Finite Group Databasebeta

← C11×#21503 #14598696

Subgroups — C11×#21503 #14598696

Order 2816.

1260 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#459C211yesmaximal, characteristic
2C2×C11×#442C212yesmaximal, complemented
3C4×C11×#127C211yesmaximal, characteristic, complemented
4C42×D4×C11C211yesmaximal, characteristic, complemented
5C11×#1982C211yesmaximal, characteristic, complemented
6C11×#1948C211yesmaximal, characteristic, complemented
7C11×#1926C212yesmaximal, complemented
8C11×#1879C212yesmaximal, complemented
9C11×#1802C211yesmaximal, characteristic, complemented
10C11×#1767C211yesmaximal, characteristic, complemented
11C11×#1762C212yesmaximal, complemented
12C22×C11×D8C2212yes—
13C2×C11×#127C2211yescharacteristic
14C2×C4×D4×C11—21no—
15C2×C4×D4×C11—21no—
16C2×C4×D4×C11C2211yescharacteristic
17C2×C4×D4×C11C2212yes—
18C2×C4×D4×C11C2211yescharacteristic
19C2×C4×D4×C11C2211yescharacteristic
20C22×C42×C11—21no—
21C11×#459C418yescomplemented
22C11×#442—28no—
23C2×C11×#106C2212yes—
24C2×C11×C4⋊C8C2211yescharacteristic
25C2×C11×C4⋊C8C2211yescharacteristic
26C2×C11×#102C2212yes—
27C2×C11×#102C2212yes—
28C2×C11×#102C2212yes—
29C2×C11×#102C2212yes—
30C2×C11×#97C2212yes—
31C11×#390—21no—
32C11×#390—21no—
33C11×#390C2212yes—
34C11×#384C2211yescharacteristic
35C4×C11×C4⋊C4C2211yescharacteristic
36C4×C11×C4⋊C4C2211yescharacteristic
37C4×C11×C4⋊C4C2211yescharacteristic
38C4×C11×C22⋊C4—21no—
39C4×C11×C22⋊C4—21no—
40C4×C11×C22⋊C4—21no—
41C43×C11C2211yescharacteristic
42C11×#340C2212yes—
43C11×#340C2212yes—
44C11×#336C2212yes—
45C22×D4×C11—21no—
46C22×D4×C11—21no—
47C22×D4×C11C2312yes—
48C22×D4×C11C2311yescharacteristic
49C23×C4×C11—21no—
50C23×C4×C11—21no—
51C23×C4×C11—21no—
52C23×C4×C11—22no—
53C2×C11×D8—24no—
54C2×C11×D8—24no—
55C2×C11×D8C2×C418yescomplemented
56C22×C8×C11C2312yes—
57C22×C8×C11C2312yes—
58C11×#127—22no—
59C11×#127C2×C414yescomplemented
60C4×D4×C11—22no—
61C4×D4×C11—22no—
62C4×D4×C11—24no—
63C4×D4×C11—22no—
64C4×D4×C11—22no—
65C4×D4×C11—24no—
66C4×D4×C11—44no—
67C4×D4×C11—44no—
68C4×D4×C11C2×C414yescomplemented
69C4×D4×C11D414yescomplemented
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4C2312yes—
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C22⋊C4—21no—
77C2×C11×C22⋊C4—21no—
78C2×C11×C22⋊C4—21no—
79C2×C11×C22⋊C4—22no—
80C2×C11×C22⋊C4—22no—
81C2×C11×C22⋊C4—22no—
82C2×C42×C11—21no—
83C2×C42×C11—21no—
84C2×C42×C11—21no—
85C2×C42×C11—44no—
86C2×C42×C11D411yescharacteristic
87C2×C42×C11D411yescharacteristic
88C2×C42×C11D411yescharacteristic
89C2×C42×C11D411yescharacteristic
90C2×C42×C11C2311yescharacteristic
91C2×C42×C11C2311yescharacteristic
92C2×C42×C11C2311yescharacteristic
93C11×#106—24no—
94C11×C4⋊C8—22no—
95C11×C4⋊C8C2×C414yescomplemented
96C11×#102—24no—
97C11×#102—24no—
98C11×#102—24no—
99C11×#102C2×C418yescomplemented
100C11×#97—24no—
101C11×#95—21no—
102C11×#95—21no—
103C11×#95—21no—
104#21503C1111yesmaximal, characteristic, direct product factor, Sylow
105C24×C11—21no—
106C24×C11—22no—
107C2×D4×C11—24no—
108C2×D4×C11—24no—
109C2×D4×C11—22no—
110C2×D4×C11—21no—
111C2×D4×C11—21no—
112C2×D4×C11—21no—
113C2×D4×C11—22no—
114C2×D4×C11—22no—
115C2×D4×C11—22no—
116C2×D4×C11—22no—
117C2×D4×C11—42no—
118C2×D4×C11—42no—
119C2×D4×C11—42no—
120C2×D4×C11—42no—
121C2×D4×C11C22×C414yes—
122C2×D4×C11C22×C412yes—
123C2×D4×C11C2×D412yes—
124C2×D4×C11#4112yes—
125C22×C4×C11—24no—
126C22×C4×C11—21no—
127C22×C4×C11—21no—
128C22×C4×C11—21no—
129C22×C4×C11—24no—
130C22×C4×C11—24no—
131C22×C4×C11—22no—
132C22×C4×C11—42no—
133C22×C4×C11—42no—
134C22×C4×C11—42no—
135C22×C4×C11—44no—
136C22×C4×C11—44no—
137C22×C4×C11—42no—
138C22×C4×C11—42no—
139C22×C4×C11—42no—
140C22×C4×C11—44no—
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2411yescharacteristic
148C11×D8—216no—
149C2×C8×C11—22no—
150C2×C8×C11—22no—
151C2×C8×C11—22no—
152C2×C8×C11—22no—
153C2×C8×C11—22no—
154C2×C8×C11C22×C414yes—
155C11×C4⋊C4—21no—
156C11×C4⋊C4—21no—
157C11×C4⋊C4—21no—
158C11×C4⋊C4—22no—
159C11×C4⋊C4—22no—
160C11×C4⋊C4—42no—
161C11×C4⋊C4—42no—
162C11×C4⋊C4C22×C412yes—
163C11×C4⋊C4C2×D412yes—
164C11×C4⋊C4#4112yes—
165C11×C22⋊C4—24no—
166C11×C22⋊C4—24no—
167C11×C22⋊C4—24no—
168C11×C22⋊C4—44no—
169C11×C22⋊C4—44no—
170C11×C22⋊C4—44no—
171C42×C11—22no—
172C42×C11—22no—
173C42×C11—22no—
174C42×C11—21no—
175C42×C11—21no—
176C42×C11—41no—
177C42×C11—42no—
178C42×C11—42no—
179C42×C11—42no—
180C42×C11C22×C412yes—
181C42×C11C2×D412yes—
182C42×C11#4112yes—
183C42×C11#4112yes—
184C2×#459C2×C1111yescharacteristic
185C2×#442C2×C1112yescomplemented
186C4×#127C2×C1111yescharacteristic, complemented
187C42×D4C2×C1111yescharacteristic, complemented
188#1982C2×C1111yescharacteristic, complemented
189#1948C2×C1111yescharacteristic, complemented
190#1926C2×C1112yescomplemented
191#1879C2×C1112yescomplemented
192#1802C2×C1111yescharacteristic, complemented
193#1767C2×C1111yescharacteristic, complemented
194#1762C2×C1112yescomplemented
195C23×C11—22no—
196C23×C11—22no—
197C23×C11—22no—
198C23×C11—24no—
199C23×C11—41no—
200C23×C11—41no—
201C23×C11—41no—
202C23×C11—41no—
203C23×C11—42no—
204C23×C11—42no—
205C23×C11—42no—
206C23×C11—42no—
207C23×C11—42no—
208C23×C11—42no—
209C23×C11C22×D411yescharacteristic
210D4×C11—24no—
211D4×C11—22no—
212D4×C11—24no—
213D4×C11—22no—
214D4×C11—22no—
215D4×C11—48no—
216D4×C11—42no—
217D4×C11—42no—
218D4×C11—48no—
219D4×C11C4×D414yescomplemented
220C2×C4×C11—21no—
221C2×C4×C11—21no—
222C2×C4×C11—21no—
223C2×C4×C11—21no—
224C2×C4×C11—21no—
225C2×C4×C11—21no—
226C2×C4×C11—21no—
227C2×C4×C11—21no—
228C2×C4×C11—22no—
229C2×C4×C11—22no—
230C2×C4×C11—21no—
231C2×C4×C11—22no—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
234C2×C4×C11—48no—
235C2×C4×C11—48no—
236C2×C4×C11—41no—
237C2×C4×C11—41no—
238C2×C4×C11—41no—
239C2×C4×C11—41no—
240C2×C4×C11—41no—
241C2×C4×C11—41no—
242C2×C4×C11—48no—
243C2×C4×C11—42no—
244C2×C4×C11—42no—
245C2×C4×C11—42no—
246C2×C4×C11—88no—
247C2×C4×C11C4×D412yes—
248C2×C4×C11C4×D412yes—
249C2×C4×C11#12112yes—
250C2×C4×C11#12112yes—
251C2×C4×C11AGL(1,ℤ/8)12yes—
252C2×C4×C11AGL(1,ℤ/8)12yes—
253C2×C4×C11AGL(1,ℤ/8)12yes—
254C2×C4×C11C23×C411yescharacteristic
255C2×C4×C11C22×D411yescharacteristic
256C2×C4×C11C2×#4111yescharacteristic
257C2×C4×C11C2×#4111yescharacteristic
258C2×C4×C11C2×#4111yescharacteristic
259C2×C4×C11C2×#4111yescharacteristic
260C8×C11—24no—
261C8×C11—42no—
262C22×D8C22×C1112yes—
263C2×#127C22×C1111yescharacteristic
264C2×C4×D4—21no—
265C2×C4×D4—21no—
266C2×C4×D4C22×C1112yes—
267C2×C4×D4C22×C1111yescharacteristic
268C2×C4×D4C22×C1111yescharacteristic
269C2×C4×D4C22×C1111yescharacteristic
270C22×C42—21no—
271#459C4×C1118yescomplemented
272#442—28no—
273C2×#106C22×C1112yes—
274C2×C4⋊C8C22×C1111yescharacteristic
275C2×C4⋊C8C22×C1111yescharacteristic
276C2×#102C22×C1112yes—
277C2×#102C22×C1112yes—
278C2×#102C22×C1112yes—
279C2×#102C22×C1112yes—
280C2×#97C22×C1112yes—
281#390—21no—
282#390—21no—
283#390C22×C1112yes—
284#384C22×C1111yescharacteristic
285C4×C4⋊C4C22×C1111yescharacteristic
286C4×C4⋊C4C22×C1111yescharacteristic
287C4×C4⋊C4C22×C1111yescharacteristic
288C4×C22⋊C4—21no—
289C4×C22⋊C4—21no—
290C4×C22⋊C4—21no—
291C43C22×C1111yescharacteristic
292#340C22×C1112yes—
293#340C22×C1112yes—
294#336C22×C1112yes—
295C22×C11—24no—
296C22×C11—42no—
297C22×C11—42no—
298C22×C11—42no—
299C22×C11—42no—
300C22×C11—42no—
301C22×C11—42no—
302C22×C11—44no—
303C22×C11—44no—
304C22×C11—44no—
305C22×C11—82no—
306C22×C11—82no—
307C22×C11—82no—
308C22×C11—82no—
309C22×C11C2×C4×D411yescharacteristic
310C22×C11C2×#12111yescharacteristic
311C22×C11#52511yescharacteristic
312C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
313C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
314C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
315C22×C11#57511yescharacteristic
316C4×C11—22no—
317C4×C11—22no—
318C4×C11—22no—
319C4×C11—22no—
320C4×C11—42no—
321C4×C11—41no—
322C4×C11—42no—
323C4×C11—42no—
324C4×C11—82no—
325C4×C11#44214yescomplemented
326C4×C11C2×C4×D411yescharacteristic
327C4×C11C4×#4111yescharacteristic
328C4×C11#52911yescharacteristic
329C4×C11#53211yescharacteristic
330C22×D4—21no—
331C22×D4—21no—
332C22×D4C23×C1112yes—
333C22×D4C23×C1111yescharacteristic
334C23×C4—21no—
335C23×C4—21no—
336C23×C4—21no—
337C23×C4—22no—
338C2×D8—24no—
339C2×D8—24no—
340C2×D8C2×C4×C1118yescomplemented
341C22×C8C23×C1112yes—
342C22×C8C23×C1112yes—
343#127—22no—
344#127C2×C4×C1114yescomplemented
345C4×D4—22no—
346C4×D4—22no—
347C4×D4—24no—
348C4×D4—22no—
349C4×D4—22no—
350C4×D4—24no—
351C4×D4—44no—
352C4×D4—44no—
353C4×D4C2×C4×C1114yescomplemented
354C4×D4D4×C1114yescomplemented
355C2×C4⋊C4—21no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4C23×C1112yes—
358C2×C4⋊C4C23×C1111yescharacteristic
359C2×C4⋊C4C23×C1111yescharacteristic
360C2×C4⋊C4C23×C1111yescharacteristic
361C2×C22⋊C4—21no—
362C2×C22⋊C4—21no—
363C2×C22⋊C4—21no—
364C2×C22⋊C4—22no—
365C2×C22⋊C4—22no—
366C2×C22⋊C4—22no—
367C2×C42—21no—
368C2×C42—21no—
369C2×C42—21no—
370C2×C42—44no—
371C2×C42D4×C1111yescharacteristic
372C2×C42D4×C1111yescharacteristic
373C2×C42D4×C1111yescharacteristic
374C2×C42D4×C1111yescharacteristic
375C2×C42C23×C1111yescharacteristic
376C2×C42C23×C1111yescharacteristic
377C2×C42C23×C1111yescharacteristic
378#106—24no—
379C4⋊C8—22no—
380C4⋊C8C2×C4×C1114yescomplemented
381#102—24no—
382#102—24no—
383#102—24no—
384#102C2×C4×C1118yescomplemented
385#97—24no—
386#95—21no—
387#95—21no—
388#95—21no—
389C2×C11—44no—
390C2×C11—84no—
391C2×C11C4×#12111yescharacteristic
392C2×C11C2×#44211yescharacteristic
393C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
394C2×C11#303611yescharacteristic
395C2×C11#303811yescharacteristic
396C2×C11#310911yescharacteristic
397C2×C11#311511yescharacteristic
398C24—21no—
399C24—22no—
400C2×D4—24no—
401C2×D4—24no—
402C2×D4—22no—
403C2×D4—21no—
404C2×D4—21no—
405C2×D4—21no—
406C2×D4—22no—
407C2×D4—22no—
408C2×D4—22no—
409C2×D4—22no—
410C2×D4—42no—
411C2×D4—42no—
412C2×D4—42no—
413C2×D4—42no—
414C2×D4C22×C4×C1114yes—
415C2×D4C22×C4×C1112yes—
416C2×D4C2×D4×C1112yes—
417C2×D4C11×#4112yes—
418C22×C4—24no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—24no—
423C22×C4—24no—
424C22×C4—22no—
425C22×C4—42no—
426C22×C4—42no—
427C22×C4—42no—
428C22×C4—44no—
429C22×C4—44no—
430C22×C4—42no—
431C22×C4—42no—
432C22×C4—42no—
433C22×C4—44no—
434C22×C4C2×D4×C1111yescharacteristic
435C22×C4C2×D4×C1111yescharacteristic
436C22×C4C2×D4×C1111yescharacteristic
437C22×C4C2×D4×C1111yescharacteristic
438C22×C4C2×D4×C1111yescharacteristic
439C22×C4C2×D4×C1111yescharacteristic
440C22×C4C24×C1111yescharacteristic
441D8—216no—
442C2×C8—22no—
443C2×C8—22no—
444C2×C8—22no—
445C2×C8—22no—
446C2×C8—22no—
447C2×C8C22×C4×C1114yes—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—22no—
452C4⋊C4—22no—
453C4⋊C4—42no—
454C4⋊C4—42no—
455C4⋊C4C22×C4×C1112yes—
456C4⋊C4C2×D4×C1112yes—
457C4⋊C4C11×#4112yes—
458C22⋊C4—24no—
459C22⋊C4—24no—
460C22⋊C4—24no—
461C22⋊C4—44no—
462C22⋊C4—44no—
463C22⋊C4—44no—
464C42—22no—
465C42—22no—
466C42—22no—
467C42—21no—
468C42—21no—
469C42—41no—
470C42—42no—
471C42—42no—
472C42—42no—
473C42C22×C4×C1112yes—
474C42C2×D4×C1112yes—
475C42C11×#4112yes—
476C42C11×#4112yes—
477C11#2150311yescharacteristic, direct product factor, Sylow
478C23—22no—
479C23—22no—
480C23—22no—
481C23—24no—
482C23—41no—
483C23—41no—
484C23—41no—
485C23—41no—
486C23—42no—
487C23—42no—
488C23—42no—
489C23—42no—
490C23—42no—
491C23—42no—
492C23C22×D4×C1111yescharacteristic
493D4—24no—
494D4—22no—
495D4—24no—
496D4—22no—
497D4—22no—
498D4—48no—
499D4—42no—
500D4—42no—
501D4—48no—
502D4C4×D4×C1114yescomplemented
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—21no—
514C2×C4—22no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—48no—
518C2×C4—48no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—48no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—88no—
530C2×C4C4×D4×C1112yes—
531C2×C4C4×D4×C1112yes—
532C2×C4C11×#12112yes—
533C2×C4C11×#12112yes—
534C2×C4C11×AGL(1,ℤ/8)12yes—
535C2×C4C11×AGL(1,ℤ/8)12yes—
536C2×C4C11×AGL(1,ℤ/8)12yes—
537C2×C4C23×C4×C1111yescharacteristic
538C2×C4C22×D4×C1111yescharacteristic
539C2×C4C2×C11×#4111yescharacteristic
540C2×C4C2×C11×#4111yescharacteristic
541C2×C4C2×C11×#4111yescharacteristic
542C2×C4C2×C11×#4111yescharacteristic
543C8—24no—
544C8—42no—
545C22—24no—
546C22—42no—
547C22—42no—
548C22—42no—
549C22—42no—
550C22—42no—
551C22—42no—
552C22—44no—
553C22—44no—
554C22—44no—
555C22—82no—
556C22—82no—
557C22—82no—
558C22—82no—
559C22C2×C4×D4×C1111yescharacteristic
560C22C2×C11×#12111yescharacteristic
561C22C11×#52511yescharacteristic
562C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
563C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
564C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
565C22C11×#57511yescharacteristic
566C4—22no—
567C4—22no—
568C4—22no—
569C4—22no—
570C4—42no—
571C4—42no—
572C4—42no—
573C4—41no—
574C4—82no—
575C4C11×#44214yescomplemented
576C4C2×C4×D4×C1111yescharacteristic
577C4C4×C11×#4111yescharacteristic
578C4C11×#52911yescharacteristic
579C4C11×#53211yescharacteristic
580C2—44no—
581C2—84no—
582C2C4×C11×#12111yescharacteristic
583C2C2×C11×#44211yescharacteristic
584C2C4×C11×AGL(1,ℤ/8)11yescharacteristic
585C2C11×#303611yescharacteristic
586C2C11×#303811yescharacteristic
587C2C11×#310911yescharacteristic
588C2C11×#311511yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#459C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C43×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#442C2semidirect
3. C4×C11×#127C2semidirect
4. C42×D4×C11C2semidirect
5. C11×#1982C2semidirect
6. C11×#1948C2semidirect
7. C11×#1926C2semidirect
8. C11×#1879C2semidirect
9. C11×#1802C2semidirect
10. C11×#1767C2semidirect
11. C11×#1762C2semidirect
21. C11×#459C4semidirect
55. C2×C11×D8C2×C4semidirect
59. C11×#127C2×C4semidirect
68. C4×D4×C11C2×C4semidirect
69. C4×D4×C11D4semidirect
95. C11×C4⋊C8C2×C4semidirect
99. C11×#102C2×C4semidirect
104. #21503C11direct (N × H)
185. C2×#442C2×C11semidirect
186. C4×#127C2×C11semidirect
187. C42×D4C2×C11semidirect
188. #1982C2×C11semidirect
189. #1948C2×C11semidirect
190. #1926C2×C11semidirect
191. #1879C2×C11semidirect
192. #1802C2×C11semidirect
193. #1767C2×C11semidirect
194. #1762C2×C11semidirect
219. D4×C11C4×D4semidirect
271. #459C4×C11semidirect
325. C4×C11#442semidirect
340. C2×D8C2×C4×C11semidirect
344. #127C2×C4×C11semidirect
353. C4×D4C2×C4×C11semidirect
354. C4×D4D4×C11semidirect
380. C4⋊C8C2×C4×C11semidirect
384. #102C2×C4×C11semidirect
477. C11#21503direct (N × H)
502. D4C4×D4×C11semidirect
575. C4C11×#442semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#4592
C2×C11×#4422
C4×C11×#1272
C42×D4×C112
C11×#19822
C11×#19482
C11×#19262
C11×#18792
C11×#18022
C11×#17672
C11×#17622
#2150311