Finite Group Databasebeta

← C11×#14410 #14591603

Subgroups — C11×#14410 #14591603

Order 2816.

1866 conjugacy classes of subgroups.

The subgroup lattice has 666 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#388C212yesmaximal, complemented
2C2×C11×#386C211yesmaximal, characteristic
3C2×C11×#380C212yesmaximal, complemented
4C11×#1442C212yesmaximal, complemented
5C11×#1439C212yesmaximal, complemented
6C11×#1438C211yesmaximal, characteristic
7C11×#1438C211yesmaximal, characteristic
8C11×#1437C212yesmaximal, complemented
9C11×#1436C212yesmaximal, complemented
10C23×D4×C11C2211yescharacteristic
11C24×C4×C11C2211yescharacteristic
12C22×C11×C4⋊C4C2212yes—
13C22×C11×C4⋊C4C2212yes—
14C22×C11×C22⋊C4C2212yes—
15C22×C11×C22⋊C4C2212yes—
16C22×C11×C22⋊C4C2211yescharacteristic
17C22×C11×C22⋊C4C2212yes—
18C22×C11×C22⋊C4C2212yes—
19C22×C11×C22⋊C4C2211yescharacteristic
20C22×C11×C22⋊C4C2211yescharacteristic
21C22×C42×C11C2212yes—
22C11×#388—28no—
23C11×#386C418yescomplemented
24C11×#380—28no—
25C2×C11×#95C2212yes—
26C2×C11×#95C2212yes—
27C2×C11×#95C2211yescharacteristic
28C2×C11×#95C2212yes—
29C2×C11×#95C2212yes—
30C2×C11×#95C2212yes—
31C2×C11×#95C2211yescharacteristic
32C2×C11×#95C2212yes—
33C2×C11×#95C2212yes—
34C25×C11C2311yescharacteristic
35C25×C11C2311yescharacteristic
36C22×D4×C11—24no—
37C22×D4×C11—42no—
38C22×D4×C11—41no—
39C22×D4×C11—41no—
40C22×D4×C11C2×C414yes—
41C23×C4×C11—24no—
42C23×C4×C11—24no—
43C23×C4×C11—41no—
44C23×C4×C11—41no—
45C23×C4×C11C2×C414yes—
46C23×C4×C11C2312yes—
47C23×C4×C11C2312yes—
48C23×C4×C11C2312yes—
49C23×C4×C11C2311yescharacteristic
50C23×C4×C11C2312yes—
51C23×C4×C11C2312yes—
52C23×C4×C11C2312yes—
53C2×C11×C4⋊C4—24no—
54C2×C11×C4⋊C4—24no—
55C2×C11×C4⋊C4—24no—
56C2×C11×C4⋊C4—24no—
57C2×C11×C4⋊C4—42no—
58C2×C11×C4⋊C4—42no—
59C2×C11×C22⋊C4—24no—
60C2×C11×C22⋊C4—24no—
61C2×C11×C22⋊C4—24no—
62C2×C11×C22⋊C4—24no—
63C2×C11×C22⋊C4—24no—
64C2×C11×C22⋊C4—24no—
65C2×C11×C22⋊C4—24no—
66C2×C11×C22⋊C4—24no—
67C2×C11×C22⋊C4—42no—
68C2×C11×C22⋊C4—41no—
69C2×C11×C22⋊C4—42no—
70C2×C11×C22⋊C4—42no—
71C2×C11×C22⋊C4—42no—
72C2×C11×C22⋊C4—42no—
73C2×C11×C22⋊C4—42no—
74C2×C11×C22⋊C4—41no—
75C2×C11×C22⋊C4C2×C418yes—
76C2×C11×C22⋊C4C2×C414yes—
77C2×C42×C11—24no—
78C2×C42×C11—42no—
79C2×C42×C11—42no—
80C11×#95—24no—
81C11×#95—24no—
82C11×#95—42no—
83C11×#95—42no—
84C11×#95—42no—
85C11×#95—41no—
86C11×#95—41no—
87C11×#95C2×C418yes—
88C11×#95D418yescomplemented
89#14410C1111yesmaximal, characteristic, direct product factor, Sylow
90C24×C11—22no—
91C24×C11—22no—
92C24×C11—22no—
93C24×C11—22no—
94C24×C11—21no—
95C24×C11—21no—
96C24×C11—22no—
97C24×C11—22no—
98C24×C11—22no—
99C24×C11—22no—
100C24×C11—22no—
101C24×C11—22no—
102C24×C11—21no—
103C24×C11—21no—
104C24×C11—22no—
105C24×C11C22×C412yes—
106C24×C11C22×C412yes—
107C24×C11#4114yes—
108C24×C11C2411yescharacteristic
109C2×D4×C11—28no—
110C2×D4×C11—44no—
111C2×D4×C11—44no—
112C2×D4×C11—48no—
113C2×D4×C11—48no—
114C22×C4×C11—22no—
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—22no—
120C22×C4×C11—22no—
121C22×C4×C11—22no—
122C22×C4×C11—22no—
123C22×C4×C11—22no—
124C22×C4×C11—22no—
125C22×C4×C11—22no—
126C22×C4×C11—22no—
127C22×C4×C11—22no—
128C22×C4×C11—22no—
129C22×C4×C11—22no—
130C22×C4×C11—22no—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—22no—
134C22×C4×C11—22no—
135C22×C4×C11—22no—
136C22×C4×C11—22no—
137C22×C4×C11—22no—
138C22×C4×C11—22no—
139C22×C4×C11—22no—
140C22×C4×C11—216no—
141C22×C4×C11—22no—
142C22×C4×C11—22no—
143C22×C4×C11—22no—
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—22no—
153C22×C4×C11—22no—
154C22×C4×C11—22no—
155C22×C4×C11—44no—
156C22×C4×C11—44no—
157C22×C4×C11—48no—
158C22×C4×C11—44no—
159C22×C4×C11C22×C412yes—
160C22×C4×C11C22×C414yes—
161C22×C4×C11C22×C414yes—
162C22×C4×C11C2×D414yes—
163C22×C4×C11C2×D414yes—
164C22×C4×C11C2×D414yes—
165C22×C4×C11#4114yes—
166C11×C4⋊C4—48no—
167C11×C4⋊C4—48no—
168C11×C22⋊C4—216no—
169C11×C22⋊C4—44no—
170C11×C22⋊C4—44no—
171C11×C22⋊C4—48no—
172C11×C22⋊C4—48no—
173C11×C22⋊C4—48no—
174C11×C22⋊C4—44no—
175C42×C11—48no—
176C2×#388C2×C1112yescomplemented
177C2×#386C2×C1111yescharacteristic
178C2×#380C2×C1112yescomplemented
179#1442C2×C1112yescomplemented
180#1439C2×C1112yescomplemented
181#1438C2×C1111yescharacteristic
182#1438C2×C1111yescharacteristic
183#1437C2×C1112yescomplemented
184#1436C2×C1112yescomplemented
185C23×C11—24no—
186C23×C11—22no—
187C23×C11—22no—
188C23×C11—24no—
189C23×C11—24no—
190C23×C11—24no—
191C23×C11—24no—
192C23×C11—24no—
193C23×C11—24no—
194C23×C11—24no—
195C23×C11—22no—
196C23×C11—24no—
197C23×C11—22no—
198C23×C11—22no—
199C23×C11—24no—
200C23×C11—42no—
201C23×C11—42no—
202C23×C11—42no—
203C23×C11—42no—
204C23×C11—41no—
205C23×C11—42no—
206C23×C11—41no—
207C23×C11—41no—
208C23×C11—42no—
209C23×C11—41no—
210C23×C11—42no—
211C23×C11—42no—
212C23×C11—42no—
213C23×C11—42no—
214C23×C11—42no—
215C23×C11—42no—
216C23×C11—41no—
217C23×C11—42no—
218C23×C11—42no—
219C23×C11—42no—
220C23×C11—41no—
221C23×C11—42no—
222C23×C11—42no—
223C23×C11—41no—
224C23×C11—42no—
225C23×C11—41no—
226C23×C11#11714yes—
227C23×C11C23×C411yescharacteristic
228C23×C11C22×D412yes—
229C23×C11C2×#4112yes—
230C23×C11C2×#4112yes—
231C23×C11H(5,𝔽2)12yes—
232C23×C11H(5,𝔽2)11yescharacteristic
233C23×C11H(5,𝔽2)11yescharacteristic
234C23×C11H(5,𝔽2)12yes—
235C23×C112−1+412yes—
236D4×C11—416no—
237C2×C4×C11—24no—
238C2×C4×C11—24no—
239C2×C4×C11—24no—
240C2×C4×C11—24no—
241C2×C4×C11—24no—
242C2×C4×C11—24no—
243C2×C4×C11—22no—
244C2×C4×C11—24no—
245C2×C4×C11—24no—
246C2×C4×C11—22no—
247C2×C4×C11—22no—
248C2×C4×C11—24no—
249C2×C4×C11—24no—
250C2×C4×C11—24no—
251C2×C4×C11—24no—
252C2×C4×C11—24no—
253C2×C4×C11—24no—
254C2×C4×C11—24no—
255C2×C4×C11—416no—
256C2×C4×C11—42no—
257C2×C4×C11—42no—
258C2×C4×C11—42no—
259C2×C4×C11—42no—
260C2×C4×C11—42no—
261C2×C4×C11—42no—
262C2×C4×C11—42no—
263C2×C4×C11—42no—
264C2×C4×C11—42no—
265C2×C4×C11—42no—
266C2×C4×C11—42no—
267C2×C4×C11—42no—
268C2×C4×C11—42no—
269C2×C4×C11—42no—
270C2×C4×C11—42no—
271C2×C4×C11—42no—
272C2×C4×C11—42no—
273C2×C4×C11—42no—
274C2×C4×C11—42no—
275C2×C4×C11—42no—
276C2×C4×C11—42no—
277C2×C4×C11—42no—
278C2×C4×C11—42no—
279C2×C4×C11—42no—
280C2×C4×C11—42no—
281C2×C4×C11—42no—
282C2×C4×C11—42no—
283C2×C4×C11—42no—
284C2×C4×C11C4×D418yes—
285C23×D4C22×C1111yescharacteristic
286C24×C4C22×C1111yescharacteristic
287C22×C4⋊C4C22×C1112yes—
288C22×C4⋊C4C22×C1112yes—
289C22×C22⋊C4C22×C1112yes—
290C22×C22⋊C4C22×C1112yes—
291C22×C22⋊C4C22×C1111yescharacteristic
292C22×C22⋊C4C22×C1112yes—
293C22×C22⋊C4C22×C1112yes—
294C22×C22⋊C4C22×C1111yescharacteristic
295C22×C22⋊C4C22×C1111yescharacteristic
296C22×C42C22×C1112yes—
297#388—28no—
298#386C4×C1118yescomplemented
299#380—28no—
300C2×#95C22×C1112yes—
301C2×#95C22×C1112yes—
302C2×#95C22×C1111yescharacteristic
303C2×#95C22×C1112yes—
304C2×#95C22×C1112yes—
305C2×#95C22×C1112yes—
306C2×#95C22×C1111yescharacteristic
307C2×#95C22×C1112yes—
308C2×#95C22×C1112yes—
309C22×C11—24no—
310C22×C11—28no—
311C22×C11—44no—
312C22×C11—42no—
313C22×C11—42no—
314C22×C11—44no—
315C22×C11—44no—
316C22×C11—44no—
317C22×C11—44no—
318C22×C11—42no—
319C22×C11—44no—
320C22×C11—44no—
321C22×C11—42no—
322C22×C11—42no—
323C22×C11—82no—
324C22×C11—82no—
325C22×C11—82no—
326C22×C11—82no—
327C22×C11C2×#11711yescharacteristic
328C22×C11C2×C4×D412yes—
329C22×C11#51811yescharacteristic
330C22×C11#51811yescharacteristic
331C22×C11#52012yes—
332C22×C11#53512yes—
333C22×C11#53712yes—
334C22×C11#53812yes—
335C22×C11#53812yes—
336C22×C11#54012yes—
337C22×C11#54212yes—
338C22×C11D4211yescharacteristic
339C22×C11#54612yes—
340C22×C11#54612yes—
341C22×C11#54812yes—
342C22×C11#55111yescharacteristic
343C22×C11#55212yes—
344C22×C11#55312yes—
345C22×C11#56011yescharacteristic
346C22×C11#56212yes—
347C22×C11#56311yescharacteristic
348C4×C11—28no—
349C4×C11—42no—
350C4×C11—44no—
351C4×C11—44no—
352C4×C11—44no—
353C4×C11—82no—
354C4×C11—82no—
355C25C23×C1111yescharacteristic
356C25C23×C1111yescharacteristic
357C22×D4—24no—
358C22×D4—42no—
359C22×D4—41no—
360C22×D4—41no—
361C22×D4C2×C4×C1114yes—
362C23×C4—24no—
363C23×C4—24no—
364C23×C4—41no—
365C23×C4—41no—
366C23×C4C2×C4×C1114yes—
367C23×C4C23×C1112yes—
368C23×C4C23×C1112yes—
369C23×C4C23×C1112yes—
370C23×C4C23×C1111yescharacteristic
371C23×C4C23×C1112yes—
372C23×C4C23×C1112yes—
373C23×C4C23×C1112yes—
374C2×C4⋊C4—24no—
375C2×C4⋊C4—24no—
376C2×C4⋊C4—24no—
377C2×C4⋊C4—24no—
378C2×C4⋊C4—42no—
379C2×C4⋊C4—42no—
380C2×C22⋊C4—24no—
381C2×C22⋊C4—24no—
382C2×C22⋊C4—24no—
383C2×C22⋊C4—24no—
384C2×C22⋊C4—24no—
385C2×C22⋊C4—24no—
386C2×C22⋊C4—24no—
387C2×C22⋊C4—24no—
388C2×C22⋊C4—42no—
389C2×C22⋊C4—41no—
390C2×C22⋊C4—42no—
391C2×C22⋊C4—42no—
392C2×C22⋊C4—42no—
393C2×C22⋊C4—42no—
394C2×C22⋊C4—42no—
395C2×C22⋊C4—41no—
396C2×C22⋊C4C2×C4×C1118yes—
397C2×C22⋊C4C2×C4×C1114yes—
398C2×C42—24no—
399C2×C42—42no—
400C2×C42—42no—
401#95—24no—
402#95—24no—
403#95—42no—
404#95—42no—
405#95—42no—
406#95—41no—
407#95—41no—
408#95C2×C4×C1118yes—
409#95D4×C1118yescomplemented
410C2×C11—44no—
411C2×C11—82no—
412C2×C11#231211yescharacteristic
413C2×C11#232412yes—
414C2×C11#235212yes—
415C2×C11#235811yescharacteristic
416C2×C11#237611yescharacteristic
417C2×C11#267612yes—
418C2×C11#270212yes—
419C2×C11#270312yes—
420C2×C11#274112yes—
421C24—22no—
422C24—22no—
423C24—22no—
424C24—22no—
425C24—21no—
426C24—21no—
427C24—22no—
428C24—22no—
429C24—22no—
430C24—22no—
431C24—22no—
432C24—22no—
433C24—21no—
434C24—21no—
435C24—22no—
436C24C22×C4×C1112yes—
437C24C22×C4×C1112yes—
438C24C11×#4114yes—
439C24C24×C1111yescharacteristic
440C2×D4—28no—
441C2×D4—44no—
442C2×D4—44no—
443C2×D4—48no—
444C2×D4—48no—
445C22×C4—22no—
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—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—216no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—44no—
487C22×C4—44no—
488C22×C4—48no—
489C22×C4—44no—
490C22×C4C22×C4×C1112yes—
491C22×C4C22×C4×C1114yes—
492C22×C4C22×C4×C1114yes—
493C22×C4C2×D4×C1114yes—
494C22×C4C2×D4×C1114yes—
495C22×C4C2×D4×C1114yes—
496C22×C4C11×#4114yes—
497C4⋊C4—48no—
498C4⋊C4—48no—
499C22⋊C4—216no—
500C22⋊C4—44no—
501C22⋊C4—44no—
502C22⋊C4—48no—
503C22⋊C4—48no—
504C22⋊C4—48no—
505C22⋊C4—44no—
506C42—48no—
507C11#1441011yescharacteristic, direct product factor, Sylow
508C23—24no—
509C23—22no—
510C23—22no—
511C23—24no—
512C23—24no—
513C23—24no—
514C23—24no—
515C23—24no—
516C23—24no—
517C23—24no—
518C23—22no—
519C23—24no—
520C23—22no—
521C23—22no—
522C23—24no—
523C23—42no—
524C23—42no—
525C23—42no—
526C23—42no—
527C23—41no—
528C23—42no—
529C23—41no—
530C23—41no—
531C23—42no—
532C23—41no—
533C23—42no—
534C23—42no—
535C23—42no—
536C23—42no—
537C23—42no—
538C23—42no—
539C23—41no—
540C23—42no—
541C23—42no—
542C23—42no—
543C23—41no—
544C23—42no—
545C23—42no—
546C23—41no—
547C23—42no—
548C23—41no—
549C23C11×#11714yes—
550C23C23×C4×C1111yescharacteristic
551C23C22×D4×C1112yes—
552C23C2×C11×#4112yes—
553C23C2×C11×#4112yes—
554C23C11×H(5,𝔽2)12yes—
555C23C11×H(5,𝔽2)11yescharacteristic
556C23C11×H(5,𝔽2)11yescharacteristic
557C23C11×H(5,𝔽2)12yes—
558C23C11×2−1+412yes—
559D4—416no—
560C2×C4—24no—
561C2×C4—24no—
562C2×C4—24no—
563C2×C4—24no—
564C2×C4—24no—
565C2×C4—24no—
566C2×C4—22no—
567C2×C4—24no—
568C2×C4—24no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—24no—
572C2×C4—24no—
573C2×C4—24no—
574C2×C4—24no—
575C2×C4—24no—
576C2×C4—24no—
577C2×C4—24no—
578C2×C4—416no—
579C2×C4—42no—
580C2×C4—42no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—42no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—42no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—42no—
599C2×C4—42no—
600C2×C4—42no—
601C2×C4—42no—
602C2×C4—42no—
603C2×C4—42no—
604C2×C4—42no—
605C2×C4—42no—
606C2×C4—42no—
607C2×C4C4×D4×C1118yes—
608C22—24no—
609C22—28no—
610C22—44no—
611C22—44no—
612C22—44no—
613C22—44no—
614C22—44no—
615C22—42no—
616C22—42no—
617C22—42no—
618C22—44no—
619C22—44no—
620C22—42no—
621C22—42no—
622C22—82no—
623C22—82no—
624C22—82no—
625C22—82no—
626C22C2×C11×#11711yescharacteristic
627C22C2×C4×D4×C1112yes—
628C22C11×#51811yescharacteristic
629C22C11×#51811yescharacteristic
630C22C11×#52012yes—
631C22C11×#53512yes—
632C22C11×#53712yes—
633C22C11×#53812yes—
634C22C11×#53812yes—
635C22C11×#54012yes—
636C22C11×#54212yes—
637C22D42×C1111yescharacteristic
638C22C11×#54612yes—
639C22C11×#54612yes—
640C22C11×#54812yes—
641C22C11×#55111yescharacteristic
642C22C11×#55212yes—
643C22C11×#55312yes—
644C22C11×#56011yescharacteristic
645C22C11×#56212yes—
646C22C11×#56311yescharacteristic
647C4—28no—
648C4—44no—
649C4—44no—
650C4—42no—
651C4—44no—
652C4—82no—
653C4—82no—
654C2—44no—
655C2—82no—
656C2C11×#231211yescharacteristic
657C2C11×#232412yes—
658C2C11×#235212yes—
659C2C11×#235811yescharacteristic
660C2C11×#237611yescharacteristic
661C2C11×#267612yes—
662C2C11×#270212yes—
663C2C11×#270312yes—
664C2C11×#274112yes—
subgroupG/H
center, socleC24×C11C24
commutatorC23C23×C4×C11
Frattini, cosocleC24C24×C11
prime radicalC23×D4×C11C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#388C2semidirect
3. C2×C11×#380C2semidirect
4. C11×#1442C2semidirect
5. C11×#1439C2semidirect
8. C11×#1437C2semidirect
9. C11×#1436C2semidirect
23. C11×#386C4semidirect
88. C11×#95D4semidirect
89. #14410C11direct (N × H)
176. C2×#388C2×C11semidirect
178. C2×#380C2×C11semidirect
179. #1442C2×C11semidirect
180. #1439C2×C11semidirect
183. #1437C2×C11semidirect
184. #1436C2×C11semidirect
298. #386C4×C11semidirect
409. #95D4×C11semidirect
507. C11#14410direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#3882
C2×C11×#3862
C2×C11×#3802
C11×#14422
C11×#14392
C11×#14382
C11×#14372
C11×#14362
#1441011