Finite Group Databasebeta

← C11×#24681 #14601874

Subgroups — C11×#24681 #14601874

Order 2816.

822 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#474C211yesmaximal, characteristic
2C2×C4×C11×SD16C211yesmaximal, characteristic
3C11×#2568C211yesmaximal, characteristic, complemented
4C11×#2354C211yesmaximal, characteristic
5C11×#2073C212yesmaximal
6C11×#2055C212yesmaximal
7C11×#1990C211yesmaximal, characteristic, complemented
8C11×#1949C212yesmaximal, complemented
9C11×#1939C211yesmaximal, characteristic, complemented
10C11×#1928C212yesmaximal, 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×#474—24no—
18C4×C11×SD16—24no—
19C2×C11×#107C2212yes—
20C2×C11×#106C2211yescharacteristic
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×#400—22no—
29C11×#391—21no—
30C11×#391—21no—
31C11×#391C2212yes—
32C11×#390C2212yes—
33C11×#388—22no—
34C11×#384C2211yescharacteristic
35C11×#382C2212yes—
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⋊C4D411yescharacteristic
65C2×C11×C4⋊C4D411yescharacteristic
66C2×C11×C4⋊C4C2312yes—
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C4⋊C4C2312yes—
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C22⋊C4—21no—
71C2×C11×C22⋊C4—22no—
72C2×C11×C22⋊C4—22no—
73C2×C42×C11—22no—
74C2×C42×C11—21no—
75C2×C42×C11C2312yes—
76C2×C42×C11C2311yescharacteristic
77C11×#107—24no—
78C11×#106—22no—
79C11×C4⋊C8—24no—
80C11×C4⋊C8—22no—
81C11×#103—24no—
82C11×#103—22no—
83C11×#102—22no—
84C11×#102—24no—
85C4×C8×C11—22no—
86C11×#95—22no—
87C11×#95—22no—
88C11×#95—22no—
89C11×#95—22no—
90C11×#95—22no—
91C11×#95D412yes—
92#24681C1111yesmaximal, 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—42no—
101C2×Q8×C11—42no—
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—21no—
113C22×C4×C11—22no—
114C22×C4×C11—22no—
115C22×C4×C11—42no—
116C22×C4×C11—42no—
117C22×C4×C11C2×D412yes—
118C22×C4×C11C2×D412yes—
119C22×C4×C11C2×D411yescharacteristic
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—22no—
134C11×C4⋊C4—21no—
135C11×C4⋊C4—21no—
136C11×C4⋊C4—22no—
137C11×C4⋊C4—22no—
138C11×C4⋊C4—21no—
139C11×C4⋊C4—22no—
140C11×C4⋊C4—22no—
141C11×C4⋊C4—42no—
142C11×C4⋊C4—42no—
143C11×C4⋊C4—42no—
144C11×C4⋊C4—81no—
145C11×C4⋊C4C2×D412yes—
146C11×C22⋊C4—24no—
147C11×C22⋊C4—44no—
148C11×C22⋊C4—82no—
149C42×C11—22no—
150C42×C11—22no—
151C42×C11—44no—
152C42×C11—42no—
153C42×C11C2×D412yes—
154C42×C11#4112yes—
155C2×#474C2×C1111yescharacteristic
156C2×C4×SD16C2×C1111yescharacteristic
157#2568C2×C1111yescharacteristic, complemented
158#2354C2×C1111yescharacteristic
159#2073C2×C1112yes—
160#2055C2×C1112yes—
161#1990C2×C1111yescharacteristic, complemented
162#1949C2×C1112yescomplemented
163#1939C2×C1111yescharacteristic, complemented
164#1928C2×C1112yescomplemented
165#1803C2×C1111yescharacteristic, complemented
166C23×C11—22no—
167C23×C11—41no—
168C23×C11—41no—
169C23×C11—41no—
170C23×C11—41no—
171C23×C11—41no—
172C23×C11—41no—
173C23×C11C22×D411yescharacteristic
174Q8×C11—22no—
175Q8×C11—22no—
176Q8×C11—41no—
177Q8×C11—41no—
178Q8×C11—84no—
179D4×C11—22no—
180D4×C11—22no—
181D4×C11—41no—
182D4×C11—41no—
183C2×C4×C11—21no—
184C2×C4×C11—21no—
185C2×C4×C11—22no—
186C2×C4×C11—22no—
187C2×C4×C11—22no—
188C2×C4×C11—22no—
189C2×C4×C11—22no—
190C2×C4×C11—22no—
191C2×C4×C11—22no—
192C2×C4×C11—22no—
193C2×C4×C11—41no—
194C2×C4×C11—41no—
195C2×C4×C11—41no—
196C2×C4×C11—41no—
197C2×C4×C11—48no—
198C2×C4×C11—41no—
199C2×C4×C11—42no—
200C2×C4×C11—42no—
201C2×C4×C11—42no—
202C2×C4×C11—42no—
203C2×C4×C11—42no—
204C2×C4×C11—42no—
205C2×C4×C11—41no—
206C2×C4×C11—41no—
207C2×C4×C11#12112yes—
208C2×C4×C11#12112yes—
209C2×C4×C11#13512yes—
210C2×C4×C11AGL(1,ℤ/8)12yes—
211C2×C4×C11C22×D411yescharacteristic
212C2×C4×C11C2×#4111yescharacteristic
213C2×C4×C11C2×#4111yescharacteristic
214C2×C4×C11C2×#4111yescharacteristic
215C2×C4×C112−1+411yescharacteristic
216C2×C4×C112−1+411yescharacteristic
217C8×C11—22no—
218C8×C11—42no—
219C8×C11—41no—
220C22×SD16C22×C1111yescharacteristic
221C2×C4⋊Q8C22×C1111yescharacteristic
222C2×C4×Q8C22×C1111yescharacteristic
223C2×C4×D4C22×C1111yescharacteristic
224C2×#117—21no—
225#474—24no—
226C4×SD16—24no—
227C2×#107C22×C1112yes—
228C2×#106C22×C1111yescharacteristic
229C2×C4⋊C8C22×C1112yes—
230C2×C4⋊C8C22×C1111yescharacteristic
231C2×#103C22×C1112yes—
232C2×#103C22×C1111yescharacteristic
233C2×#102C22×C1112yes—
234C2×#102C22×C1111yescharacteristic
235C2×C4×C8C22×C1111yescharacteristic
236#400—22no—
237#391—21no—
238#391—21no—
239#391C22×C1112yes—
240#390C22×C1112yes—
241#388—22no—
242#384C22×C1111yescharacteristic
243#382C22×C1112yes—
244#380—21no—
245C4×C4⋊C4C22×C1112yes—
246C4×C4⋊C4C22×C1111yescharacteristic
247#340C22×C1112yes—
248#340C22×C1112yes—
249#340C22×C1112yes—
250#336C22×C1112yes—
251C22×C11—42no—
252C22×C11—42no—
253C22×C11—42no—
254C22×C11—81no—
255C22×C11—81no—
256C22×C11—81no—
257C22×C11—81no—
258C22×C11C2×#12111yescharacteristic
259C22×C11#54711yescharacteristic
260C22×C11#54811yescharacteristic
261C22×C11C2×#13511yescharacteristic
262C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
263C22×C11#57711yescharacteristic
264C22×C11#57811yescharacteristic
265C4×C11—22no—
266C4×C11—42no—
267C4×C11—42no—
268C4×C11—42no—
269C4×C11—42no—
270C4×C11—82no—
271C4×C11—82no—
272C4×C11—81no—
273C4×C11#46314yes—
274C4×C11#52511yescharacteristic
275C4×C11#53611yescharacteristic
276C4×C11#55211yescharacteristic
277C4×C11#55611yescharacteristic
278C22×Q8—21no—
279C22×Q8C23×C1111yescharacteristic
280C22×D4C23×C1111yescharacteristic
281C23×C4—21no—
282C2×SD16—22no—
283C2×SD16—22no—
284C2×SD16—22no—
285C22×C8C23×C1111yescharacteristic
286C22×C8C23×C1112yes—
287C22×C8C23×C1111yescharacteristic
288C4⋊Q8—22no—
289C4⋊Q8—22no—
290C4×Q8—22no—
291C4×Q8—22no—
292C4×D4—22no—
293C4×D4D4×C1114yes—
294#117—44no—
295C2×C4⋊C4—21no—
296C2×C4⋊C4—21no—
297C2×C4⋊C4—21no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4D4×C1111yescharacteristic
300C2×C4⋊C4D4×C1111yescharacteristic
301C2×C4⋊C4C23×C1111yescharacteristic
302C2×C4⋊C4C23×C1112yes—
303C2×C4⋊C4C23×C1112yes—
304C2×C4⋊C4C23×C1111yescharacteristic
305C2×C22⋊C4—21no—
306C2×C22⋊C4—22no—
307C2×C22⋊C4—22no—
308C2×C42—22no—
309C2×C42—21no—
310C2×C42C23×C1112yes—
311C2×C42C23×C1111yescharacteristic
312#107—24no—
313#106—22no—
314C4⋊C8—24no—
315C4⋊C8—22no—
316#103—24no—
317#103—22no—
318#102—22no—
319#102—24no—
320C4×C8—22no—
321#95—22no—
322#95—22no—
323#95—22no—
324#95—22no—
325#95—22no—
326#95D4×C1112yes—
327C2×C11—82no—
328C2×C11#241511yescharacteristic
329C2×C11C2×#46311yescharacteristic
330C2×C11#304611yescharacteristic
331C2×C11#334011yescharacteristic
332C2×C11#335311yescharacteristic
333C2×C11#336411yescharacteristic
334C2×C11#336811yescharacteristic
335C24—21no—
336C2×Q8—21no—
337C2×Q8—21no—
338C2×Q8—21no—
339C2×Q8—21no—
340C2×Q8—21no—
341C2×Q8—42no—
342C2×Q8—42no—
343C2×Q8—42no—
344C2×Q8C11×#4112yes—
345C2×D4—21no—
346C2×D4—21no—
347C2×D4—21no—
348C2×D4—21no—
349C2×D4—21no—
350C2×D4C2×D4×C1112yes—
351C22×C4—21no—
352C22×C4—21no—
353C22×C4—24no—
354C22×C4—21no—
355C22×C4—22no—
356C22×C4—22no—
357C22×C4—42no—
358C22×C4—42no—
359C22×C4C2×D4×C1112yes—
360C22×C4C2×D4×C1112yes—
361C22×C4C2×D4×C1111yescharacteristic
362C22×C4C2×D4×C1111yescharacteristic
363C22×C4C24×C1111yescharacteristic
364SD16—28no—
365C2×C8—21no—
366C2×C8—21no—
367C2×C8—21no—
368C2×C8—22no—
369C2×C8—22no—
370C2×C8—22no—
371C2×C8—21no—
372C2×C8—21no—
373C2×C8C11×#4112yes—
374C4⋊C4—22no—
375C4⋊C4—22no—
376C4⋊C4—21no—
377C4⋊C4—21no—
378C4⋊C4—22no—
379C4⋊C4—22no—
380C4⋊C4—21no—
381C4⋊C4—22no—
382C4⋊C4—22no—
383C4⋊C4—42no—
384C4⋊C4—42no—
385C4⋊C4—42no—
386C4⋊C4—81no—
387C4⋊C4C2×D4×C1112yes—
388C22⋊C4—24no—
389C22⋊C4—44no—
390C22⋊C4—82no—
391C42—22no—
392C42—22no—
393C42—44no—
394C42—42no—
395C42C2×D4×C1112yes—
396C42C11×#4112yes—
397C11#2468111yescharacteristic, direct product factor, Sylow
398C23—22no—
399C23—41no—
400C23—41no—
401C23—41no—
402C23—41no—
403C23—41no—
404C23—41no—
405C23C22×D4×C1111yescharacteristic
406Q8—22no—
407Q8—22no—
408Q8—41no—
409Q8—41no—
410Q8—84no—
411D4—22no—
412D4—22no—
413D4—41no—
414D4—41no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—22no—
421C2×C4—22no—
422C2×C4—22no—
423C2×C4—22no—
424C2×C4—22no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—48no—
430C2×C4—41no—
431C2×C4—42no—
432C2×C4—42no—
433C2×C4—42no—
434C2×C4—42no—
435C2×C4—42no—
436C2×C4—42no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4C11×#12112yes—
440C2×C4C11×#12112yes—
441C2×C4C11×#13512yes—
442C2×C4C11×AGL(1,ℤ/8)12yes—
443C2×C4C22×D4×C1111yescharacteristic
444C2×C4C2×C11×#4111yescharacteristic
445C2×C4C2×C11×#4111yescharacteristic
446C2×C4C2×C11×#4111yescharacteristic
447C2×C4C11×2−1+411yescharacteristic
448C2×C4C11×2−1+411yescharacteristic
449C8—22no—
450C8—42no—
451C8—41no—
452C22—42no—
453C22—42no—
454C22—42no—
455C22—81no—
456C22—81no—
457C22—81no—
458C22—81no—
459C22C2×C11×#12111yescharacteristic
460C22C11×#54711yescharacteristic
461C22C11×#54811yescharacteristic
462C22C2×C11×#13511yescharacteristic
463C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
464C22C11×#57711yescharacteristic
465C22C11×#57811yescharacteristic
466C4—22no—
467C4—42no—
468C4—42no—
469C4—42no—
470C4—42no—
471C4—82no—
472C4—81no—
473C4—82no—
474C4C11×#46314yes—
475C4C11×#52511yescharacteristic
476C4C11×#53611yescharacteristic
477C4C11×#55211yescharacteristic
478C4C11×#55611yescharacteristic
479C2—82no—
480C2C11×#241511yescharacteristic
481C2C2×C11×#46311yescharacteristic
482C2C11×#304611yescharacteristic
483C2C11×#334011yescharacteristic
484C2C11×#335311yescharacteristic
485C2C11×#336411yescharacteristic
486C2C11×#336811yescharacteristic
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×#2568C2semidirect
7. C11×#1990C2semidirect
8. C11×#1949C2semidirect
9. C11×#1939C2semidirect
10. C11×#1928C2semidirect
11. C11×#1803C2semidirect
92. #24681C11direct (N × H)
157. #2568C2×C11semidirect
161. #1990C2×C11semidirect
162. #1949C2×C11semidirect
163. #1939C2×C11semidirect
164. #1928C2×C11semidirect
165. #1803C2×C11semidirect
397. C11#24681direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4742
C2×C4×C11×SD162
C11×#25682
C11×#23542
C11×#20732
C11×#20552
C11×#19902
C11×#19492
C11×#19392
C11×#19282
C11×#18032
#2468111