Finite Group Databasebeta

← C2×C11×#1900 #14598180

Subgroups — C2×C11×#1900 #14598180

Order 2816.

2198 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C11×M16C211yesmaximal, characteristic, complemented
2C22×C11×#121C211yesmaximal, characteristic
3C22×C11×#100C212yesmaximal, complemented
4C2×C11×#407C211yesmaximal, characteristic, complemented
5C11×#1900C218yesmaximal, direct product factor
6C2×C11×#343C212yesmaximal, complemented
7C23×D4×C11C412yes—
8C23×D4×C11C2211yescharacteristic
9C24×C4×C11C2211yescharacteristic
10C22×C11×M16—21no—
11C22×C11×M16—22no—
12C22×C11×M16—28no—
13C22×C11×M16C2212yes—
14C22×C11×M16C2212yes—
15C22×C11×M16C2214yescomplemented
16C23×C8×C11—21no—
17C2×C11×#121—21no—
18C2×C11×#121—21no—
19C2×C11×#121—22no—
20C2×C11×#121—21no—
21C2×C11×#121—22no—
22C2×C11×#121—21no—
23C2×C11×#121C414yes—
24C2×C11×#121C2214yes—
25C22×C11×C4⋊C4C2211yescharacteristic
26C22×C11×C22⋊C4C412yes—
27C2×C11×#100—28no—
28C2×C11×#100C2218yescomplemented
29C11×#407—22no—
30C11×#407C2214yescomplemented
31C2×C11×C22⋊C8—21no—
32C2×C11×C22⋊C8—21no—
33C11×#343C2218yescomplemented
34C25×C11C2×C411yescharacteristic
35C25×C11C2×C412yes—
36C22×D4×C11—24no—
37C22×D4×C11—22no—
38C22×D4×C11—22no—
39C22×D4×C11—21no—
40C22×D4×C11—21no—
41C22×D4×C11—21no—
42C22×D4×C11—21no—
43C22×D4×C11—24no—
44C22×D4×C11—24no—
45C22×D4×C11—48no—
46C22×D4×C11C2×C412yes—
47C22×D4×C11C2×C418yes—
48C22×D4×C11C2312yes—
49C23×C4×C11—24no—
50C23×C4×C11—24no—
51C23×C4×C11C2×C411yescharacteristic
52C23×C4×C11C2×C412yes—
53C23×C4×C11C2×C412yes—
54C23×C4×C11D411yescharacteristic
55C23×C4×C11D411yescharacteristic
56C23×C4×C11D412yes—
57C23×C4×C11D411yescharacteristic
58C23×C4×C11D412yes—
59C23×C4×C11D411yescharacteristic
60C23×C4×C11C2312yes—
61C23×C4×C11C2311yescharacteristic
62C2×C11×M16—216no—
63C2×C11×M16—28no—
64C2×C11×M16—24no—
65C2×C11×M16—22no—
66C2×C11×M16—24no—
67C2×C11×M16—216no—
68C2×C11×M16—22no—
69C2×C11×M16—24no—
70C2×C11×M16—24no—
71C2×C11×M16D418yescomplemented
72C2×C11×M16C2314yes—
73C2×C11×M16C2314yes—
74C22×C8×C11—28no—
75C22×C8×C11—22no—
76C22×C8×C11—24no—
77C22×C8×C11—22no—
78C11×#121—24no—
79C11×#121—24no—
80C11×#121—24no—
81C11×#121—24no—
82C11×#121—24no—
83C11×#121—24no—
84C11×#121—24no—
85C11×#121—24no—
86C2×C11×C4⋊C4—21no—
87C2×C11×C4⋊C4—21no—
88C2×C11×C4⋊C4—21no—
89C2×C11×C4⋊C4—21no—
90C2×C11×C4⋊C4C2×C412yes—
91C2×C11×C4⋊C4C2312yes—
92C2×C11×C22⋊C4—24no—
93C2×C11×C22⋊C4—22no—
94C2×C11×C22⋊C4—22no—
95C2×C11×C22⋊C4C2×C418yes—
96C11×#100—216no—
97C11×C22⋊C8—24no—
98C11×C22⋊C8—24no—
99C2×#1900C1111yesmaximal, characteristic, direct product factor, Sylow
100C24×C11—24no—
101C24×C11—24no—
102C24×C11—22no—
103C24×C11—22no—
104C24×C11—28no—
105C24×C11—42no—
106C24×C11—44no—
107C24×C11—44no—
108C24×C11C22⋊C411yescharacteristic
109C24×C11C22⋊C412yes—
110C24×C11C22⋊C411yescharacteristic
111C24×C11C22×C412yes—
112C24×C11C22×C411yescharacteristic
113C24×C11C22×C414yes—
114C2×D4×C11—28no—
115C2×D4×C11—28no—
116C2×D4×C11—22no—
117C2×D4×C11—22no—
118C2×D4×C11—28no—
119C2×D4×C11—24no—
120C2×D4×C11—22no—
121C2×D4×C11—22no—
122C2×D4×C11—24no—
123C2×D4×C11—416no—
124C2×D4×C11—48no—
125C2×D4×C11—48no—
126C2×D4×C11—416no—
127C2×D4×C11—42no—
128C2×D4×C11—42no—
129C2×D4×C11—44no—
130C2×D4×C11—44no—
131C2×D4×C11—42no—
132C2×D4×C11—42no—
133C22×C4×C11—24no—
134C22×C4×C11—28no—
135C22×C4×C11—22no—
136C22×C4×C11—24no—
137C22×C4×C11—22no—
138C22×C4×C11—24no—
139C22×C4×C11—24no—
140C22×C4×C11—28no—
141C22×C4×C11—22no—
142C22×C4×C11—24no—
143C22×C4×C11—22no—
144C22×C4×C11—24no—
145C22×C4×C11—24no—
146C22×C4×C11—22no—
147C22×C4×C11—22no—
148C22×C4×C11—44no—
149C22×C4×C11C22⋊C412yes—
150C22×C4×C11C22⋊C412yes—
151C22×C4×C11C22⋊C412yes—
152C22×C4×C11C22⋊C412yes—
153C22×C4×C11C22⋊C412yes—
154C22×C4×C11C22⋊C411yescharacteristic
155C22×C4×C11C22⋊C411yescharacteristic
156C22×C4×C11C22×C412yes—
157C22×C4×C11C22×C414yes—
158C22×C4×C11C22×C411yescharacteristic
159C22×C4×C11C2×D412yes—
160C22×C4×C11C2×D412yes—
161C22×C4×C11C2×D412yes—
162C22×C4×C11C2×D412yes—
163C22×C4×C11C2×D411yescharacteristic
164C22×C4×C11C2×D411yescharacteristic
165C22×C4×C11C2×D411yescharacteristic
166C22×C4×C11C2×D411yescharacteristic
167C22×C4×C11C2×D414yes—
168C22×C4×C11#4114yes—
169C22×C4×C11C2411yescharacteristic
170C11×M16—216no—
171C11×M16—28no—
172C11×M16—24no—
173C11×M16—24no—
174C11×M16—24no—
175C11×M16—44no—
176C11×M16C2×D418yescomplemented
177C2×C8×C11—216no—
178C2×C8×C11—28no—
179C2×C8×C11—24no—
180C2×C8×C11—24no—
181C2×C8×C11—44no—
182C11×C4⋊C4—22no—
183C11×C4⋊C4—22no—
184C11×C4⋊C4—22no—
185C11×C4⋊C4—22no—
186C11×C22⋊C4—28no—
187C11×C22⋊C4—28no—
188C23×M16C2×C1111yescharacteristic, complemented
189C22×#121C2×C1111yescharacteristic
190C22×#100C2×C1112yescomplemented
191C2×#407C2×C1111yescharacteristic, complemented
192#1900C2×C1118yesdirect product factor
193C2×#343C2×C1112yescomplemented
194C23×C11—22no—
195C23×C11—22no—
196C23×C11—22no—
197C23×C11—22no—
198C23×C11—24no—
199C23×C11—24no—
200C23×C11—22no—
201C23×C11—22no—
202C23×C11—24no—
203C23×C11—24no—
204C23×C11—22no—
205C23×C11—24no—
206C23×C11—28no—
207C23×C11—42no—
208C23×C11—42no—
209C23×C11—416no—
210C23×C11—44no—
211C23×C11—44no—
212C23×C11—44no—
213C23×C11—44no—
214C23×C11—44no—
215C23×C11—44no—
216C23×C11—44no—
217C23×C11—44no—
218C23×C11—816no—
219C23×C11#10014yescomplemented
220C23×C11C2×C22⋊C412yes—
221C23×C11C2×C22⋊C411yescharacteristic
222C23×C11C2×C22⋊C412yes—
223C23×C11C2×C22⋊C411yescharacteristic
224C23×C11C4×D414yes—
225C23×C11C23×C411yescharacteristic
226D4×C11—416no—
227D4×C11—416no—
228D4×C11—42no—
229D4×C11—44no—
230D4×C11—42no—
231D4×C11—44no—
232D4×C11—44no—
233C2×C4×C11—24no—
234C2×C4×C11—24no—
235C2×C4×C11—22no—
236C2×C4×C11—22no—
237C2×C4×C11—22no—
238C2×C4×C11—22no—
239C2×C4×C11—24no—
240C2×C4×C11—24no—
241C2×C4×C11—22no—
242C2×C4×C11—22no—
243C2×C4×C11—24no—
244C2×C4×C11—24no—
245C2×C4×C11—24no—
246C2×C4×C11—24no—
247C2×C4×C11—24no—
248C2×C4×C11—44no—
249C2×C4×C11—44no—
250C2×C4×C11—44no—
251C2×C4×C11C2×C22⋊C412yes—
252C2×C4×C11C2×C22⋊C412yes—
253C2×C4×C11C2×C22⋊C411yescharacteristic
254C2×C4×C11C2×C22⋊C411yescharacteristic
255C2×C4×C11C4×D414yes—
256C2×C4×C11#12012yes—
257C2×C4×C11#12012yes—
258C2×C4×C11#12114yes—
259C2×C4×C11#12114yes—
260C2×C4×C11#12312yes—
261C2×C4×C11#12312yes—
262C2×C4×C11C22×D412yes—
263C2×C4×C11C22×D411yescharacteristic
264C2×C4×C11C22×D411yescharacteristic
265C2×C4×C11C2×#4112yes—
266C8×C11—28no—
267C8×C11—44no—
268C23×D4C4×C1112yes—
269C23×D4C22×C1111yescharacteristic
270C24×C4C22×C1111yescharacteristic
271C22×M16—21no—
272C22×M16—22no—
273C22×M16—28no—
274C22×M16C22×C1112yes—
275C22×M16C22×C1112yes—
276C22×M16C22×C1114yescomplemented
277C23×C8—21no—
278C2×#121—21no—
279C2×#121—21no—
280C2×#121—22no—
281C2×#121—21no—
282C2×#121—21no—
283C2×#121—22no—
284C2×#121C4×C1114yes—
285C2×#121C22×C1114yes—
286C22×C4⋊C4C22×C1111yescharacteristic
287C22×C22⋊C4C4×C1112yes—
288C2×#100—28no—
289C2×#100C22×C1118yescomplemented
290#407—22no—
291#407C22×C1114yescomplemented
292C2×C22⋊C8—21no—
293C2×C22⋊C8—21no—
294#343C22×C1118yescomplemented
295C22×C11—21no—
296C22×C11—21no—
297C22×C11—21no—
298C22×C11—21no—
299C22×C11—22no—
300C22×C11—28no—
301C22×C11—28no—
302C22×C11—22no—
303C22×C11—22no—
304C22×C11—22no—
305C22×C11—22no—
306C22×C11—48no—
307C22×C11—48no—
308C22×C11—44no—
309C22×C11—44no—
310C22×C11—44no—
311C22×C11—44no—
312C22×C11—88no—
313C22×C11—88no—
314C22×C11—88no—
315C22×C11#38612yes—
316C22×C11#38612yes—
317C22×C11C2×#10012yes—
318C22×C11C2×#10014yescomplemented
319C22×C11#41312yes—
320C22×C11C22×C22⋊C411yescharacteristic
321C22×C11C2×C4×D412yes—
322C4×C11—22no—
323C4×C11—22no—
324C4×C11—44no—
325C4×C11#38612yes—
326C4×C11#38612yes—
327C4×C11C2×#12011yescharacteristic
328C4×C11C2×#12112yes—
329C4×C11C2×#12311yescharacteristic
330C25C2×C4×C1111yescharacteristic
331C25C2×C4×C1112yes—
332C22×D4—22no—
333C22×D4—24no—
334C22×D4—22no—
335C22×D4—21no—
336C22×D4—21no—
337C22×D4—21no—
338C22×D4—21no—
339C22×D4—24no—
340C22×D4—24no—
341C22×D4—48no—
342C22×D4C2×C4×C1112yes—
343C22×D4C2×C4×C1118yes—
344C22×D4C23×C1112yes—
345C23×C4—24no—
346C23×C4—24no—
347C23×C4C2×C4×C1111yescharacteristic
348C23×C4C2×C4×C1112yes—
349C23×C4C2×C4×C1112yes—
350C23×C4D4×C1111yescharacteristic
351C23×C4D4×C1112yes—
352C23×C4D4×C1111yescharacteristic
353C23×C4D4×C1111yescharacteristic
354C23×C4D4×C1111yescharacteristic
355C23×C4D4×C1112yes—
356C23×C4C23×C1112yes—
357C23×C4C23×C1111yescharacteristic
358C2×M16—216no—
359C2×M16—28no—
360C2×M16—24no—
361C2×M16—22no—
362C2×M16—24no—
363C2×M16—216no—
364C2×M16—22no—
365C2×M16—24no—
366C2×M16—24no—
367C2×M16D4×C1118yescomplemented
368C2×M16C23×C1114yes—
369C2×M16C23×C1114yes—
370C22×C8—28no—
371C22×C8—22no—
372C22×C8—24no—
373C22×C8—22no—
374#121—24no—
375#121—24no—
376#121—24no—
377#121—24no—
378#121—24no—
379#121—24no—
380#121—24no—
381#121—24no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4C2×C4×C1112yes—
387C2×C4⋊C4C23×C1112yes—
388C2×C22⋊C4—24no—
389C2×C22⋊C4—22no—
390C2×C22⋊C4—22no—
391C2×C22⋊C4C2×C4×C1118yes—
392#100—216no—
393C22⋊C8—24no—
394C22⋊C8—24no—
395C2×C11—22no—
396C2×C11—22no—
397C2×C11—24no—
398C2×C11—42no—
399C2×C11—84no—
400C2×C11#190014yesdirect product factor
401C2×C11C2×#38611yescharacteristic
402C2×C11C22×#10011yescharacteristic
403C2×C11C2×#41311yescharacteristic
404C24—24no—
405C24—24no—
406C24—22no—
407C24—22no—
408C24—28no—
409C24—42no—
410C24—44no—
411C24—44no—
412C24C11×C22⋊C411yescharacteristic
413C24C11×C22⋊C412yes—
414C24C11×C22⋊C411yescharacteristic
415C24C22×C4×C1112yes—
416C24C22×C4×C1111yescharacteristic
417C24C22×C4×C1114yes—
418C2×D4—28no—
419C2×D4—28no—
420C2×D4—22no—
421C2×D4—22no—
422C2×D4—28no—
423C2×D4—24no—
424C2×D4—22no—
425C2×D4—22no—
426C2×D4—24no—
427C2×D4—416no—
428C2×D4—48no—
429C2×D4—48no—
430C2×D4—416no—
431C2×D4—42no—
432C2×D4—42no—
433C2×D4—44no—
434C2×D4—44no—
435C2×D4—42no—
436C2×D4—42no—
437C22×C4—24no—
438C22×C4—28no—
439C22×C4—22no—
440C22×C4—24no—
441C22×C4—22no—
442C22×C4—24no—
443C22×C4—24no—
444C22×C4—28no—
445C22×C4—22no—
446C22×C4—24no—
447C22×C4—22no—
448C22×C4—24no—
449C22×C4—24no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—44no—
453C22×C4C11×C22⋊C412yes—
454C22×C4C11×C22⋊C411yescharacteristic
455C22×C4C11×C22⋊C411yescharacteristic
456C22×C4C11×C22⋊C412yes—
457C22×C4C11×C22⋊C412yes—
458C22×C4C11×C22⋊C412yes—
459C22×C4C11×C22⋊C412yes—
460C22×C4C22×C4×C1112yes—
461C22×C4C22×C4×C1114yes—
462C22×C4C22×C4×C1111yescharacteristic
463C22×C4C2×D4×C1112yes—
464C22×C4C2×D4×C1112yes—
465C22×C4C2×D4×C1112yes—
466C22×C4C2×D4×C1112yes—
467C22×C4C2×D4×C1111yescharacteristic
468C22×C4C2×D4×C1111yescharacteristic
469C22×C4C2×D4×C1111yescharacteristic
470C22×C4C2×D4×C1111yescharacteristic
471C22×C4C2×D4×C1114yes—
472C22×C4C11×#4114yes—
473C22×C4C24×C1111yescharacteristic
474M16—216no—
475M16—28no—
476M16—24no—
477M16—24no—
478M16—24no—
479M16—44no—
480M16C2×D4×C1118yescomplemented
481C2×C8—216no—
482C2×C8—28no—
483C2×C8—24no—
484C2×C8—24no—
485C2×C8—44no—
486C4⋊C4—22no—
487C4⋊C4—22no—
488C4⋊C4—22no—
489C4⋊C4—22no—
490C22⋊C4—28no—
491C22⋊C4—28no—
492C11C2×#190011yescharacteristic, direct product factor, Sylow
493C23—22no—
494C23—22no—
495C23—22no—
496C23—22no—
497C23—24no—
498C23—24no—
499C23—22no—
500C23—22no—
501C23—24no—
502C23—24no—
503C23—22no—
504C23—24no—
505C23—28no—
506C23—42no—
507C23—42no—
508C23—416no—
509C23—44no—
510C23—44no—
511C23—44no—
512C23—44no—
513C23—44no—
514C23—44no—
515C23—44no—
516C23—44no—
517C23—816no—
518C23C11×#10014yescomplemented
519C23C2×C11×C22⋊C412yes—
520C23C2×C11×C22⋊C411yescharacteristic
521C23C2×C11×C22⋊C412yes—
522C23C2×C11×C22⋊C411yescharacteristic
523C23C4×D4×C1114yes—
524C23C23×C4×C1111yescharacteristic
525D4—416no—
526D4—416no—
527D4—42no—
528D4—44no—
529D4—44no—
530D4—44no—
531D4—42no—
532C2×C4—24no—
533C2×C4—24no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—24no—
539C2×C4—24no—
540C2×C4—24no—
541C2×C4—24no—
542C2×C4—24no—
543C2×C4—24no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—24no—
547C2×C4—44no—
548C2×C4—44no—
549C2×C4—44no—
550C2×C4C2×C11×C22⋊C412yes—
551C2×C4C2×C11×C22⋊C412yes—
552C2×C4C2×C11×C22⋊C411yescharacteristic
553C2×C4C2×C11×C22⋊C411yescharacteristic
554C2×C4C4×D4×C1114yes—
555C2×C4C11×#12012yes—
556C2×C4C11×#12012yes—
557C2×C4C11×#12114yes—
558C2×C4C11×#12114yes—
559C2×C4C11×#12312yes—
560C2×C4C11×#12312yes—
561C2×C4C22×D4×C1112yes—
562C2×C4C22×D4×C1111yescharacteristic
563C2×C4C22×D4×C1111yescharacteristic
564C2×C4C2×C11×#4112yes—
565C8—28no—
566C8—44no—
567C22—28no—
568C22—28no—
569C22—22no—
570C22—21no—
571C22—21no—
572C22—21no—
573C22—21no—
574C22—22no—
575C22—22no—
576C22—22no—
577C22—22no—
578C22—48no—
579C22—48no—
580C22—44no—
581C22—44no—
582C22—44no—
583C22—44no—
584C22—88no—
585C22—88no—
586C22—88no—
587C22C11×#38612yes—
588C22C11×#38612yes—
589C22C2×C11×#10012yes—
590C22C2×C11×#10014yescomplemented
591C22C11×#41312yes—
592C22C22×C11×C22⋊C411yescharacteristic
593C22C2×C4×D4×C1112yes—
594C4—22no—
595C4—22no—
596C4—44no—
597C4C11×#38612yes—
598C4C11×#38612yes—
599C4C2×C11×#12011yescharacteristic
600C4C2×C11×#12112yes—
601C4C2×C11×#12311yescharacteristic
602C2—22no—
603C2—22no—
604C2—24no—
605C2—42no—
606C2—84no—
607C2C11×#190014yesdirect product factor
608C2C2×C11×#38611yescharacteristic
609C2C22×C11×#10011yescharacteristic
610C2C2×C11×#41311yescharacteristic
subgroupG/H
center, socleC23×C11C2×C22⋊C4
commutatorC23C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC22×C11×#121C2
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C24×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C23×C11×M16C2semidirect
3. C22×C11×#100C2semidirect
4. C2×C11×#407C2semidirect
5. C11×#1900C2direct (N × H)
6. C2×C11×#343C2semidirect
15. C22×C11×M16C22semidirect
28. C2×C11×#100C22semidirect
30. C11×#407C22semidirect
33. C11×#343C22semidirect
71. C2×C11×M16D4semidirect
99. C2×#1900C11direct (N × H)
176. C11×M16C2×D4semidirect
188. C23×M16C2×C11semidirect
190. C22×#100C2×C11semidirect
191. C2×#407C2×C11semidirect
192. #1900C2×C11direct (N × H)
193. C2×#343C2×C11semidirect
219. C23×C11#100semidirect
276. C22×M16C22×C11semidirect
289. C2×#100C22×C11semidirect
291. #407C22×C11semidirect
294. #343C22×C11semidirect
318. C22×C11C2×#100semidirect
367. C2×M16D4×C11semidirect
400. C2×C11#1900direct (N × H)
480. M16C2×D4×C11semidirect
492. C11C2×#1900direct (N × H)
518. C23C11×#100semidirect
590. C22C2×C11×#100semidirect
607. C2C11×#1900direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C11×M162
C22×C11×#1212
C22×C11×#1002
C2×C11×#4072
C11×#19002
C2×C11×#3432
C2×#190011