Finite Group Databasebeta

← C11×#32891 #14610084

Subgroups — C11×#32891 #14610084

Order 2816.

3940 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
1C22×C11×H(5,𝔽2)C211yesmaximal, characteristic
2C2×C11×#455C214yesmaximal, complemented
3C11×#3007C212yesmaximal, complemented
4C11×#2435C211yesmaximal, characteristic, complemented
5C11×#1792C214yesmaximal, complemented
6C11×#1789C212yesmaximal, complemented
7C11×#1783C211yesmaximal, characteristic, complemented
8C2×C11×H(5,𝔽2)—216no—
9C2×C11×H(5,𝔽2)—24no—
10C2×C11×H(5,𝔽2)—22no—
11C2×C11×H(5,𝔽2)C2214yes—
12C22×C11×#41—22no—
13C22×C11×#41C2212yes—
14C23×D4×C11—22no—
15C23×D4×C11—22no—
16C23×D4×C11C2211yescharacteristic
17C2×C11×#137C2214yescomplemented
18C2×C11×#124C2212yescomplemented
19C2×C11×C22⋊Q8C2211yescharacteristic, complemented
20C11×#455—216no—
21C11×#452—24no—
22C11×#451—22no—
23C11×#450—22no—
24C2×C11×#104C2218yescomplemented
25C11×#417C2214yescomplemented
26C2×C11×#100C2214yescomplemented
27C11×#407C2212yescomplemented
28C11×#394—22no—
29C11×#390C2212yescomplemented
30C11×#379—22no—
31C4×C11×C22⋊C4C2211yescharacteristic, complemented
32C25×C11—22no—
33C25×C11D412yes—
34C11×H(5,𝔽2)—232no—
35C11×H(5,𝔽2)—232no—
36C11×H(5,𝔽2)—232no—
37C11×H(5,𝔽2)—216no—
38C11×H(5,𝔽2)—28no—
39C11×H(5,𝔽2)D4116yes—
40C2×C11×#41—232no—
41C2×C11×#41—28no—
42C2×C11×#41—216no—
43C2×C11×#41—28no—
44C2×C11×#41—22no—
45C2×C11×#41—22no—
46C2×C11×#41D414yes—
47C2×C11×#41C2314yes—
48C22×Q8×C11D412yes—
49C22×Q8×C11C2311yescharacteristic, complemented
50C22×D4×C11—24no—
51C22×D4×C11—232no—
52C22×D4×C11—232no—
53C22×D4×C11—28no—
54C22×D4×C11—28no—
55C22×D4×C11—22no—
56C22×D4×C11—28no—
57C22×D4×C11—28no—
58C22×D4×C11—28no—
59C22×D4×C11—22no—
60C22×D4×C11—22no—
61C22×D4×C11D412yes—
62C22×D4×C11D412yes—
63C22×D4×C11C2312yes—
64C23×C4×C11—22no—
65C23×C4×C11—22no—
66C23×C4×C11C2311yescharacteristic
67C11×#137—216no—
68C2×C11×Q16—24no—
69C2×C11×SD16—24no—
70C2×C11×M16C2314yescomplemented
71C11×#124—28no—
72C11×C22⋊Q8—22no—
73C11×C22⋊Q8—22no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4C2311yescharacteristic, complemented
76C2×C11×C22⋊C4—21no—
77C2×C11×C22⋊C4—21no—
78C2×C11×C22⋊C4—24no—
79C2×C11×C22⋊C4—24no—
80C2×C42×C11C2312yescomplemented
81C11×#104—216no—
82C11×#103—24no—
83C11×#102—24no—
84C11×#100—28no—
85C11×C22⋊C8—22no—
86C11×C22⋊C8—22no—
87C11×#95—21no—
88#32891C1111yesmaximal, characteristic, direct product factor, Sylow
89C24×C11—216no—
90C24×C11—28no—
91C24×C11—22no—
92C24×C11—22no—
93C24×C11—28no—
94C24×C11—22no—
95C24×C11—44no—
96C24×C11—82no—
97C24×C11—84no—
98C24×C11—84no—
99C24×C11C2×D411yescharacteristic
100C24×C11C2×D414yes—
101C11×#41—264no—
102C11×#41—216no—
103C11×#41—232no—
104C11×#41—216no—
105C11×#41—232no—
106C11×#41—28no—
107C11×#41—28no—
108C11×#41—28no—
109C11×#41C2×D4116yes—
110C2×Q8×C11—28no—
111C2×Q8×C11—22no—
112C2×Q8×C11—22no—
113C2×Q8×C11—24no—
114C2×Q8×C11C2×D414yes—
115C2×D4×C11—232no—
116C2×D4×C11—216no—
117C2×D4×C11—216no—
118C2×D4×C11—216no—
119C2×D4×C11—264no—
120C2×D4×C11—264no—
121C2×D4×C11—232no—
122C2×D4×C11—232no—
123C2×D4×C11—216no—
124C2×D4×C11—24no—
125C2×D4×C11—232no—
126C2×D4×C11—28no—
127C2×D4×C11—24no—
128C2×D4×C11—28no—
129C2×D4×C11—232no—
130C2×D4×C11—24no—
131C2×D4×C11—22no—
132C2×D4×C11—24no—
133C2×D4×C11—24no—
134C2×D4×C11C2×D418yes—
135C2×D4×C11C2×D414yes—
136C22×C4×C11—216no—
137C22×C4×C11—216no—
138C22×C4×C11—28no—
139C22×C4×C11—22no—
140C22×C4×C11—24no—
141C22×C4×C11—24no—
142C22×C4×C11—24no—
143C22×C4×C11—22no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D412yes—
148C22×C4×C11C2×D412yes—
149C22×C4×C11C2411yescharacteristic
150C11×Q16—48no—
151C11×SD16—48no—
152C11×M16—28no—
153C2×C8×C11—24no—
154C11×C4⋊C4—22no—
155C11×C4⋊C4—42no—
156C11×C22⋊C4—42no—
157C11×C22⋊C4—41no—
158C11×C22⋊C4—41no—
159C11×C22⋊C4—48no—
160C11×C22⋊C4—84no—
161C42×C11—24no—
162C22×H(5,𝔽2)C2×C1111yescharacteristic
163C2×#455C2×C1114yescomplemented
164#3007C2×C1112yescomplemented
165#2435C2×C1111yescharacteristic, complemented
166#1792C2×C1114yescomplemented
167#1789C2×C1112yescomplemented
168#1783C2×C1111yescharacteristic, complemented
169C23×C11—28no—
170C23×C11—28no—
171C23×C11—28no—
172C23×C11—232no—
173C23×C11—22no—
174C23×C11—24no—
175C23×C11—24no—
176C23×C11—22no—
177C23×C11—24no—
178C23×C11—41no—
179C23×C11—44no—
180C23×C11—44no—
181C23×C11—44no—
182C23×C11—44no—
183C23×C11—44no—
184C23×C11—44no—
185C23×C11—82no—
186C23×C11—82no—
187C23×C11—816no—
188C23×C11—832no—
189C23×C11—88no—
190C23×C11—88no—
191C23×C11#12011yescharacteristic
192C23×C11#12011yescharacteristic
193C23×C11#12018yes—
194C23×C11C22×D411yescharacteristic
195Q8×C11—28no—
196Q8×C11—24no—
197Q8×C11—44no—
198Q8×C11#12018yes—
199D4×C11—264no—
200D4×C11—216no—
201D4×C11—216no—
202D4×C11—28no—
203D4×C11—216no—
204D4×C11—216no—
205D4×C11—24no—
206D4×C11#12018yes—
207C2×C4×C11—28no—
208C2×C4×C11—232no—
209C2×C4×C11—216no—
210C2×C4×C11—22no—
211C2×C4×C11—24no—
212C2×C4×C11—24no—
213C2×C4×C11—216no—
214C2×C4×C11—24no—
215C2×C4×C11—42no—
216C2×C4×C11—42no—
217C2×C4×C11—42no—
218C2×C4×C11—42no—
219C2×C4×C11—42no—
220C2×C4×C11—41no—
221C2×C4×C11—41no—
222C2×C4×C11#12012yes—
223C2×C4×C11C22×D414yes—
224C2×C4×C11C22×D412yes—
225C8×C11—44no—
226C2×H(5,𝔽2)—216no—
227C2×H(5,𝔽2)—24no—
228C2×H(5,𝔽2)—22no—
229C2×H(5,𝔽2)C22×C1114yes—
230C22×#41—22no—
231C22×#41C22×C1112yes—
232C23×D4—22no—
233C23×D4—22no—
234C23×D4C22×C1111yescharacteristic
235C2×#137C22×C1114yescomplemented
236C2×#124C22×C1112yescomplemented
237C2×C22⋊Q8C22×C1111yescharacteristic, complemented
238#455—216no—
239#452—24no—
240#451—22no—
241#450—22no—
242C2×#104C22×C1118yescomplemented
243#417C22×C1114yescomplemented
244C2×#100C22×C1114yescomplemented
245#407C22×C1112yescomplemented
246#394—22no—
247#390C22×C1112yescomplemented
248#379—22no—
249C4×C22⋊C4C22×C1111yescharacteristic, complemented
250C22×C11—21no—
251C22×C11—21no—
252C22×C11—21no—
253C22×C11—21no—
254C22×C11—21no—
255C22×C11—28no—
256C22×C11—28no—
257C22×C11—21no—
258C22×C11—21no—
259C22×C11—44no—
260C22×C11—48no—
261C22×C11—416no—
262C22×C11—416no—
263C22×C11—44no—
264C22×C11—44no—
265C22×C11—44no—
266C22×C11—44no—
267C22×C11—84no—
268C22×C11—88no—
269C22×C11—832no—
270C22×C11#45512yescomplemented
271C22×C11C2×#12012yes—
272C22×C11C2×#12011yescharacteristic
273C4×C11—28no—
274C4×C11—22no—
275C4×C11—82no—
276C4×C11—81no—
277C4×C11—81no—
278C4×C11C2×#12014yes—
279C25—22no—
280C25D4×C1112yes—
281H(5,𝔽2)—232no—
282H(5,𝔽2)—232no—
283H(5,𝔽2)—232no—
284H(5,𝔽2)—216no—
285H(5,𝔽2)—28no—
286H(5,𝔽2)D4×C11116yes—
287C2×#41—232no—
288C2×#41—28no—
289C2×#41—216no—
290C2×#41—28no—
291C2×#41—22no—
292C2×#41—22no—
293C2×#41D4×C1114yes—
294C2×#41C23×C1114yes—
295C22×Q8D4×C1112yes—
296C22×Q8C23×C1111yescharacteristic, complemented
297C22×D4—24no—
298C22×D4—232no—
299C22×D4—232no—
300C22×D4—28no—
301C22×D4—28no—
302C22×D4—22no—
303C22×D4—28no—
304C22×D4—28no—
305C22×D4—28no—
306C22×D4—22no—
307C22×D4—22no—
308C22×D4D4×C1112yes—
309C22×D4D4×C1112yes—
310C22×D4C23×C1112yes—
311C23×C4—22no—
312C23×C4—22no—
313C23×C4C23×C1111yescharacteristic
314#137—216no—
315C2×Q16—24no—
316C2×SD16—24no—
317C2×M16C23×C1114yescomplemented
318#124—28no—
319C22⋊Q8—22no—
320C22⋊Q8—22no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4C23×C1111yescharacteristic, complemented
323C2×C22⋊C4—21no—
324C2×C22⋊C4—24no—
325C2×C22⋊C4—21no—
326C2×C22⋊C4—24no—
327C2×C42C23×C1112yescomplemented
328#104—216no—
329#103—24no—
330#102—24no—
331#100—28no—
332C22⋊C8—22no—
333C22⋊C8—22no—
334#95—21no—
335C2×C11—22no—
336C2×C11—22no—
337C2×C11—41no—
338C2×C11—48no—
339C2×C11—48no—
340C2×C11#284611yescharacteristic
341C2×C11C2×#45511yescharacteristic
342C2×C11#301911yescharacteristic
343C24—216no—
344C24—28no—
345C24—22no—
346C24—22no—
347C24—28no—
348C24—22no—
349C24—44no—
350C24—82no—
351C24—84no—
352C24—84no—
353C24C2×D4×C1111yescharacteristic
354C24C2×D4×C1114yes—
355#41—264no—
356#41—216no—
357#41—232no—
358#41—216no—
359#41—232no—
360#41—28no—
361#41—28no—
362#41—28no—
363#41C2×D4×C11116yes—
364C2×Q8—28no—
365C2×Q8—22no—
366C2×Q8—22no—
367C2×Q8—24no—
368C2×Q8C2×D4×C1114yes—
369C2×D4—232no—
370C2×D4—216no—
371C2×D4—216no—
372C2×D4—216no—
373C2×D4—264no—
374C2×D4—264no—
375C2×D4—232no—
376C2×D4—232no—
377C2×D4—216no—
378C2×D4—24no—
379C2×D4—232no—
380C2×D4—28no—
381C2×D4—24no—
382C2×D4—28no—
383C2×D4—232no—
384C2×D4—24no—
385C2×D4—22no—
386C2×D4—24no—
387C2×D4—24no—
388C2×D4C2×D4×C1118yes—
389C2×D4C2×D4×C1114yes—
390C22×C4—216no—
391C22×C4—216no—
392C22×C4—28no—
393C22×C4—22no—
394C22×C4—24no—
395C22×C4—24no—
396C22×C4—24no—
397C22×C4—22no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4C2×D4×C1111yescharacteristic
401C22×C4C2×D4×C1112yes—
402C22×C4C2×D4×C1112yes—
403C22×C4C24×C1111yescharacteristic
404Q16—48no—
405SD16—48no—
406M16—28no—
407C2×C8—24no—
408C4⋊C4—22no—
409C4⋊C4—42no—
410C22⋊C4—42no—
411C22⋊C4—41no—
412C22⋊C4—41no—
413C22⋊C4—48no—
414C22⋊C4—84no—
415C42—24no—
416C11#3289111yescharacteristic, direct product factor, Sylow
417C23—28no—
418C23—28no—
419C23—28no—
420C23—232no—
421C23—22no—
422C23—24no—
423C23—24no—
424C23—22no—
425C23—24no—
426C23—41no—
427C23—44no—
428C23—44no—
429C23—44no—
430C23—44no—
431C23—44no—
432C23—44no—
433C23—82no—
434C23—82no—
435C23—816no—
436C23—832no—
437C23—88no—
438C23—88no—
439C23C11×#12011yescharacteristic
440C23C11×#12011yescharacteristic
441C23C11×#12018yes—
442C23C22×D4×C1111yescharacteristic
443Q8—28no—
444Q8—24no—
445Q8—44no—
446Q8C11×#12018yes—
447D4—264no—
448D4—216no—
449D4—216no—
450D4—28no—
451D4—216no—
452D4—216no—
453D4—24no—
454D4C11×#12018yes—
455C2×C4—28no—
456C2×C4—232no—
457C2×C4—216no—
458C2×C4—24no—
459C2×C4—22no—
460C2×C4—24no—
461C2×C4—216no—
462C2×C4—24no—
463C2×C4—42no—
464C2×C4—42no—
465C2×C4—42no—
466C2×C4—42no—
467C2×C4—42no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4C11×#12012yes—
471C2×C4C22×D4×C1114yes—
472C2×C4C22×D4×C1112yes—
473C8—44no—
474C22—21no—
475C22—21no—
476C22—21no—
477C22—21no—
478C22—21no—
479C22—21no—
480C22—21no—
481C22—28no—
482C22—28no—
483C22—44no—
484C22—48no—
485C22—416no—
486C22—416no—
487C22—44no—
488C22—44no—
489C22—44no—
490C22—44no—
491C22—84no—
492C22—88no—
493C22—832no—
494C22C11×#45512yescomplemented
495C22C2×C11×#12012yes—
496C22C2×C11×#12011yescharacteristic
497C4—28no—
498C4—22no—
499C4—82no—
500C4—81no—
501C4—81no—
502C4C2×C11×#12014yes—
503C2—22no—
504C2—22no—
505C2—41no—
506C2—48no—
507C2—48no—
508C2C11×#284611yescharacteristic
509C2C2×C11×#45511yescharacteristic
510C2C11×#301911yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC22×C11×H(5,𝔽2)C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#455C2semidirect
3. C11×#3007C2semidirect
4. C11×#2435C2semidirect
5. C11×#1792C2semidirect
6. C11×#1789C2semidirect
7. C11×#1783C2semidirect
17. C2×C11×#137C22semidirect
18. C2×C11×#124C22semidirect
19. C2×C11×C22⋊Q8C22semidirect
24. C2×C11×#104C22semidirect
25. C11×#417C22semidirect
26. C2×C11×#100C22semidirect
27. C11×#407C22semidirect
29. C11×#390C22semidirect
31. C4×C11×C22⋊C4C22semidirect
49. C22×Q8×C11C23semidirect
70. C2×C11×M16C23semidirect
75. C2×C11×C4⋊C4C23semidirect
80. C2×C42×C11C23semidirect
88. #32891C11direct (N × H)
163. C2×#455C2×C11semidirect
164. #3007C2×C11semidirect
165. #2435C2×C11semidirect
166. #1792C2×C11semidirect
167. #1789C2×C11semidirect
168. #1783C2×C11semidirect
235. C2×#137C22×C11semidirect
236. C2×#124C22×C11semidirect
237. C2×C22⋊Q8C22×C11semidirect
242. C2×#104C22×C11semidirect
243. #417C22×C11semidirect
244. C2×#100C22×C11semidirect
245. #407C22×C11semidirect
247. #390C22×C11semidirect
249. C4×C22⋊C4C22×C11semidirect
270. C22×C11#455semidirect
296. C22×Q8C23×C11semidirect
317. C2×M16C23×C11semidirect
322. C2×C4⋊C4C23×C11semidirect
327. C2×C42C23×C11semidirect
416. C11#32891direct (N × H)
494. C22C11×#455semidirect

Maximal subgroups

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

subgroupindex
C22×C11×H(5,𝔽2)2
C2×C11×#4552
C11×#30072
C11×#24352
C11×#17922
C11×#17892
C11×#17832
#3289111