Finite Group Databasebeta

← C11×#24016 #14601209

Subgroups — C11×#24016 #14601209

Order 2816.

1276 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#536C211yesmaximal, characteristic
2C2×C11×#485C212yesmaximal, complemented
3C11×#2311C211yesmaximal, characteristic
4C11×#2036C212yesmaximal, complemented
5C11×#2035C212yesmaximal, complemented
6C11×#1872C212yesmaximal, complemented
7C11×#1854C212yesmaximal, complemented
8C11×#1787C212yesmaximal, complemented
9C11×#1780C211yesmaximal, characteristic
10C22×C11×#41C2211yescharacteristic
11C23×Q8×C11C2211yescharacteristic
12C11×#536—28no—
13C2×C11×C4⋊Q8—21no—
14C2×C11×#124—21no—
15C2×C11×#123—21no—
16C2×C11×#123—21no—
17C2×C11×C22⋊Q8C2212yes—
18C2×C11×C22⋊Q8C2212yes—
19C2×C11×#117C2211yescharacteristic
20C2×C11×#117C2211yescharacteristic
21C22×C11×C4⋊C4C2211yescharacteristic
22C11×#485—28no—
23C2×C11×#107C2212yes—
24C2×C11×#106C2212yes—
25C2×C11×#103C2212yes—
26C2×C11×#103C2212yes—
27C2×C11×#103C2212yes—
28C2×C11×#103C2212yes—
29C2×C11×C22⋊C8C2212yes—
30C2×C11×C22⋊C8C2212yes—
31C2×C11×C22⋊C8C2211yescharacteristic
32C2×C11×C22⋊C8C2211yescharacteristic
33C11×#391—21no—
34C11×#390—21no—
35C11×#386—21no—
36C11×#386—21no—
37C11×#380C2212yes—
38C11×#380C2212yes—
39C11×#340C2212yes—
40C11×#340C2212yes—
41C2×C11×#41—24no—
42C2×C11×#41—24no—
43C2×C11×#41—41no—
44C2×C11×#41—41no—
45C22×Q8×C11—24no—
46C22×Q8×C11—21no—
47C22×Q8×C11—24no—
48C22×Q8×C11—41no—
49C22×Q8×C11—41no—
50C22×Q8×C11D411yescharacteristic
51C22×Q8×C11C2312yes—
52C22×D4×C11D411yescharacteristic
53C22×D4×C11D411yescharacteristic
54C22×D4×C11D411yescharacteristic
55C23×C4×C11—21no—
56C23×C4×C11—21no—
57C23×C4×C11C2311yescharacteristic
58C23×C4×C11C2311yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C22×C8×C11C2312yes—
61C22×C8×C11C2312yes—
62C11×C4⋊Q8—28no—
63C11×#124—28no—
64C11×#123—28no—
65C11×#123—28no—
66C11×C22⋊Q8—24no—
67C11×C22⋊Q8—24no—
68C11×C22⋊Q8—24no—
69C11×C22⋊Q8D418yes—
70C11×#117—24no—
71C11×#117—24no—
72C2×C11×C4⋊C4—22no—
73C2×C11×C4⋊C4—22no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4—41no—
76C2×C11×C4⋊C4—41no—
77C2×C11×C4⋊C4C2312yes—
78C2×C11×C4⋊C4C2312yes—
79C2×C11×C4⋊C4C2312yes—
80C2×C11×C22⋊C4—21no—
81C2×C11×C22⋊C4—22no—
82C2×C11×C22⋊C4—22no—
83C2×C11×C22⋊C4—21no—
84C2×C11×C22⋊C4—22no—
85C2×C11×C22⋊C4—22no—
86C2×C42×C11—21no—
87C2×C42×C11—21no—
88C11×#107—24no—
89C11×#106—24no—
90C11×#103—24no—
91C11×#103—24no—
92C11×#103—42no—
93C11×#103—42no—
94C11×C22⋊C8—24no—
95C11×C22⋊C8—24no—
96C11×C22⋊C8—41no—
97C11×C22⋊C8—41no—
98C11×#95—22no—
99C11×#95—22no—
100#24016C1111yesmaximal, characteristic, direct product factor, Sylow
101C24×C11C2×D411yescharacteristic
102C24×C11C2×D411yescharacteristic
103C24×C11C2×D411yescharacteristic
104C11×#41—48no—
105C11×#41—48no—
106C2×Q8×C11—24no—
107C2×Q8×C11—22no—
108C2×Q8×C11—22no—
109C2×Q8×C11—22no—
110C2×Q8×C11—22no—
111C2×Q8×C11—22no—
112C2×Q8×C11—22no—
113C2×Q8×C11—22no—
114C2×Q8×C11—41no—
115C2×Q8×C11—48no—
116C2×Q8×C11—48no—
117C2×Q8×C11—42no—
118C2×Q8×C11—42no—
119C2×Q8×C11C2×D414yes—
120C2×D4×C11—22no—
121C2×D4×C11—22no—
122C2×D4×C11—22no—
123C2×D4×C11—22no—
124C2×D4×C11—22no—
125C2×D4×C11—22no—
126C2×D4×C11—41no—
127C2×D4×C11—41no—
128C2×D4×C11—41no—
129C22×C4×C11—22no—
130C22×C4×C11—22no—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—24no—
136C22×C4×C11—22no—
137C22×C4×C11—22no—
138C22×C4×C11—22no—
139C22×C4×C11—22no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—22no—
143C22×C4×C11—22no—
144C22×C4×C11—42no—
145C22×C4×C11—42no—
146C22×C4×C11—42no—
147C22×C4×C11—82no—
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D414yes—
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11#4114yes—
153C22×C4×C11C2411yescharacteristic
154C2×C8×C11—22no—
155C2×C8×C11—22no—
156C2×C8×C11—22no—
157C2×C8×C11—22no—
158C2×C8×C11—22no—
159C2×C8×C11—22no—
160C11×C4⋊C4—28no—
161C11×C4⋊C4—28no—
162C11×C4⋊C4—22no—
163C11×C4⋊C4—22no—
164C11×C4⋊C4—22no—
165C11×C4⋊C4—22no—
166C11×C4⋊C4—22no—
167C11×C4⋊C4—42no—
168C11×C4⋊C4C2×D414yes—
169C11×C22⋊C4—24no—
170C11×C22⋊C4—28no—
171C11×C22⋊C4—28no—
172C11×C22⋊C4—42no—
173C11×C22⋊C4—82no—
174C11×C22⋊C4—82no—
175C42×C11—24no—
176C42×C11—42no—
177C2×#536C2×C1111yescharacteristic
178C2×#485C2×C1112yescomplemented
179#2311C2×C1111yescharacteristic
180#2036C2×C1112yescomplemented
181#2035C2×C1112yescomplemented
182#1872C2×C1112yescomplemented
183#1854C2×C1112yescomplemented
184#1787C2×C1112yescomplemented
185#1780C2×C1111yescharacteristic
186C23×C11—21no—
187C23×C11—21no—
188C23×C11—21no—
189C23×C11—21no—
190C23×C11—22no—
191C23×C11—22no—
192C23×C11—22no—
193C23×C11—22no—
194C23×C11—21no—
195C23×C11—21no—
196C23×C11—21no—
197C23×C11—22no—
198C23×C11—22no—
199C23×C11#12012yes—
200C23×C11#12312yes—
201C23×C11C22×D411yescharacteristic
202Q8×C11—24no—
203Q8×C11—24no—
204Q8×C11—44no—
205Q8×C11—48no—
206Q8×C11—42no—
207Q8×C11—42no—
208D4×C11—44no—
209D4×C11—44no—
210D4×C11—44no—
211C2×C4×C11—21no—
212C2×C4×C11—21no—
213C2×C4×C11—21no—
214C2×C4×C11—21no—
215C2×C4×C11—24no—
216C2×C4×C11—24no—
217C2×C4×C11—24no—
218C2×C4×C11—24no—
219C2×C4×C11—24no—
220C2×C4×C11—24no—
221C2×C4×C11—21no—
222C2×C4×C11—21no—
223C2×C4×C11—21no—
224C2×C4×C11—48no—
225C2×C4×C11—42no—
226C2×C4×C11—42no—
227C2×C4×C11—42no—
228C2×C4×C11—42no—
229C2×C4×C11—42no—
230C2×C4×C11—42no—
231C2×C4×C11—42no—
232C2×C4×C11—42no—
233C2×C4×C11—42no—
234C2×C4×C11—42no—
235C2×C4×C11—42no—
236C2×C4×C11—42no—
237C2×C4×C11—84no—
238C2×C4×C11#12012yes—
239C2×C4×C11#12312yes—
240C2×C4×C11C22×D412yes—
241C2×C4×C11C2×#4112yes—
242C2×C4×C11H(5,𝔽2)11yescharacteristic
243C2×C4×C11H(5,𝔽2)11yescharacteristic
244C8×C11—42no—
245C8×C11—42no—
246C22×#41C22×C1111yescharacteristic
247C23×Q8C22×C1111yescharacteristic
248#536—28no—
249C2×C4⋊Q8—21no—
250C2×#124—21no—
251C2×#123—21no—
252C2×#123—21no—
253C2×C22⋊Q8C22×C1112yes—
254C2×C22⋊Q8C22×C1112yes—
255C2×#117C22×C1111yescharacteristic
256C2×#117C22×C1111yescharacteristic
257C22×C4⋊C4C22×C1111yescharacteristic
258#485—28no—
259C2×#107C22×C1112yes—
260C2×#106C22×C1112yes—
261C2×#103C22×C1112yes—
262C2×#103C22×C1112yes—
263C2×#103C22×C1112yes—
264C2×#103C22×C1112yes—
265C2×C22⋊C8C22×C1112yes—
266C2×C22⋊C8C22×C1112yes—
267C2×C22⋊C8C22×C1111yescharacteristic
268C2×C22⋊C8C22×C1111yescharacteristic
269#391—21no—
270#390—21no—
271#386—21no—
272#386—21no—
273#380C22×C1112yes—
274#380C22×C1112yes—
275#340C22×C1112yes—
276#340C22×C1112yes—
277C22×C11—24no—
278C22×C11—22no—
279C22×C11—22no—
280C22×C11—24no—
281C22×C11—42no—
282C22×C11—41no—
283C22×C11—41no—
284C22×C11—41no—
285C22×C11—41no—
286C22×C11—42no—
287C22×C11—42no—
288C22×C11—41no—
289C22×C11—41no—
290C22×C11—41no—
291C22×C11—42no—
292C22×C11C2×#12011yescharacteristic
293C22×C11C2×#12311yescharacteristic
294C22×C11#53411yescharacteristic
295C22×C11#57712yes—
296C22×C11#57812yes—
297C4×C11—22no—
298C4×C11—22no—
299C4×C11—41no—
300C4×C11—44no—
301C4×C11—44no—
302C4×C11—82no—
303C4×C11—82no—
304C4×C11#54612yes—
305C4×C11#54612yes—
306C2×#41—24no—
307C2×#41—24no—
308C2×#41—41no—
309C2×#41—41no—
310C22×Q8—24no—
311C22×Q8—21no—
312C22×Q8—24no—
313C22×Q8—41no—
314C22×Q8—41no—
315C22×Q8D4×C1111yescharacteristic
316C22×Q8C23×C1112yes—
317C22×D4D4×C1111yescharacteristic
318C22×D4D4×C1111yescharacteristic
319C22×D4D4×C1111yescharacteristic
320C23×C4—21no—
321C23×C4—21no—
322C23×C4C23×C1111yescharacteristic
323C23×C4C23×C1111yescharacteristic
324C23×C4C23×C1111yescharacteristic
325C22×C8C23×C1112yes—
326C22×C8C23×C1112yes—
327C4⋊Q8—28no—
328#124—28no—
329#123—28no—
330#123—28no—
331C22⋊Q8—24no—
332C22⋊Q8—24no—
333C22⋊Q8—24no—
334C22⋊Q8D4×C1118yes—
335#117—24no—
336#117—24no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—41no—
341C2×C4⋊C4—41no—
342C2×C4⋊C4C23×C1112yes—
343C2×C4⋊C4C23×C1112yes—
344C2×C4⋊C4C23×C1112yes—
345C2×C22⋊C4—21no—
346C2×C22⋊C4—22no—
347C2×C22⋊C4—22no—
348C2×C22⋊C4—21no—
349C2×C22⋊C4—22no—
350C2×C22⋊C4—22no—
351C2×C42—21no—
352C2×C42—21no—
353#107—24no—
354#106—24no—
355#103—24no—
356#103—24no—
357#103—42no—
358#103—42no—
359C22⋊C8—24no—
360C22⋊C8—24no—
361C22⋊C8—41no—
362C22⋊C8—41no—
363#95—22no—
364#95—22no—
365C2×C11—42no—
366C2×C11—42no—
367C2×C11—81no—
368C2×C11#240511yescharacteristic
369C2×C11#301312yes—
370C2×C11#309712yes—
371C2×C11#320011yescharacteristic
372C2×C11#320211yescharacteristic
373C24C2×D4×C1111yescharacteristic
374C24C2×D4×C1111yescharacteristic
375C24C2×D4×C1111yescharacteristic
376#41—48no—
377#41—48no—
378C2×Q8—24no—
379C2×Q8—22no—
380C2×Q8—22no—
381C2×Q8—22no—
382C2×Q8—22no—
383C2×Q8—22no—
384C2×Q8—22no—
385C2×Q8—22no—
386C2×Q8—41no—
387C2×Q8—48no—
388C2×Q8—48no—
389C2×Q8—42no—
390C2×Q8—42no—
391C2×Q8C2×D4×C1114yes—
392C2×D4—22no—
393C2×D4—22no—
394C2×D4—22no—
395C2×D4—22no—
396C2×D4—22no—
397C2×D4—22no—
398C2×D4—41no—
399C2×D4—41no—
400C2×D4—41no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—21no—
404C22×C4—21no—
405C22×C4—21no—
406C22×C4—21no—
407C22×C4—24no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—42no—
417C22×C4—42no—
418C22×C4—42no—
419C22×C4—82no—
420C22×C4C2×D4×C1111yescharacteristic
421C22×C4C2×D4×C1111yescharacteristic
422C22×C4C2×D4×C1114yes—
423C22×C4C2×D4×C1111yescharacteristic
424C22×C4C11×#4114yes—
425C22×C4C24×C1111yescharacteristic
426C2×C8—22no—
427C2×C8—22no—
428C2×C8—22no—
429C2×C8—22no—
430C2×C8—22no—
431C2×C8—22no—
432C4⋊C4—28no—
433C4⋊C4—28no—
434C4⋊C4—22no—
435C4⋊C4—22no—
436C4⋊C4—22no—
437C4⋊C4—22no—
438C4⋊C4—22no—
439C4⋊C4—42no—
440C4⋊C4C2×D4×C1114yes—
441C22⋊C4—24no—
442C22⋊C4—28no—
443C22⋊C4—28no—
444C22⋊C4—42no—
445C22⋊C4—82no—
446C22⋊C4—82no—
447C42—24no—
448C42—42no—
449C11#2401611yescharacteristic, direct product factor, Sylow
450C23—21no—
451C23—21no—
452C23—21no—
453C23—21no—
454C23—22no—
455C23—22no—
456C23—22no—
457C23—22no—
458C23—21no—
459C23—21no—
460C23—21no—
461C23—22no—
462C23—22no—
463C23C11×#12012yes—
464C23C11×#12312yes—
465C23C22×D4×C1111yescharacteristic
466Q8—24no—
467Q8—24no—
468Q8—44no—
469Q8—48no—
470Q8—42no—
471Q8—42no—
472D4—44no—
473D4—44no—
474D4—44no—
475C2×C4—21no—
476C2×C4—21no—
477C2×C4—21no—
478C2×C4—21no—
479C2×C4—24no—
480C2×C4—24no—
481C2×C4—24no—
482C2×C4—24no—
483C2×C4—24no—
484C2×C4—24no—
485C2×C4—21no—
486C2×C4—21no—
487C2×C4—21no—
488C2×C4—48no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—84no—
502C2×C4C11×#12012yes—
503C2×C4C11×#12312yes—
504C2×C4C22×D4×C1112yes—
505C2×C4C2×C11×#4112yes—
506C2×C4C11×H(5,𝔽2)11yescharacteristic
507C2×C4C11×H(5,𝔽2)11yescharacteristic
508C8—42no—
509C8—42no—
510C22—22no—
511C22—22no—
512C22—24no—
513C22—24no—
514C22—41no—
515C22—41no—
516C22—41no—
517C22—41no—
518C22—42no—
519C22—42no—
520C22—41no—
521C22—41no—
522C22—41no—
523C22—42no—
524C22—42no—
525C22C2×C11×#12011yescharacteristic
526C22C2×C11×#12311yescharacteristic
527C22C11×#53411yescharacteristic
528C22C11×#57712yes—
529C22C11×#57812yes—
530C4—22no—
531C4—22no—
532C4—41no—
533C4—44no—
534C4—44no—
535C4—82no—
536C4—82no—
537C4C11×#54612yes—
538C4C11×#54612yes—
539C2—42no—
540C2—42no—
541C2—81no—
542C2C11×#240511yescharacteristic
543C2C11×#301312yes—
544C2C11×#309712yes—
545C2C11×#320011yescharacteristic
546C2C11×#320211yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC22×C11×#41C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C22×C11×#41 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#485C2semidirect
4. C11×#2036C2semidirect
5. C11×#2035C2semidirect
6. C11×#1872C2semidirect
7. C11×#1854C2semidirect
8. C11×#1787C2semidirect
100. #24016C11direct (N × H)
178. C2×#485C2×C11semidirect
180. #2036C2×C11semidirect
181. #2035C2×C11semidirect
182. #1872C2×C11semidirect
183. #1854C2×C11semidirect
184. #1787C2×C11semidirect
449. C11#24016direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5362
C2×C11×#4852
C11×#23112
C11×#20362
C11×#20352
C11×#18722
C11×#18542
C11×#17872
C11×#17802
#2401611