Finite Group Databasebeta

← C11×#24243 #14601436

Subgroups — C11×#24243 #14601436

Order 2816.

1406 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×D4×Q8×C11C211yesmaximal, characteristic
2C2×C11×#462C211yesmaximal, characteristic, complemented
3C2×C11×#451C212yesmaximal, complemented
4C2×C4×C11×Q16C211yesmaximal, characteristic, complemented
5C11×#2538C211yesmaximal, characteristic
6C11×#2036C212yesmaximal, complemented
7C11×#2001C212yesmaximal, complemented
8C11×#1956C211yesmaximal, characteristic, complemented
9C11×#1954C211yesmaximal, characteristic
10C11×#1803C211yesmaximal, characteristic, complemented
11C11×#1787C212yesmaximal, complemented
12C23×Q8×C11C2212yes—
13C22×C11×Q16C2212yes—
14C22×C11×Q16C2211yescharacteristic
15D4×Q8×C11—24no—
16D4×Q8×C11—24no—
17C2×C11×C4⋊Q8—21no—
18C2×C11×C4⋊Q8C2211yescharacteristic
19C2×C11×C22⋊Q8—22no—
20C2×C11×C22⋊Q8C2212yes—
21C2×C11×C22⋊Q8C2212yes—
22C2×C4×Q8×C11C2211yescharacteristic
23C2×C4×Q8×C11C2211yescharacteristic
24C2×C4×D4×C11—21no—
25C2×C4×D4×C11C2211yescharacteristic
26C11×#462—24no—
27C11×#451—28no—
28C4×C11×Q16—24no—
29C2×C11×#107C2211yescharacteristic
30C2×C11×C4⋊C8C2211yescharacteristic
31C2×C11×#103C2211yescharacteristic
32C2×C11×#103C2211yescharacteristic
33C2×C11×#103C2212yes—
34C2×C11×#103C2212yes—
35C2×C11×#103C2212yes—
36C2×C11×#103C2212yes—
37C2×C11×C22⋊C8C2212yes—
38C2×C11×C22⋊C8C2212yes—
39C2×C4×C8×C11C2211yescharacteristic
40C11×#396—22no—
41C11×#390—21no—
42C11×#389—21no—
43C11×#384C2211yescharacteristic
44C11×#380C2212yes—
45C11×#340C2212yes—
46C22×Q8×C11—24no—
47C22×Q8×C11—24no—
48C22×Q8×C11—22no—
49C22×Q8×C11—24no—
50C22×Q8×C11—24no—
51C22×Q8×C11—42no—
52C22×Q8×C11—42no—
53C22×Q8×C11C2311yescharacteristic
54C22×Q8×C11C2312yes—
55C22×Q8×C11C2311yescharacteristic
56C22×D4×C11D411yescharacteristic
57C23×C4×C11—22no—
58C23×C4×C11C2312yes—
59C2×C11×Q16—22no—
60C2×C11×Q16—22no—
61C2×C11×Q16—24no—
62C2×C11×Q16—24no—
63C2×C11×Q16—42no—
64C2×C11×Q16D414yescomplemented
65C22×C8×C11C2312yes—
66C22×C8×C11C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C11×C4⋊Q8—28no—
69C11×C4⋊Q8—22no—
70C11×C4⋊Q8D414yes—
71C11×C22⋊Q8—216no—
72C11×C22⋊Q8—24no—
73C11×C22⋊Q8—24no—
74C11×C22⋊Q8—24no—
75C11×C22⋊Q8—42no—
76C4×Q8×C11—22no—
77C4×Q8×C11—22no—
78C4×Q8×C11—22no—
79C4×Q8×C11D414yes—
80C4×D4×C11—28no—
81C4×D4×C11—22no—
82C4×D4×C11—22no—
83C2×C11×C4⋊C4—21no—
84C2×C11×C4⋊C4—21no—
85C2×C11×C4⋊C4—21no—
86C2×C11×C4⋊C4—22no—
87C2×C11×C4⋊C4—21no—
88C2×C11×C4⋊C4—21no—
89C2×C11×C4⋊C4—22no—
90C2×C11×C4⋊C4—21no—
91C2×C11×C4⋊C4D411yescharacteristic
92C2×C11×C4⋊C4C2312yes—
93C2×C11×C4⋊C4C2311yescharacteristic
94C2×C11×C4⋊C4C2311yescharacteristic
95C2×C11×C22⋊C4—22no—
96C2×C11×C22⋊C4—22no—
97C2×C11×C22⋊C4—22no—
98C2×C11×C22⋊C4D412yes—
99C2×C42×C11—21no—
100C2×C42×C11—21no—
101C2×C42×C11C2311yescharacteristic
102C11×#107—22no—
103C11×C4⋊C8—22no—
104C11×#103—22no—
105C11×#103—24no—
106C11×#103—24no—
107C11×#103—24no—
108C11×#103—22no—
109C11×#103—42no—
110C11×C22⋊C8—24no—
111C11×C22⋊C8—42no—
112C4×C8×C11—22no—
113C11×#95—22no—
114#24243C1111yesmaximal, characteristic, direct product factor, Sylow
115C24×C11C2×D412yes—
116C2×Q8×C11—28no—
117C2×Q8×C11—21no—
118C2×Q8×C11—22no—
119C2×Q8×C11—21no—
120C2×Q8×C11—21no—
121C2×Q8×C11—21no—
122C2×Q8×C11—21no—
123C2×Q8×C11—22no—
124C2×Q8×C11—21no—
125C2×Q8×C11—21no—
126C2×Q8×C11—22no—
127C2×Q8×C11—22no—
128C2×Q8×C11—21no—
129C2×Q8×C11—22no—
130C2×Q8×C11—44no—
131C2×Q8×C11—44no—
132C2×Q8×C11—48no—
133C2×Q8×C11—48no—
134C2×Q8×C11—48no—
135C2×Q8×C11—48no—
136C2×Q8×C11C2×D414yes—
137C2×Q8×C11C2×D412yes—
138C2×Q8×C11C2×D412yes—
139C2×Q8×C11C2×D412yes—
140C2×Q8×C11#4112yes—
141C2×D4×C11—22no—
142C2×D4×C11—22no—
143C2×D4×C11Q1614yescomplemented
144C22×C4×C11—21no—
145C22×C4×C11—28no—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
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—22no—
155C22×C4×C11—21no—
156C22×C4×C11—22no—
157C22×C4×C11—44no—
158C22×C4×C11—44no—
159C22×C4×C11C2×D412yes—
160C22×C4×C11C2×D411yescharacteristic
161C22×C4×C11C2×D411yescharacteristic
162C22×C4×C11C2411yescharacteristic
163C11×Q16—28no—
164C11×Q16—48no—
165C2×C8×C11—21no—
166C2×C8×C11—21no—
167C2×C8×C11—22no—
168C2×C8×C11—22no—
169C2×C8×C11—21no—
170C2×C8×C11—21no—
171C2×C8×C11—22no—
172C2×C8×C11—21no—
173C2×C8×C11C2×D412yes—
174C11×C4⋊C4—28no—
175C11×C4⋊C4—24no—
176C11×C4⋊C4—24no—
177C11×C4⋊C4—24no—
178C11×C4⋊C4—22no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—22no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—22no—
184C11×C4⋊C4—44no—
185C11×C4⋊C4—42no—
186C11×C4⋊C4—42no—
187C11×C4⋊C4—81no—
188C11×C4⋊C4C2×D412yes—
189C11×C22⋊C4—28no—
190C11×C22⋊C4—24no—
191C11×C22⋊C4—44no—
192C11×C22⋊C4—82no—
193C42×C11—24no—
194C42×C11—42no—
195C42×C11C2×D412yes—
196C42×C11C2×D412yes—
197C2×D4×Q8C2×C1111yescharacteristic
198C2×#462C2×C1111yescharacteristic, complemented
199C2×#451C2×C1112yescomplemented
200C2×C4×Q16C2×C1111yescharacteristic, complemented
201#2538C2×C1111yescharacteristic
202#2036C2×C1112yescomplemented
203#2001C2×C1112yescomplemented
204#1956C2×C1111yescharacteristic, complemented
205#1954C2×C1111yescharacteristic
206#1803C2×C1111yescharacteristic, complemented
207#1787C2×C1112yescomplemented
208C23×C11—22no—
209C23×C11—22no—
210C23×C11—22no—
211C23×C11—22no—
212C23×C11—22no—
213C23×C11—22no—
214C23×C11C2×Q1614yes—
215C23×C11C22×D411yescharacteristic
216Q8×C11—22no—
217Q8×C11—22no—
218Q8×C11—22no—
219Q8×C11—22no—
220Q8×C11—22no—
221Q8×C11—24no—
222Q8×C11—24no—
223Q8×C11—416no—
224Q8×C11—42no—
225Q8×C11—41no—
226Q8×C11—42no—
227Q8×C11—41no—
228Q8×C11#12114yes—
229D4×C11—28no—
230C2×C4×C11—22no—
231C2×C4×C11—22no—
232C2×C4×C11—22no—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—22no—
236C2×C4×C11—24no—
237C2×C4×C11—22no—
238C2×C4×C11—22no—
239C2×C4×C11—22no—
240C2×C4×C11—22no—
241C2×C4×C11—416no—
242C2×C4×C11—41no—
243C2×C4×C11—42no—
244C2×C4×C11—42no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11—41no—
248C2×C4×C11—42no—
249C2×C4×C11—42no—
250C2×C4×C11—42no—
251C2×C4×C11—42no—
252C2×C4×C11—41no—
253C2×C4×C11—42no—
254C2×C4×C11—42no—
255C2×C4×C11—41no—
256C2×C4×C11—42no—
257C2×C4×C11—41no—
258C2×C4×C11#12012yes—
259C2×C4×C11#12012yes—
260C2×C4×C11C2×Q1612yes—
261C2×C4×C11#13712yes—
262C2×C4×C11C22×D411yescharacteristic
263C2×C4×C11C22×D411yescharacteristic
264C2×C4×C11C22×D411yescharacteristic
265C2×C4×C11C2×#4111yescharacteristic
266C2×C4×C11H(5,𝔽2)11yescharacteristic
267C2×C4×C11H(5,𝔽2)11yescharacteristic
268C8×C11—22no—
269C8×C11—41no—
270C8×C11—42no—
271C23×Q8C22×C1112yes—
272C22×Q16C22×C1112yes—
273C22×Q16C22×C1111yescharacteristic
274D4×Q8—24no—
275D4×Q8—24no—
276C2×C4⋊Q8—21no—
277C2×C4⋊Q8C22×C1111yescharacteristic
278C2×C22⋊Q8—22no—
279C2×C22⋊Q8C22×C1112yes—
280C2×C22⋊Q8C22×C1112yes—
281C2×C4×Q8C22×C1111yescharacteristic
282C2×C4×Q8C22×C1111yescharacteristic
283C2×C4×D4—21no—
284C2×C4×D4C22×C1111yescharacteristic
285#462—24no—
286#451—28no—
287C4×Q16—24no—
288C2×#107C22×C1111yescharacteristic
289C2×C4⋊C8C22×C1111yescharacteristic
290C2×#103C22×C1112yes—
291C2×#103C22×C1111yescharacteristic
292C2×#103C22×C1111yescharacteristic
293C2×#103C22×C1112yes—
294C2×#103C22×C1112yes—
295C2×#103C22×C1112yes—
296C2×C22⋊C8C22×C1112yes—
297C2×C22⋊C8C22×C1112yes—
298C2×C4×C8C22×C1111yescharacteristic
299#396—22no—
300#390—21no—
301#389—21no—
302#384C22×C1111yescharacteristic
303#380C22×C1112yes—
304#340C22×C1112yes—
305C22×C11—24no—
306C22×C11—24no—
307C22×C11—24no—
308C22×C11—42no—
309C22×C11—42no—
310C22×C11—42no—
311C22×C11—42no—
312C22×C11C2×#12011yescharacteristic
313C22×C11D4211yescharacteristic
314C22×C11#54611yescharacteristic
315C22×C11C22×Q1611yescharacteristic
316C22×C11C2×#13711yescharacteristic
317C22×C11#57711yescharacteristic
318C22×C11#57811yescharacteristic
319C4×C11—24no—
320C4×C11—22no—
321C4×C11—42no—
322C4×C11—44no—
323C4×C11—42no—
324C4×C11—42no—
325C4×C11—81no—
326C4×C11—82no—
327C4×C11#45114yescomplemented
328C4×C11C2×#12111yescharacteristic
329C4×C11#53511yescharacteristic
330C4×C11D4211yescharacteristic
331C4×C11#54611yescharacteristic
332C22×Q8—24no—
333C22×Q8—24no—
334C22×Q8—22no—
335C22×Q8—24no—
336C22×Q8—24no—
337C22×Q8—42no—
338C22×Q8—42no—
339C22×Q8C23×C1111yescharacteristic
340C22×Q8C23×C1112yes—
341C22×Q8C23×C1111yescharacteristic
342C22×D4D4×C1111yescharacteristic
343C23×C4—22no—
344C23×C4C23×C1112yes—
345C2×Q16—22no—
346C2×Q16—22no—
347C2×Q16—24no—
348C2×Q16—24no—
349C2×Q16—42no—
350C2×Q16D4×C1114yescomplemented
351C22×C8C23×C1112yes—
352C22×C8C23×C1111yescharacteristic
353C22×C8C23×C1111yescharacteristic
354C4⋊Q8—28no—
355C4⋊Q8—22no—
356C4⋊Q8D4×C1114yes—
357C22⋊Q8—216no—
358C22⋊Q8—24no—
359C22⋊Q8—24no—
360C22⋊Q8—24no—
361C22⋊Q8—42no—
362C4×Q8—22no—
363C4×Q8—22no—
364C4×Q8—22no—
365C4×Q8D4×C1114yes—
366C4×D4—28no—
367C4×D4—22no—
368C4×D4—22no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4D4×C1111yescharacteristic
378C2×C4⋊C4C23×C1111yescharacteristic
379C2×C4⋊C4C23×C1112yes—
380C2×C4⋊C4C23×C1111yescharacteristic
381C2×C22⋊C4—22no—
382C2×C22⋊C4—22no—
383C2×C22⋊C4—22no—
384C2×C22⋊C4D4×C1112yes—
385C2×C42—21no—
386C2×C42—21no—
387C2×C42C23×C1111yescharacteristic
388#107—22no—
389C4⋊C8—22no—
390#103—22no—
391#103—24no—
392#103—24no—
393#103—24no—
394#103—22no—
395#103—42no—
396C22⋊C8—24no—
397C22⋊C8—42no—
398C4×C8—22no—
399#95—22no—
400C2×C11—44no—
401C2×C11#240811yescharacteristic
402C2×C11C2×#45111yescharacteristic
403C2×C11#301311yescharacteristic
404C2×C11#327811yescharacteristic
405C2×C11D4×Q1611yescharacteristic
406C2×C11#329911yescharacteristic
407C2×C11#332811yescharacteristic
408C24C2×D4×C1112yes—
409C2×Q8—28no—
410C2×Q8—21no—
411C2×Q8—22no—
412C2×Q8—21no—
413C2×Q8—21no—
414C2×Q8—21no—
415C2×Q8—21no—
416C2×Q8—22no—
417C2×Q8—21no—
418C2×Q8—21no—
419C2×Q8—22no—
420C2×Q8—22no—
421C2×Q8—21no—
422C2×Q8—22no—
423C2×Q8—44no—
424C2×Q8—44no—
425C2×Q8—48no—
426C2×Q8—48no—
427C2×Q8—48no—
428C2×Q8—48no—
429C2×Q8C2×D4×C1114yes—
430C2×Q8C2×D4×C1112yes—
431C2×Q8C2×D4×C1112yes—
432C2×Q8C2×D4×C1112yes—
433C2×Q8C11×#4112yes—
434C2×D4—22no—
435C2×D4—22no—
436C2×D4C11×Q1614yescomplemented
437C22×C4—21no—
438C22×C4—28no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—21no—
449C22×C4—22no—
450C22×C4—44no—
451C22×C4—44no—
452C22×C4C2×D4×C1112yes—
453C22×C4C2×D4×C1111yescharacteristic
454C22×C4C2×D4×C1111yescharacteristic
455C22×C4C24×C1111yescharacteristic
456Q16—28no—
457Q16—48no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—22no—
462C2×C8—22no—
463C2×C8—21no—
464C2×C8—22no—
465C2×C8—21no—
466C2×C8C2×D4×C1112yes—
467C4⋊C4—28no—
468C4⋊C4—24no—
469C4⋊C4—24no—
470C4⋊C4—24no—
471C4⋊C4—22no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—22no—
475C4⋊C4—21no—
476C4⋊C4—22no—
477C4⋊C4—44no—
478C4⋊C4—42no—
479C4⋊C4—42no—
480C4⋊C4—81no—
481C4⋊C4C2×D4×C1112yes—
482C22⋊C4—28no—
483C22⋊C4—24no—
484C22⋊C4—44no—
485C22⋊C4—82no—
486C42—24no—
487C42—42no—
488C42C2×D4×C1112yes—
489C42C2×D4×C1112yes—
490C11#2424311yescharacteristic, direct product factor, Sylow
491C23—22no—
492C23—22no—
493C23—22no—
494C23—22no—
495C23—22no—
496C23—22no—
497C23C2×C11×Q1614yes—
498C23C22×D4×C1111yescharacteristic
499Q8—22no—
500Q8—22no—
501Q8—22no—
502Q8—22no—
503Q8—22no—
504Q8—24no—
505Q8—24no—
506Q8—416no—
507Q8—42no—
508Q8—41no—
509Q8—42no—
510Q8—41no—
511Q8C11×#12114yes—
512D4—28no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—22no—
519C2×C4—24no—
520C2×C4—22no—
521C2×C4—22no—
522C2×C4—22no—
523C2×C4—22no—
524C2×C4—416no—
525C2×C4—41no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—41no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—41no—
539C2×C4—42no—
540C2×C4—41no—
541C2×C4C11×#12012yes—
542C2×C4C11×#12012yes—
543C2×C4C2×C11×Q1612yes—
544C2×C4C11×#13712yes—
545C2×C4C22×D4×C1111yescharacteristic
546C2×C4C22×D4×C1111yescharacteristic
547C2×C4C22×D4×C1111yescharacteristic
548C2×C4C2×C11×#4111yescharacteristic
549C2×C4C11×H(5,𝔽2)11yescharacteristic
550C2×C4C11×H(5,𝔽2)11yescharacteristic
551C8—22no—
552C8—41no—
553C8—42no—
554C22—24no—
555C22—24no—
556C22—24no—
557C22—42no—
558C22—42no—
559C22—42no—
560C22—42no—
561C22C2×C11×#12011yescharacteristic
562C22D42×C1111yescharacteristic
563C22C11×#54611yescharacteristic
564C22C22×C11×Q1611yescharacteristic
565C22C2×C11×#13711yescharacteristic
566C22C11×#57711yescharacteristic
567C22C11×#57811yescharacteristic
568C4—24no—
569C4—22no—
570C4—42no—
571C4—44no—
572C4—42no—
573C4—42no—
574C4—81no—
575C4—82no—
576C4C11×#45114yescomplemented
577C4C2×C11×#12111yescharacteristic
578C4C11×#53511yescharacteristic
579C4D42×C1111yescharacteristic
580C4C11×#54611yescharacteristic
581C2—44no—
582C2C11×#240811yescharacteristic
583C2C2×C11×#45111yescharacteristic
584C2C11×#301311yescharacteristic
585C2C11×#327811yescharacteristic
586C2D4×C11×Q1611yescharacteristic
587C2C11×#329911yescharacteristic
588C2C11×#332811yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC22×D4×C11D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C4×D4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#462C2semidirect
3. C2×C11×#451C2semidirect
4. C2×C4×C11×Q16C2semidirect
6. C11×#2036C2semidirect
7. C11×#2001C2semidirect
8. C11×#1956C2semidirect
10. C11×#1803C2semidirect
11. C11×#1787C2semidirect
64. C2×C11×Q16D4semidirect
114. #24243C11direct (N × H)
143. C2×D4×C11Q16semidirect
198. C2×#462C2×C11semidirect
199. C2×#451C2×C11semidirect
200. C2×C4×Q16C2×C11semidirect
202. #2036C2×C11semidirect
203. #2001C2×C11semidirect
204. #1956C2×C11semidirect
206. #1803C2×C11semidirect
207. #1787C2×C11semidirect
327. C4×C11#451semidirect
350. C2×Q16D4×C11semidirect
436. C2×D4C11×Q16semidirect
490. C11#24243direct (N × H)
576. C4C11×#451semidirect

Maximal subgroups

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

subgroupindex
C2×D4×Q8×C112
C2×C11×#4622
C2×C11×#4512
C2×C4×C11×Q162
C11×#25382
C11×#20362
C11×#20012
C11×#19562
C11×#19542
C11×#18032
C11×#17872
#2424311