Finite Group Databasebeta

← C2×C11×#2033 #14600668

Subgroups — C2×C11×#2033 #14600668

Order 2816.

2006 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×#121C211yesmaximal, characteristic
2C22×C11×#107C211yesmaximal, characteristic, complemented
3C22×C11×#102C211yesmaximal, characteristic, complemented
4C22×C11×#102C211yesmaximal, characteristic, complemented
5C22×C11×C22⋊C8C211yesmaximal, characteristic, complemented
6C2×C11×#380C211yesmaximal, characteristic, complemented
7C11×#2033C218yesmaximal, direct product factor
8C2×C11×#340C211yesmaximal, characteristic, complemented
9C23×D4×C11—21no—
10C23×D4×C11C2211yescharacteristic
11C24×C4×C11C2211yescharacteristic
12C23×C8×C11C2211yescharacteristic
13C23×C8×C11C2211yescharacteristic
14C2×C11×#121—24no—
15C2×C11×#121—22no—
16C2×C11×#121—24no—
17C2×C11×#121C2214yes—
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×C11×C4⋊C4C2211yescharacteristic
20C22×C11×C4⋊C4C2211yescharacteristic
21C22×C11×C22⋊C4—21no—
22C22×C11×C22⋊C4—21no—
23C2×C11×#107—24no—
24C2×C11×#107C2214yescomplemented
25C2×C11×#102—24no—
26C2×C11×#102—24no—
27C2×C11×#102C2214yescomplemented
28C2×C11×#102C2214yescomplemented
29C2×C11×C22⋊C8—24no—
30C2×C11×C22⋊C8C2214yescomplemented
31C11×#380—22no—
32C11×#380C2214yescomplemented
33C2×C11×#95—21no—
34C11×#340C2214yescomplemented
35C25×C11—21no—
36C25×C11D411yescharacteristic
37C22×D4×C11—28no—
38C22×D4×C11—24no—
39C22×D4×C11—22no—
40C22×D4×C11—21no—
41C22×D4×C11—22no—
42C22×D4×C11—22no—
43C22×D4×C11—22no—
44C22×D4×C11—22no—
45C22×D4×C11—44no—
46C22×D4×C11—44no—
47C22×D4×C11D414yes—
48C22×D4×C11C2312yes—
49C23×C4×C11—21no—
50C23×C4×C11—22no—
51C23×C4×C11—22no—
52C23×C4×C11—22no—
53C23×C4×C11—22no—
54C23×C4×C11—22no—
55C23×C4×C11—22no—
56C23×C4×C11—21no—
57C23×C4×C11—21no—
58C23×C4×C11D412yes—
59C23×C4×C11D411yescharacteristic
60C23×C4×C11C2312yes—
61C23×C4×C11C2311yescharacteristic
62C22×C8×C11—22no—
63C22×C8×C11—22no—
64C22×C8×C11—22no—
65C22×C8×C11—22no—
66C22×C8×C11—22no—
67C22×C8×C11D414yescomplemented
68C22×C8×C11C2312yes—
69C22×C8×C11C2312yes—
70C11×#121—216no—
71C11×#121—28no—
72C11×#121—28no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4—22no—
75C2×C11×C4⋊C4—22no—
76C2×C11×C4⋊C4—22no—
77C2×C11×C4⋊C4—22no—
78C2×C11×C4⋊C4—22no—
79C2×C11×C4⋊C4—21no—
80C2×C11×C4⋊C4—21no—
81C2×C11×C4⋊C4D414yes—
82C2×C11×C4⋊C4C2312yes—
83C2×C11×C4⋊C4C2312yes—
84C2×C11×C4⋊C4C2312yes—
85C2×C11×C22⋊C4—28no—
86C2×C11×C22⋊C4—24no—
87C2×C11×C22⋊C4—24no—
88C2×C11×C22⋊C4—44no—
89C11×#107—28no—
90C11×#102—28no—
91C11×#102—28no—
92C11×C22⋊C8—28no—
93C11×#95—24no—
94C2×#2033C1111yesmaximal, characteristic, direct product factor, Sylow
95C24×C11—22no—
96C24×C11—22no—
97C24×C11—22no—
98C24×C11—22no—
99C24×C11—22no—
100C24×C11—22no—
101C24×C11—24no—
102C24×C11—22no—
103C24×C11—42no—
104C24×C11—42no—
105C24×C11—42no—
106C24×C11—42no—
107C24×C11—42no—
108C24×C11—42no—
109C24×C11D814yes—
110C24×C11C2×D412yes—
111C24×C11C2×D411yescharacteristic
112C2×D4×C11—216no—
113C2×D4×C11—24no—
114C2×D4×C11—28no—
115C2×D4×C11—28no—
116C2×D4×C11—22no—
117C2×D4×C11—22no—
118C2×D4×C11—22no—
119C2×D4×C11—22no—
120C2×D4×C11—22no—
121C2×D4×C11—48no—
122C2×D4×C11—432no—
123C2×D4×C11—48no—
124C2×D4×C11—44no—
125C2×D4×C11—42no—
126C2×D4×C11—42no—
127C2×D4×C11—44no—
128C2×D4×C11C2×D414yes—
129C22×C4×C11—22no—
130C22×C4×C11—24no—
131C22×C4×C11—22no—
132C22×C4×C11—22no—
133C22×C4×C11—22no—
134C22×C4×C11—24no—
135C22×C4×C11—24no—
136C22×C4×C11—24no—
137C22×C4×C11—22no—
138C22×C4×C11—22no—
139C22×C4×C11—22no—
140C22×C4×C11—22no—
141C22×C4×C11—22no—
142C22×C4×C11—22no—
143C22×C4×C11—22no—
144C22×C4×C11—22no—
145C22×C4×C11—42no—
146C22×C4×C11—42no—
147C22×C4×C11—44no—
148C22×C4×C11—44no—
149C22×C4×C11—44no—
150C22×C4×C11—44no—
151C22×C4×C11—42no—
152C22×C4×C11—42no—
153C22×C4×C11—42no—
154C22×C4×C11—42no—
155C22×C4×C11—42no—
156C22×C4×C11—42no—
157C22×C4×C11C2×D412yes—
158C22×C4×C11C2×D411yescharacteristic
159C22×C4×C11C2×D412yes—
160C22×C4×C11C2×D412yes—
161C22×C4×C11C2×D412yes—
162C22×C4×C11#4112yes—
163C22×C4×C11#4112yes—
164C22×C4×C11#4112yes—
165C22×C4×C11C2411yescharacteristic
166C2×C8×C11—28no—
167C2×C8×C11—22no—
168C2×C8×C11—22no—
169C2×C8×C11—22no—
170C2×C8×C11—22no—
171C2×C8×C11—22no—
172C2×C8×C11—44no—
173C2×C8×C11C2×D414yescomplemented
174C11×C4⋊C4—24no—
175C11×C4⋊C4—22no—
176C11×C4⋊C4—22no—
177C11×C4⋊C4—22no—
178C11×C4⋊C4—22no—
179C11×C4⋊C4—22no—
180C11×C4⋊C4—42no—
181C11×C4⋊C4—42no—
182C11×C4⋊C4C2×D414yes—
183C11×C22⋊C4—216no—
184C11×C22⋊C4—48no—
185C22×#121C2×C1111yescharacteristic
186C22×#107C2×C1111yescharacteristic, complemented
187C22×#102C2×C1111yescharacteristic, complemented
188C22×#102C2×C1111yescharacteristic, complemented
189C22×C22⋊C8C2×C1111yescharacteristic, complemented
190C2×#380C2×C1111yescharacteristic, complemented
191#2033C2×C1118yesdirect product factor
192C2×#340C2×C1111yescharacteristic, complemented
193C23×C11—22no—
194C23×C11—22no—
195C23×C11—22no—
196C23×C11—22no—
197C23×C11—22no—
198C23×C11—22no—
199C23×C11—28no—
200C23×C11—28no—
201C23×C11—28no—
202C23×C11—24no—
203C23×C11—44no—
204C23×C11—44no—
205C23×C11—44no—
206C23×C11—44no—
207C23×C11—42no—
208C23×C11—42no—
209C23×C11—42no—
210C23×C11—42no—
211C23×C11—42no—
212C23×C11—42no—
213C23×C11—48no—
214C23×C11—48no—
215C23×C11—48no—
216C23×C11—84no—
217C23×C11—84no—
218C23×C11—84no—
219C23×C11—84no—
220C23×C11#12012yes—
221C23×C11#12112yes—
222C23×C11#12312yes—
223C23×C11C2×D814yes—
224C23×C11C2×D812yes—
225C23×C11#13512yes—
226C23×C11AGL(1,ℤ/8)12yes—
227C23×C11#13712yes—
228C23×C11C22×D411yescharacteristic
229D4×C11—24no—
230D4×C11—24no—
231D4×C11—432no—
232D4×C11—42no—
233D4×C11—42no—
234D4×C11—48no—
235C2×C4×C11—22no—
236C2×C4×C11—24no—
237C2×C4×C11—22no—
238C2×C4×C11—22no—
239C2×C4×C11—42no—
240C2×C4×C11—42no—
241C2×C4×C11—44no—
242C2×C4×C11—48no—
243C2×C4×C11—42no—
244C2×C4×C11—42no—
245C2×C4×C11—42no—
246C2×C4×C11—42no—
247C2×C4×C11—48no—
248C2×C4×C11—42no—
249C2×C4×C11—42no—
250C2×C4×C11—42no—
251C2×C4×C11—42no—
252C2×C4×C11—42no—
253C2×C4×C11—42no—
254C2×C4×C11—84no—
255C2×C4×C11—84no—
256C2×C4×C11#12012yes—
257C2×C4×C11#12114yes—
258C2×C4×C11#12114yes—
259C2×C4×C11#12112yes—
260C2×C4×C11#12314yes—
261C2×C4×C11#12312yes—
262C2×C4×C11#12414yes—
263C2×C4×C11C22×D411yescharacteristic
264C2×C4×C11C22×D411yescharacteristic
265C2×C4×C11C22×D411yescharacteristic
266C2×C4×C11C2×#4111yescharacteristic
267C2×C4×C11C2×#4111yescharacteristic
268C2×C4×C11C2×#4111yescharacteristic
269C8×C11—24no—
270C8×C11—42no—
271C23×D4—21no—
272C23×D4C22×C1111yescharacteristic
273C24×C4C22×C1111yescharacteristic
274C23×C8C22×C1111yescharacteristic
275C23×C8C22×C1111yescharacteristic
276C2×#121—24no—
277C2×#121—22no—
278C2×#121—24no—
279C2×#121C22×C1114yes—
280C22×C4⋊C4C22×C1111yescharacteristic
281C22×C4⋊C4C22×C1111yescharacteristic
282C22×C4⋊C4C22×C1111yescharacteristic
283C22×C22⋊C4—21no—
284C22×C22⋊C4—21no—
285C2×#107—24no—
286C2×#107C22×C1114yescomplemented
287C2×#102—24no—
288C2×#102—24no—
289C2×#102C22×C1114yescomplemented
290C2×#102C22×C1114yescomplemented
291C2×C22⋊C8—24no—
292C2×C22⋊C8C22×C1114yescomplemented
293#380—22no—
294#380C22×C1114yescomplemented
295C2×#95—21no—
296#340C22×C1114yescomplemented
297C22×C11—24no—
298C22×C11—24no—
299C22×C11—24no—
300C22×C11—42no—
301C22×C11—42no—
302C22×C11—42no—
303C22×C11—42no—
304C22×C11—416no—
305C22×C11—44no—
306C22×C11—44no—
307C22×C11—44no—
308C22×C11—82no—
309C22×C11—82no—
310C22×C11—82no—
311C22×C11—82no—
312C22×C11—816no—
313C22×C11#39414yes—
314C22×C11#44714yes—
315C22×C11#45214yes—
316C22×C11#46614yes—
317C22×C11#46814yes—
318C22×C11#48014yes—
319C22×C11#48214yes—
320C22×C11C2×#12011yescharacteristic
321C22×C11C2×#12111yescharacteristic
322C22×C11C2×#12311yescharacteristic
323C22×C11C22×D811yescharacteristic
324C22×C11C2×#13511yescharacteristic
325C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
326C22×C11C2×#13711yescharacteristic
327C4×C11—42no—
328C4×C11—44no—
329C4×C11—82no—
330C4×C11—82no—
331C4×C11#39414yes—
332C4×C11C2×#12111yescharacteristic
333C4×C11C2×#12111yescharacteristic
334C4×C11C2×#12311yescharacteristic
335C4×C11C2×#12411yescharacteristic
336C25—21no—
337C25D4×C1111yescharacteristic
338C22×D4—28no—
339C22×D4—24no—
340C22×D4—22no—
341C22×D4—21no—
342C22×D4—22no—
343C22×D4—22no—
344C22×D4—22no—
345C22×D4—22no—
346C22×D4—44no—
347C22×D4—44no—
348C22×D4D4×C1114yes—
349C22×D4C23×C1112yes—
350C23×C4—21no—
351C23×C4—22no—
352C23×C4—22no—
353C23×C4—22no—
354C23×C4—22no—
355C23×C4—22no—
356C23×C4—22no—
357C23×C4—21no—
358C23×C4—21no—
359C23×C4D4×C1111yescharacteristic
360C23×C4D4×C1112yes—
361C23×C4C23×C1112yes—
362C23×C4C23×C1111yescharacteristic
363C22×C8—22no—
364C22×C8—22no—
365C22×C8—22no—
366C22×C8—22no—
367C22×C8—22no—
368C22×C8D4×C1114yescomplemented
369C22×C8C23×C1112yes—
370C22×C8C23×C1112yes—
371#121—216no—
372#121—28no—
373#121—28no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4—22no—
377C2×C4⋊C4—22no—
378C2×C4⋊C4—22no—
379C2×C4⋊C4—22no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4D4×C1114yes—
383C2×C4⋊C4C23×C1112yes—
384C2×C4⋊C4C23×C1112yes—
385C2×C4⋊C4C23×C1112yes—
386C2×C22⋊C4—28no—
387C2×C22⋊C4—24no—
388C2×C22⋊C4—24no—
389C2×C22⋊C4—44no—
390#107—28no—
391#102—28no—
392#102—28no—
393C22⋊C8—28no—
394#95—24no—
395C2×C11—44no—
396C2×C11—84no—
397C2×C11#203318yesdirect product factor
398C2×C11C2×#39411yescharacteristic
399C2×C11C2×#44711yescharacteristic
400C2×C11C2×#45211yescharacteristic
401C2×C11C2×#46611yescharacteristic
402C2×C11C2×#46811yescharacteristic
403C2×C11C2×#48011yescharacteristic
404C2×C11C2×#48211yescharacteristic
405C24—22no—
406C24—22no—
407C24—22no—
408C24—22no—
409C24—22no—
410C24—22no—
411C24—24no—
412C24—22no—
413C24—42no—
414C24—42no—
415C24—42no—
416C24—42no—
417C24—42no—
418C24—42no—
419C24C11×D814yes—
420C24C2×D4×C1112yes—
421C24C2×D4×C1111yescharacteristic
422C2×D4—216no—
423C2×D4—24no—
424C2×D4—28no—
425C2×D4—28no—
426C2×D4—22no—
427C2×D4—22no—
428C2×D4—22no—
429C2×D4—22no—
430C2×D4—22no—
431C2×D4—48no—
432C2×D4—432no—
433C2×D4—48no—
434C2×D4—44no—
435C2×D4—42no—
436C2×D4—42no—
437C2×D4—44no—
438C2×D4C2×D4×C1114yes—
439C22×C4—22no—
440C22×C4—24no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—24no—
445C22×C4—24no—
446C22×C4—24no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—42no—
456C22×C4—42no—
457C22×C4—44no—
458C22×C4—44no—
459C22×C4—44no—
460C22×C4—44no—
461C22×C4—42no—
462C22×C4—42no—
463C22×C4—42no—
464C22×C4—42no—
465C22×C4—42no—
466C22×C4—42no—
467C22×C4C2×D4×C1112yes—
468C22×C4C2×D4×C1111yescharacteristic
469C22×C4C2×D4×C1112yes—
470C22×C4C2×D4×C1112yes—
471C22×C4C2×D4×C1112yes—
472C22×C4C11×#4112yes—
473C22×C4C11×#4112yes—
474C22×C4C11×#4112yes—
475C22×C4C24×C1111yescharacteristic
476C2×C8—28no—
477C2×C8—22no—
478C2×C8—22no—
479C2×C8—22no—
480C2×C8—22no—
481C2×C8—22no—
482C2×C8—44no—
483C2×C8C2×D4×C1114yescomplemented
484C4⋊C4—24no—
485C4⋊C4—22no—
486C4⋊C4—22no—
487C4⋊C4—22no—
488C4⋊C4—22no—
489C4⋊C4—22no—
490C4⋊C4—42no—
491C4⋊C4—42no—
492C4⋊C4C2×D4×C1114yes—
493C22⋊C4—216no—
494C22⋊C4—48no—
495C11C2×#203311yescharacteristic, direct product factor, Sylow
496C23—22no—
497C23—22no—
498C23—22no—
499C23—22no—
500C23—22no—
501C23—22no—
502C23—28no—
503C23—28no—
504C23—28no—
505C23—24no—
506C23—44no—
507C23—44no—
508C23—44no—
509C23—44no—
510C23—42no—
511C23—42no—
512C23—48no—
513C23—42no—
514C23—42no—
515C23—42no—
516C23—42no—
517C23—48no—
518C23—48no—
519C23—84no—
520C23—84no—
521C23—84no—
522C23—84no—
523C23C11×#12012yes—
524C23C11×#12112yes—
525C23C11×#12312yes—
526C23C2×C11×D814yes—
527C23C2×C11×D812yes—
528C23C11×#13512yes—
529C23C11×AGL(1,ℤ/8)12yes—
530C23C11×#13712yes—
531C23C22×D4×C1111yescharacteristic
532D4—24no—
533D4—24no—
534D4—432no—
535D4—42no—
536D4—42no—
537D4—48no—
538C2×C4—22no—
539C2×C4—24no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—44no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—48no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—48no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—84no—
558C2×C4—84no—
559C2×C4C11×#12012yes—
560C2×C4C11×#12114yes—
561C2×C4C11×#12114yes—
562C2×C4C11×#12112yes—
563C2×C4C11×#12314yes—
564C2×C4C11×#12312yes—
565C2×C4C11×#12414yes—
566C2×C4C22×D4×C1111yescharacteristic
567C2×C4C22×D4×C1111yescharacteristic
568C2×C4C22×D4×C1111yescharacteristic
569C2×C4C2×C11×#4111yescharacteristic
570C2×C4C2×C11×#4111yescharacteristic
571C2×C4C2×C11×#4111yescharacteristic
572C8—24no—
573C8—42no—
574C22—24no—
575C22—24no—
576C22—24no—
577C22—42no—
578C22—42no—
579C22—42no—
580C22—416no—
581C22—42no—
582C22—44no—
583C22—44no—
584C22—44no—
585C22—82no—
586C22—82no—
587C22—816no—
588C22—82no—
589C22—82no—
590C22C11×#39414yes—
591C22C11×#44714yes—
592C22C11×#45214yes—
593C22C11×#46614yes—
594C22C11×#46814yes—
595C22C11×#48014yes—
596C22C11×#48214yes—
597C22C2×C11×#12011yescharacteristic
598C22C2×C11×#12111yescharacteristic
599C22C2×C11×#12311yescharacteristic
600C22C22×C11×D811yescharacteristic
601C22C2×C11×#13511yescharacteristic
602C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
603C22C2×C11×#13711yescharacteristic
604C4—42no—
605C4—44no—
606C4—82no—
607C4—82no—
608C4C11×#39414yes—
609C4C2×C11×#12111yescharacteristic
610C4C2×C11×#12111yescharacteristic
611C4C2×C11×#12311yescharacteristic
612C4C2×C11×#12411yescharacteristic
613C2—44no—
614C2—84no—
615C2C11×#203318yesdirect product factor
616C2C2×C11×#39411yescharacteristic
617C2C2×C11×#44711yescharacteristic
618C2C2×C11×#45211yescharacteristic
619C2C2×C11×#46611yescharacteristic
620C2C2×C11×#46811yescharacteristic
621C2C2×C11×#48011yescharacteristic
622C2C2×C11×#48211yescharacteristic
subgroupG/H
center, socleC24×C11C2×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC22×C11×#121C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24×C11 ◁ C24×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×C11×#107C2semidirect
3. C22×C11×#102C2semidirect
4. C22×C11×#102C2semidirect
5. C22×C11×C22⋊C8C2semidirect
6. C2×C11×#380C2semidirect
7. C11×#2033C2direct (N × H)
8. C2×C11×#340C2semidirect
24. C2×C11×#107C22semidirect
27. C2×C11×#102C22semidirect
28. C2×C11×#102C22semidirect
30. C2×C11×C22⋊C8C22semidirect
32. C11×#380C22semidirect
34. C11×#340C22semidirect
67. C22×C8×C11D4semidirect
94. C2×#2033C11direct (N × H)
173. C2×C8×C11C2×D4semidirect
186. C22×#107C2×C11semidirect
187. C22×#102C2×C11semidirect
188. C22×#102C2×C11semidirect
189. C22×C22⋊C8C2×C11semidirect
190. C2×#380C2×C11semidirect
191. #2033C2×C11direct (N × H)
192. C2×#340C2×C11semidirect
286. C2×#107C22×C11semidirect
289. C2×#102C22×C11semidirect
290. C2×#102C22×C11semidirect
292. C2×C22⋊C8C22×C11semidirect
294. #380C22×C11semidirect
296. #340C22×C11semidirect
368. C22×C8D4×C11semidirect
397. C2×C11#2033direct (N × H)
483. C2×C8C2×D4×C11semidirect
495. C11C2×#2033direct (N × H)
615. C2C11×#2033direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C11×#1212
C22×C11×#1072
C22×C11×#1022
C22×C11×C22⋊C82
C2×C11×#3802
C11×#20332
C2×C11×#3402
C2×#203311