Finite Group Databasebeta

← C2×C11×#1896 #14598170

Subgroups — C2×C11×#1896 #14598170

Order 2816.

2514 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#525C211yesmaximal, characteristic
2C23×C42×C11C211yesmaximal, characteristic, complemented
3C22×C11×#104C212yesmaximal, complemented
4C2×C11×#407C211yesmaximal, characteristic, complemented
5C11×#1896C218yesmaximal, direct product factor
6C2×C11×#339C212yesmaximal, complemented
7C22×C11×#41C2211yescharacteristic
8C24×C4×C11—21no—
9C24×C4×C11C2211yescharacteristic
10C22×C11×M16C2212yes—
11C11×#525—22no—
12C11×#525—22no—
13C11×#525C414yescomplemented
14C11×#525C2214yes—
15C2×C11×#123—21no—
16C2×C11×C22⋊Q8C412yescomplemented
17C2×C11×#121C412yescomplemented
18C2×C11×#120—21no—
19C2×C4×D4×C11—22no—
20C2×C11×#117C2211yescharacteristic
21C22×C42×C11—22no—
22C22×C42×C11—21no—
23C22×C42×C11—28no—
24C22×C42×C11C2212yes—
25C22×C42×C11C2214yescomplemented
26C2×C11×#104—28no—
27C2×C11×#104C2218yescomplemented
28C11×#407—22no—
29C11×#407C2214yescomplemented
30C2×C11×C22⋊C8—22no—
31C11×#339C2218yescomplemented
32C25×C11D411yescharacteristic
33C2×C11×#41—21no—
34C2×C11×#41—21no—
35C2×C11×#41—24no—
36C2×C11×#41—24no—
37C2×C11×#41C2×C412yescomplemented
38C2×C11×#41C2312yes—
39C22×Q8×C11C2×C411yescharacteristic, complemented
40C22×D4×C11—22no—
41C22×D4×C11—21no—
42C22×D4×C11C2×C411yescharacteristic, complemented
43C23×C4×C11—28no—
44C23×C4×C11—216no—
45C23×C4×C11—22no—
46C23×C4×C11—24no—
47C23×C4×C11—24no—
48C23×C4×C11—24no—
49C23×C4×C11—21no—
50C23×C4×C11C2×C412yes—
51C23×C4×C11C2×C412yes—
52C23×C4×C11D411yescharacteristic
53C23×C4×C11D412yes—
54C23×C4×C11D412yes—
55C23×C4×C11D412yes—
56C23×C4×C11C2312yes—
57C23×C4×C11C2311yescharacteristic
58C2×C11×M16—22no—
59C2×C11×M16—24no—
60C2×C11×M16—24no—
61C2×C11×M16C2314yes—
62C22×C8×C11—22no—
63C11×#123—24no—
64C11×#123—24no—
65C11×C22⋊Q8—24no—
66C11×C22⋊Q8C2×C418yescomplemented
67C11×#121—24no—
68C11×#121C2×C418yescomplemented
69C11×#120—24no—
70C11×#120—24no—
71C4×D4×C11—28no—
72C4×D4×C11—28no—
73C11×#117—21no—
74C11×#117—21no—
75C11×#117C2×C412yescomplemented
76C11×#117C2312yes—
77C2×C11×C4⋊C4—22no—
78C2×C11×C4⋊C4C2×C412yescomplemented
79C2×C11×C22⋊C4—22no—
80C2×C11×C22⋊C4—21no—
81C2×C11×C22⋊C4—22no—
82C2×C42×C11—28no—
83C2×C42×C11—216no—
84C2×C42×C11—22no—
85C2×C42×C11—24no—
86C2×C42×C11—24no—
87C2×C42×C11—21no—
88C2×C42×C11—216no—
89C2×C42×C11D418yescomplemented
90C2×C42×C11C2314yes—
91C11×#104—216no—
92C11×C22⋊C8—28no—
93C2×#1896C1111yesmaximal, characteristic, direct product factor, Sylow
94C24×C11—28no—
95C24×C11—22no—
96C24×C11—22no—
97C24×C11—21no—
98C24×C11C22⋊C412yes—
99C24×C11C22⋊C412yes—
100C24×C11C2×D412yes—
101C24×C11C2×D411yescharacteristic
102C11×#41—28no—
103C11×#41—24no—
104C11×#41—24no—
105C11×#41—42no—
106C11×#41—44no—
107C11×#41—42no—
108C2×Q8×C11—21no—
109C2×Q8×C11—24no—
110C2×Q8×C11C22×C412yescomplemented
111C2×D4×C11—28no—
112C2×D4×C11—22no—
113C2×D4×C11—22no—
114C2×D4×C11—21no—
115C2×D4×C11—24no—
116C2×D4×C11—48no—
117C2×D4×C11—42no—
118C2×D4×C11—42no—
119C2×D4×C11C22×C412yescomplemented
120C22×C4×C11—216no—
121C22×C4×C11—264no—
122C22×C4×C11—216no—
123C22×C4×C11—232no—
124C22×C4×C11—22no—
125C22×C4×C11—28no—
126C22×C4×C11—22no—
127C22×C4×C11—24no—
128C22×C4×C11—28no—
129C22×C4×C11—28no—
130C22×C4×C11—24no—
131C22×C4×C11—28no—
132C22×C4×C11—28no—
133C22×C4×C11—24no—
134C22×C4×C11—24no—
135C22×C4×C11—24no—
136C22×C4×C11—22no—
137C22×C4×C11—21no—
138C22×C4×C11—22no—
139C22×C4×C11—22no—
140C22×C4×C11—44no—
141C22×C4×C11C22⋊C412yes—
142C22×C4×C11C22⋊C414yes—
143C22×C4×C11C22⋊C414yes—
144C22×C4×C11C22⋊C412yes—
145C22×C4×C11C22×C414yes—
146C22×C4×C11C22×C411yescharacteristic
147C22×C4×C11C22×C411yescharacteristic
148C22×C4×C11C2×D412yes—
149C22×C4×C11C2×D414yes—
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D414yes—
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11#4114yes—
155C22×C4×C11C2411yescharacteristic
156C11×M16—24no—
157C11×M16—24no—
158C11×M16—44no—
159C2×C8×C11—24no—
160C2×C8×C11—44no—
161C11×C4⋊C4—28no—
162C11×C4⋊C4—22no—
163C11×C4⋊C4C22×C414yescomplemented
164C11×C22⋊C4—22no—
165C11×C22⋊C4—28no—
166C11×C22⋊C4—22no—
167C11×C22⋊C4—28no—
168C42×C11—216no—
169C42×C11—22no—
170C42×C11—28no—
171C42×C11—24no—
172C42×C11—22no—
173C42×C11C2×D418yescomplemented
174C2×#525C2×C1111yescharacteristic
175C23×C42C2×C1111yescharacteristic, complemented
176C22×#104C2×C1112yescomplemented
177C2×#407C2×C1111yescharacteristic, complemented
178#1896C2×C1118yesdirect product factor
179C2×#339C2×C1112yescomplemented
180C23×C11—216no—
181C23×C11—216no—
182C23×C11—22no—
183C23×C11—22no—
184C23×C11—24no—
185C23×C11—24no—
186C23×C11—24no—
187C23×C11—24no—
188C23×C11—28no—
189C23×C11—28no—
190C23×C11—22no—
191C23×C11—42no—
192C23×C11—44no—
193C23×C11#10418yescomplemented
194C23×C11C2×C22⋊C411yescharacteristic
195C23×C11C2×C22⋊C414yes—
196C23×C11C2×C22⋊C411yescharacteristic
197C23×C11#12012yes—
198C23×C11#12312yes—
199C23×C11C22×D411yescharacteristic
200Q8×C11—24no—
201Q8×C11—42no—
202D4×C11—24no—
203D4×C11—42no—
204D4×C11—42no—
205D4×C11—44no—
206D4×C11—416no—
207D4×C11—42no—
208C2×C4×C11—264no—
209C2×C4×C11—216no—
210C2×C4×C11—232no—
211C2×C4×C11—22no—
212C2×C4×C11—28no—
213C2×C4×C11—22no—
214C2×C4×C11—24no—
215C2×C4×C11—24no—
216C2×C4×C11—28no—
217C2×C4×C11—28no—
218C2×C4×C11—28no—
219C2×C4×C11—28no—
220C2×C4×C11—24no—
221C2×C4×C11—22no—
222C2×C4×C11—42no—
223C2×C4×C11—44no—
224C2×C4×C11—44no—
225C2×C4×C11—44no—
226C2×C4×C11C2×C22⋊C414yes—
227C2×C4×C11C2×C22⋊C411yescharacteristic
228C2×C4×C11C2×C22⋊C411yescharacteristic
229C2×C4×C11C4×D414yes—
230C2×C4×C11C4×D414yes—
231C2×C4×C11#12012yes—
232C2×C4×C11#12114yes—
233C2×C4×C11#12114yes—
234C2×C4×C11#12312yes—
235C2×C4×C11C23×C411yescharacteristic
236C2×C4×C11C22×D412yes—
237C2×C4×C11C22×D411yescharacteristic
238C2×C4×C11C2×#4112yes—
239C8×C11—44no—
240C22×#41C22×C1111yescharacteristic
241C24×C4—21no—
242C24×C4C22×C1111yescharacteristic
243C22×M16C22×C1112yes—
244#525—22no—
245#525—22no—
246#525C4×C1114yescomplemented
247#525C22×C1114yes—
248C2×#123—21no—
249C2×C22⋊Q8C4×C1112yescomplemented
250C2×#121C4×C1112yescomplemented
251C2×#120—21no—
252C2×C4×D4—22no—
253C2×#117C22×C1111yescharacteristic
254C22×C42—22no—
255C22×C42—21no—
256C22×C42—28no—
257C22×C42C22×C1112yes—
258C22×C42C22×C1114yescomplemented
259C2×#104—28no—
260C2×#104C22×C1118yescomplemented
261#407—22no—
262#407C22×C1114yescomplemented
263C2×C22⋊C8—22no—
264#339C22×C1118yescomplemented
265C22×C11—28no—
266C22×C11—28no—
267C22×C11—216no—
268C22×C11—22no—
269C22×C11—22no—
270C22×C11—24no—
271C22×C11—24no—
272C22×C11—216no—
273C22×C11—24no—
274C22×C11—24no—
275C22×C11—44no—
276C22×C11—42no—
277C22×C11—84no—
278C22×C11#38612yes—
279C22×C11#38612yes—
280C22×C11C2×#10414yes—
281C22×C11C2×#10418yescomplemented
282C22×C11C22×C22⋊C411yescharacteristic
283C22×C11C2×#12011yescharacteristic
284C22×C11C2×#12311yescharacteristic
285C4×C11—216no—
286C4×C11—24no—
287C4×C11—44no—
288C4×C11—42no—
289C4×C11#38612yes—
290C4×C11#38612yes—
291C4×C11C2×C4×D412yes—
292C4×C11C2×#12112yes—
293C25D4×C1111yescharacteristic
294C2×#41—21no—
295C2×#41—21no—
296C2×#41—24no—
297C2×#41—24no—
298C2×#41C2×C4×C1112yescomplemented
299C2×#41C23×C1112yes—
300C22×Q8C2×C4×C1111yescharacteristic, complemented
301C22×D4—22no—
302C22×D4—21no—
303C22×D4C2×C4×C1111yescharacteristic, complemented
304C23×C4—216no—
305C23×C4—28no—
306C23×C4—22no—
307C23×C4—24no—
308C23×C4—24no—
309C23×C4—24no—
310C23×C4—21no—
311C23×C4C2×C4×C1112yes—
312C23×C4C2×C4×C1112yes—
313C23×C4D4×C1111yescharacteristic
314C23×C4D4×C1112yes—
315C23×C4D4×C1112yes—
316C23×C4D4×C1112yes—
317C23×C4C23×C1112yes—
318C23×C4C23×C1111yescharacteristic
319C2×M16—22no—
320C2×M16—24no—
321C2×M16—24no—
322C2×M16C23×C1114yes—
323C22×C8—22no—
324#123—24no—
325#123—24no—
326C22⋊Q8—24no—
327C22⋊Q8C2×C4×C1118yescomplemented
328#121—24no—
329#121C2×C4×C1118yescomplemented
330#120—24no—
331#120—24no—
332C4×D4—28no—
333C4×D4—28no—
334#117—21no—
335#117—21no—
336#117C2×C4×C1112yescomplemented
337#117C23×C1112yes—
338C2×C4⋊C4—22no—
339C2×C4⋊C4C2×C4×C1112yescomplemented
340C2×C22⋊C4—22no—
341C2×C22⋊C4—21no—
342C2×C22⋊C4—22no—
343C2×C42—28no—
344C2×C42—216no—
345C2×C42—21no—
346C2×C42—22no—
347C2×C42—24no—
348C2×C42—24no—
349C2×C42—216no—
350C2×C42D4×C1118yescomplemented
351C2×C42C23×C1114yes—
352#104—216no—
353C22⋊C8—28no—
354C2×C11—21no—
355C2×C11—21no—
356C2×C11—22no—
357C2×C11—28no—
358C2×C11—82no—
359C2×C11#189614yesdirect product factor
360C2×C11C2×#38611yescharacteristic
361C2×C11C22×#10412yes—
362C24—28no—
363C24—22no—
364C24—22no—
365C24—21no—
366C24C11×C22⋊C412yes—
367C24C11×C22⋊C412yes—
368C24C2×D4×C1112yes—
369C24C2×D4×C1111yescharacteristic
370#41—28no—
371#41—24no—
372#41—24no—
373#41—42no—
374#41—44no—
375#41—42no—
376C2×Q8—21no—
377C2×Q8—24no—
378C2×Q8C22×C4×C1112yescomplemented
379C2×D4—28no—
380C2×D4—22no—
381C2×D4—22no—
382C2×D4—21no—
383C2×D4—24no—
384C2×D4—48no—
385C2×D4—42no—
386C2×D4—42no—
387C2×D4C22×C4×C1112yescomplemented
388C22×C4—216no—
389C22×C4—264no—
390C22×C4—216no—
391C22×C4—232no—
392C22×C4—22no—
393C22×C4—28no—
394C22×C4—22no—
395C22×C4—24no—
396C22×C4—28no—
397C22×C4—28no—
398C22×C4—24no—
399C22×C4—28no—
400C22×C4—28no—
401C22×C4—24no—
402C22×C4—24no—
403C22×C4—24no—
404C22×C4—22no—
405C22×C4—21no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—44no—
409C22×C4C11×C22⋊C412yes—
410C22×C4C11×C22⋊C414yes—
411C22×C4C11×C22⋊C414yes—
412C22×C4C11×C22⋊C412yes—
413C22×C4C22×C4×C1114yes—
414C22×C4C22×C4×C1111yescharacteristic
415C22×C4C22×C4×C1111yescharacteristic
416C22×C4C2×D4×C1112yes—
417C22×C4C2×D4×C1114yes—
418C22×C4C2×D4×C1111yescharacteristic
419C22×C4C2×D4×C1111yescharacteristic
420C22×C4C2×D4×C1111yescharacteristic
421C22×C4C2×D4×C1114yes—
422C22×C4C11×#4114yes—
423C22×C4C24×C1111yescharacteristic
424M16—24no—
425M16—24no—
426M16—44no—
427C2×C8—24no—
428C2×C8—44no—
429C4⋊C4—28no—
430C4⋊C4—22no—
431C4⋊C4C22×C4×C1114yescomplemented
432C22⋊C4—22no—
433C22⋊C4—28no—
434C22⋊C4—22no—
435C22⋊C4—28no—
436C42—216no—
437C42—22no—
438C42—28no—
439C42—24no—
440C42—22no—
441C42C2×D4×C1118yescomplemented
442C11C2×#189611yescharacteristic, direct product factor, Sylow
443C23—216no—
444C23—216no—
445C23—22no—
446C23—24no—
447C23—24no—
448C23—22no—
449C23—24no—
450C23—24no—
451C23—28no—
452C23—28no—
453C23—22no—
454C23—42no—
455C23—44no—
456C23C11×#10418yescomplemented
457C23C2×C11×C22⋊C411yescharacteristic
458C23C2×C11×C22⋊C414yes—
459C23C2×C11×C22⋊C411yescharacteristic
460C23C11×#12012yes—
461C23C11×#12312yes—
462C23C22×D4×C1111yescharacteristic
463Q8—24no—
464Q8—42no—
465D4—24no—
466D4—42no—
467D4—44no—
468D4—42no—
469D4—416no—
470D4—42no—
471C2×C4—264no—
472C2×C4—216no—
473C2×C4—232no—
474C2×C4—22no—
475C2×C4—28no—
476C2×C4—24no—
477C2×C4—24no—
478C2×C4—22no—
479C2×C4—28no—
480C2×C4—28no—
481C2×C4—28no—
482C2×C4—28no—
483C2×C4—24no—
484C2×C4—22no—
485C2×C4—42no—
486C2×C4—44no—
487C2×C4—44no—
488C2×C4—44no—
489C2×C4C2×C11×C22⋊C414yes—
490C2×C4C2×C11×C22⋊C411yescharacteristic
491C2×C4C2×C11×C22⋊C411yescharacteristic
492C2×C4C4×D4×C1114yes—
493C2×C4C4×D4×C1114yes—
494C2×C4C11×#12012yes—
495C2×C4C11×#12114yes—
496C2×C4C11×#12114yes—
497C2×C4C11×#12312yes—
498C2×C4C23×C4×C1111yescharacteristic
499C2×C4C22×D4×C1112yes—
500C2×C4C22×D4×C1111yescharacteristic
501C2×C4C2×C11×#4112yes—
502C8—44no—
503C22—28no—
504C22—216no—
505C22—28no—
506C22—22no—
507C22—22no—
508C22—24no—
509C22—24no—
510C22—216no—
511C22—24no—
512C22—24no—
513C22—44no—
514C22—42no—
515C22—84no—
516C22C11×#38612yes—
517C22C11×#38612yes—
518C22C2×C11×#10414yes—
519C22C2×C11×#10418yescomplemented
520C22C22×C11×C22⋊C411yescharacteristic
521C22C2×C11×#12011yescharacteristic
522C22C2×C11×#12311yescharacteristic
523C4—216no—
524C4—24no—
525C4—44no—
526C4—42no—
527C4C11×#38612yes—
528C4C11×#38612yes—
529C4C2×C4×D4×C1112yes—
530C4C2×C11×#12112yes—
531C2—21no—
532C2—22no—
533C2—21no—
534C2—28no—
535C2—82no—
536C2C11×#189614yesdirect product factor
537C2C2×C11×#38611yescharacteristic
538C2C22×C11×#10412yes—
subgroupG/H
centerC22×C4×C11C2×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
socleC23×C11C2×C22⋊C4
prime radicalC2×C11×#525C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4×C11 ◁ C24×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C23×C42×C11C2semidirect
3. C22×C11×#104C2semidirect
4. C2×C11×#407C2semidirect
5. C11×#1896C2direct (N × H)
6. C2×C11×#339C2semidirect
13. C11×#525C4semidirect
16. C2×C11×C22⋊Q8C4semidirect
17. C2×C11×#121C4semidirect
25. C22×C42×C11C22semidirect
27. C2×C11×#104C22semidirect
29. C11×#407C22semidirect
31. C11×#339C22semidirect
37. C2×C11×#41C2×C4semidirect
39. C22×Q8×C11C2×C4semidirect
42. C22×D4×C11C2×C4semidirect
66. C11×C22⋊Q8C2×C4semidirect
68. C11×#121C2×C4semidirect
75. C11×#117C2×C4semidirect
78. C2×C11×C4⋊C4C2×C4semidirect
89. C2×C42×C11D4semidirect
93. C2×#1896C11direct (N × H)
110. C2×Q8×C11C22×C4semidirect
119. C2×D4×C11C22×C4semidirect
163. C11×C4⋊C4C22×C4semidirect
173. C42×C11C2×D4semidirect
175. C23×C42C2×C11semidirect
176. C22×#104C2×C11semidirect
177. C2×#407C2×C11semidirect
178. #1896C2×C11direct (N × H)
179. C2×#339C2×C11semidirect
193. C23×C11#104semidirect
246. #525C4×C11semidirect
249. C2×C22⋊Q8C4×C11semidirect
250. C2×#121C4×C11semidirect
258. C22×C42C22×C11semidirect
260. C2×#104C22×C11semidirect
262. #407C22×C11semidirect
264. #339C22×C11semidirect
281. C22×C11C2×#104semidirect
298. C2×#41C2×C4×C11semidirect
300. C22×Q8C2×C4×C11semidirect
303. C22×D4C2×C4×C11semidirect
327. C22⋊Q8C2×C4×C11semidirect
329. #121C2×C4×C11semidirect
336. #117C2×C4×C11semidirect
339. C2×C4⋊C4C2×C4×C11semidirect
350. C2×C42D4×C11semidirect
359. C2×C11#1896direct (N × H)
378. C2×Q8C22×C4×C11semidirect
387. C2×D4C22×C4×C11semidirect
431. C4⋊C4C22×C4×C11semidirect
441. C42C2×D4×C11semidirect
442. C11C2×#1896direct (N × H)
456. C23C11×#104semidirect
519. C22C2×C11×#104semidirect
536. C2C11×#1896direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5252
C23×C42×C112
C22×C11×#1042
C2×C11×#4072
C11×#18962
C2×C11×#3392
C2×#189611