Finite Group Databasebeta

← C11×#22656 #14599849

Subgroups — C11×#22656 #14599849

Order 2816.

1010 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C8×D4×C11C211yesmaximal, characteristic
2C2×C11×#427C211yesmaximal, characteristic, complemented
3C22×C11×#107C211yesmaximal, characteristic, complemented
4C11×#2352C212yesmaximal
5C11×#1949C212yesmaximal, complemented
6C11×#1854C212yesmaximal, complemented
7C11×#1853C212yesmaximal, complemented
8C11×#1846C211yesmaximal, characteristic, complemented
9C11×#1808C211yesmaximal, characteristic, complemented
10C11×#1808C211yesmaximal, characteristic, complemented
11C4×C11×#107C211yesmaximal, characteristic, complemented
12C23×C8×C11C2211yescharacteristic
13C23×C8×C11C2211yescharacteristic
14C2×C4×D4×C11C2211yescharacteristic
15C2×C11×#117C2212yes—
16C22×C11×C4⋊C4C2212yes—
17C8×D4×C11C418yescomplemented
18C11×#427—24no—
19C2×C11×#107—24no—
20C2×C11×#107C2212yes—
21C2×C11×#107C2211yescharacteristic
22C2×C11×#107C2211yescharacteristic
23C2×C11×#107C2211yescharacteristic
24C2×C11×#107C2211yescharacteristic
25C2×C11×#106C2212yes—
26C2×C11×#106C2212yes—
27C2×C11×C4⋊C8C2211yescharacteristic
28C2×C11×C22⋊C8C2211yescharacteristic
29C2×C11×C22⋊C8C2211yescharacteristic
30C2×C4×C8×C11C2211yescharacteristic
31C11×#388—22no—
32C11×#387—22no—
33C11×#386—22no—
34C11×#382C2212yes—
35C11×#380C2212yes—
36C11×#380C2212yes—
37C4×C11×C4⋊C4C2212yes—
38C4×C11×C22⋊C4—22no—
39C11×#340C2212yes—
40C11×#340C2212yes—
41C11×#340C2212yes—
42C22×D4×C11D411yescharacteristic
43C23×C4×C11—22no—
44C23×C4×C11C2311yescharacteristic
45C23×C4×C11C2311yescharacteristic
46C22×C8×C11—22no—
47C22×C8×C11—22no—
48C22×C8×C11—22no—
49C22×C8×C11—22no—
50C22×C8×C11C2×C414yes—
51C22×C8×C11C2×C414yescomplemented
52C22×C8×C11C2311yescharacteristic
53C22×C8×C11C2311yescharacteristic
54C22×C8×C11C2311yescharacteristic
55C22×C8×C11C2311yescharacteristic
56C4×D4×C11C2×C414yes—
57C4×D4×C11Q814yes—
58C11×#117—24no—
59C11×#117—42no—
60C2×C11×C4⋊C4—24no—
61C2×C11×C4⋊C4—22no—
62C2×C11×C4⋊C4—42no—
63C2×C11×C4⋊C4D411yescharacteristic
64C2×C11×C4⋊C4C2312yes—
65C2×C11×C4⋊C4C2312yes—
66C2×C11×C4⋊C4C2312yes—
67C2×C11×C4⋊C4C2312yes—
68C2×C11×C22⋊C4—22no—
69C2×C11×C22⋊C4—22no—
70C2×C11×C22⋊C4—22no—
71C2×C11×C22⋊C4D411yescharacteristic
72C2×C11×C22⋊C4D411yescharacteristic
73C2×C42×C11—22no—
74C2×C42×C11—22no—
75C2×C42×C11C2311yescharacteristic
76C11×#107—22no—
77C11×#107—22no—
78C11×#107—22no—
79C11×#107—24no—
80C11×#107D414yescomplemented
81C11×#106—24no—
82C11×#106—42no—
83C11×C4⋊C8C2×C414yescomplemented
84C11×C22⋊C8C2×C414yes—
85C11×C22⋊C8C2×C414yescomplemented
86C4×C8×C11C2×C414yescomplemented
87C11×#95—22no—
88C11×#95—22no—
89C11×#95—22no—
90C11×#95—22no—
91C11×#95—22no—
92#22656C1111yesmaximal, characteristic, direct product factor, Sylow
93C24×C11C2×D411yescharacteristic
94C24×C11C2×D411yescharacteristic
95C2×D4×C11—22no—
96C2×D4×C11—22no—
97C2×D4×C11C4⋊C414yes—
98C22×C4×C11—21no—
99C22×C4×C11—21no—
100C22×C4×C11—21no—
101C22×C4×C11—21no—
102C22×C4×C11—21no—
103C22×C4×C11—21no—
104C22×C4×C11—21no—
105C22×C4×C11—21no—
106C22×C4×C11—22no—
107C22×C4×C11—22no—
108C22×C4×C11—22no—
109C22×C4×C11—22no—
110C22×C4×C11—44no—
111C22×C4×C11—44no—
112C22×C4×C11—82no—
113C22×C4×C11C22×C412yes—
114C22×C4×C11C22×C412yes—
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11C2×D411yescharacteristic
117C22×C4×C11C2×D411yescharacteristic
118C22×C4×C11C2×D411yescharacteristic
119C22×C4×C11C2×Q812yes—
120C22×C4×C11C2×Q812yes—
121C22×C4×C11C2411yescharacteristic
122C2×C8×C11—28no—
123C2×C8×C11—28no—
124C2×C8×C11—21no—
125C2×C8×C11—21no—
126C2×C8×C11—21no—
127C2×C8×C11—21no—
128C2×C8×C11—21no—
129C2×C8×C11—21no—
130C2×C8×C11C22×C412yes—
131C2×C8×C11C22×C412yes—
132C2×C8×C11C22×C412yes—
133C2×C8×C11C22×C412yes—
134C2×C8×C11C2×D412yes—
135C2×C8×C11#4112yes—
136C11×C4⋊C4—22no—
137C11×C4⋊C4—22no—
138C11×C4⋊C4—22no—
139C11×C4⋊C4—22no—
140C11×C4⋊C4—22no—
141C11×C4⋊C4—22no—
142C11×C4⋊C4—22no—
143C11×C4⋊C4—44no—
144C11×C4⋊C4C4⋊C414yes—
145C11×C4⋊C4C2×D414yes—
146C11×C22⋊C4—44no—
147C11×C22⋊C4—44no—
148C11×C22⋊C4—82no—
149C11×C22⋊C4C4⋊C414yes—
150C11×C22⋊C4C4⋊C414yes—
151C42×C11—44no—
152C42×C11—82no—
153C42×C11C22×C412yes—
154C42×C11C2×Q812yes—
155C2×C8×D4C2×C1111yescharacteristic
156C2×#427C2×C1111yescharacteristic, complemented
157C22×#107C2×C1111yescharacteristic, complemented
158#2352C2×C1112yes—
159#1949C2×C1112yescomplemented
160#1854C2×C1112yescomplemented
161#1853C2×C1112yescomplemented
162#1846C2×C1111yescharacteristic, complemented
163#1808C2×C1111yescharacteristic, complemented
164#1808C2×C1111yescharacteristic, complemented
165C4×#107C2×C1111yescharacteristic, complemented
166C23×C11—21no—
167C23×C11—21no—
168C23×C11—21no—
169C23×C11—21no—
170C23×C11—21no—
171C23×C11—21no—
172C23×C11—21no—
173C23×C11—21no—
174C23×C11—21no—
175C23×C11—21no—
176C23×C11C2×C4⋊C412yes—
177C23×C11C2×C4⋊C412yes—
178C23×C11#13512yes—
179C23×C11#13512yes—
180C23×C11C22×D411yescharacteristic
181D4×C11—28no—
182C2×C4×C11—21no—
183C2×C4×C11—21no—
184C2×C4×C11—21no—
185C2×C4×C11—21no—
186C2×C4×C11—21no—
187C2×C4×C11—21no—
188C2×C4×C11—21no—
189C2×C4×C11—21no—
190C2×C4×C11—22no—
191C2×C4×C11—22no—
192C2×C4×C11—22no—
193C2×C4×C11—22no—
194C2×C4×C11—22no—
195C2×C4×C11—22no—
196C2×C4×C11—22no—
197C2×C4×C11—22no—
198C2×C4×C11—24no—
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—42no—
206C2×C4×C11—42no—
207C2×C4×C11—42no—
208C2×C4×C11—42no—
209C2×C4×C11—42no—
210C2×C4×C11—88no—
211C2×C4×C11C2×C4⋊C412yes—
212C2×C4×C11C2×C4⋊C412yes—
213C2×C4×C11C2×C4⋊C412yes—
214C2×C4×C11C2×C4⋊C412yes—
215C2×C4×C11C23×C411yescharacteristic
216C2×C4×C11C22×D411yescharacteristic
217C2×C4×C11C22×Q811yescharacteristic
218C2×C4×C11C2×#4111yescharacteristic
219C2×C4×C11H(5,𝔽2)11yescharacteristic
220C2×C4×C112−1+411yescharacteristic
221C8×C11—22no—
222C8×C11—22no—
223C8×C11—22no—
224C8×C11C4×D414yes—
225C23×C8C22×C1111yescharacteristic
226C23×C8C22×C1111yescharacteristic
227C2×C4×D4C22×C1111yescharacteristic
228C2×#117C22×C1112yes—
229C22×C4⋊C4C22×C1112yes—
230C8×D4C4×C1118yescomplemented
231#427—24no—
232C2×#107—24no—
233C2×#107C22×C1111yescharacteristic
234C2×#107C22×C1111yescharacteristic
235C2×#107C22×C1111yescharacteristic
236C2×#107C22×C1112yes—
237C2×#107C22×C1111yescharacteristic
238C2×#106C22×C1112yes—
239C2×#106C22×C1112yes—
240C2×C4⋊C8C22×C1111yescharacteristic
241C2×C22⋊C8C22×C1111yescharacteristic
242C2×C22⋊C8C22×C1111yescharacteristic
243C2×C4×C8C22×C1111yescharacteristic
244#388—22no—
245#387—22no—
246#386—22no—
247#382C22×C1112yes—
248#380C22×C1112yes—
249#380C22×C1112yes—
250C4×C4⋊C4C22×C1112yes—
251C4×C22⋊C4—22no—
252#340C22×C1112yes—
253#340C22×C1112yes—
254#340C22×C1112yes—
255C22×C11—22no—
256C22×C11—22no—
257C22×C11—22no—
258C22×C11—22no—
259C22×C11—22no—
260C22×C11—22no—
261C22×C11—22no—
262C22×C11—22no—
263C22×C11—22no—
264C22×C11—41no—
265C22×C11—41no—
266C22×C11—41no—
267C22×C11—41no—
268C22×C11#42714yescomplemented
269C22×C11C22×C4⋊C411yescharacteristic
270C22×C11D4211yescharacteristic
271C22×C11#54711yescharacteristic
272C22×C11C2×#13511yescharacteristic
273C22×C11C2×#13511yescharacteristic
274C22×C11#57611yescharacteristic
275C22×C11#57811yescharacteristic
276C4×C11—22no—
277C4×C11—22no—
278C4×C11—22no—
279C4×C11—22no—
280C4×C11—44no—
281C4×C11—82no—
282C4×C11—82no—
283C4×C11—82no—
284C4×C11C2×C4×D411yescharacteristic
285C4×C11#52011yescharacteristic
286C4×C11D4×Q811yescharacteristic
287C4×C11#55411yescharacteristic
288C22×D4D4×C1111yescharacteristic
289C23×C4—22no—
290C23×C4C23×C1111yescharacteristic
291C23×C4C23×C1111yescharacteristic
292C22×C8—22no—
293C22×C8—22no—
294C22×C8—22no—
295C22×C8—22no—
296C22×C8C2×C4×C1114yes—
297C22×C8C2×C4×C1114yescomplemented
298C22×C8C23×C1111yescharacteristic
299C22×C8C23×C1111yescharacteristic
300C22×C8C23×C1111yescharacteristic
301C22×C8C23×C1111yescharacteristic
302C4×D4C2×C4×C1114yes—
303C4×D4Q8×C1114yes—
304#117—24no—
305#117—42no—
306C2×C4⋊C4—24no—
307C2×C4⋊C4—22no—
308C2×C4⋊C4—42no—
309C2×C4⋊C4D4×C1111yescharacteristic
310C2×C4⋊C4C23×C1112yes—
311C2×C4⋊C4C23×C1112yes—
312C2×C4⋊C4C23×C1112yes—
313C2×C4⋊C4C23×C1112yes—
314C2×C22⋊C4—22no—
315C2×C22⋊C4—22no—
316C2×C22⋊C4—22no—
317C2×C22⋊C4D4×C1111yescharacteristic
318C2×C22⋊C4D4×C1111yescharacteristic
319C2×C42—22no—
320C2×C42—22no—
321C2×C42C23×C1111yescharacteristic
322#107—22no—
323#107—22no—
324#107—22no—
325#107—24no—
326#107D4×C1114yescomplemented
327#106—24no—
328#106—42no—
329C4⋊C8C2×C4×C1114yescomplemented
330C22⋊C8C2×C4×C1114yes—
331C22⋊C8C2×C4×C1114yescomplemented
332C4×C8C2×C4×C1114yescomplemented
333#95—22no—
334#95—22no—
335#95—22no—
336#95—22no—
337#95—22no—
338C2×C11—24no—
339C2×C11—42no—
340C2×C11D4×C4⋊C411yescharacteristic
341C2×C11C2×#42711yescharacteristic
342C2×C11#291311yescharacteristic
343C2×C11#328011yescharacteristic
344C2×C11#328511yescharacteristic
345C2×C11#333611yescharacteristic
346C2×C11#333911yescharacteristic
347C24C2×D4×C1111yescharacteristic
348C24C2×D4×C1111yescharacteristic
349C2×D4—22no—
350C2×D4—22no—
351C2×D4C11×C4⋊C414yes—
352C22×C4—21no—
353C22×C4—21no—
354C22×C4—21no—
355C22×C4—21no—
356C22×C4—21no—
357C22×C4—21no—
358C22×C4—21no—
359C22×C4—21no—
360C22×C4—22no—
361C22×C4—22no—
362C22×C4—22no—
363C22×C4—22no—
364C22×C4—44no—
365C22×C4—44no—
366C22×C4—82no—
367C22×C4C22×C4×C1112yes—
368C22×C4C22×C4×C1112yes—
369C22×C4C2×D4×C1111yescharacteristic
370C22×C4C2×D4×C1111yescharacteristic
371C22×C4C2×D4×C1111yescharacteristic
372C22×C4C2×D4×C1111yescharacteristic
373C22×C4C2×Q8×C1112yes—
374C22×C4C2×Q8×C1112yes—
375C22×C4C24×C1111yescharacteristic
376C2×C8—21no—
377C2×C8—21no—
378C2×C8—21no—
379C2×C8—21no—
380C2×C8—21no—
381C2×C8—21no—
382C2×C8—28no—
383C2×C8—28no—
384C2×C8C22×C4×C1112yes—
385C2×C8C22×C4×C1112yes—
386C2×C8C22×C4×C1112yes—
387C2×C8C22×C4×C1112yes—
388C2×C8C2×D4×C1112yes—
389C2×C8C11×#4112yes—
390C4⋊C4—22no—
391C4⋊C4—22no—
392C4⋊C4—22no—
393C4⋊C4—22no—
394C4⋊C4—22no—
395C4⋊C4—22no—
396C4⋊C4—22no—
397C4⋊C4—44no—
398C4⋊C4C11×C4⋊C414yes—
399C4⋊C4C2×D4×C1114yes—
400C22⋊C4—44no—
401C22⋊C4—44no—
402C22⋊C4—82no—
403C22⋊C4C11×C4⋊C414yes—
404C22⋊C4C11×C4⋊C414yes—
405C42—44no—
406C42—82no—
407C42C22×C4×C1112yes—
408C42C2×Q8×C1112yes—
409C11#2265611yescharacteristic, direct product factor, Sylow
410C23—21no—
411C23—21no—
412C23—21no—
413C23—21no—
414C23—21no—
415C23—21no—
416C23—21no—
417C23—21no—
418C23—21no—
419C23—21no—
420C23C2×C11×C4⋊C412yes—
421C23C2×C11×C4⋊C412yes—
422C23C11×#13512yes—
423C23C11×#13512yes—
424C23C22×D4×C1111yescharacteristic
425D4—28no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—21no—
429C2×C4—21no—
430C2×C4—21no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—22no—
435C2×C4—22no—
436C2×C4—22no—
437C2×C4—22no—
438C2×C4—22no—
439C2×C4—22no—
440C2×C4—22no—
441C2×C4—22no—
442C2×C4—24no—
443C2×C4—42no—
444C2×C4—42no—
445C2×C4—42no—
446C2×C4—42no—
447C2×C4—42no—
448C2×C4—42no—
449C2×C4—42no—
450C2×C4—42no—
451C2×C4—42no—
452C2×C4—42no—
453C2×C4—42no—
454C2×C4—88no—
455C2×C4C2×C11×C4⋊C412yes—
456C2×C4C2×C11×C4⋊C412yes—
457C2×C4C2×C11×C4⋊C412yes—
458C2×C4C2×C11×C4⋊C412yes—
459C2×C4C23×C4×C1111yescharacteristic
460C2×C4C22×D4×C1111yescharacteristic
461C2×C4C22×Q8×C1111yescharacteristic
462C2×C4C2×C11×#4111yescharacteristic
463C2×C4C11×H(5,𝔽2)11yescharacteristic
464C2×C4C11×2−1+411yescharacteristic
465C8—22no—
466C8—22no—
467C8—22no—
468C8C4×D4×C1114yes—
469C22—22no—
470C22—22no—
471C22—22no—
472C22—22no—
473C22—22no—
474C22—22no—
475C22—22no—
476C22—22no—
477C22—22no—
478C22—41no—
479C22—41no—
480C22—41no—
481C22—41no—
482C22C11×#42714yescomplemented
483C22C22×C11×C4⋊C411yescharacteristic
484C22D42×C1111yescharacteristic
485C22C11×#54711yescharacteristic
486C22C2×C11×#13511yescharacteristic
487C22C2×C11×#13511yescharacteristic
488C22C11×#57611yescharacteristic
489C22C11×#57811yescharacteristic
490C4—22no—
491C4—22no—
492C4—22no—
493C4—22no—
494C4—44no—
495C4—82no—
496C4—82no—
497C4—82no—
498C4C2×C4×D4×C1111yescharacteristic
499C4C11×#52011yescharacteristic
500C4D4×Q8×C1111yescharacteristic
501C4C11×#55411yescharacteristic
502C2—24no—
503C2—42no—
504C2D4×C11×C4⋊C411yescharacteristic
505C2C2×C11×#42711yescharacteristic
506C2C11×#291311yescharacteristic
507C2C11×#328011yescharacteristic
508C2C11×#328511yescharacteristic
509C2C11×#333611yescharacteristic
510C2C11×#333911yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC22×D4×C11D4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C4×D4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#427C2semidirect
3. C22×C11×#107C2semidirect
5. C11×#1949C2semidirect
6. C11×#1854C2semidirect
7. C11×#1853C2semidirect
8. C11×#1846C2semidirect
9. C11×#1808C2semidirect
10. C11×#1808C2semidirect
11. C4×C11×#107C2semidirect
17. C8×D4×C11C4semidirect
51. C22×C8×C11C2×C4semidirect
80. C11×#107D4semidirect
83. C11×C4⋊C8C2×C4semidirect
85. C11×C22⋊C8C2×C4semidirect
86. C4×C8×C11C2×C4semidirect
92. #22656C11direct (N × H)
156. C2×#427C2×C11semidirect
157. C22×#107C2×C11semidirect
159. #1949C2×C11semidirect
160. #1854C2×C11semidirect
161. #1853C2×C11semidirect
162. #1846C2×C11semidirect
163. #1808C2×C11semidirect
164. #1808C2×C11semidirect
165. C4×#107C2×C11semidirect
230. C8×D4C4×C11semidirect
268. C22×C11#427semidirect
297. C22×C8C2×C4×C11semidirect
326. #107D4×C11semidirect
329. C4⋊C8C2×C4×C11semidirect
331. C22⋊C8C2×C4×C11semidirect
332. C4×C8C2×C4×C11semidirect
409. C11#22656direct (N × H)
482. C22C11×#427semidirect

Maximal subgroups

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

subgroupindex
C2×C8×D4×C112
C2×C11×#4272
C22×C11×#1072
C11×#23522
C11×#19492
C11×#18542
C11×#18532
C11×#18462
C11×#18082
C4×C11×#1072
#2265611