Finite Group Databasebeta

← C11×#9039 #14586232

Subgroups — C11×#9039 #14586232

Order 2816.

834 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#448C211yesmaximal, characteristic
2C11×#2325C211yesmaximal, characteristic
3C11×#1787C211yesmaximal, characteristic, complemented
4C2×C11×#327C211yesmaximal, characteristic
5C11×#1446C211yesmaximal, characteristic, complemented
6C11×#1294C211yesmaximal, characteristic, complemented
7C11×#1280C211yesmaximal, characteristic, complemented
8C23×Q8×C11C2211yescharacteristic
9C22×C11×SD16—21no—
10C2×C11×#121C2211yescharacteristic
11C2×C4×D4×C11—21no—
12C11×#448—22no—
13C11×#448C414yescomplemented
14C2×C11×#103—21no—
15C2×C11×#103—21no—
16C2×C11×#103—21no—
17C2×C11×C22⋊C8C2211yescharacteristic
18C2×C11×C22⋊C8C2211yescharacteristic
19C11×#388—21no—
20C11×#387—21no—
21C11×#386—21no—
22C11×#386—21no—
23C11×#385—21no—
24C11×#380C2211yescharacteristic
25C2×C11×#95—21no—
26C2×C11×#95—21no—
27C2×C11×#95C2211yescharacteristic
28C2×C11×#95C2211yescharacteristic
29C11×#327—22no—
30C22×Q8×C11—21no—
31C22×Q8×C11—21no—
32C22×Q8×C11—21no—
33C22×Q8×C11—21no—
34C22×Q8×C11—21no—
35C22×Q8×C11—42no—
36C22×Q8×C11—42no—
37C22×Q8×C11C2×C412yescomplemented
38C22×D4×C11—21no—
39C22×D4×C11D411yescharacteristic
40C23×C4×C11—21no—
41C23×C4×C11—21no—
42C23×C4×C11—21no—
43C23×C4×C11D411yescharacteristic
44C23×C4×C11D411yescharacteristic
45C23×C4×C11C2311yescharacteristic
46C2×C11×SD16—24no—
47C2×C11×SD16—42no—
48C2×C11×SD16—42no—
49C22×C8×C11—21no—
50C22×C8×C11—21no—
51C11×#121—21no—
52C11×#121—21no—
53C11×#121C2×C412yes—
54C11×#121D412yes—
55C4×D4×C11—42no—
56C4×D4×C11—42no—
57C2×C11×C4⋊C4—21no—
58C2×C11×C4⋊C4D411yescharacteristic
59C2×C11×C4⋊C4D411yescharacteristic
60C2×C11×C4⋊C4D411yescharacteristic
61C2×C11×C22⋊C4—21no—
62C2×C11×C22⋊C4—21no—
63C2×C11×C22⋊C4—21no—
64C2×C11×C22⋊C4—21no—
65C2×C11×C22⋊C4—21no—
66C2×C42×C11—21no—
67C11×#103—24no—
68C11×#103—42no—
69C11×#103—42no—
70C11×C22⋊C8—21no—
71C11×C22⋊C8—21no—
72C11×C22⋊C8—21no—
73C11×C22⋊C8C2×C412yescomplemented
74C11×#95—21no—
75C11×#95—21no—
76C11×#95—21no—
77C11×#95—21no—
78C11×#95—21no—
79C11×#95—21no—
80C11×#95—21no—
81C11×#95—42no—
82C11×#95—42no—
83#9039C1111yesmaximal, characteristic, direct product factor, Sylow
84C24×C11—21no—
85C24×C11C2×D411yescharacteristic
86C2×Q8×C11—22no—
87C2×Q8×C11—22no—
88C2×Q8×C11—22no—
89C2×Q8×C11—22no—
90C2×Q8×C11—22no—
91C2×Q8×C11—22no—
92C2×Q8×C11—44no—
93C2×Q8×C11—41no—
94C2×Q8×C11—41no—
95C2×Q8×C11—41no—
96C2×Q8×C11—41no—
97C2×Q8×C11—44no—
98C2×Q8×C11—44no—
99C2×Q8×C11—44no—
100C2×Q8×C11—41no—
101C2×Q8×C11—41no—
102C2×D4×C11—22no—
103C2×D4×C11—22no—
104C2×D4×C11—21no—
105C2×D4×C11—41no—
106C2×D4×C11—41no—
107C2×D4×C11—41no—
108C2×D4×C11—41no—
109C2×D4×C11—41no—
110C2×D4×C11—41no—
111C2×D4×C11C22⋊C412yes—
112C22×C4×C11—22no—
113C22×C4×C11—22no—
114C22×C4×C11—22no—
115C22×C4×C11—21no—
116C22×C4×C11—21no—
117C22×C4×C11—21no—
118C22×C4×C11—22no—
119C22×C4×C11—21no—
120C22×C4×C11—21no—
121C22×C4×C11—21no—
122C22×C4×C11—21no—
123C22×C4×C11—21no—
124C22×C4×C11—41no—
125C22×C4×C11—41no—
126C22×C4×C11—42no—
127C22×C4×C11—41no—
128C22×C4×C11—41no—
129C22×C4×C11—41no—
130C22×C4×C11—41no—
131C22×C4×C11—41no—
132C22×C4×C11—41no—
133C22×C4×C11—41no—
134C22×C4×C11—41no—
135C22×C4×C11—41no—
136C22×C4×C11—41no—
137C22×C4×C11—41no—
138C22×C4×C11—41no—
139C22×C4×C11—41no—
140C22×C4×C11—41no—
141C22×C4×C11—81no—
142C22×C4×C11—81no—
143C22×C4×C11SD1612yescomplemented
144C22×C4×C11C22×C411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11#4111yescharacteristic
149C22×C4×C11#4111yescharacteristic
150C11×SD16—48no—
151C2×C8×C11—22no—
152C2×C8×C11—41no—
153C2×C8×C11—41no—
154C2×C8×C11—41no—
155C2×C8×C11—41no—
156C2×C8×C11—41no—
157C11×C4⋊C4—21no—
158C11×C4⋊C4—42no—
159C11×C4⋊C4—41no—
160C11×C4⋊C4—41no—
161C11×C4⋊C4C22⋊C412yes—
162C11×C22⋊C4—22no—
163C11×C22⋊C4—22no—
164C11×C22⋊C4—42no—
165C11×C22⋊C4—41no—
166C11×C22⋊C4—41no—
167C11×C22⋊C4—81no—
168C11×C22⋊C4—81no—
169C42×C11—42no—
170C2×#448C2×C1111yescharacteristic
171#2325C2×C1111yescharacteristic
172#1787C2×C1111yescharacteristic, complemented
173C2×#327C2×C1111yescharacteristic
174#1446C2×C1111yescharacteristic, complemented
175#1294C2×C1111yescharacteristic, complemented
176#1280C2×C1111yescharacteristic, complemented
177C23×C11—21no—
178C23×C11—21no—
179C23×C11—21no—
180C23×C11—21no—
181C23×C11—22no—
182C23×C11—41no—
183C23×C11—41no—
184C23×C11—41no—
185C23×C11—41no—
186C23×C11—41no—
187C23×C11—41no—
188C23×C11C4×D411yescharacteristic
189C23×C11#12011yescharacteristic
190C23×C11#12111yescharacteristic
191C23×C11C2×SD1611yescharacteristic
192C23×C11#13511yescharacteristic
193C23×C11AGL(1,ℤ/8)11yescharacteristic
194C23×C11#13711yescharacteristic
195Q8×C11—24no—
196Q8×C11—24no—
197Q8×C11—42no—
198Q8×C11—42no—
199Q8×C11—42no—
200Q8×C11—42no—
201Q8×C11—42no—
202Q8×C11—42no—
203D4×C11—42no—
204D4×C11—42no—
205D4×C11—42no—
206D4×C11—42no—
207D4×C11—42no—
208D4×C11—81no—
209C2×C4×C11—21no—
210C2×C4×C11—21no—
211C2×C4×C11—21no—
212C2×C4×C11—21no—
213C2×C4×C11—24no—
214C2×C4×C11—22no—
215C2×C4×C11—22no—
216C2×C4×C11—41no—
217C2×C4×C11—41no—
218C2×C4×C11—41no—
219C2×C4×C11—41no—
220C2×C4×C11—42no—
221C2×C4×C11—42no—
222C2×C4×C11—42no—
223C2×C4×C11—42no—
224C2×C4×C11—41no—
225C2×C4×C11—41no—
226C2×C4×C11—41no—
227C2×C4×C11—42no—
228C2×C4×C11—42no—
229C2×C4×C11—41no—
230C2×C4×C11—42no—
231C2×C4×C11—42no—
232C2×C4×C11—42no—
233C2×C4×C11—42no—
234C2×C4×C11—42no—
235C2×C4×C11—41no—
236C2×C4×C11—41no—
237C2×C4×C11—41no—
238C2×C4×C11—41no—
239C2×C4×C11—41no—
240C2×C4×C11—41no—
241C2×C4×C11—41no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11—81no—
245C2×C4×C11—84no—
246C2×C4×C11—81no—
247C2×C4×C11—81no—
248C2×C4×C11—81no—
249C2×C4×C11—81no—
250C2×C4×C11—81no—
251C2×C4×C11C2×C22⋊C411yescharacteristic
252C2×C4×C11C4×D411yescharacteristic
253C2×C4×C11#12111yescharacteristic
254C2×C4×C11#12311yescharacteristic
255C8×C11—42no—
256C8×C11—81no—
257C23×Q8C22×C1111yescharacteristic
258C22×SD16—21no—
259C2×#121C22×C1111yescharacteristic
260C2×C4×D4—21no—
261#448—22no—
262#448C4×C1114yescomplemented
263C2×#103—21no—
264C2×#103—21no—
265C2×#103—21no—
266C2×C22⋊C8C22×C1111yescharacteristic
267C2×C22⋊C8C22×C1111yescharacteristic
268#388—21no—
269#387—21no—
270#386—21no—
271#386—21no—
272#385—21no—
273#380C22×C1111yescharacteristic
274C2×#95—21no—
275C2×#95—21no—
276C2×#95C22×C1111yescharacteristic
277C2×#95C22×C1111yescharacteristic
278#327—22no—
279C22×C11—21no—
280C22×C11—21no—
281C22×C11—21no—
282C22×C11—21no—
283C22×C11—21no—
284C22×C11—21no—
285C22×C11—21no—
286C22×C11—21no—
287C22×C11—21no—
288C22×C11—21no—
289C22×C11—21no—
290C22×C11—21no—
291C22×C11—42no—
292C22×C11—42no—
293C22×C11—42no—
294C22×C11—81no—
295C22×C11—81no—
296C22×C11—81no—
297C22×C11—81no—
298C22×C11#38611yescharacteristic
299C22×C11C4×SD1611yescharacteristic
300C22×C11#44011yescharacteristic
301C22×C11#45011yescharacteristic
302C22×C11#45211yescharacteristic
303C22×C11#45511yescharacteristic
304C22×C11#45611yescharacteristic
305C22×C11B(4,𝔽2)11yescharacteristic
306C22×C11B(4,𝔽2)11yescharacteristic
307C22×C11#46111yescharacteristic
308C22×C11#46311yescharacteristic
309C4×C11—21no—
310C4×C11—21no—
311C4×C11—21no—
312C4×C11—21no—
313C4×C11—42no—
314C4×C11—42no—
315C4×C11—44no—
316C4×C11—82no—
317C4×C11—81no—
318C4×C11—81no—
319C4×C11—81no—
320C22×Q8—21no—
321C22×Q8—21no—
322C22×Q8—21no—
323C22×Q8—21no—
324C22×Q8—21no—
325C22×Q8—42no—
326C22×Q8—42no—
327C22×Q8C2×C4×C1112yescomplemented
328C22×D4—21no—
329C22×D4D4×C1111yescharacteristic
330C23×C4—21no—
331C23×C4—21no—
332C23×C4—21no—
333C23×C4D4×C1111yescharacteristic
334C23×C4D4×C1111yescharacteristic
335C23×C4C23×C1111yescharacteristic
336C2×SD16—24no—
337C2×SD16—42no—
338C2×SD16—42no—
339C22×C8—21no—
340C22×C8—21no—
341#121—21no—
342#121—21no—
343#121C2×C4×C1112yes—
344#121D4×C1112yes—
345C4×D4—42no—
346C4×D4—42no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4D4×C1111yescharacteristic
349C2×C4⋊C4D4×C1111yescharacteristic
350C2×C4⋊C4D4×C1111yescharacteristic
351C2×C22⋊C4—21no—
352C2×C22⋊C4—21no—
353C2×C22⋊C4—21no—
354C2×C22⋊C4—21no—
355C2×C22⋊C4—21no—
356C2×C42—21no—
357#103—24no—
358#103—42no—
359#103—42no—
360C22⋊C8—21no—
361C22⋊C8—21no—
362C22⋊C8—21no—
363C22⋊C8C2×C4×C1112yescomplemented
364#95—21no—
365#95—21no—
366#95—21no—
367#95—21no—
368#95—21no—
369#95—21no—
370#95—21no—
371#95—42no—
372#95—42no—
373C2×C11—21no—
374C2×C11—21no—
375C2×C11—21no—
376C2×C11—21no—
377C2×C11—82no—
378C2×C11#160111yescharacteristic
379C2×C11#160311yescharacteristic
380C2×C11#160411yescharacteristic
381C2×C11#160611yescharacteristic
382C2×C11#187711yescharacteristic
383C2×C11#188211yescharacteristic
384C2×C11#188911yescharacteristic
385C24—21no—
386C24C2×D4×C1111yescharacteristic
387C2×Q8—22no—
388C2×Q8—22no—
389C2×Q8—22no—
390C2×Q8—22no—
391C2×Q8—22no—
392C2×Q8—22no—
393C2×Q8—44no—
394C2×Q8—41no—
395C2×Q8—41no—
396C2×Q8—41no—
397C2×Q8—41no—
398C2×Q8—44no—
399C2×Q8—44no—
400C2×Q8—44no—
401C2×Q8—41no—
402C2×Q8—41no—
403C2×D4—22no—
404C2×D4—22no—
405C2×D4—21no—
406C2×D4—41no—
407C2×D4—41no—
408C2×D4—41no—
409C2×D4—41no—
410C2×D4—41no—
411C2×D4—41no—
412C2×D4C11×C22⋊C412yes—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—22no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—41no—
426C22×C4—41no—
427C22×C4—42no—
428C22×C4—41no—
429C22×C4—41no—
430C22×C4—41no—
431C22×C4—41no—
432C22×C4—41no—
433C22×C4—41no—
434C22×C4—41no—
435C22×C4—41no—
436C22×C4—41no—
437C22×C4—41no—
438C22×C4—41no—
439C22×C4—41no—
440C22×C4—41no—
441C22×C4—41no—
442C22×C4—81no—
443C22×C4—81no—
444C22×C4C11×SD1612yescomplemented
445C22×C4C22×C4×C1111yescharacteristic
446C22×C4C2×D4×C1111yescharacteristic
447C22×C4C2×D4×C1111yescharacteristic
448C22×C4C2×D4×C1111yescharacteristic
449C22×C4C11×#4111yescharacteristic
450C22×C4C11×#4111yescharacteristic
451SD16—48no—
452C2×C8—22no—
453C2×C8—41no—
454C2×C8—41no—
455C2×C8—41no—
456C2×C8—41no—
457C2×C8—41no—
458C4⋊C4—21no—
459C4⋊C4—41no—
460C4⋊C4—41no—
461C4⋊C4—42no—
462C4⋊C4C11×C22⋊C412yes—
463C22⋊C4—22no—
464C22⋊C4—22no—
465C22⋊C4—42no—
466C22⋊C4—41no—
467C22⋊C4—41no—
468C22⋊C4—81no—
469C22⋊C4—81no—
470C42—42no—
471C11#903911yescharacteristic, direct product factor, Sylow
472C23—21no—
473C23—21no—
474C23—21no—
475C23—21no—
476C23—22no—
477C23—41no—
478C23—41no—
479C23—41no—
480C23—41no—
481C23—41no—
482C23—41no—
483C23C4×D4×C1111yescharacteristic
484C23C11×#12011yescharacteristic
485C23C11×#12111yescharacteristic
486C23C2×C11×SD1611yescharacteristic
487C23C11×#13511yescharacteristic
488C23C11×AGL(1,ℤ/8)11yescharacteristic
489C23C11×#13711yescharacteristic
490Q8—24no—
491Q8—24no—
492Q8—42no—
493Q8—42no—
494Q8—42no—
495Q8—42no—
496Q8—42no—
497Q8—42no—
498D4—42no—
499D4—42no—
500D4—42no—
501D4—42no—
502D4—42no—
503D4—81no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—24no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—41no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—81no—
540C2×C4—84no—
541C2×C4—81no—
542C2×C4—81no—
543C2×C4—81no—
544C2×C4—81no—
545C2×C4—81no—
546C2×C4C2×C11×C22⋊C411yescharacteristic
547C2×C4C4×D4×C1111yescharacteristic
548C2×C4C11×#12111yescharacteristic
549C2×C4C11×#12311yescharacteristic
550C8—42no—
551C8—81no—
552C22—21no—
553C22—21no—
554C22—21no—
555C22—21no—
556C22—21no—
557C22—21no—
558C22—21no—
559C22—21no—
560C22—21no—
561C22—21no—
562C22—21no—
563C22—21no—
564C22—42no—
565C22—42no—
566C22—42no—
567C22—81no—
568C22—81no—
569C22—81no—
570C22—81no—
571C22C11×#38611yescharacteristic
572C22C4×C11×SD1611yescharacteristic
573C22C11×#44011yescharacteristic
574C22C11×#45011yescharacteristic
575C22C11×#45211yescharacteristic
576C22C11×#45511yescharacteristic
577C22C11×#45611yescharacteristic
578C22C11×B(4,𝔽2)11yescharacteristic
579C22C11×B(4,𝔽2)11yescharacteristic
580C22C11×#46111yescharacteristic
581C22C11×#46311yescharacteristic
582C4—21no—
583C4—21no—
584C4—21no—
585C4—21no—
586C4—42no—
587C4—44no—
588C4—42no—
589C4—82no—
590C4—81no—
591C4—81no—
592C4—81no—
593C2—21no—
594C2—21no—
595C2—21no—
596C2—21no—
597C2—82no—
598C2C11×#160111yescharacteristic
599C2C11×#160311yescharacteristic
600C2C11×#160411yescharacteristic
601C2C11×#160611yescharacteristic
602C2C11×#187711yescharacteristic
603C2C11×#188211yescharacteristic
604C2C11×#188911yescharacteristic
subgroupG/H
center, socleC23×C11#120
commutatorC22×C4C22×C4×C11
Frattini, cosocleC23×C4C23×C11
prime radicalC2×C11×#121C22
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
3. C11×#1787C2semidirect
5. C11×#1446C2semidirect
6. C11×#1294C2semidirect
7. C11×#1280C2semidirect
13. C11×#448C4semidirect
37. C22×Q8×C11C2×C4semidirect
73. C11×C22⋊C8C2×C4semidirect
83. #9039C11direct (N × H)
143. C22×C4×C11SD16semidirect
172. #1787C2×C11semidirect
174. #1446C2×C11semidirect
175. #1294C2×C11semidirect
176. #1280C2×C11semidirect
262. #448C4×C11semidirect
327. C22×Q8C2×C4×C11semidirect
363. C22⋊C8C2×C4×C11semidirect
444. C22×C4C11×SD16semidirect
471. C11#9039direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4482
C11×#23252
C11×#17872
C2×C11×#3272
C11×#14462
C11×#12942
C11×#12802
#903911