Finite Group Databasebeta

← C2×C11×#1889 #14598150

Subgroups — C2×C11×#1889 #14598150

Order 2816.

3566 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×#120C211yesmaximal, characteristic
2C2×C11×#518C211yesmaximal, characteristic, complemented
3C22×C11×#99C211yesmaximal, characteristic, complemented
4C2×C11×#379C212yesmaximal, complemented
5C11×#1889C218yesmaximal, direct product factor
6C2×C11×#342C212yesmaximal, complemented
7C26×C11C2211yescharacteristic
8C23×D4×C11—21no—
9C23×D4×C11C2211yescharacteristic
10C2×C11×#120—24no—
11C2×C11×#120—22no—
12C2×C11×#120C418yescomplemented
13C2×C11×#120C2214yes—
14C11×#518—22no—
15C11×#518—24no—
16C11×#518C2214yescomplemented
17C2×C4×D4×C11—24no—
18C2×C11×#117—21no—
19C22×C11×C22⋊C4—21no—
20C22×C11×C22⋊C4—21no—
21C22×C11×C22⋊C4—24no—
22C22×C11×C22⋊C4C2212yes—
23C22×C11×C22⋊C4C2212yes—
24C22×C11×C22⋊C4C2211yescharacteristic
25C2×C11×#99—24no—
26C2×C11×#99C2214yescomplemented
27C11×#379—24no—
28C11×#379C2218yescomplemented
29C11×#342C2218yescomplemented
30C25×C11—22no—
31C25×C11—21no—
32C25×C11—22no—
33C25×C11—22no—
34C25×C11—21no—
35C25×C11—24no—
36C25×C11—48no—
37C25×C11C2×C414yescomplemented
38C25×C11D411yescharacteristic
39C25×C11C2312yes—
40C25×C11C2311yescharacteristic
41C22×D4×C11—22no—
42C22×D4×C11—22no—
43C22×D4×C11—24no—
44C22×D4×C11—28no—
45C22×D4×C11—24no—
46C22×D4×C11—48no—
47C22×D4×C11C2×C414yes—
48C22×D4×C11D414yes—
49C22×D4×C11D412yes—
50C22×D4×C11C2312yes—
51C23×C4×C11—21no—
52C23×C4×C11—22no—
53C23×C4×C11—22no—
54C23×C4×C11D411yescharacteristic
55C23×C4×C11D414yescomplemented
56C11×#120—216no—
57C11×#120—28no—
58C11×#120C2×C4116yescomplemented
59C4×D4×C11—216no—
60C4×D4×C11—216no—
61C11×#117—24no—
62C11×#117—24no—
63C2×C11×C4⋊C4—22no—
64C2×C11×C22⋊C4—22no—
65C2×C11×C22⋊C4—24no—
66C2×C11×C22⋊C4—22no—
67C2×C11×C22⋊C4—24no—
68C2×C11×C22⋊C4—22no—
69C2×C11×C22⋊C4—22no—
70C2×C11×C22⋊C4—22no—
71C2×C11×C22⋊C4—21no—
72C2×C11×C22⋊C4—22no—
73C2×C11×C22⋊C4—28no—
74C2×C11×C22⋊C4—24no—
75C2×C11×C22⋊C4—24no—
76C2×C11×C22⋊C4—24no—
77C2×C11×C22⋊C4—22no—
78C2×C11×C22⋊C4—216no—
79C2×C11×C22⋊C4—416no—
80C2×C11×C22⋊C4C2×C414yescomplemented
81C2×C11×C22⋊C4D414yescomplemented
82C2×C11×C22⋊C4C2314yes—
83C2×C11×C22⋊C4C2314yes—
84C2×C11×C22⋊C4C2312yes—
85C2×C42×C11—22no—
86C11×#99—28no—
87C2×#1889C1111yesmaximal, characteristic, direct product factor, Sylow
88C24×C11—216no—
89C24×C11—28no—
90C24×C11—24no—
91C24×C11—28no—
92C24×C11—21no—
93C24×C11—24no—
94C24×C11—22no—
95C24×C11—21no—
96C24×C11—22no—
97C24×C11—24no—
98C24×C11—28no—
99C24×C11—22no—
100C24×C11—24no—
101C24×C11—416no—
102C24×C11—48no—
103C24×C11—44no—
104C24×C11—48no—
105C24×C11—44no—
106C24×C11—416no—
107C24×C11—416no—
108C24×C11—48no—
109C24×C11—432no—
110C24×C11—44no—
111C24×C11—41no—
112C24×C11—42no—
113C24×C11—41no—
114C24×C11—44no—
115C24×C11—44no—
116C24×C11—42no—
117C24×C11—42no—
118C24×C11C22⋊C414yescomplemented
119C24×C11C22×C412yes—
120C24×C11C22×C414yescomplemented
121C24×C11C2×D411yescharacteristic
122C24×C11C2×D412yes—
123C24×C11C2×D412yes—
124C24×C11C2×D411yescharacteristic
125C24×C11C2×D412yes—
126C24×C11C2×D412yes—
127C24×C11#4114yes—
128C24×C11C2411yescharacteristic
129C2×D4×C11—28no—
130C2×D4×C11—28no—
131C2×D4×C11—24no—
132C2×D4×C11—28no—
133C2×D4×C11—28no—
134C2×D4×C11—24no—
135C2×D4×C11—24no—
136C2×D4×C11—24no—
137C2×D4×C11—216no—
138C2×D4×C11—432no—
139C2×D4×C11—416no—
140C2×D4×C11C22⋊C418yescomplemented
141C2×D4×C11C22×C414yes—
142C2×D4×C11C2×D414yes—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—22no—
146C22×C4×C11—24no—
147C22×C4×C11—24no—
148C22×C4×C11—22no—
149C22×C4×C11—28no—
150C22×C4×C11—24no—
151C22×C4×C11—24no—
152C22×C4×C11—44no—
153C22×C4×C11—48no—
154C22×C4×C11—48no—
155C22×C4×C11—44no—
156C22×C4×C11—84no—
157C22×C4×C11C22⋊C414yescomplemented
158C22×C4×C11C2×D412yes—
159C22×C4×C11C2×D418yescomplemented
160C11×C4⋊C4—28no—
161C11×C22⋊C4—28no—
162C11×C22⋊C4—24no—
163C11×C22⋊C4—24no—
164C11×C22⋊C4—24no—
165C11×C22⋊C4—24no—
166C11×C22⋊C4—24no—
167C11×C22⋊C4—22no—
168C11×C22⋊C4—216no—
169C11×C22⋊C4—24no—
170C11×C22⋊C4—24no—
171C11×C22⋊C4—432no—
172C11×C22⋊C4—44no—
173C11×C22⋊C4C22×C414yescomplemented
174C42×C11—28no—
175C22×#120C2×C1111yescharacteristic
176C2×#518C2×C1111yescharacteristic, complemented
177C22×#99C2×C1111yescharacteristic, complemented
178C2×#379C2×C1112yescomplemented
179#1889C2×C1118yesdirect product factor
180C2×#342C2×C1112yescomplemented
181C23×C11—28no—
182C23×C11—24no—
183C23×C11—216no—
184C23×C11—216no—
185C23×C11—28no—
186C23×C11—232no—
187C23×C11—24no—
188C23×C11—28no—
189C23×C11—22no—
190C23×C11—24no—
191C23×C11—22no—
192C23×C11—24no—
193C23×C11—44no—
194C23×C11—48no—
195C23×C11—44no—
196C23×C11—44no—
197C23×C11—42no—
198C23×C11—48no—
199C23×C11—42no—
200C23×C11—48no—
201C23×C11—432no—
202C23×C11—416no—
203C23×C11—416no—
204C23×C11—48no—
205C23×C11—44no—
206C23×C11—416no—
207C23×C11—48no—
208C23×C11—416no—
209C23×C11—48no—
210C23×C11—432no—
211C23×C11—416no—
212C23×C11—48no—
213C23×C11—44no—
214C23×C11—432no—
215C23×C11—416no—
216C23×C11—42no—
217C23×C11—44no—
218C23×C11—42no—
219C23×C11—44no—
220C23×C11—48no—
221C23×C11—44no—
222C23×C11—44no—
223C23×C11—48no—
224C23×C11—84no—
225C23×C11—82no—
226C23×C11C2×C22⋊C412yes—
227C23×C11C2×C22⋊C412yes—
228C23×C11C2×C22⋊C414yescomplemented
229C23×C11C4×D414yes—
230C23×C11C4×D414yes—
231C23×C11#12011yescharacteristic
232C23×C11#12012yes—
233C23×C11#12011yescharacteristic
234C23×C11#12114yes—
235C23×C11#12114yes—
236C23×C11#12312yes—
237C23×C11#12312yes—
238C23×C11C23×C411yescharacteristic
239C23×C11C22×D411yescharacteristic
240C23×C11C22×D412yes—
241C23×C11C22×D411yescharacteristic
242C23×C11C2×#4112yes—
243D4×C11—28no—
244D4×C11—28no—
245D4×C11—216no—
246D4×C11—432no—
247C2×C4×C11—22no—
248C2×C4×C11—22no—
249C2×C4×C11—24no—
250C2×C4×C11—24no—
251C2×C4×C11—24no—
252C2×C4×C11—28no—
253C2×C4×C11—48no—
254C2×C4×C11—44no—
255C2×C4×C11—48no—
256C2×C4×C11—48no—
257C2×C4×C11—48no—
258C2×C4×C11—44no—
259C2×C4×C11—84no—
260C2×C4×C11—88no—
261C2×C4×C11—88no—
262C2×C4×C11C2×C22⋊C414yescomplemented
263C26C22×C1111yescharacteristic
264C23×D4—21no—
265C23×D4C22×C1111yescharacteristic
266C2×#120—24no—
267C2×#120—22no—
268C2×#120C4×C1118yescomplemented
269C2×#120C22×C1114yes—
270#518—22no—
271#518—24no—
272#518C22×C1114yescomplemented
273C2×C4×D4—24no—
274C2×#117—21no—
275C22×C22⋊C4—21no—
276C22×C22⋊C4—21no—
277C22×C22⋊C4—24no—
278C22×C22⋊C4C22×C1112yes—
279C22×C22⋊C4C22×C1112yes—
280C22×C22⋊C4C22×C1111yescharacteristic
281C2×#99—24no—
282C2×#99C22×C1114yescomplemented
283#379—24no—
284#379C22×C1118yescomplemented
285#342C22×C1118yescomplemented
286C22×C11—24no—
287C22×C11—28no—
288C22×C11—28no—
289C22×C11—24no—
290C22×C11—24no—
291C22×C11—22no—
292C22×C11—24no—
293C22×C11—22no—
294C22×C11—28no—
295C22×C11—216no—
296C22×C11—24no—
297C22×C11—42no—
298C22×C11—44no—
299C22×C11—44no—
300C22×C11—42no—
301C22×C11—41no—
302C22×C11—41no—
303C22×C11—42no—
304C22×C11—44no—
305C22×C11—44no—
306C22×C11—416no—
307C22×C11—48no—
308C22×C11—48no—
309C22×C11—416no—
310C22×C11—432no—
311C22×C11—416no—
312C22×C11—48no—
313C22×C11—44no—
314C22×C11—48no—
315C22×C11—44no—
316C22×C11—82no—
317C22×C11—84no—
318C22×C11#38612yes—
319C22×C11#38614yes—
320C22×C11#38612yes—
321C22×C11B(4,𝔽2)14yes—
322C22×C11C22×C22⋊C411yescharacteristic
323C22×C11C2×C4×D412yes—
324C22×C11C2×#12011yescharacteristic
325C22×C11C2×#12112yes—
326C22×C11C2×#12311yescharacteristic
327C4×C11—24no—
328C4×C11—44no—
329C4×C11—48no—
330C4×C11—84no—
331C25—22no—
332C25—21no—
333C25—22no—
334C25—21no—
335C25—22no—
336C25—24no—
337C25—48no—
338C25C2×C4×C1114yescomplemented
339C25D4×C1111yescharacteristic
340C25C23×C1112yes—
341C25C23×C1111yescharacteristic
342C22×D4—22no—
343C22×D4—22no—
344C22×D4—24no—
345C22×D4—28no—
346C22×D4—24no—
347C22×D4—48no—
348C22×D4C2×C4×C1114yes—
349C22×D4D4×C1114yes—
350C22×D4D4×C1112yes—
351C22×D4C23×C1112yes—
352C23×C4—21no—
353C23×C4—22no—
354C23×C4—22no—
355C23×C4D4×C1111yescharacteristic
356C23×C4D4×C1114yescomplemented
357#120—216no—
358#120—28no—
359#120C2×C4×C11116yescomplemented
360C4×D4—216no—
361C4×D4—216no—
362#117—24no—
363#117—24no—
364C2×C4⋊C4—22no—
365C2×C22⋊C4—22no—
366C2×C22⋊C4—24no—
367C2×C22⋊C4—22no—
368C2×C22⋊C4—24no—
369C2×C22⋊C4—22no—
370C2×C22⋊C4—22no—
371C2×C22⋊C4—22no—
372C2×C22⋊C4—21no—
373C2×C22⋊C4—22no—
374C2×C22⋊C4—28no—
375C2×C22⋊C4—24no—
376C2×C22⋊C4—24no—
377C2×C22⋊C4—24no—
378C2×C22⋊C4—22no—
379C2×C22⋊C4—216no—
380C2×C22⋊C4—416no—
381C2×C22⋊C4C2×C4×C1114yescomplemented
382C2×C22⋊C4D4×C1114yescomplemented
383C2×C22⋊C4C23×C1114yes—
384C2×C22⋊C4C23×C1114yes—
385C2×C22⋊C4C23×C1112yes—
386C2×C42—22no—
387#99—28no—
388C2×C11—21no—
389C2×C11—22no—
390C2×C11—22no—
391C2×C11—21no—
392C2×C11—22no—
393C2×C11—24no—
394C2×C11—48no—
395C2×C11—44no—
396C2×C11#188914yesdirect product factor
397C2×C11C2×#38611yescharacteristic
398C2×C11C2×B(4,𝔽2)12yes—
399C24—216no—
400C24—28no—
401C24—24no—
402C24—28no—
403C24—21no—
404C24—24no—
405C24—22no—
406C24—21no—
407C24—22no—
408C24—24no—
409C24—28no—
410C24—22no—
411C24—24no—
412C24—416no—
413C24—44no—
414C24—48no—
415C24—48no—
416C24—44no—
417C24—416no—
418C24—416no—
419C24—48no—
420C24—432no—
421C24—44no—
422C24—41no—
423C24—42no—
424C24—41no—
425C24—44no—
426C24—44no—
427C24—42no—
428C24—42no—
429C24C11×C22⋊C414yescomplemented
430C24C22×C4×C1112yes—
431C24C22×C4×C1114yescomplemented
432C24C2×D4×C1111yescharacteristic
433C24C2×D4×C1112yes—
434C24C2×D4×C1112yes—
435C24C2×D4×C1111yescharacteristic
436C24C2×D4×C1112yes—
437C24C2×D4×C1112yes—
438C24C11×#4114yes—
439C24C24×C1111yescharacteristic
440C2×D4—28no—
441C2×D4—28no—
442C2×D4—24no—
443C2×D4—28no—
444C2×D4—28no—
445C2×D4—24no—
446C2×D4—24no—
447C2×D4—24no—
448C2×D4—216no—
449C2×D4—432no—
450C2×D4—416no—
451C2×D4C11×C22⋊C418yescomplemented
452C2×D4C22×C4×C1114yes—
453C2×D4C2×D4×C1114yes—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—22no—
457C22×C4—24no—
458C22×C4—24no—
459C22×C4—22no—
460C22×C4—28no—
461C22×C4—24no—
462C22×C4—24no—
463C22×C4—44no—
464C22×C4—48no—
465C22×C4—48no—
466C22×C4—44no—
467C22×C4—84no—
468C22×C4C11×C22⋊C414yescomplemented
469C22×C4C2×D4×C1112yes—
470C22×C4C2×D4×C1118yescomplemented
471C4⋊C4—28no—
472C22⋊C4—28no—
473C22⋊C4—24no—
474C22⋊C4—24no—
475C22⋊C4—24no—
476C22⋊C4—24no—
477C22⋊C4—24no—
478C22⋊C4—22no—
479C22⋊C4—216no—
480C22⋊C4—24no—
481C22⋊C4—24no—
482C22⋊C4—432no—
483C22⋊C4—44no—
484C22⋊C4C22×C4×C1114yescomplemented
485C42—28no—
486C11C2×#188911yescharacteristic, direct product factor, Sylow
487C23—28no—
488C23—24no—
489C23—216no—
490C23—216no—
491C23—28no—
492C23—232no—
493C23—24no—
494C23—28no—
495C23—22no—
496C23—24no—
497C23—24no—
498C23—22no—
499C23—44no—
500C23—48no—
501C23—44no—
502C23—44no—
503C23—42no—
504C23—48no—
505C23—42no—
506C23—48no—
507C23—432no—
508C23—416no—
509C23—416no—
510C23—48no—
511C23—44no—
512C23—416no—
513C23—48no—
514C23—416no—
515C23—48no—
516C23—432no—
517C23—416no—
518C23—48no—
519C23—44no—
520C23—432no—
521C23—416no—
522C23—42no—
523C23—44no—
524C23—44no—
525C23—48no—
526C23—44no—
527C23—42no—
528C23—44no—
529C23—48no—
530C23—84no—
531C23—82no—
532C23C2×C11×C22⋊C412yes—
533C23C2×C11×C22⋊C412yes—
534C23C2×C11×C22⋊C414yescomplemented
535C23C4×D4×C1114yes—
536C23C4×D4×C1114yes—
537C23C11×#12011yescharacteristic
538C23C11×#12012yes—
539C23C11×#12011yescharacteristic
540C23C11×#12114yes—
541C23C11×#12114yes—
542C23C11×#12312yes—
543C23C11×#12312yes—
544C23C23×C4×C1111yescharacteristic
545C23C22×D4×C1111yescharacteristic
546C23C22×D4×C1112yes—
547C23C22×D4×C1111yescharacteristic
548C23C2×C11×#4112yes—
549D4—28no—
550D4—28no—
551D4—216no—
552D4—432no—
553C2×C4—22no—
554C2×C4—24no—
555C2×C4—24no—
556C2×C4—22no—
557C2×C4—24no—
558C2×C4—28no—
559C2×C4—48no—
560C2×C4—44no—
561C2×C4—48no—
562C2×C4—48no—
563C2×C4—48no—
564C2×C4—44no—
565C2×C4—84no—
566C2×C4—88no—
567C2×C4—88no—
568C2×C4C2×C11×C22⋊C414yescomplemented
569C22—24no—
570C22—28no—
571C22—28no—
572C22—24no—
573C22—24no—
574C22—22no—
575C22—24no—
576C22—22no—
577C22—28no—
578C22—216no—
579C22—24no—
580C22—42no—
581C22—44no—
582C22—44no—
583C22—42no—
584C22—41no—
585C22—41no—
586C22—42no—
587C22—44no—
588C22—44no—
589C22—416no—
590C22—48no—
591C22—416no—
592C22—48no—
593C22—432no—
594C22—416no—
595C22—48no—
596C22—44no—
597C22—48no—
598C22—44no—
599C22—84no—
600C22—82no—
601C22C11×#38612yes—
602C22C11×#38614yes—
603C22C11×#38612yes—
604C22C11×B(4,𝔽2)14yes—
605C22C22×C11×C22⋊C411yescharacteristic
606C22C2×C4×D4×C1112yes—
607C22C2×C11×#12011yescharacteristic
608C22C2×C11×#12112yes—
609C22C2×C11×#12311yescharacteristic
610C4—24no—
611C4—44no—
612C4—48no—
613C4—84no—
614C2—21no—
615C2—22no—
616C2—22no—
617C2—22no—
618C2—21no—
619C2—24no—
620C2—48no—
621C2—44no—
622C2C11×#188914yesdirect product factor
623C2C2×C11×#38611yescharacteristic
624C2C2×C11×B(4,𝔽2)12yes—
subgroupG/H
center, socleC23×C11#120
commutatorC23C23×C4×C11
Frattini, cosocleC24C24×C11
prime radicalC22×C11×#120C2
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C25×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#518C2semidirect
3. C22×C11×#99C2semidirect
4. C2×C11×#379C2semidirect
5. C11×#1889C2direct (N × H)
6. C2×C11×#342C2semidirect
12. C2×C11×#120C4semidirect
16. C11×#518C22semidirect
26. C2×C11×#99C22semidirect
28. C11×#379C22semidirect
29. C11×#342C22semidirect
37. C25×C11C2×C4semidirect
55. C23×C4×C11D4semidirect
58. C11×#120C2×C4semidirect
80. C2×C11×C22⋊C4C2×C4semidirect
81. C2×C11×C22⋊C4D4semidirect
87. C2×#1889C11direct (N × H)
118. C24×C11C22⋊C4semidirect
120. C24×C11C22×C4semidirect
140. C2×D4×C11C22⋊C4semidirect
157. C22×C4×C11C22⋊C4semidirect
159. C22×C4×C11C2×D4semidirect
173. C11×C22⋊C4C22×C4semidirect
176. C2×#518C2×C11semidirect
177. C22×#99C2×C11semidirect
178. C2×#379C2×C11semidirect
179. #1889C2×C11direct (N × H)
180. C2×#342C2×C11semidirect
228. C23×C11C2×C22⋊C4semidirect
262. C2×C4×C11C2×C22⋊C4semidirect
268. C2×#120C4×C11semidirect
272. #518C22×C11semidirect
282. C2×#99C22×C11semidirect
284. #379C22×C11semidirect
285. #342C22×C11semidirect
338. C25C2×C4×C11semidirect
356. C23×C4D4×C11semidirect
359. #120C2×C4×C11semidirect
381. C2×C22⋊C4C2×C4×C11semidirect
382. C2×C22⋊C4D4×C11semidirect
396. C2×C11#1889direct (N × H)
429. C24C11×C22⋊C4semidirect
431. C24C22×C4×C11semidirect
451. C2×D4C11×C22⋊C4semidirect
468. C22×C4C11×C22⋊C4semidirect
470. C22×C4C2×D4×C11semidirect
484. C22⋊C4C22×C4×C11semidirect
486. C11C2×#1889direct (N × H)
534. C23C2×C11×C22⋊C4semidirect
568. C2×C4C2×C11×C22⋊C4semidirect
622. C2C11×#1889direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C11×#1202
C2×C11×#5182
C22×C11×#992
C2×C11×#3792
C11×#18892
C2×C11×#3422
C2×#188911