Finite Group Databasebeta

← C11×#24815 #14602008

Subgroups — C11×#24815 #14602008

Order 2816.

910 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#476C211yesmaximal, characteristic
2C2×C4×C11×SD16C211yesmaximal, characteristic
3C11×#2567C211yesmaximal, characteristic, complemented
4D4×C11×C4⋊C4C211yesmaximal, characteristic
5C11×#2084C212yesmaximal, complemented
6C11×#2066C212yesmaximal, complemented
7C11×#1990C211yesmaximal, characteristic, complemented
8C11×#1939C211yesmaximal, characteristic, complemented
9C11×#1877C212yesmaximal
10C11×#1803C211yesmaximal, characteristic, complemented
11C11×#1802C212yesmaximal
12C22×C11×SD16C2211yescharacteristic
13C2×C11×C4⋊Q8C2211yescharacteristic
14C2×C4×Q8×C11C2211yescharacteristic
15C2×C4×D4×C11C2212yes—
16C2×C4×D4×C11C2211yescharacteristic
17C22×C11×C4⋊C4—21no—
18C11×#476—24no—
19C4×C11×SD16—24no—
20C2×C11×#106C2211yescharacteristic
21C2×C11×#106C2212yes—
22C2×C11×C4⋊C8C2211yescharacteristic
23C2×C11×C4⋊C8C2212yes—
24C2×C11×#103C2211yescharacteristic
25C2×C11×#103C2212yes—
26C2×C11×#102C2212yes—
27C2×C11×#102C2211yescharacteristic
28C2×C4×C8×C11C2211yescharacteristic
29C11×#395—22no—
30C11×#391C2212yes—
31C11×#389—21no—
32C11×#389—21no—
33C11×#389C2212yes—
34C11×#385—22no—
35C11×#384C2211yescharacteristic
36C11×#384C2212yes—
37C11×#380—21no—
38C4×C11×C4⋊C4C2211yescharacteristic
39C11×#340C2212yes—
40C11×#340C2212yes—
41C11×#340C2212yes—
42C11×#336C2212yes—
43C22×Q8×C11—21no—
44C22×Q8×C11C2311yescharacteristic
45C22×D4×C11C2311yescharacteristic
46C23×C4×C11—21no—
47C23×C4×C11—22no—
48C2×C11×SD16—22no—
49C2×C11×SD16—22no—
50C2×C11×SD16Q814yescomplemented
51C22×C8×C11C2312yes—
52C22×C8×C11C2311yescharacteristic
53C22×C8×C11C2311yescharacteristic
54C11×C4⋊Q8—22no—
55C11×C4⋊Q8—22no—
56C4×Q8×C11—22no—
57C4×Q8×C11—22no—
58C4×D4×C11—24no—
59C4×D4×C11—22no—
60C4×D4×C11—42no—
61C4×D4×C11D414yes—
62C2×C11×C4⋊C4—21no—
63C2×C11×C4⋊C4—22no—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4—22no—
68C2×C11×C4⋊C4—22no—
69C2×C11×C4⋊C4—44no—
70C2×C11×C4⋊C4D411yescharacteristic
71C2×C11×C4⋊C4D411yescharacteristic
72C2×C11×C4⋊C4C2312yes—
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C4⋊C4C2312yes—
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C22⋊C4—21no—
77C2×C11×C22⋊C4—22no—
78C2×C42×C11—21no—
79C2×C42×C11C2312yes—
80C2×C42×C11C2311yescharacteristic
81C11×#106—22no—
82C11×#106—24no—
83C11×C4⋊C8—22no—
84C11×C4⋊C8—42no—
85C11×#103—22no—
86C11×#103—42no—
87C11×#102—22no—
88C11×#102—24no—
89C4×C8×C11—22no—
90C11×#95—22no—
91C11×#95—22no—
92C11×#95—22no—
93C11×#95D412yes—
94#24815C1111yesmaximal, characteristic, direct product factor, Sylow
95C24×C11—21no—
96C2×Q8×C11—21no—
97C2×Q8×C11—21no—
98C2×Q8×C11—21no—
99C2×Q8×C11—21no—
100C2×Q8×C11—21no—
101C2×Q8×C11—42no—
102C2×Q8×C11—81no—
103C2×Q8×C11—81no—
104C2×Q8×C11C2×Q812yes—
105C2×D4×C11—21no—
106C2×D4×C11—21no—
107C2×D4×C11—21no—
108C2×D4×C11C2×D412yes—
109C2×D4×C11C2×Q812yes—
110C2×D4×C11#4112yes—
111C22×C4×C11—21no—
112C22×C4×C11—21no—
113C22×C4×C11—24no—
114C22×C4×C11—22no—
115C22×C4×C11—22no—
116C22×C4×C11—21no—
117C22×C4×C11—44no—
118C22×C4×C11—42no—
119C22×C4×C11—42no—
120C22×C4×C11—44no—
121C22×C4×C11—82no—
122C22×C4×C11C2×D412yes—
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2×D412yes—
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2411yescharacteristic
127C11×SD16—28no—
128C2×C8×C11—21no—
129C2×C8×C11—21no—
130C2×C8×C11—22no—
131C2×C8×C11—21no—
132C2×C8×C11—22no—
133C2×C8×C11—21no—
134C2×C8×C11—22no—
135C2×C8×C11—21no—
136C2×C8×C11C2×Q812yes—
137C11×C4⋊C4—22no—
138C11×C4⋊C4—21no—
139C11×C4⋊C4—21no—
140C11×C4⋊C4—22no—
141C11×C4⋊C4—22no—
142C11×C4⋊C4—21no—
143C11×C4⋊C4—22no—
144C11×C4⋊C4—22no—
145C11×C4⋊C4—42no—
146C11×C4⋊C4—42no—
147C11×C4⋊C4—44no—
148C11×C4⋊C4—42no—
149C11×C4⋊C4—82no—
150C11×C4⋊C4—81no—
151C11×C4⋊C4—82no—
152C11×C4⋊C4SD1614yescomplemented
153C11×C4⋊C4C2×D412yes—
154C11×C22⋊C4—24no—
155C11×C22⋊C4—44no—
156C42×C11—22no—
157C42×C11—22no—
158C42×C11—42no—
159C42×C11C2×D412yes—
160C42×C11#4112yes—
161C2×#476C2×C1111yescharacteristic
162C2×C4×SD16C2×C1111yescharacteristic
163#2567C2×C1111yescharacteristic, complemented
164D4×C4⋊C4C2×C1111yescharacteristic
165#2084C2×C1112yescomplemented
166#2066C2×C1112yescomplemented
167#1990C2×C1111yescharacteristic, complemented
168#1939C2×C1111yescharacteristic, complemented
169#1877C2×C1112yes—
170#1803C2×C1111yescharacteristic, complemented
171#1802C2×C1112yes—
172C23×C11—22no—
173C23×C11—22no—
174C23×C11—22no—
175C23×C11—41no—
176C23×C11—41no—
177C23×C11—41no—
178C23×C11—41no—
179C23×C11C22×D411yescharacteristic
180Q8×C11—22no—
181Q8×C11—22no—
182Q8×C11—41no—
183Q8×C11—41no—
184Q8×C11—84no—
185D4×C11—22no—
186D4×C11—22no—
187D4×C11—22no—
188D4×C11C22⋊Q814yes—
189C2×C4×C11—22no—
190C2×C4×C11—22no—
191C2×C4×C11—21no—
192C2×C4×C11—21no—
193C2×C4×C11—22no—
194C2×C4×C11—22no—
195C2×C4×C11—22no—
196C2×C4×C11—22no—
197C2×C4×C11—22no—
198C2×C4×C11—41no—
199C2×C4×C11—41no—
200C2×C4×C11—41no—
201C2×C4×C11—41no—
202C2×C4×C11—48no—
203C2×C4×C11—41no—
204C2×C4×C11—42no—
205C2×C4×C11—42no—
206C2×C4×C11—42no—
207C2×C4×C11—41no—
208C2×C4×C11—42no—
209C2×C4×C11—42no—
210C2×C4×C11—41no—
211C2×C4×C11—42no—
212C2×C4×C11—88no—
213C2×C4×C11#12112yes—
214C2×C4×C11#12112yes—
215C2×C4×C11C2×SD1614yes—
216C2×C4×C11C2×SD1612yes—
217C2×C4×C11#13712yes—
218C2×C4×C11C22×D411yescharacteristic
219C2×C4×C11C22×Q811yescharacteristic
220C2×C4×C11C2×#4111yescharacteristic
221C2×C4×C11C2×#4111yescharacteristic
222C2×C4×C11H(5,𝔽2)11yescharacteristic
223C2×C4×C112−1+411yescharacteristic
224C8×C11—22no—
225C8×C11—41no—
226C8×C11—42no—
227C22×SD16C22×C1111yescharacteristic
228C2×C4⋊Q8C22×C1111yescharacteristic
229C2×C4×Q8C22×C1111yescharacteristic
230C2×C4×D4C22×C1112yes—
231C2×C4×D4C22×C1111yescharacteristic
232C22×C4⋊C4—21no—
233#476—24no—
234C4×SD16—24no—
235C2×#106C22×C1112yes—
236C2×#106C22×C1111yescharacteristic
237C2×C4⋊C8C22×C1111yescharacteristic
238C2×C4⋊C8C22×C1112yes—
239C2×#103C22×C1111yescharacteristic
240C2×#103C22×C1112yes—
241C2×#102C22×C1111yescharacteristic
242C2×#102C22×C1112yes—
243C2×C4×C8C22×C1111yescharacteristic
244#395—22no—
245#391C22×C1112yes—
246#389—21no—
247#389—21no—
248#389C22×C1112yes—
249#385—22no—
250#384C22×C1112yes—
251#384C22×C1111yescharacteristic
252#380—21no—
253C4×C4⋊C4C22×C1111yescharacteristic
254#340C22×C1112yes—
255#340C22×C1112yes—
256#340C22×C1112yes—
257#336C22×C1112yes—
258C22×C11—24no—
259C22×C11—42no—
260C22×C11—42no—
261C22×C11—42no—
262C22×C11—42no—
263C22×C11—42no—
264C22×C11—42no—
265C22×C11C2×#12111yescharacteristic
266C22×C11#54611yescharacteristic
267C22×C11D4×Q811yescharacteristic
268C22×C11C22×SD1611yescharacteristic
269C22×C11C2×#13711yescharacteristic
270C22×C11#57611yescharacteristic
271C22×C11#57711yescharacteristic
272C4×C11—24no—
273C4×C11—22no—
274C4×C11—42no—
275C4×C11—42no—
276C4×C11—42no—
277C4×C11—82no—
278C4×C11—81no—
279C4×C11—82no—
280C4×C11#46114yes—
281C4×C11C2×C22⋊Q811yescharacteristic
282C4×C11#53711yescharacteristic
283C4×C11#55211yescharacteristic
284C4×C11#55411yescharacteristic
285C22×Q8—21no—
286C22×Q8C23×C1111yescharacteristic
287C22×D4C23×C1111yescharacteristic
288C23×C4—21no—
289C23×C4—22no—
290C2×SD16—22no—
291C2×SD16—22no—
292C2×SD16Q8×C1114yescomplemented
293C22×C8C23×C1112yes—
294C22×C8C23×C1111yescharacteristic
295C22×C8C23×C1111yescharacteristic
296C4⋊Q8—22no—
297C4⋊Q8—22no—
298C4×Q8—22no—
299C4×Q8—22no—
300C4×D4—24no—
301C4×D4—22no—
302C4×D4—42no—
303C4×D4D4×C1114yes—
304C2×C4⋊C4—21no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4—21no—
307C2×C4⋊C4—21no—
308C2×C4⋊C4—21no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—22no—
311C2×C4⋊C4—44no—
312C2×C4⋊C4D4×C1111yescharacteristic
313C2×C4⋊C4D4×C1111yescharacteristic
314C2×C4⋊C4C23×C1112yes—
315C2×C4⋊C4C23×C1111yescharacteristic
316C2×C4⋊C4C23×C1112yes—
317C2×C4⋊C4C23×C1111yescharacteristic
318C2×C22⋊C4—21no—
319C2×C22⋊C4—22no—
320C2×C42—21no—
321C2×C42C23×C1112yes—
322C2×C42C23×C1111yescharacteristic
323#106—22no—
324#106—24no—
325C4⋊C8—22no—
326C4⋊C8—42no—
327#103—22no—
328#103—42no—
329#102—22no—
330#102—24no—
331C4×C8—22no—
332#95—22no—
333#95—22no—
334#95—22no—
335#95D4×C1112yes—
336C2×C11—44no—
337C2×C11#241711yescharacteristic
338C2×C11C2×#46111yescharacteristic
339C2×C11#304511yescharacteristic
340C2×C11#329511yescharacteristic
341C2×C11#333111yescharacteristic
342C2×C11Q8×SD1611yescharacteristic
343C2×C11#338511yescharacteristic
344C24—21no—
345C2×Q8—21no—
346C2×Q8—21no—
347C2×Q8—21no—
348C2×Q8—21no—
349C2×Q8—21no—
350C2×Q8—42no—
351C2×Q8—81no—
352C2×Q8—81no—
353C2×Q8C2×Q8×C1112yes—
354C2×D4—21no—
355C2×D4—21no—
356C2×D4—21no—
357C2×D4C2×D4×C1112yes—
358C2×D4C2×Q8×C1112yes—
359C2×D4C11×#4112yes—
360C22×C4—21no—
361C22×C4—21no—
362C22×C4—24no—
363C22×C4—22no—
364C22×C4—22no—
365C22×C4—21no—
366C22×C4—44no—
367C22×C4—42no—
368C22×C4—42no—
369C22×C4—44no—
370C22×C4—82no—
371C22×C4C2×D4×C1112yes—
372C22×C4C2×D4×C1111yescharacteristic
373C22×C4C2×D4×C1112yes—
374C22×C4C2×D4×C1111yescharacteristic
375C22×C4C24×C1111yescharacteristic
376SD16—28no—
377C2×C8—21no—
378C2×C8—21no—
379C2×C8—21no—
380C2×C8—22no—
381C2×C8—22no—
382C2×C8—21no—
383C2×C8—22no—
384C2×C8—21no—
385C2×C8C2×Q8×C1112yes—
386C4⋊C4—22no—
387C4⋊C4—21no—
388C4⋊C4—21no—
389C4⋊C4—22no—
390C4⋊C4—22no—
391C4⋊C4—21no—
392C4⋊C4—22no—
393C4⋊C4—22no—
394C4⋊C4—42no—
395C4⋊C4—42no—
396C4⋊C4—44no—
397C4⋊C4—42no—
398C4⋊C4—82no—
399C4⋊C4—81no—
400C4⋊C4—82no—
401C4⋊C4C11×SD1614yescomplemented
402C4⋊C4C2×D4×C1112yes—
403C22⋊C4—24no—
404C22⋊C4—44no—
405C42—22no—
406C42—22no—
407C42—42no—
408C42C2×D4×C1112yes—
409C42C11×#4112yes—
410C11#2481511yescharacteristic, direct product factor, Sylow
411C23—22no—
412C23—22no—
413C23—22no—
414C23—41no—
415C23—41no—
416C23—41no—
417C23—41no—
418C23C22×D4×C1111yescharacteristic
419Q8—22no—
420Q8—22no—
421Q8—41no—
422Q8—41no—
423Q8—84no—
424D4—22no—
425D4—22no—
426D4—22no—
427D4C11×C22⋊Q814yes—
428C2×C4—22no—
429C2×C4—22no—
430C2×C4—21no—
431C2×C4—21no—
432C2×C4—22no—
433C2×C4—22no—
434C2×C4—22no—
435C2×C4—22no—
436C2×C4—22no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—41no—
441C2×C4—48no—
442C2×C4—41no—
443C2×C4—42no—
444C2×C4—42no—
445C2×C4—42no—
446C2×C4—41no—
447C2×C4—42no—
448C2×C4—42no—
449C2×C4—41no—
450C2×C4—42no—
451C2×C4—88no—
452C2×C4C11×#12112yes—
453C2×C4C11×#12112yes—
454C2×C4C2×C11×SD1614yes—
455C2×C4C2×C11×SD1612yes—
456C2×C4C11×#13712yes—
457C2×C4C22×D4×C1111yescharacteristic
458C2×C4C22×Q8×C1111yescharacteristic
459C2×C4C2×C11×#4111yescharacteristic
460C2×C4C2×C11×#4111yescharacteristic
461C2×C4C11×H(5,𝔽2)11yescharacteristic
462C2×C4C11×2−1+411yescharacteristic
463C8—22no—
464C8—41no—
465C8—42no—
466C22—24no—
467C22—42no—
468C22—42no—
469C22—42no—
470C22—42no—
471C22—42no—
472C22—42no—
473C22C2×C11×#12111yescharacteristic
474C22C11×#54611yescharacteristic
475C22D4×Q8×C1111yescharacteristic
476C22C22×C11×SD1611yescharacteristic
477C22C2×C11×#13711yescharacteristic
478C22C11×#57611yescharacteristic
479C22C11×#57711yescharacteristic
480C4—24no—
481C4—22no—
482C4—42no—
483C4—42no—
484C4—42no—
485C4—82no—
486C4—82no—
487C4—81no—
488C4C11×#46114yes—
489C4C2×C11×C22⋊Q811yescharacteristic
490C4C11×#53711yescharacteristic
491C4C11×#55211yescharacteristic
492C4C11×#55411yescharacteristic
493C2—44no—
494C2C11×#241711yescharacteristic
495C2C2×C11×#46111yescharacteristic
496C2C11×#304511yescharacteristic
497C2C11×#329511yescharacteristic
498C2C11×#333111yescharacteristic
499C2Q8×C11×SD1611yescharacteristic
500C2C11×#338511yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC22×D4×C11C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C4×C11×C4⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
3. C11×#2567C2semidirect
5. C11×#2084C2semidirect
6. C11×#2066C2semidirect
7. C11×#1990C2semidirect
8. C11×#1939C2semidirect
10. C11×#1803C2semidirect
50. C2×C11×SD16Q8semidirect
94. #24815C11direct (N × H)
152. C11×C4⋊C4SD16semidirect
163. #2567C2×C11semidirect
165. #2084C2×C11semidirect
166. #2066C2×C11semidirect
167. #1990C2×C11semidirect
168. #1939C2×C11semidirect
170. #1803C2×C11semidirect
292. C2×SD16Q8×C11semidirect
401. C4⋊C4C11×SD16semidirect
410. C11#24815direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4762
C2×C4×C11×SD162
C11×#25672
D4×C11×C4⋊C42
C11×#20842
C11×#20662
C11×#19902
C11×#19392
C11×#18772
C11×#18032
C11×#18022
#2481511