Finite Group Databasebeta

← C11×#32944 #14610137

Subgroups — C11×#32944 #14610137

Order 2816.

1320 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#568C211yesmaximal, characteristic, complemented
2C2×C11×#471C212yesmaximal, complemented
3C2×C11×#468C211yesmaximal, characteristic, complemented
4C11×#3007C211yesmaximal, characteristic, complemented
5C11×#3006C211yesmaximal, characteristic
6C11×#1908C212yesmaximal, complemented
7C11×#1907C212yesmaximal, complemented
8C11×#1901C211yesmaximal, characteristic, complemented
9C11×#1900C211yesmaximal, characteristic, complemented
10C11×#1816C212yesmaximal, complemented
11C11×#1811C211yesmaximal, characteristic, complemented
12C22×C11×#41C2211yescharacteristic
13C2×C11×#137C2212yes—
14C2×C11×AGL(1,ℤ/8)C2212yes—
15C22×C11×SD16C2211yescharacteristic, complemented
16C11×#568—28no—
17C2×C11×#131—22no—
18C2×C11×#131C2212yes—
19C2×C11×#131C2212yes—
20C22×C11×M16—22no—
21C22×C11×M16C2211yescharacteristic
22C22×C11×M16C2211yescharacteristic
23C2×C11×C22⋊Q8C2211yescharacteristic
24C2×C11×#121C2211yescharacteristic
25C11×#471—28no—
26C11×#468—22no—
27C11×#468—22no—
28C11×#452—22no—
29C11×#451—21no—
30C11×#450—21no—
31C11×#449—22no—
32C11×#448—21no—
33C11×#447—21no—
34C2×C11×#108C2212yescomplemented
35C2×C11×#107C2211yescharacteristic, complemented
36C11×#417C2212yes—
37C11×#417C2212yes—
38C2×C11×#103C2211yescharacteristic, complemented
39C2×C11×#102C2211yescharacteristic, complemented
40C2×C11×#101C2212yescomplemented
41C2×C11×#100C2212yescomplemented
42C11×#407C2211yescharacteristic
43C11×#407C2211yescharacteristic
44C11×#343C2212yescomplemented
45C11×#343C2212yescomplemented
46C11×#341C2212yescomplemented
47C2×C11×#41—24no—
48C2×C11×#41—24no—
49C2×C11×#41—21no—
50C2×C11×#41—21no—
51C2×C11×#41D412yes—
52C2×C11×#41C2312yes—
53C22×Q8×C11D411yescharacteristic
54C22×Q8×C11C2311yescharacteristic
55C22×D4×C11—21no—
56C22×D4×C11—21no—
57C22×D4×C11D411yescharacteristic
58C22×D4×C11C2311yescharacteristic
59C23×C4×C11—21no—
60C23×C4×C11C2311yescharacteristic
61C11×#137—24no—
62C11×#137—24no—
63C11×AGL(1,ℤ/8)—24no—
64C11×AGL(1,ℤ/8)—24no—
65C2×C11×Q16—22no—
66C2×C11×SD16—22no—
67C2×C11×SD16—22no—
68C2×C11×SD16—22no—
69C2×C11×SD16—24no—
70C2×C11×D8—22no—
71C11×#131—216no—
72C11×#131—24no—
73C11×#131—24no—
74C11×#131—24no—
75C11×#131D418yescomplemented
76C2×C11×M16—216no—
77C2×C11×M16—21no—
78C2×C11×M16—24no—
79C2×C11×M16—22no—
80C2×C11×M16—22no—
81C2×C11×M16—24no—
82C2×C11×M16D412yes—
83C2×C11×M16D412yes—
84C2×C11×M16C2312yes—
85C2×C11×M16C2312yes—
86C2×C11×M16C2312yes—
87C22×C8×C11—21no—
88C22×C8×C11—22no—
89C22×C8×C11—22no—
90C22×C8×C11C2311yescharacteristic
91C22×C8×C11C2311yescharacteristic
92C11×C22⋊Q8—21no—
93C11×C22⋊Q8—21no—
94C11×C22⋊Q8—21no—
95C11×C22⋊Q8—21no—
96C11×#121—21no—
97C11×#121—21no—
98C11×#121—21no—
99C11×#121—21no—
100C2×C11×C4⋊C4—21no—
101C2×C11×C4⋊C4C2311yescharacteristic
102C2×C11×C4⋊C4C2311yescharacteristic
103C2×C11×C22⋊C4—21no—
104C2×C11×C22⋊C4—21no—
105C11×#108—24no—
106C11×#107—22no—
107C11×#103—22no—
108C11×#103—22no—
109C11×#103—22no—
110C11×#102—22no—
111C11×#102—22no—
112C11×#102—22no—
113C11×#101—24no—
114C11×#100—24no—
115C11×C22⋊C8—21no—
116C11×C22⋊C8—21no—
117C11×C22⋊C8—21no—
118C11×C22⋊C8—21no—
119#32944C1111yesmaximal, characteristic, direct product factor, Sylow
120C24×C11—21no—
121C24×C11—21no—
122C24×C11#4111yescharacteristic
123C11×#41—24no—
124C11×#41—28no—
125C11×#41—24no—
126C11×#41—24no—
127C11×#41—24no—
128C11×#41—22no—
129C11×#41—22no—
130C11×#41C2×D414yes—
131C11×#41#4114yes—
132C2×Q8×C11—24no—
133C2×Q8×C11—21no—
134C2×Q8×C11—22no—
135C2×Q8×C11—21no—
136C2×Q8×C11—21no—
137C2×Q8×C11—22no—
138C2×Q8×C11C2×D412yes—
139C2×D4×C11—28no—
140C2×D4×C11—22no—
141C2×D4×C11—22no—
142C2×D4×C11—24no—
143C2×D4×C11—21no—
144C2×D4×C11—22no—
145C2×D4×C11—21no—
146C2×D4×C11—21no—
147C2×D4×C11—22no—
148C2×D4×C11—41no—
149C2×D4×C11—41no—
150C2×D4×C11—82no—
151C2×D4×C11C2×D412yes—
152C22×C4×C11—24no—
153C22×C4×C11—24no—
154C22×C4×C11—21no—
155C22×C4×C11—22no—
156C22×C4×C11—22no—
157C22×C4×C11—22no—
158C22×C4×C11—22no—
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11—21no—
162C22×C4×C11C2×D411yescharacteristic
163C22×C4×C11C2×D411yescharacteristic
164C22×C4×C11C2×D411yescharacteristic
165C22×C4×C11C2×D411yescharacteristic
166C22×C4×C11#4111yescharacteristic
167C22×C4×C11C2411yescharacteristic
168C11×Q16—44no—
169C11×SD16—44no—
170C11×SD16—44no—
171C11×SD16—44no—
172C11×D8—44no—
173C11×M16—24no—
174C11×M16—28no—
175C11×M16—24no—
176C11×M16—28no—
177C11×M16—24no—
178C11×M16—22no—
179C11×M16—22no—
180C11×M16—22no—
181C11×M16—22no—
182C11×M16—22no—
183C11×M16C2×D414yes—
184C2×C8×C11—28no—
185C2×C8×C11—24no—
186C2×C8×C11—28no—
187C2×C8×C11—22no—
188C2×C8×C11—22no—
189C2×C8×C11—22no—
190C2×C8×C11—22no—
191C2×C8×C11C2×D412yes—
192C2×C8×C11C2×D412yes—
193C2×C8×C11C2×D414yes—
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×C22⋊C4—41no—
201C11×C22⋊C4—41no—
202C11×C22⋊C4—41no—
203C11×C22⋊C4—41no—
204C2×#568C2×C1111yescharacteristic, complemented
205C2×#471C2×C1112yescomplemented
206C2×#468C2×C1111yescharacteristic, complemented
207#3007C2×C1111yescharacteristic, complemented
208#3006C2×C1111yescharacteristic
209#1908C2×C1112yescomplemented
210#1907C2×C1112yescomplemented
211#1901C2×C1111yescharacteristic, complemented
212#1900C2×C1111yescharacteristic, complemented
213#1816C2×C1112yescomplemented
214#1811C2×C1111yescharacteristic, complemented
215C23×C11—24no—
216C23×C11—22no—
217C23×C11—22no—
218C23×C11—41no—
219C23×C11—41no—
220C23×C11—41no—
221C23×C11—42no—
222C23×C11—81no—
223C23×C11—81no—
224C23×C11—81no—
225C23×C11—81no—
226C23×C11#12111yescharacteristic
227C23×C11#12111yescharacteristic
228C23×C11C2×#4111yescharacteristic
229Q8×C11—24no—
230Q8×C11—22no—
231Q8×C11—41no—
232Q8×C11—42no—
233Q8×C11—41no—
234Q8×C11#12114yes—
235D4×C11—28no—
236D4×C11—24no—
237D4×C11—24no—
238D4×C11—24no—
239D4×C11—22no—
240D4×C11—41no—
241D4×C11—42no—
242D4×C11—41no—
243D4×C11—82no—
244D4×C11—82no—
245D4×C11#12114yes—
246C2×C4×C11—24no—
247C2×C4×C11—28no—
248C2×C4×C11—22no—
249C2×C4×C11—22no—
250C2×C4×C11—24no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—22no—
254C2×C4×C11—22no—
255C2×C4×C11—21no—
256C2×C4×C11—24no—
257C2×C4×C11—21no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11—42no—
262C2×C4×C11—81no—
263C2×C4×C11—81no—
264C2×C4×C11#12111yescharacteristic
265C2×C4×C11#12111yescharacteristic
266C2×C4×C11C22×D412yes—
267C2×C4×C11C22×D411yescharacteristic
268C2×C4×C11C22×D411yescharacteristic
269C2×C4×C11C2×#4112yes—
270C8×C11—24no—
271C8×C11—22no—
272C8×C11—42no—
273C8×C11—42no—
274C8×C11#12014yes—
275C22×#41C22×C1111yescharacteristic
276C2×#137C22×C1112yes—
277C2×AGL(1,ℤ/8)C22×C1112yes—
278C22×SD16C22×C1111yescharacteristic, complemented
279#568—28no—
280C2×#131—22no—
281C2×#131C22×C1112yes—
282C2×#131C22×C1112yes—
283C22×M16—22no—
284C22×M16C22×C1111yescharacteristic
285C22×M16C22×C1111yescharacteristic
286C2×C22⋊Q8C22×C1111yescharacteristic
287C2×#121C22×C1111yescharacteristic
288#471—28no—
289#468—22no—
290#468—22no—
291#452—22no—
292#451—21no—
293#450—21no—
294#449—22no—
295#448—21no—
296#447—21no—
297C2×#108C22×C1112yescomplemented
298C2×#107C22×C1111yescharacteristic, complemented
299#417C22×C1112yes—
300#417C22×C1112yes—
301C2×#103C22×C1111yescharacteristic, complemented
302C2×#102C22×C1111yescharacteristic, complemented
303C2×#101C22×C1112yescomplemented
304C2×#100C22×C1112yescomplemented
305#407C22×C1111yescharacteristic
306#407C22×C1111yescharacteristic
307#343C22×C1112yescomplemented
308#343C22×C1112yescomplemented
309#341C22×C1112yescomplemented
310C22×C11—21no—
311C22×C11—21no—
312C22×C11—21no—
313C22×C11—21no—
314C22×C11—24no—
315C22×C11—21no—
316C22×C11—21no—
317C22×C11—21no—
318C22×C11—21no—
319C22×C11—42no—
320C22×C11—42no—
321C22×C11—82no—
322C22×C11—84no—
323C22×C11—81no—
324C22×C11—81no—
325C22×C11—81no—
326C22×C11—162no—
327C22×C11C2×#12111yescharacteristic
328C22×C11#52512yes—
329C4×C11—21no—
330C4×C11—24no—
331C4×C11—21no—
332C4×C11—81no—
333C4×C11—81no—
334C4×C11—81no—
335C4×C11C2×#12011yescharacteristic
336C4×C11C2×#12112yes—
337C4×C11#52511yescharacteristic
338C2×#41—24no—
339C2×#41—24no—
340C2×#41—21no—
341C2×#41—21no—
342C2×#41D4×C1112yes—
343C2×#41C23×C1112yes—
344C22×Q8D4×C1111yescharacteristic
345C22×Q8C23×C1111yescharacteristic
346C22×D4—21no—
347C22×D4—21no—
348C22×D4D4×C1111yescharacteristic
349C22×D4C23×C1111yescharacteristic
350C23×C4—21no—
351C23×C4C23×C1111yescharacteristic
352#137—24no—
353#137—24no—
354AGL(1,ℤ/8)—24no—
355AGL(1,ℤ/8)—24no—
356C2×Q16—22no—
357C2×SD16—22no—
358C2×SD16—22no—
359C2×SD16—22no—
360C2×SD16—24no—
361C2×D8—22no—
362#131—216no—
363#131—24no—
364#131—24no—
365#131—24no—
366#131D4×C1118yescomplemented
367C2×M16—216no—
368C2×M16—21no—
369C2×M16—24no—
370C2×M16—22no—
371C2×M16—22no—
372C2×M16—24no—
373C2×M16D4×C1112yes—
374C2×M16D4×C1112yes—
375C2×M16C23×C1112yes—
376C2×M16C23×C1112yes—
377C2×M16C23×C1112yes—
378C22×C8—21no—
379C22×C8—22no—
380C22×C8—22no—
381C22×C8C23×C1111yescharacteristic
382C22×C8C23×C1111yescharacteristic
383C22⋊Q8—21no—
384C22⋊Q8—21no—
385C22⋊Q8—21no—
386C22⋊Q8—21no—
387#121—21no—
388#121—21no—
389#121—21no—
390#121—21no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4C23×C1111yescharacteristic
393C2×C4⋊C4C23×C1111yescharacteristic
394C2×C22⋊C4—21no—
395C2×C22⋊C4—21no—
396#108—24no—
397#107—22no—
398#103—22no—
399#103—22no—
400#103—22no—
401#102—22no—
402#102—22no—
403#102—22no—
404#101—24no—
405#100—24no—
406C22⋊C8—21no—
407C22⋊C8—21no—
408C22⋊C8—21no—
409C22⋊C8—21no—
410C2×C11—22no—
411C2×C11—41no—
412C2×C11—41no—
413C2×C11—44no—
414C2×C11—161no—
415C2×C11#284711yescharacteristic
416C2×C11#306811yescharacteristic
417C2×C11#306911yescharacteristic
418C24—21no—
419C24—21no—
420C24C11×#4111yescharacteristic
421#41—24no—
422#41—28no—
423#41—24no—
424#41—24no—
425#41—24no—
426#41—22no—
427#41—22no—
428#41C2×D4×C1114yes—
429#41C11×#4114yes—
430C2×Q8—24no—
431C2×Q8—21no—
432C2×Q8—22no—
433C2×Q8—21no—
434C2×Q8—21no—
435C2×Q8—22no—
436C2×Q8C2×D4×C1112yes—
437C2×D4—28no—
438C2×D4—22no—
439C2×D4—22no—
440C2×D4—24no—
441C2×D4—21no—
442C2×D4—22no—
443C2×D4—21no—
444C2×D4—21no—
445C2×D4—22no—
446C2×D4—41no—
447C2×D4—41no—
448C2×D4—82no—
449C2×D4C2×D4×C1112yes—
450C22×C4—24no—
451C22×C4—24no—
452C22×C4—21no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4C2×D4×C1111yescharacteristic
461C22×C4C2×D4×C1111yescharacteristic
462C22×C4C2×D4×C1111yescharacteristic
463C22×C4C2×D4×C1111yescharacteristic
464C22×C4C11×#4111yescharacteristic
465C22×C4C24×C1111yescharacteristic
466Q16—44no—
467SD16—44no—
468SD16—44no—
469SD16—44no—
470D8—44no—
471M16—24no—
472M16—28no—
473M16—22no—
474M16—24no—
475M16—28no—
476M16—24no—
477M16—22no—
478M16—22no—
479M16—22no—
480M16—22no—
481M16C2×D4×C1114yes—
482C2×C8—24no—
483C2×C8—28no—
484C2×C8—22no—
485C2×C8—22no—
486C2×C8—28no—
487C2×C8—22no—
488C2×C8—22no—
489C2×C8C2×D4×C1112yes—
490C2×C8C2×D4×C1112yes—
491C2×C8C2×D4×C1114yes—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—41no—
497C4⋊C4—41no—
498C22⋊C4—41no—
499C22⋊C4—41no—
500C22⋊C4—41no—
501C22⋊C4—41no—
502C11#3294411yescharacteristic, direct product factor, Sylow
503C23—24no—
504C23—22no—
505C23—22no—
506C23—41no—
507C23—41no—
508C23—41no—
509C23—42no—
510C23—81no—
511C23—81no—
512C23—81no—
513C23—81no—
514C23C11×#12111yescharacteristic
515C23C11×#12111yescharacteristic
516C23C2×C11×#4111yescharacteristic
517Q8—24no—
518Q8—22no—
519Q8—41no—
520Q8—42no—
521Q8—41no—
522Q8C11×#12114yes—
523D4—28no—
524D4—24no—
525D4—24no—
526D4—24no—
527D4—22no—
528D4—41no—
529D4—42no—
530D4—41no—
531D4—82no—
532D4—82no—
533D4C11×#12114yes—
534C2×C4—24no—
535C2×C4—28no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—24no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—21no—
544C2×C4—24no—
545C2×C4—21no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—42no—
550C2×C4—81no—
551C2×C4—81no—
552C2×C4C11×#12111yescharacteristic
553C2×C4C11×#12111yescharacteristic
554C2×C4C22×D4×C1112yes—
555C2×C4C22×D4×C1111yescharacteristic
556C2×C4C22×D4×C1111yescharacteristic
557C2×C4C2×C11×#4112yes—
558C8—24no—
559C8—22no—
560C8—42no—
561C8—42no—
562C8C11×#12014yes—
563C22—21no—
564C22—21no—
565C22—21no—
566C22—21no—
567C22—21no—
568C22—21no—
569C22—21no—
570C22—21no—
571C22—24no—
572C22—42no—
573C22—42no—
574C22—82no—
575C22—84no—
576C22—81no—
577C22—81no—
578C22—81no—
579C22—162no—
580C22C2×C11×#12111yescharacteristic
581C22C11×#52512yes—
582C4—21no—
583C4—24no—
584C4—21no—
585C4—81no—
586C4—81no—
587C4—81no—
588C4C2×C11×#12011yescharacteristic
589C4C2×C11×#12112yes—
590C4C11×#52511yescharacteristic
591C2—22no—
592C2—41no—
593C2—41no—
594C2—44no—
595C2—161no—
596C2C11×#284711yescharacteristic
597C2C11×#306811yescharacteristic
598C2C11×#306911yescharacteristic
subgroupG/H
center, socleC22×C11C2×#121
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#3006C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#568C2semidirect
2. C2×C11×#471C2semidirect
3. C2×C11×#468C2semidirect
4. C11×#3007C2semidirect
6. C11×#1908C2semidirect
7. C11×#1907C2semidirect
8. C11×#1901C2semidirect
9. C11×#1900C2semidirect
10. C11×#1816C2semidirect
11. C11×#1811C2semidirect
15. C22×C11×SD16C22semidirect
34. C2×C11×#108C22semidirect
35. C2×C11×#107C22semidirect
38. C2×C11×#103C22semidirect
39. C2×C11×#102C22semidirect
40. C2×C11×#101C22semidirect
41. C2×C11×#100C22semidirect
44. C11×#343C22semidirect
45. C11×#343C22semidirect
46. C11×#341C22semidirect
75. C11×#131D4semidirect
119. #32944C11direct (N × H)
204. C2×#568C2×C11semidirect
205. C2×#471C2×C11semidirect
206. C2×#468C2×C11semidirect
207. #3007C2×C11semidirect
209. #1908C2×C11semidirect
210. #1907C2×C11semidirect
211. #1901C2×C11semidirect
212. #1900C2×C11semidirect
213. #1816C2×C11semidirect
214. #1811C2×C11semidirect
278. C22×SD16C22×C11semidirect
297. C2×#108C22×C11semidirect
298. C2×#107C22×C11semidirect
301. C2×#103C22×C11semidirect
302. C2×#102C22×C11semidirect
303. C2×#101C22×C11semidirect
304. C2×#100C22×C11semidirect
307. #343C22×C11semidirect
308. #343C22×C11semidirect
309. #341C22×C11semidirect
366. #131D4×C11semidirect
502. C11#32944direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5682
C2×C11×#4712
C2×C11×#4682
C11×#30072
C11×#30062
C11×#19082
C11×#19072
C11×#19012
C11×#19002
C11×#18162
C11×#18112
#3294411