Finite Group Databasebeta

← C11×#24130 #14601323

Subgroups — C11×#24130 #14601323

Order 2816.

1184 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#554C211yesmaximal, characteristic, complemented
2C2×C11×#474C211yesmaximal, characteristic, complemented
3C2×C11×#440C211yesmaximal, characteristic, complemented
4C11×#2535C211yesmaximal, characteristic
5C11×#2036C212yesmaximal, complemented
6C11×#2000C212yesmaximal, complemented
7C11×#1993C211yesmaximal, characteristic, complemented
8C11×#1955C211yesmaximal, characteristic, complemented
9C11×#1874C212yesmaximal, complemented
10C11×#1852C212yesmaximal, complemented
11C11×#1805C211yesmaximal, characteristic, complemented
12C22×C11×SD16C2211yescharacteristic
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×#121C2212yes—
20C2×C4×Q8×C11C2211yescharacteristic
21C2×C4×D4×C11—21no—
22C2×C4×D4×C11C2211yescharacteristic
23C2×C4×D4×C11C2211yescharacteristic
24C22×C11×C4⋊C4C2212yes—
25C11×#474—24no—
26C11×#440—24no—
27C2×C11×#107C2211yescharacteristic
28C2×C11×#107C2212yes—
29C2×C11×C4⋊C8C2211yescharacteristic
30C2×C11×#103C2211yescharacteristic
31C2×C11×#103C2212yes—
32C2×C11×#102C2211yescharacteristic
33C2×C11×#102C2212yes—
34C2×C11×C22⋊C8C2212yes—
35C2×C11×C22⋊C8C2212yes—
36C2×C11×#97C2211yescharacteristic
37C11×#397—21no—
38C11×#392—21no—
39C11×#386—22no—
40C11×#382C2211yescharacteristic
41C11×#380C2212yes—
42C11×#340C2212yes—
43C11×#340C2212yes—
44C11×#340C2212yes—
45C22×Q8×C11—21no—
46C22×Q8×C11C2311yescharacteristic
47C22×D4×C11—22no—
48C22×D4×C11D411yescharacteristic
49C22×D4×C11C2311yescharacteristic
50C23×C4×C11—22no—
51C23×C4×C11—21no—
52C23×C4×C11C2312yes—
53C2×C11×SD16—22no—
54C2×C11×SD16—22no—
55C2×C11×SD16—22no—
56C22×C8×C11C2311yescharacteristic
57C22×C8×C11C2312yes—
58C22×C8×C11C2311yescharacteristic
59C11×C4⋊Q8—22no—
60C11×C4⋊Q8D414yescomplemented
61C11×#125—28no—
62C11×C22⋊Q8—216no—
63C11×C22⋊Q8—24no—
64C11×C22⋊Q8—24no—
65C11×#121—24no—
66C11×#121—42no—
67C4×Q8×C11—22no—
68C4×Q8×C11D414yescomplemented
69C4×D4×C11—28no—
70C4×D4×C11—22no—
71C4×D4×C11—22no—
72C4×D4×C11—22no—
73C4×D4×C11—22no—
74C2×C11×C4⋊C4—22no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4—22no—
78C2×C11×C4⋊C4—24no—
79C2×C11×C4⋊C4—24no—
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—21no—
87C2×C11×C22⋊C4—22no—
88C2×C11×C22⋊C4—22no—
89C2×C11×C22⋊C4D412yes—
90C2×C42×C11—21no—
91C2×C42×C11C2311yescharacteristic
92C11×#107—22no—
93C11×#107—24no—
94C11×C4⋊C8—22no—
95C11×#103—22no—
96C11×#103—42no—
97C11×#102—22no—
98C11×#102—24no—
99C11×C22⋊C8—24no—
100C11×C22⋊C8—42no—
101C11×#97—22no—
102C11×#95—22no—
103C11×#95—21no—
104C11×#95—21no—
105#24130C1111yesmaximal, characteristic, direct product factor, Sylow
106C24×C11—21no—
107C24×C11C2×D412yes—
108C2×Q8×C11—24no—
109C2×Q8×C11—21no—
110C2×Q8×C11—21no—
111C2×Q8×C11—21no—
112C2×Q8×C11—21no—
113C2×Q8×C11—21no—
114C2×Q8×C11—82no—
115C2×Q8×C11C2×D412yes—
116C2×D4×C11—24no—
117C2×D4×C11—22no—
118C2×D4×C11—21no—
119C2×D4×C11—21no—
120C2×D4×C11—21no—
121C2×D4×C11—21no—
122C2×D4×C11—21no—
123C2×D4×C11—44no—
124C2×D4×C11—44no—
125C2×D4×C11—82no—
126C2×D4×C11#4112yes—
127C22×C4×C11—21no—
128C22×C4×C11—21no—
129C22×C4×C11—22no—
130C22×C4×C11—28no—
131C22×C4×C11—22no—
132C22×C4×C11—22no—
133C22×C4×C11—22no—
134C22×C4×C11—22no—
135C22×C4×C11—22no—
136C22×C4×C11—22no—
137C22×C4×C11—22no—
138C22×C4×C11—21no—
139C22×C4×C11—42no—
140C22×C4×C11—82no—
141C22×C4×C11—82no—
142C22×C4×C11—82no—
143C22×C4×C11C2×D412yes—
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2411yescharacteristic
147C11×SD16—28no—
148C2×C8×C11—21no—
149C2×C8×C11—21no—
150C2×C8×C11—22no—
151C2×C8×C11—21no—
152C2×C8×C11—22no—
153C2×C8×C11—21no—
154C2×C8×C11—22no—
155C2×C8×C11—21no—
156C2×C8×C11#4112yes—
157C11×C4⋊C4—28no—
158C11×C4⋊C4—28no—
159C11×C4⋊C4—24no—
160C11×C4⋊C4—24no—
161C11×C4⋊C4—22no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—22no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—22no—
167C11×C4⋊C4—22no—
168C11×C4⋊C4C2×D412yes—
169C11×C4⋊C4C2×D414yes—
170C11×C22⋊C4—28no—
171C11×C22⋊C4—24no—
172C11×C22⋊C4—44no—
173C11×C22⋊C4—42no—
174C11×C22⋊C4—82no—
175C42×C11—24no—
176C42×C11C2×D412yes—
177C42×C11C2×D412yes—
178C2×#554C2×C1111yescharacteristic, complemented
179C2×#474C2×C1111yescharacteristic, complemented
180C2×#440C2×C1111yescharacteristic, complemented
181#2535C2×C1111yescharacteristic
182#2036C2×C1112yescomplemented
183#2000C2×C1112yescomplemented
184#1993C2×C1111yescharacteristic, complemented
185#1955C2×C1111yescharacteristic, complemented
186#1874C2×C1112yescomplemented
187#1852C2×C1112yescomplemented
188#1805C2×C1111yescharacteristic, complemented
189C23×C11—22no—
190C23×C11—22no—
191C23×C11—22no—
192C23×C11—22no—
193C23×C11—22no—
194C23×C11—22no—
195C23×C11—22no—
196C23×C11—41no—
197C23×C11—41no—
198C23×C11—42no—
199C23×C11—42no—
200C23×C11#13714yes—
201C23×C11C22×D411yescharacteristic
202Q8×C11—22no—
203Q8×C11—22no—
204Q8×C11—41no—
205Q8×C11—41no—
206Q8×C11—84no—
207D4×C11—28no—
208D4×C11—22no—
209D4×C11—22no—
210D4×C11—41no—
211D4×C11—41no—
212D4×C11—88no—
213C2×C4×C11—22no—
214C2×C4×C11—22no—
215C2×C4×C11—22no—
216C2×C4×C11—22no—
217C2×C4×C11—22no—
218C2×C4×C11—24no—
219C2×C4×C11—22no—
220C2×C4×C11—22no—
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—42no—
228C2×C4×C11—42no—
229C2×C4×C11—42no—
230C2×C4×C11—41no—
231C2×C4×C11—42no—
232C2×C4×C11—42no—
233C2×C4×C11—42no—
234C2×C4×C11—42no—
235C2×C4×C11—84no—
236C2×C4×C11—88no—
237C2×C4×C11#12012yes—
238C2×C4×C11#12012yes—
239C2×C4×C11C22×D411yescharacteristic
240C2×C4×C11C22×D411yescharacteristic
241C2×C4×C11C2×#4111yescharacteristic
242C2×C4×C11C2×#4111yescharacteristic
243C2×C4×C11H(5,𝔽2)11yescharacteristic
244C2×C4×C112−1+411yescharacteristic
245C8×C11—22no—
246C8×C11—41no—
247C8×C11—42no—
248C22×SD16C22×C1111yescharacteristic
249#554—24no—
250#554—24no—
251C2×C4⋊Q8C22×C1111yescharacteristic
252C2×#125—21no—
253C2×C22⋊Q8—22no—
254C2×C22⋊Q8C22×C1112yes—
255C2×#121C22×C1112yes—
256C2×C4×Q8C22×C1111yescharacteristic
257C2×C4×D4—21no—
258C2×C4×D4C22×C1111yescharacteristic
259C2×C4×D4C22×C1111yescharacteristic
260C22×C4⋊C4C22×C1112yes—
261#474—24no—
262#440—24no—
263C2×#107C22×C1111yescharacteristic
264C2×#107C22×C1112yes—
265C2×C4⋊C8C22×C1111yescharacteristic
266C2×#103C22×C1111yescharacteristic
267C2×#103C22×C1112yes—
268C2×#102C22×C1111yescharacteristic
269C2×#102C22×C1112yes—
270C2×C22⋊C8C22×C1112yes—
271C2×C22⋊C8C22×C1112yes—
272C2×#97C22×C1111yescharacteristic
273#397—21no—
274#392—21no—
275#386—22no—
276#382C22×C1111yescharacteristic
277#380C22×C1112yes—
278#340C22×C1112yes—
279#340C22×C1112yes—
280#340C22×C1112yes—
281C22×C11—24no—
282C22×C11—24no—
283C22×C11—24no—
284C22×C11—42no—
285C22×C11—42no—
286C22×C11—42no—
287C22×C11—42no—
288C22×C11—42no—
289C22×C11—44no—
290C22×C11—82no—
291C22×C11—81no—
292C22×C11—81no—
293C22×C11C2×#12011yescharacteristic
294C22×C11#54611yescharacteristic
295C22×C11#54711yescharacteristic
296C22×C11C2×#13712yes—
297C22×C11#57612yes—
298C4×C11—22no—
299C4×C11—22no—
300C4×C11—42no—
301C4×C11—42no—
302C4×C11—42no—
303C4×C11—44no—
304C4×C11—81no—
305C4×C11—82no—
306C4×C11#52511yescharacteristic
307C4×C11#53711yescharacteristic
308C4×C11#54811yescharacteristic
309C4×C11#55011yescharacteristic
310C22×Q8—21no—
311C22×Q8C23×C1111yescharacteristic
312C22×D4—22no—
313C22×D4D4×C1111yescharacteristic
314C22×D4C23×C1111yescharacteristic
315C23×C4—22no—
316C23×C4—21no—
317C23×C4C23×C1112yes—
318C2×SD16—22no—
319C2×SD16—22no—
320C2×SD16—22no—
321C22×C8C23×C1111yescharacteristic
322C22×C8C23×C1112yes—
323C22×C8C23×C1111yescharacteristic
324C4⋊Q8—22no—
325C4⋊Q8D4×C1114yescomplemented
326#125—28no—
327C22⋊Q8—216no—
328C22⋊Q8—24no—
329C22⋊Q8—24no—
330#121—24no—
331#121—42no—
332C4×Q8—22no—
333C4×Q8D4×C1114yescomplemented
334C4×D4—28no—
335C4×D4—22no—
336C4×D4—22no—
337C4×D4—22no—
338C4×D4—22no—
339C2×C4⋊C4—22no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—24no—
344C2×C4⋊C4—24no—
345C2×C4⋊C4D4×C1111yescharacteristic
346C2×C4⋊C4C23×C1111yescharacteristic
347C2×C4⋊C4C23×C1112yes—
348C2×C4⋊C4C23×C1111yescharacteristic
349C2×C4⋊C4C23×C1112yes—
350C2×C22⋊C4—22no—
351C2×C22⋊C4—21no—
352C2×C22⋊C4—22no—
353C2×C22⋊C4—22no—
354C2×C22⋊C4D4×C1112yes—
355C2×C42—21no—
356C2×C42C23×C1111yescharacteristic
357#107—22no—
358#107—24no—
359C4⋊C8—22no—
360#103—22no—
361#103—42no—
362#102—22no—
363#102—24no—
364C22⋊C8—24no—
365C22⋊C8—42no—
366#97—22no—
367#95—22no—
368#95—21no—
369#95—21no—
370C2×C11—44no—
371C2×C11—82no—
372C2×C11#240711yescharacteristic
373C2×C11#300411yescharacteristic
374C2×C11#300811yescharacteristic
375C2×C11#331412yes—
376C2×C11#334612yes—
377C24—21no—
378C24C2×D4×C1112yes—
379C2×Q8—24no—
380C2×Q8—21no—
381C2×Q8—21no—
382C2×Q8—21no—
383C2×Q8—21no—
384C2×Q8—21no—
385C2×Q8—82no—
386C2×Q8C2×D4×C1112yes—
387C2×D4—24no—
388C2×D4—22no—
389C2×D4—21no—
390C2×D4—21no—
391C2×D4—21no—
392C2×D4—21no—
393C2×D4—21no—
394C2×D4—44no—
395C2×D4—44no—
396C2×D4—82no—
397C2×D4C11×#4112yes—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—22no—
401C22×C4—28no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—21no—
410C22×C4—42no—
411C22×C4—82no—
412C22×C4—82no—
413C22×C4—82no—
414C22×C4C2×D4×C1112yes—
415C22×C4C2×D4×C1111yescharacteristic
416C22×C4C2×D4×C1111yescharacteristic
417C22×C4C24×C1111yescharacteristic
418SD16—28no—
419C2×C8—21no—
420C2×C8—21no—
421C2×C8—21no—
422C2×C8—22no—
423C2×C8—22no—
424C2×C8—21no—
425C2×C8—22no—
426C2×C8—21no—
427C2×C8C11×#4112yes—
428C4⋊C4—28no—
429C4⋊C4—28no—
430C4⋊C4—24no—
431C4⋊C4—24no—
432C4⋊C4—22no—
433C4⋊C4—21no—
434C4⋊C4—22no—
435C4⋊C4—21no—
436C4⋊C4—21no—
437C4⋊C4—22no—
438C4⋊C4—22no—
439C4⋊C4C2×D4×C1112yes—
440C4⋊C4C2×D4×C1114yes—
441C22⋊C4—28no—
442C22⋊C4—24no—
443C22⋊C4—44no—
444C22⋊C4—42no—
445C22⋊C4—82no—
446C42—24no—
447C42C2×D4×C1112yes—
448C42C2×D4×C1112yes—
449C11#2413011yescharacteristic, direct product factor, Sylow
450C23—22no—
451C23—22no—
452C23—22no—
453C23—22no—
454C23—22no—
455C23—22no—
456C23—22no—
457C23—41no—
458C23—41no—
459C23—42no—
460C23—42no—
461C23C11×#13714yes—
462C23C22×D4×C1111yescharacteristic
463Q8—22no—
464Q8—22no—
465Q8—41no—
466Q8—41no—
467Q8—84no—
468D4—28no—
469D4—22no—
470D4—22no—
471D4—41no—
472D4—41no—
473D4—88no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—22no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—24no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—41no—
483C2×C4—41no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—42no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—41no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—84no—
497C2×C4—88no—
498C2×C4C11×#12012yes—
499C2×C4C11×#12012yes—
500C2×C4C22×D4×C1111yescharacteristic
501C2×C4C22×D4×C1111yescharacteristic
502C2×C4C2×C11×#4111yescharacteristic
503C2×C4C2×C11×#4111yescharacteristic
504C2×C4C11×H(5,𝔽2)11yescharacteristic
505C2×C4C11×2−1+411yescharacteristic
506C8—22no—
507C8—41no—
508C8—42no—
509C22—24no—
510C22—24no—
511C22—24no—
512C22—42no—
513C22—42no—
514C22—42no—
515C22—42no—
516C22—42no—
517C22—44no—
518C22—81no—
519C22—81no—
520C22—82no—
521C22C2×C11×#12011yescharacteristic
522C22C11×#54611yescharacteristic
523C22C11×#54711yescharacteristic
524C22C2×C11×#13712yes—
525C22C11×#57612yes—
526C4—22no—
527C4—22no—
528C4—42no—
529C4—42no—
530C4—42no—
531C4—44no—
532C4—81no—
533C4—82no—
534C4C11×#52511yescharacteristic
535C4C11×#53711yescharacteristic
536C4C11×#54811yescharacteristic
537C4C11×#55011yescharacteristic
538C2—44no—
539C2—82no—
540C2C11×#240711yescharacteristic
541C2C11×#300411yescharacteristic
542C2C11×#300811yescharacteristic
543C2C11×#331412yes—
544C2C11×#334612yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#2535C2
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
1. C2×C11×#554C2semidirect
2. C2×C11×#474C2semidirect
3. C2×C11×#440C2semidirect
5. C11×#2036C2semidirect
6. C11×#2000C2semidirect
7. C11×#1993C2semidirect
8. C11×#1955C2semidirect
9. C11×#1874C2semidirect
10. C11×#1852C2semidirect
11. C11×#1805C2semidirect
60. C11×C4⋊Q8D4semidirect
68. C4×Q8×C11D4semidirect
105. #24130C11direct (N × H)
178. C2×#554C2×C11semidirect
179. C2×#474C2×C11semidirect
180. C2×#440C2×C11semidirect
182. #2036C2×C11semidirect
183. #2000C2×C11semidirect
184. #1993C2×C11semidirect
185. #1955C2×C11semidirect
186. #1874C2×C11semidirect
187. #1852C2×C11semidirect
188. #1805C2×C11semidirect
325. C4⋊Q8D4×C11semidirect
333. C4×Q8D4×C11semidirect
449. C11#24130direct (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×#4742
C2×C11×#4402
C11×#25352
C11×#20362
C11×#20002
C11×#19932
C11×#19552
C11×#18742
C11×#18522
C11×#18052
#2413011