Finite Group Databasebeta

← C11×#32960 #14610153

Subgroups — C11×#32960 #14610153

Order 2816.

1288 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×Q8×C11C211yesmaximal, characteristic
2C2×C11×#479C212yesmaximal, complemented
3C11×#2851C211yesmaximal, characteristic
4C11×#1865C212yesmaximal, complemented
5C11×#1863C212yesmaximal, complemented
6C11×#1853C211yesmaximal, characteristic
7C11×#1852C211yesmaximal, characteristic
8C11×#1805C212yesmaximal, complemented
9C11×#1797C211yesmaximal, characteristic
10C11×#1787C211yesmaximal, characteristic
11C11×#1787C211yesmaximal, characteristic
12C23×Q8×C11C2211yescharacteristic
13C2×C11×#125C2211yescharacteristic
14C2×C4×Q8×C11—28no—
15C2×C4×Q8×C11—21no—
16C2×C4×Q8×C11—21no—
17C2×C4×Q8×C11C2212yes—
18C2×C4×Q8×C11C2212yes—
19C22×C11×C4⋊C4—21no—
20C22×C11×C4⋊C4C2211yescharacteristic
21C22×C42×C11—21no—
22C22×C42×C11C2211yescharacteristic
23C11×#479—28no—
24C2×C11×#107C2212yes—
25C2×C11×#106C2212yes—
26C2×C11×C4⋊C8C2212yes—
27C2×C11×#103C2212yes—
28C2×C11×#103C2212yes—
29C2×C11×#103C2212yes—
30C2×C11×#103C2212yes—
31C2×C11×C22⋊C8C2211yescharacteristic
32C2×C11×C22⋊C8C2211yescharacteristic
33C11×#389C2211yescharacteristic
34C11×#389C2211yescharacteristic
35C11×#387—21no—
36C11×#387—21no—
37C11×#385—21no—
38C11×#385—21no—
39C11×#382C2211yescharacteristic
40C11×#380C2211yescharacteristic
41C11×#380C2211yescharacteristic
42C11×#340C2212yes—
43C11×#340C2212yes—
44C11×#336C2212yes—
45C22×Q8×C11—24no—
46C22×Q8×C11—24no—
47C22×Q8×C11—21no—
48C22×Q8×C11—22no—
49C22×Q8×C11Q814yes—
50C22×Q8×C11C2312yes—
51C23×C4×C11—21no—
52C23×C4×C11—21no—
53C23×C4×C11D411yescharacteristic
54C23×C4×C11D411yescharacteristic
55C23×C4×C11C2311yescharacteristic
56C22×C8×C11C2312yes—
57C22×C8×C11C2312yes—
58C11×#125—24no—
59C4×Q8×C11—28no—
60C4×Q8×C11—28no—
61C4×Q8×C11—24no—
62C4×Q8×C11—24no—
63C4×Q8×C11—24no—
64C4×Q8×C11D418yes—
65C2×C11×C4⋊C4—28no—
66C2×C11×C4⋊C4—22no—
67C2×C11×C4⋊C4—22no—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4—24no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C4⋊C4C2312yes—
79C2×C11×C22⋊C4—21no—
80C2×C11×C22⋊C4—21no—
81C2×C42×C11—28no—
82C2×C42×C11—22no—
83C2×C42×C11—22no—
84C2×C42×C11—24no—
85C2×C42×C11D411yescharacteristic
86C2×C42×C11D411yescharacteristic
87C2×C42×C11C2311yescharacteristic
88C2×C42×C11C2311yescharacteristic
89C11×#107—24no—
90C11×#106—24no—
91C11×C4⋊C8—24no—
92C11×#103—24no—
93C11×#103—24no—
94C11×#103—24no—
95C11×#103—24no—
96C11×C22⋊C8—22no—
97C11×C22⋊C8—22no—
98C11×#95—21no—
99C11×#95—21no—
100C11×#95—21no—
101C11×#95—21no—
102C11×#95—21no—
103C11×#95—21no—
104#32960C1111yesmaximal, characteristic, direct product factor, Sylow
105C24×C11C2×D411yescharacteristic
106C2×Q8×C11—24no—
107C2×Q8×C11—216no—
108C2×Q8×C11—24no—
109C2×Q8×C11—216no—
110C2×Q8×C11—24no—
111C2×Q8×C11—22no—
112C2×Q8×C11—22no—
113C2×Q8×C11—22no—
114C2×Q8×C11C2×D414yes—
115C2×Q8×C11C2×Q814yes—
116C2×Q8×C11#4114yes—
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—22no—
126C22×C4×C11—24no—
127C22×C4×C11—22no—
128C22×C4×C11—22no—
129C22×C4×C11—22no—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—41no—
135C22×C4×C11—42no—
136C22×C4×C11—42no—
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2×Q812yes—
143C22×C4×C11#4112yes—
144C22×C4×C11C2411yescharacteristic
145C2×C8×C11—22no—
146C2×C8×C11—22no—
147C2×C8×C11—22no—
148C2×C8×C11—22no—
149C2×C8×C11—22no—
150C2×C8×C11—22no—
151C11×C4⋊C4—28no—
152C11×C4⋊C4—24no—
153C11×C4⋊C4—28no—
154C11×C4⋊C4—22no—
155C11×C4⋊C4—22no—
156C11×C4⋊C4—22no—
157C11×C4⋊C4—22no—
158C11×C4⋊C4—22no—
159C11×C4⋊C4—42no—
160C11×C4⋊C4—42no—
161C11×C4⋊C4—42no—
162C11×C4⋊C4—42no—
163C11×C4⋊C4C2×D414yes—
164C11×C22⋊C4—42no—
165C11×C22⋊C4—42no—
166C42×C11—28no—
167C42×C11—28no—
168C42×C11—22no—
169C42×C11—22no—
170C42×C11—22no—
171C42×C11C2×D414yes—
172C22×C4×Q8C2×C1111yescharacteristic
173C2×#479C2×C1112yescomplemented
174#2851C2×C1111yescharacteristic
175#1865C2×C1112yescomplemented
176#1863C2×C1112yescomplemented
177#1853C2×C1111yescharacteristic
178#1852C2×C1111yescharacteristic
179#1805C2×C1112yescomplemented
180#1797C2×C1111yescharacteristic
181#1787C2×C1111yescharacteristic
182#1787C2×C1111yescharacteristic
183C23×C11—21no—
184C23×C11—21no—
185C23×C11—21no—
186C23×C11—21no—
187C23×C11C22⋊Q812yes—
188C23×C11#13512yes—
189C23×C11#13712yes—
190C23×C11C22×D411yescharacteristic
191Q8×C11—216no—
192Q8×C11—24no—
193Q8×C11—24no—
194Q8×C11—24no—
195Q8×C11C22⋊Q818yes—
196C2×C4×C11—28no—
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—21no—
208C2×C4×C11—21no—
209C2×C4×C11—24no—
210C2×C4×C11—24no—
211C2×C4×C11—21no—
212C2×C4×C11—24no—
213C2×C4×C11—21no—
214C2×C4×C11—21no—
215C2×C4×C11—44no—
216C2×C4×C11—48no—
217C2×C4×C11—42no—
218C2×C4×C11—42no—
219C2×C4×C11—41no—
220C2×C4×C11—41no—
221C2×C4×C11—41no—
222C2×C4×C11—41no—
223C2×C4×C11—41no—
224C2×C4×C11—41no—
225C2×C4×C11—41no—
226C2×C4×C11—41no—
227C2×C4×C11—41no—
228C2×C4×C11—41no—
229C2×C4×C11—41no—
230C2×C4×C11—41no—
231C2×C4×C11#12012yes—
232C2×C4×C11#12012yes—
233C2×C4×C11C22⋊Q812yes—
234C2×C4×C11#13712yes—
235C2×C4×C11C22×D412yes—
236C2×C4×C11C22×Q811yescharacteristic
237C2×C4×C11C2×#4112yes—
238C2×C4×C11C2×#4111yescharacteristic
239C8×C11—42no—
240C8×C11—42no—
241C23×Q8C22×C1111yescharacteristic
242C2×#125C22×C1111yescharacteristic
243C2×C4×Q8—28no—
244C2×C4×Q8—21no—
245C2×C4×Q8—21no—
246C2×C4×Q8C22×C1112yes—
247C2×C4×Q8C22×C1112yes—
248C22×C4⋊C4—21no—
249C22×C4⋊C4C22×C1111yescharacteristic
250C22×C42—21no—
251C22×C42C22×C1111yescharacteristic
252#479—28no—
253C2×#107C22×C1112yes—
254C2×#106C22×C1112yes—
255C2×C4⋊C8C22×C1112yes—
256C2×#103C22×C1112yes—
257C2×#103C22×C1112yes—
258C2×#103C22×C1112yes—
259C2×#103C22×C1112yes—
260C2×C22⋊C8C22×C1111yescharacteristic
261C2×C22⋊C8C22×C1111yescharacteristic
262#389C22×C1111yescharacteristic
263#389C22×C1111yescharacteristic
264#387—21no—
265#387—21no—
266#385—21no—
267#385—21no—
268#382C22×C1111yescharacteristic
269#380C22×C1111yescharacteristic
270#380C22×C1111yescharacteristic
271#340C22×C1112yes—
272#340C22×C1112yes—
273#336C22×C1112yes—
274C22×C11—22no—
275C22×C11—22no—
276C22×C11—22no—
277C22×C11—22no—
278C22×C11—22no—
279C22×C11—22no—
280C22×C11#47914yescomplemented
281C22×C11C2×#12011yescharacteristic
282C22×C11C2×C22⋊Q811yescharacteristic
283C22×C11#52511yescharacteristic
284C22×C11C2×#13511yescharacteristic
285C22×C11C2×#13711yescharacteristic
286C22×C11C2×#13711yescharacteristic
287C22×C11#57511yescharacteristic
288C4×C11—28no—
289C4×C11—22no—
290C4×C11—22no—
291C4×C11—22no—
292C4×C11—22no—
293C4×C11—41no—
294C4×C11—44no—
295C4×C11—81no—
296C4×C11—81no—
297C4×C11—81no—
298C4×C11—81no—
299C4×C11C2×C22⋊Q812yes—
300C4×C11#52512yes—
301C22×Q8—24no—
302C22×Q8—24no—
303C22×Q8—21no—
304C22×Q8—22no—
305C22×Q8Q8×C1114yes—
306C22×Q8C23×C1112yes—
307C23×C4—21no—
308C23×C4—21no—
309C23×C4D4×C1111yescharacteristic
310C23×C4D4×C1111yescharacteristic
311C23×C4C23×C1111yescharacteristic
312C22×C8C23×C1112yes—
313C22×C8C23×C1112yes—
314#125—24no—
315C4×Q8—28no—
316C4×Q8—28no—
317C4×Q8—24no—
318C4×Q8—24no—
319C4×Q8—24no—
320C4×Q8D4×C1118yes—
321C2×C4⋊C4—28no—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—22no—
324C2×C4⋊C4—21no—
325C2×C4⋊C4—24no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—21no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4C23×C1111yescharacteristic
331C2×C4⋊C4C23×C1111yescharacteristic
332C2×C4⋊C4C23×C1111yescharacteristic
333C2×C4⋊C4C23×C1111yescharacteristic
334C2×C4⋊C4C23×C1112yes—
335C2×C22⋊C4—21no—
336C2×C22⋊C4—21no—
337C2×C42—28no—
338C2×C42—22no—
339C2×C42—22no—
340C2×C42—24no—
341C2×C42D4×C1111yescharacteristic
342C2×C42D4×C1111yescharacteristic
343C2×C42C23×C1111yescharacteristic
344C2×C42C23×C1111yescharacteristic
345#107—24no—
346#106—24no—
347C4⋊C8—24no—
348#103—24no—
349#103—24no—
350#103—24no—
351#103—24no—
352C22⋊C8—22no—
353C22⋊C8—22no—
354#95—21no—
355#95—21no—
356#95—21no—
357#95—21no—
358#95—21no—
359#95—21no—
360C2×C11—24no—
361C2×C11#284811yescharacteristic
362C2×C11#300211yescharacteristic
363C2×C11#300411yescharacteristic
364C2×C11C2×#47911yescharacteristic
365C2×C11#307811yescharacteristic
366C2×C11#310811yescharacteristic
367C2×C11#311711yescharacteristic
368C24C2×D4×C1111yescharacteristic
369C2×Q8—24no—
370C2×Q8—216no—
371C2×Q8—24no—
372C2×Q8—216no—
373C2×Q8—24no—
374C2×Q8—22no—
375C2×Q8—22no—
376C2×Q8—22no—
377C2×Q8C2×D4×C1114yes—
378C2×Q8C2×Q8×C1114yes—
379C2×Q8C11×#4114yes—
380C22×C4—24no—
381C22×C4—24no—
382C22×C4—24no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—24no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—41no—
398C22×C4—42no—
399C22×C4—42no—
400C22×C4C2×D4×C1111yescharacteristic
401C22×C4C2×D4×C1111yescharacteristic
402C22×C4C2×D4×C1111yescharacteristic
403C22×C4C2×D4×C1111yescharacteristic
404C22×C4C2×D4×C1111yescharacteristic
405C22×C4C2×Q8×C1112yes—
406C22×C4C11×#4112yes—
407C22×C4C24×C1111yescharacteristic
408C2×C8—22no—
409C2×C8—22no—
410C2×C8—22no—
411C2×C8—22no—
412C2×C8—22no—
413C2×C8—22no—
414C4⋊C4—28no—
415C4⋊C4—24no—
416C4⋊C4—28no—
417C4⋊C4—22no—
418C4⋊C4—22no—
419C4⋊C4—22no—
420C4⋊C4—22no—
421C4⋊C4—22no—
422C4⋊C4—42no—
423C4⋊C4—42no—
424C4⋊C4—42no—
425C4⋊C4—42no—
426C4⋊C4C2×D4×C1114yes—
427C22⋊C4—42no—
428C22⋊C4—42no—
429C42—28no—
430C42—28no—
431C42—22no—
432C42—22no—
433C42—22no—
434C42C2×D4×C1114yes—
435C11#3296011yescharacteristic, direct product factor, Sylow
436C23—21no—
437C23—21no—
438C23—21no—
439C23—21no—
440C23C11×C22⋊Q812yes—
441C23C11×#13512yes—
442C23C11×#13712yes—
443C23C22×D4×C1111yescharacteristic
444Q8—216no—
445Q8—24no—
446Q8—24no—
447Q8—24no—
448Q8C11×C22⋊Q818yes—
449C2×C4—28no—
450C2×C4—216no—
451C2×C4—21no—
452C2×C4—24no—
453C2×C4—21no—
454C2×C4—24no—
455C2×C4—24no—
456C2×C4—21no—
457C2×C4—21no—
458C2×C4—21no—
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—24no—
463C2×C4—24no—
464C2×C4—21no—
465C2×C4—24no—
466C2×C4—21no—
467C2×C4—21no—
468C2×C4—44no—
469C2×C4—48no—
470C2×C4—42no—
471C2×C4—42no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—41no—
475C2×C4—41no—
476C2×C4—41no—
477C2×C4—41no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—41no—
482C2×C4—41no—
483C2×C4—41no—
484C2×C4C11×#12012yes—
485C2×C4C11×#12012yes—
486C2×C4C11×C22⋊Q812yes—
487C2×C4C11×#13712yes—
488C2×C4C22×D4×C1112yes—
489C2×C4C22×Q8×C1111yescharacteristic
490C2×C4C2×C11×#4112yes—
491C2×C4C2×C11×#4111yescharacteristic
492C8—42no—
493C8—42no—
494C22—22no—
495C22—22no—
496C22—22no—
497C22—22no—
498C22—22no—
499C22—22no—
500C22C11×#47914yescomplemented
501C22C2×C11×#12011yescharacteristic
502C22C2×C11×C22⋊Q811yescharacteristic
503C22C11×#52511yescharacteristic
504C22C2×C11×#13511yescharacteristic
505C22C2×C11×#13711yescharacteristic
506C22C2×C11×#13711yescharacteristic
507C22C11×#57511yescharacteristic
508C4—22no—
509C4—22no—
510C4—22no—
511C4—28no—
512C4—22no—
513C4—41no—
514C4—44no—
515C4—81no—
516C4—81no—
517C4—81no—
518C4—81no—
519C4C2×C11×C22⋊Q812yes—
520C4C11×#52512yes—
521C2—24no—
522C2C11×#284811yescharacteristic
523C2C11×#300211yescharacteristic
524C2C11×#300411yescharacteristic
525C2C2×C11×#47911yescharacteristic
526C2C11×#307811yescharacteristic
527C2C11×#310811yescharacteristic
528C2C11×#311711yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC24×C11C2×D4
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
2. C2×C11×#479C2semidirect
4. C11×#1865C2semidirect
5. C11×#1863C2semidirect
8. C11×#1805C2semidirect
104. #32960C11direct (N × H)
173. C2×#479C2×C11semidirect
175. #1865C2×C11semidirect
176. #1863C2×C11semidirect
179. #1805C2×C11semidirect
280. C22×C11#479semidirect
435. C11#32960direct (N × H)
500. C22C11×#479semidirect

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×#4792
C11×#28512
C11×#18652
C11×#18632
C11×#18532
C11×#18522
C11×#18052
C11×#17972
C11×#17872
#3296011