Finite Group Databasebeta

← C11×#24779 #14601972

Subgroups — C11×#24779 #14601972

Order 2816.

966 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#467C211yesmaximal, characteristic, complemented
2C2×C11×#467C211yesmaximal, characteristic, complemented
3C2×C8×D4×C11C211yesmaximal, characteristic
4C2×C11×#427C211yesmaximal, characteristic, complemented
5C11×#2415C212yesmaximal
6C11×#2066C212yesmaximal, complemented
7C11×#2035C212yesmaximal, complemented
8C11×#1969C211yesmaximal, characteristic, complemented
9C11×#1942C211yesmaximal, characteristic, complemented
10C11×#1873C212yesmaximal, complemented
11C11×#1808C211yesmaximal, characteristic, complemented
12C22×C11×Q16C2211yescharacteristic
13C23×C8×C11C2211yescharacteristic
14C23×C8×C11C2211yescharacteristic
15C2×C11×C22⋊Q8C2212yes—
16C2×C11×C22⋊Q8C2212yes—
17C2×C4×D4×C11C2211yescharacteristic
18C2×C11×#117C2212yes—
19C11×#467—24no—
20C11×#467—24no—
21C8×D4×C11—24no—
22C11×#427—24no—
23C2×C11×#107C2211yescharacteristic
24C2×C11×#107C2211yescharacteristic
25C2×C11×#107C2211yescharacteristic
26C2×C11×#106C2212yes—
27C2×C11×C4⋊C8C2211yescharacteristic
28C2×C11×#103C2212yes—
29C2×C11×#103C2212yes—
30C2×C11×#103C2212yes—
31C2×C11×C22⋊C8C2211yescharacteristic
32C2×C11×C22⋊C8C2211yescharacteristic
33C2×C4×C8×C11C2211yescharacteristic
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—
50C22×C8×C11—22no—
51C22×C8×C11—22no—
52C22×C8×C11—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—22no—
85C11×#107D414yescomplemented
86C11×#106—24no—
87C11×C4⋊C8—22no—
88C11×#103—24no—
89C11×#103—24no—
90C11×#103—42no—
91C11×C22⋊C8—22no—
92C11×C22⋊C8—22no—
93C4×C8×C11—22no—
94C11×#95—22no—
95C11×#95—22no—
96C11×#95—22no—
97C11×#95—22no—
98#24779C1111yesmaximal, 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—22no—
109C2×D4×C11—22no—
110C22×C4×C11—21no—
111C22×C4×C11—21no—
112C22×C4×C11—21no—
113C22×C4×C11—21no—
114C22×C4×C11—22no—
115C22×C4×C11—21no—
116C22×C4×C11—21no—
117C22×C4×C11—21no—
118C22×C4×C11—21no—
119C22×C4×C11—21no—
120C22×C4×C11—21no—
121C22×C4×C11—22no—
122C22×C4×C11—22no—
123C22×C4×C11—22no—
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2×D411yescharacteristic
127C22×C4×C11C2×D412yes—
128C22×C4×C11C2×D411yescharacteristic
129C22×C4×C11#4112yes—
130C22×C4×C11C2411yescharacteristic
131C11×Q16—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×C11—44no—
142C2×C8×C11C2×D412yes—
143C2×C8×C11C2×D412yes—
144C2×C8×C11C2×D412yes—
145C2×C8×C11#4112yes—
146C11×C4⋊C4—22no—
147C11×C4⋊C4—22no—
148C11×C4⋊C4—22no—
149C11×C4⋊C4—22no—
150C11×C4⋊C4—22no—
151C11×C4⋊C4—22no—
152C11×C4⋊C4—44no—
153C11×C4⋊C4—44no—
154C11×C4⋊C4—44no—
155C11×C4⋊C4C2×D414yes—
156C11×C22⋊C4—22no—
157C11×C22⋊C4—22no—
158C11×C22⋊C4—44no—
159C11×C22⋊C4—44no—
160C11×C22⋊C4—44no—
161C11×C22⋊C4—44no—
162C42×C11—21no—
163C42×C11—21no—
164C42×C11—44no—
165C2×#467C2×C1111yescharacteristic, complemented
166C2×#467C2×C1111yescharacteristic, complemented
167C2×C8×D4C2×C1111yescharacteristic
168C2×#427C2×C1111yescharacteristic, complemented
169#2415C2×C1112yes—
170#2066C2×C1112yescomplemented
171#2035C2×C1112yescomplemented
172#1969C2×C1111yescharacteristic, complemented
173#1942C2×C1111yescharacteristic, complemented
174#1873C2×C1112yescomplemented
175#1808C2×C1111yescharacteristic, complemented
176C23×C11—21no—
177C23×C11—21no—
178C23×C11—21no—
179C23×C11—21no—
180C23×C11—21no—
181C23×C11—21no—
182C23×C11—21no—
183C23×C11—21no—
184C23×C11—21no—
185C23×C11—21no—
186C23×C11—21no—
187C23×C11—21no—
188C23×C11#12112yes—
189C23×C11#13512yes—
190C23×C11C22×D411yescharacteristic
191Q8×C11—42no—
192Q8×C11—42no—
193Q8×C11—42no—
194Q8×C11—42no—
195D4×C11—28no—
196C2×C4×C11—21no—
197C2×C4×C11—21no—
198C2×C4×C11—21no—
199C2×C4×C11—21no—
200C2×C4×C11—22no—
201C2×C4×C11—22no—
202C2×C4×C11—22no—
203C2×C4×C11—22no—
204C2×C4×C11—21no—
205C2×C4×C11—21no—
206C2×C4×C11—24no—
207C2×C4×C11—21no—
208C2×C4×C11—21no—
209C2×C4×C11—21no—
210C2×C4×C11—21no—
211C2×C4×C11—42no—
212C2×C4×C11—42no—
213C2×C4×C11—41no—
214C2×C4×C11—41no—
215C2×C4×C11—41no—
216C2×C4×C11—41no—
217C2×C4×C11—42no—
218C2×C4×C11—42no—
219C2×C4×C11—42no—
220C2×C4×C11—42no—
221C2×C4×C11—42no—
222C2×C4×C11—42no—
223C2×C4×C11—42no—
224C2×C4×C11—42no—
225C2×C4×C11—42no—
226C2×C4×C11#12112yes—
227C2×C4×C11#13512yes—
228C2×C4×C11C22×D411yescharacteristic
229C2×C4×C11C22×D411yescharacteristic
230C2×C4×C11C2×#4111yescharacteristic
231C2×C4×C11C2×#4111yescharacteristic
232C2×C4×C11H(5,𝔽2)11yescharacteristic
233C2×C4×C112−1+411yescharacteristic
234C8×C11—22no—
235C8×C11—41no—
236C8×C11—41no—
237C8×C11#12114yes—
238C22×Q16C22×C1111yescharacteristic
239C23×C8C22×C1111yescharacteristic
240C23×C8C22×C1111yescharacteristic
241C2×C22⋊Q8C22×C1112yes—
242C2×C22⋊Q8C22×C1112yes—
243C2×C4×D4C22×C1111yescharacteristic
244C2×#117C22×C1112yes—
245#467—24no—
246#467—24no—
247C8×D4—24no—
248#427—24no—
249C2×#107C22×C1111yescharacteristic
250C2×#107C22×C1111yescharacteristic
251C2×#107C22×C1111yescharacteristic
252C2×#106C22×C1112yes—
253C2×C4⋊C8C22×C1111yescharacteristic
254C2×#103C22×C1112yes—
255C2×#103C22×C1112yes—
256C2×#103C22×C1112yes—
257C2×C22⋊C8C22×C1111yescharacteristic
258C2×C22⋊C8C22×C1111yescharacteristic
259C2×C4×C8C22×C1111yescharacteristic
260#397—22no—
261#394—22no—
262#391C22×C1112yes—
263#389—22no—
264#389C22×C1112yes—
265#388—22no—
266#380C22×C1112yes—
267#340C22×C1112yes—
268#340C22×C1112yes—
269C22×C11—22no—
270C22×C11—22no—
271C22×C11—22no—
272C22×C11—22no—
273C22×C11—22no—
274C22×C11—22no—
275C22×C11—41no—
276C22×C11—41no—
277C22×C11—41no—
278C22×C11—41no—
279C22×C11—41no—
280C22×C11—41no—
281C22×C11—41no—
282C22×C11—41no—
283C22×C11C2×#12111yescharacteristic
284C22×C11D4211yescharacteristic
285C22×C11#54711yescharacteristic
286C22×C11C2×#13511yescharacteristic
287C22×C11C2×#13511yescharacteristic
288C22×C11#57811yescharacteristic
289C22×C11#57811yescharacteristic
290C4×C11—22no—
291C4×C11—22no—
292C4×C11—41no—
293C4×C11—44no—
294C4×C11—41no—
295C4×C11—82no—
296C4×C11—82no—
297C4×C11—82no—
298C4×C11C2×#12111yescharacteristic
299C4×C11#53711yescharacteristic
300C4×C11#54811yescharacteristic
301C4×C11#55311yescharacteristic
302C22×Q8C23×C1112yes—
303C22×D4D4×C1111yescharacteristic
304C23×C4C23×C1111yescharacteristic
305C23×C4C23×C1111yescharacteristic
306C2×Q16—22no—
307C2×Q16—22no—
308C2×Q16—22no—
309C22×C8—22no—
310C22×C8—22no—
311C22×C8—22no—
312C22×C8—22no—
313C22×C8—22no—
314C22×C8D4×C1114yes—
315C22×C8C23×C1111yescharacteristic
316C22×C8C23×C1111yescharacteristic
317C22×C8C23×C1111yescharacteristic
318C22×C8C23×C1111yescharacteristic
319C22⋊Q8—24no—
320C22⋊Q8—24no—
321C22⋊Q8—24no—
322C22⋊Q8—42no—
323C4×D4—22no—
324C4×D4—22no—
325#117—24no—
326#117—42no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—22no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4D4×C1111yescharacteristic
331C2×C4⋊C4C23×C1112yes—
332C2×C4⋊C4C23×C1112yes—
333C2×C4⋊C4C23×C1112yes—
334C2×C22⋊C4—22no—
335C2×C22⋊C4—22no—
336C2×C22⋊C4—22no—
337C2×C22⋊C4—22no—
338C2×C22⋊C4D4×C1111yescharacteristic
339C2×C22⋊C4D4×C1111yescharacteristic
340C2×C42—22no—
341C2×C42C23×C1111yescharacteristic
342#107—22no—
343#107—22no—
344#107D4×C1114yescomplemented
345#106—24no—
346C4⋊C8—22no—
347#103—24no—
348#103—24no—
349#103—42no—
350C22⋊C8—22no—
351C22⋊C8—22no—
352C4×C8—22no—
353#95—22no—
354#95—22no—
355#95—22no—
356#95—22no—
357C2×C11—42no—
358C2×C11—42no—
359C2×C11#241611yescharacteristic
360C2×C11#305011yescharacteristic
361C2×C11#305911yescharacteristic
362C2×C11#328311yescharacteristic
363C2×C11#328511yescharacteristic
364C2×C11#333611yescharacteristic
365C2×C11#334211yescharacteristic
366C24C2×D4×C1111yescharacteristic
367C24C2×D4×C1111yescharacteristic
368C2×Q8—22no—
369C2×Q8—22no—
370C2×Q8—22no—
371C2×Q8—22no—
372C2×Q8—22no—
373C2×Q8—22no—
374C2×D4—22no—
375C2×D4—22no—
376C2×D4—22no—
377C22×C4—21no—
378C22×C4—21no—
379C22×C4—21no—
380C22×C4—21no—
381C22×C4—22no—
382C22×C4—21no—
383C22×C4—21no—
384C22×C4—21no—
385C22×C4—21no—
386C22×C4—21no—
387C22×C4—21no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4C2×D4×C1111yescharacteristic
392C22×C4C2×D4×C1111yescharacteristic
393C22×C4C2×D4×C1111yescharacteristic
394C22×C4C2×D4×C1112yes—
395C22×C4C2×D4×C1111yescharacteristic
396C22×C4C11×#4112yes—
397C22×C4C24×C1111yescharacteristic
398Q16—44no—
399C2×C8—21no—
400C2×C8—21no—
401C2×C8—28no—
402C2×C8—21no—
403C2×C8—21no—
404C2×C8—21no—
405C2×C8—21no—
406C2×C8—21no—
407C2×C8—21no—
408C2×C8—44no—
409C2×C8C2×D4×C1112yes—
410C2×C8C2×D4×C1112yes—
411C2×C8C2×D4×C1112yes—
412C2×C8C11×#4112yes—
413C4⋊C4—22no—
414C4⋊C4—22no—
415C4⋊C4—22no—
416C4⋊C4—22no—
417C4⋊C4—22no—
418C4⋊C4—22no—
419C4⋊C4—44no—
420C4⋊C4—44no—
421C4⋊C4—44no—
422C4⋊C4C2×D4×C1114yes—
423C22⋊C4—22no—
424C22⋊C4—22no—
425C22⋊C4—44no—
426C22⋊C4—44no—
427C22⋊C4—44no—
428C22⋊C4—44no—
429C42—21no—
430C42—21no—
431C42—44no—
432C11#2477911yescharacteristic, direct product factor, Sylow
433C23—21no—
434C23—21no—
435C23—21no—
436C23—21no—
437C23—21no—
438C23—21no—
439C23—21no—
440C23—21no—
441C23—21no—
442C23—21no—
443C23—21no—
444C23—21no—
445C23C11×#12112yes—
446C23C11×#13512yes—
447C23C22×D4×C1111yescharacteristic
448Q8—42no—
449Q8—42no—
450Q8—42no—
451Q8—42no—
452D4—28no—
453C2×C4—21no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—21no—
457C2×C4—22no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—21no—
462C2×C4—21no—
463C2×C4—24no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—21no—
467C2×C4—21no—
468C2×C4—42no—
469C2×C4—42no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—42no—
475C2×C4—42no—
476C2×C4—42no—
477C2×C4—42no—
478C2×C4—42no—
479C2×C4—42no—
480C2×C4—42no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4C11×#12112yes—
484C2×C4C11×#13512yes—
485C2×C4C22×D4×C1111yescharacteristic
486C2×C4C22×D4×C1111yescharacteristic
487C2×C4C2×C11×#4111yescharacteristic
488C2×C4C2×C11×#4111yescharacteristic
489C2×C4C11×H(5,𝔽2)11yescharacteristic
490C2×C4C11×2−1+411yescharacteristic
491C8—22no—
492C8—41no—
493C8—41no—
494C8C11×#12114yes—
495C22—22no—
496C22—22no—
497C22—22no—
498C22—22no—
499C22—22no—
500C22—22no—
501C22—41no—
502C22—41no—
503C22—41no—
504C22—41no—
505C22—41no—
506C22—41no—
507C22—41no—
508C22—41no—
509C22C2×C11×#12111yescharacteristic
510C22D42×C1111yescharacteristic
511C22C11×#54711yescharacteristic
512C22C2×C11×#13511yescharacteristic
513C22C2×C11×#13511yescharacteristic
514C22C11×#57811yescharacteristic
515C22C11×#57811yescharacteristic
516C4—22no—
517C4—22no—
518C4—41no—
519C4—44no—
520C4—41no—
521C4—82no—
522C4—82no—
523C4—82no—
524C4C2×C11×#12111yescharacteristic
525C4C11×#53711yescharacteristic
526C4C11×#54811yescharacteristic
527C4C11×#55311yescharacteristic
528C2—42no—
529C2—42no—
530C2C11×#241611yescharacteristic
531C2C11×#305011yescharacteristic
532C2C11×#305911yescharacteristic
533C2C11×#328311yescharacteristic
534C2C11×#328511yescharacteristic
535C2C11×#333611yescharacteristic
536C2C11×#334211yescharacteristic
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×#467C2semidirect
2. C2×C11×#467C2semidirect
4. C2×C11×#427C2semidirect
6. C11×#2066C2semidirect
7. C11×#2035C2semidirect
8. C11×#1969C2semidirect
9. C11×#1942C2semidirect
10. C11×#1873C2semidirect
11. C11×#1808C2semidirect
85. C11×#107D4semidirect
98. #24779C11direct (N × H)
165. C2×#467C2×C11semidirect
166. C2×#467C2×C11semidirect
168. C2×#427C2×C11semidirect
170. #2066C2×C11semidirect
171. #2035C2×C11semidirect
172. #1969C2×C11semidirect
173. #1942C2×C11semidirect
174. #1873C2×C11semidirect
175. #1808C2×C11semidirect
344. #107D4×C11semidirect
432. C11#24779direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4672
C2×C8×D4×C112
C2×C11×#4272
C11×#24152
C11×#20662
C11×#20352
C11×#19692
C11×#19422
C11×#18732
C11×#18082
#2477911