Finite Group Databasebeta

← C11×#32903 #14610096

Subgroups — C11×#32903 #14610096

Order 2816.

1576 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×Q8×C11C211yesmaximal, characteristic, complemented
2C2×C11×#460C212yesmaximal, complemented
3C2×C11×#448C212yesmaximal, complemented
4C11×#2856C211yesmaximal, characteristic
5C11×#1880C214yesmaximal, complemented
6C11×#1874C212yesmaximal, complemented
7C11×#1803C212yesmaximal, complemented
8C11×#1797C211yesmaximal, characteristic, complemented
9C23×Q8×C11C2211yescharacteristic
10C22×C11×SD16C2214yes—
11C2×C11×#127C2211yescharacteristic
12C2×C11×#121—21no—
13C2×C11×#121—21no—
14C2×C11×#121C2212yes—
15C2×C4×Q8×C11—28no—
16C2×C4×Q8×C11—21no—
17C2×C4×Q8×C11—21no—
18C2×C4×Q8×C11C2212yes—
19C2×C4×Q8×C11C2212yes—
20C22×C11×C4⋊C4—21no—
21C22×C11×C4⋊C4C2211yescharacteristic
22C22×C42×C11—21no—
23C22×C42×C11C2211yescharacteristic
24C11×#460—28no—
25C11×#448—28no—
26C2×C11×C4⋊C8C2212yes—
27C2×C11×#103C2214yes—
28C2×C11×#102C2214yes—
29C2×C11×C22⋊C8C2212yes—
30C11×#390—21no—
31C11×#390—21no—
32C11×#390C2212yes—
33C11×#384C2211yescharacteristic
34C11×#340C2214yes—
35C11×#336C2212yes—
36C22×Q8×C11—24no—
37C22×Q8×C11—24no—
38C22×Q8×C11—21no—
39C22×Q8×C11—22no—
40C22×Q8×C11D414yescomplemented
41C22×Q8×C11C2312yes—
42C22×D4×C11—22no—
43C22×D4×C11—21no—
44C22×D4×C11—21no—
45C22×D4×C11C2312yes—
46C23×C4×C11—21no—
47C23×C4×C11—21no—
48C23×C4×C11D411yescharacteristic
49C23×C4×C11D411yescharacteristic
50C23×C4×C11C2311yescharacteristic
51C2×C11×SD16—28no—
52C2×C11×SD16—28no—
53C2×C11×SD16—28no—
54C22×C8×C11C2314yes—
55C11×#127—24no—
56C11×#121—24no—
57C11×#121—24no—
58C11×#121—44no—
59C11×#121—44no—
60C4×Q8×C11—28no—
61C4×Q8×C11—28no—
62C4×Q8×C11—24no—
63C4×Q8×C11—24no—
64C4×Q8×C11—24no—
65C4×Q8×C11D418yescomplemented
66C2×C11×C4⋊C4—28no—
67C2×C11×C4⋊C4—22no—
68C2×C11×C4⋊C4—22no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4—24no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4C2312yes—
74C2×C11×C4⋊C4C2312yes—
75C2×C11×C22⋊C4—22no—
76C2×C11×C22⋊C4—22no—
77C2×C11×C22⋊C4—22no—
78C2×C42×C11—28no—
79C2×C42×C11—22no—
80C2×C42×C11—22no—
81C2×C42×C11—24no—
82C2×C42×C11D411yescharacteristic
83C2×C42×C11D411yescharacteristic
84C2×C42×C11C2311yescharacteristic
85C2×C42×C11C2311yescharacteristic
86C11×C4⋊C8—24no—
87C11×#103—28no—
88C11×#102—28no—
89C11×C22⋊C8—24no—
90#32903C1111yesmaximal, characteristic, direct product factor, Sylow
91C24×C11—22no—
92C24×C11C2×D411yescharacteristic
93C2×Q8×C11—24no—
94C2×Q8×C11—216no—
95C2×Q8×C11—24no—
96C2×Q8×C11—216no—
97C2×Q8×C11—24no—
98C2×Q8×C11—22no—
99C2×Q8×C11—22no—
100C2×Q8×C11—22no—
101C2×Q8×C11C2×D414yes—
102C2×Q8×C11C2×D414yes—
103C2×Q8×C11#4114yes—
104C2×D4×C11—24no—
105C2×D4×C11—22no—
106C2×D4×C11—22no—
107C2×D4×C11—24no—
108C2×D4×C11—42no—
109C2×D4×C11—42no—
110C2×D4×C11—44no—
111C2×D4×C11—44no—
112C2×D4×C11—44no—
113C2×D4×C11—42no—
114C2×D4×C11—42no—
115C2×D4×C11—42no—
116C2×D4×C11—42no—
117C22×C4×C11—24no—
118C22×C4×C11—24no—
119C22×C4×C11—24no—
120C22×C4×C11—22no—
121C22×C4×C11—22no—
122C22×C4×C11—22no—
123C22×C4×C11—22no—
124C22×C4×C11—22no—
125C22×C4×C11—24no—
126C22×C4×C11—22no—
127C22×C4×C11—22no—
128C22×C4×C11—22no—
129C22×C4×C11—22no—
130C22×C4×C11—41no—
131C22×C4×C11—42no—
132C22×C4×C11—42no—
133C22×C4×C11SD1614yescomplemented
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2×D412yes—
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11#4112yes—
141C22×C4×C11C2411yescharacteristic
142C11×SD16—416no—
143C2×C8×C11—24no—
144C2×C8×C11—24no—
145C2×C8×C11—24no—
146C11×C4⋊C4—28no—
147C11×C4⋊C4—24no—
148C11×C4⋊C4—28no—
149C11×C4⋊C4—22no—
150C11×C4⋊C4—22no—
151C11×C4⋊C4—22no—
152C11×C4⋊C4—42no—
153C11×C4⋊C4—42no—
154C11×C4⋊C4C2×D414yes—
155C11×C22⋊C4—44no—
156C11×C22⋊C4—44no—
157C11×C22⋊C4—44no—
158C42×C11—28no—
159C42×C11—28no—
160C42×C11—22no—
161C42×C11—22no—
162C42×C11—22no—
163C42×C11C2×D414yes—
164C22×C4×Q8C2×C1111yescharacteristic, complemented
165C2×#460C2×C1112yescomplemented
166C2×#448C2×C1112yescomplemented
167#2856C2×C1111yescharacteristic
168#1880C2×C1114yescomplemented
169#1874C2×C1112yescomplemented
170#1803C2×C1112yescomplemented
171#1797C2×C1111yescharacteristic, complemented
172C23×C11—21no—
173C23×C11—21no—
174C23×C11—21no—
175C23×C11—21no—
176C23×C11—42no—
177C23×C11—42no—
178C23×C11—42no—
179C23×C11—42no—
180C23×C11—42no—
181C23×C11—42no—
182C23×C11—42no—
183C23×C11#12112yes—
184C23×C11C2×SD1612yes—
185C23×C11AGL(1,ℤ/8)12yes—
186C23×C11C22×D411yescharacteristic
187Q8×C11—216no—
188Q8×C11—24no—
189Q8×C11—24no—
190Q8×C11—24no—
191Q8×C11#12118yescomplemented
192D4×C11—44no—
193D4×C11—44no—
194D4×C11—84no—
195D4×C11—88no—
196D4×C11—84no—
197C2×C4×C11—216no—
198C2×C4×C11—21no—
199C2×C4×C11—24no—
200C2×C4×C11—21no—
201C2×C4×C11—24no—
202C2×C4×C11—24no—
203C2×C4×C11—21no—
204C2×C4×C11—21no—
205C2×C4×C11—21no—
206C2×C4×C11—21no—
207C2×C4×C11—24no—
208C2×C4×C11—24no—
209C2×C4×C11—28no—
210C2×C4×C11—21no—
211C2×C4×C11—24no—
212C2×C4×C11—21no—
213C2×C4×C11—21no—
214C2×C4×C11—44no—
215C2×C4×C11—48no—
216C2×C4×C11—42no—
217C2×C4×C11—42no—
218C2×C4×C11—42no—
219C2×C4×C11—42no—
220C2×C4×C11—42no—
221C2×C4×C11#12012yes—
222C2×C4×C11#12012yes—
223C2×C4×C11#12112yes—
224C2×C4×C11C2×SD1612yes—
225C2×C4×C11C2×SD1612yes—
226C2×C4×C11#13712yes—
227C2×C4×C11C22×D411yescharacteristic
228C2×C4×C11C22×D412yes—
229C2×C4×C11C2×#4112yes—
230C2×C4×C11C2×#4111yescharacteristic
231C8×C11—44no—
232C23×Q8C22×C1111yescharacteristic
233C22×SD16C22×C1114yes—
234C2×#127C22×C1111yescharacteristic
235C2×#121—21no—
236C2×#121—21no—
237C2×#121C22×C1112yes—
238C2×C4×Q8—28no—
239C2×C4×Q8—21no—
240C2×C4×Q8—21no—
241C2×C4×Q8C22×C1112yes—
242C2×C4×Q8C22×C1112yes—
243C22×C4⋊C4—21no—
244C22×C4⋊C4C22×C1111yescharacteristic
245C22×C42—21no—
246C22×C42C22×C1111yescharacteristic
247#460—28no—
248#448—28no—
249C2×C4⋊C8C22×C1112yes—
250C2×#103C22×C1114yes—
251C2×#102C22×C1114yes—
252C2×C22⋊C8C22×C1112yes—
253#390—21no—
254#390—21no—
255#390C22×C1112yes—
256#384C22×C1111yescharacteristic
257#340C22×C1114yes—
258#336C22×C1112yes—
259C22×C11—22no—
260C22×C11—22no—
261C22×C11—22no—
262C22×C11—22no—
263C22×C11—22no—
264C22×C11—22no—
265C22×C11—82no—
266C22×C11—82no—
267C22×C11—82no—
268C22×C11—82no—
269C22×C11—82no—
270C22×C11—82no—
271C22×C11—82no—
272C22×C11#46014yescomplemented
273C22×C11C2×#12011yescharacteristic
274C22×C11C2×#12111yescharacteristic
275C22×C11#52511yescharacteristic
276C22×C11C22×SD1611yescharacteristic
277C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
278C22×C11C2×#13711yescharacteristic
279C22×C11#57511yescharacteristic
280C4×C11—28no—
281C4×C11—22no—
282C4×C11—22no—
283C4×C11—22no—
284C4×C11—41no—
285C4×C11—44no—
286C4×C11—82no—
287C4×C11#44814yescomplemented
288C4×C11C2×#12112yes—
289C4×C11#52512yes—
290C22×Q8—24no—
291C22×Q8—24no—
292C22×Q8—21no—
293C22×Q8—22no—
294C22×Q8D4×C1114yescomplemented
295C22×Q8C23×C1112yes—
296C22×D4—22no—
297C22×D4—21no—
298C22×D4—21no—
299C22×D4C23×C1112yes—
300C23×C4—21no—
301C23×C4—21no—
302C23×C4D4×C1111yescharacteristic
303C23×C4D4×C1111yescharacteristic
304C23×C4C23×C1111yescharacteristic
305C2×SD16—28no—
306C2×SD16—28no—
307C2×SD16—28no—
308C22×C8C23×C1114yes—
309#127—24no—
310#121—24no—
311#121—24no—
312#121—44no—
313#121—44no—
314C4×Q8—28no—
315C4×Q8—28no—
316C4×Q8—24no—
317C4×Q8—24no—
318C4×Q8—24no—
319C4×Q8D4×C1118yescomplemented
320C2×C4⋊C4—28no—
321C2×C4⋊C4—22no—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—21no—
324C2×C4⋊C4—24no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4C23×C1112yes—
328C2×C4⋊C4C23×C1112yes—
329C2×C22⋊C4—22no—
330C2×C22⋊C4—22no—
331C2×C22⋊C4—22no—
332C2×C42—28no—
333C2×C42—22no—
334C2×C42—22no—
335C2×C42—24no—
336C2×C42D4×C1111yescharacteristic
337C2×C42D4×C1111yescharacteristic
338C2×C42C23×C1111yescharacteristic
339C2×C42C23×C1111yescharacteristic
340C4⋊C8—24no—
341#103—28no—
342#102—28no—
343C22⋊C8—24no—
344C2×C11—24no—
345C2×C11—162no—
346C2×C11#284711yescharacteristic
347C2×C11C2×#44811yescharacteristic
348C2×C11#300611yescharacteristic
349C2×C11C2×#46011yescharacteristic
350C2×C11#303711yescharacteristic
351C2×C11#310311yescharacteristic
352C2×C11#311211yescharacteristic
353C24—22no—
354C24C2×D4×C1111yescharacteristic
355C2×Q8—24no—
356C2×Q8—216no—
357C2×Q8—24no—
358C2×Q8—216no—
359C2×Q8—24no—
360C2×Q8—22no—
361C2×Q8—22no—
362C2×Q8—22no—
363C2×Q8C2×D4×C1114yes—
364C2×Q8C2×D4×C1114yes—
365C2×Q8C11×#4114yes—
366C2×D4—24no—
367C2×D4—22no—
368C2×D4—22no—
369C2×D4—24no—
370C2×D4—42no—
371C2×D4—42no—
372C2×D4—44no—
373C2×D4—44no—
374C2×D4—44no—
375C2×D4—42no—
376C2×D4—42no—
377C2×D4—42no—
378C2×D4—42no—
379C22×C4—24no—
380C22×C4—24no—
381C22×C4—24no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—24no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—41no—
393C22×C4—42no—
394C22×C4—42no—
395C22×C4C11×SD1614yescomplemented
396C22×C4C2×D4×C1111yescharacteristic
397C22×C4C2×D4×C1111yescharacteristic
398C22×C4C2×D4×C1111yescharacteristic
399C22×C4C2×D4×C1112yes—
400C22×C4C2×D4×C1111yescharacteristic
401C22×C4C2×D4×C1111yescharacteristic
402C22×C4C11×#4112yes—
403C22×C4C24×C1111yescharacteristic
404SD16—416no—
405C2×C8—24no—
406C2×C8—24no—
407C2×C8—24no—
408C4⋊C4—28no—
409C4⋊C4—24no—
410C4⋊C4—28no—
411C4⋊C4—22no—
412C4⋊C4—22no—
413C4⋊C4—22no—
414C4⋊C4—42no—
415C4⋊C4—42no—
416C4⋊C4C2×D4×C1114yes—
417C22⋊C4—44no—
418C22⋊C4—44no—
419C22⋊C4—44no—
420C42—28no—
421C42—28no—
422C42—22no—
423C42—22no—
424C42—22no—
425C42C2×D4×C1114yes—
426C11#3290311yescharacteristic, direct product factor, Sylow
427C23—21no—
428C23—21no—
429C23—21no—
430C23—21no—
431C23—42no—
432C23—42no—
433C23—42no—
434C23—42no—
435C23—42no—
436C23—42no—
437C23—42no—
438C23C11×#12112yes—
439C23C2×C11×SD1612yes—
440C23C11×AGL(1,ℤ/8)12yes—
441C23C22×D4×C1111yescharacteristic
442Q8—216no—
443Q8—24no—
444Q8—24no—
445Q8—24no—
446Q8C11×#12118yescomplemented
447D4—44no—
448D4—44no—
449D4—84no—
450D4—88no—
451D4—84no—
452C2×C4—216no—
453C2×C4—21no—
454C2×C4—24no—
455C2×C4—21no—
456C2×C4—24no—
457C2×C4—24no—
458C2×C4—21no—
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—24no—
463C2×C4—24no—
464C2×C4—28no—
465C2×C4—21no—
466C2×C4—24no—
467C2×C4—21no—
468C2×C4—21no—
469C2×C4—44no—
470C2×C4—48no—
471C2×C4—42no—
472C2×C4—42no—
473C2×C4—42no—
474C2×C4—42no—
475C2×C4—42no—
476C2×C4C11×#12012yes—
477C2×C4C11×#12012yes—
478C2×C4C11×#12112yes—
479C2×C4C2×C11×SD1612yes—
480C2×C4C2×C11×SD1612yes—
481C2×C4C11×#13712yes—
482C2×C4C22×D4×C1111yescharacteristic
483C2×C4C22×D4×C1112yes—
484C2×C4C2×C11×#4112yes—
485C2×C4C2×C11×#4111yescharacteristic
486C8—44no—
487C22—22no—
488C22—22no—
489C22—22no—
490C22—22no—
491C22—22no—
492C22—22no—
493C22—82no—
494C22—82no—
495C22—82no—
496C22—82no—
497C22—82no—
498C22—82no—
499C22—82no—
500C22C11×#46014yescomplemented
501C22C2×C11×#12011yescharacteristic
502C22C2×C11×#12111yescharacteristic
503C22C11×#52511yescharacteristic
504C22C22×C11×SD1611yescharacteristic
505C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
506C22C2×C11×#13711yescharacteristic
507C22C11×#57511yescharacteristic
508C4—22no—
509C4—22no—
510C4—28no—
511C4—22no—
512C4—41no—
513C4—44no—
514C4—82no—
515C4C11×#44814yescomplemented
516C4C2×C11×#12112yes—
517C4C11×#52512yes—
518C2—24no—
519C2—162no—
520C2C11×#284711yescharacteristic
521C2C2×C11×#44811yescharacteristic
522C2C11×#300611yescharacteristic
523C2C2×C11×#46011yescharacteristic
524C2C11×#303711yescharacteristic
525C2C11×#310311yescharacteristic
526C2C11×#311211yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#2856C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C22×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C4×Q8×C11C2semidirect
2. C2×C11×#460C2semidirect
3. C2×C11×#448C2semidirect
5. C11×#1880C2semidirect
6. C11×#1874C2semidirect
7. C11×#1803C2semidirect
8. C11×#1797C2semidirect
40. C22×Q8×C11D4semidirect
65. C4×Q8×C11D4semidirect
90. #32903C11direct (N × H)
133. C22×C4×C11SD16semidirect
164. C22×C4×Q8C2×C11semidirect
165. C2×#460C2×C11semidirect
166. C2×#448C2×C11semidirect
168. #1880C2×C11semidirect
169. #1874C2×C11semidirect
170. #1803C2×C11semidirect
171. #1797C2×C11semidirect
191. Q8×C11#121semidirect
272. C22×C11#460semidirect
287. C4×C11#448semidirect
294. C22×Q8D4×C11semidirect
319. C4×Q8D4×C11semidirect
395. C22×C4C11×SD16semidirect
426. C11#32903direct (N × H)
446. Q8C11×#121semidirect
500. C22C11×#460semidirect
515. C4C11×#448semidirect

Maximal subgroups

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

subgroupindex
C22×C4×Q8×C112
C2×C11×#4602
C2×C11×#4482
C11×#28562
C11×#18802
C11×#18742
C11×#18032
C11×#17972
#3290311