Finite Group Databasebeta

← C11×#24647 #14601840

Subgroups — C11×#24647 #14601840

Order 2816.

932 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#459C211yesmaximal, characteristic
2C2×C11×#440C211yesmaximal, characteristic, complemented
3C11×#2548C211yesmaximal, characteristic, complemented
4C11×#2357C211yesmaximal, characteristic, complemented
5C11×#2054C212yesmaximal, complemented
6C11×#2012C212yesmaximal, complemented
7C11×#1983C212yesmaximal, complemented
8C11×#1961C211yesmaximal, characteristic, complemented
9C11×#1940C211yesmaximal, characteristic, complemented
10C11×#1925C212yesmaximal, complemented
11C11×#1805C211yesmaximal, characteristic, complemented
12C22×C11×SD16C2211yescharacteristic
13C22×C11×D8C2212yes—
14C2×C11×#127C2211yescharacteristic
15C2×C11×#124C2212yes—
16C2×C4×Q8×C11C2211yescharacteristic
17C2×C4×D4×C11C2211yescharacteristic
18C11×#459—24no—
19C11×#440—24no—
20C2×C11×#107C2211yescharacteristic
21C2×C11×C4⋊C8C2211yescharacteristic
22C2×C11×C4⋊C8C2212yes—
23C2×C11×#103C2211yescharacteristic
24C2×C11×#103C2212yes—
25C2×C11×#102C2211yescharacteristic
26C2×C11×#102C2212yes—
27C2×C11×#102C2212yes—
28C2×C11×#102C2212yes—
29C2×C11×#97C2211yescharacteristic
30C11×#394—21no—
31C11×#394—21no—
32C11×#390—22no—
33C11×#390C2212yes—
34C11×#390C2212yes—
35C11×#388—22no—
36C11×#382C2211yescharacteristic
37C11×#381—21no—
38C4×C11×C4⋊C4C2212yes—
39C4×C11×C4⋊C4C2211yescharacteristic
40C4×C11×C22⋊C4—21no—
41C11×#340C2212yes—
42C11×#336C2212yes—
43C22×Q8×C11C2311yescharacteristic
44C22×D4×C11—21no—
45C22×D4×C11—21no—
46C22×D4×C11C2312yes—
47C22×D4×C11C2311yescharacteristic
48C23×C4×C11—21no—
49C2×C11×SD16—22no—
50C2×C11×SD16—22no—
51C2×C11×SD16—22no—
52C2×C11×D8—24no—
53C2×C11×D8—42no—
54C2×C11×D8—42no—
55C22×C8×C11C2312yes—
56C22×C8×C11C2311yescharacteristic
57C22×C8×C11C2311yescharacteristic
58C11×#127—22no—
59C11×#127—22no—
60C11×#124—24no—
61C11×#124—42no—
62C4×Q8×C11—22no—
63C4×Q8×C11—22no—
64C4×D4×C11—22no—
65C4×D4×C11D414yes—
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4D412yes—
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C4⋊C4C2312yes—
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C22⋊C4—21no—
72C2×C11×C22⋊C4—22no—
73C2×C11×C22⋊C4—22no—
74C2×C11×C22⋊C4—22no—
75C2×C11×C22⋊C4—22no—
76C2×C11×C22⋊C4—22no—
77C2×C11×C22⋊C4—22no—
78C2×C42×C11—21no—
79C2×C42×C11—22no—
80C2×C42×C11C2312yes—
81C2×C42×C11C2311yescharacteristic
82C11×#107—22no—
83C11×C4⋊C8—22no—
84C11×C4⋊C8—42no—
85C11×#103—22no—
86C11×#103—42no—
87C11×#102—22no—
88C11×#102—24no—
89C11×#102—24no—
90C11×#102—42no—
91C11×#97—22no—
92C11×#95—21no—
93C11×#95—22no—
94C11×#95—21no—
95C11×#95D411yescharacteristic
96C11×#95D411yescharacteristic
97#24647C1111yesmaximal, characteristic, direct product factor, Sylow
98C24×C11—21no—
99C24×C11—22no—
100C2×Q8×C11—21no—
101C2×Q8×C11—21no—
102C2×Q8×C11—21no—
103C2×Q8×C11—21no—
104C2×Q8×C11—21no—
105C2×Q8×C11#4112yes—
106C2×D4×C11—22no—
107C2×D4×C11—21no—
108C2×D4×C11—21no—
109C2×D4×C11—21no—
110C2×D4×C11—22no—
111C2×D4×C11—22no—
112C2×D4×C11—22no—
113C2×D4×C11—21no—
114C2×D4×C11—21no—
115C2×D4×C11—22no—
116C2×D4×C11—22no—
117C2×D4×C11—44no—
118C2×D4×C11—42no—
119C2×D4×C11—42no—
120C2×D4×C11—82no—
121C2×D4×C11C2×D412yes—
122C22×C4×C11—21no—
123C22×C4×C11—21no—
124C22×C4×C11—24no—
125C22×C4×C11—22no—
126C22×C4×C11—21no—
127C22×C4×C11—82no—
128C22×C4×C11C2×D412yes—
129C22×C4×C11C2×D412yes—
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11C2×D411yescharacteristic
132C22×C4×C11C2411yescharacteristic
133C11×SD16—28no—
134C11×D8—48no—
135C2×C8×C11—21no—
136C2×C8×C11—21no—
137C2×C8×C11—22no—
138C2×C8×C11—21no—
139C2×C8×C11—21no—
140C2×C8×C11—22no—
141C2×C8×C11—21no—
142C2×C8×C11—22no—
143C2×C8×C11#4112yes—
144C11×C4⋊C4—21no—
145C11×C4⋊C4—21no—
146C11×C4⋊C4—22no—
147C11×C4⋊C4—21no—
148C11×C4⋊C4—22no—
149C11×C4⋊C4—42no—
150C11×C4⋊C4—42no—
151C11×C4⋊C4C2×D412yes—
152C11×C22⋊C4—24no—
153C11×C22⋊C4—44no—
154C11×C22⋊C4—44no—
155C11×C22⋊C4—44no—
156C11×C22⋊C4—82no—
157C11×C22⋊C4—82no—
158C11×C22⋊C4—82no—
159C42×C11—22no—
160C42×C11—22no—
161C42×C11—42no—
162C42×C11—82no—
163C42×C11C2×D412yes—
164C42×C11#4112yes—
165C2×#459C2×C1111yescharacteristic
166C2×#440C2×C1111yescharacteristic, complemented
167#2548C2×C1111yescharacteristic, complemented
168#2357C2×C1111yescharacteristic, complemented
169#2054C2×C1112yescomplemented
170#2012C2×C1112yescomplemented
171#1983C2×C1112yescomplemented
172#1961C2×C1111yescharacteristic, complemented
173#1940C2×C1111yescharacteristic, complemented
174#1925C2×C1112yescomplemented
175#1805C2×C1111yescharacteristic, complemented
176C23×C11—22no—
177C23×C11—41no—
178C23×C11—41no—
179C23×C11—42no—
180C23×C11—42no—
181C23×C11—42no—
182C23×C11—42no—
183C23×C11—42no—
184C23×C11—42no—
185C23×C11—42no—
186C23×C11—42no—
187C23×C11—42no—
188C23×C11C22×D411yescharacteristic
189Q8×C11—22no—
190Q8×C11—22no—
191Q8×C11—41no—
192Q8×C11—41no—
193D4×C11—22no—
194D4×C11—22no—
195D4×C11—42no—
196D4×C11—42no—
197D4×C11—41no—
198D4×C11—42no—
199D4×C11—41no—
200D4×C11—42no—
201D4×C11—84no—
202D4×C11—84no—
203C2×C4×C11—22no—
204C2×C4×C11—22no—
205C2×C4×C11—22no—
206C2×C4×C11—22no—
207C2×C4×C11—22no—
208C2×C4×C11—22no—
209C2×C4×C11—22no—
210C2×C4×C11—22no—
211C2×C4×C11—22no—
212C2×C4×C11—22no—
213C2×C4×C11—41no—
214C2×C4×C11—41no—
215C2×C4×C11—42no—
216C2×C4×C11—41no—
217C2×C4×C11—42no—
218C2×C4×C11—42no—
219C2×C4×C11—42no—
220C2×C4×C11—42no—
221C2×C4×C11—84no—
222C2×C4×C11#12112yes—
223C2×C4×C11#12112yes—
224C2×C4×C11C22×D411yescharacteristic
225C2×C4×C11C2×#4111yescharacteristic
226C2×C4×C11C2×#4111yescharacteristic
227C2×C4×C11C2×#4111yescharacteristic
228C2×C4×C11H(5,𝔽2)11yescharacteristic
229C2×C4×C11H(5,𝔽2)11yescharacteristic
230C8×C11—22no—
231C8×C11—41no—
232C8×C11—42no—
233C22×SD16C22×C1111yescharacteristic
234C22×D8C22×C1112yes—
235C2×#127C22×C1111yescharacteristic
236C2×#124C22×C1112yes—
237C2×C4×Q8C22×C1111yescharacteristic
238C2×C4×D4C22×C1111yescharacteristic
239#459—24no—
240#440—24no—
241C2×#107C22×C1111yescharacteristic
242C2×C4⋊C8C22×C1111yescharacteristic
243C2×C4⋊C8C22×C1112yes—
244C2×#103C22×C1111yescharacteristic
245C2×#103C22×C1112yes—
246C2×#102C22×C1111yescharacteristic
247C2×#102C22×C1112yes—
248C2×#102C22×C1112yes—
249C2×#102C22×C1112yes—
250C2×#97C22×C1111yescharacteristic
251#394—21no—
252#394—21no—
253#390—22no—
254#390C22×C1112yes—
255#390C22×C1112yes—
256#388—22no—
257#382C22×C1111yescharacteristic
258#381—21no—
259C4×C4⋊C4C22×C1112yes—
260C4×C4⋊C4C22×C1111yescharacteristic
261C4×C22⋊C4—21no—
262#340C22×C1112yes—
263#336C22×C1112yes—
264C22×C11—42no—
265C22×C11—42no—
266C22×C11—42no—
267C22×C11—82no—
268C22×C11—82no—
269C22×C11—82no—
270C22×C11—82no—
271C22×C11—82no—
272C22×C11—82no—
273C22×C11—82no—
274C22×C11—82no—
275C22×C11—82no—
276C22×C11C2×#12111yescharacteristic
277C22×C11#54611yescharacteristic
278C22×C11#55011yescharacteristic
279C22×C11#57512yes—
280C22×C11#57612yes—
281C4×C11—22no—
282C4×C11—22no—
283C4×C11—42no—
284C4×C11—42no—
285C4×C11—42no—
286C4×C11—42no—
287C4×C11—82no—
288C4×C11—81no—
289C4×C11#52511yescharacteristic
290C4×C11#53511yescharacteristic
291C4×C11#55311yescharacteristic
292C4×C11#55511yescharacteristic
293C22×Q8C23×C1111yescharacteristic
294C22×D4—21no—
295C22×D4—21no—
296C22×D4C23×C1112yes—
297C22×D4C23×C1111yescharacteristic
298C23×C4—21no—
299C2×SD16—22no—
300C2×SD16—22no—
301C2×SD16—22no—
302C2×D8—24no—
303C2×D8—42no—
304C2×D8—42no—
305C22×C8C23×C1112yes—
306C22×C8C23×C1111yescharacteristic
307C22×C8C23×C1111yescharacteristic
308#127—22no—
309#127—22no—
310#124—24no—
311#124—42no—
312C4×Q8—22no—
313C4×Q8—22no—
314C4×D4—22no—
315C4×D4D4×C1114yes—
316C2×C4⋊C4—21no—
317C2×C4⋊C4D4×C1112yes—
318C2×C4⋊C4C23×C1111yescharacteristic
319C2×C4⋊C4C23×C1112yes—
320C2×C4⋊C4C23×C1111yescharacteristic
321C2×C22⋊C4—21no—
322C2×C22⋊C4—22no—
323C2×C22⋊C4—22no—
324C2×C22⋊C4—22no—
325C2×C22⋊C4—22no—
326C2×C22⋊C4—22no—
327C2×C22⋊C4—22no—
328C2×C42—21no—
329C2×C42—22no—
330C2×C42C23×C1112yes—
331C2×C42C23×C1111yescharacteristic
332#107—22no—
333C4⋊C8—22no—
334C4⋊C8—42no—
335#103—22no—
336#103—42no—
337#102—22no—
338#102—24no—
339#102—24no—
340#102—42no—
341#97—22no—
342#95—21no—
343#95—22no—
344#95—21no—
345#95D4×C1111yescharacteristic
346#95D4×C1111yescharacteristic
347C2×C11—82no—
348C2×C11—162no—
349C2×C11#241411yescharacteristic
350C2×C11#304011yescharacteristic
351C2×C11#304111yescharacteristic
352C2×C11#330912yes—
353C2×C11#340312yes—
354C24—21no—
355C24—22no—
356C2×Q8—21no—
357C2×Q8—21no—
358C2×Q8—21no—
359C2×Q8—21no—
360C2×Q8—21no—
361C2×Q8C11×#4112yes—
362C2×D4—22no—
363C2×D4—21no—
364C2×D4—21no—
365C2×D4—21no—
366C2×D4—22no—
367C2×D4—22no—
368C2×D4—22no—
369C2×D4—21no—
370C2×D4—21no—
371C2×D4—22no—
372C2×D4—22no—
373C2×D4—44no—
374C2×D4—42no—
375C2×D4—42no—
376C2×D4—82no—
377C2×D4C2×D4×C1112yes—
378C22×C4—21no—
379C22×C4—21no—
380C22×C4—24no—
381C22×C4—22no—
382C22×C4—21no—
383C22×C4—82no—
384C22×C4C2×D4×C1112yes—
385C22×C4C2×D4×C1112yes—
386C22×C4C2×D4×C1111yescharacteristic
387C22×C4C2×D4×C1111yescharacteristic
388C22×C4C24×C1111yescharacteristic
389SD16—28no—
390D8—48no—
391C2×C8—21no—
392C2×C8—21no—
393C2×C8—21no—
394C2×C8—22no—
395C2×C8—21no—
396C2×C8—22no—
397C2×C8—21no—
398C2×C8—22no—
399C2×C8C11×#4112yes—
400C4⋊C4—21no—
401C4⋊C4—21no—
402C4⋊C4—22no—
403C4⋊C4—21no—
404C4⋊C4—22no—
405C4⋊C4—42no—
406C4⋊C4—42no—
407C4⋊C4C2×D4×C1112yes—
408C22⋊C4—24no—
409C22⋊C4—44no—
410C22⋊C4—44no—
411C22⋊C4—44no—
412C22⋊C4—82no—
413C22⋊C4—82no—
414C22⋊C4—82no—
415C42—22no—
416C42—22no—
417C42—42no—
418C42—82no—
419C42C2×D4×C1112yes—
420C42C11×#4112yes—
421C11#2464711yescharacteristic, direct product factor, Sylow
422C23—22no—
423C23—41no—
424C23—41no—
425C23—42no—
426C23—42no—
427C23—42no—
428C23—42no—
429C23—42no—
430C23—42no—
431C23—42no—
432C23—42no—
433C23—42no—
434C23C22×D4×C1111yescharacteristic
435Q8—22no—
436Q8—22no—
437Q8—41no—
438Q8—41no—
439D4—22no—
440D4—22no—
441D4—42no—
442D4—42no—
443D4—41no—
444D4—42no—
445D4—41no—
446D4—42no—
447D4—84no—
448D4—84no—
449C2×C4—22no—
450C2×C4—22no—
451C2×C4—22no—
452C2×C4—22no—
453C2×C4—22no—
454C2×C4—22no—
455C2×C4—22no—
456C2×C4—22no—
457C2×C4—22no—
458C2×C4—22no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—42no—
462C2×C4—41no—
463C2×C4—42no—
464C2×C4—42no—
465C2×C4—42no—
466C2×C4—42no—
467C2×C4—84no—
468C2×C4C11×#12112yes—
469C2×C4C11×#12112yes—
470C2×C4C22×D4×C1111yescharacteristic
471C2×C4C2×C11×#4111yescharacteristic
472C2×C4C2×C11×#4111yescharacteristic
473C2×C4C2×C11×#4111yescharacteristic
474C2×C4C11×H(5,𝔽2)11yescharacteristic
475C2×C4C11×H(5,𝔽2)11yescharacteristic
476C8—22no—
477C8—42no—
478C8—41no—
479C22—42no—
480C22—42no—
481C22—42no—
482C22—82no—
483C22—82no—
484C22—82no—
485C22—82no—
486C22—82no—
487C22—82no—
488C22—82no—
489C22—82no—
490C22—82no—
491C22C2×C11×#12111yescharacteristic
492C22C11×#54611yescharacteristic
493C22C11×#55011yescharacteristic
494C22C11×#57512yes—
495C22C11×#57612yes—
496C4—22no—
497C4—22no—
498C4—42no—
499C4—42no—
500C4—42no—
501C4—42no—
502C4—82no—
503C4—81no—
504C4C11×#52511yescharacteristic
505C4C11×#53511yescharacteristic
506C4C11×#55311yescharacteristic
507C4C11×#55511yescharacteristic
508C2—82no—
509C2—162no—
510C2C11×#241411yescharacteristic
511C2C11×#304011yescharacteristic
512C2C11×#304111yescharacteristic
513C2C11×#330912yes—
514C2C11×#340312yes—
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
2. C2×C11×#440C2semidirect
3. C11×#2548C2semidirect
4. C11×#2357C2semidirect
5. C11×#2054C2semidirect
6. C11×#2012C2semidirect
7. C11×#1983C2semidirect
8. C11×#1961C2semidirect
9. C11×#1940C2semidirect
10. C11×#1925C2semidirect
11. C11×#1805C2semidirect
97. #24647C11direct (N × H)
166. C2×#440C2×C11semidirect
167. #2548C2×C11semidirect
168. #2357C2×C11semidirect
169. #2054C2×C11semidirect
170. #2012C2×C11semidirect
171. #1983C2×C11semidirect
172. #1961C2×C11semidirect
173. #1940C2×C11semidirect
174. #1925C2×C11semidirect
175. #1805C2×C11semidirect
421. C11#24647direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4592
C2×C11×#4402
C11×#25482
C11×#23572
C11×#20542
C11×#20122
C11×#19832
C11×#19612
C11×#19402
C11×#19252
C11×#18052
#2464711