Finite Group Databasebeta

← C11×#22482 #14599675

Subgroups — C11×#22482 #14599675

Order 2816.

1132 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#553C211yesmaximal, characteristic
2D4×C11×M16C212yesmaximal, complemented
3C11×#1998C212yesmaximal, complemented
4C11×#1900C212yesmaximal, complemented
5C11×#1900C212yesmaximal, complemented
6C11×#1822C211yesmaximal, characteristic, complemented
7C11×#1821C211yesmaximal, characteristic, complemented
8C11×#1800C211yesmaximal, characteristic, complemented
9C4×C11×#100C211yesmaximal, characteristic, complemented
10C11×#1742C211yesmaximal, characteristic, complemented
11C2×C11×#343C211yesmaximal, characteristic, complemented
12C22×C11×M16C2212yes—
13C22×C11×M16C2212yes—
14C11×#553—22no—
15C11×#553—22no—
16C11×#553—22no—
17C11×#553—22no—
18C2×C11×#126C412yes—
19C2×C11×#125C2211yescharacteristic
20C2×C11×#123C412yes—
21C2×C11×#121C412yes—
22C2×C11×#121C2211yescharacteristic
23C2×C11×#121C2211yescharacteristic
24C2×C4×D4×C11C412yes—
25C2×C4×D4×C11C2211yescharacteristic
26C2×C4×D4×C11C2211yescharacteristic
27C2×C11×#117C2211yescharacteristic
28C22×C11×C4⋊C4C2211yescharacteristic
29C11×#436—22no—
30C11×#435—22no—
31C11×#435—22no—
32C8×D4×C11—22no—
33C11×#423C2212yes—
34C2×C11×#100C2212yes—
35C2×C11×#100C2212yes—
36C11×#407C2212yes—
37C11×#407C2212yes—
38C4×C11×M16C2212yes—
39C11×#343C2212yes—
40C11×#343C2212yes—
41C11×#343C2212yes—
42C11×#343C2212yes—
43C11×#343C2211yescharacteristic
44C11×#343C2211yescharacteristic
45C11×#343C2211yescharacteristic
46C11×#343C2211yescharacteristic
47C22×D4×C11C2×C412yes—
48C22×D4×C11C2×C412yes—
49C22×D4×C11C2×C411yescharacteristic
50C22×D4×C11C2311yescharacteristic
51C23×C4×C11C2×C412yes—
52C23×C4×C11C2×C412yes—
53C23×C4×C11C2311yescharacteristic
54C23×C4×C11C2311yescharacteristic
55C2×C11×M16—22no—
56C2×C11×M16—22no—
57C2×C11×M16—24no—
58C2×C11×M16—24no—
59C2×C11×M16—42no—
60C2×C11×M16—42no—
61C2×C11×M16C2312yes—
62C2×C11×M16C2312yes—
63C2×C11×M16C2312yes—
64C2×C11×M16C2312yes—
65C22×C8×C11—22no—
66C22×C8×C11—22no—
67C11×#126—24no—
68C11×#126—24no—
69C11×#125—22no—
70C11×#125—22no—
71C11×#123—24no—
72C11×#123—24no—
73C11×#121—24no—
74C11×#121—24no—
75C11×#121—22no—
76C11×#121—22no—
77C11×#121—22no—
78C11×#121—22no—
79C4×D4×C11—22no—
80C4×D4×C11—22no—
81C4×D4×C11—22no—
82C4×D4×C11—22no—
83C4×D4×C11—22no—
84C4×D4×C11—22no—
85C4×D4×C11D412yes—
86C4×D4×C11D412yes—
87C4×D4×C11D412yes—
88C4×D4×C11D412yes—
89C11×#117—22no—
90C11×#117—22no—
91C2×C11×C4⋊C4—22no—
92C2×C11×C4⋊C4—22no—
93C2×C11×C4⋊C4C2×C412yes—
94C2×C11×C4⋊C4C2×C412yes—
95C2×C11×C4⋊C4C2×C412yes—
96C2×C11×C4⋊C4C2×C411yescharacteristic
97C2×C11×C4⋊C4C2311yescharacteristic
98C2×C11×C4⋊C4C2311yescharacteristic
99C2×C11×C4⋊C4C2311yescharacteristic
100C2×C11×C22⋊C4C2×C412yes—
101C2×C11×C22⋊C4C2×C412yes—
102C2×C11×C22⋊C4C2×C412yes—
103C2×C11×C22⋊C4C2×C412yes—
104C2×C11×C22⋊C4C2×C411yescharacteristic
105C2×C11×C22⋊C4C2×C411yescharacteristic
106C2×C42×C11C2×C412yes—
107C2×C42×C11C2311yescharacteristic
108C11×C4⋊C8—22no—
109C11×C4⋊C8—22no—
110C11×#100—24no—
111C11×#100—42no—
112C11×C22⋊C8—22no—
113C11×C22⋊C8—22no—
114C11×C22⋊C8—22no—
115C11×C22⋊C8—22no—
116C11×#97—22no—
117C4×C8×C11—22no—
118#22482C1111yesmaximal, characteristic, direct product factor, Sylow
119C24×C11C22×C411yescharacteristic
120C24×C11C22×C412yes—
121C24×C11C22×C411yescharacteristic
122C2×D4×C11—22no—
123C2×D4×C11—22no—
124C2×D4×C11—24no—
125C2×D4×C11—22no—
126C2×D4×C11—22no—
127C2×D4×C11—21no—
128C2×D4×C11—21no—
129C2×D4×C11—42no—
130C2×D4×C11—44no—
131C2×D4×C11—82no—
132C2×D4×C11C22⋊C412yes—
133C2×D4×C11C22⋊C412yes—
134C22×C4×C11—22no—
135C22×C4×C11—22no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—22no—
141C22×C4×C11—22no—
142C22×C4×C11—22no—
143C22×C4×C11—22no—
144C22×C4×C11—82no—
145C22×C4×C11—82no—
146C22×C4×C11C22×C411yescharacteristic
147C22×C4×C11C22×C411yescharacteristic
148C22×C4×C11C22×C412yes—
149C22×C4×C11C22×C412yes—
150C22×C4×C11C22×C412yes—
151C22×C4×C11C22×C411yescharacteristic
152C22×C4×C11C22×C411yescharacteristic
153C22×C4×C11C2×D412yes—
154C22×C4×C11C2×D412yes—
155C22×C4×C11C2×D412yes—
156C22×C4×C11C2×D412yes—
157C22×C4×C11C2411yescharacteristic
158C11×M16—22no—
159C11×M16—22no—
160C11×M16—22no—
161C11×M16—22no—
162C11×M16—22no—
163C11×M16—22no—
164C11×M16—22no—
165C11×M16—44no—
166C11×M16—44no—
167C11×M16#4114yes—
168C2×C8×C11—22no—
169C2×C8×C11—22no—
170C2×C8×C11—22no—
171C2×C8×C11—22no—
172C2×C8×C11—44no—
173C2×C8×C11—44no—
174C11×C4⋊C4—24no—
175C11×C4⋊C4—22no—
176C11×C4⋊C4—22no—
177C11×C4⋊C4—24no—
178C11×C4⋊C4—22no—
179C11×C4⋊C4—22no—
180C11×C4⋊C4—22no—
181C11×C4⋊C4C22⋊C412yes—
182C11×C4⋊C4C22⋊C412yes—
183C11×C22⋊C4—24no—
184C11×C22⋊C4—24no—
185C11×C22⋊C4—22no—
186C11×C22⋊C4—22no—
187C11×C22⋊C4—24no—
188C11×C22⋊C4C22⋊C411yescharacteristic
189C11×C22⋊C4C22⋊C411yescharacteristic
190C11×C22⋊C4C22⋊C411yescharacteristic
191C11×C22⋊C4C22⋊C411yescharacteristic
192C11×C22⋊C4C22⋊C412yes—
193C11×C22⋊C4C22⋊C412yes—
194C42×C11—22no—
195C42×C11—22no—
196C42×C11C2×D412yes—
197C42×C11C2×D412yes—
198C2×#553C2×C1111yescharacteristic
199D4×M16C2×C1112yescomplemented
200#1998C2×C1112yescomplemented
201#1900C2×C1112yescomplemented
202#1900C2×C1112yescomplemented
203#1822C2×C1111yescharacteristic, complemented
204#1821C2×C1111yescharacteristic, complemented
205#1800C2×C1111yescharacteristic, complemented
206C4×#100C2×C1111yescharacteristic, complemented
207#1742C2×C1111yescharacteristic, complemented
208C2×#343C2×C1111yescharacteristic, complemented
209C23×C11—21no—
210C23×C11—21no—
211C23×C11—22no—
212C23×C11—21no—
213C23×C11—21no—
214C23×C11—22no—
215C23×C11—22no—
216C23×C11—22no—
217C23×C11—41no—
218C23×C11—41no—
219C23×C11—41no—
220C23×C11—42no—
221C23×C11—42no—
222C23×C11C2×C22⋊C412yes—
223C23×C11C2×C22⋊C411yescharacteristic
224C23×C11C2×C22⋊C411yescharacteristic
225C23×C11C23×C411yescharacteristic
226D4×C11—24no—
227D4×C11—42no—
228D4×C11—44no—
229D4×C11—44no—
230D4×C11—42no—
231D4×C11—42no—
232D4×C11—84no—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—22no—
238C2×C4×C11—22no—
239C2×C4×C11—22no—
240C2×C4×C11—22no—
241C2×C4×C11—22no—
242C2×C4×C11—22no—
243C2×C4×C11—22no—
244C2×C4×C11—22no—
245C2×C4×C11—22no—
246C2×C4×C11—22no—
247C2×C4×C11—22no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11—42no—
251C2×C4×C11—42no—
252C2×C4×C11—42no—
253C2×C4×C11—82no—
254C2×C4×C11—82no—
255C2×C4×C11—82no—
256C2×C4×C11—82no—
257C2×C4×C11C2×C22⋊C411yescharacteristic
258C2×C4×C11C2×C22⋊C411yescharacteristic
259C2×C4×C11C2×C22⋊C412yes—
260C2×C4×C11C2×C22⋊C411yescharacteristic
261C2×C4×C11C2×C22⋊C411yescharacteristic
262C2×C4×C11C2×C22⋊C412yes—
263C2×C4×C11C22×D412yes—
264C2×C4×C11C2×#4112yes—
265C2×C4×C11H(5,𝔽2)11yescharacteristic
266C2×C4×C112−1+411yescharacteristic
267C8×C11—24no—
268C8×C11—42no—
269C8×C11—42no—
270C8×C11—42no—
271C22×M16C22×C1112yes—
272C22×M16C22×C1112yes—
273#553—22no—
274#553—22no—
275#553—22no—
276#553—22no—
277C2×#126C4×C1112yes—
278C2×#125C22×C1111yescharacteristic
279C2×#123C4×C1112yes—
280C2×#121C4×C1112yes—
281C2×#121C22×C1111yescharacteristic
282C2×#121C22×C1111yescharacteristic
283C2×C4×D4C4×C1112yes—
284C2×C4×D4C22×C1111yescharacteristic
285C2×C4×D4C22×C1111yescharacteristic
286C2×#117C22×C1111yescharacteristic
287C22×C4⋊C4C22×C1111yescharacteristic
288#436—22no—
289#435—22no—
290#435—22no—
291C8×D4—22no—
292#423C22×C1112yes—
293C2×#100C22×C1112yes—
294C2×#100C22×C1112yes—
295#407C22×C1112yes—
296#407C22×C1112yes—
297C4×M16C22×C1112yes—
298#343C22×C1111yescharacteristic
299#343C22×C1111yescharacteristic
300#343C22×C1111yescharacteristic
301#343C22×C1112yes—
302#343C22×C1112yes—
303#343C22×C1112yes—
304#343C22×C1112yes—
305#343C22×C1111yescharacteristic
306C22×C11—21no—
307C22×C11—21no—
308C22×C11—21no—
309C22×C11—21no—
310C22×C11—21no—
311C22×C11—22no—
312C22×C11—22no—
313C22×C11—21no—
314C22×C11—21no—
315C22×C11—22no—
316C22×C11—42no—
317C22×C11—42no—
318C22×C11—42no—
319C22×C11—42no—
320C22×C11—42no—
321C22×C11—81no—
322C22×C11—81no—
323C22×C11—82no—
324C22×C11—82no—
325C22×C11#41312yes—
326C22×C11C22×C22⋊C411yescharacteristic
327C22×C11C4×#4111yescharacteristic
328C22×C11#52011yescharacteristic
329C4×C11—21no—
330C4×C11—22no—
331C4×C11—21no—
332C4×C11—22no—
333C4×C11—21no—
334C4×C11—21no—
335C4×C11—42no—
336C4×C11—42no—
337C4×C11—42no—
338C4×C11#54612yes—
339C4×C11#54712yes—
340C22×D4C2×C4×C1112yes—
341C22×D4C2×C4×C1112yes—
342C22×D4C2×C4×C1111yescharacteristic
343C22×D4C23×C1111yescharacteristic
344C23×C4C2×C4×C1112yes—
345C23×C4C2×C4×C1112yes—
346C23×C4C23×C1111yescharacteristic
347C23×C4C23×C1111yescharacteristic
348C2×M16—22no—
349C2×M16—22no—
350C2×M16—24no—
351C2×M16—24no—
352C2×M16—42no—
353C2×M16—42no—
354C2×M16C23×C1112yes—
355C2×M16C23×C1112yes—
356C2×M16C23×C1112yes—
357C2×M16C23×C1112yes—
358C22×C8—22no—
359C22×C8—22no—
360#126—24no—
361#126—24no—
362#125—22no—
363#125—22no—
364#123—24no—
365#123—24no—
366#121—24no—
367#121—24no—
368#121—22no—
369#121—22no—
370#121—22no—
371#121—22no—
372C4×D4—22no—
373C4×D4—22no—
374C4×D4—22no—
375C4×D4—22no—
376C4×D4—22no—
377C4×D4—22no—
378C4×D4D4×C1112yes—
379C4×D4D4×C1112yes—
380C4×D4D4×C1112yes—
381C4×D4D4×C1112yes—
382#117—22no—
383#117—22no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—22no—
386C2×C4⋊C4C2×C4×C1112yes—
387C2×C4⋊C4C2×C4×C1112yes—
388C2×C4⋊C4C2×C4×C1112yes—
389C2×C4⋊C4C2×C4×C1111yescharacteristic
390C2×C4⋊C4C23×C1111yescharacteristic
391C2×C4⋊C4C23×C1111yescharacteristic
392C2×C4⋊C4C23×C1111yescharacteristic
393C2×C22⋊C4C2×C4×C1112yes—
394C2×C22⋊C4C2×C4×C1112yes—
395C2×C22⋊C4C2×C4×C1112yes—
396C2×C22⋊C4C2×C4×C1112yes—
397C2×C22⋊C4C2×C4×C1111yescharacteristic
398C2×C22⋊C4C2×C4×C1111yescharacteristic
399C2×C42C2×C4×C1112yes—
400C2×C42C23×C1111yescharacteristic
401C4⋊C8—22no—
402C4⋊C8—22no—
403#100—24no—
404#100—42no—
405C22⋊C8—22no—
406C22⋊C8—22no—
407C22⋊C8—22no—
408C22⋊C8—22no—
409#97—22no—
410C4×C8—22no—
411C2×C11—21no—
412C2×C11—21no—
413C2×C11—22no—
414C2×C11—41no—
415C2×C11—42no—
416C2×C11—82no—
417C2×C11#233911yescharacteristic
418C2×C11C2×#41311yescharacteristic
419C2×C11#288811yescharacteristic
420C24C22×C4×C1111yescharacteristic
421C24C22×C4×C1112yes—
422C24C22×C4×C1111yescharacteristic
423C2×D4—22no—
424C2×D4—22no—
425C2×D4—24no—
426C2×D4—22no—
427C2×D4—22no—
428C2×D4—21no—
429C2×D4—21no—
430C2×D4—42no—
431C2×D4—44no—
432C2×D4—82no—
433C2×D4C11×C22⋊C412yes—
434C2×D4C11×C22⋊C412yes—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—82no—
446C22×C4—82no—
447C22×C4C22×C4×C1111yescharacteristic
448C22×C4C22×C4×C1111yescharacteristic
449C22×C4C22×C4×C1112yes—
450C22×C4C22×C4×C1112yes—
451C22×C4C22×C4×C1112yes—
452C22×C4C22×C4×C1111yescharacteristic
453C22×C4C22×C4×C1111yescharacteristic
454C22×C4C2×D4×C1112yes—
455C22×C4C2×D4×C1112yes—
456C22×C4C2×D4×C1112yes—
457C22×C4C2×D4×C1112yes—
458C22×C4C24×C1111yescharacteristic
459M16—22no—
460M16—22no—
461M16—22no—
462M16—22no—
463M16—22no—
464M16—22no—
465M16—22no—
466M16—44no—
467M16—44no—
468M16C11×#4114yes—
469C2×C8—22no—
470C2×C8—22no—
471C2×C8—22no—
472C2×C8—22no—
473C2×C8—44no—
474C2×C8—44no—
475C4⋊C4—24no—
476C4⋊C4—22no—
477C4⋊C4—22no—
478C4⋊C4—24no—
479C4⋊C4—22no—
480C4⋊C4—22no—
481C4⋊C4—22no—
482C4⋊C4C11×C22⋊C412yes—
483C4⋊C4C11×C22⋊C412yes—
484C22⋊C4—24no—
485C22⋊C4—24no—
486C22⋊C4—22no—
487C22⋊C4—22no—
488C22⋊C4—24no—
489C22⋊C4C11×C22⋊C411yescharacteristic
490C22⋊C4C11×C22⋊C411yescharacteristic
491C22⋊C4C11×C22⋊C411yescharacteristic
492C22⋊C4C11×C22⋊C411yescharacteristic
493C22⋊C4C11×C22⋊C412yes—
494C22⋊C4C11×C22⋊C412yes—
495C42—22no—
496C42—22no—
497C42C2×D4×C1112yes—
498C42C2×D4×C1112yes—
499C11#2248211yescharacteristic, direct product factor, Sylow
500C23—21no—
501C23—21no—
502C23—22no—
503C23—21no—
504C23—21no—
505C23—22no—
506C23—22no—
507C23—22no—
508C23—41no—
509C23—41no—
510C23—41no—
511C23—42no—
512C23—42no—
513C23C2×C11×C22⋊C412yes—
514C23C2×C11×C22⋊C411yescharacteristic
515C23C2×C11×C22⋊C411yescharacteristic
516C23C23×C4×C1111yescharacteristic
517D4—24no—
518D4—42no—
519D4—44no—
520D4—44no—
521D4—42no—
522D4—42no—
523D4—84no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—82no—
545C2×C4—82no—
546C2×C4—82no—
547C2×C4—82no—
548C2×C4C2×C11×C22⋊C411yescharacteristic
549C2×C4C2×C11×C22⋊C411yescharacteristic
550C2×C4C2×C11×C22⋊C412yes—
551C2×C4C2×C11×C22⋊C411yescharacteristic
552C2×C4C2×C11×C22⋊C411yescharacteristic
553C2×C4C2×C11×C22⋊C412yes—
554C2×C4C22×D4×C1112yes—
555C2×C4C2×C11×#4112yes—
556C2×C4C11×H(5,𝔽2)11yescharacteristic
557C2×C4C11×2−1+411yescharacteristic
558C8—24no—
559C8—42no—
560C8—42no—
561C8—42no—
562C22—21no—
563C22—21no—
564C22—21no—
565C22—21no—
566C22—21no—
567C22—22no—
568C22—22no—
569C22—21no—
570C22—21no—
571C22—22no—
572C22—42no—
573C22—42no—
574C22—42no—
575C22—42no—
576C22—42no—
577C22—81no—
578C22—81no—
579C22—82no—
580C22—82no—
581C22C11×#41312yes—
582C22C22×C11×C22⋊C411yescharacteristic
583C22C4×C11×#4111yescharacteristic
584C22C11×#52011yescharacteristic
585C4—21no—
586C4—22no—
587C4—21no—
588C4—22no—
589C4—21no—
590C4—21no—
591C4—42no—
592C4—42no—
593C4—42no—
594C4C11×#54612yes—
595C4C11×#54712yes—
596C2—21no—
597C2—21no—
598C2—22no—
599C2—41no—
600C2—42no—
601C2—82no—
602C2C11×#233911yescharacteristic
603C2C2×C11×#41311yescharacteristic
604C2C11×#288811yescharacteristic
subgroupG/H
center, socleC22×C11C22×C22⋊C4
commutatorC23C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#553C2
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C4×D4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. D4×C11×M16C2semidirect
3. C11×#1998C2semidirect
4. C11×#1900C2semidirect
5. C11×#1900C2semidirect
6. C11×#1822C2semidirect
7. C11×#1821C2semidirect
8. C11×#1800C2semidirect
9. C4×C11×#100C2semidirect
10. C11×#1742C2semidirect
11. C2×C11×#343C2semidirect
118. #22482C11direct (N × H)
199. D4×M16C2×C11semidirect
200. #1998C2×C11semidirect
201. #1900C2×C11semidirect
202. #1900C2×C11semidirect
203. #1822C2×C11semidirect
204. #1821C2×C11semidirect
205. #1800C2×C11semidirect
206. C4×#100C2×C11semidirect
207. #1742C2×C11semidirect
208. C2×#343C2×C11semidirect
499. C11#22482direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5532
D4×C11×M162
C11×#19982
C11×#19002
C11×#18222
C11×#18212
C11×#18002
C4×C11×#1002
C11×#17422
C2×C11×#3432
#2248211