Finite Group Databasebeta

← C11×#18883 #14596076

Subgroups — C11×#18883 #14596076

Order 2816.

1096 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3499C211yesmaximal, characteristic
2C11×#3246C211yesmaximal, characteristic, complemented
3C11×#3229C211yesmaximal, characteristic, complemented
4C11×#3076C211yesmaximal, characteristic, complemented
5C11×#1654C212yesmaximal, complemented
6C11×#1651C212yesmaximal, complemented
7C11×#1637C212yesmaximal, complemented
8C11×#1635C212yesmaximal, complemented
9C2×C11×#332C211yesmaximal, characteristic, complemented
10C11×#1480C211yesmaximal, characteristic, complemented
11C11×#1477C211yesmaximal, characteristic, complemented
12C2×C11×2−1+4—21no—
13D4×Q8×C11—21no—
14D4×Q8×C11C2212yes—
15C11×#547—22no—
16C11×#547—21no—
17C11×#547—22no—
18C11×#547C2212yes—
19C11×#536—22no—
20C11×#536—21no—
21C11×#533C2211yescharacteristic
22C11×#532—21no—
23C11×#532C2211yescharacteristic
24C2×C11×C4⋊Q8—21no—
25C2×C11×C4⋊Q8C2211yescharacteristic
26C4×C11×#41C2211yescharacteristic
27C11×#498C2212yes—
28C11×#487C2212yes—
29C11×#483—22no—
30C11×#479—21no—
31C11×#478—21no—
32C11×#477C2211yescharacteristic
33C11×#476C2211yescharacteristic
34C11×#476C2212yes—
35C11×#475—22no—
36C11×#475—21no—
37C11×#475C2211yescharacteristic
38C11×#474C2211yescharacteristic
39C11×#465—22no—
40C11×#461C2212yes—
41C11×#460—21no—
42C11×#431C2211yescharacteristic
43C11×#427—21no—
44C2×C11×C4⋊C8C2211yescharacteristic
45C2×C11×C4⋊C8C2211yescharacteristic
46C11×#416—21no—
47C11×#332C2212yes—
48C11×#332C2212yes—
49C11×Q8⋊C8C2212yes—
50C11×D4⋊C8C2212yes—
51C11×D4⋊C8C2212yes—
52C11×D4⋊C8C2212yes—
53C11×2−1+4—44no—
54C11×2−1+4—44no—
55C2×C11×#41—22no—
56C2×C11×#41—24no—
57C2×C11×#41—22no—
58C2×C11×#41—21no—
59C2×C11×#41D411yescharacteristic
60C22×Q8×C11—22no—
61C22×Q8×C11—22no—
62C22×Q8×C11—21no—
63C2×C11×SD16—22no—
64C22×C8×C11—21no—
65C22×C8×C11—21no—
66C11×C4⋊Q8—22no—
67C11×C4⋊Q8—22no—
68C11×C4⋊Q8—22no—
69C11×C4⋊Q8—21no—
70C11×C4⋊Q8—21no—
71C11×C4⋊Q8D411yescharacteristic
72C11×C4⋊Q8D412yes—
73C11×C4⋊Q8C2311yescharacteristic
74C11×C4⋊Q8C2311yescharacteristic
75C11×C4⋊Q8C2312yes—
76C11×#127D411yescharacteristic
77C11×#125—21no—
78C11×#124—22no—
79C11×#124—21no—
80C11×#123—24no—
81C11×#123—24no—
82C11×#123—24no—
83C11×C22⋊Q8—24no—
84C11×C22⋊Q8—22no—
85C11×C22⋊Q8—24no—
86C11×C22⋊Q8—22no—
87C11×C22⋊Q8—21no—
88C11×C22⋊Q8—21no—
89C11×#121—22no—
90C11×#121—22no—
91C11×#121—21no—
92C11×#121D412yes—
93C4×Q8×C11—21no—
94C4×Q8×C11—21no—
95C4×Q8×C11D411yescharacteristic
96C4×Q8×C11C2311yescharacteristic
97C4×D4×C11—22no—
98C4×D4×C11—22no—
99C4×D4×C11—21no—
100C4×D4×C11—21no—
101C4×D4×C11—21no—
102C4×D4×C11D411yescharacteristic
103C4×D4×C11C2311yescharacteristic
104C4×D4×C11C2312yes—
105C11×#117—21no—
106C11×#117—21no—
107C11×#117D411yescharacteristic
108C2×C11×C4⋊C4—22no—
109C2×C11×C4⋊C4—21no—
110C2×C11×C4⋊C4—22no—
111C2×C11×C4⋊C4D412yes—
112C2×C42×C11—21no—
113C2×C42×C11C2311yescharacteristic
114C11×#107—21no—
115C11×#107—21no—
116C11×#106—24no—
117C11×#106—21no—
118C11×#106—21no—
119C11×#106—22no—
120C11×C4⋊C8—21no—
121C11×C4⋊C8—21no—
122C11×C4⋊C8—21no—
123C11×C4⋊C8C2311yescharacteristic
124C11×C4⋊C8C2311yescharacteristic
125C11×C4⋊C8C2312yes—
126C11×#103—21no—
127C11×#103—21no—
128C11×#103—22no—
129C11×#103—24no—
130C11×#102—21no—
131C11×#102—21no—
132C11×#102—22no—
133C11×C22⋊C8—21no—
134C4×C8×C11C2312yes—
135#18883C1111yesmaximal, characteristic, direct product factor, Sylow
136C11×#41—22no—
137C11×#41—48no—
138C11×#41—416no—
139C11×#41—44no—
140C11×#41—44no—
141C11×#41—42no—
142C11×#41—42no—
143C11×#41SD1614yescomplemented
144C2×Q8×C11—24no—
145C2×Q8×C11—22no—
146C2×Q8×C11—21no—
147C2×Q8×C11—22no—
148C2×Q8×C11—21no—
149C2×Q8×C11—21no—
150C2×Q8×C11—48no—
151C2×Q8×C11—44no—
152C2×Q8×C11—44no—
153C2×Q8×C11—42no—
154C2×Q8×C11—42no—
155C2×Q8×C11C2×D411yescharacteristic
156C2×D4×C11—21no—
157C2×D4×C11—24no—
158C2×D4×C11—22no—
159C2×D4×C11—21no—
160C2×D4×C11—21no—
161C2×D4×C11C2×D412yes—
162C2×D4×C11C2×D411yescharacteristic
163C22×C4×C11—21no—
164C22×C4×C11—24no—
165C22×C4×C11—24no—
166C22×C4×C11—22no—
167C22×C4×C11—21no—
168C22×C4×C11—21no—
169C22×C4×C11—22no—
170C22×C4×C11C2×D411yescharacteristic
171C22×C4×C11C2×D411yescharacteristic
172C22×C4×C11C2×D411yescharacteristic
173C11×SD16—82no—
174C2×C8×C11—22no—
175C2×C8×C11—21no—
176C2×C8×C11—22no—
177C2×C8×C11—21no—
178C2×C8×C11—42no—
179C2×C8×C11—81no—
180C11×C4⋊C4—24no—
181C11×C4⋊C4—24no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—22no—
184C11×C4⋊C4—22no—
185C11×C4⋊C4—21no—
186C11×C4⋊C4—22no—
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×D412yes—
195C11×C4⋊C4C2×D414yes—
196C11×C4⋊C4C2×D411yescharacteristic
197C11×C4⋊C4C2×D411yescharacteristic
198C11×C22⋊C4—24no—
199C11×C22⋊C4—24no—
200C11×C22⋊C4—21no—
201C11×C22⋊C4—21no—
202C11×C22⋊C4—22no—
203C11×C22⋊C4—21no—
204C11×C22⋊C4—22no—
205C11×C22⋊C4—41no—
206C42×C11—21no—
207C42×C11—21no—
208C42×C11—21no—
209C42×C11—41no—
210C42×C11C2×D411yescharacteristic
211C42×C11C2×D411yescharacteristic
212C42×C11C2×D411yescharacteristic
213C42×C11C2411yescharacteristic
214#3499C2×C1111yescharacteristic
215#3246C2×C1111yescharacteristic, complemented
216#3229C2×C1111yescharacteristic, complemented
217#3076C2×C1111yescharacteristic, complemented
218#1654C2×C1112yescomplemented
219#1651C2×C1112yescomplemented
220#1637C2×C1112yescomplemented
221#1635C2×C1112yescomplemented
222C2×#332C2×C1111yescharacteristic, complemented
223#1480C2×C1111yescharacteristic, complemented
224#1477C2×C1111yescharacteristic, complemented
225C23×C11—21no—
226C23×C11—22no—
227C23×C11#12011yescharacteristic
228Q8×C11—21no—
229Q8×C11—48no—
230Q8×C11—42no—
231Q8×C11—42no—
232Q8×C11—42no—
233Q8×C11—42no—
234Q8×C11—44no—
235Q8×C11—41no—
236Q8×C11—41no—
237Q8×C11C2×SD1612yes—
238D4×C11—24no—
239D4×C11—21no—
240D4×C11—22no—
241D4×C11—22no—
242D4×C11—42no—
243D4×C11—48no—
244D4×C11—44no—
245D4×C11—42no—
246D4×C11C2×SD1612yes—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—24no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—24no—
254C2×C4×C11—22no—
255C2×C4×C11—41no—
256C2×C4×C11—42no—
257C2×C4×C11—48no—
258C2×C4×C11—48no—
259C2×C4×C11—44no—
260C2×C4×C11—42no—
261C2×C4×C11—42no—
262C2×C4×C11—41no—
263C2×C4×C11—41no—
264C2×C4×C11—41no—
265C2×C4×C11—41no—
266C2×C4×C11#12011yescharacteristic
267C2×C4×C11#12011yescharacteristic
268C2×C4×C11#12011yescharacteristic
269C2×C4×C11C2×SD1612yes—
270C2×C4×C11AGL(1,ℤ/8)12yes—
271C2×C4×C11C22×D411yescharacteristic
272C2×C4×C11C22×D411yescharacteristic
273C2×C4×C11C22×D411yescharacteristic
274C8×C11—42no—
275C8×C11—41no—
276C8×C11—41no—
277C8×C11—42no—
278C2×2−1+4—21no—
279D4×Q8—21no—
280D4×Q8C22×C1112yes—
281#547—22no—
282#547—21no—
283#547—22no—
284#547C22×C1112yes—
285#536—22no—
286#536—21no—
287#533C22×C1111yescharacteristic
288#532—21no—
289#532C22×C1111yescharacteristic
290C2×C4⋊Q8—21no—
291C2×C4⋊Q8C22×C1111yescharacteristic
292C4×#41C22×C1111yescharacteristic
293#498C22×C1112yes—
294#487C22×C1112yes—
295#483—22no—
296#479—21no—
297#478—21no—
298#477C22×C1111yescharacteristic
299#476C22×C1111yescharacteristic
300#476C22×C1112yes—
301#475—22no—
302#475—21no—
303#475C22×C1111yescharacteristic
304#474C22×C1111yescharacteristic
305#465—22no—
306#461C22×C1112yes—
307#460—21no—
308#431C22×C1111yescharacteristic
309#427—21no—
310C2×C4⋊C8C22×C1111yescharacteristic
311C2×C4⋊C8C22×C1111yescharacteristic
312#416—21no—
313#332C22×C1112yes—
314#332C22×C1112yes—
315Q8⋊C8C22×C1112yes—
316D4⋊C8C22×C1112yes—
317D4⋊C8C22×C1112yes—
318D4⋊C8C22×C1112yes—
319C22×C11—21no—
320C22×C11—21no—
321C22×C11—22no—
322C22×C11—41no—
323C22×C11—41no—
324C22×C11—42no—
325C22×C11—42no—
326C22×C11—42no—
327C22×C11#45012yes—
328C22×C11C2×#12011yescharacteristic
329C4×C11—22no—
330C4×C11—21no—
331C4×C11—21no—
332C4×C11—21no—
333C4×C11—44no—
334C4×C11—42no—
335C4×C11—41no—
336C4×C11—41no—
337C4×C11—81no—
338C4×C11—81no—
339C4×C11#45012yes—
340C4×C11C22×SD1611yescharacteristic
341C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
342C4×C11#57711yescharacteristic
343C4×C11#57811yescharacteristic
3442−1+4—44no—
3452−1+4—44no—
346C2×#41—22no—
347C2×#41—24no—
348C2×#41—22no—
349C2×#41—21no—
350C2×#41D4×C1111yescharacteristic
351C22×Q8—22no—
352C22×Q8—22no—
353C22×Q8—21no—
354C2×SD16—22no—
355C22×C8—21no—
356C22×C8—21no—
357C4⋊Q8—22no—
358C4⋊Q8—22no—
359C4⋊Q8—22no—
360C4⋊Q8—21no—
361C4⋊Q8—21no—
362C4⋊Q8D4×C1111yescharacteristic
363C4⋊Q8D4×C1112yes—
364C4⋊Q8C23×C1111yescharacteristic
365C4⋊Q8C23×C1111yescharacteristic
366C4⋊Q8C23×C1112yes—
367#127D4×C1111yescharacteristic
368#125—21no—
369#124—22no—
370#124—21no—
371#123—24no—
372#123—24no—
373#123—24no—
374C22⋊Q8—24no—
375C22⋊Q8—22no—
376C22⋊Q8—24no—
377C22⋊Q8—22no—
378C22⋊Q8—21no—
379C22⋊Q8—21no—
380#121—22no—
381#121—22no—
382#121—21no—
383#121D4×C1112yes—
384C4×Q8—21no—
385C4×Q8—21no—
386C4×Q8D4×C1111yescharacteristic
387C4×Q8C23×C1111yescharacteristic
388C4×D4—22no—
389C4×D4—22no—
390C4×D4—21no—
391C4×D4—21no—
392C4×D4—21no—
393C4×D4D4×C1111yescharacteristic
394C4×D4C23×C1111yescharacteristic
395C4×D4C23×C1112yes—
396#117—21no—
397#117—21no—
398#117D4×C1111yescharacteristic
399C2×C4⋊C4—22no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4—22no—
402C2×C4⋊C4D4×C1112yes—
403C2×C42—21no—
404C2×C42C23×C1111yescharacteristic
405#107—21no—
406#107—21no—
407#106—21no—
408#106—21no—
409#106—22no—
410#106—24no—
411C4⋊C8—21no—
412C4⋊C8—21no—
413C4⋊C8—21no—
414C4⋊C8C23×C1111yescharacteristic
415C4⋊C8C23×C1111yescharacteristic
416C4⋊C8C23×C1112yes—
417#103—21no—
418#103—21no—
419#103—22no—
420#103—24no—
421#102—21no—
422#102—21no—
423#102—22no—
424C22⋊C8—21no—
425C4×C8C23×C1112yes—
426C2×C11—22no—
427C2×C11—42no—
428C2×C11—82no—
429C2×C11C2×#45011yescharacteristic
430C2×C11#301311yescharacteristic
431C2×C11#302011yescharacteristic
432#41—22no—
433#41—48no—
434#41—416no—
435#41—44no—
436#41—44no—
437#41—42no—
438#41—42no—
439#41C11×SD1614yescomplemented
440C2×Q8—24no—
441C2×Q8—22no—
442C2×Q8—21no—
443C2×Q8—22no—
444C2×Q8—21no—
445C2×Q8—21no—
446C2×Q8—48no—
447C2×Q8—44no—
448C2×Q8—44no—
449C2×Q8—42no—
450C2×Q8—42no—
451C2×Q8C2×D4×C1111yescharacteristic
452C2×D4—21no—
453C2×D4—24no—
454C2×D4—22no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4C2×D4×C1112yes—
458C2×D4C2×D4×C1111yescharacteristic
459C22×C4—21no—
460C22×C4—24no—
461C22×C4—24no—
462C22×C4—22no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—22no—
466C22×C4C2×D4×C1111yescharacteristic
467C22×C4C2×D4×C1111yescharacteristic
468C22×C4C2×D4×C1111yescharacteristic
469SD16—82no—
470C2×C8—22no—
471C2×C8—21no—
472C2×C8—22no—
473C2×C8—21no—
474C2×C8—42no—
475C2×C8—81no—
476C4⋊C4—24no—
477C4⋊C4—24no—
478C4⋊C4—21no—
479C4⋊C4—22no—
480C4⋊C4—22no—
481C4⋊C4—21no—
482C4⋊C4—22no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—41no—
489C4⋊C4—41no—
490C4⋊C4C2×D4×C1112yes—
491C4⋊C4C2×D4×C1114yes—
492C4⋊C4C2×D4×C1111yescharacteristic
493C4⋊C4C2×D4×C1111yescharacteristic
494C22⋊C4—24no—
495C22⋊C4—24no—
496C22⋊C4—21no—
497C22⋊C4—21no—
498C22⋊C4—22no—
499C22⋊C4—21no—
500C22⋊C4—22no—
501C22⋊C4—41no—
502C42—21no—
503C42—21no—
504C42—21no—
505C42—41no—
506C42C2×D4×C1111yescharacteristic
507C42C2×D4×C1111yescharacteristic
508C42C2×D4×C1111yescharacteristic
509C42C24×C1111yescharacteristic
510C11#1888311yescharacteristic, direct product factor, Sylow
511C23—21no—
512C23—22no—
513C23C11×#12011yescharacteristic
514Q8—21no—
515Q8—48no—
516Q8—42no—
517Q8—42no—
518Q8—42no—
519Q8—42no—
520Q8—44no—
521Q8—41no—
522Q8—41no—
523Q8C2×C11×SD1612yes—
524D4—24no—
525D4—21no—
526D4—22no—
527D4—22no—
528D4—42no—
529D4—48no—
530D4—44no—
531D4—42no—
532D4C2×C11×SD1612yes—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—24no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—24no—
540C2×C4—22no—
541C2×C4—41no—
542C2×C4—42no—
543C2×C4—48no—
544C2×C4—48no—
545C2×C4—44no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4C11×#12011yescharacteristic
553C2×C4C11×#12011yescharacteristic
554C2×C4C11×#12011yescharacteristic
555C2×C4C2×C11×SD1612yes—
556C2×C4C11×AGL(1,ℤ/8)12yes—
557C2×C4C22×D4×C1111yescharacteristic
558C2×C4C22×D4×C1111yescharacteristic
559C2×C4C22×D4×C1111yescharacteristic
560C8—42no—
561C8—41no—
562C8—41no—
563C8—42no—
564C22—21no—
565C22—21no—
566C22—22no—
567C22—41no—
568C22—41no—
569C22—42no—
570C22—42no—
571C22—42no—
572C22C11×#45012yes—
573C22C2×C11×#12011yescharacteristic
574C4—22no—
575C4—21no—
576C4—21no—
577C4—21no—
578C4—44no—
579C4—42no—
580C4—41no—
581C4—41no—
582C4—81no—
583C4—81no—
584C4C11×#45012yes—
585C4C22×C11×SD1611yescharacteristic
586C4C2×C11×AGL(1,ℤ/8)11yescharacteristic
587C4C11×#57711yescharacteristic
588C4C11×#57811yescharacteristic
589C2—22no—
590C2—42no—
591C2—82no—
592C2C2×C11×#45011yescharacteristic
593C2C11×#301311yescharacteristic
594C2C11×#302011yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC42C24×C11
prime radicalC11×#3499C2
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
2. C11×#3246C2semidirect
3. C11×#3229C2semidirect
4. C11×#3076C2semidirect
5. C11×#1654C2semidirect
6. C11×#1651C2semidirect
7. C11×#1637C2semidirect
8. C11×#1635C2semidirect
9. C2×C11×#332C2semidirect
10. C11×#1480C2semidirect
11. C11×#1477C2semidirect
135. #18883C11direct (N × H)
143. C11×#41SD16semidirect
215. #3246C2×C11semidirect
216. #3229C2×C11semidirect
217. #3076C2×C11semidirect
218. #1654C2×C11semidirect
219. #1651C2×C11semidirect
220. #1637C2×C11semidirect
221. #1635C2×C11semidirect
222. C2×#332C2×C11semidirect
223. #1480C2×C11semidirect
224. #1477C2×C11semidirect
439. #41C11×SD16semidirect
510. C11#18883direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#34992
C11×#32462
C11×#32292
C11×#30762
C11×#16542
C11×#16512
C11×#16372
C11×#16352
C2×C11×#3322
C11×#14802
C11×#14772
#1888311