Finite Group Databasebeta

← C11×#10256 #14587449

Subgroups — C11×#10256 #14587449

Order 2816.

580 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3246C211yesmaximal, characteristic, complemented
2C11×#3077C211yesmaximal, characteristic, complemented
3C11×#3036C211yesmaximal, characteristic
4C11×#1954C211yesmaximal, characteristic, complemented
5C11×#1493C211yesmaximal, characteristic, complemented
6C11×#1492C211yesmaximal, characteristic, complemented
7C11×#1292C211yesmaximal, characteristic, complemented
8C2×C11×AGL(1,ℤ/8)—21no—
9C11×#533C2211yescharacteristic
10C11×#532C2211yescharacteristic
11C2×C4×D4×C11C2211yescharacteristic
12C11×#478—22no—
13C11×#476—21no—
14C11×#476—21no—
15C11×#475—21no—
16C11×#474—21no—
17C11×#465—22no—
18C11×#463—22no—
19C11×#461—21no—
20C11×#461—21no—
21C11×#460—21no—
22C11×#459—21no—
23C11×#428—21no—
24C11×#423C2211yescharacteristic
25C11×#423C2211yescharacteristic
26C2×C11×C4⋊C8C2211yescharacteristic
27C11×#418—21no—
28C11×#417—21no—
29C2×C11×C22⋊C8—22no—
30C2×C4×C8×C11C2211yescharacteristic
31C11×Q8⋊C8—22no—
32C11×D4⋊C8—22no—
33C2×C11×#41—21no—
34C22×D4×C11D411yescharacteristic
35C23×C4×C11—21no—
36C11×AGL(1,ℤ/8)—42no—
37C11×AGL(1,ℤ/8)—42no—
38C2×C11×SD16—22no—
39C2×C11×SD16—22no—
40C2×C11×D8—22no—
41C2×C11×M16—21no—
42C2×C11×M16—21no—
43C22×C8×C11—21no—
44C22×C8×C11D412yes—
45C11×C4⋊Q8D411yescharacteristic
46C11×C4⋊Q8D411yescharacteristic
47C11×C4⋊Q8D411yescharacteristic
48C11×#127D411yescharacteristic
49C11×#125—21no—
50C11×#124—21no—
51C11×C22⋊Q8—21no—
52C11×C22⋊Q8—21no—
53C11×#121—21no—
54C11×#121—21no—
55C4×Q8×C11—21no—
56C4×Q8×C11—21no—
57C4×D4×C11—21no—
58C4×D4×C11—21no—
59C4×D4×C11—21no—
60C4×D4×C11—21no—
61C4×D4×C11—21no—
62C4×D4×C11—21no—
63C11×#117—21no—
64C2×C11×C4⋊C4D411yescharacteristic
65C2×C11×C22⋊C4—21no—
66C2×C42×C11C2311yescharacteristic
67C11×#107—22no—
68C11×#106—22no—
69C11×#106—22no—
70C11×C4⋊C8—21no—
71C11×C4⋊C8—21no—
72C11×C4⋊C8—21no—
73C11×C4⋊C8—21no—
74C11×C4⋊C8D412yes—
75C11×C4⋊C8D412yes—
76C11×#103—22no—
77C11×#103—22no—
78C11×#102—22no—
79C11×#102—22no—
80C11×#102—22no—
81C11×#102—22no—
82C11×C22⋊C8—44no—
83C4×C8×C11—21no—
84C4×C8×C11—21no—
85#10256C1111yesmaximal, characteristic, direct product factor, Sylow
86C24×C11—21no—
87C11×#41—41no—
88C11×#41—41no—
89C11×#41—41no—
90C11×#41—41no—
91C2×Q8×C11—21no—
92C2×Q8×C11—21no—
93C2×Q8×C11—21no—
94C2×D4×C11—21no—
95C2×D4×C11—21no—
96C2×D4×C11—21no—
97C2×D4×C11—21no—
98C2×D4×C11—21no—
99C2×D4×C11—21no—
100C2×D4×C11—21no—
101C2×D4×C11—21no—
102C2×D4×C11—41no—
103C2×D4×C11SD1612yescomplemented
104C22×C4×C11—21no—
105C22×C4×C11—42no—
106C22×C4×C11—42no—
107C22×C4×C11—41no—
108C22×C4×C11—41no—
109C22×C4×C11—41no—
110C22×C4×C11C2×D411yescharacteristic
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11#4111yescharacteristic
113C11×SD16—44no—
114C11×SD16—82no—
115C11×D8—44no—
116C11×M16—41no—
117C11×M16—41no—
118C11×M16—41no—
119C11×M16—41no—
120C2×C8×C11—22no—
121C2×C8×C11—22no—
122C2×C8×C11—22no—
123C2×C8×C11—22no—
124C2×C8×C11—42no—
125C2×C8×C11—41no—
126C2×C8×C11—41no—
127C11×C4⋊C4—21no—
128C11×C4⋊C4—21no—
129C11×C4⋊C4—21no—
130C11×C4⋊C4—21no—
131C11×C4⋊C4—21no—
132C11×C4⋊C4—21no—
133C11×C4⋊C4—21no—
134C11×C4⋊C4—21no—
135C11×C4⋊C4—41no—
136C11×C4⋊C4—41no—
137C11×C22⋊C4—41no—
138C11×C22⋊C4—41no—
139C11×C22⋊C4—41no—
140C11×C22⋊C4—41no—
141C11×C22⋊C4—41no—
142C42×C11—41no—
143C42×C11C2×D411yescharacteristic
144C42×C11C2×D411yescharacteristic
145C42×C11C2×D411yescharacteristic
146C42×C11C2×D411yescharacteristic
147#3246C2×C1111yescharacteristic, complemented
148#3077C2×C1111yescharacteristic, complemented
149#3036C2×C1111yescharacteristic
150#1954C2×C1111yescharacteristic, complemented
151#1493C2×C1111yescharacteristic, complemented
152#1492C2×C1111yescharacteristic, complemented
153#1292C2×C1111yescharacteristic, complemented
154C23×C11—22no—
155C23×C11—42no—
156C23×C11—42no—
157C23×C11—41no—
158C23×C11—41no—
159C23×C11—41no—
160C23×C11#12111yescharacteristic
161Q8×C11—42no—
162Q8×C11—41no—
163Q8×C11—41no—
164Q8×C11—41no—
165Q8×C11—41no—
166D4×C11—22no—
167D4×C11—22no—
168D4×C11—42no—
169D4×C11—41no—
170D4×C11—41no—
171D4×C11—41no—
172D4×C11—41no—
173D4×C11—41no—
174D4×C11—41no—
175D4×C11—81no—
176D4×C11—81no—
177C2×C4×C11—21no—
178C2×C4×C11—21no—
179C2×C4×C11—41no—
180C2×C4×C11—42no—
181C2×C4×C11—41no—
182C2×C4×C11—41no—
183C2×C4×C11—41no—
184C2×C4×C11—41no—
185C2×C4×C11—82no—
186C2×C4×C11—81no—
187C2×C4×C11—81no—
188C2×C4×C11—81no—
189C2×C4×C11—81no—
190C2×C4×C11#12011yescharacteristic
191C2×C4×C11#12011yescharacteristic
192C2×C4×C11#12011yescharacteristic
193C2×C4×C11#12111yescharacteristic
194C2×C4×C11#12111yescharacteristic
195C2×C4×C11#12711yescharacteristic
196C2×C4×C11C2×SD1611yescharacteristic
197C2×C4×C11#13511yescharacteristic
198C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
199C2×C4×C11#13711yescharacteristic
200C8×C11—42no—
201C8×C11—42no—
202C8×C11—42no—
203C8×C11—42no—
204C2×AGL(1,ℤ/8)—21no—
205#533C22×C1111yescharacteristic
206#532C22×C1111yescharacteristic
207C2×C4×D4C22×C1111yescharacteristic
208#478—22no—
209#476—21no—
210#476—21no—
211#475—21no—
212#474—21no—
213#465—22no—
214#463—22no—
215#461—21no—
216#461—21no—
217#460—21no—
218#459—21no—
219#428—21no—
220#423C22×C1111yescharacteristic
221#423C22×C1111yescharacteristic
222C2×C4⋊C8C22×C1111yescharacteristic
223#418—21no—
224#417—21no—
225C2×C22⋊C8—22no—
226C2×C4×C8C22×C1111yescharacteristic
227Q8⋊C8—22no—
228D4⋊C8—22no—
229C22×C11—21no—
230C22×C11—21no—
231C22×C11—44no—
232C22×C11—42no—
233C22×C11—82no—
234C22×C11—81no—
235C22×C11—81no—
236C22×C11—81no—
237C22×C11—81no—
238C22×C11—81no—
239C22×C11#39211yescharacteristic
240C22×C11#46511yescharacteristic
241C22×C11#46811yescharacteristic
242C4×C11—21no—
243C4×C11—21no—
244C4×C11—21no—
245C4×C11—81no—
246C4×C11—81no—
247C4×C11—81no—
248C4×C11—81no—
249C4×C11#44811yescharacteristic
250C4×C11#44911yescharacteristic
251C4×C11#45011yescharacteristic
252C4×C11#45211yescharacteristic
253C4×C11#45311yescharacteristic
254C4×C11#45411yescharacteristic
255C2×#41—21no—
256C22×D4D4×C1111yescharacteristic
257C23×C4—21no—
258AGL(1,ℤ/8)—42no—
259AGL(1,ℤ/8)—42no—
260C2×SD16—22no—
261C2×SD16—22no—
262C2×D8—22no—
263C2×M16—21no—
264C2×M16—21no—
265C22×C8—21no—
266C22×C8D4×C1112yes—
267C4⋊Q8D4×C1111yescharacteristic
268C4⋊Q8D4×C1111yescharacteristic
269C4⋊Q8D4×C1111yescharacteristic
270#127D4×C1111yescharacteristic
271#125—21no—
272#124—21no—
273C22⋊Q8—21no—
274C22⋊Q8—21no—
275#121—21no—
276#121—21no—
277C4×Q8—21no—
278C4×Q8—21no—
279C4×D4—21no—
280C4×D4—21no—
281C4×D4—21no—
282C4×D4—21no—
283C4×D4—21no—
284C4×D4—21no—
285#117—21no—
286C2×C4⋊C4D4×C1111yescharacteristic
287C2×C22⋊C4—21no—
288C2×C42C23×C1111yescharacteristic
289#107—22no—
290#106—22no—
291#106—22no—
292C4⋊C8—21no—
293C4⋊C8—21no—
294C4⋊C8—21no—
295C4⋊C8—21no—
296C4⋊C8D4×C1112yes—
297C4⋊C8D4×C1112yes—
298#103—22no—
299#103—22no—
300#102—22no—
301#102—22no—
302#102—22no—
303#102—22no—
304C22⋊C8—44no—
305C4×C8—21no—
306C4×C8—21no—
307C2×C11—21no—
308C2×C11—21no—
309C2×C11—82no—
310C2×C11—161no—
311C2×C11#200011yescharacteristic
312C2×C11#200611yescharacteristic
313C2×C11#201711yescharacteristic
314C24—21no—
315#41—41no—
316#41—41no—
317#41—41no—
318#41—41no—
319C2×Q8—21no—
320C2×Q8—21no—
321C2×Q8—21no—
322C2×D4—21no—
323C2×D4—21no—
324C2×D4—21no—
325C2×D4—21no—
326C2×D4—21no—
327C2×D4—21no—
328C2×D4—21no—
329C2×D4—21no—
330C2×D4—41no—
331C2×D4C11×SD1612yescomplemented
332C22×C4—21no—
333C22×C4—42no—
334C22×C4—42no—
335C22×C4—41no—
336C22×C4—41no—
337C22×C4—41no—
338C22×C4C2×D4×C1111yescharacteristic
339C22×C4C2×D4×C1111yescharacteristic
340C22×C4C11×#4111yescharacteristic
341SD16—44no—
342SD16—82no—
343D8—44no—
344M16—41no—
345M16—41no—
346M16—41no—
347M16—41no—
348C2×C8—22no—
349C2×C8—22no—
350C2×C8—22no—
351C2×C8—22no—
352C2×C8—41no—
353C2×C8—41no—
354C2×C8—42no—
355C4⋊C4—21no—
356C4⋊C4—21no—
357C4⋊C4—21no—
358C4⋊C4—21no—
359C4⋊C4—21no—
360C4⋊C4—21no—
361C4⋊C4—21no—
362C4⋊C4—21no—
363C4⋊C4—41no—
364C4⋊C4—41no—
365C22⋊C4—41no—
366C22⋊C4—41no—
367C22⋊C4—41no—
368C22⋊C4—41no—
369C22⋊C4—41no—
370C42—41no—
371C42C2×D4×C1111yescharacteristic
372C42C2×D4×C1111yescharacteristic
373C42C2×D4×C1111yescharacteristic
374C42C2×D4×C1111yescharacteristic
375C11#1025611yescharacteristic, direct product factor, Sylow
376C23—22no—
377C23—42no—
378C23—42no—
379C23—41no—
380C23—41no—
381C23—41no—
382C23C11×#12111yescharacteristic
383Q8—42no—
384Q8—41no—
385Q8—41no—
386Q8—41no—
387Q8—41no—
388D4—22no—
389D4—22no—
390D4—42no—
391D4—41no—
392D4—41no—
393D4—41no—
394D4—41no—
395D4—41no—
396D4—41no—
397D4—81no—
398D4—81no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—41no—
402C2×C4—42no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—82no—
408C2×C4—81no—
409C2×C4—81no—
410C2×C4—81no—
411C2×C4—81no—
412C2×C4C11×#12011yescharacteristic
413C2×C4C11×#12011yescharacteristic
414C2×C4C11×#12011yescharacteristic
415C2×C4C11×#12111yescharacteristic
416C2×C4C11×#12111yescharacteristic
417C2×C4C11×#12711yescharacteristic
418C2×C4C2×C11×SD1611yescharacteristic
419C2×C4C11×#13511yescharacteristic
420C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
421C2×C4C11×#13711yescharacteristic
422C8—42no—
423C8—42no—
424C8—42no—
425C8—42no—
426C22—21no—
427C22—21no—
428C22—44no—
429C22—42no—
430C22—82no—
431C22—81no—
432C22—81no—
433C22—81no—
434C22—81no—
435C22—81no—
436C22C11×#39211yescharacteristic
437C22C11×#46511yescharacteristic
438C22C11×#46811yescharacteristic
439C4—21no—
440C4—21no—
441C4—21no—
442C4—81no—
443C4—81no—
444C4—81no—
445C4—81no—
446C4C11×#44811yescharacteristic
447C4C11×#44911yescharacteristic
448C4C11×#45011yescharacteristic
449C4C11×#45211yescharacteristic
450C4C11×#45311yescharacteristic
451C4C11×#45411yescharacteristic
452C2—21no—
453C2—21no—
454C2—82no—
455C2—161no—
456C2C11×#200011yescharacteristic
457C2C11×#200611yescharacteristic
458C2C11×#201711yescharacteristic
subgroupG/H
center, socleC22×C11#392
commutator, Frattini, cosocleC2×C42C23×C11
prime radicalC11×#3036C2
LCSG ▷ C2×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. C11×#3246C2semidirect
2. C11×#3077C2semidirect
4. C11×#1954C2semidirect
5. C11×#1493C2semidirect
6. C11×#1492C2semidirect
7. C11×#1292C2semidirect
85. #10256C11direct (N × H)
103. C2×D4×C11SD16semidirect
147. #3246C2×C11semidirect
148. #3077C2×C11semidirect
150. #1954C2×C11semidirect
151. #1493C2×C11semidirect
152. #1492C2×C11semidirect
153. #1292C2×C11semidirect
331. C2×D4C11×SD16semidirect
375. C11#10256direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#32462
C11×#30772
C11×#30362
C11×#19542
C11×#14932
C11×#14922
C11×#12922
#1025611