Finite Group Databasebeta

← C2×C11×#1897 #14598171

Subgroups — C2×C11×#1897 #14598171

Order 2816.

1954 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#525C211yesmaximal, characteristic
2C22×C11×#117C211yesmaximal, characteristic, complemented
3C22×C11×#104C212yesmaximal, complemented
4C2×C11×#407C211yesmaximal, characteristic, complemented
5C11×#1897C218yesmaximal, direct product factor
6C2×C11×#339C212yesmaximal, complemented
7C22×C11×#41C2211yescharacteristic
8C24×C4×C11C2211yescharacteristic
9C22×C11×M16C2212yes—
10C11×#525—22no—
11C11×#525—22no—
12C11×#525C414yescomplemented
13C11×#525C2214yes—
14C2×C11×#123—21no—
15C2×C11×C22⋊Q8C412yescomplemented
16C2×C11×#121C412yescomplemented
17C2×C11×#120—21no—
18C2×C4×D4×C11—22no—
19C2×C11×#117—22no—
20C2×C11×#117—28no—
21C2×C11×#117C2211yescharacteristic
22C2×C11×#117C2214yescomplemented
23C22×C11×C4⋊C4—21no—
24C22×C11×C22⋊C4—21no—
25C22×C42×C11C2212yes—
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×C412yes—
38C2×C11×#41C2312yes—
39C22×Q8×C11C2×C411yescharacteristic
40C22×D4×C11—22no—
41C22×D4×C11—21no—
42C22×D4×C11C2×C411yescharacteristic
43C23×C4×C11—24no—
44C23×C4×C11—24no—
45C23×C4×C11—22no—
46C23×C4×C11—21no—
47C23×C4×C11C2×C412yes—
48C23×C4×C11C2×C412yes—
49C23×C4×C11D411yescharacteristic
50C23×C4×C11D412yes—
51C23×C4×C11D412yes—
52C23×C4×C11D412yes—
53C23×C4×C11C2312yes—
54C23×C4×C11C2311yescharacteristic
55C2×C11×M16—22no—
56C2×C11×M16—24no—
57C2×C11×M16—24no—
58C2×C11×M16C2314yes—
59C22×C8×C11—22no—
60C11×#123—24no—
61C11×#123—24no—
62C11×C22⋊Q8—24no—
63C11×C22⋊Q8C2×C418yescomplemented
64C11×#121—24no—
65C11×#121C2×C418yescomplemented
66C11×#120—24no—
67C11×#120—24no—
68C4×D4×C11—28no—
69C4×D4×C11—28no—
70C11×#117—216no—
71C11×#117—21no—
72C11×#117—21no—
73C11×#117—216no—
74C11×#117C2×C412yes—
75C11×#117C2312yes—
76C2×C11×C4⋊C4—28no—
77C2×C11×C4⋊C4—22no—
78C2×C11×C4⋊C4—24no—
79C2×C11×C4⋊C4C2×C412yes—
80C2×C11×C22⋊C4—28no—
81C2×C11×C22⋊C4—22no—
82C2×C11×C22⋊C4—24no—
83C2×C11×C22⋊C4—21no—
84C2×C11×C22⋊C4—22no—
85C2×C42×C11—22no—
86C2×C42×C11—24no—
87C2×C42×C11—21no—
88C2×C42×C11D418yescomplemented
89C2×C42×C11C2314yes—
90C11×#104—216no—
91C11×C22⋊C8—28no—
92C2×#1897C1111yesmaximal, characteristic, direct product factor, Sylow
93C24×C11—22no—
94C24×C11—22no—
95C24×C11—21no—
96C24×C11—44no—
97C24×C11C22⋊C412yes—
98C24×C11C22⋊C412yes—
99C24×C11C2×D411yescharacteristic
100C24×C11C2×D412yes—
101C11×#41—28no—
102C11×#41—24no—
103C11×#41—24no—
104C11×#41—42no—
105C11×#41—44no—
106C11×#41—42no—
107C2×Q8×C11—21no—
108C2×Q8×C11—24no—
109C2×Q8×C11C22×C412yes—
110C2×D4×C11—28no—
111C2×D4×C11—22no—
112C2×D4×C11—22no—
113C2×D4×C11—21no—
114C2×D4×C11—24no—
115C2×D4×C11—48no—
116C2×D4×C11—42no—
117C2×D4×C11—42no—
118C2×D4×C11C22×C412yes—
119C22×C4×C11—22no—
120C22×C4×C11—22no—
121C22×C4×C11—28no—
122C22×C4×C11—28no—
123C22×C4×C11—24no—
124C22×C4×C11—28no—
125C22×C4×C11—28no—
126C22×C4×C11—24no—
127C22×C4×C11—24no—
128C22×C4×C11—24no—
129C22×C4×C11—22no—
130C22×C4×C11—21no—
131C22×C4×C11—28no—
132C22×C4×C11—24no—
133C22×C4×C11—22no—
134C22×C4×C11—22no—
135C22×C4×C11—48no—
136C22×C4×C11—44no—
137C22×C4×C11C22⋊C412yes—
138C22×C4×C11C22⋊C414yes—
139C22×C4×C11C22⋊C414yes—
140C22×C4×C11C22⋊C412yes—
141C22×C4×C11C22×C414yes—
142C22×C4×C11C22×C411yescharacteristic
143C22×C4×C11C22×C411yescharacteristic
144C22×C4×C11C2×D412yes—
145C22×C4×C11C2×D414yes—
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D414yes—
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11#4114yes—
151C22×C4×C11C2411yescharacteristic
152C11×M16—24no—
153C11×M16—24no—
154C11×M16—44no—
155C2×C8×C11—24no—
156C2×C8×C11—44no—
157C11×C4⋊C4—216no—
158C11×C4⋊C4—28no—
159C11×C4⋊C4—22no—
160C11×C4⋊C4C22×C414yes—
161C11×C22⋊C4—216no—
162C11×C22⋊C4—22no—
163C11×C22⋊C4—28no—
164C11×C22⋊C4—22no—
165C11×C22⋊C4—28no—
166C42×C11—22no—
167C42×C11—28no—
168C42×C11—24no—
169C42×C11—22no—
170C42×C11C2×D418yescomplemented
171C2×#525C2×C1111yescharacteristic
172C22×#117C2×C1111yescharacteristic, complemented
173C22×#104C2×C1112yescomplemented
174C2×#407C2×C1111yescharacteristic, complemented
175#1897C2×C1118yesdirect product factor
176C2×#339C2×C1112yescomplemented
177C23×C11—24no—
178C23×C11—22no—
179C23×C11—22no—
180C23×C11—24no—
181C23×C11—24no—
182C23×C11—24no—
183C23×C11—24no—
184C23×C11—22no—
185C23×C11—44no—
186C23×C11—44no—
187C23×C11—48no—
188C23×C11—48no—
189C23×C11—42no—
190C23×C11—44no—
191C23×C11C2×C22⋊C414yes—
192C23×C11C2×C22⋊C411yescharacteristic
193C23×C11C2×C22⋊C411yescharacteristic
194C23×C11#12012yes—
195C23×C11#12312yes—
196C23×C11C22×D411yescharacteristic
197Q8×C11—24no—
198Q8×C11—42no—
199D4×C11—24no—
200D4×C11—416no—
201D4×C11—42no—
202D4×C11—42no—
203D4×C11—44no—
204D4×C11—42no—
205C2×C4×C11—22no—
206C2×C4×C11—22no—
207C2×C4×C11—24no—
208C2×C4×C11—24no—
209C2×C4×C11—28no—
210C2×C4×C11—28no—
211C2×C4×C11—28no—
212C2×C4×C11—28no—
213C2×C4×C11—24no—
214C2×C4×C11—22no—
215C2×C4×C11—28no—
216C2×C4×C11—48no—
217C2×C4×C11—416no—
218C2×C4×C11—42no—
219C2×C4×C11—44no—
220C2×C4×C11—44no—
221C2×C4×C11—44no—
222C2×C4×C11C2×C22⋊C414yes—
223C2×C4×C11C2×C22⋊C411yescharacteristic
224C2×C4×C11C2×C22⋊C411yescharacteristic
225C2×C4×C11C4×D414yes—
226C2×C4×C11C4×D414yes—
227C2×C4×C11#12012yes—
228C2×C4×C11#12114yes—
229C2×C4×C11#12114yes—
230C2×C4×C11#12312yes—
231C2×C4×C11C23×C411yescharacteristic
232C2×C4×C11C22×D412yes—
233C2×C4×C11C22×D411yescharacteristic
234C2×C4×C11C2×#4112yes—
235C8×C11—44no—
236C22×#41C22×C1111yescharacteristic
237C24×C4C22×C1111yescharacteristic
238C22×M16C22×C1112yes—
239#525—22no—
240#525—22no—
241#525C4×C1114yescomplemented
242#525C22×C1114yes—
243C2×#123—21no—
244C2×C22⋊Q8C4×C1112yescomplemented
245C2×#121C4×C1112yescomplemented
246C2×#120—21no—
247C2×C4×D4—22no—
248C2×#117—22no—
249C2×#117—28no—
250C2×#117C22×C1111yescharacteristic
251C2×#117C22×C1114yescomplemented
252C22×C4⋊C4—21no—
253C22×C22⋊C4—21no—
254C22×C42C22×C1112yes—
255C2×#104—28no—
256C2×#104C22×C1118yescomplemented
257#407—22no—
258#407C22×C1114yescomplemented
259C2×C22⋊C8—22no—
260#339C22×C1118yescomplemented
261C22×C11—22no—
262C22×C11—22no—
263C22×C11—24no—
264C22×C11—24no—
265C22×C11—24no—
266C22×C11—24no—
267C22×C11—24no—
268C22×C11—44no—
269C22×C11—44no—
270C22×C11—48no—
271C22×C11—48no—
272C22×C11—44no—
273C22×C11—42no—
274C22×C11—84no—
275C22×C11#38612yes—
276C22×C11#38612yes—
277C22×C11#42114yes—
278C22×C11C22×C22⋊C411yescharacteristic
279C22×C11C2×#12011yescharacteristic
280C22×C11C2×#12311yescharacteristic
281C4×C11—24no—
282C4×C11—48no—
283C4×C11—44no—
284C4×C11—42no—
285C4×C11#38612yes—
286C4×C11#38612yes—
287C4×C11C2×C4×D412yes—
288C4×C11C2×#12112yes—
289C25D4×C1111yescharacteristic
290C2×#41—21no—
291C2×#41—21no—
292C2×#41—24no—
293C2×#41—24no—
294C2×#41C2×C4×C1112yes—
295C2×#41C23×C1112yes—
296C22×Q8C2×C4×C1111yescharacteristic
297C22×D4—22no—
298C22×D4—21no—
299C22×D4C2×C4×C1111yescharacteristic
300C23×C4—24no—
301C23×C4—24no—
302C23×C4—22no—
303C23×C4—21no—
304C23×C4C2×C4×C1112yes—
305C23×C4C2×C4×C1112yes—
306C23×C4D4×C1111yescharacteristic
307C23×C4D4×C1112yes—
308C23×C4D4×C1112yes—
309C23×C4D4×C1112yes—
310C23×C4C23×C1112yes—
311C23×C4C23×C1111yescharacteristic
312C2×M16—22no—
313C2×M16—24no—
314C2×M16—24no—
315C2×M16C23×C1114yes—
316C22×C8—22no—
317#123—24no—
318#123—24no—
319C22⋊Q8—24no—
320C22⋊Q8C2×C4×C1118yescomplemented
321#121—24no—
322#121C2×C4×C1118yescomplemented
323#120—24no—
324#120—24no—
325C4×D4—28no—
326C4×D4—28no—
327#117—216no—
328#117—21no—
329#117—21no—
330#117—216no—
331#117C2×C4×C1112yes—
332#117C23×C1112yes—
333C2×C4⋊C4—28no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—24no—
336C2×C4⋊C4C2×C4×C1112yes—
337C2×C22⋊C4—28no—
338C2×C22⋊C4—22no—
339C2×C22⋊C4—24no—
340C2×C22⋊C4—21no—
341C2×C22⋊C4—22no—
342C2×C42—22no—
343C2×C42—24no—
344C2×C42—21no—
345C2×C42D4×C1118yescomplemented
346C2×C42C23×C1114yes—
347#104—216no—
348C22⋊C8—28no—
349C2×C11—21no—
350C2×C11—21no—
351C2×C11—22no—
352C2×C11—44no—
353C2×C11—82no—
354C2×C11#189714yesdirect product factor
355C2×C11C2×#38611yescharacteristic
356C2×C11C2×#42112yes—
357C24—22no—
358C24—22no—
359C24—21no—
360C24—44no—
361C24C11×C22⋊C412yes—
362C24C11×C22⋊C412yes—
363C24C2×D4×C1111yescharacteristic
364C24C2×D4×C1112yes—
365#41—28no—
366#41—24no—
367#41—24no—
368#41—42no—
369#41—44no—
370#41—42no—
371C2×Q8—21no—
372C2×Q8—24no—
373C2×Q8C22×C4×C1112yes—
374C2×D4—28no—
375C2×D4—22no—
376C2×D4—22no—
377C2×D4—21no—
378C2×D4—24no—
379C2×D4—48no—
380C2×D4—42no—
381C2×D4—42no—
382C2×D4C22×C4×C1112yes—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—28no—
386C22×C4—28no—
387C22×C4—24no—
388C22×C4—28no—
389C22×C4—28no—
390C22×C4—24no—
391C22×C4—24no—
392C22×C4—24no—
393C22×C4—22no—
394C22×C4—21no—
395C22×C4—28no—
396C22×C4—24no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—48no—
400C22×C4—44no—
401C22×C4C11×C22⋊C412yes—
402C22×C4C11×C22⋊C414yes—
403C22×C4C11×C22⋊C414yes—
404C22×C4C11×C22⋊C412yes—
405C22×C4C22×C4×C1114yes—
406C22×C4C22×C4×C1111yescharacteristic
407C22×C4C22×C4×C1111yescharacteristic
408C22×C4C2×D4×C1112yes—
409C22×C4C2×D4×C1114yes—
410C22×C4C2×D4×C1111yescharacteristic
411C22×C4C2×D4×C1111yescharacteristic
412C22×C4C2×D4×C1111yescharacteristic
413C22×C4C2×D4×C1114yes—
414C22×C4C11×#4114yes—
415C22×C4C24×C1111yescharacteristic
416M16—24no—
417M16—24no—
418M16—44no—
419C2×C8—24no—
420C2×C8—44no—
421C4⋊C4—216no—
422C4⋊C4—28no—
423C4⋊C4—22no—
424C4⋊C4C22×C4×C1114yes—
425C22⋊C4—216no—
426C22⋊C4—22no—
427C22⋊C4—28no—
428C22⋊C4—22no—
429C22⋊C4—28no—
430C42—22no—
431C42—28no—
432C42—24no—
433C42—22no—
434C42C2×D4×C1118yescomplemented
435C11C2×#189711yescharacteristic, direct product factor, Sylow
436C23—24no—
437C23—22no—
438C23—24no—
439C23—24no—
440C23—22no—
441C23—24no—
442C23—24no—
443C23—22no—
444C23—44no—
445C23—44no—
446C23—48no—
447C23—48no—
448C23—42no—
449C23—44no—
450C23C2×C11×C22⋊C414yes—
451C23C2×C11×C22⋊C411yescharacteristic
452C23C2×C11×C22⋊C411yescharacteristic
453C23C11×#12012yes—
454C23C11×#12312yes—
455C23C22×D4×C1111yescharacteristic
456Q8—24no—
457Q8—42no—
458D4—24no—
459D4—416no—
460D4—42no—
461D4—44no—
462D4—42no—
463D4—42no—
464C2×C4—22no—
465C2×C4—24no—
466C2×C4—24no—
467C2×C4—22no—
468C2×C4—28no—
469C2×C4—28no—
470C2×C4—28no—
471C2×C4—28no—
472C2×C4—24no—
473C2×C4—22no—
474C2×C4—28no—
475C2×C4—48no—
476C2×C4—416no—
477C2×C4—42no—
478C2×C4—44no—
479C2×C4—44no—
480C2×C4—44no—
481C2×C4C2×C11×C22⋊C414yes—
482C2×C4C2×C11×C22⋊C411yescharacteristic
483C2×C4C2×C11×C22⋊C411yescharacteristic
484C2×C4C4×D4×C1114yes—
485C2×C4C4×D4×C1114yes—
486C2×C4C11×#12012yes—
487C2×C4C11×#12114yes—
488C2×C4C11×#12114yes—
489C2×C4C11×#12312yes—
490C2×C4C23×C4×C1111yescharacteristic
491C2×C4C22×D4×C1112yes—
492C2×C4C22×D4×C1111yescharacteristic
493C2×C4C2×C11×#4112yes—
494C8—44no—
495C22—22no—
496C22—22no—
497C22—24no—
498C22—24no—
499C22—24no—
500C22—24no—
501C22—24no—
502C22—44no—
503C22—48no—
504C22—44no—
505C22—48no—
506C22—44no—
507C22—42no—
508C22—84no—
509C22C11×#38612yes—
510C22C11×#38612yes—
511C22C11×#42114yes—
512C22C22×C11×C22⋊C411yescharacteristic
513C22C2×C11×#12011yescharacteristic
514C22C2×C11×#12311yescharacteristic
515C4—24no—
516C4—48no—
517C4—44no—
518C4—42no—
519C4C11×#38612yes—
520C4C11×#38612yes—
521C4C2×C4×D4×C1112yes—
522C4C2×C11×#12112yes—
523C2—21no—
524C2—22no—
525C2—21no—
526C2—44no—
527C2—82no—
528C2C11×#189714yesdirect product factor
529C2C2×C11×#38611yescharacteristic
530C2C2×C11×#42112yes—
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. C22×C11×#117C2semidirect
3. C22×C11×#104C2semidirect
4. C2×C11×#407C2semidirect
5. C11×#1897C2direct (N × H)
6. C2×C11×#339C2semidirect
12. C11×#525C4semidirect
15. C2×C11×C22⋊Q8C4semidirect
16. C2×C11×#121C4semidirect
22. C2×C11×#117C22semidirect
27. C2×C11×#104C22semidirect
29. C11×#407C22semidirect
31. C11×#339C22semidirect
63. C11×C22⋊Q8C2×C4semidirect
65. C11×#121C2×C4semidirect
88. C2×C42×C11D4semidirect
92. C2×#1897C11direct (N × H)
170. C42×C11C2×D4semidirect
172. C22×#117C2×C11semidirect
173. C22×#104C2×C11semidirect
174. C2×#407C2×C11semidirect
175. #1897C2×C11direct (N × H)
176. C2×#339C2×C11semidirect
241. #525C4×C11semidirect
244. C2×C22⋊Q8C4×C11semidirect
245. C2×#121C4×C11semidirect
251. C2×#117C22×C11semidirect
256. C2×#104C22×C11semidirect
258. #407C22×C11semidirect
260. #339C22×C11semidirect
320. C22⋊Q8C2×C4×C11semidirect
322. #121C2×C4×C11semidirect
345. C2×C42D4×C11semidirect
354. C2×C11#1897direct (N × H)
434. C42C2×D4×C11semidirect
435. C11C2×#1897direct (N × H)
528. C2C11×#1897direct (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
C22×C11×#1172
C22×C11×#1042
C2×C11×#4072
C11×#18972
C2×C11×#3392
C2×#189711