Finite Group Databasebeta

← C11×#24542 #14601735

Subgroups — C11×#24542 #14601735

Order 2816.

1078 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×#449C211yesmaximal, characteristic
2C2×C11×#417C211yesmaximal, characteristic, complemented
3C11×#2501C211yesmaximal, characteristic, complemented
4C11×#2341C211yesmaximal, characteristic, complemented
5C11×#2071C212yesmaximal, complemented
6C11×#2054C212yesmaximal, complemented
7C11×#1895C211yesmaximal, characteristic, complemented
8C11×#1880C212yesmaximal, complemented
9C11×#1851C211yesmaximal, characteristic, complemented
10C11×#1824C211yesmaximal, characteristic, complemented
11C11×#1803C212yesmaximal, complemented
12C22×C11×#41C2211yescharacteristic
13C22×C11×SD16C2211yescharacteristic
14C22×C11×D8C2211yescharacteristic
15C22×C11×M16C2211yescharacteristic
16C2×C11×#123—22no—
17C2×C11×#121C2211yescharacteristic
18C2×C4×Q8×C11C2212yes—
19C22×C11×C4⋊C4C2211yescharacteristic
20C11×#449—24no—
21C2×C11×C4⋊C8C2212yes—
22C11×#417—24no—
23C2×C11×#103C2212yes—
24C2×C11×#103C2211yescharacteristic
25C2×C11×#102C2212yes—
26C2×C11×#102C2211yescharacteristic
27C2×C11×#102C2212yes—
28C2×C11×C22⋊C8C2211yescharacteristic
29C11×#399—21no—
30C11×#399—21no—
31C11×#390—22no—
32C11×#390C2212yes—
33C11×#390C2212yes—
34C11×#384C2212yes—
35C11×#380—21no—
36C11×#380C2211yescharacteristic
37C4×C11×C22⋊C4—21no—
38C4×C11×C22⋊C4C2211yescharacteristic
39C11×#340C2212yes—
40C11×#340C2212yes—
41C11×#340C2212yes—
42C11×#336C2212yes—
43C2×C11×#41—22no—
44C2×C11×#41—24no—
45C2×C11×#41—42no—
46C2×C11×#41D414yes—
47C22×Q8×C11C2311yescharacteristic
48C22×D4×C11—21no—
49C22×D4×C11—21no—
50C22×D4×C11C2311yescharacteristic
51C22×D4×C11C2311yescharacteristic
52C23×C4×C11—21no—
53C23×C4×C11—21no—
54C23×C4×C11C2311yescharacteristic
55C2×C11×SD16—22no—
56C2×C11×SD16—24no—
57C2×C11×D8—22no—
58C2×C11×D8—42no—
59C2×C11×M16—22no—
60C2×C11×M16—42no—
61C22×C8×C11C2311yescharacteristic
62C22×C8×C11C2312yes—
63C22×C8×C11C2311yescharacteristic
64C11×#123—48no—
65C11×#121—22no—
66C11×#121—22no—
67C4×Q8×C11—24no—
68C4×Q8×C11—42no—
69C2×C11×C4⋊C4—22no—
70C2×C11×C4⋊C4—22no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—22no—
73C2×C11×C4⋊C4—22no—
74C2×C11×C4⋊C4—22no—
75C2×C11×C4⋊C4C2312yes—
76C2×C11×C4⋊C4C2312yes—
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C22⋊C4—22no—
79C2×C11×C22⋊C4—21no—
80C2×C11×C22⋊C4—22no—
81C2×C11×C22⋊C4—22no—
82C2×C11×C22⋊C4—21no—
83C2×C11×C22⋊C4—22no—
84C2×C11×C22⋊C4D412yes—
85C2×C42×C11—22no—
86C2×C42×C11C2312yes—
87C11×C4⋊C8—42no—
88C11×#103—24no—
89C11×#103—22no—
90C11×#102—24no—
91C11×#102—22no—
92C11×#102—42no—
93C11×C22⋊C8—22no—
94C11×#95—21no—
95C11×#95D411yescharacteristic
96C11×#95D411yescharacteristic
97#24542C1111yesmaximal, characteristic, direct product factor, Sylow
98C24×C11—21no—
99C24×C11—21no—
100C24×C11C2×D411yescharacteristic
101C11×#41—28no—
102C11×#41—44no—
103C11×#41—48no—
104C2×Q8×C11—21no—
105C2×Q8×C11—22no—
106C2×Q8×C11C2×D412yes—
107C2×Q8×C11#4114yes—
108C2×D4×C11—24no—
109C2×D4×C11—21no—
110C2×D4×C11—22no—
111C2×D4×C11—21no—
112C2×D4×C11—21no—
113C2×D4×C11—22no—
114C2×D4×C11—22no—
115C2×D4×C11—22no—
116C2×D4×C11—44no—
117C2×D4×C11—44no—
118C2×D4×C11—42no—
119C2×D4×C11C2×D412yes—
120C22×C4×C11—21no—
121C22×C4×C11—22no—
122C22×C4×C11—22no—
123C22×C4×C11—24no—
124C22×C4×C11—22no—
125C22×C4×C11—22no—
126C22×C4×C11—21no—
127C22×C4×C11—44no—
128C22×C4×C11—44no—
129C22×C4×C11—42no—
130C22×C4×C11C2×D412yes—
131C22×C4×C11C2×D411yescharacteristic
132C22×C4×C11C2×D412yes—
133C22×C4×C11C2×D412yes—
134C22×C4×C11#4112yes—
135C22×C4×C11C2411yescharacteristic
136C11×SD16—44no—
137C11×D8—44no—
138C11×M16—44no—
139C2×C8×C11—21no—
140C2×C8×C11—21no—
141C2×C8×C11—22no—
142C2×C8×C11—22no—
143C2×C8×C11—22no—
144C2×C8×C11—22no—
145C2×C8×C11—22no—
146C11×C4⋊C4—22no—
147C11×C4⋊C4—21no—
148C11×C4⋊C4—22no—
149C11×C4⋊C4—22no—
150C11×C4⋊C4—21no—
151C11×C4⋊C4—22no—
152C11×C4⋊C4—44no—
153C11×C4⋊C4—44no—
154C11×C4⋊C4—42no—
155C11×C4⋊C4—44no—
156C11×C22⋊C4—24no—
157C11×C22⋊C4—44no—
158C11×C22⋊C4—42no—
159C11×C22⋊C4—44no—
160C11×C22⋊C4—44no—
161C11×C22⋊C4—82no—
162C11×C22⋊C4—81no—
163C42×C11—22no—
164C42×C11—22no—
165C42×C11—44no—
166C2×#449C2×C1111yescharacteristic
167C2×#417C2×C1111yescharacteristic, complemented
168#2501C2×C1111yescharacteristic, complemented
169#2341C2×C1111yescharacteristic, complemented
170#2071C2×C1112yescomplemented
171#2054C2×C1112yescomplemented
172#1895C2×C1111yescharacteristic, complemented
173#1880C2×C1112yescomplemented
174#1851C2×C1111yescharacteristic, complemented
175#1824C2×C1111yescharacteristic, complemented
176#1803C2×C1112yescomplemented
177C23×C11—22no—
178C23×C11—22no—
179C23×C11—21no—
180C23×C11—21no—
181C23×C11—22no—
182C23×C11—42no—
183C23×C11—42no—
184C23×C11—41no—
185C23×C11—41no—
186C23×C11—41no—
187C23×C11—42no—
188C23×C11—42no—
189C23×C11—41no—
190C23×C11—41no—
191C23×C11#12112yes—
192C23×C11C22×D411yescharacteristic
193Q8×C11—22no—
194Q8×C11—24no—
195Q8×C11#12314yescomplemented
196D4×C11—22no—
197D4×C11—22no—
198D4×C11—48no—
199D4×C11—41no—
200D4×C11—41no—
201D4×C11—42no—
202D4×C11—42no—
203D4×C11—84no—
204C2×C4×C11—22no—
205C2×C4×C11—22no—
206C2×C4×C11—24no—
207C2×C4×C11—22no—
208C2×C4×C11—22no—
209C2×C4×C11—22no—
210C2×C4×C11—22no—
211C2×C4×C11—24no—
212C2×C4×C11—22no—
213C2×C4×C11—22no—
214C2×C4×C11—22no—
215C2×C4×C11—48no—
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—84no—
225C2×C4×C11#12112yes—
226C2×C4×C11AGL(1,ℤ/8)14yes—
227C2×C4×C11C22×D411yescharacteristic
228C2×C4×C11C2×#4112yes—
229C2×C4×C11C2×#4111yescharacteristic
230C2×C4×C11H(5,𝔽2)12yes—
231C8×C11—41no—
232C8×C11—42no—
233C8×C11—41no—
234C22×#41C22×C1111yescharacteristic
235C22×SD16C22×C1111yescharacteristic
236C22×D8C22×C1111yescharacteristic
237C22×M16C22×C1111yescharacteristic
238C2×#123—22no—
239C2×#121C22×C1111yescharacteristic
240C2×C4×Q8C22×C1112yes—
241C22×C4⋊C4C22×C1111yescharacteristic
242#449—24no—
243C2×C4⋊C8C22×C1112yes—
244#417—24no—
245C2×#103C22×C1111yescharacteristic
246C2×#103C22×C1112yes—
247C2×#102C22×C1112yes—
248C2×#102C22×C1111yescharacteristic
249C2×#102C22×C1112yes—
250C2×C22⋊C8C22×C1111yescharacteristic
251#399—21no—
252#399—21no—
253#390—22no—
254#390C22×C1112yes—
255#390C22×C1112yes—
256#384C22×C1112yes—
257#380—21no—
258#380C22×C1111yescharacteristic
259C4×C22⋊C4—21no—
260C4×C22⋊C4C22×C1111yescharacteristic
261#340C22×C1112yes—
262#340C22×C1112yes—
263#340C22×C1112yes—
264#336C22×C1112yes—
265C22×C11—22no—
266C22×C11—22no—
267C22×C11—22no—
268C22×C11—42no—
269C22×C11—42no—
270C22×C11—42no—
271C22×C11—42no—
272C22×C11—42no—
273C22×C11—82no—
274C22×C11—82no—
275C22×C11—82no—
276C22×C11—81no—
277C22×C11—81no—
278C22×C11—81no—
279C22×C11—82no—
280C22×C11C2×#12111yescharacteristic
281C22×C11#54612yes—
282C22×C11C2×AGL(1,ℤ/8)12yes—
283C22×C11#57711yescharacteristic
284C22×C11#57811yescharacteristic
285C4×C11—22no—
286C4×C11—24no—
287C4×C11—24no—
288C4×C11—42no—
289C4×C11—82no—
290C4×C11—82no—
291C4×C11—81no—
292C4×C11C2×#12311yescharacteristic
293C4×C11#53411yescharacteristic
294C4×C11#55112yes—
295C2×#41—22no—
296C2×#41—24no—
297C2×#41—42no—
298C2×#41D4×C1114yes—
299C22×Q8C23×C1111yescharacteristic
300C22×D4—21no—
301C22×D4—21no—
302C22×D4C23×C1111yescharacteristic
303C22×D4C23×C1111yescharacteristic
304C23×C4—21no—
305C23×C4—21no—
306C23×C4C23×C1111yescharacteristic
307C2×SD16—22no—
308C2×SD16—24no—
309C2×D8—22no—
310C2×D8—42no—
311C2×M16—22no—
312C2×M16—42no—
313C22×C8C23×C1112yes—
314C22×C8C23×C1111yescharacteristic
315C22×C8C23×C1111yescharacteristic
316#123—48no—
317#121—22no—
318#121—22no—
319C4×Q8—24no—
320C4×Q8—42no—
321C2×C4⋊C4—22no—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—21no—
324C2×C4⋊C4—22no—
325C2×C4⋊C4—22no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4C23×C1112yes—
328C2×C4⋊C4C23×C1112yes—
329C2×C4⋊C4C23×C1111yescharacteristic
330C2×C22⋊C4—21no—
331C2×C22⋊C4—22no—
332C2×C22⋊C4—22no—
333C2×C22⋊C4—22no—
334C2×C22⋊C4—21no—
335C2×C22⋊C4—22no—
336C2×C22⋊C4D4×C1112yes—
337C2×C42—22no—
338C2×C42C23×C1112yes—
339C4⋊C8—42no—
340#103—24no—
341#103—22no—
342#102—24no—
343#102—22no—
344#102—42no—
345C22⋊C8—22no—
346#95—21no—
347#95D4×C1111yescharacteristic
348#95D4×C1111yescharacteristic
349C2×C11—42no—
350C2×C11—82no—
351C2×C11—161no—
352C2×C11#241211yescharacteristic
353C2×C11#303811yescharacteristic
354C2×C11#304611yescharacteristic
355C2×C11#330812yes—
356C2×C11#333212yes—
357C24—21no—
358C24—21no—
359C24C2×D4×C1111yescharacteristic
360#41—28no—
361#41—44no—
362#41—48no—
363C2×Q8—21no—
364C2×Q8—22no—
365C2×Q8C2×D4×C1112yes—
366C2×Q8C11×#4114yes—
367C2×D4—24no—
368C2×D4—21no—
369C2×D4—22no—
370C2×D4—21no—
371C2×D4—21no—
372C2×D4—22no—
373C2×D4—22no—
374C2×D4—22no—
375C2×D4—44no—
376C2×D4—44no—
377C2×D4—42no—
378C2×D4C2×D4×C1112yes—
379C22×C4—21no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—24no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—21no—
386C22×C4—44no—
387C22×C4—44no—
388C22×C4—42no—
389C22×C4C2×D4×C1112yes—
390C22×C4C2×D4×C1111yescharacteristic
391C22×C4C2×D4×C1112yes—
392C22×C4C2×D4×C1112yes—
393C22×C4C11×#4112yes—
394C22×C4C24×C1111yescharacteristic
395SD16—44no—
396D8—44no—
397M16—44no—
398C2×C8—21no—
399C2×C8—21no—
400C2×C8—22no—
401C2×C8—22no—
402C2×C8—22no—
403C2×C8—22no—
404C2×C8—22no—
405C4⋊C4—22no—
406C4⋊C4—21no—
407C4⋊C4—22no—
408C4⋊C4—22no—
409C4⋊C4—21no—
410C4⋊C4—22no—
411C4⋊C4—44no—
412C4⋊C4—44no—
413C4⋊C4—42no—
414C4⋊C4—44no—
415C22⋊C4—24no—
416C22⋊C4—44no—
417C22⋊C4—42no—
418C22⋊C4—44no—
419C22⋊C4—44no—
420C22⋊C4—82no—
421C22⋊C4—81no—
422C42—22no—
423C42—22no—
424C42—44no—
425C11#2454211yescharacteristic, direct product factor, Sylow
426C23—22no—
427C23—22no—
428C23—21no—
429C23—21no—
430C23—22no—
431C23—42no—
432C23—42no—
433C23—41no—
434C23—41no—
435C23—41no—
436C23—42no—
437C23—42no—
438C23—41no—
439C23—41no—
440C23C11×#12112yes—
441C23C22×D4×C1111yescharacteristic
442Q8—22no—
443Q8—24no—
444Q8C11×#12314yescomplemented
445D4—22no—
446D4—22no—
447D4—48no—
448D4—41no—
449D4—41no—
450D4—42no—
451D4—42no—
452D4—84no—
453C2×C4—22no—
454C2×C4—22no—
455C2×C4—24no—
456C2×C4—22no—
457C2×C4—22no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—24no—
461C2×C4—22no—
462C2×C4—22no—
463C2×C4—22no—
464C2×C4—48no—
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—84no—
474C2×C4C11×#12112yes—
475C2×C4C11×AGL(1,ℤ/8)14yes—
476C2×C4C22×D4×C1111yescharacteristic
477C2×C4C2×C11×#4112yes—
478C2×C4C2×C11×#4111yescharacteristic
479C2×C4C11×H(5,𝔽2)12yes—
480C8—41no—
481C8—42no—
482C8—41no—
483C22—22no—
484C22—22no—
485C22—22no—
486C22—42no—
487C22—42no—
488C22—42no—
489C22—42no—
490C22—42no—
491C22—82no—
492C22—82no—
493C22—81no—
494C22—81no—
495C22—81no—
496C22—82no—
497C22—82no—
498C22C2×C11×#12111yescharacteristic
499C22C11×#54612yes—
500C22C2×C11×AGL(1,ℤ/8)12yes—
501C22C11×#57711yescharacteristic
502C22C11×#57811yescharacteristic
503C4—22no—
504C4—24no—
505C4—24no—
506C4—42no—
507C4—82no—
508C4—81no—
509C4—82no—
510C4C2×C11×#12311yescharacteristic
511C4C11×#53411yescharacteristic
512C4C11×#55112yes—
513C2—42no—
514C2—82no—
515C2—161no—
516C2C11×#241211yescharacteristic
517C2C11×#303811yescharacteristic
518C2C11×#304611yescharacteristic
519C2C11×#330812yes—
520C2C11×#333212yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#449C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C4×C11×C22⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#417C2semidirect
3. C11×#2501C2semidirect
4. C11×#2341C2semidirect
5. C11×#2071C2semidirect
6. C11×#2054C2semidirect
7. C11×#1895C2semidirect
8. C11×#1880C2semidirect
9. C11×#1851C2semidirect
10. C11×#1824C2semidirect
11. C11×#1803C2semidirect
97. #24542C11direct (N × H)
167. C2×#417C2×C11semidirect
168. #2501C2×C11semidirect
169. #2341C2×C11semidirect
170. #2071C2×C11semidirect
171. #2054C2×C11semidirect
172. #1895C2×C11semidirect
173. #1880C2×C11semidirect
174. #1851C2×C11semidirect
175. #1824C2×C11semidirect
176. #1803C2×C11semidirect
195. Q8×C11#123semidirect
425. C11#24542direct (N × H)
444. Q8C11×#123semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#4492
C2×C11×#4172
C11×#25012
C11×#23412
C11×#20712
C11×#20542
C11×#18952
C11×#18802
C11×#18512
C11×#18242
C11×#18032
#2454211