Finite Group Databasebeta

← C11×#19781 #14596974

Subgroups — C11×#19781 #14596974

Order 2816.

616 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3380C211yesmaximal, characteristic, complemented
2C11×#3358C211yesmaximal, characteristic
3C11×#3333C211yesmaximal, characteristic, complemented
4C11×#3299C211yesmaximal, characteristic, complemented
5C11×#1719C211yesmaximal, characteristic, complemented
6C11×#1703C211yesmaximal, characteristic, complemented
7C11×#1682C211yesmaximal, characteristic, complemented
8C11×#1677C211yesmaximal, characteristic, complemented
9C11×#1676C211yesmaximal, characteristic, complemented
10C11×#1644C211yesmaximal, characteristic, complemented
11C11×#1637C211yesmaximal, characteristic, complemented
12C11×#1631C211yesmaximal, characteristic, complemented
13C11×#1622C211yesmaximal, characteristic, complemented
14C11×#1581C211yesmaximal, characteristic, complemented
15C11×#1579C211yesmaximal, characteristic, complemented
16C11×#554C2211yescharacteristic
17C11×#554C2211yescharacteristic
18C11×#550C2211yescharacteristic
19D4×Q8×C11C2211yescharacteristic
20C11×#500C2211yescharacteristic
21C11×#499—21no—
22C11×#492C2211yescharacteristic
23C11×#487C2211yescharacteristic
24C11×#487C2211yescharacteristic
25C11×#486—21no—
26C11×#486C2211yescharacteristic
27C11×#486C2211yescharacteristic
28C11×#484—21no—
29C11×#480—21no—
30C11×#478—21no—
31C11×#478—21no—
32C11×#477C2211yescharacteristic
33C11×#477C2211yescharacteristic
34C11×#476C2211yescharacteristic
35C11×#476C2211yescharacteristic
36C11×#474—21no—
37C11×#474C2211yescharacteristic
38C11×#468—21no—
39C11×#467—21no—
40C11×#462C2211yescharacteristic
41C11×#460C2211yescharacteristic
42C11×#459—21no—
43C11×#459C2211yescharacteristic
44C11×#452—21no—
45C11×#451—21no—
46C8×Q8×C11C2211yescharacteristic
47C8×Q8×C11C2211yescharacteristic
48C4×C11×Q16C2211yescharacteristic
49C4×C11×D8—21no—
50C4×C11×D8—21no—
51C4×C11×D8C2211yescharacteristic
52C11×#436C2211yescharacteristic
53C8×D4×C11C2211yescharacteristic
54C11×#417—21no—
55C2×C11×#103—21no—
56C11×#335C2211yescharacteristic
57C11×#334C2211yescharacteristic
58C11×#333C2211yescharacteristic
59C11×#333C2211yescharacteristic
60C11×#332C2211yescharacteristic
61C11×#331C2211yescharacteristic
62C11×Q8⋊C8C2211yescharacteristic
63C11×Q8⋊C8C2211yescharacteristic
64C11×D4⋊C8C2211yescharacteristic
65C11×D4⋊C8C2211yescharacteristic
66C11×#322C2211yescharacteristic
67C2×C11×#41—21no—
68C22×Q8×C11—21no—
69C2×C11×Q16—21no—
70C2×C11×Q16D411yescharacteristic
71C2×C11×SD16—21no—
72C2×C11×SD16—41no—
73C2×C11×D8—21no—
74C2×C11×D8D411yescharacteristic
75C2×C11×M16—21no—
76C22×C8×C11—21no—
77C11×C4⋊Q8—21no—
78C11×C4⋊Q8C2311yescharacteristic
79C11×C4⋊Q8C2311yescharacteristic
80C11×C4⋊Q8C2311yescharacteristic
81C11×#127—21no—
82C11×#127C2311yescharacteristic
83C11×#125—21no—
84C11×#125—21no—
85C11×C22⋊Q8—21no—
86C11×C22⋊Q8—21no—
87C11×C22⋊Q8—21no—
88C11×C22⋊Q8—41no—
89C11×C22⋊Q8—41no—
90C11×C22⋊Q8—41no—
91C11×#121—21no—
92C11×#121—41no—
93C4×Q8×C11C2311yescharacteristic
94C4×Q8×C11C2311yescharacteristic
95C4×D4×C11—21no—
96C4×D4×C11—21no—
97C4×D4×C11—21no—
98C4×D4×C11—21no—
99C4×D4×C11C2311yescharacteristic
100C4×D4×C11C2311yescharacteristic
101C2×C11×C4⋊C4—21no—
102C2×C11×C4⋊C4—21no—
103C11×#107—21no—
104C11×#107—21no—
105C11×#107—21no—
106C11×#107—21no—
107C11×#107—21no—
108C11×#107D411yescharacteristic
109C11×#107D411yescharacteristic
110C11×#106—21no—
111C11×#106—21no—
112C11×C4⋊C8—21no—
113C11×C4⋊C8—21no—
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—41no—
124C11×#103D411yescharacteristic
125C11×#103D411yescharacteristic
126C11×#102—21no—
127C11×#102—21no—
128C11×#102—21no—
129C11×#102—21no—
130C11×#102—21no—
131C11×#102—21no—
132C11×#102—21no—
133C11×#102—21no—
134C11×#102—21no—
135C11×#102D411yescharacteristic
136C11×#102D411yescharacteristic
137C11×C22⋊C8—21no—
138C11×C22⋊C8—21no—
139C4×C8×C11—21no—
140C4×C8×C11—21no—
141C4×C8×C11C2311yescharacteristic
142C4×C8×C11C2311yescharacteristic
143C4×C8×C11C2311yescharacteristic
144#19781C1111yesmaximal, characteristic, direct product factor, Sylow
145C11×#41—42no—
146C11×#41—81no—
147C2×Q8×C11—21no—
148C2×Q8×C11—21no—
149C2×Q8×C11—21no—
150C2×Q8×C11—41no—
151C2×Q8×C11—42no—
152C2×Q8×C11—81no—
153C2×Q8×C11C2×D411yescharacteristic
154C2×Q8×C11C2×D411yescharacteristic
155C2×D4×C11—21no—
156C2×D4×C11—21no—
157C2×D4×C11—21no—
158C2×D4×C11—41no—
159C2×D4×C11—41no—
160C2×D4×C11C2×D411yescharacteristic
161C2×D4×C11C2×D411yescharacteristic
162C22×C4×C11—21no—
163C22×C4×C11—21no—
164C22×C4×C11—41no—
165C22×C4×C11—41no—
166C22×C4×C11—41no—
167C22×C4×C11—41no—
168C11×Q16—22no—
169C11×Q16—81no—
170C11×SD16—81no—
171C11×SD16—82no—
172C11×D8—22no—
173C11×D8—42no—
174C11×M16—81no—
175C2×C8×C11—21no—
176C2×C8×C11—21no—
177C2×C8×C11—21no—
178C2×C8×C11—21no—
179C2×C8×C11—21no—
180C2×C8×C11—81no—
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⋊C4—41no—
196C11×C4⋊C4—41no—
197C11×C4⋊C4—41no—
198C11×C4⋊C4C2×D411yescharacteristic
199C11×C4⋊C4C2×D411yescharacteristic
200C11×C4⋊C4C2×D411yescharacteristic
201C11×C4⋊C4C2×D411yescharacteristic
202C11×C22⋊C4—21no—
203C11×C22⋊C4—21no—
204C11×C22⋊C4—41no—
205C11×C22⋊C4—41no—
206C11×C22⋊C4—41no—
207C11×C22⋊C4—41no—
208C42×C11—21no—
209C42×C11—21no—
210C42×C11C2411yescharacteristic
211#3380C2×C1111yescharacteristic, complemented
212#3358C2×C1111yescharacteristic
213#3333C2×C1111yescharacteristic, complemented
214#3299C2×C1111yescharacteristic, complemented
215#1719C2×C1111yescharacteristic, complemented
216#1703C2×C1111yescharacteristic, complemented
217#1682C2×C1111yescharacteristic, complemented
218#1677C2×C1111yescharacteristic, complemented
219#1676C2×C1111yescharacteristic, complemented
220#1644C2×C1111yescharacteristic, complemented
221#1637C2×C1111yescharacteristic, complemented
222#1631C2×C1111yescharacteristic, complemented
223#1622C2×C1111yescharacteristic, complemented
224#1581C2×C1111yescharacteristic, complemented
225#1579C2×C1111yescharacteristic, complemented
226C23×C11—21no—
227C23×C11—21no—
228C23×C11—41no—
229Q8×C11—21no—
230Q8×C11—21no—
231Q8×C11—21no—
232Q8×C11—41no—
233Q8×C11—41no—
234Q8×C11—82no—
235Q8×C11—81no—
236Q8×C11—81no—
237Q8×C11#13512yes—
238D4×C11—21no—
239D4×C11—21no—
240D4×C11—21no—
241D4×C11—41no—
242D4×C11—41no—
243D4×C11—41no—
244D4×C11—41no—
245D4×C11—82no—
246D4×C11—81no—
247D4×C11—161no—
248D4×C11#13712yes—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11—82no—
263C2×C4×C11—82no—
264C2×C4×C11—161no—
265C2×C4×C11—161no—
266C2×C4×C11C22×D411yescharacteristic
267C2×C4×C11C22×D411yescharacteristic
268C2×C4×C11H(5,𝔽2)11yescharacteristic
269C8×C11—21no—
270C8×C11—21no—
271C8×C11—21no—
272C8×C11—21no—
273C8×C11—41no—
274C8×C11—41no—
275C8×C11—41no—
276C8×C11—41no—
277C8×C11—41no—
278#554C22×C1111yescharacteristic
279#554C22×C1111yescharacteristic
280#550C22×C1111yescharacteristic
281D4×Q8C22×C1111yescharacteristic
282#500C22×C1111yescharacteristic
283#499—21no—
284#492C22×C1111yescharacteristic
285#487C22×C1111yescharacteristic
286#487C22×C1111yescharacteristic
287#486—21no—
288#486C22×C1111yescharacteristic
289#486C22×C1111yescharacteristic
290#484—21no—
291#480—21no—
292#478—21no—
293#478—21no—
294#477C22×C1111yescharacteristic
295#477C22×C1111yescharacteristic
296#476C22×C1111yescharacteristic
297#476C22×C1111yescharacteristic
298#474—21no—
299#474C22×C1111yescharacteristic
300#468—21no—
301#467—21no—
302#462C22×C1111yescharacteristic
303#460C22×C1111yescharacteristic
304#459—21no—
305#459C22×C1111yescharacteristic
306#452—21no—
307#451—21no—
308C8×Q8C22×C1111yescharacteristic
309C8×Q8C22×C1111yescharacteristic
310C4×Q16C22×C1111yescharacteristic
311C4×D8—21no—
312C4×D8—21no—
313C4×D8C22×C1111yescharacteristic
314#436C22×C1111yescharacteristic
315C8×D4C22×C1111yescharacteristic
316#417—21no—
317C2×#103—21no—
318#335C22×C1111yescharacteristic
319#334C22×C1111yescharacteristic
320#333C22×C1111yescharacteristic
321#333C22×C1111yescharacteristic
322#332C22×C1111yescharacteristic
323#331C22×C1111yescharacteristic
324Q8⋊C8C22×C1111yescharacteristic
325Q8⋊C8C22×C1111yescharacteristic
326D4⋊C8C22×C1111yescharacteristic
327D4⋊C8C22×C1111yescharacteristic
328#322C22×C1111yescharacteristic
329C22×C11—22no—
330C22×C11—41no—
331C22×C11—41no—
332C22×C11—41no—
333C22×C11—41no—
334C22×C11—41no—
335C22×C11—81no—
336C22×C11—81no—
337C22×C11—81no—
338C22×C11D4211yescharacteristic
339C4×C11—22no—
340C4×C11—21no—
341C4×C11—41no—
342C4×C11—41no—
343C4×C11—41no—
344C4×C11—41no—
345C4×C11—41no—
346C4×C11—81no—
347C4×C11—81no—
348C4×C11—81no—
349C4×C11C2×#13511yescharacteristic
350C4×C11C2×#13711yescharacteristic
351C4×C11#57611yescharacteristic
352C4×C11#57811yescharacteristic
353C2×#41—21no—
354C22×Q8—21no—
355C2×Q16—21no—
356C2×Q16D4×C1111yescharacteristic
357C2×SD16—21no—
358C2×SD16—41no—
359C2×D8—21no—
360C2×D8D4×C1111yescharacteristic
361C2×M16—21no—
362C22×C8—21no—
363C4⋊Q8—21no—
364C4⋊Q8C23×C1111yescharacteristic
365C4⋊Q8C23×C1111yescharacteristic
366C4⋊Q8C23×C1111yescharacteristic
367#127—21no—
368#127C23×C1111yescharacteristic
369#125—21no—
370#125—21no—
371C22⋊Q8—21no—
372C22⋊Q8—21no—
373C22⋊Q8—21no—
374C22⋊Q8—41no—
375C22⋊Q8—41no—
376C22⋊Q8—41no—
377#121—21no—
378#121—41no—
379C4×Q8C23×C1111yescharacteristic
380C4×Q8C23×C1111yescharacteristic
381C4×D4—21no—
382C4×D4—21no—
383C4×D4—21no—
384C4×D4—21no—
385C4×D4C23×C1111yescharacteristic
386C4×D4C23×C1111yescharacteristic
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389#107—21no—
390#107—21no—
391#107—21no—
392#107—21no—
393#107—21no—
394#107D4×C1111yescharacteristic
395#107D4×C1111yescharacteristic
396#106—21no—
397#106—21no—
398C4⋊C8—21no—
399C4⋊C8—21no—
400C4⋊C8C23×C1111yescharacteristic
401C4⋊C8C23×C1111yescharacteristic
402C4⋊C8C23×C1111yescharacteristic
403C4⋊C8C23×C1111yescharacteristic
404#103—21no—
405#103—21no—
406#103—21no—
407#103—21no—
408#103—21no—
409#103—41no—
410#103D4×C1111yescharacteristic
411#103D4×C1111yescharacteristic
412#102—21no—
413#102—21no—
414#102—21no—
415#102—21no—
416#102—21no—
417#102—21no—
418#102—21no—
419#102—21no—
420#102—21no—
421#102D4×C1111yescharacteristic
422#102D4×C1111yescharacteristic
423C22⋊C8—21no—
424C22⋊C8—21no—
425C4×C8—21no—
426C4×C8—21no—
427C4×C8C23×C1111yescharacteristic
428C4×C8C23×C1111yescharacteristic
429C4×C8C23×C1111yescharacteristic
430C2×C11—42no—
431C2×C11—81no—
432C2×C11—161no—
433C2×C11#327011yescharacteristic
434C2×C11#328011yescharacteristic
435C2×C11#328811yescharacteristic
436#41—42no—
437#41—81no—
438C2×Q8—21no—
439C2×Q8—21no—
440C2×Q8—21no—
441C2×Q8—41no—
442C2×Q8—42no—
443C2×Q8—81no—
444C2×Q8C2×D4×C1111yescharacteristic
445C2×Q8C2×D4×C1111yescharacteristic
446C2×D4—21no—
447C2×D4—21no—
448C2×D4—21no—
449C2×D4—41no—
450C2×D4—41no—
451C2×D4C2×D4×C1111yescharacteristic
452C2×D4C2×D4×C1111yescharacteristic
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—41no—
456C22×C4—41no—
457C22×C4—41no—
458C22×C4—41no—
459Q16—22no—
460Q16—81no—
461SD16—81no—
462SD16—82no—
463D8—22no—
464D8—42no—
465M16—81no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—81no—
472C2×C8C2×D4×C1111yescharacteristic
473C2×C8C2×D4×C1111yescharacteristic
474C2×C8C2×D4×C1111yescharacteristic
475C2×C8C2×D4×C1111yescharacteristic
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—41no—
485C4⋊C4—41no—
486C4⋊C4—41no—
487C4⋊C4—41no—
488C4⋊C4—41no—
489C4⋊C4C2×D4×C1111yescharacteristic
490C4⋊C4C2×D4×C1111yescharacteristic
491C4⋊C4C2×D4×C1111yescharacteristic
492C4⋊C4C2×D4×C1111yescharacteristic
493C22⋊C4—21no—
494C22⋊C4—21no—
495C22⋊C4—41no—
496C22⋊C4—41no—
497C22⋊C4—41no—
498C22⋊C4—41no—
499C42—21no—
500C42—21no—
501C42C24×C1111yescharacteristic
502C11#1978111yescharacteristic, direct product factor, Sylow
503C23—21no—
504C23—21no—
505C23—41no—
506Q8—21no—
507Q8—21no—
508Q8—21no—
509Q8—41no—
510Q8—41no—
511Q8—82no—
512Q8—81no—
513Q8—81no—
514Q8C11×#13512yes—
515D4—21no—
516D4—21no—
517D4—21no—
518D4—41no—
519D4—41no—
520D4—41no—
521D4—41no—
522D4—82no—
523D4—81no—
524D4—161no—
525D4C11×#13712yes—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—82no—
540C2×C4—82no—
541C2×C4—161no—
542C2×C4—161no—
543C2×C4C22×D4×C1111yescharacteristic
544C2×C4C22×D4×C1111yescharacteristic
545C2×C4C11×H(5,𝔽2)11yescharacteristic
546C8—21no—
547C8—21no—
548C8—21no—
549C8—21no—
550C8—41no—
551C8—41no—
552C8—41no—
553C8—41no—
554C8—41no—
555C22—22no—
556C22—41no—
557C22—41no—
558C22—41no—
559C22—41no—
560C22—41no—
561C22—81no—
562C22—81no—
563C22—81no—
564C22D42×C1111yescharacteristic
565C4—22no—
566C4—21no—
567C4—41no—
568C4—41no—
569C4—41no—
570C4—41no—
571C4—41no—
572C4—81no—
573C4—81no—
574C4—81no—
575C4C2×C11×#13511yescharacteristic
576C4C2×C11×#13711yescharacteristic
577C4C11×#57611yescharacteristic
578C4C11×#57811yescharacteristic
579C2—42no—
580C2—81no—
581C2—161no—
582C2C11×#327011yescharacteristic
583C2C11×#328011yescharacteristic
584C2C11×#328811yescharacteristic
subgroupG/H
center, socleC22×C11D42
commutator, Frattini, cosocleC42C24×C11
prime radicalC11×#3358C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3380C2semidirect
3. C11×#3333C2semidirect
4. C11×#3299C2semidirect
5. C11×#1719C2semidirect
6. C11×#1703C2semidirect
7. C11×#1682C2semidirect
8. C11×#1677C2semidirect
9. C11×#1676C2semidirect
10. C11×#1644C2semidirect
11. C11×#1637C2semidirect
12. C11×#1631C2semidirect
13. C11×#1622C2semidirect
14. C11×#1581C2semidirect
15. C11×#1579C2semidirect
144. #19781C11direct (N × H)
211. #3380C2×C11semidirect
213. #3333C2×C11semidirect
214. #3299C2×C11semidirect
215. #1719C2×C11semidirect
216. #1703C2×C11semidirect
217. #1682C2×C11semidirect
218. #1677C2×C11semidirect
219. #1676C2×C11semidirect
220. #1644C2×C11semidirect
221. #1637C2×C11semidirect
222. #1631C2×C11semidirect
223. #1622C2×C11semidirect
224. #1581C2×C11semidirect
225. #1579C2×C11semidirect
502. C11#19781direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#33802
C11×#33582
C11×#33332
C11×#32992
C11×#17192
C11×#17032
C11×#16822
C11×#16772
C11×#16762
C11×#16442
C11×#16372
C11×#16312
C11×#16222
C11×#15812
C11×#15792
#1978111