Finite Group Databasebeta

← C11×#24771 #14601964

Subgroups — C11×#24771 #14601964

Order 2816.

872 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#471C212yesmaximal
2C11×#3039C211yesmaximal, characteristic, complemented
3C2×C11×#461C211yesmaximal, characteristic, complemented
4C4×C11×AGL(1,ℤ/8)C211yesmaximal, characteristic
5C11×#2906C211yesmaximal, characteristic, complemented
6C11×#2064C212yesmaximal, complemented
7C11×#2046C212yesmaximal, complemented
8C11×#1966C211yesmaximal, characteristic, complemented
9C11×#1950C211yesmaximal, characteristic, complemented
10C11×#1908C212yesmaximal, complemented
11C11×#1800C211yesmaximal, characteristic, complemented
12C2×C11×#137C2212yes—
13C2×C11×AGL(1,ℤ/8)C2211yescharacteristic
14C22×C11×SD16C2212yes—
15C2×C11×#131C2212yes—
16C2×C11×C4⋊Q8C2211yescharacteristic
17C4×C11×#41C2211yescharacteristic
18C2×C4×D4×C11C2211yescharacteristic
19C11×#471—28no—
20C11×#462—21no—
21C11×#462—21no—
22C11×#461—21no—
23C11×#461—21no—
24C11×#461—21no—
25C11×#461—21no—
26C11×#461—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×#419C2212yes—
41C11×#418C2211yescharacteristic
42C11×#417C2211yescharacteristic
43C2×C11×#103C2212yes—
44C2×C11×#101C2212yes—
45C2×C11×#101C2212yes—
46C2×C11×#100C2212yes—
47C4×C11×M16C2211yescharacteristic
48C11×#343C2212yes—
49C11×#341C2212yes—
50C2×C11×#41C2311yescharacteristic
51C22×Q8×C11C2312yes—
52C22×D4×C11C2311yescharacteristic
53C23×C4×C11—21no—
54C11×#137—24no—
55C11×#137—24no—
56C11×AGL(1,ℤ/8)—22no—
57C11×AGL(1,ℤ/8)D414yes—
58C2×C11×Q16—22no—
59C2×C11×SD16—21no—
60C2×C11×SD16—24no—
61C2×C11×SD16—22no—
62C2×C11×SD16—22no—
63C2×C11×SD16—22no—
64C2×C11×SD16—42no—
65C2×C11×D8—21no—
66C11×#131—24no—
67C11×#131—42no—
68C2×C11×M16—22no—
69C2×C11×M16C2311yescharacteristic
70C2×C11×M16C2312yes—
71C2×C11×M16C2312yes—
72C2×C11×M16C2311yescharacteristic
73C22×C8×C11—22no—
74C22×C8×C11C2312yes—
75C11×C4⋊Q8—21no—
76C11×C4⋊Q8—21no—
77C11×C4⋊Q8—21no—
78C11×C4⋊Q8—21no—
79C4×Q8×C11D411yescharacteristic
80C4×Q8×C11D411yescharacteristic
81C4×D4×C11—21no—
82C4×D4×C11—21no—
83C4×D4×C11—21no—
84C4×D4×C11—21no—
85C4×D4×C11—21no—
86C4×D4×C11—21no—
87C4×D4×C11D411yescharacteristic
88C4×D4×C11D411yescharacteristic
89C11×#117—21no—
90C11×#117C2311yescharacteristic
91C2×C11×C4⋊C4—21no—
92C2×C11×C4⋊C4—21no—
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×#103—22no—
111C11×#103—22no—
112C11×#103—22no—
113C11×#103—22no—
114C11×#102—21no—
115C11×#102—21no—
116C11×#102—21no—
117C11×#101—24no—
118C11×#101—42no—
119C11×#100—24no—
120C11×#97—21no—
121C4×C8×C11—21no—
122#24771C1111yesmaximal, characteristic, direct product factor, Sylow
123C24×C11—21no—
124C11×#41—21no—
125C11×#41—21no—
126C11×#41C2×D412yes—
127C11×#41#4112yes—
128C2×Q8×C11—22no—
129C2×Q8×C11—22no—
130C2×Q8×C11—22no—
131C2×Q8×C11—22no—
132C2×Q8×C11—22no—
133C2×Q8×C11—22no—
134C2×Q8×C11C2×D411yescharacteristic
135C2×D4×C11—21no—
136C2×D4×C11—21no—
137C2×D4×C11—21no—
138C2×D4×C11—21no—
139C2×D4×C11—21no—
140C2×D4×C11—21no—
141C2×D4×C11C2×D412yes—
142C2×D4×C11C2×D411yescharacteristic
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—22no—
147C22×C4×C11—21no—
148C22×C4×C11—41no—
149C22×C4×C11—41no—
150C22×C4×C11—82no—
151C22×C4×C11#4111yescharacteristic
152C22×C4×C11#4111yescharacteristic
153C22×C4×C11C2411yescharacteristic
154C11×Q16—44no—
155C11×SD16—24no—
156C11×SD16—44no—
157C11×SD16—44no—
158C11×SD16—44no—
159C11×D8—24no—
160C11×M16—22no—
161C11×M16—22no—
162C11×M16—21no—
163C11×M16—22no—
164C11×M16—21no—
165C11×M16—22no—
166C11×M16—21no—
167C11×M16—44no—
168C11×M16C2×D412yes—
169C2×C8×C11—21no—
170C2×C8×C11—22no—
171C2×C8×C11—21no—
172C2×C8×C11—22no—
173C2×C8×C11—22no—
174C2×C8×C11—22no—
175C2×C8×C11—44no—
176C2×C8×C11C2×D412yes—
177C2×C8×C11C2×D412yes—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—41no—
183C11×C4⋊C4—41no—
184C11×C4⋊C4—41no—
185C11×C4⋊C4—41no—
186C11×C4⋊C4C2×D411yescharacteristic
187C11×C4⋊C4C2×D411yescharacteristic
188C11×C22⋊C4—21no—
189C11×C22⋊C4—21no—
190C11×C22⋊C4—21no—
191C11×C22⋊C4—41no—
192C11×C22⋊C4—41no—
193C42×C11—21no—
194C42×C11—21no—
195C42×C11—21no—
196C42×C11C2×D411yescharacteristic
197C42×C11C2×D411yescharacteristic
198C42×C11C2×D411yescharacteristic
199C42×C11C2×D411yescharacteristic
200C2×#471C2×C1112yes—
201#3039C2×C1111yescharacteristic, complemented
202C2×#461C2×C1111yescharacteristic, complemented
203C4×AGL(1,ℤ/8)C2×C1111yescharacteristic
204#2906C2×C1111yescharacteristic, complemented
205#2064C2×C1112yescomplemented
206#2046C2×C1112yescomplemented
207#1966C2×C1111yescharacteristic, complemented
208#1950C2×C1111yescharacteristic, complemented
209#1908C2×C1112yescomplemented
210#1800C2×C1111yescharacteristic, complemented
211C23×C11—21no—
212C23×C11—22no—
213C23×C11—41no—
214C23×C11—41no—
215C23×C11—81no—
216C23×C11—81no—
217C23×C11C2×#4111yescharacteristic
218Q8×C11—21no—
219Q8×C11—42no—
220Q8×C11—42no—
221Q8×C11—42no—
222Q8×C11—42no—
223Q8×C11#12112yes—
224D4×C11—22no—
225D4×C11—22no—
226D4×C11—22no—
227D4×C11—21no—
228D4×C11—22no—
229D4×C11—41no—
230D4×C11—41no—
231D4×C11#12112yes—
232C2×C4×C11—21no—
233C2×C4×C11—22no—
234C2×C4×C11—22no—
235C2×C4×C11—22no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—41no—
239C2×C4×C11—42no—
240C2×C4×C11—41no—
241C2×C4×C11—42no—
242C2×C4×C11—42no—
243C2×C4×C11—42no—
244C2×C4×C11—81no—
245C2×C4×C11—82no—
246C2×C4×C11—82no—
247C2×C4×C11—81no—
248C2×C4×C11#12111yescharacteristic
249C2×C4×C11#12111yescharacteristic
250C2×C4×C11#12111yescharacteristic
251C2×C4×C11#12111yescharacteristic
252C2×C4×C11C22×D411yescharacteristic
253C2×C4×C11C22×D411yescharacteristic
254C2×C4×C11C22×D411yescharacteristic
255C2×C4×C11C2×#4111yescharacteristic
256C2×C4×C11H(5,𝔽2)11yescharacteristic
257C2×C4×C112−1+411yescharacteristic
258C8×C11—22no—
259C8×C11—22no—
260C8×C11—22no—
261C8×C11—42no—
262C8×C11—41no—
263C8×C11—42no—
264C2×#137C22×C1112yes—
265C2×AGL(1,ℤ/8)C22×C1111yescharacteristic
266C22×SD16C22×C1112yes—
267C2×#131C22×C1112yes—
268C2×C4⋊Q8C22×C1111yescharacteristic
269C4×#41C22×C1111yescharacteristic
270C2×C4×D4C22×C1111yescharacteristic
271#471—28no—
272#462—21no—
273#462—21no—
274#461—21no—
275#461—21no—
276#461—21no—
277#461—21no—
278#461—22no—
279#442—21no—
280#440—21no—
281C4×SD16—21no—
282C4×D8—21no—
283C2×#108C22×C1112yes—
284#428C22×C1111yescharacteristic
285#424—22no—
286#424C22×C1112yes—
287#423—21no—
288#423C22×C1111yescharacteristic
289#423C22×C1111yescharacteristic
290C2×C4⋊C8—21no—
291C2×C4⋊C8C22×C1111yescharacteristic
292#419C22×C1112yes—
293#418C22×C1111yescharacteristic
294#417C22×C1111yescharacteristic
295C2×#103C22×C1112yes—
296C2×#101C22×C1112yes—
297C2×#101C22×C1112yes—
298C2×#100C22×C1112yes—
299C4×M16C22×C1111yescharacteristic
300#343C22×C1112yes—
301#341C22×C1112yes—
302C22×C11—21no—
303C22×C11—21no—
304C22×C11—22no—
305C22×C11—41no—
306C22×C11—41no—
307C22×C11—42no—
308C22×C11—82no—
309C22×C11—82no—
310C22×C11—81no—
311C22×C11—81no—
312C22×C11C2×#12111yescharacteristic
313C22×C11#54711yescharacteristic
314C22×C11#55311yescharacteristic
315C4×C11—22no—
316C4×C11—21no—
317C4×C11—21no—
318C4×C11—21no—
319C4×C11—41no—
320C4×C11—41no—
321C4×C11—82no—
322C4×C11—81no—
323C4×C11#47112yescomplemented
324C4×C11C2×#12111yescharacteristic
325C4×C11#53711yescharacteristic
326C4×C11D4211yescharacteristic
327C4×C11#54811yescharacteristic
328C2×#41C23×C1111yescharacteristic
329C22×Q8C23×C1112yes—
330C22×D4C23×C1111yescharacteristic
331C23×C4—21no—
332#137—24no—
333#137—24no—
334AGL(1,ℤ/8)—22no—
335AGL(1,ℤ/8)D4×C1114yes—
336C2×Q16—22no—
337C2×SD16—21no—
338C2×SD16—24no—
339C2×SD16—22no—
340C2×SD16—22no—
341C2×SD16—22no—
342C2×SD16—42no—
343C2×D8—21no—
344#131—24no—
345#131—42no—
346C2×M16—22no—
347C2×M16C23×C1112yes—
348C2×M16C23×C1112yes—
349C2×M16C23×C1111yescharacteristic
350C2×M16C23×C1111yescharacteristic
351C22×C8—22no—
352C22×C8C23×C1112yes—
353C4⋊Q8—21no—
354C4⋊Q8—21no—
355C4⋊Q8—21no—
356C4⋊Q8—21no—
357C4×Q8D4×C1111yescharacteristic
358C4×Q8D4×C1111yescharacteristic
359C4×D4—21no—
360C4×D4—21no—
361C4×D4—21no—
362C4×D4—21no—
363C4×D4—21no—
364C4×D4—21no—
365C4×D4D4×C1111yescharacteristic
366C4×D4D4×C1111yescharacteristic
367#117—21no—
368#117C23×C1111yescharacteristic
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4C23×C1111yescharacteristic
372C2×C22⋊C4—21no—
373C2×C42—21no—
374C2×C42C23×C1111yescharacteristic
375#108—24no—
376#107—21no—
377#106—21no—
378C4⋊C8—22no—
379C4⋊C8—22no—
380C4⋊C8—21no—
381C4⋊C8—21no—
382C4⋊C8—21no—
383C4⋊C8—21no—
384C4⋊C8D4×C1111yescharacteristic
385C4⋊C8D4×C1111yescharacteristic
386C4⋊C8D4×C1112yes—
387#103—21no—
388#103—22no—
389#103—22no—
390#103—22no—
391#103—22no—
392#102—21no—
393#102—21no—
394#102—21no—
395#101—24no—
396#101—42no—
397#100—24no—
398#97—21no—
399C4×C8—21no—
400C2×C11—21no—
401C2×C11—21no—
402C2×C11—42no—
403C2×C11—82no—
404C2×C11#241611yescharacteristic
405C2×C11C2×#47111yescharacteristic
406C2×C11#306911yescharacteristic
407C24—21no—
408#41—21no—
409#41—21no—
410#41C2×D4×C1112yes—
411#41C11×#4112yes—
412C2×Q8—22no—
413C2×Q8—22no—
414C2×Q8—22no—
415C2×Q8—22no—
416C2×Q8—22no—
417C2×Q8—22no—
418C2×Q8C2×D4×C1111yescharacteristic
419C2×D4—21no—
420C2×D4—21no—
421C2×D4—21no—
422C2×D4—21no—
423C2×D4—21no—
424C2×D4—21no—
425C2×D4C2×D4×C1112yes—
426C2×D4C2×D4×C1111yescharacteristic
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—22no—
431C22×C4—21no—
432C22×C4—41no—
433C22×C4—41no—
434C22×C4—82no—
435C22×C4C11×#4111yescharacteristic
436C22×C4C11×#4111yescharacteristic
437C22×C4C24×C1111yescharacteristic
438Q16—44no—
439SD16—24no—
440SD16—44no—
441SD16—44no—
442SD16—44no—
443D8—24no—
444M16—21no—
445M16—22no—
446M16—22no—
447M16—22no—
448M16—21no—
449M16—22no—
450M16—21no—
451M16—44no—
452M16C2×D4×C1112yes—
453C2×C8—21no—
454C2×C8—22no—
455C2×C8—22no—
456C2×C8—21no—
457C2×C8—22no—
458C2×C8—22no—
459C2×C8—44no—
460C2×C8C2×D4×C1112yes—
461C2×C8C2×D4×C1112yes—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—41no—
467C4⋊C4—41no—
468C4⋊C4—41no—
469C4⋊C4—41no—
470C4⋊C4C2×D4×C1111yescharacteristic
471C4⋊C4C2×D4×C1111yescharacteristic
472C22⋊C4—21no—
473C22⋊C4—21no—
474C22⋊C4—21no—
475C22⋊C4—41no—
476C22⋊C4—41no—
477C42—21no—
478C42—21no—
479C42—21no—
480C42C2×D4×C1111yescharacteristic
481C42C2×D4×C1111yescharacteristic
482C42C2×D4×C1111yescharacteristic
483C42C2×D4×C1111yescharacteristic
484C11#2477111yescharacteristic, direct product factor, Sylow
485C23—21no—
486C23—22no—
487C23—41no—
488C23—41no—
489C23—81no—
490C23—81no—
491C23C2×C11×#4111yescharacteristic
492Q8—21no—
493Q8—42no—
494Q8—42no—
495Q8—42no—
496Q8—42no—
497Q8C11×#12112yes—
498D4—22no—
499D4—22no—
500D4—22no—
501D4—21no—
502D4—22no—
503D4—41no—
504D4—41no—
505D4C11×#12112yes—
506C2×C4—21no—
507C2×C4—22no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—41no—
513C2×C4—42no—
514C2×C4—41no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—81no—
519C2×C4—82no—
520C2×C4—82no—
521C2×C4—81no—
522C2×C4C11×#12111yescharacteristic
523C2×C4C11×#12111yescharacteristic
524C2×C4C11×#12111yescharacteristic
525C2×C4C11×#12111yescharacteristic
526C2×C4C22×D4×C1111yescharacteristic
527C2×C4C22×D4×C1111yescharacteristic
528C2×C4C22×D4×C1111yescharacteristic
529C2×C4C2×C11×#4111yescharacteristic
530C2×C4C11×H(5,𝔽2)11yescharacteristic
531C2×C4C11×2−1+411yescharacteristic
532C8—22no—
533C8—22no—
534C8—22no—
535C8—42no—
536C8—41no—
537C8—42no—
538C22—21no—
539C22—21no—
540C22—22no—
541C22—41no—
542C22—41no—
543C22—42no—
544C22—82no—
545C22—82no—
546C22—81no—
547C22—81no—
548C22C2×C11×#12111yescharacteristic
549C22C11×#54711yescharacteristic
550C22C11×#55311yescharacteristic
551C4—22no—
552C4—21no—
553C4—21no—
554C4—21no—
555C4—41no—
556C4—41no—
557C4—82no—
558C4—81no—
559C4C11×#47112yescomplemented
560C4C2×C11×#12111yescharacteristic
561C4C11×#53711yescharacteristic
562C4D42×C1111yescharacteristic
563C4C11×#54811yescharacteristic
564C2—21no—
565C2—21no—
566C2—42no—
567C2—82no—
568C2C11×#241611yescharacteristic
569C2C2×C11×#47111yescharacteristic
570C2C11×#306911yescharacteristic
subgroupG/H
center, socleC22×C11C2×#121
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×AGL(1,ℤ/8)C22
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
2. C11×#3039C2semidirect
3. C2×C11×#461C2semidirect
5. C11×#2906C2semidirect
6. C11×#2064C2semidirect
7. C11×#2046C2semidirect
8. C11×#1966C2semidirect
9. C11×#1950C2semidirect
10. C11×#1908C2semidirect
11. C11×#1800C2semidirect
122. #24771C11direct (N × H)
201. #3039C2×C11semidirect
202. C2×#461C2×C11semidirect
204. #2906C2×C11semidirect
205. #2064C2×C11semidirect
206. #2046C2×C11semidirect
207. #1966C2×C11semidirect
208. #1950C2×C11semidirect
209. #1908C2×C11semidirect
210. #1800C2×C11semidirect
323. C4×C11#471semidirect
484. C11#24771direct (N × H)
559. C4C11×#471semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#4712
C11×#30392
C2×C11×#4612
C4×C11×AGL(1,ℤ/8)2
C11×#29062
C11×#20642
C11×#20462
C11×#19662
C11×#19502
C11×#19082
C11×#18002
#2477111