Finite Group Databasebeta

← C2×C11×#2044 #14600706

Subgroups — C2×C11×#2044 #14600706

Order 2816.

2046 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#534C211yesmaximal, characteristic
2C22×C11×#99C212yesmaximal, complemented
3C2×C11×#386C212yesmaximal, complemented
4C2×C11×#385C211yesmaximal, characteristic, complemented
5C11×#2044C218yesmaximal, direct product factor
6C2×C11×#342C211yesmaximal, characteristic, complemented
7C23×D4×C11C2212yes—
8C24×C4×C11C2211yescharacteristic
9C11×#534—24no—
10C11×#534—22no—
11C11×#534C2214yes—
12C2×C11×#123—22no—
13C2×C11×#121—21no—
14C2×C11×#121—21no—
15C2×C11×#120—22no—
16C22×C11×C4⋊C4—21no—
17C22×C11×C22⋊C4—22no—
18C22×C11×C22⋊C4C2212yes—
19C22×C11×C22⋊C4C2211yescharacteristic
20C22×C11×C22⋊C4C2211yescharacteristic
21C2×C11×#99—28no—
22C2×C11×#99C2218yescomplemented
23C11×#386—24no—
24C11×#386C2218yescomplemented
25C11×#385—22no—
26C11×#385C2214yescomplemented
27C2×C11×#95—21no—
28C2×C11×#95—22no—
29C11×#342C2214yescomplemented
30C25×C11D412yes—
31C25×C11C2311yescharacteristic
32C22×D4×C11—22no—
33C22×D4×C11—22no—
34C22×D4×C11—22no—
35C22×D4×C11—22no—
36C22×D4×C11—24no—
37C22×D4×C11—24no—
38C22×D4×C11—24no—
39C22×D4×C11—24no—
40C22×D4×C11—21no—
41C22×D4×C11—21no—
42C22×D4×C11D414yes—
43C22×D4×C11C2314yes—
44C23×C4×C11—22no—
45C23×C4×C11—21no—
46C23×C4×C11—21no—
47C23×C4×C11—22no—
48C23×C4×C11—21no—
49C23×C4×C11—22no—
50C23×C4×C11—44no—
51C23×C4×C11D412yes—
52C23×C4×C11D411yescharacteristic
53C23×C4×C11D411yescharacteristic
54C23×C4×C11C2312yes—
55C11×#123—28no—
56C11×#123—28no—
57C11×#121—24no—
58C11×#121—24no—
59C11×#121—24no—
60C11×#121—24no—
61C11×#120—28no—
62C11×#120—28no—
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4—24no—
66C2×C11×C4⋊C4—44no—
67C2×C11×C22⋊C4—22no—
68C2×C11×C22⋊C4—22no—
69C2×C11×C22⋊C4—22no—
70C2×C11×C22⋊C4—21no—
71C2×C11×C22⋊C4—22no—
72C2×C11×C22⋊C4—22no—
73C2×C11×C22⋊C4—24no—
74C2×C11×C22⋊C4—24no—
75C2×C11×C22⋊C4—28no—
76C2×C11×C22⋊C4—22no—
77C2×C11×C22⋊C4—48no—
78C2×C11×C22⋊C4D412yes—
79C2×C11×C22⋊C4D414yescomplemented
80C2×C11×C22⋊C4C2314yes—
81C2×C11×C22⋊C4C2312yes—
82C2×C11×C22⋊C4C2312yes—
83C11×#99—216no—
84C11×#95—24no—
85C11×#95—28no—
86C2×#2044C1111yesmaximal, characteristic, direct product factor, Sylow
87C24×C11—22no—
88C24×C11—24no—
89C24×C11—22no—
90C24×C11—24no—
91C24×C11—42no—
92C24×C11—42no—
93C24×C11—44no—
94C24×C11—44no—
95C24×C11C2×D412yes—
96C24×C11C2×D411yescharacteristic
97C24×C11C2×D414yes—
98C24×C11C2×D412yes—
99C24×C11C2×D411yescharacteristic
100C24×C11C2×D412yes—
101C24×C11#4112yes—
102C24×C11#4114yes—
103C24×C11C2411yescharacteristic
104C2×D4×C11—24no—
105C2×D4×C11—24no—
106C2×D4×C11—28no—
107C2×D4×C11—28no—
108C2×D4×C11—24no—
109C2×D4×C11—24no—
110C2×D4×C11—24no—
111C2×D4×C11—24no—
112C2×D4×C11—24no—
113C2×D4×C11—24no—
114C2×D4×C11—24no—
115C2×D4×C11—24no—
116C2×D4×C11—44no—
117C2×D4×C11—44no—
118C2×D4×C11—44no—
119C2×D4×C11—44no—
120C2×D4×C11—44no—
121C2×D4×C11—44no—
122C2×D4×C11—44no—
123C2×D4×C11—44no—
124C2×D4×C11—82no—
125C2×D4×C11—82no—
126C22×C4×C11—28no—
127C22×C4×C11—24no—
128C22×C4×C11—22no—
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11—22no—
132C22×C4×C11—24no—
133C22×C4×C11—24no—
134C22×C4×C11—24no—
135C22×C4×C11—24no—
136C22×C4×C11—22no—
137C22×C4×C11—22no—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—24no—
141C22×C4×C11—44no—
142C22×C4×C11—48no—
143C22×C4×C11—44no—
144C22×C4×C11—42no—
145C22×C4×C11—42no—
146C22×C4×C11—42no—
147C22×C4×C11—44no—
148C22×C4×C11—42no—
149C22×C4×C11—41no—
150C22×C4×C11—41no—
151C22×C4×C11—42no—
152C22×C4×C11—42no—
153C22×C4×C11—44no—
154C22×C4×C11—44no—
155C22×C4×C11—44no—
156C22×C4×C11C2×D414yes—
157C22×C4×C11C2×D412yes—
158C22×C4×C11C2×D412yes—
159C11×C4⋊C4—24no—
160C11×C4⋊C4—24no—
161C11×C4⋊C4—48no—
162C11×C22⋊C4—28no—
163C11×C22⋊C4—28no—
164C11×C22⋊C4—24no—
165C11×C22⋊C4—24no—
166C11×C22⋊C4—24no—
167C11×C22⋊C4—22no—
168C11×C22⋊C4—24no—
169C11×C22⋊C4—24no—
170C11×C22⋊C4—416no—
171C11×C22⋊C4—44no—
172C11×C22⋊C4C2×D414yescomplemented
173C2×#534C2×C1111yescharacteristic
174C22×#99C2×C1112yescomplemented
175C2×#386C2×C1112yescomplemented
176C2×#385C2×C1111yescharacteristic, complemented
177#2044C2×C1118yesdirect product factor
178C2×#342C2×C1111yescharacteristic, complemented
179C23×C11—22no—
180C23×C11—24no—
181C23×C11—22no—
182C23×C11—24no—
183C23×C11—24no—
184C23×C11—24no—
185C23×C11—24no—
186C23×C11—41no—
187C23×C11—42no—
188C23×C11—41no—
189C23×C11—41no—
190C23×C11—42no—
191C23×C11—44no—
192C23×C11—44no—
193C23×C11—48no—
194C23×C11—41no—
195C23×C11—44no—
196C23×C11—44no—
197C23×C11—416no—
198C23×C11—44no—
199C23×C11—44no—
200C23×C11—44no—
201C23×C11—44no—
202C23×C11—82no—
203C23×C11—82no—
204C23×C11—88no—
205C23×C11#12012yes—
206C23×C11#12011yescharacteristic
207C23×C11#12011yescharacteristic
208C23×C11#12112yes—
209C23×C11#12114yes—
210C23×C11#12112yes—
211C23×C11#12114yes—
212C23×C11#12314yes—
213C23×C11#12314yes—
214C23×C11#12412yes—
215C23×C11#12412yes—
216C23×C11C22×D412yes—
217C23×C11C22×D411yescharacteristic
218C23×C11C22×D411yescharacteristic
219C23×C11C2×#4111yescharacteristic
220C23×C11C2×#4112yes—
221D4×C11—44no—
222D4×C11—44no—
223D4×C11—44no—
224D4×C11—44no—
225D4×C11—48no—
226D4×C11—48no—
227D4×C11—84no—
228D4×C11—84no—
229C2×C4×C11—28no—
230C2×C4×C11—24no—
231C2×C4×C11—22no—
232C2×C4×C11—22no—
233C2×C4×C11—24no—
234C2×C4×C11—24no—
235C2×C4×C11—24no—
236C2×C4×C11—24no—
237C2×C4×C11—42no—
238C2×C4×C11—42no—
239C2×C4×C11—48no—
240C2×C4×C11—42no—
241C2×C4×C11—44no—
242C2×C4×C11—44no—
243C2×C4×C11—48no—
244C2×C4×C11—42no—
245C2×C4×C11—44no—
246C2×C4×C11—44no—
247C2×C4×C11—44no—
248C2×C4×C11—42no—
249C2×C4×C11—42no—
250C2×C4×C11—42no—
251C2×C4×C11—42no—
252C2×C4×C11—44no—
253C2×C4×C11—44no—
254C2×C4×C11—44no—
255C2×C4×C11—81no—
256C2×C4×C11—81no—
257C2×C4×C11—88no—
258C23×D4C22×C1112yes—
259C24×C4C22×C1111yescharacteristic
260#534—24no—
261#534—22no—
262#534C22×C1114yes—
263C2×#123—22no—
264C2×#121—21no—
265C2×#121—21no—
266C2×#120—22no—
267C22×C4⋊C4—21no—
268C22×C22⋊C4—22no—
269C22×C22⋊C4C22×C1112yes—
270C22×C22⋊C4C22×C1111yescharacteristic
271C22×C22⋊C4C22×C1111yescharacteristic
272C2×#99—28no—
273C2×#99C22×C1118yescomplemented
274#386—24no—
275#386C22×C1118yescomplemented
276#385—22no—
277#385C22×C1114yescomplemented
278C2×#95—21no—
279C2×#95—22no—
280#342C22×C1114yescomplemented
281C22×C11—21no—
282C22×C11—22no—
283C22×C11—21no—
284C22×C11—22no—
285C22×C11—21no—
286C22×C11—22no—
287C22×C11—21no—
288C22×C11—22no—
289C22×C11—24no—
290C22×C11—28no—
291C22×C11—28no—
292C22×C11—24no—
293C22×C11—42no—
294C22×C11—44no—
295C22×C11—44no—
296C22×C11—42no—
297C22×C11—41no—
298C22×C11—41no—
299C22×C11—42no—
300C22×C11—48no—
301C22×C11—44no—
302C22×C11—44no—
303C22×C11—44no—
304C22×C11—84no—
305C22×C11—88no—
306C22×C11—88no—
307C22×C11#39414yes—
308C22×C11#39412yes—
309C22×C11#39412yes—
310C22×C11B(4,𝔽2)12yes—
311C22×C11#45812yes—
312C22×C11C2×#12011yescharacteristic
313C22×C11C2×#12111yescharacteristic
314C22×C11C2×#12112yes—
315C22×C11C2×#12312yes—
316C22×C11C2×#12411yescharacteristic
317C4×C11—44no—
318C4×C11—44no—
319C4×C11—44no—
320C4×C11—42no—
321C4×C11—42no—
322C4×C11—84no—
323C25D4×C1112yes—
324C25C23×C1111yescharacteristic
325C22×D4—22no—
326C22×D4—22no—
327C22×D4—22no—
328C22×D4—22no—
329C22×D4—24no—
330C22×D4—24no—
331C22×D4—24no—
332C22×D4—24no—
333C22×D4—21no—
334C22×D4—21no—
335C22×D4D4×C1114yes—
336C22×D4C23×C1114yes—
337C23×C4—22no—
338C23×C4—21no—
339C23×C4—21no—
340C23×C4—22no—
341C23×C4—21no—
342C23×C4—22no—
343C23×C4—44no—
344C23×C4D4×C1112yes—
345C23×C4D4×C1111yescharacteristic
346C23×C4D4×C1111yescharacteristic
347C23×C4C23×C1112yes—
348#123—28no—
349#123—28no—
350#121—24no—
351#121—24no—
352#121—24no—
353#121—24no—
354#120—28no—
355#120—28no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—24no—
359C2×C4⋊C4—44no—
360C2×C22⋊C4—22no—
361C2×C22⋊C4—22no—
362C2×C22⋊C4—22no—
363C2×C22⋊C4—22no—
364C2×C22⋊C4—21no—
365C2×C22⋊C4—22no—
366C2×C22⋊C4—24no—
367C2×C22⋊C4—24no—
368C2×C22⋊C4—28no—
369C2×C22⋊C4—22no—
370C2×C22⋊C4—48no—
371C2×C22⋊C4D4×C1112yes—
372C2×C22⋊C4D4×C1114yescomplemented
373C2×C22⋊C4C23×C1114yes—
374C2×C22⋊C4C23×C1112yes—
375C2×C22⋊C4C23×C1112yes—
376#99—216no—
377#95—24no—
378#95—28no—
379C2×C11—21no—
380C2×C11—22no—
381C2×C11—22no—
382C2×C11—24no—
383C2×C11—21no—
384C2×C11—22no—
385C2×C11—84no—
386C2×C11#204414yesdirect product factor
387C2×C11C2×#39411yescharacteristic
388C2×C11C2×B(4,𝔽2)11yescharacteristic
389C2×C11C2×#45811yescharacteristic
390C24—22no—
391C24—24no—
392C24—22no—
393C24—24no—
394C24—42no—
395C24—42no—
396C24—44no—
397C24—44no—
398C24C2×D4×C1112yes—
399C24C2×D4×C1111yescharacteristic
400C24C2×D4×C1114yes—
401C24C2×D4×C1112yes—
402C24C2×D4×C1111yescharacteristic
403C24C2×D4×C1112yes—
404C24C11×#4112yes—
405C24C11×#4114yes—
406C24C24×C1111yescharacteristic
407C2×D4—24no—
408C2×D4—24no—
409C2×D4—28no—
410C2×D4—28no—
411C2×D4—24no—
412C2×D4—24no—
413C2×D4—24no—
414C2×D4—24no—
415C2×D4—24no—
416C2×D4—24no—
417C2×D4—24no—
418C2×D4—24no—
419C2×D4—44no—
420C2×D4—44no—
421C2×D4—44no—
422C2×D4—44no—
423C2×D4—44no—
424C2×D4—44no—
425C2×D4—44no—
426C2×D4—44no—
427C2×D4—82no—
428C2×D4—82no—
429C22×C4—28no—
430C22×C4—24no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—24no—
436C22×C4—24no—
437C22×C4—24no—
438C22×C4—24no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—24no—
444C22×C4—44no—
445C22×C4—48no—
446C22×C4—44no—
447C22×C4—42no—
448C22×C4—42no—
449C22×C4—44no—
450C22×C4—42no—
451C22×C4—42no—
452C22×C4—41no—
453C22×C4—41no—
454C22×C4—42no—
455C22×C4—42no—
456C22×C4—44no—
457C22×C4—44no—
458C22×C4—44no—
459C22×C4C2×D4×C1114yes—
460C22×C4C2×D4×C1112yes—
461C22×C4C2×D4×C1112yes—
462C4⋊C4—24no—
463C4⋊C4—24no—
464C4⋊C4—48no—
465C22⋊C4—28no—
466C22⋊C4—28no—
467C22⋊C4—24no—
468C22⋊C4—24no—
469C22⋊C4—24no—
470C22⋊C4—22no—
471C22⋊C4—24no—
472C22⋊C4—24no—
473C22⋊C4—416no—
474C22⋊C4—44no—
475C22⋊C4C2×D4×C1114yescomplemented
476C11C2×#204411yescharacteristic, direct product factor, Sylow
477C23—22no—
478C23—24no—
479C23—22no—
480C23—24no—
481C23—24no—
482C23—24no—
483C23—24no—
484C23—41no—
485C23—42no—
486C23—41no—
487C23—41no—
488C23—42no—
489C23—44no—
490C23—44no—
491C23—48no—
492C23—41no—
493C23—44no—
494C23—44no—
495C23—416no—
496C23—44no—
497C23—44no—
498C23—44no—
499C23—44no—
500C23—82no—
501C23—82no—
502C23—88no—
503C23C11×#12012yes—
504C23C11×#12011yescharacteristic
505C23C11×#12011yescharacteristic
506C23C11×#12112yes—
507C23C11×#12114yes—
508C23C11×#12112yes—
509C23C11×#12114yes—
510C23C11×#12314yes—
511C23C11×#12314yes—
512C23C11×#12412yes—
513C23C11×#12412yes—
514C23C22×D4×C1112yes—
515C23C22×D4×C1111yescharacteristic
516C23C22×D4×C1111yescharacteristic
517C23C2×C11×#4111yescharacteristic
518C23C2×C11×#4112yes—
519D4—44no—
520D4—44no—
521D4—44no—
522D4—44no—
523D4—48no—
524D4—48no—
525D4—84no—
526D4—84no—
527C2×C4—28no—
528C2×C4—24no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—24no—
532C2×C4—24no—
533C2×C4—24no—
534C2×C4—24no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—48no—
538C2×C4—42no—
539C2×C4—44no—
540C2×C4—44no—
541C2×C4—48no—
542C2×C4—42no—
543C2×C4—44no—
544C2×C4—44no—
545C2×C4—44no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—44no—
551C2×C4—44no—
552C2×C4—44no—
553C2×C4—81no—
554C2×C4—81no—
555C2×C4—88no—
556C22—21no—
557C22—22no—
558C22—21no—
559C22—22no—
560C22—21no—
561C22—22no—
562C22—21no—
563C22—22no—
564C22—24no—
565C22—28no—
566C22—28no—
567C22—24no—
568C22—42no—
569C22—44no—
570C22—44no—
571C22—42no—
572C22—41no—
573C22—41no—
574C22—42no—
575C22—48no—
576C22—44no—
577C22—44no—
578C22—44no—
579C22—84no—
580C22—88no—
581C22—88no—
582C22C11×#39414yes—
583C22C11×#39412yes—
584C22C11×#39412yes—
585C22C11×B(4,𝔽2)12yes—
586C22C11×#45812yes—
587C22C2×C11×#12011yescharacteristic
588C22C2×C11×#12111yescharacteristic
589C22C2×C11×#12112yes—
590C22C2×C11×#12312yes—
591C22C2×C11×#12411yescharacteristic
592C4—44no—
593C4—44no—
594C4—44no—
595C4—42no—
596C4—42no—
597C4—84no—
598C2—21no—
599C2—22no—
600C2—22no—
601C2—24no—
602C2—21no—
603C2—22no—
604C2—84no—
605C2C11×#204414yesdirect product factor
606C2C2×C11×#39411yescharacteristic
607C2C2×C11×B(4,𝔽2)11yescharacteristic
608C2C2×C11×#45811yescharacteristic
subgroupG/H
center, socleC23×C11#120
commutator, Frattini, cosocleC24C24×C11
prime radicalC2×C11×#534C2
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C25×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×C11×#99C2semidirect
3. C2×C11×#386C2semidirect
4. C2×C11×#385C2semidirect
5. C11×#2044C2direct (N × H)
6. C2×C11×#342C2semidirect
22. C2×C11×#99C22semidirect
24. C11×#386C22semidirect
26. C11×#385C22semidirect
29. C11×#342C22semidirect
79. C2×C11×C22⋊C4D4semidirect
86. C2×#2044C11direct (N × H)
172. C11×C22⋊C4C2×D4semidirect
174. C22×#99C2×C11semidirect
175. C2×#386C2×C11semidirect
176. C2×#385C2×C11semidirect
177. #2044C2×C11direct (N × H)
178. C2×#342C2×C11semidirect
273. C2×#99C22×C11semidirect
275. #386C22×C11semidirect
277. #385C22×C11semidirect
280. #342C22×C11semidirect
372. C2×C22⋊C4D4×C11semidirect
386. C2×C11#2044direct (N × H)
475. C22⋊C4C2×D4×C11semidirect
476. C11C2×#2044direct (N × H)
605. C2C11×#2044direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5342
C22×C11×#992
C2×C11×#3862
C2×C11×#3852
C11×#20442
C2×C11×#3422
C2×#204411