Finite Group Databasebeta

← C11×#19419 #14596612

Subgroups — C11×#19419 #14596612

Order 2816.

616 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3228C211yesmaximal, characteristic, complemented
2C11×#3116C211yesmaximal, characteristic, complemented
3C11×#3106C211yesmaximal, characteristic
4C11×#2988C211yesmaximal, characteristic, complemented
5C11×#1682C211yesmaximal, characteristic, complemented
6C11×#1681C211yesmaximal, characteristic, complemented
7C11×#1678C211yesmaximal, characteristic, complemented
8C11×#1677C211yesmaximal, characteristic, complemented
9C11×#1676C211yesmaximal, characteristic, complemented
10C11×#1675C211yesmaximal, characteristic, complemented
11C11×#1672C211yesmaximal, characteristic, complemented
12C11×#1671C211yesmaximal, characteristic, complemented
13C11×#1572C211yesmaximal, characteristic, complemented
14C11×#1551C211yesmaximal, characteristic, complemented
15C11×#1542C211yesmaximal, characteristic, complemented
16C11×#533C2211yescharacteristic
17C11×#532C2211yescharacteristic
18C4×C11×#41C2211yescharacteristic
19C11×#500C2211yescharacteristic
20C11×#498C2211yescharacteristic
21C11×#486C2211yescharacteristic
22C11×#486C2211yescharacteristic
23C11×#485—21no—
24C11×#482—21no—
25C11×#482—21no—
26C11×#482—21no—
27C11×#478—21no—
28C11×#478—21no—
29C11×#477C2211yescharacteristic
30C11×#477C2211yescharacteristic
31C11×#476C2211yescharacteristic
32C11×#476C2211yescharacteristic
33C11×#462C2211yescharacteristic
34C11×#461C2211yescharacteristic
35C11×#460C2211yescharacteristic
36C11×#459C2211yescharacteristic
37C11×#452—21no—
38C11×#449—21no—
39C8×Q8×C11C2211yescharacteristic
40C8×Q8×C11C2211yescharacteristic
41C11×#441—21no—
42C11×#440—21no—
43C4×C11×SD16—21no—
44C4×C11×D8—21no—
45C8×D4×C11—21no—
46C8×D4×C11—21no—
47C8×D4×C11C2211yescharacteristic
48C8×D4×C11C2211yescharacteristic
49C11×#432C2211yescharacteristic
50C11×#431—21no—
51C11×#431C2211yescharacteristic
52C11×#431C2211yescharacteristic
53C2×C11×C4⋊C8—21no—
54C2×C11×C4⋊C8C2211yescharacteristic
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×Q16—21no—
70C2×C11×SD16—21no—
71C2×C11×SD16—21no—
72C2×C11×D8—21no—
73C22×C8×C11—21no—
74C22×C8×C11—21no—
75C22×C8×C11—21no—
76C11×C4⋊Q8C2311yescharacteristic
77C11×C4⋊Q8C2311yescharacteristic
78C11×C4⋊Q8C2311yescharacteristic
79C11×#127C2311yescharacteristic
80C11×#125—21no—
81C11×#124—21no—
82C11×C22⋊Q8—21no—
83C11×C22⋊Q8—21no—
84C11×#121—21no—
85C11×#121—21no—
86C4×Q8×C11—21no—
87C4×Q8×C11—21no—
88C4×Q8×C11D411yescharacteristic
89C4×Q8×C11C2311yescharacteristic
90C4×D4×C11—21no—
91C4×D4×C11—21no—
92C4×D4×C11—21no—
93C4×D4×C11—21no—
94C4×D4×C11D411yescharacteristic
95C4×D4×C11C2311yescharacteristic
96C11×#117—21no—
97C11×#117—21no—
98C11×#117D411yescharacteristic
99C2×C42×C11—21no—
100C2×C42×C11C2311yescharacteristic
101C11×#107—21no—
102C11×#107—21no—
103C11×#107—21no—
104C11×#107—21no—
105C11×#106—21no—
106C11×#106—21no—
107C11×#106—21no—
108C11×#106—21no—
109C11×C4⋊C8—21no—
110C11×C4⋊C8—21no—
111C11×C4⋊C8—21no—
112C11×C4⋊C8D411yescharacteristic
113C11×C4⋊C8D411yescharacteristic
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×#102—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×C22⋊C8D411yescharacteristic
137C11×C22⋊C8D411yescharacteristic
138C11×#97—21no—
139C4×C8×C11—21no—
140C4×C8×C11—21no—
141C4×C8×C11—21no—
142C4×C8×C11C2311yescharacteristic
143C4×C8×C11C2311yescharacteristic
144#19419C1111yesmaximal, characteristic, direct product factor, Sylow
145C11×#41—22no—
146C11×#41—22no—
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×D8—42no—
169C2×C8×C11—21no—
170C2×C8×C11—21no—
171C2×C8×C11—21no—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11—81no—
176C2×C8×C11—81no—
177C2×C8×C11—81no—
178C2×C8×C11C2×D411yescharacteristic
179C2×C8×C11C2×D411yescharacteristic
180C2×C8×C11C2×D411yescharacteristic
181C2×C8×C11C2×D411yescharacteristic
182C11×C4⋊C4—21no—
183C11×C4⋊C4—21no—
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—41no—
191C11×C4⋊C4—41no—
192C11×C4⋊C4C2×D411yescharacteristic
193C11×C4⋊C4C2×D411yescharacteristic
194C11×C22⋊C4—21no—
195C11×C22⋊C4—21no—
196C11×C22⋊C4—21no—
197C11×C22⋊C4—41no—
198C11×C22⋊C4—41no—
199C11×C22⋊C4—41no—
200C42×C11—21no—
201C42×C11—21no—
202C42×C11—21no—
203C42×C11—41no—
204C42×C11C2×D411yescharacteristic
205C42×C11C2×D411yescharacteristic
206C42×C11#4111yescharacteristic
207C42×C11C2411yescharacteristic
208#3228C2×C1111yescharacteristic, complemented
209#3116C2×C1111yescharacteristic, complemented
210#3106C2×C1111yescharacteristic
211#2988C2×C1111yescharacteristic, complemented
212#1682C2×C1111yescharacteristic, complemented
213#1681C2×C1111yescharacteristic, complemented
214#1678C2×C1111yescharacteristic, complemented
215#1677C2×C1111yescharacteristic, complemented
216#1676C2×C1111yescharacteristic, complemented
217#1675C2×C1111yescharacteristic, complemented
218#1672C2×C1111yescharacteristic, complemented
219#1671C2×C1111yescharacteristic, complemented
220#1572C2×C1111yescharacteristic, complemented
221#1551C2×C1111yescharacteristic, complemented
222#1542C2×C1111yescharacteristic, complemented
223C23×C11—21no—
224C23×C11—41no—
225C23×C11#12111yescharacteristic
226Q8×C11—21no—
227Q8×C11—41no—
228Q8×C11—41no—
229Q8×C11—81no—
230Q8×C11—81no—
231Q8×C11#13512yes—
232D4×C11—24no—
233D4×C11—21no—
234D4×C11—41no—
235D4×C11—41no—
236D4×C11—41no—
237D4×C11—41no—
238D4×C11—81no—
239D4×C11—82no—
240D4×C11#13512yes—
241C2×C4×C11—24no—
242C2×C4×C11—21no—
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—41no—
250C2×C4×C11—41no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11—81no—
256C2×C4×C11—82no—
257C2×C4×C11#12111yescharacteristic
258C2×C4×C11#12111yescharacteristic
259C2×C4×C11#12111yescharacteristic
260C2×C4×C11C22×D411yescharacteristic
261C2×C4×C11C22×D411yescharacteristic
262C2×C4×C11C2×#4111yescharacteristic
263C8×C11—21no—
264C8×C11—21no—
265C8×C11—21no—
266C8×C11—21no—
267C8×C11—41no—
268C8×C11—41no—
269C8×C11—41no—
270C8×C11—41no—
271C8×C11—41no—
272C8×C11—41no—
273#533C22×C1111yescharacteristic
274#532C22×C1111yescharacteristic
275C4×#41C22×C1111yescharacteristic
276#500C22×C1111yescharacteristic
277#498C22×C1111yescharacteristic
278#486C22×C1111yescharacteristic
279#486C22×C1111yescharacteristic
280#485—21no—
281#482—21no—
282#482—21no—
283#482—21no—
284#478—21no—
285#478—21no—
286#477C22×C1111yescharacteristic
287#477C22×C1111yescharacteristic
288#476C22×C1111yescharacteristic
289#476C22×C1111yescharacteristic
290#462C22×C1111yescharacteristic
291#461C22×C1111yescharacteristic
292#460C22×C1111yescharacteristic
293#459C22×C1111yescharacteristic
294#452—21no—
295#449—21no—
296C8×Q8C22×C1111yescharacteristic
297C8×Q8C22×C1111yescharacteristic
298#441—21no—
299#440—21no—
300C4×SD16—21no—
301C4×D8—21no—
302C8×D4—21no—
303C8×D4—21no—
304C8×D4C22×C1111yescharacteristic
305C8×D4C22×C1111yescharacteristic
306#432C22×C1111yescharacteristic
307#431—21no—
308#431C22×C1111yescharacteristic
309#431C22×C1111yescharacteristic
310C2×C4⋊C8—21no—
311C2×C4⋊C8C22×C1111yescharacteristic
312#335C22×C1111yescharacteristic
313#335C22×C1111yescharacteristic
314#334C22×C1111yescharacteristic
315#334C22×C1111yescharacteristic
316#333C22×C1111yescharacteristic
317#333C22×C1111yescharacteristic
318#333C22×C1111yescharacteristic
319#333C22×C1111yescharacteristic
320#332C22×C1111yescharacteristic
321#332C22×C1111yescharacteristic
322#331C22×C1111yescharacteristic
323#331C22×C1111yescharacteristic
324C22×C11—21no—
325C22×C11—21no—
326C22×C11—22no—
327C22×C11—21no—
328C22×C11—41no—
329C22×C11—41no—
330C22×C11—81no—
331C22×C11—81no—
332C22×C11—81no—
333C22×C11C2×#12111yescharacteristic
334C4×C11—21no—
335C4×C11—21no—
336C4×C11—22no—
337C4×C11—21no—
338C4×C11—21no—
339C4×C11—41no—
340C4×C11—41no—
341C4×C11—81no—
342C4×C11—81no—
343C4×C11—81no—
344C4×C11C2×#13511yescharacteristic
345C4×C11C2×#13511yescharacteristic
346C4×C11#57711yescharacteristic
347C4×C11#57811yescharacteristic
348C2×#41—21no—
349C2×#41D4×C1111yescharacteristic
350C2×Q16—21no—
351C2×SD16—21no—
352C2×SD16—21no—
353C2×D8—21no—
354C22×C8—21no—
355C22×C8—21no—
356C22×C8—21no—
357C4⋊Q8C23×C1111yescharacteristic
358C4⋊Q8C23×C1111yescharacteristic
359C4⋊Q8C23×C1111yescharacteristic
360#127C23×C1111yescharacteristic
361#125—21no—
362#124—21no—
363C22⋊Q8—21no—
364C22⋊Q8—21no—
365#121—21no—
366#121—21no—
367C4×Q8—21no—
368C4×Q8—21no—
369C4×Q8D4×C1111yescharacteristic
370C4×Q8C23×C1111yescharacteristic
371C4×D4—21no—
372C4×D4—21no—
373C4×D4—21no—
374C4×D4—21no—
375C4×D4D4×C1111yescharacteristic
376C4×D4C23×C1111yescharacteristic
377#117—21no—
378#117—21no—
379#117D4×C1111yescharacteristic
380C2×C42—21no—
381C2×C42C23×C1111yescharacteristic
382#107—21no—
383#107—21no—
384#107—21no—
385#107—21no—
386#106—21no—
387#106—21no—
388#106—21no—
389#106—21no—
390C4⋊C8—21no—
391C4⋊C8—21no—
392C4⋊C8—21no—
393C4⋊C8D4×C1111yescharacteristic
394C4⋊C8D4×C1111yescharacteristic
395C4⋊C8C23×C1111yescharacteristic
396C4⋊C8C23×C1111yescharacteristic
397C4⋊C8C23×C1111yescharacteristic
398C4⋊C8C23×C1111yescharacteristic
399C4⋊C8C23×C1111yescharacteristic
400C4⋊C8C23×C1111yescharacteristic
401#103—21no—
402#103—21no—
403#103—21no—
404#103—21no—
405#102—21no—
406#102—21no—
407#102—21no—
408#102—21no—
409#102—21no—
410#102—21no—
411#102—21no—
412#102—21no—
413C22⋊C8—21no—
414C22⋊C8—21no—
415C22⋊C8—21no—
416C22⋊C8—21no—
417C22⋊C8D4×C1111yescharacteristic
418C22⋊C8D4×C1111yescharacteristic
419#97—21no—
420C4×C8—21no—
421C4×C8—21no—
422C4×C8—21no—
423C4×C8C23×C1111yescharacteristic
424C4×C8C23×C1111yescharacteristic
425C2×C11—41no—
426C2×C11—42no—
427C2×C11—161no—
428C2×C11#304611yescharacteristic
429C2×C11#305011yescharacteristic
430C2×C11#306811yescharacteristic
431#41—22no—
432#41—22no—
433#41—82no—
434C2×Q8—21no—
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8C2×D4×C1111yescharacteristic
438C2×D4—21no—
439C2×D4—21no—
440C2×D4—21no—
441C2×D4—21no—
442C2×D4—41no—
443C2×D4C2×D4×C1111yescharacteristic
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—41no—
448C22×C4C2×D4×C1111yescharacteristic
449C22×C4C2×D4×C1111yescharacteristic
450C22×C4C11×#4111yescharacteristic
451Q16—42no—
452SD16—42no—
453SD16—42no—
454D8—42no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—81no—
462C2×C8—81no—
463C2×C8—81no—
464C2×C8C2×D4×C1111yescharacteristic
465C2×C8C2×D4×C1111yescharacteristic
466C2×C8C2×D4×C1111yescharacteristic
467C2×C8C2×D4×C1111yescharacteristic
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—41no—
477C4⋊C4—41no—
478C4⋊C4C2×D4×C1111yescharacteristic
479C4⋊C4C2×D4×C1111yescharacteristic
480C22⋊C4—21no—
481C22⋊C4—21no—
482C22⋊C4—21no—
483C22⋊C4—41no—
484C22⋊C4—41no—
485C22⋊C4—41no—
486C42—21no—
487C42—21no—
488C42—21no—
489C42—41no—
490C42C2×D4×C1111yescharacteristic
491C42C2×D4×C1111yescharacteristic
492C42C11×#4111yescharacteristic
493C42C24×C1111yescharacteristic
494C11#1941911yescharacteristic, direct product factor, Sylow
495C23—21no—
496C23—41no—
497C23C11×#12111yescharacteristic
498Q8—21no—
499Q8—41no—
500Q8—41no—
501Q8—81no—
502Q8—81no—
503Q8C11×#13512yes—
504D4—24no—
505D4—21no—
506D4—41no—
507D4—41no—
508D4—41no—
509D4—41no—
510D4—81no—
511D4—82no—
512D4C11×#13512yes—
513C2×C4—24no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—81no—
528C2×C4—82no—
529C2×C4C11×#12111yescharacteristic
530C2×C4C11×#12111yescharacteristic
531C2×C4C11×#12111yescharacteristic
532C2×C4C22×D4×C1111yescharacteristic
533C2×C4C22×D4×C1111yescharacteristic
534C2×C4C2×C11×#4111yescharacteristic
535C8—21no—
536C8—21no—
537C8—21no—
538C8—21no—
539C8—41no—
540C8—41no—
541C8—41no—
542C8—41no—
543C8—41no—
544C8—41no—
545C22—21no—
546C22—21no—
547C22—22no—
548C22—21no—
549C22—41no—
550C22—41no—
551C22—81no—
552C22—81no—
553C22—81no—
554C22C2×C11×#12111yescharacteristic
555C4—21no—
556C4—21no—
557C4—22no—
558C4—21no—
559C4—21no—
560C4—41no—
561C4—41no—
562C4—81no—
563C4—81no—
564C4—81no—
565C4C2×C11×#13511yescharacteristic
566C4C2×C11×#13511yescharacteristic
567C4C11×#57711yescharacteristic
568C4C11×#57811yescharacteristic
569C2—41no—
570C2—42no—
571C2—161no—
572C2C11×#304611yescharacteristic
573C2C11×#305011yescharacteristic
574C2C11×#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×#3228C2semidirect
2. C11×#3116C2semidirect
4. C11×#2988C2semidirect
5. C11×#1682C2semidirect
6. C11×#1681C2semidirect
7. C11×#1678C2semidirect
8. C11×#1677C2semidirect
9. C11×#1676C2semidirect
10. C11×#1675C2semidirect
11. C11×#1672C2semidirect
12. C11×#1671C2semidirect
13. C11×#1572C2semidirect
14. C11×#1551C2semidirect
15. C11×#1542C2semidirect
144. #19419C11direct (N × H)
208. #3228C2×C11semidirect
209. #3116C2×C11semidirect
211. #2988C2×C11semidirect
212. #1682C2×C11semidirect
213. #1681C2×C11semidirect
214. #1678C2×C11semidirect
215. #1677C2×C11semidirect
216. #1676C2×C11semidirect
217. #1675C2×C11semidirect
218. #1672C2×C11semidirect
219. #1671C2×C11semidirect
220. #1572C2×C11semidirect
221. #1551C2×C11semidirect
222. #1542C2×C11semidirect
494. C11#19419direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#32282
C11×#31162
C11×#31062
C11×#29882
C11×#16822
C11×#16812
C11×#16782
C11×#16772
C11×#16762
C11×#16752
C11×#16722
C11×#16712
C11×#15722
C11×#15512
C11×#15422
#1941911