Finite Group Databasebeta

← C2×C11×#1891 #14598156

Subgroups — C2×C11×#1891 #14598156

Order 2816.

1870 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#568C211yesmaximal, characteristic, complemented
2C2×C11×#525C211yesmaximal, characteristic
3C2×C11×#413C211yesmaximal, characteristic, complemented
4C2×C11×#407C212yesmaximal, complemented
5C11×#1891C218yesmaximal, direct product factor
6C2×C11×#344C212yesmaximal, complemented
7C22×C11×#41C2211yescharacteristic
8C24×C4×C11C2211yescharacteristic
9C11×#568—22no—
10C11×#568—24no—
11C11×#568C2214yescomplemented
12C2×C11×#131—24no—
13C22×C11×M16—22no—
14C22×C11×M16C2212yes—
15C22×C11×M16C2212yes—
16C11×#525—22no—
17C11×#525—22no—
18C11×#525C414yes—
19C11×#525C2214yes—
20C2×C11×#123C412yes—
21C2×C11×C22⋊Q8—21no—
22C2×C11×#121—21no—
23C2×C11×#120C412yes—
24C2×C4×D4×C11—22no—
25C2×C11×#117C2211yescharacteristic
26C11×#413—22no—
27C11×#413C2214yescomplemented
28C2×C11×#101—21no—
29C2×C11×#100—21no—
30C11×#407—24no—
31C11×#407C2218yescomplemented
32C2×C11×C22⋊C8—24no—
33C11×#344C2218yescomplemented
34C25×C11C2×C411yescharacteristic
35C2×C11×#41—22no—
36C2×C11×#41—22no—
37C2×C11×#41—22no—
38C2×C11×#41—22no—
39C2×C11×#41C2×C412yes—
40C2×C11×#41D412yes—
41C2×C11×#41D412yes—
42C2×C11×#41C2312yes—
43C22×Q8×C11D411yescharacteristic
44C22×D4×C11—22no—
45C22×D4×C11C2×C412yes—
46C22×D4×C11D411yescharacteristic
47C23×C4×C11—21no—
48C23×C4×C11—21no—
49C23×C4×C11—21no—
50C23×C4×C11—21no—
51C23×C4×C11—22no—
52C23×C4×C11—22no—
53C23×C4×C11—22no—
54C23×C4×C11—22no—
55C23×C4×C11C2×C411yescharacteristic
56C23×C4×C11C2×C412yes—
57C23×C4×C11D412yes—
58C23×C4×C11C2312yes—
59C23×C4×C11C2311yescharacteristic
60C11×#131—216no—
61C11×#131—216no—
62C2×C11×M16—24no—
63C2×C11×M16—28no—
64C2×C11×M16—22no—
65C2×C11×M16—28no—
66C2×C11×M16—22no—
67C2×C11×M16—22no—
68C2×C11×M16—22no—
69C2×C11×M16—22no—
70C2×C11×M16—22no—
71C2×C11×M16—22no—
72C2×C11×M16—22no—
73C2×C11×M16—22no—
74C2×C11×M16D414yescomplemented
75C2×C11×M16C2314yes—
76C2×C11×M16C2314yes—
77C22×C8×C11—24no—
78C22×C8×C11—22no—
79C22×C8×C11D414yescomplemented
80C11×#123—24no—
81C11×#123C2×C418yes—
82C11×C22⋊Q8—24no—
83C11×C22⋊Q8—24no—
84C11×#121—24no—
85C11×#121—24no—
86C11×#120—24no—
87C11×#120C2×C418yes—
88C4×D4×C11—28no—
89C4×D4×C11—28no—
90C11×#117—21no—
91C11×#117—21no—
92C11×#117C2×C412yes—
93C11×#117C2312yes—
94C2×C11×C4⋊C4—22no—
95C2×C11×C4⋊C4—21no—
96C2×C11×C22⋊C4—22no—
97C2×C11×C22⋊C4—22no—
98C2×C11×C22⋊C4C2×C412yes—
99C2×C42×C11—21no—
100C11×#101—24no—
101C11×#100—24no—
102C11×C22⋊C8—216no—
103C2×#1891C1111yesmaximal, characteristic, direct product factor, Sylow
104C24×C11—21no—
105C24×C11—22no—
106C24×C11—21no—
107C24×C11—22no—
108C24×C11—44no—
109C24×C11C22⋊C412yes—
110C24×C11C22×C412yes—
111C24×C11C22×C411yescharacteristic
112C11×#41—24no—
113C11×#41—24no—
114C11×#41—24no—
115C11×#41—24no—
116C11×#41—24no—
117C11×#41—24no—
118C11×#41—24no—
119C11×#41—24no—
120C2×Q8×C11—22no—
121C2×Q8×C11—22no—
122C2×Q8×C11C22⋊C412yes—
123C2×Q8×C11C2×D412yes—
124C2×D4×C11—24no—
125C2×D4×C11—24no—
126C2×D4×C11—28no—
127C2×D4×C11—22no—
128C2×D4×C11—22no—
129C2×D4×C11—48no—
130C2×D4×C11C22⋊C414yes—
131C2×D4×C11C22⋊C412yes—
132C2×D4×C11C22×C414yes—
133C2×D4×C11C2×D412yes—
134C22×C4×C11—22no—
135C22×C4×C11—22no—
136C22×C4×C11—22no—
137C22×C4×C11—22no—
138C22×C4×C11—22no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—22no—
142C22×C4×C11—22no—
143C22×C4×C11—22no—
144C22×C4×C11—22no—
145C22×C4×C11—24no—
146C22×C4×C11—24no—
147C22×C4×C11—24no—
148C22×C4×C11—22no—
149C22×C4×C11—22no—
150C22×C4×C11—24no—
151C22×C4×C11—42no—
152C22×C4×C11—41no—
153C22×C4×C11—41no—
154C22×C4×C11—42no—
155C22×C4×C11—42no—
156C22×C4×C11—42no—
157C22×C4×C11—42no—
158C22×C4×C11—41no—
159C22×C4×C11—41no—
160C22×C4×C11—42no—
161C22×C4×C11C22⋊C412yes—
162C22×C4×C11C22⋊C414yes—
163C22×C4×C11C22×C412yes—
164C22×C4×C11C22×C411yescharacteristic
165C22×C4×C11C2×D414yes—
166C22×C4×C11C2×D411yescharacteristic
167C22×C4×C11C2×D411yescharacteristic
168C22×C4×C11C2×D411yescharacteristic
169C22×C4×C11C2×D411yescharacteristic
170C22×C4×C11C2×D412yes—
171C22×C4×C11C2×D412yes—
172C22×C4×C11#4112yes—
173C22×C4×C11#4112yes—
174C22×C4×C11C2411yescharacteristic
175C11×M16—216no—
176C11×M16—24no—
177C11×M16—24no—
178C11×M16—24no—
179C11×M16—24no—
180C11×M16—24no—
181C11×M16—24no—
182C11×M16—42no—
183C11×M16—42no—
184C2×C8×C11—216no—
185C2×C8×C11—24no—
186C2×C8×C11—24no—
187C2×C8×C11—24no—
188C2×C8×C11—42no—
189C2×C8×C11—42no—
190C2×C8×C11C2×D418yescomplemented
191C11×C4⋊C4—22no—
192C11×C4⋊C4—28no—
193C11×C4⋊C4—22no—
194C11×C22⋊C4—28no—
195C11×C22⋊C4—22no—
196C11×C22⋊C4—28no—
197C11×C22⋊C4C22×C414yes—
198C42×C11—22no—
199C42×C11—22no—
200C2×#568C2×C1111yescharacteristic, complemented
201C2×#525C2×C1111yescharacteristic
202C2×#413C2×C1111yescharacteristic, complemented
203C2×#407C2×C1112yescomplemented
204#1891C2×C1118yesdirect product factor
205C2×#344C2×C1112yescomplemented
206C23×C11—24no—
207C23×C11—28no—
208C23×C11—22no—
209C23×C11—24no—
210C23×C11—22no—
211C23×C11—22no—
212C23×C11—42no—
213C23×C11—44no—
214C23×C11—42no—
215C23×C11—44no—
216C23×C11—44no—
217C23×C11—48no—
218C23×C11—44no—
219C23×C11—41no—
220C23×C11—42no—
221C23×C11—41no—
222C23×C11C2×C22⋊C411yescharacteristic
223C23×C11C2×C22⋊C414yes—
224C23×C11C2×C22⋊C411yescharacteristic
225C23×C11C4×D412yes—
226C23×C11C4×D412yes—
227C23×C11C23×C411yescharacteristic
228Q8×C11—24no—
229Q8×C11—24no—
230D4×C11—28no—
231D4×C11—28no—
232D4×C11—24no—
233D4×C11—24no—
234D4×C11—416no—
235C2×C4×C11—22no—
236C2×C4×C11—22no—
237C2×C4×C11—24no—
238C2×C4×C11—24no—
239C2×C4×C11—24no—
240C2×C4×C11—24no—
241C2×C4×C11—24no—
242C2×C4×C11—22no—
243C2×C4×C11—24no—
244C2×C4×C11—44no—
245C2×C4×C11—41no—
246C2×C4×C11—42no—
247C2×C4×C11—41no—
248C2×C4×C11—42no—
249C2×C4×C11—44no—
250C2×C4×C11—42no—
251C2×C4×C11—42no—
252C2×C4×C11—42no—
253C2×C4×C11—44no—
254C2×C4×C11C2×C22⋊C414yes—
255C2×C4×C11C2×C22⋊C411yescharacteristic
256C2×C4×C11C2×C22⋊C411yescharacteristic
257C2×C4×C11C4×D412yes—
258C2×C4×C11C4×D412yes—
259C2×C4×C11#12012yes—
260C2×C4×C11#12011yescharacteristic
261C2×C4×C11#12011yescharacteristic
262C2×C4×C11#12112yes—
263C2×C4×C11#12112yes—
264C2×C4×C11#12112yes—
265C2×C4×C11#12112yes—
266C2×C4×C11#12311yescharacteristic
267C2×C4×C11#12311yescharacteristic
268C2×C4×C11#12312yes—
269C2×C4×C11C22×D412yes—
270C2×C4×C11C22×D411yescharacteristic
271C2×C4×C11C22×D411yescharacteristic
272C2×C4×C11C2×#4112yes—
273C8×C11—28no—
274C8×C11—44no—
275C22×#41C22×C1111yescharacteristic
276C24×C4C22×C1111yescharacteristic
277#568—22no—
278#568—24no—
279#568C22×C1114yescomplemented
280C2×#131—24no—
281C22×M16—22no—
282C22×M16C22×C1112yes—
283C22×M16C22×C1112yes—
284#525—22no—
285#525—22no—
286#525C4×C1114yes—
287#525C22×C1114yes—
288C2×#123C4×C1112yes—
289C2×C22⋊Q8—21no—
290C2×#121—21no—
291C2×#120C4×C1112yes—
292C2×C4×D4—22no—
293C2×#117C22×C1111yescharacteristic
294#413—22no—
295#413C22×C1114yescomplemented
296C2×#101—21no—
297C2×#100—21no—
298#407—24no—
299#407C22×C1118yescomplemented
300C2×C22⋊C8—24no—
301#344C22×C1118yescomplemented
302C22×C11—22no—
303C22×C11—24no—
304C22×C11—24no—
305C22×C11—28no—
306C22×C11—24no—
307C22×C11—41no—
308C22×C11—42no—
309C22×C11—41no—
310C22×C11—44no—
311C22×C11—42no—
312C22×C11—44no—
313C22×C11—44no—
314C22×C11—48no—
315C22×C11—44no—
316C22×C11—44no—
317C22×C11—42no—
318C22×C11—82no—
319C22×C11#38611yescharacteristic
320C22×C11#38612yes—
321C22×C11#38611yescharacteristic
322C22×C11C22×C22⋊C411yescharacteristic
323C22×C11C2×C4×D412yes—
324C4×C11—24no—
325C4×C11—44no—
326C4×C11—42no—
327C4×C11#38611yescharacteristic
328C4×C11#38611yescharacteristic
329C4×C11#38612yes—
330C4×C11C2×#12011yescharacteristic
331C4×C11C2×#12112yes—
332C4×C11C2×#12311yescharacteristic
333C25C2×C4×C1111yescharacteristic
334C2×#41—22no—
335C2×#41—22no—
336C2×#41—22no—
337C2×#41—22no—
338C2×#41C2×C4×C1112yes—
339C2×#41D4×C1112yes—
340C2×#41D4×C1112yes—
341C2×#41C23×C1112yes—
342C22×Q8D4×C1111yescharacteristic
343C22×D4—22no—
344C22×D4C2×C4×C1112yes—
345C22×D4D4×C1111yescharacteristic
346C23×C4—21no—
347C23×C4—21no—
348C23×C4—21no—
349C23×C4—21no—
350C23×C4—22no—
351C23×C4—22no—
352C23×C4—22no—
353C23×C4—22no—
354C23×C4C2×C4×C1111yescharacteristic
355C23×C4C2×C4×C1112yes—
356C23×C4D4×C1112yes—
357C23×C4C23×C1112yes—
358C23×C4C23×C1111yescharacteristic
359#131—216no—
360#131—216no—
361C2×M16—24no—
362C2×M16—28no—
363C2×M16—22no—
364C2×M16—28no—
365C2×M16—22no—
366C2×M16—22no—
367C2×M16—22no—
368C2×M16—22no—
369C2×M16—22no—
370C2×M16—22no—
371C2×M16—22no—
372C2×M16—22no—
373C2×M16D4×C1114yescomplemented
374C2×M16C23×C1114yes—
375C2×M16C23×C1114yes—
376C22×C8—24no—
377C22×C8—22no—
378C22×C8D4×C1114yescomplemented
379#123—24no—
380#123C2×C4×C1118yes—
381C22⋊Q8—24no—
382C22⋊Q8—24no—
383#121—24no—
384#121—24no—
385#120—24no—
386#120C2×C4×C1118yes—
387C4×D4—28no—
388C4×D4—28no—
389#117—21no—
390#117—21no—
391#117C2×C4×C1112yes—
392#117C23×C1112yes—
393C2×C4⋊C4—22no—
394C2×C4⋊C4—21no—
395C2×C22⋊C4—22no—
396C2×C22⋊C4—22no—
397C2×C22⋊C4C2×C4×C1112yes—
398C2×C42—21no—
399#101—24no—
400#100—24no—
401C22⋊C8—216no—
402C2×C11—21no—
403C2×C11—22no—
404C2×C11—21no—
405C2×C11—22no—
406C2×C11—44no—
407C2×C11—44no—
408C2×C11#189112yesdirect product factor
409C2×C11C2×#38611yescharacteristic
410C24—21no—
411C24—22no—
412C24—21no—
413C24—22no—
414C24—44no—
415C24C11×C22⋊C412yes—
416C24C22×C4×C1112yes—
417C24C22×C4×C1111yescharacteristic
418#41—24no—
419#41—24no—
420#41—24no—
421#41—24no—
422#41—24no—
423#41—24no—
424#41—24no—
425#41—24no—
426C2×Q8—22no—
427C2×Q8—22no—
428C2×Q8C11×C22⋊C412yes—
429C2×Q8C2×D4×C1112yes—
430C2×D4—24no—
431C2×D4—24no—
432C2×D4—28no—
433C2×D4—22no—
434C2×D4—22no—
435C2×D4—48no—
436C2×D4C11×C22⋊C414yes—
437C2×D4C11×C22⋊C412yes—
438C2×D4C22×C4×C1114yes—
439C2×D4C2×D4×C1112yes—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—24no—
452C22×C4—24no—
453C22×C4—24no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—24no—
457C22×C4—42no—
458C22×C4—41no—
459C22×C4—41no—
460C22×C4—42no—
461C22×C4—42no—
462C22×C4—42no—
463C22×C4—42no—
464C22×C4—41no—
465C22×C4—41no—
466C22×C4—42no—
467C22×C4C11×C22⋊C412yes—
468C22×C4C11×C22⋊C414yes—
469C22×C4C22×C4×C1112yes—
470C22×C4C22×C4×C1111yescharacteristic
471C22×C4C2×D4×C1114yes—
472C22×C4C2×D4×C1111yescharacteristic
473C22×C4C2×D4×C1111yescharacteristic
474C22×C4C2×D4×C1111yescharacteristic
475C22×C4C2×D4×C1111yescharacteristic
476C22×C4C2×D4×C1112yes—
477C22×C4C2×D4×C1112yes—
478C22×C4C11×#4112yes—
479C22×C4C11×#4112yes—
480C22×C4C24×C1111yescharacteristic
481M16—216no—
482M16—24no—
483M16—24no—
484M16—24no—
485M16—24no—
486M16—24no—
487M16—24no—
488M16—42no—
489M16—42no—
490C2×C8—216no—
491C2×C8—24no—
492C2×C8—24no—
493C2×C8—24no—
494C2×C8—42no—
495C2×C8—42no—
496C2×C8C2×D4×C1118yescomplemented
497C4⋊C4—22no—
498C4⋊C4—28no—
499C4⋊C4—22no—
500C22⋊C4—28no—
501C22⋊C4—22no—
502C22⋊C4—28no—
503C22⋊C4C22×C4×C1114yes—
504C42—22no—
505C42—22no—
506C11C2×#189111yescharacteristic, direct product factor, Sylow
507C23—24no—
508C23—28no—
509C23—22no—
510C23—24no—
511C23—22no—
512C23—22no—
513C23—42no—
514C23—44no—
515C23—42no—
516C23—44no—
517C23—44no—
518C23—48no—
519C23—44no—
520C23—41no—
521C23—42no—
522C23—41no—
523C23C2×C11×C22⋊C411yescharacteristic
524C23C2×C11×C22⋊C414yes—
525C23C2×C11×C22⋊C411yescharacteristic
526C23C4×D4×C1112yes—
527C23C4×D4×C1112yes—
528C23C23×C4×C1111yescharacteristic
529Q8—24no—
530Q8—24no—
531D4—28no—
532D4—28no—
533D4—24no—
534D4—24no—
535D4—416no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—24no—
539C2×C4—24no—
540C2×C4—24no—
541C2×C4—24no—
542C2×C4—24no—
543C2×C4—22no—
544C2×C4—24no—
545C2×C4—44no—
546C2×C4—41no—
547C2×C4—42no—
548C2×C4—41no—
549C2×C4—42no—
550C2×C4—44no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—44no—
554C2×C4—42no—
555C2×C4C2×C11×C22⋊C414yes—
556C2×C4C2×C11×C22⋊C411yescharacteristic
557C2×C4C2×C11×C22⋊C411yescharacteristic
558C2×C4C4×D4×C1112yes—
559C2×C4C4×D4×C1112yes—
560C2×C4C11×#12012yes—
561C2×C4C11×#12011yescharacteristic
562C2×C4C11×#12011yescharacteristic
563C2×C4C11×#12112yes—
564C2×C4C11×#12112yes—
565C2×C4C11×#12112yes—
566C2×C4C11×#12112yes—
567C2×C4C11×#12311yescharacteristic
568C2×C4C11×#12311yescharacteristic
569C2×C4C11×#12312yes—
570C2×C4C22×D4×C1112yes—
571C2×C4C22×D4×C1111yescharacteristic
572C2×C4C22×D4×C1111yescharacteristic
573C2×C4C2×C11×#4112yes—
574C8—28no—
575C8—44no—
576C22—22no—
577C22—24no—
578C22—24no—
579C22—28no—
580C22—24no—
581C22—41no—
582C22—42no—
583C22—41no—
584C22—44no—
585C22—42no—
586C22—44no—
587C22—44no—
588C22—48no—
589C22—44no—
590C22—44no—
591C22—42no—
592C22—82no—
593C22C11×#38611yescharacteristic
594C22C11×#38612yes—
595C22C11×#38611yescharacteristic
596C22C22×C11×C22⋊C411yescharacteristic
597C22C2×C4×D4×C1112yes—
598C4—24no—
599C4—44no—
600C4—42no—
601C4C11×#38611yescharacteristic
602C4C11×#38611yescharacteristic
603C4C11×#38612yes—
604C4C2×C11×#12011yescharacteristic
605C4C2×C11×#12112yes—
606C4C2×C11×#12311yescharacteristic
607C2—21no—
608C2—22no—
609C2—21no—
610C2—22no—
611C2—44no—
612C2—44no—
613C2C11×#189112yesdirect product factor
614C2C2×C11×#38611yescharacteristic
subgroupG/H
centerC2×C4×C11#120
commutatorC23C23×C4×C11
Frattini, cosocleC22×C4C24×C11
socleC22×C11#386
prime radicalC2×C11×#525C2
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#568C2semidirect
3. C2×C11×#413C2semidirect
4. C2×C11×#407C2semidirect
5. C11×#1891C2direct (N × H)
6. C2×C11×#344C2semidirect
11. C11×#568C22semidirect
27. C11×#413C22semidirect
31. C11×#407C22semidirect
33. C11×#344C22semidirect
74. C2×C11×M16D4semidirect
79. C22×C8×C11D4semidirect
103. C2×#1891C11direct (N × H)
190. C2×C8×C11C2×D4semidirect
200. C2×#568C2×C11semidirect
202. C2×#413C2×C11semidirect
203. C2×#407C2×C11semidirect
204. #1891C2×C11direct (N × H)
205. C2×#344C2×C11semidirect
279. #568C22×C11semidirect
295. #413C22×C11semidirect
299. #407C22×C11semidirect
301. #344C22×C11semidirect
373. C2×M16D4×C11semidirect
378. C22×C8D4×C11semidirect
408. C2×C11#1891direct (N × H)
496. C2×C8C2×D4×C11semidirect
506. C11C2×#1891direct (N × H)
613. C2C11×#1891direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5682
C2×C11×#5252
C2×C11×#4132
C2×C11×#4072
C11×#18912
C2×C11×#3442
C2×#189111