Finite Group Databasebeta

← C11×#23576 #14600769

Subgroups — C11×#23576 #14600769

Order 2816.

1424 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#532C211yesmaximal, characteristic
2C2×C11×#440C212yesmaximal, complemented
3C4×C11×C22⋊Q8C211yesmaximal, characteristic, complemented
4C11×#2057C211yesmaximal, characteristic, complemented
5C11×#2041C211yesmaximal, characteristic, complemented
6C11×#2033C212yesmaximal, complemented
7C11×#2024C211yesmaximal, characteristic, complemented
8C11×#2014C211yesmaximal, characteristic, complemented
9C11×#2000C212yesmaximal, complemented
10C11×#1762C212yesmaximal, complemented
11C11×#1749C211yesmaximal, characteristic, complemented
12C22×C11×#41—21no—
13C22×C11×SD16C2212yes—
14C11×#532—28no—
15C2×C11×C4⋊Q8C2211yescharacteristic
16C2×C11×#127C2211yescharacteristic
17C2×C11×#124—21no—
18C2×C11×C22⋊Q8C2211yescharacteristic
19C2×C11×#121—21no—
20C2×C11×#121C2212yes—
21C2×C4×Q8×C11C2211yescharacteristic
22C2×C4×D4×C11—21no—
23C2×C4×D4×C11C2212yes—
24C22×C42×C11C2211yescharacteristic
25C11×#440—28no—
26C2×C11×#107C2212yes—
27C2×C11×#103C2212yes—
28C2×C11×#102C2212yes—
29C2×C11×#102C2212yes—
30C2×C11×#102C2212yes—
31C2×C11×C22⋊C8C2212yes—
32C2×C11×#97C2212yes—
33C11×#391C2211yescharacteristic
34C11×#389C2211yescharacteristic
35C11×#387—21no—
36C11×#385—21no—
37C11×#380C2211yescharacteristic
38C4×C11×C4⋊C4—21no—
39C4×C11×C4⋊C4C2211yescharacteristic
40C4×C11×C22⋊C4—21no—
41C11×#340C2212yes—
42C11×#340C2212yes—
43C11×#336C2211yescharacteristic
44C11×#336C2211yescharacteristic
45C2×C11×#41—28no—
46C2×C11×#41—44no—
47C2×C11×#41—44no—
48C22×Q8×C11—21no—
49C22×Q8×C11C2311yescharacteristic
50C22×D4×C11—22no—
51C22×D4×C11—21no—
52C22×D4×C11—21no—
53C22×D4×C11C2312yes—
54C23×C4×C11—22no—
55C23×C4×C11D411yescharacteristic
56C23×C4×C11D411yescharacteristic
57C23×C4×C11C2311yescharacteristic
58C2×C11×SD16—24no—
59C2×C11×SD16—24no—
60C2×C11×SD16—24no—
61C22×C8×C11C2312yes—
62C22×C8×C11C2312yes—
63C11×C4⋊Q8—24no—
64C11×#127—24no—
65C11×#124—28no—
66C11×C22⋊Q8—22no—
67C11×C22⋊Q8—22no—
68C11×#121—28no—
69C11×#121—24no—
70C11×#121—24no—
71C4×Q8×C11—24no—
72C4×D4×C11—28no—
73C4×D4×C11—24no—
74C4×D4×C11D418yes—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4—21no—
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C11×C4⋊C4C2312yes—
82C2×C11×C4⋊C4C2311yescharacteristic
83C2×C11×C22⋊C4—21no—
84C2×C11×C22⋊C4—22no—
85C2×C11×C22⋊C4—22no—
86C2×C11×C22⋊C4—21no—
87C2×C42×C11—24no—
88C2×C42×C11—21no—
89C2×C42×C11—21no—
90C2×C42×C11D411yescharacteristic
91C2×C42×C11D411yescharacteristic
92C2×C42×C11C2311yescharacteristic
93C2×C42×C11C2311yescharacteristic
94C11×#107—24no—
95C11×#103—24no—
96C11×#102—24no—
97C11×#102—24no—
98C11×#102—24no—
99C11×C22⋊C8—24no—
100C11×#97—24no—
101C11×#95—21no—
102C11×#95—21no—
103C11×#95—21no—
104C11×#95—21no—
105C11×#95—21no—
106#23576C1111yesmaximal, characteristic, direct product factor, Sylow
107C24×C11—22no—
108C24×C11C2×D411yescharacteristic
109C11×#41—432no—
110C2×Q8×C11—24no—
111C2×Q8×C11—21no—
112C2×Q8×C11—22no—
113C2×Q8×C11—22no—
114C2×Q8×C11—42no—
115C2×Q8×C11—42no—
116C2×Q8×C11#4112yescomplemented
117C2×D4×C11—24no—
118C2×D4×C11—28no—
119C2×D4×C11—24no—
120C2×D4×C11—22no—
121C2×D4×C11—22no—
122C2×D4×C11—22no—
123C2×D4×C11—22no—
124C2×D4×C11—22no—
125C2×D4×C11—42no—
126C2×D4×C11—42no—
127C2×D4×C11—44no—
128C2×D4×C11—44no—
129C2×D4×C11—42no—
130C2×D4×C11—42no—
131C2×D4×C11C2×D414yes—
132C22×C4×C11—22no—
133C22×C4×C11—22no—
134C22×C4×C11—22no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—22no—
138C22×C4×C11—22no—
139C22×C4×C11—28no—
140C22×C4×C11—22no—
141C22×C4×C11—22no—
142C22×C4×C11—22no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—41no—
148C22×C4×C11—44no—
149C22×C4×C11—44no—
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2411yescharacteristic
156C11×SD16—216no—
157C2×C8×C11—22no—
158C2×C8×C11—22no—
159C2×C8×C11—22no—
160C2×C8×C11—22no—
161C2×C8×C11—22no—
162C2×C8×C11#4114yescomplemented
163C11×C4⋊C4—24no—
164C11×C4⋊C4—24no—
165C11×C4⋊C4—22no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—22no—
168C11×C4⋊C4—22no—
169C11×C4⋊C4—42no—
170C11×C4⋊C4—42no—
171C11×C4⋊C4C2×D414yes—
172C11×C4⋊C4#4112yescomplemented
173C11×C22⋊C4—28no—
174C11×C22⋊C4—24no—
175C11×C22⋊C4—28no—
176C11×C22⋊C4—42no—
177C42×C11—22no—
178C42×C11—22no—
179C42×C11—22no—
180C42×C11—42no—
181C42×C11—42no—
182C42×C11C2×D414yes—
183C2×#532C2×C1111yescharacteristic
184C2×#440C2×C1112yescomplemented
185C4×C22⋊Q8C2×C1111yescharacteristic, complemented
186#2057C2×C1111yescharacteristic, complemented
187#2041C2×C1111yescharacteristic, complemented
188#2033C2×C1112yescomplemented
189#2024C2×C1111yescharacteristic, complemented
190#2014C2×C1111yescharacteristic, complemented
191#2000C2×C1112yescomplemented
192#1762C2×C1112yescomplemented
193#1749C2×C1111yescharacteristic, complemented
194C23×C11—21no—
195C23×C11—21no—
196C23×C11—21no—
197C23×C11—21no—
198C23×C11—21no—
199C23×C11—21no—
200C23×C11—24no—
201C23×C11—42no—
202C23×C11—42no—
203C23×C11—42no—
204C23×C11—42no—
205C23×C11—42no—
206C23×C11—42no—
207C23×C11AGL(1,ℤ/8)12yes—
208C23×C11C22×D411yescharacteristic
209Q8×C11—24no—
210Q8×C11—48no—
211Q8×C11—42no—
212D4×C11—24no—
213D4×C11—24no—
214D4×C11—48no—
215D4×C11—48no—
216D4×C11—416no—
217D4×C11—42no—
218D4×C11—42no—
219C2×C4×C11—28no—
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—21no—
229C2×C4×C11—24no—
230C2×C4×C11—22no—
231C2×C4×C11—22no—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
234C2×C4×C11—44no—
235C2×C4×C11—416no—
236C2×C4×C11—41no—
237C2×C4×C11—41no—
238C2×C4×C11—41no—
239C2×C4×C11—42no—
240C2×C4×C11—42no—
241C2×C4×C11—41no—
242C2×C4×C11—42no—
243C2×C4×C11—42no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11#12012yes—
251C2×C4×C11#12012yes—
252C2×C4×C11AGL(1,ℤ/8)12yes—
253C2×C4×C11#13712yes—
254C2×C4×C11C22×D412yes—
255C2×C4×C11C2×#4111yescharacteristic
256C2×C4×C11C2×#4112yes—
257C2×C4×C11C2×#4111yescharacteristic
258C8×C11—24no—
259C8×C11—42no—
260C22×#41—21no—
261C22×SD16C22×C1112yes—
262#532—28no—
263C2×C4⋊Q8C22×C1111yescharacteristic
264C2×#127C22×C1111yescharacteristic
265C2×#124—21no—
266C2×C22⋊Q8C22×C1111yescharacteristic
267C2×#121—21no—
268C2×#121C22×C1112yes—
269C2×C4×Q8C22×C1111yescharacteristic
270C2×C4×D4—21no—
271C2×C4×D4C22×C1112yes—
272C22×C42C22×C1111yescharacteristic
273#440—28no—
274C2×#107C22×C1112yes—
275C2×#103C22×C1112yes—
276C2×#102C22×C1112yes—
277C2×#102C22×C1112yes—
278C2×#102C22×C1112yes—
279C2×C22⋊C8C22×C1112yes—
280C2×#97C22×C1112yes—
281#391C22×C1111yescharacteristic
282#389C22×C1111yescharacteristic
283#387—21no—
284#385—21no—
285#380C22×C1111yescharacteristic
286C4×C4⋊C4—21no—
287C4×C4⋊C4C22×C1111yescharacteristic
288C4×C22⋊C4—21no—
289#340C22×C1112yes—
290#340C22×C1112yes—
291#336C22×C1111yescharacteristic
292#336C22×C1111yescharacteristic
293C22×C11—22no—
294C22×C11—22no—
295C22×C11—22no—
296C22×C11—41no—
297C22×C11—41no—
298C22×C11—41no—
299C22×C11—41no—
300C22×C11—44no—
301C22×C11—44no—
302C22×C11—44no—
303C22×C11—82no—
304C22×C11—82no—
305C22×C11—82no—
306C22×C11—82no—
307C22×C11C2×#12011yescharacteristic
308C22×C11#52511yescharacteristic
309C22×C11#53211yescharacteristic
310C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
311C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
312C22×C11C2×#13711yescharacteristic
313C22×C11#57511yescharacteristic
314C4×C11—22no—
315C4×C11—22no—
316C4×C11—22no—
317C4×C11—22no—
318C4×C11—42no—
319C4×C11—41no—
320C4×C11—42no—
321C4×C11—44no—
322C4×C11—81no—
323C4×C11—81no—
324C4×C11#52512yes—
325C4×C11#53212yes—
326C2×#41—28no—
327C2×#41—44no—
328C2×#41—44no—
329C22×Q8—21no—
330C22×Q8C23×C1111yescharacteristic
331C22×D4—22no—
332C22×D4—21no—
333C22×D4—21no—
334C22×D4C23×C1112yes—
335C23×C4—22no—
336C23×C4D4×C1111yescharacteristic
337C23×C4D4×C1111yescharacteristic
338C23×C4C23×C1111yescharacteristic
339C2×SD16—24no—
340C2×SD16—24no—
341C2×SD16—24no—
342C22×C8C23×C1112yes—
343C22×C8C23×C1112yes—
344C4⋊Q8—24no—
345#127—24no—
346#124—28no—
347C22⋊Q8—22no—
348C22⋊Q8—22no—
349#121—28no—
350#121—24no—
351#121—24no—
352C4×Q8—24no—
353C4×D4—28no—
354C4×D4—24no—
355C4×D4D4×C1118yes—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4C23×C1111yescharacteristic
361C2×C4⋊C4C23×C1111yescharacteristic
362C2×C4⋊C4C23×C1112yes—
363C2×C4⋊C4C23×C1111yescharacteristic
364C2×C22⋊C4—21no—
365C2×C22⋊C4—22no—
366C2×C22⋊C4—22no—
367C2×C22⋊C4—21no—
368C2×C42—24no—
369C2×C42—21no—
370C2×C42—21no—
371C2×C42D4×C1111yescharacteristic
372C2×C42D4×C1111yescharacteristic
373C2×C42C23×C1111yescharacteristic
374C2×C42C23×C1111yescharacteristic
375#107—24no—
376#103—24no—
377#102—24no—
378#102—24no—
379#102—24no—
380C22⋊C8—24no—
381#97—24no—
382#95—21no—
383#95—21no—
384#95—21no—
385#95—21no—
386#95—21no—
387C2×C11—42no—
388C2×C11—84no—
389C2×C11#238811yescharacteristic
390C2×C11#300311yescharacteristic
391C2×C11#300711yescharacteristic
392C2×C11#311211yescharacteristic
393C2×C11#311511yescharacteristic
394C2×C11#318011yescharacteristic
395C2×C11#318211yescharacteristic
396C24—22no—
397C24C2×D4×C1111yescharacteristic
398#41—432no—
399C2×Q8—24no—
400C2×Q8—21no—
401C2×Q8—22no—
402C2×Q8—22no—
403C2×Q8—42no—
404C2×Q8—42no—
405C2×Q8C11×#4112yescomplemented
406C2×D4—24no—
407C2×D4—28no—
408C2×D4—24no—
409C2×D4—22no—
410C2×D4—22no—
411C2×D4—22no—
412C2×D4—22no—
413C2×D4—22no—
414C2×D4—42no—
415C2×D4—42no—
416C2×D4—44no—
417C2×D4—44no—
418C2×D4—42no—
419C2×D4—42no—
420C2×D4C2×D4×C1114yes—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—28no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—41no—
437C22×C4—44no—
438C22×C4—44no—
439C22×C4C2×D4×C1111yescharacteristic
440C22×C4C2×D4×C1111yescharacteristic
441C22×C4C2×D4×C1111yescharacteristic
442C22×C4C2×D4×C1111yescharacteristic
443C22×C4C2×D4×C1111yescharacteristic
444C22×C4C24×C1111yescharacteristic
445SD16—216no—
446C2×C8—22no—
447C2×C8—22no—
448C2×C8—22no—
449C2×C8—22no—
450C2×C8—22no—
451C2×C8C11×#4114yescomplemented
452C4⋊C4—24no—
453C4⋊C4—24no—
454C4⋊C4—22no—
455C4⋊C4—21no—
456C4⋊C4—22no—
457C4⋊C4—22no—
458C4⋊C4—42no—
459C4⋊C4—42no—
460C4⋊C4C2×D4×C1114yes—
461C4⋊C4C11×#4112yescomplemented
462C22⋊C4—28no—
463C22⋊C4—24no—
464C22⋊C4—28no—
465C22⋊C4—42no—
466C42—22no—
467C42—22no—
468C42—22no—
469C42—42no—
470C42—42no—
471C42C2×D4×C1114yes—
472C11#2357611yescharacteristic, direct product factor, Sylow
473C23—21no—
474C23—21no—
475C23—21no—
476C23—21no—
477C23—21no—
478C23—21no—
479C23—24no—
480C23—42no—
481C23—42no—
482C23—42no—
483C23—42no—
484C23—42no—
485C23—42no—
486C23C11×AGL(1,ℤ/8)12yes—
487C23C22×D4×C1111yescharacteristic
488Q8—24no—
489Q8—48no—
490Q8—42no—
491D4—24no—
492D4—24no—
493D4—48no—
494D4—48no—
495D4—416no—
496D4—42no—
497D4—42no—
498C2×C4—28no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—24no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—44no—
514C2×C4—416no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—41no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4C11×#12012yes—
530C2×C4C11×#12012yes—
531C2×C4C11×AGL(1,ℤ/8)12yes—
532C2×C4C11×#13712yes—
533C2×C4C22×D4×C1112yes—
534C2×C4C2×C11×#4111yescharacteristic
535C2×C4C2×C11×#4112yes—
536C2×C4C2×C11×#4111yescharacteristic
537C8—24no—
538C8—42no—
539C22—22no—
540C22—22no—
541C22—22no—
542C22—41no—
543C22—41no—
544C22—41no—
545C22—41no—
546C22—44no—
547C22—44no—
548C22—44no—
549C22—82no—
550C22—82no—
551C22—82no—
552C22—82no—
553C22C2×C11×#12011yescharacteristic
554C22C11×#52511yescharacteristic
555C22C11×#53211yescharacteristic
556C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
557C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
558C22C2×C11×#13711yescharacteristic
559C22C11×#57511yescharacteristic
560C4—22no—
561C4—22no—
562C4—22no—
563C4—22no—
564C4—41no—
565C4—42no—
566C4—44no—
567C4—42no—
568C4—81no—
569C4—81no—
570C4C11×#52512yes—
571C4C11×#53212yes—
572C2—42no—
573C2—84no—
574C2C11×#238811yescharacteristic
575C2C11×#300311yescharacteristic
576C2C11×#300711yescharacteristic
577C2C11×#311211yescharacteristic
578C2C11×#311511yescharacteristic
579C2C11×#318011yescharacteristic
580C2C11×#318211yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#532C2
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×#440C2semidirect
3. C4×C11×C22⋊Q8C2semidirect
4. C11×#2057C2semidirect
5. C11×#2041C2semidirect
6. C11×#2033C2semidirect
7. C11×#2024C2semidirect
8. C11×#2014C2semidirect
9. C11×#2000C2semidirect
10. C11×#1762C2semidirect
11. C11×#1749C2semidirect
106. #23576C11direct (N × H)
116. C2×Q8×C11#41semidirect
162. C2×C8×C11#41semidirect
172. C11×C4⋊C4#41semidirect
184. C2×#440C2×C11semidirect
185. C4×C22⋊Q8C2×C11semidirect
186. #2057C2×C11semidirect
187. #2041C2×C11semidirect
188. #2033C2×C11semidirect
189. #2024C2×C11semidirect
190. #2014C2×C11semidirect
191. #2000C2×C11semidirect
192. #1762C2×C11semidirect
193. #1749C2×C11semidirect
405. C2×Q8C11×#41semidirect
451. C2×C8C11×#41semidirect
461. C4⋊C4C11×#41semidirect
472. C11#23576direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5322
C2×C11×#4402
C4×C11×C22⋊Q82
C11×#20572
C11×#20412
C11×#20332
C11×#20242
C11×#20142
C11×#20002
C11×#17622
C11×#17492
#2357611