Finite Group Databasebeta

← C11×#24546 #14601739

Subgroups — C11×#24546 #14601739

Order 2816.

996 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#452C211yesmaximal, characteristic
2C2×C11×#417C211yesmaximal, characteristic
3C11×#2502C211yesmaximal, characteristic, complemented
4C11×#2341C211yesmaximal, characteristic
5C11×#2071C212yesmaximal, complemented
6C11×#2055C212yesmaximal, complemented
7C11×#1894C211yesmaximal, characteristic, complemented
8C11×#1878C212yesmaximal, complemented
9C11×#1851C211yesmaximal, characteristic, complemented
10C11×#1823C211yesmaximal, characteristic, complemented
11C11×#1803C212yesmaximal, complemented
12C22×C11×#41C2211yescharacteristic
13C22×C11×Q16C2211yescharacteristic
14C22×C11×SD16C2211yescharacteristic
15C22×C11×M16C2211yescharacteristic
16C2×C11×C22⋊Q8C2211yescharacteristic
17C2×C4×Q8×C11C2212yes—
18C22×C11×C4⋊C4C2211yescharacteristic
19C11×#452—24no—
20C2×C11×C4⋊C8C2212yes—
21C11×#417—24no—
22C2×C11×#103C2212yes—
23C2×C11×#103C2211yescharacteristic
24C2×C11×#103C2212yes—
25C2×C11×#102C2212yes—
26C2×C11×#102C2211yescharacteristic
27C2×C11×C22⋊C8C2211yescharacteristic
28C11×#398—21no—
29C11×#398—21no—
30C11×#391C2212yes—
31C11×#390—22no—
32C11×#390C2212yes—
33C11×#385—22no—
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×Q8×C11C2311yescharacteristic
49C22×D4×C11—21no—
50C22×D4×C11C2311yescharacteristic
51C23×C4×C11—21no—
52C23×C4×C11—21no—
53C23×C4×C11C2311yescharacteristic
54C2×C11×Q16—22no—
55C2×C11×Q16—24no—
56C2×C11×SD16—22no—
57C2×C11×SD16—42no—
58C2×C11×M16—22no—
59C2×C11×M16—42no—
60C22×C8×C11C2311yescharacteristic
61C22×C8×C11C2312yes—
62C22×C8×C11C2311yescharacteristic
63C11×C22⋊Q8—22no—
64C11×C22⋊Q8—22no—
65C4×Q8×C11—24no—
66C4×Q8×C11—42no—
67C2×C11×C4⋊C4—22no—
68C2×C11×C4⋊C4—22no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4—22no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—22no—
73C2×C11×C4⋊C4—22no—
74C2×C11×C4⋊C4C2312yes—
75C2×C11×C4⋊C4C2312yes—
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C22⋊C4—21no—
78C2×C11×C22⋊C4—22no—
79C2×C11×C22⋊C4—21no—
80C2×C11×C22⋊C4—22no—
81C2×C11×C22⋊C4D412yes—
82C2×C42×C11—22no—
83C2×C42×C11C2312yes—
84C11×C4⋊C8—42no—
85C11×#103—24no—
86C11×#103—22no—
87C11×#103—42no—
88C11×#102—24no—
89C11×#102—22no—
90C11×C22⋊C8—22no—
91C11×#95—21no—
92C11×#95—22no—
93C11×#95—22no—
94C11×#95D411yescharacteristic
95C11×#95D411yescharacteristic
96#24546C1111yesmaximal, characteristic, direct product factor, Sylow
97C24×C11—21no—
98C24×C11C2×D411yescharacteristic
99C11×#41—28no—
100C11×#41—44no—
101C11×#41—48no—
102C2×Q8×C11—21no—
103C2×Q8×C11—22no—
104C2×Q8×C11—21no—
105C2×Q8×C11—21no—
106C2×Q8×C11—22no—
107C2×Q8×C11—22no—
108C2×Q8×C11C2×D412yes—
109C2×Q8×C11#4114yes—
110C2×D4×C11—24no—
111C2×D4×C11—22no—
112C2×D4×C11—21no—
113C2×D4×C11—22no—
114C2×D4×C11—44no—
115C2×D4×C11C2×D412yes—
116C22×C4×C11—21no—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—24no—
120C22×C4×C11—21no—
121C22×C4×C11—22no—
122C22×C4×C11—22no—
123C22×C4×C11—21no—
124C22×C4×C11—44no—
125C22×C4×C11—42no—
126C22×C4×C11—81no—
127C22×C4×C11—81no—
128C22×C4×C11C2×D412yes—
129C22×C4×C11C2×D411yescharacteristic
130C22×C4×C11C2×D412yes—
131C22×C4×C11C2×D412yes—
132C22×C4×C11#4112yes—
133C22×C4×C11C2411yescharacteristic
134C11×Q16—44no—
135C11×SD16—44no—
136C11×M16—44no—
137C2×C8×C11—21no—
138C2×C8×C11—21no—
139C2×C8×C11—22no—
140C2×C8×C11—22no—
141C2×C8×C11—22no—
142C2×C8×C11—22no—
143C2×C8×C11—22no—
144C11×C4⋊C4—22no—
145C11×C4⋊C4—21no—
146C11×C4⋊C4—22no—
147C11×C4⋊C4—22no—
148C11×C4⋊C4—21no—
149C11×C4⋊C4—22no—
150C11×C4⋊C4—44no—
151C11×C4⋊C4—42no—
152C11×C4⋊C4—42no—
153C11×C4⋊C4—82no—
154C11×C4⋊C4—82no—
155C11×C22⋊C4—24no—
156C11×C22⋊C4—42no—
157C11×C22⋊C4—44no—
158C11×C22⋊C4—82no—
159C11×C22⋊C4—81no—
160C42×C11—22no—
161C42×C11—22no—
162C42×C11—44no—
163C2×#452C2×C1111yescharacteristic
164C2×#417C2×C1111yescharacteristic
165#2502C2×C1111yescharacteristic, complemented
166#2341C2×C1111yescharacteristic
167#2071C2×C1112yescomplemented
168#2055C2×C1112yescomplemented
169#1894C2×C1111yescharacteristic, complemented
170#1878C2×C1112yescomplemented
171#1851C2×C1111yescharacteristic, complemented
172#1823C2×C1111yescharacteristic, complemented
173#1803C2×C1112yescomplemented
174C23×C11—22no—
175C23×C11—22no—
176C23×C11—21no—
177C23×C11—21no—
178C23×C11—22no—
179C23×C11—42no—
180C23×C11—42no—
181C23×C11—41no—
182C23×C11—41no—
183C23×C11#12112yes—
184C23×C11C22×D411yescharacteristic
185Q8×C11—22no—
186Q8×C11—24no—
187Q8×C11—41no—
188Q8×C11—41no—
189Q8×C11—42no—
190Q8×C11#12314yes—
191D4×C11—22no—
192D4×C11—22no—
193D4×C11—48no—
194D4×C11—42no—
195C2×C4×C11—22no—
196C2×C4×C11—22no—
197C2×C4×C11—24no—
198C2×C4×C11—22no—
199C2×C4×C11—22no—
200C2×C4×C11—22no—
201C2×C4×C11—22no—
202C2×C4×C11—24no—
203C2×C4×C11—22no—
204C2×C4×C11—22no—
205C2×C4×C11—22no—
206C2×C4×C11—48no—
207C2×C4×C11—41no—
208C2×C4×C11—41no—
209C2×C4×C11—42no—
210C2×C4×C11—42no—
211C2×C4×C11—42no—
212C2×C4×C11—42no—
213C2×C4×C11—42no—
214C2×C4×C11—41no—
215C2×C4×C11—42no—
216C2×C4×C11—41no—
217C2×C4×C11—42no—
218C2×C4×C11—84no—
219C2×C4×C11#12112yes—
220C2×C4×C11#13714yes—
221C2×C4×C11C22×D411yescharacteristic
222C2×C4×C11C2×#4112yes—
223C2×C4×C11C2×#4111yescharacteristic
224C2×C4×C11H(5,𝔽2)12yes—
225C8×C11—41no—
226C8×C11—42no—
227C8×C11—41no—
228C22×#41C22×C1111yescharacteristic
229C22×Q16C22×C1111yescharacteristic
230C22×SD16C22×C1111yescharacteristic
231C22×M16C22×C1111yescharacteristic
232C2×C22⋊Q8C22×C1111yescharacteristic
233C2×C4×Q8C22×C1112yes—
234C22×C4⋊C4C22×C1111yescharacteristic
235#452—24no—
236C2×C4⋊C8C22×C1112yes—
237#417—24no—
238C2×#103C22×C1111yescharacteristic
239C2×#103C22×C1112yes—
240C2×#103C22×C1112yes—
241C2×#102C22×C1112yes—
242C2×#102C22×C1111yescharacteristic
243C2×C22⋊C8C22×C1111yescharacteristic
244#398—21no—
245#398—21no—
246#391C22×C1112yes—
247#390—22no—
248#390C22×C1112yes—
249#385—22no—
250#384C22×C1112yes—
251#380—21no—
252#380C22×C1111yescharacteristic
253C4×C22⋊C4—21no—
254C4×C22⋊C4C22×C1111yescharacteristic
255#340C22×C1112yes—
256#340C22×C1112yes—
257#340C22×C1112yes—
258#336C22×C1112yes—
259C22×C11—22no—
260C22×C11—22no—
261C22×C11—22no—
262C22×C11—42no—
263C22×C11—42no—
264C22×C11—42no—
265C22×C11—42no—
266C22×C11—42no—
267C22×C11—82no—
268C22×C11—82no—
269C22×C11C2×#12111yescharacteristic
270C22×C11#54612yes—
271C22×C11C2×#13712yes—
272C22×C11#57611yescharacteristic
273C22×C11#57711yescharacteristic
274C4×C11—22no—
275C4×C11—24no—
276C4×C11—24no—
277C4×C11—42no—
278C4×C11—82no—
279C4×C11—81no—
280C4×C11—81no—
281C4×C11—82no—
282C4×C11C2×#12311yescharacteristic
283C4×C11#53411yescharacteristic
284C4×C11#55112yes—
285C2×#41—22no—
286C2×#41—24no—
287C2×#41—42no—
288C2×#41D4×C1114yes—
289C22×Q8C23×C1111yescharacteristic
290C22×Q8C23×C1111yescharacteristic
291C22×D4—21no—
292C22×D4C23×C1111yescharacteristic
293C23×C4—21no—
294C23×C4—21no—
295C23×C4C23×C1111yescharacteristic
296C2×Q16—22no—
297C2×Q16—24no—
298C2×SD16—22no—
299C2×SD16—42no—
300C2×M16—22no—
301C2×M16—42no—
302C22×C8C23×C1112yes—
303C22×C8C23×C1111yescharacteristic
304C22×C8C23×C1111yescharacteristic
305C22⋊Q8—22no—
306C22⋊Q8—22no—
307C4×Q8—24no—
308C4×Q8—42no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—22no—
311C2×C4⋊C4—21no—
312C2×C4⋊C4—22no—
313C2×C4⋊C4—21no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—22no—
316C2×C4⋊C4C23×C1112yes—
317C2×C4⋊C4C23×C1112yes—
318C2×C4⋊C4C23×C1111yescharacteristic
319C2×C22⋊C4—21no—
320C2×C22⋊C4—22no—
321C2×C22⋊C4—21no—
322C2×C22⋊C4—22no—
323C2×C22⋊C4D4×C1112yes—
324C2×C42—22no—
325C2×C42C23×C1112yes—
326C4⋊C8—42no—
327#103—24no—
328#103—22no—
329#103—42no—
330#102—24no—
331#102—22no—
332C22⋊C8—22no—
333#95—21no—
334#95—22no—
335#95—22no—
336#95D4×C1111yescharacteristic
337#95D4×C1111yescharacteristic
338C2×C11—42no—
339C2×C11—82no—
340C2×C11#241211yescharacteristic
341C2×C11#303911yescharacteristic
342C2×C11#304511yescharacteristic
343C2×C11#331612yes—
344C2×C11#333312yes—
345C24—21no—
346C24C2×D4×C1111yescharacteristic
347#41—28no—
348#41—44no—
349#41—48no—
350C2×Q8—21no—
351C2×Q8—22no—
352C2×Q8—21no—
353C2×Q8—21no—
354C2×Q8—22no—
355C2×Q8—22no—
356C2×Q8C2×D4×C1112yes—
357C2×Q8C11×#4114yes—
358C2×D4—24no—
359C2×D4—22no—
360C2×D4—21no—
361C2×D4—22no—
362C2×D4—44no—
363C2×D4C2×D4×C1112yes—
364C22×C4—21no—
365C22×C4—22no—
366C22×C4—22no—
367C22×C4—24no—
368C22×C4—21no—
369C22×C4—22no—
370C22×C4—22no—
371C22×C4—21no—
372C22×C4—44no—
373C22×C4—42no—
374C22×C4—81no—
375C22×C4—81no—
376C22×C4C2×D4×C1112yes—
377C22×C4C2×D4×C1111yescharacteristic
378C22×C4C2×D4×C1112yes—
379C22×C4C2×D4×C1112yes—
380C22×C4C11×#4112yes—
381C22×C4C24×C1111yescharacteristic
382Q16—44no—
383SD16—44no—
384M16—44no—
385C2×C8—21no—
386C2×C8—21no—
387C2×C8—22no—
388C2×C8—22no—
389C2×C8—22no—
390C2×C8—22no—
391C2×C8—22no—
392C4⋊C4—22no—
393C4⋊C4—21no—
394C4⋊C4—22no—
395C4⋊C4—22no—
396C4⋊C4—21no—
397C4⋊C4—22no—
398C4⋊C4—44no—
399C4⋊C4—42no—
400C4⋊C4—42no—
401C4⋊C4—82no—
402C4⋊C4—82no—
403C22⋊C4—24no—
404C22⋊C4—42no—
405C22⋊C4—44no—
406C22⋊C4—82no—
407C22⋊C4—81no—
408C42—22no—
409C42—22no—
410C42—44no—
411C11#2454611yescharacteristic, direct product factor, Sylow
412C23—22no—
413C23—22no—
414C23—21no—
415C23—21no—
416C23—22no—
417C23—42no—
418C23—42no—
419C23—41no—
420C23—41no—
421C23C11×#12112yes—
422C23C22×D4×C1111yescharacteristic
423Q8—22no—
424Q8—24no—
425Q8—41no—
426Q8—41no—
427Q8—42no—
428Q8C11×#12314yes—
429D4—22no—
430D4—22no—
431D4—48no—
432D4—42no—
433C2×C4—22no—
434C2×C4—22no—
435C2×C4—24no—
436C2×C4—22no—
437C2×C4—22no—
438C2×C4—22no—
439C2×C4—22no—
440C2×C4—24no—
441C2×C4—22no—
442C2×C4—22no—
443C2×C4—22no—
444C2×C4—48no—
445C2×C4—41no—
446C2×C4—41no—
447C2×C4—42no—
448C2×C4—42no—
449C2×C4—42no—
450C2×C4—42no—
451C2×C4—42no—
452C2×C4—41no—
453C2×C4—42no—
454C2×C4—41no—
455C2×C4—42no—
456C2×C4—84no—
457C2×C4C11×#12112yes—
458C2×C4C11×#13714yes—
459C2×C4C22×D4×C1111yescharacteristic
460C2×C4C2×C11×#4112yes—
461C2×C4C2×C11×#4111yescharacteristic
462C2×C4C11×H(5,𝔽2)12yes—
463C8—41no—
464C8—42no—
465C8—41no—
466C22—22no—
467C22—22no—
468C22—22no—
469C22—42no—
470C22—42no—
471C22—42no—
472C22—42no—
473C22—42no—
474C22—82no—
475C22—82no—
476C22C2×C11×#12111yescharacteristic
477C22C11×#54612yes—
478C22C2×C11×#13712yes—
479C22C11×#57611yescharacteristic
480C22C11×#57711yescharacteristic
481C4—22no—
482C4—24no—
483C4—24no—
484C4—42no—
485C4—81no—
486C4—82no—
487C4—81no—
488C4—82no—
489C4C2×C11×#12311yescharacteristic
490C4C11×#53411yescharacteristic
491C4C11×#55112yes—
492C2—42no—
493C2—82no—
494C2C11×#241211yescharacteristic
495C2C11×#303911yescharacteristic
496C2C11×#304511yescharacteristic
497C2C11×#331612yes—
498C2C11×#333312yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC22×C11×#41C22
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
3. C11×#2502C2semidirect
5. C11×#2071C2semidirect
6. C11×#2055C2semidirect
7. C11×#1894C2semidirect
8. C11×#1878C2semidirect
9. C11×#1851C2semidirect
10. C11×#1823C2semidirect
11. C11×#1803C2semidirect
96. #24546C11direct (N × H)
165. #2502C2×C11semidirect
167. #2071C2×C11semidirect
168. #2055C2×C11semidirect
169. #1894C2×C11semidirect
170. #1878C2×C11semidirect
171. #1851C2×C11semidirect
172. #1823C2×C11semidirect
173. #1803C2×C11semidirect
411. C11#24546direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4522
C2×C11×#4172
C11×#25022
C11×#23412
C11×#20712
C11×#20552
C11×#18942
C11×#18782
C11×#18512
C11×#18232
C11×#18032
#2454611