Finite Group Databasebeta

← C11×#19002 #14596195

Subgroups — C11×#19002 #14596195

Order 2816.

884 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#563C211yesmaximal, characteristic, complemented
2C11×#3234C211yesmaximal, characteristic, complemented
3C11×#3213C211yesmaximal, characteristic
4C11×#3142C211yesmaximal, characteristic, complemented
5C11×#1664C214yesmaximal, complemented
6C11×#1657C214yesmaximal, complemented
7C11×#1534C211yesmaximal, characteristic, complemented
8C11×#1528C211yesmaximal, characteristic, complemented
9C11×#1527C211yesmaximal, characteristic, complemented
10C11×#563—22no—
11C11×#563—22no—
12C11×#563—22no—
13C11×#563C2214yes—
14C11×#532C2211yescharacteristic
15C2×C11×C4⋊Q8—21no—
16C2×C11×#126—21no—
17C2×C11×#126—21no—
18C2×C11×#125C2211yescharacteristic
19C2×C11×#125C2211yescharacteristic
20C2×C11×#124C2211yescharacteristic
21C2×C11×#123—21no—
22C2×C11×C22⋊Q8—21no—
23C2×C11×C22⋊Q8—21no—
24C11×#501C2212yescomplemented
25C11×#496C2212yes—
26C11×#491C2212yescomplemented
27C11×#490C2212yescomplemented
28C11×#490C2212yescomplemented
29C11×#489C2212yes—
30C11×#488—22no—
31C11×#481—21no—
32C11×#480—21no—
33C11×#478—22no—
34C11×#463—22no—
35C11×#448—21no—
36C11×#447—21no—
37C11×#432C2211yescharacteristic
38C11×#432C2211yescharacteristic
39C11×#417—21no—
40C11×#417—21no—
41C4×C11×M16C2211yescharacteristic
42C11×#330C2214yescomplemented
43C11×#330C2214yescomplemented
44C11×#329C2214yes—
45C2×C11×#41—21no—
46C22×Q8×C11—21no—
47C22×Q8×C11D411yescharacteristic
48C22×D4×C11D411yescharacteristic
49C23×C4×C11—21no—
50C2×C11×SD16—22no—
51C2×C11×D8—22no—
52C2×C11×M16—21no—
53C11×C4⋊Q8—24no—
54C11×C4⋊Q8—24no—
55C11×C4⋊Q8C2311yescharacteristic
56C11×#127C2311yescharacteristic
57C11×#126—24no—
58C11×#126—24no—
59C11×#126—24no—
60C11×#126—24no—
61C11×#125—21no—
62C11×#125—21no—
63C11×#125—21no—
64C11×#125—21no—
65C11×#125D412yes—
66C11×#125D412yes—
67C11×#125C2312yes—
68C11×#125C2312yes—
69C11×#124—21no—
70C11×#124—21no—
71C11×#124—21no—
72C11×#124D412yes—
73C11×#124C2312yes—
74C11×#123—24no—
75C11×#123—24no—
76C11×C22⋊Q8—24no—
77C11×C22⋊Q8—24no—
78C11×C22⋊Q8—24no—
79C11×C22⋊Q8—24no—
80C11×#121—21no—
81C11×#121—21no—
82C4×D4×C11—21no—
83C4×D4×C11—21no—
84C2×C11×C4⋊C4—21no—
85C2×C11×C4⋊C4—21no—
86C2×C11×C4⋊C4—21no—
87C2×C11×C4⋊C4—21no—
88C2×C11×C4⋊C4—21no—
89C2×C11×C4⋊C4—21no—
90C2×C11×C4⋊C4D411yescharacteristic
91C2×C11×C4⋊C4D411yescharacteristic
92C2×C11×C4⋊C4D411yescharacteristic
93C2×C11×C4⋊C4D411yescharacteristic
94C2×C11×C22⋊C4—21no—
95C2×C11×C22⋊C4—21no—
96C2×C11×C22⋊C4—21no—
97C2×C11×C22⋊C4—21no—
98C2×C11×C22⋊C4—21no—
99C2×C42×C11—21no—
100C2×C42×C11C2311yescharacteristic
101C11×#107—22no—
102C11×#106—22no—
103C11×C4⋊C8—21no—
104C11×C4⋊C8—21no—
105C11×#103—22no—
106C11×#103—22no—
107C11×#103—22no—
108C11×#102—22no—
109C11×#102—22no—
110C11×#102—22no—
111C11×#102—22no—
112C11×#102—22no—
113C11×C22⋊C8—21no—
114C11×C22⋊C8—21no—
115C11×#97C2312yes—
116C11×#97C2312yes—
117C11×#97C2312yes—
118C4×C8×C11—21no—
119#19002C1111yesmaximal, characteristic, direct product factor, Sylow
120C24×C11—21no—
121C11×#41—44no—
122C2×Q8×C11—24no—
123C2×Q8×C11—21no—
124C2×Q8×C11—21no—
125C2×Q8×C11—81no—
126C2×Q8×C11—82no—
127C2×Q8×C11C2×D412yes—
128C2×D4×C11—21no—
129C2×D4×C11—21no—
130C2×D4×C11—21no—
131C2×D4×C11—21no—
132C2×D4×C11—41no—
133C2×D4×C11—81no—
134C2×D4×C11C2×D412yes—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—24no—
141C22×C4×C11—41no—
142C22×C4×C11—82no—
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C11×SD16—82no—
147C11×D8—82no—
148C11×M16—42no—
149C2×C8×C11—22no—
150C2×C8×C11—22no—
151C2×C8×C11—22no—
152C11×C4⋊C4—24no—
153C11×C4⋊C4—24no—
154C11×C4⋊C4—22no—
155C11×C4⋊C4—22no—
156C11×C4⋊C4—22no—
157C11×C4⋊C4—22no—
158C11×C4⋊C4—21no—
159C11×C4⋊C4—21no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—22no—
163C11×C4⋊C4—22no—
164C11×C4⋊C4—22no—
165C11×C4⋊C4—22no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4C2×D412yes—
169C11×C4⋊C4C2×D412yes—
170C11×C4⋊C4C2×D412yes—
171C11×C4⋊C4C2×D412yes—
172C11×C22⋊C4—24no—
173C11×C22⋊C4—24no—
174C11×C22⋊C4—24no—
175C11×C22⋊C4—22no—
176C11×C22⋊C4—22no—
177C11×C22⋊C4—22no—
178C11×C22⋊C4—22no—
179C11×C22⋊C4—41no—
180C11×C22⋊C4—41no—
181C42×C11—24no—
182C42×C11C2×D411yescharacteristic
183C42×C11C2×D411yescharacteristic
184C42×C11C2×D411yescharacteristic
185C42×C11C2411yescharacteristic
186C2×#563C2×C1111yescharacteristic, complemented
187#3234C2×C1111yescharacteristic, complemented
188#3213C2×C1111yescharacteristic
189#3142C2×C1111yescharacteristic, complemented
190#1664C2×C1114yescomplemented
191#1657C2×C1114yescomplemented
192#1534C2×C1111yescharacteristic, complemented
193#1528C2×C1111yescharacteristic, complemented
194#1527C2×C1111yescharacteristic, complemented
195C23×C11—22no—
196C23×C11—42no—
197C23×C11—42no—
198C23×C11—42no—
199C23×C11—41no—
200C23×C11#12011yescharacteristic
201Q8×C11—42no—
202Q8×C11—42no—
203Q8×C11—81no—
204Q8×C11—84no—
205D4×C11—42no—
206D4×C11—42no—
207D4×C11—42no—
208D4×C11—42no—
209D4×C11—81no—
210D4×C11—82no—
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—41no—
218C2×C4×C11—41no—
219C2×C4×C11—42no—
220C2×C4×C11—42no—
221C2×C4×C11—42no—
222C2×C4×C11—42no—
223C2×C4×C11—42no—
224C2×C4×C11—41no—
225C2×C4×C11—82no—
226C2×C4×C11—84no—
227C2×C4×C11#12011yescharacteristic
228C2×C4×C11#12011yescharacteristic
229C2×C4×C11#12011yescharacteristic
230C2×C4×C11C22×D411yescharacteristic
231C2×C4×C11C22×D411yescharacteristic
232C2×C4×C11C22×D411yescharacteristic
233C8×C11—42no—
234C8×C11—42no—
235C8×C11—42no—
236#563—22no—
237#563—22no—
238#563—22no—
239#563C22×C1114yes—
240#532C22×C1111yescharacteristic
241C2×C4⋊Q8—21no—
242C2×#126—21no—
243C2×#126—21no—
244C2×#125C22×C1111yescharacteristic
245C2×#125C22×C1111yescharacteristic
246C2×#124C22×C1111yescharacteristic
247C2×#123—21no—
248C2×C22⋊Q8—21no—
249C2×C22⋊Q8—21no—
250#501C22×C1112yescomplemented
251#496C22×C1112yes—
252#491C22×C1112yescomplemented
253#490C22×C1112yescomplemented
254#490C22×C1112yescomplemented
255#489C22×C1112yes—
256#488—22no—
257#481—21no—
258#480—21no—
259#478—22no—
260#463—22no—
261#448—21no—
262#447—21no—
263#432C22×C1111yescharacteristic
264#432C22×C1111yescharacteristic
265#417—21no—
266#417—21no—
267C4×M16C22×C1111yescharacteristic
268#330C22×C1114yescomplemented
269#330C22×C1114yescomplemented
270#329C22×C1114yes—
271C22×C11—21no—
272C22×C11—21no—
273C22×C11—42no—
274C22×C11—42no—
275C22×C11—42no—
276C22×C11—84no—
277C22×C11—81no—
278C22×C11—81no—
279C22×C11—81no—
280C22×C11#45412yes—
281C22×C11C2×#12011yescharacteristic
282C4×C11—21no—
283C4×C11—21no—
284C4×C11—21no—
285C4×C11—21no—
286C4×C11—21no—
287C4×C11—21no—
288C4×C11—42no—
289C4×C11—42no—
290C4×C11—42no—
291C4×C11—42no—
292C4×C11—42no—
293C4×C11—81no—
294C2×#41—21no—
295C22×Q8—21no—
296C22×Q8D4×C1111yescharacteristic
297C22×D4D4×C1111yescharacteristic
298C23×C4—21no—
299C2×SD16—22no—
300C2×D8—22no—
301C2×M16—21no—
302C4⋊Q8—24no—
303C4⋊Q8—24no—
304C4⋊Q8C23×C1111yescharacteristic
305#127C23×C1111yescharacteristic
306#126—24no—
307#126—24no—
308#126—24no—
309#126—24no—
310#125—21no—
311#125—21no—
312#125—21no—
313#125—21no—
314#125D4×C1112yes—
315#125D4×C1112yes—
316#125C23×C1112yes—
317#125C23×C1112yes—
318#124—21no—
319#124—21no—
320#124—21no—
321#124D4×C1112yes—
322#124C23×C1112yes—
323#123—24no—
324#123—24no—
325C22⋊Q8—24no—
326C22⋊Q8—24no—
327C22⋊Q8—24no—
328C22⋊Q8—24no—
329#121—21no—
330#121—21no—
331C4×D4—21no—
332C4×D4—21no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4—21no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4D4×C1111yescharacteristic
340C2×C4⋊C4D4×C1111yescharacteristic
341C2×C4⋊C4D4×C1111yescharacteristic
342C2×C4⋊C4D4×C1111yescharacteristic
343C2×C22⋊C4—21no—
344C2×C22⋊C4—21no—
345C2×C22⋊C4—21no—
346C2×C22⋊C4—21no—
347C2×C22⋊C4—21no—
348C2×C42—21no—
349C2×C42C23×C1111yescharacteristic
350#107—22no—
351#106—22no—
352C4⋊C8—21no—
353C4⋊C8—21no—
354#103—22no—
355#103—22no—
356#103—22no—
357#102—22no—
358#102—22no—
359#102—22no—
360#102—22no—
361#102—22no—
362C22⋊C8—21no—
363C22⋊C8—21no—
364#97C23×C1112yes—
365#97C23×C1112yes—
366#97C23×C1112yes—
367C4×C8—21no—
368C2×C11—22no—
369C2×C11—82no—
370C2×C11—161no—
371C2×C11C2×#45411yescharacteristic
372C2×C11#301911yescharacteristic
373C2×C11#302011yescharacteristic
374C24—21no—
375#41—44no—
376C2×Q8—24no—
377C2×Q8—21no—
378C2×Q8—21no—
379C2×Q8—81no—
380C2×Q8—82no—
381C2×Q8C2×D4×C1112yes—
382C2×D4—21no—
383C2×D4—21no—
384C2×D4—21no—
385C2×D4—21no—
386C2×D4—41no—
387C2×D4—81no—
388C2×D4C2×D4×C1112yes—
389C22×C4—21no—
390C22×C4—21no—
391C22×C4—21no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—24no—
395C22×C4—41no—
396C22×C4—82no—
397C22×C4C2×D4×C1111yescharacteristic
398C22×C4C2×D4×C1111yescharacteristic
399C22×C4C2×D4×C1111yescharacteristic
400SD16—82no—
401D8—82no—
402M16—42no—
403C2×C8—22no—
404C2×C8—22no—
405C2×C8—22no—
406C4⋊C4—24no—
407C4⋊C4—24no—
408C4⋊C4—22no—
409C4⋊C4—22no—
410C4⋊C4—22no—
411C4⋊C4—22no—
412C4⋊C4—21no—
413C4⋊C4—21no—
414C4⋊C4—21no—
415C4⋊C4—21no—
416C4⋊C4—22no—
417C4⋊C4—22no—
418C4⋊C4—22no—
419C4⋊C4—22no—
420C4⋊C4—21no—
421C4⋊C4—21no—
422C4⋊C4C2×D4×C1112yes—
423C4⋊C4C2×D4×C1112yes—
424C4⋊C4C2×D4×C1112yes—
425C4⋊C4C2×D4×C1112yes—
426C22⋊C4—24no—
427C22⋊C4—24no—
428C22⋊C4—24no—
429C22⋊C4—22no—
430C22⋊C4—22no—
431C22⋊C4—22no—
432C22⋊C4—22no—
433C22⋊C4—41no—
434C22⋊C4—41no—
435C42—24no—
436C42C2×D4×C1111yescharacteristic
437C42C2×D4×C1111yescharacteristic
438C42C2×D4×C1111yescharacteristic
439C42C24×C1111yescharacteristic
440C11#1900211yescharacteristic, direct product factor, Sylow
441C23—22no—
442C23—42no—
443C23—42no—
444C23—42no—
445C23—41no—
446C23C11×#12011yescharacteristic
447Q8—42no—
448Q8—42no—
449Q8—81no—
450Q8—84no—
451D4—42no—
452D4—42no—
453D4—42no—
454D4—42no—
455D4—81no—
456D4—82no—
457C2×C4—22no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—22no—
463C2×C4—41no—
464C2×C4—41no—
465C2×C4—42no—
466C2×C4—42no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—42no—
470C2×C4—41no—
471C2×C4—82no—
472C2×C4—84no—
473C2×C4C11×#12011yescharacteristic
474C2×C4C11×#12011yescharacteristic
475C2×C4C11×#12011yescharacteristic
476C2×C4C22×D4×C1111yescharacteristic
477C2×C4C22×D4×C1111yescharacteristic
478C2×C4C22×D4×C1111yescharacteristic
479C8—42no—
480C8—42no—
481C8—42no—
482C22—21no—
483C22—21no—
484C22—42no—
485C22—42no—
486C22—42no—
487C22—84no—
488C22—81no—
489C22—81no—
490C22—81no—
491C22C11×#45412yes—
492C22C2×C11×#12011yescharacteristic
493C4—21no—
494C4—21no—
495C4—21no—
496C4—21no—
497C4—21no—
498C4—21no—
499C4—42no—
500C4—42no—
501C4—42no—
502C4—42no—
503C4—42no—
504C4—81no—
505C2—22no—
506C2—82no—
507C2—161no—
508C2C2×C11×#45411yescharacteristic
509C2C11×#301911yescharacteristic
510C2C11×#302011yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC42C24×C11
prime radicalC11×#3213C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#563C2semidirect
2. C11×#3234C2semidirect
4. C11×#3142C2semidirect
5. C11×#1664C2semidirect
6. C11×#1657C2semidirect
7. C11×#1534C2semidirect
8. C11×#1528C2semidirect
9. C11×#1527C2semidirect
24. C11×#501C22semidirect
26. C11×#491C22semidirect
27. C11×#490C22semidirect
28. C11×#490C22semidirect
42. C11×#330C22semidirect
43. C11×#330C22semidirect
119. #19002C11direct (N × H)
186. C2×#563C2×C11semidirect
187. #3234C2×C11semidirect
189. #3142C2×C11semidirect
190. #1664C2×C11semidirect
191. #1657C2×C11semidirect
192. #1534C2×C11semidirect
193. #1528C2×C11semidirect
194. #1527C2×C11semidirect
250. #501C22×C11semidirect
252. #491C22×C11semidirect
253. #490C22×C11semidirect
254. #490C22×C11semidirect
268. #330C22×C11semidirect
269. #330C22×C11semidirect
440. C11#19002direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5632
C11×#32342
C11×#32132
C11×#31422
C11×#16642
C11×#16572
C11×#15342
C11×#15282
C11×#15272
#1900211