Finite Group Databasebeta

← C11×#24749 #14601942

Subgroups — C11×#24749 #14601942

Order 2816.

1044 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#463C212yesmaximal, complemented
2C2×C11×#459C211yesmaximal, characteristic
3C2×C11×#440C211yesmaximal, characteristic, complemented
4C11×#2548C211yesmaximal, characteristic, complemented
5C11×#2349C211yesmaximal, characteristic, complemented
6C11×#2067C212yesmaximal, complemented
7C11×#2042C212yesmaximal, complemented
8C11×#1961C211yesmaximal, characteristic, complemented
9C11×#1940C211yesmaximal, characteristic, complemented
10C11×#1879C212yesmaximal, complemented
11C11×#1805C211yesmaximal, characteristic, complemented
12C22×C11×SD16C2211yescharacteristic
13C22×C11×D8C2212yes—
14C2×C11×#127C2211yescharacteristic
15C2×C11×#124C2212yes—
16C2×C4×Q8×C11C2211yescharacteristic
17C2×C4×D4×C11C2212yes—
18C2×C4×D4×C11C2211yescharacteristic
19C11×#463—28no—
20C11×#459—24no—
21C11×#440—24no—
22C2×C11×#107C2211yescharacteristic
23C2×C11×C4⋊C8C2211yescharacteristic
24C2×C11×C4⋊C8C2212yes—
25C2×C11×#103C2211yescharacteristic
26C2×C11×#103C2212yes—
27C2×C11×#102C2211yescharacteristic
28C2×C11×#102C2212yes—
29C2×C11×#102C2212yes—
30C2×C11×#102C2212yes—
31C2×C11×#97C2211yescharacteristic
32C11×#394—21no—
33C11×#394—21no—
34C11×#390—22no—
35C11×#390C2212yes—
36C11×#389C2212yes—
37C11×#385—22no—
38C11×#382C2211yescharacteristic
39C11×#380—21no—
40C4×C11×C4⋊C4C2211yescharacteristic
41C2×C11×#95—21no—
42C11×#340C2212yes—
43C11×#336C2212yes—
44C22×Q8×C11C2311yescharacteristic
45C22×D4×C11—21no—
46C22×D4×C11—21no—
47C22×D4×C11C2312yes—
48C22×D4×C11C2311yescharacteristic
49C23×C4×C11—21no—
50C23×C4×C11—22no—
51C2×C11×SD16—22no—
52C2×C11×SD16—22no—
53C2×C11×SD16D414yescomplemented
54C2×C11×D8—24no—
55C2×C11×D8—24no—
56C2×C11×D8—24no—
57C22×C8×C11C2311yescharacteristic
58C22×C8×C11C2312yes—
59C22×C8×C11C2311yescharacteristic
60C11×#127—22no—
61C11×#127—22no—
62C11×#124—24no—
63C11×#124—42no—
64C4×Q8×C11—22no—
65C4×Q8×C11—22no—
66C4×D4×C11—24no—
67C4×D4×C11—22no—
68C4×D4×C11—42no—
69C4×D4×C11D414yes—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—22no—
72C2×C11×C4⋊C4D412yes—
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C4⋊C4C2312yes—
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C22⋊C4—21no—
77C2×C11×C22⋊C4—22no—
78C2×C11×C22⋊C4—22no—
79C2×C11×C22⋊C4—22no—
80C2×C11×C22⋊C4—22no—
81C2×C11×C22⋊C4—22no—
82C2×C42×C11—21no—
83C2×C42×C11C2312yes—
84C2×C42×C11C2311yescharacteristic
85C11×#107—22no—
86C11×C4⋊C8—24no—
87C11×C4⋊C8—22no—
88C11×#103—24no—
89C11×#103—22no—
90C11×#102—22no—
91C11×#102—24no—
92C11×#102—24no—
93C11×#102—42no—
94C11×#97—22no—
95C11×#95—21no—
96C11×#95—22no—
97C11×#95—21no—
98C11×#95D411yescharacteristic
99C11×#95D411yescharacteristic
100#24749C1111yesmaximal, characteristic, direct product factor, Sylow
101C24×C11—21no—
102C24×C11—22no—
103C2×Q8×C11—21no—
104C2×Q8×C11—21no—
105C2×Q8×C11—21no—
106C2×Q8×C11—21no—
107C2×Q8×C11—21no—
108C2×Q8×C11C2×D412yes—
109C2×D4×C11—22no—
110C2×D4×C11—22no—
111C2×D4×C11—21no—
112C2×D4×C11—22no—
113C2×D4×C11—22no—
114C2×D4×C11—21no—
115C2×D4×C11—22no—
116C2×D4×C11—21no—
117C2×D4×C11—22no—
118C2×D4×C11—44no—
119C2×D4×C11—42no—
120C2×D4×C11—42no—
121C2×D4×C11—82no—
122C2×D4×C11C2×D412yes—
123C2×D4×C11C2×D412yes—
124C2×D4×C11#4112yes—
125C22×C4×C11—21no—
126C22×C4×C11—21no—
127C22×C4×C11—24no—
128C22×C4×C11—22no—
129C22×C4×C11—21no—
130C22×C4×C11—44no—
131C22×C4×C11—44no—
132C22×C4×C11—82no—
133C22×C4×C11—82no—
134C22×C4×C11C2×D412yes—
135C22×C4×C11C2×D412yes—
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2411yescharacteristic
139C11×SD16—28no—
140C11×D8—48no—
141C2×C8×C11—21no—
142C2×C8×C11—21no—
143C2×C8×C11—22no—
144C2×C8×C11—22no—
145C2×C8×C11—21no—
146C2×C8×C11—22no—
147C2×C8×C11—21no—
148C2×C8×C11—21no—
149C2×C8×C11C2×D412yes—
150C11×C4⋊C4—21no—
151C11×C4⋊C4—22no—
152C11×C4⋊C4—21no—
153C11×C4⋊C4—21no—
154C11×C4⋊C4—22no—
155C11×C4⋊C4—42no—
156C11×C4⋊C4—42no—
157C11×C4⋊C4—82no—
158C11×C4⋊C4C2×D412yes—
159C11×C22⋊C4—24no—
160C11×C22⋊C4—44no—
161C11×C22⋊C4—44no—
162C11×C22⋊C4—44no—
163C11×C22⋊C4—82no—
164C11×C22⋊C4—82no—
165C42×C11—22no—
166C42×C11—22no—
167C42×C11—42no—
168C42×C11C2×D412yes—
169C42×C11#4112yes—
170C2×#463C2×C1112yescomplemented
171C2×#459C2×C1111yescharacteristic
172C2×#440C2×C1111yescharacteristic, complemented
173#2548C2×C1111yescharacteristic, complemented
174#2349C2×C1111yescharacteristic, complemented
175#2067C2×C1112yescomplemented
176#2042C2×C1112yescomplemented
177#1961C2×C1111yescharacteristic, complemented
178#1940C2×C1111yescharacteristic, complemented
179#1879C2×C1112yescomplemented
180#1805C2×C1111yescharacteristic, complemented
181C23×C11—22no—
182C23×C11—22no—
183C23×C11—22no—
184C23×C11—42no—
185C23×C11—42no—
186C23×C11—42no—
187C23×C11—42no—
188C23×C11—42no—
189C23×C11—42no—
190C23×C11—42no—
191C23×C11—42no—
192C23×C11—42no—
193C23×C11C22×D411yescharacteristic
194Q8×C11—22no—
195Q8×C11—22no—
196Q8×C11—41no—
197Q8×C11—41no—
198D4×C11—22no—
199D4×C11—22no—
200D4×C11—22no—
201D4×C11—42no—
202D4×C11—42no—
203D4×C11—42no—
204D4×C11—42no—
205D4×C11—84no—
206D4×C11—84no—
207D4×C11#12114yes—
208C2×C4×C11—22no—
209C2×C4×C11—22no—
210C2×C4×C11—22no—
211C2×C4×C11—22no—
212C2×C4×C11—22no—
213C2×C4×C11—22no—
214C2×C4×C11—22no—
215C2×C4×C11—22no—
216C2×C4×C11—22no—
217C2×C4×C11—22no—
218C2×C4×C11—41no—
219C2×C4×C11—41no—
220C2×C4×C11—42no—
221C2×C4×C11—41no—
222C2×C4×C11—42no—
223C2×C4×C11—42no—
224C2×C4×C11—42no—
225C2×C4×C11—42no—
226C2×C4×C11—84no—
227C2×C4×C11—88no—
228C2×C4×C11#12112yes—
229C2×C4×C11#12112yes—
230C2×C4×C11C22×D411yescharacteristic
231C2×C4×C11C22×D411yescharacteristic
232C2×C4×C11C2×#4111yescharacteristic
233C2×C4×C11C2×#4111yescharacteristic
234C2×C4×C11H(5,𝔽2)11yescharacteristic
235C2×C4×C112−1+411yescharacteristic
236C8×C11—22no—
237C8×C11—42no—
238C8×C11—41no—
239C22×SD16C22×C1111yescharacteristic
240C22×D8C22×C1112yes—
241C2×#127C22×C1111yescharacteristic
242C2×#124C22×C1112yes—
243C2×C4×Q8C22×C1111yescharacteristic
244C2×C4×D4C22×C1112yes—
245C2×C4×D4C22×C1111yescharacteristic
246#463—28no—
247#459—24no—
248#440—24no—
249C2×#107C22×C1111yescharacteristic
250C2×C4⋊C8C22×C1111yescharacteristic
251C2×C4⋊C8C22×C1112yes—
252C2×#103C22×C1112yes—
253C2×#103C22×C1111yescharacteristic
254C2×#102C22×C1112yes—
255C2×#102C22×C1112yes—
256C2×#102C22×C1111yescharacteristic
257C2×#102C22×C1112yes—
258C2×#97C22×C1111yescharacteristic
259#394—21no—
260#394—21no—
261#390—22no—
262#390C22×C1112yes—
263#389C22×C1112yes—
264#385—22no—
265#382C22×C1111yescharacteristic
266#380—21no—
267C4×C4⋊C4C22×C1111yescharacteristic
268C2×#95—21no—
269#340C22×C1112yes—
270#336C22×C1112yes—
271C22×C11—24no—
272C22×C11—44no—
273C22×C11—44no—
274C22×C11—42no—
275C22×C11—42no—
276C22×C11—82no—
277C22×C11—82no—
278C22×C11—82no—
279C22×C11—82no—
280C22×C11—82no—
281C22×C11—82no—
282C22×C11—82no—
283C22×C11C2×#12111yescharacteristic
284C22×C11D4211yescharacteristic
285C22×C11#54811yescharacteristic
286C22×C11#57512yes—
287C22×C11#57612yes—
288C4×C11—22no—
289C4×C11—22no—
290C4×C11—42no—
291C4×C11—42no—
292C4×C11—42no—
293C4×C11—42no—
294C4×C11—82no—
295C4×C11—81no—
296C4×C11C2×#12111yescharacteristic
297C4×C11#53711yescharacteristic
298C4×C11#54711yescharacteristic
299C4×C11#55311yescharacteristic
300C22×Q8C23×C1111yescharacteristic
301C22×D4—21no—
302C22×D4—21no—
303C22×D4C23×C1112yes—
304C22×D4C23×C1111yescharacteristic
305C23×C4—21no—
306C23×C4—22no—
307C2×SD16—22no—
308C2×SD16—22no—
309C2×SD16D4×C1114yescomplemented
310C2×D8—24no—
311C2×D8—24no—
312C2×D8—24no—
313C22×C8C23×C1112yes—
314C22×C8C23×C1111yescharacteristic
315C22×C8C23×C1111yescharacteristic
316#127—22no—
317#127—22no—
318#124—24no—
319#124—42no—
320C4×Q8—22no—
321C4×Q8—22no—
322C4×D4—24no—
323C4×D4—22no—
324C4×D4—42no—
325C4×D4D4×C1114yes—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4D4×C1112yes—
329C2×C4⋊C4C23×C1112yes—
330C2×C4⋊C4C23×C1111yescharacteristic
331C2×C4⋊C4C23×C1111yescharacteristic
332C2×C22⋊C4—21no—
333C2×C22⋊C4—22no—
334C2×C22⋊C4—22no—
335C2×C22⋊C4—22no—
336C2×C22⋊C4—22no—
337C2×C22⋊C4—22no—
338C2×C42—21no—
339C2×C42C23×C1112yes—
340C2×C42C23×C1111yescharacteristic
341#107—22no—
342C4⋊C8—24no—
343C4⋊C8—22no—
344#103—24no—
345#103—22no—
346#102—22no—
347#102—24no—
348#102—24no—
349#102—42no—
350#97—22no—
351#95—21no—
352#95—22no—
353#95—21no—
354#95D4×C1111yescharacteristic
355#95D4×C1111yescharacteristic
356C2×C11—44no—
357C2×C11—162no—
358C2×C11#241611yescharacteristic
359C2×C11#304011yescharacteristic
360C2×C11#304111yescharacteristic
361C2×C11#326812yes—
362C2×C11#337012yes—
363C24—21no—
364C24—22no—
365C2×Q8—21no—
366C2×Q8—21no—
367C2×Q8—21no—
368C2×Q8—21no—
369C2×Q8—21no—
370C2×Q8C2×D4×C1112yes—
371C2×D4—22no—
372C2×D4—22no—
373C2×D4—21no—
374C2×D4—22no—
375C2×D4—22no—
376C2×D4—21no—
377C2×D4—22no—
378C2×D4—21no—
379C2×D4—22no—
380C2×D4—44no—
381C2×D4—42no—
382C2×D4—42no—
383C2×D4—82no—
384C2×D4C2×D4×C1112yes—
385C2×D4C2×D4×C1112yes—
386C2×D4C11×#4112yes—
387C22×C4—21no—
388C22×C4—21no—
389C22×C4—24no—
390C22×C4—22no—
391C22×C4—21no—
392C22×C4—44no—
393C22×C4—44no—
394C22×C4—82no—
395C22×C4—82no—
396C22×C4C2×D4×C1112yes—
397C22×C4C2×D4×C1112yes—
398C22×C4C2×D4×C1111yescharacteristic
399C22×C4C2×D4×C1111yescharacteristic
400C22×C4C24×C1111yescharacteristic
401SD16—28no—
402D8—48no—
403C2×C8—21no—
404C2×C8—21no—
405C2×C8—21no—
406C2×C8—22no—
407C2×C8—22no—
408C2×C8—22no—
409C2×C8—21no—
410C2×C8—21no—
411C2×C8C2×D4×C1112yes—
412C4⋊C4—21no—
413C4⋊C4—22no—
414C4⋊C4—21no—
415C4⋊C4—21no—
416C4⋊C4—22no—
417C4⋊C4—42no—
418C4⋊C4—42no—
419C4⋊C4—82no—
420C4⋊C4C2×D4×C1112yes—
421C22⋊C4—24no—
422C22⋊C4—44no—
423C22⋊C4—44no—
424C22⋊C4—44no—
425C22⋊C4—82no—
426C22⋊C4—82no—
427C42—22no—
428C42—22no—
429C42—42no—
430C42C2×D4×C1112yes—
431C42C11×#4112yes—
432C11#2474911yescharacteristic, direct product factor, Sylow
433C23—22no—
434C23—22no—
435C23—22no—
436C23—42no—
437C23—42no—
438C23—42no—
439C23—42no—
440C23—42no—
441C23—42no—
442C23—42no—
443C23—42no—
444C23—42no—
445C23C22×D4×C1111yescharacteristic
446Q8—22no—
447Q8—22no—
448Q8—41no—
449Q8—41no—
450D4—22no—
451D4—22no—
452D4—22no—
453D4—42no—
454D4—42no—
455D4—42no—
456D4—42no—
457D4—84no—
458D4—84no—
459D4C11×#12114yes—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—22no—
463C2×C4—22no—
464C2×C4—22no—
465C2×C4—22no—
466C2×C4—22no—
467C2×C4—22no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—42no—
473C2×C4—41no—
474C2×C4—42no—
475C2×C4—42no—
476C2×C4—42no—
477C2×C4—42no—
478C2×C4—84no—
479C2×C4—88no—
480C2×C4C11×#12112yes—
481C2×C4C11×#12112yes—
482C2×C4C22×D4×C1111yescharacteristic
483C2×C4C22×D4×C1111yescharacteristic
484C2×C4C2×C11×#4111yescharacteristic
485C2×C4C2×C11×#4111yescharacteristic
486C2×C4C11×H(5,𝔽2)11yescharacteristic
487C2×C4C11×2−1+411yescharacteristic
488C8—22no—
489C8—42no—
490C8—41no—
491C22—24no—
492C22—44no—
493C22—42no—
494C22—42no—
495C22—44no—
496C22—82no—
497C22—82no—
498C22—82no—
499C22—82no—
500C22—82no—
501C22—82no—
502C22—82no—
503C22C2×C11×#12111yescharacteristic
504C22D42×C1111yescharacteristic
505C22C11×#54811yescharacteristic
506C22C11×#57512yes—
507C22C11×#57612yes—
508C4—22no—
509C4—22no—
510C4—42no—
511C4—42no—
512C4—42no—
513C4—42no—
514C4—82no—
515C4—81no—
516C4C2×C11×#12111yescharacteristic
517C4C11×#53711yescharacteristic
518C4C11×#54711yescharacteristic
519C4C11×#55311yescharacteristic
520C2—44no—
521C2—162no—
522C2C11×#241611yescharacteristic
523C2C11×#304011yescharacteristic
524C2C11×#304111yescharacteristic
525C2C11×#326812yes—
526C2C11×#337012yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#459C2
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
1. C2×C11×#463C2semidirect
3. C2×C11×#440C2semidirect
4. C11×#2548C2semidirect
5. C11×#2349C2semidirect
6. C11×#2067C2semidirect
7. C11×#2042C2semidirect
8. C11×#1961C2semidirect
9. C11×#1940C2semidirect
10. C11×#1879C2semidirect
11. C11×#1805C2semidirect
53. C2×C11×SD16D4semidirect
100. #24749C11direct (N × H)
170. C2×#463C2×C11semidirect
172. C2×#440C2×C11semidirect
173. #2548C2×C11semidirect
174. #2349C2×C11semidirect
175. #2067C2×C11semidirect
176. #2042C2×C11semidirect
177. #1961C2×C11semidirect
178. #1940C2×C11semidirect
179. #1879C2×C11semidirect
180. #1805C2×C11semidirect
309. C2×SD16D4×C11semidirect
432. C11#24749direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4632
C2×C11×#4592
C2×C11×#4402
C11×#25482
C11×#23492
C11×#20672
C11×#20422
C11×#19612
C11×#19402
C11×#18792
C11×#18052
#2474911