Finite Group Databasebeta

← C11×#23493 #14600686

Subgroups — C11×#23493 #14600686

Order 2816.

1586 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#535C211yesmaximal, characteristic
2C11×#2911C211yesmaximal, characteristic, complemented
3C2×C11×#421C211yesmaximal, characteristic, complemented
4C11×#2896C211yesmaximal, characteristic, complemented
5C22×C11×#100C211yesmaximal, characteristic, complemented
6C11×#2309C211yesmaximal, characteristic, complemented
7C11×#2037C218yesmaximal, complemented
8C11×#1733C211yesmaximal, characteristic, complemented
9C22×C11×#41C2211yescharacteristic
10C23×D4×C11C2211yescharacteristic
11C22×C11×M16C2211yescharacteristic
12C22×C11×M16C2211yescharacteristic
13C11×#535—22no—
14C11×#535—22no—
15C11×#535—22no—
16C11×#535C2214yes—
17C2×C11×#127—21no—
18C2×C11×#124—21no—
19C2×C11×#121—22no—
20C2×C11×#120—22no—
21C2×C11×#117C2211yescharacteristic
22C2×C11×#117C2211yescharacteristic
23C2×C11×#117C2211yescharacteristic
24C11×#428—22no—
25C11×#428C2214yescomplemented
26C11×#427—22no—
27C11×#421—24no—
28C2×C11×#104C2214yescomplemented
29C11×#419—21no—
30C11×#418—21no—
31C11×#417C2214yescomplemented
32C11×#416—22no—
33C2×C11×#100—24no—
34C2×C11×#100C2214yescomplemented
35C11×#390—22no—
36C11×#390C2214yescomplemented
37C11×#379—22no—
38C11×#339C2214yescomplemented
39C25×C11D412yes—
40C2×C11×#41—21no—
41C2×C11×#41—21no—
42C2×C11×#41—22no—
43C2×C11×#41—22no—
44C2×C11×#41—22no—
45C2×C11×#41—22no—
46C2×C11×#41D412yes—
47C2×C11×#41C2312yes—
48C22×Q8×C11D411yescharacteristic
49C22×D4×C11—21no—
50C22×D4×C11—24no—
51C22×D4×C11—21no—
52C22×D4×C11—21no—
53C22×D4×C11—21no—
54C22×D4×C11—21no—
55C22×D4×C11—22no—
56C22×D4×C11—22no—
57C22×D4×C11—22no—
58C22×D4×C11—22no—
59C22×D4×C11D412yes—
60C22×D4×C11D411yescharacteristic
61C22×D4×C11C2312yes—
62C23×C4×C11—21no—
63C23×C4×C11C2311yescharacteristic
64C2×C11×M16—21no—
65C2×C11×M16—22no—
66C2×C11×M16—21no—
67C2×C11×M16—22no—
68C2×C11×M16—22no—
69C2×C11×M16D414yescomplemented
70C2×C11×M16C2312yes—
71C2×C11×M16C2312yes—
72C22×C8×C11—21no—
73C22×C8×C11—21no—
74C11×#127—24no—
75C11×#127—24no—
76C11×#124—24no—
77C11×#124—24no—
78C11×#121—28no—
79C11×#121—28no—
80C11×#120—28no—
81C11×#120—28no—
82C11×#117—21no—
83C11×#117—21no—
84C11×#117—22no—
85C11×#117—22no—
86C11×#117—21no—
87C11×#117—21no—
88C11×#117—21no—
89C11×#117—21no—
90C11×#117D412yes—
91C11×#117C2312yes—
92C2×C11×C4⋊C4—21no—
93C2×C11×C4⋊C4D412yes—
94C2×C11×C4⋊C4C2312yes—
95C2×C11×C22⋊C4—24no—
96C2×C11×C22⋊C4—21no—
97C2×C11×C22⋊C4—21no—
98C2×C11×C22⋊C4—21no—
99C2×C11×C22⋊C4—28no—
100C2×C42×C11—21no—
101C2×C42×C11—21no—
102C2×C42×C11C2312yes—
103C11×#107—24no—
104C11×#106—24no—
105C11×#104—28no—
106C11×#103—24no—
107C11×#102—24no—
108C11×#100—28no—
109#23493C1111yesmaximal, characteristic, direct product factor, Sylow
110C24×C11—22no—
111C24×C11—21no—
112C24×C11—22no—
113C24×C11—24no—
114C24×C11—24no—
115C24×C11—84no—
116C24×C11C2×D414yes—
117C24×C11C2×D411yescharacteristic
118C11×#41—24no—
119C11×#41—24no—
120C11×#41—22no—
121C11×#41—22no—
122C11×#41—22no—
123C11×#41—22no—
124C11×#41—42no—
125C11×#41—42no—
126C11×#41—42no—
127C11×#41—42no—
128C2×Q8×C11—21no—
129C2×Q8×C11—22no—
130C2×Q8×C11—22no—
131C2×Q8×C11C2×D412yes—
132C2×D4×C11—22no—
133C2×D4×C11—22no—
134C2×D4×C11—216no—
135C2×D4×C11—22no—
136C2×D4×C11—22no—
137C2×D4×C11—21no—
138C2×D4×C11—22no—
139C2×D4×C11—24no—
140C2×D4×C11—22no—
141C2×D4×C11—24no—
142C2×D4×C11—22no—
143C2×D4×C11—22no—
144C2×D4×C11—22no—
145C2×D4×C11—22no—
146C2×D4×C11—22no—
147C2×D4×C11—22no—
148C2×D4×C11—42no—
149C2×D4×C11—42no—
150C2×D4×C11—42no—
151C2×D4×C11—42no—
152C2×D4×C11—42no—
153C2×D4×C11—42no—
154C2×D4×C11—42no—
155C2×D4×C11—42no—
156C2×D4×C11—42no—
157C2×D4×C11—42no—
158C2×D4×C11—88no—
159C2×D4×C11C2×D412yes—
160C22×C4×C11—22no—
161C22×C4×C11—21no—
162C22×C4×C11—22no—
163C22×C4×C11—22no—
164C22×C4×C11—22no—
165C22×C4×C11—22no—
166C22×C4×C11—42no—
167C22×C4×C11—42no—
168C22×C4×C11C2×D411yescharacteristic
169C22×C4×C11C2×D411yescharacteristic
170C22×C4×C11C2×D411yescharacteristic
171C22×C4×C11C2×D411yescharacteristic
172C22×C4×C11C2×D411yescharacteristic
173C22×C4×C11C2×D412yes—
174C22×C4×C11#4112yes—
175C22×C4×C11#4112yes—
176C22×C4×C11#4112yes—
177C22×C4×C11C2411yescharacteristic
178C11×M16—24no—
179C11×M16—22no—
180C11×M16—22no—
181C11×M16—22no—
182C11×M16—42no—
183C11×M16C2×D414yescomplemented
184C2×C8×C11—24no—
185C2×C8×C11—22no—
186C2×C8×C11—22no—
187C2×C8×C11—42no—
188C11×C4⋊C4—22no—
189C11×C4⋊C4—22no—
190C11×C4⋊C4—22no—
191C11×C4⋊C4—42no—
192C11×C4⋊C4C2×D414yes—
193C11×C22⋊C4—216no—
194C11×C22⋊C4—22no—
195C11×C22⋊C4—22no—
196C11×C22⋊C4—41no—
197C11×C22⋊C4—41no—
198C11×C22⋊C4—42no—
199C11×C22⋊C4—88no—
200C42×C11—22no—
201C42×C11—22no—
202C42×C11—22no—
203C42×C11—22no—
204C42×C11—41no—
205C42×C11—41no—
206C2×#535C2×C1111yescharacteristic
207#2911C2×C1111yescharacteristic, complemented
208C2×#421C2×C1111yescharacteristic, complemented
209#2896C2×C1111yescharacteristic, complemented
210C22×#100C2×C1111yescharacteristic, complemented
211#2309C2×C1111yescharacteristic, complemented
212#2037C2×C1118yescomplemented
213#1733C2×C1111yescharacteristic, complemented
214C23×C11—24no—
215C23×C11—22no—
216C23×C11—24no—
217C23×C11—24no—
218C23×C11—42no—
219C23×C11—48no—
220C23×C11—44no—
221C23×C11—48no—
222C23×C11—42no—
223C23×C11—44no—
224C23×C11—44no—
225C23×C11—84no—
226C23×C11—88no—
227C23×C11—88no—
228C23×C11#12011yescharacteristic
229C23×C11#12011yescharacteristic
230C23×C11#12112yes—
231C23×C11#12312yes—
232C23×C11C22×D411yescharacteristic
233Q8×C11—22no—
234Q8×C11—22no—
235Q8×C11—42no—
236D4×C11—22no—
237D4×C11—22no—
238D4×C11—42no—
239D4×C11—42no—
240D4×C11—44no—
241D4×C11—42no—
242D4×C11—42no—
243D4×C11—42no—
244D4×C11—42no—
245D4×C11—44no—
246D4×C11—44no—
247D4×C11—42no—
248D4×C11—816no—
249C2×C4×C11—24no—
250C2×C4×C11—22no—
251C2×C4×C11—44no—
252C2×C4×C11—42no—
253C2×C4×C11—42no—
254C2×C4×C11—42no—
255C2×C4×C11—44no—
256C2×C4×C11—44no—
257C2×C4×C11—44no—
258C2×C4×C11—42no—
259C2×C4×C11—42no—
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#12112yes—
267C2×C4×C11#12312yes—
268C2×C4×C11#12312yes—
269C2×C4×C11#12312yes—
270C2×C4×C11#12412yes—
271C2×C4×C11#12412yes—
272C2×C4×C11C22×D411yescharacteristic
273C2×C4×C11C22×D411yescharacteristic
274C2×C4×C11C22×D411yescharacteristic
275C2×C4×C11C2×#4111yescharacteristic
276C2×C4×C11C2×#4111yescharacteristic
277C2×C4×C11C2×#4111yescharacteristic
278C8×C11—24no—
279C8×C11—42no—
280C22×#41C22×C1111yescharacteristic
281C23×D4C22×C1111yescharacteristic
282C22×M16C22×C1111yescharacteristic
283C22×M16C22×C1111yescharacteristic
284#535—22no—
285#535—22no—
286#535—22no—
287#535C22×C1114yes—
288C2×#127—21no—
289C2×#124—21no—
290C2×#121—22no—
291C2×#120—22no—
292C2×#117C22×C1111yescharacteristic
293C2×#117C22×C1111yescharacteristic
294C2×#117C22×C1111yescharacteristic
295#428—22no—
296#428C22×C1114yescomplemented
297#427—22no—
298#421—24no—
299C2×#104C22×C1114yescomplemented
300#419—21no—
301#418—21no—
302#417C22×C1114yescomplemented
303#416—22no—
304C2×#100—24no—
305C2×#100C22×C1114yescomplemented
306#390—22no—
307#390C22×C1114yescomplemented
308#379—22no—
309#339C22×C1114yescomplemented
310C22×C11—22no—
311C22×C11—22no—
312C22×C11—22no—
313C22×C11—42no—
314C22×C11—42no—
315C22×C11—48no—
316C22×C11—42no—
317C22×C11—44no—
318C22×C11—44no—
319C22×C11—48no—
320C22×C11—84no—
321C22×C11—84no—
322C22×C11—88no—
323C22×C11—88no—
324C22×C11#39412yes—
325C22×C11#39412yes—
326C22×C11C2×#12011yescharacteristic
327C22×C11C2×#12111yescharacteristic
328C22×C11C2×#12311yescharacteristic
329C4×C11—42no—
330C4×C11—44no—
331C4×C11—82no—
332C4×C11—82no—
333C4×C11#39412yes—
334C4×C11#39412yes—
335C4×C11C2×#12111yescharacteristic
336C4×C11C2×#12111yescharacteristic
337C4×C11C2×#12311yescharacteristic
338C4×C11C2×#12411yescharacteristic
339C25D4×C1112yes—
340C2×#41—21no—
341C2×#41—21no—
342C2×#41—22no—
343C2×#41—22no—
344C2×#41—22no—
345C2×#41—22no—
346C2×#41D4×C1112yes—
347C2×#41C23×C1112yes—
348C22×Q8D4×C1111yescharacteristic
349C22×D4—21no—
350C22×D4—24no—
351C22×D4—21no—
352C22×D4—21no—
353C22×D4—21no—
354C22×D4—21no—
355C22×D4—22no—
356C22×D4—22no—
357C22×D4—22no—
358C22×D4—22no—
359C22×D4D4×C1112yes—
360C22×D4D4×C1111yescharacteristic
361C22×D4C23×C1112yes—
362C23×C4—21no—
363C23×C4C23×C1111yescharacteristic
364C2×M16—21no—
365C2×M16—22no—
366C2×M16—21no—
367C2×M16—22no—
368C2×M16—22no—
369C2×M16D4×C1114yescomplemented
370C2×M16C23×C1112yes—
371C2×M16C23×C1112yes—
372C22×C8—21no—
373C22×C8—21no—
374#127—24no—
375#127—24no—
376#124—24no—
377#124—24no—
378#121—28no—
379#121—28no—
380#120—28no—
381#120—28no—
382#117—21no—
383#117—21no—
384#117—22no—
385#117—22no—
386#117—21no—
387#117—21no—
388#117—21no—
389#117—21no—
390#117D4×C1112yes—
391#117C23×C1112yes—
392C2×C4⋊C4—21no—
393C2×C4⋊C4D4×C1112yes—
394C2×C4⋊C4C23×C1112yes—
395C2×C22⋊C4—24no—
396C2×C22⋊C4—21no—
397C2×C22⋊C4—21no—
398C2×C22⋊C4—21no—
399C2×C22⋊C4—28no—
400C2×C42—21no—
401C2×C42—21no—
402C2×C42C23×C1112yes—
403#107—24no—
404#106—24no—
405#104—28no—
406#103—24no—
407#102—24no—
408#100—28no—
409C2×C11—21no—
410C2×C11—21no—
411C2×C11—22no—
412C2×C11—22no—
413C2×C11—84no—
414C2×C11—82no—
415C2×C11C2×#39411yescharacteristic
416C2×C11#301912yes—
417C24—22no—
418C24—21no—
419C24—22no—
420C24—24no—
421C24—24no—
422C24—84no—
423C24C2×D4×C1114yes—
424C24C2×D4×C1111yescharacteristic
425#41—24no—
426#41—24no—
427#41—22no—
428#41—22no—
429#41—22no—
430#41—22no—
431#41—42no—
432#41—42no—
433#41—42no—
434#41—42no—
435C2×Q8—21no—
436C2×Q8—22no—
437C2×Q8—22no—
438C2×Q8C2×D4×C1112yes—
439C2×D4—22no—
440C2×D4—22no—
441C2×D4—216no—
442C2×D4—22no—
443C2×D4—22no—
444C2×D4—21no—
445C2×D4—22no—
446C2×D4—24no—
447C2×D4—22no—
448C2×D4—24no—
449C2×D4—22no—
450C2×D4—22no—
451C2×D4—22no—
452C2×D4—22no—
453C2×D4—22no—
454C2×D4—22no—
455C2×D4—42no—
456C2×D4—42no—
457C2×D4—42no—
458C2×D4—42no—
459C2×D4—42no—
460C2×D4—42no—
461C2×D4—42no—
462C2×D4—42no—
463C2×D4—42no—
464C2×D4—42no—
465C2×D4—88no—
466C2×D4C2×D4×C1112yes—
467C22×C4—22no—
468C22×C4—21no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—42no—
474C22×C4—42no—
475C22×C4C2×D4×C1111yescharacteristic
476C22×C4C2×D4×C1111yescharacteristic
477C22×C4C2×D4×C1111yescharacteristic
478C22×C4C2×D4×C1111yescharacteristic
479C22×C4C2×D4×C1111yescharacteristic
480C22×C4C2×D4×C1112yes—
481C22×C4C11×#4112yes—
482C22×C4C11×#4112yes—
483C22×C4C11×#4112yes—
484C22×C4C24×C1111yescharacteristic
485M16—24no—
486M16—22no—
487M16—22no—
488M16—22no—
489M16—42no—
490M16C2×D4×C1114yescomplemented
491C2×C8—24no—
492C2×C8—22no—
493C2×C8—22no—
494C2×C8—42no—
495C4⋊C4—22no—
496C4⋊C4—22no—
497C4⋊C4—22no—
498C4⋊C4—42no—
499C4⋊C4C2×D4×C1114yes—
500C22⋊C4—216no—
501C22⋊C4—22no—
502C22⋊C4—22no—
503C22⋊C4—41no—
504C22⋊C4—41no—
505C22⋊C4—42no—
506C22⋊C4—88no—
507C42—22no—
508C42—22no—
509C42—22no—
510C42—22no—
511C42—41no—
512C42—41no—
513C11#2349311yescharacteristic, direct product factor, Sylow
514C23—24no—
515C23—22no—
516C23—24no—
517C23—24no—
518C23—42no—
519C23—48no—
520C23—44no—
521C23—48no—
522C23—42no—
523C23—44no—
524C23—44no—
525C23—84no—
526C23—88no—
527C23—88no—
528C23C11×#12011yescharacteristic
529C23C11×#12011yescharacteristic
530C23C11×#12112yes—
531C23C11×#12312yes—
532C23C22×D4×C1111yescharacteristic
533Q8—22no—
534Q8—22no—
535Q8—42no—
536D4—22no—
537D4—22no—
538D4—42no—
539D4—42no—
540D4—44no—
541D4—42no—
542D4—42no—
543D4—42no—
544D4—42no—
545D4—44no—
546D4—44no—
547D4—42no—
548D4—816no—
549C2×C4—24no—
550C2×C4—22no—
551C2×C4—44no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—44no—
556C2×C4—44no—
557C2×C4—44no—
558C2×C4—42no—
559C2×C4—42no—
560C2×C4C11×#12011yescharacteristic
561C2×C4C11×#12011yescharacteristic
562C2×C4C11×#12112yes—
563C2×C4C11×#12112yes—
564C2×C4C11×#12112yes—
565C2×C4C11×#12112yes—
566C2×C4C11×#12112yes—
567C2×C4C11×#12312yes—
568C2×C4C11×#12312yes—
569C2×C4C11×#12312yes—
570C2×C4C11×#12412yes—
571C2×C4C11×#12412yes—
572C2×C4C22×D4×C1111yescharacteristic
573C2×C4C22×D4×C1111yescharacteristic
574C2×C4C22×D4×C1111yescharacteristic
575C2×C4C2×C11×#4111yescharacteristic
576C2×C4C2×C11×#4111yescharacteristic
577C2×C4C2×C11×#4111yescharacteristic
578C8—24no—
579C8—42no—
580C22—22no—
581C22—22no—
582C22—22no—
583C22—42no—
584C22—42no—
585C22—48no—
586C22—42no—
587C22—44no—
588C22—44no—
589C22—48no—
590C22—84no—
591C22—88no—
592C22—84no—
593C22—88no—
594C22C11×#39412yes—
595C22C11×#39412yes—
596C22C2×C11×#12011yescharacteristic
597C22C2×C11×#12111yescharacteristic
598C22C2×C11×#12311yescharacteristic
599C4—42no—
600C4—44no—
601C4—82no—
602C4—82no—
603C4C11×#39412yes—
604C4C11×#39412yes—
605C4C2×C11×#12111yescharacteristic
606C4C2×C11×#12111yescharacteristic
607C4C2×C11×#12311yescharacteristic
608C4C2×C11×#12411yescharacteristic
609C2—21no—
610C2—21no—
611C2—22no—
612C2—22no—
613C2—84no—
614C2—82no—
615C2C2×C11×#39411yescharacteristic
616C2C11×#301912yes—
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#535C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#2911C2semidirect
3. C2×C11×#421C2semidirect
4. C11×#2896C2semidirect
5. C22×C11×#100C2semidirect
6. C11×#2309C2semidirect
7. C11×#2037C2semidirect
8. C11×#1733C2semidirect
25. C11×#428C22semidirect
28. C2×C11×#104C22semidirect
31. C11×#417C22semidirect
34. C2×C11×#100C22semidirect
36. C11×#390C22semidirect
38. C11×#339C22semidirect
69. C2×C11×M16D4semidirect
109. #23493C11direct (N × H)
183. C11×M16C2×D4semidirect
207. #2911C2×C11semidirect
208. C2×#421C2×C11semidirect
209. #2896C2×C11semidirect
210. C22×#100C2×C11semidirect
211. #2309C2×C11semidirect
212. #2037C2×C11semidirect
213. #1733C2×C11semidirect
296. #428C22×C11semidirect
299. C2×#104C22×C11semidirect
302. #417C22×C11semidirect
305. C2×#100C22×C11semidirect
307. #390C22×C11semidirect
309. #339C22×C11semidirect
369. C2×M16D4×C11semidirect
490. M16C2×D4×C11semidirect
513. C11#23493direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5352
C11×#29112
C2×C11×#4212
C11×#28962
C22×C11×#1002
C11×#23092
C11×#20372
C11×#17332
#2349311