Finite Group Databasebeta

← C11×#24333 #14601526

Subgroups — C11×#24333 #14601526

Order 2816.

1034 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q82×C11C211yesmaximal, characteristic
2C2×C11×#477C211yesmaximal, characteristic
3C2×C4×C11×Q16C211yesmaximal, characteristic
4C11×#2582C211yesmaximal, characteristic
5C11×#2057C212yesmaximal
6C11×#2024C212yesmaximal
7C11×#1990C211yesmaximal, characteristic
8C11×#1984C211yesmaximal, characteristic
9C11×#1878C212yesmaximal
10C11×#1863C212yesmaximal
11C11×#1803C211yesmaximal, characteristic
12C22×C11×Q16C2211yescharacteristic
13Q82×C11—24no—
14Q82×C11—24no—
15C2×C11×C4⋊Q8—21no—
16C2×C11×C4⋊Q8—22no—
17C2×C11×C4⋊Q8C2212yes—
18C2×C11×C4⋊Q8C2211yescharacteristic
19C2×C4×Q8×C11—21no—
20C2×C4×Q8×C11C2212yes—
21C2×C4×Q8×C11C2211yescharacteristic
22C2×C4×Q8×C11C2211yescharacteristic
23C2×C4×Q8×C11C2211yescharacteristic
24C11×#477—24no—
25C4×C11×Q16—24no—
26C2×C11×#107C2211yescharacteristic
27C2×C11×#107C2212yes—
28C2×C11×C4⋊C8C2211yescharacteristic
29C2×C11×#103C2212yes—
30C2×C11×#103C2212yes—
31C2×C11×#103C2211yescharacteristic
32C2×C11×#103C2211yescharacteristic
33C2×C4×C8×C11C2211yescharacteristic
34C11×#398—22no—
35C11×#391—21no—
36C11×#391C2212yes—
37C11×#389—21no—
38C11×#389C2212yes—
39C11×#384C2211yescharacteristic
40C11×#340C2212yes—
41C11×#340C2212yes—
42C11×#340C2212yes—
43C11×#336C2212yes—
44C11×#336C2212yes—
45C22×Q8×C11—22no—
46C22×Q8×C11—21no—
47C22×Q8×C11D411yescharacteristic
48C22×Q8×C11C2311yescharacteristic
49C22×Q8×C11C2311yescharacteristic
50C2×C11×Q16—22no—
51C2×C11×Q16—22no—
52C2×C11×Q16Q814yescomplemented
53C22×C8×C11C2311yescharacteristic
54C22×C8×C11C2312yes—
55C22×C8×C11C2311yescharacteristic
56C11×C4⋊Q8—216no—
57C11×C4⋊Q8—28no—
58C11×C4⋊Q8—24no—
59C11×C4⋊Q8—24no—
60C11×C4⋊Q8—22no—
61C11×C4⋊Q8D414yes—
62C4×Q8×C11—28no—
63C4×Q8×C11—24no—
64C4×Q8×C11—24no—
65C4×Q8×C11—22no—
66C4×Q8×C11—22no—
67C4×Q8×C11—22no—
68C4×Q8×C11—22no—
69C4×Q8×C11—22no—
70C4×Q8×C11D414yes—
71C2×C11×C4⋊C4—22no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—22no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4—22no—
79C2×C11×C4⋊C4D411yescharacteristic
80C2×C11×C4⋊C4D412yes—
81C2×C11×C4⋊C4C2312yes—
82C2×C11×C4⋊C4C2311yescharacteristic
83C2×C11×C4⋊C4C2312yes—
84C2×C11×C4⋊C4C2311yescharacteristic
85C2×C42×C11—22no—
86C2×C42×C11—21no—
87C2×C42×C11—21no—
88C2×C42×C11C2312yes—
89C2×C42×C11C2311yescharacteristic
90C11×#107—22no—
91C11×#107—24no—
92C11×C4⋊C8—22no—
93C11×#103—22no—
94C11×#103—24no—
95C11×#103—22no—
96C11×#103—24no—
97C4×C8×C11—22no—
98C11×#95—22no—
99C11×#95—22no—
100C11×#95—22no—
101#24333C1111yesmaximal, characteristic, direct product factor, Sylow
102C2×Q8×C11—28no—
103C2×Q8×C11—22no—
104C2×Q8×C11—24no—
105C2×Q8×C11—22no—
106C2×Q8×C11—21no—
107C2×Q8×C11—21no—
108C2×Q8×C11—21no—
109C2×Q8×C11—21no—
110C2×Q8×C11—21no—
111C2×Q8×C11—21no—
112C2×Q8×C11—21no—
113C2×Q8×C11—21no—
114C2×Q8×C11—81no—
115C2×Q8×C11—81no—
116C2×Q8×C11—82no—
117C2×Q8×C11—82no—
118C2×Q8×C11Q1614yescomplemented
119C2×Q8×C11C2×D412yes—
120C2×Q8×C11C2×Q812yes—
121C2×Q8×C11C2×Q812yes—
122C2×Q8×C11#4112yes—
123C22×C4×C11—21no—
124C22×C4×C11—21no—
125C22×C4×C11—22no—
126C22×C4×C11—21no—
127C22×C4×C11—22no—
128C22×C4×C11—21no—
129C22×C4×C11C2×D412yes—
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11C2×D412yes—
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2411yescharacteristic
134C11×Q16—28no—
135C2×C8×C11—21no—
136C2×C8×C11—21no—
137C2×C8×C11—22no—
138C2×C8×C11—21no—
139C2×C8×C11—22no—
140C2×C8×C11—21no—
141C2×C8×C11—22no—
142C2×C8×C11—21no—
143C2×C8×C11C2×Q812yes—
144C11×C4⋊C4—28no—
145C11×C4⋊C4—28no—
146C11×C4⋊C4—24no—
147C11×C4⋊C4—24no—
148C11×C4⋊C4—24no—
149C11×C4⋊C4—22no—
150C11×C4⋊C4—22no—
151C11×C4⋊C4—21no—
152C11×C4⋊C4—21no—
153C11×C4⋊C4—21no—
154C11×C4⋊C4—22no—
155C11×C4⋊C4—22no—
156C11×C4⋊C4—42no—
157C11×C4⋊C4—42no—
158C11×C4⋊C4—81no—
159C11×C4⋊C4—82no—
160C11×C4⋊C4C2×D414yes—
161C11×C4⋊C4C2×D412yes—
162C42×C11—28no—
163C42×C11—24no—
164C42×C11—22no—
165C42×C11—22no—
166C42×C11—42no—
167C42×C11C2×D412yes—
168C42×C11C2×D412yes—
169C2×Q82C2×C1111yescharacteristic
170C2×#477C2×C1111yescharacteristic
171C2×C4×Q16C2×C1111yescharacteristic
172#2582C2×C1111yescharacteristic
173#2057C2×C1112yes—
174#2024C2×C1112yes—
175#1990C2×C1111yescharacteristic
176#1984C2×C1111yescharacteristic
177#1878C2×C1112yes—
178#1863C2×C1112yes—
179#1803C2×C1111yescharacteristic
180C23×C11C22×D411yescharacteristic
181Q8×C11—22no—
182Q8×C11—22no—
183Q8×C11—22no—
184Q8×C11—28no—
185Q8×C11—22no—
186Q8×C11—22no—
187Q8×C11—41no—
188Q8×C11—41no—
189Q8×C11—84no—
190Q8×C11—88no—
191Q8×C11C22⋊Q814yes—
192C2×C4×C11—22no—
193C2×C4×C11—22no—
194C2×C4×C11—22no—
195C2×C4×C11—22no—
196C2×C4×C11—22no—
197C2×C4×C11—21no—
198C2×C4×C11—21no—
199C2×C4×C11—22no—
200C2×C4×C11—24no—
201C2×C4×C11—22no—
202C2×C4×C11—22no—
203C2×C4×C11—22no—
204C2×C4×C11—22no—
205C2×C4×C11—41no—
206C2×C4×C11—41no—
207C2×C4×C11—42no—
208C2×C4×C11—41no—
209C2×C4×C11—42no—
210C2×C4×C11—41no—
211C2×C4×C11—41no—
212C2×C4×C11—42no—
213C2×C4×C11—42no—
214C2×C4×C11—42no—
215C2×C4×C11—41no—
216C2×C4×C11—41no—
217C2×C4×C11#12012yes—
218C2×C4×C11#12012yes—
219C2×C4×C11C2×Q1614yes—
220C2×C4×C11C2×Q1612yes—
221C2×C4×C11#13712yes—
222C2×C4×C11C22×D411yescharacteristic
223C2×C4×C11C22×D411yescharacteristic
224C2×C4×C11C22×Q811yescharacteristic
225C2×C4×C11C2×#4111yescharacteristic
226C2×C4×C112−1+411yescharacteristic
227C2×C4×C112−1+411yescharacteristic
228C8×C11—22no—
229C8×C11—41no—
230C8×C11—42no—
231C22×Q16C22×C1111yescharacteristic
232Q82—24no—
233Q82—24no—
234C2×C4⋊Q8—21no—
235C2×C4⋊Q8—22no—
236C2×C4⋊Q8C22×C1112yes—
237C2×C4⋊Q8C22×C1111yescharacteristic
238C2×C4×Q8—21no—
239C2×C4×Q8C22×C1111yescharacteristic
240C2×C4×Q8C22×C1112yes—
241C2×C4×Q8C22×C1111yescharacteristic
242C2×C4×Q8C22×C1111yescharacteristic
243#477—24no—
244C4×Q16—24no—
245C2×#107C22×C1112yes—
246C2×#107C22×C1111yescharacteristic
247C2×C4⋊C8C22×C1111yescharacteristic
248C2×#103C22×C1112yes—
249C2×#103C22×C1112yes—
250C2×#103C22×C1111yescharacteristic
251C2×#103C22×C1111yescharacteristic
252C2×C4×C8C22×C1111yescharacteristic
253#398—22no—
254#391—21no—
255#391C22×C1112yes—
256#389—21no—
257#389C22×C1112yes—
258#384C22×C1111yescharacteristic
259#340C22×C1112yes—
260#340C22×C1112yes—
261#340C22×C1112yes—
262#336C22×C1112yes—
263#336C22×C1112yes—
264C22×C11C2×#12011yescharacteristic
265C22×C11#54811yescharacteristic
266C22×C11D4×Q811yescharacteristic
267C22×C11C22×Q1611yescharacteristic
268C22×C11C2×#13711yescharacteristic
269C22×C11#57611yescharacteristic
270C22×C11#57711yescharacteristic
271C4×C11—24no—
272C4×C11—24no—
273C4×C11—22no—
274C4×C11—42no—
275C4×C11—42no—
276C4×C11—44no—
277C4×C11—42no—
278C4×C11—82no—
279C4×C11—81no—
280C4×C11#45114yes—
281C4×C11C2×C22⋊Q811yescharacteristic
282C4×C11#53611yescharacteristic
283C4×C11#54811yescharacteristic
284C4×C11D4×Q811yescharacteristic
285C22×Q8—22no—
286C22×Q8—21no—
287C22×Q8D4×C1111yescharacteristic
288C22×Q8C23×C1111yescharacteristic
289C22×Q8C23×C1111yescharacteristic
290C2×Q16—22no—
291C2×Q16—22no—
292C2×Q16Q8×C1114yescomplemented
293C22×C8C23×C1111yescharacteristic
294C22×C8C23×C1112yes—
295C22×C8C23×C1111yescharacteristic
296C4⋊Q8—216no—
297C4⋊Q8—28no—
298C4⋊Q8—24no—
299C4⋊Q8—24no—
300C4⋊Q8—22no—
301C4⋊Q8D4×C1114yes—
302C4×Q8—28no—
303C4×Q8—24no—
304C4×Q8—24no—
305C4×Q8—22no—
306C4×Q8—22no—
307C4×Q8—22no—
308C4×Q8—22no—
309C4×Q8—22no—
310C4×Q8D4×C1114yes—
311C2×C4⋊C4—22no—
312C2×C4⋊C4—21no—
313C2×C4⋊C4—22no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—21no—
318C2×C4⋊C4—22no—
319C2×C4⋊C4D4×C1111yescharacteristic
320C2×C4⋊C4D4×C1112yes—
321C2×C4⋊C4C23×C1111yescharacteristic
322C2×C4⋊C4C23×C1112yes—
323C2×C4⋊C4C23×C1112yes—
324C2×C4⋊C4C23×C1111yescharacteristic
325C2×C42—22no—
326C2×C42—21no—
327C2×C42—21no—
328C2×C42C23×C1112yes—
329C2×C42C23×C1111yescharacteristic
330#107—22no—
331#107—24no—
332C4⋊C8—22no—
333#103—22no—
334#103—24no—
335#103—22no—
336#103—24no—
337C4×C8—22no—
338#95—22no—
339#95—22no—
340#95—22no—
341C2×C11#240911yescharacteristic
342C2×C11C2×#45111yescharacteristic
343C2×C11#301211yescharacteristic
344C2×C11#336311yescharacteristic
345C2×C11#337511yescharacteristic
346C2×C11Q8×Q1611yescharacteristic
347C2×C11#338711yescharacteristic
348C2×Q8—28no—
349C2×Q8—22no—
350C2×Q8—24no—
351C2×Q8—22no—
352C2×Q8—21no—
353C2×Q8—21no—
354C2×Q8—21no—
355C2×Q8—21no—
356C2×Q8—21no—
357C2×Q8—21no—
358C2×Q8—21no—
359C2×Q8—21no—
360C2×Q8—81no—
361C2×Q8—81no—
362C2×Q8—82no—
363C2×Q8—82no—
364C2×Q8C11×Q1614yescomplemented
365C2×Q8C2×D4×C1112yes—
366C2×Q8C2×Q8×C1112yes—
367C2×Q8C2×Q8×C1112yes—
368C2×Q8C11×#4112yes—
369C22×C4—21no—
370C22×C4—21no—
371C22×C4—22no—
372C22×C4—21no—
373C22×C4—22no—
374C22×C4—21no—
375C22×C4C2×D4×C1112yes—
376C22×C4C2×D4×C1111yescharacteristic
377C22×C4C2×D4×C1112yes—
378C22×C4C2×D4×C1111yescharacteristic
379C22×C4C24×C1111yescharacteristic
380Q16—28no—
381C2×C8—21no—
382C2×C8—21no—
383C2×C8—21no—
384C2×C8—22no—
385C2×C8—22no—
386C2×C8—21no—
387C2×C8—21no—
388C2×C8—22no—
389C2×C8C2×Q8×C1112yes—
390C4⋊C4—28no—
391C4⋊C4—28no—
392C4⋊C4—24no—
393C4⋊C4—24no—
394C4⋊C4—24no—
395C4⋊C4—22no—
396C4⋊C4—22no—
397C4⋊C4—21no—
398C4⋊C4—21no—
399C4⋊C4—21no—
400C4⋊C4—22no—
401C4⋊C4—22no—
402C4⋊C4—42no—
403C4⋊C4—42no—
404C4⋊C4—81no—
405C4⋊C4—82no—
406C4⋊C4C2×D4×C1114yes—
407C4⋊C4C2×D4×C1112yes—
408C42—28no—
409C42—24no—
410C42—22no—
411C42—22no—
412C42—42no—
413C42C2×D4×C1112yes—
414C42C2×D4×C1112yes—
415C11#2433311yescharacteristic, direct product factor, Sylow
416C23C22×D4×C1111yescharacteristic
417Q8—22no—
418Q8—22no—
419Q8—22no—
420Q8—28no—
421Q8—22no—
422Q8—22no—
423Q8—41no—
424Q8—41no—
425Q8—84no—
426Q8—88no—
427Q8C11×C22⋊Q814yes—
428C2×C4—22no—
429C2×C4—22no—
430C2×C4—22no—
431C2×C4—22no—
432C2×C4—22no—
433C2×C4—21no—
434C2×C4—21no—
435C2×C4—22no—
436C2×C4—24no—
437C2×C4—22no—
438C2×C4—22no—
439C2×C4—22no—
440C2×C4—22no—
441C2×C4—41no—
442C2×C4—41no—
443C2×C4—42no—
444C2×C4—41no—
445C2×C4—42no—
446C2×C4—41no—
447C2×C4—41no—
448C2×C4—42no—
449C2×C4—42no—
450C2×C4—41no—
451C2×C4—42no—
452C2×C4—41no—
453C2×C4C11×#12012yes—
454C2×C4C11×#12012yes—
455C2×C4C2×C11×Q1614yes—
456C2×C4C2×C11×Q1612yes—
457C2×C4C11×#13712yes—
458C2×C4C22×D4×C1111yescharacteristic
459C2×C4C22×D4×C1111yescharacteristic
460C2×C4C22×Q8×C1111yescharacteristic
461C2×C4C2×C11×#4111yescharacteristic
462C2×C4C11×2−1+411yescharacteristic
463C2×C4C11×2−1+411yescharacteristic
464C8—22no—
465C8—41no—
466C8—42no—
467C22C2×C11×#12011yescharacteristic
468C22C11×#54811yescharacteristic
469C22D4×Q8×C1111yescharacteristic
470C22C22×C11×Q1611yescharacteristic
471C22C2×C11×#13711yescharacteristic
472C22C11×#57611yescharacteristic
473C22C11×#57711yescharacteristic
474C4—24no—
475C4—24no—
476C4—22no—
477C4—42no—
478C4—42no—
479C4—44no—
480C4—42no—
481C4—81no—
482C4—82no—
483C4C11×#45114yes—
484C4C2×C11×C22⋊Q811yescharacteristic
485C4C11×#53611yescharacteristic
486C4C11×#54811yescharacteristic
487C4D4×Q8×C1111yescharacteristic
488C2C11×#240911yescharacteristic
489C2C2×C11×#45111yescharacteristic
490C2C11×#301211yescharacteristic
491C2C11×#336311yescharacteristic
492C2C11×#337511yescharacteristic
493C2Q8×C11×Q1611yescharacteristic
494C2C11×#338711yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C4×Q8×C11 ◁ G

Complements

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

NH ≅ G/Ntype
52. C2×C11×Q16Q8semidirect
101. #24333C11direct (N × H)
118. C2×Q8×C11Q16semidirect
292. C2×Q16Q8×C11semidirect
364. C2×Q8C11×Q16semidirect
415. C11#24333direct (N × H)

Maximal subgroups

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

subgroupindex
C2×Q82×C112
C2×C11×#4772
C2×C4×C11×Q162
C11×#25822
C11×#20572
C11×#20242
C11×#19902
C11×#19842
C11×#18782
C11×#18632
C11×#18032
#2433311