Finite Group Databasebeta

← C11×#13046 #14590239

Subgroups — C11×#13046 #14590239

Order 2816.

644 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3025C211yesmaximal, characteristic
2C11×#2978C211yesmaximal, characteristic, complemented
3C11×#2120C211yesmaximal, characteristic, complemented
4C11×#1794C211yesmaximal, characteristic, complemented
5C11×#1791C211yesmaximal, characteristic, complemented
6C11×#1395C211yesmaximal, characteristic, complemented
7C11×#1391C211yesmaximal, characteristic, complemented
8C11×#585C2211yescharacteristic
9C11×#525—21no—
10C11×#525C2211yescharacteristic
11C11×#458—21no—
12C11×#458C412yescomplemented
13C11×B(4,𝔽2)—21no—
14C11×B(4,𝔽2)C412yescomplemented
15C11×#436—21no—
16C11×#436—21no—
17C11×#435—21no—
18C11×#435—21no—
19C11×#433—21no—
20C11×#421—21no—
21C11×#416—21no—
22C11×#413—21no—
23C11×#413C2211yescharacteristic
24C11×#410—21no—
25C11×#410C2211yescharacteristic
26C11×#410C2211yescharacteristic
27C11×#408—21no—
28C11×#408C2211yescharacteristic
29C11×#408C2211yescharacteristic
30C11×#407—21no—
31C11×#352—21no—
32C11×AΣL(1,𝔽16)—21no—
33C11×2−1+4—21no—
34C11×2−1+4—41no—
35C11×H(5,𝔽2)—21no—
36C11×H(5,𝔽2)—21no—
37C11×H(5,𝔽2)—41no—
38C11×H(5,𝔽2)C2×C412yes—
39C2×C11×#41—21no—
40C2×C11×#41—21no—
41C2×C11×#41—21no—
42C2×C11×#41—42no—
43C2×C11×#41C2311yescharacteristic
44C23×C4×C11D411yescharacteristic
45C2×C11×M16—21no—
46C2×C11×M16—21no—
47C2×C11×M16—21no—
48C2×C11×M16D411yescharacteristic, complemented
49C2×C11×M16D411yescharacteristic, complemented
50C22×C8×C11D411yescharacteristic, complemented
51C22×C8×C11D411yescharacteristic, complemented
52C11×#123—22no—
53C11×#123C2×C411yescharacteristic
54C11×#123D411yescharacteristic
55C11×C22⋊Q8—21no—
56C11×C22⋊Q8—41no—
57C11×#121—21no—
58C11×#121—41no—
59C11×#120—22no—
60C11×#120C2×C411yescharacteristic
61C11×#120D411yescharacteristic
62C4×D4×C11—21no—
63C4×D4×C11—21no—
64C4×D4×C11—42no—
65C11×#117—21no—
66C11×#117—21no—
67C11×#117D411yescharacteristic
68C11×C4⋊C8—21no—
69C11×C4⋊C8—21no—
70C11×#104—42no—
71C11×#103—41no—
72C11×#102—41no—
73C11×#101—21no—
74C11×#101—41no—
75C11×#100—21no—
76C11×#100—41no—
77C11×#99—21no—
78C11×#99—22no—
79C11×#99—22no—
80C11×#99—21no—
81C11×#99—21no—
82C11×#99C2×C412yes—
83C11×C22⋊C8—21no—
84C11×C22⋊C8—21no—
85C11×C22⋊C8—21no—
86C11×C22⋊C8—21no—
87C11×C22⋊C8—21no—
88C11×C22⋊C8—21no—
89C11×C22⋊C8—42no—
90C11×#97—21no—
91C4×C8×C11—21no—
92#13046C1111yesmaximal, characteristic, direct product factor, Sylow
93C24×C11C22⋊C411yescharacteristic
94C11×#41—22no—
95C11×#41—22no—
96C11×#41—41no—
97C11×#41—41no—
98C11×#41—42no—
99C11×#41—41no—
100C11×#41—41no—
101C11×#41—41no—
102C11×#41—41no—
103C11×#41—41no—
104C11×#41—42no—
105C11×#41—42no—
106C11×#41—42no—
107C11×#41—41no—
108C11×#41—41no—
109C11×#41—41no—
110C2×Q8×C11—21no—
111C2×Q8×C11—21no—
112C2×Q8×C11—21no—
113C2×Q8×C11—42no—
114C2×Q8×C11#4111yescharacteristic
115C2×D4×C11—21no—
116C2×D4×C11—21no—
117C2×D4×C11—21no—
118C2×D4×C11—22no—
119C2×D4×C11—22no—
120C2×D4×C11—21no—
121C2×D4×C11—21no—
122C2×D4×C11—42no—
123C2×D4×C11—42no—
124C2×D4×C11—42no—
125C2×D4×C11—41no—
126C2×D4×C11—42no—
127C2×D4×C11C22×C411yescharacteristic
128C2×D4×C11C2×D411yescharacteristic
129C2×D4×C11#4111yescharacteristic
130C22×C4×C11—22no—
131C22×C4×C11—22no—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—41no—
135C22×C4×C11—41no—
136C22×C4×C11—41no—
137C22×C4×C11C22⋊C411yescharacteristic
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2×D411yescharacteristic
141C11×M16—41no—
142C11×M16—41no—
143C11×M16—41no—
144C11×M16—41no—
145C11×M16—81no—
146C11×M16—81no—
147C2×C8×C11—21no—
148C2×C8×C11—21no—
149C2×C8×C11—21no—
150C2×C8×C11—21no—
151C2×C8×C11—41no—
152C2×C8×C11—41no—
153C2×C8×C11—41no—
154C11×C4⋊C4—21no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4—21no—
157C11×C4⋊C4—41no—
158C11×C4⋊C4—42no—
159C11×C4⋊C4—41no—
160C11×C22⋊C4—21no—
161C11×C22⋊C4—21no—
162C11×C22⋊C4—21no—
163C11×C22⋊C4—21no—
164C11×C22⋊C4—22no—
165C11×C22⋊C4—42no—
166C11×C22⋊C4—42no—
167C11×C22⋊C4—41no—
168C11×C22⋊C4C22⋊C411yescharacteristic
169C11×C22⋊C4C22⋊C411yescharacteristic
170C42×C11—21no—
171C42×C11—41no—
172C42×C11—41no—
173#3025C2×C1111yescharacteristic
174#2978C2×C1111yescharacteristic, complemented
175#2120C2×C1111yescharacteristic, complemented
176#1794C2×C1111yescharacteristic, complemented
177#1791C2×C1111yescharacteristic, complemented
178#1395C2×C1111yescharacteristic, complemented
179#1391C2×C1111yescharacteristic, complemented
180C23×C11—22no—
181C23×C11—22no—
182C23×C11—21no—
183C23×C11—41no—
184C23×C11—41no—
185C23×C11—81no—
186C23×C11C2×C22⋊C411yescharacteristic
187C23×C11C4×D411yescharacteristic
188C23×C11#12111yescharacteristic
189Q8×C11—22no—
190Q8×C11—41no—
191Q8×C11—41no—
192Q8×C11—41no—
193Q8×C11—41no—
194D4×C11—22no—
195D4×C11—41no—
196D4×C11—41no—
197D4×C11—41no—
198D4×C11—41no—
199D4×C11—41no—
200D4×C11—42no—
201D4×C11—42no—
202D4×C11—42no—
203D4×C11—42no—
204D4×C11—41no—
205D4×C11—81no—
206D4×C11—81no—
207D4×C11—84no—
208C2×C4×C11—21no—
209C2×C4×C11—21no—
210C2×C4×C11—21no—
211C2×C4×C11—21no—
212C2×C4×C11—21no—
213C2×C4×C11—21no—
214C2×C4×C11—22no—
215C2×C4×C11—22no—
216C2×C4×C11—21no—
217C2×C4×C11—21no—
218C2×C4×C11—21no—
219C2×C4×C11—42no—
220C2×C4×C11—42no—
221C2×C4×C11—42no—
222C2×C4×C11—41no—
223C2×C4×C11—41no—
224C2×C4×C11—41no—
225C2×C4×C11—42no—
226C2×C4×C11—41no—
227C2×C4×C11—42no—
228C2×C4×C11—81no—
229C2×C4×C11—81no—
230C2×C4×C11C4×D411yescharacteristic
231C2×C4×C11#12011yescharacteristic
232C2×C4×C11#12111yescharacteristic
233C2×C4×C11#12311yescharacteristic
234C8×C11—41no—
235C8×C11—41no—
236C8×C11—41no—
237C8×C11—41no—
238C8×C11—81no—
239#585C22×C1111yescharacteristic
240#525—21no—
241#525C22×C1111yescharacteristic
242#458—21no—
243#458C4×C1112yescomplemented
244B(4,𝔽2)—21no—
245B(4,𝔽2)C4×C1112yescomplemented
246#436—21no—
247#436—21no—
248#435—21no—
249#435—21no—
250#433—21no—
251#421—21no—
252#416—21no—
253#413—21no—
254#413C22×C1111yescharacteristic
255#410—21no—
256#410C22×C1111yescharacteristic
257#410C22×C1111yescharacteristic
258#408—21no—
259#408C22×C1111yescharacteristic
260#408C22×C1111yescharacteristic
261#407—21no—
262#352—21no—
263AΣL(1,𝔽16)—21no—
264C22×C11—21no—
265C22×C11—21no—
266C22×C11—21no—
267C22×C11—41no—
268C22×C11—41no—
269C22×C11—41no—
270C22×C11—41no—
271C22×C11—41no—
272C22×C11—42no—
273C22×C11—42no—
274C22×C11—41no—
275C22×C11—82no—
276C22×C11—82no—
277C22×C11—81no—
278C22×C11—161no—
279C22×C11#38611yescharacteristic
280C4×C11—21no—
281C4×C11—21no—
282C4×C11—21no—
283C4×C11—41no—
284C4×C11—41no—
285C4×C11—42no—
286C4×C11—41no—
287C4×C11—82no—
288C4×C11—161no—
289C4×C11B(4,𝔽2)11yescharacteristic
290C4×C11B(4,𝔽2)11yescharacteristic
2912−1+4—21no—
2922−1+4—41no—
293H(5,𝔽2)—21no—
294H(5,𝔽2)—21no—
295H(5,𝔽2)—41no—
296H(5,𝔽2)C2×C4×C1112yes—
297C2×#41—21no—
298C2×#41—21no—
299C2×#41—21no—
300C2×#41—42no—
301C2×#41C23×C1111yescharacteristic
302C23×C4D4×C1111yescharacteristic
303C2×M16—21no—
304C2×M16—21no—
305C2×M16—21no—
306C2×M16D4×C1111yescharacteristic, complemented
307C2×M16D4×C1111yescharacteristic, complemented
308C22×C8D4×C1111yescharacteristic, complemented
309C22×C8D4×C1111yescharacteristic, complemented
310#123—22no—
311#123C2×C4×C1111yescharacteristic
312#123D4×C1111yescharacteristic
313C22⋊Q8—21no—
314C22⋊Q8—41no—
315#121—21no—
316#121—41no—
317#120—22no—
318#120C2×C4×C1111yescharacteristic
319#120D4×C1111yescharacteristic
320C4×D4—21no—
321C4×D4—21no—
322C4×D4—42no—
323#117—21no—
324#117—21no—
325#117D4×C1111yescharacteristic
326C4⋊C8—21no—
327C4⋊C8—21no—
328#104—42no—
329#103—41no—
330#102—41no—
331#101—21no—
332#101—41no—
333#100—21no—
334#100—41no—
335#99—21no—
336#99—22no—
337#99—22no—
338#99—21no—
339#99—21no—
340#99C2×C4×C1112yes—
341C22⋊C8—21no—
342C22⋊C8—21no—
343C22⋊C8—21no—
344C22⋊C8—21no—
345C22⋊C8—21no—
346C22⋊C8—21no—
347C22⋊C8—42no—
348#97—21no—
349C4×C8—21no—
350C2×C11—21no—
351C2×C11—41no—
352C2×C11—41no—
353C2×C11—41no—
354C2×C11—81no—
355C2×C11—82no—
356C2×C11#188911yescharacteristic
357C24C11×C22⋊C411yescharacteristic
358#41—22no—
359#41—22no—
360#41—41no—
361#41—41no—
362#41—42no—
363#41—41no—
364#41—41no—
365#41—41no—
366#41—41no—
367#41—41no—
368#41—42no—
369#41—42no—
370#41—42no—
371#41—41no—
372#41—41no—
373#41—41no—
374C2×Q8—21no—
375C2×Q8—21no—
376C2×Q8—21no—
377C2×Q8—42no—
378C2×Q8C11×#4111yescharacteristic
379C2×D4—21no—
380C2×D4—21no—
381C2×D4—21no—
382C2×D4—22no—
383C2×D4—22no—
384C2×D4—21no—
385C2×D4—21no—
386C2×D4—42no—
387C2×D4—42no—
388C2×D4—42no—
389C2×D4—41no—
390C2×D4—42no—
391C2×D4C22×C4×C1111yescharacteristic
392C2×D4C2×D4×C1111yescharacteristic
393C2×D4C11×#4111yescharacteristic
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—41no—
399C22×C4—41no—
400C22×C4—41no—
401C22×C4C11×C22⋊C411yescharacteristic
402C22×C4C2×D4×C1111yescharacteristic
403C22×C4C2×D4×C1111yescharacteristic
404C22×C4C2×D4×C1111yescharacteristic
405M16—41no—
406M16—41no—
407M16—41no—
408M16—41no—
409M16—81no—
410M16—81no—
411C2×C8—21no—
412C2×C8—21no—
413C2×C8—21no—
414C2×C8—21no—
415C2×C8—41no—
416C2×C8—41no—
417C2×C8—41no—
418C4⋊C4—21no—
419C4⋊C4—21no—
420C4⋊C4—21no—
421C4⋊C4—41no—
422C4⋊C4—42no—
423C4⋊C4—41no—
424C22⋊C4—21no—
425C22⋊C4—21no—
426C22⋊C4—21no—
427C22⋊C4—21no—
428C22⋊C4—22no—
429C22⋊C4—42no—
430C22⋊C4—42no—
431C22⋊C4—41no—
432C22⋊C4C11×C22⋊C411yescharacteristic
433C22⋊C4C11×C22⋊C411yescharacteristic
434C42—21no—
435C42—41no—
436C42—41no—
437C11#1304611yescharacteristic, direct product factor, Sylow
438C23—22no—
439C23—22no—
440C23—21no—
441C23—41no—
442C23—41no—
443C23—81no—
444C23C2×C11×C22⋊C411yescharacteristic
445C23C4×D4×C1111yescharacteristic
446C23C11×#12111yescharacteristic
447Q8—22no—
448Q8—41no—
449Q8—41no—
450Q8—41no—
451Q8—41no—
452D4—22no—
453D4—41no—
454D4—41no—
455D4—41no—
456D4—41no—
457D4—41no—
458D4—42no—
459D4—42no—
460D4—42no—
461D4—42no—
462D4—41no—
463D4—81no—
464D4—81no—
465D4—84no—
466C2×C4—21no—
467C2×C4—21no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—21no—
475C2×C4—21no—
476C2×C4—21no—
477C2×C4—42no—
478C2×C4—42no—
479C2×C4—42no—
480C2×C4—41no—
481C2×C4—41no—
482C2×C4—41no—
483C2×C4—42no—
484C2×C4—41no—
485C2×C4—42no—
486C2×C4—81no—
487C2×C4—81no—
488C2×C4C4×D4×C1111yescharacteristic
489C2×C4C11×#12011yescharacteristic
490C2×C4C11×#12111yescharacteristic
491C2×C4C11×#12311yescharacteristic
492C8—41no—
493C8—41no—
494C8—41no—
495C8—41no—
496C8—81no—
497C22—21no—
498C22—21no—
499C22—21no—
500C22—41no—
501C22—41no—
502C22—41no—
503C22—41no—
504C22—41no—
505C22—42no—
506C22—42no—
507C22—41no—
508C22—82no—
509C22—82no—
510C22—81no—
511C22—161no—
512C22C11×#38611yescharacteristic
513C4—21no—
514C4—21no—
515C4—21no—
516C4—41no—
517C4—41no—
518C4—42no—
519C4—41no—
520C4—82no—
521C4—161no—
522C4C11×B(4,𝔽2)11yescharacteristic
523C4C11×B(4,𝔽2)11yescharacteristic
524C2—21no—
525C2—41no—
526C2—41no—
527C2—41no—
528C2—81no—
529C2—82no—
530C2C11×#188911yescharacteristic
subgroupG/H
centerC4×C11B(4,𝔽2)
commutatorC2×D4C22×C4×C11
Frattini, cosocleC2×#41C23×C11
socleC2×C11#1889
prime radicalC11×#3025C2
LCSG ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C4×C11 ◁ C2×C4×C11 ◁ C2×C11×#41 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#2978C2semidirect
3. C11×#2120C2semidirect
4. C11×#1794C2semidirect
5. C11×#1791C2semidirect
6. C11×#1395C2semidirect
7. C11×#1391C2semidirect
12. C11×#458C4semidirect
14. C11×B(4,𝔽2)C4semidirect
48. C2×C11×M16D4semidirect
49. C2×C11×M16D4semidirect
50. C22×C8×C11D4semidirect
51. C22×C8×C11D4semidirect
92. #13046C11direct (N × H)
174. #2978C2×C11semidirect
175. #2120C2×C11semidirect
176. #1794C2×C11semidirect
177. #1791C2×C11semidirect
178. #1395C2×C11semidirect
179. #1391C2×C11semidirect
243. #458C4×C11semidirect
245. B(4,𝔽2)C4×C11semidirect
306. C2×M16D4×C11semidirect
307. C2×M16D4×C11semidirect
308. C22×C8D4×C11semidirect
309. C22×C8D4×C11semidirect
437. C11#13046direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#30252
C11×#29782
C11×#21202
C11×#17942
C11×#17912
C11×#13952
C11×#13912
#1304611