Finite Group Databasebeta

← C11×#22844 #14600037

Subgroups — C11×#22844 #14600037

Order 2816.

1326 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#435C212yesmaximal, complemented
2C22×C11×C22⋊C8C212yesmaximal, complemented
3C4×C11×#120C211yesmaximal, characteristic
4C11×#1955C211yesmaximal, characteristic, complemented
5C11×#1924C212yesmaximal, complemented
6C11×#1870C211yesmaximal, characteristic, complemented
7C11×#1869C212yesmaximal, complemented
8C11×#1850C212yesmaximal, complemented
9C11×#1752C212yesmaximal, complemented
10C24×C4×C11C2211yescharacteristic
11C22×C11×M16C2211yescharacteristic, complemented
12C23×C8×C11C2212yes—
13C23×C8×C11C2212yes—
14C2×C11×#120C411yescharacteristic
15C2×C4×D4×C11C2212yes—
16C2×C4×D4×C11C2211yescharacteristic
17C11×#435—28no—
18C2×C11×C4⋊C8C2212yescomplemented
19C2×C11×C4⋊C8C2211yescharacteristic, complemented
20C2×C11×C22⋊C8—28no—
21C2×C11×C22⋊C8C2212yes—
22C2×C11×C22⋊C8C2212yes—
23C2×C11×C22⋊C8C2212yes—
24C2×C11×C22⋊C8C2212yes—
25C2×C11×C22⋊C8C2212yescomplemented
26C2×C11×C22⋊C8C2211yescharacteristic, complemented
27C2×C11×#97C2212yescomplemented
28C2×C11×#97C2211yescharacteristic, complemented
29C11×#386C412yes—
30C11×#386C411yescharacteristic
31C11×#385C412yes—
32C11×#385C411yescharacteristic
33C11×#379C411yescharacteristic
34C4×C11×C22⋊C4C2211yescharacteristic
35C4×C11×C22⋊C4C2212yes—
36C11×#336C2212yescomplemented
37C11×#336C2212yescomplemented
38C11×#336C2212yescomplemented
39C25×C11C2×C411yescharacteristic
40C22×D4×C11C2×C412yes—
41C22×D4×C11C2×C411yescharacteristic
42C23×C4×C11—24no—
43C23×C4×C11—24no—
44C23×C4×C11—41no—
45C23×C4×C11—41no—
46C23×C4×C11C2×C412yes—
47C23×C4×C11C2×C411yescharacteristic
48C23×C4×C11C2311yescharacteristic
49C23×C4×C11C2311yescharacteristic
50C23×C4×C11C2312yes—
51C2×C11×M16—24no—
52C2×C11×M16—41no—
53C22×C8×C11—24no—
54C22×C8×C11—24no—
55C22×C8×C11—24no—
56C22×C8×C11—24no—
57C22×C8×C11—42no—
58C22×C8×C11—42no—
59C22×C8×C11C2312yes—
60C22×C8×C11C2312yes—
61C22×C8×C11C2312yes—
62C22×C8×C11C2312yes—
63C11×#120—24no—
64C4×D4×C11—24no—
65C4×D4×C11—24no—
66C4×D4×C11—41no—
67C4×D4×C11—41no—
68C2×C11×C4⋊C4C2×C412yes—
69C2×C11×C4⋊C4C2×C411yescharacteristic
70C2×C11×C22⋊C4C2×C412yes—
71C2×C11×C22⋊C4C2×C411yescharacteristic
72C2×C11×C22⋊C4C2×C412yes—
73C2×C11×C22⋊C4C2×C412yes—
74C2×C11×C22⋊C4C2×C412yes—
75C2×C11×C22⋊C4C2×C411yescharacteristic
76C2×C11×C22⋊C4C2×C411yescharacteristic
77C2×C11×C22⋊C4C2×C411yescharacteristic
78C2×C42×C11C2312yes—
79C2×C42×C11C2311yescharacteristic
80C11×C4⋊C8—24no—
81C11×C4⋊C8—41no—
82C11×C22⋊C8—24no—
83C11×C22⋊C8—24no—
84C11×C22⋊C8—24no—
85C11×C22⋊C8—24no—
86C11×C22⋊C8—41no—
87C11×C22⋊C8D418yescomplemented
88C11×#97—24no—
89C11×#97—41no—
90C11×#95C2×C412yes—
91C11×#95C2×C412yes—
92C11×#95C2×C412yes—
93#22844C1111yesmaximal, characteristic, direct product factor, Sylow
94C24×C11—24no—
95C24×C11—24no—
96C24×C11—41no—
97C24×C11—41no—
98C24×C11M1614yescomplemented
99C24×C11C22×C411yescharacteristic
100C24×C11C22×C411yescharacteristic
101C24×C11C22×C412yes—
102C2×D4×C11—24no—
103C2×D4×C11—22no—
104C2×D4×C11—24no—
105C2×D4×C11—24no—
106C2×D4×C11—41no—
107C2×D4×C11—41no—
108C22×C4×C11—22no—
109C22×C4×C11—22no—
110C22×C4×C11—22no—
111C22×C4×C11—22no—
112C22×C4×C11—24no—
113C22×C4×C11—24no—
114C22×C4×C11—24no—
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—21no—
120C22×C4×C11—21no—
121C22×C4×C11—21no—
122C22×C4×C11—21no—
123C22×C4×C11—41no—
124C22×C4×C11—42no—
125C22×C4×C11—44no—
126C22×C4×C11—48no—
127C22×C4×C11—44no—
128C22×C4×C11C22×C412yes—
129C22×C4×C11C22×C411yescharacteristic
130C22×C4×C11C22×C412yes—
131C22×C4×C11C22×C411yescharacteristic
132C22×C4×C11C22×C411yescharacteristic
133C22×C4×C11C22×C411yescharacteristic
134C22×C4×C11C22×C412yes—
135C22×C4×C11C2×D414yes—
136C22×C4×C11#4114yes—
137C22×C4×C11C2411yescharacteristic
138C11×M16—44no—
139C2×C8×C11—22no—
140C2×C8×C11—22no—
141C2×C8×C11—22no—
142C2×C8×C11—22no—
143C2×C8×C11—22no—
144C2×C8×C11—22no—
145C2×C8×C11—22no—
146C2×C8×C11—22no—
147C2×C8×C11—22no—
148C2×C8×C11—22no—
149C2×C8×C11—48no—
150C2×C8×C11—48no—
151C2×C8×C11C2×D414yes—
152C2×C8×C11C2×D414yes—
153C11×C4⋊C4—24no—
154C11×C4⋊C4—41no—
155C11×C22⋊C4—24no—
156C11×C22⋊C4—22no—
157C11×C22⋊C4—24no—
158C11×C22⋊C4—24no—
159C11×C22⋊C4—24no—
160C11×C22⋊C4—41no—
161C11×C22⋊C4—41no—
162C11×C22⋊C4—41no—
163C42×C11—22no—
164C42×C11—22no—
165C42×C11—21no—
166C42×C11—21no—
167C2×#435C2×C1112yescomplemented
168C22×C22⋊C8C2×C1112yescomplemented
169C4×#120C2×C1111yescharacteristic
170#1955C2×C1111yescharacteristic, complemented
171#1924C2×C1112yescomplemented
172#1870C2×C1111yescharacteristic, complemented
173#1869C2×C1112yescomplemented
174#1850C2×C1112yescomplemented
175#1752C2×C1112yescomplemented
176C23×C11—22no—
177C23×C11—22no—
178C23×C11—22no—
179C23×C11—22no—
180C23×C11—22no—
181C23×C11—21no—
182C23×C11—22no—
183C23×C11—21no—
184C23×C11—216no—
185C23×C11—22no—
186C23×C11—21no—
187C23×C11—21no—
188C23×C11—22no—
189C23×C11—21no—
190C23×C11—44no—
191C23×C11—44no—
192C23×C11—48no—
193C23×C11—44no—
194C23×C11C4×D414yes—
195C23×C11C2×M1612yes—
196C23×C11C2×M1614yes—
197C23×C11#13114yes—
198C23×C11C23×C411yescharacteristic
199D4×C11—44no—
200D4×C11—48no—
201C2×C4×C11—22no—
202C2×C4×C11—22no—
203C2×C4×C11—24no—
204C2×C4×C11—24no—
205C2×C4×C11—24no—
206C2×C4×C11—24no—
207C2×C4×C11—22no—
208C2×C4×C11—22no—
209C2×C4×C11—22no—
210C2×C4×C11—22no—
211C2×C4×C11—21no—
212C2×C4×C11—21no—
213C2×C4×C11—21no—
214C2×C4×C11—21no—
215C2×C4×C11—22no—
216C2×C4×C11—21no—
217C2×C4×C11—22no—
218C2×C4×C11—22no—
219C2×C4×C11—22no—
220C2×C4×C11—22no—
221C2×C4×C11—21no—
222C2×C4×C11—44no—
223C2×C4×C11—48no—
224C2×C4×C11—41no—
225C2×C4×C11—41no—
226C2×C4×C11—42no—
227C2×C4×C11—42no—
228C2×C4×C11—41no—
229C2×C4×C11—41no—
230C2×C4×C11C4×D414yes—
231C2×C4×C11C22×D412yes—
232C2×C4×C11C2×#4112yes—
233C2×C4×C11H(5,𝔽2)11yescharacteristic
234C2×C4×C11H(5,𝔽2)11yescharacteristic
235C8×C11—24no—
236C8×C11—24no—
237C8×C11—42no—
238C8×C11—42no—
239C24×C4C22×C1111yescharacteristic
240C22×M16C22×C1111yescharacteristic, complemented
241C23×C8C22×C1112yes—
242C23×C8C22×C1112yes—
243C2×#120C4×C1111yescharacteristic
244C2×C4×D4C22×C1112yes—
245C2×C4×D4C22×C1111yescharacteristic
246#435—28no—
247C2×C4⋊C8C22×C1112yescomplemented
248C2×C4⋊C8C22×C1111yescharacteristic, complemented
249C2×C22⋊C8—28no—
250C2×C22⋊C8C22×C1112yes—
251C2×C22⋊C8C22×C1112yes—
252C2×C22⋊C8C22×C1112yes—
253C2×C22⋊C8C22×C1112yes—
254C2×C22⋊C8C22×C1112yescomplemented
255C2×C22⋊C8C22×C1111yescharacteristic, complemented
256C2×#97C22×C1112yescomplemented
257C2×#97C22×C1111yescharacteristic, complemented
258#386C4×C1111yescharacteristic
259#386C4×C1112yes—
260#385C4×C1112yes—
261#385C4×C1111yescharacteristic
262#379C4×C1111yescharacteristic
263C4×C22⋊C4C22×C1112yes—
264C4×C22⋊C4C22×C1111yescharacteristic
265#336C22×C1112yescomplemented
266#336C22×C1112yescomplemented
267#336C22×C1112yescomplemented
268C22×C11—24no—
269C22×C11—24no—
270C22×C11—24no—
271C22×C11—24no—
272C22×C11—24no—
273C22×C11—24no—
274C22×C11—24no—
275C22×C11—22no—
276C22×C11—416no—
277C22×C11—41no—
278C22×C11—42no—
279C22×C11—41no—
280C22×C11—41no—
281C22×C11—42no—
282C22×C11—42no—
283C22×C11—41no—
284C22×C11—41no—
285C22×C11#43518yescomplemented
286C22×C11C2×C4×D412yes—
287C22×C11#51811yescharacteristic
288C22×C11C22×M1611yescharacteristic
289C22×C11C2×#13112yes—
290C22×C11#56811yescharacteristic
291C4×C11—24no—
292C4×C11—41no—
293C4×C11—41no—
294C4×C11—42no—
295C4×C11—42no—
296C4×C11—41no—
297C4×C11—41no—
298C4×C11D4211yescharacteristic
299C4×C11#54612yes—
300C4×C11#55111yescharacteristic
301C25C2×C4×C1111yescharacteristic
302C22×D4C2×C4×C1112yes—
303C22×D4C2×C4×C1111yescharacteristic
304C23×C4—24no—
305C23×C4—24no—
306C23×C4—41no—
307C23×C4—41no—
308C23×C4C2×C4×C1112yes—
309C23×C4C2×C4×C1111yescharacteristic
310C23×C4C23×C1111yescharacteristic
311C23×C4C23×C1111yescharacteristic
312C23×C4C23×C1112yes—
313C2×M16—24no—
314C2×M16—41no—
315C22×C8—24no—
316C22×C8—24no—
317C22×C8—24no—
318C22×C8—24no—
319C22×C8—42no—
320C22×C8—42no—
321C22×C8C23×C1112yes—
322C22×C8C23×C1112yes—
323C22×C8C23×C1112yes—
324C22×C8C23×C1112yes—
325#120—24no—
326C4×D4—24no—
327C4×D4—24no—
328C4×D4—41no—
329C4×D4—41no—
330C2×C4⋊C4C2×C4×C1112yes—
331C2×C4⋊C4C2×C4×C1111yescharacteristic
332C2×C22⋊C4C2×C4×C1112yes—
333C2×C22⋊C4C2×C4×C1112yes—
334C2×C22⋊C4C2×C4×C1111yescharacteristic
335C2×C22⋊C4C2×C4×C1112yes—
336C2×C22⋊C4C2×C4×C1112yes—
337C2×C22⋊C4C2×C4×C1111yescharacteristic
338C2×C22⋊C4C2×C4×C1111yescharacteristic
339C2×C22⋊C4C2×C4×C1111yescharacteristic
340C2×C42C23×C1112yes—
341C2×C42C23×C1111yescharacteristic
342C4⋊C8—24no—
343C4⋊C8—41no—
344C22⋊C8—24no—
345C22⋊C8—24no—
346C22⋊C8—24no—
347C22⋊C8—24no—
348C22⋊C8—41no—
349C22⋊C8D4×C1118yescomplemented
350#97—24no—
351#97—41no—
352#95C2×C4×C1112yes—
353#95C2×C4×C1112yes—
354#95C2×C4×C1112yes—
355C2×C11—28no—
356C2×C11—42no—
357C2×C11—81no—
358C2×C11#235811yescharacteristic
359C2×C11C2×#43512yes—
360C2×C11#293312yes—
361C2×C11#297311yescharacteristic
362C2×C11#297711yescharacteristic
363C24—24no—
364C24—24no—
365C24—41no—
366C24—41no—
367C24C11×M1614yescomplemented
368C24C22×C4×C1111yescharacteristic
369C24C22×C4×C1111yescharacteristic
370C24C22×C4×C1112yes—
371C2×D4—24no—
372C2×D4—22no—
373C2×D4—24no—
374C2×D4—24no—
375C2×D4—41no—
376C2×D4—41no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—24no—
382C22×C4—24no—
383C22×C4—24no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—21no—
389C22×C4—21no—
390C22×C4—21no—
391C22×C4—21no—
392C22×C4—41no—
393C22×C4—42no—
394C22×C4—44no—
395C22×C4—48no—
396C22×C4—44no—
397C22×C4C22×C4×C1112yes—
398C22×C4C22×C4×C1111yescharacteristic
399C22×C4C22×C4×C1112yes—
400C22×C4C22×C4×C1111yescharacteristic
401C22×C4C22×C4×C1111yescharacteristic
402C22×C4C22×C4×C1111yescharacteristic
403C22×C4C22×C4×C1112yes—
404C22×C4C2×D4×C1114yes—
405C22×C4C11×#4114yes—
406C22×C4C24×C1111yescharacteristic
407M16—44no—
408C2×C8—22no—
409C2×C8—22no—
410C2×C8—22no—
411C2×C8—22no—
412C2×C8—22no—
413C2×C8—22no—
414C2×C8—22no—
415C2×C8—22no—
416C2×C8—22no—
417C2×C8—22no—
418C2×C8—48no—
419C2×C8—48no—
420C2×C8C2×D4×C1114yes—
421C2×C8C2×D4×C1114yes—
422C4⋊C4—24no—
423C4⋊C4—41no—
424C22⋊C4—24no—
425C22⋊C4—22no—
426C22⋊C4—24no—
427C22⋊C4—24no—
428C22⋊C4—24no—
429C22⋊C4—41no—
430C22⋊C4—41no—
431C22⋊C4—41no—
432C42—22no—
433C42—22no—
434C42—21no—
435C42—21no—
436C11#2284411yescharacteristic, direct product factor, Sylow
437C23—22no—
438C23—22no—
439C23—22no—
440C23—22no—
441C23—22no—
442C23—21no—
443C23—22no—
444C23—21no—
445C23—216no—
446C23—22no—
447C23—21no—
448C23—21no—
449C23—22no—
450C23—21no—
451C23—44no—
452C23—44no—
453C23—48no—
454C23—44no—
455C23C4×D4×C1114yes—
456C23C2×C11×M1612yes—
457C23C2×C11×M1614yes—
458C23C11×#13114yes—
459C23C23×C4×C1111yescharacteristic
460D4—44no—
461D4—48no—
462C2×C4—22no—
463C2×C4—22no—
464C2×C4—24no—
465C2×C4—24no—
466C2×C4—24no—
467C2×C4—24no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—22no—
472C2×C4—21no—
473C2×C4—21no—
474C2×C4—21no—
475C2×C4—21no—
476C2×C4—22no—
477C2×C4—21no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—21no—
483C2×C4—44no—
484C2×C4—48no—
485C2×C4—41no—
486C2×C4—41no—
487C2×C4—42no—
488C2×C4—42no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4C4×D4×C1114yes—
492C2×C4C22×D4×C1112yes—
493C2×C4C2×C11×#4112yes—
494C2×C4C11×H(5,𝔽2)11yescharacteristic
495C2×C4C11×H(5,𝔽2)11yescharacteristic
496C8—24no—
497C8—24no—
498C8—42no—
499C8—42no—
500C22—24no—
501C22—24no—
502C22—24no—
503C22—24no—
504C22—24no—
505C22—24no—
506C22—24no—
507C22—22no—
508C22—416no—
509C22—42no—
510C22—41no—
511C22—41no—
512C22—42no—
513C22—42no—
514C22—41no—
515C22—41no—
516C22—41no—
517C22C11×#43518yescomplemented
518C22C2×C4×D4×C1112yes—
519C22C11×#51811yescharacteristic
520C22C22×C11×M1611yescharacteristic
521C22C2×C11×#13112yes—
522C22C11×#56811yescharacteristic
523C4—24no—
524C4—42no—
525C4—42no—
526C4—41no—
527C4—41no—
528C4—41no—
529C4—41no—
530C4D42×C1111yescharacteristic
531C4C11×#54612yes—
532C4C11×#55111yescharacteristic
533C2—28no—
534C2—42no—
535C2—81no—
536C2C11×#235811yescharacteristic
537C2C2×C11×#43512yes—
538C2C11×#293312yes—
539C2C11×#297311yescharacteristic
540C2C11×#297711yescharacteristic
subgroupG/H
centerC22×C4×C11C24
commutatorC23C23×C4×C11
Frattini, cosocleC22×C4C24×C11
socleC23×C11C23×C4
prime radicalC2×C11×#120C4
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#435C2semidirect
2. C22×C11×C22⋊C8C2semidirect
4. C11×#1955C2semidirect
5. C11×#1924C2semidirect
6. C11×#1870C2semidirect
7. C11×#1869C2semidirect
8. C11×#1850C2semidirect
9. C11×#1752C2semidirect
11. C22×C11×M16C22semidirect
18. C2×C11×C4⋊C8C22semidirect
19. C2×C11×C4⋊C8C22semidirect
25. C2×C11×C22⋊C8C22semidirect
26. C2×C11×C22⋊C8C22semidirect
27. C2×C11×#97C22semidirect
28. C2×C11×#97C22semidirect
36. C11×#336C22semidirect
37. C11×#336C22semidirect
38. C11×#336C22semidirect
87. C11×C22⋊C8D4semidirect
93. #22844C11direct (N × H)
98. C24×C11M16semidirect
167. C2×#435C2×C11semidirect
168. C22×C22⋊C8C2×C11semidirect
170. #1955C2×C11semidirect
171. #1924C2×C11semidirect
172. #1870C2×C11semidirect
173. #1869C2×C11semidirect
174. #1850C2×C11semidirect
175. #1752C2×C11semidirect
240. C22×M16C22×C11semidirect
247. C2×C4⋊C8C22×C11semidirect
248. C2×C4⋊C8C22×C11semidirect
254. C2×C22⋊C8C22×C11semidirect
255. C2×C22⋊C8C22×C11semidirect
256. C2×#97C22×C11semidirect
257. C2×#97C22×C11semidirect
265. #336C22×C11semidirect
266. #336C22×C11semidirect
267. #336C22×C11semidirect
285. C22×C11#435semidirect
349. C22⋊C8D4×C11semidirect
367. C24C11×M16semidirect
436. C11#22844direct (N × H)
517. C22C11×#435semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#4352
C22×C11×C22⋊C82
C4×C11×#1202
C11×#19552
C11×#19242
C11×#18702
C11×#18692
C11×#18502
C11×#17522
#2284411