Finite Group Databasebeta

← C11×#19159 #14596352

Subgroups — C11×#19159 #14596352

Order 2816.

620 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3167C211yesmaximal, characteristic, complemented
2C11×#3107C211yesmaximal, characteristic, complemented
3C11×#3106C211yesmaximal, characteristic
4C11×#2965C211yesmaximal, characteristic, complemented
5C11×#1704C211yesmaximal, characteristic, complemented
6C11×#1703C211yesmaximal, characteristic, complemented
7C11×#1702C211yesmaximal, characteristic, complemented
8C11×#1701C211yesmaximal, characteristic, complemented
9C11×#1692C211yesmaximal, characteristic, complemented
10C11×#1691C211yesmaximal, characteristic, complemented
11C11×#1686C211yesmaximal, characteristic, complemented
12C11×#1685C211yesmaximal, characteristic, complemented
13C11×#1564C211yesmaximal, characteristic, complemented
14C11×#1544C211yesmaximal, characteristic, complemented
15C11×#1543C211yesmaximal, characteristic, complemented
16C11×#533C2211yescharacteristic
17C11×#532C2211yescharacteristic
18C4×C11×#41C2211yescharacteristic
19C11×#498C2211yescharacteristic
20C11×#492C2211yescharacteristic
21C11×#487C2211yescharacteristic
22C11×#486C2211yescharacteristic
23C11×#485—21no—
24C11×#482—21no—
25C11×#477C2211yescharacteristic
26C11×#476C2211yescharacteristic
27C11×#475C2211yescharacteristic
28C11×#474C2211yescharacteristic
29C11×#465—21no—
30C11×#465—21no—
31C11×#462C2211yescharacteristic
32C11×#461C2211yescharacteristic
33C11×#460C2211yescharacteristic
34C11×#459C2211yescharacteristic
35C11×#452—21no—
36C11×#449—21no—
37C11×#446C2211yescharacteristic
38C11×#446C2211yescharacteristic
39C4×C11×Q16—21no—
40C4×C11×SD16—21no—
41C4×C11×SD16—21no—
42C4×C11×SD16—21no—
43C4×C11×SD16—21no—
44C4×C11×D8—21no—
45C11×#436C2211yescharacteristic
46C11×#436C2211yescharacteristic
47C11×#435—21no—
48C11×#435—21no—
49C11×#431—21no—
50C11×#431C2211yescharacteristic
51C11×#431C2211yescharacteristic
52C11×#431C2211yescharacteristic
53C4×C11×M16—21no—
54C2×C4×C8×C11C2211yescharacteristic
55C11×#335C2211yescharacteristic
56C11×#335C2211yescharacteristic
57C11×#334C2211yescharacteristic
58C11×#334C2211yescharacteristic
59C11×#333C2211yescharacteristic
60C11×#333C2211yescharacteristic
61C11×#332C2211yescharacteristic
62C11×#332C2211yescharacteristic
63C11×#332C2211yescharacteristic
64C11×#332C2211yescharacteristic
65C11×#331C2211yescharacteristic
66C11×#331C2211yescharacteristic
67C2×C11×#41—21no—
68C2×C11×#41D411yescharacteristic
69C2×C11×Q16—21no—
70C2×C11×SD16—21no—
71C2×C11×SD16—21no—
72C2×C11×SD16—21no—
73C2×C11×SD16—21no—
74C2×C11×D8—21no—
75C2×C11×M16—21no—
76C2×C11×M16—21no—
77C22×C8×C11D411yescharacteristic
78C22×C8×C11D411yescharacteristic
79C11×C4⋊Q8C2311yescharacteristic
80C11×C4⋊Q8C2311yescharacteristic
81C11×C4⋊Q8C2311yescharacteristic
82C11×#127C2311yescharacteristic
83C11×#125—21no—
84C11×#124—21no—
85C11×C22⋊Q8—21no—
86C11×C22⋊Q8—21no—
87C11×#121—21no—
88C11×#121—21no—
89C4×Q8×C11—21no—
90C4×Q8×C11—21no—
91C4×Q8×C11D411yescharacteristic
92C4×Q8×C11C2311yescharacteristic
93C4×D4×C11—21no—
94C4×D4×C11—21no—
95C4×D4×C11—21no—
96C4×D4×C11—21no—
97C4×D4×C11D411yescharacteristic
98C4×D4×C11C2311yescharacteristic
99C11×#117—21no—
100C11×#117—21no—
101C11×#117D411yescharacteristic
102C2×C42×C11—21no—
103C2×C42×C11C2311yescharacteristic
104C11×#107—21no—
105C11×#107—21no—
106C11×#106—21no—
107C11×#106—21no—
108C11×#106—21no—
109C11×#106—21no—
110C11×C4⋊C8—21no—
111C11×C4⋊C8—21no—
112C11×C4⋊C8C2311yescharacteristic
113C11×C4⋊C8C2311yescharacteristic
114C11×C4⋊C8C2311yescharacteristic
115C11×C4⋊C8C2311yescharacteristic
116C11×C4⋊C8C2311yescharacteristic
117C11×C4⋊C8C2311yescharacteristic
118C11×#103—21no—
119C11×#103—21no—
120C11×#103—21no—
121C11×#103—21no—
122C11×#103—21no—
123C11×#103—21no—
124C11×#102—21no—
125C11×#102—21no—
126C11×#102—21no—
127C11×#102—21no—
128C11×#102—21no—
129C11×#102—21no—
130C11×C22⋊C8—21no—
131C11×C22⋊C8—21no—
132C11×C22⋊C8—21no—
133C11×C22⋊C8—21no—
134C11×C22⋊C8—21no—
135C11×#97—21no—
136C11×#97—21no—
137C4×C8×C11—21no—
138C4×C8×C11—21no—
139C4×C8×C11—21no—
140C4×C8×C11D411yescharacteristic
141C4×C8×C11D411yescharacteristic
142C4×C8×C11C2311yescharacteristic
143C4×C8×C11C2311yescharacteristic
144#19159C1111yesmaximal, characteristic, direct product factor, Sylow
145C11×#41—41no—
146C11×#41—41no—
147C11×#41—82no—
148C2×Q8×C11—21no—
149C2×Q8×C11—21no—
150C2×Q8×C11—21no—
151C2×Q8×C11C2×D411yescharacteristic
152C2×D4×C11—21no—
153C2×D4×C11—21no—
154C2×D4×C11—21no—
155C2×D4×C11—21no—
156C2×D4×C11—41no—
157C2×D4×C11C2×D411yescharacteristic
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11—41no—
162C22×C4×C11C2×D411yescharacteristic
163C22×C4×C11C2×D411yescharacteristic
164C22×C4×C11#4111yescharacteristic
165C11×Q16—42no—
166C11×SD16—42no—
167C11×SD16—42no—
168C11×SD16—42no—
169C11×SD16—42no—
170C11×D8—42no—
171C11×M16—42no—
172C11×M16—42no—
173C2×C8×C11—22no—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C2×C8×C11—21no—
177C2×C8×C11—21no—
178C2×C8×C11—21no—
179C2×C8×C11—21no—
180C2×C8×C11—41no—
181C2×C8×C11C2×D411yescharacteristic
182C2×C8×C11C2×D411yescharacteristic
183C2×C8×C11C2×D411yescharacteristic
184C2×C8×C11C2×D411yescharacteristic
185C11×C4⋊C4—21no—
186C11×C4⋊C4—21no—
187C11×C4⋊C4—21no—
188C11×C4⋊C4—21no—
189C11×C4⋊C4—21no—
190C11×C4⋊C4—21no—
191C11×C4⋊C4—21no—
192C11×C4⋊C4—21no—
193C11×C4⋊C4—41no—
194C11×C4⋊C4—41no—
195C11×C4⋊C4C2×D411yescharacteristic
196C11×C4⋊C4C2×D411yescharacteristic
197C11×C22⋊C4—21no—
198C11×C22⋊C4—21no—
199C11×C22⋊C4—21no—
200C11×C22⋊C4—41no—
201C11×C22⋊C4—41no—
202C11×C22⋊C4—41no—
203C42×C11—21no—
204C42×C11—21no—
205C42×C11—21no—
206C42×C11—41no—
207C42×C11C2×D411yescharacteristic
208C42×C11C2×D411yescharacteristic
209C42×C11#4111yescharacteristic
210C42×C11C2411yescharacteristic
211#3167C2×C1111yescharacteristic, complemented
212#3107C2×C1111yescharacteristic, complemented
213#3106C2×C1111yescharacteristic
214#2965C2×C1111yescharacteristic, complemented
215#1704C2×C1111yescharacteristic, complemented
216#1703C2×C1111yescharacteristic, complemented
217#1702C2×C1111yescharacteristic, complemented
218#1701C2×C1111yescharacteristic, complemented
219#1692C2×C1111yescharacteristic, complemented
220#1691C2×C1111yescharacteristic, complemented
221#1686C2×C1111yescharacteristic, complemented
222#1685C2×C1111yescharacteristic, complemented
223#1564C2×C1111yescharacteristic, complemented
224#1544C2×C1111yescharacteristic, complemented
225#1543C2×C1111yescharacteristic, complemented
226C23×C11—21no—
227C23×C11—41no—
228C23×C11#12111yescharacteristic
229Q8×C11—21no—
230Q8×C11—21no—
231Q8×C11—41no—
232Q8×C11—41no—
233Q8×C11—41no—
234Q8×C11—41no—
235Q8×C11—81no—
236D4×C11—21no—
237D4×C11—21no—
238D4×C11—42no—
239D4×C11—41no—
240D4×C11—41no—
241D4×C11—41no—
242D4×C11—41no—
243D4×C11—81no—
244D4×C11—82no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—22no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—42no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—42no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11—82no—
261C2×C4×C11#12111yescharacteristic
262C2×C4×C11#12111yescharacteristic
263C2×C4×C11#12111yescharacteristic
264C2×C4×C11C22×D411yescharacteristic
265C2×C4×C11C22×D411yescharacteristic
266C2×C4×C11C2×#4111yescharacteristic
267C8×C11—21no—
268C8×C11—21no—
269C8×C11—21no—
270C8×C11—41no—
271C8×C11—41no—
272C8×C11—41no—
273C8×C11—41no—
274C8×C11—41no—
275C8×C11—41no—
276C8×C11#13512yes—
277#533C22×C1111yescharacteristic
278#532C22×C1111yescharacteristic
279C4×#41C22×C1111yescharacteristic
280#498C22×C1111yescharacteristic
281#492C22×C1111yescharacteristic
282#487C22×C1111yescharacteristic
283#486C22×C1111yescharacteristic
284#485—21no—
285#482—21no—
286#477C22×C1111yescharacteristic
287#476C22×C1111yescharacteristic
288#475C22×C1111yescharacteristic
289#474C22×C1111yescharacteristic
290#465—21no—
291#465—21no—
292#462C22×C1111yescharacteristic
293#461C22×C1111yescharacteristic
294#460C22×C1111yescharacteristic
295#459C22×C1111yescharacteristic
296#452—21no—
297#449—21no—
298#446C22×C1111yescharacteristic
299#446C22×C1111yescharacteristic
300C4×Q16—21no—
301C4×SD16—21no—
302C4×SD16—21no—
303C4×SD16—21no—
304C4×SD16—21no—
305C4×D8—21no—
306#436C22×C1111yescharacteristic
307#436C22×C1111yescharacteristic
308#435—21no—
309#435—21no—
310#431—21no—
311#431C22×C1111yescharacteristic
312#431C22×C1111yescharacteristic
313#431C22×C1111yescharacteristic
314C4×M16—21no—
315C2×C4×C8C22×C1111yescharacteristic
316#335C22×C1111yescharacteristic
317#335C22×C1111yescharacteristic
318#334C22×C1111yescharacteristic
319#334C22×C1111yescharacteristic
320#333C22×C1111yescharacteristic
321#333C22×C1111yescharacteristic
322#332C22×C1111yescharacteristic
323#332C22×C1111yescharacteristic
324#332C22×C1111yescharacteristic
325#332C22×C1111yescharacteristic
326#331C22×C1111yescharacteristic
327#331C22×C1111yescharacteristic
328C22×C11—21no—
329C22×C11—21no—
330C22×C11—21no—
331C22×C11—41no—
332C22×C11—41no—
333C22×C11—41no—
334C22×C11—81no—
335C22×C11—81no—
336C22×C11—81no—
337C22×C11C2×#12111yescharacteristic
338C4×C11—21no—
339C4×C11—21no—
340C4×C11—21no—
341C4×C11—41no—
342C4×C11—41no—
343C4×C11—41no—
344C4×C11—81no—
345C4×C11—81no—
346C4×C11—81no—
347C4×C11#47112yes—
348C4×C11C2×#13511yescharacteristic
349C4×C11#57511yescharacteristic
350C4×C11#57511yescharacteristic
351C4×C11#57511yescharacteristic
352C2×#41—21no—
353C2×#41D4×C1111yescharacteristic
354C2×Q16—21no—
355C2×SD16—21no—
356C2×SD16—21no—
357C2×SD16—21no—
358C2×SD16—21no—
359C2×D8—21no—
360C2×M16—21no—
361C2×M16—21no—
362C22×C8D4×C1111yescharacteristic
363C22×C8D4×C1111yescharacteristic
364C4⋊Q8C23×C1111yescharacteristic
365C4⋊Q8C23×C1111yescharacteristic
366C4⋊Q8C23×C1111yescharacteristic
367#127C23×C1111yescharacteristic
368#125—21no—
369#124—21no—
370C22⋊Q8—21no—
371C22⋊Q8—21no—
372#121—21no—
373#121—21no—
374C4×Q8—21no—
375C4×Q8—21no—
376C4×Q8D4×C1111yescharacteristic
377C4×Q8C23×C1111yescharacteristic
378C4×D4—21no—
379C4×D4—21no—
380C4×D4—21no—
381C4×D4—21no—
382C4×D4D4×C1111yescharacteristic
383C4×D4C23×C1111yescharacteristic
384#117—21no—
385#117—21no—
386#117D4×C1111yescharacteristic
387C2×C42—21no—
388C2×C42C23×C1111yescharacteristic
389#107—21no—
390#107—21no—
391#106—21no—
392#106—21no—
393#106—21no—
394#106—21no—
395C4⋊C8—21no—
396C4⋊C8—21no—
397C4⋊C8C23×C1111yescharacteristic
398C4⋊C8C23×C1111yescharacteristic
399C4⋊C8C23×C1111yescharacteristic
400C4⋊C8C23×C1111yescharacteristic
401C4⋊C8C23×C1111yescharacteristic
402C4⋊C8C23×C1111yescharacteristic
403#103—21no—
404#103—21no—
405#103—21no—
406#103—21no—
407#103—21no—
408#103—21no—
409#102—21no—
410#102—21no—
411#102—21no—
412#102—21no—
413#102—21no—
414#102—21no—
415C22⋊C8—21no—
416C22⋊C8—21no—
417C22⋊C8—21no—
418C22⋊C8—21no—
419C22⋊C8—21no—
420#97—21no—
421#97—21no—
422C4×C8—21no—
423C4×C8—21no—
424C4×C8—21no—
425C4×C8D4×C1111yescharacteristic
426C4×C8D4×C1111yescharacteristic
427C4×C8C23×C1111yescharacteristic
428C4×C8C23×C1111yescharacteristic
429C2×C11—41no—
430C2×C11—81no—
431C2×C11—161no—
432C2×C11#303511yescharacteristic
433C2×C11#305411yescharacteristic
434C2×C11C2×#47111yescharacteristic
435#41—41no—
436#41—41no—
437#41—82no—
438C2×Q8—21no—
439C2×Q8—21no—
440C2×Q8—21no—
441C2×Q8C2×D4×C1111yescharacteristic
442C2×D4—21no—
443C2×D4—21no—
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—41no—
447C2×D4C2×D4×C1111yescharacteristic
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—41no—
452C22×C4C2×D4×C1111yescharacteristic
453C22×C4C2×D4×C1111yescharacteristic
454C22×C4C11×#4111yescharacteristic
455Q16—42no—
456SD16—42no—
457SD16—42no—
458SD16—42no—
459SD16—42no—
460D8—42no—
461M16—42no—
462M16—42no—
463C2×C8—22no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—41no—
471C2×C8C2×D4×C1111yescharacteristic
472C2×C8C2×D4×C1111yescharacteristic
473C2×C8C2×D4×C1111yescharacteristic
474C2×C8C2×D4×C1111yescharacteristic
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—41no—
484C4⋊C4—41no—
485C4⋊C4C2×D4×C1111yescharacteristic
486C4⋊C4C2×D4×C1111yescharacteristic
487C22⋊C4—21no—
488C22⋊C4—21no—
489C22⋊C4—21no—
490C22⋊C4—41no—
491C22⋊C4—41no—
492C22⋊C4—41no—
493C42—21no—
494C42—21no—
495C42—21no—
496C42—41no—
497C42C2×D4×C1111yescharacteristic
498C42C2×D4×C1111yescharacteristic
499C42C11×#4111yescharacteristic
500C42C24×C1111yescharacteristic
501C11#1915911yescharacteristic, direct product factor, Sylow
502C23—21no—
503C23—41no—
504C23C11×#12111yescharacteristic
505Q8—21no—
506Q8—21no—
507Q8—41no—
508Q8—41no—
509Q8—41no—
510Q8—41no—
511Q8—81no—
512D4—21no—
513D4—21no—
514D4—42no—
515D4—41no—
516D4—41no—
517D4—41no—
518D4—41no—
519D4—81no—
520D4—82no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—22no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—42no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—42no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—82no—
537C2×C4C11×#12111yescharacteristic
538C2×C4C11×#12111yescharacteristic
539C2×C4C11×#12111yescharacteristic
540C2×C4C22×D4×C1111yescharacteristic
541C2×C4C22×D4×C1111yescharacteristic
542C2×C4C2×C11×#4111yescharacteristic
543C8—21no—
544C8—21no—
545C8—21no—
546C8—41no—
547C8—41no—
548C8—41no—
549C8—41no—
550C8—41no—
551C8—41no—
552C8C11×#13512yes—
553C22—21no—
554C22—21no—
555C22—21no—
556C22—41no—
557C22—41no—
558C22—41no—
559C22—81no—
560C22—81no—
561C22—81no—
562C22C2×C11×#12111yescharacteristic
563C4—21no—
564C4—21no—
565C4—21no—
566C4—41no—
567C4—41no—
568C4—41no—
569C4—81no—
570C4—81no—
571C4—81no—
572C4C11×#47112yes—
573C4C2×C11×#13511yescharacteristic
574C4C11×#57511yescharacteristic
575C4C11×#57511yescharacteristic
576C4C11×#57511yescharacteristic
577C2—41no—
578C2—81no—
579C2—161no—
580C2C11×#303511yescharacteristic
581C2C11×#305411yescharacteristic
582C2C2×C11×#47111yescharacteristic
subgroupG/H
centerC2×C4×C11#121
commutator, Frattini, cosocleC42C24×C11
socleC22×C11C2×#121
prime radicalC11×#3106C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3167C2semidirect
2. C11×#3107C2semidirect
4. C11×#2965C2semidirect
5. C11×#1704C2semidirect
6. C11×#1703C2semidirect
7. C11×#1702C2semidirect
8. C11×#1701C2semidirect
9. C11×#1692C2semidirect
10. C11×#1691C2semidirect
11. C11×#1686C2semidirect
12. C11×#1685C2semidirect
13. C11×#1564C2semidirect
14. C11×#1544C2semidirect
15. C11×#1543C2semidirect
144. #19159C11direct (N × H)
211. #3167C2×C11semidirect
212. #3107C2×C11semidirect
214. #2965C2×C11semidirect
215. #1704C2×C11semidirect
216. #1703C2×C11semidirect
217. #1702C2×C11semidirect
218. #1701C2×C11semidirect
219. #1692C2×C11semidirect
220. #1691C2×C11semidirect
221. #1686C2×C11semidirect
222. #1685C2×C11semidirect
223. #1564C2×C11semidirect
224. #1544C2×C11semidirect
225. #1543C2×C11semidirect
501. C11#19159direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#31672
C11×#31072
C11×#31062
C11×#29652
C11×#17042
C11×#17032
C11×#17022
C11×#17012
C11×#16922
C11×#16912
C11×#16862
C11×#16852
C11×#15642
C11×#15442
C11×#15432
#1915911