Finite Group Databasebeta

← C11×#22081 #14599274

Subgroups — C11×#22081 #14599274

Order 2816.

968 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#480C211yesmaximal, characteristic
2C4×C11×#121C211yesmaximal, characteristic
3C2×C11×#389C211yesmaximal, characteristic, complemented
4C11×#1943C212yesmaximal, complemented
5C11×#1936C212yesmaximal, complemented
6C11×#1921C212yesmaximal, complemented
7C11×#1874C211yesmaximal, characteristic
8C11×#1864C212yesmaximal, complemented
9C11×#1853C211yesmaximal, characteristic, complemented
10C11×#1823C211yesmaximal, characteristic, complemented
11C11×#1749C211yesmaximal, characteristic, complemented
12C2×C11×#121C2211yescharacteristic
13C2×C4×D4×C11—21no—
14C2×C4×D4×C11C2211yescharacteristic
15C22×C11×C4⋊C4—21no—
16C22×C11×C4⋊C4C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C42×C11C2211yescharacteristic
19C11×#480C418yescomplemented
20C2×C11×#107C2212yes—
21C2×C11×#106C2212yes—
22C2×C11×#102C2212yes—
23C2×C11×#102C2212yes—
24C2×C11×C22⋊C8C2211yescharacteristic
25C2×C11×C22⋊C8C2211yescharacteristic
26C2×C11×#97C2212yes—
27C11×#390C2211yescharacteristic
28C11×#389—21no—
29C11×#389—21no—
30C11×#389C2212yes—
31C11×#389C2212yes—
32C11×#389C2211yescharacteristic
33C11×#388—21no—
34C11×#386—21no—
35C11×#380C2211yescharacteristic
36C4×C11×C4⋊C4C2211yescharacteristic
37C4×C11×C22⋊C4—21no—
38C2×C11×#95—21no—
39C11×#340C2212yes—
40C11×#340C2212yes—
41C11×#340C2212yes—
42C11×#340C2212yes—
43C11×#336C2212yes—
44C22×D4×C11—21no—
45C22×D4×C11C2311yescharacteristic
46C23×C4×C11—21no—
47C23×C4×C11—21no—
48C23×C4×C11—21no—
49C23×C4×C11D411yescharacteristic
50C23×C4×C11D411yescharacteristic
51C23×C4×C11C2311yescharacteristic
52C22×C8×C11C2312yes—
53C22×C8×C11C2312yes—
54C11×#121—22no—
55C11×#121C2×C414yes—
56C4×D4×C11—42no—
57C4×D4×C11—44no—
58C2×C11×C4⋊C4—21no—
59C2×C11×C4⋊C4—22no—
60C2×C11×C4⋊C4—22no—
61C2×C11×C4⋊C4—22no—
62C2×C11×C4⋊C4—21no—
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4—42no—
65C2×C11×C4⋊C4—44no—
66C2×C11×C4⋊C4C2×C414yescomplemented
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C4⋊C4C2312yes—
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C4⋊C4C2312yes—
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C22⋊C4—21no—
73C2×C11×C22⋊C4—21no—
74C2×C11×C22⋊C4—21no—
75C2×C11×C22⋊C4—21no—
76C2×C11×C22⋊C4—21no—
77C2×C42×C11—21no—
78C2×C42×C11—42no—
79C2×C42×C11D411yescharacteristic
80C2×C42×C11D411yescharacteristic
81C2×C42×C11C2311yescharacteristic
82C2×C42×C11C2311yescharacteristic
83C11×#107C2×C418yescomplemented
84C11×#106—42no—
85C11×#102—42no—
86C11×#102C2×C418yescomplemented
87C11×C22⋊C8—22no—
88C11×C22⋊C8C2×C414yescomplemented
89C11×#97—42no—
90C11×#95—22no—
91C11×#95—22no—
92C11×#95—21no—
93C11×#95—21no—
94C11×#95—21no—
95#22081C1111yesmaximal, characteristic, direct product factor, Sylow
96C24×C11—21no—
97C24×C11C2×D411yescharacteristic
98C2×D4×C11—24no—
99C2×D4×C11—21no—
100C2×D4×C11—22no—
101C2×D4×C11—22no—
102C2×D4×C11—42no—
103C2×D4×C11—42no—
104C2×D4×C11C22×C412yes—
105C22×C4×C11—22no—
106C22×C4×C11—22no—
107C22×C4×C11—24no—
108C22×C4×C11—22no—
109C22×C4×C11—22no—
110C22×C4×C11—21no—
111C22×C4×C11—22no—
112C22×C4×C11—22no—
113C22×C4×C11—21no—
114C22×C4×C11—21no—
115C22×C4×C11—22no—
116C22×C4×C11—41no—
117C22×C4×C11—41no—
118C22×C4×C11—41no—
119C22×C4×C11—42no—
120C22×C4×C11—42no—
121C22×C4×C11—42no—
122C22×C4×C11—42no—
123C22×C4×C11—42no—
124C22×C4×C11—42no—
125C22×C4×C11—42no—
126C22×C4×C11—42no—
127C22×C4×C11C22×C412yes—
128C22×C4×C11C2×D411yescharacteristic
129C22×C4×C11C2×D411yescharacteristic
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11C2×D411yescharacteristic
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11#4112yes—
134C22×C4×C11C2411yescharacteristic
135C2×C8×C11—22no—
136C2×C8×C11—22no—
137C2×C8×C11—22no—
138C2×C8×C11—22no—
139C2×C8×C11—22no—
140C2×C8×C11C22×C414yes—
141C11×C4⋊C4—24no—
142C11×C4⋊C4—22no—
143C11×C4⋊C4—21no—
144C11×C4⋊C4—22no—
145C11×C4⋊C4—22no—
146C11×C4⋊C4—22no—
147C11×C4⋊C4—22no—
148C11×C4⋊C4—42no—
149C11×C4⋊C4—44no—
150C11×C4⋊C4—44no—
151C11×C4⋊C4—42no—
152C11×C4⋊C4C22×C414yes—
153C11×C4⋊C4C22×C412yes—
154C11×C22⋊C4—24no—
155C11×C22⋊C4—42no—
156C11×C22⋊C4—42no—
157C11×C22⋊C4—42no—
158C11×C22⋊C4—42no—
159C42×C11—22no—
160C42×C11—22no—
161C42×C11—41no—
162C42×C11—41no—
163C42×C11—42no—
164C2×#480C2×C1111yescharacteristic
165C4×#121C2×C1111yescharacteristic
166C2×#389C2×C1111yescharacteristic, complemented
167#1943C2×C1112yescomplemented
168#1936C2×C1112yescomplemented
169#1921C2×C1112yescomplemented
170#1874C2×C1111yescharacteristic
171#1864C2×C1112yescomplemented
172#1853C2×C1111yescharacteristic, complemented
173#1823C2×C1111yescharacteristic, complemented
174#1749C2×C1111yescharacteristic, complemented
175C23×C11—21no—
176C23×C11—21no—
177C23×C11—21no—
178C23×C11—21no—
179C23×C11—22no—
180C23×C11—41no—
181C23×C11—41no—
182C23×C11—41no—
183C23×C11—41no—
184C23×C11—41no—
185C23×C11—41no—
186C23×C11C4×D412yes—
187C23×C11AGL(1,ℤ/8)12yes—
188C23×C11AGL(1,ℤ/8)12yes—
189C23×C11C22×D411yescharacteristic
190D4×C11—24no—
191D4×C11—48no—
192D4×C11—42no—
193C2×C4×C11—21no—
194C2×C4×C11—21no—
195C2×C4×C11—21no—
196C2×C4×C11—21no—
197C2×C4×C11—24no—
198C2×C4×C11—24no—
199C2×C4×C11—22no—
200C2×C4×C11—24no—
201C2×C4×C11—21no—
202C2×C4×C11—21no—
203C2×C4×C11—21no—
204C2×C4×C11—21no—
205C2×C4×C11—21no—
206C2×C4×C11—21no—
207C2×C4×C11—21no—
208C2×C4×C11—21no—
209C2×C4×C11—21no—
210C2×C4×C11—44no—
211C2×C4×C11—44no—
212C2×C4×C11—41no—
213C2×C4×C11—42no—
214C2×C4×C11—42no—
215C2×C4×C11—41no—
216C2×C4×C11—48no—
217C2×C4×C11—41no—
218C2×C4×C11—42no—
219C2×C4×C11—41no—
220C2×C4×C11—41no—
221C2×C4×C11—41no—
222C2×C4×C11—42no—
223C2×C4×C11—41no—
224C2×C4×C11—41no—
225C2×C4×C11—42no—
226C2×C4×C11—84no—
227C2×C4×C11—84no—
228C2×C4×C11C4×D412yes—
229C2×C4×C11#13712yes—
230C2×C4×C11C23×C411yescharacteristic
231C2×C4×C11C2×#4111yescharacteristic
232C2×C4×C11H(5,𝔽2)12yes—
233C2×C4×C112−1+412yes—
234C8×C11—24no—
235C8×C11—42no—
236C2×#121C22×C1111yescharacteristic
237C2×C4×D4—21no—
238C2×C4×D4C22×C1111yescharacteristic
239C22×C4⋊C4—21no—
240C22×C4⋊C4C22×C1111yescharacteristic
241C22×C4⋊C4C22×C1111yescharacteristic
242C22×C42C22×C1111yescharacteristic
243#480C4×C1118yescomplemented
244C2×#107C22×C1112yes—
245C2×#106C22×C1112yes—
246C2×#102C22×C1112yes—
247C2×#102C22×C1112yes—
248C2×C22⋊C8C22×C1111yescharacteristic
249C2×C22⋊C8C22×C1111yescharacteristic
250C2×#97C22×C1112yes—
251#390C22×C1111yescharacteristic
252#389—21no—
253#389—21no—
254#389C22×C1112yes—
255#389C22×C1112yes—
256#389C22×C1111yescharacteristic
257#388—21no—
258#386—21no—
259#380C22×C1111yescharacteristic
260C4×C4⋊C4C22×C1111yescharacteristic
261C4×C22⋊C4—21no—
262C2×#95—21no—
263#340C22×C1112yes—
264#340C22×C1112yes—
265#340C22×C1112yes—
266#340C22×C1112yes—
267#336C22×C1112yes—
268C22×C11—22no—
269C22×C11—22no—
270C22×C11—22no—
271C22×C11—22no—
272C22×C11—22no—
273C22×C11—22no—
274C22×C11—42no—
275C22×C11—42no—
276C22×C11—42no—
277C22×C11—81no—
278C22×C11—81no—
279C22×C11—81no—
280C22×C11—81no—
281C22×C11#44214yes—
282C22×C11C2×C4×D411yescharacteristic
283C22×C11#53411yescharacteristic
284C22×C11#53611yescharacteristic
285C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
286C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
287C22×C11C2×#13711yescharacteristic
288C22×C11#57511yescharacteristic
289C4×C11—22no—
290C4×C11—22no—
291C4×C11—41no—
292C4×C11—41no—
293C4×C11—41no—
294C4×C11—44no—
295C4×C11—42no—
296C4×C11—81no—
297C4×C11—82no—
298C4×C11—81no—
299C4×C11#52012yes—
300C4×C11#53912yes—
301C22×D4—21no—
302C22×D4C23×C1111yescharacteristic
303C23×C4—21no—
304C23×C4—21no—
305C23×C4—21no—
306C23×C4D4×C1111yescharacteristic
307C23×C4D4×C1111yescharacteristic
308C23×C4C23×C1111yescharacteristic
309C22×C8C23×C1112yes—
310C22×C8C23×C1112yes—
311#121—22no—
312#121C2×C4×C1114yes—
313C4×D4—42no—
314C4×D4—44no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—22no—
317C2×C4⋊C4—22no—
318C2×C4⋊C4—22no—
319C2×C4⋊C4—21no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—42no—
322C2×C4⋊C4—44no—
323C2×C4⋊C4C2×C4×C1114yescomplemented
324C2×C4⋊C4C23×C1112yes—
325C2×C4⋊C4C23×C1111yescharacteristic
326C2×C4⋊C4C23×C1111yescharacteristic
327C2×C4⋊C4C23×C1112yes—
328C2×C4⋊C4C23×C1111yescharacteristic
329C2×C22⋊C4—21no—
330C2×C22⋊C4—21no—
331C2×C22⋊C4—21no—
332C2×C22⋊C4—21no—
333C2×C22⋊C4—21no—
334C2×C42—21no—
335C2×C42—42no—
336C2×C42D4×C1111yescharacteristic
337C2×C42D4×C1111yescharacteristic
338C2×C42C23×C1111yescharacteristic
339C2×C42C23×C1111yescharacteristic
340#107C2×C4×C1118yescomplemented
341#106—42no—
342#102—42no—
343#102C2×C4×C1118yescomplemented
344C22⋊C8—22no—
345C22⋊C8C2×C4×C1114yescomplemented
346#97—42no—
347#95—22no—
348#95—22no—
349#95—21no—
350#95—21no—
351#95—21no—
352C2×C11—24no—
353C2×C11—82no—
354C2×C11#232211yescharacteristic
355C2×C11C2×#44211yescharacteristic
356C2×C11C4×#13711yescharacteristic
357C2×C11#319311yescharacteristic
358C2×C11#319411yescharacteristic
359C2×C11#323411yescharacteristic
360C2×C11#323811yescharacteristic
361C24—21no—
362C24C2×D4×C1111yescharacteristic
363C2×D4—24no—
364C2×D4—21no—
365C2×D4—22no—
366C2×D4—22no—
367C2×D4—42no—
368C2×D4—42no—
369C2×D4C22×C4×C1112yes—
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—24no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—21no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—21no—
379C22×C4—21no—
380C22×C4—22no—
381C22×C4—41no—
382C22×C4—41no—
383C22×C4—41no—
384C22×C4—42no—
385C22×C4—42no—
386C22×C4—42no—
387C22×C4—42no—
388C22×C4—42no—
389C22×C4—42no—
390C22×C4—42no—
391C22×C4—42no—
392C22×C4C22×C4×C1112yes—
393C22×C4C2×D4×C1111yescharacteristic
394C22×C4C2×D4×C1111yescharacteristic
395C22×C4C2×D4×C1111yescharacteristic
396C22×C4C2×D4×C1111yescharacteristic
397C22×C4C2×D4×C1111yescharacteristic
398C22×C4C11×#4112yes—
399C22×C4C24×C1111yescharacteristic
400C2×C8—22no—
401C2×C8—22no—
402C2×C8—22no—
403C2×C8—22no—
404C2×C8—22no—
405C2×C8C22×C4×C1114yes—
406C4⋊C4—24no—
407C4⋊C4—22no—
408C4⋊C4—21no—
409C4⋊C4—22no—
410C4⋊C4—22no—
411C4⋊C4—22no—
412C4⋊C4—22no—
413C4⋊C4—42no—
414C4⋊C4—44no—
415C4⋊C4—44no—
416C4⋊C4—42no—
417C4⋊C4C22×C4×C1114yes—
418C4⋊C4C22×C4×C1112yes—
419C22⋊C4—24no—
420C22⋊C4—42no—
421C22⋊C4—42no—
422C22⋊C4—42no—
423C22⋊C4—42no—
424C42—22no—
425C42—22no—
426C42—41no—
427C42—41no—
428C42—42no—
429C11#2208111yescharacteristic, direct product factor, Sylow
430C23—21no—
431C23—21no—
432C23—21no—
433C23—21no—
434C23—22no—
435C23—41no—
436C23—41no—
437C23—41no—
438C23—41no—
439C23—41no—
440C23—41no—
441C23C4×D4×C1112yes—
442C23C11×AGL(1,ℤ/8)12yes—
443C23C11×AGL(1,ℤ/8)12yes—
444C23C22×D4×C1111yescharacteristic
445D4—24no—
446D4—48no—
447D4—42no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—24no—
453C2×C4—24no—
454C2×C4—22no—
455C2×C4—24no—
456C2×C4—21no—
457C2×C4—21no—
458C2×C4—21no—
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—21no—
463C2×C4—21no—
464C2×C4—21no—
465C2×C4—44no—
466C2×C4—44no—
467C2×C4—41no—
468C2×C4—42no—
469C2×C4—42no—
470C2×C4—41no—
471C2×C4—48no—
472C2×C4—41no—
473C2×C4—42no—
474C2×C4—41no—
475C2×C4—41no—
476C2×C4—41no—
477C2×C4—42no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—42no—
481C2×C4—84no—
482C2×C4—84no—
483C2×C4C4×D4×C1112yes—
484C2×C4C11×#13712yes—
485C2×C4C23×C4×C1111yescharacteristic
486C2×C4C2×C11×#4111yescharacteristic
487C2×C4C11×H(5,𝔽2)12yes—
488C2×C4C11×2−1+412yes—
489C8—24no—
490C8—42no—
491C22—22no—
492C22—22no—
493C22—22no—
494C22—22no—
495C22—22no—
496C22—22no—
497C22—42no—
498C22—42no—
499C22—42no—
500C22—81no—
501C22—81no—
502C22—81no—
503C22—81no—
504C22C11×#44214yes—
505C22C2×C4×D4×C1111yescharacteristic
506C22C11×#53411yescharacteristic
507C22C11×#53611yescharacteristic
508C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
509C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
510C22C2×C11×#13711yescharacteristic
511C22C11×#57511yescharacteristic
512C4—22no—
513C4—22no—
514C4—41no—
515C4—41no—
516C4—41no—
517C4—44no—
518C4—42no—
519C4—81no—
520C4—82no—
521C4—81no—
522C4C11×#52012yes—
523C4C11×#53912yes—
524C2—24no—
525C2—82no—
526C2C11×#232211yescharacteristic
527C2C2×C11×#44211yescharacteristic
528C2C4×C11×#13711yescharacteristic
529C2C11×#319311yescharacteristic
530C2C11×#319411yescharacteristic
531C2C11×#323411yescharacteristic
532C2C11×#323811yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#121C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C22×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C11×#389C2semidirect
4. C11×#1943C2semidirect
5. C11×#1936C2semidirect
6. C11×#1921C2semidirect
8. C11×#1864C2semidirect
9. C11×#1853C2semidirect
10. C11×#1823C2semidirect
11. C11×#1749C2semidirect
19. C11×#480C4semidirect
66. C2×C11×C4⋊C4C2×C4semidirect
83. C11×#107C2×C4semidirect
86. C11×#102C2×C4semidirect
88. C11×C22⋊C8C2×C4semidirect
95. #22081C11direct (N × H)
166. C2×#389C2×C11semidirect
167. #1943C2×C11semidirect
168. #1936C2×C11semidirect
169. #1921C2×C11semidirect
171. #1864C2×C11semidirect
172. #1853C2×C11semidirect
173. #1823C2×C11semidirect
174. #1749C2×C11semidirect
243. #480C4×C11semidirect
323. C2×C4⋊C4C2×C4×C11semidirect
340. #107C2×C4×C11semidirect
343. #102C2×C4×C11semidirect
345. C22⋊C8C2×C4×C11semidirect
429. C11#22081direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4802
C4×C11×#1212
C2×C11×#3892
C11×#19432
C11×#19362
C11×#19212
C11×#18742
C11×#18642
C11×#18532
C11×#18232
C11×#17492
#2208111