Finite Group Databasebeta

← C11×#16303 #14593496

Subgroups — C11×#16303 #14593496

Order 2816.

1682 conjugacy classes of subgroups.

The subgroup lattice has 634 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#399C211yesmaximal, characteristic
2C2×C11×#395C212yesmaximal, complemented
3C2×C11×#393C211yesmaximal, characteristic
4C2×C11×#380C212yesmaximal
5C11×#1444C212yesmaximal, complemented
6C11×#1442C212yesmaximal, complemented
7C11×#1441C212yesmaximal, complemented
8C11×#1439C212yesmaximal
9C11×C22⋊#95C211yesmaximal, characteristic
10C23×Q8×C11C2211yescharacteristic
11C24×C4×C11C2211yescharacteristic
12C22×C11×C4⋊C4C2212yes—
13C22×C11×C4⋊C4C2212yes—
14C22×C11×C4⋊C4C2212yes—
15C22×C11×C4⋊C4C2212yes—
16C22×C11×C4⋊C4C2211yescharacteristic
17C22×C11×C22⋊C4C2212yes—
18C22×C11×C22⋊C4C2212yes—
19C22×C11×C22⋊C4C2211yescharacteristic
20C22×C11×C22⋊C4C2211yescharacteristic
21C11×#399—24no—
22C11×#395—28no—
23C11×#393—24no—
24C11×#380—28no—
25C2×C11×#95C2211yescharacteristic
26C2×C11×#95C2212yes—
27C2×C11×#95C2212yes—
28C2×C11×#95C2212yes—
29C2×C11×#95C2211yescharacteristic
30C2×C11×#95C2212yes—
31C2×C11×#95C2212yes—
32C2×C11×#95C2212yes—
33C2×C11×#95C2212yes—
34C2×C11×#95C2212yes—
35C25×C11C2311yescharacteristic
36C22×Q8×C11—22no—
37C22×Q8×C11—24no—
38C22×Q8×C11—41no—
39C22×Q8×C11—42no—
40C22×Q8×C11—41no—
41C23×C4×C11—24no—
42C23×C4×C11—24no—
43C23×C4×C11—41no—
44C23×C4×C11—41no—
45C23×C4×C11Q814yescomplemented
46C23×C4×C11C2312yes—
47C23×C4×C11C2312yes—
48C23×C4×C11C2311yescharacteristic
49C23×C4×C11C2312yes—
50C23×C4×C11C2312yes—
51C23×C4×C11C2311yescharacteristic
52C23×C4×C11C2312yes—
53C23×C4×C11C2312yes—
54C2×C11×C4⋊C4—24no—
55C2×C11×C4⋊C4—24no—
56C2×C11×C4⋊C4—24no—
57C2×C11×C4⋊C4—24no—
58C2×C11×C4⋊C4—24no—
59C2×C11×C4⋊C4—24no—
60C2×C11×C4⋊C4—22no—
61C2×C11×C4⋊C4—24no—
62C2×C11×C4⋊C4—42no—
63C2×C11×C4⋊C4—42no—
64C2×C11×C4⋊C4—42no—
65C2×C11×C4⋊C4—42no—
66C2×C11×C4⋊C4—42no—
67C2×C11×C4⋊C4—41no—
68C2×C11×C4⋊C4—41no—
69C2×C11×C22⋊C4—24no—
70C2×C11×C22⋊C4—24no—
71C2×C11×C22⋊C4—24no—
72C2×C11×C22⋊C4—24no—
73C2×C11×C22⋊C4—41no—
74C2×C11×C22⋊C4—41no—
75C2×C11×C22⋊C4—41no—
76C2×C11×C22⋊C4—41no—
77C2×C11×C22⋊C4—42no—
78C2×C11×C22⋊C4—42no—
79C2×C11×C22⋊C4D414yes—
80C2×C11×C22⋊C4Q814yescomplemented
81C11×#95—24no—
82C11×#95—24no—
83C11×#95—22no—
84C11×#95—24no—
85C11×#95—24no—
86C11×#95—22no—
87C11×#95—24no—
88C11×#95—42no—
89C11×#95—42no—
90C11×#95D418yes—
91#16303C1111yesmaximal, characteristic, direct product factor, Sylow
92C24×C11—22no—
93C24×C11—22no—
94C24×C11—21no—
95C24×C11—22no—
96C24×C11—21no—
97C24×C11—21no—
98C24×C11—21no—
99C24×C11—22no—
100C24×C11C2×D412yes—
101C24×C11C2×Q812yes—
102C24×C11C2×Q812yes—
103C24×C11C2411yescharacteristic
104C2×Q8×C11—48no—
105C2×Q8×C11—44no—
106C2×Q8×C11—44no—
107C2×Q8×C11—48no—
108C2×Q8×C11—44no—
109C22×C4×C11—22no—
110C22×C4×C11—22no—
111C22×C4×C11—22no—
112C22×C4×C11—22no—
113C22×C4×C11—22no—
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—21no—
125C22×C4×C11—21no—
126C22×C4×C11—22no—
127C22×C4×C11—22no—
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11—22no—
131C22×C4×C11—22no—
132C22×C4×C11—22no—
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—216no—
140C22×C4×C11—22no—
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—44no—
155C22×C4×C11—44no—
156C22×C4×C11—48no—
157C22×C4×C11—44no—
158C22×C4×C11C2×D412yes—
159C22×C4×C11C2×D414yes—
160C22×C4×C11C2×D412yes—
161C22×C4×C11C2×D414yes—
162C22×C4×C11C2×D414yes—
163C22×C4×C11C2×Q814yes—
164C22×C4×C11C2×Q814yes—
165C22×C4×C11#4114yes—
166C11×C4⋊C4—48no—
167C11×C4⋊C4—48no—
168C11×C4⋊C4—48no—
169C11×C4⋊C4—44no—
170C11×C4⋊C4—48no—
171C11×C22⋊C4—44no—
172C11×C22⋊C4—44no—
173C11×C22⋊C4—48no—
174C11×C22⋊C4—48no—
175C2×#399C2×C1111yescharacteristic
176C2×#395C2×C1112yescomplemented
177C2×#393C2×C1111yescharacteristic
178C2×#380C2×C1112yes—
179#1444C2×C1112yescomplemented
180#1442C2×C1112yescomplemented
181#1441C2×C1112yescomplemented
182#1439C2×C1112yes—
183C22⋊#95C2×C1111yescharacteristic
184C23×C11—24no—
185C23×C11—22no—
186C23×C11—22no—
187C23×C11—22no—
188C23×C11—22no—
189C23×C11—22no—
190C23×C11—22no—
191C23×C11—24no—
192C23×C11—24no—
193C23×C11—24no—
194C23×C11—24no—
195C23×C11—24no—
196C23×C11—42no—
197C23×C11—42no—
198C23×C11—42no—
199C23×C11—42no—
200C23×C11—41no—
201C23×C11—42no—
202C23×C11—41no—
203C23×C11—41no—
204C23×C11—42no—
205C23×C11—41no—
206C23×C11C4⋊Q814yes—
207C23×C11C22×D412yes—
208C23×C11C22×D411yescharacteristic
209C23×C11C22×Q811yescharacteristic
210C23×C11C22×Q811yescharacteristic
211C23×C11C2×#4112yes—
212C23×C11H(5,𝔽2)11yescharacteristic
213C23×C11H(5,𝔽2)11yescharacteristic
214C23×C11H(5,𝔽2)12yes—
215C23×C11H(5,𝔽2)11yescharacteristic
216C23×C112−1+411yescharacteristic
217C23×C112−1+412yes—
218Q8×C11—416no—
219C2×C4×C11—24no—
220C2×C4×C11—24no—
221C2×C4×C11—24no—
222C2×C4×C11—24no—
223C2×C4×C11—24no—
224C2×C4×C11—24no—
225C2×C4×C11—22no—
226C2×C4×C11—22no—
227C2×C4×C11—24no—
228C2×C4×C11—24no—
229C2×C4×C11—24no—
230C2×C4×C11—24no—
231C2×C4×C11—24no—
232C2×C4×C11—24no—
233C2×C4×C11—24no—
234C2×C4×C11—24no—
235C2×C4×C11—24no—
236C2×C4×C11—24no—
237C2×C4×C11—24no—
238C2×C4×C11—416no—
239C2×C4×C11—42no—
240C2×C4×C11—42no—
241C2×C4×C11—42no—
242C2×C4×C11—42no—
243C2×C4×C11—42no—
244C2×C4×C11—42no—
245C2×C4×C11—42no—
246C2×C4×C11—42no—
247C2×C4×C11—42no—
248C2×C4×C11—41no—
249C2×C4×C11—42no—
250C2×C4×C11—42no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—42no—
254C2×C4×C11—42no—
255C2×C4×C11—42no—
256C2×C4×C11—41no—
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×C11C22⋊Q818yes—
272C23×Q8C22×C1111yescharacteristic
273C24×C4C22×C1111yescharacteristic
274C22×C4⋊C4C22×C1112yes—
275C22×C4⋊C4C22×C1112yes—
276C22×C4⋊C4C22×C1112yes—
277C22×C4⋊C4C22×C1112yes—
278C22×C4⋊C4C22×C1111yescharacteristic
279C22×C22⋊C4C22×C1112yes—
280C22×C22⋊C4C22×C1112yes—
281C22×C22⋊C4C22×C1111yescharacteristic
282C22×C22⋊C4C22×C1111yescharacteristic
283#399—24no—
284#395—28no—
285#393—24no—
286#380—28no—
287C2×#95C22×C1111yescharacteristic
288C2×#95C22×C1112yes—
289C2×#95C22×C1112yes—
290C2×#95C22×C1112yes—
291C2×#95C22×C1111yescharacteristic
292C2×#95C22×C1112yes—
293C2×#95C22×C1112yes—
294C2×#95C22×C1112yes—
295C2×#95C22×C1112yes—
296C2×#95C22×C1112yes—
297C22×C11—24no—
298C22×C11—28no—
299C22×C11—42no—
300C22×C11—44no—
301C22×C11—42no—
302C22×C11—44no—
303C22×C11—42no—
304C22×C11—44no—
305C22×C11—42no—
306C22×C11—42no—
307C22×C11—42no—
308C22×C11C2×C22⋊Q812yes—
309C22×C11C2×C4⋊Q811yescharacteristic
310C22×C11#53411yescharacteristic
311C22×C11#53512yes—
312C22×C11#53612yes—
313C22×C11#53711yescharacteristic
314C22×C11#54212yes—
315C22×C11#54212yes—
316C22×C11#54311yescharacteristic
317C22×C11#54311yescharacteristic
318C22×C11#54412yes—
319C22×C11#54411yescharacteristic
320C22×C11#54411yescharacteristic
321C22×C11D4212yes—
322C22×C11D4211yescharacteristic
323C22×C11#54612yes—
324C22×C11#54712yes—
325C22×C11D4×Q812yes—
326C22×C11#55111yescharacteristic
327C22×C11#55412yes—
328C22×C11#56011yescharacteristic
329C22×C11#56212yes—
330C22×C11#56311yescharacteristic
331C4×C11—28no—
332C4×C11—42no—
333C4×C11—44no—
334C4×C11—44no—
335C4×C11—44no—
336C4×C11—42no—
337C4×C11—82no—
338C4×C11—82no—
339C25C23×C1111yescharacteristic
340C22×Q8—22no—
341C22×Q8—24no—
342C22×Q8—41no—
343C22×Q8—42no—
344C22×Q8—41no—
345C23×C4—24no—
346C23×C4—24no—
347C23×C4—41no—
348C23×C4—41no—
349C23×C4Q8×C1114yescomplemented
350C23×C4C23×C1112yes—
351C23×C4C23×C1112yes—
352C23×C4C23×C1112yes—
353C23×C4C23×C1111yescharacteristic
354C23×C4C23×C1112yes—
355C23×C4C23×C1111yescharacteristic
356C23×C4C23×C1112yes—
357C23×C4C23×C1112yes—
358C2×C4⋊C4—24no—
359C2×C4⋊C4—24no—
360C2×C4⋊C4—24no—
361C2×C4⋊C4—24no—
362C2×C4⋊C4—24no—
363C2×C4⋊C4—24no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—24no—
366C2×C4⋊C4—42no—
367C2×C4⋊C4—42no—
368C2×C4⋊C4—42no—
369C2×C4⋊C4—42no—
370C2×C4⋊C4—42no—
371C2×C4⋊C4—41no—
372C2×C4⋊C4—41no—
373C2×C22⋊C4—24no—
374C2×C22⋊C4—24no—
375C2×C22⋊C4—24no—
376C2×C22⋊C4—24no—
377C2×C22⋊C4—41no—
378C2×C22⋊C4—41no—
379C2×C22⋊C4—41no—
380C2×C22⋊C4—41no—
381C2×C22⋊C4—42no—
382C2×C22⋊C4—42no—
383C2×C22⋊C4D4×C1114yes—
384C2×C22⋊C4Q8×C1114yescomplemented
385#95—24no—
386#95—24no—
387#95—22no—
388#95—24no—
389#95—24no—
390#95—22no—
391#95—24no—
392#95—42no—
393#95—42no—
394#95D4×C1118yes—
395C2×C11—44no—
396C2×C11#243711yescharacteristic
397C2×C11#244012yes—
398C2×C11#262812yes—
399C2×C11#265911yescharacteristic
400C2×C11#266911yescharacteristic
401C2×C11#267212yes—
402C2×C11#267711yescharacteristic
403C2×C11#269212yes—
404C2×C11#271711yescharacteristic
405C2×C11#274211yescharacteristic
406C2×C11#284111yescharacteristic
407C24—22no—
408C24—22no—
409C24—21no—
410C24—22no—
411C24—21no—
412C24—21no—
413C24—21no—
414C24—22no—
415C24C2×D4×C1112yes—
416C24C2×Q8×C1112yes—
417C24C2×Q8×C1112yes—
418C24C24×C1111yescharacteristic
419C2×Q8—48no—
420C2×Q8—44no—
421C2×Q8—44no—
422C2×Q8—48no—
423C2×Q8—44no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—21no—
444C22×C4—21no—
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—216no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—44no—
470C22×C4—44no—
471C22×C4—48no—
472C22×C4—44no—
473C22×C4C2×D4×C1112yes—
474C22×C4C2×D4×C1114yes—
475C22×C4C2×D4×C1112yes—
476C22×C4C2×D4×C1114yes—
477C22×C4C2×D4×C1114yes—
478C22×C4C2×Q8×C1114yes—
479C22×C4C2×Q8×C1114yes—
480C22×C4C11×#4114yes—
481C4⋊C4—48no—
482C4⋊C4—48no—
483C4⋊C4—48no—
484C4⋊C4—44no—
485C4⋊C4—48no—
486C22⋊C4—44no—
487C22⋊C4—44no—
488C22⋊C4—48no—
489C22⋊C4—48no—
490C11#1630311yescharacteristic, direct product factor, Sylow
491C23—24no—
492C23—22no—
493C23—22no—
494C23—22no—
495C23—22no—
496C23—22no—
497C23—22no—
498C23—24no—
499C23—24no—
500C23—24no—
501C23—24no—
502C23—24no—
503C23—42no—
504C23—42no—
505C23—42no—
506C23—42no—
507C23—41no—
508C23—42no—
509C23—41no—
510C23—41no—
511C23—42no—
512C23—41no—
513C23C11×C4⋊Q814yes—
514C23C22×D4×C1112yes—
515C23C22×D4×C1111yescharacteristic
516C23C22×Q8×C1111yescharacteristic
517C23C22×Q8×C1111yescharacteristic
518C23C2×C11×#4112yes—
519C23C11×H(5,𝔽2)11yescharacteristic
520C23C11×H(5,𝔽2)11yescharacteristic
521C23C11×H(5,𝔽2)12yes—
522C23C11×H(5,𝔽2)11yescharacteristic
523C23C11×2−1+411yescharacteristic
524C23C11×2−1+412yes—
525Q8—416no—
526C2×C4—24no—
527C2×C4—24no—
528C2×C4—24no—
529C2×C4—24no—
530C2×C4—24no—
531C2×C4—24no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—24no—
535C2×C4—24no—
536C2×C4—24no—
537C2×C4—24no—
538C2×C4—24no—
539C2×C4—24no—
540C2×C4—24no—
541C2×C4—24no—
542C2×C4—24no—
543C2×C4—24no—
544C2×C4—24no—
545C2×C4—416no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—41no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—42no—
563C2×C4—41no—
564C2×C4—42no—
565C2×C4—42no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4C11×C22⋊Q818yes—
579C22—24no—
580C22—28no—
581C22—42no—
582C22—44no—
583C22—42no—
584C22—44no—
585C22—42no—
586C22—42no—
587C22—42no—
588C22—42no—
589C22—44no—
590C22C2×C11×C22⋊Q812yes—
591C22C2×C11×C4⋊Q811yescharacteristic
592C22C11×#53411yescharacteristic
593C22C11×#53512yes—
594C22C11×#53612yes—
595C22C11×#53711yescharacteristic
596C22C11×#54212yes—
597C22C11×#54212yes—
598C22C11×#54311yescharacteristic
599C22C11×#54311yescharacteristic
600C22C11×#54411yescharacteristic
601C22C11×#54411yescharacteristic
602C22C11×#54412yes—
603C22D42×C1112yes—
604C22D42×C1111yescharacteristic
605C22C11×#54612yes—
606C22C11×#54712yes—
607C22D4×Q8×C1112yes—
608C22C11×#55111yescharacteristic
609C22C11×#55412yes—
610C22C11×#56011yescharacteristic
611C22C11×#56212yes—
612C22C11×#56311yescharacteristic
613C4—28no—
614C4—42no—
615C4—44no—
616C4—44no—
617C4—44no—
618C4—42no—
619C4—82no—
620C4—82no—
621C2—44no—
622C2C11×#243711yescharacteristic
623C2C11×#244012yes—
624C2C11×#262812yes—
625C2C11×#265911yescharacteristic
626C2C11×#266911yescharacteristic
627C2C11×#267212yes—
628C2C11×#267711yescharacteristic
629C2C11×#269212yes—
630C2C11×#271711yescharacteristic
631C2C11×#274211yescharacteristic
632C2C11×#284111yescharacteristic
subgroupG/H
center, socleC24×C11C24
commutator, Frattini, cosocleC24C24×C11
prime radicalC25×C11C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#395C2semidirect
5. C11×#1444C2semidirect
6. C11×#1442C2semidirect
7. C11×#1441C2semidirect
45. C23×C4×C11Q8semidirect
80. C2×C11×C22⋊C4Q8semidirect
91. #16303C11direct (N × H)
176. C2×#395C2×C11semidirect
179. #1444C2×C11semidirect
180. #1442C2×C11semidirect
181. #1441C2×C11semidirect
349. C23×C4Q8×C11semidirect
384. C2×C22⋊C4Q8×C11semidirect
490. C11#16303direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#3992
C2×C11×#3952
C2×C11×#3932
C2×C11×#3802
C11×#14442
C11×#14422
C11×#14412
C11×#14392
C11×C22⋊#952
#1630311