Finite Group Databasebeta

← C11×#24770 #14601963

Subgroups — C11×#24770 #14601963

Order 2816.

924 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#472C212yesmaximal, complemented
2C11×#3038C211yesmaximal, characteristic, complemented
3C2×C11×#459C211yesmaximal, characteristic, complemented
4C4×C11×AGL(1,ℤ/8)C211yesmaximal, characteristic, complemented
5C11×#2906C211yesmaximal, characteristic, complemented
6C11×#2063C212yesmaximal, complemented
7C11×#2045C212yesmaximal, complemented
8C11×#1965C211yesmaximal, characteristic, complemented
9C11×#1950C211yesmaximal, characteristic, complemented
10C11×#1907C212yesmaximal, complemented
11C11×#1800C211yesmaximal, characteristic, complemented
12C2×C11×AGL(1,ℤ/8)C2212yes—
13C2×C11×AGL(1,ℤ/8)C2211yescharacteristic
14C22×C11×D8C2212yes—
15C2×C11×#131C2212yes—
16C2×C11×#127C2211yescharacteristic
17C4×C11×#41C2211yescharacteristic
18C2×C4×D4×C11C2211yescharacteristic
19C11×#472—28no—
20C11×#460—21no—
21C11×#460—21no—
22C11×#459—21no—
23C11×#459—21no—
24C11×#459—21no—
25C11×#459—21no—
26C11×#459—22no—
27C11×#442—21no—
28C11×#440—21no—
29C4×C11×SD16—21no—
30C4×C11×D8—21no—
31C2×C11×#108C2212yes—
32C11×#428C2211yescharacteristic
33C11×#424—22no—
34C11×#424C2212yes—
35C11×#423—21no—
36C11×#423C2211yescharacteristic
37C11×#423C2211yescharacteristic
38C2×C11×C4⋊C8—21no—
39C2×C11×C4⋊C8C2211yescharacteristic
40C11×#418C2211yescharacteristic
41C11×#418C2212yes—
42C11×#417C2211yescharacteristic
43C2×C11×#102C2212yes—
44C2×C11×#100C2212yes—
45C2×C11×#100C2212yes—
46C2×C11×#100C2212yes—
47C4×C11×M16C2211yescharacteristic
48C11×#343C2212yes—
49C11×#341C2212yes—
50C2×C11×#41C2311yescharacteristic
51C22×D4×C11—21no—
52C22×D4×C11—21no—
53C22×D4×C11C2312yes—
54C22×D4×C11C2311yescharacteristic
55C23×C4×C11—21no—
56C11×AGL(1,ℤ/8)—22no—
57C11×AGL(1,ℤ/8)—24no—
58C11×AGL(1,ℤ/8)—24no—
59C11×AGL(1,ℤ/8)D414yescomplemented
60C2×C11×SD16—21no—
61C2×C11×SD16—22no—
62C2×C11×D8—21no—
63C2×C11×D8—24no—
64C2×C11×D8—22no—
65C2×C11×D8—22no—
66C2×C11×D8—22no—
67C2×C11×D8—42no—
68C11×#131—24no—
69C11×#131—42no—
70C2×C11×M16—22no—
71C2×C11×M16C2311yescharacteristic
72C2×C11×M16C2312yes—
73C2×C11×M16C2312yes—
74C2×C11×M16C2311yescharacteristic
75C22×C8×C11—22no—
76C22×C8×C11C2312yes—
77C11×#127—21no—
78C11×#127—21no—
79C11×#127—21no—
80C11×#127—21no—
81C4×Q8×C11D411yescharacteristic
82C4×Q8×C11D411yescharacteristic
83C4×D4×C11—21no—
84C4×D4×C11—21no—
85C4×D4×C11—21no—
86C4×D4×C11—21no—
87C4×D4×C11—21no—
88C4×D4×C11—21no—
89C4×D4×C11D411yescharacteristic
90C4×D4×C11D411yescharacteristic
91C11×#117—21no—
92C11×#117C2311yescharacteristic
93C2×C11×C4⋊C4C2311yescharacteristic
94C2×C11×C22⋊C4—21no—
95C2×C42×C11—21no—
96C2×C42×C11C2311yescharacteristic
97C11×#108—24no—
98C11×#107—21no—
99C11×#106—21no—
100C11×C4⋊C8—22no—
101C11×C4⋊C8—22no—
102C11×C4⋊C8—21no—
103C11×C4⋊C8—21no—
104C11×C4⋊C8—21no—
105C11×C4⋊C8—21no—
106C11×C4⋊C8D411yescharacteristic
107C11×C4⋊C8D411yescharacteristic
108C11×C4⋊C8D412yes—
109C11×#103—21no—
110C11×#102—21no—
111C11×#102—22no—
112C11×#102—22no—
113C11×#102—21no—
114C11×#102—21no—
115C11×#102—22no—
116C11×#102—22no—
117C11×#100—24no—
118C11×#100—24no—
119C11×#100—42no—
120C11×#97—21no—
121C4×C8×C11—21no—
122#24770C1111yesmaximal, characteristic, direct product factor, Sylow
123C24×C11—21no—
124C24×C11—22no—
125C11×#41—21no—
126C11×#41—21no—
127C11×#41C2×D412yes—
128C11×#41#4112yes—
129C2×Q8×C11C2×D411yescharacteristic
130C2×D4×C11—21no—
131C2×D4×C11—21no—
132C2×D4×C11—21no—
133C2×D4×C11—22no—
134C2×D4×C11—22no—
135C2×D4×C11—22no—
136C2×D4×C11—21no—
137C2×D4×C11—22no—
138C2×D4×C11—21no—
139C2×D4×C11—22no—
140C2×D4×C11—21no—
141C2×D4×C11—22no—
142C2×D4×C11—41no—
143C2×D4×C11—41no—
144C2×D4×C11—41no—
145C2×D4×C11—41no—
146C2×D4×C11—82no—
147C2×D4×C11—82no—
148C2×D4×C11C2×D412yes—
149C2×D4×C11C2×D411yescharacteristic
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11—41no—
155C22×C4×C11—41no—
156C22×C4×C11—82no—
157C22×C4×C11#4111yescharacteristic
158C22×C4×C11#4111yescharacteristic
159C22×C4×C11C2411yescharacteristic
160C11×SD16—24no—
161C11×SD16—44no—
162C11×D8—24no—
163C11×D8—44no—
164C11×D8—44no—
165C11×D8—44no—
166C11×M16—22no—
167C11×M16—22no—
168C11×M16—21no—
169C11×M16—22no—
170C11×M16—21no—
171C11×M16—22no—
172C11×M16—21no—
173C11×M16—44no—
174C11×M16C2×D412yes—
175C2×C8×C11—21no—
176C2×C8×C11—22no—
177C2×C8×C11—21no—
178C2×C8×C11—22no—
179C2×C8×C11—22no—
180C2×C8×C11—22no—
181C2×C8×C11—44no—
182C2×C8×C11C2×D412yes—
183C2×C8×C11C2×D412yes—
184C11×C4⋊C4—21no—
185C11×C4⋊C4—21no—
186C11×C4⋊C4—21no—
187C11×C4⋊C4—21no—
188C11×C4⋊C4C2×D411yescharacteristic
189C11×C4⋊C4C2×D411yescharacteristic
190C11×C22⋊C4—21no—
191C11×C22⋊C4—21no—
192C11×C22⋊C4—21no—
193C11×C22⋊C4—41no—
194C11×C22⋊C4—41no—
195C42×C11—21no—
196C42×C11—21no—
197C42×C11—21no—
198C42×C11C2×D411yescharacteristic
199C42×C11C2×D411yescharacteristic
200C42×C11C2×D411yescharacteristic
201C42×C11C2×D411yescharacteristic
202C2×#472C2×C1112yescomplemented
203#3038C2×C1111yescharacteristic, complemented
204C2×#459C2×C1111yescharacteristic, complemented
205C4×AGL(1,ℤ/8)C2×C1111yescharacteristic, complemented
206#2906C2×C1111yescharacteristic, complemented
207#2063C2×C1112yescomplemented
208#2045C2×C1112yescomplemented
209#1965C2×C1111yescharacteristic, complemented
210#1950C2×C1111yescharacteristic, complemented
211#1907C2×C1112yescomplemented
212#1800C2×C1111yescharacteristic, complemented
213C23×C11—21no—
214C23×C11—22no—
215C23×C11—41no—
216C23×C11—41no—
217C23×C11—42no—
218C23×C11—42no—
219C23×C11—42no—
220C23×C11—81no—
221C23×C11—81no—
222C23×C11—82no—
223C23×C11—82no—
224C23×C11C2×#4111yescharacteristic
225Q8×C11—21no—
226Q8×C11#12112yes—
227D4×C11—22no—
228D4×C11—22no—
229D4×C11—22no—
230D4×C11—21no—
231D4×C11—22no—
232D4×C11—42no—
233D4×C11—41no—
234D4×C11—42no—
235D4×C11—42no—
236D4×C11—41no—
237D4×C11—42no—
238D4×C11—82no—
239D4×C11—82no—
240D4×C11—82no—
241D4×C11—82no—
242D4×C11#12112yes—
243C2×C4×C11—21no—
244C2×C4×C11—22no—
245C2×C4×C11—22no—
246C2×C4×C11—22no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—41no—
250C2×C4×C11—42no—
251C2×C4×C11—41no—
252C2×C4×C11—81no—
253C2×C4×C11—82no—
254C2×C4×C11—82no—
255C2×C4×C11—81no—
256C2×C4×C11#12111yescharacteristic
257C2×C4×C11#12111yescharacteristic
258C2×C4×C11#12111yescharacteristic
259C2×C4×C11#12111yescharacteristic
260C2×C4×C11C22×D411yescharacteristic
261C2×C4×C11C22×D411yescharacteristic
262C2×C4×C11C22×D411yescharacteristic
263C2×C4×C11C2×#4111yescharacteristic
264C2×C4×C11H(5,𝔽2)11yescharacteristic
265C2×C4×C112−1+411yescharacteristic
266C8×C11—22no—
267C8×C11—22no—
268C8×C11—22no—
269C8×C11—42no—
270C8×C11—41no—
271C8×C11—42no—
272C2×AGL(1,ℤ/8)C22×C1112yes—
273C2×AGL(1,ℤ/8)C22×C1111yescharacteristic
274C22×D8C22×C1112yes—
275C2×#131C22×C1112yes—
276C2×#127C22×C1111yescharacteristic
277C4×#41C22×C1111yescharacteristic
278C2×C4×D4C22×C1111yescharacteristic
279#472—28no—
280#460—21no—
281#460—21no—
282#459—21no—
283#459—21no—
284#459—21no—
285#459—21no—
286#459—22no—
287#442—21no—
288#440—21no—
289C4×SD16—21no—
290C4×D8—21no—
291C2×#108C22×C1112yes—
292#428C22×C1111yescharacteristic
293#424—22no—
294#424C22×C1112yes—
295#423—21no—
296#423C22×C1111yescharacteristic
297#423C22×C1111yescharacteristic
298C2×C4⋊C8—21no—
299C2×C4⋊C8C22×C1111yescharacteristic
300#418C22×C1112yes—
301#418C22×C1111yescharacteristic
302#417C22×C1111yescharacteristic
303C2×#102C22×C1112yes—
304C2×#100C22×C1112yes—
305C2×#100C22×C1112yes—
306C2×#100C22×C1112yes—
307C4×M16C22×C1111yescharacteristic
308#343C22×C1112yes—
309#341C22×C1112yes—
310C22×C11—21no—
311C22×C11—21no—
312C22×C11—22no—
313C22×C11—41no—
314C22×C11—41no—
315C22×C11—42no—
316C22×C11—82no—
317C22×C11—82no—
318C22×C11—81no—
319C22×C11—81no—
320C22×C11—82no—
321C22×C11—82no—
322C22×C11—82no—
323C22×C11—162no—
324C22×C11—162no—
325C22×C11C2×#12111yescharacteristic
326C22×C11#54711yescharacteristic
327C22×C11#55311yescharacteristic
328C4×C11—22no—
329C4×C11—21no—
330C4×C11—21no—
331C4×C11—21no—
332C4×C11—41no—
333C4×C11—41no—
334C4×C11—81no—
335C4×C11#47212yescomplemented
336C4×C11C2×#12111yescharacteristic
337C4×C11#53711yescharacteristic
338C4×C11D4211yescharacteristic
339C4×C11#54811yescharacteristic
340C2×#41C23×C1111yescharacteristic
341C22×D4—21no—
342C22×D4—21no—
343C22×D4C23×C1112yes—
344C22×D4C23×C1111yescharacteristic
345C23×C4—21no—
346AGL(1,ℤ/8)—22no—
347AGL(1,ℤ/8)—24no—
348AGL(1,ℤ/8)—24no—
349AGL(1,ℤ/8)D4×C1114yescomplemented
350C2×SD16—21no—
351C2×SD16—22no—
352C2×D8—21no—
353C2×D8—24no—
354C2×D8—22no—
355C2×D8—22no—
356C2×D8—22no—
357C2×D8—42no—
358#131—24no—
359#131—42no—
360C2×M16—22no—
361C2×M16C23×C1112yes—
362C2×M16C23×C1112yes—
363C2×M16C23×C1111yescharacteristic
364C2×M16C23×C1111yescharacteristic
365C22×C8—22no—
366C22×C8C23×C1112yes—
367#127—21no—
368#127—21no—
369#127—21no—
370#127—21no—
371C4×Q8D4×C1111yescharacteristic
372C4×Q8D4×C1111yescharacteristic
373C4×D4—21no—
374C4×D4—21no—
375C4×D4—21no—
376C4×D4—21no—
377C4×D4—21no—
378C4×D4—21no—
379C4×D4D4×C1111yescharacteristic
380C4×D4D4×C1111yescharacteristic
381#117—21no—
382#117C23×C1111yescharacteristic
383C2×C4⋊C4C23×C1111yescharacteristic
384C2×C22⋊C4—21no—
385C2×C42—21no—
386C2×C42C23×C1111yescharacteristic
387#108—24no—
388#107—21no—
389#106—21no—
390C4⋊C8—22no—
391C4⋊C8—22no—
392C4⋊C8—21no—
393C4⋊C8—21no—
394C4⋊C8—21no—
395C4⋊C8—21no—
396C4⋊C8D4×C1111yescharacteristic
397C4⋊C8D4×C1111yescharacteristic
398C4⋊C8D4×C1112yes—
399#103—21no—
400#102—21no—
401#102—22no—
402#102—22no—
403#102—21no—
404#102—21no—
405#102—22no—
406#102—22no—
407#100—24no—
408#100—24no—
409#100—42no—
410#97—21no—
411C4×C8—21no—
412C2×C11—21no—
413C2×C11—21no—
414C2×C11—42no—
415C2×C11—82no—
416C2×C11—162no—
417C2×C11#241611yescharacteristic
418C2×C11C2×#47211yescharacteristic
419C2×C11#306811yescharacteristic
420C24—21no—
421C24—22no—
422#41—21no—
423#41—21no—
424#41C2×D4×C1112yes—
425#41C11×#4112yes—
426C2×Q8C2×D4×C1111yescharacteristic
427C2×D4—21no—
428C2×D4—21no—
429C2×D4—21no—
430C2×D4—22no—
431C2×D4—22no—
432C2×D4—22no—
433C2×D4—21no—
434C2×D4—22no—
435C2×D4—21no—
436C2×D4—22no—
437C2×D4—21no—
438C2×D4—22no—
439C2×D4—41no—
440C2×D4—41no—
441C2×D4—41no—
442C2×D4—41no—
443C2×D4—82no—
444C2×D4—82no—
445C2×D4C2×D4×C1112yes—
446C2×D4C2×D4×C1111yescharacteristic
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—41no—
452C22×C4—41no—
453C22×C4—82no—
454C22×C4C11×#4111yescharacteristic
455C22×C4C11×#4111yescharacteristic
456C22×C4C24×C1111yescharacteristic
457SD16—24no—
458SD16—44no—
459D8—24no—
460D8—44no—
461D8—44no—
462D8—44no—
463M16—21no—
464M16—22no—
465M16—22no—
466M16—22no—
467M16—21no—
468M16—22no—
469M16—21no—
470M16—44no—
471M16C2×D4×C1112yes—
472C2×C8—21no—
473C2×C8—22no—
474C2×C8—22no—
475C2×C8—21no—
476C2×C8—22no—
477C2×C8—22no—
478C2×C8—44no—
479C2×C8C2×D4×C1112yes—
480C2×C8C2×D4×C1112yes—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4C2×D4×C1111yescharacteristic
486C4⋊C4C2×D4×C1111yescharacteristic
487C22⋊C4—21no—
488C22⋊C4—21no—
489C22⋊C4—21no—
490C22⋊C4—41no—
491C22⋊C4—41no—
492C42—21no—
493C42—21no—
494C42—21no—
495C42C2×D4×C1111yescharacteristic
496C42C2×D4×C1111yescharacteristic
497C42C2×D4×C1111yescharacteristic
498C42C2×D4×C1111yescharacteristic
499C11#2477011yescharacteristic, direct product factor, Sylow
500C23—21no—
501C23—22no—
502C23—41no—
503C23—41no—
504C23—42no—
505C23—42no—
506C23—42no—
507C23—81no—
508C23—81no—
509C23—82no—
510C23—82no—
511C23C2×C11×#4111yescharacteristic
512Q8—21no—
513Q8C11×#12112yes—
514D4—22no—
515D4—22no—
516D4—22no—
517D4—21no—
518D4—22no—
519D4—42no—
520D4—41no—
521D4—42no—
522D4—42no—
523D4—41no—
524D4—42no—
525D4—82no—
526D4—82no—
527D4—82no—
528D4—82no—
529D4C11×#12112yes—
530C2×C4—21no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—41no—
537C2×C4—42no—
538C2×C4—41no—
539C2×C4—81no—
540C2×C4—82no—
541C2×C4—82no—
542C2×C4—81no—
543C2×C4C11×#12111yescharacteristic
544C2×C4C11×#12111yescharacteristic
545C2×C4C11×#12111yescharacteristic
546C2×C4C11×#12111yescharacteristic
547C2×C4C22×D4×C1111yescharacteristic
548C2×C4C22×D4×C1111yescharacteristic
549C2×C4C22×D4×C1111yescharacteristic
550C2×C4C2×C11×#4111yescharacteristic
551C2×C4C11×H(5,𝔽2)11yescharacteristic
552C2×C4C11×2−1+411yescharacteristic
553C8—22no—
554C8—22no—
555C8—22no—
556C8—42no—
557C8—41no—
558C8—42no—
559C22—21no—
560C22—21no—
561C22—22no—
562C22—41no—
563C22—41no—
564C22—42no—
565C22—82no—
566C22—82no—
567C22—81no—
568C22—81no—
569C22—82no—
570C22—82no—
571C22—82no—
572C22—162no—
573C22—162no—
574C22C2×C11×#12111yescharacteristic
575C22C11×#54711yescharacteristic
576C22C11×#55311yescharacteristic
577C4—22no—
578C4—21no—
579C4—21no—
580C4—21no—
581C4—41no—
582C4—41no—
583C4—81no—
584C4C11×#47212yescomplemented
585C4C2×C11×#12111yescharacteristic
586C4C11×#53711yescharacteristic
587C4D42×C1111yescharacteristic
588C4C11×#54811yescharacteristic
589C2—21no—
590C2—21no—
591C2—42no—
592C2—82no—
593C2—162no—
594C2C11×#241611yescharacteristic
595C2C2×C11×#47211yescharacteristic
596C2C11×#306811yescharacteristic
subgroupG/H
center, socleC22×C11C2×#121
commutator, Frattini, cosocleC22×C4C24×C11
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#472C2semidirect
2. C11×#3038C2semidirect
3. C2×C11×#459C2semidirect
4. C4×C11×AGL(1,ℤ/8)C2semidirect
5. C11×#2906C2semidirect
6. C11×#2063C2semidirect
7. C11×#2045C2semidirect
8. C11×#1965C2semidirect
9. C11×#1950C2semidirect
10. C11×#1907C2semidirect
11. C11×#1800C2semidirect
59. C11×AGL(1,ℤ/8)D4semidirect
122. #24770C11direct (N × H)
202. C2×#472C2×C11semidirect
203. #3038C2×C11semidirect
204. C2×#459C2×C11semidirect
205. C4×AGL(1,ℤ/8)C2×C11semidirect
206. #2906C2×C11semidirect
207. #2063C2×C11semidirect
208. #2045C2×C11semidirect
209. #1965C2×C11semidirect
210. #1950C2×C11semidirect
211. #1907C2×C11semidirect
212. #1800C2×C11semidirect
335. C4×C11#472semidirect
349. AGL(1,ℤ/8)D4×C11semidirect
499. C11#24770direct (N × H)
584. C4C11×#472semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#4722
C11×#30382
C2×C11×#4592
C4×C11×AGL(1,ℤ/8)2
C11×#29062
C11×#20632
C11×#20452
C11×#19652
C11×#19502
C11×#19072
C11×#18002
#2477011