Finite Group Databasebeta

← C11×#24360 #14601553

Subgroups — C11×#24360 #14601553

Order 2816.

1382 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C11×Q16C211yesmaximal, characteristic
2C2×C11×#462C212yesmaximal, complemented
3C2×C11×#451C211yesmaximal, characteristic
4C11×#2434C211yesmaximal, characteristic
5Q8×C11×C22⋊C4C211yesmaximal, characteristic
6C11×#2056C212yesmaximal, complemented
7C11×#2016C212yesmaximal, complemented
8C11×#1892C211yesmaximal, characteristic
9C11×#1878C212yesmaximal, complemented
10C11×#1850C211yesmaximal, characteristic
11C11×#1787C211yesmaximal, characteristic
12C23×Q8×C11C2211yescharacteristic
13C23×Q8×C11C2211yescharacteristic
14C22×C11×Q16—24no—
15C22×C11×Q16—28no—
16C22×C11×Q16C2211yescharacteristic
17C22×C11×Q16C2212yes—
18C22×C11×Q16C2212yes—
19C22×C11×Q16C2211yescharacteristic
20C23×C8×C11C2211yescharacteristic
21C2×C11×C4⋊Q8C2212yes—
22C2×C11×C22⋊Q8C2211yescharacteristic
23C2×C4×Q8×C11C2212yes—
24C11×#462—28no—
25C11×#451—24no—
26C2×C11×C4⋊C8C2212yes—
27C2×C11×#103C2211yescharacteristic
28C2×C11×#103C2212yes—
29C2×C11×#103C2211yescharacteristic
30C2×C11×#103C2212yes—
31C2×C11×#103C2212yes—
32C2×C11×C22⋊C8C2211yescharacteristic
33C11×#395—22no—
34C11×#391—22no—
35C11×#391C2212yes—
36C11×#391C2212yes—
37C11×#385—21no—
38C11×#385—21no—
39C11×#380—21no—
40C11×#380C2211yescharacteristic
41C4×C11×C22⋊C4—21no—
42C4×C11×C22⋊C4C2211yescharacteristic
43C11×#340C2212yes—
44C11×#336C2212yes—
45C22×Q8×C11—21no—
46C22×Q8×C11—21no—
47C22×Q8×C11—22no—
48C22×Q8×C11—24no—
49C22×Q8×C11—24no—
50C22×Q8×C11—22no—
51C22×Q8×C11—22no—
52C22×Q8×C11—42no—
53C22×Q8×C11—42no—
54C22×Q8×C11D414yes—
55C22×Q8×C11C2311yescharacteristic
56C22×Q8×C11C2311yescharacteristic
57C22×Q8×C11C2312yes—
58C22×Q8×C11C2311yescharacteristic
59C23×C4×C11—21no—
60C23×C4×C11—21no—
61C23×C4×C11C2311yescharacteristic
62C2×C11×Q16—232no—
63C2×C11×Q16—24no—
64C2×C11×Q16—24no—
65C2×C11×Q16—24no—
66C2×C11×Q16—24no—
67C2×C11×Q16—22no—
68C2×C11×Q16—22no—
69C2×C11×Q16—24no—
70C2×C11×Q16—24no—
71C2×C11×Q16—42no—
72C2×C11×Q16D418yes—
73C22×C8×C11—22no—
74C22×C8×C11—24no—
75C22×C8×C11C2311yescharacteristic
76C22×C8×C11C2311yescharacteristic
77C22×C8×C11C2312yes—
78C11×C4⋊Q8—24no—
79C11×C4⋊Q8—42no—
80C11×C22⋊Q8—22no—
81C11×C22⋊Q8—22no—
82C4×Q8×C11—24no—
83C4×Q8×C11—42no—
84C2×C11×C4⋊C4—22no—
85C2×C11×C4⋊C4—22no—
86C2×C11×C4⋊C4—22no—
87C2×C11×C4⋊C4—21no—
88C2×C11×C4⋊C4C2311yescharacteristic
89C2×C11×C4⋊C4C2312yes—
90C2×C11×C22⋊C4—21no—
91C2×C11×C22⋊C4—21no—
92C2×C11×C22⋊C4D411yescharacteristic
93C2×C11×C22⋊C4D411yescharacteristic
94C2×C42×C11—22no—
95C2×C42×C11C2312yes—
96C11×C4⋊C8—24no—
97C11×#103—22no—
98C11×#103—22no—
99C11×#103—24no—
100C11×#103—24no—
101C11×#103—42no—
102C11×C22⋊C8—22no—
103C11×#95—22no—
104C11×#95—22no—
105C11×#95—21no—
106C11×#95—22no—
107C11×#95—22no—
108C11×#95D412yes—
109#24360C1111yesmaximal, characteristic, direct product factor, Sylow
110C24×C11C2×D411yescharacteristic
111C2×Q8×C11—24no—
112C2×Q8×C11—21no—
113C2×Q8×C11—21no—
114C2×Q8×C11—22no—
115C2×Q8×C11—22no—
116C2×Q8×C11—28no—
117C2×Q8×C11—28no—
118C2×Q8×C11—22no—
119C2×Q8×C11—22no—
120C2×Q8×C11—22no—
121C2×Q8×C11—22no—
122C2×Q8×C11—21no—
123C2×Q8×C11—22no—
124C2×Q8×C11—21no—
125C2×Q8×C11—22no—
126C2×Q8×C11—22no—
127C2×Q8×C11—22no—
128C2×Q8×C11—44no—
129C2×Q8×C11—44no—
130C2×Q8×C11—44no—
131C2×Q8×C11—48no—
132C2×Q8×C11—48no—
133C2×Q8×C11—44no—
134C2×Q8×C11—42no—
135C2×Q8×C11C2×D414yes—
136C2×Q8×C11C2×D412yes—
137C2×Q8×C11C2×D412yes—
138C2×Q8×C11C2×D414yes—
139C22×C4×C11—21no—
140C22×C4×C11—22no—
141C22×C4×C11—22no—
142C22×C4×C11—24no—
143C22×C4×C11—21no—
144C22×C4×C11—22no—
145C22×C4×C11—21no—
146C22×C4×C11—22no—
147C22×C4×C11—21no—
148C22×C4×C11—44no—
149C22×C4×C11—44no—
150C22×C4×C11—42no—
151C22×C4×C11C2×D412yes—
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D412yes—
154C22×C4×C11C2×D412yes—
155C22×C4×C11#4112yes—
156C22×C4×C11C2411yescharacteristic
157C11×Q16—216no—
158C11×Q16—216no—
159C11×Q16—44no—
160C11×Q16—44no—
161C2×C8×C11—28no—
162C2×C8×C11—22no—
163C2×C8×C11—22no—
164C2×C8×C11—21no—
165C2×C8×C11—21no—
166C2×C8×C11—22no—
167C2×C8×C11—22no—
168C2×C8×C11C2×D414yes—
169C11×C4⋊C4—22no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—22no—
173C11×C4⋊C4—44no—
174C11×C4⋊C4—44no—
175C11×C4⋊C4—44no—
176C11×C4⋊C4—42no—
177C11×C22⋊C4—22no—
178C11×C22⋊C4—42no—
179C11×C22⋊C4—42no—
180C11×C22⋊C4Q1614yescomplemented
181C42×C11—22no—
182C42×C11—22no—
183C42×C11—44no—
184C23×Q16C2×C1111yescharacteristic
185C2×#462C2×C1112yescomplemented
186C2×#451C2×C1111yescharacteristic
187#2434C2×C1111yescharacteristic
188Q8×C22⋊C4C2×C1111yescharacteristic
189#2056C2×C1112yescomplemented
190#2016C2×C1112yescomplemented
191#1892C2×C1111yescharacteristic
192#1878C2×C1112yescomplemented
193#1850C2×C1111yescharacteristic
194#1787C2×C1111yescharacteristic
195C23×C11—22no—
196C23×C11—22no—
197C23×C11#12112yes—
198C23×C11C2×Q1612yes—
199C23×C11#13712yes—
200C23×C11C22×D411yescharacteristic
201Q8×C11—22no—
202Q8×C11—24no—
203Q8×C11—22no—
204Q8×C11—24no—
205Q8×C11—22no—
206Q8×C11—24no—
207Q8×C11—48no—
208Q8×C11—48no—
209Q8×C11—42no—
210Q8×C11—42no—
211Q8×C11—42no—
212Q8×C11—41no—
213Q8×C11—41no—
214Q8×C11—42no—
215Q8×C11#12014yes—
216C2×C4×C11—22no—
217C2×C4×C11—22no—
218C2×C4×C11—24no—
219C2×C4×C11—22no—
220C2×C4×C11—22no—
221C2×C4×C11—22no—
222C2×C4×C11—22no—
223C2×C4×C11—24no—
224C2×C4×C11—22no—
225C2×C4×C11—22no—
226C2×C4×C11—24no—
227C2×C4×C11—22no—
228C2×C4×C11—22no—
229C2×C4×C11—48no—
230C2×C4×C11—48no—
231C2×C4×C11—42no—
232C2×C4×C11—42no—
233C2×C4×C11—42no—
234C2×C4×C11—41no—
235C2×C4×C11—41no—
236C2×C4×C11—42no—
237C2×C4×C11—42no—
238C2×C4×C11—42no—
239C2×C4×C11—42no—
240C2×C4×C11—42no—
241C2×C4×C11#12112yes—
242C2×C4×C11C2×Q1614yescomplemented
243C2×C4×C11C22×D411yescharacteristic
244C2×C4×C11C22×D412yes—
245C2×C4×C11C2×#4111yescharacteristic
246C2×C4×C11H(5,𝔽2)12yes—
247C8×C11—24no—
248C8×C11—41no—
249C8×C11—41no—
250C23×Q8C22×C1111yescharacteristic
251C23×Q8C22×C1111yescharacteristic
252C22×Q16—24no—
253C22×Q16—28no—
254C22×Q16C22×C1112yes—
255C22×Q16C22×C1111yescharacteristic
256C22×Q16C22×C1112yes—
257C22×Q16C22×C1111yescharacteristic
258C23×C8C22×C1111yescharacteristic
259C2×C4⋊Q8C22×C1112yes—
260C2×C22⋊Q8C22×C1111yescharacteristic
261C2×C4×Q8C22×C1112yes—
262#462—28no—
263#451—24no—
264C2×C4⋊C8C22×C1112yes—
265C2×#103C22×C1111yescharacteristic
266C2×#103C22×C1112yes—
267C2×#103C22×C1111yescharacteristic
268C2×#103C22×C1112yes—
269C2×#103C22×C1112yes—
270C2×C22⋊C8C22×C1111yescharacteristic
271#395—22no—
272#391—22no—
273#391C22×C1112yes—
274#391C22×C1112yes—
275#385—21no—
276#385—21no—
277#380—21no—
278#380C22×C1111yescharacteristic
279C4×C22⋊C4—21no—
280C4×C22⋊C4C22×C1111yescharacteristic
281#340C22×C1112yes—
282#336C22×C1112yes—
283C22×C11—22no—
284C22×C11—24no—
285C22×C11—24no—
286C22×C11—22no—
287C22×C11#46214yescomplemented
288C22×C11C2×#12111yescharacteristic
289C22×C11D4212yes—
290C22×C11C22×Q1611yescharacteristic
291C22×C11C2×#13711yescharacteristic
292C22×C11#57812yes—
293C4×C11—22no—
294C4×C11—24no—
295C4×C11—24no—
296C4×C11—42no—
297C4×C11—44no—
298C4×C11—42no—
299C4×C11—81no—
300C4×C11—82no—
301C4×C11—81no—
302C4×C11C2×#12011yescharacteristic
303C4×C11#53411yescharacteristic
304C4×C11#54612yes—
305C22×Q8—21no—
306C22×Q8—21no—
307C22×Q8—22no—
308C22×Q8—24no—
309C22×Q8—24no—
310C22×Q8—22no—
311C22×Q8—22no—
312C22×Q8—42no—
313C22×Q8—42no—
314C22×Q8D4×C1114yes—
315C22×Q8C23×C1111yescharacteristic
316C22×Q8C23×C1112yes—
317C22×Q8C23×C1111yescharacteristic
318C22×Q8C23×C1111yescharacteristic
319C23×C4—21no—
320C23×C4—21no—
321C23×C4C23×C1111yescharacteristic
322C2×Q16—232no—
323C2×Q16—24no—
324C2×Q16—24no—
325C2×Q16—24no—
326C2×Q16—24no—
327C2×Q16—22no—
328C2×Q16—22no—
329C2×Q16—24no—
330C2×Q16—24no—
331C2×Q16—42no—
332C2×Q16D4×C1118yes—
333C22×C8—22no—
334C22×C8—24no—
335C22×C8C23×C1111yescharacteristic
336C22×C8C23×C1111yescharacteristic
337C22×C8C23×C1112yes—
338C4⋊Q8—24no—
339C4⋊Q8—42no—
340C22⋊Q8—22no—
341C22⋊Q8—22no—
342C4×Q8—24no—
343C4×Q8—42no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4C23×C1112yes—
349C2×C4⋊C4C23×C1111yescharacteristic
350C2×C22⋊C4—21no—
351C2×C22⋊C4—21no—
352C2×C22⋊C4D4×C1111yescharacteristic
353C2×C22⋊C4D4×C1111yescharacteristic
354C2×C42—22no—
355C2×C42C23×C1112yes—
356C4⋊C8—24no—
357#103—22no—
358#103—22no—
359#103—24no—
360#103—24no—
361#103—42no—
362C22⋊C8—22no—
363#95—22no—
364#95—22no—
365#95—21no—
366#95—22no—
367#95—22no—
368#95D4×C1112yes—
369C2×C11—24no—
370C2×C11#241011yescharacteristic
371C2×C11C2×#46211yescharacteristic
372C2×C11#304411yescharacteristic
373C2×C11#327012yes—
374C2×C11D4×Q1612yes—
375C24C2×D4×C1111yescharacteristic
376C2×Q8—24no—
377C2×Q8—21no—
378C2×Q8—21no—
379C2×Q8—22no—
380C2×Q8—22no—
381C2×Q8—28no—
382C2×Q8—28no—
383C2×Q8—22no—
384C2×Q8—22no—
385C2×Q8—22no—
386C2×Q8—22no—
387C2×Q8—21no—
388C2×Q8—22no—
389C2×Q8—21no—
390C2×Q8—22no—
391C2×Q8—22no—
392C2×Q8—22no—
393C2×Q8—44no—
394C2×Q8—44no—
395C2×Q8—44no—
396C2×Q8—48no—
397C2×Q8—48no—
398C2×Q8—44no—
399C2×Q8—42no—
400C2×Q8C2×D4×C1114yes—
401C2×Q8C2×D4×C1112yes—
402C2×Q8C2×D4×C1112yes—
403C2×Q8C2×D4×C1114yes—
404C22×C4—21no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—24no—
408C22×C4—21no—
409C22×C4—22no—
410C22×C4—21no—
411C22×C4—22no—
412C22×C4—21no—
413C22×C4—44no—
414C22×C4—44no—
415C22×C4—42no—
416C22×C4C2×D4×C1112yes—
417C22×C4C2×D4×C1111yescharacteristic
418C22×C4C2×D4×C1112yes—
419C22×C4C2×D4×C1112yes—
420C22×C4C11×#4112yes—
421C22×C4C24×C1111yescharacteristic
422Q16—216no—
423Q16—216no—
424Q16—44no—
425Q16—44no—
426C2×C8—28no—
427C2×C8—22no—
428C2×C8—22no—
429C2×C8—21no—
430C2×C8—21no—
431C2×C8—22no—
432C2×C8—22no—
433C2×C8C2×D4×C1114yes—
434C4⋊C4—22no—
435C4⋊C4—21no—
436C4⋊C4—21no—
437C4⋊C4—22no—
438C4⋊C4—44no—
439C4⋊C4—44no—
440C4⋊C4—44no—
441C4⋊C4—42no—
442C22⋊C4—22no—
443C22⋊C4—42no—
444C22⋊C4—42no—
445C22⋊C4C11×Q1614yescomplemented
446C42—22no—
447C42—22no—
448C42—44no—
449C11#2436011yescharacteristic, direct product factor, Sylow
450C23—22no—
451C23—22no—
452C23C11×#12112yes—
453C23C2×C11×Q1612yes—
454C23C11×#13712yes—
455C23C22×D4×C1111yescharacteristic
456Q8—22no—
457Q8—24no—
458Q8—22no—
459Q8—24no—
460Q8—22no—
461Q8—24no—
462Q8—48no—
463Q8—48no—
464Q8—42no—
465Q8—42no—
466Q8—42no—
467Q8—41no—
468Q8—41no—
469Q8—42no—
470Q8C11×#12014yes—
471C2×C4—22no—
472C2×C4—22no—
473C2×C4—24no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—22no—
477C2×C4—22no—
478C2×C4—24no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—24no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—48no—
485C2×C4—48no—
486C2×C4—42no—
487C2×C4—42no—
488C2×C4—42no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4C11×#12112yes—
497C2×C4C2×C11×Q1614yescomplemented
498C2×C4C22×D4×C1111yescharacteristic
499C2×C4C22×D4×C1112yes—
500C2×C4C2×C11×#4111yescharacteristic
501C2×C4C11×H(5,𝔽2)12yes—
502C8—24no—
503C8—41no—
504C8—41no—
505C22—22no—
506C22—24no—
507C22—24no—
508C22—22no—
509C22C11×#46214yescomplemented
510C22C2×C11×#12111yescharacteristic
511C22D42×C1112yes—
512C22C22×C11×Q1611yescharacteristic
513C22C2×C11×#13711yescharacteristic
514C22C11×#57812yes—
515C4—22no—
516C4—24no—
517C4—24no—
518C4—42no—
519C4—44no—
520C4—42no—
521C4—81no—
522C4—82no—
523C4—81no—
524C4C2×C11×#12011yescharacteristic
525C4C11×#53411yescharacteristic
526C4C11×#54612yes—
527C2—24no—
528C2C11×#241011yescharacteristic
529C2C2×C11×#46211yescharacteristic
530C2C11×#304411yescharacteristic
531C2C11×#327012yes—
532C2D4×C11×Q1612yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC24×C11C2×D4
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×#462C2semidirect
6. C11×#2056C2semidirect
7. C11×#2016C2semidirect
9. C11×#1878C2semidirect
109. #24360C11direct (N × H)
180. C11×C22⋊C4Q16semidirect
185. C2×#462C2×C11semidirect
189. #2056C2×C11semidirect
190. #2016C2×C11semidirect
192. #1878C2×C11semidirect
242. C2×C4×C11C2×Q16semidirect
287. C22×C11#462semidirect
445. C22⋊C4C11×Q16semidirect
449. C11#24360direct (N × H)
497. C2×C4C2×C11×Q16semidirect
509. C22C11×#462semidirect

Maximal subgroups

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

subgroupindex
C23×C11×Q162
C2×C11×#4622
C2×C11×#4512
C11×#24342
Q8×C11×C22⋊C42
C11×#20562
C11×#20162
C11×#18922
C11×#18782
C11×#18502
C11×#17872
#2436011