Finite Group Databasebeta

← C11×#24626 #14601819

Subgroups — C11×#24626 #14601819

Order 2816.

1110 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#459C211yesmaximal, characteristic, complemented
2C2×C4×C11×D8C211yesmaximal, characteristic, complemented
3C11×#2541C211yesmaximal, characteristic, complemented
4C11×#2354C211yesmaximal, characteristic, complemented
5C11×#2054C212yesmaximal, complemented
6C11×#2011C212yesmaximal, complemented
7C11×#1982C212yesmaximal, complemented
8C11×#1957C211yesmaximal, characteristic, complemented
9C11×#1939C211yesmaximal, characteristic, complemented
10C11×#1925C212yesmaximal, complemented
11C11×#1802C211yesmaximal, characteristic, complemented
12C22×C11×D8C2211yescharacteristic
13C22×C11×D8C2212yes—
14C2×C11×#127C2211yescharacteristic
15C2×C11×#127C2212yes—
16C2×C11×#121—21no—
17C2×C11×#121—21no—
18C2×C4×D4×C11C2211yescharacteristic
19C2×C4×D4×C11C2211yescharacteristic
20C2×C11×#117—21no—
21C11×#459—24no—
22C4×C11×D8—24no—
23C2×C11×#107C2211yescharacteristic
24C2×C11×C4⋊C8C2211yescharacteristic
25C2×C11×C4⋊C8C2212yes—
26C2×C11×#102C2211yescharacteristic
27C2×C11×#102C2211yescharacteristic
28C2×C11×#102C2212yes—
29C2×C11×#102C2212yes—
30C2×C11×#102C2212yes—
31C2×C11×#102C2212yes—
32C2×C4×C8×C11C2211yescharacteristic
33C11×#392—22no—
34C11×#390C2212yes—
35C11×#390C2212yes—
36C11×#388—22no—
37C11×#384C2211yescharacteristic
38C11×#380—21no—
39C4×C11×C4⋊C4C2212yes—
40C4×C11×C4⋊C4C2211yescharacteristic
41C11×#340C2212yes—
42C11×#336C2212yes—
43C22×D4×C11—21no—
44C22×D4×C11—22no—
45C22×D4×C11—22no—
46C22×D4×C11—21no—
47C22×D4×C11C2312yes—
48C22×D4×C11C2311yescharacteristic
49C22×D4×C11C2311yescharacteristic
50C23×C4×C11—21no—
51C23×C4×C11—21no—
52C2×C11×D8—22no—
53C2×C11×D8—22no—
54C2×C11×D8—24no—
55C2×C11×D8—22no—
56C2×C11×D8—42no—
57C2×C11×D8—42no—
58C22×C8×C11C2312yes—
59C22×C8×C11C2311yescharacteristic
60C22×C8×C11C2311yescharacteristic
61C11×#127—24no—
62C11×#127—22no—
63C11×#127—22no—
64C11×#127—42no—
65C11×#121—44no—
66C11×#121—44no—
67C4×D4×C11—22no—
68C4×D4×C11—22no—
69C4×D4×C11—22no—
70C4×D4×C11D414yescomplemented
71C11×#117—44no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4D411yescharacteristic
75C2×C11×C4⋊C4D411yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C4⋊C4C2312yes—
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C11×C22⋊C4—21no—
80C2×C11×C22⋊C4—22no—
81C2×C11×C22⋊C4—21no—
82C2×C11×C22⋊C4—22no—
83C2×C11×C22⋊C4—22no—
84C2×C11×C22⋊C4—22no—
85C2×C42×C11—22no—
86C2×C42×C11C2312yes—
87C2×C42×C11C2311yescharacteristic
88C11×#107—22no—
89C11×C4⋊C8—22no—
90C11×C4⋊C8—42no—
91C11×#102—22no—
92C11×#102—24no—
93C11×#102—22no—
94C11×#102—24no—
95C11×#102—42no—
96C11×#102—42no—
97C4×C8×C11—22no—
98C11×#95—22no—
99C11×#95D412yes—
100#24626C1111yesmaximal, characteristic, direct product factor, Sylow
101C24×C11—21no—
102C24×C11—21no—
103C24×C11—22no—
104C2×D4×C11—21no—
105C2×D4×C11—22no—
106C2×D4×C11—21no—
107C2×D4×C11—21no—
108C2×D4×C11—21no—
109C2×D4×C11—21no—
110C2×D4×C11—21no—
111C2×D4×C11—22no—
112C2×D4×C11—22no—
113C2×D4×C11—22no—
114C2×D4×C11—21no—
115C2×D4×C11—21no—
116C2×D4×C11—21no—
117C2×D4×C11—21no—
118C2×D4×C11—22no—
119C2×D4×C11—22no—
120C2×D4×C11—44no—
121C2×D4×C11—44no—
122C2×D4×C11—44no—
123C2×D4×C11—42no—
124C2×D4×C11—42no—
125C2×D4×C11—44no—
126C2×D4×C11—42no—
127C2×D4×C11—42no—
128C2×D4×C11—81no—
129C2×D4×C11—82no—
130C2×D4×C11—81no—
131C2×D4×C11—82no—
132C2×D4×C11C2×D412yes—
133C2×D4×C11#4112yes—
134C22×C4×C11—21no—
135C22×C4×C11—24no—
136C22×C4×C11—22no—
137C22×C4×C11—21no—
138C22×C4×C11—42no—
139C22×C4×C11—42no—
140C22×C4×C11—42no—
141C22×C4×C11—42no—
142C22×C4×C11—42no—
143C22×C4×C11C2×D412yes—
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D412yes—
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2411yescharacteristic
148C11×D8—28no—
149C11×D8—48no—
150C2×C8×C11—21no—
151C2×C8×C11—21no—
152C2×C8×C11—22no—
153C2×C8×C11—21no—
154C2×C8×C11—21no—
155C2×C8×C11—22no—
156C2×C8×C11—21no—
157C2×C8×C11—22no—
158C2×C8×C11#4112yes—
159C11×C4⋊C4—22no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—22no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—22no—
165C11×C4⋊C4—42no—
166C11×C4⋊C4—81no—
167C11×C4⋊C4D814yescomplemented
168C11×C4⋊C4C2×D412yes—
169C11×C22⋊C4—24no—
170C11×C22⋊C4—44no—
171C11×C22⋊C4—42no—
172C11×C22⋊C4—44no—
173C11×C22⋊C4—44no—
174C11×C22⋊C4—82no—
175C42×C11—22no—
176C42×C11—22no—
177C42×C11—44no—
178C42×C11C2×D412yes—
179C42×C11#4112yes—
180C2×#459C2×C1111yescharacteristic, complemented
181C2×C4×D8C2×C1111yescharacteristic, complemented
182#2541C2×C1111yescharacteristic, complemented
183#2354C2×C1111yescharacteristic, complemented
184#2054C2×C1112yescomplemented
185#2011C2×C1112yescomplemented
186#1982C2×C1112yescomplemented
187#1957C2×C1111yescharacteristic, complemented
188#1939C2×C1111yescharacteristic, complemented
189#1925C2×C1112yescomplemented
190#1802C2×C1111yescharacteristic, complemented
191C23×C11—22no—
192C23×C11—22no—
193C23×C11—41no—
194C23×C11—41no—
195C23×C11—41no—
196C23×C11—41no—
197C23×C11—41no—
198C23×C11—41no—
199C23×C11—41no—
200C23×C11—41no—
201C23×C11—41no—
202C23×C11—41no—
203C23×C11—41no—
204C23×C11—41no—
205C23×C11—42no—
206C23×C11—42no—
207C23×C11—42no—
208C23×C11—42no—
209C23×C11—42no—
210C23×C11—42no—
211C23×C11—42no—
212C23×C11C22×D411yescharacteristic
213D4×C11—22no—
214D4×C11—22no—
215D4×C11—22no—
216D4×C11—22no—
217D4×C11—42no—
218D4×C11—41no—
219D4×C11—42no—
220D4×C11—41no—
221D4×C11—42no—
222D4×C11—41no—
223D4×C11—41no—
224D4×C11—42no—
225D4×C11—88no—
226D4×C11—84no—
227D4×C11—88no—
228D4×C11—84no—
229C2×C4×C11—22no—
230C2×C4×C11—21no—
231C2×C4×C11—22no—
232C2×C4×C11—21no—
233C2×C4×C11—22no—
234C2×C4×C11—22no—
235C2×C4×C11—22no—
236C2×C4×C11—22no—
237C2×C4×C11—41no—
238C2×C4×C11—41no—
239C2×C4×C11—48no—
240C2×C4×C11—41no—
241C2×C4×C11—42no—
242C2×C4×C11—42no—
243C2×C4×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11—42no—
246C2×C4×C11—84no—
247C2×C4×C11#12112yes—
248C2×C4×C11#12112yes—
249C2×C4×C11C2×D814yes—
250C2×C4×C11C2×D812yes—
251C2×C4×C11AGL(1,ℤ/8)12yes—
252C2×C4×C11C22×D411yescharacteristic
253C2×C4×C11C2×#4111yescharacteristic
254C2×C4×C11C2×#4111yescharacteristic
255C2×C4×C11C2×#4111yescharacteristic
256C2×C4×C11H(5,𝔽2)11yescharacteristic
257C2×C4×C11H(5,𝔽2)11yescharacteristic
258C8×C11—22no—
259C8×C11—41no—
260C8×C11—42no—
261C22×D8C22×C1111yescharacteristic
262C22×D8C22×C1112yes—
263C2×#127C22×C1111yescharacteristic
264C2×#127C22×C1112yes—
265C2×#121—21no—
266C2×#121—21no—
267C2×C4×D4C22×C1111yescharacteristic
268C2×C4×D4C22×C1111yescharacteristic
269C2×#117—21no—
270#459—24no—
271C4×D8—24no—
272C2×#107C22×C1111yescharacteristic
273C2×C4⋊C8C22×C1111yescharacteristic
274C2×C4⋊C8C22×C1112yes—
275C2×#102C22×C1111yescharacteristic
276C2×#102C22×C1111yescharacteristic
277C2×#102C22×C1112yes—
278C2×#102C22×C1112yes—
279C2×#102C22×C1112yes—
280C2×#102C22×C1112yes—
281C2×C4×C8C22×C1111yescharacteristic
282#392—22no—
283#390C22×C1112yes—
284#390C22×C1112yes—
285#388—22no—
286#384C22×C1111yescharacteristic
287#380—21no—
288C4×C4⋊C4C22×C1112yes—
289C4×C4⋊C4C22×C1111yescharacteristic
290#340C22×C1112yes—
291#336C22×C1112yes—
292C22×C11—42no—
293C22×C11—42no—
294C22×C11—42no—
295C22×C11—42no—
296C22×C11—42no—
297C22×C11—42no—
298C22×C11—81no—
299C22×C11—81no—
300C22×C11—81no—
301C22×C11—81no—
302C22×C11—81no—
303C22×C11—81no—
304C22×C11—81no—
305C22×C11—81no—
306C22×C11—82no—
307C22×C11—82no—
308C22×C11—82no—
309C22×C11—82no—
310C22×C11—82no—
311C22×C11—82no—
312C22×C11—82no—
313C22×C11C2×#12111yescharacteristic
314C22×C11#54611yescharacteristic
315C22×C11#55011yescharacteristic
316C22×C11C22×D811yescharacteristic
317C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
318C22×C11#57611yescharacteristic
319C22×C11#57711yescharacteristic
320C4×C11—24no—
321C4×C11—22no—
322C4×C11—42no—
323C4×C11—42no—
324C4×C11—82no—
325C4×C11—81no—
326C4×C11#45914yes—
327C4×C11#52511yescharacteristic
328C4×C11#53511yescharacteristic
329C4×C11#55311yescharacteristic
330C4×C11#55511yescharacteristic
331C22×D4—21no—
332C22×D4—22no—
333C22×D4—22no—
334C22×D4—21no—
335C22×D4C23×C1112yes—
336C22×D4C23×C1111yescharacteristic
337C22×D4C23×C1111yescharacteristic
338C23×C4—21no—
339C23×C4—21no—
340C2×D8—22no—
341C2×D8—22no—
342C2×D8—24no—
343C2×D8—22no—
344C2×D8—42no—
345C2×D8—42no—
346C22×C8C23×C1112yes—
347C22×C8C23×C1111yescharacteristic
348C22×C8C23×C1111yescharacteristic
349#127—24no—
350#127—22no—
351#127—22no—
352#127—42no—
353#121—44no—
354#121—44no—
355C4×D4—22no—
356C4×D4—22no—
357C4×D4—22no—
358C4×D4D4×C1114yescomplemented
359#117—44no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4D4×C1111yescharacteristic
363C2×C4⋊C4D4×C1111yescharacteristic
364C2×C4⋊C4C23×C1111yescharacteristic
365C2×C4⋊C4C23×C1112yes—
366C2×C4⋊C4C23×C1111yescharacteristic
367C2×C22⋊C4—21no—
368C2×C22⋊C4—22no—
369C2×C22⋊C4—21no—
370C2×C22⋊C4—22no—
371C2×C22⋊C4—22no—
372C2×C22⋊C4—22no—
373C2×C42—22no—
374C2×C42C23×C1112yes—
375C2×C42C23×C1111yescharacteristic
376#107—22no—
377C4⋊C8—22no—
378C4⋊C8—42no—
379#102—22no—
380#102—24no—
381#102—22no—
382#102—24no—
383#102—42no—
384#102—42no—
385C4×C8—22no—
386#95—22no—
387#95D4×C1112yes—
388C2×C11—82no—
389C2×C11—82no—
390C2×C11—162no—
391C2×C11#241411yescharacteristic
392C2×C11C2×#45911yescharacteristic
393C2×C11#304511yescharacteristic
394C2×C11#329411yescharacteristic
395C2×C11#332511yescharacteristic
396C2×C11#339111yescharacteristic
397C2×C11#339711yescharacteristic
398C24—21no—
399C24—21no—
400C24—22no—
401C2×D4—21no—
402C2×D4—22no—
403C2×D4—21no—
404C2×D4—21no—
405C2×D4—21no—
406C2×D4—21no—
407C2×D4—21no—
408C2×D4—22no—
409C2×D4—22no—
410C2×D4—22no—
411C2×D4—21no—
412C2×D4—21no—
413C2×D4—21no—
414C2×D4—21no—
415C2×D4—22no—
416C2×D4—22no—
417C2×D4—44no—
418C2×D4—44no—
419C2×D4—44no—
420C2×D4—42no—
421C2×D4—42no—
422C2×D4—44no—
423C2×D4—42no—
424C2×D4—42no—
425C2×D4—81no—
426C2×D4—82no—
427C2×D4—81no—
428C2×D4—82no—
429C2×D4C2×D4×C1112yes—
430C2×D4C11×#4112yes—
431C22×C4—21no—
432C22×C4—24no—
433C22×C4—22no—
434C22×C4—21no—
435C22×C4—42no—
436C22×C4—42no—
437C22×C4—42no—
438C22×C4—42no—
439C22×C4—42no—
440C22×C4C2×D4×C1112yes—
441C22×C4C2×D4×C1111yescharacteristic
442C22×C4C2×D4×C1112yes—
443C22×C4C2×D4×C1111yescharacteristic
444C22×C4C24×C1111yescharacteristic
445D8—28no—
446D8—48no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—22no—
451C2×C8—21no—
452C2×C8—22no—
453C2×C8—21no—
454C2×C8—22no—
455C2×C8C11×#4112yes—
456C4⋊C4—22no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—22no—
460C4⋊C4—21no—
461C4⋊C4—22no—
462C4⋊C4—42no—
463C4⋊C4—81no—
464C4⋊C4C11×D814yescomplemented
465C4⋊C4C2×D4×C1112yes—
466C22⋊C4—24no—
467C22⋊C4—44no—
468C22⋊C4—42no—
469C22⋊C4—44no—
470C22⋊C4—44no—
471C22⋊C4—82no—
472C42—22no—
473C42—22no—
474C42—44no—
475C42C2×D4×C1112yes—
476C42C11×#4112yes—
477C11#2462611yescharacteristic, direct product factor, Sylow
478C23—22no—
479C23—22no—
480C23—41no—
481C23—41no—
482C23—41no—
483C23—41no—
484C23—41no—
485C23—41no—
486C23—41no—
487C23—41no—
488C23—41no—
489C23—41no—
490C23—41no—
491C23—41no—
492C23—42no—
493C23—42no—
494C23—42no—
495C23—42no—
496C23—42no—
497C23—42no—
498C23—42no—
499C23C22×D4×C1111yescharacteristic
500D4—22no—
501D4—22no—
502D4—22no—
503D4—22no—
504D4—42no—
505D4—41no—
506D4—42no—
507D4—41no—
508D4—42no—
509D4—41no—
510D4—41no—
511D4—42no—
512D4—88no—
513D4—84no—
514D4—88no—
515D4—84no—
516C2×C4—22no—
517C2×C4—21no—
518C2×C4—22no—
519C2×C4—21no—
520C2×C4—22no—
521C2×C4—22no—
522C2×C4—22no—
523C2×C4—22no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—48no—
527C2×C4—41no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—42no—
533C2×C4—84no—
534C2×C4C11×#12112yes—
535C2×C4C11×#12112yes—
536C2×C4C2×C11×D814yes—
537C2×C4C2×C11×D812yes—
538C2×C4C11×AGL(1,ℤ/8)12yes—
539C2×C4C22×D4×C1111yescharacteristic
540C2×C4C2×C11×#4111yescharacteristic
541C2×C4C2×C11×#4111yescharacteristic
542C2×C4C2×C11×#4111yescharacteristic
543C2×C4C11×H(5,𝔽2)11yescharacteristic
544C2×C4C11×H(5,𝔽2)11yescharacteristic
545C8—22no—
546C8—42no—
547C8—41no—
548C22—42no—
549C22—42no—
550C22—42no—
551C22—42no—
552C22—42no—
553C22—42no—
554C22—81no—
555C22—81no—
556C22—81no—
557C22—81no—
558C22—81no—
559C22—81no—
560C22—81no—
561C22—81no—
562C22—82no—
563C22—82no—
564C22—82no—
565C22—82no—
566C22—82no—
567C22—82no—
568C22—82no—
569C22C2×C11×#12111yescharacteristic
570C22C11×#54611yescharacteristic
571C22C11×#55011yescharacteristic
572C22C22×C11×D811yescharacteristic
573C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
574C22C11×#57611yescharacteristic
575C22C11×#57711yescharacteristic
576C4—24no—
577C4—22no—
578C4—42no—
579C4—42no—
580C4—81no—
581C4—82no—
582C4C11×#45914yes—
583C4C11×#52511yescharacteristic
584C4C11×#53511yescharacteristic
585C4C11×#55311yescharacteristic
586C4C11×#55511yescharacteristic
587C2—82no—
588C2—82no—
589C2—162no—
590C2C11×#241411yescharacteristic
591C2C2×C11×#45911yescharacteristic
592C2C11×#304511yescharacteristic
593C2C11×#329411yescharacteristic
594C2C11×#332511yescharacteristic
595C2C11×#339111yescharacteristic
596C2C11×#339711yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C4×C11×C4⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#459C2semidirect
2. C2×C4×C11×D8C2semidirect
3. C11×#2541C2semidirect
4. C11×#2354C2semidirect
5. C11×#2054C2semidirect
6. C11×#2011C2semidirect
7. C11×#1982C2semidirect
8. C11×#1957C2semidirect
9. C11×#1939C2semidirect
10. C11×#1925C2semidirect
11. C11×#1802C2semidirect
70. C4×D4×C11D4semidirect
100. #24626C11direct (N × H)
167. C11×C4⋊C4D8semidirect
180. C2×#459C2×C11semidirect
181. C2×C4×D8C2×C11semidirect
182. #2541C2×C11semidirect
183. #2354C2×C11semidirect
184. #2054C2×C11semidirect
185. #2011C2×C11semidirect
186. #1982C2×C11semidirect
187. #1957C2×C11semidirect
188. #1939C2×C11semidirect
189. #1925C2×C11semidirect
190. #1802C2×C11semidirect
358. C4×D4D4×C11semidirect
464. C4⋊C4C11×D8semidirect
477. C11#24626direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4592
C2×C4×C11×D82
C11×#25412
C11×#23542
C11×#20542
C11×#20112
C11×#19822
C11×#19572
C11×#19392
C11×#19252
C11×#18022
#2462611