Finite Group Databasebeta

← C11×#24672 #14601865

Subgroups — C11×#24672 #14601865

Order 2816.

754 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3039C211yesmaximal, characteristic
2C2×C11×#462C211yesmaximal, characteristic, complemented
3C4×C11×#137C211yesmaximal, characteristic
4C11×#2925C211yesmaximal, characteristic
5C11×#2052C212yesmaximal
6C11×#2020C212yesmaximal
7C11×#1979C212yesmaximal, complemented
8C11×#1966C211yesmaximal, characteristic, complemented
9C11×#1950C211yesmaximal, characteristic, complemented
10C11×#1930C212yesmaximal, complemented
11C11×#1801C211yesmaximal, characteristic, complemented
12C2×C11×#137C2211yescharacteristic
13C2×C11×#137C2212yes—
14C22×C11×Q16C2212yes—
15C2×C11×C4⋊Q8C2211yescharacteristic
16C4×C11×#41C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C11×#462—21no—
19C11×#462—21no—
20C11×#462—21no—
21C11×#462—21no—
22C11×#462—22no—
23C11×#461—21no—
24C11×#461—21no—
25C11×#441—21no—
26C11×#440—21no—
27C4×C11×Q16—21no—
28C4×C11×SD16—21no—
29C11×#433—22no—
30C11×#432—21no—
31C11×#431—21no—
32C2×C11×#108C2212yes—
33C11×#428C2211yescharacteristic
34C11×#423C2211yescharacteristic
35C11×#423C2211yescharacteristic
36C2×C11×C4⋊C8C2211yescharacteristic
37C11×#419C2211yescharacteristic
38C11×#419C2212yes—
39C11×#417C2211yescharacteristic
40C2×C11×#103C2212yes—
41C2×C11×#101C2212yes—
42C2×C11×#101C2212yes—
43C2×C11×#101C2212yes—
44C11×#408C2212yes—
45C11×#405C2212yes—
46C4×C11×M16C2211yescharacteristic
47C11×#343C2212yes—
48C11×#341C2212yes—
49C2×C11×#41C2311yescharacteristic
50C22×Q8×C11C2312yes—
51C22×Q8×C11C2311yescharacteristic
52C11×#137—22no—
53C11×#137—22no—
54C11×#137—42no—
55C11×#137—42no—
56C2×C11×Q16—21no—
57C2×C11×Q16—22no—
58C2×C11×Q16—24no—
59C2×C11×Q16—22no—
60C2×C11×Q16—22no—
61C2×C11×Q16—42no—
62C2×C11×SD16—21no—
63C2×C11×SD16—22no—
64C2×C11×M16C2312yes—
65C2×C11×M16C2312yes—
66C2×C11×M16C2311yescharacteristic
67C2×C11×M16C2311yescharacteristic
68C22×C8×C11C2312yes—
69C11×C4⋊Q8—21no—
70C11×C4⋊Q8—21no—
71C11×C4⋊Q8—21no—
72C11×C4⋊Q8—21no—
73C4×Q8×C11—21no—
74C4×Q8×C11—21no—
75C4×Q8×C11—21no—
76C4×Q8×C11—21no—
77C4×Q8×C11D411yescharacteristic
78C4×Q8×C11D411yescharacteristic
79C4×D4×C11—21no—
80C4×D4×C11—21no—
81C4×D4×C11D411yescharacteristic
82C4×D4×C11D411yescharacteristic
83C11×#117—21no—
84C11×#117C2311yescharacteristic
85C2×C11×C4⋊C4—21no—
86C2×C11×C4⋊C4—21no—
87C2×C11×C4⋊C4—21no—
88C2×C11×C4⋊C4C2311yescharacteristic
89C2×C42×C11—21no—
90C2×C42×C11—21no—
91C2×C42×C11C2311yescharacteristic
92C11×#108—42no—
93C11×#107—21no—
94C11×#106—21no—
95C11×C4⋊C8—21no—
96C11×C4⋊C8—21no—
97C11×C4⋊C8—21no—
98C11×C4⋊C8—21no—
99C11×C4⋊C8D411yescharacteristic
100C11×C4⋊C8D411yescharacteristic
101C11×C4⋊C8D412yes—
102C11×#103—21no—
103C11×#103—22no—
104C11×#103—22no—
105C11×#103—21no—
106C11×#103—21no—
107C11×#103—22no—
108C11×#103—22no—
109C11×#102—21no—
110C11×#101—24no—
111C11×#101—42no—
112C11×#101—42no—
113C11×C22⋊C8—22no—
114C11×C22⋊C8—22no—
115C11×#97—22no—
116C11×#97—21no—
117C4×C8×C11—22no—
118C4×C8×C11—21no—
119#24672C1111yesmaximal, characteristic, direct product factor, Sylow
120C11×#41—21no—
121C11×#41—21no—
122C11×#41—21no—
123C11×#41—21no—
124C2×Q8×C11—21no—
125C2×Q8×C11—21no—
126C2×Q8×C11—21no—
127C2×Q8×C11—22no—
128C2×Q8×C11—22no—
129C2×Q8×C11—21no—
130C2×Q8×C11—22no—
131C2×Q8×C11—22no—
132C2×Q8×C11—21no—
133C2×Q8×C11—22no—
134C2×Q8×C11—22no—
135C2×Q8×C11C2×D411yescharacteristic
136C2×Q8×C11#4112yes—
137C2×D4×C11—21no—
138C2×D4×C11C2×D411yescharacteristic
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—22no—
144C22×C4×C11—21no—
145C22×C4×C11#4111yescharacteristic
146C22×C4×C11#4111yescharacteristic
147C22×C4×C11C2411yescharacteristic
148C11×Q16—24no—
149C11×Q16—44no—
150C11×Q16—44no—
151C11×Q16—44no—
152C11×SD16—24no—
153C11×SD16—44no—
154C11×M16—21no—
155C11×M16—22no—
156C11×M16—21no—
157C11×M16—22no—
158C11×M16—22no—
159C11×M16—21no—
160C11×M16—22no—
161C11×M16#4112yes—
162C2×C8×C11—21no—
163C2×C8×C11—22no—
164C2×C8×C11—21no—
165C2×C8×C11—22no—
166C2×C8×C11—22no—
167C2×C8×C11—22no—
168C2×C8×C11C2×D412yes—
169C2×C8×C11C2×D412yes—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—41no—
175C11×C4⋊C4—41no—
176C11×C4⋊C4—41no—
177C11×C4⋊C4—41no—
178C11×C4⋊C4—41no—
179C11×C4⋊C4—41no—
180C11×C4⋊C4C2×D411yescharacteristic
181C11×C4⋊C4C2×D411yescharacteristic
182C11×C22⋊C4—21no—
183C11×C22⋊C4—21no—
184C11×C22⋊C4—21no—
185C42×C11—21no—
186C42×C11—21no—
187C42×C11—21no—
188C42×C11—41no—
189C42×C11—41no—
190C42×C11C2×D411yescharacteristic
191C42×C11C2×D411yescharacteristic
192C42×C11C2×D411yescharacteristic
193C42×C11C2×D411yescharacteristic
194#3039C2×C1111yescharacteristic
195C2×#462C2×C1111yescharacteristic, complemented
196C4×#137C2×C1111yescharacteristic
197#2925C2×C1111yescharacteristic
198#2052C2×C1112yes—
199#2020C2×C1112yes—
200#1979C2×C1112yescomplemented
201#1966C2×C1111yescharacteristic, complemented
202#1950C2×C1111yescharacteristic, complemented
203#1930C2×C1112yescomplemented
204#1801C2×C1111yescharacteristic, complemented
205C23×C11—21no—
206C23×C11C2×#4111yescharacteristic
207Q8×C11—22no—
208Q8×C11—21no—
209Q8×C11—21no—
210Q8×C11—22no—
211Q8×C11—41no—
212Q8×C11—41no—
213Q8×C11—42no—
214Q8×C11—42no—
215Q8×C11—42no—
216Q8×C11—42no—
217D4×C11—21no—
218D4×C11—21no—
219D4×C11—41no—
220D4×C11—41no—
221C2×C4×C11—22no—
222C2×C4×C11—21no—
223C2×C4×C11—21no—
224C2×C4×C11—21no—
225C2×C4×C11—22no—
226C2×C4×C11—41no—
227C2×C4×C11—41no—
228C2×C4×C11—41no—
229C2×C4×C11—41no—
230C2×C4×C11—41no—
231C2×C4×C11—42no—
232C2×C4×C11—41no—
233C2×C4×C11—42no—
234C2×C4×C11—42no—
235C2×C4×C11—42no—
236C2×C4×C11—81no—
237C2×C4×C11—81no—
238C2×C4×C11#12111yescharacteristic
239C2×C4×C11#12111yescharacteristic
240C2×C4×C11#12111yescharacteristic
241C2×C4×C11#12111yescharacteristic
242C2×C4×C11C22×D411yescharacteristic
243C2×C4×C11C22×D411yescharacteristic
244C2×C4×C11C2×#4111yescharacteristic
245C2×C4×C11C2×#4111yescharacteristic
246C2×C4×C11H(5,𝔽2)11yescharacteristic
247C2×C4×C11H(5,𝔽2)11yescharacteristic
248C8×C11—22no—
249C8×C11—22no—
250C8×C11—22no—
251C8×C11—41no—
252C8×C11—42no—
253C8×C11—42no—
254C2×#137C22×C1111yescharacteristic
255C2×#137C22×C1112yes—
256C22×Q16C22×C1112yes—
257C2×C4⋊Q8C22×C1111yescharacteristic
258C4×#41C22×C1111yescharacteristic
259C2×C4×Q8C22×C1111yescharacteristic
260#462—21no—
261#462—21no—
262#462—21no—
263#462—21no—
264#462—22no—
265#461—21no—
266#461—21no—
267#441—21no—
268#440—21no—
269C4×Q16—21no—
270C4×SD16—21no—
271#433—22no—
272#432—21no—
273#431—21no—
274C2×#108C22×C1112yes—
275#428C22×C1111yescharacteristic
276#423C22×C1111yescharacteristic
277#423C22×C1111yescharacteristic
278C2×C4⋊C8C22×C1111yescharacteristic
279#419C22×C1111yescharacteristic
280#419C22×C1112yes—
281#417C22×C1111yescharacteristic
282C2×#103C22×C1112yes—
283C2×#101C22×C1112yes—
284C2×#101C22×C1112yes—
285C2×#101C22×C1112yes—
286#408C22×C1112yes—
287#405C22×C1112yes—
288C4×M16C22×C1111yescharacteristic
289#343C22×C1112yes—
290#341C22×C1112yes—
291C22×C11—21no—
292C22×C11—21no—
293C22×C11—41no—
294C22×C11—41no—
295C22×C11—41no—
296C22×C11C2×#12111yescharacteristic
297C22×C11#55311yescharacteristic
298C22×C11#55511yescharacteristic
299C4×C11—21no—
300C4×C11—21no—
301C4×C11—21no—
302C4×C11—41no—
303C4×C11—42no—
304C4×C11—41no—
305C4×C11—41no—
306C4×C11—82no—
307C4×C11—81no—
308C4×C11#47312yes—
309C4×C11#52511yescharacteristic
310C4×C11#53511yescharacteristic
311C4×C11#54611yescharacteristic
312C4×C11#55011yescharacteristic
313C2×#41C23×C1111yescharacteristic
314C22×Q8C23×C1112yes—
315C22×Q8C23×C1111yescharacteristic
316#137—22no—
317#137—22no—
318#137—42no—
319#137—42no—
320C2×Q16—21no—
321C2×Q16—22no—
322C2×Q16—24no—
323C2×Q16—22no—
324C2×Q16—22no—
325C2×Q16—42no—
326C2×SD16—21no—
327C2×SD16—22no—
328C2×M16C23×C1112yes—
329C2×M16C23×C1112yes—
330C2×M16C23×C1111yescharacteristic
331C2×M16C23×C1111yescharacteristic
332C22×C8C23×C1112yes—
333C4⋊Q8—21no—
334C4⋊Q8—21no—
335C4⋊Q8—21no—
336C4⋊Q8—21no—
337C4×Q8—21no—
338C4×Q8—21no—
339C4×Q8—21no—
340C4×Q8—21no—
341C4×Q8D4×C1111yescharacteristic
342C4×Q8D4×C1111yescharacteristic
343C4×D4—21no—
344C4×D4—21no—
345C4×D4D4×C1111yescharacteristic
346C4×D4D4×C1111yescharacteristic
347#117—21no—
348#117C23×C1111yescharacteristic
349C2×C4⋊C4—21no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4C23×C1111yescharacteristic
353C2×C42—21no—
354C2×C42—21no—
355C2×C42C23×C1111yescharacteristic
356#108—42no—
357#107—21no—
358#106—21no—
359C4⋊C8—21no—
360C4⋊C8—21no—
361C4⋊C8—21no—
362C4⋊C8—21no—
363C4⋊C8D4×C1111yescharacteristic
364C4⋊C8D4×C1111yescharacteristic
365C4⋊C8D4×C1112yes—
366#103—21no—
367#103—22no—
368#103—22no—
369#103—21no—
370#103—21no—
371#103—22no—
372#103—22no—
373#102—21no—
374#101—24no—
375#101—42no—
376#101—42no—
377C22⋊C8—22no—
378C22⋊C8—22no—
379#97—22no—
380#97—21no—
381C4×C8—22no—
382C4×C8—21no—
383C2×C11—21no—
384C2×C11—21no—
385C2×C11—81no—
386C2×C11#241411yescharacteristic
387C2×C11C2×#47311yescharacteristic
388C2×C11#306911yescharacteristic
389#41—21no—
390#41—21no—
391#41—21no—
392#41—21no—
393C2×Q8—21no—
394C2×Q8—21no—
395C2×Q8—21no—
396C2×Q8—22no—
397C2×Q8—22no—
398C2×Q8—21no—
399C2×Q8—22no—
400C2×Q8—22no—
401C2×Q8—21no—
402C2×Q8—22no—
403C2×Q8—22no—
404C2×Q8C2×D4×C1111yescharacteristic
405C2×Q8C11×#4112yes—
406C2×D4—21no—
407C2×D4C2×D4×C1111yescharacteristic
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—22no—
413C22×C4—21no—
414C22×C4C11×#4111yescharacteristic
415C22×C4C11×#4111yescharacteristic
416C22×C4C24×C1111yescharacteristic
417Q16—24no—
418Q16—44no—
419Q16—44no—
420Q16—44no—
421SD16—24no—
422SD16—44no—
423M16—21no—
424M16—22no—
425M16—21no—
426M16—22no—
427M16—22no—
428M16—21no—
429M16—22no—
430M16C11×#4112yes—
431C2×C8—21no—
432C2×C8—22no—
433C2×C8—22no—
434C2×C8—22no—
435C2×C8—21no—
436C2×C8—22no—
437C2×C8C2×D4×C1112yes—
438C2×C8C2×D4×C1112yes—
439C4⋊C4—21no—
440C4⋊C4—21no—
441C4⋊C4—21no—
442C4⋊C4—21no—
443C4⋊C4—41no—
444C4⋊C4—41no—
445C4⋊C4—41no—
446C4⋊C4—41no—
447C4⋊C4—41no—
448C4⋊C4—41no—
449C4⋊C4C2×D4×C1111yescharacteristic
450C4⋊C4C2×D4×C1111yescharacteristic
451C22⋊C4—21no—
452C22⋊C4—21no—
453C22⋊C4—21no—
454C42—21no—
455C42—21no—
456C42—21no—
457C42—41no—
458C42—41no—
459C42C2×D4×C1111yescharacteristic
460C42C2×D4×C1111yescharacteristic
461C42C2×D4×C1111yescharacteristic
462C42C2×D4×C1111yescharacteristic
463C11#2467211yescharacteristic, direct product factor, Sylow
464C23—21no—
465C23C2×C11×#4111yescharacteristic
466Q8—22no—
467Q8—21no—
468Q8—21no—
469Q8—22no—
470Q8—41no—
471Q8—41no—
472Q8—42no—
473Q8—42no—
474Q8—42no—
475Q8—42no—
476D4—21no—
477D4—21no—
478D4—41no—
479D4—41no—
480C2×C4—22no—
481C2×C4—21no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—22no—
485C2×C4—41no—
486C2×C4—41no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—42no—
491C2×C4—41no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—81no—
496C2×C4—81no—
497C2×C4C11×#12111yescharacteristic
498C2×C4C11×#12111yescharacteristic
499C2×C4C11×#12111yescharacteristic
500C2×C4C11×#12111yescharacteristic
501C2×C4C22×D4×C1111yescharacteristic
502C2×C4C22×D4×C1111yescharacteristic
503C2×C4C2×C11×#4111yescharacteristic
504C2×C4C2×C11×#4111yescharacteristic
505C2×C4C11×H(5,𝔽2)11yescharacteristic
506C2×C4C11×H(5,𝔽2)11yescharacteristic
507C8—22no—
508C8—22no—
509C8—22no—
510C8—42no—
511C8—41no—
512C8—42no—
513C22—21no—
514C22—21no—
515C22—41no—
516C22—41no—
517C22—41no—
518C22C2×C11×#12111yescharacteristic
519C22C11×#55311yescharacteristic
520C22C11×#55511yescharacteristic
521C4—21no—
522C4—21no—
523C4—21no—
524C4—41no—
525C4—42no—
526C4—41no—
527C4—41no—
528C4—82no—
529C4—81no—
530C4C11×#47312yes—
531C4C11×#52511yescharacteristic
532C4C11×#53511yescharacteristic
533C4C11×#54611yescharacteristic
534C4C11×#55011yescharacteristic
535C2—21no—
536C2—21no—
537C2—81no—
538C2C11×#241411yescharacteristic
539C2C2×C11×#47311yescharacteristic
540C2C11×#306911yescharacteristic
subgroupG/H
center, socleC22×C11C2×#121
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#41C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#462C2semidirect
7. C11×#1979C2semidirect
8. C11×#1966C2semidirect
9. C11×#1950C2semidirect
10. C11×#1930C2semidirect
11. C11×#1801C2semidirect
119. #24672C11direct (N × H)
195. C2×#462C2×C11semidirect
200. #1979C2×C11semidirect
201. #1966C2×C11semidirect
202. #1950C2×C11semidirect
203. #1930C2×C11semidirect
204. #1801C2×C11semidirect
463. C11#24672direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#30392
C2×C11×#4622
C4×C11×#1372
C11×#29252
C11×#20522
C11×#20202
C11×#19792
C11×#19662
C11×#19502
C11×#19302
C11×#18012
#2467211