Finite Group Databasebeta

← C11×#24528 #14601721

Subgroups — C11×#24528 #14601721

Order 2816.

1064 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#448C211yesmaximal, characteristic
2C22×C11×#103C211yesmaximal, characteristic, complemented
3C11×#2501C211yesmaximal, characteristic
4Q8×C11×C22⋊C4C211yesmaximal, characteristic, complemented
5C11×#2072C212yesmaximal, complemented
6C11×#2055C212yesmaximal, complemented
7C11×#1893C211yesmaximal, characteristic
8C11×#1880C212yesmaximal, complemented
9C11×#1850C211yesmaximal, characteristic, complemented
10C11×#1823C211yesmaximal, characteristic, complemented
11C11×#1803C212yesmaximal, complemented
12C23×Q8×C11C2211yescharacteristic
13C22×C11×SD16C2211yescharacteristic
14C22×C11×SD16C2211yescharacteristic
15C23×C8×C11C2211yescharacteristic
16C2×C11×#123—21no—
17C2×C11×#123—21no—
18C2×C11×#121C2211yescharacteristic
19C2×C4×Q8×C11C2212yes—
20C22×C11×C4⋊C4C2211yescharacteristic
21C11×#448—24no—
22C2×C11×C4⋊C8C2212yes—
23C2×C11×#103—24no—
24C2×C11×#103C2212yes—
25C2×C11×#103C2212yes—
26C2×C11×#103C2211yescharacteristic
27C2×C11×#103C2211yescharacteristic
28C2×C11×#102C2212yes—
29C2×C11×C22⋊C8C2211yescharacteristic
30C11×#399—22no—
31C11×#391—22no—
32C11×#391C2212yes—
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—
43C22×Q8×C11—21no—
44C22×Q8×C11—22no—
45C22×Q8×C11—24no—
46C22×Q8×C11—42no—
47C22×Q8×C11D414yes—
48C22×Q8×C11C2311yescharacteristic
49C22×Q8×C11C2311yescharacteristic
50C22×D4×C11—21no—
51C22×D4×C11C2311yescharacteristic
52C23×C4×C11—21no—
53C23×C4×C11—21no—
54C23×C4×C11C2311yescharacteristic
55C2×C11×SD16—22no—
56C2×C11×SD16—22no—
57C2×C11×SD16—24no—
58C2×C11×SD16—42no—
59C22×C8×C11—22no—
60C22×C8×C11—42no—
61C22×C8×C11C2311yescharacteristic
62C22×C8×C11C2312yes—
63C22×C8×C11C2311yescharacteristic
64C11×#123—44no—
65C11×#123—44no—
66C11×#121—22no—
67C11×#121—22no—
68C4×Q8×C11—24no—
69C4×Q8×C11—42no—
70C2×C11×C4⋊C4—22no—
71C2×C11×C4⋊C4—22no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—22no—
74C2×C11×C4⋊C4—22no—
75C2×C11×C4⋊C4—22no—
76C2×C11×C4⋊C4C2312yes—
77C2×C11×C4⋊C4C2312yes—
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C11×C22⋊C4—21no—
80C2×C11×C22⋊C4—21no—
81C2×C11×C22⋊C4—22no—
82C2×C11×C22⋊C4—22no—
83C2×C11×C22⋊C4D411yescharacteristic
84C2×C11×C22⋊C4D411yescharacteristic
85C2×C42×C11—22no—
86C2×C42×C11C2312yes—
87C11×C4⋊C8—42no—
88C11×#103—24no—
89C11×#103—24no—
90C11×#103—22no—
91C11×#103—22no—
92C11×#102—42no—
93C11×C22⋊C8—22no—
94C11×#95—22no—
95C11×#95—22no—
96C11×#95—21no—
97C11×#95D412yes—
98#24528C1111yesmaximal, characteristic, direct product factor, Sylow
99C24×C11—21no—
100C24×C11C2×D411yescharacteristic
101C2×Q8×C11—24no—
102C2×Q8×C11—21no—
103C2×Q8×C11—21no—
104C2×Q8×C11—22no—
105C2×Q8×C11—28no—
106C2×Q8×C11—22no—
107C2×Q8×C11—22no—
108C2×Q8×C11—44no—
109C2×Q8×C11—44no—
110C2×Q8×C11—48no—
111C2×Q8×C11C2×D412yes—
112C2×Q8×C11C2×D412yes—
113C2×Q8×C11#4114yes—
114C2×D4×C11—21no—
115C2×D4×C11—21no—
116C2×D4×C11—22no—
117C2×D4×C11—22no—
118C2×D4×C11—42no—
119C2×D4×C11—42no—
120C2×D4×C11—42no—
121C22×C4×C11—21no—
122C22×C4×C11—22no—
123C22×C4×C11—22no—
124C22×C4×C11—24no—
125C22×C4×C11—21no—
126C22×C4×C11—22no—
127C22×C4×C11—22no—
128C22×C4×C11—21no—
129C22×C4×C11—44no—
130C22×C4×C11—42no—
131C22×C4×C11—42no—
132C22×C4×C11—42no—
133C22×C4×C11C2×D412yes—
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2×D412yes—
136C22×C4×C11C2×D412yes—
137C22×C4×C11#4112yes—
138C22×C4×C11C2411yescharacteristic
139C11×SD16—44no—
140C11×SD16—44no—
141C2×C8×C11—21no—
142C2×C8×C11—21no—
143C2×C8×C11—22no—
144C2×C8×C11—22no—
145C2×C8×C11—22no—
146C2×C8×C11—22no—
147C2×C8×C11—22no—
148C2×C8×C11—44no—
149C11×C4⋊C4—22no—
150C11×C4⋊C4—21no—
151C11×C4⋊C4—22no—
152C11×C4⋊C4—22no—
153C11×C4⋊C4—21no—
154C11×C4⋊C4—22no—
155C11×C4⋊C4—44no—
156C11×C4⋊C4—44no—
157C11×C4⋊C4—42no—
158C11×C4⋊C4—44no—
159C11×C22⋊C4—22no—
160C11×C22⋊C4—44no—
161C11×C22⋊C4—42no—
162C11×C22⋊C4—42no—
163C11×C22⋊C4—44no—
164C11×C22⋊C4SD1614yescomplemented
165C42×C11—22no—
166C42×C11—22no—
167C42×C11—44no—
168C2×#448C2×C1111yescharacteristic
169C22×#103C2×C1111yescharacteristic, complemented
170#2501C2×C1111yescharacteristic
171Q8×C22⋊C4C2×C1111yescharacteristic, complemented
172#2072C2×C1112yescomplemented
173#2055C2×C1112yescomplemented
174#1893C2×C1111yescharacteristic
175#1880C2×C1112yescomplemented
176#1850C2×C1111yescharacteristic, complemented
177#1823C2×C1111yescharacteristic, complemented
178#1803C2×C1112yescomplemented
179C23×C11—22no—
180C23×C11—22no—
181C23×C11—41no—
182C23×C11—42no—
183C23×C11—41no—
184C23×C11—41no—
185C23×C11—42no—
186C23×C11#12112yes—
187C23×C11C2×SD1612yes—
188C23×C11AGL(1,ℤ/8)12yes—
189C23×C11C22×D411yescharacteristic
190Q8×C11—22no—
191Q8×C11—24no—
192Q8×C11—22no—
193Q8×C11—22no—
194Q8×C11—48no—
195Q8×C11—42no—
196Q8×C11#12314yescomplemented
197D4×C11—41no—
198D4×C11—41no—
199D4×C11—42no—
200D4×C11—84no—
201C2×C4×C11—22no—
202C2×C4×C11—22no—
203C2×C4×C11—24no—
204C2×C4×C11—22no—
205C2×C4×C11—22no—
206C2×C4×C11—22no—
207C2×C4×C11—22no—
208C2×C4×C11—24no—
209C2×C4×C11—22no—
210C2×C4×C11—22no—
211C2×C4×C11—22no—
212C2×C4×C11—22no—
213C2×C4×C11—48no—
214C2×C4×C11—42no—
215C2×C4×C11—41no—
216C2×C4×C11—42no—
217C2×C4×C11—42no—
218C2×C4×C11—42no—
219C2×C4×C11—41no—
220C2×C4×C11—42no—
221C2×C4×C11—42no—
222C2×C4×C11—41no—
223C2×C4×C11—42no—
224C2×C4×C11—84no—
225C2×C4×C11#12112yes—
226C2×C4×C11C2×SD1614yes—
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—
234C23×Q8C22×C1111yescharacteristic
235C22×SD16C22×C1111yescharacteristic
236C22×SD16C22×C1111yescharacteristic
237C23×C8C22×C1111yescharacteristic
238C2×#123—21no—
239C2×#123—21no—
240C2×#121C22×C1111yescharacteristic
241C2×C4×Q8C22×C1112yes—
242C22×C4⋊C4C22×C1111yescharacteristic
243#448—24no—
244C2×C4⋊C8C22×C1112yes—
245C2×#103—24no—
246C2×#103C22×C1112yes—
247C2×#103C22×C1111yescharacteristic
248C2×#103C22×C1112yes—
249C2×#103C22×C1111yescharacteristic
250C2×#102C22×C1112yes—
251C2×C22⋊C8C22×C1111yescharacteristic
252#399—22no—
253#391—22no—
254#391C22×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—24no—
267C22×C11—22no—
268C22×C11—24no—
269C22×C11—81no—
270C22×C11—81no—
271C22×C11—82no—
272C22×C11—81no—
273C22×C11—82no—
274C22×C11#46014yes—
275C22×C11C2×#12111yescharacteristic
276C22×C11#54612yes—
277C22×C11C22×SD1611yescharacteristic
278C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
279C22×C11#57812yes—
280C4×C11—22no—
281C4×C11—24no—
282C4×C11—24no—
283C4×C11—42no—
284C4×C11—42no—
285C4×C11—82no—
286C4×C11—81no—
287C4×C11—82no—
288C4×C11C2×#12311yescharacteristic
289C4×C11#53411yescharacteristic
290C4×C11#55112yes—
291C22×Q8—21no—
292C22×Q8—22no—
293C22×Q8—24no—
294C22×Q8—42no—
295C22×Q8D4×C1114yes—
296C22×Q8C23×C1111yescharacteristic
297C22×Q8C23×C1111yescharacteristic
298C22×D4—21no—
299C22×D4C23×C1111yescharacteristic
300C23×C4—21no—
301C23×C4—21no—
302C23×C4C23×C1111yescharacteristic
303C2×SD16—22no—
304C2×SD16—22no—
305C2×SD16—24no—
306C2×SD16—42no—
307C22×C8—22no—
308C22×C8—42no—
309C22×C8C23×C1112yes—
310C22×C8C23×C1111yescharacteristic
311C22×C8C23×C1111yescharacteristic
312#123—44no—
313#123—44no—
314#121—22no—
315#121—22no—
316C4×Q8—24no—
317C4×Q8—42no—
318C2×C4⋊C4—22no—
319C2×C4⋊C4—22no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—22no—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—22no—
324C2×C4⋊C4C23×C1112yes—
325C2×C4⋊C4C23×C1112yes—
326C2×C4⋊C4C23×C1111yescharacteristic
327C2×C22⋊C4—21no—
328C2×C22⋊C4—21no—
329C2×C22⋊C4—22no—
330C2×C22⋊C4—22no—
331C2×C22⋊C4D4×C1111yescharacteristic
332C2×C22⋊C4D4×C1111yescharacteristic
333C2×C42—22no—
334C2×C42C23×C1112yes—
335C4⋊C8—42no—
336#103—24no—
337#103—24no—
338#103—22no—
339#103—22no—
340#102—42no—
341C22⋊C8—22no—
342#95—22no—
343#95—22no—
344#95—21no—
345#95D4×C1112yes—
346C2×C11—24no—
347C2×C11—161no—
348C2×C11#241211yescharacteristic
349C2×C11C2×#46011yescharacteristic
350C2×C11#304411yescharacteristic
351C2×C11#329812yes—
352C2×C11#330812yes—
353C24—21no—
354C24C2×D4×C1111yescharacteristic
355C2×Q8—24no—
356C2×Q8—21no—
357C2×Q8—21no—
358C2×Q8—22no—
359C2×Q8—28no—
360C2×Q8—22no—
361C2×Q8—22no—
362C2×Q8—44no—
363C2×Q8—44no—
364C2×Q8—48no—
365C2×Q8C2×D4×C1112yes—
366C2×Q8C2×D4×C1112yes—
367C2×Q8C11×#4114yes—
368C2×D4—21no—
369C2×D4—21no—
370C2×D4—22no—
371C2×D4—22no—
372C2×D4—42no—
373C2×D4—42no—
374C2×D4—42no—
375C22×C4—21no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—24no—
379C22×C4—21no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—21no—
383C22×C4—44no—
384C22×C4—42no—
385C22×C4—42no—
386C22×C4—42no—
387C22×C4C2×D4×C1112yes—
388C22×C4C2×D4×C1111yescharacteristic
389C22×C4C2×D4×C1112yes—
390C22×C4C2×D4×C1112yes—
391C22×C4C11×#4112yes—
392C22×C4C24×C1111yescharacteristic
393SD16—44no—
394SD16—44no—
395C2×C8—21no—
396C2×C8—21no—
397C2×C8—22no—
398C2×C8—22no—
399C2×C8—22no—
400C2×C8—22no—
401C2×C8—22no—
402C2×C8—44no—
403C4⋊C4—22no—
404C4⋊C4—21no—
405C4⋊C4—22no—
406C4⋊C4—22no—
407C4⋊C4—21no—
408C4⋊C4—22no—
409C4⋊C4—44no—
410C4⋊C4—44no—
411C4⋊C4—42no—
412C4⋊C4—44no—
413C22⋊C4—22no—
414C22⋊C4—44no—
415C22⋊C4—42no—
416C22⋊C4—42no—
417C22⋊C4—44no—
418C22⋊C4C11×SD1614yescomplemented
419C42—22no—
420C42—22no—
421C42—44no—
422C11#2452811yescharacteristic, direct product factor, Sylow
423C23—22no—
424C23—22no—
425C23—41no—
426C23—42no—
427C23—41no—
428C23—41no—
429C23—42no—
430C23C11×#12112yes—
431C23C2×C11×SD1612yes—
432C23C11×AGL(1,ℤ/8)12yes—
433C23C22×D4×C1111yescharacteristic
434Q8—22no—
435Q8—24no—
436Q8—22no—
437Q8—22no—
438Q8—48no—
439Q8—42no—
440Q8C11×#12314yescomplemented
441D4—41no—
442D4—41no—
443D4—42no—
444D4—84no—
445C2×C4—22no—
446C2×C4—22no—
447C2×C4—24no—
448C2×C4—22no—
449C2×C4—22no—
450C2×C4—22no—
451C2×C4—22no—
452C2×C4—24no—
453C2×C4—22no—
454C2×C4—22no—
455C2×C4—22no—
456C2×C4—22no—
457C2×C4—48no—
458C2×C4—42no—
459C2×C4—41no—
460C2×C4—42no—
461C2×C4—42no—
462C2×C4—42no—
463C2×C4—41no—
464C2×C4—42no—
465C2×C4—42no—
466C2×C4—41no—
467C2×C4—42no—
468C2×C4—84no—
469C2×C4C11×#12112yes—
470C2×C4C2×C11×SD1614yes—
471C2×C4C22×D4×C1111yescharacteristic
472C2×C4C2×C11×#4112yes—
473C2×C4C2×C11×#4111yescharacteristic
474C2×C4C11×H(5,𝔽2)12yes—
475C8—41no—
476C8—42no—
477C8—41no—
478C22—22no—
479C22—24no—
480C22—22no—
481C22—24no—
482C22—81no—
483C22—81no—
484C22—82no—
485C22—81no—
486C22—82no—
487C22C11×#46014yes—
488C22C2×C11×#12111yescharacteristic
489C22C11×#54612yes—
490C22C22×C11×SD1611yescharacteristic
491C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
492C22C11×#57812yes—
493C4—22no—
494C4—24no—
495C4—24no—
496C4—42no—
497C4—42no—
498C4—82no—
499C4—81no—
500C4—82no—
501C4C2×C11×#12311yescharacteristic
502C4C11×#53411yescharacteristic
503C4C11×#55112yes—
504C2—24no—
505C2—161no—
506C2C11×#241211yescharacteristic
507C2C2×C11×#46011yescharacteristic
508C2C11×#304411yescharacteristic
509C2C11×#329812yes—
510C2C11×#330812yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#121C22
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. C22×C11×#103C2semidirect
4. Q8×C11×C22⋊C4C2semidirect
5. C11×#2072C2semidirect
6. C11×#2055C2semidirect
8. C11×#1880C2semidirect
9. C11×#1850C2semidirect
10. C11×#1823C2semidirect
11. C11×#1803C2semidirect
98. #24528C11direct (N × H)
164. C11×C22⋊C4SD16semidirect
169. C22×#103C2×C11semidirect
171. Q8×C22⋊C4C2×C11semidirect
172. #2072C2×C11semidirect
173. #2055C2×C11semidirect
175. #1880C2×C11semidirect
176. #1850C2×C11semidirect
177. #1823C2×C11semidirect
178. #1803C2×C11semidirect
196. Q8×C11#123semidirect
418. C22⋊C4C11×SD16semidirect
422. C11#24528direct (N × H)
440. Q8C11×#123semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#4482
C22×C11×#1032
C11×#25012
Q8×C11×C22⋊C42
C11×#20722
C11×#20552
C11×#18932
C11×#18802
C11×#18502
C11×#18232
C11×#18032
#2452811