Finite Group Databasebeta

← C11×#24785 #14601978

Subgroups — C11×#24785 #14601978

Order 2816.

940 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#470C211yesmaximal, characteristic, complemented
2C2×C11×#467C211yesmaximal, characteristic, complemented
3C2×C11×#435C211yesmaximal, characteristic
4C2×C11×#427C211yesmaximal, characteristic, complemented
5C11×#2415C212yesmaximal
6C11×#2068C212yesmaximal, complemented
7C11×#2036C212yesmaximal, complemented
8C11×#1971C211yesmaximal, characteristic, complemented
9C11×#1944C211yesmaximal, characteristic, complemented
10C11×#1873C212yesmaximal, complemented
11C11×#1809C211yesmaximal, characteristic, complemented
12C22×C11×Q16C2211yescharacteristic
13C22×C11×M16C2211yescharacteristic
14C23×C8×C11C2211yescharacteristic
15C2×C11×C22⋊Q8C2212yes—
16C2×C11×C22⋊Q8C2212yes—
17C2×C4×D4×C11C2211yescharacteristic
18C2×C11×#117C2212yes—
19C11×#470—24no—
20C11×#467—24no—
21C11×#435—24no—
22C11×#427—24no—
23C2×C11×#107C2212yes—
24C2×C11×#107C2211yescharacteristic
25C2×C11×#106C2211yescharacteristic
26C2×C11×#106C2211yescharacteristic
27C2×C11×C4⋊C8C2211yescharacteristic
28C2×C11×#103C2212yes—
29C2×C11×#103C2212yes—
30C2×C11×#103C2212yes—
31C2×C11×C22⋊C8C2211yescharacteristic
32C2×C11×C22⋊C8C2211yescharacteristic
33C2×C11×#97C2211yescharacteristic
34C11×#397—22no—
35C11×#394—22no—
36C11×#391C2212yes—
37C11×#389—22no—
38C11×#389C2212yes—
39C11×#388—22no—
40C11×#380C2212yes—
41C11×#340C2212yes—
42C11×#340C2212yes—
43C22×Q8×C11C2312yes—
44C22×D4×C11D411yescharacteristic
45C23×C4×C11C2311yescharacteristic
46C23×C4×C11C2311yescharacteristic
47C2×C11×Q16—22no—
48C2×C11×Q16—22no—
49C2×C11×Q16—22no—
50C2×C11×M16—22no—
51C2×C11×M16—22no—
52C2×C11×M16—22no—
53C22×C8×C11—22no—
54C22×C8×C11—22no—
55C22×C8×C11D414yes—
56C22×C8×C11C2311yescharacteristic
57C22×C8×C11C2311yescharacteristic
58C22×C8×C11C2311yescharacteristic
59C22×C8×C11C2311yescharacteristic
60C11×C22⋊Q8—24no—
61C11×C22⋊Q8—24no—
62C11×C22⋊Q8—24no—
63C11×C22⋊Q8—42no—
64C4×D4×C11—22no—
65C4×D4×C11—22no—
66C11×#117—24no—
67C11×#117—42no—
68C2×C11×C4⋊C4—22no—
69C2×C11×C4⋊C4—22no—
70C2×C11×C4⋊C4—22no—
71C2×C11×C4⋊C4D411yescharacteristic
72C2×C11×C4⋊C4C2312yes—
73C2×C11×C4⋊C4C2312yes—
74C2×C11×C4⋊C4C2312yes—
75C2×C11×C22⋊C4—22no—
76C2×C11×C22⋊C4—22no—
77C2×C11×C22⋊C4—22no—
78C2×C11×C22⋊C4—22no—
79C2×C11×C22⋊C4D411yescharacteristic
80C2×C11×C22⋊C4D411yescharacteristic
81C2×C42×C11—22no—
82C2×C42×C11C2311yescharacteristic
83C11×#107—22no—
84C11×#107—24no—
85C11×#106—22no—
86C11×#106D414yescomplemented
87C11×C4⋊C8—22no—
88C11×#103—24no—
89C11×#103—24no—
90C11×#103—42no—
91C11×C22⋊C8—22no—
92C11×C22⋊C8—22no—
93C11×#97—22no—
94C11×#95—22no—
95C11×#95—22no—
96C11×#95—22no—
97C11×#95—22no—
98#24785C1111yesmaximal, characteristic, direct product factor, Sylow
99C24×C11C2×D411yescharacteristic
100C24×C11C2×D411yescharacteristic
101C2×Q8×C11—22no—
102C2×Q8×C11—22no—
103C2×Q8×C11—22no—
104C2×Q8×C11—22no—
105C2×Q8×C11—22no—
106C2×Q8×C11—22no—
107C2×D4×C11—22no—
108C2×D4×C11—42no—
109C22×C4×C11—21no—
110C22×C4×C11—21no—
111C22×C4×C11—21no—
112C22×C4×C11—21no—
113C22×C4×C11—22no—
114C22×C4×C11—21no—
115C22×C4×C11—21no—
116C22×C4×C11—21no—
117C22×C4×C11—21no—
118C22×C4×C11—21no—
119C22×C4×C11—21no—
120C22×C4×C11—22no—
121C22×C4×C11—22no—
122C22×C4×C11—22no—
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2×D411yescharacteristic
127C22×C4×C11C2×D412yes—
128C22×C4×C11#4112yes—
129C22×C4×C11C2411yescharacteristic
130C11×Q16—44no—
131C11×M16—44no—
132C2×C8×C11—28no—
133C2×C8×C11—21no—
134C2×C8×C11—21no—
135C2×C8×C11—21no—
136C2×C8×C11—21no—
137C2×C8×C11—21no—
138C2×C8×C11—21no—
139C2×C8×C11—21no—
140C2×C8×C11—21no—
141C2×C8×C11C2×D412yes—
142C2×C8×C11C2×D412yes—
143C2×C8×C11C2×D412yes—
144C2×C8×C11#4112yes—
145C11×C4⋊C4—22no—
146C11×C4⋊C4—22no—
147C11×C4⋊C4—22no—
148C11×C4⋊C4—22no—
149C11×C4⋊C4—22no—
150C11×C4⋊C4—22no—
151C11×C4⋊C4—44no—
152C11×C4⋊C4—44no—
153C11×C4⋊C4—44no—
154C11×C4⋊C4C2×D414yes—
155C11×C22⋊C4—22no—
156C11×C22⋊C4—22no—
157C11×C22⋊C4—44no—
158C11×C22⋊C4—44no—
159C11×C22⋊C4—44no—
160C11×C22⋊C4—44no—
161C42×C11—21no—
162C42×C11—21no—
163C42×C11—44no—
164C2×#470C2×C1111yescharacteristic, complemented
165C2×#467C2×C1111yescharacteristic, complemented
166C2×#435C2×C1111yescharacteristic
167C2×#427C2×C1111yescharacteristic, complemented
168#2415C2×C1112yes—
169#2068C2×C1112yescomplemented
170#2036C2×C1112yescomplemented
171#1971C2×C1111yescharacteristic, complemented
172#1944C2×C1111yescharacteristic, complemented
173#1873C2×C1112yescomplemented
174#1809C2×C1111yescharacteristic, complemented
175C23×C11—21no—
176C23×C11—21no—
177C23×C11—22no—
178C23×C11—22no—
179C23×C11—21no—
180C23×C11—21no—
181C23×C11—21no—
182C23×C11—22no—
183C23×C11—22no—
184C23×C11#12112yes—
185C23×C11C22×D411yescharacteristic
186Q8×C11—42no—
187Q8×C11—42no—
188Q8×C11—42no—
189Q8×C11—42no—
190D4×C11—44no—
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—21no—
198C2×C4×C11—21no—
199C2×C4×C11—21no—
200C2×C4×C11—24no—
201C2×C4×C11—21no—
202C2×C4×C11—21no—
203C2×C4×C11—22no—
204C2×C4×C11—22no—
205C2×C4×C11—42no—
206C2×C4×C11—42no—
207C2×C4×C11—41no—
208C2×C4×C11—41no—
209C2×C4×C11—41no—
210C2×C4×C11—41no—
211C2×C4×C11—42no—
212C2×C4×C11—42no—
213C2×C4×C11—42no—
214C2×C4×C11—42no—
215C2×C4×C11—42no—
216C2×C4×C11—42no—
217C2×C4×C11—42no—
218C2×C4×C11—42no—
219C2×C4×C11—42no—
220C2×C4×C11#12112yes—
221C2×C4×C11C22×D411yescharacteristic
222C2×C4×C11C22×D411yescharacteristic
223C2×C4×C11C2×#4111yescharacteristic
224C2×C4×C11C2×#4111yescharacteristic
225C2×C4×C11H(5,𝔽2)11yescharacteristic
226C2×C4×C112−1+411yescharacteristic
227C8×C11—22no—
228C8×C11—41no—
229C8×C11—41no—
230C8×C11#12114yes—
231C22×Q16C22×C1111yescharacteristic
232C22×M16C22×C1111yescharacteristic
233C23×C8C22×C1111yescharacteristic
234C2×C22⋊Q8C22×C1112yes—
235C2×C22⋊Q8C22×C1112yes—
236C2×C4×D4C22×C1111yescharacteristic
237C2×#117C22×C1112yes—
238#470—24no—
239#467—24no—
240#435—24no—
241#427—24no—
242C2×#107C22×C1111yescharacteristic
243C2×#107C22×C1112yes—
244C2×#106C22×C1111yescharacteristic
245C2×#106C22×C1111yescharacteristic
246C2×C4⋊C8C22×C1111yescharacteristic
247C2×#103C22×C1112yes—
248C2×#103C22×C1112yes—
249C2×#103C22×C1112yes—
250C2×C22⋊C8C22×C1111yescharacteristic
251C2×C22⋊C8C22×C1111yescharacteristic
252C2×#97C22×C1111yescharacteristic
253#397—22no—
254#394—22no—
255#391C22×C1112yes—
256#389—22no—
257#389C22×C1112yes—
258#388—22no—
259#380C22×C1112yes—
260#340C22×C1112yes—
261#340C22×C1112yes—
262C22×C11—22no—
263C22×C11—22no—
264C22×C11—22no—
265C22×C11—42no—
266C22×C11—42no—
267C22×C11—42no—
268C22×C11—41no—
269C22×C11—42no—
270C22×C11—41no—
271C22×C11—41no—
272C22×C11C2×#12111yescharacteristic
273C22×C11D4211yescharacteristic
274C22×C11#54711yescharacteristic
275C22×C11#57512yes—
276C22×C11#57812yes—
277C4×C11—22no—
278C4×C11—41no—
279C4×C11—44no—
280C4×C11—41no—
281C4×C11—41no—
282C4×C11—82no—
283C4×C11—82no—
284C4×C11—82no—
285C4×C11C2×#12111yescharacteristic
286C4×C11#53711yescharacteristic
287C4×C11#54811yescharacteristic
288C4×C11#55311yescharacteristic
289C22×Q8C23×C1112yes—
290C22×D4D4×C1111yescharacteristic
291C23×C4C23×C1111yescharacteristic
292C23×C4C23×C1111yescharacteristic
293C2×Q16—22no—
294C2×Q16—22no—
295C2×Q16—22no—
296C2×M16—22no—
297C2×M16—22no—
298C2×M16—22no—
299C22×C8—22no—
300C22×C8—22no—
301C22×C8D4×C1114yes—
302C22×C8C23×C1111yescharacteristic
303C22×C8C23×C1111yescharacteristic
304C22×C8C23×C1111yescharacteristic
305C22×C8C23×C1111yescharacteristic
306C22⋊Q8—24no—
307C22⋊Q8—24no—
308C22⋊Q8—24no—
309C22⋊Q8—42no—
310C4×D4—22no—
311C4×D4—22no—
312#117—24no—
313#117—42no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—22no—
316C2×C4⋊C4—22no—
317C2×C4⋊C4D4×C1111yescharacteristic
318C2×C4⋊C4C23×C1112yes—
319C2×C4⋊C4C23×C1112yes—
320C2×C4⋊C4C23×C1112yes—
321C2×C22⋊C4—22no—
322C2×C22⋊C4—22no—
323C2×C22⋊C4—22no—
324C2×C22⋊C4—22no—
325C2×C22⋊C4D4×C1111yescharacteristic
326C2×C22⋊C4D4×C1111yescharacteristic
327C2×C42—22no—
328C2×C42C23×C1111yescharacteristic
329#107—22no—
330#107—24no—
331#106—22no—
332#106D4×C1114yescomplemented
333C4⋊C8—22no—
334#103—24no—
335#103—24no—
336#103—42no—
337C22⋊C8—22no—
338C22⋊C8—22no—
339#97—22no—
340#95—22no—
341#95—22no—
342#95—22no—
343#95—22no—
344C2×C11—42no—
345C2×C11—81no—
346C2×C11#241611yescharacteristic
347C2×C11#305411yescharacteristic
348C2×C11#305911yescharacteristic
349C2×C11#326912yes—
350C2×C11#334912yes—
351C24C2×D4×C1111yescharacteristic
352C24C2×D4×C1111yescharacteristic
353C2×Q8—22no—
354C2×Q8—22no—
355C2×Q8—22no—
356C2×Q8—22no—
357C2×Q8—22no—
358C2×Q8—22no—
359C2×D4—22no—
360C2×D4—42no—
361C22×C4—21no—
362C22×C4—21no—
363C22×C4—21no—
364C22×C4—21no—
365C22×C4—22no—
366C22×C4—21no—
367C22×C4—21no—
368C22×C4—21no—
369C22×C4—21no—
370C22×C4—21no—
371C22×C4—21no—
372C22×C4—22no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4C2×D4×C1111yescharacteristic
376C22×C4C2×D4×C1111yescharacteristic
377C22×C4C2×D4×C1111yescharacteristic
378C22×C4C2×D4×C1111yescharacteristic
379C22×C4C2×D4×C1112yes—
380C22×C4C11×#4112yes—
381C22×C4C24×C1111yescharacteristic
382Q16—44no—
383M16—44no—
384C2×C8—21no—
385C2×C8—21no—
386C2×C8—28no—
387C2×C8—21no—
388C2×C8—21no—
389C2×C8—21no—
390C2×C8—21no—
391C2×C8—21no—
392C2×C8—21no—
393C2×C8C2×D4×C1112yes—
394C2×C8C2×D4×C1112yes—
395C2×C8C2×D4×C1112yes—
396C2×C8C11×#4112yes—
397C4⋊C4—22no—
398C4⋊C4—22no—
399C4⋊C4—22no—
400C4⋊C4—22no—
401C4⋊C4—22no—
402C4⋊C4—22no—
403C4⋊C4—44no—
404C4⋊C4—44no—
405C4⋊C4—44no—
406C4⋊C4C2×D4×C1114yes—
407C22⋊C4—22no—
408C22⋊C4—22no—
409C22⋊C4—44no—
410C22⋊C4—44no—
411C22⋊C4—44no—
412C22⋊C4—44no—
413C42—21no—
414C42—21no—
415C42—44no—
416C11#2478511yescharacteristic, direct product factor, Sylow
417C23—21no—
418C23—21no—
419C23—22no—
420C23—22no—
421C23—21no—
422C23—21no—
423C23—21no—
424C23—22no—
425C23—22no—
426C23C11×#12112yes—
427C23C22×D4×C1111yescharacteristic
428Q8—42no—
429Q8—42no—
430Q8—42no—
431Q8—42no—
432D4—44no—
433C2×C4—21no—
434C2×C4—21no—
435C2×C4—22no—
436C2×C4—22no—
437C2×C4—22no—
438C2×C4—22no—
439C2×C4—21no—
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—24no—
443C2×C4—21no—
444C2×C4—21no—
445C2×C4—22no—
446C2×C4—22no—
447C2×C4—42no—
448C2×C4—42no—
449C2×C4—41no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—41no—
453C2×C4—42no—
454C2×C4—42no—
455C2×C4—42no—
456C2×C4—42no—
457C2×C4—42no—
458C2×C4—42no—
459C2×C4—42no—
460C2×C4—42no—
461C2×C4—42no—
462C2×C4C11×#12112yes—
463C2×C4C22×D4×C1111yescharacteristic
464C2×C4C22×D4×C1111yescharacteristic
465C2×C4C2×C11×#4111yescharacteristic
466C2×C4C2×C11×#4111yescharacteristic
467C2×C4C11×H(5,𝔽2)11yescharacteristic
468C2×C4C11×2−1+411yescharacteristic
469C8—22no—
470C8—41no—
471C8—41no—
472C8C11×#12114yes—
473C22—22no—
474C22—22no—
475C22—22no—
476C22—42no—
477C22—42no—
478C22—41no—
479C22—42no—
480C22—41no—
481C22—41no—
482C22—42no—
483C22C2×C11×#12111yescharacteristic
484C22D42×C1111yescharacteristic
485C22C11×#54711yescharacteristic
486C22C11×#57512yes—
487C22C11×#57812yes—
488C4—22no—
489C4—41no—
490C4—44no—
491C4—41no—
492C4—41no—
493C4—82no—
494C4—82no—
495C4—82no—
496C4C2×C11×#12111yescharacteristic
497C4C11×#53711yescharacteristic
498C4C11×#54811yescharacteristic
499C4C11×#55311yescharacteristic
500C2—42no—
501C2—81no—
502C2C11×#241611yescharacteristic
503C2C11×#305411yescharacteristic
504C2C11×#305911yescharacteristic
505C2C11×#326912yes—
506C2C11×#334912yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC22×D4×C11D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C4×D4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#470C2semidirect
2. C2×C11×#467C2semidirect
4. C2×C11×#427C2semidirect
6. C11×#2068C2semidirect
7. C11×#2036C2semidirect
8. C11×#1971C2semidirect
9. C11×#1944C2semidirect
10. C11×#1873C2semidirect
11. C11×#1809C2semidirect
86. C11×#106D4semidirect
98. #24785C11direct (N × H)
164. C2×#470C2×C11semidirect
165. C2×#467C2×C11semidirect
167. C2×#427C2×C11semidirect
169. #2068C2×C11semidirect
170. #2036C2×C11semidirect
171. #1971C2×C11semidirect
172. #1944C2×C11semidirect
173. #1873C2×C11semidirect
174. #1809C2×C11semidirect
332. #106D4×C11semidirect
416. C11#24785direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4702
C2×C11×#4672
C2×C11×#4352
C2×C11×#4272
C11×#24152
C11×#20682
C11×#20362
C11×#19712
C11×#19442
C11×#18732
C11×#18092
#2478511