Finite Group Databasebeta

← C11×#24652 #14601845

Subgroups — C11×#24652 #14601845

Order 2816.

896 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×#462C211yesmaximal, characteristic, complemented
2C2×C11×#431C211yesmaximal, characteristic
3C11×#2857C211yesmaximal, characteristic
4C4×C11×C22⋊Q8C211yesmaximal, characteristic
5C11×#2036C212yesmaximal
6C11×#2001C212yesmaximal
7C11×#1981C211yesmaximal, characteristic, complemented
8C11×#1969C212yesmaximal, complemented
9C11×#1947C211yesmaximal, characteristic, complemented
10C11×#1933C212yesmaximal, complemented
11C11×#1803C211yesmaximal, characteristic, complemented
12C22×C11×Q16C2212yes—
13C2×C11×C4⋊Q8C2211yescharacteristic
14C2×C11×C22⋊Q8C2211yescharacteristic
15C2×C11×C22⋊Q8C2212yes—
16C2×C4×Q8×C11C2211yescharacteristic
17C22×C42×C11C2211yescharacteristic
18C11×#462—24no—
19C11×#431—24no—
20C2×C11×#107C2212yes—
21C2×C11×C4⋊C8C2211yescharacteristic
22C2×C11×C4⋊C8C2211yescharacteristic
23C2×C11×#103C2212yes—
24C2×C11×#103C2212yes—
25C2×C11×#103C2212yes—
26C2×C11×#103C2212yes—
27C2×C11×C22⋊C8C2212yes—
28C2×C4×C8×C11C2212yes—
29C11×#391C2212yes—
30C11×#391C2211yescharacteristic
31C11×#389—21no—
32C11×#389—21no—
33C11×#389C2211yescharacteristic
34C11×#387—21no—
35C11×#385—21no—
36C11×#384C2211yescharacteristic
37C11×#380—21no—
38C11×#380—21no—
39C11×#380C2211yescharacteristic
40C4×C11×C4⋊C4—21no—
41C4×C11×C4⋊C4C2211yescharacteristic
42C4×C11×C22⋊C4—21no—
43C11×#340C2212yes—
44C11×#340C2212yes—
45C22×Q8×C11C2312yes—
46C22×Q8×C11C2311yescharacteristic
47C23×C4×C11D411yescharacteristic
48C23×C4×C11D411yescharacteristic
49C23×C4×C11C2311yescharacteristic
50C2×C11×Q16—24no—
51C2×C11×Q16—24no—
52C2×C11×Q16—42no—
53C22×C8×C11C2312yes—
54C22×C8×C11C2312yes—
55C11×C4⋊Q8—22no—
56C11×C4⋊Q8—22no—
57C11×C22⋊Q8—22no—
58C11×C22⋊Q8—22no—
59C11×C22⋊Q8—42no—
60C11×C22⋊Q8—42no—
61C4×Q8×C11—22no—
62C4×Q8×C11—22no—
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4—21no—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4—22no—
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2312yes—
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C22⋊C4—21no—
76C2×C11×C22⋊C4—21no—
77C2×C11×C22⋊C4—22no—
78C2×C42×C11—22no—
79C2×C42×C11—22no—
80C2×C42×C11—21no—
81C2×C42×C11—21no—
82C2×C42×C11D411yescharacteristic
83C2×C42×C11D411yescharacteristic
84C2×C42×C11C2311yescharacteristic
85C2×C42×C11C2311yescharacteristic
86C11×#107—42no—
87C11×C4⋊C8—22no—
88C11×C4⋊C8D414yes—
89C11×#103—24no—
90C11×#103—24no—
91C11×#103—42no—
92C11×#103—42no—
93C11×C22⋊C8—24no—
94C4×C8×C11—24no—
95C11×#95—21no—
96C11×#95—21no—
97C11×#95—21no—
98C11×#95—21no—
99C11×#95—21no—
100C11×#95—22no—
101C11×#95—22no—
102#24652C1111yesmaximal, characteristic, direct product factor, Sylow
103C24×C11C2×D411yescharacteristic
104C2×Q8×C11—21no—
105C2×Q8×C11—21no—
106C2×Q8×C11—22no—
107C2×Q8×C11—21no—
108C2×Q8×C11—22no—
109C2×Q8×C11—22no—
110C2×Q8×C11—22no—
111C2×Q8×C11—21no—
112C2×Q8×C11—21no—
113C2×Q8×C11—22no—
114C2×Q8×C11—22no—
115C2×Q8×C11#4112yes—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—21no—
119C22×C4×C11—21no—
120C22×C4×C11—22no—
121C22×C4×C11—22no—
122C22×C4×C11—21no—
123C22×C4×C11—21no—
124C22×C4×C11—21no—
125C22×C4×C11—21no—
126C22×C4×C11—21no—
127C22×C4×C11—21no—
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11—22no—
131C22×C4×C11—22no—
132C22×C4×C11—41no—
133C22×C4×C11Q1614yescomplemented
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2411yescharacteristic
140C11×Q16—48no—
141C2×C8×C11—22no—
142C2×C8×C11—22no—
143C2×C8×C11—22no—
144C2×C8×C11—22no—
145C2×C8×C11—22no—
146C2×C8×C11C2×D414yes—
147C11×C4⋊C4—24no—
148C11×C4⋊C4—21no—
149C11×C4⋊C4—21no—
150C11×C4⋊C4—21no—
151C11×C4⋊C4—21no—
152C11×C4⋊C4—22no—
153C11×C4⋊C4—21no—
154C11×C4⋊C4—22no—
155C11×C4⋊C4—42no—
156C11×C4⋊C4—44no—
157C11×C4⋊C4—42no—
158C11×C4⋊C4—42no—
159C11×C4⋊C4—42no—
160C11×C4⋊C4—42no—
161C11×C4⋊C4—42no—
162C11×C4⋊C4#4112yes—
163C11×C22⋊C4—24no—
164C11×C22⋊C4—42no—
165C11×C22⋊C4—44no—
166C42×C11—22no—
167C42×C11—22no—
168C42×C11—21no—
169C42×C11—21no—
170C42×C11—42no—
171C42×C11—42no—
172C42×C11C2×D412yes—
173C42×C11#4112yes—
174C2×#462C2×C1111yescharacteristic, complemented
175C2×#431C2×C1111yescharacteristic
176#2857C2×C1111yescharacteristic
177C4×C22⋊Q8C2×C1111yescharacteristic
178#2036C2×C1112yes—
179#2001C2×C1112yes—
180#1981C2×C1111yescharacteristic, complemented
181#1969C2×C1112yescomplemented
182#1947C2×C1111yescharacteristic, complemented
183#1933C2×C1112yescomplemented
184#1803C2×C1111yescharacteristic, complemented
185C23×C11—21no—
186C23×C11—21no—
187C23×C11—21no—
188C23×C11—21no—
189C23×C11—21no—
190C23×C11—21no—
191C23×C11C2×Q1612yes—
192C23×C11C22×D411yescharacteristic
193Q8×C11—22no—
194Q8×C11—22no—
195Q8×C11—41no—
196Q8×C11—41no—
197Q8×C11—42no—
198Q8×C11—42no—
199Q8×C11—42no—
200Q8×C11—42no—
201C2×C4×C11—21no—
202C2×C4×C11—21no—
203C2×C4×C11—21no—
204C2×C4×C11—21no—
205C2×C4×C11—21no—
206C2×C4×C11—21no—
207C2×C4×C11—28no—
208C2×C4×C11—21no—
209C2×C4×C11—22no—
210C2×C4×C11—22no—
211C2×C4×C11—21no—
212C2×C4×C11—21no—
213C2×C4×C11—44no—
214C2×C4×C11—41no—
215C2×C4×C11—41no—
216C2×C4×C11—41no—
217C2×C4×C11—41no—
218C2×C4×C11—41no—
219C2×C4×C11—41no—
220C2×C4×C11—41no—
221C2×C4×C11—41no—
222C2×C4×C11—41no—
223C2×C4×C11—42no—
224C2×C4×C11—42no—
225C2×C4×C11—42no—
226C2×C4×C11—42no—
227C2×C4×C11—41no—
228C2×C4×C11—41no—
229C2×C4×C11—42no—
230C2×C4×C11—41no—
231C2×C4×C11—41no—
232C2×C4×C11—41no—
233C2×C4×C11—42no—
234C2×C4×C11#12112yes—
235C2×C4×C11#12112yes—
236C2×C4×C11C2×Q1612yes—
237C2×C4×C11C2×Q1612yes—
238C2×C4×C11#13512yes—
239C2×C4×C11#13712yes—
240C2×C4×C11C22×D411yescharacteristic
241C2×C4×C11C2×#4111yescharacteristic
242C2×C4×C11C2×#4111yescharacteristic
243C2×C4×C11C2×#4111yescharacteristic
244C2×C4×C11H(5,𝔽2)11yescharacteristic
245C2×C4×C11H(5,𝔽2)11yescharacteristic
246C8×C11—24no—
247C8×C11—42no—
248C22×Q16C22×C1112yes—
249C2×C4⋊Q8C22×C1111yescharacteristic
250C2×C22⋊Q8C22×C1111yescharacteristic
251C2×C22⋊Q8C22×C1112yes—
252C2×C4×Q8C22×C1111yescharacteristic
253C22×C42C22×C1111yescharacteristic
254#462—24no—
255#431—24no—
256C2×#107C22×C1112yes—
257C2×C4⋊C8C22×C1111yescharacteristic
258C2×C4⋊C8C22×C1111yescharacteristic
259C2×#103C22×C1112yes—
260C2×#103C22×C1112yes—
261C2×#103C22×C1112yes—
262C2×#103C22×C1112yes—
263C2×C22⋊C8C22×C1112yes—
264C2×C4×C8C22×C1112yes—
265#391C22×C1112yes—
266#391C22×C1111yescharacteristic
267#389—21no—
268#389—21no—
269#389C22×C1111yescharacteristic
270#387—21no—
271#385—21no—
272#384C22×C1111yescharacteristic
273#380—21no—
274#380—21no—
275#380C22×C1111yescharacteristic
276C4×C4⋊C4—21no—
277C4×C4⋊C4C22×C1111yescharacteristic
278C4×C22⋊C4—21no—
279#340C22×C1112yes—
280#340C22×C1112yes—
281C22×C11—22no—
282C22×C11—22no—
283C22×C11—22no—
284C22×C11—41no—
285C22×C11—41no—
286C22×C11—41no—
287C22×C11—41no—
288C22×C11C2×#12111yescharacteristic
289C22×C11#52511yescharacteristic
290C22×C11#53511yescharacteristic
291C22×C11C22×Q1611yescharacteristic
292C22×C11C2×#13511yescharacteristic
293C22×C11C2×#13711yescharacteristic
294C22×C11#57511yescharacteristic
295C4×C11—22no—
296C4×C11—22no—
297C4×C11—22no—
298C4×C11—42no—
299C4×C11—41no—
300C4×C11—42no—
301C4×C11—82no—
302C4×C11—82no—
303C4×C11—81no—
304C4×C11—81no—
305C4×C11#46714yes—
306C4×C11#54611yescharacteristic
307C4×C11#55011yescharacteristic
308C4×C11#55311yescharacteristic
309C4×C11#55511yescharacteristic
310C22×Q8C23×C1112yes—
311C22×Q8C23×C1111yescharacteristic
312C23×C4D4×C1111yescharacteristic
313C23×C4D4×C1111yescharacteristic
314C23×C4C23×C1111yescharacteristic
315C2×Q16—24no—
316C2×Q16—24no—
317C2×Q16—42no—
318C22×C8C23×C1112yes—
319C22×C8C23×C1112yes—
320C4⋊Q8—22no—
321C4⋊Q8—22no—
322C22⋊Q8—22no—
323C22⋊Q8—22no—
324C22⋊Q8—42no—
325C22⋊Q8—42no—
326C4×Q8—22no—
327C4×Q8—22no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—22no—
331C2×C4⋊C4—21no—
332C2×C4⋊C4—21no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4C23×C1111yescharacteristic
337C2×C4⋊C4C23×C1112yes—
338C2×C4⋊C4C23×C1111yescharacteristic
339C2×C4⋊C4C23×C1111yescharacteristic
340C2×C22⋊C4—21no—
341C2×C22⋊C4—22no—
342C2×C22⋊C4—21no—
343C2×C42—22no—
344C2×C42—22no—
345C2×C42—21no—
346C2×C42—21no—
347C2×C42D4×C1111yescharacteristic
348C2×C42D4×C1111yescharacteristic
349C2×C42C23×C1111yescharacteristic
350C2×C42C23×C1111yescharacteristic
351#107—42no—
352C4⋊C8—22no—
353C4⋊C8D4×C1114yes—
354#103—24no—
355#103—24no—
356#103—42no—
357#103—42no—
358C22⋊C8—24no—
359C4×C8—24no—
360#95—21no—
361#95—21no—
362#95—21no—
363#95—21no—
364#95—21no—
365#95—22no—
366#95—22no—
367C2×C11—42no—
368C2×C11#241411yescharacteristic
369C2×C11C2×#46711yescharacteristic
370C2×C11#305611yescharacteristic
371C2×C11#310411yescharacteristic
372C2×C11#310711yescharacteristic
373C2×C11#320911yescharacteristic
374C2×C11#321211yescharacteristic
375C24C2×D4×C1111yescharacteristic
376C2×Q8—21no—
377C2×Q8—21no—
378C2×Q8—22no—
379C2×Q8—21no—
380C2×Q8—22no—
381C2×Q8—22no—
382C2×Q8—22no—
383C2×Q8—21no—
384C2×Q8—21no—
385C2×Q8—22no—
386C2×Q8—22no—
387C2×Q8C11×#4112yes—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—21no—
391C22×C4—21no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—41no—
405C22×C4C11×Q1614yescomplemented
406C22×C4C2×D4×C1111yescharacteristic
407C22×C4C2×D4×C1111yescharacteristic
408C22×C4C2×D4×C1111yescharacteristic
409C22×C4C2×D4×C1111yescharacteristic
410C22×C4C2×D4×C1111yescharacteristic
411C22×C4C24×C1111yescharacteristic
412Q16—48no—
413C2×C8—22no—
414C2×C8—22no—
415C2×C8—22no—
416C2×C8—22no—
417C2×C8—22no—
418C2×C8C2×D4×C1114yes—
419C4⋊C4—24no—
420C4⋊C4—21no—
421C4⋊C4—21no—
422C4⋊C4—21no—
423C4⋊C4—21no—
424C4⋊C4—22no—
425C4⋊C4—21no—
426C4⋊C4—22no—
427C4⋊C4—44no—
428C4⋊C4—42no—
429C4⋊C4—42no—
430C4⋊C4—42no—
431C4⋊C4—42no—
432C4⋊C4—42no—
433C4⋊C4—42no—
434C4⋊C4C11×#4112yes—
435C22⋊C4—24no—
436C22⋊C4—44no—
437C22⋊C4—42no—
438C42—22no—
439C42—22no—
440C42—21no—
441C42—21no—
442C42—42no—
443C42—42no—
444C42C2×D4×C1112yes—
445C42C11×#4112yes—
446C11#2465211yescharacteristic, direct product factor, Sylow
447C23—21no—
448C23—21no—
449C23—21no—
450C23—21no—
451C23—21no—
452C23—21no—
453C23C2×C11×Q1612yes—
454C23C22×D4×C1111yescharacteristic
455Q8—22no—
456Q8—22no—
457Q8—41no—
458Q8—41no—
459Q8—42no—
460Q8—42no—
461Q8—42no—
462Q8—42no—
463C2×C4—21no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—21no—
467C2×C4—21no—
468C2×C4—21no—
469C2×C4—28no—
470C2×C4—21no—
471C2×C4—22no—
472C2×C4—22no—
473C2×C4—21no—
474C2×C4—21no—
475C2×C4—44no—
476C2×C4—41no—
477C2×C4—41no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—41no—
482C2×C4—41no—
483C2×C4—41no—
484C2×C4—41no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—42no—
488C2×C4—42no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4—42no—
492C2×C4—41no—
493C2×C4—41no—
494C2×C4—41no—
495C2×C4—42no—
496C2×C4C11×#12112yes—
497C2×C4C11×#12112yes—
498C2×C4C2×C11×Q1612yes—
499C2×C4C2×C11×Q1612yes—
500C2×C4C11×#13512yes—
501C2×C4C11×#13712yes—
502C2×C4C22×D4×C1111yescharacteristic
503C2×C4C2×C11×#4111yescharacteristic
504C2×C4C2×C11×#4111yescharacteristic
505C2×C4C2×C11×#4111yescharacteristic
506C2×C4C11×H(5,𝔽2)11yescharacteristic
507C2×C4C11×H(5,𝔽2)11yescharacteristic
508C8—24no—
509C8—42no—
510C22—22no—
511C22—22no—
512C22—22no—
513C22—41no—
514C22—41no—
515C22—41no—
516C22—41no—
517C22C2×C11×#12111yescharacteristic
518C22C11×#52511yescharacteristic
519C22C11×#53511yescharacteristic
520C22C22×C11×Q1611yescharacteristic
521C22C2×C11×#13511yescharacteristic
522C22C2×C11×#13711yescharacteristic
523C22C11×#57511yescharacteristic
524C4—22no—
525C4—22no—
526C4—22no—
527C4—41no—
528C4—42no—
529C4—42no—
530C4—82no—
531C4—82no—
532C4—81no—
533C4—81no—
534C4C11×#46714yes—
535C4C11×#54611yescharacteristic
536C4C11×#55011yescharacteristic
537C4C11×#55311yescharacteristic
538C4C11×#55511yescharacteristic
539C2—42no—
540C2C11×#241411yescharacteristic
541C2C2×C11×#46711yescharacteristic
542C2C11×#305611yescharacteristic
543C2C11×#310411yescharacteristic
544C2C11×#310711yescharacteristic
545C2C11×#320911yescharacteristic
546C2C11×#321211yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC24×C11C2×D4
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
1. C2×C11×#462C2semidirect
7. C11×#1981C2semidirect
8. C11×#1969C2semidirect
9. C11×#1947C2semidirect
10. C11×#1933C2semidirect
11. C11×#1803C2semidirect
102. #24652C11direct (N × H)
133. C22×C4×C11Q16semidirect
174. C2×#462C2×C11semidirect
180. #1981C2×C11semidirect
181. #1969C2×C11semidirect
182. #1947C2×C11semidirect
183. #1933C2×C11semidirect
184. #1803C2×C11semidirect
405. C22×C4C11×Q16semidirect
446. C11#24652direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4622
C2×C11×#4312
C11×#28572
C4×C11×C22⋊Q82
C11×#20362
C11×#20012
C11×#19812
C11×#19692
C11×#19472
C11×#19332
C11×#18032
#2465211