Finite Group Databasebeta

← C11×#22805 #14599998

Subgroups — C11×#22805 #14599998

Order 2816.

858 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C11×SD16C211yesmaximal, characteristic
2C11×#2355C211yesmaximal, characteristic, complemented
3C11×#2354C211yesmaximal, characteristic
4C11×#1968C212yesmaximal
5C11×#1927C212yesmaximal, complemented
6C11×#1926C212yesmaximal
7C11×#1844C211yesmaximal, characteristic, complemented
8C11×#1803C211yesmaximal, characteristic, complemented
9C11×#1802C211yesmaximal, characteristic
10C4×C11×#106C212yesmaximal, complemented
11C8×C11×C4⋊C4C211yesmaximal, characteristic, complemented
12C22×C11×SD16C2211yescharacteristic
13C2×C4×Q8×C11C2211yescharacteristic
14C2×C4×D4×C11C2211yescharacteristic
15C2×C11×#117—21no—
16C4×C11×SD16C418yescomplemented
17C2×C11×#106C2212yes—
18C2×C11×#106C2212yes—
19C2×C11×#106C2211yescharacteristic
20C2×C11×C4⋊C8C2211yescharacteristic
21C2×C11×#103C2212yes—
22C2×C11×#103C2211yescharacteristic
23C2×C11×#102C2212yes—
24C2×C11×#102C2211yescharacteristic
25C2×C4×C8×C11C2212yes—
26C2×C4×C8×C11C2211yescharacteristic
27C11×#391C2212yes—
28C11×#390C2212yes—
29C11×#388—22no—
30C11×#387—22no—
31C11×#384C2211yescharacteristic
32C11×#384C2211yescharacteristic
33C11×#382—21no—
34C11×#380—21no—
35C4×C11×C4⋊C4—21no—
36C4×C11×C4⋊C4C2212yes—
37C4×C11×C4⋊C4C2212yes—
38C4×C11×C4⋊C4C2211yescharacteristic
39C11×#340C2212yes—
40C11×#340C2212yes—
41C11×#336C2212yes—
42C22×Q8×C11C2311yescharacteristic
43C22×D4×C11C2311yescharacteristic
44C23×C4×C11—21no—
45C2×C11×SD16—22no—
46C2×C11×SD16—22no—
47C2×C11×SD16C2×C414yes—
48C22×C8×C11C2312yes—
49C22×C8×C11C2311yescharacteristic
50C22×C8×C11C2311yescharacteristic
51C4×Q8×C11—22no—
52C4×Q8×C11C2×C414yes—
53C4×D4×C11—22no—
54C4×D4×C11C2×C414yes—
55C11×#117—44no—
56C2×C11×C4⋊C4—21no—
57C2×C11×C4⋊C4—21no—
58C2×C11×C4⋊C4—21no—
59C2×C11×C4⋊C4—21no—
60C2×C11×C4⋊C4—21no—
61C2×C11×C4⋊C4D411yescharacteristic
62C2×C11×C4⋊C4D411yescharacteristic
63C2×C11×C4⋊C4C2312yes—
64C2×C11×C4⋊C4C2312yes—
65C2×C11×C4⋊C4C2311yescharacteristic
66C2×C11×C4⋊C4C2311yescharacteristic
67C2×C11×C22⋊C4—21no—
68C2×C11×C22⋊C4—22no—
69C2×C11×C22⋊C4—22no—
70C2×C42×C11—21no—
71C2×C42×C11—22no—
72C2×C42×C11—22no—
73C2×C42×C11C2312yes—
74C2×C42×C11C2311yescharacteristic
75C11×#106—24no—
76C11×#106—42no—
77C11×#106C2×C414yes—
78C11×C4⋊C8—22no—
79C11×#103—42no—
80C11×#103C2×C414yes—
81C11×#102—42no—
82C11×#102C2×C414yes—
83C4×C8×C11—24no—
84C4×C8×C11C2×C414yes—
85C11×#95—22no—
86C11×#95—22no—
87C11×#95—22no—
88C11×#95—22no—
89C11×#95D412yes—
90#22805C1111yesmaximal, characteristic, direct product factor, Sylow
91C24×C11—21no—
92C2×Q8×C11—21no—
93C2×Q8×C11—21no—
94C2×Q8×C11—21no—
95C2×Q8×C11—21no—
96C2×Q8×C11—21no—
97C2×Q8×C11C22×C412yes—
98C2×D4×C11—21no—
99C2×D4×C11—21no—
100C2×D4×C11—21no—
101C2×D4×C11—21no—
102C2×D4×C11—21no—
103C2×D4×C11C22×C412yes—
104C22×C4×C11—21no—
105C22×C4×C11—21no—
106C22×C4×C11—21no—
107C22×C4×C11—24no—
108C22×C4×C11—22no—
109C22×C4×C11—22no—
110C22×C4×C11—42no—
111C22×C4×C11—42no—
112C22×C4×C11C2×D412yes—
113C22×C4×C11C2×D411yescharacteristic
114C22×C4×C11C2×D412yes—
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11C2411yescharacteristic
117C11×SD16—28no—
118C2×C8×C11—22no—
119C2×C8×C11—22no—
120C2×C8×C11—21no—
121C2×C8×C11—22no—
122C2×C8×C11—21no—
123C2×C8×C11C22×C412yes—
124C2×C8×C11C22×C412yes—
125C2×C8×C11#4112yes—
126C2×C8×C11#4112yes—
127C11×C4⋊C4—24no—
128C11×C4⋊C4—22no—
129C11×C4⋊C4—21no—
130C11×C4⋊C4—21no—
131C11×C4⋊C4—22no—
132C11×C4⋊C4—22no—
133C11×C4⋊C4—22no—
134C11×C4⋊C4—22no—
135C11×C4⋊C4—42no—
136C11×C4⋊C4—42no—
137C11×C4⋊C4—81no—
138C11×C4⋊C4—81no—
139C11×C4⋊C4SD1614yescomplemented
140C11×C4⋊C4C22×C412yes—
141C11×C4⋊C4C22×C412yes—
142C11×C22⋊C4—24no—
143C11×C22⋊C4—44no—
144C11×C22⋊C4—82no—
145C42×C11—24no—
146C42×C11—22no—
147C42×C11—22no—
148C42×C11—44no—
149C42×C11—82no—
150C42×C11C22×C412yes—
151C42×C11#4112yes—
152C2×C4×SD16C2×C1111yescharacteristic
153#2355C2×C1111yescharacteristic, complemented
154#2354C2×C1111yescharacteristic
155#1968C2×C1112yes—
156#1927C2×C1112yescomplemented
157#1926C2×C1112yes—
158#1844C2×C1111yescharacteristic, complemented
159#1803C2×C1111yescharacteristic, complemented
160#1802C2×C1111yescharacteristic
161C4×#106C2×C1112yescomplemented
162C8×C4⋊C4C2×C1111yescharacteristic, complemented
163C23×C11—22no—
164C23×C11—41no—
165C23×C11—41no—
166C23×C11—41no—
167C23×C11—41no—
168C23×C11—41no—
169C23×C11—41no—
170C23×C11C22×D411yescharacteristic
171Q8×C11—22no—
172Q8×C11—22no—
173Q8×C11—41no—
174Q8×C11—41no—
175D4×C11—22no—
176D4×C11—22no—
177D4×C11—41no—
178D4×C11—41no—
179C2×C4×C11—22no—
180C2×C4×C11—22no—
181C2×C4×C11—21no—
182C2×C4×C11—21no—
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—41no—
190C2×C4×C11—41no—
191C2×C4×C11—41no—
192C2×C4×C11—41no—
193C2×C4×C11—41no—
194C2×C4×C11—41no—
195C2×C4×C11—48no—
196C2×C4×C11—42no—
197C2×C4×C11—42no—
198C2×C4×C11—42no—
199C2×C4×C11—42no—
200C2×C4×C11—42no—
201C2×C4×C11—42no—
202C2×C4×C11C4×D412yes—
203C2×C4×C11C4×D412yes—
204C2×C4×C11C2×SD1614yes—
205C2×C4×C11C2×SD1612yes—
206C2×C4×C11#13512yes—
207C2×C4×C11C23×C411yescharacteristic
208C2×C4×C11C2×#4111yescharacteristic
209C2×C4×C11C2×#4111yescharacteristic
210C2×C4×C11C2×#4111yescharacteristic
211C2×C4×C11H(5,𝔽2)11yescharacteristic
212C2×C4×C112−1+411yescharacteristic
213C8×C11—22no—
214C8×C11—42no—
215C8×C11#11714yescomplemented
216C22×SD16C22×C1111yescharacteristic
217C2×C4×Q8C22×C1111yescharacteristic
218C2×C4×D4C22×C1111yescharacteristic
219C2×#117—21no—
220C4×SD16C4×C1118yescomplemented
221C2×#106C22×C1112yes—
222C2×#106C22×C1112yes—
223C2×#106C22×C1111yescharacteristic
224C2×C4⋊C8C22×C1111yescharacteristic
225C2×#103C22×C1112yes—
226C2×#103C22×C1111yescharacteristic
227C2×#102C22×C1112yes—
228C2×#102C22×C1111yescharacteristic
229C2×C4×C8C22×C1112yes—
230C2×C4×C8C22×C1111yescharacteristic
231#391C22×C1112yes—
232#390C22×C1112yes—
233#388—22no—
234#387—22no—
235#384C22×C1111yescharacteristic
236#384C22×C1111yescharacteristic
237#382—21no—
238#380—21no—
239C4×C4⋊C4—21no—
240C4×C4⋊C4C22×C1112yes—
241C4×C4⋊C4C22×C1112yes—
242C4×C4⋊C4C22×C1111yescharacteristic
243#340C22×C1112yes—
244#340C22×C1112yes—
245#336C22×C1112yes—
246C22×C11—42no—
247C22×C11—42no—
248C22×C11—42no—
249C22×C11—81no—
250C22×C11—81no—
251C22×C11—81no—
252C22×C11—81no—
253C22×C11C2×C4×D411yescharacteristic
254C22×C11#54711yescharacteristic
255C22×C11#55011yescharacteristic
256C22×C11C22×SD1611yescharacteristic
257C22×C11C2×#13511yescharacteristic
258C22×C11#57711yescharacteristic
259C22×C11#57711yescharacteristic
260C4×C11—24no—
261C4×C11—22no—
262C4×C11—42no—
263C4×C11—42no—
264C4×C11—42no—
265C4×C11—42no—
266C4×C11—82no—
267C4×C11—82no—
268C4×C11C4×SD1614yes—
269C4×C11C2×#11711yescharacteristic
270C4×C11#52011yescharacteristic
271C4×C11#55511yescharacteristic
272C4×C11#55611yescharacteristic
273C22×Q8C23×C1111yescharacteristic
274C22×D4C23×C1111yescharacteristic
275C23×C4—21no—
276C2×SD16—22no—
277C2×SD16—22no—
278C2×SD16C2×C4×C1114yes—
279C22×C8C23×C1112yes—
280C22×C8C23×C1111yescharacteristic
281C22×C8C23×C1111yescharacteristic
282C4×Q8—22no—
283C4×Q8C2×C4×C1114yes—
284C4×D4—22no—
285C4×D4C2×C4×C1114yes—
286#117—44no—
287C2×C4⋊C4—21no—
288C2×C4⋊C4—21no—
289C2×C4⋊C4—21no—
290C2×C4⋊C4—21no—
291C2×C4⋊C4—21no—
292C2×C4⋊C4D4×C1111yescharacteristic
293C2×C4⋊C4D4×C1111yescharacteristic
294C2×C4⋊C4C23×C1112yes—
295C2×C4⋊C4C23×C1112yes—
296C2×C4⋊C4C23×C1111yescharacteristic
297C2×C4⋊C4C23×C1111yescharacteristic
298C2×C22⋊C4—21no—
299C2×C22⋊C4—22no—
300C2×C22⋊C4—22no—
301C2×C42—21no—
302C2×C42—22no—
303C2×C42—22no—
304C2×C42C23×C1112yes—
305C2×C42C23×C1111yescharacteristic
306#106—24no—
307#106—42no—
308#106C2×C4×C1114yes—
309C4⋊C8—22no—
310#103—42no—
311#103C2×C4×C1114yes—
312#102—42no—
313#102C2×C4×C1114yes—
314C4×C8—24no—
315C4×C8C2×C4×C1114yes—
316#95—22no—
317#95—22no—
318#95—22no—
319#95—22no—
320#95D4×C1112yes—
321C2×C11—82no—
322C2×C11#235411yescharacteristic
323C2×C11C2×C4×SD1611yescharacteristic
324C2×C11#295211yescharacteristic
325C2×C11#333511yescharacteristic
326C2×C11#334011yescharacteristic
327C2×C11#339211yescharacteristic
328C2×C11#339411yescharacteristic
329C24—21no—
330C2×Q8—21no—
331C2×Q8—21no—
332C2×Q8—21no—
333C2×Q8—21no—
334C2×Q8—21no—
335C2×Q8C22×C4×C1112yes—
336C2×D4—21no—
337C2×D4—21no—
338C2×D4—21no—
339C2×D4—21no—
340C2×D4—21no—
341C2×D4C22×C4×C1112yes—
342C22×C4—21no—
343C22×C4—21no—
344C22×C4—21no—
345C22×C4—24no—
346C22×C4—22no—
347C22×C4—22no—
348C22×C4—42no—
349C22×C4—42no—
350C22×C4C2×D4×C1112yes—
351C22×C4C2×D4×C1111yescharacteristic
352C22×C4C2×D4×C1112yes—
353C22×C4C2×D4×C1111yescharacteristic
354C22×C4C24×C1111yescharacteristic
355SD16—28no—
356C2×C8—21no—
357C2×C8—21no—
358C2×C8—22no—
359C2×C8—22no—
360C2×C8—22no—
361C2×C8C22×C4×C1112yes—
362C2×C8C22×C4×C1112yes—
363C2×C8C11×#4112yes—
364C2×C8C11×#4112yes—
365C4⋊C4—24no—
366C4⋊C4—22no—
367C4⋊C4—21no—
368C4⋊C4—21no—
369C4⋊C4—22no—
370C4⋊C4—22no—
371C4⋊C4—22no—
372C4⋊C4—22no—
373C4⋊C4—42no—
374C4⋊C4—42no—
375C4⋊C4—81no—
376C4⋊C4—81no—
377C4⋊C4C11×SD1614yescomplemented
378C4⋊C4C22×C4×C1112yes—
379C4⋊C4C22×C4×C1112yes—
380C22⋊C4—24no—
381C22⋊C4—44no—
382C22⋊C4—82no—
383C42—24no—
384C42—22no—
385C42—22no—
386C42—44no—
387C42—82no—
388C42C22×C4×C1112yes—
389C42C11×#4112yes—
390C11#2280511yescharacteristic, direct product factor, Sylow
391C23—22no—
392C23—41no—
393C23—41no—
394C23—41no—
395C23—41no—
396C23—41no—
397C23—41no—
398C23C22×D4×C1111yescharacteristic
399Q8—22no—
400Q8—22no—
401Q8—41no—
402Q8—41no—
403D4—22no—
404D4—22no—
405D4—41no—
406D4—41no—
407C2×C4—22no—
408C2×C4—22no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—22no—
412C2×C4—22no—
413C2×C4—22no—
414C2×C4—22no—
415C2×C4—22no—
416C2×C4—22no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—48no—
424C2×C4—42no—
425C2×C4—42no—
426C2×C4—42no—
427C2×C4—42no—
428C2×C4—42no—
429C2×C4—42no—
430C2×C4C4×D4×C1112yes—
431C2×C4C4×D4×C1112yes—
432C2×C4C2×C11×SD1614yes—
433C2×C4C2×C11×SD1612yes—
434C2×C4C11×#13512yes—
435C2×C4C23×C4×C1111yescharacteristic
436C2×C4C2×C11×#4111yescharacteristic
437C2×C4C2×C11×#4111yescharacteristic
438C2×C4C2×C11×#4111yescharacteristic
439C2×C4C11×H(5,𝔽2)11yescharacteristic
440C2×C4C11×2−1+411yescharacteristic
441C8—22no—
442C8—42no—
443C8C11×#11714yescomplemented
444C22—42no—
445C22—42no—
446C22—42no—
447C22—81no—
448C22—81no—
449C22—81no—
450C22—81no—
451C22C2×C4×D4×C1111yescharacteristic
452C22C11×#54711yescharacteristic
453C22C11×#55011yescharacteristic
454C22C22×C11×SD1611yescharacteristic
455C22C2×C11×#13511yescharacteristic
456C22C11×#57711yescharacteristic
457C22C11×#57711yescharacteristic
458C4—22no—
459C4—24no—
460C4—42no—
461C4—42no—
462C4—42no—
463C4—42no—
464C4—82no—
465C4—82no—
466C4C4×C11×SD1614yes—
467C4C2×C11×#11711yescharacteristic
468C4C11×#52011yescharacteristic
469C4C11×#55511yescharacteristic
470C4C11×#55611yescharacteristic
471C2—82no—
472C2C11×#235411yescharacteristic
473C2C2×C4×C11×SD1611yescharacteristic
474C2C11×#295211yescharacteristic
475C2C11×#333511yescharacteristic
476C2C11×#334011yescharacteristic
477C2C11×#339211yescharacteristic
478C2C11×#339411yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC22×D4×C11C23
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×#2355C2semidirect
5. C11×#1927C2semidirect
7. C11×#1844C2semidirect
8. C11×#1803C2semidirect
10. C4×C11×#106C2semidirect
11. C8×C11×C4⋊C4C2semidirect
16. C4×C11×SD16C4semidirect
90. #22805C11direct (N × H)
139. C11×C4⋊C4SD16semidirect
153. #2355C2×C11semidirect
156. #1927C2×C11semidirect
158. #1844C2×C11semidirect
159. #1803C2×C11semidirect
161. C4×#106C2×C11semidirect
162. C8×C4⋊C4C2×C11semidirect
215. C8×C11#117semidirect
220. C4×SD16C4×C11semidirect
377. C4⋊C4C11×SD16semidirect
390. C11#22805direct (N × H)
443. C8C11×#117semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C11×SD162
C11×#23552
C11×#23542
C11×#19682
C11×#19272
C11×#19262
C11×#18442
C11×#18032
C11×#18022
C4×C11×#1062
C8×C11×C4⋊C42
#2280511