Finite Group Databasebeta

← C11×#24307 #14601500

Subgroups — C11×#24307 #14601500

Order 2816.

1078 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
1C22×C11×#125C211yesmaximal, characteristic
2C2×C11×#479C212yesmaximal, complemented
3C4×C11×C22⋊Q8C211yesmaximal, characteristic
4C11×#2059C212yesmaximal, complemented
5C11×#2026C212yesmaximal, complemented
6C11×#1989C212yesmaximal, complemented
7C11×#1872C211yesmaximal, characteristic
8C11×#1872C211yesmaximal, characteristic
9C11×#1853C211yesmaximal, characteristic
10C11×#1852C211yesmaximal, characteristic
11C11×#1797C211yesmaximal, characteristic
12C2×C11×#125—28no—
13C2×C11×#125—21no—
14C2×C11×#125—21no—
15C2×C11×#125C2212yes—
16C2×C11×#125C2212yes—
17C2×C11×C22⋊Q8C2211yescharacteristic
18C2×C4×Q8×C11C2211yescharacteristic
19C22×C11×C4⋊C4—21no—
20C22×C11×C4⋊C4—21no—
21C22×C11×C4⋊C4C2211yescharacteristic
22C22×C11×C4⋊C4C2211yescharacteristic
23C22×C42×C11C2211yescharacteristic
24C11×#479—28no—
25C2×C11×#107C2212yes—
26C2×C11×#106C2212yes—
27C2×C11×C4⋊C8C2212yes—
28C2×C11×#103C2212yes—
29C2×C11×#103C2212yes—
30C2×C11×C22⋊C8C2211yescharacteristic
31C2×C11×C22⋊C8C2211yescharacteristic
32C11×#391C2211yescharacteristic
33C11×#389C2211yescharacteristic
34C11×#387—21no—
35C11×#385—21no—
36C11×#380C2211yescharacteristic
37C4×C11×C4⋊C4—21no—
38C4×C11×C4⋊C4C2211yescharacteristic
39C4×C11×C22⋊C4—21no—
40C11×#340C2212yes—
41C11×#340C2212yes—
42C11×#340C2212yes—
43C11×#340C2212yes—
44C11×#336C2212yes—
45C22×Q8×C11C2311yescharacteristic
46C23×C4×C11—21no—
47C23×C4×C11—21no—
48C23×C4×C11D411yescharacteristic
49C23×C4×C11D411yescharacteristic
50C23×C4×C11C2311yescharacteristic
51C22×C8×C11C2312yes—
52C22×C8×C11C2312yes—
53C11×#125—28no—
54C11×#125—28no—
55C11×#125—24no—
56C11×#125—24no—
57C11×#125—24no—
58C11×#125D418yes—
59C11×C22⋊Q8—22no—
60C11×C22⋊Q8Q814yes—
61C4×Q8×C11—24no—
62C2×C11×C4⋊C4—28no—
63C2×C11×C4⋊C4—28no—
64C2×C11×C4⋊C4—22no—
65C2×C11×C4⋊C4—22no—
66C2×C11×C4⋊C4—22no—
67C2×C11×C4⋊C4—22no—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—24no—
72C2×C11×C4⋊C4—24no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C4⋊C4C2312yes—
78C2×C11×C4⋊C4C2312yes—
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C22⋊C4—21no—
81C2×C11×C22⋊C4—21no—
82C2×C42×C11—24no—
83C2×C42×C11—21no—
84C2×C42×C11—21no—
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×C22⋊C8—22no—
95C11×C22⋊C8—22no—
96C11×#95—21no—
97C11×#95—21no—
98C11×#95—21no—
99C11×#95—21no—
100C11×#95—21no—
101#24307C1111yesmaximal, characteristic, direct product factor, Sylow
102C24×C11C2×D411yescharacteristic
103C2×Q8×C11—21no—
104C2×Q8×C11—22no—
105C2×Q8×C11—22no—
106C2×Q8×C11C2×Q812yes—
107C22×C4×C11—22no—
108C22×C4×C11—22no—
109C22×C4×C11—24no—
110C22×C4×C11—24no—
111C22×C4×C11—22no—
112C22×C4×C11—22no—
113C22×C4×C11—21no—
114C22×C4×C11—21no—
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—21no—
120C22×C4×C11—21no—
121C22×C4×C11—41no—
122C22×C4×C11—41no—
123C22×C4×C11—42no—
124C22×C4×C11—42no—
125C22×C4×C11—42no—
126C22×C4×C11—42no—
127C22×C4×C11C2×D411yescharacteristic
128C22×C4×C11C2×D411yescharacteristic
129C22×C4×C11C2×D411yescharacteristic
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11C2×D411yescharacteristic
132C22×C4×C11C2×Q812yes—
133C22×C4×C11#4112yes—
134C22×C4×C11C2411yescharacteristic
135C2×C8×C11—22no—
136C2×C8×C11—22no—
137C2×C8×C11—22no—
138C2×C8×C11—22no—
139C2×C8×C11—22no—
140C2×C8×C11—22no—
141C11×C4⋊C4—24no—
142C11×C4⋊C4—24no—
143C11×C4⋊C4—28no—
144C11×C4⋊C4—28no—
145C11×C4⋊C4—28no—
146C11×C4⋊C4—28no—
147C11×C4⋊C4—24no—
148C11×C4⋊C4—22no—
149C11×C4⋊C4—22no—
150C11×C4⋊C4—21no—
151C11×C4⋊C4—22no—
152C11×C4⋊C4—22no—
153C11×C4⋊C4—42no—
154C11×C4⋊C4—42no—
155C11×C4⋊C4C2×D414yes—
156C11×C4⋊C4C2×D414yes—
157C11×C4⋊C4C2×Q812yes—
158C11×C22⋊C4—24no—
159C11×C22⋊C4—42no—
160C42×C11—22no—
161C42×C11—22no—
162C42×C11—22no—
163C42×C11—42no—
164C42×C11—42no—
165C42×C11C2×D414yes—
166C22×#125C2×C1111yescharacteristic
167C2×#479C2×C1112yescomplemented
168C4×C22⋊Q8C2×C1111yescharacteristic
169#2059C2×C1112yescomplemented
170#2026C2×C1112yescomplemented
171#1989C2×C1112yescomplemented
172#1872C2×C1111yescharacteristic
173#1872C2×C1111yescharacteristic
174#1853C2×C1111yescharacteristic
175#1852C2×C1111yescharacteristic
176#1797C2×C1111yescharacteristic
177C23×C11—21no—
178C23×C11—21no—
179C23×C11—21no—
180C23×C11—21no—
181C23×C11C22⋊Q812yes—
182C23×C11#13512yes—
183C23×C11#13712yes—
184C23×C11C22×D411yescharacteristic
185Q8×C11—24no—
186Q8×C11—42no—
187C2×C4×C11—21no—
188C2×C4×C11—21no—
189C2×C4×C11—21no—
190C2×C4×C11—21no—
191C2×C4×C11—21no—
192C2×C4×C11—21no—
193C2×C4×C11—24no—
194C2×C4×C11—24no—
195C2×C4×C11—21no—
196C2×C4×C11—21no—
197C2×C4×C11—24no—
198C2×C4×C11—24no—
199C2×C4×C11—22no—
200C2×C4×C11—22no—
201C2×C4×C11—21no—
202C2×C4×C11—21no—
203C2×C4×C11—21no—
204C2×C4×C11—21no—
205C2×C4×C11—44no—
206C2×C4×C11—44no—
207C2×C4×C11—48no—
208C2×C4×C11—48no—
209C2×C4×C11—41no—
210C2×C4×C11—41no—
211C2×C4×C11—42no—
212C2×C4×C11—42no—
213C2×C4×C11—41no—
214C2×C4×C11—41no—
215C2×C4×C11—42no—
216C2×C4×C11—42no—
217C2×C4×C11—41no—
218C2×C4×C11—41no—
219C2×C4×C11—41no—
220C2×C4×C11—41no—
221C2×C4×C11—41no—
222C2×C4×C11—41no—
223C2×C4×C11#12012yes—
224C2×C4×C11#12012yes—
225C2×C4×C11C22⋊Q812yes—
226C2×C4×C11C22×D412yes—
227C2×C4×C11C22×Q811yescharacteristic
228C2×C4×C11C2×#4111yescharacteristic
229C2×C4×C112−1+412yes—
230C8×C11—42no—
231C8×C11—42no—
232C2×#125—28no—
233C2×#125—21no—
234C2×#125—21no—
235C2×#125C22×C1112yes—
236C2×#125C22×C1112yes—
237C2×C22⋊Q8C22×C1111yescharacteristic
238C2×C4×Q8C22×C1111yescharacteristic
239C22×C4⋊C4—21no—
240C22×C4⋊C4—21no—
241C22×C4⋊C4C22×C1111yescharacteristic
242C22×C4⋊C4C22×C1111yescharacteristic
243C22×C42C22×C1111yescharacteristic
244#479—28no—
245C2×#107C22×C1112yes—
246C2×#106C22×C1112yes—
247C2×C4⋊C8C22×C1112yes—
248C2×#103C22×C1112yes—
249C2×#103C22×C1112yes—
250C2×C22⋊C8C22×C1111yescharacteristic
251C2×C22⋊C8C22×C1111yescharacteristic
252#391C22×C1111yescharacteristic
253#389C22×C1111yescharacteristic
254#387—21no—
255#385—21no—
256#380C22×C1111yescharacteristic
257C4×C4⋊C4—21no—
258C4×C4⋊C4C22×C1111yescharacteristic
259C4×C22⋊C4—21no—
260#340C22×C1112yes—
261#340C22×C1112yes—
262#340C22×C1112yes—
263#340C22×C1112yes—
264#336C22×C1112yes—
265C22×C11—22no—
266C22×C11—22no—
267C22×C11—22no—
268C22×C11—22no—
269C22×C11—22no—
270C22×C11—22no—
271C22×C11#47914yescomplemented
272C22×C11C2×#12011yescharacteristic
273C22×C11C2×C22⋊Q811yescharacteristic
274C22×C11#53611yescharacteristic
275C22×C11C2×#13511yescharacteristic
276C22×C11C2×#13711yescharacteristic
277C22×C11#57511yescharacteristic
278C22×C11#57511yescharacteristic
279C4×C11—22no—
280C4×C11—22no—
281C4×C11—22no—
282C4×C11—42no—
283C4×C11—42no—
284C4×C11—41no—
285C4×C11—44no—
286C4×C11—41no—
287C4×C11—44no—
288C4×C11—81no—
289C4×C11—81no—
290C4×C11#54812yes—
291C4×C11D4×Q812yes—
292C22×Q8C23×C1111yescharacteristic
293C23×C4—21no—
294C23×C4—21no—
295C23×C4D4×C1111yescharacteristic
296C23×C4D4×C1111yescharacteristic
297C23×C4C23×C1111yescharacteristic
298C22×C8C23×C1112yes—
299C22×C8C23×C1112yes—
300#125—28no—
301#125—28no—
302#125—24no—
303#125—24no—
304#125—24no—
305#125D4×C1118yes—
306C22⋊Q8—22no—
307C22⋊Q8Q8×C1114yes—
308C4×Q8—24no—
309C2×C4⋊C4—28no—
310C2×C4⋊C4—28no—
311C2×C4⋊C4—22no—
312C2×C4⋊C4—22no—
313C2×C4⋊C4—22no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—21no—
318C2×C4⋊C4—24no—
319C2×C4⋊C4—24no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4C23×C1111yescharacteristic
323C2×C4⋊C4C23×C1111yescharacteristic
324C2×C4⋊C4C23×C1112yes—
325C2×C4⋊C4C23×C1112yes—
326C2×C4⋊C4C23×C1111yescharacteristic
327C2×C22⋊C4—21no—
328C2×C22⋊C4—21no—
329C2×C42—24no—
330C2×C42—21no—
331C2×C42—21no—
332C2×C42D4×C1111yescharacteristic
333C2×C42D4×C1111yescharacteristic
334C2×C42C23×C1111yescharacteristic
335C2×C42C23×C1111yescharacteristic
336#107—24no—
337#106—24no—
338C4⋊C8—24no—
339#103—24no—
340#103—24no—
341C22⋊C8—22no—
342C22⋊C8—22no—
343#95—21no—
344#95—21no—
345#95—21no—
346#95—21no—
347#95—21no—
348C2×C11—24no—
349C2×C11#240911yescharacteristic
350C2×C11#300211yescharacteristic
351C2×C11#300711yescharacteristic
352C2×C11C2×#47911yescharacteristic
353C2×C11#308011yescharacteristic
354C2×C11#323211yescharacteristic
355C2×C11#323611yescharacteristic
356C24C2×D4×C1111yescharacteristic
357C2×Q8—21no—
358C2×Q8—22no—
359C2×Q8—22no—
360C2×Q8C2×Q8×C1112yes—
361C22×C4—22no—
362C22×C4—22no—
363C22×C4—24no—
364C22×C4—24no—
365C22×C4—22no—
366C22×C4—22no—
367C22×C4—21no—
368C22×C4—21no—
369C22×C4—22no—
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—21no—
374C22×C4—21no—
375C22×C4—41no—
376C22×C4—41no—
377C22×C4—42no—
378C22×C4—42no—
379C22×C4—42no—
380C22×C4—42no—
381C22×C4C2×D4×C1111yescharacteristic
382C22×C4C2×D4×C1111yescharacteristic
383C22×C4C2×D4×C1111yescharacteristic
384C22×C4C2×D4×C1111yescharacteristic
385C22×C4C2×D4×C1111yescharacteristic
386C22×C4C2×Q8×C1112yes—
387C22×C4C11×#4112yes—
388C22×C4C24×C1111yescharacteristic
389C2×C8—22no—
390C2×C8—22no—
391C2×C8—22no—
392C2×C8—22no—
393C2×C8—22no—
394C2×C8—22no—
395C4⋊C4—24no—
396C4⋊C4—24no—
397C4⋊C4—28no—
398C4⋊C4—28no—
399C4⋊C4—28no—
400C4⋊C4—28no—
401C4⋊C4—24no—
402C4⋊C4—22no—
403C4⋊C4—22no—
404C4⋊C4—21no—
405C4⋊C4—22no—
406C4⋊C4—22no—
407C4⋊C4—42no—
408C4⋊C4—42no—
409C4⋊C4C2×D4×C1114yes—
410C4⋊C4C2×D4×C1114yes—
411C4⋊C4C2×Q8×C1112yes—
412C22⋊C4—24no—
413C22⋊C4—42no—
414C42—22no—
415C42—22no—
416C42—22no—
417C42—42no—
418C42—42no—
419C42C2×D4×C1114yes—
420C11#2430711yescharacteristic, direct product factor, Sylow
421C23—21no—
422C23—21no—
423C23—21no—
424C23—21no—
425C23C11×C22⋊Q812yes—
426C23C11×#13512yes—
427C23C11×#13712yes—
428C23C22×D4×C1111yescharacteristic
429Q8—24no—
430Q8—42no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—21no—
435C2×C4—21no—
436C2×C4—21no—
437C2×C4—24no—
438C2×C4—24no—
439C2×C4—21no—
440C2×C4—21no—
441C2×C4—24no—
442C2×C4—24no—
443C2×C4—22no—
444C2×C4—22no—
445C2×C4—21no—
446C2×C4—21no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—44no—
450C2×C4—44no—
451C2×C4—48no—
452C2×C4—48no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—42no—
456C2×C4—42no—
457C2×C4—41no—
458C2×C4—41no—
459C2×C4—42no—
460C2×C4—42no—
461C2×C4—41no—
462C2×C4—41no—
463C2×C4—41no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4C11×#12012yes—
468C2×C4C11×#12012yes—
469C2×C4C11×C22⋊Q812yes—
470C2×C4C22×D4×C1112yes—
471C2×C4C22×Q8×C1111yescharacteristic
472C2×C4C2×C11×#4111yescharacteristic
473C2×C4C11×2−1+412yes—
474C8—42no—
475C8—42no—
476C22—22no—
477C22—22no—
478C22—22no—
479C22—22no—
480C22—22no—
481C22—22no—
482C22C11×#47914yescomplemented
483C22C2×C11×#12011yescharacteristic
484C22C2×C11×C22⋊Q811yescharacteristic
485C22C11×#53611yescharacteristic
486C22C2×C11×#13511yescharacteristic
487C22C2×C11×#13711yescharacteristic
488C22C11×#57511yescharacteristic
489C22C11×#57511yescharacteristic
490C4—22no—
491C4—22no—
492C4—22no—
493C4—42no—
494C4—41no—
495C4—44no—
496C4—41no—
497C4—44no—
498C4—42no—
499C4—81no—
500C4—81no—
501C4C11×#54812yes—
502C4D4×Q8×C1112yes—
503C2—24no—
504C2C11×#240911yescharacteristic
505C2C11×#300211yescharacteristic
506C2C11×#300711yescharacteristic
507C2C2×C11×#47911yescharacteristic
508C2C11×#308011yescharacteristic
509C2C11×#323211yescharacteristic
510C2C11×#323611yescharacteristic
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×#2059C2semidirect
5. C11×#2026C2semidirect
6. C11×#1989C2semidirect
101. #24307C11direct (N × H)
167. C2×#479C2×C11semidirect
169. #2059C2×C11semidirect
170. #2026C2×C11semidirect
171. #1989C2×C11semidirect
271. C22×C11#479semidirect
420. C11#24307direct (N × H)
482. C22C11×#479semidirect

Maximal subgroups

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

subgroupindex
C22×C11×#1252
C2×C11×#4792
C4×C11×C22⋊Q82
C11×#20592
C11×#20262
C11×#19892
C11×#18722
C11×#18532
C11×#18522
C11×#17972
#2430711