Finite Group Databasebeta

← C11×#24340 #14601533

Subgroups — C11×#24340 #14601533

Order 2816.

1036 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#557C211yesmaximal, characteristic, complemented
2C2×C11×#476C211yesmaximal, characteristic
3C2×C11×#440C211yesmaximal, characteristic
4C11×#2580C211yesmaximal, characteristic
5C11×#2059C212yesmaximal, complemented
6C11×#2025C212yesmaximal
7C11×#1993C211yesmaximal, characteristic, complemented
8C11×#1985C211yesmaximal, characteristic, complemented
9C11×#1880C212yesmaximal
10C11×#1865C212yesmaximal, complemented
11C11×#1805C211yesmaximal, characteristic, complemented
12C22×C11×SD16C2211yescharacteristic
13C11×#557—24no—
14C11×#557—24no—
15C2×C11×C4⋊Q8—21no—
16C2×C11×C4⋊Q8C2211yescharacteristic
17C2×C11×#125—22no—
18C2×C11×#125C2212yes—
19C2×C4×Q8×C11—21no—
20C2×C4×Q8×C11C2212yes—
21C2×C4×Q8×C11C2211yescharacteristic
22C2×C4×Q8×C11C2211yescharacteristic
23C2×C4×D4×C11C2211yescharacteristic
24C11×#476—24no—
25C11×#440—24no—
26C2×C11×#107C2211yescharacteristic
27C2×C11×#106C2212yes—
28C2×C11×C4⋊C8C2211yescharacteristic
29C2×C11×#103C2212yes—
30C2×C11×#103C2211yescharacteristic
31C2×C11×#102C2212yes—
32C2×C11×#102C2211yescharacteristic
33C2×C11×#97C2211yescharacteristic
34C11×#399—21no—
35C11×#393—21no—
36C11×#390C2212yes—
37C11×#389C2212yes—
38C11×#385—22no—
39C11×#382C2211yescharacteristic
40C11×#340C2212yes—
41C11×#340C2212yes—
42C11×#340C2212yes—
43C11×#336C2212yes—
44C11×#336C2212yes—
45C22×Q8×C11—21no—
46C22×Q8×C11D411yescharacteristic
47C22×Q8×C11C2311yescharacteristic
48C22×D4×C11C2311yescharacteristic
49C23×C4×C11—21no—
50C2×C11×SD16—22no—
51C2×C11×SD16—22no—
52C2×C11×SD16Q814yescomplemented
53C22×C8×C11C2311yescharacteristic
54C22×C8×C11C2312yes—
55C22×C8×C11C2311yescharacteristic
56C11×C4⋊Q8—28no—
57C11×C4⋊Q8—22no—
58C11×C4⋊Q8D414yes—
59C11×#125—216no—
60C11×#125—24no—
61C11×#125—24no—
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×C11D414yes—
69C4×D4×C11—22no—
70C4×D4×C11—22no—
71C2×C11×C4⋊C4—22no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—22no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4—22no—
76C2×C11×C4⋊C4—22no—
77C2×C11×C4⋊C4D411yescharacteristic
78C2×C11×C4⋊C4D412yes—
79C2×C11×C4⋊C4C2312yes—
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C11×C4⋊C4C2311yescharacteristic
82C2×C11×C4⋊C4C2312yes—
83C2×C11×C22⋊C4—21no—
84C2×C11×C22⋊C4—22no—
85C2×C11×C22⋊C4—22no—
86C2×C42×C11—22no—
87C2×C42×C11—21no—
88C2×C42×C11C2312yes—
89C2×C42×C11C2311yescharacteristic
90C11×#107—22no—
91C11×#106—24no—
92C11×C4⋊C8—22no—
93C11×#103—22no—
94C11×#103—24no—
95C11×#102—22no—
96C11×#102—24no—
97C11×#97—22no—
98C11×#95—21no—
99C11×#95—21no—
100C11×#95—22no—
101#24340C1111yesmaximal, characteristic, direct product factor, Sylow
102C24×C11—21no—
103C2×Q8×C11—22no—
104C2×Q8×C11—24no—
105C2×Q8×C11—21no—
106C2×Q8×C11—21no—
107C2×Q8×C11—21no—
108C2×Q8×C11—42no—
109C2×Q8×C11—44no—
110C2×Q8×C11C2×D412yes—
111C2×Q8×C11C2×Q812yes—
112C2×Q8×C11#4112yes—
113C2×D4×C11—21no—
114C2×D4×C11—21no—
115C2×D4×C11—21no—
116C2×D4×C11—21no—
117C2×D4×C11—21no—
118C2×D4×C11C2×Q812yes—
119C22×C4×C11—21no—
120C22×C4×C11—21no—
121C22×C4×C11—22no—
122C22×C4×C11—22no—
123C22×C4×C11—21no—
124C22×C4×C11—42no—
125C22×C4×C11—82no—
126C22×C4×C11C2×D412yes—
127C22×C4×C11C2×D412yes—
128C22×C4×C11C2×D411yescharacteristic
129C22×C4×C11C2×D411yescharacteristic
130C22×C4×C11C2411yescharacteristic
131C11×SD16—28no—
132C2×C8×C11—21no—
133C2×C8×C11—21no—
134C2×C8×C11—22no—
135C2×C8×C11—21no—
136C2×C8×C11—22no—
137C2×C8×C11—21no—
138C2×C8×C11—22no—
139C2×C8×C11—21no—
140C2×C8×C11C2×Q812yes—
141C11×C4⋊C4—28no—
142C11×C4⋊C4—28no—
143C11×C4⋊C4—28no—
144C11×C4⋊C4—24no—
145C11×C4⋊C4—24no—
146C11×C4⋊C4—22no—
147C11×C4⋊C4—24no—
148C11×C4⋊C4—21no—
149C11×C4⋊C4—22no—
150C11×C4⋊C4—21no—
151C11×C4⋊C4—21no—
152C11×C4⋊C4—22no—
153C11×C4⋊C4—22no—
154C11×C4⋊C4—82no—
155C11×C4⋊C4C2×D414yes—
156C11×C4⋊C4C2×D412yes—
157C11×C22⋊C4—44no—
158C11×C22⋊C4—42no—
159C11×C22⋊C4—82no—
160C42×C11—28no—
161C42×C11—24no—
162C42×C11—22no—
163C42×C11—22no—
164C42×C11C2×D412yes—
165C42×C11C2×D412yes—
166C2×#557C2×C1111yescharacteristic, complemented
167C2×#476C2×C1111yescharacteristic
168C2×#440C2×C1111yescharacteristic
169#2580C2×C1111yescharacteristic
170#2059C2×C1112yescomplemented
171#2025C2×C1112yes—
172#1993C2×C1111yescharacteristic, complemented
173#1985C2×C1111yescharacteristic, complemented
174#1880C2×C1112yes—
175#1865C2×C1112yescomplemented
176#1805C2×C1111yescharacteristic, complemented
177C23×C11—22no—
178C23×C11—41no—
179C23×C11—41no—
180C23×C11—42no—
181C23×C11—42no—
182C23×C11C22×D411yescharacteristic
183Q8×C11—22no—
184Q8×C11—22no—
185Q8×C11—22no—
186Q8×C11—44no—
187Q8×C11—48no—
188Q8×C11C22⋊Q814yes—
189D4×C11—22no—
190D4×C11—22no—
191D4×C11—41no—
192D4×C11—41no—
193C2×C4×C11—22no—
194C2×C4×C11—22no—
195C2×C4×C11—22no—
196C2×C4×C11—22no—
197C2×C4×C11—22no—
198C2×C4×C11—22no—
199C2×C4×C11—22no—
200C2×C4×C11—22no—
201C2×C4×C11—24no—
202C2×C4×C11—22no—
203C2×C4×C11—22no—
204C2×C4×C11—22no—
205C2×C4×C11—22no—
206C2×C4×C11—44no—
207C2×C4×C11—42no—
208C2×C4×C11—41no—
209C2×C4×C11—42no—
210C2×C4×C11—42no—
211C2×C4×C11—42no—
212C2×C4×C11—42no—
213C2×C4×C11—84no—
214C2×C4×C11#12012yes—
215C2×C4×C11#12012yes—
216C2×C4×C11C22×D411yescharacteristic
217C2×C4×C11C22×D411yescharacteristic
218C2×C4×C11C22×Q811yescharacteristic
219C2×C4×C11C2×#4111yescharacteristic
220C2×C4×C112−1+411yescharacteristic
221C2×C4×C112−1+411yescharacteristic
222C8×C11—22no—
223C8×C11—41no—
224C8×C11—42no—
225C22×SD16C22×C1111yescharacteristic
226#557—24no—
227#557—24no—
228C2×C4⋊Q8—21no—
229C2×C4⋊Q8C22×C1111yescharacteristic
230C2×#125—22no—
231C2×#125C22×C1112yes—
232C2×C4×Q8—21no—
233C2×C4×Q8C22×C1112yes—
234C2×C4×Q8C22×C1111yescharacteristic
235C2×C4×Q8C22×C1111yescharacteristic
236C2×C4×D4C22×C1111yescharacteristic
237#476—24no—
238#440—24no—
239C2×#107C22×C1111yescharacteristic
240C2×#106C22×C1112yes—
241C2×C4⋊C8C22×C1111yescharacteristic
242C2×#103C22×C1112yes—
243C2×#103C22×C1111yescharacteristic
244C2×#102C22×C1112yes—
245C2×#102C22×C1111yescharacteristic
246C2×#97C22×C1111yescharacteristic
247#399—21no—
248#393—21no—
249#390C22×C1112yes—
250#389C22×C1112yes—
251#385—22no—
252#382C22×C1111yescharacteristic
253#340C22×C1112yes—
254#340C22×C1112yes—
255#340C22×C1112yes—
256#336C22×C1112yes—
257#336C22×C1112yes—
258C22×C11—44no—
259C22×C11—42no—
260C22×C11—82no—
261C22×C11—81no—
262C22×C11—81no—
263C22×C11C2×#12011yescharacteristic
264C22×C11#54811yescharacteristic
265C22×C11D4×Q811yescharacteristic
266C22×C11#57512yes—
267C22×C11#57712yes—
268C4×C11—24no—
269C4×C11—22no—
270C4×C11—22no—
271C4×C11—42no—
272C4×C11—44no—
273C4×C11—42no—
274C4×C11—42no—
275C4×C11—82no—
276C4×C11—81no—
277C4×C11C2×C22⋊Q811yescharacteristic
278C4×C11#53611yescharacteristic
279C4×C11#54811yescharacteristic
280C4×C11D4×Q811yescharacteristic
281C22×Q8—21no—
282C22×Q8D4×C1111yescharacteristic
283C22×Q8C23×C1111yescharacteristic
284C22×D4C23×C1111yescharacteristic
285C23×C4—21no—
286C2×SD16—22no—
287C2×SD16—22no—
288C2×SD16Q8×C1114yescomplemented
289C22×C8C23×C1111yescharacteristic
290C22×C8C23×C1112yes—
291C22×C8C23×C1111yescharacteristic
292C4⋊Q8—28no—
293C4⋊Q8—22no—
294C4⋊Q8D4×C1114yes—
295#125—216no—
296#125—24no—
297#125—24no—
298C4×Q8—28no—
299C4×Q8—24no—
300C4×Q8—24no—
301C4×Q8—22no—
302C4×Q8—22no—
303C4×Q8—22no—
304C4×Q8D4×C1114yes—
305C4×D4—22no—
306C4×D4—22no—
307C2×C4⋊C4—22no—
308C2×C4⋊C4—21no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—21no—
311C2×C4⋊C4—22no—
312C2×C4⋊C4—22no—
313C2×C4⋊C4D4×C1111yescharacteristic
314C2×C4⋊C4D4×C1112yes—
315C2×C4⋊C4C23×C1111yescharacteristic
316C2×C4⋊C4C23×C1112yes—
317C2×C4⋊C4C23×C1111yescharacteristic
318C2×C4⋊C4C23×C1112yes—
319C2×C22⋊C4—21no—
320C2×C22⋊C4—22no—
321C2×C22⋊C4—22no—
322C2×C42—22no—
323C2×C42—21no—
324C2×C42C23×C1112yes—
325C2×C42C23×C1111yescharacteristic
326#107—22no—
327#106—24no—
328C4⋊C8—22no—
329#103—22no—
330#103—24no—
331#102—22no—
332#102—24no—
333#97—22no—
334#95—21no—
335#95—21no—
336#95—22no—
337C2×C11—82no—
338C2×C11#240911yescharacteristic
339C2×C11#300511yescharacteristic
340C2×C11#301011yescharacteristic
341C2×C11#337112yes—
342C2×C11#338812yes—
343C24—21no—
344C2×Q8—22no—
345C2×Q8—24no—
346C2×Q8—21no—
347C2×Q8—21no—
348C2×Q8—21no—
349C2×Q8—42no—
350C2×Q8—44no—
351C2×Q8C2×D4×C1112yes—
352C2×Q8C2×Q8×C1112yes—
353C2×Q8C11×#4112yes—
354C2×D4—21no—
355C2×D4—21no—
356C2×D4—21no—
357C2×D4—21no—
358C2×D4—21no—
359C2×D4C2×Q8×C1112yes—
360C22×C4—21no—
361C22×C4—21no—
362C22×C4—22no—
363C22×C4—22no—
364C22×C4—21no—
365C22×C4—42no—
366C22×C4—82no—
367C22×C4C2×D4×C1112yes—
368C22×C4C2×D4×C1112yes—
369C22×C4C2×D4×C1111yescharacteristic
370C22×C4C2×D4×C1111yescharacteristic
371C22×C4C24×C1111yescharacteristic
372SD16—28no—
373C2×C8—21no—
374C2×C8—21no—
375C2×C8—21no—
376C2×C8—22no—
377C2×C8—22no—
378C2×C8—21no—
379C2×C8—21no—
380C2×C8—22no—
381C2×C8C2×Q8×C1112yes—
382C4⋊C4—28no—
383C4⋊C4—28no—
384C4⋊C4—28no—
385C4⋊C4—24no—
386C4⋊C4—24no—
387C4⋊C4—22no—
388C4⋊C4—24no—
389C4⋊C4—21no—
390C4⋊C4—22no—
391C4⋊C4—21no—
392C4⋊C4—21no—
393C4⋊C4—22no—
394C4⋊C4—22no—
395C4⋊C4—82no—
396C4⋊C4C2×D4×C1114yes—
397C4⋊C4C2×D4×C1112yes—
398C22⋊C4—44no—
399C22⋊C4—42no—
400C22⋊C4—82no—
401C42—28no—
402C42—24no—
403C42—22no—
404C42—22no—
405C42C2×D4×C1112yes—
406C42C2×D4×C1112yes—
407C11#2434011yescharacteristic, direct product factor, Sylow
408C23—22no—
409C23—41no—
410C23—41no—
411C23—42no—
412C23—42no—
413C23C22×D4×C1111yescharacteristic
414Q8—22no—
415Q8—22no—
416Q8—22no—
417Q8—44no—
418Q8—48no—
419Q8C11×C22⋊Q814yes—
420D4—22no—
421D4—22no—
422D4—41no—
423D4—41no—
424C2×C4—22no—
425C2×C4—22no—
426C2×C4—22no—
427C2×C4—22no—
428C2×C4—22no—
429C2×C4—22no—
430C2×C4—22no—
431C2×C4—22no—
432C2×C4—24no—
433C2×C4—22no—
434C2×C4—22no—
435C2×C4—22no—
436C2×C4—22no—
437C2×C4—44no—
438C2×C4—42no—
439C2×C4—41no—
440C2×C4—42no—
441C2×C4—42no—
442C2×C4—42no—
443C2×C4—42no—
444C2×C4—84no—
445C2×C4C11×#12012yes—
446C2×C4C11×#12012yes—
447C2×C4C22×D4×C1111yescharacteristic
448C2×C4C22×D4×C1111yescharacteristic
449C2×C4C22×Q8×C1111yescharacteristic
450C2×C4C2×C11×#4111yescharacteristic
451C2×C4C11×2−1+411yescharacteristic
452C2×C4C11×2−1+411yescharacteristic
453C8—22no—
454C8—41no—
455C8—42no—
456C22—42no—
457C22—44no—
458C22—81no—
459C22—81no—
460C22—82no—
461C22C2×C11×#12011yescharacteristic
462C22C11×#54811yescharacteristic
463C22D4×Q8×C1111yescharacteristic
464C22C11×#57512yes—
465C22C11×#57712yes—
466C4—24no—
467C4—22no—
468C4—22no—
469C4—42no—
470C4—44no—
471C4—42no—
472C4—42no—
473C4—81no—
474C4—82no—
475C4C2×C11×C22⋊Q811yescharacteristic
476C4C11×#53611yescharacteristic
477C4C11×#54811yescharacteristic
478C4D4×Q8×C1111yescharacteristic
479C2—82no—
480C2C11×#240911yescharacteristic
481C2C11×#300511yescharacteristic
482C2C11×#301011yescharacteristic
483C2C11×#337112yes—
484C2C11×#338812yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC22×D4×C11C23
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
1. C2×C11×#557C2semidirect
5. C11×#2059C2semidirect
7. C11×#1993C2semidirect
8. C11×#1985C2semidirect
10. C11×#1865C2semidirect
11. C11×#1805C2semidirect
52. C2×C11×SD16Q8semidirect
101. #24340C11direct (N × H)
166. C2×#557C2×C11semidirect
170. #2059C2×C11semidirect
172. #1993C2×C11semidirect
173. #1985C2×C11semidirect
175. #1865C2×C11semidirect
176. #1805C2×C11semidirect
288. C2×SD16Q8×C11semidirect
407. C11#24340direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5572
C2×C11×#4762
C2×C11×#4402
C11×#25802
C11×#20592
C11×#20252
C11×#19932
C11×#19852
C11×#18802
C11×#18652
C11×#18052
#2434011