4×C11—42no—
208C2×C4×C11—42no—
209C2×C4×C11—42no—
210C2×C4×C11—42no—
211C2×C4×C11—44no—
212C2×C4×C11—42no—
213C2×C4×C11—41no—
214C2×C4×C11—41no—
215C2×C4×C11—84no—
216C2×C4×C11#12112yes—
217C2×C4×C11C22×D411yescharacteristic
218C2×C4×C11C2×#4112yes—
219C2×C4×C11C2×#4111yescharacteristic
220C2×C4×C11H(5,𝔽2)12yes—
221C8×C11—41no—
222C8×C11—42no—
223C8×C11—41no—
224C22×#41C22×C1111yescharacteristic
225C22×Q16C22×C1111yescharacteristic
226C22×SD16C22×C1111yescharacteristic
227C22×M16C22×C1111yescharacteristic
228C2×C22⋊Q8C22×C1111yescharacteristic
229C2×C4×Q8C22×C1112yes—
230C22×C4⋊C4C22×C1111yescharacteristic
231#452—24no—
232C2×C4⋊C8C22×C1112yes—
233#417—24no—
234C2×#103C22×C1111yescharacteristic
235C2×#103C22×C1112yes—
236C2×#103C22×C1112yes—
237C2×#102C22×C1112yes—
238C2×#102C22×C1111yescharacteristic
239C2×C22⋊C8C22×C1111yescharacteristic
240#400—21no—
241#400—21no—
242#391C22×C1112yes—
243#390—22no—
244#390C22×C1112yes—
245#382C22×C1112yes—
246#381—22no—
247#380—21no—
248#380C22×C1111yescharacteristic
249C4×C22⋊C4—21no—
250C4×C22⋊C4C22×C1111yescharacteristic
251#340C22×C1112yes—
252#340C22×C1112yes—
253#340C22×C1112yes—
254#336C22×C1112yes—
255C22×C11—22no—
256C22×C11—22no—
257C22×C11—22no—
258C22×C11—42no—
259C22×C11—42no—
260C22×C11—42no—
261C22×C11—42no—
262C22×C11—42no—
263C22×C11—82no—
264C22×C11—82no—
265C22×C11C2×#12111yescharacteristic
266C22×C11#54612yes—
267C22×C11#57512yes—
268C22×C11#57711yescharacteristic
269C22×C11#57811yescharacteristic
270C4×C11—22no—
271C4×C11—24no—
272C4×C11—42no—
273C4×C11—42no—
274C4×C11—81no—
275C4×C11—82no—
276C4×C11—81no—
277C4×C11—82no—
278C4×C11C2×#12311yescharacteristic
279C4×C11#53411yescharacteristic
280C4×C11#55112yes—
281C2×#41—22no—
282C2×#41—24no—
283C2×#41—42no—
284C2×#41D4×C1114yes—
285C22×Q8C23×C1111yescharacteristic
286C22×Q8C23×C1111yescharacteristic
287C22×D4—21no—
288C22×D4C23×C1111yescharacteristic
289C23×C4—21no—
290C23×C4—21no—
291C23×C4C23×C1111yescharacteristic
292C2×Q16—22no—
293C2×Q16—24no—
294C2×SD16—22no—
295C2×SD16—42no—
296C2×M16—22no—
297C2×M16—42no—
298C22×C8C23×C1112yes—
299C22×C8C23×C1111yescharacteristic
300C22×C8C23×C1111yescharacteristic
301C22⋊Q8—22no—
302C22⋊Q8—22no—
303C4×Q8—24no—
304C4×Q8—42no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—21no—
308C2×C4⋊C4—22no—
309C2×C4⋊C4—21no—
310C2×C4⋊C4C23×C1112yes—
311C2×C4⋊C4C23×C1112yes—
312C2×C4⋊C4C23×C1111yescharacteristic
313C2×C22⋊C4—21no—
314C2×C22⋊C4—22no—
315C2×C22⋊C4—21no—
316C2×C22⋊C4—22no—
317C2×C22⋊C4D4×C1112yes—
318C2×C42—22no—
319C2×C42C23×C1112yes—
320C4⋊C8—42no—
321#103—24no—
322#103—22no—
323#103—42no—
324#102—24no—
325#102—22no—
326C22⋊C8—22no—
327#95—21no—
328#95—22no—
329#95—22no—
330#95—22no—
331#95—22no—
332#95D4×C1111yescharacteristic
333#95D4×C1111yescharacteristic
334C2×C11—42no—
335C2×C11—82no—
336C2×C11#241211yescharacteristic
337C2×C11#304011yescharacteristic
338C2×C11#304611yescharacteristic
339C2×C11#331712yes—
340C2×C11#332712yes—
341C24—21no—
342C24C2×D4×C1111yescharacteristic
343#41—28no—
344#41—44no—
345#41—48no—
346C2×Q8—21no—
347C2×Q8—22no—
348C2×Q8—21no—
349C2×Q8—21no—
350C2×Q8—22no—
351C2×Q8—22no—
352C2×Q8C2×D4×C1112yes—
353C2×Q8C11×#4114yes—
354C2×D4—24no—
355C2×D4—22no—
356C2×D4—21no—
357C2×D4—22no—
358C2×D4—44no—
359C2×D4C2×D4×C1112yes—
360C22×C4—21no—
361C22×C4—22no—
362C22×C4—22no—
363C22×C4—24no—
364C22×C4—21no—
365C22×C4—21no—
366C22×C4—22no—
367C22×C4—22no—
368C22×C4—44no—
369C22×C4—44no—
370C22×C4—42no—
371C22×C4C2×D4×C1112yes—
372C22×C4C2×D4×C1112yes—
373C22×C4C2×D4×C1111yescharacteristic
374C22×C4C2×D4×C1112yes—
375C22×C4C11×#4112yes—
376C22×C4C24×C1111yescharacteristic
377Q16—44no—
378SD16—44no—
379M16—44no—
380C2×C8—21no—
381C2×C8—21no—
382C2×C8—22no—
383C2×C8—22no—
384C2×C8—22no—
385C2×C8—22no—
386C2×C8—22no—
387C4⋊C4—22no—
388C4⋊C4—21no—
389C4⋊C4—22no—
390C4⋊C4—22no—
391C4⋊C4—21no—
392C4⋊C4—22no—
393C4⋊C4—44no—
394C4⋊C4—42no—
395C4⋊C4—42no—
396C22⋊C4—42no—
397C22⋊C4—44no—
398C22⋊C4—42no—
399C22⋊C4—82no—
400C22⋊C4—81no—
401C42—22no—
402C42—22no—
403C42—44no—
404C11#2454311yescharacteristic, direct product factor, Sylow
405C23—22no—
406C23—22no—
407C23—21no—
408C23—21no—
409C23—22no—
410C23—42no—
411C23—42no—
412C23—41no—
413C23—41no—
414C23C11×#12112yes—
415C23C22×D4×C1111yescharacteristic
416Q8—22no—
417Q8—24no—
418Q8—41no—
419Q8—41no—
420Q8—42no—
421Q8C11×#12314yes—
422D4—22no—
423D4—22no—
424D4—48no—
425D4—42no—
426C2×C4—22no—
427C2×C4—24no—
428C2×C4—22no—
429C2×C4—22no—
430C2×C4—22no—
431C2×C4—24no—
432C2×C4—22no—
433C2×C4—22no—
434C2×C4—22no—
435C2×C4—22no—
436C2×C4—22no—
437C2×C4—22no—
438C2×C4—48no—
439C2×C4—41no—
440C2×C4—41no—
441C2×C4—42no—
442C2×C4—42no—
443C2×C4—42no—
444C2×C4—42no—
445C2×C4—44no—
446C2×C4—42no—
447C2×C4—41no—
448C2×C4—41no—
449C2×C4—84no—
450C2×C4C11×#12112yes—
451C2×C4C22×D4×C1111yescharacteristic
452C2×C4C2×C11×#4112yes—
453C2×C4C2×C11×#4111yescharacteristic
454C2×C4C11×H(5,𝔽2)12yes—
455C8—41no—
456C8—42no—
457C8—41no—
458C22—22no—
459C22—22no—
460C22—22no—
461C22—42no—
462C22—42no—
463C22—42no—
464C22—42no—
465C22—42no—
466C22—82no—
467C22—82no—
468C22C2×C11×#12111yescharacteristic
469C22C11×#54612yes—
470C22C11×#57512yes—
471C22C11×#57711yescharacteristic
472C22C11×#57811yescharacteristic
473C4—22no—
474C4—24no—
475C4—42no—
476C4—42no—
477C4—81no—
478C4—82no—
479C4—81no—
480C4—82no—
481C4C2×C11×#12311yescharacteristic
482C4C11×#53411yescharacteristic
483C4C11×#55112yes—
484C2—42no—
485C2—82no—
486C2C11×#241211yescharacteristic
487C2C11×#304011yescharacteristic
488C2C11×#304611yescharacteristic
489C2C11×#331712yes—
490C2C11×#332712yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC22×C11×#41C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C4×C11×C22⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
3. C11×#2503C2semidirect
5. C11×#2073C2semidirect
6. C11×#2055C2semidirect
7. C11×#1894C2semidirect
8. C11×#1878C2semidirect
9. C11×#1851C2semidirect
10. C11×#1824C2semidirect
11. C11×#1805C2semidirect
96. #24543C11direct (N × H)
162. #2503C2×C11semidirect
164. #2073C2×C11semidirect
165. #2055C2×C11semidirect
166. #1894C2×C11semidirect
167. #1878C2×C11semidirect
168. #1851C2×C11semidirect
169. #1824C2×C11semidirect
170. #1805C2×C11semidirect
404. C11#24543direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4522
C2×C11×#4172
C11×#25032
C11×#23412
C11×#20732
C11×#20552
C11×#18942
C11×#18782
C11×#18512
C11×#18242
C11×#18052
#2454311