Finite Group Databasebeta

← C11×#19183 #14596376

Subgroups — C11×#19183 #14596376

Order 2816.

614 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3182C211yesmaximal, characteristic, complemented
2C11×#3106C211yesmaximal, characteristic
3C11×#3076C211yesmaximal, characteristic, complemented
4C11×#2971C211yesmaximal, characteristic, complemented
5C11×#1703C211yesmaximal, characteristic, complemented
6C11×#1697C211yesmaximal, characteristic, complemented
7C11×#1695C211yesmaximal, characteristic, complemented
8C11×#1685C211yesmaximal, characteristic, complemented
9C11×#1684C211yesmaximal, characteristic, complemented
10C11×#1678C211yesmaximal, characteristic, complemented
11C11×#1676C211yesmaximal, characteristic, complemented
12C11×#1666C211yesmaximal, characteristic, complemented
13C11×#1565C211yesmaximal, characteristic, complemented
14C11×#1554C211yesmaximal, characteristic, complemented
15C11×#1551C211yesmaximal, characteristic, complemented
16C11×#533C2211yescharacteristic
17C11×#532C2211yescharacteristic
18C4×C11×#41C2211yescharacteristic
19C11×#500C2211yescharacteristic
20C11×#492C2211yescharacteristic
21C11×#487C2211yescharacteristic
22C11×#486C2211yescharacteristic
23C11×#482—21no—
24C11×#479—21no—
25C11×#478—21no—
26C11×#477C2211yescharacteristic
27C11×#477C2211yescharacteristic
28C11×#476C2211yescharacteristic
29C11×#476C2211yescharacteristic
30C11×#475C2211yescharacteristic
31C11×#474C2211yescharacteristic
32C11×#468—21no—
33C11×#468—21no—
34C11×#460C2211yescharacteristic
35C11×#459C2211yescharacteristic
36C11×#449—21no—
37C8×Q8×C11C2211yescharacteristic
38C8×Q8×C11C2211yescharacteristic
39C11×#440—21no—
40C11×#440—21no—
41C4×C11×SD16—21no—
42C4×C11×D8—21no—
43C11×#436—21no—
44C11×#436—21no—
45C11×#436C2211yescharacteristic
46C11×#436C2211yescharacteristic
47C11×#432—21no—
48C11×#432C2211yescharacteristic
49C11×#431C2211yescharacteristic
50C11×#427—21no—
51C2×C11×C4⋊C8C2211yescharacteristic
52C11×#416—21no—
53C4×C11×M16—21no—
54C4×C11×M16C2211yescharacteristic
55C11×#335C2211yescharacteristic
56C11×#335C2211yescharacteristic
57C11×#334C2211yescharacteristic
58C11×#334C2211yescharacteristic
59C11×#333C2211yescharacteristic
60C11×#333C2211yescharacteristic
61C11×#333C2211yescharacteristic
62C11×#333C2211yescharacteristic
63C11×#332C2211yescharacteristic
64C11×#332C2211yescharacteristic
65C11×#331C2211yescharacteristic
66C11×#331C2211yescharacteristic
67C2×C11×#41—21no—
68C2×C11×#41D411yescharacteristic
69C2×C11×SD16—21no—
70C2×C11×SD16—21no—
71C2×C11×SD16—21no—
72C2×C11×D8—21no—
73C2×C11×M16—21no—
74C2×C11×M16—21no—
75C2×C11×M16D411yescharacteristic
76C2×C11×M16D411yescharacteristic
77C22×C8×C11—21no—
78C11×C4⋊Q8C2311yescharacteristic
79C11×C4⋊Q8C2311yescharacteristic
80C11×C4⋊Q8C2311yescharacteristic
81C11×#127C2311yescharacteristic
82C11×#125—21no—
83C11×#124—21no—
84C11×C22⋊Q8—21no—
85C11×C22⋊Q8—21no—
86C11×#121—21no—
87C11×#121—21no—
88C4×Q8×C11—21no—
89C4×Q8×C11—21no—
90C4×Q8×C11D411yescharacteristic
91C4×Q8×C11C2311yescharacteristic
92C4×D4×C11—21no—
93C4×D4×C11—21no—
94C4×D4×C11—21no—
95C4×D4×C11—21no—
96C4×D4×C11D411yescharacteristic
97C4×D4×C11C2311yescharacteristic
98C11×#117—21no—
99C11×#117—21no—
100C11×#117D411yescharacteristic
101C2×C42×C11—21no—
102C2×C42×C11C2311yescharacteristic
103C11×#107—21no—
104C11×#107—21no—
105C11×#107—21no—
106C11×#107—21no—
107C11×#107—21no—
108C11×#106—21no—
109C11×#106—21no—
110C11×#106—21no—
111C11×C4⋊C8—21no—
112C11×C4⋊C8—21no—
113C11×C4⋊C8—21no—
114C11×C4⋊C8C2311yescharacteristic
115C11×C4⋊C8C2311yescharacteristic
116C11×C4⋊C8C2311yescharacteristic
117C11×C4⋊C8C2311yescharacteristic
118C11×C4⋊C8C2311yescharacteristic
119C11×C4⋊C8C2311yescharacteristic
120C11×#103—21no—
121C11×#103—21no—
122C11×#103—21no—
123C11×#103—21no—
124C11×#103—21no—
125C11×#102—21no—
126C11×#102—21no—
127C11×#102—21no—
128C11×#102—21no—
129C11×#102—21no—
130C11×#102—21no—
131C11×#102—21no—
132C11×C22⋊C8—21no—
133C11×C22⋊C8—21no—
134C11×C22⋊C8—21no—
135C11×C22⋊C8—21no—
136C11×#97—21no—
137C11×#97D411yescharacteristic
138C11×#97D411yescharacteristic
139C4×C8×C11—21no—
140C4×C8×C11—21no—
141C4×C8×C11—21no—
142C4×C8×C11C2311yescharacteristic
143C4×C8×C11C2311yescharacteristic
144#19183C1111yesmaximal, characteristic, direct product factor, Sylow
145C11×#41—22no—
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×SD16—42no—
166C11×SD16—42no—
167C11×SD16—42no—
168C11×D8—42no—
169C11×M16—22no—
170C11×M16—41no—
171C11×M16—42no—
172C11×M16—42no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C2×C8×C11—21no—
177C2×C8×C11—21no—
178C2×C8×C11—21no—
179C2×C8×C11—42no—
180C2×C8×C11C2×D411yescharacteristic
181C2×C8×C11C2×D411yescharacteristic
182C2×C8×C11C2×D411yescharacteristic
183C2×C8×C11C2×D411yescharacteristic
184C11×C4⋊C4—21no—
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—41no—
193C11×C4⋊C4—41no—
194C11×C4⋊C4C2×D411yescharacteristic
195C11×C4⋊C4C2×D411yescharacteristic
196C11×C22⋊C4—21no—
197C11×C22⋊C4—21no—
198C11×C22⋊C4—21no—
199C11×C22⋊C4—41no—
200C11×C22⋊C4—41no—
201C11×C22⋊C4—41no—
202C42×C11—21no—
203C42×C11—21no—
204C42×C11—21no—
205C42×C11—41no—
206C42×C11C2×D411yescharacteristic
207C42×C11C2×D411yescharacteristic
208C42×C11#4111yescharacteristic
209C42×C11C2411yescharacteristic
210#3182C2×C1111yescharacteristic, complemented
211#3106C2×C1111yescharacteristic
212#3076C2×C1111yescharacteristic, complemented
213#2971C2×C1111yescharacteristic, complemented
214#1703C2×C1111yescharacteristic, complemented
215#1697C2×C1111yescharacteristic, complemented
216#1695C2×C1111yescharacteristic, complemented
217#1685C2×C1111yescharacteristic, complemented
218#1684C2×C1111yescharacteristic, complemented
219#1678C2×C1111yescharacteristic, complemented
220#1676C2×C1111yescharacteristic, complemented
221#1666C2×C1111yescharacteristic, complemented
222#1565C2×C1111yescharacteristic, complemented
223#1554C2×C1111yescharacteristic, complemented
224#1551C2×C1111yescharacteristic, complemented
225C23×C11—21no—
226C23×C11—41no—
227C23×C11#12111yescharacteristic
228Q8×C11—21no—
229Q8×C11—41no—
230Q8×C11—41no—
231Q8×C11—81no—
232Q8×C11—81no—
233Q8×C11#13712yes—
234D4×C11—21no—
235D4×C11—21no—
236D4×C11—42no—
237D4×C11—41no—
238D4×C11—41no—
239D4×C11—41no—
240D4×C11—41no—
241D4×C11—81no—
242D4×C11—82no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—41no—
251C2×C4×C11—42no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11—81no—
258C2×C4×C11—82no—
259C2×C4×C11#12111yescharacteristic
260C2×C4×C11#12111yescharacteristic
261C2×C4×C11#12111yescharacteristic
262C2×C4×C11C22×D411yescharacteristic
263C2×C4×C11C22×D411yescharacteristic
264C2×C4×C11C2×#4111yescharacteristic
265C8×C11—21no—
266C8×C11—21no—
267C8×C11—21no—
268C8×C11—41no—
269C8×C11—41no—
270C8×C11—41no—
271C8×C11—41no—
272C8×C11—41no—
273C8×C11—41no—
274C8×C11#13512yes—
275#533C22×C1111yescharacteristic
276#532C22×C1111yescharacteristic
277C4×#41C22×C1111yescharacteristic
278#500C22×C1111yescharacteristic
279#492C22×C1111yescharacteristic
280#487C22×C1111yescharacteristic
281#486C22×C1111yescharacteristic
282#482—21no—
283#479—21no—
284#478—21no—
285#477C22×C1111yescharacteristic
286#477C22×C1111yescharacteristic
287#476C22×C1111yescharacteristic
288#476C22×C1111yescharacteristic
289#475C22×C1111yescharacteristic
290#474C22×C1111yescharacteristic
291#468—21no—
292#468—21no—
293#460C22×C1111yescharacteristic
294#459C22×C1111yescharacteristic
295#449—21no—
296C8×Q8C22×C1111yescharacteristic
297C8×Q8C22×C1111yescharacteristic
298#440—21no—
299#440—21no—
300C4×SD16—21no—
301C4×D8—21no—
302#436—21no—
303#436—21no—
304#436C22×C1111yescharacteristic
305#436C22×C1111yescharacteristic
306#432—21no—
307#432C22×C1111yescharacteristic
308#431C22×C1111yescharacteristic
309#427—21no—
310C2×C4⋊C8C22×C1111yescharacteristic
311#416—21no—
312C4×M16—21no—
313C4×M16C22×C1111yescharacteristic
314#335C22×C1111yescharacteristic
315#335C22×C1111yescharacteristic
316#334C22×C1111yescharacteristic
317#334C22×C1111yescharacteristic
318#333C22×C1111yescharacteristic
319#333C22×C1111yescharacteristic
320#333C22×C1111yescharacteristic
321#333C22×C1111yescharacteristic
322#332C22×C1111yescharacteristic
323#332C22×C1111yescharacteristic
324#331C22×C1111yescharacteristic
325#331C22×C1111yescharacteristic
326C22×C11—21no—
327C22×C11—21no—
328C22×C11—21no—
329C22×C11—41no—
330C22×C11—41no—
331C22×C11—41no—
332C22×C11—81no—
333C22×C11—81no—
334C22×C11—81no—
335C22×C11C2×#12111yescharacteristic
336C4×C11—21no—
337C4×C11—21no—
338C4×C11—22no—
339C4×C11—21no—
340C4×C11—21no—
341C4×C11—41no—
342C4×C11—41no—
343C4×C11—81no—
344C4×C11—81no—
345C4×C11—81no—
346C4×C11C2×#13511yescharacteristic
347C4×C11C2×#13711yescharacteristic
348C4×C11#57511yescharacteristic
349C4×C11#57511yescharacteristic
350C2×#41—21no—
351C2×#41D4×C1111yescharacteristic
352C2×SD16—21no—
353C2×SD16—21no—
354C2×SD16—21no—
355C2×D8—21no—
356C2×M16—21no—
357C2×M16—21no—
358C2×M16D4×C1111yescharacteristic
359C2×M16D4×C1111yescharacteristic
360C22×C8—21no—
361C4⋊Q8C23×C1111yescharacteristic
362C4⋊Q8C23×C1111yescharacteristic
363C4⋊Q8C23×C1111yescharacteristic
364#127C23×C1111yescharacteristic
365#125—21no—
366#124—21no—
367C22⋊Q8—21no—
368C22⋊Q8—21no—
369#121—21no—
370#121—21no—
371C4×Q8—21no—
372C4×Q8—21no—
373C4×Q8D4×C1111yescharacteristic
374C4×Q8C23×C1111yescharacteristic
375C4×D4—21no—
376C4×D4—21no—
377C4×D4—21no—
378C4×D4—21no—
379C4×D4D4×C1111yescharacteristic
380C4×D4C23×C1111yescharacteristic
381#117—21no—
382#117—21no—
383#117D4×C1111yescharacteristic
384C2×C42—21no—
385C2×C42C23×C1111yescharacteristic
386#107—21no—
387#107—21no—
388#107—21no—
389#107—21no—
390#107—21no—
391#106—21no—
392#106—21no—
393#106—21no—
394C4⋊C8—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#102—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—
419#97—21no—
420#97D4×C1111yescharacteristic
421#97D4×C1111yescharacteristic
422C4×C8—21no—
423C4×C8—21no—
424C4×C8—21no—
425C4×C8C23×C1111yescharacteristic
426C4×C8C23×C1111yescharacteristic
427C2×C11—41no—
428C2×C11—81no—
429C2×C11—161no—
430C2×C11#303511yescharacteristic
431C2×C11#305611yescharacteristic
432C2×C11#306811yescharacteristic
433#41—22no—
434#41—41no—
435#41—82no—
436C2×Q8—21no—
437C2×Q8—21no—
438C2×Q8—21no—
439C2×Q8C2×D4×C1111yescharacteristic
440C2×D4—21no—
441C2×D4—21no—
442C2×D4—21no—
443C2×D4—21no—
444C2×D4—41no—
445C2×D4C2×D4×C1111yescharacteristic
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—41no—
450C22×C4C2×D4×C1111yescharacteristic
451C22×C4C2×D4×C1111yescharacteristic
452C22×C4C11×#4111yescharacteristic
453SD16—42no—
454SD16—42no—
455SD16—42no—
456D8—42no—
457M16—22no—
458M16—41no—
459M16—42no—
460M16—42no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—42no—
468C2×C8C2×D4×C1111yescharacteristic
469C2×C8C2×D4×C1111yescharacteristic
470C2×C8C2×D4×C1111yescharacteristic
471C2×C8C2×D4×C1111yescharacteristic
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—41no—
481C4⋊C4—41no—
482C4⋊C4C2×D4×C1111yescharacteristic
483C4⋊C4C2×D4×C1111yescharacteristic
484C22⋊C4—21no—
485C22⋊C4—21no—
486C22⋊C4—21no—
487C22⋊C4—41no—
488C22⋊C4—41no—
489C22⋊C4—41no—
490C42—21no—
491C42—21no—
492C42—21no—
493C42—41no—
494C42C2×D4×C1111yescharacteristic
495C42C2×D4×C1111yescharacteristic
496C42C11×#4111yescharacteristic
497C42C24×C1111yescharacteristic
498C11#1918311yescharacteristic, direct product factor, Sylow
499C23—21no—
500C23—41no—
501C23C11×#12111yescharacteristic
502Q8—21no—
503Q8—41no—
504Q8—41no—
505Q8—81no—
506Q8—81no—
507Q8C11×#13712yes—
508D4—21no—
509D4—21no—
510D4—42no—
511D4—41no—
512D4—41no—
513D4—41no—
514D4—41no—
515D4—81no—
516D4—82no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—41no—
525C2×C4—42no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—81no—
532C2×C4—82no—
533C2×C4C11×#12111yescharacteristic
534C2×C4C11×#12111yescharacteristic
535C2×C4C11×#12111yescharacteristic
536C2×C4C22×D4×C1111yescharacteristic
537C2×C4C22×D4×C1111yescharacteristic
538C2×C4C2×C11×#4111yescharacteristic
539C8—21no—
540C8—21no—
541C8—21no—
542C8—41no—
543C8—41no—
544C8—41no—
545C8—41no—
546C8—41no—
547C8—41no—
548C8C11×#13512yes—
549C22—21no—
550C22—21no—
551C22—21no—
552C22—41no—
553C22—41no—
554C22—41no—
555C22—81no—
556C22—81no—
557C22—81no—
558C22C2×C11×#12111yescharacteristic
559C4—21no—
560C4—21no—
561C4—22no—
562C4—21no—
563C4—21no—
564C4—41no—
565C4—41no—
566C4—81no—
567C4—81no—
568C4—81no—
569C4C2×C11×#13511yescharacteristic
570C4C2×C11×#13711yescharacteristic
571C4C11×#57511yescharacteristic
572C4C11×#57511yescharacteristic
573C2—41no—
574C2—81no—
575C2—161no—
576C2C11×#303511yescharacteristic
577C2C11×#305611yescharacteristic
578C2C11×#306811yescharacteristic
subgroupG/H
center, socleC22×C11C2×#121
commutator, Frattini, cosocleC42C24×C11
prime radicalC11×#3106C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3182C2semidirect
3. C11×#3076C2semidirect
4. C11×#2971C2semidirect
5. C11×#1703C2semidirect
6. C11×#1697C2semidirect
7. C11×#1695C2semidirect
8. C11×#1685C2semidirect
9. C11×#1684C2semidirect
10. C11×#1678C2semidirect
11. C11×#1676C2semidirect
12. C11×#1666C2semidirect
13. C11×#1565C2semidirect
14. C11×#1554C2semidirect
15. C11×#1551C2semidirect
144. #19183C11direct (N × H)
210. #3182C2×C11semidirect
212. #3076C2×C11semidirect
213. #2971C2×C11semidirect
214. #1703C2×C11semidirect
215. #1697C2×C11semidirect
216. #1695C2×C11semidirect
217. #1685C2×C11semidirect
218. #1684C2×C11semidirect
219. #1678C2×C11semidirect
220. #1676C2×C11semidirect
221. #1666C2×C11semidirect
222. #1565C2×C11semidirect
223. #1554C2×C11semidirect
224. #1551C2×C11semidirect
498. C11#19183direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#31822
C11×#31062
C11×#30762
C11×#29712
C11×#17032
C11×#16972
C11×#16952
C11×#16852
C11×#16842
C11×#16782
C11×#16762
C11×#16662
C11×#15652
C11×#15542
C11×#15512
#1918311