Finite Group Databasebeta

← C11×#24326 #14601519

Subgroups — C11×#24326 #14601519

Order 2816.

1330 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×Q8×C11C211yesmaximal, characteristic, complemented
2C2×C11×#474C211yesmaximal, characteristic, complemented
3C2×C4×C11×D8C211yesmaximal, characteristic
4C11×#2538C211yesmaximal, characteristic, complemented
5C11×#2057C212yesmaximal, complemented
6C11×#2023C212yesmaximal, complemented
7C11×#1990C211yesmaximal, characteristic, complemented
8C11×#1984C211yesmaximal, characteristic, complemented
9C11×#1879C212yesmaximal
10C11×#1862C212yesmaximal, complemented
11C11×#1802C211yesmaximal, characteristic, complemented
12C23×Q8×C11—21no—
13C22×C11×D8C2211yescharacteristic
14D4×Q8×C11—24no—
15D4×Q8×C11—24no—
16C2×C11×C4⋊Q8C2212yes—
17C2×C11×C4⋊Q8C2211yescharacteristic
18C2×C11×C22⋊Q8—21no—
19C2×C11×C22⋊Q8—21no—
20C2×C11×C22⋊Q8—22no—
21C2×C4×Q8×C11C2211yescharacteristic
22C2×C4×D4×C11C2212yes—
23C2×C4×D4×C11C2211yescharacteristic
24C2×C4×D4×C11C2211yescharacteristic
25C11×#474—24no—
26C4×C11×D8—24no—
27C2×C11×#107C2211yescharacteristic
28C2×C11×#107C2212yes—
29C2×C11×C4⋊C8C2211yescharacteristic
30C2×C11×#102C2212yes—
31C2×C11×#102C2212yes—
32C2×C11×#102C2211yescharacteristic
33C2×C11×#102C2211yescharacteristic
34C2×C4×C8×C11C2211yescharacteristic
35C11×#396—22no—
36C11×#390C2212yes—
37C11×#389C2212yes—
38C11×#384C2211yescharacteristic
39C11×#380—21no—
40C11×#340C2212yes—
41C11×#340C2212yes—
42C11×#340C2212yes—
43C11×#336C2212yes—
44C11×#336C2212yes—
45C22×Q8×C11—28no—
46C22×Q8×C11—22no—
47C22×Q8×C11—21no—
48C22×Q8×C11—44no—
49C22×Q8×C11—44no—
50C22×Q8×C11D411yescharacteristic
51C22×D4×C11C2311yescharacteristic
52C22×D4×C11C2311yescharacteristic
53C23×C4×C11—22no—
54C23×C4×C11—21no—
55C23×C4×C11—21no—
56C2×C11×D8—22no—
57C2×C11×D8—22no—
58C2×C11×D8Q814yescomplemented
59C22×C8×C11C2311yescharacteristic
60C22×C8×C11C2312yes—
61C22×C8×C11C2311yescharacteristic
62C11×C4⋊Q8—24no—
63C11×C4⋊Q8—24no—
64C11×C4⋊Q8—22no—
65C11×C4⋊Q8D414yes—
66C11×C22⋊Q8—28no—
67C11×C22⋊Q8—216no—
68C11×C22⋊Q8—44no—
69C4×Q8×C11—22no—
70C4×Q8×C11—22no—
71C4×D4×C11—24no—
72C4×D4×C11—24no—
73C4×D4×C11—22no—
74C4×D4×C11—22no—
75C4×D4×C11—22no—
76C4×D4×C11D414yes—
77C2×C11×C4⋊C4—22no—
78C2×C11×C4⋊C4—21no—
79C2×C11×C4⋊C4—21no—
80C2×C11×C4⋊C4—22no—
81C2×C11×C4⋊C4—21no—
82C2×C11×C4⋊C4D411yescharacteristic
83C2×C11×C4⋊C4D412yes—
84C2×C11×C4⋊C4C2312yes—
85C2×C11×C4⋊C4C2311yescharacteristic
86C2×C11×C4⋊C4C2312yes—
87C2×C11×C4⋊C4C2311yescharacteristic
88C2×C11×C22⋊C4—22no—
89C2×C11×C22⋊C4—21no—
90C2×C11×C22⋊C4—21no—
91C2×C11×C22⋊C4—22no—
92C2×C11×C22⋊C4—22no—
93C2×C42×C11C2312yes—
94C2×C42×C11C2311yescharacteristic
95C11×#107—22no—
96C11×#107—24no—
97C11×C4⋊C8—22no—
98C11×#102—22no—
99C11×#102—24no—
100C11×#102—22no—
101C11×#102—24no—
102C4×C8×C11—22no—
103C11×#95—22no—
104#24326C1111yesmaximal, characteristic, direct product factor, Sylow
105C24×C11—21no—
106C24×C11—21no—
107C2×Q8×C11—28no—
108C2×Q8×C11—22no—
109C2×Q8×C11—24no—
110C2×Q8×C11—22no—
111C2×Q8×C11—44no—
112C2×Q8×C11—432no—
113C2×Q8×C11—44no—
114C2×Q8×C11—42no—
115C2×Q8×C11—42no—
116C2×Q8×C11D814yescomplemented
117C2×D4×C11—21no—
118C2×D4×C11—21no—
119C2×D4×C11—21no—
120C2×D4×C11—21no—
121C2×D4×C11—21no—
122C2×D4×C11—21no—
123C2×D4×C11—21no—
124C2×D4×C11—21no—
125C2×D4×C11C2×D412yes—
126C2×D4×C11C2×Q812yes—
127C2×D4×C11C2×Q812yescomplemented
128C2×D4×C11#4112yes—
129C22×C4×C11—28no—
130C22×C4×C11—22no—
131C22×C4×C11—21no—
132C22×C4×C11—24no—
133C22×C4×C11—21no—
134C22×C4×C11—22no—
135C22×C4×C11—44no—
136C22×C4×C11—44no—
137C22×C4×C11—42no—
138C22×C4×C11—42no—
139C22×C4×C11—42no—
140C22×C4×C11—42no—
141C22×C4×C11—42no—
142C22×C4×C11C2×D412yes—
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×D412yes—
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2411yescharacteristic
147C11×D8—28no—
148C2×C8×C11—21no—
149C2×C8×C11—21no—
150C2×C8×C11—22no—
151C2×C8×C11—21no—
152C2×C8×C11—22no—
153C2×C8×C11—21no—
154C2×C8×C11—22no—
155C2×C8×C11—21no—
156C2×C8×C11C2×Q812yescomplemented
157C11×C4⋊C4—28no—
158C11×C4⋊C4—24no—
159C11×C4⋊C4—24no—
160C11×C4⋊C4—22no—
161C11×C4⋊C4—22no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—22no—
166C11×C4⋊C4—22no—
167C11×C4⋊C4—42no—
168C11×C4⋊C4—44no—
169C11×C4⋊C4—81no—
170C11×C4⋊C4C2×D414yes—
171C11×C4⋊C4C2×D412yes—
172C11×C22⋊C4—28no—
173C11×C22⋊C4—24no—
174C11×C22⋊C4—42no—
175C11×C22⋊C4—44no—
176C11×C22⋊C4—82no—
177C42×C11—22no—
178C42×C11—22no—
179C42×C11C2×D412yes—
180C42×C11C2×D412yes—
181C2×D4×Q8C2×C1111yescharacteristic, complemented
182C2×#474C2×C1111yescharacteristic, complemented
183C2×C4×D8C2×C1111yescharacteristic
184#2538C2×C1111yescharacteristic, complemented
185#2057C2×C1112yescomplemented
186#2023C2×C1112yescomplemented
187#1990C2×C1111yescharacteristic, complemented
188#1984C2×C1111yescharacteristic, complemented
189#1879C2×C1112yes—
190#1862C2×C1112yescomplemented
191#1802C2×C1111yescharacteristic, complemented
192C23×C11—22no—
193C23×C11—22no—
194C23×C11—22no—
195C23×C11—22no—
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—41no—
206C23×C11C22×D411yescharacteristic
207Q8×C11—28no—
208Q8×C11—416no—
209Q8×C11—48no—
210D4×C11—22no—
211D4×C11—22no—
212D4×C11—22no—
213D4×C11—22no—
214D4×C11—22no—
215D4×C11—41no—
216D4×C11—41no—
217D4×C11C22⋊Q814yescomplemented
218C2×C4×C11—22no—
219C2×C4×C11—22no—
220C2×C4×C11—21no—
221C2×C4×C11—21no—
222C2×C4×C11—22no—
223C2×C4×C11—24no—
224C2×C4×C11—22no—
225C2×C4×C11—22no—
226C2×C4×C11—22no—
227C2×C4×C11—416no—
228C2×C4×C11—42no—
229C2×C4×C11—41no—
230C2×C4×C11—42no—
231C2×C4×C11—41no—
232C2×C4×C11—48no—
233C2×C4×C11—41no—
234C2×C4×C11—42no—
235C2×C4×C11—42no—
236C2×C4×C11—41no—
237C2×C4×C11—41no—
238C2×C4×C11—42no—
239C2×C4×C11—84no—
240C2×C4×C11#12012yes—
241C2×C4×C11#12012yes—
242C2×C4×C11C2×D814yes—
243C2×C4×C11C2×D812yes—
244C2×C4×C11AGL(1,ℤ/8)12yes—
245C2×C4×C11C22×D411yescharacteristic
246C2×C4×C11C22×D411yescharacteristic
247C2×C4×C11C22×Q811yescharacteristic
248C2×C4×C11C2×#4111yescharacteristic
249C2×C4×C112−1+411yescharacteristic
250C2×C4×C112−1+411yescharacteristic
251C8×C11—22no—
252C8×C11—41no—
253C8×C11—42no—
254C23×Q8—21no—
255C22×D8C22×C1111yescharacteristic
256D4×Q8—24no—
257D4×Q8—24no—
258C2×C4⋊Q8C22×C1112yes—
259C2×C4⋊Q8C22×C1111yescharacteristic
260C2×C22⋊Q8—21no—
261C2×C22⋊Q8—21no—
262C2×C22⋊Q8—22no—
263C2×C4×Q8C22×C1111yescharacteristic
264C2×C4×D4C22×C1112yes—
265C2×C4×D4C22×C1111yescharacteristic
266C2×C4×D4C22×C1111yescharacteristic
267#474—24no—
268C4×D8—24no—
269C2×#107C22×C1111yescharacteristic
270C2×#107C22×C1112yes—
271C2×C4⋊C8C22×C1111yescharacteristic
272C2×#102C22×C1112yes—
273C2×#102C22×C1111yescharacteristic
274C2×#102C22×C1112yes—
275C2×#102C22×C1111yescharacteristic
276C2×C4×C8C22×C1111yescharacteristic
277#396—22no—
278#390C22×C1112yes—
279#389C22×C1112yes—
280#384C22×C1111yescharacteristic
281#380—21no—
282#340C22×C1112yes—
283#340C22×C1112yes—
284#340C22×C1112yes—
285#336C22×C1112yes—
286#336C22×C1112yes—
287C22×C11—24no—
288C22×C11—42no—
289C22×C11—42no—
290C22×C11—42no—
291C22×C11—42no—
292C22×C11—42no—
293C22×C11—42no—
294C22×C11—42no—
295C22×C11—42no—
296C22×C11—42no—
297C22×C11—81no—
298C22×C11—81no—
299C22×C11—81no—
300C22×C11—81no—
301C22×C11C2×#12011yescharacteristic
302C22×C11#54811yescharacteristic
303C22×C11D4×Q811yescharacteristic
304C22×C11C22×D811yescharacteristic
305C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
306C22×C11#57711yescharacteristic
307C22×C11#57811yescharacteristic
308C4×C11—24no—
309C4×C11—22no—
310C4×C11—44no—
311C4×C11—42no—
312C4×C11—42no—
313C4×C11—82no—
314C4×C11—81no—
315C4×C11#44714yes—
316C4×C11C2×C22⋊Q811yescharacteristic
317C4×C11#53611yescharacteristic
318C4×C11#54811yescharacteristic
319C4×C11D4×Q811yescharacteristic
320C22×Q8—28no—
321C22×Q8—22no—
322C22×Q8—21no—
323C22×Q8—44no—
324C22×Q8—44no—
325C22×Q8D4×C1111yescharacteristic
326C22×D4C23×C1111yescharacteristic
327C22×D4C23×C1111yescharacteristic
328C23×C4—22no—
329C23×C4—21no—
330C23×C4—21no—
331C2×D8—22no—
332C2×D8—22no—
333C2×D8Q8×C1114yescomplemented
334C22×C8C23×C1111yescharacteristic
335C22×C8C23×C1112yes—
336C22×C8C23×C1111yescharacteristic
337C4⋊Q8—24no—
338C4⋊Q8—24no—
339C4⋊Q8—22no—
340C4⋊Q8D4×C1114yes—
341C22⋊Q8—28no—
342C22⋊Q8—216no—
343C22⋊Q8—44no—
344C4×Q8—22no—
345C4×Q8—22no—
346C4×D4—24no—
347C4×D4—24no—
348C4×D4—22no—
349C4×D4—22no—
350C4×D4—22no—
351C4×D4D4×C1114yes—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4D4×C1111yescharacteristic
358C2×C4⋊C4D4×C1112yes—
359C2×C4⋊C4C23×C1111yescharacteristic
360C2×C4⋊C4C23×C1112yes—
361C2×C4⋊C4C23×C1112yes—
362C2×C4⋊C4C23×C1111yescharacteristic
363C2×C22⋊C4—22no—
364C2×C22⋊C4—21no—
365C2×C22⋊C4—21no—
366C2×C22⋊C4—22no—
367C2×C22⋊C4—22no—
368C2×C42C23×C1112yes—
369C2×C42C23×C1111yescharacteristic
370#107—22no—
371#107—24no—
372C4⋊C8—22no—
373#102—22no—
374#102—24no—
375#102—22no—
376#102—24no—
377C4×C8—22no—
378#95—22no—
379C2×C11—44no—
380C2×C11—82no—
381C2×C11#240911yescharacteristic
382C2×C11C2×#44711yescharacteristic
383C2×C11#301311yescharacteristic
384C2×C11#335811yescharacteristic
385C2×C11#336711yescharacteristic
386C2×C11Q8×D811yescharacteristic
387C2×C11#338411yescharacteristic
388C24—21no—
389C24—21no—
390C2×Q8—28no—
391C2×Q8—22no—
392C2×Q8—24no—
393C2×Q8—22no—
394C2×Q8—44no—
395C2×Q8—432no—
396C2×Q8—44no—
397C2×Q8—42no—
398C2×Q8—42no—
399C2×Q8C11×D814yescomplemented
400C2×D4—21no—
401C2×D4—21no—
402C2×D4—21no—
403C2×D4—21no—
404C2×D4—21no—
405C2×D4—21no—
406C2×D4—21no—
407C2×D4—21no—
408C2×D4C2×D4×C1112yes—
409C2×D4C2×Q8×C1112yes—
410C2×D4C2×Q8×C1112yescomplemented
411C2×D4C11×#4112yes—
412C22×C4—28no—
413C22×C4—22no—
414C22×C4—21no—
415C22×C4—24no—
416C22×C4—21no—
417C22×C4—22no—
418C22×C4—44no—
419C22×C4—44no—
420C22×C4—42no—
421C22×C4—42no—
422C22×C4—42no—
423C22×C4—42no—
424C22×C4—42no—
425C22×C4C2×D4×C1112yes—
426C22×C4C2×D4×C1111yescharacteristic
427C22×C4C2×D4×C1112yes—
428C22×C4C2×D4×C1111yescharacteristic
429C22×C4C24×C1111yescharacteristic
430D8—28no—
431C2×C8—21no—
432C2×C8—21no—
433C2×C8—21no—
434C2×C8—22no—
435C2×C8—22no—
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—22no—
439C2×C8C2×Q8×C1112yescomplemented
440C4⋊C4—28no—
441C4⋊C4—24no—
442C4⋊C4—24no—
443C4⋊C4—22no—
444C4⋊C4—22no—
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—22no—
449C4⋊C4—22no—
450C4⋊C4—42no—
451C4⋊C4—44no—
452C4⋊C4—81no—
453C4⋊C4C2×D4×C1114yes—
454C4⋊C4C2×D4×C1112yes—
455C22⋊C4—28no—
456C22⋊C4—24no—
457C22⋊C4—42no—
458C22⋊C4—44no—
459C22⋊C4—82no—
460C42—22no—
461C42—22no—
462C42C2×D4×C1112yes—
463C42C2×D4×C1112yes—
464C11#2432611yescharacteristic, direct product factor, Sylow
465C23—22no—
466C23—22no—
467C23—22no—
468C23—22no—
469C23—41no—
470C23—41no—
471C23—41no—
472C23—41no—
473C23—41no—
474C23—41no—
475C23—41no—
476C23—41no—
477C23—41no—
478C23—41no—
479C23C22×D4×C1111yescharacteristic
480Q8—28no—
481Q8—416no—
482Q8—48no—
483D4—22no—
484D4—22no—
485D4—22no—
486D4—22no—
487D4—22no—
488D4—41no—
489D4—41no—
490D4C11×C22⋊Q814yescomplemented
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—22no—
496C2×C4—24no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—416no—
501C2×C4—42no—
502C2×C4—41no—
503C2×C4—42no—
504C2×C4—41no—
505C2×C4—48no—
506C2×C4—41no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—42no—
512C2×C4—84no—
513C2×C4C11×#12012yes—
514C2×C4C11×#12012yes—
515C2×C4C2×C11×D814yes—
516C2×C4C2×C11×D812yes—
517C2×C4C11×AGL(1,ℤ/8)12yes—
518C2×C4C22×D4×C1111yescharacteristic
519C2×C4C22×D4×C1111yescharacteristic
520C2×C4C22×Q8×C1111yescharacteristic
521C2×C4C2×C11×#4111yescharacteristic
522C2×C4C11×2−1+411yescharacteristic
523C2×C4C11×2−1+411yescharacteristic
524C8—22no—
525C8—41no—
526C8—42no—
527C22—24no—
528C22—42no—
529C22—42no—
530C22—42no—
531C22—42no—
532C22—42no—
533C22—42no—
534C22—42no—
535C22—42no—
536C22—42no—
537C22—81no—
538C22—81no—
539C22—81no—
540C22—81no—
541C22C2×C11×#12011yescharacteristic
542C22C11×#54811yescharacteristic
543C22D4×Q8×C1111yescharacteristic
544C22C22×C11×D811yescharacteristic
545C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
546C22C11×#57711yescharacteristic
547C22C11×#57811yescharacteristic
548C4—24no—
549C4—22no—
550C4—44no—
551C4—42no—
552C4—42no—
553C4—81no—
554C4—82no—
555C4C11×#44714yes—
556C4C2×C11×C22⋊Q811yescharacteristic
557C4C11×#53611yescharacteristic
558C4C11×#54811yescharacteristic
559C4D4×Q8×C1111yescharacteristic
560C2—44no—
561C2—82no—
562C2C11×#240911yescharacteristic
563C2C2×C11×#44711yescharacteristic
564C2C11×#301311yescharacteristic
565C2C11×#335811yescharacteristic
566C2C11×#336711yescharacteristic
567C2Q8×C11×D811yescharacteristic
568C2C11×#338411yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC22×C11×D8C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C4×Q8×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×D4×Q8×C11C2semidirect
2. C2×C11×#474C2semidirect
4. C11×#2538C2semidirect
5. C11×#2057C2semidirect
6. C11×#2023C2semidirect
7. C11×#1990C2semidirect
8. C11×#1984C2semidirect
10. C11×#1862C2semidirect
11. C11×#1802C2semidirect
58. C2×C11×D8Q8semidirect
104. #24326C11direct (N × H)
116. C2×Q8×C11D8semidirect
127. C2×D4×C11C2×Q8semidirect
156. C2×C8×C11C2×Q8semidirect
181. C2×D4×Q8C2×C11semidirect
182. C2×#474C2×C11semidirect
184. #2538C2×C11semidirect
185. #2057C2×C11semidirect
186. #2023C2×C11semidirect
187. #1990C2×C11semidirect
188. #1984C2×C11semidirect
190. #1862C2×C11semidirect
191. #1802C2×C11semidirect
217. D4×C11C22⋊Q8semidirect
333. C2×D8Q8×C11semidirect
399. C2×Q8C11×D8semidirect
410. C2×D4C2×Q8×C11semidirect
439. C2×C8C2×Q8×C11semidirect
464. C11#24326direct (N × H)
490. D4C11×C22⋊Q8semidirect

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×#4742
C2×C4×C11×D82
C11×#25382
C11×#20572
C11×#20232
C11×#19902
C11×#19842
C11×#18792
C11×#18622
C11×#18022
#2432611