Finite Group Databasebeta

← C11×#22772 #14599965

Subgroups — C11×#22772 #14599965

Order 2816.

918 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C11×D8C211yesmaximal, characteristic
2C11×#2357C211yesmaximal, characteristic, complemented
3C11×#2349C211yesmaximal, characteristic, complemented
4C11×#1934C212yesmaximal, complemented
5C11×#1921C212yesmaximal, complemented
6C11×#1879C212yesmaximal
7C11×#1835C211yesmaximal, characteristic, complemented
8C11×#1804C211yesmaximal, characteristic, complemented
9C11×#1804C211yesmaximal, characteristic, complemented
10C8×C11×C4⋊C4C211yesmaximal, characteristic, complemented
11C4×C11×#102C212yesmaximal, complemented
12C22×C11×D8C2211yescharacteristic
13C2×C4×D4×C11C2212yes—
14C2×C4×D4×C11C2211yescharacteristic
15C2×C4×D4×C11C2211yescharacteristic
16C4×C11×D8C418yescomplemented
17C2×C11×#107C2211yescharacteristic
18C2×C11×C4⋊C8C2211yescharacteristic
19C2×C11×#102C2212yes—
20C2×C11×#102C2212yes—
21C2×C11×#102C2211yescharacteristic
22C2×C11×#102C2211yescharacteristic
23C2×C4×C8×C11C2212yes—
24C2×C4×C8×C11C2211yescharacteristic
25C11×#390C2212yes—
26C11×#389C2212yes—
27C11×#388—22no—
28C11×#385—22no—
29C11×#382C2211yescharacteristic
30C11×#382C2211yescharacteristic
31C11×#381—21no—
32C11×#380—21no—
33C4×C11×C4⋊C4C2212yes—
34C4×C11×C4⋊C4C2211yescharacteristic
35C4×C11×C22⋊C4—21no—
36C2×C11×#95—21no—
37C11×#340C2212yes—
38C11×#340C2212yes—
39C11×#340C2212yes—
40C11×#340C2212yes—
41C11×#336C2212yes—
42C22×D4×C11C2311yescharacteristic
43C22×D4×C11C2311yescharacteristic
44C23×C4×C11—21no—
45C23×C4×C11—21no—
46C23×C4×C11—22no—
47C2×C11×D8—22no—
48C2×C11×D8—22no—
49C2×C11×D8C2×C414yes—
50C22×C8×C11C2312yes—
51C22×C8×C11C2311yescharacteristic
52C22×C8×C11C2311yescharacteristic
53C4×D4×C11—24no—
54C4×D4×C11—22no—
55C4×D4×C11—22no—
56C4×D4×C11—42no—
57C4×D4×C11C2×C414yes—
58C4×D4×C11C2×C414yescomplemented
59C2×C11×C4⋊C4—22no—
60C2×C11×C4⋊C4D412yes—
61C2×C11×C4⋊C4C2312yes—
62C2×C11×C4⋊C4C2312yes—
63C2×C11×C4⋊C4C2311yescharacteristic
64C2×C11×C4⋊C4C2311yescharacteristic
65C2×C11×C22⋊C4—21no—
66C2×C11×C22⋊C4—21no—
67C2×C11×C22⋊C4—22no—
68C2×C11×C22⋊C4—22no—
69C2×C11×C22⋊C4—22no—
70C2×C42×C11—22no—
71C2×C42×C11C2312yes—
72C2×C42×C11C2311yescharacteristic
73C11×#107C2×C414yescomplemented
74C11×C4⋊C8—22no—
75C11×#102—24no—
76C11×#102—42no—
77C11×#102C2×C414yes—
78C11×#102C2×C414yescomplemented
79C4×C8×C11—42no—
80C4×C8×C11C2×C414yescomplemented
81C11×#95—21no—
82C11×#95—22no—
83C11×#95—21no—
84C11×#95—22no—
85C11×#95—21no—
86C11×#95—21no—
87C11×#95D411yescharacteristic
88C11×#95D411yescharacteristic
89#22772C1111yesmaximal, characteristic, direct product factor, Sylow
90C24×C11—21no—
91C24×C11—21no—
92C2×D4×C11—21no—
93C2×D4×C11—21no—
94C2×D4×C11—21no—
95C2×D4×C11—21no—
96C2×D4×C11—21no—
97C2×D4×C11—21no—
98C2×D4×C11—21no—
99C2×D4×C11—21no—
100C2×D4×C11C22×C412yes—
101C2×D4×C11C22×C412yes—
102C2×D4×C11#4112yes—
103C2×D4×C11#4112yes—
104C22×C4×C11—21no—
105C22×C4×C11—21no—
106C22×C4×C11—24no—
107C22×C4×C11—24no—
108C22×C4×C11—22no—
109C22×C4×C11—22no—
110C22×C4×C11—44no—
111C22×C4×C11—44no—
112C22×C4×C11—82no—
113C22×C4×C11—82no—
114C22×C4×C11—82no—
115C22×C4×C11C2×D412yes—
116C22×C4×C11C2×D411yescharacteristic
117C22×C4×C11C2×D411yescharacteristic
118C22×C4×C11C2×D412yes—
119C22×C4×C11C2411yescharacteristic
120C11×D8—28no—
121C2×C8×C11—21no—
122C2×C8×C11—21no—
123C2×C8×C11—22no—
124C2×C8×C11—22no—
125C2×C8×C11—21no—
126C2×C8×C11—22no—
127C2×C8×C11—21no—
128C2×C8×C11C22×C412yes—
129C2×C8×C11C22×C412yes—
130C11×C4⋊C4—24no—
131C11×C4⋊C4—21no—
132C11×C4⋊C4—21no—
133C11×C4⋊C4—22no—
134C11×C4⋊C4—22no—
135C11×C4⋊C4—22no—
136C11×C4⋊C4—22no—
137C11×C4⋊C4—82no—
138C11×C4⋊C4C22×C412yes—
139C11×C4⋊C4C22×C412yes—
140C11×C22⋊C4—24no—
141C11×C22⋊C4—24no—
142C11×C22⋊C4—44no—
143C11×C22⋊C4—44no—
144C11×C22⋊C4—82no—
145C42×C11—22no—
146C42×C11—22no—
147C42×C11—82no—
148C42×C11C22×C412yes—
149C42×C11#4112yes—
150C2×C4×D8C2×C1111yescharacteristic
151#2357C2×C1111yescharacteristic, complemented
152#2349C2×C1111yescharacteristic, complemented
153#1934C2×C1112yescomplemented
154#1921C2×C1112yescomplemented
155#1879C2×C1112yes—
156#1835C2×C1111yescharacteristic, complemented
157#1804C2×C1111yescharacteristic, complemented
158#1804C2×C1111yescharacteristic, complemented
159C8×C4⋊C4C2×C1111yescharacteristic, complemented
160C4×#102C2×C1112yescomplemented
161C23×C11—22no—
162C23×C11—22no—
163C23×C11—22no—
164C23×C11—22no—
165C23×C11—42no—
166C23×C11—42no—
167C23×C11—41no—
168C23×C11—41no—
169C23×C11—42no—
170C23×C11—42no—
171C23×C11C22×D411yescharacteristic
172D4×C11—22no—
173D4×C11—22no—
174D4×C11—22no—
175D4×C11—22no—
176D4×C11—22no—
177D4×C11—41no—
178D4×C11—41no—
179D4×C11#11714yes—
180C2×C4×C11—22no—
181C2×C4×C11—22no—
182C2×C4×C11—22no—
183C2×C4×C11—22no—
184C2×C4×C11—22no—
185C2×C4×C11—22no—
186C2×C4×C11—22no—
187C2×C4×C11—22no—
188C2×C4×C11—22no—
189C2×C4×C11—42no—
190C2×C4×C11—42no—
191C2×C4×C11—42no—
192C2×C4×C11—42no—
193C2×C4×C11—42no—
194C2×C4×C11—42no—
195C2×C4×C11—42no—
196C2×C4×C11—42no—
197C2×C4×C11—84no—
198C2×C4×C11—84no—
199C2×C4×C11—88no—
200C2×C4×C11C4×D412yes—
201C2×C4×C11C4×D412yes—
202C2×C4×C11#13514yes—
203C2×C4×C11C23×C411yescharacteristic
204C2×C4×C11C2×#4111yescharacteristic
205C2×C4×C11C2×#4111yescharacteristic
206C2×C4×C11C2×#4111yescharacteristic
207C2×C4×C11H(5,𝔽2)11yescharacteristic
208C2×C4×C112−1+411yescharacteristic
209C8×C11—22no—
210C8×C11—22no—
211C8×C11—42no—
212C22×D8C22×C1111yescharacteristic
213C2×C4×D4C22×C1112yes—
214C2×C4×D4C22×C1111yescharacteristic
215C2×C4×D4C22×C1111yescharacteristic
216C4×D8C4×C1118yescomplemented
217C2×#107C22×C1111yescharacteristic
218C2×C4⋊C8C22×C1111yescharacteristic
219C2×#102C22×C1112yes—
220C2×#102C22×C1112yes—
221C2×#102C22×C1111yescharacteristic
222C2×#102C22×C1111yescharacteristic
223C2×C4×C8C22×C1112yes—
224C2×C4×C8C22×C1111yescharacteristic
225#390C22×C1112yes—
226#389C22×C1112yes—
227#388—22no—
228#385—22no—
229#382C22×C1111yescharacteristic
230#382C22×C1111yescharacteristic
231#381—21no—
232#380—21no—
233C4×C4⋊C4C22×C1112yes—
234C4×C4⋊C4C22×C1111yescharacteristic
235C4×C22⋊C4—21no—
236C2×#95—21no—
237#340C22×C1112yes—
238#340C22×C1112yes—
239#340C22×C1112yes—
240#340C22×C1112yes—
241#336C22×C1112yes—
242C22×C11—24no—
243C22×C11—44no—
244C22×C11—42no—
245C22×C11—42no—
246C22×C11—44no—
247C22×C11—42no—
248C22×C11—42no—
249C22×C11—42no—
250C22×C11—82no—
251C22×C11—82no—
252C22×C11C2×C4×D411yescharacteristic
253C22×C11#54611yescharacteristic
254C22×C11#54811yescharacteristic
255C22×C11C2×#13512yes—
256C22×C11#57612yes—
257C4×C11—22no—
258C4×C11—22no—
259C4×C11—24no—
260C4×C11—42no—
261C4×C11—42no—
262C4×C11—42no—
263C4×C11—82no—
264C4×C11—82no—
265C4×C11C2×#11711yescharacteristic
266C4×C11#52011yescharacteristic
267C4×C11#55211yescharacteristic
268C4×C11#55311yescharacteristic
269C22×D4C23×C1111yescharacteristic
270C22×D4C23×C1111yescharacteristic
271C23×C4—21no—
272C23×C4—21no—
273C23×C4—22no—
274C2×D8—22no—
275C2×D8—22no—
276C2×D8C2×C4×C1114yes—
277C22×C8C23×C1112yes—
278C22×C8C23×C1111yescharacteristic
279C22×C8C23×C1111yescharacteristic
280C4×D4—24no—
281C4×D4—22no—
282C4×D4—22no—
283C4×D4—42no—
284C4×D4C2×C4×C1114yes—
285C4×D4C2×C4×C1114yescomplemented
286C2×C4⋊C4—22no—
287C2×C4⋊C4D4×C1112yes—
288C2×C4⋊C4C23×C1112yes—
289C2×C4⋊C4C23×C1112yes—
290C2×C4⋊C4C23×C1111yescharacteristic
291C2×C4⋊C4C23×C1111yescharacteristic
292C2×C22⋊C4—21no—
293C2×C22⋊C4—21no—
294C2×C22⋊C4—22no—
295C2×C22⋊C4—22no—
296C2×C22⋊C4—22no—
297C2×C42—22no—
298C2×C42C23×C1112yes—
299C2×C42C23×C1111yescharacteristic
300#107C2×C4×C1114yescomplemented
301C4⋊C8—22no—
302#102—24no—
303#102—42no—
304#102C2×C4×C1114yes—
305#102C2×C4×C1114yescomplemented
306C4×C8—42no—
307C4×C8C2×C4×C1114yescomplemented
308#95—21no—
309#95—22no—
310#95—21no—
311#95—22no—
312#95—21no—
313#95—21no—
314#95D4×C1111yescharacteristic
315#95D4×C1111yescharacteristic
316C2×C11—44no—
317C2×C11—82no—
318C2×C11#235211yescharacteristic
319C2×C11C4×#13511yescharacteristic
320C2×C11#294811yescharacteristic
321C2×C11#329712yes—
322C2×C11#336112yes—
323C24—21no—
324C24—21no—
325C2×D4—21no—
326C2×D4—21no—
327C2×D4—21no—
328C2×D4—21no—
329C2×D4—21no—
330C2×D4—21no—
331C2×D4—21no—
332C2×D4—21no—
333C2×D4C22×C4×C1112yes—
334C2×D4C22×C4×C1112yes—
335C2×D4C11×#4112yes—
336C2×D4C11×#4112yes—
337C22×C4—21no—
338C22×C4—21no—
339C22×C4—24no—
340C22×C4—24no—
341C22×C4—22no—
342C22×C4—22no—
343C22×C4—44no—
344C22×C4—44no—
345C22×C4—82no—
346C22×C4—82no—
347C22×C4—82no—
348C22×C4C2×D4×C1112yes—
349C22×C4C2×D4×C1111yescharacteristic
350C22×C4C2×D4×C1111yescharacteristic
351C22×C4C2×D4×C1112yes—
352C22×C4C24×C1111yescharacteristic
353D8—28no—
354C2×C8—21no—
355C2×C8—21no—
356C2×C8—21no—
357C2×C8—21no—
358C2×C8—22no—
359C2×C8—22no—
360C2×C8—22no—
361C2×C8C22×C4×C1112yes—
362C2×C8C22×C4×C1112yes—
363C4⋊C4—24no—
364C4⋊C4—21no—
365C4⋊C4—21no—
366C4⋊C4—22no—
367C4⋊C4—22no—
368C4⋊C4—22no—
369C4⋊C4—22no—
370C4⋊C4—82no—
371C4⋊C4C22×C4×C1112yes—
372C4⋊C4C22×C4×C1112yes—
373C22⋊C4—24no—
374C22⋊C4—24no—
375C22⋊C4—44no—
376C22⋊C4—44no—
377C22⋊C4—82no—
378C42—22no—
379C42—22no—
380C42—82no—
381C42C22×C4×C1112yes—
382C42C11×#4112yes—
383C11#2277211yescharacteristic, direct product factor, Sylow
384C23—22no—
385C23—22no—
386C23—22no—
387C23—22no—
388C23—42no—
389C23—42no—
390C23—41no—
391C23—41no—
392C23—42no—
393C23—42no—
394C23C22×D4×C1111yescharacteristic
395D4—22no—
396D4—22no—
397D4—22no—
398D4—22no—
399D4—22no—
400D4—41no—
401D4—41no—
402D4C11×#11714yes—
403C2×C4—22no—
404C2×C4—22no—
405C2×C4—22no—
406C2×C4—22no—
407C2×C4—22no—
408C2×C4—22no—
409C2×C4—22no—
410C2×C4—22no—
411C2×C4—22no—
412C2×C4—42no—
413C2×C4—42no—
414C2×C4—42no—
415C2×C4—42no—
416C2×C4—42no—
417C2×C4—42no—
418C2×C4—42no—
419C2×C4—42no—
420C2×C4—84no—
421C2×C4—84no—
422C2×C4—88no—
423C2×C4C4×D4×C1112yes—
424C2×C4C4×D4×C1112yes—
425C2×C4C11×#13514yes—
426C2×C4C23×C4×C1111yescharacteristic
427C2×C4C2×C11×#4111yescharacteristic
428C2×C4C2×C11×#4111yescharacteristic
429C2×C4C2×C11×#4111yescharacteristic
430C2×C4C11×H(5,𝔽2)11yescharacteristic
431C2×C4C11×2−1+411yescharacteristic
432C8—22no—
433C8—22no—
434C8—42no—
435C22—24no—
436C22—42no—
437C22—42no—
438C22—44no—
439C22—44no—
440C22—42no—
441C22—42no—
442C22—42no—
443C22—82no—
444C22—82no—
445C22C2×C4×D4×C1111yescharacteristic
446C22C11×#54611yescharacteristic
447C22C11×#54811yescharacteristic
448C22C2×C11×#13512yes—
449C22C11×#57612yes—
450C4—22no—
451C4—22no—
452C4—24no—
453C4—42no—
454C4—42no—
455C4—42no—
456C4—82no—
457C4—82no—
458C4C2×C11×#11711yescharacteristic
459C4C11×#52011yescharacteristic
460C4C11×#55211yescharacteristic
461C4C11×#55311yescharacteristic
462C2—44no—
463C2—82no—
464C2C11×#235211yescharacteristic
465C2C4×C11×#13511yescharacteristic
466C2C11×#294811yescharacteristic
467C2C11×#329712yes—
468C2C11×#336112yes—
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC22×C11×D8C22
LCSG ▷ C2×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
2. C11×#2357C2semidirect
3. C11×#2349C2semidirect
4. C11×#1934C2semidirect
5. C11×#1921C2semidirect
7. C11×#1835C2semidirect
8. C11×#1804C2semidirect
9. C11×#1804C2semidirect
10. C8×C11×C4⋊C4C2semidirect
11. C4×C11×#102C2semidirect
16. C4×C11×D8C4semidirect
58. C4×D4×C11C2×C4semidirect
73. C11×#107C2×C4semidirect
78. C11×#102C2×C4semidirect
80. C4×C8×C11C2×C4semidirect
89. #22772C11direct (N × H)
151. #2357C2×C11semidirect
152. #2349C2×C11semidirect
153. #1934C2×C11semidirect
154. #1921C2×C11semidirect
156. #1835C2×C11semidirect
157. #1804C2×C11semidirect
158. #1804C2×C11semidirect
159. C8×C4⋊C4C2×C11semidirect
160. C4×#102C2×C11semidirect
216. C4×D8C4×C11semidirect
285. C4×D4C2×C4×C11semidirect
300. #107C2×C4×C11semidirect
305. #102C2×C4×C11semidirect
307. C4×C8C2×C4×C11semidirect
383. C11#22772direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×C11×D82
C11×#23572
C11×#23492
C11×#19342
C11×#19212
C11×#18792
C11×#18352
C11×#18042
C8×C11×C4⋊C42
C4×C11×#1022
#2277211