Finite Group Databasebeta

← C11×#24545 #14601738

Subgroups — C11×#24545 #14601738

Order 2816.

1008 conjugacy classes of subgroups.

The subgroup lattice has 494 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×#2503C211yesmaximal, characteristic, complemented
4C11×#2339C211yesmaximal, characteristic
5C11×#2074C212yesmaximal, complemented
6C11×#2056C212yesmaximal, complemented
7C11×#1894C211yesmaximal, characteristic, complemented
8C11×#1877C212yesmaximal, complemented
9C11×#1851C211yesmaximal, characteristic, complemented
10C11×#1824C211yesmaximal, characteristic, complemented
11C11×#1804C212yesmaximal, complemented
12C22×C11×#41C2211yescharacteristic
13C22×C11×Q16C2211yescharacteristic
14C22×C11×SD16C2211yescharacteristic
15C22×C11×M16C2211yescharacteristic
16C2×C11×C22⋊Q8C2211yescharacteristic
17C2×C4×D4×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×#400—21no—
29C11×#400—21no—
30C11×#391C2212yes—
31C11×#391C2212yes—
32C11×#386—22no—
33C11×#382C2212yes—
34C11×#381—22no—
35C11×#381—21no—
36C11×#380C2211yescharacteristic
37C4×C11×C22⋊C4C2211yescharacteristic
38C2×C11×#95—21no—
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×C11—22no—
54C23×C4×C11C2311yescharacteristic
55C2×C11×Q16—22no—
56C2×C11×Q16—42no—
57C2×C11×SD16—22no—
58C2×C11×SD16—24no—
59C2×C11×M16—22no—
60C2×C11×M16—42no—
61C22×C8×C11C2311yescharacteristic
62C22×C8×C11C2312yes—
63C22×C8×C11C2311yescharacteristic
64C11×C22⋊Q8—22no—
65C11×C22⋊Q8—22no—
66C4×D4×C11—24no—
67C4×D4×C11—42no—
68C2×C11×C4⋊C4—22no—
69C2×C11×C4⋊C4—22no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4C2312yes—
73C2×C11×C4⋊C4C2312yes—
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C22⋊C4—21no—
76C2×C11×C22⋊C4—22no—
77C2×C11×C22⋊C4—21no—
78C2×C11×C22⋊C4D412yes—
79C2×C42×C11C2312yes—
80C11×C4⋊C8—42no—
81C11×#103—24no—
82C11×#103—22no—
83C11×#103—42no—
84C11×#102—24no—
85C11×#102—22no—
86C11×C22⋊C8—22no—
87C11×#95—21no—
88C11×#95—22no—
89C11×#95—22no—
90C11×#95—22no—
91C11×#95—22no—
92C11×#95—22no—
93C11×#95—22no—
94C11×#95D411yescharacteristic
95C11×#95D411yescharacteristic
96#24545C1111yesmaximal, 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—21no—
104C2×Q8×C11—22no—
105C2×Q8×C11—21no—
106C2×Q8×C11—22no—
107C2×Q8×C11—22no—
108C2×Q8×C11—22no—
109C2×Q8×C11C2×D412yes—
110C2×D4×C11—24no—
111C2×D4×C11—21no—
112C2×D4×C11—22no—
113C2×D4×C11—44no—
114C2×D4×C11C2×D412yes—
115C2×D4×C11#4114yes—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—21no—
119C22×C4×C11—24no—
120C22×C4×C11—21no—
121C22×C4×C11—21no—
122C22×C4×C11—22no—
123C22×C4×C11—22no—
124C22×C4×C11—44no—
125C22×C4×C11—44no—
126C22×C4×C11—44no—
127C22×C4×C11—44no—
128C22×C4×C11—42no—
129C22×C4×C11—82no—
130C22×C4×C11C2×D412yes—
131C22×C4×C11C2×D412yes—
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2×D412yes—
134C22×C4×C11#4112yes—
135C22×C4×C11C2411yescharacteristic
136C11×Q16—44no—
137C11×SD16—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—42no—
153C11×C4⋊C4—42no—
154C11×C22⋊C4—42no—
155C11×C22⋊C4—44no—
156C11×C22⋊C4—42no—
157C11×C22⋊C4—81no—
158C42×C11—22no—
159C42×C11—22no—
160C2×#452C2×C1111yescharacteristic
161C2×#417C2×C1111yescharacteristic
162#2503C2×C1111yescharacteristic, complemented
163#2339C2×C1111yescharacteristic
164#2074C2×C1112yescomplemented
165#2056C2×C1112yescomplemented
166#1894C2×C1111yescharacteristic, complemented
167#1877C2×C1112yescomplemented
168#1851C2×C1111yescharacteristic, complemented
169#1824C2×C1111yescharacteristic, complemented
170#1804C2×C1112yescomplemented
171C23×C11—22no—
172C23×C11—24no—
173C23×C11—22no—
174C23×C11—22no—
175C23×C11—21no—
176C23×C11—21no—
177C23×C11—42no—
178C23×C11—41no—
179C23×C11—41no—
180C23×C11#12112yes—
181C23×C11C22×D411yescharacteristic
182Q8×C11—22no—
183Q8×C11—22no—
184Q8×C11—42no—
185Q8×C11—41no—
186Q8×C11—41no—
187Q8×C11—42no—
188D4×C11—22no—
189D4×C11—24no—
190D4×C11—48no—
191D4×C11#12314yes—
192C2×C4×C11—22no—
193C2×C4×C11—22no—
194C2×C4×C11—22no—
195C2×C4×C11—24no—
196C2×C4×C11—22no—
197C2×C4×C11—22no—
198C2×C4×C11—22no—
199C2×C4×C11—22no—
200C2×C4×C11—22no—
201C2×C4×C11—22no—
202C2×C4×C11—22no—
203C2×C4×C11—48no—
204C2×C4×C11—42no—
205C2×C4×C11—41no—
206C2×C4×C11—41no—
207C2×C4×C11—42no—
208C2×C4×C11—42no—
209C2×C4×C11—42no—
210C2×C4×C11—44no—
211C2×C4×C11—42no—
212C2×C4×C11—42no—
213C2×C4×C11—41no—
214C2×C4×C11—41no—
215C2×C4×C11—88no—
216C2×C4×C11—84no—
217C2×C4×C11#12112yes—
218C2×C4×C11C22×D411yescharacteristic
219C2×C4×C11C2×#4112yes—
220C2×C4×C11C2×#4111yescharacteristic
221C2×C4×C11H(5,𝔽2)12yes—
222C8×C11—41no—
223C8×C11—42no—
224C8×C11—41no—
225C22×#41C22×C1111yescharacteristic
226C22×Q16C22×C1111yescharacteristic
227C22×SD16C22×C1111yescharacteristic
228C22×M16C22×C1111yescharacteristic
229C2×C22⋊Q8C22×C1111yescharacteristic
230C2×C4×D4C22×C1112yes—
231C22×C4⋊C4C22×C1111yescharacteristic
232#452—24no—
233C2×C4⋊C8C22×C1112yes—
234#417—24no—
235C2×#103C22×C1112yes—
236C2×#103C22×C1111yescharacteristic
237C2×#103C22×C1112yes—
238C2×#102C22×C1111yescharacteristic
239C2×#102C22×C1112yes—
240C2×C22⋊C8C22×C1111yescharacteristic
241#400—21no—
242#400—21no—
243#391C22×C1112yes—
244#391C22×C1112yes—
245#386—22no—
246#382C22×C1112yes—
247#381—22no—
248#381—21no—
249#380C22×C1111yescharacteristic
250C4×C22⋊C4C22×C1111yescharacteristic
251C2×#95—21no—
252#340C22×C1112yes—
253#340C22×C1112yes—
254#340C22×C1112yes—
255#336C22×C1112yes—
256C22×C11—22no—
257C22×C11—24no—
258C22×C11—22no—
259C22×C11—22no—
260C22×C11—42no—
261C22×C11—42no—
262C22×C11—42no—
263C22×C11—44no—
264C22×C11—44no—
265C22×C11—42no—
266C22×C11C2×#12111yescharacteristic
267C22×C11#54612yes—
268C22×C11#57512yes—
269C22×C11#57711yescharacteristic
270C22×C11#57811yescharacteristic
271C4×C11—22no—
272C4×C11—42no—
273C4×C11—42no—
274C4×C11—42no—
275C4×C11—81no—
276C4×C11—82no—
277C4×C11—81no—
278C4×C11—82no—
279C4×C11C2×#12311yescharacteristic
280C4×C11#53411yescharacteristic
281C4×C11#55112yes—
282C2×#41—22no—
283C2×#41—24no—
284C2×#41—42no—
285C2×#41D4×C1114yes—
286C22×Q8C23×C1111yescharacteristic
287C22×Q8C23×C1111yescharacteristic
288C22×D4—21no—
289C22×D4C23×C1111yescharacteristic
290C23×C4—21no—
291C23×C4—21no—
292C23×C4—22no—
293C23×C4C23×C1111yescharacteristic
294C2×Q16—22no—
295C2×Q16—42no—
296C2×SD16—22no—
297C2×SD16—24no—
298C2×M16—22no—
299C2×M16—42no—
300C22×C8C23×C1112yes—
301C22×C8C23×C1111yescharacteristic
302C22×C8C23×C1111yescharacteristic
303C22⋊Q8—22no—
304C22⋊Q8—22no—
305C4×D4—24no—
306C4×D4—42no—
307C2×C4⋊C4—22no—
308C2×C4⋊C4—22no—
309C2×C4⋊C4—21no—
310C2×C4⋊C4—21no—
311C2×C4⋊C4C23×C1112yes—
312C2×C4⋊C4C23×C1112yes—
313C2×C4⋊C4C23×C1111yescharacteristic
314C2×C22⋊C4—21no—
315C2×C22⋊C4—22no—
316C2×C22⋊C4—21no—
317C2×C22⋊C4D4×C1112yes—
318C2×C42C23×C1112yes—
319C4⋊C8—42no—
320#103—24no—
321#103—22no—
322#103—42no—
323#102—24no—
324#102—22no—
325C22⋊C8—22no—
326#95—21no—
327#95—22no—
328#95—22no—
329#95—22no—
330#95—22no—
331#95—22no—
332#95—22no—
333#95D4×C1111yescharacteristic
334#95D4×C1111yescharacteristic
335C2×C11—42no—
336C2×C11—44no—
337C2×C11#241211yescharacteristic
338C2×C11#304011yescharacteristic
339C2×C11#304611yescharacteristic
340C2×C11#331512yes—
341C2×C11#332312yes—
342C24—21no—
343C24C2×D4×C1111yescharacteristic
344#41—28no—
345#41—44no—
346#41—48no—
347C2×Q8—21no—
348C2×Q8—21no—
349C2×Q8—22no—
350C2×Q8—21no—
351C2×Q8—22no—
352C2×Q8—22no—
353C2×Q8—22no—
354C2×Q8C2×D4×C1112yes—
355C2×D4—24no—
356C2×D4—21no—
357C2×D4—22no—
358C2×D4—44no—
359C2×D4C2×D4×C1112yes—
360C2×D4C11×#4114yes—
361C22×C4—22no—
362C22×C4—22no—
363C22×C4—21no—
364C22×C4—24no—
365C22×C4—21no—
366C22×C4—21no—
367C22×C4—22no—
368C22×C4—22no—
369C22×C4—44no—
370C22×C4—44no—
371C22×C4—44no—
372C22×C4—44no—
373C22×C4—42no—
374C22×C4—82no—
375C22×C4C2×D4×C1112yes—
376C22×C4C2×D4×C1112yes—
377C22×C4C2×D4×C1111yescharacteristic
378C22×C4C2×D4×C1112yes—
379C22×C4C11×#4112yes—
380C22×C4C24×C1111yescharacteristic
381Q16—44no—
382SD16—44no—
383M16—44no—
384C2×C8—21no—
385C2×C8—21no—
386C2×C8—22no—
387C2×C8—22no—
388C2×C8—22no—
389C2×C8—22no—
390C2×C8—22no—
391C4⋊C4—22no—
392C4⋊C4—21no—
393C4⋊C4—22no—
394C4⋊C4—22no—
395C4⋊C4—21no—
396C4⋊C4—22no—
397C4⋊C4—42no—
398C4⋊C4—42no—
399C22⋊C4—42no—
400C22⋊C4—44no—
401C22⋊C4—42no—
402C22⋊C4—81no—
403C42—22no—
404C42—22no—
405C11#2454511yescharacteristic, direct product factor, Sylow
406C23—22no—
407C23—24no—
408C23—22no—
409C23—22no—
410C23—21no—
411C23—21no—
412C23—42no—
413C23—41no—
414C23—41no—
415C23C11×#12112yes—
416C23C22×D4×C1111yescharacteristic
417Q8—22no—
418Q8—22no—
419Q8—42no—
420Q8—41no—
421Q8—41no—
422Q8—42no—
423D4—22no—
424D4—24no—
425D4—48no—
426D4C11×#12314yes—
427C2×C4—22no—
428C2×C4—22no—
429C2×C4—22no—
430C2×C4—24no—
431C2×C4—22no—
432C2×C4—22no—
433C2×C4—22no—
434C2×C4—22no—
435C2×C4—22no—
436C2×C4—22no—
437C2×C4—22no—
438C2×C4—48no—
439C2×C4—42no—
440C2×C4—41no—
441C2×C4—41no—
442C2×C4—42no—
443C2×C4—42no—
444C2×C4—42no—
445C2×C4—44no—
446C2×C4—42no—
447C2×C4—42no—
448C2×C4—41no—
449C2×C4—41no—
450C2×C4—88no—
451C2×C4—84no—
452C2×C4C11×#12112yes—
453C2×C4C22×D4×C1111yescharacteristic
454C2×C4C2×C11×#4112yes—
455C2×C4C2×C11×#4111yescharacteristic
456C2×C4C11×H(5,𝔽2)12yes—
457C8—41no—
458C8—42no—
459C8—41no—
460C22—22no—
461C22—24no—
462C22—22no—
463C22—22no—
464C22—42no—
465C22—42no—
466C22—42no—
467C22—44no—
468C22—44no—
469C22—42no—
470C22C2×C11×#12111yescharacteristic
471C22C11×#54612yes—
472C22C11×#57512yes—
473C22C11×#57711yescharacteristic
474C22C11×#57811yescharacteristic
475C4—22no—
476C4—42no—
477C4—42no—
478C4—42no—
479C4—81no—
480C4—82no—
481C4—81no—
482C4—82no—
483C4C2×C11×#12311yescharacteristic
484C4C11×#53411yescharacteristic
485C4C11×#55112yes—
486C2—42no—
487C2—44no—
488C2C11×#241211yescharacteristic
489C2C11×#304011yescharacteristic
490C2C11×#304611yescharacteristic
491C2C11×#331512yes—
492C2C11×#332312yes—
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×#2503C2semidirect
5. C11×#2074C2semidirect
6. C11×#2056C2semidirect
7. C11×#1894C2semidirect
8. C11×#1877C2semidirect
9. C11×#1851C2semidirect
10. C11×#1824C2semidirect
11. C11×#1804C2semidirect
96. #24545C11direct (N × H)
162. #2503C2×C11semidirect
164. #2074C2×C11semidirect
165. #2056C2×C11semidirect
166. #1894C2×C11semidirect
167. #1877C2×C11semidirect
168. #1851C2×C11semidirect
169. #1824C2×C11semidirect
170. #1804C2×C11semidirect
405. C11#24545direct (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×#25032
C11×#23392
C11×#20742
C11×#20562
C11×#18942
C11×#18772
C11×#18512
C11×#18242
C11×#18042
#2454511