Finite Group Databasebeta

← C11×#14287 #14591480

Subgroups — C11×#14287 #14591480

Order 2816.

1978 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×#123C211yesmaximal, characteristic
2C2×C11×#380C211yesmaximal, characteristic, complemented
3C2×C4×C11×C22⋊C4C211yesmaximal, characteristic, complemented
4C11×#1441C212yesmaximal, complemented
5C11×#1440C212yesmaximal, complemented
6C11×#1439C212yesmaximal, complemented
7C11×#1438C212yesmaximal
8C11×#1437C212yesmaximal, complemented
9C11×#1436C212yesmaximal, complemented
10C23×D4×C11C2211yescharacteristic
11C24×C4×C11C2211yescharacteristic
12C2×C11×#123—24no—
13C2×C11×#123—24no—
14C2×C11×#123C418yescomplemented
15C22×C11×C4⋊C4C2211yescharacteristic
16C22×C11×C4⋊C4C2211yescharacteristic
17C22×C11×C4⋊C4C2212yes—
18C22×C11×C22⋊C4C2212yes—
19C22×C11×C22⋊C4C2211yescharacteristic
20C22×C11×C22⋊C4C2211yescharacteristic
21C22×C11×C22⋊C4C2211yescharacteristic
22C22×C11×C22⋊C4C2214yes—
23C22×C11×C22⋊C4C2212yes—
24C22×C42×C11C2212yes—
25C11×#380—24no—
26C4×C11×C22⋊C4—24no—
27C2×C11×#95C2212yes—
28C2×C11×#95C2214yes—
29C2×C11×#95C2212yes—
30C2×C11×#95C2214yes—
31C2×C11×#95C2214yes—
32C25×C11C2311yescharacteristic
33C25×C11C2311yescharacteristic
34C22×D4×C11—22no—
35C22×D4×C11—22no—
36C22×D4×C11—44no—
37C22×D4×C11C2×C414yes—
38C23×C4×C11—44no—
39C23×C4×C11C2×C414yes—
40C23×C4×C11D414yes—
41C23×C4×C11D414yes—
42C23×C4×C11C2314yes—
43C23×C4×C11C2311yescharacteristic
44C23×C4×C11C2311yescharacteristic
45C23×C4×C11C2311yescharacteristic
46C23×C4×C11C2314yes—
47C23×C4×C11C2311yescharacteristic
48C23×C4×C11C2311yescharacteristic
49C11×#123—232no—
50C2×C11×C4⋊C4—22no—
51C2×C11×C4⋊C4—22no—
52C2×C11×C4⋊C4—22no—
53C2×C11×C4⋊C4—22no—
54C2×C11×C4⋊C4—24no—
55C2×C11×C4⋊C4—44no—
56C2×C11×C4⋊C4C2×C414yes—
57C2×C11×C4⋊C4C2×C414yes—
58C2×C11×C22⋊C4—24no—
59C2×C11×C22⋊C4—22no—
60C2×C11×C22⋊C4—22no—
61C2×C11×C22⋊C4—22no—
62C2×C11×C22⋊C4—22no—
63C2×C11×C22⋊C4—22no—
64C2×C11×C22⋊C4—22no—
65C2×C11×C22⋊C4—28no—
66C2×C11×C22⋊C4—24no—
67C2×C11×C22⋊C4—28no—
68C2×C11×C22⋊C4—44no—
69C2×C11×C22⋊C4—44no—
70C2×C11×C22⋊C4—44no—
71C2×C11×C22⋊C4C2×C414yes—
72C2×C11×C22⋊C4C2×C414yes—
73C2×C11×C22⋊C4C2×C414yes—
74C2×C42×C11—24no—
75C2×C42×C11—44no—
76C11×#95—24no—
77C11×#95—24no—
78C11×#95—28no—
79C11×#95—44no—
80C11×#95—44no—
81#14287C1111yesmaximal, characteristic, direct product factor, Sylow
82C24×C11—24no—
83C24×C11—22no—
84C24×C11—24no—
85C24×C11—22no—
86C24×C11—21no—
87C24×C11—21no—
88C24×C11—24no—
89C24×C11—22no—
90C24×C11—24no—
91C24×C11—22no—
92C24×C11C22×C412yes—
93C24×C11C22×C412yes—
94C24×C11C2×D412yes—
95C24×C11C2×D412yes—
96C24×C11C2411yescharacteristic
97C2×D4×C11—28no—
98C2×D4×C11—48no—
99C2×D4×C11—48no—
100C2×D4×C11—48no—
101C22×C4×C11—24no—
102C22×C4×C11—24no—
103C22×C4×C11—24no—
104C22×C4×C11—21no—
105C22×C4×C11—21no—
106C22×C4×C11—21no—
107C22×C4×C11—21no—
108C22×C4×C11—21no—
109C22×C4×C11—21no—
110C22×C4×C11—24no—
111C22×C4×C11—24no—
112C22×C4×C11—22no—
113C22×C4×C11—24no—
114C22×C4×C11—24no—
115C22×C4×C11—24no—
116C22×C4×C11—24no—
117C22×C4×C11—22no—
118C22×C4×C11—24no—
119C22×C4×C11—24no—
120C22×C4×C11—24no—
121C22×C4×C11—24no—
122C22×C4×C11—24no—
123C22×C4×C11—24no—
124C22×C4×C11—24no—
125C22×C4×C11—24no—
126C22×C4×C11—48no—
127C22×C4×C11—48no—
128C22×C4×C11—48no—
129C22×C4×C11C22⋊C4116yescomplemented
130C22×C4×C11C22×C412yes—
131C22×C4×C11C22×C412yes—
132C22×C4×C11C22×C412yes—
133C22×C4×C11C22×C412yes—
134C22×C4×C11C22×C412yes—
135C22×C4×C11C2×D412yes—
136C22×C4×C11C2×D412yes—
137C22×C4×C11C2×D412yes—
138C22×C4×C11C2×D412yes—
139C22×C4×C11#4118yes—
140C11×C4⋊C4—28no—
141C11×C4⋊C4—28no—
142C11×C4⋊C4—48no—
143C11×C22⋊C4—216no—
144C11×C22⋊C4—28no—
145C11×C22⋊C4—28no—
146C11×C22⋊C4—28no—
147C11×C22⋊C4—416no—
148C11×C22⋊C4—48no—
149C42×C11—48no—
150C22×#123C2×C1111yescharacteristic
151C2×#380C2×C1111yescharacteristic, complemented
152C2×C4×C22⋊C4C2×C1111yescharacteristic, complemented
153#1441C2×C1112yescomplemented
154#1440C2×C1112yescomplemented
155#1439C2×C1112yescomplemented
156#1438C2×C1112yes—
157#1437C2×C1112yescomplemented
158#1436C2×C1112yescomplemented
159C23×C11—24no—
160C23×C11—24no—
161C23×C11—24no—
162C23×C11—24no—
163C23×C11—24no—
164C23×C11—24no—
165C23×C11—24no—
166C23×C11—22no—
167C23×C11—22no—
168C23×C11—24no—
169C23×C11—22no—
170C23×C11—24no—
171C23×C11—24no—
172C23×C11—24no—
173C23×C11—44no—
174C23×C11—44no—
175C23×C11—44no—
176C23×C11—44no—
177C23×C11—42no—
178C23×C11—42no—
179C23×C11—42no—
180C23×C11—42no—
181C23×C11—41no—
182C23×C11—41no—
183C23×C11—42no—
184C23×C11—44no—
185C23×C11—44no—
186C23×C11—44no—
187C23×C11—44no—
188C23×C11C2×C22⋊C414yes—
189C23×C11C23×C411yescharacteristic
190C23×C11C22×D411yescharacteristic
191C23×C11C22×D411yescharacteristic
192C23×C11C2×#4114yes—
193C23×C11H(5,𝔽2)14yes—
194C23×C11H(5,𝔽2)12yes—
195C23×C112−1+412yes—
196D4×C11—416no—
197C2×C4×C11—24no—
198C2×C4×C11—24no—
199C2×C4×C11—24no—
200C2×C4×C11—24no—
201C2×C4×C11—24no—
202C2×C4×C11—24no—
203C2×C4×C11—22no—
204C2×C4×C11—22no—
205C2×C4×C11—22no—
206C2×C4×C11—24no—
207C2×C4×C11—24no—
208C2×C4×C11—24no—
209C2×C4×C11—28no—
210C2×C4×C11—28no—
211C2×C4×C11—28no—
212C2×C4×C11—416no—
213C2×C4×C11—42no—
214C2×C4×C11—42no—
215C2×C4×C11—44no—
216C2×C4×C11—42no—
217C2×C4×C11—42no—
218C2×C4×C11—41no—
219C2×C4×C11—41no—
220C2×C4×C11—42no—
221C2×C4×C11—44no—
222C2×C4×C11—44no—
223C2×C4×C11—44no—
224C2×C4×C11—44no—
225C2×C4×C11—44no—
226C2×C4×C11—44no—
227C2×C4×C11—44no—
228C2×C4×C11—44no—
229C2×C4×C11—44no—
230C2×C4×C11—44no—
231C2×C4×C11C2×C22⋊C414yes—
232C2×C4×C11C2×C22⋊C414yes—
233C23×D4C22×C1111yescharacteristic
234C24×C4C22×C1111yescharacteristic
235C2×#123—24no—
236C2×#123—24no—
237C2×#123C4×C1118yescomplemented
238C22×C4⋊C4C22×C1111yescharacteristic
239C22×C4⋊C4C22×C1111yescharacteristic
240C22×C4⋊C4C22×C1112yes—
241C22×C22⋊C4C22×C1112yes—
242C22×C22⋊C4C22×C1111yescharacteristic
243C22×C22⋊C4C22×C1111yescharacteristic
244C22×C22⋊C4C22×C1111yescharacteristic
245C22×C22⋊C4C22×C1114yes—
246C22×C22⋊C4C22×C1112yes—
247C22×C42C22×C1112yes—
248#380—24no—
249C4×C22⋊C4—24no—
250C2×#95C22×C1112yes—
251C2×#95C22×C1114yes—
252C2×#95C22×C1112yes—
253C2×#95C22×C1114yes—
254C2×#95C22×C1114yes—
255C22×C11—24no—
256C22×C11—24no—
257C22×C11—24no—
258C22×C11—48no—
259C22×C11—48no—
260C22×C11—44no—
261C22×C11—44no—
262C22×C11—42no—
263C22×C11—42no—
264C22×C11—48no—
265C22×C11—42no—
266C22×C11—84no—
267C22×C11—82no—
268C22×C11—82no—
269C22×C11C22×C22⋊C411yescharacteristic
270C22×C11C4×#4112yes—
271C22×C11#51812yes—
272C22×C11#52012yes—
273C22×C11#52512yes—
274C22×C11#53212yes—
275C22×C11#53412yes—
276C22×C11#53412yes—
277C22×C11#53511yescharacteristic
278C22×C11#53611yescharacteristic
279C22×C11#53712yes—
280C22×C11#53814yes—
281C22×C11#53914yes—
282C22×C11#54014yes—
283C22×C11#54214yes—
284C4×C11—24no—
285C4×C11—24no—
286C4×C11—42no—
287C4×C11—42no—
288C4×C11—48no—
289C4×C11—42no—
290C4×C11—84no—
291C25C23×C1111yescharacteristic
292C25C23×C1111yescharacteristic
293C22×D4—22no—
294C22×D4—22no—
295C22×D4—44no—
296C22×D4C2×C4×C1114yes—
297C23×C4—44no—
298C23×C4C2×C4×C1114yes—
299C23×C4D4×C1114yes—
300C23×C4D4×C1114yes—
301C23×C4C23×C1114yes—
302C23×C4C23×C1111yescharacteristic
303C23×C4C23×C1111yescharacteristic
304C23×C4C23×C1111yescharacteristic
305C23×C4C23×C1114yes—
306C23×C4C23×C1111yescharacteristic
307C23×C4C23×C1111yescharacteristic
308#123—232no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—22no—
311C2×C4⋊C4—22no—
312C2×C4⋊C4—22no—
313C2×C4⋊C4—24no—
314C2×C4⋊C4—44no—
315C2×C4⋊C4C2×C4×C1114yes—
316C2×C4⋊C4C2×C4×C1114yes—
317C2×C22⋊C4—22no—
318C2×C22⋊C4—22no—
319C2×C22⋊C4—24no—
320C2×C22⋊C4—22no—
321C2×C22⋊C4—22no—
322C2×C22⋊C4—22no—
323C2×C22⋊C4—22no—
324C2×C22⋊C4—28no—
325C2×C22⋊C4—24no—
326C2×C22⋊C4—28no—
327C2×C22⋊C4—44no—
328C2×C22⋊C4—44no—
329C2×C22⋊C4—44no—
330C2×C22⋊C4C2×C4×C1114yes—
331C2×C22⋊C4C2×C4×C1114yes—
332C2×C22⋊C4C2×C4×C1114yes—
333C2×C42—24no—
334C2×C42—44no—
335#95—24no—
336#95—24no—
337#95—28no—
338#95—44no—
339#95—44no—
340C2×C11—44no—
341C2×C11—82no—
342C2×C11#229711yescharacteristic
343C2×C11#230811yescharacteristic
344C2×C11#231111yescharacteristic
345C2×C11#233514yes—
346C2×C11#263014yes—
347C2×C11#266112yes—
348C2×C11#266312yes—
349C24—24no—
350C24—22no—
351C24—24no—
352C24—22no—
353C24—21no—
354C24—21no—
355C24—24no—
356C24—22no—
357C24—24no—
358C24—22no—
359C24C22×C4×C1112yes—
360C24C22×C4×C1112yes—
361C24C2×D4×C1112yes—
362C24C2×D4×C1112yes—
363C24C24×C1111yescharacteristic
364C2×D4—28no—
365C2×D4—48no—
366C2×D4—48no—
367C2×D4—48no—
368C22×C4—24no—
369C22×C4—24no—
370C22×C4—24no—
371C22×C4—21no—
372C22×C4—21no—
373C22×C4—21no—
374C22×C4—21no—
375C22×C4—21no—
376C22×C4—21no—
377C22×C4—24no—
378C22×C4—24no—
379C22×C4—22no—
380C22×C4—24no—
381C22×C4—24no—
382C22×C4—24no—
383C22×C4—24no—
384C22×C4—22no—
385C22×C4—24no—
386C22×C4—24no—
387C22×C4—24no—
388C22×C4—24no—
389C22×C4—24no—
390C22×C4—24no—
391C22×C4—24no—
392C22×C4—24no—
393C22×C4—48no—
394C22×C4—48no—
395C22×C4—48no—
396C22×C4C11×C22⋊C4116yescomplemented
397C22×C4C22×C4×C1112yes—
398C22×C4C22×C4×C1112yes—
399C22×C4C22×C4×C1112yes—
400C22×C4C22×C4×C1112yes—
401C22×C4C22×C4×C1112yes—
402C22×C4C2×D4×C1112yes—
403C22×C4C2×D4×C1112yes—
404C22×C4C2×D4×C1112yes—
405C22×C4C2×D4×C1112yes—
406C22×C4C11×#4118yes—
407C4⋊C4—28no—
408C4⋊C4—28no—
409C4⋊C4—48no—
410C22⋊C4—216no—
411C22⋊C4—28no—
412C22⋊C4—28no—
413C22⋊C4—28no—
414C22⋊C4—416no—
415C22⋊C4—48no—
416C42—48no—
417C11#1428711yescharacteristic, direct product factor, Sylow
418C23—24no—
419C23—24no—
420C23—24no—
421C23—24no—
422C23—24no—
423C23—24no—
424C23—24no—
425C23—22no—
426C23—22no—
427C23—24no—
428C23—22no—
429C23—24no—
430C23—24no—
431C23—24no—
432C23—44no—
433C23—44no—
434C23—44no—
435C23—44no—
436C23—42no—
437C23—42no—
438C23—42no—
439C23—42no—
440C23—41no—
441C23—41no—
442C23—42no—
443C23—44no—
444C23—44no—
445C23—44no—
446C23—44no—
447C23C2×C11×C22⋊C414yes—
448C23C23×C4×C1111yescharacteristic
449C23C22×D4×C1111yescharacteristic
450C23C22×D4×C1111yescharacteristic
451C23C2×C11×#4114yes—
452C23C11×H(5,𝔽2)14yes—
453C23C11×H(5,𝔽2)12yes—
454C23C11×2−1+412yes—
455D4—416no—
456C2×C4—24no—
457C2×C4—24no—
458C2×C4—24no—
459C2×C4—24no—
460C2×C4—24no—
461C2×C4—24no—
462C2×C4—22no—
463C2×C4—22no—
464C2×C4—22no—
465C2×C4—24no—
466C2×C4—24no—
467C2×C4—24no—
468C2×C4—28no—
469C2×C4—28no—
470C2×C4—28no—
471C2×C4—416no—
472C2×C4—42no—
473C2×C4—42no—
474C2×C4—44no—
475C2×C4—42no—
476C2×C4—42no—
477C2×C4—41no—
478C2×C4—41no—
479C2×C4—42no—
480C2×C4—44no—
481C2×C4—44no—
482C2×C4—44no—
483C2×C4—44no—
484C2×C4—44no—
485C2×C4—44no—
486C2×C4—44no—
487C2×C4—44no—
488C2×C4—44no—
489C2×C4—44no—
490C2×C4C2×C11×C22⋊C414yes—
491C2×C4C2×C11×C22⋊C414yes—
492C22—24no—
493C22—24no—
494C22—24no—
495C22—44no—
496C22—44no—
497C22—48no—
498C22—48no—
499C22—42no—
500C22—42no—
501C22—42no—
502C22—48no—
503C22—82no—
504C22—82no—
505C22—84no—
506C22C22×C11×C22⋊C411yescharacteristic
507C22C4×C11×#4112yes—
508C22C11×#51812yes—
509C22C11×#52012yes—
510C22C11×#52512yes—
511C22C11×#53212yes—
512C22C11×#53412yes—
513C22C11×#53412yes—
514C22C11×#53511yescharacteristic
515C22C11×#53611yescharacteristic
516C22C11×#53712yes—
517C22C11×#53814yes—
518C22C11×#53914yes—
519C22C11×#54014yes—
520C22C11×#54214yes—
521C4—24no—
522C4—24no—
523C4—42no—
524C4—42no—
525C4—42no—
526C4—48no—
527C4—84no—
528C2—44no—
529C2—82no—
530C2C11×#229711yescharacteristic
531C2C11×#230811yescharacteristic
532C2C11×#231111yescharacteristic
533C2C11×#233514yes—
534C2C11×#263014yes—
535C2C11×#266112yes—
536C2C11×#266312yes—
subgroupG/H
center, socleC24×C11C24
commutatorC23C23×C4×C11
Frattini, cosocleC24C24×C11
prime radicalC23×D4×C11C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#380C2semidirect
3. C2×C4×C11×C22⋊C4C2semidirect
4. C11×#1441C2semidirect
5. C11×#1440C2semidirect
6. C11×#1439C2semidirect
8. C11×#1437C2semidirect
9. C11×#1436C2semidirect
14. C2×C11×#123C4semidirect
81. #14287C11direct (N × H)
129. C22×C4×C11C22⋊C4semidirect
151. C2×#380C2×C11semidirect
152. C2×C4×C22⋊C4C2×C11semidirect
153. #1441C2×C11semidirect
154. #1440C2×C11semidirect
155. #1439C2×C11semidirect
157. #1437C2×C11semidirect
158. #1436C2×C11semidirect
237. C2×#123C4×C11semidirect
396. C22×C4C11×C22⋊C4semidirect
417. C11#14287direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C11×#1232
C2×C11×#3802
C2×C4×C11×C22⋊C42
C11×#14412
C11×#14402
C11×#14392
C11×#14382
C11×#14372
C11×#14362
#1428711