Finite Group Databasebeta

← C11×#24134 #14601327

Subgroups — C11×#24134 #14601327

Order 2816.

1120 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#554C211yesmaximal, characteristic
2C2×C11×#475C211yesmaximal, characteristic, complemented
3C2×C11×#441C211yesmaximal, characteristic, complemented
4C11×#2536C211yesmaximal, characteristic
5C11×#2035C212yesmaximal, complemented
6C11×#2001C212yesmaximal, complemented
7C11×#1993C211yesmaximal, characteristic, complemented
8C11×#1955C211yesmaximal, characteristic
9C11×#1872C212yesmaximal, complemented
10C11×#1853C212yesmaximal, complemented
11C11×#1805C211yesmaximal, characteristic, complemented
12C22×C11×Q16C2211yescharacteristic
13C11×#554—24no—
14C11×#554—24no—
15C2×C11×C4⋊Q8C2211yescharacteristic
16C2×C11×#125—21no—
17C2×C11×C22⋊Q8—22no—
18C2×C11×C22⋊Q8C2212yes—
19C2×C11×C22⋊Q8C2212yes—
20C2×C4×Q8×C11C2211yescharacteristic
21C2×C4×Q8×C11C2211yescharacteristic
22C2×C4×D4×C11—21no—
23C2×C4×D4×C11C2211yescharacteristic
24C22×C11×C4⋊C4C2212yes—
25C11×#475—24no—
26C11×#441—24no—
27C2×C11×#106C2211yescharacteristic
28C2×C11×#106C2212yes—
29C2×C11×C4⋊C8C2211yescharacteristic
30C2×C11×#103C2211yescharacteristic
31C2×C11×#103C2212yes—
32C2×C11×#103C2211yescharacteristic
33C2×C11×#103C2212yes—
34C2×C11×C22⋊C8C2212yes—
35C2×C11×C22⋊C8C2212yes—
36C2×C11×#97C2211yescharacteristic
37C11×#398—21no—
38C11×#394—21no—
39C11×#388—22no—
40C11×#382C2211yescharacteristic
41C11×#380C2212yes—
42C11×#340C2212yes—
43C11×#340C2212yes—
44C11×#340C2212yes—
45C22×Q8×C11—21no—
46C22×Q8×C11C2311yescharacteristic
47C22×Q8×C11C2311yescharacteristic
48C22×D4×C11D411yescharacteristic
49C23×C4×C11—22no—
50C23×C4×C11C2312yes—
51C2×C11×Q16—22no—
52C2×C11×Q16—22no—
53C2×C11×Q16—22no—
54C22×C8×C11C2311yescharacteristic
55C22×C8×C11C2312yes—
56C22×C8×C11C2311yescharacteristic
57C11×C4⋊Q8—22no—
58C11×C4⋊Q8D414yes—
59C11×#125—28no—
60C11×C22⋊Q8—216no—
61C11×C22⋊Q8—24no—
62C11×C22⋊Q8—24no—
63C11×C22⋊Q8—24no—
64C11×C22⋊Q8—42no—
65C4×Q8×C11—22no—
66C4×Q8×C11—22no—
67C4×Q8×C11—22no—
68C4×Q8×C11D414yes—
69C4×D4×C11—28no—
70C4×D4×C11—22no—
71C4×D4×C11—22no—
72C2×C11×C4⋊C4—22no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4—22no—
76C2×C11×C4⋊C4—24no—
77C2×C11×C4⋊C4—24no—
78C2×C11×C4⋊C4—21no—
79C2×C11×C4⋊C4—22no—
80C2×C11×C4⋊C4D411yescharacteristic
81C2×C11×C4⋊C4C2312yes—
82C2×C11×C4⋊C4C2311yescharacteristic
83C2×C11×C4⋊C4C2311yescharacteristic
84C2×C11×C4⋊C4C2312yes—
85C2×C11×C22⋊C4—22no—
86C2×C11×C22⋊C4—22no—
87C2×C11×C22⋊C4—22no—
88C2×C11×C22⋊C4D412yes—
89C2×C42×C11—21no—
90C2×C42×C11—21no—
91C2×C42×C11C2311yescharacteristic
92C11×#106—22no—
93C11×#106—24no—
94C11×C4⋊C8—22no—
95C11×#103—22no—
96C11×#103—22no—
97C11×#103—24no—
98C11×#103—42no—
99C11×C22⋊C8—24no—
100C11×C22⋊C8—42no—
101C11×#97—22no—
102C11×#95—22no—
103C11×#95—21no—
104C11×#95—21no—
105#24134C1111yesmaximal, characteristic, direct product factor, Sylow
106C24×C11C2×D412yes—
107C2×Q8×C11—24no—
108C2×Q8×C11—21no—
109C2×Q8×C11—21no—
110C2×Q8×C11—21no—
111C2×Q8×C11—21no—
112C2×Q8×C11—21no—
113C2×Q8×C11—21no—
114C2×Q8×C11—21no—
115C2×Q8×C11—21no—
116C2×Q8×C11—21no—
117C2×Q8×C11—21no—
118C2×Q8×C11—82no—
119C2×Q8×C11C2×D412yes—
120C2×Q8×C11#4112yes—
121C2×D4×C11—24no—
122C2×D4×C11—22no—
123C22×C4×C11—21no—
124C22×C4×C11—21no—
125C22×C4×C11—21no—
126C22×C4×C11—22no—
127C22×C4×C11—28no—
128C22×C4×C11—22no—
129C22×C4×C11—22no—
130C22×C4×C11—22no—
131C22×C4×C11—22no—
132C22×C4×C11—22no—
133C22×C4×C11—22no—
134C22×C4×C11—22no—
135C22×C4×C11—21no—
136C22×C4×C11—82no—
137C22×C4×C11—82no—
138C22×C4×C11C2×D412yes—
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2411yescharacteristic
142C11×Q16—28no—
143C2×C8×C11—21no—
144C2×C8×C11—21no—
145C2×C8×C11—22no—
146C2×C8×C11—21no—
147C2×C8×C11—22no—
148C2×C8×C11—21no—
149C2×C8×C11—22no—
150C2×C8×C11—21no—
151C2×C8×C11#4112yes—
152C11×C4⋊C4—28no—
153C11×C4⋊C4—28no—
154C11×C4⋊C4—24no—
155C11×C4⋊C4—24no—
156C11×C4⋊C4—22no—
157C11×C4⋊C4—21no—
158C11×C4⋊C4—22no—
159C11×C4⋊C4—21no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—22no—
162C11×C4⋊C4—22no—
163C11×C4⋊C4—44no—
164C11×C4⋊C4—42no—
165C11×C4⋊C4C2×D412yes—
166C11×C4⋊C4C2×D414yes—
167C11×C22⋊C4—28no—
168C11×C22⋊C4—24no—
169C11×C22⋊C4—44no—
170C11×C22⋊C4—44no—
171C42×C11—24no—
172C42×C11—42no—
173C42×C11C2×D412yes—
174C42×C11C2×D412yes—
175C2×#554C2×C1111yescharacteristic
176C2×#475C2×C1111yescharacteristic, complemented
177C2×#441C2×C1111yescharacteristic, complemented
178#2536C2×C1111yescharacteristic
179#2035C2×C1112yescomplemented
180#2001C2×C1112yescomplemented
181#1993C2×C1111yescharacteristic, complemented
182#1955C2×C1111yescharacteristic
183#1872C2×C1112yescomplemented
184#1853C2×C1112yescomplemented
185#1805C2×C1111yescharacteristic, complemented
186C23×C11—22no—
187C23×C11—22no—
188C23×C11—22no—
189C23×C11—22no—
190C23×C11—22no—
191C23×C11—22no—
192C23×C11#13714yes—
193C23×C11C22×D411yescharacteristic
194Q8×C11—22no—
195Q8×C11—22no—
196Q8×C11—22no—
197Q8×C11—22no—
198Q8×C11—41no—
199Q8×C11—41no—
200Q8×C11—41no—
201Q8×C11—41no—
202Q8×C11—84no—
203D4×C11—28no—
204C2×C4×C11—22no—
205C2×C4×C11—22no—
206C2×C4×C11—22no—
207C2×C4×C11—22no—
208C2×C4×C11—22no—
209C2×C4×C11—24no—
210C2×C4×C11—22no—
211C2×C4×C11—22no—
212C2×C4×C11—22no—
213C2×C4×C11—41no—
214C2×C4×C11—41no—
215C2×C4×C11—41no—
216C2×C4×C11—41no—
217C2×C4×C11—42no—
218C2×C4×C11—42no—
219C2×C4×C11—42no—
220C2×C4×C11—42no—
221C2×C4×C11—42no—
222C2×C4×C11—42no—
223C2×C4×C11—42no—
224C2×C4×C11—41no—
225C2×C4×C11—42no—
226C2×C4×C11—42no—
227C2×C4×C11—42no—
228C2×C4×C11—42no—
229C2×C4×C11—88no—
230C2×C4×C11#12012yes—
231C2×C4×C11#12012yes—
232C2×C4×C11C22×D411yescharacteristic
233C2×C4×C11C22×D411yescharacteristic
234C2×C4×C11C2×#4111yescharacteristic
235C2×C4×C11C2×#4111yescharacteristic
236C2×C4×C11H(5,𝔽2)11yescharacteristic
237C2×C4×C112−1+411yescharacteristic
238C8×C11—22no—
239C8×C11—41no—
240C8×C11—42no—
241C22×Q16C22×C1111yescharacteristic
242#554—24no—
243#554—24no—
244C2×C4⋊Q8C22×C1111yescharacteristic
245C2×#125—21no—
246C2×C22⋊Q8—22no—
247C2×C22⋊Q8C22×C1112yes—
248C2×C22⋊Q8C22×C1112yes—
249C2×C4×Q8C22×C1111yescharacteristic
250C2×C4×Q8C22×C1111yescharacteristic
251C2×C4×D4—21no—
252C2×C4×D4C22×C1111yescharacteristic
253C22×C4⋊C4C22×C1112yes—
254#475—24no—
255#441—24no—
256C2×#106C22×C1112yes—
257C2×#106C22×C1111yescharacteristic
258C2×C4⋊C8C22×C1111yescharacteristic
259C2×#103C22×C1112yes—
260C2×#103C22×C1111yescharacteristic
261C2×#103C22×C1111yescharacteristic
262C2×#103C22×C1112yes—
263C2×C22⋊C8C22×C1112yes—
264C2×C22⋊C8C22×C1112yes—
265C2×#97C22×C1111yescharacteristic
266#398—21no—
267#394—21no—
268#388—22no—
269#382C22×C1111yescharacteristic
270#380C22×C1112yes—
271#340C22×C1112yes—
272#340C22×C1112yes—
273#340C22×C1112yes—
274C22×C11—24no—
275C22×C11—24no—
276C22×C11—24no—
277C22×C11—42no—
278C22×C11—42no—
279C22×C11—42no—
280C22×C11—42no—
281C22×C11C2×#12011yescharacteristic
282C22×C11#54611yescharacteristic
283C22×C11#54711yescharacteristic
284C22×C11C2×#13712yes—
285C22×C11#57712yes—
286C4×C11—22no—
287C4×C11—22no—
288C4×C11—42no—
289C4×C11—42no—
290C4×C11—42no—
291C4×C11—42no—
292C4×C11—44no—
293C4×C11—81no—
294C4×C11—82no—
295C4×C11#52511yescharacteristic
296C4×C11#53711yescharacteristic
297C4×C11#54811yescharacteristic
298C4×C11#55011yescharacteristic
299C22×Q8—21no—
300C22×Q8C23×C1111yescharacteristic
301C22×Q8C23×C1111yescharacteristic
302C22×D4D4×C1111yescharacteristic
303C23×C4—22no—
304C23×C4C23×C1112yes—
305C2×Q16—22no—
306C2×Q16—22no—
307C2×Q16—22no—
308C22×C8C23×C1111yescharacteristic
309C22×C8C23×C1112yes—
310C22×C8C23×C1111yescharacteristic
311C4⋊Q8—22no—
312C4⋊Q8D4×C1114yes—
313#125—28no—
314C22⋊Q8—216no—
315C22⋊Q8—24no—
316C22⋊Q8—24no—
317C22⋊Q8—24no—
318C22⋊Q8—42no—
319C4×Q8—22no—
320C4×Q8—22no—
321C4×Q8—22no—
322C4×Q8D4×C1114yes—
323C4×D4—28no—
324C4×D4—22no—
325C4×D4—22no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—21no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4—24no—
331C2×C4⋊C4—24no—
332C2×C4⋊C4—21no—
333C2×C4⋊C4—22no—
334C2×C4⋊C4D4×C1111yescharacteristic
335C2×C4⋊C4C23×C1111yescharacteristic
336C2×C4⋊C4C23×C1112yes—
337C2×C4⋊C4C23×C1111yescharacteristic
338C2×C4⋊C4C23×C1112yes—
339C2×C22⋊C4—22no—
340C2×C22⋊C4—22no—
341C2×C22⋊C4—22no—
342C2×C22⋊C4D4×C1112yes—
343C2×C42—21no—
344C2×C42—21no—
345C2×C42C23×C1111yescharacteristic
346#106—22no—
347#106—24no—
348C4⋊C8—22no—
349#103—22no—
350#103—22no—
351#103—24no—
352#103—42no—
353C22⋊C8—24no—
354C22⋊C8—42no—
355#97—22no—
356#95—22no—
357#95—21no—
358#95—21no—
359C2×C11—44no—
360C2×C11#240711yescharacteristic
361C2×C11#300411yescharacteristic
362C2×C11#300911yescharacteristic
363C2×C11#331612yes—
364C2×C11#334412yes—
365C24C2×D4×C1112yes—
366C2×Q8—24no—
367C2×Q8—21no—
368C2×Q8—21no—
369C2×Q8—21no—
370C2×Q8—21no—
371C2×Q8—21no—
372C2×Q8—21no—
373C2×Q8—21no—
374C2×Q8—21no—
375C2×Q8—21no—
376C2×Q8—21no—
377C2×Q8—82no—
378C2×Q8C2×D4×C1112yes—
379C2×Q8C11×#4112yes—
380C2×D4—24no—
381C2×D4—22no—
382C22×C4—21no—
383C22×C4—21no—
384C22×C4—21no—
385C22×C4—22no—
386C22×C4—28no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—21no—
395C22×C4—82no—
396C22×C4—82no—
397C22×C4C2×D4×C1112yes—
398C22×C4C2×D4×C1111yescharacteristic
399C22×C4C2×D4×C1111yescharacteristic
400C22×C4C24×C1111yescharacteristic
401Q16—28no—
402C2×C8—21no—
403C2×C8—21no—
404C2×C8—21no—
405C2×C8—22no—
406C2×C8—22no—
407C2×C8—21no—
408C2×C8—22no—
409C2×C8—21no—
410C2×C8C11×#4112yes—
411C4⋊C4—28no—
412C4⋊C4—28no—
413C4⋊C4—24no—
414C4⋊C4—24no—
415C4⋊C4—22no—
416C4⋊C4—21no—
417C4⋊C4—22no—
418C4⋊C4—21no—
419C4⋊C4—21no—
420C4⋊C4—22no—
421C4⋊C4—22no—
422C4⋊C4—44no—
423C4⋊C4—42no—
424C4⋊C4C2×D4×C1112yes—
425C4⋊C4C2×D4×C1114yes—
426C22⋊C4—28no—
427C22⋊C4—24no—
428C22⋊C4—44no—
429C22⋊C4—44no—
430C42—24no—
431C42—42no—
432C42C2×D4×C1112yes—
433C42C2×D4×C1112yes—
434C11#2413411yescharacteristic, direct product factor, Sylow
435C23—22no—
436C23—22no—
437C23—22no—
438C23—22no—
439C23—22no—
440C23—22no—
441C23C11×#13714yes—
442C23C22×D4×C1111yescharacteristic
443Q8—22no—
444Q8—22no—
445Q8—22no—
446Q8—22no—
447Q8—41no—
448Q8—41no—
449Q8—41no—
450Q8—41no—
451Q8—84no—
452D4—28no—
453C2×C4—22no—
454C2×C4—22no—
455C2×C4—22no—
456C2×C4—22no—
457C2×C4—22no—
458C2×C4—24no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—41no—
463C2×C4—41no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—42no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—42no—
470C2×C4—42no—
471C2×C4—42no—
472C2×C4—42no—
473C2×C4—41no—
474C2×C4—42no—
475C2×C4—42no—
476C2×C4—42no—
477C2×C4—42no—
478C2×C4—88no—
479C2×C4C11×#12012yes—
480C2×C4C11×#12012yes—
481C2×C4C22×D4×C1111yescharacteristic
482C2×C4C22×D4×C1111yescharacteristic
483C2×C4C2×C11×#4111yescharacteristic
484C2×C4C2×C11×#4111yescharacteristic
485C2×C4C11×H(5,𝔽2)11yescharacteristic
486C2×C4C11×2−1+411yescharacteristic
487C8—22no—
488C8—41no—
489C8—42no—
490C22—24no—
491C22—24no—
492C22—24no—
493C22—42no—
494C22—42no—
495C22—42no—
496C22—42no—
497C22C2×C11×#12011yescharacteristic
498C22C11×#54611yescharacteristic
499C22C11×#54711yescharacteristic
500C22C2×C11×#13712yes—
501C22C11×#57712yes—
502C4—22no—
503C4—22no—
504C4—42no—
505C4—42no—
506C4—42no—
507C4—42no—
508C4—44no—
509C4—81no—
510C4—82no—
511C4C11×#52511yescharacteristic
512C4C11×#53711yescharacteristic
513C4C11×#54811yescharacteristic
514C4C11×#55011yescharacteristic
515C2—44no—
516C2C11×#240711yescharacteristic
517C2C11×#300411yescharacteristic
518C2C11×#300911yescharacteristic
519C2C11×#331612yes—
520C2C11×#334412yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC22×D4×C11D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C4×D4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#475C2semidirect
3. C2×C11×#441C2semidirect
5. C11×#2035C2semidirect
6. C11×#2001C2semidirect
7. C11×#1993C2semidirect
9. C11×#1872C2semidirect
10. C11×#1853C2semidirect
11. C11×#1805C2semidirect
105. #24134C11direct (N × H)
176. C2×#475C2×C11semidirect
177. C2×#441C2×C11semidirect
179. #2035C2×C11semidirect
180. #2001C2×C11semidirect
181. #1993C2×C11semidirect
183. #1872C2×C11semidirect
184. #1853C2×C11semidirect
185. #1805C2×C11semidirect
434. C11#24134direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5542
C2×C11×#4752
C2×C11×#4412
C11×#25362
C11×#20352
C11×#20012
C11×#19932
C11×#19552
C11×#18722
C11×#18532
C11×#18052
#2413411