Finite Group Databasebeta

← C11×#19178 #14596371

Subgroups — C11×#19178 #14596371

Order 2816.

648 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×#3182C211yesmaximal, characteristic, complemented
2C11×#3107C211yesmaximal, characteristic, complemented
3C11×#3035C211yesmaximal, characteristic
4C11×#2970C211yesmaximal, characteristic, complemented
5C11×#1702C211yesmaximal, characteristic, complemented
6C11×#1700C211yesmaximal, characteristic, complemented
7C11×#1694C211yesmaximal, characteristic, complemented
8C11×#1686C211yesmaximal, characteristic, complemented
9C11×#1681C211yesmaximal, characteristic, complemented
10C11×#1679C211yesmaximal, characteristic, complemented
11C11×#1673C211yesmaximal, characteristic, complemented
12C11×#1665C211yesmaximal, characteristic, complemented
13C11×#1565C211yesmaximal, characteristic, complemented
14C11×#1553C211yesmaximal, characteristic, complemented
15C11×#1552C211yesmaximal, characteristic, complemented
16C2×C11×#135—21no—
17C11×#533C2211yescharacteristic
18C11×#532C2211yescharacteristic
19C4×C11×#41C2211yescharacteristic
20C11×#500C2211yescharacteristic
21C11×#492C2211yescharacteristic
22C11×#487C2211yescharacteristic
23C11×#486C2211yescharacteristic
24C11×#485—21no—
25C11×#475C2211yescharacteristic
26C11×#474C2211yescharacteristic
27C11×#468—21no—
28C11×#468—21no—
29C11×#464—21no—
30C11×#463—21no—
31C11×#462C2211yescharacteristic
32C11×#462C2211yescharacteristic
33C11×#461C2211yescharacteristic
34C11×#461C2211yescharacteristic
35C11×#460C2211yescharacteristic
36C11×#459C2211yescharacteristic
37C11×#452—21no—
38C11×#446C2211yescharacteristic
39C11×#446C2211yescharacteristic
40C11×#440—21no—
41C11×#440—21no—
42C4×C11×Q16—21no—
43C4×C11×SD16—21no—
44C11×#435—21no—
45C11×#435—21no—
46C8×D4×C11C2211yescharacteristic
47C8×D4×C11C2211yescharacteristic
48C11×#432—21no—
49C11×#432C2211yescharacteristic
50C11×#431C2211yescharacteristic
51C2×C11×C4⋊C8C2211yescharacteristic
52C11×#416—21no—
53C4×C11×M16C2211yescharacteristic
54C2×C11×#97—21no—
55C11×#335C2211yescharacteristic
56C11×#335C2211yescharacteristic
57C11×#334C2211yescharacteristic
58C11×#334C2211yescharacteristic
59C11×#332C2211yescharacteristic
60C11×#332C2211yescharacteristic
61C11×#332C2211yescharacteristic
62C11×#332C2211yescharacteristic
63C11×#332C2211yescharacteristic
64C11×#332C2211yescharacteristic
65C11×#331C2211yescharacteristic
66C11×#331C2211yescharacteristic
67C2×C11×#41—21no—
68C2×C11×#41D411yescharacteristic
69C11×#135—44no—
70C2×C11×Q16—21no—
71C2×C11×Q16—21no—
72C2×C11×SD16—21no—
73C2×C11×SD16—21no—
74C2×C11×SD16—21no—
75C2×C11×SD16—21no—
76C2×C11×SD16—21no—
77C2×C11×D8—21no—
78C2×C11×M16D411yescharacteristic
79C2×C11×M16D411yescharacteristic
80C22×C8×C11—21no—
81C22×C8×C11—21no—
82C22×C8×C11—21no—
83C11×C4⋊Q8C2311yescharacteristic
84C11×C4⋊Q8C2311yescharacteristic
85C11×C4⋊Q8C2311yescharacteristic
86C11×#127C2311yescharacteristic
87C11×#125—21no—
88C11×#124—21no—
89C11×C22⋊Q8—21no—
90C11×C22⋊Q8—21no—
91C11×#121—21no—
92C11×#121—21no—
93C4×Q8×C11—21no—
94C4×Q8×C11—21no—
95C4×Q8×C11D411yescharacteristic
96C4×Q8×C11C2311yescharacteristic
97C4×D4×C11—21no—
98C4×D4×C11—21no—
99C4×D4×C11—21no—
100C4×D4×C11—21no—
101C4×D4×C11D411yescharacteristic
102C4×D4×C11C2311yescharacteristic
103C11×#117—21no—
104C11×#117—21no—
105C11×#117D411yescharacteristic
106C2×C42×C11—21no—
107C2×C42×C11C2311yescharacteristic
108C11×#107—21no—
109C11×#107—21no—
110C11×#107—21no—
111C11×#106—21no—
112C11×C4⋊C8—21no—
113C11×C4⋊C8—21no—
114C11×C4⋊C8—21no—
115C11×C4⋊C8C2311yescharacteristic
116C11×C4⋊C8C2311yescharacteristic
117C11×C4⋊C8C2311yescharacteristic
118C11×C4⋊C8C2311yescharacteristic
119C11×C4⋊C8C2311yescharacteristic
120C11×C4⋊C8C2311yescharacteristic
121C11×#103—21no—
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×C22⋊C8—21no—
134C11×C22⋊C8—21no—
135C11×C22⋊C8—21no—
136C11×C22⋊C8—21no—
137C11×#97—21no—
138C11×#97—21no—
139C11×#97—21no—
140C11×#97D411yescharacteristic
141C11×#97D411yescharacteristic
142C4×C8×C11—21no—
143C4×C8×C11C2311yescharacteristic
144C4×C8×C11C2311yescharacteristic
145#19178C1111yesmaximal, characteristic, direct product factor, Sylow
146C11×#41—22no—
147C11×#41—41no—
148C11×#41—42no—
149C11×#41—42no—
150C2×Q8×C11—21no—
151C2×Q8×C11—21no—
152C2×Q8×C11—21no—
153C2×Q8×C11C2×D411yescharacteristic
154C2×D4×C11—21no—
155C2×D4×C11—21no—
156C2×D4×C11—21no—
157C2×D4×C11—21no—
158C2×D4×C11—41no—
159C2×D4×C11C2×D411yescharacteristic
160C22×C4×C11—21no—
161C22×C4×C11—21no—
162C22×C4×C11—21no—
163C22×C4×C11—41no—
164C22×C4×C11C2×D411yescharacteristic
165C22×C4×C11C2×D411yescharacteristic
166C22×C4×C11#4111yescharacteristic
167C11×Q16—42no—
168C11×Q16—42no—
169C11×SD16—42no—
170C11×SD16—42no—
171C11×SD16—42no—
172C11×SD16—42no—
173C11×SD16—42no—
174C11×D8—42no—
175C11×M16—22no—
176C11×M16—41no—
177C2×C8×C11—21no—
178C2×C8×C11—21no—
179C2×C8×C11—21no—
180C2×C8×C11—21no—
181C2×C8×C11—21no—
182C2×C8×C11—21no—
183C2×C8×C11—42no—
184C2×C8×C11—42no—
185C2×C8×C11—42no—
186C2×C8×C11C2×D411yescharacteristic
187C2×C8×C11C2×D411yescharacteristic
188C2×C8×C11C2×D411yescharacteristic
189C2×C8×C11C2×D411yescharacteristic
190C11×C4⋊C4—21no—
191C11×C4⋊C4—21no—
192C11×C4⋊C4—21no—
193C11×C4⋊C4—21no—
194C11×C4⋊C4—21no—
195C11×C4⋊C4—21no—
196C11×C4⋊C4—21no—
197C11×C4⋊C4—21no—
198C11×C4⋊C4—41no—
199C11×C4⋊C4—41no—
200C11×C4⋊C4C2×D411yescharacteristic
201C11×C4⋊C4C2×D411yescharacteristic
202C11×C22⋊C4—21no—
203C11×C22⋊C4—21no—
204C11×C22⋊C4—21no—
205C11×C22⋊C4—41no—
206C11×C22⋊C4—41no—
207C11×C22⋊C4—41no—
208C42×C11—21no—
209C42×C11—21no—
210C42×C11—21no—
211C42×C11—41no—
212C42×C11C2×D411yescharacteristic
213C42×C11C2×D411yescharacteristic
214C42×C11#4111yescharacteristic
215C42×C11C2411yescharacteristic
216#3182C2×C1111yescharacteristic, complemented
217#3107C2×C1111yescharacteristic, complemented
218#3035C2×C1111yescharacteristic
219#2970C2×C1111yescharacteristic, complemented
220#1702C2×C1111yescharacteristic, complemented
221#1700C2×C1111yescharacteristic, complemented
222#1694C2×C1111yescharacteristic, complemented
223#1686C2×C1111yescharacteristic, complemented
224#1681C2×C1111yescharacteristic, complemented
225#1679C2×C1111yescharacteristic, complemented
226#1673C2×C1111yescharacteristic, complemented
227#1665C2×C1111yescharacteristic, complemented
228#1565C2×C1111yescharacteristic, complemented
229#1553C2×C1111yescharacteristic, complemented
230#1552C2×C1111yescharacteristic, complemented
231C23×C11—21no—
232C23×C11—41no—
233C23×C11#12111yescharacteristic
234Q8×C11—21no—
235Q8×C11—21no—
236Q8×C11—41no—
237Q8×C11—41no—
238Q8×C11—41no—
239Q8×C11—41no—
240Q8×C11—41no—
241Q8×C11—41no—
242D4×C11—21no—
243D4×C11—42no—
244D4×C11—41no—
245D4×C11—41no—
246D4×C11—41no—
247D4×C11—41no—
248D4×C11—81no—
249D4×C11—82no—
250D4×C11AGL(1,ℤ/8)12yes—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—41no—
259C2×C4×C11—42no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11—41no—
263C2×C4×C11—41no—
264C2×C4×C11—41no—
265C2×C4×C11—81no—
266C2×C4×C11—82no—
267C2×C4×C11#12111yescharacteristic
268C2×C4×C11#12111yescharacteristic
269C2×C4×C11#12111yescharacteristic
270C2×C4×C11C22×D411yescharacteristic
271C2×C4×C11C22×D411yescharacteristic
272C2×C4×C11C2×#4111yescharacteristic
273C8×C11—21no—
274C8×C11—21no—
275C8×C11—21no—
276C8×C11—41no—
277C8×C11—41no—
278C8×C11—41no—
279C8×C11—41no—
280C8×C11—41no—
281C8×C11—41no—
282C8×C11#13512yescomplemented
283C2×#135—21no—
284#533C22×C1111yescharacteristic
285#532C22×C1111yescharacteristic
286C4×#41C22×C1111yescharacteristic
287#500C22×C1111yescharacteristic
288#492C22×C1111yescharacteristic
289#487C22×C1111yescharacteristic
290#486C22×C1111yescharacteristic
291#485—21no—
292#475C22×C1111yescharacteristic
293#474C22×C1111yescharacteristic
294#468—21no—
295#468—21no—
296#464—21no—
297#463—21no—
298#462C22×C1111yescharacteristic
299#462C22×C1111yescharacteristic
300#461C22×C1111yescharacteristic
301#461C22×C1111yescharacteristic
302#460C22×C1111yescharacteristic
303#459C22×C1111yescharacteristic
304#452—21no—
305#446C22×C1111yescharacteristic
306#446C22×C1111yescharacteristic
307#440—21no—
308#440—21no—
309C4×Q16—21no—
310C4×SD16—21no—
311#435—21no—
312#435—21no—
313C8×D4C22×C1111yescharacteristic
314C8×D4C22×C1111yescharacteristic
315#432—21no—
316#432C22×C1111yescharacteristic
317#431C22×C1111yescharacteristic
318C2×C4⋊C8C22×C1111yescharacteristic
319#416—21no—
320C4×M16C22×C1111yescharacteristic
321C2×#97—21no—
322#335C22×C1111yescharacteristic
323#335C22×C1111yescharacteristic
324#334C22×C1111yescharacteristic
325#334C22×C1111yescharacteristic
326#332C22×C1111yescharacteristic
327#332C22×C1111yescharacteristic
328#332C22×C1111yescharacteristic
329#332C22×C1111yescharacteristic
330#332C22×C1111yescharacteristic
331#332C22×C1111yescharacteristic
332#331C22×C1111yescharacteristic
333#331C22×C1111yescharacteristic
334C22×C11—21no—
335C22×C11—21no—
336C22×C11—22no—
337C22×C11—21no—
338C22×C11—41no—
339C22×C11—41no—
340C22×C11—81no—
341C22×C11—81no—
342C22×C11—81no—
343C22×C11C2×#12111yescharacteristic
344C4×C11—21no—
345C4×C11—21no—
346C4×C11—21no—
347C4×C11—21no—
348C4×C11—41no—
349C4×C11—41no—
350C4×C11—41no—
351C4×C11—81no—
352C4×C11—81no—
353C4×C11—81no—
354C4×C11C2×#13511yescharacteristic
355C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
356C4×C11#57511yescharacteristic
357C4×C11#57511yescharacteristic
358C2×#41—21no—
359C2×#41D4×C1111yescharacteristic
360#135—44no—
361C2×Q16—21no—
362C2×Q16—21no—
363C2×SD16—21no—
364C2×SD16—21no—
365C2×SD16—21no—
366C2×SD16—21no—
367C2×SD16—21no—
368C2×D8—21no—
369C2×M16D4×C1111yescharacteristic
370C2×M16D4×C1111yescharacteristic
371C22×C8—21no—
372C22×C8—21no—
373C22×C8—21no—
374C4⋊Q8C23×C1111yescharacteristic
375C4⋊Q8C23×C1111yescharacteristic
376C4⋊Q8C23×C1111yescharacteristic
377#127C23×C1111yescharacteristic
378#125—21no—
379#124—21no—
380C22⋊Q8—21no—
381C22⋊Q8—21no—
382#121—21no—
383#121—21no—
384C4×Q8—21no—
385C4×Q8—21no—
386C4×Q8D4×C1111yescharacteristic
387C4×Q8C23×C1111yescharacteristic
388C4×D4—21no—
389C4×D4—21no—
390C4×D4—21no—
391C4×D4—21no—
392C4×D4D4×C1111yescharacteristic
393C4×D4C23×C1111yescharacteristic
394#117—21no—
395#117—21no—
396#117D4×C1111yescharacteristic
397C2×C42—21no—
398C2×C42C23×C1111yescharacteristic
399#107—21no—
400#107—21no—
401#107—21no—
402#106—21no—
403C4⋊C8—21no—
404C4⋊C8—21no—
405C4⋊C8—21no—
406C4⋊C8C23×C1111yescharacteristic
407C4⋊C8C23×C1111yescharacteristic
408C4⋊C8C23×C1111yescharacteristic
409C4⋊C8C23×C1111yescharacteristic
410C4⋊C8C23×C1111yescharacteristic
411C4⋊C8C23×C1111yescharacteristic
412#103—21no—
413#103—21no—
414#103—21no—
415#103—21no—
416#103—21no—
417#103—21no—
418#103—21no—
419#102—21no—
420#102—21no—
421#102—21no—
422#102—21no—
423#102—21no—
424C22⋊C8—21no—
425C22⋊C8—21no—
426C22⋊C8—21no—
427C22⋊C8—21no—
428#97—21no—
429#97—21no—
430#97—21no—
431#97D4×C1111yescharacteristic
432#97D4×C1111yescharacteristic
433C4×C8—21no—
434C4×C8C23×C1111yescharacteristic
435C4×C8C23×C1111yescharacteristic
436C2×C11—41no—
437C2×C11—42no—
438C2×C11—161no—
439C2×C11#303511yescharacteristic
440C2×C11#305511yescharacteristic
441C2×C11#306911yescharacteristic
442#41—22no—
443#41—41no—
444#41—42no—
445#41—42no—
446C2×Q8—21no—
447C2×Q8—21no—
448C2×Q8—21no—
449C2×Q8C2×D4×C1111yescharacteristic
450C2×D4—21no—
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—41no—
455C2×D4C2×D4×C1111yescharacteristic
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—41no—
460C22×C4C2×D4×C1111yescharacteristic
461C22×C4C2×D4×C1111yescharacteristic
462C22×C4C11×#4111yescharacteristic
463Q16—42no—
464Q16—42no—
465SD16—42no—
466SD16—42no—
467SD16—42no—
468SD16—42no—
469SD16—42no—
470D8—42no—
471M16—22no—
472M16—41no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—42no—
480C2×C8—42no—
481C2×C8—42no—
482C2×C8C2×D4×C1111yescharacteristic
483C2×C8C2×D4×C1111yescharacteristic
484C2×C8C2×D4×C1111yescharacteristic
485C2×C8C2×D4×C1111yescharacteristic
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—41no—
495C4⋊C4—41no—
496C4⋊C4C2×D4×C1111yescharacteristic
497C4⋊C4C2×D4×C1111yescharacteristic
498C22⋊C4—21no—
499C22⋊C4—21no—
500C22⋊C4—21no—
501C22⋊C4—41no—
502C22⋊C4—41no—
503C22⋊C4—41no—
504C42—21no—
505C42—21no—
506C42—21no—
507C42—41no—
508C42C2×D4×C1111yescharacteristic
509C42C2×D4×C1111yescharacteristic
510C42C11×#4111yescharacteristic
511C42C24×C1111yescharacteristic
512C11#1917811yescharacteristic, direct product factor, Sylow
513C23—21no—
514C23—41no—
515C23C11×#12111yescharacteristic
516Q8—21no—
517Q8—21no—
518Q8—41no—
519Q8—41no—
520Q8—41no—
521Q8—41no—
522Q8—41no—
523Q8—41no—
524D4—21no—
525D4—42no—
526D4—41no—
527D4—41no—
528D4—41no—
529D4—41no—
530D4—81no—
531D4—82no—
532D4C11×AGL(1,ℤ/8)12yes—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—41no—
541C2×C4—42no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—81no—
548C2×C4—82no—
549C2×C4C11×#12111yescharacteristic
550C2×C4C11×#12111yescharacteristic
551C2×C4C11×#12111yescharacteristic
552C2×C4C22×D4×C1111yescharacteristic
553C2×C4C22×D4×C1111yescharacteristic
554C2×C4C2×C11×#4111yescharacteristic
555C8—21no—
556C8—21no—
557C8—21no—
558C8—41no—
559C8—41no—
560C8—41no—
561C8—41no—
562C8—41no—
563C8—41no—
564C8C11×#13512yescomplemented
565C22—21no—
566C22—21no—
567C22—22no—
568C22—21no—
569C22—41no—
570C22—41no—
571C22—81no—
572C22—81no—
573C22—81no—
574C22C2×C11×#12111yescharacteristic
575C4—21no—
576C4—21no—
577C4—21no—
578C4—21no—
579C4—41no—
580C4—41no—
581C4—41no—
582C4—81no—
583C4—81no—
584C4—81no—
585C4C2×C11×#13511yescharacteristic
586C4C2×C11×AGL(1,ℤ/8)11yescharacteristic
587C4C11×#57511yescharacteristic
588C4C11×#57511yescharacteristic
589C2—41no—
590C2—42no—
591C2—161no—
592C2C11×#303511yescharacteristic
593C2C11×#305511yescharacteristic
594C2C11×#306911yescharacteristic
subgroupG/H
center, socleC22×C11C2×#121
commutator, Frattini, cosocleC42C24×C11
prime radicalC11×#3035C2
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
2. C11×#3107C2semidirect
4. C11×#2970C2semidirect
5. C11×#1702C2semidirect
6. C11×#1700C2semidirect
7. C11×#1694C2semidirect
8. C11×#1686C2semidirect
9. C11×#1681C2semidirect
10. C11×#1679C2semidirect
11. C11×#1673C2semidirect
12. C11×#1665C2semidirect
13. C11×#1565C2semidirect
14. C11×#1553C2semidirect
15. C11×#1552C2semidirect
145. #19178C11direct (N × H)
216. #3182C2×C11semidirect
217. #3107C2×C11semidirect
219. #2970C2×C11semidirect
220. #1702C2×C11semidirect
221. #1700C2×C11semidirect
222. #1694C2×C11semidirect
223. #1686C2×C11semidirect
224. #1681C2×C11semidirect
225. #1679C2×C11semidirect
226. #1673C2×C11semidirect
227. #1665C2×C11semidirect
228. #1565C2×C11semidirect
229. #1553C2×C11semidirect
230. #1552C2×C11semidirect
282. C8×C11#135semidirect
512. C11#19178direct (N × H)
564. C8C11×#135semidirect

Maximal subgroups

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

subgroupindex
C11×#31822
C11×#31072
C11×#30352
C11×#29702
C11×#17022
C11×#17002
C11×#16942
C11×#16862
C11×#16812
C11×#16792
C11×#16732
C11×#16652
C11×#15652
C11×#15532
C11×#15522
#1917811