Finite Group Databasebeta

← C2×C11×#2055 #14600730

Subgroups — C2×C11×#2055 #14600730

Order 2816.

1702 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C11×SD16C211yesmaximal, characteristic
2C22×C11×C4⋊C8C211yesmaximal, characteristic, complemented
3C22×C11×#103C211yesmaximal, characteristic, complemented
4C22×C11×#102C211yesmaximal, characteristic
5C2×C11×#391C211yesmaximal, characteristic, complemented
6C2×C11×#390C211yesmaximal, characteristic
7C11×#2055C218yesmaximal, direct product factor
8C2×C11×#340C211yesmaximal, characteristic, complemented
9C23×Q8×C11C2211yescharacteristic
10C23×D4×C11C2211yescharacteristic
11C22×C11×SD16—24no—
12C22×C11×SD16—24no—
13C22×C11×SD16—24no—
14C22×C11×SD16C2214yes—
15C23×C8×C11C2211yescharacteristic
16C23×C8×C11C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×C11×C22⋊C4—21no—
20C22×C11×C22⋊C4—21no—
21C22×C42×C11C2211yescharacteristic
22C2×C11×C4⋊C8—24no—
23C2×C11×C4⋊C8C2214yescomplemented
24C2×C11×#103—24no—
25C2×C11×#103C2214yescomplemented
26C2×C11×#102—24no—
27C2×C11×#102C2214yes—
28C11×#391—22no—
29C11×#391C2214yescomplemented
30C11×#390—22no—
31C11×#390C2214yes—
32C2×C11×#95—21no—
33C2×C11×#95—21no—
34C11×#340C2214yescomplemented
35C25×C11—21no—
36C22×Q8×C11—21no—
37C22×Q8×C11—22no—
38C22×Q8×C11—22no—
39C22×Q8×C11—22no—
40C22×Q8×C11—22no—
41C22×Q8×C11—22no—
42C22×Q8×C11D414yes—
43C22×Q8×C11C2312yes—
44C22×D4×C11—22no—
45C22×D4×C11—22no—
46C22×D4×C11—21no—
47C22×D4×C11—22no—
48C22×D4×C11—22no—
49C22×D4×C11—22no—
50C22×D4×C11D414yes—
51C22×D4×C11C2312yes—
52C23×C4×C11—21no—
53C23×C4×C11—21no—
54C23×C4×C11—21no—
55C23×C4×C11D411yescharacteristic
56C23×C4×C11D411yescharacteristic
57C23×C4×C11C2311yescharacteristic
58C2×C11×SD16—232no—
59C2×C11×SD16—28no—
60C2×C11×SD16—28no—
61C2×C11×SD16—28no—
62C22×C8×C11—22no—
63C22×C8×C11—22no—
64C22×C8×C11—22no—
65C22×C8×C11—22no—
66C22×C8×C11—22no—
67C22×C8×C11D414yes—
68C22×C8×C11C2312yes—
69C22×C8×C11C2312yes—
70C2×C11×C4⋊C4—22no—
71C2×C11×C4⋊C4—22no—
72C2×C11×C4⋊C4—22no—
73C2×C11×C4⋊C4—22no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4C2312yes—
77C2×C11×C4⋊C4C2312yes—
78C2×C11×C22⋊C4—24no—
79C2×C11×C22⋊C4—24no—
80C2×C11×C22⋊C4—44no—
81C2×C11×C22⋊C4—44no—
82C2×C42×C11—22no—
83C2×C42×C11—22no—
84C2×C42×C11D412yes—
85C2×C42×C11C2312yes—
86C11×C4⋊C8—28no—
87C11×#103—28no—
88C11×#102—28no—
89C11×#95—24no—
90C11×#95—24no—
91C2×#2055C1111yesmaximal, characteristic, direct product factor, Sylow
92C24×C11—24no—
93C24×C11—22no—
94C24×C11—42no—
95C24×C11—42no—
96C24×C11—42no—
97C24×C11—42no—
98C24×C11—42no—
99C24×C11—42no—
100C24×C11C2×D411yescharacteristic
101C2×Q8×C11—24no—
102C2×Q8×C11—22no—
103C2×Q8×C11—28no—
104C2×Q8×C11—28no—
105C2×Q8×C11—22no—
106C2×Q8×C11—22no—
107C2×Q8×C11—22no—
108C2×Q8×C11—22no—
109C2×Q8×C11—42no—
110C2×Q8×C11—42no—
111C2×Q8×C11—44no—
112C2×Q8×C11—44no—
113C2×Q8×C11C2×D414yes—
114C2×D4×C11—28no—
115C2×D4×C11—24no—
116C2×D4×C11—28no—
117C2×D4×C11—22no—
118C2×D4×C11—22no—
119C2×D4×C11—22no—
120C2×D4×C11—22no—
121C2×D4×C11—22no—
122C2×D4×C11—42no—
123C2×D4×C11—42no—
124C2×D4×C11—44no—
125C2×D4×C11—44no—
126C2×D4×C11C2×D414yes—
127C22×C4×C11—22no—
128C22×C4×C11—22no—
129C22×C4×C11—22no—
130C22×C4×C11—24no—
131C22×C4×C11—22no—
132C22×C4×C11—22no—
133C22×C4×C11—22no—
134C22×C4×C11—22no—
135C22×C4×C11—22no—
136C22×C4×C11—42no—
137C22×C4×C11—42no—
138C22×C4×C11—42no—
139C22×C4×C11—42no—
140C22×C4×C11—42no—
141C22×C4×C11—42no—
142C22×C4×C11—42no—
143C22×C4×C11—42no—
144C22×C4×C11SD1614yescomplemented
145C22×C4×C11C2×D412yes—
146C22×C4×C11C2×D412yes—
147C22×C4×C11C2×D412yes—
148C22×C4×C11C2×D412yes—
149C22×C4×C11C2×D412yes—
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11#4112yes—
152C22×C4×C11#4112yes—
153C22×C4×C11#4112yes—
154C22×C4×C11C2411yescharacteristic
155C11×SD16—232no—
156C2×C8×C11—28no—
157C2×C8×C11—22no—
158C2×C8×C11—22no—
159C2×C8×C11—22no—
160C2×C8×C11—22no—
161C2×C8×C11—22no—
162C2×C8×C11—44no—
163C2×C8×C11C2×D414yes—
164C11×C4⋊C4—22no—
165C11×C4⋊C4—22no—
166C11×C4⋊C4—22no—
167C11×C4⋊C4—22no—
168C11×C4⋊C4—42no—
169C11×C4⋊C4—42no—
170C11×C22⋊C4—48no—
171C11×C22⋊C4—48no—
172C42×C11—24no—
173C42×C11—22no—
174C42×C11—22no—
175C23×SD16C2×C1111yescharacteristic
176C22×C4⋊C8C2×C1111yescharacteristic, complemented
177C22×#103C2×C1111yescharacteristic, complemented
178C22×#102C2×C1111yescharacteristic
179C2×#391C2×C1111yescharacteristic, complemented
180C2×#390C2×C1111yescharacteristic
181#2055C2×C1118yesdirect product factor
182C2×#340C2×C1111yescharacteristic, complemented
183C23×C11—24no—
184C23×C11—42no—
185C23×C11—42no—
186C23×C11—42no—
187C23×C11—42no—
188C23×C11—42no—
189C23×C11—42no—
190C23×C11—48no—
191C23×C11—48no—
192C23×C11—48no—
193C23×C11—84no—
194C23×C11—84no—
195C23×C11—84no—
196C23×C11—84no—
197C23×C11#12112yes—
198C23×C11#12112yes—
199C23×C11#12112yes—
200C23×C11C2×SD1612yes—
201C23×C11#13512yes—
202C23×C11AGL(1,ℤ/8)12yes—
203C23×C11#13712yes—
204C23×C11C22×D411yescharacteristic
205Q8×C11—24no—
206Q8×C11—24no—
207Q8×C11—42no—
208Q8×C11—42no—
209Q8×C11—48no—
210D4×C11—24no—
211D4×C11—24no—
212D4×C11—42no—
213D4×C11—42no—
214D4×C11—48no—
215C2×C4×C11—22no—
216C2×C4×C11—22no—
217C2×C4×C11—28no—
218C2×C4×C11—22no—
219C2×C4×C11—24no—
220C2×C4×C11—22no—
221C2×C4×C11—22no—
222C2×C4×C11—42no—
223C2×C4×C11—42no—
224C2×C4×C11—48no—
225C2×C4×C11—44no—
226C2×C4×C11—42no—
227C2×C4×C11—42no—
228C2×C4×C11—42no—
229C2×C4×C11—42no—
230C2×C4×C11—42no—
231C2×C4×C11—42no—
232C2×C4×C11—84no—
233C2×C4×C11—84no—
234C2×C4×C11#12014yes—
235C2×C4×C11#12112yes—
236C2×C4×C11#12112yes—
237C2×C4×C11#12112yes—
238C2×C4×C11#12314yes—
239C2×C4×C11#12314yes—
240C2×C4×C11#12414yes—
241C2×C4×C11C2×SD1614yescomplemented
242C2×C4×C11C22×D411yescharacteristic
243C2×C4×C11C22×D411yescharacteristic
244C2×C4×C11C22×D411yescharacteristic
245C2×C4×C11C2×#4111yescharacteristic
246C2×C4×C11C2×#4111yescharacteristic
247C2×C4×C11C2×#4111yescharacteristic
248C8×C11—24no—
249C8×C11—42no—
250C23×Q8C22×C1111yescharacteristic
251C23×D4C22×C1111yescharacteristic
252C22×SD16—24no—
253C22×SD16—24no—
254C22×SD16—24no—
255C22×SD16C22×C1114yes—
256C23×C8C22×C1111yescharacteristic
257C23×C8C22×C1111yescharacteristic
258C22×C4⋊C4C22×C1111yescharacteristic
259C22×C4⋊C4C22×C1111yescharacteristic
260C22×C22⋊C4—21no—
261C22×C22⋊C4—21no—
262C22×C42C22×C1111yescharacteristic
263C2×C4⋊C8—24no—
264C2×C4⋊C8C22×C1114yescomplemented
265C2×#103—24no—
266C2×#103C22×C1114yescomplemented
267C2×#102—24no—
268C2×#102C22×C1114yes—
269#391—22no—
270#391C22×C1114yescomplemented
271#390—22no—
272#390C22×C1114yes—
273C2×#95—21no—
274C2×#95—21no—
275#340C22×C1114yescomplemented
276C22×C11—44no—
277C22×C11—44no—
278C22×C11—44no—
279C22×C11—816no—
280C22×C11—82no—
281C22×C11—82no—
282C22×C11—82no—
283C22×C11—82no—
284C22×C11#39414yes—
285C22×C11#46014yes—
286C22×C11#46114yes—
287C22×C11#46314yes—
288C22×C11#46414yes—
289C22×C11#46514yes—
290C22×C11#46814yes—
291C22×C11C2×#12111yescharacteristic
292C22×C11C2×#12111yescharacteristic
293C22×C11C2×#12111yescharacteristic
294C22×C11C22×SD1611yescharacteristic
295C22×C11C2×#13511yescharacteristic
296C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
297C22×C11C2×#13711yescharacteristic
298C4×C11—24no—
299C4×C11—44no—
300C4×C11—42no—
301C4×C11—82no—
302C4×C11—82no—
303C4×C11#39414yes—
304C4×C11C2×#12011yescharacteristic
305C4×C11C2×#12311yescharacteristic
306C4×C11C2×#12311yescharacteristic
307C4×C11C2×#12411yescharacteristic
308C25—21no—
309C22×Q8—21no—
310C22×Q8—22no—
311C22×Q8—22no—
312C22×Q8—22no—
313C22×Q8—22no—
314C22×Q8—22no—
315C22×Q8D4×C1114yes—
316C22×Q8C23×C1112yes—
317C22×D4—22no—
318C22×D4—22no—
319C22×D4—21no—
320C22×D4—22no—
321C22×D4—22no—
322C22×D4—22no—
323C22×D4D4×C1114yes—
324C22×D4C23×C1112yes—
325C23×C4—21no—
326C23×C4—21no—
327C23×C4—21no—
328C23×C4D4×C1111yescharacteristic
329C23×C4D4×C1111yescharacteristic
330C23×C4C23×C1111yescharacteristic
331C2×SD16—232no—
332C2×SD16—28no—
333C2×SD16—28no—
334C2×SD16—28no—
335C22×C8—22no—
336C22×C8—22no—
337C22×C8—22no—
338C22×C8—22no—
339C22×C8—22no—
340C22×C8D4×C1114yes—
341C22×C8C23×C1112yes—
342C22×C8C23×C1112yes—
343C2×C4⋊C4—22no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4C23×C1112yes—
350C2×C4⋊C4C23×C1112yes—
351C2×C22⋊C4—24no—
352C2×C22⋊C4—24no—
353C2×C22⋊C4—44no—
354C2×C22⋊C4—44no—
355C2×C42—22no—
356C2×C42—22no—
357C2×C42D4×C1112yes—
358C2×C42C23×C1112yes—
359C4⋊C8—28no—
360#103—28no—
361#102—28no—
362#95—24no—
363#95—24no—
364C2×C11—84no—
365C2×C11#205518yesdirect product factor
366C2×C11C2×#39411yescharacteristic
367C2×C11C2×#46111yescharacteristic
368C2×C11C2×#46311yescharacteristic
369C2×C11C2×#46011yescharacteristic
370C2×C11C2×#46411yescharacteristic
371C2×C11C2×#46511yescharacteristic
372C2×C11C2×#46811yescharacteristic
373C24—24no—
374C24—22no—
375C24—42no—
376C24—42no—
377C24—42no—
378C24—42no—
379C24—42no—
380C24—42no—
381C24C2×D4×C1111yescharacteristic
382C2×Q8—24no—
383C2×Q8—22no—
384C2×Q8—28no—
385C2×Q8—28no—
386C2×Q8—22no—
387C2×Q8—22no—
388C2×Q8—22no—
389C2×Q8—22no—
390C2×Q8—42no—
391C2×Q8—42no—
392C2×Q8—44no—
393C2×Q8—44no—
394C2×Q8C2×D4×C1114yes—
395C2×D4—28no—
396C2×D4—24no—
397C2×D4—28no—
398C2×D4—22no—
399C2×D4—22no—
400C2×D4—22no—
401C2×D4—22no—
402C2×D4—22no—
403C2×D4—42no—
404C2×D4—42no—
405C2×D4—44no—
406C2×D4—44no—
407C2×D4C2×D4×C1114yes—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—24no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—42no—
418C22×C4—42no—
419C22×C4—42no—
420C22×C4—42no—
421C22×C4—42no—
422C22×C4—42no—
423C22×C4—42no—
424C22×C4—42no—
425C22×C4C11×SD1614yescomplemented
426C22×C4C2×D4×C1112yes—
427C22×C4C2×D4×C1112yes—
428C22×C4C2×D4×C1112yes—
429C22×C4C2×D4×C1112yes—
430C22×C4C2×D4×C1112yes—
431C22×C4C2×D4×C1111yescharacteristic
432C22×C4C11×#4112yes—
433C22×C4C11×#4112yes—
434C22×C4C11×#4112yes—
435C22×C4C24×C1111yescharacteristic
436SD16—232no—
437C2×C8—28no—
438C2×C8—22no—
439C2×C8—22no—
440C2×C8—22no—
441C2×C8—22no—
442C2×C8—22no—
443C2×C8—44no—
444C2×C8C2×D4×C1114yes—
445C4⋊C4—22no—
446C4⋊C4—22no—
447C4⋊C4—22no—
448C4⋊C4—22no—
449C4⋊C4—42no—
450C4⋊C4—42no—
451C22⋊C4—48no—
452C22⋊C4—48no—
453C42—24no—
454C42—22no—
455C42—22no—
456C11C2×#205511yescharacteristic, direct product factor, Sylow
457C23—24no—
458C23—42no—
459C23—42no—
460C23—48no—
461C23—42no—
462C23—42no—
463C23—42no—
464C23—42no—
465C23—48no—
466C23—48no—
467C23—84no—
468C23—84no—
469C23—84no—
470C23—84no—
471C23C11×#12112yes—
472C23C11×#12112yes—
473C23C11×#12112yes—
474C23C2×C11×SD1612yes—
475C23C11×#13512yes—
476C23C11×AGL(1,ℤ/8)12yes—
477C23C11×#13712yes—
478C23C22×D4×C1111yescharacteristic
479Q8—24no—
480Q8—24no—
481Q8—42no—
482Q8—42no—
483Q8—48no—
484D4—24no—
485D4—24no—
486D4—42no—
487D4—42no—
488D4—48no—
489C2×C4—22no—
490C2×C4—22no—
491C2×C4—28no—
492C2×C4—22no—
493C2×C4—24no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—48no—
499C2×C4—44no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—84no—
507C2×C4—84no—
508C2×C4C11×#12014yes—
509C2×C4C11×#12112yes—
510C2×C4C11×#12112yes—
511C2×C4C11×#12112yes—
512C2×C4C11×#12314yes—
513C2×C4C11×#12314yes—
514C2×C4C11×#12414yes—
515C2×C4C2×C11×SD1614yescomplemented
516C2×C4C22×D4×C1111yescharacteristic
517C2×C4C22×D4×C1111yescharacteristic
518C2×C4C22×D4×C1111yescharacteristic
519C2×C4C2×C11×#4111yescharacteristic
520C2×C4C2×C11×#4111yescharacteristic
521C2×C4C2×C11×#4111yescharacteristic
522C8—24no—
523C8—42no—
524C22—44no—
525C22—44no—
526C22—44no—
527C22—82no—
528C22—82no—
529C22—82no—
530C22—82no—
531C22—816no—
532C22C11×#39414yes—
533C22C11×#46014yes—
534C22C11×#46114yes—
535C22C11×#46314yes—
536C22C11×#46414yes—
537C22C11×#46514yes—
538C22C11×#46814yes—
539C22C2×C11×#12111yescharacteristic
540C22C2×C11×#12111yescharacteristic
541C22C2×C11×#12111yescharacteristic
542C22C22×C11×SD1611yescharacteristic
543C22C2×C11×#13511yescharacteristic
544C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
545C22C2×C11×#13711yescharacteristic
546C4—24no—
547C4—44no—
548C4—42no—
549C4—82no—
550C4—82no—
551C4C11×#39414yes—
552C4C2×C11×#12011yescharacteristic
553C4C2×C11×#12311yescharacteristic
554C4C2×C11×#12311yescharacteristic
555C4C2×C11×#12411yescharacteristic
556C2—84no—
557C2C11×#205518yesdirect product factor
558C2C2×C11×#39411yescharacteristic
559C2C2×C11×#46111yescharacteristic
560C2C2×C11×#46311yescharacteristic
561C2C2×C11×#46011yescharacteristic
562C2C2×C11×#46411yescharacteristic
563C2C2×C11×#46511yescharacteristic
564C2C2×C11×#46811yescharacteristic
subgroupG/H
center, socleC24×C11C2×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC23×D4×C11C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24×C11 ◁ C22×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×C11×C4⋊C8C2semidirect
3. C22×C11×#103C2semidirect
5. C2×C11×#391C2semidirect
7. C11×#2055C2direct (N × H)
8. C2×C11×#340C2semidirect
23. C2×C11×C4⋊C8C22semidirect
25. C2×C11×#103C22semidirect
29. C11×#391C22semidirect
34. C11×#340C22semidirect
91. C2×#2055C11direct (N × H)
144. C22×C4×C11SD16semidirect
176. C22×C4⋊C8C2×C11semidirect
177. C22×#103C2×C11semidirect
179. C2×#391C2×C11semidirect
181. #2055C2×C11direct (N × H)
182. C2×#340C2×C11semidirect
241. C2×C4×C11C2×SD16semidirect
264. C2×C4⋊C8C22×C11semidirect
266. C2×#103C22×C11semidirect
270. #391C22×C11semidirect
275. #340C22×C11semidirect
365. C2×C11#2055direct (N × H)
425. C22×C4C11×SD16semidirect
456. C11C2×#2055direct (N × H)
515. C2×C4C2×C11×SD16semidirect
557. C2C11×#2055direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C11×SD162
C22×C11×C4⋊C82
C22×C11×#1032
C22×C11×#1022
C2×C11×#3912
C2×C11×#3902
C11×#20552
C2×C11×#3402
C2×#205511