Finite Group Databasebeta

← C11×#24500 #14601693

Subgroups — C11×#24500 #14601693

Order 2816.

1270 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#447C211yesmaximal, characteristic
2C2×C11×#431C211yesmaximal, characteristic, complemented
3C11×#2854C211yesmaximal, characteristic, complemented
4C2×C11×#390C211yesmaximal, characteristic, complemented
5C11×#2067C212yesmaximal, complemented
6C11×#2054C212yesmaximal, complemented
7C11×#1970C212yesmaximal, complemented
8C11×#1934C212yesmaximal, complemented
9C11×#1874C211yesmaximal, characteristic, complemented
10C11×#1852C211yesmaximal, characteristic, complemented
11C11×#1786C211yesmaximal, characteristic, complemented
12C23×D4×C11C2211yescharacteristic
13C22×C11×D8C2212yes—
14C2×C11×#123—21no—
15C2×C11×#121C2211yescharacteristic
16C22×C11×C4⋊C4C2211yescharacteristic
17C22×C11×C22⋊C4—21no—
18C22×C11×C22⋊C4—21no—
19C22×C42×C11C2211yescharacteristic
20C11×#447—24no—
21C11×#431—24no—
22C2×C11×#107C2212yescomplemented
23C2×C11×C4⋊C8C2212yescomplemented
24C2×C11×#102C2212yes—
25C2×C11×#102C2212yes—
26C2×C11×#102C2212yes—
27C2×C11×#102C2212yescomplemented
28C2×C11×C22⋊C8C2211yescharacteristic
29C2×C11×C22⋊C8C2211yescharacteristic
30C2×C4×C8×C11C2212yescomplemented
31C11×#390—21no—
32C11×#390—21no—
33C11×#390C2212yes—
34C11×#390C2212yes—
35C11×#390C2211yescharacteristic, complemented
36C11×#390C2211yescharacteristic, complemented
37C11×#389C2211yescharacteristic, complemented
38C11×#389C2211yescharacteristic, complemented
39C11×#388—21no—
40C11×#388—21no—
41C11×#386—21no—
42C11×#380C2211yescharacteristic
43C11×#340C2212yescomplemented
44C11×#340C2212yescomplemented
45C25×C11—21no—
46C22×D4×C11—24no—
47C22×D4×C11—21no—
48C22×D4×C11—21no—
49C22×D4×C11—22no—
50C22×D4×C11—22no—
51C22×D4×C11—42no—
52C22×D4×C11C2311yescharacteristic
53C22×D4×C11C2312yes—
54C23×C4×C11—21no—
55C23×C4×C11D411yescharacteristic
56C23×C4×C11D411yescharacteristic
57C23×C4×C11C2311yescharacteristic
58C2×C11×D8—24no—
59C2×C11×D8—24no—
60C2×C11×D8—42no—
61C22×C8×C11C2312yes—
62C22×C8×C11C2312yes—
63C11×#123—44no—
64C11×#121—22no—
65C11×#121—22no—
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4—21no—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4—42no—
70C2×C11×C4⋊C4C2312yes—
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C22⋊C4—21no—
75C2×C11×C22⋊C4—22no—
76C2×C11×C22⋊C4—22no—
77C2×C11×C22⋊C4—22no—
78C2×C11×C22⋊C4—22no—
79C2×C11×C22⋊C4—21no—
80C2×C11×C22⋊C4—21no—
81C2×C11×C22⋊C4—21no—
82C2×C11×C22⋊C4—21no—
83C2×C11×C22⋊C4—21no—
84C2×C11×C22⋊C4—44no—
85C2×C11×C22⋊C4—44no—
86C2×C42×C11—22no—
87C2×C42×C11—22no—
88C2×C42×C11D411yescharacteristic
89C2×C42×C11D411yescharacteristic
90C2×C42×C11C2311yescharacteristic
91C2×C42×C11C2311yescharacteristic
92C11×#107—42no—
93C11×C4⋊C8—24no—
94C11×#102—24no—
95C11×#102—24no—
96C11×#102—42no—
97C11×#102—42no—
98C11×C22⋊C8—22no—
99C11×C22⋊C8D414yes—
100C4×C8×C11—24no—
101C11×#95—21no—
102C11×#95—21no—
103C11×#95—21no—
104#24500C1111yesmaximal, characteristic, direct product factor, Sylow
105C24×C11—24no—
106C24×C11—22no—
107C24×C11—21no—
108C24×C11—42no—
109C24×C11—42no—
110C24×C11—42no—
111C24×C11—42no—
112C24×C11—42no—
113C24×C11—42no—
114C24×C11C2×D411yescharacteristic
115C2×D4×C11—24no—
116C2×D4×C11—22no—
117C2×D4×C11—21no—
118C2×D4×C11—22no—
119C2×D4×C11—22no—
120C2×D4×C11—21no—
121C2×D4×C11—22no—
122C2×D4×C11—22no—
123C2×D4×C11—22no—
124C2×D4×C11—22no—
125C2×D4×C11—48no—
126C2×D4×C11—48no—
127C2×D4×C11—42no—
128C2×D4×C11—42no—
129C2×D4×C11—42no—
130C2×D4×C11—42no—
131C2×D4×C11—42no—
132C2×D4×C11#4114yes—
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—21no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—22no—
143C22×C4×C11—41no—
144C22×C4×C11—42no—
145C22×C4×C11—42no—
146C22×C4×C11—42no—
147C22×C4×C11D814yescomplemented
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D412yes—
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11#4112yes—
155C22×C4×C11C2411yescharacteristic
156C11×D8—48no—
157C2×C8×C11—22no—
158C2×C8×C11—22no—
159C2×C8×C11—22no—
160C2×C8×C11—22no—
161C2×C8×C11—22no—
162C2×C8×C11C2×D414yes—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—22no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—22no—
167C11×C4⋊C4—22no—
168C11×C4⋊C4—22no—
169C11×C4⋊C4—42no—
170C11×C4⋊C4—42no—
171C11×C4⋊C4—42no—
172C11×C22⋊C4—42no—
173C11×C22⋊C4—44no—
174C11×C22⋊C4—42no—
175C11×C22⋊C4—42no—
176C11×C22⋊C4—44no—
177C11×C22⋊C4—44no—
178C11×C22⋊C4—42no—
179C11×C22⋊C4—42no—
180C11×C22⋊C4—42no—
181C11×C22⋊C4—44no—
182C42×C11—22no—
183C42×C11—22no—
184C42×C11—21no—
185C42×C11—21no—
186C42×C11—21no—
187C42×C11—21no—
188C2×#447C2×C1111yescharacteristic
189C2×#431C2×C1111yescharacteristic, complemented
190#2854C2×C1111yescharacteristic, complemented
191C2×#390C2×C1111yescharacteristic, complemented
192#2067C2×C1112yescomplemented
193#2054C2×C1112yescomplemented
194#1970C2×C1112yescomplemented
195#1934C2×C1112yescomplemented
196#1874C2×C1111yescharacteristic, complemented
197#1852C2×C1111yescharacteristic, complemented
198#1786C2×C1111yescharacteristic, complemented
199C23×C11—21no—
200C23×C11—21no—
201C23×C11—21no—
202C23×C11—21no—
203C23×C11—24no—
204C23×C11—48no—
205C23×C11—48no—
206C23×C11—48no—
207C23×C11—42no—
208C23×C11—42no—
209C23×C11—42no—
210C23×C11—42no—
211C23×C11—42no—
212C23×C11—42no—
213C23×C11—41no—
214C23×C11—41no—
215C23×C11—41no—
216C23×C11—41no—
217C23×C11—41no—
218C23×C11—41no—
219C23×C11—41no—
220C23×C11—84no—
221C23×C11—84no—
222C23×C11—84no—
223C23×C11—84no—
224C23×C11#12112yes—
225C23×C11C2×D812yes—
226C23×C11#13512yes—
227C23×C11C22×D411yescharacteristic
228D4×C11—24no—
229D4×C11—24no—
230D4×C11—48no—
231D4×C11—42no—
232D4×C11—42no—
233D4×C11—42no—
234D4×C11—42no—
235D4×C11—84no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—28no—
245C2×C4×C11—24no—
246C2×C4×C11—24no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—44no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—42no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11—42no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11—42no—
261C2×C4×C11—41no—
262C2×C4×C11—41no—
263C2×C4×C11—84no—
264C2×C4×C11#12112yes—
265C2×C4×C11C2×D812yes—
266C2×C4×C11C2×D812yes—
267C2×C4×C11AGL(1,ℤ/8)12yes—
268C2×C4×C11C22×D411yescharacteristic
269C2×C4×C11C2×#4112yes—
270C2×C4×C11C2×#4111yescharacteristic
271C2×C4×C11H(5,𝔽2)12yes—
272C8×C11—24no—
273C8×C11—42no—
274C23×D4C22×C1111yescharacteristic
275C22×D8C22×C1112yes—
276C2×#123—21no—
277C2×#121C22×C1111yescharacteristic
278C22×C4⋊C4C22×C1111yescharacteristic
279C22×C22⋊C4—21no—
280C22×C22⋊C4—21no—
281C22×C42C22×C1111yescharacteristic
282#447—24no—
283#431—24no—
284C2×#107C22×C1112yescomplemented
285C2×C4⋊C8C22×C1112yescomplemented
286C2×#102C22×C1112yes—
287C2×#102C22×C1112yes—
288C2×#102C22×C1112yes—
289C2×#102C22×C1112yescomplemented
290C2×C22⋊C8C22×C1111yescharacteristic
291C2×C22⋊C8C22×C1111yescharacteristic
292C2×C4×C8C22×C1112yescomplemented
293#390—21no—
294#390—21no—
295#390C22×C1112yes—
296#390C22×C1112yes—
297#390C22×C1111yescharacteristic, complemented
298#390C22×C1111yescharacteristic, complemented
299#389C22×C1111yescharacteristic, complemented
300#389C22×C1111yescharacteristic, complemented
301#388—21no—
302#388—21no—
303#386—21no—
304#380C22×C1111yescharacteristic
305#340C22×C1112yescomplemented
306#340C22×C1112yescomplemented
307C22×C11—22no—
308C22×C11—22no—
309C22×C11—22no—
310C22×C11—22no—
311C22×C11—22no—
312C22×C11—22no—
313C22×C11—44no—
314C22×C11—44no—
315C22×C11—44no—
316C22×C11—816no—
317C22×C11—82no—
318C22×C11—82no—
319C22×C11—82no—
320C22×C11—82no—
321C22×C11—81no—
322C22×C11—81no—
323C22×C11—81no—
324C22×C11—81no—
325C22×C11—81no—
326C22×C11—81no—
327C22×C11—81no—
328C22×C11#46614yes—
329C22×C11C2×#12111yescharacteristic
330C22×C11#52511yescharacteristic
331C22×C11#53511yescharacteristic
332C22×C11C22×D811yescharacteristic
333C22×C11C2×#13511yescharacteristic
334C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
335C22×C11#57511yescharacteristic
336C4×C11—22no—
337C4×C11—22no—
338C4×C11—22no—
339C4×C11—22no—
340C4×C11—41no—
341C4×C11—81no—
342C4×C11—81no—
343C4×C11—82no—
344C4×C11—81no—
345C4×C11#54612yes—
346C4×C11#55112yes—
347C25—21no—
348C22×D4—24no—
349C22×D4—21no—
350C22×D4—21no—
351C22×D4—22no—
352C22×D4—22no—
353C22×D4—42no—
354C22×D4C23×C1111yescharacteristic
355C22×D4C23×C1112yes—
356C23×C4—21no—
357C23×C4D4×C1111yescharacteristic
358C23×C4D4×C1111yescharacteristic
359C23×C4C23×C1111yescharacteristic
360C2×D8—24no—
361C2×D8—24no—
362C2×D8—42no—
363C22×C8C23×C1112yes—
364C22×C8C23×C1112yes—
365#123—44no—
366#121—22no—
367#121—22no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—42no—
372C2×C4⋊C4C23×C1112yes—
373C2×C4⋊C4C23×C1111yescharacteristic
374C2×C4⋊C4C23×C1111yescharacteristic
375C2×C4⋊C4C23×C1111yescharacteristic
376C2×C22⋊C4—21no—
377C2×C22⋊C4—22no—
378C2×C22⋊C4—22no—
379C2×C22⋊C4—22no—
380C2×C22⋊C4—22no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—21no—
384C2×C22⋊C4—21no—
385C2×C22⋊C4—21no—
386C2×C22⋊C4—44no—
387C2×C22⋊C4—44no—
388C2×C42—22no—
389C2×C42—22no—
390C2×C42D4×C1111yescharacteristic
391C2×C42D4×C1111yescharacteristic
392C2×C42C23×C1111yescharacteristic
393C2×C42C23×C1111yescharacteristic
394#107—42no—
395C4⋊C8—24no—
396#102—24no—
397#102—24no—
398#102—42no—
399#102—42no—
400C22⋊C8—22no—
401C22⋊C8D4×C1114yes—
402C4×C8—24no—
403#95—21no—
404#95—21no—
405#95—21no—
406C2×C11—24no—
407C2×C11—84no—
408C2×C11—161no—
409C2×C11#241111yescharacteristic
410C2×C11C2×#46611yescharacteristic
411C2×C11#305511yescharacteristic
412C2×C11#310011yescharacteristic
413C2×C11#310511yescharacteristic
414C2×C11#320511yescharacteristic
415C2×C11#321111yescharacteristic
416C24—24no—
417C24—22no—
418C24—21no—
419C24—42no—
420C24—42no—
421C24—42no—
422C24—42no—
423C24—42no—
424C24—42no—
425C24C2×D4×C1111yescharacteristic
426C2×D4—24no—
427C2×D4—22no—
428C2×D4—21no—
429C2×D4—22no—
430C2×D4—22no—
431C2×D4—21no—
432C2×D4—22no—
433C2×D4—22no—
434C2×D4—22no—
435C2×D4—22no—
436C2×D4—48no—
437C2×D4—48no—
438C2×D4—42no—
439C2×D4—42no—
440C2×D4—42no—
441C2×D4—42no—
442C2×D4—42no—
443C2×D4C11×#4114yes—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—22no—
454C22×C4—41no—
455C22×C4—42no—
456C22×C4—42no—
457C22×C4—42no—
458C22×C4C11×D814yescomplemented
459C22×C4C2×D4×C1111yescharacteristic
460C22×C4C2×D4×C1111yescharacteristic
461C22×C4C2×D4×C1112yes—
462C22×C4C2×D4×C1111yescharacteristic
463C22×C4C2×D4×C1111yescharacteristic
464C22×C4C2×D4×C1111yescharacteristic
465C22×C4C11×#4112yes—
466C22×C4C24×C1111yescharacteristic
467D8—48no—
468C2×C8—22no—
469C2×C8—22no—
470C2×C8—22no—
471C2×C8—22no—
472C2×C8—22no—
473C2×C8C2×D4×C1114yes—
474C4⋊C4—21no—
475C4⋊C4—22no—
476C4⋊C4—21no—
477C4⋊C4—22no—
478C4⋊C4—22no—
479C4⋊C4—22no—
480C4⋊C4—42no—
481C4⋊C4—42no—
482C4⋊C4—42no—
483C22⋊C4—44no—
484C22⋊C4—42no—
485C22⋊C4—42no—
486C22⋊C4—42no—
487C22⋊C4—44no—
488C22⋊C4—44no—
489C22⋊C4—42no—
490C22⋊C4—42no—
491C22⋊C4—44no—
492C22⋊C4—42no—
493C42—22no—
494C42—22no—
495C42—21no—
496C42—21no—
497C42—21no—
498C42—21no—
499C11#2450011yescharacteristic, direct product factor, Sylow
500C23—21no—
501C23—21no—
502C23—21no—
503C23—21no—
504C23—24no—
505C23—48no—
506C23—48no—
507C23—48no—
508C23—42no—
509C23—42no—
510C23—42no—
511C23—42no—
512C23—42no—
513C23—42no—
514C23—41no—
515C23—41no—
516C23—41no—
517C23—41no—
518C23—41no—
519C23—41no—
520C23—41no—
521C23—84no—
522C23—84no—
523C23—84no—
524C23—84no—
525C23C11×#12112yes—
526C23C2×C11×D812yes—
527C23C11×#13512yes—
528C23C22×D4×C1111yescharacteristic
529D4—24no—
530D4—24no—
531D4—48no—
532D4—42no—
533D4—42no—
534D4—42no—
535D4—42no—
536D4—84no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—28no—
546C2×C4—24no—
547C2×C4—24no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—44no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—42no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—42no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—42no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—84no—
565C2×C4C11×#12112yes—
566C2×C4C2×C11×D812yes—
567C2×C4C2×C11×D812yes—
568C2×C4C11×AGL(1,ℤ/8)12yes—
569C2×C4C22×D4×C1111yescharacteristic
570C2×C4C2×C11×#4112yes—
571C2×C4C2×C11×#4111yescharacteristic
572C2×C4C11×H(5,𝔽2)12yes—
573C8—24no—
574C8—42no—
575C22—22no—
576C22—22no—
577C22—22no—
578C22—22no—
579C22—22no—
580C22—22no—
581C22—44no—
582C22—44no—
583C22—44no—
584C22—816no—
585C22—82no—
586C22—82no—
587C22—82no—
588C22—82no—
589C22—81no—
590C22—81no—
591C22—81no—
592C22—81no—
593C22—81no—
594C22—81no—
595C22—81no—
596C22C11×#46614yes—
597C22C2×C11×#12111yescharacteristic
598C22C11×#52511yescharacteristic
599C22C11×#53511yescharacteristic
600C22C22×C11×D811yescharacteristic
601C22C2×C11×#13511yescharacteristic
602C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
603C22C11×#57511yescharacteristic
604C4—22no—
605C4—22no—
606C4—22no—
607C4—22no—
608C4—41no—
609C4—82no—
610C4—81no—
611C4—81no—
612C4—81no—
613C4C11×#54612yes—
614C4C11×#55112yes—
615C2—24no—
616C2—84no—
617C2—161no—
618C2C11×#241111yescharacteristic
619C2C2×C11×#46611yescharacteristic
620C2C11×#305511yescharacteristic
621C2C11×#310011yescharacteristic
622C2C11×#310511yescharacteristic
623C2C11×#320511yescharacteristic
624C2C11×#321111yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#447C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C22×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#431C2semidirect
3. C11×#2854C2semidirect
4. C2×C11×#390C2semidirect
5. C11×#2067C2semidirect
6. C11×#2054C2semidirect
7. C11×#1970C2semidirect
8. C11×#1934C2semidirect
9. C11×#1874C2semidirect
10. C11×#1852C2semidirect
11. C11×#1786C2semidirect
22. C2×C11×#107C22semidirect
23. C2×C11×C4⋊C8C22semidirect
27. C2×C11×#102C22semidirect
30. C2×C4×C8×C11C22semidirect
35. C11×#390C22semidirect
36. C11×#390C22semidirect
37. C11×#389C22semidirect
38. C11×#389C22semidirect
43. C11×#340C22semidirect
44. C11×#340C22semidirect
104. #24500C11direct (N × H)
147. C22×C4×C11D8semidirect
189. C2×#431C2×C11semidirect
190. #2854C2×C11semidirect
191. C2×#390C2×C11semidirect
192. #2067C2×C11semidirect
193. #2054C2×C11semidirect
194. #1970C2×C11semidirect
195. #1934C2×C11semidirect
196. #1874C2×C11semidirect
197. #1852C2×C11semidirect
198. #1786C2×C11semidirect
284. C2×#107C22×C11semidirect
285. C2×C4⋊C8C22×C11semidirect
289. C2×#102C22×C11semidirect
292. C2×C4×C8C22×C11semidirect
297. #390C22×C11semidirect
298. #390C22×C11semidirect
299. #389C22×C11semidirect
300. #389C22×C11semidirect
305. #340C22×C11semidirect
306. #340C22×C11semidirect
458. C22×C4C11×D8semidirect
499. C11#24500direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4472
C2×C11×#4312
C11×#28542
C2×C11×#3902
C11×#20672
C11×#20542
C11×#19702
C11×#19342
C11×#18742
C11×#18522
C11×#17862
#2450011