Finite Group Databasebeta

← C11×#23388 #14600581

Subgroups — C11×#23388 #14600581

Order 2816.

2142 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C11×SD16C211yesmaximal, characteristic, complemented
2C2×C11×#536C211yesmaximal, characteristic, complemented
3C2×C11×#535C211yesmaximal, characteristic
4C2×C11×#419C211yesmaximal, characteristic, complemented
5C2×C11×#418C211yesmaximal, characteristic, complemented
6C2×C11×#408C211yesmaximal, characteristic, complemented
7C11×#2000C218yesmaximal, complemented
8C11×#1735C211yesmaximal, characteristic, complemented
9C22×C11×#41C2211yescharacteristic
10C23×Q8×C11C2211yescharacteristic
11C23×D4×C11C2211yescharacteristic
12C22×C11×SD16—24no—
13C22×C11×SD16—24no—
14C22×C11×SD16—24no—
15C22×C11×SD16C2214yes—
16C22×C11×M16C2211yescharacteristic
17C23×C8×C11C2211yescharacteristic
18C11×#536—24no—
19C11×#536—24no—
20C11×#535—24no—
21C11×#535—24no—
22C2×C11×C4⋊Q8—21no—
23C2×C11×#127—21no—
24C2×C11×#124—21no—
25C2×C11×#124—21no—
26C2×C11×#123—22no—
27C2×C11×C22⋊Q8C2214yescomplemented
28C2×C11×#121C2214yes—
29C2×C11×#120—22no—
30C2×C11×#117C2211yescharacteristic
31C2×C11×#117C2211yescharacteristic
32C11×#419—24no—
33C11×#418—24no—
34C2×C11×#103C2214yescomplemented
35C2×C11×#102C2214yes—
36C11×#408—24no—
37C2×C11×C22⋊C8C2214yescomplemented
38C11×#340C2214yescomplemented
39C25×C11—21no—
40C2×C11×#41—22no—
41C2×C11×#41—22no—
42C2×C11×#41—22no—
43C2×C11×#41—22no—
44C2×C11×#41—22no—
45C2×C11×#41—22no—
46C22×Q8×C11—21no—
47C22×Q8×C11—22no—
48C22×Q8×C11—22no—
49C22×Q8×C11—22no—
50C22×Q8×C11—22no—
51C22×Q8×C11—22no—
52C22×Q8×C11D411yescharacteristic
53C22×Q8×C11D414yescomplemented
54C22×Q8×C11C2312yes—
55C22×D4×C11—24no—
56C22×D4×C11—22no—
57C22×D4×C11—22no—
58C22×D4×C11—22no—
59C22×D4×C11—21no—
60C22×D4×C11—22no—
61C22×D4×C11—22no—
62C22×D4×C11D412yes—
63C22×D4×C11D411yescharacteristic
64C22×D4×C11D414yes—
65C22×D4×C11C2312yes—
66C23×C4×C11—21no—
67C23×C4×C11C2312yes—
68C23×C4×C11C2311yescharacteristic
69C2×C11×SD16—232no—
70C2×C11×SD16—28no—
71C2×C11×SD16—28no—
72C2×C11×SD16—28no—
73C2×C11×M16—22no—
74C2×C11×M16—22no—
75C2×C11×M16—22no—
76C22×C8×C11—22no—
77C22×C8×C11—22no—
78C22×C8×C11D414yescomplemented
79C22×C8×C11C2312yes—
80C22×C8×C11C2312yes—
81C11×C4⋊Q8—28no—
82C11×#127—28no—
83C11×#124—28no—
84C11×#124—28no—
85C11×#123—216no—
86C11×C22⋊Q8—28no—
87C11×C22⋊Q8—28no—
88C11×#121—28no—
89C11×#121—28no—
90C11×#120—216no—
91C11×#117—22no—
92C11×#117—22no—
93C11×#117D414yes—
94C11×#117D414yescomplemented
95C2×C11×C4⋊C4—24no—
96C2×C11×C4⋊C4C2312yes—
97C2×C11×C4⋊C4C2312yes—
98C2×C11×C22⋊C4—21no—
99C2×C11×C22⋊C4—21no—
100C2×C11×C22⋊C4—24no—
101C2×C11×C22⋊C4—24no—
102C2×C42×C11—21no—
103C2×C42×C11—21no—
104C11×#103—28no—
105C11×#102—28no—
106C11×C22⋊C8—28no—
107#23388C1111yesmaximal, characteristic, direct product factor, Sylow
108C24×C11—22no—
109C24×C11—24no—
110C24×C11—42no—
111C24×C11—42no—
112C24×C11—84no—
113C24×C11C2×D412yes—
114C24×C11C2×D411yescharacteristic
115C11×#41—44no—
116C11×#41—44no—
117C11×#41—44no—
118C11×#41—44no—
119C2×Q8×C11—22no—
120C2×Q8×C11—24no—
121C2×Q8×C11—22no—
122C2×Q8×C11—22no—
123C2×Q8×C11—22no—
124C2×Q8×C11—28no—
125C2×Q8×C11—28no—
126C2×Q8×C11—22no—
127C2×Q8×C11—22no—
128C2×Q8×C11—22no—
129C2×Q8×C11—22no—
130C2×Q8×C11—42no—
131C2×Q8×C11—42no—
132C2×Q8×C11—44no—
133C2×Q8×C11—44no—
134C2×Q8×C11C2×D414yes—
135C2×D4×C11—24no—
136C2×D4×C11—24no—
137C2×D4×C11—24no—
138C2×D4×C11—216no—
139C2×D4×C11—28no—
140C2×D4×C11—22no—
141C2×D4×C11—24no—
142C2×D4×C11—22no—
143C2×D4×C11—28no—
144C2×D4×C11—22no—
145C2×D4×C11—22no—
146C2×D4×C11—22no—
147C2×D4×C11—22no—
148C2×D4×C11—22no—
149C2×D4×C11—22no—
150C2×D4×C11—42no—
151C2×D4×C11—44no—
152C2×D4×C11—42no—
153C2×D4×C11—44no—
154C2×D4×C11—88no—
155C2×D4×C11C2×D414yes—
156C22×C4×C11—24no—
157C22×C4×C11—22no—
158C22×C4×C11—22no—
159C22×C4×C11—22no—
160C22×C4×C11—22no—
161C22×C4×C11—22no—
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×D412yes—
169C22×C4×C11C2×D411yescharacteristic
170C22×C4×C11C2×D412yes—
171C22×C4×C11C2×D412yes—
172C22×C4×C11C2×D412yes—
173C22×C4×C11C2×D412yes—
174C22×C4×C11C2×D412yes—
175C22×C4×C11#4112yes—
176C22×C4×C11C2411yescharacteristic
177C11×SD16—232no—
178C11×M16—44no—
179C2×C8×C11—28no—
180C2×C8×C11—22no—
181C2×C8×C11—22no—
182C2×C8×C11—22no—
183C2×C8×C11—22no—
184C2×C8×C11—22no—
185C2×C8×C11C2×D414yes—
186C11×C4⋊C4—216no—
187C11×C4⋊C4—22no—
188C11×C4⋊C4—22no—
189C11×C4⋊C4C2×D414yes—
190C11×C4⋊C4C2×D414yes—
191C11×C22⋊C4—216no—
192C11×C22⋊C4—216no—
193C11×C22⋊C4—24no—
194C11×C22⋊C4—24no—
195C42×C11—24no—
196C42×C11—24no—
197C23×SD16C2×C1111yescharacteristic, complemented
198C2×#536C2×C1111yescharacteristic, complemented
199C2×#535C2×C1111yescharacteristic
200C2×#419C2×C1111yescharacteristic, complemented
201C2×#418C2×C1111yescharacteristic, complemented
202C2×#408C2×C1111yescharacteristic, complemented
203#2000C2×C1118yescomplemented
204#1735C2×C1111yescharacteristic, complemented
205C23×C11—24no—
206C23×C11—22no—
207C23×C11—24no—
208C23×C11—22no—
209C23×C11—22no—
210C23×C11—28no—
211C23×C11—42no—
212C23×C11—42no—
213C23×C11—48no—
214C23×C11—48no—
215C23×C11—88no—
216C23×C11—88no—
217C23×C11—88no—
218C23×C11#12012yes—
219C23×C11#12012yes—
220C23×C11#12112yes—
221C23×C11C22×D411yescharacteristic
222Q8×C11—24no—
223Q8×C11—24no—
224Q8×C11—42no—
225Q8×C11—42no—
226Q8×C11—48no—
227Q8×C11—44no—
228D4×C11—24no—
229D4×C11—24no—
230D4×C11—48no—
231D4×C11—42no—
232D4×C11—42no—
233D4×C11—48no—
234D4×C11—44no—
235D4×C11—816no—
236C2×C4×C11—24no—
237C2×C4×C11—24no—
238C2×C4×C11—22no—
239C2×C4×C11—24no—
240C2×C4×C11—22no—
241C2×C4×C11—22no—
242C2×C4×C11—42no—
243C2×C4×C11—42no—
244C2×C4×C11—44no—
245C2×C4×C11—44no—
246C2×C4×C11—48no—
247C2×C4×C11—42no—
248C2×C4×C11—42no—
249C2×C4×C11—42no—
250C2×C4×C11—42no—
251C2×C4×C11#12014yes—
252C2×C4×C11#12012yes—
253C2×C4×C11#12012yes—
254C2×C4×C11#12114yes—
255C2×C4×C11#12114yes—
256C2×C4×C11#12112yes—
257C2×C4×C11#12714yes—
258C2×C4×C11C22×D411yescharacteristic
259C2×C4×C11C22×D411yescharacteristic
260C2×C4×C11C22×D411yescharacteristic
261C2×C4×C11C22×D411yescharacteristic
262C2×C4×C11C22×D411yescharacteristic
263C2×C4×C11C2×#4111yescharacteristic
264C8×C11—24no—
265C8×C11—42no—
266C22×#41C22×C1111yescharacteristic
267C23×Q8C22×C1111yescharacteristic
268C23×D4C22×C1111yescharacteristic
269C22×SD16—24no—
270C22×SD16—24no—
271C22×SD16—24no—
272C22×SD16C22×C1114yes—
273C22×M16C22×C1111yescharacteristic
274C23×C8C22×C1111yescharacteristic
275#536—24no—
276#536—24no—
277#535—24no—
278#535—24no—
279C2×C4⋊Q8—21no—
280C2×#127—21no—
281C2×#124—21no—
282C2×#124—21no—
283C2×#123—22no—
284C2×C22⋊Q8C22×C1114yescomplemented
285C2×#121C22×C1114yes—
286C2×#120—22no—
287C2×#117C22×C1111yescharacteristic
288C2×#117C22×C1111yescharacteristic
289#419—24no—
290#418—24no—
291C2×#103C22×C1114yescomplemented
292C2×#102C22×C1114yes—
293#408—24no—
294C2×C22⋊C8C22×C1114yescomplemented
295#340C22×C1114yescomplemented
296C22×C11—24no—
297C22×C11—24no—
298C22×C11—24no—
299C22×C11—42no—
300C22×C11—44no—
301C22×C11—44no—
302C22×C11—48no—
303C22×C11—44no—
304C22×C11—44no—
305C22×C11—816no—
306C22×C11—84no—
307C22×C11—84no—
308C22×C11#39214yes—
309C22×C11C2×#12011yescharacteristic
310C22×C11C2×#12011yescharacteristic
311C22×C11C2×#12111yescharacteristic
312C22×C11#57714yes—
313C4×C11—42no—
314C4×C11—44no—
315C4×C11—44no—
316C4×C11—44no—
317C4×C11#39214yes—
318C4×C11C2×#12011yescharacteristic
319C4×C11C2×#12111yescharacteristic
320C4×C11C2×#12111yescharacteristic
321C4×C11C2×#12711yescharacteristic
322C25—21no—
323C2×#41—22no—
324C2×#41—22no—
325C2×#41—22no—
326C2×#41—22no—
327C2×#41—22no—
328C2×#41—22no—
329C22×Q8—21no—
330C22×Q8—22no—
331C22×Q8—22no—
332C22×Q8—22no—
333C22×Q8—22no—
334C22×Q8—22no—
335C22×Q8D4×C1111yescharacteristic
336C22×Q8D4×C1114yescomplemented
337C22×Q8C23×C1112yes—
338C22×D4—24no—
339C22×D4—22no—
340C22×D4—22no—
341C22×D4—22no—
342C22×D4—21no—
343C22×D4—22no—
344C22×D4—22no—
345C22×D4D4×C1112yes—
346C22×D4D4×C1111yescharacteristic
347C22×D4D4×C1114yes—
348C22×D4C23×C1112yes—
349C23×C4—21no—
350C23×C4C23×C1112yes—
351C23×C4C23×C1111yescharacteristic
352C2×SD16—232no—
353C2×SD16—28no—
354C2×SD16—28no—
355C2×SD16—28no—
356C2×M16—22no—
357C2×M16—22no—
358C2×M16—22no—
359C22×C8—22no—
360C22×C8—22no—
361C22×C8D4×C1114yescomplemented
362C22×C8C23×C1112yes—
363C22×C8C23×C1112yes—
364C4⋊Q8—28no—
365#127—28no—
366#124—28no—
367#124—28no—
368#123—216no—
369C22⋊Q8—28no—
370C22⋊Q8—28no—
371#121—28no—
372#121—28no—
373#120—216no—
374#117—22no—
375#117—22no—
376#117D4×C1114yes—
377#117D4×C1114yescomplemented
378C2×C4⋊C4—24no—
379C2×C4⋊C4C23×C1112yes—
380C2×C4⋊C4C23×C1112yes—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—24no—
384C2×C22⋊C4—24no—
385C2×C42—21no—
386C2×C42—21no—
387#103—28no—
388#102—28no—
389C22⋊C8—28no—
390C2×C11—24no—
391C2×C11—82no—
392C2×C11—84no—
393C2×C11C2×#39211yescharacteristic
394C2×C11#300912yes—
395C2×C11#301012yes—
396C2×C11#305712yes—
397C24—22no—
398C24—24no—
399C24—42no—
400C24—42no—
401C24—84no—
402C24C2×D4×C1112yes—
403C24C2×D4×C1111yescharacteristic
404#41—44no—
405#41—44no—
406#41—44no—
407#41—44no—
408C2×Q8—22no—
409C2×Q8—24no—
410C2×Q8—22no—
411C2×Q8—22no—
412C2×Q8—22no—
413C2×Q8—28no—
414C2×Q8—28no—
415C2×Q8—22no—
416C2×Q8—22no—
417C2×Q8—22no—
418C2×Q8—22no—
419C2×Q8—42no—
420C2×Q8—42no—
421C2×Q8—44no—
422C2×Q8—44no—
423C2×Q8C2×D4×C1114yes—
424C2×D4—24no—
425C2×D4—24no—
426C2×D4—24no—
427C2×D4—216no—
428C2×D4—28no—
429C2×D4—22no—
430C2×D4—24no—
431C2×D4—22no—
432C2×D4—28no—
433C2×D4—22no—
434C2×D4—22no—
435C2×D4—22no—
436C2×D4—22no—
437C2×D4—22no—
438C2×D4—22no—
439C2×D4—42no—
440C2×D4—44no—
441C2×D4—42no—
442C2×D4—44no—
443C2×D4—88no—
444C2×D4C2×D4×C1114yes—
445C22×C4—24no—
446C22×C4—22no—
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×C4C2×D4×C1112yes—
458C22×C4C2×D4×C1111yescharacteristic
459C22×C4C2×D4×C1112yes—
460C22×C4C2×D4×C1112yes—
461C22×C4C2×D4×C1112yes—
462C22×C4C2×D4×C1112yes—
463C22×C4C2×D4×C1112yes—
464C22×C4C11×#4112yes—
465C22×C4C24×C1111yescharacteristic
466SD16—232no—
467M16—44no—
468C2×C8—28no—
469C2×C8—22no—
470C2×C8—22no—
471C2×C8—22no—
472C2×C8—22no—
473C2×C8—22no—
474C2×C8C2×D4×C1114yes—
475C4⋊C4—216no—
476C4⋊C4—22no—
477C4⋊C4—22no—
478C4⋊C4C2×D4×C1114yes—
479C4⋊C4C2×D4×C1114yes—
480C22⋊C4—216no—
481C22⋊C4—216no—
482C22⋊C4—24no—
483C22⋊C4—24no—
484C42—24no—
485C42—24no—
486C11#2338811yescharacteristic, direct product factor, Sylow
487C23—24no—
488C23—22no—
489C23—24no—
490C23—22no—
491C23—22no—
492C23—28no—
493C23—42no—
494C23—42no—
495C23—48no—
496C23—48no—
497C23—88no—
498C23—88no—
499C23—88no—
500C23C11×#12012yes—
501C23C11×#12012yes—
502C23C11×#12112yes—
503C23C22×D4×C1111yescharacteristic
504Q8—24no—
505Q8—24no—
506Q8—42no—
507Q8—48no—
508Q8—44no—
509Q8—42no—
510D4—24no—
511D4—24no—
512D4—48no—
513D4—42no—
514D4—48no—
515D4—44no—
516D4—42no—
517D4—816no—
518C2×C4—24no—
519C2×C4—24no—
520C2×C4—22no—
521C2×C4—24no—
522C2×C4—22no—
523C2×C4—22no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—48no—
527C2×C4—44no—
528C2×C4—44no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4C11×#12014yes—
534C2×C4C11×#12012yes—
535C2×C4C11×#12012yes—
536C2×C4C11×#12114yes—
537C2×C4C11×#12114yes—
538C2×C4C11×#12112yes—
539C2×C4C11×#12714yes—
540C2×C4C22×D4×C1111yescharacteristic
541C2×C4C22×D4×C1111yescharacteristic
542C2×C4C22×D4×C1111yescharacteristic
543C2×C4C22×D4×C1111yescharacteristic
544C2×C4C22×D4×C1111yescharacteristic
545C2×C4C2×C11×#4111yescharacteristic
546C8—24no—
547C8—42no—
548C22—24no—
549C22—24no—
550C22—24no—
551C22—42no—
552C22—44no—
553C22—44no—
554C22—48no—
555C22—44no—
556C22—44no—
557C22—816no—
558C22—84no—
559C22—84no—
560C22C11×#39214yes—
561C22C2×C11×#12011yescharacteristic
562C22C2×C11×#12011yescharacteristic
563C22C2×C11×#12111yescharacteristic
564C22C11×#57714yes—
565C4—42no—
566C4—44no—
567C4—44no—
568C4—44no—
569C4C11×#39214yes—
570C4C2×C11×#12011yescharacteristic
571C4C2×C11×#12111yescharacteristic
572C4C2×C11×#12111yescharacteristic
573C4C2×C11×#12711yescharacteristic
574C2—24no—
575C2—82no—
576C2—84no—
577C2C2×C11×#39211yescharacteristic
578C2C11×#300912yes—
579C2C11×#301012yes—
580C2C11×#305712yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#535C2
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
1. C23×C11×SD16C2semidirect
2. C2×C11×#536C2semidirect
4. C2×C11×#419C2semidirect
5. C2×C11×#418C2semidirect
6. C2×C11×#408C2semidirect
7. C11×#2000C2semidirect
8. C11×#1735C2semidirect
27. C2×C11×C22⋊Q8C22semidirect
34. C2×C11×#103C22semidirect
37. C2×C11×C22⋊C8C22semidirect
38. C11×#340C22semidirect
53. C22×Q8×C11D4semidirect
78. C22×C8×C11D4semidirect
94. C11×#117D4semidirect
107. #23388C11direct (N × H)
197. C23×SD16C2×C11semidirect
198. C2×#536C2×C11semidirect
200. C2×#419C2×C11semidirect
201. C2×#418C2×C11semidirect
202. C2×#408C2×C11semidirect
203. #2000C2×C11semidirect
204. #1735C2×C11semidirect
284. C2×C22⋊Q8C22×C11semidirect
291. C2×#103C22×C11semidirect
294. C2×C22⋊C8C22×C11semidirect
295. #340C22×C11semidirect
336. C22×Q8D4×C11semidirect
361. C22×C8D4×C11semidirect
377. #117D4×C11semidirect
486. C11#23388direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C11×SD162
C2×C11×#5362
C2×C11×#5352
C2×C11×#4192
C2×C11×#4182
C2×C11×#4082
C11×#20002
C11×#17352
#2338811