Finite Group Databasebeta

← C2×C11×#1877 #14598113

Subgroups — C2×C11×#1877 #14598113

Order 2816.

2254 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C11×SD16C211yesmaximal, characteristic
2C22×C4×D4×C11C211yesmaximal, characteristic
3C22×C11×#103C211yesmaximal, characteristic, complemented
4C22×C11×#102C211yesmaximal, characteristic
5C2×C11×#391C211yesmaximal, characteristic, complemented
6C11×#1877C218yesmaximal, direct product factor
7C2×C11×#340C211yesmaximal, characteristic, complemented
8C2×C11×#336C211yesmaximal, characteristic, complemented
9C23×Q8×C11C2211yescharacteristic
10C23×D4×C11C2211yescharacteristic
11C24×C4×C11—21no—
12C22×C11×SD16—24no—
13C22×C11×SD16—24no—
14C22×C11×SD16C418yescomplemented
15C22×C11×SD16C2214yes—
16C23×C8×C11C2211yescharacteristic
17C23×C8×C11C2211yescharacteristic
18C2×C4×D4×C11—24no—
19C2×C4×D4×C11—24no—
20C2×C4×D4×C11—22no—
21C2×C4×D4×C11C2214yes—
22C22×C11×C4⋊C4C2211yescharacteristic
23C22×C11×C4⋊C4C2211yescharacteristic
24C22×C11×C22⋊C4—21no—
25C22×C42×C11C2211yescharacteristic
26C2×C11×#103—24no—
27C2×C11×#103C2214yescomplemented
28C2×C11×#102—24no—
29C2×C11×#102C2214yes—
30C11×#391—22no—
31C11×#391C2214yescomplemented
32C2×C11×#95—21no—
33C2×C11×#95—21no—
34C11×#340C2214yescomplemented
35C11×#336C2214yescomplemented
36C25×C11—21no—
37C22×Q8×C11—21no—
38C22×Q8×C11—22no—
39C22×Q8×C11—22no—
40C22×Q8×C11—22no—
41C22×Q8×C11—22no—
42C22×Q8×C11—22no—
43C22×Q8×C11C2×C414yescomplemented
44C22×Q8×C11C2312yes—
45C22×D4×C11—21no—
46C22×D4×C11—22no—
47C22×D4×C11—22no—
48C22×D4×C11—22no—
49C22×D4×C11C2×C414yes—
50C22×D4×C11D414yes—
51C22×D4×C11D414yes—
52C22×D4×C11C2312yes—
53C23×C4×C11—28no—
54C23×C4×C11—21no—
55C23×C4×C11—21no—
56C23×C4×C11—24no—
57C23×C4×C11—21no—
58C23×C4×C11—44no—
59C23×C4×C11—44no—
60C23×C4×C11D411yescharacteristic
61C23×C4×C11D411yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C2×C11×SD16—232no—
64C2×C11×SD16—28no—
65C2×C11×SD16—28no—
66C2×C11×SD16C2×C4116yescomplemented
67C22×C8×C11—22no—
68C22×C8×C11—22no—
69C22×C8×C11—22no—
70C22×C8×C11—22no—
71C22×C8×C11—22no—
72C22×C8×C11C2×C414yescomplemented
73C22×C8×C11C2312yes—
74C22×C8×C11C2312yes—
75C4×D4×C11—216no—
76C4×D4×C11—28no—
77C4×D4×C11—28no—
78C2×C11×C4⋊C4—21no—
79C2×C11×C4⋊C4—22no—
80C2×C11×C4⋊C4—22no—
81C2×C11×C4⋊C4—22no—
82C2×C11×C4⋊C4—21no—
83C2×C11×C4⋊C4D414yes—
84C2×C11×C4⋊C4C2312yes—
85C2×C11×C4⋊C4C2312yes—
86C2×C11×C22⋊C4—28no—
87C2×C11×C22⋊C4—24no—
88C2×C42×C11—22no—
89C2×C42×C11—22no—
90C2×C42×C11D412yes—
91C2×C42×C11C2312yes—
92C11×#103—28no—
93C11×#102—28no—
94C11×#95—24no—
95C11×#95—24no—
96C2×#1877C1111yesmaximal, characteristic, direct product factor, Sylow
97C24×C11—24no—
98C24×C11—24no—
99C24×C11—24no—
100C24×C11—22no—
101C24×C11—42no—
102C24×C11—42no—
103C24×C11—42no—
104C24×C11—42no—
105C24×C11C2×D411yescharacteristic
106C2×Q8×C11—24no—
107C2×Q8×C11—22no—
108C2×Q8×C11—28no—
109C2×Q8×C11—28no—
110C2×Q8×C11—22no—
111C2×Q8×C11—22no—
112C2×Q8×C11—22no—
113C2×Q8×C11—22no—
114C2×Q8×C11—42no—
115C2×Q8×C11—42no—
116C2×Q8×C11—44no—
117C2×Q8×C11—44no—
118C2×Q8×C11C22×C414yescomplemented
119C2×D4×C11—28no—
120C2×D4×C11—24no—
121C2×D4×C11—24no—
122C2×D4×C11—28no—
123C2×D4×C11—24no—
124C2×D4×C11—28no—
125C2×D4×C11—22no—
126C2×D4×C11—22no—
127C2×D4×C11—22no—
128C2×D4×C11C22⋊C4116yes—
129C2×D4×C11C22×C414yes—
130C2×D4×C11C2×D414yes—
131C2×D4×C11C2×D414yes—
132C22×C4×C11—22no—
133C22×C4×C11—22no—
134C22×C4×C11—216no—
135C22×C4×C11—24no—
136C22×C4×C11—22no—
137C22×C4×C11—24no—
138C22×C4×C11—22no—
139C22×C4×C11—22no—
140C22×C4×C11—22no—
141C22×C4×C11—22no—
142C22×C4×C11—22no—
143C22×C4×C11—48no—
144C22×C4×C11—432no—
145C22×C4×C11—42no—
146C22×C4×C11—42no—
147C22×C4×C11—42no—
148C22×C4×C11—42no—
149C22×C4×C11—48no—
150C22×C4×C11—42no—
151C22×C4×C11—42no—
152C22×C4×C11—42no—
153C22×C4×C11SD1614yescomplemented
154C22×C4×C11C22×C412yes—
155C22×C4×C11C2×D412yes—
156C22×C4×C11C2×D412yes—
157C22×C4×C11C2×D412yes—
158C22×C4×C11C2×D412yes—
159C22×C4×C11C2×D411yescharacteristic
160C22×C4×C11C2×D412yes—
161C22×C4×C11#4112yes—
162C22×C4×C11#4112yes—
163C22×C4×C11C2411yescharacteristic
164C11×SD16—232no—
165C2×C8×C11—28no—
166C2×C8×C11—22no—
167C2×C8×C11—22no—
168C2×C8×C11—22no—
169C2×C8×C11—22no—
170C2×C8×C11—22no—
171C2×C8×C11—44no—
172C2×C8×C11C22×C414yescomplemented
173C11×C4⋊C4—24no—
174C11×C4⋊C4—22no—
175C11×C4⋊C4—22no—
176C11×C4⋊C4—22no—
177C11×C4⋊C4—42no—
178C11×C4⋊C4C2×D414yes—
179C11×C22⋊C4—216no—
180C42×C11—24no—
181C42×C11—22no—
182C42×C11—22no—
183C23×SD16C2×C1111yescharacteristic
184C22×C4×D4C2×C1111yescharacteristic
185C22×#103C2×C1111yescharacteristic, complemented
186C22×#102C2×C1111yescharacteristic
187C2×#391C2×C1111yescharacteristic, complemented
188#1877C2×C1118yesdirect product factor
189C2×#340C2×C1111yescharacteristic, complemented
190C2×#336C2×C1111yescharacteristic, complemented
191C23×C11—24no—
192C23×C11—24no—
193C23×C11—24no—
194C23×C11—216no—
195C23×C11—42no—
196C23×C11—42no—
197C23×C11—42no—
198C23×C11—42no—
199C23×C11—48no—
200C23×C11—48no—
201C23×C11—48no—
202C23×C11—48no—
203C23×C11—48no—
204C23×C11—48no—
205C23×C11C4×D412yes—
206C23×C11#12012yes—
207C23×C11#12112yes—
208C23×C11C2×SD1612yes—
209C23×C11#13512yes—
210C23×C11AGL(1,ℤ/8)12yes—
211C23×C11#13712yes—
212C23×C11C22×D411yescharacteristic
213Q8×C11—24no—
214Q8×C11—24no—
215Q8×C11—42no—
216Q8×C11—42no—
217Q8×C11—48no—
218D4×C11—24no—
219D4×C11—24no—
220D4×C11—24no—
221D4×C11—216no—
222D4×C11C2×C22⋊C418yes—
223C2×C4×C11—22no—
224C2×C4×C11—22no—
225C2×C4×C11—28no—
226C2×C4×C11—24no—
227C2×C4×C11—22no—
228C2×C4×C11—24no—
229C2×C4×C11—22no—
230C2×C4×C11—22no—
231C2×C4×C11—432no—
232C2×C4×C11—42no—
233C2×C4×C11—42no—
234C2×C4×C11—42no—
235C2×C4×C11—42no—
236C2×C4×C11—48no—
237C2×C4×C11—48no—
238C2×C4×C11—44no—
239C2×C4×C11—42no—
240C2×C4×C11—42no—
241C2×C4×C11—42no—
242C2×C4×C11—84no—
243C2×C4×C11C2×C22⋊C414yes—
244C2×C4×C11C4×D414yes—
245C2×C4×C11C4×D412yes—
246C2×C4×C11#12012yes—
247C2×C4×C11#12114yes—
248C2×C4×C11#12112yes—
249C2×C4×C11#12314yes—
250C2×C4×C11C2×SD1614yescomplemented
251C2×C4×C11C23×C411yescharacteristic
252C2×C4×C11C22×D411yescharacteristic
253C2×C4×C11C22×D411yescharacteristic
254C2×C4×C11C22×D411yescharacteristic
255C2×C4×C11C2×#4111yescharacteristic
256C2×C4×C11C2×#4111yescharacteristic
257C8×C11—24no—
258C8×C11—42no—
259C23×Q8C22×C1111yescharacteristic
260C23×D4C22×C1111yescharacteristic
261C24×C4—21no—
262C22×SD16—24no—
263C22×SD16—24no—
264C22×SD16C4×C1118yescomplemented
265C22×SD16C22×C1114yes—
266C23×C8C22×C1111yescharacteristic
267C23×C8C22×C1111yescharacteristic
268C2×C4×D4—24no—
269C2×C4×D4—24no—
270C2×C4×D4—22no—
271C2×C4×D4C22×C1114yes—
272C22×C4⋊C4C22×C1111yescharacteristic
273C22×C4⋊C4C22×C1111yescharacteristic
274C22×C22⋊C4—21no—
275C22×C42C22×C1111yescharacteristic
276C2×#103—24no—
277C2×#103C22×C1114yescomplemented
278C2×#102—24no—
279C2×#102C22×C1114yes—
280#391—22no—
281#391C22×C1114yescomplemented
282C2×#95—21no—
283C2×#95—21no—
284#340C22×C1114yescomplemented
285#336C22×C1114yescomplemented
286C22×C11—28no—
287C22×C11—432no—
288C22×C11—44no—
289C22×C11—44no—
290C22×C11—44no—
291C22×C11—44no—
292C22×C11—44no—
293C22×C11—44no—
294C22×C11#38614yes—
295C22×C11C4×SD1614yes—
296C22×C11#44014yes—
297C22×C11#45014yes—
298C22×C11#45214yes—
299C22×C11#46114yes—
300C22×C11#46314yes—
301C22×C11C2×C4×D411yescharacteristic
302C22×C11C2×#12011yescharacteristic
303C22×C11C2×#12111yescharacteristic
304C22×C11C22×SD1611yescharacteristic
305C22×C11C2×#13511yescharacteristic
306C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
307C22×C11C2×#13711yescharacteristic
308C4×C11—24no—
309C4×C11—44no—
310C4×C11—42no—
311C4×C11—44no—
312C4×C11—82no—
313C4×C11#38614yes—
314C4×C11C22×C22⋊C411yescharacteristic
315C4×C11C2×C4×D411yescharacteristic
316C4×C11C2×#12111yescharacteristic
317C4×C11C2×#12311yescharacteristic
318C25—21no—
319C22×Q8—21no—
320C22×Q8—22no—
321C22×Q8—22no—
322C22×Q8—22no—
323C22×Q8—22no—
324C22×Q8—22no—
325C22×Q8C2×C4×C1114yescomplemented
326C22×Q8C23×C1112yes—
327C22×D4—21no—
328C22×D4—22no—
329C22×D4—22no—
330C22×D4—22no—
331C22×D4C2×C4×C1114yes—
332C22×D4D4×C1114yes—
333C22×D4D4×C1114yes—
334C22×D4C23×C1112yes—
335C23×C4—28no—
336C23×C4—21no—
337C23×C4—21no—
338C23×C4—24no—
339C23×C4—21no—
340C23×C4—44no—
341C23×C4—44no—
342C23×C4D4×C1111yescharacteristic
343C23×C4D4×C1111yescharacteristic
344C23×C4C23×C1111yescharacteristic
345C2×SD16—232no—
346C2×SD16—28no—
347C2×SD16—28no—
348C2×SD16C2×C4×C11116yescomplemented
349C22×C8—22no—
350C22×C8—22no—
351C22×C8—22no—
352C22×C8—22no—
353C22×C8—22no—
354C22×C8C2×C4×C1114yescomplemented
355C22×C8C23×C1112yes—
356C22×C8C23×C1112yes—
357C4×D4—216no—
358C4×D4—28no—
359C4×D4—28no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4D4×C1114yes—
366C2×C4⋊C4C23×C1112yes—
367C2×C4⋊C4C23×C1112yes—
368C2×C22⋊C4—28no—
369C2×C22⋊C4—24no—
370C2×C42—22no—
371C2×C42—22no—
372C2×C42D4×C1112yes—
373C2×C42C23×C1112yes—
374#103—28no—
375#102—28no—
376#95—24no—
377#95—24no—
378C2×C11—48no—
379C2×C11#187718yesdirect product factor
380C2×C11C2×#38611yescharacteristic
381C2×C11C2×C4×SD1611yescharacteristic
382C2×C11C2×#44011yescharacteristic
383C2×C11C2×#45011yescharacteristic
384C2×C11C2×#45211yescharacteristic
385C2×C11C2×#46111yescharacteristic
386C2×C11C2×#46311yescharacteristic
387C24—24no—
388C24—24no—
389C24—24no—
390C24—22no—
391C24—42no—
392C24—42no—
393C24—42no—
394C24—42no—
395C24C2×D4×C1111yescharacteristic
396C2×Q8—24no—
397C2×Q8—22no—
398C2×Q8—28no—
399C2×Q8—28no—
400C2×Q8—22no—
401C2×Q8—22no—
402C2×Q8—22no—
403C2×Q8—22no—
404C2×Q8—42no—
405C2×Q8—42no—
406C2×Q8—44no—
407C2×Q8—44no—
408C2×Q8C22×C4×C1114yescomplemented
409C2×D4—28no—
410C2×D4—24no—
411C2×D4—24no—
412C2×D4—28no—
413C2×D4—24no—
414C2×D4—28no—
415C2×D4—22no—
416C2×D4—22no—
417C2×D4—22no—
418C2×D4C11×C22⋊C4116yes—
419C2×D4C22×C4×C1114yes—
420C2×D4C2×D4×C1114yes—
421C2×D4C2×D4×C1114yes—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—216no—
425C22×C4—24no—
426C22×C4—22no—
427C22×C4—24no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—48no—
434C22×C4—432no—
435C22×C4—42no—
436C22×C4—42no—
437C22×C4—42no—
438C22×C4—42no—
439C22×C4—48no—
440C22×C4—42no—
441C22×C4—42no—
442C22×C4—42no—
443C22×C4C11×SD1614yescomplemented
444C22×C4C22×C4×C1112yes—
445C22×C4C2×D4×C1112yes—
446C22×C4C2×D4×C1112yes—
447C22×C4C2×D4×C1112yes—
448C22×C4C2×D4×C1112yes—
449C22×C4C2×D4×C1111yescharacteristic
450C22×C4C2×D4×C1112yes—
451C22×C4C11×#4112yes—
452C22×C4C11×#4112yes—
453C22×C4C24×C1111yescharacteristic
454SD16—232no—
455C2×C8—28no—
456C2×C8—22no—
457C2×C8—22no—
458C2×C8—22no—
459C2×C8—22no—
460C2×C8—22no—
461C2×C8—44no—
462C2×C8C22×C4×C1114yescomplemented
463C4⋊C4—24no—
464C4⋊C4—22no—
465C4⋊C4—22no—
466C4⋊C4—22no—
467C4⋊C4—42no—
468C4⋊C4C2×D4×C1114yes—
469C22⋊C4—216no—
470C42—24no—
471C42—22no—
472C42—22no—
473C11C2×#187711yescharacteristic, direct product factor, Sylow
474C23—24no—
475C23—24no—
476C23—24no—
477C23—216no—
478C23—42no—
479C23—42no—
480C23—42no—
481C23—42no—
482C23—48no—
483C23—48no—
484C23—48no—
485C23—48no—
486C23—48no—
487C23—48no—
488C23C4×D4×C1112yes—
489C23C11×#12012yes—
490C23C11×#12112yes—
491C23C2×C11×SD1612yes—
492C23C11×#13512yes—
493C23C11×AGL(1,ℤ/8)12yes—
494C23C11×#13712yes—
495C23C22×D4×C1111yescharacteristic
496Q8—24no—
497Q8—24no—
498Q8—42no—
499Q8—48no—
500Q8—42no—
501D4—24no—
502D4—24no—
503D4—216no—
504D4—24no—
505D4C2×C11×C22⋊C418yes—
506C2×C4—22no—
507C2×C4—22no—
508C2×C4—28no—
509C2×C4—24no—
510C2×C4—22no—
511C2×C4—24no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—432no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—48no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—48no—
521C2×C4—44no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—84no—
526C2×C4C2×C11×C22⋊C414yes—
527C2×C4C4×D4×C1114yes—
528C2×C4C4×D4×C1112yes—
529C2×C4C11×#12012yes—
530C2×C4C11×#12114yes—
531C2×C4C11×#12112yes—
532C2×C4C11×#12314yes—
533C2×C4C2×C11×SD1614yescomplemented
534C2×C4C23×C4×C1111yescharacteristic
535C2×C4C22×D4×C1111yescharacteristic
536C2×C4C22×D4×C1111yescharacteristic
537C2×C4C22×D4×C1111yescharacteristic
538C2×C4C2×C11×#4111yescharacteristic
539C2×C4C2×C11×#4111yescharacteristic
540C8—24no—
541C8—42no—
542C22—28no—
543C22—432no—
544C22—44no—
545C22—44no—
546C22—44no—
547C22—44no—
548C22—44no—
549C22—44no—
550C22C11×#38614yes—
551C22C4×C11×SD1614yes—
552C22C11×#44014yes—
553C22C11×#45014yes—
554C22C11×#45214yes—
555C22C11×#46114yes—
556C22C11×#46314yes—
557C22C2×C4×D4×C1111yescharacteristic
558C22C2×C11×#12011yescharacteristic
559C22C2×C11×#12111yescharacteristic
560C22C22×C11×SD1611yescharacteristic
561C22C2×C11×#13511yescharacteristic
562C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
563C22C2×C11×#13711yescharacteristic
564C4—24no—
565C4—44no—
566C4—42no—
567C4—44no—
568C4—82no—
569C4C11×#38614yes—
570C4C22×C11×C22⋊C411yescharacteristic
571C4C2×C4×D4×C1111yescharacteristic
572C4C2×C11×#12111yescharacteristic
573C4C2×C11×#12311yescharacteristic
574C2—48no—
575C2C11×#187718yesdirect product factor
576C2C2×C11×#38611yescharacteristic
577C2C2×C4×C11×SD1611yescharacteristic
578C2C2×C11×#44011yescharacteristic
579C2C2×C11×#45011yescharacteristic
580C2C2×C11×#45211yescharacteristic
581C2C2×C11×#46111yescharacteristic
582C2C2×C11×#46311yescharacteristic
subgroupG/H
center, socleC24×C11C2×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC23×D4×C11C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24×C11 ◁ C22×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
3. C22×C11×#103C2semidirect
5. C2×C11×#391C2semidirect
6. C11×#1877C2direct (N × H)
7. C2×C11×#340C2semidirect
8. C2×C11×#336C2semidirect
14. C22×C11×SD16C4semidirect
27. C2×C11×#103C22semidirect
31. C11×#391C22semidirect
34. C11×#340C22semidirect
35. C11×#336C22semidirect
43. C22×Q8×C11C2×C4semidirect
66. C2×C11×SD16C2×C4semidirect
72. C22×C8×C11C2×C4semidirect
96. C2×#1877C11direct (N × H)
118. C2×Q8×C11C22×C4semidirect
153. C22×C4×C11SD16semidirect
172. C2×C8×C11C22×C4semidirect
185. C22×#103C2×C11semidirect
187. C2×#391C2×C11semidirect
188. #1877C2×C11direct (N × H)
189. C2×#340C2×C11semidirect
190. C2×#336C2×C11semidirect
250. C2×C4×C11C2×SD16semidirect
264. C22×SD16C4×C11semidirect
277. C2×#103C22×C11semidirect
281. #391C22×C11semidirect
284. #340C22×C11semidirect
285. #336C22×C11semidirect
325. C22×Q8C2×C4×C11semidirect
348. C2×SD16C2×C4×C11semidirect
354. C22×C8C2×C4×C11semidirect
379. C2×C11#1877direct (N × H)
408. C2×Q8C22×C4×C11semidirect
443. C22×C4C11×SD16semidirect
462. C2×C8C22×C4×C11semidirect
473. C11C2×#1877direct (N × H)
533. C2×C4C2×C11×SD16semidirect
575. C2C11×#1877direct (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×C4×D4×C112
C22×C11×#1032
C22×C11×#1022
C2×C11×#3912
C11×#18772
C2×C11×#3402
C2×C11×#3362
C2×#187711