Finite Group Databasebeta

← C11×#24680 #14601873

Subgroups — C11×#24680 #14601873

Order 2816.

838 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×#476C211yesmaximal, characteristic
2C2×C4×C11×SD16C211yesmaximal, characteristic
3C11×#2567C211yesmaximal, characteristic, complemented
4C11×#2354C211yesmaximal, characteristic
5C11×#2071C212yesmaximal
6C11×#2055C212yesmaximal
7C11×#1990C211yesmaximal, characteristic, complemented
8C11×#1948C212yesmaximal, complemented
9C11×#1939C211yesmaximal, characteristic, complemented
10C11×#1927C212yesmaximal, complemented
11C11×#1803C211yesmaximal, characteristic, complemented
12C22×C11×SD16C2211yescharacteristic
13C2×C11×C4⋊Q8C2211yescharacteristic
14C2×C4×Q8×C11C2211yescharacteristic
15C2×C4×D4×C11C2211yescharacteristic
16C2×C11×#117—21no—
17C11×#476—24no—
18C4×C11×SD16—24no—
19C2×C11×#106C2211yescharacteristic
20C2×C11×#106C2212yes—
21C2×C11×C4⋊C8C2212yes—
22C2×C11×C4⋊C8C2211yescharacteristic
23C2×C11×#103C2211yescharacteristic
24C2×C11×#103C2212yes—
25C2×C11×#102C2211yescharacteristic
26C2×C11×#102C2212yes—
27C2×C4×C8×C11C2211yescharacteristic
28C11×#395—22no—
29C11×#391C2212yes—
30C11×#390C2212yes—
31C11×#389—21no—
32C11×#389—21no—
33C11×#388—22no—
34C11×#384C2212yes—
35C11×#384C2211yescharacteristic
36C11×#380—21no—
37C4×C11×C4⋊C4C2212yes—
38C4×C11×C4⋊C4C2211yescharacteristic
39C11×#340C2212yes—
40C11×#340C2212yes—
41C11×#340C2212yes—
42C11×#336C2212yes—
43C22×Q8×C11—21no—
44C22×Q8×C11C2311yescharacteristic
45C22×D4×C11C2311yescharacteristic
46C23×C4×C11—21no—
47C2×C11×SD16—22no—
48C2×C11×SD16—22no—
49C2×C11×SD16—22no—
50C22×C8×C11C2311yescharacteristic
51C22×C8×C11C2312yes—
52C22×C8×C11C2311yescharacteristic
53C11×C4⋊Q8—22no—
54C11×C4⋊Q8—22no—
55C4×Q8×C11—22no—
56C4×Q8×C11—22no—
57C4×D4×C11—22no—
58C4×D4×C11D414yes—
59C11×#117—44no—
60C2×C11×C4⋊C4—21no—
61C2×C11×C4⋊C4—21no—
62C2×C11×C4⋊C4—21no—
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4—22no—
65C2×C11×C4⋊C4—22no—
66C2×C11×C4⋊C4D411yescharacteristic
67C2×C11×C4⋊C4D411yescharacteristic
68C2×C11×C4⋊C4C2312yes—
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C4⋊C4C2312yes—
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C22⋊C4—21no—
73C2×C11×C22⋊C4—22no—
74C2×C11×C22⋊C4—22no—
75C2×C42×C11—22no—
76C2×C42×C11—21no—
77C2×C42×C11C2312yes—
78C2×C42×C11C2311yescharacteristic
79C11×#106—22no—
80C11×#106—24no—
81C11×C4⋊C8—24no—
82C11×C4⋊C8—22no—
83C11×#103—24no—
84C11×#103—22no—
85C11×#102—22no—
86C11×#102—24no—
87C4×C8×C11—22no—
88C11×#95—22no—
89C11×#95—22no—
90C11×#95—22no—
91C11×#95D412yes—
92#24680C1111yesmaximal, characteristic, direct product factor, Sylow
93C24×C11—21no—
94C2×Q8×C11—21no—
95C2×Q8×C11—21no—
96C2×Q8×C11—21no—
97C2×Q8×C11—21no—
98C2×Q8×C11—21no—
99C2×Q8×C11—42no—
100C2×Q8×C11—81no—
101C2×Q8×C11—81no—
102C2×Q8×C11#4112yes—
103C2×D4×C11—21no—
104C2×D4×C11—21no—
105C2×D4×C11—21no—
106C2×D4×C11—21no—
107C2×D4×C11—21no—
108C2×D4×C11C2×D412yes—
109C22×C4×C11—21no—
110C22×C4×C11—21no—
111C22×C4×C11—24no—
112C22×C4×C11—22no—
113C22×C4×C11—22no—
114C22×C4×C11—21no—
115C22×C4×C11—42no—
116C22×C4×C11—42no—
117C22×C4×C11C2×D412yes—
118C22×C4×C11C2×D411yescharacteristic
119C22×C4×C11C2×D412yes—
120C22×C4×C11C2×D411yescharacteristic
121C22×C4×C11C2411yescharacteristic
122C11×SD16—28no—
123C2×C8×C11—21no—
124C2×C8×C11—21no—
125C2×C8×C11—22no—
126C2×C8×C11—21no—
127C2×C8×C11—22no—
128C2×C8×C11—22no—
129C2×C8×C11—21no—
130C2×C8×C11—21no—
131C2×C8×C11#4112yes—
132C11×C4⋊C4—22no—
133C11×C4⋊C4—21no—
134C11×C4⋊C4—21no—
135C11×C4⋊C4—22no—
136C11×C4⋊C4—22no—
137C11×C4⋊C4—21no—
138C11×C4⋊C4—22no—
139C11×C4⋊C4—22no—
140C11×C4⋊C4—42no—
141C11×C4⋊C4—42no—
142C11×C4⋊C4—42no—
143C11×C4⋊C4—81no—
144C11×C4⋊C4—82no—
145C11×C4⋊C4—82no—
146C11×C4⋊C4SD1614yescomplemented
147C11×C4⋊C4C2×D412yes—
148C11×C22⋊C4—24no—
149C11×C22⋊C4—44no—
150C11×C22⋊C4—82no—
151C42×C11—22no—
152C42×C11—22no—
153C42×C11—42no—
154C42×C11—44no—
155C42×C11C2×D412yes—
156C42×C11#4112yes—
157C2×#476C2×C1111yescharacteristic
158C2×C4×SD16C2×C1111yescharacteristic
159#2567C2×C1111yescharacteristic, complemented
160#2354C2×C1111yescharacteristic
161#2071C2×C1112yes—
162#2055C2×C1112yes—
163#1990C2×C1111yescharacteristic, complemented
164#1948C2×C1112yescomplemented
165#1939C2×C1111yescharacteristic, complemented
166#1927C2×C1112yescomplemented
167#1803C2×C1111yescharacteristic, complemented
168C23×C11—22no—
169C23×C11—41no—
170C23×C11—41no—
171C23×C11—41no—
172C23×C11—41no—
173C23×C11—41no—
174C23×C11—41no—
175C23×C11C22×D411yescharacteristic
176Q8×C11—22no—
177Q8×C11—22no—
178Q8×C11—41no—
179Q8×C11—41no—
180Q8×C11—84no—
181D4×C11—22no—
182D4×C11—22no—
183D4×C11—41no—
184D4×C11—41no—
185C2×C4×C11—22no—
186C2×C4×C11—21no—
187C2×C4×C11—22no—
188C2×C4×C11—21no—
189C2×C4×C11—22no—
190C2×C4×C11—22no—
191C2×C4×C11—22no—
192C2×C4×C11—22no—
193C2×C4×C11—22no—
194C2×C4×C11—41no—
195C2×C4×C11—41no—
196C2×C4×C11—41no—
197C2×C4×C11—41no—
198C2×C4×C11—48no—
199C2×C4×C11—41no—
200C2×C4×C11—42no—
201C2×C4×C11—42no—
202C2×C4×C11—42no—
203C2×C4×C11—42no—
204C2×C4×C11—41no—
205C2×C4×C11—42no—
206C2×C4×C11—41no—
207C2×C4×C11—42no—
208C2×C4×C11#12112yes—
209C2×C4×C11#12112yes—
210C2×C4×C11C2×SD1614yes—
211C2×C4×C11C2×SD1612yes—
212C2×C4×C11#13712yes—
213C2×C4×C11C22×D411yescharacteristic
214C2×C4×C11C2×#4111yescharacteristic
215C2×C4×C11C2×#4111yescharacteristic
216C2×C4×C11C2×#4111yescharacteristic
217C2×C4×C112−1+411yescharacteristic
218C2×C4×C112−1+411yescharacteristic
219C8×C11—22no—
220C8×C11—42no—
221C8×C11—41no—
222C22×SD16C22×C1111yescharacteristic
223C2×C4⋊Q8C22×C1111yescharacteristic
224C2×C4×Q8C22×C1111yescharacteristic
225C2×C4×D4C22×C1111yescharacteristic
226C2×#117—21no—
227#476—24no—
228C4×SD16—24no—
229C2×#106C22×C1111yescharacteristic
230C2×#106C22×C1112yes—
231C2×C4⋊C8C22×C1112yes—
232C2×C4⋊C8C22×C1111yescharacteristic
233C2×#103C22×C1112yes—
234C2×#103C22×C1111yescharacteristic
235C2×#102C22×C1112yes—
236C2×#102C22×C1111yescharacteristic
237C2×C4×C8C22×C1111yescharacteristic
238#395—22no—
239#391C22×C1112yes—
240#390C22×C1112yes—
241#389—21no—
242#389—21no—
243#388—22no—
244#384C22×C1112yes—
245#384C22×C1111yescharacteristic
246#380—21no—
247C4×C4⋊C4C22×C1112yes—
248C4×C4⋊C4C22×C1111yescharacteristic
249#340C22×C1112yes—
250#340C22×C1112yes—
251#340C22×C1112yes—
252#336C22×C1112yes—
253C22×C11—42no—
254C22×C11—42no—
255C22×C11—42no—
256C22×C11—81no—
257C22×C11—81no—
258C22×C11—81no—
259C22×C11—81no—
260C22×C11C2×#12111yescharacteristic
261C22×C11#54711yescharacteristic
262C22×C11#54811yescharacteristic
263C22×C11C22×SD1611yescharacteristic
264C22×C11C2×#13711yescharacteristic
265C22×C11#57611yescharacteristic
266C22×C11#57711yescharacteristic
267C4×C11—24no—
268C4×C11—22no—
269C4×C11—42no—
270C4×C11—42no—
271C4×C11—42no—
272C4×C11—82no—
273C4×C11—81no—
274C4×C11—82no—
275C4×C11#46114yes—
276C4×C11#52511yescharacteristic
277C4×C11#53611yescharacteristic
278C4×C11#55211yescharacteristic
279C4×C11#55611yescharacteristic
280C22×Q8—21no—
281C22×Q8C23×C1111yescharacteristic
282C22×D4C23×C1111yescharacteristic
283C23×C4—21no—
284C2×SD16—22no—
285C2×SD16—22no—
286C2×SD16—22no—
287C22×C8C23×C1111yescharacteristic
288C22×C8C23×C1112yes—
289C22×C8C23×C1111yescharacteristic
290C4⋊Q8—22no—
291C4⋊Q8—22no—
292C4×Q8—22no—
293C4×Q8—22no—
294C4×D4—22no—
295C4×D4D4×C1114yes—
296#117—44no—
297C2×C4⋊C4—21no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4—21no—
300C2×C4⋊C4—21no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4—22no—
303C2×C4⋊C4D4×C1111yescharacteristic
304C2×C4⋊C4D4×C1111yescharacteristic
305C2×C4⋊C4C23×C1111yescharacteristic
306C2×C4⋊C4C23×C1112yes—
307C2×C4⋊C4C23×C1112yes—
308C2×C4⋊C4C23×C1111yescharacteristic
309C2×C22⋊C4—21no—
310C2×C22⋊C4—22no—
311C2×C22⋊C4—22no—
312C2×C42—22no—
313C2×C42—21no—
314C2×C42C23×C1112yes—
315C2×C42C23×C1111yescharacteristic
316#106—22no—
317#106—24no—
318C4⋊C8—24no—
319C4⋊C8—22no—
320#103—24no—
321#103—22no—
322#102—22no—
323#102—24no—
324C4×C8—22no—
325#95—22no—
326#95—22no—
327#95—22no—
328#95D4×C1112yes—
329C2×C11—82no—
330C2×C11#241511yescharacteristic
331C2×C11C2×#46111yescharacteristic
332C2×C11#304511yescharacteristic
333C2×C11#333511yescharacteristic
334C2×C11#335711yescharacteristic
335C2×C11#336211yescharacteristic
336C2×C11#336911yescharacteristic
337C24—21no—
338C2×Q8—21no—
339C2×Q8—21no—
340C2×Q8—21no—
341C2×Q8—21no—
342C2×Q8—21no—
343C2×Q8—42no—
344C2×Q8—81no—
345C2×Q8—81no—
346C2×Q8C11×#4112yes—
347C2×D4—21no—
348C2×D4—21no—
349C2×D4—21no—
350C2×D4—21no—
351C2×D4—21no—
352C2×D4C2×D4×C1112yes—
353C22×C4—21no—
354C22×C4—21no—
355C22×C4—24no—
356C22×C4—22no—
357C22×C4—22no—
358C22×C4—21no—
359C22×C4—42no—
360C22×C4—42no—
361C22×C4C2×D4×C1112yes—
362C22×C4C2×D4×C1111yescharacteristic
363C22×C4C2×D4×C1112yes—
364C22×C4C2×D4×C1111yescharacteristic
365C22×C4C24×C1111yescharacteristic
366SD16—28no—
367C2×C8—21no—
368C2×C8—21no—
369C2×C8—21no—
370C2×C8—22no—
371C2×C8—22no—
372C2×C8—22no—
373C2×C8—21no—
374C2×C8—21no—
375C2×C8C11×#4112yes—
376C4⋊C4—22no—
377C4⋊C4—21no—
378C4⋊C4—21no—
379C4⋊C4—22no—
380C4⋊C4—22no—
381C4⋊C4—21no—
382C4⋊C4—22no—
383C4⋊C4—22no—
384C4⋊C4—42no—
385C4⋊C4—42no—
386C4⋊C4—42no—
387C4⋊C4—81no—
388C4⋊C4—82no—
389C4⋊C4—82no—
390C4⋊C4C11×SD1614yescomplemented
391C4⋊C4C2×D4×C1112yes—
392C22⋊C4—24no—
393C22⋊C4—44no—
394C22⋊C4—82no—
395C42—22no—
396C42—22no—
397C42—42no—
398C42—44no—
399C42C2×D4×C1112yes—
400C42C11×#4112yes—
401C11#2468011yescharacteristic, direct product factor, Sylow
402C23—22no—
403C23—41no—
404C23—41no—
405C23—41no—
406C23—41no—
407C23—41no—
408C23—41no—
409C23C22×D4×C1111yescharacteristic
410Q8—22no—
411Q8—22no—
412Q8—41no—
413Q8—41no—
414Q8—84no—
415D4—22no—
416D4—22no—
417D4—41no—
418D4—41no—
419C2×C4—22no—
420C2×C4—21no—
421C2×C4—22no—
422C2×C4—21no—
423C2×C4—22no—
424C2×C4—22no—
425C2×C4—22no—
426C2×C4—22no—
427C2×C4—22no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—48no—
433C2×C4—41no—
434C2×C4—42no—
435C2×C4—42no—
436C2×C4—42no—
437C2×C4—42no—
438C2×C4—41no—
439C2×C4—42no—
440C2×C4—41no—
441C2×C4—42no—
442C2×C4C11×#12112yes—
443C2×C4C11×#12112yes—
444C2×C4C2×C11×SD1614yes—
445C2×C4C2×C11×SD1612yes—
446C2×C4C11×#13712yes—
447C2×C4C22×D4×C1111yescharacteristic
448C2×C4C2×C11×#4111yescharacteristic
449C2×C4C2×C11×#4111yescharacteristic
450C2×C4C2×C11×#4111yescharacteristic
451C2×C4C11×2−1+411yescharacteristic
452C2×C4C11×2−1+411yescharacteristic
453C8—22no—
454C8—42no—
455C8—41no—
456C22—42no—
457C22—42no—
458C22—42no—
459C22—81no—
460C22—81no—
461C22—81no—
462C22—81no—
463C22C2×C11×#12111yescharacteristic
464C22C11×#54711yescharacteristic
465C22C11×#54811yescharacteristic
466C22C22×C11×SD1611yescharacteristic
467C22C2×C11×#13711yescharacteristic
468C22C11×#57611yescharacteristic
469C22C11×#57711yescharacteristic
470C4—22no—
471C4—24no—
472C4—42no—
473C4—42no—
474C4—42no—
475C4—82no—
476C4—81no—
477C4—82no—
478C4C11×#46114yes—
479C4C11×#52511yescharacteristic
480C4C11×#53611yescharacteristic
481C4C11×#55211yescharacteristic
482C4C11×#55611yescharacteristic
483C2—82no—
484C2C11×#241511yescharacteristic
485C2C2×C11×#46111yescharacteristic
486C2C11×#304511yescharacteristic
487C2C11×#333511yescharacteristic
488C2C11×#335711yescharacteristic
489C2C11×#336211yescharacteristic
490C2C11×#336911yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC22×D4×C11C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C4×C11×C4⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
3. C11×#2567C2semidirect
7. C11×#1990C2semidirect
8. C11×#1948C2semidirect
9. C11×#1939C2semidirect
10. C11×#1927C2semidirect
11. C11×#1803C2semidirect
92. #24680C11direct (N × H)
146. C11×C4⋊C4SD16semidirect
159. #2567C2×C11semidirect
163. #1990C2×C11semidirect
164. #1948C2×C11semidirect
165. #1939C2×C11semidirect
166. #1927C2×C11semidirect
167. #1803C2×C11semidirect
390. C4⋊C4C11×SD16semidirect
401. C11#24680direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4762
C2×C4×C11×SD162
C11×#25672
C11×#23542
C11×#20712
C11×#20552
C11×#19902
C11×#19482
C11×#19392
C11×#19272
C11×#18032
#2468011