Finite Group Databasebeta

← C11×#24633 #14601826

Subgroups — C11×#24633 #14601826

Order 2816.

898 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#460C211yesmaximal, characteristic
2C2×C4×C11×Q16C211yesmaximal, characteristic, complemented
3C11×#2548C211yesmaximal, characteristic
4C11×#2355C211yesmaximal, characteristic, complemented
5C11×#2055C212yesmaximal, complemented
6C11×#2015C212yesmaximal, complemented
7C11×#1983C212yesmaximal, complemented
8C11×#1957C211yesmaximal, characteristic
9C11×#1939C211yesmaximal, characteristic, complemented
10C11×#1925C212yesmaximal, complemented
11C11×#1803C211yesmaximal, characteristic, complemented
12C22×C11×Q16C2211yescharacteristic
13C22×C11×SD16C2212yes—
14C2×C11×#127C2211yescharacteristic
15C2×C11×#124C2212yes—
16C2×C4×Q8×C11C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C11×#460—24no—
19C4×C11×Q16—24no—
20C2×C11×#107C2211yescharacteristic
21C2×C11×C4⋊C8C2211yescharacteristic
22C2×C11×C4⋊C8C2212yes—
23C2×C11×#103C2211yescharacteristic
24C2×C11×#103C2211yescharacteristic
25C2×C11×#103C2212yes—
26C2×C11×#102C2212yes—
27C2×C11×#102C2212yes—
28C2×C11×#102C2212yes—
29C2×C4×C8×C11C2211yescharacteristic
30C11×#394—22no—
31C11×#391C2212yes—
32C11×#390—21no—
33C11×#390—21no—
34C11×#390C2212yes—
35C11×#387—22no—
36C11×#384C2211yescharacteristic
37C11×#382—21no—
38C4×C11×C4⋊C4—21no—
39C4×C11×C4⋊C4C2212yes—
40C4×C11×C4⋊C4C2211yescharacteristic
41C11×#340C2212yes—
42C11×#336C2212yes—
43C22×Q8×C11C2311yescharacteristic
44C22×Q8×C11C2311yescharacteristic
45C22×D4×C11—21no—
46C22×D4×C11—21no—
47C22×D4×C11C2312yes—
48C2×C11×Q16—22no—
49C2×C11×Q16—22no—
50C2×C11×Q16—22no—
51C2×C11×SD16—24no—
52C2×C11×SD16—42no—
53C2×C11×SD16—42no—
54C22×C8×C11C2312yes—
55C22×C8×C11C2311yescharacteristic
56C22×C8×C11C2311yescharacteristic
57C11×#127—22no—
58C11×#127—22no—
59C11×#124—24no—
60C11×#124—42no—
61C4×Q8×C11—22no—
62C4×Q8×C11—22no—
63C4×Q8×C11—22no—
64C4×Q8×C11D414yes—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4—21no—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4D411yescharacteristic
70C2×C11×C4⋊C4D411yescharacteristic
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2312yes—
73C2×C11×C4⋊C4C2311yescharacteristic
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—21no—
80C2×C42×C11—22no—
81C2×C42×C11C2312yes—
82C2×C42×C11C2311yescharacteristic
83C11×#107—22no—
84C11×C4⋊C8—22no—
85C11×C4⋊C8—42no—
86C11×#103—22no—
87C11×#103—22no—
88C11×#103—42no—
89C11×#102—24no—
90C11×#102—24no—
91C11×#102—42no—
92C4×C8×C11—22no—
93C11×#95—22no—
94C11×#95—22no—
95C11×#95—22no—
96C11×#95D412yes—
97#24633C1111yesmaximal, characteristic, direct product factor, Sylow
98C24×C11—22no—
99C2×Q8×C11—21no—
100C2×Q8×C11—21no—
101C2×Q8×C11—21no—
102C2×Q8×C11—21no—
103C2×Q8×C11—21no—
104C2×Q8×C11—21no—
105C2×Q8×C11—21no—
106C2×Q8×C11—21no—
107C2×Q8×C11—21no—
108C2×Q8×C11—21no—
109C2×Q8×C11C2×D412yes—
110C2×Q8×C11#4112yes—
111C2×D4×C11—22no—
112C2×D4×C11—22no—
113C2×D4×C11—22no—
114C2×D4×C11—22no—
115C2×D4×C11—22no—
116C2×D4×C11—22no—
117C2×D4×C11—42no—
118C2×D4×C11—42no—
119C2×D4×C11—42no—
120C2×D4×C11—42no—
121C2×D4×C11—81no—
122C2×D4×C11—81no—
123C22×C4×C11—21no—
124C22×C4×C11—21no—
125C22×C4×C11—21no—
126C22×C4×C11—22no—
127C22×C4×C11—21no—
128C22×C4×C11C2×D412yes—
129C22×C4×C11C2×D412yes—
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11C2×D411yescharacteristic
132C22×C4×C11C2411yescharacteristic
133C11×Q16—28no—
134C11×SD16—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—24no—
145C11×C4⋊C4—22no—
146C11×C4⋊C4—22no—
147C11×C4⋊C4—21no—
148C11×C4⋊C4—21no—
149C11×C4⋊C4—22no—
150C11×C4⋊C4—21no—
151C11×C4⋊C4—22no—
152C11×C4⋊C4—42no—
153C11×C4⋊C4—42no—
154C11×C4⋊C4—81no—
155C11×C4⋊C4C2×D412yes—
156C11×C22⋊C4—44no—
157C11×C22⋊C4—44no—
158C11×C22⋊C4—82no—
159C11×C22⋊C4—82no—
160C42×C11—24no—
161C42×C11—22no—
162C42×C11—22no—
163C42×C11—42no—
164C42×C11—82no—
165C42×C11C2×D412yes—
166C42×C11#4112yes—
167C2×#460C2×C1111yescharacteristic
168C2×C4×Q16C2×C1111yescharacteristic, complemented
169#2548C2×C1111yescharacteristic
170#2355C2×C1111yescharacteristic, complemented
171#2055C2×C1112yescomplemented
172#2015C2×C1112yescomplemented
173#1983C2×C1112yescomplemented
174#1957C2×C1111yescharacteristic
175#1939C2×C1111yescharacteristic, complemented
176#1925C2×C1112yescomplemented
177#1803C2×C1111yescharacteristic, complemented
178C23×C11—42no—
179C23×C11—42no—
180C23×C11—42no—
181C23×C11—42no—
182C23×C11—42no—
183C23×C11—42no—
184C23×C11—42no—
185C23×C11C22×D411yescharacteristic
186Q8×C11—22no—
187Q8×C11—22no—
188Q8×C11—22no—
189Q8×C11—22no—
190Q8×C11—41no—
191Q8×C11—41no—
192Q8×C11—41no—
193Q8×C11—41no—
194D4×C11—42no—
195D4×C11—42no—
196D4×C11—42no—
197D4×C11—42no—
198D4×C11—84no—
199D4×C11—84no—
200C2×C4×C11—21no—
201C2×C4×C11—21no—
202C2×C4×C11—22no—
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—41no—
212C2×C4×C11—41no—
213C2×C4×C11—41no—
214C2×C4×C11—41no—
215C2×C4×C11—41no—
216C2×C4×C11—41no—
217C2×C4×C11—41no—
218C2×C4×C11—42no—
219C2×C4×C11—42no—
220C2×C4×C11—42no—
221C2×C4×C11—41no—
222C2×C4×C11—41no—
223C2×C4×C11#12112yes—
224C2×C4×C11#12112yes—
225C2×C4×C11#13512yes—
226C2×C4×C11#13712yes—
227C2×C4×C11C22×D411yescharacteristic
228C2×C4×C11C2×#4111yescharacteristic
229C2×C4×C11C2×#4111yescharacteristic
230C2×C4×C11C2×#4111yescharacteristic
231C2×C4×C11H(5,𝔽2)11yescharacteristic
232C2×C4×C11H(5,𝔽2)11yescharacteristic
233C8×C11—22no—
234C8×C11—41no—
235C8×C11—42no—
236C22×Q16C22×C1111yescharacteristic
237C22×SD16C22×C1112yes—
238C2×#127C22×C1111yescharacteristic
239C2×#124C22×C1112yes—
240C2×C4×Q8C22×C1111yescharacteristic
241C2×C4×Q8C22×C1111yescharacteristic
242#460—24no—
243C4×Q16—24no—
244C2×#107C22×C1111yescharacteristic
245C2×C4⋊C8C22×C1111yescharacteristic
246C2×C4⋊C8C22×C1112yes—
247C2×#103C22×C1111yescharacteristic
248C2×#103C22×C1111yescharacteristic
249C2×#103C22×C1112yes—
250C2×#102C22×C1112yes—
251C2×#102C22×C1112yes—
252C2×#102C22×C1112yes—
253C2×C4×C8C22×C1111yescharacteristic
254#394—22no—
255#391C22×C1112yes—
256#390—21no—
257#390—21no—
258#390C22×C1112yes—
259#387—22no—
260#384C22×C1111yescharacteristic
261#382—21no—
262C4×C4⋊C4—21no—
263C4×C4⋊C4C22×C1112yes—
264C4×C4⋊C4C22×C1111yescharacteristic
265#340C22×C1112yes—
266#336C22×C1112yes—
267C22×C11—82no—
268C22×C11—82no—
269C22×C11—82no—
270C22×C11—82no—
271C22×C11—82no—
272C22×C11—82no—
273C22×C11—82no—
274C22×C11C2×#12111yescharacteristic
275C22×C11#54611yescharacteristic
276C22×C11#55011yescharacteristic
277C22×C11C2×#13511yescharacteristic
278C22×C11C2×#13711yescharacteristic
279C22×C11#57611yescharacteristic
280C22×C11#57711yescharacteristic
281C4×C11—22no—
282C4×C11—42no—
283C4×C11—42no—
284C4×C11—42no—
285C4×C11—42no—
286C4×C11—42no—
287C4×C11—82no—
288C4×C11—81no—
289C4×C11#46414yes—
290C4×C11#52511yescharacteristic
291C4×C11#53511yescharacteristic
292C4×C11#55311yescharacteristic
293C4×C11#55511yescharacteristic
294C22×Q8C23×C1111yescharacteristic
295C22×Q8C23×C1111yescharacteristic
296C22×D4—21no—
297C22×D4—21no—
298C22×D4C23×C1112yes—
299C2×Q16—22no—
300C2×Q16—22no—
301C2×Q16—22no—
302C2×SD16—24no—
303C2×SD16—42no—
304C2×SD16—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×Q8—22no—
315C4×Q8D4×C1114yes—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—21no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4—21no—
320C2×C4⋊C4D4×C1111yescharacteristic
321C2×C4⋊C4D4×C1111yescharacteristic
322C2×C4⋊C4C23×C1111yescharacteristic
323C2×C4⋊C4C23×C1112yes—
324C2×C4⋊C4C23×C1111yescharacteristic
325C2×C22⋊C4—22no—
326C2×C22⋊C4—22no—
327C2×C22⋊C4—22no—
328C2×C22⋊C4—22no—
329C2×C42—21no—
330C2×C42—21no—
331C2×C42—22no—
332C2×C42C23×C1112yes—
333C2×C42C23×C1111yescharacteristic
334#107—22no—
335C4⋊C8—22no—
336C4⋊C8—42no—
337#103—22no—
338#103—22no—
339#103—42no—
340#102—24no—
341#102—24no—
342#102—42no—
343C4×C8—22no—
344#95—22no—
345#95—22no—
346#95—22no—
347#95D4×C1112yes—
348C2×C11—162no—
349C2×C11#241411yescharacteristic
350C2×C11C2×#46411yescharacteristic
351C2×C11#304511yescharacteristic
352C2×C11#330411yescharacteristic
353C2×C11#333311yescharacteristic
354C2×C11#339611yescharacteristic
355C2×C11#340011yescharacteristic
356C24—22no—
357C2×Q8—21no—
358C2×Q8—21no—
359C2×Q8—21no—
360C2×Q8—21no—
361C2×Q8—21no—
362C2×Q8—21no—
363C2×Q8—21no—
364C2×Q8—21no—
365C2×Q8—21no—
366C2×Q8—21no—
367C2×Q8C2×D4×C1112yes—
368C2×Q8C11×#4112yes—
369C2×D4—22no—
370C2×D4—22no—
371C2×D4—22no—
372C2×D4—22no—
373C2×D4—22no—
374C2×D4—22no—
375C2×D4—42no—
376C2×D4—42no—
377C2×D4—42no—
378C2×D4—42no—
379C2×D4—81no—
380C2×D4—81no—
381C22×C4—21no—
382C22×C4—21no—
383C22×C4—21no—
384C22×C4—22no—
385C22×C4—21no—
386C22×C4C2×D4×C1112yes—
387C22×C4C2×D4×C1112yes—
388C22×C4C2×D4×C1111yescharacteristic
389C22×C4C2×D4×C1111yescharacteristic
390C22×C4C24×C1111yescharacteristic
391Q16—28no—
392SD16—48no—
393C2×C8—21no—
394C2×C8—21no—
395C2×C8—21no—
396C2×C8—22no—
397C2×C8—21no—
398C2×C8—22no—
399C2×C8—21no—
400C2×C8—22no—
401C2×C8C11×#4112yes—
402C4⋊C4—24no—
403C4⋊C4—22no—
404C4⋊C4—22no—
405C4⋊C4—21no—
406C4⋊C4—21no—
407C4⋊C4—22no—
408C4⋊C4—21no—
409C4⋊C4—22no—
410C4⋊C4—42no—
411C4⋊C4—42no—
412C4⋊C4—81no—
413C4⋊C4C2×D4×C1112yes—
414C22⋊C4—44no—
415C22⋊C4—44no—
416C22⋊C4—82no—
417C22⋊C4—82no—
418C42—24no—
419C42—22no—
420C42—22no—
421C42—42no—
422C42—82no—
423C42C2×D4×C1112yes—
424C42C11×#4112yes—
425C11#2463311yescharacteristic, direct product factor, Sylow
426C23—42no—
427C23—42no—
428C23—42no—
429C23—42no—
430C23—42no—
431C23—42no—
432C23—42no—
433C23C22×D4×C1111yescharacteristic
434Q8—22no—
435Q8—22no—
436Q8—22no—
437Q8—22no—
438Q8—41no—
439Q8—41no—
440Q8—41no—
441Q8—41no—
442D4—42no—
443D4—42no—
444D4—42no—
445D4—42no—
446D4—84no—
447D4—84no—
448C2×C4—21no—
449C2×C4—21no—
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—41no—
462C2×C4—41no—
463C2×C4—41no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—42no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4C11×#12112yes—
472C2×C4C11×#12112yes—
473C2×C4C11×#13512yes—
474C2×C4C11×#13712yes—
475C2×C4C22×D4×C1111yescharacteristic
476C2×C4C2×C11×#4111yescharacteristic
477C2×C4C2×C11×#4111yescharacteristic
478C2×C4C2×C11×#4111yescharacteristic
479C2×C4C11×H(5,𝔽2)11yescharacteristic
480C2×C4C11×H(5,𝔽2)11yescharacteristic
481C8—22no—
482C8—42no—
483C8—41no—
484C22—82no—
485C22—82no—
486C22—82no—
487C22—82no—
488C22—82no—
489C22—82no—
490C22—82no—
491C22C2×C11×#12111yescharacteristic
492C22C11×#54611yescharacteristic
493C22C11×#55011yescharacteristic
494C22C2×C11×#13511yescharacteristic
495C22C2×C11×#13711yescharacteristic
496C22C11×#57611yescharacteristic
497C22C11×#57711yescharacteristic
498C4—22no—
499C4—42no—
500C4—42no—
501C4—42no—
502C4—42no—
503C4—42no—
504C4—81no—
505C4—82no—
506C4C11×#46414yes—
507C4C11×#52511yescharacteristic
508C4C11×#53511yescharacteristic
509C4C11×#55311yescharacteristic
510C4C11×#55511yescharacteristic
511C2—162no—
512C2C11×#241411yescharacteristic
513C2C2×C11×#46411yescharacteristic
514C2C11×#304511yescharacteristic
515C2C11×#330411yescharacteristic
516C2C11×#333311yescharacteristic
517C2C11×#339611yescharacteristic
518C2C11×#340011yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#127C22
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×C4×C11×Q16C2semidirect
4. C11×#2355C2semidirect
5. C11×#2055C2semidirect
6. C11×#2015C2semidirect
7. C11×#1983C2semidirect
9. C11×#1939C2semidirect
10. C11×#1925C2semidirect
11. C11×#1803C2semidirect
97. #24633C11direct (N × H)
168. C2×C4×Q16C2×C11semidirect
170. #2355C2×C11semidirect
171. #2055C2×C11semidirect
172. #2015C2×C11semidirect
173. #1983C2×C11semidirect
175. #1939C2×C11semidirect
176. #1925C2×C11semidirect
177. #1803C2×C11semidirect
425. C11#24633direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4602
C2×C4×C11×Q162
C11×#25482
C11×#23552
C11×#20552
C11×#20152
C11×#19832
C11×#19572
C11×#19392
C11×#19252
C11×#18032
#2463311