Finite Group Databasebeta

← C2×C11×#1884 #14598139

Subgroups — C2×C11×#1884 #14598139

Order 2816.

1794 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#568C211yesmaximal, characteristic, complemented
2C2×C11×#532C211yesmaximal, characteristic
3C2×C11×#421C212yesmaximal, complemented
4C2×C11×#410C211yesmaximal, characteristic, complemented
5C11×#1884C218yesmaximal, direct product factor
6C2×C11×#339C212yesmaximal, complemented
7C22×C11×#41C2211yescharacteristic
8C22×C11×#41C2211yescharacteristic
9C11×#568—22no—
10C11×#568—24no—
11C11×#568C2214yescomplemented
12C2×C11×#131—24no—
13C22×C11×M16—22no—
14C22×C11×M16C2212yes—
15C11×#532—22no—
16C11×#532—22no—
17C11×#532C414yescomplemented
18C11×#532C2214yes—
19C2×C11×C4⋊Q8C411yescharacteristic, complemented
20C2×C11×#127C411yescharacteristic, complemented
21C2×C11×#124C411yescharacteristic, complemented
22C2×C11×#124C411yescharacteristic, complemented
23C2×C11×#121—22no—
24C2×C4×D4×C11—22no—
25C2×C11×#117C2212yes—
26C22×C42×C11C2211yescharacteristic
27C11×#421—24no—
28C11×#421C2218yescomplemented
29C2×C11×#104—24no—
30C11×#410—22no—
31C11×#410C2214yescomplemented
32C2×C11×#99—22no—
33C11×#339C2218yescomplemented
34C2×C11×#41—22no—
35C2×C11×#41—22no—
36C2×C11×#41—21no—
37C2×C11×#41—21no—
38C2×C11×#41—22no—
39C2×C11×#41—22no—
40C2×C11×#41—22no—
41C2×C11×#41—22no—
42C2×C11×#41—22no—
43C2×C11×#41—22no—
44C2×C11×#41C2×C412yes—
45C2×C11×#41C2×C412yes—
46C2×C11×#41D412yes—
47C2×C11×#41D412yes—
48C2×C11×#41C2312yes—
49C2×C11×#41C2312yes—
50C22×Q8×C11C2×C411yescharacteristic
51C22×Q8×C11C2×C411yescharacteristic
52C22×D4×C11—22no—
53C22×D4×C11—21no—
54C22×D4×C11C2×C411yescharacteristic
55C22×D4×C11C2×C411yescharacteristic
56C22×D4×C11D412yes—
57C23×C4×C11—21no—
58C23×C4×C11—21no—
59C23×C4×C11D412yes—
60C23×C4×C11C2311yescharacteristic
61C11×#131—216no—
62C11×#131—216no—
63C2×C11×M16—24no—
64C2×C11×M16—28no—
65C2×C11×M16—22no—
66C2×C11×M16—28no—
67C2×C11×M16—22no—
68C2×C11×M16—22no—
69C2×C11×M16D414yescomplemented
70C2×C11×M16D414yescomplemented
71C2×C11×M16C2314yes—
72C22×C8×C11—24no—
73C22×C8×C11—22no—
74C11×C4⋊Q8—22no—
75C11×C4⋊Q8C2×C414yescomplemented
76C11×#127—22no—
77C11×#127C2×C414yescomplemented
78C11×#124—22no—
79C11×#124—22no—
80C11×#124C2×C414yescomplemented
81C11×#124C2×C414yescomplemented
82C11×#121—28no—
83C11×#121—28no—
84C4×D4×C11—28no—
85C4×D4×C11—28no—
86C11×#117—22no—
87C11×#117—22no—
88C11×#117—22no—
89C11×#117C2314yes—
90C2×C11×C4⋊C4—22no—
91C2×C11×C4⋊C4—22no—
92C2×C11×C22⋊C4—22no—
93C2×C11×C22⋊C4—22no—
94C2×C11×C22⋊C4—22no—
95C2×C42×C11—21no—
96C2×C42×C11—21no—
97C2×C42×C11—21no—
98C2×C42×C11—22no—
99C2×C42×C11C2×C411yescharacteristic
100C2×C42×C11C2×C411yescharacteristic
101C2×C42×C11C2×C412yes—
102C2×C42×C11C2312yes—
103C11×#104—216no—
104C11×#99—28no—
105C2×#1884C1111yesmaximal, characteristic, direct product factor, Sylow
106C24×C11—21no—
107C24×C11C22⋊C412yes—
108C24×C11C2×D411yescharacteristic
109C11×#41—24no—
110C11×#41—24no—
111C11×#41—24no—
112C11×#41—24no—
113C11×#41—24no—
114C11×#41—24no—
115C11×#41—24no—
116C11×#41—24no—
117C11×#41—24no—
118C11×#41—24no—
119C11×#41—24no—
120C11×#41—24no—
121C11×#41—42no—
122C11×#41—42no—
123C11×#41—42no—
124C11×#41—42no—
125C2×Q8×C11—21no—
126C2×Q8×C11—22no—
127C2×Q8×C11—22no—
128C2×Q8×C11—22no—
129C2×Q8×C11—22no—
130C2×Q8×C11C22⋊C412yes—
131C2×Q8×C11C22×C412yes—
132C2×Q8×C11C22×C412yes—
133C2×D4×C11—24no—
134C2×D4×C11—24no—
135C2×D4×C11—28no—
136C2×D4×C11—22no—
137C2×D4×C11—22no—
138C2×D4×C11—21no—
139C2×D4×C11—22no—
140C2×D4×C11—22no—
141C2×D4×C11—22no—
142C2×D4×C11—22no—
143C2×D4×C11—48no—
144C2×D4×C11—42no—
145C2×D4×C11—42no—
146C2×D4×C11C22⋊C414yes—
147C2×D4×C11C22⋊C412yes—
148C2×D4×C11C22×C412yes—
149C2×D4×C11C22×C412yes—
150C2×D4×C11C2×D414yes—
151C22×C4×C11—21no—
152C22×C4×C11—22no—
153C22×C4×C11—22no—
154C22×C4×C11—22no—
155C22×C4×C11—22no—
156C22×C4×C11—21no—
157C22×C4×C11—22no—
158C22×C4×C11—21no—
159C22×C4×C11—22no—
160C22×C4×C11—22no—
161C22×C4×C11—22no—
162C22×C4×C11—44no—
163C22×C4×C11—41no—
164C22×C4×C11—41no—
165C22×C4×C11—41no—
166C22×C4×C11—41no—
167C22×C4×C11—42no—
168C22×C4×C11C22⋊C412yes—
169C22×C4×C11C22⋊C414yes—
170C22×C4×C11C22×C411yescharacteristic
171C22×C4×C11C22×C411yescharacteristic
172C22×C4×C11C2×D414yes—
173C22×C4×C11C2×D411yescharacteristic
174C22×C4×C11C2×D411yescharacteristic
175C22×C4×C11C2×D411yescharacteristic
176C22×C4×C11C2×D412yes—
177C22×C4×C11C2×D412yes—
178C22×C4×C11#4112yes—
179C22×C4×C11#4112yes—
180C22×C4×C11C2411yescharacteristic
181C11×M16—216no—
182C11×M16—24no—
183C11×M16—24no—
184C11×M16—24no—
185C11×M16C2×D418yescomplemented
186C2×C8×C11—216no—
187C2×C8×C11—24no—
188C2×C8×C11—24no—
189C2×C8×C11—24no—
190C11×C4⋊C4—28no—
191C11×C4⋊C4—24no—
192C11×C4⋊C4—42no—
193C11×C22⋊C4—28no—
194C11×C22⋊C4—28no—
195C11×C22⋊C4—24no—
196C11×C22⋊C4—42no—
197C42×C11—22no—
198C42×C11—21no—
199C42×C11—21no—
200C42×C11—22no—
201C42×C11—24no—
202C42×C11—42no—
203C42×C11C22×C412yes—
204C42×C11C22×C412yes—
205C2×#568C2×C1111yescharacteristic, complemented
206C2×#532C2×C1111yescharacteristic
207C2×#421C2×C1112yescomplemented
208C2×#410C2×C1111yescharacteristic, complemented
209#1884C2×C1118yesdirect product factor
210C2×#339C2×C1112yescomplemented
211C23×C11—22no—
212C23×C11—22no—
213C23×C11—22no—
214C23×C11—42no—
215C23×C11—44no—
216C23×C11—44no—
217C23×C11—41no—
218C23×C11—41no—
219C23×C11C2×C22⋊C411yescharacteristic
220C23×C11C2×C22⋊C414yes—
221C23×C11C2×C22⋊C411yescharacteristic
222C23×C11#12112yes—
223C23×C11#12112yes—
224C23×C11C22×D411yescharacteristic
225Q8×C11—24no—
226Q8×C11—24no—
227Q8×C11—24no—
228Q8×C11—42no—
229D4×C11—28no—
230D4×C11—28no—
231D4×C11—24no—
232D4×C11—24no—
233D4×C11—24no—
234D4×C11—416no—
235D4×C11—44no—
236D4×C11—44no—
237D4×C11—42no—
238C2×C4×C11—24no—
239C2×C4×C11—22no—
240C2×C4×C11—22no—
241C2×C4×C11—22no—
242C2×C4×C11—24no—
243C2×C4×C11—24no—
244C2×C4×C11—24no—
245C2×C4×C11—24no—
246C2×C4×C11—22no—
247C2×C4×C11—22no—
248C2×C4×C11—44no—
249C2×C4×C11—44no—
250C2×C4×C11—42no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—42no—
254C2×C4×C11—42no—
255C2×C4×C11—42no—
256C2×C4×C11—42no—
257C2×C4×C11—44no—
258C2×C4×C11—84no—
259C2×C4×C11C2×C22⋊C414yes—
260C2×C4×C11C2×C22⋊C411yescharacteristic
261C2×C4×C11C2×C22⋊C411yescharacteristic
262C2×C4×C11C4×D412yes—
263C2×C4×C11C4×D412yes—
264C2×C4×C11C4×D412yes—
265C2×C4×C11C4×D412yes—
266C2×C4×C11#12012yes—
267C2×C4×C11#12011yescharacteristic
268C2×C4×C11#12011yescharacteristic
269C2×C4×C11#12112yes—
270C2×C4×C11#12112yes—
271C2×C4×C11#12311yescharacteristic
272C2×C4×C11#12311yescharacteristic
273C2×C4×C11#12312yes—
274C2×C4×C11C23×C411yescharacteristic
275C2×C4×C11C22×D412yes—
276C2×C4×C11C22×D411yescharacteristic
277C2×C4×C11C2×#4112yes—
278C8×C11—28no—
279C22×#41C22×C1111yescharacteristic
280C22×#41C22×C1111yescharacteristic
281#568—22no—
282#568—24no—
283#568C22×C1114yescomplemented
284C2×#131—24no—
285C22×M16—22no—
286C22×M16C22×C1112yes—
287#532—22no—
288#532—22no—
289#532C4×C1114yescomplemented
290#532C22×C1114yes—
291C2×C4⋊Q8C4×C1111yescharacteristic, complemented
292C2×#127C4×C1111yescharacteristic, complemented
293C2×#124C4×C1111yescharacteristic, complemented
294C2×#124C4×C1111yescharacteristic, complemented
295C2×#121—22no—
296C2×C4×D4—22no—
297C2×#117C22×C1112yes—
298C22×C42C22×C1111yescharacteristic
299#421—24no—
300#421C22×C1118yescomplemented
301C2×#104—24no—
302#410—22no—
303#410C22×C1114yescomplemented
304C2×#99—22no—
305#339C22×C1118yescomplemented
306C22×C11—22no—
307C22×C11—24no—
308C22×C11—24no—
309C22×C11—41no—
310C22×C11—41no—
311C22×C11—42no—
312C22×C11—44no—
313C22×C11—44no—
314C22×C11—44no—
315C22×C11—42no—
316C22×C11—82no—
317C22×C11—82no—
318C22×C11—82no—
319C22×C11#38611yescharacteristic
320C22×C11#38612yes—
321C22×C11#38611yescharacteristic
322C22×C11C22×C22⋊C411yescharacteristic
323C22×C11C2×#12112yes—
324C4×C11—24no—
325C4×C11—24no—
326C4×C11—42no—
327C4×C11—42no—
328C4×C11—84no—
329C4×C11#38611yescharacteristic
330C4×C11#38611yescharacteristic
331C4×C11#38612yes—
332C4×C11C2×C4×D412yes—
333C4×C11C2×#12011yescharacteristic
334C4×C11C2×#12311yescharacteristic
335C2×#41—22no—
336C2×#41—22no—
337C2×#41—21no—
338C2×#41—21no—
339C2×#41—22no—
340C2×#41—22no—
341C2×#41—22no—
342C2×#41—22no—
343C2×#41—22no—
344C2×#41—22no—
345C2×#41C2×C4×C1112yes—
346C2×#41C2×C4×C1112yes—
347C2×#41D4×C1112yes—
348C2×#41D4×C1112yes—
349C2×#41C23×C1112yes—
350C2×#41C23×C1112yes—
351C22×Q8C2×C4×C1111yescharacteristic
352C22×Q8C2×C4×C1111yescharacteristic
353C22×D4—22no—
354C22×D4—21no—
355C22×D4C2×C4×C1111yescharacteristic
356C22×D4C2×C4×C1111yescharacteristic
357C22×D4D4×C1112yes—
358C23×C4—21no—
359C23×C4—21no—
360C23×C4D4×C1112yes—
361C23×C4C23×C1111yescharacteristic
362#131—216no—
363#131—216no—
364C2×M16—24no—
365C2×M16—28no—
366C2×M16—22no—
367C2×M16—28no—
368C2×M16—22no—
369C2×M16—22no—
370C2×M16D4×C1114yescomplemented
371C2×M16D4×C1114yescomplemented
372C2×M16C23×C1114yes—
373C22×C8—24no—
374C22×C8—22no—
375C4⋊Q8—22no—
376C4⋊Q8C2×C4×C1114yescomplemented
377#127—22no—
378#127C2×C4×C1114yescomplemented
379#124—22no—
380#124—22no—
381#124C2×C4×C1114yescomplemented
382#124C2×C4×C1114yescomplemented
383#121—28no—
384#121—28no—
385C4×D4—28no—
386C4×D4—28no—
387#117—22no—
388#117—22no—
389#117—22no—
390#117C23×C1114yes—
391C2×C4⋊C4—22no—
392C2×C4⋊C4—22no—
393C2×C22⋊C4—22no—
394C2×C22⋊C4—22no—
395C2×C22⋊C4—22no—
396C2×C42—21no—
397C2×C42—21no—
398C2×C42—21no—
399C2×C42—22no—
400C2×C42C2×C4×C1111yescharacteristic
401C2×C42C2×C4×C1111yescharacteristic
402C2×C42C2×C4×C1112yes—
403C2×C42C23×C1112yes—
404#104—216no—
405#99—28no—
406C2×C11—21no—
407C2×C11—22no—
408C2×C11—21no—
409C2×C11—22no—
410C2×C11—44no—
411C2×C11—82no—
412C2×C11#188412yesdirect product factor
413C2×C11C2×#38611yescharacteristic
414C24—21no—
415C24C11×C22⋊C412yes—
416C24C2×D4×C1111yescharacteristic
417#41—24no—
418#41—24no—
419#41—24no—
420#41—24no—
421#41—24no—
422#41—24no—
423#41—24no—
424#41—24no—
425#41—24no—
426#41—24no—
427#41—24no—
428#41—24no—
429#41—42no—
430#41—42no—
431#41—42no—
432#41—42no—
433C2×Q8—21no—
434C2×Q8—22no—
435C2×Q8—22no—
436C2×Q8—22no—
437C2×Q8—22no—
438C2×Q8C11×C22⋊C412yes—
439C2×Q8C22×C4×C1112yes—
440C2×Q8C22×C4×C1112yes—
441C2×D4—24no—
442C2×D4—24no—
443C2×D4—28no—
444C2×D4—22no—
445C2×D4—22no—
446C2×D4—21no—
447C2×D4—22no—
448C2×D4—22no—
449C2×D4—22no—
450C2×D4—22no—
451C2×D4—48no—
452C2×D4—42no—
453C2×D4—42no—
454C2×D4C11×C22⋊C414yes—
455C2×D4C11×C22⋊C412yes—
456C2×D4C22×C4×C1112yes—
457C2×D4C22×C4×C1112yes—
458C2×D4C2×D4×C1114yes—
459C22×C4—21no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—21no—
465C22×C4—22no—
466C22×C4—21no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—44no—
471C22×C4—41no—
472C22×C4—41no—
473C22×C4—41no—
474C22×C4—41no—
475C22×C4—42no—
476C22×C4C11×C22⋊C412yes—
477C22×C4C11×C22⋊C414yes—
478C22×C4C22×C4×C1111yescharacteristic
479C22×C4C22×C4×C1111yescharacteristic
480C22×C4C2×D4×C1114yes—
481C22×C4C2×D4×C1111yescharacteristic
482C22×C4C2×D4×C1111yescharacteristic
483C22×C4C2×D4×C1111yescharacteristic
484C22×C4C2×D4×C1112yes—
485C22×C4C2×D4×C1112yes—
486C22×C4C11×#4112yes—
487C22×C4C11×#4112yes—
488C22×C4C24×C1111yescharacteristic
489M16—216no—
490M16—24no—
491M16—24no—
492M16—24no—
493M16C2×D4×C1118yescomplemented
494C2×C8—216no—
495C2×C8—24no—
496C2×C8—24no—
497C2×C8—24no—
498C4⋊C4—28no—
499C4⋊C4—24no—
500C4⋊C4—42no—
501C22⋊C4—28no—
502C22⋊C4—28no—
503C22⋊C4—24no—
504C22⋊C4—42no—
505C42—22no—
506C42—21no—
507C42—21no—
508C42—22no—
509C42—24no—
510C42—42no—
511C42C22×C4×C1112yes—
512C42C22×C4×C1112yes—
513C11C2×#188411yescharacteristic, direct product factor, Sylow
514C23—22no—
515C23—22no—
516C23—22no—
517C23—42no—
518C23—44no—
519C23—44no—
520C23—41no—
521C23—41no—
522C23C2×C11×C22⋊C411yescharacteristic
523C23C2×C11×C22⋊C414yes—
524C23C2×C11×C22⋊C411yescharacteristic
525C23C11×#12112yes—
526C23C11×#12112yes—
527C23C22×D4×C1111yescharacteristic
528Q8—24no—
529Q8—24no—
530Q8—24no—
531Q8—42no—
532D4—28no—
533D4—28no—
534D4—24no—
535D4—24no—
536D4—24no—
537D4—416no—
538D4—44no—
539D4—44no—
540D4—42no—
541C2×C4—24no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—24no—
546C2×C4—24no—
547C2×C4—24no—
548C2×C4—24no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—44no—
552C2×C4—44no—
553C2×C4—42no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—42no—
560C2×C4—44no—
561C2×C4—84no—
562C2×C4C2×C11×C22⋊C414yes—
563C2×C4C2×C11×C22⋊C411yescharacteristic
564C2×C4C2×C11×C22⋊C411yescharacteristic
565C2×C4C4×D4×C1112yes—
566C2×C4C4×D4×C1112yes—
567C2×C4C4×D4×C1112yes—
568C2×C4C4×D4×C1112yes—
569C2×C4C11×#12012yes—
570C2×C4C11×#12011yescharacteristic
571C2×C4C11×#12011yescharacteristic
572C2×C4C11×#12112yes—
573C2×C4C11×#12112yes—
574C2×C4C11×#12311yescharacteristic
575C2×C4C11×#12311yescharacteristic
576C2×C4C11×#12312yes—
577C2×C4C23×C4×C1111yescharacteristic
578C2×C4C22×D4×C1112yes—
579C2×C4C22×D4×C1111yescharacteristic
580C2×C4C2×C11×#4112yes—
581C8—28no—
582C22—22no—
583C22—24no—
584C22—24no—
585C22—41no—
586C22—41no—
587C22—42no—
588C22—44no—
589C22—44no—
590C22—44no—
591C22—42no—
592C22—82no—
593C22—82no—
594C22—82no—
595C22C11×#38611yescharacteristic
596C22C11×#38612yes—
597C22C11×#38611yescharacteristic
598C22C22×C11×C22⋊C411yescharacteristic
599C22C2×C11×#12112yes—
600C4—24no—
601C4—24no—
602C4—42no—
603C4—42no—
604C4—84no—
605C4C11×#38611yescharacteristic
606C4C11×#38611yescharacteristic
607C4C11×#38612yes—
608C4C2×C4×D4×C1112yes—
609C4C2×C11×#12011yescharacteristic
610C4C2×C11×#12311yescharacteristic
611C2—21no—
612C2—22no—
613C2—21no—
614C2—22no—
615C2—44no—
616C2—82no—
617C2C11×#188412yesdirect product factor
618C2C2×C11×#38611yescharacteristic
subgroupG/H
centerC2×C4×C11#120
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
socleC22×C11#386
prime radicalC2×C11×#532C2
LCSG ▷ C2×C4 ▷ 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×#421C2semidirect
4. C2×C11×#410C2semidirect
5. C11×#1884C2direct (N × H)
6. C2×C11×#339C2semidirect
11. C11×#568C22semidirect
17. C11×#532C4semidirect
19. C2×C11×C4⋊Q8C4semidirect
20. C2×C11×#127C4semidirect
21. C2×C11×#124C4semidirect
22. C2×C11×#124C4semidirect
28. C11×#421C22semidirect
31. C11×#410C22semidirect
33. C11×#339C22semidirect
69. C2×C11×M16D4semidirect
70. C2×C11×M16D4semidirect
75. C11×C4⋊Q8C2×C4semidirect
77. C11×#127C2×C4semidirect
80. C11×#124C2×C4semidirect
81. C11×#124C2×C4semidirect
105. C2×#1884C11direct (N × H)
185. C11×M16C2×D4semidirect
205. C2×#568C2×C11semidirect
207. C2×#421C2×C11semidirect
208. C2×#410C2×C11semidirect
209. #1884C2×C11direct (N × H)
210. C2×#339C2×C11semidirect
283. #568C22×C11semidirect
289. #532C4×C11semidirect
291. C2×C4⋊Q8C4×C11semidirect
292. C2×#127C4×C11semidirect
293. C2×#124C4×C11semidirect
294. C2×#124C4×C11semidirect
300. #421C22×C11semidirect
303. #410C22×C11semidirect
305. #339C22×C11semidirect
370. C2×M16D4×C11semidirect
371. C2×M16D4×C11semidirect
376. C4⋊Q8C2×C4×C11semidirect
378. #127C2×C4×C11semidirect
381. #124C2×C4×C11semidirect
382. #124C2×C4×C11semidirect
412. C2×C11#1884direct (N × H)
493. M16C2×D4×C11semidirect
513. C11C2×#1884direct (N × H)
617. C2C11×#1884direct (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×#5322
C2×C11×#4212
C2×C11×#4102
C11×#18842
C2×C11×#3392
C2×#188411