Finite Group Databasebeta

← C11×#23489 #14600682

Subgroups — C11×#23489 #14600682

Order 2816.

1482 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#537C211yesmaximal, characteristic
2C22×C11×#106C211yesmaximal, characteristic, complemented
3C2×C11×#417C211yesmaximal, characteristic, complemented
4C2×C11×#416C211yesmaximal, characteristic, complemented
5C2×C11×#408C211yesmaximal, characteristic, complemented
6C11×#2311C211yesmaximal, characteristic, complemented
7C11×#2035C214yesmaximal, complemented
8C11×#2034C214yesmaximal, complemented
9C11×#1736C211yesmaximal, characteristic, complemented
10C22×C11×#41C2211yescharacteristic
11C22×C11×#41C2211yescharacteristic
12C22×C11×M16C2211yescharacteristic
13C23×C8×C11C2211yescharacteristic
14C11×#537—24no—
15C11×#537—24no—
16C2×C11×C22⋊Q8—21no—
17C2×C11×C22⋊Q8C2212yes—
18C2×C11×#121—21no—
19C2×C11×#121—22no—
20C2×C11×#121C2212yes—
21C2×C11×#117C2211yescharacteristic
22C22×C11×C4⋊C4C2211yescharacteristic
23C22×C11×C4⋊C4C2211yescharacteristic
24C2×C11×#106—24no—
25C2×C11×#106C2214yes—
26C11×#417—24no—
27C11×#416—24no—
28C2×C11×#103C2212yes—
29C2×C11×#103C2212yes—
30C2×C11×#102C2212yes—
31C2×C11×#102C2212yes—
32C11×#408—24no—
33C2×C11×C22⋊C8C2214yes—
34C11×#391—21no—
35C11×#390—21no—
36C11×#386—22no—
37C11×#380C2214yes—
38C11×#340C2214yes—
39C2×C11×#41—22no—
40C2×C11×#41—22no—
41C2×C11×#41—22no—
42C2×C11×#41—22no—
43C2×C11×#41—22no—
44C2×C11×#41—22no—
45C2×C11×#41—22no—
46C2×C11×#41—22no—
47C2×C11×#41—22no—
48C2×C11×#41—22no—
49C2×C11×#41—22no—
50C2×C11×#41D414yes—
51C22×Q8×C11D411yescharacteristic
52C22×Q8×C11C2311yescharacteristic
53C22×D4×C11—21no—
54C22×D4×C11—22no—
55C22×D4×C11D412yes—
56C22×D4×C11D411yescharacteristic
57C22×D4×C11C2311yescharacteristic
58C23×C4×C11—21no—
59C23×C4×C11—21no—
60C23×C4×C11—21no—
61C23×C4×C11C2312yes—
62C23×C4×C11C2311yescharacteristic
63C2×C11×M16—22no—
64C2×C11×M16—22no—
65C2×C11×M16—22no—
66C22×C8×C11—22no—
67C22×C8×C11—22no—
68C22×C8×C11D414yescomplemented
69C22×C8×C11C2312yes—
70C22×C8×C11C2312yes—
71C11×C22⋊Q8—28no—
72C11×C22⋊Q8—24no—
73C11×C22⋊Q8—24no—
74C11×#121—216no—
75C11×#121—28no—
76C11×#121—24no—
77C11×#121—24no—
78C11×#117—22no—
79C11×#117—22no—
80C2×C11×C4⋊C4—21no—
81C2×C11×C4⋊C4—22no—
82C2×C11×C4⋊C4—22no—
83C2×C11×C4⋊C4—22no—
84C2×C11×C4⋊C4—22no—
85C2×C11×C4⋊C4—21no—
86C2×C11×C4⋊C4D414yes—
87C2×C11×C4⋊C4C2312yes—
88C2×C11×C4⋊C4C2312yes—
89C2×C11×C4⋊C4C2312yes—
90C2×C11×C22⋊C4—22no—
91C2×C11×C22⋊C4—22no—
92C2×C11×C22⋊C4—21no—
93C2×C11×C22⋊C4—24no—
94C2×C42×C11—21no—
95C11×#106—28no—
96C11×#103—24no—
97C11×#103—24no—
98C11×#102—24no—
99C11×#102—24no—
100C11×C22⋊C8—28no—
101C11×#95—24no—
102#23489C1111yesmaximal, characteristic, direct product factor, Sylow
103C24×C11—21no—
104C24×C11C2×D412yes—
105C24×C11C2×D411yescharacteristic
106C11×#41—28no—
107C11×#41—28no—
108C11×#41—44no—
109C11×#41—44no—
110C11×#41—44no—
111C11×#41—44no—
112C11×#41—44no—
113C11×#41—44no—
114C2×Q8×C11—22no—
115C2×Q8×C11—22no—
116C2×Q8×C11—22no—
117C2×Q8×C11—21no—
118C2×Q8×C11—21no—
119C2×Q8×C11—21no—
120C2×Q8×C11—21no—
121C2×Q8×C11—21no—
122C2×Q8×C11C2×D412yes—
123C2×D4×C11—24no—
124C2×D4×C11—24no—
125C2×D4×C11—24no—
126C2×D4×C11—24no—
127C2×D4×C11—28no—
128C2×D4×C11—22no—
129C2×D4×C11—22no—
130C2×D4×C11—22no—
131C2×D4×C11—21no—
132C2×D4×C11—21no—
133C2×D4×C11—21no—
134C2×D4×C11—21no—
135C2×D4×C11—21no—
136C2×D4×C11—42no—
137C2×D4×C11—42no—
138C2×D4×C11—84no—
139C2×D4×C11C2×D412yes—
140C22×C4×C11—22no—
141C22×C4×C11—21no—
142C22×C4×C11—24no—
143C22×C4×C11—24no—
144C22×C4×C11—22no—
145C22×C4×C11—22no—
146C22×C4×C11—22no—
147C22×C4×C11—22no—
148C22×C4×C11—22no—
149C22×C4×C11—22no—
150C22×C4×C11—22no—
151C22×C4×C11—22no—
152C22×C4×C11—42no—
153C22×C4×C11—42no—
154C22×C4×C11—42no—
155C22×C4×C11—82no—
156C22×C4×C11—82no—
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
166C11×M16—44no—
167C2×C8×C11—28no—
168C2×C8×C11—22no—
169C2×C8×C11—22no—
170C2×C8×C11—22no—
171C2×C8×C11—22no—
172C2×C8×C11—22no—
173C2×C8×C11C2×D414yes—
174C11×C4⋊C4—28no—
175C11×C4⋊C4—24no—
176C11×C4⋊C4—22no—
177C11×C4⋊C4—22no—
178C11×C4⋊C4—22no—
179C11×C4⋊C4—22no—
180C11×C4⋊C4—22no—
181C11×C4⋊C4—42no—
182C11×C4⋊C4C2×D414yes—
183C11×C22⋊C4—28no—
184C11×C22⋊C4—28no—
185C11×C22⋊C4—42no—
186C11×C22⋊C4—84no—
187C42×C11—42no—
188C2×#537C2×C1111yescharacteristic
189C22×#106C2×C1111yescharacteristic, complemented
190C2×#417C2×C1111yescharacteristic, complemented
191C2×#416C2×C1111yescharacteristic, complemented
192C2×#408C2×C1111yescharacteristic, complemented
193#2311C2×C1111yescharacteristic, complemented
194#2035C2×C1114yescomplemented
195#2034C2×C1114yescomplemented
196#1736C2×C1111yescharacteristic, complemented
197C23×C11—22no—
198C23×C11—22no—
199C23×C11—22no—
200C23×C11—22no—
201C23×C11—22no—
202C23×C11—22no—
203C23×C11—24no—
204C23×C11—24no—
205C23×C11—41no—
206C23×C11—41no—
207C23×C11—42no—
208C23×C11—42no—
209C23×C11#12012yes—
210C23×C11#12112yes—
211C23×C11#12312yes—
212C23×C11C22×D411yescharacteristic
213Q8×C11—22no—
214Q8×C11—22no—
215Q8×C11—41no—
216Q8×C11—41no—
217Q8×C11—44no—
218D4×C11—22no—
219D4×C11—22no—
220D4×C11—48no—
221D4×C11—48no—
222D4×C11—41no—
223D4×C11—41no—
224D4×C11—44no—
225D4×C11—88no—
226C2×C4×C11—24no—
227C2×C4×C11—22no—
228C2×C4×C11—22no—
229C2×C4×C11—22no—
230C2×C4×C11—22no—
231C2×C4×C11—41no—
232C2×C4×C11—41no—
233C2×C4×C11—44no—
234C2×C4×C11—42no—
235C2×C4×C11—42no—
236C2×C4×C11—42no—
237C2×C4×C11—42no—
238C2×C4×C11—48no—
239C2×C4×C11—42no—
240C2×C4×C11—42no—
241C2×C4×C11—42no—
242C2×C4×C11—44no—
243C2×C4×C11—42no—
244C2×C4×C11—84no—
245C2×C4×C11—84no—
246C2×C4×C11#12012yes—
247C2×C4×C11#12114yes—
248C2×C4×C11#12114yes—
249C2×C4×C11#12112yes—
250C2×C4×C11#12314yes—
251C2×C4×C11#12312yes—
252C2×C4×C11#12414yes—
253C2×C4×C11C22×D411yescharacteristic
254C2×C4×C11C22×D411yescharacteristic
255C2×C4×C11C22×D411yescharacteristic
256C2×C4×C11C2×#4111yescharacteristic
257C2×C4×C11C2×#4111yescharacteristic
258C2×C4×C11C2×#4111yescharacteristic
259C8×C11—24no—
260C8×C11—42no—
261C22×#41C22×C1111yescharacteristic
262C22×#41C22×C1111yescharacteristic
263C22×M16C22×C1111yescharacteristic
264C23×C8C22×C1111yescharacteristic
265#537—24no—
266#537—24no—
267C2×C22⋊Q8—21no—
268C2×C22⋊Q8C22×C1112yes—
269C2×#121—21no—
270C2×#121—22no—
271C2×#121C22×C1112yes—
272C2×#117C22×C1111yescharacteristic
273C22×C4⋊C4C22×C1111yescharacteristic
274C22×C4⋊C4C22×C1111yescharacteristic
275C2×#106—24no—
276C2×#106C22×C1114yes—
277#417—24no—
278#416—24no—
279C2×#103C22×C1112yes—
280C2×#103C22×C1112yes—
281C2×#102C22×C1112yes—
282C2×#102C22×C1112yes—
283#408—24no—
284C2×C22⋊C8C22×C1114yes—
285#391—21no—
286#390—21no—
287#386—22no—
288#380C22×C1114yes—
289#340C22×C1114yes—
290C22×C11—24no—
291C22×C11—22no—
292C22×C11—22no—
293C22×C11—24no—
294C22×C11—44no—
295C22×C11—42no—
296C22×C11—42no—
297C22×C11—42no—
298C22×C11—42no—
299C22×C11—42no—
300C22×C11—42no—
301C22×C11—44no—
302C22×C11—82no—
303C22×C11—82no—
304C22×C11#39414yes—
305C22×C11C2×#12011yescharacteristic
306C22×C11C2×#12111yescharacteristic
307C22×C11C2×#12311yescharacteristic
308C22×C11#57712yes—
309C22×C11#57712yes—
310C4×C11—42no—
311C4×C11—42no—
312C4×C11—44no—
313C4×C11—82no—
314C4×C11—82no—
315C4×C11#39414yes—
316C4×C11C2×#12111yescharacteristic
317C4×C11C2×#12111yescharacteristic
318C4×C11C2×#12311yescharacteristic
319C4×C11C2×#12411yescharacteristic
320C2×#41—22no—
321C2×#41—22no—
322C2×#41—22no—
323C2×#41—22no—
324C2×#41—22no—
325C2×#41—22no—
326C2×#41—22no—
327C2×#41—22no—
328C2×#41—22no—
329C2×#41—22no—
330C2×#41—22no—
331C2×#41D4×C1114yes—
332C22×Q8D4×C1111yescharacteristic
333C22×Q8C23×C1111yescharacteristic
334C22×D4—21no—
335C22×D4—22no—
336C22×D4D4×C1112yes—
337C22×D4D4×C1111yescharacteristic
338C22×D4C23×C1111yescharacteristic
339C23×C4—21no—
340C23×C4—21no—
341C23×C4—21no—
342C23×C4C23×C1112yes—
343C23×C4C23×C1111yescharacteristic
344C2×M16—22no—
345C2×M16—22no—
346C2×M16—22no—
347C22×C8—22no—
348C22×C8—22no—
349C22×C8D4×C1114yescomplemented
350C22×C8C23×C1112yes—
351C22×C8C23×C1112yes—
352C22⋊Q8—28no—
353C22⋊Q8—24no—
354C22⋊Q8—24no—
355#121—216no—
356#121—28no—
357#121—24no—
358#121—24no—
359#117—22no—
360#117—22no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4D4×C1114yes—
368C2×C4⋊C4C23×C1112yes—
369C2×C4⋊C4C23×C1112yes—
370C2×C4⋊C4C23×C1112yes—
371C2×C22⋊C4—22no—
372C2×C22⋊C4—22no—
373C2×C22⋊C4—21no—
374C2×C22⋊C4—24no—
375C2×C42—21no—
376#106—28no—
377#103—24no—
378#103—24no—
379#102—24no—
380#102—24no—
381C22⋊C8—28no—
382#95—24no—
383C2×C11—24no—
384C2×C11—82no—
385C2×C11—82no—
386C2×C11C2×#39411yescharacteristic
387C2×C11#300911yescharacteristic
388C2×C11#301011yescharacteristic
389C2×C11#306012yes—
390C2×C11#309912yes—
391C24—21no—
392C24C2×D4×C1112yes—
393C24C2×D4×C1111yescharacteristic
394#41—28no—
395#41—28no—
396#41—44no—
397#41—44no—
398#41—44no—
399#41—44no—
400#41—44no—
401#41—44no—
402C2×Q8—22no—
403C2×Q8—22no—
404C2×Q8—22no—
405C2×Q8—21no—
406C2×Q8—21no—
407C2×Q8—21no—
408C2×Q8—21no—
409C2×Q8—21no—
410C2×Q8C2×D4×C1112yes—
411C2×D4—24no—
412C2×D4—24no—
413C2×D4—24no—
414C2×D4—24no—
415C2×D4—28no—
416C2×D4—22no—
417C2×D4—22no—
418C2×D4—22no—
419C2×D4—21no—
420C2×D4—21no—
421C2×D4—21no—
422C2×D4—21no—
423C2×D4—21no—
424C2×D4—42no—
425C2×D4—42no—
426C2×D4—84no—
427C2×D4C2×D4×C1112yes—
428C22×C4—22no—
429C22×C4—21no—
430C22×C4—24no—
431C22×C4—24no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—42no—
441C22×C4—42no—
442C22×C4—42no—
443C22×C4—82no—
444C22×C4—82no—
445C22×C4C2×D4×C1112yes—
446C22×C4C2×D4×C1111yescharacteristic
447C22×C4C2×D4×C1112yes—
448C22×C4C2×D4×C1112yes—
449C22×C4C2×D4×C1112yes—
450C22×C4C11×#4112yes—
451C22×C4C11×#4112yes—
452C22×C4C11×#4112yes—
453C22×C4C24×C1111yescharacteristic
454M16—44no—
455C2×C8—28no—
456C2×C8—22no—
457C2×C8—22no—
458C2×C8—22no—
459C2×C8—22no—
460C2×C8—22no—
461C2×C8C2×D4×C1114yes—
462C4⋊C4—28no—
463C4⋊C4—24no—
464C4⋊C4—22no—
465C4⋊C4—22no—
466C4⋊C4—22no—
467C4⋊C4—22no—
468C4⋊C4—22no—
469C4⋊C4—42no—
470C4⋊C4C2×D4×C1114yes—
471C22⋊C4—28no—
472C22⋊C4—28no—
473C22⋊C4—42no—
474C22⋊C4—84no—
475C42—42no—
476C11#2348911yescharacteristic, direct product factor, Sylow
477C23—22no—
478C23—22no—
479C23—22no—
480C23—22no—
481C23—22no—
482C23—22no—
483C23—24no—
484C23—24no—
485C23—41no—
486C23—41no—
487C23—42no—
488C23—42no—
489C23C11×#12012yes—
490C23C11×#12112yes—
491C23C11×#12312yes—
492C23C22×D4×C1111yescharacteristic
493Q8—22no—
494Q8—22no—
495Q8—41no—
496Q8—41no—
497Q8—44no—
498D4—22no—
499D4—22no—
500D4—48no—
501D4—48no—
502D4—41no—
503D4—41no—
504D4—44no—
505D4—88no—
506C2×C4—24no—
507C2×C4—22no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—44no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—48no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—44no—
523C2×C4—42no—
524C2×C4—84no—
525C2×C4—84no—
526C2×C4C11×#12012yes—
527C2×C4C11×#12114yes—
528C2×C4C11×#12114yes—
529C2×C4C11×#12112yes—
530C2×C4C11×#12314yes—
531C2×C4C11×#12312yes—
532C2×C4C11×#12414yes—
533C2×C4C22×D4×C1111yescharacteristic
534C2×C4C22×D4×C1111yescharacteristic
535C2×C4C22×D4×C1111yescharacteristic
536C2×C4C2×C11×#4111yescharacteristic
537C2×C4C2×C11×#4111yescharacteristic
538C2×C4C2×C11×#4111yescharacteristic
539C8—24no—
540C8—42no—
541C22—22no—
542C22—22no—
543C22—24no—
544C22—24no—
545C22—42no—
546C22—42no—
547C22—42no—
548C22—42no—
549C22—42no—
550C22—42no—
551C22—44no—
552C22—44no—
553C22—82no—
554C22—82no—
555C22C11×#39414yes—
556C22C2×C11×#12011yescharacteristic
557C22C2×C11×#12111yescharacteristic
558C22C2×C11×#12311yescharacteristic
559C22C11×#57712yes—
560C22C11×#57712yes—
561C4—42no—
562C4—42no—
563C4—44no—
564C4—82no—
565C4—82no—
566C4C11×#39414yes—
567C4C2×C11×#12111yescharacteristic
568C4C2×C11×#12111yescharacteristic
569C4C2×C11×#12311yescharacteristic
570C4C2×C11×#12411yescharacteristic
571C2—24no—
572C2—82no—
573C2—82no—
574C2C2×C11×#39411yescharacteristic
575C2C11×#300911yescharacteristic
576C2C11×#301011yescharacteristic
577C2C11×#306012yes—
578C2C11×#309912yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#537C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C22×C11×#41 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×C11×#106C2semidirect
3. C2×C11×#417C2semidirect
4. C2×C11×#416C2semidirect
5. C2×C11×#408C2semidirect
6. C11×#2311C2semidirect
7. C11×#2035C2semidirect
8. C11×#2034C2semidirect
9. C11×#1736C2semidirect
68. C22×C8×C11D4semidirect
102. #23489C11direct (N × H)
189. C22×#106C2×C11semidirect
190. C2×#417C2×C11semidirect
191. C2×#416C2×C11semidirect
192. C2×#408C2×C11semidirect
193. #2311C2×C11semidirect
194. #2035C2×C11semidirect
195. #2034C2×C11semidirect
196. #1736C2×C11semidirect
349. C22×C8D4×C11semidirect
476. C11#23489direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5372
C22×C11×#1062
C2×C11×#4172
C2×C11×#4162
C2×C11×#4082
C11×#23112
C11×#20352
C11×#20342
C11×#17362
#2348911