Finite Group Databasebeta

← C11×#19221 #14596414

Subgroups — C11×#19221 #14596414

Order 2816.

606 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×#3248C211yesmaximal, characteristic, complemented
2C11×#3247C211yesmaximal, characteristic
3C11×#3167C211yesmaximal, characteristic, complemented
4C11×#2966C211yesmaximal, characteristic, complemented
5C11×#1704C211yesmaximal, characteristic, complemented
6C11×#1703C211yesmaximal, characteristic, complemented
7C11×#1702C211yesmaximal, characteristic, complemented
8C11×#1701C211yesmaximal, characteristic, complemented
9C11×#1672C211yesmaximal, characteristic, complemented
10C11×#1671C211yesmaximal, characteristic, complemented
11C11×#1666C211yesmaximal, characteristic, complemented
12C11×#1665C211yesmaximal, characteristic, complemented
13C2×C11×#334C211yesmaximal, characteristic, complemented
14C11×#1552C211yesmaximal, characteristic, complemented
15C11×#1551C211yesmaximal, characteristic, complemented
16C11×#533C2211yescharacteristic
17C11×#532C2211yescharacteristic
18C11×#529C2211yescharacteristic
19C11×#498C2211yescharacteristic
20C11×#492C2211yescharacteristic
21C11×#487C2211yescharacteristic
22C11×#486C2211yescharacteristic
23C11×#479—21no—
24C11×#478—21no—
25C11×#477C2211yescharacteristic
26C11×#476C2211yescharacteristic
27C11×#475C2211yescharacteristic
28C11×#474C2211yescharacteristic
29C11×#467—21no—
30C11×#466—21no—
31C11×#465—21no—
32C11×#465—21no—
33C11×#465—21no—
34C11×#465—21no—
35C11×#464—21no—
36C11×#463—21no—
37C11×#462C2211yescharacteristic
38C11×#461C2211yescharacteristic
39C11×#460C2211yescharacteristic
40C11×#459C2211yescharacteristic
41C11×#446C2211yescharacteristic
42C8×Q8×C11C2211yescharacteristic
43C4×C11×SD16—21no—
44C4×C11×SD16—21no—
45C11×#436C2211yescharacteristic
46C11×#435—21no—
47C8×D4×C11—21no—
48C8×D4×C11C2211yescharacteristic
49C11×#433—21no—
50C11×#432C2211yescharacteristic
51C2×C11×C4⋊C8C2211yescharacteristic
52C2×C11×C4⋊C8C2211yescharacteristic
53C11×#405—21no—
54C2×C4×C8×C11C2211yescharacteristic
55C11×#334C2211yescharacteristic
56C11×#334C2211yescharacteristic
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×Q16—21no—
69C2×C11×SD16—21no—
70C2×C11×SD16—21no—
71C2×C11×SD16—21no—
72C2×C11×SD16—21no—
73C2×C11×D8—21no—
74C2×C11×M16—21no—
75C22×C8×C11—21no—
76C22×C8×C11—21no—
77C22×C8×C11—21no—
78C22×C8×C11D411yescharacteristic
79C22×C8×C11D411yescharacteristic
80C11×C4⋊Q8C2311yescharacteristic
81C11×C4⋊Q8C2311yescharacteristic
82C11×C4⋊Q8C2311yescharacteristic
83C11×#127C2311yescharacteristic
84C11×#126—21no—
85C11×#125—21no—
86C11×#125D411yescharacteristic
87C11×#124—21no—
88C11×#124D411yescharacteristic
89C11×#123—21no—
90C11×C22⋊Q8—21no—
91C11×C22⋊Q8—21no—
92C11×C22⋊Q8D411yescharacteristic
93C11×#121—21no—
94C11×#121—21no—
95C11×#121D411yescharacteristic
96C4×Q8×C11—21no—
97C4×Q8×C11—21no—
98C4×Q8×C11C2311yescharacteristic
99C4×D4×C11—21no—
100C4×D4×C11—21no—
101C4×D4×C11—21no—
102C4×D4×C11C2311yescharacteristic
103C11×#117—21no—
104C11×#117—21no—
105C2×C42×C11C2311yescharacteristic
106C11×#107—21no—
107C11×#107—21no—
108C11×#106—21no—
109C11×#106—21no—
110C11×#106—21no—
111C11×#106—21no—
112C11×C4⋊C8—21no—
113C11×C4⋊C8—21no—
114C11×C4⋊C8—21no—
115C11×C4⋊C8—21no—
116C11×C4⋊C8C2311yescharacteristic
117C11×C4⋊C8C2311yescharacteristic
118C11×C4⋊C8C2311yescharacteristic
119C11×C4⋊C8C2311yescharacteristic
120C11×C4⋊C8C2311yescharacteristic
121C11×C4⋊C8C2311yescharacteristic
122C11×#103—21no—
123C11×#103—21no—
124C11×#103—21no—
125C11×#103—21no—
126C11×#103—21no—
127C11×#103—21no—
128C11×#102—21no—
129C11×#102—21no—
130C11×#102—21no—
131C11×#102—21no—
132C11×#102—21no—
133C11×#102—21no—
134C11×C22⋊C8—21no—
135C11×C22⋊C8—21no—
136C11×C22⋊C8—21no—
137C11×#97—21no—
138C11×#97—21no—
139C4×C8×C11—21no—
140C4×C8×C11D411yescharacteristic
141C4×C8×C11D411yescharacteristic
142C4×C8×C11C2311yescharacteristic
143C4×C8×C11C2311yescharacteristic
144#19221C1111yesmaximal, characteristic, direct product factor, Sylow
145C11×#41—82no—
146C2×Q8×C11—21no—
147C2×Q8×C11—21no—
148C2×Q8×C11—21no—
149C2×Q8×C11C2×D411yescharacteristic
150C2×D4×C11—21no—
151C2×D4×C11—21no—
152C2×D4×C11—21no—
153C2×D4×C11—21no—
154C2×D4×C11—41no—
155C2×D4×C11C2×D411yescharacteristic
156C22×C4×C11—21no—
157C22×C4×C11—41no—
158C22×C4×C11C2×D411yescharacteristic
159C22×C4×C11C2×D411yescharacteristic
160C22×C4×C11#4111yescharacteristic
161C11×Q16—81no—
162C11×SD16—42no—
163C11×SD16—42no—
164C11×SD16—81no—
165C11×SD16—81no—
166C11×D8—81no—
167C11×M16—42no—
168C2×C8×C11—22no—
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—41no—
176C2×C8×C11—42no—
177C2×C8×C11—81no—
178C2×C8×C11—81no—
179C2×C8×C11C2×D411yescharacteristic
180C2×C8×C11C2×D411yescharacteristic
181C2×C8×C11C2×D411yescharacteristic
182C2×C8×C11C2×D411yescharacteristic
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—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—21no—
201C11×C22⋊C4—21no—
202C11×C22⋊C4—41no—
203C11×C22⋊C4—41no—
204C11×C22⋊C4—41no—
205C42×C11—21no—
206C42×C11—41no—
207C42×C11C2×D411yescharacteristic
208C42×C11C2×D411yescharacteristic
209C42×C11#4111yescharacteristic
210C42×C11C2411yescharacteristic
211#3248C2×C1111yescharacteristic, complemented
212#3247C2×C1111yescharacteristic
213#3167C2×C1111yescharacteristic, complemented
214#2966C2×C1111yescharacteristic, complemented
215#1704C2×C1111yescharacteristic, complemented
216#1703C2×C1111yescharacteristic, complemented
217#1702C2×C1111yescharacteristic, complemented
218#1701C2×C1111yescharacteristic, complemented
219#1672C2×C1111yescharacteristic, complemented
220#1671C2×C1111yescharacteristic, complemented
221#1666C2×C1111yescharacteristic, complemented
222#1665C2×C1111yescharacteristic, complemented
223C2×#334C2×C1111yescharacteristic, complemented
224#1552C2×C1111yescharacteristic, complemented
225#1551C2×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—22no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
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
277#529C22×C1111yescharacteristic
278#498C22×C1111yescharacteristic
279#492C22×C1111yescharacteristic
280#487C22×C1111yescharacteristic
281#486C22×C1111yescharacteristic
282#479—21no—
283#478—21no—
284#477C22×C1111yescharacteristic
285#476C22×C1111yescharacteristic
286#475C22×C1111yescharacteristic
287#474C22×C1111yescharacteristic
288#467—21no—
289#466—21no—
290#465—21no—
291#465—21no—
292#465—21no—
293#465—21no—
294#464—21no—
295#463—21no—
296#462C22×C1111yescharacteristic
297#461C22×C1111yescharacteristic
298#460C22×C1111yescharacteristic
299#459C22×C1111yescharacteristic
300#446C22×C1111yescharacteristic
301C8×Q8C22×C1111yescharacteristic
302C4×SD16—21no—
303C4×SD16—21no—
304#436C22×C1111yescharacteristic
305#435—21no—
306C8×D4—21no—
307C8×D4C22×C1111yescharacteristic
308#433—21no—
309#432C22×C1111yescharacteristic
310C2×C4⋊C8C22×C1111yescharacteristic
311C2×C4⋊C8C22×C1111yescharacteristic
312#405—21no—
313C2×C4×C8C22×C1111yescharacteristic
314#334C22×C1111yescharacteristic
315#334C22×C1111yescharacteristic
316#334C22×C1111yescharacteristic
317#334C22×C1111yescharacteristic
318#333C22×C1111yescharacteristic
319#333C22×C1111yescharacteristic
320#332C22×C1111yescharacteristic
321#332C22×C1111yescharacteristic
322#332C22×C1111yescharacteristic
323#332C22×C1111yescharacteristic
324#331C22×C1111yescharacteristic
325#331C22×C1111yescharacteristic
326C22×C11—21no—
327C22×C11—21no—
328C22×C11—41no—
329C22×C11—41no—
330C22×C11—41no—
331C22×C11—81no—
332C22×C11—81no—
333C22×C11—81no—
334C22×C11#47112yes—
335C22×C11C2×#12111yescharacteristic
336C4×C11—21no—
337C4×C11—21no—
338C4×C11—21no—
339C4×C11—21no—
340C4×C11—41no—
341C4×C11—41no—
342C4×C11—41no—
343C4×C11—81no—
344C4×C11—81no—
345C4×C11—81no—
346C4×C11C2×#13511yescharacteristic
347C4×C11#57511yescharacteristic
348C4×C11#57711yescharacteristic
349C4×C11#57711yescharacteristic
350C2×#41—21no—
351C2×Q16—21no—
352C2×SD16—21no—
353C2×SD16—21no—
354C2×SD16—21no—
355C2×SD16—21no—
356C2×D8—21no—
357C2×M16—21no—
358C22×C8—21no—
359C22×C8—21no—
360C22×C8—21no—
361C22×C8D4×C1111yescharacteristic
362C22×C8D4×C1111yescharacteristic
363C4⋊Q8C23×C1111yescharacteristic
364C4⋊Q8C23×C1111yescharacteristic
365C4⋊Q8C23×C1111yescharacteristic
366#127C23×C1111yescharacteristic
367#126—21no—
368#125—21no—
369#125D4×C1111yescharacteristic
370#124—21no—
371#124D4×C1111yescharacteristic
372#123—21no—
373C22⋊Q8—21no—
374C22⋊Q8—21no—
375C22⋊Q8D4×C1111yescharacteristic
376#121—21no—
377#121—21no—
378#121D4×C1111yescharacteristic
379C4×Q8—21no—
380C4×Q8—21no—
381C4×Q8C23×C1111yescharacteristic
382C4×D4—21no—
383C4×D4—21no—
384C4×D4—21no—
385C4×D4C23×C1111yescharacteristic
386#117—21no—
387#117—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⋊C8—21no—
398C4⋊C8—21no—
399C4⋊C8C23×C1111yescharacteristic
400C4⋊C8C23×C1111yescharacteristic
401C4⋊C8C23×C1111yescharacteristic
402C4⋊C8C23×C1111yescharacteristic
403C4⋊C8C23×C1111yescharacteristic
404C4⋊C8C23×C1111yescharacteristic
405#103—21no—
406#103—21no—
407#103—21no—
408#103—21no—
409#103—21no—
410#103—21no—
411#102—21no—
412#102—21no—
413#102—21no—
414#102—21no—
415#102—21no—
416#102—21no—
417C22⋊C8—21no—
418C22⋊C8—21no—
419C22⋊C8—21no—
420#97—21no—
421#97—21no—
422C4×C8—21no—
423C4×C8D4×C1111yescharacteristic
424C4×C8D4×C1111yescharacteristic
425C4×C8C23×C1111yescharacteristic
426C4×C8C23×C1111yescharacteristic
427C2×C11—22no—
428C2×C11—81no—
429C2×C11—161no—
430C2×C11#303511yescharacteristic
431C2×C11#306011yescharacteristic
432C2×C11C2×#47111yescharacteristic
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—41no—
446C22×C4C2×D4×C1111yescharacteristic
447C22×C4C2×D4×C1111yescharacteristic
448C22×C4C11×#4111yescharacteristic
449Q16—81no—
450SD16—42no—
451SD16—42no—
452SD16—81no—
453SD16—81no—
454D8—81no—
455M16—42no—
456C2×C8—22no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—41no—
464C2×C8—42no—
465C2×C8—81no—
466C2×C8—81no—
467C2×C8C2×D4×C1111yescharacteristic
468C2×C8C2×D4×C1111yescharacteristic
469C2×C8C2×D4×C1111yescharacteristic
470C2×C8C2×D4×C1111yescharacteristic
471C4⋊C4—21no—
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—21no—
481C4⋊C4—41no—
482C4⋊C4—41no—
483C4⋊C4C2×D4×C1111yescharacteristic
484C4⋊C4C2×D4×C1111yescharacteristic
485C22⋊C4—21no—
486C22⋊C4—21no—
487C22⋊C4—21no—
488C22⋊C4—21no—
489C22⋊C4—21no—
490C22⋊C4—41no—
491C22⋊C4—41no—
492C22⋊C4—41no—
493C42—21no—
494C42—41no—
495C42C2×D4×C1111yescharacteristic
496C42C2×D4×C1111yescharacteristic
497C42C11×#4111yescharacteristic
498C42C24×C1111yescharacteristic
499C11#1922111yescharacteristic, direct product factor, Sylow
500C23—21no—
501C23—41no—
502C23C11×#12111yescharacteristic
503Q8—21no—
504Q8—21no—
505Q8—41no—
506Q8—41no—
507Q8—41no—
508Q8—41no—
509Q8—81no—
510D4—21no—
511D4—21no—
512D4—42no—
513D4—41no—
514D4—41no—
515D4—41no—
516D4—41no—
517D4—81no—
518D4—82no—
519C2×C4—22no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
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—41no—
552C22—41no—
553C22—41no—
554C22—81no—
555C22—81no—
556C22—81no—
557C22C11×#47112yes—
558C22C2×C11×#12111yescharacteristic
559C4—21no—
560C4—21no—
561C4—21no—
562C4—21no—
563C4—41no—
564C4—41no—
565C4—41no—
566C4—81no—
567C4—81no—
568C4—81no—
569C4C2×C11×#13511yescharacteristic
570C4C11×#57511yescharacteristic
571C4C11×#57711yescharacteristic
572C4C11×#57711yescharacteristic
573C2—22no—
574C2—81no—
575C2—161no—
576C2C11×#303511yescharacteristic
577C2C11×#306011yescharacteristic
578C2C2×C11×#47111yescharacteristic
subgroupG/H
center, socleC22×C11C2×#121
commutator, Frattini, cosocleC42C24×C11
prime radicalC11×#3247C2
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×#3248C2semidirect
3. C11×#3167C2semidirect
4. C11×#2966C2semidirect
5. C11×#1704C2semidirect
6. C11×#1703C2semidirect
7. C11×#1702C2semidirect
8. C11×#1701C2semidirect
9. C11×#1672C2semidirect
10. C11×#1671C2semidirect
11. C11×#1666C2semidirect
12. C11×#1665C2semidirect
13. C2×C11×#334C2semidirect
14. C11×#1552C2semidirect
15. C11×#1551C2semidirect
144. #19221C11direct (N × H)
211. #3248C2×C11semidirect
213. #3167C2×C11semidirect
214. #2966C2×C11semidirect
215. #1704C2×C11semidirect
216. #1703C2×C11semidirect
217. #1702C2×C11semidirect
218. #1701C2×C11semidirect
219. #1672C2×C11semidirect
220. #1671C2×C11semidirect
221. #1666C2×C11semidirect
222. #1665C2×C11semidirect
223. C2×#334C2×C11semidirect
224. #1552C2×C11semidirect
225. #1551C2×C11semidirect
499. C11#19221direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#32482
C11×#32472
C11×#31672
C11×#29662
C11×#17042
C11×#17032
C11×#17022
C11×#17012
C11×#16722
C11×#16712
C11×#16662
C11×#16652
C2×C11×#3342
C11×#15522
C11×#15512
#1922111