Finite Group Databasebeta

← C11×#22565 #14599758

Subgroups — C11×#22565 #14599758

Order 2816.

966 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#416C211yesmaximal, characteristic
2C11×#2346C211yesmaximal, characteristic, complemented
3C11×#2341C211yesmaximal, characteristic
4C11×#1936C212yesmaximal, complemented
5C11×#1926C212yesmaximal, complemented
6C11×#1865C212yesmaximal, complemented
7C11×#1825C211yesmaximal, characteristic, complemented
8C11×#1807C211yesmaximal, characteristic, complemented
9C11×#1788C211yesmaximal, characteristic
10C11×#1763C212yesmaximal, complemented
11C11×#1752C211yesmaximal, characteristic, complemented
12C22×C11×#41C2211yescharacteristic
13C23×C8×C11C2211yescharacteristic
14C2×C4×Q8×C11C2212yes—
15C2×C11×#117C2211yescharacteristic
16C2×C11×#106C2212yes—
17C11×#416C418yescomplemented
18C2×C11×#103C2212yes—
19C2×C11×#103C2211yescharacteristic
20C2×C11×#103C2211yescharacteristic
21C2×C11×#102C2212yes—
22C2×C11×#102C2211yescharacteristic
23C2×C11×#102C2211yescharacteristic
24C2×C11×C22⋊C8C2211yescharacteristic
25C2×C11×#97C2212yes—
26C11×#390—22no—
27C11×#390C2212yes—
28C11×#389C2212yes—
29C11×#388—22no—
30C11×#382—21no—
31C11×#380—21no—
32C11×#380C2211yescharacteristic
33C11×#380C2211yescharacteristic
34C4×C11×C4⋊C4C2212yes—
35C4×C11×C22⋊C4—21no—
36C4×C11×C22⋊C4C2211yescharacteristic
37C11×#376—21no—
38C11×#340C2212yes—
39C11×#340C2212yes—
40C11×#340C2212yes—
41C11×#336C2212yes—
42C2×C11×#41—22no—
43C2×C11×#41—24no—
44C2×C11×#41—42no—
45C2×C11×#41C2×C414yes—
46C22×Q8×C11C2311yescharacteristic
47C22×D4×C11—21no—
48C22×D4×C11C2311yescharacteristic
49C23×C4×C11—21no—
50C23×C4×C11C2311yescharacteristic
51C22×C8×C11—42no—
52C22×C8×C11C2×C414yes—
53C22×C8×C11C2312yes—
54C22×C8×C11C2311yescharacteristic
55C22×C8×C11C2311yescharacteristic
56C4×Q8×C11—24no—
57C4×Q8×C11—42no—
58C11×#117—22no—
59C11×#117C2×C414yes—
60C2×C11×C4⋊C4—22no—
61C2×C11×C4⋊C4—22no—
62C2×C11×C4⋊C4C2312yes—
63C2×C11×C4⋊C4C2312yes—
64C2×C11×C4⋊C4C2311yescharacteristic
65C2×C11×C4⋊C4C2311yescharacteristic
66C2×C11×C22⋊C4—21no—
67C2×C11×C22⋊C4—22no—
68C2×C11×C22⋊C4—21no—
69C2×C11×C22⋊C4—21no—
70C2×C11×C22⋊C4—22no—
71C2×C11×C22⋊C4D412yes—
72C2×C42×C11—21no—
73C2×C42×C11—22no—
74C2×C42×C11—22no—
75C2×C42×C11C2312yes—
76C11×#106—42no—
77C11×#103—24no—
78C11×#103C2×C414yes—
79C11×#103C2×C414yes—
80C11×#102—42no—
81C11×#102C2×C414yes—
82C11×#102C2×C414yes—
83C11×C22⋊C8—22no—
84C11×#97—42no—
85C11×#95—21no—
86C11×#95—22no—
87C11×#95—21no—
88C11×#95—22no—
89C11×#95D411yescharacteristic
90C11×#95D411yescharacteristic
91#22565C1111yesmaximal, characteristic, direct product factor, Sylow
92C24×C11—21no—
93C24×C11C2×D411yescharacteristic
94C11×#41—28no—
95C11×#41—44no—
96C11×#41—48no—
97C2×Q8×C11—21no—
98C2×Q8×C11—22no—
99C2×Q8×C11C22×C412yes—
100C2×Q8×C11#4114yes—
101C2×D4×C11—24no—
102C2×D4×C11—22no—
103C2×D4×C11—21no—
104C2×D4×C11—22no—
105C2×D4×C11—44no—
106C2×D4×C11C22×C412yes—
107C22×C4×C11—21no—
108C22×C4×C11—22no—
109C22×C4×C11—22no—
110C22×C4×C11—21no—
111C22×C4×C11—21no—
112C22×C4×C11—24no—
113C22×C4×C11—22no—
114C22×C4×C11—22no—
115C22×C4×C11—44no—
116C22×C4×C11C22×C412yes—
117C22×C4×C11C2×D412yes—
118C22×C4×C11C2×D412yes—
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11#4112yes—
121C22×C4×C11C2411yescharacteristic
122C2×C8×C11—22no—
123C2×C8×C11—22no—
124C2×C8×C11—22no—
125C2×C8×C11—22no—
126C2×C8×C11—22no—
127C2×C8×C11—44no—
128C2×C8×C11C22×C412yes—
129C2×C8×C11C22×C412yes—
130C11×C4⋊C4—21no—
131C11×C4⋊C4—21no—
132C11×C4⋊C4—22no—
133C11×C4⋊C4—22no—
134C11×C4⋊C4—22no—
135C11×C4⋊C4—22no—
136C11×C4⋊C4—44no—
137C11×C4⋊C4—82no—
138C11×C4⋊C4C22×C412yes—
139C11×C4⋊C4C22×C412yes—
140C11×C22⋊C4—24no—
141C11×C22⋊C4—42no—
142C11×C22⋊C4—44no—
143C11×C22⋊C4—82no—
144C11×C22⋊C4—81no—
145C11×C22⋊C4—81no—
146C42×C11—24no—
147C42×C11—22no—
148C42×C11—22no—
149C42×C11—44no—
150C42×C11—44no—
151C2×#416C2×C1111yescharacteristic
152#2346C2×C1111yescharacteristic, complemented
153#2341C2×C1111yescharacteristic
154#1936C2×C1112yescomplemented
155#1926C2×C1112yescomplemented
156#1865C2×C1112yescomplemented
157#1825C2×C1111yescharacteristic, complemented
158#1807C2×C1111yescharacteristic, complemented
159#1788C2×C1111yescharacteristic
160#1763C2×C1112yescomplemented
161#1752C2×C1111yescharacteristic, complemented
162C23×C11—22no—
163C23×C11—22no—
164C23×C11—21no—
165C23×C11—21no—
166C23×C11—22no—
167C23×C11—42no—
168C23×C11—42no—
169C23×C11—41no—
170C23×C11—41no—
171C23×C11C4×D412yes—
172C23×C11C22×D411yescharacteristic
173Q8×C11—22no—
174Q8×C11—24no—
175Q8×C11#11714yes—
176D4×C11—22no—
177D4×C11—22no—
178D4×C11—48no—
179D4×C11—42no—
180C2×C4×C11—22no—
181C2×C4×C11—24no—
182C2×C4×C11—22no—
183C2×C4×C11—22no—
184C2×C4×C11—22no—
185C2×C4×C11—24no—
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—22no—
194C2×C4×C11—48no—
195C2×C4×C11—42no—
196C2×C4×C11—41no—
197C2×C4×C11—41no—
198C2×C4×C11—42no—
199C2×C4×C11—42no—
200C2×C4×C11—42no—
201C2×C4×C11—42no—
202C2×C4×C11—42no—
203C2×C4×C11—42no—
204C2×C4×C11C4×D412yes—
205C2×C4×C11C23×C411yescharacteristic
206C2×C4×C11C2×#4112yes—
207C2×C4×C11C2×#4111yescharacteristic
208C2×C4×C11H(5,𝔽2)12yes—
209C8×C11—22no—
210C8×C11—22no—
211C8×C11—42no—
212C22×#41C22×C1111yescharacteristic
213C23×C8C22×C1111yescharacteristic
214C2×C4×Q8C22×C1112yes—
215C2×#117C22×C1111yescharacteristic
216C2×#106C22×C1112yes—
217#416C4×C1118yescomplemented
218C2×#103C22×C1112yes—
219C2×#103C22×C1111yescharacteristic
220C2×#103C22×C1111yescharacteristic
221C2×#102C22×C1112yes—
222C2×#102C22×C1111yescharacteristic
223C2×#102C22×C1111yescharacteristic
224C2×C22⋊C8C22×C1111yescharacteristic
225C2×#97C22×C1112yes—
226#390—22no—
227#390C22×C1112yes—
228#389C22×C1112yes—
229#388—22no—
230#382—21no—
231#380—21no—
232#380C22×C1111yescharacteristic
233#380C22×C1111yescharacteristic
234C4×C4⋊C4C22×C1112yes—
235C4×C22⋊C4—21no—
236C4×C22⋊C4C22×C1111yescharacteristic
237#376—21no—
238#340C22×C1112yes—
239#340C22×C1112yes—
240#340C22×C1112yes—
241#336C22×C1112yes—
242C22×C11—22no—
243C22×C11—22no—
244C22×C11—22no—
245C22×C11—42no—
246C22×C11—42no—
247C22×C11—42no—
248C22×C11—42no—
249C22×C11—42no—
250C22×C11—82no—
251C22×C11—82no—
252C22×C11C2×C4×D411yescharacteristic
253C22×C11#54612yes—
254C22×C11#57512yes—
255C22×C11#57711yescharacteristic
256C22×C11#57711yescharacteristic
257C4×C11—22no—
258C4×C11—24no—
259C4×C11—42no—
260C4×C11—42no—
261C4×C11—42no—
262C4×C11—42no—
263C4×C11—82no—
264C4×C11—82no—
265C4×C11C2×#11711yescharacteristic
266C4×C11#51811yescharacteristic
267C4×C11#55112yes—
268C2×#41—22no—
269C2×#41—24no—
270C2×#41—42no—
271C2×#41C2×C4×C1114yes—
272C22×Q8C23×C1111yescharacteristic
273C22×D4—21no—
274C22×D4C23×C1111yescharacteristic
275C23×C4—21no—
276C23×C4C23×C1111yescharacteristic
277C22×C8—42no—
278C22×C8C2×C4×C1114yes—
279C22×C8C23×C1112yes—
280C22×C8C23×C1111yescharacteristic
281C22×C8C23×C1111yescharacteristic
282C4×Q8—24no—
283C4×Q8—42no—
284#117—22no—
285#117C2×C4×C1114yes—
286C2×C4⋊C4—22no—
287C2×C4⋊C4—22no—
288C2×C4⋊C4C23×C1112yes—
289C2×C4⋊C4C23×C1112yes—
290C2×C4⋊C4C23×C1111yescharacteristic
291C2×C4⋊C4C23×C1111yescharacteristic
292C2×C22⋊C4—21no—
293C2×C22⋊C4—22no—
294C2×C22⋊C4—21no—
295C2×C22⋊C4—21no—
296C2×C22⋊C4—22no—
297C2×C22⋊C4D4×C1112yes—
298C2×C42—21no—
299C2×C42—22no—
300C2×C42—22no—
301C2×C42C23×C1112yes—
302#106—42no—
303#103—24no—
304#103C2×C4×C1114yes—
305#103C2×C4×C1114yes—
306#102—42no—
307#102C2×C4×C1114yes—
308#102C2×C4×C1114yes—
309C22⋊C8—22no—
310#97—42no—
311#95—21no—
312#95—22no—
313#95—21no—
314#95—22no—
315#95D4×C1111yescharacteristic
316#95D4×C1111yescharacteristic
317C2×C11—42no—
318C2×C11—82no—
319C2×C11#234211yescharacteristic
320C2×C11#294311yescharacteristic
321C2×C11#295211yescharacteristic
322C2×C11#331712yes—
323C2×C11#332112yes—
324C24—21no—
325C24C2×D4×C1111yescharacteristic
326#41—28no—
327#41—44no—
328#41—48no—
329C2×Q8—21no—
330C2×Q8—22no—
331C2×Q8C22×C4×C1112yes—
332C2×Q8C11×#4114yes—
333C2×D4—24no—
334C2×D4—22no—
335C2×D4—21no—
336C2×D4—22no—
337C2×D4—44no—
338C2×D4C22×C4×C1112yes—
339C22×C4—21no—
340C22×C4—22no—
341C22×C4—22no—
342C22×C4—21no—
343C22×C4—21no—
344C22×C4—24no—
345C22×C4—22no—
346C22×C4—22no—
347C22×C4—44no—
348C22×C4C22×C4×C1112yes—
349C22×C4C2×D4×C1112yes—
350C22×C4C2×D4×C1112yes—
351C22×C4C2×D4×C1111yescharacteristic
352C22×C4C11×#4112yes—
353C22×C4C24×C1111yescharacteristic
354C2×C8—22no—
355C2×C8—22no—
356C2×C8—22no—
357C2×C8—22no—
358C2×C8—22no—
359C2×C8—44no—
360C2×C8C22×C4×C1112yes—
361C2×C8C22×C4×C1112yes—
362C4⋊C4—21no—
363C4⋊C4—21no—
364C4⋊C4—22no—
365C4⋊C4—22no—
366C4⋊C4—22no—
367C4⋊C4—22no—
368C4⋊C4—44no—
369C4⋊C4—82no—
370C4⋊C4C22×C4×C1112yes—
371C4⋊C4C22×C4×C1112yes—
372C22⋊C4—24no—
373C22⋊C4—42no—
374C22⋊C4—44no—
375C22⋊C4—82no—
376C22⋊C4—81no—
377C22⋊C4—81no—
378C42—24no—
379C42—22no—
380C42—22no—
381C42—44no—
382C42—44no—
383C11#2256511yescharacteristic, direct product factor, Sylow
384C23—22no—
385C23—22no—
386C23—21no—
387C23—21no—
388C23—22no—
389C23—42no—
390C23—42no—
391C23—41no—
392C23—41no—
393C23C4×D4×C1112yes—
394C23C22×D4×C1111yescharacteristic
395Q8—22no—
396Q8—24no—
397Q8C11×#11714yes—
398D4—22no—
399D4—22no—
400D4—48no—
401D4—42no—
402C2×C4—22no—
403C2×C4—24no—
404C2×C4—22no—
405C2×C4—22no—
406C2×C4—22no—
407C2×C4—24no—
408C2×C4—22no—
409C2×C4—22no—
410C2×C4—22no—
411C2×C4—22no—
412C2×C4—22no—
413C2×C4—22no—
414C2×C4—22no—
415C2×C4—22no—
416C2×C4—48no—
417C2×C4—42no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—42no—
421C2×C4—42no—
422C2×C4—42no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—42no—
426C2×C4C4×D4×C1112yes—
427C2×C4C23×C4×C1111yescharacteristic
428C2×C4C2×C11×#4112yes—
429C2×C4C2×C11×#4111yescharacteristic
430C2×C4C11×H(5,𝔽2)12yes—
431C8—22no—
432C8—22no—
433C8—42no—
434C22—22no—
435C22—22no—
436C22—22no—
437C22—42no—
438C22—42no—
439C22—42no—
440C22—42no—
441C22—42no—
442C22—82no—
443C22—82no—
444C22C2×C4×D4×C1111yescharacteristic
445C22C11×#54612yes—
446C22C11×#57512yes—
447C22C11×#57711yescharacteristic
448C22C11×#57711yescharacteristic
449C4—22no—
450C4—24no—
451C4—42no—
452C4—42no—
453C4—42no—
454C4—42no—
455C4—82no—
456C4—82no—
457C4C2×C11×#11711yescharacteristic
458C4C11×#51811yescharacteristic
459C4C11×#55112yes—
460C2—42no—
461C2—82no—
462C2C11×#234211yescharacteristic
463C2C11×#294311yescharacteristic
464C2C11×#295211yescharacteristic
465C2C11×#331712yes—
466C2C11×#332112yes—
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC22×C11×#41C22
LCSG ▷ C2×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
2. C11×#2346C2semidirect
4. C11×#1936C2semidirect
5. C11×#1926C2semidirect
6. C11×#1865C2semidirect
7. C11×#1825C2semidirect
8. C11×#1807C2semidirect
10. C11×#1763C2semidirect
11. C11×#1752C2semidirect
17. C11×#416C4semidirect
91. #22565C11direct (N × H)
152. #2346C2×C11semidirect
154. #1936C2×C11semidirect
155. #1926C2×C11semidirect
156. #1865C2×C11semidirect
157. #1825C2×C11semidirect
158. #1807C2×C11semidirect
160. #1763C2×C11semidirect
161. #1752C2×C11semidirect
217. #416C4×C11semidirect
383. C11#22565direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4162
C11×#23462
C11×#23412
C11×#19362
C11×#19262
C11×#18652
C11×#18252
C11×#18072
C11×#17882
C11×#17632
C11×#17522
#2256511